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  • lfunc_lfunctions • Show schema
    {'Lhash': '1350041910011586587802333722229,1386221469779102186566837080839,2256246197540860602648648096255', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': -2, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 172768.2590114603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [1]], [5, [1]], [31, [1, -3, 3, -1]]], 'bad_primes': [3, 5, 31], 'central_character': '6975.1', 'coefficient_field': '1.1.1.1', 'conductor': 339338109375, 'conductor_radical': 465, 'degree': 6, 'euler_factors': [[1, -1, 3, -3, 6, -4, 8], [1], [1], [1, 2, 19, 26, 133, 98, 343], [1, 6, 45, 140, 495, 726, 1331], [1, -2, 17, -54, 221, -338, 2197], [1, 0, 23, 52, 391, 0, 4913], [1, 0, 57, 0, 1083, 0, 6859], [1, -2, 65, -88, 1495, -1058, 12167], [1, 8, 71, 334, 2059, 6728, 24389], [1, -3, 3, -1], [1, 0, -7, 358, -259, 0, 50653], [1, 8, 91, 528, 3731, 13448, 68921], [1, -10, 125, -852, 5375, -18490, 79507], [1, 6, 105, 496, 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-5.762346688408216], 'positive_zeros': ['1.06499528321804395605277008259428', '1.09353592348674401071897324502714', '1.77986441779354911505611110712125', '1.97258035879966970335370864855679', '2.48137204834009977009648708535594', '2.53614409617627261213368552688008', '3.13449898224920744790392401721512', '3.31015447868465147053041711440099', '3.31261516881152094632871440041412', '3.66977219552438767209883282014178', '4.10113061551044184170404355609966', '4.17308871497055973180974324056649', '4.67893067772266809225876693529512', '4.78452315927123161398707979616997', '4.82819335139974406541011627273777', '5.33232268331931568463788583481547', '5.33985071932240847474394849970495', '5.58442063299519439737090647975309', '6.04908150527819694849604987795403', '6.06390088885855882096725084877959', '6.35963975527518870178408288859330', '6.61445485503462271045324375993568', '6.94900759820036747110681987551625', '7.03384945539502868544046238666409', '7.46204491122111712583361452489981', '7.68047715395338600647163429936562', '7.83085096376450162095131925783744'], 'prelabel': '6-6975e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.4629521913143115, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1e3-0', 'trace_hash': 1745617416377923402, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06499528321804395605277008259', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.09353592348674401071897324503', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.77986441779354911505611110712', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 172768.2590114603, 'bad_primes': [3, 5, 31], 'central_character': '1.1', 'conductor': 339338109375, 'conductor_radical': 465, 'degree': 6, 'dirichlet_coefficients': [1, 1, 0, -2, 0, 0, -2, -2, 0, 0, -6, 0, 2, -2, 0, 1, 0, 0, 0, 0, 0, -6, 2, 0, 0, 2, 0, 4, -8, 0, 3, -1, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 10, 12, 0, 2, -6, 0, -15, 0, 0, -4, 0, 0, 0, 4, 0, -8, -14, 0, -2, 3, 0, -2, 0, 0, 16, 0, 0, 0, -20, 0, 0, 0, 0, 0, 12, 0, 8, 0, 0, -8, 2, 0, 0, 10, 0, 12, 6, 0, -4, -4, 0, -6, 0, 0, 36, -15, 0, 0], 'euler11': [1, 6, 45, 140, 495, 726, 1331], 'euler13': [1, -2, 17, -54, 221, -338, 2197], 'euler17': [1, 0, 23, 52, 391, 0, 4913], 'euler19': [1, 0, 57, 0, 1083, 0, 6859], 'euler2': [1, -1, 3, -3, 6, -4, 8], 'euler23': [1, -2, 65, -88, 1495, -1058, 12167], 'euler29': [1, 8, 71, 334, 2059, 6728, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -3, 3, -1, 0, 0, 0], 'euler37': [1, 0, -7, 358, -259, 0, 50653], 'euler41': [1, 8, 91, 528, 3731, 13448, 68921], 'euler43': [1, -10, 125, -852, 5375, -18490, 79507], 'euler47': [1, 6, 105, 496, 4935, 13254, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, 119, 76, 6307, 0, 148877], 'euler59': [1, 14, 149, 982, 8791, 48734, 205379], 'euler61': [1, 2, 147, 140, 8967, 7442, 226981], 'euler67': [1, -16, 203, -1842, 13601, -71824, 300763], 'euler7': [1, 2, 19, 26, 133, 98, 343], 'euler71': [1, 20, 297, 2706, 21087, 100820, 357911], 'euler73': [1, 0, 149, -86, 10877, 0, 389017], 'euler79': [1, -8, 145, -884, 11455, -49928, 493039], 'euler83': [1, -2, 117, -336, 9711, -13778, 571787], 'euler89': [1, -6, 83, 2, 7387, -47526, 704969], 'euler97': [1, -36, 723, -8712, 70131, -338724, 912673], 'euler_factors': [[1, -1, 3, -3, 6, -4, 8], [1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 2, 19, 26, 133, 98, 343], [1, 6, 45, 140, 495, 726, 1331], [1, -2, 17, -54, 221, -338, 2197], [1, 0, 23, 52, 391, 0, 4913], [1, 0, 57, 0, 1083, 0, 6859], [1, -2, 65, -88, 1495, -1058, 12167], [1, 8, 71, 334, 2059, 6728, 24389], [1, -3, 3, -1, 0, 0, 0], [1, 0, -7, 358, -259, 0, 50653], [1, 8, 91, 528, 3731, 13448, 68921], [1, -10, 125, -852, 5375, -18490, 79507], [1, 6, 105, 496, 4935, 13254, 103823], [1, 0, 119, 76, 6307, 0, 148877], [1, 14, 149, 982, 8791, 48734, 205379], [1, 2, 147, 140, 8967, 7442, 226981], [1, -16, 203, -1842, 13601, -71824, 300763], [1, 20, 297, 2706, 21087, 100820, 357911], [1, 0, 149, -86, 10877, 0, 389017], [1, -8, 145, -884, 11455, -49928, 493039], [1, -2, 117, -336, 9711, -13778, 571787], [1, -6, 83, 2, 7387, -47526, 704969], [1, -36, 723, -8712, 70131, -338724, 912673]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6975/2/a/be'], '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': '6-6975e3-1.1-c1e3-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-6975e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.4629521913143115, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1745617416377923402, 'z1': {'__RealLiteral__': 0, 'data': '1.06499528321804395605277008259', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1350041910011586587802333722229,1386221469779102186566837080839,2256246197540860602648648096255', 'Lhash_array': ['1350041910011586587802333722229', '1386221469779102186566837080839', '2256246197540860602648648096255'], 'factors': ['2-6975-1.1-c1-0-133', '2-6975-1.1-c1-0-143', '2-6975-1.1-c1-0-228'], 'label': '6-6975e3-1.1-c1e3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6975/2/a/be'}