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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '1647680407005070488', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 1], [1, -1], [1, 2, 13], [1, -6, 17], [1, 4, 19], [1, -4, 23], [1, -2, 29], [1, 4, 31], [1, 2, 37], [1, 2, 41], [1, 12, 43], [1, 0, 47], [1, 2, 53], [1, 0, 59], [1, -14, 61], [1, 8, 67], [1, 16, 71], [1, 10, 73], [1, -16, 79], [1, 4, 83], [1, 6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 13, 'label': '2-369600-1.1-c1-0-13', 'leading_term': '0.534929055519', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/369600/eg', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.5349290555191621, -0.2504116427690977, -1.869397054368282, -2.601394800238865, -1.429392908349655, 0.2871106459730585, -0.04639477271845402, -2.603793257998243, -4.01515867438198, -1.720202910777833, 1.720369187858793, 1.68717623455336, -1.504885568069653, -2.827303447423156, -0.6369858148600847, 0.5357287614607465, -2.077043551086182, -4.307095520802461, -2.300952088397989, 0.5636235896777736, 0.004360050045661864, -1.366297796973119, 0.2754722393499676, 2.109133305606998, 0.5727528151430508, -0.9768838751805303, 0.9062935422323847, 2.400489244288069, 0.5941529397311018, 0.09335140646301968, 2.826285207058639, 2.533321651542753, -2.245115623046357, -3.526077500704608, 0.4016281050035541, 1.050130284852005, -2.88858109267802, -2.974709831384474, 1.219263887628093, 1.879342396884347, -0.3801571056463428, 0.289170043929947, 0.9827752208230874, -2.143040720496619, -3.403924752394189, -0.08637454942040718, 0.946752245755124, -1.476523076490549, -1.096681966758013, 0.5988498018330818, -1.128372541869953, -1.888695769494362, 0.6513199014485149, -0.271166063673151, -3.495687717207829, -0.2232326109316909, 5.168094392028186, 3.028586519193944, -0.7725530270460726, 0.970957358332114, 1.468277546409513, -1.235432819896325, 1.239917614670583, 6.079470701281459, 4.136906331159692, 0.1491112728959058, 0.498440083146725, 0.3342344273103093, -0.9377889895364819, 1.203488092884194, 2.02415128025835, -1.064773699072601, -0.1971137102753447, 3.35755290084166, 0.9509145935131128, -2.481474080784676, -0.7139759135702242, -0.2369066883516409, -0.8616456681792377, 4.033410170572069, 6.451459441565503, 0.1399551450408081, -3.039374910085915, 0.003696077096609138, -1.551218187322543, -4.639101013872891, -1.509290723726901, 0.6733235007400336, -0.7373214796125352, 1.099936563757872, 2.215226402968691, -1.420008652536393, -2.021777470923171, 0.3675644165092455, -0.05966672003032704, 1.240356922047472, 3.441716854527283, -1.284272695282549, -5.26175417611444, -1.033666915637829, 1.065596182390884, -0.9629114180069764, 0.5686474458177677, -0.8244195207114903, -7.08722885357012, -5.402596296664405, 0.8075251387252468, -0.1167517418284089, -0.8525582906401521, 2.635466684943743, 1.618249239788421, -0.3057707278807889, 1.910174169337565, 1.096804894596982, -0.4596889546026491, 2.906029268265165, 3.038769739556372, -0.6387019589098147, -0.01776927861362221, 0.5563007428914833, -0.2136119859272017], 'positive_zeros': ['0.2035181319225544', '1.193994544645858', '1.493324543942802', '2.362343128364787', '2.889419533073189', '3.565910596332073', '3.833252367706312', '4.677324833386943', '5.000572485222939', '5.474077320609462', '6.057415646303130', '6.415010430124998', '7.081353917179076', '7.234898054692980', '7.888788623496416', '8.474403670374517', '8.825877441376743', '9.424264679608376', '9.943143451576450', '10.21079299228438', '10.60324609053894', '11.25636950195244', '11.60311148498665', '12.12053002410792', '12.38528729542293', '12.93261124938969', '13.23036100546364', '13.75857498450798', '14.41158261684569', '14.66444565262798', '15.12402084838520', '15.43842598052570', '16.27546738451192', '16.39549696965021', '16.79713510575913', '17.14733362101222', '17.66309747516526', '18.01245184090514', '18.54857680343466', '19.09889297285787', '19.20162637870589', '19.57137644469657'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1647680407005070488, 'z1': {'__RealLiteral__': 0, 'data': '0.2035181319225544', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.193994544645858', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.493324543942802', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 1, 0, -2, 0, 0, 0, 6, 0, -4, 0, 1, 0, 4, 0, 0, 0, -1, 0, 2, 0, -4, 0, -1, 0, 0, 0, -2, 0, 2, 0, -2, 0, -12, 0, 0, 0, 0, 0, 1, 0, -6, 0, -2, 0, 0, 0, 4, 0, 0, 0, 14, 0, -1, 0, 0, 0, -8, 0, -4, 0, -16, 0, -10, 0, 0, 0, -1, 0, 16, 0, 1, 0, -4, 0, 0, 0, -2, 0, -6, 0, 2, 0, 4, 0, 0, 0, -2, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, 2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 2, 41], 'euler43': [1, 12, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, 0, 59], 'euler61': [1, -14, 61], 'euler67': [1, 8, 67], 'euler7': [1, 1, 0], 'euler71': [1, 16, 71], 'euler73': [1, 10, 73], 'euler79': [1, -16, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 2, 13], [1, -6, 17], [1, 4, 19], [1, -4, 23], [1, -2, 29], [1, 4, 31], [1, 2, 37], [1, 2, 41], [1, 12, 43], [1, 0, 47], [1, 2, 53], [1, 0, 59], [1, -14, 61], [1, 8, 67], [1, 16, 71], [1, 10, 73], [1, -16, 79], [1, 4, 83], [1, 6, 89], [1, 2, 97]], 'index': 13, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/eg'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-369600-1.1-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1647680407005070488, 'z1': {'__RealLiteral__': 0, 'data': '0.2035181319225544', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1647680407005070488', 'Lhash_array': ['1647680407005070488'], 'label': '2-369600-1.1-c1-0-13', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/eg'}