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lfunc_lfunctions • Show schema
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{'Lhash': '1378061675488418090613190274318', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [3.414213562373095, 0.0], 'a6': [0.0, 0.0], 'a7': [0.585786437626905, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.795065251406015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '4608.1', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.414213562373095, 0], [5.0, 0]], [[1.0, 0], [-0.585786437626905, 0], [7.0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [13.0, 0]], [[1.0, 0], [-7.656854249492381, 0], [17.0, 0]], [[1.0, 0], [5.656854249492381, 0], [19.0, 0]], [[1.0, 0], [6.82842712474619, 0], [23.0, 0]], [[1.0, 0], 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'label': '2-4608-1.1-c1-0-39', 'leading_term': '3.15150530309703486720778217311', '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/4608/2/a/r/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.151505303097035, 3.1443135379360556, 3.1226653511761597, 3.086350662648792, 3.03504737463259, 2.968361361804368, 2.8858785662123556, 2.7872258094950775, 2.6721365738678453, 2.540517938823302, 2.3925150376829802, 2.22856974481972, 2.0494707485789694, 1.85639264792239, 1.6509221931634446, 1.4350702527937043, 1.211268524767955, 0.9823504272091005, 0.7515160103897173, 0.52228113934994, 0.2984116121801901, 0.08384330600325551, -0.11741012077496443, -0.3013600019578746, -0.46415351338202926, -0.6021897904885891, -0.7122381347903002, -0.7915548170413373, -0.8379947468745051, 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'6.51938349739942481526667437843792', '7.73767693179721289177421371332628', '8.331855736467897710675438440363027'], 'prelabel': '2-4608-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08709898077617771084790018006', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.83619650703641114579002383234', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75837890263118224056386816817', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.795065251406015, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 4608, 'conductor_radical': 6, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4608/2/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': '2-4608-1.1-c1-0-39', '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': '2-4608-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08709898077617771084790018006', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1378061675488418090613190274318', 'Lhash_array': ['1378061675488418090613190274318'], 'label': '2-4608-1.1-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4608/2/a/r/1/2'}