LMFDB - Embedded newform 405.2.r.a.152.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 27])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$405 = 3^{4} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	405.r (of order $36$ , degree $12$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			152.14
Character	$\chi$	$=$	405.152
Dual form			405.2.r.a.8.14

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66533 + 1.16608i) q^{2} +(0.729546 + 2.00441i) q^{4} +(1.48319 + 1.67336i) q^{5} +(1.13512 + 2.43427i) q^{7} +(-0.0700073 + 0.261271i) q^{8} +(0.518731 + 4.51621i) q^{10} +(-4.08386 - 4.86695i) q^{11} +(1.19516 + 1.70687i) q^{13} +(-0.948196 + 5.37749i) q^{14} +(2.84677 - 2.38873i) q^{16} +(0.174154 + 0.649952i) q^{17} +(-2.70632 + 1.56249i) q^{19} +(-2.27205 + 4.19372i) q^{20} +(-1.12573 - 12.8672i) q^{22} +(0.409999 + 0.191186i) q^{23} +(-0.600292 + 4.96383i) q^{25} +4.23615i q^{26} +(-4.05115 + 4.05115i) q^{28} +(-1.39473 - 7.90988i) q^{29} +(-1.53858 + 0.559998i) q^{31} +(8.06517 - 0.705611i) q^{32} +(-0.467869 + 1.28546i) q^{34} +(-2.38982 + 5.50995i) q^{35} +(2.76163 - 0.739977i) q^{37} +(-6.32889 - 0.553706i) q^{38} +(-0.541035 + 0.270367i) q^{40} +(9.28604 + 1.63738i) q^{41} +(0.307907 - 3.51939i) q^{43} +(6.77601 - 11.7364i) q^{44} +(0.459846 + 0.796477i) q^{46} +(-5.68707 + 2.65193i) q^{47} +(-0.137652 + 0.164047i) q^{49} +(-6.78789 + 7.56643i) q^{50} +(-2.54934 + 3.64084i) q^{52} +(-5.99520 - 5.99520i) q^{53} +(2.08704 - 14.0524i) q^{55} +(-0.715470 + 0.126157i) q^{56} +(6.90084 - 14.7989i) q^{58} +(-6.07856 - 5.10051i) q^{59} +(-1.53937 - 0.560286i) q^{61} +(-3.21525 - 0.861522i) q^{62} +(7.81729 + 4.51332i) q^{64} +(-1.08356 + 4.53156i) q^{65} +(4.38163 - 3.06805i) q^{67} +(-1.17572 + 0.823246i) q^{68} +(-10.4048 + 6.38916i) q^{70} +(-2.05039 - 1.18380i) q^{71} +(-1.33738 - 0.358350i) q^{73} +(5.46189 + 1.98796i) q^{74} +(-5.10626 - 4.28466i) q^{76} +(7.21181 - 15.4658i) q^{77} +(-6.73243 + 1.18711i) q^{79} +(8.21952 + 1.22075i) q^{80} +(13.5550 + 13.5550i) q^{82} +(2.27065 - 3.24283i) q^{83} +(-0.829302 + 1.25543i) q^{85} +(4.61664 - 5.50190i) q^{86} +(1.55749 - 0.726271i) q^{88} +(-0.428822 - 0.742742i) q^{89} +(-2.79833 + 4.84685i) q^{91} +(-0.0841016 + 0.961286i) q^{92} +(-12.5632 - 2.21523i) q^{94} +(-6.62860 - 2.21118i) q^{95} +(-3.88639 - 0.340015i) q^{97} +(-0.420527 + 0.112680i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100})$ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$ .

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	1.66533	+	1.16608i	1.17756	+	0.824540i	0.987560	−	0.157243i	$-0.0502607\pi$
$2$	1.66533	+	1.16608i	1.17756	+	0.824540i	0.190005	+	0.981783i	$0.439150\pi$
$3$		0			0
$3$		0			0
$4$	0.729546	+	2.00441i	0.364773	+	1.00221i
$5$	1.48319	+	1.67336i	0.663303	+	0.748351i
$5$	1.48319	+	1.67336i	0.663303	+	0.748351i
$6$		0			0
$7$	1.13512	+	2.43427i	0.429034	+	0.920067i	0.995390	+	0.0959060i	$0.0305748\pi$
$7$	1.13512	+	2.43427i	0.429034	+	0.920067i	−0.566356	+	0.824160i	$0.691647\pi$
$8$	−0.0700073	+	0.261271i	−0.0247513	+	0.0923732i
$9$		0			0
$10$	0.518731	+	4.51621i	0.164037	+	1.42815i
$11$	−4.08386	−	4.86695i	−1.23133	−	1.46744i	−0.835842	−	0.548970i	$-0.815020\pi$
$11$	−4.08386	−	4.86695i	−1.23133	−	1.46744i	−0.395488	−	0.918471i	$-0.629424\pi$
$12$		0			0
$13$	1.19516	+	1.70687i	0.331479	+	0.473401i	0.949948	−	0.312408i	$-0.101136\pi$
$13$	1.19516	+	1.70687i	0.331479	+	0.473401i	−0.618469	+	0.785809i	$0.712247\pi$
$14$	−0.948196	+	5.37749i	−0.253416	+	1.43719i
$15$		0			0
$16$	2.84677	−	2.38873i	0.711694	−	0.597182i
$17$	0.174154	+	0.649952i	0.0422386	+	0.157637i	0.983824	−	0.179138i	$-0.0573308\pi$
$17$	0.174154	+	0.649952i	0.0422386	+	0.157637i	−0.941585	+	0.336774i	$0.890664\pi$
$18$		0			0
$19$	−2.70632	+	1.56249i	−0.620871	+	0.358460i	−0.777208	−	0.629243i	$-0.783365\pi$
$19$	−2.70632	+	1.56249i	−0.620871	+	0.358460i	0.156337	+	0.987704i	$0.450031\pi$
$20$	−2.27205	+	4.19372i	−0.508046	+	0.937744i
$21$		0			0
$22$	−1.12573	−	12.8672i	−0.240007	−	2.74329i
$23$	0.409999	+	0.191186i	0.0854907	+	0.0398650i	0.464893	−	0.885367i	$-0.346093\pi$
$23$	0.409999	+	0.191186i	0.0854907	+	0.0398650i	−0.379403	+	0.925232i	$0.623870\pi$
$24$		0			0
$25$	−0.600292	+	4.96383i	−0.120058	+	0.992767i
$26$			4.23615i			0.830778i
$27$		0			0
$28$	−4.05115	+	4.05115i	−0.765596	+	0.765596i
$29$	−1.39473	−	7.90988i	−0.258994	−	1.46883i	−0.785608	−	0.618724i	$-0.787650\pi$
$29$	−1.39473	−	7.90988i	−0.258994	−	1.46883i	0.526614	−	0.850104i	$-0.323461\pi$
$30$		0			0
$31$	−1.53858	+	0.559998i	−0.276338	+	0.100579i	−0.476472	−	0.879190i	$-0.658084\pi$
$31$	−1.53858	+	0.559998i	−0.276338	+	0.100579i	0.200134	+	0.979769i	$0.435862\pi$
$32$	8.06517	−	0.705611i	1.42573	−	0.124735i
$33$		0			0
$34$	−0.467869	+	1.28546i	−0.0802389	+	0.220455i
$35$	−2.38982	+	5.50995i	−0.403953	+	0.931351i
$36$		0			0
$37$	2.76163	−	0.739977i	0.454009	−	0.121651i	−0.0245656	−	0.999698i	$-0.507820\pi$
$37$	2.76163	−	0.739977i	0.454009	−	0.121651i	0.478575	+	0.878047i	$0.341154\pi$
$38$	−6.32889	−	0.553706i	−1.02668	−	0.0898230i
$39$		0			0
$40$	−0.541035	+	0.270367i	−0.0855452	+	0.0427487i
$41$	9.28604	+	1.63738i	1.45024	+	0.255716i	0.842617	−	0.538514i	$-0.181014\pi$
$41$	9.28604	+	1.63738i	1.45024	+	0.255716i	0.607618	+	0.794229i	$0.292125\pi$
$42$		0			0
$43$	0.307907	−	3.51939i	0.0469554	−	0.536702i	−0.935893	−	0.352285i	$-0.885405\pi$
$43$	0.307907	−	3.51939i	0.0469554	−	0.536702i	0.982848	−	0.184417i	$-0.0590397\pi$
$44$	6.77601	−	11.7364i	1.02152	−	1.76933i
$45$		0			0
$46$	0.459846	+	0.796477i	0.0678006	+	0.117434i
$47$	−5.68707	+	2.65193i	−0.829545	+	0.386823i	−0.790536	−	0.612416i	$-0.790198\pi$
$47$	−5.68707	+	2.65193i	−0.829545	+	0.386823i	−0.0390089	+	0.999239i	$0.512420\pi$
$48$		0			0
$49$	−0.137652	+	0.164047i	−0.0196646	+	0.0234353i
$50$	−6.78789	+	7.56643i	−0.959952	+	1.07005i
$51$		0			0
$52$	−2.54934	+	3.64084i	−0.353530	+	0.504894i
$53$	−5.99520	−	5.99520i	−0.823504	−	0.823504i	0.163105	−	0.986609i	$-0.447849\pi$
$53$	−5.99520	−	5.99520i	−0.823504	−	0.823504i	−0.986609	+	0.163105i	$0.947849\pi$
$54$		0			0
$55$	2.08704	−	14.0524i	0.281417	−	1.89483i
$56$	−0.715470	+	0.126157i	−0.0956087	+	0.0168584i
$57$		0			0
$58$	6.90084	−	14.7989i	0.906125	−	1.94319i
$59$	−6.07856	−	5.10051i	−0.791361	−	0.664030i	0.154721	−	0.987958i	$-0.450552\pi$
$59$	−6.07856	−	5.10051i	−0.791361	−	0.664030i	−0.946082	+	0.323928i	$0.894997\pi$
$60$		0			0
$61$	−1.53937	−	0.560286i	−0.197096	−	0.0717372i	0.241586	−	0.970379i	$-0.422332\pi$
$61$	−1.53937	−	0.560286i	−0.197096	−	0.0717372i	−0.438682	+	0.898642i	$0.644555\pi$
$62$	−3.21525	−	0.861522i	−0.408337	−	0.109413i
$63$		0			0
$64$	7.81729	+	4.51332i	0.977162	+	0.564165i
$65$	−1.08356	+	4.53156i	−0.134399	+	0.562071i
$66$		0			0
$67$	4.38163	−	3.06805i	0.535302	−	0.374822i	−0.274444	−	0.961603i	$-0.588494\pi$
$67$	4.38163	−	3.06805i	0.535302	−	0.374822i	0.809746	+	0.586781i	$0.199605\pi$
$68$	−1.17572	+	0.823246i	−0.142577	+	0.0998333i
$69$		0			0
$70$	−10.4048	+	6.38916i	−1.24362	+	0.763651i
$71$	−2.05039	−	1.18380i	−0.243337	−	0.140491i	0.373372	−	0.927682i	$-0.378201\pi$
$71$	−2.05039	−	1.18380i	−0.243337	−	0.140491i	−0.616710	+	0.787191i	$0.711535\pi$
$72$		0			0
$73$	−1.33738	−	0.358350i	−0.156529	−	0.0419417i	0.179704	−	0.983721i	$-0.442486\pi$
$73$	−1.33738	−	0.358350i	−0.156529	−	0.0419417i	−0.336232	+	0.941779i	$0.609153\pi$
$74$	5.46189	+	1.98796i	0.634932	+	0.231096i
$75$		0			0
$76$	−5.10626	−	4.28466i	−0.585728	−	0.491484i
$77$	7.21181	−	15.4658i	0.821861	−	1.76249i
$78$		0			0
$79$	−6.73243	+	1.18711i	−0.757458	+	0.133560i	−0.539023	−	0.842291i	$-0.681206\pi$
$79$	−6.73243	+	1.18711i	−0.757458	+	0.133560i	−0.218435	+	0.975851i	$0.570095\pi$
$80$	8.21952	+	1.22075i	0.918970	+	0.136484i
$81$		0			0
$82$	13.5550	+	13.5550i	1.49690	+	1.49690i
$83$	2.27065	−	3.24283i	0.249236	−	0.355946i	−0.674966	−	0.737848i	$-0.735842\pi$
$83$	2.27065	−	3.24283i	0.249236	−	0.355946i	0.924203	+	0.381902i	$0.124731\pi$
$84$		0			0
$85$	−0.829302	+	1.25543i	−0.0899505	+	0.136170i
$86$	4.61664	−	5.50190i	0.497825	−	0.593285i
$87$		0			0
$88$	1.55749	−	0.726271i	0.166029	−	0.0774208i
$89$	−0.428822	−	0.742742i	−0.0454551	−	0.0787305i	0.842403	−	0.538848i	$-0.181140\pi$
$89$	−0.428822	−	0.742742i	−0.0454551	−	0.0787305i	−0.887858	+	0.460118i	$0.847807\pi$
$90$		0			0
$91$	−2.79833	+	4.84685i	−0.293345	+	0.508088i
$92$	−0.0841016	+	0.961286i	−0.00876820	+	0.100221i
$93$		0			0
$94$	−12.5632	−	2.21523i	−1.29579	−	0.228483i
$95$	−6.62860	−	2.21118i	−0.680080	−	0.226862i
$96$		0			0
$97$	−3.88639	−	0.340015i	−0.394603	−	0.0345233i	−0.111872	−	0.993723i	$-0.535685\pi$
$97$	−3.88639	−	0.340015i	−0.394603	−	0.0345233i	−0.282731	+	0.959199i	$0.591240\pi$
$98$	−0.420527	+	0.112680i	−0.0424797	+	0.0113824i
$99$		0			0
$100$	−10.3875	+	2.41811i	−1.03875	+	0.241811i
$101$	−4.66297	+	12.8114i	−0.463983	+	1.27478i	0.458482	+	0.888704i	$0.348393\pi$
$101$	−4.66297	+	12.8114i	−0.463983	+	1.27478i	−0.922465	+	0.386080i	$0.873829\pi$
$102$		0			0
$103$	6.33428	−	0.554178i	0.624135	−	0.0546047i	0.229299	−	0.973356i	$-0.426357\pi$
$103$	6.33428	−	0.554178i	0.624135	−	0.0546047i	0.394837	+	0.918751i	$0.370801\pi$
$104$	−0.529626	+	0.192768i	−0.0519341	+	0.0189025i
$105$		0			0
$106$	−2.99312	−	16.9748i	−0.290718	−	1.64874i
$107$	7.42914	−	7.42914i	0.718202	−	0.718202i	−0.250035	−	0.968237i	$-0.580442\pi$
$107$	7.42914	−	7.42914i	0.718202	−	0.718202i	0.968237	+	0.250035i	$0.0804420\pi$
$108$		0			0
$109$			2.73749i			0.262204i	0.991369	+	0.131102i	$0.0418515\pi$
$109$			2.73749i			0.262204i	−0.991369	+	0.131102i	$0.958148\pi$
$110$	19.8618	−	20.9682i	1.89374	−	1.99924i
$111$		0			0
$112$	9.04622	+	4.21832i	0.854788	+	0.398594i
$113$	1.76514	+	20.1756i	0.166050	+	1.89796i	0.386073	+	0.922468i	$0.373831\pi$
$113$	1.76514	+	20.1756i	0.166050	+	1.89796i	−0.220022	+	0.975495i	$0.570613\pi$
$114$		0			0
$115$	0.288184	+	0.969643i	0.0268733	+	0.0904197i
$116$	14.8371	−	8.56623i	1.37759	−	0.795354i
$117$		0			0
$118$	−4.17521	−	15.5821i	−0.384359	−	1.43445i
$119$	−1.38447	+	1.16171i	−0.126914	+	0.106494i
$120$		0			0
$121$	−5.09920	+	28.9190i	−0.463564	+	2.62900i
$122$	−1.91022	−	2.72808i	−0.172944	−	0.246989i
$123$		0			0
$124$	−2.24493	−	2.67541i	−0.201601	−	0.240259i
$125$	−9.19665	+	6.35781i	−0.822573	+	0.568659i
$126$		0			0
$127$	−0.371696	+	1.38719i	−0.0329827	+	0.123093i	−0.980454	−	0.196747i	$-0.936962\pi$
$127$	−0.371696	+	1.38719i	−0.0329827	+	0.123093i	0.947472	+	0.319840i	$0.103629\pi$
$128$	0.912480	+	1.95682i	0.0806526	+	0.172960i
$129$		0			0
$130$	−7.08862	+	6.28302i	−0.621713	+	0.551057i
$131$	6.84812	+	18.8151i	0.598323	+	1.64388i	0.754614	+	0.656168i	$0.227824\pi$
$131$	6.84812	+	18.8151i	0.598323	+	1.64388i	−0.156291	+	0.987711i	$0.549954\pi$
$132$		0			0
$133$	−6.87551	−	4.81428i	−0.596182	−	0.417451i
$134$	10.8744			0.939409
$135$		0			0
$136$	−0.182006			−0.0156069
$137$	10.7088	+	7.49837i	0.914913	+	0.640629i	0.933260	−	0.359202i	$-0.116951\pi$
$137$	10.7088	+	7.49837i	0.914913	+	0.640629i	−0.0183463	+	0.999832i	$0.505840\pi$
$138$		0			0
$139$	4.79900	+	13.1851i	0.407046	+	1.11835i	0.958735	+	0.284300i	$0.0917610\pi$
$139$	4.79900	+	13.1851i	0.407046	+	1.11835i	−0.551690	+	0.834049i	$0.686017\pi$
$140$	−12.7877	−	0.770420i	−1.08076	−	0.0651124i
$141$		0			0
$142$	−2.03418	−	4.36232i	−0.170705	−	0.366078i
$143$	3.42638	−	12.7874i	0.286528	−	1.06934i
$144$		0			0
$145$	11.1675	−	14.0658i	0.927408	−	1.16810i
$146$	−1.80932	−	2.15626i	−0.149740	−	0.178453i
$147$		0			0
$148$	3.49795	+	4.99559i	0.287530	+	0.410635i
$149$	−0.199237	+	1.12993i	−0.0163222	+	0.0925675i	−0.991881	−	0.127173i	$-0.959410\pi$
$149$	−0.199237	+	1.12993i	−0.0163222	+	0.0925675i	0.975558	+	0.219740i	$0.0705209\pi$
$150$		0			0
$151$	1.20809	−	1.01370i	0.0983127	−	0.0824941i	−0.592307	−	0.805713i	$-0.701783\pi$
$151$	1.20809	−	1.01370i	0.0983127	−	0.0824941i	0.690619	+	0.723219i	$0.257338\pi$
$152$	−0.218772	−	0.816468i	−0.0177447	−	0.0662243i
$153$		0			0
$154$	30.0443	−	17.3461i	2.42104	−	1.39779i
$155$	−3.21909	−	1.74402i	−0.258564	−	0.140083i
$156$		0			0
$157$	−1.15466	−	13.1978i	−0.0921516	−	1.05330i	−0.891679	−	0.452668i	$-0.850472\pi$
$157$	−1.15466	−	13.1978i	−0.0921516	−	1.05330i	0.799528	−	0.600629i	$-0.205083\pi$
$158$	−12.5960	−	5.87360i	−1.00208	−	0.467278i
$159$		0			0
$160$	13.1429	+	12.4494i	1.03904	+	0.984211i
$161$			1.21507i			0.0957606i
$162$		0			0
$163$	−13.2225	+	13.2225i	−1.03567	+	1.03567i	−0.0363256	+	0.999340i	$0.511565\pi$
$163$	−13.2225	+	13.2225i	−1.03567	+	1.03567i	−0.999340	+	0.0363256i	$0.988435\pi$
$164$	3.49261	+	19.8076i	0.272727	+	1.54671i
$165$		0			0
$166$	7.56276	−	2.75262i	0.586984	−	0.213645i
$167$	−7.51125	+	0.657149i	−0.581238	+	0.0508517i	−0.373983	−	0.927435i	$-0.622008\pi$
$167$	−7.51125	+	0.657149i	−0.581238	+	0.0508517i	−0.207254	+	0.978287i	$0.566453\pi$
$168$		0			0
$169$	2.96127	−	8.13602i	0.227790	−	0.625848i
$170$	−2.84498	+	1.12367i	−0.218200	+	0.0861813i
$171$		0			0
$172$	7.27894	−	1.95039i	0.555014	−	0.148715i
$173$	−7.48506	−	0.654858i	−0.569078	−	0.0497879i	−0.201014	−	0.979588i	$-0.564424\pi$
$173$	−7.48506	−	0.654858i	−0.569078	−	0.0497879i	−0.368064	+	0.929800i	$0.619979\pi$
$174$		0			0
$175$	−12.7647	+	4.17326i	−0.964921	+	0.315469i
$176$	−23.2516	−	4.09989i	−1.75266	−	0.309041i
$177$		0			0
$178$	0.151963	−	1.73695i	0.0113901	−	0.130190i
$179$	−6.45949	+	11.1882i	−0.482805	+	0.836242i	−0.999805	−	0.0197428i	$-0.993715\pi$
$179$	−6.45949	+	11.1882i	−0.482805	+	0.836242i	0.517000	+	0.855985i	$0.327049\pi$
$180$		0			0
$181$	−2.64164	−	4.57545i	−0.196351	−	0.340091i	0.750991	−	0.660312i	$-0.229576\pi$
$181$	−2.64164	−	4.57545i	−0.196351	−	0.340091i	−0.947343	+	0.320222i	$0.896243\pi$
$182$	−10.3119	+	4.80853i	−0.764371	+	0.356432i
$183$		0			0
$184$	−0.0786542	+	0.0937365i	−0.00579847	+	0.00691034i
$185$	5.33427	+	3.52369i	0.392184	+	0.259066i
$186$		0			0
$187$	2.45207	−	3.50191i	0.179313	−	0.256085i
$188$	−9.46453	−	9.46453i	−0.690272	−	0.690272i
$189$		0			0
$190$	−8.46039	−	11.4118i	−0.613782	−	0.827898i
$191$	−18.3259	+	3.23135i	−1.32602	+	0.233812i	−0.791408	−	0.611288i	$-0.790652\pi$
$191$	−18.3259	+	3.23135i	−1.32602	+	0.233812i	−0.534607	+	0.845101i	$0.679540\pi$
$192$		0			0
$193$	−2.42548	+	5.20146i	−0.174590	+	0.374410i	−0.974058	−	0.226300i	$-0.927337\pi$
$193$	−2.42548	+	5.20146i	−0.174590	+	0.374410i	0.799468	+	0.600709i	$0.205115\pi$
$194$	−6.07563	−	5.09806i	−0.436205	−	0.366020i
$195$		0			0
$196$	−0.429242	−	0.156231i	−0.0306601	−	0.0111594i
$197$	−16.4402	−	4.40513i	−1.17131	−	0.313852i	−0.379837	−	0.925053i	$-0.624020\pi$
$197$	−16.4402	−	4.40513i	−1.17131	−	0.313852i	−0.791475	+	0.611201i	$0.790687\pi$
$198$		0			0
$199$	−20.0824	−	11.5946i	−1.42361	−	0.821920i	−0.427002	−	0.904251i	$-0.640430\pi$
$199$	−20.0824	−	11.5946i	−1.42361	−	0.821920i	−0.996605	+	0.0823307i	$0.973764\pi$
$200$	−1.25488	−	0.504344i	−0.0887335	−	0.0356625i
$201$		0			0
$202$	−22.7045	+	15.8978i	−1.59748	+	1.11857i
$203$	17.6716	−	12.3738i	1.24030	−	0.868469i
$204$		0			0
$205$	11.0330	+	17.9675i	0.770580	+	1.25490i
$206$	11.1949	+	6.46336i	0.779983	+	0.450324i
$207$		0			0
$208$	7.47961	+	2.00416i	0.518618	+	0.138963i
$209$	18.6568	+	6.79052i	1.29052	+	0.469710i
$210$		0			0
$211$	−1.99032	−	1.67007i	−0.137019	−	0.114973i	0.571702	−	0.820461i	$-0.306283\pi$
$211$	−1.99032	−	1.67007i	−0.137019	−	0.114973i	−0.708721	+	0.705488i	$0.750728\pi$
$212$	7.64307	−	16.3906i	0.524928	−	1.12571i
$213$		0			0
$214$	21.0349	−	3.70902i	1.43792	−	0.253543i
$215$	6.34591	−	4.70469i	0.432787	−	0.320857i
$216$		0			0
$217$	−3.10966	−	3.10966i	−0.211097	−	0.211097i
$218$	−3.19212	+	4.55882i	−0.216198	+	0.308762i
$219$		0			0
$220$	29.6894	−	6.06858i	2.00166	−	0.409143i
$221$	−0.901242	+	1.07406i	−0.0606241	+	0.0722490i
$222$		0			0
$223$	4.57405	−	2.13291i	0.306301	−	0.142831i	−0.263390	−	0.964689i	$-0.584841\pi$
$223$	4.57405	−	2.13291i	0.306301	−	0.142831i	0.569691	+	0.821859i	$0.307063\pi$
$224$	10.8726	+	18.8318i	0.726453	+	1.25825i
$225$		0			0
$226$	−20.5868	+	35.6573i	−1.36941	+	2.37189i
$227$	1.72288	−	19.6926i	0.114352	−	1.30705i	−0.694696	−	0.719304i	$-0.744461\pi$
$227$	1.72288	−	19.6926i	0.114352	−	1.30705i	0.809048	−	0.587743i	$-0.199983\pi$
$228$		0			0
$229$	24.6362	+	4.34402i	1.62800	+	0.287061i	0.911740	−	0.410768i	$-0.134739\pi$
$229$	24.6362	+	4.34402i	1.62800	+	0.287061i	0.716264	+	0.697829i	$0.245850\pi$
$230$	−0.650756	+	1.95082i	−0.0429096	+	0.128633i
$231$		0			0
$232$	2.16426	+	0.189349i	0.142091	+	0.0124313i
$233$	−7.90321	+	2.11766i	−0.517756	+	0.138732i	−0.508229	−	0.861222i	$-0.669699\pi$
$233$	−7.90321	+	2.11766i	−0.517756	+	0.138732i	−0.00952771	+	0.999955i	$0.503033\pi$
$234$		0			0
$235$	−12.8726	−	5.58323i	−0.839719	−	0.364210i
$236$	5.78894	−	15.9050i	0.376828	−	1.03533i
$237$		0			0
$238$	−3.66024	+	0.320230i	−0.237258	+	0.0207574i
$239$	−15.0785	+	5.48812i	−0.975347	+	0.354997i	−0.780029	−	0.625743i	$-0.784796\pi$
$239$	−15.0785	+	5.48812i	−0.975347	+	0.354997i	−0.195317	+	0.980740i	$0.562574\pi$
$240$		0			0
$241$	2.00152	+	11.3512i	0.128929	+	0.731194i	0.978896	+	0.204358i	$0.0655107\pi$
$241$	2.00152	+	11.3512i	0.128929	+	0.731194i	−0.849967	+	0.526836i	$0.823378\pi$
$242$	−42.2136	+	42.2136i	−2.71359	+	2.71359i
$243$		0			0
$244$		−	3.49429i		−	0.223699i
$245$	−0.478675	+	0.0129715i	−0.0305814	+	0.000828719i
$246$		0			0
$247$	−5.90147	−	2.75190i	−0.375501	−	0.175099i
$248$	−0.0385992	−	0.441191i	−0.00245105	−	0.0280157i
$249$		0			0
$250$	−22.7291	−	0.136151i	−1.43752	−	0.00861094i
$251$	−0.521180	+	0.300903i	−0.0328966	+	0.0189928i	−0.516358	−	0.856373i	$-0.672713\pi$
$251$	−0.521180	+	0.300903i	−0.0328966	+	0.0189928i	0.483462	+	0.875366i	$0.339379\pi$
$252$		0			0
$253$	−0.743887	−	2.77622i	−0.0467677	−	0.174540i
$254$	−2.23656	+	1.87670i	−0.140334	+	0.117755i
$255$		0			0
$256$	2.37270	−	13.4562i	0.148294	−	0.841014i
$257$	5.05815	+	7.22379i	0.315519	+	0.450608i	0.945318	−	0.326151i	$-0.105752\pi$
$257$	5.05815	+	7.22379i	0.315519	+	0.450608i	−0.629799	+	0.776758i	$0.716863\pi$
$258$		0			0
$259$	4.93607	+	5.88259i	0.306713	+	0.365526i
$260$	−9.87361	+	1.13408i	−0.612336	+	0.0703327i
$261$		0			0
$262$	−10.5354	+	39.3187i	−0.650880	+	2.42912i
$263$	−5.05420	−	10.8388i	−0.311656	−	0.668347i	0.686622	−	0.727015i	$-0.259093\pi$
$263$	−5.05420	−	10.8388i	−0.311656	−	0.668347i	−0.998278	+	0.0586671i	$0.981315\pi$
$264$		0			0
$265$	1.14013	−	18.9242i	0.0700374	−	1.16250i
$266$	−5.83616	−	16.0347i	−0.357838	−	0.983152i
$267$		0			0
$268$	9.34624	+	6.54431i	0.570913	+	0.399757i
$269$	15.6712			0.955492			0.477746	−	0.878498i	$-0.341454\pi$
$269$	15.6712			0.955492			0.477746	+	0.878498i	$0.341454\pi$
$270$		0			0
$271$	15.3544			0.932711			0.466355	−	0.884597i	$-0.345567\pi$
$271$	15.3544			0.932711			0.466355	+	0.884597i	$0.345567\pi$
$272$	2.04834	+	1.43426i	0.124199	+	0.0869648i
$273$		0			0
$274$	9.08998	+	24.9745i	0.549146	+	1.50876i
$275$	26.6103	−	17.3500i	1.60466	−	1.04624i
$276$		0			0
$277$	1.83097	+	3.92654i	0.110013	+	0.235923i	0.953605	−	0.301062i	$-0.0973411\pi$
$277$	1.83097	+	3.92654i	0.110013	+	0.235923i	−0.843592	+	0.536985i	$0.819563\pi$
$278$	−7.38296	+	27.5536i	−0.442800	+	1.65255i
$279$		0			0
$280$	−1.27228	−	1.01013i	−0.0760335	−	0.0603666i
$281$	11.4406	+	13.6344i	0.682490	+	0.813360i	0.990426	−	0.138047i	$-0.0440825\pi$
$281$	11.4406	+	13.6344i	0.682490	+	0.813360i	−0.307935	+	0.951407i	$0.599638\pi$
$282$		0			0
$283$	−11.3847	−	16.2591i	−0.676752	−	0.966501i	−0.999798	−	0.0201182i	$-0.993596\pi$
$283$	−11.3847	−	16.2591i	−0.676752	−	0.966501i	0.323046	−	0.946383i	$-0.395293\pi$
$284$	0.876956	−	4.97347i	0.0520378	−	0.295121i
$285$		0			0
$286$	20.6172	−	17.2998i	1.21912	−	1.02296i
$287$	6.55492	+	24.4633i	0.386925	+	1.44402i
$288$		0			0
$289$	14.3303	−	8.27362i	0.842960	−	0.486683i
$290$	34.9992	−	10.4020i	2.05523	−	0.610825i
$291$		0			0
$292$	−0.257400	−	2.94209i	−0.0150632	−	0.172173i
$293$	14.9126	+	6.95384i	0.871201	+	0.406248i	0.806204	−	0.591638i	$-0.201518\pi$
$293$	14.9126	+	6.95384i	0.871201	+	0.406248i	0.0649974	+	0.997885i	$0.479296\pi$
$294$		0			0
$295$	−0.480642	−	17.7367i	−0.0279840	−	1.03267i
$296$			0.773337i			0.0449493i
$297$		0			0
$298$	−1.64938	+	1.64938i	−0.0955460	+	0.0955460i
$299$	0.163687	+	0.928314i	0.00946626	+	0.0536858i
$300$		0			0
$301$	8.91665	−	3.24540i	0.513947	−	0.187061i
$302$	3.19392	−	0.279431i	0.183789	−	0.0160795i
$303$		0			0
$304$	−3.97190	+	10.9127i	−0.227804	+	0.625887i
$305$	−1.34562	−	3.40694i	−0.0770500	−	0.195081i
$306$		0			0
$307$	−2.83491	+	0.759611i	−0.161797	+	0.0433533i	−0.338808	−	0.940856i	$-0.610024\pi$
$307$	−2.83491	+	0.759611i	−0.161797	+	0.0433533i	0.177011	+	0.984209i	$0.443357\pi$
$308$	36.2611	+	3.17243i	2.06617	+	0.180766i
$309$		0			0
$310$	−3.32718	−	6.65808i	−0.188971	−	0.378153i
$311$	3.75166	+	0.661519i	0.212737	+	0.0375113i	0.279001	−	0.960291i	$-0.409997\pi$
$311$	3.75166	+	0.661519i	0.212737	+	0.0375113i	−0.0662637	+	0.997802i	$0.521108\pi$
$312$		0			0
$313$	0.0495580	−	0.566450i	0.00280118	−	0.0320177i	−0.994665	−	0.103153i	$-0.967107\pi$
$313$	0.0495580	−	0.566450i	0.00280118	−	0.0320177i	0.997467	+	0.0711357i	$0.0226623\pi$
$314$	13.4667	−	23.3250i	0.759971	−	1.31631i
$315$		0			0
$316$	−7.29107	−	12.6285i	−0.410155	−	0.710409i
$317$	10.3800	−	4.84025i	0.582997	−	0.271856i	−0.108664	−	0.994079i	$-0.534657\pi$
$317$	10.3800	−	4.84025i	0.582997	−	0.271856i	0.691661	+	0.722223i	$0.256879\pi$
$318$		0			0
$319$	−32.8012	+	39.0909i	−1.83651	+	2.18867i
$320$	4.04212	+	19.7753i	0.225961	+	1.10547i
$321$		0			0
$322$	−1.41686	+	2.02348i	−0.0789584	+	0.112764i
$323$	−1.48686	−	1.48686i	−0.0827312	−	0.0827312i
$324$		0			0
$325$	−9.19007	+	4.90798i	−0.509774	+	0.272246i
$326$	−37.4382	+	6.60137i	−2.07351	+	0.365616i
$327$		0			0
$328$	−1.07789	+	2.31154i	−0.0595165	+	0.127634i
$329$	−12.9110	−	10.8336i	−0.711806	−	0.597276i
$330$		0			0
$331$	24.0043	+	8.73685i	1.31940	+	0.480221i	0.903265	−	0.429084i	$-0.141164\pi$
$331$	24.0043	+	8.73685i	1.31940	+	0.480221i	0.416131	+	0.909305i	$0.363386\pi$
$332$	8.15650	+	2.18553i	0.447646	+	0.119946i
$333$		0			0
$334$	−13.2750	−	7.66431i	−0.726374	−	0.419372i
$335$	11.6328	+	2.78156i	0.635566	+	0.151973i
$336$		0			0
$337$	14.4868	−	10.1438i	0.789147	−	0.552566i	−0.108077	−	0.994143i	$-0.534469\pi$
$337$	14.4868	−	10.1438i	0.789147	−	0.552566i	0.897224	+	0.441576i	$0.145580\pi$
$338$	14.4187	−	10.0961i	0.784274	−	0.549154i
$339$		0			0
$340$	−3.12140	−	0.746372i	−0.169282	−	0.0404777i
$341$	9.00884	+	5.20126i	0.487856	+	0.281664i
$342$		0			0
$343$	17.6052	+	4.71730i	0.950591	+	0.254710i
$344$	0.897959	+	0.326830i	0.0484147	+	0.0176215i
$345$		0			0
$346$	−11.7015	−	9.81869i	−0.629075	−	0.527856i
$347$	−0.943762	+	2.02390i	−0.0506638	+	0.108649i	−0.930010	−	0.367534i	$-0.880202\pi$
$347$	−0.943762	+	2.02390i	−0.0506638	+	0.108649i	0.879346	+	0.476183i	$0.157980\pi$
$348$		0			0
$349$	−18.9031	+	3.33312i	−1.01186	+	0.178418i	−0.654910	−	0.755707i	$-0.727294\pi$
$349$	−18.9031	+	3.33312i	−1.01186	+	0.178418i	−0.356948	+	0.934124i	$0.616183\pi$
$350$	−26.1238	−	7.93475i	−1.39637	−	0.424130i
$351$		0			0
$352$	−36.3712	−	36.3712i	−1.93859	−	1.93859i
$353$	−17.0436	+	24.3407i	−0.907137	+	1.29553i	0.0478427	+	0.998855i	$0.484765\pi$
$353$	−17.0436	+	24.3407i	−0.907137	+	1.29553i	−0.954980	+	0.296671i	$0.904124\pi$
$354$		0			0
$355$	−1.06020	−	5.18685i	−0.0562698	−	0.275289i
$356$	1.17591	−	1.40140i	0.0623233	−	0.0742741i
$357$		0			0
$358$	−23.8034	+	11.0997i	−1.25805	+	0.586638i
$359$	−14.0984	−	24.4191i	−0.744085	−	1.28879i	−0.950621	−	0.310354i	$-0.899552\pi$
$359$	−14.0984	−	24.4191i	−0.744085	−	1.28879i	0.206536	−	0.978439i	$-0.433781\pi$
$360$		0			0
$361$	−4.61724	+	7.99729i	−0.243012	+	0.420910i
$362$	0.936127	−	10.7000i	0.0492017	−	0.562378i
$363$		0			0
$364$	−11.7566	−	2.07300i	−0.616212	−	0.108655i
$365$	−1.38394	−	2.76943i	−0.0724388	−	0.144958i
$366$		0			0
$367$	23.9655	+	2.09671i	1.25099	+	0.109447i	0.693328	−	0.720622i	$-0.256144\pi$
$367$	23.9655	+	2.09671i	1.25099	+	0.109447i	0.557660	+	0.830069i	$0.311699\pi$
$368$	1.62387	−	0.435114i	0.0846499	−	0.0226819i
$369$		0			0
$370$	4.77443	+	12.0883i	0.248211	+	0.628438i
$371$	7.78866	−	21.3992i	0.404367	−	1.11099i
$372$		0			0
$373$	7.15282	−	0.625791i	0.370359	−	0.0324022i	0.0995428	−	0.995033i	$-0.468262\pi$
$373$	7.15282	−	0.625791i	0.370359	−	0.0324022i	0.270816	+	0.962631i	$0.412706\pi$
$374$	8.16699	−	2.97254i	0.422305	−	0.153706i
$375$		0			0
$376$	−0.294734	−	1.67152i	−0.0151998	−	0.0862021i
$377$	11.8342	−	11.8342i	0.609494	−	0.609494i
$378$		0			0
$379$		−	6.61098i		−	0.339583i	−0.985480	−	0.169792i	$-0.945691\pi$
$379$		−	6.61098i		−	0.339583i	0.985480	−	0.169792i	$-0.0543094\pi$
$380$	−0.403760	−	14.8996i	−0.0207125	−	0.764333i
$381$		0			0
$382$	−34.2866	−	15.9881i	−1.75426	−	0.818023i
$383$	−0.852747	−	9.74694i	−0.0435733	−	0.498046i	−0.986355	−	0.164634i	$-0.947356\pi$
$383$	−0.852747	−	9.74694i	−0.0435733	−	0.498046i	0.942781	−	0.333412i	$-0.108200\pi$
$384$		0			0
$385$	36.5763	−	10.8707i	1.86410	−	0.554022i
$386$	−10.1045	+	5.83385i	−0.514307	+	0.296935i
$387$		0			0
$388$	−2.15377	−	8.03798i	−0.109341	−	0.408067i
$389$	−7.47118	+	6.26906i	−0.378804	+	0.317854i	−0.812233	−	0.583334i	$-0.801748\pi$
$389$	−7.47118	+	6.26906i	−0.378804	+	0.317854i	0.433429	+	0.901188i	$0.357304\pi$
$390$		0			0
$391$	−0.0528585	+	0.299776i	−0.00267317	+	0.0151603i
$392$	−0.0332242	−	0.0474490i	−0.00167807	−	0.00239654i
$393$		0			0
$394$	−22.2415	−	26.5064i	−1.12051	−	1.33538i
$395$	−11.9719	−	9.50510i	−0.602374	−	0.478253i
$396$		0			0
$397$	−5.87091	+	21.9105i	−0.294653	+	1.09966i	0.646840	+	0.762626i	$0.276090\pi$
$397$	−5.87091	+	21.9105i	−0.294653	+	1.09966i	−0.941493	+	0.337033i	$0.890577\pi$
$398$	−19.9237	−	42.7265i	−0.998684	−	2.14168i
$399$		0			0
$400$	10.1484	+	15.5648i	0.507418	+	0.778242i
$401$	−10.7416	−	29.5124i	−0.536411	−	1.47378i	−0.851316	−	0.524654i	$-0.824195\pi$
$401$	−10.7416	−	29.5124i	−0.536411	−	1.47378i	0.314905	−	0.949123i	$-0.398027\pi$
$402$		0			0
$403$	−2.79470	−	1.95687i	−0.139214	−	0.0974788i
$404$	−29.0812			−1.44684
$405$		0			0
$406$	43.8578			2.17662
$407$	−14.8795	−	10.4188i	−0.737551	−	0.516439i
$408$		0			0
$409$	−9.77070	−	26.8448i	−0.483130	−	1.32739i	−0.906796	−	0.421570i	$-0.861479\pi$
$409$	−9.77070	−	26.8448i	−0.483130	−	1.32739i	0.423666	−	0.905818i	$-0.360743\pi$
$410$	−2.57779	+	42.7871i	−0.127308	+	2.11310i
$411$		0			0
$412$	5.73195	+	12.2922i	0.282393	+	0.605593i
$413$	5.51614	−	20.5865i	0.271432	−	1.01300i
$414$		0			0
$415$	8.79424	−	1.01010i	0.431692	−	0.0495840i
$416$	10.8436	+	12.9229i	0.531650	+	0.633596i
$417$		0			0
$418$	23.1514	+	33.0637i	1.13237	+	1.61720i
$419$	−0.704690	+	3.99650i	−0.0344264	+	0.195242i	−0.997171	−	0.0751721i	$-0.976049\pi$
$419$	−0.704690	+	3.99650i	−0.0344264	+	0.195242i	0.962744	+	0.270414i	$0.0871605\pi$
$420$		0			0
$421$	−7.52582	+	6.31491i	−0.366786	+	0.307770i	−0.807489	−	0.589883i	$-0.799174\pi$
$421$	−7.52582	+	6.31491i	−0.366786	+	0.307770i	0.440703	+	0.897653i	$0.354729\pi$
$422$	−1.36710	−	5.10208i	−0.0665493	−	0.248366i
$423$		0			0
$424$	1.98608	−	1.14666i	0.0964525	−	0.0556869i
$425$	−3.33080	+	0.474311i	−0.161567	+	0.0230075i
$426$		0			0
$427$	−0.383483	−	4.38323i	−0.0185581	−	0.212119i
$428$	20.3110	+	9.47115i	0.981767	+	0.457805i
$429$		0			0
$430$	16.0540	−	0.435044i	0.774194	−	0.0209797i
$431$			3.57709i			0.172302i	0.996282	+	0.0861512i	$0.0274568\pi$
$431$			3.57709i			0.172302i	−0.996282	+	0.0861512i	$0.972543\pi$
$432$		0			0
$433$	0.671243	−	0.671243i	0.0322579	−	0.0322579i	−0.690794	−	0.723052i	$-0.742739\pi$
$433$	0.671243	−	0.671243i	0.0322579	−	0.0322579i	0.723052	+	0.690794i	$0.242739\pi$
$434$	−1.55251	−	8.80470i	−0.0745227	−	0.422639i
$435$		0			0
$436$	−5.48705	+	1.99712i	−0.262782	+	0.0956449i
$437$	−1.40831	+	0.123211i	−0.0673688	+	0.00589400i
$438$		0			0
$439$	11.2524	−	30.9157i	0.537048	−	1.47553i	−0.313479	−	0.949595i	$-0.601495\pi$
$439$	11.2524	−	30.9157i	0.537048	−	1.47553i	0.850527	−	0.525932i	$-0.176283\pi$
$440$	3.52537	+	1.52905i	0.168066	+	0.0728948i
$441$		0			0
$442$	−2.75330	+	0.737744i	−0.130961	+	0.0350909i
$443$	22.3331	+	1.95389i	1.06108	+	0.0928322i	0.604306	−	0.796752i	$-0.293450\pi$
$443$	22.3331	+	1.95389i	1.06108	+	0.0928322i	0.456771	+	0.889585i	$0.349006\pi$
$444$		0			0
$445$	0.606852	−	1.81920i	0.0287676	−	0.0862385i
$446$	10.1044	+	1.78168i	0.478459	+	0.0843652i
$447$		0			0
$448$	−2.11307	+	24.1525i	−0.0998333	+	1.14110i
$449$	−4.96273	+	8.59571i	−0.234206	+	0.405656i	−0.959042	−	0.283265i	$-0.908582\pi$
$449$	−4.96273	+	8.59571i	−0.234206	+	0.405656i	0.724836	+	0.688922i	$0.241916\pi$
$450$		0			0
$451$	−29.9538	−	51.8815i	−1.41047	−	2.44301i
$452$	−39.1525	+	18.2571i	−1.84158	+	0.858742i
$453$		0			0
$454$	25.8323	−	30.7857i	1.21237	−	1.44484i
$455$	−12.2610	+	2.50618i	−0.574804	+	0.117491i
$456$		0			0
$457$	19.8172	−	28.3019i	0.927010	−	1.32391i	−0.0190173	−	0.999819i	$-0.506054\pi$
$457$	19.8172	−	28.3019i	0.927010	−	1.32391i	0.946027	−	0.324088i	$-0.105057\pi$
$458$	35.9619	+	35.9619i	1.68039	+	1.68039i
$459$		0			0
$460$	−1.73332	+	1.28504i	−0.0808164	+	0.0599152i
$461$	10.2855	−	1.81362i	0.479046	−	0.0844687i	0.0710890	−	0.997470i	$-0.477353\pi$
$461$	10.2855	−	1.81362i	0.479046	−	0.0844687i	0.407957	+	0.913001i	$0.366241\pi$
$462$		0			0
$463$	−7.80727	+	16.7427i	−0.362835	+	0.778101i	0.637138	+	0.770749i	$0.280118\pi$
$463$	−7.80727	+	16.7427i	−0.362835	+	0.778101i	−0.999973	+	0.00735185i	$0.997660\pi$
$464$	−22.8650	−	19.1860i	−1.06148	−	0.890689i
$465$		0			0
$466$	−15.6308	−	5.68914i	−0.724082	−	0.263544i
$467$	37.1950	+	9.96636i	1.72118	+	0.461188i	0.978120	−	0.208040i	$-0.0667084\pi$
$467$	37.1950	+	9.96636i	1.72118	+	0.461188i	0.743057	+	0.669228i	$0.233375\pi$
$468$		0			0
$469$	12.4421	+	7.18347i	0.574524	+	0.331702i
$470$	−14.9267	−	24.3084i	−0.688518	−	1.12126i
$471$		0			0
$472$	1.75816	−	1.23108i	0.0809259	−	0.0566649i
$473$	−18.3862	+	12.8741i	−0.845397	+	0.591953i
$474$		0			0
$475$	−6.13137	−	14.3717i	−0.281327	−	0.659417i
$476$	−3.33858	−	1.92753i	−0.153024	−	0.0883482i
$477$		0			0
$478$	−31.5102	−	8.44313i	−1.44124	−	0.386180i
$479$	−13.8251	−	5.03191i	−0.631684	−	0.229914i	0.00628038	−	0.999980i	$-0.498001\pi$
$479$	−13.8251	−	5.03191i	−0.631684	−	0.229914i	−0.637964	+	0.770066i	$0.720223\pi$
$480$		0			0
$481$	4.56365	+	3.82935i	0.208084	+	0.174604i
$482$	−9.90315	+	21.2374i	−0.451076	+	0.967336i
$483$		0			0
$484$	−61.6857	+	10.8768i	−2.80389	+	0.494402i
$485$	−5.19529	−	7.00765i	−0.235906	−	0.318201i
$486$		0			0
$487$	3.40980	+	3.40980i	0.154513	+	0.154513i	0.780130	−	0.625617i	$-0.215153\pi$
$487$	3.40980	+	3.40980i	0.154513	+	0.154513i	−0.625617	+	0.780130i	$0.715153\pi$
$488$	0.254154	−	0.362969i	0.0115050	−	0.0164308i
$489$		0			0
$490$	−0.812277	−	0.536569i	−0.0366949	−	0.0242397i
$491$	4.15599	−	4.95292i	0.187557	−	0.223522i	−0.664069	−	0.747671i	$-0.731172\pi$
$491$	4.15599	−	4.95292i	0.187557	−	0.223522i	0.851627	+	0.524149i	$0.175617\pi$
$492$		0			0
$493$	4.89815	−	2.28404i	0.220602	−	0.102868i
$494$	−6.61896	−	11.4644i	−0.297801	−	0.515806i
$495$		0			0
$496$	−3.04231	+	5.26944i	−0.136604	+	0.236605i
$497$	0.554237	−	6.33496i	0.0248609	−	0.284162i
$498$		0			0
$499$	−24.8022	−	4.37330i	−1.11030	−	0.195776i	−0.411722	−	0.911309i	$-0.635073\pi$
$499$	−24.8022	−	4.37330i	−1.11030	−	0.195776i	−0.698578	+	0.715534i	$0.746184\pi$
$500$	−19.4530	−	13.7955i	−0.869966	−	0.616956i
$501$		0			0
$502$	−1.21881	−	0.106632i	−0.0543982	−	0.00475922i
$503$	37.5360	−	10.0577i	1.67365	−	0.448452i	0.707556	−	0.706657i	$-0.249798\pi$
$503$	37.5360	−	10.0577i	1.67365	−	0.448452i	0.966090	+	0.258205i	$0.0831310\pi$
$504$		0			0
$505$	−28.3542	+	11.1989i	−1.26175	+	0.498345i
$506$	1.99847	−	5.49075i	0.0888428	−	0.244094i
$507$		0			0
$508$	−3.05166	+	0.266986i	−0.135396	+	0.0118456i
$509$	−5.50573	+	2.00392i	−0.244037	+	0.0888223i	−0.461143	−	0.887326i	$-0.652561\pi$
$509$	−5.50573	+	2.00392i	−0.244037	+	0.0888223i	0.217106	+	0.976148i	$0.430338\pi$
$510$		0			0
$511$	−0.645765	−	3.66231i	−0.0285669	−	0.162011i
$512$	22.6957	−	22.6957i	1.00302	−	1.00302i
$513$		0			0
$514$			17.9282i			0.790777i
$515$	10.3223	+	9.77760i	0.454854	+	0.430853i
$516$		0			0
$517$	36.1320	+	16.8486i	1.58908	+	0.741002i
$518$	1.36065	+	15.5523i	0.0597834	+	0.683327i
$519$		0			0
$520$	−1.10811	−	0.600345i	−0.0485937	−	0.0263269i
$521$	−16.6908	+	9.63645i	−0.731238	+	0.422180i	−0.818875	−	0.573972i	$-0.805402\pi$
$521$	−16.6908	+	9.63645i	−0.731238	+	0.422180i	0.0876370	+	0.996152i	$0.472068\pi$
$522$		0			0
$523$	5.63988	+	21.0483i	0.246615	+	0.920379i	0.972565	+	0.232631i	$0.0747336\pi$
$523$	5.63988	+	21.0483i	0.246615	+	0.920379i	−0.725950	+	0.687747i	$0.758600\pi$
$524$	−32.7171	+	27.4529i	−1.42925	+	1.19929i
$525$		0			0
$526$	4.22192	−	23.9437i	0.184084	−	1.04399i
$527$	−0.631923	−	0.902479i	−0.0275270	−	0.0393126i
$528$		0			0
$529$	−14.6526	−	17.4623i	−0.637068	−	0.759228i
$530$	23.9657	−	30.1855i	1.04100	−	1.31117i
$531$		0			0
$532$	4.63380	−	17.2936i	0.200901	−	0.749772i
$533$	8.30354	+	17.8070i	0.359666	+	0.771307i
$534$		0			0
$535$	23.4505	+	1.41282i	1.01385	+	0.0610817i
$536$	0.494847	+	1.35958i	0.0213741	+	0.0587249i
$537$		0			0
$538$	26.0978	+	18.2738i	1.12515	+	0.787841i
$539$	1.36056			0.0586036
$540$		0			0
$541$	17.4882			0.751877			0.375938	−	0.926645i	$-0.377320\pi$
$541$	17.4882			0.751877			0.375938	+	0.926645i	$0.377320\pi$
$542$	25.5700	+	17.9043i	1.09833	+	0.769057i
$543$		0			0
$544$	1.86319	+	5.11909i	0.0798838	+	0.219479i
$545$	−4.58081	+	4.06022i	−0.196221	+	0.173921i
$546$		0			0
$547$	−15.2727	−	32.7524i	−0.653013	−	1.40039i	−0.901937	−	0.431868i	$-0.857855\pi$
$547$	−15.2727	−	32.7524i	−0.653013	−	1.40039i	0.248924	−	0.968523i	$-0.419923\pi$
$548$	−7.21727	+	26.9352i	−0.308306	+	1.15062i
$549$		0			0
$550$	64.5462	+	2.13611i	2.75226	+	0.0910841i
$551$	16.1337	+	19.2274i	0.687319	+	0.819115i
$552$		0			0
$553$	−10.5318	−	15.0410i	−0.447859	−	0.639610i
$554$	−1.52946	+	8.67402i	−0.0649807	+	0.368524i
$555$		0			0
$556$	−22.9273	+	19.2383i	−0.972336	+	0.815887i
$557$	0.942784	+	3.51852i	0.0399470	+	0.149084i	0.983019	−	0.183505i	$-0.0587444\pi$
$557$	0.942784	+	3.51852i	0.0399470	+	0.149084i	−0.943072	+	0.332589i	$0.892078\pi$
$558$		0			0
$559$	6.37515	−	3.68069i	0.269640	−	0.155677i
$560$	6.35848	+	21.3942i	0.268695	+	0.904070i
$561$		0			0
$562$	3.15365	+	36.0464i	0.133029	+	1.52053i
$563$	−7.85254	−	3.66170i	−0.330945	−	0.154322i	0.250042	−	0.968235i	$-0.419556\pi$
$563$	−7.85254	−	3.66170i	−0.330945	−	0.154322i	−0.580987	+	0.813913i	$0.697333\pi$
$564$		0			0
$565$	−31.1431	+	32.8780i	−1.31020	+	1.38319i
$566$		−	40.3521i		−	1.69613i
$567$		0			0
$568$	0.452834	−	0.452834i	0.0190005	−	0.0190005i
$569$	6.84317	+	38.8095i	0.286881	+	1.62698i	0.698490	+	0.715620i	$0.253856\pi$
$569$	6.84317	+	38.8095i	0.286881	+	1.62698i	−0.411609	+	0.911361i	$0.635033\pi$
$570$		0			0
$571$	−4.05495	+	1.47588i	−0.169694	+	0.0617636i	−0.425470	−	0.904972i	$-0.639891\pi$
$571$	−4.05495	+	1.47588i	−0.169694	+	0.0617636i	0.255776	+	0.966736i	$0.417669\pi$
$572$	28.1310	−	2.46114i	1.17621	−	0.102905i
$573$		0			0
$574$	−17.6100	+	48.3830i	−0.735026	+	2.01947i
$575$	−1.19513	+	1.92040i	−0.0498405	+	0.0800863i
$576$		0			0
$577$	29.3682	−	7.86919i	1.22261	−	0.327598i	0.410915	−	0.911674i	$-0.365209\pi$
$577$	29.3682	−	7.86919i	1.22261	−	0.327598i	0.811699	+	0.584075i	$0.198543\pi$
$578$	33.5123	+	2.93195i	1.39393	+	0.121953i
$579$		0			0
$580$	36.3407	+	12.1226i	1.50897	+	0.503363i
$581$	10.4714	+	1.84638i	0.434425	+	0.0766009i
$582$		0			0
$583$	−4.69481	+	53.6619i	−0.194439	+	2.22245i
$584$	0.187253	−	0.324332i	0.00774858	−	0.0134209i
$585$		0			0
$586$	16.7256	+	28.9696i	0.690929	+	1.19672i
$587$	−17.8591	+	8.32785i	−0.737126	+	0.343727i	−0.754657	−	0.656119i	$-0.772197\pi$
$587$	−17.8591	+	8.32785i	−0.737126	+	0.343727i	0.0175318	+	0.999846i	$0.494419\pi$
$588$		0			0
$589$	3.28890	−	3.91956i	0.135517	−	0.161503i
$590$	19.8819	−	30.0978i	0.818524	−	1.23911i
$591$		0			0
$592$	6.09413	−	8.70333i	0.250467	−	0.357705i
$593$	1.60584	+	1.60584i	0.0659438	+	0.0659438i	0.739310	−	0.673366i	$-0.235152\pi$
$593$	1.60584	+	1.60584i	0.0659438	+	0.0659438i	−0.673366	+	0.739310i	$0.735152\pi$
$594$		0			0
$595$	−3.99740	−	0.593688i	−0.163877	−	0.0243388i
$596$	−2.41020	+	0.424983i	−0.0987255	+	0.0174080i
$597$		0			0
$598$	−0.809892	+	1.73682i	−0.0331190	+	0.0710238i
$599$	16.1072	+	13.5155i	0.658122	+	0.552230i	0.909523	−	0.415653i	$-0.136447\pi$
$599$	16.1072	+	13.5155i	0.658122	+	0.552230i	−0.251401	+	0.967883i	$0.580891\pi$
$600$		0			0
$601$	−25.6301	−	9.32859i	−1.04547	−	0.380521i	−0.238521	−	0.971137i	$-0.576662\pi$
$601$	−25.6301	−	9.32859i	−1.04547	−	0.380521i	−0.806952	+	0.590616i	$0.798885\pi$
$602$	18.6335	+	4.99284i	0.759446	+	0.203493i
$603$		0			0
$604$	2.91323	+	1.68196i	0.118538	+	0.0684378i
$605$	−55.9551	+	34.3596i	−2.27490	+	1.39692i
$606$		0			0
$607$	−27.5055	+	19.2596i	−1.11641	+	0.781721i	−0.977990	−	0.208652i	$-0.933092\pi$
$607$	−27.5055	+	19.2596i	−1.11641	+	0.781721i	−0.138424	+	0.990373i	$0.544204\pi$
$608$	−20.7244	+	14.5114i	−0.840484	+	0.588513i
$609$		0			0
$610$	1.73185	−	7.24277i	0.0701205	−	0.293251i
$611$	−11.3235	−	6.53761i	−0.458099	−	0.264484i
$612$		0			0
$613$	42.7632	+	11.4584i	1.72719	+	0.462799i	0.979532	−	0.201288i	$-0.0645126\pi$
$613$	42.7632	+	11.4584i	1.72719	+	0.462799i	0.747656	+	0.664086i	$0.231179\pi$
$614$	−5.60681	−	2.04071i	−0.226272	−	0.0823564i
$615$		0			0
$616$	3.53588	+	2.96695i	0.142464	+	0.119542i
$617$	−5.99691	+	12.8604i	−0.241427	+	0.517741i	−0.989264	−	0.146141i	$-0.953315\pi$
$617$	−5.99691	+	12.8604i	−0.241427	+	0.517741i	0.747837	+	0.663882i	$0.231092\pi$
$618$		0			0
$619$	21.7592	−	3.83673i	0.874576	−	0.154211i	0.281697	−	0.959503i	$-0.409103\pi$
$619$	21.7592	−	3.83673i	0.874576	−	0.154211i	0.592878	+	0.805292i	$0.297991\pi$
$620$	1.14727	−	7.72473i	0.0460753	−	0.310233i
$621$		0			0
$622$	5.47637	+	5.47637i	0.219582	+	0.219582i
$623$	1.32127	−	1.88697i	0.0529355	−	0.0755998i
$624$		0			0
$625$	−24.2793	−	5.95950i	−0.971172	−	0.238380i
$626$	0.743054	−	0.885537i	0.0296984	−	0.0353932i
$627$		0			0
$628$	25.6114	−	11.9428i	1.02201	−	0.476569i
$629$	0.961899	+	1.66606i	0.0383534	+	0.0664301i
$630$		0			0
$631$	6.92272	−	11.9905i	0.275589	−	0.477334i	−0.694694	−	0.719305i	$-0.744460\pi$
$631$	6.92272	−	11.9905i	0.275589	−	0.477334i	0.970284	+	0.241971i	$0.0777937\pi$
$632$	0.161162	−	1.84210i	0.00641070	−	0.0732746i
$633$		0			0
$634$	22.9301	+	4.04320i	0.910672	+	0.160576i
$635$	−2.87257	+	1.43548i	−0.113994	+	0.0569654i
$636$		0			0
$637$	−0.444525	−	0.0388909i	−0.0176127	−	0.00154091i
$638$	−100.208	+	26.8506i	−3.96726	+	1.06302i
$639$		0			0
$640$	−1.92109	+	4.42925i	−0.0759377	+	0.175081i
$641$	7.88689	−	21.6691i	0.311513	−	0.855876i	−0.680838	−	0.732434i	$-0.738384\pi$
$641$	7.88689	−	21.6691i	0.311513	−	0.855876i	0.992352	−	0.123442i	$-0.0393934\pi$
$642$		0			0
$643$	7.31553	−	0.640026i	0.288496	−	0.0252402i	0.0580110	−	0.998316i	$-0.481524\pi$
$643$	7.31553	−	0.640026i	0.288496	−	0.0252402i	0.230485	+	0.973076i	$0.425969\pi$
$644$	−2.43549	+	0.886446i	−0.0959718	+	0.0349309i
$645$		0			0
$646$	−0.742320	−	4.20990i	−0.0292062	−	0.165636i
$647$	24.4108	−	24.4108i	0.959686	−	0.959686i	−0.0395324	−	0.999218i	$-0.512587\pi$
$647$	24.4108	−	24.4108i	0.959686	−	0.959686i	0.999218	+	0.0395324i	$0.0125868\pi$
$648$		0			0
$649$			50.4138i			1.97892i
$650$	−21.0276	−	2.54293i	−0.824769	−	0.0997418i
$651$		0			0
$652$	−36.1497	−	16.8569i	−1.41573	−	0.660167i
$653$	0.801061	+	9.15617i	0.0313480	+	0.358309i	0.995627	+	0.0934196i	$0.0297798\pi$
$653$	0.801061	+	9.15617i	0.0313480	+	0.358309i	−0.964279	+	0.264889i	$0.914665\pi$
$654$		0			0
$655$	−21.3274	+	39.3657i	−0.833329	+	1.53815i
$656$	30.3465	−	17.5206i	1.18483	−	0.684063i
$657$		0			0
$658$	−8.86823	−	33.0967i	−0.345720	−	1.29024i
$659$	23.2374	−	19.4985i	0.905199	−	0.759552i	−0.0660005	−	0.997820i	$-0.521024\pi$
$659$	23.2374	−	19.4985i	0.905199	−	0.759552i	0.971200	+	0.238267i	$0.0765795\pi$
$660$		0			0
$661$	1.43027	−	8.11147i	0.0556311	−	0.315500i	−0.944276	−	0.329156i	$-0.893236\pi$
$661$	1.43027	−	8.11147i	0.0556311	−	0.315500i	0.999907	+	0.0136561i	$0.00434700\pi$
$662$	29.7872	+	42.5405i	1.15771	+	1.65338i
$663$		0			0
$664$	0.688294	+	0.820277i	0.0267110	+	0.0318329i
$665$	−2.14164	−	18.6457i	−0.0830494	−	0.723050i
$666$		0			0
$667$	0.940421	−	3.50970i	0.0364132	−	0.135896i
$668$	−6.79699	−	14.5762i	−0.262984	−	0.563970i
$669$		0			0
$670$	16.1289	+	18.1969i	0.623112	+	0.703007i
$671$	3.55969	+	9.78018i	0.137420	+	0.377560i
$672$		0			0
$673$	−8.54498	−	5.98326i	−0.329385	−	0.230638i	0.397172	−	0.917744i	$-0.369992\pi$
$673$	−8.54498	−	5.98326i	−0.329385	−	0.230638i	−0.726557	+	0.687107i	$0.758881\pi$
$674$	35.9537			1.38488
$675$		0			0
$676$	18.4683			0.710319
$677$	−32.5175	−	22.7690i	−1.24975	−	0.875083i	−0.254000	−	0.967204i	$-0.581746\pi$
$677$	−32.5175	−	22.7690i	−1.24975	−	0.875083i	−0.995748	+	0.0921212i	$0.970635\pi$
$678$		0			0
$679$	−3.58382	−	9.84647i	−0.137535	−	0.377873i
$680$	−0.269949	−	0.304562i	−0.0103521	−	0.0116794i
$681$		0			0
$682$	8.93762	+	19.1668i	0.342239	+	0.733934i
$683$	−0.244148	+	0.911173i	−0.00934207	+	0.0348651i	−0.970440	−	0.241344i	$-0.922412\pi$
$683$	−0.244148	+	0.911173i	−0.00934207	+	0.0348651i	0.961097	+	0.276209i	$0.0890783\pi$
$684$		0			0
$685$	3.33567	+	29.0412i	0.127449	+	1.10961i
$686$	23.8177	+	28.3848i	0.909364	+	1.08374i
$687$		0			0
$688$	−7.53032	−	10.7544i	−0.287091	−	0.410008i
$689$	3.06779	−	17.3983i	0.116873	−	0.662822i
$690$		0			0
$691$	−8.89879	+	7.46697i	−0.338526	+	0.284057i	−0.796163	−	0.605082i	$-0.793140\pi$
$691$	−8.89879	+	7.46697i	−0.338526	+	0.284057i	0.457637	+	0.889139i	$0.348696\pi$
$692$	−4.14809	−	15.4809i	−0.157687	−	0.588495i
$693$		0			0
$694$	−3.93170	+	2.26997i	−0.149245	+	0.0861668i
$695$	−14.9457	+	27.5865i	−0.566923	+	1.04642i
$696$		0			0
$697$	0.552984	+	6.32063i	0.0209458	+	0.239411i
$698$	−35.3665	−	16.4917i	−1.33864	−	0.624219i
$699$		0			0
$700$	−17.6774	−	22.5411i	−0.668142	−	0.851974i
$701$			27.3341i			1.03240i	0.856469	+	0.516198i	$0.172653\pi$
$701$			27.3341i			1.03240i	−0.856469	+	0.516198i	$0.827347\pi$
$702$		0			0
$703$	−6.31764	+	6.31764i	−0.238274	+	0.238274i
$704$	−9.95862	−	56.4781i	−0.375330	−	2.12860i
$705$		0			0
$706$	−56.7662	+	20.6612i	−2.13643	+	0.777595i
$707$	−36.4794	+	3.19154i	−1.37195	+	0.120030i
$708$		0			0
$709$	10.1733	−	27.9510i	0.382068	−	1.04972i	−0.588417	−	0.808558i	$-0.700249\pi$
$709$	10.1733	−	27.9510i	0.382068	−	1.04972i	0.970484	−	0.241164i	$-0.0775292\pi$
$710$	4.28267	−	9.87409i	0.160726	−	0.370568i
$711$		0			0
$712$	0.224078	−	0.0600414i	0.00839766	−	0.00225015i
$713$	−0.737882	−	0.0645563i	−0.0276339	−	0.00241765i
$714$		0			0
$715$	26.4800	−	13.2326i	0.990296	−	0.494872i
$716$	−27.1382	−	4.78519i	−1.01420	−	0.178831i
$717$		0			0
$718$	4.99610	−	57.1057i	0.186453	−	2.13116i
$719$	−4.04581	+	7.00756i	−0.150883	+	0.261338i	−0.931552	−	0.363607i	$-0.881545\pi$
$719$	−4.04581	+	7.00756i	−0.150883	+	0.261338i	0.780669	+	0.624945i	$0.214878\pi$
$720$		0			0
$721$	8.53917	+	14.7903i	0.318015	+	0.550819i
$722$	−17.0147	+	7.93406i	−0.633220	+	0.295275i
$723$		0			0
$724$	7.24389	−	8.63293i	0.269217	−	0.320840i
$725$	40.1006	−	2.17495i	1.48930	−	0.0807756i
$726$		0			0
$727$	−26.0879	+	37.2574i	−0.967546	+	1.38180i	−0.0436958	+	0.999045i	$0.513913\pi$
$727$	−26.0879	+	37.2574i	−0.967546	+	1.38180i	−0.923850	+	0.382754i	$0.874976\pi$
$728$	−1.07044	−	1.07044i	−0.0396730	−	0.0396730i
$729$		0			0
$730$	0.924644	−	6.22578i	0.0342226	−	0.230427i
$731$	2.34106	−	0.412792i	0.0865872	−	0.0152677i
$732$		0			0
$733$	11.4484	−	24.5512i	0.422857	−	0.906819i	−0.573309	−	0.819339i	$-0.694341\pi$
$733$	11.4484	−	24.5512i	0.422857	−	0.906819i	0.996166	−	0.0874805i	$-0.0278815\pi$
$734$	37.4655	+	31.4373i	1.38288	+	1.16037i
$735$		0			0
$736$	3.44161	+	1.25265i	0.126860	+	0.0461731i
$737$	−32.8260	−	8.79571i	−1.20916	−	0.323994i
$738$		0			0
$739$	−13.2893	−	7.67257i	−0.488854	−	0.282240i	0.235245	−	0.971936i	$-0.424411\pi$
$739$	−13.2893	−	7.67257i	−0.488854	−	0.282240i	−0.724099	+	0.689696i	$0.757744\pi$
$740$	−3.17131	+	13.2628i	−0.116580	+	0.487549i
$741$		0			0
$742$	37.9237	−	26.5545i	1.39222	−	0.974846i
$743$	−31.3637	+	21.9611i	−1.15062	+	0.805674i	−0.983615	−	0.180282i	$-0.942299\pi$
$743$	−31.3637	+	21.9611i	−1.15062	+	0.805674i	−0.167007	+	0.985956i	$0.553410\pi$
$744$		0			0
$745$	−2.18629	+	1.34251i	−0.0800995	+	0.0491856i
$746$	12.6415	+	7.29858i	0.462839	+	0.267220i
$747$		0			0
$748$	8.80816	+	2.36014i	0.322058	+	0.0862953i
$749$	26.5175	+	9.65157i	0.968927	+	0.352661i
$750$		0			0
$751$	−6.83954	−	5.73906i	−0.249578	−	0.209421i	0.509412	−	0.860523i	$-0.329863\pi$
$751$	−6.83954	−	5.73906i	−0.249578	−	0.209421i	−0.758991	+	0.651101i	$0.774307\pi$
$752$	−9.85508	+	21.1343i	−0.359378	+	0.770688i
$753$		0			0
$754$	33.5075	−	5.90827i	1.22027	−	0.215167i
$755$	3.48812	+	0.518050i	0.126946	+	0.0188538i
$756$		0			0
$757$	−12.0849	−	12.0849i	−0.439232	−	0.439232i	0.452522	−	0.891753i	$-0.350525\pi$
$757$	−12.0849	−	12.0849i	−0.439232	−	0.439232i	−0.891753	+	0.452522i	$0.850525\pi$
$758$	7.70890	−	11.0094i	0.280000	−	0.399881i
$759$		0			0
$760$	1.04177	−	1.57706i	0.0377889	−	0.0572060i
$761$	28.7638	−	34.2794i	1.04269	−	1.24263i	0.0732447	−	0.997314i	$-0.476665\pi$
$761$	28.7638	−	34.2794i	1.04269	−	1.24263i	0.969444	−	0.245314i	$-0.0788910\pi$
$762$		0			0
$763$	−6.66378	+	3.10737i	−0.241245	+	0.112494i
$764$	−19.8465	−	34.3752i	−0.718022	−	1.24365i
$765$		0			0
$766$	9.94557	−	17.2262i	0.359348	−	0.622409i
$767$	1.44105	−	16.4713i	0.0520333	−	0.594743i
$768$		0			0
$769$	22.4692	+	3.96193i	0.810262	+	0.142871i	0.563405	−	0.826181i	$-0.309491\pi$
$769$	22.4692	+	3.96193i	0.810262	+	0.142871i	0.246857	+	0.969052i	$0.420602\pi$
$770$	73.5877	+	24.5475i	2.65191	+	0.884629i
$771$		0			0
$772$	−12.1954	−	1.06696i	−0.438921	−	0.0384006i
$773$	40.1817	−	10.7667i	1.44524	−	0.387250i	0.550872	−	0.834589i	$-0.314295\pi$
$773$	40.1817	−	10.7667i	1.44524	−	0.387250i	0.894364	+	0.447339i	$0.147628\pi$
$774$		0			0
$775$	−1.85614	−	7.97343i	−0.0666745	−	0.286414i
$776$	0.360912	−	0.991598i	0.0129560	−	0.0355963i
$777$		0			0
$778$	−19.7522	+	1.72809i	−0.708149	+	0.0619550i
$779$	−27.6893	+	10.0781i	−0.992074	+	0.361085i
$780$		0			0
$781$	2.61204	+	14.8136i	0.0934662	+	0.530073i
$782$	−0.437588	+	0.437588i	−0.0156481	+	0.0156481i
$783$		0			0
$784$			0.795819i			0.0284221i
$785$	20.3721	−	21.5070i	0.727112	−	0.767617i
$786$		0			0
$787$	−0.509559	−	0.237611i	−0.0181638	−	0.00846992i	0.413515	−	0.910497i	$-0.364301\pi$
$787$	−0.509559	−	0.237611i	−0.0181638	−	0.00846992i	−0.431679	+	0.902027i	$0.642079\pi$
$788$	−3.16416	−	36.1666i	−0.112719	−	1.28838i
$789$		0			0
$790$	−8.85356	−	29.7893i	−0.314995	−	1.05986i
$791$	−47.1092	+	27.1985i	−1.67501	+	0.967068i
$792$		0			0
$793$	−0.883467	−	3.29714i	−0.0313728	−	0.117085i
$794$	−35.3263	+	29.6423i	−1.25368	+	1.05197i
$795$		0			0
$796$	8.58929	−	48.7123i	0.304439	−	1.72656i
$797$	−29.3985	−	41.9854i	−1.04135	−	1.48720i	−0.864288	−	0.502998i	$-0.832230\pi$
$797$	−29.3985	−	41.9854i	−1.04135	−	1.48720i	−0.177060	−	0.984200i	$-0.556659\pi$
$798$		0			0
$799$	−2.71405	−	3.23448i	−0.0960162	−	0.114428i
$800$	−1.33892	+	40.4577i	−0.0473379	+	1.43040i
$801$		0			0
$802$	16.5253	−	61.6733i	0.583529	−	2.17776i
$803$	3.71760	+	7.97242i	0.131191	+	0.281341i
$804$		0			0
$805$	−2.03325	+	1.80217i	−0.0716626	+	0.0635183i
$806$	−2.37224	−	6.51767i	−0.0835585	−	0.229575i
$807$		0			0
$808$	−3.02081	−	2.11519i	−0.106272	−	0.0744122i
$809$	−10.4010			−0.365681			−0.182841	−	0.983143i	$-0.558529\pi$
$809$	−10.4010			−0.365681			−0.182841	+	0.983143i	$0.558529\pi$
$810$		0			0
$811$	3.01122			0.105738			0.0528692	−	0.998601i	$-0.483163\pi$
$811$	3.01122			0.105738			0.0528692	+	0.998601i	$0.483163\pi$
$812$	37.6944	+	26.3939i	1.32281	+	0.926244i
$813$		0			0
$814$	−12.6302	−	34.7013i	−0.442690	−	1.21628i
$815$	−41.7375	−	2.51456i	−1.46200	−	0.0880813i
$816$		0			0
$817$	4.66573	+	10.0057i	0.163233	+	0.350055i
$818$	15.0316	−	56.0987i	0.525568	−	1.96145i
$819$		0			0
$820$	−27.9651	+	35.2228i	−0.976582	+	1.23003i
$821$	−23.3489	−	27.8262i	−0.814883	−	0.971140i	0.185050	−	0.982729i	$-0.440755\pi$
$821$	−23.3489	−	27.8262i	−0.814883	−	0.971140i	−0.999933	+	0.0115894i	$0.996311\pi$
$822$		0			0
$823$	−4.70013	−	6.71249i	−0.163836	−	0.233983i	0.728836	−	0.684688i	$-0.240061\pi$
$823$	−4.70013	−	6.71249i	−0.163836	−	0.233983i	−0.892673	+	0.450705i	$0.851173\pi$
$824$	−0.298656	+	1.69376i	−0.0104042	+	0.0590049i
$825$		0			0
$826$	33.1916	−	27.8511i	1.15488	−	0.969063i
$827$	−2.16528	−	8.08092i	−0.0752940	−	0.281001i	0.918006	−	0.396567i	$-0.129799\pi$
$827$	−2.16528	−	8.08092i	−0.0752940	−	0.281001i	−0.993300	+	0.115566i	$0.963132\pi$
$828$		0			0
$829$	−24.2355	+	13.9924i	−0.841734	+	0.485975i	−0.857853	−	0.513895i	$-0.828202\pi$
$829$	−24.2355	+	13.9924i	−0.841734	+	0.485975i	0.0161192	+	0.999870i	$0.494869\pi$
$830$	15.8231	+	8.57259i	0.549229	+	0.297559i
$831$		0			0
$832$	1.63930	+	18.7373i	0.0568325	+	0.649598i
$833$	−0.130596	−	0.0608977i	−0.00452487	−	0.00210998i
$834$		0			0
$835$	−12.2403	−	11.5944i	−0.423592	−	0.401240i
$836$			42.3499i			1.46470i
$837$		0			0
$838$	−5.83376	+	5.83376i	−0.201524	+	0.201524i
$839$	−4.76834	−	27.0426i	−0.164621	−	0.933615i	−0.949454	−	0.313907i	$-0.898362\pi$
$839$	−4.76834	−	27.0426i	−0.164621	−	0.933615i	0.784832	−	0.619708i	$-0.212749\pi$
$840$		0			0
$841$	−33.3699	+	12.1457i	−1.15069	+	0.418816i
$842$	−19.8966	+	1.74073i	−0.685683	+	0.0599895i
$843$		0			0
$844$	1.89549	−	5.20781i	0.0652454	−	0.179260i
$845$	18.0066	−	7.11199i	0.619448	−	0.244660i
$846$		0			0
$847$	−76.1848	+	20.4137i	−2.61774	+	0.701421i
$848$	−31.3879	−	2.74608i	−1.07786	−	0.0943009i
$849$		0			0
$850$	−6.09995	−	3.09408i	−0.209227	−	0.106126i
$851$	1.27374	+	0.224595i	0.0436632	+	0.00769900i
$852$		0			0
$853$	1.45086	−	16.5834i	0.0496766	−	0.567806i	−0.930045	−	0.367444i	$-0.880233\pi$
$853$	1.45086	−	16.5834i	0.0496766	−	0.567806i	0.979722	−	0.200361i	$-0.0642116\pi$
$854$	4.47255	−	7.74669i	0.153048	−	0.265086i
$855$		0			0
$856$	1.42092	+	2.46111i	0.0485662	+	0.0841191i
$857$	−9.84971	+	4.59299i	−0.336460	+	0.156894i	−0.583504	−	0.812111i	$-0.698319\pi$
$857$	−9.84971	+	4.59299i	−0.336460	+	0.156894i	0.247044	+	0.969004i	$0.420541\pi$
$858$		0			0
$859$	0.275808	−	0.328695i	0.00941045	−	0.0112149i	−0.761319	−	0.648378i	$-0.775448\pi$
$859$	0.275808	−	0.328695i	0.00941045	−	0.0112149i	0.770729	+	0.637163i	$0.219892\pi$
$860$	14.0598	+	9.28752i	0.479434	+	0.316702i
$861$		0			0
$862$	−4.17115	+	5.95703i	−0.142070	+	0.202897i
$863$	7.52083	+	7.52083i	0.256012	+	0.256012i	0.823430	−	0.567418i	$-0.192058\pi$
$863$	7.52083	+	7.52083i	0.256012	+	0.256012i	−0.567418	+	0.823430i	$0.692058\pi$
$864$		0			0
$865$	−10.0060	−	13.4965i	−0.340213	−	0.458895i
$866$	1.90056	−	0.335120i	0.0645837	−	0.0113878i
$867$		0			0
$868$	3.96439	−	8.50167i	0.134560	−	0.288565i
$869$	33.2719	+	27.9184i	1.12867	+	0.947068i
$870$		0			0
$871$	10.4735	+	3.81206i	0.354883	+	0.129167i
$872$	−0.715226	−	0.191644i	−0.0242206	−	0.00648989i
$873$		0			0
$874$	−2.48898	−	1.43701i	−0.0841909	−	0.0486077i
$875$	−25.9159	−	15.1702i	−0.876116	−	0.512848i
$876$		0			0
$877$	4.01504	−	2.81136i	0.135578	−	0.0949330i	−0.503820	−	0.863809i	$-0.668072\pi$
$877$	4.01504	−	2.81136i	0.135578	−	0.0949330i	0.639398	+	0.768876i	$0.279184\pi$
$878$	54.7890	−	38.3637i	1.84904	−	1.29471i
$879$		0			0
$880$	−27.6260	−	44.9894i	−0.931273	−	1.51659i
$881$	0.734747	+	0.424206i	0.0247542	+	0.0142919i	0.512326	−	0.858791i	$-0.328784\pi$
$881$	0.734747	+	0.424206i	0.0247542	+	0.0142919i	−0.487572	+	0.873083i	$0.662117\pi$
$882$		0			0
$883$	33.9530	+	9.09767i	1.14261	+	0.306161i	0.779999	−	0.625781i	$-0.215219\pi$
$883$	33.9530	+	9.09767i	1.14261	+	0.306161i	0.362609	+	0.931941i	$0.381886\pi$
$884$	−2.81035	−	1.02288i	−0.0945223	−	0.0344033i
$885$		0			0
$886$	34.9135	+	29.2959i	1.17294	+	0.984216i
$887$	−9.41211	+	20.1843i	−0.316028	+	0.677724i	−0.998589	−	0.0531048i	$-0.983088\pi$
$887$	−9.41211	+	20.1843i	−0.316028	+	0.677724i	0.682561	+	0.730828i	$0.260866\pi$
$888$		0			0
$889$	−3.79871	+	0.669814i	−0.127405	+	0.0224649i
$890$	3.13194	−	2.32194i	0.104983	−	0.0778314i
$891$		0			0
$892$	7.61222	+	7.61222i	0.254876	+	0.254876i
$893$	11.2474	−	16.0630i	0.376380	−	0.537526i
$894$		0			0
$895$	−28.3025	+	5.78510i	−0.946049	+	0.193375i
$896$	−3.72765	+	4.44244i	−0.124532	+	0.148412i
$897$		0			0
$898$	−18.2878	+	8.52775i	−0.610272	+	0.284575i
$899$	6.57542	+	11.3890i	0.219303	+	0.379843i
$900$		0			0
$901$	2.85250	−	4.94068i	0.0950307	−	0.164598i
$902$	10.6148	−	121.328i	0.353435	−	4.03979i
$903$		0			0
$904$	−5.39488	−	0.951262i	−0.179431	−	0.0316385i
$905$	3.73834	−	11.2067i	0.124267	−	0.372523i
$906$		0			0
$907$	50.6679	+	4.43286i	1.68240	+	0.147191i	0.887888	−	0.460060i	$-0.152172\pi$
$907$	50.6679	+	4.43286i	1.68240	+	0.147191i	0.794511	+	0.607250i	$0.207727\pi$
$908$	40.7291	−	10.9133i	1.35164	−	0.362171i
$909$		0			0
$910$	−23.3410	−	10.1236i	−0.773746	−	0.335595i
$911$	1.01302	−	2.78325i	0.0335629	−	0.0922132i	−0.921779	−	0.387715i	$-0.873265\pi$
$911$	1.01302	−	2.78325i	0.0335629	−	0.0922132i	0.955342	+	0.295502i	$0.0954868\pi$
$912$		0			0
$913$	−25.0557	+	2.19209i	−0.829223	+	0.0725476i
$914$	66.0043	−	24.0236i	2.18323	−	0.794630i
$915$		0			0
$916$	9.26601	+	52.5502i	0.306158	+	1.73631i
$917$	−38.0275	+	38.0275i	−1.25578	+	1.25578i
$918$		0			0
$919$		−	4.33194i		−	0.142897i	−0.997444	−	0.0714487i	$-0.977238\pi$
$919$		−	4.33194i		−	0.142897i	0.997444	−	0.0714487i	$-0.0227622\pi$
$920$	−0.273514	+	0.00741190i	−0.00901750	+	0.000244363i
$921$		0			0
$922$	19.2436	+	8.97345i	0.633755	+	0.295525i
$923$	−0.429971	−	4.91459i	−0.0141527	−	0.161766i
$924$		0			0
$925$	2.01534	+	14.1525i	0.0662639	+	0.465331i
$926$	−32.5250	+	18.7783i	−1.06884	+	0.617093i
$927$		0			0
$928$	−16.8300	−	62.8104i	−0.552472	−	2.06185i
$929$	24.5535	−	20.6028i	0.805574	−	0.675957i	−0.143973	−	0.989582i	$-0.545988\pi$
$929$	24.5535	−	20.6028i	0.805574	−	0.675957i	0.949547	+	0.313625i	$0.101543\pi$
$930$		0			0
$931$	0.116207	−	0.659044i	0.00380854	−	0.0215993i
$932$	−10.0104	−	14.2963i	−0.327902	−	0.468292i
$933$		0			0
$934$	50.3203	+	59.9694i	1.64653	+	1.96226i
$935$	9.49685	−	1.09081i	0.310580	−	0.0356732i
$936$		0			0
$937$	−3.81043	+	14.2207i	−0.124481	+	0.464571i	−0.999821	−	0.0189383i	$-0.993971\pi$
$937$	−3.81043	+	14.2207i	−0.124481	+	0.464571i	0.875339	+	0.483509i	$0.160638\pi$
$938$	12.3438	+	26.4713i	0.403038	+	0.864318i
$939$		0			0
$940$	1.79990	−	29.8753i	0.0587062	−	0.974425i
$941$	0.647073	+	1.77782i	0.0210940	+	0.0579552i	0.949793	−	0.312880i	$-0.101294\pi$
$941$	0.647073	+	1.77782i	0.0210940	+	0.0579552i	−0.928699	+	0.370835i	$0.879072\pi$
$942$		0			0
$943$	3.49422	+	2.44668i	0.113788	+	0.0796749i
$944$	−29.4880			−0.959753
$945$		0			0
$946$	−45.6312			−1.48360
$947$	27.3760	+	19.1689i	0.889601	+	0.622906i	0.926451	−	0.376415i	$-0.122843\pi$
$947$	27.3760	+	19.1689i	0.889601	+	0.622906i	−0.0368497	+	0.999321i	$0.511732\pi$
$948$		0			0
$949$	−0.986732	−	2.71103i	−0.0320307	−	0.0880036i
$950$	6.54768	−	31.0832i	0.212435	−	1.00847i
$951$		0			0
$952$	−0.206598	−	0.443050i	−0.00669587	−	0.0143593i
$953$	−4.71015	+	17.5785i	−0.152577	+	0.569424i	0.846724	+	0.532032i	$0.178572\pi$
$953$	−4.71015	+	17.5785i	−0.152577	+	0.569424i	−0.999301	+	0.0373915i	$0.988095\pi$
$954$		0			0
$955$	−32.5880	−	25.8732i	−1.05452	−	0.837236i
$956$	−22.0009	−	26.2197i	−0.711560	−	0.848004i
$957$		0			0
$958$	−17.1557	−	24.5009i	−0.554275	−	0.791587i
$959$	−6.09731	+	34.5796i	−0.196893	+	1.11663i
$960$		0			0
$961$	−21.6937	+	18.2032i	−0.699798	+	0.587200i
$962$	3.13465	+	11.6987i	0.101065	+	0.377181i
$963$		0			0
$964$	−21.2922	+	12.2931i	−0.685777	+	0.395934i
$965$	−12.3014	+	3.65605i	−0.395996	+	0.117692i
$966$		0			0
$967$	3.69964	+	42.2870i	0.118972	+	1.35986i	0.787566	+	0.616231i	$0.211341\pi$
$967$	3.69964	+	42.2870i	0.118972	+	1.35986i	−0.668593	+	0.743628i	$0.733103\pi$
$968$	−7.19871	−	3.35682i	−0.231375	−	0.107892i
$969$		0			0
$970$	−0.480411	−	17.7281i	−0.0154251	−	0.569216i
$971$			8.10739i			0.260179i	0.991502	+	0.130089i	$0.0415264\pi$
$971$			8.10739i			0.260179i	−0.991502	+	0.130089i	$0.958474\pi$
$972$		0			0
$973$	−26.6487	+	26.6487i	−0.854319	+	0.854319i
$974$	1.70235	+	9.65451i	0.0545468	+	0.309350i
$975$		0			0
$976$	−5.72061	+	2.08213i	−0.183112	+	0.0666475i
$977$	42.0388	−	3.67792i	1.34494	−	0.117667i	0.608168	−	0.793808i	$-0.291905\pi$
$977$	42.0388	−	3.67792i	1.34494	−	0.117667i	0.736772	+	0.676141i	$0.236349\pi$
$978$		0			0
$979$	−1.86364	+	5.12031i	−0.0595622	+	0.163646i
$980$	−0.375216	−	0.949998i	−0.0119858	−	0.0303466i
$981$		0			0
$982$	12.6966	−	3.40203i	0.405163	−	0.108563i
$983$	−14.2769	−	1.24906i	−0.455362	−	0.0398390i	−0.142832	−	0.989747i	$-0.545621\pi$
$983$	−14.2769	−	1.24906i	−0.455362	−	0.0398390i	−0.312530	+	0.949908i	$0.601176\pi$
$984$		0			0
$985$	−17.0125	−	34.0440i	−0.542064	−	1.08473i
$986$	10.8204	+	1.90793i	0.344592	+	0.0607608i
$987$		0			0
$988$	1.21055	−	13.8366i	0.0385126	−	0.440201i
$989$	0.799099	−	1.38408i	0.0254099	−	0.0440112i
$990$		0			0
$991$	15.7989	+	27.3646i	0.501870	+	0.869265i	0.999998	+	0.00216080i	$0.000687805\pi$
$991$	15.7989	+	27.3646i	0.501870	+	0.869265i	−0.498128	+	0.867104i	$0.665979\pi$
$992$	−12.0138	+	5.60212i	−0.381438	+	0.177867i
$993$		0			0
$994$	8.31002	−	9.90350i	0.263578	−	0.314120i
$995$	−10.3841	−	50.8023i	−0.329198	−	1.61054i
$996$		0			0
$997$	7.09629	−	10.1346i	0.224742	−	0.320965i	−0.690907	−	0.722944i	$-0.742789\pi$
$997$	7.09629	−	10.1346i	0.224742	−	0.320965i	0.915649	+	0.401979i	$0.131678\pi$
$998$	−36.2043	−	36.2043i	−1.14603	−	1.14603i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.152.14		192
3.2	odd	2		135.2.q.a.122.3	yes	192
5.3	odd	4	inner	405.2.r.a.233.14		192
15.2	even	4		675.2.ba.b.68.14		192
15.8	even	4		135.2.q.a.68.3	yes	192
15.14	odd	2		675.2.ba.b.257.14		192
27.2	odd	18	inner	405.2.r.a.332.14		192
27.25	even	9		135.2.q.a.2.3	✓	192
135.52	odd	36		675.2.ba.b.218.14		192
135.79	even	18		675.2.ba.b.407.14		192
135.83	even	36	inner	405.2.r.a.8.14		192
135.133	odd	36		135.2.q.a.83.3	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.3	✓	192	27.25	even	9
135.2.q.a.68.3	yes	192	15.8	even	4
135.2.q.a.83.3	yes	192	135.133	odd	36
135.2.q.a.122.3	yes	192	3.2	odd	2
405.2.r.a.8.14		192	135.83	even	36	inner
405.2.r.a.152.14		192	1.1	even	1	trivial
405.2.r.a.233.14		192	5.3	odd	4	inner
405.2.r.a.332.14		192	27.2	odd	18	inner
675.2.ba.b.68.14		192	15.2	even	4
675.2.ba.b.218.14		192	135.52	odd	36
675.2.ba.b.257.14		192	15.14	odd	2
675.2.ba.b.407.14		192	135.79	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	405.2.r.a.152.14

Level	$405$
Weight	$2$
Character	405.152
Analytic conductor	$3.234$
Analytic rank	$0$
Dimension	$192$
Inner twists	$4$