data: - - Lhash: '1903186700956924621544106186140' a10: 0 a2: 0 a3: 0 a4: 0 a5: 5 a6: 0 a7: -34 a8: 0 a9: 0 accuracy: 100 algebraic: true analytic_conductor: 42.481375204133265 analytic_normalization: __RealLiteral__: 0 data: '1.5' prec: 10 bad_lfactors: - - 2 - - 1 - - 3 - - 1 - - 5 - - 1 - -5 bad_primes: - 2 - 3 - 5 central_character: '720.1' coefficient_field: 1.1.1.1 conductor: 720 conductor_radical: 30 degree: 2 euler_factors: - - 1 - - 1 - - 1 - -5 - - 1 - 34 - 343 - - 1 - -18 - 1331 - - 1 - -12 - 2197 - - 1 - -106 - 4913 - - 1 - -44 - 6859 - - 1 - -56 - 12167 - - 1 - 270 - 24389 - - 1 - 204 - 29791 - - 1 - -120 - 50653 - - 1 - 80 - 68921 - - 1 - 536 - 79507 - - 1 - 536 - 103823 - - 1 - 542 - 148877 - - 1 - 174 - 205379 - - 1 - -186 - 226981 - - 1 - 332 - 300763 - - 1 - 132 - 357911 - - 1 - 602 - 389017 - - 1 - -548 - 493039 - - 1 - 492 - 571787 - - 1 - -1052 - 704969 - - 1 - -482 - 912673 - - 1 - 1214 - 1030301 - - 1 - 898 - 1092727 - - 1 - -1364 - 1225043 - - 1 - -218 - 1295029 - - 1 - 1386 - 1442897 euler_factors_factorization: - - 1 - - 1 - - - - 1 - -5 - 1 - - - - 1 - 34 - 343 - 1 - - - - 1 - -18 - 1331 - 1 - - - - 1 - -12 - 2197 - 1 - - - - 1 - -106 - 4913 - 1 - - - - 1 - -44 - 6859 - 1 - - - - 1 - -56 - 12167 - 1 - - - - 1 - 270 - 24389 - 1 - - - - 1 - 204 - 29791 - 1 - - - - 1 - -120 - 50653 - 1 - - - - 1 - 80 - 68921 - 1 - - - - 1 - 536 - 79507 - 1 - - - - 1 - 536 - 103823 - 1 - - - - 1 - 542 - 148877 - 1 - - - - 1 - 174 - 205379 - 1 - - - - 1 - -186 - 226981 - 1 - - - - 1 - 332 - 300763 - 1 - - - - 1 - 132 - 357911 - 1 - - - - 1 - 602 - 389017 - 1 - - - - 1 - -548 - 493039 - 1 - - - - 1 - 492 - 571787 - 1 - - - - 1 - -1052 - 704969 - 1 - - - - 1 - -482 - 912673 - 1 - - - - 1 - 1214 - 1030301 - 1 - - - - 1 - 898 - 1092727 - 1 - - - - 1 - -1364 - 1225043 - 1 - - - - 1 - -218 - 1295029 - 1 - - - - 1 - 1386 - 1442897 - 1 gamma_factors: - [] - - 0 group: GL2 id: 20193391 index: 19 label: 2-720-1.1-c3-0-19 load_key: CMFs-workshop motivic_weight: 3 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 3 order_of_vanishing: 1 origin: ModularForm/GL2/Q/holomorphic/720/4/a/p plot_delta: __RealLiteral__: 0 data: '0.05859375' prec: 34 plot_values: - -1.4123327642333294e-60 - 0.21283658200407712 - 0.42314847966625474 - 0.6284223024912917 - 0.826167912753224 - 1.0139316797781277 - 1.1893115916745485 - 1.3499746876887506 - 1.493677148578099 - 1.618287234518086 - 1.7218110955644232 - 1.8024213045087736 - 1.858487782238565 - 1.8886106075939966 - 1.891654033213372 - 1.8667808717009782 - 1.8134862780072216 - 1.7316298391226017 - 1.6214647955296229 - 1.4836631642916969 - 1.3193355145853667 - 1.1300441656773166 - 0.9178086368834194 - 0.6851022801994106 - 0.4348391694354565 - 0.1703505041810966 - -0.10464998898527404 - -0.38611191491825286 - -0.6697052917577077 - -0.9508885001458423 - -1.2249864039916822 - -1.4872775955013153 - -1.7330893633617543 - -1.9578986371306475 - -2.1574368342042693 - -2.3277962399030354 - -2.4655352981254377 - -2.567779991415421 - -2.6323183563369836 - -2.6576851229290543 - -2.64323349445986 - -2.5891912025693204 - -2.496698187735346 - -2.3678235676947796 - -2.205559965846891 - -2.013793773351544 - -1.7972505047541127 - -1.5614150661780277 - -1.3124274726394891 - -1.0569553088236856 - -0.8020450047558858 - -0.5549547707713716 - -0.3229727797216076 - -0.1132248719680566 - 0.0675233364197283 - 0.21306456599599258 - 0.3179424684352301 - 0.3776327586730329 - 0.388706908618032 - 0.3489725835674984 - 0.25758535720257997 - 0.11512679596119654 - -0.07635524540663648 - -0.31334733943356863 - -0.590914332826349 - -0.9027872020402503 - -1.2414944441891147 - -1.5985351100397673 - -1.9645901408359234 - -2.329767248722921 - -2.6838732323317434 - -3.0167063962904597 - -3.318360696818158 - -3.5795324130232298 - -3.7918195881382544 - -3.9480042329499545 - -4.042307362765093 - -4.070607366754388 - -4.030612990149316 - -3.9219833385718537 - -3.7463887695180023 - -3.507508285045518 - -3.2109610353582063 - -2.8641717264451922 - -2.4761720267804095 - -2.057342410194471 - -1.6191011700562337 - -1.1735495061520358 - -0.7330835322805752 - -0.3099856950090341 - 0.08399064554131544 - 0.43802891114343107 - 0.7426344081029382 - 0.9899822018055905 - 1.1742139212578169 - 1.291671002362407 - 1.3410537623348775 - 1.3234980677604193 - 1.2425641470380366 - 1.1041352158853988 - 0.9162269259528447 - 0.6887120907395444 - 0.4329685589048691 - 0.16146135615690319 - -0.11272683364561482 - -0.37640026118704917 - -0.6167712283315031 - -0.8219778732248717 - -0.9815782019041601 - -1.0870001726297736 - -1.1319286874073142 - -1.112612206211686 - -1.0280743319194263 - -0.8802190425008043 - -0.673822163665944 - -0.4164060423488539 - -0.11799903640715025 - 0.20921380349638846 - 0.5513378124887947 - 0.8932981206845537 - 1.2194320654930313 - 1.5141220506920265 - 1.7624438989276665 - 1.9508043134110344 - 2.0675406980240267 - 2.1034573390731555 - 2.052273836448269 - 1.9109646480019093 - 1.6799725903032776 - 1.3632839857086507 - 0.9683586804924276 - 0.5059141646758684 - -0.010430745140753043 - -0.5646410090932847 - -1.138861728590151 - -1.7141029592812163 - -2.2709857127592414 - -2.790518507831888 - -3.2548717069684 - -3.648116139435917 - -3.9568932484680017 - -4.170986220240062 - -4.283765204854646 - -4.292484703852357 - -4.198417290290803 - -4.006814803043638 - -3.726695724178048 - -3.37046527704168 - -2.9533825195279793 - -2.4928959906817902 - -2.0078759472002377 - -1.517776573385301 - -1.0417654801216554 - -0.5978600994416915 - -0.2021110755729666 - 0.13212862419107202 - 0.3948133932653443 - 0.5796629757178938 - 0.684444841579511 - 0.7110648948093021 - 0.6654592883005234 - 0.557289507899864 - 0.39945239743779043 - 0.20742597171535118 - -0.0015197508941929329 - -0.20921050041161915 - -0.39751213577760675 - -0.5492860576899088 - -0.649308567871849 - -0.6851078809391865 - -0.6476755904710924 - -0.5320146974624097 - -0.3374936217767318 - -0.06798462398083455 - 0.2682246394952308 - 0.6587466025217397 - 1.0876251185561991 - 1.5360603568722346 - 1.9832947728009653 - 2.4076188421107507 - 2.7874483149144926 - 3.1024200917868145 - 3.3344517483173606 - 3.468710404436331 - 3.494440085461533 - 3.405602844706244 - 3.201297463697794 - 2.8859301347274213 - 2.469123664822105 - 1.9653648302210067 - 1.3934029008467559 - 0.7754253572406592 - 0.1360487527085192 - -0.4988271155524238 - -1.1032456434473064 - -1.6524392213787114 - -2.1240310863544924 - -2.4991311093774153 - -2.7632678777347914 - -2.907107018414796 - -2.926916072218083 - -2.8247488772452836 - -2.608336730490184 - -2.2906888386968305 - -1.8894199487844925 - -1.4258377425415354 - -0.9238357865311666 - -0.40864880499263034 - 0.0944648461992371 - 0.561543878430476 - 0.9711772538437015 - 1.3056219183500009 - 1.5517236410899165 - 1.7015894648028433 - 1.7529731950381982 - 1.7093506015372697 - 1.5796777759883764 - 1.3778434886745352 - 1.1218434602326948 - 0.8327202595728497 - 0.5333261518124792 - 0.2469768506177699 - -0.0039288724026636706 - -0.19924586233635266 - -0.32229910550402224 - -0.36090942542360577 - -0.3081675133778066 - -0.1629089030656255 - 0.07014114601785719 - 0.38056550330791106 - 0.752788994270902 - 1.1669220859623213 - 1.599870140283532 - 2.026648001057436 - 2.4218269273489175 - 2.761032112799345 - 3.0224048173264175 - 3.187943810024206 - 3.244646431176403 - 3.18537989273035 - 3.0094279386312377 - 2.7226759136469703 - 2.3374176617823443 - 1.8717893513117672 - 1.3488570626345149 - 0.7954055095509405 - 0.24049337223646827 - -0.2861447018298939 - -0.7557592409830243 - -1.1422150351433635 - -1.4234934507035748 - -1.582979315144211 - -1.6104550693151136 - -1.502740963472012 - -1.2639399988229563 - -0.9052689714669601 - -0.4444810593259611 positive_zeros: - '1.50134958372147065178214757112118' - '3.14091650863687332822324609739340' - '3.61113749066029937377856775328109' - '5.26048846395843449438972536185450' - '6.06954826095111377752373881003659' - '6.81847892209639060270204661908913' - '7.73323846350184087475417457616255' - '9.057427983709098036792655771257432' - '9.608953731299650841890066401626815' prelabel: 2-720-1.1-c3-0 primitive: true rational: true root_analytic_conductor: 6.517773792034613 root_angle: 1.0 root_number: '-1' self_dual: true sign_arg: __RealLiteral__: 0 data: '0.5' prec: 10 spectral_label: c3-0 trace_hash: 1220729169783329338 types: - CMF z1: __RealLiteral__: 0 data: '1.50134958372147065178214757112' prec: 103 z2: __RealLiteral__: 0 data: '3.14091650863687332822324609739' prec: 103 z3: __RealLiteral__: 0 data: '3.61113749066029937377856775328' prec: 103 - - algebraic: true analytic_conductor: 42.481375204133265 bad_primes: - 2 - 3 - 5 central_character: '1.1' conductor: 720 conductor_radical: 30 degree: 2 dirichlet_coefficients: - 1 - 0 - 0 - 0 - 5 - 0 - -34 - 0 - 0 - 0 - 18 - 0 - 12 - 0 - 0 - 0 - 106 - 0 - 44 - 0 - 0 - 0 - 56 - 0 - 25 - 0 - 0 - 0 - -270 - 0 - -204 - 0 - 0 - 0 - -170 - 0 - 120 - 0 - 0 - 0 - -80 - 0 - -536 - 0 - 0 - 0 - -536 - 0 - 813 - 0 - 0 - 0 - -542 - 0 - 90 - 0 - 0 - 0 - -174 - 0 - 186 - 0 - 0 - 0 - 60 - 0 - -332 - 0 - 0 - 0 - -132 - 0 - -602 - 0 - 0 - 0 - -612 - 0 - 548 - 0 - 0 - 0 - -492 - 0 - 530 - 0 - 0 - 0 - 1052 - 0 - -408 - 0 - 0 - 0 - 220 - 0 - 482 - 0 - 0 - 0 euler11: - 1 - -18 - 1331 euler13: - 1 - -12 - 2197 euler17: - 1 - -106 - 4913 euler19: - 1 - -44 - 6859 euler2: - 1 - 0 - 0 euler23: - 1 - -56 - 12167 euler29: - 1 - 270 - 24389 euler3: - 1 - 0 - 0 euler31: - 1 - 204 - 29791 euler37: - 1 - -120 - 50653 euler41: - 1 - 80 - 68921 euler43: - 1 - 536 - 79507 euler47: - 1 - 536 - 103823 euler5: - 1 - -5 - 0 euler53: - 1 - 542 - 148877 euler59: - 1 - 174 - 205379 euler61: - 1 - -186 - 226981 euler67: - 1 - 332 - 300763 euler7: - 1 - 34 - 343 euler71: - 1 - 132 - 357911 euler73: - 1 - 602 - 389017 euler79: - 1 - -548 - 493039 euler83: - 1 - 492 - 571787 euler89: - 1 - -1052 - 704969 euler97: - 1 - -482 - 912673 euler_factors: - - 1 - 0 - 0 - - 1 - 0 - 0 - - 1 - -5 - 0 - - 1 - 34 - 343 - - 1 - -18 - 1331 - - 1 - -12 - 2197 - - 1 - -106 - 4913 - - 1 - -44 - 6859 - - 1 - -56 - 12167 - - 1 - 270 - 24389 - - 1 - 204 - 29791 - - 1 - -120 - 50653 - - 1 - 80 - 68921 - - 1 - 536 - 79507 - - 1 - 536 - 103823 - - 1 - 542 - 148877 - - 1 - 174 - 205379 - - 1 - -186 - 226981 - - 1 - 332 - 300763 - - 1 - 132 - 357911 - - 1 - 602 - 389017 - - 1 - -548 - 493039 - - 1 - 492 - 571787 - - 1 - -1052 - 704969 - - 1 - -482 - 912673 id: 20193391 index: 19 instance_types: - CMF - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/720/4/a/p/1/1 - ModularForm/GL2/Q/holomorphic/720/4/a/p 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: 2-720-1.1-c3-0-19 motivic_weight: 3 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 3 order_of_vanishing: 1 prelabel: 2-720-1.1-c3-0 primitive: true rational: true root_analytic_conductor: 6.517773792034613 root_angle: 0.5 self_dual: true spectral_label: c3-0 trace_hash: 1220729169783329338 z1: __RealLiteral__: 0 data: '1.50134958372147065178214757112' prec: 103 - - Lhash: '1903186700956924621544106186140' Lhash_array: - '1903186700956924621544106186140' id: 19979588 label: 2-720-1.1-c3-0-19 type: CMF url: ModularForm/GL2/Q/holomorphic/720/4/a/p - Lhash: '1903186700956924621544106186140' Lhash_array: - '1903186700956924621544106186140' id: 24569823 label: 2-720-1.1-c3-0-19 type: CMF url: ModularForm/GL2/Q/holomorphic/720/4/a/p/1/1 label_cols: - label - label - label labels: - 2-720-1.1-c3-0-19 - 2-720-1.1-c3-0-19 - 2-720-1.1-c3-0-19 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-23T21:02:05.046013'