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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': -3, 'A5': -4, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '284912283351601962,2236197294291727863', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [-1.5, 0], 'a5': [-1.788854381999832, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.14908216899752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [1, -3, 11]], [83, [1, 0, -1]]], 'bad_primes': [11, 83], 'central_character': '833569.1', 'coefficient_field': '1.1.1.1', 'conductor': 833569, 'conductor_radical': 913, 'degree': 4, 'euler_factors': [[1, 0, 3, 0, 4], [1, 2, 7, 6, 9], [1, 4, 14, 20, 25], [1, 0, 5, 0, 49], [1, -3, 11], [1, 0, -10, 0, 169], [1, 0, 9, 0, 289], [1, 0, 34, 0, 361], [1, 8, 62, 184, 529], [1, 0, 9, 0, 841], [1, -10, 87, -310, 961], [1, 22, 195, 814, 1369], [1, 0, 78, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, 94, 0, 2209], [1, -12, 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0.0034762547196905353, -0.35181841440954464, -0.9029090878302835, -1.6180067409052026, -2.4259907196444543], 'positive_zeros': ['1.02383200139573404740051201822150', '2.27615150194359396668418676132972', '3.31355572200378673558994513482524', '3.65475901244453246589839654025875', '4.05031920828601961060326774392732', '4.49871079624823310774196588430642', '5.10251401460890303589286087658373', '5.31327024180315445602831381887930', '6.00831015099480609083754328355441', '6.24077886297520789663122777595720', '6.97450299304430271706246705191916', '7.24884684342390107531743170326326', '8.118927993931557797577222055682638'], 'prelabel': '4-913e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.700063277877558, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 215266568429635874, 'z1': {'__RealLiteral__': 0, 'data': '1.02383200139573404740051201822150', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.27615150194359396668418676132972', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.31355572200378673558994513482524', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.14908216899752, 'bad_primes': [11, 83], 'central_character': '1.1', 'conductor': 833569, 'conductor_radical': 913, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, -3, -4, 0, 0, 0, -3, 0, 3, 6, 0, 0, 8, 5, 0, 0, 0, 12, 0, 0, -8, 0, 2, 0, 14, 0, 0, 0, 10, 0, -6, 0, 0, 9, -22, 0, 0, 0, 0, 0, 0, -9, 12, 0, 0, -10, -5, 0, 0, 0, 12, 0, -12, 0, 0, 0, 10, -24, 0, 0, 0, -3, 0, 0, -4, 0, 16, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, -20, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, -20, 0, 0, 0, -16, 0, -9, -6], 'euler11': [1, -3, 11, 0, 0], 'euler13': [1, 0, -10, 0, 169], 'euler17': [1, 0, 9, 0, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, 3, 0, 4], 'euler23': [1, 8, 62, 184, 529], 'euler29': [1, 0, 9, 0, 841], 'euler3': [1, 2, 7, 6, 9], 'euler31': [1, -10, 87, -310, 961], 'euler37': [1, 22, 195, 814, 1369], 'euler41': [1, 0, 78, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 4, 14, 20, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, -10, 143, -590, 3481], 'euler61': [1, 0, 97, 0, 3721], 'euler67': [1, 4, 138, 268, 4489], 'euler7': [1, 0, 5, 0, 49], 'euler71': [1, -4, 146, -284, 5041], 'euler73': [1, 0, 146, 0, 5329], 'euler79': [1, 0, -38, 0, 6241], 'euler83': [1, 0, -1, 0, 0], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 16, 258, 1552, 9409], 'euler_factors': [[1, 0, 3, 0, 4], [1, 2, 7, 6, 9], [1, 4, 14, 20, 25], [1, 0, 5, 0, 49], [1, -3, 11, 0, 0], [1, 0, -10, 0, 169], [1, 0, 9, 0, 289], [1, 0, 34, 0, 361], [1, 8, 62, 184, 529], [1, 0, 9, 0, 841], [1, -10, 87, -310, 961], [1, 22, 195, 814, 1369], [1, 0, 78, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, 94, 0, 2209], [1, -12, 142, -636, 2809], [1, -10, 143, -590, 3481], [1, 0, 97, 0, 3721], [1, 4, 138, 268, 4489], [1, -4, 146, -284, 5041], [1, 0, 146, 0, 5329], [1, 0, -38, 0, 6241], [1, 0, -1, 0, 0], [1, 0, 178, 0, 7921], [1, 16, 258, 1552, 9409]], 'index': 0, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.11.1/6889.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/6889.1/a'], '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': '4-913e2-1.1-c1e2-0-0', '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': 2, 'prelabel': '4-913e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.700063277877558, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 215266568429635874, 'z1': {'__RealLiteral__': 0, 'data': '1.02383200139573404740051201822150', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9945754
{'Lhash': '284912283351601962,2236197294291727863', 'Lhash_array': ['284912283351601962', '2236197294291727863'], 'label': '4-913e2-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/6889.1/a'}
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id: 9945307
{'Lhash': '284912283351601962,2236197294291727863', 'Lhash_array': ['284912283351601962', '2236197294291727863'], 'label': '4-913e2-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/6889.1/a'}