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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': 0, 'A8': 0, 'A9': 1, 'Lhash': '304241147297165012', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1878.0814555405154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '235200.1', 'coefficient_field': '1.1.1.1', 'conductor': 235200, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1], [1, 0, 11], [1, 6, 13], [1, 2, 17], [1, 4, 19], [1, -4, 23], [1, 6, 29], [1, 0, 31], [1, -6, 37], [1, -2, 41], [1, -4, 43], [1, 8, 47], [1, 2, 53], [1, -12, 59], [1, -6, 61], [1, -4, 67], [1, -12, 71], [1, -10, 73], [1, -8, 79], [1, 12, 83], [1, 14, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 111, 'label': '2-235200-1.1-c1-0-111', 'leading_term': '1.76465668954', '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/235200/ui', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.764656689541137, 0.8251066223844187, -1.298048341673065, -2.771800987555404, -1.907993783818919, 0.9092986474852796, 3.085219841675026, 2.579456976033589, 0.5184106757244306, -0.2609579882820728, 0.7030776598281548, 0.8133105736042927, -1.238369772562849, -2.756281769163062, -1.064467721416078, 1.70886392722733, 1.613677965666244, -0.5008991507293897, -0.2694420101138251, 2.379868143558819, 2.777959021968283, 0.2424045673125709, 0.2286923114652222, 4.563732093256596, 6.99132526404404, 3.430924599555384, -0.8250227986091754, -0.4286749721053718, 1.185561652898594, -0.4054992108039407, -1.971491178719926, 0.04226438947805934, 1.803156108413741, 0.1206541999307239, -0.6731044270496713, 2.11834615203899, 3.502127064248067, 1.011267283460922, -0.517443351793726, 0.05516922675679671, -2.159952265900325, -5.844355582117646, -4.381484238618709, -0.08468757335663983, -0.46237337091781, -2.546479626351778, 0.741510309837266, 4.665382727643707, 1.887920384609206, -2.22207054830508, -0.9345642057245089, 0.9088242548269846, -0.4628697497371452, 0.2754332821878854, 3.342935743671373, 1.863589851816835, -2.388126782883466, -2.141197709074411, 0.2436897291998566, -0.0826777149220587, 0.3634961746211303, 2.41975232642668, 0.6525349922144281, -1.907974501877441, 1.83462703293074, 5.977286610627812, 2.962321029135912, -0.3511552809524406, 1.060749865619897, -0.1290529968615719, -4.187313489595014, -2.757945767289045, 0.3568123157519534, -2.976122483388548, -6.073461733457796, -2.499148390199507, 0.2391585483375892, -0.9680680741474258, -0.02913215349882665, 1.405421050542719, -0.3953306616105585, 0.114396210528353, 3.309232559300247, 1.696485227477845, -1.652518121387655, -0.2742122398364535, -0.09607214999174539, -3.563162916240862, -2.649374231026641, 0.4344505033826315, -1.500280290268027, -1.415724333136053, 4.234680064061344, 3.98498333012688, -2.128239784405124, -1.898224566273022, 1.633839962838677, 0.2075795587539112, -0.5795087445819641, 1.192432539271259, -0.9355841741067173, -2.951022134491039, -0.2126347659871019, 0.1305666994811351, -1.917229803713201, 0.8132466816362731, 3.2370324712913, 0.7552369300921711, 0.07694640963727689, 0.02169414827729279, -4.007605144223843, -3.872622478044096, 1.011111278622089, -1.127415443416757, -5.60043216463259, -1.783286161654281, 1.311312501607254, -1.817766174662369, -1.353752385512457, 1.2287499484595, -0.4777544646750505], 'positive_zeros': ['0.3538777843105362', '1.175748685157772', '2.085762372108251', '2.343850784573075', '2.871163642334820', '3.585625164368980', '4.183082474170732', '4.530497726551482', '5.278843366564529', '5.476335054791451', '6.428637007418048', '6.798214866500853', '7.210648423223445', '7.746405121877473', '8.263298844154547', '8.583681481269131', '9.350836453556093', '9.691531084167416', '9.785257793539634', '10.75828122735755', '10.95379890156464', '11.46487268224074', '12.09020564208676', '12.58126123937350', '12.92936183482511', '13.22494094014722', '13.85001488902411', '14.45741698291755', '14.72748708441241', '14.94716421782199', '15.54307744659296', '15.91865114492878', '16.68281098575747', '16.86184621398368', '17.24175620888106', '17.93004855554648', '18.07810143180346', '18.92640728367427', '19.08228724256656', '19.50309541485928', '19.95224419445670'], 'prelabel': '2-235200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.336837165862896, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 304241147297165012, 'z1': {'__RealLiteral__': 0, 'data': '0.3538777843105362', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.175748685157772', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.085762372108251', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1878.0814555405154, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 235200, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, 0, 0, 0, -2, 0, -4, 0, 0, 0, 4, 0, 0, 0, 1, 0, -6, 0, 0, 0, 0, 0, 0, 0, 6, 0, -6, 0, 2, 0, 4, 0, 0, 0, -8, 0, 0, 0, -2, 0, -2, 0, 0, 0, -4, 0, 12, 0, 6, 0, 0, 0, 0, 0, 4, 0, 4, 0, 12, 0, 10, 0, 0, 0, 0, 0, 8, 0, 1, 0, -12, 0, 0, 0, -6, 0, -14, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 6, 13], 'euler17': [1, 2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, -12, 59], 'euler61': [1, -6, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, -10, 73], 'euler79': [1, -8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 14, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 0, 0], [1, 0, 11], [1, 6, 13], [1, 2, 17], [1, 4, 19], [1, -4, 23], [1, 6, 29], [1, 0, 31], [1, -6, 37], [1, -2, 41], [1, -4, 43], [1, 8, 47], [1, 2, 53], [1, -12, 59], [1, -6, 61], [1, -4, 67], [1, -12, 71], [1, -10, 73], [1, -8, 79], [1, 12, 83], [1, 14, 89], [1, -2, 97]], 'index': 111, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/235200/ui'], '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': '2-235200-1.1-c1-0-111', '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': '2-235200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.336837165862896, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 304241147297165012, 'z1': {'__RealLiteral__': 0, 'data': '0.3538777843105362', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '304241147297165012', 'Lhash_array': ['304241147297165012'], 'factors': ['2-235200-1.1-c1-0-111'], 'label': '2-235200-1.1-c1-0-111', 'type': 'ECQ', 'url': 'EllipticCurve/Q/235200/ui'}