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lfunc_lfunctions • Show schema
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{'Lhash': '266116324843056551399855693555', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0.7245696892229471], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -2.338401535794995], 'a8': [0, 0], 'a9': [2.474998765459362, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.731184929788995, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '4600.4049', 'coefficient_field': 'CDF', 'conductor': 4600, 'conductor_radical': 230, 'conjugate': '1767723289348876796094269013076', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -0.7245696892229471], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.338401535794995], [-7.0, 0]], [[1.0, 0], [2.627831328424641, 0], [11.0, 0]], [[1.0, 0], [0, -4.296306815480615], [-13.0, 0]], [[1.0, 0], [0, -6.85404445988569], [-17.0, 0]], [[1.0, 0], [2.8730268240481887, 0], 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'2.59278825920438505816928972652527', '3.10461940884640374115077382064226', '4.39378948114668665695359884182824', '5.21391532929184479035799970497415', '5.64883710720481608155154968285094', '6.78285341533769777834560158662124', '7.16130639554780205002507434500087', '8.184608711534520757624610871620097'], 'prelabel': '2-4600-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.06062578697852, 'root_angle': -0.8524163823495667, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20992876490978242350656714206', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.50202874673285258162631824811', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.59278825920438505816928972653', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.731184929788995, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 4600, 'conductor_radical': 230, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4600/2/e/v/4049/6'], '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': '2-4600-5.4-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4600-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.06062578697852, 'root_angle': -0.42620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.20992876490978242350656714206', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '266116324843056551399855693555', 'Lhash_array': ['266116324843056551399855693555'], 'label': '2-4600-5.4-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4600/2/e/v/4049/6'}