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lfunc_lfunctions • Show schema
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{'Lhash': '1258294262471512707850099922183', 'a10': [-0.9888877762179195, -0.8568761358243677], 'a2': [-2.4981411479892577, 0.11900112973628188], 'a3': [-0.0685285434280837, -1.730694611633036], 'a4': [4.235604081252405, -0.4044511510944622], 'a5': [0.37865084974643864, 0.36104285598344243], 'a6': [0.37714858816229163, 4.315364449836651], 'a7': [0.8241810180134599, 4.276257184261369], 'a8': [-5.581971508251807, 0.8025663405849929], 'a9': [-2.9906076774712504, 0.23720396170808994], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6529033218405047, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.0685285434280837, 1.730694611633036]]], [23, [[1.0, 0], [-4.583904299677046, -1.4099011920706663]]]], 'bad_primes': [3, 23], 'central_character': '207.11', 'coefficient_field': 'CDF', 'conductor': 207, 'conductor_radical': 69, 'conjugate': '1896471199847074971151983286822', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[62.098194484680214, -48.83455991142781]], [[1.0, 0], [1.2956685906193481, -1.2354175058064845], [3.9492990133706107, -82.90598915218966]], [[1.0, 0], [-0.8596570423331319, 5.979046060757868], [-85.39487465169027, -25.074197558887242]], [[1.0, 0], [-12.98758861371452, -3.15075490579496], [86.21703851952758, 44.44797260755881]], [[1.0, 0], [-1.4532291707204357, -1.5241028904193046], [-4.805773498197972, 100.8856012574838]], [[1.0, 0], [1.3346386909880015, 0.0635766766602283], [102.53360802502772, 9.790772460330814]], [[1.0, 0], [-1.047940081426456, -7.288583361985734], [-102.66574817675122, 30.145383582032977]], [[1.0, 0], [-14.535437670495714, 6.638111961446293], [71.37982000003608, -82.37670360461415]], [[1.0, 0], [13.174322983020833, 6.791835548141848], [65.5464307815454, 92.04708258168793]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-207-207.11-c1-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2856528776619702, 'root_angle': -0.03866936992172973, 'root_number': '0.9706284808535717 - 0.24058335801939335*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0386693699217', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.992619150927682938121678904987', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.26219012043716451709111196804', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82757769882967377370173113907', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6529033218405047, 'bad_primes': [3, 23], 'central_character': '207.11', 'conductor': 207, 'conductor_radical': 69, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/207/2/o/a/11/2'], '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': '2-207-207.11-c1-0-4', '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': '2-207-207.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2856528776619702, 'root_angle': -0.03866936992172973, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.992619150927682938121678904987', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1258294262471512707850099922183', 'Lhash_array': ['1258294262471512707850099922183'], 'factors': ['2-207-207.11-c1-0-4'], 'label': '2-207-207.11-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/207/2/o/a/11/2'}