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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': -3, 'A5': 0, 'A6': 0, 'A7': -8, 'A8': 0, 'A9': 1, 'Lhash': '854949074168896706,1364169308829084149', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [-1.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-3.0237157840738176, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.4245069688005803, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 3]], [5, [1, 0, -1]], [13, [1, 2, 1]]], 'bad_primes': [3, 5, 13], 'central_character': '38025.1', 'coefficient_field': '1.1.1.1', 'conductor': 38025, 'conductor_radical': 195, 'degree': 4, 'euler_factors': [[1, 0, 3, 0, 4], [1, 2, 3], [1, 0, -1], [1, 8, 30, 56, 49], [1, 0, 18, 0, 121], [1, 2, 1], [1, 0, 30, 0, 289], [1, 12, 74, 228, 361], [1, 0, 10, 0, 529], [1, 0, 54, 0, 841], [1, 20, 162, 620, 961], [1, 4, 78, 148, 1369], [1, 0, 46, 0, 1681], [1, -20, 186, -860, 1849], [1, 0, 78, 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-4.8510364068932015, -4.276108364383605, -3.087178523982968, -1.365863487473004, 0.7301078853190702], 'positive_zeros': ['2.53409816778618263405222233424558', '3.51994456797006266949922249859162', '4.03550878858777485512286959394243', '4.59731852050444182415870036677213', '5.66957165960173077695586779199567', '5.80677556175820100036715333303852', '6.35831289645710659676663930684764', '7.04231773996815600274218157257619', '7.36945570129601409328488904448187', '8.679150483937958571354498819427294', '8.903866275348653436076253219749813', '9.238371497422229278947323218386275', '9.844976583062747102624785032359495'], 'prelabel': '4-195e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2478312543829668, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2219118382997980855, 'z1': {'__RealLiteral__': 0, 'data': '2.53409816778618263405222233424558', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.51994456797006266949922249859162', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.03550878858777485512286959394243', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4245069688005803, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 38025, 'conductor_radical': 195, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, -3, 0, 0, -8, 0, 1, 0, 0, 6, -2, 0, 0, 5, 0, 0, -12, 0, 16, 0, 0, 0, 1, 0, 4, 24, 0, 0, -20, 0, 0, 0, 0, -3, -4, 0, 4, 0, 0, 0, 20, 0, 0, 0, 0, -10, 34, 0, 0, 6, 0, 0, 0, 0, 24, 0, 0, 0, 4, 0, -8, -3, 0, 0, -8, 0, 0, 0, 0, 0, -12, 0, -2, 36, 0, 0, -24, 0, -11, 0, 0, -48, 0, 0, 0, 0, 0, 0, 16, 0, 40, 0, 0, 0, -4, 0, 0, -3], 'euler11': [1, 0, 18, 0, 121], 'euler13': [1, 2, 1, 0, 0], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 12, 74, 228, 361], 'euler2': [1, 0, 3, 0, 4], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, 0, 54, 0, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 20, 162, 620, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, -20, 186, -860, 1849], 'euler47': [1, 0, 78, 0, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 0, 102, 0, 2809], 'euler59': [1, 0, 82, 0, 3481], 'euler61': [1, -4, 126, -244, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 8, 30, 56, 49], 'euler71': [1, 0, 106, 0, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, 24, 302, 1896, 6241], 'euler83': [1, 0, -90, 0, 6889], 'euler89': [1, 0, 174, 0, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 0, 3, 0, 4], [1, 2, 3, 0, 0], [1, 0, -1, 0, 0], [1, 8, 30, 56, 49], [1, 0, 18, 0, 121], [1, 2, 1, 0, 0], [1, 0, 30, 0, 289], [1, 12, 74, 228, 361], [1, 0, 10, 0, 529], [1, 0, 54, 0, 841], [1, 20, 162, 620, 961], [1, 4, 78, 148, 1369], [1, 0, 46, 0, 1681], [1, -20, 186, -860, 1849], [1, 0, 78, 0, 2209], [1, 0, 102, 0, 2809], [1, 0, 82, 0, 3481], [1, -4, 126, -244, 3721], [1, 8, 150, 536, 4489], [1, 0, 106, 0, 5041], [1, 12, 182, 876, 5329], [1, 24, 302, 1896, 6241], [1, 0, -90, 0, 6889], [1, 0, 174, 0, 7921], [1, 4, 198, 388, 9409]], 'index': 13, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/4225.2/a', 'EllipticCurve/2.0.3.1/4225.2/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': '4-195e2-1.1-c1e2-0-13', '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': '4-195e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2478312543829668, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2219118382997980855, 'z1': {'__RealLiteral__': 0, 'data': '2.53409816778618263405222233424558', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9766900
{'Lhash': '854949074168896706,1364169308829084149', 'Lhash_array': ['854949074168896706', '1364169308829084149'], 'label': '4-195e2-1.1-c1e2-0-13', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/4225.2/a'}
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id: 9766781
{'Lhash': '854949074168896706,1364169308829084149', 'Lhash_array': ['854949074168896706', '1364169308829084149'], 'label': '4-195e2-1.1-c1e2-0-13', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/4225.2/a'}