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lfunc_lfunctions • Show schema
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{'Lhash': '925921007130613144316403404214', 'a10': [3.732050807568877, 0.0], 'a2': [-1.0, 0.0], 'a3': [1.7320508075688772, 0.0], 'a4': [1.0, 0.0], 'a5': [-3.732050807568877, 0.0], 'a6': [-1.7320508075688772, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [-1.2125640181566132e-75, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.892605118234947, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7, 13], 'central_character': '2366.1', 'coefficient_field': 'CDF', 'conductor': 2366, 'conductor_radical': 182, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [3.0, 0]], [[1.0, 0], [3.732050807568877, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.4641016151377546, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [17.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], 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[[1.0, 0], [-2.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-2366-1.1-c1-0-16', 'leading_term': '1.1907807468108935908524547093056', '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/2366/2/a/r/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.1907807468108935, 1.1854515404024617, 1.1694121631877852, 1.1425121813706083, 1.104516705698683, 1.055129125921487, 0.9940210232013391, 0.9208675915292847, 0.8353867188194575, 0.7373798401822954, 0.6267727512652697, 0.5036547211652287, 0.36831443552075466, 0.22127150143327035, 0.06330243757772706, -0.10453975368409187, -0.2809131807325462, -0.4641824313485737, -0.6524221883981562, -0.8434294280720049, -1.0347443892679642, -1.2236803407579577, -1.4073619928803345, 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'5.92066937541887510734909664509986', '7.35849111478084463727392316474228', '7.65111527987991316272985377896757', '8.014670133378411148586388291916603', '8.985482468481825860122979382925427'], 'prelabel': '2-2366-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.346562448445317, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73042288384820641168491640541', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21925446904970875547353981392', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27772453528571475243015271567', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.892605118234947, 'bad_primes': [2, 7, 13], 'central_character': '1.1', 'conductor': 2366, 'conductor_radical': 182, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2366/2/a/r/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': '2-2366-1.1-c1-0-16', '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': '2-2366-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.346562448445317, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.73042288384820641168491640541', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '925921007130613144316403404214', 'Lhash_array': ['925921007130613144316403404214'], 'label': '2-2366-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2366/2/a/r/1/2'}