data: - - Lhash: '1748631566078318561493435628141' a10: 0 a2: 0 a3: -3 a4: 0 a5: 0 a6: 0 a7: -1 a8: 0 a9: 6 accuracy: 100 algebraic: true analytic_conductor: 9.7098088857877 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 2 - - 1 - - 19 - - 1 - -1 bad_primes: - 2 - 19 central_character: '1216.1' coefficient_field: 1.1.1.1 conductor: 1216 conductor_radical: 38 degree: 2 euler_factors: - - 1 - - 1 - 3 - 3 - - 1 - 0 - 5 - - 1 - 1 - 7 - - 1 - 2 - 11 - - 1 - -1 - 13 - - 1 - -3 - 17 - - 1 - -1 - - 1 - -3 - 23 - - 1 - 3 - 29 - - 1 - -8 - 31 - - 1 - -10 - 37 - - 1 - 12 - 41 - - 1 - 8 - 43 - - 1 - 8 - 47 - - 1 - -9 - 53 - - 1 - -5 - 59 - - 1 - 10 - 61 - - 1 - 7 - 67 - - 1 - 10 - 71 - - 1 - -1 - 73 - - 1 - 14 - 79 - - 1 - 6 - 83 - - 1 - 4 - 89 - - 1 - 6 - 97 - - 1 - 10 - 101 - - 1 - -14 - 103 - - 1 - 5 - 107 - - 1 - 9 - 109 - - 1 - -2 - 113 euler_factors_factorization: - - 1 - - - - 1 - 3 - 3 - 1 - - - - 1 - 0 - 5 - 1 - - - - 1 - 1 - 7 - 1 - - - - 1 - 2 - 11 - 1 - - - - 1 - -1 - 13 - 1 - - - - 1 - -3 - 17 - 1 - - - - 1 - -1 - 1 - - - - 1 - -3 - 23 - 1 - - - - 1 - 3 - 29 - 1 - - - - 1 - -8 - 31 - 1 - - - - 1 - -10 - 37 - 1 - - - - 1 - 12 - 41 - 1 - - - - 1 - 8 - 43 - 1 - - - - 1 - 8 - 47 - 1 - - - - 1 - -9 - 53 - 1 - - - - 1 - -5 - 59 - 1 - - - - 1 - 10 - 61 - 1 - - - - 1 - 7 - 67 - 1 - - - - 1 - 10 - 71 - 1 - - - - 1 - -1 - 73 - 1 - - - - 1 - 14 - 79 - 1 - - - - 1 - 6 - 83 - 1 - - - - 1 - 4 - 89 - 1 - - - - 1 - 6 - 97 - 1 - - - - 1 - 10 - 101 - 1 - - - - 1 - -14 - 103 - 1 - - - - 1 - 5 - 107 - 1 - - - - 1 - 9 - 109 - 1 - - - - 1 - -2 - 113 - 1 gamma_factors: - [] - - 0 group: GL2 id: 20373781 index: 15 label: 2-1216-1.1-c1-0-15 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: 1 origin: ModularForm/GL2/Q/holomorphic/1216/2/a/a plot_delta: __RealLiteral__: 0 data: '0.05859375' prec: 34 plot_values: - -6.903657573877204e-61 - 0.0968506633009704 - 0.19338483368717396 - 0.28923159945361515 - 0.38391467939191487 - 0.4768080581184629 - 0.5671007021223449 - 0.6537720819946222 - 0.735579447932663 - 0.8110571270116427 - 0.878527591876174 - 0.9361237010691578 - 0.9818213034114107 - 1.013481286038026 - 1.0289000790660603 - 1.025867569380647 - 1.0022312952631935 - 0.9559656799541353 - 0.8852449146362081 - 0.7885179269014682 - 0.6645836818921768 - 0.5126648751037509 - 0.33247790441448366 - 0.12429687015260069 - -0.1109907392013186 - -0.3718390484526149 - -0.6560118152857255 - -0.9605656761918984 - -1.2818506167601889 - -1.6155293636550025 - -1.9566170043937403 - -2.2995416628996845 - -2.6382265010059673 - -2.96619268966069 - -3.276682313291374 - -3.562799454941043 - -3.8176669799308183 - -4.0345958162309765 - -4.2072628468501945 - -4.329892911134113 - -4.3974398860689465 - -4.4057614130651 - -4.351781576063407 - -4.233635746070315 - -4.050791904216036 - -3.8041430537581125 - -3.4960658384903747 - -3.1304412009928737 - -2.712633831470885 - -2.2494282607053386 - -1.7489207145738017 - -1.2203672401533636 - -0.6739900943195626 - -0.12074590792083519 - 0.4279393506174692 - 0.9604621456379684 - 1.465352095830321 - 1.9315927334597154 - 2.348942498084555 - 2.7082455644519565 - 3.001721843245507 - 3.2232256023984056 - 3.3684626577213397 - 3.435156982745577 - 3.4231588818073524 - 3.3344885341965935 - 3.1733107109001915 - 2.9458387332478937 - 2.6601682137948224 - 2.3260437100652376 - 1.9545640367242532 - 1.5578345192798448 - 1.1485768267971128 - 0.7397090870892294 - 0.34391066519878943 - -0.02681281591526006 - -0.3615479911701769 - -0.6508595556586309 - -0.887127724438648 - -1.0648230020293261 - -1.1807058386292606 - -1.233941273296656 - -1.2261217124798147 - -1.1611944649108568 - -1.0452944262461068 - -0.8864862339134495 - -0.6944241342070218 - -0.4799415505698854 - -0.2545857430669084 - -0.030115838696159906 - 0.1820152617782508 - 0.3711731634883486 - 0.5280259728995936 - 0.6449779702949514 - 0.7165323466209285 - 0.7395647969445189 - 0.713493086099871 - 0.6403318381636337 - 0.5246266016417536 - 0.37326651970118624 - 0.19518047056718024 - 0.0009270950088881454 - -0.1978055600566482 - -0.38877023819695683 - -0.5597758973811308 - -0.6993206497670538 - -0.7972125696361403 - -0.8451480936933904 - -0.8372185095846427 - -0.7703172292782327 - -0.6444241366743199 - -0.4627481777446735 - -0.2317153540114127 - 0.039203848514214365 - 0.33782610137985625 - 0.6497367329629499 - 0.9589042522139968 - 1.2484039188615108 - 1.5012200778871927 - 1.7010918568528164 - 1.8333631926540155 - 1.8857962531502885 - 1.8493073189752043 - 1.718586176171549 - 1.4925640316840072 - 1.174700793749855 - 0.7730700531383481 - 0.3002289626448691 - -0.22712993617631325 - -0.788737491637663 - -1.3614994230822954 - -1.9204126031602669 - -2.4396092108753247 - -2.893484251761414 - -3.2578562569916314 - -3.5111075334023694 - -3.6352493987318977 - -3.6168595422895686 - -3.447843014202314 - -3.1259752456841703 - -2.655194684439993 - -2.0456237136676814 - -1.3133090193833923 - -0.47968589808560397 - 0.42921548926143105 - 1.3837908870947062 - 2.3520668505951843 - 3.301036843165748 - 4.19806789790611 - 5.012312362889549 - 5.716057561237288 - 6.285947847787083 - 6.704018542112824 - 6.958489395348832 - 7.044276266334633 - 6.9631930421113974 - 6.723830901801298 - 6.341118046094805 - 5.835579180015742 - 5.232329497585562 - 4.559851841835211 - 3.8486173314015524 - 3.1296183892898006 - 2.4328882578550437 - 1.7860823909925778 - 1.2131944350677824 - 0.7334729138215356 - 0.36059450541077676 - 0.10213643444041436 - -0.04062532453960287 - -0.07258279430382675 - -0.004336608442559897 - 0.14856274256291996 - 0.36662971872430045 - 0.6276569815917127 - 0.9080582756015242 - 1.1842646969348745 - 1.4340949319009553 - 1.6380213716482601 - 1.7802598262215694 - 1.8496206000679811 - 1.8400724338423158 - 1.7509875182017987 - 1.5870545105683178 - 1.357866164298162 - 1.077207662411068 - 0.7620898746731624 - 0.43158742444193277 - 0.10555368188778028 - -0.19670719918106014 - -0.4577278665266562 - -0.6630434850856793 - -0.8021609693232323 - -0.8692687004563008 - -0.8636393564261717 - -0.7896973310447833 - -0.656743151271778 - -0.47834906007006167 - -0.2714611790031269 - -0.055263062720155444 - 0.15012824675472541 - 0.32505045458737303 - 0.45167826891057516 - 0.5153079609886023 - 0.5054568933075263 - 0.41670075094202713 - 0.249186475106219 - 0.008778513291437976 - -0.2931811686229304 - -0.6404941901833778 - -1.01307785475391 - -1.3882343841750082 - -1.7421425047061745 - -2.0514798951347264 - -2.2950737095661706 - -2.4554713675220445 - -2.5203255605641086 - -2.4834960387462206 - -2.3457858587412828 - -2.115250621510472 - -1.8070446372715492 - -1.4427964421333734 - -1.049535928932328 - -0.6582246845533734 - -0.3019680673277486 - -0.014010330272499883 - 0.17436886600032936 - 0.23592814627677533 - 0.1493776655218108 - -0.09899282835693586 - -0.5140819083725042 - -1.0912298608334727 - -1.8160195625780908 - -2.6646547262780085 - -3.6049105561682113 - -4.597616428797544 - -5.5985964194893265 - -6.560963505724644 - -7.437639073499463 - -8.18395258936491 - -8.760168200343934 - -9.13378628209524 - -9.28147868656122 - -9.190536155689866 - -8.859733995592503 - -8.299556046475365 - -7.531755203837027 - -6.588268899645138 - -5.509547526075518 - -4.3423902599437465 - -3.137413761188146 - -1.9463027252354292 - -0.8190056710430053 - 0.19895638692880133 - 1.0689069928384956 - 1.7610121341202685 - 2.2557398333702983 positive_zeros: - '1.37942708011457790071691730372484' - '3.11827862407422559284554596551673' - '4.39011552338323920878309071486365' - '5.22289133265133441977616849928471' - '5.91824238738469752095279165719534' - '6.61303503651954034437075836395682' - '7.47536575646542499937872009351946' - '8.410316400065169823569354161047042' - '9.880157654161737946048525039668674' prelabel: 2-1216-1.1-c1-0 primitive: true rational: true root_analytic_conductor: 3.11605662429098 root_angle: 1.0 root_number: '-1' self_dual: true sign_arg: __RealLiteral__: 0 data: '0.5' prec: 10 spectral_label: c1-0 trace_hash: 1934663668760385422 types: - CMF z1: __RealLiteral__: 0 data: '1.37942708011457790071691730372' prec: 103 z2: __RealLiteral__: 0 data: '3.11827862407422559284554596552' prec: 103 z3: __RealLiteral__: 0 data: '4.39011552338323920878309071486' prec: 103 - - algebraic: true analytic_conductor: 9.7098088857877 bad_primes: - 2 - 19 central_character: '1.1' conductor: 1216 conductor_radical: 38 degree: 2 dirichlet_coefficients: - 1 - 0 - -3 - 0 - 0 - 0 - -1 - 0 - 6 - 0 - -2 - 0 - 1 - 0 - 0 - 0 - 3 - 0 - 1 - 0 - 3 - 0 - 3 - 0 - -5 - 0 - -9 - 0 - -3 - 0 - 8 - 0 - 6 - 0 - 0 - 0 - 10 - 0 - -3 - 0 - -12 - 0 - -8 - 0 - 0 - 0 - -8 - 0 - -6 - 0 - -9 - 0 - 9 - 0 - 0 - 0 - -3 - 0 - 5 - 0 - -10 - 0 - -6 - 0 - 0 - 0 - -7 - 0 - -9 - 0 - -10 - 0 - 1 - 0 - 15 - 0 - 2 - 0 - -14 - 0 - 9 - 0 - -6 - 0 - 0 - 0 - 9 - 0 - -4 - 0 - -1 - 0 - -24 - 0 - 0 - 0 - -6 - 0 - -12 - 0 euler11: - 1 - 2 - 11 euler13: - 1 - -1 - 13 euler17: - 1 - -3 - 17 euler19: - 1 - -1 - 0 euler2: - 1 - 0 - 0 euler23: - 1 - -3 - 23 euler29: - 1 - 3 - 29 euler3: - 1 - 3 - 3 euler31: - 1 - -8 - 31 euler37: - 1 - -10 - 37 euler41: - 1 - 12 - 41 euler43: - 1 - 8 - 43 euler47: - 1 - 8 - 47 euler5: - 1 - 0 - 5 euler53: - 1 - -9 - 53 euler59: - 1 - -5 - 59 euler61: - 1 - 10 - 61 euler67: - 1 - 7 - 67 euler7: - 1 - 1 - 7 euler71: - 1 - 10 - 71 euler73: - 1 - -1 - 73 euler79: - 1 - 14 - 79 euler83: - 1 - 6 - 83 euler89: - 1 - 4 - 89 euler97: - 1 - 6 - 97 euler_factors: - - 1 - 0 - 0 - - 1 - 3 - 3 - - 1 - 0 - 5 - - 1 - 1 - 7 - - 1 - 2 - 11 - - 1 - -1 - 13 - - 1 - -3 - 17 - - 1 - -1 - 0 - - 1 - -3 - 23 - - 1 - 3 - 29 - - 1 - -8 - 31 - - 1 - -10 - 37 - - 1 - 12 - 41 - - 1 - 8 - 43 - - 1 - 8 - 47 - - 1 - -9 - 53 - - 1 - -5 - 59 - - 1 - 10 - 61 - - 1 - 7 - 67 - - 1 - 10 - 71 - - 1 - -1 - 73 - - 1 - 14 - 79 - - 1 - 6 - 83 - - 1 - 4 - 89 - - 1 - 6 - 97 id: 20373781 index: 15 instance_types: - ECQ - CMF - CMF instance_urls: - EllipticCurve/Q/1216/a - ModularForm/GL2/Q/holomorphic/1216/2/a/a/1/1 - ModularForm/GL2/Q/holomorphic/1216/2/a/a is_instance_Artin: false is_instance_BMF: false is_instance_CMF: true is_instance_DIR: false is_instance_ECNF: false is_instance_ECQ: true 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: 2-1216-1.1-c1-0-15 motivic_weight: 1 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 1 order_of_vanishing: 1 prelabel: 2-1216-1.1-c1-0 primitive: true rational: true root_analytic_conductor: 3.11605662429098 root_angle: 0.5 self_dual: true spectral_label: c1-0 trace_hash: 1934663668760385422 z1: __RealLiteral__: 0 data: '1.37942708011457790071691730372' prec: 103 - - Lhash: '1748631566078318561493435628141' Lhash_array: - '1748631566078318561493435628141' id: 20709645 label: 2-1216-1.1-c1-0-15 type: CMF url: ModularForm/GL2/Q/holomorphic/1216/2/a/a - Lhash: '1748631566078318561493435628141' Lhash_array: - '1748631566078318561493435628141' id: 24552222 label: 2-1216-1.1-c1-0-15 type: CMF url: ModularForm/GL2/Q/holomorphic/1216/2/a/a/1/1 - Lhash: '1934663668760385422' Lhash_array: - '1934663668760385422' id: 89870 label: 2-1216-1.1-c1-0-15 type: ECQ url: EllipticCurve/Q/1216/a label_cols: - label - label - label labels: - 2-1216-1.1-c1-0-15 - 2-1216-1.1-c1-0-15 - 2-1216-1.1-c1-0-15 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-24T16:38:59.781991'