data: - - Lhash: '1429112177444346038152611044612' a10: 0 a2: 0 a3: 0 a4: 0 a5: 1 a6: 0 a7: -4 a8: 0 a9: 0 accuracy: 100 algebraic: true analytic_conductor: 68.99074734638629 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 2 - - 1 - - 3 - - 1 - - 5 - - 1 - -1 bad_primes: - 2 - 3 - 5 central_character: '8640.1' coefficient_field: 1.1.1.1 conductor: 8640 conductor_radical: 30 degree: 2 euler_factors: - - 1 - - 1 - - 1 - -1 - - 1 - 4 - 7 - - 1 - 2 - 11 - - 1 - 4 - 13 - - 1 - -1 - 17 - - 1 - -5 - 19 - - 1 - -5 - 23 - - 1 - 8 - 29 - - 1 - -7 - 31 - - 1 - -6 - 37 - - 1 - -6 - 41 - - 1 - -2 - 43 - - 1 - -8 - 47 - - 1 - 9 - 53 - - 1 - 4 - 59 - - 1 - 13 - 61 - - 1 - -10 - 67 - - 1 - 6 - 71 - - 1 - 6 - 73 - - 1 - -9 - 79 - - 1 - -17 - 83 - - 1 - 6 - 89 - - 1 - 8 - 97 - - 1 - 12 - 101 - - 1 - -4 - 103 - - 1 - 12 - 107 - - 1 - 17 - 109 - - 1 - -6 - 113 euler_factors_factorization: - - 1 - - 1 - - - - 1 - -1 - 1 - - - - 1 - 4 - 7 - 1 - - - - 1 - 2 - 11 - 1 - - - - 1 - 4 - 13 - 1 - - - - 1 - -1 - 17 - 1 - - - - 1 - -5 - 19 - 1 - - - - 1 - -5 - 23 - 1 - - - - 1 - 8 - 29 - 1 - - - - 1 - -7 - 31 - 1 - - - - 1 - -6 - 37 - 1 - - - - 1 - -6 - 41 - 1 - - - - 1 - -2 - 43 - 1 - - - - 1 - -8 - 47 - 1 - - - - 1 - 9 - 53 - 1 - - - - 1 - 4 - 59 - 1 - - - - 1 - 13 - 61 - 1 - - - - 1 - -10 - 67 - 1 - - - - 1 - 6 - 71 - 1 - - - - 1 - 6 - 73 - 1 - - - - 1 - -9 - 79 - 1 - - - - 1 - -17 - 83 - 1 - - - - 1 - 6 - 89 - 1 - - - - 1 - 8 - 97 - 1 - - - - 1 - 12 - 101 - 1 - - - - 1 - -4 - 103 - 1 - - - - 1 - 12 - 107 - 1 - - - - 1 - 17 - 109 - 1 - - - - 1 - -6 - 113 - 1 gamma_factors: - [] - - 0 group: GL2 id: 22271506 index: 81 label: 2-8640-1.1-c1-0-81 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/8640/2/a/bf plot_delta: __RealLiteral__: 0 data: '0.046875' prec: 27 plot_values: - -5.420829714699354e-61 - 0.18091664947317032 - 0.3601707822066091 - 0.5360627178373546 - 0.7068219073492866 - 0.8705798900939828 - 1.025352637401379 - 1.1690343606011997 - 1.2994041160147245 - 1.4141457655366891 - 1.5108811086019276 - 1.5872153328183274 - 1.6407933611678298 - 1.6693652120287685 - 1.670858131238985 - 1.643452993355543 - 1.5856622905848297 - 1.4964069222975682 - 1.3750889584720893 - 1.2216575733186954 - 1.03666543041955 - 0.8213129498838633 - 0.5774781041904165 - 0.30772967529217105 - 0.015322262640102988 - -0.2958282406463862 - -0.6211894916441999 - -0.955678094740331 - -1.29374517986655 - -1.629481147351346 - -1.9567379019500417 - -2.2692662343510257 - -2.560865364331266 - -2.825541058787 - -3.057668203933592 - -3.2521532678209226 - -3.404591759712621 - -3.5114155976191377 - -3.5700252521952964 - -3.5789016582576405 - -3.5376931835237135 - -3.447273421472571 - -3.3097662289768537 - -3.128535250490441 - -2.908136143232961 - -2.6542308193770277 - -2.3734642226365983 - -2.0733054229007504 - -1.7618561036297093 - -1.4476307886573225 - -1.1393143612597685 - -0.8455035212517898 - -0.574439758544899 - -0.33374214965325916 - -0.13014876706715908 - 0.030724303514845386 - 0.14459744214471904 - 0.20870699316159752 - 0.22194205163951736 - 0.18493187009674888 - 0.10007858193540403 - -0.028468429236345384 - -0.1948983277430263 - -0.3918845775500629 - -0.6107883017392266 - -0.8419147405127045 - -1.074816182443706 - -1.2986327570132075 - -1.5024607011619509 - -1.6757362274501182 - -1.8086219987501877 - -1.8923825167184751 - -1.9197345082502724 - -1.8851586797467201 - -1.7851600194008157 - -1.618465159286327 - -1.3861471375732617 - -1.0916701815485998 - -0.74084979883224 - -0.34172643295263194 - 0.09564589049952883 - 0.5594912436982291 - 1.0366758980891786 - 1.513133887212517 - 1.9743403075486405 - 2.405816287280216 - 2.7936477344316883 - 3.1249987821610477 - 3.3886003556766626 - 3.5751945430423455 - 3.677916483408952 - 3.692597282681904 - 3.6179739881421153 - 3.455795828159655 - 3.210819648655892 - 2.8906916247070247 - 2.505716740677484 - 2.0685220446554364 - 1.593624110380371 - 1.0969152957083974 - 0.5950870879002098 - 0.10501190113805191 - -0.3568930113712859 - -0.7752944747493192 - -1.1365396847490041 - -1.4291950697964104 - -1.6445046245843227 - -1.776747346508916 - -1.823477077348773 - -1.7856325405880042 - -1.6675105046906358 - -1.476600594812604 - -1.2232860930402605 - -0.9204208651611314 - -0.5827980770093335 - -0.22653136528079357 - 0.13162662971663305 - 0.4750001893708956 - 0.7877105925359746 - 1.0553691813746768 - 1.265712756044786 - 1.4091525071106055 - 1.479210893411806 - 1.4728252969457993 - 1.3905027722840702 - 1.2363165395561064 - 1.017741784765993 - 0.7453355315426862 - 0.4322725139756889 - 0.09375578183981939 - -0.25367311557372285 - -0.5928943939229153 - -0.9070068995534617 - -1.1801253233899287 - -1.398140724618377 - -1.549408243282441 - -1.6253285055644215 - -1.620793481552308 - -1.5344732876117844 - -1.368927404448635 - -1.130531711871055 - -0.8292212723785224 - -0.47805753917621424 - -0.0926372095407768 - 0.30963212145820906 - 0.710357424910103 - 1.0910491768074662 - 1.4340322373268146 - 1.7233351460989934 - 1.9455143658409515 - 2.0903721617981073 - 2.151531008056896 - 2.126833513106109 - 2.0185446083786536 - 1.8333418096436027 - 1.5820893331293813 - 1.2794022615750633 - 0.9430173111498232 - 0.5929965388839107 - 0.25079905685144677 - -0.0617369717920889 - -0.32345448104742797 - -0.5149291397603403 - -0.61946116611462 - -0.6239578613747944 - -0.5196617399059668 - -0.3026857882583676 - 0.02567391553938167 - 0.458867638377044 - 0.9852713731588802 - 1.5886119041837883 - 2.2486211203797795 - 2.9418915486571997 - 3.64289466890367 - 4.325114891530119 - 4.962245601953079 - 5.529389776121463 - 6.0042065958797135 - 6.367947352051093 - 6.606328677800134 - 6.710198616465245 - 6.6759608644563535 - 6.505734279148502 - 6.207237833524981 - 5.793404981861927 - 5.281745173148811 - 4.693483296910106 - 4.052519479125107 - 3.38426123420749 - 2.7143869879347364 - 2.067604006859412 - 1.4664645431643415 - 0.9303014382320478 - 0.47433860695909397 - 0.1090230063850696 - -0.16038670052334267 - -0.33395297373045574 - -0.4169066237112753 - -0.4192166120999488 - -0.3549056047707053 - -0.24114838476157496 - -0.0972023134330143 - 0.05677142156400561 - 0.20093057193361424 - 0.31695043659892846 - 0.3891308742865021 - 0.4053487404193598 - 0.35780076159480084 - 0.24349300670111576 - 0.06444684634212929 - -0.17239310674559824 - -0.4555469491506704 - -0.7696644426918173 - -1.0964321324731745 - -1.4156735390064874 - -1.7065816247508068 - -1.9490142570741402 - -2.124778675770616 - -2.2188303542696453 - -2.2203152265309427 - -2.123391909397346 - -1.927781924467578 - -1.639010440004937 - -1.2683169497798106 - -0.8322336711993494 - -0.35184826864554286 - 0.14821426623233483 - 0.6410391592699297 - 1.0988334273315867 - 1.4944255527527048 - 1.802770904334898 - 2.002378666840592 - 2.076578887306298 - 2.014555744560675 - 1.812084953385742 - 1.4719287304162194 - 1.0038601564688636 - 0.42430907133239465 - -0.24435729167683834 - -0.9748850700668119 - -1.736463020807863 - -2.4962609976391104 - -3.221095747057045 - -3.879133923700801 - -4.441539035774352 - -4.883971095040009 - -5.187855019572652 - -5.341345975224522 - -5.339936211541261 - -5.186667663217936 - -4.891936555685297 - -4.472899233166521 - -3.952511103222889 - -3.358251646479614 - -2.7206066334988743 - -2.0713929327752654 - -1.4420207115847108 positive_zeros: - '1.12737072596111806526309478814964' - '2.56805366284799917081919448512489' - '2.85015981870912461136487956706930' - '3.74003194570339284765478358434300' - '4.74472917965118669238450357257207' - '5.42016231751570044953010087520414' - '6.05954716596321482019902208948638' - '6.71401739160618710686470724247308' - '7.49021375169655068173068034665104' prelabel: 2-8640-1.1-c1-0 primitive: true rational: true root_analytic_conductor: 8.306066899946465 root_angle: 1.0 root_number: '-1' self_dual: true sign_arg: __RealLiteral__: 0 data: '0.5' prec: 10 spectral_label: c1-0 trace_hash: 1794528052930445543 types: - CMF z1: __RealLiteral__: 0 data: '1.12737072596111806526309478815' prec: 103 z2: __RealLiteral__: 0 data: '2.56805366284799917081919448512' prec: 103 z3: __RealLiteral__: 0 data: '2.85015981870912461136487956707' prec: 103 - - algebraic: true analytic_conductor: 68.99074734638629 bad_primes: - 2 - 3 - 5 central_character: '1.1' conductor: 8640 conductor_radical: 30 degree: 2 dirichlet_coefficients: - 1 - 0 - 0 - 0 - 1 - 0 - -4 - 0 - 0 - 0 - -2 - 0 - -4 - 0 - 0 - 0 - 1 - 0 - 5 - 0 - 0 - 0 - 5 - 0 - 1 - 0 - 0 - 0 - -8 - 0 - 7 - 0 - 0 - 0 - -4 - 0 - 6 - 0 - 0 - 0 - 6 - 0 - 2 - 0 - 0 - 0 - 8 - 0 - 9 - 0 - 0 - 0 - -9 - 0 - -2 - 0 - 0 - 0 - -4 - 0 - -13 - 0 - 0 - 0 - -4 - 0 - 10 - 0 - 0 - 0 - -6 - 0 - -6 - 0 - 0 - 0 - 8 - 0 - 9 - 0 - 0 - 0 - 17 - 0 - 1 - 0 - 0 - 0 - -6 - 0 - 16 - 0 - 0 - 0 - 5 - 0 - -8 - 0 - 0 - 0 euler11: - 1 - 2 - 11 euler13: - 1 - 4 - 13 euler17: - 1 - -1 - 17 euler19: - 1 - -5 - 19 euler2: - 1 - 0 - 0 euler23: - 1 - -5 - 23 euler29: - 1 - 8 - 29 euler3: - 1 - 0 - 0 euler31: - 1 - -7 - 31 euler37: - 1 - -6 - 37 euler41: - 1 - -6 - 41 euler43: - 1 - -2 - 43 euler47: - 1 - -8 - 47 euler5: - 1 - -1 - 0 euler53: - 1 - 9 - 53 euler59: - 1 - 4 - 59 euler61: - 1 - 13 - 61 euler67: - 1 - -10 - 67 euler7: - 1 - 4 - 7 euler71: - 1 - 6 - 71 euler73: - 1 - 6 - 73 euler79: - 1 - -9 - 79 euler83: - 1 - -17 - 83 euler89: - 1 - 6 - 89 euler97: - 1 - 8 - 97 euler_factors: - - 1 - 0 - 0 - - 1 - 0 - 0 - - 1 - -1 - 0 - - 1 - 4 - 7 - - 1 - 2 - 11 - - 1 - 4 - 13 - - 1 - -1 - 17 - - 1 - -5 - 19 - - 1 - -5 - 23 - - 1 - 8 - 29 - - 1 - -7 - 31 - - 1 - -6 - 37 - - 1 - -6 - 41 - - 1 - -2 - 43 - - 1 - -8 - 47 - - 1 - 9 - 53 - - 1 - 4 - 59 - - 1 - 13 - 61 - - 1 - -10 - 67 - - 1 - 6 - 71 - - 1 - 6 - 73 - - 1 - -9 - 79 - - 1 - -17 - 83 - - 1 - 6 - 89 - - 1 - 8 - 97 id: 22271506 index: 81 instance_types: - ECQ - CMF - CMF instance_urls: - EllipticCurve/Q/8640/bf - ModularForm/GL2/Q/holomorphic/8640/2/a/bf/1/1 - ModularForm/GL2/Q/holomorphic/8640/2/a/bf 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: 2-8640-1.1-c1-0-81 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: 2-8640-1.1-c1-0 primitive: true rational: true root_analytic_conductor: 8.306066899946465 root_angle: 0.5 self_dual: true spectral_label: c1-0 trace_hash: 1794528052930445543 z1: __RealLiteral__: 0 data: '1.12737072596111806526309478815' prec: 103 - - Lhash: '1429112177444346038152611044612' Lhash_array: - '1429112177444346038152611044612' id: 22269743 label: 2-8640-1.1-c1-0-81 type: CMF url: ModularForm/GL2/Q/holomorphic/8640/2/a/bf - Lhash: '1429112177444346038152611044612' Lhash_array: - '1429112177444346038152611044612' id: 24584914 label: 2-8640-1.1-c1-0-81 type: CMF url: ModularForm/GL2/Q/holomorphic/8640/2/a/bf/1/1 - Lhash: '1794528052930445543' Lhash_array: - '1794528052930445543' id: 30133 label: 2-8640-1.1-c1-0-81 type: ECQ url: EllipticCurve/Q/8640/bf label_cols: - label - label - label labels: - 2-8640-1.1-c1-0-81 - 2-8640-1.1-c1-0-81 - 2-8640-1.1-c1-0-81 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-05-22T08:34:18.945463'