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lfunc_lfunctions • Show schema
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{'Lhash': '1698616591517135791410824581368', 'a10': [0.0, 0.0], 'a2': [1.4460703197968103, -1.4460703197968103], 'a3': [-2.952400829552802, 1.2229244651623472], 'a4': [0.0, -2.182238739594498], 'a5': [0.0, 0.0], 'a6': [-2.50094443933513, 6.037813984184447], 'a7': [-0.45058390354093353, 1.0878057709155322], 'a8': [-0.2635300324447836, -0.2635300324447836], 'a9': [5.099806067291818, -5.099806067291818], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.393642085904418, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-3.891413562985862, 1.3626813574015306]]]], 'bad_primes': [5, 17], 'central_character': '425.49', 'coefficient_field': 'CDF', 'conductor': 425, 'conductor_radical': 85, 'conjugate': '1407577050787462385678897138397', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4460703197968103, 1.4460703197968103], [0, -2.0]], [[1.0, 0], [2.952400829552802, -1.2229244651623472], 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[[1.0, 0], [10.459270609296555, 4.332371738900938], [77.07463914933368, 77.07463914933368]], [[1.0, 0], [-5.405513897195411, -2.2390371678145833], [79.90306627407988, 79.90306627407988]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-425-85.49-c1-0-14', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/425/2/n/c/49/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4975282674633985, 1.551745076723014, 1.5952588945983766, 1.622491210805815, 1.6241115900134324, 1.5879347424810473, 1.5000723564819713, 1.3461971127083228, 1.1128603529892986, 0.7888463021279808, 0.36654010036995854, -0.15674520467057507, -0.7775753826112518, -1.4854584307053327, -2.262303254527571, -3.082409375730728, -3.9131003161804925, -4.716069754909664, -5.449447374774836, 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'4.88442510698282404124103815262169', '5.70286878034356913423375331295735', '6.54258680109066430863922825059661', '7.09042517240848524651956965884016', '7.88057625132665371967559314239514', '9.799279351911628443269925628601907', '10.59221242787113999481567504147908', '11.71345434167423060412125896983406'], 'prelabel': '2-425-85.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': 0.31454517688798245, 'root_number': '0.5502165163157734 + 0.835022026759375*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.157272588444', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33997222200763738301375314793', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.96275842548863895628544637880', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.88442510698282404124103815262', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.393642085904418, 'bad_primes': [5, 17], 'central_character': '85.49', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/2/n/c/49/6'], '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': '2-425-85.49-c1-0-14', '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': '2-425-85.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': 0.15727258844399122, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33997222200763738301375314793', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1698616591517135791410824581368', 'Lhash_array': ['1698616591517135791410824581368'], 'label': '2-425-85.49-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/2/n/c/49/6'}