data: - - Lhash: '4550156540727536811956799645442' a10: - -1.7320508075688772 - 6.873352803342883e-62 a2: - 0.8660254037844386 - -0.5 a3: - 0.36602540378443865 - -0.6339745962155614 a4: - 0.5 - -0.8660254037844386 a5: - -1.5 - -0.8660254037844386 a6: - -6.076624599100714e-61 - -0.7320508075688773 a7: - -2.0 - 3.4641016151377544 a8: - 0.0 - -1.0 a9: - 1.2320508075688772 - 2.133974596215561 accuracy: 100 algebraic: true analytic_conductor: 0.5908929749574752 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 2 - - - 1.0 - 0 - - -0.8660254037844386 - 0.5 - - 37 - - - 1.0 - 0 - - 0.5 - 6.06217782649107 bad_primes: - 2 - 37 central_character: '74.11' coefficient_field: CDF conductor: 74 conductor_radical: 74 conjugate: '3186580474100743147525674365857' degree: 2 euler_factors: - - - 1.0 - 0 - - -0.8660254037844386 - 0.5 - - - 1.0 - 0 - - -0.36602540378443865 - 0.6339745962155614 - - -1.5 - -2.598076211353316 - - - 1.0 - 0 - - 1.5 - 0.8660254037844386 - - 2.5 - 4.330127018922194 - - - 1.0 - 0 - - 2.0 - -3.4641016151377544 - - -3.5 - -6.06217782649107 - - - 1.0 - 0 - - -4.732050807568878 - 0 - - 11.0 - 0 - - - 1.0 - 0 - - 5.196152422706632 - 3.0 - - 6.5 - 11.258330249197702 - - - 1.0 - 0 - - 1.5 - -0.8660254037844386 - - 8.5 - -14.722431864335457 - - - 1.0 - 0 - - 1.098076211353316 - 0.6339745962155614 - - 9.5 - 16.454482671904334 - - - 1.0 - 0 - - 0 - -1.2679491924311228 - - -23.0 - 0 - - - 1.0 - 0 - - 0 - 4.267949192431122 - - -29.0 - 0 - - - 1.0 - 0 - - 0 - 1.2679491924311228 - - -31.0 - 0 - - - 1.0 - 0 - - 0.5 - 6.06217782649107 - - - 1.0 - 0 - - 0.2320508075688773 - -0.40192378864668404 - - -20.5 - -35.50704155516198 - - - 1.0 - 0 - - 0 - -9.464101615137755 - - -43.0 - 0 - - - 1.0 - 0 - - -11.660254037844387 - 0 - - 47.0 - 0 - - - 1.0 - 0 - - -1.2679491924311228 - -2.196152422706632 - - -26.5 - 45.89934640057525 - - - 1.0 - 0 - - 2.196152422706632 - -1.2679491924311228 - - 29.5 - -51.09549882328188 - - - 1.0 - 0 - - -12.696152422706632 - -7.330127018922194 - - 30.5 - 52.827549630850754 - - - 1.0 - 0 - - 3.098076211353316 - -5.366025403784438 - - -33.5 - -58.023702053557386 - - - 1.0 - 0 - - 1.2679491924311228 - -2.196152422706632 - - -35.5 - -61.48780366869514 - - - 1.0 - 0 - - 12.392304845413264 - 0 - - 73.0 - 0 - - - 1.0 - 0 - - 7.098076211353316 - 4.098076211353316 - - 39.5 - 68.41600689897065 - - - 1.0 - 0 - - 5.830127018922194 - 10.098076211353316 - - -41.5 - 71.88010851410841 - - - 1.0 - 0 - - -4.5 - 2.598076211353316 - - 44.5 - -77.07626093681505 - - - 1.0 - 0 - - 0 - -5.196152422706632 - - -97.0 - 0 - - - 1.0 - 0 - - 0.4641016151377546 - 0 - - 101.0 - 0 - - - 1.0 - 0 - - 0 - -6.928203230275509 - - -103.0 - 0 - - - 1.0 - 0 - - -8.196152422706632 - 14.196152422706632 - - -53.5 - -92.66471820493493 - - - 1.0 - 0 - - 6.696152422706632 - -3.866025403784439 - - 54.5 - -94.39676901250381 - - - 1.0 - 0 - - -17.196152422706632 - 9.928203230275509 - - 56.5 - -97.86087062764156 gamma_factors: - [] - - 0 group: GL2 id: 9593062 index: 3 label: 2-74-37.11-c1-0-3 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/74/2/e/a/11/2 plot_delta: __RealLiteral__: 0 data: '0.125' prec: 17 plot_values: - 1.1838196814510902 - 1.217155640831172 - 1.2692326494733097 - 1.3397106302870614 - 1.4273079371465007 - 1.5299836784586929 - 1.645099468938697 - 1.769524388224122 - 1.8996858255246443 - 2.031589718264807 - 2.1608374398250714 - 2.2826616267949214 - 2.391996099338494 - 2.4835885868632945 - 2.552159756180583 - 2.5926076948481223 - 2.6002530653612093 - 2.571116322511131 - 2.502214594510836 - 2.3918621638851882 - 2.2399551719181137 - 2.048218521639106 - 1.8203913259096076 - 1.562327003707914 - 1.2819856019050027 - 0.9892993714358939 - 0.6958982011882112 - 0.414689201997789 - 0.1592943420171305 - -0.05663884089707241 - -0.22022640588503473 - -0.32019792670156677 - -0.3477568824818097 - -0.2973921455154105 - -0.1675752948261014 - 0.03872312022993731 - 0.3137616487446924 - 0.6450542231156027 - 1.0157331475981617 - 1.4052662048406694 - 1.7905194415579377 - 2.1471280566757778 - 2.4511074501072407 - 2.680607419119837 - 2.8176875343029932 - 2.849973788731526 - 2.7720483995295675 - 2.5864283663422865 - 2.30400547923171 - 1.943851278390581 - 1.5323340876310414 - 1.1015493787407509 - 0.6871257133042065 - 0.32553148411577304 - 0.051066876481672054 - -0.10722531230240184 - -0.12846318854641078 - -0.0023649764516281225 - 0.26904134778981836 - 0.6706629339105984 - 1.1746997595153155 - 1.7421840805914641 - 2.3256646977416926 - 2.8728855684621006 - 3.3311977475084493 - 3.6523477172927747 - 3.7972153543081992 - 3.740041110759937 - 3.471691814293139 - 3.001571308565937 - 2.357884800834473 - 1.5861079822757627 - 0.7456824932465962 - -0.09485741462058185 - -0.8639446592939863 - -1.4936912397886069 - -1.926610475078262 - -2.121660507356666 - -2.0589434692877306 - -1.7424923620154236 - -1.2007448442351965 - -0.484526718366548 - 0.33737282981031474 - 1.184683925961287 - 1.9735991165021103 - 2.625383295014384 - 3.074738419424545 - 3.276989642042743 - 3.2132445571937596 - 2.8928660630810543 - 2.3528763454447534 - 1.654247324655496 - 0.8753947058718716 - 0.10353607149276954 - -0.5751448978412196 - -1.0854044203292694 - -1.3717381256506829 - -1.4049868998891926 - -1.1858907553884535 - -0.7450793426859096 - -0.13941478489143894 - 0.5549409736407029 - 1.2519337970720794 - 1.8663567314613234 - 2.3245701733027775 - 2.5738134448268792 - 2.58886266518636 - 2.3751062388347326 - 1.967563208792194 - 1.4259056473861538 - 0.8260942631602378 - 0.24972104561238087 - -0.22749662921192365 - -0.5464650433478628 - -0.6731612643494007 - -0.6035166037526197 - -0.36395066114713026 - -0.007379055049174865 - 0.39482281320839024 - 0.7638022633371904 - 1.0255818826277925 - 1.1229419028730598 - 1.0249927344819383 - 0.7328761611803363 - 0.2805615611790438 - -0.2695861840861582 - -0.8359964072276223 - -1.330608548957254 - -1.67327375425597 - -1.8056462548368197 - -1.702335287633576 - -1.3773996776293378 - -0.8848937471114144 - -0.31303467659006884 - 0.22746354064416324 - 0.61940179584 - 0.7572043306780706 - 0.5644243756775965 - 0.007894358680889122 - -0.8938577528086866 - -2.0695393781144102 - -3.4019290217728924 - -4.741978794597525 - -5.928392102540634 - -6.8099568133088155 - -7.267369072227558 - -7.231224592917383 - -6.693313813748595 - -5.709284459315231 - -4.392002137537343 - -2.8963586618397055 - -1.397628223418723 - -0.06653460812500718 - 0.9552126899259832 - 1.5751413647206578 - 1.7628138706499694 - 1.5531289281739133 - 1.039530367520545 - 0.35813097670613725 - -0.3347662815593302 - -0.888168714093395 - -1.1808039770986596 - -1.1404663645804467 - -0.755126464986223 - -0.07397405799326344 - 0.8017663379956891 - 1.7366883655781058 - 2.584689489151785 - 3.2140778961253136 - 3.5299920629739674 - 3.490270043196078 - 3.1120292389039843 - 2.4678337021148264 - 1.6721579052793822 - 0.8605817031462041 - 0.16546073211034976 - -0.3075327024982852 - -0.49774016351714717 - -0.3993746901925831 - -0.06109864294451104 - 0.4245947163060972 - 0.9402116959012664 - 1.3667580351347577 - 1.6074469680391847 - 1.6070612886932398 - 1.3631831410828494 - 0.9270082572866212 - 0.3934311446038977 - -0.11784002062086243 - -0.48659933633347435 - -0.6172109299885771 - -0.4594878520794848 - -0.021132613208766093 - 0.6309728397808371 - 1.3812302833171681 - 2.0858555645341488 - 2.5997635987335515 - 2.8047348777705903 - 2.6333829475081645 - 2.084098245175834 - 1.2237682118382718 - 0.17737842809361776 - -0.8938473476393973 - -1.8218046674007822 - -2.462805454307007 - -2.7247126926767127 - -2.584459805392657 - -2.092254436719068 - -1.361310761838366 - -0.5448101026919192 - 0.1956028240616105 - 0.7236506734316029 - 0.9577838817013193 - 0.8899553725754719 - 0.5896274074621252 - 0.19166780242555578 - -0.13000059338452596 - -0.19819059208761922 - 0.1292037912167347 - 0.9259605323579277 - 2.176294890246676 - 3.7704004625736305 - 5.5183563810726595 - 7.180398326597937 - 8.508246256420628 - 9.289835403899904 - 9.388906109276002 - 8.771689739875677 - 7.515268141509933 - 5.795650988245748 - 3.857539179440852 - 1.9713454027488941 - 0.3855956805006637 - -0.7161929461283489 - -1.245893083766375 - -1.2226276713849724 - -0.7639928294671039 - -0.05862718214915798 - 0.6741763772133735 - 1.2295612701798315 - 1.4577702800088703 - 1.2922489469592193 - 0.759726905657388 - -0.0293955774215774 - -0.9079104532448917 - -1.6898883222305694 - -2.21167774957504 - -2.3670035748628537 - -2.1287363097313277 - -1.5528813804972337 - -0.7642600961992126 - 0.07262987644843656 - 0.7908571864068368 - 1.2579541723081231 - 1.404174273380742 - 1.2358248827750484 - 0.8308149509273728 positive_zeros: - '3.58944060761563235987323413754741' - '4.35454702863015530219870428383506' - '6.78100534759549792262131656320118' - '7.12647051850906816776564857635823' - '9.110551508020049280683057617744602' - '10.19986489249041837987230741305943' - '11.64267762420174043955853688278114' - '12.52591161735497669367802514913748' - '13.93607461460691835680073444993368' - '14.62734859744811519789407056603691' prelabel: 2-74-37.11-c1-0 primitive: true rational: false root_analytic_conductor: 0.7686956321961738 root_angle: 0.2134907334186144 root_number: 0.7833862120526783 + 0.6215352305105127*I self_dual: false sign_arg: __RealLiteral__: 0 data: '0.106745366709' prec: 47 spectral_label: c1-0 types: - CMF z1: __RealLiteral__: 0 data: '3.58944060761563235987323413755' prec: 103 z2: __RealLiteral__: 0 data: '4.35454702863015530219870428384' prec: 103 z3: __RealLiteral__: 0 data: '6.78100534759549792262131656320' prec: 103 - - algebraic: true analytic_conductor: 0.5908929749574752 bad_primes: - 2 - 37 central_character: '37.11' conductor: 74 conductor_radical: 74 degree: 2 id: 9593062 index: 3 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/74/2/e/a/11/2 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: 2-74-37.11-c1-0-3 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: 2-74-37.11-c1-0 primitive: true rational: false root_analytic_conductor: 0.7686956321961738 root_angle: 0.1067453667093072 self_dual: false spectral_label: c1-0 z1: __RealLiteral__: 0 data: '3.58944060761563235987323413755' prec: 103 - - Lhash: '4550156540727536811956799645442' Lhash_array: - '4550156540727536811956799645442' id: 9959095 label: 2-74-37.11-c1-0-3 type: CMF url: ModularForm/GL2/Q/holomorphic/74/2/e/a/11/2 label_cols: - label - label - label labels: - 2-74-37.11-c1-0-3 - 2-74-37.11-c1-0-3 - 2-74-37.11-c1-0-3 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-05-05T18:05:56.156296'