LMFDB - Embedded newform 722.2.e.r.245.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			245.2
Character	$\chi$	$=$	722.245
Dual form			722.2.e.r.389.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(0.338947 + 0.284410i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.837728 - 0.304908i) q^{5} +(0.338947 - 0.284410i) q^{6} +(-1.26007 - 2.18251i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.486949 - 2.76162i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(0.338947 + 0.284410i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.837728 - 0.304908i) q^{5} +(0.338947 - 0.284410i) q^{6} +(-1.26007 - 2.18251i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.486949 - 2.76162i) q^{9} +(-0.154806 - 0.877948i) q^{10} +(-0.975994 + 1.69047i) q^{11} +(-0.221232 - 0.383185i) q^{12} +(4.94838 - 4.15218i) q^{13} +(-2.36816 + 0.861941i) q^{14} +(0.370664 + 0.134911i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.594269 + 3.37027i) q^{17} -2.80423 q^{18} -0.891491 q^{20} +(0.193630 - 1.09813i) q^{21} +(1.49531 + 1.25471i) q^{22} +(-7.69142 - 2.79945i) q^{23} +(-0.415780 + 0.151331i) q^{24} +(-3.22140 + 2.70308i) q^{25} +(-3.22982 - 5.59422i) q^{26} +(1.28408 - 2.22409i) q^{27} +(0.437619 + 2.48186i) q^{28} +(-0.795421 - 4.51105i) q^{29} +(0.197226 - 0.341606i) q^{30} +(-4.39680 - 7.61548i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-0.811597 + 0.295397i) q^{33} +(3.21587 + 1.17048i) q^{34} +(-1.72106 - 1.44414i) q^{35} +(-0.486949 + 2.76162i) q^{36} +5.97980 q^{37} +2.85816 q^{39} +(-0.154806 + 0.877948i) q^{40} +(2.67298 + 2.24289i) q^{41} +(-1.04783 - 0.381377i) q^{42} +(5.86997 - 2.13649i) q^{43} +(1.49531 - 1.25471i) q^{44} +(-1.24997 - 2.16501i) q^{45} +(-4.09252 + 7.08845i) q^{46} +(-1.83196 - 10.3895i) q^{47} +(0.0768330 + 0.435741i) q^{48} +(0.324429 - 0.561928i) q^{49} +(2.10262 + 3.64185i) q^{50} +(-1.15996 + 0.973325i) q^{51} +(-6.07009 + 2.20933i) q^{52} +(3.53586 + 1.28695i) q^{53} +(-1.96732 - 1.65078i) q^{54} +(-0.302179 + 1.71374i) q^{55} +2.52015 q^{56} -4.58064 q^{58} +(-0.493441 + 2.79845i) q^{59} +(-0.302168 - 0.253549i) q^{60} +(2.30690 + 0.839642i) q^{61} +(-8.26329 + 3.00759i) q^{62} +(-5.41368 + 4.54262i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.87936 - 4.98720i) q^{65} +(0.149977 + 0.850563i) q^{66} +(0.464094 + 2.63201i) q^{67} +(1.71113 - 2.96376i) q^{68} +(-1.81079 - 3.13638i) q^{69} +(-1.72106 + 1.44414i) q^{70} +(0.0530366 - 0.0193038i) q^{71} +(2.63511 + 0.959102i) q^{72} +(-5.33870 - 4.47970i) q^{73} +(1.03838 - 5.88895i) q^{74} -1.86067 q^{75} +4.91930 q^{77} +(0.496314 - 2.81474i) q^{78} +(6.99522 + 5.86969i) q^{79} +(0.837728 + 0.304908i) q^{80} +(-6.83754 + 2.48866i) q^{81} +(2.67298 - 2.24289i) q^{82} +(7.06195 + 12.2317i) q^{83} +(-0.557537 + 0.965682i) q^{84} +(0.529786 + 3.00457i) q^{85} +(-1.08473 - 6.15179i) q^{86} +(1.01338 - 1.75523i) q^{87} +(-0.975994 - 1.69047i) q^{88} +(-1.43077 + 1.20056i) q^{89} +(-2.34918 + 0.855031i) q^{90} +(-15.2975 - 5.56784i) q^{91} +(6.27010 + 5.26124i) q^{92} +(0.675639 - 3.83174i) q^{93} -10.5498 q^{94} +0.442463 q^{96} +(-1.35868 + 7.70545i) q^{97} +(-0.497055 - 0.417079i) q^{98} +(5.14371 + 1.87216i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{7} - 12 q^{8}+O(q^{10}) $ 24 * q + 6 * q^7 - 12 * q^8	$ 24 q + 6 q^{7} - 12 q^{8} - 6 q^{11} - 6 q^{12} + 24 q^{18} - 12 q^{20} - 54 q^{26} + 12 q^{27} - 12 q^{30} - 78 q^{31} + 24 q^{37} - 36 q^{39} + 66 q^{45} + 30 q^{46} + 36 q^{49} - 18 q^{50} - 12 q^{56} - 12 q^{58} - 12 q^{64} + 12 q^{65} - 18 q^{68} + 60 q^{69} + 48 q^{75} + 24 q^{77} + 36 q^{83} - 12 q^{84} + 78 q^{87} - 6 q^{88} - 72 q^{94} + 12 q^{96}+O(q^{100}) $ 24 * q + 6 * q^7 - 12 * q^8 - 6 * q^11 - 6 * q^12 + 24 * q^18 - 12 * q^20 - 54 * q^26 + 12 * q^27 - 12 * q^30 - 78 * q^31 + 24 * q^37 - 36 * q^39 + 66 * q^45 + 30 * q^46 + 36 * q^49 - 18 * q^50 - 12 * q^56 - 12 * q^58 - 12 * q^64 + 12 * q^65 - 18 * q^68 + 60 * q^69 + 48 * q^75 + 24 * q^77 + 36 * q^83 - 12 * q^84 + 78 * q^87 - 6 * q^88 - 72 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	0.338947	+	0.284410i	0.195691	+	0.164204i	0.735368	−	0.677668i	$-0.237009\pi$
$3$	0.338947	+	0.284410i	0.195691	+	0.164204i	−0.539677	+	0.841872i	$0.681454\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	0.837728	−	0.304908i	0.374643	−	0.136359i	−0.147834	−	0.989012i	$-0.547230\pi$
$5$	0.837728	−	0.304908i	0.374643	−	0.136359i	0.522477	+	0.852653i	$0.325008\pi$
$6$	0.338947	−	0.284410i	0.138374	−	0.116110i
$7$	−1.26007	−	2.18251i	−0.476263	−	0.824912i	0.523367	−	0.852107i	$-0.324676\pi$
$7$	−1.26007	−	2.18251i	−0.476263	−	0.824912i	−0.999630	+	0.0271956i	$0.991342\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.486949	−	2.76162i	−0.162316	−	0.920541i
$10$	−0.154806	−	0.877948i	−0.0489539	−	0.277631i
$11$	−0.975994	+	1.69047i	−0.294273	+	0.509696i	−0.974816	−	0.223012i	$-0.928411\pi$
$11$	−0.975994	+	1.69047i	−0.294273	+	0.509696i	0.680542	+	0.732709i	$0.261744\pi$
$12$	−0.221232	−	0.383185i	−0.0638641	−	0.110616i
$13$	4.94838	−	4.15218i	1.37243	−	1.15161i	0.400515	−	0.916290i	$-0.368831\pi$
$13$	4.94838	−	4.15218i	1.37243	−	1.15161i	0.971918	−	0.235318i	$-0.0756132\pi$
$14$	−2.36816	+	0.861941i	−0.632918	+	0.230363i
$15$	0.370664	+	0.134911i	0.0957050	+	0.0348338i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−0.594269	+	3.37027i	−0.144131	+	0.817410i	0.823929	+	0.566693i	$0.191777\pi$
$17$	−0.594269	+	3.37027i	−0.144131	+	0.817410i	−0.968060	+	0.250717i	$0.919334\pi$
$18$	−2.80423			−0.660962
$19$		0			0
$19$		0			0
$20$	−0.891491			−0.199344
$21$	0.193630	−	1.09813i	0.0422536	−	0.239632i
$22$	1.49531	+	1.25471i	0.318801	+	0.267506i
$23$	−7.69142	−	2.79945i	−1.60377	−	0.583725i	−0.623577	−	0.781762i	$-0.714321\pi$
$23$	−7.69142	−	2.79945i	−1.60377	−	0.583725i	−0.980195	+	0.198036i	$0.936544\pi$
$24$	−0.415780	+	0.151331i	−0.0848707	+	0.0308904i
$25$	−3.22140	+	2.70308i	−0.644281	+	0.540616i
$26$	−3.22982	−	5.59422i	−0.633421	−	1.09712i
$27$	1.28408	−	2.22409i	0.247121	−	0.428026i
$28$	0.437619	+	2.48186i	0.0827022	+	0.469028i
$29$	−0.795421	−	4.51105i	−0.147706	−	0.837682i	−0.965155	−	0.261680i	$-0.915723\pi$
$29$	−0.795421	−	4.51105i	−0.147706	−	0.837682i	0.817449	−	0.576001i	$-0.195388\pi$
$30$	0.197226	−	0.341606i	0.0360084	−	0.0623684i
$31$	−4.39680	−	7.61548i	−0.789689	−	1.36778i	−0.926157	−	0.377137i	$-0.876909\pi$
$31$	−4.39680	−	7.61548i	−0.789689	−	1.36778i	0.136468	−	0.990644i	$-0.456425\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−0.811597	+	0.295397i	−0.141281	+	0.0514221i
$34$	3.21587	+	1.17048i	0.551518	+	0.200736i
$35$	−1.72106	−	1.44414i	−0.290913	−	0.244105i
$36$	−0.486949	+	2.76162i	−0.0811581	+	0.460271i
$37$	5.97980			0.983073			0.491536	−	0.870857i	$-0.336436\pi$
$37$	5.97980			0.983073			0.491536	+	0.870857i	$0.336436\pi$
$38$		0			0
$39$	2.85816			0.457672
$40$	−0.154806	+	0.877948i	−0.0244770	+	0.138816i
$41$	2.67298	+	2.24289i	0.417449	+	0.350281i	0.827192	−	0.561920i	$-0.189937\pi$
$41$	2.67298	+	2.24289i	0.417449	+	0.350281i	−0.409743	+	0.912201i	$0.634382\pi$
$42$	−1.04783	−	0.381377i	−0.161683	−	0.0588478i
$43$	5.86997	−	2.13649i	0.895162	−	0.325812i	0.146849	−	0.989159i	$-0.453087\pi$
$43$	5.86997	−	2.13649i	0.895162	−	0.325812i	0.748312	+	0.663347i	$0.230864\pi$
$44$	1.49531	−	1.25471i	0.225427	−	0.189155i
$45$	−1.24997	−	2.16501i	−0.186335	−	0.322741i
$46$	−4.09252	+	7.08845i	−0.603409	+	1.04514i
$47$	−1.83196	−	10.3895i	−0.267218	−	1.51547i	−0.762643	−	0.646820i	$-0.776099\pi$
$47$	−1.83196	−	10.3895i	−0.267218	−	1.51547i	0.495425	−	0.868651i	$-0.335013\pi$
$48$	0.0768330	+	0.435741i	0.0110899	+	0.0628939i
$49$	0.324429	−	0.561928i	0.0463471	−	0.0802755i
$50$	2.10262	+	3.64185i	0.297356	+	0.515035i
$51$	−1.15996	+	0.973325i	−0.162427	+	0.136293i
$52$	−6.07009	+	2.20933i	−0.841769	+	0.306379i
$53$	3.53586	+	1.28695i	0.485687	+	0.176776i	0.573245	−	0.819384i	$-0.305684\pi$
$53$	3.53586	+	1.28695i	0.485687	+	0.176776i	−0.0875582	+	0.996159i	$0.527906\pi$
$54$	−1.96732	−	1.65078i	−0.267719	−	0.224643i
$55$	−0.302179	+	1.71374i	−0.0407459	+	0.231081i
$56$	2.52015			0.336769
$57$		0			0
$58$	−4.58064			−0.601468
$59$	−0.493441	+	2.79845i	−0.0642406	+	0.364327i	0.935693	+	0.352815i	$0.114775\pi$
$59$	−0.493441	+	2.79845i	−0.0642406	+	0.364327i	−0.999934	+	0.0115116i	$0.996336\pi$
$60$	−0.302168	−	0.253549i	−0.0390097	−	0.0327331i
$61$	2.30690	+	0.839642i	0.295368	+	0.107505i	0.485454	−	0.874262i	$-0.338654\pi$
$61$	2.30690	+	0.839642i	0.295368	+	0.107505i	−0.190086	+	0.981767i	$0.560877\pi$
$62$	−8.26329	+	3.00759i	−1.04944	+	0.381964i
$63$	−5.41368	+	4.54262i	−0.682060	+	0.572316i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.87936	−	4.98720i	0.357141	−	0.618586i
$66$	0.149977	+	0.850563i	0.0184609	+	0.104697i
$67$	0.464094	+	2.63201i	0.0566981	+	0.321551i	0.999944	−	0.0105431i	$-0.00335603\pi$
$67$	0.464094	+	2.63201i	0.0566981	+	0.321551i	−0.943246	+	0.332094i	$0.892245\pi$
$68$	1.71113	−	2.96376i	0.207505	−	0.359409i
$69$	−1.81079	−	3.13638i	−0.217994	−	0.377576i
$70$	−1.72106	+	1.44414i	−0.205706	+	0.172608i
$71$	0.0530366	−	0.0193038i	0.00629429	−	0.00229093i	−0.338871	−	0.940833i	$-0.610045\pi$
$71$	0.0530366	−	0.0193038i	0.00629429	−	0.00229093i	0.345165	+	0.938542i	$0.387823\pi$
$72$	2.63511	+	0.959102i	0.310551	+	0.113031i
$73$	−5.33870	−	4.47970i	−0.624847	−	0.524309i	0.274476	−	0.961594i	$-0.411496\pi$
$73$	−5.33870	−	4.47970i	−0.624847	−	0.524309i	−0.899323	+	0.437285i	$0.855940\pi$
$74$	1.03838	−	5.88895i	0.120709	−	0.684577i
$75$	−1.86067			−0.214851
$76$		0			0
$77$	4.91930			0.560606
$78$	0.496314	−	2.81474i	0.0561965	−	0.318706i
$79$	6.99522	+	5.86969i	0.787024	+	0.660392i	0.945007	−	0.327050i	$-0.106055\pi$
$79$	6.99522	+	5.86969i	0.787024	+	0.660392i	−0.157983	+	0.987442i	$0.550499\pi$
$80$	0.837728	+	0.304908i	0.0936608	+	0.0340898i
$81$	−6.83754	+	2.48866i	−0.759727	+	0.276518i
$82$	2.67298	−	2.24289i	0.295181	−	0.247686i
$83$	7.06195	+	12.2317i	0.775150	+	1.34260i	0.934710	+	0.355411i	$0.115659\pi$
$83$	7.06195	+	12.2317i	0.775150	+	1.34260i	−0.159561	+	0.987188i	$0.551008\pi$
$84$	−0.557537	+	0.965682i	−0.0608322	+	0.105364i
$85$	0.529786	+	3.00457i	0.0574634	+	0.325891i
$86$	−1.08473	−	6.15179i	−0.116969	−	0.663364i
$87$	1.01338	−	1.75523i	0.108646	−	0.188181i
$88$	−0.975994	−	1.69047i	−0.104041	−	0.180205i
$89$	−1.43077	+	1.20056i	−0.151662	+	0.127259i	−0.715461	−	0.698652i	$-0.753783\pi$
$89$	−1.43077	+	1.20056i	−0.151662	+	0.127259i	0.563800	+	0.825912i	$0.309339\pi$
$90$	−2.34918	+	0.855031i	−0.247625	+	0.0901282i
$91$	−15.2975	−	5.56784i	−1.60361	−	0.583668i
$92$	6.27010	+	5.26124i	0.653704	+	0.548522i
$93$	0.675639	−	3.83174i	0.0700605	−	0.397333i
$94$	−10.5498			−1.08813
$95$		0			0
$96$	0.442463			0.0451587
$97$	−1.35868	+	7.70545i	−0.137953	+	0.782370i	0.834805	+	0.550546i	$0.185580\pi$
$97$	−1.35868	+	7.70545i	−0.137953	+	0.782370i	−0.972758	+	0.231824i	$0.925531\pi$
$98$	−0.497055	−	0.417079i	−0.0502101	−	0.0421313i
$99$	5.14371	+	1.87216i	0.516962	+	0.188159i
$100$	3.95164	−	1.43828i	0.395164	−	0.143828i
$101$	−4.12505	+	3.46133i	−0.410458	+	0.344415i	−0.824519	−	0.565834i	$-0.808554\pi$
$101$	−4.12505	+	3.46133i	−0.410458	+	0.344415i	0.414061	+	0.910249i	$0.364110\pi$
$102$	0.757113	+	1.31136i	0.0749653	+	0.129844i
$103$	−2.34734	+	4.06571i	−0.231290	+	0.400606i	−0.958188	−	0.286139i	$-0.907628\pi$
$103$	−2.34734	+	4.06571i	−0.231290	+	0.400606i	0.726898	+	0.686746i	$0.240961\pi$
$104$	1.12171	+	6.36151i	0.109992	+	0.623798i
$105$	−0.172620	−	0.978976i	−0.0168460	−	0.0955383i
$106$	1.88139	−	3.25866i	0.182737	−	0.316509i
$107$	8.01864	+	13.8887i	0.775191	+	1.34267i	0.934687	+	0.355472i	$0.115680\pi$
$107$	8.01864	+	13.8887i	0.775191	+	1.34267i	−0.159496	+	0.987199i	$0.550987\pi$
$108$	−1.96732	+	1.65078i	−0.189306	+	0.158846i
$109$	13.2504	−	4.82275i	1.26916	−	0.461936i	0.382327	−	0.924027i	$-0.375123\pi$
$109$	13.2504	−	4.82275i	1.26916	−	0.461936i	0.886832	+	0.462091i	$0.152901\pi$
$110$	1.63524	+	0.595177i	0.155914	+	0.0567479i
$111$	2.02683	+	1.70071i	0.192378	+	0.161425i
$112$	0.437619	−	2.48186i	0.0413511	−	0.234514i
$113$	12.7224			1.19682			0.598410	−	0.801190i	$-0.295799\pi$
$113$	12.7224			1.19682			0.598410	+	0.801190i	$0.295799\pi$
$114$		0			0
$115$	−7.29689			−0.680439
$116$	−0.795421	+	4.51105i	−0.0738529	+	0.418841i
$117$	−13.8764	−	11.6437i	−1.28287	−	1.07646i
$118$	2.67025	+	0.971890i	0.245816	+	0.0894697i
$119$	8.10447	−	2.94979i	0.742936	−	0.270406i
$120$	−0.302168	+	0.253549i	−0.0275840	+	0.0231458i
$121$	3.59487	+	6.22650i	0.326806	+	0.566045i
$122$	1.22747	−	2.12605i	0.111130	−	0.192483i
$123$	0.268095	+	1.52044i	0.0241733	+	0.137094i
$124$	1.52699	+	8.66001i	0.137128	+	0.777692i
$125$	−4.10320	+	7.10695i	−0.367001	+	0.635665i
$126$	3.53353	+	6.12026i	0.314792	+	0.545236i
$127$	−5.49592	+	4.61163i	−0.487684	+	0.409216i	−0.853196	−	0.521591i	$-0.825339\pi$
$127$	−5.49592	+	4.61163i	−0.487684	+	0.409216i	0.365511	+	0.930807i	$0.380894\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	2.59725	+	0.945320i	0.228675	+	0.0832308i
$130$	−4.41144	−	3.70164i	−0.386909	−	0.324655i
$131$	−0.611703	+	3.46914i	−0.0534447	+	0.303100i	−0.999799	−	0.0200298i	$-0.993624\pi$
$131$	−0.611703	+	3.46914i	−0.0534447	+	0.303100i	0.946355	+	0.323130i	$0.104735\pi$
$132$	0.863684			0.0751740
$133$		0			0
$134$	2.67261			0.230878
$135$	0.397566	−	2.25471i	0.0342170	−	0.194054i
$136$	−2.62160	−	2.19979i	−0.224801	−	0.188630i
$137$	10.3400	+	3.76343i	0.883402	+	0.321532i	0.743582	−	0.668645i	$-0.233125\pi$
$137$	10.3400	+	3.76343i	0.883402	+	0.321532i	0.139820	+	0.990177i	$0.455348\pi$
$138$	−3.40317	+	1.23865i	−0.289697	+	0.105441i
$139$	16.6681	−	13.9862i	1.41377	−	1.18629i	0.459185	−	0.888341i	$-0.348141\pi$
$139$	16.6681	−	13.9862i	1.41377	−	1.18629i	0.954581	−	0.297950i	$-0.0963030\pi$
$140$	1.12334	+	1.94569i	0.0949400	+	0.164441i
$141$	2.33395	−	4.04253i	0.196554	−	0.340442i
$142$	−0.00980077	−	0.0555829i	−0.000822462	−	0.00466442i
$143$	2.18956	+	12.4176i	0.183100	+	1.03841i
$144$	1.40211	−	2.42853i	0.116843	−	0.202378i
$145$	−2.04180	−	3.53651i	−0.169562	−	0.293691i
$146$	−5.33870	+	4.47970i	−0.441834	+	0.370743i
$147$	0.269782	−	0.0981928i	0.0222513	−	0.00809880i
$148$	−5.61917	−	2.04521i	−0.461893	−	0.168115i
$149$	11.0231	+	9.24944i	0.903043	+	0.757743i	0.970783	−	0.239960i	$-0.0771342\pi$
$149$	11.0231	+	9.24944i	0.903043	+	0.757743i	−0.0677394	+	0.997703i	$0.521579\pi$
$150$	−0.323101	+	1.83240i	−0.0263811	+	0.149615i
$151$	−12.4068			−1.00965			−0.504824	−	0.863222i	$-0.668443\pi$
$151$	−12.4068			−1.00965			−0.504824	+	0.863222i	$0.668443\pi$
$152$		0			0
$153$	9.59679			0.775855
$154$	0.854227	−	4.84456i	0.0688356	−	0.390386i
$155$	−6.00535	−	5.03908i	−0.482361	−	0.404749i
$156$	−2.68579	−	0.977548i	−0.215035	−	0.0782665i
$157$	0.424008	−	0.154326i	0.0338395	−	0.0123166i	−0.325045	−	0.945699i	$-0.605379\pi$
$157$	0.424008	−	0.154326i	0.0338395	−	0.0123166i	0.358884	+	0.933382i	$0.383157\pi$
$158$	6.99522	−	5.86969i	0.556510	−	0.466967i
$159$	0.832446	+	1.44184i	0.0660173	+	0.114345i
$160$	0.445746	−	0.772054i	0.0352393	−	0.0610362i
$161$	3.58193	+	20.3141i	0.282295	+	1.60098i
$162$	1.26353	+	7.16582i	0.0992721	+	0.563000i
$163$	0.0346271	−	0.0599759i	0.00271220	−	0.00469768i	−0.864666	−	0.502347i	$-0.832470\pi$
$163$	0.0346271	−	0.0599759i	0.00271220	−	0.00469768i	0.867378	+	0.497649i	$0.165803\pi$
$164$	−1.74466	−	3.02184i	−0.136235	−	0.235966i
$165$	−0.589829	+	0.494925i	−0.0459181	+	0.0385299i
$166$	13.2721	−	4.83066i	1.03012	−	0.374932i
$167$	2.04262	+	0.743451i	0.158062	+	0.0575300i	0.419840	−	0.907598i	$-0.362086\pi$
$167$	2.04262	+	0.743451i	0.158062	+	0.0575300i	−0.261777	+	0.965128i	$0.584309\pi$
$168$	0.854195	+	0.716755i	0.0659026	+	0.0552989i
$169$	4.98840	−	28.2906i	0.383723	−	2.17620i
$170$	3.05092			0.233995
$171$		0			0
$172$	−6.24669			−0.476306
$173$	2.92585	−	16.5933i	0.222448	−	1.26157i	−0.645056	−	0.764136i	$-0.723166\pi$
$173$	2.92585	−	16.5933i	0.222448	−	1.26157i	0.867504	−	0.497431i	$-0.165723\pi$
$174$	−1.55259	−	1.30278i	−0.117702	−	0.0987636i
$175$	9.95870	+	3.62467i	0.752807	+	0.273999i
$176$	−1.83427	+	0.667620i	−0.138263	+	0.0503237i
$177$	−0.963156	+	0.808184i	−0.0723953	+	0.0607468i
$178$	0.933870	+	1.61751i	0.0699965	+	0.121238i
$179$	9.48276	−	16.4246i	0.708775	−	1.22763i	−0.256537	−	0.966534i	$-0.582582\pi$
$179$	9.48276	−	16.4246i	0.708775	−	1.22763i	0.965312	−	0.261099i	$-0.0840850\pi$
$180$	0.434111	+	2.46196i	0.0323567	+	0.183504i
$181$	0.345017	+	1.95669i	0.0256449	+	0.145439i	0.994942	−	0.100454i	$-0.0320297\pi$
$181$	0.345017	+	1.95669i	0.0256449	+	0.145439i	−0.969297	+	0.245894i	$0.920919\pi$
$182$	−8.13963	+	14.0983i	−0.603350	+	1.04503i
$183$	0.543113	+	0.940699i	0.0401481	+	0.0695385i
$184$	6.27010	−	5.26124i	0.462238	−	0.387864i
$185$	5.00944	−	1.82329i	0.368302	−	0.134051i
$186$	−3.65620	−	1.33075i	−0.268086	−	0.0975752i
$187$	−5.11734	−	4.29396i	−0.374217	−	0.314005i
$188$	−1.83196	+	10.3895i	−0.133609	+	0.757735i
$189$	−6.47214			−0.470779
$190$		0			0
$191$	−20.9259			−1.51415			−0.757074	−	0.653329i	$-0.773372\pi$
$191$	−20.9259			−1.51415			−0.757074	+	0.653329i	$0.773372\pi$
$192$	0.0768330	−	0.435741i	0.00554494	−	0.0314469i
$193$	−5.96656	−	5.00654i	−0.429482	−	0.360379i	0.402274	−	0.915519i	$-0.368220\pi$
$193$	−5.96656	−	5.00654i	−0.429482	−	0.360379i	−0.831756	+	0.555141i	$0.812664\pi$
$194$	7.35245	+	2.67607i	0.527875	+	0.192131i
$195$	2.39436	−	0.871476i	0.171464	−	0.0624077i
$196$	−0.497055	+	0.417079i	−0.0355039	+	0.0297913i
$197$	−0.912571	−	1.58062i	−0.0650180	−	0.112614i	0.831684	−	0.555249i	$-0.187377\pi$
$197$	−0.912571	−	1.58062i	−0.0650180	−	0.112614i	−0.896702	+	0.442635i	$0.854044\pi$
$198$	2.73691	−	4.74047i	0.194504	−	0.336890i
$199$	0.409680	+	2.32341i	0.0290415	+	0.164702i	0.995879	−	0.0906888i	$-0.0289069\pi$
$199$	0.409680	+	2.32341i	0.0290415	+	0.164702i	−0.966838	+	0.255391i	$0.917796\pi$
$200$	−0.730233	−	4.14136i	−0.0516353	−	0.292838i
$201$	−0.591266	+	1.02410i	−0.0417047	+	0.0722346i
$202$	2.69244	+	4.66343i	0.189439	+	0.328118i
$203$	−8.84314	+	7.42027i	−0.620667	+	0.520801i
$204$	1.42291	−	0.517895i	0.0996234	−	0.0362599i
$205$	2.92310	+	1.06392i	0.204158	+	0.0743076i
$206$	3.59633	+	3.01768i	0.250568	+	0.210252i
$207$	−3.98569	+	22.6040i	−0.277025	+	1.57109i
$208$	6.45965			0.447896
$209$		0			0
$210$	−0.994078			−0.0685979
$211$	0.0626957	−	0.355565i	0.00431615	−	0.0244781i	−0.982574	−	0.185874i	$-0.940488\pi$
$211$	0.0626957	−	0.355565i	0.00431615	−	0.0244781i	0.986890	+	0.161396i	$0.0515995\pi$
$212$	−2.88246	−	2.41867i	−0.197968	−	0.166115i
$213$	0.0234668	+	0.00854121i	0.00160792	+	0.000585234i
$214$	15.0701	−	5.48507i	1.03017	−	0.374952i
$215$	4.26600	−	3.57960i	0.290939	−	0.244127i
$216$	1.28408	+	2.22409i	0.0873705	+	0.151330i
$217$	−11.0806	+	19.1921i	−0.752199	+	1.30285i
$218$	−2.44858	−	13.8866i	−0.165839	−	0.940517i
$219$	−0.535462	−	3.03676i	−0.0361832	−	0.205205i
$220$	0.870091	−	1.50704i	0.0586615	−	0.101605i
$221$	11.0533	+	19.1449i	0.743525	+	1.28782i
$222$	2.02683	−	1.70071i	0.136032	−	0.114144i
$223$	16.9601	−	6.17299i	1.13574	−	0.413374i	0.295364	−	0.955385i	$-0.404559\pi$
$223$	16.9601	−	6.17299i	1.13574	−	0.413374i	0.840371	+	0.542011i	$0.182337\pi$
$224$	−2.36816	−	0.861941i	−0.158230	−	0.0575909i
$225$	9.03354	+	7.58004i	0.602236	+	0.505336i
$226$	2.20922	−	12.5291i	0.146955	−	0.833423i
$227$	−12.2845			−0.815349			−0.407675	−	0.913127i	$-0.633660\pi$
$227$	−12.2845			−0.815349			−0.407675	+	0.913127i	$0.633660\pi$
$228$		0			0
$229$	6.79174			0.448811			0.224405	−	0.974496i	$-0.427956\pi$
$229$	6.79174			0.448811			0.224405	+	0.974496i	$0.427956\pi$
$230$	−1.26709	+	7.18604i	−0.0835496	+	0.473833i
$231$	1.66738	+	1.39910i	0.109706	+	0.0920539i
$232$	4.30440	+	1.56667i	0.282598	+	0.102857i
$233$	−20.1370	+	7.32927i	−1.31922	+	0.480156i	−0.903208	−	0.429203i	$-0.858794\pi$
$233$	−20.1370	+	7.32927i	−1.31922	+	0.480156i	−0.416011	+	0.909360i	$0.636572\pi$
$234$	−13.8764	+	11.6437i	−0.907127	+	0.761170i
$235$	−4.70254	−	8.14503i	−0.306760	−	0.531323i
$236$	1.42081	−	2.46091i	0.0924867	−	0.160192i
$237$	0.701609	+	3.97902i	0.0455744	+	0.258465i
$238$	−1.49765	−	8.49357i	−0.0970780	−	0.550556i
$239$	5.91881	−	10.2517i	0.382856	−	0.663126i	−0.608613	−	0.793467i	$-0.708274\pi$
$239$	5.91881	−	10.2517i	0.382856	−	0.663126i	0.991469	+	0.130341i	$0.0416071\pi$
$240$	0.197226	+	0.341606i	0.0127309	+	0.0220506i
$241$	16.6586	−	13.9783i	1.07308	−	0.900419i	0.0777494	−	0.996973i	$-0.475227\pi$
$241$	16.6586	−	13.9783i	1.07308	−	0.900419i	0.995328	+	0.0965543i	$0.0307822\pi$
$242$	6.75614	−	2.45904i	0.434301	−	0.158073i
$243$	−10.2652	−	3.73623i	−0.658513	−	0.239679i
$244$	−1.88060	−	1.57801i	−0.120393	−	0.101022i
$245$	0.100447	−	0.569664i	0.00641733	−	0.0363945i
$246$	1.54390			0.0984353
$247$		0			0
$248$	8.79360			0.558394
$249$	−1.08518	+	6.15437i	−0.0687706	+	0.390017i
$250$	6.28646	+	5.27497i	0.397591	+	0.333618i
$251$	−22.2153	−	8.08571i	−1.40222	−	0.510365i	−0.473382	−	0.880857i	$-0.656967\pi$
$251$	−22.2153	−	8.08571i	−1.40222	−	0.510365i	−0.928836	+	0.370492i	$0.879189\pi$
$252$	6.64087	−	2.41708i	0.418335	−	0.152262i
$253$	12.2392	−	10.2699i	0.769470	−	0.645662i
$254$	3.58721	+	6.21323i	0.225082	+	0.389853i
$255$	−0.674959	+	1.16906i	−0.0422676	+	0.0732096i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	0.160359	+	0.909439i	0.0100029	+	0.0567293i	0.989401	−	0.145211i	$-0.0463863\pi$
$257$	0.160359	+	0.909439i	0.0100029	+	0.0567293i	−0.979398	+	0.201941i	$0.935275\pi$
$258$	1.38197	−	2.39364i	0.0860374	−	0.149021i
$259$	−7.53498	−	13.0510i	−0.468201	−	0.810948i
$260$	−4.41144	+	3.70164i	−0.273586	+	0.229566i
$261$	−12.0705	+	4.39330i	−0.747145	+	0.271939i
$262$	3.31021	+	1.20482i	0.204506	+	0.0744340i
$263$	3.30906	+	2.77663i	0.204045	+	0.171214i	0.739084	−	0.673613i	$-0.235259\pi$
$263$	3.30906	+	2.77663i	0.204045	+	0.171214i	−0.535039	+	0.844828i	$0.679703\pi$
$264$	0.149977	−	0.850563i	0.00923045	−	0.0523485i
$265$	3.35449			0.206064
$266$		0			0
$267$	−0.826407			−0.0505753
$268$	0.464094	−	2.63201i	0.0283490	−	0.160775i
$269$	8.26972	+	6.93912i	0.504214	+	0.423086i	0.859088	−	0.511829i	$-0.171032\pi$
$269$	8.26972	+	6.93912i	0.504214	+	0.423086i	−0.354874	+	0.934914i	$0.615476\pi$
$270$	−2.15142	−	0.783052i	−0.130931	−	0.0476550i
$271$	−0.758561	+	0.276094i	−0.0460793	+	0.0167715i	−0.364957	−	0.931024i	$-0.618916\pi$
$271$	−0.758561	+	0.276094i	−0.0460793	+	0.0167715i	0.318878	+	0.947796i	$0.396694\pi$
$272$	−2.62160	+	2.19979i	−0.158958	+	0.133382i
$273$	−3.60149	−	6.23796i	−0.217972	−	0.377539i
$274$	5.50177	−	9.52935i	0.332374	−	0.575689i
$275$	−1.42541	−	8.08388i	−0.0859552	−	0.487476i
$276$	0.628881	+	3.56656i	0.0378542	+	0.214682i
$277$	4.57434	−	7.92300i	0.274846	−	0.476047i	−0.695250	−	0.718768i	$-0.744707\pi$
$277$	4.57434	−	7.92300i	0.274846	−	0.476047i	0.970096	+	0.242721i	$0.0780399\pi$
$278$	−10.8793	−	18.8435i	−0.652497	−	1.13016i
$279$	−18.8901	+	15.8507i	−1.13092	+	0.948954i
$280$	2.11120	−	0.768413i	0.126168	−	0.0459215i
$281$	19.9363	+	7.25621i	1.18930	+	0.432869i	0.859477	−	0.511174i	$-0.170789\pi$
$281$	19.9363	+	7.25621i	1.18930	+	0.432869i	0.329822	+	0.944043i	$0.393011\pi$
$282$	−3.57583	−	3.00047i	−0.212937	−	0.178676i
$283$	0.901208	−	5.11101i	0.0535713	−	0.303818i	−0.946235	−	0.323479i	$-0.895148\pi$
$283$	0.901208	−	5.11101i	0.0535713	−	0.303818i	0.999807	+	0.0196610i	$0.00625868\pi$
$284$	−0.0564404			−0.00334912
$285$		0			0
$286$	12.6092			0.745596
$287$	1.52699	−	8.66001i	0.0901356	−	0.511184i
$288$	−2.14816	−	1.80252i	−0.126582	−	0.106215i
$289$	4.96922	+	1.80865i	0.292307	+	0.106391i
$290$	−3.83733	+	1.39668i	−0.225336	+	0.0820156i
$291$	−2.65203	+	2.22531i	−0.155465	+	0.130450i
$292$	3.48459	+	6.03548i	0.203920	+	0.353200i
$293$	−8.78298	+	15.2126i	−0.513107	+	0.888728i	0.486777	+	0.873526i	$0.338172\pi$
$293$	−8.78298	+	15.2126i	−0.513107	+	0.888728i	−0.999884	+	0.0152018i	$0.995161\pi$
$294$	−0.0498538	−	0.282735i	−0.00290753	−	0.0164894i
$295$	0.439899	+	2.49479i	0.0256119	+	0.145252i
$296$	−2.98990	+	5.17866i	−0.173784	+	0.301003i
$297$	2.50651	+	4.34140i	0.145442	+	0.251914i
$298$	11.0231	−	9.24944i	0.638548	−	0.535806i
$299$	−49.6839	+	18.0835i	−2.87329	+	1.04579i
$300$	1.74845	+	0.636385i	0.100947	+	0.0367417i
$301$	−12.0595	−	10.1191i	−0.695099	−	0.583257i
$302$	−2.15441	+	12.2183i	−0.123972	+	0.703082i
$303$	−2.38261			−0.136877
$304$		0			0
$305$	2.18857			0.125317
$306$	1.66647	−	9.45099i	0.0952655	−	0.540277i
$307$	16.5223	+	13.8639i	0.942979	+	0.791253i	0.978101	−	0.208130i	$-0.0667377\pi$
$307$	16.5223	+	13.8639i	0.942979	+	0.791253i	−0.0351224	+	0.999383i	$0.511182\pi$
$308$	−4.62263	−	1.68250i	−0.263399	−	0.0958693i
$309$	−1.95195	+	0.710452i	−0.111043	+	0.0404162i
$310$	−6.00535	+	5.03908i	−0.341081	+	0.286201i
$311$	1.28684	+	2.22887i	0.0729701	+	0.126388i	0.900202	−	0.435473i	$-0.143419\pi$
$311$	1.28684	+	2.22887i	0.0729701	+	0.126388i	−0.827232	+	0.561861i	$0.810086\pi$
$312$	−1.42908	+	2.47524i	−0.0809057	+	0.140133i
$313$	−0.900173	−	5.10513i	−0.0508808	−	0.288559i	0.948741	−	0.316054i	$-0.102358\pi$
$313$	−0.900173	−	5.10513i	−0.0508808	−	0.288559i	−0.999622	+	0.0274949i	$0.991247\pi$
$314$	−0.0783536	−	0.444365i	−0.00442175	−	0.0250770i
$315$	−3.15011	+	5.45616i	−0.177489	+	0.307420i
$316$	−4.56581	−	7.90821i	−0.256847	−	0.444872i
$317$	15.5171	−	13.0204i	0.871528	−	0.731299i	−0.0928912	−	0.995676i	$-0.529611\pi$
$317$	15.5171	−	13.0204i	0.871528	−	0.731299i	0.964419	+	0.264377i	$0.0851664\pi$
$318$	1.56449	−	0.569427i	0.0877321	−	0.0319319i
$319$	8.40214	+	3.05813i	0.470429	+	0.171222i
$320$	−0.682922	−	0.573040i	−0.0381765	−	0.0320339i
$321$	−1.23219	+	6.98811i	−0.0687742	+	0.390038i
$322$	20.6275			1.14953
$323$		0			0
$324$	7.27636			0.404242
$325$	−4.71705	+	26.7517i	−0.261655	+	1.48392i
$326$	−0.0530518	−	0.0445157i	−0.00293827	−	0.00246550i
$327$	5.86282	+	2.13389i	0.324215	+	0.118005i
$328$	−3.27889	+	1.19342i	−0.181046	+	0.0658955i
$329$	−20.3669	+	17.0899i	−1.12286	+	0.942194i
$330$	0.384983	+	0.666811i	0.0211926	+	0.0367067i
$331$	−10.6640	+	18.4706i	−0.586146	+	1.01523i	0.408585	+	0.912720i	$0.366022\pi$
$331$	−10.6640	+	18.4706i	−0.586146	+	1.01523i	−0.994731	+	0.102515i	$0.967311\pi$
$332$	−2.45259	−	13.9093i	−0.134603	−	0.763373i
$333$	−2.91185	−	16.5139i	−0.159569	−	0.904959i
$334$	1.08685	−	1.88248i	0.0594699	−	0.103005i
$335$	1.19130	+	2.06340i	0.0650879	+	0.112736i
$336$	0.854195	−	0.716755i	0.0466002	−	0.0391022i
$337$	−21.3568	+	7.77325i	−1.16338	+	0.423436i	−0.850304	−	0.526292i	$-0.823582\pi$
$337$	−21.3568	+	7.77325i	−1.16338	+	0.423436i	−0.313077	+	0.949728i	$0.601360\pi$
$338$	−26.9946	−	9.82524i	−1.46831	−	0.534422i
$339$	4.31221	+	3.61837i	0.234207	+	0.196523i
$340$	0.529786	−	3.00457i	0.0287317	−	0.162945i
$341$	17.1650			0.929538
$342$		0			0
$343$	−19.2762			−1.04082
$344$	−1.08473	+	6.15179i	−0.0584845	+	0.331682i
$345$	−2.47326	−	2.07531i	−0.133156	−	0.111731i
$346$	−15.8332	−	5.76280i	−0.851196	−	0.309810i
$347$	4.63133	−	1.68566i	0.248623	−	0.0904912i	−0.214703	−	0.976679i	$-0.568878\pi$
$347$	4.63133	−	1.68566i	0.248623	−	0.0904912i	0.463325	+	0.886188i	$0.346656\pi$
$348$	−1.55259	+	1.30278i	−0.0832278	+	0.0698364i
$349$	−13.0808	−	22.6565i	−0.700197	−	1.21278i	−0.968397	−	0.249413i	$-0.919762\pi$
$349$	−13.0808	−	22.6565i	−0.700197	−	1.21278i	0.268201	−	0.963363i	$-0.413571\pi$
$350$	5.29892	−	9.17799i	0.283239	−	0.490584i
$351$	−2.88072	−	16.3374i	−0.153761	−	0.872024i
$352$	0.338959	+	1.92233i	0.0180666	+	0.102461i
$353$	−1.35407	+	2.34531i	−0.0720697	+	0.124828i	−0.899808	−	0.436286i	$-0.856294\pi$
$353$	−1.35407	+	2.34531i	−0.0720697	+	0.124828i	0.827739	+	0.561114i	$0.189627\pi$
$354$	0.628656	+	1.08886i	0.0334127	+	0.0578724i
$355$	0.0385444	−	0.0323426i	0.00204572	−	0.00171657i
$356$	1.75510	−	0.638805i	0.0930202	−	0.0338566i
$357$	3.58593	+	1.30517i	0.189788	+	0.0690771i
$358$	−14.5284	−	12.1908i	−0.767851	−	0.644304i
$359$	−1.61667	+	9.16858i	−0.0853245	+	0.483899i	0.911962	+	0.410276i	$0.134567\pi$
$359$	−1.61667	+	9.16858i	−0.0853245	+	0.483899i	−0.997286	+	0.0736237i	$0.976544\pi$
$360$	2.49994			0.131759
$361$		0			0
$362$	1.98687			0.104428
$363$	−0.552409	+	3.13287i	−0.0289940	+	0.164433i
$364$	12.4706	+	10.4641i	0.653639	+	0.548468i
$365$	−5.83827	−	2.12496i	−0.305589	−	0.111225i
$366$	1.02072	−	0.371511i	0.0533538	−	0.0194192i
$367$	5.94023	−	4.98445i	0.310077	−	0.260186i	−0.474447	−	0.880284i	$-0.657352\pi$
$367$	5.94023	−	4.98445i	0.310077	−	0.260186i	0.784524	+	0.620098i	$0.212907\pi$
$368$	−4.09252	−	7.08845i	−0.213337	−	0.369511i
$369$	4.89242	−	8.47393i	0.254689	−	0.441135i
$370$	−0.925708	−	5.24995i	−0.0481252	−	0.272932i
$371$	−1.64666	−	9.33869i	−0.0854905	−	0.484841i
$372$	−1.94542	+	3.36957i	−0.100866	+	0.174704i
$373$	−12.5062	−	21.6614i	−0.647546	−	1.12158i	−0.983707	−	0.179778i	$-0.942462\pi$
$373$	−12.5062	−	21.6614i	−0.647546	−	1.12158i	0.336161	−	0.941804i	$-0.390871\pi$
$374$	−5.11734	+	4.29396i	−0.264611	+	0.222035i
$375$	−3.41205	+	1.24189i	−0.176198	+	0.0641307i
$376$	9.91359	+	3.60825i	0.511254	+	0.186081i
$377$	−22.6668	−	19.0197i	−1.16740	−	0.979563i
$378$	−1.12387	+	6.37381i	−0.0578059	+	0.327833i
$379$	−19.1802			−0.985222			−0.492611	−	0.870250i	$-0.663957\pi$
$379$	−19.1802			−0.985222			−0.492611	+	0.870250i	$0.663957\pi$
$380$		0			0
$381$	−3.17442			−0.162630
$382$	−3.63375	+	20.6080i	−0.185919	+	1.05440i
$383$	3.70244	+	3.10671i	0.189186	+	0.158746i	0.732461	−	0.680809i	$-0.238372\pi$
$383$	3.70244	+	3.10671i	0.189186	+	0.158746i	−0.543275	+	0.839555i	$0.682816\pi$
$384$	−0.415780	−	0.151331i	−0.0212177	−	0.00772260i
$385$	4.12103	−	1.49993i	0.210027	−	0.0764437i
$386$	−5.96656	+	5.00654i	−0.303690	+	0.254826i
$387$	−8.75856	−	15.1703i	−0.445223	−	0.771149i
$388$	3.91216	−	6.77606i	0.198610	−	0.344002i
$389$	3.77322	+	21.3990i	0.191310	+	1.08497i	0.917576	+	0.397559i	$0.130143\pi$
$389$	3.77322	+	21.3990i	0.191310	+	1.08497i	−0.726266	+	0.687413i	$0.758746\pi$
$390$	−0.442460	−	2.50931i	−0.0224048	−	0.127064i
$391$	14.0057	−	24.2585i	0.708297	−	1.22681i
$392$	0.324429	+	0.561928i	0.0163862	+	0.0283817i
$393$	−1.19399	+	1.00188i	−0.0602289	+	0.0505381i
$394$	−1.71507	+	0.624235i	−0.0864041	+	0.0314485i
$395$	7.64981	+	2.78430i	0.384904	+	0.140094i
$396$	−4.19319	−	3.51850i	−0.210716	−	0.176811i
$397$	2.03412	−	11.5361i	0.102089	−	0.578978i	−0.890254	−	0.455465i	$-0.849473\pi$
$397$	2.03412	−	11.5361i	0.102089	−	0.578978i	0.992343	−	0.123513i	$-0.0394159\pi$
$398$	2.35926			0.118259
$399$		0			0
$400$	−4.20524			−0.210262
$401$	2.05119	−	11.6329i	0.102432	−	0.580919i	−0.889784	−	0.456383i	$-0.849145\pi$
$401$	2.05119	−	11.6329i	0.102432	−	0.580919i	0.992215	−	0.124536i	$-0.0397441\pi$
$402$	0.905872	+	0.760117i	0.0451808	+	0.0379112i
$403$	−53.3779	−	19.4280i	−2.65894	−	0.967776i
$404$	5.06012	−	1.84173i	0.251751	−	0.0916297i
$405$	−4.96919	+	4.16964i	−0.246921	+	0.207191i
$406$	5.77195	+	9.99731i	0.286457	+	0.496158i
$407$	−5.83625	+	10.1087i	−0.289292	+	0.501069i
$408$	−0.262942	−	1.49122i	−0.0130176	−	0.0738264i
$409$	−4.38744	−	24.8824i	−0.216945	−	1.23036i	−0.877499	−	0.479578i	$-0.840790\pi$
$409$	−4.38744	−	24.8824i	−0.216945	−	1.23036i	0.660554	−	0.750778i	$-0.270321\pi$
$410$	1.55535	−	2.69395i	0.0768133	−	0.133045i
$411$	2.43433	+	4.21639i	0.120077	+	0.207979i
$412$	3.59633	−	3.01768i	0.177179	−	0.148670i
$413$	6.72941	−	2.44931i	0.331133	−	0.120522i
$414$	21.5685	+	7.85029i	1.06003	+	0.385821i
$415$	9.64552	+	8.09355i	0.473480	+	0.397297i
$416$	1.12171	−	6.36151i	0.0549962	−	0.311899i
$417$	9.62739			0.471455
$418$		0			0
$419$	31.6143			1.54446			0.772229	−	0.635344i	$-0.219142\pi$
$419$	31.6143			1.54446			0.772229	+	0.635344i	$0.219142\pi$
$420$	−0.172620	+	0.978976i	−0.00842299	+	0.0477691i
$421$	1.67742	+	1.40752i	0.0817526	+	0.0685985i	0.682748	−	0.730654i	$-0.260785\pi$
$421$	1.67742	+	1.40752i	0.0817526	+	0.0685985i	−0.600996	+	0.799252i	$0.705229\pi$
$422$	−0.339276	−	0.123486i	−0.0165157	−	0.00601123i
$423$	−27.7999	+	10.1184i	−1.35168	+	0.491971i
$424$	−2.88246	+	2.41867i	−0.139984	+	0.117461i
$425$	−7.19572	−	12.4633i	−0.349044	−	0.604561i
$426$	0.0124864	−	0.0216271i	0.000604968	−	0.00104784i
$427$	−1.07433	−	6.09284i	−0.0519906	−	0.294853i
$428$	−2.78484	−	15.7936i	−0.134611	−	0.763414i
$429$	−2.78955	+	4.83164i	−0.134681	+	0.233274i
$430$	−2.78444	−	4.82278i	−0.134277	−	0.232575i
$431$	1.38173	−	1.15941i	0.0665554	−	0.0558466i	−0.608903	−	0.793245i	$-0.708390\pi$
$431$	1.38173	−	1.15941i	0.0665554	−	0.0558466i	0.675459	+	0.737398i	$0.263946\pi$
$432$	2.41328	−	0.878362i	0.116109	−	0.0422602i
$433$	−6.17597	−	2.24787i	−0.296798	−	0.108026i	0.189329	−	0.981914i	$-0.439369\pi$
$433$	−6.17597	−	2.24787i	−0.296798	−	0.108026i	−0.486127	+	0.873888i	$0.661591\pi$
$434$	16.9764	+	14.2449i	0.814895	+	0.683778i
$435$	0.313756	−	1.77940i	0.0150434	−	0.0853155i
$436$	−14.1008			−0.675305
$437$		0			0
$438$	−3.08361			−0.147340
$439$	1.58551	−	8.99188i	0.0756723	−	0.429159i	−0.923310	−	0.384056i	$-0.874527\pi$
$439$	1.58551	−	8.99188i	0.0756723	−	0.429159i	0.998982	−	0.0451036i	$-0.0143618\pi$
$440$	−1.33306	−	1.11857i	−0.0635510	−	0.0533256i
$441$	−1.70982	−	0.622322i	−0.0814198	−	0.0296344i
$442$	20.7734	−	7.56090i	0.988090	−	0.359635i
$443$	−21.0422	+	17.6565i	−0.999744	+	0.838885i	−0.986949	−	0.161033i	$-0.948517\pi$
$443$	−21.0422	+	17.6565i	−0.999744	+	0.838885i	−0.0127949	+	0.999918i	$0.504073\pi$
$444$	−1.32292	−	2.29137i	−0.0627830	−	0.108743i
$445$	−0.832538	+	1.44200i	−0.0394661	+	0.0683572i
$446$	−3.13411	−	17.7744i	−0.148404	−	0.841643i
$447$	1.10559	+	6.27013i	0.0522928	+	0.296567i
$448$	−1.26007	+	2.18251i	−0.0595329	+	0.103114i
$449$	−3.78646	−	6.55835i	−0.178694	−	0.309508i	0.762739	−	0.646706i	$-0.223854\pi$
$449$	−3.78646	−	6.55835i	−0.178694	−	0.309508i	−0.941434	+	0.337199i	$0.890521\pi$
$450$	9.03354	−	7.58004i	0.425845	−	0.357327i
$451$	−6.40036	+	2.32954i	−0.301381	+	0.109694i
$452$	−11.9551	−	4.35131i	−0.562322	−	0.204668i
$453$	−4.20523	−	3.52861i	−0.197579	−	0.165788i
$454$	−2.13318	+	12.0978i	−0.100115	+	0.567780i
$455$	−14.5128			−0.680372
$456$		0			0
$457$	−21.7675			−1.01824			−0.509120	−	0.860696i	$-0.670029\pi$
$457$	−21.7675			−1.01824			−0.509120	+	0.860696i	$0.670029\pi$
$458$	1.17937	−	6.68856i	0.0551085	−	0.312536i
$459$	6.73269	+	5.64940i	0.314255	+	0.263691i
$460$	6.85684	+	2.49568i	0.319702	+	0.116362i
$461$	−11.2241	+	4.08522i	−0.522756	+	0.190268i	−0.589901	−	0.807476i	$-0.700833\pi$
$461$	−11.2241	+	4.08522i	−0.522756	+	0.190268i	0.0671449	+	0.997743i	$0.478611\pi$
$462$	1.66738	−	1.39910i	0.0775735	−	0.0650919i
$463$	4.37685	+	7.58093i	0.203410	+	0.352316i	0.949625	−	0.313389i	$-0.101464\pi$
$463$	4.37685	+	7.58093i	0.203410	+	0.352316i	−0.746215	+	0.665705i	$0.768131\pi$
$464$	2.29032	−	3.96695i	0.106326	−	0.184161i
$465$	−0.602326	−	3.41596i	−0.0279322	−	0.158411i
$466$	3.72117	+	21.1038i	0.172380	+	0.977614i
$467$	−14.6784	+	25.4238i	−0.679236	+	1.17647i	0.295975	+	0.955196i	$0.404355\pi$
$467$	−14.6784	+	25.4238i	−0.679236	+	1.17647i	−0.975211	+	0.221276i	$0.928978\pi$
$468$	9.05716	+	15.6875i	0.418667	+	0.725153i
$469$	5.15959	−	4.32941i	0.238248	−	0.199914i
$470$	−8.83788	+	3.21672i	−0.407661	+	0.148376i
$471$	0.187608	+	0.0682838i	0.00864453	+	0.00314635i
$472$	−2.17680	−	1.82656i	−0.100196	−	0.0840740i
$473$	−2.11737	+	12.0082i	−0.0973569	+	0.552139i
$474$	4.04041			0.185582
$475$		0			0
$476$	−8.62460			−0.395308
$477$	1.83228	−	10.3914i	0.0838944	−	0.475789i
$478$	−9.06815	−	7.60908i	−0.414767	−	0.348031i
$479$	23.3706	+	8.50620i	1.06783	+	0.388658i	0.815365	−	0.578948i	$-0.196537\pi$
$479$	23.3706	+	8.50620i	1.06783	+	0.388658i	0.252465	+	0.967606i	$0.418759\pi$
$480$	0.370664	−	0.134911i	0.0169184	−	0.00615780i
$481$	29.5903	−	24.8292i	1.34920	−	1.13211i
$482$	−10.8732	−	18.8329i	−0.495259	−	0.857813i
$483$	−4.56346	+	7.90414i	−0.207645	+	0.359651i
$484$	−1.24849	−	7.08051i	−0.0567493	−	0.321841i
$485$	1.21125	+	6.86934i	0.0550000	+	0.311921i
$486$	−5.46200	+	9.46046i	−0.247761	+	0.429135i
$487$	−4.26883	−	7.39383i	−0.193439	−	0.335046i	0.752949	−	0.658079i	$-0.228631\pi$
$487$	−4.26883	−	7.39383i	−0.193439	−	0.335046i	−0.946388	+	0.323033i	$0.895298\pi$
$488$	−1.88060	+	1.57801i	−0.0851308	+	0.0714332i
$489$	0.0287945	−	0.0104803i	0.00130213	−	0.000473937i
$490$	−0.543567	−	0.197842i	−0.0245559	−	0.00893761i
$491$	−8.83993	−	7.41758i	−0.398940	−	0.334751i	0.421144	−	0.906994i	$-0.361629\pi$
$491$	−8.83993	−	7.41758i	−0.398940	−	0.334751i	−0.820084	+	0.572243i	$0.806073\pi$
$492$	0.268095	−	1.52044i	0.0120867	−	0.0685468i
$493$	15.6762			0.706019
$494$		0			0
$495$	4.87986			0.219333
$496$	1.52699	−	8.66001i	0.0685640	−	0.388846i
$497$	−0.108961	−	0.0914289i	−0.00488756	−	0.00410115i
$498$	5.87243	+	2.13739i	0.263150	+	0.0957787i
$499$	27.8234	−	10.1269i	1.24555	−	0.453342i	0.366652	−	0.930358i	$-0.380504\pi$
$499$	27.8234	−	10.1269i	1.24555	−	0.453342i	0.878895	+	0.477016i	$0.158282\pi$
$500$	6.28646	−	5.27497i	0.281139	−	0.235904i
$501$	0.480893	+	0.832931i	0.0214847	+	0.0372126i
$502$	−11.8205	+	20.4737i	−0.527575	+	0.913787i
$503$	1.01901	+	5.77912i	0.0454356	+	0.257678i	0.999061	−	0.0433166i	$-0.0137924\pi$
$503$	1.01901	+	5.77912i	0.0454356	+	0.257678i	−0.953626	+	0.300995i	$0.902681\pi$
$504$	−1.22718	−	6.95970i	−0.0546631	−	0.310010i
$505$	−2.40028	+	4.15741i	−0.106811	+	0.185002i
$506$	−7.98855	−	13.8366i	−0.355135	−	0.615111i
$507$	9.73695	−	8.17027i	0.432433	−	0.362854i
$508$	6.74175	−	2.45380i	0.299117	−	0.108870i
$509$	24.0267	+	8.74501i	1.06497	+	0.387616i	0.814292	−	0.580456i	$-0.197126\pi$
$509$	24.0267	+	8.74501i	1.06497	+	0.387616i	0.250674	+	0.968072i	$0.419348\pi$
$510$	1.03410	+	0.867711i	0.0457906	+	0.0384229i
$511$	−3.04984	+	17.2965i	−0.134917	+	0.765153i
$512$	1.00000			0.0441942
$513$		0			0
$514$	0.923469			0.0407325
$515$	−0.726764	+	4.12168i	−0.0320250	+	0.181623i
$516$	−2.11729	−	1.77662i	−0.0932087	−	0.0782114i
$517$	19.3512	+	7.04327i	0.851065	+	0.309762i
$518$	−14.1611	+	5.15423i	−0.622205	+	0.226464i
$519$	5.71101	−	4.79211i	0.250686	−	0.210350i
$520$	2.87936	+	4.98720i	0.126268	+	0.218703i
$521$	7.01661	−	12.1531i	0.307403	−	0.532438i	−0.670390	−	0.742009i	$-0.733873\pi$
$521$	7.01661	−	12.1531i	0.307403	−	0.532438i	0.977794	+	0.209571i	$0.0672066\pi$
$522$	2.23054	+	12.6500i	0.0976280	+	0.553676i
$523$	5.39671	+	30.6062i	0.235982	+	1.33832i	0.840537	+	0.541754i	$0.182240\pi$
$523$	5.39671	+	30.6062i	0.235982	+	1.33832i	−0.604555	+	0.796563i	$0.706649\pi$
$524$	1.76133	−	3.05071i	0.0769439	−	0.133271i
$525$	2.34458	+	4.06093i	0.102326	+	0.177233i
$526$	3.30906	−	2.77663i	0.144282	−	0.121067i
$527$	28.2791	−	10.2928i	1.23186	−	0.448359i
$528$	−0.811597	−	0.295397i	−0.0353202	−	0.0128555i
$529$	33.7020	+	28.2794i	1.46531	+	1.22954i
$530$	0.582500	−	3.30352i	0.0253022	−	0.143496i
$531$	7.96853			0.345805
$532$		0			0
$533$	22.5398			0.976307
$534$	−0.143504	+	0.813852i	−0.00621003	+	0.0352188i
$535$	10.9522	+	9.19000i	0.473505	+	0.397318i
$536$	−2.51143	−	0.914086i	−0.108477	−	0.0394825i
$537$	7.88548	−	2.87008i	0.340283	−	0.123853i
$538$	8.26972	−	6.93912i	0.356533	−	0.299167i
$539$	0.633283	+	1.09688i	0.0272774	+	0.0472459i
$540$	−1.14475	+	1.98276i	−0.0492620	+	0.0853243i
$541$	0.502899	+	2.85208i	0.0216213	+	0.122621i	0.993708	−	0.112001i	$-0.0357260\pi$
$541$	0.502899	+	2.85208i	0.0216213	+	0.122621i	−0.972087	+	0.234622i	$0.924615\pi$
$542$	0.140176	+	0.794980i	0.00602109	+	0.0341473i
$543$	−0.439559	+	0.761338i	−0.0188633	+	0.0326722i
$544$	1.71113	+	2.96376i	0.0733641	+	0.127070i
$545$	9.62974	−	8.08031i	0.412493	−	0.346123i
$546$	−6.76859	+	2.46356i	−0.289669	+	0.105431i
$547$	−28.5536	−	10.3927i	−1.22086	−	0.444358i	−0.350405	−	0.936598i	$-0.613956\pi$
$547$	−28.5536	−	10.3927i	−1.22086	−	0.444358i	−0.870459	+	0.492240i	$0.836178\pi$
$548$	−8.42921	−	7.07294i	−0.360078	−	0.302141i
$549$	1.19543	−	6.77965i	0.0510199	−	0.289348i
$550$	−8.20859			−0.350015
$551$		0			0
$552$	3.62158			0.154145
$553$	3.99617	−	22.6634i	0.169934	−	0.963746i
$554$	−7.00830	−	5.88066i	−0.297754	−	0.249845i
$555$	2.21650	+	0.806738i	0.0940850	+	0.0342441i
$556$	−20.4464	+	7.44188i	−0.867121	+	0.315606i
$557$	−4.69901	+	3.94294i	−0.199104	+	0.167068i	−0.736888	−	0.676014i	$-0.763706\pi$
$557$	−4.69901	+	3.94294i	−0.199104	+	0.167068i	0.537785	+	0.843082i	$0.319261\pi$
$558$	12.3296	+	21.3555i	0.521955	+	0.904052i
$559$	20.1757	−	34.9454i	0.853342	−	1.47803i
$560$	−0.390134	−	2.21256i	−0.0164862	−	0.0934976i
$561$	−0.513261	−	2.91085i	−0.0216699	−	0.122896i
$562$	10.6079	−	18.3734i	0.447466	−	0.775034i
$563$	14.0958	+	24.4147i	0.594069	+	1.02896i	0.993678	+	0.112271i	$0.0358126\pi$
$563$	14.0958	+	24.4147i	0.594069	+	1.02896i	−0.399609	+	0.916686i	$0.630854\pi$
$564$	−3.57583	+	3.00047i	−0.150569	+	0.126343i
$565$	10.6579	−	3.87915i	0.448381	−	0.163197i
$566$	−4.87687	−	1.77503i	−0.204990	−	0.0746102i
$567$	14.0473	+	11.7871i	0.589933	+	0.495012i
$568$	−0.00980077	+	0.0555829i	−0.000411231	+	0.00233221i
$569$	−42.1145			−1.76553			−0.882766	−	0.469812i	$-0.844322\pi$
$569$	−42.1145			−1.76553			−0.882766	+	0.469812i	$0.844322\pi$
$570$		0			0
$571$	0.166927			0.00698566			0.00349283	−	0.999994i	$-0.498888\pi$
$571$	0.166927			0.00698566			0.00349283	+	0.999994i	$0.498888\pi$
$572$	2.18956	−	12.4176i	0.0915500	−	0.519206i
$573$	−7.09278	−	5.95155i	−0.296305	−	0.248629i
$574$	−8.26329	−	3.00759i	−0.344903	−	0.125534i
$575$	32.3443	−	11.7724i	1.34885	−	0.490941i
$576$	−2.14816	+	1.80252i	−0.0895067	+	0.0751051i
$577$	9.98157	+	17.2886i	0.415538	+	0.719733i	0.995485	−	0.0949212i	$-0.0302599\pi$
$577$	9.98157	+	17.2886i	0.415538	+	0.719733i	−0.579947	+	0.814655i	$0.696927\pi$
$578$	2.64407	−	4.57966i	0.109979	−	0.190489i
$579$	−0.598436	−	3.39390i	−0.0248702	−	0.141046i
$580$	0.709111	+	4.02157i	0.0294442	+	0.166986i
$581$	17.7972	−	30.8256i	0.738350	−	1.27886i
$582$	1.73099	+	2.99816i	0.0717517	+	0.124278i
$583$	−5.62652	+	4.72121i	−0.233027	+	0.195533i
$584$	6.54888	−	2.38360i	0.270995	−	0.0986340i
$585$	−15.1749	−	5.52320i	−0.627404	−	0.228356i
$586$	13.4563	+	11.2912i	0.555875	+	0.466435i
$587$	1.76149	−	9.98992i	0.0727046	−	0.412328i	−0.926634	−	0.375965i	$-0.877311\pi$
$587$	1.76149	−	9.98992i	0.0727046	−	0.412328i	0.999339	−	0.0363636i	$-0.0115775\pi$
$588$	−0.287096			−0.0118397
$589$		0			0
$590$	2.53328			0.104293
$591$	0.140231	−	0.795290i	0.00576834	−	0.0327139i
$592$	4.58079	+	3.84374i	0.188269	+	0.157977i
$593$	−7.00367	−	2.54913i	−0.287606	−	0.104680i	0.194188	−	0.980964i	$-0.437793\pi$
$593$	−7.00367	−	2.54913i	−0.287606	−	0.104680i	−0.481795	+	0.876284i	$0.660015\pi$
$594$	4.71069	−	1.71455i	0.193282	−	0.0703489i
$595$	5.88993	−	4.94224i	0.241464	−	0.202612i
$596$	−7.19479	−	12.4617i	−0.294710	−	0.510452i
$597$	−0.521942	+	0.904030i	−0.0213617	+	0.0369995i
$598$	9.18121	+	52.0692i	0.375448	+	2.12927i
$599$	−1.10638	−	6.27462i	−0.0452056	−	0.256374i	0.953827	−	0.300358i	$-0.0971061\pi$
$599$	−1.10638	−	6.27462i	−0.0452056	−	0.256374i	−0.999032	+	0.0439839i	$0.985995\pi$
$600$	0.930333	−	1.61138i	0.0379807	−	0.0657845i
$601$	−0.873153	−	1.51235i	−0.0356166	−	0.0616898i	0.847668	−	0.530528i	$-0.178006\pi$
$601$	−0.873153	−	1.51235i	−0.0356166	−	0.0616898i	−0.883284	+	0.468838i	$0.844673\pi$
$602$	−12.0595	+	10.1191i	−0.491509	+	0.412425i
$603$	7.04262	−	2.56330i	0.286798	−	0.104386i
$604$	11.6585	+	4.24336i	0.474379	+	0.172660i
$605$	4.91003	+	4.12001i	0.199621	+	0.167502i
$606$	−0.413736	+	2.34641i	−0.0168069	+	0.0953164i
$607$	32.1612			1.30538			0.652691	−	0.757624i	$-0.273640\pi$
$607$	32.1612			1.30538			0.652691	+	0.757624i	$0.273640\pi$
$608$		0			0
$609$	−5.10775			−0.206977
$610$	0.380041	−	2.15532i	0.0153874	−	0.0872663i
$611$	−52.2045	−	43.8048i	−2.11197	−	1.77215i
$612$	−9.01803	−	3.28230i	−0.364532	−	0.132679i
$613$	−11.9947	+	4.36570i	−0.484460	+	0.176329i	−0.572692	−	0.819771i	$-0.694101\pi$
$613$	−11.9947	+	4.36570i	−0.484460	+	0.176329i	0.0882314	+	0.996100i	$0.471879\pi$
$614$	16.5223	−	13.8639i	0.666787	−	0.559500i
$615$	0.688186	+	1.19197i	0.0277503	+	0.0480650i
$616$	−2.45965	+	4.26024i	−0.0991021	+	0.171650i
$617$	−0.292290	−	1.65766i	−0.0117672	−	0.0667348i	0.978359	−	0.206916i	$-0.0663426\pi$
$617$	−0.292290	−	1.65766i	−0.0117672	−	0.0667348i	−0.990126	+	0.140181i	$0.955232\pi$
$618$	0.360706	+	2.04567i	0.0145097	+	0.0822887i
$619$	−15.7642	+	27.3045i	−0.633618	+	1.09746i	0.353188	+	0.935552i	$0.385098\pi$
$619$	−15.7642	+	27.3045i	−0.633618	+	1.09746i	−0.986806	+	0.161906i	$0.948236\pi$
$620$	3.91971	+	6.78914i	0.157419	+	0.272658i
$621$	−16.1026	+	13.5117i	−0.646176	+	0.542206i
$622$	2.41847	−	0.880251i	0.0969718	−	0.0352949i
$623$	4.42312	+	1.60988i	0.177208	+	0.0644986i
$624$	2.18948	+	1.83719i	0.0876492	+	0.0735464i
$625$	2.38077	−	13.5020i	0.0952306	−	0.540080i
$626$	−5.18389			−0.207190
$627$		0			0
$628$	−0.451220			−0.0180056
$629$	−3.55361	+	20.1535i	−0.141692	+	0.803573i
$630$	4.82625	+	4.04971i	0.192283	+	0.161344i
$631$	29.8505	+	10.8647i	1.18833	+	0.432516i	0.859136	−	0.511747i	$-0.171001\pi$
$631$	29.8505	+	10.8647i	1.18833	+	0.432516i	0.329192	+	0.944263i	$0.393224\pi$
$632$	−8.58091	+	3.12320i	−0.341330	+	0.124234i
$633$	0.122377	−	0.102686i	0.00486404	−	0.00408142i
$634$	−10.1281	−	17.5423i	−0.402237	−	0.696696i
$635$	−3.19797	+	5.53904i	−0.126907	+	0.219810i
$636$	−0.289106	−	1.63960i	−0.0114638	−	0.0650143i
$637$	−0.727829	−	4.12772i	−0.0288376	−	0.163546i
$638$	4.47068	−	7.74345i	0.176996	−	0.306566i
$639$	−0.0791358	−	0.137067i	−0.00313056	−	0.00542230i
$640$	−0.682922	+	0.573040i	−0.0269949	+	0.0226514i
$641$	38.0047	−	13.8326i	1.50109	−	0.546353i	0.544750	−	0.838598i	$-0.316625\pi$
$641$	38.0047	−	13.8326i	1.50109	−	0.546353i	0.956343	+	0.292245i	$0.0944023\pi$
$642$	6.66797	+	2.42694i	0.263164	+	0.0957838i
$643$	−19.9963	−	16.7788i	−0.788575	−	0.661693i	0.156817	−	0.987628i	$-0.449877\pi$
$643$	−19.9963	−	16.7788i	−0.788575	−	0.661693i	−0.945392	+	0.325934i	$0.894321\pi$
$644$	3.58193	−	20.3141i	0.141148	−	0.800489i
$645$	2.46402			0.0970208
$646$		0			0
$647$	−48.7713			−1.91740			−0.958699	−	0.284423i	$-0.908198\pi$
$647$	−48.7713			−1.91740			−0.958699	+	0.284423i	$0.908198\pi$
$648$	1.26353	−	7.16582i	0.0496360	−	0.281500i
$649$	−4.24910	−	3.56542i	−0.166792	−	0.139955i
$650$	25.5262	+	9.29077i	1.00122	+	0.364414i
$651$	−9.21417	+	3.35368i	−0.361132	+	0.131441i
$652$	−0.0530518	+	0.0445157i	−0.00207767	+	0.00174337i
$653$	21.5915	+	37.3976i	0.844942	+	1.46348i	0.885672	+	0.464312i	$0.153698\pi$
$653$	21.5915	+	37.3976i	0.844942	+	1.46348i	−0.0407298	+	0.999170i	$0.512968\pi$
$654$	3.11954	−	5.40321i	0.121984	−	0.211282i
$655$	0.545328	+	3.09271i	0.0213077	+	0.120842i
$656$	0.605914	+	3.43631i	0.0236570	+	0.134165i
$657$	−9.77157	+	16.9249i	−0.381225	+	0.660302i
$658$	13.2935	+	23.0251i	0.518236	+	0.897612i
$659$	−10.9367	+	9.17700i	−0.426034	+	0.357485i	−0.830453	−	0.557089i	$-0.811918\pi$
$659$	−10.9367	+	9.17700i	−0.426034	+	0.357485i	0.404419	+	0.914574i	$0.367474\pi$
$660$	0.723532	−	0.263344i	0.0281634	−	0.0102507i
$661$	−33.5937	−	12.2271i	−1.30664	−	0.475579i	−0.407489	−	0.913210i	$-0.633595\pi$
$661$	−33.5937	−	12.2271i	−1.30664	−	0.475579i	−0.899155	+	0.437631i	$0.855818\pi$
$662$	16.3382	+	13.7094i	0.635002	+	0.532830i
$663$	−1.69852	+	9.63276i	−0.0659649	+	0.374106i
$664$	−14.1239			−0.548114
$665$		0			0
$666$	−16.7687			−0.649774
$667$	−6.51055	+	36.9232i	−0.252089	+	1.42967i
$668$	−1.66516	−	1.39723i	−0.0644268	−	0.0540605i
$669$	7.50425	+	2.73132i	0.290131	+	0.105599i
$670$	2.23892	−	0.814900i	0.0864970	−	0.0314823i
$671$	−3.67091	+	3.08026i	−0.141714	+	0.118912i
$672$	−0.557537	−	0.965682i	−0.0215074	−	0.0372520i
$673$	−5.17870	+	8.96976i	−0.199624	+	0.345759i	−0.948407	−	0.317057i	$-0.897305\pi$
$673$	−5.17870	+	8.96976i	−0.199624	+	0.345759i	0.748783	+	0.662816i	$0.230639\pi$
$674$	3.94658	+	22.3822i	0.152017	+	0.862130i
$675$	1.87535	+	10.6357i	0.0721824	+	0.409367i
$676$	−14.3635	+	24.8784i	−0.552444	+	0.956861i
$677$	5.35854	+	9.28126i	0.205945	+	0.356708i	0.950434	−	0.310928i	$-0.100640\pi$
$677$	5.35854	+	9.28126i	0.205945	+	0.356708i	−0.744488	+	0.667636i	$0.767306\pi$
$678$	4.31221	−	3.61837i	0.165609	−	0.138963i
$679$	18.5293	−	6.74410i	0.711088	−	0.258815i
$680$	−2.86692	−	1.04347i	−0.109941	−	0.0400154i
$681$	−4.16378	−	3.49383i	−0.159556	−	0.133884i
$682$	2.98067	−	16.9042i	0.114136	−	0.647297i
$683$	0.122930			0.00470377			0.00235188	−	0.999997i	$-0.499251\pi$
$683$	0.122930			0.00470377			0.00235188	+	0.999997i	$0.499251\pi$
$684$		0			0
$685$	9.80957			0.374804
$686$	−3.34729	+	18.9834i	−0.127800	+	0.724790i
$687$	2.30204	+	1.93164i	0.0878282	+	0.0736966i
$688$	5.86997	+	2.13649i	0.223790	+	0.0814531i
$689$	22.8404	−	8.31322i	0.870150	−	0.316709i
$690$	−2.47326	+	2.07531i	−0.0941553	+	0.0790057i
$691$	12.6407	+	21.8944i	0.480876	+	0.832902i	0.999759	−	0.0219435i	$-0.00698538\pi$
$691$	12.6407	+	21.8944i	0.480876	+	0.832902i	−0.518883	+	0.854845i	$0.673652\pi$
$692$	−8.42464	+	14.5919i	−0.320257	+	0.554701i
$693$	−2.39545	−	13.5853i	−0.0909955	−	0.516061i
$694$	−0.855834	−	4.85368i	−0.0324870	−	0.184243i
$695$	9.69881	−	16.7988i	0.367897	−	0.637216i
$696$	1.01338	+	1.75523i	0.0384122	+	0.0665319i
$697$	−9.14762	+	7.67576i	−0.346491	+	0.290740i
$698$	−24.5838	+	8.94776i	−0.930509	+	0.338678i
$699$	−8.90989	−	3.24293i	−0.337003	−	0.122659i
$700$	−8.11841	−	6.81215i	−0.306847	−	0.257475i
$701$	−0.898259	+	5.09428i	−0.0339268	+	0.192408i	−0.997061	−	0.0766135i	$-0.975589\pi$
$701$	−0.898259	+	5.09428i	−0.0339268	+	0.192408i	0.963134	+	0.269022i	$0.0867004\pi$
$702$	−16.5894			−0.626127
$703$		0			0
$704$	1.95199			0.0735684
$705$	0.722620	−	4.09818i	0.0272154	−	0.154346i
$706$	2.07455	+	1.74076i	0.0780768	+	0.0655142i
$707$	12.7523	+	4.64144i	0.479598	+	0.174559i
$708$	1.18149	−	0.430026i	0.0444030	−	0.0161614i
$709$	−22.9742	+	19.2777i	−0.862815	+	0.723987i	−0.962572	−	0.271024i	$-0.912638\pi$
$709$	−22.9742	+	19.2777i	−0.862815	+	0.723987i	0.0997579	+	0.995012i	$0.468193\pi$
$710$	−0.0251581	−	0.0435750i	−0.000944165	−	0.00163534i
$711$	12.8036	−	22.1764i	0.480171	−	0.831680i
$712$	−0.324330	−	1.83937i	−0.0121548	−	0.0689331i
$713$	12.4985	+	70.8825i	0.468073	+	2.65457i
$714$	1.90803	−	3.30481i	0.0714064	−	0.123680i
$715$	5.62048	+	9.73496i	0.210194	+	0.364067i
$716$	−14.5284	+	12.1908i	−0.542953	+	0.455592i
$717$	4.92185	−	1.79141i	0.183810	−	0.0669013i
$718$	8.74856	+	3.18422i	0.326493	+	0.118834i
$719$	−17.3917	−	14.5934i	−0.648601	−	0.544241i	0.258045	−	0.966133i	$-0.416922\pi$
$719$	−17.3917	−	14.5934i	−0.648601	−	0.544241i	−0.906646	+	0.421892i	$0.861366\pi$
$720$	0.434111	−	2.46196i	0.0161783	−	0.0917520i
$721$	11.8313			0.440620
$722$		0			0
$723$	9.62195			0.357844
$724$	0.345017	−	1.95669i	0.0128224	−	0.0727197i
$725$	14.7561	+	12.3818i	0.548028	+	0.459850i
$726$	2.98935	+	1.08803i	0.110945	+	0.0403807i
$727$	−34.3869	+	12.5158i	−1.27534	+	0.464185i	−0.888888	−	0.458125i	$-0.848521\pi$
$727$	−34.3869	+	12.5158i	−1.27534	+	0.464185i	−0.386450	+	0.922310i	$0.626299\pi$
$728$	12.4706	−	10.4641i	0.462193	−	0.387826i
$729$	8.49781	+	14.7186i	0.314734	+	0.545135i
$730$	−3.10648	+	5.38058i	−0.114976	+	0.199144i
$731$	3.71222	+	21.0530i	0.137301	+	0.778674i
$732$	−0.188621	−	1.06972i	−0.00697164	−	0.0395381i
$733$	−10.5761	+	18.3184i	−0.390637	+	0.676604i	−0.992534	−	0.121970i	$-0.961079\pi$
$733$	−10.5761	+	18.3184i	−0.390637	+	0.676604i	0.601896	+	0.798574i	$0.294412\pi$
$734$	−3.87721	−	6.71552i	−0.143110	−	0.247875i
$735$	0.196064	−	0.164518i	0.00723195	−	0.00606832i
$736$	−7.69142	+	2.79945i	−0.283510	+	0.103189i
$737$	−4.90229	−	1.78429i	−0.180578	−	0.0657250i
$738$	−7.49563	−	6.28958i	−0.275918	−	0.231523i
$739$	8.38836	−	47.5727i	0.308571	−	1.74999i	−0.297631	−	0.954681i	$-0.596197\pi$
$739$	8.38836	−	47.5727i	0.308571	−	1.74999i	0.606202	−	0.795311i	$-0.292692\pi$
$740$	−5.33094			−0.195969
$741$		0			0
$742$	−9.48276			−0.348123
$743$	5.53240	−	31.3758i	0.202964	−	1.15107i	−0.697647	−	0.716442i	$-0.745770\pi$
$743$	5.53240	−	31.3758i	0.202964	−	1.15107i	0.900611	−	0.434626i	$-0.143119\pi$
$744$	2.98056	+	2.50099i	0.109273	+	0.0916907i
$745$	12.0545	+	4.38750i	0.441644	+	0.160745i
$746$	−23.5039	+	8.55474i	−0.860540	+	0.313211i
$747$	30.3404	−	25.4586i	1.11010	−	0.931483i
$748$	3.34011	+	5.78523i	0.122126	+	0.211529i
$749$	20.2081	−	35.0015i	0.738390	−	1.27893i
$750$	0.630522	+	3.57587i	0.0230234	+	0.130572i
$751$	−7.11892	−	40.3734i	−0.259773	−	1.47325i	−0.783517	−	0.621371i	$-0.786576\pi$
$751$	−7.11892	−	40.3734i	−0.259773	−	1.47325i	0.523743	−	0.851876i	$-0.324535\pi$
$752$	5.27491	−	9.13641i	0.192356	−	0.333171i
$753$	−5.23015	−	9.05888i	−0.190597	−	0.330124i
$754$	−22.6668	+	19.0197i	−0.825475	+	0.692656i
$755$	−10.3935	+	3.78292i	−0.378258	+	0.137675i
$756$	6.08182	+	2.21360i	0.221194	+	0.0805079i
$757$	−9.82186	−	8.24152i	−0.356981	−	0.299543i	0.446605	−	0.894731i	$-0.352633\pi$
$757$	−9.82186	−	8.24152i	−0.356981	−	0.299543i	−0.803586	+	0.595188i	$0.797077\pi$
$758$	−3.33061	+	18.8888i	−0.120973	+	0.686073i
$759$	7.06929			0.256599
$760$		0			0
$761$	35.6382			1.29188			0.645942	−	0.763386i	$-0.276465\pi$
$761$	35.6382			1.29188			0.645942	+	0.763386i	$0.276465\pi$
$762$	−0.551232	+	3.12619i	−0.0199690	+	0.113250i
$763$	−27.2222	−	22.8421i	−0.985510	−	0.826941i
$764$	19.6639	+	7.15709i	0.711417	+	0.258934i
$765$	8.03950	−	2.92614i	0.290669	−	0.105795i
$766$	3.70244	−	3.10671i	0.133774	−	0.112250i
$767$	9.17792	+	15.8966i	0.331395	+	0.573994i
$768$	−0.221232	+	0.383185i	−0.00798301	+	0.0138270i
$769$	−0.967917	−	5.48933i	−0.0349040	−	0.197950i	0.962370	−	0.271744i	$-0.0876004\pi$
$769$	−0.967917	−	5.48933i	−0.0349040	−	0.197950i	−0.997274	+	0.0737938i	$0.976489\pi$
$770$	−0.761536	−	4.31889i	−0.0274439	−	0.155642i
$771$	−0.204301	+	0.353859i	−0.00735771	+	0.0127439i
$772$	3.89440	+	6.74529i	0.140162	+	0.242768i
$773$	−27.8932	+	23.4051i	−1.00325	+	0.841824i	−0.987431	−	0.158051i	$-0.949479\pi$
$773$	−27.8932	+	23.4051i	−1.00325	+	0.841824i	−0.0158159	+	0.999875i	$0.505035\pi$
$774$	−16.4607	+	5.99121i	−0.591668	+	0.215350i
$775$	34.7491	+	12.6476i	1.24823	+	0.454317i
$776$	−5.99377	−	5.02937i	−0.215164	−	0.180544i
$777$	1.15787	−	6.56661i	0.0415384	−	0.235576i
$778$	21.7291			0.779027
$779$		0			0
$780$	−2.54802			−0.0912339
$781$	−0.0191310	+	0.108497i	−0.000684561	+	0.00388234i
$782$	−21.4579	−	18.0053i	−0.767334	−	0.643870i
$783$	−11.0544	−	4.02346i	−0.395051	−	0.143787i
$784$	0.609728	−	0.221923i	0.0217760	−	0.00792582i
$785$	0.308148	−	0.258567i	0.0109983	−	0.00922865i
$786$	0.779323	+	1.34983i	0.0277975	+	0.0481467i
$787$	15.9523	−	27.6302i	0.568638	−	0.984909i	−0.428063	−	0.903749i	$-0.640804\pi$
$787$	15.9523	−	27.6302i	0.568638	−	0.984909i	0.996701	−	0.0811606i	$-0.0258627\pi$
$788$	0.316933	+	1.79741i	0.0112903	+	0.0640302i
$789$	0.331893	+	1.88226i	0.0118157	+	0.0670103i
$790$	4.07038	−	7.05010i	0.144818	−	0.250831i
$791$	−16.0311	−	27.7667i	−0.570001	−	0.987271i
$792$	−4.19319	+	3.51850i	−0.148998	+	0.125025i
$793$	14.9018	−	5.42380i	0.529177	−	0.192605i
$794$	−11.0076	−	4.00643i	−0.390644	−	0.142183i
$795$	1.13699	+	0.954049i	0.0403249	+	0.0338366i
$796$	0.409680	−	2.32341i	0.0145207	−	0.0823512i
$797$	2.09165			0.0740900			0.0370450	−	0.999314i	$-0.488206\pi$
$797$	2.09165			0.0740900			0.0370450	+	0.999314i	$0.488206\pi$
$798$		0			0
$799$	36.1042			1.27728
$800$	−0.730233	+	4.14136i	−0.0258176	+	0.146419i
$801$	4.01221	+	3.36664i	0.141764	+	0.118955i
$802$	−11.1000	−	4.04006i	−0.391954	−	0.142659i
$803$	12.7833	−	4.65276i	0.451114	−	0.164192i
$804$	0.905872	−	0.760117i	0.0319476	−	0.0268073i
$805$	9.19462	+	15.9256i	0.324068	+	0.561302i
$806$	−28.4018	+	49.1934i	−1.00041	+	1.73276i
$807$	0.829439	+	4.70398i	0.0291976	+	0.165588i
$808$	−0.935073	−	5.30306i	−0.0328958	−	0.186561i
$809$	15.0360	−	26.0430i	0.528636	−	0.915625i	−0.470806	−	0.882237i	$-0.656037\pi$
$809$	15.0360	−	26.0430i	0.528636	−	0.915625i	0.999442	−	0.0333880i	$-0.0106297\pi$
$810$	3.24341	+	5.61775i	0.113962	+	0.197387i
$811$	−0.630908	+	0.529395i	−0.0221542	+	0.0185896i	−0.653797	−	0.756670i	$-0.726825\pi$
$811$	−0.630908	+	0.529395i	−0.0221542	+	0.0185896i	0.631643	+	0.775259i	$0.282381\pi$
$812$	10.8477	−	3.94825i	0.380680	−	0.138556i
$813$	−0.335635	−	0.122161i	−0.0117712	−	0.00428438i
$814$	8.94165	+	7.50294i	0.313405	+	0.262978i
$815$	0.0107210	−	0.0608016i	0.000375539	−	0.00212979i
$816$	−1.51423			−0.0530085
$817$		0			0
$818$	−25.2663			−0.883414
$819$	−7.92717	+	44.9572i	−0.276998	+	1.57093i
$820$	−2.38294	−	1.99952i	−0.0832157	−	0.0698263i
$821$	−7.24620	−	2.63740i	−0.252894	−	0.0920459i	0.212463	−	0.977169i	$-0.431852\pi$
$821$	−7.24620	−	2.63740i	−0.252894	−	0.0920459i	−0.465357	+	0.885123i	$0.654074\pi$
$822$	4.57505	−	1.66518i	0.159573	−	0.0580799i
$823$	−19.0071	+	15.9489i	−0.662547	+	0.555943i	−0.910849	−	0.412740i	$-0.864572\pi$
$823$	−19.0071	+	15.9489i	−0.662547	+	0.555943i	0.248302	+	0.968683i	$0.420127\pi$
$824$	−2.34734	−	4.06571i	−0.0817734	−	0.141636i
$825$	1.81600	−	3.14540i	0.0632250	−	0.109509i
$826$	−1.24354	−	7.05249i	−0.0432685	−	0.245388i
$827$	−1.84561	−	10.4670i	−0.0641783	−	0.363973i	−0.999936	−	0.0113292i	$-0.996394\pi$
$827$	−1.84561	−	10.4670i	−0.0641783	−	0.363973i	0.935758	−	0.352644i	$-0.114717\pi$
$828$	11.4764	−	19.8776i	0.398831	−	0.690795i
$829$	10.7355	+	18.5944i	0.372859	+	0.645811i	0.990004	−	0.141039i	$-0.0450442\pi$
$829$	10.7355	+	18.5944i	0.372859	+	0.645811i	−0.617145	+	0.786849i	$0.711711\pi$
$830$	9.64552	−	8.09355i	0.334801	−	0.280931i
$831$	3.80384	−	1.38448i	0.131954	−	0.0480272i
$832$	−6.07009	−	2.20933i	−0.210442	−	0.0765947i
$833$	1.70105	+	1.42735i	0.0589379	+	0.0494548i
$834$	1.67178	−	9.48113i	0.0578890	−	0.328305i
$835$	1.93784			0.0670617
$836$		0			0
$837$	−22.5834			−0.780595
$838$	5.48976	−	31.1340i	0.189641	−	1.07551i
$839$	37.4013	+	31.3834i	1.29123	+	1.08347i	0.991589	+	0.129424i	$0.0413129\pi$
$839$	37.4013	+	31.3834i	1.29123	+	1.08347i	0.299646	+	0.954051i	$0.403132\pi$
$840$	0.934128	+	0.339995i	0.0322305	+	0.0117309i
$841$	7.53417	−	2.74221i	0.259799	−	0.0945591i
$842$	1.67742	−	1.40752i	0.0578078	−	0.0485065i
$843$	4.69360	+	8.12955i	0.161656	+	0.279997i
$844$	−0.180525	+	0.312679i	−0.00621393	+	0.0107628i
$845$	−4.44712	−	25.2209i	−0.152986	−	0.867624i
$846$	5.13722	+	29.1346i	0.176621	+	1.00167i
$847$	9.05960	−	15.6917i	0.311292	−	0.539173i
$848$	1.88139	+	3.25866i	0.0646072	+	0.111903i
$849$	1.75908	−	1.47605i	0.0603716	−	0.0506578i
$850$	−13.5235	+	4.92216i	−0.463853	+	0.168829i
$851$	−45.9931	−	16.7401i	−1.57662	−	0.573844i
$852$	−0.0191303	−	0.0160522i	−0.000655393	−	0.000549940i
$853$	−3.64853	+	20.6918i	−0.124923	+	0.708475i	0.856430	+	0.516263i	$0.172677\pi$
$853$	−3.64853	+	20.6918i	−0.124923	+	0.708475i	−0.981353	+	0.192212i	$0.938434\pi$
$854$	−6.18683			−0.211709
$855$		0			0
$856$	−16.0373			−0.548143
$857$	−5.59828	+	31.7494i	−0.191233	+	1.08454i	0.726448	+	0.687222i	$0.241170\pi$
$857$	−5.59828	+	31.7494i	−0.191233	+	1.08454i	−0.917681	+	0.397317i	$0.869941\pi$
$858$	4.27383	+	3.58617i	0.145906	+	0.122430i
$859$	38.7411	+	14.1006i	1.32183	+	0.481106i	0.904044	−	0.427439i	$-0.140584\pi$
$859$	38.7411	+	14.1006i	1.32183	+	0.481106i	0.417785	+	0.908546i	$0.362806\pi$
$860$	−5.23303	+	1.90467i	−0.178445	+	0.0649486i
$861$	2.98056	−	2.50099i	0.101577	−	0.0852335i
$862$	−0.901858	−	1.56206i	−0.0307174	−	0.0532041i
$863$	−21.0325	+	36.4293i	−0.715953	+	1.24007i	0.246637	+	0.969108i	$0.420674\pi$
$863$	−21.0325	+	36.4293i	−0.715953	+	1.24007i	−0.962591	+	0.270960i	$0.912659\pi$
$864$	−0.445956	−	2.52914i	−0.0151717	−	0.0860432i
$865$	−2.60837	−	14.7928i	−0.0886872	−	0.502970i
$866$	−3.28616	+	5.69180i	−0.111668	+	0.193415i
$867$	1.16990	+	2.02633i	0.0397320	+	0.0688179i
$868$	16.9764	−	14.2449i	0.576218	−	0.483504i
$869$	−16.7498	+	6.09645i	−0.568200	+	0.206808i
$870$	−1.69788	−	0.617978i	−0.0575635	−	0.0209514i
$871$	13.2251	+	11.0972i	0.448115	+	0.376013i
$872$	−2.44858	+	13.8866i	−0.0829193	+	0.470259i
$873$	21.9412			0.742596
$874$		0			0
$875$	20.6813			0.699156
$876$	−0.535462	+	3.03676i	−0.0180916	+	0.102603i
$877$	1.80443	+	1.51409i	0.0609312	+	0.0511273i	0.672745	−	0.739875i	$-0.265115\pi$
$877$	1.80443	+	1.51409i	0.0609312	+	0.0511273i	−0.611813	+	0.791002i	$0.709560\pi$
$878$	−8.57995	−	3.12285i	−0.289559	−	0.105391i
$879$	−7.30357	+	2.65828i	−0.246343	+	0.0896616i
$880$	−1.33306	+	1.11857i	−0.0449373	+	0.0377069i
$881$	−11.5677	−	20.0358i	−0.389725	−	0.675024i	0.602687	−	0.797977i	$-0.294097\pi$
$881$	−11.5677	−	20.0358i	−0.389725	−	0.675024i	−0.992412	+	0.122954i	$0.960763\pi$
$882$	−0.909774	+	1.57577i	−0.0306337	+	0.0530591i
$883$	1.21760	+	6.90538i	0.0409757	+	0.232385i	0.998417	−	0.0562430i	$-0.0179122\pi$
$883$	1.21760	+	6.90538i	0.0409757	+	0.232385i	−0.957441	+	0.288628i	$0.906801\pi$
$884$	−3.83877	−	21.7708i	−0.129112	−	0.732230i
$885$	−0.560441	+	0.970712i	−0.0188390	+	0.0326301i
$886$	13.7343	+	23.7885i	0.461413	+	0.799191i
$887$	37.4820	−	31.4511i	1.25852	−	1.05603i	0.262685	−	0.964882i	$-0.415392\pi$
$887$	37.4820	−	31.4511i	1.25852	−	1.05603i	0.995838	−	0.0911446i	$-0.0290525\pi$
$888$	−2.48628	+	0.904931i	−0.0834340	+	0.0303675i
$889$	16.9902	+	6.18393i	0.569833	+	0.207402i
$890$	1.27552	+	1.07029i	0.0427556	+	0.0358762i
$891$	2.46639	−	13.9876i	0.0826272	−	0.468602i
$892$	−18.0486			−0.604312
$893$		0			0
$894$	6.36686			0.212940
$895$	2.93597	−	16.6507i	0.0981388	−	0.556573i
$896$	1.93054	+	1.61992i	0.0644950	+	0.0541177i
$897$	−21.9833	−	8.00127i	−0.734001	−	0.267155i
$898$	−7.11622	+	2.59009i	−0.237471	+	0.0864325i
$899$	−30.8566	+	25.8917i	−1.02912	+	0.863537i
$900$	−5.89623	−	10.2126i	−0.196541	−	0.340419i
$901$	−6.43860	+	11.1520i	−0.214501	+	0.371527i
$902$	1.18274	+	6.70764i	0.0393809	+	0.223340i
$903$	−1.20955	−	6.85969i	−0.0402513	−	0.228276i
$904$	−6.36119	+	11.0179i	−0.211570	+	0.366450i
$905$	0.885639	+	1.53397i	0.0294396	+	0.0509910i
$906$	−4.20523	+	3.52861i	−0.139709	+	0.117230i
$907$	1.12109	−	0.408044i	0.0372252	−	0.0135489i	−0.323340	−	0.946283i	$-0.604806\pi$
$907$	1.12109	−	0.408044i	0.0372252	−	0.0135489i	0.360566	+	0.932734i	$0.382584\pi$
$908$	11.5436	+	4.20154i	0.383089	+	0.139433i
$909$	11.5676	+	9.70635i	0.383672	+	0.321939i
$910$	−2.52013	+	14.2923i	−0.0835414	+	0.473787i
$911$	37.6344			1.24688			0.623442	−	0.781870i	$-0.285734\pi$
$911$	37.6344			1.24688			0.623442	+	0.781870i	$0.285734\pi$
$912$		0			0
$913$	−27.5697			−0.912424
$914$	−3.77988	+	21.4368i	−0.125027	+	0.709066i
$915$	0.741808	+	0.622450i	0.0245234	+	0.0205776i
$916$	−6.38215	−	2.32291i	−0.210872	−	0.0767512i
$917$	8.34222	−	3.03632i	0.275484	−	0.100268i
$918$	6.73269	−	5.64940i	0.222212	−	0.186458i
$919$	−13.4738	−	23.3373i	−0.444460	−	0.769828i	0.553554	−	0.832813i	$-0.313271\pi$
$919$	−13.4738	−	23.3373i	−0.444460	−	0.769828i	−0.998014	+	0.0629854i	$0.979938\pi$
$920$	3.64845	−	6.31929i	0.120286	−	0.208341i
$921$	1.65716	+	9.39823i	0.0546053	+	0.309682i
$922$	2.07412	+	11.7629i	0.0683075	+	0.387391i
$923$	0.182293	−	0.315740i	0.00600023	−	0.0103927i
$924$	−1.08831	−	1.88500i	−0.0358026	−	0.0620119i
$925$	−19.2633	+	16.1639i	−0.633375	+	0.531464i
$926$	8.22579	−	2.99394i	0.270316	−	0.0983871i
$927$	12.3710	+	4.50267i	0.406317	+	0.147887i
$928$	−3.50898	−	2.94438i	−0.115188	−	0.0966541i
$929$	−3.10049	+	17.5838i	−0.101724	+	0.576904i	0.890755	+	0.454484i	$0.150177\pi$
$929$	−3.10049	+	17.5838i	−0.101724	+	0.576904i	−0.992478	+	0.122420i	$0.960935\pi$
$930$	−3.46866			−0.113742
$931$		0			0
$932$	21.4294			0.701942
$933$	−0.197744	+	1.12146i	−0.00647384	+	0.0367150i
$934$	22.4886	+	18.8702i	0.735851	+	0.617452i
$935$	−5.59620	−	2.03685i	−0.183015	−	0.0666121i
$936$	17.0219	−	6.19546i	0.556378	−	0.202505i
$937$	−18.2568	+	15.3193i	−0.596424	+	0.500459i	−0.890294	−	0.455386i	$-0.849501\pi$
$937$	−18.2568	+	15.3193i	−0.596424	+	0.500459i	0.293870	+	0.955845i	$0.405057\pi$
$938$	−3.36768	−	5.83300i	−0.109959	−	0.190454i
$939$	1.14684	−	1.98639i	0.0374257	−	0.0648232i
$940$	1.63317	+	9.26219i	0.0532683	+	0.302099i
$941$	3.53636	+	20.0557i	0.115282	+	0.653796i	0.986610	+	0.163096i	$0.0521480\pi$
$941$	3.53636	+	20.0557i	0.115282	+	0.653796i	−0.871328	+	0.490700i	$0.836741\pi$
$942$	0.0998242	−	0.172901i	0.00325245	−	0.00563341i
$943$	−14.2801	−	24.7339i	−0.465025	−	0.805446i
$944$	−2.17680	+	1.82656i	−0.0708489	+	0.0594493i
$945$	−5.42189	+	1.97341i	−0.176374	+	0.0641949i
$946$	11.4581	+	4.17041i	0.372535	+	0.135592i
$947$	−2.61673	−	2.19570i	−0.0850323	−	0.0713506i	0.599281	−	0.800539i	$-0.295453\pi$
$947$	−2.61673	−	2.19570i	−0.0850323	−	0.0713506i	−0.684313	+	0.729188i	$0.739898\pi$
$948$	0.701609	−	3.97902i	0.0227872	−	0.129233i
$949$	−45.0184			−1.46136
$950$		0			0
$951$	8.96261			0.290633
$952$	−1.49765	+	8.49357i	−0.0485390	+	0.275278i
$953$	−13.5891	−	11.4026i	−0.440195	−	0.369367i	0.395587	−	0.918428i	$-0.370541\pi$
$953$	−13.5891	−	11.4026i	−0.440195	−	0.369367i	−0.835782	+	0.549061i	$0.814985\pi$
$954$	−9.91534	−	3.60889i	−0.321021	−	0.116842i
$955$	−17.5302	+	6.38049i	−0.567265	+	0.206468i
$956$	−9.06815	+	7.60908i	−0.293285	+	0.246095i
$957$	1.97811	+	3.42619i	0.0639434	+	0.110753i
$958$	12.4352	−	21.5385i	0.401764	−	0.695876i
$959$	−4.81536	−	27.3093i	−0.155496	−	0.881862i
$960$	−0.0684959	−	0.388460i	−0.00221070	−	0.0125375i
$961$	−23.1637	+	40.1208i	−0.747217	+	1.29422i
$962$	−19.3137	−	33.4523i	−0.622699	−	1.07855i
$963$	34.4507	−	28.9075i	1.11016	−	0.931532i
$964$	−20.4348	+	7.43767i	−0.658162	+	0.239551i
$965$	−6.52489	−	2.37487i	−0.210044	−	0.0764496i
$966$	6.99162	+	5.86667i	0.224952	+	0.188757i
$967$	−7.42435	+	42.1056i	−0.238751	+	1.35402i	0.595817	+	0.803120i	$0.296828\pi$
$967$	−7.42435	+	42.1056i	−0.238751	+	1.35402i	−0.834568	+	0.550904i	$0.814283\pi$
$968$	−7.18974			−0.231087
$969$		0			0
$970$	6.97531			0.223964
$971$	9.21181	−	52.2428i	0.295621	−	1.67655i	−0.369047	−	0.929411i	$-0.620316\pi$
$971$	9.21181	−	52.2428i	0.295621	−	1.67655i	0.664668	−	0.747139i	$-0.268573\pi$
$972$	8.36827	+	7.02181i	0.268412	+	0.225225i
$973$	−51.5279	−	18.7546i	−1.65191	−	0.601246i
$974$	−8.02278	+	2.92005i	−0.257066	+	0.0935645i
$975$	−9.20728	+	7.72583i	−0.294869	+	0.247424i
$976$	1.22747	+	2.12605i	0.0392905	+	0.0680532i
$977$	6.16319	−	10.6750i	0.197178	−	0.341522i	−0.750434	−	0.660945i	$-0.770156\pi$
$977$	6.16319	−	10.6750i	0.197178	−	0.341522i	0.947612	+	0.319423i	$0.103489\pi$
$978$	−0.00532101	−	0.0301769i	−0.000170147	−	0.000964952i
$979$	−0.633088	−	3.59042i	−0.0202336	−	0.114750i
$980$	−0.289226	+	0.500954i	−0.00923899	+	0.0160024i
$981$	−19.7709	−	34.2442i	−0.631236	−	1.09333i
$982$	−8.83993	+	7.41758i	−0.282093	+	0.236705i
$983$	30.3102	−	11.0320i	0.966744	−	0.351866i	0.190071	−	0.981770i	$-0.439128\pi$
$983$	30.3102	−	11.0320i	0.966744	−	0.351866i	0.776673	+	0.629904i	$0.216906\pi$
$984$	−1.45079	−	0.528044i	−0.0462495	−	0.0168334i
$985$	−1.24643	−	1.04588i	−0.0397146	−	0.0333245i
$986$	2.72214	−	15.4380i	0.0866905	−	0.491646i
$987$	−11.7638			−0.374446
$988$		0			0
$989$	−51.1294			−1.62582
$990$	0.847379	−	4.80573i	0.0269315	−	0.152736i
$991$	21.3241	+	17.8930i	0.677381	+	0.568390i	0.915240	−	0.402910i	$-0.132001\pi$
$991$	21.3241	+	17.8930i	0.677381	+	0.568390i	−0.237859	+	0.971300i	$0.576446\pi$
$992$	−8.26329	−	3.00759i	−0.262360	−	0.0954911i
$993$	−8.86774	+	3.22760i	−0.281409	+	0.102425i
$994$	−0.108961	+	0.0914289i	−0.00345602	+	0.00289995i
$995$	1.05163	+	1.82147i	0.0333388	+	0.0577446i
$996$	3.12465	−	5.41206i	0.0990085	−	0.171488i
$997$	−7.52441	−	42.6730i	−0.238300	−	1.35147i	−0.835551	−	0.549414i	$-0.814851\pi$
$997$	−7.52441	−	42.6730i	−0.238300	−	1.35147i	0.597250	−	0.802055i	$-0.296260\pi$
$998$	−5.14156	−	29.1592i	−0.162753	−	0.923019i
$999$	7.67853	−	13.2996i	0.242938	−	0.420781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.r.245.2		24
19.2	odd	18		722.2.c.n.429.2		8
19.3	odd	18		722.2.a.m.1.3	✓	4
19.4	even	9	inner	722.2.e.r.595.3		24
19.5	even	9		722.2.c.m.653.3		8
19.6	even	9	inner	722.2.e.r.99.2		24
19.7	even	3	inner	722.2.e.r.415.3		24
19.8	odd	6		722.2.e.s.423.3		24
19.9	even	9	inner	722.2.e.r.389.2		24
19.10	odd	18		722.2.e.s.389.3		24
19.11	even	3	inner	722.2.e.r.423.2		24
19.12	odd	6		722.2.e.s.415.2		24
19.13	odd	18		722.2.e.s.99.3		24
19.14	odd	18		722.2.c.n.653.2		8
19.15	odd	18		722.2.e.s.595.2		24
19.16	even	9		722.2.a.n.1.2	yes	4
19.17	even	9		722.2.c.m.429.3		8
19.18	odd	2		722.2.e.s.245.3		24
57.35	odd	18		6498.2.a.bx.1.2		4
57.41	even	18		6498.2.a.ca.1.2		4
76.3	even	18		5776.2.a.bv.1.2		4
76.35	odd	18		5776.2.a.bt.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.3	✓	4	19.3	odd	18
722.2.a.n.1.2	yes	4	19.16	even	9
722.2.c.m.429.3		8	19.17	even	9
722.2.c.m.653.3		8	19.5	even	9
722.2.c.n.429.2		8	19.2	odd	18
722.2.c.n.653.2		8	19.14	odd	18
722.2.e.r.99.2		24	19.6	even	9	inner
722.2.e.r.245.2		24	1.1	even	1	trivial
722.2.e.r.389.2		24	19.9	even	9	inner
722.2.e.r.415.3		24	19.7	even	3	inner
722.2.e.r.423.2		24	19.11	even	3	inner
722.2.e.r.595.3		24	19.4	even	9	inner
722.2.e.s.99.3		24	19.13	odd	18
722.2.e.s.245.3		24	19.18	odd	2
722.2.e.s.389.3		24	19.10	odd	18
722.2.e.s.415.2		24	19.12	odd	6
722.2.e.s.423.3		24	19.8	odd	6
722.2.e.s.595.2		24	19.15	odd	18
5776.2.a.bt.1.3		4	76.35	odd	18
5776.2.a.bv.1.2		4	76.3	even	18
6498.2.a.bx.1.2		4	57.35	odd	18
6498.2.a.ca.1.2		4	57.41	even	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(0.338947 + 0.284410i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.837728 - 0.304908i) q^{5} +(0.338947 - 0.284410i) q^{6} +(-1.26007 - 2.18251i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.486949 - 2.76162i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(0.338947 + 0.284410i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.837728 - 0.304908i) q^{5} +(0.338947 - 0.284410i) q^{6} +(-1.26007 - 2.18251i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.486949 - 2.76162i) q^{9} +(-0.154806 - 0.877948i) q^{10} +(-0.975994 + 1.69047i) q^{11} +(-0.221232 - 0.383185i) q^{12} +(4.94838 - 4.15218i) q^{13} +(-2.36816 + 0.861941i) q^{14} +(0.370664 + 0.134911i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.594269 + 3.37027i) q^{17} -2.80423 q^{18} -0.891491 q^{20} +(0.193630 - 1.09813i) q^{21} +(1.49531 + 1.25471i) q^{22} +(-7.69142 - 2.79945i) q^{23} +(-0.415780 + 0.151331i) q^{24} +(-3.22140 + 2.70308i) q^{25} +(-3.22982 - 5.59422i) q^{26} +(1.28408 - 2.22409i) q^{27} +(0.437619 + 2.48186i) q^{28} +(-0.795421 - 4.51105i) q^{29} +(0.197226 - 0.341606i) q^{30} +(-4.39680 - 7.61548i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-0.811597 + 0.295397i) q^{33} +(3.21587 + 1.17048i) q^{34} +(-1.72106 - 1.44414i) q^{35} +(-0.486949 + 2.76162i) q^{36} +5.97980 q^{37} +2.85816 q^{39} +(-0.154806 + 0.877948i) q^{40} +(2.67298 + 2.24289i) q^{41} +(-1.04783 - 0.381377i) q^{42} +(5.86997 - 2.13649i) q^{43} +(1.49531 - 1.25471i) q^{44} +(-1.24997 - 2.16501i) q^{45} +(-4.09252 + 7.08845i) q^{46} +(-1.83196 - 10.3895i) q^{47} +(0.0768330 + 0.435741i) q^{48} +(0.324429 - 0.561928i) q^{49} +(2.10262 + 3.64185i) q^{50} +(-1.15996 + 0.973325i) q^{51} +(-6.07009 + 2.20933i) q^{52} +(3.53586 + 1.28695i) q^{53} +(-1.96732 - 1.65078i) q^{54} +(-0.302179 + 1.71374i) q^{55} +2.52015 q^{56} -4.58064 q^{58} +(-0.493441 + 2.79845i) q^{59} +(-0.302168 - 0.253549i) q^{60} +(2.30690 + 0.839642i) q^{61} +(-8.26329 + 3.00759i) q^{62} +(-5.41368 + 4.54262i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.87936 - 4.98720i) q^{65} +(0.149977 + 0.850563i) q^{66} +(0.464094 + 2.63201i) q^{67} +(1.71113 - 2.96376i) q^{68} +(-1.81079 - 3.13638i) q^{69} +(-1.72106 + 1.44414i) q^{70} +(0.0530366 - 0.0193038i) q^{71} +(2.63511 + 0.959102i) q^{72} +(-5.33870 - 4.47970i) q^{73} +(1.03838 - 5.88895i) q^{74} -1.86067 q^{75} +4.91930 q^{77} +(0.496314 - 2.81474i) q^{78} +(6.99522 + 5.86969i) q^{79} +(0.837728 + 0.304908i) q^{80} +(-6.83754 + 2.48866i) q^{81} +(2.67298 - 2.24289i) q^{82} +(7.06195 + 12.2317i) q^{83} +(-0.557537 + 0.965682i) q^{84} +(0.529786 + 3.00457i) q^{85} +(-1.08473 - 6.15179i) q^{86} +(1.01338 - 1.75523i) q^{87} +(-0.975994 - 1.69047i) q^{88} +(-1.43077 + 1.20056i) q^{89} +(-2.34918 + 0.855031i) q^{90} +(-15.2975 - 5.56784i) q^{91} +(6.27010 + 5.26124i) q^{92} +(0.675639 - 3.83174i) q^{93} -10.5498 q^{94} +0.442463 q^{96} +(-1.35868 + 7.70545i) q^{97} +(-0.497055 - 0.417079i) q^{98} +(5.14371 + 1.87216i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{7} - 12 q^{8}+O(q^{10}) \) 24 * q + 6 * q^7 - 12 * q^8	\( 24 q + 6 q^{7} - 12 q^{8} - 6 q^{11} - 6 q^{12} + 24 q^{18} - 12 q^{20} - 54 q^{26} + 12 q^{27} - 12 q^{30} - 78 q^{31} + 24 q^{37} - 36 q^{39} + 66 q^{45} + 30 q^{46} + 36 q^{49} - 18 q^{50} - 12 q^{56} - 12 q^{58} - 12 q^{64} + 12 q^{65} - 18 q^{68} + 60 q^{69} + 48 q^{75} + 24 q^{77} + 36 q^{83} - 12 q^{84} + 78 q^{87} - 6 q^{88} - 72 q^{94} + 12 q^{96}+O(q^{100}) \) 24 * q + 6 * q^7 - 12 * q^8 - 6 * q^11 - 6 * q^12 + 24 * q^18 - 12 * q^20 - 54 * q^26 + 12 * q^27 - 12 * q^30 - 78 * q^31 + 24 * q^37 - 36 * q^39 + 66 * q^45 + 30 * q^46 + 36 * q^49 - 18 * q^50 - 12 * q^56 - 12 * q^58 - 12 * q^64 + 12 * q^65 - 18 * q^68 + 60 * q^69 + 48 * q^75 + 24 * q^77 + 36 * q^83 - 12 * q^84 + 78 * q^87 - 6 * q^88 - 72 * q^94 + 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more