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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': -3, 'Lhash': '399798456654841633', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 232.5243706859686, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [7, [1, -1]], [13, [1, -1]]], 'bad_primes': [2, 5, 7, 13], 'central_character': '29120.1', 'coefficient_field': '1.1.1.1', 'conductor': 29120, 'conductor_radical': 910, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, 1], [1, -1], [1, -2, 11], [1, -1], [1, 4, 17], [1, 4, 19], [1, -4, 23], [1, -2, 29], [1, 2, 31], [1, 6, 37], [1, 0, 41], [1, -2, 43], [1, 8, 47], [1, -12, 53], [1, -4, 59], [1, -2, 61], [1, -16, 67], [1, 12, 71], [1, -6, 73], [1, 0, 79], [1, -4, 83], [1, 0, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 37, 'label': '2-29120-1.1-c1-0-37', 'leading_term': '4.83501995672', '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/29120/bd', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.112707870727474, 1.649850138257947, 1.14677024785773, -0.3719293595259, -2.095978698841298, -2.78246794101665, -1.760785345042508, 0.2418419578788035, 1.465719903743895, 0.6911204031733441, -1.396910605079942, -2.677511976672352, -1.772950116501589, 0.3114254078699538, 1.175436108448259, -0.165659192120218, -1.949627322704993, -1.745338182134256, 0.3664174987798039, 1.667832654555986, 0.2943352962540322, -2.071685190266198, -2.186211331018474, 0.3889188222020289, 2.530035442901385, 1.808538687184568, -0.03866824166640156, 0.4147558551538247, 3.152999945964015, 4.484290129105797, 2.354160993785683, -0.5928160730075372, -0.9383904287127617, 0.5359479966043623, 0.6161216857500976, -0.6532713429035146, 0.1985362084215636, 3.939864392701134, 6.205984319758787, 3.576992226482526, -0.9486799347167493, -2.0892938818022, 0.132925566507406, 1.284241115996769, 0.03800016427969556, -0.3464002899691255, 1.357817780844611, 1.719517395620956, -0.9755618814431984, -2.784448293544479, -0.4451600225901498, 2.600624752790712, 1.594812590478561, -1.465614170340551, -1.20890226919382, 1.928511717100811, 2.769067297630651, 0.5904208925120328, -0.1703730253166953, 1.389754041595965, 1.029681623268152, -2.044002465273857, -2.868483540901731, 0.2257502656432594, 1.987340426415973, -0.5696624451632286, -2.902151725430509, -1.429701868072444, 0.2298043325629677, -1.065180448800998, -1.589263881125481, 1.569897932689327, 3.74375137274624, 0.844112198962157, -2.616761553068825, -1.386702627403401, 1.362411632386513, 0.7389487723150223, -0.8241617200323806, 0.3837824563420026, 1.238503293694843, -1.54794822157115, -3.779455040947253, -1.682846120691673, 0.05491048914906461, -2.852838499926552, -5.470166354780476, -2.845523166053278, 0.5184104495413872, -0.4391213803744543, -2.037952222274463, -0.330726956028385, 0.8625305183140998, -1.170840242864552, -1.590511501422014, 1.822994662951865, 3.300089504323249, 0.6056692152391328, -0.3127154296733429, 2.279920501113292, 2.229117489361967, -1.473401781863894, -2.268553130142485, 0.4288478404004353, 0.209992539377534, -2.589145942435581, -1.525996861102179, 2.220358078686538, 2.159262349714251, -0.2859349558813544, 0.2302687888235258, 1.174044419709958, -1.495494149627639, -3.252233446192088, -0.361366896610389, 1.390041101961636, -1.335701261476945, -2.052782247202043, 1.637629843863629, 2.348624010977978], 'positive_zeros': ['0.9478674089519174', '1.969313638728767', '2.589172881891947', '3.460061258337159', '3.979359995720126', '4.710006184775839', '5.279577881183802', '5.967887431896378', '6.741662493001865', '6.937855970634521', '7.935957799369266', '8.407518364062865', '8.866974576139000', '9.230466198405256', '10.18888883580771', '10.73637383109033', '11.25664287019067', '11.56815751579892', '12.17460808928961', '12.77952727141265', '13.37050506642358', '13.85126566150195', '14.58033834556426', '14.78910445604298', '15.34274676062562', '15.98417219544176', '16.45972560712795', '17.16871188968618', '17.34718786791504', '17.89809815442426', '18.54701862635607', '19.10663804768414', '19.58827355413543', '19.95191960493129'], 'prelabel': '2-29120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.248749807311043, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 399798456654841633, 'z1': {'__RealLiteral__': 0, 'data': '0.9478674089519174', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.969313638728767', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.589172881891947', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 232.5243706859686, 'bad_primes': [2, 5, 7, 13], 'central_character': '1.1', 'conductor': 29120, 'conductor_radical': 910, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 1, 0, -3, 0, 2, 0, 1, 0, 0, 0, -4, 0, -4, 0, 0, 0, 4, 0, 1, 0, 0, 0, 2, 0, -2, 0, 0, 0, -1, 0, -6, 0, 0, 0, 0, 0, 2, 0, 3, 0, -8, 0, 1, 0, 0, 0, 12, 0, -2, 0, 0, 0, 4, 0, 2, 0, -3, 0, -1, 0, 16, 0, 0, 0, -12, 0, 6, 0, 0, 0, 2, 0, 0, 0, 9, 0, 4, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 10, 0, -6, 0], 'euler11': [1, -2, 11], 'euler13': [1, -1, 0], 'euler17': [1, 4, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 3], 'euler31': [1, 2, 31], 'euler37': [1, 6, 37], 'euler41': [1, 0, 41], 'euler43': [1, -2, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -12, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, -16, 67], 'euler7': [1, -1, 0], 'euler71': [1, 12, 71], 'euler73': [1, -6, 73], 'euler79': [1, 0, 79], 'euler83': [1, -4, 83], 'euler89': [1, 0, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, 1, 0], [1, -1, 0], [1, -2, 11], [1, -1, 0], [1, 4, 17], [1, 4, 19], [1, -4, 23], [1, -2, 29], [1, 2, 31], [1, 6, 37], [1, 0, 41], [1, -2, 43], [1, 8, 47], [1, -12, 53], [1, -4, 59], [1, -2, 61], [1, -16, 67], [1, 12, 71], [1, -6, 73], [1, 0, 79], [1, -4, 83], [1, 0, 89], [1, -10, 97]], 'index': 37, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/29120/bd'], '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': '2-29120-1.1-c1-0-37', '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': '2-29120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.248749807311043, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 399798456654841633, 'z1': {'__RealLiteral__': 0, 'data': '0.9478674089519174', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '399798456654841633', 'Lhash_array': ['399798456654841633'], 'label': '2-29120-1.1-c1-0-37', 'type': 'ECQ', 'url': 'EllipticCurve/Q/29120/bd'}