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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -4, 'A4': 1, 'A5': -4, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 6, 'Lhash': '1061891762443100711,1205027419215220824', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-2.309401076758503, 0], 'a4': [0.5, 0], 'a5': [-1.788854381999832, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 51.87609645875153, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [11, [1, 2, 11]], [41, [1, 0, -1]]], 'bad_primes': [2, 11, 41], 'central_character': '813604.1', 'coefficient_field': '1.1.1.1', 'conductor': 813604, 'conductor_radical': 902, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, 4, 10, 12, 9], [1, 4, 14, 20, 25], [1, 0, -2, 0, 49], [1, 2, 11], [1, 0, 10, 0, 169], [1, 0, 30, 0, 289], [1, 0, 2, 0, 361], [1, 16, 110, 368, 529], [1, 0, 58, 0, 841], [1, 16, 126, 496, 961], [1, -4, 78, -148, 1369], [1, 0, -1], [1, 0, -58, 0, 1849], [1, -8, 110, -376, 2209], 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0.2197432182479206, 0.00026521817772282567, -0.1670332746050588, -0.23714250626745803, -0.18423126493673317], 'positive_zeros': ['0.51007563820159210654692309037406', '1.81218327277471613539827363634983', '2.49154151345673781514406094737327', '3.54075497823589975288034605375193', '3.86994574951596423396651108732690', '4.29503464325844101707308794985160', '4.86924096907948566839386350025114', '5.64804010098781556115362461940269', '5.69856539643665466176583402942537', '5.94236815873722182165691595934562', '6.70748925180204914131686110029889', '7.04169032820714443488725174992820', '7.50501018771004978536853111924378', '8.024357451025613311326857967234058'], 'prelabel': '4-902e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6837485467754787, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2266919181658321535, 'z1': {'__RealLiteral__': 0, 'data': '0.51007563820159210654692309037406', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.81218327277471613539827363634983', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.49154151345673781514406094737327', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 51.87609645875153, 'bad_primes': [2, 11, 41], 'central_character': '1.1', 'conductor': 813604, 'conductor_radical': 902, 'degree': 4, 'dirichlet_coefficients': [1, 0, -4, 1, -4, 0, 0, 0, 6, 0, -2, -4, 0, 0, 16, 1, 0, 0, 0, -4, 0, 0, -16, 0, 2, 0, 4, 0, 0, 0, -16, 0, 8, 0, 0, 6, 4, 0, 0, 0, 0, 0, 0, -2, -24, 0, 8, -4, 2, 0, 0, 0, -8, 0, 8, 0, 0, 0, 16, 16, 0, 0, 0, 1, 0, 0, -4, 0, 64, 0, 16, 0, 0, 0, -8, 0, 0, 0, 0, -4, -37, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, -16, 64, 0, 0, 0, 12, 0, -12, 2], 'euler11': [1, 2, 11, 0, 0], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 0, 2, 0, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 16, 110, 368, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 4, 10, 12, 9], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, -1, 0, 0], 'euler43': [1, 0, -58, 0, 1849], 'euler47': [1, -8, 110, -376, 2209], 'euler5': [1, 4, 14, 20, 25], 'euler53': [1, 8, 122, 424, 2809], 'euler59': [1, -16, 182, -944, 3481], 'euler61': [1, 0, -74, 0, 3721], 'euler67': [1, 4, 138, 268, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, 0, 46, 0, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 28, 374, 2492, 7921], 'euler97': [1, -12, 230, -1164, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 4, 10, 12, 9], [1, 4, 14, 20, 25], [1, 0, -2, 0, 49], [1, 2, 11, 0, 0], [1, 0, 10, 0, 169], [1, 0, 30, 0, 289], [1, 0, 2, 0, 361], [1, 16, 110, 368, 529], [1, 0, 58, 0, 841], [1, 16, 126, 496, 961], [1, -4, 78, -148, 1369], [1, 0, -1, 0, 0], [1, 0, -58, 0, 1849], [1, -8, 110, -376, 2209], [1, 8, 122, 424, 2809], [1, -16, 182, -944, 3481], [1, 0, -74, 0, 3721], [1, 4, 138, 268, 4489], [1, -16, 206, -1136, 5041], [1, 0, 46, 0, 5329], [1, 0, 142, 0, 6241], [1, 0, 22, 0, 6889], [1, 28, 374, 2492, 7921], [1, -12, 230, -1164, 9409]], 'index': 0, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/6724.1/a', 'EllipticCurve/2.0.11.1/6724.1/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': '4-902e2-1.1-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': 1, 'prelabel': '4-902e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6837485467754787, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2266919181658321535, 'z1': {'__RealLiteral__': 0, 'data': '0.51007563820159210654692309037406', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9945873
{'Lhash': '1061891762443100711,1205027419215220824', 'Lhash_array': ['1061891762443100711', '1205027419215220824'], 'label': '4-902e2-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/6724.1/a'}
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id: 9945643
{'Lhash': '1061891762443100711,1205027419215220824', 'Lhash_array': ['1061891762443100711', '1205027419215220824'], 'label': '4-902e2-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/6724.1/a'}