LMFDB - Embedded newform 975.2.bn.d.257.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(218,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.218"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,2,0,0,-12,12,0,0,0,0,12,24,0,0,16,0,0,0,0,0,-20,0,0,0,0, 32,36,0,0,0,0,-30,0,0,-4,84,0,0,0,0,48,-8,0,0,0,0,28,0,0,-16,-28,0,0,0, 0,0,-84,0,0,-32,0,-90,0,0,0,-36,0,0,0,0,-90,0,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(76)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			257.13
Character	$\chi$	$=$	975.257
Dual form			975.2.bn.d.368.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0288234 - 0.107570i) q^{2} +(-0.895534 - 1.48257i) q^{3} +(1.72131 + 0.993799i) q^{4} +(-0.185293 + 0.0536002i) q^{6} +(1.03453 + 3.86093i) q^{7} +(0.314011 - 0.314011i) q^{8} +(-1.39604 + 2.65539i) q^{9} +(-2.60494 - 4.51189i) q^{11} +(-0.0681144 - 3.44195i) q^{12} +(3.33885 - 1.36091i) q^{13} +0.445140 q^{14} +(1.96287 + 3.39979i) q^{16} +(0.878092 + 3.27708i) q^{17} +(0.245402 + 0.226709i) q^{18} +(0.210416 - 0.364452i) q^{19} +(4.79764 - 4.99136i) q^{21} +(-0.560429 + 0.150166i) q^{22} +(-0.705071 + 2.63136i) q^{23} +(-0.746752 - 0.184336i) q^{24} +(-0.0501565 - 0.398387i) q^{26} +(5.18700 - 0.308267i) q^{27} +(-2.05624 + 7.67398i) q^{28} +(2.52506 + 4.37354i) q^{29} +4.23553i q^{31} +(1.28019 - 0.343025i) q^{32} +(-4.35638 + 7.90256i) q^{33} +0.377826 q^{34} +(-5.04193 + 3.18337i) q^{36} +(5.74223 + 1.53863i) q^{37} +(-0.0331393 - 0.0331393i) q^{38} +(-5.00770 - 3.73134i) q^{39} +(0.973131 + 1.68551i) q^{41} +(-0.398638 - 0.659952i) q^{42} +(0.242554 + 0.905224i) q^{43} -10.3551i q^{44} +(0.262734 + 0.151689i) q^{46} +(-1.29449 - 1.29449i) q^{47} +(3.28262 - 5.95473i) q^{48} +(-7.77434 + 4.48852i) q^{49} +(4.07215 - 4.23657i) q^{51} +(7.09967 + 0.975600i) q^{52} +(2.45762 + 2.45762i) q^{53} +(0.116347 - 0.566853i) q^{54} +(1.53723 + 0.887520i) q^{56} +(-0.728761 + 0.0144218i) q^{57} +(0.543244 - 0.145562i) q^{58} +(7.83433 + 4.52315i) q^{59} +(2.65934 - 4.60611i) q^{61} +(0.455618 + 0.122082i) q^{62} +(-11.6965 - 2.64291i) q^{63} +7.70388i q^{64} +(0.724516 + 0.696396i) q^{66} +(-7.41523 - 1.98691i) q^{67} +(-1.74529 + 6.51352i) q^{68} +(4.53259 - 1.31116i) q^{69} +(6.09876 - 10.5634i) q^{71} +(0.395450 + 1.27219i) q^{72} +(-1.29733 - 1.29733i) q^{73} +(0.331021 - 0.573345i) q^{74} +(0.724384 - 0.418223i) q^{76} +(14.7252 - 14.7252i) q^{77} +(-0.545721 + 0.431130i) q^{78} -2.49102i q^{79} +(-5.10216 - 7.41404i) q^{81} +(0.209360 - 0.0560979i) q^{82} +(9.55183 - 9.55183i) q^{83} +(13.2186 - 3.82379i) q^{84} +0.104367 q^{86} +(4.22280 - 7.66024i) q^{87} +(-2.23476 - 0.598803i) q^{88} +(-3.74597 + 2.16273i) q^{89} +(8.70853 + 11.4832i) q^{91} +(-3.82869 + 3.82869i) q^{92} +(6.27948 - 3.79307i) q^{93} +(-0.176560 + 0.101937i) q^{94} +(-1.65501 - 1.59078i) q^{96} +(0.740590 + 2.76392i) q^{97} +(0.258749 + 0.965663i) q^{98} +(15.6174 - 0.618364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0288234	−	0.107570i	0.0203812	−	0.0760637i	−0.954986	−	0.296650i	$-0.904130\pi$
$2$	0.0288234	−	0.107570i	0.0203812	−	0.0760637i	0.975367	+	0.220586i	$0.0707971\pi$
$3$	−0.895534	−	1.48257i	−0.517037	−	0.855963i
$3$	−0.895534	−	1.48257i	−0.517037	−	0.855963i
$4$	1.72131	+	0.993799i	0.860655	+	0.496899i
$5$		0			0
$5$		0			0
$6$	−0.185293	+	0.0536002i	−0.0756456	+	0.0218822i
$7$	1.03453	+	3.86093i	0.391017	+	1.45929i	0.828460	+	0.560048i	$0.189217\pi$
$7$	1.03453	+	3.86093i	0.391017	+	1.45929i	−0.437443	+	0.899246i	$0.644116\pi$
$8$	0.314011	−	0.314011i	0.111020	−	0.111020i
$9$	−1.39604	+	2.65539i	−0.465346	+	0.885129i
$10$		0			0
$11$	−2.60494	−	4.51189i	−0.785419	−	1.36039i	−0.928748	−	0.370711i	$-0.879114\pi$
$11$	−2.60494	−	4.51189i	−0.785419	−	1.36039i	0.143329	−	0.989675i	$-0.454219\pi$
$12$	−0.0681144	−	3.44195i	−0.0196629	−	0.993604i
$13$	3.33885	−	1.36091i	0.926031	−	0.377448i
$13$	3.33885	−	1.36091i	0.926031	−	0.377448i
$14$	0.445140			0.118969
$15$		0			0
$16$	1.96287	+	3.39979i	0.490718	+	0.849948i
$17$	0.878092	+	3.27708i	0.212969	+	0.794809i	0.986872	+	0.161506i	$0.0516350\pi$
$17$	0.878092	+	3.27708i	0.212969	+	0.794809i	−0.773903	+	0.633304i	$0.781698\pi$
$18$	0.245402	+	0.226709i	0.0578419	+	0.0534359i
$19$	0.210416	−	0.364452i	0.0482728	−	0.0836110i	−0.840879	−	0.541223i	$-0.817962\pi$
$19$	0.210416	−	0.364452i	0.0482728	−	0.0836110i	0.889152	+	0.457612i	$0.151295\pi$
$20$		0			0
$21$	4.79764	−	4.99136i	1.04693	−	1.08920i
$22$	−0.560429	+	0.150166i	−0.119484	+	0.0320156i
$23$	−0.705071	+	2.63136i	−0.147017	+	0.548676i	0.852640	+	0.522499i	$0.175000\pi$
$23$	−0.705071	+	2.63136i	−0.147017	+	0.548676i	−0.999657	+	0.0261774i	$0.991667\pi$
$24$	−0.746752	−	0.184336i	−0.152430	−	0.0376275i
$25$		0			0
$26$	−0.0501565	−	0.398387i	−0.00983649	−	0.0781302i
$27$	5.18700	−	0.308267i	0.998239	−	0.0593259i
$28$	−2.05624	+	7.67398i	−0.388592	+	1.45024i
$29$	2.52506	+	4.37354i	0.468892	+	0.812146i	0.999368	−	0.0355548i	$-0.0113198\pi$
$29$	2.52506	+	4.37354i	0.468892	+	0.812146i	−0.530475	+	0.847700i	$0.677987\pi$
$30$		0			0
$31$			4.23553i			0.760724i	0.924838	+	0.380362i	$0.124201\pi$
$31$			4.23553i			0.760724i	−0.924838	+	0.380362i	$0.875799\pi$
$32$	1.28019	−	0.343025i	0.226307	−	0.0606389i
$33$	−4.35638	+	7.90256i	−0.758349	+	1.37566i
$34$	0.377826			0.0647967
$35$		0			0
$36$	−5.04193	+	3.18337i	−0.840322	+	0.530561i
$37$	5.74223	+	1.53863i	0.944017	+	0.252949i	0.697822	−	0.716272i	$-0.254153\pi$
$37$	5.74223	+	1.53863i	0.944017	+	0.252949i	0.246195	+	0.969220i	$0.420820\pi$
$38$	−0.0331393	−	0.0331393i	−0.00537590	−	0.00537590i
$39$	−5.00770	−	3.73134i	−0.801874	−	0.597493i
$40$		0			0
$41$	0.973131	+	1.68551i	0.151978	+	0.263233i	0.931954	−	0.362576i	$-0.118103\pi$
$41$	0.973131	+	1.68551i	0.151978	+	0.263233i	−0.779977	+	0.625808i	$0.784769\pi$
$42$	−0.398638	−	0.659952i	−0.0615112	−	0.101833i
$43$	0.242554	+	0.905224i	0.0369892	+	0.138045i	0.981951	−	0.189135i	$-0.0605683\pi$
$43$	0.242554	+	0.905224i	0.0369892	+	0.138045i	−0.944962	+	0.327180i	$0.893902\pi$
$44$		−	10.3551i		−	1.56110i
$45$		0			0
$46$	0.262734	+	0.151689i	0.0387380	+	0.0223654i
$47$	−1.29449	−	1.29449i	−0.188821	−	0.188821i	0.606365	−	0.795186i	$-0.292627\pi$
$47$	−1.29449	−	1.29449i	−0.188821	−	0.188821i	−0.795186	+	0.606365i	$0.792627\pi$
$48$	3.28262	−	5.95473i	0.473805	−	0.859491i
$49$	−7.77434	+	4.48852i	−1.11062	+	0.641217i
$50$		0			0
$51$	4.07215	−	4.23657i	0.570215	−	0.593239i
$52$	7.09967	+	0.975600i	0.984547	+	0.135291i
$53$	2.45762	+	2.45762i	0.337580	+	0.337580i	0.855456	−	0.517876i	$-0.173277\pi$
$53$	2.45762	+	2.45762i	0.337580	+	0.337580i	−0.517876	+	0.855456i	$0.673277\pi$
$54$	0.116347	−	0.566853i	0.0158328	−	0.0771389i
$55$		0			0
$56$	1.53723	+	0.887520i	0.205421	+	0.118600i
$57$	−0.728761	+	0.0144218i	−0.0965268	+	0.00191022i
$58$	0.543244	−	0.145562i	0.0713314	−	0.0191132i
$59$	7.83433	+	4.52315i	1.01994	+	0.588865i	0.914088	−	0.405517i	$-0.132908\pi$
$59$	7.83433	+	4.52315i	1.01994	+	0.588865i	0.105856	+	0.994381i	$0.466242\pi$
$60$		0			0
$61$	2.65934	−	4.60611i	0.340493	−	0.589752i	−0.644031	−	0.764999i	$-0.722739\pi$
$61$	2.65934	−	4.60611i	0.340493	−	0.589752i	0.984524	+	0.175248i	$0.0560726\pi$
$62$	0.455618	+	0.122082i	0.0578635	+	0.0155045i
$63$	−11.6965	−	2.64291i	−1.47362	−	0.332976i
$64$			7.70388i			0.962986i
$65$		0			0
$66$	0.724516	+	0.696396i	0.0891817	+	0.0857205i
$67$	−7.41523	−	1.98691i	−0.905915	−	0.242739i	−0.224360	−	0.974506i	$-0.572029\pi$
$67$	−7.41523	−	1.98691i	−0.905915	−	0.242739i	−0.681555	+	0.731767i	$0.738696\pi$
$68$	−1.74529	+	6.51352i	−0.211648	+	0.789881i
$69$	4.53259	−	1.31116i	0.545660	−	0.157845i
$70$		0			0
$71$	6.09876	−	10.5634i	0.723789	−	1.25364i	−0.235681	−	0.971830i	$-0.575732\pi$
$71$	6.09876	−	10.5634i	0.723789	−	1.25364i	0.959470	−	0.281809i	$-0.0909346\pi$
$72$	0.395450	+	1.27219i	0.0466043	+	0.149929i
$73$	−1.29733	−	1.29733i	−0.151841	−	0.151841i	0.627099	−	0.778940i	$-0.284242\pi$
$73$	−1.29733	−	1.29733i	−0.151841	−	0.151841i	−0.778940	+	0.627099i	$0.784242\pi$
$74$	0.331021	−	0.573345i	0.0384804	−	0.0666500i
$75$		0			0
$76$	0.724384	−	0.418223i	0.0830925	−	0.0479735i
$77$	14.7252	−	14.7252i	1.67809	−	1.67809i
$78$	−0.545721	+	0.431130i	−0.0617907	+	0.0488159i
$79$		−	2.49102i		−	0.280262i	−0.990133	−	0.140131i	$-0.955248\pi$
$79$		−	2.49102i		−	0.280262i	0.990133	−	0.140131i	$-0.0447523\pi$
$80$		0			0
$81$	−5.10216	−	7.41404i	−0.566907	−	0.823782i
$82$	0.209360	−	0.0560979i	0.0231200	−	0.00619497i
$83$	9.55183	−	9.55183i	1.04845	−	1.04845i	0.0496844	−	0.998765i	$-0.484178\pi$
$83$	9.55183	−	9.55183i	1.04845	−	1.04845i	0.998765	−	0.0496844i	$-0.0158216\pi$
$84$	13.2186	−	3.82379i	1.44227	−	0.417210i
$85$		0			0
$86$	0.104367			0.0112541
$87$	4.22280	−	7.66024i	0.452732	−	0.821264i
$88$	−2.23476	−	0.598803i	−0.238227	−	0.0638326i
$89$	−3.74597	+	2.16273i	−0.397072	+	0.229249i	−0.685220	−	0.728336i	$-0.740294\pi$
$89$	−3.74597	+	2.16273i	−0.397072	+	0.229249i	0.288148	+	0.957586i	$0.406960\pi$
$90$		0			0
$91$	8.70853	+	11.4832i	0.912901	+	1.20376i
$92$	−3.82869	+	3.82869i	−0.399168	+	0.399168i
$93$	6.27948	−	3.79307i	0.651152	−	0.393323i
$94$	−0.176560	+	0.101937i	−0.0182108	+	0.0105140i
$95$		0			0
$96$	−1.65501	−	1.59078i	−0.168914	−	0.162358i
$97$	0.740590	+	2.76392i	0.0751955	+	0.280633i	0.993278	−	0.115757i	$-0.0369294\pi$
$97$	0.740590	+	2.76392i	0.0751955	+	0.280633i	−0.918082	+	0.396390i	$0.870263\pi$
$98$	0.258749	+	0.965663i	0.0261376	+	0.0975467i
$99$	15.6174	−	0.618364i	1.56961	−	0.0621479i
$100$		0			0
$101$	−2.39453	+	1.38248i	−0.238265	+	0.137562i	−0.614379	−	0.789011i	$-0.710593\pi$
$101$	−2.39453	+	1.38248i	−0.238265	+	0.137562i	0.376114	+	0.926573i	$0.377260\pi$
$102$	−0.338357	−	0.560155i	−0.0335023	−	0.0554636i
$103$	−0.0455864	+	0.0455864i	−0.00449176	+	0.00449176i	−0.709349	−	0.704857i	$-0.751011\pi$
$103$	−0.0455864	+	0.0455864i	−0.00449176	+	0.00449176i	0.704857	+	0.709349i	$0.251011\pi$
$104$	0.621096	−	1.47578i	0.0609035	−	0.144712i
$105$		0			0
$106$	0.335204	−	0.193530i	0.0325579	−	0.0187973i
$107$	−16.4075	−	4.39639i	−1.58618	−	0.425015i	−0.645346	−	0.763890i	$-0.723287\pi$
$107$	−16.4075	−	4.39639i	−1.58618	−	0.425015i	−0.940831	+	0.338875i	$0.889954\pi$
$108$	9.23479	+	4.62421i	0.888618	+	0.444965i
$109$	4.73152			0.453198			0.226599	−	0.973988i	$-0.427239\pi$
$109$	4.73152			0.453198			0.226599	+	0.973988i	$0.427239\pi$
$110$		0			0
$111$	−2.86124	−	9.89116i	−0.271577	−	0.938827i
$112$	−11.0957	+	11.0957i	−1.04845	+	1.04845i
$113$	−2.72351	+	0.729762i	−0.256206	+	0.0686502i	−0.384636	−	0.923068i	$-0.625673\pi$
$113$	−2.72351	+	0.729762i	−0.256206	+	0.0686502i	0.128430	+	0.991719i	$0.459006\pi$
$114$	−0.0194540	+	0.0788088i	−0.00182203	+	0.00738112i
$115$		0			0
$116$			10.0376i			0.931970i
$117$	−1.04742	+	10.7658i	−0.0968338	+	0.995301i
$118$	0.712369	−	0.712369i	0.0655789	−	0.0655789i
$119$	−11.7442	+	6.78050i	−1.07659	+	0.621567i
$120$		0			0
$121$	−8.07143	+	13.9801i	−0.733766	+	1.27092i
$122$	−0.418829	−	0.418829i	−0.0379190	−	0.0379190i
$123$	1.62742	−	2.95217i	0.146740	−	0.266188i
$124$	−4.20927	+	7.29067i	−0.378003	+	0.654721i
$125$		0			0
$126$	−0.621432	+	1.18202i	−0.0553616	+	0.105303i
$127$	−0.468909	+	1.74999i	−0.0416089	+	0.155287i	−0.983605	−	0.180338i	$-0.942281\pi$
$127$	−0.468909	+	1.74999i	−0.0416089	+	0.155287i	0.941996	+	0.335625i	$0.108947\pi$
$128$	3.38909	+	0.908103i	0.299556	+	0.0802657i
$129$	1.12484	−	1.17026i	0.0990370	−	0.103036i
$130$		0			0
$131$			20.2873i			1.77251i	0.463200	+	0.886254i	$0.346701\pi$
$131$			20.2873i			1.77251i	−0.463200	+	0.886254i	$0.653299\pi$
$132$	−15.3522	+	9.27339i	−1.33624	+	0.807145i
$133$	1.62481	+	0.435365i	0.140889	+	0.0377510i
$134$	−0.427464	+	0.740390i	−0.0369273	+	0.0639599i
$135$		0			0
$136$	1.30477	+	0.753310i	0.111883	+	0.0645958i
$137$	12.9118	−	3.45972i	1.10313	−	0.295584i	0.339093	−	0.940753i	$-0.389880\pi$
$137$	12.9118	−	3.45972i	1.10313	−	0.295584i	0.764040	+	0.645169i	$0.223213\pi$
$138$	−0.0103967	−	0.525365i	−0.000885026	−	0.0447220i
$139$	−17.9438	−	10.3598i	−1.52197	−	0.878710i	−0.999663	−	0.0259523i	$-0.991738\pi$
$139$	−17.9438	−	10.3598i	−1.52197	−	0.878710i	−0.522307	−	0.852758i	$-0.674928\pi$
$140$		0			0
$141$	−0.759913	+	3.07843i	−0.0639962	+	0.259251i
$142$	−0.960517	−	0.960517i	−0.0806048	−	0.0806048i
$143$	−14.8378	−	11.5194i	−1.24080	−	0.963304i
$144$	−11.7680	+	0.465948i	−0.980667	+	0.0388290i
$145$		0			0
$146$	−0.176948	+	0.102161i	−0.0146443	+	0.00845490i
$147$	13.6167	+	7.50639i	1.12309	+	0.619117i
$148$	8.35507	+	8.35507i	0.686783	+	0.686783i
$149$	−7.82540	−	4.51800i	−0.641082	−	0.370129i	0.143949	−	0.989585i	$-0.454020\pi$
$149$	−7.82540	−	4.51800i	−0.641082	−	0.370129i	−0.785031	+	0.619456i	$0.787353\pi$
$150$		0			0
$151$		−	11.7129i		−	0.953180i	−0.879126	−	0.476590i	$-0.841873\pi$
$151$		−	11.7129i		−	0.953180i	0.879126	−	0.476590i	$-0.158127\pi$
$152$	−0.0483689	−	0.180515i	−0.00392323	−	0.0146417i
$153$	−9.92777	−	2.24325i	−0.802613	−	0.181356i
$154$	−1.15956	−	2.00842i	−0.0934403	−	0.161843i
$155$		0			0
$156$	−4.91160	−	11.3994i	−0.393243	−	0.912686i
$157$	−11.2708	−	11.2708i	−0.899508	−	0.899508i	0.0958846	−	0.995392i	$-0.469432\pi$
$157$	−11.2708	−	11.2708i	−0.899508	−	0.899508i	−0.995392	+	0.0958846i	$0.969432\pi$
$158$	−0.267960	−	0.0717997i	−0.0213177	−	0.00571207i
$159$	1.44271	−	5.84448i	0.114415	−	0.463497i
$160$		0			0
$161$	−10.8889			−0.858167
$162$	−0.944592	+	0.335144i	−0.0742142	+	0.0263314i
$163$	12.3808	−	3.31744i	0.969742	−	0.259842i	0.261023	−	0.965333i	$-0.415940\pi$
$163$	12.3808	−	3.31744i	0.969742	−	0.259842i	0.708719	+	0.705491i	$0.249273\pi$
$164$			3.86839i			0.302070i
$165$		0			0
$166$	−0.752177	−	1.30281i	−0.0583803	−	0.101118i
$167$	−5.83706	+	21.7842i	−0.451685	+	1.68571i	0.245968	+	0.969278i	$0.420894\pi$
$167$	−5.83706	+	21.7842i	−0.451685	+	1.68571i	−0.697654	+	0.716435i	$0.745773\pi$
$168$	−0.0608301	−	3.07386i	−0.00469315	−	0.237153i
$169$	9.29585	−	9.08774i	0.715066	−	0.699057i
$170$		0			0
$171$	0.674012	+	1.06753i	0.0515430	+	0.0816357i
$172$	−0.482100	+	1.79922i	−0.0367598	+	0.137189i
$173$	−3.49516	+	0.936524i	−0.265732	+	0.0712026i	−0.389225	−	0.921143i	$-0.627257\pi$
$173$	−3.49516	+	0.936524i	−0.265732	+	0.0712026i	0.123493	+	0.992345i	$0.460590\pi$
$174$	−0.702299	−	0.675042i	−0.0532412	−	0.0511748i
$175$		0			0
$176$	10.2263	−	17.7125i	0.770838	−	1.33513i
$177$	−0.310014	−	15.6656i	−0.0233021	−	1.17750i
$178$	0.124675	+	0.465292i	0.00934476	+	0.0348751i
$179$	−2.91155	−	5.04296i	−0.217620	−	0.376928i	0.736460	−	0.676481i	$-0.236496\pi$
$179$	−2.91155	−	5.04296i	−0.217620	−	0.376928i	−0.954080	+	0.299553i	$0.903163\pi$
$180$		0			0
$181$	9.95426			0.739894			0.369947	−	0.929053i	$-0.379376\pi$
$181$	9.95426			0.739894			0.369947	+	0.929053i	$0.379376\pi$
$182$	1.48626	−	0.605795i	0.110169	−	0.0449045i
$183$	−9.21041	+	0.182270i	−0.680853	+	0.0134738i
$184$	0.604876	+	1.04768i	0.0445921	+	0.0772357i
$185$		0			0
$186$	−0.227025	−	0.784815i	−0.0166463	−	0.0575454i
$187$	12.4985	−	12.4985i	0.913978	−	0.913978i
$188$	−0.941755	−	3.51468i	−0.0686846	−	0.256334i
$189$	6.55632	+	19.7077i	0.476902	+	1.43353i
$190$		0			0
$191$	−19.8105	−	11.4376i	−1.43343	−	0.827594i	−0.436053	−	0.899921i	$-0.643624\pi$
$191$	−19.8105	−	11.4376i	−1.43343	−	0.827594i	−0.997381	+	0.0723271i	$0.976957\pi$
$192$	11.4216	−	6.89909i	0.824280	−	0.497899i
$193$	4.42994	−	16.5328i	0.318874	−	1.19005i	−0.601454	−	0.798908i	$-0.705412\pi$
$193$	4.42994	−	16.5328i	0.318874	−	1.19005i	0.920328	−	0.391147i	$-0.127922\pi$
$194$	0.318662			0.0228786
$195$		0			0
$196$	−17.8427			−1.27448
$197$	0.382929	−	1.42911i	0.0272826	−	0.101820i	−0.950942	−	0.309369i	$-0.899882\pi$
$197$	0.382929	−	1.42911i	0.0272826	−	0.101820i	0.978225	+	0.207549i	$0.0665488\pi$
$198$	0.383629	−	1.69779i	0.0272633	−	0.120657i
$199$	−20.6928	−	11.9470i	−1.46687	−	0.846899i	−0.467558	−	0.883962i	$-0.654866\pi$
$199$	−20.6928	−	11.9470i	−1.46687	−	0.846899i	−0.999313	+	0.0370636i	$0.988200\pi$
$200$		0			0
$201$	3.69487	+	12.7730i	0.260616	+	0.900935i
$202$	0.0796957	+	0.297429i	0.00560737	+	0.0209270i
$203$	−14.2737	+	14.2737i	−1.00181	+	1.00181i
$204$	11.2197	−	3.24556i	0.785538	−	0.227235i
$205$		0			0
$206$	0.00358979	+	0.00621770i	0.000250113	+	0.000433208i
$207$	−6.00297	−	5.54571i	−0.417236	−	0.385453i
$208$	11.1805	+	8.68011i	0.775231	+	0.601857i
$209$	−2.19249			−0.151658
$210$		0			0
$211$	1.53923	+	2.66603i	0.105965	+	0.183537i	0.914132	−	0.405416i	$-0.132873\pi$
$211$	1.53923	+	2.66603i	0.105965	+	0.183537i	−0.808167	+	0.588953i	$0.799540\pi$
$212$	1.78795	+	6.67270i	0.122797	+	0.458283i
$213$	−21.1226	+	0.418005i	−1.44730	+	0.0286413i
$214$	−0.945842	+	1.63825i	−0.0646565	+	0.111988i
$215$		0			0
$216$	1.53198	−	1.72558i	0.104238	−	0.117411i
$217$	−16.3531	+	4.38180i	−1.11012	+	0.297456i
$218$	0.136379	−	0.508972i	0.00923672	−	0.0344719i
$219$	−0.761582	+	3.08519i	−0.0514629	+	0.208478i
$220$		0			0
$221$	7.39163	+	9.74669i	0.497215	+	0.655633i
$222$	−1.14647	+	0.0226880i	−0.0769458	+	0.00152272i
$223$	1.49616	−	5.58375i	0.100190	−	0.373916i	−0.897565	−	0.440883i	$-0.854666\pi$
$223$	1.49616	−	5.58375i	0.100190	−	0.373916i	0.997755	+	0.0669668i	$0.0213322\pi$
$224$	2.64879	+	4.58784i	0.176980	+	0.306538i
$225$		0			0
$226$			0.314003i			0.0208872i
$227$	−14.1812	+	3.79984i	−0.941238	+	0.252204i	−0.696640	−	0.717421i	$-0.745323\pi$
$227$	−14.1812	+	3.79984i	−0.941238	+	0.252204i	−0.244598	+	0.969625i	$0.578656\pi$
$228$	−1.26876	−	0.699418i	−0.0840254	−	0.0463201i
$229$	3.60574			0.238274			0.119137	−	0.992878i	$-0.461987\pi$
$229$	3.60574			0.238274			0.119137	+	0.992878i	$0.461987\pi$
$230$		0			0
$231$	−35.0181	−	8.64423i	−2.30402	−	0.568749i
$232$	2.16624	+	0.580442i	0.142220	+	0.0381079i
$233$	7.88221	+	7.88221i	0.516381	+	0.516381i	0.916474	−	0.400093i	$-0.131022\pi$
$233$	7.88221	+	7.88221i	0.516381	+	0.516381i	−0.400093	+	0.916474i	$0.631022\pi$
$234$	1.12789	+	0.422979i	0.0737327	+	0.0276510i
$235$		0			0
$236$	8.99021	+	15.5715i	0.585213	+	1.01362i
$237$	−3.69312	+	2.23079i	−0.239894	+	0.144906i
$238$	0.390874	+	1.45876i	0.0253366	+	0.0945575i
$239$			0.0947772i			0.00613063i	0.999995	+	0.00306532i	$0.000975722\pi$
$239$			0.0947772i			0.00613063i	−0.999995	+	0.00306532i	$0.999024\pi$
$240$		0			0
$241$	9.34499	+	5.39533i	0.601964	+	0.347544i	0.769814	−	0.638269i	$-0.220349\pi$
$241$	9.34499	+	5.39533i	0.601964	+	0.347544i	−0.167850	+	0.985813i	$0.553682\pi$
$242$	1.27120	+	1.27120i	0.0817159	+	0.0817159i
$243$	−6.42267	+	14.2038i	−0.412015	+	0.911177i
$244$	9.15509	−	5.28569i	0.586095	−	0.338382i
$245$		0			0
$246$	−0.270658	−	0.260154i	−0.0172565	−	0.0165868i
$247$	0.206563	−	1.50321i	0.0131433	−	0.0956468i
$248$	1.33000	+	1.33000i	0.0844554	+	0.0844554i
$249$	−22.7153	−	5.60728i	−1.43952	−	0.355347i
$250$		0			0
$251$	18.5242	+	10.6949i	1.16923	+	0.675058i	0.953500	−	0.301394i	$-0.0974521\pi$
$251$	18.5242	+	10.6949i	1.16923	+	0.675058i	0.215735	+	0.976452i	$0.430785\pi$
$252$	−17.5068	−	16.1733i	−1.10282	−	1.01882i
$253$	13.7091	−	3.67333i	0.861882	−	0.230941i
$254$	0.174732	+	0.100881i	0.0109636	+	0.00632986i
$255$		0			0
$256$	−7.50851	+	13.0051i	−0.469282	+	0.812821i
$257$	−15.6729	−	4.19954i	−0.977648	−	0.261960i	−0.265594	−	0.964085i	$-0.585568\pi$
$257$	−15.6729	−	4.19954i	−0.977648	−	0.261960i	−0.712054	+	0.702125i	$0.752235\pi$
$258$	−0.0934638	−	0.154731i	−0.00581880	−	0.00963312i
$259$			23.7621i			1.47651i
$260$		0			0
$261$	−15.1385	+	0.599402i	−0.937051	+	0.0371021i
$262$	2.18231	+	0.584748i	0.134824	+	0.0361259i
$263$	5.94046	−	22.1701i	0.366304	−	1.36707i	−0.499340	−	0.866406i	$-0.666424\pi$
$263$	5.94046	−	22.1701i	0.366304	−	1.36707i	0.865644	−	0.500660i	$-0.166909\pi$
$264$	1.11354	+	3.84945i	0.0685336	+	0.236917i
$265$		0			0
$266$	0.0936648	−	0.162232i	0.00574296	−	0.00994709i
$267$	6.56105	+	3.61686i	0.401530	+	0.221348i
$268$	−10.7893	−	10.7893i	−0.659063	−	0.659063i
$269$	−1.73455	+	3.00433i	−0.105758	+	0.183177i	−0.914047	−	0.405607i	$-0.867060\pi$
$269$	−1.73455	+	3.00433i	−0.105758	+	0.183177i	0.808290	+	0.588785i	$0.200393\pi$
$270$		0			0
$271$	10.2881	−	5.93984i	0.624958	−	0.360819i	−0.153839	−	0.988096i	$-0.549164\pi$
$271$	10.2881	−	5.93984i	0.624958	−	0.360819i	0.778797	+	0.627277i	$0.215830\pi$
$272$	−9.41782	+	9.41782i	−0.571039	+	0.571039i
$273$	9.22583	−	23.1946i	0.558373	−	1.40380i
$274$		−	1.48865i		−	0.0899328i
$275$		0			0
$276$	9.10502	+	2.24758i	0.548058	+	0.135289i
$277$	−16.6029	+	4.44872i	−0.997570	+	0.267298i	−0.720427	−	0.693531i	$-0.756054\pi$
$277$	−16.6029	+	4.44872i	−0.997570	+	0.267298i	−0.277143	+	0.960829i	$0.589387\pi$
$278$	−1.63161	+	1.63161i	−0.0978575	+	0.0978575i
$279$	−11.2470	−	5.91296i	−0.673339	−	0.354000i
$280$		0			0
$281$	−22.1387			−1.32068			−0.660341	−	0.750966i	$-0.729588\pi$
$281$	−22.1387			−1.32068			−0.660341	+	0.750966i	$0.729588\pi$
$282$	0.309245	+	0.170475i	0.0184153	+	0.0101516i
$283$	−2.73331	−	0.732387i	−0.162478	−	0.0435359i	0.176663	−	0.984271i	$-0.443470\pi$
$283$	−2.73331	−	0.732387i	−0.162478	−	0.0435359i	−0.339141	+	0.940736i	$0.610136\pi$
$284$	20.9957	−	12.1219i	1.24587	−	0.719301i
$285$		0			0
$286$	−1.66682	+	1.26408i	−0.0985614	+	0.0747464i
$287$	−5.50091	+	5.50091i	−0.324708	+	0.324708i
$288$	−0.876324	+	3.87827i	−0.0516379	+	0.228529i
$289$	4.75421	−	2.74484i	0.279659	−	0.161461i
$290$		0			0
$291$	3.43448	−	3.57316i	0.201333	−	0.209462i
$292$	−0.943823	−	3.52240i	−0.0552331	−	0.206133i
$293$	−2.04676	−	7.63862i	−0.119573	−	0.446253i	0.880015	−	0.474946i	$-0.157532\pi$
$293$	−2.04676	−	7.63862i	−0.119573	−	0.446253i	−0.999588	+	0.0286927i	$0.990866\pi$
$294$	1.19995	−	1.24840i	0.0699823	−	0.0728080i
$295$		0			0
$296$	2.28627	−	1.31998i	0.132887	−	0.0767222i
$297$	−14.9027	−	22.6002i	−0.864742	−	1.31139i
$298$	−0.711557	+	0.711557i	−0.0412194	+	0.0412194i
$299$	1.22691	+	9.74525i	0.0709543	+	0.563583i
$300$		0			0
$301$	−3.24408	+	1.87297i	−0.186985	+	0.107956i
$302$	−1.25996	−	0.337605i	−0.0725024	−	0.0194270i
$303$	4.19402	+	2.31200i	0.240940	+	0.132821i
$304$	1.65208			0.0947533
$305$		0			0
$306$	−0.527460	+	1.00328i	−0.0301529	+	0.0573535i
$307$	10.6962	−	10.6962i	0.610465	−	0.610465i	−0.332602	−	0.943067i	$-0.607927\pi$
$307$	10.6962	−	10.6962i	0.610465	−	0.610465i	0.943067	+	0.332602i	$0.107927\pi$
$308$	39.9805	−	10.7127i	2.27810	−	0.610415i
$309$	0.108409	+	0.0267609i	0.00616719	+	0.00152238i
$310$		0			0
$311$		−	12.0194i		−	0.681560i	−0.940143	−	0.340780i	$-0.889309\pi$
$311$		−	12.0194i		−	0.681560i	0.940143	−	0.340780i	$-0.110691\pi$
$312$	−2.74416	+	0.400790i	−0.155357	+	0.0226903i
$313$	−16.5079	+	16.5079i	−0.933082	+	0.933082i	−0.997897	−	0.0648148i	$-0.979354\pi$
$313$	−16.5079	+	16.5079i	−0.933082	+	0.933082i	0.0648148	+	0.997897i	$0.479354\pi$
$314$	−1.53727	+	0.887541i	−0.0867530	+	0.0500869i
$315$		0			0
$316$	2.47557	−	4.28782i	0.139262	−	0.241209i
$317$	−0.778692	−	0.778692i	−0.0437357	−	0.0437357i	0.684901	−	0.728636i	$-0.259846\pi$
$317$	−0.778692	−	0.778692i	−0.0437357	−	0.0437357i	−0.728636	+	0.684901i	$0.759846\pi$
$318$	−0.587109	−	0.323651i	−0.0329234	−	0.0181494i
$319$	13.1553	−	22.7856i	0.736554	−	1.27575i
$320$		0			0
$321$	8.17556	+	28.2625i	0.456315	+	1.57746i
$322$	−0.313855	+	1.17132i	−0.0174905	+	0.0652753i
$323$	1.37910	+	0.369530i	0.0767354	+	0.0205612i
$324$	−1.41435	−	17.8324i	−0.0785748	−	0.990688i
$325$		0			0
$326$		−	1.42743i		−	0.0790581i
$327$	−4.23724	−	7.01482i	−0.234320	−	0.387921i
$328$	0.834844	+	0.223696i	0.0460965	+	0.0123515i
$329$	3.65874	−	6.33712i	0.201713	−	0.349377i
$330$		0			0
$331$	−24.3850	−	14.0787i	−1.34032	−	0.773834i	−0.353466	−	0.935448i	$-0.614997\pi$
$331$	−24.3850	−	14.0787i	−1.34032	−	0.773834i	−0.986854	+	0.161614i	$0.948330\pi$
$332$	25.9343	−	6.94906i	1.42333	−	0.381379i
$333$	−12.1020	+	13.0999i	−0.663186	+	0.717868i
$334$	2.17509	+	1.25579i	0.119016	+	0.0687138i
$335$		0			0
$336$	26.3867	+	6.51359i	1.43952	+	0.355345i
$337$	17.9435	+	17.9435i	0.977446	+	0.977446i	0.999751	−	0.0223051i	$-0.00710052\pi$
$337$	17.9435	+	17.9435i	0.977446	+	0.977446i	−0.0223051	+	0.999751i	$0.507101\pi$
$338$	−0.709634	−	1.26190i	−0.0385990	−	0.0686382i
$339$	3.52092	+	3.38427i	0.191230	+	0.183808i
$340$		0			0
$341$	19.1103	−	11.0333i	1.03488	−	0.597487i
$342$	0.134261	−	0.0417340i	0.00726002	−	0.00225672i
$343$	−5.58789	−	5.58789i	−0.301717	−	0.301717i
$344$	0.360415	+	0.208086i	0.0194323	+	0.0112192i
$345$		0			0
$346$			0.402969i			0.0216637i
$347$	0.129801	+	0.484424i	0.00696808	+	0.0260052i	0.969322	−	0.245793i	$-0.0790483\pi$
$347$	0.129801	+	0.484424i	0.00696808	+	0.0260052i	−0.962354	+	0.271798i	$0.912382\pi$
$348$	14.8815	−	8.98903i	0.797732	−	0.481863i
$349$	4.63210	+	8.02304i	0.247951	+	0.429463i	0.962957	−	0.269655i	$-0.0869095\pi$
$349$	4.63210	+	8.02304i	0.247951	+	0.429463i	−0.715006	+	0.699118i	$0.753576\pi$
$350$		0			0
$351$	16.8991	−	8.08829i	0.902007	−	0.431721i
$352$	−4.88250	−	4.88250i	−0.260238	−	0.260238i
$353$	−20.4549	−	5.48087i	−1.08870	−	0.291717i	−0.330547	−	0.943790i	$-0.607233\pi$
$353$	−20.4549	−	5.48087i	−1.08870	−	0.291717i	−0.758157	+	0.652072i	$0.773900\pi$
$354$	−1.69409	−	0.418187i	−0.0900398	−	0.0222264i
$355$		0			0
$356$	−8.59729			−0.455656
$357$	20.5699	+	11.3394i	1.08867	+	0.600145i
$358$	−0.626394	+	0.167842i	−0.0331059	+	0.00887071i
$359$		−	17.7610i		−	0.937391i	−0.883360	−	0.468695i	$-0.844724\pi$
$359$		−	17.7610i		−	0.937391i	0.883360	−	0.468695i	$-0.155276\pi$
$360$		0			0
$361$	9.41145	+	16.3011i	0.495339	+	0.857953i
$362$	0.286915	−	1.07078i	0.0150799	−	0.0562791i
$363$	27.9548	−	0.553211i	1.46724	−	0.0290361i
$364$	3.57812	+	28.4206i	0.187544	+	1.48964i
$365$		0			0
$366$	−0.245868	+	0.996021i	−0.0128518	+	0.0520628i
$367$	0.292041	−	1.08991i	0.0152444	−	0.0568929i	−0.957885	−	0.287153i	$-0.907291\pi$
$367$	0.292041	−	1.08991i	0.0152444	−	0.0568929i	0.973129	+	0.230260i	$0.0739578\pi$
$368$	−10.3300	+	2.76792i	−0.538490	+	0.144288i
$369$	−5.83421	+	0.231003i	−0.303717	+	0.0120255i
$370$		0			0
$371$	−6.94621	+	12.0312i	−0.360629	+	0.624628i
$372$	14.5785	−	0.288501i	0.755859	−	0.0149581i
$373$	4.61559	+	17.2256i	0.238986	+	0.891908i	0.976311	+	0.216370i	$0.0694218\pi$
$373$	4.61559	+	17.2256i	0.238986	+	0.891908i	−0.737325	+	0.675538i	$0.763912\pi$
$374$	−0.984215	−	1.70471i	−0.0508926	−	0.0881485i
$375$		0			0
$376$	−0.812968			−0.0419256
$377$	14.3828	+	11.1662i	0.740752	+	0.575089i
$378$	2.30894	−	0.137222i	0.118759	−	0.00705793i
$379$	−5.17481	−	8.96303i	−0.265812	−	0.460400i	0.701964	−	0.712212i	$-0.252307\pi$
$379$	−5.17481	−	8.96303i	−0.265812	−	0.460400i	−0.967776	+	0.251813i	$0.918973\pi$
$380$		0			0
$381$	3.01441	−	0.871986i	0.154433	−	0.0446732i
$382$	−1.80135	+	1.80135i	−0.0921650	+	0.0921650i
$383$	4.29989	+	16.0474i	0.219714	+	0.819985i	0.984454	+	0.175645i	$0.0562011\pi$
$383$	4.29989	+	16.0474i	0.219714	+	0.819985i	−0.764739	+	0.644340i	$0.777132\pi$
$384$	−1.68872	−	5.83780i	−0.0861769	−	0.297909i
$385$		0			0
$386$	−1.65075	−	0.953061i	−0.0840210	−	0.0485095i
$387$	−2.74234	−	0.619651i	−0.139401	−	0.0314986i
$388$	−1.47199	+	5.49356i	−0.0747292	+	0.278893i
$389$	24.1762			1.22578			0.612891	−	0.790167i	$-0.290006\pi$
$389$	24.1762			1.22578			0.612891	+	0.790167i	$0.290006\pi$
$390$		0			0
$391$	−9.24230			−0.467403
$392$	−1.03179	+	3.85068i	−0.0521130	+	0.194488i
$393$	30.0773	−	18.1680i	1.51720	−	0.916452i
$394$	−0.142693	−	0.0823836i	−0.00718875	−	0.00415043i
$395$		0			0
$396$	27.4969	+	14.4562i	1.38177	+	0.726450i
$397$	−2.21309	−	8.25936i	−0.111072	−	0.414525i	0.887891	−	0.460053i	$-0.152170\pi$
$397$	−2.21309	−	8.25936i	−0.111072	−	0.414525i	−0.998963	+	0.0455279i	$0.985503\pi$
$398$	−1.88158	+	1.88158i	−0.0943149	+	0.0943149i
$399$	−0.809609	−	2.79878i	−0.0405311	−	0.140114i
$400$		0			0
$401$	−13.7400	−	23.7983i	−0.686142	−	1.18843i	−0.973076	−	0.230482i	$-0.925970\pi$
$401$	−13.7400	−	23.7983i	−0.686142	−	1.18843i	0.286935	−	0.957950i	$-0.407364\pi$
$402$	1.48049	−	0.0292982i	0.0738401	−	0.00146126i
$403$	5.76418	+	14.1418i	0.287134	+	0.704454i
$404$	−5.49564			−0.273418
$405$		0			0
$406$	1.12401	+	1.94684i	0.0557835	+	0.0966199i
$407$	−8.01606	−	29.9163i	−0.397341	−	1.48290i
$408$	−0.0516315	−	2.60903i	−0.00255614	−	0.129166i
$409$	−18.6648	+	32.3284i	−0.922916	+	1.59854i	−0.128038	+	0.991769i	$0.540868\pi$
$409$	−18.6648	+	32.3284i	−0.922916	+	1.59854i	−0.794878	+	0.606769i	$0.792465\pi$
$410$		0			0
$411$	−16.6923	−	16.0444i	−0.823369	−	0.791414i
$412$	−0.123772	+	0.0331646i	−0.00609781	+	0.00163390i
$413$	−9.35870	+	34.9272i	−0.460512	+	1.71865i
$414$	−0.769580	+	0.485896i	−0.0378228	+	0.0238805i
$415$		0			0
$416$	3.80753	−	2.88753i	0.186680	−	0.141573i
$417$	0.710057	+	35.8805i	0.0347717	+	1.75708i
$418$	−0.0631949	+	0.235847i	−0.00309097	+	0.0115356i
$419$	−14.8413	−	25.7059i	−0.725046	−	1.25582i	−0.958955	−	0.283558i	$-0.908485\pi$
$419$	−14.8413	−	25.7059i	−0.725046	−	1.25582i	0.233909	−	0.972259i	$-0.424848\pi$
$420$		0			0
$421$		−	21.3437i		−	1.04023i	−0.854097	−	0.520114i	$-0.825889\pi$
$421$		−	21.3437i		−	1.04023i	0.854097	−	0.520114i	$-0.174111\pi$
$422$	0.331151	−	0.0887317i	0.0161202	−	0.00431939i
$423$	5.24452	−	1.63022i	0.254997	−	0.0792638i
$424$	1.54344			0.0749561
$425$		0			0
$426$	−0.563859	+	2.28421i	−0.0273191	+	0.110670i
$427$	20.5350	+	5.50234i	0.993760	+	0.266277i
$428$	−23.8734	−	23.8734i	−1.15396	−	1.15396i
$429$	−3.79065	+	32.3141i	−0.183014	+	1.56014i
$430$		0			0
$431$	−1.45407	−	2.51852i	−0.0700400	−	0.121313i	0.828879	−	0.559429i	$-0.188979\pi$
$431$	−1.45407	−	2.51852i	−0.0700400	−	0.121313i	−0.898919	+	0.438116i	$0.855646\pi$
$432$	11.2295	+	17.0296i	0.540277	+	0.819339i
$433$	−6.84446	−	25.5439i	−0.328924	−	1.22756i	−0.910308	−	0.413932i	$-0.864155\pi$
$433$	−6.84446	−	25.5439i	−0.328924	−	1.22756i	0.581384	−	0.813629i	$-0.302511\pi$
$434$			1.88541i			0.0905024i
$435$		0			0
$436$	8.14442	+	4.70218i	0.390047	+	0.225194i
$437$	0.810645	+	0.810645i	0.0387784	+	0.0387784i
$438$	0.309924	+	0.170849i	0.0148087	+	0.00816349i
$439$	23.2175	−	13.4046i	1.10811	−	0.639768i	0.169771	−	0.985484i	$-0.445697\pi$
$439$	23.2175	−	13.4046i	1.10811	−	0.639768i	0.938339	+	0.345716i	$0.112364\pi$
$440$		0			0
$441$	−1.06549	−	26.9100i	−0.0507376	−	1.28143i
$442$	1.26151	−	0.514187i	0.0600037	−	0.0244574i
$443$	19.3624	+	19.3624i	0.919937	+	0.919937i	0.997024	−	0.0770872i	$-0.0245620\pi$
$443$	19.3624	+	19.3624i	0.919937	+	0.919937i	−0.0770872	+	0.997024i	$0.524562\pi$
$444$	4.90474	−	19.8693i	0.232769	−	0.942953i
$445$		0			0
$446$	−0.557522	−	0.321885i	−0.0263994	−	0.0152417i
$447$	0.309661	+	15.6477i	0.0146465	+	0.740113i
$448$	−29.7442	+	7.96992i	−1.40528	+	0.376543i
$449$	3.02917	+	1.74889i	0.142956	+	0.0825354i	0.569772	−	0.821803i	$-0.307032\pi$
$449$	3.02917	+	1.74889i	0.142956	+	0.0825354i	−0.426816	+	0.904338i	$0.640365\pi$
$450$		0			0
$451$	5.06990	−	8.78132i	0.238732	−	0.413496i
$452$	−5.41324	−	1.45047i	−0.254617	−	0.0682245i
$453$	−17.3652	+	10.4893i	−0.815887	+	0.492829i
$454$			1.63500i			0.0767343i
$455$		0			0
$456$	−0.224311	+	0.233368i	−0.0105043	+	0.0109284i
$457$	33.6949	+	9.02853i	1.57618	+	0.422337i	0.937742	−	0.347334i	$-0.112913\pi$
$457$	33.6949	+	9.02853i	1.57618	+	0.422337i	0.638441	+	0.769671i	$0.279580\pi$
$458$	0.103930	−	0.387870i	0.00485631	−	0.0181240i
$459$	5.56488	+	16.7275i	0.259746	+	0.780775i
$460$		0			0
$461$	5.43399	−	9.41194i	0.253086	−	0.438358i	−0.711288	−	0.702901i	$-0.751888\pi$
$461$	5.43399	−	9.41194i	0.253086	−	0.438358i	0.964374	+	0.264543i	$0.0852211\pi$
$462$	−1.93920	+	3.51775i	−0.0902198	+	0.163660i
$463$	−6.69797	−	6.69797i	−0.311281	−	0.311281i	0.534125	−	0.845406i	$-0.320641\pi$
$463$	−6.69797	−	6.69797i	−0.311281	−	0.311281i	−0.845406	+	0.534125i	$0.820641\pi$
$464$	−9.91274	+	17.1694i	−0.460188	+	0.797068i
$465$		0			0
$466$	1.07508	−	0.620700i	0.0498023	−	0.0287534i
$467$	4.56632	−	4.56632i	0.211304	−	0.211304i	−0.593517	−	0.804821i	$-0.702261\pi$
$467$	4.56632	−	4.56632i	0.211304	−	0.211304i	0.804821	+	0.593517i	$0.202261\pi$
$468$	−12.5020	+	17.4904i	−0.577905	+	0.808494i
$469$		−	30.6852i		−	1.41691i
$470$		0			0
$471$	−6.61638	+	26.8032i	−0.304867	+	1.23502i
$472$	3.88039	−	1.03975i	0.178609	−	0.0478582i
$473$	3.45243	−	3.45243i	0.158743	−	0.158743i
$474$	0.133519	+	0.461569i	0.00613274	+	0.0212006i
$475$		0			0
$476$	−26.9538			−1.23543
$477$	−9.95686	+	3.09500i	−0.455893	+	0.141711i
$478$	0.0101952	+	0.00273180i	0.000466319	+	0.000124950i
$479$	−13.8170	+	7.97728i	−0.631317	+	0.364491i	−0.781262	−	0.624203i	$-0.785424\pi$
$479$	−13.8170	+	7.97728i	−0.631317	+	0.364491i	0.149945	+	0.988694i	$0.452090\pi$
$480$		0			0
$481$	21.2664	−	2.67741i	0.969664	−	0.122079i
$482$	0.849732	−	0.849732i	0.0387042	−	0.0387042i
$483$	9.75139	+	16.1436i	0.443704	+	0.734559i
$484$	−27.7869	+	16.0427i	−1.26304	+	0.729216i
$485$		0			0
$486$	1.34279	+	1.10029i	0.0609102	+	0.0499103i
$487$	−8.49708	−	31.7115i	−0.385040	−	1.43699i	−0.838104	−	0.545510i	$-0.816336\pi$
$487$	−8.49708	−	31.7115i	−0.385040	−	1.43699i	0.453065	−	0.891478i	$-0.350331\pi$
$488$	−0.611308	−	2.28143i	−0.0276726	−	0.103276i
$489$	−16.0058	−	15.3846i	−0.723807	−	0.695716i
$490$		0			0
$491$	25.2561	−	14.5816i	1.13979	−	0.658058i	0.193412	−	0.981118i	$-0.438045\pi$
$491$	25.2561	−	14.5816i	1.13979	−	0.658058i	0.946379	+	0.323059i	$0.104711\pi$
$492$	5.73516	−	3.46427i	0.258561	−	0.156181i
$493$	−12.1152	+	12.1152i	−0.545642	+	0.545642i
$494$	−0.155747	−	0.0655476i	−0.00700738	−	0.00294913i
$495$		0			0
$496$	−14.3999	+	8.31380i	−0.646576	+	0.373301i
$497$	47.0937	+	12.6187i	2.11244	+	0.566027i
$498$	−1.25791	+	2.28187i	−0.0563682	+	0.102253i
$499$	16.7557			0.750087			0.375044	−	0.927007i	$-0.377628\pi$
$499$	16.7557			0.750087			0.375044	+	0.927007i	$0.377628\pi$
$500$		0			0
$501$	37.5239	−	10.8546i	1.67645	−	0.484950i
$502$	1.68439	−	1.68439i	0.0751778	−	0.0751778i
$503$	−8.90077	+	2.38495i	−0.396866	+	0.106340i	−0.451732	−	0.892154i	$-0.649194\pi$
$503$	−8.90077	+	2.38495i	−0.396866	+	0.106340i	0.0548660	+	0.998494i	$0.482527\pi$
$504$	−4.50274	+	2.84293i	−0.200568	+	0.126634i
$505$		0			0
$506$		−	1.58057i		−	0.0702648i
$507$	−21.7980	−	5.64338i	−0.968083	−	0.250631i
$508$	−2.54628	+	2.54628i	−0.112973	+	0.112973i
$509$	0.476859	−	0.275315i	0.0211364	−	0.0122031i	−0.489395	−	0.872062i	$-0.662782\pi$
$509$	0.476859	−	0.275315i	0.0211364	−	0.0122031i	0.510531	+	0.859859i	$0.329449\pi$
$510$		0			0
$511$	3.66677	−	6.35104i	0.162208	−	0.280953i
$512$	6.14451	+	6.14451i	0.271552	+	0.271552i
$513$	0.979082	−	1.95528i	0.0432275	−	0.0863276i
$514$	−0.903491	+	1.56489i	−0.0398513	+	0.0690245i
$515$		0			0
$516$	3.09921	−	0.896517i	0.136435	−	0.0394670i
$517$	−2.46852	+	9.21266i	−0.108566	+	0.405172i
$518$	2.55610	+	0.684904i	0.112308	+	0.0300930i
$519$	4.51850	+	4.34313i	0.198340	+	0.190642i
$520$		0			0
$521$			32.2002i			1.41072i	0.708852	+	0.705358i	$0.249214\pi$
$521$			32.2002i			1.41072i	−0.708852	+	0.705358i	$0.750786\pi$
$522$	−0.371865	+	1.64573i	−0.0162761	+	0.0720318i
$523$	−13.6311	−	3.65245i	−0.596048	−	0.159711i	−0.0518323	−	0.998656i	$-0.516506\pi$
$523$	−13.6311	−	3.65245i	−0.596048	−	0.159711i	−0.544216	+	0.838945i	$0.683173\pi$
$524$	−20.1615	+	34.9207i	−0.880758	+	1.52552i
$525$		0			0
$526$	−2.21362	−	1.27803i	−0.0965184	−	0.0557249i
$527$	−13.8802	+	3.71919i	−0.604631	+	0.162010i
$528$	−35.4181	+	0.700906i	−1.54137	+	0.0305030i
$529$	13.4917	+	7.78941i	0.586594	+	0.338670i
$530$		0			0
$531$	−22.9477	+	14.4887i	−0.995847	+	0.628756i
$532$	2.36413	+	2.36413i	0.102498	+	0.102498i
$533$	5.54297	+	4.30333i	0.240093	+	0.186398i
$534$	0.578179	−	0.601524i	0.0250202	−	0.0260305i
$535$		0			0
$536$	−2.95238	+	1.70456i	−0.127523	+	0.0736256i
$537$	−4.86915	+	8.83273i	−0.210119	+	0.381160i
$538$	0.273182	+	0.273182i	0.0117777	+	0.0117777i
$539$	40.5034	+	23.3846i	1.74460	+	1.00725i
$540$		0			0
$541$		−	22.8149i		−	0.980890i	−0.871472	−	0.490445i	$-0.836834\pi$
$541$		−	22.8149i		−	0.980890i	0.871472	−	0.490445i	$-0.163166\pi$
$542$	−0.342412	−	1.27790i	−0.0147079	−	0.0548905i
$543$	−8.91438	−	14.7579i	−0.382553	−	0.633322i
$544$	2.24824	+	3.89407i	0.0963927	+	0.166957i
$545$		0			0
$546$	−2.22913	−	1.66097i	−0.0953979	−	0.0710830i
$547$	−10.0470	−	10.0470i	−0.429577	−	0.429577i	0.458907	−	0.888484i	$-0.348241\pi$
$547$	−10.0470	−	10.0470i	−0.429577	−	0.429577i	−0.888484	+	0.458907i	$0.848241\pi$
$548$	25.6636	+	6.87653i	1.09629	+	0.293751i
$549$	8.51847	+	13.4919i	0.363559	+	0.575819i
$550$		0			0
$551$	2.12526			0.0905391
$552$	1.01157	−	1.83500i	0.0430552	−	0.0781029i
$553$	9.61765	−	2.57704i	0.408984	−	0.109587i
$554$			1.91420i			0.0813267i
$555$		0			0
$556$	−20.5912	−	35.6650i	−0.873261	−	1.51253i
$557$	6.81604	−	25.4378i	0.288805	−	1.07783i	−0.657209	−	0.753708i	$-0.728263\pi$
$557$	6.81604	−	25.4378i	0.288805	−	1.07783i	0.946014	−	0.324126i	$-0.105070\pi$
$558$	−0.960235	+	1.03941i	−0.0406500	+	0.0440017i
$559$	2.04178	+	2.69231i	0.0863581	+	0.113873i
$560$		0			0
$561$	−29.7227	−	7.33706i	−1.25489	−	0.309771i
$562$	−0.638111	+	2.38146i	−0.0269171	+	0.100456i
$563$	18.9045	−	5.06546i	0.796732	−	0.213484i	0.162583	−	0.986695i	$-0.448017\pi$
$563$	18.9045	−	5.06546i	0.796732	−	0.213484i	0.634149	+	0.773211i	$0.281351\pi$
$564$	−4.36739	+	4.54374i	−0.183900	+	0.191326i
$565$		0			0
$566$	−0.157566	+	0.272913i	−0.00662300	+	0.0114714i
$567$	23.3467	−	27.3692i	0.980470	−	1.14940i
$568$	−1.40193	−	5.23209i	−0.0588239	−	0.219534i
$569$	2.45559	+	4.25321i	0.102944	+	0.178304i	0.912896	−	0.408192i	$-0.133841\pi$
$569$	2.45559	+	4.25321i	0.102944	+	0.178304i	−0.809952	+	0.586495i	$0.800507\pi$
$570$		0			0
$571$	−17.2440			−0.721639			−0.360819	−	0.932636i	$-0.617503\pi$
$571$	−17.2440			−0.721639			−0.360819	+	0.932636i	$0.617503\pi$
$572$	−14.0924	−	34.5743i	−0.589233	−	1.44562i
$573$	0.783925	+	39.6132i	0.0327489	+	1.65486i
$574$	0.433180	+	0.750289i	0.0180806	+	0.0313165i
$575$		0			0
$576$	−20.4568	−	10.7549i	−0.852367	−	0.448121i
$577$	−16.3463	+	16.3463i	−0.680507	+	0.680507i	−0.960114	−	0.279607i	$-0.909796\pi$
$577$	−16.3463	+	16.3463i	−0.680507	+	0.680507i	0.279607	+	0.960114i	$0.409796\pi$
$578$	−0.158231	−	0.590527i	−0.00658156	−	0.0245627i
$579$	−28.4782	+	8.23796i	−1.18351	+	0.342358i
$580$		0			0
$581$	46.7606	+	26.9973i	1.93996	+	1.12003i
$582$	−0.285373	−	0.472439i	−0.0118291	−	0.0195832i
$583$	4.68655	−	17.4905i	0.194097	−	0.724381i
$584$	−0.814753			−0.0337147
$585$		0			0
$586$	−0.880683			−0.0363807
$587$	−0.347066	+	1.29527i	−0.0143250	+	0.0534615i	−0.972718	−	0.231989i	$-0.925477\pi$
$587$	−0.347066	+	1.29527i	−0.0143250	+	0.0534615i	0.958393	+	0.285451i	$0.0921433\pi$
$588$	15.9788	+	26.4531i	0.658954	+	1.09091i
$589$	1.54365	+	0.891226i	0.0636049	+	0.0367223i
$590$		0			0
$591$	−2.46169	+	0.712098i	−0.101260	+	0.0292918i
$592$	6.04025	+	22.5425i	0.248253	+	0.926491i
$593$	16.7430	−	16.7430i	0.687552	−	0.687552i	−0.274138	−	0.961690i	$-0.588393\pi$
$593$	16.7430	−	16.7430i	0.687552	−	0.687552i	0.961690	+	0.274138i	$0.0883925\pi$
$594$	−2.86065	+	0.951675i	−0.117374	+	0.0390477i
$595$		0			0
$596$	−8.97996	−	15.5537i	−0.367834	−	0.637106i
$597$	0.818839	+	41.3774i	0.0335129	+	1.69347i
$598$	1.08366	+	0.148912i	0.0443143	+	0.00608945i
$599$	−29.1006			−1.18902			−0.594509	−	0.804089i	$-0.702653\pi$
$599$	−29.1006			−1.18902			−0.594509	+	0.804089i	$0.702653\pi$
$600$		0			0
$601$	15.9418	+	27.6120i	0.650280	+	1.12632i	0.983055	+	0.183311i	$0.0586816\pi$
$601$	15.9418	+	27.6120i	0.650280	+	1.12632i	−0.332775	+	0.943006i	$0.607985\pi$
$602$	0.107971	+	0.402952i	0.00440055	+	0.0164231i
$603$	15.6279	−	16.9165i	0.636419	−	0.688894i
$604$	11.6402	−	20.1615i	0.473635	−	0.820359i
$605$		0			0
$606$	0.369589	−	0.384512i	0.0150135	−	0.0156197i
$607$	14.1691	−	3.79661i	0.575107	−	0.154100i	0.0404693	−	0.999181i	$-0.487115\pi$
$607$	14.1691	−	3.79661i	0.575107	−	0.154100i	0.534638	+	0.845081i	$0.320448\pi$
$608$	0.144356	−	0.538745i	0.00585442	−	0.0218490i
$609$	33.9443	+	8.37917i	1.37549	+	0.339541i
$610$		0			0
$611$	−6.08379	−	2.56042i	−0.246124	−	0.103584i
$612$	−14.8594	−	13.7275i	−0.600657	−	0.554903i
$613$	−5.37967	+	20.0772i	−0.217283	+	0.810911i	0.768067	+	0.640369i	$0.221219\pi$
$613$	−5.37967	+	20.0772i	−0.217283	+	0.810911i	−0.985350	+	0.170542i	$0.945448\pi$
$614$	−0.842294	−	1.45890i	−0.0339922	−	0.0588762i
$615$		0			0
$616$		−	9.24775i		−	0.372602i
$617$	39.2451	−	10.5157i	1.57995	−	0.423345i	0.641037	−	0.767510i	$-0.278504\pi$
$617$	39.2451	−	10.5157i	1.57995	−	0.423345i	0.938909	+	0.344164i	$0.111838\pi$
$618$	0.00600341	−	0.0108903i	0.000241492	−	0.000438072i
$619$	21.9052			0.880445			0.440222	−	0.897889i	$-0.354900\pi$
$619$	21.9052			0.880445			0.440222	+	0.897889i	$0.354900\pi$
$620$		0			0
$621$	−2.84604	+	13.8662i	−0.114208	+	0.556432i
$622$	−1.29293	−	0.346441i	−0.0518420	−	0.0138910i
$623$	−12.2255	−	12.2255i	−0.489804	−	0.489804i
$624$	2.85633	−	24.3493i	0.114345	−	0.974751i
$625$		0			0
$626$	1.29995	+	2.25158i	0.0519564	+	0.0899911i
$627$	1.96345	+	3.25052i	0.0784126	+	0.129813i
$628$	−8.19964	−	30.6015i	−0.327201	−	1.22113i
$629$			20.1688i			0.804183i
$630$		0			0
$631$	16.2845	+	9.40185i	0.648275	+	0.374282i	0.787795	−	0.615937i	$-0.211223\pi$
$631$	16.2845	+	9.40185i	0.648275	+	0.374282i	−0.139520	+	0.990219i	$0.544556\pi$
$632$	−0.782208	−	0.782208i	−0.0311146	−	0.0311146i
$633$	2.57414	−	4.66954i	0.102313	−	0.185598i
$634$	−0.106209	+	0.0613196i	−0.00421809	+	0.00243531i
$635$		0			0
$636$	8.29159	−	8.62639i	0.328783	−	0.342059i
$637$	−19.8489	+	25.5667i	−0.786442	+	1.01299i
$638$	−2.07188	−	2.07188i	−0.0820264	−	0.0820264i
$639$	19.5357	+	30.9414i	0.772821	+	1.22402i
$640$		0			0
$641$	18.6204	+	10.7505i	0.735461	+	0.424619i	0.820417	−	0.571766i	$-0.193742\pi$
$641$	18.6204	+	10.7505i	0.735461	+	0.424619i	−0.0849557	+	0.996385i	$0.527075\pi$
$642$	3.27585	−	0.0648275i	0.129288	−	0.00255854i
$643$	−2.64106	+	0.707671i	−0.104153	+	0.0279078i	−0.310519	−	0.950567i	$-0.600503\pi$
$643$	−2.64106	+	0.707671i	−0.104153	+	0.0279078i	0.206366	+	0.978475i	$0.433836\pi$
$644$	−18.7432	−	10.8214i	−0.738585	−	0.426422i
$645$		0			0
$646$	0.0795009	−	0.137700i	0.00312792	−	0.00541772i
$647$	−39.8449	−	10.6764i	−1.56647	−	0.419733i	−0.631762	−	0.775162i	$-0.717668\pi$
$647$	−39.8449	−	10.6764i	−1.56647	−	0.419733i	−0.934703	+	0.355429i	$0.884335\pi$
$648$	−3.93023	−	0.725954i	−0.154394	−	0.0285182i
$649$		−	47.1302i		−	1.85002i
$650$		0			0
$651$	21.1411	+	20.3206i	0.828585	+	0.796426i
$652$	24.6081	+	6.59373i	0.963729	+	0.258230i
$653$	−4.49795	+	16.7866i	−0.176018	+	0.656909i	0.820358	+	0.571851i	$0.193774\pi$
$653$	−4.49795	+	16.7866i	−0.176018	+	0.656909i	−0.996376	+	0.0850584i	$0.972892\pi$
$654$	−0.876719	+	0.253611i	−0.0342824	+	0.00991696i
$655$		0			0
$656$	−3.82026	+	6.61688i	−0.149156	+	0.258346i
$657$	5.25604	−	1.63380i	0.205058	−	0.0637404i
$658$	−0.576229	−	0.576229i	−0.0224638	−	0.0224638i
$659$	9.34358	−	16.1835i	0.363974	−	0.630422i	−0.624637	−	0.780915i	$-0.714753\pi$
$659$	9.34358	−	16.1835i	0.363974	−	0.630422i	0.988611	+	0.150494i	$0.0480863\pi$
$660$		0			0
$661$	36.7989	−	21.2459i	1.43131	−	0.826368i	0.434091	−	0.900869i	$-0.357070\pi$
$661$	36.7989	−	21.2459i	1.43131	−	0.826368i	0.997221	+	0.0745005i	$0.0237362\pi$
$662$	−2.21731	+	2.21731i	−0.0861780	+	0.0861780i
$663$	7.83071	−	19.6871i	0.304119	−	0.764584i
$664$		−	5.99876i		−	0.232797i
$665$		0			0
$666$	1.06034	+	1.67940i	0.0410872	+	0.0650754i
$667$	−13.2887	+	3.56070i	−0.514540	+	0.137871i
$668$	−31.6965	+	31.6965i	−1.22638	+	1.22638i
$669$	−9.61818	+	2.78228i	−0.371860	+	0.107569i
$670$		0			0
$671$	−27.7097			−1.06972
$672$	4.42972	−	8.03560i	0.170880	−	0.309980i
$673$	0.980547	+	0.262737i	0.0377973	+	0.0101278i	0.277668	−	0.960677i	$-0.410438\pi$
$673$	0.980547	+	0.262737i	0.0377973	+	0.0101278i	−0.239871	+	0.970805i	$0.577105\pi$
$674$	2.44738	−	1.41300i	0.0942697	−	0.0544267i
$675$		0			0
$676$	25.0324	−	6.40462i	0.962786	−	0.246331i
$677$	2.15255	−	2.15255i	0.0827291	−	0.0827291i	−0.664531	−	0.747260i	$-0.731369\pi$
$677$	2.15255	−	2.15255i	0.0827291	−	0.0827291i	0.747260	+	0.664531i	$0.231369\pi$
$678$	0.465532	−	0.281201i	0.0178786	−	0.0107994i
$679$	−9.90513	+	5.71873i	−0.380124	+	0.219465i
$680$		0			0
$681$	18.3333	+	17.6217i	0.702532	+	0.675266i
$682$	−0.636035	−	2.37371i	−0.0243550	−	0.0908942i
$683$	−8.32509	−	31.0697i	−0.318551	−	1.18885i	−0.920638	−	0.390418i	$-0.872331\pi$
$683$	−8.32509	−	31.0697i	−0.318551	−	1.18885i	0.602087	−	0.798430i	$-0.294336\pi$
$684$	0.0992783	+	2.50737i	0.00379600	+	0.0958718i
$685$		0			0
$686$	−0.762153	+	0.440029i	−0.0290991	+	0.0168004i
$687$	−3.22906	−	5.34576i	−0.123196	−	0.203954i
$688$	−2.60147	+	2.60147i	−0.0991802	+	0.0991802i
$689$	11.5502	+	4.86103i	0.440028	+	0.185190i
$690$		0			0
$691$	−15.5777	+	8.99379i	−0.592603	+	0.342140i	−0.766126	−	0.642690i	$-0.777818\pi$
$691$	−15.5777	+	8.99379i	−0.592603	+	0.342140i	0.173523	+	0.984830i	$0.444485\pi$
$692$	−6.94696	−	1.86143i	−0.264084	−	0.0707611i
$693$	18.5442	+	59.6580i	0.704435	+	2.26622i
$694$	0.0558510			0.00212007
$695$		0			0
$696$	−1.07939	−	3.73141i	−0.0409143	−	0.141439i
$697$	−4.66906	+	4.66906i	−0.176853	+	0.176853i
$698$	0.996554	−	0.267026i	0.0377201	−	0.0101071i
$699$	4.62715	−	18.7447i	0.175015	−	0.708991i
$700$		0			0
$701$		−	36.5117i		−	1.37903i	−0.724272	−	0.689515i	$-0.757824\pi$
$701$		−	36.5117i		−	1.37903i	0.724272	−	0.689515i	$-0.242176\pi$
$702$	−0.382971	−	2.05097i	−0.0144543	−	0.0774090i
$703$	1.76901	−	1.76901i	0.0667196	−	0.0667196i
$704$	34.7591	−	20.0682i	1.31003	−	0.756347i
$705$		0			0
$706$	−1.17916	+	2.04236i	−0.0443782	+	0.0768653i
$707$	−7.81490	−	7.81490i	−0.293909	−	0.293909i
$708$	15.0348	−	27.2734i	0.565043	−	1.02500i
$709$	−17.1761	+	29.7499i	−0.645063	+	1.11728i	0.339224	+	0.940706i	$0.389836\pi$
$709$	−17.1761	+	29.7499i	−0.645063	+	1.11728i	−0.984287	+	0.176577i	$0.943498\pi$
$710$		0			0
$711$	6.61462	+	3.47756i	0.248068	+	0.130419i
$712$	−0.497153	+	1.85540i	−0.0186316	+	0.0695340i
$713$	−11.1452	−	2.98635i	−0.417391	−	0.111840i
$714$	1.81268	−	1.88587i	0.0678377	−	0.0705769i
$715$		0			0
$716$		−	11.5740i		−	0.432540i
$717$	0.140514	−	0.0848763i	0.00524759	−	0.00316976i
$718$	−1.91056	−	0.511933i	−0.0713014	−	0.0191052i
$719$	5.50044	−	9.52704i	0.205132	−	0.355299i	−0.745043	−	0.667016i	$-0.767571\pi$
$719$	5.50044	−	9.52704i	0.205132	−	0.355299i	0.950175	+	0.311718i	$0.100904\pi$
$720$		0			0
$721$	−0.223167	−	0.128845i	−0.00831116	−	0.00479845i
$722$	2.02479	−	0.542540i	0.0753547	−	0.0201912i
$723$	−0.369793	−	18.6863i	−0.0137528	−	0.694952i
$724$	17.1344	+	9.89253i	0.636794	+	0.367653i
$725$		0			0
$726$	0.746242	−	3.02305i	0.0276956	−	0.112196i
$727$	−13.9424	−	13.9424i	−0.517094	−	0.517094i	0.399597	−	0.916691i	$-0.369150\pi$
$727$	−13.9424	−	13.9424i	−0.517094	−	0.517094i	−0.916691	+	0.399597i	$0.869150\pi$
$728$	6.34042	+	0.871268i	0.234991	+	0.0322913i
$729$	26.8099	−	3.19796i	0.992961	−	0.118443i
$730$		0			0
$731$	−2.75351	+	1.58974i	−0.101842	+	0.0587986i
$732$	−16.0351	−	8.83955i	−0.592675	−	0.326719i
$733$	−10.0007	−	10.0007i	−0.369383	−	0.369383i	0.497869	−	0.867252i	$-0.334116\pi$
$733$	−10.0007	−	10.0007i	−0.369383	−	0.369383i	−0.867252	+	0.497869i	$0.834116\pi$
$734$	−0.108825	−	0.0628299i	−0.00401679	−	0.00231909i
$735$		0			0
$736$			3.61049i			0.133084i
$737$	10.3515	+	38.6325i	0.381304	+	1.42305i
$738$	−0.143313	+	0.634247i	−0.00527542	+	0.0233469i
$739$	−5.27257	−	9.13236i	−0.193955	−	0.335939i	0.752603	−	0.658475i	$-0.228798\pi$
$739$	−5.27257	−	9.13236i	−0.193955	−	0.335939i	−0.946557	+	0.322536i	$0.895465\pi$
$740$		0			0
$741$	−2.41360	+	1.03993i	−0.0886657	+	0.0382028i
$742$	1.09399	+	1.09399i	0.0401615	+	0.0401615i
$743$	33.1343	+	8.87832i	1.21558	+	0.325714i	0.808949	−	0.587878i	$-0.200037\pi$
$743$	33.1343	+	8.87832i	1.21558	+	0.325714i	0.406632	+	0.913592i	$0.366703\pi$
$744$	0.780762	−	3.16289i	0.0286241	−	0.115957i
$745$		0			0
$746$	1.98600			0.0727127
$747$	12.0291	+	38.6985i	0.440122	+	1.41590i
$748$	33.9347	−	9.09277i	1.24077	−	0.332465i
$749$		−	67.8966i		−	2.48089i
$750$		0			0
$751$	−7.98474	−	13.8300i	−0.291367	−	0.504663i	0.682766	−	0.730637i	$-0.260777\pi$
$751$	−7.98474	−	13.8300i	−0.291367	−	0.504663i	−0.974133	+	0.225974i	$0.927444\pi$
$752$	1.86008	−	6.94191i	0.0678301	−	0.253145i
$753$	−0.733024	−	37.0411i	−0.0267129	−	1.34985i
$754$	1.61571	−	1.22531i	0.0588408	−	0.0446233i
$755$		0			0
$756$	−8.30006	+	40.4388i	−0.301870	+	1.47074i
$757$	10.9112	−	40.7211i	0.396574	−	1.48003i	−0.422510	−	0.906358i	$-0.638851\pi$
$757$	10.9112	−	40.7211i	0.396574	−	1.48003i	0.819083	−	0.573675i	$-0.194483\pi$
$758$	−1.11331	+	0.298311i	−0.0404373	+	0.0108351i
$759$	−17.7229	−	17.0351i	−0.643301	−	0.618334i
$760$		0			0
$761$	−2.02411	+	3.50585i	−0.0733738	+	0.127087i	−0.900378	−	0.435109i	$-0.856710\pi$
$761$	−2.02411	+	3.50585i	−0.0733738	+	0.127087i	0.827004	+	0.562196i	$0.190043\pi$
$762$	−0.00691435	−	0.349395i	−0.000250480	−	0.0126572i
$763$	4.89492	+	18.2681i	0.177208	+	0.661349i
$764$	−22.7333	−	39.3752i	−0.822462	−	1.42455i
$765$		0			0
$766$	1.85016			0.0668492
$767$	32.3133	+	4.44032i	1.16676	+	0.160331i
$768$	26.0052	−	0.514629i	0.938381	−	0.0185701i
$769$	−9.59863	−	16.6253i	−0.346135	−	0.599524i	0.639424	−	0.768854i	$-0.279173\pi$
$769$	−9.59863	−	16.6253i	−0.346135	−	0.599524i	−0.985559	+	0.169330i	$0.945840\pi$
$770$		0			0
$771$	7.80949	+	26.9970i	0.281252	+	0.972273i
$772$	24.0556	−	24.0556i	0.865778	−	0.865778i
$773$	−0.891235	−	3.32613i	−0.0320555	−	0.119633i	0.948044	−	0.318139i	$-0.103058\pi$
$773$	−0.891235	−	3.32613i	−0.0320555	−	0.119633i	−0.980100	+	0.198506i	$0.936391\pi$
$774$	−0.145699	+	0.277134i	−0.00523706	+	0.00996136i
$775$		0			0
$776$	1.10045	+	0.635348i	0.0395040	+	0.0228077i
$777$	35.2290	−	21.2798i	1.26383	−	0.763408i
$778$	0.696840	−	2.60064i	0.0249829	−	0.0932375i
$779$	0.819051			0.0293455
$780$		0			0
$781$	−63.5476			−2.27391
$782$	−0.266394	+	0.994197i	−0.00952624	+	0.0355524i
$783$	14.4457	+	21.9071i	0.516248	+	0.782898i
$784$	−30.5200	−	17.6208i	−1.09000	−	0.629313i
$785$		0			0
$786$	−1.08740	−	3.75909i	−0.0387864	−	0.134082i
$787$	−8.97719	−	33.5033i	−0.320002	−	1.19426i	−0.919241	−	0.393694i	$-0.871197\pi$
$787$	−8.97719	−	33.5033i	−0.320002	−	1.19426i	0.599239	−	0.800570i	$-0.295470\pi$
$788$	2.07939	−	2.07939i	0.0740752	−	0.0740752i
$789$	−38.1886	+	11.0469i	−1.35955	+	0.393281i
$790$		0			0
$791$	−5.63512	−	9.76031i	−0.200362	−	0.347037i
$792$	4.70987	−	5.09821i	0.167358	−	0.181157i
$793$	2.61064	−	18.9982i	0.0927065	−	0.674647i
$794$	−0.952251			−0.0337941
$795$		0			0
$796$	−23.7458	−	41.1289i	−0.841647	−	1.45778i
$797$	7.97400	+	29.7594i	0.282454	+	1.05413i	0.950680	+	0.310173i	$0.100387\pi$
$797$	7.97400	+	29.7594i	0.282454	+	1.05413i	−0.668226	+	0.743958i	$0.732946\pi$
$798$	−0.324401	+	0.00641973i	−0.0114837	+	0.000227256i
$799$	3.10547	−	5.37883i	0.109864	−	0.190289i
$800$		0			0
$801$	−0.513392	−	12.9662i	−0.0181398	−	0.458140i
$802$	−2.95603	+	0.792066i	−0.104381	+	0.0279688i
$803$	−2.47394	+	9.23288i	−0.0873036	+	0.325821i
$804$	−6.33374	+	25.6582i	−0.223374	+	0.904894i
$805$		0			0
$806$	1.68738	−	0.212439i	0.0594355	−	0.00748286i
$807$	6.00749	−	0.118885i	0.211474	−	0.00418496i
$808$	−0.317795	+	1.18603i	−0.0111800	+	0.0417242i
$809$	18.8982	+	32.7327i	0.664427	+	1.15082i	0.979440	+	0.201734i	$0.0646576\pi$
$809$	18.8982	+	32.7327i	0.664427	+	1.15082i	−0.315013	+	0.949087i	$0.602009\pi$
$810$		0			0
$811$		−	11.6051i		−	0.407512i	−0.979022	−	0.203756i	$-0.934685\pi$
$811$		−	11.6051i		−	0.407512i	0.979022	−	0.203756i	$-0.0653148\pi$
$812$	−38.7545	+	10.3842i	−1.36002	+	0.364416i
$813$	−18.0196	−	9.93352i	−0.631974	−	0.348384i
$814$	−3.44916			−0.120893
$815$		0			0
$816$	22.3966	+	5.52861i	0.784037	+	0.193540i
$817$	0.380948	+	0.102075i	0.0133277	+	0.00357114i
$818$	2.93960	+	2.93960i	0.102781	+	0.102781i
$819$	−42.6497	+	7.09359i	−1.49030	+	0.247870i
$820$		0			0
$821$	21.9513	+	38.0208i	0.766107	+	1.32694i	0.939659	+	0.342111i	$0.111142\pi$
$821$	21.9513	+	38.0208i	0.766107	+	1.32694i	−0.173553	+	0.984825i	$0.555525\pi$
$822$	−2.20703	+	1.33314i	−0.0769791	+	0.0464986i
$823$	11.4601	+	42.7695i	0.399472	+	1.49085i	0.814027	+	0.580827i	$0.197271\pi$
$823$	11.4601	+	42.7695i	0.399472	+	1.49085i	−0.414554	+	0.910025i	$0.636063\pi$
$824$			0.0286293i			0.000997349i
$825$		0			0
$826$	3.48738	+	2.01344i	0.121341	+	0.0700565i
$827$	−6.22326	−	6.22326i	−0.216404	−	0.216404i	0.590577	−	0.806981i	$-0.298900\pi$
$827$	−6.22326	−	6.22326i	−0.216404	−	0.216404i	−0.806981	+	0.590577i	$0.798900\pi$
$828$	−4.82166	−	15.5116i	−0.167564	−	0.539067i
$829$	34.6858	−	20.0259i	1.20469	−	0.695527i	0.243094	−	0.970003i	$-0.421838\pi$
$829$	34.6858	−	20.0259i	1.20469	−	0.695527i	0.961594	+	0.274475i	$0.0885042\pi$
$830$		0			0
$831$	21.4640	+	20.6310i	0.744578	+	0.715680i
$832$	10.4843	+	25.7221i	0.363477	+	0.891754i
$833$	−21.5358	−	21.5358i	−0.746172	−	0.746172i
$834$	3.88014	+	0.957816i	0.134358	+	0.0331665i
$835$		0			0
$836$	−3.77395	−	2.17889i	−0.130525	−	0.0753586i
$837$	1.30567	+	21.9697i	0.0451307	+	0.759384i
$838$	−3.19297	+	0.855555i	−0.110299	+	0.0295546i
$839$	3.62533	+	2.09309i	0.125160	+	0.0722614i	0.561273	−	0.827631i	$-0.310312\pi$
$839$	3.62533	+	2.09309i	0.125160	+	0.0722614i	−0.436113	+	0.899892i	$0.643645\pi$
$840$		0			0
$841$	1.74811	−	3.02782i	0.0602797	−	0.104407i
$842$	−2.29595	−	0.615198i	−0.0791236	−	0.0212011i
$843$	19.8259	+	32.8222i	0.682842	+	1.13046i
$844$			6.11875i			0.210616i
$845$		0			0
$846$	−0.0241979	−	0.611144i	−0.000831942	−	0.0210116i
$847$	−62.3264	−	16.7003i	−2.14156	−	0.573830i
$848$	−3.53140	+	13.1794i	−0.121269	+	0.452582i
$849$	1.36195	+	4.70820i	0.0467421	+	0.161585i
$850$		0			0
$851$	−8.09736	+	14.0250i	−0.277574	+	0.480772i
$852$	−36.7739	−	20.2721i	−1.25985	−	0.694510i
$853$	1.57958	+	1.57958i	0.0540837	+	0.0540837i	0.733631	−	0.679548i	$-0.237824\pi$
$853$	1.57958	+	1.57958i	0.0540837	+	0.0540837i	−0.679548	+	0.733631i	$0.737824\pi$
$854$	1.18378	−	2.05036i	0.0405081	−	0.0701620i
$855$		0			0
$856$	−6.53267	+	3.77164i	−0.223282	+	0.128912i
$857$	−31.1740	+	31.1740i	−1.06488	+	1.06488i	−0.0671414	+	0.997743i	$0.521388\pi$
$857$	−31.1740	+	31.1740i	−1.06488	+	1.06488i	−0.997743	+	0.0671414i	$0.978612\pi$
$858$	3.36678	+	1.33916i	0.114940	+	0.0457183i
$859$			17.7932i			0.607095i	0.952816	+	0.303547i	$0.0981711\pi$
$859$			17.7932i			0.607095i	−0.952816	+	0.303547i	$0.901829\pi$
$860$		0			0
$861$	13.0817	+	3.22924i	0.445825	+	0.110052i
$862$	−0.312829	+	0.0838223i	−0.0106550	+	0.00285500i
$863$	−4.49895	+	4.49895i	−0.153146	+	0.153146i	−0.779522	−	0.626375i	$-0.784538\pi$
$863$	−4.49895	+	4.49895i	−0.153146	+	0.153146i	0.626375	+	0.779522i	$0.284538\pi$
$864$	6.53459	−	2.17391i	0.222311	−	0.0739580i
$865$		0			0
$866$	−2.94505			−0.100077
$867$	−8.32698	−	4.59035i	−0.282799	−	0.155896i
$868$	−32.5034	−	8.70925i	−1.10324	−	0.295611i
$869$	−11.2392	+	6.48896i	−0.381264	+	0.220123i
$870$		0			0
$871$	−27.4624	+	3.45747i	−0.930526	+	0.117152i
$872$	1.48575	−	1.48575i	0.0503139	−	0.0503139i
$873$	−8.37316	−	1.89198i	−0.283389	−	0.0640338i
$874$	0.110567	−	0.0638359i	0.00373998	−	0.00215928i
$875$		0			0
$876$	−4.37698	+	4.55371i	−0.147884	+	0.153856i
$877$	−1.58848	−	5.92830i	−0.0536393	−	0.200184i	0.933906	−	0.357518i	$-0.116377\pi$
$877$	−1.58848	−	5.92830i	−0.0536393	−	0.200184i	−0.987546	+	0.157334i	$0.949710\pi$
$878$	−0.772733	−	2.88388i	−0.0260785	−	0.0973262i
$879$	−9.49185	+	9.87511i	−0.320152	+	0.333079i
$880$		0			0
$881$	−36.9093	+	21.3096i	−1.24350	+	0.717938i	−0.969806	−	0.243878i	$-0.921581\pi$
$881$	−36.9093	+	21.3096i	−1.24350	+	0.717938i	−0.273699	+	0.961815i	$0.588247\pi$
$882$	−2.92543	−	0.661023i	−0.0985044	−	0.0222578i
$883$	13.2826	−	13.2826i	0.446996	−	0.446996i	−0.447358	−	0.894355i	$-0.647635\pi$
$883$	13.2826	−	13.2826i	0.446996	−	0.446996i	0.894355	+	0.447358i	$0.147635\pi$
$884$	3.03704	+	24.1229i	0.102147	+	0.811340i
$885$		0			0
$886$	2.64092	−	1.52473i	0.0887233	−	0.0512244i
$887$	0.0708297	+	0.0189788i	0.00237823	+	0.000637244i	0.260008	−	0.965606i	$-0.416275\pi$
$887$	0.0708297	+	0.0189788i	0.00237823	+	0.000637244i	−0.257630	+	0.966244i	$0.582941\pi$
$888$	−4.00440	−	2.20747i	−0.134379	−	0.0740779i
$889$	−7.24169			−0.242879
$890$		0			0
$891$	−20.1605	+	42.3335i	−0.675401	+	1.41823i
$892$	8.12449	−	8.12449i	0.272028	−	0.272028i
$893$	−0.744161	+	0.199397i	−0.0249024	+	0.00667257i
$894$	1.69216	+	0.417710i	0.0565942	+	0.0139703i
$895$		0			0
$896$			14.0245i			0.468525i
$897$	13.3493	−	10.5462i	0.445720	−	0.352127i
$898$	0.275440	−	0.275440i	0.00919156	−	0.00919156i
$899$	−18.5243	+	10.6950i	−0.617819	+	0.356698i
$900$		0			0
$901$	−5.89581	+	10.2118i	−0.196418	+	0.340206i
$902$	−0.798478	−	0.798478i	−0.0265864	−	0.0265864i
$903$	5.68199	+	3.13227i	0.189085	+	0.104235i
$904$	−0.626059	+	1.08437i	−0.0208224	+	0.0360655i
$905$		0			0
$906$	0.627812	+	2.17031i	0.0208577	+	0.0721039i
$907$	3.44596	−	12.8605i	0.114421	−	0.427026i	−0.884822	−	0.465930i	$-0.845720\pi$
$907$	3.44596	−	12.8605i	0.114421	−	0.427026i	0.999243	+	0.0389038i	$0.0123866\pi$
$908$	−28.1865	−	7.55255i	−0.935401	−	0.250640i
$909$	−0.328176	−	8.28841i	−0.0108849	−	0.274909i
$910$		0			0
$911$		−	26.2784i		−	0.870641i	−0.900276	−	0.435321i	$-0.856635\pi$
$911$		−	26.2784i		−	0.870641i	0.900276	−	0.435321i	$-0.143365\pi$
$912$	−1.47949	−	2.44933i	−0.0489910	−	0.0811053i
$913$	−67.9787	−	18.2148i	−2.24977	−	0.602823i
$914$	1.94240	−	3.36434i	0.0642490	−	0.111283i
$915$		0			0
$916$	6.20659	+	3.58338i	0.205072	+	0.118398i
$917$	−78.3277	+	20.9879i	−2.58661	+	0.693080i
$918$	1.95979	−	0.116471i	0.0646826	−	0.00384412i
$919$	−12.6380	−	7.29655i	−0.416889	−	0.240691i	0.276856	−	0.960911i	$-0.410707\pi$
$919$	−12.6380	−	7.29655i	−0.416889	−	0.240691i	−0.693746	+	0.720220i	$0.744041\pi$
$920$		0			0
$921$	−25.4367	−	6.27907i	−0.838168	−	0.206902i
$922$	−0.855820	−	0.855820i	−0.0281849	−	0.0281849i
$923$	5.98707	−	43.5693i	0.197067	−	1.43410i
$924$	−51.6863	−	49.6803i	−1.70035	−	1.63436i
$925$		0			0
$926$	−0.913562	+	0.527445i	−0.0300215	+	0.0173329i
$927$	−0.0574093	−	0.184690i	−0.00188557	−	0.00606601i
$928$	4.73279	+	4.73279i	0.155361	+	0.155361i
$929$	−38.3045	−	22.1151i	−1.25673	−	0.725573i	−0.284292	−	0.958738i	$-0.591758\pi$
$929$	−38.3045	−	22.1151i	−1.25673	−	0.725573i	−0.972437	+	0.233165i	$0.925092\pi$
$930$		0			0
$931$			3.77783i			0.123813i
$932$	5.73440	+	21.4011i	0.187836	+	0.701015i
$933$	−17.8197	+	10.7638i	−0.583390	+	0.352392i
$934$	−0.359584	−	0.622817i	−0.0117659	−	0.0203792i
$935$		0			0
$936$	3.05169	+	3.70949i	0.0997475	+	0.121248i
$937$	−22.4956	−	22.4956i	−0.734898	−	0.734898i	0.236688	−	0.971586i	$-0.423938\pi$
$937$	−22.4956	−	22.4956i	−0.734898	−	0.734898i	−0.971586	+	0.236688i	$0.923938\pi$
$938$	−3.30082	−	0.884452i	−0.107776	−	0.0288784i
$939$	39.2576	+	9.69076i	1.28112	+	0.316246i
$940$		0			0
$941$	−37.4186			−1.21981			−0.609905	−	0.792474i	$-0.708793\pi$
$941$	−37.4186			−1.21981			−0.609905	+	0.792474i	$0.708793\pi$
$942$	2.69252	+	1.48428i	0.0877270	+	0.0483606i
$943$	−5.12131	+	1.37225i	−0.166773	+	0.0446867i
$944$			35.5135i			1.15586i
$945$		0			0
$946$	−0.271869	−	0.470890i	−0.00883921	−	0.0153100i
$947$	−0.895335	+	3.34143i	−0.0290945	+	0.108582i	−0.978946	−	0.204119i	$-0.934567\pi$
$947$	−0.895335	+	3.34143i	−0.0290945	+	0.108582i	0.949852	+	0.312701i	$0.101234\pi$
$948$	−8.57396	+	0.169674i	−0.278469	+	0.00551077i
$949$	−6.09715	−	2.56605i	−0.197922	−	0.0832974i
$950$		0			0
$951$	−0.457121	+	1.85181i	−0.0148232	+	0.0600491i
$952$	−1.55865	+	5.81695i	−0.0505161	+	0.188529i
$953$	28.6007	−	7.66352i	0.926466	−	0.248246i	0.236119	−	0.971724i	$-0.424124\pi$
$953$	28.6007	−	7.66352i	0.926466	−	0.248246i	0.690347	+	0.723478i	$0.257458\pi$
$954$	0.0459404	+	1.16027i	0.00148737	+	0.0375652i
$955$		0			0
$956$	−0.0941895	+	0.163141i	−0.00304631	+	0.00527636i
$957$	−45.5623	+	0.901655i	−1.47282	+	0.0291464i
$958$	0.459864	+	1.71624i	0.0148575	+	0.0554491i
$959$	26.7155	+	46.2725i	0.862687	+	1.49422i
$960$		0			0
$961$	13.0603			0.421299
$962$	0.324959	−	2.36480i	0.0104771	−	0.0762443i
$963$	34.5797	−	37.4309i	1.11431	−	1.20619i
$964$	10.7238	+	18.5741i	0.345389	+	0.598231i
$965$		0			0
$966$	2.01764	−	0.583648i	0.0649165	−	0.0187786i
$967$	−18.5880	+	18.5880i	−0.597750	+	0.597750i	−0.939713	−	0.341963i	$-0.888908\pi$
$967$	−18.5880	+	18.5880i	−0.597750	+	0.597750i	0.341963	+	0.939713i	$0.388908\pi$
$968$	1.85540	+	6.92443i	0.0596347	+	0.222560i
$969$	−0.687180	−	2.37555i	−0.0220754	−	0.0763135i
$970$		0			0
$971$	6.10879	+	3.52691i	0.196040	+	0.113184i	0.594807	−	0.803868i	$-0.297228\pi$
$971$	6.10879	+	3.52691i	0.196040	+	0.113184i	−0.398767	+	0.917052i	$0.630562\pi$
$972$	−25.1712	+	18.0664i	−0.807366	+	0.579479i
$973$	21.4352	−	79.9972i	0.687180	−	2.56459i
$974$	−3.65614			−0.117150
$975$		0			0
$976$	20.8797			0.668344
$977$	−5.28126	+	19.7099i	−0.168963	+	0.630577i	0.828539	+	0.559932i	$0.189173\pi$
$977$	−5.28126	+	19.7099i	−0.168963	+	0.630577i	−0.997501	+	0.0706455i	$0.977494\pi$
$978$	−2.11627	+	1.27831i	−0.0676708	+	0.0408760i
$979$	19.5160	+	11.2676i	0.623735	+	0.360114i
$980$		0			0
$981$	−6.60538	+	12.5640i	−0.210894	+	0.401139i
$982$	−0.840582	−	3.13710i	−0.0268241	−	0.100109i
$983$	−30.8727	+	30.8727i	−0.984687	+	0.984687i	−0.999885	−	0.0151975i	$-0.995162\pi$
$983$	−30.8727	+	30.8727i	−0.984687	+	0.984687i	0.0151975	+	0.999885i	$0.495162\pi$
$984$	−0.415986	−	1.43804i	−0.0132612	−	0.0458431i
$985$		0			0
$986$	0.954036	+	1.65244i	0.0303827	+	0.0526244i
$987$	−12.6718	+	0.250768i	−0.403347	+	0.00798203i
$988$	1.84945	−	2.38221i	0.0588387	−	0.0757880i
$989$	−2.55299			−0.0811803
$990$		0			0
$991$	−6.36105	−	11.0177i	−0.202065	−	0.349988i	0.747128	−	0.664680i	$-0.231432\pi$
$991$	−6.36105	−	11.0177i	−0.202065	−	0.349988i	−0.949194	+	0.314692i	$0.898099\pi$
$992$	1.45290	+	5.42228i	0.0461295	+	0.172158i
$993$	0.964945	+	48.7604i	0.0306216	+	1.54736i
$994$	2.71480	−	4.70218i	0.0861083	−	0.149144i
$995$		0			0
$996$	−33.5275	−	32.2263i	−1.06236	−	1.02113i
$997$	8.75218	−	2.34514i	0.277184	−	0.0742713i	−0.117549	−	0.993067i	$-0.537504\pi$
$997$	8.75218	−	2.34514i	0.277184	−	0.0742713i	0.394733	+	0.918796i	$0.370837\pi$
$998$	0.482956	−	1.80241i	0.0152877	−	0.0570544i
$999$	30.2593	+	6.21072i	0.957360	+	0.196498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.257.13		96
3.2	odd	2	inner	975.2.bn.d.257.12		96
5.2	odd	4		195.2.bf.a.23.13	yes	96
5.3	odd	4	inner	975.2.bn.d.218.12		96
5.4	even	2		195.2.bf.a.62.12	yes	96
13.4	even	6	inner	975.2.bn.d.407.13		96
15.2	even	4		195.2.bf.a.23.12	yes	96
15.8	even	4	inner	975.2.bn.d.218.13		96
15.14	odd	2		195.2.bf.a.62.13	yes	96
39.17	odd	6	inner	975.2.bn.d.407.12		96
65.4	even	6		195.2.bf.a.17.12	✓	96
65.17	odd	12		195.2.bf.a.173.13	yes	96
65.43	odd	12	inner	975.2.bn.d.368.12		96
195.17	even	12		195.2.bf.a.173.12	yes	96
195.134	odd	6		195.2.bf.a.17.13	yes	96
195.173	even	12	inner	975.2.bn.d.368.13		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.12	✓	96	65.4	even	6
195.2.bf.a.17.13	yes	96	195.134	odd	6
195.2.bf.a.23.12	yes	96	15.2	even	4
195.2.bf.a.23.13	yes	96	5.2	odd	4
195.2.bf.a.62.12	yes	96	5.4	even	2
195.2.bf.a.62.13	yes	96	15.14	odd	2
195.2.bf.a.173.12	yes	96	195.17	even	12
195.2.bf.a.173.13	yes	96	65.17	odd	12
975.2.bn.d.218.12		96	5.3	odd	4	inner
975.2.bn.d.218.13		96	15.8	even	4	inner
975.2.bn.d.257.12		96	3.2	odd	2	inner
975.2.bn.d.257.13		96	1.1	even	1	trivial
975.2.bn.d.368.12		96	65.43	odd	12	inner
975.2.bn.d.368.13		96	195.173	even	12	inner
975.2.bn.d.407.12		96	39.17	odd	6	inner
975.2.bn.d.407.13		96	13.4	even	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0288234 - 0.107570i) q^{2} +(-0.895534 - 1.48257i) q^{3} +(1.72131 + 0.993799i) q^{4} +(-0.185293 + 0.0536002i) q^{6} +(1.03453 + 3.86093i) q^{7} +(0.314011 - 0.314011i) q^{8} +(-1.39604 + 2.65539i) q^{9} +(-2.60494 - 4.51189i) q^{11} +(-0.0681144 - 3.44195i) q^{12} +(3.33885 - 1.36091i) q^{13} +0.445140 q^{14} +(1.96287 + 3.39979i) q^{16} +(0.878092 + 3.27708i) q^{17} +(0.245402 + 0.226709i) q^{18} +(0.210416 - 0.364452i) q^{19} +(4.79764 - 4.99136i) q^{21} +(-0.560429 + 0.150166i) q^{22} +(-0.705071 + 2.63136i) q^{23} +(-0.746752 - 0.184336i) q^{24} +(-0.0501565 - 0.398387i) q^{26} +(5.18700 - 0.308267i) q^{27} +(-2.05624 + 7.67398i) q^{28} +(2.52506 + 4.37354i) q^{29} +4.23553i q^{31} +(1.28019 - 0.343025i) q^{32} +(-4.35638 + 7.90256i) q^{33} +0.377826 q^{34} +(-5.04193 + 3.18337i) q^{36} +(5.74223 + 1.53863i) q^{37} +(-0.0331393 - 0.0331393i) q^{38} +(-5.00770 - 3.73134i) q^{39} +(0.973131 + 1.68551i) q^{41} +(-0.398638 - 0.659952i) q^{42} +(0.242554 + 0.905224i) q^{43} -10.3551i q^{44} +(0.262734 + 0.151689i) q^{46} +(-1.29449 - 1.29449i) q^{47} +(3.28262 - 5.95473i) q^{48} +(-7.77434 + 4.48852i) q^{49} +(4.07215 - 4.23657i) q^{51} +(7.09967 + 0.975600i) q^{52} +(2.45762 + 2.45762i) q^{53} +(0.116347 - 0.566853i) q^{54} +(1.53723 + 0.887520i) q^{56} +(-0.728761 + 0.0144218i) q^{57} +(0.543244 - 0.145562i) q^{58} +(7.83433 + 4.52315i) q^{59} +(2.65934 - 4.60611i) q^{61} +(0.455618 + 0.122082i) q^{62} +(-11.6965 - 2.64291i) q^{63} +7.70388i q^{64} +(0.724516 + 0.696396i) q^{66} +(-7.41523 - 1.98691i) q^{67} +(-1.74529 + 6.51352i) q^{68} +(4.53259 - 1.31116i) q^{69} +(6.09876 - 10.5634i) q^{71} +(0.395450 + 1.27219i) q^{72} +(-1.29733 - 1.29733i) q^{73} +(0.331021 - 0.573345i) q^{74} +(0.724384 - 0.418223i) q^{76} +(14.7252 - 14.7252i) q^{77} +(-0.545721 + 0.431130i) q^{78} -2.49102i q^{79} +(-5.10216 - 7.41404i) q^{81} +(0.209360 - 0.0560979i) q^{82} +(9.55183 - 9.55183i) q^{83} +(13.2186 - 3.82379i) q^{84} +0.104367 q^{86} +(4.22280 - 7.66024i) q^{87} +(-2.23476 - 0.598803i) q^{88} +(-3.74597 + 2.16273i) q^{89} +(8.70853 + 11.4832i) q^{91} +(-3.82869 + 3.82869i) q^{92} +(6.27948 - 3.79307i) q^{93} +(-0.176560 + 0.101937i) q^{94} +(-1.65501 - 1.59078i) q^{96} +(0.740590 + 2.76392i) q^{97} +(0.258749 + 0.965663i) q^{98} +(15.6174 - 0.618364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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