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lfunc_lfunctions • Show schema
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{'Lhash': '2862967495253038464212995551671', 'a10': [0.0, 0.0], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [0.0, 0.0], 'a4': [0.0, -1.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.0, -2.0], 'a8': [-2.1213203435596424, 2.1213203435596424], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.143', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1193927374010203718760461205772', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 0.7071067811865476], [0, 2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 2.0], [0, -7.0]], [[1.0, 0], [0, 2.8284271247461903], [-11.0, 0]], [[1.0, 0], [1.0, 1.0], [0, 13.0]], [[1.0, 0], [2.8284271247461903, 2.8284271247461903], [0, 17.0]], [[1.0, 0], 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'9.251053975480417444355696257081595', '10.54996192158307526478698564559011', '11.77595465101173436169065162725382', '12.37564912344075466035146942045333'], 'prelabel': '2-15e2-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.627878532809913, 'root_number': '-0.39102247747950375 + 0.9203811287210266*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.313939266405', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25848312992364474183984224563', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.01941594741982611705807245109', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.36123438529372113779581079301', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/f/a/143/1'], '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': '2-15e2-15.8-c1-0-5', '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': '2-15e2-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.3139392664049565, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25848312992364474183984224563', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2862967495253038464212995551671', 'Lhash_array': ['2862967495253038464212995551671'], 'label': '2-15e2-15.8-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/f/a/143/1'}