data: - - Lhash: '3614324641899719930679170306866' a10: - -1.746979603717467 - -3.025857433425196 a2: - 1.0799160148203788 - -0.6234898018587335 a3: - -0.5 - -0.8660254037844386 a4: - -0.2225209339563144 - 0.38541756336001515 a5: - 0.0 - -2.801937735804838 a6: - -1.0799160148203788 - -0.6234898018587335 a7: - -4.158600066598118 - -2.400968867902419 a8: - 0.0 - 3.0489173395223053 a9: - -0.5 - 0.8660254037844386 accuracy: 100 algebraic: true analytic_conductor: 4.048415382478917 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 3 - - - 1.0 - 0 - - 0.5 - 0.8660254037844386 - - 13 - - - 1.0 - 0 - - 0 - 0 bad_primes: - 3 - 13 central_character: '507.361' coefficient_field: CDF conductor: 507 conductor_radical: 39 conjugate: '469467426716300557323203164480' degree: 2 euler_factors: - - - 1.0 - 0 - - -1.0799160148203788 - 0.6234898018587335 - - 1.0 - -1.7320508075688772 - - - 1.0 - 0 - - 0.5 - 0.8660254037844386 - - - 1.0 - 0 - - 0 - 2.801937735804838 - - -5.0 - 0 - - - 1.0 - 0 - - 4.158600066598118 - 2.400968867902419 - - 3.5 - 6.06217782649107 - - - 1.0 - 0 - - 1.2702965689491954 - -0.7334060660334759 - - 5.5 - -9.526279441628825 - - - 1.0 - 0 - - 0 - 0 - - - 1.0 - 0 - - 1.2225209339563143 - -2.1174683709288926 - - -8.5 - -14.722431864335457 - - - 1.0 - 0 - - 2.202195688352622 - 1.2714382734786198 - - 9.5 - 16.454482671904334 - - - 1.0 - 0 - - 1.7578647357946287 - 3.0447110352299376 - - -11.5 - 19.91858428704209 - - - 1.0 - 0 - - 0.9254275376635718 - 1.6028875139566672 - - -14.5 - 25.11473670974872 - - - 1.0 - 0 - - 0 - 7.6310225469776585 - - -31.0 - 0 - - - 1.0 - 0 - - -3.9447094555621782 - 2.2774790660436857 - - 18.5 - -32.04293994002423 - - - 1.0 - 0 - - -1.0799160148203788 - 0.6234898018587335 - - 20.5 - -35.50704155516198 - - - 1.0 - 0 - - -1.1920214716300959 - 2.064641752576349 - - -21.5 - -37.239092362730865 - - - 1.0 - 0 - - 0 - 12.817003226042688 - - -47.0 - 0 - - - 1.0 - 0 - - 8.850855075327143 - 0 - - 53.0 - 0 - - - 1.0 - 0 - - -1.884724158088211 - -1.0881460000204193 - - 29.5 - 51.09549882328188 - - - 1.0 - 0 - - -3.91454240558641 - 6.780186334858557 - - -30.5 - -52.827549630850754 - - - 1.0 - 0 - - 3.102194108684863 - -1.7910526037276768 - - 33.5 - -58.023702053557386 - - - 1.0 - 0 - - -7.654602380807059 - -4.419386745098506 - - 35.5 - 61.48780366869514 - - - 1.0 - 0 - - 0 - -7.692021471630096 - - -73.0 - 0 - - - 1.0 - 0 - - 4.021770264154323 - 0 - - 79.0 - 0 - - - 1.0 - 0 - - 0 - 0.6527928111319818 - - -83.0 - 0 - - - 1.0 - 0 - - 5.452406692454437 - -3.1479484716198862 - - 44.5 - -77.07626093681505 - - - 1.0 - 0 - - -8.687498281813191 - -5.015729471589257 - - 48.5 - 84.00446416709055 - - - 1.0 - 0 - - -6.943845414859658 - -12.027093058441118 - - -50.5 - 87.4685657822283 - - - 1.0 - 0 - - -17.403420301308575 - 0 - - 103.0 - 0 - - - 1.0 - 0 - - 5.276282612990715 - 9.138789560792194 - - -53.5 - 92.66471820493493 - - - 1.0 - 0 - - 0 - -1.0706876036766284 - - -109.0 - 0 - - - 1.0 - 0 - - -8.265397480913554 - 14.316088381694085 - - -56.5 - -97.86087062764156 gamma_factors: - [] - - 0 group: GL2 id: 10856240 index: 26 label: 2-507-13.10-c1-0-26 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/507/2/j/h/361/5 plot_delta: __RealLiteral__: 0 data: '0.125' prec: 17 plot_values: - 0.8107145062618306 - 1.1007160769806086 - 1.4117137018640884 - 1.7488496280932209 - 2.1135004034454217 - 2.5024945650303945 - 2.9078650132988657 - 3.317032882616159 - 3.7133438572096824 - 4.076928876041602 - 4.385890415141153 - 4.617809793349561 - 4.7515372815508226 - 4.769177688084376 - 4.658131222897983 - 4.413002736141947 - 4.037160501182629 - 3.5437160199145294 - 2.955714691698498 - 2.3053769202829106 - 1.6323101542232943 - 0.9807199823395322 - 0.39577358028797976 - -0.08060203884940385 - -0.4140883348507868 - -0.5820268251319234 - -0.5766352419554641 - -0.40689737237412227 - -0.09873411904552896 - 0.30676931027847437 - 0.7570811191394703 - 1.193628798276846 - 1.558377015612732 - 1.8008382434750672 - 1.884628701584434 - 1.7926425710747012 - 1.5300084037668222 - 1.124218295166687 - 0.622167121617767 - 0.08426883502626926 - -0.42372659337486357 - -0.8401772101029437 - -1.1169146934877503 - -1.2270684026752356 - -1.1699814417352412 - -0.9721818830530365 - -0.6839096269862515 - -0.371380803773845 - -0.10570035300578254 - 0.0500083110895028 - 0.05322084700356879 - -0.10783084206751137 - -0.40848125249878525 - -0.7878949003357553 - -1.1558576690657296 - -1.4056088692362545 - -1.4311203709679066 - -1.146282030438139 - -0.502851330308987 - 0.4960847601224956 - 1.7899331461004613 - 3.2635030725119547 - 4.759382060202045 - 6.098537591075488 - 7.106346186329414 - 7.64005235036475 - 7.6130712814248875 - 7.011735833048797 - 5.901085533721862 - 4.417990308781024 - 2.752038768936613 - 1.1168387594343439 - -0.2837324194421267 - -1.2886099183745456 - -1.8060415591156254 - -1.828490587867632 - -1.4328217749123449 - -0.7652498956778331 - -0.013373071195998235 - 0.6298355088394995 - 1.003462721648755 - 1.0103627536142452 - 0.6368197725567671 - -0.04402384408244394 - -0.8861041422769387 - -1.6994433838920022 - -2.288823266184184 - -2.494569866832195 - -2.2272020347561057 - -1.4886674005033373 - -0.375405566179124 - 0.9379193730627363 - 2.231194492156632 - 3.2817867593894907 - 3.9089545086862336 - 4.010517714038332 - 3.5839588387561485 - 2.727243005307565 - 1.6188697412495736 - 0.48111449087110786 - -0.4658829563971713 - -1.0494153997266362 - -1.1791185805635576 - -0.8638878224664914 - -0.20710098150450934 - 0.6187417193697066 - 1.4122112246881924 - 1.9888296205948708 - 2.2221505698251933 - 2.0706330370451127 - 1.5841982490888096 - 0.8891424695931973 - 0.15523567820009623 - -0.44686612441452794 - -0.7873930265239926 - -0.8080904609877836 - -0.5341185584068677 - -0.06432006170977032 - 0.45754157928934513 - 0.8830240427692042 - 1.10006550479764 - 1.0637823371425754 - 0.8084056481438582 - 0.436593910006827 - 0.0883775698229495 - -0.10234438212023644 - -0.05204235180722906 - 0.2400094986714677 - 0.6811244681706717 - 1.1010768900282284 - 1.292172740447183 - 1.0644737729793232 - 0.3023693787825464 - -0.9926887599693149 - -2.6858987420241016 - -4.52578937518254 - -6.192190507974307 - -7.365535425788054 - -7.801358982142187 - -7.391519657335912 - -6.196010067209074 - -4.435870951083194 - -2.4471753305304618 - -0.605973232086153 - 0.7580876770366437 - 1.4381676397972405 - 1.397155766848659 - 0.7725155018256302 - -0.16308547319017233 - -1.0761219867050411 - -1.662944037375957 - -1.7335154714451544 - -1.2659747057939192 - -0.41689975530089124 - 0.5165835024034119 - 1.174116228891818 - 1.2294795451178722 - 0.48286972536792466 - -1.0763632741252376 - -3.25375985734064 - -5.685923300615786 - -7.920635206762639 - -9.521146288202962 - -10.168366613558014 - -9.735051993733533 - -8.313306313088228 - -6.188901642756573 - -3.7697964595052653 - -1.4880553270998014 - 0.29906663841444525 - 1.3835792312614918 - 1.7387694479784321 - 1.5028491129080126 - 0.9217031245916155 - 0.2691300950601853 - -0.2316304694646739 - -0.4628682211183836 - -0.42963212349877367 - -0.2369128049913713 - -0.036742063692613965 - 0.03590422297766383 - -0.08337837067742308 - -0.36328387653690114 - -0.688230216576982 - -0.9023527599712976 - -0.8710659642009668 - -0.5389692827307027 - 0.0365360956718789 - 0.6891743417920098 - 1.1865414416699127 - 1.300078266925563 - 0.8810296861513195 - -0.08205480188943484 - -1.4441942672944694 - -2.9319970248091374 - -4.213112474087907 - -4.98801663458861 - -5.077048958682949 - -4.475786249440328 - -3.360456655295102 - -2.0398061760070947 - -0.8662608815939549 - -0.13229293596605823 - 0.016630656589322966 - -0.37473584919124114 - -1.086503557168025 - -1.793760228810331 - -2.171116870537794 - -1.9996775090567156 - -1.2426813315792455 - -0.06488954950377092 - 1.2122473187915124 - 2.207576167838516 - 2.600434799077253 - 2.2368015420958165 - 1.1873255478460458 - -0.2628161861729498 - -1.6915024622241583 - -2.662757048678973 - -2.8584660241745508 - -2.1780611962548875 - -0.7743907960543985 - 0.9869047603463506 - 2.6336384890290176 - 3.7273723350504824 - 3.9949472252701947 - 3.4104022311797277 - 2.201277610592407 - 0.7765732012292282 - -0.4018566841041615 - -0.9646829855110225 - -0.7517692707855471 - 0.1367612758462436 - 1.3715888206681903 - 2.4981273333086005 - 3.0809794226321054 - 2.843578080270024 - 1.758992925535846 - 0.06317707520373159 - -1.8136054670982193 - -3.3755983813516517 - -4.2101134245036365 - -4.10937115775638 - -3.1280595367946993 - -1.559869777331238 - 0.15778977370569405 - 1.5790887246931702 - 2.3812985258273964 - 2.451215307349894 - 1.9010076545634647 - 1.0118334828058395 - 0.12731270448986953 - -0.46531420810114077 - -0.625905570771224 - -0.3947379893204249 - 0.040001032551536024 - 0.4257827294469311 positive_zeros: - '2.85119940877162239821246398307291' - '3.53272781393754365451363220863484' - '4.89482941618729772251283644567380' - '6.07136252398558104498640416294083' - '6.30663280108642489957909219142919' - '7.31812354288205105141540348057498' - '8.972036189036442456646302633903832' - '9.752298723013442265836713988262188' - '10.36799811216535513792756046320072' - '11.28681881026712450336213328027489' prelabel: 2-507-13.10-c1-0 primitive: true rational: false root_analytic_conductor: 2.0120674398436345 root_angle: -0.9731934556051499 root_number: -0.9964559917413861 - 0.08411573290824204*I self_dual: false sign_arg: __RealLiteral__: 0 data: '-0.486596727803' prec: 50 spectral_label: c1-0 types: - CMF z1: __RealLiteral__: 0 data: '2.85119940877162239821246398307' prec: 103 z2: __RealLiteral__: 0 data: '3.53272781393754365451363220863' prec: 103 z3: __RealLiteral__: 0 data: '4.89482941618729772251283644567' prec: 103 - - algebraic: true analytic_conductor: 4.048415382478917 bad_primes: - 3 - 13 central_character: '13.10' conductor: 507 conductor_radical: 39 degree: 2 id: 10856240 index: 26 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/507/2/j/h/361/5 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: 2-507-13.10-c1-0-26 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: 2-507-13.10-c1-0 primitive: true rational: false root_analytic_conductor: 2.0120674398436345 root_angle: -0.48659672780257496 self_dual: false spectral_label: c1-0 z1: __RealLiteral__: 0 data: '2.85119940877162239821246398307' prec: 103 - - Lhash: '3614324641899719930679170306866' Lhash_array: - '3614324641899719930679170306866' id: 11222298 label: 2-507-13.10-c1-0-26 type: CMF url: ModularForm/GL2/Q/holomorphic/507/2/j/h/361/5 label_cols: - label - label - label labels: - 2-507-13.10-c1-0-26 - 2-507-13.10-c1-0-26 - 2-507-13.10-c1-0-26 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-24T12:41:21.482607'