LMFDB - Embedded newform 864.2.w.b.107.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(107,864)]

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([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (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			107.20
Character	$\chi$	$=$	864.107
Dual form			864.2.w.b.323.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535739 - 1.30881i) q^{2} +(-1.42597 - 1.40236i) q^{4} +(0.682524 + 0.282711i) q^{5} +(-1.19295 + 1.19295i) q^{7} +(-2.59937 + 1.11502i) q^{8} +O(q^{10})$	\(q+(0.535739 - 1.30881i) q^{2} +(-1.42597 - 1.40236i) q^{4} +(0.682524 + 0.282711i) q^{5} +(-1.19295 + 1.19295i) q^{7} +(-2.59937 + 1.11502i) q^{8} +(0.735670 - 0.741835i) q^{10} +(5.62168 + 2.32858i) q^{11} +(2.15399 + 5.20018i) q^{13} +(0.922234 + 2.20045i) q^{14} +(0.0667630 + 3.99944i) q^{16} +0.831881 q^{17} +(5.77328 - 2.39137i) q^{19} +(-0.576794 - 1.36028i) q^{20} +(6.05942 - 6.11020i) q^{22} +(-4.88515 + 4.88515i) q^{23} +(-3.14962 - 3.14962i) q^{25} +(7.96002 - 0.0332164i) q^{26} +(3.37405 - 0.0281597i) q^{28} +(-0.233848 - 0.564559i) q^{29} -9.42163i q^{31} +(5.27028 + 2.05528i) q^{32} +(0.445671 - 1.08877i) q^{34} +(-1.15148 + 0.476957i) q^{35} +(0.970846 - 2.34383i) q^{37} +(-0.0368772 - 8.83728i) q^{38} +(-2.08936 + 0.0261574i) q^{40} +(6.47604 + 6.47604i) q^{41} +(3.74978 - 9.05277i) q^{43} +(-4.75082 - 11.2041i) q^{44} +(3.77656 + 9.01089i) q^{46} -3.11389i q^{47} +4.15374i q^{49} +(-5.80963 + 2.43488i) q^{50} +(4.22102 - 10.4360i) q^{52} +(-4.92335 + 11.8860i) q^{53} +(3.17862 + 3.17862i) q^{55} +(1.77076 - 4.43108i) q^{56} +(-0.864182 + 0.00360615i) q^{58} +(-1.32483 + 3.19841i) q^{59} +(1.27224 - 0.526977i) q^{61} +(-12.3311 - 5.04754i) q^{62} +(5.51346 - 5.79670i) q^{64} +4.15820i q^{65} +(1.88604 + 4.55331i) q^{67} +(-1.18623 - 1.16660i) q^{68} +(0.00735512 + 1.76259i) q^{70} +(8.26529 + 8.26529i) q^{71} +(-4.12286 + 4.12286i) q^{73} +(-2.54751 - 2.52633i) q^{74} +(-11.5861 - 4.68621i) q^{76} +(-9.48426 + 3.92851i) q^{77} +4.13671 q^{79} +(-1.08512 + 2.74859i) q^{80} +(11.9454 - 5.00644i) q^{82} +(-4.96034 - 11.9753i) q^{83} +(0.567779 + 0.235182i) q^{85} +(-9.83945 - 9.75767i) q^{86} +(-17.2092 + 0.215448i) q^{88} +(6.98174 - 6.98174i) q^{89} +(-8.77315 - 3.63396i) q^{91} +(13.8168 - 0.115314i) q^{92} +(-4.07549 - 1.66823i) q^{94} +4.61647 q^{95} -2.26985 q^{97} +(5.43646 + 2.22532i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) $ 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	0.535739	−	1.30881i	0.378825	−	0.925468i
$2$	0.535739	−	1.30881i	0.378825	−	0.925468i
$3$		0			0
$3$		0			0
$4$	−1.42597	−	1.40236i	−0.712983	−	0.701181i
$5$	0.682524	+	0.282711i	0.305234	+	0.126432i	0.530043	−	0.847971i	$-0.322176\pi$
$5$	0.682524	+	0.282711i	0.305234	+	0.126432i	−0.224809	+	0.974403i	$0.572176\pi$
$6$		0			0
$7$	−1.19295	+	1.19295i	−0.450893	+	0.450893i	−0.895651	−	0.444758i	$-0.853290\pi$
$7$	−1.19295	+	1.19295i	−0.450893	+	0.450893i	0.444758	+	0.895651i	$0.353290\pi$
$8$	−2.59937	+	1.11502i	−0.919017	+	0.394219i
$9$		0			0
$10$	0.735670	−	0.741835i	0.232639	−	0.234589i
$11$	5.62168	+	2.32858i	1.69500	+	0.702092i	0.999859	−	0.0167807i	$-0.00534171\pi$
$11$	5.62168	+	2.32858i	1.69500	+	0.702092i	0.695141	+	0.718873i	$0.255342\pi$
$12$		0			0
$13$	2.15399	+	5.20018i	0.597408	+	1.44227i	0.876214	+	0.481923i	$0.160062\pi$
$13$	2.15399	+	5.20018i	0.597408	+	1.44227i	−0.278806	+	0.960348i	$0.589938\pi$
$14$	0.922234	+	2.20045i	0.246477	+	0.588096i
$15$		0			0
$16$	0.0667630	+	3.99944i	0.0166908	+	0.999861i
$17$	0.831881			0.201761			0.100880	−	0.994899i	$-0.467834\pi$
$17$	0.831881			0.201761			0.100880	+	0.994899i	$0.467834\pi$
$18$		0			0
$19$	5.77328	−	2.39137i	1.32448	−	0.548618i	0.395406	−	0.918507i	$-0.370604\pi$
$19$	5.77328	−	2.39137i	1.32448	−	0.548618i	0.929076	+	0.369888i	$0.120604\pi$
$20$	−0.576794	−	1.36028i	−0.128975	−	0.304168i
$21$		0			0
$22$	6.05942	−	6.11020i	1.29187	−	1.30270i
$23$	−4.88515	+	4.88515i	−1.01862	+	1.01862i	−0.0187999	+	0.999823i	$0.505985\pi$
$23$	−4.88515	+	4.88515i	−1.01862	+	1.01862i	−0.999823	+	0.0187999i	$0.994015\pi$
$24$		0			0
$25$	−3.14962	−	3.14962i	−0.629924	−	0.629924i
$26$	7.96002	−	0.0332164i	1.56109	−	0.00651428i
$27$		0			0
$28$	3.37405	−	0.0281597i	0.637636	−	0.00532169i
$29$	−0.233848	−	0.564559i	−0.0434245	−	0.104836i	0.900679	−	0.434485i	$-0.143070\pi$
$29$	−0.233848	−	0.564559i	−0.0434245	−	0.104836i	−0.944104	+	0.329649i	$0.893070\pi$
$30$		0			0
$31$		−	9.42163i		−	1.69217i	−0.533044	−	0.846087i	$-0.678952\pi$
$31$		−	9.42163i		−	1.69217i	0.533044	−	0.846087i	$-0.321048\pi$
$32$	5.27028	+	2.05528i	0.931662	+	0.363325i
$33$		0			0
$34$	0.445671	−	1.08877i	0.0764320	−	0.186723i
$35$	−1.15148	+	0.476957i	−0.194635	+	0.0806205i
$36$		0			0
$37$	0.970846	−	2.34383i	0.159606	−	0.385323i	−0.823765	−	0.566932i	$-0.808130\pi$
$37$	0.970846	−	2.34383i	0.159606	−	0.385323i	0.983371	+	0.181608i	$0.0581304\pi$
$38$	−0.0368772	−	8.83728i	−0.00598226	−	1.43360i
$39$		0			0
$40$	−2.08936	+	0.0261574i	−0.330357	+	0.00413584i
$41$	6.47604	+	6.47604i	1.01139	+	1.01139i	0.999934	+	0.0114529i	$0.00364566\pi$
$41$	6.47604	+	6.47604i	1.01139	+	1.01139i	0.0114529	+	0.999934i	$0.496354\pi$
$42$		0			0
$43$	3.74978	−	9.05277i	0.571836	−	1.38053i	−0.328154	−	0.944624i	$-0.606427\pi$
$43$	3.74978	−	9.05277i	0.571836	−	1.38053i	0.899990	−	0.435910i	$-0.143573\pi$
$44$	−4.75082	−	11.2041i	−0.716214	−	1.68908i
$45$		0			0
$46$	3.77656	+	9.01089i	0.556824	+	1.32858i
$47$		−	3.11389i		−	0.454208i	−0.973871	−	0.227104i	$-0.927074\pi$
$47$		−	3.11389i		−	0.454208i	0.973871	−	0.227104i	$-0.0729257\pi$
$48$		0			0
$49$			4.15374i			0.593392i
$50$	−5.80963	+	2.43488i	−0.821606	+	0.344344i
$51$		0			0
$52$	4.22102	−	10.4360i	0.585351	−	1.44721i
$53$	−4.92335	+	11.8860i	−0.676274	+	1.63267i	0.0944728	+	0.995527i	$0.469883\pi$
$53$	−4.92335	+	11.8860i	−0.676274	+	1.63267i	−0.770747	+	0.637142i	$0.780117\pi$
$54$		0			0
$55$	3.17862	+	3.17862i	0.428605	+	0.428605i
$56$	1.77076	−	4.43108i	0.236627	−	0.592128i
$57$		0			0
$58$	−0.864182	+	0.00360615i	−0.113473	+	0.000473511i
$59$	−1.32483	+	3.19841i	−0.172478	+	0.416398i	−0.986354	−	0.164641i	$-0.947354\pi$
$59$	−1.32483	+	3.19841i	−0.172478	+	0.416398i	0.813876	+	0.581039i	$0.197354\pi$
$60$		0			0
$61$	1.27224	−	0.526977i	0.162893	−	0.0674725i	−0.299747	−	0.954019i	$-0.596902\pi$
$61$	1.27224	−	0.526977i	0.162893	−	0.0674725i	0.462640	+	0.886546i	$0.346902\pi$
$62$	−12.3311	−	5.04754i	−1.56605	−	0.641038i
$63$		0			0
$64$	5.51346	−	5.79670i	0.689183	−	0.724587i
$65$			4.15820i			0.515762i
$66$		0			0
$67$	1.88604	+	4.55331i	0.230417	+	0.556275i	0.996226	−	0.0867922i	$-0.0276616\pi$
$67$	1.88604	+	4.55331i	0.230417	+	0.556275i	−0.765810	+	0.643067i	$0.777662\pi$
$68$	−1.18623	−	1.16660i	−0.143852	−	0.141471i
$69$		0			0
$70$	0.00735512	+	1.76259i	0.000879105	+	0.210670i
$71$	8.26529	+	8.26529i	0.980909	+	0.980909i	0.999821	−	0.0189118i	$-0.00602018\pi$
$71$	8.26529	+	8.26529i	0.980909	+	0.980909i	−0.0189118	+	0.999821i	$0.506020\pi$
$72$		0			0
$73$	−4.12286	+	4.12286i	−0.482545	+	0.482545i	−0.905943	−	0.423399i	$-0.860837\pi$
$73$	−4.12286	+	4.12286i	−0.482545	+	0.482545i	0.423399	+	0.905943i	$0.360837\pi$
$74$	−2.54751	−	2.52633i	−0.296142	−	0.293680i
$75$		0			0
$76$	−11.5861	−	4.68621i	−1.32901	−	0.537546i
$77$	−9.48426	+	3.92851i	−1.08083	+	0.447695i
$78$		0			0
$79$	4.13671			0.465417			0.232708	−	0.972547i	$-0.425241\pi$
$79$	4.13671			0.465417			0.232708	+	0.972547i	$0.425241\pi$
$80$	−1.08512	+	2.74859i	−0.121320	+	0.307302i
$81$		0			0
$82$	11.9454	−	5.00644i	1.31915	−	0.552868i
$83$	−4.96034	−	11.9753i	−0.544468	−	1.31446i	−0.921542	−	0.388278i	$-0.873070\pi$
$83$	−4.96034	−	11.9753i	−0.544468	−	1.31446i	0.377074	−	0.926183i	$-0.376930\pi$
$84$		0			0
$85$	0.567779	+	0.235182i	0.0615842	+	0.0255090i
$86$	−9.83945	−	9.75767i	−1.06101	−	1.05220i
$87$		0			0
$88$	−17.2092	+	0.215448i	−1.83451	+	0.0229668i
$89$	6.98174	−	6.98174i	0.740063	−	0.740063i	−0.232527	−	0.972590i	$-0.574699\pi$
$89$	6.98174	−	6.98174i	0.740063	−	0.740063i	0.972590	+	0.232527i	$0.0746994\pi$
$90$		0			0
$91$	−8.77315	−	3.63396i	−0.919676	−	0.380942i
$92$	13.8168	−	0.115314i	1.44050	−	0.0120224i
$93$		0			0
$94$	−4.07549	−	1.66823i	−0.420355	−	0.172065i
$95$	4.61647			0.473640
$96$		0			0
$97$	−2.26985			−0.230468			−0.115234	−	0.993338i	$-0.536762\pi$
$97$	−2.26985			−0.230468			−0.115234	+	0.993338i	$0.536762\pi$
$98$	5.43646	+	2.22532i	0.549165	+	0.224792i
$99$		0			0
$100$	0.0743472	+	8.90816i	0.00743472	+	0.890816i
$101$	4.38924	+	1.81808i	0.436745	+	0.180906i	0.590213	−	0.807248i	$-0.299044\pi$
$101$	4.38924	+	1.81808i	0.436745	+	0.180906i	−0.153467	+	0.988154i	$0.549044\pi$
$102$		0			0
$103$	0.707652	−	0.707652i	0.0697270	−	0.0697270i	−0.671383	−	0.741110i	$-0.734300\pi$
$103$	0.707652	−	0.707652i	0.0697270	−	0.0697270i	0.741110	+	0.671383i	$0.234300\pi$
$104$	−11.3973	−	11.1155i	−1.11760	−	1.08996i
$105$		0			0
$106$	12.9189	+	12.8115i	1.25479	+	1.24437i
$107$	−7.75646	−	3.21283i	−0.749845	−	0.310596i	−0.0251667	−	0.999683i	$-0.508012\pi$
$107$	−7.75646	−	3.21283i	−0.749845	−	0.310596i	−0.724678	+	0.689087i	$0.758012\pi$
$108$		0			0
$109$	0.437998	+	1.05742i	0.0419526	+	0.101282i	0.943467	−	0.331467i	$-0.107544\pi$
$109$	0.437998	+	1.05742i	0.0419526	+	0.101282i	−0.901514	+	0.432749i	$0.857544\pi$
$110$	5.86312	−	2.45730i	0.559026	−	0.234294i
$111$		0			0
$112$	−4.85078	−	4.69149i	−0.458355	−	0.443304i
$113$	−1.69342			−0.159303			−0.0796515	−	0.996823i	$-0.525381\pi$
$113$	−1.69342			−0.159303			−0.0796515	+	0.996823i	$0.525381\pi$
$114$		0			0
$115$	−4.71531	+	1.95315i	−0.439705	+	0.182132i
$116$	−0.458257	+	1.13298i	−0.0425481	+	0.105195i
$117$		0			0
$118$	3.47635	+	3.44746i	0.320024	+	0.317365i
$119$	−0.992392	+	0.992392i	−0.0909724	+	0.0909724i
$120$		0			0
$121$	18.4029	+	18.4029i	1.67299	+	1.67299i
$122$	−0.00812647	−	1.94744i	−0.000735736	−	0.176313i
$123$		0			0
$124$	−13.2125	+	13.4349i	−1.18652	+	1.20649i
$125$	−2.67281	−	6.45274i	−0.239064	−	0.577151i
$126$		0			0
$127$		−	17.4098i		−	1.54487i	−0.635095	−	0.772434i	$-0.719039\pi$
$127$		−	17.4098i		−	1.54487i	0.635095	−	0.772434i	$-0.280961\pi$
$128$	−4.63300	−	10.3216i	−0.409503	−	0.912309i
$129$		0			0
$130$	5.44230	+	2.22771i	0.477321	+	0.195383i
$131$	−3.15837	+	1.30824i	−0.275948	+	0.114301i	−0.516366	−	0.856368i	$-0.672716\pi$
$131$	−3.15837	+	1.30824i	−0.275948	+	0.114301i	0.240418	+	0.970669i	$0.422716\pi$
$132$		0			0
$133$	−4.03445	+	9.74002i	−0.349831	+	0.844567i
$134$	6.96984	−	0.0290845i	0.602102	−	0.00251252i
$135$		0			0
$136$	−2.16237	+	0.927563i	−0.185421	+	0.0795379i
$137$	0.0343534	+	0.0343534i	0.00293501	+	0.00293501i	0.708573	−	0.705638i	$-0.249339\pi$
$137$	0.0343534	+	0.0343534i	0.00293501	+	0.00293501i	−0.705638	+	0.708573i	$0.749339\pi$
$138$		0			0
$139$	−4.55777	+	11.0034i	−0.386585	+	0.933298i	0.604073	+	0.796929i	$0.293543\pi$
$139$	−4.55777	+	11.0034i	−0.386585	+	0.933298i	−0.990658	+	0.136370i	$0.956457\pi$
$140$	2.31083	+	0.934661i	0.195301	+	0.0789933i
$141$		0			0
$142$	15.2457	−	6.38965i	1.27939	−	0.536208i
$143$			34.2495i			2.86409i
$144$		0			0
$145$		−	0.451437i		−	0.0374898i
$146$	3.18727	+	7.60483i	0.263780	+	0.629380i
$147$		0			0
$148$	−4.67129	+	1.98075i	−0.383978	+	0.162816i
$149$	−0.302934	+	0.731346i	−0.0248173	+	0.0599142i	−0.935802	−	0.352525i	$-0.885323\pi$
$149$	−0.302934	+	0.731346i	−0.0248173	+	0.0599142i	0.910985	+	0.412439i	$0.135323\pi$
$150$		0			0
$151$	−12.9039	−	12.9039i	−1.05010	−	1.05010i	−0.998677	−	0.0514275i	$-0.983623\pi$
$151$	−12.9039	−	12.9039i	−1.05010	−	1.05010i	−0.0514275	−	0.998677i	$-0.516377\pi$
$152$	−12.3405	+	12.6534i	−1.00095	+	1.02633i
$153$		0			0
$154$	0.0605812	+	14.5177i	0.00488177	+	1.16987i
$155$	2.66360	−	6.43049i	0.213945	−	0.516509i
$156$		0			0
$157$	−15.0170	+	6.22023i	−1.19848	+	0.496428i	−0.890509	−	0.454966i	$-0.849651\pi$
$157$	−15.0170	+	6.22023i	−1.19848	+	0.496428i	−0.307975	+	0.951394i	$0.599651\pi$
$158$	2.21620	−	5.41417i	0.176311	−	0.430728i
$159$		0			0
$160$	3.01604	+	2.89274i	0.238439	+	0.228691i
$161$		−	11.6555i		−	0.918579i
$162$		0			0
$163$	−7.97203	−	19.2462i	−0.624418	−	1.50748i	−0.846467	−	0.532442i	$-0.821274\pi$
$163$	−7.97203	−	19.2462i	−0.624418	−	1.50748i	0.222049	−	0.975036i	$-0.428726\pi$
$164$	−0.152868	−	18.3164i	−0.0119370	−	1.43027i
$165$		0			0
$166$	−18.3309	+	0.0764930i	−1.42275	+	0.00593701i
$167$	3.21960	+	3.21960i	0.249140	+	0.249140i	0.820618	−	0.571478i	$-0.193630\pi$
$167$	3.21960	+	3.21960i	0.249140	+	0.249140i	−0.571478	+	0.820618i	$0.693630\pi$
$168$		0			0
$169$	−13.2098	+	13.2098i	−1.01614	+	1.01614i
$170$	0.611989	−	0.617118i	0.0469374	−	0.0473308i
$171$		0			0
$172$	−18.0423	+	7.65040i	−1.37571	+	0.583337i
$173$	−5.16253	+	2.13839i	−0.392500	+	0.162579i	−0.570200	−	0.821506i	$-0.693134\pi$
$173$	−5.16253	+	2.13839i	−0.392500	+	0.162579i	0.177700	+	0.984085i	$0.443134\pi$
$174$		0			0
$175$	7.51468			0.568056
$176$	−8.93769	+	22.6391i	−0.673704	+	1.70648i
$177$		0			0
$178$	−5.39738	−	12.8782i	−0.404551	−	0.965259i
$179$	3.72910	+	9.00285i	0.278726	+	0.672904i	0.999801	−	0.0199528i	$-0.00635160\pi$
$179$	3.72910	+	9.00285i	0.278726	+	0.672904i	−0.721075	+	0.692857i	$0.756352\pi$
$180$		0			0
$181$	−1.61408	−	0.668576i	−0.119974	−	0.0496948i	0.321889	−	0.946777i	$-0.395682\pi$
$181$	−1.61408	−	0.668576i	−0.119974	−	0.0496948i	−0.441863	+	0.897083i	$0.645682\pi$
$182$	−9.45628	+	9.53553i	−0.700946	+	0.706821i
$183$		0			0
$184$	7.25128	−	18.1453i	0.534571	−	1.33769i
$185$	1.32525	−	1.32525i	0.0974344	−	0.0974344i
$186$		0			0
$187$	4.67657	+	1.93710i	0.341984	+	0.141655i
$188$	−4.36680	+	4.44031i	−0.318482	+	0.323843i
$189$		0			0
$190$	2.47322	−	6.04208i	0.179427	−	0.438339i
$191$	−2.08075			−0.150558			−0.0752790	−	0.997163i	$-0.523985\pi$
$191$	−2.08075			−0.150558			−0.0752790	+	0.997163i	$0.523985\pi$
$192$		0			0
$193$	−10.5440			−0.758973			−0.379487	−	0.925197i	$-0.623899\pi$
$193$	−10.5440			−0.758973			−0.379487	+	0.925197i	$0.623899\pi$
$194$	−1.21605	+	2.97080i	−0.0873072	+	0.213291i
$195$		0			0
$196$	5.82505	−	5.92310i	0.416075	−	0.423079i
$197$	−17.5666	−	7.27633i	−1.25157	−	0.518417i	−0.344257	−	0.938875i	$-0.611869\pi$
$197$	−17.5666	−	7.27633i	−1.25157	−	0.518417i	−0.907312	+	0.420458i	$0.861869\pi$
$198$		0			0
$199$	−4.66813	+	4.66813i	−0.330915	+	0.330915i	−0.852934	−	0.522019i	$-0.825179\pi$
$199$	−4.66813	+	4.66813i	−0.330915	+	0.330915i	0.522019	+	0.852934i	$0.325179\pi$
$200$	11.6989	+	4.67515i	0.827239	+	0.330583i
$201$		0			0
$202$	4.73101	−	4.77066i	0.332873	−	0.335662i
$203$	0.952460	+	0.394522i	0.0668496	+	0.0276900i
$204$		0			0
$205$	2.58921	+	6.25090i	0.180838	+	0.436582i
$206$	−0.547065	−	1.30530i	−0.0381158	−	0.0909445i
$207$		0			0
$208$	−20.6540	+	8.96192i	−1.43210	+	0.621397i
$209$	38.0240			2.63018
$210$		0			0
$211$	15.5535	−	6.44246i	1.07075	−	0.443517i	0.223492	−	0.974706i	$-0.428254\pi$
$211$	15.5535	−	6.44246i	1.07075	−	0.443517i	0.847254	+	0.531189i	$0.178254\pi$
$212$	23.6890	−	10.0447i	1.62697	−	0.689876i
$213$		0			0
$214$	−8.36042	+	8.43049i	−0.571507	+	0.576296i
$215$	5.11863	−	5.11863i	0.349088	−	0.349088i
$216$		0			0
$217$	11.2395	+	11.2395i	0.762989	+	0.762989i
$218$	1.61861	−	0.00675433i	0.109626	−	0.000457461i
$219$		0			0
$220$	−0.0750317	−	8.99018i	−0.00505863	−	0.606118i
$221$	1.79186	+	4.32593i	0.120533	+	0.290993i
$222$		0			0
$223$		−	3.20646i		−	0.214721i	−0.994220	−	0.107360i	$-0.965760\pi$
$223$		−	3.20646i		−	0.214721i	0.994220	−	0.107360i	$-0.0342398\pi$
$224$	−8.73902	+	3.83533i	−0.583900	+	0.256259i
$225$		0			0
$226$	−0.907229	+	2.21636i	−0.0603480	+	0.147430i
$227$	17.0798	−	7.07468i	1.13362	−	0.469563i	0.264613	−	0.964355i	$-0.414756\pi$
$227$	17.0798	−	7.07468i	1.13362	−	0.469563i	0.869011	+	0.494792i	$0.164756\pi$
$228$		0			0
$229$	3.95791	−	9.55523i	0.261546	−	0.631428i	−0.737489	−	0.675360i	$-0.763988\pi$
$229$	3.95791	−	9.55523i	0.261546	−	0.631428i	0.999035	+	0.0439319i	$0.0139885\pi$
$230$	0.0301193	+	7.21782i	0.00198601	+	0.475929i
$231$		0			0
$232$	1.23735	+	1.20675i	0.0812362	+	0.0792273i
$233$	0.222203	+	0.222203i	0.0145570	+	0.0145570i	0.714348	−	0.699791i	$-0.246723\pi$
$233$	0.222203	+	0.222203i	0.0145570	+	0.0145570i	−0.699791	+	0.714348i	$0.746723\pi$
$234$		0			0
$235$	0.880330	−	2.12531i	0.0574264	−	0.138640i
$236$	6.37449	−	2.70295i	0.414944	−	0.175947i
$237$		0			0
$238$	0.767189	+	1.83052i	0.0497295	+	0.118655i
$239$		−	4.31400i		−	0.279050i	−0.990219	−	0.139525i	$-0.955442\pi$
$239$		−	4.31400i		−	0.279050i	0.990219	−	0.139525i	$-0.0445575\pi$
$240$		0			0
$241$		−	21.3101i		−	1.37270i	−0.727270	−	0.686352i	$-0.759211\pi$
$241$		−	21.3101i		−	1.37270i	0.727270	−	0.686352i	$-0.240789\pi$
$242$	33.9450	−	14.2267i	2.18207	−	0.914527i
$243$		0			0
$244$	−2.55318	−	1.03268i	−0.163450	−	0.0661107i
$245$	−1.17431	+	2.83503i	−0.0750238	+	0.181123i
$246$		0			0
$247$	24.8711	+	24.8711i	1.58251	+	1.58251i
$248$	10.5053	+	24.4903i	0.667087	+	1.55514i
$249$		0			0
$250$	−9.87735	+	0.0412172i	−0.624698	+	0.00260681i
$251$	5.01752	−	12.1134i	0.316703	−	0.764589i	−0.682722	−	0.730678i	$-0.739204\pi$
$251$	5.01752	−	12.1134i	0.316703	−	0.764589i	0.999425	−	0.0339103i	$-0.0107961\pi$
$252$		0			0
$253$	−38.8382	+	16.0873i	−2.44173	+	1.01140i
$254$	−22.7861	−	9.32711i	−1.42973	−	0.585235i
$255$		0			0
$256$	−15.9911	+	0.534030i	−0.999443	+	0.0333769i
$257$			10.2030i			0.636443i	0.948016	+	0.318222i	$0.103086\pi$
$257$			10.2030i			0.636443i	−0.948016	+	0.318222i	$0.896914\pi$
$258$		0			0
$259$	1.63790	+	3.95424i	0.101774	+	0.245705i
$260$	5.83130	−	5.92946i	0.361642	−	0.367729i
$261$		0			0
$262$	0.0201742	+	4.83458i	0.00124637	+	0.298681i
$263$	7.14987	+	7.14987i	0.440880	+	0.440880i	0.892308	−	0.451428i	$-0.149085\pi$
$263$	7.14987	+	7.14987i	0.440880	+	0.440880i	−0.451428	+	0.892308i	$0.649085\pi$
$264$		0			0
$265$	−6.72061	+	6.72061i	−0.412844	+	0.412844i
$266$	10.5864	+	10.4984i	0.649095	+	0.643701i
$267$		0			0
$268$	3.69595	−	9.13778i	0.225766	−	0.558179i
$269$	−7.57384	+	3.13719i	−0.461785	+	0.191278i	−0.601432	−	0.798924i	$-0.705403\pi$
$269$	−7.57384	+	3.13719i	−0.461785	+	0.191278i	0.139647	+	0.990201i	$0.455403\pi$
$270$		0			0
$271$	−2.63980			−0.160356			−0.0801782	−	0.996781i	$-0.525549\pi$
$271$	−2.63980			−0.160356			−0.0801782	+	0.996781i	$0.525549\pi$
$272$	0.0555389	+	3.32706i	0.00336754	+	0.201733i
$273$		0			0
$274$	0.0633665	−	0.0265576i	0.00382811	−	0.00160440i
$275$	−10.3720	−	25.0403i	−0.625457	−	1.50999i
$276$		0			0
$277$	26.3061	+	10.8964i	1.58058	+	0.654699i	0.988506	−	0.151183i	$-0.0483084\pi$
$277$	26.3061	+	10.8964i	1.58058	+	0.654699i	0.592076	+	0.805882i	$0.298308\pi$
$278$	11.9596	+	11.8602i	0.717290	+	0.711329i
$279$		0			0
$280$	2.46130	−	2.52371i	0.147091	−	0.150820i
$281$	−11.5211	+	11.5211i	−0.687292	+	0.687292i	−0.961632	−	0.274341i	$-0.911540\pi$
$281$	−11.5211	+	11.5211i	−0.687292	+	0.687292i	0.274341	+	0.961632i	$0.411540\pi$
$282$		0			0
$283$	−16.3549	−	6.77441i	−0.972197	−	0.402697i	−0.160667	−	0.987009i	$-0.551365\pi$
$283$	−16.3549	−	6.77441i	−0.972197	−	0.402697i	−0.811529	+	0.584312i	$0.801365\pi$
$284$	−0.195103	−	23.3770i	−0.0115772	−	1.38717i
$285$		0			0
$286$	44.8261	+	18.3488i	2.65062	+	1.08499i
$287$	−15.4512			−0.912054
$288$		0			0
$289$	−16.3080			−0.959293
$290$	−0.590845	−	0.241852i	−0.0346956	−	0.0142021i
$291$		0			0
$292$	11.6608	−	0.0973207i	0.682398	−	0.00569526i
$293$	−12.9255	−	5.35393i	−0.755118	−	0.312780i	−0.0282899	−	0.999600i	$-0.509006\pi$
$293$	−12.9255	−	5.35393i	−0.755118	−	0.312780i	−0.726828	+	0.686820i	$0.759006\pi$
$294$		0			0
$295$	−1.80845	+	1.80845i	−0.105292	+	0.105292i
$296$	0.0898259	+	7.17499i	0.00522103	+	0.417038i
$297$		0			0
$298$	0.794900	+	0.788293i	0.0460473	+	0.0456646i
$299$	−35.9262	−	14.8811i	−2.07766	−	0.860597i
$300$		0			0
$301$	6.32620	+	15.2728i	0.364636	+	0.880309i
$302$	−23.8019	+	9.97562i	−1.36964	+	0.574033i
$303$		0			0
$304$	9.94960	+	22.9303i	0.570648	+	1.31514i
$305$	1.01731			0.0582512
$306$		0			0
$307$	4.77503	−	1.97788i	0.272525	−	0.112884i	−0.242236	−	0.970217i	$-0.577881\pi$
$307$	4.77503	−	1.97788i	0.272525	−	0.112884i	0.514761	+	0.857334i	$0.327881\pi$
$308$	19.0334	+	7.69844i	1.08453	+	0.438659i
$309$		0			0
$310$	−6.98930	−	6.93121i	−0.396965	−	0.393666i
$311$	−4.07077	+	4.07077i	−0.230832	+	0.230832i	−0.813040	−	0.582208i	$-0.802189\pi$
$311$	−4.07077	+	4.07077i	−0.230832	+	0.230832i	0.582208	+	0.813040i	$0.302189\pi$
$312$		0			0
$313$	−3.97918	−	3.97918i	−0.224917	−	0.224917i	0.585648	−	0.810565i	$-0.300840\pi$
$313$	−3.97918	−	3.97918i	−0.224917	−	0.224917i	−0.810565	+	0.585648i	$0.800840\pi$
$314$	0.0959217	+	22.9868i	0.00541317	+	1.29722i
$315$		0			0
$316$	−5.89882	−	5.80117i	−0.331834	−	0.326341i
$317$	4.05858	+	9.79829i	0.227953	+	0.550327i	0.995928	−	0.0901530i	$-0.0287356\pi$
$317$	4.05858	+	9.79829i	0.227953	+	0.550327i	−0.767975	+	0.640480i	$0.778736\pi$
$318$		0			0
$319$		−	3.71831i		−	0.208185i
$320$	5.40186	−	2.39767i	0.301973	−	0.134034i
$321$		0			0
$322$	−15.2548	−	6.24429i	−0.850116	−	0.347981i
$323$	4.80268	−	1.98934i	0.267228	−	0.110690i
$324$		0			0
$325$	9.59436	−	23.1628i	0.532199	−	1.28484i
$326$	−29.4605	+	0.122936i	−1.63167	+	0.00680880i
$327$		0			0
$328$	−24.0545	−	9.61272i	−1.32819	−	0.530774i
$329$	3.71472	+	3.71472i	0.204799	+	0.204799i
$330$		0			0
$331$	8.74444	−	21.1110i	0.480638	−	1.16036i	−0.478668	−	0.877996i	$-0.658880\pi$
$331$	8.74444	−	21.1110i	0.480638	−	1.16036i	0.959306	−	0.282367i	$-0.0911196\pi$
$332$	−9.72044	+	24.0326i	−0.533479	+	1.31896i
$333$		0			0
$334$	5.93871	−	2.48898i	0.324952	−	0.136191i
$335$			3.64095i			0.198926i
$336$		0			0
$337$		−	2.85209i		−	0.155363i	−0.996978	−	0.0776815i	$-0.975248\pi$
$337$		−	2.85209i		−	0.155363i	0.996978	−	0.0776815i	$-0.0247517\pi$
$338$	10.2121	+	24.3662i	0.555467	+	1.32535i
$339$		0			0
$340$	−0.479824	−	1.13159i	−0.0260221	−	0.0613692i
$341$	21.9390	−	52.9654i	1.18806	−	2.86824i
$342$		0			0
$343$	−13.3059	−	13.3059i	−0.718449	−	0.718449i
$344$	0.346942	+	27.7126i	0.0187059	+	1.49416i
$345$		0			0
$346$	0.0329760	+	7.90240i	0.00177280	+	0.424836i
$347$	11.8246	−	28.5470i	0.634776	−	1.53249i	−0.198776	−	0.980045i	$-0.563697\pi$
$347$	11.8246	−	28.5470i	0.634776	−	1.53249i	0.833552	−	0.552440i	$-0.186303\pi$
$348$		0			0
$349$	−5.89443	+	2.44155i	−0.315522	+	0.130693i	−0.534824	−	0.844964i	$-0.679622\pi$
$349$	−5.89443	+	2.44155i	−0.315522	+	0.130693i	0.219302	+	0.975657i	$0.429622\pi$
$350$	4.02591	−	9.83528i	0.215194	−	0.525718i
$351$		0			0
$352$	24.8420	+	23.8264i	1.32408	+	1.26995i
$353$		−	12.8423i		−	0.683525i	−0.939786	−	0.341763i	$-0.888976\pi$
$353$		−	12.8423i		−	0.683525i	0.939786	−	0.341763i	$-0.111024\pi$
$354$		0			0
$355$	3.30457	+	7.97794i	0.175389	+	0.423425i
$356$	−19.7467	+	0.164805i	−1.04657	+	0.00873464i
$357$		0			0
$358$	13.7808	−	0.0575062i	0.728340	−	0.00303930i
$359$	−2.77398	−	2.77398i	−0.146405	−	0.146405i	0.630105	−	0.776510i	$-0.283012\pi$
$359$	−2.77398	−	2.77398i	−0.146405	−	0.146405i	−0.776510	+	0.630105i	$0.783012\pi$
$360$		0			0
$361$	14.1771	−	14.1771i	0.746163	−	0.746163i
$362$	−1.73977	+	1.75435i	−0.0914401	+	0.0922064i
$363$		0			0
$364$	7.41410	+	17.4850i	0.388604	+	0.916465i
$365$	−3.97953	+	1.64838i	−0.208298	+	0.0862799i
$366$		0			0
$367$	−28.3204			−1.47832			−0.739158	−	0.673532i	$-0.764776\pi$
$367$	−28.3204			−1.47832			−0.739158	+	0.673532i	$0.764776\pi$
$368$	−19.8640	−	19.2117i	−1.03548	−	1.00148i
$369$		0			0
$370$	−1.02451	−	2.44449i	−0.0532619	−	0.127083i
$371$	−8.30611	−	20.0527i	−0.431232	−	1.04109i
$372$		0			0
$373$	20.7080	+	8.57752i	1.07222	+	0.444127i	0.847773	−	0.530360i	$-0.177943\pi$
$373$	20.7080	+	8.57752i	1.07222	+	0.444127i	0.224445	+	0.974487i	$0.427943\pi$
$374$	5.04071	−	5.08296i	0.260649	−	0.262834i
$375$		0			0
$376$	3.47205	+	8.09416i	0.179057	+	0.417424i
$377$	2.43210	−	2.43210i	0.125260	−	0.125260i
$378$		0			0
$379$	−23.3918	−	9.68919i	−1.20155	−	0.497700i	−0.310054	−	0.950719i	$-0.600347\pi$
$379$	−23.3918	−	9.68919i	−1.20155	−	0.497700i	−0.891501	+	0.453019i	$0.850347\pi$
$380$	−6.58293	−	6.47396i	−0.337697	−	0.332107i
$381$		0			0
$382$	−1.11474	+	2.72331i	−0.0570351	+	0.139337i
$383$	15.5823			0.796217			0.398109	−	0.917338i	$-0.369667\pi$
$383$	15.5823			0.796217			0.398109	+	0.917338i	$0.369667\pi$
$384$		0			0
$385$	−7.58386			−0.386510
$386$	−5.64883	+	13.8001i	−0.287518	+	0.702406i
$387$		0			0
$388$	3.23673	+	3.18315i	0.164320	+	0.161600i
$389$	−25.6466	−	10.6232i	−1.30033	−	0.538615i	−0.378284	−	0.925690i	$-0.623486\pi$
$389$	−25.6466	−	10.6232i	−1.30033	−	0.538615i	−0.922048	+	0.387075i	$0.873486\pi$
$390$		0			0
$391$	−4.06386	+	4.06386i	−0.205518	+	0.205518i
$392$	−4.63150	−	10.7971i	−0.233926	−	0.545337i
$393$		0			0
$394$	−18.9345	+	19.0931i	−0.953904	+	0.961898i
$395$	2.82341	+	1.16949i	0.142061	+	0.0588436i
$396$		0			0
$397$	−3.50601	−	8.46425i	−0.175962	−	0.424809i	0.811151	−	0.584837i	$-0.198841\pi$
$397$	−3.50601	−	8.46425i	−0.175962	−	0.424809i	−0.987112	+	0.160028i	$0.948841\pi$
$398$	3.60880	+	8.61060i	0.180893	+	0.431610i
$399$		0			0
$400$	12.3864	−	12.8070i	0.619322	−	0.640350i
$401$	15.0054			0.749336			0.374668	−	0.927159i	$-0.377757\pi$
$401$	15.0054			0.749336			0.374668	+	0.927159i	$0.377757\pi$
$402$		0			0
$403$	48.9942	−	20.2941i	2.44057	−	1.01092i
$404$	−3.70930	−	8.74782i	−0.184545	−	0.435220i
$405$		0			0
$406$	1.02662	−	1.03523i	0.0509505	−	0.0513775i
$407$	10.9156	−	10.9156i	0.541065	−	0.541065i
$408$		0			0
$409$	15.5473	+	15.5473i	0.768763	+	0.768763i	0.977889	−	0.209126i	$-0.0670619\pi$
$409$	15.5473	+	15.5473i	0.768763	+	0.768763i	−0.209126	+	0.977889i	$0.567062\pi$
$410$	9.56838	−	0.0399280i	0.472548	−	0.00197190i
$411$		0			0
$412$	−2.00147	+	0.0167042i	−0.0986055	+	0.000822957i
$413$	−2.23510	−	5.39600i	−0.109982	−	0.265520i
$414$		0			0
$415$		−	9.57578i		−	0.470057i
$416$	0.664282	+	31.8334i	0.0325691	+	1.56076i
$417$		0			0
$418$	20.3710	−	49.7662i	0.996377	−	2.43415i
$419$	−12.7893	+	5.29749i	−0.624797	+	0.258799i	−0.672541	−	0.740060i	$-0.734797\pi$
$419$	−12.7893	+	5.29749i	−0.624797	+	0.258799i	0.0477435	+	0.998860i	$0.484797\pi$
$420$		0			0
$421$	−2.20238	+	5.31702i	−0.107338	+	0.259136i	−0.968418	−	0.249333i	$-0.919788\pi$
$421$	−2.20238	+	5.31702i	−0.107338	+	0.259136i	0.861080	+	0.508469i	$0.169788\pi$
$422$	−0.0993487	−	23.8080i	−0.00483622	−	1.15896i
$423$		0			0
$424$	−0.455525	−	36.3858i	−0.0221222	−	1.76705i
$425$	−2.62011	−	2.62011i	−0.127094	−	0.127094i
$426$		0			0
$427$	−0.889055	+	2.14637i	−0.0430244	+	0.103870i
$428$	6.55490	+	15.4587i	0.316843	+	0.747227i
$429$		0			0
$430$	−3.95706	−	9.44156i	−0.190826	−	0.455313i
$431$			1.85356i			0.0892829i	0.999003	+	0.0446414i	$0.0142145\pi$
$431$			1.85356i			0.0892829i	−0.999003	+	0.0446414i	$0.985785\pi$
$432$		0			0
$433$		−	13.2013i		−	0.634414i	−0.948356	−	0.317207i	$-0.897255\pi$
$433$		−	13.2013i		−	0.634414i	0.948356	−	0.317207i	$-0.102745\pi$
$434$	20.7319	−	8.68895i	0.995161	−	0.417083i
$435$		0			0
$436$	0.858315	−	2.12208i	0.0411059	−	0.101629i
$437$	−16.5211	+	39.8855i	−0.790312	+	1.90798i
$438$		0			0
$439$	20.9943	+	20.9943i	1.00201	+	1.00201i	0.999998	+	0.00200743i	$0.000638984\pi$
$439$	20.9943	+	20.9943i	1.00201	+	1.00201i	0.00200743	+	0.999998i	$0.499361\pi$
$440$	−11.8066	−	4.71819i	−0.562859	−	0.224931i
$441$		0			0
$442$	6.62179	−	0.0276321i	0.314966	−	0.00131433i
$443$	3.14533	−	7.59351i	0.149439	−	0.360778i	−0.831378	−	0.555707i	$-0.812448\pi$
$443$	3.14533	−	7.59351i	0.149439	−	0.360778i	0.980817	+	0.194929i	$0.0624476\pi$
$444$		0			0
$445$	6.73902	−	2.79139i	0.319460	−	0.132325i
$446$	−4.19665	−	1.71783i	−0.198717	−	0.0813415i
$447$		0			0
$448$	0.337885	+	13.4925i	0.0159636	+	0.637459i
$449$		−	28.5624i		−	1.34794i	−0.738756	−	0.673972i	$-0.764587\pi$
$449$		−	28.5624i		−	1.34794i	0.738756	−	0.673972i	$-0.235413\pi$
$450$		0			0
$451$	21.3263	+	51.4862i	1.00422	+	2.42439i
$452$	2.41475	+	2.37478i	0.113580	+	0.111700i
$453$		0			0
$454$	−0.109098	−	26.1444i	−0.00512022	−	1.22702i
$455$	−4.96053	−	4.96053i	−0.232553	−	0.232553i
$456$		0			0
$457$	24.5606	−	24.5606i	1.14890	−	1.14890i	0.162129	−	0.986770i	$-0.448164\pi$
$457$	24.5606	−	24.5606i	1.14890	−	1.14890i	0.986770	−	0.162129i	$-0.0518360\pi$
$458$	−10.3856	−	10.2993i	−0.485286	−	0.481253i
$459$		0			0
$460$	9.46290	+	3.82745i	0.441210	+	0.178456i
$461$	−22.7019	+	9.40342i	−1.05733	+	0.437961i	−0.842503	−	0.538691i	$-0.818919\pi$
$461$	−22.7019	+	9.40342i	−1.05733	+	0.437961i	−0.214828	+	0.976652i	$0.568919\pi$
$462$		0			0
$463$	13.7861			0.640693			0.320346	−	0.947300i	$-0.396201\pi$
$463$	13.7861			0.640693			0.320346	+	0.947300i	$0.396201\pi$
$464$	2.24231	−	0.972954i	0.104097	−	0.0451682i
$465$		0			0
$466$	0.409865	−	0.171779i	0.0189866	−	0.00795751i
$467$	10.2478	+	24.7404i	0.474212	+	1.14485i	0.962284	+	0.272046i	$0.0877002\pi$
$467$	10.2478	+	24.7404i	0.474212	+	1.14485i	−0.488072	+	0.872803i	$0.662300\pi$
$468$		0			0
$469$	−7.68182	−	3.18191i	−0.354713	−	0.146927i
$470$	−2.30999	−	2.29079i	−0.106552	−	0.105666i
$471$		0			0
$472$	−0.122577	−	9.79107i	−0.00564208	−	0.450671i
$473$	42.1601	−	42.1601i	1.93852	−	1.93852i
$474$		0			0
$475$	−25.7156	−	10.6517i	−1.17991	−	0.488735i
$476$	2.80681	−	0.0234255i	0.128650	−	0.00107371i
$477$		0			0
$478$	−5.64621	−	2.31118i	−0.258252	−	0.105711i
$479$	−8.56568			−0.391376			−0.195688	−	0.980666i	$-0.562694\pi$
$479$	−8.56568			−0.391376			−0.195688	+	0.980666i	$0.562694\pi$
$480$		0			0
$481$	14.2795			0.651090
$482$	−27.8909	−	11.4166i	−1.27039	−	0.520014i
$483$		0			0
$484$	−0.434402	−	52.0493i	−0.0197455	−	2.36588i
$485$	−1.54923	−	0.641711i	−0.0703468	−	0.0291386i
$486$		0			0
$487$	5.19658	−	5.19658i	0.235480	−	0.235480i	−0.579496	−	0.814975i	$-0.696750\pi$
$487$	5.19658	−	5.19658i	0.235480	−	0.235480i	0.814975	+	0.579496i	$0.196750\pi$
$488$	−2.71942	+	2.78838i	−0.123102	+	0.126224i
$489$		0			0
$490$	3.08139	+	3.05578i	0.139203	+	0.138046i
$491$	5.82100	+	2.41114i	0.262698	+	0.108813i	0.510145	−	0.860088i	$-0.329592\pi$
$491$	5.82100	+	2.41114i	0.262698	+	0.108813i	−0.247447	+	0.968901i	$0.579592\pi$
$492$		0			0
$493$	−0.194534	−	0.469646i	−0.00876136	−	0.0211518i
$494$	45.8760	−	19.2271i	2.06406	−	0.865070i
$495$		0			0
$496$	37.6813	−	0.629017i	1.69194	−	0.0282437i
$497$	−19.7201			−0.884569
$498$		0			0
$499$	−12.1439	+	5.03015i	−0.543634	+	0.225180i	−0.637563	−	0.770398i	$-0.720057\pi$
$499$	−12.1439	+	5.03015i	−0.543634	+	0.225180i	0.0939291	+	0.995579i	$0.470057\pi$
$500$	−5.23774	+	12.9496i	−0.234239	+	0.579126i
$501$		0			0
$502$	−13.1660	−	13.0566i	−0.587628	−	0.582744i
$503$	−24.8835	+	24.8835i	−1.10950	+	1.10950i	−0.116286	+	0.993216i	$0.537099\pi$
$503$	−24.8835	+	24.8835i	−1.10950	+	1.10950i	−0.993216	+	0.116286i	$0.962901\pi$
$504$		0			0
$505$	2.48177	+	2.48177i	0.110437	+	0.110437i
$506$	0.248081	+	59.4504i	0.0110285	+	2.64289i
$507$		0			0
$508$	−24.4148	+	24.8258i	−1.08323	+	1.10147i
$509$	−14.9572	−	36.1098i	−0.662965	−	1.60054i	−0.793134	−	0.609048i	$-0.791552\pi$
$509$	−14.9572	−	36.1098i	−0.662965	−	1.60054i	0.130169	−	0.991492i	$-0.458448\pi$
$510$		0			0
$511$		−	9.83674i		−	0.435152i
$512$	−7.86811	+	21.2154i	−0.347725	+	0.937597i
$513$		0			0
$514$	13.3537	+	5.46613i	0.589008	+	0.241101i
$515$	0.683050	−	0.282929i	0.0300988	−	0.0124673i
$516$		0			0
$517$	7.25093	−	17.5053i	0.318896	−	0.769882i
$518$	6.05284	−	0.0252579i	0.265946	−	0.00110977i
$519$		0			0
$520$	−4.63648	−	10.8087i	−0.203323	−	0.473993i
$521$	−19.0341	−	19.0341i	−0.833897	−	0.833897i	0.154150	−	0.988047i	$-0.450736\pi$
$521$	−19.0341	−	19.0341i	−0.833897	−	0.833897i	−0.988047	+	0.154150i	$0.950736\pi$
$522$		0			0
$523$	−11.2496	+	27.1590i	−0.491912	+	1.18758i	0.461833	+	0.886967i	$0.347192\pi$
$523$	−11.2496	+	27.1590i	−0.491912	+	1.18758i	−0.953746	+	0.300615i	$0.902808\pi$
$524$	6.33835	+	2.56367i	0.276892	+	0.111994i
$525$		0			0
$526$	13.1883	−	5.52735i	0.575036	−	0.241004i
$527$		−	7.83767i		−	0.341414i
$528$		0			0
$529$		−	24.7293i		−	1.07519i
$530$	5.19550	+	12.3965i	0.225678	+	0.538469i
$531$		0			0
$532$	19.4120	−	8.23119i	0.841618	−	0.356867i
$533$	−19.7273	+	47.6259i	−0.854483	+	2.06291i
$534$		0			0
$535$	−4.38567	−	4.38567i	−0.189609	−	0.189609i
$536$	−9.97955	−	9.73276i	−0.431051	−	0.420391i
$537$		0			0
$538$	0.0483783	+	11.5934i	0.00208574	+	0.499828i
$539$	−9.67231	+	23.3510i	−0.416616	+	1.00580i
$540$		0			0
$541$	25.6059	−	10.6063i	1.10088	−	0.456000i	0.243093	−	0.970003i	$-0.421838\pi$
$541$	25.6059	−	10.6063i	1.10088	−	0.456000i	0.857789	+	0.514003i	$0.171838\pi$
$542$	−1.41424	+	3.45500i	−0.0607470	+	0.148405i
$543$		0			0
$544$	4.38424	+	1.70975i	0.187973	+	0.0733048i
$545$			0.845541i			0.0362190i
$546$		0			0
$547$	1.44828	+	3.49645i	0.0619239	+	0.149497i	0.951813	−	0.306680i	$-0.0992182\pi$
$547$	1.44828	+	3.49645i	0.0619239	+	0.149497i	−0.889889	+	0.456178i	$0.849218\pi$
$548$	−0.000810915	−	0.0971626i	−3.46406e−5	−	0.00415058i
$549$		0			0
$550$	−38.3297	+	0.159946i	−1.63438	+	0.00682013i
$551$	−2.70014	−	2.70014i	−0.115030	−	0.115030i
$552$		0			0
$553$	−4.93489	+	4.93489i	−0.209853	+	0.209853i
$554$	28.3545	−	28.5921i	1.20467	−	1.21476i
$555$		0			0
$556$	21.9300	−	9.29888i	0.930040	−	0.394360i
$557$	−0.812580	+	0.336582i	−0.0344301	+	0.0142614i	−0.399832	−	0.916588i	$-0.630932\pi$
$557$	−0.812580	+	0.336582i	−0.0344301	+	0.0142614i	0.365402	+	0.930850i	$0.380932\pi$
$558$		0			0
$559$	55.1530			2.33272
$560$	−1.98444	−	4.57342i	−0.0838578	−	0.193262i
$561$		0			0
$562$	8.90663	+	21.2512i	0.375703	+	0.896430i
$563$	−14.1727	−	34.2160i	−0.597310	−	1.44203i	−0.876313	−	0.481743i	$-0.840004\pi$
$563$	−14.1727	−	34.2160i	−0.597310	−	1.44203i	0.279003	−	0.960290i	$-0.409996\pi$
$564$		0			0
$565$	−1.15580	−	0.478747i	−0.0486247	−	0.0201410i
$566$	−17.6284	+	17.7761i	−0.740976	+	0.747186i
$567$		0			0
$568$	−30.7005	−	12.2686i	−1.28816	−	0.514779i
$569$	19.9512	−	19.9512i	0.836398	−	0.836398i	−0.151985	−	0.988383i	$-0.548567\pi$
$569$	19.9512	−	19.9512i	0.836398	−	0.836398i	0.988383	+	0.151985i	$0.0485666\pi$
$570$		0			0
$571$	−24.3708	−	10.0947i	−1.01989	−	0.422451i	−0.190835	−	0.981622i	$-0.561120\pi$
$571$	−24.3708	−	10.0947i	−1.01989	−	0.422451i	−0.829052	+	0.559171i	$0.811120\pi$
$572$	48.0302	−	48.8386i	2.00824	−	2.04205i
$573$		0			0
$574$	−8.27780	+	20.2227i	−0.345509	+	0.844077i
$575$	30.7727			1.28331
$576$		0			0
$577$	5.95177			0.247776			0.123888	−	0.992296i	$-0.460464\pi$
$577$	5.95177			0.247776			0.123888	+	0.992296i	$0.460464\pi$
$578$	−8.73682	+	21.3440i	−0.363404	+	0.887795i
$579$		0			0
$580$	−0.633077	+	0.643734i	−0.0262871	+	0.0267296i
$581$	20.2034	+	8.36851i	0.838177	+	0.347184i
$582$		0			0
$583$	−55.3550	+	55.3550i	−2.29257	+	2.29257i
$584$	6.11978	−	15.3139i	0.253238	−	0.633695i
$585$		0			0
$586$	−13.9320	+	14.0488i	−0.575525	+	0.580349i
$587$	−5.33151	−	2.20839i	−0.220055	−	0.0911498i	0.269932	−	0.962879i	$-0.412999\pi$
$587$	−5.33151	−	2.20839i	−0.220055	−	0.0911498i	−0.489987	+	0.871729i	$0.662999\pi$
$588$		0			0
$589$	−22.5306	−	54.3937i	−0.928358	−	2.24125i
$590$	1.39806	+	3.33578i	0.0575573	+	0.137332i
$591$		0			0
$592$	9.43883	+	3.72636i	0.387933	+	0.153153i
$593$	28.3544			1.16437			0.582187	−	0.813055i	$-0.302197\pi$
$593$	28.3544			1.16437			0.582187	+	0.813055i	$0.302197\pi$
$594$		0			0
$595$	−0.957891	+	0.396771i	−0.0392697	+	0.0162660i
$596$	1.45759	−	0.618053i	0.0597050	−	0.0253164i
$597$		0			0
$598$	−38.7236	+	39.0481i	−1.58353	+	1.59680i
$599$	−5.32217	+	5.32217i	−0.217458	+	0.217458i	−0.807426	−	0.589968i	$-0.799140\pi$
$599$	−5.32217	+	5.32217i	−0.217458	+	0.217458i	0.589968	+	0.807426i	$0.299140\pi$
$600$		0			0
$601$	6.32507	+	6.32507i	0.258005	+	0.258005i	0.824242	−	0.566237i	$-0.191601\pi$
$601$	6.32507	+	6.32507i	0.258005	+	0.258005i	−0.566237	+	0.824242i	$0.691601\pi$
$602$	23.3784	−	0.0975558i	0.952831	−	0.00397608i
$603$		0			0
$604$	0.304598	+	36.4965i	0.0123939	+	1.48502i
$605$	7.35771	+	17.7631i	0.299133	+	0.722172i
$606$		0			0
$607$		−	24.1871i		−	0.981724i	−0.871237	−	0.490862i	$-0.836682\pi$
$607$		−	24.1871i		−	0.981724i	0.871237	−	0.490862i	$-0.163318\pi$
$608$	35.3417	−	0.737492i	1.43330	−	0.0299092i
$609$		0			0
$610$	0.545015	−	1.33147i	0.0220670	−	0.0539096i
$611$	16.1928	−	6.70728i	0.655090	−	0.271347i
$612$		0			0
$613$	8.83387	−	21.3268i	0.356796	−	0.861383i	−0.638950	−	0.769248i	$-0.720631\pi$
$613$	8.83387	−	21.3268i	0.356796	−	0.861383i	0.995747	−	0.0921347i	$-0.0293690\pi$
$614$	−0.0305008	−	7.30924i	−0.00123091	−	0.294977i
$615$		0			0
$616$	20.2727	−	20.7868i	0.816812	−	0.837523i
$617$	18.8549	+	18.8549i	0.759069	+	0.759069i	0.976153	−	0.217084i	$-0.0696544\pi$
$617$	18.8549	+	18.8549i	0.759069	+	0.759069i	−0.217084	+	0.976153i	$0.569654\pi$
$618$		0			0
$619$	−8.40383	+	20.2886i	−0.337779	+	0.815470i	0.660150	+	0.751134i	$0.270493\pi$
$619$	−8.40383	+	20.2886i	−0.337779	+	0.815470i	−0.997928	+	0.0643356i	$0.979507\pi$
$620$	−12.8161	+	5.43434i	−0.514706	+	0.218248i
$621$		0			0
$622$	3.14699	+	7.50874i	0.126183	+	0.301073i
$623$			16.6577i			0.667378i
$624$		0			0
$625$			17.1114i			0.684456i
$626$	−7.33980	+	3.07619i	−0.293357	+	0.122949i
$627$		0			0
$628$	30.1367	+	12.1894i	1.20259	+	0.486409i
$629$	0.807628	−	1.94979i	0.0322022	−	0.0777431i
$630$		0			0
$631$	16.0770	+	16.0770i	0.640015	+	0.640015i	0.950559	−	0.310544i	$-0.100511\pi$
$631$	16.0770	+	16.0770i	0.640015	+	0.640015i	−0.310544	+	0.950559i	$0.600511\pi$
$632$	−10.7529	+	4.61252i	−0.427726	+	0.183476i
$633$		0			0
$634$	14.9984	−	0.0625871i	0.595664	−	0.00248565i
$635$	4.92193	−	11.8826i	0.195321	−	0.471547i
$636$		0			0
$637$	−21.6002	+	8.94710i	−0.855832	+	0.354497i
$638$	−4.86656	−	1.99204i	−0.192669	−	0.0788657i
$639$		0			0
$640$	−0.244107	−	8.35454i	−0.00964917	−	0.330242i
$641$			30.2820i			1.19607i	0.801470	+	0.598034i	$0.204051\pi$
$641$			30.2820i			1.19607i	−0.801470	+	0.598034i	$0.795949\pi$
$642$		0			0
$643$	11.0640	+	26.7109i	0.436322	+	1.05337i	0.977209	+	0.212279i	$0.0680887\pi$
$643$	11.0640	+	26.7109i	0.436322	+	1.05337i	−0.540887	+	0.841095i	$0.681911\pi$
$644$	−16.3452	+	16.6203i	−0.644090	+	0.654932i
$645$		0			0
$646$	−0.0306774	−	7.35156i	−0.00120699	−	0.289243i
$647$	18.4284	+	18.4284i	0.724495	+	0.724495i	0.969517	−	0.245023i	$-0.0787954\pi$
$647$	18.4284	+	18.4284i	0.724495	+	0.724495i	−0.245023	+	0.969517i	$0.578795\pi$
$648$		0			0
$649$	−14.8955	+	14.8955i	−0.584700	+	0.584700i
$650$	−25.1757	−	24.9664i	−0.987471	−	0.979264i
$651$		0			0
$652$	−15.6223	+	38.6241i	−0.611815	+	1.51264i
$653$	17.8407	−	7.38987i	0.698161	−	0.289188i	−0.00523453	−	0.999986i	$-0.501666\pi$
$653$	17.8407	−	7.38987i	0.698161	−	0.289188i	0.703396	+	0.710798i	$0.251666\pi$
$654$		0			0
$655$	−2.52551			−0.0986800
$656$	−25.4682	+	26.3329i	−0.994366	+	1.02813i
$657$		0			0
$658$	6.85197	−	2.87174i	0.267118	−	0.111952i
$659$	7.71681	+	18.6300i	0.300604	+	0.725723i	0.999940	+	0.0109299i	$0.00347916\pi$
$659$	7.71681	+	18.6300i	0.300604	+	0.725723i	−0.699336	+	0.714793i	$0.746521\pi$
$660$		0			0
$661$	−34.0397	−	14.0997i	−1.32399	−	0.548415i	−0.395056	−	0.918657i	$-0.629275\pi$
$661$	−34.0397	−	14.0997i	−1.32399	−	0.548415i	−0.928936	+	0.370241i	$0.879275\pi$
$662$	−22.9455	−	22.7548i	−0.891801	−	0.884390i
$663$		0			0
$664$	26.2465	+	25.5974i	1.01856	+	0.993372i
$665$	−5.50722	+	5.50722i	−0.213561	+	0.213561i
$666$		0			0
$667$	3.90034	+	1.61557i	0.151022	+	0.0625552i
$668$	−0.0759991	−	9.10609i	−0.00294049	−	0.352325i
$669$		0			0
$670$	4.76531	+	1.95060i	0.184100	+	0.0753582i
$671$	8.37921			0.323476
$672$		0			0
$673$	−44.4459			−1.71326			−0.856632	−	0.515929i	$-0.827447\pi$
$673$	−44.4459			−1.71326			−0.856632	+	0.515929i	$0.827447\pi$
$674$	−3.73284	−	1.52797i	−0.143784	−	0.0588554i
$675$		0			0
$676$	37.3618	−	0.311820i	1.43699	−	0.0119931i
$677$	32.6371	+	13.5187i	1.25434	+	0.519567i	0.908169	−	0.418603i	$-0.137480\pi$
$677$	32.6371	+	13.5187i	1.25434	+	0.519567i	0.346176	+	0.938170i	$0.387480\pi$
$678$		0			0
$679$	2.70782	−	2.70782i	0.103917	−	0.103917i
$680$	−1.73810	+	0.0217598i	−0.0666531	+	0.000834450i
$681$		0			0
$682$	−57.5681	−	57.0896i	−2.20440	−	2.18607i
$683$	8.81684	+	3.65205i	0.337367	+	0.139742i	0.544934	−	0.838479i	$-0.316555\pi$
$683$	8.81684	+	3.65205i	0.337367	+	0.139742i	−0.207567	+	0.978221i	$0.566555\pi$
$684$		0			0
$685$	0.0137349	+	0.0331591i	0.000524785	+	0.00126694i
$686$	−24.5433	+	10.2864i	−0.937068	+	0.392735i
$687$		0			0
$688$	36.4564	+	14.3926i	1.38989	+	0.548714i
$689$	−72.4142			−2.75876
$690$		0			0
$691$	15.1938	−	6.29348i	0.578000	−	0.239415i	−0.0744787	−	0.997223i	$-0.523729\pi$
$691$	15.1938	−	6.29348i	0.578000	−	0.239415i	0.652478	+	0.757807i	$0.273729\pi$
$692$	10.3604	+	4.19047i	0.393843	+	0.159298i
$693$		0			0
$694$	−31.0278	−	30.7699i	−1.17780	−	1.16801i
$695$	−6.22157	+	6.22157i	−0.235998	+	0.235998i
$696$		0			0
$697$	5.38729	+	5.38729i	0.204058	+	0.204058i
$698$	0.0376510	+	9.02273i	0.00142511	+	0.341515i
$699$		0			0
$700$	−10.7157	−	10.5383i	−0.405015	−	0.398310i
$701$	1.91025	+	4.61175i	0.0721492	+	0.174184i	0.955840	−	0.293888i	$-0.0949491\pi$
$701$	1.91025	+	4.61175i	0.0721492	+	0.174184i	−0.883691	+	0.468071i	$0.844949\pi$
$702$		0			0
$703$		−	15.8532i		−	0.597916i
$704$	44.4930	−	19.7487i	1.67689	−	0.744306i
$705$		0			0
$706$	−16.8081	−	6.88011i	−0.632581	−	0.258936i
$707$	−7.40502	+	3.06726i	−0.278494	+	0.115356i
$708$		0			0
$709$	14.6364	−	35.3355i	0.549683	−	1.32705i	−0.368033	−	0.929813i	$-0.619969\pi$
$709$	14.6364	−	35.3355i	0.549683	−	1.32705i	0.917715	−	0.397239i	$-0.130031\pi$
$710$	12.2120	−	0.0509596i	0.458308	−	0.00191248i
$711$		0			0
$712$	−10.3634	+	25.9329i	−0.388383	+	0.971877i
$713$	46.0260	+	46.0260i	1.72369	+	1.72369i
$714$		0			0
$715$	−9.68269	+	23.3761i	−0.362112	+	0.874216i
$716$	7.30767	−	18.0673i	0.273101	−	0.675207i
$717$		0			0
$718$	−5.11675	+	2.14449i	−0.190955	+	0.0800315i
$719$		−	16.0726i		−	0.599405i	−0.954033	−	0.299703i	$-0.903113\pi$
$719$		−	16.0726i		−	0.599405i	0.954033	−	0.299703i	$-0.0968875\pi$
$720$		0			0
$721$			1.68839i			0.0628788i
$722$	−10.9599	−	26.1504i	−0.407885	−	0.973216i
$723$		0			0
$724$	1.36405	+	3.21690i	0.0506944	+	0.119555i
$725$	−1.04161	+	2.51468i	−0.0386846	+	0.0933929i
$726$		0			0
$727$	19.9154	+	19.9154i	0.738623	+	0.738623i	0.972312	−	0.233689i	$-0.0750796\pi$
$727$	19.9154	+	19.9154i	0.738623	+	0.738623i	−0.233689	+	0.972312i	$0.575080\pi$
$728$	26.8566	−	0.336226i	0.995372	−	0.0124614i
$729$		0			0
$730$	0.0254195	+	6.09155i	0.000940817	+	0.225458i
$731$	3.11937	−	7.53082i	0.115374	−	0.278537i
$732$		0			0
$733$	−25.2364	+	10.4533i	−0.932129	+	0.386100i	−0.796486	−	0.604657i	$-0.793310\pi$
$733$	−25.2364	+	10.4533i	−0.932129	+	0.386100i	−0.135643	+	0.990758i	$0.543310\pi$
$734$	−15.1724	+	37.0661i	−0.560023	+	1.36813i
$735$		0			0
$736$	−35.7864	+	15.7057i	−1.31910	+	0.578921i
$737$			29.9890i			1.10466i
$738$		0			0
$739$	−9.18129	−	22.1656i	−0.337739	−	0.815374i	−0.997932	−	0.0642783i	$-0.979525\pi$
$739$	−9.18129	−	22.1656i	−0.337739	−	0.815374i	0.660193	−	0.751096i	$-0.270475\pi$
$740$	−3.74825	+	0.0312827i	−0.137788	+	0.00114998i
$741$		0			0
$742$	−30.6951	+	0.128088i	−1.12685	+	0.00470225i
$743$	1.56336	+	1.56336i	0.0573540	+	0.0573540i	0.735202	−	0.677848i	$-0.237087\pi$
$743$	1.56336	+	1.56336i	0.0573540	+	0.0573540i	−0.677848	+	0.735202i	$0.737087\pi$
$744$		0			0
$745$	−0.413519	+	0.413519i	−0.0151502	+	0.0151502i
$746$	22.3204	−	22.5075i	0.817209	−	0.824057i
$747$		0			0
$748$	−3.95212	−	9.32048i	−0.144504	−	0.340790i
$749$	13.0858	−	5.42032i	0.478145	−	0.198054i
$750$		0			0
$751$	7.06766			0.257903			0.128951	−	0.991651i	$-0.458839\pi$
$751$	7.06766			0.257903			0.128951	+	0.991651i	$0.458839\pi$
$752$	12.4538	−	0.207893i	0.454144	−	0.00758107i
$753$		0			0
$754$	−1.88019	−	4.48614i	−0.0684724	−	0.163375i
$755$	−5.15915	−	12.4553i	−0.187761	−	0.453294i
$756$		0			0
$757$	40.2770	+	16.6833i	1.46389	+	0.606364i	0.965457	−	0.260564i	$-0.0839084\pi$
$757$	40.2770	+	16.6833i	1.46389	+	0.606364i	0.498435	+	0.866927i	$0.333908\pi$
$758$	−25.2132	+	25.4245i	−0.915785	+	0.923460i
$759$		0			0
$760$	−11.9999	+	5.14745i	−0.435283	+	0.186718i
$761$	−4.77305	+	4.77305i	−0.173023	+	0.173023i	−0.788306	−	0.615283i	$-0.789042\pi$
$761$	−4.77305	+	4.77305i	−0.173023	+	0.173023i	0.615283	+	0.788306i	$0.289042\pi$
$762$		0			0
$763$	−1.78396	−	0.738940i	−0.0645836	−	0.0267514i
$764$	2.96708	+	2.91797i	0.107345	+	0.105568i
$765$		0			0
$766$	8.34804	−	20.3942i	0.301627	−	0.736874i
$767$	−19.4860			−0.703598
$768$		0			0
$769$	0.0609393			0.00219753			0.00109876	−	0.999999i	$-0.499650\pi$
$769$	0.0609393			0.00219753			0.00109876	+	0.999999i	$0.499650\pi$
$770$	−4.06297	+	9.92584i	−0.146419	+	0.357702i
$771$		0			0
$772$	15.0354	+	14.7865i	0.541136	+	0.532178i
$773$	−41.9526	−	17.3773i	−1.50893	−	0.625019i	−0.533593	−	0.845742i	$-0.679158\pi$
$773$	−41.9526	−	17.3773i	−1.50893	−	0.625019i	−0.975337	+	0.220723i	$0.929158\pi$
$774$		0			0
$775$	−29.6746	+	29.6746i	−1.06594	+	1.06594i
$776$	5.90019	−	2.53093i	0.211804	−	0.0908550i
$777$		0			0
$778$	−27.6436	+	27.8752i	−0.991069	+	0.999375i
$779$	52.8746	+	21.9014i	1.89443	+	0.784698i
$780$		0			0
$781$	27.2185	+	65.7112i	0.973953	+	2.35133i
$782$	3.14165	+	7.49598i	0.112345	+	0.268056i
$783$		0			0
$784$	−16.6127	+	0.277316i	−0.593309	+	0.00990416i
$785$	−12.0080			−0.428583
$786$		0			0
$787$	−19.1010	+	7.91188i	−0.680876	+	0.282028i	−0.696193	−	0.717855i	$-0.745124\pi$
$787$	−19.1010	+	7.91188i	−0.680876	+	0.282028i	0.0153170	+	0.999883i	$0.495124\pi$
$788$	14.8454	+	35.0105i	0.528844	+	1.24720i
$789$		0			0
$790$	3.04325	−	3.06876i	0.108274	−	0.109182i
$791$	2.02016	−	2.02016i	0.0718286	−	0.0718286i
$792$		0			0
$793$	5.48075	+	5.48075i	0.194627	+	0.194627i
$794$	−12.9564	+	0.0540659i	−0.459806	+	0.00191873i
$795$		0			0
$796$	13.2030	−	0.110192i	0.467968	−	0.00390564i
$797$	−4.56396	−	11.0184i	−0.161664	−	0.390291i	0.822203	−	0.569195i	$-0.192745\pi$
$797$	−4.56396	−	11.0184i	−0.161664	−	0.390291i	−0.983867	+	0.178904i	$0.942745\pi$
$798$		0			0
$799$		−	2.59039i		−	0.0916413i
$800$	−10.1260	−	23.0727i	−0.358009	−	0.815744i
$801$		0			0
$802$	8.03900	−	19.6393i	0.283867	−	0.693487i
$803$	−32.7778	+	13.5770i	−1.15670	+	0.479123i
$804$		0			0
$805$	3.29512	−	7.95513i	0.116138	−	0.280382i
$806$	−0.312953	−	74.9964i	−0.0110233	−	2.64164i
$807$		0			0
$808$	−13.4365	+	0.168215i	−0.472693	+	0.00591778i
$809$	−17.2857	−	17.2857i	−0.607733	−	0.607733i	0.334620	−	0.942353i	$-0.391392\pi$
$809$	−17.2857	−	17.2857i	−0.607733	−	0.607733i	−0.942353	+	0.334620i	$0.891392\pi$
$810$		0			0
$811$	−8.60645	+	20.7778i	−0.302213	+	0.729608i	0.697699	+	0.716391i	$0.254207\pi$
$811$	−8.60645	+	20.7778i	−0.302213	+	0.729608i	−0.999913	+	0.0132170i	$0.995793\pi$
$812$	−0.804914	−	1.89827i	−0.0282469	−	0.0666161i
$813$		0			0
$814$	−8.43851	−	20.1343i	−0.295770	−	0.705707i
$815$		−	15.3898i		−	0.539080i
$816$		0			0
$817$		−	61.2313i		−	2.14221i
$818$	28.6777	−	12.0191i	1.00269	−	0.420239i
$819$		0			0
$820$	5.07390	−	12.5446i	0.177188	−	0.438076i
$821$	19.7476	−	47.6749i	0.689195	−	1.66386i	−0.0572007	−	0.998363i	$-0.518217\pi$
$821$	19.7476	−	47.6749i	0.689195	−	1.66386i	0.746396	−	0.665502i	$-0.231783\pi$
$822$		0			0
$823$	−25.0801	−	25.0801i	−0.874237	−	0.874237i	0.118694	−	0.992931i	$-0.462129\pi$
$823$	−25.0801	−	25.0801i	−0.874237	−	0.874237i	−0.992931	+	0.118694i	$0.962129\pi$
$824$	−1.05040	+	2.62850i	−0.0365926	+	0.0915680i
$825$		0			0
$826$	−8.25976	+	0.0344672i	−0.287394	+	0.00119927i
$827$	−5.36911	+	12.9622i	−0.186702	+	0.450739i	−0.989321	−	0.145753i	$-0.953439\pi$
$827$	−5.36911	+	12.9622i	−0.186702	+	0.450739i	0.802619	+	0.596492i	$0.203439\pi$
$828$		0			0
$829$	−6.27737	+	2.60017i	−0.218022	+	0.0903077i	−0.489021	−	0.872272i	$-0.662646\pi$
$829$	−6.27737	+	2.60017i	−0.218022	+	0.0903077i	0.270999	+	0.962580i	$0.412646\pi$
$830$	−12.5329	−	5.13012i	−0.435022	−	0.178069i
$831$		0			0
$832$	42.0198	+	16.1850i	1.45677	+	0.561114i
$833$			3.45542i			0.119723i
$834$		0			0
$835$	1.28724	+	3.10767i	0.0445468	+	0.107545i
$836$	−54.2210	−	53.3235i	−1.87527	−	1.84423i
$837$		0			0
$838$	0.0816922	+	19.5768i	0.00282201	+	0.676270i
$839$	−11.1915	−	11.1915i	−0.386373	−	0.386373i	0.487018	−	0.873392i	$-0.338084\pi$
$839$	−11.1915	−	11.1915i	−0.386373	−	0.386373i	−0.873392	+	0.487018i	$0.838084\pi$
$840$		0			0
$841$	20.2421	−	20.2421i	0.698002	−	0.698002i
$842$	5.77907	+	5.73104i	0.199160	+	0.197505i
$843$		0			0
$844$	−31.2134	−	12.6249i	−1.07441	−	0.434566i
$845$	−12.7506	+	5.28147i	−0.438634	+	0.181688i
$846$		0			0
$847$	−43.9074			−1.50867
$848$	−47.8661	−	18.8971i	−1.64373	−	0.648929i
$849$		0			0
$850$	−4.83292	+	2.02553i	−0.165768	+	0.0694751i
$851$	6.70722	+	16.1927i	0.229921	+	0.555078i
$852$		0			0
$853$	23.7303	+	9.82940i	0.812509	+	0.336552i	0.749955	−	0.661489i	$-0.230075\pi$
$853$	23.7303	+	9.82940i	0.812509	+	0.336552i	0.0625546	+	0.998042i	$0.480075\pi$
$854$	2.33289	+	2.31350i	0.0798298	+	0.0791663i
$855$		0			0
$856$	23.7443	−	0.297262i	0.811563	−	0.0101602i
$857$	−35.8087	+	35.8087i	−1.22320	+	1.22320i	−0.256717	+	0.966487i	$0.582641\pi$
$857$	−35.8087	+	35.8087i	−1.22320	+	1.22320i	−0.966487	+	0.256717i	$0.917359\pi$
$858$		0			0
$859$	4.34986	+	1.80177i	0.148415	+	0.0614757i	0.455655	−	0.890157i	$-0.349405\pi$
$859$	4.34986	+	1.80177i	0.148415	+	0.0614757i	−0.307239	+	0.951632i	$0.599405\pi$
$860$	−14.4772	+	0.120826i	−0.493667	+	0.00412013i
$861$		0			0
$862$	2.42596	+	0.993025i	0.0826285	+	0.0338226i
$863$	10.4293			0.355017			0.177508	−	0.984119i	$-0.443196\pi$
$863$	10.4293			0.355017			0.177508	+	0.984119i	$0.443196\pi$
$864$		0			0
$865$	−4.12810			−0.140360
$866$	−17.2780	−	7.07245i	−0.587130	−	0.240332i
$867$		0			0
$868$	−0.265310	−	31.7891i	−0.00900522	−	1.07899i
$869$	23.2553	+	9.63265i	0.788881	+	0.326765i
$870$		0			0
$871$	−19.6155	+	19.6155i	−0.664646	+	0.664646i
$872$	−2.31756	−	2.26025i	−0.0784826	−	0.0765418i
$873$		0			0
$874$	43.3515	+	42.9912i	1.46639	+	1.45420i
$875$	10.8863	+	4.50927i	0.368025	+	0.152441i
$876$		0			0
$877$	−10.9876	−	26.5265i	−0.371026	−	0.895736i	−0.993577	−	0.113157i	$-0.963904\pi$
$877$	−10.9876	−	26.5265i	−0.371026	−	0.895736i	0.622551	−	0.782579i	$-0.286096\pi$
$878$	38.7251	−	16.2301i	1.30691	−	0.547740i
$879$		0			0
$880$	−12.5005	+	12.9249i	−0.421391	+	0.435699i
$881$	50.1783			1.69055			0.845275	−	0.534332i	$-0.179437\pi$
$881$	50.1783			1.69055			0.845275	+	0.534332i	$0.179437\pi$
$882$		0			0
$883$	−0.738499	+	0.305896i	−0.0248525	+	0.0102942i	−0.395075	−	0.918649i	$-0.629281\pi$
$883$	−0.738499	+	0.305896i	−0.0248525	+	0.0102942i	0.370223	+	0.928943i	$0.379281\pi$
$884$	3.51139	−	8.68147i	0.118101	−	0.291989i
$885$		0			0
$886$	−8.25338	−	8.18478i	−0.277278	−	0.274973i
$887$	−30.7355	+	30.7355i	−1.03200	+	1.03200i	−0.0325277	+	0.999471i	$0.510356\pi$
$887$	−30.7355	+	30.7355i	−1.03200	+	1.03200i	−0.999471	+	0.0325277i	$0.989644\pi$
$888$		0			0
$889$	20.7690	+	20.7690i	0.696570	+	0.696570i
$890$	−0.0430459	−	10.3156i	−0.00144290	−	0.345778i
$891$		0			0
$892$	−4.49662	+	4.57231i	−0.150558	+	0.153092i
$893$	−7.44647	−	17.9774i	−0.249187	−	0.601590i
$894$		0			0
$895$			7.19892i			0.240633i
$896$	17.8401	+	6.78621i	0.595995	+	0.226711i
$897$		0			0
$898$	−37.3828	−	15.3020i	−1.24748	−	0.510635i
$899$	−5.31907	+	2.20323i	−0.177401	+	0.0734818i
$900$		0			0
$901$	−4.09564	+	9.88774i	−0.136445	+	0.329408i
$902$	78.8109	−	0.328871i	2.62412	−	0.0109502i
$903$		0			0
$904$	4.40182	−	1.88819i	0.146402	−	0.0628003i
$905$	−0.912638	−	0.912638i	−0.0303371	−	0.0303371i
$906$		0			0
$907$	4.17152	−	10.0709i	0.138513	−	0.334400i	−0.839367	−	0.543565i	$-0.817074\pi$
$907$	4.17152	−	10.0709i	0.138513	−	0.334400i	0.977881	+	0.209164i	$0.0670743\pi$
$908$	−34.2765	−	13.8638i	−1.13750	−	0.460086i
$909$		0			0
$910$	−9.14993	+	3.83484i	−0.303317	+	0.127124i
$911$		−	16.8358i		−	0.557794i	−0.960321	−	0.278897i	$-0.910031\pi$
$911$		−	16.8358i		−	0.557794i	0.960321	−	0.278897i	$-0.0899689\pi$
$912$		0			0
$913$		−	78.8719i		−	2.61028i
$914$	−18.9871	−	45.3033i	−0.628038	−	1.49850i
$915$		0			0
$916$	−19.0437	+	8.07503i	−0.629223	+	0.266806i
$917$	2.20711	−	5.32844i	0.0728852	−	0.175960i
$918$		0			0
$919$	25.6724	+	25.6724i	0.846855	+	0.846855i	0.989739	−	0.142885i	$-0.0456378\pi$
$919$	25.6724	+	25.6724i	0.846855	+	0.846855i	−0.142885	+	0.989739i	$0.545638\pi$
$920$	10.0791	−	10.3346i	0.332296	−	0.340722i
$921$		0			0
$922$	0.145009	+	34.7502i	0.00477563	+	1.14444i
$923$	−25.1777	+	60.7843i	−0.828734	+	2.00074i
$924$		0			0
$925$	−10.4400	+	4.32438i	−0.343264	+	0.142185i
$926$	7.38574	−	18.0433i	0.242710	−	0.592941i
$927$		0			0
$928$	−0.0721180	−	3.45601i	−0.00236739	−	0.113449i
$929$			20.3207i			0.666702i	0.942803	+	0.333351i	$0.108179\pi$
$929$			20.3207i			0.666702i	−0.942803	+	0.333351i	$0.891821\pi$
$930$		0			0
$931$	9.93314	+	23.9807i	0.325546	+	0.785937i
$932$	−0.00524514	−	0.628464i	−0.000171810	−	0.0205860i
$933$		0			0
$934$	37.8706	−	0.158031i	1.23916	−	0.00517092i
$935$	2.64423	+	2.64423i	0.0864756	+	0.0864756i
$936$		0			0
$937$	−22.4306	+	22.4306i	−0.732777	+	0.732777i	−0.971169	−	0.238392i	$-0.923380\pi$
$937$	−22.4306	+	22.4306i	−0.732777	+	0.732777i	0.238392	+	0.971169i	$0.423380\pi$
$938$	−8.27997	+	8.34936i	−0.270351	+	0.272616i
$939$		0			0
$940$	−4.23577	+	1.79607i	−0.138156	+	0.0585815i
$941$	36.4356	−	15.0921i	1.18777	−	0.491989i	0.300739	−	0.953707i	$-0.402767\pi$
$941$	36.4356	−	15.0921i	1.18777	−	0.491989i	0.887027	+	0.461718i	$0.152767\pi$
$942$		0			0
$943$	−63.2728			−2.06045
$944$	−12.8803	−	5.08503i	−0.419219	−	0.165504i
$945$		0			0
$946$	−32.5928	−	77.7664i	−1.05968	−	2.52840i
$947$	17.0628	+	41.1933i	0.554467	+	1.33860i	0.914092	+	0.405506i	$0.132905\pi$
$947$	17.0628	+	41.1933i	0.554467	+	1.33860i	−0.359625	+	0.933097i	$0.617095\pi$
$948$		0			0
$949$	−30.3202	−	12.5590i	−0.984236	−	0.407684i
$950$	−27.7179	+	27.9502i	−0.899288	+	0.906825i
$951$		0			0
$952$	1.47306	−	3.68613i	0.0477421	−	0.119468i
$953$	−22.0729	+	22.0729i	−0.715012	+	0.715012i	−0.967579	−	0.252567i	$-0.918725\pi$
$953$	−22.0729	+	22.0729i	−0.715012	+	0.715012i	0.252567	+	0.967579i	$0.418725\pi$
$954$		0			0
$955$	−1.42016	−	0.588251i	−0.0459554	−	0.0190354i
$956$	−6.04979	+	6.15163i	−0.195664	+	0.198958i
$957$		0			0
$958$	−4.58897	+	11.2108i	−0.148263	+	0.362206i
$959$	−0.0819637			−0.00264674
$960$		0			0
$961$	−57.7671			−1.86346
$962$	7.65010	−	18.6892i	0.246649	−	0.602563i
$963$		0			0
$964$	−29.8844	+	30.3875i	−0.962513	+	0.978715i
$965$	−7.19653	−	2.98090i	−0.231665	−	0.0959586i
$966$		0			0
$967$	1.21138	−	1.21138i	0.0389555	−	0.0389555i	−0.687361	−	0.726316i	$-0.741231\pi$
$967$	1.21138	−	1.21138i	0.0389555	−	0.0389555i	0.726316	+	0.687361i	$0.241231\pi$
$968$	−68.3554	−	27.3163i	−2.19703	−	0.877980i
$969$		0			0
$970$	−1.66986	+	1.68386i	−0.0536160	+	0.0540653i
$971$	−36.7679	−	15.2298i	−1.17994	−	0.488746i	−0.295472	−	0.955351i	$-0.595477\pi$
$971$	−36.7679	−	15.2298i	−1.17994	−	0.488746i	−0.884466	+	0.466605i	$0.845477\pi$
$972$		0			0
$973$	−7.68934	−	18.5637i	−0.246509	−	0.595126i
$974$	−4.01733	−	9.58535i	−0.128723	−	0.307135i
$975$		0			0
$976$	2.19255	+	5.05305i	0.0701819	+	0.161744i
$977$	−2.64835			−0.0847282			−0.0423641	−	0.999102i	$-0.513489\pi$
$977$	−2.64835			−0.0847282			−0.0423641	+	0.999102i	$0.513489\pi$
$978$		0			0
$979$	55.5066	−	22.9916i	1.77400	−	0.734815i
$980$	5.65026	−	2.39585i	0.180491	−	0.0765327i
$981$		0			0
$982$	6.27426	−	6.32684i	0.200220	−	0.201898i
$983$	10.8449	−	10.8449i	0.345898	−	0.345898i	−0.512681	−	0.858579i	$-0.671348\pi$
$983$	10.8449	−	10.8449i	0.345898	−	0.345898i	0.858579	+	0.512681i	$0.171348\pi$
$984$		0			0
$985$	−9.93254	−	9.93254i	−0.316477	−	0.316477i
$986$	−0.718897	+	0.00299989i	−0.0228943	+	9.55359e-5i
$987$		0			0
$988$	−0.587086	−	70.3437i	−0.0186777	−	2.23793i
$989$	25.9059	+	62.5423i	0.823759	+	1.98873i
$990$		0			0
$991$			29.7431i			0.944819i	0.881379	+	0.472410i	$0.156616\pi$
$991$			29.7431i			0.944819i	−0.881379	+	0.472410i	$0.843384\pi$
$992$	19.3641	−	49.6546i	0.614810	−	1.57654i
$993$		0			0
$994$	−10.5649	+	25.8099i	−0.335097	+	0.818641i
$995$	−4.50584	+	1.86638i	−0.142845	+	0.0591683i
$996$		0			0
$997$	15.1979	−	36.6911i	0.481324	−	1.16202i	−0.477657	−	0.878547i	$-0.658514\pi$
$997$	15.1979	−	36.6911i	0.481324	−	1.16202i	0.958981	−	0.283472i	$-0.0914863\pi$
$998$	0.0775695	+	18.5888i	0.00245542	+	0.588420i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.b.107.20	yes	128
3.2	odd	2	inner	864.2.w.b.107.13	✓	128
32.3	odd	8	inner	864.2.w.b.323.13	yes	128
96.35	even	8	inner	864.2.w.b.323.20	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.b.107.13	✓	128	3.2	odd	2	inner
864.2.w.b.107.20	yes	128	1.1	even	1	trivial
864.2.w.b.323.13	yes	128	32.3	odd	8	inner
864.2.w.b.323.20	yes	128	96.35	even	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.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.535739 - 1.30881i) q^{2} +(-1.42597 - 1.40236i) q^{4} +(0.682524 + 0.282711i) q^{5} +(-1.19295 + 1.19295i) q^{7} +(-2.59937 + 1.11502i) q^{8} +O(q^{10})\)	\(q+(0.535739 - 1.30881i) q^{2} +(-1.42597 - 1.40236i) q^{4} +(0.682524 + 0.282711i) q^{5} +(-1.19295 + 1.19295i) q^{7} +(-2.59937 + 1.11502i) q^{8} +(0.735670 - 0.741835i) q^{10} +(5.62168 + 2.32858i) q^{11} +(2.15399 + 5.20018i) q^{13} +(0.922234 + 2.20045i) q^{14} +(0.0667630 + 3.99944i) q^{16} +0.831881 q^{17} +(5.77328 - 2.39137i) q^{19} +(-0.576794 - 1.36028i) q^{20} +(6.05942 - 6.11020i) q^{22} +(-4.88515 + 4.88515i) q^{23} +(-3.14962 - 3.14962i) q^{25} +(7.96002 - 0.0332164i) q^{26} +(3.37405 - 0.0281597i) q^{28} +(-0.233848 - 0.564559i) q^{29} -9.42163i q^{31} +(5.27028 + 2.05528i) q^{32} +(0.445671 - 1.08877i) q^{34} +(-1.15148 + 0.476957i) q^{35} +(0.970846 - 2.34383i) q^{37} +(-0.0368772 - 8.83728i) q^{38} +(-2.08936 + 0.0261574i) q^{40} +(6.47604 + 6.47604i) q^{41} +(3.74978 - 9.05277i) q^{43} +(-4.75082 - 11.2041i) q^{44} +(3.77656 + 9.01089i) q^{46} -3.11389i q^{47} +4.15374i q^{49} +(-5.80963 + 2.43488i) q^{50} +(4.22102 - 10.4360i) q^{52} +(-4.92335 + 11.8860i) q^{53} +(3.17862 + 3.17862i) q^{55} +(1.77076 - 4.43108i) q^{56} +(-0.864182 + 0.00360615i) q^{58} +(-1.32483 + 3.19841i) q^{59} +(1.27224 - 0.526977i) q^{61} +(-12.3311 - 5.04754i) q^{62} +(5.51346 - 5.79670i) q^{64} +4.15820i q^{65} +(1.88604 + 4.55331i) q^{67} +(-1.18623 - 1.16660i) q^{68} +(0.00735512 + 1.76259i) q^{70} +(8.26529 + 8.26529i) q^{71} +(-4.12286 + 4.12286i) q^{73} +(-2.54751 - 2.52633i) q^{74} +(-11.5861 - 4.68621i) q^{76} +(-9.48426 + 3.92851i) q^{77} +4.13671 q^{79} +(-1.08512 + 2.74859i) q^{80} +(11.9454 - 5.00644i) q^{82} +(-4.96034 - 11.9753i) q^{83} +(0.567779 + 0.235182i) q^{85} +(-9.83945 - 9.75767i) q^{86} +(-17.2092 + 0.215448i) q^{88} +(6.98174 - 6.98174i) q^{89} +(-8.77315 - 3.63396i) q^{91} +(13.8168 - 0.115314i) q^{92} +(-4.07549 - 1.66823i) q^{94} +4.61647 q^{95} -2.26985 q^{97} +(5.43646 + 2.22532i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) \) 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

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