LMFDB - Embedded newform 980.2.k.k.687.13

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			687.13
Character	$\chi$	$=$	980.687
Dual form			980.2.k.k.883.13

$q$-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 $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

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

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	$-0.354907\pi$
$3$	−0.792756	−	0.792756i	−0.457698	−	0.457698i	−0.897899	+	0.440201i	$0.854907\pi$
$4$	−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	$-0.851495\pi$
$11$		−	2.98364i		−	0.899601i	0.893129	−	0.449800i	$-0.148505\pi$
$12$	−0.0868916	+	2.24057i	−0.0250834	+	0.646796i
$13$	4.05418	−	4.05418i	1.12443	−	1.12443i	0.133359	−	0.991068i	$-0.457424\pi$
$13$	4.05418	−	4.05418i	1.12443	−	1.12443i	0.991068	−	0.133359i	$-0.0425763\pi$
$14$		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	$-0.156559\pi$
$17$	1.68722	+	1.68722i	0.409211	+	0.409211i	−0.472252	+	0.881463i	$0.656559\pi$
$18$	−2.25873	−	0.987305i	−0.532388	−	0.232710i
$19$	−2.51388			−0.576723			−0.288362	−	0.957522i	$-0.593111\pi$
$19$	−2.51388			−0.576723			−0.288362	+	0.957522i	$0.593111\pi$
$20$	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	0.109545	−	0.993982i	$-0.465060\pi$
$23$	−4.24161	−	4.24161i	−0.884436	−	0.884436i	−0.993982	+	0.109545i	$0.965060\pi$
$24$	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	$0.0762177\pi$
$29$			2.55433i			0.474327i	−0.971470	+	0.237163i	$0.923782\pi$
$30$	−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	0.373006	−	0.927829i	$-0.378327\pi$
$37$	−3.37486	−	3.37486i	−0.554823	−	0.554823i	−0.927829	+	0.373006i	$0.878327\pi$
$38$	−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	$-0.712785\pi$
$41$	−7.93727			−1.23959			−0.619797	+	0.784763i	$0.712785\pi$
$42$		0			0
$43$	−7.62646	−	7.62646i	−1.16302	−	1.16302i	−0.983810	−	0.179215i	$-0.942644\pi$
$43$	−7.62646	−	7.62646i	−1.16302	−	1.16302i	−0.179215	−	0.983810i	$-0.557356\pi$
$44$	−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	$-0.819251\pi$
$47$	−2.09272	+	2.09272i	−0.305254	+	0.305254i	0.537811	+	0.843065i	$0.319251\pi$
$48$	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	−0.571787	−	0.820402i	$-0.693750\pi$
$53$	1.80994	−	1.80994i	0.248615	−	0.248615i	0.820402	+	0.571787i	$0.193750\pi$
$54$	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	$-0.456479\pi$
$59$	2.09389			0.272601			0.136301	+	0.990668i	$0.456479\pi$
$60$	−4.95484	+	0.766842i	−0.639667	+	0.0989988i
$61$	−1.90096			−0.243393			−0.121696	−	0.992567i	$-0.538833\pi$
$61$	−1.90096			−0.243393			−0.121696	+	0.992567i	$0.538833\pi$
$62$	−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	−0.559840	−	0.828601i	$-0.689137\pi$
$67$	2.19990	−	2.19990i	0.268761	−	0.268761i	0.828601	+	0.559840i	$0.189137\pi$
$68$	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	$-0.840462\pi$
$71$		−	8.09721i		−	0.960962i	0.877005	−	0.480481i	$-0.159538\pi$
$72$	1.61882	+	4.65682i	0.190780	+	0.548811i
$73$	6.89558	−	6.89558i	0.807067	−	0.807067i	−0.177122	−	0.984189i	$-0.556679\pi$
$73$	6.89558	−	6.89558i	0.807067	−	0.807067i	0.984189	+	0.177122i	$0.0566788\pi$
$74$	−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	$-0.0958646\pi$
$83$	5.99790	+	5.99790i	0.658356	+	0.658356i	−0.296635	+	0.954991i	$0.595865\pi$
$84$		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	$-0.0920425\pi$
$97$	6.63160	+	6.63160i	0.673337	+	0.673337i	−0.285147	+	0.958484i	$0.592042\pi$
$98$		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	$-0.621129\pi$
$101$	−7.46547			−0.742842			−0.371421	+	0.928465i	$0.621129\pi$
$102$	−3.46648	−	1.51522i	−0.343233	−	0.150029i
$103$	−2.91433	−	2.91433i	−0.287157	−	0.287157i	0.548798	−	0.835955i	$-0.315086\pi$
$103$	−2.91433	−	2.91433i	−0.287157	−	0.287157i	−0.835955	+	0.548798i	$0.815086\pi$
$104$	−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	−0.254904	−	0.966966i	$-0.582044\pi$
$107$	7.36564	−	7.36564i	0.712063	−	0.712063i	0.966966	+	0.254904i	$0.0820437\pi$
$108$	10.6272	+	0.412133i	1.02260	+	0.0396575i
$109$			10.2630i			0.983013i	0.870874	+	0.491507i	$0.163554\pi$
$109$			10.2630i			0.983013i	−0.870874	+	0.491507i	$0.836446\pi$
$110$	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	−0.270712	−	0.962660i	$-0.587259\pi$
$113$	7.35551	−	7.35551i	0.691948	−	0.691948i	0.962660	+	0.270712i	$0.0872592\pi$
$114$	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	0.209826	−	0.977739i	$-0.432710\pi$
$127$	13.3832	−	13.3832i	1.18756	−	1.18756i	0.977739	−	0.209826i	$-0.0672898\pi$
$128$	−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	0.834965	−	0.550302i	$-0.185488\pi$
$137$	3.33190	+	3.33190i	0.284663	+	0.284663i	−0.550302	+	0.834965i	$0.685488\pi$
$138$	8.71460	+	3.80921i	0.741836	+	0.324261i
$139$	−10.3065			−0.874185			−0.437093	−	0.899417i	$-0.643992\pi$
$139$	−10.3065			−0.874185			−0.437093	+	0.899417i	$0.643992\pi$
$140$		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	$0.129671\pi$
$149$			9.67244i			0.792398i	−0.918165	+	0.396199i	$0.870329\pi$
$150$	5.75743	−	5.44960i	0.470092	−	0.444958i
$151$		−	1.10382i		−	0.0898272i	−0.998991	−	0.0449136i	$-0.985699\pi$
$151$		−	1.10382i		−	0.0898272i	0.998991	−	0.0449136i	$-0.0143013\pi$
$152$	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	$-0.362702\pi$
$157$	−6.14377	−	6.14377i	−0.490326	−	0.490326i	−0.908409	+	0.418083i	$0.862702\pi$
$158$	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	0.736324	−	0.676629i	$-0.236560\pi$
$163$	0.762126	+	0.762126i	0.0596944	+	0.0596944i	−0.676629	+	0.736324i	$0.736560\pi$
$164$	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	$-0.711917\pi$
$167$	2.18132	−	2.18132i	0.168796	−	0.168796i	0.786450	+	0.617654i	$0.211917\pi$
$168$		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	0.321157	−	0.947026i	$-0.395928\pi$
$173$	16.6803	−	16.6803i	1.26818	−	1.26818i	0.947026	−	0.321157i	$-0.104072\pi$
$174$	−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	$-0.528123\pi$
$181$	−2.37419			−0.176472			−0.0882360	+	0.996100i	$0.528123\pi$
$182$		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	$0.0733816\pi$
$191$			6.31582i			0.456997i	−0.973544	+	0.228498i	$0.926618\pi$
$192$	−8.90843	−	1.04061i	−0.642911	−	0.0750996i
$193$	14.9354	−	14.9354i	1.07508	−	1.07508i	0.0781335	−	0.996943i	$-0.475104\pi$
$193$	14.9354	−	14.9354i	1.07508	−	1.07508i	0.996943	−	0.0781335i	$-0.0248961\pi$
$194$	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	0.670078	−	0.742290i	$-0.266260\pi$
$197$	−1.01354	−	1.01354i	−0.0722120	−	0.0722120i	−0.742290	+	0.670078i	$0.766260\pi$
$198$	−2.94576	+	6.73923i	−0.209346	+	0.478936i
$199$	−9.51476			−0.674484			−0.337242	−	0.941418i	$-0.609494\pi$
$199$	−9.51476			−0.674484			−0.337242	+	0.941418i	$0.609494\pi$
$200$	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	$0.378112\pi$
$211$			26.9476i			1.85515i	−0.373634	+	0.927576i	$0.621888\pi$
$212$	−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	$-0.283617\pi$
$223$	−2.22624	−	2.22624i	−0.149080	−	0.149080i	−0.777707	+	0.628627i	$0.783617\pi$
$224$		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	$-0.836252\pi$
$227$	−5.70319	+	5.70319i	−0.378534	+	0.378534i	0.492039	+	0.870573i	$0.336252\pi$
$228$	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	−0.421767	−	0.906704i	$-0.638590\pi$
$233$	7.40225	−	7.40225i	0.484937	−	0.484937i	0.906704	+	0.421767i	$0.138590\pi$
$234$	−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	$-0.472141\pi$
$241$	2.71390			0.174817			0.0874087	+	0.996173i	$0.472141\pi$
$242$	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	$-0.0783222\pi$
$257$	11.6435	+	11.6435i	0.726299	+	0.726299i	−0.243581	+	0.969881i	$0.578322\pi$
$258$	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	0.944659	+	0.328054i	$0.106393\pi$
$263$	20.6399	+	20.6399i	1.27271	+	1.27271i	0.328054	+	0.944659i	$0.393607\pi$
$264$	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	0.265066	−	0.964230i	$-0.414606\pi$
$277$	−11.6364	−	11.6364i	−0.699165	−	0.699165i	−0.964230	+	0.265066i	$0.914606\pi$
$278$	−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	$-0.123264\pi$
$283$	9.22409	+	9.22409i	0.548315	+	0.548315i	−0.377638	+	0.925953i	$0.623264\pi$
$284$	−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	$-0.766949\pi$
$293$	−1.28839	+	1.28839i	−0.0752688	+	0.0752688i	0.668470	+	0.743739i	$0.266949\pi$
$294$		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	$-0.905751\pi$
$307$	−11.6465	+	11.6465i	−0.664701	+	0.664701i	0.291783	+	0.956484i	$0.405751\pi$
$308$		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	$-0.535699\pi$
$313$	15.6006	−	15.6006i	0.881800	−	0.881800i	0.993717	+	0.111918i	$0.0356993\pi$
$314$	−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	0.677738	−	0.735304i	$-0.262961\pi$
$317$	−1.02494	−	1.02494i	−0.0575664	−	0.0575664i	−0.735304	+	0.677738i	$0.762961\pi$
$318$	−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	$-0.715297\pi$
$331$		−	28.3761i		−	1.55969i	0.625971	−	0.779846i	$-0.284703\pi$
$332$	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	0.309155	−	0.951012i	$-0.399954\pi$
$337$	−11.7829	−	11.7829i	−0.641857	−	0.641857i	−0.951012	+	0.309155i	$0.899954\pi$
$338$	−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	−0.941899	−	0.335896i	$-0.890961\pi$
$347$	−11.2886	+	11.2886i	−0.606002	+	0.606002i	0.335896	+	0.941899i	$0.390961\pi$
$348$	−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	$-0.702329\pi$
$353$	3.96442	−	3.96442i	0.211005	−	0.211005i	0.804694	+	0.593689i	$0.202329\pi$
$354$	−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	0.234769	−	0.972051i	$-0.424567\pi$
$367$	23.1194	−	23.1194i	1.20682	−	1.20682i	0.972051	−	0.234769i	$-0.0754335\pi$
$368$	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	−0.999133	−	0.0416212i	$-0.986748\pi$
$373$	−18.4926	+	18.4926i	−0.957512	+	0.957512i	0.0416212	+	0.999133i	$0.486748\pi$
$374$	−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	$-0.476217\pi$
$383$	−18.0549	−	18.0549i	−0.922564	−	0.922564i	−0.997210	+	0.0746461i	$0.976217\pi$
$384$	−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	$0.151278\pi$
$389$			18.0492i			0.915129i	−0.889176	+	0.457564i	$0.848722\pi$
$390$	−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	0.997532	+	0.0702120i	$0.0223676\pi$
$397$	21.2747	+	21.2747i	1.06774	+	1.06774i	0.0702120	+	0.997532i	$0.477632\pi$
$398$	−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	$-0.151761\pi$
$419$	36.3735			1.77696			0.888481	+	0.458914i	$0.151761\pi$
$420$		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	$-0.730358\pi$
$431$		−	31.1145i		−	1.49873i	0.662154	−	0.749367i	$-0.269642\pi$
$432$	−13.8304	−	16.1600i	−0.665416	−	0.777501i
$433$	7.14603	−	7.14603i	0.343416	−	0.343416i	−0.514234	−	0.857650i	$-0.671924\pi$
$433$	7.14603	−	7.14603i	0.343416	−	0.343416i	0.857650	+	0.514234i	$0.171924\pi$
$434$		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	$-0.504232\pi$
$439$	−0.557131			−0.0265904			−0.0132952	+	0.999912i	$0.504232\pi$
$440$	−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	0.986020	−	0.166629i	$-0.0532882\pi$
$443$	17.2462	+	17.2462i	0.819391	+	0.819391i	−0.166629	+	0.986020i	$0.553288\pi$
$444$	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	$0.0653870\pi$
$449$			8.64441i			0.407955i	−0.978976	+	0.203978i	$0.934613\pi$
$450$	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	0.750868	−	0.660453i	$-0.229636\pi$
$457$	1.93285	+	1.93285i	0.0904150	+	0.0904150i	−0.660453	+	0.750868i	$0.729636\pi$
$458$	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	$-0.144398\pi$
$461$	38.5986			1.79772			0.898858	+	0.438239i	$0.144398\pi$
$462$		0			0
$463$	−13.5055	−	13.5055i	−0.627652	−	0.627652i	0.319824	−	0.947477i	$-0.396376\pi$
$463$	−13.5055	−	13.5055i	−0.627652	−	0.627652i	−0.947477	+	0.319824i	$0.896376\pi$
$464$	−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	$-0.649945\pi$
$467$	9.44901	−	9.44901i	0.437248	−	0.437248i	0.891085	+	0.453837i	$0.149945\pi$
$468$	−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	$-0.557267\pi$
$479$	−7.83260			−0.357881			−0.178940	+	0.983860i	$0.557267\pi$
$480$	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	−0.745113	−	0.666938i	$-0.767605\pi$
$487$	−1.72517	+	1.72517i	−0.0781749	+	0.0781749i	0.666938	+	0.745113i	$0.267605\pi$
$488$	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	$0.273035\pi$
$491$			33.5206i			1.51276i	−0.654130	+	0.756382i	$0.726965\pi$
$492$	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	$-0.206113\pi$
$503$	4.35918	+	4.35918i	0.194366	+	0.194366i	−0.603214	+	0.797580i	$0.706113\pi$
$504$		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	$-0.434230\pi$
$521$	9.36545			0.410308			0.205154	+	0.978730i	$0.434230\pi$
$522$	2.52190	−	5.76954i	0.110381	−	0.252526i
$523$	−23.1360	−	23.1360i	−1.01167	−	1.01167i	−0.999931	−	0.0117350i	$-0.996265\pi$
$523$	−23.1360	−	23.1360i	−1.01167	−	1.01167i	−0.0117350	−	0.999931i	$-0.503735\pi$
$524$	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	−0.799461	−	0.600718i	$-0.794882\pi$
$547$	−4.64823	+	4.64823i	−0.198744	+	0.198744i	0.600718	+	0.799461i	$0.294882\pi$
$548$	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	0.868865	−	0.495049i	$-0.164850\pi$
$557$	8.82237	+	8.82237i	0.373816	+	0.373816i	−0.495049	+	0.868865i	$0.664850\pi$
$558$	−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	$-0.381036\pi$
$563$	−13.4268	−	13.4268i	−0.565873	−	0.565873i	−0.930970	+	0.365097i	$0.881036\pi$
$564$	−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	$-0.843253\pi$
$569$		−	22.5548i		−	0.945547i	0.881184	−	0.472773i	$-0.156747\pi$
$570$	4.77661	+	7.52438i	0.200070	+	0.315162i
$571$			26.3826i			1.10408i	0.833819	+	0.552038i	$0.186150\pi$
$571$			26.3826i			1.10408i	−0.833819	+	0.552038i	$0.813850\pi$
$572$	−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	$-0.481157\pi$
$577$	−22.5576	−	22.5576i	−0.939086	−	0.939086i	−0.998248	+	0.0591623i	$0.981157\pi$
$578$	−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	$-0.606942\pi$
$587$	14.8860	−	14.8860i	0.614410	−	0.614410i	0.944092	+	0.329682i	$0.106942\pi$
$588$		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	$-0.986818\pi$
$593$	−23.3225	+	23.3225i	−0.957741	+	0.957741i	0.0414014	+	0.999143i	$0.486818\pi$
$594$	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	$-0.618055\pi$
$601$	−17.7704			−0.724871			−0.362436	+	0.932009i	$0.618055\pi$
$602$		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	$-0.812773\pi$
$607$	−6.82673	+	6.82673i	−0.277088	+	0.277088i	0.554857	+	0.831946i	$0.312773\pi$
$608$	−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	−0.571749	−	0.820429i	$-0.693735\pi$
$613$	6.15701	−	6.15701i	0.248679	−	0.248679i	0.820429	+	0.571749i	$0.193735\pi$
$614$	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	0.989587	−	0.143938i	$-0.0459767\pi$
$617$	21.0055	+	21.0055i	0.845648	+	0.845648i	−0.143938	+	0.989587i	$0.545977\pi$
$618$	5.98764	+	2.61724i	0.240858	+	0.105281i
$619$	−14.0231			−0.563634			−0.281817	−	0.959468i	$-0.590937\pi$
$619$	−14.0231			−0.563634			−0.281817	+	0.959468i	$0.590937\pi$
$620$	−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	$-0.827264\pi$
$631$		−	25.9447i		−	1.03284i	0.856334	−	0.516422i	$-0.172736\pi$
$632$	−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	$-0.199319\pi$
$643$	5.68565	+	5.68565i	0.224220	+	0.224220i	−0.586053	+	0.810273i	$0.699319\pi$
$644$		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	$-0.875282\pi$
$647$	−13.7954	+	13.7954i	−0.542352	+	0.542352i	0.381865	+	0.924218i	$0.375282\pi$
$648$	−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	−0.973208	−	0.229925i	$-0.926152\pi$
$653$	−18.9938	+	18.9938i	−0.743283	+	0.743283i	0.229925	+	0.973208i	$0.426152\pi$
$654$	−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	$-0.424480\pi$
$661$	12.0854			0.470068			0.235034	+	0.971987i	$0.424480\pi$
$662$	−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	0.395511	−	0.918461i	$-0.370568\pi$
$673$	34.0874	−	34.0874i	1.31397	−	1.31397i	0.918461	−	0.395511i	$-0.129432\pi$
$674$	−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	$-0.475064\pi$
$677$	−23.9032	−	23.9032i	−0.918675	−	0.918675i	−0.996933	+	0.0782577i	$0.975064\pi$
$678$	−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	0.801176	−	0.598429i	$-0.204208\pi$
$683$	5.29866	+	5.29866i	0.202747	+	0.202747i	−0.598429	+	0.801176i	$0.704208\pi$
$684$	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	$-0.828197\pi$
$709$		−	27.3678i		−	1.02782i	0.857845	−	0.513909i	$-0.171803\pi$
$710$	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	$-0.198802\pi$
$719$	43.5045			1.62245			0.811223	+	0.584737i	$0.198802\pi$
$720$	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	$-0.621723\pi$
$727$	14.9542	−	14.9542i	0.554620	−	0.554620i	0.927771	+	0.373151i	$0.121723\pi$
$728$		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	$-0.949616\pi$
$733$	−22.4679	+	22.4679i	−0.829871	+	0.829871i	0.157627	+	0.987499i	$0.449616\pi$
$734$	−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	0.852656	−	0.522472i	$-0.174990\pi$
$743$	9.00016	+	9.00016i	0.330184	+	0.330184i	−0.522472	+	0.852656i	$0.674990\pi$
$744$	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	$-0.923294\pi$
$751$		−	13.0803i		−	0.477307i	0.971105	−	0.238653i	$-0.0767060\pi$
$752$	−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	0.774907	−	0.632076i	$-0.217797\pi$
$757$	3.92981	+	3.92981i	0.142831	+	0.142831i	−0.632076	+	0.774907i	$0.717797\pi$
$758$	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	$-0.632593\pi$
$761$	−22.3234			−0.809223			−0.404612	+	0.914489i	$0.632593\pi$
$762$	−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	−0.142823	+	0.989748i	$0.545618\pi$
$773$	−31.4887	+	31.4887i	−1.13257	+	1.13257i	−0.989748	+	0.142823i	$0.954382\pi$
$774$	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	0.0202524	−	0.999795i	$-0.493553\pi$
$787$	28.6159	−	28.6159i	1.02005	−	1.02005i	0.999795	−	0.0202524i	$-0.00644697\pi$
$788$	−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	$-0.225207\pi$
$797$	3.10654	+	3.10654i	0.110039	+	0.110039i	−0.649943	+	0.759983i	$0.725207\pi$
$798$		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	$-0.818896\pi$
$809$		−	30.6474i		−	1.07751i	0.842464	−	0.538753i	$-0.181104\pi$
$810$	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	0.709952	−	0.704250i	$-0.248716\pi$
$823$	0.163598	+	0.163598i	0.00570267	+	0.00570267i	−0.704250	+	0.709952i	$0.748716\pi$
$824$	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	−0.707081	−	0.707133i	$-0.749988\pi$
$827$	0.00150949	−	0.00150949i	5.24902e−5	−	5.24902e-5i	0.707133	+	0.707081i	$0.249988\pi$
$828$	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	$-0.174168\pi$
$839$	49.4733			1.70801			0.854004	+	0.520267i	$0.174168\pi$
$840$		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	$-0.678763\pi$
$853$	9.16674	−	9.16674i	0.313863	−	0.313863i	0.846404	+	0.532541i	$0.178763\pi$
$854$		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	$-0.124587\pi$
$857$	15.8929	+	15.8929i	0.542890	+	0.542890i	−0.381485	+	0.924375i	$0.624587\pi$
$858$	24.8523	+	10.8631i	0.848443	+	0.370860i
$859$	−8.11716			−0.276954			−0.138477	−	0.990366i	$-0.544221\pi$
$859$	−8.11716			−0.276954			−0.138477	+	0.990366i	$0.544221\pi$
$860$	−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	0.701226	−	0.712939i	$-0.252636\pi$
$863$	−0.344094	−	0.344094i	−0.0117131	−	0.0117131i	−0.712939	+	0.701226i	$0.752636\pi$
$864$	−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	0.887555	−	0.460701i	$-0.152402\pi$
$877$	12.6409	+	12.6409i	0.426854	+	0.426854i	−0.460701	+	0.887555i	$0.652402\pi$
$878$	−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	$-0.528320\pi$
$881$	−5.27459			−0.177705			−0.0888527	+	0.996045i	$0.528320\pi$
$882$		0			0
$883$	−5.20270	−	5.20270i	−0.175085	−	0.175085i	0.614124	−	0.789209i	$-0.289509\pi$
$883$	−5.20270	−	5.20270i	−0.175085	−	0.175085i	−0.789209	+	0.614124i	$0.789509\pi$
$884$	−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	−0.0634967	+	0.997982i	$0.520225\pi$
$887$	−31.6135	+	31.6135i	−1.06148	+	1.06148i	−0.997982	+	0.0634967i	$0.979775\pi$
$888$	−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	−0.812590	−	0.582836i	$-0.801943\pi$
$907$	−6.91939	+	6.91939i	−0.229755	+	0.229755i	0.582836	+	0.812590i	$0.301943\pi$
$908$	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	$-0.969301\pi$
$911$		−	5.81294i		−	0.192591i	0.995353	−	0.0962957i	$-0.0306994\pi$
$912$	−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	$-0.212756\pi$
$937$	5.05360	+	5.05360i	0.165094	+	0.165094i	−0.619725	+	0.784819i	$0.712756\pi$
$938$		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	$-0.515025\pi$
$941$	−2.89484			−0.0943690			−0.0471845	+	0.998886i	$0.515025\pi$
$942$	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	−0.204057	−	0.978959i	$-0.565413\pi$
$947$	23.8463	−	23.8463i	0.774902	−	0.774902i	0.978959	+	0.204057i	$0.0654128\pi$
$948$	−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	−0.204379	−	0.978892i	$-0.565517\pi$
$953$	23.9098	−	23.9098i	0.774513	−	0.774513i	0.978892	+	0.204379i	$0.0655173\pi$
$954$	−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	−0.671925	−	0.740620i	$-0.734532\pi$
$967$	2.13618	−	2.13618i	0.0686949	−	0.0686949i	0.740620	+	0.671925i	$0.234532\pi$
$968$	−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	0.703558	−	0.710638i	$-0.251594\pi$
$977$	−0.221322	−	0.221322i	−0.00708071	−	0.00708071i	−0.710638	+	0.703558i	$0.751594\pi$
$978$	−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	−0.927172	−	0.374636i	$-0.877768\pi$
$983$	−40.8154	−	40.8154i	−1.30181	−	1.30181i	−0.374636	−	0.927172i	$-0.622232\pi$
$984$	−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	$-0.886541\pi$
$991$		−	21.9695i		−	0.697885i	0.937144	−	0.348942i	$-0.113459\pi$
$992$	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	$-0.292638\pi$
$997$	−5.96367	−	5.96367i	−0.188871	−	0.188871i	−0.795208	+	0.606337i	$0.792638\pi$
$998$	−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.k.687.13		36
4.3	odd	2	inner	980.2.k.k.687.3		36
5.3	odd	4	inner	980.2.k.k.883.3		36
7.2	even	3		140.2.w.b.67.2	yes	72
7.3	odd	6		980.2.x.m.667.13		72
7.4	even	3		140.2.w.b.107.13	yes	72
7.5	odd	6		980.2.x.m.67.2		72
7.6	odd	2		980.2.k.j.687.13		36
20.3	even	4	inner	980.2.k.k.883.13		36
28.3	even	6		980.2.x.m.667.10		72
28.11	odd	6		140.2.w.b.107.10	yes	72
28.19	even	6		980.2.x.m.67.14		72
28.23	odd	6		140.2.w.b.67.14	yes	72
28.27	even	2		980.2.k.j.687.3		36
35.2	odd	12		700.2.be.e.543.9		72
35.3	even	12		980.2.x.m.863.14		72
35.4	even	6		700.2.be.e.107.6		72
35.9	even	6		700.2.be.e.207.17		72
35.13	even	4		980.2.k.j.883.3		36
35.18	odd	12		140.2.w.b.23.14	yes	72
35.23	odd	12		140.2.w.b.123.10	yes	72
35.32	odd	12		700.2.be.e.443.5		72
35.33	even	12		980.2.x.m.263.10		72
140.3	odd	12		980.2.x.m.863.2		72
140.23	even	12		140.2.w.b.123.13	yes	72
140.39	odd	6		700.2.be.e.107.9		72
140.67	even	12		700.2.be.e.443.17		72
140.79	odd	6		700.2.be.e.207.5		72
140.83	odd	4		980.2.k.j.883.13		36
140.103	odd	12		980.2.x.m.263.13		72
140.107	even	12		700.2.be.e.543.6		72
140.123	even	12		140.2.w.b.23.2	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.2	✓	72	140.123	even	12
140.2.w.b.23.14	yes	72	35.18	odd	12
140.2.w.b.67.2	yes	72	7.2	even	3
140.2.w.b.67.14	yes	72	28.23	odd	6
140.2.w.b.107.10	yes	72	28.11	odd	6
140.2.w.b.107.13	yes	72	7.4	even	3
140.2.w.b.123.10	yes	72	35.23	odd	12
140.2.w.b.123.13	yes	72	140.23	even	12
700.2.be.e.107.6		72	35.4	even	6
700.2.be.e.107.9		72	140.39	odd	6
700.2.be.e.207.5		72	140.79	odd	6
700.2.be.e.207.17		72	35.9	even	6
700.2.be.e.443.5		72	35.32	odd	12
700.2.be.e.443.17		72	140.67	even	12
700.2.be.e.543.6		72	140.107	even	12
700.2.be.e.543.9		72	35.2	odd	12
980.2.k.j.687.3		36	28.27	even	2
980.2.k.j.687.13		36	7.6	odd	2
980.2.k.j.883.3		36	35.13	even	4
980.2.k.j.883.13		36	140.83	odd	4
980.2.k.k.687.3		36	4.3	odd	2	inner
980.2.k.k.687.13		36	1.1	even	1	trivial
980.2.k.k.883.3		36	5.3	odd	4	inner
980.2.k.k.883.13		36	20.3	even	4	inner
980.2.x.m.67.2		72	7.5	odd	6
980.2.x.m.67.14		72	28.19	even	6
980.2.x.m.263.10		72	35.33	even	12
980.2.x.m.263.13		72	140.103	odd	12
980.2.x.m.667.10		72	28.3	even	6
980.2.x.m.667.13		72	7.3	odd	6
980.2.x.m.863.2		72	140.3	odd	12
980.2.x.m.863.14		72	35.3	even	12

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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