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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': '1443606385090846283', '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, 6, 13], [1, 6, 17], [1, -2, 19], [1, -6, 23], [1, 2, 29], [1, 6, 31], [1, -4, 37], [1, 4, 41], [1, -12, 43], [1, -12, 47], [1, -10, 53], [1, -4, 59], [1, -2, 61], [1, -4, 67], [1, -16, 71], [1, 14, 73], [1, 4, 79], [1, 4, 83], [1, -8, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 142, 'label': '2-369600-1.1-c1-0-142', 'leading_term': '1.65394458918', '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/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.653944589179151, 1.024729770591923, -0.1266599069854942, -0.1144143548054824, 1.944904018201248, 4.426443264184911, 4.3849069449591, 1.345089760940904, -1.395627335289445, -0.9916652953701717, 0.6137379387175934, -0.4735663943214542, -3.455135061339137, -3.352048297403504, 0.8596850810222413, 3.752071653395053, 1.861018496162967, -0.7655690669317123, 0.189750614689311, 2.018404419392762, 0.8162331221249156, -0.9479893699310445, 0.1115606035463623, 0.9436758800764361, -1.70508098285898, -3.806314876456911, -1.472084954044546, 1.175150644844059, 0.2496877732963865, -0.5937251991916357, 0.4541467081618171, -1.911487384593797, -7.71562266844394, -8.08276050822856, -1.6259181366011, 1.814741569783755, -0.5449492278420442, -0.9125316269278169, 1.671056771799447, 0.671966025074438, -2.131364851876818, -0.5711895770328962, 1.763539504989644, -0.1638687864907486, -1.523845030735818, 0.5181287661939072, 0.1245488904508513, -2.75439391975955, -1.577067397119883, 1.377515118771141, 0.2542054894243015, -0.9421157914067639, 0.7685313539732146, -0.4985523423910081, -3.508287889801067, -0.2513150505849274, 4.304256381008356, 1.072549891985917, -2.793723985465905, 0.3783484690007007, 2.562298278470616, -0.1047534396198, 0.2388448875090482, 2.464854054485136, -0.2235874767346518, -2.464949006770544, 0.384908233024267, 1.218443617129122, -1.0515066041524, -0.4122129702651649, -0.02562292944786521, -2.47727232971376, -0.9672265836239253, 2.853913242994651, 1.177001459437566, -0.5052767783987551, 2.796215700141171, 2.391916081154376, -2.036938909595175, -1.342584543516601, 0.02742913913454051, -3.146044715844393, -1.646545195787055, 3.963485119226335, 1.811168369752745, -2.962938414893, -0.3520438600935517, 2.223739184997965, 0.2137963882475581, 0.03190343205899416, -0.1637348221944896, -2.408958359803899, -0.1017597743799431, 3.311721002237939, 0.6493727556813639, -0.7698037990608227, 1.902977535335559, 0.5379225207659537, -1.513156014315886, 0.2515004080953881, -1.967068154792544, -4.892942744853007, 0.7214487406215881, 4.299672904837544, -0.7902816474909627, -1.638606583600966, 2.059346153927875, 0.5679263889238738, -0.5272668048143467, 1.311110905308312, -0.7153703209290956, -0.4694041831653133, 5.531303048185151, 5.492505178088105, 0.2154865322858835, -0.4096291302726525, 0.02400030562102181, -0.382928860168343, 1.036302152292598, -2.092350358578353, -6.815254348441765], 'positive_zeros': ['0.4662426293048429', '0.7742100158454484', '1.848032119181547', '2.382628794036468', '2.702155397000907', '3.454885404760819', '4.146691109549467', '4.479214906304524', '5.086682809239897', '5.485244764600889', '5.871322689012150', '6.605915702982348', '7.034956095203057', '7.383744393898126', '7.624563616463581', '8.567639163095051', '8.952577148022736', '9.337466860704941', '9.800094229861112', '10.29233907360886', '10.73612200197250', '11.19025285785883', '11.51128927083012', '12.10994550937221', '12.52618664727285', '12.89354201825835', '13.21269740070036', '13.76032018177250', '14.29586452503668', '14.72979819310781', '15.23928866823896', '15.47724115822688', '15.98671234251899', '16.47146595886306', '16.87637145931024', '17.31270376392280', '17.49616349438327', '18.05354704378960', '18.58903957130037', '18.80805881148183', '19.37477556158844', '19.88137679131292'], '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': 1443606385090846283, 'z1': {'__RealLiteral__': 0, 'data': '0.4662426293048429', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.7742100158454484', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.848032119181547', '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, -6, 0, 0, 0, -6, 0, 2, 0, 1, 0, 6, 0, 0, 0, -1, 0, -2, 0, -6, 0, 1, 0, 0, 0, 4, 0, 6, 0, -4, 0, 12, 0, 0, 0, 12, 0, 1, 0, 6, 0, 10, 0, 0, 0, -2, 0, 4, 0, 2, 0, -1, 0, 0, 0, 4, 0, -6, 0, 16, 0, -14, 0, 0, 0, 1, 0, -4, 0, 1, 0, -4, 0, 0, 0, 2, 0, 8, 0, 6, 0, 6, 0, 0, 0, -14, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 6, 13], 'euler17': [1, 6, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 6, 31], 'euler37': [1, -4, 37], 'euler41': [1, 4, 41], 'euler43': [1, -12, 43], 'euler47': [1, -12, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, -16, 71], 'euler73': [1, 14, 73], 'euler79': [1, 4, 79], 'euler83': [1, 4, 83], 'euler89': [1, -8, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 6, 13], [1, 6, 17], [1, -2, 19], [1, -6, 23], [1, 2, 29], [1, 6, 31], [1, -4, 37], [1, 4, 41], [1, -12, 43], [1, -12, 47], [1, -10, 53], [1, -4, 59], [1, -2, 61], [1, -4, 67], [1, -16, 71], [1, 14, 73], [1, 4, 79], [1, 4, 83], [1, -8, 89], [1, 14, 97]], 'index': 142, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/c'], '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-c1-0-142', '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': 1443606385090846283, 'z1': {'__RealLiteral__': 0, 'data': '0.4662426293048429', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1443606385090846283', 'Lhash_array': ['1443606385090846283'], 'label': '2-369600-1.1-c1-0-142', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/c'}