-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4105382204012680241078642910491', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': -3, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [19, [1, -1]]], 'bad_primes': [3, 19], 'central_character': '171.1', 'coefficient_field': '1.1.1.1', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'euler_factors': [[1, 0, 2], [1], [1, 3, 5], [1, 1, 7], [1, 3, 11], [1, 4, 13], [1, -3, 17], [1, -1], [1, 0, 23], [1, 6, 29], [1, 4, 31], [1, -2, 37], [1, -6, 41], [1, 1, 43], [1, -3, 47], [1, 12, 53], [1, -6, 59], [1, 1, 61], [1, 4, 67], [1, 6, 71], [1, 7, 73], [1, -8, 79], [1, 12, 83], [1, 12, 89], [1, -8, 97], [1, 6, 101], [1, -14, 103], [1, -18, 107], [1, 16, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [1], [[[1, 3, 5], 1]], [[[1, 1, 7], 1]], [[[1, 3, 11], 1]], [[[1, 4, 13], 1]], [[[1, -3, 17], 1]], [[[1, -1], 1]], [[[1, 0, 23], 1]], [[[1, 6, 29], 1]], [[[1, 4, 31], 1]], [[[1, -2, 37], 1]], [[[1, -6, 41], 1]], [[[1, 1, 43], 1]], [[[1, -3, 47], 1]], [[[1, 12, 53], 1]], [[[1, -6, 59], 1]], [[[1, 1, 61], 1]], [[[1, 4, 67], 1]], [[[1, 6, 71], 1]], [[[1, 7, 73], 1]], [[[1, -8, 79], 1]], [[[1, 12, 83], 1]], [[[1, 12, 89], 1]], [[[1, -8, 97], 1]], [[[1, 6, 101], 1]], [[[1, -14, 103], 1]], [[[1, -18, 107], 1]], [[[1, 16, 109], 1]], [[[1, 6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-171-1.1-c1-0-7', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/171/2/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-2.1233418427384003e-120, 0.1355829293921456, 0.27689043239750755, 0.42902601877861435, 0.595962240013052, 0.7801929346626157, 0.9825303019044119, 1.2019983348904157, 1.435782871347853, 1.679224463514164, 1.9258635284834626, 2.1675601682975305, 2.394714049822632, 2.596605561975566, 2.7618705035553766, 2.8791083354848883, 2.9376095930745234, 2.9281723416518486, 2.843961681555231, 2.6813516368041093, 2.440676905618511, 2.1268146507144934, 1.7495154630600098, 1.3234092916971065, 0.8676274549912544, 0.4050060801377337, -0.039131208825291426, -0.4385745280400477, -0.7681333166960901, -1.005723963163661, -1.134479017000717, -1.1446888780074425, -1.0353725416473787, -0.8152781595163318, -0.50313968786553, -0.12706369265136072, 0.27701096935131536, 0.6677524390614055, 1.0016504586028605, 1.23678610473844, 1.3368495796205768, 1.2750330429863355, 1.0373911303074026, 0.6252676689406714, 0.056438327730990244, -0.6352839886495877, -1.4020962190676438, -2.18585169770351, -2.923070573872771, -3.5509013770554487, -4.0134713061052505, -4.267962042810446, -4.2897142660502015, -4.075709729632689, -3.6459084225153617, -3.04212348682789, -2.32438113987816, -1.5650100012777488, -0.8409997173506055, -0.2254245902418868, 0.22109305874941776, 0.45783391339052737, 0.46935800135129957, 0.2680070654092376, -0.10695599092379214, -0.5936588748292246, -1.115025868210344, -1.5884874654532737, -1.9368419166386925, -2.0988840975997034, -2.038356230242317, -1.7499091684810089, -1.2610897107569816, -0.6298582517594455, 0.062264593227420104, 0.7207009730557892, 1.2506836147290645, 1.570786422570404, 1.625216988603542, 1.3930355202013613, 0.8928041626818233, 0.18175356734613704, -0.6506902509367555, -1.4943482347549082, -2.2332513016443087, -2.7620695030590876, -3.001623346570886, -2.9111097837585094, -2.4950576770303, -1.8037392554104168, -0.9267138317583783, 0.019767765368140896, 0.9097763039870564, 1.626641255394823, 2.080905340738869, 2.224423398353526, 2.058232256261866, 1.6327286451655798, 1.0398856412402553, 0.3985321828852716, -0.16509554336209786, -0.5384520151011561, -0.6419580512203028, -0.4431585398241289, 0.03679022015518439, 0.7256441893113893, 1.5114521835952504, 2.261106871193307, 2.84307468788395, 3.1504752755584864, 3.1204800411021254, 2.746501083502456, 2.080789854807891, 1.2266844751464059, 0.3215666404180713, -0.4867057933417825, -1.065850423204503, -1.3230642924385574, -1.222377673242039, -0.7920993784576679, -0.12069791692157199, 0.6584630328927465, 1.3910402331968528, 1.9300923262258105, 2.1637697102492983, 2.0371146714246624, 1.5637102390499766, 0.8246925731674992, -0.04504649403850164, -0.8812131345710774, -1.520686349567555, -1.8326568666493885, -1.7443947168723388, -1.2565685991678268, -0.4449104416984653, 0.5524277687660315, 1.559716900210013, 2.396153085405497, 2.909867499774983, 3.0068472658852765, 2.6690221846867974, 1.9577902689372164, 1.0020731156677318, -0.026932727735998283, -0.9494246538258039, -1.612403058361575, -1.9196606363366997, -1.850167186830447, -1.460938680299197, -0.8736197959319517, -0.24738990959030643, 0.25627503293328835, 0.5096150327684003, 0.447671418671367, 0.08403432412622532, -0.49046780600924894, -1.1262940667214056, -1.6473873701145356, -1.8904420697433217, -1.7429142374398379, -1.171456003545733, -0.23425986043002003, 0.9259334099023014, 2.1073378292159526, 3.088291607394763, 3.6721547335570555, 3.728530261896852, 3.22193377237115, 2.2215034778333123, 0.8892669111594048, -0.5509593388208167, -1.8577461146588465, -2.820081243473368, -3.299056499318065, -3.25426498535787, -2.749204768860408, -1.9345423955923555, -1.0129707071017102, -0.19350932459653536, 0.3545002553591748, 0.537338018610282, 0.35466435136251123, -0.10489332003746292, -0.6892021535849651, -1.2230833046394127, -1.5541257310236645, -1.5928185794451875, -1.3371500083698797, -0.8753620897357015, -0.3656734922757654, 0.0026874872144369176, 0.058158048814639235, -0.30637774979513466, -1.1002248808022563, -2.223617560519304, -3.482251681903731, -4.625263168732469, -5.39864444904483, -5.602162327524837, -5.136629690220503, -4.0302546577372995, -2.4373810027830114, -0.6092191958349549, 1.1573083513224596, 2.581272091754697, 3.4560272572093402, 3.690767976618652, 3.3258296368185096, 2.518347881971116, 1.5018771069576693, 0.5297585775191495, -0.1841052169343916, -0.5128403507785663, -0.4412264989852363, -0.061729192733686995, 0.4565664963088995, 0.9178388096186255, 1.1551957812528402, 1.0776001279547476, 0.6957168883950281, 0.11972021444277933, -0.47066603752766834, -0.8763329264571751, -0.9361299726340119, -0.576161927481659, 0.16247952079021674, 1.1258002120096684, 2.0794994283557195, 2.764820516385281, 2.964094500169681, 2.5594289715361263, 1.5691875615171778, 0.1520824133571406, -1.4233637193590174, -2.837506605236138, -3.792651435908082, -4.082782183486477, -3.6426962452163414, -2.564155236240577, -1.074755427546669, 0.5154801468509911, 1.8866536519620134, 2.782699019353964, 3.0679687724236775, 2.752834424946316, 1.9824320233006567, 0.9922155447877978, 0.042557861256467724, -0.6500038600227039, -0.966583739923695, -0.9107079342550314, -0.597876588503609, -0.21343331837187654, 0.04901752963853757, 0.05097122513090986, -0.24412542033923762, -0.75437046415822], 'positive_zeros': ['3.23857552173567549926694025030601', '4.41466206651142691425988858089376', '5.51097905283736056328679977780922', '7.43141403312000422638829977686362', '7.968751144610877316457317025190196', '9.238767264318381906771348588363811', '10.15333178148614777799832547131897', '11.37237044309941020825023181952267', '12.45987383937424874038080001139914'], 'prelabel': '2-171-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 356985413515069152, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.23857552173567549926694025031', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.41466206651142691425988858089', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.51097905283736056328679977781', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, -2, -3, 0, -1, 0, 0, 0, -3, 0, -4, 0, 0, 4, 3, 0, 1, 6, 0, 0, 0, 0, 4, 0, 0, 2, -6, 0, -4, 0, 0, 0, 3, 0, 2, 0, 0, 0, 6, 0, -1, 6, 0, 0, 3, 0, -6, 0, 0, 8, -12, 0, 9, 0, 0, 0, 6, 0, -1, 0, 0, -8, 12, 0, -4, -6, 0, 0, -6, 0, -7, 0, 0, -2, 3, 0, 8, -12, 0, 0, -12, 0, -9, 0, 0, 0, -12, 0, 4, 0, 0, 0, -3, 0, 8, 0, 0, -8], 'euler11': [1, 3, 11], 'euler13': [1, 4, 13], 'euler17': [1, -3, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 2], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 1, 43], 'euler47': [1, -3, 47], 'euler5': [1, 3, 5], 'euler53': [1, 12, 53], 'euler59': [1, -6, 59], 'euler61': [1, 1, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 7], 'euler71': [1, 6, 71], 'euler73': [1, 7, 73], 'euler79': [1, -8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 12, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 2], [1, 0, 0], [1, 3, 5], [1, 1, 7], [1, 3, 11], [1, 4, 13], [1, -3, 17], [1, -1, 0], [1, 0, 23], [1, 6, 29], [1, 4, 31], [1, -2, 37], [1, -6, 41], [1, 1, 43], [1, -3, 47], [1, 12, 53], [1, -6, 59], [1, 1, 61], [1, 4, 67], [1, 6, 71], [1, 7, 73], [1, -8, 79], [1, 12, 83], [1, 12, 89], [1, -8, 97]], 'index': 7, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/171/b', 'ModularForm/GL2/Q/holomorphic/171/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/171/2/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-171-1.1-c1-0-7', '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': '2-171-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 356985413515069152, 'z1': {'__RealLiteral__': 0, 'data': '3.23857552173567549926694025031', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 10002611
{'Lhash': '4105382204012680241078642910491', 'Lhash_array': ['4105382204012680241078642910491'], 'label': '2-171-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/a/b'}
-
id: 24547629
{'Lhash': '4105382204012680241078642910491', 'Lhash_array': ['4105382204012680241078642910491'], 'label': '2-171-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/a/b/1/1'}
-
id: 22057
{'Lhash': '356985413515069152', 'Lhash_array': ['356985413515069152'], 'label': '2-171-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/171/b'}