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lfunc_lfunctions • Show schema
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{'Lhash': '394023049076666989652536441611', 'a10': [1.372971034288733, 0.0], 'a2': [0.0, 3.9761834067762587], 'a3': [-1.0030641610456885, 0.0], 'a4': [-7.810034484322854, 0.0], 'a5': [0.0, -0.34529871835109505], 'a6': [0.0, -3.9883670730818155], 'a7': [0.0, 17.753771158952617], 'a8': [0.0, 0.7553377312951647], 'a9': [-25.99386228882571, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.437273130820913, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [0, 11.0]]], [13, [[1.0, 0], [39.77470403156909, 24.798647527659284]]]], 'bad_primes': [11, 13], 'central_character': '143.12', 'coefficient_field': 'CDF', 'conductor': 143, 'conductor_radical': 143, 'conjugate': '3463810798065591123446805818256', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -3.9761834067762587], [-8.0, 0]], [[1.0, 0], [1.0030641610456885, 0], [27.0, 0]], [[1.0, 0], [0, 0.34529871835109505], [-125.0, 0]], [[1.0, 0], [0, -17.753771158952617], 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-0.27602030125238997, -0.4033362785716137, 0.02580073340821736, 1.0051794202873248], 'positive_zeros': ['0.31082937917256268129119383232644', '2.08800124419272009791916284141833', '3.52839383427264743769569343932736', '4.73813830303420615620628904864135', '6.47493419440676062927841451906456', '7.81761624698043664448468239877387', '9.299167754212244254687763056969767', '10.20027511370292350173932366649685', '10.98052637673624088544792856787107', '11.92901903874071325994819268773542'], 'prelabel': '2-143-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.904698457812947, 'root_angle': 0.6774590338524265, 'root_number': '-0.5290697942197267 + 0.8485783127350687*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.338729516926', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31082937917256268129119383233', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08800124419272009791916284142', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52839383427264743769569343933', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.437273130820913, 'bad_primes': [11, 13], 'central_character': '13.12', 'conductor': 143, 'conductor_radical': 143, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/143/4/b/a/12/29'], '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': '2-143-13.12-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-143-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.904698457812947, 'root_angle': 0.3387295169262132, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31082937917256268129119383233', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '394023049076666989652536441611', 'Lhash_array': ['394023049076666989652536441611'], 'label': '2-143-13.12-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/143/4/b/a/12/29'}