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lfunc_lfunctions • Show schema
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{'Lhash': '1561105251504374233644172398602', 'a10': [-0.8090169943749475, 0.5877852522924731], 'a2': [0.8090169943749475, 0.5877852522924731], 'a3': [0.0, 0.0], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [-0.30901699437494745, 0.9510565162951535], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4491585113697022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]]], 'bad_primes': [2, 3, 5], 'central_character': '900.91', 'coefficient_field': 'CDF', 'conductor': 900, 'conductor_radical': 30, 'conjugate': '3137063611814434624004947206706', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.30901699437494745, 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[[1.0, 0], [0.5, 0.36327126400268045], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.5, 0.36327126400268045], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [1.3090169943749475, 0.9510565162951535], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0.5, 1.5388417685876268], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.5, -0.36327126400268045], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [1.3090169943749475, -0.9510565162951535], [0.30901699437494745, -0.9510565162951535]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-30e2-100.91-c0-0-0', 'leading_term': '1.42396316189849894471540203578', '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/900/1/x/a/91/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.423963161898499, 1.3757171106805832, 1.3442001803123027, 1.3253300208828689, 1.314562218769175, 1.3073283363277104, 1.2993589115801079, 1.2868676687266016, 1.2666247464043383, 1.2359627500315233, 1.192752789928541, 1.1353740872236784, 1.0626888205567813, 0.9740260113816323, 0.8691738825822329, 0.74837808111824, 0.6123424319742532, 0.46222884594738006, 0.2996532793564274, 0.12667505915186228, -0.05422263972637851, -0.2401628787830885, -0.4279168011878862, -0.6139579074028072, -0.7945288875646247, -0.9657205822761366, -1.1235620831901032, -1.264120428421077, -1.3836078083264922, 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'8.385713789739642149276021526796876', '9.500281353636004488824856649603088', '10.13110540383176579835939850246179'], 'prelabel': '2-30e2-100.91-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6701928911661942, 'root_angle': -0.56, 'root_number': '-0.18738131458572463054255073444767 - 0.98228725072868868108564174286545*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.28', 'prec': 17}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23149490184701595948393562657', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61240193002872695376815841275', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.91436252679634624073741527626', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4491585113697022, 'bad_primes': [2, 3, 5], 'central_character': '100.91', 'conductor': 900, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/900/1/x/a/91/1'], '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': '2-30e2-100.91-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': '2-30e2-100.91-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6701928911661942, 'root_angle': -0.28, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23149490184701595948393562657', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1561105251504374233644172398602', 'Lhash_array': ['1561105251504374233644172398602'], 'label': '2-30e2-100.91-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/900/1/x/a/91/1'}