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lfunc_lfunctions • Show schema
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{'Lhash': '1323040707935635099722047184741', 'a10': [15.833788495652591, 0.0], 'a2': [-0.6333515398261037, 0.0], 'a3': [-19.51711384666374, 0.0], 'a4': [-31.598865826999905, 0.0], 'a5': [-25.0, 0.0], 'a6': [12.361194107745849, 0.0], 'a7': [0.0, 0.0], 'a8': [40.28043960272415, 0.0], 'a9': [137.91773290363352, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.294035854180265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [25.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 7], 'central_character': '245.1', 'coefficient_field': 'CDF', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6333515398261037, 0], [32.0, 0]], [[1.0, 0], [19.51711384666374, 0], [243.0, 0]], [[1.0, 0], [25.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-76.23435007585846, 0], [161051.0, 0]], [[1.0, 0], [266.4951069407524, 0], [371293.0, 0]], [[1.0, 0], [267.518358752691, 0], [1419857.0, 0]], [[1.0, 0], 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'positive_zeros': ['1.04369509050635340201056558030747', '3.37036683996665923230889462949302', '4.77962573700529298773484414889846', '5.31512544355711873295994374702644', '6.64134823976724354452919321843286', '7.72809976403210896955453859306940', '8.932894461174331474090058783437780', '9.810998314153366364890863783085735', '10.91713477306078661841818579353374'], 'prelabel': '2-245-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.268495501647925, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04369509050635340201056558031', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.37036683996665923230889462949', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.77962573700529298773484414890', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.294035854180265, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/6/a/l/1/5'], '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': '2-245-1.1-c5-0-30', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-245-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.268495501647925, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04369509050635340201056558031', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1323040707935635099722047184741', 'Lhash_array': ['1323040707935635099722047184741'], 'label': '2-245-1.1-c5-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/6/a/l/1/5'}