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lfunc_lfunctions • Show schema
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{'Lhash': '2414207245125402913033727825216', 'a10': [-2.618033988749895, 0.0], 'a2': [2.618033988749895, 0.0], 'a3': [2.618033988749895, 0.0], 'a4': [4.854101966249685, 0.0], 'a5': [-1.0, 0.0], 'a6': [6.854101966249685, 0.0], 'a7': [0.2360679774997897, 0.0], 'a8': [7.47213595499958, 0.0], 'a9': [3.8541019662496847, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.412997564841117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 19], 'central_character': '1805.1', 'coefficient_field': 'CDF', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.618033988749895, 0], [2.0, 0]], [[1.0, 0], [-2.618033988749895, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.2360679774997897, 0], [7.0, 0]], [[1.0, 0], [4.618033988749895, 0], [11.0, 0]], [[1.0, 0], [-5.0, 0], [13.0, 0]], [[1.0, 0], [6.0, 0], [17.0, 0]], [[1.0, 0], [0, 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 95, 'label': '2-1805-1.1-c1-0-95', 'leading_term': '8.00563240753746548163425993223', '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/1805/2/a/e/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [8.005632407537465, 8.00451982895836, 8.000817852444321, 7.993453630046548, 7.980703630174633, 7.960284816139656, 7.9294720138099954, 7.885233236080778, 7.824374668292514, 7.743687821516064, 7.640092672648029, 7.510772073884099, 7.353294055738162, 7.165719711856691, 6.9466950950424255, 6.695526005683323, 6.412234792363512, 6.097598398517941, 5.753166960034816, 5.381262350885004, 4.98495623109188, 4.568027398477942, 4.134898591362617, 3.6905533297752204, 3.2404339042464625, 2.7903222033013266, 2.3462056878766204, 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'5.96046546573772756684310601277854', '6.75852679799842559231476869127622', '7.71588748756469928128942260478655', '8.205402875684973851902928915517696', '9.047443828937567089998162044728892'], 'prelabel': '2-1805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90447371278075048234866366222', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70341147120747461778621637303', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41215051482841317071662253214', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.412997564841117, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'index': 95, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1805/2/a/e/1/2'], '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': '2-1805-1.1-c1-0-95', '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': '2-1805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90447371278075048234866366222', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2414207245125402913033727825216', 'Lhash_array': ['2414207245125402913033727825216'], 'label': '2-1805-1.1-c1-0-95', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/a/e/1/2'}