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lfunc_lfunctions • Show schema
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{'Lhash': '2258779957293258202862783019041', 'a10': [0, 0], 'a2': [3.8046013914980503, 0], 'a3': [0, -1.7320508075688772], 'a4': [10.4749917481889, 0], 'a5': [0, 0], 'a6': [0, -6.589762912621873], 'a7': [-2.4462052029268775, 6.5586645062217865], 'a8': [24.634762615097884, 0], 'a9': [-3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.30521387891559, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.7320508075688772]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.4462052029268775, -6.5586645062217865]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.76', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': '2116026884341773502642714491039', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.8046013914980503, 0], [4.0, 0]], [[1.0, 0], [0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.4462052029268775, -6.5586645062217865]], [[1.0, 0], [-14.448905364923622, 0], 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-15.319828304919449, -18.118678129427032, -20.70990333825204, -22.969064560179074], 'positive_zeros': ['1.78186320180543805269821874407094', '3.32801829787824733695463310171264', '4.14998588138403513711984210217515', '4.59161992830263020721711124110626', '6.06068064268588563425594701970788', '6.60225652803154682195882544934621', '7.50970656792414431499801579664327', '9.102661787279524038560499716013125', '10.10250556703072204376730409361416', '11.20310468884322756558356998521899'], 'prelabel': '2-525-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.782223404152059, 'root_angle': 0.11363422555989904, 'root_number': '0.93695207231739809982482751384379827470083709397923380547 + 0.34945788613241109877579897405929978111451206549975753796*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.05681711277994952', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78186320180543805269821874407', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.32801829787824733695463310171', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14998588138403513711984210218', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.30521387891559, 'bad_primes': [3, 5, 7], 'central_character': '7.6', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/3/h/d/76/11'], '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': '2-525-7.6-c2-0-42', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-525-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.782223404152059, 'root_angle': 0.05681711277994952, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78186320180543805269821874407', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2258779957293258202862783019041', 'Lhash_array': ['2258779957293258202862783019041'], 'label': '2-525-7.6-c2-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/3/h/d/76/11'}