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lfunc_lfunctions • Show schema
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{'Lhash': '1635903958097604770821023270506', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.1637219122004232, -1.1637219122004232], 'a6': [0, 0], 'a7': [3.7416573867739413, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.397532625703008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '2304.1727', 'coefficient_field': 'CDF', 'conductor': 2304, 'conductor_radical': 6, 'conjugate': '773507114257373214335919279827', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.1637219122004232, 1.1637219122004232], [0, 5.0]], [[1.0, 0], [-3.7416573867739413, 0], [7.0, 0]], [[1.0, 0], [1.6457513110645905, -1.6457513110645905], [0, -11.0]], [[1.0, 0], [-0.6457513110645906, -0.6457513110645906], [0, 13.0]], [[1.0, 0], [0, 6.570084511520132], [-17.0, 0]], [[1.0, 0], 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0.010214715730254537, 0.13865732917872492], 'positive_zeros': ['1.29050067723951266510153439638115', '2.32878331314280958794470295794768', '3.62990224156568803687136199172688', '4.13379460910137007616243850808531', '5.45880333944757938962819115085370', '5.76143139687334168249034041981441', '7.07557635536242022966855536286364', '7.80754315401646725900367728478419', '8.155969693258835455806741158791303', '9.006039080724196545779790453976180'], 'prelabel': '2-48e2-48.35-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.289234503463644, 'root_angle': 0.42908672398469644, 'root_number': '0.2209423826903945243437902445352700888116450720800593275 + 0.9752868621749660655411321790127824695546674729636444888*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2145433619923482', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29050067723951266510153439638', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.397532625703008, 'bad_primes': [2, 3], 'central_character': '48.35', 'conductor': 2304, 'conductor_radical': 6, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2304/2/l/e/1727/2'], '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': '2-48e2-48.35-c1-0-21', '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': '2-48e2-48.35-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.289234503463644, 'root_angle': 0.21454336199234822, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29050067723951266510153439638', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1635903958097604770821023270506', 'Lhash_array': ['1635903958097604770821023270506'], 'label': '2-48e2-48.35-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2304/2/l/e/1727/2'}