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lfunc_lfunctions • Show schema
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{'Lhash': '1028071062918741029578614602868', 'a10': [-0.23475117961519423, 0.0], 'a2': [-0.18588534642645962, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.965446637983915, 0.0], 'a5': [1.2628815779627203, 0.0], 'a6': [0.18588534642645962, 0.0], 'a7': [0.0, 0.0], 'a8': [0.7371184220372796, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.911810006841044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '1617.1', 'coefficient_field': 'CDF', 'conductor': 1617, 'conductor_radical': 231, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.18588534642645962, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.2628815779627203, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-6.93089327596783, 0], [13.0, 0]], [[1.0, 0], [5.6079884163036455, 0], [17.0, 0]], [[1.0, 0], 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'3.76962624284713139715448467457317', '4.30095782427232958149108879344881', '5.37972755374541224558996189727359', '6.12520072590224000855260687645062', '6.73688619343504748590370269700589', '8.022533065910066859354693254722593', '8.830617784380916206243921015209116', '9.192802459770363803223370618838449'], 'prelabel': '2-1617-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.593300711997403, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.811005069325605831761243431284', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.06340802795815706750767146859', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.76962624284713139715448467457', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.911810006841044, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 1617, 'conductor_radical': 231, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1617/2/a/u/1/3'], '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': '2-1617-1.1-c1-0-11', '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': '2-1617-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.593300711997403, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.811005069325605831761243431284', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1028071062918741029578614602868', 'Lhash_array': ['1028071062918741029578614602868'], 'factors': ['2-1617-1.1-c1-0-11'], 'label': '2-1617-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1617/2/a/u/1/3'}