LMFDB - Embedded newform 864.2.v.b.109.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.5
Character	$\chi$	$=$	864.109
Dual form			864.2.v.b.325.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19327 + 0.759019i) q^{2} +(0.847781 - 1.81143i) q^{4} +(2.08348 - 0.863006i) q^{5} +(-2.85037 + 2.85037i) q^{7} +(0.363276 + 2.80500i) q^{8} +O(q^{10})$	\(q+(-1.19327 + 0.759019i) q^{2} +(0.847781 - 1.81143i) q^{4} +(2.08348 - 0.863006i) q^{5} +(-2.85037 + 2.85037i) q^{7} +(0.363276 + 2.80500i) q^{8} +(-1.83111 + 2.61120i) q^{10} +(-1.60584 - 3.87685i) q^{11} +(-4.07396 - 1.68749i) q^{13} +(1.23777 - 5.56473i) q^{14} +(-2.56253 - 3.07139i) q^{16} -2.43357i q^{17} +(5.59078 + 2.31578i) q^{19} +(0.203063 - 4.50571i) q^{20} +(4.85880 + 3.40725i) q^{22} +(-3.00850 - 3.00850i) q^{23} +(0.0605754 - 0.0605754i) q^{25} +(6.14217 - 1.07858i) q^{26} +(2.74674 + 7.57972i) q^{28} +(3.80631 - 9.18924i) q^{29} -8.41072 q^{31} +(5.38903 + 1.71998i) q^{32} +(1.84713 + 2.90390i) q^{34} +(-3.47880 + 8.39856i) q^{35} +(-0.565027 + 0.234042i) q^{37} +(-8.42902 + 1.48016i) q^{38} +(3.17761 + 5.53065i) q^{40} +(-0.301316 - 0.301316i) q^{41} +(-2.97363 - 7.17897i) q^{43} +(-8.38402 - 0.377851i) q^{44} +(5.87346 + 1.30644i) q^{46} +8.16538i q^{47} -9.24917i q^{49} +(-0.0263049 + 0.118261i) q^{50} +(-6.51059 + 5.94906i) q^{52} +(-4.15977 - 10.0426i) q^{53} +(-6.69148 - 6.69148i) q^{55} +(-9.03075 - 6.95981i) q^{56} +(2.43286 + 13.8543i) q^{58} +(-1.89160 + 0.783525i) q^{59} +(2.77585 - 6.70150i) q^{61} +(10.0362 - 6.38389i) q^{62} +(-7.73606 + 2.03798i) q^{64} -9.94433 q^{65} +(-3.15764 + 7.62322i) q^{67} +(-4.40823 - 2.06313i) q^{68} +(-2.22352 - 12.6622i) q^{70} +(-3.64048 + 3.64048i) q^{71} +(2.01970 + 2.01970i) q^{73} +(0.496587 - 0.708141i) q^{74} +(8.93461 - 8.16401i) q^{76} +(15.6277 + 6.47319i) q^{77} -14.0780i q^{79} +(-7.98961 - 4.18769i) q^{80} +(0.588256 + 0.130847i) q^{82} +(9.22437 + 3.82086i) q^{83} +(-2.10018 - 5.07029i) q^{85} +(8.99730 + 6.30940i) q^{86} +(10.2912 - 5.91275i) q^{88} +(6.86945 - 6.86945i) q^{89} +(16.4222 - 6.80232i) q^{91} +(-8.00023 + 2.89913i) q^{92} +(-6.19768 - 9.74350i) q^{94} +13.6468 q^{95} -0.463135 q^{97} +(7.02029 + 11.0367i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) $ 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.19327	+	0.759019i	−0.843769	+	0.536707i
$2$	−1.19327	+	0.759019i	−0.843769	+	0.536707i
$3$		0			0
$3$		0			0
$4$	0.847781	−	1.81143i	0.423891	−	0.905713i
$5$	2.08348	−	0.863006i	0.931760	−	0.385948i	0.135414	−	0.990789i	$-0.456763\pi$
$5$	2.08348	−	0.863006i	0.931760	−	0.385948i	0.796346	+	0.604841i	$0.206763\pi$
$6$		0			0
$7$	−2.85037	+	2.85037i	−1.07734	+	1.07734i	−0.0805896	+	0.996747i	$0.525680\pi$
$7$	−2.85037	+	2.85037i	−1.07734	+	1.07734i	−0.996747	+	0.0805896i	$0.974320\pi$
$8$	0.363276	+	2.80500i	0.128437	+	0.991718i
$9$		0			0
$10$	−1.83111	+	2.61120i	−0.579049	+	0.825733i
$11$	−1.60584	−	3.87685i	−0.484180	−	1.16891i	−0.957606	−	0.288080i	$-0.906983\pi$
$11$	−1.60584	−	3.87685i	−0.484180	−	1.16891i	0.473427	−	0.880833i	$-0.343017\pi$
$12$		0			0
$13$	−4.07396	−	1.68749i	−1.12991	−	0.468026i	−0.262162	−	0.965024i	$-0.584436\pi$
$13$	−4.07396	−	1.68749i	−1.12991	−	0.468026i	−0.867752	+	0.496998i	$0.834436\pi$
$14$	1.23777	−	5.56473i	0.330808	−	1.48724i
$15$		0			0
$16$	−2.56253	−	3.07139i	−0.640634	−	0.767847i
$17$		−	2.43357i		−	0.590227i	−0.955462	−	0.295114i	$-0.904642\pi$
$17$		−	2.43357i		−	0.590227i	0.955462	−	0.295114i	$-0.0953575\pi$
$18$		0			0
$19$	5.59078	+	2.31578i	1.28261	+	0.531275i	0.916775	−	0.399403i	$-0.130783\pi$
$19$	5.59078	+	2.31578i	1.28261	+	0.531275i	0.365837	+	0.930679i	$0.380783\pi$
$20$	0.203063	−	4.50571i	0.0454064	−	1.00751i
$21$		0			0
$22$	4.85880	+	3.40725i	1.03590	+	0.726429i
$23$	−3.00850	−	3.00850i	−0.627316	−	0.627316i	0.320076	−	0.947392i	$-0.396292\pi$
$23$	−3.00850	−	3.00850i	−0.627316	−	0.627316i	−0.947392	+	0.320076i	$0.896292\pi$
$24$		0			0
$25$	0.0605754	−	0.0605754i	0.0121151	−	0.0121151i
$26$	6.14217	−	1.07858i	1.20458	−	0.211528i
$27$		0			0
$28$	2.74674	+	7.57972i	0.519086	+	1.43243i
$29$	3.80631	−	9.18924i	0.706813	−	1.70640i	−0.00100092	−	0.999999i	$-0.500319\pi$
$29$	3.80631	−	9.18924i	0.706813	−	1.70640i	0.707814	−	0.706399i	$-0.249681\pi$
$30$		0			0
$31$	−8.41072			−1.51061			−0.755305	−	0.655374i	$-0.772511\pi$
$31$	−8.41072			−1.51061			−0.755305	+	0.655374i	$0.772511\pi$
$32$	5.38903	+	1.71998i	0.952655	+	0.304052i
$33$		0			0
$34$	1.84713	+	2.90390i	0.316779	+	0.498015i
$35$	−3.47880	+	8.39856i	−0.588024	+	1.41962i
$36$		0			0
$37$	−0.565027	+	0.234042i	−0.0928899	+	0.0384762i	−0.428644	−	0.903473i	$-0.641009\pi$
$37$	−0.565027	+	0.234042i	−0.0928899	+	0.0384762i	0.335755	+	0.941949i	$0.391009\pi$
$38$	−8.42902	+	1.48016i	−1.36737	+	0.240114i
$39$		0			0
$40$	3.17761	+	5.53065i	0.502424	+	0.874473i
$41$	−0.301316	−	0.301316i	−0.0470577	−	0.0470577i	0.683186	−	0.730244i	$-0.260594\pi$
$41$	−0.301316	−	0.301316i	−0.0470577	−	0.0470577i	−0.730244	+	0.683186i	$0.760594\pi$
$42$		0			0
$43$	−2.97363	−	7.17897i	−0.453474	−	1.09478i	−0.970992	−	0.239110i	$-0.923144\pi$
$43$	−2.97363	−	7.17897i	−0.453474	−	1.09478i	0.517519	−	0.855672i	$-0.326856\pi$
$44$	−8.38402	−	0.377851i	−1.26394	−	0.0569632i
$45$		0			0
$46$	5.87346	+	1.30644i	0.865994	+	0.192624i
$47$			8.16538i			1.19104i	0.803339	+	0.595522i	$0.203055\pi$
$47$			8.16538i			1.19104i	−0.803339	+	0.595522i	$0.796945\pi$
$48$		0			0
$49$		−	9.24917i		−	1.32131i
$50$	−0.0263049	+	0.118261i	−0.00372007	+	0.0167246i
$51$		0			0
$52$	−6.51059	+	5.94906i	−0.902857	+	0.824986i
$53$	−4.15977	−	10.0426i	−0.571389	−	1.37945i	−0.900373	−	0.435119i	$-0.856706\pi$
$53$	−4.15977	−	10.0426i	−0.571389	−	1.37945i	0.328984	−	0.944336i	$-0.393294\pi$
$54$		0			0
$55$	−6.69148	−	6.69148i	−0.902279	−	0.902279i
$56$	−9.03075	−	6.95981i	−1.20678	−	0.930044i
$57$		0			0
$58$	2.43286	+	13.8543i	0.319450	+	1.81916i
$59$	−1.89160	+	0.783525i	−0.246265	+	0.102006i	−0.502402	−	0.864634i	$-0.667550\pi$
$59$	−1.89160	+	0.783525i	−0.246265	+	0.102006i	0.256137	+	0.966640i	$0.417550\pi$
$60$		0			0
$61$	2.77585	−	6.70150i	0.355412	−	0.858040i	−0.640521	−	0.767941i	$-0.721282\pi$
$61$	2.77585	−	6.70150i	0.355412	−	0.858040i	0.995933	−	0.0900992i	$-0.0287184\pi$
$62$	10.0362	−	6.38389i	1.27460	−	0.810755i
$63$		0			0
$64$	−7.73606	+	2.03798i	−0.967008	+	0.254747i
$65$	−9.94433			−1.23344
$66$		0			0
$67$	−3.15764	+	7.62322i	−0.385767	+	0.931325i	0.605059	+	0.796181i	$0.293150\pi$
$67$	−3.15764	+	7.62322i	−0.385767	+	0.931325i	−0.990826	+	0.135144i	$0.956850\pi$
$68$	−4.40823	−	2.06313i	−0.534577	−	0.250192i
$69$		0			0
$70$	−2.22352	−	12.6622i	−0.265762	−	1.51342i
$71$	−3.64048	+	3.64048i	−0.432045	+	0.432045i	−0.889324	−	0.457278i	$-0.848824\pi$
$71$	−3.64048	+	3.64048i	−0.432045	+	0.432045i	0.457278	+	0.889324i	$0.348824\pi$
$72$		0			0
$73$	2.01970	+	2.01970i	0.236388	+	0.236388i	0.815353	−	0.578965i	$-0.196543\pi$
$73$	2.01970	+	2.01970i	0.236388	+	0.236388i	−0.578965	+	0.815353i	$0.696543\pi$
$74$	0.496587	−	0.708141i	0.0577271	−	0.0823197i
$75$		0			0
$76$	8.93461	−	8.16401i	1.02487	−	0.936477i
$77$	15.6277	+	6.47319i	1.78094	+	0.737688i
$78$		0			0
$79$		−	14.0780i		−	1.58390i	−0.610585	−	0.791951i	$-0.709065\pi$
$79$		−	14.0780i		−	1.58390i	0.610585	−	0.791951i	$-0.290935\pi$
$80$	−7.98961	−	4.18769i	−0.893266	−	0.468198i
$81$		0			0
$82$	0.588256	+	0.130847i	0.0649620	+	0.0144496i
$83$	9.22437	+	3.82086i	1.01251	+	0.419394i	0.826369	−	0.563130i	$-0.190403\pi$
$83$	9.22437	+	3.82086i	1.01251	+	0.419394i	0.186138	+	0.982524i	$0.440403\pi$
$84$		0			0
$85$	−2.10018	−	5.07029i	−0.227797	−	0.549951i
$86$	8.99730	+	6.30940i	0.970204	+	0.680360i
$87$		0			0
$88$	10.2912	−	5.91275i	1.09704	−	0.630302i
$89$	6.86945	−	6.86945i	0.728160	−	0.728160i	−0.242093	−	0.970253i	$-0.577834\pi$
$89$	6.86945	−	6.86945i	0.728160	−	0.728160i	0.970253	+	0.242093i	$0.0778339\pi$
$90$		0			0
$91$	16.4222	−	6.80232i	1.72152	−	0.713076i
$92$	−8.00023	+	2.89913i	−0.834082	+	0.302255i
$93$		0			0
$94$	−6.19768	−	9.74350i	−0.639242	−	1.00496i
$95$	13.6468			1.40013
$96$		0			0
$97$	−0.463135			−0.0470242			−0.0235121	−	0.999724i	$-0.507485\pi$
$97$	−0.463135			−0.0470242			−0.0235121	+	0.999724i	$0.507485\pi$
$98$	7.02029	+	11.0367i	0.709157	+	1.11488i
$99$		0			0
$100$	−0.0583732	−	0.161083i	−0.00583732	−	0.0161083i
$101$	−6.53443	+	2.70665i	−0.650200	+	0.269322i	−0.683308	−	0.730130i	$-0.739460\pi$
$101$	−6.53443	+	2.70665i	−0.650200	+	0.269322i	0.0331079	+	0.999452i	$0.489460\pi$
$102$		0			0
$103$	2.75457	−	2.75457i	0.271415	−	0.271415i	−0.558254	−	0.829670i	$-0.688529\pi$
$103$	2.75457	−	2.75457i	0.271415	−	0.271415i	0.829670	+	0.558254i	$0.188529\pi$
$104$	3.25344	−	12.0405i	0.319026	−	1.18067i
$105$		0			0
$106$	12.5862	+	8.82616i	1.22248	+	0.857272i
$107$	−6.80158	−	16.4205i	−0.657533	−	1.58743i	−0.801602	−	0.597858i	$-0.796019\pi$
$107$	−6.80158	−	16.4205i	−0.657533	−	1.58743i	0.144069	−	0.989568i	$-0.453981\pi$
$108$		0			0
$109$	2.86933	+	1.18851i	0.274832	+	0.113839i	0.515843	−	0.856683i	$-0.327479\pi$
$109$	2.86933	+	1.18851i	0.274832	+	0.113839i	−0.241011	+	0.970522i	$0.577479\pi$
$110$	13.0637	+	2.90578i	1.24557	+	0.277055i
$111$		0			0
$112$	16.0587	+	1.45042i	1.51741	+	0.137052i
$113$			3.44216i			0.323811i	0.986806	+	0.161906i	$0.0517640\pi$
$113$			3.44216i			0.323811i	−0.986806	+	0.161906i	$0.948236\pi$
$114$		0			0
$115$	−8.86450	−	3.67180i	−0.826619	−	0.342397i
$116$	−13.4187	−	14.6853i	−1.24590	−	1.36350i
$117$		0			0
$118$	1.66247	−	2.37071i	0.153043	−	0.218242i
$119$	6.93657	+	6.93657i	0.635874	+	0.635874i
$120$		0			0
$121$	−4.67303	+	4.67303i	−0.424821	+	0.424821i
$122$	1.77423	+	10.1036i	0.160631	+	0.914739i
$123$		0			0
$124$	−7.13045	+	15.2354i	−0.640333	+	1.36818i
$125$	−4.24110	+	10.2389i	−0.379335	+	0.915796i
$126$		0			0
$127$	−8.85490			−0.785746			−0.392873	−	0.919593i	$-0.628519\pi$
$127$	−8.85490			−0.785746			−0.392873	+	0.919593i	$0.628519\pi$
$128$	7.68434	−	8.30367i	0.679206	−	0.733948i
$129$		0			0
$130$	11.8663	−	7.54793i	1.04074	−	0.661997i
$131$	1.03111	−	2.48932i	0.0900885	−	0.217493i	−0.872413	−	0.488770i	$-0.837446\pi$
$131$	1.03111	−	2.48932i	0.0900885	−	0.217493i	0.962501	+	0.271277i	$0.0874459\pi$
$132$		0			0
$133$	−22.5366	+	9.33495i	−1.95417	+	0.809443i
$134$	−2.01825	−	11.4933i	−0.174350	−	0.992866i
$135$		0			0
$136$	6.82617	−	0.884058i	0.585339	−	0.0758073i
$137$	−6.97938	−	6.97938i	−0.596289	−	0.596289i	0.343034	−	0.939323i	$-0.388545\pi$
$137$	−6.97938	−	6.97938i	−0.596289	−	0.596289i	−0.939323	+	0.343034i	$0.888545\pi$
$138$		0			0
$139$	1.01039	+	2.43930i	0.0857003	+	0.206899i	0.960920	−	0.276827i	$-0.0892830\pi$
$139$	1.01039	+	2.43930i	0.0857003	+	0.206899i	−0.875219	+	0.483726i	$0.839283\pi$
$140$	12.2641	+	13.4217i	1.03651	+	1.13434i
$141$		0			0
$142$	1.58088	−	7.10726i	0.132664	−	0.596428i
$143$			18.5040i			1.54738i
$144$		0			0
$145$		−	22.4304i		−	1.86275i
$146$	−3.94303	−	0.877055i	−0.326328	−	0.0725856i
$147$		0			0
$148$	−0.0550696	+	1.22192i	−0.00452669	+	0.100441i
$149$	−7.50184	−	18.1111i	−0.614575	−	1.48372i	−0.857924	−	0.513777i	$-0.828246\pi$
$149$	−7.50184	−	18.1111i	−0.614575	−	1.48372i	0.243349	−	0.969939i	$-0.421754\pi$
$150$		0			0
$151$	8.74013	+	8.74013i	0.711261	+	0.711261i	0.966799	−	0.255538i	$-0.0822525\pi$
$151$	8.74013	+	8.74013i	0.711261	+	0.711261i	−0.255538	+	0.966799i	$0.582252\pi$
$152$	−4.46476	+	16.5234i	−0.362140	+	1.34022i
$153$		0			0
$154$	−23.5613	+	4.13743i	−1.89862	+	0.333404i
$155$	−17.5236	+	7.25850i	−1.40753	+	0.583016i
$156$		0			0
$157$	−6.47700	+	15.6369i	−0.516921	+	1.24796i	0.422865	+	0.906193i	$0.361024\pi$
$157$	−6.47700	+	15.6369i	−0.516921	+	1.24796i	−0.939786	+	0.341764i	$0.888976\pi$
$158$	10.6855	+	16.7989i	0.850092	+	1.33645i
$159$		0			0
$160$	12.7123	−	1.06722i	1.00499	−	0.0843714i
$161$	17.1507			1.35166
$162$		0			0
$163$	−0.272097	+	0.656899i	−0.0213123	+	0.0514523i	−0.934177	−	0.356809i	$-0.883865\pi$
$163$	−0.272097	+	0.656899i	−0.0213123	+	0.0514523i	0.912865	+	0.408261i	$0.133865\pi$
$164$	−0.801262	+	0.290362i	−0.0625681	+	0.0226735i
$165$		0			0
$166$	−13.9073	+	2.44216i	−1.07941	+	0.189548i
$167$	−7.15054	+	7.15054i	−0.553326	+	0.553326i	−0.927399	−	0.374073i	$-0.877961\pi$
$167$	−7.15054	+	7.15054i	−0.553326	+	0.553326i	0.374073	+	0.927399i	$0.377961\pi$
$168$		0			0
$169$	4.55715	+	4.55715i	0.350550	+	0.350550i
$170$	6.35453	+	4.45614i	0.487370	+	0.341771i
$171$		0			0
$172$	−15.5252	−	0.699688i	−1.18378	−	0.0533507i
$173$	1.45722	+	0.603599i	0.110790	+	0.0458908i	0.437390	−	0.899272i	$-0.355903\pi$
$173$	1.45722	+	0.603599i	0.110790	+	0.0458908i	−0.326600	+	0.945163i	$0.605903\pi$
$174$		0			0
$175$			0.345324i			0.0261040i
$176$	−7.79227	+	14.8667i	−0.587364	+	1.12062i
$177$		0			0
$178$	−2.98306	+	13.4111i	−0.223590	+	1.00521i
$179$	3.93633	+	1.63048i	0.294215	+	0.121868i	0.524909	−	0.851159i	$-0.324100\pi$
$179$	3.93633	+	1.63048i	0.294215	+	0.121868i	−0.230694	+	0.973026i	$0.574100\pi$
$180$		0			0
$181$	6.45799	+	15.5910i	0.480018	+	1.15887i	0.959600	+	0.281369i	$0.0907886\pi$
$181$	6.45799	+	15.5910i	0.480018	+	1.15887i	−0.479581	+	0.877497i	$0.659211\pi$
$182$	−14.4331	+	20.5818i	−1.06985	+	1.52562i
$183$		0			0
$184$	7.34593	−	9.53176i	0.541549	−	0.702691i
$185$	−0.975243	+	0.975243i	−0.0717013	+	0.0717013i
$186$		0			0
$187$	−9.43457	+	3.90793i	−0.689924	+	0.285776i
$188$	14.7910	+	6.92246i	1.07874	+	0.504872i
$189$		0			0
$190$	−16.2843	+	10.3582i	−1.18139	+	0.751461i
$191$	−14.4897			−1.04844			−0.524220	−	0.851583i	$-0.675643\pi$
$191$	−14.4897			−1.04844			−0.524220	+	0.851583i	$0.675643\pi$
$192$		0			0
$193$	−8.86055			−0.637796			−0.318898	−	0.947789i	$-0.603313\pi$
$193$	−8.86055			−0.637796			−0.318898	+	0.947789i	$0.603313\pi$
$194$	0.552644	−	0.351528i	0.0396775	−	0.0252382i
$195$		0			0
$196$	−16.7542	−	7.84127i	−1.19673	−	0.560091i
$197$	3.01070	−	1.24707i	0.214503	−	0.0888502i	−0.272844	−	0.962058i	$-0.587964\pi$
$197$	3.01070	−	1.24707i	0.214503	−	0.0888502i	0.487348	+	0.873208i	$0.337964\pi$
$198$		0			0
$199$	7.41133	−	7.41133i	0.525375	−	0.525375i	−0.393815	−	0.919190i	$-0.628845\pi$
$199$	7.41133	−	7.41133i	0.525375	−	0.525375i	0.919190	+	0.393815i	$0.128845\pi$
$200$	0.191920	+	0.147908i	0.0135708	+	0.0104587i
$201$		0			0
$202$	5.74294	−	8.18952i	0.404072	−	0.576213i
$203$	15.3433	+	37.0420i	1.07689	+	2.59984i
$204$		0			0
$205$	−0.887824	−	0.367749i	−0.0620083	−	0.0256847i
$206$	−1.19617	+	5.37771i	−0.0833412	+	0.374683i
$207$		0			0
$208$	5.25673	+	16.8370i	0.364489	+	1.16743i
$209$		−	25.3933i		−	1.75649i
$210$		0			0
$211$	25.9727	+	10.7583i	1.78804	+	0.740629i	0.990526	+	0.137322i	$0.0438494\pi$
$211$	25.9727	+	10.7583i	1.78804	+	0.740629i	0.797509	+	0.603307i	$0.206151\pi$
$212$	−21.7180	−	0.978786i	−1.49160	−	0.0672233i
$213$		0			0
$214$	20.5795	+	14.4315i	1.40679	+	0.986517i
$215$	−12.3910	−	12.3910i	−0.845058	−	0.845058i
$216$		0			0
$217$	23.9736	−	23.9736i	1.62744	−	1.62744i
$218$	−4.32598	+	0.759656i	−0.292993	+	0.0514504i
$219$		0			0
$220$	−17.7940	+	6.44821i	−1.19967	+	0.434738i
$221$	−4.10663	+	9.91427i	−0.276242	+	0.666906i
$222$		0			0
$223$	4.20275			0.281437			0.140718	−	0.990050i	$-0.455059\pi$
$223$	4.20275			0.281437			0.140718	+	0.990050i	$0.455059\pi$
$224$	−20.2633	+	10.4581i	−1.35390	+	0.698764i
$225$		0			0
$226$	−2.61267	−	4.10743i	−0.173792	−	0.273222i
$227$	−4.67917	+	11.2965i	−0.310567	+	0.749776i	0.689117	+	0.724650i	$0.257999\pi$
$227$	−4.67917	+	11.2965i	−0.310567	+	0.749776i	−0.999684	+	0.0251256i	$0.992001\pi$
$228$		0			0
$229$	−9.42870	+	3.90550i	−0.623066	+	0.258083i	−0.671804	−	0.740729i	$-0.734480\pi$
$229$	−9.42870	+	3.90550i	−0.623066	+	0.258083i	0.0487375	+	0.998812i	$0.484480\pi$
$230$	13.3647	−	2.34688i	0.881242	−	0.154749i
$231$		0			0
$232$	27.1586	+	7.33846i	1.78305	+	0.481794i
$233$	14.7860	+	14.7860i	0.968661	+	0.968661i	0.999524	−	0.0308622i	$-0.00982531\pi$
$233$	14.7860	+	14.7860i	0.968661	+	0.968661i	−0.0308622	+	0.999524i	$0.509825\pi$
$234$		0			0
$235$	7.04677	+	17.0124i	0.459681	+	1.10977i
$236$	−0.184362	+	4.09075i	−0.0120009	+	0.266285i
$237$		0			0
$238$	−13.5422	−	3.01220i	−0.877808	−	0.195252i
$239$			6.57134i			0.425064i	0.977154	+	0.212532i	$0.0681710\pi$
$239$			6.57134i			0.425064i	−0.977154	+	0.212532i	$0.931829\pi$
$240$		0			0
$241$		−	1.59471i		−	0.102725i	−0.998680	−	0.0513623i	$-0.983644\pi$
$241$		−	1.59471i		−	0.102725i	0.998680	−	0.0513623i	$-0.0163563\pi$
$242$	2.02926	−	9.12309i	0.130446	−	0.586455i
$243$		0			0
$244$	−9.78597	−	10.7097i	−0.626482	−	0.685616i
$245$	−7.98209	−	19.2705i	−0.509957	−	1.23114i
$246$		0			0
$247$	−18.8688	−	18.8688i	−1.20059	−	1.20059i
$248$	−3.05541	−	23.5921i	−0.194019	−	1.49810i
$249$		0			0
$250$	−2.71076	−	15.4368i	−0.171443	−	0.976312i
$251$	−11.3850	+	4.71583i	−0.718616	+	0.297661i	−0.711865	−	0.702317i	$-0.752149\pi$
$251$	−11.3850	+	4.71583i	−0.718616	+	0.297661i	−0.00675143	+	0.999977i	$0.502149\pi$
$252$		0			0
$253$	−6.83232	+	16.4947i	−0.429544	+	1.03701i
$254$	10.5663	−	6.72104i	0.662987	−	0.421715i
$255$		0			0
$256$	−2.86684	+	15.7411i	−0.179177	+	0.983817i
$257$	25.0023			1.55960			0.779802	−	0.626027i	$-0.215320\pi$
$257$	25.0023			1.55960			0.779802	+	0.626027i	$0.215320\pi$
$258$		0			0
$259$	0.943429	−	2.27764i	0.0586218	−	0.141526i
$260$	−8.43062	+	18.0134i	−0.522845	+	1.11715i
$261$		0			0
$262$	0.659049	+	3.75306i	0.0407162	+	0.231865i
$263$	10.3998	−	10.3998i	0.641280	−	0.641280i	−0.309590	−	0.950870i	$-0.600192\pi$
$263$	10.3998	−	10.3998i	0.641280	−	0.641280i	0.950870	+	0.309590i	$0.100192\pi$
$264$		0			0
$265$	−17.3336	−	17.3336i	−1.06480	−	1.06480i
$266$	19.8068	−	28.2448i	1.21443	−	1.73180i
$267$		0			0
$268$	11.1319	+	12.1827i	0.679990	+	0.744174i
$269$	7.95160	+	3.29366i	0.484817	+	0.200818i	0.611685	−	0.791102i	$-0.290492\pi$
$269$	7.95160	+	3.29366i	0.484817	+	0.200818i	−0.126867	+	0.991920i	$0.540492\pi$
$270$		0			0
$271$		−	2.89487i		−	0.175851i	−0.996127	−	0.0879254i	$-0.971976\pi$
$271$		−	2.89487i		−	0.175851i	0.996127	−	0.0879254i	$-0.0280237\pi$
$272$	−7.47444	+	6.23611i	−0.453204	+	0.378120i
$273$		0			0
$274$	13.6258	+	3.03080i	0.823162	+	0.183097i
$275$	−0.332116	−	0.137567i	−0.0200273	−	0.00829559i
$276$		0			0
$277$	8.83346	+	21.3259i	0.530751	+	1.28135i	0.931026	+	0.364952i	$0.118915\pi$
$277$	8.83346	+	21.3259i	0.530751	+	1.28135i	−0.400275	+	0.916395i	$0.631085\pi$
$278$	−3.05714	−	2.14384i	−0.183355	−	0.128579i
$279$		0			0
$280$	−24.8217	−	6.70704i	−1.48338	−	0.400822i
$281$	−10.2412	+	10.2412i	−0.610937	+	0.610937i	−0.943190	−	0.332253i	$-0.892191\pi$
$281$	−10.2412	+	10.2412i	−0.610937	+	0.610937i	0.332253	+	0.943190i	$0.392191\pi$
$282$		0			0
$283$	−0.560906	+	0.232335i	−0.0333424	+	0.0138109i	−0.399292	−	0.916824i	$-0.630744\pi$
$283$	−0.560906	+	0.232335i	−0.0333424	+	0.0138109i	0.365950	+	0.930635i	$0.380744\pi$
$284$	3.50813	+	9.68079i	0.208169	+	0.574449i
$285$		0			0
$286$	−14.0449	−	22.0802i	−0.830490	−	1.30563i
$287$	1.71772			0.101394
$288$		0			0
$289$	11.0777			0.651632
$290$	17.0251	+	26.7656i	0.999750	+	1.57173i
$291$		0			0
$292$	5.37080	−	1.94627i	0.314302	−	0.113897i
$293$	16.6992	−	6.91702i	0.975576	−	0.404097i	0.162791	−	0.986661i	$-0.447950\pi$
$293$	16.6992	−	6.91702i	0.975576	−	0.404097i	0.812785	+	0.582564i	$0.197950\pi$
$294$		0			0
$295$	−3.26492	+	3.26492i	−0.190091	+	0.190091i
$296$	−0.861748	−	1.49988i	−0.0500881	−	0.0871787i
$297$		0			0
$298$	22.6983	+	15.9173i	1.31488	+	0.922065i
$299$	7.17970	+	17.3333i	0.415213	+	1.00241i
$300$		0			0
$301$	28.9386	+	11.9868i	1.66799	+	0.690905i
$302$	−17.0632	−	3.79540i	−0.981879	−	0.218401i
$303$		0			0
$304$	−7.21391	−	23.1057i	−0.413746	−	1.32520i
$305$		−	16.3580i		−	0.936658i
$306$		0			0
$307$	−9.90260	−	4.10179i	−0.565172	−	0.234102i	0.0817571	−	0.996652i	$-0.473947\pi$
$307$	−9.90260	−	4.10179i	−0.565172	−	0.234102i	−0.646929	+	0.762551i	$0.723947\pi$
$308$	24.9745	−	22.8205i	1.42306	−	1.30032i
$309$		0			0
$310$	15.4010	−	21.9620i	0.874717	−	1.24736i
$311$	−15.5621	−	15.5621i	−0.882447	−	0.882447i	0.111336	−	0.993783i	$-0.464487\pi$
$311$	−15.5621	−	15.5621i	−0.882447	−	0.882447i	−0.993783	+	0.111336i	$0.964487\pi$
$312$		0			0
$313$	21.4835	−	21.4835i	1.21432	−	1.21432i	0.244731	−	0.969591i	$-0.421300\pi$
$313$	21.4835	−	21.4835i	1.21432	−	1.21432i	0.969591	−	0.244731i	$-0.0786996\pi$
$314$	−4.13987	−	23.5751i	−0.233626	−	1.33042i
$315$		0			0
$316$	−25.5013	−	11.9351i	−1.43456	−	0.671401i
$317$	4.35244	−	10.5077i	0.244457	−	0.590172i	−0.753258	−	0.657725i	$-0.771519\pi$
$317$	4.35244	−	10.5077i	0.244457	−	0.590172i	0.997716	+	0.0675523i	$0.0215190\pi$
$318$		0			0
$319$	−41.7376			−2.33686
$320$	−14.3591	+	10.9224i	−0.802700	+	0.610578i
$321$		0			0
$322$	−20.4653	+	13.0177i	−1.14049	+	0.725446i
$323$	5.63560	−	13.6055i	0.313573	−	0.757033i
$324$		0			0
$325$	−0.349002	+	0.144561i	−0.0193592	+	0.00801882i
$326$	−0.173914	−	0.990384i	−0.00963223	−	0.0548523i
$327$		0			0
$328$	0.735731	−	0.954653i	0.0406240	−	0.0527119i
$329$	−23.2743	−	23.2743i	−1.28316	−	1.28316i
$330$		0			0
$331$	9.81816	+	23.7031i	0.539655	+	1.30284i	0.924964	+	0.380054i	$0.124095\pi$
$331$	9.81816	+	23.7031i	0.539655	+	1.30284i	−0.385309	+	0.922787i	$0.625905\pi$
$332$	14.7415	−	13.4700i	0.809043	−	0.739264i
$333$		0			0
$334$	3.10512	−	13.9599i	0.169905	−	0.763853i
$335$			18.6079i			1.01666i
$336$		0			0
$337$			18.6782i			1.01747i	0.860924	+	0.508734i	$0.169886\pi$
$337$			18.6782i			1.01747i	−0.860924	+	0.508734i	$0.830114\pi$
$338$	−8.89687	−	1.97894i	−0.483926	−	0.107640i
$339$		0			0
$340$	−10.9650	−	0.494169i	−0.594659	−	0.0268001i
$341$	13.5063	+	32.6070i	0.731406	+	1.76577i
$342$		0			0
$343$	6.41096	+	6.41096i	0.346159	+	0.346159i
$344$	19.0568	−	10.9490i	1.02747	−	0.590329i
$345$		0			0
$346$	−2.19699	+	0.385799i	−0.118111	+	0.0207407i
$347$	−18.2190	+	7.54656i	−0.978048	+	0.405121i	−0.813702	−	0.581282i	$-0.802551\pi$
$347$	−18.2190	+	7.54656i	−0.978048	+	0.405121i	−0.164346	+	0.986403i	$0.552551\pi$
$348$		0			0
$349$	−4.81063	+	11.6139i	−0.257507	+	0.621677i	−0.998772	−	0.0495349i	$-0.984226\pi$
$349$	−4.81063	+	11.6139i	−0.257507	+	0.621677i	0.741265	+	0.671212i	$0.234226\pi$
$350$	−0.262107	−	0.412064i	−0.0140102	−	0.0220258i
$351$		0			0
$352$	−1.98584	−	23.6545i	−0.105846	−	1.26079i
$353$	18.1486			0.965951			0.482975	−	0.875634i	$-0.339556\pi$
$353$	18.1486			0.965951			0.482975	+	0.875634i	$0.339556\pi$
$354$		0			0
$355$	−4.44311	+	10.7266i	−0.235816	+	0.569310i
$356$	−6.61971	−	18.2673i	−0.350844	−	0.968165i
$357$		0			0
$358$	−5.93466	+	1.04214i	−0.313657	+	0.0550791i
$359$	3.93767	−	3.93767i	0.207822	−	0.207822i	−0.595519	−	0.803341i	$-0.703054\pi$
$359$	3.93767	−	3.93767i	0.207822	−	0.207822i	0.803341	+	0.595519i	$0.203054\pi$
$360$		0			0
$361$	12.4589	+	12.4589i	0.655734	+	0.655734i
$362$	−19.5399	−	13.7025i	−1.02700	−	0.720186i
$363$		0			0
$364$	1.60057	−	35.5146i	0.0838927	−	1.86147i
$365$	5.95101	+	2.46499i	0.311490	+	0.129024i
$366$		0			0
$367$			18.7048i			0.976380i	0.872737	+	0.488190i	$0.162343\pi$
$367$			18.7048i			0.976380i	−0.872737	+	0.488190i	$0.837657\pi$
$368$	−1.53088	+	16.9497i	−0.0798029	+	0.883562i
$369$		0			0
$370$	0.423499	−	1.90395i	0.0220167	−	0.0989819i
$371$	40.4819	+	16.7682i	2.10172	+	0.870559i
$372$		0			0
$373$	−0.457926	−	1.10553i	−0.0237105	−	0.0572422i	0.911581	−	0.411121i	$-0.134863\pi$
$373$	−0.457926	−	1.10553i	−0.0237105	−	0.0572422i	−0.935291	+	0.353879i	$0.884863\pi$
$374$	8.29179	−	11.8242i	0.428758	−	0.611416i
$375$		0			0
$376$	−22.9039	+	2.96629i	−1.18118	+	0.152975i
$377$	−31.0135	+	31.0135i	−1.59728	+	1.59728i
$378$		0			0
$379$	21.1834	−	8.77447i	1.08812	−	0.450714i	0.234769	−	0.972051i	$-0.424566\pi$
$379$	21.1834	−	8.77447i	1.08812	−	0.450714i	0.853351	+	0.521337i	$0.174566\pi$
$380$	11.5695	−	24.7202i	0.593503	−	1.26812i
$381$		0			0
$382$	17.2901	−	10.9980i	0.884640	−	0.562705i
$383$	−29.7938			−1.52239			−0.761197	−	0.648521i	$-0.775388\pi$
$383$	−29.7938			−1.52239			−0.761197	+	0.648521i	$0.775388\pi$
$384$		0			0
$385$	38.1463			1.94412
$386$	10.5730	−	6.72532i	0.538152	−	0.342310i
$387$		0			0
$388$	−0.392637	+	0.838935i	−0.0199331	+	0.0425905i
$389$	−31.6813	+	13.1228i	−1.60630	+	0.665353i	−0.992290	−	0.123941i	$-0.960446\pi$
$389$	−31.6813	+	13.1228i	−1.60630	+	0.665353i	−0.614015	+	0.789295i	$0.710446\pi$
$390$		0			0
$391$	−7.32140	+	7.32140i	−0.370259	+	0.370259i
$392$	25.9439	−	3.36000i	1.31037	−	0.169706i
$393$		0			0
$394$	−2.64602	+	3.77327i	−0.133305	+	0.190094i
$395$	−12.1494	−	29.3313i	−0.611304	−	1.47582i
$396$		0			0
$397$	−0.757512	−	0.313772i	−0.0380184	−	0.0157478i	0.363593	−	0.931558i	$-0.381550\pi$
$397$	−0.757512	−	0.313772i	−0.0380184	−	0.0157478i	−0.401612	+	0.915810i	$0.631550\pi$
$398$	−3.21837	+	14.4690i	−0.161322	+	0.725267i
$399$		0			0
$400$	−0.341277	−	0.0308240i	−0.0170638	−	0.00154120i
$401$		−	10.0557i		−	0.502160i	−0.967966	−	0.251080i	$-0.919214\pi$
$401$		−	10.0557i		−	0.502160i	0.967966	−	0.251080i	$-0.0807857\pi$
$402$		0			0
$403$	34.2649	+	14.1930i	1.70686	+	0.707004i
$404$	−0.636870	+	14.1313i	−0.0316854	+	0.703058i
$405$		0			0
$406$	−46.4243	−	32.5553i	−2.30400	−	1.61569i
$407$	1.81469	+	1.81469i	0.0899508	+	0.0899508i
$408$		0			0
$409$	−12.4532	+	12.4532i	−0.615773	+	0.615773i	−0.944444	−	0.328672i	$-0.893399\pi$
$409$	−12.4532	+	12.4532i	−0.615773	+	0.615773i	0.328672	+	0.944444i	$0.393399\pi$
$410$	1.33854	−	0.235052i	0.0661058	−	0.0116084i
$411$		0			0
$412$	−2.65443	−	7.32496i	−0.130774	−	0.360875i
$413$	3.15841	−	7.62507i	0.155415	−	0.375205i
$414$		0			0
$415$	22.5162			1.10528
$416$	−19.0523	−	16.1011i	−0.934114	−	0.789420i
$417$		0			0
$418$	19.2740	+	30.3011i	0.942724	+	1.48207i
$419$	10.6919	−	25.8126i	0.522335	−	1.26103i	−0.414115	−	0.910225i	$-0.635909\pi$
$419$	10.6919	−	25.8126i	0.522335	−	1.26103i	0.936449	−	0.350803i	$-0.114091\pi$
$420$		0			0
$421$	−7.69993	+	3.18942i	−0.375272	+	0.155443i	−0.562344	−	0.826904i	$-0.690100\pi$
$421$	−7.69993	+	3.18942i	−0.375272	+	0.155443i	0.187072	+	0.982346i	$0.440100\pi$
$422$	−39.1582	+	6.87629i	−1.90619	+	0.334733i
$423$		0			0
$424$	26.6583	−	15.3164i	1.29464	−	0.743830i
$425$	−0.147414	−	0.147414i	−0.00715065	−	0.00715065i
$426$		0			0
$427$	11.1895	+	27.0139i	0.541500	+	1.30730i
$428$	−35.5107	−	1.60040i	−1.71647	−	0.0773581i
$429$		0			0
$430$	24.1907	+	5.38078i	1.16658	+	0.259484i
$431$		−	21.9728i		−	1.05839i	−0.848500	−	0.529196i	$-0.822494\pi$
$431$		−	21.9728i		−	1.05839i	0.848500	−	0.529196i	$-0.177506\pi$
$432$		0			0
$433$		−	3.88947i		−	0.186916i	−0.995623	−	0.0934581i	$-0.970208\pi$
$433$		−	3.88947i		−	0.186916i	0.995623	−	0.0934581i	$-0.0297921\pi$
$434$	−10.4105	+	46.8034i	−0.499722	+	2.24663i
$435$		0			0
$436$	4.58547	−	4.18998i	0.219604	−	0.200663i
$437$	−9.85285	−	23.7869i	−0.471326	−	1.13788i
$438$		0			0
$439$	7.39884	+	7.39884i	0.353127	+	0.353127i	0.861272	−	0.508145i	$-0.169668\pi$
$439$	7.39884	+	7.39884i	0.353127	+	0.353127i	−0.508145	+	0.861272i	$0.669668\pi$
$440$	16.3387	−	21.2005i	0.778919	−	1.01069i
$441$		0			0
$442$	−2.62481	−	14.9474i	−0.124849	−	0.710975i
$443$	22.6781	−	9.39359i	1.07747	−	0.446303i	0.227849	−	0.973696i	$-0.426831\pi$
$443$	22.6781	−	9.39359i	1.07747	−	0.446303i	0.849621	+	0.527394i	$0.176831\pi$
$444$		0			0
$445$	8.38399	−	20.2407i	0.397439	−	0.959503i
$446$	−5.01501	+	3.18996i	−0.237468	+	0.151049i
$447$		0			0
$448$	16.2416	−	27.8596i	0.767344	−	1.31624i
$449$	11.7065			0.552464			0.276232	−	0.961091i	$-0.410914\pi$
$449$	11.7065			0.552464			0.276232	+	0.961091i	$0.410914\pi$
$450$		0			0
$451$	−0.684290	+	1.65202i	−0.0322220	+	0.0777907i
$452$	6.23523	+	2.91820i	0.293280	+	0.137261i
$453$		0			0
$454$	−2.99076	−	17.0313i	−0.140363	−	0.799321i
$455$	28.3450	−	28.3450i	1.32883	−	1.32883i
$456$		0			0
$457$	−24.3492	−	24.3492i	−1.13901	−	1.13901i	−0.988628	−	0.150380i	$-0.951950\pi$
$457$	−24.3492	−	24.3492i	−1.13901	−	1.13901i	−0.150380	−	0.988628i	$-0.548050\pi$
$458$	8.28663	−	11.8169i	0.387209	−	0.552166i
$459$		0			0
$460$	−14.1664	+	12.9445i	−0.660510	+	0.603541i
$461$	−19.8716	−	8.23110i	−0.925514	−	0.383360i	−0.131539	−	0.991311i	$-0.541992\pi$
$461$	−19.8716	−	8.23110i	−0.925514	−	0.383360i	−0.793975	+	0.607951i	$0.791992\pi$
$462$		0			0
$463$		−	30.7142i		−	1.42741i	−0.700445	−	0.713706i	$-0.747015\pi$
$463$		−	30.7142i		−	1.42741i	0.700445	−	0.713706i	$-0.252985\pi$
$464$	−37.9775	+	11.8571i	−1.76306	+	0.550452i
$465$		0			0
$466$	−28.8665	−	6.42081i	−1.33721	−	0.297438i
$467$	6.37272	+	2.63967i	0.294894	+	0.122149i	0.525226	−	0.850963i	$-0.323981\pi$
$467$	6.37272	+	2.63967i	0.294894	+	0.122149i	−0.230331	+	0.973112i	$0.573981\pi$
$468$		0			0
$469$	−12.7285	−	30.7294i	−0.587749	−	1.41895i
$470$	−21.3214	−	14.9517i	−0.983484	−	0.689673i
$471$		0			0
$472$	−2.88496	−	5.02129i	−0.132791	−	0.231124i
$473$	−23.0566	+	23.0566i	−1.06014	+	1.06014i
$474$		0			0
$475$	0.478942	−	0.198384i	0.0219754	−	0.00910250i
$476$	18.4458	−	6.68439i	0.845460	−	0.306379i
$477$		0			0
$478$	−4.98777	−	7.84137i	−0.228135	−	0.358656i
$479$	18.1283			0.828305			0.414153	−	0.910207i	$-0.364078\pi$
$479$	18.1283			0.828305			0.414153	+	0.910207i	$0.364078\pi$
$480$		0			0
$481$	2.69684			0.122965
$482$	1.21042	+	1.90292i	0.0551330	+	0.0866758i
$483$		0			0
$484$	4.50314	+	12.4265i	0.204688	+	0.564843i
$485$	−0.964932	+	0.399688i	−0.0438153	+	0.0181489i
$486$		0			0
$487$	1.87257	−	1.87257i	0.0848542	−	0.0848542i	−0.663406	−	0.748260i	$-0.730890\pi$
$487$	1.87257	−	1.87257i	0.0848542	−	0.0848542i	0.748260	+	0.663406i	$0.230890\pi$
$488$	19.8061	+	5.35178i	0.896581	+	0.242264i
$489$		0			0
$490$	24.1514	+	16.9363i	1.09105	+	0.765103i
$491$	−12.7120	−	30.6894i	−0.573684	−	1.38499i	−0.898398	−	0.439183i	$-0.855268\pi$
$491$	−12.7120	−	30.6894i	−0.573684	−	1.38499i	0.324714	−	0.945812i	$-0.394732\pi$
$492$		0			0
$493$	−22.3626	−	9.26291i	−1.00716	−	0.417181i
$494$	36.8373	+	8.19376i	1.65739	+	0.368655i
$495$		0			0
$496$	21.5527	+	25.8326i	0.967747	+	1.15992i
$497$		−	20.7534i		−	0.930917i
$498$		0			0
$499$	−3.71314	−	1.53803i	−0.166223	−	0.0688518i	0.298020	−	0.954560i	$-0.403674\pi$
$499$	−3.71314	−	1.53803i	−0.166223	−	0.0688518i	−0.464243	+	0.885708i	$0.653674\pi$
$500$	14.9515	+	16.3628i	0.668652	+	0.731766i
$501$		0			0
$502$	10.0060	−	14.2687i	0.446589	−	0.636843i
$503$	−16.4875	−	16.4875i	−0.735143	−	0.735143i	0.236491	−	0.971634i	$-0.424003\pi$
$503$	−16.4875	−	16.4875i	−0.735143	−	0.735143i	−0.971634	+	0.236491i	$0.924003\pi$
$504$		0			0
$505$	−11.2785	+	11.2785i	−0.501887	+	0.501887i
$506$	−4.36697	−	24.8684i	−0.194136	−	1.10554i
$507$		0			0
$508$	−7.50702	+	16.0400i	−0.333070	+	0.711660i
$509$	−6.26960	+	15.1361i	−0.277895	+	0.670898i	−0.999777	−	0.0211183i	$-0.993277\pi$
$509$	−6.26960	+	15.1361i	−0.277895	+	0.670898i	0.721882	+	0.692016i	$0.243277\pi$
$510$		0			0
$511$	−11.5138			−0.509339
$512$	−8.52686	−	20.9593i	−0.376837	−	0.926279i
$513$		0			0
$514$	−29.8345	+	18.9772i	−1.31594	+	0.837050i
$515$	3.36188	−	8.11629i	0.148142	−	0.357646i
$516$		0			0
$517$	31.6559	−	13.1123i	1.39223	−	0.576679i
$518$	0.603006	+	3.43392i	0.0264946	+	0.150878i
$519$		0			0
$520$	−3.61254	−	27.8939i	−0.158420	−	1.22323i
$521$	23.0991	+	23.0991i	1.01199	+	1.01199i	0.999927	+	0.0120622i	$0.00383961\pi$
$521$	23.0991	+	23.0991i	1.01199	+	1.01199i	0.0120622	+	0.999927i	$0.496160\pi$
$522$		0			0
$523$	−5.00460	−	12.0822i	−0.218836	−	0.528317i	0.775892	−	0.630866i	$-0.217300\pi$
$523$	−5.00460	−	12.0822i	−0.218836	−	0.528317i	−0.994728	+	0.102549i	$0.967300\pi$
$524$	−3.63506	−	3.97818i	−0.158798	−	0.173787i
$525$		0			0
$526$	−4.51612	+	20.3034i	−0.196912	+	0.885271i
$527$			20.4681i			0.891603i
$528$		0			0
$529$		−	4.89784i		−	0.212950i
$530$	33.8402	+	7.52712i	1.46992	+	0.326957i
$531$		0			0
$532$	−2.19650	+	48.7373i	−0.0952302	+	2.11303i
$533$	0.719082	+	1.73602i	0.0311469	+	0.0751953i
$534$		0			0
$535$	−28.3419	−	28.3419i	−1.22533	−	1.22533i
$536$	−22.5302	−	6.08785i	−0.973158	−	0.262955i
$537$		0			0
$538$	−11.9883	+	2.10519i	−0.516854	+	0.0907612i
$539$	−35.8576	+	14.8527i	−1.54450	+	0.639751i
$540$		0			0
$541$	−10.8290	+	26.1435i	−0.465574	+	1.12400i	0.500501	+	0.865736i	$0.333149\pi$
$541$	−10.8290	+	26.1435i	−0.465574	+	1.12400i	−0.966075	+	0.258260i	$0.916851\pi$
$542$	2.19726	+	3.45436i	0.0943804	+	0.148377i
$543$		0			0
$544$	4.18569	−	13.1146i	0.179460	−	0.562283i
$545$	7.00388			0.300013
$546$		0			0
$547$	14.4643	−	34.9200i	0.618450	−	1.49307i	−0.235053	−	0.971982i	$-0.575527\pi$
$547$	14.4643	−	34.9200i	0.618450	−	1.49307i	0.853503	−	0.521087i	$-0.174473\pi$
$548$	−18.5596	+	6.72565i	−0.792828	+	0.287305i
$549$		0			0
$550$	0.500719	−	0.0879279i	0.0213507	−	0.00374926i
$551$	42.5604	−	42.5604i	1.81313	−	1.81313i
$552$		0			0
$553$	40.1275	+	40.1275i	1.70640	+	1.70640i
$554$	−26.7274	−	18.7427i	−1.13554	−	0.796302i
$555$		0			0
$556$	5.27521	+	0.237743i	0.223719	+	0.0100826i
$557$	1.60723	+	0.665734i	0.0681003	+	0.0282081i	0.416474	−	0.909148i	$-0.363266\pi$
$557$	1.60723	+	0.665734i	0.0681003	+	0.0282081i	−0.348373	+	0.937356i	$0.613266\pi$
$558$		0			0
$559$			34.2648i			1.44925i
$560$	34.7098	−	10.8369i	1.46676	−	0.457941i
$561$		0			0
$562$	4.44723	−	19.9937i	0.187595	−	0.843384i
$563$	−19.2851	−	7.98816i	−0.812771	−	0.336661i	−0.0627123	−	0.998032i	$-0.519975\pi$
$563$	−19.2851	−	7.98816i	−0.812771	−	0.336661i	−0.750059	+	0.661371i	$0.769975\pi$
$564$		0			0
$565$	2.97061	+	7.17168i	0.124974	+	0.301715i
$566$	0.492965	−	0.702976i	0.0207209	−	0.0295483i
$567$		0			0
$568$	−11.5340	−	8.88905i	−0.483958	−	0.372976i
$569$	9.58320	−	9.58320i	0.401749	−	0.401749i	−0.477100	−	0.878849i	$-0.658312\pi$
$569$	9.58320	−	9.58320i	0.401749	−	0.401749i	0.878849	+	0.477100i	$0.158312\pi$
$570$		0			0
$571$	23.4595	−	9.71724i	0.981749	−	0.406654i	0.166676	−	0.986012i	$-0.446697\pi$
$571$	23.4595	−	9.71724i	0.981749	−	0.406654i	0.815073	+	0.579358i	$0.196697\pi$
$572$	33.5186	+	15.6873i	1.40148	+	0.655919i
$573$		0			0
$574$	−2.04970	+	1.30378i	−0.0855530	+	0.0544189i
$575$	−0.364482			−0.0152000
$576$		0			0
$577$	−8.54443			−0.355709			−0.177855	−	0.984057i	$-0.556916\pi$
$577$	−8.54443			−0.355709			−0.177855	+	0.984057i	$0.556916\pi$
$578$	−13.2187	+	8.40821i	−0.549826	+	0.349735i
$579$		0			0
$580$	−40.6311	−	19.0161i	−1.68712	−	0.789601i
$581$	−37.1837	+	15.4020i	−1.54264	+	0.638982i
$582$		0			0
$583$	−32.2536	+	32.2536i	−1.33581	+	1.33581i
$584$	−4.93155	+	6.39897i	−0.204069	+	0.264791i
$585$		0			0
$586$	−14.6765	+	20.9289i	−0.606279	+	0.864563i
$587$	−0.337800	−	0.815522i	−0.0139425	−	0.0336602i	0.916755	−	0.399450i	$-0.130799\pi$
$587$	−0.337800	−	0.815522i	−0.0139425	−	0.0336602i	−0.930697	+	0.365790i	$0.880799\pi$
$588$		0			0
$589$	−47.0224	−	19.4773i	−1.93753	−	0.802550i
$590$	1.41779	−	6.37406i	0.0583695	−	0.262416i
$591$		0			0
$592$	2.16673	+	1.13568i	0.0890522	+	0.0466760i
$593$		−	39.5130i		−	1.62260i	−0.584628	−	0.811301i	$-0.698760\pi$
$593$		−	39.5130i		−	1.62260i	0.584628	−	0.811301i	$-0.301240\pi$
$594$		0			0
$595$	20.4385	+	8.46590i	0.837896	+	0.347068i
$596$	−39.1668	−	1.76517i	−1.60433	−	0.0723041i
$597$		0			0
$598$	−21.7236	−	15.2338i	−0.888346	−	0.622956i
$599$	19.3067	+	19.3067i	0.788852	+	0.788852i	0.981306	−	0.192454i	$-0.0616447\pi$
$599$	19.3067	+	19.3067i	0.788852	+	0.788852i	−0.192454	+	0.981306i	$0.561645\pi$
$600$		0			0
$601$	9.25969	−	9.25969i	0.377711	−	0.377711i	−0.492565	−	0.870276i	$-0.663941\pi$
$601$	9.25969	−	9.25969i	0.377711	−	0.377711i	0.870276	+	0.492565i	$0.163941\pi$
$602$	−43.6297	+	7.66151i	−1.77821	+	0.312260i
$603$		0			0
$604$	23.2418	−	8.42239i	0.945696	−	0.342702i
$605$	−5.70331	+	13.7690i	−0.231872	+	0.559790i
$606$		0			0
$607$	41.1980			1.67218			0.836088	−	0.548595i	$-0.184837\pi$
$607$	41.1980			1.67218			0.836088	+	0.548595i	$0.184837\pi$
$608$	26.1458	+	22.0958i	1.06035	+	0.896104i
$609$		0			0
$610$	12.4160	+	19.5195i	0.502711	+	0.790322i
$611$	13.7790	−	33.2655i	0.557439	−	1.34578i
$612$		0			0
$613$	29.3158	−	12.1430i	1.18406	−	0.490452i	0.298241	−	0.954491i	$-0.403600\pi$
$613$	29.3158	−	12.1430i	1.18406	−	0.490452i	0.885815	+	0.464039i	$0.153600\pi$
$614$	14.9298	−	2.62172i	0.602518	−	0.105804i
$615$		0			0
$616$	−12.4802	+	46.1872i	−0.502840	+	1.86093i
$617$	1.14955	+	1.14955i	0.0462792	+	0.0462792i	0.729868	−	0.683588i	$-0.239582\pi$
$617$	1.14955	+	1.14955i	0.0462792	+	0.0462792i	−0.683588	+	0.729868i	$0.739582\pi$
$618$		0			0
$619$	−17.8628	−	43.1245i	−0.717965	−	1.73332i	−0.679065	−	0.734078i	$-0.737615\pi$
$619$	−17.8628	−	43.1245i	−0.717965	−	1.73332i	−0.0388998	−	0.999243i	$-0.512385\pi$
$620$	−1.70791	+	37.8963i	−0.0685913	+	1.52195i
$621$		0			0
$622$	30.3817	+	6.75785i	1.21820	+	0.270965i
$623$			39.1609i			1.56895i
$624$		0			0
$625$			25.4210i			1.01684i
$626$	−9.32923	+	41.9421i	−0.372871	+	1.67634i
$627$		0			0
$628$	22.8339	+	24.9892i	0.911173	+	0.997179i
$629$	0.569557	+	1.37503i	0.0227097	+	0.0548262i
$630$		0			0
$631$	−12.8227	−	12.8227i	−0.510465	−	0.510465i	0.404204	−	0.914669i	$-0.367549\pi$
$631$	−12.8227	−	12.8227i	−0.510465	−	0.510465i	−0.914669	+	0.404204i	$0.867549\pi$
$632$	39.4889	−	5.11421i	1.57078	−	0.203432i
$633$		0			0
$634$	2.78193	+	15.8421i	0.110484	+	0.629171i
$635$	−18.4490	+	7.64183i	−0.732127	+	0.303257i
$636$		0			0
$637$	−15.6079	+	37.6808i	−0.618407	+	1.49297i
$638$	49.8041	−	31.6796i	1.97176	−	1.25421i
$639$		0			0
$640$	8.84404	−	23.9322i	0.349592	−	0.946002i
$641$	−41.8175			−1.65169			−0.825846	−	0.563896i	$-0.809302\pi$
$641$	−41.8175			−1.65169			−0.825846	+	0.563896i	$0.809302\pi$
$642$		0			0
$643$	−5.37358	+	12.9730i	−0.211913	+	0.511604i	−0.993717	−	0.111920i	$-0.964300\pi$
$643$	−5.37358	+	12.9730i	−0.211913	+	0.511604i	0.781804	+	0.623525i	$0.214300\pi$
$644$	14.5400	−	31.0672i	0.572956	−	1.22422i
$645$		0			0
$646$	3.60208	+	20.5126i	0.141722	+	0.807058i
$647$	−6.96582	+	6.96582i	−0.273854	+	0.273854i	−0.830650	−	0.556795i	$-0.812031\pi$
$647$	−6.96582	+	6.96582i	−0.273854	+	0.273854i	0.556795	+	0.830650i	$0.312031\pi$
$648$		0			0
$649$	6.07521	+	6.07521i	0.238473	+	0.238473i
$650$	0.306729	−	0.437400i	0.0120309	−	0.0171562i
$651$		0			0
$652$	0.959247	+	1.04979i	0.0375670	+	0.0411129i
$653$	33.1423	+	13.7280i	1.29696	+	0.537218i	0.921052	−	0.389440i	$-0.127331\pi$
$653$	33.1423	+	13.7280i	1.29696	+	0.537218i	0.375906	+	0.926658i	$0.377331\pi$
$654$		0			0
$655$		−	6.07630i		−	0.237421i
$656$	−0.153326	+	1.69759i	−0.00598636	+	0.0662798i
$657$		0			0
$658$	45.4382	+	10.1069i	1.77136	+	0.394007i
$659$	7.43115	+	3.07808i	0.289477	+	0.119905i	0.522696	−	0.852519i	$-0.324926\pi$
$659$	7.43115	+	3.07808i	0.289477	+	0.119905i	−0.233220	+	0.972424i	$0.574926\pi$
$660$		0			0
$661$	11.6998	+	28.2458i	0.455069	+	1.09863i	0.970370	+	0.241625i	$0.0776804\pi$
$661$	11.6998	+	28.2458i	0.455069	+	1.09863i	−0.515300	+	0.857010i	$0.672320\pi$
$662$	−29.7068	−	20.8320i	−1.15459	−	0.809660i
$663$		0			0
$664$	−7.36652	+	27.2624i	−0.285877	+	1.05799i
$665$	−38.8984	+	38.8984i	−1.50841	+	1.50841i
$666$		0			0
$667$	−39.0971	+	16.1945i	−1.51385	+	0.627055i
$668$	6.89059	+	19.0148i	0.266605	+	0.735704i
$669$		0			0
$670$	−14.1237	−	22.2042i	−0.545647	−	0.857823i
$671$	−30.4383			−1.17506
$672$		0			0
$673$	6.05688			0.233475			0.116738	−	0.993163i	$-0.462756\pi$
$673$	6.05688			0.233475			0.116738	+	0.993163i	$0.462756\pi$
$674$	−14.1771	−	22.2882i	−0.546083	−	0.858508i
$675$		0			0
$676$	12.1184	−	4.39148i	0.466093	−	0.168903i
$677$	24.4632	−	10.1330i	0.940197	−	0.389442i	0.140659	−	0.990058i	$-0.455078\pi$
$677$	24.4632	−	10.1330i	0.940197	−	0.389442i	0.799538	+	0.600616i	$0.205078\pi$
$678$		0			0
$679$	1.32010	−	1.32010i	0.0506609	−	0.0506609i
$680$	13.4592	−	7.73294i	0.516138	−	0.296545i
$681$		0			0
$682$	−40.8660	−	28.6575i	−1.56484	−	1.09735i
$683$	−1.74140	−	4.20410i	−0.0666327	−	0.160865i	0.887055	−	0.461663i	$-0.152747\pi$
$683$	−1.74140	−	4.20410i	−0.0666327	−	0.160865i	−0.953688	+	0.300798i	$0.902747\pi$
$684$		0			0
$685$	−20.5646	−	8.51815i	−0.785734	−	0.325462i
$686$	−12.5160	−	2.78396i	−0.477864	−	0.106292i
$687$		0			0
$688$	−14.4294	+	27.5295i	−0.550115	+	1.04955i
$689$			47.9327i			1.82609i
$690$		0			0
$691$	3.11071	+	1.28850i	0.118337	+	0.0490167i	0.441066	−	0.897475i	$-0.354600\pi$
$691$	3.11071	+	1.28850i	0.118337	+	0.0490167i	−0.322729	+	0.946491i	$0.604600\pi$
$692$	2.32878	−	2.12792i	0.0885267	−	0.0808914i
$693$		0			0
$694$	16.0122	−	22.8336i	0.607815	−	0.866753i
$695$	4.21026	+	4.21026i	0.159704	+	0.159704i
$696$		0			0
$697$	−0.733274	+	0.733274i	−0.0277747	+	0.0277747i
$698$	−3.07478	−	17.5099i	−0.116382	−	0.662758i
$699$		0			0
$700$	0.625529	+	0.292759i	0.0236428	+	0.0110653i
$701$	3.22162	−	7.77768i	0.121679	−	0.293759i	−0.851290	−	0.524696i	$-0.824179\pi$
$701$	3.22162	−	7.77768i	0.121679	−	0.293759i	0.972969	+	0.230937i	$0.0741791\pi$
$702$		0			0
$703$	−3.70093			−0.139583
$704$	20.3238	+	26.7188i	0.765983	+	1.00700i
$705$		0			0
$706$	−21.6561	+	13.7751i	−0.815039	+	0.518433i
$707$	10.9106	−	26.3405i	0.410335	−	0.990635i
$708$		0			0
$709$	−39.9776	+	16.5592i	−1.50139	+	0.621896i	−0.973760	−	0.227579i	$-0.926919\pi$
$709$	−39.9776	+	16.5592i	−1.50139	+	0.621896i	−0.527629	+	0.849475i	$0.676919\pi$
$710$	−2.83988	−	16.1721i	−0.106579	−	0.606930i
$711$		0			0
$712$	21.7643	+	16.7733i	0.815652	+	0.628606i
$713$	25.3037	+	25.3037i	0.947629	+	0.947629i
$714$		0			0
$715$	15.9690	+	38.5526i	0.597208	+	1.44179i
$716$	6.29064	−	5.74808i	0.235092	−	0.214816i
$717$		0			0
$718$	−1.70993	+	7.68746i	−0.0638141	+	0.286893i
$719$			12.6156i			0.470482i	0.971937	+	0.235241i	$0.0755879\pi$
$719$			12.6156i			0.470482i	−0.971937	+	0.235241i	$0.924412\pi$
$720$		0			0
$721$			15.7030i			0.584812i
$722$	−24.3234	−	5.41030i	−0.905225	−	0.201351i
$723$		0			0
$724$	33.7168	+	1.51955i	1.25308	+	0.0564737i
$725$	−0.326073	−	0.787210i	−0.0121100	−	0.0292362i
$726$		0			0
$727$	−25.6586	−	25.6586i	−0.951625	−	0.951625i	0.0472578	−	0.998883i	$-0.484952\pi$
$727$	−25.6586	−	25.6586i	−0.951625	−	0.951625i	−0.998883	+	0.0472578i	$0.984952\pi$
$728$	25.0463	+	43.5933i	0.928278	+	1.61567i
$729$		0			0
$730$	−8.97213	+	1.57553i	−0.332074	+	0.0583131i
$731$	−17.4705	+	7.23653i	−0.646170	+	0.267653i
$732$		0			0
$733$	3.96810	−	9.57983i	0.146565	−	0.353839i	−0.833499	−	0.552521i	$-0.813666\pi$
$733$	3.96810	−	9.57983i	0.146565	−	0.353839i	0.980064	+	0.198682i	$0.0636660\pi$
$734$	−14.1973	−	22.3198i	−0.524030	−	0.823839i
$735$		0			0
$736$	−11.0384	−	21.3875i	−0.406879	−	0.788353i
$737$	34.6247			1.27542
$738$		0			0
$739$	10.0007	−	24.1438i	0.367881	−	0.888143i	−0.626216	−	0.779650i	$-0.715397\pi$
$739$	10.0007	−	24.1438i	0.367881	−	0.888143i	0.994097	−	0.108494i	$-0.0346028\pi$
$740$	0.939789	+	2.59337i	0.0345473	+	0.0953343i
$741$		0			0
$742$	−61.0332	+	10.7176i	−2.24060	+	0.393456i
$743$	19.5551	−	19.5551i	0.717406	−	0.717406i	−0.250667	−	0.968073i	$-0.580650\pi$
$743$	19.5551	−	19.5551i	0.717406	−	0.717406i	0.968073	+	0.250667i	$0.0806500\pi$
$744$		0			0
$745$	−31.2599	−	31.2599i	−1.14527	−	1.14527i
$746$	1.38555	+	0.971622i	0.0507285	+	0.0355736i
$747$		0			0
$748$	−0.919528	+	20.4031i	−0.0336213	+	0.746012i
$749$	66.1913	+	27.4173i	2.41858	+	1.00181i
$750$		0			0
$751$		−	11.3314i		−	0.413488i	−0.978395	−	0.206744i	$-0.933713\pi$
$751$		−	11.3314i		−	0.413488i	0.978395	−	0.206744i	$-0.0662867\pi$
$752$	25.0790	−	20.9241i	0.914539	−	0.763022i
$753$		0			0
$754$	13.4676	−	60.5472i	0.490461	−	2.20500i
$755$	25.7527	+	10.6671i	0.937235	+	0.388215i
$756$		0			0
$757$	9.52720	+	23.0007i	0.346272	+	0.835974i	0.997054	+	0.0767093i	$0.0244413\pi$
$757$	9.52720	+	23.0007i	0.346272	+	0.835974i	−0.650782	+	0.759265i	$0.725559\pi$
$758$	−18.6176	+	26.5489i	−0.676220	+	0.964301i
$759$		0			0
$760$	4.95755	+	38.2793i	0.179829	+	1.38854i
$761$	7.15967	−	7.15967i	0.259538	−	0.259538i	−0.565328	−	0.824866i	$-0.691250\pi$
$761$	7.15967	−	7.15967i	0.259538	−	0.259538i	0.824866	+	0.565328i	$0.191250\pi$
$762$		0			0
$763$	−11.5663	+	4.79093i	−0.418729	+	0.173443i
$764$	−12.2841	+	26.2471i	−0.444423	+	0.949585i
$765$		0			0
$766$	35.5521	−	22.6141i	1.28455	−	0.817080i
$767$	9.02848			0.326000
$768$		0			0
$769$	−34.3231			−1.23772			−0.618861	−	0.785500i	$-0.712406\pi$
$769$	−34.3231			−1.23772			−0.618861	+	0.785500i	$0.712406\pi$
$770$	−45.5188	+	28.9538i	−1.64038	+	1.04342i
$771$		0			0
$772$	−7.51180	+	16.0502i	−0.270356	+	0.577660i
$773$	22.9617	−	9.51107i	0.825876	−	0.342089i	0.0706075	−	0.997504i	$-0.477506\pi$
$773$	22.9617	−	9.51107i	0.825876	−	0.342089i	0.755269	+	0.655415i	$0.227506\pi$
$774$		0			0
$775$	−0.509482	+	0.509482i	−0.0183011	+	0.0183011i
$776$	−0.168246	−	1.29909i	−0.00603967	−	0.0466347i
$777$		0			0
$778$	27.8438	−	39.7057i	0.998249	−	1.42352i
$779$	−0.986811	−	2.38237i	−0.0353562	−	0.0853573i
$780$		0			0
$781$	19.9596	+	8.26754i	0.714211	+	0.295836i
$782$	3.17932	−	14.2935i	0.113692	−	0.511134i
$783$		0			0
$784$	−28.4078	+	23.7013i	−1.01456	+	0.846476i
$785$			38.1688i			1.36230i
$786$		0			0
$787$	−5.00037	−	2.07122i	−0.178244	−	0.0738311i	0.291777	−	0.956486i	$-0.405754\pi$
$787$	−5.00037	−	2.07122i	−0.178244	−	0.0738311i	−0.470021	+	0.882655i	$0.655754\pi$
$788$	0.293433	−	6.51090i	0.0104531	−	0.231941i
$789$		0			0
$790$	36.7605	+	25.7785i	1.30788	+	0.917157i
$791$	−9.81142	−	9.81142i	−0.348854	−	0.348854i
$792$		0			0
$793$	−22.6174	+	22.6174i	−0.803169	+	0.803169i
$794$	1.14207	−	0.200552i	0.0405307	−	0.00711731i
$795$		0			0
$796$	−7.14189	−	19.7083i	−0.253138	−	0.698541i
$797$	−13.4012	+	32.3532i	−0.474693	+	1.14601i	0.487373	+	0.873194i	$0.337955\pi$
$797$	−13.4012	+	32.3532i	−0.474693	+	1.14601i	−0.962066	+	0.272817i	$0.912045\pi$
$798$		0			0
$799$	19.8710			0.702987
$800$	0.430631	−	0.222254i	0.0152251	−	0.00785788i
$801$		0			0
$802$	7.63249	+	11.9992i	0.269513	+	0.423706i
$803$	4.58674	−	11.0734i	0.161863	−	0.390771i
$804$		0			0
$805$	35.7330	−	14.8011i	1.25942	−	0.521671i
$806$	−51.6600	+	9.07166i	−1.81965	+	0.319536i
$807$		0			0
$808$	−9.96596	−	17.3458i	−0.350601	−	0.610224i
$809$	−21.2492	−	21.2492i	−0.747081	−	0.747081i	0.226849	−	0.973930i	$-0.427158\pi$
$809$	−21.2492	−	21.2492i	−0.747081	−	0.747081i	−0.973930	+	0.226849i	$0.927158\pi$
$810$		0			0
$811$	5.57542	+	13.4602i	0.195779	+	0.472653i	0.991032	−	0.133625i	$-0.0426618\pi$
$811$	5.57542	+	13.4602i	0.195779	+	0.472653i	−0.795253	+	0.606278i	$0.792662\pi$
$812$	80.1067	+	3.61025i	2.81120	+	0.126695i
$813$		0			0
$814$	−3.54279	−	0.788029i	−0.124175	−	0.0276204i
$815$			1.60346i			0.0561667i
$816$		0			0
$817$		−	47.0223i		−	1.64510i
$818$	5.40782	−	24.3123i	0.189080	−	0.850059i
$819$		0			0
$820$	−1.41883	+	1.29646i	−0.0495477	+	0.0452742i
$821$	−20.2070	−	48.7840i	−0.705229	−	1.70257i	−0.711591	−	0.702594i	$-0.752025\pi$
$821$	−20.2070	−	48.7840i	−0.705229	−	1.70257i	0.00636188	−	0.999980i	$-0.497975\pi$
$822$		0			0
$823$	−0.0550181	−	0.0550181i	−0.00191781	−	0.00191781i	0.706147	−	0.708065i	$-0.250432\pi$
$823$	−0.0550181	−	0.0550181i	−0.00191781	−	0.00191781i	−0.708065	+	0.706147i	$0.750432\pi$
$824$	8.72723	+	6.72589i	0.304027	+	0.234308i
$825$		0			0
$826$	2.01874	+	11.4961i	0.0702410	+	0.399999i
$827$	5.73683	−	2.37627i	0.199489	−	0.0826310i	−0.280702	−	0.959795i	$-0.590567\pi$
$827$	5.73683	−	2.37627i	0.199489	−	0.0826310i	0.480191	+	0.877164i	$0.340567\pi$
$828$		0			0
$829$	11.8640	−	28.6423i	0.412055	−	0.994790i	−0.572530	−	0.819884i	$-0.694038\pi$
$829$	11.8640	−	28.6423i	0.412055	−	0.994790i	0.984585	−	0.174906i	$-0.0559621\pi$
$830$	−26.8679	+	17.0902i	−0.932599	+	0.593211i
$831$		0			0
$832$	34.9555	+	4.75188i	1.21186	+	0.164742i
$833$	−22.5085			−0.779873
$834$		0			0
$835$	−8.72705	+	21.0690i	−0.302012	+	0.729122i
$836$	−45.9982	−	21.5280i	−1.59088	−	0.744562i
$837$		0			0
$838$	6.83390	+	38.9167i	0.236073	+	1.34436i
$839$	−24.2642	+	24.2642i	−0.837694	+	0.837694i	−0.988555	−	0.150861i	$-0.951795\pi$
$839$	−24.2642	+	24.2642i	−0.837694	+	0.837694i	0.150861	+	0.988555i	$0.451795\pi$
$840$		0			0
$841$	−49.4480	−	49.4480i	−1.70510	−	1.70510i
$842$	6.76726	−	9.65023i	0.233215	−	0.332569i
$843$		0			0
$844$	41.5070	−	37.9270i	1.42873	−	1.30550i
$845$	13.4276	+	5.56188i	0.461923	+	0.191335i
$846$		0			0
$847$		−	26.6397i		−	0.915350i
$848$	−20.1851	+	38.5107i	−0.693159	+	1.32246i
$849$		0			0
$850$	0.287795	+	0.0640147i	0.00987130	+	0.00219569i
$851$	2.40400	+	0.995769i	0.0824081	+	0.0341345i
$852$		0			0
$853$	−7.92253	−	19.1267i	−0.271262	−	0.654885i	0.728276	−	0.685284i	$-0.240322\pi$
$853$	−7.92253	−	19.1267i	−0.271262	−	0.654885i	−0.999538	+	0.0303994i	$0.990322\pi$
$854$	−33.8562	−	23.7418i	−1.15854	−	0.812428i
$855$		0			0
$856$	43.5885	−	25.0436i	1.48983	−	0.855972i
$857$	−26.8084	+	26.8084i	−0.915758	+	0.915758i	−0.996717	−	0.0809594i	$-0.974202\pi$
$857$	−26.8084	+	26.8084i	−0.915758	+	0.915758i	0.0809594	+	0.996717i	$0.474202\pi$
$858$		0			0
$859$	−4.81751	+	1.99548i	−0.164371	+	0.0680848i	−0.463352	−	0.886174i	$-0.653353\pi$
$859$	−4.81751	+	1.99548i	−0.164371	+	0.0680848i	0.298981	+	0.954259i	$0.403353\pi$
$860$	−32.9502	+	11.9405i	−1.12359	+	0.407168i
$861$		0			0
$862$	16.6778	+	26.2195i	0.568047	+	0.893038i
$863$	37.7248			1.28417			0.642084	−	0.766634i	$-0.278070\pi$
$863$	37.7248			1.28417			0.642084	+	0.766634i	$0.278070\pi$
$864$		0			0
$865$	3.55699			0.120941
$866$	2.95218	+	4.64119i	0.100319	+	0.157714i
$867$		0			0
$868$	−23.1021	−	63.7508i	−0.784135	−	2.16384i
$869$	−54.5783	+	22.6071i	−1.85144	+	0.766893i
$870$		0			0
$871$	25.7282	−	25.7282i	0.871767	−	0.871767i
$872$	−2.29143	+	8.48022i	−0.0775975	+	0.287177i
$873$		0			0
$874$	29.8118	+	20.9056i	1.00840	+	0.707144i
$875$	−17.0960	−	41.2733i	−0.577949	−	1.39529i
$876$		0			0
$877$	30.3851	+	12.5859i	1.02603	+	0.424996i	0.831279	−	0.555856i	$-0.187609\pi$
$877$	30.3851	+	12.5859i	1.02603	+	0.424996i	0.194754	+	0.980852i	$0.437609\pi$
$878$	−14.4447	−	3.21295i	−0.487484	−	0.108432i
$879$		0			0
$880$	−3.40498	+	37.6993i	−0.114782	+	1.27084i
$881$			31.6972i			1.06790i	0.845515	+	0.533952i	$0.179294\pi$
$881$			31.6972i			1.06790i	−0.845515	+	0.533952i	$0.820706\pi$
$882$		0			0
$883$	−43.6690	−	18.0883i	−1.46958	−	0.608719i	−0.502815	−	0.864394i	$-0.667702\pi$
$883$	−43.6690	−	18.0883i	−1.46958	−	0.608719i	−0.966763	+	0.255675i	$0.917702\pi$
$884$	14.4775	+	15.8440i	0.486930	+	0.532891i
$885$		0			0
$886$	−19.9312	+	28.4222i	−0.669601	+	0.954862i
$887$	−25.0660	−	25.0660i	−0.841633	−	0.841633i	0.147438	−	0.989071i	$-0.452897\pi$
$887$	−25.0660	−	25.0660i	−0.841633	−	0.841633i	−0.989071	+	0.147438i	$0.952897\pi$
$888$		0			0
$889$	25.2397	−	25.2397i	0.846513	−	0.846513i
$890$	5.35874	+	30.5162i	0.179626	+	1.02291i
$891$		0			0
$892$	3.56301	−	7.61297i	0.119298	−	0.254901i
$893$	−18.9092	+	45.6508i	−0.632772	+	1.52765i
$894$		0			0
$895$	9.60837			0.321172
$896$	1.76533	+	45.5717i	0.0589756	+	1.52244i
$897$		0			0
$898$	−13.9690	+	8.88546i	−0.466152	+	0.296512i
$899$	−32.0138	+	77.2881i	−1.06772	+	2.57770i
$900$		0			0
$901$	−24.4393	+	10.1231i	−0.814192	+	0.337249i
$902$	−0.437374	−	2.49070i	−0.0145630	−	0.0829311i
$903$		0			0
$904$	−9.65527	+	1.25046i	−0.321129	+	0.0415895i
$905$	26.9102	+	26.9102i	0.894524	+	0.894524i
$906$		0			0
$907$	−19.7109	−	47.5863i	−0.654489	−	1.58008i	−0.806194	−	0.591651i	$-0.798476\pi$
$907$	−19.7109	−	47.5863i	−0.654489	−	1.58008i	0.151705	−	0.988426i	$-0.451524\pi$
$908$	16.4959	+	18.0529i	0.547435	+	0.599108i
$909$		0			0
$910$	−12.3088	+	55.3375i	−0.408033	+	1.83442i
$911$			11.5753i			0.383506i	0.981443	+	0.191753i	$0.0614173\pi$
$911$			11.5753i			0.383506i	−0.981443	+	0.191753i	$0.938583\pi$
$912$		0			0
$913$		−	41.8972i		−	1.38659i
$914$	47.5367	+	10.5736i	1.57237	+	0.349745i
$915$		0			0
$916$	−0.918956	+	20.3904i	−0.0303631	+	0.673718i
$917$	4.15643	+	10.0345i	0.137257	+	0.331369i
$918$		0			0
$919$	0.632326	+	0.632326i	0.0208585	+	0.0208585i	0.717459	−	0.696601i	$-0.245305\pi$
$919$	0.632326	+	0.632326i	0.0208585	+	0.0208585i	−0.696601	+	0.717459i	$0.745305\pi$
$920$	7.07914	−	26.1988i	0.233392	−	0.863749i
$921$		0			0
$922$	29.9597	−	5.26102i	0.986672	−	0.173263i
$923$	20.9744	−	8.68790i	0.690382	−	0.285966i
$924$		0			0
$925$	−0.0200496	+	0.0484039i	−0.000659225	+	0.00159151i
$926$	23.3127	+	36.6503i	0.766102	+	1.20441i
$927$		0			0
$928$	36.3176	−	42.9743i	1.19218	−	1.41070i
$929$	17.1062			0.561236			0.280618	−	0.959820i	$-0.409461\pi$
$929$	17.1062			0.561236			0.280618	+	0.959820i	$0.409461\pi$
$930$		0			0
$931$	21.4190	−	51.7101i	0.701980	−	1.69473i
$932$	39.3190	−	14.2484i	1.28794	−	0.466723i
$933$		0			0
$934$	−9.60793	+	1.68718i	−0.314381	+	0.0552063i
$935$	−16.2842	+	16.2842i	−0.532550	+	0.532550i
$936$		0			0
$937$	−26.7705	−	26.7705i	−0.874553	−	0.874553i	0.118412	−	0.992965i	$-0.462220\pi$
$937$	−26.7705	−	26.7705i	−0.874553	−	0.874553i	−0.992965	+	0.118412i	$0.962220\pi$
$938$	38.5127	+	27.0072i	1.25749	+	0.881818i
$939$		0			0
$940$	36.7909	+	1.65809i	1.19999	+	0.0540810i
$941$	20.3204	+	8.41699i	0.662427	+	0.274386i	0.688459	−	0.725275i	$-0.258287\pi$
$941$	20.3204	+	8.41699i	0.662427	+	0.274386i	−0.0260325	+	0.999661i	$0.508287\pi$
$942$		0			0
$943$			1.81302i			0.0590401i
$944$	7.25379	+	3.80202i	0.236091	+	0.123745i
$945$		0			0
$946$	10.0123	−	45.0131i	0.325529	−	1.46350i
$947$	−5.02768	−	2.08253i	−0.163378	−	0.0676733i	0.299496	−	0.954098i	$-0.403182\pi$
$947$	−5.02768	−	2.08253i	−0.163378	−	0.0676733i	−0.462873	+	0.886424i	$0.653182\pi$
$948$		0			0
$949$	−4.81995	−	11.6364i	−0.156462	−	0.377733i
$950$	−0.420930	+	0.600252i	−0.0136568	+	0.0194748i
$951$		0			0
$952$	−16.9372	+	21.9770i	−0.548937	+	0.712277i
$953$	−27.5589	+	27.5589i	−0.892719	+	0.892719i	−0.994778	−	0.102059i	$-0.967457\pi$
$953$	−27.5589	+	27.5589i	−0.892719	+	0.892719i	0.102059	+	0.994778i	$0.467457\pi$
$954$		0			0
$955$	−30.1890	+	12.5047i	−0.976894	+	0.404643i
$956$	11.9035	+	5.57105i	0.384986	+	0.180181i
$957$		0			0
$958$	−21.6320	+	13.7598i	−0.698898	+	0.444557i
$959$	39.7876			1.28481
$960$		0			0
$961$	39.7402			1.28194
$962$	−3.21806	+	2.04695i	−0.103754	+	0.0659964i
$963$		0			0
$964$	−2.88871	−	1.35197i	−0.0930390	−	0.0435440i
$965$	−18.4608	+	7.64670i	−0.594273	+	0.246156i
$966$		0			0
$967$	16.5604	−	16.5604i	0.532547	−	0.532547i	−0.388783	−	0.921329i	$-0.627104\pi$
$967$	16.5604	−	16.5604i	0.532547	−	0.532547i	0.921329	+	0.388783i	$0.127104\pi$
$968$	−14.8054	−	11.4102i	−0.475865	−	0.366739i
$969$		0			0
$970$	0.848052	−	1.20934i	0.0272293	−	0.0388294i
$971$	−10.1344	−	24.4667i	−0.325230	−	0.785174i	−0.998933	−	0.0461727i	$-0.985298\pi$
$971$	−10.1344	−	24.4667i	−0.325230	−	0.785174i	0.673704	−	0.739002i	$-0.264702\pi$
$972$		0			0
$973$	−9.83288	−	4.07291i	−0.315228	−	0.130572i
$974$	−0.813164	+	3.65580i	−0.0260554	+	0.117139i
$975$		0			0
$976$	−27.6961	+	8.64711i	−0.886532	+	0.276787i
$977$		−	22.8534i		−	0.731144i	−0.930783	−	0.365572i	$-0.880873\pi$
$977$		−	22.8534i		−	0.731144i	0.930783	−	0.365572i	$-0.119127\pi$
$978$		0			0
$979$	−37.6630	−	15.6005i	−1.20372	−	0.498595i
$980$	−41.6741	−	1.87817i	−1.33123	−	0.0599959i
$981$		0			0
$982$	38.4627	+	26.9721i	1.22739	+	0.860715i
$983$	−37.4286	−	37.4286i	−1.19379	−	1.19379i	−0.975996	−	0.217790i	$-0.930115\pi$
$983$	−37.4286	−	37.4286i	−1.19379	−	1.19379i	−0.217790	−	0.975996i	$-0.569885\pi$
$984$		0			0
$985$	5.19650	−	5.19650i	0.165574	−	0.165574i
$986$	33.7154	−	5.92052i	1.07372	−	0.188548i
$987$		0			0
$988$	−50.1760	+	18.1828i	−1.59631	+	0.578472i
$989$	−12.6518	+	30.5441i	−0.402303	+	0.971245i
$990$		0			0
$991$	−8.18399			−0.259973			−0.129987	−	0.991516i	$-0.541493\pi$
$991$	−8.18399			−0.259973			−0.129987	+	0.991516i	$0.541493\pi$
$992$	−45.3256	−	14.4663i	−1.43909	−	0.459304i
$993$		0			0
$994$	15.7522	+	24.7644i	0.499630	+	0.785478i
$995$	9.04533	−	21.8374i	0.286756	−	0.692291i
$996$		0			0
$997$	−2.09960	+	0.869684i	−0.0664951	+	0.0275432i	−0.415683	−	0.909510i	$-0.636457\pi$
$997$	−2.09960	+	0.869684i	−0.0664951	+	0.0275432i	0.349188	+	0.937053i	$0.386457\pi$
$998$	5.59817	−	0.983055i	0.177207	−	0.0311181i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.b.109.5	✓	128
3.2	odd	2	inner	864.2.v.b.109.28	yes	128
32.5	even	8	inner	864.2.v.b.325.5	yes	128
96.5	odd	8	inner	864.2.v.b.325.28	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.b.109.5	✓	128	1.1	even	1	trivial
864.2.v.b.109.28	yes	128	3.2	odd	2	inner
864.2.v.b.325.5	yes	128	32.5	even	8	inner
864.2.v.b.325.28	yes	128	96.5	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19327 + 0.759019i) q^{2} +(0.847781 - 1.81143i) q^{4} +(2.08348 - 0.863006i) q^{5} +(-2.85037 + 2.85037i) q^{7} +(0.363276 + 2.80500i) q^{8} +O(q^{10})\)	\(q+(-1.19327 + 0.759019i) q^{2} +(0.847781 - 1.81143i) q^{4} +(2.08348 - 0.863006i) q^{5} +(-2.85037 + 2.85037i) q^{7} +(0.363276 + 2.80500i) q^{8} +(-1.83111 + 2.61120i) q^{10} +(-1.60584 - 3.87685i) q^{11} +(-4.07396 - 1.68749i) q^{13} +(1.23777 - 5.56473i) q^{14} +(-2.56253 - 3.07139i) q^{16} -2.43357i q^{17} +(5.59078 + 2.31578i) q^{19} +(0.203063 - 4.50571i) q^{20} +(4.85880 + 3.40725i) q^{22} +(-3.00850 - 3.00850i) q^{23} +(0.0605754 - 0.0605754i) q^{25} +(6.14217 - 1.07858i) q^{26} +(2.74674 + 7.57972i) q^{28} +(3.80631 - 9.18924i) q^{29} -8.41072 q^{31} +(5.38903 + 1.71998i) q^{32} +(1.84713 + 2.90390i) q^{34} +(-3.47880 + 8.39856i) q^{35} +(-0.565027 + 0.234042i) q^{37} +(-8.42902 + 1.48016i) q^{38} +(3.17761 + 5.53065i) q^{40} +(-0.301316 - 0.301316i) q^{41} +(-2.97363 - 7.17897i) q^{43} +(-8.38402 - 0.377851i) q^{44} +(5.87346 + 1.30644i) q^{46} +8.16538i q^{47} -9.24917i q^{49} +(-0.0263049 + 0.118261i) q^{50} +(-6.51059 + 5.94906i) q^{52} +(-4.15977 - 10.0426i) q^{53} +(-6.69148 - 6.69148i) q^{55} +(-9.03075 - 6.95981i) q^{56} +(2.43286 + 13.8543i) q^{58} +(-1.89160 + 0.783525i) q^{59} +(2.77585 - 6.70150i) q^{61} +(10.0362 - 6.38389i) q^{62} +(-7.73606 + 2.03798i) q^{64} -9.94433 q^{65} +(-3.15764 + 7.62322i) q^{67} +(-4.40823 - 2.06313i) q^{68} +(-2.22352 - 12.6622i) q^{70} +(-3.64048 + 3.64048i) q^{71} +(2.01970 + 2.01970i) q^{73} +(0.496587 - 0.708141i) q^{74} +(8.93461 - 8.16401i) q^{76} +(15.6277 + 6.47319i) q^{77} -14.0780i q^{79} +(-7.98961 - 4.18769i) q^{80} +(0.588256 + 0.130847i) q^{82} +(9.22437 + 3.82086i) q^{83} +(-2.10018 - 5.07029i) q^{85} +(8.99730 + 6.30940i) q^{86} +(10.2912 - 5.91275i) q^{88} +(6.86945 - 6.86945i) q^{89} +(16.4222 - 6.80232i) q^{91} +(-8.00023 + 2.89913i) q^{92} +(-6.19768 - 9.74350i) q^{94} +13.6468 q^{95} -0.463135 q^{97} +(7.02029 + 11.0367i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

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