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lfunc_lfunctions • Show schema
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{'Lhash': '2012574328555604593645237892818', 'a10': [102.5466074463031, 0], 'a2': [0, 4.837500676934202], 'a3': [3.0, 0], 'a4': [-15.40141279933887, 0], 'a5': [0, -21.198262138806083], 'a6': [0, 14.512502030802608], 'a7': [0, 16.280608771553837], 'a8': [0, -35.80433942707125], 'a9': [9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.913968372910507, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.337', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '270025785712850101880491125340', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -4.837500676934202], [-8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [0, 21.198262138806083], [-125.0, 0]], [[1.0, 0], [0, -16.280608771553837], [-343.0, 0]], [[1.0, 0], [0, -30.753237296192424], [-1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [46.237126934217606, 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['1.58764120664894426844451116799769', '2.69857159354379117953208204263579', '3.52200562011416810422488841753592', '4.05045527924138206545689739423883', '5.98115367317070440320982540805726', '7.14001892148921336226860245051456', '8.025969065700759238334236012205235', '9.278336517291027318023402754128966', '10.13966927119719435330797694597215', '10.70254443381968895390093615314470'], 'prelabel': '2-507-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.2568621317591576, 'root_number': '0.691699830870937428708049193858132763203004138512164386 + 0.722185117523974289552500875697739383571207580751487481*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1284310658795788', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58764120664894426844451116800', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69857159354379117953208204264', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52200562011416810422488841754', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.913968372910507, 'bad_primes': [3, 13], 'central_character': '13.12', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 58, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/4/b/k/337/17'], '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': '2-507-13.12-c3-0-58', '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': '2-507-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.1284310658795788, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58764120664894426844451116800', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2012574328555604593645237892818', 'Lhash_array': ['2012574328555604593645237892818'], 'label': '2-507-13.12-c3-0-58', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/b/k/337/17'}