LMFDB - Embedded newform 980.2.x.l.667.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(67,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("980.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not 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:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			667.14
Character	$\chi$	$=$	980.667
Dual form			980.2.x.l.263.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996542 - 1.00345i) q^{2} +(0.463343 - 1.72922i) q^{3} +(-0.0138066 - 1.99995i) q^{4} +(1.91033 - 1.16218i) q^{5} +(-1.27344 - 2.18818i) q^{6} +(-2.02060 - 1.97918i) q^{8} +(-0.177443 - 0.102447i) q^{9} +O(q^{10})$	\(q+(0.996542 - 1.00345i) q^{2} +(0.463343 - 1.72922i) q^{3} +(-0.0138066 - 1.99995i) q^{4} +(1.91033 - 1.16218i) q^{5} +(-1.27344 - 2.18818i) q^{6} +(-2.02060 - 1.97918i) q^{8} +(-0.177443 - 0.102447i) q^{9} +(0.737542 - 3.07507i) q^{10} +(-1.83014 + 1.05663i) q^{11} +(-3.46476 - 0.902790i) q^{12} +(-2.86476 + 2.86476i) q^{13} +(-1.12452 - 3.84186i) q^{15} +(-3.99962 + 0.0552250i) q^{16} +(1.63626 - 6.10660i) q^{17} +(-0.279629 + 0.0759618i) q^{18} +(1.47623 - 2.55691i) q^{19} +(-2.35067 - 3.80452i) q^{20} +(-0.763541 + 2.88943i) q^{22} +(-5.38640 + 1.44328i) q^{23} +(-4.35868 + 2.57703i) q^{24} +(2.29870 - 4.44027i) q^{25} +(0.0197764 + 5.72949i) q^{26} +(3.53826 - 3.53826i) q^{27} +2.86818i q^{29} +(-4.97573 - 2.70019i) q^{30} +(5.20796 - 3.00682i) q^{31} +(-3.93037 + 4.06843i) q^{32} +(0.979169 + 3.65431i) q^{33} +(-4.49704 - 7.72739i) q^{34} +(-0.202439 + 0.356292i) q^{36} +(-5.34722 + 1.43278i) q^{37} +(-1.09459 - 4.02938i) q^{38} +(3.62644 + 6.28117i) q^{39} +(-6.16017 - 1.43259i) q^{40} +7.98984 q^{41} +(5.64967 + 5.64967i) q^{43} +(2.13849 + 3.64561i) q^{44} +(-0.458035 + 0.0105130i) q^{45} +(-3.91952 + 6.84325i) q^{46} +(1.57515 + 5.87853i) q^{47} +(-1.75770 + 6.94181i) q^{48} +(-2.16482 - 6.73153i) q^{50} +(-9.80152 - 5.65891i) q^{51} +(5.76894 + 5.68983i) q^{52} +(0.766587 + 0.205406i) q^{53} +(-0.0244258 - 7.07649i) q^{54} +(-2.26818 + 4.14546i) q^{55} +(-3.73746 - 3.73746i) q^{57} +(2.87806 + 2.85826i) q^{58} +(2.48910 + 4.31124i) q^{59} +(-7.66802 + 2.30203i) q^{60} +(0.843662 - 1.46127i) q^{61} +(2.17278 - 8.22233i) q^{62} +(0.165668 + 7.99828i) q^{64} +(-2.14328 + 8.80198i) q^{65} +(4.64268 + 2.65913i) q^{66} +(11.0122 + 2.95071i) q^{67} +(-12.2355 - 3.18813i) q^{68} +9.98301i q^{69} +0.610925i q^{71} +(0.155781 + 0.558196i) q^{72} +(-4.41548 - 1.18312i) q^{73} +(-3.89101 + 6.79348i) q^{74} +(-6.61312 - 6.03233i) q^{75} +(-5.13407 - 2.91709i) q^{76} +(9.91671 + 2.62052i) q^{78} +(7.12694 - 12.3442i) q^{79} +(-7.57640 + 4.75376i) q^{80} +(-4.78635 - 8.29020i) q^{81} +(7.96221 - 8.01737i) q^{82} +(-5.51624 - 5.51624i) q^{83} +(-3.97115 - 13.5672i) q^{85} +(11.2993 - 0.0390015i) q^{86} +(4.95971 + 1.32895i) q^{87} +(5.78927 + 1.48715i) q^{88} +(1.80030 + 1.03940i) q^{89} +(-0.445902 + 0.470090i) q^{90} +(2.96086 + 10.7526i) q^{92} +(-2.78638 - 10.3989i) q^{93} +(7.46849 + 4.27763i) q^{94} +(-0.151490 - 6.60017i) q^{95} +(5.21411 + 8.68157i) q^{96} +(1.95542 + 1.95542i) q^{97} +0.432994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 16 q^{6}+O(q^{10}) $ 72 * q + 16 * q^6	$ 72 q + 16 q^{6} - 16 q^{10} - 16 q^{12} + 8 q^{13} + 8 q^{16} - 20 q^{17} - 28 q^{18} - 40 q^{20} + 8 q^{22} + 20 q^{25} - 32 q^{26} + 4 q^{30} - 20 q^{37} - 36 q^{40} + 20 q^{45} - 16 q^{46} + 48 q^{48} + 80 q^{50} + 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} - 64 q^{61} - 80 q^{62} - 4 q^{65} + 32 q^{66} + 80 q^{68} - 80 q^{72} + 52 q^{73} - 16 q^{76} - 152 q^{78} - 20 q^{80} + 36 q^{81} + 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} + 32 q^{90} - 112 q^{92} - 32 q^{93} + 120 q^{96} - 40 q^{97}+O(q^{100}) $ 72 * q + 16 * q^6 - 16 * q^10 - 16 * q^12 + 8 * q^13 + 8 * q^16 - 20 * q^17 - 28 * q^18 - 40 * q^20 + 8 * q^22 + 20 * q^25 - 32 * q^26 + 4 * q^30 - 20 * q^37 - 36 * q^40 + 20 * q^45 - 16 * q^46 + 48 * q^48 + 80 * q^50 + 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 - 64 * q^61 - 80 * q^62 - 4 * q^65 + 32 * q^66 + 80 * q^68 - 80 * q^72 + 52 * q^73 - 16 * q^76 - 152 * q^78 - 20 * q^80 + 36 * q^81 + 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 + 32 * q^90 - 112 * q^92 - 32 * q^93 + 120 * q^96 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.996542	−	1.00345i	0.704662	−	0.709543i
$2$	0.996542	−	1.00345i	0.704662	−	0.709543i
$3$	0.463343	−	1.72922i	0.267511	−	0.998366i	−0.693184	−	0.720761i	$-0.743793\pi$
$3$	0.463343	−	1.72922i	0.267511	−	0.998366i	0.960695	−	0.277605i	$-0.0895408\pi$
$4$	−0.0138066	−	1.99995i	−0.00690329	−	0.999976i
$5$	1.91033	−	1.16218i	0.854324	−	0.519741i
$5$	1.91033	−	1.16218i	0.854324	−	0.519741i
$6$	−1.27344	−	2.18818i	−0.519879	−	0.893322i
$7$		0			0
$7$		0			0
$8$	−2.02060	−	1.97918i	−0.714391	−	0.699747i
$9$	−0.177443	−	0.102447i	−0.0591476	−	0.0341489i
$10$	0.737542	−	3.07507i	0.233231	−	0.972421i
$11$	−1.83014	+	1.05663i	−0.551809	+	0.318587i	−0.749851	−	0.661606i	$-0.769875\pi$
$11$	−1.83014	+	1.05663i	−0.551809	+	0.318587i	0.198042	+	0.980193i	$0.436542\pi$
$12$	−3.46476	−	0.902790i	−1.00019	−	0.260613i
$13$	−2.86476	+	2.86476i	−0.794542	+	0.794542i	−0.982229	−	0.187687i	$-0.939901\pi$
$13$	−2.86476	+	2.86476i	−0.794542	+	0.794542i	0.187687	+	0.982229i	$0.439901\pi$
$14$		0			0
$15$	−1.12452	−	3.84186i	−0.290350	−	0.991965i
$16$	−3.99962	+	0.0552250i	−0.999905	+	0.0138062i
$17$	1.63626	−	6.10660i	0.396851	−	1.48107i	−0.421753	−	0.906711i	$-0.638585\pi$
$17$	1.63626	−	6.10660i	0.396851	−	1.48107i	0.818604	−	0.574358i	$-0.194748\pi$
$18$	−0.279629	+	0.0759618i	−0.0659092	+	0.0179044i
$19$	1.47623	−	2.55691i	0.338671	−	0.586595i	−0.645512	−	0.763750i	$-0.723356\pi$
$19$	1.47623	−	2.55691i	0.338671	−	0.586595i	0.984183	+	0.177155i	$0.0566894\pi$
$20$	−2.35067	−	3.80452i	−0.525626	−	0.850716i
$21$		0			0
$22$	−0.763541	+	2.88943i	−0.162788	+	0.616029i
$23$	−5.38640	+	1.44328i	−1.12314	+	0.300945i	−0.772154	−	0.635435i	$-0.780821\pi$
$23$	−5.38640	+	1.44328i	−1.12314	+	0.300945i	−0.350988	+	0.936380i	$0.614154\pi$
$24$	−4.35868	+	2.57703i	−0.889711	+	0.526033i
$25$	2.29870	−	4.44027i	0.459740	−	0.888054i
$26$	0.0197764	+	5.72949i	0.00387847	+	1.12364i
$27$	3.53826	−	3.53826i	0.680939	−	0.680939i
$28$		0			0
$29$			2.86818i			0.532607i	0.963889	+	0.266303i	$0.0858023\pi$
$29$			2.86818i			0.532607i	−0.963889	+	0.266303i	$0.914198\pi$
$30$	−4.97573	−	2.70019i	−0.908441	−	0.492984i
$31$	5.20796	−	3.00682i	0.935378	−	0.540041i	0.0468695	−	0.998901i	$-0.485076\pi$
$31$	5.20796	−	3.00682i	0.935378	−	0.540041i	0.888508	+	0.458860i	$0.151742\pi$
$32$	−3.93037	+	4.06843i	−0.694799	+	0.719204i
$33$	0.979169	+	3.65431i	0.170451	+	0.636133i
$34$	−4.49704	−	7.72739i	−0.771237	−	1.32524i
$35$		0			0
$36$	−0.202439	+	0.356292i	−0.0337398	+	0.0593819i
$37$	−5.34722	+	1.43278i	−0.879078	+	0.235548i	−0.670009	−	0.742353i	$-0.733710\pi$
$37$	−5.34722	+	1.43278i	−0.879078	+	0.235548i	−0.209069	+	0.977901i	$0.567043\pi$
$38$	−1.09459	−	4.02938i	−0.177566	−	0.653652i
$39$	3.62644	+	6.28117i	0.580695	+	1.00579i
$40$	−6.16017	−	1.43259i	−0.974008	−	0.226513i
$41$	7.98984			1.24780			0.623902	−	0.781503i	$-0.285547\pi$
$41$	7.98984			1.24780			0.623902	+	0.781503i	$0.285547\pi$
$42$		0			0
$43$	5.64967	+	5.64967i	0.861567	+	0.861567i	0.991520	−	0.129954i	$-0.0414828\pi$
$43$	5.64967	+	5.64967i	0.861567	+	0.861567i	−0.129954	+	0.991520i	$0.541483\pi$
$44$	2.13849	+	3.64561i	0.322389	+	0.549597i
$45$	−0.458035	+	0.0105130i	−0.0682798	+	0.00156719i
$46$	−3.91952	+	6.84325i	−0.577902	+	1.00898i
$47$	1.57515	+	5.87853i	0.229759	+	0.857472i	0.980442	+	0.196810i	$0.0630581\pi$
$47$	1.57515	+	5.87853i	0.229759	+	0.857472i	−0.750683	+	0.660663i	$0.770275\pi$
$48$	−1.75770	+	6.94181i	−0.253702	+	1.00196i
$49$		0			0
$50$	−2.16482	−	6.73153i	−0.306152	−	0.951983i
$51$	−9.80152	−	5.65891i	−1.37249	−	0.792406i
$52$	5.76894	+	5.68983i	0.800008	+	0.789038i
$53$	0.766587	+	0.205406i	0.105299	+	0.0282147i	0.311084	−	0.950383i	$-0.399308\pi$
$53$	0.766587	+	0.205406i	0.105299	+	0.0282147i	−0.205785	+	0.978597i	$0.565975\pi$
$54$	−0.0244258	−	7.07649i	−0.00332393	−	0.962988i
$55$	−2.26818	+	4.14546i	−0.305841	+	0.558974i
$56$		0			0
$57$	−3.73746	−	3.73746i	−0.495038	−	0.495038i
$58$	2.87806	+	2.85826i	0.377908	+	0.375308i
$59$	2.48910	+	4.31124i	0.324053	+	0.561276i	0.981320	−	0.192382i	$-0.0616212\pi$
$59$	2.48910	+	4.31124i	0.324053	+	0.561276i	−0.657268	+	0.753657i	$0.728288\pi$
$60$	−7.66802	+	2.30203i	−0.989937	+	0.297191i
$61$	0.843662	−	1.46127i	0.108020	−	0.187096i	−0.806948	−	0.590622i	$-0.798882\pi$
$61$	0.843662	−	1.46127i	0.108020	−	0.187096i	0.914968	+	0.403526i	$0.132216\pi$
$62$	2.17278	−	8.22233i	0.275943	−	1.04424i
$63$		0			0
$64$	0.165668	+	7.99828i	0.0207085	+	0.999786i
$65$	−2.14328	+	8.80198i	−0.265841	+	1.09175i
$66$	4.64268	+	2.65913i	0.571475	+	0.327316i
$67$	11.0122	+	2.95071i	1.34535	+	0.360486i	0.858417	−	0.512952i	$-0.171448\pi$
$67$	11.0122	+	2.95071i	1.34535	+	0.360486i	0.486935	+	0.873438i	$0.338115\pi$
$68$	−12.2355	−	3.18813i	−1.48377	−	0.386618i
$69$			9.98301i			1.20181i
$70$		0			0
$71$			0.610925i			0.0725035i	0.999343	+	0.0362518i	$0.0115418\pi$
$71$			0.610925i			0.0725035i	−0.999343	+	0.0362518i	$0.988458\pi$
$72$	0.155781	+	0.558196i	0.0183589	+	0.0657840i
$73$	−4.41548	−	1.18312i	−0.516793	−	0.138474i	−0.00901016	−	0.999959i	$-0.502868\pi$
$73$	−4.41548	−	1.18312i	−0.516793	−	0.138474i	−0.507783	+	0.861485i	$0.669535\pi$
$74$	−3.89101	+	6.79348i	−0.452321	+	0.789726i
$75$	−6.61312	−	6.03233i	−0.763617	−	0.696553i
$76$	−5.13407	−	2.91709i	−0.588919	−	0.334613i
$77$		0			0
$78$	9.91671	+	2.62052i	1.12285	+	0.296716i
$79$	7.12694	−	12.3442i	0.801843	−	1.38883i	−0.116558	−	0.993184i	$-0.537186\pi$
$79$	7.12694	−	12.3442i	0.801843	−	1.38883i	0.918401	−	0.395650i	$-0.129481\pi$
$80$	−7.57640	+	4.75376i	−0.847067	+	0.531486i
$81$	−4.78635	−	8.29020i	−0.531817	−	0.921133i
$82$	7.96221	−	8.01737i	0.879279	−	0.885370i
$83$	−5.51624	−	5.51624i	−0.605486	−	0.605486i	0.336277	−	0.941763i	$-0.390832\pi$
$83$	−5.51624	−	5.51624i	−0.605486	−	0.605486i	−0.941763	+	0.336277i	$0.890832\pi$
$84$		0			0
$85$	−3.97115	−	13.5672i	−0.430732	−	1.47157i
$86$	11.2993	−	0.0390015i	1.21843	−	0.00420564i
$87$	4.95971	+	1.32895i	0.531737	+	0.142478i
$88$	5.78927	+	1.48715i	0.617138	+	0.158531i
$89$	1.80030	+	1.03940i	0.190831	+	0.110176i	0.592372	−	0.805665i	$-0.298192\pi$
$89$	1.80030	+	1.03940i	0.190831	+	0.110176i	−0.401540	+	0.915841i	$0.631525\pi$
$90$	−0.445902	+	0.470090i	−0.0470022	+	0.0495518i
$91$		0			0
$92$	2.96086	+	10.7526i	0.308691	+	1.12104i
$93$	−2.78638	−	10.3989i	−0.288934	−	1.07832i
$94$	7.46849	+	4.27763i	0.770316	+	0.441204i
$95$	−0.151490	−	6.60017i	−0.0155426	−	0.677163i
$96$	5.21411	+	8.68157i	0.532163	+	0.886059i
$97$	1.95542	+	1.95542i	0.198543	+	0.198543i	0.799375	−	0.600832i	$-0.205164\pi$
$97$	1.95542	+	1.95542i	0.198543	+	0.198543i	−0.600832	+	0.799375i	$0.705164\pi$
$98$		0			0
$99$	0.432994			0.0435176
$100$	−8.91206	−	4.53598i	−0.891206	−	0.453598i
$101$	0.631568	+	1.09391i	0.0628434	+	0.108848i	0.895735	−	0.444588i	$-0.146650\pi$
$101$	0.631568	+	1.09391i	0.0628434	+	0.108848i	−0.832892	+	0.553436i	$0.813316\pi$
$102$	−15.4460	+	4.19595i	−1.52939	+	0.415461i
$103$	−12.5525	+	3.36344i	−1.23684	+	0.331409i	−0.817238	−	0.576300i	$-0.804496\pi$
$103$	−12.5525	+	3.36344i	−1.23684	+	0.331409i	−0.419599	+	0.907710i	$0.637829\pi$
$104$	11.4584	−	0.118656i	1.12359	−	0.0116352i
$105$		0			0
$106$	0.970051	−	0.564533i	0.0942197	−	0.0548322i
$107$	5.00010	+	18.6606i	0.483378	+	1.80399i	0.587255	+	0.809402i	$0.300209\pi$
$107$	5.00010	+	18.6606i	0.483378	+	1.80399i	−0.103877	+	0.994590i	$0.533125\pi$
$108$	−7.12521	−	7.02751i	−0.685624	−	0.676222i
$109$	11.7830	−	6.80291i	1.12860	−	0.651600i	0.185021	−	0.982735i	$-0.440765\pi$
$109$	11.7830	−	6.80291i	1.12860	−	0.651600i	0.943584	+	0.331134i	$0.107431\pi$
$110$	1.89941	+	6.40713i	0.181102	+	0.610895i
$111$			9.91040i			0.940654i
$112$		0			0
$113$	−7.72607	+	7.72607i	−0.726807	+	0.726807i	−0.969982	−	0.243175i	$-0.921811\pi$
$113$	−7.72607	+	7.72607i	−0.726807	+	0.726807i	0.243175	+	0.969982i	$0.421811\pi$
$114$	−7.47487	+	0.0258009i	−0.700086	+	0.00241647i
$115$	−8.61244	+	9.01708i	−0.803114	+	0.840847i
$116$	5.73621	−	0.0395997i	0.532594	−	0.00367674i
$117$	0.801816	−	0.214846i	0.0741279	−	0.0198625i
$118$	6.80658	+	1.79866i	0.626597	+	0.165580i
$119$		0			0
$120$	−5.33154	+	9.98851i	−0.486701	+	0.911822i
$121$	−3.26705	+	5.65869i	−0.297004	+	0.514427i
$122$	−0.625556	−	2.30278i	−0.0566352	−	0.208484i
$123$	3.70204	−	13.8162i	0.333802	−	1.24576i
$124$	−6.08540	−	10.3742i	−0.546485	−	0.931628i
$125$	−0.769107	−	11.1539i	−0.0687910	−	0.997631i
$126$		0			0
$127$	−3.84193	+	3.84193i	−0.340917	+	0.340917i	−0.856712	−	0.515795i	$-0.827496\pi$
$127$	−3.84193	+	3.84193i	−0.340917	+	0.340917i	0.515795	+	0.856712i	$0.327496\pi$
$128$	8.19094	+	7.80439i	0.723984	+	0.689817i
$129$	12.3873	−	7.15179i	1.09064	−	0.629680i
$130$	6.69645	+	10.9222i	0.587317	+	0.957941i
$131$	10.0683	+	5.81295i	0.879674	+	0.507880i	0.870551	−	0.492078i	$-0.163763\pi$
$131$	10.0683	+	5.81295i	0.879674	+	0.507880i	0.00912320	+	0.999958i	$0.497096\pi$
$132$	7.29492	−	2.00874i	0.634942	−	0.174839i
$133$		0			0
$134$	13.9350	−	8.10963i	1.20380	−	0.700565i
$135$	2.64716	−	10.8713i	0.227831	−	0.935654i
$136$	−15.3923	+	9.10056i	−1.31988	+	0.780367i
$137$	5.52298	−	20.6120i	0.471860	−	1.76101i	−0.161219	−	0.986919i	$-0.551543\pi$
$137$	5.52298	−	20.6120i	0.471860	−	1.76101i	0.633079	−	0.774087i	$-0.281791\pi$
$138$	10.0174	+	9.94849i	0.852738	+	0.846872i
$139$	−5.05787			−0.429003			−0.214501	−	0.976724i	$-0.568813\pi$
$139$	−5.05787			−0.429003			−0.214501	+	0.976724i	$0.568813\pi$
$140$		0			0
$141$	10.8951			0.917535
$142$	0.613030	+	0.608813i	0.0514444	+	0.0510905i
$143$	2.21592	−	8.26993i	0.185305	−	0.691566i
$144$	0.715361	+	0.399948i	0.0596134	+	0.0333290i
$145$	3.33332	+	5.47915i	0.276817	+	0.455019i
$146$	−5.58741	+	3.25166i	−0.462418	+	0.269109i
$147$		0			0
$148$	2.93933	+	10.6744i	0.241611	+	0.877431i
$149$	6.53199	+	3.77124i	0.535121	+	0.308952i	0.743099	−	0.669181i	$-0.233355\pi$
$149$	6.53199	+	3.77124i	0.535121	+	0.308952i	−0.207978	+	0.978133i	$0.566688\pi$
$150$	−12.6434	+	0.624439i	−1.03233	+	0.0509852i
$151$	−12.0674	+	6.96711i	−0.982030	+	0.566975i	−0.902883	−	0.429887i	$-0.858553\pi$
$151$	−12.0674	+	6.96711i	−0.982030	+	0.566975i	−0.0791478	+	0.996863i	$0.525220\pi$
$152$	−8.04346	+	2.24476i	−0.652411	+	0.182074i
$153$	−0.915944	+	0.915944i	−0.0740496	+	0.0740496i
$154$		0			0
$155$	6.45446	−	11.7966i	0.518435	−	0.947524i
$156$	12.5120	−	7.33942i	1.00176	−	0.587624i
$157$	2.06532	−	7.70790i	0.164831	−	0.615157i	−0.833231	−	0.552925i	$-0.813512\pi$
$157$	2.06532	−	7.70790i	0.164831	−	0.615157i	0.998062	−	0.0622318i	$-0.0198218\pi$
$158$	−5.28446	−	19.4530i	−0.420409	−	1.54760i
$159$	0.710386	−	1.23043i	0.0563373	−	0.0975791i
$160$	−2.78007	+	12.3398i	−0.219784	+	0.975549i
$161$		0			0
$162$	−13.0886	−	3.45869i	−1.02833	−	0.271741i
$163$	13.4557	−	3.60545i	1.05393	−	0.282400i	0.310057	−	0.950718i	$-0.399652\pi$
$163$	13.4557	−	3.60545i	1.05393	−	0.282400i	0.743876	+	0.668318i	$0.232985\pi$
$164$	−0.110312	−	15.9793i	−0.00861395	−	1.24777i
$165$	6.11748	+	5.84296i	0.476245	+	0.454874i
$166$	−11.0324	+	0.0380804i	−0.856282	+	0.00295561i
$167$	−14.0288	+	14.0288i	−1.08558	+	1.08558i	−0.0896054	+	0.995977i	$0.528561\pi$
$167$	−14.0288	+	14.0288i	−1.08558	+	1.08558i	−0.995977	+	0.0896054i	$0.971439\pi$
$168$		0			0
$169$		−	3.41370i		−	0.262592i
$170$	−17.5714	−	9.53548i	−1.34767	−	0.731338i
$171$	−0.523893	+	0.302470i	−0.0400631	+	0.0231304i
$172$	11.2211	−	11.3771i	0.855598	−	0.867494i
$173$	−3.24936	−	12.1268i	−0.247044	−	0.921982i	−0.972345	−	0.233550i	$-0.924966\pi$
$173$	−3.24936	−	12.1268i	−0.247044	−	0.921982i	0.725300	−	0.688432i	$-0.241701\pi$
$174$	6.27609	−	3.65244i	0.475789	−	0.276891i
$175$		0			0
$176$	7.26153	−	4.32720i	0.547358	−	0.326175i
$177$	8.60839	−	2.30661i	0.647046	−	0.173376i
$178$	2.83706	−	0.770693i	0.212647	−	0.0577659i
$179$	1.72867	+	2.99414i	0.129207	+	0.223792i	0.923369	−	0.383913i	$-0.125424\pi$
$179$	1.72867	+	2.99414i	0.129207	+	0.223792i	−0.794163	+	0.607705i	$0.792090\pi$
$180$	0.0273495	+	0.915902i	0.00203851	+	0.0682673i
$181$	16.0960			1.19640			0.598202	−	0.801345i	$-0.295882\pi$
$181$	16.0960			1.19640			0.598202	+	0.801345i	$0.295882\pi$
$182$		0			0
$183$	−2.13595	−	2.13595i	−0.157894	−	0.157894i
$184$	13.7403	+	7.74437i	1.01295	+	0.570923i
$185$	−8.54980	+	8.95149i	−0.628594	+	0.658127i
$186$	−13.2115	−	7.56697i	−0.968713	−	0.554838i
$187$	3.45786	+	12.9049i	0.252863	+	0.943699i
$188$	11.7350	−	3.23138i	0.855866	−	0.235673i
$189$		0			0
$190$	−6.77388	−	6.42533i	−0.491429	−	0.466143i
$191$	4.59262	+	2.65155i	0.332310	+	0.191860i	0.656866	−	0.754007i	$-0.271882\pi$
$191$	4.59262	+	2.65155i	0.332310	+	0.191860i	−0.324556	+	0.945866i	$0.605215\pi$
$192$	13.9076	+	3.41948i	1.00369	+	0.246779i
$193$	−21.6160	−	5.79200i	−1.55596	−	0.416917i	−0.624576	−	0.780964i	$-0.714728\pi$
$193$	−21.6160	−	5.79200i	−1.55596	−	0.416917i	−0.931381	+	0.364047i	$0.881395\pi$
$194$	3.91081	−	0.0134989i	0.280780	−	0.000969164i
$195$	14.2275	+	7.78454i	1.01885	+	0.557462i
$196$		0			0
$197$	5.33556	+	5.33556i	0.380143	+	0.380143i	0.871154	−	0.491011i	$-0.163372\pi$
$197$	5.33556	+	5.33556i	0.380143	+	0.380143i	−0.491011	+	0.871154i	$0.663372\pi$
$198$	0.431497	−	0.434486i	0.0306652	−	0.0308776i
$199$	5.94289	+	10.2934i	0.421280	+	0.729679i	0.996065	−	0.0886258i	$-0.0282475\pi$
$199$	5.94289	+	10.2934i	0.421280	+	0.729679i	−0.574785	+	0.818305i	$0.694914\pi$
$200$	−13.4329	+	4.42247i	−0.949847	+	0.312716i
$201$	10.2048	−	17.6753i	0.719795	−	1.24672i
$202$	1.72706	+	0.456381i	0.121516	+	0.0321109i
$203$		0			0
$204$	−11.1822	+	19.6807i	−0.782912	+	1.37792i
$205$	15.2632	−	9.28559i	1.06603	−	0.648534i
$206$	−9.13409	+	15.9476i	−0.636402	+	1.11112i
$207$	1.10364	+	0.295719i	0.0767081	+	0.0205539i
$208$	11.2997	−	11.6162i	0.783496	−	0.805435i
$209$			6.23934i			0.431584i
$210$		0			0
$211$		−	2.04430i		−	0.140735i	−0.997521	−	0.0703677i	$-0.977583\pi$
$211$		−	2.04430i		−	0.140735i	0.997521	−	0.0703677i	$-0.0224173\pi$
$212$	0.400219	−	1.53597i	0.0274872	−	0.105491i
$213$	1.05643	+	0.283068i	0.0723851	+	0.0193955i
$214$	23.7078	+	13.5788i	1.62063	+	0.928227i
$215$	17.3586	+	4.22681i	1.18385	+	0.288266i
$216$	−14.1523	+	0.146552i	−0.962942	+	0.00997163i
$217$		0			0
$218$	4.91589	−	18.6030i	0.332946	−	1.25995i
$219$	−4.09177	+	7.08715i	−0.276496	+	0.478905i
$220$	8.32205	+	4.47902i	0.561072	+	0.301975i
$221$	12.8065	+	22.1815i	0.861456	+	1.49209i
$222$	9.94455	+	9.87613i	0.667434	+	0.662843i
$223$	−13.1600	−	13.1600i	−0.881261	−	0.881261i	0.112402	−	0.993663i	$-0.464146\pi$
$223$	−13.1600	−	13.1600i	−0.881261	−	0.881261i	−0.993663	+	0.112402i	$0.964146\pi$
$224$		0			0
$225$	−0.862778	+	0.552400i	−0.0575185	+	0.0368267i
$226$	0.0533356	+	15.4520i	0.00354783	+	1.02785i
$227$	−5.37597	−	1.44049i	−0.356816	−	0.0956085i	0.0759580	−	0.997111i	$-0.475798\pi$
$227$	−5.37597	−	1.44049i	−0.356816	−	0.0956085i	−0.432774	+	0.901502i	$0.642465\pi$
$228$	−7.42313	+	7.52634i	−0.491609	+	0.498444i
$229$	7.11068	+	4.10535i	0.469887	+	0.271289i	0.716192	−	0.697903i	$-0.245883\pi$
$229$	7.11068	+	4.10535i	0.469887	+	0.271289i	−0.246305	+	0.969192i	$0.579217\pi$
$230$	0.465490	+	17.6280i	0.0306935	+	1.16236i
$231$		0			0
$232$	5.67664	−	5.79544i	0.372690	−	0.380489i
$233$	−3.10326	−	11.5815i	−0.203302	−	0.758732i	−0.989961	−	0.141344i	$-0.954858\pi$
$233$	−3.10326	−	11.5815i	−0.203302	−	0.758732i	0.786659	−	0.617388i	$-0.211809\pi$
$234$	0.583457	−	1.01868i	0.0381418	−	0.0665933i
$235$	9.84094	+	9.39932i	0.641952	+	0.613144i
$236$	8.58791	−	5.03760i	0.559025	−	0.327920i
$237$	−18.0437	−	18.0437i	−1.17206	−	1.17206i
$238$		0			0
$239$	−18.5038			−1.19691			−0.598456	−	0.801155i	$-0.704219\pi$
$239$	−18.5038			−1.19691			−0.598456	+	0.801155i	$0.704219\pi$
$240$	4.70982	+	15.3039i	0.304018	+	0.987862i
$241$	0.0411841	+	0.0713330i	0.00265290	+	0.00459496i	0.867349	−	0.497701i	$-0.165822\pi$
$241$	0.0411841	+	0.0713330i	0.00265290	+	0.00459496i	−0.864696	+	0.502296i	$0.832489\pi$
$242$	2.42244	+	8.91743i	0.155720	+	0.573234i
$243$	−2.05324	+	0.550164i	−0.131715	+	0.0352930i
$244$	−2.93411	−	1.66711i	−0.187837	−	0.106726i
$245$		0			0
$246$	−10.1746	−	17.4832i	−0.648707	−	1.11469i
$247$	3.09588	+	11.5540i	0.196986	+	0.735162i
$248$	−16.4743	−	4.23193i	−1.04612	−	0.268728i
$249$	−12.0947	+	6.98289i	−0.766471	+	0.442522i
$250$	−11.9587	−	10.3435i	−0.756337	−	0.654182i
$251$		−	9.07743i		−	0.572963i	−0.958086	−	0.286481i	$-0.907514\pi$
$251$		−	9.07743i		−	0.572963i	0.958086	−	0.286481i	$-0.0924856\pi$
$252$		0			0
$253$	8.33287	−	8.33287i	0.523883	−	0.523883i
$254$	0.0265221	+	7.68382i	0.00166415	+	0.482126i
$255$	−25.3008	+	0.580715i	−1.58439	+	0.0363658i
$256$	15.9939	−	0.441758i	0.999619	−	0.0276099i
$257$	−7.03925	+	1.88616i	−0.439097	+	0.117656i	−0.471593	−	0.881816i	$-0.656321\pi$
$257$	−7.03925	+	1.88616i	−0.439097	+	0.117656i	0.0324965	+	0.999472i	$0.489654\pi$
$258$	5.16800	−	19.5570i	0.321746	−	1.21757i
$259$		0			0
$260$	17.6331	+	4.16492i	1.09356	+	0.258298i
$261$	0.293835	−	0.508937i	0.0181879	−	0.0315024i
$262$	15.8665	−	4.31017i	0.980236	−	0.266283i
$263$	1.38891	−	5.18349i	0.0856441	−	0.319628i	−0.909791	−	0.415066i	$-0.863759\pi$
$263$	1.38891	−	5.18349i	0.0856441	−	0.319628i	0.995435	+	0.0954380i	$0.0304252\pi$
$264$	5.25403	−	9.32186i	0.323363	−	0.573721i
$265$	1.70315	−	0.498515i	0.104624	−	0.0306236i
$266$		0			0
$267$	2.63151	−	2.63151i	0.161046	−	0.161046i
$268$	5.74923	−	22.0646i	0.351190	−	1.34781i
$269$	−4.69186	+	2.70885i	−0.286068	+	0.165161i	−0.636167	−	0.771551i	$-0.719481\pi$
$269$	−4.69186	+	2.70885i	−0.286068	+	0.165161i	0.350099	+	0.936713i	$0.386148\pi$
$270$	−8.27078	−	13.4900i	−0.503343	−	0.820976i
$271$	7.10365	+	4.10129i	0.431516	+	0.249136i	0.699992	−	0.714151i	$-0.253187\pi$
$271$	7.10365	+	4.10129i	0.431516	+	0.249136i	−0.268476	+	0.963286i	$0.586520\pi$
$272$	−6.20718	+	24.5145i	−0.376365	+	1.48641i
$273$		0			0
$274$	−15.1792	−	26.0828i	−0.917008	−	1.57572i
$275$	0.484792	+	10.5552i	0.0292341	+	0.636503i
$276$	19.9655	−	0.137831i	1.20178	−	0.00829646i
$277$	−3.92432	+	14.6458i	−0.235790	+	0.879979i	0.742002	+	0.670398i	$0.233877\pi$
$277$	−3.92432	+	14.6458i	−0.235790	+	0.879979i	−0.977791	+	0.209581i	$0.932790\pi$
$278$	−5.04038	+	5.07530i	−0.302302	+	0.304396i
$279$	−1.23215			−0.0737671
$280$		0			0
$281$	−23.7586			−1.41732			−0.708659	−	0.705551i	$-0.750700\pi$
$281$	−23.7586			−1.41732			−0.708659	+	0.705551i	$0.750700\pi$
$282$	10.8575	−	10.9327i	0.646552	−	0.651031i
$283$	6.13117	−	22.8818i	0.364460	−	1.36018i	−0.503691	−	0.863884i	$-0.668025\pi$
$283$	6.13117	−	22.8818i	0.364460	−	1.36018i	0.868151	−	0.496300i	$-0.165308\pi$
$284$	1.22182	−	0.00843479i	0.0725018	−	0.000500513i
$285$	−11.4833	−	2.79618i	−0.680214	−	0.165632i
$286$	−6.09016	−	10.4649i	−0.360119	−	0.618802i
$287$		0			0
$288$	1.11421	−	0.319261i	0.0656557	−	0.0188126i
$289$	−19.8908	−	11.4840i	−1.17005	−	0.675528i
$290$	8.81983	+	2.11540i	0.517918	+	0.124221i
$291$	4.28738	−	2.47532i	0.251331	−	0.145106i
$292$	−2.30523	+	8.84709i	−0.134903	+	0.517736i
$293$	−18.6078	+	18.6078i	−1.08708	+	1.08708i	−0.0912527	+	0.995828i	$0.529087\pi$
$293$	−18.6078	+	18.6078i	−1.08708	+	1.08708i	−0.995828	+	0.0912527i	$0.970913\pi$
$294$		0			0
$295$	9.76540	+	5.34311i	0.568564	+	0.311088i
$296$	13.6404	+	7.68804i	0.792829	+	0.446859i
$297$	−2.73688	+	10.2142i	−0.158810	+	0.592687i
$298$	10.2936	−	2.79629i	0.596295	−	0.161985i
$299$	11.2961	−	19.5654i	0.653270	−	1.13150i
$300$	−11.9731	+	13.3092i	−0.691265	+	0.768408i
$301$		0			0
$302$	−5.03455	+	19.0520i	−0.289706	+	1.09632i
$303$	2.18424	−	0.585266i	0.125481	−	0.0336226i
$304$	−5.76316	+	10.3082i	−0.330540	+	0.591215i
$305$	−0.0865763	−	3.77198i	−0.00495734	−	0.215983i
$306$	0.00632306	+	1.83188i	0.000361465	+	0.104721i
$307$	19.1930	−	19.1930i	1.09540	−	1.09540i	0.100459	−	0.994941i	$-0.467969\pi$
$307$	19.1930	−	19.1930i	1.09540	−	1.09540i	0.994941	−	0.100459i	$-0.0320312\pi$
$308$		0			0
$309$			23.2645i			1.32347i
$310$	−5.40508	−	18.2325i	−0.306988	−	1.03554i
$311$	−11.9923	+	6.92373i	−0.680018	+	0.392609i	−0.799862	−	0.600184i	$-0.795094\pi$
$311$	−11.9923	+	6.92373i	−0.680018	+	0.392609i	0.119844	+	0.992793i	$0.461761\pi$
$312$	5.10400	−	19.8691i	0.288957	−	1.12487i
$313$	6.08759	+	22.7192i	0.344091	+	1.28417i	0.893670	+	0.448724i	$0.148121\pi$
$313$	6.08759	+	22.7192i	0.344091	+	1.28417i	−0.549579	+	0.835441i	$0.685212\pi$
$314$	−5.67627	−	9.75368i	−0.320331	−	0.550432i
$315$		0			0
$316$	−24.7863	−	14.0831i	−1.39434	−	0.792237i
$317$	0.796585	−	0.213444i	0.0447407	−	0.0119882i	−0.236379	−	0.971661i	$-0.575961\pi$
$317$	0.796585	−	0.213444i	0.0447407	−	0.0119882i	0.281120	+	0.959673i	$0.409294\pi$
$318$	−0.526735	−	1.93901i	−0.0295378	−	0.108734i
$319$	−3.03061	−	5.24917i	−0.169682	−	0.293897i
$320$	9.61189	+	15.0868i	0.537321	+	0.843378i
$321$	34.5851			1.93035
$322$		0			0
$323$	−13.1985	−	13.1985i	−0.734386	−	0.734386i
$324$	−16.5139	+	9.68693i	−0.917440	+	0.538163i
$325$	6.13509	+	19.3055i	0.340313	+	1.07088i
$326$	9.79131	−	17.0951i	0.542291	−	0.946807i
$327$	−6.30416	−	23.5275i	−0.348621	−	1.30107i
$328$	−16.1443	−	15.8134i	−0.891419	−	0.873146i
$329$		0			0
$330$	11.9594	−	0.315804i	0.658344	−	0.0173844i
$331$	−12.4271	−	7.17480i	−0.683056	−	0.394363i	0.117949	−	0.993020i	$-0.462368\pi$
$331$	−12.4271	−	7.17480i	−0.683056	−	0.394363i	−0.801006	+	0.598657i	$0.795701\pi$
$332$	−10.9561	+	11.1084i	−0.601292	+	0.609652i
$333$	1.09561	+	0.293568i	0.0600390	+	0.0160874i
$334$	0.0968456	+	28.0575i	0.00529915	+	1.53524i
$335$	24.4661	−	7.16128i	1.33673	−	0.391262i
$336$		0			0
$337$	0.0624771	+	0.0624771i	0.00340335	+	0.00340335i	0.708806	−	0.705403i	$-0.249234\pi$
$337$	0.0624771	+	0.0624771i	0.00340335	+	0.00340335i	−0.705403	+	0.708806i	$0.749234\pi$
$338$	−3.42546	−	3.40190i	−0.186321	−	0.185039i
$339$	9.78026	+	16.9399i	0.531191	+	0.920049i
$340$	−27.0790	+	8.12943i	−1.46856	+	0.440880i
$341$	−6.35422	+	11.0058i	−0.344100	+	0.595999i
$342$	−0.218570	+	0.827122i	−0.0118189	+	0.0447256i
$343$		0			0
$344$	−0.234005	−	22.5975i	−0.0126167	−	1.21837i
$345$	11.6020	+	19.0708i	0.624631	+	1.02674i
$346$	−15.4067	−	8.82430i	−0.828269	−	0.474397i
$347$	−8.52161	−	2.28336i	−0.457464	−	0.122577i	0.0227259	−	0.999742i	$-0.492766\pi$
$347$	−8.52161	−	2.28336i	−0.457464	−	0.122577i	−0.480190	+	0.877165i	$0.659432\pi$
$348$	2.58936	−	9.93753i	0.138804	−	0.532708i
$349$			3.77799i			0.202231i	0.994875	+	0.101116i	$0.0322412\pi$
$349$			3.77799i			0.202231i	−0.994875	+	0.101116i	$0.967759\pi$
$350$		0			0
$351$			20.2726i			1.08207i
$352$	2.89430	−	11.5988i	0.154267	−	0.618217i
$353$	−1.20055	−	0.321686i	−0.0638987	−	0.0171216i	0.226728	−	0.973958i	$-0.427197\pi$
$353$	−1.20055	−	0.321686i	−0.0638987	−	0.0171216i	−0.290627	+	0.956836i	$0.593864\pi$
$354$	6.26407	−	10.9367i	0.332932	−	0.581279i
$355$	0.710002	+	1.16707i	0.0376830	+	0.0619415i
$356$	2.05390	−	3.61486i	0.108856	−	0.191587i
$357$		0			0
$358$	4.72714	+	1.24916i	0.249837	+	0.0660203i
$359$	−8.75216	+	15.1592i	−0.461922	+	0.800072i	−0.999057	−	0.0434246i	$-0.986173\pi$
$359$	−8.75216	+	15.1592i	−0.461922	+	0.800072i	0.537135	+	0.843496i	$0.319507\pi$
$360$	0.946313	+	0.885292i	0.0498751	+	0.0466590i
$361$	5.14148	+	8.90531i	0.270604	+	0.468701i
$362$	16.0403	−	16.1514i	0.843061	−	0.848901i
$363$	8.27137	+	8.27137i	0.434134	+	0.434134i
$364$		0			0
$365$	−9.81001	+	2.87141i	−0.513479	+	0.150296i
$366$	−4.27187	+	0.0147451i	−0.223294	+	0.000770741i
$367$	15.0382	+	4.02948i	0.784988	+	0.210337i	0.628983	−	0.777419i	$-0.283472\pi$
$367$	15.0382	+	4.02948i	0.784988	+	0.210337i	0.156006	+	0.987756i	$0.450138\pi$
$368$	21.4638	−	6.07004i	1.11888	−	0.316423i
$369$	−1.41774	−	0.818532i	−0.0738046	−	0.0426111i
$370$	0.462104	+	17.4998i	0.0240237	+	0.909771i
$371$		0			0
$372$	−20.7589	+	5.71620i	−1.07630	+	0.296371i
$373$	0.203640	+	0.759994i	0.0105441	+	0.0393510i	0.970997	−	0.239090i	$-0.0768490\pi$
$373$	0.203640	+	0.759994i	0.0105441	+	0.0393510i	−0.960453	+	0.278441i	$0.910182\pi$
$374$	16.3953	+	9.39050i	0.847779	+	0.485571i
$375$	−19.6438	−	3.83811i	−1.01440	−	0.198199i
$376$	8.45195	−	14.9957i	0.435876	−	0.773344i
$377$	−8.21663	−	8.21663i	−0.423178	−	0.423178i
$378$		0			0
$379$	9.14995			0.470001			0.235001	−	0.971995i	$-0.424491\pi$
$379$	9.14995			0.470001			0.235001	+	0.971995i	$0.424491\pi$
$380$	−13.1979	+	0.394099i	−0.677039	+	0.0202168i
$381$	4.86342	+	8.42369i	0.249161	+	0.431559i
$382$	7.23743	−	1.96606i	0.370299	−	0.100593i
$383$	−8.15515	+	2.18517i	−0.416709	+	0.111657i	−0.461080	−	0.887358i	$-0.652538\pi$
$383$	−8.15515	+	2.18517i	−0.416709	+	0.111657i	0.0443718	+	0.999015i	$0.485871\pi$
$384$	17.2907	−	10.5478i	0.882364	−	0.538267i
$385$		0			0
$386$	−27.3533	+	15.9185i	−1.39224	+	0.810233i
$387$	−0.423703	−	1.58128i	−0.0215381	−	0.0803811i
$388$	3.88375	−	3.93774i	0.197167	−	0.199908i
$389$	−24.8832	+	14.3663i	−1.26163	+	0.728400i	−0.973389	−	0.229159i	$-0.926402\pi$
$389$	−24.8832	+	14.3663i	−1.26163	+	0.728400i	−0.288237	+	0.957559i	$0.593069\pi$
$390$	21.9897	−	6.51890i	1.11349	−	0.330098i
$391$			35.2542i			1.78288i
$392$		0			0
$393$	14.7170	−	14.7170i	0.742373	−	0.742373i
$394$	10.6711	−	0.0368331i	0.537600	−	0.00185563i
$395$	−0.731364	−	31.8643i	−0.0367989	−	1.60326i
$396$	−0.00597817	−	0.865968i	−0.000300414	−	0.0435165i
$397$	−24.6559	+	6.60652i	−1.23744	+	0.331572i	−0.817473	−	0.575967i	$-0.804626\pi$
$397$	−24.6559	+	6.60652i	−1.23744	+	0.331572i	−0.419969	+	0.907538i	$0.637959\pi$
$398$	16.2512	+	4.29443i	0.814599	+	0.215260i
$399$		0			0
$400$	−8.94870	+	17.8863i	−0.447435	+	0.894316i
$401$	−13.0839	+	22.6620i	−0.653380	+	1.13169i	0.328917	+	0.944359i	$0.393316\pi$
$401$	−13.0839	+	22.6620i	−0.653380	+	1.13169i	−0.982297	+	0.187329i	$0.940017\pi$
$402$	−7.56666	−	27.8542i	−0.377391	−	1.38924i
$403$	−6.30575	+	23.5334i	−0.314112	+	1.17228i
$404$	2.17904	−	1.27821i	0.108411	−	0.0635933i
$405$	−18.7782	−	10.2744i	−0.933094	−	0.510540i
$406$		0			0
$407$	8.27226	−	8.27226i	0.410041	−	0.410041i
$408$	8.60496	+	30.8334i	0.426009	+	1.52648i
$409$	−0.853122	+	0.492550i	−0.0421842	+	0.0243550i	−0.520944	−	0.853591i	$-0.674420\pi$
$409$	−0.853122	+	0.492550i	−0.0421842	+	0.0243550i	0.478760	+	0.877946i	$0.341087\pi$
$410$	5.89284	−	24.5693i	0.291027	−	1.21339i
$411$	−33.0837	−	19.1009i	−1.63190	−	0.942178i
$412$	6.90002	+	25.0580i	0.339940	+	1.23452i
$413$		0			0
$414$	1.39656	−	0.812743i	0.0686371	−	0.0399442i
$415$	−16.9487	−	4.12699i	−0.831977	−	0.202586i
$416$	−0.395509	−	22.9147i	−0.0193914	−	1.12348i
$417$	−2.34353	+	8.74617i	−0.114763	+	0.428302i
$418$	6.26084	+	6.21777i	0.306228	+	0.304121i
$419$	16.7317			0.817399			0.408699	−	0.912669i	$-0.365982\pi$
$419$	16.7317			0.817399			0.408699	+	0.912669i	$0.365982\pi$
$420$		0			0
$421$	35.5024			1.73028			0.865140	−	0.501530i	$-0.167229\pi$
$421$	35.5024			1.73028			0.865140	+	0.501530i	$0.167229\pi$
$422$	−2.05134	−	2.03723i	−0.0998578	−	0.0991708i
$423$	0.322737	−	1.20447i	0.0156920	−	0.0585634i
$424$	−1.14243	−	1.93226i	−0.0554814	−	0.0938389i
$425$	−23.3537	−	21.3027i	−1.13282	−	1.03333i
$426$	1.33682	−	0.777976i	0.0647689	−	0.0376930i
$427$		0			0
$428$	37.2514	−	10.2576i	1.80061	−	0.495820i
$429$	−13.2738	−	7.66363i	−0.640865	−	0.370004i
$430$	21.5400	−	13.2062i	1.03875	−	0.636861i
$431$	−0.906153	+	0.523167i	−0.0436478	+	0.0252001i	−0.521665	−	0.853150i	$-0.674689\pi$
$431$	−0.906153	+	0.523167i	−0.0436478	+	0.0252001i	0.478017	+	0.878350i	$0.341356\pi$
$432$	−13.9563	+	14.3471i	−0.671473	+	0.690275i
$433$	−9.24591	+	9.24591i	−0.444330	+	0.444330i	−0.893464	−	0.449134i	$-0.851733\pi$
$433$	−9.24591	+	9.24591i	−0.444330	+	0.444330i	0.449134	+	0.893464i	$0.351733\pi$
$434$		0			0
$435$	11.0191	−	3.22532i	0.528327	−	0.154642i
$436$	−13.7682	−	23.4715i	−0.659376	−	1.12408i
$437$	−4.26123	+	15.9031i	−0.203842	+	0.760750i
$438$	3.03395	+	11.1685i	0.144968	+	0.533652i
$439$	−11.3657	+	19.6860i	−0.542455	+	0.939559i	0.456307	+	0.889822i	$0.349172\pi$
$439$	−11.3657	+	19.6860i	−0.542455	+	0.939559i	−0.998762	+	0.0497373i	$0.984162\pi$
$440$	12.7877	−	3.88719i	0.609631	−	0.185315i
$441$		0			0
$442$	35.0201	+	9.25416i	1.66573	+	0.440176i
$443$	22.5471	−	6.04148i	1.07125	−	0.287040i	0.320241	−	0.947336i	$-0.396236\pi$
$443$	22.5471	−	6.04148i	1.07125	−	0.287040i	0.751005	+	0.660296i	$0.229569\pi$
$444$	19.8203	−	0.136829i	0.940631	−	0.00649360i
$445$	4.64713	−	0.106663i	0.220295	−	0.00505632i
$446$	−26.3199	+	0.0908480i	−1.24628	+	0.00430178i
$447$	9.54787	−	9.54787i	0.451599	−	0.451599i
$448$		0			0
$449$			18.0937i			0.853895i	0.904276	+	0.426947i	$0.140411\pi$
$449$			18.0937i			0.853895i	−0.904276	+	0.426947i	$0.859589\pi$
$450$	−0.305492	+	1.41624i	−0.0144010	+	0.0667622i
$451$	−14.6226	+	8.44234i	−0.688549	+	0.397534i
$452$	15.5584	+	15.3451i	0.731807	+	0.721773i
$453$	6.45633	+	24.0954i	0.303345	+	1.13210i
$454$	−6.80284	+	3.95899i	−0.319273	+	0.185805i
$455$		0			0
$456$	0.154803	+	14.9490i	0.00724931	+	0.700052i
$457$	17.5625	−	4.70586i	0.821540	−	0.220131i	0.176520	−	0.984297i	$-0.443516\pi$
$457$	17.5625	−	4.70586i	0.821540	−	0.220131i	0.645020	+	0.764166i	$0.276849\pi$
$458$	11.2056	−	3.04402i	0.523603	−	0.142238i
$459$	−15.8173	−	27.3963i	−0.738286	−	1.27875i
$460$	18.1526	+	17.1000i	0.846371	+	0.797290i
$461$	−30.3805			−1.41496			−0.707481	−	0.706733i	$-0.750168\pi$
$461$	−30.3805			−1.41496			−0.707481	+	0.706733i	$0.750168\pi$
$462$		0			0
$463$	20.1652	+	20.1652i	0.937156	+	0.937156i	0.998139	−	0.0609833i	$-0.0194236\pi$
$463$	20.1652	+	20.1652i	0.937156	+	0.937156i	−0.0609833	+	0.998139i	$0.519424\pi$
$464$	−0.158395	−	11.4716i	−0.00735330	−	0.532556i
$465$	−17.4083	−	16.6271i	−0.807288	−	0.771061i
$466$	−14.7140	−	8.42754i	−0.681612	−	0.390398i
$467$	−5.42798	−	20.2575i	−0.251177	−	0.937405i	−0.970177	−	0.242396i	$-0.922067\pi$
$467$	−5.42798	−	20.2575i	−0.251177	−	0.937405i	0.719001	−	0.695009i	$-0.244600\pi$
$468$	−0.440752	−	1.60063i	−0.0203738	−	0.0739890i
$469$		0			0
$470$	19.2386	−	0.508020i	0.887411	−	0.0234332i
$471$	−12.3717	−	7.14281i	−0.570058	−	0.329123i
$472$	3.50326	−	13.6377i	0.161251	−	0.627725i
$473$	−16.3093	−	4.37008i	−0.749904	−	0.200936i
$474$	−36.0871	+	0.124561i	−1.65754	+	0.00572129i
$475$	−7.95995	−	12.4324i	−0.365227	−	0.570439i
$476$		0			0
$477$	−0.114982	−	0.114982i	−0.00526467	−	0.00526467i
$478$	−18.4398	+	18.5676i	−0.843419	+	0.849261i
$479$	−13.9452	−	24.1538i	−0.637172	−	1.10361i	−0.986051	−	0.166446i	$-0.946771\pi$
$479$	−13.9452	−	24.1538i	−0.637172	−	1.10361i	0.348879	−	0.937168i	$-0.386562\pi$
$480$	20.0502	+	10.5249i	0.915160	+	0.480395i
$481$	11.2139	−	19.4231i	0.511311	−	0.885617i
$482$	0.112621	+	0.0297603i	0.00512972	+	0.00135555i
$483$		0			0
$484$	11.3622	+	6.45581i	0.516465	+	0.293446i
$485$	6.00803	+	1.46295i	0.272810	+	0.0664291i
$486$	−1.49408	+	2.60858i	−0.0677729	+	0.118327i
$487$	−3.75898	−	1.00721i	−0.170335	−	0.0456412i	0.172643	−	0.984984i	$-0.444769\pi$
$487$	−3.75898	−	1.00721i	−0.170335	−	0.0456412i	−0.342979	+	0.939343i	$0.611436\pi$
$488$	−4.59682	+	1.28288i	−0.208088	+	0.0580730i
$489$		−	24.9385i		−	1.12776i
$490$		0			0
$491$			14.4151i			0.650544i	0.945620	+	0.325272i	$0.105456\pi$
$491$			14.4151i			0.650544i	−0.945620	+	0.325272i	$0.894544\pi$
$492$	−27.6829	−	7.21315i	−1.24804	−	0.325194i
$493$	17.5148	+	4.69308i	0.788827	+	0.211366i
$494$	14.6790	+	8.40748i	0.660438	+	0.378270i
$495$	0.827161	−	0.503215i	0.0371781	−	0.0226178i
$496$	−20.6638	+	12.3137i	−0.927833	+	0.552903i
$497$		0			0
$498$	−5.04595	+	19.0951i	−0.226114	+	0.855673i
$499$	1.47517	−	2.55507i	0.0660377	−	0.114381i	−0.831116	−	0.556099i	$-0.812298\pi$
$499$	1.47517	−	2.55507i	0.0660377	−	0.114381i	0.897154	+	0.441718i	$0.145631\pi$
$500$	−22.2966	+	1.69217i	−0.997132	+	0.0756763i
$501$	17.7588	+	30.7591i	0.793403	+	1.37422i
$502$	−9.10871	−	9.04605i	−0.406542	−	0.403745i
$503$	−17.2036	−	17.2036i	−0.767071	−	0.767071i	0.210518	−	0.977590i	$-0.432485\pi$
$503$	−17.2036	−	17.2036i	−0.767071	−	0.767071i	−0.977590	+	0.210518i	$0.932485\pi$
$504$		0			0
$505$	2.47781	+	1.35573i	0.110261	+	0.0603291i
$506$	−0.0575245	−	16.6656i	−0.00255728	−	0.740878i
$507$	−5.90305	−	1.58172i	−0.262163	−	0.0702465i
$508$	7.73673	+	7.63064i	0.343262	+	0.338555i
$509$	2.32094	+	1.34000i	0.102874	+	0.0593944i	0.550554	−	0.834799i	$-0.314416\pi$
$509$	2.32094	+	1.34000i	0.102874	+	0.0593944i	−0.447680	+	0.894194i	$0.647750\pi$
$510$	−24.6306	+	25.9666i	−1.09066	+	1.14982i
$511$		0			0
$512$	15.4953	−	16.4892i	0.684803	−	0.728728i
$513$	−3.82372	−	14.2703i	−0.168821	−	0.630049i
$514$	−5.12225	+	8.94315i	−0.225933	+	0.394465i
$515$	−20.0705	+	21.0135i	−0.884412	+	0.925965i
$516$	−14.4743	−	24.6752i	−0.637194	−	1.08627i
$517$	−9.09421	−	9.09421i	−0.399963	−	0.399963i
$518$		0			0
$519$	−22.4755			−0.986563
$520$	21.7514	−	13.5434i	0.953864	−	0.593916i
$521$	−22.5104	−	38.9891i	−0.986196	−	1.70814i	−0.636495	−	0.771281i	$-0.719616\pi$
$521$	−22.5104	−	38.9891i	−0.986196	−	1.70814i	−0.349702	−	0.936861i	$-0.613717\pi$
$522$	−0.217872	−	0.802025i	−0.00953598	−	0.0351037i
$523$	6.11620	−	1.63883i	0.267443	−	0.0716610i	−0.122606	−	0.992455i	$-0.539125\pi$
$523$	6.11620	−	1.63883i	0.267443	−	0.0716610i	0.390048	+	0.920794i	$0.372458\pi$
$524$	11.4866	−	20.2164i	0.501795	−	0.883159i
$525$		0			0
$526$	−3.81724	−	6.55927i	−0.166440	−	0.285998i
$527$	−9.83987	−	36.7229i	−0.428632	−	1.59968i
$528$	−4.11811	−	14.5618i	−0.179218	−	0.633720i
$529$	7.01165	−	4.04818i	0.304854	−	0.176008i
$530$	1.19703	−	2.20581i	0.0519956	−	0.0958143i
$531$		−	1.02000i		−	0.0442641i
$532$		0			0
$533$	−22.8890	+	22.8890i	−0.991432	+	0.991432i
$534$	−0.0181662	−	5.26300i	−0.000786129	−	0.227752i
$535$	31.2388	+	29.8369i	1.35057	+	1.28996i
$536$	−16.4113	−	27.7573i	−0.708859	−	1.19893i
$537$	5.97849	−	1.60193i	0.257991	−	0.0691285i
$538$	−1.95746	+	7.40751i	−0.0843919	+	0.319360i
$539$		0			0
$540$	−21.7787	−	5.14409i	−0.937205	−	0.221367i
$541$	−8.37685	+	14.5091i	−0.360149	+	0.623796i	−0.987985	−	0.154549i	$-0.950607\pi$
$541$	−8.37685	+	14.5091i	−0.360149	+	0.623796i	0.627836	+	0.778345i	$0.283941\pi$
$542$	11.1945	−	3.04101i	0.480845	−	0.130623i
$543$	7.45797	−	27.8335i	0.320052	−	1.19445i
$544$	18.4132	+	30.6583i	0.789460	+	1.31446i
$545$	14.6032	−	26.6897i	0.625531	−	1.14326i
$546$		0			0
$547$	−12.5910	+	12.5910i	−0.538352	+	0.538352i	−0.923045	−	0.384693i	$-0.874307\pi$
$547$	−12.5910	+	12.5910i	−0.538352	+	0.538352i	0.384693	+	0.923045i	$0.374307\pi$
$548$	−41.2994	−	10.7611i	−1.76422	−	0.459692i
$549$	−0.299404	+	0.172861i	−0.0127782	+	0.00737752i
$550$	11.0747	+	10.0323i	0.472227	+	0.427777i
$551$	7.33366	+	4.23409i	0.312424	+	0.180378i
$552$	19.7582	−	20.1717i	0.840965	−	0.858564i
$553$		0			0
$554$	10.7855	+	18.5330i	0.458231	+	0.787391i
$555$	11.5176	+	18.9321i	0.488896	+	0.803623i
$556$	0.0698318	+	10.1155i	0.00296153	+	0.428993i
$557$	−8.56509	+	31.9653i	−0.362914	+	1.35441i	0.507312	+	0.861763i	$0.330639\pi$
$557$	−8.56509	+	31.9653i	−0.362914	+	1.35441i	−0.870226	+	0.492652i	$0.836027\pi$
$558$	−1.22789	+	1.23640i	−0.0519809	+	0.0523410i
$559$	−32.3699			−1.36910
$560$		0			0
$561$	23.9176			1.00980
$562$	−23.6764	+	23.8404i	−0.998730	+	1.00565i
$563$	−5.05720	+	18.8737i	−0.213136	+	0.795433i	0.773679	+	0.633578i	$0.218414\pi$
$563$	−5.05720	+	18.8737i	−0.213136	+	0.795433i	−0.986815	+	0.161855i	$0.948252\pi$
$564$	−0.150424	−	21.7897i	−0.00633401	−	0.917513i
$565$	−5.78027	+	23.7384i	−0.243178	+	0.998680i
$566$	−16.8507	−	28.9550i	−0.708288	−	1.21707i
$567$		0			0
$568$	1.20913	−	1.23444i	0.0507341	−	0.0517958i
$569$	33.7127	+	19.4640i	1.41331	+	0.815974i	0.995699	−	0.0926518i	$-0.0295344\pi$
$569$	33.7127	+	19.4640i	1.41331	+	0.815974i	0.417610	+	0.908626i	$0.362868\pi$
$570$	−14.2495	+	8.73639i	−0.596844	+	0.365927i
$571$	−17.7481	+	10.2468i	−0.742733	+	0.428817i	−0.823062	−	0.567951i	$-0.807736\pi$
$571$	−17.7481	+	10.2468i	−0.742733	+	0.428817i	0.0803293	+	0.996768i	$0.474403\pi$
$572$	−16.5701	−	4.31756i	−0.692829	−	0.180526i
$573$	6.71308	−	6.71308i	0.280443	−	0.280443i
$574$		0			0
$575$	−5.97315	+	27.2347i	−0.249097	+	1.13577i
$576$	0.790001	−	1.43621i	0.0329167	−	0.0598421i
$577$	1.81990	−	6.79196i	0.0757634	−	0.282753i	−0.917642	−	0.397408i	$-0.869910\pi$
$577$	1.81990	−	6.79196i	0.0757634	−	0.282753i	0.993405	+	0.114655i	$0.0365764\pi$
$578$	−31.3456	+	8.51511i	−1.30381	+	0.354182i
$579$	−20.0313	+	34.6952i	−0.832472	+	1.44188i
$580$	10.9120	−	6.74213i	0.453097	−	0.279952i
$581$		0			0
$582$	1.78871	−	6.76892i	0.0741443	−	0.280581i
$583$	−1.62000	+	0.434079i	−0.0670937	+	0.0179777i
$584$	6.58031	+	11.1297i	0.272295	+	0.460549i
$585$	1.28204	−	1.34228i	0.0530059	−	0.0554963i
$586$	0.128456	+	37.2154i	0.00530646	+	1.53735i
$587$	4.00401	−	4.00401i	0.165263	−	0.165263i	−0.619631	−	0.784894i	$-0.712718\pi$
$587$	4.00401	−	4.00401i	0.165263	−	0.165263i	0.784894	+	0.619631i	$0.212718\pi$
$588$		0			0
$589$		−	17.7550i		−	0.731584i
$590$	15.0932	−	4.47441i	0.621376	−	0.184209i
$591$	11.6986	−	6.75417i	0.481215	−	0.277829i
$592$	21.3077	−	6.02589i	0.875742	−	0.247663i
$593$	−9.08806	−	33.9171i	−0.373202	−	1.39281i	−0.855954	−	0.517051i	$-0.827030\pi$
$593$	−9.08806	−	33.9171i	−0.373202	−	1.39281i	0.482753	−	0.875757i	$-0.339637\pi$
$594$	7.52196	+	12.9252i	0.308630	+	0.530326i
$595$		0			0
$596$	7.45212	−	13.1157i	0.305251	−	0.537241i
$597$	20.5531	−	5.50720i	0.841184	−	0.225395i
$598$	−8.37578	−	30.8328i	−0.342511	−	1.26085i
$599$	−0.687491	−	1.19077i	−0.0280901	−	0.0486535i	0.851639	−	0.524129i	$-0.175609\pi$
$599$	−0.687491	−	1.19077i	−0.0280901	−	0.0486535i	−0.879729	+	0.475476i	$0.842276\pi$
$600$	1.42341	+	25.2775i	0.0581105	+	1.03195i
$601$	8.86739			0.361708			0.180854	−	0.983510i	$-0.442114\pi$
$601$	8.86739			0.361708			0.180854	+	0.983510i	$0.442114\pi$
$602$		0			0
$603$	−1.65174	−	1.65174i	−0.0672642	−	0.0672642i
$604$	14.1005	+	24.0380i	0.573741	+	0.978093i
$605$	0.335263	+	14.6068i	0.0136304	+	0.593852i
$606$	1.58941	−	2.77501i	0.0645652	−	0.112727i
$607$	−4.40882	−	16.4539i	−0.178948	−	0.667845i	−0.995845	−	0.0910609i	$-0.970974\pi$
$607$	−4.40882	−	16.4539i	−0.178948	−	0.667845i	0.816897	−	0.576784i	$-0.195692\pi$
$608$	4.60047	+	16.0556i	0.186574	+	0.651139i
$609$		0			0
$610$	−3.87125	−	3.67206i	−0.156742	−	0.148677i
$611$	−21.3530	−	12.3282i	−0.863851	−	0.498744i
$612$	1.84449	+	1.81920i	0.0745591	+	0.0735367i
$613$	27.5042	+	7.36973i	1.11088	+	0.297661i	0.767189	−	0.641421i	$-0.221655\pi$
$613$	27.5042	+	7.36973i	1.11088	+	0.297661i	0.343695	+	0.939081i	$0.388321\pi$
$614$	−0.132495	−	38.3857i	−0.00534708	−	1.54912i
$615$	−8.98474	−	30.6959i	−0.362300	−	1.23778i
$616$		0			0
$617$	0.247352	+	0.247352i	0.00995801	+	0.00995801i	0.712068	−	0.702110i	$-0.247759\pi$
$617$	0.247352	+	0.247352i	0.00995801	+	0.00995801i	−0.702110	+	0.712068i	$0.747759\pi$
$618$	23.3447	+	23.1841i	0.939060	+	0.932600i
$619$	4.44950	+	7.70677i	0.178841	+	0.309761i	0.941484	−	0.337059i	$-0.109432\pi$
$619$	4.44950	+	7.70677i	0.178841	+	0.309761i	−0.762643	+	0.646820i	$0.776099\pi$
$620$	−23.6817	−	12.7457i	−0.951080	−	0.511881i
$621$	−13.9518	+	24.1652i	−0.559866	+	0.969716i
$622$	−5.00320	+	18.9334i	−0.200610	+	0.759159i
$623$		0			0
$624$	−14.8512	−	24.9220i	−0.594525	−	0.997679i
$625$	−14.4320	−	20.4137i	−0.577279	−	0.816547i
$626$	28.8640	+	16.5321i	1.15364	+	0.660755i
$627$	10.7892	+	2.89096i	0.430879	+	0.115454i
$628$	−15.4439	−	4.02413i	−0.616280	−	0.160580i
$629$			34.9978i			1.39545i
$630$		0			0
$631$		−	30.9594i		−	1.23248i	−0.787560	−	0.616238i	$-0.788656\pi$
$631$		−	30.9594i		−	1.23248i	0.787560	−	0.616238i	$-0.211344\pi$
$632$	−38.8322	+	10.8372i	−1.54466	+	0.431083i
$633$	−3.53505	−	0.947212i	−0.140505	−	0.0376483i
$634$	0.579651	−	1.01204i	0.0230209	−	0.0401931i
$635$	−2.87435	+	11.8044i	−0.114065	+	0.468441i
$636$	−2.47060	−	1.40375i	−0.0979657	−	0.0556624i
$637$		0			0
$638$	−8.28739	−	2.18997i	−0.328101	−	0.0867017i
$639$	0.0625872	−	0.108404i	0.00247591	−	0.00428841i
$640$	24.7174	+	5.38963i	0.977043	+	0.213044i
$641$	−6.18079	−	10.7055i	−0.244127	−	0.422840i	0.717759	−	0.696292i	$-0.245168\pi$
$641$	−6.18079	−	10.7055i	−0.244127	−	0.422840i	−0.961886	+	0.273452i	$0.911835\pi$
$642$	34.4656	−	34.7043i	1.36025	−	1.36967i
$643$	−2.95024	−	2.95024i	−0.116346	−	0.116346i	0.646537	−	0.762883i	$-0.276217\pi$
$643$	−2.95024	−	2.95024i	−0.116346	−	0.116346i	−0.762883	+	0.646537i	$0.776217\pi$
$644$		0			0
$645$	15.3521	−	28.0584i	0.604488	−	1.10480i
$646$	−26.3969	+	0.0911138i	−1.03857	+	0.00358482i
$647$	−4.60847	−	1.23483i	−0.181178	−	0.0485464i	0.167090	−	0.985942i	$-0.446563\pi$
$647$	−4.60847	−	1.23483i	−0.181178	−	0.0485464i	−0.348267	+	0.937395i	$0.613230\pi$
$648$	−6.73652	+	26.2243i	−0.264635	+	1.03019i
$649$	−9.11081	−	5.26013i	−0.357630	−	0.206478i
$650$	25.4859	+	13.0825i	0.999640	+	0.513140i
$651$		0			0
$652$	−7.39650	−	26.8610i	−0.289669	−	1.05196i
$653$	2.16858	+	8.09326i	0.0848632	+	0.316714i	0.995288	−	0.0969603i	$-0.0309120\pi$
$653$	2.16858	+	8.09326i	0.0848632	+	0.316714i	−0.910425	+	0.413674i	$0.864245\pi$
$654$	−29.8909	−	17.1202i	−1.16883	−	0.669454i
$655$	25.9895	−	0.596523i	1.01549	−	0.0233081i
$656$	−31.9563	+	0.441239i	−1.24768	+	0.0172275i
$657$	0.662288	+	0.662288i	0.0258383	+	0.0258383i
$658$		0			0
$659$	−35.0426			−1.36507			−0.682534	−	0.730854i	$-0.739122\pi$
$659$	−35.0426			−1.36507			−0.682534	+	0.730854i	$0.739122\pi$
$660$	11.6012	−	12.3153i	0.451575	−	0.479374i
$661$	9.52109	+	16.4910i	0.370328	+	0.641426i	0.989616	−	0.143737i	$-0.0459121\pi$
$661$	9.52109	+	16.4910i	0.370328	+	0.641426i	−0.619288	+	0.785164i	$0.712579\pi$
$662$	−19.5837	+	5.31995i	−0.761141	+	0.206766i
$663$	44.2904	−	11.8676i	1.72010	−	0.460899i
$664$	0.228479	+	22.0638i	0.00886670	+	0.856241i
$665$		0			0
$666$	1.38640	−	0.806832i	0.0537219	−	0.0312641i
$667$	−4.13958	−	15.4491i	−0.160285	−	0.598193i
$668$	28.2507	+	27.8633i	1.09305	+	1.07806i
$669$	−28.8542	+	16.6590i	−1.11557	+	0.644074i
$670$	17.1956	−	31.6869i	0.664323	−	1.22417i
$671$			3.56577i			0.137655i
$672$		0			0
$673$	−25.9196	+	25.9196i	−0.999127	+	0.999127i	−1.00000		0.000872915i	$-0.999722\pi$
$673$	−25.9196	+	25.9196i	−0.999127	+	0.999127i	0.000872915		1.00000i	$0.499722\pi$
$674$	0.124954		0.000431300i	0.00481303		1.66131e-5i
$675$	−7.57744	−	23.8442i	−0.291656	−	0.917765i
$676$	−6.82724	+	0.0471315i	−0.262586	+	0.00181275i
$677$	13.2916	−	3.56148i	0.510838	−	0.136879i	0.00581271	−	0.999983i	$-0.498150\pi$
$677$	13.2916	−	3.56148i	0.510838	−	0.136879i	0.505026	+	0.863104i	$0.331483\pi$
$678$	26.7447	+	7.06737i	1.02712	+	0.271421i
$679$		0			0
$680$	−18.8279	+	35.2736i	−0.722018	+	1.35268i
$681$	−4.98184	+	8.62881i	−0.190905	+	0.330657i
$682$	4.71150	+	17.3439i	0.180413	+	0.664132i
$683$	2.14974	−	8.02293i	0.0822574	−	0.306989i	−0.912523	−	0.409025i	$-0.865869\pi$
$683$	2.14974	−	8.02293i	0.0822574	−	0.306989i	0.994781	+	0.102036i	$0.0325357\pi$
$684$	0.612158	+	1.04359i	0.0234065	+	0.0399025i
$685$	−13.4041	−	45.7944i	−0.512145	−	1.74971i
$686$		0			0
$687$	10.3937	−	10.3937i	0.396546	−	0.396546i
$688$	−22.9085	−	22.2845i	−0.873379	−	0.849589i
$689$	−2.78453	+	1.60765i	−0.106082	+	0.0612465i
$690$	30.6984	+	7.36289i	1.16867	+	0.280300i
$691$	7.15943	+	4.13350i	0.272357	+	0.157246i	0.629958	−	0.776629i	$-0.283072\pi$
$691$	7.15943	+	4.13350i	0.272357	+	0.157246i	−0.357601	+	0.933874i	$0.616405\pi$
$692$	−24.2081	+	6.66600i	−0.920255	+	0.253403i
$693$		0			0
$694$	−10.7834	+	6.27551i	−0.409331	+	0.238215i
$695$	−9.66218	+	5.87813i	−0.366507	+	0.222970i
$696$	−7.39136	−	12.5015i	−0.280169	−	0.473866i
$697$	13.0735	−	48.7908i	0.495192	−	1.84808i
$698$	3.79101	+	3.76493i	0.143492	+	0.142505i
$699$	−21.4649			−0.811878
$700$		0			0
$701$	−14.1462			−0.534296			−0.267148	−	0.963656i	$-0.586081\pi$
$701$	−14.1462			−0.534296			−0.267148	+	0.963656i	$0.586081\pi$
$702$	20.3424	+	20.2025i	0.767775	+	0.762493i
$703$	−4.23024	+	15.7875i	−0.159547	+	0.595436i
$704$	−8.75446	−	14.4630i	−0.329946	−	0.545093i
$705$	20.8132	−	12.6620i	0.783872	−	0.476880i
$706$	−1.51919	+	0.884111i	−0.0571755	+	0.0332740i
$707$		0			0
$708$	−4.73197	−	17.1845i	−0.177838	−	0.645834i
$709$	−10.2057	−	5.89228i	−0.383284	−	0.221289i	0.295962	−	0.955200i	$-0.404360\pi$
$709$	−10.2057	−	5.89228i	−0.383284	−	0.221289i	−0.679246	+	0.733910i	$0.737693\pi$
$710$	1.87864	+	0.450583i	0.0705040	+	0.0169101i
$711$	−2.52925	+	1.46026i	−0.0948542	+	0.0547641i
$712$	−1.58052	−	5.66334i	−0.0592325	−	0.212243i
$713$	−23.7125	+	23.7125i	−0.888039	+	0.888039i
$714$		0			0
$715$	−5.37797	−	18.3736i	−0.201125	−	0.687132i
$716$	5.96426	−	3.49859i	0.222895	−	0.130748i
$717$	−8.57362	+	31.9972i	−0.320188	+	1.19496i
$718$	6.48952	+	23.8891i	0.242187	+	0.891533i
$719$	−9.74435	+	16.8777i	−0.363403	+	0.629433i	−0.988519	−	0.151100i	$-0.951719\pi$
$719$	−9.74435	+	16.8777i	−0.363403	+	0.629433i	0.625115	+	0.780532i	$0.285052\pi$
$720$	1.83138	−	0.0673431i	0.0682516	−	0.00250973i
$721$		0			0
$722$	14.0597	+	3.71532i	0.523248	+	0.138270i
$723$	0.142433	−	0.0381648i	0.00529714	−	0.00141936i
$724$	−0.222230	−	32.1912i	−0.00825913	−	1.19638i
$725$	12.7355	+	6.59307i	0.472983	+	0.244860i
$726$	16.5426	−	0.0571000i	0.613955	−	0.00211918i
$727$	21.7062	−	21.7062i	0.805039	−	0.805039i	−0.178839	−	0.983878i	$-0.557234\pi$
$727$	21.7062	−	21.7062i	0.805039	−	0.805039i	0.983878	+	0.178839i	$0.0572342\pi$
$728$		0			0
$729$		−	24.9127i		−	0.922692i
$730$	−6.89479	+	12.7053i	−0.255188	+	0.470244i
$731$	43.7446	−	25.2560i	1.61795	−	0.934126i
$732$	−4.24230	+	4.30128i	−0.156800	+	0.158980i
$733$	6.04984	+	22.5783i	0.223456	+	0.833949i	0.983017	+	0.183513i	$0.0587469\pi$
$733$	6.04984	+	22.5783i	0.223456	+	0.833949i	−0.759561	+	0.650436i	$0.774586\pi$
$734$	19.0296	−	11.0745i	0.702395	−	0.408767i
$735$		0			0
$736$	15.2987	−	27.5868i	0.563916	−	1.01686i
$737$	−23.2717	+	6.23563i	−0.857224	+	0.229693i
$738$	−2.23419	+	0.606922i	−0.0822417	+	0.0223411i
$739$	−4.82260	−	8.35299i	−0.177402	−	0.307270i	0.763588	−	0.645704i	$-0.223436\pi$
$739$	−4.82260	−	8.35299i	−0.177402	−	0.307270i	−0.940990	+	0.338434i	$0.890103\pi$
$740$	18.0206	+	16.9756i	0.662451	+	0.624035i
$741$	21.4138			0.786657
$742$		0			0
$743$	−24.5711	−	24.5711i	−0.901426	−	0.901426i	0.0941337	−	0.995560i	$-0.469992\pi$
$743$	−24.5711	−	24.5711i	−0.901426	−	0.901426i	−0.995560	+	0.0941337i	$0.969992\pi$
$744$	−14.9512	+	26.5268i	−0.548137	+	0.972520i
$745$	16.8611	−	0.387004i	0.617742	−	0.0141787i
$746$	0.965548	+	0.553025i	0.0353512	+	0.0202477i
$747$	0.413697	+	1.54394i	0.0151364	+	0.0564897i
$748$	25.7614	−	7.09372i	0.941931	−	0.259372i
$749$		0			0
$750$	−23.4273	+	15.8867i	−0.855442	+	0.580100i
$751$	45.6939	+	26.3814i	1.66739	+	0.962671i	0.969035	+	0.246923i	$0.0794195\pi$
$751$	45.6939	+	26.3814i	1.66739	+	0.962671i	0.698359	+	0.715747i	$0.253914\pi$
$752$	−6.62464	−	23.4249i	−0.241576	−	0.854219i
$753$	−15.6969	−	4.20597i	−0.572027	−	0.153274i
$754$	−16.4332	+	0.0567221i	−0.598461	+	0.00206570i
$755$	−14.9557	+	27.3339i	−0.544292	+	0.994782i
$756$		0			0
$757$	−4.54052	−	4.54052i	−0.165028	−	0.165028i	0.619762	−	0.784790i	$-0.287229\pi$
$757$	−4.54052	−	4.54052i	−0.165028	−	0.165028i	−0.784790	+	0.619762i	$0.787229\pi$
$758$	9.11832	−	9.18148i	0.331192	−	0.333486i
$759$	−10.5484	−	18.2703i	−0.382882	−	0.663172i
$760$	−12.7568	+	13.6361i	−0.462739	+	0.494635i
$761$	5.96614	−	10.3337i	0.216272	−	0.374595i	−0.737393	−	0.675464i	$-0.763943\pi$
$761$	5.96614	−	10.3337i	0.216272	−	0.374595i	0.953665	+	0.300869i	$0.0972767\pi$
$762$	13.2993	+	3.51439i	0.481783	+	0.127313i
$763$		0			0
$764$	5.23957	−	9.22163i	0.189561	−	0.333627i
$765$	−0.685265	+	2.81424i	−0.0247758	+	0.101749i
$766$	−5.93426	+	10.3609i	−0.214413	+	0.374353i
$767$	−19.4813	−	5.22001i	−0.703430	−	0.188484i
$768$	6.64677	−	27.8617i	0.239845	−	1.00537i
$769$			29.2063i			1.05321i	0.850111	+	0.526603i	$0.176535\pi$
$769$			29.2063i			1.05321i	−0.850111	+	0.526603i	$0.823465\pi$
$770$		0			0
$771$			13.0464i			0.469854i
$772$	−11.2853	+	43.3110i	−0.406166	+	1.55880i
$773$	−34.7584	−	9.31348i	−1.25017	−	0.334982i	−0.427769	−	0.903888i	$-0.640700\pi$
$773$	−34.7584	−	9.31348i	−1.25017	−	0.334982i	−0.822403	+	0.568906i	$0.807367\pi$
$774$	−2.00897	−	1.15065i	−0.0722109	−	0.0413593i
$775$	−1.37955	−	30.0365i	−0.0495550	−	1.07894i
$776$	−0.0809921	−	7.82125i	−0.00290745	−	0.280767i
$777$		0			0
$778$	−10.3813	+	39.2855i	−0.372188	+	1.40845i
$779$	11.7948	−	20.4293i	0.422594	−	0.731955i
$780$	15.3723	−	28.5618i	0.550416	−	1.02268i
$781$	−0.645525	−	1.11808i	−0.0230987	−	0.0400081i
$782$	35.3757	+	35.1323i	1.26503	+	1.25633i
$783$	10.1484	+	10.1484i	0.362673	+	0.362673i
$784$		0			0
$785$	−5.01248	−	17.1249i	−0.178903	−	0.611213i
$786$	−0.101596	−	29.4338i	−0.00362381	−	1.04987i
$787$	−17.3841	−	4.65805i	−0.619675	−	0.166042i	−0.0646952	−	0.997905i	$-0.520608\pi$
$787$	−17.3841	−	4.65805i	−0.619675	−	0.166042i	−0.554980	+	0.831864i	$0.687274\pi$
$788$	10.5972	−	10.7445i	0.377510	−	0.382758i
$789$	−8.31986	−	4.80348i	−0.296195	−	0.171008i
$790$	−32.7029	−	31.0202i	−1.16352	−	1.10365i
$791$		0			0
$792$	−0.874910	−	0.856975i	−0.0310886	−	0.0304513i
$793$	1.76929	+	6.60307i	0.0628292	+	0.234482i
$794$	−17.9413	+	31.3245i	−0.636714	+	1.11166i
$795$	−0.0728996	−	3.17611i	−0.00258548	−	0.112645i
$796$	20.5042	−	12.0276i	0.726753	−	0.426307i
$797$	26.2293	+	26.2293i	0.929091	+	0.929091i	0.997647	−	0.0685567i	$-0.0218394\pi$
$797$	26.2293	+	26.2293i	0.929091	+	0.929091i	−0.0685567	+	0.997647i	$0.521839\pi$
$798$		0			0
$799$	38.4752			1.36116
$800$	9.03020	+	26.8040i	0.319266	+	0.947665i
$801$	−0.212967	−	0.368869i	−0.00752481	−	0.0130333i
$802$	9.70143	+	35.7127i	0.342569	+	1.26106i
$803$	9.33109	−	2.50026i	0.329287	−	0.0882322i
$804$	−35.4907	−	20.1652i	−1.25166	−	0.711171i
$805$		0			0
$806$	17.3305	+	29.7795i	0.610442	+	1.04894i
$807$	2.51025	+	9.36839i	0.0883651	+	0.329783i
$808$	0.888896	−	3.46034i	0.0312713	−	0.121734i
$809$	28.7418	−	16.5941i	1.01051	−	0.583418i	0.0991688	−	0.995071i	$-0.468382\pi$
$809$	28.7418	−	16.5941i	1.01051	−	0.583418i	0.911341	+	0.411653i	$0.135048\pi$
$810$	−29.0230	+	8.60397i	−1.01977	+	0.302313i
$811$			44.6901i			1.56928i	0.619950	+	0.784641i	$0.287153\pi$
$811$			44.6901i			1.56928i	−0.619950	+	0.784641i	$0.712847\pi$
$812$		0			0
$813$	10.3835	−	10.3835i	0.364164	−	0.364164i
$814$	−0.0571061	−	16.5444i	−0.00200157	−	0.579882i
$815$	21.5146	−	22.5255i	0.753625	−	0.789033i
$816$	39.5149	+	22.0922i	1.38330	+	0.773382i
$817$	22.7859	−	6.10546i	0.797178	−	0.213603i
$818$	−0.355925	+	1.34691i	−0.0124446	+	0.0470936i
$819$		0			0
$820$	−18.7815	−	30.3975i	−0.655878	−	1.06153i
$821$	3.13055	−	5.42227i	0.109257	−	0.189238i	−0.806213	−	0.591626i	$-0.798486\pi$
$821$	3.13055	−	5.42227i	0.109257	−	0.189238i	0.915469	+	0.402388i	$0.131820\pi$
$822$	−52.1361	+	14.1629i	−1.81845	+	0.493987i
$823$	−5.59854	+	20.8940i	−0.195153	+	0.728320i	0.797074	+	0.603881i	$0.206380\pi$
$823$	−5.59854	+	20.8940i	−0.195153	+	0.728320i	−0.992227	+	0.124439i	$0.960287\pi$
$824$	32.0205	+	18.0476i	1.11549	+	0.628717i
$825$	18.4769	+	4.05238i	0.643284	+	0.141086i
$826$		0			0
$827$	−2.73070	+	2.73070i	−0.0949558	+	0.0949558i	−0.752989	−	0.658033i	$-0.771389\pi$
$827$	−2.73070	+	2.73070i	−0.0949558	+	0.0949558i	0.658033	+	0.752989i	$0.271389\pi$
$828$	0.576186	−	2.21130i	0.0200238	−	0.0768481i
$829$	36.5986	−	21.1302i	1.27112	−	0.733883i	0.295924	−	0.955212i	$-0.404373\pi$
$829$	36.5986	−	21.1302i	1.27112	−	0.733883i	0.975199	+	0.221328i	$0.0710392\pi$
$830$	−21.0313	+	12.8943i	−0.730006	+	0.447569i
$831$	23.5075	+	13.5720i	0.815465	+	0.470809i
$832$	−23.3878	−	22.4386i	−0.810825	−	0.777917i
$833$		0			0
$834$	6.44088	+	11.0675i	0.223030	+	0.383238i
$835$	−10.4957	+	43.1036i	−0.363218	+	1.49166i
$836$	12.4784	−	0.0861440i	0.431574	−	0.00297935i
$837$	7.78823	−	29.0661i	0.269201	−	1.00467i
$838$	16.6739	−	16.7894i	0.575990	−	0.579980i
$839$	27.3666			0.944801			0.472400	−	0.881384i	$-0.343388\pi$
$839$	27.3666			0.944801			0.472400	+	0.881384i	$0.343388\pi$
$840$		0			0
$841$	20.7736			0.716330
$842$	35.3796	−	35.6247i	1.21926	−	1.22771i
$843$	−11.0084	+	41.0838i	−0.379149	+	1.41500i
$844$	−4.08850	+	0.0282248i	−0.140732	+	0.000971537i
$845$	−3.96732	−	6.52129i	−0.136480	−	0.224339i
$846$	−0.887001	−	1.52416i	−0.0304957	−	0.0524016i
$847$		0			0
$848$	−3.07740	−	0.779213i	−0.105678	−	0.0267583i
$849$	−36.7269	−	21.2043i	−1.26046	−	0.727729i
$850$	−44.6490	+	2.20516i	−1.53145	+	0.0756362i
$851$	26.7344	−	15.4351i	0.916442	−	0.529108i
$852$	0.551537	−	2.11671i	0.0188954	−	0.0725172i
$853$	15.4514	−	15.4514i	0.529044	−	0.529044i	−0.391243	−	0.920287i	$-0.627955\pi$
$853$	15.4514	−	15.4514i	0.529044	−	0.529044i	0.920287	+	0.391243i	$0.127955\pi$
$854$		0			0
$855$	−0.649284	+	1.18667i	−0.0222050	+	0.0405833i
$856$	26.8296	−	47.6019i	0.917017	−	1.62700i
$857$	4.58257	−	17.1024i	0.156537	−	0.584206i	−0.842431	−	0.538804i	$-0.818876\pi$
$857$	4.58257	−	17.1024i	0.156537	−	0.584206i	0.998969	−	0.0454021i	$-0.0144569\pi$
$858$	−20.9179	+	5.68240i	−0.714127	+	0.193994i
$859$	4.41256	−	7.64278i	0.150555	−	0.260768i	−0.780877	−	0.624685i	$-0.785227\pi$
$859$	4.41256	−	7.64278i	0.150555	−	0.260768i	0.931432	+	0.363917i	$0.118561\pi$
$860$	8.21376	−	34.7748i	0.280087	−	1.18581i
$861$		0			0
$862$	−0.378049	+	1.43063i	−0.0128764	+	0.0487276i
$863$	−30.4985	+	8.17206i	−1.03818	+	0.278180i	−0.737360	−	0.675500i	$-0.763928\pi$
$863$	−30.4985	+	8.17206i	−1.03818	+	0.278180i	−0.300822	+	0.953680i	$0.597261\pi$
$864$	0.488493	+	28.3019i	0.0166189	+	0.962850i
$865$	−20.3008	−	19.3898i	−0.690248	−	0.659273i
$866$	0.0638276	+	18.4917i	0.00216895	+	0.628374i
$867$	−29.0746	+	29.0746i	−0.987427	+	0.987427i
$868$		0			0
$869$			30.1223i			1.02183i
$870$	7.74460	−	14.2713i	0.262567	−	0.483842i
$871$	−40.0003	+	23.0942i	−1.35536	+	0.782517i
$872$	−37.2729	−	9.57471i	−1.26222	−	0.324240i
$873$	−0.146649	−	0.547301i	−0.00496331	−	0.0185233i
$874$	11.7114	+	20.1241i	0.396145	+	0.680707i
$875$		0			0
$876$	14.2305	+	8.08549i	0.480803	+	0.273183i
$877$	15.3977	−	4.12581i	0.519945	−	0.139319i	0.0107038	−	0.999943i	$-0.496593\pi$
$877$	15.3977	−	4.12581i	0.519945	−	0.139319i	0.509241	+	0.860624i	$0.329926\pi$
$878$	8.42739	+	31.0227i	0.284411	+	1.04697i
$879$	23.5552	+	40.7988i	0.794498	+	1.37611i
$880$	8.84292	−	16.7055i	0.298095	−	0.563144i
$881$	33.9704			1.14449			0.572245	−	0.820082i	$-0.306073\pi$
$881$	33.9704			1.14449			0.572245	+	0.820082i	$0.306073\pi$
$882$		0			0
$883$	−5.75604	−	5.75604i	−0.193706	−	0.193706i	0.603589	−	0.797295i	$-0.293737\pi$
$883$	−5.75604	−	5.75604i	−0.193706	−	0.193706i	−0.797295	+	0.603589i	$0.793737\pi$
$884$	44.1850	−	25.9186i	1.48610	−	0.871736i
$885$	13.7642	−	14.4108i	0.462677	−	0.484415i
$886$	16.4069	−	28.6454i	0.551199	−	0.962361i
$887$	−4.70474	−	17.5583i	−0.157970	−	0.589551i	−0.998833	−	0.0483029i	$-0.984619\pi$
$887$	−4.70474	−	17.5583i	−0.157970	−	0.589551i	0.840863	−	0.541248i	$-0.182048\pi$
$888$	19.6145	−	20.0250i	0.658219	−	0.671994i
$889$		0			0
$890$	4.52403	−	4.76943i	0.151646	−	0.159872i
$891$	17.5194	+	10.1148i	0.586923	+	0.338860i
$892$	−26.1377	+	26.5011i	−0.875156	+	0.887323i
$893$	17.3562	+	4.65057i	0.580801	+	0.155625i
$894$	−0.0659121	−	19.0956i	−0.00220443	−	0.638653i
$895$	6.78203	+	3.71077i	0.226698	+	0.124037i
$896$		0			0
$897$	−28.5989	−	28.5989i	−0.954890	−	0.954890i
$898$	18.1561	+	18.0311i	0.605875	+	0.601707i
$899$	8.62408	+	14.9374i	0.287629	+	0.498189i
$900$	1.11669	+	1.71789i	0.0372228	+	0.0572629i
$901$	2.50867	−	4.34515i	0.0835760	−	0.144758i
$902$	−6.10057	+	23.0861i	−0.203127	+	0.768683i
$903$		0			0
$904$	30.9026	−	0.320008i	1.02781	−	0.0106433i
$905$	30.7486	−	18.7063i	1.02212	−	0.621820i
$906$	30.6124	+	17.5335i	1.01703	+	0.582510i
$907$	43.7702	+	11.7282i	1.45337	+	0.389428i	0.897193	−	0.441639i	$-0.145603\pi$
$907$	43.7702	+	11.7282i	1.45337	+	0.389428i	0.556172	+	0.831067i	$0.312269\pi$
$908$	−2.80668	+	10.7716i	−0.0931431	+	0.357467i
$909$		−	0.258808i		−	0.00858412i
$910$		0			0
$911$		−	55.7310i		−	1.84645i	−0.384261	−	0.923225i	$-0.625544\pi$
$911$		−	55.7310i		−	1.84645i	0.384261	−	0.923225i	$-0.374456\pi$
$912$	15.1548	+	14.7420i	0.501826	+	0.488156i
$913$	15.9242	+	4.26687i	0.527013	+	0.141213i
$914$	12.7797	−	22.3126i	0.422715	−	0.738036i
$915$	−6.56270	−	1.59801i	−0.216956	−	0.0528287i
$916$	8.11234	−	14.2777i	0.268039	−	0.471748i
$917$		0			0
$918$	−43.2533	−	11.4298i	−1.42757	−	0.377240i
$919$	1.00568	−	1.74189i	0.0331743	−	0.0574596i	−0.848962	−	0.528455i	$-0.822772\pi$
$919$	1.00568	−	1.74189i	0.0331743	−	0.0574596i	0.882136	+	0.470995i	$0.156105\pi$
$920$	35.2488	−	1.17434i	1.16212	−	0.0387168i
$921$	−24.2959	−	42.0818i	−0.800579	−	1.38664i
$922$	−30.2755	+	30.4852i	−0.997069	+	1.00398i
$923$	−1.75015	−	1.75015i	−0.0576070	−	0.0576070i
$924$		0			0
$925$	−5.92970	+	27.0366i	−0.194967	+	0.888959i
$926$	40.3301	−	0.139207i	1.32533	−	0.00457462i
$927$	2.57193	+	0.689146i	0.0844731	+	0.0226345i
$928$	−11.6690	−	11.2730i	−0.383053	−	0.370054i
$929$	12.0757	+	6.97192i	0.396192	+	0.228741i	0.684839	−	0.728694i	$-0.259872\pi$
$929$	12.0757	+	6.97192i	0.396192	+	0.228741i	−0.288648	+	0.957435i	$0.593206\pi$
$930$	−34.0324	+	0.898669i	−1.11597	+	0.0294685i
$931$		0			0
$932$	−23.1197	+	6.36628i	−0.757310	+	0.208534i
$933$	6.41613	+	23.9453i	0.210055	+	0.783935i
$934$	−25.7365	−	14.7408i	−0.842124	−	0.482333i
$935$	21.6034	+	20.6339i	0.706506	+	0.674802i
$936$	−2.04537	−	1.15282i	−0.0668550	−	0.0376812i
$937$	10.0820	+	10.0820i	0.329363	+	0.329363i	0.852344	−	0.522981i	$-0.175180\pi$
$937$	10.0820	+	10.0820i	0.329363	+	0.329363i	−0.522981	+	0.852344i	$0.675180\pi$
$938$		0			0
$939$	42.1072			1.37412
$940$	18.6623	−	19.8112i	0.608698	−	0.646169i
$941$	8.57804	+	14.8576i	0.279636	+	0.484344i	0.971294	−	0.237881i	$-0.0764528\pi$
$941$	8.57804	+	14.8576i	0.279636	+	0.484344i	−0.691658	+	0.722225i	$0.743119\pi$
$942$	−19.4963	+	5.29622i	−0.635225	+	0.172560i
$943$	−43.0365	+	11.5316i	−1.40146	+	0.375520i
$944$	−10.1935	−	17.1059i	−0.331771	−	0.556748i
$945$		0			0
$946$	−20.6381	+	12.0106i	−0.671002	+	0.390497i
$947$	−7.87222	−	29.3795i	−0.255813	−	0.954707i	−0.967636	−	0.252348i	$-0.918797\pi$
$947$	−7.87222	−	29.3795i	−0.255813	−	0.954707i	0.711824	−	0.702358i	$-0.247870\pi$
$948$	−35.8374	+	36.3356i	−1.16394	+	1.18013i
$949$	16.0387	−	9.25992i	0.520637	−	0.300590i
$950$	−20.4077	−	4.40206i	−0.662113	−	0.142822i
$951$		−	1.47637i		−	0.0478746i
$952$		0			0
$953$	−36.7987	+	36.7987i	−1.19203	+	1.19203i	−0.215529	+	0.976497i	$0.569148\pi$
$953$	−36.7987	+	36.7987i	−1.19203	+	1.19203i	−0.976497	+	0.215529i	$0.930852\pi$
$954$	−0.229963		0.000793760i	−0.00744533		2.56989e-5i
$955$	11.8550	−	0.272101i	0.383618	−	0.00880499i
$956$	0.255474	+	37.0068i	0.00826263	+	1.19688i
$957$	−10.4812	+	2.80843i	−0.338809	+	0.0907836i
$958$	−38.1340	−	10.0770i	−1.23205	−	0.325574i
$959$		0			0
$960$	30.5420	−	9.63071i	0.985740	−	0.310830i
$961$	2.58192	−	4.47202i	0.0832878	−	0.144259i
$962$	−8.31486	−	30.6085i	−0.268082	−	0.986858i
$963$	1.02449	−	3.82344i	0.0330137	−	0.123209i
$964$	0.142094	−	0.0833512i	0.00457654	−	0.00268456i
$965$	−48.0250	+	14.0570i	−1.54598	+	0.452511i
$966$		0			0
$967$	2.22247	−	2.22247i	0.0714698	−	0.0714698i	−0.670468	−	0.741938i	$-0.733907\pi$
$967$	2.22247	−	2.22247i	0.0714698	−	0.0714698i	0.741938	+	0.670468i	$0.233907\pi$
$968$	17.8010	−	4.96788i	0.572146	−	0.159674i
$969$	−28.9386	+	16.7077i	−0.929642	+	0.536729i
$970$	7.45524	−	4.57084i	0.239373	−	0.146761i
$971$	28.5473	+	16.4818i	0.916127	+	0.528926i	0.882397	−	0.470505i	$-0.155928\pi$
$971$	28.5473	+	16.4818i	0.916127	+	0.528926i	0.0337295	+	0.999431i	$0.489262\pi$
$972$	1.12865	+	4.09879i	0.0362015	+	0.131469i
$973$		0			0
$974$	−4.75666	+	2.76820i	−0.152413	+	0.0886987i
$975$	36.2262	−	1.66384i	1.16017	−	0.0532855i
$976$	−3.29363	+	5.89110i	−0.105426	+	0.188569i
$977$	1.84795	−	6.89664i	0.0591211	−	0.220643i	−0.930044	−	0.367447i	$-0.880232\pi$
$977$	1.84795	−	6.89664i	0.0591211	−	0.220643i	0.989166	+	0.146804i	$0.0468986\pi$
$978$	−25.0244	−	24.8522i	−0.800192	−	0.794687i
$979$	−4.39307			−0.140403
$980$		0			0
$981$	−2.78774			−0.0890057
$982$	14.4648	+	14.3653i	0.461589	+	0.458414i
$983$	−8.85773	+	33.0575i	−0.282518	+	1.05437i	0.668116	+	0.744057i	$0.267101\pi$
$983$	−8.85773	+	33.0575i	−0.282518	+	1.05437i	−0.950634	+	0.310314i	$0.899566\pi$
$984$	−34.8251	+	20.5900i	−1.11018	+	0.656386i
$985$	16.3935	+	3.99181i	0.522341	+	0.127190i
$986$	22.1635	−	12.8983i	0.705830	−	0.410766i
$987$		0			0
$988$	23.0647	−	6.35113i	0.733784	−	0.202056i
$989$	−38.5854	−	22.2773i	−1.22695	−	0.708377i
$990$	0.319352	−	1.33149i	0.0101497	−	0.0423174i
$991$	27.9661	−	16.1462i	0.888373	−	0.512902i	0.0149631	−	0.999888i	$-0.495237\pi$
$991$	27.9661	−	16.1462i	0.888373	−	0.512902i	0.873410	+	0.486986i	$0.161904\pi$
$992$	−8.23620	+	33.0062i	−0.261500	+	1.04795i
$993$	−18.1648	+	18.1648i	−0.576444	+	0.576444i
$994$		0			0
$995$	23.3156	+	12.7571i	0.739154	+	0.404426i
$996$	14.1324	+	24.0924i	0.447803	+	0.763398i
$997$	6.83904	−	25.5236i	0.216594	−	0.808342i	−0.769005	−	0.639243i	$-0.779248\pi$
$997$	6.83904	−	25.5236i	0.216594	−	0.808342i	0.985599	−	0.169098i	$-0.0540856\pi$
$998$	−1.09380	−	4.02649i	−0.0346238	−	0.127456i
$999$	−13.8503	+	23.9894i	−0.438205	+	0.758993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.l.667.14		72
4.3	odd	2	inner	980.2.x.l.667.17		72
5.3	odd	4	inner	980.2.x.l.863.6		72
7.2	even	3		980.2.k.l.687.2		36
7.3	odd	6		980.2.x.k.67.11		72
7.4	even	3	inner	980.2.x.l.67.11		72
7.5	odd	6		140.2.k.a.127.2	yes	36
7.6	odd	2		980.2.x.k.667.14		72
20.3	even	4	inner	980.2.x.l.863.11		72
28.3	even	6		980.2.x.k.67.6		72
28.11	odd	6	inner	980.2.x.l.67.6		72
28.19	even	6		140.2.k.a.127.9	yes	36
28.23	odd	6		980.2.k.l.687.9		36
28.27	even	2		980.2.x.k.667.17		72
35.3	even	12		980.2.x.k.263.17		72
35.12	even	12		700.2.k.b.43.10		36
35.13	even	4		980.2.x.k.863.6		72
35.18	odd	12	inner	980.2.x.l.263.17		72
35.19	odd	6		700.2.k.b.407.17		36
35.23	odd	12		980.2.k.l.883.9		36
35.33	even	12		140.2.k.a.43.9	yes	36
140.3	odd	12		980.2.x.k.263.14		72
140.19	even	6		700.2.k.b.407.10		36
140.23	even	12		980.2.k.l.883.2		36
140.47	odd	12		700.2.k.b.43.17		36
140.83	odd	4		980.2.x.k.863.11		72
140.103	odd	12		140.2.k.a.43.2	✓	36
140.123	even	12	inner	980.2.x.l.263.14		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.2	✓	36	140.103	odd	12
140.2.k.a.43.9	yes	36	35.33	even	12
140.2.k.a.127.2	yes	36	7.5	odd	6
140.2.k.a.127.9	yes	36	28.19	even	6
700.2.k.b.43.10		36	35.12	even	12
700.2.k.b.43.17		36	140.47	odd	12
700.2.k.b.407.10		36	140.19	even	6
700.2.k.b.407.17		36	35.19	odd	6
980.2.k.l.687.2		36	7.2	even	3
980.2.k.l.687.9		36	28.23	odd	6
980.2.k.l.883.2		36	140.23	even	12
980.2.k.l.883.9		36	35.23	odd	12
980.2.x.k.67.6		72	28.3	even	6
980.2.x.k.67.11		72	7.3	odd	6
980.2.x.k.263.14		72	140.3	odd	12
980.2.x.k.263.17		72	35.3	even	12
980.2.x.k.667.14		72	7.6	odd	2
980.2.x.k.667.17		72	28.27	even	2
980.2.x.k.863.6		72	35.13	even	4
980.2.x.k.863.11		72	140.83	odd	4
980.2.x.l.67.6		72	28.11	odd	6	inner
980.2.x.l.67.11		72	7.4	even	3	inner
980.2.x.l.263.14		72	140.123	even	12	inner
980.2.x.l.263.17		72	35.18	odd	12	inner
980.2.x.l.667.14		72	1.1	even	1	trivial
980.2.x.l.667.17		72	4.3	odd	2	inner
980.2.x.l.863.6		72	5.3	odd	4	inner
980.2.x.l.863.11		72	20.3	even	4	inner

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.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.996542 - 1.00345i) q^{2} +(0.463343 - 1.72922i) q^{3} +(-0.0138066 - 1.99995i) q^{4} +(1.91033 - 1.16218i) q^{5} +(-1.27344 - 2.18818i) q^{6} +(-2.02060 - 1.97918i) q^{8} +(-0.177443 - 0.102447i) q^{9} +O(q^{10})\)	\(q+(0.996542 - 1.00345i) q^{2} +(0.463343 - 1.72922i) q^{3} +(-0.0138066 - 1.99995i) q^{4} +(1.91033 - 1.16218i) q^{5} +(-1.27344 - 2.18818i) q^{6} +(-2.02060 - 1.97918i) q^{8} +(-0.177443 - 0.102447i) q^{9} +(0.737542 - 3.07507i) q^{10} +(-1.83014 + 1.05663i) q^{11} +(-3.46476 - 0.902790i) q^{12} +(-2.86476 + 2.86476i) q^{13} +(-1.12452 - 3.84186i) q^{15} +(-3.99962 + 0.0552250i) q^{16} +(1.63626 - 6.10660i) q^{17} +(-0.279629 + 0.0759618i) q^{18} +(1.47623 - 2.55691i) q^{19} +(-2.35067 - 3.80452i) q^{20} +(-0.763541 + 2.88943i) q^{22} +(-5.38640 + 1.44328i) q^{23} +(-4.35868 + 2.57703i) q^{24} +(2.29870 - 4.44027i) q^{25} +(0.0197764 + 5.72949i) q^{26} +(3.53826 - 3.53826i) q^{27} +2.86818i q^{29} +(-4.97573 - 2.70019i) q^{30} +(5.20796 - 3.00682i) q^{31} +(-3.93037 + 4.06843i) q^{32} +(0.979169 + 3.65431i) q^{33} +(-4.49704 - 7.72739i) q^{34} +(-0.202439 + 0.356292i) q^{36} +(-5.34722 + 1.43278i) q^{37} +(-1.09459 - 4.02938i) q^{38} +(3.62644 + 6.28117i) q^{39} +(-6.16017 - 1.43259i) q^{40} +7.98984 q^{41} +(5.64967 + 5.64967i) q^{43} +(2.13849 + 3.64561i) q^{44} +(-0.458035 + 0.0105130i) q^{45} +(-3.91952 + 6.84325i) q^{46} +(1.57515 + 5.87853i) q^{47} +(-1.75770 + 6.94181i) q^{48} +(-2.16482 - 6.73153i) q^{50} +(-9.80152 - 5.65891i) q^{51} +(5.76894 + 5.68983i) q^{52} +(0.766587 + 0.205406i) q^{53} +(-0.0244258 - 7.07649i) q^{54} +(-2.26818 + 4.14546i) q^{55} +(-3.73746 - 3.73746i) q^{57} +(2.87806 + 2.85826i) q^{58} +(2.48910 + 4.31124i) q^{59} +(-7.66802 + 2.30203i) q^{60} +(0.843662 - 1.46127i) q^{61} +(2.17278 - 8.22233i) q^{62} +(0.165668 + 7.99828i) q^{64} +(-2.14328 + 8.80198i) q^{65} +(4.64268 + 2.65913i) q^{66} +(11.0122 + 2.95071i) q^{67} +(-12.2355 - 3.18813i) q^{68} +9.98301i q^{69} +0.610925i q^{71} +(0.155781 + 0.558196i) q^{72} +(-4.41548 - 1.18312i) q^{73} +(-3.89101 + 6.79348i) q^{74} +(-6.61312 - 6.03233i) q^{75} +(-5.13407 - 2.91709i) q^{76} +(9.91671 + 2.62052i) q^{78} +(7.12694 - 12.3442i) q^{79} +(-7.57640 + 4.75376i) q^{80} +(-4.78635 - 8.29020i) q^{81} +(7.96221 - 8.01737i) q^{82} +(-5.51624 - 5.51624i) q^{83} +(-3.97115 - 13.5672i) q^{85} +(11.2993 - 0.0390015i) q^{86} +(4.95971 + 1.32895i) q^{87} +(5.78927 + 1.48715i) q^{88} +(1.80030 + 1.03940i) q^{89} +(-0.445902 + 0.470090i) q^{90} +(2.96086 + 10.7526i) q^{92} +(-2.78638 - 10.3989i) q^{93} +(7.46849 + 4.27763i) q^{94} +(-0.151490 - 6.60017i) q^{95} +(5.21411 + 8.68157i) q^{96} +(1.95542 + 1.95542i) q^{97} +0.432994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 16 q^{6}+O(q^{10}) \) 72 * q + 16 * q^6	\( 72 q + 16 q^{6} - 16 q^{10} - 16 q^{12} + 8 q^{13} + 8 q^{16} - 20 q^{17} - 28 q^{18} - 40 q^{20} + 8 q^{22} + 20 q^{25} - 32 q^{26} + 4 q^{30} - 20 q^{37} - 36 q^{40} + 20 q^{45} - 16 q^{46} + 48 q^{48} + 80 q^{50} + 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} - 64 q^{61} - 80 q^{62} - 4 q^{65} + 32 q^{66} + 80 q^{68} - 80 q^{72} + 52 q^{73} - 16 q^{76} - 152 q^{78} - 20 q^{80} + 36 q^{81} + 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} + 32 q^{90} - 112 q^{92} - 32 q^{93} + 120 q^{96} - 40 q^{97}+O(q^{100}) \) 72 * q + 16 * q^6 - 16 * q^10 - 16 * q^12 + 8 * q^13 + 8 * q^16 - 20 * q^17 - 28 * q^18 - 40 * q^20 + 8 * q^22 + 20 * q^25 - 32 * q^26 + 4 * q^30 - 20 * q^37 - 36 * q^40 + 20 * q^45 - 16 * q^46 + 48 * q^48 + 80 * q^50 + 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 - 64 * q^61 - 80 * q^62 - 4 * q^65 + 32 * q^66 + 80 * q^68 - 80 * q^72 + 52 * q^73 - 16 * q^76 - 152 * q^78 - 20 * q^80 + 36 * q^81 + 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 + 32 * q^90 - 112 * q^92 - 32 * q^93 + 120 * q^96 - 40 * q^97

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