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lfunc_lfunctions • Show schema
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{'Lhash': '1545865455980066753767486389577', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [23.518577752611478, 0.0], 'a4': [0.0, 0.0], 'a5': [74.27532113722259, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [310.12349950563157, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 125.74091473337684, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '784.1', 'coefficient_field': 'CDF', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-23.518577752611478, 0], [243.0, 0]], [[1.0, 0], [-74.27532113722259, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-424.2191251235921, 0], [161051.0, 0]], [[1.0, 0], [-252.2333570951518, 0], [371293.0, 0]], [[1.0, 0], [-1104.3467585722674, 0], [1419857.0, 0]], [[1.0, 0], [6.470998183574452, 0], [2476099.0, 0]], [[1.0, 0], 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['1.21947282295432763668721103643843', '1.91865051537295262688619234919017', '3.00390087799909120649706369520267', '3.74072775402439171627684324660115', '5.08013532794258773703006378564704', '6.12633707900141863610938475648785', '7.00402485784650260756494603426605', '8.002199276282416304442161762037227', '8.931459943132264806971307981586105', '9.355372912020021730241351118573907'], 'prelabel': '2-28e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.213425646669123, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21947282295432763668721103644', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91865051537295262688619234919', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00390087799909120649706369520', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 125.74091473337684, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'index': 72, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/784/6/a/bf/1/4'], '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': '2-28e2-1.1-c5-0-72', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-28e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.213425646669123, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21947282295432763668721103644', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1545865455980066753767486389577', 'Lhash_array': ['1545865455980066753767486389577'], 'label': '2-28e2-1.1-c5-0-72', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/6/a/bf/1/4'}