Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Jacobi symbol | Statement: [Legendre symbol, generalization, Jacobi symbol]

Target entity: Jacobi symbol
Context triple: [Legendre symbol, generalization, Jacobi symbol]

• A. Jacobi symbol chosen
  The Jacobi symbol is a number-theoretic function that generalizes the Legendre symbol and plays a key role in quadratic residues and primality testing in modular arithmetic.
• B. Legendre symbol
  The Legendre symbol is a number-theoretic function that indicates whether an integer is a quadratic residue modulo an odd prime, taking values 1, −1, or 0 accordingly.
• C. Jacobi
  Jacobi is a German surname most famously associated with the 19th-century mathematician Carl Gustav Jacob Jacobi, known for his foundational work in elliptic functions and number theory.
• D. quadratic reciprocity law
  The quadratic reciprocity law is a fundamental theorem in number theory that characterizes when a quadratic equation modulo one odd prime has solutions in terms of solvability modulo another, revealing a deep symmetry between primes.
• E. Jacobi’s four-square theorem
  Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.