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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -1, 'Lhash': '1085090975977872573193354247015', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 58.76201505448033, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 1]], [5, [1, -2, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '921600.1', 'coefficient_field': '1.1.1.1', 'conductor': 921600, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 0, 1], [1, -2, 1], [1, 0, -6, 0, 49], [1, 0, 6, 0, 121], [1, -4, 30, -52, 169], [1, -4, 22, -68, 289], [1, 0, -26, 0, 361], [1, 0, -6, 0, 529], [1, 4, 46, 116, 841], [1, 0, 30, 0, 961], [1, -12, 94, -444, 1369], [1, 4, 22, 164, 1681], [1, 0, 10, 0, 1849], [1, 0, -6, 0, 2209], [1, -20, 190, -1060, 2809], 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-4.594634137750791, -4.8186335593629455, -4.589767394362487, -3.9495520122626844], 'positive_zeros': ['0.855985849557055733700832379487972', '1.47110145224388845847332462271543', '2.35014419199254126013460628199774', '2.71269144652642031556550384592846', '3.53113048928162608318301357136506', '3.86850844409555418989432301854548', '4.47077099251116239108779577658068', '5.18560884013015285113930661690711', '5.60078284840423417456855955662797', '5.85154189950553561868529735768036', '6.29005983602675476263053442911368', '6.80382813403846473025826771591495', '7.28990729415394696222055218268542', '7.75607362005887971566007526051214', '8.197583128587011294573660454989594'], 'prelabel': '4-960e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.768688966648822, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1789615171152990534, 'z1': {'__RealLiteral__': 0, 'data': '0.855985849557055733700832379487972', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.47110145224388845847332462271543', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.35014419199254126013460628199774', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 58.76201505448033, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 921600, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 6, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 8, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, -4, 22, -68, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -6, 0, 529], 'euler29': [1, 4, 46, 116, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, 0, 30, 0, 961], 'euler37': [1, -12, 94, -444, 1369], 'euler41': [1, 4, 22, 164, 1681], 'euler43': [1, 0, 10, 0, 1849], 'euler47': [1, 0, -6, 0, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -20, 190, -1060, 2809], 'euler59': [1, 0, 6, 0, 3481], 'euler61': [1, -4, -18, -244, 3721], 'euler67': [1, 0, -102, 0, 4489], 'euler7': [1, 0, -6, 0, 49], 'euler71': [1, 0, 30, 0, 5041], 'euler73': [1, 4, 6, 292, 5329], 'euler79': [1, 0, 78, 0, 6241], 'euler83': [1, 0, -86, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, -12, 214, -1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 1, 0, 0], [1, -2, 1, 0, 0], [1, 0, -6, 0, 49], [1, 0, 6, 0, 121], [1, -4, 30, -52, 169], [1, -4, 22, -68, 289], [1, 0, -26, 0, 361], [1, 0, -6, 0, 529], [1, 4, 46, 116, 841], [1, 0, 30, 0, 961], [1, -12, 94, -444, 1369], [1, 4, 22, 164, 1681], [1, 0, 10, 0, 1849], [1, 0, -6, 0, 2209], [1, -20, 190, -1060, 2809], [1, 0, 6, 0, 3481], [1, -4, -18, -244, 3721], [1, 0, -102, 0, 4489], [1, 0, 30, 0, 5041], [1, 4, 6, 292, 5329], [1, 0, 78, 0, 6241], [1, 0, -86, 0, 6889], [1, 12, 214, 1068, 7921], [1, -12, 214, -1164, 9409]], 'index': 27, 'instance_types': ['BMF', 'ECNF', 'ECNF', 'BMF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/57600.2/w', 'EllipticCurve/2.0.4.1/57600.2/w', 'EllipticCurve/2.0.4.1/57600.2/x', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/57600.2/x'], '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': '4-960e2-1.1-c1e2-0-27', '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': 0, 'prelabel': '4-960e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.768688966648822, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1789615171152990534, 'z1': {'__RealLiteral__': 0, 'data': '0.855985849557055733700832379487972', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9709685
{'Lhash': '1085090975977872573193354247015', 'Lhash_array': ['1085090975977872573193354247015'], 'factors': ['4-960e2-1.1-c1e2-0-27'], 'label': '4-960e2-1.1-c1e2-0-27', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/57600.2/x'}
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id: 9709543
{'Lhash': '1085090975977872573193354247015', 'Lhash_array': ['1085090975977872573193354247015'], 'factors': ['4-960e2-1.1-c1e2-0-27'], 'label': '4-960e2-1.1-c1e2-0-27', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/57600.2/x'}
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id: 9709429
{'Lhash': '1085090975977872573193354247015', 'Lhash_array': ['1085090975977872573193354247015'], 'factors': ['4-960e2-1.1-c1e2-0-27'], 'label': '4-960e2-1.1-c1e2-0-27', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/57600.2/w'}
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id: 9709342
{'Lhash': '1085090975977872573193354247015', 'Lhash_array': ['1085090975977872573193354247015'], 'factors': ['4-960e2-1.1-c1e2-0-27'], 'label': '4-960e2-1.1-c1e2-0-27', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/57600.2/w'}