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  • lfunc_lfunctions • Show schema
    {'Lhash': '748483991682944712038389771857,3485079674248322896229173890752', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 6, 'a5': -14, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -15, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.870282844746168, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 7}, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '121.1', 'coefficient_field': '1.1.1.1', 'conductor': 14641, 'conductor_radical': 11, 'degree': 4, 'euler_factors': [[1, 0, -6, 0, 16], [1, 2, 19, 18, 81], [1, 14, 99, 350, 625], [1, 0, -48, 0, 2401], [1], [1, 0, -50, 0, 28561], [1, 0, -560, 0, 83521], [1, 0, -434, 0, 130321], [1, 18, 1139, 9522, 279841], [1, 0, -1170, 0, 707281], [1, -98, 4323, -94178, 923521], [1, -34, 3027, -46546, 1874161], [1, 0, -3074, 0, 2825761], [1, 0, -1520, 0, 3418801], [1, -64, 5442, -141376, 4879681], [1, -32, 5874, -89888, 7890481], [1, 142, 12003, 494302, 12117361], [1, 0, -7314, 0, 13845841], [1, 62, 9939, 278318, 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'12.31327984556556409245766645904571', '13.99809295019528776467839866675852'], 'prelabel': '4-11e4-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.815767385641562, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e2-0', 'trace_hash': 1096377356650673188, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59044975922244403692719338873', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.74924310659488094546090791855', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.09449157917602735179416906144', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 10.870282844746168, 'bad_primes': [11], 'central_character': '1.1', 'conductor': 14641, 'conductor_radical': 11, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 6, -14, 0, 0, 0, -15, 0, 0, -12, 0, 0, 28, 20, 0, 0, 0, -84, 0, 0, -18, 0, 97, 0, 50, 0, 0, 0, 98, 0, 0, 0, 0, -90, 34, 0, 0, 0, 0, 0, 0, 0, 210, 0, 64, -40, 48, 0, 0, 0, 32, 0, 0, 0, 0, 0, -142, 168, 0, 0, 0, 24, 0, 0, -62, 0, 36, 0, -146, 0, 0, 0, -194, 0, 0, 0, 0, -280, 140, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, -108, -196, 0, 0, 0, -34, 0, 0, 582], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, 0, -50, 0, 28561], 'euler17': [1, 0, -560, 0, 83521], 'euler19': [1, 0, -434, 0, 130321], 'euler2': [1, 0, -6, 0, 16], 'euler23': [1, 18, 1139, 9522, 279841], 'euler29': [1, 0, -1170, 0, 707281], 'euler3': [1, 2, 19, 18, 81], 'euler31': [1, -98, 4323, -94178, 923521], 'euler37': [1, -34, 3027, -46546, 1874161], 'euler41': [1, 0, -3074, 0, 2825761], 'euler43': [1, 0, -1520, 0, 3418801], 'euler47': [1, -64, 5442, -141376, 4879681], 'euler5': [1, 14, 99, 350, 625], 'euler53': [1, -32, 5874, -89888, 7890481], 'euler59': [1, 142, 12003, 494302, 12117361], 'euler61': [1, 0, -7314, 0, 13845841], 'euler67': [1, 62, 9939, 278318, 20151121], 'euler7': [1, 0, -48, 0, 2401], 'euler71': [1, 146, 15411, 735986, 25411681], 'euler73': [1, 0, -9090, 0, 28398241], 'euler79': [1, 0, 12160, 0, 38950081], 'euler83': [1, 0, -12528, 0, 47458321], 'euler89': [1, 18, 15923, 142578, 62742241], 'euler97': [1, 34, 19107, 319906, 88529281], 'euler_factors': [[1, 0, -6, 0, 16], [1, 2, 19, 18, 81], [1, 14, 99, 350, 625], [1, 0, -48, 0, 2401], [1, 0, 0, 0, 0], [1, 0, -50, 0, 28561], [1, 0, -560, 0, 83521], [1, 0, -434, 0, 130321], [1, 18, 1139, 9522, 279841], [1, 0, -1170, 0, 707281], [1, -98, 4323, -94178, 923521], [1, -34, 3027, -46546, 1874161], [1, 0, -3074, 0, 2825761], [1, 0, -1520, 0, 3418801], [1, -64, 5442, -141376, 4879681], [1, -32, 5874, -89888, 7890481], [1, 142, 12003, 494302, 12117361], [1, 0, -7314, 0, 13845841], [1, 62, 9939, 278318, 20151121], [1, 146, 15411, 735986, 25411681], [1, 0, -9090, 0, 28398241], [1, 0, 12160, 0, 38950081], [1, 0, -12528, 0, 47458321], [1, 18, 15923, 142578, 62742241], [1, 34, 19107, 319906, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/121/3/b/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-11e4-1.1-c2e2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-11e4-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.815767385641562, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 1096377356650673188, 'z1': {'__RealLiteral__': 0, 'data': '0.59044975922244403692719338873', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '748483991682944712038389771857,3485079674248322896229173890752', 'Lhash_array': ['748483991682944712038389771857', '3485079674248322896229173890752'], 'factors': ['2-11e2-11.10-c2-0-2', '2-11e2-11.10-c2-0-12'], 'label': '4-11e4-1.1-c2e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/121/3/b/a'}