data: - - Lhash: '3530998172299460347542111941674' a10: - -2.6756379191452906 - 2.5143033246678455 a2: - 1.3767386367626386 - -0.32340489489949226 a3: - 1.7087382700800293 - -0.28321992225814313 a4: - 1.7908185479100966 - -0.8904880282525828 a5: - -2.2483960518670796 - 1.29811206579035 a6: - 2.2608912873427918 - -0.9425341303196686 a7: - -2.5367843988886802 - -0.751481811859074 a8: - 2.1775008991527116 - -1.805128758340837 a9: - 2.839572951272183 - -0.9678974400231597 accuracy: 100 algebraic: true analytic_conductor: 1.341486753957511 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 2 - - - 1.0 - 0 - - -1.3767386367626386 - 0.32340489489949226 - - 3 - - - 1.0 - 0 - - -1.7087382700800293 - 0.28321992225814313 - - 7 - - - 1.0 - 0 - - 2.5367843988886802 - 0.751481811859074 bad_primes: - 2 - 3 - 7 central_character: '168.101' coefficient_field: CDF conductor: 168 conductor_radical: 42 conjugate: '3193835539169997991662474081147' degree: 2 euler_factors: - - - 1.0 - 0 - - -1.3767386367626386 - 0.32340489489949226 - - - 1.0 - 0 - - -1.7087382700800293 - 0.28321992225814313 - - - 1.0 - 0 - - 2.2483960518670796 - -1.29811206579035 - - 2.5 - -4.330127018922194 - - - 1.0 - 0 - - 2.5367843988886802 - 0.751481811859074 - - - 1.0 - 0 - - 1.6380804859691884 - -2.837238628585752 - - -5.5 - -9.526279441628825 - - - 1.0 - 0 - - 0.9126351796316271 - 0 - - 13.0 - 0 - - - 1.0 - 0 - - 2.394477502802211 - -4.147356692434078 - - -8.5 - -14.722431864335457 - - - 1.0 - 0 - - 2.6669294685992293 - 4.6192573398165315 - - -9.5 - 16.454482671904334 - - - 1.0 - 0 - - -4.455688468139663 - 2.572492936505546 - - 11.5 - -19.91858428704209 - - - 1.0 - 0 - - 1.3595025432348997 - 0 - - 29.0 - 0 - - - 1.0 - 0 - - -8.184691742069356 - -4.72543398051785 - - 15.5 - 26.846787517317598 - - - 1.0 - 0 - - 1.5974571077994633 - -0.9222922912069011 - - 18.5 - -32.04293994002423 - - - 1.0 - 0 - - 5.918328640518468 - 0 - - 41.0 - 0 - - - 1.0 - 0 - - 0 - 8.001253423780035 - - -43.0 - 0 - - - 1.0 - 0 - - 3.292430857723993 - 5.702657525985534 - - -23.5 - 40.703193977868615 - - - 1.0 - 0 - - 0.8417118818667857 - -1.4578877447276855 - - -26.5 - -45.89934640057525 - - - 1.0 - 0 - - 1.5026602587439604 - 0.8675613048863782 - - 29.5 - 51.09549882328188 - - - 1.0 - 0 - - -4.723474002337222 - -8.181296960278782 - - -30.5 - 52.827549630850754 - - - 1.0 - 0 - - -10.863393994497049 - -6.271983447035835 - - 33.5 - 58.023702053557386 - - - 1.0 - 0 - - 0 - 0.6039886131109159 - - -71.0 - 0 - - - 1.0 - 0 - - 1.2922016800577454 - 0.7460529878286261 - - 36.5 - 63.21985447626402 - - - 1.0 - 0 - - 0.06251521712205955 - 0.10827953230160696 - - -39.5 - 68.41600689897065 - - - 1.0 - 0 - - 0 - -0.24643089869960472 - - -83.0 - 0 - - - 1.0 - 0 - - 1.8067066098191384 - 3.1293076425772672 - - -44.5 - 77.07626093681505 - - - 1.0 - 0 - - 0 - 5.103235351336727 - - -97.0 - 0 - - - 1.0 - 0 - - -6.33114396718448 - -3.6552876737322344 - - 50.5 - 87.4685657822283 - - - 1.0 - 0 - - -0.670565982987915 - 0.38715145078747876 - - 51.5 - -89.20061658979718 - - - 1.0 - 0 - - 7.2643462270496775 - 12.58221674902132 - - -53.5 - 92.66471820493493 - - - 1.0 - 0 - - 12.801469237564225 - 7.390931710330419 - - 54.5 - 94.39676901250381 - - - 1.0 - 0 - - 0 - -16.270806839409936 - - -113.0 - 0 gamma_factors: - [] - - 0 group: GL2 id: 9633808 index: 25 label: 2-168-168.101-c1-0-25 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/168/2/ba/c/101/23 plot_delta: __RealLiteral__: 0 data: '0.125' prec: 17 plot_values: - 2.1050718372037887 - 2.139279998325629 - 2.1975328357048842 - 2.2769492166676137 - 2.3725247166314376 - 2.4776561252113534 - 2.5846578526154786 - 2.6851996123581454 - 2.770671951038775 - 2.832522659565295 - 2.8626073137428287 - 2.8535795816413674 - 2.7993254627395094 - 2.6954266202671433 - 2.5396231282523303 - 2.3322353147331527 - 2.0764978230126143 - 1.7787566988237449 - 1.448482643983549 - 1.0980609872378353 - 0.7423316455774459 - 0.3978702291942748 - 0.08202378969925953 - -0.1882597866849648 - -0.3977430251307141 - -0.5342596120096575 - -0.5900122995406318 - -0.5626816802377748 - -0.4562157984059938 - -0.28117938411505206 - -0.0545643329537168 - 0.2009999201799369 - 0.4586476752353422 - 0.6892419593785015 - 0.8637909886131421 - 0.956140945885948 - 0.9457156750597481 - 0.8200358313706219 - 0.5767351304567654 - 0.22480506130086267 - -0.21515521107080293 - -0.7118302616585624 - -1.225263494183608 - -1.710034663937648 - -2.119327128225204 - -2.409547101474639 - -2.5450543741418623 - -2.502498743040271 - -2.2742418588701208 - -1.8703890141901423 - -1.3190621063254826 - -0.6647087407825558 - 0.03554955849301035 - 0.7172949131756853 - 1.3154509211064522 - 1.771515748869465 - 2.040585822913091 - 2.0973105317725897 - 1.939965149084415 - 1.5919834563053739 - 1.1005455626736698 - 0.5321483085848633 - -0.03453945010215849 - -0.5178611087368776 - -0.8433984796474869 - -0.9540194881266474 - -0.8184436546463597 - -0.43710283840990455 - 0.15567414996372692 - 0.8937210038412892 - 1.685390138361448 - 2.423691533824672 - 2.999155012301876 - 3.313910860159765 - 3.2952076535489283 - 2.906533009068514 - 2.1546988178733377 - 1.0916899528691864 - -0.18928839095334754 - -1.563369932186297 - -2.8882146953241326 - -4.021149478134871 - -4.837083465175742 - -5.244798343261101 - -5.199320742681075 - -4.708529681799298 - -3.8328879091557444 - -2.6781214581241453 - -1.3816777998969443 - -0.0947220949390527 - 1.0378617213260217 - 1.8966321780793851 - 2.403128994191366 - 2.5294785866754603 - 2.300601185520567 - 1.7886544157116224 - 1.1005389455615244 - 0.3603864792688667 - -0.310231297741925 - -0.8112357699270539 - -1.079081579106634 - -1.0954728032941112 - -0.8883457657251488 - -0.5249908901536975 - -0.09851832987340785 - 0.2899723021018843 - 0.5503851822700746 - 0.6204100021689322 - 0.47706759413461913 - 0.14089404858620036 - -0.32805639518905894 - -0.8417196944157814 - -1.3009637495174826 - -1.6148224889411582 - -1.71837357590399 - -1.5857761814294773 - -1.2358198334520025 - -0.7287093682745464 - -0.15448559349687288 - 0.384852069087659 - 0.7961190719462474 - 1.0144854774525713 - 1.0177057326329297 - 0.8318293960383726 - 0.5267390930573045 - 0.20183824463485076 - -0.03575771589811314 - -0.09648600761026724 - 0.06797015507125241 - 0.4476326367731478 - 0.9679322125721587 - 1.4964230971642147 - 1.862337784581203 - 1.8862468481102026 - 1.4148829562910958 - 0.3547991343011877 - -1.3017173649279317 - -3.4640422507462088 - -5.947336764463687 - -8.4938681790773 - -10.808795282908685 - -12.604823052392401 - -13.648182154093414 - -13.797776635771699 - -13.030248322567443 - -11.446021484184838 - -9.254727579675732 - -6.7421617735295385 - -4.224379050833481 - -1.9970183310748548 - -0.28893696758029913 - 0.7714878963633992 - 1.1713790539903401 - 1.0072236536606736 - 0.4591556483093105 - -0.24900381086155984 - -0.8958826291833075 - -1.305682852478339 - -1.3798323774089434 - -1.1111437620068274 - -0.578131554626302 - 0.07871387551655416 - 0.6931398168531805 - 1.1137007530487804 - 1.2397156303985917 - 1.0447364145541376 - 0.5824507761338193 - -0.02614626467463661 - -0.6212981780370946 - -1.0422084665402491 - -1.1653064847996586 - -0.9342568930099533 - -0.37472520492778844 - 0.40967369450118013 - 1.259549685605724 - 1.9951742863722701 - 2.4572071582791084 - 2.5434079022998213 - 2.2328164951811984 - 1.5916500046123614 - 0.759303342217037 - -0.08257426270583956 - -0.7509835179563282 - -1.1030941881237863 - -1.0687378715965734 - -0.6662133675356099 - 0.002439825795875155 - 0.7757535083601333 - 1.471130824726547 - 1.9281342739462977 - 2.0464469096984317 - 1.8093274472287884 - 1.2867498036367235 - 0.6172622454244946 - -0.027216036989680868 - -0.4851738217200602 - -0.6470855335683717 - -0.4843173797759913 - -0.05779481145809082 - 0.4962714553245139 - 1.0006170558189085 - 1.2830015713750598 - 1.2227436513331693 - 0.7857817825845117 - 0.0387578000812899 - -0.8624667137474061 - -1.7081777272512255 - -2.2862499903203912 - -2.4374061578885993 - -2.1004524433123857 - -1.3354467619702886 - -0.3176411603091462 - 0.6980567341811147 - 1.4350548272895949 - 1.662512155072513 - 1.2562548069507922 - 0.23794438947570243 - -1.2182220176552476 - -2.814687058724153 - -4.190535014007535 - -4.999685167244081 - -4.989793143525457 - -4.063535453992949 - -2.3074536990036583 - 0.01933048785831003 - 2.535062253308737 - 4.813461796552552 - 6.472752992104911 - 7.25558358966134 - 7.081709369232395 - 6.0615154183962785 - 4.4675087051576625 - 2.670684053732441 - 1.056793077308051 - -0.05793227321008414 - -0.49222549461647275 - -0.23183948375712687 - 0.5781006566192352 - 1.6771178480589988 - 2.7578139906506687 - 3.541243507235769 - 3.840707736933984 - 3.599033935169012 - 2.8916321336808695 - 1.8965793706752747 - 0.8413242625539172 - -0.05881519139569396 - -0.6537703854535168 - -0.8898943704317402 - -0.8121905094037998 - -0.5388595419401736 - -0.21709348886355773 - 0.02598591349877501 - 0.1224222259653249 - 0.0810700442500181 - -0.021063691014183025 - -0.07062725874009632 positive_zeros: - '2.78546641453389050173910249535347' - '3.77747040583234867593579540976443' - '4.94148459187719850545050245285208' - '6.49367416808772968124210309629301' - '7.74201929700137100107931727553197' - '8.470549289626051456316929189478512' - '9.732384762863786199044973063856803' - '11.13465596048661886890042302585103' - '12.18924802115817814178699425731691' - '13.02942361959689160822440521062939' prelabel: 2-168-168.101-c1-0 primitive: true rational: false root_analytic_conductor: 1.1582256921505028 root_angle: 0.11205160696306983 root_number: 0.9386779690294043 + 0.3447951137397871*I self_dual: false sign_arg: __RealLiteral__: 0 data: '0.0560258034815' prec: 50 spectral_label: c1-0 types: - CMF z1: __RealLiteral__: 0 data: '2.78546641453389050173910249535' prec: 103 z2: __RealLiteral__: 0 data: '3.77747040583234867593579540976' prec: 103 z3: __RealLiteral__: 0 data: '4.94148459187719850545050245285' prec: 103 - - algebraic: true analytic_conductor: 1.341486753957511 bad_primes: - 2 - 3 - 7 central_character: '168.101' conductor: 168 conductor_radical: 42 degree: 2 id: 9633808 index: 25 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/23 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: 2-168-168.101-c1-0-25 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: 2-168-168.101-c1-0 primitive: true rational: false root_analytic_conductor: 1.1582256921505028 root_angle: 0.056025803481534915 self_dual: false spectral_label: c1-0 z1: __RealLiteral__: 0 data: '2.78546641453389050173910249535' prec: 103 - - Lhash: '3530998172299460347542111941674' Lhash_array: - '3530998172299460347542111941674' id: 9999847 label: 2-168-168.101-c1-0-25 type: CMF url: ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/23 label_cols: - label - label - label labels: - 2-168-168.101-c1-0-25 - 2-168-168.101-c1-0-25 - 2-168-168.101-c1-0-25 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-24T14:44:07.387767'