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lfunc_lfunctions • Show schema
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{'Lhash': '4736787083600932785073107969536', 'a10': [-5.411474127809773, 1.780565171543984e-60], 'a2': [0.9396926207859084, -1.6275953626987474], 'a3': [-1.7057370639048863, -0.3007674663608706], 'a4': [-0.766044443118978, -1.3268278963378768], 'a5': [-1.4396926207859084, -2.493620766483186], 'a6': [-2.092396265452048, 2.493620766483186], 'a7': [0.32635182233306964, -0.565257937423568], 'a8': [0.8793852415718167, 0.0], 'a9': [2.8190778623577253, 1.0260604299770062], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7905189800106762, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7057370639048863, 0.3007674663608706]]], [11, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [3, 11], 'central_character': '99.34', 'coefficient_field': 'CDF', 'conductor': 99, 'conductor_radical': 33, 'conjugate': '1815981478195618079524847314444', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9396926207859084, 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[[1.0, 0], [-2.5320888862379562, -4.385706600244631], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-99-9.7-c1-0-8', '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/99/2/e/d/34/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0371355019845947, 1.127034307192341, 1.2363103471302668, 1.3673811801126947, 1.521455468874041, 1.6985767865904915, 1.8976995758066908, 2.1167417205079437, 2.352596090868999, 2.6011126329420664, 2.8570759251022, 3.1142049886395946, 3.3651985619831226, 3.6018437304930213, 3.815200157442987, 3.9958663832656436, 4.134328558322294, 4.221385384389018, 4.248635975532392, 4.209010033651754, 4.097312583360169, 3.910749095228384, 3.6493918209352363, 3.3165452885626694, 2.9189688551301005, 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'8.266052948927218701638265756798612', '10.51179848334022285439567020509997', '10.86059941714504891459072775708511', '12.31907917792042465022701315280192', '13.29674243050505664512120908318743', '14.75648955819797762141413907904026'], 'prelabel': '2-99-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8891113428647034, 'root_angle': 0.6666666666666667, 'root_number': '-0.5000000000000002 + 0.8660254037844385*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.333333333333', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.73666614660862836087454104850', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.17843851421376892230602417199', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.28886996829218224912112058240', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7905189800106762, 'bad_primes': [3, 11], 'central_character': '9.7', 'conductor': 99, 'conductor_radical': 33, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/99/2/e/d/34/3'], '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': '2-99-9.7-c1-0-8', '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': '2-99-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8891113428647034, 'root_angle': 0.33333333333333337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.73666614660862836087454104850', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4736787083600932785073107969536', 'Lhash_array': ['4736787083600932785073107969536'], 'label': '2-99-9.7-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/99/2/e/d/34/3'}