LMFDB - Embedded newform 2.84.a.a.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2,84,Mod(1,2)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2.1"); S:= CuspForms(chi, 84); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 84, names="a")

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 84 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-6597069766656] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$87.2544256533$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 287609867501924274375802127400x - 41230865304567060522794640394926417995512500 $ x^3 - x^2 - 287609867501924274375802127400*x - 41230865304567060522794640394926417995512500
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{7}\cdot 5^{3}\cdot 7\cdot 11\cdot 17 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.56747e14$ 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)

$f(q)$	$=$	\(q-2.19902e12 q^{2} -7.32556e17 q^{3} +4.83570e24 q^{4} -1.23719e29 q^{5} +1.61091e30 q^{6} +6.61589e34 q^{7} -1.06338e37 q^{8} -3.99030e39 q^{9} +2.72062e41 q^{10} -2.35451e43 q^{11} -3.54242e42 q^{12} +2.17555e46 q^{13} -1.45485e47 q^{14} +9.06313e46 q^{15} +2.33840e49 q^{16} -2.06003e51 q^{17} +8.77477e51 q^{18} -1.54338e53 q^{19} -5.98270e53 q^{20} -4.84651e52 q^{21} +5.17762e55 q^{22} +3.09757e56 q^{23} +7.78987e54 q^{24} +4.96671e57 q^{25} -4.78409e58 q^{26} +5.84663e57 q^{27} +3.19925e59 q^{28} -4.67177e59 q^{29} -1.99300e59 q^{30} -1.70498e61 q^{31} -5.14220e61 q^{32} +1.72481e61 q^{33} +4.53006e63 q^{34} -8.18513e63 q^{35} -1.92959e64 q^{36} -9.03184e64 q^{37} +3.39393e65 q^{38} -1.59371e64 q^{39} +1.31561e66 q^{40} -8.21191e66 q^{41} +1.06576e65 q^{42} -5.19673e67 q^{43} -1.13857e68 q^{44} +4.93677e68 q^{45} -6.81164e68 q^{46} -3.72927e69 q^{47} -1.71301e67 q^{48} -9.52692e69 q^{49} -1.09219e70 q^{50} +1.50909e69 q^{51} +1.05203e71 q^{52} -4.87207e71 q^{53} -1.28569e70 q^{54} +2.91298e72 q^{55} -7.03522e71 q^{56} +1.13061e71 q^{57} +1.02733e72 q^{58} +2.59897e73 q^{59} +4.38266e71 q^{60} -2.95096e73 q^{61} +3.74928e73 q^{62} -2.63994e74 q^{63} +1.13078e74 q^{64} -2.69158e75 q^{65} -3.79289e73 q^{66} +9.82765e75 q^{67} -9.96170e75 q^{68} -2.26915e74 q^{69} +1.79993e76 q^{70} -2.74633e76 q^{71} +4.24322e76 q^{72} +1.97027e77 q^{73} +1.98612e77 q^{74} -3.63839e75 q^{75} -7.46332e77 q^{76} -1.55772e78 q^{77} +3.50461e76 q^{78} +2.44890e78 q^{79} -2.89306e78 q^{80} +1.59204e79 q^{81} +1.80582e79 q^{82} -4.50780e79 q^{83} -2.34363e77 q^{84} +2.54866e80 q^{85} +1.14277e80 q^{86} +3.42233e77 q^{87} +2.50374e80 q^{88} +1.00507e81 q^{89} -1.08561e81 q^{90} +1.43932e81 q^{91} +1.49790e81 q^{92} +1.24899e79 q^{93} +8.20075e81 q^{94} +1.90946e82 q^{95} +3.76695e79 q^{96} +2.37614e82 q^{97} +2.09499e82 q^{98} +9.39519e82 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6597069766656 q^{2} - 10\!\cdots\!76 q^{3} + 14\!\cdots\!12 q^{4} - 30\!\cdots\!50 q^{5} + 22\!\cdots\!52 q^{6} - 56\!\cdots\!88 q^{7} - 31\!\cdots\!24 q^{8} - 12\!\cdots\!89 q^{9} + 66\!\cdots\!00 q^{10}+ \cdots + 19\!\cdots\!32 q^{99}+O(q^{100}) $ 3 * q - 6597069766656 * q^2 - 101702746285870676076 * q^3 + 14507109835375550096474112 * q^4 - 3017971800730183156270503750 * q^5 + 223646704236134410563496760573952 * q^6 - 56868150843977452944646463510381688 * q^7 - 31901471898837980949691369446728269824 * q^8 - 1296874291714430512157132519227131713889 * q^9 + 6636590174405819175051197919076024320000 * q^10 - 14950728458111344172644916593801016887110564 * q^11 - 491804303642819560873193225250337807090581504 * q^12 - 1247981540309661732670825900285957005746323326 * q^13 + 125054386206145514986821355038283113695885131776 * q^14 + 4906492677986416590677954813004295766551257495000 * q^15 + 70152078591883340073776871970381584943484762062848 * q^16 + 308707077121944230069182989402617524752248119191702 * q^17 + 2851856727007561124341460266607934416403294194761728 * q^18 - 115503389070558091326292857695805111426543766855575900 * q^19 - 14594016131086299949534512224284046843955527024640000 * q^20 + 11732509177487968088847123014707541440900722409128681696 * q^21 + 32876999566829941323832368430603818937182001313850851328 * q^22 + 194663684763812875191113719688319482770211677377322471704 * q^23 + 1081489100891117403739876406035948694736079088282876510208 * q^24 + 12909879973100417219963359678562824650000813226633695703125 * q^25 + 2744340429640551861577672691219426502524181891794916605952 * q^26 - 290348404273186317953555961767716089388521032516233322490360 * q^27 - 274997503476095232555763502532521370272192681344292043620352 * q^28 - 13486329927712179588984433941095898960588114051806442043586670 * q^29 - 10789491502087740615267140807689853862322637644134340362240000 * q^30 - 15259967576282197636337376987931730029636327543719637765688544 * q^31 - 154266052248863066452028360864751609842131487403148112188932096 * q^32 - 1336547007031971436844230453948912193833625845633434107312028912 * q^33 - 678854041744640139306516867544963504950976601295805462823829504 * q^34 - 4715426532246777190495790364493797502235361786948801169983690000 * q^35 - 6271299264192038386568991427565833816353277190742157451493113856 * q^36 - 14494063415216183355357089013103312323277748587162249391027196198 * q^37 + 253994638661227949421879853425594813422920389098161789821832396800 * q^38 + 2251057512970717018303362982262318489471334094923390545655007255992 * q^39 + 32092580864159798905291356378425445483172353970827768920801280000 * q^40 - 14818758269141418586845700862345328527833540370975401597391422024914 * q^41 - 25800060527273309376046088034231202556535459599350794106835872776192 * q^42 - 185244954670444550871541201943532654714303102292687444038114532088196 * q^43 - 72297286620232071362282991511381118908365913109923040397065302573056 * q^44 - 445304744251191879515880421159304247588651697718013601376522535738750 * q^45 - 428069969807068049003296346049660667749219654314446370823457480900608 * q^46 - 3448406958823523161683735769272979667242315508968779579731926344222288 * q^47 - 2378219683485590377451108994563285321843377682147559120972784720674816 * q^48 - 24204657151984474899244957119159079945630782364557535531639947732611781 * q^49 - 28389126287232845662053308486508750926405703261079531118867251200000000 * q^50 - 159771856978893944372170339388872603934388296478829119559446399433647384 * q^51 - 6034868425931140751804427864360828512367115609300263711544913380245504 * q^52 - 38228075067609946992767570273872110566199949304778310964597335131494166 * q^53 + 638482893209150405286492417381461479698795761902271851111176947336478720 * q^54 + 1632368017260468921889695841941301488454386228416677729923288387359805000 * q^55 + 604725905362675374903561594720047340410969182507153225534677647364194304 * q^56 + 13669697388868679820702878590004238254426621204184980921073833602893558000 * q^57 + 29656753143086005983010235202600589534948527502759279769253966946070691840 * q^58 + 31613062218678070684199282229341608500802570309765108219439478779674808460 * q^59 + 23726342728671621972532883493096933196643847824391924780213039771156480000 * q^60 - 300977969222767422409550493089091515367954112401531859539082731681256713294 * q^61 + 33557023579214041146919698117421960784890438437795765451058589389750796288 * q^62 - 992074289040538657756858982598619777914871239570401795427028157894987504856 * q^63 + 339234636437449791279993120142640355038876908200118839959348390648182996992 * q^64 - 1917243958686383471256365173175992694077398080707307194070034549472858042500 * q^65 + 2939097950601727665997874813950879706773010366513123274278972745956588519424 * q^66 - 982637701678785800107254732493330334728874481890572467358891175920869750828 * q^67 + 1492815824921931868984511521678326816398325035943278430620923662929869406208 * q^68 - 21655460830208580430272460899997906856840259134834774174059414577437293487968 * q^69 + 10369332604257585886504029000280463291877051274072688973561080526541946880000 * q^70 + 81323855968755668931344497395237657205614815488847595977459622574528389719496 * q^71 + 13790732924484438391751897000498999873642596104530083953994562754930920128512 * q^72 + 548873577024651694456863478198166388574208592802271833905358733692520264564814 * q^73 + 31872782517505831055973500781076296651648875369662498089091954440696596791296 * q^74 + 912138201967791367839128382755536641522919078982168357289238136440309354687500 * q^75 - 558540117201567368175675431579752086015316422649958308352817055257239067033600 * q^76 - 3005028120885098102302957975353158884875680002579185981596130718386560350748256 * q^77 - 4950127820607654604433191636804447234772736136799089673740211744321710099267584 * q^78 - 4067605044230191215111847191307608889794835491462832667642191199625939386072880 * q^79 - 70572331650970498465875444222370963622121563461652994848505196398048706560000 * q^80 + 33808691764431685386797752948754870665430100591880108642034455139043697722146523 * q^81 + 32586794052245482920728996353009758149335491392120349430406306052065140332822528 * q^82 + 52320856384188709336165772408250585231532944867594284635669359634811993777696484 * q^83 + 56734933094123202469789754314629091063332551702292952842490677050041020117417984 * q^84 + 316267518620820766744316449951643581834460413806947373196136097716975356986172500 * q^85 + 407357963293983643532635012845570248041467928462558818351888431524425936710664192 * q^86 + 575303708654380961743785855428949551793413321741844564188457223801420243612082040 * q^87 + 158983414591198780636847931616474888961699234615448121130128552410941527437606912 * q^88 + 733253478112862467624920912575255942772815303482379067262950255952136468291966430 * q^89 + 979235488416006723349237105421270092547658702046078078973616575080920294359040000 * q^90 + 3958486486193561239681510386291189813367736615785635650689290525519286213694821296 * q^91 + 941335818609185126459229799669550776258775216538097901072710896698703865096175616 * q^92 + 13541048382265560471940050480602442790047804383299002720803504054466709325709234048 * q^93 + 7583127097060275514844244697156018876046698300587265525750399024903969543318142976 * q^94 + 51788977142106604382125904089728054618147393900592501799173468378425492743926275000 * q^95 + 5229760390796329962703262192937345156932680488448025329051964457649576842658578432 * q^96 + 117078360112868492279222552244621773215209350988306910045991279988287119545107278182 * q^97 + 53226603969876900450298872790891839174622038193494100284800792964463079454368858112 * q^98 + 198409433299529730956797285182513284269146472820417337852908952084356577918325681932 * q^99

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 $

$2$	−2.19902e12	−0.707107
$2$	−2.19902e12	−0.707107
$3$	−7.32556e17	−0.0115960	−0.00579801	−	0.999983i	$-0.501846\pi$
$3$	−7.32556e17	−0.0115960	−0.00579801	+	0.999983i	$0.501846\pi$
$4$	4.83570e24	0.500000
$5$	−1.23719e29	−1.21670	−0.608348	−	0.793670i	$-0.708168\pi$
$5$	−1.23719e29	−1.21670	−0.608348	+	0.793670i	$0.708168\pi$
$6$	1.61091e30	0.00819962
$7$	6.61589e34	0.561073	0.280537	−	0.959843i	$-0.409488\pi$
$7$	6.61589e34	0.561073	0.280537	+	0.959843i	$0.409488\pi$
$8$	−1.06338e37	−0.353553
$9$	−3.99030e39	−0.999866
$10$	2.72062e41	0.860334
$11$	−2.35451e43	−1.42595	−0.712974	−	0.701191i	$-0.752652\pi$
$11$	−2.35451e43	−1.42595	−0.712974	+	0.701191i	$0.752652\pi$
$12$	−3.54242e42	−0.00579801
$13$	2.17555e46	1.28505	0.642525	−	0.766265i	$-0.277887\pi$
$13$	2.17555e46	1.28505	0.642525	+	0.766265i	$0.277887\pi$
$14$	−1.45485e47	−0.396739
$15$	9.06313e46	0.0141088
$16$	2.33840e49	0.250000
$17$	−2.06003e51	−1.77928	−0.889638	−	0.456666i	$-0.849043\pi$
$17$	−2.06003e51	−1.77928	−0.889638	+	0.456666i	$0.849043\pi$
$18$	8.77477e51	0.707012
$19$	−1.54338e53	−1.31886	−0.659429	−	0.751767i	$-0.729202\pi$
$19$	−1.54338e53	−1.31886	−0.659429	+	0.751767i	$0.729202\pi$
$20$	−5.98270e53	−0.608348
$21$	−4.84651e52	−0.00650621
$22$	5.17762e55	1.00830
$23$	3.09757e56	0.953491	0.476745	−	0.879041i	$-0.341816\pi$
$23$	3.09757e56	0.953491	0.476745	+	0.879041i	$0.341816\pi$
$24$	7.78987e54	0.00409981
$25$	4.96671e57	0.480350
$26$	−4.78409e58	−0.908668
$27$	5.84663e57	0.0231905
$28$	3.19925e59	0.280537
$29$	−4.67177e59	−0.0954914	−0.0477457	−	0.998860i	$-0.515204\pi$
$29$	−4.67177e59	−0.0954914	−0.0477457	+	0.998860i	$0.515204\pi$
$30$	−1.99300e59	−0.00997645
$31$	−1.70498e61	−0.218881	−0.109441	−	0.993993i	$-0.534906\pi$
$31$	−1.70498e61	−0.218881	−0.109441	+	0.993993i	$0.534906\pi$
$32$	−5.14220e61	−0.176777
$33$	1.72481e61	0.0165353
$34$	4.53006e63	1.25814
$35$	−8.18513e63	−0.682656
$36$	−1.92959e64	−0.499933
$37$	−9.03184e64	−0.750593	−0.375297	−	0.926905i	$-0.622459\pi$
$37$	−9.03184e64	−0.750593	−0.375297	+	0.926905i	$0.622459\pi$
$38$	3.39393e65	0.932574
$39$	−1.59371e64	−0.0149015
$40$	1.31561e66	0.430167
$41$	−8.21191e66	−0.963638	−0.481819	−	0.876271i	$-0.660024\pi$
$41$	−8.21191e66	−0.963638	−0.481819	+	0.876271i	$0.660024\pi$
$42$	1.06576e65	0.00460059
$43$	−5.19673e67	−0.844869	−0.422435	−	0.906393i	$-0.638824\pi$
$43$	−5.19673e67	−0.844869	−0.422435	+	0.906393i	$0.638824\pi$
$44$	−1.13857e68	−0.712974
$45$	4.93677e68	1.21653
$46$	−6.81164e68	−0.674220
$47$	−3.72927e69	−1.51204	−0.756019	−	0.654550i	$-0.772858\pi$
$47$	−3.72927e69	−1.51204	−0.756019	+	0.654550i	$0.772858\pi$
$48$	−1.71301e67	−0.00289900
$49$	−9.52692e69	−0.685197
$50$	−1.09219e70	−0.339659
$51$	1.50909e69	0.0206325
$52$	1.05203e71	0.642525
$53$	−4.87207e71	−1.34979	−0.674893	−	0.737916i	$-0.735810\pi$
$53$	−4.87207e71	−1.34979	−0.674893	+	0.737916i	$0.735810\pi$
$54$	−1.28569e70	−0.0163981
$55$	2.91298e72	1.73495
$56$	−7.03522e71	−0.198369
$57$	1.13061e71	0.0152935
$58$	1.02733e72	0.0675226
$59$	2.59897e73	0.840316	0.420158	−	0.907451i	$-0.361975\pi$
$59$	2.59897e73	0.840316	0.420158	+	0.907451i	$0.361975\pi$
$60$	4.38266e71	0.00705441
$61$	−2.95096e73	−0.239208	−0.119604	−	0.992822i	$-0.538162\pi$
$61$	−2.95096e73	−0.239208	−0.119604	+	0.992822i	$0.538162\pi$
$62$	3.74928e73	0.154772
$63$	−2.63994e74	−0.560998
$64$	1.13078e74	0.125000
$65$	−2.69158e75	−1.56352
$66$	−3.79289e73	−0.0116922
$67$	9.82765e75	1.62310	0.811550	−	0.584283i	$-0.198624\pi$
$67$	9.82765e75	1.62310	0.811550	+	0.584283i	$0.198624\pi$
$68$	−9.96170e75	−0.889638
$69$	−2.26915e74	−0.0110567
$70$	1.79993e76	0.482711
$71$	−2.74633e76	−0.408819	−0.204410	−	0.978885i	$-0.565527\pi$
$71$	−2.74633e76	−0.408819	−0.204410	+	0.978885i	$0.565527\pi$
$72$	4.24322e76	0.353506
$73$	1.97027e77	0.926035	0.463017	−	0.886349i	$-0.346767\pi$
$73$	1.97027e77	0.926035	0.463017	+	0.886349i	$0.346767\pi$
$74$	1.98612e77	0.530750
$75$	−3.63839e75	−0.00557015
$76$	−7.46332e77	−0.659429
$77$	−1.55772e78	−0.800061
$78$	3.50461e76	0.0105369
$79$	2.44890e78	0.433957	0.216978	−	0.976176i	$-0.430380\pi$
$79$	2.44890e78	0.433957	0.216978	+	0.976176i	$0.430380\pi$
$80$	−2.89306e78	−0.304174
$81$	1.59204e79	0.999597
$82$	1.80582e79	0.681395
$83$	−4.50780e79	−1.02855	−0.514273	−	0.857627i	$-0.671938\pi$
$83$	−4.50780e79	−1.02855	−0.514273	+	0.857627i	$0.671938\pi$
$84$	−2.34363e77	−0.00325311
$85$	2.54866e80	2.16484
$86$	1.14277e80	0.597413
$87$	3.42233e77	0.00110732
$88$	2.50374e80	0.504149
$89$	1.00507e81	1.26623	0.633115	−	0.774058i	$-0.281776\pi$
$89$	1.00507e81	1.26623	0.633115	+	0.774058i	$0.281776\pi$
$90$	−1.08561e81	−0.860219
$91$	1.43932e81	0.721007
$92$	1.49790e81	0.476745
$93$	1.24899e79	0.00253815
$94$	8.20075e81	1.06917
$95$	1.90946e82	1.60465
$96$	3.76695e79	0.00204990
$97$	2.37614e82	0.841096	0.420548	−	0.907270i	$-0.361838\pi$
$97$	2.37614e82	0.841096	0.420548	+	0.907270i	$0.361838\pi$
$98$	2.09499e82	0.484507
$99$	9.39519e82	1.42576
$100$	2.40175e82	0.240175
$101$	1.86756e83	1.23577	0.617884	−	0.786269i	$-0.287990\pi$
$101$	1.86756e83	1.23577	0.617884	+	0.786269i	$0.287990\pi$
$102$	−3.31852e81	−0.0145894
$103$	−1.33705e83	−0.392105	−0.196052	−	0.980593i	$-0.562812\pi$
$103$	−1.33705e83	−0.392105	−0.196052	+	0.980593i	$0.562812\pi$
$104$	−2.31344e83	−0.454334
$105$	5.99607e81	0.00791609
$106$	1.07138e84	0.954443
$107$	−1.76716e84	−1.06623	−0.533114	−	0.846044i	$-0.678978\pi$
$107$	−1.76716e84	−1.06623	−0.533114	+	0.846044i	$0.678978\pi$
$108$	2.82726e82	0.0115952
$109$	1.72699e83	0.0483159	0.0241579	−	0.999708i	$-0.492310\pi$
$109$	1.72699e83	0.0483159	0.0241579	+	0.999708i	$0.492310\pi$
$110$	−6.40571e84	−1.22679
$111$	6.61633e82	0.00870389
$112$	1.54706e84	0.140268
$113$	−4.40696e84	−0.276302	−0.138151	−	0.990411i	$-0.544116\pi$
$113$	−4.40696e84	−0.276302	−0.138151	+	0.990411i	$0.544116\pi$
$114$	−2.48624e83	−0.0108141
$115$	−3.83230e85	−1.16011
$116$	−2.25913e84	−0.0477457
$117$	−8.68110e85	−1.28488
$118$	−5.71520e85	−0.594193
$119$	−1.36289e86	−0.998305
$120$	−9.63757e83	−0.00498822
$121$	2.81728e86	1.03333
$122$	6.48923e85	0.169145
$123$	6.01568e84	0.0111744
$124$	−8.24476e85	−0.109441
$125$	6.64750e86	0.632256
$126$	5.80529e86	0.396685
$127$	2.59885e87	1.27916	0.639582	−	0.768722i	$-0.279107\pi$
$127$	2.59885e87	1.27916	0.639582	+	0.768722i	$0.279107\pi$
$128$	−2.48662e86	−0.0883883
$129$	3.80690e85	0.00979711
$130$	5.91884e87	1.10557
$131$	7.20837e87	0.979667	0.489833	−	0.871816i	$-0.337058\pi$
$131$	7.20837e87	0.979667	0.489833	+	0.871816i	$0.337058\pi$
$132$	8.34066e85	0.00826765
$133$	−1.02108e88	−0.739976
$134$	−2.16112e88	−1.14770
$135$	−7.23341e86	−0.0282158
$136$	2.19060e88	0.629069
$137$	7.82178e88	1.65730	0.828651	−	0.559765i	$-0.189109\pi$
$137$	7.82178e88	1.65730	0.828651	+	0.559765i	$0.189109\pi$
$138$	4.98991e86	0.00781826
$139$	−1.30461e89	−1.51484	−0.757419	−	0.652929i	$-0.773540\pi$
$139$	−1.30461e89	−1.51484	−0.757419	+	0.652929i	$0.773540\pi$
$140$	−3.95809e88	−0.341328
$141$	2.73190e87	0.0175336
$142$	6.03925e88	0.289079
$143$	−5.12235e89	−1.83241
$144$	−9.33093e88	−0.249966
$145$	5.77988e88	0.116184
$146$	−4.33267e89	−0.654806
$147$	6.97900e87	0.00794555
$148$	−4.36753e89	−0.375297
$149$	−3.63174e89	−0.235985	−0.117993	−	0.993014i	$-0.537646\pi$
$149$	−3.63174e89	−0.235985	−0.117993	+	0.993014i	$0.537646\pi$
$150$	8.00090e87	0.00393869
$151$	−1.21094e90	−0.452458	−0.226229	−	0.974074i	$-0.572640\pi$
$151$	−1.21094e90	−0.452458	−0.226229	+	0.974074i	$0.572640\pi$
$152$	1.64120e90	0.466287
$153$	8.22014e90	1.77904
$154$	3.42545e90	0.565729
$155$	2.10938e90	0.266312
$156$	−7.70672e88	−0.00745073
$157$	1.43682e91	1.06554	0.532768	−	0.846262i	$-0.321152\pi$
$157$	1.43682e91	1.06554	0.532768	+	0.846262i	$0.321152\pi$
$158$	−5.38518e90	−0.306854
$159$	3.56906e89	0.0156521
$160$	6.36190e90	0.215084
$161$	2.04932e91	0.534978
$162$	−3.50093e91	−0.706822
$163$	−6.52333e90	−0.102020	−0.0510098	−	0.998698i	$-0.516244\pi$
$163$	−6.52333e90	−0.102020	−0.0510098	+	0.998698i	$0.516244\pi$
$164$	−3.97104e91	−0.481819
$165$	−2.13392e90	−0.0201184
$166$	9.91275e91	0.727292
$167$	−2.55968e92	−1.46370	−0.731849	−	0.681467i	$-0.761342\pi$
$167$	−2.55968e92	−1.46370	−0.731849	+	0.681467i	$0.761342\pi$
$168$	5.15369e89	0.00230029
$169$	1.86687e92	0.651354
$170$	−5.60455e92	−1.53077
$171$	6.15855e92	1.31868
$172$	−2.51299e92	−0.422435
$173$	−1.23154e93	−1.62755	−0.813777	−	0.581177i	$-0.802592\pi$
$173$	−1.23154e93	−1.62755	−0.813777	+	0.581177i	$0.802592\pi$
$174$	−7.52579e89	−0.000782993 0
$175$	3.28592e92	0.269512
$176$	−5.50579e92	−0.356487
$177$	−1.90389e91	−0.00974432
$178$	−2.21018e93	−0.895360
$179$	4.00341e93	1.28537	0.642687	−	0.766129i	$-0.277820\pi$
$179$	4.00341e93	1.28537	0.642687	+	0.766129i	$0.277820\pi$
$180$	2.38728e93	0.608266
$181$	7.45433e93	1.50920	0.754602	−	0.656183i	$-0.227830\pi$
$181$	7.45433e93	1.50920	0.754602	+	0.656183i	$0.227830\pi$
$182$	−3.16510e93	−0.509829
$183$	2.16174e91	0.00277386
$184$	−3.29391e93	−0.337110
$185$	1.11741e94	0.913244
$186$	−2.74656e91	−0.00179474
$187$	4.85036e94	2.53716
$188$	−1.80336e94	−0.756019
$189$	3.86807e92	0.0130116
$190$	−4.19894e94	−1.13466
$191$	−2.24626e94	−0.488176	−0.244088	−	0.969753i	$-0.578488\pi$
$191$	−2.24626e94	−0.488176	−0.244088	+	0.969753i	$0.578488\pi$
$192$	−8.28361e91	−0.00144950
$193$	−8.03970e94	−1.13400	−0.566998	−	0.823719i	$-0.691895\pi$
$193$	−8.03970e94	−1.13400	−0.566998	+	0.823719i	$0.691895\pi$
$194$	−5.22519e94	−0.594744
$195$	1.97173e93	0.0181305
$196$	−4.60694e94	−0.342598
$197$	1.17845e95	0.709516	0.354758	−	0.934958i	$-0.384563\pi$
$197$	1.17845e95	0.709516	0.354758	+	0.934958i	$0.384563\pi$
$198$	−2.06603e95	−1.00816
$199$	2.16660e95	0.857781	0.428891	−	0.903356i	$-0.358905\pi$
$199$	2.16660e95	0.857781	0.428891	+	0.903356i	$0.358905\pi$
$200$	−5.28151e94	−0.169829
$201$	−7.19930e93	−0.0188215
$202$	−4.10680e95	−0.873820
$203$	−3.09079e94	−0.0535777
$204$	7.29750e93	0.0103163
$205$	1.01597e96	1.17246
$206$	2.94020e95	0.277260
$207$	−1.23603e96	−0.953363
$208$	5.08731e95	0.321263
$209$	3.63390e96	1.88062
$210$	−1.31855e94	−0.00559752
$211$	−1.07711e96	−0.375439	−0.187719	−	0.982223i	$-0.560110\pi$
$211$	−1.07711e96	−0.375439	−0.187719	+	0.982223i	$0.560110\pi$
$212$	−2.35599e96	−0.674893
$213$	2.01184e94	0.00474067
$214$	3.88603e96	0.753936
$215$	6.42936e96	1.02795
$216$	−6.21720e94	−0.00819907
$217$	−1.12799e96	−0.122808
$218$	−3.79769e95	−0.0341645
$219$	−1.44333e95	−0.0107383
$220$	1.40863e97	0.867473
$221$	−4.48170e97	−2.28646
$222$	−1.45495e95	−0.00615458
$223$	−4.04527e97	−1.42002	−0.710011	−	0.704190i	$-0.751310\pi$
$223$	−4.04527e97	−1.42002	−0.710011	+	0.704190i	$0.751310\pi$
$224$	−3.40202e96	−0.0991847
$225$	−1.98187e97	−0.480286
$226$	9.69100e96	0.195375
$227$	−8.85082e96	−0.148563	−0.0742815	−	0.997237i	$-0.523666\pi$
$227$	−8.85082e96	−0.148563	−0.0742815	+	0.997237i	$0.523666\pi$
$228$	5.46730e95	0.00764675
$229$	−2.54255e96	−0.0296549	−0.0148274	−	0.999890i	$-0.504720\pi$
$229$	−2.54255e96	−0.0296549	−0.0148274	+	0.999890i	$0.504720\pi$
$230$	8.42731e97	0.820321
$231$	1.14111e96	0.00927752
$232$	4.96788e96	0.0337613
$233$	−1.71386e98	−0.974324	−0.487162	−	0.873312i	$-0.661968\pi$
$233$	−1.71386e98	−0.974324	−0.487162	+	0.873312i	$0.661968\pi$
$234$	1.90899e98	0.908545
$235$	4.61382e98	1.83969
$236$	1.25679e98	0.420158
$237$	−1.79395e96	−0.00503217
$238$	2.99704e98	0.705908
$239$	−6.03124e98	−1.19370	−0.596848	−	0.802354i	$-0.703580\pi$
$239$	−6.03124e98	−1.19370	−0.596848	+	0.802354i	$0.703580\pi$
$240$	2.11932e96	0.00352721
$241$	5.02162e98	0.703293	0.351646	−	0.936133i	$-0.385622\pi$
$241$	5.02162e98	0.703293	0.351646	+	0.936133i	$0.385622\pi$
$242$	−6.19527e98	−0.730673
$243$	−3.49955e97	−0.0347818
$244$	−1.42700e98	−0.119604
$245$	1.17866e99	0.833676
$246$	−1.32286e97	−0.00790147
$247$	−3.35770e99	−1.69480
$248$	1.81304e98	0.0773861
$249$	3.30221e97	0.0119270
$250$	−1.46180e99	−0.447072
$251$	5.27365e99	1.36663	0.683317	−	0.730122i	$-0.260537\pi$
$251$	5.27365e99	1.36663	0.683317	+	0.730122i	$0.260537\pi$
$252$	−1.27660e99	−0.280499
$253$	−7.29326e99	−1.35963
$254$	−5.71493e99	−0.904506
$255$	−1.86703e98	−0.0251035
$256$	5.46813e98	0.0625000
$257$	1.47183e100	1.43098	0.715488	−	0.698625i	$-0.246204\pi$
$257$	1.47183e100	1.43098	0.715488	+	0.698625i	$0.246204\pi$
$258$	−8.37145e97	−0.00692760
$259$	−5.97537e99	−0.421138
$260$	−1.30157e100	−0.781758
$261$	1.86418e99	0.0954786
$262$	−1.58514e100	−0.692729
$263$	3.80826e100	1.42090	0.710449	−	0.703749i	$-0.248492\pi$
$263$	3.80826e100	1.42090	0.710449	+	0.703749i	$0.248492\pi$
$264$	−1.83413e98	−0.00584611
$265$	6.02769e100	1.64228
$266$	2.24538e100	0.523242
$267$	−7.36273e98	−0.0146832
$268$	4.75236e100	0.811550
$269$	−5.22540e100	−0.764539	−0.382269	−	0.924051i	$-0.624857\pi$
$269$	−5.22540e100	−0.764539	−0.382269	+	0.924051i	$0.624857\pi$
$270$	1.59064e99	0.0199516
$271$	7.94839e100	0.855172	0.427586	−	0.903975i	$-0.359364\pi$
$271$	7.94839e100	0.855172	0.427586	+	0.903975i	$0.359364\pi$
$272$	−4.81718e100	−0.444819
$273$	−1.05438e99	−0.00836081
$274$	−1.72003e101	−1.17189
$275$	−1.16941e101	−0.684954
$276$	−1.09729e99	−0.00552835
$277$	−3.58227e101	−1.55327	−0.776637	−	0.629948i	$-0.783076\pi$
$277$	−3.58227e101	−1.55327	−0.776637	+	0.629948i	$0.783076\pi$
$278$	2.86887e101	1.07115
$279$	6.80337e100	0.218852
$280$	8.70393e100	0.241355
$281$	−5.10359e101	−1.22057	−0.610286	−	0.792181i	$-0.708946\pi$
$281$	−5.10359e101	−1.22057	−0.610286	+	0.792181i	$0.708946\pi$
$282$	−6.00751e99	−0.0123981
$283$	−4.70816e101	−0.838907	−0.419454	−	0.907777i	$-0.637778\pi$
$283$	−4.70816e101	−0.838907	−0.419454	+	0.907777i	$0.637778\pi$
$284$	−1.32804e101	−0.204410
$285$	−1.39878e100	−0.0186075
$286$	1.12642e102	1.29571
$287$	−5.43291e101	−0.540672
$288$	2.05189e101	0.176753
$289$	2.90325e102	2.16582
$290$	−1.27101e101	−0.0821546
$291$	−1.74066e100	−0.00975335
$292$	9.52765e101	0.463017
$293$	−7.77907e101	−0.328036	−0.164018	−	0.986457i	$-0.552446\pi$
$293$	−7.77907e101	−0.328036	−0.164018	+	0.986457i	$0.552446\pi$
$294$	−1.53470e100	−0.00561835
$295$	−3.21543e102	−1.02241
$296$	9.60430e101	0.265375
$297$	−1.37659e101	−0.0330684
$298$	7.98629e101	0.166867
$299$	6.73893e102	1.22528
$300$	−1.75942e100	−0.00278507
$301$	−3.43810e102	−0.474034
$302$	2.66288e102	0.319936
$303$	−1.36809e101	−0.0143300
$304$	−3.60904e102	−0.329715
$305$	3.65091e102	0.291043
$306$	−1.80763e103	−1.25797
$307$	−2.89674e102	−0.176062	−0.0880312	−	0.996118i	$-0.528058\pi$
$307$	−2.89674e102	−0.176062	−0.0880312	+	0.996118i	$0.528058\pi$
$308$	−7.53265e102	−0.400031
$309$	9.79462e100	0.00454685
$310$	−4.63859e102	−0.188311
$311$	−1.09171e103	−0.387749	−0.193875	−	0.981026i	$-0.562105\pi$
$311$	−1.09171e103	−0.387749	−0.193875	+	0.981026i	$0.562105\pi$
$312$	1.69473e101	0.00526846
$313$	−9.43698e102	−0.256888	−0.128444	−	0.991717i	$-0.540998\pi$
$313$	−9.43698e102	−0.256888	−0.128444	+	0.991717i	$0.540998\pi$
$314$	−3.15961e103	−0.753447
$315$	3.26612e103	0.682564
$316$	1.18421e103	0.216978
$317$	2.18142e103	0.350574	0.175287	−	0.984517i	$-0.443915\pi$
$317$	2.18142e103	0.350574	0.175287	+	0.984517i	$0.443915\pi$
$318$	−7.84845e101	−0.0110677
$319$	1.09997e103	0.136166
$320$	−1.39900e103	−0.152087
$321$	1.29455e102	0.0123640
$322$	−4.50651e103	−0.378287
$323$	3.17941e104	2.34661
$324$	7.69862e103	0.499798
$325$	1.08053e104	0.617274
$326$	1.43450e103	0.0721388
$327$	−1.26512e101	−0.000560271 0
$328$	8.73240e103	0.340698
$329$	−2.46724e104	−0.848364
$330$	4.69254e102	0.0142259
$331$	−5.37346e104	−1.43679	−0.718394	−	0.695637i	$-0.755122\pi$
$331$	−5.37346e104	−1.43679	−0.718394	+	0.695637i	$0.755122\pi$
$332$	−2.17984e104	−0.514273
$333$	3.60398e104	0.750492
$334$	5.62879e104	1.03499
$335$	−1.21587e105	−1.97482
$336$	−1.13331e102	−0.00162655
$337$	−6.28692e104	−0.797622	−0.398811	−	0.917033i	$-0.630577\pi$
$337$	−6.28692e104	−0.797622	−0.398811	+	0.917033i	$0.630577\pi$
$338$	−4.10530e104	−0.460577
$339$	3.22834e102	0.00320400
$340$	1.23245e105	1.08242
$341$	4.01438e104	0.312113
$342$	−1.35428e105	−0.932448
$343$	−1.55016e105	−0.945519
$344$	5.52611e104	0.298706
$345$	2.80737e103	0.0134526
$346$	2.70819e105	1.15085
$347$	3.23846e105	1.22086	0.610429	−	0.792071i	$-0.290997\pi$
$347$	3.23846e105	1.22086	0.610429	+	0.792071i	$0.290997\pi$
$348$	1.65494e102	0.000553660 0
$349$	−1.45038e105	−0.430752	−0.215376	−	0.976531i	$-0.569098\pi$
$349$	−1.45038e105	−0.430752	−0.215376	+	0.976531i	$0.569098\pi$
$350$	−7.22581e104	−0.190574
$351$	1.27196e104	0.0298009
$352$	1.21074e105	0.252074
$353$	−1.83016e105	−0.338718	−0.169359	−	0.985554i	$-0.554170\pi$
$353$	−1.83016e105	−0.338718	−0.169359	+	0.985554i	$0.554170\pi$
$354$	4.18670e103	0.00689027
$355$	3.39774e105	0.497409
$356$	4.86024e105	0.633115
$357$	9.98396e103	0.0115764
$358$	−8.80360e105	−0.908897
$359$	1.83689e106	1.68913	0.844566	−	0.535452i	$-0.179859\pi$
$359$	1.83689e106	1.68913	0.844566	+	0.535452i	$0.179859\pi$
$360$	−5.24968e105	−0.430109
$361$	1.01256e106	0.739387
$362$	−1.63923e106	−1.06717
$363$	−2.06382e104	−0.0119825
$364$	6.96013e105	0.360504
$365$	−2.43761e106	−1.12670
$366$	−4.75372e103	−0.00196141
$367$	−2.93248e106	−1.08042	−0.540212	−	0.841529i	$-0.681656\pi$
$367$	−2.93248e106	−1.08042	−0.540212	+	0.841529i	$0.681656\pi$
$368$	7.24338e105	0.238373
$369$	3.27680e106	0.963509
$370$	−2.45722e106	−0.645761
$371$	−3.22331e106	−0.757329
$372$	6.03975e103	0.00126907
$373$	3.30772e106	0.621745	0.310873	−	0.950452i	$-0.399379\pi$
$373$	3.30772e106	0.621745	0.310873	+	0.950452i	$0.399379\pi$
$374$	−1.06660e107	−1.79404
$375$	−4.86967e104	−0.00733165
$376$	3.96564e106	0.534586
$377$	−1.01637e106	−0.122711
$378$	−8.50597e104	−0.00920056
$379$	2.50774e106	0.243084	0.121542	−	0.992586i	$-0.461216\pi$
$379$	2.50774e106	0.243084	0.121542	+	0.992586i	$0.461216\pi$
$380$	9.23357e106	0.802325
$381$	−1.90380e105	−0.0148332
$382$	4.93959e106	0.345192
$383$	1.15247e107	0.722571	0.361286	−	0.932455i	$-0.382338\pi$
$383$	1.15247e107	0.722571	0.361286	+	0.932455i	$0.382338\pi$
$384$	1.82159e104	0.00102495
$385$	1.92720e107	0.973432
$386$	1.76795e107	0.801856
$387$	2.07365e107	0.844756
$388$	1.14903e107	0.420548
$389$	−3.97495e107	−1.30744	−0.653722	−	0.756735i	$-0.726793\pi$
$389$	−3.97495e107	−1.30744	−0.653722	+	0.756735i	$0.726793\pi$
$390$	−4.33588e105	−0.0128202
$391$	−6.38110e107	−1.69652
$392$	1.01308e107	0.242254
$393$	−5.28053e105	−0.0113602
$394$	−2.59143e107	−0.501703
$395$	−3.02976e107	−0.527994
$396$	4.54324e107	0.712878
$397$	1.94436e107	0.274770	0.137385	−	0.990518i	$-0.456130\pi$
$397$	1.94436e107	0.274770	0.137385	+	0.990518i	$0.456130\pi$
$398$	−4.76441e107	−0.606543
$399$	7.48000e105	0.00858077
$400$	1.16142e107	0.120088
$401$	−1.42569e108	−1.32903	−0.664513	−	0.747277i	$-0.731361\pi$
$401$	−1.42569e108	−1.32903	−0.664513	+	0.747277i	$0.731361\pi$
$402$	1.58314e106	0.0133088
$403$	−3.70926e107	−0.281273
$404$	9.03095e107	0.617884
$405$	−1.96966e108	−1.21621
$406$	6.79672e106	0.0378852
$407$	2.12655e108	1.07031
$408$	−1.60474e106	−0.00729469
$409$	3.38003e108	1.38804	0.694021	−	0.719955i	$-0.255837\pi$
$409$	3.38003e108	1.38804	0.694021	+	0.719955i	$0.255837\pi$
$410$	−2.23414e108	−0.829051
$411$	−5.72989e106	−0.0192181
$412$	−6.46557e107	−0.196052
$413$	1.71945e108	0.471479
$414$	2.71805e108	0.674129
$415$	5.57701e108	1.25143
$416$	−1.11871e108	−0.227167
$417$	9.55699e106	0.0175661
$418$	−7.99102e108	−1.32980
$419$	−1.08958e109	−1.64202	−0.821008	−	0.570917i	$-0.806588\pi$
$419$	−1.08958e109	−1.64202	−0.821008	+	0.570917i	$0.806588\pi$
$420$	2.89952e106	0.00395804
$421$	1.48564e109	1.83741	0.918705	−	0.394945i	$-0.129236\pi$
$421$	1.48564e109	1.83741	0.918705	+	0.394945i	$0.129236\pi$
$422$	2.36859e108	0.265475
$423$	1.48809e109	1.51183
$424$	5.18087e108	0.477221
$425$	−1.02316e109	−0.854676
$426$	−4.42408e106	−0.00335216
$427$	−1.95232e108	−0.134213
$428$	−8.54547e108	−0.533114
$429$	3.75241e107	0.0212487
$430$	−1.41383e109	−0.726870
$431$	−2.63902e109	−1.23207	−0.616035	−	0.787719i	$-0.711262\pi$
$431$	−2.63902e109	−1.23207	−0.616035	+	0.787719i	$0.711262\pi$
$432$	1.36718e107	0.00579762
$433$	7.65361e108	0.294862	0.147431	−	0.989072i	$-0.452900\pi$
$433$	7.65361e108	0.294862	0.147431	+	0.989072i	$0.452900\pi$
$434$	2.48048e108	0.0868386
$435$	−4.23408e106	−0.00134727
$436$	8.35120e107	0.0241579
$437$	−4.78073e109	−1.25752
$438$	3.17392e107	0.00759313
$439$	−3.61884e109	−0.787574	−0.393787	−	0.919202i	$-0.628835\pi$
$439$	−3.61884e109	−0.787574	−0.393787	+	0.919202i	$0.628835\pi$
$440$	−3.09761e109	−0.613396
$441$	3.80153e109	0.685105
$442$	9.85536e109	1.61677
$443$	5.85530e109	0.874570	0.437285	−	0.899323i	$-0.355940\pi$
$443$	5.85530e109	0.874570	0.437285	+	0.899323i	$0.355940\pi$
$444$	3.19946e107	0.00435194
$445$	−1.24347e110	−1.54062
$446$	8.89564e109	1.00411
$447$	2.66045e107	0.00273649
$448$	7.48113e108	0.0701342
$449$	1.16917e110	0.999206	0.499603	−	0.866255i	$-0.333479\pi$
$449$	1.16917e110	0.999206	0.499603	+	0.866255i	$0.333479\pi$
$450$	4.35817e109	0.339613
$451$	1.93350e110	1.37410
$452$	−2.13107e109	−0.138151
$453$	8.87078e107	0.00524670
$454$	1.94632e109	0.105050
$455$	−1.78072e110	−0.877247
$456$	−1.20227e108	−0.00540707
$457$	4.93283e108	0.0202570	0.0101285	−	0.999949i	$-0.496776\pi$
$457$	4.93283e108	0.0202570	0.0101285	+	0.999949i	$0.496776\pi$
$458$	5.59112e108	0.0209692
$459$	−1.20442e109	−0.0412622
$460$	−1.85319e110	−0.580055
$461$	−4.52351e110	−1.29386	−0.646930	−	0.762550i	$-0.723947\pi$
$461$	−4.52351e110	−1.29386	−0.646930	+	0.762550i	$0.723947\pi$
$462$	−2.50934e108	−0.00656020
$463$	−2.00646e110	−0.479533	−0.239766	−	0.970831i	$-0.577071\pi$
$463$	−2.00646e110	−0.479533	−0.239766	+	0.970831i	$0.577071\pi$
$464$	−1.09245e109	−0.0238729
$465$	−1.54524e108	−0.00308815
$466$	3.76881e110	0.688951
$467$	−1.74428e110	−0.291720	−0.145860	−	0.989305i	$-0.546595\pi$
$467$	−1.74428e110	−0.291720	−0.145860	+	0.989305i	$0.546595\pi$
$468$	−4.19792e110	−0.642439
$469$	6.50186e110	0.910678
$470$	−1.01459e111	−1.30086
$471$	−1.05255e109	−0.0123560
$472$	−2.76370e110	−0.297097
$473$	1.22357e111	1.20474
$474$	3.94495e108	0.00355828
$475$	−7.66551e110	−0.633514
$476$	−6.59055e110	−0.499152
$477$	1.94410e111	1.34960
$478$	1.32628e111	0.844070
$479$	1.70754e111	0.996431	0.498216	−	0.867053i	$-0.333989\pi$
$479$	1.70754e111	0.996431	0.498216	+	0.867053i	$0.333989\pi$
$480$	−4.66044e108	−0.00249411
$481$	−1.96492e111	−0.964550
$482$	−1.10426e111	−0.497303
$483$	−1.50124e109	−0.00620362
$484$	1.36236e111	0.516664
$485$	−2.93975e111	−1.02336
$486$	7.69559e109	0.0245944
$487$	5.73073e111	1.68174	0.840869	−	0.541239i	$-0.182045\pi$
$487$	5.73073e111	1.68174	0.840869	+	0.541239i	$0.182045\pi$
$488$	3.13800e110	0.0845727
$489$	4.77870e108	0.00118302
$490$	−2.59191e111	−0.589498
$491$	3.97537e111	0.830799	0.415400	−	0.909639i	$-0.363642\pi$
$491$	3.97537e111	0.830799	0.415400	+	0.909639i	$0.363642\pi$
$492$	2.90900e109	0.00558718
$493$	9.62399e110	0.169906
$494$	7.38366e111	1.19840
$495$	−1.16237e112	−1.73471
$496$	−3.98692e110	−0.0547203
$497$	−1.81694e111	−0.229378
$498$	−7.26164e109	−0.00843368
$499$	−1.46410e112	−1.56458	−0.782288	−	0.622916i	$-0.785948\pi$
$499$	−1.46410e112	−1.56458	−0.782288	+	0.622916i	$0.785948\pi$
$500$	3.21453e111	0.316128
$501$	1.87511e110	0.0169731
$502$	−1.15969e112	−0.966356
$503$	2.83844e111	0.217775	0.108888	−	0.994054i	$-0.465271\pi$
$503$	2.83844e111	0.217775	0.108888	+	0.994054i	$0.465271\pi$
$504$	2.80727e111	0.198343
$505$	−2.31053e112	−1.50355
$506$	1.60381e112	0.961402
$507$	−1.36759e110	−0.00755310
$508$	1.25673e112	0.639582
$509$	−7.25643e111	−0.340357	−0.170179	−	0.985413i	$-0.554434\pi$
$509$	−7.25643e111	−0.340357	−0.170179	+	0.985413i	$0.554434\pi$
$510$	4.10565e110	0.0177509
$511$	1.30351e112	0.519574
$512$	−1.20245e111	−0.0441942
$513$	−9.02357e110	−0.0305849
$514$	−3.23658e112	−1.01185
$515$	1.65419e112	0.477072
$516$	1.84090e110	0.00489856
$517$	8.78059e112	2.15609
$518$	1.31400e112	0.297789
$519$	9.02172e110	0.0188731
$520$	2.86217e112	0.552786
$521$	5.90803e112	1.05360	0.526802	−	0.849988i	$-0.323391\pi$
$521$	5.90803e112	1.05360	0.526802	+	0.849988i	$0.323391\pi$
$522$	−4.09937e111	−0.0675136
$523$	−6.09468e112	−0.927110	−0.463555	−	0.886068i	$-0.653426\pi$
$523$	−6.09468e112	−0.927110	−0.463555	+	0.886068i	$0.653426\pi$
$524$	3.48575e112	0.489833
$525$	−2.40712e110	−0.00312526
$526$	−8.37445e112	−1.00473
$527$	3.51230e112	0.389450
$528$	4.03330e110	0.00413383
$529$	−9.58868e111	−0.0908550
$530$	−1.32550e113	−1.16127
$531$	−1.03707e113	−0.840203
$532$	−4.93765e112	−0.369988
$533$	−1.78654e113	−1.23832
$534$	1.61908e111	0.0103826
$535$	2.18632e113	1.29727
$536$	−1.04505e113	−0.573852
$537$	−2.93272e111	−0.0149052
$538$	1.14908e113	0.540611
$539$	2.24312e113	0.977055
$540$	−3.49786e111	−0.0141079
$541$	−2.22947e113	−0.832750	−0.416375	−	0.909193i	$-0.636700\pi$
$541$	−2.22947e113	−0.832750	−0.416375	+	0.909193i	$0.636700\pi$
$542$	−1.74787e113	−0.604698
$543$	−5.46071e111	−0.0175007
$544$	1.05931e113	0.314535
$545$	−2.13662e112	−0.0587857
$546$	2.31861e111	0.00591199
$547$	−2.02028e113	−0.477460	−0.238730	−	0.971086i	$-0.576731\pi$
$547$	−2.02028e113	−0.477460	−0.238730	+	0.971086i	$0.576731\pi$
$548$	3.78238e113	0.828651
$549$	1.17752e113	0.239176
$550$	2.57157e113	0.484336
$551$	7.21031e112	0.125940
$552$	2.41297e111	0.00390913
$553$	1.62016e113	0.243482
$554$	7.87750e113	1.09833
$555$	−8.18567e111	−0.0105900
$556$	−6.30870e113	−0.757419
$557$	7.81160e113	0.870462	0.435231	−	0.900319i	$-0.356667\pi$
$557$	7.81160e113	0.870462	0.435231	+	0.900319i	$0.356667\pi$
$558$	−1.49608e113	−0.154751
$559$	−1.13058e114	−1.08570
$560$	−1.91401e113	−0.170664
$561$	−3.55316e112	−0.0294209
$562$	1.12229e114	0.863075
$563$	−8.55541e113	−0.611143	−0.305571	−	0.952169i	$-0.598847\pi$
$563$	−8.55541e113	−0.611143	−0.305571	+	0.952169i	$0.598847\pi$
$564$	1.32106e112	0.00876680
$565$	5.45225e113	0.336175
$566$	1.03534e114	0.593197
$567$	1.05327e114	0.560847
$568$	2.92040e113	0.144539
$569$	−3.03861e114	−1.39803	−0.699014	−	0.715108i	$-0.746377\pi$
$569$	−3.03861e114	−1.39803	−0.699014	+	0.715108i	$0.746377\pi$
$570$	3.07596e112	0.0131575
$571$	−2.02235e114	−0.804372	−0.402186	−	0.915558i	$-0.631749\pi$
$571$	−2.02235e114	−0.804372	−0.402186	+	0.915558i	$0.631749\pi$
$572$	−2.47702e114	−0.916207
$573$	1.64551e112	0.00566089
$574$	1.19471e114	0.382313
$575$	1.53847e114	0.458010
$576$	−4.51216e113	−0.124983
$577$	−1.99169e114	−0.513363	−0.256682	−	0.966496i	$-0.582629\pi$
$577$	−1.99169e114	−0.513363	−0.256682	+	0.966496i	$0.582629\pi$
$578$	−6.38431e114	−1.53147
$579$	5.88953e112	0.0131498
$580$	2.79498e113	0.0580920
$581$	−2.98231e114	−0.577090
$582$	3.82774e112	0.00689666
$583$	1.14713e115	1.92472
$584$	−2.09515e114	−0.327403
$585$	1.07402e115	1.56331
$586$	1.71064e114	0.231956
$587$	−7.37323e114	−0.931487	−0.465743	−	0.884920i	$-0.654213\pi$
$587$	−7.37323e114	−0.931487	−0.465743	+	0.884920i	$0.654213\pi$
$588$	3.37484e112	0.00397277
$589$	2.63143e114	0.288673
$590$	7.07080e114	0.722953
$591$	−8.63279e112	−0.00822755
$592$	−2.11201e114	−0.187648
$593$	1.20108e115	0.994954	0.497477	−	0.867477i	$-0.334260\pi$
$593$	1.20108e115	0.994954	0.497477	+	0.867477i	$0.334260\pi$
$594$	3.02716e113	0.0233829
$595$	1.68616e115	1.21463
$596$	−1.75620e114	−0.117993
$597$	−1.58716e113	−0.00994684
$598$	−1.48191e115	−0.866406
$599$	1.21792e115	0.664361	0.332181	−	0.943216i	$-0.392216\pi$
$599$	1.21792e115	0.664361	0.332181	+	0.943216i	$0.392216\pi$
$600$	3.86900e112	0.00196934
$601$	−2.21766e115	−1.05343	−0.526715	−	0.850042i	$-0.676576\pi$
$601$	−2.21766e115	−1.05343	−0.526715	+	0.850042i	$0.676576\pi$
$602$	7.56047e114	0.335192
$603$	−3.92153e115	−1.62288
$604$	−5.85573e114	−0.226229
$605$	−3.48552e115	−1.25725
$606$	3.00846e113	0.0101328
$607$	3.73785e115	1.17569	0.587844	−	0.808975i	$-0.299977\pi$
$607$	3.73785e115	1.17569	0.587844	+	0.808975i	$0.299977\pi$
$608$	7.93637e114	0.233143
$609$	2.26418e112	0.000621288 0
$610$	−8.02843e114	−0.205799
$611$	−8.11321e115	−1.94304
$612$	3.97502e115	0.889519
$613$	−3.47576e115	−0.726842	−0.363421	−	0.931625i	$-0.618391\pi$
$613$	−3.47576e115	−0.726842	−0.363421	+	0.931625i	$0.618391\pi$
$614$	6.37000e114	0.124495
$615$	−7.44256e113	−0.0135958
$616$	1.65645e115	0.282864
$617$	9.31989e115	1.48791	0.743955	−	0.668230i	$-0.232948\pi$
$617$	9.31989e115	1.48791	0.743955	+	0.668230i	$0.232948\pi$
$618$	−2.15386e113	−0.00321511
$619$	−3.57176e115	−0.498563	−0.249282	−	0.968431i	$-0.580195\pi$
$619$	−3.57176e115	−0.498563	−0.249282	+	0.968431i	$0.580195\pi$
$620$	1.02004e115	0.133156
$621$	1.81104e114	0.0221119
$622$	2.40069e115	0.274180
$623$	6.64946e115	0.710448
$624$	−3.72674e113	−0.00372536
$625$	−1.33597e116	−1.24961
$626$	2.07521e115	0.181647
$627$	−2.66203e114	−0.0218077
$628$	6.94805e115	0.532768
$629$	1.86059e116	1.33551
$630$	−7.18226e115	−0.482646
$631$	2.74127e116	1.72478	0.862388	−	0.506247i	$-0.168968\pi$
$631$	2.74127e116	1.72478	0.862388	+	0.506247i	$0.168968\pi$
$632$	−2.60411e115	−0.153427
$633$	7.89044e113	0.00435359
$634$	−4.79699e115	−0.247893
$635$	−3.21528e116	−1.55636
$636$	1.72589e114	0.00782607
$637$	−2.07263e116	−0.880512
$638$	−2.41886e115	−0.0962838
$639$	1.09587e116	0.408764
$640$	3.07642e115	0.107542
$641$	1.15285e114	0.00377714	0.00188857	−	0.999998i	$-0.499399\pi$
$641$	1.15285e114	0.00377714	0.00188857	+	0.999998i	$0.499399\pi$
$642$	−2.84673e114	−0.00874266
$643$	5.51605e116	1.58808	0.794041	−	0.607865i	$-0.207974\pi$
$643$	5.51605e116	1.58808	0.794041	+	0.607865i	$0.207974\pi$
$644$	9.90991e115	0.267489
$645$	−4.70987e114	−0.0119201
$646$	−6.99159e116	−1.65931
$647$	2.69348e116	0.599495	0.299748	−	0.954019i	$-0.403098\pi$
$647$	2.69348e116	0.599495	0.299748	+	0.954019i	$0.403098\pi$
$648$	−1.69294e116	−0.353411
$649$	−6.11930e116	−1.19825
$650$	−2.37611e116	−0.436479
$651$	8.26318e113	0.00142409
$652$	−3.15449e115	−0.0510098
$653$	1.50164e116	0.227860	0.113930	−	0.993489i	$-0.463656\pi$
$653$	1.50164e116	0.227860	0.113930	+	0.993489i	$0.463656\pi$
$654$	2.78202e113	0.000396172 0
$655$	−8.91815e116	−1.19196
$656$	−1.92027e116	−0.240910
$657$	−7.86198e116	−0.925910
$658$	5.42553e116	0.599884
$659$	6.97853e116	0.724468	0.362234	−	0.932087i	$-0.382014\pi$
$659$	6.97853e116	0.724468	0.362234	+	0.932087i	$0.382014\pi$
$660$	−1.03190e115	−0.0100592
$661$	1.28721e117	1.17839	0.589196	−	0.807990i	$-0.299445\pi$
$661$	1.28721e117	1.17839	0.589196	+	0.807990i	$0.299445\pi$
$662$	1.18164e117	1.01596
$663$	3.28310e115	0.0265138
$664$	4.79351e116	0.363646
$665$	1.26328e117	0.900327
$666$	−7.92523e116	−0.530678
$667$	−1.44712e116	−0.0910502
$668$	−1.23778e117	−0.731849
$669$	2.96338e115	0.0164666
$670$	2.67373e117	1.39641
$671$	6.94806e116	0.341098
$672$	2.49217e114	0.00115015
$673$	−1.41274e117	−0.612966	−0.306483	−	0.951876i	$-0.599152\pi$
$673$	−1.41274e117	−0.612966	−0.306483	+	0.951876i	$0.599152\pi$
$674$	1.38251e117	0.564004
$675$	2.90385e115	0.0111395
$676$	9.02765e116	0.325677
$677$	−2.45656e117	−0.833484	−0.416742	−	0.909025i	$-0.636828\pi$
$677$	−2.45656e117	−0.833484	−0.416742	+	0.909025i	$0.636828\pi$
$678$	−7.09920e114	−0.00226557
$679$	1.57203e117	0.471916
$680$	−2.71020e117	−0.765386
$681$	6.48372e114	0.00172274
$682$	−8.82771e116	−0.220697
$683$	−3.59496e117	−0.845737	−0.422869	−	0.906191i	$-0.638977\pi$
$683$	−3.59496e117	−0.845737	−0.422869	+	0.906191i	$0.638977\pi$
$684$	2.97809e117	0.659341
$685$	−9.67705e117	−2.01643
$686$	3.40884e117	0.668583
$687$	1.86256e114	0.000343878 0
$688$	−1.21521e117	−0.211217
$689$	−1.05994e118	−1.73454
$690$	−6.17348e115	−0.00951245
$691$	3.64308e117	0.528603	0.264302	−	0.964440i	$-0.414859\pi$
$691$	3.64308e117	0.528603	0.264302	+	0.964440i	$0.414859\pi$
$692$	−5.95536e117	−0.813777
$693$	6.21576e117	0.799954
$694$	−7.12144e117	−0.863276
$695$	1.61405e118	1.84310
$696$	−3.63925e114	−0.000391497 0
$697$	1.69168e118	1.71458
$698$	3.18942e117	0.304588
$699$	1.25549e116	0.0112983
$700$	1.58897e117	0.134756
$701$	−1.93265e118	−1.54474	−0.772371	−	0.635172i	$-0.780929\pi$
$701$	−1.93265e118	−1.54474	−0.772371	+	0.635172i	$0.780929\pi$
$702$	−2.79708e116	−0.0210724
$703$	1.39396e118	0.989926
$704$	−2.66243e117	−0.178243
$705$	−3.37988e116	−0.0213331
$706$	4.02456e117	0.239510
$707$	1.23556e118	0.693356
$708$	−9.20665e115	−0.00487216
$709$	2.50803e117	0.125174	0.0625870	−	0.998040i	$-0.480065\pi$
$709$	2.50803e117	0.125174	0.0625870	+	0.998040i	$0.480065\pi$
$710$	−7.47171e117	−0.351721
$711$	−9.77184e117	−0.433898
$712$	−1.06878e118	−0.447680
$713$	−5.28129e117	−0.208701
$714$	−2.19550e116	−0.00818572
$715$	6.33733e118	2.22949
$716$	1.93593e118	0.642687
$717$	4.41822e116	0.0138421
$718$	−4.03936e118	−1.19440
$719$	−4.74549e118	−1.32444	−0.662220	−	0.749309i	$-0.730386\pi$
$719$	−4.74549e118	−1.32444	−0.662220	+	0.749309i	$0.730386\pi$
$720$	1.15442e118	0.304133
$721$	−8.84576e117	−0.220000
$722$	−2.22664e118	−0.522826
$723$	−3.67861e116	−0.00815539
$724$	3.60469e118	0.754602
$725$	−2.32033e117	−0.0458693
$726$	4.53838e116	0.00847289
$727$	−7.22350e118	−1.27371	−0.636854	−	0.770985i	$-0.719764\pi$
$727$	−7.22350e118	−1.27371	−0.636854	+	0.770985i	$0.719764\pi$
$728$	−1.53055e118	−0.254915
$729$	−6.35100e118	−0.999193
$730$	5.36035e118	0.796700
$731$	1.07054e119	1.50326
$732$	1.04536e116	0.00138693
$733$	−9.11017e118	−1.14212	−0.571060	−	0.820908i	$-0.693468\pi$
$733$	−9.11017e118	−1.14212	−0.571060	+	0.820908i	$0.693468\pi$
$734$	6.44860e118	0.763975
$735$	−8.63437e116	−0.00966732
$736$	−1.59284e118	−0.168555
$737$	−2.31393e119	−2.31446
$738$	−7.20576e118	−0.681304
$739$	1.20282e119	1.07512	0.537558	−	0.843227i	$-0.319347\pi$
$739$	1.20282e119	1.07512	0.537558	+	0.843227i	$0.319347\pi$
$740$	5.40348e118	0.456622
$741$	2.45970e117	0.0196529
$742$	7.08813e118	0.535512
$743$	1.32005e119	0.943096	0.471548	−	0.881840i	$-0.343695\pi$
$743$	1.32005e119	0.943096	0.471548	+	0.881840i	$0.343695\pi$
$744$	−1.32815e116	−0.000897370 0
$745$	4.49317e118	0.287122
$746$	−7.27376e118	−0.439640
$747$	1.79875e119	1.02841
$748$	2.34549e119	1.26858
$749$	−1.16914e119	−0.598232
$750$	1.07085e117	0.00518426
$751$	1.21121e119	0.554833	0.277416	−	0.960750i	$-0.410522\pi$
$751$	1.21121e119	0.554833	0.277416	+	0.960750i	$0.410522\pi$
$752$	−8.72053e118	−0.378009
$753$	−3.86324e117	−0.0158475
$754$	2.23501e118	0.0867700
$755$	1.49816e119	0.550503
$756$	1.87048e117	0.00650578
$757$	−1.68795e118	−0.0555750	−0.0277875	−	0.999614i	$-0.508846\pi$
$757$	−1.68795e118	−0.0555750	−0.0277875	+	0.999614i	$0.508846\pi$
$758$	−5.51459e118	−0.171886
$759$	5.34272e117	0.0157663
$760$	−2.03048e119	−0.567330
$761$	−2.63589e118	−0.0697371	−0.0348686	−	0.999392i	$-0.511101\pi$
$761$	−2.63589e118	−0.0697371	−0.0348686	+	0.999392i	$0.511101\pi$
$762$	4.18650e117	0.0104887
$763$	1.14256e118	0.0271087
$764$	−1.08623e119	−0.244088
$765$	−1.01699e120	−2.16455
$766$	−2.53431e119	−0.510935
$767$	5.65419e119	1.07985
$768$	−4.00571e116	−0.000724751 0
$769$	−1.12559e119	−0.192947	−0.0964736	−	0.995336i	$-0.530756\pi$
$769$	−1.12559e119	−0.192947	−0.0964736	+	0.995336i	$0.530756\pi$
$770$	−4.23795e119	−0.688320
$771$	−1.07820e118	−0.0165936
$772$	−3.88776e119	−0.566998
$773$	1.59287e119	0.220157	0.110078	−	0.993923i	$-0.464890\pi$
$773$	1.59287e119	0.220157	0.110078	+	0.993923i	$0.464890\pi$
$774$	−4.56001e119	−0.597332
$775$	−8.46812e118	−0.105140
$776$	−2.52675e119	−0.297372
$777$	4.37729e117	0.00488352
$778$	8.74100e119	0.924502
$779$	1.26741e120	1.27090
$780$	9.53470e117	0.00906527
$781$	6.46626e119	0.582955
$782$	1.40322e120	1.19962
$783$	−2.73141e117	−0.00221449
$784$	−2.22778e119	−0.171299
$785$	−1.77763e120	−1.29643
$786$	1.16120e118	0.00803289
$787$	1.91554e120	1.25701	0.628506	−	0.777805i	$-0.283667\pi$
$787$	1.91554e120	1.25701	0.628506	+	0.777805i	$0.283667\pi$
$788$	5.69862e119	0.354758
$789$	−2.78976e118	−0.0164767
$790$	6.66251e119	0.373348
$791$	−2.91559e119	−0.155025
$792$	−9.99068e119	−0.504081
$793$	−6.41997e119	−0.307394
$794$	−4.27569e119	−0.194292
$795$	−4.41562e118	−0.0190439
$796$	1.04770e120	0.428891
$797$	−3.07246e120	−1.19390	−0.596948	−	0.802280i	$-0.703620\pi$
$797$	−3.07246e120	−1.19390	−0.596948	+	0.802280i	$0.703620\pi$
$798$	−1.64487e118	−0.00606752
$799$	7.68241e120	2.69033
$800$	−2.55398e119	−0.0849147
$801$	−4.01055e120	−1.26606
$802$	3.13512e120	0.939763
$803$	−4.63902e120	−1.32048
$804$	−3.48137e118	−0.00941074
$805$	−2.53541e120	−0.650906
$806$	8.15675e119	0.198890
$807$	3.82789e118	0.00886560
$808$	−1.98593e120	−0.436910
$809$	−7.09944e120	−1.48375	−0.741874	−	0.670539i	$-0.766063\pi$
$809$	−7.09944e120	−1.48375	−0.741874	+	0.670539i	$0.766063\pi$
$810$	4.33132e120	0.859987
$811$	1.43742e120	0.271156	0.135578	−	0.990767i	$-0.456711\pi$
$811$	1.43742e120	0.271156	0.135578	+	0.990767i	$0.456711\pi$
$812$	−1.49461e119	−0.0267888
$813$	−5.82264e118	−0.00991658
$814$	−4.67634e120	−0.756821
$815$	8.07062e119	0.124127
$816$	3.52885e118	0.00515813
$817$	8.02053e120	1.11426
$818$	−7.43275e120	−0.981494
$819$	−5.74332e120	−0.720910
$820$	4.91294e120	0.586228
$821$	−7.78548e119	−0.0883170	−0.0441585	−	0.999025i	$-0.514061\pi$
$821$	−7.78548e119	−0.0883170	−0.0441585	+	0.999025i	$0.514061\pi$
$822$	1.26002e119	0.0135892
$823$	1.65033e121	1.69230	0.846151	−	0.532943i	$-0.178914\pi$
$823$	1.65033e121	1.69230	0.846151	+	0.532943i	$0.178914\pi$
$824$	1.42179e120	0.138630
$825$	8.56661e118	0.00794274
$826$	−3.78111e120	−0.333386
$827$	−1.35079e121	−1.13269	−0.566343	−	0.824170i	$-0.691642\pi$
$827$	−1.35079e121	−1.13269	−0.566343	+	0.824170i	$0.691642\pi$
$828$	−5.97705e120	−0.476681
$829$	6.10580e120	0.463158	0.231579	−	0.972816i	$-0.425611\pi$
$829$	6.10580e120	0.463158	0.231579	+	0.972816i	$0.425611\pi$
$830$	−1.22640e121	−0.884893
$831$	2.62421e119	0.0180118
$832$	2.46007e120	0.160631
$833$	1.96257e121	1.21915
$834$	−2.10160e119	−0.0124211
$835$	3.16681e121	1.78088
$836$	1.75724e121	0.940312
$837$	−9.96837e118	−0.00507595
$838$	2.39601e121	1.16108
$839$	1.35734e121	0.625991	0.312996	−	0.949755i	$-0.398667\pi$
$839$	1.35734e121	0.625991	0.312996	+	0.949755i	$0.398667\pi$
$840$	−6.37611e118	−0.00279876
$841$	−2.37168e121	−0.990881
$842$	−3.26695e121	−1.29924
$843$	3.73867e119	0.0141538
$844$	−5.20859e120	−0.187719
$845$	−2.30968e121	−0.792500
$846$	−3.27235e121	−1.06903
$847$	1.86388e121	0.579772
$848$	−1.13929e121	−0.337446
$849$	3.44899e119	0.00972798
$850$	2.24995e121	0.604347
$851$	−2.79768e121	−0.715684
$852$	9.72866e118	0.00237034
$853$	−1.76135e121	−0.408752	−0.204376	−	0.978892i	$-0.565517\pi$
$853$	−1.76135e121	−0.408752	−0.204376	+	0.978892i	$0.565517\pi$
$854$	4.29321e120	0.0949030
$855$	−7.61931e121	−1.60443
$856$	1.87917e121	0.376968
$857$	−1.71907e121	−0.328541	−0.164270	−	0.986415i	$-0.552527\pi$
$857$	−1.71907e121	−0.328541	−0.164270	+	0.986415i	$0.552527\pi$
$858$	−8.25163e119	−0.0150251
$859$	−1.24485e121	−0.215974	−0.107987	−	0.994152i	$-0.534440\pi$
$859$	−1.24485e121	−0.215974	−0.107987	+	0.994152i	$0.534440\pi$
$860$	3.10905e121	0.513975
$861$	3.97991e119	0.00626964
$862$	5.80326e121	0.871205
$863$	−1.09444e122	−1.56583	−0.782914	−	0.622130i	$-0.786267\pi$
$863$	−1.09444e122	−1.56583	−0.782914	+	0.622130i	$0.786267\pi$
$864$	−3.00646e119	−0.00409953
$865$	1.52365e122	1.98024
$866$	−1.68305e121	−0.208499
$867$	−2.12679e120	−0.0251149
$868$	−5.45464e120	−0.0614042
$869$	−5.76595e121	−0.618800
$870$	9.31085e118	0.000952665 0
$871$	2.13805e122	2.08576
$872$	−1.83645e120	−0.0170822
$873$	−9.48152e121	−0.840983
$874$	1.05129e122	0.889201
$875$	4.39791e121	0.354742
$876$	−6.97953e119	−0.00536916
$877$	8.92250e121	0.654642	0.327321	−	0.944913i	$-0.393854\pi$
$877$	8.92250e121	0.654642	0.327321	+	0.944913i	$0.393854\pi$
$878$	7.95791e121	0.556899
$879$	5.69860e119	0.00380391
$880$	6.81172e121	0.433736
$881$	4.39476e121	0.266953	0.133476	−	0.991052i	$-0.457386\pi$
$881$	4.39476e121	0.266953	0.133476	+	0.991052i	$0.457386\pi$
$882$	−8.35965e121	−0.484442
$883$	−1.29544e122	−0.716223	−0.358112	−	0.933679i	$-0.616579\pi$
$883$	−1.29544e122	−0.716223	−0.358112	+	0.933679i	$0.616579\pi$
$884$	−2.16722e122	−1.14323
$885$	2.35548e120	0.0118559
$886$	−1.28759e122	−0.618414
$887$	−1.63443e122	−0.749092	−0.374546	−	0.927208i	$-0.622201\pi$
$887$	−1.63443e122	−0.749092	−0.374546	+	0.927208i	$0.622201\pi$
$888$	−7.03568e119	−0.00307729
$889$	1.71937e122	0.717705
$890$	2.73442e122	1.08938
$891$	−3.74846e122	−1.42537
$892$	−1.95617e122	−0.710011
$893$	5.75567e122	1.99416
$894$	−5.85040e119	−0.00193499
$895$	−4.95299e122	−1.56391
$896$	−1.64512e121	−0.0495923
$897$	−4.93664e120	−0.0142084
$898$	−2.57103e122	−0.706545
$899$	7.96526e120	0.0209013
$900$	−9.58371e121	−0.240143
$901$	1.00366e123	2.40164
$902$	−4.25181e122	−0.971634
$903$	2.51860e120	0.00549690
$904$	4.68628e121	0.0976873
$905$	−9.22245e122	−1.83624
$906$	−1.95071e120	−0.00370998
$907$	5.78479e122	1.05096	0.525479	−	0.850807i	$-0.323886\pi$
$907$	5.78479e122	1.05096	0.525479	+	0.850807i	$0.323886\pi$
$908$	−4.28000e121	−0.0742815
$909$	−7.45212e122	−1.23560
$910$	3.91584e122	0.620307
$911$	4.10656e120	0.00621534	0.00310767	−	0.999995i	$-0.499011\pi$
$911$	4.10656e120	0.00621534	0.00310767	+	0.999995i	$0.499011\pi$
$912$	2.64382e120	0.00382337
$913$	1.06136e123	1.46665
$914$	−1.08474e121	−0.0143238
$915$	−2.67449e120	−0.00337494
$916$	−1.22950e121	−0.0148274
$917$	4.76898e122	0.549665
$918$	2.64856e121	0.0291768
$919$	−8.16430e122	−0.859657	−0.429828	−	0.902911i	$-0.641426\pi$
$919$	−8.16430e122	−0.859657	−0.429828	+	0.902911i	$0.641426\pi$
$920$	4.07520e122	0.410161
$921$	2.12202e120	0.00204162
$922$	9.94730e122	0.914897
$923$	−5.97478e122	−0.525353
$924$	5.51809e120	0.00463876
$925$	−4.48585e122	−0.360548
$926$	4.41224e122	0.339081
$927$	5.33522e122	0.392052
$928$	2.40232e121	0.0168807
$929$	2.25330e123	1.51415	0.757073	−	0.653330i	$-0.226629\pi$
$929$	2.25330e123	1.51415	0.757073	+	0.653330i	$0.226629\pi$
$930$	3.39802e120	0.00218365
$931$	1.47037e123	0.903677
$932$	−8.28770e122	−0.487162
$933$	7.99738e120	0.00449634
$934$	3.83572e122	0.206277
$935$	−6.00083e123	−3.08695
$936$	9.23133e122	0.454273
$937$	8.41190e122	0.396006	0.198003	−	0.980201i	$-0.436555\pi$
$937$	8.41190e122	0.396006	0.198003	+	0.980201i	$0.436555\pi$
$938$	−1.42977e123	−0.643947
$939$	6.91311e120	0.00297887
$940$	2.23111e123	0.919845
$941$	−3.05113e123	−1.20362	−0.601812	−	0.798638i	$-0.705554\pi$
$941$	−3.05113e123	−1.20362	−0.601812	+	0.798638i	$0.705554\pi$
$942$	2.31459e121	0.00873698
$943$	−2.54370e123	−0.918820
$944$	6.07744e122	0.210079
$945$	−4.78554e121	−0.0158311
$946$	−2.69067e123	−0.851879
$947$	−5.94796e123	−1.80237	−0.901185	−	0.433436i	$-0.857301\pi$
$947$	−5.94796e123	−1.80237	−0.901185	+	0.433436i	$0.857301\pi$
$948$	−8.67503e120	−0.00251608
$949$	4.28643e123	1.19000
$950$	1.68566e123	0.447962
$951$	−1.59801e121	−0.00406526
$952$	1.44928e123	0.352954
$953$	6.37411e123	1.48615	0.743077	−	0.669206i	$-0.233365\pi$
$953$	6.37411e123	1.48615	0.743077	+	0.669206i	$0.233365\pi$
$954$	−4.27513e123	−0.954314
$955$	2.77906e123	0.593961
$956$	−2.91653e123	−0.596848
$957$	−8.05790e120	−0.00157898
$958$	−3.75492e123	−0.704583
$959$	5.17480e123	0.929868
$960$	1.02484e121	0.00176360
$961$	−5.77696e123	−0.952091
$962$	4.32091e123	0.682040
$963$	7.05151e123	1.06608
$964$	2.42830e123	0.351646
$965$	9.94666e123	1.37973
$966$	3.30127e121	0.00438662
$967$	3.24393e123	0.412927	0.206463	−	0.978454i	$-0.433805\pi$
$967$	3.24393e123	0.412927	0.206463	+	0.978454i	$0.433805\pi$
$968$	−2.99585e123	−0.365336
$969$	−2.32909e122	−0.0272114
$970$	6.46457e123	0.723623
$971$	8.24664e123	0.884462	0.442231	−	0.896901i	$-0.354187\pi$
$971$	8.24664e123	0.884462	0.442231	+	0.896901i	$0.354187\pi$
$972$	−1.69228e122	−0.0173909
$973$	−8.63115e123	−0.849936
$974$	−1.26020e124	−1.18917
$975$	−7.91550e121	−0.00715792
$976$	−6.90054e122	−0.0598020
$977$	4.25843e123	0.353692	0.176846	−	0.984239i	$-0.443411\pi$
$977$	4.25843e123	0.353692	0.176846	+	0.984239i	$0.443411\pi$
$978$	−1.05085e121	−0.000836522 0
$979$	−2.36645e124	−1.80558
$980$	5.69967e123	0.416838
$981$	−6.89120e122	−0.0483094
$982$	−8.74194e123	−0.587464
$983$	4.08523e123	0.263175	0.131588	−	0.991305i	$-0.457993\pi$
$983$	4.08523e123	0.263175	0.131588	+	0.991305i	$0.457993\pi$
$984$	−6.39697e121	−0.00395073
$985$	−1.45797e124	−0.863265
$986$	−2.11634e123	−0.120141
$987$	1.80739e122	0.00983764
$988$	−1.62368e124	−0.847400
$989$	−1.60973e124	−0.805575
$990$	2.55607e124	1.22663
$991$	3.01427e124	1.38716	0.693578	−	0.720382i	$-0.256033\pi$
$991$	3.01427e124	1.38716	0.693578	+	0.720382i	$0.256033\pi$
$992$	8.76733e122	0.0386931
$993$	3.93636e122	0.0166610
$994$	3.99550e123	0.162194
$995$	−2.68050e124	−1.04366
$996$	1.59685e122	0.00596351
$997$	4.45172e123	0.159470	0.0797350	−	0.996816i	$-0.474593\pi$
$997$	4.45172e123	0.159470	0.0797350	+	0.996816i	$0.474593\pi$
$998$	3.21958e124	1.10632
$999$	−5.28058e122	−0.0174066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.84.a.a.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.84.a.a.1.2	✓	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 84 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-2.19902e12 q^{2} -7.32556e17 q^{3} +4.83570e24 q^{4} -1.23719e29 q^{5} +1.61091e30 q^{6} +6.61589e34 q^{7} -1.06338e37 q^{8} -3.99030e39 q^{9} +2.72062e41 q^{10} -2.35451e43 q^{11} -3.54242e42 q^{12} +2.17555e46 q^{13} -1.45485e47 q^{14} +9.06313e46 q^{15} +2.33840e49 q^{16} -2.06003e51 q^{17} +8.77477e51 q^{18} -1.54338e53 q^{19} -5.98270e53 q^{20} -4.84651e52 q^{21} +5.17762e55 q^{22} +3.09757e56 q^{23} +7.78987e54 q^{24} +4.96671e57 q^{25} -4.78409e58 q^{26} +5.84663e57 q^{27} +3.19925e59 q^{28} -4.67177e59 q^{29} -1.99300e59 q^{30} -1.70498e61 q^{31} -5.14220e61 q^{32} +1.72481e61 q^{33} +4.53006e63 q^{34} -8.18513e63 q^{35} -1.92959e64 q^{36} -9.03184e64 q^{37} +3.39393e65 q^{38} -1.59371e64 q^{39} +1.31561e66 q^{40} -8.21191e66 q^{41} +1.06576e65 q^{42} -5.19673e67 q^{43} -1.13857e68 q^{44} +4.93677e68 q^{45} -6.81164e68 q^{46} -3.72927e69 q^{47} -1.71301e67 q^{48} -9.52692e69 q^{49} -1.09219e70 q^{50} +1.50909e69 q^{51} +1.05203e71 q^{52} -4.87207e71 q^{53} -1.28569e70 q^{54} +2.91298e72 q^{55} -7.03522e71 q^{56} +1.13061e71 q^{57} +1.02733e72 q^{58} +2.59897e73 q^{59} +4.38266e71 q^{60} -2.95096e73 q^{61} +3.74928e73 q^{62} -2.63994e74 q^{63} +1.13078e74 q^{64} -2.69158e75 q^{65} -3.79289e73 q^{66} +9.82765e75 q^{67} -9.96170e75 q^{68} -2.26915e74 q^{69} +1.79993e76 q^{70} -2.74633e76 q^{71} +4.24322e76 q^{72} +1.97027e77 q^{73} +1.98612e77 q^{74} -3.63839e75 q^{75} -7.46332e77 q^{76} -1.55772e78 q^{77} +3.50461e76 q^{78} +2.44890e78 q^{79} -2.89306e78 q^{80} +1.59204e79 q^{81} +1.80582e79 q^{82} -4.50780e79 q^{83} -2.34363e77 q^{84} +2.54866e80 q^{85} +1.14277e80 q^{86} +3.42233e77 q^{87} +2.50374e80 q^{88} +1.00507e81 q^{89} -1.08561e81 q^{90} +1.43932e81 q^{91} +1.49790e81 q^{92} +1.24899e79 q^{93} +8.20075e81 q^{94} +1.90946e82 q^{95} +3.76695e79 q^{96} +2.37614e82 q^{97} +2.09499e82 q^{98} +9.39519e82 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6597069766656 q^{2} - 10\!\cdots\!76 q^{3} + 14\!\cdots\!12 q^{4} - 30\!\cdots\!50 q^{5} + 22\!\cdots\!52 q^{6} - 56\!\cdots\!88 q^{7} - 31\!\cdots\!24 q^{8} - 12\!\cdots\!89 q^{9} + 66\!\cdots\!00 q^{10}+ \cdots + 19\!\cdots\!32 q^{99}+O(q^{100}) \) 3 * q - 6597069766656 * q^2 - 101702746285870676076 * q^3 + 14507109835375550096474112 * q^4 - 3017971800730183156270503750 * q^5 + 223646704236134410563496760573952 * q^6 - 56868150843977452944646463510381688 * q^7 - 31901471898837980949691369446728269824 * q^8 - 1296874291714430512157132519227131713889 * q^9 + 6636590174405819175051197919076024320000 * q^10 - 14950728458111344172644916593801016887110564 * q^11 - 491804303642819560873193225250337807090581504 * q^12 - 1247981540309661732670825900285957005746323326 * q^13 + 125054386206145514986821355038283113695885131776 * q^14 + 4906492677986416590677954813004295766551257495000 * q^15 + 70152078591883340073776871970381584943484762062848 * q^16 + 308707077121944230069182989402617524752248119191702 * q^17 + 2851856727007561124341460266607934416403294194761728 * q^18 - 115503389070558091326292857695805111426543766855575900 * q^19 - 14594016131086299949534512224284046843955527024640000 * q^20 + 11732509177487968088847123014707541440900722409128681696 * q^21 + 32876999566829941323832368430603818937182001313850851328 * q^22 + 194663684763812875191113719688319482770211677377322471704 * q^23 + 1081489100891117403739876406035948694736079088282876510208 * q^24 + 12909879973100417219963359678562824650000813226633695703125 * q^25 + 2744340429640551861577672691219426502524181891794916605952 * q^26 - 290348404273186317953555961767716089388521032516233322490360 * q^27 - 274997503476095232555763502532521370272192681344292043620352 * q^28 - 13486329927712179588984433941095898960588114051806442043586670 * q^29 - 10789491502087740615267140807689853862322637644134340362240000 * q^30 - 15259967576282197636337376987931730029636327543719637765688544 * q^31 - 154266052248863066452028360864751609842131487403148112188932096 * q^32 - 1336547007031971436844230453948912193833625845633434107312028912 * q^33 - 678854041744640139306516867544963504950976601295805462823829504 * q^34 - 4715426532246777190495790364493797502235361786948801169983690000 * q^35 - 6271299264192038386568991427565833816353277190742157451493113856 * q^36 - 14494063415216183355357089013103312323277748587162249391027196198 * q^37 + 253994638661227949421879853425594813422920389098161789821832396800 * q^38 + 2251057512970717018303362982262318489471334094923390545655007255992 * q^39 + 32092580864159798905291356378425445483172353970827768920801280000 * q^40 - 14818758269141418586845700862345328527833540370975401597391422024914 * q^41 - 25800060527273309376046088034231202556535459599350794106835872776192 * q^42 - 185244954670444550871541201943532654714303102292687444038114532088196 * q^43 - 72297286620232071362282991511381118908365913109923040397065302573056 * q^44 - 445304744251191879515880421159304247588651697718013601376522535738750 * q^45 - 428069969807068049003296346049660667749219654314446370823457480900608 * q^46 - 3448406958823523161683735769272979667242315508968779579731926344222288 * q^47 - 2378219683485590377451108994563285321843377682147559120972784720674816 * q^48 - 24204657151984474899244957119159079945630782364557535531639947732611781 * q^49 - 28389126287232845662053308486508750926405703261079531118867251200000000 * q^50 - 159771856978893944372170339388872603934388296478829119559446399433647384 * q^51 - 6034868425931140751804427864360828512367115609300263711544913380245504 * q^52 - 38228075067609946992767570273872110566199949304778310964597335131494166 * q^53 + 638482893209150405286492417381461479698795761902271851111176947336478720 * q^54 + 1632368017260468921889695841941301488454386228416677729923288387359805000 * q^55 + 604725905362675374903561594720047340410969182507153225534677647364194304 * q^56 + 13669697388868679820702878590004238254426621204184980921073833602893558000 * q^57 + 29656753143086005983010235202600589534948527502759279769253966946070691840 * q^58 + 31613062218678070684199282229341608500802570309765108219439478779674808460 * q^59 + 23726342728671621972532883493096933196643847824391924780213039771156480000 * q^60 - 300977969222767422409550493089091515367954112401531859539082731681256713294 * q^61 + 33557023579214041146919698117421960784890438437795765451058589389750796288 * q^62 - 992074289040538657756858982598619777914871239570401795427028157894987504856 * q^63 + 339234636437449791279993120142640355038876908200118839959348390648182996992 * q^64 - 1917243958686383471256365173175992694077398080707307194070034549472858042500 * q^65 + 2939097950601727665997874813950879706773010366513123274278972745956588519424 * q^66 - 982637701678785800107254732493330334728874481890572467358891175920869750828 * q^67 + 1492815824921931868984511521678326816398325035943278430620923662929869406208 * q^68 - 21655460830208580430272460899997906856840259134834774174059414577437293487968 * q^69 + 10369332604257585886504029000280463291877051274072688973561080526541946880000 * q^70 + 81323855968755668931344497395237657205614815488847595977459622574528389719496 * q^71 + 13790732924484438391751897000498999873642596104530083953994562754930920128512 * q^72 + 548873577024651694456863478198166388574208592802271833905358733692520264564814 * q^73 + 31872782517505831055973500781076296651648875369662498089091954440696596791296 * q^74 + 912138201967791367839128382755536641522919078982168357289238136440309354687500 * q^75 - 558540117201567368175675431579752086015316422649958308352817055257239067033600 * q^76 - 3005028120885098102302957975353158884875680002579185981596130718386560350748256 * q^77 - 4950127820607654604433191636804447234772736136799089673740211744321710099267584 * q^78 - 4067605044230191215111847191307608889794835491462832667642191199625939386072880 * q^79 - 70572331650970498465875444222370963622121563461652994848505196398048706560000 * q^80 + 33808691764431685386797752948754870665430100591880108642034455139043697722146523 * q^81 + 32586794052245482920728996353009758149335491392120349430406306052065140332822528 * q^82 + 52320856384188709336165772408250585231532944867594284635669359634811993777696484 * q^83 + 56734933094123202469789754314629091063332551702292952842490677050041020117417984 * q^84 + 316267518620820766744316449951643581834460413806947373196136097716975356986172500 * q^85 + 407357963293983643532635012845570248041467928462558818351888431524425936710664192 * q^86 + 575303708654380961743785855428949551793413321741844564188457223801420243612082040 * q^87 + 158983414591198780636847931616474888961699234615448121130128552410941527437606912 * q^88 + 733253478112862467624920912575255942772815303482379067262950255952136468291966430 * q^89 + 979235488416006723349237105421270092547658702046078078973616575080920294359040000 * q^90 + 3958486486193561239681510386291189813367736615785635650689290525519286213694821296 * q^91 + 941335818609185126459229799669550776258775216538097901072710896698703865096175616 * q^92 + 13541048382265560471940050480602442790047804383299002720803504054466709325709234048 * q^93 + 7583127097060275514844244697156018876046698300587265525750399024903969543318142976 * q^94 + 51788977142106604382125904089728054618147393900592501799173468378425492743926275000 * q^95 + 5229760390796329962703262192937345156932680488448025329051964457649576842658578432 * q^96 + 117078360112868492279222552244621773215209350988306910045991279988287119545107278182 * q^97 + 53226603969876900450298872790891839174622038193494100284800792964463079454368858112 * q^98 + 198409433299529730956797285182513284269146472820417337852908952084356577918325681932 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more