LMFDB - Embedded newform 2.80.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,80,Mod(1,2)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 80, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 80);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 80 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$79.0474097443$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2 x^{3} + \cdots + 18\!\cdots\!60 $ x^4 - 2x^3 - 41378554124364514550149116389619x^2 - 22942689466335514146071616491770842136426264992*x + 189651623212039036292000549473742215529785444677917055760560
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{12}\cdot 5^{5}\cdot 7\cdot 11\cdot 13 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$6.69343e15$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.49756e11 q^{2} -1.17521e19 q^{3} +3.02231e23 q^{4} -1.34628e27 q^{5} +6.46078e30 q^{6} -6.77209e32 q^{7} -1.66153e35 q^{8} +8.88420e37 q^{9} +O(q^{10})$	\(q-5.49756e11 q^{2} -1.17521e19 q^{3} +3.02231e23 q^{4} -1.34628e27 q^{5} +6.46078e30 q^{6} -6.77209e32 q^{7} -1.66153e35 q^{8} +8.88420e37 q^{9} +7.40123e38 q^{10} -5.85751e40 q^{11} -3.55185e42 q^{12} +1.58161e44 q^{13} +3.72300e44 q^{14} +1.58215e46 q^{15} +9.13439e46 q^{16} -3.21696e48 q^{17} -4.88414e49 q^{18} +5.69780e50 q^{19} -4.06887e50 q^{20} +7.95862e51 q^{21} +3.22020e52 q^{22} -3.98321e53 q^{23} +1.95265e54 q^{24} -1.47312e55 q^{25} -8.69498e55 q^{26} -4.65058e56 q^{27} -2.04674e56 q^{28} -1.05519e58 q^{29} -8.69799e57 q^{30} -6.93296e58 q^{31} -5.02168e58 q^{32} +6.88380e59 q^{33} +1.76854e60 q^{34} +9.11710e59 q^{35} +2.68508e61 q^{36} +9.16682e61 q^{37} -3.13240e62 q^{38} -1.85872e63 q^{39} +2.23688e62 q^{40} -3.37087e63 q^{41} -4.37530e63 q^{42} +2.25894e64 q^{43} -1.77032e64 q^{44} -1.19606e65 q^{45} +2.18980e65 q^{46} -1.28682e66 q^{47} -1.07348e66 q^{48} -5.33228e66 q^{49} +8.09854e66 q^{50} +3.78060e67 q^{51} +4.78012e67 q^{52} -3.09468e67 q^{53} +2.55668e68 q^{54} +7.88582e67 q^{55} +1.12521e68 q^{56} -6.69610e69 q^{57} +5.80098e69 q^{58} -7.75517e69 q^{59} +4.78177e69 q^{60} +1.98642e70 q^{61} +3.81143e70 q^{62} -6.01646e70 q^{63} +2.76070e70 q^{64} -2.12928e71 q^{65} -3.78441e71 q^{66} +1.96379e72 q^{67} -9.72266e71 q^{68} +4.68111e72 q^{69} -5.01218e71 q^{70} +1.42244e73 q^{71} -1.47614e73 q^{72} -7.35923e73 q^{73} -5.03951e73 q^{74} +1.73122e74 q^{75} +1.72205e74 q^{76} +3.96676e73 q^{77} +1.02184e75 q^{78} +7.87169e74 q^{79} -1.22974e74 q^{80} +1.08819e75 q^{81} +1.85316e75 q^{82} +2.03088e75 q^{83} +2.40535e75 q^{84} +4.33091e75 q^{85} -1.24186e76 q^{86} +1.24007e77 q^{87} +9.73246e75 q^{88} +1.65040e77 q^{89} +6.57540e76 q^{90} -1.07108e77 q^{91} -1.20385e77 q^{92} +8.14768e77 q^{93} +7.07436e77 q^{94} -7.67080e77 q^{95} +5.90152e77 q^{96} -1.14716e78 q^{97} +2.93145e78 q^{98} -5.20393e78 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2199023255552 q^{2} + 43\!\cdots\!88 q^{3}+ \cdots + 11\!\cdots\!68 q^{9}+O(q^{10}) $ 4 * q - 2199023255552 * q^2 + 4397166235394547888 * q^3 + 1208925819614629174706176 * q^4 - 2086014264921085269083726280 * q^5 - 2417367702540162666965231468544 * q^6 + 2573657218644254612276267065505504 * q^7 - 664613997892457936451903530140172288 * q^8 + 112831132354410260252452789557864274068 * q^9	$ 4 q - 2199023255552 q^{2} + 43\!\cdots\!88 q^{3}+ \cdots - 24\!\cdots\!24 q^{99}+O(q^{100}) $ 4 * q - 2199023255552 * q^2 + 4397166235394547888 * q^3 + 1208925819614629174706176 * q^4 - 2086014264921085269083726280 * q^5 - 2417367702540162666965231468544 * q^6 + 2573657218644254612276267065505504 * q^7 - 664613997892457936451903530140172288 * q^8 + 112831132354410260252452789557864274068 * q^9 + 1146798469993669280197371425077214576640 * q^10 - 197159815504598633763217332606735329596272 * q^11 + 1328961948776531811985383516987716190339072 * q^12 + 170659994114464310607333330726054349201117208 * q^13 - 1414883018904498562307037076903427761663639552 * q^14 - 59366752746116883766669164021489296326782488160 * q^15 + 365375409332725729550921208179070754913983135744 * q^16 + 2796535717206368263389203662758684400077797212104 * q^17 - 62029570999403462291345079671679661661291632656384 * q^18 + 684695990053883053631017856536943728062103032667760 * q^19 - 630459126236882801342409049071558512824740552376320 * q^20 + 45478844539030123008167232224769119704272628301033088 * q^21 + 108389754838738543311270380964644181752802447810625536 * q^22 + 488013222626121609525538789113144096441523639094824608 * q^23 - 730604557775824812131947908541401788318211250046631936 * q^24 - 1126158160782455808180245842925474538931659342186424100 * q^25 - 93821323962518616911063366814611886711982353282922184704 * q^26 + 90964799281766581383421329970064862000231385703676280800 * q^27 + 777840165614153097265631047162836375890408246806027698176 * q^28 + 3688955716580217982904251654950665317367915182498635788760 * q^29 + 32637217473829146466723501353466415224010715590746523566080 * q^30 + 47913642648243257357880153903864424303169229638564126887808 * q^31 - 200867255532373784442745261542645325315275374222849104412672 * q^32 - 1436330994448132246142996248045289777329665443300928101553984 * q^33 - 1537411769279648790296184812932091217704898416858451884900352 * q^34 - 7972883232568194700190580853845272700117553615578992904761280 * q^35 + 34101117289900531974463531653168456220619851696334705359060992 * q^36 - 38544494660546044616136325697019592074980910779612167168904776 * q^37 - 376415601277922431123690975362328720360838397733177450697850880 * q^38 - 1630430927936849113215375152201441675512550245915136857855917024 * q^39 + 346598570067474839136065505742950780970580128274082494058332160 * q^40 - 12579033250871855934974364481604046809757294442784672679492978072 * q^41 - 25002259194240329456503731622940248355911696642675347964657926144 * q^42 - 27881137628994939802008918876181036324603361539085263748281837552 * q^43 - 59587897888491494069322986810445784691835708121009085238076243968 * q^44 - 1135438665665771435983146357768830772915834005948410169448283574760 * q^45 - 268288106392929222173577110530610526457832192809366877979650555904 * q^46 + 576521573667121444294826737512354596485517945866563824315674561344 * q^47 + 401654103290330888644103718906997727081296916501704017928853127168 * q^48 + 8503633478015001303779478851572586384147456200881468883106419562532 * q^49 + 619111996247572155737523861581422862078995923674056274519837900800 * q^50 + 49232145152944155726126332673453135974534372921258319898205217633888 * q^51 + 51578818315064139446293721734708447790185110870946434382918584369152 * q^52 + 105260874204831629761192832713944871847534780950247243530744550109048 * q^53 - 50008427264306144786882182247712414885087609091846601344884827750400 * q^54 + 1706371452310384568720710819629526373211333934635788847603849120131040 * q^55 - 427622153321985447359103023662926825094203686415434933675018093068288 * q^56 - 3821140729633100507759495557501687754299260740915493042180144734143680 * q^57 - 2028024852365347993231980538542973956036692033092289571499438642298880 * q^58 - 22994083684412863891816921299052701325384953970436261646797889586232880 * q^59 - 17942500055364597755669937995231998671549764789224145784576882549719040 * q^60 - 23646778479353101184296000685935209544077325117960260112218279494132392 * q^61 - 26340803610423759642189648499781687091197367097746793648886991504277504 * q^62 + 296052075404662580137809311474829180309942987769431307228777293972598368 * q^63 + 110427941548649020598956093796432407239217743554726184882600387580788736 * q^64 + 82132500368390587233984346712328863046834885947481304582705463914927440 * q^65 + 789631314865393352379800451175068610620676517068650045775581191488929792 * q^66 + 2983897377193475990481005659832229621500411081115555050468937379296200624 * q^67 + 845201058501323396184073718414746835063213424564380916075080711537688576 * q^68 + 643705029211491925644175845796189209393168474013641254367041007578645376 * q^69 + 4383138910554516265866120926017177867674433041208106320712414756748656640 * q^70 - 16499813603455772357667749355219751026230120653663304246848158193765849632 * q^71 - 18747287490199415798185366476162474783535363057168343371131250932392656896 * q^72 - 51054101367263816819239972529705907616909197826293748520432769719012535832 * q^73 + 21190060033010161040443186271526854737062885327709199558928757895450329088 * q^74 + 460262000986235535329966978224762375148848884176930915586953670808542094800 * q^75 + 206936665240685139008136354558917581356970270387844823668726004106857021440 * q^76 + 714443940797159208758465775389654529345067448576374493435847369953921324928 * q^77 + 896338881776089560901969623433755443248364460001570610669486630165714829312 * q^78 + 3793482818758144309481153181998416908055274731698143035904870248402594032320 * q^79 - 190544578979861625266209566883798244711206501002837662257491320768645038080 * q^80 + 10503648529690173875799214665504367224948242302604410591535224882970590535844 * q^81 + 6915396662757271645124914949999791957652571306137947178046339927153297063936 * q^82 + 19346063777388756720202955274004150860046151063944560371597113890413092234608 * q^83 + 13745137352368323402233469673278639366497088684052943034064122446804913487872 * q^84 + 30655188804191738921148634717047425623385547547695664063843774112286102804720 * q^85 + 15327817509351455718286978774209871921863613181700535494963823165007961522176 * q^86 + 138979180900031985924221810974428938836250542065413584799944105485284337733920 * q^87 + 32758793301562677990645783707123711543358950986846160846900971750025890627584 * q^88 + 459737633766523870607866690314569291936758726488822645779886714468574569430440 * q^89 + 624214007762990897172297115366226393322484430862475666044697128566805894266880 * q^90 + 1085896524691399091167300270848714222149318633472628260999900307465809641228608 * q^91 + 147492946286515140464413660808083125510365694870041229233692376462835163594752 * q^92 + 2601718925395081722296014880082930112779863466567237516827989872206913506290176 * q^93 - 316946086955358898394440527309048241646153742735102720682561513107408103145472 * q^94 - 3072347992266807812950710777377746192504934105084754288221571876169908708511200 * q^95 - 220811678455830676447365536760004109230144485073979070115356395004657804509184 * q^96 + 876722878175671412672813582974525849228585033511787690974854054652742606089864 * q^97 - 4674921943711381196432668526518770776326171804720424348849116020317384570044416 * q^98 - 24079215890709128892364067000577259961482799185203811654942166618829711668703024 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−5.49756e11	−0.707107
$2$	−5.49756e11	−0.707107
$3$	−1.17521e19	−1.67427	−0.837135	−	0.546996i	$-0.815771\pi$
$3$	−1.17521e19	−1.67427	−0.837135	+	0.546996i	$0.815771\pi$
$4$	3.02231e23	0.500000
$5$	−1.34628e27	−0.330993	−0.165496	−	0.986210i	$-0.552923\pi$
$5$	−1.34628e27	−0.330993	−0.165496	+	0.986210i	$0.552923\pi$
$6$	6.46078e30	1.18389
$7$	−6.77209e32	−0.281417	−0.140708	−	0.990051i	$-0.544938\pi$
$7$	−6.77209e32	−0.281417	−0.140708	+	0.990051i	$0.544938\pi$
$8$	−1.66153e35	−0.353553
$9$	8.88420e37	1.80318
$10$	7.40123e38	0.234047
$11$	−5.85751e40	−0.429242	−0.214621	−	0.976697i	$-0.568852\pi$
$11$	−5.85751e40	−0.429242	−0.214621	+	0.976697i	$0.568852\pi$
$12$	−3.55185e42	−0.837135
$13$	1.58161e44	1.57883	0.789417	−	0.613857i	$-0.210383\pi$
$13$	1.58161e44	1.57883	0.789417	+	0.613857i	$0.210383\pi$
$14$	3.72300e44	0.198992
$15$	1.58215e46	0.554172
$16$	9.13439e46	0.250000
$17$	−3.21696e48	−0.802996	−0.401498	−	0.915860i	$-0.631510\pi$
$17$	−3.21696e48	−0.802996	−0.401498	+	0.915860i	$0.631510\pi$
$18$	−4.88414e49	−1.27504
$19$	5.69780e50	1.75768	0.878840	−	0.477117i	$-0.158318\pi$
$19$	5.69780e50	1.75768	0.878840	+	0.477117i	$0.158318\pi$
$20$	−4.06887e50	−0.165496
$21$	7.95862e51	0.471168
$22$	3.22020e52	0.303520
$23$	−3.98321e53	−0.648611	−0.324305	−	0.945952i	$-0.605131\pi$
$23$	−3.98321e53	−0.648611	−0.324305	+	0.945952i	$0.605131\pi$
$24$	1.95265e54	0.591944
$25$	−1.47312e55	−0.890444
$26$	−8.69498e55	−1.11640
$27$	−4.65058e56	−1.34474
$28$	−2.04674e56	−0.140708
$29$	−1.05519e58	−1.81389	−0.906944	−	0.421251i	$-0.861591\pi$
$29$	−1.05519e58	−1.81389	−0.906944	+	0.421251i	$0.861591\pi$
$30$	−8.69799e57	−0.391858
$31$	−6.93296e58	−0.855326	−0.427663	−	0.903938i	$-0.640663\pi$
$31$	−6.93296e58	−0.855326	−0.427663	+	0.903938i	$0.640663\pi$
$32$	−5.02168e58	−0.176777
$33$	6.88380e59	0.718667
$34$	1.76854e60	0.567804
$35$	9.11710e59	0.0931470
$36$	2.68508e61	0.901590
$37$	9.16682e61	1.04292	0.521459	−	0.853276i	$-0.325388\pi$
$37$	9.16682e61	1.04292	0.521459	+	0.853276i	$0.325388\pi$
$38$	−3.13240e62	−1.24287
$39$	−1.85872e63	−2.64339
$40$	2.23688e62	0.117024
$41$	−3.37087e63	−0.664937	−0.332468	−	0.943114i	$-0.607881\pi$
$41$	−3.37087e63	−0.664937	−0.332468	+	0.943114i	$0.607881\pi$
$42$	−4.37530e63	−0.333166
$43$	2.25894e64	0.679047	0.339524	−	0.940598i	$-0.389734\pi$
$43$	2.25894e64	0.679047	0.339524	+	0.940598i	$0.389734\pi$
$44$	−1.77032e64	−0.214621
$45$	−1.19606e65	−0.596840
$46$	2.18980e65	0.458637
$47$	−1.28682e66	−1.15253	−0.576265	−	0.817263i	$-0.695490\pi$
$47$	−1.28682e66	−1.15253	−0.576265	+	0.817263i	$0.695490\pi$
$48$	−1.07348e66	−0.418567
$49$	−5.33228e66	−0.920805
$50$	8.09854e66	0.629639
$51$	3.78060e67	1.34443
$52$	4.78012e67	0.789417
$53$	−3.09468e67	−0.240835	−0.120417	−	0.992723i	$-0.538423\pi$
$53$	−3.09468e67	−0.240835	−0.120417	+	0.992723i	$0.538423\pi$
$54$	2.55668e68	0.950875
$55$	7.88582e67	0.142076
$56$	1.12521e68	0.0994959
$57$	−6.69610e69	−2.94283
$58$	5.80098e69	1.28261
$59$	−7.75517e69	−0.872845	−0.436422	−	0.899742i	$-0.643755\pi$
$59$	−7.75517e69	−0.872845	−0.436422	+	0.899742i	$0.643755\pi$
$60$	4.78177e69	0.277086
$61$	1.98642e70	0.599161	0.299580	−	0.954071i	$-0.403153\pi$
$61$	1.98642e70	0.599161	0.299580	+	0.954071i	$0.403153\pi$
$62$	3.81143e70	0.604807
$63$	−6.01646e70	−0.507445
$64$	2.76070e70	0.125000
$65$	−2.12928e71	−0.522583
$66$	−3.78441e71	−0.508174
$67$	1.96379e72	1.45593	0.727966	−	0.685613i	$-0.240466\pi$
$67$	1.96379e72	1.45593	0.727966	+	0.685613i	$0.240466\pi$
$68$	−9.72266e71	−0.401498
$69$	4.68111e72	1.08595
$70$	−5.01218e71	−0.0658649
$71$	1.42244e73	1.06741	0.533703	−	0.845672i	$-0.320800\pi$
$71$	1.42244e73	1.06741	0.533703	+	0.845672i	$0.320800\pi$
$72$	−1.47614e73	−0.637520
$73$	−7.35923e73	−1.84323	−0.921614	−	0.388107i	$-0.873129\pi$
$73$	−7.35923e73	−1.84323	−0.921614	+	0.388107i	$0.873129\pi$
$74$	−5.03951e73	−0.737455
$75$	1.73122e74	1.49084
$76$	1.72205e74	0.878840
$77$	3.96676e73	0.120796
$78$	1.02184e75	1.86916
$79$	7.87169e74	0.870559	0.435279	−	0.900295i	$-0.356650\pi$
$79$	7.87169e74	0.870559	0.435279	+	0.900295i	$0.356650\pi$
$80$	−1.22974e74	−0.0827482
$81$	1.08819e75	0.448278
$82$	1.85316e75	0.470181
$83$	2.03088e75	0.319227	0.159613	−	0.987180i	$-0.448975\pi$
$83$	2.03088e75	0.319227	0.159613	+	0.987180i	$0.448975\pi$
$84$	2.40535e75	0.235584
$85$	4.33091e75	0.265786
$86$	−1.24186e76	−0.480159
$87$	1.24007e77	3.03694
$88$	9.73246e75	0.151760
$89$	1.65040e77	1.64697	0.823483	−	0.567341i	$-0.192028\pi$
$89$	1.65040e77	1.64697	0.823483	+	0.567341i	$0.192028\pi$
$90$	6.57540e76	0.422030
$91$	−1.07108e77	−0.444311
$92$	−1.20385e77	−0.324305
$93$	8.14768e77	1.43205
$94$	7.07436e77	0.814961
$95$	−7.67080e77	−0.581780
$96$	5.90152e77	0.295972
$97$	−1.14716e78	−0.382066	−0.191033	−	0.981584i	$-0.561184\pi$
$97$	−1.14716e78	−0.382066	−0.191033	+	0.981584i	$0.561184\pi$
$98$	2.93145e78	0.651107
$99$	−5.20393e78	−0.774000
$100$	−4.45222e78	−0.445222
$101$	−2.29951e79	−1.55218	−0.776089	−	0.630624i	$-0.782799\pi$
$101$	−2.29951e79	−1.55218	−0.776089	+	0.630624i	$0.782799\pi$
$102$	−2.07841e79	−0.950657
$103$	1.60544e79	0.499487	0.249743	−	0.968312i	$-0.419654\pi$
$103$	1.60544e79	0.499487	0.249743	+	0.968312i	$0.419654\pi$
$104$	−2.62790e79	−0.558202
$105$	−1.07145e79	−0.155953
$106$	1.70132e79	0.170296
$107$	1.44838e80	1.00052	0.500258	−	0.865876i	$-0.333239\pi$
$107$	1.44838e80	1.00052	0.500258	+	0.865876i	$0.333239\pi$
$108$	−1.40555e80	−0.672370
$109$	−5.15084e80	−1.71211	−0.856054	−	0.516886i	$-0.827091\pi$
$109$	−5.15084e80	−1.71211	−0.856054	+	0.516886i	$0.827091\pi$
$110$	−4.33528e79	−0.100463
$111$	−1.07729e81	−1.74613
$112$	−6.18589e79	−0.0703542
$113$	6.96134e80	0.557307	0.278654	−	0.960392i	$-0.410112\pi$
$113$	6.96134e80	0.557307	0.278654	+	0.960392i	$0.410112\pi$
$114$	3.68122e81	2.08089
$115$	5.36250e80	0.214686
$116$	−3.18912e81	−0.906944
$117$	1.40513e82	2.84692
$118$	4.26345e81	0.617195
$119$	2.17855e81	0.225977
$120$	−2.62881e81	−0.195929
$121$	−1.51908e82	−0.815752
$122$	−1.09205e82	−0.423671
$123$	3.96148e82	1.11328
$124$	−2.09536e82	−0.427663
$125$	4.21045e82	0.625724
$126$	3.30758e82	0.358818
$127$	−7.36587e82	−0.584760	−0.292380	−	0.956302i	$-0.594447\pi$
$127$	−7.36587e82	−0.584760	−0.292380	+	0.956302i	$0.594447\pi$
$128$	−1.51771e82	−0.0883883
$129$	−2.65472e83	−1.13691
$130$	1.17058e83	0.369522
$131$	−5.67038e83	−1.32250	−0.661251	−	0.750165i	$-0.729974\pi$
$131$	−5.67038e83	−1.32250	−0.661251	+	0.750165i	$0.729974\pi$
$132$	2.08050e83	0.359333
$133$	−3.85860e83	−0.494641
$134$	−1.07961e84	−1.02950
$135$	6.26096e83	0.445099
$136$	5.34509e83	0.283902
$137$	−1.15412e83	−0.0458975	−0.0229488	−	0.999737i	$-0.507305\pi$
$137$	−1.15412e83	−0.0458975	−0.0229488	+	0.999737i	$0.507305\pi$
$138$	−2.57347e84	−0.767882
$139$	3.62107e83	0.0812366	0.0406183	−	0.999175i	$-0.487067\pi$
$139$	3.62107e83	0.0812366	0.0406183	+	0.999175i	$0.487067\pi$
$140$	2.75547e83	0.0465735
$141$	1.51228e85	1.92964
$142$	−7.81996e84	−0.754770
$143$	−9.26428e84	−0.677701
$144$	8.11517e84	0.450795
$145$	1.42058e85	0.600384
$146$	4.04578e85	1.30336
$147$	6.26654e85	1.54168
$148$	2.77050e85	0.521459
$149$	3.85154e84	0.0555619	0.0277810	−	0.999614i	$-0.491156\pi$
$149$	3.85154e84	0.0555619	0.0277810	+	0.999614i	$0.491156\pi$
$150$	−9.51747e85	−1.05419
$151$	−5.87255e85	−0.500308	−0.250154	−	0.968206i	$-0.580481\pi$
$151$	−5.87255e85	−0.500308	−0.250154	+	0.968206i	$0.580481\pi$
$152$	−9.46709e85	−0.621434
$153$	−2.85801e86	−1.44795
$154$	−2.18075e85	−0.0854156
$155$	9.33367e85	0.283107
$156$	−5.61764e86	−1.32170
$157$	7.56706e86	1.38322	0.691609	−	0.722272i	$-0.256902\pi$
$157$	7.56706e86	1.38322	0.691609	+	0.722272i	$0.256902\pi$
$158$	−4.32751e86	−0.615578
$159$	3.63689e86	0.403222
$160$	6.76057e85	0.0585118
$161$	2.69747e86	0.182530
$162$	−5.98240e86	−0.316980
$163$	−1.69216e87	−0.703121	−0.351561	−	0.936165i	$-0.614349\pi$
$163$	−1.69216e87	−0.703121	−0.351561	+	0.936165i	$0.614349\pi$
$164$	−1.01878e87	−0.332468
$165$	−9.26749e86	−0.237874
$166$	−1.11649e87	−0.225727
$167$	3.17468e87	0.506290	0.253145	−	0.967428i	$-0.418535\pi$
$167$	3.17468e87	0.506290	0.253145	+	0.967428i	$0.418535\pi$
$168$	−1.32235e87	−0.166583
$169$	1.49797e88	1.49272
$170$	−2.38095e87	−0.187939
$171$	5.06203e88	3.16941
$172$	6.82722e87	0.339524
$173$	−1.38880e88	−0.549312	−0.274656	−	0.961543i	$-0.588564\pi$
$173$	−1.38880e88	−0.549312	−0.274656	+	0.961543i	$0.588564\pi$
$174$	−6.81736e88	−2.14744
$175$	9.97607e87	0.250586
$176$	−5.35048e87	−0.107310
$177$	9.11395e88	1.46138
$178$	−9.07318e88	−1.16458
$179$	−2.63459e88	−0.271031	−0.135515	−	0.990775i	$-0.543269\pi$
$179$	−2.63459e88	−0.271031	−0.135515	+	0.990775i	$0.543269\pi$
$180$	−3.61486e88	−0.298420
$181$	−8.28717e88	−0.549670	−0.274835	−	0.961491i	$-0.588623\pi$
$181$	−8.28717e88	−0.549670	−0.274835	+	0.961491i	$0.588623\pi$
$182$	5.88832e88	0.314175
$183$	−2.33446e89	−1.00316
$184$	6.61825e88	0.229319
$185$	−1.23411e89	−0.345199
$186$	−4.47923e89	−1.01261
$187$	1.88434e89	0.344679
$188$	−3.88917e89	−0.576265
$189$	3.14941e89	0.378433
$190$	4.21707e89	0.411380
$191$	1.19769e90	0.949571	0.474786	−	0.880102i	$-0.342526\pi$
$191$	1.19769e90	0.949571	0.474786	+	0.880102i	$0.342526\pi$
$192$	−3.24440e89	−0.209284
$193$	2.40485e90	1.26350	0.631748	−	0.775174i	$-0.282338\pi$
$193$	2.40485e90	1.26350	0.631748	+	0.775174i	$0.282338\pi$
$194$	6.30655e89	0.270162
$195$	2.50235e90	0.874945
$196$	−1.61158e90	−0.460402
$197$	−2.50243e90	−0.584718	−0.292359	−	0.956309i	$-0.594440\pi$
$197$	−2.50243e90	−0.584718	−0.292359	+	0.956309i	$0.594440\pi$
$198$	2.86089e90	0.547301
$199$	−4.90517e89	−0.0769055	−0.0384527	−	0.999260i	$-0.512243\pi$
$199$	−4.90517e89	−0.0769055	−0.0384527	+	0.999260i	$0.512243\pi$
$200$	2.44763e90	0.314819
$201$	−2.30787e91	−2.43762
$202$	1.26417e91	1.09755
$203$	7.14586e90	0.510459
$204$	1.14262e91	0.672216
$205$	4.53813e90	0.220089
$206$	−8.82600e90	−0.353190
$207$	−3.53877e91	−1.16956
$208$	1.44470e91	0.394708
$209$	−3.33749e91	−0.754469
$210$	5.89036e90	0.110276
$211$	−2.86799e90	−0.0445062	−0.0222531	−	0.999752i	$-0.507084\pi$
$211$	−2.86799e90	−0.0445062	−0.0222531	+	0.999752i	$0.507084\pi$
$212$	−9.35309e90	−0.120417
$213$	−1.67167e92	−1.78713
$214$	−7.96256e91	−0.707471
$215$	−3.04115e91	−0.224760
$216$	7.72710e91	0.475437
$217$	4.69506e91	0.240703
$218$	2.83170e92	1.21064
$219$	8.64863e92	3.08606
$220$	2.38334e91	0.0710380
$221$	−5.08797e92	−1.26780
$222$	5.92248e92	1.23470
$223$	2.01972e92	0.352574	0.176287	−	0.984339i	$-0.443591\pi$
$223$	2.01972e92	0.352574	0.176287	+	0.984339i	$0.443591\pi$
$224$	3.40073e91	0.0497480
$225$	−1.30874e93	−1.60563
$226$	−3.82704e92	−0.394076
$227$	1.46691e93	1.26877	0.634383	−	0.773019i	$-0.281254\pi$
$227$	1.46691e93	1.26877	0.634383	+	0.773019i	$0.281254\pi$
$228$	−2.02377e93	−1.47141
$229$	3.67782e92	0.224952	0.112476	−	0.993654i	$-0.464122\pi$
$229$	3.67782e92	0.224952	0.112476	+	0.993654i	$0.464122\pi$
$230$	−2.94807e92	−0.151806
$231$	−4.66177e92	−0.202245
$232$	1.75324e93	0.641306
$233$	2.97483e93	0.918128	0.459064	−	0.888403i	$-0.348185\pi$
$233$	2.97483e93	0.918128	0.459064	+	0.888403i	$0.348185\pi$
$234$	−7.72479e93	−2.01308
$235$	1.73241e93	0.381479
$236$	−2.34386e93	−0.436422
$237$	−9.25089e93	−1.45755
$238$	−1.19767e93	−0.159790
$239$	1.27190e94	1.43792	0.718961	−	0.695051i	$-0.244618\pi$
$239$	1.27190e94	1.43792	0.718961	+	0.695051i	$0.244618\pi$
$240$	1.44520e93	0.138543
$241$	−1.84851e94	−1.50365	−0.751827	−	0.659360i	$-0.770827\pi$
$241$	−1.84851e94	−1.50365	−0.751827	+	0.659360i	$0.770827\pi$
$242$	8.35122e93	0.576823
$243$	1.01247e94	0.594202
$244$	6.00360e93	0.299580
$245$	7.17871e93	0.304780
$246$	−2.17785e94	−0.787210
$247$	9.01168e94	2.77508
$248$	1.15194e94	0.302403
$249$	−2.38671e94	−0.534472
$250$	−2.31472e94	−0.442453
$251$	−4.29972e94	−0.701986	−0.350993	−	0.936378i	$-0.614156\pi$
$251$	−4.29972e94	−0.701986	−0.350993	+	0.936378i	$0.614156\pi$
$252$	−1.81836e94	−0.253723
$253$	2.33317e94	0.278411
$254$	4.04943e94	0.413487
$255$	−5.08973e94	−0.444997
$256$	8.34370e93	0.0625000
$257$	2.01519e95	1.29407	0.647033	−	0.762462i	$-0.276009\pi$
$257$	2.01519e95	1.29407	0.647033	+	0.762462i	$0.276009\pi$
$258$	1.45945e95	0.803916
$259$	−6.20785e94	−0.293495
$260$	−6.43535e94	−0.261291
$261$	−9.37453e95	−3.27077
$262$	3.11732e95	0.935149
$263$	−3.12012e95	−0.805229	−0.402614	−	0.915370i	$-0.631898\pi$
$263$	−3.12012e95	−0.805229	−0.402614	+	0.915370i	$0.631898\pi$
$264$	−1.14377e95	−0.254087
$265$	4.16629e94	0.0797145
$266$	2.12129e95	0.349764
$267$	−1.93957e96	−2.75747
$268$	5.93520e95	0.727966
$269$	1.59050e96	1.68391	0.841955	−	0.539548i	$-0.181405\pi$
$269$	1.59050e96	1.68391	0.841955	+	0.539548i	$0.181405\pi$
$270$	−3.44200e95	−0.314733
$271$	2.19628e96	1.73540	0.867702	−	0.497084i	$-0.165596\pi$
$271$	2.19628e96	1.73540	0.867702	+	0.497084i	$0.165596\pi$
$272$	−2.93849e95	−0.200749
$273$	1.25874e96	0.743896
$274$	6.34485e94	0.0324544
$275$	8.62879e95	0.382216
$276$	1.41478e96	0.542975
$277$	3.65040e96	1.21448	0.607239	−	0.794519i	$-0.292277\pi$
$277$	3.65040e96	1.21448	0.607239	+	0.794519i	$0.292277\pi$
$278$	−1.99070e95	−0.0574430
$279$	−6.15938e96	−1.54231
$280$	−1.51484e95	−0.0329324
$281$	1.87207e96	0.353526	0.176763	−	0.984253i	$-0.443437\pi$
$281$	1.87207e96	0.353526	0.176763	+	0.984253i	$0.443437\pi$
$282$	−8.31385e96	−1.36446
$283$	−1.03292e97	−1.47401	−0.737006	−	0.675886i	$-0.763761\pi$
$283$	−1.03292e97	−1.47401	−0.737006	+	0.675886i	$0.763761\pi$
$284$	4.29907e96	0.533703
$285$	9.01480e96	0.974056
$286$	5.09309e96	0.479207
$287$	2.28279e96	0.187124
$288$	−4.46136e96	−0.318760
$289$	−5.70079e96	−0.355198
$290$	−7.80972e96	−0.424536
$291$	1.34815e97	0.639682
$292$	−2.22419e97	−0.921614
$293$	3.75985e96	0.136113	0.0680564	−	0.997681i	$-0.478320\pi$
$293$	3.75985e96	0.136113	0.0680564	+	0.997681i	$0.478320\pi$
$294$	−3.44507e97	−1.09013
$295$	1.04406e97	0.288906
$296$	−1.52310e97	−0.368728
$297$	2.72408e97	0.577219
$298$	−2.11741e96	−0.0392882
$299$	−6.29988e97	−1.02405
$300$	5.23229e97	0.745422
$301$	−1.52977e97	−0.191095
$302$	3.22847e97	0.353771
$303$	2.70241e98	2.59876
$304$	5.20459e97	0.439420
$305$	−2.67427e97	−0.198318
$306$	1.57121e98	1.02385
$307$	−1.94871e98	−1.11630	−0.558152	−	0.829739i	$-0.688489\pi$
$307$	−1.94871e98	−1.11630	−0.558152	+	0.829739i	$0.688489\pi$
$308$	1.19888e97	0.0603980
$309$	−1.88673e98	−0.836275
$310$	−5.13124e97	−0.200187
$311$	−2.32009e97	−0.0797022	−0.0398511	−	0.999206i	$-0.512688\pi$
$311$	−2.32009e97	−0.0797022	−0.0398511	+	0.999206i	$0.512688\pi$
$312$	3.08833e98	0.934581
$313$	−2.22861e98	−0.594337	−0.297169	−	0.954825i	$-0.596042\pi$
$313$	−2.22861e98	−0.594337	−0.297169	+	0.954825i	$0.596042\pi$
$314$	−4.16003e98	−0.978083
$315$	8.09981e97	0.167961
$316$	2.37907e98	0.435279
$317$	−1.92375e98	−0.310675	−0.155338	−	0.987861i	$-0.549647\pi$
$317$	−1.92375e98	−0.310675	−0.155338	+	0.987861i	$0.549647\pi$
$318$	−1.99940e98	−0.285121
$319$	6.18080e98	0.778597
$320$	−3.71666e97	−0.0413741
$321$	−1.70215e99	−1.67513
$322$	−1.48295e98	−0.129068
$323$	−1.83296e99	−1.41141
$324$	3.28886e98	0.224139
$325$	−2.32989e99	−1.40586
$326$	9.30273e98	0.497182
$327$	6.05331e99	2.86653
$328$	5.60083e98	0.235091
$329$	8.71445e98	0.324341
$330$	5.09486e98	0.168202
$331$	−2.27825e97	−0.00667414	−0.00333707	−	0.999994i	$-0.501062\pi$
$331$	−2.27825e97	−0.00667414	−0.00333707	+	0.999994i	$0.501062\pi$
$332$	6.13795e98	0.159613
$333$	8.14398e99	1.88057
$334$	−1.74530e99	−0.358001
$335$	−2.64381e99	−0.481903
$336$	7.26971e98	0.117792
$337$	6.54753e99	0.943402	0.471701	−	0.881759i	$-0.343640\pi$
$337$	6.54753e99	0.943402	0.471701	+	0.881759i	$0.343640\pi$
$338$	−8.23516e99	−1.05551
$339$	−8.18103e99	−0.933082
$340$	1.30894e99	0.132893
$341$	4.06099e99	0.367142
$342$	−2.78288e100	−2.24111
$343$	7.53271e99	0.540547
$344$	−3.75330e99	−0.240079
$345$	−6.30206e99	−0.359442
$346$	7.63502e99	0.388422
$347$	1.59365e100	0.723399	0.361700	−	0.932295i	$-0.382197\pi$
$347$	1.59365e100	0.723399	0.361700	+	0.932295i	$0.382197\pi$
$348$	3.74788e100	1.51847
$349$	−2.19859e99	−0.0795317	−0.0397658	−	0.999209i	$-0.512661\pi$
$349$	−2.19859e99	−0.0795317	−0.0397658	+	0.999209i	$0.512661\pi$
$350$	−5.48440e99	−0.177191
$351$	−7.35539e100	−2.12312
$352$	2.94145e99	0.0758799
$353$	2.22001e100	0.511982	0.255991	−	0.966679i	$-0.417598\pi$
$353$	2.22001e100	0.511982	0.255991	+	0.966679i	$0.417598\pi$
$354$	−5.01045e100	−1.03335
$355$	−1.91500e100	−0.353304
$356$	4.98803e100	0.823483
$357$	−2.56026e100	−0.378346
$358$	1.44838e100	0.191648
$359$	−1.32349e101	−1.56852	−0.784261	−	0.620431i	$-0.786958\pi$
$359$	−1.32349e101	−1.56852	−0.784261	+	0.620431i	$0.786958\pi$
$360$	1.98729e100	0.211015
$361$	2.19565e101	2.08944
$362$	4.55592e100	0.388676
$363$	1.78523e101	1.36579
$364$	−3.23714e100	−0.222155
$365$	9.90755e100	0.610096
$366$	1.28338e101	0.709339
$367$	−2.99917e100	−0.148830	−0.0744152	−	0.997227i	$-0.523709\pi$
$367$	−2.99917e100	−0.148830	−0.0744152	+	0.997227i	$0.523709\pi$
$368$	−3.63842e100	−0.162153
$369$	−2.99475e101	−1.19900
$370$	6.78457e100	0.244092
$371$	2.09575e100	0.0677749
$372$	2.46248e101	0.716023
$373$	−1.64810e101	−0.431007	−0.215504	−	0.976503i	$-0.569139\pi$
$373$	−1.64810e101	−0.431007	−0.215504	+	0.976503i	$0.569139\pi$
$374$	−1.03593e101	−0.243725
$375$	−4.94815e101	−1.04763
$376$	2.13809e101	0.407481
$377$	−1.66890e102	−2.86383
$378$	−1.73141e101	−0.267592
$379$	6.11938e101	0.852038	0.426019	−	0.904714i	$-0.359916\pi$
$379$	6.11938e101	0.852038	0.426019	+	0.904714i	$0.359916\pi$
$380$	−2.31836e101	−0.290890
$381$	8.65644e101	0.979045
$382$	−6.58439e101	−0.671448
$383$	1.31846e102	1.21259	0.606295	−	0.795240i	$-0.292655\pi$
$383$	1.31846e102	1.21259	0.606295	+	0.795240i	$0.292655\pi$
$384$	1.78363e101	0.147986
$385$	−5.34035e100	−0.0399826
$386$	−1.32208e102	−0.893427
$387$	2.00688e102	1.22444
$388$	−3.46706e101	−0.191033
$389$	−2.29643e102	−1.14299	−0.571496	−	0.820605i	$-0.693637\pi$
$389$	−2.29643e102	−1.14299	−0.571496	+	0.820605i	$0.693637\pi$
$390$	−1.37568e102	−0.618679
$391$	1.28138e102	0.520832
$392$	8.85976e101	0.325554
$393$	6.66388e102	2.21422
$394$	1.37573e102	0.413458
$395$	−1.05975e102	−0.288149
$396$	−1.57279e102	−0.387000
$397$	3.23864e102	0.721336	0.360668	−	0.932694i	$-0.382549\pi$
$397$	3.23864e102	0.721336	0.360668	+	0.932694i	$0.382549\pi$
$398$	2.69664e101	0.0543804
$399$	4.53466e102	0.828162
$400$	−1.34560e102	−0.222611
$401$	−1.11293e103	−1.66826	−0.834131	−	0.551567i	$-0.814030\pi$
$401$	−1.11293e103	−1.66826	−0.834131	+	0.551567i	$0.814030\pi$
$402$	1.26876e103	1.72366
$403$	−1.09652e103	−1.35042
$404$	−6.94985e102	−0.776089
$405$	−1.46501e102	−0.148377
$406$	−3.92848e102	−0.360949
$407$	−5.36947e102	−0.447664
$408$	−6.28160e102	−0.475328
$409$	1.65120e102	0.113430	0.0567152	−	0.998390i	$-0.481937\pi$
$409$	1.65120e102	0.113430	0.0567152	+	0.998390i	$0.481937\pi$
$410$	−2.49486e102	−0.155627
$411$	1.35633e102	0.0768448
$412$	4.85215e102	0.249743
$413$	5.25187e102	0.245633
$414$	1.94546e103	0.827005
$415$	−2.73412e102	−0.105662
$416$	−7.94233e102	−0.279101
$417$	−4.25551e102	−0.136012
$418$	1.83480e103	0.533490
$419$	−2.29768e103	−0.607906	−0.303953	−	0.952687i	$-0.598307\pi$
$419$	−2.29768e103	−0.607906	−0.303953	+	0.952687i	$0.598307\pi$
$420$	−3.23826e102	−0.0779766
$421$	1.29230e103	0.283284	0.141642	−	0.989918i	$-0.454762\pi$
$421$	1.29230e103	0.283284	0.141642	+	0.989918i	$0.454762\pi$
$422$	1.57669e102	0.0314706
$423$	−1.14323e104	−2.07822
$424$	5.14192e102	0.0851479
$425$	4.73895e103	0.715022
$426$	9.19008e103	1.26369
$427$	−1.34522e103	−0.168614
$428$	4.37747e103	0.500258
$429$	1.08875e104	1.13466
$430$	1.67189e103	0.158929
$431$	2.02718e104	1.75808	0.879042	−	0.476745i	$-0.158183\pi$
$431$	2.02718e104	1.75808	0.879042	+	0.476745i	$0.158183\pi$
$432$	−4.24802e103	−0.336185
$433$	1.37148e104	0.990644	0.495322	−	0.868710i	$-0.335050\pi$
$433$	1.37148e104	0.990644	0.495322	+	0.868710i	$0.335050\pi$
$434$	−2.58114e103	−0.170203
$435$	−1.66948e104	−1.00521
$436$	−1.55675e104	−0.856054
$437$	−2.26955e104	−1.14005
$438$	−4.75463e104	−2.18218
$439$	4.00116e104	1.67818	0.839088	−	0.543996i	$-0.183090\pi$
$439$	4.00116e104	1.67818	0.839088	+	0.543996i	$0.183090\pi$
$440$	−1.31026e103	−0.0502315
$441$	−4.73730e104	−1.66038
$442$	2.79714e104	0.896468
$443$	−5.81406e103	−0.170425	−0.0852123	−	0.996363i	$-0.527157\pi$
$443$	−5.81406e103	−0.170425	−0.0852123	+	0.996363i	$0.527157\pi$
$444$	−3.25592e104	−0.873064
$445$	−2.22190e104	−0.545134
$446$	−1.11035e104	−0.249307
$447$	−4.52637e103	−0.0930256
$448$	−1.86957e103	−0.0351771
$449$	6.83786e104	1.17812	0.589060	−	0.808089i	$-0.299498\pi$
$449$	6.83786e104	1.17812	0.589060	+	0.808089i	$0.299498\pi$
$450$	7.19490e104	1.13535
$451$	1.97449e104	0.285419
$452$	2.10394e104	0.278654
$453$	6.90147e104	0.837650
$454$	−8.06441e104	−0.897153
$455$	1.44197e104	0.147064
$456$	1.11258e105	1.04045
$457$	−1.57130e105	−1.34763	−0.673814	−	0.738901i	$-0.735345\pi$
$457$	−1.57130e105	−1.34763	−0.673814	+	0.738901i	$0.735345\pi$
$458$	−2.02191e104	−0.159065
$459$	1.49607e105	1.07982
$460$	1.62072e104	0.107343
$461$	−6.17791e104	−0.375539	−0.187769	−	0.982213i	$-0.560126\pi$
$461$	−6.17791e104	−0.375539	−0.187769	+	0.982213i	$0.560126\pi$
$462$	2.56284e104	0.143009
$463$	4.20434e104	0.215402	0.107701	−	0.994183i	$-0.465651\pi$
$463$	4.20434e104	0.215402	0.107701	+	0.994183i	$0.465651\pi$
$464$	−9.63853e104	−0.453472
$465$	−1.09690e105	−0.473997
$466$	−1.63543e105	−0.649215
$467$	5.30087e105	1.93344	0.966719	−	0.255839i	$-0.0823518\pi$
$467$	5.30087e105	1.93344	0.966719	+	0.255839i	$0.0823518\pi$
$468$	4.24675e105	1.42346
$469$	−1.32990e105	−0.409724
$470$	−9.52404e104	−0.269746
$471$	−8.89287e105	−2.31588
$472$	1.28855e105	0.308597
$473$	−1.32317e105	−0.291475
$474$	5.08573e105	1.03064
$475$	−8.39351e105	−1.56511
$476$	6.58428e104	0.112988
$477$	−2.74937e105	−0.434268
$478$	−6.99233e105	−1.01676
$479$	−3.00664e105	−0.402558	−0.201279	−	0.979534i	$-0.564510\pi$
$479$	−3.00664e105	−0.402558	−0.201279	+	0.979534i	$0.564510\pi$
$480$	−7.94508e104	−0.0979646
$481$	1.44983e106	1.64660
$482$	1.01623e106	1.06324
$483$	−3.17009e105	−0.305605
$484$	−4.59113e105	−0.407876
$485$	1.54439e105	0.126461
$486$	−5.56611e105	−0.420164
$487$	−6.93688e105	−0.482803	−0.241402	−	0.970425i	$-0.577607\pi$
$487$	−6.93688e105	−0.482803	−0.241402	+	0.970425i	$0.577607\pi$
$488$	−3.30051e105	−0.211835
$489$	1.98864e106	1.17721
$490$	−3.94654e105	−0.215512
$491$	2.37777e106	1.19798	0.598991	−	0.800756i	$-0.295569\pi$
$491$	2.37777e106	1.19798	0.598991	+	0.800756i	$0.295569\pi$
$492$	1.19728e106	0.556642
$493$	3.39451e106	1.45654
$494$	−4.95422e106	−1.96228
$495$	7.00592e105	0.256189
$496$	−6.33283e105	−0.213832
$497$	−9.63291e105	−0.300386
$498$	1.31211e106	0.377929
$499$	−1.14868e106	−0.305652	−0.152826	−	0.988253i	$-0.548837\pi$
$499$	−1.14868e106	−0.305652	−0.152826	+	0.988253i	$0.548837\pi$
$500$	1.27253e106	0.312862
$501$	−3.73091e106	−0.847666
$502$	2.36380e106	0.496379
$503$	9.01248e106	1.74948	0.874739	−	0.484594i	$-0.161032\pi$
$503$	9.01248e106	1.74948	0.874739	+	0.484594i	$0.161032\pi$
$504$	9.99656e105	0.179409
$505$	3.09578e106	0.513760
$506$	−1.28267e106	−0.196866
$507$	−1.76042e107	−2.49921
$508$	−2.22620e106	−0.292380
$509$	−3.46810e106	−0.421443	−0.210721	−	0.977546i	$-0.567581\pi$
$509$	−3.46810e106	−0.421443	−0.210721	+	0.977546i	$0.567581\pi$
$510$	2.79811e106	0.314661
$511$	4.98374e106	0.518716
$512$	−4.58700e105	−0.0441942
$513$	−2.64981e107	−2.36362
$514$	−1.10786e107	−0.915043
$515$	−2.16137e106	−0.165327
$516$	−8.02341e106	−0.568454
$517$	7.53755e106	0.494714
$518$	3.41280e106	0.207532
$519$	1.63213e107	0.919697
$520$	3.53787e106	0.184761
$521$	9.43323e106	0.456636	0.228318	−	0.973587i	$-0.426677\pi$
$521$	9.43323e106	0.456636	0.228318	+	0.973587i	$0.426677\pi$
$522$	5.15370e107	2.31278
$523$	3.57980e107	1.48951	0.744753	−	0.667340i	$-0.232567\pi$
$523$	3.57980e107	1.48951	0.744753	+	0.667340i	$0.232567\pi$
$524$	−1.71377e107	−0.661251
$525$	−1.17240e107	−0.419548
$526$	1.71530e107	0.569383
$527$	2.23030e107	0.686823
$528$	6.28793e106	0.179667
$529$	−2.18477e107	−0.579304
$530$	−2.29044e106	−0.0563667
$531$	−6.88985e107	−1.57390
$532$	−1.16619e107	−0.247320
$533$	−5.33140e107	−1.04982
$534$	1.06629e108	1.94982
$535$	−1.94992e107	−0.331164
$536$	−3.26291e107	−0.514750
$537$	3.09620e107	0.453779
$538$	−8.74387e107	−1.19070
$539$	3.12339e107	0.395248
$540$	1.89226e107	0.222550
$541$	7.30589e106	0.0798696	0.0399348	−	0.999202i	$-0.487285\pi$
$541$	7.30589e106	0.0798696	0.0399348	+	0.999202i	$0.487285\pi$
$542$	−1.20742e108	−1.22712
$543$	9.73915e107	0.920297
$544$	1.61545e107	0.141951
$545$	6.93445e107	0.566696
$546$	−6.92001e107	−0.526014
$547$	4.83608e107	0.341975	0.170987	−	0.985273i	$-0.445304\pi$
$547$	4.83608e107	0.341975	0.170987	+	0.985273i	$0.445304\pi$
$548$	−3.48812e106	−0.0229488
$549$	1.76478e108	1.08039
$550$	−4.74373e107	−0.270267
$551$	−6.01227e108	−3.18823
$552$	−7.77783e107	−0.383941
$553$	−5.33078e107	−0.244990
$554$	−2.00683e108	−0.858765
$555$	1.45033e108	0.577956
$556$	1.09440e107	0.0406183
$557$	4.46527e108	1.54372	0.771858	−	0.635796i	$-0.219328\pi$
$557$	4.46527e108	1.54372	0.771858	+	0.635796i	$0.219328\pi$
$558$	3.38615e108	1.09058
$559$	3.57275e108	1.07210
$560$	8.32791e106	0.0232868
$561$	−2.21449e108	−0.577086
$562$	−1.02918e108	−0.249981
$563$	2.57215e107	0.0582390	0.0291195	−	0.999576i	$-0.490730\pi$
$563$	2.57215e107	0.0582390	0.0291195	+	0.999576i	$0.490730\pi$
$564$	4.57059e108	0.964822
$565$	−9.37189e107	−0.184465
$566$	5.67852e108	1.04228
$567$	−7.36934e107	−0.126153
$568$	−2.36344e108	−0.377385
$569$	3.74479e108	0.557819	0.278910	−	0.960317i	$-0.410027\pi$
$569$	3.74479e108	0.557819	0.278910	+	0.960317i	$0.410027\pi$
$570$	−4.95594e108	−0.688762
$571$	6.49151e108	0.841821	0.420911	−	0.907102i	$-0.361711\pi$
$571$	6.49151e108	0.841821	0.420911	+	0.907102i	$0.361711\pi$
$572$	−2.79996e108	−0.338851
$573$	−1.40754e109	−1.58984
$574$	−1.25498e108	−0.132317
$575$	5.86773e108	0.577551
$576$	2.45266e108	0.225397
$577$	7.10731e107	0.0609903	0.0304952	−	0.999535i	$-0.490292\pi$
$577$	7.10731e107	0.0609903	0.0304952	+	0.999535i	$0.490292\pi$
$578$	3.13404e108	0.251163
$579$	−2.82620e109	−2.11543
$580$	4.29344e108	0.300192
$581$	−1.37533e108	−0.0898358
$582$	−7.41152e108	−0.452324
$583$	1.81271e108	0.103376
$584$	1.22276e109	0.651680
$585$	−1.89169e109	−0.942311
$586$	−2.06700e108	−0.0962463
$587$	5.94319e108	0.258711	0.129355	−	0.991598i	$-0.458709\pi$
$587$	5.94319e108	0.258711	0.129355	+	0.991598i	$0.458709\pi$
$588$	1.89394e109	0.770838
$589$	−3.95026e109	−1.50339
$590$	−5.73978e108	−0.204287
$591$	2.94088e109	0.978976
$592$	8.37333e108	0.260730
$593$	1.29415e108	0.0376985	0.0188493	−	0.999822i	$-0.494000\pi$
$593$	1.29415e108	0.0376985	0.0188493	+	0.999822i	$0.494000\pi$
$594$	−1.49758e109	−0.408155
$595$	−2.93293e108	−0.0747967
$596$	1.16406e108	0.0277810
$597$	5.76460e108	0.128761
$598$	3.46340e109	0.724112
$599$	9.47647e109	1.85476	0.927379	−	0.374124i	$-0.122057\pi$
$599$	9.47647e109	1.85476	0.927379	+	0.374124i	$0.122057\pi$
$600$	−2.87648e109	−0.527093
$601$	3.54023e108	0.0607420	0.0303710	−	0.999539i	$-0.490331\pi$
$601$	3.54023e108	0.0607420	0.0303710	+	0.999539i	$0.490331\pi$
$602$	8.41001e108	0.135125
$603$	1.74467e110	2.62531
$604$	−1.77487e109	−0.250154
$605$	2.04510e109	0.270008
$606$	−1.48566e110	−1.83760
$607$	3.77034e109	0.436946	0.218473	−	0.975843i	$-0.429892\pi$
$607$	3.77034e109	0.436946	0.218473	+	0.975843i	$0.429892\pi$
$608$	−2.86125e109	−0.310717
$609$	−8.39787e109	−0.854646
$610$	1.47020e109	0.140232
$611$	−2.03524e110	−1.81965
$612$	−8.63781e109	−0.723973
$613$	1.00568e109	0.0790266	0.0395133	−	0.999219i	$-0.487419\pi$
$613$	1.00568e109	0.0790266	0.0395133	+	0.999219i	$0.487419\pi$
$614$	1.07132e110	0.789346
$615$	−5.33325e109	−0.368489
$616$	−6.59091e108	−0.0427078
$617$	−5.82967e109	−0.354307	−0.177154	−	0.984183i	$-0.556689\pi$
$617$	−5.82967e109	−0.354307	−0.177154	+	0.984183i	$0.556689\pi$
$618$	1.03724e110	0.591336
$619$	−2.00864e110	−1.07429	−0.537145	−	0.843490i	$-0.680497\pi$
$619$	−2.00864e110	−1.07429	−0.537145	+	0.843490i	$0.680497\pi$
$620$	2.82093e109	0.141553
$621$	1.85243e110	0.872213
$622$	1.27548e109	0.0563579
$623$	−1.11767e110	−0.463484
$624$	−1.69783e110	−0.660849
$625$	1.87022e110	0.683334
$626$	1.22519e110	0.420260
$627$	3.92225e110	1.26319
$628$	2.28700e110	0.691609
$629$	−2.94893e110	−0.837459
$630$	−4.45292e109	−0.118766
$631$	−3.85798e110	−0.966496	−0.483248	−	0.875483i	$-0.660543\pi$
$631$	−3.85798e110	−0.966496	−0.483248	+	0.875483i	$0.660543\pi$
$632$	−1.30791e110	−0.307789
$633$	3.37048e109	0.0745154
$634$	1.05759e110	0.219681
$635$	9.91650e109	0.193551
$636$	1.09918e110	0.201611
$637$	−8.43357e110	−1.45380
$638$	−3.39793e110	−0.550551
$639$	1.26373e111	1.92473
$640$	2.04326e109	0.0292559
$641$	−2.80668e110	−0.377834	−0.188917	−	0.981993i	$-0.560498\pi$
$641$	−2.80668e110	−0.377834	−0.188917	+	0.981993i	$0.560498\pi$
$642$	9.35768e110	1.18450
$643$	1.13786e111	1.35443	0.677213	−	0.735787i	$-0.263188\pi$
$643$	1.13786e111	1.35443	0.677213	+	0.735787i	$0.263188\pi$
$644$	8.15260e109	0.0912650
$645$	3.57399e110	0.376309
$646$	1.00768e111	0.998017
$647$	−1.43322e111	−1.33534	−0.667672	−	0.744456i	$-0.732709\pi$
$647$	−1.43322e111	−1.33534	−0.667672	+	0.744456i	$0.732709\pi$
$648$	−1.80807e110	−0.158490
$649$	4.54260e110	0.374661
$650$	1.28087e111	0.994095
$651$	−5.51768e110	−0.403002
$652$	−5.11423e110	−0.351561
$653$	−2.22055e111	−1.43678	−0.718388	−	0.695642i	$-0.755120\pi$
$653$	−2.22055e111	−1.43678	−0.718388	+	0.695642i	$0.755120\pi$
$654$	−3.32784e111	−2.02694
$655$	7.63389e110	0.437739
$656$	−3.07909e110	−0.166234
$657$	−6.53808e111	−3.32367
$658$	−4.79082e110	−0.229344
$659$	3.62807e111	1.63569	0.817846	−	0.575436i	$-0.195168\pi$
$659$	3.62807e111	1.63569	0.817846	+	0.575436i	$0.195168\pi$
$660$	−2.80093e110	−0.118937
$661$	7.46944e110	0.298766	0.149383	−	0.988779i	$-0.452271\pi$
$661$	7.46944e110	0.298766	0.149383	+	0.988779i	$0.452271\pi$
$662$	1.25248e109	0.00471933
$663$	5.97943e111	2.12263
$664$	−3.37438e110	−0.112864
$665$	5.19474e110	0.163723
$666$	−4.47720e111	−1.32976
$667$	4.20306e111	1.17651
$668$	9.59488e110	0.253145
$669$	−2.37360e111	−0.590304
$670$	1.45345e111	0.340757
$671$	−1.16355e111	−0.257185
$672$	−3.99657e110	−0.0832915
$673$	5.74424e111	1.12885	0.564427	−	0.825483i	$-0.309097\pi$
$673$	5.74424e111	1.12885	0.564427	+	0.825483i	$0.309097\pi$
$674$	−3.59954e111	−0.667086
$675$	6.85084e111	1.19742
$676$	4.52733e111	0.746358
$677$	−4.22338e111	−0.656761	−0.328381	−	0.944545i	$-0.606503\pi$
$677$	−4.22338e111	−0.656761	−0.328381	+	0.944545i	$0.606503\pi$
$678$	4.49757e111	0.659789
$679$	7.76864e110	0.107520
$680$	−7.19596e110	−0.0939695
$681$	−1.72392e112	−2.12426
$682$	−2.23255e111	−0.259608
$683$	1.16037e112	1.27344	0.636719	−	0.771096i	$-0.280291\pi$
$683$	1.16037e112	1.27344	0.636719	+	0.771096i	$0.280291\pi$
$684$	1.52991e112	1.58471
$685$	1.55377e110	0.0151918
$686$	−4.14115e111	−0.382224
$687$	−4.32221e111	−0.376630
$688$	2.06340e111	0.169762
$689$	−4.89457e111	−0.380238
$690$	3.46460e111	0.254164
$691$	−1.91263e112	−1.32510	−0.662548	−	0.749019i	$-0.730525\pi$
$691$	−1.91263e112	−1.32510	−0.662548	+	0.749019i	$0.730525\pi$
$692$	−4.19740e111	−0.274656
$693$	3.52415e111	0.217817
$694$	−8.76117e111	−0.511520
$695$	−4.87495e110	−0.0268888
$696$	−2.06042e112	−1.07372
$697$	1.08440e112	0.533941
$698$	1.20869e111	0.0562374
$699$	−3.49605e112	−1.53719
$700$	3.01508e111	0.125293
$701$	−3.42936e112	−1.34695	−0.673475	−	0.739210i	$-0.735199\pi$
$701$	−3.42936e112	−1.34695	−0.673475	+	0.739210i	$0.735199\pi$
$702$	4.04367e112	1.50127
$703$	5.22307e112	1.83312
$704$	−1.61708e111	−0.0536552
$705$	−2.03595e112	−0.638699
$706$	−1.22047e112	−0.362026
$707$	1.55725e112	0.436809
$708$	2.75452e112	0.730689
$709$	−1.02083e112	−0.256110	−0.128055	−	0.991767i	$-0.540873\pi$
$709$	−1.02083e112	−0.256110	−0.128055	+	0.991767i	$0.540873\pi$
$710$	1.05278e112	0.249824
$711$	6.99337e112	1.56977
$712$	−2.74220e112	−0.582290
$713$	2.76155e112	0.554774
$714$	1.40752e112	0.267531
$715$	1.24723e112	0.224314
$716$	−7.96257e111	−0.135515
$717$	−1.49475e113	−2.40747
$718$	7.27597e112	1.10911
$719$	−1.74435e112	−0.251676	−0.125838	−	0.992051i	$-0.540162\pi$
$719$	−1.74435e112	−0.251676	−0.125838	+	0.992051i	$0.540162\pi$
$720$	−1.09253e112	−0.149210
$721$	−1.08722e112	−0.140564
$722$	−1.20707e113	−1.47746
$723$	2.17238e113	2.51752
$724$	−2.50464e112	−0.274835
$725$	1.55442e113	1.61517
$726$	−9.81443e112	−0.965758
$727$	1.06400e113	0.991593	0.495797	−	0.868439i	$-0.334876\pi$
$727$	1.06400e113	0.991593	0.495797	+	0.868439i	$0.334876\pi$
$728$	1.77964e112	0.157088
$729$	−1.72601e113	−1.44313
$730$	−5.44673e112	−0.431403
$731$	−7.26691e112	−0.545272
$732$	−7.05548e112	−0.501578
$733$	1.73758e113	1.17041	0.585205	−	0.810885i	$-0.301014\pi$
$733$	1.73758e113	1.17041	0.585205	+	0.810885i	$0.301014\pi$
$734$	1.64881e112	0.105239
$735$	−8.43649e112	−0.510284
$736$	2.00024e112	0.114659
$737$	−1.15029e113	−0.624947
$738$	1.64638e113	0.847821
$739$	3.63549e113	1.77463	0.887316	−	0.461162i	$-0.152567\pi$
$739$	3.63549e113	1.77463	0.887316	+	0.461162i	$0.152567\pi$
$740$	−3.72986e112	−0.172599
$741$	−1.05906e114	−4.64624
$742$	−1.15215e112	−0.0479241
$743$	−1.30618e113	−0.515165	−0.257582	−	0.966256i	$-0.582926\pi$
$743$	−1.30618e113	−0.515165	−0.257582	+	0.966256i	$0.582926\pi$
$744$	−1.35376e113	−0.506305
$745$	−5.18524e111	−0.0183906
$746$	9.06052e112	0.304768
$747$	1.80427e113	0.575623
$748$	5.69506e112	0.172340
$749$	−9.80858e112	−0.281562
$750$	2.72028e113	0.740786
$751$	3.68235e113	0.951366	0.475683	−	0.879617i	$-0.342201\pi$
$751$	3.68235e113	0.951366	0.475683	+	0.879617i	$0.342201\pi$
$752$	−1.17543e113	−0.288132
$753$	5.05307e113	1.17531
$754$	9.17488e113	2.02503
$755$	7.90607e112	0.165598
$756$	9.51852e112	0.189216
$757$	8.41910e113	1.58847	0.794234	−	0.607612i	$-0.207872\pi$
$757$	8.41910e113	1.58847	0.794234	+	0.607612i	$0.207872\pi$
$758$	−3.36417e113	−0.602482
$759$	−2.74196e113	−0.466135
$760$	1.27453e113	0.205690
$761$	−7.92847e113	−1.21477	−0.607387	−	0.794406i	$-0.707782\pi$
$761$	−7.92847e113	−1.21477	−0.607387	+	0.794406i	$0.707782\pi$
$762$	−4.75893e113	−0.692290
$763$	3.48820e113	0.481816
$764$	3.61980e113	0.474786
$765$	3.84767e113	0.479260
$766$	−7.24829e113	−0.857430
$767$	−1.22656e114	−1.37808
$768$	−9.80559e112	−0.104642
$769$	7.01929e113	0.711546	0.355773	−	0.934572i	$-0.384218\pi$
$769$	7.01929e113	0.711546	0.355773	+	0.934572i	$0.384218\pi$
$770$	2.93589e112	0.0282720
$771$	−2.36826e114	−2.16662
$772$	7.26821e113	0.631748
$773$	−5.67593e113	−0.468757	−0.234378	−	0.972145i	$-0.575305\pi$
$773$	−5.67593e113	−0.468757	−0.234378	+	0.972145i	$0.575305\pi$
$774$	−1.10330e114	−0.865813
$775$	1.02130e114	0.761620
$776$	1.90604e113	0.135081
$777$	7.29552e113	0.491390
$778$	1.26247e114	0.808217
$779$	−1.92066e114	−1.16875
$780$	7.56289e113	0.437472
$781$	−8.33197e113	−0.458175
$782$	−7.04448e113	−0.368284
$783$	4.90725e114	2.43921
$784$	−4.87071e113	−0.230201
$785$	−1.01873e114	−0.457836
$786$	−3.66351e114	−1.56569
$787$	−2.00796e114	−0.816119	−0.408059	−	0.912955i	$-0.633794\pi$
$787$	−2.00796e114	−0.816119	−0.408059	+	0.912955i	$0.633794\pi$
$788$	−7.56314e113	−0.292359
$789$	3.66679e114	1.34817
$790$	5.82602e113	0.203752
$791$	−4.71429e113	−0.156836
$792$	8.64651e113	0.273650
$793$	3.14174e114	0.945975
$794$	−1.78046e114	−0.510062
$795$	−4.89626e113	−0.133464
$796$	−1.48250e113	−0.0384527
$797$	−3.03995e114	−0.750349	−0.375175	−	0.926954i	$-0.622417\pi$
$797$	−3.03995e114	−0.750349	−0.375175	+	0.926954i	$0.622417\pi$
$798$	−2.49296e114	−0.585599
$799$	4.13964e114	0.925476
$800$	7.39752e113	0.157410
$801$	1.46625e115	2.96978
$802$	6.11838e114	1.17964
$803$	4.31067e114	0.791191
$804$	−6.97510e114	−1.21881
$805$	−3.63154e113	−0.0604162
$806$	6.02820e114	0.954890
$807$	−1.86917e115	−2.81932
$808$	3.82072e114	0.548777
$809$	−1.39321e115	−1.90568	−0.952840	−	0.303475i	$-0.901853\pi$
$809$	−1.39321e115	−1.90568	−0.952840	+	0.303475i	$0.901853\pi$
$810$	8.05396e113	0.104918
$811$	7.11357e114	0.882600	0.441300	−	0.897360i	$-0.354517\pi$
$811$	7.11357e114	0.882600	0.441300	+	0.897360i	$0.354517\pi$
$812$	2.15970e114	0.255229
$813$	−2.58109e115	−2.90554
$814$	2.95190e114	0.316547
$815$	2.27811e114	0.232728
$816$	3.45335e114	0.336108
$817$	1.28710e115	1.19355
$818$	−9.07757e113	−0.0802074
$819$	−9.51568e114	−0.801172
$820$	1.37156e114	0.110045
$821$	1.04051e115	0.795592	0.397796	−	0.917474i	$-0.369775\pi$
$821$	1.04051e115	0.795592	0.397796	+	0.917474i	$0.369775\pi$
$822$	−7.45653e113	−0.0543375
$823$	−3.11214e114	−0.216155	−0.108078	−	0.994142i	$-0.534470\pi$
$823$	−3.11214e114	−0.216155	−0.108078	+	0.994142i	$0.534470\pi$
$824$	−2.66750e114	−0.176595
$825$	−1.01406e115	−0.639932
$826$	−2.88725e114	−0.173689
$827$	7.37008e114	0.422673	0.211337	−	0.977413i	$-0.432218\pi$
$827$	7.37008e114	0.422673	0.211337	+	0.977413i	$0.432218\pi$
$828$	−1.06953e115	−0.584781
$829$	1.42087e115	0.740712	0.370356	−	0.928890i	$-0.379236\pi$
$829$	1.42087e115	0.740712	0.370356	+	0.928890i	$0.379236\pi$
$830$	1.50310e114	0.0747142
$831$	−4.28998e115	−2.03336
$832$	4.36634e114	0.197354
$833$	1.71537e115	0.739402
$834$	2.33949e114	0.0961750
$835$	−4.27399e114	−0.167578
$836$	−1.00869e115	−0.377235
$837$	3.22423e115	1.15019
$838$	1.26316e115	0.429854
$839$	−1.04004e115	−0.337639	−0.168820	−	0.985647i	$-0.553996\pi$
$839$	−1.04004e115	−0.337639	−0.168820	+	0.985647i	$0.553996\pi$
$840$	1.78025e114	0.0551378
$841$	7.75021e115	2.29019
$842$	−7.10451e114	−0.200312
$843$	−2.20007e115	−0.591899
$844$	−8.66796e113	−0.0222531
$845$	−2.01668e115	−0.494079
$846$	6.28500e115	1.46952
$847$	1.02873e115	0.229566
$848$	−2.82680e114	−0.0602086
$849$	1.21389e116	2.46789
$850$	−2.60527e115	−0.505597
$851$	−3.65134e115	−0.676448
$852$	−5.05230e115	−0.893563
$853$	−6.12531e115	−1.03429	−0.517144	−	0.855898i	$-0.673005\pi$
$853$	−6.12531e115	−1.03429	−0.517144	+	0.855898i	$0.673005\pi$
$854$	7.39545e114	0.119228
$855$	−6.81489e115	−1.04905
$856$	−2.40654e115	−0.353736
$857$	9.45650e115	1.32736	0.663679	−	0.748018i	$-0.268994\pi$
$857$	9.45650e115	1.32736	0.663679	+	0.748018i	$0.268994\pi$
$858$	−5.98545e115	−0.802322
$859$	−5.60615e115	−0.717686	−0.358843	−	0.933398i	$-0.616829\pi$
$859$	−5.60615e115	−0.717686	−0.358843	+	0.933398i	$0.616829\pi$
$860$	−9.19131e114	−0.112380
$861$	−2.68275e115	−0.313297
$862$	−1.11445e116	−1.24315
$863$	−1.38009e116	−1.47056	−0.735278	−	0.677766i	$-0.762948\pi$
$863$	−1.38009e116	−1.47056	−0.735278	+	0.677766i	$0.762948\pi$
$864$	2.33537e115	0.237719
$865$	1.86971e115	0.181818
$866$	−7.53979e115	−0.700491
$867$	6.69962e115	0.594697
$868$	1.41900e115	0.120352
$869$	−4.61085e115	−0.373680
$870$	9.17805e115	0.710788
$871$	3.10595e116	2.29868
$872$	8.55830e115	0.605322
$873$	−1.01916e116	−0.688934
$874$	1.24770e116	0.806137
$875$	−2.85135e115	−0.176089
$876$	2.61389e116	1.54303
$877$	−9.18956e115	−0.518574	−0.259287	−	0.965800i	$-0.583488\pi$
$877$	−9.18956e115	−0.518574	−0.259287	+	0.965800i	$0.583488\pi$
$878$	−2.19966e116	−1.18665
$879$	−4.41860e115	−0.227890
$880$	7.20321e114	0.0355190
$881$	1.86628e116	0.879888	0.439944	−	0.898025i	$-0.354998\pi$
$881$	1.86628e116	0.879888	0.439944	+	0.898025i	$0.354998\pi$
$882$	2.60436e116	1.17406
$883$	−2.99656e116	−1.29174	−0.645869	−	0.763448i	$-0.723505\pi$
$883$	−2.99656e116	−1.29174	−0.645869	+	0.763448i	$0.723505\pi$
$884$	−1.53774e116	−0.633898
$885$	−1.22699e116	−0.483706
$886$	3.19631e115	0.120508
$887$	1.46162e116	0.527048	0.263524	−	0.964653i	$-0.415115\pi$
$887$	1.46162e116	0.527048	0.263524	+	0.964653i	$0.415115\pi$
$888$	1.78996e116	0.617349
$889$	4.98824e115	0.164561
$890$	1.22150e116	0.385468
$891$	−6.37410e115	−0.192420
$892$	6.10424e115	0.176287
$893$	−7.33203e116	−2.02578
$894$	2.48840e115	0.0657791
$895$	3.54689e115	0.0897093
$896$	1.02781e115	0.0248740
$897$	7.40368e116	1.71453
$898$	−3.75915e116	−0.833057
$899$	7.31560e116	1.55147
$900$	−3.95544e116	−0.802815
$901$	9.95546e115	0.193389
$902$	−1.08549e116	−0.201821
$903$	1.79780e116	0.319945
$904$	−1.15665e116	−0.197038
$905$	1.11568e116	0.181937
$906$	−3.79412e116	−0.592308
$907$	−4.20858e116	−0.628996	−0.314498	−	0.949258i	$-0.601836\pi$
$907$	−4.20858e116	−0.628996	−0.314498	+	0.949258i	$0.601836\pi$
$908$	4.43346e116	0.634383
$909$	−2.04293e117	−2.79885
$910$	−7.92730e115	−0.103990
$911$	−2.02174e116	−0.253951	−0.126975	−	0.991906i	$-0.540527\pi$
$911$	−2.02174e116	−0.253951	−0.126975	+	0.991906i	$0.540527\pi$
$912$	−6.11648e116	−0.735707
$913$	−1.18959e116	−0.137025
$914$	8.63833e116	0.952917
$915$	3.14283e116	0.332038
$916$	1.11155e116	0.112476
$917$	3.84003e116	0.372174
$918$	−8.22475e116	−0.763548
$919$	−8.04666e116	−0.715571	−0.357786	−	0.933804i	$-0.616468\pi$
$919$	−8.04666e116	−0.715571	−0.357786	+	0.933804i	$0.616468\pi$
$920$	−8.90999e115	−0.0759028
$921$	2.29015e117	1.86899
$922$	3.39634e116	0.265546
$923$	2.24975e117	1.68526
$924$	−1.40893e116	−0.101122
$925$	−1.35038e117	−0.928661
$926$	−2.31136e116	−0.152312
$927$	1.42630e117	0.900664
$928$	5.29884e116	0.320653
$929$	3.24131e117	1.87975	0.939875	−	0.341518i	$-0.110941\pi$
$929$	3.24131e117	1.87975	0.939875	+	0.341518i	$0.110941\pi$
$930$	6.03028e116	0.335167
$931$	−3.03822e117	−1.61848
$932$	8.99087e116	0.459064
$933$	2.72659e116	0.133443
$934$	−2.91418e117	−1.36715
$935$	−2.53684e116	−0.114086
$936$	−2.33468e117	−1.00654
$937$	−1.22958e116	−0.0508209	−0.0254105	−	0.999677i	$-0.508089\pi$
$937$	−1.22958e116	−0.0508209	−0.0254105	+	0.999677i	$0.508089\pi$
$938$	7.31120e116	0.289719
$939$	2.61908e117	0.995081
$940$	5.23589e116	0.190740
$941$	−2.88504e117	−1.00777	−0.503885	−	0.863771i	$-0.668096\pi$
$941$	−2.88504e117	−1.00777	−0.503885	+	0.863771i	$0.668096\pi$
$942$	4.88891e117	1.63758
$943$	1.34269e117	0.431285
$944$	−7.08387e116	−0.218211
$945$	−4.23998e116	−0.125259
$946$	7.27423e116	0.206104
$947$	−1.11408e117	−0.302755	−0.151377	−	0.988476i	$-0.548371\pi$
$947$	−1.11408e117	−0.302755	−0.151377	+	0.988476i	$0.548371\pi$
$948$	−2.79591e117	−0.728775
$949$	−1.16394e118	−2.91015
$950$	4.61438e117	1.10670
$951$	2.26080e117	0.520154
$952$	−3.61974e116	−0.0798948
$953$	−5.00821e117	−1.06051	−0.530253	−	0.847840i	$-0.677903\pi$
$953$	−5.00821e117	−1.06051	−0.530253	+	0.847840i	$0.677903\pi$
$954$	1.51148e117	0.307074
$955$	−1.61242e117	−0.314301
$956$	3.84408e117	0.718961
$957$	−7.26373e117	−1.30358
$958$	1.65292e117	0.284651
$959$	7.81582e115	0.0129163
$960$	4.36785e116	0.0692714
$961$	−1.76354e117	−0.268417
$962$	−7.97053e117	−1.16432
$963$	1.28677e118	1.80411
$964$	−5.58677e117	−0.751827
$965$	−3.23759e117	−0.418208
$966$	1.74278e117	0.216095
$967$	−4.13417e117	−0.492088	−0.246044	−	0.969259i	$-0.579131\pi$
$967$	−4.13417e117	−0.492088	−0.246044	+	0.969259i	$0.579131\pi$
$968$	2.52400e117	0.288412
$969$	2.15411e118	2.36308
$970$	−8.49036e116	−0.0894216
$971$	1.06804e118	1.08001	0.540006	−	0.841661i	$-0.318422\pi$
$971$	1.06804e118	1.08001	0.540006	+	0.841661i	$0.318422\pi$
$972$	3.06000e117	0.297101
$973$	−2.45222e116	−0.0228614
$974$	3.81359e117	0.341394
$975$	2.73811e118	2.35379
$976$	1.81448e117	0.149790
$977$	1.22999e118	0.975142	0.487571	−	0.873083i	$-0.337883\pi$
$977$	1.22999e118	0.975142	0.487571	+	0.873083i	$0.337883\pi$
$978$	−1.09326e118	−0.832416
$979$	−9.66725e117	−0.706946
$980$	2.16963e117	0.152390
$981$	−4.57611e118	−3.08724
$982$	−1.30719e118	−0.847101
$983$	9.18582e117	0.571813	0.285906	−	0.958258i	$-0.407705\pi$
$983$	9.18582e117	0.571813	0.285906	+	0.958258i	$0.407705\pi$
$984$	−6.58214e117	−0.393605
$985$	3.36897e117	0.193538
$986$	−1.86615e118	−1.02993
$987$	−1.02413e118	−0.543035
$988$	2.72361e118	1.38754
$989$	−8.99783e117	−0.440437
$990$	−3.85155e117	−0.181153
$991$	5.64226e117	0.255002	0.127501	−	0.991838i	$-0.459304\pi$
$991$	5.64226e117	0.255002	0.127501	+	0.991838i	$0.459304\pi$
$992$	3.48151e117	0.151202
$993$	2.67742e116	0.0111743
$994$	5.29575e117	0.212405
$995$	6.60371e116	0.0254552
$996$	−7.21338e117	−0.267236
$997$	2.34284e118	0.834225	0.417113	−	0.908855i	$-0.363042\pi$
$997$	2.34284e118	0.834225	0.417113	+	0.908855i	$0.363042\pi$
$998$	6.31492e117	0.216128
$999$	−4.26310e118	−1.40245

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.80.a.b.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.80.a.b.1.1	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 80 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-5.49756e11 q^{2} -1.17521e19 q^{3} +3.02231e23 q^{4} -1.34628e27 q^{5} +6.46078e30 q^{6} -6.77209e32 q^{7} -1.66153e35 q^{8} +8.88420e37 q^{9} +O(q^{10})\)	\(q-5.49756e11 q^{2} -1.17521e19 q^{3} +3.02231e23 q^{4} -1.34628e27 q^{5} +6.46078e30 q^{6} -6.77209e32 q^{7} -1.66153e35 q^{8} +8.88420e37 q^{9} +7.40123e38 q^{10} -5.85751e40 q^{11} -3.55185e42 q^{12} +1.58161e44 q^{13} +3.72300e44 q^{14} +1.58215e46 q^{15} +9.13439e46 q^{16} -3.21696e48 q^{17} -4.88414e49 q^{18} +5.69780e50 q^{19} -4.06887e50 q^{20} +7.95862e51 q^{21} +3.22020e52 q^{22} -3.98321e53 q^{23} +1.95265e54 q^{24} -1.47312e55 q^{25} -8.69498e55 q^{26} -4.65058e56 q^{27} -2.04674e56 q^{28} -1.05519e58 q^{29} -8.69799e57 q^{30} -6.93296e58 q^{31} -5.02168e58 q^{32} +6.88380e59 q^{33} +1.76854e60 q^{34} +9.11710e59 q^{35} +2.68508e61 q^{36} +9.16682e61 q^{37} -3.13240e62 q^{38} -1.85872e63 q^{39} +2.23688e62 q^{40} -3.37087e63 q^{41} -4.37530e63 q^{42} +2.25894e64 q^{43} -1.77032e64 q^{44} -1.19606e65 q^{45} +2.18980e65 q^{46} -1.28682e66 q^{47} -1.07348e66 q^{48} -5.33228e66 q^{49} +8.09854e66 q^{50} +3.78060e67 q^{51} +4.78012e67 q^{52} -3.09468e67 q^{53} +2.55668e68 q^{54} +7.88582e67 q^{55} +1.12521e68 q^{56} -6.69610e69 q^{57} +5.80098e69 q^{58} -7.75517e69 q^{59} +4.78177e69 q^{60} +1.98642e70 q^{61} +3.81143e70 q^{62} -6.01646e70 q^{63} +2.76070e70 q^{64} -2.12928e71 q^{65} -3.78441e71 q^{66} +1.96379e72 q^{67} -9.72266e71 q^{68} +4.68111e72 q^{69} -5.01218e71 q^{70} +1.42244e73 q^{71} -1.47614e73 q^{72} -7.35923e73 q^{73} -5.03951e73 q^{74} +1.73122e74 q^{75} +1.72205e74 q^{76} +3.96676e73 q^{77} +1.02184e75 q^{78} +7.87169e74 q^{79} -1.22974e74 q^{80} +1.08819e75 q^{81} +1.85316e75 q^{82} +2.03088e75 q^{83} +2.40535e75 q^{84} +4.33091e75 q^{85} -1.24186e76 q^{86} +1.24007e77 q^{87} +9.73246e75 q^{88} +1.65040e77 q^{89} +6.57540e76 q^{90} -1.07108e77 q^{91} -1.20385e77 q^{92} +8.14768e77 q^{93} +7.07436e77 q^{94} -7.67080e77 q^{95} +5.90152e77 q^{96} -1.14716e78 q^{97} +2.93145e78 q^{98} -5.20393e78 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2199023255552 q^{2} + 43\!\cdots\!88 q^{3}+ \cdots + 11\!\cdots\!68 q^{9}+O(q^{10}) \) 4 * q - 2199023255552 * q^2 + 4397166235394547888 * q^3 + 1208925819614629174706176 * q^4 - 2086014264921085269083726280 * q^5 - 2417367702540162666965231468544 * q^6 + 2573657218644254612276267065505504 * q^7 - 664613997892457936451903530140172288 * q^8 + 112831132354410260252452789557864274068 * q^9	\( 4 q - 2199023255552 q^{2} + 43\!\cdots\!88 q^{3}+ \cdots - 24\!\cdots\!24 q^{99}+O(q^{100}) \) 4 * q - 2199023255552 * q^2 + 4397166235394547888 * q^3 + 1208925819614629174706176 * q^4 - 2086014264921085269083726280 * q^5 - 2417367702540162666965231468544 * q^6 + 2573657218644254612276267065505504 * q^7 - 664613997892457936451903530140172288 * q^8 + 112831132354410260252452789557864274068 * q^9 + 1146798469993669280197371425077214576640 * q^10 - 197159815504598633763217332606735329596272 * q^11 + 1328961948776531811985383516987716190339072 * q^12 + 170659994114464310607333330726054349201117208 * q^13 - 1414883018904498562307037076903427761663639552 * q^14 - 59366752746116883766669164021489296326782488160 * q^15 + 365375409332725729550921208179070754913983135744 * q^16 + 2796535717206368263389203662758684400077797212104 * q^17 - 62029570999403462291345079671679661661291632656384 * q^18 + 684695990053883053631017856536943728062103032667760 * q^19 - 630459126236882801342409049071558512824740552376320 * q^20 + 45478844539030123008167232224769119704272628301033088 * q^21 + 108389754838738543311270380964644181752802447810625536 * q^22 + 488013222626121609525538789113144096441523639094824608 * q^23 - 730604557775824812131947908541401788318211250046631936 * q^24 - 1126158160782455808180245842925474538931659342186424100 * q^25 - 93821323962518616911063366814611886711982353282922184704 * q^26 + 90964799281766581383421329970064862000231385703676280800 * q^27 + 777840165614153097265631047162836375890408246806027698176 * q^28 + 3688955716580217982904251654950665317367915182498635788760 * q^29 + 32637217473829146466723501353466415224010715590746523566080 * q^30 + 47913642648243257357880153903864424303169229638564126887808 * q^31 - 200867255532373784442745261542645325315275374222849104412672 * q^32 - 1436330994448132246142996248045289777329665443300928101553984 * q^33 - 1537411769279648790296184812932091217704898416858451884900352 * q^34 - 7972883232568194700190580853845272700117553615578992904761280 * q^35 + 34101117289900531974463531653168456220619851696334705359060992 * q^36 - 38544494660546044616136325697019592074980910779612167168904776 * q^37 - 376415601277922431123690975362328720360838397733177450697850880 * q^38 - 1630430927936849113215375152201441675512550245915136857855917024 * q^39 + 346598570067474839136065505742950780970580128274082494058332160 * q^40 - 12579033250871855934974364481604046809757294442784672679492978072 * q^41 - 25002259194240329456503731622940248355911696642675347964657926144 * q^42 - 27881137628994939802008918876181036324603361539085263748281837552 * q^43 - 59587897888491494069322986810445784691835708121009085238076243968 * q^44 - 1135438665665771435983146357768830772915834005948410169448283574760 * q^45 - 268288106392929222173577110530610526457832192809366877979650555904 * q^46 + 576521573667121444294826737512354596485517945866563824315674561344 * q^47 + 401654103290330888644103718906997727081296916501704017928853127168 * q^48 + 8503633478015001303779478851572586384147456200881468883106419562532 * q^49 + 619111996247572155737523861581422862078995923674056274519837900800 * q^50 + 49232145152944155726126332673453135974534372921258319898205217633888 * q^51 + 51578818315064139446293721734708447790185110870946434382918584369152 * q^52 + 105260874204831629761192832713944871847534780950247243530744550109048 * q^53 - 50008427264306144786882182247712414885087609091846601344884827750400 * q^54 + 1706371452310384568720710819629526373211333934635788847603849120131040 * q^55 - 427622153321985447359103023662926825094203686415434933675018093068288 * q^56 - 3821140729633100507759495557501687754299260740915493042180144734143680 * q^57 - 2028024852365347993231980538542973956036692033092289571499438642298880 * q^58 - 22994083684412863891816921299052701325384953970436261646797889586232880 * q^59 - 17942500055364597755669937995231998671549764789224145784576882549719040 * q^60 - 23646778479353101184296000685935209544077325117960260112218279494132392 * q^61 - 26340803610423759642189648499781687091197367097746793648886991504277504 * q^62 + 296052075404662580137809311474829180309942987769431307228777293972598368 * q^63 + 110427941548649020598956093796432407239217743554726184882600387580788736 * q^64 + 82132500368390587233984346712328863046834885947481304582705463914927440 * q^65 + 789631314865393352379800451175068610620676517068650045775581191488929792 * q^66 + 2983897377193475990481005659832229621500411081115555050468937379296200624 * q^67 + 845201058501323396184073718414746835063213424564380916075080711537688576 * q^68 + 643705029211491925644175845796189209393168474013641254367041007578645376 * q^69 + 4383138910554516265866120926017177867674433041208106320712414756748656640 * q^70 - 16499813603455772357667749355219751026230120653663304246848158193765849632 * q^71 - 18747287490199415798185366476162474783535363057168343371131250932392656896 * q^72 - 51054101367263816819239972529705907616909197826293748520432769719012535832 * q^73 + 21190060033010161040443186271526854737062885327709199558928757895450329088 * q^74 + 460262000986235535329966978224762375148848884176930915586953670808542094800 * q^75 + 206936665240685139008136354558917581356970270387844823668726004106857021440 * q^76 + 714443940797159208758465775389654529345067448576374493435847369953921324928 * q^77 + 896338881776089560901969623433755443248364460001570610669486630165714829312 * q^78 + 3793482818758144309481153181998416908055274731698143035904870248402594032320 * q^79 - 190544578979861625266209566883798244711206501002837662257491320768645038080 * q^80 + 10503648529690173875799214665504367224948242302604410591535224882970590535844 * q^81 + 6915396662757271645124914949999791957652571306137947178046339927153297063936 * q^82 + 19346063777388756720202955274004150860046151063944560371597113890413092234608 * q^83 + 13745137352368323402233469673278639366497088684052943034064122446804913487872 * q^84 + 30655188804191738921148634717047425623385547547695664063843774112286102804720 * q^85 + 15327817509351455718286978774209871921863613181700535494963823165007961522176 * q^86 + 138979180900031985924221810974428938836250542065413584799944105485284337733920 * q^87 + 32758793301562677990645783707123711543358950986846160846900971750025890627584 * q^88 + 459737633766523870607866690314569291936758726488822645779886714468574569430440 * q^89 + 624214007762990897172297115366226393322484430862475666044697128566805894266880 * q^90 + 1085896524691399091167300270848714222149318633472628260999900307465809641228608 * q^91 + 147492946286515140464413660808083125510365694870041229233692376462835163594752 * q^92 + 2601718925395081722296014880082930112779863466567237516827989872206913506290176 * q^93 - 316946086955358898394440527309048241646153742735102720682561513107408103145472 * q^94 - 3072347992266807812950710777377746192504934105084754288221571876169908708511200 * q^95 - 220811678455830676447365536760004109230144485073979070115356395004657804509184 * q^96 + 876722878175671412672813582974525849228585033511787690974854054652742606089864 * q^97 - 4674921943711381196432668526518770776326171804720424348849116020317384570044416 * q^98 - 24079215890709128892364067000577259961482799185203811654942166618829711668703024 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more