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lfunc_lfunctions • Show schema
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{'Lhash': '2836599502513982723700806112240', 'a10': [2.514136929335291, 0.0], 'a2': [2.514136929335291, 0.0], 'a3': [0.0, 0.0], 'a4': [4.320884499447486, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5141369293352911, 0.0], 'a8': [5.8350214287827775, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.233941281861857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '2836599502513982723700806112240', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.514136929335291, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.5141369293352911, 0], [7.0, 0]], [[1.0, 0], [3.3208844994474864, 0], [11.0, 0]], [[1.0, 0], [1.3208844994474864, 0], [13.0, 0]], [[1.0, 0], [3.3208844994474864, 0], [17.0, 0]], [[1.0, 0], 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'7.03024273615491346463579841902481', '8.281294856092912784424661004140563', '9.699823814832895875174538969105986', '10.71476474098541103720363091295427', '11.43647010305502459602123780381801'], 'prelabel': '2-405-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7983162352216746, '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': '2.23768245130265216385360926189', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17689899663705654627478208061', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.55802444124845438928070684110', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.233941281861857, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/2/a/j/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': '2-405-1.1-c1-0-12', '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': '2-405-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.23768245130265216385360926189', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2836599502513982723700806112240', 'Lhash_array': ['2836599502513982723700806112240'], 'label': '2-405-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/2/a/j/1/3'}