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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1695923020295502031807849568276', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.120761435790342, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -5, 13, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '393984.1', 'coefficient_field': '1.1.1.1', 'conductor': 393984, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -4, 0, 25], [1, 0, 10, 0, 49], [1, 2, 14, 22, 121], [1, 0, 6, 0, 169], [1, 4, 22, 68, 289], [1, -5, 13, 19], [1, 0, 2, 0, 529], [1, 0, -34, 0, 841], [1, 0, -40, 0, 961], [1, 0, -6, 0, 1369], [1, 14, 106, 574, 1681], [1, 10, 110, 430, 1849], [1, 0, -54, 0, 2209], [1, 0, 78, 0, 2809], [1, 0, 102, 0, 3481], [1, 0, -58, 0, 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-3.3958852502767796, -3.1333947678404974], 'positive_zeros': ['1.33784736897546210879609948594140', '2.08031981858606058339953538281929', '2.90865415911878850219722299526171', '3.30751435481752369468116959995886', '3.95882121351609270736426090960067', '4.72566736895393909920154584971960', '5.12309217238773725530963190498913', '5.36638324801711127923719635815357', '6.21805662666855670434489105305522', '6.64381896006505864434012622568886', '6.97953621646410800160984453847194', '7.48608603641513830932619017379585', '8.105280168978459503690321851899784', '8.417392318980020335350764696572051'], 'prelabel': '4-393984-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.2387634076361764, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1498673009408869992, 'z1': {'__RealLiteral__': 0, 'data': '1.33784736897546210879609948594140', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.08031981858606058339953538281929', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.90865415911878850219722299526171', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.120761435790342, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 393984, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 5, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, -10, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 2, 14, 22, 121], 'euler13': [1, 0, 6, 0, 169], 'euler17': [1, 4, 22, 68, 289], 'euler19': [1, -5, 13, 19, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 2, 0, 529], 'euler29': [1, 0, -34, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -40, 0, 961], 'euler37': [1, 0, -6, 0, 1369], 'euler41': [1, 14, 106, 574, 1681], 'euler43': [1, 10, 110, 430, 1849], 'euler47': [1, 0, -54, 0, 2209], 'euler5': [1, 0, -4, 0, 25], 'euler53': [1, 0, 78, 0, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, 0, -58, 0, 3721], 'euler67': [1, 2, 14, 134, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, 62, 0, 5041], 'euler73': [1, -20, 210, -1460, 5329], 'euler79': [1, 0, 60, 0, 6241], 'euler83': [1, 14, 166, 1162, 6889], 'euler89': [1, 4, 166, 356, 7921], 'euler97': [1, 0, 190, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -4, 0, 25], [1, 0, 10, 0, 49], [1, 2, 14, 22, 121], [1, 0, 6, 0, 169], [1, 4, 22, 68, 289], [1, -5, 13, 19, 0], [1, 0, 2, 0, 529], [1, 0, -34, 0, 841], [1, 0, -40, 0, 961], [1, 0, -6, 0, 1369], [1, 14, 106, 574, 1681], [1, 10, 110, 430, 1849], [1, 0, -54, 0, 2209], [1, 0, 78, 0, 2809], [1, 0, 102, 0, 3481], [1, 0, -58, 0, 3721], [1, 2, 14, 134, 4489], [1, 0, 62, 0, 5041], [1, -20, 210, -1460, 5329], [1, 0, 60, 0, 6241], [1, 14, 166, 1162, 6889], [1, 4, 166, 356, 7921], [1, 0, 190, 0, 9409]], 'index': 18, 'instance_types': ['ECNF', 'BMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.0.8.1/6156.6/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/6156.5/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/6156.6/b', 'EllipticCurve/2.0.8.1/6156.5/d'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-393984-1.1-c1e2-0-18', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-393984-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.2387634076361764, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1498673009408869992, 'z1': {'__RealLiteral__': 0, 'data': '1.33784736897546210879609948594140', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9882159
{'Lhash': '1695923020295502031807849568276', 'Lhash_array': ['1695923020295502031807849568276'], 'label': '4-393984-1.1-c1e2-0-18', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/6156.5/d'}
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id: 9881535
{'Lhash': '1695923020295502031807849568276', 'Lhash_array': ['1695923020295502031807849568276'], 'label': '4-393984-1.1-c1e2-0-18', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/6156.6/b'}
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id: 9881533
{'Lhash': '1695923020295502031807849568276', 'Lhash_array': ['1695923020295502031807849568276'], 'label': '4-393984-1.1-c1e2-0-18', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/6156.5/d'}
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id: 9881448
{'Lhash': '1695923020295502031807849568276', 'Lhash_array': ['1695923020295502031807849568276'], 'label': '4-393984-1.1-c1e2-0-18', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/6156.6/b'}