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lfunc_lfunctions • Show schema
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{'Lhash': '868943292604477905909314251662', 'a10': [1.5179629739957365, -1.6418856262170087], 'a2': [-0.8660254037844386, 0.5], 'a3': [-0.9659258262890683, -0.25881904510252074], 'a4': [0.5, -0.8660254037844386], 'a5': [-2.1355373105929893, 0.6629331754145827], 'a6': [0.9659258262890683, -0.25881904510252074], 'a7': [0.6485164470396031, -1.1232634358166436], 'a8': [0.0, 1.0], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0.9659258262890683, 0.25881904510252074]]], [5, [[1.0, 0], [2.1355373105929893, -0.6629331754145827]]], [13, [[1.0, 0], [1.9739891295654044, 3.0171786351420455]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.37', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '1626533694406050717876379784862', 'degree': 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[-92.66471820493493, -53.5]], [[1.0, 0], [2.2068068296590906, -2.2068068296590906], [0, -109.0]], [[1.0, 0], [2.6288555137815566, 9.811022343190354], [-97.86087062764156, 56.5]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-390-65.37-c1-0-1', '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/390/2/bd/b/37/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6692292941868245, 0.5901084903953996, 0.4965260126791135, 0.38455901265966536, 0.2497897239014121, 0.08839350133969236, -0.10188100173597835, -0.3209067975867304, -0.5655682343029794, -0.8293588345435063, -1.1022160436359782, -1.370636982673733, -1.618122972853748, -1.8259889347979803, -1.9745474271868613, -2.0446387376637216, -2.0194319734541413, -1.8863725387135488, -1.6391048155881973, 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'5.06944970740880090326960491395669', '6.66787334131761456195288627876008', '7.38895744170656864269009005703934', '8.599563821229286143435491045598092', '9.243744556612418660746947188201671', '10.24418892571744004551100567143615', '11.49842018946703566575612757589390'], 'prelabel': '2-390-65.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.3853914829272772, 'root_number': '0.3523240929353167 - 0.9358780548433147*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.192695741464', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68547539238969497380705407674', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68330593609035425353406323378', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.20999929765425586298202143421', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.37', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bd/b/37/1'], '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': '2-390-65.37-c1-0-1', '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': '2-390-65.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.1926957414636386, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68547539238969497380705407674', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '868943292604477905909314251662', 'Lhash_array': ['868943292604477905909314251662'], 'label': '2-390-65.37-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bd/b/37/1'}