LMFDB - Embedded newform 980.2.k.j.883.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(687,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("980.687");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.k (of order $4$, degree $2$, minimal)

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:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			883.13
Character	$\chi$	$=$	980.883
Dual form			980.2.k.j.687.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.566415 + 1.29583i) q^{2} +(0.792756 - 0.792756i) q^{3} +(-1.35835 + 1.46795i) q^{4} +(-0.427372 + 2.19485i) q^{5} +(1.47630 + 0.578247i) q^{6} +(-2.67161 - 0.928715i) q^{8} +1.74308i q^{9} +O(q^{10})$	\(q+(0.566415 + 1.29583i) q^{2} +(0.792756 - 0.792756i) q^{3} +(-1.35835 + 1.46795i) q^{4} +(-0.427372 + 2.19485i) q^{5} +(1.47630 + 0.578247i) q^{6} +(-2.67161 - 0.928715i) q^{8} +1.74308i q^{9} +(-3.08622 + 0.689394i) q^{10} +2.98364i q^{11} +(0.0868916 + 2.24057i) q^{12} +(-4.05418 - 4.05418i) q^{13} +(1.40118 + 2.07878i) q^{15} +(-0.309783 - 3.98799i) q^{16} +(-1.68722 + 1.68722i) q^{17} +(-2.25873 + 0.987305i) q^{18} +2.51388 q^{19} +(-2.64142 - 3.60873i) q^{20} +(-3.86629 + 1.68998i) q^{22} +(-4.24161 + 4.24161i) q^{23} +(-2.85418 + 1.38169i) q^{24} +(-4.63471 - 1.87603i) q^{25} +(2.95718 - 7.54987i) q^{26} +(3.76010 + 3.76010i) q^{27} -2.55433i q^{29} +(-1.90010 + 2.99314i) q^{30} -3.60553i q^{31} +(4.99228 - 2.66028i) q^{32} +(2.36530 + 2.36530i) q^{33} +(-3.14202 - 1.23068i) q^{34} +(-2.55876 - 2.36770i) q^{36} +(-3.37486 + 3.37486i) q^{37} +(1.42390 + 3.25756i) q^{38} -6.42795 q^{39} +(3.18016 - 5.46686i) q^{40} +7.93727 q^{41} +(-7.62646 + 7.62646i) q^{43} +(-4.37985 - 4.05282i) q^{44} +(-3.82579 - 0.744942i) q^{45} +(-7.89891 - 3.09389i) q^{46} +(2.09272 + 2.09272i) q^{47} +(-3.40708 - 2.91592i) q^{48} +(-0.194151 - 7.06840i) q^{50} +2.67511i q^{51} +(11.4583 - 0.444366i) q^{52} +(1.80994 + 1.80994i) q^{53} +(-2.74267 + 7.00223i) q^{54} +(-6.54863 - 1.27512i) q^{55} +(1.99289 - 1.99289i) q^{57} +(3.30997 - 1.44681i) q^{58} -2.09389 q^{59} +(-4.95484 - 0.766842i) q^{60} +1.90096 q^{61} +(4.67216 - 2.04223i) q^{62} +(6.27498 + 4.96233i) q^{64} +(10.6309 - 7.16566i) q^{65} +(-1.72528 + 4.40476i) q^{66} +(2.19990 + 2.19990i) q^{67} +(-0.184931 - 4.76859i) q^{68} +6.72512i q^{69} +8.09721i q^{71} +(1.61882 - 4.65682i) q^{72} +(-6.89558 - 6.89558i) q^{73} +(-6.28481 - 2.46167i) q^{74} +(-5.16142 + 2.18696i) q^{75} +(-3.41472 + 3.69026i) q^{76} +(-3.64089 - 8.32952i) q^{78} +8.06116 q^{79} +(8.88541 + 1.02443i) q^{80} +0.732452 q^{81} +(4.49579 + 10.2853i) q^{82} +(-5.99790 + 5.99790i) q^{83} +(-2.98212 - 4.42426i) q^{85} +(-14.2023 - 5.56285i) q^{86} +(-2.02496 - 2.02496i) q^{87} +(2.77095 - 7.97111i) q^{88} +2.05525i q^{89} +(-1.20167 - 5.37951i) q^{90} +(-0.464910 - 11.9881i) q^{92} +(-2.85831 - 2.85831i) q^{93} +(-1.52646 + 3.89715i) q^{94} +(-1.07436 + 5.51758i) q^{95} +(1.84871 - 6.06661i) q^{96} +(-6.63160 + 6.63160i) q^{97} -5.20071 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{2} - 8 q^{5} + 8 q^{6} - 2 q^{8}+O(q^{10}) $ 36 * q - 2 * q^2 - 8 * q^5 + 8 * q^6 - 2 * q^8	$ 36 q - 2 q^{2} - 8 q^{5} + 8 q^{6} - 2 q^{8} + 2 q^{10} + 10 q^{12} + 28 q^{16} + 4 q^{17} + 20 q^{18} + 28 q^{20} - 8 q^{22} + 16 q^{25} - 4 q^{26} + 32 q^{30} + 38 q^{32} - 64 q^{33} + 8 q^{36} + 4 q^{37} + 12 q^{38} + 2 q^{40} + 20 q^{41} - 12 q^{45} + 28 q^{46} - 6 q^{48} - 14 q^{50} + 48 q^{52} + 24 q^{53} - 8 q^{57} - 30 q^{58} + 10 q^{60} - 20 q^{61} - 28 q^{62} - 4 q^{65} + 44 q^{66} - 12 q^{68} - 44 q^{72} - 12 q^{73} - 56 q^{76} + 32 q^{78} + 52 q^{80} + 52 q^{81} - 34 q^{82} + 8 q^{85} - 64 q^{86} - 16 q^{88} + 16 q^{90} + 22 q^{92} - 12 q^{93} - 48 q^{96} + 12 q^{97}+O(q^{100}) $ 36 * q - 2 * q^2 - 8 * q^5 + 8 * q^6 - 2 * q^8 + 2 * q^10 + 10 * q^12 + 28 * q^16 + 4 * q^17 + 20 * q^18 + 28 * q^20 - 8 * q^22 + 16 * q^25 - 4 * q^26 + 32 * q^30 + 38 * q^32 - 64 * q^33 + 8 * q^36 + 4 * q^37 + 12 * q^38 + 2 * q^40 + 20 * q^41 - 12 * q^45 + 28 * q^46 - 6 * q^48 - 14 * q^50 + 48 * q^52 + 24 * q^53 - 8 * q^57 - 30 * q^58 + 10 * q^60 - 20 * q^61 - 28 * q^62 - 4 * q^65 + 44 * q^66 - 12 * q^68 - 44 * q^72 - 12 * q^73 - 56 * q^76 + 32 * q^78 + 52 * q^80 + 52 * q^81 - 34 * q^82 + 8 * q^85 - 64 * q^86 - 16 * q^88 + 16 * q^90 + 22 * q^92 - 12 * q^93 - 48 * q^96 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.566415	+	1.29583i	0.400516	+	0.916290i
$2$	0.566415	+	1.29583i	0.400516	+	0.916290i
$3$	0.792756	−	0.792756i	0.457698	−	0.457698i	−0.440201	−	0.897899i	$-0.645093\pi$
$3$	0.792756	−	0.792756i	0.457698	−	0.457698i	0.897899	+	0.440201i	$0.145093\pi$
$4$	−1.35835	+	1.46795i	−0.679174	+	0.733977i
$5$	−0.427372	+	2.19485i	−0.191126	+	0.981565i
$5$	−0.427372	+	2.19485i	−0.191126	+	0.981565i
$6$	1.47630	+	0.578247i	0.602699	+	0.236068i
$7$		0			0
$7$		0			0
$8$	−2.67161	−	0.928715i	−0.944556	−	0.328350i
$9$			1.74308i			0.581026i
$10$	−3.08622	+	0.689394i	−0.975948	+	0.218005i
$11$			2.98364i			0.899601i	0.893129	+	0.449800i	$0.148505\pi$
$11$			2.98364i			0.899601i	−0.893129	+	0.449800i	$0.851495\pi$
$12$	0.0868916	+	2.24057i	0.0250834	+	0.646796i
$13$	−4.05418	−	4.05418i	−1.12443	−	1.12443i	−0.991068	−	0.133359i	$-0.957424\pi$
$13$	−4.05418	−	4.05418i	−1.12443	−	1.12443i	−0.133359	−	0.991068i	$-0.542576\pi$
$14$		0			0
$15$	1.40118	+	2.07878i	0.361782	+	0.536738i
$16$	−0.309783	−	3.98799i	−0.0774456	−	0.996997i
$17$	−1.68722	+	1.68722i	−0.409211	+	0.409211i	−0.881463	−	0.472252i	$-0.843441\pi$
$17$	−1.68722	+	1.68722i	−0.409211	+	0.409211i	0.472252	+	0.881463i	$0.343441\pi$
$18$	−2.25873	+	0.987305i	−0.532388	+	0.232710i
$19$	2.51388			0.576723			0.288362	−	0.957522i	$-0.406889\pi$
$19$	2.51388			0.576723			0.288362	+	0.957522i	$0.406889\pi$
$20$	−2.64142	−	3.60873i	−0.590639	−	0.806936i
$21$		0			0
$22$	−3.86629	+	1.68998i	−0.824295	+	0.360304i
$23$	−4.24161	+	4.24161i	−0.884436	+	0.884436i	−0.993982	−	0.109545i	$-0.965060\pi$
$23$	−4.24161	+	4.24161i	−0.884436	+	0.884436i	0.109545	+	0.993982i	$0.465060\pi$
$24$	−2.85418	+	1.38169i	−0.582606	+	0.282036i
$25$	−4.63471	−	1.87603i	−0.926941	−	0.375206i
$26$	2.95718	−	7.54987i	0.579950	−	1.48065i
$27$	3.76010	+	3.76010i	0.723632	+	0.723632i
$28$		0			0
$29$		−	2.55433i		−	0.474327i	−0.971470	−	0.237163i	$-0.923782\pi$
$29$		−	2.55433i		−	0.474327i	0.971470	−	0.237163i	$-0.0762177\pi$
$30$	−1.90010	+	2.99314i	−0.346908	+	0.546470i
$31$		−	3.60553i		−	0.647573i	−0.946130	−	0.323787i	$-0.895044\pi$
$31$		−	3.60553i		−	0.647573i	0.946130	−	0.323787i	$-0.104956\pi$
$32$	4.99228	−	2.66028i	0.882520	−	0.470276i
$33$	2.36530	+	2.36530i	0.411745	+	0.411745i
$34$	−3.14202	−	1.23068i	−0.538851	−	0.211060i
$35$		0			0
$36$	−2.55876	−	2.36770i	−0.426460	−	0.394617i
$37$	−3.37486	+	3.37486i	−0.554823	+	0.554823i	−0.927829	−	0.373006i	$-0.878327\pi$
$37$	−3.37486	+	3.37486i	−0.554823	+	0.554823i	0.373006	+	0.927829i	$0.378327\pi$
$38$	1.42390	+	3.25756i	0.230987	+	0.528446i
$39$	−6.42795			−1.02930
$40$	3.18016	−	5.46686i	0.502827	−	0.864387i
$41$	7.93727			1.23959			0.619797	−	0.784763i	$-0.287215\pi$
$41$	7.93727			1.23959			0.619797	+	0.784763i	$0.287215\pi$
$42$		0			0
$43$	−7.62646	+	7.62646i	−1.16302	+	1.16302i	−0.179215	+	0.983810i	$0.557356\pi$
$43$	−7.62646	+	7.62646i	−1.16302	+	1.16302i	−0.983810	+	0.179215i	$0.942644\pi$
$44$	−4.37985	−	4.05282i	−0.660287	−	0.610985i
$45$	−3.82579	−	0.744942i	−0.570315	−	0.111049i
$46$	−7.89891	−	3.09389i	−1.16463	−	0.456169i
$47$	2.09272	+	2.09272i	0.305254	+	0.305254i	0.843065	−	0.537811i	$-0.180749\pi$
$47$	2.09272	+	2.09272i	0.305254	+	0.305254i	−0.537811	+	0.843065i	$0.680749\pi$
$48$	−3.40708	−	2.91592i	−0.491770	−	0.420876i
$49$		0			0
$50$	−0.194151	−	7.06840i	−0.0274571	−	0.999623i
$51$			2.67511i			0.374590i
$52$	11.4583	−	0.444366i	1.58899	−	0.0616225i
$53$	1.80994	+	1.80994i	0.248615	+	0.248615i	0.820402	−	0.571787i	$-0.193750\pi$
$53$	1.80994	+	1.80994i	0.248615	+	0.248615i	−0.571787	+	0.820402i	$0.693750\pi$
$54$	−2.74267	+	7.00223i	−0.373230	+	0.952882i
$55$	−6.54863	−	1.27512i	−0.883017	−	0.171938i
$56$		0			0
$57$	1.99289	−	1.99289i	0.263965	−	0.263965i
$58$	3.30997	−	1.44681i	0.434621	−	0.189975i
$59$	−2.09389			−0.272601			−0.136301	−	0.990668i	$-0.543521\pi$
$59$	−2.09389			−0.272601			−0.136301	+	0.990668i	$0.543521\pi$
$60$	−4.95484	−	0.766842i	−0.639667	−	0.0989988i
$61$	1.90096			0.243393			0.121696	−	0.992567i	$-0.461167\pi$
$61$	1.90096			0.243393			0.121696	+	0.992567i	$0.461167\pi$
$62$	4.67216	−	2.04223i	0.593365	−	0.259363i
$63$		0			0
$64$	6.27498	+	4.96233i	0.784372	+	0.620291i
$65$	10.6309	−	7.16566i	1.31861	−	0.888791i
$66$	−1.72528	+	4.40476i	−0.212367	+	0.542188i
$67$	2.19990	+	2.19990i	0.268761	+	0.268761i	0.828601	−	0.559840i	$-0.189137\pi$
$67$	2.19990	+	2.19990i	0.268761	+	0.268761i	−0.559840	+	0.828601i	$0.689137\pi$
$68$	−0.184931	−	4.76859i	−0.0224262	−	0.578277i
$69$			6.72512i			0.809609i
$70$		0			0
$71$			8.09721i			0.960962i	0.877005	+	0.480481i	$0.159538\pi$
$71$			8.09721i			0.960962i	−0.877005	+	0.480481i	$0.840462\pi$
$72$	1.61882	−	4.65682i	0.190780	−	0.548811i
$73$	−6.89558	−	6.89558i	−0.807067	−	0.807067i	0.177122	−	0.984189i	$-0.443321\pi$
$73$	−6.89558	−	6.89558i	−0.807067	−	0.807067i	−0.984189	+	0.177122i	$0.943321\pi$
$74$	−6.28481	−	2.46167i	−0.730595	−	0.286163i
$75$	−5.16142	+	2.18696i	−0.595990	+	0.252528i
$76$	−3.41472	+	3.69026i	−0.391695	+	0.423302i
$77$		0			0
$78$	−3.64089	−	8.32952i	−0.412249	−	0.943133i
$79$	8.06116			0.906952			0.453476	−	0.891269i	$-0.350184\pi$
$79$	8.06116			0.906952			0.453476	+	0.891269i	$0.350184\pi$
$80$	8.88541	+	1.02443i	0.993419	+	0.114535i
$81$	0.732452			0.0813835
$82$	4.49579	+	10.2853i	0.496477	+	1.13583i
$83$	−5.99790	+	5.99790i	−0.658356	+	0.658356i	−0.954991	−	0.296635i	$-0.904135\pi$
$83$	−5.99790	+	5.99790i	−0.658356	+	0.658356i	0.296635	+	0.954991i	$0.404135\pi$
$84$		0			0
$85$	−2.98212	−	4.42426i	−0.323456	−	0.479878i
$86$	−14.2023	−	5.56285i	−1.53148	−	0.599858i
$87$	−2.02496	−	2.02496i	−0.217098	−	0.217098i
$88$	2.77095	−	7.97111i	0.295384	−	0.849723i
$89$			2.05525i			0.217856i	0.994050	+	0.108928i	$0.0347418\pi$
$89$			2.05525i			0.217856i	−0.994050	+	0.108928i	$0.965258\pi$
$90$	−1.20167	−	5.37951i	−0.126667	−	0.567051i
$91$		0			0
$92$	−0.464910	−	11.9881i	−0.0484702	−	1.24984i
$93$	−2.85831	−	2.85831i	−0.296393	−	0.296393i
$94$	−1.52646	+	3.89715i	−0.157442	+	0.401960i
$95$	−1.07436	+	5.51758i	−0.110227	+	0.566092i
$96$	1.84871	−	6.06661i	0.188683	−	0.619171i
$97$	−6.63160	+	6.63160i	−0.673337	+	0.673337i	−0.958484	−	0.285147i	$-0.907958\pi$
$97$	−6.63160	+	6.63160i	−0.673337	+	0.673337i	0.285147	+	0.958484i	$0.407958\pi$
$98$		0			0
$99$	−5.20071			−0.522691
$100$	9.04947	−	4.25524i	0.904947	−	0.425524i
$101$	7.46547			0.742842			0.371421	−	0.928465i	$-0.378871\pi$
$101$	7.46547			0.742842			0.371421	+	0.928465i	$0.378871\pi$
$102$	−3.46648	+	1.51522i	−0.343233	+	0.150029i
$103$	2.91433	−	2.91433i	0.287157	−	0.287157i	−0.548798	−	0.835955i	$-0.684914\pi$
$103$	2.91433	−	2.91433i	0.287157	−	0.287157i	0.835955	+	0.548798i	$0.184914\pi$
$104$	7.06600	+	14.5964i	0.692878	+	1.43129i
$105$		0			0
$106$	−1.32020	+	3.37056i	−0.128229	+	0.327377i
$107$	7.36564	+	7.36564i	0.712063	+	0.712063i	0.966966	−	0.254904i	$-0.0820437\pi$
$107$	7.36564	+	7.36564i	0.712063	+	0.712063i	−0.254904	+	0.966966i	$0.582044\pi$
$108$	−10.6272	+	0.412133i	−1.02260	+	0.0396575i
$109$		−	10.2630i		−	0.983013i	−0.870874	−	0.491507i	$-0.836446\pi$
$109$		−	10.2630i		−	0.983013i	0.870874	−	0.491507i	$-0.163554\pi$
$110$	−2.05690	−	9.20815i	−0.196118	−	0.877963i
$111$			5.35088i			0.507883i
$112$		0			0
$113$	7.35551	+	7.35551i	0.691948	+	0.691948i	0.962660	−	0.270712i	$-0.0872592\pi$
$113$	7.35551	+	7.35551i	0.691948	+	0.691948i	−0.270712	+	0.962660i	$0.587259\pi$
$114$	3.71125	+	1.45364i	0.347591	+	0.136146i
$115$	−7.49694	−	11.1224i	−0.699093	−	1.03717i
$116$	3.74964	+	3.46967i	0.348145	+	0.322150i
$117$	7.06674	−	7.06674i	0.653321	−	0.653321i
$118$	−1.18601	−	2.71332i	−0.109181	−	0.249782i
$119$		0			0
$120$	−1.81280	−	6.85497i	−0.165485	−	0.625771i
$121$	2.09791			0.190719
$122$	1.07673	+	2.46332i	0.0974826	+	0.223018i
$123$	6.29231	−	6.29231i	0.567359	−	0.567359i
$124$	5.29276	+	4.89757i	0.475304	+	0.439815i
$125$	6.09835	−	9.37071i	0.545453	−	0.838142i
$126$		0			0
$127$	13.3832	+	13.3832i	1.18756	+	1.18756i	0.977739	+	0.209826i	$0.0672898\pi$
$127$	13.3832	+	13.3832i	1.18756	+	1.18756i	0.209826	+	0.977739i	$0.432710\pi$
$128$	−2.87609	+	10.9420i	−0.254213	+	0.967148i
$129$			12.0918i			1.06463i
$130$	15.3070	+	9.71715i	1.34251	+	0.852250i
$131$			15.3563i			1.34169i	0.741598	+	0.670845i	$0.234068\pi$
$131$			15.3563i			1.34169i	−0.741598	+	0.670845i	$0.765932\pi$
$132$	−6.68504	+	0.259253i	−0.581858	+	0.0225651i
$133$		0			0
$134$	−1.60464	+	4.09675i	−0.138620	+	0.353905i
$135$	−9.85981	+	6.64589i	−0.848597	+	0.571987i
$136$	6.07454	−	2.94064i	0.520887	−	0.252158i
$137$	3.33190	−	3.33190i	0.284663	−	0.284663i	−0.550302	−	0.834965i	$-0.685488\pi$
$137$	3.33190	−	3.33190i	0.284663	−	0.284663i	0.834965	+	0.550302i	$0.185488\pi$
$138$	−8.71460	+	3.80921i	−0.741836	+	0.324261i
$139$	10.3065			0.874185			0.437093	−	0.899417i	$-0.356008\pi$
$139$	10.3065			0.874185			0.437093	+	0.899417i	$0.356008\pi$
$140$		0			0
$141$	3.31802			0.279428
$142$	−10.4926	+	4.58638i	−0.880519	+	0.384880i
$143$	12.0962	−	12.0962i	1.01154	−	1.01154i
$144$	6.95137	−	0.539975i	0.579281	−	0.0449979i
$145$	5.60636	+	1.09165i	0.465583	+	0.0906564i
$146$	5.02973	−	12.8413i	0.416264	−	1.06275i
$147$		0			0
$148$	−0.369908	−	9.53837i	−0.0304063	−	0.784049i
$149$		−	9.67244i		−	0.792398i	−0.918165	−	0.396199i	$-0.870329\pi$
$149$		−	9.67244i		−	0.792398i	0.918165	−	0.396199i	$-0.129671\pi$
$150$	−5.75743	−	5.44960i	−0.470092	−	0.444958i
$151$			1.10382i			0.0898272i	0.998991	+	0.0449136i	$0.0143013\pi$
$151$			1.10382i			0.0898272i	−0.998991	+	0.0449136i	$0.985699\pi$
$152$	−6.71610	−	2.33468i	−0.544748	−	0.189367i
$153$	−2.94095	−	2.94095i	−0.237762	−	0.237762i
$154$		0			0
$155$	7.91360	+	1.54090i	0.635635	+	0.123768i
$156$	8.73139	−	9.43593i	0.699070	−	0.755479i
$157$	6.14377	−	6.14377i	0.490326	−	0.490326i	−0.418083	−	0.908409i	$-0.637298\pi$
$157$	6.14377	−	6.14377i	0.490326	−	0.490326i	0.908409	+	0.418083i	$0.137298\pi$
$158$	4.56597	+	10.4459i	0.363249	+	0.831031i
$159$	2.86968			0.227581
$160$	3.70535	+	12.0942i	0.292933	+	0.956133i
$161$		0			0
$162$	0.414872	+	0.949133i	0.0325954	+	0.0745709i
$163$	0.762126	−	0.762126i	0.0596944	−	0.0596944i	−0.676629	−	0.736324i	$-0.736560\pi$
$163$	0.762126	−	0.762126i	0.0596944	−	0.0596944i	0.736324	+	0.676629i	$0.236560\pi$
$164$	−10.7816	+	11.6516i	−0.841899	+	0.909833i
$165$	−6.20232	+	4.18060i	−0.482850	+	0.325459i
$166$	−11.1696	−	4.37496i	−0.866926	−	0.339563i
$167$	−2.18132	−	2.18132i	−0.168796	−	0.168796i	0.617654	−	0.786450i	$-0.288083\pi$
$167$	−2.18132	−	2.18132i	−0.168796	−	0.168796i	−0.786450	+	0.617654i	$0.788083\pi$
$168$		0			0
$169$			19.8727i			1.52867i
$170$	4.04397	−	6.37028i	0.310158	−	0.488579i
$171$			4.38188i			0.335091i
$172$	−0.835914	−	21.5547i	−0.0637378	−	1.64353i
$173$	−16.6803	−	16.6803i	−1.26818	−	1.26818i	−0.947026	−	0.321157i	$-0.895928\pi$
$173$	−16.6803	−	16.6803i	−1.26818	−	1.26818i	−0.321157	−	0.947026i	$-0.604072\pi$
$174$	1.47703	−	3.77097i	0.111974	−	0.285876i
$175$		0			0
$176$	11.8987	−	0.924279i	0.896899	−	0.0696701i
$177$	−1.65994	+	1.65994i	−0.124769	+	0.124769i
$178$	−2.66326	+	1.16413i	−0.199619	+	0.0872549i
$179$	7.06310			0.527921			0.263960	−	0.964534i	$-0.414971\pi$
$179$	7.06310			0.527921			0.263960	+	0.964534i	$0.414971\pi$
$180$	6.29029	−	4.60419i	0.468851	−	0.343176i
$181$	2.37419			0.176472			0.0882360	−	0.996100i	$-0.471877\pi$
$181$	2.37419			0.176472			0.0882360	+	0.996100i	$0.471877\pi$
$182$		0			0
$183$	1.50699	−	1.50699i	0.111400	−	0.111400i
$184$	15.2712	−	7.39267i	1.12580	−	0.544995i
$185$	−5.96498	−	8.84962i	−0.438554	−	0.650637i
$186$	2.08489	−	5.32287i	0.152872	−	0.390292i
$187$	−5.03405	−	5.03405i	−0.368126	−	0.368126i
$188$	−5.91465	+	0.229376i	−0.431370	+	0.0167290i
$189$		0			0
$190$	−7.75838	+	1.73305i	−0.562852	+	0.125729i
$191$		−	6.31582i		−	0.456997i	−0.973544	−	0.228498i	$-0.926618\pi$
$191$		−	6.31582i		−	0.456997i	0.973544	−	0.228498i	$-0.0733816\pi$
$192$	8.90843	−	1.04061i	0.642911	−	0.0750996i
$193$	14.9354	+	14.9354i	1.07508	+	1.07508i	0.996943	+	0.0781335i	$0.0248961\pi$
$193$	14.9354	+	14.9354i	1.07508	+	1.07508i	0.0781335	+	0.996943i	$0.475104\pi$
$194$	−12.3497	−	4.83718i	−0.886653	−	0.347289i
$195$	2.74712	−	14.1084i	0.196726	−	1.01032i
$196$		0			0
$197$	−1.01354	+	1.01354i	−0.0722120	+	0.0722120i	−0.742290	−	0.670078i	$-0.766260\pi$
$197$	−1.01354	+	1.01354i	−0.0722120	+	0.0722120i	0.670078	+	0.742290i	$0.266260\pi$
$198$	−2.94576	−	6.73923i	−0.209346	−	0.478936i
$199$	9.51476			0.674484			0.337242	−	0.941418i	$-0.390506\pi$
$199$	9.51476			0.674484			0.337242	+	0.941418i	$0.390506\pi$
$200$	10.6398	+	9.31634i	0.752349	+	0.658765i
$201$	3.48797			0.246022
$202$	4.22855	+	9.67397i	0.297520	+	0.680658i
$203$		0			0
$204$	−3.92693	−	3.63372i	−0.274940	−	0.254412i
$205$	−3.39216	+	17.4211i	−0.236919	+	1.21674i
$206$	5.42720	+	2.12575i	0.378131	+	0.148108i
$207$	−7.39345	−	7.39345i	−0.513880	−	0.513880i
$208$	−14.9121	+	17.4239i	−1.03397	+	1.20813i
$209$			7.50050i			0.518821i
$210$		0			0
$211$		−	26.9476i		−	1.85515i	−0.373634	−	0.927576i	$-0.621888\pi$
$211$		−	26.9476i		−	1.85515i	0.373634	−	0.927576i	$-0.378112\pi$
$212$	−5.11545	+	0.198382i	−0.351330	+	0.0136250i
$213$	6.41911	+	6.41911i	0.439830	+	0.439830i
$214$	−5.37260	+	13.7166i	−0.367263	+	0.937648i
$215$	−13.4796	−	19.9983i	−0.919300	−	1.36387i
$216$	−6.55345	−	13.5376i	−0.445906	−	0.921116i
$217$		0			0
$218$	13.2990	−	5.81310i	0.900725	−	0.393712i
$219$	−10.9330			−0.738785
$220$	10.7671	−	7.88103i	0.725920	−	0.531339i
$221$	13.6806			0.920255
$222$	−6.93382	+	3.03082i	−0.465368	+	0.203415i
$223$	2.22624	−	2.22624i	0.149080	−	0.149080i	−0.628627	−	0.777707i	$-0.716383\pi$
$223$	2.22624	−	2.22624i	0.149080	−	0.149080i	0.777707	+	0.628627i	$0.216383\pi$
$224$		0			0
$225$	3.27007	−	8.07865i	0.218004	−	0.538577i
$226$	−5.36521	+	13.6978i	−0.356889	+	0.911161i
$227$	5.70319	+	5.70319i	0.378534	+	0.378534i	0.870573	−	0.492039i	$-0.163748\pi$
$227$	5.70319	+	5.70319i	0.378534	+	0.378534i	−0.492039	+	0.870573i	$0.663748\pi$
$228$	0.218435	+	5.63252i	0.0144662	+	0.373022i
$229$			2.43296i			0.160775i	0.996764	+	0.0803873i	$0.0256157\pi$
$229$			2.43296i			0.160775i	−0.996764	+	0.0803873i	$0.974384\pi$
$230$	10.1664	−	16.0147i	0.670352	−	1.05598i
$231$		0			0
$232$	−2.37224	+	6.82416i	−0.155745	+	0.448028i
$233$	7.40225	+	7.40225i	0.484937	+	0.484937i	0.906704	−	0.421767i	$-0.138590\pi$
$233$	7.40225	+	7.40225i	0.484937	+	0.484937i	−0.421767	+	0.906704i	$0.638590\pi$
$234$	13.1600	+	5.15458i	0.860297	+	0.336966i
$235$	−5.48756	+	3.69882i	−0.357969	+	0.241285i
$236$	2.84423	−	3.07373i	0.185144	−	0.200083i
$237$	6.39053	−	6.39053i	0.415110	−	0.415110i
$238$		0			0
$239$	−12.9050			−0.834754			−0.417377	−	0.908733i	$-0.637051\pi$
$239$	−12.9050			−0.834754			−0.417377	+	0.908733i	$0.637051\pi$
$240$	7.85608	−	6.23184i	0.507108	−	0.402264i
$241$	−2.71390			−0.174817			−0.0874087	−	0.996173i	$-0.527859\pi$
$241$	−2.71390			−0.174817			−0.0874087	+	0.996173i	$0.527859\pi$
$242$	1.18829	+	2.71853i	0.0763859	+	0.174754i
$243$	−10.6996	+	10.6996i	−0.686383	+	0.686383i
$244$	−2.58216	+	2.79052i	−0.165306	+	0.178645i
$245$		0			0
$246$	11.7178	+	4.58970i	0.747101	+	0.292629i
$247$	−10.1917	−	10.1917i	−0.648483	−	0.648483i
$248$	−3.34851	+	9.63257i	−0.212631	+	0.611669i
$249$			9.50975i			0.602656i
$250$	15.5970	+	2.59470i	0.986443	+	0.164103i
$251$		−	3.15358i		−	0.199052i	−0.995035	−	0.0995262i	$-0.968267\pi$
$251$		−	3.15358i		−	0.199052i	0.995035	−	0.0995262i	$-0.0317327\pi$
$252$		0			0
$253$	−12.6554	−	12.6554i	−0.795640	−	0.795640i
$254$	−9.76188	+	24.9227i	−0.612515	+	1.56379i
$255$	−5.87145	−	1.14326i	−0.367684	−	0.0715940i
$256$	−15.8081	+	2.47082i	−0.988004	+	0.154426i
$257$	−11.6435	+	11.6435i	−0.726299	+	0.726299i	−0.969881	−	0.243581i	$-0.921678\pi$
$257$	−11.6435	+	11.6435i	−0.726299	+	0.726299i	0.243581	+	0.969881i	$0.421678\pi$
$258$	−15.6690	+	6.84900i	−0.975507	+	0.426400i
$259$		0			0
$260$	−3.92165	+	25.3392i	−0.243211	+	1.57147i
$261$	4.45239			0.275596
$262$	−19.8992	+	8.69806i	−1.22938	+	0.537368i
$263$	20.6399	−	20.6399i	1.27271	−	1.27271i	0.328054	−	0.944659i	$-0.393607\pi$
$263$	20.6399	−	20.6399i	1.27271	−	1.27271i	0.944659	−	0.328054i	$-0.106393\pi$
$264$	−4.12246	−	8.51583i	−0.253720	−	0.524113i
$265$	−4.74607	+	3.19903i	−0.291549	+	0.196515i
$266$		0			0
$267$	1.62931	+	1.62931i	0.0997123	+	0.0997123i
$268$	−6.21758	+	0.241124i	−0.379799	+	0.0147290i
$269$		−	6.11072i		−	0.372577i	−0.982495	−	0.186288i	$-0.940354\pi$
$269$		−	6.11072i		−	0.372577i	0.982495	−	0.186288i	$-0.0596459\pi$
$270$	−14.1967	−	9.01230i	−0.863982	−	0.548471i
$271$			22.0200i			1.33762i	0.743434	+	0.668810i	$0.233196\pi$
$271$			22.0200i			1.33762i	−0.743434	+	0.668810i	$0.766804\pi$
$272$	7.25128	+	6.20594i	0.439673	+	0.376290i
$273$		0			0
$274$	6.20480	+	2.43033i	0.374846	+	0.146822i
$275$	5.59740	−	13.8283i	0.337536	−	0.833877i
$276$	−9.87217	−	9.13505i	−0.594235	−	0.549865i
$277$	−11.6364	+	11.6364i	−0.699165	+	0.699165i	−0.964230	−	0.265066i	$-0.914606\pi$
$277$	−11.6364	+	11.6364i	−0.699165	+	0.699165i	0.265066	+	0.964230i	$0.414606\pi$
$278$	5.83775	+	13.3555i	0.350125	+	0.801007i
$279$	6.28472			0.376257
$280$		0			0
$281$	6.79274			0.405221			0.202610	−	0.979259i	$-0.435057\pi$
$281$	6.79274			0.405221			0.202610	+	0.979259i	$0.435057\pi$
$282$	1.87938	+	4.29959i	0.111915	+	0.256037i
$283$	−9.22409	+	9.22409i	−0.548315	+	0.548315i	−0.925953	−	0.377638i	$-0.876736\pi$
$283$	−9.22409	+	9.22409i	−0.548315	+	0.548315i	0.377638	+	0.925953i	$0.376736\pi$
$284$	−11.8863	−	10.9988i	−0.705324	−	0.652660i
$285$	3.52239	+	5.22580i	0.208648	+	0.309550i
$286$	22.5261	+	8.82314i	1.33200	+	0.521723i
$287$		0			0
$288$	4.63707	+	8.70194i	0.273242	+	0.512767i
$289$			11.3066i			0.665093i
$290$	1.76094	+	7.88321i	0.103406	+	0.462918i
$291$			10.5145i			0.616369i
$292$	19.4890	−	0.755804i	1.14051	−	0.0442301i
$293$	1.28839	+	1.28839i	0.0752688	+	0.0752688i	0.743739	−	0.668470i	$-0.233051\pi$
$293$	1.28839	+	1.28839i	0.0752688	+	0.0752688i	−0.668470	+	0.743739i	$0.733051\pi$
$294$		0			0
$295$	0.894869	−	4.59577i	0.0521013	−	0.267576i
$296$	12.1506	−	5.88202i	0.706238	−	0.341885i
$297$	−11.2188	+	11.2188i	−0.650980	+	0.650980i
$298$	12.5338	−	5.47862i	0.726066	−	0.317368i
$299$	34.3925			1.98897
$300$	3.80066	−	10.5474i	0.219431	−	0.608953i
$301$		0			0
$302$	−1.43036	+	0.625218i	−0.0823078	+	0.0359772i
$303$	5.91829	−	5.91829i	0.339997	−	0.339997i
$304$	−0.778756	−	10.0253i	−0.0446647	−	0.574991i
$305$	−0.812415	+	4.17231i	−0.0465188	+	0.238906i
$306$	2.14517	−	5.47678i	0.122631	−	0.313086i
$307$	11.6465	+	11.6465i	0.664701	+	0.664701i	0.956484	−	0.291783i	$-0.0942486\pi$
$307$	11.6465	+	11.6465i	0.664701	+	0.664701i	−0.291783	+	0.956484i	$0.594249\pi$
$308$		0			0
$309$		−	4.62070i		−	0.262863i
$310$	2.48563	+	11.1275i	0.141174	+	0.631997i
$311$			30.1836i			1.71156i	0.517343	+	0.855778i	$0.326921\pi$
$311$			30.1836i			1.71156i	−0.517343	+	0.855778i	$0.673079\pi$
$312$	17.1729	+	5.96973i	0.972227	+	0.337969i
$313$	−15.6006	−	15.6006i	−0.881800	−	0.881800i	0.111918	−	0.993717i	$-0.464301\pi$
$313$	−15.6006	−	15.6006i	−0.881800	−	0.881800i	−0.993717	+	0.111918i	$0.964301\pi$
$314$	11.4412	+	4.48135i	0.645664	+	0.252897i
$315$		0			0
$316$	−10.9499	+	11.8334i	−0.615978	+	0.665682i
$317$	−1.02494	+	1.02494i	−0.0575664	+	0.0575664i	−0.735304	−	0.677738i	$-0.762961\pi$
$317$	−1.02494	+	1.02494i	−0.0575664	+	0.0575664i	0.677738	+	0.735304i	$0.262961\pi$
$318$	1.62543	+	3.71862i	0.0911498	+	0.208530i
$319$	7.62119			0.426705
$320$	−13.5733	+	11.6519i	−0.758770	+	0.651358i
$321$	11.6783			0.651819
$322$		0			0
$323$	−4.24147	+	4.24147i	−0.236001	+	0.236001i
$324$	−0.994924	+	1.07521i	−0.0552736	+	0.0597337i
$325$	11.1842	+	26.3957i	0.620386	+	1.46417i
$326$	1.41927	+	0.555906i	0.0786059	+	0.0307888i
$327$	−8.13602	−	8.13602i	−0.449923	−	0.449923i
$328$	−21.2053	−	7.37146i	−1.17087	−	0.407021i
$329$		0			0
$330$	−8.93044	−	5.66920i	−0.491604	−	0.312079i
$331$			28.3761i			1.55969i	0.625971	+	0.779846i	$0.284703\pi$
$331$			28.3761i			1.55969i	−0.625971	+	0.779846i	$0.715297\pi$
$332$	−0.657412	−	16.9519i	−0.0360802	−	0.930356i
$333$	−5.88264	−	5.88264i	−0.322367	−	0.322367i
$334$	1.59109	−	4.06216i	0.0870605	−	0.222271i
$335$	−5.76862	+	3.88827i	−0.315173	+	0.212439i
$336$		0			0
$337$	−11.7829	+	11.7829i	−0.641857	+	0.641857i	−0.951012	−	0.309155i	$-0.899954\pi$
$337$	−11.7829	+	11.7829i	−0.641857	+	0.641857i	0.309155	+	0.951012i	$0.399954\pi$
$338$	−25.7517	+	11.2562i	−1.40071	+	0.612257i
$339$	11.6622			0.633406
$340$	10.5454	+	1.63207i	0.571903	+	0.0885113i
$341$	10.7576			0.582557
$342$	−5.67817	+	2.48197i	−0.307041	+	0.134209i
$343$		0			0
$344$	27.4577	−	13.2921i	1.48042	−	0.716662i
$345$	−14.7606	−	2.87413i	−0.794684	−	0.154738i
$346$	12.1669	−	31.0629i	0.654096	−	1.66995i
$347$	−11.2886	−	11.2886i	−0.606002	−	0.606002i	0.335896	−	0.941899i	$-0.390961\pi$
$347$	−11.2886	−	11.2886i	−0.606002	−	0.606002i	−0.941899	+	0.335896i	$0.890961\pi$
$348$	5.72314	−	0.221950i	0.306793	−	0.0118977i
$349$		−	7.52656i		−	0.402888i	−0.979500	−	0.201444i	$-0.935437\pi$
$349$		−	7.52656i		−	0.402888i	0.979500	−	0.201444i	$-0.0645633\pi$
$350$		0			0
$351$		−	30.4882i		−	1.62734i
$352$	7.93732	+	14.8952i	0.423060	+	0.793915i
$353$	−3.96442	−	3.96442i	−0.211005	−	0.211005i	0.593689	−	0.804694i	$-0.297671\pi$
$353$	−3.96442	−	3.96442i	−0.211005	−	0.211005i	−0.804694	+	0.593689i	$0.797671\pi$
$354$	−3.09122	−	1.21079i	−0.164296	−	0.0643525i
$355$	−17.7721	−	3.46052i	−0.943247	−	0.183665i
$356$	−3.01702	−	2.79175i	−0.159902	−	0.147962i
$357$		0			0
$358$	4.00064	+	9.15257i	0.211441	+	0.483728i
$359$	36.4285			1.92262			0.961311	−	0.275464i	$-0.0888315\pi$
$359$	36.4285			1.92262			0.961311	+	0.275464i	$0.0888315\pi$
$360$	9.52916	+	5.54326i	0.502231	+	0.292155i
$361$	−12.6804			−0.667390
$362$	1.34478	+	3.07654i	0.0706799	+	0.161699i
$363$	1.66313	−	1.66313i	0.0872915	−	0.0872915i
$364$		0			0
$365$	18.0817	−	12.1878i	0.946440	−	0.637937i
$366$	2.80639	+	1.09922i	0.146692	+	0.0574573i
$367$	−23.1194	−	23.1194i	−1.20682	−	1.20682i	−0.972051	−	0.234769i	$-0.924567\pi$
$367$	−23.1194	−	23.1194i	−1.20682	−	1.20682i	−0.234769	−	0.972051i	$-0.575433\pi$
$368$	18.2294	+	15.6015i	0.950276	+	0.813284i
$369$			13.8353i			0.720235i
$370$	8.08894	−	12.7422i	0.420524	−	0.662433i
$371$		0			0
$372$	8.07844	−	0.313291i	0.418848	−	0.0162434i
$373$	−18.4926	−	18.4926i	−0.957512	−	0.957512i	0.0416212	−	0.999133i	$-0.486748\pi$
$373$	−18.4926	−	18.4926i	−0.957512	−	0.957512i	−0.999133	+	0.0416212i	$0.986748\pi$
$374$	3.67191	−	9.37464i	0.189870	−	0.484751i
$375$	−2.59418	−	12.2632i	−0.133963	−	0.633268i
$376$	−3.64738	−	7.53445i	−0.188099	−	0.388560i
$377$	−10.3557	+	10.3557i	−0.533346	+	0.533346i
$378$		0			0
$379$	20.3769			1.04669			0.523344	−	0.852121i	$-0.324684\pi$
$379$	20.3769			1.04669			0.523344	+	0.852121i	$0.324684\pi$
$380$	−6.64020	−	9.07191i	−0.340635	−	0.465379i
$381$	21.2192			1.08709
$382$	8.18423	−	3.57738i	0.418742	−	0.183035i
$383$	18.0549	−	18.0549i	0.922564	−	0.922564i	−0.0746461	−	0.997210i	$-0.523783\pi$
$383$	18.0549	−	18.0549i	0.922564	−	0.922564i	0.997210	+	0.0746461i	$0.0237827\pi$
$384$	6.39433	+	10.9544i	0.326309	+	0.559014i
$385$		0			0
$386$	−10.8941	+	27.8134i	−0.554496	+	1.41567i
$387$	−13.2935	−	13.2935i	−0.675747	−	0.675747i
$388$	−0.726869	−	18.7429i	−0.0369012	−	0.951526i
$389$		−	18.0492i		−	0.915129i	−0.889176	−	0.457564i	$-0.848722\pi$
$389$		−	18.0492i		−	0.915129i	0.889176	−	0.457564i	$-0.151278\pi$
$390$	19.8380	−	4.43138i	1.00454	−	0.224392i
$391$		−	14.3130i		−	0.723842i
$392$		0			0
$393$	12.1738	+	12.1738i	0.614088	+	0.614088i
$394$	−1.88747	−	0.739294i	−0.0950892	−	0.0372451i
$395$	−3.44511	+	17.6930i	−0.173343	+	0.890233i
$396$	7.06437	−	7.63441i	0.354998	−	0.383643i
$397$	−21.2747	+	21.2747i	−1.06774	+	1.06774i	−0.0702120	+	0.997532i	$0.522368\pi$
$397$	−21.2747	+	21.2747i	−1.06774	+	1.06774i	−0.997532	+	0.0702120i	$0.977632\pi$
$398$	5.38931	+	12.3295i	0.270141	+	0.618022i
$399$		0			0
$400$	−6.04584	+	19.0643i	−0.302292	+	0.953215i
$401$	4.89560			0.244475			0.122237	−	0.992501i	$-0.460993\pi$
$401$	4.89560			0.244475			0.122237	+	0.992501i	$0.460993\pi$
$402$	1.97564	+	4.51981i	0.0985358	+	0.225428i
$403$	−14.6175	+	14.6175i	−0.728149	+	0.728149i
$404$	−10.1407	+	10.9590i	−0.504519	+	0.545229i
$405$	−0.313029	+	1.60762i	−0.0155546	+	0.0798833i
$406$		0			0
$407$	−10.0694	−	10.0694i	−0.499119	−	0.499119i
$408$	2.48441	−	7.14683i	0.122997	−	0.353821i
$409$		−	33.5439i		−	1.65864i	−0.558774	−	0.829320i	$-0.688728\pi$
$409$		−	33.5439i		−	1.65864i	0.558774	−	0.829320i	$-0.311272\pi$
$410$	−24.4961	+	5.47190i	−1.20978	+	0.270238i
$411$		−	5.28276i		−	0.260579i
$412$	0.319431	+	8.23678i	0.0157372	+	0.405797i
$413$		0			0
$414$	5.39289	−	13.7684i	0.265046	−	0.676680i
$415$	−10.6011	−	15.7278i	−0.520390	−	0.772048i
$416$	−31.0249	−	9.45436i	−1.52112	−	0.463538i
$417$	8.17053	−	8.17053i	0.400112	−	0.400112i
$418$	−9.71937	+	4.24840i	−0.475390	+	0.207796i
$419$	−36.3735			−1.77696			−0.888481	−	0.458914i	$-0.848239\pi$
$419$	−36.3735			−1.77696			−0.888481	+	0.458914i	$0.848239\pi$
$420$		0			0
$421$	−33.2473			−1.62038			−0.810188	−	0.586170i	$-0.800635\pi$
$421$	−33.2473			−1.62038			−0.810188	+	0.586170i	$0.800635\pi$
$422$	34.9196	−	15.2636i	1.69986	−	0.743018i
$423$	−3.64776	+	3.64776i	−0.177360	+	0.177360i
$424$	−3.15454	−	6.51638i	−0.153198	−	0.316463i
$425$	10.9850	−	4.65449i	0.532853	−	0.225776i
$426$	−4.68219	+	11.9539i	−0.226853	+	0.579171i
$427$		0			0
$428$	−20.8175	+	0.807325i	−1.00625	+	0.0390235i
$429$		−	19.1787i		−	0.925955i
$430$	18.2793	−	28.7946i	0.881505	−	1.38860i
$431$			31.1145i			1.49873i	0.662154	+	0.749367i	$0.269642\pi$
$431$			31.1145i			1.49873i	−0.662154	+	0.749367i	$0.730358\pi$
$432$	13.8304	−	16.1600i	0.665416	−	0.777501i
$433$	−7.14603	−	7.14603i	−0.343416	−	0.343416i	0.514234	−	0.857650i	$-0.328076\pi$
$433$	−7.14603	−	7.14603i	−0.343416	−	0.343416i	−0.857650	+	0.514234i	$0.828076\pi$
$434$		0			0
$435$	5.30988	−	3.57906i	0.254589	−	0.171603i
$436$	15.0656	+	13.9407i	0.721509	+	0.667637i
$437$	−10.6629	+	10.6629i	−0.510075	+	0.510075i
$438$	−6.19263	−	14.1673i	−0.295895	−	0.676941i
$439$	0.557131			0.0265904			0.0132952	−	0.999912i	$-0.495768\pi$
$439$	0.557131			0.0265904			0.0132952	+	0.999912i	$0.495768\pi$
$440$	16.3111	+	9.48844i	0.777603	+	0.452344i
$441$		0			0
$442$	7.74889	+	17.7277i	0.368577	+	0.843221i
$443$	17.2462	−	17.2462i	0.819391	−	0.819391i	−0.166629	−	0.986020i	$-0.553288\pi$
$443$	17.2462	−	17.2462i	0.819391	−	0.819391i	0.986020	+	0.166629i	$0.0532882\pi$
$444$	−7.85485	−	7.26835i	−0.372774	−	0.344941i
$445$	−4.51096	−	0.878357i	−0.213840	−	0.0416381i
$446$	4.14581	+	1.62385i	0.196310	+	0.0768917i
$447$	−7.66789	−	7.66789i	−0.362679	−	0.362679i
$448$		0			0
$449$		−	8.64441i		−	0.407955i	−0.978976	−	0.203978i	$-0.934613\pi$
$449$		−	8.64441i		−	0.407955i	0.978976	−	0.203978i	$-0.0653870\pi$
$450$	12.3208	−	0.338420i	0.580807	−	0.0159533i
$451$			23.6819i			1.11514i
$452$	−20.7889	+	0.806215i	−0.977828	+	0.0379212i
$453$	0.875056	+	0.875056i	0.0411137	+	0.0411137i
$454$	−4.15999	+	10.6207i	−0.195238	+	0.498456i
$455$		0			0
$456$	−7.17505	+	3.47340i	−0.336003	+	0.162657i
$457$	1.93285	−	1.93285i	0.0904150	−	0.0904150i	−0.660453	−	0.750868i	$-0.729636\pi$
$457$	1.93285	−	1.93285i	0.0904150	−	0.0904150i	0.750868	+	0.660453i	$0.229636\pi$
$458$	−3.15270	+	1.37807i	−0.147316	+	0.0643928i
$459$	−12.6882			−0.592236
$460$	26.5107	+	4.10296i	1.23607	+	0.191301i
$461$	−38.5986			−1.79772			−0.898858	−	0.438239i	$-0.855602\pi$
$461$	−38.5986			−1.79772			−0.898858	+	0.438239i	$0.855602\pi$
$462$		0			0
$463$	−13.5055	+	13.5055i	−0.627652	+	0.627652i	−0.947477	−	0.319824i	$-0.896376\pi$
$463$	−13.5055	+	13.5055i	−0.627652	+	0.627652i	0.319824	+	0.947477i	$0.396376\pi$
$464$	−10.1866	+	0.791286i	−0.472902	+	0.0367345i
$465$	7.49511	−	5.05199i	0.347577	−	0.234280i
$466$	−5.39931	+	13.7848i	−0.250118	+	0.638568i
$467$	−9.44901	−	9.44901i	−0.437248	−	0.437248i	0.453837	−	0.891085i	$-0.350055\pi$
$467$	−9.44901	−	9.44901i	−0.437248	−	0.437248i	−0.891085	+	0.453837i	$0.850055\pi$
$468$	0.774565	+	19.9728i	0.0358043	+	0.923241i
$469$		0			0
$470$	−7.90128	−	5.01587i	−0.364459	−	0.231365i
$471$		−	9.74101i		−	0.448842i
$472$	5.59405	+	1.94463i	0.257487	+	0.0895087i
$473$	−22.7546	−	22.7546i	−1.04626	−	1.04626i
$474$	11.9007	+	4.66135i	0.546619	+	0.214103i
$475$	−11.6511	−	4.71612i	−0.534589	−	0.216390i
$476$		0			0
$477$	−3.15487	+	3.15487i	−0.144452	+	0.144452i
$478$	−7.30958	−	16.7227i	−0.334332	−	0.764877i
$479$	7.83260			0.357881			0.178940	−	0.983860i	$-0.442733\pi$
$479$	7.83260			0.357881			0.178940	+	0.983860i	$0.442733\pi$
$480$	12.5252	+	6.65033i	0.571695	+	0.303545i
$481$	27.3646			1.24772
$482$	−1.53719	−	3.51675i	−0.0700172	−	0.160183i
$483$		0			0
$484$	−2.84968	+	3.07963i	−0.129531	+	0.139983i
$485$	−11.7212	−	17.3895i	−0.532231	−	0.789616i
$486$	−19.9254	−	7.80448i	−0.903833	−	0.354018i
$487$	−1.72517	−	1.72517i	−0.0781749	−	0.0781749i	0.666938	−	0.745113i	$-0.267605\pi$
$487$	−1.72517	−	1.72517i	−0.0781749	−	0.0781749i	−0.745113	+	0.666938i	$0.767605\pi$
$488$	−5.07861	−	1.76545i	−0.229898	−	0.0799181i
$489$		−	1.20836i		−	0.0546439i
$490$		0			0
$491$		−	33.5206i		−	1.51276i	−0.654130	−	0.756382i	$-0.726965\pi$
$491$		−	33.5206i		−	1.51276i	0.654130	−	0.756382i	$-0.273035\pi$
$492$	0.689682	+	17.7840i	0.0310932	+	0.801764i
$493$	4.30971	+	4.30971i	0.194100	+	0.194100i
$494$	7.43398	−	18.9795i	0.334471	−	0.853926i
$495$	2.22264	−	11.4148i	0.0999001	−	0.513055i
$496$	−14.3788	+	1.11693i	−0.645628	+	0.0501517i
$497$		0			0
$498$	−12.3230	+	5.38646i	−0.552207	+	0.241373i
$499$	−20.6924			−0.926319			−0.463159	−	0.886275i	$-0.653284\pi$
$499$	−20.6924			−0.926319			−0.463159	+	0.886275i	$0.653284\pi$
$500$	5.47210	+	21.6808i	0.244720	+	0.969594i
$501$	−3.45851			−0.154515
$502$	4.08651	−	1.78624i	0.182390	−	0.0797237i
$503$	−4.35918	+	4.35918i	−0.194366	+	0.194366i	−0.797580	−	0.603214i	$-0.793887\pi$
$503$	−4.35918	+	4.35918i	−0.194366	+	0.194366i	0.603214	+	0.797580i	$0.293887\pi$
$504$		0			0
$505$	−3.19053	+	16.3856i	−0.141977	+	0.729148i
$506$	9.23105	−	23.5675i	0.410370	−	1.04770i
$507$	15.7542	+	15.7542i	0.699669	+	0.699669i
$508$	−37.8249	+	1.46689i	−1.67821	+	0.0650827i
$509$		−	30.5865i		−	1.35572i	−0.735189	−	0.677862i	$-0.762907\pi$
$509$		−	30.5865i		−	1.35572i	0.735189	−	0.677862i	$-0.237093\pi$
$510$	−1.84420	−	8.25596i	−0.0816626	−	0.365580i
$511$		0			0
$512$	−12.1557	−	19.0851i	−0.537211	−	0.843448i
$513$	9.45244	+	9.45244i	0.417335	+	0.417335i
$514$	−21.6830	−	8.49291i	−0.956395	−	0.374606i
$515$	5.15101	+	7.64201i	0.226980	+	0.336747i
$516$	−17.7503	−	16.4249i	−0.781412	−	0.723067i
$517$	−6.24391	+	6.24391i	−0.274607	+	0.274607i
$518$		0			0
$519$	−26.4469			−1.16089
$520$	−35.0566	+	9.27071i	−1.53733	+	0.406548i
$521$	−9.36545			−0.410308			−0.205154	−	0.978730i	$-0.565770\pi$
$521$	−9.36545			−0.410308			−0.205154	+	0.978730i	$0.565770\pi$
$522$	2.52190	+	5.76954i	0.110381	+	0.252526i
$523$	23.1360	−	23.1360i	1.01167	−	1.01167i	0.0117350	−	0.999931i	$-0.496265\pi$
$523$	23.1360	−	23.1360i	1.01167	−	1.01167i	0.999931	−	0.0117350i	$-0.00373545\pi$
$524$	−22.5424	−	20.8592i	−0.984770	−	0.911240i
$525$		0			0
$526$	38.4366	+	15.0551i	1.67592	+	0.656432i
$527$	6.08333	+	6.08333i	0.264994	+	0.264994i
$528$	8.70004	−	10.1655i	0.378621	−	0.442396i
$529$		−	12.9825i		−	0.564455i
$530$	−6.83364	−	4.33811i	−0.296834	−	0.188436i
$531$		−	3.64981i		−	0.158388i
$532$		0			0
$533$	−32.1791	−	32.1791i	−1.39383	−	1.39383i
$534$	−1.18844	+	3.03418i	−0.0514290	+	0.131302i
$535$	−19.3143	+	13.0186i	−0.835030	+	0.562842i
$536$	−3.83419	−	7.92035i	−0.165612	−	0.342107i
$537$	5.59931	−	5.59931i	0.241628	−	0.241628i
$538$	7.91844	−	3.46120i	0.341388	−	0.149223i
$539$		0			0
$540$	3.63719	−	23.5012i	0.156520	−	1.01133i
$541$	−5.46190			−0.234825			−0.117413	−	0.993083i	$-0.537460\pi$
$541$	−5.46190			−0.234825			−0.117413	+	0.993083i	$0.537460\pi$
$542$	−28.5342	+	12.4725i	−1.22565	+	0.535738i
$543$	1.88215	−	1.88215i	0.0807708	−	0.0807708i
$544$	−3.93460	+	12.9116i	−0.168695	+	0.553579i
$545$	22.5256	+	4.38610i	0.964892	+	0.187880i
$546$		0			0
$547$	−4.64823	−	4.64823i	−0.198744	−	0.198744i	0.600718	−	0.799461i	$-0.294882\pi$
$547$	−4.64823	−	4.64823i	−0.198744	−	0.198744i	−0.799461	+	0.600718i	$0.794882\pi$
$548$	0.365199	+	9.41694i	0.0156005	+	0.402272i
$549$			3.31351i			0.141417i
$550$	21.0896	−	0.579277i	0.899261	−	0.0247004i
$551$		−	6.42127i		−	0.273555i
$552$	6.24572	−	17.9669i	0.265835	−	0.764721i
$553$		0			0
$554$	−21.6699	−	8.48777i	−0.920664	−	0.360611i
$555$	−11.7444	−	2.28681i	−0.498520	−	0.0970698i
$556$	−13.9998	+	15.1295i	−0.593724	+	0.641632i
$557$	8.82237	−	8.82237i	0.373816	−	0.373816i	−0.495049	−	0.868865i	$-0.664850\pi$
$557$	8.82237	−	8.82237i	0.373816	−	0.373816i	0.868865	+	0.495049i	$0.164850\pi$
$558$	3.55976	+	8.14393i	0.150697	+	0.344760i
$559$	61.8381			2.61547
$560$		0			0
$561$	−7.98155			−0.336981
$562$	3.84751	+	8.80223i	0.162297	+	0.371300i
$563$	13.4268	−	13.4268i	0.565873	−	0.565873i	−0.365097	−	0.930970i	$-0.618964\pi$
$563$	13.4268	−	13.4268i	0.565873	−	0.565873i	0.930970	+	0.365097i	$0.118964\pi$
$564$	−4.50703	+	4.87071i	−0.189780	+	0.205094i
$565$	−19.2878	+	13.0007i	−0.811442	+	0.546943i
$566$	−17.1775	−	6.72818i	−0.722025	−	0.282807i
$567$		0			0
$568$	7.52000	−	21.6326i	0.315532	−	0.907682i
$569$			22.5548i			0.945547i	0.881184	+	0.472773i	$0.156747\pi$
$569$			22.5548i			0.945547i	−0.881184	+	0.472773i	$0.843253\pi$
$570$	−4.77661	+	7.52438i	−0.200070	+	0.315162i
$571$		−	26.3826i		−	1.10408i	−0.833819	−	0.552038i	$-0.813850\pi$
$571$		−	26.3826i		−	1.10408i	0.833819	−	0.552038i	$-0.186150\pi$
$572$	1.32583	+	34.1875i	0.0554357	+	1.42945i
$573$	−5.00690	−	5.00690i	−0.209166	−	0.209166i
$574$		0			0
$575$	27.6160	−	11.7012i	1.15167	−	0.487975i
$576$	−8.64972	+	10.9378i	−0.360405	+	0.455740i
$577$	22.5576	−	22.5576i	0.939086	−	0.939086i	−0.0591623	−	0.998248i	$-0.518843\pi$
$577$	22.5576	−	22.5576i	0.939086	−	0.939086i	0.998248	+	0.0591623i	$0.0188430\pi$
$578$	−14.6514	+	6.40422i	−0.609418	+	0.266380i
$579$	23.6803			0.984120
$580$	−9.21787	+	6.74704i	−0.382751	+	0.280156i
$581$		0			0
$582$	−13.6250	+	5.95556i	−0.564773	+	0.246866i
$583$	−5.40021	+	5.40021i	−0.223654	+	0.223654i
$584$	12.0183	+	24.8263i	0.497319	+	1.02732i
$585$	12.4903	+	18.5306i	0.516410	+	0.766144i
$586$	−0.939774	+	2.39931i	−0.0388217	+	0.0991144i
$587$	−14.8860	−	14.8860i	−0.614410	−	0.614410i	0.329682	−	0.944092i	$-0.393058\pi$
$587$	−14.8860	−	14.8860i	−0.614410	−	0.614410i	−0.944092	+	0.329682i	$0.893058\pi$
$588$		0			0
$589$		−	9.06388i		−	0.373471i
$590$	6.46220	−	1.44351i	0.266044	−	0.0594285i
$591$			1.60699i			0.0661026i
$592$	14.5044	+	12.4134i	0.596126	+	0.510188i
$593$	23.3225	+	23.3225i	0.957741	+	0.957741i	0.999143	−	0.0414014i	$-0.0131822\pi$
$593$	23.3225	+	23.3225i	0.957741	+	0.957741i	−0.0414014	+	0.999143i	$0.513182\pi$
$594$	−20.8921	−	8.18314i	−0.857214	−	0.335758i
$595$		0			0
$596$	14.1987	+	13.1385i	0.581602	+	0.538176i
$597$	7.54288	−	7.54288i	0.308710	−	0.308710i
$598$	19.4804	+	44.5668i	0.796613	+	1.82247i
$599$	17.5846			0.718486			0.359243	−	0.933244i	$-0.383035\pi$
$599$	17.5846			0.718486			0.359243	+	0.933244i	$0.383035\pi$
$600$	15.8204	−	1.04919i	0.645864	−	0.0428331i
$601$	17.7704			0.724871			0.362436	−	0.932009i	$-0.381945\pi$
$601$	17.7704			0.724871			0.362436	+	0.932009i	$0.381945\pi$
$602$		0			0
$603$	−3.83460	+	3.83460i	−0.156157	+	0.156157i
$604$	−1.62035	−	1.49937i	−0.0659312	−	0.0610083i
$605$	−0.896586	+	4.60458i	−0.0364514	+	0.187203i
$606$	11.0213	+	4.31689i	0.447710	+	0.175362i
$607$	6.82673	+	6.82673i	0.277088	+	0.277088i	0.831946	−	0.554857i	$-0.187227\pi$
$607$	6.82673	+	6.82673i	0.277088	+	0.277088i	−0.554857	+	0.831946i	$0.687227\pi$
$608$	12.5500	−	6.68762i	0.508970	−	0.271219i
$609$		0			0
$610$	−5.86677	+	1.31051i	−0.237538	+	0.0530609i
$611$		−	16.9685i		−	0.686471i
$612$	8.31203	−	0.322349i	0.335994	−	0.0130302i
$613$	6.15701	+	6.15701i	0.248679	+	0.248679i	0.820429	−	0.571749i	$-0.193735\pi$
$613$	6.15701	+	6.15701i	0.248679	+	0.248679i	−0.571749	+	0.820429i	$0.693735\pi$
$614$	−8.49513	+	21.6886i	−0.342836	+	0.875283i
$615$	11.1215	+	16.4998i	0.448463	+	0.665337i
$616$		0			0
$617$	21.0055	−	21.0055i	0.845648	−	0.845648i	−0.143938	−	0.989587i	$-0.545977\pi$
$617$	21.0055	−	21.0055i	0.845648	−	0.845648i	0.989587	+	0.143938i	$0.0459767\pi$
$618$	5.98764	−	2.61724i	0.240858	−	0.105281i
$619$	14.0231			0.563634			0.281817	−	0.959468i	$-0.409063\pi$
$619$	14.0231			0.563634			0.281817	+	0.959468i	$0.409063\pi$
$620$	−13.0114	+	9.52372i	−0.522550	+	0.382482i
$621$	−31.8977			−1.28001
$622$	−39.1128	+	17.0965i	−1.56828	+	0.685505i
$623$		0			0
$624$	1.99127	+	25.6346i	0.0797144	+	1.02620i
$625$	17.9610	+	17.3897i	0.718440	+	0.695588i
$626$	11.3793	−	29.0522i	0.454809	−	1.16116i
$627$	5.94607	+	5.94607i	0.237463	+	0.237463i
$628$	0.673400	+	17.3641i	0.0268716	+	0.692905i
$629$		−	11.3883i		−	0.454080i
$630$		0			0
$631$			25.9447i			1.03284i	0.856334	+	0.516422i	$0.172736\pi$
$631$			25.9447i			1.03284i	−0.856334	+	0.516422i	$0.827264\pi$
$632$	−21.5363	−	7.48653i	−0.856667	−	0.297798i
$633$	−21.3629	−	21.3629i	−0.849099	−	0.849099i
$634$	−1.90869	−	0.747606i	−0.0758038	−	0.0296912i
$635$	−35.0936	+	23.6544i	−1.39265	+	0.938697i
$636$	−3.89803	+	4.21257i	−0.154567	+	0.167039i
$637$		0			0
$638$	4.31676	+	9.87576i	0.170902	+	0.390985i
$639$	−14.1141			−0.558343
$640$	−22.7869	−	10.9889i	−0.900733	−	0.434374i
$641$	5.01605			0.198122			0.0990610	−	0.995081i	$-0.468416\pi$
$641$	5.01605			0.198122			0.0990610	+	0.995081i	$0.468416\pi$
$642$	6.61476	+	15.1331i	0.261064	+	0.597255i
$643$	−5.68565	+	5.68565i	−0.224220	+	0.224220i	−0.810273	−	0.586053i	$-0.800681\pi$
$643$	−5.68565	+	5.68565i	−0.224220	+	0.224220i	0.586053	+	0.810273i	$0.300681\pi$
$644$		0			0
$645$	−26.5397	−	5.16771i	−1.04500	−	0.203478i
$646$	−7.89865	−	3.09379i	−0.310768	−	0.121723i
$647$	13.7954	+	13.7954i	0.542352	+	0.542352i	0.924218	−	0.381865i	$-0.124718\pi$
$647$	13.7954	+	13.7954i	0.542352	+	0.542352i	−0.381865	+	0.924218i	$0.624718\pi$
$648$	−1.95682	−	0.680239i	−0.0768713	−	0.0267223i
$649$		−	6.24741i		−	0.245232i
$650$	−27.8694	+	29.4437i	−1.09313	+	1.15488i
$651$		0			0
$652$	0.0835344	+	2.15400i	0.00327146	+	0.0843572i
$653$	−18.9938	−	18.9938i	−0.743283	−	0.743283i	0.229925	−	0.973208i	$-0.426152\pi$
$653$	−18.9938	−	18.9938i	−0.743283	−	0.743283i	−0.973208	+	0.229925i	$0.926152\pi$
$654$	5.93453	−	15.1513i	0.232058	−	0.592461i
$655$	−33.7048	−	6.56287i	−1.31696	−	0.256432i
$656$	−2.45883	−	31.6537i	−0.0960011	−	1.23587i
$657$	12.0195	−	12.0195i	0.468926	−	0.468926i
$658$		0			0
$659$	−2.47864			−0.0965543			−0.0482771	−	0.998834i	$-0.515373\pi$
$659$	−2.47864			−0.0965543			−0.0482771	+	0.998834i	$0.515373\pi$
$660$	2.28798	−	14.7834i	0.0890594	−	0.575445i
$661$	−12.0854			−0.470068			−0.235034	−	0.971987i	$-0.575520\pi$
$661$	−12.0854			−0.470068			−0.235034	+	0.971987i	$0.575520\pi$
$662$	−36.7706	+	16.0727i	−1.42913	+	0.624682i
$663$	10.8454	−	10.8454i	0.421199	−	0.421199i
$664$	21.5944	−	10.4537i	0.838025	−	0.405682i
$665$		0			0
$666$	4.29088	−	10.9549i	0.166268	−	0.424494i
$667$	10.8345	+	10.8345i	0.419512	+	0.419512i
$668$	6.16508	−	0.239088i	0.238534	−	0.00925060i
$669$		−	3.52973i		−	0.136467i
$670$	−8.30597	−	5.27277i	−0.320887	−	0.203705i
$671$			5.67177i			0.218956i
$672$		0			0
$673$	34.0874	+	34.0874i	1.31397	+	1.31397i	0.918461	+	0.395511i	$0.129432\pi$
$673$	34.0874	+	34.0874i	1.31397	+	1.31397i	0.395511	+	0.918461i	$0.370568\pi$
$674$	−21.9427	−	8.59464i	−0.845201	−	0.331053i
$675$	−10.3729	−	24.4810i	−0.399253	−	0.942275i
$676$	−29.1723	−	26.9941i	−1.12201	−	1.03823i
$677$	23.9032	−	23.9032i	0.918675	−	0.918675i	−0.0782577	−	0.996933i	$-0.524936\pi$
$677$	23.9032	−	23.9032i	0.918675	−	0.918675i	0.996933	+	0.0782577i	$0.0249357\pi$
$678$	6.60567	+	15.1123i	0.253689	+	0.580384i
$679$		0			0
$680$	3.85817	+	14.5894i	0.147954	+	0.559479i
$681$	9.04247			0.346508
$682$	6.09327	+	13.9400i	0.233323	+	0.533791i
$683$	5.29866	−	5.29866i	0.202747	−	0.202747i	−0.598429	−	0.801176i	$-0.704208\pi$
$683$	5.29866	−	5.29866i	0.202747	−	0.202747i	0.801176	+	0.598429i	$0.204208\pi$
$684$	−6.43241	−	5.95212i	−0.245949	−	0.227585i
$685$	5.88904	+	8.73696i	0.225009	+	0.333822i
$686$		0			0
$687$	1.92874	+	1.92874i	0.0735862	+	0.0735862i
$688$	32.7768	+	28.0517i	1.24960	+	1.06946i
$689$		−	14.6757i		−	0.559098i
$690$	−4.63625	−	20.7552i	−0.176499	−	0.790136i
$691$			19.0813i			0.725888i	0.931811	+	0.362944i	$0.118228\pi$
$691$			19.0813i			0.725888i	−0.931811	+	0.362944i	$0.881772\pi$
$692$	47.1437	−	1.82828i	1.79213	−	0.0695009i
$693$		0			0
$694$	8.23405	−	21.0221i	0.312560	−	0.797987i
$695$	−4.40470	+	22.6212i	−0.167080	+	0.858070i
$696$	3.52928	+	7.29050i	0.133777	+	0.276346i
$697$	−13.3919	+	13.3919i	−0.507255	+	0.507255i
$698$	9.75314	−	4.26316i	0.369162	−	0.161363i
$699$	11.7363			0.443909
$700$		0			0
$701$	−30.0384			−1.13454			−0.567268	−	0.823533i	$-0.692000\pi$
$701$	−30.0384			−1.13454			−0.567268	+	0.823533i	$0.692000\pi$
$702$	39.5076	−	17.2690i	1.49112	−	0.651776i
$703$	−8.48399	+	8.48399i	−0.319980	+	0.319980i
$704$	−14.8058	+	18.7223i	−0.558014	+	0.705622i
$705$	−1.41803	+	7.28256i	−0.0534061	+	0.274277i
$706$	2.89170	−	7.38272i	0.108831	−	0.277852i
$707$		0			0
$708$	−0.181941	−	4.69150i	−0.00683777	−	0.176317i
$709$			27.3678i			1.02782i	0.857845	+	0.513909i	$0.171803\pi$
$709$			27.3678i			1.02782i	−0.857845	+	0.513909i	$0.828197\pi$
$710$	−5.58216	−	24.9897i	−0.209495	−	0.937848i
$711$			14.0512i			0.526962i
$712$	1.90874	−	5.49083i	0.0715332	−	0.205777i
$713$	15.2933	+	15.2933i	0.572737	+	0.572737i
$714$		0			0
$715$	21.3797	+	31.7189i	0.799557	+	1.18622i
$716$	−9.59414	+	10.3683i	−0.358550	+	0.387482i
$717$	−10.2305	+	10.2305i	−0.382065	+	0.382065i
$718$	20.6337	+	47.2051i	0.770041	+	1.76168i
$719$	−43.5045			−1.62245			−0.811223	−	0.584737i	$-0.801198\pi$
$719$	−43.5045			−1.62245			−0.811223	+	0.584737i	$0.801198\pi$
$720$	−1.78566	+	15.4880i	−0.0665475	+	0.577202i
$721$		0			0
$722$	−7.18238	−	16.4317i	−0.267300	−	0.611523i
$723$	−2.15146	+	2.15146i	−0.0800135	+	0.0800135i
$724$	−3.22497	+	3.48520i	−0.119855	+	0.129526i
$725$	−4.79200	+	11.8386i	−0.177970	+	0.439673i
$726$	3.09715	+	1.21311i	0.114946	+	0.0450227i
$727$	−14.9542	−	14.9542i	−0.554620	−	0.554620i	0.373151	−	0.927771i	$-0.378277\pi$
$727$	−14.9542	−	14.9542i	−0.554620	−	0.554620i	−0.927771	+	0.373151i	$0.878277\pi$
$728$		0			0
$729$			19.1618i			0.709695i
$730$	26.0350	+	16.5275i	0.963600	+	0.611710i
$731$		−	25.7350i		−	0.951845i
$732$	0.165177	+	4.25922i	0.00610512	+	0.157425i
$733$	22.4679	+	22.4679i	0.829871	+	0.829871i	0.987499	−	0.157627i	$-0.0503845\pi$
$733$	22.4679	+	22.4679i	0.829871	+	0.829871i	−0.157627	+	0.987499i	$0.550384\pi$
$734$	16.8636	−	43.0539i	0.622446	−	1.58915i
$735$		0			0
$736$	−9.89144	+	32.4592i	−0.364603	+	1.19646i
$737$	−6.56371	+	6.56371i	−0.241777	+	0.241777i
$738$	−17.9281	+	7.83651i	−0.659944	+	0.288466i
$739$	0.990905			0.0364510			0.0182255	−	0.999834i	$-0.494198\pi$
$739$	0.990905			0.0364510			0.0182255	+	0.999834i	$0.494198\pi$
$740$	21.0934	+	3.26454i	0.775407	+	0.120007i
$741$	−16.1591			−0.593619
$742$		0			0
$743$	9.00016	−	9.00016i	0.330184	−	0.330184i	−0.522472	−	0.852656i	$-0.674990\pi$
$743$	9.00016	−	9.00016i	0.330184	−	0.330184i	0.852656	+	0.522472i	$0.174990\pi$
$744$	4.98172	+	10.2908i	0.182639	+	0.377280i
$745$	21.2295	+	4.13373i	0.777790	+	0.151448i
$746$	13.4888	−	34.4378i	0.493860	−	1.26086i
$747$	−10.4548	−	10.4548i	−0.382521	−	0.382521i
$748$	14.2278	−	0.551767i	0.520218	−	0.0201746i
$749$		0			0
$750$	14.4216	−	10.3077i	0.526603	−	0.376383i
$751$			13.0803i			0.477307i	0.971105	+	0.238653i	$0.0767060\pi$
$751$			13.0803i			0.477307i	−0.971105	+	0.238653i	$0.923294\pi$
$752$	7.69743	−	8.99401i	0.280697	−	0.327978i
$753$	−2.50002	−	2.50002i	−0.0911058	−	0.0911058i
$754$	−19.2848	−	7.55360i	−0.702313	−	0.275086i
$755$	−2.42271	−	0.471740i	−0.0881713	−	0.0171684i
$756$		0			0
$757$	3.92981	−	3.92981i	0.142831	−	0.142831i	−0.632076	−	0.774907i	$-0.717797\pi$
$757$	3.92981	−	3.92981i	0.142831	−	0.142831i	0.774907	+	0.632076i	$0.217797\pi$
$758$	11.5418	+	26.4049i	0.419216	+	0.959070i
$759$	−20.0653			−0.728325
$760$	7.99453	−	13.7430i	0.289992	−	0.498512i
$761$	22.3234			0.809223			0.404612	−	0.914489i	$-0.367407\pi$
$761$	22.3234			0.809223			0.404612	+	0.914489i	$0.367407\pi$
$762$	12.0189	+	27.4964i	0.435397	+	0.996091i
$763$		0			0
$764$	9.27134	+	8.57908i	0.335425	+	0.310380i
$765$	7.71182	−	5.19806i	0.278822	−	0.187936i
$766$	33.6227	+	13.1695i	1.21484	+	0.475834i
$767$	8.48900	+	8.48900i	0.306520	+	0.306520i
$768$	−10.5732	+	14.4907i	−0.381527	+	0.522888i
$769$		−	27.9731i		−	1.00873i	−0.863489	−	0.504367i	$-0.831726\pi$
$769$		−	27.9731i		−	1.00873i	0.863489	−	0.504367i	$-0.168274\pi$
$770$		0			0
$771$			18.4608i			0.664851i
$772$	−42.2121	+	1.63703i	−1.51925	+	0.0589179i
$773$	31.4887	+	31.4887i	1.13257	+	1.13257i	0.989748	+	0.142823i	$0.0456180\pi$
$773$	31.4887	+	31.4887i	1.13257	+	1.13257i	0.142823	+	0.989748i	$0.454382\pi$
$774$	9.69648	−	24.7558i	0.348533	−	0.889828i
$775$	−6.76410	+	16.7106i	−0.242974	+	0.600262i
$776$	23.8759	−	11.5582i	0.857094	−	0.414914i
$777$		0			0
$778$	23.3886	−	10.2233i	0.838523	−	0.366524i
$779$	19.9533			0.714902
$780$	16.9789	+	23.1967i	0.607941	+	0.830575i
$781$	−24.1591			−0.864482
$782$	18.5473	−	8.10713i	0.663249	−	0.289910i
$783$	9.60453	−	9.60453i	0.343238	−	0.343238i
$784$		0			0
$785$	10.8590	+	16.1103i	0.387573	+	0.575001i
$786$	−8.87976	+	22.6706i	−0.316731	+	0.808635i
$787$	−28.6159	−	28.6159i	−1.02005	−	1.02005i	−0.999795	−	0.0202524i	$-0.993553\pi$
$787$	−28.6159	−	28.6159i	−1.02005	−	1.02005i	−0.0202524	−	0.999795i	$-0.506447\pi$
$788$	−0.111092	−	2.86458i	−0.00395747	−	0.102047i
$789$		−	32.7248i		−	1.16504i
$790$	−24.8785	+	5.55731i	−0.885137	+	0.197720i
$791$		0			0
$792$	13.8943	+	4.82998i	0.493711	+	0.171626i
$793$	−7.70682	−	7.70682i	−0.273677	−	0.273677i
$794$	−39.6186	−	15.5180i	−1.40601	−	0.550714i
$795$	−1.22642	+	6.29852i	−0.0434967	+	0.223385i
$796$	−12.9244	+	13.9672i	−0.458092	+	0.495056i
$797$	−3.10654	+	3.10654i	−0.110039	+	0.110039i	−0.759983	−	0.649943i	$-0.774793\pi$
$797$	−3.10654	+	3.10654i	−0.110039	+	0.110039i	0.649943	+	0.759983i	$0.274793\pi$
$798$		0			0
$799$	−7.06174			−0.249826
$800$	−28.1285	+	2.96394i	−0.994494	+	0.104791i
$801$	−3.58246			−0.126580
$802$	2.77294	+	6.34387i	0.0979161	+	0.224010i
$803$	20.5739	−	20.5739i	0.726038	−	0.726038i
$804$	−4.73787	+	5.12018i	−0.167092	+	0.180575i
$805$		0			0
$806$	−27.2213	−	10.6622i	−0.958830	−	0.375560i
$807$	−4.84430	−	4.84430i	−0.170528	−	0.170528i
$808$	−19.9448	−	6.93330i	−0.701656	−	0.243912i
$809$			30.6474i			1.07751i	0.842464	+	0.538753i	$0.181104\pi$
$809$			30.6474i			1.07751i	−0.842464	+	0.538753i	$0.818896\pi$
$810$	−2.26051	+	0.504948i	−0.0794261	+	0.0177420i
$811$			47.0428i			1.65190i	0.563747	+	0.825948i	$0.309359\pi$
$811$			47.0428i			1.65190i	−0.563747	+	0.825948i	$0.690641\pi$
$812$		0			0
$813$	17.4565	+	17.4565i	0.612225	+	0.612225i
$814$	7.34473	−	18.7516i	0.257433	−	0.657243i
$815$	1.34704	+	1.99846i	0.0471847	+	0.0700031i
$816$	10.6683	−	0.828701i	0.373465	−	0.0290103i
$817$	−19.1720	+	19.1720i	−0.670744	+	0.670744i
$818$	43.4672	−	18.9998i	1.51979	−	0.664312i
$819$		0			0
$820$	−20.9656	−	28.6434i	−0.732152	−	1.00027i
$821$	−0.830802			−0.0289952			−0.0144976	−	0.999895i	$-0.504615\pi$
$821$	−0.830802			−0.0289952			−0.0144976	+	0.999895i	$0.504615\pi$
$822$	6.84555	−	2.99223i	0.238766	−	0.104366i
$823$	0.163598	−	0.163598i	0.00570267	−	0.00570267i	−0.704250	−	0.709952i	$-0.748716\pi$
$823$	0.163598	−	0.163598i	0.00570267	−	0.00570267i	0.709952	+	0.704250i	$0.248716\pi$
$824$	−10.4925	+	5.07936i	−0.365525	+	0.176948i
$825$	−6.52508	−	15.3998i	−0.227174	−	0.536153i
$826$		0			0
$827$	0.00150949	+	0.00150949i	5.24902e−5	+	5.24902e-5i	0.707133	−	0.707081i	$-0.249988\pi$
$827$	0.00150949	+	0.00150949i	5.24902e−5	+	5.24902e-5i	−0.707081	+	0.707133i	$0.749988\pi$
$828$	20.8961	−	0.810374i	0.726191	−	0.0281624i
$829$			42.5293i			1.47710i	0.674197	+	0.738551i	$0.264490\pi$
$829$			42.5293i			1.47710i	−0.674197	+	0.738551i	$0.735510\pi$
$830$	14.3759	−	22.6458i	0.498995	−	0.786046i
$831$			18.4497i			0.640012i
$832$	−5.32172	−	45.5580i	−0.184497	−	1.57944i
$833$		0			0
$834$	15.2155	+	5.95970i	0.526870	+	0.206368i
$835$	5.71991	−	3.85543i	0.197946	−	0.133423i
$836$	−11.0104	−	10.1883i	−0.380803	−	0.352370i
$837$	13.5572	−	13.5572i	0.468604	−	0.468604i
$838$	−20.6025	−	47.1339i	−0.711702	−	1.62821i
$839$	−49.4733			−1.70801			−0.854004	−	0.520267i	$-0.825832\pi$
$839$	−49.4733			−1.70801			−0.854004	+	0.520267i	$0.825832\pi$
$840$		0			0
$841$	22.4754			0.775014
$842$	−18.8318	−	43.0829i	−0.648986	−	1.48473i
$843$	5.38498	−	5.38498i	0.185469	−	0.185469i
$844$	39.5579	+	36.6043i	1.36164	+	1.25997i
$845$	−43.6176	−	8.49304i	−1.50049	−	0.292170i
$846$	−6.79303	−	2.66073i	−0.233549	−	0.0914778i
$847$		0			0
$848$	6.65734	−	7.77872i	0.228614	−	0.267122i
$849$			14.6249i			0.501925i
$850$	12.2535	+	11.5984i	0.420292	+	0.397821i
$851$		−	28.6297i		−	0.981412i
$852$	−18.1423	+	0.703579i	−0.621546	+	0.0241042i
$853$	−9.16674	−	9.16674i	−0.313863	−	0.313863i	0.532541	−	0.846404i	$-0.321237\pi$
$853$	−9.16674	−	9.16674i	−0.313863	−	0.313863i	−0.846404	+	0.532541i	$0.821237\pi$
$854$		0			0
$855$	−9.61757	−	1.87269i	−0.328914	−	0.0640448i
$856$	−12.8375	−	26.5187i	−0.438777	−	0.906389i
$857$	−15.8929	+	15.8929i	−0.542890	+	0.542890i	−0.924375	−	0.381485i	$-0.875413\pi$
$857$	−15.8929	+	15.8929i	−0.542890	+	0.542890i	0.381485	+	0.924375i	$0.375413\pi$
$858$	24.8523	−	10.8631i	0.848443	−	0.370860i
$859$	8.11716			0.276954			0.138477	−	0.990366i	$-0.455779\pi$
$859$	8.11716			0.276954			0.138477	+	0.990366i	$0.455779\pi$
$860$	47.6665	+	7.37717i	1.62541	+	0.251559i
$861$		0			0
$862$	−40.3191	+	17.6237i	−1.37328	+	0.600267i
$863$	−0.344094	+	0.344094i	−0.0117131	+	0.0117131i	−0.712939	−	0.701226i	$-0.752636\pi$
$863$	−0.344094	+	0.344094i	−0.0117131	+	0.0117131i	0.701226	+	0.712939i	$0.252636\pi$
$864$	28.7744	+	8.76857i	0.978926	+	0.298313i
$865$	43.7395	−	29.4821i	1.48719	−	1.00242i
$866$	5.21242	−	13.3077i	0.177125	−	0.452213i
$867$	8.96335	+	8.96335i	0.304411	+	0.304411i
$868$		0			0
$869$			24.0516i			0.815895i
$870$	7.64545	+	4.85347i	0.259205	+	0.164548i
$871$		−	17.8376i		−	0.604403i
$872$	−9.53137	+	27.4186i	−0.322773	+	0.928511i
$873$	−11.5594	−	11.5594i	−0.391226	−	0.391226i
$874$	−19.8569	−	7.77766i	−0.671670	−	0.263083i
$875$		0			0
$876$	14.8508	−	16.0492i	0.501763	−	0.542251i
$877$	12.6409	−	12.6409i	0.426854	−	0.426854i	−0.460701	−	0.887555i	$-0.652402\pi$
$877$	12.6409	−	12.6409i	0.426854	−	0.426854i	0.887555	+	0.460701i	$0.152402\pi$
$878$	0.315567	+	0.721946i	0.0106499	+	0.0243645i
$879$	2.04276			0.0689007
$880$	−3.05652	+	26.5109i	−0.103035	+	0.893681i
$881$	5.27459			0.177705			0.0888527	−	0.996045i	$-0.471680\pi$
$881$	5.27459			0.177705			0.0888527	+	0.996045i	$0.471680\pi$
$882$		0			0
$883$	−5.20270	+	5.20270i	−0.175085	+	0.175085i	−0.789209	−	0.614124i	$-0.789509\pi$
$883$	−5.20270	+	5.20270i	−0.175085	+	0.175085i	0.614124	+	0.789209i	$0.289509\pi$
$884$	−18.5830	+	20.0825i	−0.625013	+	0.675447i
$885$	−2.93391	−	4.35273i	−0.0986222	−	0.146315i
$886$	32.1166	+	12.5796i	1.07898	+	0.422620i
$887$	31.6135	+	31.6135i	1.06148	+	1.06148i	0.997982	+	0.0634967i	$0.0202252\pi$
$887$	31.6135	+	31.6135i	1.06148	+	1.06148i	0.0634967	+	0.997982i	$0.479775\pi$
$888$	4.96944	−	14.2954i	0.166764	−	0.479724i
$889$		0			0
$890$	−1.41688	−	6.34295i	−0.0474938	−	0.212616i
$891$			2.18537i			0.0732127i
$892$	0.244012	+	6.29204i	0.00817012	+	0.210673i
$893$	5.26083	+	5.26083i	0.176047	+	0.176047i
$894$	5.59307	−	14.2795i	0.187060	−	0.477577i
$895$	−3.01857	+	15.5024i	−0.100900	+	0.518189i
$896$		0			0
$897$	27.2648	−	27.2648i	0.910346	−	0.910346i
$898$	11.2017	−	4.89633i	0.373805	−	0.163393i
$899$	−9.20972			−0.307161
$900$	7.41720	+	15.7739i	0.247240	+	0.525798i
$901$	−6.10754			−0.203472
$902$	−30.6877	+	13.4138i	−1.02179	+	0.446631i
$903$		0			0
$904$	−12.8199	−	26.4822i	−0.426382	−	0.880785i
$905$	−1.01466	+	5.21098i	−0.0337285	+	0.173219i
$906$	−0.638278	+	1.62957i	−0.0212054	+	0.0541388i
$907$	−6.91939	−	6.91939i	−0.229755	−	0.229755i	0.582836	−	0.812590i	$-0.301943\pi$
$907$	−6.91939	−	6.91939i	−0.229755	−	0.229755i	−0.812590	+	0.582836i	$0.801943\pi$
$908$	−16.1189	+	0.625110i	−0.534926	+	0.0207450i
$909$			13.0129i			0.431610i
$910$		0			0
$911$			5.81294i			0.192591i	0.995353	+	0.0962957i	$0.0306994\pi$
$911$			5.81294i			0.192591i	−0.995353	+	0.0962957i	$0.969301\pi$
$912$	−8.56499	−	7.33026i	−0.283615	−	0.242729i
$913$	−17.8956	−	17.8956i	−0.592257	−	0.592257i
$914$	3.59944	+	1.40985i	0.119059	+	0.0466337i
$915$	2.66358	+	3.95167i	0.0880551	+	0.130638i
$916$	−3.57148	−	3.30481i	−0.118005	−	0.109194i
$917$		0			0
$918$	−7.18681	−	16.4418i	−0.237200	−	0.542660i
$919$	−21.3375			−0.703861			−0.351930	−	0.936026i	$-0.614475\pi$
$919$	−21.3375			−0.703861			−0.351930	+	0.936026i	$0.614475\pi$
$920$	9.69931	+	36.6773i	0.319777	+	1.20921i
$921$	18.4657			0.608465
$922$	−21.8628	−	50.0172i	−0.720014	−	1.64723i
$923$	32.8275	−	32.8275i	1.08053	−	1.08053i
$924$		0			0
$925$	21.9728	−	9.31014i	0.722462	−	0.306115i
$926$	−25.1505	−	9.85108i	−0.826496	−	0.323727i
$927$	5.07990	+	5.07990i	0.166846	+	0.166846i
$928$	−6.79523	−	12.7519i	−0.223064	−	0.418603i
$929$			14.5405i			0.477059i	0.971135	+	0.238529i	$0.0766653\pi$
$929$			14.5405i			0.477059i	−0.971135	+	0.238529i	$0.923335\pi$
$930$	10.7919	+	6.85086i	0.353879	+	0.224649i
$931$		0			0
$932$	−20.9210	+	0.811338i	−0.685290	+	0.0265763i
$933$	23.9282	+	23.9282i	0.783375	+	0.783375i
$934$	6.89224	−	17.5964i	0.225521	−	0.575771i
$935$	13.2004	−	8.89756i	0.431699	−	0.290981i
$936$	−25.4426	+	12.3166i	−0.831616	+	0.402580i
$937$	−5.05360	+	5.05360i	−0.165094	+	0.165094i	−0.784819	−	0.619725i	$-0.787244\pi$
$937$	−5.05360	+	5.05360i	−0.165094	+	0.165094i	0.619725	+	0.784819i	$0.287244\pi$
$938$		0			0
$939$	−24.7350			−0.807195
$940$	2.02431	−	13.0798i	0.0660256	−	0.426615i
$941$	2.89484			0.0943690			0.0471845	−	0.998886i	$-0.484975\pi$
$941$	2.89484			0.0943690			0.0471845	+	0.998886i	$0.484975\pi$
$942$	12.6227	−	5.51746i	0.411270	−	0.179768i
$943$	−33.6668	+	33.6668i	−1.09634	+	1.09634i
$944$	0.648650	+	8.35040i	0.0211118	+	0.271782i
$945$		0			0
$946$	16.5975	−	42.3746i	0.539632	−	1.37772i
$947$	23.8463	+	23.8463i	0.774902	+	0.774902i	0.978959	−	0.204057i	$-0.0654128\pi$
$947$	23.8463	+	23.8463i	0.774902	+	0.774902i	−0.204057	+	0.978959i	$0.565413\pi$
$948$	0.700447	+	18.0616i	0.0227495	+	0.586613i
$949$			55.9118i			1.81497i
$950$	−0.488072	−	17.7691i	−0.0158352	−	0.576506i
$951$			1.62505i			0.0526960i
$952$		0			0
$953$	23.9098	+	23.9098i	0.774513	+	0.774513i	0.978892	−	0.204379i	$-0.0655173\pi$
$953$	23.9098	+	23.9098i	0.774513	+	0.774513i	−0.204379	+	0.978892i	$0.565517\pi$
$954$	−5.87514	−	2.30121i	−0.190215	−	0.0745043i
$955$	13.8623	+	2.69920i	0.448572	+	0.0873442i
$956$	17.5295	−	18.9439i	0.566943	−	0.612691i
$957$	6.04174	−	6.04174i	0.195302	−	0.195302i
$958$	4.43650	+	10.1497i	0.143337	+	0.327922i
$959$		0			0
$960$	−1.52323	+	19.9974i	−0.0491621	+	0.645413i
$961$	18.0001			0.580649
$962$	15.4997	+	35.4598i	0.499730	+	1.14327i
$963$	−12.8389	+	12.8389i	−0.413727	+	0.413727i
$964$	3.68641	−	3.98388i	0.118731	−	0.128312i
$965$	−39.1640	+	26.3980i	−1.26073	+	0.849782i
$966$		0			0
$967$	2.13618	+	2.13618i	0.0686949	+	0.0686949i	0.740620	−	0.671925i	$-0.234532\pi$
$967$	2.13618	+	2.13618i	0.0686949	+	0.0686949i	−0.671925	+	0.740620i	$0.734532\pi$
$968$	−5.60478	−	1.94836i	−0.180144	−	0.0626225i
$969$			6.72489i			0.216035i
$970$	15.8948	−	25.0383i	0.510350	−	0.803932i
$971$			16.5693i			0.531734i	0.964010	+	0.265867i	$0.0856582\pi$
$971$			16.5693i			0.531734i	−0.964010	+	0.265867i	$0.914342\pi$
$972$	−1.17276	−	30.2404i	−0.0376162	−	0.969963i
$973$		0			0
$974$	1.25836	−	3.21269i	0.0403206	−	0.102941i
$975$	29.7916	+	12.0590i	0.954096	+	0.386198i
$976$	−0.588883	−	7.58099i	−0.0188497	−	0.242662i
$977$	−0.221322	+	0.221322i	−0.00708071	+	0.00708071i	−0.710638	−	0.703558i	$-0.751594\pi$
$977$	−0.221322	+	0.221322i	−0.00708071	+	0.00708071i	0.703558	+	0.710638i	$0.251594\pi$
$978$	1.56583	−	0.684433i	0.0500697	−	0.0218858i
$979$	−6.13213			−0.195984
$980$		0			0
$981$	17.8891			0.571156
$982$	43.4370	−	18.9866i	1.38613	−	0.605886i
$983$	40.8154	−	40.8154i	1.30181	−	1.30181i	0.374636	−	0.927172i	$-0.377768\pi$
$983$	40.8154	−	40.8154i	1.30181	−	1.30181i	0.927172	−	0.374636i	$-0.122232\pi$
$984$	−22.6544	+	10.9668i	−0.722195	+	0.349610i
$985$	−1.79141	−	2.65774i	−0.0570792	−	0.0846825i
$986$	−3.14357	+	8.02574i	−0.100112	+	0.255592i
$987$		0			0
$988$	28.8049	−	1.11708i	0.916405	−	0.0355391i
$989$		−	64.6969i		−	2.05724i
$990$	16.0505	−	3.58534i	0.510119	−	0.113949i
$991$			21.9695i			0.697885i	0.937144	+	0.348942i	$0.113459\pi$
$991$			21.9695i			0.697885i	−0.937144	+	0.348942i	$0.886541\pi$
$992$	−9.59174	−	17.9999i	−0.304538	−	0.571496i
$993$	22.4953	+	22.4953i	0.713868	+	0.713868i
$994$		0			0
$995$	−4.06634	+	20.8834i	−0.128912	+	0.662050i
$996$	−13.9599	−	12.9175i	−0.442336	−	0.409308i
$997$	5.96367	−	5.96367i	0.188871	−	0.188871i	−0.606337	−	0.795208i	$-0.707362\pi$
$997$	5.96367	−	5.96367i	0.188871	−	0.188871i	0.795208	+	0.606337i	$0.207362\pi$
$998$	−11.7205	−	26.8138i	−0.371005	−	0.848776i
$999$	−25.3796			−0.802976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.k.j.883.13		36
4.3	odd	2	inner	980.2.k.j.883.3		36
5.2	odd	4	inner	980.2.k.j.687.3		36
7.2	even	3		980.2.x.m.263.13		72
7.3	odd	6		140.2.w.b.23.2	✓	72
7.4	even	3		980.2.x.m.863.2		72
7.5	odd	6		140.2.w.b.123.13	yes	72
7.6	odd	2		980.2.k.k.883.13		36
20.7	even	4	inner	980.2.k.j.687.13		36
28.3	even	6		140.2.w.b.23.14	yes	72
28.11	odd	6		980.2.x.m.863.14		72
28.19	even	6		140.2.w.b.123.10	yes	72
28.23	odd	6		980.2.x.m.263.10		72
28.27	even	2		980.2.k.k.883.3		36
35.2	odd	12		980.2.x.m.67.14		72
35.3	even	12		700.2.be.e.107.9		72
35.12	even	12		140.2.w.b.67.14	yes	72
35.17	even	12		140.2.w.b.107.10	yes	72
35.19	odd	6		700.2.be.e.543.6		72
35.24	odd	6		700.2.be.e.443.17		72
35.27	even	4		980.2.k.k.687.3		36
35.32	odd	12		980.2.x.m.667.10		72
35.33	even	12		700.2.be.e.207.5		72
140.3	odd	12		700.2.be.e.107.6		72
140.19	even	6		700.2.be.e.543.9		72
140.27	odd	4		980.2.k.k.687.13		36
140.47	odd	12		140.2.w.b.67.2	yes	72
140.59	even	6		700.2.be.e.443.5		72
140.67	even	12		980.2.x.m.667.13		72
140.87	odd	12		140.2.w.b.107.13	yes	72
140.103	odd	12		700.2.be.e.207.17		72
140.107	even	12		980.2.x.m.67.2		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.2	✓	72	7.3	odd	6
140.2.w.b.23.14	yes	72	28.3	even	6
140.2.w.b.67.2	yes	72	140.47	odd	12
140.2.w.b.67.14	yes	72	35.12	even	12
140.2.w.b.107.10	yes	72	35.17	even	12
140.2.w.b.107.13	yes	72	140.87	odd	12
140.2.w.b.123.10	yes	72	28.19	even	6
140.2.w.b.123.13	yes	72	7.5	odd	6
700.2.be.e.107.6		72	140.3	odd	12
700.2.be.e.107.9		72	35.3	even	12
700.2.be.e.207.5		72	35.33	even	12
700.2.be.e.207.17		72	140.103	odd	12
700.2.be.e.443.5		72	140.59	even	6
700.2.be.e.443.17		72	35.24	odd	6
700.2.be.e.543.6		72	35.19	odd	6
700.2.be.e.543.9		72	140.19	even	6
980.2.k.j.687.3		36	5.2	odd	4	inner
980.2.k.j.687.13		36	20.7	even	4	inner
980.2.k.j.883.3		36	4.3	odd	2	inner
980.2.k.j.883.13		36	1.1	even	1	trivial
980.2.k.k.687.3		36	35.27	even	4
980.2.k.k.687.13		36	140.27	odd	4
980.2.k.k.883.3		36	28.27	even	2
980.2.k.k.883.13		36	7.6	odd	2
980.2.x.m.67.2		72	140.107	even	12
980.2.x.m.67.14		72	35.2	odd	12
980.2.x.m.263.10		72	28.23	odd	6
980.2.x.m.263.13		72	7.2	even	3
980.2.x.m.667.10		72	35.32	odd	12
980.2.x.m.667.13		72	140.67	even	12
980.2.x.m.863.2		72	7.4	even	3
980.2.x.m.863.14		72	28.11	odd	6

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.566415 + 1.29583i) q^{2} +(0.792756 - 0.792756i) q^{3} +(-1.35835 + 1.46795i) q^{4} +(-0.427372 + 2.19485i) q^{5} +(1.47630 + 0.578247i) q^{6} +(-2.67161 - 0.928715i) q^{8} +1.74308i q^{9} +O(q^{10})\)	\(q+(0.566415 + 1.29583i) q^{2} +(0.792756 - 0.792756i) q^{3} +(-1.35835 + 1.46795i) q^{4} +(-0.427372 + 2.19485i) q^{5} +(1.47630 + 0.578247i) q^{6} +(-2.67161 - 0.928715i) q^{8} +1.74308i q^{9} +(-3.08622 + 0.689394i) q^{10} +2.98364i q^{11} +(0.0868916 + 2.24057i) q^{12} +(-4.05418 - 4.05418i) q^{13} +(1.40118 + 2.07878i) q^{15} +(-0.309783 - 3.98799i) q^{16} +(-1.68722 + 1.68722i) q^{17} +(-2.25873 + 0.987305i) q^{18} +2.51388 q^{19} +(-2.64142 - 3.60873i) q^{20} +(-3.86629 + 1.68998i) q^{22} +(-4.24161 + 4.24161i) q^{23} +(-2.85418 + 1.38169i) q^{24} +(-4.63471 - 1.87603i) q^{25} +(2.95718 - 7.54987i) q^{26} +(3.76010 + 3.76010i) q^{27} -2.55433i q^{29} +(-1.90010 + 2.99314i) q^{30} -3.60553i q^{31} +(4.99228 - 2.66028i) q^{32} +(2.36530 + 2.36530i) q^{33} +(-3.14202 - 1.23068i) q^{34} +(-2.55876 - 2.36770i) q^{36} +(-3.37486 + 3.37486i) q^{37} +(1.42390 + 3.25756i) q^{38} -6.42795 q^{39} +(3.18016 - 5.46686i) q^{40} +7.93727 q^{41} +(-7.62646 + 7.62646i) q^{43} +(-4.37985 - 4.05282i) q^{44} +(-3.82579 - 0.744942i) q^{45} +(-7.89891 - 3.09389i) q^{46} +(2.09272 + 2.09272i) q^{47} +(-3.40708 - 2.91592i) q^{48} +(-0.194151 - 7.06840i) q^{50} +2.67511i q^{51} +(11.4583 - 0.444366i) q^{52} +(1.80994 + 1.80994i) q^{53} +(-2.74267 + 7.00223i) q^{54} +(-6.54863 - 1.27512i) q^{55} +(1.99289 - 1.99289i) q^{57} +(3.30997 - 1.44681i) q^{58} -2.09389 q^{59} +(-4.95484 - 0.766842i) q^{60} +1.90096 q^{61} +(4.67216 - 2.04223i) q^{62} +(6.27498 + 4.96233i) q^{64} +(10.6309 - 7.16566i) q^{65} +(-1.72528 + 4.40476i) q^{66} +(2.19990 + 2.19990i) q^{67} +(-0.184931 - 4.76859i) q^{68} +6.72512i q^{69} +8.09721i q^{71} +(1.61882 - 4.65682i) q^{72} +(-6.89558 - 6.89558i) q^{73} +(-6.28481 - 2.46167i) q^{74} +(-5.16142 + 2.18696i) q^{75} +(-3.41472 + 3.69026i) q^{76} +(-3.64089 - 8.32952i) q^{78} +8.06116 q^{79} +(8.88541 + 1.02443i) q^{80} +0.732452 q^{81} +(4.49579 + 10.2853i) q^{82} +(-5.99790 + 5.99790i) q^{83} +(-2.98212 - 4.42426i) q^{85} +(-14.2023 - 5.56285i) q^{86} +(-2.02496 - 2.02496i) q^{87} +(2.77095 - 7.97111i) q^{88} +2.05525i q^{89} +(-1.20167 - 5.37951i) q^{90} +(-0.464910 - 11.9881i) q^{92} +(-2.85831 - 2.85831i) q^{93} +(-1.52646 + 3.89715i) q^{94} +(-1.07436 + 5.51758i) q^{95} +(1.84871 - 6.06661i) q^{96} +(-6.63160 + 6.63160i) q^{97} -5.20071 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{2} - 8 q^{5} + 8 q^{6} - 2 q^{8}+O(q^{10}) \) 36 * q - 2 * q^2 - 8 * q^5 + 8 * q^6 - 2 * q^8	\( 36 q - 2 q^{2} - 8 q^{5} + 8 q^{6} - 2 q^{8} + 2 q^{10} + 10 q^{12} + 28 q^{16} + 4 q^{17} + 20 q^{18} + 28 q^{20} - 8 q^{22} + 16 q^{25} - 4 q^{26} + 32 q^{30} + 38 q^{32} - 64 q^{33} + 8 q^{36} + 4 q^{37} + 12 q^{38} + 2 q^{40} + 20 q^{41} - 12 q^{45} + 28 q^{46} - 6 q^{48} - 14 q^{50} + 48 q^{52} + 24 q^{53} - 8 q^{57} - 30 q^{58} + 10 q^{60} - 20 q^{61} - 28 q^{62} - 4 q^{65} + 44 q^{66} - 12 q^{68} - 44 q^{72} - 12 q^{73} - 56 q^{76} + 32 q^{78} + 52 q^{80} + 52 q^{81} - 34 q^{82} + 8 q^{85} - 64 q^{86} - 16 q^{88} + 16 q^{90} + 22 q^{92} - 12 q^{93} - 48 q^{96} + 12 q^{97}+O(q^{100}) \) 36 * q - 2 * q^2 - 8 * q^5 + 8 * q^6 - 2 * q^8 + 2 * q^10 + 10 * q^12 + 28 * q^16 + 4 * q^17 + 20 * q^18 + 28 * q^20 - 8 * q^22 + 16 * q^25 - 4 * q^26 + 32 * q^30 + 38 * q^32 - 64 * q^33 + 8 * q^36 + 4 * q^37 + 12 * q^38 + 2 * q^40 + 20 * q^41 - 12 * q^45 + 28 * q^46 - 6 * q^48 - 14 * q^50 + 48 * q^52 + 24 * q^53 - 8 * q^57 - 30 * q^58 + 10 * q^60 - 20 * q^61 - 28 * q^62 - 4 * q^65 + 44 * q^66 - 12 * q^68 - 44 * q^72 - 12 * q^73 - 56 * q^76 + 32 * q^78 + 52 * q^80 + 52 * q^81 - 34 * q^82 + 8 * q^85 - 64 * q^86 - 16 * q^88 + 16 * q^90 + 22 * q^92 - 12 * q^93 - 48 * q^96 + 12 * q^97

Introduction

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