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lfunc_lfunctions • Show schema
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{'Lhash': '1304078566664067687964913972970', 'a10': [0.0, 0.0], 'a2': [2.6719479533035697, 0.0], 'a3': [-1.0, 0.0], 'a4': [5.139305865163135, 0.0], 'a5': [0.0, 0.0], 'a6': [-2.6719479533035697, 0.0], 'a7': [-1.0, 0.0], 'a8': [8.388061881216531, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.113607167289445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '5775.1', 'coefficient_field': 'CDF', 'conductor': 5775, 'conductor_radical': 1155, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.6719479533035697, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.4757384684040915, 0], [13.0, 0]], [[1.0, 0], [1.8468607585031354, 0], [17.0, 0]], [[1.0, 0], [-2.7457911641574, 0], [19.0, 0]], [[1.0, 0], 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[[1.0, 0], [-3.444488616950086, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 107, 'label': '2-5775-1.1-c1-0-107', 'leading_term': '5.90293896508737171392703244867', '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/5775/2/a/cj/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [5.902938965087372, 5.891600857925132, 5.857463459945106, 5.800167003911404, 5.719142863252974, 5.613658142680607, 5.482874521177141, 5.325918175014048, 5.14195720952649, 4.930282891994141, 4.690391068293392, 4.422060407911592, 4.125424494595154, 3.8010352079157936, 3.449915281423594, 3.073598347976115, 2.6741551787202558, 2.2542051867374617, 1.8169126046058628, 1.365967065798209, 0.9055486322487268, 0.44027762238987733, -0.024850089503260505, -0.48454130904848747, 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'4.56822562817859541934852726559562', '5.16513617202190110478114560405191', '5.85804561508718326014145700175747', '6.35594694387842161037503158429890', '7.23851724824535523889486714815572', '7.49205024624462763596854823862277'], 'prelabel': '2-5775-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.790700049868898, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02873659857793602572642447059', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33345773549761467370594415165', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96959777134258176761668094750', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 46.113607167289445, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 5775, 'conductor_radical': 1155, 'degree': 2, 'index': 107, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5775/2/a/cj/1/5'], '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': '2-5775-1.1-c1-0-107', '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': '2-5775-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.790700049868898, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02873659857793602572642447059', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1304078566664067687964913972970', 'Lhash_array': ['1304078566664067687964913972970'], 'label': '2-5775-1.1-c1-0-107', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5775/2/a/cj/1/5'}