data: - - Lhash: '447152261917800547379452406606' a10: 3 a2: -1 a3: -1 a4: 1 a5: -3 a6: 1 a7: 0 a8: -1 a9: 1 accuracy: 100 algebraic: true analytic_conductor: 25.82362001368209 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 2 - - 1 - 1 - - 3 - - 1 - 1 - - 7 - - 1 - - 11 - - 1 - 1 bad_primes: - 2 - 3 - 7 - 11 central_character: '3234.1' coefficient_field: 1.1.1.1 conductor: 3234 conductor_radical: 462 degree: 2 euler_factors: - - 1 - 1 - - 1 - 1 - - 1 - 3 - 5 - - 1 - - 1 - 1 - - 1 - 6 - 13 - - 1 - -5 - 17 - - 1 - 6 - 19 - - 1 - -5 - 23 - - 1 - 6 - 29 - - 1 - 4 - 31 - - 1 - 2 - 37 - - 1 - 5 - 41 - - 1 - 10 - 43 - - 1 - 9 - 47 - - 1 - -2 - 53 - - 1 - -12 - 59 - - 1 - -5 - 61 - - 1 - -5 - 67 - - 1 - -4 - 71 - - 1 - 12 - 73 - - 1 - 1 - 79 - - 1 - 1 - 83 - - 1 - 6 - 89 - - 1 - 9 - 97 - - 1 - -8 - 101 - - 1 - -2 - 103 - - 1 - 13 - 107 - - 1 - 11 - 109 - - 1 - -10 - 113 euler_factors_factorization: - - - - 1 - 1 - 1 - - - - 1 - 1 - 1 - - - - 1 - 3 - 5 - 1 - - 1 - - - - 1 - 1 - 1 - - - - 1 - 6 - 13 - 1 - - - - 1 - -5 - 17 - 1 - - - - 1 - 6 - 19 - 1 - - - - 1 - -5 - 23 - 1 - - - - 1 - 6 - 29 - 1 - - - - 1 - 4 - 31 - 1 - - - - 1 - 2 - 37 - 1 - - - - 1 - 5 - 41 - 1 - - - - 1 - 10 - 43 - 1 - - - - 1 - 9 - 47 - 1 - - - - 1 - -2 - 53 - 1 - - - - 1 - -12 - 59 - 1 - - - - 1 - -5 - 61 - 1 - - - - 1 - -5 - 67 - 1 - - - - 1 - -4 - 71 - 1 - - - - 1 - 12 - 73 - 1 - - - - 1 - 1 - 79 - 1 - - - - 1 - 1 - 83 - 1 - - - - 1 - 6 - 89 - 1 - - - - 1 - 9 - 97 - 1 - - - - 1 - -8 - 101 - 1 - - - - 1 - -2 - 103 - 1 - - - - 1 - 13 - 107 - 1 - - - - 1 - 11 - 109 - 1 - - - - 1 - -10 - 113 - 1 gamma_factors: - [] - - 0 group: GL2 id: 20176869 index: 0 label: 2-3234-1.1-c1-0-0 leading_term: '0.285036630903140513684938919367600000000000000000000000000000000000000000000000000000000000' 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/3234/2/a/a plot_delta: __RealLiteral__: 0 data: '0.05078125' prec: 34 plot_values: - 0.2850366309031405 - 0.2791438536820494 - 0.261455099148086 - 0.2319438651689841 - 0.19058154946468184 - 0.13735971388095028 - 0.07231919285039298 - -0.004415773054820945 - -0.09260042303443976 - -0.19183150524342865 - -0.30151053014763923 - -0.42081019672153475 - -0.548645751712229 - -0.6836528247798331 - -0.8241730543258756 - -0.9682485895713151 - -1.1136263259047599 - -1.2577724998103899 - -1.3978980316537968 - -1.5309947539656608 - -1.6538823957066144 - -1.7632659076903716 - -1.855802411941458 - -1.9281767420565494 - -1.9771842189523736 - -1.9998189852466202 - -1.9933659122344953 - -1.955493807595508 - -1.8843474019910844 - -1.7786353912640274 - -1.637711670432762 - -1.461646827690347 - -1.2512869814332466 - -1.0082971493567265 - -0.7351865419018887 - -0.4353134760515294 - -0.11286800967341021 - 0.22716910218879288 - 0.579091936691598 - 0.9365595561254442 - 1.2927101886741674 - 1.6402980622137757 - 1.9718507136481263 - 2.2798437945053376 - 2.5568896195027744 - 2.7959349867977195 - 2.9904631655099547 - 3.134694426245774 - 3.2237791107021705 - 3.253977021330569 - 3.2228168821435412 - 3.129229792946328 - 2.9736509817122747 - 2.7580847570398954 - 2.486128370886437 - 2.1629515095719567 - 1.7952293189222164 - 1.391028209995745 - 0.9596451502109716 - 0.5114026790907027 - 0.05740345065609032 - -0.3907503564402581 - -0.8212659597984249 - -1.2224890989841029 - -1.583244105608517 - -1.8931747662063083 - -2.1430752257532877 - -2.325199909663331 - -2.4335415334494037 - -2.4640667415694173 - -2.4148997773068914 - -2.2864458270852683 - -2.0814472841445464 - -1.8049681021420936 - -1.4643036088428905 - -1.0688155602153824 - -0.6296947607875788 - -0.159656172264381 - 0.3274260126000492 - 0.8169334356964862 - 1.293956698369644 - 1.7437726053921299 - 2.15233014025985 - 2.506728822712544 - 2.795672685450266 - 3.0098832835128246 - 3.1424559395464873 - 3.1891448316980386 - 3.1485645250304293 - 3.022298085003337 - 2.814904922080984 - 2.5338249073379626 - 2.18917895800198 - 1.7934700911637391 - 1.3611927436453037 - 0.9083618097880511 - 0.45197620909094166 - 0.009434719352573137 - -0.40207583380794687 - -0.7661982688140695 - -1.0680059647810094 - -1.294564295040135 - -1.435430696312354 - -1.4830731979437615 - -1.4331897855590756 - -1.2849142972786698 - -1.0408985433358993 - -0.7072648649187707 - -0.29342824140151863 - 0.1882078687640172 - 0.7226727097183417 - 1.2929523550232012 - 1.8805982992384505 - 2.466398256800578 - 3.031083935925107 - 3.5560485314157413 - 4.024045721277824 - 4.419842130554828 - 4.7307965685306215 - 4.947341830179098 - 5.0633484075288875 - 5.076353960965895 - 4.987647688906035 - 4.802204601803891 - 4.528470916380534 - 4.178008079041894 - 3.7650090327450485 - 3.305705987985065 - 2.8176938870755226 - 2.3191977265020127 - 1.8283147253282601 - 1.3622638445992237 - 0.9366752737708459 - 0.5649511662739535 - 0.25772615255187165 - 0.022452075688885097 - -0.1368738643598314 - -0.21982459522935038 - -0.22949624823813453 - -0.17230011561286115 - -0.05760217760359346 - 0.10277398026490021 - 0.2951585129867253 - 0.5047329742800791 - 0.7162819384704405 - 0.9149632785410788 - 1.0870604450691823 - 1.2206804537245761 - 1.3063633835574109 - 1.3375729531110652 - 1.3110430334822454 - 1.2269615566870613 - 1.088980895226026 - 0.9040520790230565 - 0.682088791888909 - 0.4354755404766617 - 0.17844229914656126 - -0.07366509506162373 - -0.3051838553182967 - -0.5009634671435913 - -0.6471840123661255 - -0.7321221773838797 - -0.746825372376223 - -0.6856582411785815 - -0.5466915567276633 - -0.33191083070426713 - -0.04723058736291941 - 0.2976902433232716 - 0.6898264276020832 - 1.113342774851741 - 1.5503041808811264 - 1.981506570305776 - 2.387389183841769 - 2.7489837683366933 - 3.0488534987928917 - 3.271974079662773 - 3.4065115085564255 - 3.4444553878308155 - 3.382073263779979 - 3.2201599674103356 - 2.9640659279001467 - 2.623499445323355 - 2.2121093942760055 - 1.7468661986136378 - 1.2472695759966936 - 0.7344209291942848 - 0.2300058429912448 - -0.24476250243724362 - -0.6701853946017434 - -1.02905247911419 - -1.3074965976304371 - -1.495684183486938 - -1.5883037986097537 - -1.584825477334226 - -1.4895152378697192 - -1.3112018374821912 - -1.0628059225977808 - -0.7606544658132871 - -0.4236150970996364 - -0.07209497567646551 - 0.2730433617036764 - 0.5915916649509989 - 0.8650716008745897 - 1.0777179749593688 - 1.2173155447242425 - 1.2758428214219164 - 1.2498863252909698 - 1.1408009945263504 - 0.9546062138107622 - 0.701621490385729 - 0.3958603698930166 - 0.054214938898640076 - -0.3045245780742408 - -0.660760764265658 - -0.9952291861615213 - -1.2901228888835208 - -1.5301363280725802 - -1.7033675761107379 - -1.802024920776185 - -1.8228944730387278 - -1.767538586427299 - -1.642210066717231 - -1.457483491208176 - -1.2276215490747746 - -0.9697102093240805 - -0.7026107888294492 - -0.44578876835876863 - -0.21808774981052803 - -0.036521690608362876 - 0.08484087654263524 - 0.13583066549128767 - 0.11090746151339942 - 0.009615691110406418 - -0.16326947991260232 - -0.3979232232382369 - -0.6799779704016552 - -0.991335366685855 - -1.3112436271861967 - -1.6175836333460187 - -1.8882928997406385 - -2.1028460621603706 - -2.2437045042069554 - -2.2976466283133896 - -2.2568942944066084 - -2.119960010541578 - -1.8921531859992227 - -1.5857014897768413 - -1.219464187769602 - -0.8182371481033444 - -0.41167274887099253 - -0.0328608625189698 - 0.28336190837706343 - 0.5022897671550531 - 0.5913135590400279 - 0.5218681372452804 - 0.2712520036407242 - -0.1757864078834014 positive_zeros: - '0.35274093810809910411564142374833' - '1.84523390935343279940589930817096' - '3.05331510142960887346457349810024' - '3.92692428639608188414387845800735' - '4.92689675195570829518821943240468' - '5.51605635968754426443992710400911' - '6.86136903500212564394979157694274' - '7.12910487439486860495499701538012' - '7.957526633191908617876120023127891' - '8.437156545038805140814932730332171' prelabel: 2-3234-1.1-c1-0 primitive: true rational: true root_analytic_conductor: 5.081694600591626 root_angle: 0.0 root_number: '1' self_dual: true sign_arg: 0 spectral_label: c1-0 trace_hash: 1822034592254675393 types: - CMF z1: __RealLiteral__: 0 data: '0.35274093810809910411564142375' prec: 103 z2: __RealLiteral__: 0 data: '1.84523390935343279940589930817' prec: 103 z3: __RealLiteral__: 0 data: '3.05331510142960887346457349810' prec: 103 - - algebraic: true analytic_conductor: 25.82362001368209 bad_primes: - 2 - 3 - 7 - 11 central_character: '1.1' conductor: 3234 conductor_radical: 462 degree: 2 dirichlet_coefficients: - 1 - -1 - -1 - 1 - -3 - 1 - 0 - -1 - 1 - 3 - -1 - -1 - -6 - 0 - 3 - 1 - 5 - -1 - -6 - -3 - 0 - 1 - 5 - 1 - 4 - 6 - -1 - 0 - -6 - -3 - -4 - -1 - 1 - -5 - 0 - 1 - -2 - 6 - 6 - 3 - -5 - 0 - -10 - -1 - -3 - -5 - -9 - -1 - 0 - -4 - -5 - -6 - 2 - 1 - 3 - 0 - 6 - 6 - 12 - 3 - 5 - 4 - 0 - 1 - 18 - -1 - 5 - 5 - -5 - 0 - 4 - -1 - -12 - 2 - -4 - -6 - 0 - -6 - -1 - -3 - 1 - 5 - -1 - 0 - -15 - 10 - 6 - 1 - -6 - 3 - 0 - 5 - 4 - 9 - 18 - 1 - -9 - 0 - -1 - 4 euler11: - 1 - 1 - 0 euler13: - 1 - 6 - 13 euler17: - 1 - -5 - 17 euler19: - 1 - 6 - 19 euler2: - 1 - 1 - 0 euler23: - 1 - -5 - 23 euler29: - 1 - 6 - 29 euler3: - 1 - 1 - 0 euler31: - 1 - 4 - 31 euler37: - 1 - 2 - 37 euler41: - 1 - 5 - 41 euler43: - 1 - 10 - 43 euler47: - 1 - 9 - 47 euler5: - 1 - 3 - 5 euler53: - 1 - -2 - 53 euler59: - 1 - -12 - 59 euler61: - 1 - -5 - 61 euler67: - 1 - -5 - 67 euler7: - 1 - 0 - 0 euler71: - 1 - -4 - 71 euler73: - 1 - 12 - 73 euler79: - 1 - 1 - 79 euler83: - 1 - 1 - 83 euler89: - 1 - 6 - 89 euler97: - 1 - 9 - 97 euler_factors: - - 1 - 1 - 0 - - 1 - 1 - 0 - - 1 - 3 - 5 - - 1 - 0 - 0 - - 1 - 1 - 0 - - 1 - 6 - 13 - - 1 - -5 - 17 - - 1 - 6 - 19 - - 1 - -5 - 23 - - 1 - 6 - 29 - - 1 - 4 - 31 - - 1 - 2 - 37 - - 1 - 5 - 41 - - 1 - 10 - 43 - - 1 - 9 - 47 - - 1 - -2 - 53 - - 1 - -12 - 59 - - 1 - -5 - 61 - - 1 - -5 - 67 - - 1 - -4 - 71 - - 1 - 12 - 73 - - 1 - 1 - 79 - - 1 - 1 - 83 - - 1 - 6 - 89 - - 1 - 9 - 97 id: 20176869 index: 0 instance_types: - ECQ - CMF - CMF instance_urls: - EllipticCurve/Q/3234/a - ModularForm/GL2/Q/holomorphic/3234/2/a/a/1/1 - ModularForm/GL2/Q/holomorphic/3234/2/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: 2-3234-1.1-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: 2-3234-1.1-c1-0 primitive: true rational: true root_analytic_conductor: 5.081694600591626 root_angle: 0.0 self_dual: true spectral_label: c1-0 trace_hash: 1822034592254675393 z1: __RealLiteral__: 0 data: '0.35274093810809910411564142375' prec: 103 - - Lhash: '447152261917800547379452406606' Lhash_array: - '447152261917800547379452406606' id: 20140279 label: 2-3234-1.1-c1-0-0 type: CMF url: ModularForm/GL2/Q/holomorphic/3234/2/a/a - Lhash: '447152261917800547379452406606' Lhash_array: - '447152261917800547379452406606' id: 24560676 label: 2-3234-1.1-c1-0-0 type: CMF url: ModularForm/GL2/Q/holomorphic/3234/2/a/a/1/1 - Lhash: '1822034592254675393' Lhash_array: - '1822034592254675393' id: 100418 label: 2-3234-1.1-c1-0-0 type: ECQ url: EllipticCurve/Q/3234/a label_cols: - label - label - label labels: - 2-3234-1.1-c1-0-0 - 2-3234-1.1-c1-0-0 - 2-3234-1.1-c1-0-0 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-23T21:04:30.878892'