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lfunc_lfunctions • Show schema
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{'Lhash': '3257007028750574418906890808710', 'a10': [-5.790630436687587, 0.24723418961631669], 'a2': [0, -2.5920079320406373], 'a3': [0, -1.0], 'a4': [-4.718505119761581, 0], 'a5': [-0.09538326891680228, -2.234032683738254], 'a6': [-2.5920079320406373, 0], 'a7': [0, -3.4183493695233285], 'a8': [0, 7.0463868337151], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.492847966862398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0.09538326891680228, 2.234032683738254]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '1815.364', 'coefficient_field': 'CDF', 'conductor': 1815, 'conductor_radical': 165, 'conjugate': '207872180873535053613840091331', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.5920079320406373], [-2.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0.09538326891680228, 2.234032683738254]], [[1.0, 0], [0, 3.4183493695233285], [-7.0, 0]], 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['2.56932551301137615903159317226802', '3.59762928136376503874410862345961', '4.66243686394487334482840258640220', '5.59044241336032980338452882848561', '5.99148821866652714960034321164623', '6.74336981594295037579938141504130', '7.72413923148258763501753711546386', '8.316114137913432813469591739459451', '8.955725552196229551559105659668801', '9.795239250493808204156489263421164'], 'prelabel': '2-1815-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.80694732914213, 'root_angle': -0.013582168746830464, 'root_number': '0.999089788959004923211773153784448049583236607024682856264 - 0.0426566946428225288846261149160305523794695906900437353*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.006791084373415233', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.56932551301137615903159317227', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.59762928136376503874410862346', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.66243686394487334482840258640', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.492847966862398, 'bad_primes': [3, 5, 11], 'central_character': '5.4', 'conductor': 1815, 'conductor_radical': 165, 'degree': 2, 'index': 107, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1815/2/c/j/364/2'], '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': '2-1815-5.4-c1-0-107', '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': '2-1815-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.80694732914213, 'root_angle': -0.006791084373415232, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.56932551301137615903159317227', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3257007028750574418906890808710', 'Lhash_array': ['3257007028750574418906890808710'], 'label': '2-1815-5.4-c1-0-107', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1815/2/c/j/364/2'}