LMFDB - Embedded newform 340.2.bd.a.73.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [340,2,Mod(57,340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(340, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 4, 15]))

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

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

chi := DirichletCharacter("340.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 340 = 2^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	340.bd (of order $16$, degree $8$, 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:	$2.71491366872$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			73.7
Character	$\chi$	$=$	340.73
Dual form			340.2.bd.a.177.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.197416 - 0.992478i) q^{3} +(-2.21386 + 0.314337i) q^{5} +(4.11814 + 2.75165i) q^{7} +(1.82560 + 0.756188i) q^{9} +(-0.593268 - 0.396409i) q^{11} -1.17074i q^{13} +(-0.125080 + 2.25927i) q^{15} +(3.61941 - 1.97480i) q^{17} +(4.66359 - 1.93172i) q^{19} +(3.54394 - 3.54394i) q^{21} +(-4.32282 + 0.859863i) q^{23} +(4.80238 - 1.39180i) q^{25} +(2.79748 - 4.18673i) q^{27} +(-0.712581 + 3.58239i) q^{29} +(0.397294 - 0.265463i) q^{31} +(-0.510548 + 0.510548i) q^{33} +(-9.98194 - 4.79730i) q^{35} +(-2.40822 - 0.479025i) q^{37} +(-1.16193 - 0.231123i) q^{39} +(1.49379 + 7.50980i) q^{41} +(-6.94077 + 2.87496i) q^{43} +(-4.27932 - 1.10024i) q^{45} -8.12736 q^{47} +(6.70869 + 16.1962i) q^{49} +(-1.24542 - 3.98205i) q^{51} +(1.07361 - 2.59192i) q^{53} +(1.43802 + 0.691109i) q^{55} +(-0.996525 - 5.00987i) q^{57} +(0.998373 - 2.41029i) q^{59} +(8.85868 - 1.76210i) q^{61} +(5.43730 + 8.13750i) q^{63} +(0.368007 + 2.59186i) q^{65} +(-8.33008 - 8.33008i) q^{67} +4.46006i q^{69} +(-4.61796 - 6.91127i) q^{71} +(-2.99656 + 2.00224i) q^{73} +(-0.433260 - 5.04103i) q^{75} +(-1.35238 - 3.26493i) q^{77} +(-4.33662 + 6.49021i) q^{79} +(0.588787 + 0.588787i) q^{81} +(-1.29740 - 0.537401i) q^{83} +(-7.39214 + 5.50966i) q^{85} +(3.41477 + 1.41444i) q^{87} +(-2.78037 - 2.78037i) q^{89} +(3.22147 - 4.82127i) q^{91} +(-0.185034 - 0.446712i) q^{93} +(-9.71735 + 5.74251i) q^{95} +(-0.201537 + 0.134663i) q^{97} +(-0.783309 - 1.17230i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{15} + 8 q^{25} - 48 q^{27} - 32 q^{31} + 16 q^{33} + 32 q^{37} - 32 q^{39} - 40 q^{41} + 80 q^{47} - 40 q^{53} + 16 q^{55} + 8 q^{57} + 112 q^{59} - 48 q^{63} - 32 q^{67} - 16 q^{71} + 8 q^{73}+ \cdots + 96 q^{99}+O(q^{100}) $ 72 * q + 24 * q^15 + 8 * q^25 - 48 * q^27 - 32 * q^31 + 16 * q^33 + 32 * q^37 - 32 * q^39 - 40 * q^41 + 80 * q^47 - 40 * q^53 + 16 * q^55 + 8 * q^57 + 112 * q^59 - 48 * q^63 - 32 * q^67 - 16 * q^71 + 8 * q^73 - 88 * q^75 - 16 * q^77 - 64 * q^79 - 48 * q^81 - 40 * q^83 - 40 * q^85 - 8 * q^87 - 48 * q^91 - 120 * q^93 - 48 * q^95 - 80 * q^97 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/340\mathbb{Z}\right)^\times$.

$n$	$137$	$171$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{16}\right)$

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			0
$2$		0			0
$3$	0.197416	−	0.992478i	0.113978	−	0.573008i	−0.881017	−	0.473085i	$-0.843140\pi$
$3$	0.197416	−	0.992478i	0.113978	−	0.573008i	0.994995	−	0.0999228i	$-0.0318596\pi$
$4$		0			0
$5$	−2.21386	+	0.314337i	−0.990070	+	0.140576i
$5$	−2.21386	+	0.314337i	−0.990070	+	0.140576i
$6$		0			0
$7$	4.11814	+	2.75165i	1.55651	+	1.04003i	0.973817	+	0.227335i	$0.0730011\pi$
$7$	4.11814	+	2.75165i	1.55651	+	1.04003i	0.582693	+	0.812692i	$0.301999\pi$
$8$		0			0
$9$	1.82560	+	0.756188i	0.608533	+	0.252063i
$10$		0			0
$11$	−0.593268	−	0.396409i	−0.178877	−	0.119522i	0.462908	−	0.886406i	$-0.346806\pi$
$11$	−0.593268	−	0.396409i	−0.178877	−	0.119522i	−0.641785	+	0.766884i	$0.721806\pi$
$12$		0			0
$13$		−	1.17074i		−	0.324705i	−0.986733	−	0.162353i	$-0.948092\pi$
$13$		−	1.17074i		−	0.324705i	0.986733	−	0.162353i	$-0.0519082\pi$
$14$		0			0
$15$	−0.125080	+	2.25927i	−0.0322956	+	0.583340i
$16$		0			0
$17$	3.61941	−	1.97480i	0.877837	−	0.478960i
$17$	3.61941	−	1.97480i	0.877837	−	0.478960i
$18$		0			0
$19$	4.66359	−	1.93172i	1.06990	−	0.443168i	0.222946	−	0.974831i	$-0.428433\pi$
$19$	4.66359	−	1.93172i	1.06990	−	0.443168i	0.846956	+	0.531663i	$0.178433\pi$
$20$		0			0
$21$	3.54394	−	3.54394i	0.773352	−	0.773352i
$22$		0			0
$23$	−4.32282	+	0.859863i	−0.901371	+	0.179294i	−0.623959	−	0.781457i	$-0.714477\pi$
$23$	−4.32282	+	0.859863i	−0.901371	+	0.179294i	−0.277412	+	0.960751i	$0.589477\pi$
$24$		0			0
$25$	4.80238	−	1.39180i	0.960477	−	0.278359i
$26$		0			0
$27$	2.79748	−	4.18673i	0.538376	−	0.805737i
$28$		0			0
$29$	−0.712581	+	3.58239i	−0.132323	+	0.665233i	0.856501	+	0.516145i	$0.172634\pi$
$29$	−0.712581	+	3.58239i	−0.132323	+	0.665233i	−0.988824	+	0.149087i	$0.952366\pi$
$30$		0			0
$31$	0.397294	−	0.265463i	0.0713561	−	0.0476786i	−0.519380	−	0.854543i	$-0.673837\pi$
$31$	0.397294	−	0.265463i	0.0713561	−	0.0476786i	0.590737	+	0.806864i	$0.298837\pi$
$32$		0			0
$33$	−0.510548	+	0.510548i	−0.0888750	+	0.0888750i
$34$		0			0
$35$	−9.98194	−	4.79730i	−1.68726	−	0.810892i
$36$		0			0
$37$	−2.40822	−	0.479025i	−0.395909	−	0.0787513i	−0.00687929	−	0.999976i	$-0.502190\pi$
$37$	−2.40822	−	0.479025i	−0.395909	−	0.0787513i	−0.389030	+	0.921225i	$0.627190\pi$
$38$		0			0
$39$	−1.16193	−	0.231123i	−0.186058	−	0.0370093i
$40$		0			0
$41$	1.49379	+	7.50980i	0.233291	+	1.17283i	0.902811	+	0.430039i	$0.141500\pi$
$41$	1.49379	+	7.50980i	0.233291	+	1.17283i	−0.669520	+	0.742794i	$0.733500\pi$
$42$		0			0
$43$	−6.94077	+	2.87496i	−1.05846	+	0.438428i	−0.842904	−	0.538064i	$-0.819156\pi$
$43$	−6.94077	+	2.87496i	−1.05846	+	0.438428i	−0.215554	+	0.976492i	$0.569156\pi$
$44$		0			0
$45$	−4.27932	−	1.10024i	−0.637924	−	0.164015i
$46$		0			0
$47$	−8.12736			−1.18550			−0.592749	−	0.805387i	$-0.701957\pi$
$47$	−8.12736			−1.18550			−0.592749	+	0.805387i	$0.701957\pi$
$48$		0			0
$49$	6.70869	+	16.1962i	0.958384	+	2.31374i
$50$		0			0
$51$	−1.24542	−	3.98205i	−0.174393	−	0.557598i
$52$		0			0
$53$	1.07361	−	2.59192i	0.147472	−	0.356028i	−0.832831	−	0.553527i	$-0.813282\pi$
$53$	1.07361	−	2.59192i	0.147472	−	0.356028i	0.980303	+	0.197498i	$0.0632817\pi$
$54$		0			0
$55$	1.43802	+	0.691109i	0.193902	+	0.0931891i
$56$		0			0
$57$	−0.996525	−	5.00987i	−0.131993	−	0.663573i
$58$		0			0
$59$	0.998373	−	2.41029i	0.129977	−	0.313793i	−0.845471	−	0.534021i	$-0.820680\pi$
$59$	0.998373	−	2.41029i	0.129977	−	0.313793i	0.975448	+	0.220228i	$0.0706803\pi$
$60$		0			0
$61$	8.85868	−	1.76210i	1.13424	−	0.225614i	0.407950	−	0.913004i	$-0.366244\pi$
$61$	8.85868	−	1.76210i	1.13424	−	0.225614i	0.726288	+	0.687390i	$0.241244\pi$
$62$		0			0
$63$	5.43730	+	8.13750i	0.685036	+	1.02523i
$64$		0			0
$65$	0.368007	+	2.59186i	0.0456456	+	0.321481i
$66$		0			0
$67$	−8.33008	−	8.33008i	−1.01768	−	1.01768i	−0.999841	−	0.0178406i	$-0.994321\pi$
$67$	−8.33008	−	8.33008i	−1.01768	−	1.01768i	−0.0178406	−	0.999841i	$-0.505679\pi$
$68$		0			0
$69$			4.46006i			0.536928i
$70$		0			0
$71$	−4.61796	−	6.91127i	−0.548051	−	0.820217i	0.449268	−	0.893397i	$-0.351685\pi$
$71$	−4.61796	−	6.91127i	−0.548051	−	0.820217i	−0.997319	+	0.0731807i	$0.976685\pi$
$72$		0			0
$73$	−2.99656	+	2.00224i	−0.350721	+	0.234344i	−0.718434	−	0.695595i	$-0.755141\pi$
$73$	−2.99656	+	2.00224i	−0.350721	+	0.234344i	0.367713	+	0.929939i	$0.380141\pi$
$74$		0			0
$75$	−0.433260	−	5.04103i	−0.0500285	−	0.582088i
$76$		0			0
$77$	−1.35238	−	3.26493i	−0.154118	−	0.372074i
$78$		0			0
$79$	−4.33662	+	6.49021i	−0.487908	+	0.730205i	−0.990976	−	0.134041i	$-0.957205\pi$
$79$	−4.33662	+	6.49021i	−0.487908	+	0.730205i	0.503068	+	0.864247i	$0.332205\pi$
$80$		0			0
$81$	0.588787	+	0.588787i	0.0654207	+	0.0654207i
$82$		0			0
$83$	−1.29740	−	0.537401i	−0.142408	−	0.0589875i	0.310341	−	0.950625i	$-0.399557\pi$
$83$	−1.29740	−	0.537401i	−0.142408	−	0.0589875i	−0.452749	+	0.891638i	$0.649557\pi$
$84$		0			0
$85$	−7.39214	+	5.50966i	−0.801790	+	0.597606i
$86$		0			0
$87$	3.41477	+	1.41444i	0.366102	+	0.151644i
$88$		0			0
$89$	−2.78037	−	2.78037i	−0.294718	−	0.294718i	0.544223	−	0.838941i	$-0.316825\pi$
$89$	−2.78037	−	2.78037i	−0.294718	−	0.294718i	−0.838941	+	0.544223i	$0.816825\pi$
$90$		0			0
$91$	3.22147	−	4.82127i	0.337702	−	0.505407i
$92$		0			0
$93$	−0.185034	−	0.446712i	−0.0191872	−	0.0463219i
$94$		0			0
$95$	−9.71735	+	5.74251i	−0.996979	+	0.589169i
$96$		0			0
$97$	−0.201537	+	0.134663i	−0.0204630	+	0.0136729i	−0.565760	−	0.824570i	$-0.691417\pi$
$97$	−0.201537	+	0.134663i	−0.0204630	+	0.0136729i	0.545297	+	0.838243i	$0.316417\pi$
$98$		0			0
$99$	−0.783309	−	1.17230i	−0.0787255	−	0.117821i
$100$		0			0
$101$			7.39481i			0.735812i	0.929863	+	0.367906i	$0.119925\pi$
$101$			7.39481i			0.735812i	−0.929863	+	0.367906i	$0.880075\pi$
$102$		0			0
$103$	−12.9168	−	12.9168i	−1.27273	−	1.27273i	−0.944652	−	0.328073i	$-0.893601\pi$
$103$	−12.9168	−	12.9168i	−1.27273	−	1.27273i	−0.328073	−	0.944652i	$-0.606399\pi$
$104$		0			0
$105$	−6.73181	+	8.95980i	−0.656958	+	0.874387i
$106$		0			0
$107$	0.923889	+	1.38270i	0.0893157	+	0.133670i	0.873437	−	0.486937i	$-0.161886\pi$
$107$	0.923889	+	1.38270i	0.0893157	+	0.133670i	−0.784121	+	0.620608i	$0.786886\pi$
$108$		0			0
$109$	−18.4061	+	3.66119i	−1.76298	+	0.350679i	−0.967026	−	0.254678i	$-0.918030\pi$
$109$	−18.4061	+	3.66119i	−1.76298	+	0.350679i	−0.795954	+	0.605357i	$0.793030\pi$
$110$		0			0
$111$	−0.950844	+	2.29554i	−0.0902501	+	0.217883i
$112$		0			0
$113$	−3.71387	−	18.6709i	−0.349372	−	1.75641i	−0.611372	−	0.791343i	$-0.709382\pi$
$113$	−3.71387	−	18.6709i	−0.349372	−	1.75641i	0.262000	−	0.965068i	$-0.415618\pi$
$114$		0			0
$115$	9.29985	−	3.26244i	0.867216	−	0.304224i
$116$		0			0
$117$	0.885300	−	2.13730i	0.0818460	−	0.197594i
$118$		0			0
$119$	20.3392	+	1.82686i	1.86449	+	0.167468i
$120$		0			0
$121$	−4.01469	−	9.69232i	−0.364972	−	0.881120i
$122$		0			0
$123$	7.74821			0.698632
$124$		0			0
$125$	−10.1943	+	4.59081i	−0.911809	+	0.410615i
$126$		0			0
$127$	2.46642	−	1.02162i	0.218859	−	0.0906545i	−0.270560	−	0.962703i	$-0.587209\pi$
$127$	2.46642	−	1.02162i	0.218859	−	0.0906545i	0.489419	+	0.872049i	$0.337209\pi$
$128$		0			0
$129$	1.48312	+	7.45613i	0.130581	+	0.656476i
$130$		0			0
$131$	7.56632	+	1.50503i	0.661072	+	0.131495i	0.514214	−	0.857662i	$-0.328084\pi$
$131$	7.56632	+	1.50503i	0.661072	+	0.131495i	0.146858	+	0.989158i	$0.453084\pi$
$132$		0			0
$133$	24.5208	+	4.87748i	2.12622	+	0.422931i
$134$		0			0
$135$	−4.87721	+	10.1482i	−0.419763	+	0.873418i
$136$		0			0
$137$	14.4500	−	14.4500i	1.23455	−	1.23455i	0.272350	−	0.962198i	$-0.412199\pi$
$137$	14.4500	−	14.4500i	1.23455	−	1.23455i	0.962198	−	0.272350i	$-0.0878008\pi$
$138$		0			0
$139$	−11.5267	+	7.70189i	−0.977681	+	0.653266i	−0.938250	−	0.345957i	$-0.887554\pi$
$139$	−11.5267	+	7.70189i	−0.977681	+	0.653266i	−0.0394305	+	0.999222i	$0.512554\pi$
$140$		0			0
$141$	−1.60447	+	8.06623i	−0.135121	+	0.679299i
$142$		0			0
$143$	−0.464092	+	0.694562i	−0.0388093	+	0.0580822i
$144$		0			0
$145$	0.451482	−	8.15491i	0.0374936	−	0.677229i
$146$		0			0
$147$	17.3988	−	3.46084i	1.43503	−	0.285445i
$148$		0			0
$149$	13.5011	−	13.5011i	1.10605	−	1.10605i	0.112390	−	0.993664i	$-0.464149\pi$
$149$	13.5011	−	13.5011i	1.10605	−	1.10605i	0.993664	−	0.112390i	$-0.0358507\pi$
$150$		0			0
$151$	20.1166	−	8.33257i	1.63707	−	0.678095i	0.641070	−	0.767483i	$-0.278491\pi$
$151$	20.1166	−	8.33257i	1.63707	−	0.678095i	0.995997	+	0.0893876i	$0.0284910\pi$
$152$		0			0
$153$	8.10092	−	0.868240i	0.654920	−	0.0701931i
$154$		0			0
$155$	−0.796110	+	0.712584i	−0.0639451	+	0.0572361i
$156$		0			0
$157$			16.4334i			1.31153i	0.754964	+	0.655766i	$0.227654\pi$
$157$			16.4334i			1.31153i	−0.754964	+	0.655766i	$0.772346\pi$
$158$		0			0
$159$	−2.36048	−	1.57722i	−0.187198	−	0.125082i
$160$		0			0
$161$	−20.1680	−	8.35387i	−1.58946	−	0.658377i
$162$		0			0
$163$	−8.94464	−	5.97662i	−0.700598	−	0.468125i	0.153559	−	0.988139i	$-0.450927\pi$
$163$	−8.94464	−	5.97662i	−0.700598	−	0.468125i	−0.854157	+	0.520015i	$0.825927\pi$
$164$		0			0
$165$	0.969799	−	1.29077i	0.0754988	−	0.100486i
$166$		0			0
$167$	−3.27605	+	16.4698i	−0.253508	+	1.27447i	0.618812	+	0.785539i	$0.287614\pi$
$167$	−3.27605	+	16.4698i	−0.253508	+	1.27447i	−0.872321	+	0.488934i	$0.837386\pi$
$168$		0			0
$169$	11.6294			0.894567
$170$		0			0
$171$	9.97459			0.762776
$172$		0			0
$173$	−3.88819	+	19.5472i	−0.295614	+	1.48615i	0.492334	+	0.870407i	$0.336144\pi$
$173$	−3.88819	+	19.5472i	−0.295614	+	1.48615i	−0.787947	+	0.615743i	$0.788856\pi$
$174$		0			0
$175$	23.6066	+	7.48288i	1.78449	+	0.565653i
$176$		0			0
$177$	−2.19506	−	1.46669i	−0.164991	−	0.110243i
$178$		0			0
$179$	−20.5760	−	8.52285i	−1.53792	−	0.637028i	−0.556839	−	0.830621i	$-0.687986\pi$
$179$	−20.5760	−	8.52285i	−1.53792	−	0.637028i	−0.981082	+	0.193593i	$0.937986\pi$
$180$		0			0
$181$	8.16840	+	5.45795i	0.607153	+	0.405686i	0.820793	−	0.571226i	$-0.193532\pi$
$181$	8.16840	+	5.45795i	0.607153	+	0.405686i	−0.213640	+	0.976912i	$0.568532\pi$
$182$		0			0
$183$		−	9.13992i		−	0.675642i
$184$		0			0
$185$	5.48205	+	0.303504i	0.403048	+	0.0223141i
$186$		0			0
$187$	−2.93011	−	0.263181i	−0.214271	−	0.0192457i
$188$		0			0
$189$	23.0409	−	9.54383i	1.67598	−	0.694212i
$190$		0			0
$191$	−13.2391	+	13.2391i	−0.957947	+	0.957947i	−0.999151	−	0.0412036i	$-0.986881\pi$
$191$	−13.2391	+	13.2391i	−0.957947	+	0.957947i	0.0412036	+	0.999151i	$0.486881\pi$
$192$		0			0
$193$	1.60060	−	0.318379i	0.115214	−	0.0229174i	−0.137147	−	0.990551i	$-0.543793\pi$
$193$	1.60060	−	0.318379i	0.115214	−	0.0229174i	0.252360	+	0.967633i	$0.418793\pi$
$194$		0			0
$195$	2.64502	+	0.146437i	0.189414	+	0.0104865i
$196$		0			0
$197$	3.25493	−	4.87135i	0.231904	−	0.347069i	−0.697207	−	0.716870i	$-0.745574\pi$
$197$	3.25493	−	4.87135i	0.231904	−	0.347069i	0.929111	+	0.369801i	$0.120574\pi$
$198$		0			0
$199$	−1.88295	+	9.46622i	−0.133479	+	0.671043i	0.854871	+	0.518841i	$0.173636\pi$
$199$	−1.88295	+	9.46622i	−0.133479	+	0.671043i	−0.988349	+	0.152202i	$0.951364\pi$
$200$		0			0
$201$	−9.91192	+	6.62293i	−0.699133	+	0.467146i
$202$		0			0
$203$	−12.7920	+	12.7920i	−0.897822	+	0.897822i
$204$		0			0
$205$	−5.66765	−	16.1561i	−0.395846	−	1.12839i
$206$		0			0
$207$	−8.54196	−	1.69910i	−0.593707	−	0.118096i
$208$		0			0
$209$	−3.53251	−	0.702660i	−0.244349	−	0.0486040i
$210$		0			0
$211$	0.128434	+	0.645683i	0.00884178	+	0.0444506i	0.984954	−	0.172815i	$-0.0552862\pi$
$211$	0.128434	+	0.645683i	0.00884178	+	0.0444506i	−0.976113	+	0.217266i	$0.930286\pi$
$212$		0			0
$213$	−7.77094	+	3.21883i	−0.532456	+	0.220551i
$214$		0			0
$215$	14.4622	−	8.54651i	0.986315	−	0.582867i
$216$		0			0
$217$	2.36657			0.160654
$218$		0			0
$219$	1.39561	+	3.36930i	0.0943066	+	0.227676i
$220$		0			0
$221$	−2.31198	−	4.23739i	−0.155521	−	0.285038i
$222$		0			0
$223$	−3.65310	+	8.81937i	−0.244630	+	0.590588i	−0.997732	−	0.0673154i	$-0.978557\pi$
$223$	−3.65310	+	8.81937i	−0.244630	+	0.590588i	0.753102	+	0.657904i	$0.228557\pi$
$224$		0			0
$225$	9.81969	+	1.09064i	0.654646	+	0.0727095i
$226$		0			0
$227$	−2.55641	−	12.8519i	−0.169675	−	0.853013i	−0.968032	−	0.250828i	$-0.919297\pi$
$227$	−2.55641	−	12.8519i	−0.169675	−	0.853013i	0.798357	−	0.602185i	$-0.205703\pi$
$228$		0			0
$229$	7.48367	−	18.0672i	0.494535	−	1.19391i	−0.457854	−	0.889027i	$-0.651382\pi$
$229$	7.48367	−	18.0672i	0.494535	−	1.19391i	0.952389	−	0.304886i	$-0.0986183\pi$
$230$		0			0
$231$	−3.50736	+	0.697656i	−0.230767	+	0.0459024i
$232$		0			0
$233$	−4.94064	−	7.39420i	−0.323672	−	0.484410i	0.633575	−	0.773682i	$-0.281587\pi$
$233$	−4.94064	−	7.39420i	−0.323672	−	0.484410i	−0.957247	+	0.289272i	$0.906587\pi$
$234$		0			0
$235$	17.9929	−	2.55473i	1.17373	−	0.166652i
$236$		0			0
$237$	5.58527	+	5.58527i	0.362802	+	0.362802i
$238$		0			0
$239$			0.496238i			0.0320990i	0.999871	+	0.0160495i	$0.00510893\pi$
$239$			0.496238i			0.0320990i	−0.999871	+	0.0160495i	$0.994891\pi$
$240$		0			0
$241$	10.0672	+	15.0666i	0.648484	+	0.970524i	0.999418	+	0.0341241i	$0.0108641\pi$
$241$	10.0672	+	15.0666i	0.648484	+	0.970524i	−0.350934	+	0.936400i	$0.614136\pi$
$242$		0			0
$243$	13.2608	−	8.86057i	0.850680	−	0.568406i
$244$		0			0
$245$	−19.9432	−	33.7474i	−1.27412	−	2.15604i
$246$		0			0
$247$	−2.26155	−	5.45986i	−0.143899	−	0.347402i
$248$		0			0
$249$	−0.789487	+	1.18155i	−0.0500317	+	0.0748778i
$250$		0			0
$251$	14.5660	+	14.5660i	0.919396	+	0.919396i	0.996985	−	0.0775894i	$-0.0247223\pi$
$251$	14.5660	+	14.5660i	0.919396	+	0.919396i	−0.0775894	+	0.996985i	$0.524722\pi$
$252$		0			0
$253$	2.90545	+	1.20348i	0.182664	+	0.0756619i
$254$		0			0
$255$	4.00889	+	8.42423i	0.251046	+	0.527546i
$256$		0			0
$257$	−19.5886	−	8.11385i	−1.22190	−	0.506128i	−0.323888	−	0.946096i	$-0.604990\pi$
$257$	−19.5886	−	8.11385i	−1.22190	−	0.506128i	−0.898014	+	0.439967i	$0.854990\pi$
$258$		0			0
$259$	−8.59928	−	8.59928i	−0.534333	−	0.534333i
$260$		0			0
$261$	−4.00985	+	6.00116i	−0.248203	+	0.371462i
$262$		0			0
$263$	2.23000	+	5.38370i	0.137508	+	0.331973i	0.977600	−	0.210470i	$-0.0674995\pi$
$263$	2.23000	+	5.38370i	0.137508	+	0.331973i	−0.840093	+	0.542443i	$0.817499\pi$
$264$		0			0
$265$	−1.56209	+	6.07564i	−0.0959584	+	0.373224i
$266$		0			0
$267$	−3.30834	+	2.21056i	−0.202467	+	0.135284i
$268$		0			0
$269$	−1.39714	−	2.09097i	−0.0851853	−	0.127489i	0.786430	−	0.617680i	$-0.211927\pi$
$269$	−1.39714	−	2.09097i	−0.0851853	−	0.127489i	−0.871615	+	0.490191i	$0.836927\pi$
$270$		0			0
$271$		−	29.5652i		−	1.79596i	−0.440037	−	0.897980i	$-0.645035\pi$
$271$		−	29.5652i		−	1.79596i	0.440037	−	0.897980i	$-0.354965\pi$
$272$		0			0
$273$	−4.14904	−	4.14904i	−0.251111	−	0.251111i
$274$		0			0
$275$	−3.40082	−	1.07800i	−0.205077	−	0.0650058i
$276$		0			0
$277$	3.97773	+	5.95310i	0.238999	+	0.357687i	0.931507	−	0.363723i	$-0.118494\pi$
$277$	3.97773	+	5.95310i	0.238999	+	0.357687i	−0.692508	+	0.721410i	$0.743494\pi$
$278$		0			0
$279$	0.926039	−	0.184201i	0.0554405	−	0.0110278i
$280$		0			0
$281$	−6.72223	+	16.2289i	−0.401015	+	0.968135i	0.586406	+	0.810017i	$0.300542\pi$
$281$	−6.72223	+	16.2289i	−0.401015	+	0.968135i	−0.987420	+	0.158117i	$0.949458\pi$
$282$		0			0
$283$	1.97818	+	9.94499i	0.117591	+	0.591168i	0.993980	+	0.109564i	$0.0349456\pi$
$283$	1.97818	+	9.94499i	0.117591	+	0.591168i	−0.876389	+	0.481604i	$0.840054\pi$
$284$		0			0
$285$	3.78096	+	10.7779i	0.223964	+	0.638429i
$286$		0			0
$287$	−14.5127	+	35.0368i	−0.856658	+	2.06816i
$288$		0			0
$289$	9.20031	−	14.2953i	0.541195	−	0.840897i
$290$		0			0
$291$	0.0938630	+	0.226605i	0.00550235	+	0.0132838i
$292$		0			0
$293$	10.3939			0.607219			0.303610	−	0.952797i	$-0.401808\pi$
$293$	10.3939			0.607219			0.303610	+	0.952797i	$0.401808\pi$
$294$		0			0
$295$	−1.45262	+	5.64987i	−0.0845749	+	0.328948i
$296$		0			0
$297$	−3.31931	+	1.37490i	−0.192606	+	0.0797801i
$298$		0			0
$299$	1.00668	+	5.06090i	0.0582176	+	0.292680i
$300$		0			0
$301$	−36.4940	−	7.25910i	−2.10348	−	0.418407i
$302$		0			0
$303$	7.33919	+	1.45986i	0.421626	+	0.0838666i
$304$		0			0
$305$	−19.0580	+	6.68566i	−1.09126	+	0.382820i
$306$		0			0
$307$	−2.82347	+	2.82347i	−0.161144	+	0.161144i	−0.783073	−	0.621929i	$-0.786349\pi$
$307$	−2.82347	+	2.82347i	−0.161144	+	0.161144i	0.621929	+	0.783073i	$0.286349\pi$
$308$		0			0
$309$	−15.3696	+	10.2696i	−0.874344	+	0.584218i
$310$		0			0
$311$	4.60636	−	23.1577i	0.261203	−	1.31316i	−0.597990	−	0.801503i	$-0.704034\pi$
$311$	4.60636	−	23.1577i	0.261203	−	1.31316i	0.859193	−	0.511652i	$-0.170966\pi$
$312$		0			0
$313$	−8.54776	+	12.7926i	−0.483148	+	0.723082i	−0.990326	−	0.138759i	$-0.955689\pi$
$313$	−8.54776	+	12.7926i	−0.483148	+	0.723082i	0.507178	+	0.861841i	$0.330689\pi$
$314$		0			0
$315$	−14.5954	−	16.3062i	−0.822355	−	0.918748i
$316$		0			0
$317$	−25.3578	+	5.04398i	−1.42424	+	0.283298i	−0.846266	−	0.532760i	$-0.821155\pi$
$317$	−25.3578	+	5.04398i	−1.42424	+	0.283298i	−0.577970	+	0.816058i	$0.696155\pi$
$318$		0			0
$319$	1.84284	−	1.84284i	0.103179	−	0.103179i
$320$		0			0
$321$	1.55469	−	0.643973i	0.0867742	−	0.0359430i
$322$		0			0
$323$	13.0647	−	16.2014i	0.726939	−	0.901469i
$324$		0			0
$325$	−1.62943	−	5.62235i	−0.0903847	−	0.311872i
$326$		0			0
$327$			18.9904i			1.05017i
$328$		0			0
$329$	−33.4696	−	22.3637i	−1.84524	−	1.23295i
$330$		0			0
$331$	−15.2803	−	6.32931i	−0.839881	−	0.347890i	−0.0790744	−	0.996869i	$-0.525196\pi$
$331$	−15.2803	−	6.32931i	−0.839881	−	0.347890i	−0.760807	+	0.648979i	$0.775196\pi$
$332$		0			0
$333$	−4.03421	−	2.69558i	−0.221074	−	0.147717i
$334$		0			0
$335$	21.0601	+	15.8232i	1.15064	+	0.864515i
$336$		0			0
$337$	−2.30348	+	11.5804i	−0.125478	+	0.630822i	0.865946	+	0.500138i	$0.166717\pi$
$337$	−2.30348	+	11.5804i	−0.125478	+	0.630822i	−0.991424	+	0.130684i	$0.958283\pi$
$338$		0			0
$339$	−19.2637			−1.04626
$340$		0			0
$341$	−0.340934			−0.0184626
$342$		0			0
$343$	−10.1753	+	51.1545i	−0.549412	+	2.76208i
$344$		0			0
$345$	−1.40196	−	9.87396i	−0.0754790	−	0.531596i
$346$		0			0
$347$	26.5873	+	17.7650i	1.42728	+	0.953677i	0.998742	+	0.0501533i	$0.0159710\pi$
$347$	26.5873	+	17.7650i	1.42728	+	0.953677i	0.428537	+	0.903524i	$0.359029\pi$
$348$		0			0
$349$	0.0914566	+	0.0378826i	0.00489556	+	0.00202781i	0.385130	−	0.922862i	$-0.374157\pi$
$349$	0.0914566	+	0.0378826i	0.00489556	+	0.00202781i	−0.380234	+	0.924890i	$0.624157\pi$
$350$		0			0
$351$	−4.90158	−	3.27513i	−0.261627	−	0.174813i
$352$		0			0
$353$		−	22.4389i		−	1.19430i	−0.802128	−	0.597152i	$-0.796299\pi$
$353$		−	22.4389i		−	1.19430i	0.802128	−	0.597152i	$-0.203701\pi$
$354$		0			0
$355$	12.3960	+	13.8490i	0.657911	+	0.735029i
$356$		0			0
$357$	5.82841	−	19.8256i	0.308472	−	1.04928i
$358$		0			0
$359$	11.3018	−	4.68137i	0.596488	−	0.247073i	−0.0639512	−	0.997953i	$-0.520370\pi$
$359$	11.3018	−	4.68137i	0.596488	−	0.247073i	0.660439	+	0.750880i	$0.270370\pi$
$360$		0			0
$361$	4.58251	−	4.58251i	0.241185	−	0.241185i
$362$		0			0
$363$	−10.4120	+	2.07107i	−0.546487	+	0.108703i
$364$		0			0
$365$	6.00461	−	5.37462i	0.314296	−	0.281320i
$366$		0			0
$367$	9.37791	−	14.0350i	0.489523	−	0.732623i	−0.501668	−	0.865060i	$-0.667280\pi$
$367$	9.37791	−	14.0350i	0.489523	−	0.732623i	0.991191	+	0.132437i	$0.0422802\pi$
$368$		0			0
$369$	−2.95175	+	14.8395i	−0.153662	+	0.772511i
$370$		0			0
$371$	11.5534	−	7.71970i	0.599820	−	0.400787i
$372$		0			0
$373$	17.6152	−	17.6152i	0.912081	−	0.912081i	−0.0843544	−	0.996436i	$-0.526883\pi$
$373$	17.6152	−	17.6152i	0.912081	−	0.912081i	0.996436	+	0.0843544i	$0.0268828\pi$
$374$		0			0
$375$	2.54376	+	11.0240i	0.131359	+	0.569275i
$376$		0			0
$377$	4.19405	+	0.834248i	0.216004	+	0.0429660i
$378$		0			0
$379$	−32.3091	−	6.42668i	−1.65961	−	0.330116i	−0.725804	−	0.687902i	$-0.758532\pi$
$379$	−32.3091	−	6.42668i	−1.65961	−	0.330116i	−0.933804	+	0.357785i	$0.883532\pi$
$380$		0			0
$381$	−0.527029	−	2.64955i	−0.0270005	−	0.135741i
$382$		0			0
$383$	12.0036	−	4.97207i	0.613357	−	0.254061i	−0.0543060	−	0.998524i	$-0.517295\pi$
$383$	12.0036	−	4.97207i	0.613357	−	0.254061i	0.667663	+	0.744463i	$0.267295\pi$
$384$		0			0
$385$	4.02027	+	6.80301i	0.204892	+	0.346714i
$386$		0			0
$387$	−14.8451			−0.754617
$388$		0			0
$389$	12.3063	+	29.7100i	0.623954	+	1.50636i	0.847023	+	0.531556i	$0.178392\pi$
$389$	12.3063	+	29.7100i	0.623954	+	1.50636i	−0.223069	+	0.974803i	$0.571608\pi$
$390$		0			0
$391$	−13.9480	+	11.6489i	−0.705382	+	0.589111i
$392$		0			0
$393$	2.98743	−	7.21229i	0.150696	−	0.363812i
$394$		0			0
$395$	7.56057	−	15.7316i	0.380414	−	0.791542i
$396$		0			0
$397$	−0.318575	−	1.60158i	−0.0159888	−	0.0803812i	0.971967	−	0.235117i	$-0.0755473\pi$
$397$	−0.318575	−	1.60158i	−0.0159888	−	0.0803812i	−0.987956	+	0.154736i	$0.950547\pi$
$398$		0			0
$399$	9.68159	−	23.3734i	0.484686	−	1.17013i
$400$		0			0
$401$	−8.12128	+	1.61542i	−0.405557	+	0.0806704i	−0.393654	−	0.919259i	$-0.628789\pi$
$401$	−8.12128	+	1.61542i	−0.405557	+	0.0806704i	−0.0119036	+	0.999929i	$0.503789\pi$
$402$		0			0
$403$	−0.310789	−	0.465128i	−0.0154815	−	0.0231697i
$404$		0			0
$405$	−1.48857	−	1.11842i	−0.0739676	−	0.0555745i
$406$		0			0
$407$	1.23883	+	1.23883i	0.0614065	+	0.0614065i
$408$		0			0
$409$		−	0.226801i		−	0.0112146i	−0.999984	−	0.00560729i	$-0.998215\pi$
$409$		−	0.226801i		−	0.0112146i	0.999984	−	0.00560729i	$-0.00178487\pi$
$410$		0			0
$411$	−11.4887	−	17.1940i	−0.566694	−	0.848117i
$412$		0			0
$413$	10.7437	−	7.17872i	0.528663	−	0.353242i
$414$		0			0
$415$	3.04120	+	0.781912i	0.149286	+	0.0383826i
$416$		0			0
$417$	5.36840	+	12.9605i	0.262892	+	0.634677i
$418$		0			0
$419$	−4.44464	+	6.65188i	−0.217135	+	0.324965i	−0.924007	−	0.382376i	$-0.875106\pi$
$419$	−4.44464	+	6.65188i	−0.217135	+	0.324965i	0.706872	+	0.707342i	$0.250106\pi$
$420$		0			0
$421$	−11.9202	−	11.9202i	−0.580957	−	0.580957i	0.354210	−	0.935166i	$-0.384750\pi$
$421$	−11.9202	−	11.9202i	−0.580957	−	0.580957i	−0.935166	+	0.354210i	$0.884750\pi$
$422$		0			0
$423$	−14.8373	−	6.14581i	−0.721414	−	0.298820i
$424$		0			0
$425$	14.6333	−	14.5212i	0.709819	−	0.704384i
$426$		0			0
$427$	41.3300	+	17.1194i	2.00010	+	0.828468i
$428$		0			0
$429$	0.597719	+	0.597719i	0.0288581	+	0.0288581i
$430$		0			0
$431$	−11.1212	+	16.6440i	−0.535688	+	0.801714i	−0.996305	−	0.0858853i	$-0.972628\pi$
$431$	−11.1212	+	16.6440i	−0.535688	+	0.801714i	0.460617	+	0.887599i	$0.347628\pi$
$432$		0			0
$433$	10.8418	+	26.1745i	0.521025	+	1.25787i	0.937267	+	0.348612i	$0.113347\pi$
$433$	10.8418	+	26.1745i	0.521025	+	1.25787i	−0.416242	+	0.909254i	$0.636653\pi$
$434$		0			0
$435$	−8.00444	−	2.05800i	−0.383784	−	0.0986735i
$436$		0			0
$437$	−18.4989	+	12.3605i	−0.884921	+	0.591285i
$438$		0			0
$439$	−11.0659	−	16.5613i	−0.528148	−	0.790429i	0.467464	−	0.884012i	$-0.345168\pi$
$439$	−11.0659	−	16.5613i	−0.528148	−	0.790429i	−0.995611	+	0.0935831i	$0.970168\pi$
$440$		0			0
$441$			34.6408i			1.64956i
$442$		0			0
$443$	3.28244	+	3.28244i	0.155953	+	0.155953i	0.780771	−	0.624817i	$-0.214827\pi$
$443$	3.28244	+	3.28244i	0.155953	+	0.155953i	−0.624817	+	0.780771i	$0.714827\pi$
$444$		0			0
$445$	7.02932	+	5.28138i	0.333222	+	0.250361i
$446$		0			0
$447$	−10.7342	−	16.0649i	−0.507711	−	0.759844i
$448$		0			0
$449$	35.0628	−	6.97442i	1.65471	−	0.329143i	0.722589	−	0.691278i	$-0.242952\pi$
$449$	35.0628	−	6.97442i	1.65471	−	0.329143i	0.932126	+	0.362134i	$0.117952\pi$
$450$		0			0
$451$	2.09073	−	5.04747i	0.0984487	−	0.237676i
$452$		0			0
$453$	−4.29855	−	21.6103i	−0.201964	−	1.01534i
$454$		0			0
$455$	−5.61640	+	11.6863i	−0.263301	+	0.547861i
$456$		0			0
$457$	−11.1833	+	26.9988i	−0.523132	+	1.26295i	0.412816	+	0.910815i	$0.364545\pi$
$457$	−11.1833	+	26.9988i	−0.523132	+	1.26295i	−0.935948	+	0.352138i	$0.885455\pi$
$458$		0			0
$459$	1.85729	−	20.6780i	0.0866907	−	0.965166i
$460$		0			0
$461$	9.32073	+	22.5022i	0.434110	+	1.04803i	0.977949	+	0.208844i	$0.0669701\pi$
$461$	9.32073	+	22.5022i	0.434110	+	1.04803i	−0.543839	+	0.839189i	$0.683030\pi$
$462$		0			0
$463$	4.78508			0.222381			0.111191	−	0.993799i	$-0.464534\pi$
$463$	4.78508			0.222381			0.111191	+	0.993799i	$0.464534\pi$
$464$		0			0
$465$	0.550059	+	0.930797i	0.0255084	+	0.0431647i
$466$		0			0
$467$	12.0107	−	4.97502i	0.555791	−	0.230216i	−0.0870657	−	0.996203i	$-0.527749\pi$
$467$	12.0107	−	4.97502i	0.555791	−	0.230216i	0.642857	+	0.765986i	$0.277749\pi$
$468$		0			0
$469$	−11.3829	−	57.2259i	−0.525615	−	2.64245i
$470$		0			0
$471$	16.3098	+	3.24423i	0.751518	+	0.149486i
$472$		0			0
$473$	5.25739	+	1.04576i	0.241735	+	0.0480841i
$474$		0			0
$475$	19.7078	−	15.7677i	0.904256	−	0.723470i
$476$		0			0
$477$	3.91996	−	3.91996i	0.179483	−	0.179483i
$478$		0			0
$479$	8.92887	−	5.96608i	0.407971	−	0.272597i	−0.334606	−	0.942358i	$-0.608603\pi$
$479$	8.92887	−	5.96608i	0.407971	−	0.272597i	0.742577	+	0.669761i	$0.233603\pi$
$480$		0			0
$481$	−0.560814	+	2.81940i	−0.0255709	+	0.128554i
$482$		0			0
$483$	−12.2725	+	18.3671i	−0.558419	+	0.835734i
$484$		0			0
$485$	0.403845	−	0.361475i	0.0183377	−	0.0164137i
$486$		0			0
$487$	−14.5275	+	2.88970i	−0.658304	+	0.130945i	−0.512928	−	0.858432i	$-0.671439\pi$
$487$	−14.5275	+	2.88970i	−0.658304	+	0.130945i	−0.145376	+	0.989377i	$0.546439\pi$
$488$		0			0
$489$	−7.69748	+	7.69748i	−0.348092	+	0.348092i
$490$		0			0
$491$	5.45568	−	2.25982i	0.246211	−	0.101984i	−0.256165	−	0.966633i	$-0.582459\pi$
$491$	5.45568	−	2.25982i	0.246211	−	0.101984i	0.502377	+	0.864649i	$0.332459\pi$
$492$		0			0
$493$	4.49538	+	14.3734i	0.202462	+	0.647343i
$494$		0			0
$495$	2.10264	+	2.34910i	0.0945065	+	0.105584i
$496$		0			0
$497$		−	41.1686i		−	1.84666i
$498$		0			0
$499$	−10.8335	−	7.23871i	−0.484974	−	0.324049i	0.288932	−	0.957350i	$-0.406700\pi$
$499$	−10.8335	−	7.23871i	−0.484974	−	0.324049i	−0.773906	+	0.633300i	$0.781700\pi$
$500$		0			0
$501$	15.6992	+	6.50282i	0.701388	+	0.290525i
$502$		0			0
$503$	20.8463	+	13.9291i	0.929492	+	0.621067i	0.925427	−	0.378925i	$-0.123706\pi$
$503$	20.8463	+	13.9291i	0.929492	+	0.621067i	0.00406480	+	0.999992i	$0.498706\pi$
$504$		0			0
$505$	−2.32446	−	16.3711i	−0.103437	−	0.728505i
$506$		0			0
$507$	2.29583	−	11.5419i	0.101961	−	0.512594i
$508$		0			0
$509$	−0.650865			−0.0288491			−0.0144245	−	0.999896i	$-0.504592\pi$
$509$	−0.650865			−0.0288491			−0.0144245	+	0.999896i	$0.504592\pi$
$510$		0			0
$511$	−17.8497			−0.789626
$512$		0			0
$513$	4.95872	−	24.9292i	0.218933	−	1.10065i
$514$		0			0
$515$	32.6561	+	24.5357i	1.43900	+	1.08117i
$516$		0			0
$517$	4.82170	+	3.22176i	0.212058	+	0.141693i
$518$		0			0
$519$	18.6326	+	7.71789i	0.817882	+	0.338778i
$520$		0			0
$521$	30.4630	+	20.3547i	1.33461	+	0.891757i	0.998742	−	0.0501523i	$-0.0159707\pi$
$521$	30.4630	+	20.3547i	1.33461	+	0.891757i	0.335867	+	0.941909i	$0.390971\pi$
$522$		0			0
$523$		−	24.3530i		−	1.06488i	−0.846467	−	0.532442i	$-0.821275\pi$
$523$		−	24.3530i		−	1.06488i	0.846467	−	0.532442i	$-0.178725\pi$
$524$		0			0
$525$	12.0869	−	21.9518i	0.527517	−	0.958056i
$526$		0			0
$527$	0.913734	−	1.74540i	0.0398029	−	0.0760308i
$528$		0			0
$529$	−3.30180	+	1.36765i	−0.143556	+	0.0594630i
$530$		0			0
$531$	3.64526	−	3.64526i	0.158191	−	0.158191i
$532$		0			0
$533$	8.79202	−	1.74884i	0.380825	−	0.0757508i
$534$		0			0
$535$	−2.48000	−	2.77069i	−0.107220	−	0.119787i
$536$		0			0
$537$	−12.5208	+	18.7387i	−0.540311	+	0.808633i
$538$		0			0
$539$	2.44027	−	12.2681i	0.105110	−	0.528423i
$540$		0			0
$541$	−26.5789	+	17.7595i	−1.14272	+	0.763539i	−0.974980	−	0.222293i	$-0.928646\pi$
$541$	−26.5789	+	17.7595i	−1.14272	+	0.763539i	−0.167737	+	0.985832i	$0.553646\pi$
$542$		0			0
$543$	7.02947	−	7.02947i	0.301664	−	0.301664i
$544$		0			0
$545$	39.5976	−	13.8911i	1.69618	−	0.595028i
$546$		0			0
$547$	0.967848	+	0.192517i	0.0413822	+	0.00823143i	0.215738	−	0.976451i	$-0.430784\pi$
$547$	0.967848	+	0.192517i	0.0413822	+	0.00823143i	−0.174356	+	0.984683i	$0.555784\pi$
$548$		0			0
$549$	17.5049	+	3.48194i	0.747090	+	0.148605i
$550$		0			0
$551$	3.59699	+	18.0833i	0.153237	+	0.770375i
$552$		0			0
$553$	−35.7176	+	14.7947i	−1.51887	+	0.629135i
$554$		0			0
$555$	1.38347	−	5.38090i	0.0587249	−	0.228407i
$556$		0			0
$557$	−11.1394			−0.471991			−0.235996	−	0.971754i	$-0.575835\pi$
$557$	−11.1394			−0.471991			−0.235996	+	0.971754i	$0.575835\pi$
$558$		0			0
$559$	3.36583	+	8.12584i	0.142360	+	0.343687i
$560$		0			0
$561$	−0.839653	+	2.85611i	−0.0354502	+	0.120585i
$562$		0			0
$563$	−1.85000	+	4.46629i	−0.0779682	+	0.188232i	−0.958057	−	0.286577i	$-0.907483\pi$
$563$	−1.85000	+	4.46629i	−0.0779682	+	0.188232i	0.880089	+	0.474809i	$0.157483\pi$
$564$		0			0
$565$	14.0910	+	40.1674i	0.592811	+	1.68986i
$566$		0			0
$567$	0.804569	+	4.04484i	0.0337887	+	0.169867i
$568$		0			0
$569$	−12.2377	+	29.5443i	−0.513029	+	1.23856i	0.429083	+	0.903265i	$0.358837\pi$
$569$	−12.2377	+	29.5443i	−0.513029	+	1.23856i	−0.942112	+	0.335297i	$0.891163\pi$
$570$		0			0
$571$	13.4709	−	2.67954i	0.563741	−	0.112135i	0.0950107	−	0.995476i	$-0.469711\pi$
$571$	13.4709	−	2.67954i	0.563741	−	0.112135i	0.468731	+	0.883341i	$0.344711\pi$
$572$		0			0
$573$	10.5259	+	15.7531i	0.439726	+	0.658096i
$574$		0			0
$575$	−19.5631	+	10.1459i	−0.815838	+	0.423113i
$576$		0			0
$577$	−20.2394	−	20.2394i	−0.842579	−	0.842579i	0.146615	−	0.989194i	$-0.453162\pi$
$577$	−20.2394	−	20.2394i	−0.842579	−	0.842579i	−0.989194	+	0.146615i	$0.953162\pi$
$578$		0			0
$579$		−	1.65142i		−	0.0686305i
$580$		0			0
$581$	−3.86414	−	5.78309i	−0.160311	−	0.239923i
$582$		0			0
$583$	−1.66440	+	1.11212i	−0.0689324	+	0.0460592i
$584$		0			0
$585$	−1.28810	+	5.00998i	−0.0532564	+	0.207137i
$586$		0			0
$587$	1.11400	+	2.68943i	0.0459796	+	0.111004i	0.945201	−	0.326490i	$-0.105866\pi$
$587$	1.11400	+	2.68943i	0.0459796	+	0.111004i	−0.899221	+	0.437494i	$0.855866\pi$
$588$		0			0
$589$	1.34002	−	2.00548i	0.0552144	−	0.0826342i
$590$		0			0
$591$	−4.19213	−	4.19213i	−0.172441	−	0.172441i
$592$		0			0
$593$	−0.856283	−	0.354684i	−0.0351633	−	0.0145651i	0.365032	−	0.930995i	$-0.381058\pi$
$593$	−0.856283	−	0.354684i	−0.0351633	−	0.0145651i	−0.400196	+	0.916430i	$0.631058\pi$
$594$		0			0
$595$	−45.6025	+	2.34895i	−1.86952	+	0.0962974i
$596$		0			0
$597$	9.02330	+	3.73757i	0.369299	+	0.152969i
$598$		0			0
$599$	11.7270	+	11.7270i	0.479151	+	0.479151i	0.904860	−	0.425709i	$-0.139975\pi$
$599$	11.7270	+	11.7270i	0.479151	+	0.479151i	−0.425709	+	0.904860i	$0.639975\pi$
$600$		0			0
$601$	14.6783	−	21.9677i	0.598741	−	0.896079i	−0.401059	−	0.916052i	$-0.631358\pi$
$601$	14.6783	−	21.9677i	0.598741	−	0.896079i	0.999801	+	0.0199727i	$0.00635792\pi$
$602$		0			0
$603$	−8.90828	−	21.5065i	−0.362773	−	0.875812i
$604$		0			0
$605$	11.9346	+	20.1955i	0.485212	+	0.821064i
$606$		0			0
$607$	15.5866	−	10.4146i	0.632639	−	0.422716i	−0.197476	−	0.980308i	$-0.563275\pi$
$607$	15.5866	−	10.4146i	0.632639	−	0.422716i	0.830115	+	0.557592i	$0.188275\pi$
$608$		0			0
$609$	10.1704	+	15.2211i	0.412127	+	0.616791i
$610$		0			0
$611$			9.51503i			0.384937i
$612$		0			0
$613$	−5.09727	−	5.09727i	−0.205877	−	0.205877i	0.596635	−	0.802512i	$-0.296504\pi$
$613$	−5.09727	−	5.09727i	−0.205877	−	0.205877i	−0.802512	+	0.596635i	$0.796504\pi$
$614$		0			0
$615$	−17.1535	+	2.43555i	−0.691695	+	0.0982107i
$616$		0			0
$617$	−0.811360	−	1.21429i	−0.0326641	−	0.0488853i	0.814778	−	0.579773i	$-0.196859\pi$
$617$	−0.811360	−	1.21429i	−0.0326641	−	0.0488853i	−0.847442	+	0.530887i	$0.821859\pi$
$618$		0			0
$619$	6.64720	−	1.32221i	0.267174	−	0.0531441i	−0.0596854	−	0.998217i	$-0.519010\pi$
$619$	6.64720	−	1.32221i	0.267174	−	0.0531441i	0.326859	+	0.945073i	$0.394010\pi$
$620$		0			0
$621$	−8.49301	+	20.5039i	−0.340813	+	0.822795i
$622$		0			0
$623$	−3.79933	−	19.1005i	−0.152217	−	0.765247i
$624$		0			0
$625$	21.1258	−	13.3679i	0.845032	−	0.534716i
$626$		0			0
$627$	−1.39475	+	3.36722i	−0.0557009	+	0.134474i
$628$		0			0
$629$	−9.66233	+	3.02197i	−0.385262	+	0.120494i
$630$		0			0
$631$	−8.45217	−	20.4054i	−0.336476	−	0.812324i	−0.998049	−	0.0624433i	$-0.980111\pi$
$631$	−8.45217	−	20.4054i	−0.336476	−	0.812324i	0.661573	−	0.749881i	$-0.269889\pi$
$632$		0			0
$633$	0.666181			0.0264783
$634$		0			0
$635$	−5.13918	+	3.03702i	−0.203942	+	0.120521i
$636$		0			0
$637$	18.9616	−	7.85414i	0.751284	−	0.311192i
$638$		0			0
$639$	−3.20433	−	16.1092i	−0.126761	−	0.637272i
$640$		0			0
$641$	25.1874	+	5.01009i	0.994844	+	0.197887i	0.665560	−	0.746344i	$-0.268193\pi$
$641$	25.1874	+	5.01009i	0.994844	+	0.197887i	0.329284	+	0.944231i	$0.393193\pi$
$642$		0			0
$643$	17.9944	+	3.57931i	0.709631	+	0.141154i	0.536692	−	0.843778i	$-0.319674\pi$
$643$	17.9944	+	3.57931i	0.709631	+	0.141154i	0.172939	+	0.984933i	$0.444674\pi$
$644$		0			0
$645$	−5.62715	−	16.0407i	−0.221569	−	0.631600i
$646$		0			0
$647$	−4.92694	+	4.92694i	−0.193698	+	0.193698i	−0.797292	−	0.603594i	$-0.793735\pi$
$647$	−4.92694	+	4.92694i	−0.193698	+	0.193698i	0.603594	+	0.797292i	$0.293735\pi$
$648$		0			0
$649$	−1.54776	+	1.03418i	−0.0607549	+	0.0405952i
$650$		0			0
$651$	0.467200	−	2.34877i	0.0183110	−	0.0920557i
$652$		0			0
$653$	−7.21656	+	10.8003i	−0.282406	+	0.422650i	−0.945369	−	0.326002i	$-0.894298\pi$
$653$	−7.21656	+	10.8003i	−0.282406	+	0.422650i	0.662963	+	0.748652i	$0.269298\pi$
$654$		0			0
$655$	−17.2239	−	0.953570i	−0.672993	−	0.0372590i
$656$		0			0
$657$	−6.98459	+	1.38932i	−0.272495	+	0.0542026i
$658$		0			0
$659$	−12.2064	+	12.2064i	−0.475495	+	0.475495i	−0.903687	−	0.428193i	$-0.859150\pi$
$659$	−12.2064	+	12.2064i	−0.475495	+	0.475495i	0.428193	+	0.903687i	$0.359150\pi$
$660$		0			0
$661$	27.0936	−	11.2225i	1.05382	−	0.436506i	0.212565	−	0.977147i	$-0.431818\pi$
$661$	27.0936	−	11.2225i	1.05382	−	0.436506i	0.841253	+	0.540641i	$0.181818\pi$
$662$		0			0
$663$	−4.66195	+	1.45806i	−0.181055	+	0.0566264i
$664$		0			0
$665$	−55.8188	−	3.09031i	−2.16456	−	0.119837i
$666$		0			0
$667$		−	16.0988i		−	0.623346i
$668$		0			0
$669$	8.03185	+	5.36671i	0.310529	+	0.207489i
$670$		0			0
$671$	−5.95408	−	2.46626i	−0.229855	−	0.0952090i
$672$		0			0
$673$	16.1038	+	10.7602i	0.620754	+	0.414775i	0.825788	−	0.563980i	$-0.190731\pi$
$673$	16.1038	+	10.7602i	0.620754	+	0.414775i	−0.205034	+	0.978755i	$0.565731\pi$
$674$		0			0
$675$	7.60752	−	23.9998i	0.292813	−	0.923754i
$676$		0			0
$677$	8.50414	−	42.7532i	0.326841	−	1.64314i	−0.372269	−	0.928125i	$-0.621420\pi$
$677$	8.50414	−	42.7532i	0.326841	−	1.64314i	0.699110	−	0.715015i	$-0.253580\pi$
$678$		0			0
$679$	−1.20050			−0.0460710
$680$		0			0
$681$	−13.2599			−0.508122
$682$		0			0
$683$	−0.116936	+	0.587877i	−0.00447443	+	0.0224945i	−0.982958	−	0.183830i	$-0.941150\pi$
$683$	−0.116936	+	0.587877i	−0.00447443	+	0.0224945i	0.978484	+	0.206325i	$0.0661503\pi$
$684$		0			0
$685$	−27.4482	+	36.5325i	−1.04874	+	1.39584i
$686$		0			0
$687$	−16.4539	−	10.9941i	−0.627755	−	0.419453i
$688$		0			0
$689$	−3.03447	−	1.25692i	−0.115604	−	0.0478848i
$690$		0			0
$691$	−28.2519	−	18.8773i	−1.07475	−	0.718126i	−0.113428	−	0.993546i	$-0.536183\pi$
$691$	−28.2519	−	18.8773i	−1.07475	−	0.718126i	−0.961324	+	0.275420i	$0.911183\pi$
$692$		0			0
$693$		−	6.98311i		−	0.265266i
$694$		0			0
$695$	23.0975	−	20.6742i	0.876139	−	0.784217i
$696$		0			0
$697$	20.2370	+	24.2311i	0.766531	+	0.917819i
$698$		0			0
$699$	−8.31394	+	3.44375i	−0.314462	+	0.130255i
$700$		0			0
$701$	22.2334	−	22.2334i	0.839745	−	0.839745i	−0.149080	−	0.988825i	$-0.547631\pi$
$701$	22.2334	−	22.2334i	0.839745	−	0.839745i	0.988825	+	0.149080i	$0.0476313\pi$
$702$		0			0
$703$	−12.1563	+	2.41804i	−0.458484	+	0.0911981i
$704$		0			0
$705$	1.01657	−	18.3619i	0.0382864	−	0.691549i
$706$		0			0
$707$	−20.3480	+	30.4529i	−0.765264	+	1.14530i
$708$		0			0
$709$	−4.75971	+	23.9287i	−0.178755	+	0.898660i	0.782427	+	0.622743i	$0.213982\pi$
$709$	−4.75971	+	23.9287i	−0.178755	+	0.898660i	−0.961181	+	0.275917i	$0.911018\pi$
$710$		0			0
$711$	−12.8247	+	8.56922i	−0.480965	+	0.321371i
$712$		0			0
$713$	−1.48917	+	1.48917i	−0.0557698	+	0.0557698i
$714$		0			0
$715$	0.809110	−	1.68355i	0.0302590	−	0.0629611i
$716$		0			0
$717$	0.492506	+	0.0979655i	0.0183930	+	0.00365859i
$718$		0			0
$719$	−26.1227	−	5.19612i	−0.974212	−	0.193783i	−0.317777	−	0.948166i	$-0.602936\pi$
$719$	−26.1227	−	5.19612i	−0.974212	−	0.193783i	−0.656435	+	0.754383i	$0.727936\pi$
$720$		0			0
$721$	−17.6506	−	88.7354i	−0.657341	−	3.30468i
$722$		0			0
$723$	16.9407	−	7.01706i	0.630031	−	0.260967i
$724$		0			0
$725$	1.56387	+	18.1958i	0.0580806	+	0.675774i
$726$		0			0
$727$	18.8277			0.698280			0.349140	−	0.937070i	$-0.386474\pi$
$727$	18.8277			0.698280			0.349140	+	0.937070i	$0.386474\pi$
$728$		0			0
$729$	−5.22009	−	12.6024i	−0.193337	−	0.466756i
$730$		0			0
$731$	−19.4440	+	24.1123i	−0.719164	+	0.891827i
$732$		0			0
$733$	−5.03431	+	12.1539i	−0.185947	+	0.448915i	−0.989172	−	0.146760i	$-0.953115\pi$
$733$	−5.03431	+	12.1539i	−0.185947	+	0.448915i	0.803225	+	0.595675i	$0.203115\pi$
$734$		0			0
$735$	−37.4307	+	13.1309i	−1.38065	+	0.484340i
$736$		0			0
$737$	1.63985	+	8.24408i	0.0604047	+	0.303675i
$738$		0			0
$739$	−17.7843	+	42.9351i	−0.654206	+	1.57939i	0.152411	+	0.988317i	$0.451296\pi$
$739$	−17.7843	+	42.9351i	−0.654206	+	1.57939i	−0.806617	+	0.591075i	$0.798704\pi$
$740$		0			0
$741$	−5.86526	+	1.16667i	−0.215466	+	0.0428588i
$742$		0			0
$743$	−14.8812	−	22.2713i	−0.545939	−	0.817055i	0.451218	−	0.892414i	$-0.350990\pi$
$743$	−14.8812	−	22.2713i	−0.545939	−	0.817055i	−0.997156	+	0.0753590i	$0.975990\pi$
$744$		0			0
$745$	−25.6457	+	34.1335i	−0.939587	+	1.25056i
$746$		0			0
$747$	−1.96216	−	1.96216i	−0.0717916	−	0.0717916i
$748$		0			0
$749$			8.23636i			0.300950i
$750$		0			0
$751$	−2.72657	−	4.08059i	−0.0994938	−	0.148903i	0.778383	−	0.627790i	$-0.216040\pi$
$751$	−2.72657	−	4.08059i	−0.0994938	−	0.148903i	−0.877877	+	0.478887i	$0.841040\pi$
$752$		0			0
$753$	17.3320	−	11.5809i	0.631612	−	0.422030i
$754$		0			0
$755$	−41.9162	+	24.7706i	−1.52549	+	0.901493i
$756$		0			0
$757$	2.57921	+	6.22675i	0.0937428	+	0.226315i	0.963795	−	0.266645i	$-0.0859150\pi$
$757$	2.57921	+	6.22675i	0.0937428	+	0.226315i	−0.870052	+	0.492960i	$0.835915\pi$
$758$		0			0
$759$	1.76801	−	2.64601i	0.0641746	−	0.0960440i
$760$		0			0
$761$	10.5965	+	10.5965i	0.384124	+	0.384124i	0.872586	−	0.488461i	$-0.162442\pi$
$761$	10.5965	+	10.5965i	0.384124	+	0.384124i	−0.488461	+	0.872586i	$0.662442\pi$
$762$		0			0
$763$	−85.8730	−	35.5698i	−3.10881	−	1.28771i
$764$		0			0
$765$	−17.6614	+	4.46858i	−0.638550	+	0.161562i
$766$		0			0
$767$	−2.82182	−	1.16884i	−0.101890	−	0.0422042i
$768$		0			0
$769$	0.755624	+	0.755624i	0.0272485	+	0.0272485i	0.720600	−	0.693351i	$-0.243867\pi$
$769$	0.755624	+	0.755624i	0.0272485	+	0.0272485i	−0.693351	+	0.720600i	$0.743867\pi$
$770$		0			0
$771$	−11.9199	+	17.8394i	−0.429286	+	0.642471i
$772$		0			0
$773$	13.4094	+	32.3732i	0.482303	+	1.16438i	0.958512	+	0.285051i	$0.0920105\pi$
$773$	13.4094	+	32.3732i	0.482303	+	1.16438i	−0.476209	+	0.879332i	$0.657989\pi$
$774$		0			0
$775$	1.53849	−	1.82781i	0.0552641	−	0.0656569i
$776$		0			0
$777$	−10.2322	+	6.83696i	−0.367080	+	0.245275i
$778$		0			0
$779$	21.4733	+	32.1370i	0.769360	+	1.15143i
$780$		0			0
$781$			5.93083i			0.212222i
$782$		0			0
$783$	13.0051	+	13.0051i	0.464763	+	0.464763i
$784$		0			0
$785$	−5.16563	−	36.3814i	−0.184369	−	1.29851i
$786$		0			0
$787$	12.7141	+	19.0280i	0.453208	+	0.678274i	0.985767	−	0.168119i	$-0.0537693\pi$
$787$	12.7141	+	19.0280i	0.453208	+	0.678274i	−0.532558	+	0.846393i	$0.678769\pi$
$788$		0			0
$789$	5.78344	−	1.15040i	0.205896	−	0.0409552i
$790$		0			0
$791$	36.0816	−	87.1087i	1.28291	−	3.09723i
$792$		0			0
$793$	−2.06296	−	10.3712i	−0.0732580	−	0.368293i
$794$		0			0
$795$	5.72156	+	2.74977i	0.202923	+	0.0975243i
$796$		0			0
$797$	17.5253	−	42.3098i	0.620778	−	1.49869i	−0.230013	−	0.973188i	$-0.573877\pi$
$797$	17.5253	−	42.3098i	0.620778	−	1.49869i	0.850791	−	0.525504i	$-0.176123\pi$
$798$		0			0
$799$	−29.4163	+	16.0499i	−1.04067	+	0.567806i
$800$		0			0
$801$	−2.97335	−	7.17831i	−0.105058	−	0.253633i
$802$		0			0
$803$	2.57147			0.0907452
$804$		0			0
$805$	47.2752	+	12.1548i	1.66623	+	0.428400i
$806$		0			0
$807$	−2.35106	+	0.973842i	−0.0827613	+	0.0342809i
$808$		0			0
$809$	3.50158	+	17.6036i	0.123109	+	0.618911i	0.992241	+	0.124330i	$0.0396783\pi$
$809$	3.50158	+	17.6036i	0.123109	+	0.618911i	−0.869132	+	0.494580i	$0.835322\pi$
$810$		0			0
$811$	19.9278	+	3.96388i	0.699758	+	0.139191i	0.532134	−	0.846660i	$-0.321390\pi$
$811$	19.9278	+	3.96388i	0.699758	+	0.139191i	0.167625	+	0.985851i	$0.446390\pi$
$812$		0			0
$813$	−29.3428	−	5.83666i	−1.02910	−	0.204700i
$814$		0			0
$815$	21.6809	+	10.4198i	0.759448	+	0.364989i
$816$		0			0
$817$	−26.8153	+	26.8153i	−0.938149	+	0.938149i
$818$		0			0
$819$	9.52690	−	6.36567i	0.332897	−	0.222435i
$820$		0			0
$821$	−1.97525	+	9.93026i	−0.0689367	+	0.346568i	−0.999824	−	0.0187371i	$-0.994035\pi$
$821$	−1.97525	+	9.93026i	−0.0689367	+	0.346568i	0.930888	+	0.365305i	$0.119035\pi$
$822$		0			0
$823$	−24.3402	+	36.4276i	−0.848445	+	1.26979i	0.112668	+	0.993633i	$0.464060\pi$
$823$	−24.3402	+	36.4276i	−0.848445	+	1.26979i	−0.961113	+	0.276155i	$0.910940\pi$
$824$		0			0
$825$	−1.74127	+	3.16243i	−0.0606232	+	0.110102i
$826$		0			0
$827$	3.23703	−	0.643886i	0.112563	−	0.0223901i	−0.138487	−	0.990364i	$-0.544224\pi$
$827$	3.23703	−	0.643886i	0.112563	−	0.0223901i	0.251050	+	0.967974i	$0.419224\pi$
$828$		0			0
$829$	−28.0827	+	28.0827i	−0.975354	+	0.975354i	−0.999704	−	0.0243494i	$-0.992249\pi$
$829$	−28.0827	+	28.0827i	−0.975354	+	0.975354i	0.0243494	+	0.999704i	$0.492249\pi$
$830$		0			0
$831$	6.69359	−	2.77258i	0.232198	−	0.0961796i
$832$		0			0
$833$	56.2658	+	45.3725i	1.94950	+	1.57206i
$834$		0			0
$835$	2.07566	−	37.4917i	0.0718313	−	1.29745i
$836$		0			0
$837$		−	2.40599i		−	0.0831633i
$838$		0			0
$839$	38.5086	+	25.7306i	1.32946	+	0.888319i	0.998469	−	0.0553139i	$-0.0176160\pi$
$839$	38.5086	+	25.7306i	1.32946	+	0.888319i	0.330994	+	0.943633i	$0.392616\pi$
$840$		0			0
$841$	14.4668	+	5.99233i	0.498854	+	0.206632i
$842$		0			0
$843$	14.7798	+	9.87551i	0.509042	+	0.340131i
$844$		0			0
$845$	−25.7458	+	3.65554i	−0.885684	+	0.125754i
$846$		0			0
$847$	10.1368	−	50.9614i	0.348306	−	1.75105i
$848$		0			0
$849$	10.2607			0.352147
$850$		0			0
$851$	10.8222			0.370981
$852$		0			0
$853$	3.15858	−	15.8793i	0.108148	−	0.543695i	−0.888284	−	0.459294i	$-0.848102\pi$
$853$	3.15858	−	15.8793i	0.108148	−	0.543695i	0.996432	−	0.0844010i	$-0.0268977\pi$
$854$		0			0
$855$	−22.0824	+	3.13538i	−0.755202	+	0.107228i
$856$		0			0
$857$	−7.54491	−	5.04135i	−0.257729	−	0.172209i	0.419993	−	0.907528i	$-0.362033\pi$
$857$	−7.54491	−	5.04135i	−0.257729	−	0.172209i	−0.677722	+	0.735318i	$0.737033\pi$
$858$		0			0
$859$	50.3770	+	20.8668i	1.71884	+	0.711967i	0.999857	+	0.0169402i	$0.00539249\pi$
$859$	50.3770	+	20.8668i	1.71884	+	0.711967i	0.718984	+	0.695027i	$0.244608\pi$
$860$		0			0
$861$	31.9082	+	21.3204i	1.08743	+	0.726596i
$862$		0			0
$863$		−	45.4598i		−	1.54747i	−0.633510	−	0.773735i	$-0.718386\pi$
$863$		−	45.4598i		−	1.54747i	0.633510	−	0.773735i	$-0.281614\pi$
$864$		0			0
$865$	2.46351	−	44.4971i	0.0837617	−	1.51295i
$866$		0			0
$867$	−12.3714	−	11.9532i	−0.420156	−	0.405953i
$868$		0			0
$869$	5.14555	−	2.13136i	0.174551	−	0.0723013i
$870$		0			0
$871$	−9.75236	+	9.75236i	−0.330446	+	0.330446i
$872$		0			0
$873$	−0.469755	+	0.0934401i	−0.0158988	+	0.00316247i
$874$		0			0
$875$	−54.6140	−	9.14565i	−1.84629	−	0.309179i
$876$		0			0
$877$	24.4613	−	36.6090i	0.826000	−	1.23620i	−0.143144	−	0.989702i	$-0.545721\pi$
$877$	24.4613	−	36.6090i	0.826000	−	1.23620i	0.969144	−	0.246495i	$-0.0792789\pi$
$878$		0			0
$879$	2.05193	−	10.3157i	0.0692098	−	0.347941i
$880$		0			0
$881$	15.9234	−	10.6396i	0.536472	−	0.358459i	−0.257630	−	0.966244i	$-0.582942\pi$
$881$	15.9234	−	10.6396i	0.536472	−	0.358459i	0.794102	+	0.607785i	$0.207942\pi$
$882$		0			0
$883$	9.86860	−	9.86860i	0.332105	−	0.332105i	−0.521281	−	0.853385i	$-0.674545\pi$
$883$	9.86860	−	9.86860i	0.332105	−	0.332105i	0.853385	+	0.521281i	$0.174545\pi$
$884$		0			0
$885$	5.32060	+	2.55707i	0.178850	+	0.0859550i
$886$		0			0
$887$	−8.35939	−	1.66279i	−0.280681	−	0.0558309i	0.0527424	−	0.998608i	$-0.483204\pi$
$887$	−8.35939	−	1.66279i	−0.280681	−	0.0558309i	−0.333423	+	0.942777i	$0.608204\pi$
$888$		0			0
$889$	12.9682	+	2.57954i	0.434940	+	0.0865149i
$890$		0			0
$891$	−0.115908	−	0.582708i	−0.00388306	−	0.0195215i
$892$		0			0
$893$	−37.9027	+	15.6998i	−1.26837	+	0.525374i
$894$		0			0
$895$	48.2315	+	12.4006i	1.61220	+	0.414508i
$896$		0			0
$897$	5.22157			0.174343
$898$		0			0
$899$	0.667889	+	1.61243i	0.0222753	+	0.0537774i
$900$		0			0
$901$	−1.23270	−	11.5014i	−0.0410672	−	0.383168i
$902$		0			0
$903$	−14.4090	+	34.7864i	−0.479501	+	1.15762i
$904$		0			0
$905$	−19.7994	−	9.51553i	−0.658153	−	0.316307i
$906$		0			0
$907$	−1.04663	−	5.26175i	−0.0347527	−	0.174714i	0.959511	−	0.281672i	$-0.0908889\pi$
$907$	−1.04663	−	5.26175i	−0.0347527	−	0.174714i	−0.994264	+	0.106958i	$0.965889\pi$
$908$		0			0
$909$	−5.59187	+	13.5000i	−0.185471	+	0.447765i
$910$		0			0
$911$	−23.9474	+	4.76343i	−0.793412	+	0.157819i	−0.575125	−	0.818065i	$-0.695047\pi$
$911$	−23.9474	+	4.76343i	−0.793412	+	0.157819i	−0.218286	+	0.975885i	$0.570047\pi$
$912$		0			0
$913$	0.556676	+	0.833124i	0.0184233	+	0.0275724i
$914$		0			0
$915$	2.87301	+	20.2345i	0.0949788	+	0.668933i
$916$		0			0
$917$	27.0178	+	27.0178i	0.892207	+	0.892207i
$918$		0			0
$919$		−	25.2143i		−	0.831744i	−0.909423	−	0.415872i	$-0.863476\pi$
$919$		−	25.2143i		−	0.831744i	0.909423	−	0.415872i	$-0.136524\pi$
$920$		0			0
$921$	2.24483	+	3.35963i	0.0739698	+	0.110704i
$922$		0			0
$923$	−8.09130	+	5.40643i	−0.266328	+	0.177955i
$924$		0			0
$925$	−12.2319	+	1.05129i	−0.402183	+	0.0345663i
$926$		0			0
$927$	−13.8133	−	33.3483i	−0.453689	−	1.09530i
$928$		0			0
$929$	19.2338	−	28.7855i	0.631042	−	0.944420i	−0.368847	−	0.929490i	$-0.620247\pi$
$929$	19.2338	−	28.7855i	0.631042	−	0.944420i	0.999889	−	0.0149303i	$-0.00475264\pi$
$930$		0			0
$931$	62.5732	+	62.5732i	2.05075	+	2.05075i
$932$		0			0
$933$	−22.0742	−	9.14343i	−0.722677	−	0.299342i
$934$		0			0
$935$	6.56959	−	0.338394i	0.214849	−	0.0110667i
$936$		0			0
$937$	−21.6351	−	8.96154i	−0.706787	−	0.292761i	0.000187415	−	1.00000i	$-0.499940\pi$
$937$	−21.6351	−	8.96154i	−0.706787	−	0.292761i	−0.706974	+	0.707239i	$0.749940\pi$
$938$		0			0
$939$	11.0089	+	11.0089i	0.359263	+	0.359263i
$940$		0			0
$941$	−1.98336	+	2.96831i	−0.0646558	+	0.0967643i	−0.862389	−	0.506247i	$-0.831033\pi$
$941$	−1.98336	+	2.96831i	−0.0646558	+	0.0967643i	0.797733	+	0.603011i	$0.206033\pi$
$942$		0			0
$943$	−12.9148	−	31.1791i	−0.420563	−	1.01533i
$944$		0			0
$945$	−48.0093	+	28.3713i	−1.56174	+	0.922919i
$946$		0			0
$947$	22.9094	−	15.3076i	0.744455	−	0.497429i	−0.124562	−	0.992212i	$-0.539752\pi$
$947$	22.9094	−	15.3076i	0.744455	−	0.497429i	0.869017	+	0.494783i	$0.164752\pi$
$948$		0			0
$949$	2.34410	+	3.50820i	0.0760928	+	0.113881i
$950$		0			0
$951$			26.1628i			0.848388i
$952$		0			0
$953$	0.563630	+	0.563630i	0.0182578	+	0.0182578i	0.716177	−	0.697919i	$-0.245890\pi$
$953$	0.563630	+	0.563630i	0.0182578	+	0.0182578i	−0.697919	+	0.716177i	$0.745890\pi$
$954$		0			0
$955$	25.1480	−	33.4711i	0.813771	−	1.08310i
$956$		0			0
$957$	−1.46517	−	2.19279i	−0.0473623	−	0.0708827i
$958$		0			0
$959$	99.2686	−	19.7457i	3.20555	−	0.637623i
$960$		0			0
$961$	−11.7758	+	28.4293i	−0.379865	+	0.917075i
$962$		0			0
$963$	0.641071	+	3.22288i	0.0206582	+	0.103856i
$964$		0			0
$965$	−3.44343	+	1.20798i	−0.110848	+	0.0388861i
$966$		0			0
$967$	−12.5402	+	30.2748i	−0.403266	+	0.973571i	0.583602	+	0.812040i	$0.301643\pi$
$967$	−12.5402	+	30.2748i	−0.403266	+	0.973571i	−0.986868	+	0.161531i	$0.948357\pi$
$968$		0			0
$969$	−13.5003	−	16.1648i	−0.433693	−	0.519290i
$970$		0			0
$971$	10.7205	+	25.8815i	0.344037	+	0.830578i	0.997299	+	0.0734464i	$0.0233998\pi$
$971$	10.7205	+	25.8815i	0.344037	+	0.830578i	−0.653263	+	0.757131i	$0.726600\pi$
$972$		0			0
$973$	−68.6614			−2.20118
$974$		0			0
$975$	−5.90173	+	0.507235i	−0.189007	+	0.0162445i
$976$		0			0
$977$	23.6357	−	9.79022i	0.756172	−	0.313217i	0.0289152	−	0.999582i	$-0.490795\pi$
$977$	23.6357	−	9.79022i	0.756172	−	0.313217i	0.727257	+	0.686365i	$0.240795\pi$
$978$		0			0
$979$	0.547340	+	2.75166i	0.0174931	+	0.0879435i
$980$		0			0
$981$	−36.3706	−	7.23456i	−1.16122	−	0.230982i
$982$		0			0
$983$	−15.4267	−	3.06857i	−0.492037	−	0.0978722i	−0.0571652	−	0.998365i	$-0.518206\pi$
$983$	−15.4267	−	3.06857i	−0.492037	−	0.0978722i	−0.434871	+	0.900493i	$0.643206\pi$
$984$		0			0
$985$	−5.67473	+	11.8076i	−0.180812	+	0.376223i
$986$		0			0
$987$	−28.8029	+	28.8029i	−0.916807	+	0.916807i
$988$		0			0
$989$	27.5317	−	18.3961i	0.875456	−	0.584961i
$990$		0			0
$991$	4.52428	−	22.7451i	0.143718	−	0.722521i	−0.839969	−	0.542634i	$-0.817427\pi$
$991$	4.52428	−	22.7451i	0.143718	−	0.722521i	0.983687	−	0.179887i	$-0.0575731\pi$
$992$		0			0
$993$	−9.29828	+	13.9159i	−0.295072	+	0.441606i
$994$		0			0
$995$	1.19301	−	21.5488i	0.0378210	−	0.683143i
$996$		0			0
$997$	−35.7376	+	7.10866i	−1.13182	+	0.225133i	−0.725250	−	0.688485i	$-0.758276\pi$
$997$	−35.7376	+	7.10866i	−1.13182	+	0.225133i	−0.406572	+	0.913619i	$0.633276\pi$
$998$		0			0
$999$	−8.74251	+	8.74251i	−0.276601	+	0.276601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	340.2.bd.a.73.7	✓	72
5.2	odd	4		340.2.bi.a.277.3	yes	72
17.7	odd	16		340.2.bi.a.313.3	yes	72
85.7	even	16	inner	340.2.bd.a.177.7	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
340.2.bd.a.73.7	✓	72	1.1	even	1	trivial
340.2.bd.a.177.7	yes	72	85.7	even	16	inner
340.2.bi.a.277.3	yes	72	5.2	odd	4
340.2.bi.a.313.3	yes	72	17.7	odd	16

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:	\( N \)	\(=\)	\( 340 = 2^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	340.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.197416 - 0.992478i) q^{3} +(-2.21386 + 0.314337i) q^{5} +(4.11814 + 2.75165i) q^{7} +(1.82560 + 0.756188i) q^{9} +(-0.593268 - 0.396409i) q^{11} -1.17074i q^{13} +(-0.125080 + 2.25927i) q^{15} +(3.61941 - 1.97480i) q^{17} +(4.66359 - 1.93172i) q^{19} +(3.54394 - 3.54394i) q^{21} +(-4.32282 + 0.859863i) q^{23} +(4.80238 - 1.39180i) q^{25} +(2.79748 - 4.18673i) q^{27} +(-0.712581 + 3.58239i) q^{29} +(0.397294 - 0.265463i) q^{31} +(-0.510548 + 0.510548i) q^{33} +(-9.98194 - 4.79730i) q^{35} +(-2.40822 - 0.479025i) q^{37} +(-1.16193 - 0.231123i) q^{39} +(1.49379 + 7.50980i) q^{41} +(-6.94077 + 2.87496i) q^{43} +(-4.27932 - 1.10024i) q^{45} -8.12736 q^{47} +(6.70869 + 16.1962i) q^{49} +(-1.24542 - 3.98205i) q^{51} +(1.07361 - 2.59192i) q^{53} +(1.43802 + 0.691109i) q^{55} +(-0.996525 - 5.00987i) q^{57} +(0.998373 - 2.41029i) q^{59} +(8.85868 - 1.76210i) q^{61} +(5.43730 + 8.13750i) q^{63} +(0.368007 + 2.59186i) q^{65} +(-8.33008 - 8.33008i) q^{67} +4.46006i q^{69} +(-4.61796 - 6.91127i) q^{71} +(-2.99656 + 2.00224i) q^{73} +(-0.433260 - 5.04103i) q^{75} +(-1.35238 - 3.26493i) q^{77} +(-4.33662 + 6.49021i) q^{79} +(0.588787 + 0.588787i) q^{81} +(-1.29740 - 0.537401i) q^{83} +(-7.39214 + 5.50966i) q^{85} +(3.41477 + 1.41444i) q^{87} +(-2.78037 - 2.78037i) q^{89} +(3.22147 - 4.82127i) q^{91} +(-0.185034 - 0.446712i) q^{93} +(-9.71735 + 5.74251i) q^{95} +(-0.201537 + 0.134663i) q^{97} +(-0.783309 - 1.17230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{15} + 8 q^{25} - 48 q^{27} - 32 q^{31} + 16 q^{33} + 32 q^{37} - 32 q^{39} - 40 q^{41} + 80 q^{47} - 40 q^{53} + 16 q^{55} + 8 q^{57} + 112 q^{59} - 48 q^{63} - 32 q^{67} - 16 q^{71} + 8 q^{73}+ \cdots + 96 q^{99}+O(q^{100}) \) 72 * q + 24 * q^15 + 8 * q^25 - 48 * q^27 - 32 * q^31 + 16 * q^33 + 32 * q^37 - 32 * q^39 - 40 * q^41 + 80 * q^47 - 40 * q^53 + 16 * q^55 + 8 * q^57 + 112 * q^59 - 48 * q^63 - 32 * q^67 - 16 * q^71 + 8 * q^73 - 88 * q^75 - 16 * q^77 - 64 * q^79 - 48 * q^81 - 40 * q^83 - 40 * q^85 - 8 * q^87 - 48 * q^91 - 120 * q^93 - 48 * q^95 - 80 * q^97 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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