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lfunc_lfunctions • Show schema
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{'Lhash': '4316207116053447043636903277354', 'a10': [-984.0, 0.0], 'a2': [0.0, -5.656854249492381], 'a3': [0.0, 0.0], 'a4': [-32.0, 0.0], 'a5': [0.0, -173.9482681718907], 'a6': [0.0, 0.0], 'a7': [-484.0, 0.0], 'a8': [0.0, 181.01933598375618], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.140973505157318, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 5.656854249492381]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '18.17', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '984154639311370948192773447136', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 5.656854249492381]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 173.9482681718907], [-15625.0, 0]], [[1.0, 0], [484.0, 0], [117649.0, 0]], [[1.0, 0], [0, 1340.674457129694], [-1771561.0, 0]], [[1.0, 0], [-3368.0, 0], [4826809.0, 0]], [[1.0, 0], [0, 12.727922061357855], [-24137569.0, 0]], [[1.0, 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'6.19948274389871141938995126914552', '7.23424034812212747387496025668526', '9.404076889061244728090908165568905', '10.75716920754941246673460170820211', '12.79943948634922932546375385270513', '14.12812289850175296566168762206650', '15.37463139302735411915003575388072', '16.32436931584549506497081861955272', '18.06910386729150301377131706948879'], 'prelabel': '2-18-3.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0349382067171766, 'root_angle': 0.8040867239846964, 'root_number': '-0.8164965809277259 + 0.5773502691896258*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.402043361992', 'prec': 47}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.40488705269129499046290458171', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.19948274389871141938995126915', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.23424034812212747387496025669', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.140973505157318, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/7/b/a/17/1'], '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': '2-18-3.2-c6-0-1', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-18-3.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0349382067171766, 'root_angle': 0.4020433619923482, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '3.40488705269129499046290458171', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4316207116053447043636903277354', 'Lhash_array': ['4316207116053447043636903277354'], 'label': '2-18-3.2-c6-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/7/b/a/17/1'}