data: - - Lhash: '852634137536462594054196749990' a10: - 3.4136473038210635 - 5.049770657120267 a2: - -1.6022549791999419 - -2.2053147853557165 a3: - -0.9510565162951535 - 0.30901699437494745 a4: - -1.6781582953876277 - 5.164840158488588 a5: - -2.234784618040114 - -0.07574767964302408 a6: - 2.2053147853557165 - 1.6022549791999419 a7: - 0.4625285464362922 - 0.15028463480712775 a8: - 8.893929820205834 - -2.889812975498067 a9: - 0.8090169943749475 - -0.5877852522924731 accuracy: 100 algebraic: true analytic_conductor: 1.3175316333511269 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 3 - - - 1.0 - 0 - - 0.9510565162951535 - -0.30901699437494745 - - 5 - - - 1.0 - 0 - - 2.234784618040114 - 0.07574767964302408 - - 11 - - - 1.0 - 0 - - -3.0656829379956356 - -1.2655386693746062 bad_primes: - 3 - 5 - 11 central_character: '165.124' coefficient_field: CDF conductor: 165 conductor_radical: 165 conjugate: '1901182455143616368452110591976' degree: 2 euler_factors: - - - 1.0 - 0 - - 1.6022549791999419 - 2.2053147853557165 - - -0.6180339887498949 - 1.902113032590307 - - - 1.0 - 0 - - 0.9510565162951535 - -0.30901699437494745 - - - 1.0 - 0 - - 2.234784618040114 - 0.07574767964302408 - - - 1.0 - 0 - - -0.4625285464362922 - -0.15028463480712775 - - 5.663118960624632 - 4.114496766047312 - - - 1.0 - 0 - - -3.0656829379956356 - -1.2655386693746062 - - - 1.0 - 0 - - -2.122101995703362 - -2.920822820281904 - - -4.017220926874317 - 12.363734711836996 - - - 1.0 - 0 - - 2.1412039566048824 - -2.9471144139123036 - - -5.253288904374106 - -16.167960777017612 - - - 1.0 - 0 - - -0.5040986838419907 - -1.5514562203722078 - - -15.371322893124 - 11.16791979355699 - - - 1.0 - 0 - - 0 - -3.5425289288932813 - - -23.0 - 0 - - - 1.0 - 0 - - 0.3263415671342078 - -1.0043760686649241 - - -23.461492836873475 - -17.04577231648172 - - - 1.0 - 0 - - 4.935718788602777 - -3.5860096061950193 - - 9.57952682562337 - -29.48275200514976 - - - 1.0 - 0 - - -8.170603391133428 - -2.6547899718866277 - - 29.933628791873055 - 21.748054334821507 - - - 1.0 - 0 - - -3.3939188444622355 - -10.445408154110282 - - -33.16969676937284 - 24.099195343991397 - - - 1.0 - 0 - - 0 - 7.417651463193187 - - -43.0 - 0 - - - 1.0 - 0 - - 4.957806317881838 - -1.6108889227877505 - - 38.02379873562253 - -27.625906857746237 - - - 1.0 - 0 - - 0.8759157458281173 - 1.2055945964138444 - - -16.377900701872214 - 50.405995363643136 - - - 1.0 - 0 - - -2.4647167798796223 - 7.585618257235116 - - -47.7320026681219 - -34.67932988525592 - - - 1.0 - 0 - - -8.789003740637668 - -6.385584996371465 - - 18.850036656871794 - 58.014447494004365 - - - 1.0 - 0 - - 0 - 0.43251505612955526 - - -67.0 - 0 - - - 1.0 - 0 - - 4.8648117643405815 - 3.534492637534226 - - 21.940206600621266 - 67.52501265695591 - - - 1.0 - 0 - - -1.107147927958097 - -0.3597341684370365 - - 59.05824058937116 - 42.90832341735054 - - - 1.0 - 0 - - 3.5798521299610355 - -2.6009148163872666 - - 24.412342555620846 - -75.13346478731714 - - - 1.0 - 0 - - 1.8675730219244355 - -2.5704937425365078 - - -25.648410533120636 - -78.93769085249775 - - - 1.0 - 0 - - 1.383537687403005 - 0 - - 89.0 - 0 - - - 1.0 - 0 - - -0.8227406368179628 - -1.132405337753184 - - -29.974648454369902 - 92.2524820806299 - - - 1.0 - 0 - - -0.09160094574376013 - 0.06655198268835338 - - 31.210716431869688 - -96.05670814581052 - - - 1.0 - 0 - - 6.893546012112622 - 2.239848876223196 - - 83.32875042061958 - 60.54188098612473 - - - 1.0 - 0 - - 8.235003353964185 - -2.675714788247008 - - 86.56481839811937 - -62.893021995294625 - - - 1.0 - 0 - - 4.415733329237201 - 0 - - 109.0 - 0 - - - 1.0 - 0 - - -17.465880371397734 - 5.675008544714832 - - 91.41892036436906 - -66.41973350904946 gamma_factors: - [] - - 0 group: GL2 id: 9631817 index: 0 label: 2-165-55.14-c1-0-0 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/165/2/s/a/124/1 plot_delta: __RealLiteral__: 0 data: '0.125' prec: 17 plot_values: - 0.40546943266199 - 0.3647511573832115 - 0.31408397776597835 - 0.24891743145715478 - 0.16350585347448301 - 0.0512674286375221 - -0.09484349974797623 - -0.2819639786343022 - -0.5169353262848304 - -0.8058804542511662 - -1.1537333814832693 - -1.5637233675424158 - -2.0368311888482498 - -2.571248299436111 - -3.1618802376831328 - -3.7999432980283343 - -4.472707687634654 - -5.163440464927117 - -5.851596804562663 - -6.513297991632386 - -7.122118782037507 - -7.650185620814925 - -8.06956152438539 - -8.353864699295922 - -8.48003832913741 - -8.430161113328163 - -8.193165174320345 - -7.766313082113703 - -7.156281997009843 - -6.379712747892212 - -5.463106522365959 - -4.441991900087435 - -3.359338762919481 - -2.263259971415738 - -1.2041117032819575 - -0.231172639454727 - 0.6108566035570877 - 1.2852469393370702 - 1.766217776186809 - 2.0411941616607483 - 2.112078838174194 - 1.995344162989526 - 1.7208477695840398 - 1.3293961724106333 - 0.8692114096110254 - 0.39158370138118337 - -0.05389707983467559 - -0.42406145846491117 - -0.6863311502548474 - -0.821863347738128 - -0.8272726066285782 - -0.7146700542954642 - -0.5099386359694953 - -0.24936781553980214 - 0.02502150199266034 - 0.27094714168689676 - 0.45148176603817963 - 0.540103172732218 - 0.5244917170430106 - 0.40850510529145057 - 0.2119641377469621 - -0.03184678212136322 - -0.28075384766654543 - -0.4898278797093086 - -0.6183040017249176 - -0.6363394415626565 - -0.5306076688099872 - -0.30781141740969714 - 0.004578271067767892 - 0.3607035890951059 - 0.7017390991859052 - 0.9638072019778515 - 1.087426424905098 - 1.0272089885172757 - 0.7603642276604101 - 0.29260475544924874 - -0.339693106981651 - -1.0717708817091656 - -1.8173062573772136 - -2.4791882953642452 - -2.9630166320466915 - -3.191561683693428 - -3.118108203127648 - -2.7365740448450193 - -2.0865814754937175 - -1.2522460863961515 - -0.35427669615106683 - 0.46405598589138525 - 1.0555589765496627 - 1.2900235853510083 - 1.0745239978772867 - 0.3700898113633697 - -0.7979642881820196 - -2.338033763244535 - -4.099437629757691 - -5.8884415102969845 - -7.491352286913517 - -8.701792274197977 - -9.348472446469595 - -9.319507059640252 - -8.57962032710283 - -7.1774757704648735 - -5.241704725631279 - -2.965835848297648 - -0.5839906565548818 - 1.6593495122496926 - 3.541220165538846 - 4.889064656123049 - 5.602379950407803 - 5.663906318553567 - 5.138729325640134 - 4.161529998514278 - 2.9140757872791934 - 1.5965837645957486 - 0.3975455537066905 - -0.5331906062892043 - -1.1038780845079865 - -1.2899687036814973 - -1.131738936504446 - -0.7213121249373291 - -0.18175603596296422 - 0.3577397026146191 - 0.7860054761404829 - 1.0289969610432665 - 1.0605524581786967 - 0.9031435354643769 - 0.6189113937631401 - 0.2931596002276967 - 0.013915465292306958 - -0.1481076603011202 - -0.15496490899022172 - -0.00916752782987307 - 0.24792512279007758 - 0.5465559215838668 - 0.8055046756376183 - 0.9517209764037072 - 0.938229407046683 - 0.7561868625699847 - 0.43818526301057076 - 0.05178293403436151 - -0.31557085377638233 - -0.5770455952674544 - -0.6678141840075731 - -0.5623231820937237 - -0.2831308607489305 - 0.10131982924051218 - 0.49024194407098837 - 0.77301022777836 - 0.856035998637811 - 0.6880410875489804 - 0.27762522914290105 - -0.30175519332884915 - -0.9218651646130548 - -1.4241293299977176 - -1.6544534188978977 - -1.5017604715470922 - -0.9321011627377807 - -0.010356530671793061 - 1.0965655940085022 - 2.137801055624434 - 2.8164311457679325 - 2.8415455690877733 - 1.9854064882379996 - 0.1348711392319161 - -2.6734693193001022 - -6.242524536445251 - -10.2321713668962 - -14.203561176467895 - -17.683623159200877 - -20.238921850709044 - -21.545781007238542 - -21.44382178692089 - -19.96282295126759 - -17.31762046889995 - -13.871713469390015 - -10.076163009249033 - -6.3950667760959155 - -3.231400609548119 - -0.8668058652571585 - 0.5740038947915236 - 1.128555223221982 - 0.9720694753839464 - 0.36937719013332687 - -0.38591438356016616 - -1.0320733102159807 - -1.3874151613098464 - -1.3769062190950603 - -1.033160108983994 - -0.47354376192946984 - 0.13972024032608846 - 0.6461196830256724 - 0.9287657221617031 - 0.9419772796083115 - 0.718701593390225 - 0.357028710707664 - -0.009822214946526214 - -0.2517403165150081 - -0.27807224695405297 - -0.06269330245566801 - 0.3485437312791352 - 0.8497289290403757 - 1.3029361471452956 - 1.5749946754099498 - 1.5733579626790808 - 1.2716615623865246 - 0.7182111461561133 - 0.025051456147834016 - -0.6596795496761727 - -1.189008129306297 - -1.4542956813633365 - -1.4125384419602 - -1.0965003383609708 - -0.6048464746856662 - -0.07474934137227605 - 0.3557975051190742 - 0.5857839019506479 - 0.5786546249943786 - 0.37154643091515305 - 0.06318301985620385 - -0.2168433117854473 - -0.3493270887456707 - -0.2657772269944484 - 0.02406094968252044 - 0.42653030405327647 - 0.7837675074200827 - 0.915470972203904 - 0.6729708556458944 - -0.008435453396548716 - -1.0737420504058144 - -2.3408583108107623 - -3.5269061428241177 - -4.305115483544279 - -4.380981283445861 - -3.570345642684587 - -1.8600228532361147 - 0.5657220647886408 - 3.3424706651440963 - 5.986421567329934 - 7.987826412478275 - 8.917768125804466 - 8.524628183837173 - 6.797707201137849 - 3.982003103166916 - 0.5387549999613368 - -2.9413752185464768 - -5.8545772782316465 - -7.704588266712718 - -8.201348604039568 - -7.315882914092521 - -5.279512804389197 - -2.528173055720422 - 0.39491698417254567 - 2.955663321401782 - 4.738105603114352 - 5.521920025669058 - 5.312350279624385 - 4.318165991905141 positive_zeros: - '0.67260973755935056253684694863108' - '4.40721581348214180297179848455743' - '5.73392295349008015950369209736653' - '6.73833954258528005486956287558253' - '7.60928947789463730392070533223965' - '8.498331085559639484454120352127876' - '9.436235379879075018131457956781182' - '10.80134342770424330041671884648652' - '11.41995535178042422596901758183687' - '13.03129617314872819539789890227919' prelabel: 2-165-55.14-c1-0 primitive: true rational: false root_analytic_conductor: 1.1478378079463696 root_angle: 0.04297035671516943 root_number: 0.9909019560995737 + 0.13458571022972146*I self_dual: false sign_arg: __RealLiteral__: 0 data: '0.0214851783576' prec: 50 spectral_label: c1-0 types: - CMF z1: __RealLiteral__: 0 data: '0.67260973755935056253684694863' prec: 103 z2: __RealLiteral__: 0 data: '4.40721581348214180297179848456' prec: 103 z3: __RealLiteral__: 0 data: '5.73392295349008015950369209737' prec: 103 - - algebraic: true analytic_conductor: 1.3175316333511269 bad_primes: - 3 - 5 - 11 central_character: '55.14' conductor: 165 conductor_radical: 165 degree: 2 id: 9631817 index: 0 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/165/2/s/a/124/1 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: 2-165-55.14-c1-0-0 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: 2-165-55.14-c1-0 primitive: true rational: false root_analytic_conductor: 1.1478378079463696 root_angle: 0.021485178357584716 self_dual: false spectral_label: c1-0 z1: __RealLiteral__: 0 data: '0.67260973755935056253684694863' prec: 103 - - Lhash: '852634137536462594054196749990' Lhash_array: - '852634137536462594054196749990' id: 9997851 label: 2-165-55.14-c1-0-0 type: CMF url: ModularForm/GL2/Q/holomorphic/165/2/s/a/124/1 label_cols: - label - label - label labels: - 2-165-55.14-c1-0-0 - 2-165-55.14-c1-0-0 - 2-165-55.14-c1-0-0 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-05-16T07:23:31.326952'