data: - - Lhash: '817536882076201932550947512410' a10: - -58.71511950137164 - 0.0 a2: - 0.0 - 4.547392645829356 a3: - 0.0 - 0.0 a4: - -12.67877987534291 - 0.0 a5: - 0.0 - 12.911820921209047 a6: - 0.0 - 0.0 a7: - 0.0 - 16.72885655075938 a8: - 0.0 - -21.276249196588736 a9: - 0.0 - 0.0 accuracy: 100 algebraic: true analytic_conductor: 6.903223470671655 analytic_normalization: __RealLiteral__: 0 data: '1.5' prec: 10 bad_lfactors: - - 3 - - - 1.0 - 0 - - 0 - 0 - - 13 - - - 1.0 - 0 - - -33.71511950137164 - 32.56210553708451 bad_primes: - 3 - 13 central_character: '117.64' coefficient_field: CDF conductor: 117 conductor_radical: 39 conjugate: '3761946146928872017976162623363' degree: 2 euler_factors: - - - 1.0 - 0 - - 0 - -4.547392645829356 - - -8.0 - 0 - - - 1.0 - 0 - - 0 - 0 - - - 1.0 - 0 - - 0 - -12.911820921209047 - - -125.0 - 0 - - - 1.0 - 0 - - 0 - -16.72885655075938 - - -343.0 - 0 - - - 1.0 - 0 - - 0 - 24.92803427798384 - - -1331.0 - 0 - - - 1.0 - 0 - - -33.71511950137164 - 32.56210553708451 - - - 1.0 - 0 - - 134.1453585041149 - 0 - - 4913.0 - 0 - - - 1.0 - 0 - - 0 - -14.937641421890879 - - -6859.0 - 0 - - - 1.0 - 0 - - -72.0 - 0 - - 12167.0 - 0 - - - 1.0 - 0 - - -206.1453585041149 - 0 - - 24389.0 - 0 - - - 1.0 - 0 - - 0 - -249.14163313252223 - - -29791.0 - 0 - - - 1.0 - 0 - - 0 - -293.9545573981949 - - -50653.0 - 0 - - - 1.0 - 0 - - 0 - -250.50645144058313 - - -68921.0 - 0 - - - 1.0 - 0 - - 432.14535850411494 - 0 - - 79507.0 - 0 - - - 1.0 - 0 - - 0 - -159.88909962030647 - - -103823.0 - 0 - - - 1.0 - 0 - - -194.58143401645967 - 0 - - 148877.0 - 0 - - - 1.0 - 0 - - 0 - 232.64738195357617 - - -205379.0 - 0 - - - 1.0 - 0 - - 185.00583650960147 - 0 - - 226981.0 - 0 - - - 1.0 - 0 - - 0 - -39.439278879067125 - - -300763.0 - 0 - - - 1.0 - 0 - - 0 - -920.4604253108955 - - -357911.0 - 0 - - - 1.0 - 0 - - 0 - 549.0777563082654 - - -389017.0 - 0 - - - 1.0 - 0 - - -933.1395219945134 - 0 - - 493039.0 - 0 - - - 1.0 - 0 - - 0 - 1095.38306207759 - - -571787.0 - 0 - - - 1.0 - 0 - - 0 - -532.1142943856927 - - -704969.0 - 0 - - - 1.0 - 0 - - 0 - -362.66119873010086 - - -912673.0 - 0 - - - 1.0 - 0 - - -1490.5814340164598 - 0 - - 1030301.0 - 0 - - - 1.0 - 0 - - 628.4360755123447 - 0 - - 1092727.0 - 0 - - - 1.0 - 0 - - 477.45358504114915 - 0 - - 1225043.0 - 0 - - - 1.0 - 0 - - 0 - -378.2067605429346 - - -1295029.0 - 0 - - - 1.0 - 0 - - 13.273207479425421 - 0 - - 1442897.0 - 0 gamma_factors: - [] - - 0 group: GL2 id: 10582196 index: 1 label: 2-117-13.12-c3-0-1 load_key: CMFs-workshop motivic_weight: 3 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 3 order_of_vanishing: 0 origin: ModularForm/GL2/Q/holomorphic/117/4/b/e/64/4 plot_delta: __RealLiteral__: 0 data: '0.125' prec: 17 plot_values: - 1.1860645975228423 - 0.9228774383932357 - 0.6738727922681107 - 0.44065460792903627 - 0.22504803210043542 - 0.029219617410586 - -0.1442704060467687 - -0.2924907137084688 - -0.4122382162926675 - -0.5002111103474358 - -0.5532478838104515 - -0.568619897998821 - -0.5443606225841793 - -0.4796101596299964 - -0.37494954933610386 - -0.2326958631619448 - -0.05712675462259604 - 0.14539747386333177 - 0.3664445444974729 - 0.595679398945515 - 0.8212101003318166 - 1.0301178265561535 - 1.2091645540511742 - 1.345655844779963 - 1.428418524732826 - 1.448835310182796 - 1.4018622419432292 - 1.2869419832651159 - 1.1087185452338866 - 0.8774586263366118 - 0.6090929586409201 - 0.32480875245114516 - 0.05015166536922402 - -0.18636811158127348 - -0.35512791015755113 - -0.42761782813519045 - -0.3789068000222296 - -0.19017415521079511 - 0.14890223572066655 - 0.6381293450308821 - 1.2653826013562384 - 2.0059972699520046 - 2.823130867466937 - 3.669193325958564 - 4.488356077277952 - 5.220052509334068 - 5.803278459567391 - 6.181402437227204 - 6.307111938548991 - 6.147065269723871 - 5.685797138990348 - 4.9284477736873935 - 3.9019526046855924 - 2.6544411926862996 - 1.2527435379748224 - -0.2219223014291598 - -1.6798211283586708 - -3.0296921836454174 - -4.1862745135745 - -5.077678296749344 - -5.651877343128654 - -5.881635405378535 - -5.767293640639961 - -5.337032725090856 - -4.644465989258288 - -3.7636965981011805 - -2.7822531213773045 - -1.792571424106732 - -0.882884656321365 - -0.12848967894120383 - 0.4156416869275218 - 0.7200522976964949 - 0.7831581750414586 - 0.6304541073217815 - 0.31061009565561265 - -0.11111947254102332 - -0.5614085174480391 - -0.9682657983439735 - -1.2701644600325248 - -1.423726546673499 - -1.4089507402775965 - -1.2312690875922807 - -0.9201246760018097 - -0.5242273783146404 - -0.10410763766746167 - 0.2770161869852241 - 0.5627728416381655 - 0.7121953118293065 - 0.7060193923936833 - 0.5497346452559586 - 0.2728501381249268 - -0.07560953049974244 - -0.43478486790929255 - -0.7417298569670988 - -0.9417474659848355 - -0.9976703264850278 - -0.8965316972002803 - -0.6524096526405465 - -0.30477922742492436 - 0.08759999086156689 - 0.4565001454915141 - 0.7363253112813676 - 0.8766012587110029 - 0.8527606332402148 - 0.6732565985394067 - 0.38149591660811305 - 0.05182174278011329 - -0.22030152951314064 - -0.33278004015410934 - -0.19407543685658452 - 0.2595072143424521 - 1.049252323831957 - 2.1448049168647607 - 3.462251553657708 - 4.870468854574127 - 6.205452935342797 - 7.29105234302544 - 7.9633955536871515 - 8.095525640138685 - 7.618479031872131 - 6.535350128066042 - 4.9257570009129745 - 2.93946001042172 - 0.7794970458663253 - -1.3231578487648727 - -3.1399950025860575 - -4.476073133768196 - -5.1971809830358655 - -5.248846382148405 - -4.664106124114518 - -3.558607757939786 - -2.113557128393176 - -0.548945661834532 - 0.9089272541166026 - 2.0606507669149297 - 2.762450960906909 - 2.9459848467380274 - 2.6260865735777488 - 1.8953174368856287 - 0.9063303657814243 - -0.15493036770063218 - -1.100658940832953 - -1.77196114217855 - -2.063837617155185 - -1.94028378801671 - -1.4371653685817318 - -0.6526881239465103 - 0.2725357021113547 - 1.1820075230383704 - 1.9315188589687244 - 2.4138479057791504 - 2.5755823270222535 - 2.4232285542841177 - 2.0178427095792437 - 1.4596199855722498 - 0.865785200064468 - 0.3463667423587667 - -0.017235801695787027 - -0.1866322271419783 - -0.17101988736031956 - -0.02127365209353893 - 0.1849316815210474 - 0.3635496437366751 - 0.44553566042958315 - 0.3943399171921439 - 0.21550577565317036 - -0.04394407699149904 - -0.30641159089585907 - -0.482676648160283 - -0.49475955554509976 - -0.2974991349869848 - 0.10629268767817611 - 0.661041460636753 - 1.265796782549785 - 1.7929619096549168 - 2.1149280221318856 - 2.1331783861833444 - 1.8035088261098764 - 1.1514304963598387 - 0.27356523771026764 - -0.676387023849263 - -1.5152724782840752 - -2.066790611435679 - -2.1993592353856304 - -1.8575778889846635 - -1.0801393021810373 - 0.0005825615781815683 - 1.1785025471974429 - 2.2105723913123403 - 2.8638527607834443 - 2.963912518063283 - 2.4347413874700816 - 1.3215326741908018 - -0.20929103771790852 - -1.8941093087312464 - -3.416688880773068 - -4.465509605689655 - -4.793113534682389 - -4.265913519836288 - -2.8943630800914124 - -0.8369472549435555 - 1.6235561654982358 - 4.127653666247086 - 6.301868040589595 - 7.824797806118371 - 8.483859074963071 - 8.211785013422137 - 7.095900921136157 - 5.358574429053523 - 3.312963366919367 - 1.303066335504618 - -0.3598938179667866 - -1.4521873878041116 - -1.8728898281848008 - -1.6534921459565743 - -0.940966497535455 - 0.04103343437715697 - 1.043750293116051 - 1.8462364785847183 - 2.2983372739003216 - 2.345104845878187 - 2.0284552135271032 - 1.4671257812685228 - 0.8208327030396029 - 0.24787113585106518 - -0.13349139940226515 - -0.2708212322643608 - -0.18494932587883156 - 0.041876058210135056 - 0.2932424357810551 - 0.4536364373269457 - 0.4419463703667402 - 0.23462461419633943 - -0.12747107057351437 - -0.5502379237774148 - -0.9124496948320303 - -1.0998504984541364 - -1.0380685299333676 - -0.7153920732584907 - -0.188988972206356 - 0.42757831499320137 - 0.9927539119054053 - 1.3741801370326014 - 1.4849586215215393 - 1.3091378109203529 - 0.9090516057229949 - 0.4116456001040381 - -0.023610723182127473 - -0.24759721634989762 - -0.16430233951624093 - 0.2380099170257764 - 0.8763097225738482 - 1.5871742750741555 - 2.163943793931299 - 2.4084861663242707 - 2.185048238346529 - 1.4622810480204405 positive_zeros: - '0.64492288484619623777322623742782' - '2.03677738579629372244051288228158' - '4.02443129768475471476256241116858' - '4.70176294154618383515049409176286' - '6.85628832495656741693293592617974' - '8.650307644997908360771824447395186' - '9.343723002851688323840401593847164' - '10.53212125852560436262777164632597' - '11.34895504646181763608019454363881' - '12.34722720571570713282008315208489' prelabel: 2-117-13.12-c3-0 primitive: true rational: false root_analytic_conductor: 2.6273986128244142 root_angle: 0.7555370260974744 root_number: -0.7192993616603038 + 0.6947002434972076*I self_dual: false sign_arg: __RealLiteral__: 0 data: '0.377768513049' prec: 47 spectral_label: c3-0 types: - CMF z1: __RealLiteral__: 0 data: '0.64492288484619623777322623743' prec: 103 z2: __RealLiteral__: 0 data: '2.03677738579629372244051288228' prec: 103 z3: __RealLiteral__: 0 data: '4.02443129768475471476256241117' prec: 103 - - algebraic: true analytic_conductor: 6.903223470671655 bad_primes: - 3 - 13 central_character: '13.12' conductor: 117 conductor_radical: 39 degree: 2 id: 10582196 index: 1 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/117/4/b/e/64/4 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: 2-117-13.12-c3-0-1 motivic_weight: 3 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 3 order_of_vanishing: 0 prelabel: 2-117-13.12-c3-0 primitive: true rational: false root_analytic_conductor: 2.6273986128244142 root_angle: 0.3777685130487372 self_dual: false spectral_label: c3-0 z1: __RealLiteral__: 0 data: '0.64492288484619623777322623743' prec: 103 - - Lhash: '817536882076201932550947512410' Lhash_array: - '817536882076201932550947512410' id: 10948231 label: 2-117-13.12-c3-0-1 type: CMF url: ModularForm/GL2/Q/holomorphic/117/4/b/e/64/4 label_cols: - label - label - label labels: - 2-117-13.12-c3-0-1 - 2-117-13.12-c3-0-1 - 2-117-13.12-c3-0-1 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-25T03:47:53.554607'