LMFDB - Embedded newform 3.70.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,70,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 70, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 70);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 70 $
Character orbit:	$[\chi]$	$=$	3.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:	$90.4544859877$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 14\!\cdots\!28 $ x^6 - 3x^5 - 1895395655112138158x^4 - 215343254036998938223429254x^3 + 753811615313247966666178630793780821x^2 + 48156657138617542519489631631312055499331993*x - 14832095927450491582029231424734280560496715550059928
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{51}\cdot 3^{33}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 17\cdot 23^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$6.69381e8$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.39528e10 q^{2} -1.66772e16 q^{3} -1.65573e19 q^{4} -4.62338e23 q^{5} -3.99466e26 q^{6} +1.66345e28 q^{7} -1.45359e31 q^{8} +2.78128e32 q^{9} +O(q^{10})$	\(q+2.39528e10 q^{2} -1.66772e16 q^{3} -1.65573e19 q^{4} -4.62338e23 q^{5} -3.99466e26 q^{6} +1.66345e28 q^{7} -1.45359e31 q^{8} +2.78128e32 q^{9} -1.10743e34 q^{10} +6.54451e35 q^{11} +2.76129e35 q^{12} +1.76455e38 q^{13} +3.98444e38 q^{14} +7.71050e39 q^{15} -3.38401e41 q^{16} +5.07009e42 q^{17} +6.66196e42 q^{18} -5.99724e43 q^{19} +7.65507e42 q^{20} -2.77417e44 q^{21} +1.56759e46 q^{22} -5.78263e46 q^{23} +2.42417e47 q^{24} -1.48031e48 q^{25} +4.22660e48 q^{26} -4.63840e48 q^{27} -2.75423e47 q^{28} +2.05342e50 q^{29} +1.84688e50 q^{30} +3.09395e50 q^{31} +4.74782e50 q^{32} -1.09144e52 q^{33} +1.21443e53 q^{34} -7.69078e51 q^{35} -4.60505e51 q^{36} +4.46611e52 q^{37} -1.43651e54 q^{38} -2.94277e54 q^{39} +6.72048e54 q^{40} -3.77578e55 q^{41} -6.64493e54 q^{42} -1.71814e56 q^{43} -1.08359e55 q^{44} -1.28589e56 q^{45} -1.38510e57 q^{46} -2.06142e57 q^{47} +5.64358e57 q^{48} -2.02238e58 q^{49} -3.54576e58 q^{50} -8.45549e58 q^{51} -2.92162e57 q^{52} -2.93028e59 q^{53} -1.11103e59 q^{54} -3.02578e59 q^{55} -2.41797e59 q^{56} +1.00017e60 q^{57} +4.91851e60 q^{58} +1.11920e61 q^{59} -1.27665e59 q^{60} +1.32213e61 q^{61} +7.41090e60 q^{62} +4.62654e60 q^{63} +2.11129e62 q^{64} -8.15819e61 q^{65} -2.61431e62 q^{66} -6.79712e62 q^{67} -8.39470e61 q^{68} +9.64380e62 q^{69} -1.84216e62 q^{70} -2.76015e63 q^{71} -4.04283e63 q^{72} -2.39218e64 q^{73} +1.06976e63 q^{74} +2.46874e64 q^{75} +9.92980e62 q^{76} +1.08865e64 q^{77} -7.04877e64 q^{78} +4.57019e65 q^{79} +1.56456e65 q^{80} +7.73554e64 q^{81} -9.04405e65 q^{82} -2.33349e65 q^{83} +4.59327e63 q^{84} -2.34410e66 q^{85} -4.11544e66 q^{86} -3.42452e66 q^{87} -9.51300e66 q^{88} -2.55589e67 q^{89} -3.08008e66 q^{90} +2.93525e66 q^{91} +9.57447e65 q^{92} -5.15984e66 q^{93} -4.93769e67 q^{94} +2.77275e67 q^{95} -7.91803e66 q^{96} -6.05089e68 q^{97} -4.84418e68 q^{98} +1.82021e68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 869363388 q^{2} - 10\!\cdots\!14 q^{3}+ \cdots + 16\!\cdots\!66 q^{9}+O(q^{10}) $ 6 * q - 869363388 * q^2 - 100063090197999414 * q^3 + 1371216641348494011408 * q^4 + 536749102286059793452020 * q^5 + 14498531184713726896175772 * q^6 - 165486212832272947603119602016 * q^7 + 29031977276772288550932250437696 * q^8 + 1668770336662161067543714657390566 * q^9	$ 6 q - 869363388 q^{2} - 10\!\cdots\!14 q^{3}+ \cdots - 53\!\cdots\!36 q^{99}+O(q^{100}) $ 6 * q - 869363388 * q^2 - 100063090197999414 * q^3 + 1371216641348494011408 * q^4 + 536749102286059793452020 * q^5 + 14498531184713726896175772 * q^6 - 165486212832272947603119602016 * q^7 + 29031977276772288550932250437696 * q^8 + 1668770336662161067543714657390566 * q^9 - 30539001465788028222087378612341640 * q^10 - 1920537066516616187668579962543158376 * q^11 - 22868029077375361513671619126882219152 * q^12 - 47217968885374199615397355356796191852 * q^13 + 7064585334174201405371837809050003141312 * q^14 - 8951462305957535762539464569043499519380 * q^15 + 377157429568235813937466329721859576398080 * q^16 - 5058270084832851177273994934925110056607412 * q^17 - 241794638945752826180250102109053616166268 * q^18 - 65818466266910893781669604806057906253992088 * q^19 - 74276832342140585406878490976963545328073760 * q^20 + 2759843640193509337740927488460262535180203104 * q^21 - 57200945629382567456443201741175335542976506864 * q^22 - 51318359662817614748704757772348805853962165488 * q^23 - 484171560145322484473355383995534830167508585024 * q^24 + 1351900008806516831015099778033783730620565906650 * q^25 - 16207493799167654397027294571148058082290306700488 * q^26 - 27830386119528611875968901007343548725913806188054 * q^27 + 121390433570468044194114098496551362783272349932288 * q^28 + 785579239339018365983000259217156564097330312249124 * q^29 + 509304476371330630546739998356596576017896314633160 * q^30 + 6912833464261058549529914367563374193660948950153296 * q^31 + 36737392694691819442392877818076822209799633285776384 * q^32 + 32029145619242227636284505564240924042938191359531944 * q^33 + 253117449563254571066779054180560057695840514055176 * q^34 + 276611165060305397158461820821003699537527995207930560 * q^35 + 381374276036647353263390282147345081660028453185929488 * q^36 - 759040697498936685975105001963916849352981208607118396 * q^37 + 2103369059703889244990286400717050872850491394651970032 * q^38 + 787462646590588064894632608232796865789891597354595788 * q^39 - 32664751344775020838298315886208043642737757270980944000 * q^40 - 25768671104884673827847532722814331858226170126017093924 * q^41 - 117817373250822824537222457055662269520721648792989198528 * q^42 - 677055351038557514071054609066516734267888940905925188840 * q^43 + 238305524760672609941760876572355183014168119775154744384 * q^44 + 149285163354170121367980976931811340477842188257753607220 * q^45 + 8376385103625214805959746309869879529208374887220505747296 * q^46 + 7598599404092453023795535768684988784173129214818972342720 * q^47 - 6289922982288665238584151982726579281690322330718011787520 * q^48 + 39520658833284024797097689208298803008912245306300761939990 * q^49 - 28568855233568347359168873341651630916131610440562956535300 * q^50 + 84357689290745289159801421813736090901392081119475734009428 * q^51 - 841291935994679864415054059209490217537323675729185299370272 * q^52 - 449047684897777378052965016724937358227157858973850840458828 * q^53 + 4032453127703594497238226593730133400050584990603665094492 * q^54 + 2254548165992828810812926827082553754343205233701600459282640 * q^55 + 1641356236071085469964848605225791359818442190977904466652160 * q^56 + 1097666521126647756280461762493305085319303708198214764106072 * q^57 + 10854840022358605054892033620996887145323506082370467922396824 * q^58 + 9739940026219086244132886290748367338175220661414782584592728 * q^59 + 1238728229045548911290208746311830657587532274639907038129440 * q^60 - 59315134126314210963145084137204520506665661947323124957508780 * q^61 - 58284415626578488701665533854996023611020152283699473273044512 * q^62 - 46026413850176360961358753239584156335498095610944326498830176 * q^63 - 196087603577998032685001038699358078224720081884631691829178368 * q^64 - 368792752455446531625971790511790913672736652263934282973351720 * q^65 + 953950563653961367781459452317768129208925530496794989139829616 * q^66 + 1284404845637086838528947432298267008623636941858083561714308648 * q^67 - 1893312213205272549692225847826950804709005883992500832775643616 * q^68 + 855845608625648963144016144920672894915758664084152710799170672 * q^69 + 5651141511141393939253777145916410305809660448417857533217598080 * q^70 - 8028908380018744267365790936955359727729274918181835022662164368 * q^71 + 8074617082354583671186761526246370992341166934797564305786862656 * q^72 + 23917666927401813793494400679686156753046201104575562189407759612 * q^73 - 66571567863995212404482808802342117220480190894464062470316692648 * q^74 - 22545882086647115963110648728416884279973448838942742394179783850 * q^75 - 117137080475037691773181405327212499216032011801755896581802226752 * q^76 - 370001686623730076506835954110410638316696132431439489747825466752 * q^77 + 270295318984938200277077861249204534384356528838329715416149585672 * q^78 + 151166116158225305435965330589298930972238439200795534257670973040 * q^79 - 103132668838130690471303376617648857617362361028013189202842042880 * q^80 + 464132406087257065130090681062365209793088477541530761100710966726 * q^81 + 37460932835681010277915179679262266245084578260611880863596729448 * q^82 - 2199869100513279294476979658003407541858593100082068956813742116504 * q^83 - 2024450317255999993413036160714996242543447082962560389819327279872 * q^84 - 6491952514505341124698414891022457176579387500885906219615755954840 * q^85 - 23144659602467499127119271177953663689526653967585956674347553430256 * q^86 - 13101247713942660717783546201323542017367838371972839670487262335556 * q^87 - 65249604729672858795836798510445455460410612360663171240882606141184 * q^88 - 6686194196194507079670325678793857718304620226396138544648538601828 * q^89 - 8493763292898219695542584151776832427456280937959354979087550828040 * q^90 - 82097466714973722451927498084842810568687277892210020260162088564544 * q^91 + 4359811041243409323098555915712612735158801326895369127311689835904 * q^92 - 115286579743017176690026802480066668815283610415364196376484636361424 * q^93 - 560087180092970937289054350368454974923005535872515030885741348295552 * q^94 - 914644999797608066644469983517358223242420981276970458662113135611600 * q^95 - 612676173141378712760794918109470208907664831994025080010863094506496 * q^96 - 1193245591335854049619056301286742793562875638671855181199561300009332 * q^97 - 3639892838212491311414089259694594431294943863329296694030071739108188 * q^98 - 534155881177182136550108656986512933865188403627723332959024704380136 * 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 $

$2$	2.39528e10	0.985876	0.492938	−	0.870065i	$-0.335923\pi$
$2$	2.39528e10	0.985876	0.492938	+	0.870065i	$0.335923\pi$
$3$	−1.66772e16	−0.577350
$3$	−1.66772e16	−0.577350
$4$	−1.65573e19	−0.0280491
$5$	−4.62338e23	−0.355218	−0.177609	−	0.984101i	$-0.556836\pi$
$5$	−4.62338e23	−0.355218	−0.177609	+	0.984101i	$0.556836\pi$
$6$	−3.99466e26	−0.569196
$7$	1.66345e28	0.116179	0.0580896	−	0.998311i	$-0.481499\pi$
$7$	1.66345e28	0.116179	0.0580896	+	0.998311i	$0.481499\pi$
$8$	−1.45359e31	−1.01353
$9$	2.78128e32	0.333333
$10$	−1.10743e34	−0.350201
$11$	6.54451e35	0.772377	0.386188	−	0.922420i	$-0.373791\pi$
$11$	6.54451e35	0.772377	0.386188	+	0.922420i	$0.373791\pi$
$12$	2.76129e35	0.0161942
$13$	1.76455e38	0.654016	0.327008	−	0.945022i	$-0.393960\pi$
$13$	1.76455e38	0.654016	0.327008	+	0.945022i	$0.393960\pi$
$14$	3.98444e38	0.114538
$15$	7.71050e39	0.205085
$16$	−3.38401e41	−0.971164
$17$	5.07009e42	1.79692	0.898459	−	0.439058i	$-0.144688\pi$
$17$	5.07009e42	1.79692	0.898459	+	0.439058i	$0.144688\pi$
$18$	6.66196e42	0.328625
$19$	−5.99724e43	−0.458091	−0.229046	−	0.973416i	$-0.573561\pi$
$19$	−5.99724e43	−0.458091	−0.229046	+	0.973416i	$0.573561\pi$
$20$	7.65507e42	0.00996355
$21$	−2.77417e44	−0.0670761
$22$	1.56759e46	0.761467
$23$	−5.78263e46	−0.606060	−0.303030	−	0.952981i	$-0.597998\pi$
$23$	−5.78263e46	−0.606060	−0.303030	+	0.952981i	$0.597998\pi$
$24$	2.42417e47	0.585161
$25$	−1.48031e48	−0.873820
$26$	4.22660e48	0.644778
$27$	−4.63840e48	−0.192450
$28$	−2.75423e47	−0.00325872
$29$	2.05342e50	0.724012	0.362006	−	0.932176i	$-0.382092\pi$
$29$	2.05342e50	0.724012	0.362006	+	0.932176i	$0.382092\pi$
$30$	1.84688e50	0.202188
$31$	3.09395e50	0.109279	0.0546393	−	0.998506i	$-0.482599\pi$
$31$	3.09395e50	0.109279	0.0546393	+	0.998506i	$0.482599\pi$
$32$	4.74782e50	0.0560816
$33$	−1.09144e52	−0.445932
$34$	1.21443e53	1.77154
$35$	−7.69078e51	−0.0412689
$36$	−4.60505e51	−0.00934971
$37$	4.46611e52	0.0352347	0.0176173	−	0.999845i	$-0.494392\pi$
$37$	4.46611e52	0.0352347	0.0176173	+	0.999845i	$0.494392\pi$
$38$	−1.43651e54	−0.451621
$39$	−2.94277e54	−0.377596
$40$	6.72048e54	0.360023
$41$	−3.77578e55	−0.862905	−0.431453	−	0.902136i	$-0.641999\pi$
$41$	−3.77578e55	−0.862905	−0.431453	+	0.902136i	$0.641999\pi$
$42$	−6.64493e54	−0.0661287
$43$	−1.71814e56	−0.759272	−0.379636	−	0.925136i	$-0.623951\pi$
$43$	−1.71814e56	−0.759272	−0.379636	+	0.925136i	$0.623951\pi$
$44$	−1.08359e55	−0.0216645
$45$	−1.28589e56	−0.118406
$46$	−1.38510e57	−0.597499
$47$	−2.06142e57	−0.423438	−0.211719	−	0.977331i	$-0.567906\pi$
$47$	−2.06142e57	−0.423438	−0.211719	+	0.977331i	$0.567906\pi$
$48$	5.64358e57	0.560702
$49$	−2.02238e58	−0.986502
$50$	−3.54576e58	−0.861478
$51$	−8.45549e58	−1.03745
$52$	−2.92162e57	−0.0183446
$53$	−2.93028e59	−0.953657	−0.476828	−	0.878996i	$-0.658214\pi$
$53$	−2.93028e59	−0.953657	−0.476828	+	0.878996i	$0.658214\pi$
$54$	−1.11103e59	−0.189732
$55$	−3.02578e59	−0.274362
$56$	−2.41797e59	−0.117751
$57$	1.00017e60	0.264479
$58$	4.91851e60	0.713786
$59$	1.11920e61	0.900565	0.450283	−	0.892886i	$-0.351323\pi$
$59$	1.11920e61	0.900565	0.450283	+	0.892886i	$0.351323\pi$
$60$	−1.27665e59	−0.00575246
$61$	1.32213e61	0.336819	0.168409	−	0.985717i	$-0.446137\pi$
$61$	1.32213e61	0.336819	0.168409	+	0.985717i	$0.446137\pi$
$62$	7.41090e60	0.107735
$63$	4.62654e60	0.0387264
$64$	2.11129e62	1.02645
$65$	−8.15819e61	−0.232318
$66$	−2.61431e62	−0.439633
$67$	−6.79712e62	−0.680368	−0.340184	−	0.940359i	$-0.610489\pi$
$67$	−6.79712e62	−0.680368	−0.340184	+	0.940359i	$0.610489\pi$
$68$	−8.39470e61	−0.0504020
$69$	9.64380e62	0.349909
$70$	−1.84216e62	−0.0406860
$71$	−2.76015e63	−0.373697	−0.186848	−	0.982389i	$-0.559827\pi$
$71$	−2.76015e63	−0.373697	−0.186848	+	0.982389i	$0.559827\pi$
$72$	−4.04283e63	−0.337843
$73$	−2.39218e64	−1.24210	−0.621049	−	0.783772i	$-0.713293\pi$
$73$	−2.39218e64	−1.24210	−0.621049	+	0.783772i	$0.713293\pi$
$74$	1.06976e63	0.0347370
$75$	2.46874e64	0.504500
$76$	9.92980e62	0.0128491
$77$	1.08865e64	0.0897341
$78$	−7.04877e64	−0.372263
$79$	4.57019e65	1.55525	0.777623	−	0.628731i	$-0.216425\pi$
$79$	4.57019e65	1.55525	0.777623	+	0.628731i	$0.216425\pi$
$80$	1.56456e65	0.344975
$81$	7.73554e64	0.111111
$82$	−9.04405e65	−0.850717
$83$	−2.33349e65	−0.144481	−0.0722406	−	0.997387i	$-0.523015\pi$
$83$	−2.33349e65	−0.144481	−0.0722406	+	0.997387i	$0.523015\pi$
$84$	4.59327e63	0.00188143
$85$	−2.34410e66	−0.638297
$86$	−4.11544e66	−0.748548
$87$	−3.42452e66	−0.418009
$88$	−9.51300e66	−0.782826
$89$	−2.55589e67	−1.42425	−0.712126	−	0.702051i	$-0.752268\pi$
$89$	−2.55589e67	−1.42425	−0.712126	+	0.702051i	$0.752268\pi$
$90$	−3.08008e66	−0.116734
$91$	2.93525e66	0.0759830
$92$	9.57447e65	0.0169994
$93$	−5.15984e66	−0.0630921
$94$	−4.93769e67	−0.417458
$95$	2.77275e67	0.162722
$96$	−7.91803e66	−0.0323787
$97$	−6.05089e68	−1.73059	−0.865296	−	0.501262i	$-0.832869\pi$
$97$	−6.05089e68	−1.73059	−0.865296	+	0.501262i	$0.832869\pi$
$98$	−4.84418e68	−0.972569
$99$	1.82021e68	0.257459
$100$	2.45099e67	0.0245099
$101$	−1.83318e69	−1.30052	−0.650261	−	0.759711i	$-0.725340\pi$
$101$	−1.83318e69	−1.30052	−0.650261	+	0.759711i	$0.725340\pi$
$102$	−2.02533e69	−1.02280
$103$	−2.55352e69	−0.920990	−0.460495	−	0.887662i	$-0.652328\pi$
$103$	−2.55352e69	−0.920990	−0.460495	+	0.887662i	$0.652328\pi$
$104$	−2.56492e69	−0.662864
$105$	1.28261e68	0.0238266
$106$	−7.01886e69	−0.940187
$107$	−7.21580e69	−0.699108	−0.349554	−	0.936916i	$-0.613667\pi$
$107$	−7.21580e69	−0.699108	−0.349554	+	0.936916i	$0.613667\pi$
$108$	7.67993e67	0.00539806
$109$	−5.39342e68	−0.0275835	−0.0137918	−	0.999905i	$-0.504390\pi$
$109$	−5.39342e68	−0.0275835	−0.0137918	+	0.999905i	$0.504390\pi$
$110$	−7.24759e69	−0.270487
$111$	−7.44822e68	−0.0203427
$112$	−5.62915e69	−0.112829
$113$	8.34297e70	1.23059	0.615297	−	0.788296i	$-0.289036\pi$
$113$	8.34297e70	1.23059	0.615297	+	0.788296i	$0.289036\pi$
$114$	2.39569e70	0.260744
$115$	2.67353e70	0.215283
$116$	−3.39990e69	−0.0203079
$117$	4.90771e70	0.218005
$118$	2.68081e71	0.887845
$119$	8.43386e70	0.208764
$120$	−1.12079e71	−0.207860
$121$	−2.89646e71	−0.403434
$122$	3.16689e71	0.332061
$123$	6.29693e71	0.498199
$124$	−5.12275e69	−0.00306517
$125$	1.46764e72	0.665614
$126$	1.10819e71	0.0381794
$127$	4.41507e72	1.15800	0.579001	−	0.815327i	$-0.303443\pi$
$127$	4.41507e72	1.15800	0.579001	+	0.815327i	$0.303443\pi$
$128$	4.77688e72	0.955874
$129$	2.86538e72	0.438366
$130$	−1.95412e72	−0.229037
$131$	7.11253e72	0.639977	0.319988	−	0.947421i	$-0.396321\pi$
$131$	7.11253e72	0.639977	0.319988	+	0.947421i	$0.396321\pi$
$132$	1.80713e71	0.0125080
$133$	−9.97613e71	−0.0532207
$134$	−1.62810e73	−0.670759
$135$	2.14451e72	0.0683617
$136$	−7.36981e73	−1.82123
$137$	−3.31264e73	−0.635792	−0.317896	−	0.948126i	$-0.602976\pi$
$137$	−3.31264e73	−0.635792	−0.317896	+	0.948126i	$0.602976\pi$
$138$	2.30996e73	0.344966
$139$	−1.65048e74	−1.92133	−0.960663	−	0.277718i	$-0.910422\pi$
$139$	−1.65048e74	−1.92133	−0.960663	+	0.277718i	$0.910422\pi$
$140$	1.27338e71	0.00115756
$141$	3.43787e73	0.244472
$142$	−6.61134e73	−0.368419
$143$	1.15481e74	0.505147
$144$	−9.41190e73	−0.323721
$145$	−9.49373e73	−0.257182
$146$	−5.72996e74	−1.22455
$147$	3.37276e74	0.569557
$148$	−7.39467e71	−0.000988302 0
$149$	1.64270e75	1.74033	0.870165	−	0.492761i	$-0.164012\pi$
$149$	1.64270e75	1.74033	0.870165	+	0.492761i	$0.164012\pi$
$150$	5.91333e74	0.497375
$151$	−2.90832e75	−1.94508	−0.972539	−	0.232739i	$-0.925231\pi$
$151$	−2.90832e75	−1.94508	−0.972539	+	0.232739i	$0.925231\pi$
$152$	8.71750e74	0.464289
$153$	1.41014e75	0.598973
$154$	2.60762e74	0.0884666
$155$	−1.43045e74	−0.0388177
$156$	4.87243e73	0.0105912
$157$	−1.23249e75	−0.214905	−0.107453	−	0.994210i	$-0.534269\pi$
$157$	−1.23249e75	−0.214905	−0.107453	+	0.994210i	$0.534269\pi$
$158$	1.09469e76	1.53328
$159$	4.88689e75	0.550594
$160$	−2.19510e74	−0.0199212
$161$	−9.61914e74	−0.0704115
$162$	1.85288e75	0.109542
$163$	8.17439e75	0.390826	0.195413	−	0.980721i	$-0.437395\pi$
$163$	8.17439e75	0.390826	0.195413	+	0.980721i	$0.437395\pi$
$164$	6.25166e74	0.0242037
$165$	5.04614e75	0.158403
$166$	−5.58937e75	−0.142441
$167$	5.16077e76	1.06905	0.534523	−	0.845154i	$-0.320491\pi$
$167$	5.16077e76	1.06905	0.534523	+	0.845154i	$0.320491\pi$
$168$	4.03249e75	0.0679835
$169$	−4.16569e76	−0.572263
$170$	−5.61478e76	−0.629282
$171$	−1.66800e76	−0.152697
$172$	2.84478e75	0.0212969
$173$	−2.51278e77	−1.54015	−0.770075	−	0.637953i	$-0.779781\pi$
$173$	−2.51278e77	−1.54015	−0.770075	+	0.637953i	$0.779781\pi$
$174$	−8.20269e76	−0.412105
$175$	−2.46242e76	−0.101520
$176$	−2.21467e77	−0.750105
$177$	−1.86652e77	−0.519942
$178$	−6.12208e77	−1.40414
$179$	4.36355e76	0.0824918	0.0412459	−	0.999149i	$-0.486867\pi$
$179$	4.36355e76	0.0824918	0.0412459	+	0.999149i	$0.486867\pi$
$180$	2.12909e75	0.00332118
$181$	1.50483e78	1.93899	0.969496	−	0.245109i	$-0.0788237\pi$
$181$	1.50483e78	1.93899	0.969496	+	0.245109i	$0.0788237\pi$
$182$	7.03075e76	0.0749098
$183$	−2.20495e77	−0.194462
$184$	8.40555e77	0.614259
$185$	−2.06485e76	−0.0125160
$186$	−1.23593e77	−0.0622009
$187$	3.31813e78	1.38790
$188$	3.41315e76	0.0118771
$189$	−7.71576e76	−0.0223587
$190$	6.64153e77	0.160424
$191$	5.37729e78	1.08371	0.541854	−	0.840473i	$-0.317723\pi$
$191$	5.37729e78	1.08371	0.541854	+	0.840473i	$0.317723\pi$
$192$	−3.52104e78	−0.592623
$193$	3.59528e78	0.505831	0.252915	−	0.967488i	$-0.418611\pi$
$193$	3.59528e78	0.505831	0.252915	+	0.967488i	$0.418611\pi$
$194$	−1.44936e79	−1.70615
$195$	1.36056e78	0.134129
$196$	3.34851e77	0.0276705
$197$	9.48795e78	0.657791	0.328895	−	0.944366i	$-0.393324\pi$
$197$	9.48795e78	0.657791	0.328895	+	0.944366i	$0.393324\pi$
$198$	4.35993e78	0.253822
$199$	1.24431e78	0.0608831	0.0304415	−	0.999537i	$-0.490309\pi$
$199$	1.24431e78	0.0608831	0.0304415	+	0.999537i	$0.490309\pi$
$200$	2.15176e79	0.885642
$201$	1.13357e79	0.392811
$202$	−4.39099e79	−1.28215
$203$	3.41576e78	0.0841151
$204$	1.40000e78	0.0290996
$205$	1.74569e79	0.306519
$206$	−6.11641e79	−0.907982
$207$	−1.60831e79	−0.202020
$208$	−5.97126e79	−0.635157
$209$	−3.92490e79	−0.353819
$210$	3.07221e78	0.0234901
$211$	−2.11110e80	−1.37014	−0.685070	−	0.728478i	$-0.740228\pi$
$211$	−2.11110e80	−1.37014	−0.685070	+	0.728478i	$0.740228\pi$
$212$	4.85175e78	0.0267492
$213$	4.60315e79	0.215754
$214$	−1.72839e80	−0.689233
$215$	7.94364e79	0.269707
$216$	6.74231e79	0.195054
$217$	5.14665e78	0.0126959
$218$	−1.29188e79	−0.0271939
$219$	3.98949e80	0.717126
$220$	5.00986e78	0.00769562
$221$	8.94643e80	1.17521
$222$	−1.78406e79	−0.0200554
$223$	7.24716e80	0.697670	0.348835	−	0.937184i	$-0.386577\pi$
$223$	7.24716e80	0.697670	0.348835	+	0.937184i	$0.386577\pi$
$224$	7.89778e78	0.00651551
$225$	−4.11716e80	−0.291273
$226$	1.99838e81	1.21321
$227$	4.15581e80	0.216652	0.108326	−	0.994115i	$-0.465451\pi$
$227$	4.15581e80	0.216652	0.108326	+	0.994115i	$0.465451\pi$
$228$	−1.65601e79	−0.00741841
$229$	2.02521e81	0.780094	0.390047	−	0.920795i	$-0.372459\pi$
$229$	2.02521e81	0.780094	0.390047	+	0.920795i	$0.372459\pi$
$230$	6.40387e80	0.212242
$231$	−1.81556e80	−0.0518080
$232$	−2.98481e81	−0.733807
$233$	−6.19330e81	−1.31263	−0.656315	−	0.754487i	$-0.727886\pi$
$233$	−6.19330e81	−1.31263	−0.656315	+	0.754487i	$0.727886\pi$
$234$	1.17554e81	0.214926
$235$	9.53073e80	0.150413
$236$	−1.85310e80	−0.0252601
$237$	−7.62178e81	−0.897922
$238$	2.02015e81	0.205816
$239$	−1.62804e82	−1.43528	−0.717641	−	0.696413i	$-0.754778\pi$
$239$	−1.62804e82	−1.43528	−0.717641	+	0.696413i	$0.754778\pi$
$240$	−2.60924e81	−0.199171
$241$	7.57628e81	0.501035	0.250518	−	0.968112i	$-0.419399\pi$
$241$	7.57628e81	0.501035	0.250518	+	0.968112i	$0.419399\pi$
$242$	−6.93785e81	−0.397736
$243$	−1.29007e81	−0.0641500
$244$	−2.18909e80	−0.00944747
$245$	9.35024e81	0.350423
$246$	1.50829e82	0.491162
$247$	−1.05824e82	−0.299599
$248$	−4.49733e81	−0.110757
$249$	3.89160e81	0.0834163
$250$	3.51540e82	0.656213
$251$	−4.97547e82	−0.809265	−0.404633	−	0.914479i	$-0.632601\pi$
$251$	−4.97547e82	−0.809265	−0.404633	+	0.914479i	$0.632601\pi$
$252$	−7.66029e79	−0.00108624
$253$	−3.78445e82	−0.468106
$254$	1.05753e83	1.14165
$255$	3.90930e82	0.368521
$256$	−1.02088e82	−0.0840806
$257$	−1.28355e83	−0.924100	−0.462050	−	0.886854i	$-0.652886\pi$
$257$	−1.28355e83	−0.924100	−0.462050	+	0.886854i	$0.652886\pi$
$258$	6.86340e82	0.432175
$259$	7.42917e80	0.00409353
$260$	1.35077e81	0.00651632
$261$	5.71113e82	0.241337
$262$	1.70365e83	0.630938
$263$	2.59449e83	0.842516	0.421258	−	0.906941i	$-0.361589\pi$
$263$	2.59449e83	0.842516	0.421258	+	0.906941i	$0.361589\pi$
$264$	1.58650e83	0.451965
$265$	1.35478e83	0.338756
$266$	−2.38957e82	−0.0524690
$267$	4.26250e83	0.822293
$268$	1.12542e82	0.0190837
$269$	1.09055e83	0.162627	0.0813136	−	0.996689i	$-0.474088\pi$
$269$	1.09055e83	0.162627	0.0813136	+	0.996689i	$0.474088\pi$
$270$	5.13671e82	0.0673961
$271$	−1.03764e84	−1.19841	−0.599206	−	0.800595i	$-0.704517\pi$
$271$	−1.03764e84	−1.19841	−0.599206	+	0.800595i	$0.704517\pi$
$272$	−1.71573e84	−1.74510
$273$	−4.89516e82	−0.0438688
$274$	−7.93472e83	−0.626812
$275$	−9.68789e83	−0.674918
$276$	−1.59675e82	−0.00981463
$277$	2.40863e84	1.30683	0.653414	−	0.757000i	$-0.273336\pi$
$277$	2.40863e84	1.30683	0.653414	+	0.757000i	$0.273336\pi$
$278$	−3.95338e84	−1.89419
$279$	8.60516e82	0.0364262
$280$	1.11792e83	0.0418272
$281$	−3.24873e84	−1.07484	−0.537421	−	0.843314i	$-0.680602\pi$
$281$	−3.24873e84	−1.07484	−0.537421	+	0.843314i	$0.680602\pi$
$282$	8.23467e83	0.241019
$283$	3.31937e84	0.859852	0.429926	−	0.902864i	$-0.358540\pi$
$283$	3.31937e84	0.859852	0.429926	+	0.902864i	$0.358540\pi$
$284$	4.57006e82	0.0104819
$285$	−4.62417e83	−0.0939477
$286$	2.76610e84	0.498012
$287$	−6.28083e83	−0.100252
$288$	1.32050e83	0.0186939
$289$	1.77447e85	2.22891
$290$	−2.27402e84	−0.253550
$291$	1.00912e85	0.999157
$292$	3.96081e83	0.0348398
$293$	−1.50273e85	−1.17476	−0.587378	−	0.809313i	$-0.699840\pi$
$293$	−1.50273e85	−1.17476	−0.587378	+	0.809313i	$0.699840\pi$
$294$	8.07872e84	0.561513
$295$	−5.17451e84	−0.319897
$296$	−6.49188e83	−0.0357113
$297$	−3.03560e84	−0.148644
$298$	3.93473e85	1.71575
$299$	−1.02037e85	−0.396373
$300$	−4.08756e83	−0.0141508
$301$	−2.85805e84	−0.0882116
$302$	−6.96625e85	−1.91761
$303$	3.05723e85	0.750857
$304$	2.02947e85	0.444882
$305$	−6.11273e84	−0.119644
$306$	3.37768e85	0.590512
$307$	−1.00148e86	−1.56447	−0.782237	−	0.622980i	$-0.785922\pi$
$307$	−1.00148e86	−1.56447	−0.782237	+	0.622980i	$0.785922\pi$
$308$	−1.80251e83	−0.00251696
$309$	4.25855e85	0.531734
$310$	−3.42634e84	−0.0382695
$311$	−1.35218e86	−1.35145	−0.675727	−	0.737152i	$-0.736170\pi$
$311$	−1.35218e86	−1.35145	−0.675727	+	0.737152i	$0.736170\pi$
$312$	4.27757e85	0.382705
$313$	2.26922e84	0.0181802	0.00909008	−	0.999959i	$-0.497106\pi$
$313$	2.26922e84	0.0181802	0.00909008	+	0.999959i	$0.497106\pi$
$314$	−2.95218e85	−0.211870
$315$	−2.13902e84	−0.0137563
$316$	−7.56699e84	−0.0436233
$317$	−1.39342e86	−0.720340	−0.360170	−	0.932887i	$-0.617281\pi$
$317$	−1.39342e86	−0.720340	−0.360170	+	0.932887i	$0.617281\pi$
$318$	1.17055e86	0.542817
$319$	1.34386e86	0.559210
$320$	−9.76132e85	−0.364615
$321$	1.20339e86	0.403630
$322$	−2.30406e85	−0.0694170
$323$	−3.04066e86	−0.823153
$324$	−1.28080e84	−0.00311657
$325$	−2.61208e86	−0.571492
$326$	1.95800e86	0.385306
$327$	8.99470e84	0.0159254
$328$	5.48841e86	0.874579
$329$	−3.42908e85	−0.0491947
$330$	1.20869e86	0.156166
$331$	1.01290e87	1.17897	0.589485	−	0.807779i	$-0.299331\pi$
$331$	1.01290e87	1.17897	0.589485	+	0.807779i	$0.299331\pi$
$332$	3.86362e84	0.00405257
$333$	1.24215e85	0.0117449
$334$	1.23615e87	1.05395
$335$	3.14257e86	0.241679
$336$	9.38783e85	0.0651419
$337$	1.58555e87	0.992998	0.496499	−	0.868037i	$-0.334619\pi$
$337$	1.58555e87	0.992998	0.496499	+	0.868037i	$0.334619\pi$
$338$	−9.97802e86	−0.564181
$339$	−1.39137e87	−0.710483
$340$	3.88119e85	0.0179037
$341$	2.02484e86	0.0844043
$342$	−3.99534e86	−0.150540
$343$	−6.77430e86	−0.230790
$344$	2.49747e87	0.769544
$345$	−4.45870e86	−0.124294
$346$	−6.01881e87	−1.51840
$347$	−7.98893e87	−1.82441	−0.912203	−	0.409739i	$-0.865620\pi$
$347$	−7.98893e87	−1.82441	−0.912203	+	0.409739i	$0.865620\pi$
$348$	5.67007e85	0.0117248
$349$	−7.84778e87	−1.46984	−0.734919	−	0.678155i	$-0.762780\pi$
$349$	−7.84778e87	−1.46984	−0.734919	+	0.678155i	$0.762780\pi$
$350$	−5.89821e86	−0.100086
$351$	−8.18468e86	−0.125865
$352$	3.10721e86	0.0433161
$353$	1.26265e88	1.59608	0.798039	−	0.602606i	$-0.205871\pi$
$353$	1.26265e88	1.59608	0.798039	+	0.602606i	$0.205871\pi$
$354$	−4.47084e87	−0.512598
$355$	1.27612e87	0.132744
$356$	4.23186e86	0.0399490
$357$	−1.40653e87	−0.120530
$358$	1.04520e87	0.0813267
$359$	1.30027e88	0.918912	0.459456	−	0.888201i	$-0.348044\pi$
$359$	1.30027e88	0.918912	0.459456	+	0.888201i	$0.348044\pi$
$360$	1.86916e87	0.120008
$361$	−1.35428e88	−0.790152
$362$	3.60449e88	1.91160
$363$	4.83048e87	0.232923
$364$	−4.85997e85	−0.00213126
$365$	1.10600e88	0.441216
$366$	−5.28147e87	−0.191716
$367$	−6.67758e87	−0.220617	−0.110309	−	0.993897i	$-0.535184\pi$
$367$	−6.67758e87	−0.220617	−0.110309	+	0.993897i	$0.535184\pi$
$368$	1.95685e88	0.588583
$369$	−1.05015e88	−0.287635
$370$	−4.94591e86	−0.0123392
$371$	−4.87439e87	−0.110795
$372$	8.54330e85	0.00176968
$373$	−8.74597e88	−1.65140	−0.825702	−	0.564106i	$-0.809221\pi$
$373$	−8.74597e88	−1.65140	−0.825702	+	0.564106i	$0.809221\pi$
$374$	7.94785e88	1.36829
$375$	−2.44760e88	−0.384293
$376$	2.99645e88	0.429167
$377$	3.62335e88	0.473515
$378$	−1.84814e87	−0.0220429
$379$	−1.94584e88	−0.211863	−0.105932	−	0.994373i	$-0.533782\pi$
$379$	−1.94584e88	−0.211863	−0.105932	+	0.994373i	$0.533782\pi$
$380$	−4.59093e86	−0.00456422
$381$	−7.36309e88	−0.668572
$382$	1.28801e89	1.06840
$383$	−6.97513e88	−0.528682	−0.264341	−	0.964429i	$-0.585154\pi$
$383$	−6.97513e88	−0.528682	−0.264341	+	0.964429i	$0.585154\pi$
$384$	−7.96649e88	−0.551874
$385$	−5.03324e87	−0.0318751
$386$	8.61171e88	0.498686
$387$	−4.77864e88	−0.253091
$388$	1.00186e88	0.0485416
$389$	−3.85925e89	−1.71097	−0.855484	−	0.517829i	$-0.826740\pi$
$389$	−3.85925e89	−1.71097	−0.855484	+	0.517829i	$0.826740\pi$
$390$	3.25892e88	0.132234
$391$	−2.93185e89	−1.08904
$392$	2.93970e89	0.999848
$393$	−1.18617e89	−0.369491
$394$	2.27263e89	0.648500
$395$	−2.11297e89	−0.552451
$396$	−3.01378e87	−0.00722150
$397$	−2.06569e89	−0.453726	−0.226863	−	0.973927i	$-0.572847\pi$
$397$	−2.06569e89	−0.453726	−0.226863	+	0.973927i	$0.572847\pi$
$398$	2.98047e88	0.0600231
$399$	1.66374e88	0.0307270
$400$	5.00939e89	0.848623
$401$	−6.82163e88	−0.106025	−0.0530124	−	0.998594i	$-0.516882\pi$
$401$	−6.82163e88	−0.106025	−0.0530124	+	0.998594i	$0.516882\pi$
$402$	2.71522e89	0.387263
$403$	5.45943e88	0.0714700
$404$	3.03525e88	0.0364785
$405$	−3.57644e88	−0.0394687
$406$	8.18172e88	0.0829270
$407$	2.92285e88	0.0272144
$408$	1.22908e90	1.05149
$409$	8.75562e89	0.688387	0.344194	−	0.938899i	$-0.388152\pi$
$409$	8.75562e89	0.688387	0.344194	+	0.938899i	$0.388152\pi$
$410$	4.18141e89	0.302190
$411$	5.52455e89	0.367075
$412$	4.22794e88	0.0258330
$413$	1.86174e89	0.104627
$414$	−3.85237e89	−0.199166
$415$	1.07886e89	0.0513223
$416$	8.37777e88	0.0366782
$417$	2.75254e90	1.10928
$418$	−9.40124e89	−0.348822
$419$	−2.00842e90	−0.686230	−0.343115	−	0.939293i	$-0.611482\pi$
$419$	−2.00842e90	−0.686230	−0.343115	+	0.939293i	$0.611482\pi$
$420$	−2.12365e87	−0.000668316 0
$421$	−4.17626e90	−1.21075	−0.605375	−	0.795940i	$-0.706977\pi$
$421$	−4.17626e90	−1.21075	−0.605375	+	0.795940i	$0.706977\pi$
$422$	−5.05669e90	−1.35079
$423$	−5.73339e89	−0.141146
$424$	4.25942e90	0.966558
$425$	−7.50531e90	−1.57018
$426$	1.10259e90	0.212707
$427$	2.19931e89	0.0391313
$428$	1.19474e89	0.0196094
$429$	−1.92590e90	−0.291647
$430$	1.90273e90	0.265898
$431$	−8.94786e90	−1.15413	−0.577063	−	0.816700i	$-0.695801\pi$
$431$	−8.94786e90	−1.15413	−0.577063	+	0.816700i	$0.695801\pi$
$432$	1.56964e90	0.186901
$433$	−7.23035e90	−0.794926	−0.397463	−	0.917618i	$-0.630109\pi$
$433$	−7.23035e90	−0.794926	−0.397463	+	0.917618i	$0.630109\pi$
$434$	1.23277e89	0.0125166
$435$	1.58329e90	0.148484
$436$	8.93003e87	0.000773694 0
$437$	3.46798e90	0.277631
$438$	9.55596e90	0.706997
$439$	2.87957e91	1.96925	0.984627	−	0.174672i	$-0.0558866\pi$
$439$	2.87957e91	1.96925	0.984627	+	0.174672i	$0.0558866\pi$
$440$	4.39822e90	0.278074
$441$	−5.62481e90	−0.328834
$442$	2.14292e91	1.15861
$443$	−9.86706e90	−0.493468	−0.246734	−	0.969083i	$-0.579357\pi$
$443$	−9.86706e90	−0.493468	−0.246734	+	0.969083i	$0.579357\pi$
$444$	1.23322e88	0.000570596 0
$445$	1.18169e91	0.505920
$446$	1.73590e91	0.687816
$447$	−2.73956e91	−1.00478
$448$	3.51204e90	0.119253
$449$	−1.44841e91	−0.455398	−0.227699	−	0.973732i	$-0.573120\pi$
$449$	−1.44841e91	−0.455398	−0.227699	+	0.973732i	$0.573120\pi$
$450$	−9.86177e90	−0.287159
$451$	−2.47106e91	−0.666488
$452$	−1.38137e90	−0.0345171
$453$	4.85025e91	1.12299
$454$	9.95433e90	0.213592
$455$	−1.35708e90	−0.0269905
$456$	−1.45383e91	−0.268057
$457$	−7.07406e91	−1.20937	−0.604686	−	0.796464i	$-0.706701\pi$
$457$	−7.07406e91	−1.20937	−0.604686	+	0.796464i	$0.706701\pi$
$458$	4.85096e91	0.769075
$459$	−2.35171e91	−0.345817
$460$	−4.42665e89	−0.00603851
$461$	1.29637e92	1.64077	0.820383	−	0.571814i	$-0.193760\pi$
$461$	1.29637e92	1.64077	0.820383	+	0.571814i	$0.193760\pi$
$462$	−4.34878e90	−0.0510762
$463$	−4.24567e91	−0.462809	−0.231405	−	0.972858i	$-0.574332\pi$
$463$	−4.24567e91	−0.462809	−0.231405	+	0.972858i	$0.574332\pi$
$464$	−6.94878e91	−0.703135
$465$	2.38559e90	0.0224114
$466$	−1.48347e92	−1.29409
$467$	1.37309e92	1.11241	0.556206	−	0.831044i	$-0.312257\pi$
$467$	1.37309e92	1.11241	0.556206	+	0.831044i	$0.312257\pi$
$468$	−8.12584e89	−0.00611486
$469$	−1.13067e91	−0.0790446
$470$	2.28288e91	0.148288
$471$	2.05545e91	0.124076
$472$	−1.62686e92	−0.912749
$473$	−1.12444e92	−0.586444
$474$	−1.82563e92	−0.885239
$475$	8.87777e91	0.400290
$476$	−1.39642e90	−0.00585566
$477$	−8.14995e91	−0.317886
$478$	−3.89962e92	−1.41501
$479$	3.66852e92	1.23855	0.619277	−	0.785172i	$-0.287426\pi$
$479$	3.66852e92	1.23855	0.619277	+	0.785172i	$0.287426\pi$
$480$	3.66081e90	0.0115015
$481$	7.88068e90	0.0230440
$482$	1.81473e92	0.493958
$483$	1.60420e91	0.0406521
$484$	4.79576e90	0.0113160
$485$	2.79756e92	0.614737
$486$	−3.09008e91	−0.0632440
$487$	7.09169e92	1.35207	0.676037	−	0.736868i	$-0.263696\pi$
$487$	7.09169e92	1.35207	0.676037	+	0.736868i	$0.263696\pi$
$488$	−1.92183e92	−0.341375
$489$	−1.36326e92	−0.225643
$490$	2.23965e92	0.345474
$491$	8.65015e92	1.24369	0.621845	−	0.783140i	$-0.286383\pi$
$491$	8.65015e92	1.24369	0.621845	+	0.783140i	$0.286383\pi$
$492$	−1.04260e91	−0.0139740
$493$	1.04110e93	1.30099
$494$	−2.53479e92	−0.295367
$495$	−8.41554e91	−0.0914540
$496$	−1.04700e92	−0.106127
$497$	−4.59138e91	−0.0434158
$498$	9.32149e91	0.0822381
$499$	1.22185e92	0.100589	0.0502945	−	0.998734i	$-0.483984\pi$
$499$	1.22185e92	0.100589	0.0502945	+	0.998734i	$0.483984\pi$
$500$	−2.43001e91	−0.0186699
$501$	−8.60671e92	−0.617214
$502$	−1.19177e93	−0.797835
$503$	−1.85218e93	−1.15768	−0.578839	−	0.815442i	$-0.696494\pi$
$503$	−1.85218e93	−1.15768	−0.578839	+	0.815442i	$0.696494\pi$
$504$	−6.72507e91	−0.0392503
$505$	8.47549e92	0.461969
$506$	−9.06483e92	−0.461495
$507$	6.94720e92	0.330396
$508$	−7.31015e91	−0.0324809
$509$	−2.21895e93	−0.921265	−0.460632	−	0.887591i	$-0.652377\pi$
$509$	−2.21895e93	−0.921265	−0.460632	+	0.887591i	$0.652377\pi$
$510$	9.36387e92	0.363316
$511$	−3.97929e92	−0.144306
$512$	−3.06430e93	−1.03877
$513$	2.78176e92	0.0881597
$514$	−3.07446e93	−0.911048
$515$	1.18059e93	0.327152
$516$	−4.74429e91	−0.0122958
$517$	−1.34910e93	−0.327054
$518$	1.77950e91	0.00403571
$519$	4.19060e93	0.889206
$520$	1.18586e93	0.235461
$521$	−2.02408e93	−0.376121	−0.188060	−	0.982157i	$-0.560220\pi$
$521$	−2.02408e93	−0.376121	−0.188060	+	0.982157i	$0.560220\pi$
$522$	1.36798e93	0.237929
$523$	5.37390e93	0.874947	0.437473	−	0.899231i	$-0.355873\pi$
$523$	5.37390e93	0.874947	0.437473	+	0.899231i	$0.355873\pi$
$524$	−1.17764e92	−0.0179508
$525$	4.10663e92	0.0586124
$526$	6.21454e93	0.830616
$527$	1.56866e93	0.196365
$528$	3.69344e93	0.433073
$529$	−5.75987e93	−0.632692
$530$	3.24509e93	0.333971
$531$	3.11283e93	0.300188
$532$	1.65178e91	0.00149279
$533$	−6.66254e93	−0.564354
$534$	1.02099e94	0.810678
$535$	3.33614e93	0.248336
$536$	9.88019e93	0.689573
$537$	−7.27718e92	−0.0476267
$538$	2.61219e93	0.160330
$539$	−1.32355e94	−0.761952
$540$	−3.55073e91	−0.00191749
$541$	3.33720e93	0.169074	0.0845369	−	0.996420i	$-0.473059\pi$
$541$	3.33720e93	0.169074	0.0845369	+	0.996420i	$0.473059\pi$
$542$	−2.48544e94	−1.18148
$543$	−2.50963e94	−1.11948
$544$	2.40719e93	0.100774
$545$	2.49358e92	0.00979816
$546$	−1.17253e93	−0.0432492
$547$	3.69661e94	1.28009	0.640046	−	0.768337i	$-0.278915\pi$
$547$	3.69661e94	1.28009	0.640046	+	0.768337i	$0.278915\pi$
$548$	5.48484e92	0.0178334
$549$	3.67723e93	0.112273
$550$	−2.32053e94	−0.665386
$551$	−1.23148e94	−0.331664
$552$	−1.40181e94	−0.354642
$553$	7.60229e93	0.180687
$554$	5.76936e94	1.28837
$555$	3.44360e92	0.00722611
$556$	2.73275e93	0.0538915
$557$	−5.03934e94	−0.934048	−0.467024	−	0.884245i	$-0.654674\pi$
$557$	−5.03934e94	−0.934048	−0.467024	+	0.884245i	$0.654674\pi$
$558$	2.06118e93	0.0359117
$559$	−3.03175e94	−0.496576
$560$	2.60257e93	0.0400789
$561$	−5.53370e94	−0.801303
$562$	−7.78162e94	−1.05966
$563$	2.97412e94	0.380907	0.190453	−	0.981696i	$-0.439004\pi$
$563$	2.97412e94	0.380907	0.190453	+	0.981696i	$0.439004\pi$
$564$	−5.69217e92	−0.00685724
$565$	−3.85728e94	−0.437129
$566$	7.95084e94	0.847707
$567$	1.28677e93	0.0129088
$568$	4.01211e94	0.378753
$569$	2.13163e94	0.189382	0.0946909	−	0.995507i	$-0.469814\pi$
$569$	2.13163e94	0.189382	0.0946909	+	0.995507i	$0.469814\pi$
$570$	−1.10762e94	−0.0926208
$571$	−4.23698e94	−0.333511	−0.166756	−	0.985998i	$-0.553329\pi$
$571$	−4.23698e94	−0.333511	−0.166756	+	0.985998i	$0.553329\pi$
$572$	−1.91205e93	−0.0141689
$573$	−8.96780e94	−0.625679
$574$	−1.50444e94	−0.0988356
$575$	8.56009e94	0.529587
$576$	5.87210e94	0.342151
$577$	1.60657e95	0.881727	0.440863	−	0.897574i	$-0.354672\pi$
$577$	1.60657e95	0.881727	0.440863	+	0.897574i	$0.354672\pi$
$578$	4.25036e95	2.19743
$579$	−5.99591e94	−0.292041
$580$	1.57190e93	0.00721373
$581$	−3.88165e93	−0.0167857
$582$	2.41712e95	0.985045
$583$	−1.91773e95	−0.736582
$584$	3.47724e95	1.25890
$585$	−2.26902e94	−0.0774394
$586$	−3.59946e95	−1.15816
$587$	3.03565e95	0.920952	0.460476	−	0.887672i	$-0.347679\pi$
$587$	3.03565e95	0.920952	0.460476	+	0.887672i	$0.347679\pi$
$588$	−5.58438e93	−0.0159756
$589$	−1.85552e94	−0.0500596
$590$	−1.23944e95	−0.315379
$591$	−1.58232e95	−0.379776
$592$	−1.51134e94	−0.0342186
$593$	−8.80139e95	−1.88003	−0.940014	−	0.341135i	$-0.889189\pi$
$593$	−8.80139e95	−1.88003	−0.940014	+	0.341135i	$0.889189\pi$
$594$	−7.27113e94	−0.146544
$595$	−3.89930e94	−0.0741568
$596$	−2.71986e94	−0.0488147
$597$	−2.07515e94	−0.0351509
$598$	−2.44409e95	−0.390774
$599$	−8.20297e95	−1.23807	−0.619036	−	0.785363i	$-0.712477\pi$
$599$	−8.20297e95	−1.23807	−0.619036	+	0.785363i	$0.712477\pi$
$600$	−3.58852e95	−0.511326
$601$	−2.80333e95	−0.377142	−0.188571	−	0.982060i	$-0.560386\pi$
$601$	−2.80333e95	−0.377142	−0.188571	+	0.982060i	$0.560386\pi$
$602$	−6.84584e94	−0.0869657
$603$	−1.89047e95	−0.226789
$604$	4.81538e94	0.0545578
$605$	1.33915e95	0.143307
$606$	7.32293e95	0.740251
$607$	1.62662e96	1.55338	0.776688	−	0.629885i	$-0.216898\pi$
$607$	1.62662e96	1.55338	0.776688	+	0.629885i	$0.216898\pi$
$608$	−2.84738e94	−0.0256905
$609$	−5.69653e94	−0.0485639
$610$	−1.46417e95	−0.117954
$611$	−3.63748e95	−0.276935
$612$	−2.33480e94	−0.0168007
$613$	1.98096e96	1.34738	0.673690	−	0.739014i	$-0.264708\pi$
$613$	1.98096e96	1.34738	0.673690	+	0.739014i	$0.264708\pi$
$614$	−2.39883e96	−1.54238
$615$	−2.91131e95	−0.176969
$616$	−1.58244e95	−0.0909481
$617$	1.25220e96	0.680512	0.340256	−	0.940333i	$-0.389486\pi$
$617$	1.25220e96	0.680512	0.340256	+	0.940333i	$0.389486\pi$
$618$	1.02004e96	0.524224
$619$	3.98006e96	1.93447	0.967235	−	0.253884i	$-0.0817081\pi$
$619$	3.98006e96	1.93447	0.967235	+	0.253884i	$0.0817081\pi$
$620$	2.36844e93	0.00108880
$621$	2.68222e95	0.116636
$622$	−3.23886e96	−1.33237
$623$	−4.25160e95	−0.165468
$624$	9.95838e95	0.366708
$625$	1.82920e96	0.637382
$626$	5.43543e94	0.0179234
$627$	6.54562e95	0.204278
$628$	2.04068e94	0.00602791
$629$	2.26436e95	0.0633138
$630$	−5.12357e94	−0.0135620
$631$	2.33099e96	0.584154	0.292077	−	0.956395i	$-0.405654\pi$
$631$	2.33099e96	0.584154	0.292077	+	0.956395i	$0.405654\pi$
$632$	−6.64315e96	−1.57629
$633$	3.52072e96	0.791050
$634$	−3.33764e96	−0.710166
$635$	−2.04126e96	−0.411343
$636$	−8.09136e94	−0.0154437
$637$	−3.56859e96	−0.645188
$638$	3.21892e96	0.551312
$639$	−7.67676e95	−0.124566
$640$	−2.20854e96	−0.339544
$641$	7.44211e96	1.08416	0.542080	−	0.840327i	$-0.317637\pi$
$641$	7.44211e96	1.08416	0.542080	+	0.840327i	$0.317637\pi$
$642$	2.88246e96	0.397929
$643$	−3.42321e96	−0.447873	−0.223937	−	0.974604i	$-0.571891\pi$
$643$	−3.42321e96	−0.447873	−0.223937	+	0.974604i	$0.571891\pi$
$644$	1.59267e94	0.00197498
$645$	−1.32477e96	−0.155715
$646$	−7.28324e96	−0.811526
$647$	−6.56125e96	−0.693089	−0.346544	−	0.938034i	$-0.612645\pi$
$647$	−6.56125e96	−0.693089	−0.346544	+	0.938034i	$0.612645\pi$
$648$	−1.12443e96	−0.112614
$649$	7.32464e96	0.695576
$650$	−6.25667e96	−0.563420
$651$	−8.58316e94	−0.00732998
$652$	−1.35346e95	−0.0109623
$653$	−7.69556e96	−0.591202	−0.295601	−	0.955312i	$-0.595520\pi$
$653$	−7.69556e96	−0.591202	−0.295601	+	0.955312i	$0.595520\pi$
$654$	2.15449e95	0.0157004
$655$	−3.28839e96	−0.227331
$656$	1.27773e97	0.838023
$657$	−6.65334e96	−0.414033
$658$	−8.21361e95	−0.0484999
$659$	6.13510e96	0.343776	0.171888	−	0.985117i	$-0.445013\pi$
$659$	6.13510e96	0.343776	0.171888	+	0.985117i	$0.445013\pi$
$660$	−8.35504e94	−0.00444307
$661$	−2.96349e96	−0.149573	−0.0747865	−	0.997200i	$-0.523828\pi$
$661$	−2.96349e96	−0.149573	−0.0747865	+	0.997200i	$0.523828\pi$
$662$	2.42619e97	1.16232
$663$	−1.49201e97	−0.678509
$664$	3.39193e96	0.146436
$665$	4.61235e95	0.0189049
$666$	2.97531e95	0.0115790
$667$	−1.18741e97	−0.438794
$668$	−8.54483e95	−0.0299858
$669$	−1.20862e97	−0.402800
$670$	7.52734e96	0.238265
$671$	8.65271e96	0.260151
$672$	−1.31713e95	−0.00376173
$673$	5.96218e97	1.61765	0.808827	−	0.588047i	$-0.200103\pi$
$673$	5.96218e97	1.61765	0.808827	+	0.588047i	$0.200103\pi$
$674$	3.79784e97	0.978973
$675$	6.86626e96	0.168167
$676$	6.89726e95	0.0160515
$677$	3.02363e97	0.668682	0.334341	−	0.942452i	$-0.391486\pi$
$677$	3.02363e97	0.668682	0.334341	+	0.942452i	$0.391486\pi$
$678$	−3.33273e97	−0.700448
$679$	−1.00654e97	−0.201059
$680$	3.40735e97	0.646933
$681$	−6.93071e96	−0.125084
$682$	4.85007e96	0.0832121
$683$	−8.41496e96	−0.137258	−0.0686291	−	0.997642i	$-0.521862\pi$
$683$	−8.41496e96	−0.137258	−0.0686291	+	0.997642i	$0.521862\pi$
$684$	2.76176e95	0.00428302
$685$	1.53156e97	0.225845
$686$	−1.62264e97	−0.227530
$687$	−3.37749e97	−0.450387
$688$	5.81422e97	0.737378
$689$	−5.17063e97	−0.623706
$690$	−1.06799e97	−0.122538
$691$	−1.60498e98	−1.75177	−0.875883	−	0.482524i	$-0.839720\pi$
$691$	−1.60498e98	−1.75177	−0.875883	+	0.482524i	$0.839720\pi$
$692$	4.16047e96	0.0431999
$693$	3.02784e96	0.0299114
$694$	−1.91357e98	−1.79864
$695$	7.63083e97	0.682489
$696$	4.97783e97	0.423664
$697$	−1.91435e98	−1.55057
$698$	−1.87977e98	−1.44908
$699$	1.03287e98	0.757848
$700$	4.07711e95	0.00284754
$701$	−2.89286e97	−0.192334	−0.0961669	−	0.995365i	$-0.530658\pi$
$701$	−2.89286e97	−0.192334	−0.0961669	+	0.995365i	$0.530658\pi$
$702$	−1.96046e97	−0.124088
$703$	−2.67843e96	−0.0161407
$704$	1.38174e98	0.792809
$705$	−1.58946e97	−0.0868409
$706$	3.02440e98	1.57353
$707$	−3.04941e97	−0.151094
$708$	3.09045e96	0.0145839
$709$	−3.51785e97	−0.158118	−0.0790592	−	0.996870i	$-0.525192\pi$
$709$	−3.51785e97	−0.158118	−0.0790592	+	0.996870i	$0.525192\pi$
$710$	3.05668e97	0.130869
$711$	1.27110e98	0.518415
$712$	3.71521e98	1.44352
$713$	−1.78912e97	−0.0662294
$714$	−3.36904e97	−0.118828
$715$	−5.33913e97	−0.179437
$716$	−7.22486e95	−0.00231382
$717$	2.71511e98	0.828661
$718$	3.11451e98	0.905933
$719$	6.76488e97	0.187548	0.0937742	−	0.995593i	$-0.470107\pi$
$719$	6.76488e97	0.187548	0.0937742	+	0.995593i	$0.470107\pi$
$720$	4.35148e97	0.114992
$721$	−4.24766e97	−0.107000
$722$	−3.24389e98	−0.778992
$723$	−1.26351e98	−0.289273
$724$	−2.49159e97	−0.0543870
$725$	−3.03969e98	−0.632656
$726$	1.15704e98	0.229633
$727$	1.87929e98	0.355678	0.177839	−	0.984060i	$-0.443089\pi$
$727$	1.87929e98	0.355678	0.177839	+	0.984060i	$0.443089\pi$
$728$	−4.26663e97	−0.0770109
$729$	2.15147e97	0.0370370
$730$	2.64918e98	0.434984
$731$	−8.71115e98	−1.36435
$732$	3.65079e96	0.00545450
$733$	1.10857e98	0.158007	0.0790036	−	0.996874i	$-0.474826\pi$
$733$	1.10857e98	0.158007	0.0790036	+	0.996874i	$0.474826\pi$
$734$	−1.59947e98	−0.217501
$735$	−1.55936e98	−0.202317
$736$	−2.74549e97	−0.0339888
$737$	−4.44838e98	−0.525501
$738$	−2.51541e98	−0.283572
$739$	9.62527e98	1.03557	0.517785	−	0.855511i	$-0.326757\pi$
$739$	9.62527e98	1.03557	0.517785	+	0.855511i	$0.326757\pi$
$740$	3.41884e95	0.000351062 0
$741$	1.76485e98	0.172974
$742$	−1.16755e98	−0.109230
$743$	1.09832e99	0.980878	0.490439	−	0.871476i	$-0.336837\pi$
$743$	1.09832e99	0.980878	0.490439	+	0.871476i	$0.336837\pi$
$744$	7.50027e97	0.0639456
$745$	−7.59482e98	−0.618196
$746$	−2.09491e99	−1.62808
$747$	−6.49010e97	−0.0481604
$748$	−5.49392e97	−0.0389293
$749$	−1.20031e98	−0.0812217
$750$	−5.86270e98	−0.378865
$751$	−5.61704e98	−0.346681	−0.173340	−	0.984862i	$-0.555456\pi$
$751$	−5.61704e98	−0.346681	−0.173340	+	0.984862i	$0.555456\pi$
$752$	6.97587e98	0.411228
$753$	8.29768e98	0.467230
$754$	8.67896e98	0.466827
$755$	1.34463e99	0.690927
$756$	1.27752e96	0.000627142 0
$757$	−3.87173e99	−1.81592	−0.907962	−	0.419053i	$-0.862362\pi$
$757$	−3.87173e99	−1.81592	−0.907962	+	0.419053i	$0.862362\pi$
$758$	−4.66085e98	−0.208871
$759$	6.31139e98	0.270261
$760$	−4.03044e98	−0.164924
$761$	3.45470e99	1.35095	0.675475	−	0.737383i	$-0.263939\pi$
$761$	3.45470e99	1.35095	0.675475	+	0.737383i	$0.263939\pi$
$762$	−1.76367e99	−0.659129
$763$	−8.97170e96	−0.00320463
$764$	−8.90333e97	−0.0303971
$765$	−6.51960e98	−0.212766
$766$	−1.67074e99	−0.521215
$767$	1.97489e99	0.588984
$768$	1.70254e98	0.0485439
$769$	4.53058e99	1.23508	0.617540	−	0.786540i	$-0.288130\pi$
$769$	4.53058e99	1.23508	0.617540	+	0.786540i	$0.288130\pi$
$770$	−1.20560e98	−0.0314249
$771$	2.14059e99	0.533529
$772$	−5.95280e97	−0.0141881
$773$	5.93829e99	1.35353	0.676766	−	0.736198i	$-0.263381\pi$
$773$	5.93829e99	1.35353	0.676766	+	0.736198i	$0.263381\pi$
$774$	−1.14462e99	−0.249516
$775$	−4.58001e98	−0.0954899
$776$	8.79549e99	1.75400
$777$	−1.23898e97	−0.00236340
$778$	−9.24401e99	−1.68680
$779$	2.26442e99	0.395290
$780$	−2.25271e97	−0.00376220
$781$	−1.80638e99	−0.288635
$782$	−7.02261e99	−1.07366
$783$	−9.52456e98	−0.139336
$784$	6.84376e99	0.958056
$785$	5.69830e98	0.0763382
$786$	−2.84121e99	−0.364272
$787$	4.48702e99	0.550592	0.275296	−	0.961360i	$-0.411224\pi$
$787$	4.48702e99	0.550592	0.275296	+	0.961360i	$0.411224\pi$
$788$	−1.57095e98	−0.0184505
$789$	−4.32688e99	−0.486427
$790$	−5.06117e99	−0.544648
$791$	1.38781e99	0.142969
$792$	−2.64583e99	−0.260942
$793$	2.33297e99	0.220285
$794$	−4.94792e99	−0.447317
$795$	−2.25939e99	−0.195581
$796$	−2.06024e97	−0.00170772
$797$	−1.29566e100	−1.02844	−0.514222	−	0.857657i	$-0.671919\pi$
$797$	−1.29566e100	−1.02844	−0.514222	+	0.857657i	$0.671919\pi$
$798$	3.98512e98	0.0302930
$799$	−1.04516e100	−0.760884
$800$	−7.02824e98	−0.0490052
$801$	−7.10866e99	−0.474751
$802$	−1.63397e99	−0.104527
$803$	−1.56557e100	−0.959368
$804$	−1.87688e98	−0.0110180
$805$	4.44730e98	0.0250114
$806$	1.30769e99	0.0704605
$807$	−1.81874e99	−0.0938929
$808$	2.66468e100	1.31812
$809$	1.40504e99	0.0665985	0.0332993	−	0.999445i	$-0.489399\pi$
$809$	1.40504e99	0.0665985	0.0332993	+	0.999445i	$0.489399\pi$
$810$	−8.56658e98	−0.0389112
$811$	7.61959e99	0.331675	0.165837	−	0.986153i	$-0.446967\pi$
$811$	7.61959e99	0.331675	0.165837	+	0.986153i	$0.446967\pi$
$812$	−5.65557e97	−0.00235936
$813$	1.73049e100	0.691903
$814$	7.00105e98	0.0268301
$815$	−3.77934e99	−0.138828
$816$	2.86135e100	1.00754
$817$	1.03041e100	0.347816
$818$	2.09722e100	0.678664
$819$	8.16375e98	0.0253277
$820$	−2.89038e98	−0.00859760
$821$	6.99852e98	0.0199603	0.00998015	−	0.999950i	$-0.496823\pi$
$821$	6.99852e98	0.0199603	0.00998015	+	0.999950i	$0.496823\pi$
$822$	1.32329e100	0.361890
$823$	8.77692e99	0.230169	0.115085	−	0.993356i	$-0.463286\pi$
$823$	8.77692e99	0.230169	0.115085	+	0.993356i	$0.463286\pi$
$824$	3.71176e100	0.933450
$825$	1.61567e100	0.389664
$826$	4.45941e99	0.103149
$827$	−3.57545e100	−0.793215	−0.396607	−	0.917988i	$-0.629813\pi$
$827$	−3.57545e100	−0.793215	−0.396607	+	0.917988i	$0.629813\pi$
$828$	2.66293e98	0.00566648
$829$	−8.84973e99	−0.180634	−0.0903168	−	0.995913i	$-0.528788\pi$
$829$	−8.84973e99	−0.180634	−0.0903168	+	0.995913i	$0.528788\pi$
$830$	2.58418e99	0.0505974
$831$	−4.01692e100	−0.754498
$832$	3.72548e100	0.671317
$833$	−1.02537e101	−1.77266
$834$	6.59312e100	1.09361
$835$	−2.38602e100	−0.379744
$836$	6.49856e98	0.00992432
$837$	−1.43510e99	−0.0210307
$838$	−4.81072e100	−0.676537
$839$	−2.50763e100	−0.338436	−0.169218	−	0.985579i	$-0.554124\pi$
$839$	−2.50763e100	−0.338436	−0.169218	+	0.985579i	$0.554124\pi$
$840$	−1.86438e99	−0.0241490
$841$	−3.82730e100	−0.475806
$842$	−1.00033e101	−1.19365
$843$	5.41796e100	0.620561
$844$	3.49541e99	0.0384312
$845$	1.92596e100	0.203278
$846$	−1.37331e100	−0.139153
$847$	−4.81813e99	−0.0468706
$848$	9.91612e100	0.926157
$849$	−5.53578e100	−0.496436
$850$	−1.79773e101	−1.54801
$851$	−2.58259e99	−0.0213543
$852$	−7.62157e98	−0.00605171
$853$	1.36550e101	1.04124	0.520620	−	0.853789i	$-0.325701\pi$
$853$	1.36550e101	1.04124	0.520620	+	0.853789i	$0.325701\pi$
$854$	5.26797e99	0.0385786
$855$	7.71182e99	0.0542408
$856$	1.04888e101	0.708566
$857$	5.89724e99	0.0382658	0.0191329	−	0.999817i	$-0.493909\pi$
$857$	5.89724e99	0.0382658	0.0191329	+	0.999817i	$0.493909\pi$
$858$	−4.61307e100	−0.287527
$859$	2.44148e101	1.46181	0.730903	−	0.682482i	$-0.239099\pi$
$859$	2.44148e101	1.46181	0.730903	+	0.682482i	$0.239099\pi$
$860$	−1.31525e99	−0.00756505
$861$	1.04746e100	0.0578803
$862$	−2.14327e101	−1.13782
$863$	−6.13218e100	−0.312783	−0.156391	−	0.987695i	$-0.549986\pi$
$863$	−6.13218e100	−0.312783	−0.156391	+	0.987695i	$0.549986\pi$
$864$	−2.20223e99	−0.0107929
$865$	1.16175e101	0.547089
$866$	−1.73187e101	−0.783699
$867$	−2.95932e101	−1.28686
$868$	−8.52145e97	−0.000356109 0
$869$	2.99096e101	1.20124
$870$	3.79242e100	0.146387
$871$	−1.19939e101	−0.444972
$872$	7.83979e99	0.0279567
$873$	−1.68292e101	−0.576864
$874$	8.30681e100	0.273709
$875$	2.44134e100	0.0773305
$876$	−6.60551e99	−0.0201148
$877$	1.13671e101	0.332784	0.166392	−	0.986060i	$-0.446788\pi$
$877$	1.13671e101	0.332784	0.166392	+	0.986060i	$0.446788\pi$
$878$	6.89739e101	1.94144
$879$	2.50613e101	0.678246
$880$	1.02393e101	0.266451
$881$	2.98798e101	0.747669	0.373834	−	0.927495i	$-0.378043\pi$
$881$	2.98798e101	0.747669	0.373834	+	0.927495i	$0.378043\pi$
$882$	−1.34730e101	−0.324190
$883$	−2.49792e101	−0.578009	−0.289004	−	0.957328i	$-0.593324\pi$
$883$	−2.49792e101	−0.578009	−0.289004	+	0.957328i	$0.593324\pi$
$884$	−1.48129e100	−0.0329637
$885$	8.62963e100	0.184693
$886$	−2.36344e101	−0.486498
$887$	2.46440e100	0.0487917	0.0243959	−	0.999702i	$-0.492234\pi$
$887$	2.46440e100	0.0487917	0.0243959	+	0.999702i	$0.492234\pi$
$888$	1.08266e100	0.0206180
$889$	7.34426e100	0.134536
$890$	2.83047e101	0.498774
$891$	5.06253e100	0.0858196
$892$	−1.19993e100	−0.0195690
$893$	1.23628e101	0.193974
$894$	−6.56202e101	−0.990588
$895$	−2.01744e100	−0.0293026
$896$	7.94612e100	0.111053
$897$	1.70170e101	0.228846
$898$	−3.46934e101	−0.448966
$899$	6.35317e100	0.0791191
$900$	6.81690e99	0.00816997
$901$	−1.48568e102	−1.71364
$902$	−5.91889e101	−0.657074
$903$	4.76642e100	0.0509290
$904$	−1.21272e102	−1.24724
$905$	−6.95739e101	−0.688764
$906$	1.16177e102	1.10713
$907$	−3.56968e100	−0.0327475	−0.0163738	−	0.999866i	$-0.505212\pi$
$907$	−3.56968e100	−0.0327475	−0.0163738	+	0.999866i	$0.505212\pi$
$908$	−6.88089e99	−0.00607691
$909$	−5.09859e101	−0.433507
$910$	−3.25058e100	−0.0266093
$911$	1.07415e102	0.846607	0.423303	−	0.905988i	$-0.360870\pi$
$911$	1.07415e102	0.846607	0.423303	+	0.905988i	$0.360870\pi$
$912$	−3.38459e101	−0.256853
$913$	−1.52715e101	−0.111594
$914$	−1.69444e102	−1.19229
$915$	1.01943e101	0.0690765
$916$	−3.35320e100	−0.0218810
$917$	1.18314e101	0.0743520
$918$	−5.63302e101	−0.340933
$919$	3.25385e102	1.89676	0.948380	−	0.317135i	$-0.102721\pi$
$919$	3.25385e102	1.89676	0.948380	+	0.317135i	$0.102721\pi$
$920$	−3.88621e101	−0.218196
$921$	1.67019e102	0.903250
$922$	3.10517e102	1.61759
$923$	−4.87042e101	−0.244404
$924$	3.00607e99	0.00145317
$925$	−6.61123e100	−0.0307888
$926$	−1.01696e102	−0.456272
$927$	−7.10206e101	−0.306997
$928$	9.74925e100	0.0406037
$929$	1.55562e102	0.624256	0.312128	−	0.950040i	$-0.398958\pi$
$929$	1.55562e102	0.624256	0.312128	+	0.950040i	$0.398958\pi$
$930$	5.71417e100	0.0220949
$931$	1.21287e102	0.451908
$932$	1.02544e101	0.0368182
$933$	2.25506e102	0.780263
$934$	3.28893e102	1.09670
$935$	−1.53410e102	−0.493006
$936$	−7.13378e101	−0.220955
$937$	7.36343e101	0.219819	0.109909	−	0.993942i	$-0.464944\pi$
$937$	7.36343e101	0.219819	0.109909	+	0.993942i	$0.464944\pi$
$938$	−2.70827e101	−0.0779282
$939$	−3.78442e100	−0.0104963
$940$	−1.57803e100	−0.00421895
$941$	−1.80601e102	−0.465456	−0.232728	−	0.972542i	$-0.574765\pi$
$941$	−1.80601e102	−0.465456	−0.232728	+	0.972542i	$0.574765\pi$
$942$	4.92340e101	0.122323
$943$	2.18339e102	0.522972
$944$	−3.78740e102	−0.874597
$945$	3.56729e100	0.00794221
$946$	−2.69335e102	−0.578161
$947$	−3.38708e102	−0.701054	−0.350527	−	0.936553i	$-0.613998\pi$
$947$	−3.38708e102	−0.701054	−0.350527	+	0.936553i	$0.613998\pi$
$948$	1.26196e101	0.0251859
$949$	−4.22113e102	−0.812352
$950$	2.12648e102	0.394636
$951$	2.32383e102	0.415889
$952$	−1.22593e102	−0.211589
$953$	−6.25100e102	−1.04050	−0.520252	−	0.854012i	$-0.674162\pi$
$953$	−6.25100e102	−1.04050	−0.520252	+	0.854012i	$0.674162\pi$
$954$	−1.95214e102	−0.313396
$955$	−2.48613e102	−0.384952
$956$	2.69559e101	0.0402584
$957$	−2.24118e102	−0.322860
$958$	8.78714e102	1.22106
$959$	−5.51043e101	−0.0738658
$960$	1.62791e102	0.210510
$961$	−7.92026e102	−0.988058
$962$	1.88765e101	0.0227185
$963$	−2.00692e102	−0.233036
$964$	−1.25443e101	−0.0140536
$965$	−1.66223e102	−0.179680
$966$	3.84252e101	0.0400779
$967$	−1.41812e103	−1.42724	−0.713622	−	0.700531i	$-0.752947\pi$
$967$	−1.41812e103	−1.42724	−0.713622	+	0.700531i	$0.752947\pi$
$968$	4.21026e102	0.408892
$969$	5.07096e102	0.475247
$970$	6.70095e102	0.606054
$971$	1.63944e103	1.43097	0.715487	−	0.698626i	$-0.246205\pi$
$971$	1.63944e103	1.43097	0.715487	+	0.698626i	$0.246205\pi$
$972$	2.13601e100	0.00179935
$973$	−2.74550e102	−0.223218
$974$	1.69866e103	1.33298
$975$	4.35621e102	0.329951
$976$	−4.47412e102	−0.327106
$977$	1.83621e101	0.0129586	0.00647932	−	0.999979i	$-0.497938\pi$
$977$	1.83621e101	0.0129586	0.00647932	+	0.999979i	$0.497938\pi$
$978$	−3.26539e102	−0.222456
$979$	−1.67270e103	−1.10006
$980$	−1.54815e101	−0.00982907
$981$	−1.50006e101	−0.00919451
$982$	2.07196e103	1.22612
$983$	−8.10458e102	−0.463057	−0.231528	−	0.972828i	$-0.574373\pi$
$983$	−8.10458e102	−0.463057	−0.231528	+	0.972828i	$0.574373\pi$
$984$	−9.15313e102	−0.504939
$985$	−4.38665e102	−0.233659
$986$	2.49373e103	1.28261
$987$	5.71873e101	0.0284026
$988$	1.75216e101	0.00840349
$989$	9.93539e102	0.460164
$990$	−2.01576e102	−0.0901623
$991$	−1.59349e103	−0.688349	−0.344174	−	0.938906i	$-0.611841\pi$
$991$	−1.59349e103	−0.688349	−0.344174	+	0.938906i	$0.611841\pi$
$992$	1.46895e101	0.00612852
$993$	−1.68924e103	−0.680679
$994$	−1.09977e102	−0.0428026
$995$	−5.75291e101	−0.0216268
$996$	−6.44344e100	−0.00233976
$997$	4.53651e103	1.59125	0.795627	−	0.605787i	$-0.207142\pi$
$997$	4.53651e103	1.59125	0.795627	+	0.605787i	$0.207142\pi$
$998$	2.92668e102	0.0991682
$999$	−2.07156e101	−0.00678091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.70.a.a.1.5	✓	6
3.2	odd	2		9.70.a.d.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.70.a.a.1.5	✓	6	1.1	even	1	trivial
9.70.a.d.1.2		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 70 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+2.39528e10 q^{2} -1.66772e16 q^{3} -1.65573e19 q^{4} -4.62338e23 q^{5} -3.99466e26 q^{6} +1.66345e28 q^{7} -1.45359e31 q^{8} +2.78128e32 q^{9} +O(q^{10})\)	\(q+2.39528e10 q^{2} -1.66772e16 q^{3} -1.65573e19 q^{4} -4.62338e23 q^{5} -3.99466e26 q^{6} +1.66345e28 q^{7} -1.45359e31 q^{8} +2.78128e32 q^{9} -1.10743e34 q^{10} +6.54451e35 q^{11} +2.76129e35 q^{12} +1.76455e38 q^{13} +3.98444e38 q^{14} +7.71050e39 q^{15} -3.38401e41 q^{16} +5.07009e42 q^{17} +6.66196e42 q^{18} -5.99724e43 q^{19} +7.65507e42 q^{20} -2.77417e44 q^{21} +1.56759e46 q^{22} -5.78263e46 q^{23} +2.42417e47 q^{24} -1.48031e48 q^{25} +4.22660e48 q^{26} -4.63840e48 q^{27} -2.75423e47 q^{28} +2.05342e50 q^{29} +1.84688e50 q^{30} +3.09395e50 q^{31} +4.74782e50 q^{32} -1.09144e52 q^{33} +1.21443e53 q^{34} -7.69078e51 q^{35} -4.60505e51 q^{36} +4.46611e52 q^{37} -1.43651e54 q^{38} -2.94277e54 q^{39} +6.72048e54 q^{40} -3.77578e55 q^{41} -6.64493e54 q^{42} -1.71814e56 q^{43} -1.08359e55 q^{44} -1.28589e56 q^{45} -1.38510e57 q^{46} -2.06142e57 q^{47} +5.64358e57 q^{48} -2.02238e58 q^{49} -3.54576e58 q^{50} -8.45549e58 q^{51} -2.92162e57 q^{52} -2.93028e59 q^{53} -1.11103e59 q^{54} -3.02578e59 q^{55} -2.41797e59 q^{56} +1.00017e60 q^{57} +4.91851e60 q^{58} +1.11920e61 q^{59} -1.27665e59 q^{60} +1.32213e61 q^{61} +7.41090e60 q^{62} +4.62654e60 q^{63} +2.11129e62 q^{64} -8.15819e61 q^{65} -2.61431e62 q^{66} -6.79712e62 q^{67} -8.39470e61 q^{68} +9.64380e62 q^{69} -1.84216e62 q^{70} -2.76015e63 q^{71} -4.04283e63 q^{72} -2.39218e64 q^{73} +1.06976e63 q^{74} +2.46874e64 q^{75} +9.92980e62 q^{76} +1.08865e64 q^{77} -7.04877e64 q^{78} +4.57019e65 q^{79} +1.56456e65 q^{80} +7.73554e64 q^{81} -9.04405e65 q^{82} -2.33349e65 q^{83} +4.59327e63 q^{84} -2.34410e66 q^{85} -4.11544e66 q^{86} -3.42452e66 q^{87} -9.51300e66 q^{88} -2.55589e67 q^{89} -3.08008e66 q^{90} +2.93525e66 q^{91} +9.57447e65 q^{92} -5.15984e66 q^{93} -4.93769e67 q^{94} +2.77275e67 q^{95} -7.91803e66 q^{96} -6.05089e68 q^{97} -4.84418e68 q^{98} +1.82021e68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 869363388 q^{2} - 10\!\cdots\!14 q^{3}+ \cdots + 16\!\cdots\!66 q^{9}+O(q^{10}) \) 6 * q - 869363388 * q^2 - 100063090197999414 * q^3 + 1371216641348494011408 * q^4 + 536749102286059793452020 * q^5 + 14498531184713726896175772 * q^6 - 165486212832272947603119602016 * q^7 + 29031977276772288550932250437696 * q^8 + 1668770336662161067543714657390566 * q^9	\( 6 q - 869363388 q^{2} - 10\!\cdots\!14 q^{3}+ \cdots - 53\!\cdots\!36 q^{99}+O(q^{100}) \) 6 * q - 869363388 * q^2 - 100063090197999414 * q^3 + 1371216641348494011408 * q^4 + 536749102286059793452020 * q^5 + 14498531184713726896175772 * q^6 - 165486212832272947603119602016 * q^7 + 29031977276772288550932250437696 * q^8 + 1668770336662161067543714657390566 * q^9 - 30539001465788028222087378612341640 * q^10 - 1920537066516616187668579962543158376 * q^11 - 22868029077375361513671619126882219152 * q^12 - 47217968885374199615397355356796191852 * q^13 + 7064585334174201405371837809050003141312 * q^14 - 8951462305957535762539464569043499519380 * q^15 + 377157429568235813937466329721859576398080 * q^16 - 5058270084832851177273994934925110056607412 * q^17 - 241794638945752826180250102109053616166268 * q^18 - 65818466266910893781669604806057906253992088 * q^19 - 74276832342140585406878490976963545328073760 * q^20 + 2759843640193509337740927488460262535180203104 * q^21 - 57200945629382567456443201741175335542976506864 * q^22 - 51318359662817614748704757772348805853962165488 * q^23 - 484171560145322484473355383995534830167508585024 * q^24 + 1351900008806516831015099778033783730620565906650 * q^25 - 16207493799167654397027294571148058082290306700488 * q^26 - 27830386119528611875968901007343548725913806188054 * q^27 + 121390433570468044194114098496551362783272349932288 * q^28 + 785579239339018365983000259217156564097330312249124 * q^29 + 509304476371330630546739998356596576017896314633160 * q^30 + 6912833464261058549529914367563374193660948950153296 * q^31 + 36737392694691819442392877818076822209799633285776384 * q^32 + 32029145619242227636284505564240924042938191359531944 * q^33 + 253117449563254571066779054180560057695840514055176 * q^34 + 276611165060305397158461820821003699537527995207930560 * q^35 + 381374276036647353263390282147345081660028453185929488 * q^36 - 759040697498936685975105001963916849352981208607118396 * q^37 + 2103369059703889244990286400717050872850491394651970032 * q^38 + 787462646590588064894632608232796865789891597354595788 * q^39 - 32664751344775020838298315886208043642737757270980944000 * q^40 - 25768671104884673827847532722814331858226170126017093924 * q^41 - 117817373250822824537222457055662269520721648792989198528 * q^42 - 677055351038557514071054609066516734267888940905925188840 * q^43 + 238305524760672609941760876572355183014168119775154744384 * q^44 + 149285163354170121367980976931811340477842188257753607220 * q^45 + 8376385103625214805959746309869879529208374887220505747296 * q^46 + 7598599404092453023795535768684988784173129214818972342720 * q^47 - 6289922982288665238584151982726579281690322330718011787520 * q^48 + 39520658833284024797097689208298803008912245306300761939990 * q^49 - 28568855233568347359168873341651630916131610440562956535300 * q^50 + 84357689290745289159801421813736090901392081119475734009428 * q^51 - 841291935994679864415054059209490217537323675729185299370272 * q^52 - 449047684897777378052965016724937358227157858973850840458828 * q^53 + 4032453127703594497238226593730133400050584990603665094492 * q^54 + 2254548165992828810812926827082553754343205233701600459282640 * q^55 + 1641356236071085469964848605225791359818442190977904466652160 * q^56 + 1097666521126647756280461762493305085319303708198214764106072 * q^57 + 10854840022358605054892033620996887145323506082370467922396824 * q^58 + 9739940026219086244132886290748367338175220661414782584592728 * q^59 + 1238728229045548911290208746311830657587532274639907038129440 * q^60 - 59315134126314210963145084137204520506665661947323124957508780 * q^61 - 58284415626578488701665533854996023611020152283699473273044512 * q^62 - 46026413850176360961358753239584156335498095610944326498830176 * q^63 - 196087603577998032685001038699358078224720081884631691829178368 * q^64 - 368792752455446531625971790511790913672736652263934282973351720 * q^65 + 953950563653961367781459452317768129208925530496794989139829616 * q^66 + 1284404845637086838528947432298267008623636941858083561714308648 * q^67 - 1893312213205272549692225847826950804709005883992500832775643616 * q^68 + 855845608625648963144016144920672894915758664084152710799170672 * q^69 + 5651141511141393939253777145916410305809660448417857533217598080 * q^70 - 8028908380018744267365790936955359727729274918181835022662164368 * q^71 + 8074617082354583671186761526246370992341166934797564305786862656 * q^72 + 23917666927401813793494400679686156753046201104575562189407759612 * q^73 - 66571567863995212404482808802342117220480190894464062470316692648 * q^74 - 22545882086647115963110648728416884279973448838942742394179783850 * q^75 - 117137080475037691773181405327212499216032011801755896581802226752 * q^76 - 370001686623730076506835954110410638316696132431439489747825466752 * q^77 + 270295318984938200277077861249204534384356528838329715416149585672 * q^78 + 151166116158225305435965330589298930972238439200795534257670973040 * q^79 - 103132668838130690471303376617648857617362361028013189202842042880 * q^80 + 464132406087257065130090681062365209793088477541530761100710966726 * q^81 + 37460932835681010277915179679262266245084578260611880863596729448 * q^82 - 2199869100513279294476979658003407541858593100082068956813742116504 * q^83 - 2024450317255999993413036160714996242543447082962560389819327279872 * q^84 - 6491952514505341124698414891022457176579387500885906219615755954840 * q^85 - 23144659602467499127119271177953663689526653967585956674347553430256 * q^86 - 13101247713942660717783546201323542017367838371972839670487262335556 * q^87 - 65249604729672858795836798510445455460410612360663171240882606141184 * q^88 - 6686194196194507079670325678793857718304620226396138544648538601828 * q^89 - 8493763292898219695542584151776832427456280937959354979087550828040 * q^90 - 82097466714973722451927498084842810568687277892210020260162088564544 * q^91 + 4359811041243409323098555915712612735158801326895369127311689835904 * q^92 - 115286579743017176690026802480066668815283610415364196376484636361424 * q^93 - 560087180092970937289054350368454974923005535872515030885741348295552 * q^94 - 914644999797608066644469983517358223242420981276970458662113135611600 * q^95 - 612676173141378712760794918109470208907664831994025080010863094506496 * q^96 - 1193245591335854049619056301286742793562875638671855181199561300009332 * q^97 - 3639892838212491311414089259694594431294943863329296694030071739108188 * q^98 - 534155881177182136550108656986512933865188403627723332959024704380136 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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