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lfunc_lfunctions • Show schema
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{'Lhash': '2877306697633358977209880892160', 'a10': [2.6457513110645907, 0.0], 'a2': [2.6457513110645907, 0.0], 'a3': [-1.0, 0.0], 'a4': [5.0, 0.0], 'a5': [1.0, 0.0], 'a6': [-2.6457513110645907, 0.0], 'a7': [-3.6457513110645907, 0.0], 'a8': [7.937253933193772, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.275736457606492, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '285.1', 'coefficient_field': 'CDF', 'conductor': 285, 'conductor_radical': 285, 'conjugate': '2877306697633358977209880892160', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.6457513110645907, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.6457513110645907, 0], [7.0, 0]], [[1.0, 0], [-5.645751311064591, 0], [11.0, 0]], [[1.0, 0], [5.645751311064591, 0], [13.0, 0]], [[1.0, 0], [4.0, 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0], [4.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-285-1.1-c1-0-7', '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/285/2/a/d/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.989732226728008, 3.0026814521506755, 3.039353817886424, 3.0935462209649174, 3.1558722566328337, 3.2148502015688845, 3.257983790515819, 3.2727177269750762, 3.247267538181449, 3.1713719361517403, 3.037007386329282, 2.8390710791788925, 2.5760032490258022, 2.2502933947521964, 1.8688004847855557, 1.4428148489070105, 0.9877986395216145, 0.5227617409074828, 0.06925965559480066, -0.3499627224144849, -0.7126153631538114, -0.9986863348185768, -1.1922961182404577, -1.283405807296331, -1.2691876460884612, -1.15487157151014, -0.9539093146045764, 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'9.308506745153719777501357755780688', '10.18739812158716040263250652269125', '11.38756509348376275999744915614243', '12.13837975172374549503100235116862'], 'prelabel': '2-285-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5085544264647834, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.26979476609353166891886826979', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65404537443948603368575444572', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61530551040323117217267653120', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.275736457606492, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 285, 'conductor_radical': 285, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/285/2/a/d/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': '2-285-1.1-c1-0-7', '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': '2-285-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5085544264647834, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.26979476609353166891886826979', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2877306697633358977209880892160', 'Lhash_array': ['2877306697633358977209880892160'], 'label': '2-285-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/285/2/a/d/1/2'}