LMFDB - Embedded newform 864.2.v.b.109.19

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			109.19
Character	$\chi$	$=$	864.109
Dual form			864.2.v.b.325.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.322202 + 1.37702i) q^{2} +(-1.79237 + 0.887359i) q^{4} +(-1.57161 + 0.650984i) q^{5} +(3.07534 - 3.07534i) q^{7} +(-1.79942 - 2.18222i) q^{8} +O(q^{10})$	\(q+(0.322202 + 1.37702i) q^{2} +(-1.79237 + 0.887359i) q^{4} +(-1.57161 + 0.650984i) q^{5} +(3.07534 - 3.07534i) q^{7} +(-1.79942 - 2.18222i) q^{8} +(-1.40280 - 1.95440i) q^{10} +(1.10590 + 2.66989i) q^{11} +(4.29788 + 1.78024i) q^{13} +(5.22569 + 3.24393i) q^{14} +(2.42519 - 3.18095i) q^{16} -5.78176i q^{17} +(1.92883 + 0.798948i) q^{19} +(2.23926 - 2.56139i) q^{20} +(-3.32016 + 2.38309i) q^{22} +(0.525810 + 0.525810i) q^{23} +(-1.48934 + 1.48934i) q^{25} +(-1.06664 + 6.49187i) q^{26} +(-2.78322 + 8.24109i) q^{28} +(-1.72922 + 4.17470i) q^{29} +6.80754 q^{31} +(5.16164 + 2.31462i) q^{32} +(7.96160 - 1.86290i) q^{34} +(-2.83125 + 6.83525i) q^{35} +(-1.09955 + 0.455448i) q^{37} +(-0.478693 + 2.91346i) q^{38} +(4.24858 + 2.25822i) q^{40} +(7.20426 + 7.20426i) q^{41} +(0.960366 + 2.31853i) q^{43} +(-4.35133 - 3.80409i) q^{44} +(-0.554634 + 0.893469i) q^{46} +5.24257i q^{47} -11.9155i q^{49} +(-2.53072 - 1.57099i) q^{50} +(-9.28311 + 0.622911i) q^{52} +(0.00485782 + 0.0117278i) q^{53} +(-3.47611 - 3.47611i) q^{55} +(-12.2449 - 1.17726i) q^{56} +(-6.30580 - 1.03607i) q^{58} +(8.86095 - 3.67033i) q^{59} +(0.439229 - 1.06039i) q^{61} +(2.19341 + 9.37412i) q^{62} +(-1.52419 + 7.85346i) q^{64} -7.91352 q^{65} +(-1.17849 + 2.84512i) q^{67} +(5.13049 + 10.3631i) q^{68} +(-10.3245 - 1.69636i) q^{70} +(-7.54709 + 7.54709i) q^{71} +(-9.04188 - 9.04188i) q^{73} +(-0.981439 - 1.36735i) q^{74} +(-4.16613 + 0.279554i) q^{76} +(11.6118 + 4.80978i) q^{77} -8.85007i q^{79} +(-1.74071 + 6.57799i) q^{80} +(-7.59918 + 12.2416i) q^{82} +(-13.0846 - 5.41983i) q^{83} +(3.76383 + 9.08669i) q^{85} +(-2.88323 + 2.06948i) q^{86} +(3.83630 - 7.21756i) q^{88} +(12.4152 - 12.4152i) q^{89} +(18.6923 - 7.74261i) q^{91} +(-1.40903 - 0.475865i) q^{92} +(-7.21913 + 1.68917i) q^{94} -3.55148 q^{95} +9.47707 q^{97} +(16.4078 - 3.83919i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.322202	+	1.37702i	0.227832	+	0.973701i
$2$	0.322202	+	1.37702i	0.227832	+	0.973701i
$3$		0			0
$3$		0			0
$4$	−1.79237	+	0.887359i	−0.896186	+	0.443679i
$5$	−1.57161	+	0.650984i	−0.702847	+	0.291129i	−0.705341	−	0.708868i	$-0.749206\pi$
$5$	−1.57161	+	0.650984i	−0.702847	+	0.291129i	0.00249383	+	0.999997i	$0.499206\pi$
$6$		0			0
$7$	3.07534	−	3.07534i	1.16237	−	1.16237i	0.178415	−	0.983955i	$-0.442903\pi$
$7$	3.07534	−	3.07534i	1.16237	−	1.16237i	0.983955	−	0.178415i	$-0.0570969\pi$
$8$	−1.79942	−	2.18222i	−0.636190	−	0.771532i
$9$		0			0
$10$	−1.40280	−	1.95440i	−0.443603	−	0.618035i
$11$	1.10590	+	2.66989i	0.333442	+	0.805001i	0.998314	+	0.0580432i	$0.0184861\pi$
$11$	1.10590	+	2.66989i	0.333442	+	0.805001i	−0.664872	+	0.746957i	$0.731514\pi$
$12$		0			0
$13$	4.29788	+	1.78024i	1.19202	+	0.493750i	0.888412	−	0.459047i	$-0.151809\pi$
$13$	4.29788	+	1.78024i	1.19202	+	0.493750i	0.303606	+	0.952798i	$0.401809\pi$
$14$	5.22569	+	3.24393i	1.39663	+	0.866976i
$15$		0			0
$16$	2.42519	−	3.18095i	0.606297	−	0.795238i
$17$		−	5.78176i		−	1.40228i	−0.713022	−	0.701141i	$-0.752674\pi$
$17$		−	5.78176i		−	1.40228i	0.713022	−	0.701141i	$-0.247326\pi$
$18$		0			0
$19$	1.92883	+	0.798948i	0.442504	+	0.183291i	0.592800	−	0.805350i	$-0.298023\pi$
$19$	1.92883	+	0.798948i	0.442504	+	0.183291i	−0.150296	+	0.988641i	$0.548023\pi$
$20$	2.23926	−	2.56139i	0.500714	−	0.572744i
$21$		0			0
$22$	−3.32016	+	2.38309i	−0.707861	+	0.508077i
$23$	0.525810	+	0.525810i	0.109639	+	0.109639i	0.759798	−	0.650159i	$-0.225298\pi$
$23$	0.525810	+	0.525810i	0.109639	+	0.109639i	−0.650159	+	0.759798i	$0.725298\pi$
$24$		0			0
$25$	−1.48934	+	1.48934i	−0.297868	+	0.297868i
$26$	−1.06664	+	6.49187i	−0.209185	+	1.27316i
$27$		0			0
$28$	−2.78322	+	8.24109i	−0.525980	+	1.55742i
$29$	−1.72922	+	4.17470i	−0.321107	+	0.775222i	0.678083	+	0.734985i	$0.262811\pi$
$29$	−1.72922	+	4.17470i	−0.321107	+	0.775222i	−0.999190	+	0.0402362i	$0.987189\pi$
$30$		0			0
$31$	6.80754			1.22267			0.611335	−	0.791372i	$-0.290633\pi$
$31$	6.80754			1.22267			0.611335	+	0.791372i	$0.290633\pi$
$32$	5.16164	+	2.31462i	0.912457	+	0.409172i
$33$		0			0
$34$	7.96160	−	1.86290i	1.36540	−	0.319484i
$35$	−2.83125	+	6.83525i	−0.478569	+	1.15537i
$36$		0			0
$37$	−1.09955	+	0.455448i	−0.180765	+	0.0748752i	−0.471230	−	0.882010i	$-0.656190\pi$
$37$	−1.09955	+	0.455448i	−0.180765	+	0.0748752i	0.290465	+	0.956885i	$0.406190\pi$
$38$	−0.478693	+	2.91346i	−0.0776543	+	0.472626i
$39$		0			0
$40$	4.24858	+	2.25822i	0.671760	+	0.357056i
$41$	7.20426	+	7.20426i	1.12512	+	1.12512i	0.990960	+	0.134156i	$0.0428322\pi$
$41$	7.20426	+	7.20426i	1.12512	+	1.12512i	0.134156	+	0.990960i	$0.457168\pi$
$42$		0			0
$43$	0.960366	+	2.31853i	0.146455	+	0.353572i	0.980035	−	0.198826i	$-0.0637128\pi$
$43$	0.960366	+	2.31853i	0.146455	+	0.353572i	−0.833580	+	0.552398i	$0.813713\pi$
$44$	−4.35133	−	3.80409i	−0.655988	−	0.573489i
$45$		0			0
$46$	−0.554634	+	0.893469i	−0.0817764	+	0.131735i
$47$			5.24257i			0.764708i	0.924016	+	0.382354i	$0.124886\pi$
$47$			5.24257i			0.764708i	−0.924016	+	0.382354i	$0.875114\pi$
$48$		0			0
$49$		−	11.9155i		−	1.70221i
$50$	−2.53072	−	1.57099i	−0.357898	−	0.222171i
$51$		0			0
$52$	−9.28311	+	0.622911i	−1.28734	+	0.0863822i
$53$	0.00485782	+	0.0117278i	0.000667273	+	0.00161094i	0.924213	−	0.381878i	$-0.124722\pi$
$53$	0.00485782	+	0.0117278i	0.000667273	+	0.00161094i	−0.923546	+	0.383489i	$0.874722\pi$
$54$		0			0
$55$	−3.47611	−	3.47611i	−0.468718	−	0.468718i
$56$	−12.2449	−	1.17726i	−1.63629	−	0.157318i
$57$		0			0
$58$	−6.30580	−	1.03607i	−0.827992	−	0.136042i
$59$	8.86095	−	3.67033i	1.15360	−	0.477836i	0.277859	−	0.960622i	$-0.410375\pi$
$59$	8.86095	−	3.67033i	1.15360	−	0.477836i	0.875738	+	0.482786i	$0.160375\pi$
$60$		0			0
$61$	0.439229	−	1.06039i	0.0562375	−	0.135769i	−0.893263	−	0.449534i	$-0.851590\pi$
$61$	0.439229	−	1.06039i	0.0562375	−	0.135769i	0.949501	+	0.313764i	$0.101590\pi$
$62$	2.19341	+	9.37412i	0.278563	+	1.19051i
$63$		0			0
$64$	−1.52419	+	7.85346i	−0.190524	+	0.981683i
$65$	−7.91352			−0.981552
$66$		0			0
$67$	−1.17849	+	2.84512i	−0.143975	+	0.347587i	−0.979374	−	0.202058i	$-0.935237\pi$
$67$	−1.17849	+	2.84512i	−0.143975	+	0.347587i	0.835398	+	0.549645i	$0.185237\pi$
$68$	5.13049	+	10.3631i	0.622164	+	1.25671i
$69$		0			0
$70$	−10.3245	−	1.69636i	−1.23402	−	0.202754i
$71$	−7.54709	+	7.54709i	−0.895675	+	0.895675i	−0.995050	−	0.0993754i	$-0.968316\pi$
$71$	−7.54709	+	7.54709i	−0.895675	+	0.895675i	0.0993754	+	0.995050i	$0.468316\pi$
$72$		0			0
$73$	−9.04188	−	9.04188i	−1.05827	−	1.05827i	−0.998194	−	0.0600782i	$-0.980865\pi$
$73$	−9.04188	−	9.04188i	−1.05827	−	1.05827i	−0.0600782	−	0.998194i	$-0.519135\pi$
$74$	−0.981439	−	1.36735i	−0.114090	−	0.158952i
$75$		0			0
$76$	−4.16613	+	0.279554i	−0.477888	+	0.0320670i
$77$	11.6118	+	4.80978i	1.32329	+	0.548126i
$78$		0			0
$79$		−	8.85007i		−	0.995711i	−0.867260	−	0.497855i	$-0.834121\pi$
$79$		−	8.85007i		−	0.995711i	0.867260	−	0.497855i	$-0.165879\pi$
$80$	−1.74071	+	6.57799i	−0.194618	+	0.735442i
$81$		0			0
$82$	−7.59918	+	12.2416i	−0.839189	+	1.35186i
$83$	−13.0846	−	5.41983i	−1.43622	−	0.594903i	−0.477344	−	0.878717i	$-0.658400\pi$
$83$	−13.0846	−	5.41983i	−1.43622	−	0.594903i	−0.958880	+	0.283813i	$0.908400\pi$
$84$		0			0
$85$	3.76383	+	9.08669i	0.408245	+	0.985590i
$86$	−2.88323	+	2.06948i	−0.310907	+	0.223158i
$87$		0			0
$88$	3.83630	−	7.21756i	0.408951	−	0.769395i
$89$	12.4152	−	12.4152i	1.31601	−	1.31601i	0.399108	−	0.916904i	$-0.369320\pi$
$89$	12.4152	−	12.4152i	1.31601	−	1.31601i	0.916904	−	0.399108i	$-0.130680\pi$
$90$		0			0
$91$	18.6923	−	7.74261i	1.95949	−	0.811646i
$92$	−1.40903	−	0.475865i	−0.146901	−	0.0496123i
$93$		0			0
$94$	−7.21913	+	1.68917i	−0.744597	+	0.174225i
$95$	−3.55148			−0.364374
$96$		0			0
$97$	9.47707			0.962250			0.481125	−	0.876652i	$-0.340228\pi$
$97$	9.47707			0.962250			0.481125	+	0.876652i	$0.340228\pi$
$98$	16.4078	−	3.83919i	1.65744	−	0.387817i
$99$		0			0
$100$	1.34787	−	3.99103i	0.134787	−	0.399103i
$101$	15.7033	−	6.50453i	1.56254	−	0.647225i	0.577011	−	0.816736i	$-0.304219\pi$
$101$	15.7033	−	6.50453i	1.56254	−	0.647225i	0.985528	+	0.169511i	$0.0542189\pi$
$102$		0			0
$103$	−9.78095	+	9.78095i	−0.963746	+	0.963746i	−0.999365	−	0.0356196i	$-0.988660\pi$
$103$	−9.78095	+	9.78095i	−0.963746	+	0.963746i	0.0356196	+	0.999365i	$0.488660\pi$
$104$	−3.84880	−	12.5823i	−0.377406	−	1.23380i
$105$		0			0
$106$	−0.0145842	+	0.0104681i	−0.00141655	+	0.00101675i
$107$	1.84303	+	4.44946i	0.178172	+	0.430145i	0.987583	−	0.157097i	$-0.0502135\pi$
$107$	1.84303	+	4.44946i	0.178172	+	0.430145i	−0.809411	+	0.587242i	$0.800214\pi$
$108$		0			0
$109$	14.1918	+	5.87844i	1.35933	+	0.563052i	0.938874	−	0.344262i	$-0.111871\pi$
$109$	14.1918	+	5.87844i	1.35933	+	0.563052i	0.420454	+	0.907314i	$0.361871\pi$
$110$	3.66666	−	5.90668i	0.349602	−	0.563180i
$111$		0			0
$112$	−2.32423	−	17.2408i	−0.219619	−	1.62910i
$113$		−	13.1265i		−	1.23483i	−0.786636	−	0.617417i	$-0.788179\pi$
$113$		−	13.1265i		−	1.23483i	0.786636	−	0.617417i	$-0.211821\pi$
$114$		0			0
$115$	−1.16867	−	0.484077i	−0.108979	−	0.0451404i
$116$	−0.605057	−	9.01704i	−0.0561781	−	0.837211i
$117$		0			0
$118$	7.90913	+	11.0191i	0.728095	+	1.01439i
$119$	−17.7809	−	17.7809i	−1.62997	−	1.62997i
$120$		0			0
$121$	1.87291	−	1.87291i	0.170264	−	0.170264i
$122$	1.60170	+	0.263166i	0.145011	+	0.0238259i
$123$		0			0
$124$	−12.2016	+	6.04073i	−1.09574	+	0.542474i
$125$	4.62605	−	11.1683i	0.413767	−	0.998921i
$126$		0			0
$127$	−16.0709			−1.42607			−0.713033	−	0.701131i	$-0.752679\pi$
$127$	−16.0709			−1.42607			−0.713033	+	0.701131i	$0.752679\pi$
$128$	−11.3055	+	0.431559i	−0.999272	+	0.0381448i
$129$		0			0
$130$	−2.54976	−	10.8971i	−0.223628	−	0.955738i
$131$	−3.38930	+	8.18249i	−0.296124	+	0.714907i	0.703865	+	0.710333i	$0.251456\pi$
$131$	−3.38930	+	8.18249i	−0.296124	+	0.714907i	−0.999990	+	0.00457365i	$0.998544\pi$
$132$		0			0
$133$	8.38885	−	3.47478i	0.727406	−	0.301301i
$134$	−4.29750	−	0.706097i	−0.371248	−	0.0609975i
$135$		0			0
$136$	−12.6171	+	10.4038i	−1.08191	+	0.892118i
$137$	9.96122	+	9.96122i	0.851044	+	0.851044i	0.990262	−	0.139218i	$-0.0444587\pi$
$137$	9.96122	+	9.96122i	0.851044	+	0.851044i	−0.139218	+	0.990262i	$0.544459\pi$
$138$		0			0
$139$	1.78163	+	4.30123i	0.151116	+	0.364826i	0.981250	−	0.192737i	$-0.0617365\pi$
$139$	1.78163	+	4.30123i	0.151116	+	0.364826i	−0.830135	+	0.557563i	$0.811737\pi$
$140$	−0.990662	−	14.7636i	−0.0837263	−	1.24776i
$141$		0			0
$142$	−12.8242	−	7.96081i	−1.07618	−	0.668056i
$143$			13.4436i			1.12421i
$144$		0			0
$145$		−	7.68670i		−	0.638346i
$146$	9.53754	−	15.3642i	0.789332	−	1.27155i
$147$		0			0
$148$	1.56665	−	1.79203i	0.128778	−	0.147304i
$149$	−4.12035	−	9.94741i	−0.337552	−	0.814923i	−0.997949	−	0.0640068i	$-0.979612\pi$
$149$	−4.12035	−	9.94741i	−0.337552	−	0.814923i	0.660397	−	0.750916i	$-0.270388\pi$
$150$		0			0
$151$	3.44757	+	3.44757i	0.280559	+	0.280559i	0.833332	−	0.552773i	$-0.186430\pi$
$151$	3.44757	+	3.44757i	0.280559	+	0.280559i	−0.552773	+	0.833332i	$0.686430\pi$
$152$	−1.72729	−	5.64678i	−0.140102	−	0.458014i
$153$		0			0
$154$	−2.88181	+	17.5395i	−0.232222	+	1.41337i
$155$	−10.6988	+	4.43160i	−0.859351	+	0.355955i
$156$		0			0
$157$	−6.79910	+	16.4145i	−0.542627	+	1.31002i	0.380236	+	0.924890i	$0.375843\pi$
$157$	−6.79910	+	16.4145i	−0.542627	+	1.31002i	−0.922863	+	0.385129i	$0.874157\pi$
$158$	12.1867	−	2.85151i	0.969524	−	0.226854i
$159$		0			0
$160$	−9.61889	−	0.277553i	−0.760440	−	0.0219425i
$161$	3.23409			0.254882
$162$		0			0
$163$	7.18090	−	17.3362i	0.562452	−	1.35788i	−0.345348	−	0.938475i	$-0.612239\pi$
$163$	7.18090	−	17.3362i	0.562452	−	1.35788i	0.907800	−	0.419404i	$-0.137761\pi$
$164$	−19.3055	−	6.51994i	−1.50750	−	0.509122i
$165$		0			0
$166$	3.24732	−	19.7641i	0.252041	−	1.53399i
$167$	−6.69386	+	6.69386i	−0.517986	+	0.517986i	−0.916962	−	0.398975i	$-0.869366\pi$
$167$	−6.69386	+	6.69386i	−0.517986	+	0.517986i	0.398975	+	0.916962i	$0.369366\pi$
$168$		0			0
$169$	6.11015	+	6.11015i	0.470012	+	0.470012i
$170$	−11.2998	+	8.11063i	−0.866659	+	0.622057i
$171$		0			0
$172$	−3.77870	−	3.30348i	−0.288123	−	0.251888i
$173$	−12.5160	−	5.18430i	−0.951575	−	0.394155i	−0.147752	−	0.989024i	$-0.547204\pi$
$173$	−12.5160	−	5.18430i	−0.951575	−	0.394155i	−0.803822	+	0.594869i	$0.797204\pi$
$174$		0			0
$175$			9.16047i			0.692467i
$176$	11.1748	+	2.95715i	0.842332	+	0.222904i
$177$		0			0
$178$	21.0962	+	13.0958i	1.58123	+	0.981573i
$179$	−8.07265	−	3.34380i	−0.603378	−	0.249928i	0.0600160	−	0.998197i	$-0.480885\pi$
$179$	−8.07265	−	3.34380i	−0.603378	−	0.249928i	−0.663394	+	0.748270i	$0.730885\pi$
$180$		0			0
$181$	−2.61334	−	6.30916i	−0.194248	−	0.468956i	0.796505	−	0.604631i	$-0.206680\pi$
$181$	−2.61334	−	6.30916i	−0.194248	−	0.468956i	−0.990753	+	0.135675i	$0.956680\pi$
$182$	16.6844	+	23.2450i	1.23673	+	1.72304i
$183$		0			0
$184$	0.201283	−	2.09359i	0.0148388	−	0.154341i
$185$	1.43158	−	1.43158i	0.105252	−	0.105252i
$186$		0			0
$187$	15.4366	−	6.39406i	1.12884	−	0.467580i
$188$	−4.65204	−	9.39664i	−0.339285	−	0.685320i
$189$		0			0
$190$	−1.14430	−	4.89046i	−0.0830159	−	0.354791i
$191$	3.99365			0.288970			0.144485	−	0.989507i	$-0.453847\pi$
$191$	3.99365			0.288970			0.144485	+	0.989507i	$0.453847\pi$
$192$		0			0
$193$	2.43219			0.175073			0.0875366	−	0.996161i	$-0.472101\pi$
$193$	2.43219			0.175073			0.0875366	+	0.996161i	$0.472101\pi$
$194$	3.05353	+	13.0501i	0.219231	+	0.936944i
$195$		0			0
$196$	10.5733	+	21.3569i	0.755235	+	1.52550i
$197$	−10.1588	+	4.20791i	−0.723783	+	0.299801i	−0.713995	−	0.700151i	$-0.753116\pi$
$197$	−10.1588	+	4.20791i	−0.723783	+	0.299801i	−0.00978883	+	0.999952i	$0.503116\pi$
$198$		0			0
$199$	−10.5481	+	10.5481i	−0.747737	+	0.747737i	−0.974054	−	0.226316i	$-0.927332\pi$
$199$	−10.5481	+	10.5481i	−0.747737	+	0.747737i	0.226316	+	0.974054i	$0.427332\pi$
$200$	5.93002	+	0.570128i	0.419316	+	0.0403141i
$201$		0			0
$202$	14.0165	+	19.5280i	0.986199	+	1.37399i
$203$	7.52069	+	18.1566i	0.527849	+	1.27434i
$204$		0			0
$205$	−16.0122	−	6.63246i	−1.11834	−	0.463231i
$206$	−16.6200	−	10.3171i	−1.15797	−	0.718828i
$207$		0			0
$208$	16.0860	−	9.35394i	1.11537	−	0.648579i
$209$			6.03331i			0.417333i
$210$		0			0
$211$	9.72448	+	4.02801i	0.669461	+	0.277300i	0.691414	−	0.722459i	$-0.256988\pi$
$211$	9.72448	+	4.02801i	0.669461	+	0.277300i	−0.0219526	+	0.999759i	$0.506988\pi$
$212$	−0.0191138	−	0.0167100i	−0.00131274	−	0.00114765i
$213$		0			0
$214$	−5.53317	+	3.97151i	−0.378240	+	0.271487i
$215$	−3.01865	−	3.01865i	−0.205870	−	0.205870i
$216$		0			0
$217$	20.9355	−	20.9355i	1.42120	−	1.42120i
$218$	−3.52209	+	21.4364i	−0.238546	+	1.45186i
$219$		0			0
$220$	9.31502	+	3.14592i	0.628019	+	0.212098i
$221$	10.2929	−	24.8493i	0.692377	−	1.67155i
$222$		0			0
$223$	−22.9813			−1.53894			−0.769470	−	0.638683i	$-0.779480\pi$
$223$	−22.9813			−1.53894			−0.769470	+	0.638683i	$0.779480\pi$
$224$	22.9921	−	8.75554i	1.53622	−	0.585004i
$225$		0			0
$226$	18.0754	−	4.22938i	1.20236	−	0.281334i
$227$	11.4882	−	27.7350i	0.762500	−	1.84084i	0.301355	−	0.953512i	$-0.402561\pi$
$227$	11.4882	−	27.7350i	0.762500	−	1.84084i	0.461145	−	0.887325i	$-0.347439\pi$
$228$		0			0
$229$	−17.5270	+	7.25994i	−1.15822	+	0.479750i	−0.877282	−	0.479976i	$-0.840646\pi$
$229$	−17.5270	+	7.25994i	−1.15822	+	0.479750i	−0.280938	+	0.959726i	$0.590646\pi$
$230$	0.290037	−	1.76525i	0.0191245	−	0.116397i
$231$		0			0
$232$	12.2217	−	3.73849i	0.802394	−	0.245444i
$233$	−12.2771	−	12.2771i	−0.804300	−	0.804300i	0.179464	−	0.983764i	$-0.442564\pi$
$233$	−12.2771	−	12.2771i	−0.804300	−	0.804300i	−0.983764	+	0.179464i	$0.942564\pi$
$234$		0			0
$235$	−3.41283	−	8.23930i	−0.222629	−	0.537473i
$236$	−12.6252	+	14.4414i	−0.821832	+	0.940057i
$237$		0			0
$238$	18.7556	−	30.2137i	1.21575	−	1.95846i
$239$		−	18.7789i		−	1.21470i	−0.794433	−	0.607351i	$-0.792232\pi$
$239$		−	18.7789i		−	1.21470i	0.794433	−	0.607351i	$-0.207768\pi$
$240$		0			0
$241$			5.58803i			0.359956i	0.983671	+	0.179978i	$0.0576027\pi$
$241$			5.58803i			0.359956i	−0.983671	+	0.179978i	$0.942397\pi$
$242$	3.18249	+	1.97558i	0.204578	+	0.126995i
$243$		0			0
$244$	0.153687	+	2.29037i	0.00983881	+	0.146626i
$245$	7.75678	+	18.7265i	0.495562	+	1.19639i
$246$		0			0
$247$	6.86757	+	6.86757i	0.436973	+	0.436973i
$248$	−12.2496	−	14.8556i	−0.777851	−	0.943330i
$249$		0			0
$250$	16.8695	+	2.77172i	1.06692	+	0.175299i
$251$	−12.1377	+	5.02760i	−0.766125	+	0.317339i	−0.731302	−	0.682054i	$-0.761087\pi$
$251$	−12.1377	+	5.02760i	−0.766125	+	0.317339i	−0.0348230	+	0.999393i	$0.511087\pi$
$252$		0			0
$253$	−0.822358	+	1.98535i	−0.0517012	+	0.124818i
$254$	−5.17810	−	22.1300i	−0.324903	−	1.38856i
$255$		0			0
$256$	−4.23692	−	15.4288i	−0.264807	−	0.964301i
$257$	−18.1239			−1.13054			−0.565268	−	0.824907i	$-0.691227\pi$
$257$	−18.1239			−1.13054			−0.565268	+	0.824907i	$0.691227\pi$
$258$		0			0
$259$	−1.98083	+	4.78215i	−0.123083	+	0.297148i
$260$	14.1840	−	7.02213i	0.879653	−	0.435494i
$261$		0			0
$262$	−12.3595	−	2.03071i	−0.763572	−	0.125458i
$263$	−3.62779	+	3.62779i	−0.223699	+	0.223699i	−0.810054	−	0.586355i	$-0.800562\pi$
$263$	−3.62779	+	3.62779i	−0.223699	+	0.223699i	0.586355	+	0.810054i	$0.300562\pi$
$264$		0			0
$265$	−0.0152692	−	0.0152692i	−0.000937982	−	0.000937982i
$266$	7.48775	+	10.4320i	0.459103	+	0.639629i
$267$		0			0
$268$	−0.412356	−	6.14526i	−0.0251886	−	0.375381i
$269$	−12.7398	−	5.27701i	−0.776761	−	0.321745i	−0.0411532	−	0.999153i	$-0.513103\pi$
$269$	−12.7398	−	5.27701i	−0.776761	−	0.321745i	−0.735607	+	0.677408i	$0.763103\pi$
$270$		0			0
$271$		−	17.2728i		−	1.04925i	−0.851335	−	0.524623i	$-0.824206\pi$
$271$		−	17.2728i		−	1.04925i	0.851335	−	0.524623i	$-0.175794\pi$
$272$	−18.3915	−	14.0219i	−1.11515	−	0.850200i
$273$		0			0
$274$	−10.5073	+	16.9263i	−0.634768	+	1.02256i
$275$	−5.62344	−	2.32931i	−0.339106	−	0.140462i
$276$		0			0
$277$	0.284800	+	0.687567i	0.0171119	+	0.0413119i	0.932205	−	0.361932i	$-0.117883\pi$
$277$	0.284800	+	0.687567i	0.0171119	+	0.0413119i	−0.915093	+	0.403244i	$0.867883\pi$
$278$	−5.34884	+	3.83921i	−0.320802	+	0.230260i
$279$		0			0
$280$	20.0107	−	6.12105i	1.19587	−	0.365802i
$281$	12.6479	−	12.6479i	0.754513	−	0.754513i	−0.220805	−	0.975318i	$-0.570869\pi$
$281$	12.6479	−	12.6479i	0.754513	−	0.754513i	0.975318	+	0.220805i	$0.0708685\pi$
$282$		0			0
$283$	−4.05155	+	1.67821i	−0.240840	+	0.0997591i	−0.499839	−	0.866118i	$-0.666607\pi$
$283$	−4.05155	+	1.67821i	−0.240840	+	0.0997591i	0.258999	+	0.965878i	$0.416607\pi$
$284$	6.83021	−	20.2242i	0.405298	−	1.20008i
$285$		0			0
$286$	−18.5122	+	4.33157i	−1.09465	+	0.256131i
$287$	44.3111			2.61560
$288$		0			0
$289$	−16.4287			−0.966396
$290$	10.5848	−	2.47667i	0.621558	−	0.145435i
$291$		0			0
$292$	24.2298	+	8.18301i	1.41794	+	0.478875i
$293$	−0.690177	+	0.285881i	−0.0403206	+	0.0167013i	−0.402753	−	0.915309i	$-0.631946\pi$
$293$	−0.690177	+	0.285881i	−0.0403206	+	0.0167013i	0.362432	+	0.932010i	$0.381946\pi$
$294$		0			0
$295$	−11.5367	+	11.5367i	−0.671691	+	0.671691i
$296$	2.97244	+	1.57992i	0.172769	+	0.0918309i
$297$		0			0
$298$	12.3702	−	8.87889i	0.716586	−	0.514340i
$299$	1.32380	+	3.19594i	0.0765574	+	0.184826i
$300$		0			0
$301$	10.0837	+	4.17682i	0.581217	+	0.240748i
$302$	−3.63656	+	5.85819i	−0.209261	+	0.337101i
$303$		0			0
$304$	7.21919	−	4.19792i	0.414049	−	0.240767i
$305$			1.95246i			0.111797i
$306$		0			0
$307$	5.14989	+	2.13316i	0.293920	+	0.121746i	0.524771	−	0.851243i	$-0.324151\pi$
$307$	5.14989	+	2.13316i	0.293920	+	0.121746i	−0.230851	+	0.972989i	$0.574151\pi$
$308$	−25.0807	+	1.68295i	−1.42911	+	0.0958952i
$309$		0			0
$310$	−9.54959	−	13.3046i	−0.542380	−	0.755652i
$311$	22.2089	+	22.2089i	1.25935	+	1.25935i	0.951404	+	0.307945i	$0.0996414\pi$
$311$	22.2089	+	22.2089i	1.25935	+	1.25935i	0.307945	+	0.951404i	$0.400359\pi$
$312$		0			0
$313$	−19.6341	+	19.6341i	−1.10978	+	1.10978i	−0.116607	+	0.993178i	$0.537202\pi$
$313$	−19.6341	+	19.6341i	−1.10978	+	1.10978i	−0.993178	+	0.116607i	$0.962798\pi$
$314$	−24.7938	−	4.07372i	−1.39919	−	0.229893i
$315$		0			0
$316$	7.85319	+	15.8626i	0.441776	+	0.892342i
$317$	3.77085	−	9.10363i	0.211792	−	0.511311i	−0.781907	−	0.623395i	$-0.785753\pi$
$317$	3.77085	−	9.10363i	0.211792	−	0.511311i	0.993699	+	0.112085i	$0.0357528\pi$
$318$		0			0
$319$	−13.0583			−0.731125
$320$	−2.71703	−	13.3348i	−0.151887	−	0.745440i
$321$		0			0
$322$	1.04203	+	4.45341i	0.0580702	+	0.248179i
$323$	4.61932	−	11.1520i	0.257026	−	0.620515i
$324$		0			0
$325$	−9.05241	+	3.74963i	−0.502137	+	0.207992i
$326$	26.1861	+	4.30247i	1.45031	+	0.238292i
$327$		0			0
$328$	2.75783	−	28.6848i	0.152276	−	1.58385i
$329$	16.1227	+	16.1227i	0.888874	+	0.888874i
$330$		0			0
$331$	8.74068	+	21.1019i	0.480431	+	1.15986i	0.959404	+	0.282034i	$0.0910090\pi$
$331$	8.74068	+	21.1019i	0.480431	+	1.15986i	−0.478973	+	0.877829i	$0.658991\pi$
$332$	28.2618	−	1.89641i	1.55107	−	0.104079i
$333$		0			0
$334$	−11.3744	−	7.06080i	−0.622377	−	0.386350i
$335$		−	5.23861i		−	0.286216i
$336$		0			0
$337$		−	8.93510i		−	0.486726i	−0.969935	−	0.243363i	$-0.921749\pi$
$337$		−	8.93510i		−	0.486726i	0.969935	−	0.243363i	$-0.0782506\pi$
$338$	−6.44510	+	10.3825i	−0.350567	+	0.564734i
$339$		0			0
$340$	−14.8093	−	12.9469i	−0.803149	−	0.702142i
$341$	7.52848	+	18.1753i	0.407690	+	0.984250i
$342$		0			0
$343$	−15.1167	−	15.1167i	−0.816227	−	0.816227i
$344$	3.33145	−	6.26774i	0.179620	−	0.337934i
$345$		0			0
$346$	3.10620	−	18.9052i	0.166990	−	1.01635i
$347$	−24.5023	+	10.1492i	−1.31535	+	0.544838i	−0.926442	−	0.376437i	$-0.877149\pi$
$347$	−24.5023	+	10.1492i	−1.31535	+	0.544838i	−0.388912	+	0.921275i	$0.627149\pi$
$348$		0			0
$349$	−6.18100	+	14.9223i	−0.330861	+	0.798770i	0.667663	+	0.744464i	$0.267295\pi$
$349$	−6.18100	+	14.9223i	−0.330861	+	0.798770i	−0.998524	+	0.0543063i	$0.982705\pi$
$350$	−12.6142	+	2.95153i	−0.674255	+	0.157766i
$351$		0			0
$352$	−0.471511	+	16.3407i	−0.0251316	+	0.870964i
$353$	4.43676			0.236145			0.118072	−	0.993005i	$-0.462329\pi$
$353$	4.43676			0.236145			0.118072	+	0.993005i	$0.462329\pi$
$354$		0			0
$355$	6.94808	−	16.7741i	0.368766	−	0.890279i
$356$	−11.2359	+	33.2695i	−0.595504	+	1.76328i
$357$		0			0
$358$	2.00346	−	12.1936i	0.105886	−	0.644451i
$359$	−15.5906	+	15.5906i	−0.822841	+	0.822841i	−0.986515	−	0.163674i	$-0.947666\pi$
$359$	−15.5906	+	15.5906i	−0.822841	+	0.822841i	0.163674	+	0.986515i	$0.447666\pi$
$360$		0			0
$361$	−10.3530	−	10.3530i	−0.544893	−	0.544893i
$362$	7.84582	−	5.63145i	0.412367	−	0.295982i
$363$		0			0
$364$	−26.6331	+	30.4644i	−1.39595	+	1.59677i
$365$	20.0965	+	8.32423i	1.05190	+	0.435710i
$366$		0			0
$367$			26.8476i			1.40143i	0.713440	+	0.700717i	$0.247136\pi$
$367$			26.8476i			1.40143i	−0.713440	+	0.700717i	$0.752864\pi$
$368$	2.94777	−	0.397388i	0.153663	−	0.0207153i
$369$		0			0
$370$	2.43257	+	1.51005i	0.126463	+	0.0785040i
$371$	0.0510065	+	0.0211276i	0.00264813	+	0.00109689i
$372$		0			0
$373$	8.30515	+	20.0504i	0.430024	+	1.03817i	0.979279	+	0.202515i	$0.0649116\pi$
$373$	8.30515	+	20.0504i	0.430024	+	1.03817i	−0.549255	+	0.835655i	$0.685088\pi$
$374$	13.7785	+	19.1964i	0.712468	+	0.992621i
$375$		0			0
$376$	11.4405	−	9.43358i	0.589997	−	0.486500i
$377$	−14.8639	+	14.8639i	−0.765532	+	0.765532i
$378$		0			0
$379$	−13.2366	+	5.48277i	−0.679917	+	0.281631i	−0.695792	−	0.718243i	$-0.744947\pi$
$379$	−13.2366	+	5.48277i	−0.679917	+	0.281631i	0.0158750	+	0.999874i	$0.494947\pi$
$380$	6.36557	−	3.15144i	0.326547	−	0.161665i
$381$		0			0
$382$	1.28676	+	5.49934i	0.0658366	+	0.281371i
$383$	−12.0126			−0.613816			−0.306908	−	0.951739i	$-0.599294\pi$
$383$	−12.0126			−0.613816			−0.306908	+	0.951739i	$0.599294\pi$
$384$		0			0
$385$	−21.3804			−1.08965
$386$	0.783659	+	3.34918i	0.0398872	+	0.170469i
$387$		0			0
$388$	−16.9864	+	8.40956i	−0.862355	+	0.426931i
$389$	−24.5778	+	10.1804i	−1.24614	+	0.516169i	−0.905629	−	0.424071i	$-0.860601\pi$
$389$	−24.5778	+	10.1804i	−1.24614	+	0.516169i	−0.340513	+	0.940240i	$0.610601\pi$
$390$		0			0
$391$	3.04011	−	3.04011i	0.153745	−	0.153745i
$392$	−26.0022	+	21.4409i	−1.31331	+	1.08293i
$393$		0			0
$394$	−9.06756	−	12.6331i	−0.456817	−	0.636444i
$395$	5.76125	+	13.9089i	0.289880	+	0.699833i
$396$		0			0
$397$	−8.40317	−	3.48071i	−0.421743	−	0.174692i	0.161710	−	0.986838i	$-0.448299\pi$
$397$	−8.40317	−	3.48071i	−0.421743	−	0.174692i	−0.583453	+	0.812147i	$0.698299\pi$
$398$	−17.9236	−	11.1264i	−0.898430	−	0.557714i
$399$		0			0
$400$	1.12559	+	8.34946i	0.0562795	+	0.417473i
$401$		−	19.5746i		−	0.977508i	−0.872422	−	0.488754i	$-0.837452\pi$
$401$		−	19.5746i		−	0.977508i	0.872422	−	0.488754i	$-0.162548\pi$
$402$		0			0
$403$	29.2580	+	12.1191i	1.45745	+	0.603694i
$404$	−22.3743	+	25.5930i	−1.11316	+	1.27330i
$405$		0			0
$406$	−22.5788	+	16.2062i	−1.12057	+	0.804302i
$407$	−2.43199	−	2.43199i	−0.120549	−	0.120549i
$408$		0			0
$409$	6.92958	−	6.92958i	0.342645	−	0.342645i	−0.514716	−	0.857361i	$-0.672102\pi$
$409$	6.92958	−	6.92958i	0.342645	−	0.342645i	0.857361	+	0.514716i	$0.172102\pi$
$410$	3.97387	−	24.1861i	0.196256	−	1.19447i
$411$		0			0
$412$	8.85188	−	26.2103i	0.436101	−	1.29129i
$413$	15.9629	−	38.5380i	0.785485	−	1.89633i
$414$		0			0
$415$	24.0922			1.18264
$416$	18.0635	+	19.1369i	0.885637	+	0.938266i
$417$		0			0
$418$	−8.30800	+	1.94395i	−0.406357	+	0.0950816i
$419$	2.24489	−	5.41965i	0.109670	−	0.264767i	−0.859511	−	0.511118i	$-0.829232\pi$
$419$	2.24489	−	5.41965i	0.109670	−	0.264767i	0.969181	+	0.246351i	$0.0792316\pi$
$420$		0			0
$421$	0.0698584	−	0.0289363i	0.00340469	−	0.00141027i	−0.380980	−	0.924583i	$-0.624413\pi$
$421$	0.0698584	−	0.0289363i	0.00340469	−	0.00141027i	0.384385	+	0.923173i	$0.374413\pi$
$422$	−2.41340	+	14.6886i	−0.117483	+	0.715032i
$423$		0			0
$424$	0.0168515	−	0.0317041i	0.000818379	−	0.00153969i
$425$	8.61102	+	8.61102i	0.417696	+	0.417696i
$426$		0			0
$427$	−1.91029	−	4.61185i	−0.0924454	−	0.223183i
$428$	−7.25165	−	6.33966i	−0.350522	−	0.306439i
$429$		0			0
$430$	3.18413	−	5.12936i	0.153552	−	0.247360i
$431$			3.28812i			0.158383i	0.996859	+	0.0791915i	$0.0252339\pi$
$431$			3.28812i			0.158383i	−0.996859	+	0.0791915i	$0.974766\pi$
$432$		0			0
$433$		−	21.9752i		−	1.05606i	−0.849225	−	0.528031i	$-0.822930\pi$
$433$		−	21.9752i		−	1.05606i	0.849225	−	0.528031i	$-0.177070\pi$
$434$	35.5741	+	22.0832i	1.70761	+	1.06003i
$435$		0			0
$436$	−30.6533	+	2.05688i	−1.46802	+	0.0985066i
$437$	0.594104	+	1.43429i	0.0284198	+	0.0686116i
$438$		0			0
$439$	−23.5627	−	23.5627i	−1.12459	−	1.12459i	−0.991043	−	0.133544i	$-0.957364\pi$
$439$	−23.5627	−	23.5627i	−1.12459	−	1.12459i	−0.133544	−	0.991043i	$-0.542636\pi$
$440$	−1.33067	+	13.8406i	−0.0634373	+	0.659825i
$441$		0			0
$442$	37.5344	+	6.16706i	1.78533	+	0.293337i
$443$	−10.4663	+	4.33528i	−0.497268	+	0.205975i	−0.617199	−	0.786807i	$-0.711733\pi$
$443$	−10.4663	+	4.33528i	−0.497268	+	0.205975i	0.119931	+	0.992782i	$0.461733\pi$
$444$		0			0
$445$	−11.4298	+	27.5941i	−0.541826	+	1.30808i
$446$	−7.40462	−	31.6457i	−0.350619	−	1.49847i
$447$		0			0
$448$	19.4647	+	28.8395i	0.919619	+	1.36254i
$449$	1.27254			0.0600548			0.0300274	−	0.999549i	$-0.490441\pi$
$449$	1.27254			0.0600548			0.0300274	+	0.999549i	$0.490441\pi$
$450$		0			0
$451$	−11.2673	+	27.2017i	−0.530558	+	1.28088i
$452$	11.6479	+	23.5275i	0.547870	+	1.10664i
$453$		0			0
$454$	41.8932	+	6.88322i	1.96615	+	0.323046i
$455$	−24.3368	+	24.3368i	−1.14093	+	1.14093i
$456$		0			0
$457$	−15.8452	−	15.8452i	−0.741205	−	0.741205i	0.231605	−	0.972810i	$-0.425602\pi$
$457$	−15.8452	−	15.8452i	−0.741205	−	0.741205i	−0.972810	+	0.231605i	$0.925602\pi$
$458$	−15.6443	−	21.7959i	−0.731012	−	1.01846i
$459$		0			0
$460$	2.52423	−	0.169380i	0.117693	−	0.00789737i
$461$	24.1001	+	9.98258i	1.12245	+	0.464935i	0.865209	−	0.501411i	$-0.167186\pi$
$461$	24.1001	+	9.98258i	1.12245	+	0.464935i	0.257244	+	0.966347i	$0.417186\pi$
$462$		0			0
$463$			6.51158i			0.302619i	0.988486	+	0.151309i	$0.0483490\pi$
$463$			6.51158i			0.302619i	−0.988486	+	0.151309i	$0.951651\pi$
$464$	9.08584	+	15.6250i	0.421799	+	0.725371i
$465$		0			0
$466$	12.9501	−	20.8615i	0.599903	−	0.966393i
$467$	−0.271505	−	0.112461i	−0.0125637	−	0.00520407i	0.376393	−	0.926460i	$-0.377164\pi$
$467$	−0.271505	−	0.112461i	−0.0125637	−	0.00520407i	−0.388956	+	0.921256i	$0.627164\pi$
$468$		0			0
$469$	5.12547	+	12.3740i	0.236672	+	0.571377i
$470$	10.2461	−	7.35426i	0.472616	−	0.339227i
$471$		0			0
$472$	−23.9540	−	12.7321i	−1.10257	−	0.586043i
$473$	−5.12814	+	5.12814i	−0.235792	+	0.235792i
$474$		0			0
$475$	−4.06259	+	1.68278i	−0.186405	+	0.0772113i
$476$	47.6480	+	16.0919i	2.18394	+	0.737572i
$477$		0			0
$478$	25.8589	−	6.05059i	1.18276	−	0.276748i
$479$	13.5118			0.617369			0.308685	−	0.951164i	$-0.400111\pi$
$479$	13.5118			0.617369			0.308685	+	0.951164i	$0.400111\pi$
$480$		0			0
$481$	−5.53654			−0.252444
$482$	−7.69483	+	1.80048i	−0.350490	+	0.0820094i
$483$		0			0
$484$	−1.69501	+	5.01889i	−0.0770457	+	0.228131i
$485$	−14.8943	+	6.16942i	−0.676315	+	0.280139i
$486$		0			0
$487$	1.42751	−	1.42751i	0.0646866	−	0.0646866i	−0.674023	−	0.738710i	$-0.735435\pi$
$487$	1.42751	−	1.42751i	0.0646866	−	0.0646866i	0.738710	+	0.674023i	$0.235435\pi$
$488$	−3.10437	+	0.949593i	−0.140528	+	0.0429860i
$489$		0			0
$490$	−23.2875	+	16.7150i	−1.05202	+	0.755105i
$491$	−0.0538443	−	0.129992i	−0.00242996	−	0.00586645i	0.922660	−	0.385615i	$-0.126011\pi$
$491$	−0.0538443	−	0.129992i	−0.00242996	−	0.00586645i	−0.925090	+	0.379748i	$0.876011\pi$
$492$		0			0
$493$	24.1371	+	9.99791i	1.08708	+	0.450283i
$494$	−7.24403	+	11.6695i	−0.325924	+	0.525037i
$495$		0			0
$496$	16.5096	−	21.6545i	0.741302	−	0.972314i
$497$			46.4198i			2.08221i
$498$		0			0
$499$	−31.1157	−	12.8885i	−1.39293	−	0.576970i	−0.445023	−	0.895519i	$-0.646804\pi$
$499$	−31.1157	−	12.8885i	−1.39293	−	0.576970i	−0.947906	+	0.318549i	$0.896804\pi$
$500$	1.61867	+	24.1227i	0.0723890	+	1.07880i
$501$		0			0
$502$	−10.8339	−	15.0940i	−0.483541	−	0.673676i
$503$	2.25575	+	2.25575i	0.100579	+	0.100579i	0.755606	−	0.655027i	$-0.227343\pi$
$503$	2.25575	+	2.25575i	0.100579	+	0.100579i	−0.655027	+	0.755606i	$0.727343\pi$
$504$		0			0
$505$	−20.4452	+	20.4452i	−0.909801	+	0.909801i
$506$	−2.99883	−	0.492720i	−0.133314	−	0.0219041i
$507$		0			0
$508$	28.8051	−	14.2607i	1.27802	−	0.632716i
$509$	−0.0379139	+	0.0915322i	−0.00168050	+	0.00405709i	−0.924718	−	0.380654i	$-0.875699\pi$
$509$	−0.0379139	+	0.0915322i	−0.00168050	+	0.00405709i	0.923037	+	0.384711i	$0.125699\pi$
$510$		0			0
$511$	−55.6137			−2.46021
$512$	19.8807	−	10.8055i	0.878609	−	0.477541i
$513$		0			0
$514$	−5.83956	−	24.9570i	−0.257572	−	1.10080i
$515$	9.00464	−	21.7391i	0.396792	−	0.957940i
$516$		0			0
$517$	−13.9971	+	5.79778i	−0.615590	+	0.254986i
$518$	−7.22334	−	1.18682i	−0.317376	−	0.0521461i
$519$		0			0
$520$	14.2397	+	17.2691i	0.624454	+	0.757299i
$521$	6.98279	+	6.98279i	0.305922	+	0.305922i	0.843325	−	0.537403i	$-0.180595\pi$
$521$	6.98279	+	6.98279i	0.305922	+	0.305922i	−0.537403	+	0.843325i	$0.680595\pi$
$522$		0			0
$523$	−8.43255	−	20.3580i	−0.368730	−	0.890192i	−0.993959	−	0.109751i	$-0.964995\pi$
$523$	−8.43255	−	20.3580i	−0.368730	−	0.890192i	0.625229	−	0.780441i	$-0.285005\pi$
$524$	−1.18592	−	17.6736i	−0.0518073	−	0.772074i
$525$		0			0
$526$	−6.16443	−	3.82666i	−0.268782	−	0.166850i
$527$		−	39.3595i		−	1.71453i
$528$		0			0
$529$		−	22.4470i		−	0.975959i
$530$	0.0161063	−	0.0259459i	0.000699612	−	0.00112702i
$531$		0			0
$532$	−11.9526	+	13.6720i	−0.518209	+	0.592757i
$533$	18.1377	+	43.7884i	0.785633	+	1.89668i
$534$		0			0
$535$	−5.79305	−	5.79305i	−0.250456	−	0.250456i
$536$	8.32928	−	2.54784i	0.359770	−	0.110050i
$537$		0			0
$538$	3.16175	−	19.2433i	0.136313	−	0.829636i
$539$	31.8129	−	13.1773i	1.37028	−	0.567588i
$540$		0			0
$541$	−3.66278	+	8.84273i	−0.157475	+	0.380179i	−0.982850	−	0.184406i	$-0.940964\pi$
$541$	−3.66278	+	8.84273i	−0.157475	+	0.380179i	0.825375	+	0.564585i	$0.190964\pi$
$542$	23.7850	−	5.56533i	1.02165	−	0.239051i
$543$		0			0
$544$	13.3826	−	29.8433i	0.573774	−	1.27952i
$545$	−26.1308			−1.11932
$546$		0			0
$547$	16.0012	−	38.6303i	0.684162	−	1.65171i	−0.0720628	−	0.997400i	$-0.522958\pi$
$547$	16.0012	−	38.6303i	0.684162	−	1.65171i	0.756224	−	0.654312i	$-0.227042\pi$
$548$	−26.6934	−	9.01503i	−1.14028	−	0.385103i
$549$		0			0
$550$	1.39561	−	8.49410i	0.0595092	−	0.362190i
$551$	−6.67073	+	6.67073i	−0.284183	+	0.284183i
$552$		0			0
$553$	−27.2170	−	27.2170i	−1.15738	−	1.15738i
$554$	−0.855031	+	0.613711i	−0.0363268	+	0.0260741i
$555$		0			0
$556$	−7.01007	−	6.12846i	−0.297293	−	0.259905i
$557$	−7.60439	−	3.14984i	−0.322209	−	0.133463i	0.215716	−	0.976456i	$-0.430791\pi$
$557$	−7.60439	−	3.14984i	−0.322209	−	0.133463i	−0.537925	+	0.842993i	$0.680791\pi$
$558$		0			0
$559$			11.6745i			0.493777i
$560$	14.8763	+	25.5829i	0.628638	+	1.08107i
$561$		0			0
$562$	21.4917	+	13.3413i	0.906571	+	0.562768i
$563$	−11.3013	−	4.68115i	−0.476293	−	0.197287i	0.131605	−	0.991302i	$-0.457987\pi$
$563$	−11.3013	−	4.68115i	−0.476293	−	0.197287i	−0.607898	+	0.794015i	$0.707987\pi$
$564$		0			0
$565$	8.54512	+	20.6297i	0.359496	+	0.867899i
$566$	−3.61635	−	5.03835i	−0.152006	−	0.211778i
$567$		0			0
$568$	30.0498	+	2.88906i	1.26086	+	0.121222i
$569$	−5.04807	+	5.04807i	−0.211626	+	0.211626i	−0.804958	−	0.593332i	$-0.797812\pi$
$569$	−5.04807	+	5.04807i	−0.211626	+	0.211626i	0.593332	+	0.804958i	$0.297812\pi$
$570$		0			0
$571$	−12.9612	+	5.36872i	−0.542411	+	0.224674i	−0.637029	−	0.770840i	$-0.719837\pi$
$571$	−12.9612	+	5.36872i	−0.542411	+	0.224674i	0.0946181	+	0.995514i	$0.469837\pi$
$572$	−11.9293	−	24.0960i	−0.498790	−	1.00750i
$573$		0			0
$574$	14.2772	+	61.0173i	0.595917	+	2.54681i
$575$	−1.56622			−0.0653160
$576$		0			0
$577$	7.48115			0.311444			0.155722	−	0.987801i	$-0.450230\pi$
$577$	7.48115			0.311444			0.155722	+	0.987801i	$0.450230\pi$
$578$	−5.29338	−	22.6227i	−0.220175	−	0.940980i
$579$		0			0
$580$	6.82086	+	13.7774i	0.283221	+	0.572077i
$581$	−56.9075	+	23.5719i	−2.36092	+	0.977925i
$582$		0			0
$583$	−0.0259396	+	0.0259396i	−0.00107431	+	0.00107431i
$584$	−3.46128	+	36.0015i	−0.143229	+	1.48975i
$585$		0			0
$586$	−0.616040	−	0.858276i	−0.0254484	−	0.0354551i
$587$	8.24039	+	19.8941i	0.340117	+	0.821116i	0.997703	+	0.0677363i	$0.0215777\pi$
$587$	8.24039	+	19.8941i	0.340117	+	0.821116i	−0.657586	+	0.753380i	$0.728422\pi$
$588$		0			0
$589$	13.1306	+	5.43887i	0.541036	+	0.224105i
$590$	−19.6034	−	12.1691i	−0.807058	−	0.500994i
$591$		0			0
$592$	−1.21786	+	4.60216i	−0.0500535	+	0.189148i
$593$		−	40.6667i		−	1.66998i	−0.550264	−	0.834991i	$-0.685473\pi$
$593$		−	40.6667i		−	1.66998i	0.550264	−	0.834991i	$-0.314527\pi$
$594$		0			0
$595$	39.5198	+	16.3696i	1.62015	+	0.671089i
$596$	16.2121	+	14.1732i	0.664074	+	0.580557i
$597$		0			0
$598$	−3.97434	+	2.85264i	−0.162523	+	0.116653i
$599$	7.41576	+	7.41576i	0.303000	+	0.303000i	0.842186	−	0.539187i	$-0.181268\pi$
$599$	7.41576	+	7.41576i	0.303000	+	0.303000i	−0.539187	+	0.842186i	$0.681268\pi$
$600$		0			0
$601$	27.4592	−	27.4592i	1.12008	−	1.12008i	0.128354	−	0.991728i	$-0.459030\pi$
$601$	27.4592	−	27.4592i	1.12008	−	1.12008i	0.991728	−	0.128354i	$-0.0409695\pi$
$602$	−2.50256	+	15.2313i	−0.101997	+	0.620781i
$603$		0			0
$604$	−9.23856	−	3.12009i	−0.375912	−	0.126955i
$605$	−1.72426	+	4.16272i	−0.0701010	+	0.169239i
$606$		0			0
$607$	35.3994			1.43682			0.718409	−	0.695621i	$-0.244871\pi$
$607$	35.3994			1.43682			0.718409	+	0.695621i	$0.244871\pi$
$608$	8.10666	+	8.58840i	0.328768	+	0.348305i
$609$		0			0
$610$	−2.68857	+	0.629087i	−0.108857	+	0.0254710i
$611$	−9.33305	+	22.5320i	−0.377575	+	0.911546i
$612$		0			0
$613$	19.0395	−	7.88644i	0.769000	−	0.318530i	0.0365328	−	0.999332i	$-0.488369\pi$
$613$	19.0395	−	7.88644i	0.769000	−	0.318530i	0.732467	+	0.680802i	$0.238369\pi$
$614$	−1.27809	+	7.77882i	−0.0515796	+	0.313928i
$615$		0			0
$616$	−10.3985	−	33.9944i	−0.418969	−	1.36967i
$617$	9.37922	+	9.37922i	0.377593	+	0.377593i	0.870233	−	0.492640i	$-0.163968\pi$
$617$	9.37922	+	9.37922i	0.377593	+	0.377593i	−0.492640	+	0.870233i	$0.663968\pi$
$618$		0			0
$619$	12.9078	+	31.1622i	0.518808	+	1.25251i	0.938636	+	0.344910i	$0.112090\pi$
$619$	12.9078	+	31.1622i	0.518808	+	1.25251i	−0.419828	+	0.907604i	$0.637910\pi$
$620$	15.2439	−	17.4368i	0.612208	−	0.700278i
$621$		0			0
$622$	−23.4263	+	37.7378i	−0.939310	+	1.51315i
$623$		−	76.3622i		−	3.05939i
$624$		0			0
$625$			10.0325i			0.401299i
$626$	−33.3627	−	20.7104i	−1.33344	−	0.827754i
$627$		0			0
$628$	−2.37902	−	35.4541i	−0.0949333	−	1.41477i
$629$	2.63329	+	6.35733i	0.104996	+	0.253483i
$630$		0			0
$631$	4.80900	+	4.80900i	0.191443	+	0.191443i	0.796319	−	0.604876i	$-0.206777\pi$
$631$	4.80900	+	4.80900i	0.191443	+	0.191443i	−0.604876	+	0.796319i	$0.706777\pi$
$632$	−19.3128	+	15.9250i	−0.768223	+	0.633461i
$633$		0			0
$634$	13.7509	+	2.25932i	0.546116	+	0.0897291i
$635$	25.2573	−	10.4619i	1.00231	−	0.415169i
$636$		0			0
$637$	21.2124	−	51.2113i	0.840466	−	2.02906i
$638$	−4.20742	−	17.9816i	−0.166573	−	0.711896i
$639$		0			0
$640$	17.4869	−	8.03793i	0.691231	−	0.317727i
$641$	−9.67074			−0.381971			−0.190986	−	0.981593i	$-0.561168\pi$
$641$	−9.67074			−0.381971			−0.190986	+	0.981593i	$0.561168\pi$
$642$		0			0
$643$	−16.0445	+	38.7348i	−0.632733	+	1.52755i	0.203440	+	0.979087i	$0.434788\pi$
$643$	−16.0445	+	38.7348i	−0.632733	+	1.52755i	−0.836173	+	0.548466i	$0.815212\pi$
$644$	−5.79670	+	2.86980i	−0.228422	+	0.113086i
$645$		0			0
$646$	16.8449	+	2.76769i	0.662755	+	0.108893i
$647$	17.1946	−	17.1946i	0.675988	−	0.675988i	−0.283102	−	0.959090i	$-0.591363\pi$
$647$	17.1946	−	17.1946i	0.675988	−	0.675988i	0.959090	+	0.283102i	$0.0913635\pi$
$648$		0			0
$649$	19.5987	+	19.5987i	0.769316	+	0.769316i
$650$	−8.08002	−	11.2572i	−0.316925	−	0.441544i
$651$		0			0
$652$	2.51262	+	37.4450i	0.0984016	+	1.46646i
$653$	−44.0250	−	18.2358i	−1.72283	−	0.713620i	−0.999738	−	0.0228702i	$-0.992720\pi$
$653$	−44.0250	−	18.2358i	−1.72283	−	0.713620i	−0.723094	−	0.690750i	$-0.757280\pi$
$654$		0			0
$655$		−	15.0661i		−	0.588681i
$656$	40.3881	−	5.44472i	1.57689	−	0.212580i
$657$		0			0
$658$	−17.0065	+	27.3961i	−0.662983	+	1.06801i
$659$	19.5624	+	8.10302i	0.762044	+	0.315649i	0.729645	−	0.683826i	$-0.239685\pi$
$659$	19.5624	+	8.10302i	0.762044	+	0.315649i	0.0323990	+	0.999475i	$0.489685\pi$
$660$		0			0
$661$	15.7189	+	37.9488i	0.611394	+	1.47604i	0.861469	+	0.507810i	$0.169545\pi$
$661$	15.7189	+	37.9488i	0.611394	+	1.47604i	−0.250075	+	0.968226i	$0.580455\pi$
$662$	−26.2414	+	18.8352i	−1.01990	+	0.732049i
$663$		0			0
$664$	11.7174	+	38.3061i	0.454724	+	1.48656i
$665$	−10.9220	+	10.9220i	−0.423538	+	0.423538i
$666$		0			0
$667$	−3.10434	+	1.28586i	−0.120200	+	0.0497887i
$668$	6.05802	−	17.9377i	0.234392	−	0.694032i
$669$		0			0
$670$	7.21368	−	1.68789i	0.278689	−	0.0652090i
$671$	3.31687			0.128046
$672$		0			0
$673$	−1.41731			−0.0546334			−0.0273167	−	0.999627i	$-0.508696\pi$
$673$	−1.41731			−0.0546334			−0.0273167	+	0.999627i	$0.508696\pi$
$674$	12.3038	−	2.87891i	0.473925	−	0.110892i
$675$		0			0
$676$	−16.3736	−	5.52976i	−0.629752	−	0.212683i
$677$	−18.8465	+	7.80647i	−0.724329	+	0.300027i	−0.714219	−	0.699922i	$-0.753218\pi$
$677$	−18.8465	+	7.80647i	−0.724329	+	0.300027i	−0.0101096	+	0.999949i	$0.503218\pi$
$678$		0			0
$679$	29.1452	−	29.1452i	1.11849	−	1.11849i
$680$	13.0565	−	24.5643i	0.500693	−	0.941997i
$681$		0			0
$682$	−22.6021	+	16.2230i	−0.865480	+	0.621211i
$683$	15.8135	+	38.1772i	0.605087	+	1.46081i	0.868284	+	0.496067i	$0.165223\pi$
$683$	15.8135	+	38.1772i	0.605087	+	1.46081i	−0.263197	+	0.964742i	$0.584777\pi$
$684$		0			0
$685$	−22.1398	−	9.17060i	−0.845918	−	0.350391i
$686$	15.9454	−	25.6867i	0.608799	−	0.980723i
$687$		0			0
$688$	9.70420	+	2.56799i	0.369969	+	0.0979038i
$689$			0.0590529i			0.00224974i
$690$		0			0
$691$	−0.368324	−	0.152565i	−0.0140117	−	0.00580384i	0.375667	−	0.926755i	$-0.377414\pi$
$691$	−0.368324	−	0.152565i	−0.0140117	−	0.00580384i	−0.389678	+	0.920951i	$0.627414\pi$
$692$	27.0337	−	1.81400i	1.02767	−	0.0689579i
$693$		0			0
$694$	−21.8704	−	30.4701i	−0.830188	−	1.15663i
$695$	−5.60007	−	5.60007i	−0.212423	−	0.212423i
$696$		0			0
$697$	41.6533	−	41.6533i	1.57773	−	1.57773i
$698$	−22.5398	−	3.70338i	−0.853143	−	0.140175i
$699$		0			0
$700$	−8.12863	−	16.4190i	−0.307233	−	0.620579i
$701$	17.5964	−	42.4815i	0.664607	−	1.60450i	−0.125895	−	0.992044i	$-0.540180\pi$
$701$	17.5964	−	42.4815i	0.664607	−	1.60450i	0.790502	−	0.612459i	$-0.209820\pi$
$702$		0			0
$703$	−2.48472			−0.0937131
$704$	−22.6534	+	4.61574i	−0.853784	+	0.173962i
$705$		0			0
$706$	1.42953	+	6.10951i	0.0538012	+	0.229934i
$707$	28.2895	−	68.2968i	1.06393	−	2.56856i
$708$		0			0
$709$	35.8877	−	14.8652i	1.34779	−	0.558274i	0.412115	−	0.911132i	$-0.364790\pi$
$709$	35.8877	−	14.8652i	1.34779	−	0.558274i	0.935677	+	0.352858i	$0.114790\pi$
$710$	25.3370	+	4.16298i	0.950882	+	0.156234i
$711$		0			0
$712$	−49.4330	−	4.75262i	−1.85258	−	0.178112i
$713$	3.57947	+	3.57947i	0.134052	+	0.134052i
$714$		0			0
$715$	−8.75159	−	21.1282i	−0.327291	−	0.790150i
$716$	17.4363	−	1.17000i	0.651627	−	0.0437251i
$717$		0			0
$718$	−26.4919	−	16.4453i	−0.988670	−	0.613732i
$719$			41.8039i			1.55902i	0.626388	+	0.779511i	$0.284533\pi$
$719$			41.8039i			1.55902i	−0.626388	+	0.779511i	$0.715467\pi$
$720$		0			0
$721$			60.1596i			2.24046i
$722$	10.9205	−	17.5920i	0.406419	−	0.654706i
$723$		0			0
$724$	10.2826	+	8.98939i	0.382148	+	0.334088i
$725$	−3.64216	−	8.79294i	−0.135266	−	0.326562i
$726$		0			0
$727$	−4.55220	−	4.55220i	−0.168832	−	0.168832i	0.617634	−	0.786466i	$-0.288091\pi$
$727$	−4.55220	−	4.55220i	−0.168832	−	0.168832i	−0.786466	+	0.617634i	$0.788091\pi$
$728$	−50.5314	−	26.8586i	−1.87282	−	0.995446i
$729$		0			0
$730$	−4.98750	+	30.3553i	−0.184596	+	1.12350i
$731$	13.4052	−	5.55261i	0.495808	−	0.205371i
$732$		0			0
$733$	3.21856	−	7.77030i	0.118880	−	0.287003i	−0.853227	−	0.521540i	$-0.825358\pi$
$733$	3.21856	−	7.77030i	0.118880	−	0.287003i	0.972107	+	0.234538i	$0.0753576\pi$
$734$	−36.9697	+	8.65036i	−1.36458	+	0.319291i
$735$		0			0
$736$	1.49699	+	3.93110i	0.0551798	+	0.144902i
$737$	−8.89944			−0.327815
$738$		0			0
$739$	−6.56067	+	15.8389i	−0.241338	+	0.582642i	−0.997416	−	0.0718394i	$-0.977113\pi$
$739$	−6.56067	+	15.8389i	−0.241338	+	0.582642i	0.756078	+	0.654482i	$0.227113\pi$
$740$	−1.29560	+	3.83624i	−0.0476270	+	0.141023i
$741$		0			0
$742$	−0.0126587	+	0.0770444i	−0.000464716	+	0.00282839i
$743$	13.8972	−	13.8972i	0.509838	−	0.509838i	−0.404639	−	0.914477i	$-0.632603\pi$
$743$	13.8972	−	13.8972i	0.509838	−	0.509838i	0.914477	+	0.404639i	$0.132603\pi$
$744$		0			0
$745$	12.9512	+	12.9512i	0.474495	+	0.474495i
$746$	−24.9339	+	17.8966i	−0.912894	+	0.655243i
$747$		0			0
$748$	−21.9943	+	25.1584i	−0.804193	+	0.919881i
$749$	19.3515	+	8.01567i	0.707090	+	0.292886i
$750$		0			0
$751$			16.1406i			0.588977i	0.955655	+	0.294489i	$0.0951493\pi$
$751$			16.1406i			0.588977i	−0.955655	+	0.294489i	$0.904851\pi$
$752$	16.6764	+	12.7142i	0.608125	+	0.463640i
$753$		0			0
$754$	−25.2571	−	15.6787i	−0.919811	−	0.570986i
$755$	−7.66257	−	3.17394i	−0.278869	−	0.115511i
$756$		0			0
$757$	−8.62137	−	20.8138i	−0.313349	−	0.756492i	−0.999576	−	0.0291046i	$-0.990734\pi$
$757$	−8.62137	−	20.8138i	−0.313349	−	0.756492i	0.686227	−	0.727387i	$-0.259266\pi$
$758$	−11.8147	−	16.4605i	−0.429131	−	0.597871i
$759$		0			0
$760$	6.39059	+	7.75012i	0.231811	+	0.281126i
$761$	22.0688	−	22.0688i	0.799993	−	0.799993i	−0.183101	−	0.983094i	$-0.558613\pi$
$761$	22.0688	−	22.0688i	0.799993	−	0.799993i	0.983094	+	0.183101i	$0.0586135\pi$
$762$		0			0
$763$	61.7229	−	25.5664i	2.23452	−	0.925567i
$764$	−7.15810	+	3.54380i	−0.258971	+	0.128210i
$765$		0			0
$766$	−3.87049	−	16.5416i	−0.139847	−	0.597673i
$767$	44.6174			1.61104
$768$		0			0
$769$	8.43463			0.304160			0.152080	−	0.988368i	$-0.451403\pi$
$769$	8.43463			0.304160			0.152080	+	0.988368i	$0.451403\pi$
$770$	−6.88883	−	29.4413i	−0.248256	−	1.06099i
$771$		0			0
$772$	−4.35939	+	2.15823i	−0.156898	+	0.0776763i
$773$	−13.8656	+	5.74334i	−0.498712	+	0.206573i	−0.617837	−	0.786306i	$-0.711991\pi$
$773$	−13.8656	+	5.74334i	−0.498712	+	0.206573i	0.119125	+	0.992879i	$0.461991\pi$
$774$		0			0
$775$	−10.1388	+	10.1388i	−0.364195	+	0.364195i
$776$	−17.0532	−	20.6811i	−0.612174	−	0.742407i
$777$		0			0
$778$	−21.9377	−	30.5639i	−0.786505	−	1.09577i
$779$	8.13996	+	19.6516i	0.291644	+	0.704092i
$780$		0			0
$781$	−28.4962	−	11.8035i	−1.01967	−	0.422363i
$782$	5.16582	+	3.20676i	0.184729	+	0.114674i
$783$		0			0
$784$	−37.9025	−	28.8973i	−1.35366	−	1.03204i
$785$		−	30.2233i		−	1.07872i
$786$		0			0
$787$	−22.1687	−	9.18256i	−0.790227	−	0.327323i	−0.0491923	−	0.998789i	$-0.515665\pi$
$787$	−22.1687	−	9.18256i	−0.790227	−	0.327323i	−0.741035	+	0.671466i	$0.765665\pi$
$788$	14.4744	−	16.5566i	0.515629	−	0.589805i
$789$		0			0
$790$	−17.2965	+	12.4148i	−0.615384	+	0.441700i
$791$	−40.3684	−	40.3684i	−1.43533	−	1.43533i
$792$		0			0
$793$	3.77551	−	3.77551i	0.134072	−	0.134072i
$794$	2.08548	−	12.6928i	0.0740110	−	0.450452i
$795$		0			0
$796$	9.54619	−	28.2662i	0.338356	−	1.00187i
$797$	−19.6093	+	47.3410i	−0.694596	+	1.67690i	0.0407118	+	0.999171i	$0.487037\pi$
$797$	−19.6093	+	47.3410i	−0.694596	+	1.67690i	−0.735308	+	0.677733i	$0.762963\pi$
$798$		0			0
$799$	30.3113			1.07234
$800$	−11.1347	+	4.24018i	−0.393672	+	0.149913i
$801$		0			0
$802$	26.9546	−	6.30698i	0.951800	−	0.222707i
$803$	14.1413	−	34.1402i	0.499037	−	1.20478i
$804$		0			0
$805$	−5.08275	+	2.10534i	−0.179143	+	0.0742036i
$806$	−7.26120	+	44.1937i	−0.255765	+	1.55666i
$807$		0			0
$808$	−42.4512	−	22.5638i	−1.49343	−	0.793791i
$809$	−5.78299	−	5.78299i	−0.203319	−	0.203319i	0.598101	−	0.801420i	$-0.295922\pi$
$809$	−5.78299	−	5.78299i	−0.203319	−	0.203319i	−0.801420	+	0.598101i	$0.795922\pi$
$810$		0			0
$811$	6.52847	+	15.7611i	0.229245	+	0.553448i	0.996086	−	0.0883902i	$-0.0281722\pi$
$811$	6.52847	+	15.7611i	0.229245	+	0.553448i	−0.766840	+	0.641838i	$0.778172\pi$
$812$	−29.5912	−	25.8697i	−1.03845	−	0.907850i
$813$		0			0
$814$	2.56530	−	4.13249i	0.0899139	−	0.144844i
$815$			31.9205i			1.11813i
$816$		0			0
$817$			5.23933i			0.183301i
$818$	11.7749	+	7.30944i	0.411700	+	0.255569i
$819$		0			0
$820$	34.5851	−	2.32071i	1.20776	−	0.0810428i
$821$	−5.94613	−	14.3552i	−0.207521	−	0.501001i	0.785510	−	0.618848i	$-0.212400\pi$
$821$	−5.94613	−	14.3552i	−0.207521	−	0.501001i	−0.993032	+	0.117848i	$0.962400\pi$
$822$		0			0
$823$	32.1607	+	32.1607i	1.12105	+	1.12105i	0.991583	+	0.129470i	$0.0413275\pi$
$823$	32.1607	+	32.1607i	1.12105	+	1.12105i	0.129470	+	0.991583i	$0.458673\pi$
$824$	38.9442	+	3.74420i	1.35669	+	0.130435i
$825$		0			0
$826$	58.2109	+	9.56428i	2.02542	+	0.332784i
$827$	46.9380	−	19.4424i	1.63219	−	0.676077i	0.636719	−	0.771096i	$-0.280291\pi$
$827$	46.9380	−	19.4424i	1.63219	−	0.676077i	0.995475	+	0.0950194i	$0.0302913\pi$
$828$		0			0
$829$	16.4161	−	39.6321i	0.570156	−	1.37648i	−0.331266	−	0.943537i	$-0.607476\pi$
$829$	16.4161	−	39.6321i	0.570156	−	1.37648i	0.901422	−	0.432941i	$-0.142524\pi$
$830$	7.76256	+	33.1754i	0.269442	+	1.15154i
$831$		0			0
$832$	−20.5319	+	31.0398i	−0.711814	+	1.07611i
$833$	−68.8923			−2.38698
$834$		0			0
$835$	6.16257	−	14.8778i	0.213264	−	0.514866i
$836$	−5.35371	−	10.8139i	−0.185162	−	0.374008i
$837$		0			0
$838$	8.18627	+	1.34504i	0.282790	+	0.0464636i
$839$	−8.83959	+	8.83959i	−0.305177	+	0.305177i	−0.843035	−	0.537858i	$-0.819233\pi$
$839$	−8.83959	+	8.83959i	−0.305177	+	0.305177i	0.537858	+	0.843035i	$0.319233\pi$
$840$		0			0
$841$	6.06820	+	6.06820i	0.209248	+	0.209248i
$842$	0.0623544	+	0.0868730i	0.00214887	+	0.00299384i
$843$		0			0
$844$	−21.0042	+	1.40941i	−0.722993	+	0.0485139i
$845$	−13.5804	−	5.62519i	−0.467180	−	0.193512i
$846$		0			0
$847$		−	11.5197i		−	0.395821i
$848$	0.0490868	+	0.0129897i	0.00168565	+	0.000446067i
$849$		0			0
$850$	−9.08306	+	14.6320i	−0.311546	+	0.501875i
$851$	−0.817633	−	0.338675i	−0.0280281	−	0.0116096i
$852$		0			0
$853$	−0.745799	−	1.80052i	−0.0255357	−	0.0616486i	0.910597	−	0.413295i	$-0.135622\pi$
$853$	−0.745799	−	1.80052i	−0.0255357	−	0.0616486i	−0.936133	+	0.351646i	$0.885622\pi$
$854$	5.73511	−	4.11646i	0.196251	−	0.140862i
$855$		0			0
$856$	6.39334	−	12.0283i	0.218520	−	0.411120i
$857$	−12.3830	+	12.3830i	−0.422996	+	0.422996i	−0.886234	−	0.463238i	$-0.846688\pi$
$857$	−12.3830	+	12.3830i	−0.422996	+	0.422996i	0.463238	+	0.886234i	$0.346688\pi$
$858$		0			0
$859$	−5.84385	+	2.42060i	−0.199390	+	0.0825899i	−0.480144	−	0.877190i	$-0.659415\pi$
$859$	−5.84385	+	2.42060i	−0.199390	+	0.0825899i	0.280754	+	0.959780i	$0.409415\pi$
$860$	8.08917	+	2.73192i	0.275838	+	0.0931576i
$861$		0			0
$862$	−4.52781	+	1.05944i	−0.154218	+	0.0360847i
$863$	33.2873			1.13311			0.566556	−	0.824023i	$-0.308275\pi$
$863$	33.2873			1.13311			0.566556	+	0.824023i	$0.308275\pi$
$864$		0			0
$865$	23.0452			0.783562
$866$	30.2603	−	7.08047i	1.02829	−	0.240604i
$867$		0			0
$868$	−18.9469	+	56.1015i	−0.643100	+	1.90421i
$869$	23.6287	−	9.78732i	0.801548	−	0.332012i
$870$		0			0
$871$	−10.1300	+	10.1300i	−0.343242	+	0.343242i
$872$	−12.7089	−	41.5474i	−0.430378	−	1.40697i
$873$		0			0
$874$	−1.78363	+	1.28023i	−0.0603322	+	0.0433043i
$875$	−20.1196	−	48.5730i	−0.680166	−	1.64207i
$876$		0			0
$877$	−48.8456	−	20.2325i	−1.64940	−	0.683204i	−0.652205	−	0.758043i	$-0.726156\pi$
$877$	−48.8456	−	20.2325i	−1.64940	−	0.683204i	−0.997196	+	0.0748390i	$0.976156\pi$
$878$	24.8544	−	40.0383i	0.838795	−	1.35123i
$879$		0			0
$880$	−19.4875	+	2.62711i	−0.656925	+	0.0885600i
$881$		−	11.8046i		−	0.397707i	−0.980029	−	0.198853i	$-0.936278\pi$
$881$		−	11.8046i		−	0.397707i	0.980029	−	0.198853i	$-0.0637217\pi$
$882$		0			0
$883$	−25.9909	−	10.7658i	−0.874663	−	0.362297i	−0.100239	−	0.994963i	$-0.531961\pi$
$883$	−25.9909	−	10.7658i	−0.874663	−	0.362297i	−0.774425	+	0.632666i	$0.781961\pi$
$884$	3.60152	+	53.6727i	0.121132	+	1.80521i
$885$		0			0
$886$	−9.34203	−	13.0155i	−0.313852	−	0.437263i
$887$	−15.5470	−	15.5470i	−0.522016	−	0.522016i	0.396164	−	0.918180i	$-0.370341\pi$
$887$	−15.5470	−	15.5470i	−0.522016	−	0.522016i	−0.918180	+	0.396164i	$0.870341\pi$
$888$		0			0
$889$	−49.4236	+	49.4236i	−1.65762	+	1.65762i
$890$	−41.6803	−	6.84825i	−1.39713	−	0.229554i
$891$		0			0
$892$	41.1910	−	20.3926i	1.37918	−	0.682796i
$893$	−4.18854	+	10.1120i	−0.140164	+	0.338386i
$894$		0			0
$895$	14.8639			0.496844
$896$	−33.4410	+	36.0954i	−1.11719	+	1.20586i
$897$		0			0
$898$	0.410015	+	1.75231i	0.0136824	+	0.0584754i
$899$	−11.7717	+	28.4194i	−0.392608	+	0.947840i
$900$		0			0
$901$	0.0678074	−	0.0280867i	0.00225899	−	0.000935705i
$902$	−41.0877	−	6.75088i	−1.36807	−	0.224780i
$903$		0			0
$904$	−28.6449	+	23.6200i	−0.952714	+	0.785589i
$905$	8.21432	+	8.21432i	0.273053	+	0.273053i
$906$		0			0
$907$	−18.3127	−	44.2108i	−0.608064	−	1.46800i	−0.865102	−	0.501595i	$-0.832747\pi$
$907$	−18.3127	−	44.2108i	−0.608064	−	1.46800i	0.257038	−	0.966401i	$-0.417253\pi$
$908$	4.01975	+	59.9056i	0.133400	+	1.98804i
$909$		0			0
$910$	−41.3536	−	25.6709i	−1.37086	−	0.850982i
$911$			5.60062i			0.185557i	0.995687	+	0.0927785i	$0.0295748\pi$
$911$			5.60062i			0.185557i	−0.995687	+	0.0927785i	$0.970425\pi$
$912$		0			0
$913$		−	40.9282i		−	1.35453i
$914$	16.7138	−	26.9245i	0.552842	−	0.890582i
$915$		0			0
$916$	24.9728	−	28.5653i	0.825125	−	0.943824i
$917$	14.7407	+	35.5872i	0.486781	+	1.17519i
$918$		0			0
$919$	−7.05061	−	7.05061i	−0.232578	−	0.232578i	0.581190	−	0.813768i	$-0.302587\pi$
$919$	−7.05061	−	7.05061i	−0.232578	−	0.232578i	−0.813768	+	0.581190i	$0.802587\pi$
$920$	1.04655	+	3.42134i	0.0345038	+	0.112798i
$921$		0			0
$922$	−5.98111	+	36.4027i	−0.196978	+	1.19886i
$923$	−45.8721	+	19.0009i	−1.50990	+	0.625421i
$924$		0			0
$925$	0.959286	−	2.31592i	0.0315411	−	0.0761471i
$926$	−8.96658	+	2.09805i	−0.294660	+	0.0689461i
$927$		0			0
$928$	−18.5884	+	17.5458i	−0.610195	+	0.575969i
$929$	−44.4709			−1.45904			−0.729521	−	0.683958i	$-0.760257\pi$
$929$	−44.4709			−1.45904			−0.729521	+	0.683958i	$0.760257\pi$
$930$		0			0
$931$	9.51983	−	22.9829i	0.312000	−	0.753234i
$932$	32.8993	+	11.1109i	1.07765	+	0.363951i
$933$		0			0
$934$	0.0673815	−	0.410103i	0.00220479	−	0.0134190i
$935$	−20.0980	+	20.0980i	−0.657275	+	0.657275i
$936$		0			0
$937$	27.1801	+	27.1801i	0.887936	+	0.887936i	0.994325	−	0.106389i	$-0.0339288\pi$
$937$	27.1801	+	27.1801i	0.887936	+	0.887936i	−0.106389	+	0.994325i	$0.533929\pi$
$938$	−15.3878	+	11.0448i	−0.502429	+	0.360626i
$939$		0			0
$940$	13.4283	+	11.7395i	0.437982	+	0.382900i
$941$	11.0146	+	4.56238i	0.359064	+	0.148729i	0.554921	−	0.831903i	$-0.312749\pi$
$941$	11.0146	+	4.56238i	0.359064	+	0.148729i	−0.195856	+	0.980633i	$0.562749\pi$
$942$		0			0
$943$			7.57615i			0.246713i
$944$	9.81435	−	37.0875i	0.319430	−	1.20710i
$945$		0			0
$946$	−8.71385	−	5.40925i	−0.283312	−	0.175870i
$947$	−45.3993	−	18.8050i	−1.47528	−	0.611080i	−0.507222	−	0.861816i	$-0.669328\pi$
$947$	−45.3993	−	18.8050i	−1.47528	−	0.611080i	−0.968056	+	0.250736i	$0.919328\pi$
$948$		0			0
$949$	−22.7642	−	54.9577i	−0.738957	−	1.78400i
$950$	−3.62620	−	5.05208i	−0.117650	−	0.163911i
$951$		0			0
$952$	−6.80662	+	70.7971i	−0.220604	+	2.29455i
$953$	9.51614	−	9.51614i	0.308258	−	0.308258i	−0.535975	−	0.844234i	$-0.680056\pi$
$953$	9.51614	−	9.51614i	0.308258	−	0.308258i	0.844234	+	0.535975i	$0.180056\pi$
$954$		0			0
$955$	−6.27648	+	2.59980i	−0.203102	+	0.0841276i
$956$	16.6636	+	33.6587i	0.538939	+	1.08860i
$957$		0			0
$958$	4.35353	+	18.6060i	0.140656	+	0.601133i
$959$	61.2683			1.97846
$960$		0			0
$961$	15.3426			0.494922
$962$	−1.78389	−	7.62393i	−0.0575148	−	0.245805i
$963$		0			0
$964$	−4.95858	−	10.0158i	−0.159705	−	0.322588i
$965$	−3.82247	+	1.58332i	−0.123050	+	0.0509688i
$966$		0			0
$967$	7.29264	−	7.29264i	0.234515	−	0.234515i	−0.580059	−	0.814574i	$-0.696971\pi$
$967$	7.29264	−	7.29264i	0.234515	−	0.234515i	0.814574	+	0.580059i	$0.196971\pi$
$968$	−7.45725	−	0.716959i	−0.239685	−	0.0230439i
$969$		0			0
$970$	−13.2944	−	18.5219i	−0.426857	−	0.594704i
$971$	−0.333431	−	0.804973i	−0.0107003	−	0.0258328i	0.918439	−	0.395562i	$-0.129450\pi$
$971$	−0.333431	−	0.804973i	−0.0107003	−	0.0258328i	−0.929139	+	0.369730i	$0.879450\pi$
$972$		0			0
$973$	18.7069	+	7.74864i	0.599715	+	0.248410i
$974$	2.42566	+	1.50576i	0.0777230	+	0.0482477i
$975$		0			0
$976$	−2.30784	−	3.96882i	−0.0738723	−	0.127039i
$977$			27.1522i			0.868676i	0.900750	+	0.434338i	$0.143018\pi$
$977$			27.1522i			0.868676i	−0.900750	+	0.434338i	$0.856982\pi$
$978$		0			0
$979$	46.8773	+	19.4172i	1.49820	+	0.620577i
$980$	−30.5202	−	26.6818i	−0.974931	−	0.852320i
$981$		0			0
$982$	0.161653	−	0.116028i	0.00515854	−	0.00370262i
$983$	1.48996	+	1.48996i	0.0475224	+	0.0475224i	0.730469	−	0.682946i	$-0.239302\pi$
$983$	1.48996	+	1.48996i	0.0475224	+	0.0475224i	−0.682946	+	0.730469i	$0.739302\pi$
$984$		0			0
$985$	13.2264	−	13.2264i	0.421429	−	0.421429i
$986$	−5.99030	+	36.4586i	−0.190770	+	1.16108i
$987$		0			0
$988$	−18.4032	−	6.21523i	−0.585484	−	0.197733i
$989$	−0.714136	+	1.72408i	−0.0227082	+	0.0548225i
$990$		0			0
$991$	−15.6787			−0.498050			−0.249025	−	0.968497i	$-0.580110\pi$
$991$	−15.6787			−0.498050			−0.249025	+	0.968497i	$0.580110\pi$
$992$	35.1381	+	15.7569i	1.11563	+	0.500282i
$993$		0			0
$994$	−63.9210	+	14.9566i	−2.02745	+	0.474393i
$995$	9.71093	−	23.4443i	0.307857	−	0.743233i
$996$		0			0
$997$	−36.0601	+	14.9366i	−1.14204	+	0.473047i	−0.871856	−	0.489763i	$-0.837083\pi$
$997$	−36.0601	+	14.9366i	−1.14204	+	0.473047i	−0.270180	+	0.962810i	$0.587083\pi$
$998$	7.72223	−	46.9997i	0.244443	−	1.48775i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.b.109.19	yes	128
3.2	odd	2	inner	864.2.v.b.109.14	✓	128
32.5	even	8	inner	864.2.v.b.325.19	yes	128
96.5	odd	8	inner	864.2.v.b.325.14	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.b.109.14	✓	128	3.2	odd	2	inner
864.2.v.b.109.19	yes	128	1.1	even	1	trivial
864.2.v.b.325.14	yes	128	96.5	odd	8	inner
864.2.v.b.325.19	yes	128	32.5	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.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.322202 + 1.37702i) q^{2} +(-1.79237 + 0.887359i) q^{4} +(-1.57161 + 0.650984i) q^{5} +(3.07534 - 3.07534i) q^{7} +(-1.79942 - 2.18222i) q^{8} +O(q^{10})\)	\(q+(0.322202 + 1.37702i) q^{2} +(-1.79237 + 0.887359i) q^{4} +(-1.57161 + 0.650984i) q^{5} +(3.07534 - 3.07534i) q^{7} +(-1.79942 - 2.18222i) q^{8} +(-1.40280 - 1.95440i) q^{10} +(1.10590 + 2.66989i) q^{11} +(4.29788 + 1.78024i) q^{13} +(5.22569 + 3.24393i) q^{14} +(2.42519 - 3.18095i) q^{16} -5.78176i q^{17} +(1.92883 + 0.798948i) q^{19} +(2.23926 - 2.56139i) q^{20} +(-3.32016 + 2.38309i) q^{22} +(0.525810 + 0.525810i) q^{23} +(-1.48934 + 1.48934i) q^{25} +(-1.06664 + 6.49187i) q^{26} +(-2.78322 + 8.24109i) q^{28} +(-1.72922 + 4.17470i) q^{29} +6.80754 q^{31} +(5.16164 + 2.31462i) q^{32} +(7.96160 - 1.86290i) q^{34} +(-2.83125 + 6.83525i) q^{35} +(-1.09955 + 0.455448i) q^{37} +(-0.478693 + 2.91346i) q^{38} +(4.24858 + 2.25822i) q^{40} +(7.20426 + 7.20426i) q^{41} +(0.960366 + 2.31853i) q^{43} +(-4.35133 - 3.80409i) q^{44} +(-0.554634 + 0.893469i) q^{46} +5.24257i q^{47} -11.9155i q^{49} +(-2.53072 - 1.57099i) q^{50} +(-9.28311 + 0.622911i) q^{52} +(0.00485782 + 0.0117278i) q^{53} +(-3.47611 - 3.47611i) q^{55} +(-12.2449 - 1.17726i) q^{56} +(-6.30580 - 1.03607i) q^{58} +(8.86095 - 3.67033i) q^{59} +(0.439229 - 1.06039i) q^{61} +(2.19341 + 9.37412i) q^{62} +(-1.52419 + 7.85346i) q^{64} -7.91352 q^{65} +(-1.17849 + 2.84512i) q^{67} +(5.13049 + 10.3631i) q^{68} +(-10.3245 - 1.69636i) q^{70} +(-7.54709 + 7.54709i) q^{71} +(-9.04188 - 9.04188i) q^{73} +(-0.981439 - 1.36735i) q^{74} +(-4.16613 + 0.279554i) q^{76} +(11.6118 + 4.80978i) q^{77} -8.85007i q^{79} +(-1.74071 + 6.57799i) q^{80} +(-7.59918 + 12.2416i) q^{82} +(-13.0846 - 5.41983i) q^{83} +(3.76383 + 9.08669i) q^{85} +(-2.88323 + 2.06948i) q^{86} +(3.83630 - 7.21756i) q^{88} +(12.4152 - 12.4152i) q^{89} +(18.6923 - 7.74261i) q^{91} +(-1.40903 - 0.475865i) q^{92} +(-7.21913 + 1.68917i) q^{94} -3.55148 q^{95} +9.47707 q^{97} +(16.4078 - 3.83919i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 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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