data: - - Lhash: '1793503083573933978399311001293' a10: - 0.0 - 0.0 a2: - 0.0 - 0.0 a3: - 1.0 - 0.0 a4: - 0.0 - 0.0 a5: - 1.3271911668031888 - 0.0 a6: - 0.0 - 0.0 a7: - -1.0 - 0.0 a8: - 0.0 - 0.0 a9: - 1.0 - 0.0 accuracy: 100 algebraic: true analytic_conductor: 61.70839068204551 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 2 - - - 1.0 - 0 - - 0 - 0 - - 3 - - - 1.0 - 0 - - -1.0 - 0 - - 7 - - - 1.0 - 0 - - 1.0 - 0 - - 23 - - - 1.0 - 0 - - -1.0 - 0 bad_primes: - 2 - 3 - 7 - 23 central_character: '7728.1' coefficient_field: CDF conductor: 7728 conductor_radical: 966 degree: 2 euler_factors: - - - 1.0 - 0 - - 0 - 0 - - - 1.0 - 0 - - -1.0 - 0 - - - 1.0 - 0 - - -1.3271911668031888 - 0 - - 5.0 - 0 - - - 1.0 - 0 - - 1.0 - 0 - - - 1.0 - 0 - - 3.743009893649977 - 0 - - 11.0 - 0 - - - 1.0 - 0 - - 5.070201060453166 - 0 - - 13.0 - 0 - - - 1.0 - 0 - - -3.3835083949559803 - 0 - - 17.0 - 0 - - - 1.0 - 0 - - -3.743009893649977 - 0 - - 19.0 - 0 - - - 1.0 - 0 - - -1.0 - 0 - - - 1.0 - 0 - - 8.01012306396161 - 0 - - 29.0 - 0 - - - 1.0 - 0 - - -10.215145848649556 - 0 - - 31.0 - 0 - - - 1.0 - 0 - - 0.911372439956401 - 0 - - 37.0 - 0 - - - 1.0 - 0 - - 7.383508394955981 - 0 - - 41.0 - 0 - - - 1.0 - 0 - - -4.084084892753539 - 0 - - 43.0 - 0 - - - 1.0 - 0 - - 0.8316374536935757 - 0 - - 47.0 - 0 - - - 1.0 - 0 - - -10.066440292114402 - 0 - - 53.0 - 0 - - - 1.0 - 0 - - 6.425941790808398 - 0 - - 59.0 - 0 - - - 1.0 - 0 - - -2.860187017245619 - 0 - - 61.0 - 0 - - - 1.0 - 0 - - 2.700576497797559 - 0 - - 67.0 - 0 - - - 1.0 - 0 - - 0.21079594215884184 - 0 - - 71.0 - 0 - - - 1.0 - 0 - - 12.841760517655185 - 0 - - 73.0 - 0 - - - 1.0 - 0 - - 10.215145848649556 - 0 - - 79.0 - 0 - - - 1.0 - 0 - - -1.201262016349182 - 0 - - 83.0 - 0 - - - 1.0 - 0 - - 14.892945940365967 - 0 - - 89.0 - 0 - - - 1.0 - 0 - - 12.841760517655185 - 0 - - 97.0 - 0 - - - 1.0 - 0 - - -9.108091789015523 - 0 - - 101.0 - 0 - - - 1.0 - 0 - - 2.027767664600748 - 0 - - 103.0 - 0 - - - 1.0 - 0 - - -14.076563356076012 - 0 - - 107.0 - 0 - - - 1.0 - 0 - - 8.2436954122016 - 0 - - 109.0 - 0 - - - 1.0 - 0 - - 8.518330119190761 - 0 - - 113.0 - 0 gamma_factors: - [] - - 0 group: GL2 id: 21641742 index: 114 label: 2-7728-1.1-c1-0-114 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/7728/2/a/cb/1/4 plot_delta: __RealLiteral__: 0 data: '0.046875' prec: 27 plot_values: - -1.1449375765127335e-60 - 0.23840517390994156 - 0.47553024943686073 - 0.7100493643894561 - 0.9405486486290308 - 1.1654907614064571 - 1.3831889889954725 - 1.591793031663448 - 1.7892878643234893 - 1.9735062876059715 - 2.142155056466068 - 2.292853824789025 - 2.4231856001074075 - 2.530756968648276 - 2.613266021351166 - 2.668575673437561 - 2.694789909024364 - 2.6903303853814364 - 2.6540107896556346 - 2.585106349390536 - 2.483415955954939 - 2.349314468867997 - 2.1837929323696508 - 1.9884846571671824 - 1.7656754030660664 - 1.5182962434836504 - 1.2498980996425582 - 0.9646073967744364 - 0.6670628101534394 - 0.3623336253791756 - 0.055820822244494674 - -0.24685741073464545 - -0.5399934312693252 - -0.8179282996205602 - -1.0751969452007912 - -1.3066764958163037 - -1.5077335526621236 - -1.6743659319115316 - -1.8033342561318608 - -1.8922787806295702 - -1.9398169923443238 - -1.945617828844831 - -1.9104488340781278 - -1.8361931920255814 - -1.725834349723144 - -1.5834068416429496 - -1.4139129367588454 - -1.2232058207133636 - -1.017841166337004 - -0.8049001000854088 - -0.5917877002861361 - -0.3860122239589878 - -0.194951210322269 - -0.025611409771489093 - 0.11560990150595883 - 0.223154273495437 - 0.29251401794166937 - 0.32041878330013873 - 0.3049892501899083 - 0.24585114368695385 - 0.14420375640945682 - 0.0028384379974022043 - -0.1738959971311275 - -0.3801823010422307 - -0.6088777844585156 - -0.8517088703353662 - -1.09951286748489 - -1.3425207310203882 - -1.570672807427078 - -1.7739579887587928 - -1.9427653925726172 - -2.068236705596976 - -2.1426067348710314 - -2.159519543815644 - -2.114307842135233 - -2.00422406143873 - -1.8286127794259284 - -1.5890158325129515 - -1.2892035394233579 - -0.9351278880716197 - -0.5347962397725379 - -0.0980669884482875 - 0.3636284238858228 - 0.837629801037595 - 1.310448674340133 - 1.7682123243907506 - 2.197136541140958 - 2.584010640828638 - 2.916677140711029 - 3.1844880074380812 - 3.3787195904575413 - 3.492929251342768 - 3.523238299431214 - 3.4685281112421276 - 3.330539184817159 - 3.1138662719095853 - 2.8258465271392623 - 2.4763416783922954 - 2.0774194042616454 - 1.6429432379319253 - 1.1880842329931487 - 0.7287711571044647 - 0.28109896472016604 - -0.13928240353472293 - -0.517775361050492 - -0.8414140377575505 - -1.0993919258163047 - -1.2835154296646787 - -1.3885632646925552 - -1.412534873623939 - -1.3567750547116293 - -1.2259666816386248 - -1.0279885685970962 - -0.7736409949253271 - -0.47624693152282505 - -0.15114237441783307 - 0.18492584388990493 - 0.5144720520717483 - 0.8199873194542062 - 1.084669882681978 - 1.2931403241251624 - 1.4321112879975235 - 1.4909826882963955 - 1.4623358073729735 - 1.3423033386530658 - 1.1307971697279964 - 0.8315813586186799 - 0.452184106188455 - 0.0036493131673572 - -0.49986475495271915 - -1.0416253896181822 - -1.6029833168074674 - -2.164122325399325 - -2.704869886535941 - -3.2055347005925428 - -3.6477352375820455 - -4.015183021163494 - -4.2943857011509685 - -4.475237848048918 - -4.5514717958863065 - -4.5209465952182315 - -4.385759989076133 - -4.152176005575274 - -3.830368940260449 - -3.433992815310548 - -2.979593471494777 - -2.4858878935286683 - -1.9729418305068853 - -1.4612819272504087 - -0.9709821594735373 - -0.5207661626877598 - -0.1271669375894245 - 0.19621663380470966 - 0.4393309627166222 - 0.5961167979683715 - 0.6647735068858758 - 0.6478243471598973 - 0.5519776967727102 - 0.38778882308497775 - 0.16913633427949012 - -0.0874634947869926 - -0.36367324193249195 - -0.6402437049161354 - -0.8979731274106573 - -1.1186703047494877 - -1.2860747883700725 - -1.386688875298657 - -1.4104797779768485 - -1.3514161807768128 - -1.2078110560141075 - -0.9824517898858581 - -0.6825089305114724 - -0.3192257257252829 - 0.09259846322036984 - 0.5353073495398627 - 0.9892365662449618 - 1.4336713104545664 - 1.84786594794841 - 2.212075030625624 - 2.5085439717510907 - 2.722409023382824 - 2.8424601826173888 - 2.861727060910322 - 2.7778562985878903 - 2.5932593936088604 - 2.3150213405572324 - 1.954572669318251 - 1.5271397132364475 - 1.0509995890631052 - 0.546576818692862 - 0.035427198985797256 - -0.46083905447387363 - -0.9216390778023116 - -1.328447324976039 - -1.6657190833330857 - -1.9216578865228597 - -2.0887848779259124 - -2.164278232722579 - -2.150062659699012 - -2.0526421729714515 - -1.8826830680825863 - -1.6543676305611972 - -1.3845518152737242 - -1.09177126118546 - -0.7951489185424474 - -0.51326374015354 - -0.2630429383389544 - -0.05874000794146686 - 0.08894298603658363 - 0.17353732634151034 - 0.1932521586928359 - 0.15115238922035495 - 0.05505498740084163 - -0.08285593891292833 - -0.24667929820869192 - -0.4176813318622563 - -0.5753693544548769 - -0.6986986886137818 - -0.7673479297953067 - -0.7629924319229826 - -0.6705044115926057 - -0.47901048890470604 - -0.18274376750860782 - 0.21836255786390601 - 0.718380058138072 - 1.305412878021611 - 1.961955793707339 - 2.6655718555028933 - 3.3898611863241523 - 4.105675922880707 - 4.7825218198106185 - 5.390075527670464 - 5.899738697040372 - 6.286146358775748 - 6.528547770557997 - 6.611983148078556 - 6.528189213478089 - 6.27617985067525 - 5.862464692045807 - 5.300887319835354 - 4.612084950178001 - 3.822591887334047 - 2.9636285679095287 - 2.069635566282638 - 1.176626501710501 - 0.32044452253379724 - -0.4649867085816761 - -1.149325254284257 - -1.7072977856599403 - -2.119931127219432 - -2.3754615760581337 - -2.4698720242544168 - -2.407026757280567 - -2.1983954986887317 - -1.8623806303082344 - -1.4232832922242773 - -0.9099640294796115 positive_zeros: - '1.41482446602480954712250837880346' - '2.49217517576195735640266702169684' - '2.86020545742159243800374438649975' - '3.80700374528165022178462090809861' - '4.81214804430731404100551257583922' - '5.41175101172213511998256277433318' - '6.00035724978743530936790746270398' - '7.09528812815843418153476615235367' - '7.48458646483744408839370175005189' prelabel: 2-7728-1.1-c1-0 primitive: true rational: false root_analytic_conductor: 7.855468839098371 root_angle: 1.0 root_number: '-1' self_dual: true sign_arg: __RealLiteral__: 0 data: '0.5' prec: 10 spectral_label: c1-0 types: - CMF z1: __RealLiteral__: 0 data: '1.41482446602480954712250837880' prec: 103 z2: __RealLiteral__: 0 data: '2.49217517576195735640266702170' prec: 103 z3: __RealLiteral__: 0 data: '2.86020545742159243800374438650' prec: 103 - - algebraic: true analytic_conductor: 61.70839068204551 bad_primes: - 2 - 3 - 7 - 23 central_character: '1.1' conductor: 7728 conductor_radical: 966 degree: 2 id: 21641742 index: 114 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/7728/2/a/cb/1/4 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: 2-7728-1.1-c1-0-114 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: 2-7728-1.1-c1-0 primitive: true rational: false root_analytic_conductor: 7.855468839098371 root_angle: 0.5 self_dual: true spectral_label: c1-0 z1: __RealLiteral__: 0 data: '1.41482446602480954712250837880' prec: 103 - - Lhash: '1793503083573933978399311001293' Lhash_array: - '1793503083573933978399311001293' id: 22013133 label: 2-7728-1.1-c1-0-114 type: CMF url: ModularForm/GL2/Q/holomorphic/7728/2/a/cb/1/4 label_cols: - label - label - label labels: - 2-7728-1.1-c1-0-114 - 2-7728-1.1-c1-0-114 - 2-7728-1.1-c1-0-114 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-18T12:14:22.134445'