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lfunc_lfunctions • Show schema
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{'Lhash': '891070300969460895161129742537', 'a10': [3.8541019662496847, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-3.8541019662496847, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.23606797749979, 0.0], 'a8': [-1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.318036774617276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 37], 'central_character': '666.1', 'coefficient_field': 'CDF', 'conductor': 666, 'conductor_radical': 222, 'conjugate': '891070300969460895161129742537', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.8541019662496847, 0], [5.0, 0]], [[1.0, 0], [3.23606797749979, 0], [7.0, 0]], [[1.0, 0], [-1.381966011250105, 0], [11.0, 0]], [[1.0, 0], [2.8541019662496847, 0], [13.0, 0]], [[1.0, 0], [-4.47213595499958, 0], [17.0, 0]], [[1.0, 0], 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[-2.9442719099991588, 0], [109.0, 0]], [[1.0, 0], [-6.944271909999159, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-666-1.1-c1-0-0', '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/666/2/a/i/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5772984426724909, 0.562161915933719, 0.5152183706083413, 0.43224238000209225, 0.3073419046745233, 0.13438299405712203, -0.09144937580465304, -0.3721523648130997, -0.705600544448295, -1.0845402149488048, -1.4959900774763306, -1.9211632797964044, -2.336018625783746, -2.7125162778559972, -3.020593444032367, -3.2307920439401663, -3.31737146576571, -3.261637350602628, -3.0551269126923417, -2.7022292123159835, -2.2218011383464074, -1.647379682836934, -1.0256956620179087, -0.41336231689922565, 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'7.14044343528659801100496828379734', '7.956053490775710793649126002139719', '8.638109233435591597672701580597245', '9.879949479711905537275271281385608', '10.16084379052051402647932147892579'], 'prelabel': '2-666-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70293052423832835508495182842', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96807548835528318907132220424', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65445389378952927062629006311', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.318036774617276, 'bad_primes': [2, 3, 37], 'central_character': '1.1', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/666/2/a/i/1/1'], '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': '2-666-1.1-c1-0-0', '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': '2-666-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70293052423832835508495182842', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '891070300969460895161129742537', 'Lhash_array': ['891070300969460895161129742537'], 'label': '2-666-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/i/1/1'}