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lfunc_lfunctions • Show schema
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{'Lhash': '792099404494286399338581779164', 'a10': [2.3168022081811563, -1.3524460246969313e-60], 'a2': [-1.1055369250363998, -0.6382820412688365], 'a3': [-1.1679251832085003, 0.0], 'a4': [-0.1851920715873747, -0.32076207714826566], 'a5': [-1.5717264767783825, 0.9074367044604613], 'a6': [1.291184415716899, 0.7454656699876013], 'a7': [0.0, 0.0], 'a8': [0.0, 3.025947258993722], 'a9': [-1.6359507664273911, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [3.583053402592878, 0.4021545898875171]]]], 'bad_primes': [7, 13], 'central_character': '637.361', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '840360457374249933108262255733', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1055369250363998, 0.6382820412688365], [1.0, 1.7320508075688772]], [[1.0, 0], [1.1679251832085003, 0], [3.0, 0]], 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'7.42641379500887011769601821808863', '7.78474900522153232446424359303835', '9.088968947717241797720838438071915', '9.423172467330113019450064214729100', '10.58473210903519205419259819525161'], 'prelabel': '2-637-91.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.16598021848749378, 'root_number': '0.8671016594298616 + 0.498131219874824*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0829901092437', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62485625325438715576426232441', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87301618836448227733386951655', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36864964685276662884593438192', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '91.88', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/u/h/361/2'], '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': '2-637-91.88-c1-0-9', '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': '2-637-91.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.08299010924374689, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62485625325438715576426232441', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '792099404494286399338581779164', 'Lhash_array': ['792099404494286399338581779164'], 'label': '2-637-91.88-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/u/h/361/2'}