data: - - Lhash: '4172211247534646306959853011364' a10: - 5040.0 - 0.0 a2: - 0.0 - 22.44994432064365 a3: - 45.0 - -67.34983296193094 a4: - -248.0 - 0.0 a5: - 0.0 - -224.4994432064365 a6: - 1512.0 - 1010.2474944289642 a7: - -1750.0 - 0.0 a8: - 0.0 - 179.5995545651492 a9: - -2511.0 - -6061.484966573785 accuracy: 100 algebraic: true analytic_conductor: 1.222135830183382 analytic_normalization: __RealLiteral__: 0 data: '4.0' prec: 10 bad_lfactors: - - 3 - - - 1.0 - 0 - - -45.0 - 67.34983296193094 bad_primes: - 3 central_character: '3.2' coefficient_field: CDF conductor: 3 conductor_radical: 3 conjugate: '8317160875811187030144230999328' degree: 2 euler_factors: - - - 1.0 - 0 - - 0 - -22.44994432064365 - - -256.0 - 0 - - - 1.0 - 0 - - -45.0 - 67.34983296193094 - - - 1.0 - 0 - - 0 - 224.4994432064365 - - -390625.0 - 0 - - - 1.0 - 0 - - 1750.0 - 0 - - 5764801.0 - 0 - - - 1.0 - 0 - - 0 - -6959.482739399531 - - -214358881.0 - 0 - - - 1.0 - 0 - - -25730.0 - 0 - - 815730721.0 - 0 - - - 1.0 - 0 - - 0 - -74893.0142536672 - - -6975757441.0 - 0 - - - 1.0 - 0 - - -18938.0 - 0 - - 16983563041.0 - 0 - - - 1.0 - 0 - - 0 - 470461.0331834083 - - -78310985281.0 - 0 - - - 1.0 - 0 - - 0 - -460897.3569028141 - - -500246412961.0 - 0 - - - 1.0 - 0 - - 351478.0 - 0 - - 852891037441.0 - 0 - - - 1.0 - 0 - - -1335170.0 - 0 - - 3512479453921.0 - 0 - - - 1.0 - 0 - - 0 - -1875468.3485465704 - - -7984925229121.0 - 0 - - - 1.0 - 0 - - 3526150.0 - 0 - - 11688200277601.0 - 0 - - - 1.0 - 0 - - 0 - 4081040.678383885 - - -23811286661761.0 - 0 - - - 1.0 - 0 - - 0 - 6601765.326594395 - - -62259690411361.0 - 0 - - - 1.0 - 0 - - 0 - -13714895.484924411 - - -146830437604321.0 - 0 - - - 1.0 - 0 - - -753602.0 - 0 - - 191707312997281.0 - 0 - - - 1.0 - 0 - - -2268890.0 - 0 - - 406067677556641.0 - 0 - - - 1.0 - 0 - - 0 - -17021996.782798428 - - -645753531245761.0 - 0 - - - 1.0 - 0 - - -27672770.0 - 0 - - 806460091894081.0 - 0 - - - 1.0 - 0 - - 22980982.0 - 0 - - 1517108809906561.0 - 0 - - - 1.0 - 0 - - 0 - 46395189.63270809 - - -2252292232139041.0 - 0 - - - 1.0 - 0 - - 0 - -72615242.9028947 - - -3936588805702081.0 - 0 - - - 1.0 - 0 - - -147271010.0 - 0 - - 7837433594376961.0 - 0 - - - 1.0 - 0 - - 0 - 103544755.69288866 - - -10828567056280800 - 0 - - - 1.0 - 0 - - 166063510.0 - 0 - - 12667700813876160 - 0 - - - 1.0 - 0 - - 0 - 22553977.36262551 - - -17181861798319200 - 0 - - - 1.0 - 0 - - 109975102.0 - 0 - - 19925626416901920 - 0 - - - 1.0 - 0 - - 0 - -287747761.1407631 - - -26584441929064320 - 0 gamma_factors: - [] - - 0 group: GL2 id: 9591300 index: 0 label: 2-3-3.2-c8-0-0 load_key: CMFs-workshop motivic_weight: 8 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 8 order_of_vanishing: 0 origin: ModularForm/GL2/Q/holomorphic/3/9/b/a/2/2 plot_delta: __RealLiteral__: 0 data: '0.17578125' prec: 34 plot_values: - 1.1759734143799212 - 1.1396751235866436 - 1.1035528519359223 - 1.06722759446425 - 1.0302625931053793 - 0.9921651793395808 - 0.952388779198516 - 0.91033530021826 - 0.8653581494461836 - 0.8167661578804655 - 0.7638287083859245 - 0.70578237943625 - 0.641839423895054 - 0.5711983981068295 - 0.4930572392643747 - 0.4066290556831028 - 0.31116084258080046 - 0.2059552627165864 - 0.09039553459171962 - -0.036026650797487465 - -0.17368041130400674 - -0.322762553083252 - -0.483262645674446 - -0.6549271086267077 - -0.8372233596453708 - -1.0293053165044848 - -1.2299817855969204 - -1.4376894966299085 - -1.6504727408433892 - -1.865971722244011 - -2.0814218189394684 - -2.2936659548316087 - -2.499182180569218 - -2.6941283376023804 - -2.8744053135990426 - -3.0357398785303698 - -3.173787411304602 - -3.284253987438331 - -3.3630363088453166 - -3.4063768384403685 - -3.4110302883779124 - -3.3744363481161024 - -3.294892287271279 - -3.1717179012359953 - -3.0054042685200213 - -2.7977370494593288 - -2.551884671853265 - -2.272441814169837 - -1.9654191970043482 - -1.638171898692122 - -1.299260267914818 - -0.958240029515175 - -0.6253813446767449 - -0.3113203220601708 - -0.026650660396457145 - 0.218532439635603 - 0.41511945245946297 - 0.555483874349786 - 0.6339650793911222 - 0.6473091506422394 - 0.5950384810099919 - 0.4797207825777772 - 0.30710976986315525 - 0.08613338342727601 - -0.17128891574676558 - -0.4506105631557634 - -0.7352052782445607 - -1.0070876737241286 - -1.247785359206232 - -1.4393285312967543 - -1.5653112611935045 - -1.6119683030595844 - -1.5692031871328627 - -1.4314985420173498 - -1.1986388240789019 - -0.8761795541063374 - -0.4756061522743677 - -0.014139575073912733 - 0.4858351372551053 - 0.9977183427700856 - 1.491998417314139 - 1.9378554632244955 - 2.304987457480084 - 2.565556237858872 - 2.696131594753367 - 2.679499503220338 - 2.5061969910697237 - 2.1756426192960805 - 1.696748726368588 - 1.087929336623801 - 0.37645493942184033 - -0.40284973295794724 - -1.2095190879949886 - -1.9998744433013822 - -2.7298213617320854 - -3.357830894291234 - -3.847889663350921 - -4.172189416742847 - -4.313330253591475 - -4.265834642432504 - -4.03681152096374 - -3.6456693292642446 - -3.1228501416868544 - -2.507638833020842 - -1.8451848106702975 - -1.1829517807946224 - -0.5668755782309675 - -0.037554058147230666 - 0.3731895423937849 - 0.6450414976369475 - 0.7709475400724836 - 0.7576700725930726 - 0.6250458488122248 - 0.4039561329791859 - 0.13314769419558933 - -0.14483513592607686 - -0.3882423646932713 - -0.5607936571064204 - -0.635960284400495 - -0.600386938684001 - -0.45604566198136204 - -0.22081992250090543 - 0.0726379570865599 - 0.37976050266617933 - 0.6484311894449571 - 0.8244889019046358 - 0.8578488854823114 - 0.7086161816498948 - 0.3525257917189913 - -0.21492830035583588 - -0.9762133616597148 - -1.8916995248339676 - -2.9019762285815522 - -3.9324461597712976 - -4.899842390243947 - -5.720079813844491 - -6.316668034189896 - -6.628804065139337 - -6.618247227508568 - -6.274163570821319 - -5.615309880412756 - -4.689192952712019 - -3.5681625616040074 - -2.3427420270087342 - -1.1128290934296987 - 0.02232814127400074 - 0.9742960717529644 - 1.6746170600248302 - 2.0818968160678413 - 2.185952121685959 - 2.0084721284919014 - 1.6000454956457897 - 1.033839448344358 - 0.3966329134667563 - -0.22174906415454385 - -0.7393256137935216 - -1.0918270591023187 - -1.2402862128857768 - -1.1753619110081108 - -0.9178014891116826 - -0.5149396237449417 - -0.033652563213048575 - 0.4493292169852901 - 0.8584674820701198 - 1.1303208124634498 - 1.2227856931508254 - 1.1213416773473812 - 0.8413502578604919 - 0.4259874026189653 - -0.05999960990725882 - -0.5399122448549766 - -0.9367800801826067 - -1.1854313096668248 - -1.243162521798073 - -1.0973482738598344 - -0.7687129065998852 - -0.30957523549745725 - 0.20290467884666083 - 0.6776977818876398 - 1.0236468863715882 - 1.1640361689823053 - 1.049824158742431 - 0.6694618651572432 - 0.053619976377719036 - -0.7261767575777608 - -1.5651506013568786 - -2.3383251649487056 - -2.917396097113408 - -3.189129099079892 - -3.0726551851087907 - -2.5330700925881557 - -1.5891723982327308 - -0.3139468422039627 - 1.1725857896290024 - 2.7174166635795594 - 4.153711188539734 - 5.322483044302036 - 6.093722107432421 - 6.383910747374411 - 6.167320519198073 - 5.479349626130834 - 4.411319540824029 - 3.097425432085147 - 1.695733076382018 - 0.3660437434420025 - -0.7520463519020472 - -1.557575507173013 - -2.000354680189689 - -2.085022417441059 - -1.866514425078764 - -1.4378321167030312 - -0.9122507533521367 - -0.40302205097092686 - -0.004037821504235243 - 0.2252498784876654 - 0.26809380228731206 - 0.1505325064649929 - -0.06663680028662752 - -0.30246251363481563 - -0.47427962296198045 - -0.5165043502785738 - -0.3961690039210021 - -0.12210757340080766 - 0.2541925230359858 - 0.6465516039769358 - 0.9497039961717519 - 1.0598883709858968 - 0.8967005407039177 - 0.42207114509061566 - -0.34743721231113833 - -1.337767123598734 - -2.4250815367639222 - -3.453302675604033 - -4.258869772183976 - -4.698648629531981 - -4.6761380926185465 - -4.16117919323831 - -3.199308673844784 - -1.9085770563453812 - -0.46379777076884815 - 0.929563963587123 - 2.0677207894706413 - 2.7817102836418726 - 2.965627442286143 - 2.5949018495720497 - 1.7312010243305966 - 0.5128283973703472 - -0.8679620656817 - -2.196952914252071 - -3.2737434094781803 - -3.945054650187117 - -4.129662327157222 - -3.830517679999748 - -3.1319132251398147 - -2.1822710479938077 - -1.1657748956518887 - -0.2681334730263627 positive_zeros: - '3.29129434150346804494000997655351' - '9.509896719961398489491287140506669' - '11.13538667100853805576196445480373' - '13.54027667979888221166920257282738' - '15.90659526368572752200092385993594' - '18.82264965358014825023913936401877' - '20.12216169702305363155548438681581' - '21.40363457458476111200117821822673' - '22.61633771030336282354266566174812' - '25.48457455056030862586971118300870' prelabel: 2-3-3.2-c8-0 primitive: true rational: false root_analytic_conductor: 1.1055025238249716 root_angle: -0.31250561891173007 root_number: 0.5555555555555556 - 0.8314794192830981*I self_dual: false sign_arg: __RealLiteral__: 0 data: '-0.156252809456' prec: 50 spectral_label: c8-0 types: - CMF z1: __RealLiteral__: 0 data: '3.29129434150346804494000997655' prec: 103 z2: __RealLiteral__: 0 data: '9.509896719961398489491287140507' prec: 107 z3: __RealLiteral__: 0 data: '11.13538667100853805576196445480' prec: 107 - - algebraic: true analytic_conductor: 1.222135830183382 bad_primes: - 3 central_character: '3.2' conductor: 3 conductor_radical: 3 degree: 2 id: 9591300 index: 0 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/3/9/b/a/2/2 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: 2-3-3.2-c8-0-0 motivic_weight: 8 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 8 order_of_vanishing: 0 prelabel: 2-3-3.2-c8-0 primitive: true rational: false root_analytic_conductor: 1.1055025238249716 root_angle: -0.15625280945586503 self_dual: false spectral_label: c8-0 z1: __RealLiteral__: 0 data: '3.29129434150346804494000997655' prec: 103 - - Lhash: '4172211247534646306959853011364' Lhash_array: - '4172211247534646306959853011364' id: 9957325 label: 2-3-3.2-c8-0-0 type: CMF url: ModularForm/GL2/Q/holomorphic/3/9/b/a/2/2 label_cols: - label - label - label labels: - 2-3-3.2-c8-0-0 - 2-3-3.2-c8-0-0 - 2-3-3.2-c8-0-0 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-25T15:50:32.334531'