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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '2202657796088506576', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 626.0271518468385, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '78400.1', 'coefficient_field': '1.1.1.1', 'conductor': 78400, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1], [1], [1, 2, 11], [1, 0, 13], [1, 7, 17], [1, 0, 19], [1, 3, 23], [1, 6, 29], [1, -7, 31], [1, -4, 37], [1, 7, 41], [1, 8, 43], [1, -7, 47], [1, 4, 53], [1, 14, 59], [1, -14, 61], [1, -12, 67], [1, -1, 71], [1, -14, 73], [1, -11, 79], [1, -14, 83], [1, -7, 89], [1, 7, 97]], 'gamma_factors': [[], [0]], 'index': 144, 'label': '2-280e2-1.1-c1-0-144', 'leading_term': '4.58843949614', '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/78400/fh', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9797781516118323, 1.018447250029417, -0.3859724836833284, -2.686745481612745, -4.287356112977489, -3.781949131020722, -1.525946200887167, 0.3736934647667728, 0.2067159375672164, -1.247944610154841, -1.508991114566667, 0.3857010722957234, 2.280818213395089, 1.562939876803216, -1.044720640533219, -2.022578000307704, 0.1698898142710358, 2.701359179363702, 2.29259822813037, 0.05740939693590944, -0.1998370977573942, 2.016379932553402, 3.008318692562815, 0.8783640591969062, -1.223727547783407, -0.3331195655208558, 1.073748137329169, -0.9248321891517173, -4.661204420528098, -5.020285854678758, -1.751087023746078, 0.2067040443704073, -0.8454479611394226, -0.9371099725335184, 1.725894012362209, 3.130212277569093, 1.072509937273071, -0.1363542487435944, 2.597438052250668, 4.920288850750796, 2.503758955153577, -1.082025465778307, -0.859535279965822, 0.7763585905306664, -0.511237849834638, -2.285194108679027, -0.637456245125746, 1.177444321449233, -1.249060036097377, -4.147075530359745, -2.076193287067262, 1.699503041138324, 1.453910906205065, -0.3923842504807675, 0.7110362524830836, 1.630473809881697, -1.530740550012535, -4.241586468596586, -1.944937428127713, 0.7752374671963967, -0.4990577053910939, -1.406317045447515, 1.120609795717902, 1.677351089500868, -2.078644140303875, -3.591554316639756, -0.4124379791402621, 1.05208160445964, -0.9508902212449782, -0.622711950932882, 2.005699158812386, 1.154996810817289, -1.349471279620164, 0.3937131617919693, 2.958045463321169, 0.3946400028813974, -2.609425059385907, -0.1624148808702945, 2.740157670254692, 1.248067257485821, -0.04056583437318721, 0.7909259332407256, -1.537503290552744, -5.573599330063587, -3.795234414487692, 1.288524076489858, 1.515516693073045, -0.5800475763469751, 1.037900376642139, 2.269525599566313, -0.5606804157011003, -1.373954245044537, 1.693564775914562, 1.765731539953864, -0.7814213224272148, 0.8337055933831652, 3.631426862814396, 1.416444483601992, -0.6578420180662921, 2.199154937078103, 3.259758979995874, -0.1835403642512171, -0.6389542794634282, 2.300299937136035, 1.770232865138103, -0.1836619124902188, 0.8708099806699715, -0.4980016275581681, -5.907684588943249, -6.03777915566706, -0.08568656648414438, 1.85142088368782, -0.469969283542848, -0.09168628880293225, 0.5114493527206093, -1.551345595715242, -0.3532257546915913, 3.433013072560786, 1.531336117217035, -2.664194272000491], 'positive_zeros': ['0.7003823003846423', '1.928084130098106', '2.290436649349630', '2.960217864110551', '3.651263557151073', '4.236177715148181', '5.008228221030165', '5.282160097832501', '6.078098287208241', '6.541587644594721', '6.930898487913833', '7.924822929371540', '8.098440930565484', '8.605684840824361', '9.375964242405938', '9.529204229439644', '10.40376050956771', '10.85487708396305', '11.19573100538473', '11.80702904264485', '12.16432917165764', '12.87029265460694', '13.41691773631184', '13.65891636587168', '14.15690664463300', '14.88971620665236', '15.19445730314384', '15.65576642784974', '16.12715850999024', '16.78072018614708', '17.14139792707659', '17.55789510270727', '18.09406011352394', '18.47174734031554', '19.02262771642325', '19.50975585077337'], 'prelabel': '2-280e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.02053460353792, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2202657796088506576, 'z1': {'__RealLiteral__': 0, 'data': '0.7003823003846423', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.928084130098106', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.290436649349630', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 626.0271518468385, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 78400, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -6, 0, 7, 0, 0, 0, 0, 0, 4, 0, 0, 0, -7, 0, -8, 0, 0, 0, 7, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -14, 0, 14, 0, 0, 0, 0, 0, 12, 0, 0, 0, 1, 0, 14, 0, 0, 0, 0, 0, 11, 0, 9, 0, 14, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, -7, 0, 6, 0], 'euler11': [1, 2, 11], 'euler13': [1, 0, 13], 'euler17': [1, 7, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 3, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 3], 'euler31': [1, -7, 31], 'euler37': [1, -4, 37], 'euler41': [1, 7, 41], 'euler43': [1, 8, 43], 'euler47': [1, -7, 47], 'euler5': [1, 0, 0], 'euler53': [1, 4, 53], 'euler59': [1, 14, 59], 'euler61': [1, -14, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 0], 'euler71': [1, -1, 71], 'euler73': [1, -14, 73], 'euler79': [1, -11, 79], 'euler83': [1, -14, 83], 'euler89': [1, -7, 89], 'euler97': [1, 7, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, 0, 0], [1, 0, 0], [1, 2, 11], [1, 0, 13], [1, 7, 17], [1, 0, 19], [1, 3, 23], [1, 6, 29], [1, -7, 31], [1, -4, 37], [1, 7, 41], [1, 8, 43], [1, -7, 47], [1, 4, 53], [1, 14, 59], [1, -14, 61], [1, -12, 67], [1, -1, 71], [1, -14, 73], [1, -11, 79], [1, -14, 83], [1, -7, 89], [1, 7, 97]], 'index': 144, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/78400/fh'], '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': '2-280e2-1.1-c1-0-144', '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': '2-280e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.02053460353792, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2202657796088506576, 'z1': {'__RealLiteral__': 0, 'data': '0.7003823003846423', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2202657796088506576', 'Lhash_array': ['2202657796088506576'], 'label': '2-280e2-1.1-c1-0-144', 'type': 'ECQ', 'url': 'EllipticCurve/Q/78400/fh'}