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lfunc_lfunctions • Show schema
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{'Lhash': '529717070534947583193126732910', 'a10': [6.898979485566356, -1.550510257216822], 'a2': [-0.7071067811865476, -1.224744871391589], 'a3': [-2.598076211353316, -1.5], 'a4': [-1.0, 1.7320508075688772], 'a5': [-1.4896678459722468, 4.772933029980245], 'a6': [2.0609719246925658e-60, 4.242640687119285], 'a7': [-1.8195371393717854, 1.050510257216822], 'a8': [2.8284271247461903, 0.0], 'a9': [4.5, 7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.4523223792426725, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 1.224744871391589]]], [3, [[1.0, 0], [2.598076211353316, 1.5]]], [5, [[1.0, 0], [1.4896678459722468, -4.772933029980245]]]], 'bad_primes': [2, 3, 5], 'central_character': '90.59', 'coefficient_field': 'CDF', 'conductor': 90, 'conductor_radical': 30, 'conjugate': '2814698476339163962588608983908', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 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[[1.0, 0], [40.012141237689995, -69.30306154330093], [-6384.5, -11058.278380923497]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-90-45.14-c2-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/90/3/j/a/59/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.4322854263829097, 0.3168612965520607, 0.19064309364286336, 0.05128066255786491, -0.10375644773211974, -0.2769548928956165, -0.4705288405187534, -0.6861947804935752, -0.9249550818303284, -1.1868943789978612, -1.4709936138760813, -1.7749686637846818, -2.0951431202533928, -2.426367164950701, -2.7619960271789195, -3.0939418071442626, -3.4128112701124853, -3.7081394335241775, -3.9687243579279454, -4.183062595331577, -4.339877449906079, -4.428723909618036, -4.440645305172526, 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'8.171526920668069783027975219316916', '8.998045387260377605204920271018927', '10.48889237908264551955019521316953', '11.14474765716074733399202054938265', '12.76852362224601810829881193633485', '13.37789012351399090671358281570961'], 'prelabel': '2-90-45.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5659892653663603, 'root_angle': -0.4592581628139682, 'root_number': '0.1276450642688189 - 0.9918199118629395*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.229629081407', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41787308777322131072163347470', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.13116839415141454397131056197', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.42872315185409107087711385738', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4523223792426725, 'bad_primes': [2, 3, 5], 'central_character': '45.14', 'conductor': 90, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/90/3/j/a/59/1'], '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': '2-90-45.14-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-90-45.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5659892653663603, 'root_angle': -0.2296290814069841, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41787308777322131072163347470', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '529717070534947583193126732910', 'Lhash_array': ['529717070534947583193126732910'], 'label': '2-90-45.14-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/90/3/j/a/59/1'}