LMFDB - Embedded newform 864.2.v.b.109.14

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			109.14
Character	$\chi$	$=$	864.109
Dual form			864.2.v.b.325.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.322202 - 1.37702i) q^{2} +(-1.79237 + 0.887359i) q^{4} +(1.57161 - 0.650984i) q^{5} +(3.07534 - 3.07534i) q^{7} +(1.79942 + 2.18222i) q^{8} +O(q^{10})$	\(q+(-0.322202 - 1.37702i) q^{2} +(-1.79237 + 0.887359i) q^{4} +(1.57161 - 0.650984i) q^{5} +(3.07534 - 3.07534i) q^{7} +(1.79942 + 2.18222i) q^{8} +(-1.40280 - 1.95440i) q^{10} +(-1.10590 - 2.66989i) q^{11} +(4.29788 + 1.78024i) q^{13} +(-5.22569 - 3.24393i) q^{14} +(2.42519 - 3.18095i) q^{16} +5.78176i q^{17} +(1.92883 + 0.798948i) q^{19} +(-2.23926 + 2.56139i) q^{20} +(-3.32016 + 2.38309i) q^{22} +(-0.525810 - 0.525810i) q^{23} +(-1.48934 + 1.48934i) q^{25} +(1.06664 - 6.49187i) q^{26} +(-2.78322 + 8.24109i) q^{28} +(1.72922 - 4.17470i) q^{29} +6.80754 q^{31} +(-5.16164 - 2.31462i) q^{32} +(7.96160 - 1.86290i) q^{34} +(2.83125 - 6.83525i) q^{35} +(-1.09955 + 0.455448i) q^{37} +(0.478693 - 2.91346i) q^{38} +(4.24858 + 2.25822i) q^{40} +(-7.20426 - 7.20426i) q^{41} +(0.960366 + 2.31853i) q^{43} +(4.35133 + 3.80409i) q^{44} +(-0.554634 + 0.893469i) q^{46} -5.24257i q^{47} -11.9155i q^{49} +(2.53072 + 1.57099i) q^{50} +(-9.28311 + 0.622911i) q^{52} +(-0.00485782 - 0.0117278i) q^{53} +(-3.47611 - 3.47611i) q^{55} +(12.2449 + 1.17726i) q^{56} +(-6.30580 - 1.03607i) q^{58} +(-8.86095 + 3.67033i) q^{59} +(0.439229 - 1.06039i) q^{61} +(-2.19341 - 9.37412i) q^{62} +(-1.52419 + 7.85346i) q^{64} +7.91352 q^{65} +(-1.17849 + 2.84512i) q^{67} +(-5.13049 - 10.3631i) q^{68} +(-10.3245 - 1.69636i) q^{70} +(7.54709 - 7.54709i) q^{71} +(-9.04188 - 9.04188i) q^{73} +(0.981439 + 1.36735i) q^{74} +(-4.16613 + 0.279554i) q^{76} +(-11.6118 - 4.80978i) q^{77} -8.85007i q^{79} +(1.74071 - 6.57799i) q^{80} +(-7.59918 + 12.2416i) q^{82} +(13.0846 + 5.41983i) q^{83} +(3.76383 + 9.08669i) q^{85} +(2.88323 - 2.06948i) q^{86} +(3.83630 - 7.21756i) q^{88} +(-12.4152 + 12.4152i) q^{89} +(18.6923 - 7.74261i) q^{91} +(1.40903 + 0.475865i) q^{92} +(-7.21913 + 1.68917i) q^{94} +3.55148 q^{95} +9.47707 q^{97} +(-16.4078 + 3.83919i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.00249383	−	0.999997i	$-0.500794\pi$
$5$	1.57161	−	0.650984i	0.702847	−	0.291129i	0.705341	+	0.708868i	$0.250794\pi$
$6$		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	$-0.981514\pi$
$11$	−1.10590	−	2.66989i	−0.333442	−	0.805001i	0.664872	−	0.746957i	$-0.268486\pi$
$12$		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	$0.247326\pi$
$17$			5.78176i			1.40228i	−0.713022	+	0.701141i	$0.752674\pi$
$18$		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	0.650159	−	0.759798i	$-0.274702\pi$
$23$	−0.525810	−	0.525810i	−0.109639	−	0.109639i	−0.759798	+	0.650159i	$0.774702\pi$
$24$		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	$-0.737189\pi$
$29$	1.72922	−	4.17470i	0.321107	−	0.775222i	0.999190	−	0.0402362i	$-0.0128110\pi$
$30$		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	$-0.957168\pi$
$41$	−7.20426	−	7.20426i	−1.12512	−	1.12512i	−0.134156	−	0.990960i	$-0.542832\pi$
$42$		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	$-0.875114\pi$
$47$		−	5.24257i		−	0.764708i	0.924016	−	0.382354i	$-0.124886\pi$
$48$		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	0.923546	−	0.383489i	$-0.125278\pi$
$53$	−0.00485782	−	0.0117278i	−0.000667273	−	0.00161094i	−0.924213	+	0.381878i	$0.875278\pi$
$54$		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	−0.875738	−	0.482786i	$-0.839625\pi$
$59$	−8.86095	+	3.67033i	−1.15360	+	0.477836i	−0.277859	+	0.960622i	$0.589625\pi$
$60$		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	−0.0993754	−	0.995050i	$-0.531684\pi$
$71$	7.54709	−	7.54709i	0.895675	−	0.895675i	0.995050	+	0.0993754i	$0.0316845\pi$
$72$		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	0.958880	−	0.283813i	$-0.0915997\pi$
$83$	13.0846	+	5.41983i	1.43622	+	0.594903i	0.477344	+	0.878717i	$0.341600\pi$
$84$		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	$0.630680\pi$
$89$	−12.4152	+	12.4152i	−1.31601	+	1.31601i	−0.916904	+	0.399108i	$0.869320\pi$
$90$		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	−0.985528	−	0.169511i	$-0.945781\pi$
$101$	−15.7033	+	6.50453i	−1.56254	+	0.647225i	−0.577011	+	0.816736i	$0.695781\pi$
$102$		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	0.809411	−	0.587242i	$-0.199786\pi$
$107$	−1.84303	−	4.44946i	−0.178172	−	0.430145i	−0.987583	+	0.157097i	$0.949786\pi$
$108$		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	$0.211821\pi$
$113$			13.1265i			1.23483i	−0.786636	+	0.617417i	$0.788179\pi$
$114$		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	$-0.748544\pi$
$131$	3.38930	−	8.18249i	0.296124	−	0.714907i	0.999990	−	0.00457365i	$-0.00145584\pi$
$132$		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	0.139218	−	0.990262i	$-0.455541\pi$
$137$	−9.96122	−	9.96122i	−0.851044	−	0.851044i	−0.990262	+	0.139218i	$0.955541\pi$
$138$		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	$0.0203879\pi$
$149$	4.12035	+	9.94741i	0.337552	+	0.814923i	−0.660397	+	0.750916i	$0.729612\pi$
$150$		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	−0.398975	−	0.916962i	$-0.630634\pi$
$167$	6.69386	−	6.69386i	0.517986	−	0.517986i	0.916962	+	0.398975i	$0.130634\pi$
$168$		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	0.803822	−	0.594869i	$-0.202796\pi$
$173$	12.5160	+	5.18430i	0.951575	+	0.394155i	0.147752	+	0.989024i	$0.452796\pi$
$174$		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	0.663394	−	0.748270i	$-0.269115\pi$
$179$	8.07265	+	3.34380i	0.603378	+	0.249928i	−0.0600160	+	0.998197i	$0.519115\pi$
$180$		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	$-0.546153\pi$
$191$	−3.99365			−0.288970			−0.144485	+	0.989507i	$0.546153\pi$
$192$		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	0.00978883	−	0.999952i	$-0.496884\pi$
$197$	10.1588	−	4.20791i	0.723783	−	0.299801i	0.713995	+	0.700151i	$0.246884\pi$
$198$		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	$0.597439\pi$
$227$	−11.4882	+	27.7350i	−0.762500	+	1.84084i	−0.461145	+	0.887325i	$0.652561\pi$
$228$		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	0.983764	−	0.179464i	$-0.0574364\pi$
$233$	12.2771	+	12.2771i	0.804300	+	0.804300i	−0.179464	+	0.983764i	$0.557436\pi$
$234$		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	$0.207768\pi$
$239$			18.7789i			1.21470i	−0.794433	+	0.607351i	$0.792232\pi$
$240$		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	0.0348230	−	0.999393i	$-0.488913\pi$
$251$	12.1377	−	5.02760i	0.766125	−	0.317339i	0.731302	+	0.682054i	$0.238913\pi$
$252$		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	$-0.308773\pi$
$257$	18.1239			1.13054			0.565268	+	0.824907i	$0.308773\pi$
$258$		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	−0.586355	−	0.810054i	$-0.699438\pi$
$263$	3.62779	−	3.62779i	0.223699	−	0.223699i	0.810054	+	0.586355i	$0.199438\pi$
$264$		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	0.735607	−	0.677408i	$-0.236897\pi$
$269$	12.7398	+	5.27701i	0.776761	+	0.321745i	0.0411532	+	0.999153i	$0.486897\pi$
$270$		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	−0.975318	−	0.220805i	$-0.929131\pi$
$281$	−12.6479	+	12.6479i	−0.754513	+	0.754513i	0.220805	+	0.975318i	$0.429131\pi$
$282$		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	−0.362432	−	0.932010i	$-0.618054\pi$
$293$	0.690177	−	0.285881i	0.0403206	−	0.0167013i	0.402753	+	0.915309i	$0.368054\pi$
$294$		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	$-0.900359\pi$
$311$	−22.2089	−	22.2089i	−1.25935	−	1.25935i	−0.307945	−	0.951404i	$-0.599641\pi$
$312$		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	−0.993699	−	0.112085i	$-0.964247\pi$
$317$	−3.77085	+	9.10363i	−0.211792	+	0.511311i	0.781907	+	0.623395i	$0.214247\pi$
$318$		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	0.388912	−	0.921275i	$-0.372851\pi$
$347$	24.5023	−	10.1492i	1.31535	−	0.544838i	0.926442	+	0.376437i	$0.122851\pi$
$348$		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	$-0.537671\pi$
$353$	−4.43676			−0.236145			−0.118072	+	0.993005i	$0.537671\pi$
$354$		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	−0.163674	−	0.986515i	$-0.552334\pi$
$359$	15.5906	−	15.5906i	0.822841	−	0.822841i	0.986515	+	0.163674i	$0.0523344\pi$
$360$		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	$-0.400706\pi$
$383$	12.0126			0.613816			0.306908	+	0.951739i	$0.400706\pi$
$384$		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	0.340513	−	0.940240i	$-0.389399\pi$
$389$	24.5778	−	10.1804i	1.24614	−	0.516169i	0.905629	+	0.424071i	$0.139399\pi$
$390$		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	$0.162548\pi$
$401$			19.5746i			0.977508i	−0.872422	+	0.488754i	$0.837452\pi$
$402$		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	−0.969181	−	0.246351i	$-0.920768\pi$
$419$	−2.24489	+	5.41965i	−0.109670	+	0.264767i	0.859511	+	0.511118i	$0.170768\pi$
$420$		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	$-0.974766\pi$
$431$		−	3.28812i		−	0.158383i	0.996859	−	0.0791915i	$-0.0252339\pi$
$432$		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	−0.119931	−	0.992782i	$-0.538267\pi$
$443$	10.4663	−	4.33528i	0.497268	−	0.205975i	0.617199	+	0.786807i	$0.288267\pi$
$444$		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	$-0.509559\pi$
$449$	−1.27254			−0.0600548			−0.0300274	+	0.999549i	$0.509559\pi$
$450$		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	−0.257244	−	0.966347i	$-0.582814\pi$
$461$	−24.1001	−	9.98258i	−1.12245	−	0.464935i	−0.865209	+	0.501411i	$0.832814\pi$
$462$		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	0.388956	−	0.921256i	$-0.372836\pi$
$467$	0.271505	+	0.112461i	0.0125637	+	0.00520407i	−0.376393	+	0.926460i	$0.622836\pi$
$468$		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	$-0.599889\pi$
$479$	−13.5118			−0.617369			−0.308685	+	0.951164i	$0.599889\pi$
$480$		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	0.925090	−	0.379748i	$-0.123989\pi$
$491$	0.0538443	+	0.129992i	0.00242996	+	0.00586645i	−0.922660	+	0.385615i	$0.873989\pi$
$492$		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	0.655027	−	0.755606i	$-0.272657\pi$
$503$	−2.25575	−	2.25575i	−0.100579	−	0.100579i	−0.755606	+	0.655027i	$0.772657\pi$
$504$		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	−0.923037	−	0.384711i	$-0.874301\pi$
$509$	0.0379139	−	0.0915322i	0.00168050	−	0.00405709i	0.924718	+	0.380654i	$0.124301\pi$
$510$		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	0.537403	−	0.843325i	$-0.319405\pi$
$521$	−6.98279	−	6.98279i	−0.305922	−	0.305922i	−0.843325	+	0.537403i	$0.819405\pi$
$522$		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	0.537925	−	0.842993i	$-0.319209\pi$
$557$	7.60439	+	3.14984i	0.322209	+	0.133463i	−0.215716	+	0.976456i	$0.569209\pi$
$558$		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	0.607898	−	0.794015i	$-0.292013\pi$
$563$	11.3013	+	4.68115i	0.476293	+	0.197287i	−0.131605	+	0.991302i	$0.542013\pi$
$564$		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	−0.593332	−	0.804958i	$-0.702188\pi$
$569$	5.04807	−	5.04807i	0.211626	−	0.211626i	0.804958	+	0.593332i	$0.202188\pi$
$570$		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	$-0.978422\pi$
$587$	−8.24039	−	19.8941i	−0.340117	−	0.821116i	0.657586	−	0.753380i	$-0.271578\pi$
$588$		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	$0.314527\pi$
$593$			40.6667i			1.66998i	−0.550264	+	0.834991i	$0.685473\pi$
$594$		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	0.539187	−	0.842186i	$-0.318732\pi$
$599$	−7.41576	−	7.41576i	−0.303000	−	0.303000i	−0.842186	+	0.539187i	$0.818732\pi$
$600$		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	0.492640	−	0.870233i	$-0.336032\pi$
$617$	−9.37922	−	9.37922i	−0.377593	−	0.377593i	−0.870233	+	0.492640i	$0.836032\pi$
$618$		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	$-0.438832\pi$
$641$	9.67074			0.381971			0.190986	+	0.981593i	$0.438832\pi$
$642$		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	−0.959090	−	0.283102i	$-0.908637\pi$
$647$	−17.1946	+	17.1946i	−0.675988	+	0.675988i	0.283102	+	0.959090i	$0.408637\pi$
$648$		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	$0.00728045\pi$
$653$	44.0250	+	18.2358i	1.72283	+	0.713620i	0.723094	+	0.690750i	$0.242720\pi$
$654$		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	−0.0323990	−	0.999475i	$-0.510315\pi$
$659$	−19.5624	−	8.10302i	−0.762044	−	0.315649i	−0.729645	+	0.683826i	$0.760315\pi$
$660$		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	0.0101096	−	0.999949i	$-0.496782\pi$
$677$	18.8465	−	7.80647i	0.724329	−	0.300027i	0.714219	+	0.699922i	$0.246782\pi$
$678$		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	$-0.834777\pi$
$683$	−15.8135	−	38.1772i	−0.605087	−	1.46081i	0.263197	−	0.964742i	$-0.415223\pi$
$684$		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	$0.459820\pi$
$701$	−17.5964	+	42.4815i	−0.664607	+	1.60450i	−0.790502	+	0.612459i	$0.790180\pi$
$702$		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	$-0.715467\pi$
$719$		−	41.8039i		−	1.55902i	0.626388	−	0.779511i	$-0.284533\pi$
$720$		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	−0.914477	−	0.404639i	$-0.867397\pi$
$743$	−13.8972	+	13.8972i	−0.509838	+	0.509838i	0.404639	+	0.914477i	$0.367397\pi$
$744$		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	−0.983094	−	0.183101i	$-0.941387\pi$
$761$	−22.0688	+	22.0688i	−0.799993	+	0.799993i	0.183101	+	0.983094i	$0.441387\pi$
$762$		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	−0.119125	−	0.992879i	$-0.538009\pi$
$773$	13.8656	−	5.74334i	0.498712	−	0.206573i	0.617837	+	0.786306i	$0.288009\pi$
$774$		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	$-0.512963\pi$
$797$	19.6093	−	47.3410i	0.694596	−	1.67690i	0.735308	−	0.677733i	$-0.237037\pi$
$798$		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	0.801420	−	0.598101i	$-0.204078\pi$
$809$	5.78299	+	5.78299i	0.203319	+	0.203319i	−0.598101	+	0.801420i	$0.704078\pi$
$810$		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	0.993032	−	0.117848i	$-0.0375995\pi$
$821$	5.94613	+	14.3552i	0.207521	+	0.501001i	−0.785510	+	0.618848i	$0.787600\pi$
$822$		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	−0.995475	−	0.0950194i	$-0.969709\pi$
$827$	−46.9380	+	19.4424i	−1.63219	+	0.676077i	−0.636719	+	0.771096i	$0.719709\pi$
$828$		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	−0.537858	−	0.843035i	$-0.680767\pi$
$839$	8.83959	−	8.83959i	0.305177	−	0.305177i	0.843035	+	0.537858i	$0.180767\pi$
$840$		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	−0.463238	−	0.886234i	$-0.653312\pi$
$857$	12.3830	−	12.3830i	0.422996	−	0.422996i	0.886234	+	0.463238i	$0.153312\pi$
$858$		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	$-0.691725\pi$
$863$	−33.2873			−1.13311			−0.566556	+	0.824023i	$0.691725\pi$
$864$		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	$0.0637217\pi$
$881$			11.8046i			0.397707i	−0.980029	+	0.198853i	$0.936278\pi$
$882$		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	0.918180	−	0.396164i	$-0.129659\pi$
$887$	15.5470	+	15.5470i	0.522016	+	0.522016i	−0.396164	+	0.918180i	$0.629659\pi$
$888$		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	$-0.970425\pi$
$911$		−	5.60062i		−	0.185557i	0.995687	−	0.0927785i	$-0.0295748\pi$
$912$		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	$-0.239743\pi$
$929$	44.4709			1.45904			0.729521	+	0.683958i	$0.239743\pi$
$930$		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	0.195856	−	0.980633i	$-0.437251\pi$
$941$	−11.0146	−	4.56238i	−0.359064	−	0.148729i	−0.554921	+	0.831903i	$0.687251\pi$
$942$		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	0.968056	−	0.250736i	$-0.0806725\pi$
$947$	45.3993	+	18.8050i	1.47528	+	0.611080i	0.507222	+	0.861816i	$0.330672\pi$
$948$		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	−0.844234	−	0.535975i	$-0.819944\pi$
$953$	−9.51614	+	9.51614i	−0.308258	+	0.308258i	0.535975	+	0.844234i	$0.319944\pi$
$954$		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	0.929139	−	0.369730i	$-0.120550\pi$
$971$	0.333431	+	0.804973i	0.0107003	+	0.0258328i	−0.918439	+	0.395562i	$0.870550\pi$
$972$		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	$-0.856982\pi$
$977$		−	27.1522i		−	0.868676i	0.900750	−	0.434338i	$-0.143018\pi$
$978$		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	0.682946	−	0.730469i	$-0.260698\pi$
$983$	−1.48996	−	1.48996i	−0.0475224	−	0.0475224i	−0.730469	+	0.682946i	$0.760698\pi$
$984$		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.109.14	✓	128
3.2	odd	2	inner	864.2.v.b.109.19	yes	128
32.5	even	8	inner	864.2.v.b.325.14	yes	128
96.5	odd	8	inner	864.2.v.b.325.19	yes	128

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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