data: - - Lhash: '993714538652549188058601419717' a10: - -26475307663.425148 - 36707560376.9826 a2: - 1174.530992096673 - 847.1298298397982 a3: - 0.0 - -178661.65845923455 a4: - 661894.1027911891 - 1989960.4789528477 a5: - 0.0 - 31252951.709222574 a6: - 151349620.3294675 - -209843654.95976165 a7: - 298845786.4702691 - 0.0 a8: - -908339744.7089766 - 2897980494.247124 a9: - -21459635000.40417 - 0.0 accuracy: 100 algebraic: true analytic_conductor: 22.35818754296497 analytic_normalization: __RealLiteral__: 0 data: '10.5' prec: 14 bad_lfactors: - - 2 - - - 1.0 - 0 - - -1174.530992096673 - -847.1298298397982 bad_primes: - 2 central_character: '8.5' coefficient_field: CDF conductor: 8 conductor_radical: 2 conjugate: '2279332467119074732692386110569' degree: 2 euler_factors: - - - 1.0 - 0 - - -1174.530992096673 - -847.1298298397982 - - - 1.0 - 0 - - 0 - 178661.65845923455 - - -10460353203.0 - 0 - - - 1.0 - 0 - - 0 - -31252951.709222574 - - -476837158203125.0 - 0 - - - 1.0 - 0 - - -298845786.4702691 - 0 - - 558545864083284030 - 0 - - - 1.0 - 0 - - 0 - 16932699325.676397 - - -7400249944258161000000 - 0 - - - 1.0 - 0 - - 0 - -506807225944.0664 - - -247064529073450400000000 - 0 - - - 1.0 - 0 - - -9279064445579.28 - 0 - - 69091933913008730000000000 - 0 - - - 1.0 - 0 - - 0 - -51892804334994.37 - - -714209495693373300000000000 - 0 - - - 1.0 - 0 - - -252325529791247.16 - 0 - - 39471584120695487000000000000 - 0 - - - 1.0 - 0 - - 0 - 359359461180396.94 - - -5132842708382183000000000000000 - 0 - - - 1.0 - 0 - - -741345378023071.8 - 0 - - 20825506393391553000000000000000 - 0 - - - 1.0 - 0 - - 0 - 35613412907048900 - - -855531895666462800000000000000000 - 0 - - - 1.0 - 0 - - 43883316586227810 - 0 - - 7386879101213258000000000000000000 - 0 - - - 1.0 - 0 - - 0 - -66741950809571350 - - -20083415214428110000000000000000000 - 0 - - - 1.0 - 0 - - 154354866565337600 - 0 - - 130033429462229770000000000000000000 - 0 - - - 1.0 - 0 - - 0 - -1641023511871898400 - - -1621038246414955000000000000000000000 - 0 - - - 1.0 - 0 - - 0 - 4375490125386005000 - - -15413179794770735000000000000000000000 - 0 - - - 1.0 - 0 - - 0 - -359041786066732900 - - -31040344686800427000000000000000000000 - 0 - - - 1.0 - 0 - - 0 - 10461214990088708000 - - -222623423334106740000000000000000000000 - 0 - - - 1.0 - 0 - - -25261957693967565000 - 0 - - 752359350923790900000000000000000000000 - 0 - - - 1.0 - 0 - - 9669385240006195000 - 0 - - 1348279907365869100000000000000000000000 - 0 - - - 1.0 - 0 - - 54743849271384580000 - 0 - - 7082211906170644000000000000000000000000 - 0 - - - 1.0 - 0 - - 0 - -131782886218553920000 - - -19982045332214680000000000000000000000000 - 0 - - - 1.0 - 0 - - 200106712542461230000 - 0 - - 86534669543385680000000000000000000000000 - 0 - - - 1.0 - 0 - - -1401406720338771800000 - 0 - - 527480512638944850000000000000000000000000 - 0 - - - 1.0 - 0 - - 0 - 748915996511366800000 - - -1232391940347446500000000000000000000000000 - 0 - - - 1.0 - 0 - - -1859520226302446500000 - 0 - - 1860294571709496000000000000000000000000000 - 0 - - - 1.0 - 0 - - 0 - 1847169427733824400000 - - -4140562374860212000000000000000000000000000 - 0 - - - 1.0 - 0 - - 0 - 3168593948946082000000 - - -6108807736878339000000000000000000000000000 - 0 - - - 1.0 - 0 - - 105801567449357480000 - 0 - - 13021089174137413000000000000000000000000000 - 0 gamma_factors: - [] - - 0 group: GL2 id: 18502830 index: 7 label: 2-2e3-8.5-c21-0-7 load_key: CMFs-workshop motivic_weight: 21 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 21 order_of_vanishing: 0 origin: ModularForm/GL2/Q/holomorphic/8/22/b/a/5/16 plot_delta: __RealLiteral__: 0 data: '0.17578125' prec: 34 plot_values: - 2.856597890284839 - 2.3613824492006326 - 1.750778240480343 - 1.0613594279518905 - 0.33456868918908494 - -0.38613822950993454 - -1.0582756613740099 - -1.6432333561898584 - -2.10890218547315 - -2.4318353951108107 - -2.598790109895739 - -2.607534293250591 - -2.466853566192642 - -2.1957472899628723 - -1.821860715172831 - -1.3792560661931905 - -0.9056763082854871 - -0.4394972910816026 - -0.016593589009655293 - 0.3326421061426161 - 0.5858886618406407 - 0.7308782131245893 - 0.7665906995920567 - 0.7035356683902827 - 0.5630622198011743 - 0.37571297806813153 - 0.1787162873135513 - 0.012786487808120604 - -0.08153116692509166 - -0.06768276346216995 - 0.08322414498533803 - 0.389228195668444 - 0.8551043985338299 - 1.4709929743516625 - 2.2122486226103644 - 3.040596292826713 - 3.906569215569274 - 4.75308870333477 - 5.519933117164051 - 6.1487460533727765 - 6.588161512255351 - 6.798585454757327 - 6.756175221770561 - 6.455603977966846 - 5.9112858787682505 - 5.156863966884617 - 4.242917553018693 - 3.2330159459104846 - 2.1984150031658025 - 1.211844786876283 - 0.34095359155993216 - -0.35795917252510845 - -0.8452823289218376 - -1.1019254640719427 - -1.131190546600247 - -0.9584102104103043 - -0.6283032234884711 - -0.20024052082136606 - 0.25814754752046526 - 0.6783874906640193 - 0.9988209333151895 - 1.1716564922314516 - 1.1685931817414326 - 0.9843164290124378 - 0.6373804398168189 - 0.16827401209060275 - -0.36520798872811255 - -0.894834852776652 - -1.3503036919106572 - -1.668126571692363 - -1.7999563028222858 - -1.7192802919494439 - -1.4255625424889364 - -0.9451915316086266 - -0.3289694635255078 - 0.35368577097996506 - 1.0232138404470548 - 1.6000606865480256 - 2.0152239845545368 - 2.2197916208894917 - 2.1921263974520593 - 1.9415943328231844 - 1.5081451914044304 - 0.9575873389869743 - 0.37298921276745556 - -0.1567919686087471 - -0.5499887429059303 - -0.7444554483565831 - -0.7080420362188738 - -0.4451947161723043 - 0.0013903143146014232 - 0.5545949591498625 - 1.111966630735199 - 1.559068890572757 - 1.7854217454761998 - 1.7008827757687823 - 1.250130884770658 - 0.4230576286335622 - -0.7406532974824522 - -2.1537201845390452 - -3.6902498037536002 - -5.200538079674605 - -6.529804117035679 - -7.538311582929653 - -8.120018972138094 - -8.217007744018476 - -7.8274700406036715 - -7.005934136526912 - -5.855543036359279 - -4.513411380562398 - -3.131178742422329 - -1.853672887483487 - -0.7989529847447225 - -0.0428432722661443 - 0.3896030349968712 - 0.5243615201411701 - 0.4304151129714978 - 0.20483807014069555 - -0.0464403076268431 - -0.22883631322111372 - -0.27669914840117676 - -0.16510673770273573 - 0.08633227782531275 - 0.41846983220554085 - 0.7456057931845881 - 0.974163568076888 - 1.0236004111833599 - 0.8455449926769015 - 0.4373233480373366 - -0.15307002249920604 - -0.8320060435305094 - -1.4748674246363962 - -1.9480497382757789 - -2.1345213393460947 - -1.9582433323095794 - -1.4026890189829604 - -0.5195403297781456 - 0.5747318745283758 - 1.7145411630414362 - 2.7109487589775316 - 3.3833355359315522 - 3.591467971056952 - 3.2620837092020833 - 2.4048564039778566 - 1.1143423053856156 - -0.44302117724680423 - -2.0550406467768987 - -3.4986671996761527 - -4.577526433926034 - -5.155240466381274 - -5.178298471950539 - -4.684047877066481 - -3.7921078064559905 - -2.6806479840239654 - -1.5519255742668374 - -0.5936388900499983 - 0.05641640127206451 - 0.3354407728165766 - 0.26546554813674755 - -0.054089103723246365 - -0.4696865018234033 - -0.8080865544761799 - -0.914861058750697 - -0.6890279148644697 - -0.10651467671240543 - 0.7726077455930679 - 1.8148421758466131 - 2.8398850857519267 - 3.657691970019641 - 4.108218816232996 - 4.095380232409828 - 3.607886431006927 - 2.7223561311080706 - 1.587893179228214 - 0.3953547030119644 - -0.6620586363183263 - -1.4282666050611972 - -1.8151019045011016 - -1.8175665680472963 - -1.5101423008171653 - -1.025049849035314 - -0.5175453490757819 - -0.12645232263425443 - 0.06059834549039271 - 0.028668494122011178 - -0.1618245957161964 - -0.39245676444231364 - -0.5204835127225569 - -0.4210309382562083 - -0.0275014440221374 - 0.6401875872908562 - 1.4675119098319158 - 2.260932878313132 - 2.785187824854068 - 2.814945660150228 - 2.189603133819347 - 0.8585519311374163 - -1.0942922058951274 - -3.453746016423189 - -5.905440299893906 - -8.091236352821129 - -9.676940861293575 - -10.41805363880647 - -10.209209498798979 - -9.106184485103844 - -7.315183963920803 - -5.1513285481645505 - -2.9751584939254374 - -1.1209674724440217 - 0.16735420465296152 - 0.7790293447414869 - 0.7487101090520838 - 0.2365433528297461 - -0.5183615432663502 - -1.259280971636555 - -1.7730065350127513 - -1.9361454046084425 - -1.7359877409107085 - -1.2619347147921358 - -0.671017082427275 - -0.1376017379128258 - 0.19870095170871327 - 0.27267590286700266 - 0.10995586197619489 - -0.18405516797758667 - -0.4595325515357045 - -0.5718041376296245 - -0.43093863283411155 - -0.03680456644315743 - 0.5112794705485764 - 1.034400911465637 - 1.319367985986855 - 1.1781035182946955 - 0.5052487126416917 - -0.6822085158994194 - -2.2353620267569525 - -3.898371105614121 - -5.363355839460809 - -6.342276261515422 - -6.637716950303414 - -6.193998470886844 - -5.1145023408859895 - -3.6395114114369793 - -2.0891112325790955 - -0.7850772218456686 - 0.02836738034103554 - 0.24421466105179576 - -0.08325282152962854 - -0.7568614238362694 - -1.4930939547215358 - -2.002128896378444 - -2.0700901373418232 - -1.6212030975645824 - -0.7425549686112384 - 0.33602680331115026 - 1.3023917833948755 - 1.8471092817575228 positive_zeros: - '0.78390255049273007730040633419641' - '3.17156184786151191438899533520956' - '4.76297274304642844193177515423167' - '5.19774308542985226974402675659356' - '8.868746480560423340584468994064695' - '10.09617749302770534695643821563745' - '11.48250711693640019042062989987933' - '13.09342140591813658847899917966826' - '14.88567227066064373770295822320115' - '15.81983804234260215623435672693372' prelabel: 2-2e3-8.5-c21-0 primitive: true rational: false root_analytic_conductor: 4.728444516219364 root_angle: -0.40331656012889083 root_number: 0.299091075130261 - 0.954224569363745*I self_dual: false sign_arg: __RealLiteral__: 0 data: '-0.201658280064' prec: 50 spectral_label: c21-0 types: - CMF z1: __RealLiteral__: 0 data: '0.78390255049273007730040633420' prec: 103 z2: __RealLiteral__: 0 data: '3.17156184786151191438899533521' prec: 103 z3: __RealLiteral__: 0 data: '4.76297274304642844193177515423' prec: 103 - - algebraic: true analytic_conductor: 22.35818754296497 bad_primes: - 2 central_character: '8.5' conductor: 8 conductor_radical: 2 degree: 2 id: 18502830 index: 7 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/8/22/b/a/5/16 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: 2-2e3-8.5-c21-0-7 motivic_weight: 21 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 21 order_of_vanishing: 0 prelabel: 2-2e3-8.5-c21-0 primitive: true rational: false root_analytic_conductor: 4.728444516219364 root_angle: -0.20165828006444542 self_dual: false spectral_label: c21-0 z1: __RealLiteral__: 0 data: '0.78390255049273007730040633420' prec: 103 - - Lhash: '993714538652549188058601419717' Lhash_array: - '993714538652549188058601419717' id: 18868856 label: 2-2e3-8.5-c21-0-7 type: CMF url: ModularForm/GL2/Q/holomorphic/8/22/b/a/5/16 label_cols: - label - label - label labels: - 2-2e3-8.5-c21-0-7 - 2-2e3-8.5-c21-0-7 - 2-2e3-8.5-c21-0-7 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-05-23T21:14:17.489381'