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lfunc_lfunctions • Show schema
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{'Lhash': '1677255889196941644378527656915', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [0.0, 0.0], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [1.0, 1.0], 'a8': [0.0, 0.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.47910241212768234, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5], 'central_character': '960.863', 'coefficient_field': 'CDF', 'conductor': 960, 'conductor_radical': 30, 'conjugate': '2393543312912434395162548735881', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-1.0, -1.0], [0, 1.0]], [[1.0, 0], [0, -1.4142135623730951], 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'1.2279948268676711864103054150113', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/960/1/u/b/863/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.2279948268676713, 1.2206538685575388, 1.2270385656782548, 1.2447214480258773, 1.2704857361393738, 1.3006866752939479, 1.3315573121079218, 1.3594167656379035, 1.3807876638356107, 1.392451299441516, 1.3914699468584912, 1.375197731875738, 1.341292508730617, 1.287734446589426, 1.212852760981259, 1.115359616805985, 0.9943889871790997, 0.8495376762601949, 0.6809055002511888, 0.4891316035379611, 0.27542398504948434, 0.04157948817099218, -0.21000824572255425, -0.4763550460570812, -0.7539085067263466, -1.038587652772836, -1.3258408037758418, -1.610721867872037, -1.8879846541863852, -2.1521941022567717, -2.3978526123892405, 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'9.139610230471446349653445292439027', '10.29452669782892380090668272234162'], 'prelabel': '2-960-120.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6921722416622053, 'root_angle': -0.07379180882521663, 'root_number': '0.97324898946773016378805774830813 - 0.22975292054736118352393736938184*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.036895904412608316', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32312159903917246102550372418', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12005835630262607581159194448', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97586843559610315052751947091', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.47910241212768234, 'bad_primes': [2, 3, 5], 'central_character': '120.83', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/1/u/b/863/2'], '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': '2-960-120.83-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-960-120.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6921722416622053, 'root_angle': -0.036895904412608316, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32312159903917246102550372418', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1677255889196941644378527656915', 'Lhash_array': ['1677255889196941644378527656915'], 'label': '2-960-120.83-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/1/u/b/863/2'}