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lfunc_lfunctions • Show schema
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{'Lhash': '1609764623364523881741055059812', 'a10': [1.820249250653002, 0.0], 'a2': [1.820249250653002, 0.0], 'a3': [0.0, 0.0], 'a4': [1.3133073345028148, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.7291260613496027, 0.0], 'a8': [-1.2499518098001638, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.420477463777095, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 29], 'central_character': '1305.1', 'coefficient_field': 'CDF', 'conductor': 1305, 'conductor_radical': 435, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.820249250653002, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.7291260613496027, 0], [7.0, 0]], [[1.0, 0], [0.7291260613496027, 0], [11.0, 0]], [[1.0, 0], [-3.3835083949559803, 0], [13.0, 0]], [[1.0, 0], [-5.743009893649977, 0], [17.0, 0]], [[1.0, 0], 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0], [109.0, 0]], [[1.0, 0], [8.510026683561938, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-1305-1.1-c1-0-21', 'leading_term': '3.44925277120017784367517312943', '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/1305/2/a/r/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [3.449252771200178, 3.4454191632003783, 3.433713739494771, 3.4135343664682196, 3.38391544108851, 3.3435817216057258, 3.2910180320007076, 3.2245502812372187, 3.142433164727703, 3.0429403088127107, 2.924453288500734, 2.785546702221397, 2.625067177381773, 2.4422047227107697, 2.236555212685178, 2.0081730036936984, 1.7576127826555172, 1.485959785747641, 1.194847543674123, 0.8864623476871095, 0.5635337138696137, 0.22931026830642828, -0.1124793098241379, 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'5.34064961383050596117241062738580', '6.07866951918344313202125584354507', '6.88022676623477708125217688283248', '7.892762914151509364177961979057084', '8.989283979204674971476991372226722', '9.595574847194210332318906549944566'], 'prelabel': '2-1305-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2280764340047923, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26988037798009943994208634503', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08369922037493253462869783834', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29358622387056447369279713306', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.420477463777095, 'bad_primes': [3, 5, 29], 'central_character': '1.1', 'conductor': 1305, 'conductor_radical': 435, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1305/2/a/r/1/3'], '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': '2-1305-1.1-c1-0-21', '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': '2-1305-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2280764340047923, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26988037798009943994208634503', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1609764623364523881741055059812', 'Lhash_array': ['1609764623364523881741055059812'], 'label': '2-1305-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1305/2/a/r/1/3'}