LMFDB - Embedded newform 952.2.cw.a.129.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [952,2,Mod(73,952)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("952.73"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(952, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 0, 8, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 952 = 2^{3} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	952.cw (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [288,0,0,0,0,0,0,0,0,0,0,0,0,0,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.60175827243$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			129.13
Character	$\chi$	$=$	952.129
Dual form			952.2.cw.a.369.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.601180 + 1.21907i) q^{3} +(-2.48941 + 2.18316i) q^{5} +(0.983031 - 2.45635i) q^{7} +(0.701565 - 0.914297i) q^{9} +(-5.80510 + 0.380487i) q^{11} +(-2.18132 - 2.18132i) q^{13} +(-4.15801 - 1.72230i) q^{15} +(1.19088 - 3.94738i) q^{17} +(-0.966899 - 7.34432i) q^{19} +(3.58544 - 0.278322i) q^{21} +(4.46998 + 2.20435i) q^{23} +(0.778374 - 5.91234i) q^{25} +(5.53575 + 1.10113i) q^{27} +(-0.698157 - 3.50987i) q^{29} +(-2.84016 + 1.40061i) q^{31} +(-3.95375 - 6.84810i) q^{33} +(2.91543 + 8.26098i) q^{35} +(-0.496882 + 7.58095i) q^{37} +(1.34782 - 3.97055i) q^{39} +(-1.21967 + 6.13169i) q^{41} +(-1.36255 - 3.28950i) q^{43} +(0.249569 + 3.80769i) q^{45} +(2.04372 - 7.62725i) q^{47} +(-5.06730 - 4.82933i) q^{49} +(5.52807 - 0.921314i) q^{51} +(5.85990 + 7.63677i) q^{53} +(13.6206 - 13.6206i) q^{55} +(8.37198 - 5.59398i) q^{57} +(-10.5527 - 1.38929i) q^{59} +(-2.85314 - 8.40508i) q^{61} +(-1.55617 - 2.62207i) q^{63} +(10.1924 + 0.668043i) q^{65} +(-7.45397 - 4.30355i) q^{67} +6.77444i q^{69} +(1.85403 + 1.23882i) q^{71} +(-5.71087 - 1.93858i) q^{73} +(7.67551 - 2.60548i) q^{75} +(-4.77199 + 14.6334i) q^{77} +(6.30295 - 12.7811i) q^{79} +(1.09080 + 4.07092i) q^{81} +(5.13043 - 12.3860i) q^{83} +(5.65315 + 12.4265i) q^{85} +(3.85907 - 2.96117i) q^{87} +(-5.15912 - 1.38238i) q^{89} +(-7.50238 + 3.21378i) q^{91} +(-3.41489 - 2.62034i) q^{93} +(18.4408 + 16.1722i) q^{95} +(-14.6476 + 2.91359i) q^{97} +(-3.72478 + 5.57452i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 32 q^{15} - 48 q^{21} + 32 q^{29} + 72 q^{31} + 32 q^{35} + 48 q^{37} + 32 q^{39} - 32 q^{43} - 24 q^{47} + 48 q^{49} + 16 q^{53} + 128 q^{57} - 72 q^{61} + 184 q^{63} - 32 q^{65} - 80 q^{71} - 96 q^{73}+ \cdots + 64 q^{99}+O(q^{100}) $ 288 * q - 32 * q^15 - 48 * q^21 + 32 * q^29 + 72 * q^31 + 32 * q^35 + 48 * q^37 + 32 * q^39 - 32 * q^43 - 24 * q^47 + 48 * q^49 + 16 * q^53 + 128 * q^57 - 72 * q^61 + 184 * q^63 - 32 * q^65 - 80 * q^71 - 96 * q^73 - 216 * q^75 + 56 * q^77 - 32 * q^79 - 64 * q^81 + 160 * q^85 - 144 * q^87 + 144 * q^89 - 32 * q^93 - 64 * q^95 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/952\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.601180	+	1.21907i	0.347091	+	0.703832i	0.998492	−	0.0549026i	$-0.0174848\pi$
$3$	0.601180	+	1.21907i	0.347091	+	0.703832i	−0.651400	+	0.758734i	$0.725818\pi$
$4$		0			0
$5$	−2.48941	+	2.18316i	−1.11330	+	0.976337i	−0.999852	−	0.0172065i	$-0.994523\pi$
$5$	−2.48941	+	2.18316i	−1.11330	+	0.976337i	−0.113448	+	0.993544i	$0.536189\pi$
$6$		0			0
$7$	0.983031	−	2.45635i	0.371551	−	0.928413i
$7$	0.983031	−	2.45635i	0.371551	−	0.928413i
$8$		0			0
$9$	0.701565	−	0.914297i	0.233855	−	0.304766i
$10$		0			0
$11$	−5.80510	+	0.380487i	−1.75030	+	0.114721i	−0.906574	−	0.422047i	$-0.861312\pi$
$11$	−5.80510	+	0.380487i	−1.75030	+	0.114721i	−0.843730	+	0.536768i	$0.819645\pi$
$12$		0			0
$13$	−2.18132	−	2.18132i	−0.604989	−	0.604989i	0.336643	−	0.941632i	$-0.390708\pi$
$13$	−2.18132	−	2.18132i	−0.604989	−	0.604989i	−0.941632	+	0.336643i	$0.890708\pi$
$14$		0			0
$15$	−4.15801	−	1.72230i	−1.07359	−	0.444697i
$16$		0			0
$17$	1.19088	−	3.94738i	0.288831	−	0.957380i
$17$	1.19088	−	3.94738i	0.288831	−	0.957380i
$18$		0			0
$19$	−0.966899	−	7.34432i	−0.221822	−	1.68490i	−0.633633	−	0.773634i	$-0.718437\pi$
$19$	−0.966899	−	7.34432i	−0.221822	−	1.68490i	0.411811	−	0.911269i	$-0.364896\pi$
$20$		0			0
$21$	3.58544	−	0.278322i	0.782408	−	0.0607348i
$22$		0			0
$23$	4.46998	+	2.20435i	0.932056	+	0.459639i	0.843920	−	0.536469i	$-0.180242\pi$
$23$	4.46998	+	2.20435i	0.932056	+	0.459639i	0.0881359	+	0.996108i	$0.471909\pi$
$24$		0			0
$25$	0.778374	−	5.91234i	0.155675	−	1.18247i
$26$		0			0
$27$	5.53575	+	1.10113i	1.06536	+	0.211912i
$28$		0			0
$29$	−0.698157	−	3.50987i	−0.129645	−	0.651767i	−0.989884	−	0.141877i	$-0.954686\pi$
$29$	−0.698157	−	3.50987i	−0.129645	−	0.651767i	0.860240	−	0.509890i	$-0.170314\pi$
$30$		0			0
$31$	−2.84016	+	1.40061i	−0.510108	+	0.251557i	−0.679081	−	0.734063i	$-0.737622\pi$
$31$	−2.84016	+	1.40061i	−0.510108	+	0.251557i	0.168973	+	0.985621i	$0.445955\pi$
$32$		0			0
$33$	−3.95375	−	6.84810i	−0.688260	−	1.19210i
$34$		0			0
$35$	2.91543	+	8.26098i	0.492797	+	1.39636i
$36$		0			0
$37$	−0.496882	+	7.58095i	−0.0816869	+	1.24630i	0.738519	+	0.674233i	$0.235525\pi$
$37$	−0.496882	+	7.58095i	−0.0816869	+	1.24630i	−0.820206	+	0.572068i	$0.806141\pi$
$38$		0			0
$39$	1.34782	−	3.97055i	0.215824	−	0.635797i
$40$		0			0
$41$	−1.21967	+	6.13169i	−0.190480	+	0.957609i	0.760731	+	0.649068i	$0.224841\pi$
$41$	−1.21967	+	6.13169i	−0.190480	+	0.957609i	−0.951211	+	0.308541i	$0.900159\pi$
$42$		0			0
$43$	−1.36255	−	3.28950i	−0.207787	−	0.501643i	0.785287	−	0.619132i	$-0.212516\pi$
$43$	−1.36255	−	3.28950i	−0.207787	−	0.501643i	−0.993074	+	0.117489i	$0.962516\pi$
$44$		0			0
$45$	0.249569	+	3.80769i	0.0372036	+	0.567617i
$46$		0			0
$47$	2.04372	−	7.62725i	0.298107	−	1.11255i	−0.640612	−	0.767865i	$-0.721319\pi$
$47$	2.04372	−	7.62725i	0.298107	−	1.11255i	0.938719	−	0.344685i	$-0.112014\pi$
$48$		0			0
$49$	−5.06730	−	4.82933i	−0.723900	−	0.689905i
$50$		0			0
$51$	5.52807	−	0.921314i	0.774085	−	0.129010i
$52$		0			0
$53$	5.85990	+	7.63677i	0.804919	+	1.04899i	0.997702	+	0.0677500i	$0.0215820\pi$
$53$	5.85990	+	7.63677i	0.804919	+	1.04899i	−0.192783	+	0.981241i	$0.561751\pi$
$54$		0			0
$55$	13.6206	−	13.6206i	1.83661	−	1.83661i
$56$		0			0
$57$	8.37198	−	5.59398i	1.10890	−	0.740941i
$58$		0			0
$59$	−10.5527	−	1.38929i	−1.37384	−	0.180870i	−0.592800	−	0.805349i	$-0.701978\pi$
$59$	−10.5527	−	1.38929i	−1.37384	−	0.180870i	−0.781041	+	0.624480i	$0.785311\pi$
$60$		0			0
$61$	−2.85314	−	8.40508i	−0.365307	−	1.07616i	−0.961850	−	0.273579i	$-0.911793\pi$
$61$	−2.85314	−	8.40508i	−0.365307	−	1.07616i	0.596542	−	0.802582i	$-0.296541\pi$
$62$		0			0
$63$	−1.55617	−	2.62207i	−0.196059	−	0.330350i
$64$		0			0
$65$	10.1924	+	0.668043i	1.26421	+	0.0828605i
$66$		0			0
$67$	−7.45397	−	4.30355i	−0.910648	−	0.525763i	−0.0300081	−	0.999550i	$-0.509553\pi$
$67$	−7.45397	−	4.30355i	−0.910648	−	0.525763i	−0.880639	+	0.473787i	$0.842887\pi$
$68$		0			0
$69$			6.77444i			0.815547i
$70$		0			0
$71$	1.85403	+	1.23882i	0.220033	+	0.147021i	0.660702	−	0.750648i	$-0.270259\pi$
$71$	1.85403	+	1.23882i	0.220033	+	0.147021i	−0.440669	+	0.897670i	$0.645259\pi$
$72$		0			0
$73$	−5.71087	−	1.93858i	−0.668407	−	0.226894i	−0.0334492	−	0.999440i	$-0.510649\pi$
$73$	−5.71087	−	1.93858i	−0.668407	−	0.226894i	−0.634958	+	0.772547i	$0.718983\pi$
$74$		0			0
$75$	7.67551	−	2.60548i	0.886291	−	0.300855i
$76$		0			0
$77$	−4.77199	+	14.6334i	−0.543818	+	1.66763i
$78$		0			0
$79$	6.30295	−	12.7811i	0.709137	−	1.43799i	−0.181554	−	0.983381i	$-0.558113\pi$
$79$	6.30295	−	12.7811i	0.709137	−	1.43799i	0.890692	−	0.454608i	$-0.150221\pi$
$80$		0			0
$81$	1.09080	+	4.07092i	0.121200	+	0.452325i
$82$		0			0
$83$	5.13043	−	12.3860i	0.563138	−	1.35954i	−0.344106	−	0.938931i	$-0.611818\pi$
$83$	5.13043	−	12.3860i	0.563138	−	1.35954i	0.907244	−	0.420605i	$-0.138182\pi$
$84$		0			0
$85$	5.65315	+	12.4265i	0.613170	+	1.34785i
$86$		0			0
$87$	3.85907	−	2.96117i	0.413736	−	0.317471i
$88$		0			0
$89$	−5.15912	−	1.38238i	−0.546866	−	0.146532i	−0.0252004	−	0.999682i	$-0.508022\pi$
$89$	−5.15912	−	1.38238i	−0.546866	−	0.146532i	−0.521665	+	0.853150i	$0.674689\pi$
$90$		0			0
$91$	−7.50238	+	3.21378i	−0.786464	+	0.336895i
$92$		0			0
$93$	−3.41489	−	2.62034i	−0.354108	−	0.271717i
$94$		0			0
$95$	18.4408	+	16.1722i	1.89199	+	1.65923i
$96$		0			0
$97$	−14.6476	+	2.91359i	−1.48724	+	0.295831i	−0.870826	−	0.491591i	$-0.836416\pi$
$97$	−14.6476	+	2.91359i	−1.48724	+	0.295831i	−0.616415	+	0.787421i	$0.711416\pi$
$98$		0			0
$99$	−3.72478	+	5.57452i	−0.374354	+	0.560261i
$100$		0			0
$101$	−4.94534	+	8.56557i	−0.492079	+	0.852307i	−0.999958	−	0.00912189i	$-0.997096\pi$
$101$	−4.94534	+	8.56557i	−0.492079	+	0.852307i	0.507879	+	0.861428i	$0.330430\pi$
$102$		0			0
$103$	4.89151	−	2.82411i	0.481974	−	0.278268i	−0.239265	−	0.970954i	$-0.576906\pi$
$103$	4.89151	−	2.82411i	0.481974	−	0.278268i	0.721239	+	0.692686i	$0.243573\pi$
$104$		0			0
$105$	−8.31803	+	8.52045i	−0.811757	+	0.831510i
$106$		0			0
$107$	−1.91897	−	2.18817i	−0.185514	−	0.211538i	0.651606	−	0.758558i	$-0.274096\pi$
$107$	−1.91897	−	2.18817i	−0.185514	−	0.211538i	−0.837120	+	0.547020i	$0.815762\pi$
$108$		0			0
$109$	1.33164	−	1.51845i	0.127548	−	0.145441i	−0.684541	−	0.728975i	$-0.739997\pi$
$109$	1.33164	−	1.51845i	0.127548	−	0.145441i	0.812089	+	0.583534i	$0.198331\pi$
$110$		0			0
$111$	−9.54044	+	3.95178i	−0.905539	+	0.375086i
$112$		0			0
$113$	3.80621	+	5.69639i	0.358058	+	0.535872i	0.966145	−	0.257999i	$-0.0830630\pi$
$113$	3.80621	+	5.69639i	0.358058	+	0.535872i	−0.608087	+	0.793870i	$0.708063\pi$
$114$		0			0
$115$	−15.9401	+	4.27113i	−1.48642	+	0.398285i
$116$		0			0
$117$	−3.52471	+	0.464037i	−0.325860	+	0.0429002i
$118$		0			0
$119$	−8.52547	−	6.80562i	−0.781528	−	0.623870i
$120$		0			0
$121$	22.6485	−	2.98174i	2.05896	−	0.271067i
$122$		0			0
$123$	−8.20821	+	2.19938i	−0.740109	+	0.198312i
$124$		0			0
$125$	1.77213	+	2.65219i	0.158504	+	0.237219i
$126$		0			0
$127$	−7.37133	+	3.05330i	−0.654100	+	0.270937i	−0.684953	−	0.728587i	$-0.740177\pi$
$127$	−7.37133	+	3.05330i	−0.654100	+	0.270937i	0.0308537	+	0.999524i	$0.490177\pi$
$128$		0			0
$129$	3.19099	−	3.63863i	0.280951	−	0.320363i
$130$		0			0
$131$	−9.53164	−	10.8687i	−0.832783	−	0.949607i	0.166554	−	0.986032i	$-0.446736\pi$
$131$	−9.53164	−	10.8687i	−0.832783	−	0.949607i	−0.999336	+	0.0364256i	$0.988403\pi$
$132$		0			0
$133$	−18.9907	−	4.84466i	−1.64670	−	0.420085i
$134$		0			0
$135$	−16.1847	+	9.34425i	−1.39296	+	0.804225i
$136$		0			0
$137$	−2.89024	+	5.00604i	−0.246930	+	0.427695i	−0.962672	−	0.270669i	$-0.912755\pi$
$137$	−2.89024	+	5.00604i	−0.246930	+	0.427695i	0.715743	+	0.698364i	$0.246088\pi$
$138$		0			0
$139$	2.79590	−	4.18436i	0.237145	−	0.354913i	−0.693739	−	0.720226i	$-0.744038\pi$
$139$	2.79590	−	4.18436i	0.237145	−	0.354913i	0.930885	+	0.365313i	$0.119038\pi$
$140$		0			0
$141$	10.5268	−	2.09391i	0.886518	−	0.176339i
$142$		0			0
$143$	13.4927	+	11.8328i	1.12832	+	0.989510i
$144$		0			0
$145$	9.40061	+	7.21334i	0.780678	+	0.599035i
$146$		0			0
$147$	2.84095	−	9.08070i	0.234317	−	0.748964i
$148$		0			0
$149$	−1.85463	−	0.496945i	−0.151937	−	0.0407114i	0.182049	−	0.983289i	$-0.441727\pi$
$149$	−1.85463	−	0.496945i	−0.151937	−	0.0407114i	−0.333986	+	0.942578i	$0.608394\pi$
$150$		0			0
$151$	−11.5320	+	8.84881i	−0.938461	+	0.720106i	−0.960099	−	0.279660i	$-0.909778\pi$
$151$	−11.5320	+	8.84881i	−0.938461	+	0.720106i	0.0216385	+	0.999766i	$0.493112\pi$
$152$		0			0
$153$	−2.77360	−	3.85816i	−0.224232	−	0.311914i
$154$		0			0
$155$	4.01258	−	9.68722i	0.322298	−	0.778096i
$156$		0			0
$157$	5.29337	+	19.7551i	0.422457	+	1.57663i	0.769414	+	0.638750i	$0.220548\pi$
$157$	5.29337	+	19.7551i	0.422457	+	1.57663i	−0.346957	+	0.937881i	$0.612785\pi$
$158$		0			0
$159$	−5.78692	+	11.7347i	−0.458933	+	0.930623i
$160$		0			0
$161$	9.80879	−	8.81289i	0.773041	−	0.694553i
$162$		0			0
$163$	18.3471	−	6.22800i	1.43706	−	0.487815i	0.509165	−	0.860669i	$-0.329954\pi$
$163$	18.3471	−	6.22800i	1.43706	−	0.487815i	0.927890	+	0.372854i	$0.121621\pi$
$164$		0			0
$165$	24.7930	+	8.41609i	1.93013	+	0.655191i
$166$		0			0
$167$	−2.33896	−	1.56284i	−0.180994	−	0.120936i	0.461773	−	0.886998i	$-0.347214\pi$
$167$	−2.33896	−	1.56284i	−0.180994	−	0.120936i	−0.642767	+	0.766062i	$0.722214\pi$
$168$		0			0
$169$		−	3.48370i		−	0.267977i
$170$		0			0
$171$	−7.39324	−	4.26849i	−0.565375	−	0.326419i
$172$		0			0
$173$	0.962306	+	0.0630729i	0.0731628	+	0.00479534i	0.101941	−	0.994790i	$-0.467495\pi$
$173$	0.962306	+	0.0630729i	0.0731628	+	0.00479534i	−0.0287778	+	0.999586i	$0.509162\pi$
$174$		0			0
$175$	−13.7576	−	7.72397i	−1.03998	−	0.583877i
$176$		0			0
$177$	−4.65042	−	13.6997i	−0.349547	−	1.02973i
$178$		0			0
$179$	5.57223	+	0.733598i	0.416488	+	0.0548317i	0.335858	−	0.941912i	$-0.390974\pi$
$179$	5.57223	+	0.733598i	0.416488	+	0.0548317i	0.0806295	+	0.996744i	$0.474307\pi$
$180$		0			0
$181$	6.56110	−	4.38398i	0.487682	−	0.325859i	−0.287301	−	0.957840i	$-0.592758\pi$
$181$	6.56110	−	4.38398i	0.487682	−	0.325859i	0.774984	+	0.631981i	$0.217758\pi$
$182$		0			0
$183$	8.53115	−	8.53115i	0.630641	−	0.630641i
$184$		0			0
$185$	−15.3135	−	19.9569i	−1.12587	−	1.46726i
$186$		0			0
$187$	−5.41127	+	23.3681i	−0.395711	+	1.70884i
$188$		0			0
$189$	8.14657	−	12.5153i	0.592576	−	0.910353i
$190$		0			0
$191$	−2.52033	+	9.40600i	−0.182365	+	0.680594i	0.812815	+	0.582522i	$0.197934\pi$
$191$	−2.52033	+	9.40600i	−0.182365	+	0.680594i	−0.995179	+	0.0980718i	$0.968733\pi$
$192$		0			0
$193$	−0.877074	−	13.3816i	−0.0631332	−	0.963226i	−0.905507	−	0.424332i	$-0.860509\pi$
$193$	−0.877074	−	13.3816i	−0.0631332	−	0.963226i	0.842373	−	0.538894i	$-0.181158\pi$
$194$		0			0
$195$	5.31305	+	12.8268i	0.380476	+	0.918549i
$196$		0			0
$197$	−2.84169	+	14.2861i	−0.202462	+	1.01785i	0.737183	+	0.675693i	$0.236156\pi$
$197$	−2.84169	+	14.2861i	−0.202462	+	1.01785i	−0.939645	+	0.342152i	$0.888844\pi$
$198$		0			0
$199$	0.379216	−	1.11713i	0.0268819	−	0.0791916i	−0.932661	−	0.360754i	$-0.882519\pi$
$199$	0.379216	−	1.11713i	0.0268819	−	0.0791916i	0.959543	+	0.281563i	$0.0908527\pi$
$200$		0			0
$201$	0.765163	−	11.6741i	0.0539705	−	0.823430i
$202$		0			0
$203$	−9.30779	−	1.73540i	−0.653279	−	0.121801i
$204$		0			0
$205$	−10.3502	−	17.9270i	−0.722888	−	1.25208i
$206$		0			0
$207$	5.15141	−	2.54040i	0.358048	−	0.176570i
$208$		0			0
$209$	8.40736	+	42.2667i	0.581549	+	2.92365i
$210$		0			0
$211$	8.23850	+	1.63874i	0.567162	+	0.112816i	0.470339	−	0.882486i	$-0.344132\pi$
$211$	8.23850	+	1.63874i	0.567162	+	0.112816i	0.0968234	+	0.995302i	$0.469132\pi$
$212$		0			0
$213$	−0.395610	+	3.00496i	−0.0271067	+	0.205896i
$214$		0			0
$215$	10.5734	+	5.21425i	0.721103	+	0.355609i
$216$		0			0
$217$	0.648427	+	8.35327i	0.0440181	+	0.567057i
$218$		0			0
$219$	−1.06999	−	8.12740i	−0.0723034	−	0.549199i
$220$		0			0
$221$	−11.2082	+	6.01280i	−0.753944	+	0.404465i
$222$		0			0
$223$	15.5795	+	6.45324i	1.04328	+	0.432141i	0.837488	−	0.546455i	$-0.184023\pi$
$223$	15.5795	+	6.45324i	1.04328	+	0.432141i	0.205792	+	0.978596i	$0.434023\pi$
$224$		0			0
$225$	−4.85955	−	4.85955i	−0.323970	−	0.323970i
$226$		0			0
$227$	2.47234	−	0.162046i	0.164095	−	0.0107554i	0.0168659	−	0.999858i	$-0.494631\pi$
$227$	2.47234	−	0.162046i	0.164095	−	0.0107554i	0.147229	+	0.989102i	$0.452964\pi$
$228$		0			0
$229$	−5.63206	+	7.33984i	−0.372177	+	0.485030i	−0.941466	−	0.337107i	$-0.890552\pi$
$229$	−5.63206	+	7.33984i	−0.372177	+	0.485030i	0.569289	+	0.822137i	$0.307218\pi$
$230$		0			0
$231$	−20.7080	+	2.97990i	−1.36248	+	0.196063i
$232$		0			0
$233$	−14.2160	+	12.4671i	−0.931319	+	0.816744i	−0.983317	−	0.181903i	$-0.941774\pi$
$233$	−14.2160	+	12.4671i	−0.931319	+	0.816744i	0.0519980	+	0.998647i	$0.483441\pi$
$234$		0			0
$235$	11.5638	+	23.4491i	0.754342	+	1.52965i
$236$		0			0
$237$	19.3703			1.25824
$238$		0			0
$239$	−11.5655			−0.748110			−0.374055	−	0.927407i	$-0.622033\pi$
$239$	−11.5655			−0.748110			−0.374055	+	0.927407i	$0.622033\pi$
$240$		0			0
$241$	3.80790	+	7.72165i	0.245288	+	0.497395i	0.984346	−	0.176247i	$-0.0563957\pi$
$241$	3.80790	+	7.72165i	0.245288	+	0.497395i	−0.739058	+	0.673642i	$0.764729\pi$
$242$		0			0
$243$	8.42363	−	7.38732i	0.540376	−	0.473897i
$244$		0			0
$245$	23.1578	+	0.959495i	1.47950	+	0.0612999i
$246$		0			0
$247$	−13.9112	+	18.1294i	−0.885148	+	1.15355i
$248$		0			0
$249$	18.1837	−	1.19182i	1.15234	−	0.0755286i
$250$		0			0
$251$	−9.78574	−	9.78574i	−0.617670	−	0.617670i	0.327263	−	0.944933i	$-0.393874\pi$
$251$	−9.78574	−	9.78574i	−0.617670	−	0.617670i	−0.944933	+	0.327263i	$0.893874\pi$
$252$		0			0
$253$	−26.7874	−	11.0957i	−1.68411	−	0.697582i
$254$		0			0
$255$	−11.7503	+	14.3622i	−0.735832	+	0.899395i
$256$		0			0
$257$	−0.0988408	−	0.750770i	−0.00616552	−	0.0468318i	0.988086	−	0.153906i	$-0.0491852\pi$
$257$	−0.0988408	−	0.750770i	−0.00616552	−	0.0468318i	−0.994251	+	0.107074i	$0.965852\pi$
$258$		0			0
$259$	18.1330	+	8.67283i	1.12673	+	0.538903i
$260$		0			0
$261$	−3.69887	−	1.82408i	−0.228954	−	0.112908i
$262$		0			0
$263$	2.67449	−	20.3148i	0.164916	−	1.25266i	−0.686094	−	0.727513i	$-0.740676\pi$
$263$	2.67449	−	20.3148i	0.164916	−	1.25266i	0.851010	−	0.525149i	$-0.175991\pi$
$264$		0			0
$265$	−31.2600	−	6.21800i	−1.92029	−	0.381969i
$266$		0			0
$267$	−1.41634	−	7.12040i	−0.0866783	−	0.435761i
$268$		0			0
$269$	8.52143	−	4.20231i	0.519561	−	0.256219i	−0.163548	−	0.986535i	$-0.552294\pi$
$269$	8.52143	−	4.20231i	0.519561	−	0.256219i	0.683109	+	0.730316i	$0.260627\pi$
$270$		0			0
$271$	13.0688	+	22.6358i	0.793871	+	1.37502i	0.923554	+	0.383469i	$0.125271\pi$
$271$	13.0688	+	22.6358i	0.793871	+	1.37502i	−0.129683	+	0.991556i	$0.541396\pi$
$272$		0			0
$273$	−8.42811	−	7.21389i	−0.510092	−	0.436604i
$274$		0			0
$275$	−2.26898	+	34.6179i	−0.136824	+	2.08754i
$276$		0			0
$277$	−7.60365	+	22.3996i	−0.456859	+	1.34586i	0.437783	+	0.899080i	$0.355764\pi$
$277$	−7.60365	+	22.3996i	−0.456859	+	1.34586i	−0.894642	+	0.446783i	$0.852570\pi$
$278$		0			0
$279$	−0.711981	+	3.57937i	−0.0426252	+	0.214291i
$280$		0			0
$281$	6.96533	+	16.8158i	0.415517	+	1.00315i	0.983631	+	0.180196i	$0.0576733\pi$
$281$	6.96533	+	16.8158i	0.415517	+	1.00315i	−0.568114	+	0.822950i	$0.692327\pi$
$282$		0			0
$283$	1.14974	+	17.5417i	0.0683450	+	1.04274i	0.884992	+	0.465606i	$0.154164\pi$
$283$	1.14974	+	17.5417i	0.0683450	+	1.04274i	−0.816647	+	0.577138i	$0.804170\pi$
$284$		0			0
$285$	−8.62879	+	32.2031i	−0.511125	+	1.90755i
$286$		0			0
$287$	13.8626	+	9.02357i	0.818283	+	0.532645i
$288$		0			0
$289$	−14.1636	−	9.40172i	−0.833153	−	0.553043i
$290$		0			0
$291$	−12.3577	−	16.1049i	−0.724424	−	0.944087i
$292$		0			0
$293$	13.8390	−	13.8390i	0.808481	−	0.808481i	−0.175923	−	0.984404i	$-0.556291\pi$
$293$	13.8390	−	13.8390i	0.808481	−	0.808481i	0.984404	+	0.175923i	$0.0562909\pi$
$294$		0			0
$295$	29.3030	−	19.5796i	1.70609	−	1.13997i
$296$		0			0
$297$	−32.5546	−	4.28589i	−1.88901	−	0.248693i
$298$		0			0
$299$	−4.94206	−	14.5588i	−0.285807	−	0.841960i
$300$		0			0
$301$	−9.41958	+	0.113232i	−0.542936	+	0.00652657i
$302$		0			0
$303$	−13.4151	−	0.879271i	−0.770677	−	0.0505128i
$304$		0			0
$305$	25.4523	+	14.6949i	1.45739	+	0.841426i
$306$		0			0
$307$		−	22.8849i		−	1.30611i	−0.757312	−	0.653054i	$-0.773488\pi$
$307$		−	22.8849i		−	1.30611i	0.757312	−	0.653054i	$-0.226512\pi$
$308$		0			0
$309$	6.38347	+	4.26530i	0.363143	+	0.242644i
$310$		0			0
$311$	−15.0077	−	5.09442i	−0.851007	−	0.288878i	−0.138344	−	0.990384i	$-0.544178\pi$
$311$	−15.0077	−	5.09442i	−0.851007	−	0.288878i	−0.712663	+	0.701506i	$0.752511\pi$
$312$		0			0
$313$	−2.01817	+	0.685076i	−0.114074	+	0.0387228i	−0.377893	−	0.925849i	$-0.623351\pi$
$313$	−2.01817	+	0.685076i	−0.114074	+	0.0387228i	0.263819	+	0.964572i	$0.415018\pi$
$314$		0			0
$315$	9.59835	+	3.13005i	0.540806	+	0.176358i
$316$		0			0
$317$	−0.358601	+	0.727172i	−0.0201411	+	0.0408420i	−0.906711	−	0.421753i	$-0.861415\pi$
$317$	−0.358601	+	0.727172i	−0.0201411	+	0.0408420i	0.886570	+	0.462595i	$0.153082\pi$
$318$		0			0
$319$	5.38834	+	20.1095i	0.301689	+	1.12592i
$320$		0			0
$321$	1.51389	−	3.65484i	0.0844968	−	0.203993i
$322$		0			0
$323$	−30.1423	−	4.92951i	−1.67716	−	0.274285i
$324$		0			0
$325$	−14.5946	+	11.1988i	−0.809561	+	0.621198i
$326$		0			0
$327$	2.65165	+	0.710508i	0.146637	+	0.0392912i
$328$		0			0
$329$	−16.7262	−	12.5179i	−0.922143	−	0.690135i
$330$		0			0
$331$	11.7753	+	9.03548i	0.647227	+	0.496635i	0.879427	−	0.476033i	$-0.157926\pi$
$331$	11.7753	+	9.03548i	0.647227	+	0.496635i	−0.232200	+	0.972668i	$0.574592\pi$
$332$		0			0
$333$	6.58265	+	5.77283i	0.360727	+	0.316349i
$334$		0			0
$335$	27.9513	−	5.55987i	1.52715	−	0.303768i
$336$		0			0
$337$	13.7773	−	20.6192i	0.750497	−	1.12320i	−0.237898	−	0.971290i	$-0.576458\pi$
$337$	13.7773	−	20.6192i	0.750497	−	1.12320i	0.988395	−	0.151908i	$-0.0485416\pi$
$338$		0			0
$339$	−4.65610	+	8.06460i	−0.252885	+	0.438009i
$340$		0			0
$341$	15.9545	−	9.21134i	0.863985	−	0.498822i
$342$		0			0
$343$	−16.8438	+	7.69967i	−0.909482	+	0.415743i
$344$		0			0
$345$	−14.7897	−	16.8644i	−0.796249	−	0.907948i
$346$		0			0
$347$	2.36764	−	2.69978i	0.127102	−	0.144932i	−0.684788	−	0.728742i	$-0.740105\pi$
$347$	2.36764	−	2.69978i	0.127102	−	0.144932i	0.811890	+	0.583810i	$0.198439\pi$
$348$		0			0
$349$	5.18690	−	2.14848i	0.277648	−	0.115006i	−0.239514	−	0.970893i	$-0.576988\pi$
$349$	5.18690	−	2.14848i	0.277648	−	0.115006i	0.517163	+	0.855887i	$0.326988\pi$
$350$		0			0
$351$	−9.67332	−	14.4772i	−0.516324	−	0.772733i
$352$		0			0
$353$	19.5759	−	5.24534i	1.04192	−	0.279181i	0.303010	−	0.952987i	$-0.402008\pi$
$353$	19.5759	−	5.24534i	1.04192	−	0.279181i	0.738908	+	0.673806i	$0.235342\pi$
$354$		0			0
$355$	−7.32000	+	0.963697i	−0.388505	+	0.0511477i
$356$		0			0
$357$	3.17120	−	14.4846i	0.167838	−	0.766604i
$358$		0			0
$359$	32.6000	−	4.29187i	1.72056	−	0.226516i	0.795399	−	0.606087i	$-0.207262\pi$
$359$	32.6000	−	4.29187i	1.72056	−	0.226516i	0.925163	+	0.379571i	$0.123928\pi$
$360$		0			0
$361$	−34.6516	+	9.28487i	−1.82377	+	0.488678i
$362$		0			0
$363$	17.2508	+	25.8177i	0.905432	+	1.35508i
$364$		0			0
$365$	18.4489	−	7.64180i	0.965662	−	0.399990i
$366$		0			0
$367$	−3.21721	+	3.66852i	−0.167937	+	0.191495i	−0.829687	−	0.558230i	$-0.811481\pi$
$367$	−3.21721	+	3.66852i	−0.167937	+	0.191495i	0.661750	+	0.749725i	$0.269814\pi$
$368$		0			0
$369$	4.75051	+	5.41692i	0.247302	+	0.281993i
$370$		0			0
$371$	24.5190	−	6.88678i	1.27297	−	0.357544i
$372$		0			0
$373$	13.0819	−	7.55285i	0.677357	−	0.391072i	−0.121502	−	0.992591i	$-0.538771\pi$
$373$	13.0819	−	7.55285i	0.677357	−	0.391072i	0.798858	+	0.601519i	$0.205438\pi$
$374$		0			0
$375$	−2.16783	+	3.75480i	−0.111946	+	0.193897i
$376$		0			0
$377$	−6.13325	+	9.17906i	−0.315879	+	0.472746i
$378$		0			0
$379$	16.3828	−	3.25874i	0.841526	−	0.167390i	0.244538	−	0.969640i	$-0.421364\pi$
$379$	16.3828	−	3.25874i	0.841526	−	0.167390i	0.596989	+	0.802250i	$0.296364\pi$
$380$		0			0
$381$	−8.15369	−	7.15059i	−0.417726	−	0.366336i
$382$		0			0
$383$	−10.0331	−	7.69871i	−0.512670	−	0.393386i	0.319775	−	0.947494i	$-0.396393\pi$
$383$	−10.0331	−	7.69871i	−0.512670	−	0.393386i	−0.832445	+	0.554108i	$0.813059\pi$
$384$		0			0
$385$	−20.0675	−	46.8465i	−1.02274	−	2.38752i
$386$		0			0
$387$	−3.96350	−	1.06202i	−0.201476	−	0.0539853i
$388$		0			0
$389$	13.7039	−	10.5154i	0.694817	−	0.533152i	−0.199883	−	0.979820i	$-0.564056\pi$
$389$	13.7039	−	10.5154i	0.694817	−	0.533152i	0.894700	+	0.446668i	$0.147389\pi$
$390$		0			0
$391$	14.0246	−	15.0196i	0.709256	−	0.759573i
$392$		0			0
$393$	7.51956	−	18.1538i	0.379312	−	0.915739i
$394$		0			0
$395$	12.2125	+	45.5778i	0.614480	+	2.29327i
$396$		0			0
$397$	9.55522	−	19.3761i	0.479563	−	0.972457i	−0.513852	−	0.857879i	$-0.671782\pi$
$397$	9.55522	−	19.3761i	0.479563	−	0.972457i	0.993414	−	0.114578i	$-0.0365515\pi$
$398$		0			0
$399$	−5.51085	−	26.0636i	−0.275887	−	1.30481i
$400$		0			0
$401$	12.1443	−	4.12242i	0.606455	−	0.205864i	−0.00128582	−	0.999999i	$-0.500409\pi$
$401$	12.1443	−	4.12242i	0.606455	−	0.205864i	0.607741	+	0.794135i	$0.292076\pi$
$402$		0			0
$403$	9.25048	+	3.14011i	0.460799	+	0.156420i
$404$		0			0
$405$	−11.6029	−	7.75282i	−0.576553	−	0.385241i
$406$		0			0
$407$		−	44.1973i		−	2.19078i
$408$		0			0
$409$	22.8815	+	13.2106i	1.13142	+	0.653223i	0.944291	−	0.329113i	$-0.106750\pi$
$409$	22.8815	+	13.2106i	1.13142	+	0.653223i	0.187126	+	0.982336i	$0.440083\pi$
$410$		0			0
$411$	−7.84028	−	0.513879i	−0.386733	−	0.0253478i
$412$		0			0
$413$	−13.7862	+	24.5553i	−0.678374	+	1.20829i
$414$		0			0
$415$	14.2687	+	42.0343i	0.700424	+	2.06338i
$416$		0			0
$417$	6.78188	+	0.892851i	0.332110	+	0.0437231i
$418$		0			0
$419$	5.72944	−	3.82829i	0.279901	−	0.187024i	−0.407693	−	0.913119i	$-0.633667\pi$
$419$	5.72944	−	3.82829i	0.279901	−	0.187024i	0.687595	+	0.726095i	$0.258667\pi$
$420$		0			0
$421$	3.91350	−	3.91350i	0.190732	−	0.190732i	−0.605280	−	0.796013i	$-0.706939\pi$
$421$	3.91350	−	3.91350i	0.190732	−	0.190732i	0.796013	+	0.605280i	$0.206939\pi$
$422$		0			0
$423$	−5.53978	−	7.21958i	−0.269353	−	0.351028i
$424$		0			0
$425$	−22.4113	−	10.1134i	−1.08711	−	0.490573i
$426$		0			0
$427$	−23.4505	−	1.25415i	−1.13485	−	0.0606923i
$428$		0			0
$429$	−6.31349	+	23.5623i	−0.304818	+	1.13760i
$430$		0			0
$431$	1.97055	+	30.0648i	0.0949182	+	1.44817i	0.734061	+	0.679084i	$0.237623\pi$
$431$	1.97055	+	30.0648i	0.0949182	+	1.44817i	−0.639143	+	0.769088i	$0.720711\pi$
$432$		0			0
$433$	−2.88330	−	6.96090i	−0.138563	−	0.334520i	0.839332	−	0.543620i	$-0.182947\pi$
$433$	−2.88330	−	6.96090i	−0.138563	−	0.334520i	−0.977894	+	0.209100i	$0.932947\pi$
$434$		0			0
$435$	−3.14213	+	15.7965i	−0.150653	+	0.757386i
$436$		0			0
$437$	11.8675	−	34.9604i	0.567697	−	1.67238i
$438$		0			0
$439$	−0.0159292	+	0.243033i	−0.000760261	+	0.0115993i	−0.998222	−	0.0596024i	$-0.981017\pi$
$439$	−0.0159292	+	0.243033i	−0.000760261	+	0.0115993i	0.997462	+	0.0712017i	$0.0226834\pi$
$440$		0			0
$441$	−7.97049	+	1.24493i	−0.379547	+	0.0592823i
$442$		0			0
$443$	7.59431	+	13.1537i	0.360816	+	0.624952i	0.988095	−	0.153842i	$-0.0491647\pi$
$443$	7.59431	+	13.1537i	0.360816	+	0.624952i	−0.627279	+	0.778795i	$0.715831\pi$
$444$		0			0
$445$	15.8611	−	7.82185i	0.751890	−	0.370791i
$446$		0			0
$447$	−0.509151	−	2.55968i	−0.0240820	−	0.121069i
$448$		0			0
$449$	1.19363	+	0.237428i	0.0563310	+	0.0112049i	0.223175	−	0.974778i	$-0.428358\pi$
$449$	1.19363	+	0.237428i	0.0563310	+	0.0112049i	−0.166844	+	0.985983i	$0.553358\pi$
$450$		0			0
$451$	4.74728	−	36.0591i	0.223541	−	1.69796i
$452$		0			0
$453$	−17.7201	−	8.73861i	−0.832565	−	0.410576i
$454$		0			0
$455$	11.6604	−	24.3793i	0.546646	−	1.14292i
$456$		0			0
$457$	−4.16118	−	31.6073i	−0.194652	−	1.47853i	−0.757972	−	0.652288i	$-0.773809\pi$
$457$	−4.16118	−	31.6073i	−0.194652	−	1.47853i	0.563320	−	0.826239i	$-0.309524\pi$
$458$		0			0
$459$	10.9390	−	20.5404i	0.510589	−	0.958743i
$460$		0			0
$461$	−32.6611	−	13.5287i	−1.52118	−	0.630093i	−0.543352	−	0.839505i	$-0.682845\pi$
$461$	−32.6611	−	13.5287i	−1.52118	−	0.630093i	−0.977828	+	0.209412i	$0.932845\pi$
$462$		0			0
$463$	−25.6721	−	25.6721i	−1.19308	−	1.19308i	−0.976197	−	0.216885i	$-0.930410\pi$
$463$	−25.6721	−	25.6721i	−1.19308	−	1.19308i	−0.216885	−	0.976197i	$-0.569590\pi$
$464$		0			0
$465$	14.2217	−	0.932139i	0.659516	−	0.0432269i
$466$		0			0
$467$	−9.46954	+	12.3410i	−0.438198	+	0.571071i	−0.959288	−	0.282431i	$-0.908859\pi$
$467$	−9.46954	+	12.3410i	−0.438198	+	0.571071i	0.521089	+	0.853502i	$0.325526\pi$
$468$		0			0
$469$	−17.8985	+	14.0790i	−0.826476	+	0.650109i
$470$		0			0
$471$	−20.9007	+	18.3294i	−0.963052	+	0.844574i
$472$		0			0
$473$	9.16137	+	18.5774i	0.421240	+	0.854191i
$474$		0			0
$475$	−44.1747			−2.02688
$476$		0			0
$477$	11.0934			0.507931
$478$		0			0
$479$	−2.75468	−	5.58594i	−0.125865	−	0.255228i	0.824815	−	0.565403i	$-0.191279\pi$
$479$	−2.75468	−	5.58594i	−0.125865	−	0.255228i	−0.950680	+	0.310174i	$0.899613\pi$
$480$		0			0
$481$	17.6203	−	15.4526i	0.803418	−	0.704579i
$482$		0			0
$483$	16.6404	+	6.65948i	0.757164	+	0.303017i
$484$		0			0
$485$	30.1032	−	39.2312i	1.36691	−	1.78140i
$486$		0			0
$487$	−12.6056	+	0.826214i	−0.571214	+	0.0374393i	−0.348274	−	0.937393i	$-0.613232\pi$
$487$	−12.6056	+	0.826214i	−0.571214	+	0.0374393i	−0.222940	+	0.974832i	$0.571565\pi$
$488$		0			0
$489$	18.6223	+	18.6223i	0.842129	+	0.842129i
$490$		0			0
$491$	−16.1549	−	6.69159i	−0.729062	−	0.301987i	−0.0128955	−	0.999917i	$-0.504105\pi$
$491$	−16.1549	−	6.69159i	−0.729062	−	0.301987i	−0.716167	+	0.697929i	$0.754105\pi$
$492$		0			0
$493$	−14.6862	−	1.42395i	−0.661434	−	0.0641316i
$494$		0			0
$495$	−2.89755	−	22.0091i	−0.130235	−	0.989234i
$496$		0			0
$497$	4.86556	−	3.33635i	0.218250	−	0.149656i
$498$		0			0
$499$	−5.15249	−	2.54093i	−0.230657	−	0.113747i	0.323288	−	0.946301i	$-0.395212\pi$
$499$	−5.15249	−	2.54093i	−0.230657	−	0.113747i	−0.553945	+	0.832553i	$0.686878\pi$
$500$		0			0
$501$	0.499083	−	3.79091i	0.0222974	−	0.169365i
$502$		0			0
$503$	−38.3313	−	7.62457i	−1.70911	−	0.339963i	−0.758812	−	0.651310i	$-0.774220\pi$
$503$	−38.3313	−	7.62457i	−1.70911	−	0.339963i	−0.950296	+	0.311347i	$0.899220\pi$
$504$		0			0
$505$	−6.38901	−	32.1197i	−0.284307	−	1.42931i
$506$		0			0
$507$	4.24688	−	2.09433i	0.188610	−	0.0930123i
$508$		0			0
$509$	21.1034	+	36.5521i	0.935390	+	1.62014i	0.773937	+	0.633263i	$0.218285\pi$
$509$	21.1034	+	36.5521i	0.935390	+	1.62014i	0.161454	+	0.986880i	$0.448382\pi$
$510$		0			0
$511$	−10.3758	+	12.1222i	−0.458998	+	0.536255i
$512$		0			0
$513$	2.73454	−	41.7210i	0.120733	−	1.84203i
$514$		0			0
$515$	−6.01150	+	17.7093i	−0.264898	+	0.780365i
$516$		0			0
$517$	−8.96192	+	45.0546i	−0.394145	+	1.98150i
$518$		0			0
$519$	0.501628	+	1.21104i	0.0220190	+	0.0531587i
$520$		0			0
$521$	2.26296	+	34.5261i	0.0991420	+	1.51261i	0.700510	+	0.713642i	$0.252956\pi$
$521$	2.26296	+	34.5261i	0.0991420	+	1.51261i	−0.601368	+	0.798972i	$0.705377\pi$
$522$		0			0
$523$	10.3197	−	38.5136i	0.451249	−	1.68408i	−0.247640	−	0.968852i	$-0.579655\pi$
$523$	10.3197	−	38.5136i	0.451249	−	1.68408i	0.698889	−	0.715230i	$-0.253678\pi$
$524$		0			0
$525$	1.14528	−	21.4150i	0.0499843	−	0.934627i
$526$		0			0
$527$	2.14645	+	12.8792i	0.0935009	+	0.561025i
$528$		0			0
$529$	1.12006	+	1.45969i	0.0486983	+	0.0634649i
$530$		0			0
$531$	−8.67361	+	8.67361i	−0.376403	+	0.376403i
$532$		0			0
$533$	16.0357	−	10.7147i	0.694581	−	0.464104i
$534$		0			0
$535$	9.55422	+	1.25784i	0.413065	+	0.0543810i
$536$		0			0
$537$	2.45560	+	7.23397i	0.105967	+	0.312169i
$538$		0			0
$539$	31.2537	+	26.1067i	1.34619	+	1.12450i
$540$		0			0
$541$	30.5053	+	1.99942i	1.31152	+	0.0859618i	0.705059	−	0.709149i	$-0.250921\pi$
$541$	30.5053	+	1.99942i	1.31152	+	0.0859618i	0.606464	+	0.795111i	$0.292587\pi$
$542$		0			0
$543$	9.28879	+	5.36289i	0.398620	+	0.230143i
$544$		0			0
$545$			6.68722i			0.286449i
$546$		0			0
$547$	29.4093	+	19.6507i	1.25745	+	0.840201i	0.992282	−	0.124001i	$-0.0395725\pi$
$547$	29.4093	+	19.6507i	1.25745	+	0.840201i	0.265168	+	0.964202i	$0.414573\pi$
$548$		0			0
$549$	−9.68641	−	3.28809i	−0.413406	−	0.140332i
$550$		0			0
$551$	−25.1026	+	8.52119i	−1.06941	+	0.363015i
$552$		0			0
$553$	−25.1989	−	28.0465i	−1.07157	−	1.19266i
$554$		0			0
$555$	15.1227	−	30.6659i	0.641925	−	1.30169i
$556$		0			0
$557$	−10.1665	−	37.9421i	−0.430770	−	1.60766i	−0.750990	−	0.660313i	$-0.770423\pi$
$557$	−10.1665	−	37.9421i	−0.430770	−	1.60766i	0.320220	−	0.947343i	$-0.396243\pi$
$558$		0			0
$559$	−4.20327	+	10.1476i	−0.177780	+	0.429198i
$560$		0			0
$561$	−31.7405	+	7.45168i	−1.34008	+	0.314610i
$562$		0			0
$563$	−3.35778	+	2.57651i	−0.141514	+	0.108587i	−0.677092	−	0.735898i	$-0.736760\pi$
$563$	−3.35778	+	2.57651i	−0.141514	+	0.108587i	0.535579	+	0.844485i	$0.320094\pi$
$564$		0			0
$565$	−21.9113	−	5.87113i	−0.921817	−	0.247000i
$566$		0			0
$567$	11.0719	+	1.32246i	0.464976	+	0.0555379i
$568$		0			0
$569$	6.38383	+	4.89848i	0.267624	+	0.205355i	0.733852	−	0.679310i	$-0.237721\pi$
$569$	6.38383	+	4.89848i	0.267624	+	0.205355i	−0.466228	+	0.884665i	$0.654387\pi$
$570$		0			0
$571$	−5.88327	−	5.15949i	−0.246207	−	0.215918i	0.527344	−	0.849652i	$-0.323188\pi$
$571$	−5.88327	−	5.15949i	−0.246207	−	0.215918i	−0.773551	+	0.633734i	$0.781521\pi$
$572$		0			0
$573$	−12.9818	+	2.58223i	−0.542321	+	0.107874i
$574$		0			0
$575$	16.5122	−	24.7122i	0.688606	−	1.03057i
$576$		0			0
$577$	−8.65385	+	14.9889i	−0.360264	+	0.623996i	−0.988004	−	0.154427i	$-0.950647\pi$
$577$	−8.65385	+	14.9889i	−0.360264	+	0.623996i	0.627740	+	0.778423i	$0.283980\pi$
$578$		0			0
$579$	15.7858	−	9.11394i	0.656036	−	0.378763i
$580$		0			0
$581$	−25.3809	−	24.7779i	−1.05298	−	1.02796i
$582$		0			0
$583$	−36.9230	−	42.1026i	−1.52920	−	1.74371i
$584$		0			0
$585$	7.76140	−	8.85018i	0.320894	−	0.365910i
$586$		0			0
$587$	−31.1888	+	12.9188i	−1.28730	+	0.533217i	−0.918180	−	0.396164i	$-0.870341\pi$
$587$	−31.1888	+	12.9188i	−1.28730	+	0.533217i	−0.369121	+	0.929381i	$0.620341\pi$
$588$		0			0
$589$	13.0327	+	19.5048i	0.537003	+	0.803682i
$590$		0			0
$591$	−19.1242	+	5.12431i	−0.786664	+	0.210786i
$592$		0			0
$593$	−3.54325	+	0.466478i	−0.145504	+	0.0191559i	−0.202926	−	0.979194i	$-0.565045\pi$
$593$	−3.54325	+	0.466478i	−0.145504	+	0.0191559i	0.0574224	+	0.998350i	$0.481712\pi$
$594$		0			0
$595$	36.0811	−	1.67044i	1.47918	−	0.0684814i
$596$		0			0
$597$	1.58984	−	0.209307i	0.0650680	−	0.00856636i
$598$		0			0
$599$	2.70628	−	0.725146i	0.110576	−	0.0296286i	−0.203107	−	0.979157i	$-0.565104\pi$
$599$	2.70628	−	0.725146i	0.110576	−	0.0296286i	0.313683	+	0.949528i	$0.398437\pi$
$600$		0			0
$601$	−10.4755	−	15.6777i	−0.427304	−	0.639505i	0.553877	−	0.832599i	$-0.313148\pi$
$601$	−10.4755	−	15.6777i	−0.427304	−	0.639505i	−0.981180	+	0.193093i	$0.938148\pi$
$602$		0			0
$603$	−9.16417	+	3.79592i	−0.373194	+	0.154582i
$604$		0			0
$605$	−49.8720	+	56.8681i	−2.02759	+	2.31202i
$606$		0			0
$607$	0.997292	+	1.13719i	0.0404788	+	0.0461573i	0.771725	−	0.635956i	$-0.219394\pi$
$607$	0.997292	+	1.13719i	0.0404788	+	0.0461573i	−0.731246	+	0.682114i	$0.761061\pi$
$608$		0			0
$609$	−3.48008	−	12.3901i	−0.141020	−	0.502074i
$610$		0			0
$611$	−21.0955	+	12.1795i	−0.853432	+	0.492729i
$612$		0			0
$613$	11.1256	−	19.2701i	0.449359	−	0.778312i	−0.548985	−	0.835832i	$-0.684986\pi$
$613$	11.1256	−	19.2701i	0.449359	−	0.778312i	0.998344	+	0.0575194i	$0.0183191\pi$
$614$		0			0
$615$	15.6320	−	23.3950i	0.630344	−	0.943377i
$616$		0			0
$617$	18.5984	−	3.69945i	0.748743	−	0.148934i	0.194052	−	0.980991i	$-0.437837\pi$
$617$	18.5984	−	3.69945i	0.748743	−	0.148934i	0.554690	+	0.832057i	$0.312837\pi$
$618$		0			0
$619$	3.68754	+	3.23389i	0.148215	+	0.129981i	0.730242	−	0.683188i	$-0.239407\pi$
$619$	3.68754	+	3.23389i	0.148215	+	0.129981i	−0.582028	+	0.813169i	$0.697740\pi$
$620$		0			0
$621$	22.3174	+	17.1248i	0.895568	+	0.687193i
$622$		0			0
$623$	−8.46719	+	11.3137i	−0.339231	+	0.453273i
$624$		0			0
$625$	18.5991	+	4.98361i	0.743963	+	0.199344i
$626$		0			0
$627$	−46.4718	+	35.6590i	−1.85590	+	1.42408i
$628$		0			0
$629$	29.3332	+	10.9894i	1.16959	+	0.438176i
$630$		0			0
$631$	−11.1945	+	27.0259i	−0.445645	+	1.07588i	0.528292	+	0.849063i	$0.322833\pi$
$631$	−11.1945	+	27.0259i	−0.445645	+	1.07588i	−0.973937	+	0.226819i	$0.927167\pi$
$632$		0			0
$633$	2.95508	+	11.0285i	0.117454	+	0.438344i
$634$		0			0
$635$	11.6844	−	23.6937i	0.463683	−	0.940256i
$636$		0			0
$637$	0.519082	+	21.5877i	0.0205668	+	0.855336i
$638$		0			0
$639$	2.43338	−	0.826021i	0.0962630	−	0.0326769i
$640$		0			0
$641$	−44.7807	−	15.2010i	−1.76873	−	0.600404i	−0.769465	−	0.638689i	$-0.779477\pi$
$641$	−44.7807	−	15.2010i	−1.76873	−	0.600404i	−0.999267	+	0.0382856i	$0.987810\pi$
$642$		0			0
$643$	16.0241	+	10.7070i	0.631930	+	0.422242i	0.829858	−	0.557975i	$-0.188421\pi$
$643$	16.0241	+	10.7070i	0.631930	+	0.422242i	−0.197928	+	0.980216i	$0.563421\pi$
$644$		0			0
$645$			16.0245i			0.630964i
$646$		0			0
$647$	−7.11239	−	4.10634i	−0.279617	−	0.161437i	0.353633	−	0.935384i	$-0.384946\pi$
$647$	−7.11239	−	4.10634i	−0.279617	−	0.161437i	−0.633250	+	0.773947i	$0.718280\pi$
$648$		0			0
$649$	61.7880	+	4.04980i	2.42539	+	0.158968i
$650$		0			0
$651$	−9.79342	+	5.81230i	−0.383834	+	0.227802i
$652$		0			0
$653$	8.81386	+	25.9648i	0.344913	+	1.01608i	0.971563	+	0.236780i	$0.0760922\pi$
$653$	8.81386	+	25.9648i	0.344913	+	1.01608i	−0.626650	+	0.779301i	$0.715575\pi$
$654$		0			0
$655$	47.4564	+	6.24775i	1.85427	+	0.244120i
$656$		0			0
$657$	−5.77898	+	3.86139i	−0.225460	+	0.150647i
$658$		0			0
$659$	7.49891	−	7.49891i	0.292116	−	0.292116i	−0.545800	−	0.837916i	$-0.683774\pi$
$659$	7.49891	−	7.49891i	0.292116	−	0.292116i	0.837916	+	0.545800i	$0.183774\pi$
$660$		0			0
$661$	−13.9295	−	18.1532i	−0.541794	−	0.706079i	0.439577	−	0.898205i	$-0.355128\pi$
$661$	−13.9295	−	18.1532i	−0.541794	−	0.706079i	−0.981370	+	0.192126i	$0.938462\pi$
$662$		0			0
$663$	−14.0682	−	10.0488i	−0.546362	−	0.390264i
$664$		0			0
$665$	57.8524	−	29.3994i	2.24342	−	1.14006i
$666$		0			0
$667$	4.61624	−	17.2281i	0.178742	−	0.667073i
$668$		0			0
$669$	1.49912	+	22.8721i	0.0579592	+	0.884286i
$670$		0			0
$671$	19.7608	+	47.7068i	0.762857	+	1.84170i
$672$		0			0
$673$	0.227268	−	1.14255i	0.00876052	−	0.0440421i	−0.976158	−	0.217062i	$-0.930353\pi$
$673$	0.227268	−	1.14255i	0.00876052	−	0.0440421i	0.984918	+	0.173020i	$0.0553526\pi$
$674$		0			0
$675$	10.8191	−	31.8721i	0.416429	−	1.22676i
$676$		0			0
$677$	1.03912	−	15.8538i	0.0399364	−	0.609312i	−0.930246	−	0.366937i	$-0.880407\pi$
$677$	1.03912	−	15.8538i	0.0399364	−	0.609312i	0.970182	−	0.242376i	$-0.0779267\pi$
$678$		0			0
$679$	−7.24227	+	38.8438i	−0.277933	+	1.49069i
$680$		0			0
$681$	1.68387	+	2.91655i	0.0645260	+	0.111762i
$682$		0			0
$683$	19.1936	−	9.46525i	0.734424	−	0.362178i	−0.0363052	−	0.999341i	$-0.511559\pi$
$683$	19.1936	−	9.46525i	0.734424	−	0.362178i	0.770729	+	0.637163i	$0.219892\pi$
$684$		0			0
$685$	−3.73397	−	18.7720i	−0.142668	−	0.717240i
$686$		0			0
$687$	−12.3337	−	2.45332i	−0.470559	−	0.0936000i
$688$		0			0
$689$	3.87592	−	29.4406i	0.147661	−	1.12160i
$690$		0			0
$691$	5.63662	+	2.77967i	0.214427	+	0.105744i	0.546331	−	0.837570i	$-0.316024\pi$
$691$	5.63662	+	2.77967i	0.214427	+	0.105744i	−0.331904	+	0.943313i	$0.607691\pi$
$692$		0			0
$693$	10.0314	+	14.6293i	0.381062	+	0.555721i
$694$		0			0
$695$	2.17497	+	16.5205i	0.0825011	+	0.626658i
$696$		0			0
$697$	22.7516	+	12.1166i	0.861779	+	0.458949i
$698$		0			0
$699$	−23.7446	−	9.83533i	−0.898103	−	0.372006i
$700$		0			0
$701$	34.0896	+	34.0896i	1.28755	+	1.28755i	0.936273	+	0.351273i	$0.114251\pi$
$701$	34.0896	+	34.0896i	1.28755	+	1.28755i	0.351273	+	0.936273i	$0.385749\pi$
$702$		0			0
$703$	56.1574	−	3.68075i	2.11802	−	0.138822i
$704$		0			0
$705$	−21.6343	+	28.1943i	−0.814793	+	1.06186i
$706$		0			0
$707$	16.1786	+	20.5677i	0.608460	+	0.773528i
$708$		0			0
$709$	−9.47615	+	8.31036i	−0.355884	+	0.312102i	−0.818555	−	0.574428i	$-0.805224\pi$
$709$	−9.47615	+	8.31036i	−0.355884	+	0.312102i	0.462671	+	0.886530i	$0.346891\pi$
$710$		0			0
$711$	−7.26381	−	14.7296i	−0.272414	−	0.552402i
$712$		0			0
$713$	−15.7829			−0.591075
$714$		0			0
$715$	−59.4219			−2.22225
$716$		0			0
$717$	−6.95294	−	14.0992i	−0.259662	−	0.526543i
$718$		0			0
$719$	6.52266	−	5.72022i	0.243254	−	0.213328i	−0.529034	−	0.848601i	$-0.677446\pi$
$719$	6.52266	−	5.72022i	0.243254	−	0.213328i	0.772288	+	0.635273i	$0.219112\pi$
$720$		0			0
$721$	−2.12850	−	14.7914i	−0.0792696	−	0.550862i
$722$		0			0
$723$	−7.12402	+	9.28420i	−0.264945	+	0.345283i
$724$		0			0
$725$	−21.2950	+	1.39575i	−0.790876	+	0.0518368i
$726$		0			0
$727$	9.59962	+	9.59962i	0.356030	+	0.356030i	0.862347	−	0.506317i	$-0.168994\pi$
$727$	9.59962	+	9.59962i	0.356030	+	0.356030i	−0.506317	+	0.862347i	$0.668994\pi$
$728$		0			0
$729$	25.7509	+	10.6664i	0.953739	+	0.395051i
$730$		0			0
$731$	−14.6075	+	1.46112i	−0.540279	+	0.0540413i
$732$		0			0
$733$	−5.36364	−	40.7409i	−0.198111	−	1.50480i	−0.744700	−	0.667399i	$-0.767408\pi$
$733$	−5.36364	−	40.7409i	−0.198111	−	1.50480i	0.546590	−	0.837401i	$-0.315926\pi$
$734$		0			0
$735$	12.7523	+	28.8079i	0.470376	+	1.06259i
$736$		0			0
$737$	44.9085	+	22.1464i	1.65423	+	0.815774i
$738$		0			0
$739$	3.10794	−	23.6071i	0.114327	−	0.868402i	−0.834146	−	0.551544i	$-0.814039\pi$
$739$	3.10794	−	23.6071i	0.114327	−	0.868402i	0.948473	−	0.316858i	$-0.102628\pi$
$740$		0			0
$741$	−30.4642	−	6.05971i	−1.11913	−	0.222609i
$742$		0			0
$743$	4.24741	+	21.3532i	0.155822	+	0.783372i	0.977090	+	0.212828i	$0.0682676\pi$
$743$	4.24741	+	21.3532i	0.155822	+	0.783372i	−0.821267	+	0.570544i	$0.806732\pi$
$744$		0			0
$745$	5.70184	−	2.81184i	0.208899	−	0.103018i
$746$		0			0
$747$	−7.72511	−	13.3803i	−0.282647	−	0.489559i
$748$		0			0
$749$	−7.26130	+	2.56262i	−0.265322	+	0.0936363i
$750$		0			0
$751$	1.82063	−	27.7775i	0.0664358	−	1.01361i	−0.826357	−	0.563147i	$-0.809591\pi$
$751$	1.82063	−	27.7775i	0.0664358	−	1.01361i	0.892793	−	0.450468i	$-0.148743\pi$
$752$		0			0
$753$	6.04653	−	17.8125i	0.220348	−	0.649124i
$754$		0			0
$755$	9.38956	−	47.2045i	0.341721	−	1.71795i
$756$		0			0
$757$	9.55015	+	23.0561i	0.347106	+	0.837988i	0.996959	+	0.0779283i	$0.0248305\pi$
$757$	9.55015	+	23.0561i	0.347106	+	0.837988i	−0.649853	+	0.760060i	$0.725169\pi$
$758$		0			0
$759$	−2.57758	−	39.3263i	−0.0935604	−	1.42746i
$760$		0			0
$761$	3.03034	−	11.3094i	0.109850	−	0.409965i	−0.889000	−	0.457907i	$-0.848599\pi$
$761$	3.03034	−	11.3094i	0.109850	−	0.409965i	0.998850	+	0.0479414i	$0.0152661\pi$
$762$		0			0
$763$	−2.42079	−	4.76365i	−0.0876384	−	0.172456i
$764$		0			0
$765$	15.3276	+	3.54936i	0.554171	+	0.128328i
$766$		0			0
$767$	19.9883	+	26.0492i	0.721735	+	0.940583i
$768$		0			0
$769$	27.0723	−	27.0723i	0.976251	−	0.976251i	−0.0234734	−	0.999724i	$-0.507472\pi$
$769$	27.0723	−	27.0723i	0.976251	−	0.976251i	0.999724	+	0.0234734i	$0.00747249\pi$
$770$		0			0
$771$	0.855822	−	0.571842i	0.0308217	−	0.0205944i
$772$		0			0
$773$	1.88065	+	0.247592i	0.0676422	+	0.00890527i	0.164271	−	0.986415i	$-0.447473\pi$
$773$	1.88065	+	0.247592i	0.0676422	+	0.00890527i	−0.0966291	+	0.995320i	$0.530806\pi$
$774$		0			0
$775$	6.07018	+	17.8822i	0.218047	+	0.642347i
$776$		0			0
$777$	0.328403	+	27.3194i	0.0117814	+	0.980077i
$778$		0			0
$779$	46.2124	+	3.02892i	1.65573	+	0.108522i
$780$		0			0
$781$	−11.2342	−	6.48607i	−0.401991	−	0.232090i
$782$		0			0
$783$		−	20.1986i		−	0.721837i
$784$		0			0
$785$	−56.3060	−	37.6224i	−2.00965	−	1.34280i
$786$		0			0
$787$	−22.9921	−	7.80477i	−0.819580	−	0.278210i	−0.120009	−	0.992773i	$-0.538292\pi$
$787$	−22.9921	−	7.80477i	−0.819580	−	0.278210i	−0.699571	+	0.714563i	$0.746626\pi$
$788$		0			0
$789$	26.3730	−	8.95243i	0.938904	−	0.318715i
$790$		0			0
$791$	17.7339	−	3.74965i	0.630547	−	0.133322i
$792$		0			0
$793$	−12.1106	+	24.5578i	−0.430058	+	0.872072i
$794$		0			0
$795$	−11.2127	−	41.8463i	−0.397673	−	1.48414i
$796$		0			0
$797$	19.5356	−	47.1631i	0.691986	−	1.67060i	−0.0487554	−	0.998811i	$-0.515525\pi$
$797$	19.5356	−	47.1631i	0.691986	−	1.67060i	0.740741	−	0.671791i	$-0.234475\pi$
$798$		0			0
$799$	−27.6738	−	17.1505i	−0.979030	−	0.606740i
$800$		0			0
$801$	−4.88337	+	3.74714i	−0.172545	+	0.132399i
$802$		0			0
$803$	33.8898	+	9.08074i	1.19594	+	0.320452i
$804$		0			0
$805$	−5.17820	+	43.3530i	−0.182508	+	1.52799i
$806$		0			0
$807$	10.2458	+	7.86190i	0.360670	+	0.276752i
$808$		0			0
$809$	10.6289	+	9.32132i	0.373693	+	0.327720i	0.825507	−	0.564392i	$-0.190889\pi$
$809$	10.6289	+	9.32132i	0.373693	+	0.327720i	−0.451814	+	0.892112i	$0.649223\pi$
$810$		0			0
$811$	40.1377	−	7.98388i	1.40942	−	0.280352i	0.569025	−	0.822320i	$-0.307321\pi$
$811$	40.1377	−	7.98388i	1.40942	−	0.280352i	0.840399	+	0.541968i	$0.182321\pi$
$812$		0			0
$813$	−19.7379	+	29.5399i	−0.692240	+	1.03601i
$814$		0			0
$815$	−32.0768	+	55.5587i	−1.12360	+	1.94613i
$816$		0			0
$817$	−22.8417	+	13.1876i	−0.799129	+	0.461377i
$818$		0			0
$819$	−2.32506	+	9.11408i	−0.0812443	+	0.318472i
$820$		0			0
$821$	31.4882	+	35.9054i	1.09895	+	1.25311i	0.965037	+	0.262114i	$0.0844198\pi$
$821$	31.4882	+	35.9054i	1.09895	+	1.25311i	0.133909	+	0.990994i	$0.457247\pi$
$822$		0			0
$823$	−9.43369	+	10.7571i	−0.328838	+	0.374967i	−0.892507	−	0.451033i	$-0.851056\pi$
$823$	−9.43369	+	10.7571i	−0.328838	+	0.374967i	0.563670	+	0.826000i	$0.309389\pi$
$824$		0			0
$825$	−43.5658	+	18.0455i	−1.51676	+	0.628265i
$826$		0			0
$827$	−11.9584	−	17.8969i	−0.415833	−	0.622338i	0.563132	−	0.826367i	$-0.309596\pi$
$827$	−11.9584	−	17.8969i	−0.415833	−	0.622338i	−0.978965	+	0.204029i	$0.934596\pi$
$828$		0			0
$829$	−15.6726	+	4.19947i	−0.544334	+	0.145854i	−0.520499	−	0.853862i	$-0.674254\pi$
$829$	−15.6726	+	4.19947i	−0.544334	+	0.145854i	−0.0238344	+	0.999716i	$0.507587\pi$
$830$		0			0
$831$	−31.8779	+	4.19681i	−1.10583	+	0.145586i
$832$		0			0
$833$	−25.0978	+	14.2514i	−0.869586	+	0.493781i
$834$		0			0
$835$	9.23457	−	1.21575i	0.319576	−	0.0420729i
$836$		0			0
$837$	−17.2647	+	4.62606i	−0.596755	+	0.159900i
$838$		0			0
$839$	5.52749	+	8.27247i	0.190830	+	0.285597i	0.914531	−	0.404517i	$-0.132560\pi$
$839$	5.52749	+	8.27247i	0.190830	+	0.285597i	−0.723701	+	0.690114i	$0.757560\pi$
$840$		0			0
$841$	14.9607	−	6.19693i	0.515887	−	0.213687i
$842$		0			0
$843$	−16.3122	+	18.6006i	−0.561824	+	0.640637i
$844$		0			0
$845$	7.60545	+	8.67236i	0.261636	+	0.298338i
$846$		0			0
$847$	14.9400	−	58.5639i	0.513346	−	2.01228i
$848$		0			0
$849$	−20.6934	+	11.9473i	−0.710194	+	0.410031i
$850$		0			0
$851$	−18.9321	+	32.7914i	−0.648985	+	1.12408i
$852$		0			0
$853$	−7.03920	+	10.5349i	−0.241018	+	0.360708i	−0.932182	−	0.361989i	$-0.882098\pi$
$853$	−7.03920	+	10.5349i	−0.241018	+	0.360708i	0.691165	+	0.722697i	$0.257098\pi$
$854$		0			0
$855$	27.7236	−	5.51457i	0.948127	−	0.188594i
$856$		0			0
$857$	−32.3917	−	28.4067i	−1.10648	−	0.970355i	−0.106765	−	0.994284i	$-0.534049\pi$
$857$	−32.3917	−	28.4067i	−1.10648	−	0.970355i	−0.999714	+	0.0239288i	$0.992382\pi$
$858$		0			0
$859$	−2.93633	−	2.25313i	−0.100186	−	0.0768757i	0.557454	−	0.830208i	$-0.311778\pi$
$859$	−2.93633	−	2.25313i	−0.100186	−	0.0768757i	−0.657640	+	0.753332i	$0.728445\pi$
$860$		0			0
$861$	−2.66647	+	22.3243i	−0.0908731	+	0.760810i
$862$		0			0
$863$	−31.4584	−	8.42924i	−1.07086	−	0.286935i	−0.320011	−	0.947414i	$-0.603687\pi$
$863$	−31.4584	−	8.42924i	−1.07086	−	0.286935i	−0.750844	+	0.660479i	$0.770353\pi$
$864$		0			0
$865$	−2.53328	+	1.94385i	−0.0861339	+	0.0660929i
$866$		0			0
$867$	2.94651	−	22.9186i	0.100069	−	0.778356i
$868$		0			0
$869$	−31.7262	+	76.5939i	−1.07624	+	2.59827i
$870$		0			0
$871$	6.87207	+	25.6469i	0.232851	+	0.869012i
$872$		0			0
$873$	−7.61237	+	15.4364i	−0.257640	+	0.522442i
$874$		0			0
$875$	8.25676	−	1.74580i	0.279129	−	0.0590188i
$876$		0			0
$877$	−34.3851	+	11.6722i	−1.16110	+	0.394141i	−0.834493	−	0.551018i	$-0.814239\pi$
$877$	−34.3851	+	11.6722i	−1.16110	+	0.394141i	−0.326609	+	0.945160i	$0.605906\pi$
$878$		0			0
$879$	25.1904	+	8.55099i	0.849651	+	0.288418i
$880$		0			0
$881$	18.2430	+	12.1896i	0.614622	+	0.410677i	0.823542	−	0.567255i	$-0.191995\pi$
$881$	18.2430	+	12.1896i	0.614622	+	0.410677i	−0.208920	+	0.977933i	$0.566995\pi$
$882$		0			0
$883$			48.1771i			1.62129i	0.585539	+	0.810644i	$0.300883\pi$
$883$			48.1771i			1.62129i	−0.585539	+	0.810644i	$0.699117\pi$
$884$		0			0
$885$	41.4854	+	23.9516i	1.39452	+	0.805124i
$886$		0			0
$887$	−2.06984	−	0.135664i	−0.0694983	−	0.00455516i	0.0306143	−	0.999531i	$-0.490254\pi$
$887$	−2.06984	−	0.135664i	−0.0694983	−	0.00455516i	−0.100113	+	0.994976i	$0.531920\pi$
$888$		0			0
$889$	0.253737	+	21.1080i	0.00851008	+	0.707941i
$890$		0			0
$891$	−7.88114	−	23.2171i	−0.264028	−	0.777802i
$892$		0			0
$893$	−57.9931	−	7.63494i	−1.94067	−	0.255493i
$894$		0			0
$895$	−15.4731	+	10.3388i	−0.517210	+	0.345589i
$896$		0			0
$897$	14.7772	−	14.7772i	0.493397	−	0.493397i
$898$		0			0
$899$	6.89885	+	8.99076i	0.230090	+	0.299859i
$900$		0			0
$901$	37.1237	−	14.0368i	1.23677	−	0.467632i
$902$		0			0
$903$	−5.80090	−	11.4151i	−0.193042	−	0.379870i
$904$		0			0
$905$	−6.76236	+	25.2375i	−0.224788	+	0.838921i
$906$		0			0
$907$	−1.50190	−	22.9146i	−0.0498699	−	0.760867i	−0.947428	−	0.319970i	$-0.896327\pi$
$907$	−1.50190	−	22.9146i	−0.0498699	−	0.760867i	0.897558	−	0.440897i	$-0.145340\pi$
$908$		0			0
$909$	4.36201	+	10.5308i	0.144679	+	0.349285i
$910$		0			0
$911$	5.03939	−	25.3347i	0.166962	−	0.839376i	−0.802973	−	0.596015i	$-0.796750\pi$
$911$	5.03939	−	25.3347i	0.166962	−	0.839376i	0.969936	−	0.243361i	$-0.0782501\pi$
$912$		0			0
$913$	−25.0700	+	73.8538i	−0.829696	+	2.44420i
$914$		0			0
$915$	−2.61272	+	39.8624i	−0.0863738	+	1.31781i
$916$		0			0
$917$	−36.0673	+	12.7287i	−1.19105	+	0.420339i
$918$		0			0
$919$	−5.61978	−	9.73374i	−0.185379	−	0.321086i	0.758325	−	0.651877i	$-0.226018\pi$
$919$	−5.61978	−	9.73374i	−0.185379	−	0.321086i	−0.943704	+	0.330790i	$0.892685\pi$
$920$		0			0
$921$	27.8983	−	13.7579i	0.919280	−	0.453339i
$922$		0			0
$923$	−1.34196	−	6.74651i	−0.0441713	−	0.222064i
$924$		0			0
$925$	44.4344	+	8.83855i	1.46099	+	0.290610i
$926$		0			0
$927$	0.849631	−	6.45359i	0.0279055	−	0.211964i
$928$		0			0
$929$	−30.6551	−	15.1174i	−1.00576	−	0.495987i	−0.136659	−	0.990618i	$-0.543637\pi$
$929$	−30.6551	−	15.1174i	−1.00576	−	0.495987i	−0.869103	+	0.494631i	$0.835303\pi$
$930$		0			0
$931$	−30.5686	+	41.8854i	−1.00185	+	1.37274i
$932$		0			0
$933$	−2.81185	−	21.3581i	−0.0920557	−	0.699232i
$934$		0			0
$935$	−37.5453	−	69.9864i	−1.22786	−	2.28880i
$936$		0			0
$937$	−7.89033	−	3.26828i	−0.257766	−	0.106770i	0.250059	−	0.968231i	$-0.419550\pi$
$937$	−7.89033	−	3.26828i	−0.257766	−	0.106770i	−0.507824	+	0.861461i	$0.669550\pi$
$938$		0			0
$939$	−2.04844	−	2.04844i	−0.0668483	−	0.0668483i
$940$		0			0
$941$	36.1010	−	2.36619i	1.17686	−	0.0771355i	0.535609	−	0.844466i	$-0.320082\pi$
$941$	36.1010	−	2.36619i	1.17686	−	0.0771355i	0.641251	+	0.767331i	$0.278416\pi$
$942$		0			0
$943$	−18.9683	+	24.7200i	−0.617693	+	0.804993i
$944$		0			0
$945$	7.04266	+	48.9410i	0.229098	+	1.59205i
$946$		0			0
$947$	−9.93756	+	8.71501i	−0.322927	+	0.283200i	−0.805425	−	0.592698i	$-0.798063\pi$
$947$	−9.93756	+	8.71501i	−0.322927	+	0.283200i	0.482498	+	0.875897i	$0.339730\pi$
$948$		0			0
$949$	8.22857	+	16.6859i	0.267111	+	0.541647i
$950$		0			0
$951$	−1.10206			−0.0357367
$952$		0			0
$953$	−47.7702			−1.54743			−0.773715	−	0.633534i	$-0.781604\pi$
$953$	−47.7702			−1.54743			−0.773715	+	0.633534i	$0.781604\pi$
$954$		0			0
$955$	−14.2606	−	28.9177i	−0.461463	−	0.935755i
$956$		0			0
$957$	−21.2756	+	18.6582i	−0.687743	+	0.603135i
$958$		0			0
$959$	9.45539	+	12.0205i	0.305331	+	0.388163i
$960$		0			0
$961$	−12.7668	+	16.6380i	−0.411832	+	0.536710i
$962$		0			0
$963$	−3.34691	+	0.219368i	−0.107853	+	0.00706905i
$964$		0			0
$965$	31.3975	+	31.3975i	1.01072	+	1.01072i
$966$		0			0
$967$	−7.69912	−	3.18908i	−0.247587	−	0.102554i	0.255439	−	0.966825i	$-0.417780\pi$
$967$	−7.69912	−	3.18908i	−0.247587	−	0.102554i	−0.503026	+	0.864271i	$0.667780\pi$
$968$		0			0
$969$	−12.1115	−	39.7091i	−0.389078	−	1.27564i
$970$		0			0
$971$	3.16907	+	24.0715i	0.101700	+	0.772490i	0.963964	+	0.266031i	$0.0857125\pi$
$971$	3.16907	+	24.0715i	0.101700	+	0.772490i	−0.862264	+	0.506459i	$0.830954\pi$
$972$		0			0
$973$	−7.52980	−	10.9811i	−0.241394	−	0.352037i
$974$		0			0
$975$	−22.4261	−	11.0593i	−0.718211	−	0.354182i
$976$		0			0
$977$	−0.0157590	+	0.119701i	−0.000504174	+	0.00382958i	−0.991695	−	0.128611i	$-0.958948\pi$
$977$	−0.0157590	+	0.119701i	−0.000504174	+	0.00382958i	0.991191	+	0.132441i	$0.0422814\pi$
$978$		0			0
$979$	30.4752	+	6.06190i	0.973992	+	0.193739i
$980$		0			0
$981$	−0.454078	−	2.28280i	−0.0144976	−	0.0728843i
$982$		0			0
$983$	−20.2113	+	9.96713i	−0.644642	+	0.317902i	−0.735060	−	0.678002i	$-0.762846\pi$
$983$	−20.2113	+	9.96713i	−0.644642	+	0.317902i	0.0904187	+	0.995904i	$0.471179\pi$
$984$		0			0
$985$	−24.1147	−	41.7680i	−0.768359	−	1.33084i
$986$		0			0
$987$	5.20480	−	27.9159i	0.165671	−	0.888573i
$988$		0			0
$989$	1.16061	−	17.7075i	0.0369053	−	0.563067i
$990$		0			0
$991$	7.31143	−	21.5388i	0.232255	−	0.684202i	−0.766847	−	0.641830i	$-0.778175\pi$
$991$	7.31143	−	21.5388i	0.232255	−	0.684202i	0.999102	−	0.0423714i	$-0.0134913\pi$
$992$		0			0
$993$	−3.93585	+	19.7868i	−0.124900	+	0.627916i
$994$		0			0
$995$	1.49485	+	3.60890i	0.0473901	+	0.114410i
$996$		0			0
$997$	−2.06677	−	31.5329i	−0.0654554	−	0.998656i	−0.896669	−	0.442702i	$-0.854020\pi$
$997$	−2.06677	−	31.5329i	−0.0654554	−	0.998656i	0.831213	−	0.555954i	$-0.187647\pi$
$998$		0			0
$999$	−11.0982	+	41.4191i	−0.351132	+	1.31044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.cw.a.129.13	✓	288
7.5	odd	6	inner	952.2.cw.a.537.13	yes	288
17.12	odd	16	inner	952.2.cw.a.913.13	yes	288
119.12	even	48	inner	952.2.cw.a.369.13	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.cw.a.129.13	✓	288	1.1	even	1	trivial
952.2.cw.a.369.13	yes	288	119.12	even	48	inner
952.2.cw.a.537.13	yes	288	7.5	odd	6	inner
952.2.cw.a.913.13	yes	288	17.12	odd	16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.cw (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.601180 + 1.21907i) q^{3} +(-2.48941 + 2.18316i) q^{5} +(0.983031 - 2.45635i) q^{7} +(0.701565 - 0.914297i) q^{9} +(-5.80510 + 0.380487i) q^{11} +(-2.18132 - 2.18132i) q^{13} +(-4.15801 - 1.72230i) q^{15} +(1.19088 - 3.94738i) q^{17} +(-0.966899 - 7.34432i) q^{19} +(3.58544 - 0.278322i) q^{21} +(4.46998 + 2.20435i) q^{23} +(0.778374 - 5.91234i) q^{25} +(5.53575 + 1.10113i) q^{27} +(-0.698157 - 3.50987i) q^{29} +(-2.84016 + 1.40061i) q^{31} +(-3.95375 - 6.84810i) q^{33} +(2.91543 + 8.26098i) q^{35} +(-0.496882 + 7.58095i) q^{37} +(1.34782 - 3.97055i) q^{39} +(-1.21967 + 6.13169i) q^{41} +(-1.36255 - 3.28950i) q^{43} +(0.249569 + 3.80769i) q^{45} +(2.04372 - 7.62725i) q^{47} +(-5.06730 - 4.82933i) q^{49} +(5.52807 - 0.921314i) q^{51} +(5.85990 + 7.63677i) q^{53} +(13.6206 - 13.6206i) q^{55} +(8.37198 - 5.59398i) q^{57} +(-10.5527 - 1.38929i) q^{59} +(-2.85314 - 8.40508i) q^{61} +(-1.55617 - 2.62207i) q^{63} +(10.1924 + 0.668043i) q^{65} +(-7.45397 - 4.30355i) q^{67} +6.77444i q^{69} +(1.85403 + 1.23882i) q^{71} +(-5.71087 - 1.93858i) q^{73} +(7.67551 - 2.60548i) q^{75} +(-4.77199 + 14.6334i) q^{77} +(6.30295 - 12.7811i) q^{79} +(1.09080 + 4.07092i) q^{81} +(5.13043 - 12.3860i) q^{83} +(5.65315 + 12.4265i) q^{85} +(3.85907 - 2.96117i) q^{87} +(-5.15912 - 1.38238i) q^{89} +(-7.50238 + 3.21378i) q^{91} +(-3.41489 - 2.62034i) q^{93} +(18.4408 + 16.1722i) q^{95} +(-14.6476 + 2.91359i) q^{97} +(-3.72478 + 5.57452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 32 q^{15} - 48 q^{21} + 32 q^{29} + 72 q^{31} + 32 q^{35} + 48 q^{37} + 32 q^{39} - 32 q^{43} - 24 q^{47} + 48 q^{49} + 16 q^{53} + 128 q^{57} - 72 q^{61} + 184 q^{63} - 32 q^{65} - 80 q^{71} - 96 q^{73}+ \cdots + 64 q^{99}+O(q^{100}) \) 288 * q - 32 * q^15 - 48 * q^21 + 32 * q^29 + 72 * q^31 + 32 * q^35 + 48 * q^37 + 32 * q^39 - 32 * q^43 - 24 * q^47 + 48 * q^49 + 16 * q^53 + 128 * q^57 - 72 * q^61 + 184 * q^63 - 32 * q^65 - 80 * q^71 - 96 * q^73 - 216 * q^75 + 56 * q^77 - 32 * q^79 - 64 * q^81 + 160 * q^85 - 144 * q^87 + 144 * q^89 - 32 * q^93 - 64 * q^95 + 64 * q^99

Introduction

L-functions

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Database

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