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lfunc_lfunctions • Show schema
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{'Lhash': '1085790549232518397499705531579', 'a10': [0.0, 0.0], 'a2': [0.14168949117801832, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.9799240880897142, 0.0], 'a5': [0.0, 0.0], 'a6': [0.14168949117801832, 0.0], 'a7': [0.8583105088219817, 0.0], 'a8': [-0.5639134189685702, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.14168949117801832, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8583105088219817, 0], [7.0, 0]], [[1.0, 0], [3.679928967245675, 0], [11.0, 0]], [[1.0, 0], [4.581341938351606, 0], [13.0, 0]], [[1.0, 0], [-5.307020760408481, 0], [17.0, 0]], [[1.0, 0], [-6.368699664264897, 0], [19.0, 0]], 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[109.0, 0]], [[1.0, 0], [-16.035362284525362, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-1875-1.1-c1-0-15', 'leading_term': '1.6784265267619107208632062031803', '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/1875/2/a/k/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.6784265267619107, 1.6717665029822497, 1.6516565822387579, 1.6177186271126733, 1.5693595469765402, 1.505824005863861, 1.4262626835906662, 1.3298115230484735, 1.2156771792813887, 1.0832240999406562, 0.9320591560930469, 0.7621103477345635, 0.573696705486906, 0.3675870263528741, 0.14504549403469355, -0.09213744360521803, -0.3416303024504493, -0.6005630104719338, -0.8655474251405776, -1.1327164551583986, -1.397781943959051, -1.6561110232909202, 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'5.17374481116315082295259049768263', '5.66128034187107831961246804693680', '7.18990851863678683779871782323253', '7.87014104890890060345456342503111', '8.251855647310923108055862150133459', '9.359537575932472272154972535948143'], 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.856537715547984048065638683635', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.45983449347866886788809852174', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29303920924863327017785265227', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/k/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': '2-1875-1.1-c1-0-15', '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': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.856537715547984048065638683635', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1085790549232518397499705531579', 'Lhash_array': ['1085790549232518397499705531579'], 'label': '2-1875-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/k/1/4'}