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lfunc_lfunctions • Show schema
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{'Lhash': '1518910108549826121239251336215', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.15479212008828522, 0.26810781660421307], 'a4': [0, 0], 'a5': [2.5, -4.330127018922194], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [13.452078799117148, -23.29968394749103], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.821871805625825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.5, 4.330127018922194]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '980.961', 'coefficient_field': 'CDF', 'conductor': 980, 'conductor_radical': 70, 'conjugate': '881407655462859801290614794476', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.15479212008828522, -0.26810781660421307], [-13.5, 23.382685902179844]], [[1.0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [8.309584240176571, 14.392622093759444], [-665.5, 1152.6798124370878]], [[1.0, 0], 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'9.795184946351451958266276756671043'], 'prelabel': '2-980-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.604069424040382, 'root_angle': 0.3736792394412256, 'root_number': '0.3865135727591552881869185769990697126707082293252108640 + 0.92228371885930696567151377458672511248388364307843616327*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1868396197206128', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19820880317996113694215721389', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22934373085073754533585797002', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49640639115996367059006491458', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.821871805625825, 'bad_primes': [2, 5, 7], 'central_character': '7.2', 'conductor': 980, 'conductor_radical': 70, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/980/4/i/w/961/1'], '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': '2-980-7.2-c3-0-27', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-980-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.604069424040382, 'root_angle': 0.1868396197206128, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19820880317996113694215721389', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1518910108549826121239251336215', 'Lhash_array': ['1518910108549826121239251336215'], 'label': '2-980-7.2-c3-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/980/4/i/w/961/1'}