data: - - Lhash: '277337483463553400984214315404' a10: - -12533.676193595436 - -839.9735319664426 a2: - -6.355819394998424 - -6.355819394998424 a3: - -140.2956981199847 - 0.34218273789954506 a4: - 0.0 - -431.20711963632374 a5: - 1052.0791179250616 - -919.920936616851 a6: - 893.8689708280183 - 889.5192674636671 a7: - -7865.99943425172 - 7865.99943425172 a8: - -5994.8541044851445 - 5994.8541044851445 a9: - 19682.765821947767 - -96.01353219644886 accuracy: 100 algebraic: true analytic_conductor: 7.725537542458099 analytic_normalization: __RealLiteral__: 0 data: '4.5' prec: 10 bad_lfactors: - - 3 - - - 1.0 - 0 - - 140.2956981199847 - -0.34218273789954506 - - 5 - - - 1.0 - 0 - - -1052.0791179250616 - 919.920936616851 bad_primes: - 3 - 5 central_character: '15.8' coefficient_field: CDF conductor: 15 conductor_radical: 15 conjugate: '2248614130548872162813988774764' degree: 2 euler_factors: - - - 1.0 - 0 - - 6.355819394998424 - 6.355819394998424 - - 0 - 512.0 - - - 1.0 - 0 - - 140.2956981199847 - -0.34218273789954506 - - - 1.0 - 0 - - -1052.0791179250616 - 919.920936616851 - - - 1.0 - 0 - - 7865.99943425172 - -7865.99943425172 - - 0 - -40353607.0 - - - 1.0 - 0 - - 0 - -50710.17998792417 - - -2357947691.0 - 0 - - - 1.0 - 0 - - 4944.613730674769 - 4944.613730674769 - - 0 - 10604499373.0 - - - 1.0 - 0 - - -174648.32690349733 - -174648.32690349733 - - 0 - 118587876497.0 - - - 1.0 - 0 - - 0 - 36012.92917072996 - - -322687697779.0 - 0 - - - 1.0 - 0 - - 995471.4861695406 - -995471.4861695406 - - 0 - -1801152661463.0 - - - 1.0 - 0 - - 1376898.9045467132 - 0 - - 14507145975869.0 - 0 - - - 1.0 - 0 - - 5367760.819038696 - 0 - - 26439622160671.0 - 0 - - - 1.0 - 0 - - 4186395.585439863 - -4186395.585439863 - - 0 - -129961739795077.0 - - - 1.0 - 0 - - 0 - -16984457.445722584 - - -327381934393961.0 - 0 - - - 1.0 - 0 - - -4048620.565993183 - -4048620.565993183 - - 0 - 502592611936843.0 - - - 1.0 - 0 - - 39336711.413144745 - 39336711.413144745 - - 0 - 1119130473102767.0 - - - 1.0 - 0 - - 43411449.722220615 - -43411449.722220615 - - 0 - -3299763591802133.0 - - - 1.0 - 0 - - -126411564.73515567 - 0 - - 8662995818654939.0 - 0 - - - 1.0 - 0 - - 156468044.08830607 - 0 - - 11694146092834140 - 0 - - - 1.0 - 0 - - 70075597.20995381 - -70075597.20995381 - - 0 - -27206534396294948 - - - 1.0 - 0 - - 0 - 37841355.91855645 - - -45848500718449030 - 0 - - - 1.0 - 0 - - -107957151.16795713 - -107957151.16795713 - - 0 - 58871586708267910 - - - 1.0 - 0 - - 0 - 66007455.82231677 - - -119851595982618320 - 0 - - - 1.0 - 0 - - -305096143.9478996 - 305096143.9478996 - - 0 - -186940255267540400 - - - 1.0 - 0 - - 44925677.01325122 - 0 - - 350356403707485200 - 0 - - - 1.0 - 0 - - 177816671.1942521 - -177816671.1942521 - - 0 - -760231058654565200 - - - 1.0 - 0 - - 0 - -1399736950.8929358 - - -1093685272684361000 - 0 - - - 1.0 - 0 - - 551323526.6728214 - 551323526.6728214 - - 0 - 1304773183829244700 - - - 1.0 - 0 - - -791408255.0051498 - -791408255.0051498 - - 0 - 1838459212420154600 - - - 1.0 - 0 - - 0 - -527319089.99858236 - - -2171893279442309400 - 0 - - - 1.0 - 0 - - 316112486.91973555 - -316112486.91973555 - - 0 - -3004041937984268300 gamma_factors: - [] - - 0 group: GL2 id: 10095325 index: 0 label: 2-15-15.8-c9-0-0 load_key: CMFs-workshop motivic_weight: 9 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 9 order_of_vanishing: 0 origin: ModularForm/GL2/Q/holomorphic/15/10/e/a/8/7 plot_delta: __RealLiteral__: 0 data: '0.17578125' prec: 34 plot_values: - 0.34852228917002276 - 0.0726915023935745 - -0.2349720273073443 - -0.5643619172314324 - -0.9045615271324813 - -1.2440286071967286 - -1.5708086884026304 - -1.872786040789895 - -2.1379791182625816 - -2.3548842923758073 - -2.5128674081504783 - -2.6025974059470163 - -2.616510170469486 - -2.5492842206652098 - -2.3983032824141617 - -2.1640747366340243 - -1.850568048146594 - -1.4654342566431948 - -1.0200671663531575 - -0.5294696721762129 - -0.01189524538011741 - 0.5117547076662264 - 1.0187820933945768 - 1.4857779245482767 - 1.889907165885709 - 2.21033414882569 - 2.429707337456536 - 2.5356019703035386 - 2.521803813350492 - 2.3893095026267908 - 2.1469210992566974 - 1.8113263972396876 - 1.4065832613879525 - 0.9629657443061149 - 0.515180469326425 - 0.10002077548401664 - -0.24641111941585897 - -0.4917230293439565 - -0.6102501367225514 - -0.585792438954015 - -0.4137811296857915 - -0.10259812633796929 - 0.32618019551328564 - 0.8387655207675917 - 1.3914102159767263 - 1.9338466086500727 - 2.4136927285882512 - 2.781472420349942 - 2.9957868746564253 - 3.0281011291077333 - 2.866587384449953 - 2.5185074111389283 - 2.0107230829990796 - 1.3880936366596275 - 0.70973851406311 - 0.04339511566360115 - -0.54164601990066 - -0.9823221102724187 - -1.229426534840214 - -1.254145197994556 - -1.0526024061662962 - -0.64767977203601 - -0.08764788876960675 - 0.5584821946440597 - 1.208561262171836 - 1.777111350281479 - 2.1862326846128113 - 2.3762499413976976 - 2.314653321854034 - 2.001996090194544 - 1.4737146502530247 - 0.7973172430476924 - 0.06499161579314207 - -0.6176651883906578 - -1.1454819680238364 - -1.4283287650376812 - -1.4044785423859358 - -1.0507132249892075 - -0.387507177878892 - 0.5217645730806709 - 1.5778226750168816 - 2.6579913341559354 - 3.6326403952982087 - 4.383281657986848 - 4.81964639858173 - 4.893076318591814 - 4.6039947173002265 - 4.002050784018882 - 3.178640572176135 - 2.2527389962477655 - 1.3521290358878106 - 0.5929849950093123 - 0.0611858894075476 - -0.20140240389366143 - -0.20314724634849854 - -3.942142749282247e-05 - 0.31557394886122214 - 0.633177362154725 - 0.8461161050281537 - 0.8735249799338947 - 0.6780263907070487 - 0.27563420833949526 - -0.26443181954450073 - -0.8305361246553443 - -1.288546139615017 - -1.507567399978472 - -1.3868618791687677 - -0.8788019332566287 - -0.0031585277265914714 - 1.1505915411223018 - 2.434135818548256 - 3.6630845958604183 - 4.647941147427391 - 5.227796737909287 - 5.300425677585232 - 4.842819453791685 - 3.917765778960315 - 2.6646063621807436 - 1.27534300209467 - -0.03978109406965779 - -1.090826233793543 - -1.7433461713336207 - -1.9431351608286394 - -1.7253100128127503 - -1.205530665641247 - -0.5547732555364092 - 0.03746642805170989 - 0.404084614609545 - 0.4368435561986219 - 0.11053921639595161 - -0.5106053637629817 - -1.2861152935410312 - -2.029600152800737 - -2.5500132163075278 - -2.6949976498669583 - -2.386748737016901 - -1.64219227436393 - -0.5725373005225095 - 0.6382505061436778 - 1.7717579833624786 - 2.621979967052757 - 3.0402930341894 - 2.968250963042716 - 2.4504224184868444 - 1.6239017766297186 - 0.6864689998128106 - -0.14956802439947386 - -0.707253402688766 - -0.8868289414755602 - -0.6893984655327295 - -0.21636258239100153 - 0.355730720645014 - 0.8193077278083174 - 0.9884570346988263 - 0.7473773345393802 - 0.08245433181559766 - -0.9104594714601894 - -2.0460593225100125 - -3.0926348047925853 - -3.8279594936825174 - -4.094267008133091 - -3.8383445579696787 - -3.1261068434377117 - -2.1271827748653207 - -1.072592022212796 - -0.19562745789219949 - 0.32924053495621464 - 0.4335722027216647 - 0.17543779367276074 - -0.27318955552053925 - -0.6700854705202888 - -0.767223547810292 - -0.37991689686707786 - 0.5573344388297636 - 1.9635254074262676 - 3.6207447499976664 - 5.219772329859887 - 6.431346694165739 - 6.985735398406123 - 6.740513615881241 - 5.718909543422526 - 4.108227505139933 - 2.217959495804116 - 0.4076440332305631 - -0.9974475233592742 - -1.781327896468815 - -1.8838042242600797 - -1.4066910214500168 - -0.5786050840728184 - 0.31170403138533126 - 0.9950823354937571 - 1.2928942722874024 - 1.1598453953513703 - 0.6873781402852529 - 0.06751656018906274 - -0.47165531479721245 - -0.7395109744713224 - -0.6433697172474219 - -0.21767814800228233 - 0.3872076265769852 - 0.9536842903634456 - 1.2686288830033547 - 1.1964141207866918 - 0.7303792819384872 - 0.005724368818279101 - -0.7320602972311788 - -1.1957829905693416 - -1.1431099246529315 - -0.4557235160973373 - 0.8132383364832365 - 2.439381970748314 - 4.077309912800502 - 5.348574163470566 - 5.943330695553994 - 5.706758753580605 - 4.684797090809003 - 3.114903338204034 - 1.3632719594304141 - -0.17431888968241094 - -1.1798375354012864 - -1.4974379990195843 - -1.1702903117024877 - -0.41896528547172307 - 0.43207956018349924 - 1.057684736213949 - 1.2334537593857064 - 0.9044028820239567 - 0.19955104719425026 - -0.6122379632560926 - -1.2115840990551172 - -1.3351866215638122 - -0.8659474111083132 - 0.1224581836713766 - 1.3817317148009758 - 2.5620119590917056 - 3.319868263317419 - 3.427664789284659 - 2.849546949786791 - 1.7591196880609414 - 0.49182975934691414 - -0.5544058368054057 - -1.040153361145757 - -0.7894788281085325 - 0.15403379498527284 - 1.5382786124906436 - 2.9776687986241708 - 4.068978759828441 - 4.5117181385706555 - 4.19528885385016 - 3.2258510947480916 - 1.8853008563709088 - 0.5367526532372784 - -0.4917787970580224 - -1.006949915641094 - -1.0003209947125933 - -0.6335457215892468 - -0.16505292562551885 positive_zeros: - '0.21878069825677612834486054859455' - '3.51961274540368439748814843123649' - '6.19897463264964757868351767423403' - '7.25328366448422053722713781448379' - '9.679997859180825897423152639575047' - '10.92321286411559377859671107608593' - '12.67204768065423243394151261361790' - '13.79073183254233479226081432043202' - '16.20034037799159283563974055325922' - '16.69924376910559785529676440009636' prelabel: 2-15-15.8-c9-0 primitive: true rational: false root_analytic_conductor: 2.77948512182708 root_angle: -0.5532677403472392 root_number: -0.16656556248034993 - 0.9860303815783795*I self_dual: false sign_arg: __RealLiteral__: 0 data: '-0.276633870174' prec: 50 spectral_label: c9-0 types: - CMF z1: __RealLiteral__: 0 data: '0.21878069825677612834486054859' prec: 103 z2: __RealLiteral__: 0 data: '3.51961274540368439748814843124' prec: 103 z3: __RealLiteral__: 0 data: '6.19897463264964757868351767423' prec: 103 - - algebraic: true analytic_conductor: 7.725537542458099 bad_primes: - 3 - 5 central_character: '15.8' conductor: 15 conductor_radical: 15 degree: 2 id: 10095325 index: 0 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/15/10/e/a/8/7 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: 2-15-15.8-c9-0-0 motivic_weight: 9 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 9 order_of_vanishing: 0 prelabel: 2-15-15.8-c9-0 primitive: true rational: false root_analytic_conductor: 2.77948512182708 root_angle: -0.2766338701736196 self_dual: false spectral_label: c9-0 z1: __RealLiteral__: 0 data: '0.21878069825677612834486054859' prec: 103 - - Lhash: '277337483463553400984214315404' Lhash_array: - '277337483463553400984214315404' id: 10461350 label: 2-15-15.8-c9-0-0 type: CMF url: ModularForm/GL2/Q/holomorphic/15/10/e/a/8/7 label_cols: - label - label - label labels: - 2-15-15.8-c9-0-0 - 2-15-15.8-c9-0-0 - 2-15-15.8-c9-0-0 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-05-18T04:55:54.915967'