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lfunc_lfunctions • Show schema
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{'Lhash': '2929684595782463022386691520596', 'a10': [0.12072644448896801, -0.3473561733856997], 'a2': [0.16086361332313168, 0.034192616545780825], 'a3': [1.486770900375071, 0.8885450409505982], 'a4': [-1.8023829482200746, -0.8024725904585472], 'a5': [0.2789103567330721, -2.218605195366456], 'a6': [0.20878565934914084, 0.19377115317561333], 'a7': [2.0666338491049414, -3.579514827291391], 'a8': [-0.5285968624276591, -0.3840481007238934], 'a9': [1.4209754204041998, 2.6421258211158505], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.486770900375071, -0.8885450409505982]]], [5, [[1.0, 0], [-0.2789103567330721, 2.218605195366456]]]], 'bad_primes': [3, 5], 'central_character': '225.106', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1779883828681789139932524113452', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0.19143654258954962, 'root_number': '0.8245354600649508 + 0.5658102818926851*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0957182712948', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.31111364224100784476981310817', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34322791704339675153971674314', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.91317502338120856137709543609', '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': '225.106', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/q/a/106/14'], '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': '2-15e2-225.106-c1-0-20', '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': '2-15e2-225.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.09571827129477481, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.31111364224100784476981310817', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2929684595782463022386691520596', 'Lhash_array': ['2929684595782463022386691520596'], 'label': '2-15e2-225.106-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/q/a/106/14'}