-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': -2, 'Lhash': '1630457097073100931', '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': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 3138.184679757938, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]], [11, [1]], [29, [1, 1]]], 'bad_primes': [2, 7, 11, 29], 'central_character': '393008.1', 'coefficient_field': '1.1.1.1', 'conductor': 393008, 'conductor_radical': 4466, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, 0, 5], [1, -1], [1], [1, 2, 13], [1, 6, 17], [1, 7, 19], [1, -3, 23], [1, 1], [1, -4, 31], [1, -2, 37], [1, 9, 41], [1, 4, 43], [1, -9, 47], [1, -9, 53], [1, -6, 59], [1, 2, 61], [1, -13, 67], [1, -9, 71], [1, -1, 73], [1, 10, 79], [1, 6, 83], [1, 15, 89], [1, 7, 97]], 'gamma_factors': [[], [0]], 'index': 1, 'label': '2-393008-1.1-c1-0-1', 'leading_term': '0.598512154506', '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/393008/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.5985121545056467, -0.07385310630996832, -1.312015686352474, -1.333139425457946, 0.8186210267038679, 3.521093271064702, 3.822313846219804, 1.271337785992414, -0.9314240281636358, -0.303022465848496, 0.8748158203874798, -1.060337271321973, -4.572679179830273, -4.303708280558827, 0.3286080397999018, 3.381803112701124, 1.564438790477916, -0.7808220635404107, 0.2877036239056241, 1.665696039970625, -0.02212728512155405, -1.621147500850445, -0.05496289937268815, 1.11002024115488, -1.04087921176437, -2.47710424848936, -0.5814028487205346, 0.2241031771839, -1.610423861946274, -0.358321198282377, 4.617860850919252, 5.467421007606491, 0.7908199721790704, -1.454113818499293, 0.1420072782240242, -0.7509285811578515, -2.67529266204252, 0.7295876112140399, 5.051811672799663, 2.565427880017191, -1.688709489036709, -0.3648920244741806, 1.701129497430499, -0.3668400652638134, -1.464362704655608, 0.3299689901122829, 0.2091373884189784, -0.3265005768681009, 2.507864831994501, 3.552570738702992, 0.1869647642150477, -0.1389247180458598, 2.996108789332886, 1.355388113474276, -2.292859216052638, -0.215603588700035, 1.676351752688153, -2.219999453483695, -3.333717823932546, 1.105189404204474, 1.935250119819289, -0.253419166190748, 1.108110595247484, 0.4589154689977468, -5.467022937561441, -6.499843179019723, -0.9837694481096376, 1.080899863573192, -0.183772411872096, 0.3280421280933272, -0.5583428646150183, -2.035726238632381, 0.6982781274456163, 1.691433647592384, -2.259880787722698, -1.414826227792908, 3.688480233256325, 2.394431217812486, -0.7246814785209159, 1.747572678871871, 2.155341024533356, -0.3741951117180429, 2.997908498835151, 6.041219463488029, 1.019354697477719, -2.031876352921362, 0.6282876140492264, 0.1633091813999472, -0.8650565381687655, 2.126639753583273, 1.794753653401446, -1.280904143899829, 0.153427569032011, 1.098266166537428, -0.9690131825515229, 0.4620674836672279, 1.307338210633942, -2.251674886183668, -1.222664422805797, 2.410180029560818, -0.6627537530028633, -2.719275034427385, 0.3979286808075389, -1.527592430030338, -4.074358021107231, 1.426880234812606, 3.947986180903622, -0.173835148622749, 0.02311582549695582, 1.061819478946382, -2.365869534386203, -1.86013463429572, 0.7922871468702313, -1.462288443058489, -1.833746723105156, 0.6097220161090734, -0.6689489973689406, -0.7060242550949561, 0.6766177179692864, -3.341727446340477, -4.598440728470768], 'positive_zeros': ['0.2344304402506960', '0.9261529764466067', '1.862561875506650', '2.294965061671894', '2.664643584239997', '3.483722819631537', '4.131233500396952', '4.466043752271162', '4.997840850923417', '5.505927037743880', '5.906798397801825', '6.571822780969507', '6.791367482354918', '7.271167521971922', '8.044446879806716', '8.473838027583615', '8.665921929376342', '9.216808563600242', '9.873525980251672', '10.27797537781323', '10.71753104305819', '11.20144120124908', '11.53803468604778', '11.79912102579917', '12.51525988869370', '12.76251652352109', '13.32379439730110', '13.76375316291364', '14.13184601096864', '14.68847090493171', '15.19671462234663', '15.36786207682455', '15.77515466385509', '16.55397081354073', '16.94379907852447', '17.15085428169323', '17.42996121288161', '17.95259005875854', '18.36564264881050', '18.81541395106056', '19.39381858026867', '19.61909021754910'], 'prelabel': '2-393008-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 56.01950267324709, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1630457097073100931, 'z1': {'__RealLiteral__': 0, 'data': '0.2344304402506960', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9261529764466067', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.862561875506650', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3138.184679757938, 'bad_primes': [2, 7, 11, 29], 'central_character': '1.1', 'conductor': 393008, 'conductor_radical': 4466, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 1, 0, -2, 0, 0, 0, -2, 0, 0, 0, -6, 0, -7, 0, -1, 0, 3, 0, -5, 0, 5, 0, -1, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, 0, -9, 0, -4, 0, 0, 0, 9, 0, 1, 0, 6, 0, 9, 0, 0, 0, 7, 0, 6, 0, -2, 0, -2, 0, 0, 0, 13, 0, -3, 0, 9, 0, 1, 0, 5, 0, 0, 0, -10, 0, 1, 0, -6, 0, 0, 0, 1, 0, -15, 0, -2, 0, -4, 0, 0, 0, -7, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 7, 19], 'euler2': [1, 0, 0], 'euler23': [1, -3, 23], 'euler29': [1, 1, 0], 'euler3': [1, 1, 3], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 9, 41], 'euler43': [1, 4, 43], 'euler47': [1, -9, 47], 'euler5': [1, 0, 5], 'euler53': [1, -9, 53], 'euler59': [1, -6, 59], 'euler61': [1, 2, 61], 'euler67': [1, -13, 67], 'euler7': [1, -1, 0], 'euler71': [1, -9, 71], 'euler73': [1, -1, 73], 'euler79': [1, 10, 79], 'euler83': [1, 6, 83], 'euler89': [1, 15, 89], 'euler97': [1, 7, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 0, 5], [1, -1, 0], [1, 0, 0], [1, 2, 13], [1, 6, 17], [1, 7, 19], [1, -3, 23], [1, 1, 0], [1, -4, 31], [1, -2, 37], [1, 9, 41], [1, 4, 43], [1, -9, 47], [1, -9, 53], [1, -6, 59], [1, 2, 61], [1, -13, 67], [1, -9, 71], [1, -1, 73], [1, 10, 79], [1, 6, 83], [1, 15, 89], [1, 7, 97]], 'index': 1, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/393008/u'], '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': '2-393008-1.1-c1-0-1', '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': '2-393008-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 56.01950267324709, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1630457097073100931, 'z1': {'__RealLiteral__': 0, 'data': '0.2344304402506960', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1630457097073100931', 'Lhash_array': ['1630457097073100931'], 'label': '2-393008-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/393008/u'}