-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2314344471933184770061072358260', 'a10': [0.14461630763275488, -0.25048279242294225], 'a2': [0.6691306063588582, -0.7431448254773942], 'a3': [0.9135454576426009, -0.4067366430758002], 'a4': [-0.10452846326765347, -0.9945218953682733], 'a5': [0.2829121886759222, -0.0601348420794946], 'a6': [0.30901699437494745, -0.9510565162951535], 'a7': [1.345673285028357, 2.2779735314443386], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [0.6691306063588582, -0.7431448254773942], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6691306063588582, 0.7431448254773942]]], [3, [[1.0, 0], [-0.9135454576426009, 0.4067366430758002]]], [7, [[1.0, 0], [-1.345673285028357, -2.2779735314443386]]], [11, [[1.0, 0], [-3.2735831103087527, 0.5325914192899391]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.445', 'coefficient_field': 'CDF', 'conductor': 462, 'conductor_radical': 462, 'conjugate': '1919808984903375929846133715530', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6691306063588582, 0.7431448254773942]], [[1.0, 0], [-0.9135454576426009, 0.4067366430758002]], [[1.0, 0], [-0.2829121886759222, 0.0601348420794946], [4.567727288213004, -2.033683215379001]], [[1.0, 0], [-1.345673285028357, -2.2779735314443386]], [[1.0, 0], [-3.2735831103087527, 0.5325914192899391]], [[1.0, 0], [0.97341768111714, 2.9958715719695324], [-10.517220926874316, 7.641208279802151]], [[1.0, 0], [-2.657311819356382, -2.951243762380729], [-1.776983875550109, 16.906872221260645]], [[1.0, 0], [-0.6169440280548675, 5.8698303307701325], [-18.584804413942308, -3.9503221255374275]], [[1.0, 0], [-0.008531662538344049, -0.014777272989443946], [-11.5, 19.91858428704209]], [[1.0, 0], [4.104899647075815, -2.9823841667947764], [8.961492836873475, -27.580638972559452]], [[1.0, 0], [4.308699252451266, 0.9158422983712358], [28.31990918692063, 12.608835935349806]], [[1.0, 0], [-7.013691068762172, -3.1226964537052035], [24.757832435277756, 27.496358542663586]], [[1.0, 0], [3.3015324872067753, 2.398703759547037], [12.669696769372845, 38.9933171681013]], [[1.0, 0], [8.895179417711496, 0], [43.0, 0]], [[1.0, 0], [0.4273530064567615, -4.065992254037366], [-45.97293723448887, -9.77184946843469]], [[1.0, 0], [-5.396175763881116, -1.146992566537675], [48.41790925505785, 21.55704208301741]], [[1.0, 0], [-1.1349250454351942, -10.798090510495564], [-57.710708443294536, 12.266789758247802]], [[1.0, 0], [-5.851574709076732, 1.2437906005166102], [55.72627291619865, -24.810935227623812]], [[1.0, 0], [-5.12350068359966, 8.874163496608487], [-33.5, -58.023702053557386]], [[1.0, 0], [4.249652141923991, -13.07908443592102], [-57.440206600621266, -41.73275291276559]], [[1.0, 0], [0.7633794618231217, 7.263070416653475], [-71.40477485356782, 15.177553429696431]], [[1.0, 0], [9.907594875066959, -11.003498860106939], [-8.257748598144625, -78.56722973409359]], [[1.0, 0], [-1.5400823149790979, 4.739885986705922], [-67.14841053312064, -48.78617594027527]], [[1.0, 0], [-0.8352449443962427, -1.4466866804593344], [-44.5, 77.07626093681505]], [[1.0, 0], [4.625001179159575, 14.23428998851556], [-78.4746484543699, 57.01516947236989]], [[1.0, 0], [8.713666101997704, 1.8521469061812563], [92.2680912219027, 41.08040095065582]], [[1.0, 0], [7.5761841562628796, 3.373134511548283], [68.9204524549624, 76.5439170241716]], [[1.0, 0], [1.692734132121527, -16.105289457106373], [-104.66179327851721, -22.246550917500247]], [[1.0, 0], [-2.5094716488973154, 4.346532396043798], [-54.5, -94.39676901250381]], [[1.0, 0], [-8.07468115353905, -5.866599258129505], [34.91892036436906, 107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-462-77.60-c1-0-8', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/462/2/y/b/445/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.2854905842225137, 2.3715326759526643, 2.4623019642487756, 2.5527075790783575, 2.6335628915443565, 2.6925861670060014, 2.715660658205482, 2.688176677597707, 2.596383554810885, 2.4287334462180303, 2.1771965197988945, 1.8384935600668988, 1.4151527575895368, 0.9162679915211518, 0.3578241522919928, -0.23753546585120944, -0.8413928635841454, -1.4211301331495056, -1.942164164184551, -2.3707267777182572, -2.6769890311138234, -2.8382490331344257, -2.841842741868253, -2.687408953414241, -2.388153234166491, -1.970817359155816, -1.474171833093616, -0.9460034040613781, -0.43875387678044586, -0.004160848031202369, 0.3125701603969463, 0.47839711167857674, 0.47714550134119454, 0.31257886710923044, 0.009255862731540682, -0.38918055440574, -0.824329360267308, -1.2296652222009523, -1.5388134727446885, -1.6944917419287349, -1.6569390238404065, -1.4105971368115278, -0.9679310969901007, -0.3695784484387813, 0.3195206452017428, 1.0177930933904367, 1.6376858825878828, 2.097950971609146, 2.335830977015352, 2.317269651118051, 2.043411586775302, 1.5520904357881589, 0.9136948497293804, 0.22165907622599992, -0.42127546398993615, -0.9190880842231527, -1.1983159471448461, -1.221050541301768, -0.9927120143744006, -0.5629228770066638, -0.018859556436126503, 0.5282812626691888, 0.9618091411488068, 1.1801394192193924, 1.115952800312903, 0.7503906028144057, 0.1193867316311046, -0.6895576023632707, -1.550236346588188, -2.3185580927580594, -2.8580512519829893, -3.065673452347403, -2.8931638926596954, -2.359660517431544, -1.5526292761608038, -0.6161362796751989, 0.2721912678523705, 0.9319410131388233, 1.2131476870494204, 1.0258859220083678, 0.3604275273815568, -0.7063968021335102, -2.0206194226730005, -3.3754223580552414, -4.546463434836255, -5.332084791044156, -5.590986405452891, -5.270074013655607, -4.416760007429776, -3.1727744385827066, -1.7500377176033923, -0.392688549393038, 0.6677658226144983, 1.255621898768057, 1.2839999213498754, 0.7710405153212682, -0.16416904062095672, -1.3253574950557574, -2.4779206037724006, -3.3950960596890263, -3.902087707424614, -3.909098053453616, -3.4264896086733843, -2.559047490519803, -1.480777739434906, -0.3958843964236915, 0.5054148014522675, 1.0864494620989735, 1.2903104687279459, 1.1470432628299707, 0.7605274921526459, 0.2784737814022428, -0.14706118311144914, -0.39897499815994963, -0.4245858952511973, -0.24796354151973862, 0.0380088033529802, 0.297953339470104, 0.3921473037776793, 0.2168104632331886, -0.2639522366669022, -1.0031967639835802, -1.8777197456916563, -2.7153092224403848, -3.33640945199322, -3.5999378296399187, -3.4414611520416503, -2.8933856460791554, -2.0810064345430024, -1.1942483069703471, -0.44125326960844874, 0.004986595694226733, 0.05336035775516474, -0.2778416062687641, -0.8608560021335417, -1.4873512030264016, -1.9203687999955452, -1.9570361506238585, -1.4862993766041737, -0.5263382831449237, 0.7692682556108602, 2.140089270920141, 3.2768099494918785, 3.8954908304548406, 3.810135036827213, 2.9851123683539904, 1.5532311441115156, -0.20668067689553982, -1.9288396363535345, -3.2429684289625875, -3.8605340333536766, -3.643553978769141, -2.6385388838883466, -1.06648035537626, 0.7293194198179689, 2.3650959281230577, 3.507967128206891, 3.9539523438692656, 3.673061140993158, 2.810198154259942, 1.6420068407539843, 0.5012229823444827, -0.3114084412966041, -0.6043814153872803, -0.3415418758249643, 0.35480663470586526, 1.2440181420803806, 2.0389060923754507, 2.4890735465859493, 2.4525112794945776, 1.9355280911091661, 1.089960695133615, 0.16862017003259447, -0.5482730163163673, -0.8346589178203464, -0.5848626369725181, 0.15458545441858199, 1.1968226214534754, 2.266999980704388, 3.08020033586317, 3.4225488582094545, 3.212076304163634, 2.521629790140923, 1.5570662996297533, 0.596973122818616, -0.08855149942102813, -0.3162946592286824, -0.04246578908555296, 0.6261128521455939, 1.4654408095118163, 2.2023942318346896, 2.596999554835253, 2.5141736402564203, 1.9632596444943802, 1.09336554976746, 0.1459332095454424, -0.6209127100328404, -1.0128886439979043, -0.9599009085550175, -0.5372104198683474, 0.059552257068463184, 0.578073839514809, 0.7919695315255723, 0.5762024696712559, -0.049021194714195235, -0.9206727493563723, -1.781944094358368, -2.3632501633339116, -2.469814020249417, -2.0475476603409963, -1.2050197018838749, -0.1827379458181923, 0.7222591464036408, 1.2536515281573903, 1.2839615697349316, 0.8640895322057119, 0.21584754567088255, -0.3334308472063938, -0.4564840802449849, 0.05972589436022469, 1.2275195725618022, 2.829223898535, 4.458378942681258, 5.623436594935172, 5.886171249080704, 4.9949178537698335, 2.9723897453280714, 0.1297583560582239, -3.000344160531321, -5.795355850987062, -7.702739594398074, -8.383078542852957, -7.795265937805146, -6.199337322452204, -4.07657020075203, -1.990784185430098, -0.4319063546940259, 0.31243378309099873, 0.22068654719837455, -0.47987140136186585, -1.4029435993525385, -2.13523978220957, -2.3683613282908453, -1.9896319541806549, -1.1052316242717615, 0.008637996010717186, 1.0076420028135344, 1.5988159052649455, 1.6376297311485304, 1.1711618216946456, 0.4147181867808042, -0.3281663067683404, -0.7735733950946148, -0.755313501674439, -0.2797944498332699, 0.4804263571058726, 1.2510371711514667], 'positive_zeros': ['1.82569587512245668732920118023637', '3.62636256332634953695860099689977', '4.25320671593650508190611894706768', '5.44318511211982160790494413605623', '6.66607302876339282318535203641321', '7.50417021072377538430058968826027', '8.269837690984954968463373143609244', '9.459357171042273448334118103997546', '10.04695108551103565085681685755609', '11.41622683063524937649762694337249'], 'prelabel': '2-462-77.60-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': 0.3135585147449871, 'root_number': '0.552802178787605 + 0.833312517083283*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.156779257372', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82569587512245668732920118024', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.62636256332634953695860099690', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.25320671593650508190611894707', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'bad_primes': [2, 3, 7, 11], 'central_character': '77.60', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/462/2/y/b/445/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-462-77.60-c1-0-8', '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': '2-462-77.60-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': 0.15677925737249354, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82569587512245668732920118024', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2314344471933184770061072358260', 'Lhash_array': ['2314344471933184770061072358260'], 'label': '2-462-77.60-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/y/b/445/1'}