data: - - Lhash: '397394384490502315551377112964' a10: - 0 - 0 a2: - 0 - 0 a3: - 1.5235855629996726 - 2.6389276047938655 a4: - 0 - 0 a5: - -0.5 - -0.8660254037844386 a6: - 0 - 0 a7: - 0.6091753400508947 - 0 a8: - 0 - 0 a9: - -3.1426259355620583 - 5.443187789577162 accuracy: 100 algebraic: true analytic_conductor: 12.137261107234623 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 2 - - - 1.0 - 0 - - 0 - 0 - - 5 - - - 1.0 - 0 - - 0.5 - 0.8660254037844386 - - 19 - - - 1.0 - 0 - - 3.6053198420742043 - 2.4498303688921066 bad_primes: - 2 - 5 - 19 central_character: '1520.881' coefficient_field: CDF conductor: 1520 conductor_radical: 190 conjugate: '2799111791532962737984489137818' degree: 2 euler_factors: - - - 1.0 - 0 - - 0 - 0 - - - 1.0 - 0 - - -1.5235855629996726 - -2.6389276047938655 - - -1.5 - 2.598076211353316 - - - 1.0 - 0 - - 0.5 - 0.8660254037844386 - - - 1.0 - 0 - - -0.6091753400508947 - 0 - - 7.0 - 0 - - - 1.0 - 0 - - 4.485166911947796 - 0 - - 11.0 - 0 - - - 1.0 - 0 - - 2.218997892974225 - -3.843417092519644 - - -6.5 - -11.258330249197702 - - - 1.0 - 0 - - 1.4517163164366318 - 2.514446418244984 - - -8.5 - 14.722431864335457 - - - 1.0 - 0 - - 3.6053198420742043 - 2.4498303688921066 - - - 1.0 - 0 - - 1.4236280425878332 - -2.465796100841956 - - -11.5 - -19.91858428704209 - - - 1.0 - 0 - - 0.5581487160748592 - -0.9667419344209919 - - -14.5 - -25.11473670974872 - - - 1.0 - 0 - - -6.229075323426519 - 0 - - 31.0 - 0 - - - 1.0 - 0 - - 3.7726438981999584 - 0 - - 37.0 - 0 - - - 1.0 - 0 - - -4.151843755201114 - -7.191204329095889 - - -20.5 - 35.50704155516198 - - - 1.0 - 0 - - 4.994384731586851 - 8.650528107654676 - - -21.5 - 37.239092362730865 - - - 1.0 - 0 - - 2.9424984967975765 - -5.09655689764845 - - -23.5 - -40.703193977868615 - - - 1.0 - 0 - - 4.22436021463659 - -7.316806521223142 - - -26.5 - -45.89934640057525 - - - 1.0 - 0 - - -5.117927814998363 - -8.864511005047135 - - -29.5 - 51.09549882328188 - - - 1.0 - 0 - - -2.4909945783017475 - 4.314529170997237 - - -30.5 - -52.827549630850754 - - - 1.0 - 0 - - -4.238080745124772 - 7.34057117713547 - - -33.5 - -58.023702053557386 - - - 1.0 - 0 - - -5.809949991687812 - -10.063128575037666 - - -35.5 - 61.48780366869514 - - - 1.0 - 0 - - 1.8616238285362836 - 3.224427055605735 - - -36.5 - 63.21985447626402 - - - 1.0 - 0 - - -4.519082852150547 - -7.827281103538019 - - -39.5 - 68.41600689897065 - - - 1.0 - 0 - - -2.121783312975053 - 0 - - 83.0 - 0 - - - 1.0 - 0 - - 3.9660840597972493 - -6.8694590986578765 - - -44.5 - -77.07626093681505 - - - 1.0 - 0 - - -4.836278495100152 - -8.376680073066213 - - -48.5 - 84.00446416709055 - - - 1.0 - 0 - - -0.4856322566393827 - 0.841139742293739 - - -50.5 - -87.4685657822283 - - - 1.0 - 0 - - -3.3414284188217143 - 0 - - 103.0 - 0 - - - 1.0 - 0 - - 9.516552309678682 - 0 - - 107.0 - 0 - - - 1.0 - 0 - - 2.7717842873867196 - 4.800871213374893 - - -54.5 - 94.39676901250381 - - - 1.0 - 0 - - -1.541343459645393 - 0 - - 113.0 - 0 gamma_factors: - [] - - 0 group: GL2 id: 23325253 index: 4 label: 2-1520-19.7-c1-0-4 leading_term: '0.995544792814330066145452689546789164588651334813733035' 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/1520/2/q/o/881/4 plot_delta: __RealLiteral__: 0 data: '0.05078125' prec: 34 plot_values: - 0.9955447928143301 - 0.828393757373529 - 0.6637865363398414 - 0.5014803982836776 - 0.3412804752699537 - 0.18307471349990742 - 0.026863772650307198 - -0.12721528377191554 - -0.27887225109933966 - -0.4276543392877666 - -0.5729440087881984 - -0.7139637949800368 - -0.8497876320001215 - -0.9793580624234374 - -1.1015086521427069 - -1.2149909009716042 - -1.3185049311291117 - -1.4107332336680949 - -1.4903767475436271 - -1.5561925323682952 - -1.607032272783482 - -1.641880821454873 - -1.6598939525465204 - -1.6604344627941066 - -1.643105728084098 - -1.6077818048310466 - -1.5546331621654481 - -1.4841471471684404 - -1.3971423245703558 - -1.2947758971006753 - -1.1785435047747828 - -1.0502708216141932 - -0.912096516415021 - -0.7664463189778677 - -0.615998132433142 - -0.46363835265705455 - -0.3124097929981266 - -0.16545186140456802 - -0.02593389148384279 - 0.1030172177841485 - 0.21839365444398598 - 0.3173860108505653 - 0.3974634352515865 - 0.45645261640374746 - 0.4926134698313476 - 0.5047093120847364 - 0.4920692815383232 - 0.4546407963903722 - 0.39302993678295967 - 0.3085278009844792 - 0.20312111622508072 - 0.07948568194342612 - -0.05903841630891809 - -0.20849046562844212 - -0.36435183170851015 - -0.5216273770468272 - -0.6749447181203647 - -0.8186698945287032 - -0.9470374691664004 - -1.0542925406268755 - -1.1348416443649998 - -1.1834090650642812 - -1.1951946963645461 - -1.1660292820308187 - -1.0925226698531156 - -0.972200619193408 - -0.8036257357720404 - -0.5864982706145337 - -0.32173281816589466 - -0.011507381639481312 - 0.34071816226388457 - 0.7302164803765033 - 1.1510415662209814 - 1.5961124840641328 - 2.057331707164032 - 2.5257366749759846 - 2.991682166359164 - 3.4450500692032016 - 3.8754821532672152 - 4.272630554952441 - 4.626419892419488 - 4.927314277685229 - 5.1665820073298105 - 5.336550419821099 - 5.430843325162928 - 5.4445935559149286 - 5.37462356549188 - 5.219587610805993 - 4.980069894987008 - 4.658634097541501 - 4.259820961578567 - 3.7900920108590266 - 3.2577189967556888 - 2.672620284034412 - 2.046147027029572 - 1.3908236130431315 - 0.7200484043388777 - 0.04776224028040072 - -0.6119065852088226 - -1.2450111274437696 - -1.8381578734060648 - -2.3788711466632466 - -2.855938758890083 - -3.2597280641545914 - -3.5824621628749544 - -3.8184469467312474 - -3.964240956412549 - -4.018761611135108 - -3.983323220732783 - -3.861604255171876 - -3.6595435603318336 - -3.3851675027246886 - -3.048352323701989 - -2.660528206581455 - -2.234333628442685 - -1.7832304048337246 - -1.3210913682598044 - -0.8617737861237217 - -0.41869236753944633 - -0.004405991095075746 - 0.36976791766165734 - 0.6940981276185993 - 0.9607314128078017 - 1.1639210214170146 - 1.3001834418478815 - 1.3683775031731757 - 1.369702517325823 - 1.3076150214105065 - 1.1876666104774907 - 1.0172682572838383 - 0.8053892866897959 - 0.5622017005387198 - 0.29868273193125516 - 0.02619025331337173 - -0.2439731079131958 - -0.5009906408268577 - -0.7349404708704984 - -0.9371667932521448 - -1.1005987194388416 - -1.2200038707658203 - -1.2921662320557732 - -1.315980622644008 - -1.292459352542174 - -1.2246500900934505 - -1.117467543139009 - -0.9774451082988175 - -0.8124160287835016 - -0.6311366786473633 - -0.4428672269751887 - -0.2569270092610562 - -0.08224334434819108 - 0.07308679320789022 - 0.20220295269698904 - 0.29983687017651545 - 0.3626009626612343 - 0.3891954624864061 - 0.38052312601693045 - 0.3397041298580426 - 0.27198786315758766 - 0.1845626772961289 - 0.08626908904756819 - -0.012773734245755865 - -0.10161433498256899 - -0.1689707233050794 - -0.20376714469812202 - -0.19568330872318088 - -0.1356922666902854 - -0.01656284145487085 - 0.16669674938294435 - 0.416475673323526 - 0.7322965179906384 - 1.1106657925892003 - 1.5450496962471696 - 2.0259809367165587 - 2.541296954900369 - 3.076504290803698 - 3.6152582493677294 - 4.1399417306428274 - 4.632322313933059 - 5.074262651223492 - 5.448456127921972 - 5.739157751125488 - 5.932879447385922 - 6.019019464543789 - 5.990397393297571 - 5.84366941539761 - 5.579602652139919 - 5.203192780802139 - 4.723615210391992 - 4.154006822221804 - 3.511082313294621 - 2.814596237388334 - 2.086668616579431 - 1.3509981947554055 - 0.6319927411960116 - -0.04614996693032958 - -0.6603739610154685 - -1.1896717678284456 - -1.6159282170701599 - -1.9246654159823124 - -2.1056563117263223 - -2.1533791061926673 - -2.0672909250787272 - -1.8519063358321048 - -1.5166742674045632 - -1.0756552779750086 - -0.5470095871879499 - 0.0476855322809202 - 0.6842628874868303 - 1.3369043845650033 - 1.9791540818920732 - 2.584963769955833 - 3.1297276669632987 - 3.5912627809208906 - 3.950693349751212 - 4.193201479655278 - 4.308611522707259 - 4.291782651940182 - 4.142792218547556 - 3.8669014638485018 - 3.474304615634125 - 2.97967190366178 - 2.401506152465781 - 1.7613409319711448 - 1.0828153785642523 - 0.39066640117688656 - -0.29031721580604075 - -0.9363325030244348 - -1.5255457858243235 - -2.038978365675773 - -2.4612552523846674 - -2.781184065016476 - -2.9921390442916036 - -3.092234146478416 - -3.0842790033630725 - -2.975521676873421 - -2.777192131132266 - -2.503869711201843 - -2.172706203077802 - -1.8025428468931215 - -1.4129646453452 - -1.0233381974211522 - -0.651879937468347 - -0.31480002312017014 - -0.025563255799075413 - 0.2056974920311667 - 0.3725875512178791 - 0.47265772783372334 - 0.507403919223256 - 0.4820609390863898 - 0.40520287803485555 - 0.28817220291347334 - 0.14436858565297778 - -0.011564305194576472 - -0.16461050269220193 - -0.3002652851068859 - -0.40538322105569063 positive_zeros: - '0.31348889387892447092718346522347' - '1.93953733543096489774511647581567' - '2.61955652257050509348914854237607' - '3.50566300119912289913359451543091' - '4.92941285733746910279880201276206' - '6.04353408180393833287352503144259' - '6.75877697559628381508127988671234' - '7.64313229693958104142871155145751' - '8.169056033435400965594280203909563' - '8.485929060140432133405246738435393' prelabel: 2-1520-19.7-c1-0 primitive: true rational: false root_analytic_conductor: 3.483857216826577 root_angle: 0.9243992705553778 root_number: -0.97192761990213015686051708235892785675821591458005268462 + 0.23528004945464544723972947543700548796203666387328035265*I self_dual: false sign_arg: __RealLiteral__: 0 data: '0.4621996352776889' prec: 60 spectral_label: c1-0 types: - CMF z1: __RealLiteral__: 0 data: '0.31348889387892447092718346522' prec: 103 z2: __RealLiteral__: 0 data: '1.93953733543096489774511647582' prec: 103 z3: __RealLiteral__: 0 data: '2.61955652257050509348914854238' prec: 103 - - algebraic: true analytic_conductor: 12.137261107234623 bad_primes: - 2 - 5 - 19 central_character: '19.7' conductor: 1520 conductor_radical: 190 degree: 2 id: 23325253 index: 4 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/1520/2/q/o/881/4 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: 2-1520-19.7-c1-0-4 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: 2-1520-19.7-c1-0 primitive: true rational: false root_analytic_conductor: 3.483857216826577 root_angle: 0.4621996352776889 self_dual: false spectral_label: c1-0 z1: __RealLiteral__: 0 data: '0.31348889387892447092718346522' prec: 103 - - Lhash: '397394384490502315551377112964' Lhash_array: - '397394384490502315551377112964' id: 23691993 label: 2-1520-19.7-c1-0-4 type: CMF url: ModularForm/GL2/Q/holomorphic/1520/2/q/o/881/4 label_cols: - label - label - label labels: - 2-1520-19.7-c1-0-4 - 2-1520-19.7-c1-0-4 - 2-1520-19.7-c1-0-4 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-25T04:09:29.851805'