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lfunc_lfunctions • Show schema
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{'Lhash': '2924200384618490421237802322538', 'a10': [-0.6347144046920767, 0.0], 'a2': [1.0, 0.0], 'a3': [0.2433159645600324, 0.0], 'a4': [1.0, 0.0], 'a5': [-0.6347144046920767, 0.0], 'a6': [0.2433159645600324, 0.0], 'a7': [0.7950803277574229, 0.0], 'a8': [1.0, 0.0], 'a9': [-2.940797341390221, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.652043629638808, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 23, 29], 'central_character': '1334.1', 'coefficient_field': 'CDF', 'conductor': 1334, 'conductor_radical': 1334, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.2433159645600324, 0], [3.0, 0]], [[1.0, 0], [0.6347144046920767, 0], [5.0, 0]], [[1.0, 0], [-0.7950803277574229, 0], [7.0, 0]], [[1.0, 0], [4.9234036305311015, 0], [11.0, 0]], [[1.0, 0], [6.904962726177992, 0], [13.0, 0]], [[1.0, 0], 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[[1.0, 0], [8.839589519863772, 0], [109.0, 0]], [[1.0, 0], [19.55576566412863, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 51, 'label': '2-1334-1.1-c1-0-51', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1334/2/a/h/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [9.250354204293298e-59, 0.21286154647426228, 0.4263462378284443, 0.6409919457328013, 0.8571710771850558, 1.0750199808602923, 1.294381464894962, 1.5147627133181196, 1.7353096658729312, 1.9547978876000833, 2.1716391977089997, 2.3839028648437717, 2.5893499585289437, 2.7854793942026497, 2.9695842387446545, 3.1388168868510387, 3.290261730814678, 3.4210139047373738, 3.528262584862186, 3.6093771794112945, 3.6619945606592017, 3.6841052993614882, 3.6741366785073093, 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'5.45751342097612836382367565938598', '6.77334931793313568775068090791043', '7.73426520766397712002284909196407', '8.027369592323741110075744495212089', '9.304271033766650126261537006435204'], 'prelabel': '2-1334-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2637468697248577, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.30678736245777323982168759370', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81948994167351736342867874467', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09832992105826826671064971682', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.652043629638808, 'bad_primes': [2, 23, 29], 'central_character': '1.1', 'conductor': 1334, 'conductor_radical': 1334, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1334/2/a/h/1/4'], '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': '2-1334-1.1-c1-0-51', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1334-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2637468697248577, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.30678736245777323982168759370', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2924200384618490421237802322538', 'Lhash_array': ['2924200384618490421237802322538'], 'label': '2-1334-1.1-c1-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1334/2/a/h/1/4'}