data: - - Lhash: '4695332391707879906425245155924' a10: - -123.73679659309838 - 214.31841846506194 a2: - -3.194933459514875 - -5.533787078681566 a3: - 4.5 - -7.794228634059948 a4: - -4.415199621455375 - 7.647350069919583 a5: - -19.364534216604124 - -33.54035712806433 a6: - -57.50880227126775 - 5.48568260085501e-61 a7: - -87.5 - 95.65955258101513 a8: - -148.05066540485126 - 0.0 a9: - -40.5 - -70.14805770653953 accuracy: 100 algebraic: true analytic_conductor: 3.368060216072594 analytic_normalization: __RealLiteral__: 0 data: '2.5' prec: 10 bad_lfactors: - - 3 - - - 1.0 - 0 - - -4.5 - 7.794228634059948 - - 7 - - - 1.0 - 0 - - 87.5 - -95.65955258101513 bad_primes: - 3 - 7 central_character: '21.4' coefficient_field: CDF conductor: 21 conductor_radical: 21 conjugate: '1073782582287085393379894598584' degree: 2 euler_factors: - - - 1.0 - 0 - - 3.194933459514875 - 5.533787078681566 - - -16.0 - 27.712812921102035 - - - 1.0 - 0 - - -4.5 - 7.794228634059948 - - - 1.0 - 0 - - 19.364534216604124 - 33.54035712806433 - - -1562.5 - 2706.329386826371 - - - 1.0 - 0 - - 87.5 - -95.65955258101513 - - - 1.0 - 0 - - -288.19493345951486 - 499.1682672358116 - - -80525.5 - -139474.25730488764 - - - 1.0 - 0 - - -391.49119772873223 - 0 - - 371293.0 - 0 - - - 1.0 - 0 - - -664.8501520082015 - 1151.5542426980962 - - -709928.5 - -1229632.2317411618 - - - 1.0 - 0 - - 471.23679659309835 - 816.2060740952468 - - -1238049.5 - 2144364.636285245 - - - 1.0 - 0 - - -816.0395055305816 - -1413.421884562351 - - -3218171.5 - 5574036.5454701455 - - - 1.0 - 0 - - 1463.5440113563388 - 0 - - 20511149.0 - 0 - - - 1.0 - 0 - - -1956.208896907424 - 3388.2531996619264 - - -14314575.5 - -24793572.054780666 - - - 1.0 - 0 - - -8150.168107885218 - -14116.5052530847 - - -34671978.5 - 60053628.36093575 - - - 1.0 - 0 - - 13103.827413499168 - 0 - - 115856201.0 - 0 - - - 1.0 - 0 - - -14733.498115577779 - 0 - - 147008443.0 - 0 - - - 1.0 - 0 - - -3407.2601904530156 - -5901.547764471432 - - -114672503.5 - 198618602.2931199 - - - 1.0 - 0 - - -1005.6715123894538 - 1741.8741551831677 - - -209097746.5 - -362167920.6861574 - - - 1.0 - 0 - - 25726.554360919767 - -44559.6992567957 - - -357462149.5 - -619142604.7167817 - - - 1.0 - 0 - - 20548.910721005843 - 35591.75740897893 - - -422298150.5 - 731441852.6083683 - - - 1.0 - 0 - - 25289.098162895858 - -43802.00289573238 - - -675062553.5 - -1169242640.9491835 - - - 1.0 - 0 - - -39970.62684568223 - 0 - - 1804229351.0 - 0 - - - 1.0 - 0 - - -27843.31586207455 - 48226.037724301554 - - -1036535796.5 - -1795332663.4018745 - - - 1.0 - 0 - - -31575.675262324658 - -54690.67383764204 - - -1538528199.5 - 2664809010.4114656 - - - 1.0 - 0 - - -45572.3572792375 - 0 - - 3939040643.0 - 0 - - - 1.0 - 0 - - 7843.341349736934 - 13585.065718850225 - - -2792029724.5 - 4835937339.076535 - - - 1.0 - 0 - - -3128.494656653256 - 0 - - 8587340257.0 - 0 - - - 1.0 - 0 - - -84505.46128587102 - 146367.7524641734 - - -5255050250.5 - -9102014030.193556 - - - 1.0 - 0 - - 56410.061387609385 - 97705.09238141878 - - -5796370371.5 - 10039607982.924889 - - - 1.0 - 0 - - -11154.738890395565 - -19320.5745033296 - - -7012758653.5 - 12146454289.080307 - - - 1.0 - 0 - - -41909.7632034069 - 72589.83920148134 - - -7693119774.5 - -13324874318.146824 - - - 1.0 - 0 - - 40928.42658778521 - 0 - - 18424351793.0 - 0 gamma_factors: - [] - - 0 group: GL2 id: 9652737 index: 6 label: 2-21-7.4-c5-0-6 load_key: CMFs-workshop motivic_weight: 5 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 5 order_of_vanishing: 0 origin: ModularForm/GL2/Q/holomorphic/21/6/e/b/4/1 plot_delta: __RealLiteral__: 0 data: '0.17578125' prec: 34 plot_values: - 0.9473367581633526 - 1.151101179171459 - 1.3542488480285189 - 1.555132853434276 - 1.7516289991456147 - 1.9409844784728854 - 2.1197048670049825 - 2.2834901755621178 - 2.427230416999055 - 2.5450704983212633 - 2.6305529561204244 - 2.676844772666768 - 2.677050931582887 - 2.6246122800918323 - 2.5137786023735704 - 2.3401397294383313 - 2.1011884161450296 - 1.796879270530833 - 1.4301391459599155 - 1.007277243280799 - 0.538239004878874 - 0.036648036484868945 - -0.4804140275202883 - -0.9929276818128755 - -1.4787747214773852 - -1.914889848161694 - -2.278687080209638 - -2.549688857866584 - -2.711250835623444 - -2.752243866825445 - -2.6685310073486295 - -2.464066043016438 - -2.1514452335900285 - -1.7517687884489856 - -1.2937144747399987 - -0.8117918376656325 - -0.3438281720583902 - 0.07216990608681786 - 0.401541941390642 - 0.6165659192367396 - 0.6997372072796968 - 0.6463292013267962 - 0.465850856623684 - 0.18208730676169307 - -0.16846803905632174 - -0.5398147529768683 - -0.8811073975555728 - -1.1423983865115466 - -1.28089069074586 - -1.266983068621062 - -1.0893164647032862 - -0.7580506205720416 - -0.3057273427805738 - 0.21468936423625998 - 0.734682111628574 - 1.1776614804877996 - 1.4683688235068721 - 1.5431572253577137 - 1.3598549461028198 - 0.9058143287265614 - 0.20283508429574795 - -0.6920627437518688 - -1.690569550072686 - -2.681664173322261 - -3.544108359670319 - -4.161482786620285 - -4.4378782926207725 - -4.312072158523493 - -3.768034074695844 - -2.8399517140758204 - -1.6106240012824913 - -0.20297051894897125 - 1.2345707109437682 - 2.546990318356905 - 3.5934324470414807 - 4.266674301368772 - 4.508333486504713 - 4.31726636039771 - 3.7495655115998807 - 2.909842139845666 - 1.934897440534528 - 0.972211019945425 - 0.15666407296210186 - -0.4106306319508587 - -0.6777224940463853 - -0.6486418902893184 - -0.3802727891429439 - 0.030333361937400247 - 0.4660314291493743 - 0.8134008388338297 - 0.9858075978860701 - 0.941174620369626 - 0.6907755854949473 - 0.2969958955274946 - -0.1398616766261834 - -0.5034048776185616 - -0.687386446742246 - -0.6209671312313011 - -0.2875242436922012 - 0.2674387725942524 - 0.9416792096839376 - 1.594598622440586 - 2.0755012493878473 - 2.256252905799747 - 2.0615236711305847 - 1.4898322525797913 - 0.6201185434618063 - -0.3986623717535035 - -1.373914964646622 - -2.107183708618173 - -2.4359634662990284 - -2.270766010280328 - -1.6190977891994627 - -0.5902971919243946 - 0.6210390318135329 - 1.7707776439627847 - 2.6135309533563977 - 2.9537726916332745 - 2.6888903878095376 - 1.8344597764710409 - 0.5254405187211874 - -1.0080028582003475 - -2.485799626777254 - -3.635271138689396 - -4.248277335814598 - -4.2256493123753325 - -3.598775965460134 - -2.5230519539971947 - -1.244122532836281 - -0.04408076080488849 - 0.8204771997074836 - 1.1745291524914072 - 0.961962102113283 - 0.25550152675848997 - -0.7630624609828761 - -1.8476058839728942 - -2.746594736835888 - -3.2619547989507502 - -3.293619962135736 - -2.8590226723595293 - -2.083063624411615 - -1.1615776511261366 - -0.3081021887050891 - 0.30192469617430906 - 0.5747475383369532 - 0.5181275788206072 - 0.23230443834349118 - -0.12512734774155454 - -0.3903365568571795 - -0.4456073400052982 - -0.25750835354479107 - 0.11084908561785597 - 0.5180225790967568 - 0.7887055708956937 - 0.7722755722115489 - 0.3984125670991238 - -0.2873921468330589 - -1.1208117868049008 - -1.8518337855761864 - -2.2074645604833627 - -1.9682931379542503 - -1.038040994607714 - 0.5143319953011085 - 2.454113348560669 - 4.4253681908039 - 6.0316224530374525 - 6.933204999272167 - 6.935980535359062 - 6.047146903235025 - 4.48151348125109 - 2.6143869576874024 - 0.8915374364640589 - -0.28124473619175394 - -0.640227938126063 - -0.13016281004114247 - 1.0831647348022864 - 2.6581128306064157 - 4.168225115671459 - 5.214566499964398 - 5.528790373262988 - 5.038916263498779 - 3.8802861327311353 - 2.3496941192475513 - 0.8168120343286858 - -0.3809298234848868 - -1.0294589898833306 - -1.089227387694016 - -0.692740993990324 - -0.09103327992105445 - 0.4329703687502888 - 0.6564752480793149 - 0.4853462595259363 - -0.0218904162336346 - -0.6811710114729879 - -1.2512393952517593 - -1.5199832402470252 - -1.3796903099163367 - -0.8657816535100915 - -0.14563184591064732 - 0.5392405800753831 - 0.9584449139351611 - 0.9764790947741055 - 0.6057128416479278 - 0.00892929783080031 - -0.551635075450546 - -0.8035432327001857 - -0.5626504835322337 - 0.19278294894150075 - 1.2993366088302396 - 2.447898259939324 - 3.2756475058043386 - 3.48253201093463 - 2.934433903619525 - 1.7176744840793214 - 0.12394926737275117 - -1.433047730676372 - -2.5452176384876553 - -2.9418774079129224 - -2.582481474427498 - -1.6778251839123468 - -0.6294566586825446 - 0.09647085612395023 - 0.12242509559038749 - -0.7091335970640456 - -2.2699197135842994 - -4.169440549172101 - -5.863720397312738 - -6.817102617235641 - -6.667124202918371 - -5.340350253070948 - -3.0818625255995897 - -0.38826153824590254 - 2.1351920187622118 - 3.9484075417779256 - 4.726689289403386 - 4.44094555173965 - 3.344802527329052 - 1.8762157523583947 - 0.5088529689599209 - -0.39611207818743405 - -0.6892000761037462 - -0.45275874566011026 - 0.05965700867188992 - 0.5381750016141157 - 0.7412541968615955 - 0.5839591282385888 - 0.15886998386078152 - -0.31517020466646084 - -0.5937690162781903 - -0.5158792027188309 - -0.07690031103296197 - 0.5637315458472146 - 1.144288060424777 - 1.4079130482159075 - 1.2124066169275918 - 0.5973451363473706 - -0.22137141835018226 positive_zeros: - '3.70396416083621652751346224855503' - '6.47103772572418322098874192106900' - '7.65268311827782394120043657193470' - '9.245271005216166249143835702643790' - '10.58961778243552219371916689167335' - '12.50507141260342186601110567731130' - '14.45488707215421780811473907422939' - '15.28091175938255730592532770559124' - '16.46621334729973753839585077465655' - '17.32457896799792680685549169209191' prelabel: 2-21-7.4-c5-0 primitive: true rational: false root_analytic_conductor: 1.8352275652007284 root_angle: 0.9226686410332108 root_number: -0.9706340591692696 + 0.24056085130500113*I self_dual: false sign_arg: __RealLiteral__: 0 data: '0.461334320517' prec: 47 spectral_label: c5-0 types: - CMF z1: __RealLiteral__: 0 data: '3.70396416083621652751346224856' prec: 103 z2: __RealLiteral__: 0 data: '6.47103772572418322098874192107' prec: 103 z3: __RealLiteral__: 0 data: '7.65268311827782394120043657193' prec: 103 - - algebraic: true analytic_conductor: 3.368060216072594 bad_primes: - 3 - 7 central_character: '7.4' conductor: 21 conductor_radical: 21 degree: 2 id: 9652737 index: 6 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/21/6/e/b/4/1 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: 2-21-7.4-c5-0-6 motivic_weight: 5 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 5 order_of_vanishing: 0 prelabel: 2-21-7.4-c5-0 primitive: true rational: false root_analytic_conductor: 1.8352275652007284 root_angle: 0.4613343205166054 self_dual: false spectral_label: c5-0 z1: __RealLiteral__: 0 data: '3.70396416083621652751346224856' prec: 103 - - Lhash: '4695332391707879906425245155924' Lhash_array: - '4695332391707879906425245155924' id: 10018762 label: 2-21-7.4-c5-0-6 type: CMF url: ModularForm/GL2/Q/holomorphic/21/6/e/b/4/1 label_cols: - label - label - label labels: - 2-21-7.4-c5-0-6 - 2-21-7.4-c5-0-6 - 2-21-7.4-c5-0-6 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-20T01:56:41.447658'