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lfunc_lfunctions • Show schema
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{'Lhash': '818625373063300533381526442272', 'a10': [0, 0], 'a2': [0, 0], 'a3': [2.241121254753591, -4.688003361932635], 'a4': [0, 0], 'a5': [-5.801934880806753, 10.049245995763373], 'a6': [0, 0], 'a7': [18.401755440007516, 2.0917448998751804], 'a8': [0, 0], 'a9': [-16.95475104298338, -21.01276795356704], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.824641761928856, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-2.241121254753591, 4.688003361932635]]], [7, [[1.0, 0], [-18.401755440007516, -2.0917448998751804]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.257', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '1884266100382291111622654295738', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.241121254753591, 4.688003361932635]], [[1.0, 0], [5.801934880806753, -10.049245995763373], [-62.5, -108.25317547305482]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-336-21.5-c3-0-15', 'leading_term': '1.818243804404458216679556456881742429702620411675606175', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/336/4/bc/d/257/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.8182438044044582, 1.701242527745073, 1.569234950329698, 1.4229047528766876, 1.263016866322782, 1.090425455963468, 0.9060830121371803, 0.7110499742792648, 0.5065042674140717, 0.2937501018283281, 0.07422537813471647, -0.15049294903392374, -0.37868616554587475, -0.6084943195668, -0.8379204752440184, -1.064839123110664, -1.2870090783075963, -1.5020910914566634, -1.7076702797072085, -1.901283358707946, -2.080450521787198, -2.2427116724512666, -2.3856665727267465, -2.5070183255155976, 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'7.70106436085459786416878545792944', '8.187436982924762638873549230994703', '8.980274948836794367330897774889126', '10.13795196281853396695106670030664', '10.89427445827534719178146289544409'], 'prelabel': '2-336-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.452487143376032, 'root_angle': -0.2816798016594403, 'root_number': '0.6333489397292919071182807165299697173276760538770030815 - 0.7738663454006652738712273201961271839919140310240728933*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.14083990082972017', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64578155283160375270690354003', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59422633061877871388284351459', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99387681509463886786834327904', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.824641761928856, 'bad_primes': [2, 3, 7], 'central_character': '21.5', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/4/bc/d/257/4'], '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': '2-336-21.5-c3-0-15', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-336-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.452487143376032, 'root_angle': -0.14083990082972014, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64578155283160375270690354003', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '818625373063300533381526442272', 'Lhash_array': ['818625373063300533381526442272'], 'label': '2-336-21.5-c3-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/4/bc/d/257/4'}