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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '1624722576410009521', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 3014.5123771073786, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [11, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '377520.1', 'coefficient_field': '1.1.1.1', 'conductor': 377520, 'conductor_radical': 4290, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, 4, 7], [1], [1, 1], [1, 2, 17], [1, 4, 19], [1, -8, 23], [1, 6, 29], [1, -10, 31], [1, 8, 37], [1, 0, 41], [1, 10, 43], [1, -8, 47], [1, -8, 53], [1, 0, 59], [1, -4, 61], [1, 8, 67], [1, 8, 71], [1, -2, 73], [1, -4, 79], [1, -2, 83], [1, 10, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 112, 'label': '2-377520-1.1-c1-0-112', 'leading_term': '6.29314665314', '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': 1, 'origin': 'EllipticCurve/Q/377520/dw', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.254518605633915, 0.8879843777793803, -1.252828739337868, -3.120885760084374, -2.199762352166943, 1.206113463681606, 3.539181995072919, 2.210216964322088, -0.787403563432242, -1.627498306233217, -0.2295294656522854, 0.140376227458443, -1.229615546023445, -1.387014579442504, 0.3035737793450641, 0.3442773443849729, -2.053736650101019, -2.285449505789972, 1.241484024424899, 2.669774647314591, -1.34697103894753, -4.451158884792981, -1.072161053665414, 3.484032347311498, 2.513717056355715, -0.6302310384982427, -0.4719822249330444, 0.2296867172605639, -1.663517284351808, -1.701538216563193, 2.28365533357711, 3.9664592394334, 0.7793465992425147, -0.9546579708925036, 0.8094780363989399, 0.8347311192612181, -0.6163536077634619, 1.155655266250886, 3.146072367424107, 0.7439415479392314, -1.21337017565939, 0.5214270819670332, -0.8635725658706054, -6.233338064685839, -5.82072296415844, 0.2525851191336663, 1.051171053558696, -2.74214830083562, -1.789984530353596, 1.508675971163786, 0.559987897557533, -0.5081992673481677, 1.256240396138394, 0.8610123031624964, 0.07085546781995063, 4.279329596405462, 7.036632620707979, 2.381026025052109, -1.539642454131511, -0.04853105157739811, 0.3684146715381043, -0.3094701972860281, 2.063356708713068, 2.248321242054728, -1.493133035106633, -1.190980457312268, 1.414305062191747, -0.8642129064534517, -1.294113222010963, 4.035603730934363, 2.712717683146478, -6.228913356435453, -7.35647445758541, -0.8547738349597607, 0.9921817857214116, -0.2229529722850994, 0.5224793844957342, -0.1261756608257312, -0.4203164083569128, 2.187295437595435, 1.369645142979957, -1.751830414781807, 0.4138171285799376, 1.969685246656864, -1.927987026267065, -1.314080813230857, 3.513897938720319, 1.504304314579235, -2.204259670758094, 0.0152421883072311, 0.6318784531681634, -0.9058774145382625, 1.830131997270768, 1.740153953723261, -3.436522242909736, -2.153393246600144, 2.337258236785945, -0.5206035093386944, -3.029896914333864, -0.04199978271933404, 0.1648529431264715, -0.4677385636983099, 2.665755044237134, 2.623566036342537, 0.003187394481916148, 0.6128004327059433, -0.4778783614036839, -2.128931955748678, 1.934896814848906, 2.423584481659299, -4.021318221409156, -4.00168120890291, 0.1745306907560235, -1.429811042641509, -0.4164543621895448, 4.685966120473112, 2.785787458178158, -0.6546906162064434, 0.4170956291457619, -2.170363697708344], 'positive_zeros': ['0.6202471942925619', '1.418037109008819', '2.177266688657783', '2.795054617632952', '3.036338595988809', '3.704273531615953', '4.045500328759520', '4.671570290560811', '5.184460417294832', '5.797633734987838', '6.432304587166268', '6.834220809825657', '7.051679008730105', '7.620874837222536', '8.307755197849800', '8.650023008248342', '9.114837134870136', '9.396075031317868', '10.05486684871117', '10.43236800679566', '10.69533511993749', '11.48756153792889', '11.82006124720359', '12.36383866413582', '12.81370401316437', '13.08848424864288', '13.62697315522627', '13.73782623635235', '14.60637732533722', '15.00597891699215', '15.32216057549278', '15.55679055992866', '16.14846066167954', '16.58839149657200', '16.93817327773017', '17.32088090472565', '17.82969107708287', '18.54413936181109', '18.91598179217790', '19.11359629732966', '19.47902758739705', '19.80104558804678'], 'prelabel': '2-377520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.90457519285054, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1624722576410009521, 'z1': {'__RealLiteral__': 0, 'data': '0.6202471942925619', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.418037109008819', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.177266688657783', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3014.5123771073786, 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '1.1', 'conductor': 377520, 'conductor_radical': 4290, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, -4, 0, 1, 0, 0, 0, -1, 0, -1, 0, -2, 0, -4, 0, -4, 0, 8, 0, 1, 0, 1, 0, -6, 0, 10, 0, 0, 0, 4, 0, -8, 0, -1, 0, 0, 0, -10, 0, -1, 0, 8, 0, 9, 0, -2, 0, 8, 0, 0, 0, -4, 0, 0, 0, 4, 0, -4, 0, 1, 0, -8, 0, 8, 0, -8, 0, 2, 0, 1, 0, 0, 0, 4, 0, 1, 0, 2, 0, 2, 0, -6, 0, -10, 0, 4, 0, 10, 0, 4, 0, 12, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 1, 0], 'euler17': [1, 2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -10, 31], 'euler37': [1, 8, 37], 'euler41': [1, 0, 41], 'euler43': [1, 10, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -8, 53], 'euler59': [1, 0, 59], 'euler61': [1, -4, 61], 'euler67': [1, 8, 67], 'euler7': [1, 4, 7], 'euler71': [1, 8, 71], 'euler73': [1, -2, 73], 'euler79': [1, -4, 79], 'euler83': [1, -2, 83], 'euler89': [1, 10, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, 4, 7], [1, 0, 0], [1, 1, 0], [1, 2, 17], [1, 4, 19], [1, -8, 23], [1, 6, 29], [1, -10, 31], [1, 8, 37], [1, 0, 41], [1, 10, 43], [1, -8, 47], [1, -8, 53], [1, 0, 59], [1, -4, 61], [1, 8, 67], [1, 8, 71], [1, -2, 73], [1, -4, 79], [1, -2, 83], [1, 10, 89], [1, -12, 97]], 'index': 112, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/377520/dw'], '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': '2-377520-1.1-c1-0-112', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-377520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.90457519285054, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1624722576410009521, 'z1': {'__RealLiteral__': 0, 'data': '0.6202471942925619', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1624722576410009521', 'Lhash_array': ['1624722576410009521'], 'label': '2-377520-1.1-c1-0-112', 'type': 'ECQ', 'url': 'EllipticCurve/Q/377520/dw'}