LMFDB - Embedded newform 864.2.w.a.107.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.9
Character	$\chi$	$=$	864.107
Dual form			864.2.w.a.323.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.948429 - 1.04904i) q^{2} +(-0.200965 + 1.98988i) q^{4} +(1.78263 + 0.738390i) q^{5} +(-0.622002 + 0.622002i) q^{7} +(2.27806 - 1.67644i) q^{8} +O(q^{10})$	\(q+(-0.948429 - 1.04904i) q^{2} +(-0.200965 + 1.98988i) q^{4} +(1.78263 + 0.738390i) q^{5} +(-0.622002 + 0.622002i) q^{7} +(2.27806 - 1.67644i) q^{8} +(-0.916100 - 2.57036i) q^{10} +(0.156498 + 0.0648236i) q^{11} +(1.19856 + 2.89359i) q^{13} +(1.24243 + 0.0625795i) q^{14} +(-3.91923 - 0.799791i) q^{16} +4.81317 q^{17} +(-3.67470 + 1.52211i) q^{19} +(-1.82755 + 3.39883i) q^{20} +(-0.0804248 - 0.225653i) q^{22} +(1.56750 - 1.56750i) q^{23} +(-0.902976 - 0.902976i) q^{25} +(1.89874 - 4.00171i) q^{26} +(-1.11271 - 1.36271i) q^{28} +(1.08392 + 2.61682i) q^{29} +2.74627i q^{31} +(2.87810 + 4.86997i) q^{32} +(-4.56495 - 5.04920i) q^{34} +(-1.56808 + 0.649520i) q^{35} +(-1.96490 + 4.74369i) q^{37} +(5.08195 + 2.41129i) q^{38} +(5.29881 - 1.30637i) q^{40} +(3.95321 + 3.95321i) q^{41} +(-0.627273 + 1.51437i) q^{43} +(-0.160442 + 0.298385i) q^{44} +(-3.13103 - 0.157706i) q^{46} +9.33089i q^{47} +6.22623i q^{49} +(-0.0908483 + 1.80367i) q^{50} +(-5.99876 + 1.80349i) q^{52} +(0.182908 - 0.441579i) q^{53} +(0.231113 + 0.231113i) q^{55} +(-0.374210 + 2.45971i) q^{56} +(1.71712 - 3.61895i) q^{58} +(3.02418 - 7.30102i) q^{59} +(11.6637 - 4.83126i) q^{61} +(2.88094 - 2.60464i) q^{62} +(2.37911 - 7.63805i) q^{64} +6.04322i q^{65} +(4.45039 + 10.7442i) q^{67} +(-0.967277 + 9.57761i) q^{68} +(2.16859 + 1.02895i) q^{70} +(-6.22714 - 6.22714i) q^{71} +(-0.573022 + 0.573022i) q^{73} +(6.83988 - 2.43779i) q^{74} +(-2.29033 - 7.61810i) q^{76} +(-0.137662 + 0.0570216i) q^{77} +12.6432 q^{79} +(-6.39598 - 4.31965i) q^{80} +(0.397731 - 7.89640i) q^{82} +(-4.21199 - 10.1686i) q^{83} +(8.58010 + 3.55400i) q^{85} +(2.18356 - 0.778239i) q^{86} +(0.465184 - 0.114687i) q^{88} +(6.68154 - 6.68154i) q^{89} +(-2.54533 - 1.05431i) q^{91} +(2.80412 + 3.43415i) q^{92} +(9.78847 - 8.84969i) q^{94} -7.67456 q^{95} -5.92342 q^{97} +(6.53155 - 5.90513i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) $ 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.948429	−	1.04904i	−0.670641	−	0.741782i
$2$	−0.948429	−	1.04904i	−0.670641	−	0.741782i
$3$		0			0
$3$		0			0
$4$	−0.200965	+	1.98988i	−0.100482	+	0.994939i
$5$	1.78263	+	0.738390i	0.797217	+	0.330218i	0.743841	−	0.668356i	$-0.233002\pi$
$5$	1.78263	+	0.738390i	0.797217	+	0.330218i	0.0533761	+	0.998574i	$0.483002\pi$
$6$		0			0
$7$	−0.622002	+	0.622002i	−0.235095	+	0.235095i	−0.814815	−	0.579721i	$-0.803162\pi$
$7$	−0.622002	+	0.622002i	−0.235095	+	0.235095i	0.579721	+	0.814815i	$0.303162\pi$
$8$	2.27806	−	1.67644i	0.805416	−	0.592710i
$9$		0			0
$10$	−0.916100	−	2.57036i	−0.289696	−	0.812820i
$11$	0.156498	+	0.0648236i	0.0471859	+	0.0195450i	0.406152	−	0.913806i	$-0.366870\pi$
$11$	0.156498	+	0.0648236i	0.0471859	+	0.0195450i	−0.358966	+	0.933351i	$0.616870\pi$
$12$		0			0
$13$	1.19856	+	2.89359i	0.332422	+	0.802538i	0.998399	+	0.0565653i	$0.0180149\pi$
$13$	1.19856	+	2.89359i	0.332422	+	0.802538i	−0.665977	+	0.745972i	$0.731985\pi$
$14$	1.24243	+	0.0625795i	0.332053	+	0.0167251i
$15$		0			0
$16$	−3.91923	−	0.799791i	−0.979807	−	0.199948i
$17$	4.81317			1.16736			0.583682	−	0.811982i	$-0.301611\pi$
$17$	4.81317			1.16736			0.583682	+	0.811982i	$0.301611\pi$
$18$		0			0
$19$	−3.67470	+	1.52211i	−0.843035	+	0.349196i	−0.762049	−	0.647519i	$-0.775807\pi$
$19$	−3.67470	+	1.52211i	−0.843035	+	0.349196i	−0.0809854	+	0.996715i	$0.525807\pi$
$20$	−1.82755	+	3.39883i	−0.408653	+	0.760001i
$21$		0			0
$22$	−0.0804248	−	0.225653i	−0.0171466	−	0.0481094i
$23$	1.56750	−	1.56750i	0.326846	−	0.326846i	−0.524540	−	0.851386i	$-0.675763\pi$
$23$	1.56750	−	1.56750i	0.326846	−	0.326846i	0.851386	+	0.524540i	$0.175763\pi$
$24$		0			0
$25$	−0.902976	−	0.902976i	−0.180595	−	0.180595i
$26$	1.89874	−	4.00171i	0.372373	−	0.784799i
$27$		0			0
$28$	−1.11271	−	1.36271i	−0.210282	−	0.257528i
$29$	1.08392	+	2.61682i	0.201279	+	0.485932i	0.991999	−	0.126247i	$-0.0402932\pi$
$29$	1.08392	+	2.61682i	0.201279	+	0.485932i	−0.790719	+	0.612179i	$0.790293\pi$
$30$		0			0
$31$			2.74627i			0.493245i	0.969112	+	0.246622i	$0.0793207\pi$
$31$			2.74627i			0.493245i	−0.969112	+	0.246622i	$0.920679\pi$
$32$	2.87810	+	4.86997i	0.508780	+	0.860896i
$33$		0			0
$34$	−4.56495	−	5.04920i	−0.782882	−	0.865930i
$35$	−1.56808	+	0.649520i	−0.265054	+	0.109789i
$36$		0			0
$37$	−1.96490	+	4.74369i	−0.323028	+	0.779857i	0.676048	+	0.736858i	$0.263691\pi$
$37$	−1.96490	+	4.74369i	−0.323028	+	0.779857i	−0.999075	+	0.0429995i	$0.986309\pi$
$38$	5.08195	+	2.41129i	0.824401	+	0.391163i
$39$		0			0
$40$	5.29881	−	1.30637i	0.837815	−	0.206556i
$41$	3.95321	+	3.95321i	0.617387	+	0.617387i	0.944860	−	0.327473i	$-0.106197\pi$
$41$	3.95321	+	3.95321i	0.617387	+	0.617387i	−0.327473	+	0.944860i	$0.606197\pi$
$42$		0			0
$43$	−0.627273	+	1.51437i	−0.0956582	+	0.230939i	−0.964464	−	0.264213i	$-0.914888\pi$
$43$	−0.627273	+	1.51437i	−0.0956582	+	0.230939i	0.868806	+	0.495152i	$0.164888\pi$
$44$	−0.160442	+	0.298385i	−0.0241875	+	0.0449832i
$45$		0			0
$46$	−3.13103	−	0.157706i	−0.461645	−	0.0232525i
$47$			9.33089i			1.36105i	0.732725	+	0.680525i	$0.238248\pi$
$47$			9.33089i			1.36105i	−0.732725	+	0.680525i	$0.761752\pi$
$48$		0			0
$49$			6.22623i			0.889461i
$50$	−0.0908483	+	1.80367i	−0.0128479	+	0.255077i
$51$		0			0
$52$	−5.99876	+	1.80349i	−0.831878	+	0.250099i
$53$	0.182908	−	0.441579i	0.0251243	−	0.0606555i	−0.910819	−	0.412805i	$-0.864549\pi$
$53$	0.182908	−	0.441579i	0.0251243	−	0.0606555i	0.935944	+	0.352149i	$0.114549\pi$
$54$		0			0
$55$	0.231113	+	0.231113i	0.0311633	+	0.0311633i
$56$	−0.374210	+	2.45971i	−0.0500059	+	0.328692i
$57$		0			0
$58$	1.71712	−	3.61895i	0.225469	−	0.475191i
$59$	3.02418	−	7.30102i	0.393715	−	0.950512i	−0.595408	−	0.803423i	$-0.703010\pi$
$59$	3.02418	−	7.30102i	0.393715	−	0.950512i	0.989123	−	0.147089i	$-0.0469904\pi$
$60$		0			0
$61$	11.6637	−	4.83126i	1.49338	−	0.618580i	0.521334	−	0.853353i	$-0.325435\pi$
$61$	11.6637	−	4.83126i	1.49338	−	0.618580i	0.972050	+	0.234773i	$0.0754346\pi$
$62$	2.88094	−	2.60464i	0.365880	−	0.330790i
$63$		0			0
$64$	2.37911	−	7.63805i	0.297389	−	0.954756i
$65$			6.04322i			0.749569i
$66$		0			0
$67$	4.45039	+	10.7442i	0.543701	+	1.31261i	0.922094	+	0.386966i	$0.126477\pi$
$67$	4.45039	+	10.7442i	0.543701	+	1.31261i	−0.378393	+	0.925645i	$0.623523\pi$
$68$	−0.967277	+	9.57761i	−0.117300	+	1.16146i
$69$		0			0
$70$	2.16859	+	1.02895i	0.259196	+	0.122984i
$71$	−6.22714	−	6.22714i	−0.739025	−	0.739025i	0.233364	−	0.972389i	$-0.425027\pi$
$71$	−6.22714	−	6.22714i	−0.739025	−	0.739025i	−0.972389	+	0.233364i	$0.925027\pi$
$72$		0			0
$73$	−0.573022	+	0.573022i	−0.0670672	+	0.0670672i	−0.739845	−	0.672778i	$-0.765101\pi$
$73$	−0.573022	+	0.573022i	−0.0670672	+	0.0670672i	0.672778	+	0.739845i	$0.265101\pi$
$74$	6.83988	−	2.43779i	0.795120	−	0.283388i
$75$		0			0
$76$	−2.29033	−	7.61810i	−0.262719	−	0.873856i
$77$	−0.137662	+	0.0570216i	−0.0156881	+	0.00649822i
$78$		0			0
$79$	12.6432			1.42247			0.711233	−	0.702956i	$-0.248137\pi$
$79$	12.6432			1.42247			0.711233	+	0.702956i	$0.248137\pi$
$80$	−6.39598	−	4.31965i	−0.715092	−	0.482952i
$81$		0			0
$82$	0.397731	−	7.89640i	0.0439221	−	0.872012i
$83$	−4.21199	−	10.1686i	−0.462326	−	1.11615i	−0.967440	−	0.253101i	$-0.918550\pi$
$83$	−4.21199	−	10.1686i	−0.462326	−	1.11615i	0.505114	−	0.863053i	$-0.331450\pi$
$84$		0			0
$85$	8.58010	+	3.55400i	0.930643	+	0.385485i
$86$	2.18356	−	0.778239i	0.235459	−	0.0839197i
$87$		0			0
$88$	0.465184	−	0.114687i	0.0495888	−	0.0122257i
$89$	6.68154	−	6.68154i	0.708241	−	0.708241i	−0.257924	−	0.966165i	$-0.583038\pi$
$89$	6.68154	−	6.68154i	0.708241	−	0.708241i	0.966165	+	0.257924i	$0.0830384\pi$
$90$		0			0
$91$	−2.54533	−	1.05431i	−0.266823	−	0.110522i
$92$	2.80412	+	3.43415i	0.292350	+	0.358034i
$93$		0			0
$94$	9.78847	−	8.84969i	1.00960	−	0.912776i
$95$	−7.67456			−0.787393
$96$		0			0
$97$	−5.92342			−0.601432			−0.300716	−	0.953714i	$-0.597226\pi$
$97$	−5.92342			−0.601432			−0.300716	+	0.953714i	$0.597226\pi$
$98$	6.53155	−	5.90513i	0.659787	−	0.596509i
$99$		0			0
$100$	1.97828	−	1.61535i	0.197828	−	0.161535i
$101$	4.59423	+	1.90299i	0.457143	+	0.189355i	0.599358	−	0.800481i	$-0.295423\pi$
$101$	4.59423	+	1.90299i	0.457143	+	0.189355i	−0.142215	+	0.989836i	$0.545423\pi$
$102$		0			0
$103$	0.254297	−	0.254297i	0.0250566	−	0.0250566i	−0.694467	−	0.719524i	$-0.744360\pi$
$103$	0.254297	−	0.254297i	0.0250566	−	0.0250566i	0.719524	+	0.694467i	$0.244360\pi$
$104$	7.58133	+	4.58245i	0.743410	+	0.449347i
$105$		0			0
$106$	−0.636709	+	0.226929i	−0.0618426	+	0.0220413i
$107$	−4.13143	−	1.71129i	−0.399401	−	0.165437i	0.173936	−	0.984757i	$-0.444351\pi$
$107$	−4.13143	−	1.71129i	−0.399401	−	0.165437i	−0.573337	+	0.819320i	$0.694351\pi$
$108$		0			0
$109$	4.89484	+	11.8172i	0.468840	+	1.13188i	0.964670	+	0.263461i	$0.0848640\pi$
$109$	4.89484	+	11.8172i	0.468840	+	1.13188i	−0.495830	+	0.868420i	$0.665136\pi$
$110$	0.0232523	−	0.461641i	0.00221702	−	0.0440158i
$111$		0			0
$112$	2.93524	−	1.94029i	0.277354	−	0.183341i
$113$	12.6188			1.18708			0.593538	−	0.804806i	$-0.297731\pi$
$113$	12.6188			1.18708			0.593538	+	0.804806i	$0.297731\pi$
$114$		0			0
$115$	3.95170	−	1.63685i	0.368498	−	0.152637i
$116$	−5.42499	+	1.63099i	−0.503697	+	0.151433i
$117$		0			0
$118$	−10.5273	+	3.75202i	−0.969115	+	0.345401i
$119$	−2.99380	+	2.99380i	−0.274441	+	0.274441i
$120$		0			0
$121$	−7.75789	−	7.75789i	−0.705262	−	0.705262i
$122$	−16.1304	−	7.65357i	−1.46038	−	0.692921i
$123$		0			0
$124$	−5.46474	−	0.551904i	−0.490748	−	0.0495624i
$125$	−4.63488	−	11.1896i	−0.414556	−	1.00083i
$126$		0			0
$127$		−	17.0615i		−	1.51396i	−0.653438	−	0.756980i	$-0.726674\pi$
$127$		−	17.0615i		−	1.51396i	0.653438	−	0.756980i	$-0.273326\pi$
$128$	−10.2690	+	4.74837i	−0.907663	+	0.419700i
$129$		0			0
$130$	6.33957	−	5.73156i	0.556017	−	0.502691i
$131$	−11.9542	+	4.95158i	−1.04444	+	0.432621i	−0.837904	−	0.545818i	$-0.816219\pi$
$131$	−11.9542	+	4.95158i	−1.04444	+	0.432621i	−0.206536	+	0.978439i	$0.566219\pi$
$132$		0			0
$133$	1.33892	−	3.23243i	0.116099	−	0.280287i
$134$	7.05019	−	14.8587i	0.609044	−	1.28360i
$135$		0			0
$136$	10.9647	−	8.06897i	0.940213	−	0.691909i
$137$	0.560971	+	0.560971i	0.0479270	+	0.0479270i	0.730664	−	0.682737i	$-0.239211\pi$
$137$	0.560971	+	0.560971i	0.0479270	+	0.0479270i	−0.682737	+	0.730664i	$0.739211\pi$
$138$		0			0
$139$	−4.35315	+	10.5094i	−0.369229	+	0.891398i	0.624648	+	0.780907i	$0.285243\pi$
$139$	−4.35315	+	10.5094i	−0.369229	+	0.891398i	−0.993877	+	0.110492i	$0.964757\pi$
$140$	−0.977337	−	3.25082i	−0.0826001	−	0.274744i
$141$		0			0
$142$	−0.626511	+	12.4385i	−0.0525757	+	1.04382i
$143$			0.530536i			0.0443657i
$144$		0			0
$145$			5.46519i			0.453859i
$146$	1.14459	+	0.0576517i	0.0947272	+	0.00477128i
$147$		0			0
$148$	−9.04448	−	4.86322i	−0.743452	−	0.399755i
$149$	−7.37477	+	17.8043i	−0.604164	+	1.45858i	0.265093	+	0.964223i	$0.414597\pi$
$149$	−7.37477	+	17.8043i	−0.604164	+	1.45858i	−0.869258	+	0.494359i	$0.835403\pi$
$150$		0			0
$151$	2.98204	+	2.98204i	0.242675	+	0.242675i	0.817956	−	0.575281i	$-0.195107\pi$
$151$	2.98204	+	2.98204i	0.242675	+	0.242675i	−0.575281	+	0.817956i	$0.695107\pi$
$152$	−5.81947	+	9.62787i	−0.472021	+	0.780924i
$153$		0			0
$154$	0.190381	+	0.0903323i	0.0153413	+	0.00727918i
$155$	−2.02782	+	4.89559i	−0.162878	+	0.393223i
$156$		0			0
$157$	−3.24732	+	1.34508i	−0.259164	+	0.107349i	−0.508483	−	0.861072i	$-0.669793\pi$
$157$	−3.24732	+	1.34508i	−0.259164	+	0.107349i	0.249318	+	0.968422i	$0.419793\pi$
$158$	−11.9911	−	13.2632i	−0.953964	−	1.05516i
$159$		0			0
$160$	1.53465	+	10.8065i	0.121325	+	0.854330i
$161$			1.94998i			0.153680i
$162$		0			0
$163$	6.91012	+	16.6825i	0.541242	+	1.30667i	0.923847	+	0.382762i	$0.125027\pi$
$163$	6.91012	+	16.6825i	0.541242	+	1.30667i	−0.382605	+	0.923912i	$0.624973\pi$
$164$	−8.66085	+	7.07194i	−0.676299	+	0.552226i
$165$		0			0
$166$	−6.67253	+	14.0628i	−0.517889	+	1.09148i
$167$	−11.6859	−	11.6859i	−0.904286	−	0.904286i	0.0915178	−	0.995803i	$-0.470828\pi$
$167$	−11.6859	−	11.6859i	−0.904286	−	0.904286i	−0.995803	+	0.0915178i	$0.970828\pi$
$168$		0			0
$169$	2.25608	−	2.25608i	0.173545	−	0.173545i
$170$	−4.40934	−	12.3716i	−0.338181	−	0.948856i
$171$		0			0
$172$	−2.88735	−	1.55253i	−0.220158	−	0.118379i
$173$	20.9504	−	8.67794i	1.59283	−	0.659772i	0.602451	−	0.798156i	$-0.294191\pi$
$173$	20.9504	−	8.67794i	1.59283	−	0.659772i	0.990379	+	0.138384i	$0.0441908\pi$
$174$		0			0
$175$	1.12331			0.0849140
$176$	−0.561506	−	0.379224i	−0.0423251	−	0.0285851i
$177$		0			0
$178$	−13.3462	−	0.672228i	−1.00034	−	0.0503856i
$179$	−0.893419	−	2.15690i	−0.0667773	−	0.161215i	0.886968	−	0.461831i	$-0.152807\pi$
$179$	−0.893419	−	2.15690i	−0.0667773	−	0.161215i	−0.953745	+	0.300617i	$0.902807\pi$
$180$		0			0
$181$	−8.91096	−	3.69104i	−0.662347	−	0.274353i	0.0260791	−	0.999660i	$-0.491698\pi$
$181$	−8.91096	−	3.69104i	−0.662347	−	0.274353i	−0.688426	+	0.725307i	$0.741698\pi$
$182$	1.30805	+	3.67009i	0.0969592	+	0.272045i
$183$		0			0
$184$	0.943043	−	6.19868i	0.0695220	−	0.456972i
$185$	−7.00539	+	7.00539i	−0.515046	+	0.515046i
$186$		0			0
$187$	0.753251	+	0.312007i	0.0550831	+	0.0228162i
$188$	−18.5673	−	1.87518i	−1.35416	−	0.136762i
$189$		0			0
$190$	7.27877	+	8.05091i	0.528058	+	0.584074i
$191$	2.43569			0.176240			0.0881200	−	0.996110i	$-0.471914\pi$
$191$	2.43569			0.176240			0.0881200	+	0.996110i	$0.471914\pi$
$192$		0			0
$193$	−23.6589			−1.70301			−0.851504	−	0.524349i	$-0.824309\pi$
$193$	−23.6589			−1.70301			−0.851504	+	0.524349i	$0.824309\pi$
$194$	5.61795	+	6.21390i	0.403345	+	0.446132i
$195$		0			0
$196$	−12.3894	−	1.25125i	−0.884959	−	0.0893752i
$197$	3.36182	+	1.39251i	0.239520	+	0.0992122i	0.499214	−	0.866478i	$-0.333622\pi$
$197$	3.36182	+	1.39251i	0.239520	+	0.0992122i	−0.259695	+	0.965691i	$0.583622\pi$
$198$		0			0
$199$	4.56361	−	4.56361i	0.323506	−	0.323506i	−0.526604	−	0.850110i	$-0.676535\pi$
$199$	4.56361	−	4.56361i	0.323506	−	0.323506i	0.850110	+	0.526604i	$0.176535\pi$
$200$	−3.57082	−	0.543250i	−0.252495	−	0.0384136i
$201$		0			0
$202$	−2.36099	−	6.62438i	−0.166119	−	0.466090i
$203$	−2.30187	−	0.953466i	−0.161560	−	0.0669202i
$204$		0			0
$205$	4.12810	+	9.96612i	0.288319	+	0.696064i
$206$	−0.507950	−	0.0255847i	−0.0353905	−	0.00178257i
$207$		0			0
$208$	−2.38318	−	12.2992i	−0.165244	−	0.852799i
$209$	−0.673752			−0.0466044
$210$		0			0
$211$	−3.67647	+	1.52284i	−0.253098	+	0.104837i	−0.505626	−	0.862753i	$-0.668738\pi$
$211$	−3.67647	+	1.52284i	−0.253098	+	0.104837i	0.252527	+	0.967590i	$0.418738\pi$
$212$	0.841930	+	0.452706i	0.0578240	+	0.0310920i
$213$		0			0
$214$	2.12315	+	5.95707i	0.145136	+	0.407217i
$215$	−2.23639	+	2.23639i	−0.152521	+	0.152521i
$216$		0			0
$217$	−1.70819	−	1.70819i	−0.115959	−	0.115959i
$218$	7.75428	−	16.3426i	0.525186	−	1.10686i
$219$		0			0
$220$	−0.506333	+	0.413441i	−0.0341369	+	0.0278742i
$221$	5.76889	+	13.9273i	0.388057	+	0.936854i
$222$		0			0
$223$		−	15.1287i		−	1.01309i	−0.862213	−	0.506545i	$-0.830922\pi$
$223$		−	15.1287i		−	1.01309i	0.862213	−	0.506545i	$-0.169078\pi$
$224$	−4.81931	−	1.23895i	−0.322004	−	0.0827806i
$225$		0			0
$226$	−11.9680	−	13.2376i	−0.796102	−	0.880552i
$227$	−14.4739	+	5.99529i	−0.960666	+	0.397921i	−0.807230	−	0.590237i	$-0.799034\pi$
$227$	−14.4739	+	5.99529i	−0.960666	+	0.397921i	−0.153437	+	0.988158i	$0.549034\pi$
$228$		0			0
$229$	−2.24557	+	5.42129i	−0.148391	+	0.358249i	−0.980544	−	0.196298i	$-0.937108\pi$
$229$	−2.24557	+	5.42129i	−0.148391	+	0.358249i	0.832153	+	0.554546i	$0.187108\pi$
$230$	−5.46503	−	2.59306i	−0.360353	−	0.170981i
$231$		0			0
$232$	6.85618	+	4.14415i	0.450130	+	0.272077i
$233$	−21.4875	−	21.4875i	−1.40769	−	1.40769i	−0.771675	−	0.636017i	$-0.780581\pi$
$233$	−21.4875	−	21.4875i	−1.40769	−	1.40769i	−0.636017	−	0.771675i	$-0.719419\pi$
$234$		0			0
$235$	−6.88984	+	16.6336i	−0.449444	+	1.08505i
$236$	13.9204	+	7.48500i	0.906140	+	0.487232i
$237$		0			0
$238$	5.98002	+	0.301205i	0.387627	+	0.0195243i
$239$		−	15.5320i		−	1.00468i	−0.864671	−	0.502339i	$-0.832473\pi$
$239$		−	15.5320i		−	1.00468i	0.864671	−	0.502339i	$-0.167527\pi$
$240$		0			0
$241$		−	25.7287i		−	1.65733i	−0.559743	−	0.828666i	$-0.689100\pi$
$241$		−	25.7287i		−	1.65733i	0.559743	−	0.828666i	$-0.310900\pi$
$242$	−0.780519	+	15.4961i	−0.0501737	+	0.996129i
$243$		0			0
$244$	7.26963	+	24.1803i	0.465390	+	1.54798i
$245$	−4.59739	+	11.0991i	−0.293716	+	0.709094i
$246$		0			0
$247$	−8.80874	−	8.80874i	−0.560487	−	0.560487i
$248$	4.60395	+	6.25617i	0.292351	+	0.397267i
$249$		0			0
$250$	−7.34246	+	15.4747i	−0.464378	+	0.978706i
$251$	0.0305865	−	0.0738424i	0.00193060	−	0.00466089i	−0.922911	−	0.385013i	$-0.874197\pi$
$251$	0.0305865	−	0.0738424i	0.00193060	−	0.00466089i	0.924842	+	0.380352i	$0.124197\pi$
$252$		0			0
$253$	0.346922	−	0.143700i	0.0218108	−	0.00903432i
$254$	−17.8981	+	16.1816i	−1.12303	+	1.01532i
$255$		0			0
$256$	14.7207	+	6.26912i	0.920042	+	0.391820i
$257$			27.2896i			1.70228i	0.524938	+	0.851141i	$0.324089\pi$
$257$			27.2896i			1.70228i	−0.524938	+	0.851141i	$0.675911\pi$
$258$		0			0
$259$	−1.72841	−	4.17275i	−0.107398	−	0.259282i
$260$	−12.0253	−	1.21447i	−0.745775	−	0.0753185i
$261$		0			0
$262$	16.5321	+	7.84416i	1.02136	+	0.484614i
$263$	−14.9965	−	14.9965i	−0.924725	−	0.924725i	0.0726334	−	0.997359i	$-0.476860\pi$
$263$	−14.9965	−	14.9965i	−0.924725	−	0.924725i	−0.997359	+	0.0726334i	$0.976860\pi$
$264$		0			0
$265$	0.652115	−	0.652115i	0.0400591	−	0.0400591i
$266$	−4.66081	+	1.66115i	−0.285773	+	0.101852i
$267$		0			0
$268$	−22.2740	+	6.69652i	−1.36060	+	0.409055i
$269$	19.0608	−	7.89523i	1.16216	−	0.481381i	0.283564	−	0.958953i	$-0.408483\pi$
$269$	19.0608	−	7.89523i	1.16216	−	0.481381i	0.878592	+	0.477573i	$0.158483\pi$
$270$		0			0
$271$	6.04647			0.367297			0.183648	−	0.982992i	$-0.441209\pi$
$271$	6.04647			0.367297			0.183648	+	0.982992i	$0.441209\pi$
$272$	−18.8639	−	3.84953i	−1.14379	−	0.233412i
$273$		0			0
$274$	0.0564392	−	1.12052i	0.00340962	−	0.0676932i
$275$	−0.0827798	−	0.199848i	−0.00499181	−	0.0120513i
$276$		0			0
$277$	17.5872	+	7.28485i	1.05671	+	0.437704i	0.842283	−	0.539036i	$-0.181211\pi$
$277$	17.5872	+	7.28485i	1.05671	+	0.437704i	0.214428	+	0.976740i	$0.431211\pi$
$278$	15.1535	−	5.40083i	0.908844	−	0.323920i
$279$		0			0
$280$	−2.48330	+	4.10844i	−0.148406	+	0.245526i
$281$	−3.99083	+	3.99083i	−0.238073	+	0.238073i	−0.816052	−	0.577979i	$-0.803842\pi$
$281$	−3.99083	+	3.99083i	−0.238073	+	0.238073i	0.577979	+	0.816052i	$0.303842\pi$
$282$		0			0
$283$	−23.8200	−	9.86659i	−1.41595	−	0.586508i	−0.462114	−	0.886821i	$-0.652909\pi$
$283$	−23.8200	−	9.86659i	−1.41595	−	0.586508i	−0.953841	+	0.300313i	$0.902909\pi$
$284$	13.6427	−	11.1398i	0.809544	−	0.661026i
$285$		0			0
$286$	0.556553	−	0.503176i	0.0329097	−	0.0297534i
$287$	−4.91780			−0.290289
$288$		0			0
$289$	6.16656			0.362739
$290$	5.73320	−	5.18335i	0.336665	−	0.304377i
$291$		0			0
$292$	−1.02509	−	1.25540i	−0.0599887	−	0.0734668i
$293$	2.98858	+	1.23791i	0.174595	+	0.0723195i	0.468269	−	0.883586i	$-0.344878\pi$
$293$	2.98858	+	1.23791i	0.174595	+	0.0723195i	−0.293674	+	0.955906i	$0.594878\pi$
$294$		0			0
$295$	10.7820	−	10.7820i	0.627753	−	0.627753i
$296$	3.47634	+	14.1004i	0.202058	+	0.819571i
$297$		0			0
$298$	25.6718	−	9.14966i	1.48713	−	0.530026i
$299$	6.41445	+	2.65695i	0.370957	+	0.153656i
$300$		0			0
$301$	−0.551776	−	1.33211i	−0.0318039	−	0.0767813i
$302$	0.300022	−	5.95652i	0.0172643	−	0.342759i
$303$		0			0
$304$	15.6194	−	3.02651i	0.895832	−	0.173582i
$305$	24.3595			1.39482
$306$		0			0
$307$	−27.9645	+	11.5833i	−1.59602	+	0.661092i	−0.990845	−	0.135002i	$-0.956896\pi$
$307$	−27.9645	+	11.5833i	−1.59602	+	0.661092i	−0.605173	+	0.796094i	$0.706896\pi$
$308$	−0.0858008	−	0.285391i	−0.00488895	−	0.0162616i
$309$		0			0
$310$	7.05891	−	2.51586i	0.400919	−	0.142891i
$311$	19.5213	−	19.5213i	1.10695	−	1.10695i	0.113401	−	0.993549i	$-0.463826\pi$
$311$	19.5213	−	19.5213i	1.10695	−	1.10695i	0.993549	−	0.113401i	$-0.0361745\pi$
$312$		0			0
$313$	−15.3194	−	15.3194i	−0.865901	−	0.865901i	0.126114	−	0.992016i	$-0.459749\pi$
$313$	−15.3194	−	15.3194i	−0.865901	−	0.865901i	−0.992016	+	0.126114i	$0.959749\pi$
$314$	4.49090	+	2.13085i	0.253436	+	0.120251i
$315$		0			0
$316$	−2.54083	+	25.1583i	−0.142933	+	1.41527i
$317$	−8.07700	−	19.4996i	−0.453649	−	1.09521i	−0.970924	−	0.239387i	$-0.923053\pi$
$317$	−8.07700	−	19.4996i	−0.453649	−	1.09521i	0.517275	−	0.855819i	$-0.326947\pi$
$318$		0			0
$319$			0.479791i			0.0268631i
$320$	9.88095	−	11.8591i	0.552362	−	0.662945i
$321$		0			0
$322$	2.04560	−	1.84941i	0.113997	−	0.103064i
$323$	−17.6870	+	7.32618i	−0.984129	+	0.407639i
$324$		0			0
$325$	1.53057	−	3.69512i	0.0849007	−	0.204968i
$326$	10.9468	−	23.0711i	0.606289	−	1.27779i
$327$		0			0
$328$	15.6329	+	2.37834i	0.863185	+	0.131322i
$329$	−5.80383	−	5.80383i	−0.319976	−	0.319976i
$330$		0			0
$331$	8.08547	−	19.5200i	0.444417	−	1.07292i	−0.529965	−	0.848020i	$-0.677795\pi$
$331$	8.08547	−	19.5200i	0.444417	−	1.07292i	0.974382	−	0.224899i	$-0.0722052\pi$
$332$	21.0808	−	6.33781i	1.15696	−	0.347832i
$333$		0			0
$334$	−1.17572	+	23.3423i	−0.0643326	+	1.27723i
$335$			22.4391i			1.22598i
$336$		0			0
$337$			7.13608i			0.388727i	0.980930	+	0.194364i	$0.0622642\pi$
$337$			7.13608i			0.388727i	−0.980930	+	0.194364i	$0.937736\pi$
$338$	−4.50645	−	0.226984i	−0.245118	−	0.0123463i
$339$		0			0
$340$	−8.79632	+	16.3591i	−0.477047	+	0.887198i
$341$	−0.178023	+	0.429786i	−0.00964049	+	0.0232742i
$342$		0			0
$343$	−8.22674	−	8.22674i	−0.444202	−	0.444202i
$344$	1.10978	+	4.50141i	0.0598355	+	0.242700i
$345$		0			0
$346$	−28.9735	−	13.7474i	−1.55762	−	0.739064i
$347$	10.8574	−	26.2122i	0.582858	−	1.40714i	−0.307354	−	0.951595i	$-0.599443\pi$
$347$	10.8574	−	26.2122i	0.582858	−	1.40714i	0.890211	−	0.455548i	$-0.150557\pi$
$348$		0			0
$349$	21.7373	−	9.00387i	1.16357	−	0.481966i	0.284508	−	0.958674i	$-0.408170\pi$
$349$	21.7373	−	9.00387i	1.16357	−	0.481966i	0.879062	+	0.476707i	$0.158170\pi$
$350$	−1.06538	−	1.17839i	−0.0569467	−	0.0629877i
$351$		0			0
$352$	0.134728	+	0.948708i	0.00718100	+	0.0505663i
$353$		−	20.0677i		−	1.06810i	−0.845454	−	0.534048i	$-0.820670\pi$
$353$		−	20.0677i		−	1.06810i	0.845454	−	0.534048i	$-0.179330\pi$
$354$		0			0
$355$	−6.50264	−	15.6988i	−0.345124	−	0.833204i
$356$	11.9527	+	14.6382i	0.633491	+	0.775823i
$357$		0			0
$358$	−1.41533	+	2.98290i	−0.0748026	+	0.157651i
$359$	2.29736	+	2.29736i	0.121250	+	0.121250i	0.765128	−	0.643878i	$-0.222676\pi$
$359$	2.29736	+	2.29736i	0.121250	+	0.121250i	−0.643878	+	0.765128i	$0.722676\pi$
$360$		0			0
$361$	−2.24841	+	2.24841i	−0.118337	+	0.118337i
$362$	4.57937	+	12.8486i	0.240686	+	0.675309i
$363$		0			0
$364$	2.60947	−	4.85301i	0.136773	−	0.254367i
$365$	−1.44460	+	0.598374i	−0.0756139	+	0.0313203i
$366$		0			0
$367$	−7.23365			−0.377594			−0.188797	−	0.982016i	$-0.560459\pi$
$367$	−7.23365			−0.377594			−0.188797	+	0.982016i	$0.560459\pi$
$368$	−7.39706	+	4.88972i	−0.385598	+	0.254894i
$369$		0			0
$370$	13.9930	+	0.704811i	0.727463	+	0.0366414i
$371$	0.160894	+	0.388432i	0.00835319	+	0.0201664i
$372$		0			0
$373$	16.5680	+	6.86267i	0.857856	+	0.355336i	0.767869	−	0.640607i	$-0.221317\pi$
$373$	16.5680	+	6.86267i	0.857856	+	0.355336i	0.0899875	+	0.995943i	$0.471317\pi$
$374$	−0.387098	−	1.08611i	−0.0200163	−	0.0561612i
$375$		0			0
$376$	15.6427	+	21.2563i	0.806709	+	1.09621i
$377$	−6.27286	+	6.27286i	−0.323069	+	0.323069i
$378$		0			0
$379$	20.4951	+	8.48935i	1.05276	+	0.436069i	0.840877	−	0.541226i	$-0.182040\pi$
$379$	20.4951	+	8.48935i	1.05276	+	0.436069i	0.211885	+	0.977295i	$0.432040\pi$
$380$	1.54232	−	15.2714i	0.0791192	−	0.783408i
$381$		0			0
$382$	−2.31008	−	2.55513i	−0.118194	−	0.130732i
$383$	−2.58370			−0.132021			−0.0660103	−	0.997819i	$-0.521027\pi$
$383$	−2.58370			−0.132021			−0.0660103	+	0.997819i	$0.521027\pi$
$384$		0			0
$385$	−0.287506			−0.0146526
$386$	22.4388	+	24.8191i	1.14211	+	1.26326i
$387$		0			0
$388$	1.19040	−	11.7869i	0.0604334	−	0.598388i
$389$	−4.93427	−	2.04384i	−0.250177	−	0.103627i	0.254071	−	0.967186i	$-0.418230\pi$
$389$	−4.93427	−	2.04384i	−0.250177	−	0.103627i	−0.504248	+	0.863559i	$0.668230\pi$
$390$		0			0
$391$	7.54464	−	7.54464i	0.381549	−	0.381549i
$392$	10.4379	+	14.1837i	0.527193	+	0.716386i
$393$		0			0
$394$	−1.72765	−	4.84737i	−0.0870376	−	0.244207i
$395$	22.5381	+	9.33559i	1.13402	+	0.469725i
$396$		0			0
$397$	−6.50861	−	15.7132i	−0.326658	−	0.788622i	−0.998836	−	0.0482326i	$-0.984641\pi$
$397$	−6.50861	−	15.7132i	−0.326658	−	0.788622i	0.672178	−	0.740389i	$-0.265359\pi$
$398$	−9.11567	−	0.459144i	−0.456927	−	0.0230148i
$399$		0			0
$400$	2.81678	+	4.26116i	0.140839	+	0.213058i
$401$	13.5140			0.674856			0.337428	−	0.941351i	$-0.390443\pi$
$401$	13.5140			0.674856			0.337428	+	0.941351i	$0.390443\pi$
$402$		0			0
$403$	−7.94658	+	3.29158i	−0.395847	+	0.163965i
$404$	−4.71000	+	8.75952i	−0.234331	+	0.435802i
$405$		0			0
$406$	1.18294	+	3.31905i	0.0587082	+	0.164722i
$407$	−0.615006	+	0.615006i	−0.0304847	+	0.0304847i
$408$		0			0
$409$	−15.3092	−	15.3092i	−0.756990	−	0.756990i	0.218783	−	0.975773i	$-0.429791\pi$
$409$	−15.3092	−	15.3092i	−0.756990	−	0.756990i	−0.975773	+	0.218783i	$0.929791\pi$
$410$	6.53964	−	13.7827i	0.322970	−	0.680679i
$411$		0			0
$412$	0.454915	+	0.557124i	0.0224120	+	0.0274475i
$413$	2.66020	+	6.42230i	0.130900	+	0.316021i
$414$		0			0
$415$		−	21.2370i		−	1.04249i
$416$	−10.6421	+	14.1650i	−0.521772	+	0.694496i
$417$		0			0
$418$	0.639006	+	0.706792i	0.0312548	+	0.0345703i
$419$	−7.00151	+	2.90012i	−0.342046	+	0.141680i	−0.547093	−	0.837072i	$-0.684265\pi$
$419$	−7.00151	+	2.90012i	−0.342046	+	0.141680i	0.205046	+	0.978752i	$0.434265\pi$
$420$		0			0
$421$	4.44827	−	10.7391i	0.216796	−	0.523391i	−0.777643	−	0.628706i	$-0.783585\pi$
$421$	4.44827	−	10.7391i	0.216796	−	0.523391i	0.994439	+	0.105315i	$0.0335850\pi$
$422$	5.08439	+	2.41245i	0.247504	+	0.117436i
$423$		0			0
$424$	−0.323604	−	1.31258i	−0.0157156	−	0.0637444i
$425$	−4.34617	−	4.34617i	−0.210820	−	0.210820i
$426$		0			0
$427$	−4.24979	+	10.2599i	−0.205662	+	0.496511i
$428$	4.23554	−	7.87713i	0.204733	−	0.380756i
$429$		0			0
$430$	4.46712	+	0.225003i	0.215424	+	0.0108506i
$431$			35.7388i			1.72148i	0.509046	+	0.860739i	$0.329998\pi$
$431$			35.7388i			1.72148i	−0.509046	+	0.860739i	$0.670002\pi$
$432$		0			0
$433$		−	36.2711i		−	1.74308i	−0.490326	−	0.871539i	$-0.663122\pi$
$433$		−	36.2711i		−	1.74308i	0.490326	−	0.871539i	$-0.336878\pi$
$434$	−0.171860	+	3.41205i	−0.00824955	+	0.163783i
$435$		0			0
$436$	−24.4984	+	7.36529i	−1.17326	+	0.352733i
$437$	−3.37419	+	8.14601i	−0.161409	+	0.389676i
$438$		0			0
$439$	−4.44721	−	4.44721i	−0.212254	−	0.212254i	0.592970	−	0.805224i	$-0.297955\pi$
$439$	−4.44721	−	4.44721i	−0.212254	−	0.212254i	−0.805224	+	0.592970i	$0.797955\pi$
$440$	0.913937	+	0.139043i	0.0435702	+	0.00662861i
$441$		0			0
$442$	9.13893	−	19.2609i	0.434694	−	0.916146i
$443$	−0.302597	+	0.730534i	−0.0143768	+	0.0347087i	−0.930905	−	0.365262i	$-0.880980\pi$
$443$	−0.302597	+	0.730534i	−0.0143768	+	0.0347087i	0.916528	+	0.399970i	$0.130980\pi$
$444$		0			0
$445$	16.8443	−	6.97714i	0.798497	−	0.330748i
$446$	−15.8706	+	14.3485i	−0.751493	+	0.679420i
$447$		0			0
$448$	3.27107	+	6.23070i	0.154544	+	0.294373i
$449$			9.45413i			0.446168i	0.974799	+	0.223084i	$0.0716124\pi$
$449$			9.45413i			0.446168i	−0.974799	+	0.223084i	$0.928388\pi$
$450$		0			0
$451$	0.362408	+	0.874930i	0.0170651	+	0.0411988i
$452$	−2.53593	+	25.1099i	−0.119280	+	1.18107i
$453$		0			0
$454$	20.0168	+	9.49758i	0.939433	+	0.445744i
$455$	−3.75889	−	3.75889i	−0.176220	−	0.176220i
$456$		0			0
$457$	−8.41071	+	8.41071i	−0.393437	+	0.393437i	−0.875910	−	0.482474i	$-0.839738\pi$
$457$	−8.41071	+	8.41071i	−0.393437	+	0.393437i	0.482474	+	0.875910i	$0.339738\pi$
$458$	7.81690	−	2.78601i	0.365260	−	0.130182i
$459$		0			0
$460$	2.46298	+	8.19236i	0.114837	+	0.381971i
$461$	22.6364	−	9.37632i	1.05428	−	0.436699i	0.212865	−	0.977082i	$-0.431721\pi$
$461$	22.6364	−	9.37632i	1.05428	−	0.436699i	0.841419	+	0.540383i	$0.181721\pi$
$462$		0			0
$463$	2.98464			0.138708			0.0693541	−	0.997592i	$-0.477906\pi$
$463$	2.98464			0.138708			0.0693541	+	0.997592i	$0.477906\pi$
$464$	−2.15523	−	11.1228i	−0.100054	−	0.516364i
$465$		0			0
$466$	−2.16185	+	42.9206i	−0.100146	+	1.98826i
$467$	14.7083	+	35.5089i	0.680618	+	1.64316i	0.762874	+	0.646547i	$0.223788\pi$
$467$	14.7083	+	35.5089i	0.680618	+	1.64316i	−0.0822559	+	0.996611i	$0.526212\pi$
$468$		0			0
$469$	−9.45105	−	3.91475i	−0.436409	−	0.180767i
$470$	23.9838	−	8.54803i	1.10629	−	0.394291i
$471$		0			0
$472$	−5.35044	−	21.7020i	−0.246274	−	0.998917i
$473$	−0.196334	+	0.196334i	−0.00902744	+	0.00902744i
$474$		0			0
$475$	4.69260	+	1.94374i	0.215311	+	0.0891849i
$476$	−5.35564	−	6.55894i	−0.245476	−	0.300629i
$477$		0			0
$478$	−16.2936	+	14.7310i	−0.745253	+	0.673778i
$479$	39.8284			1.81980			0.909902	−	0.414823i	$-0.136156\pi$
$479$	39.8284			1.81980			0.909902	+	0.414823i	$0.136156\pi$
$480$		0			0
$481$	−16.0813			−0.733246
$482$	−26.9904	+	24.4019i	−1.22938	+	1.11147i
$483$		0			0
$484$	16.9963	−	13.8782i	0.772559	−	0.630826i
$485$	−10.5593	−	4.37380i	−0.479472	−	0.198604i
$486$		0			0
$487$	21.5914	−	21.5914i	0.978400	−	0.978400i	−0.0213713	−	0.999772i	$-0.506803\pi$
$487$	21.5914	−	21.5914i	0.978400	−	0.978400i	0.999772	+	0.0213713i	$0.00680320\pi$
$488$	18.4713	−	30.5594i	0.836156	−	1.38336i
$489$		0			0
$490$	16.0037	−	5.70385i	0.722971	−	0.257674i
$491$	26.9379	+	11.1580i	1.21569	+	0.503555i	0.896037	−	0.443980i	$-0.146434\pi$
$491$	26.9379	+	11.1580i	1.21569	+	0.503555i	0.319652	+	0.947535i	$0.396434\pi$
$492$		0			0
$493$	5.21710	+	12.5952i	0.234966	+	0.567259i
$494$	−0.886245	+	17.5952i	−0.0398741	+	0.791644i
$495$		0			0
$496$	2.19644	−	10.7633i	0.0986232	−	0.483284i
$497$	7.74658			0.347482
$498$		0			0
$499$	11.3562	−	4.70388i	0.508372	−	0.210575i	−0.113729	−	0.993512i	$-0.536279\pi$
$499$	11.3562	−	4.70388i	0.508372	−	0.210575i	0.622101	+	0.782937i	$0.286279\pi$
$500$	23.1974	−	6.97413i	1.03742	−	0.311892i
$501$		0			0
$502$	−0.106473	+	0.0379478i	−0.00475211	+	0.00169369i
$503$	8.97393	−	8.97393i	0.400128	−	0.400128i	−0.478150	−	0.878278i	$-0.658693\pi$
$503$	8.97393	−	8.97393i	0.400128	−	0.400128i	0.878278	+	0.478150i	$0.158693\pi$
$504$		0			0
$505$	6.78467	+	6.78467i	0.301914	+	0.301914i
$506$	−0.479777	−	0.227645i	−0.0213287	−	0.0101201i
$507$		0			0
$508$	33.9502	+	3.42876i	1.50630	+	0.152126i
$509$	−2.41200	−	5.82308i	−0.106910	−	0.258104i	0.861367	−	0.507983i	$-0.169609\pi$
$509$	−2.41200	−	5.82308i	−0.106910	−	0.258104i	−0.968277	+	0.249880i	$0.919609\pi$
$510$		0			0
$511$		−	0.712842i		−	0.0315343i
$512$	−7.38496	−	21.3884i	−0.326372	−	0.945241i
$513$		0			0
$514$	28.6279	−	25.8823i	1.26272	−	1.14162i
$515$	0.641088	−	0.265547i	0.0282497	−	0.0117014i
$516$		0			0
$517$	−0.604862	+	1.46027i	−0.0266018	+	0.0642224i
$518$	−2.73811	+	5.77073i	−0.120305	+	0.253551i
$519$		0			0
$520$	10.1311	+	13.7668i	0.444277	+	0.603714i
$521$	−0.969806	−	0.969806i	−0.0424880	−	0.0424880i	0.685544	−	0.728032i	$-0.259565\pi$
$521$	−0.969806	−	0.969806i	−0.0424880	−	0.0424880i	−0.728032	+	0.685544i	$0.759565\pi$
$522$		0			0
$523$	−13.6100	+	32.8575i	−0.595125	+	1.43676i	0.283372	+	0.959010i	$0.408547\pi$
$523$	−13.6100	+	32.8575i	−0.595125	+	1.43676i	−0.878497	+	0.477748i	$0.841453\pi$
$524$	−7.45067	−	24.7824i	−0.325484	−	1.08263i
$525$		0			0
$526$	−1.50880	+	29.9551i	−0.0657867	+	1.30610i
$527$			13.2183i			0.575796i
$528$		0			0
$529$			18.0859i			0.786343i
$530$	−1.30258	−	0.0656092i	−0.0565804	−	0.00284988i
$531$		0			0
$532$	6.16306	+	3.31388i	0.267203	+	0.143675i
$533$	−6.70079	+	16.1771i	−0.290243	+	0.700709i
$534$		0			0
$535$	−6.10122	−	6.10122i	−0.263779	−	0.263779i
$536$	28.1502	+	17.0151i	1.21590	+	0.734940i
$537$		0			0
$538$	−26.3602	−	12.5074i	−1.13647	−	0.539233i
$539$	−0.403606	+	0.974392i	−0.0173846	+	0.0419700i
$540$		0			0
$541$	−22.0030	+	9.11394i	−0.945983	+	0.391839i	−0.801720	−	0.597700i	$-0.796081\pi$
$541$	−22.0030	+	9.11394i	−0.945983	+	0.391839i	−0.144263	+	0.989539i	$0.546081\pi$
$542$	−5.73464	−	6.34298i	−0.246324	−	0.272454i
$543$		0			0
$544$	13.8528	+	23.4399i	0.593932	+	1.00498i
$545$			24.6800i			1.05717i
$546$		0			0
$547$	−2.89886	−	6.99847i	−0.123946	−	0.299233i	0.849711	−	0.527248i	$-0.176776\pi$
$547$	−2.89886	−	6.99847i	−0.123946	−	0.299233i	−0.973657	+	0.228016i	$0.926776\pi$
$548$	−1.22900	+	1.00353i	−0.0525003	+	0.0428686i
$549$		0			0
$550$	−0.131138	+	0.276381i	−0.00559173	+	0.0117849i
$551$	−7.96619	−	7.96619i	−0.339371	−	0.339371i
$552$		0			0
$553$	−7.86407	+	7.86407i	−0.334414	+	0.334414i
$554$	−9.03810	−	25.3588i	−0.383992	−	1.07739i
$555$		0			0
$556$	−20.0377	−	10.7743i	−0.849786	−	0.456930i
$557$	−5.71563	+	2.36749i	−0.242179	+	0.100314i	−0.500472	−	0.865753i	$-0.666840\pi$
$557$	−5.71563	+	2.36749i	−0.242179	+	0.100314i	0.258293	+	0.966067i	$0.416840\pi$
$558$		0			0
$559$	−5.13379			−0.217136
$560$	6.66515	−	1.29148i	0.281654	−	0.0545750i
$561$		0			0
$562$	7.97156	+	0.401517i	0.336260	+	0.0169370i
$563$	−11.5978	−	27.9995i	−0.488787	−	1.18004i	−0.955331	−	0.295538i	$-0.904501\pi$
$563$	−11.5978	−	27.9995i	−0.488787	−	1.18004i	0.466544	−	0.884498i	$-0.345499\pi$
$564$		0			0
$565$	22.4947	+	9.31760i	0.946358	+	0.391994i
$566$	12.2412	+	34.3459i	0.514536	+	1.44367i
$567$		0			0
$568$	−24.6252	−	3.74638i	−1.03325	−	0.157195i
$569$	−8.09693	+	8.09693i	−0.339441	+	0.339441i	−0.856157	−	0.516716i	$-0.827154\pi$
$569$	−8.09693	+	8.09693i	−0.339441	+	0.339441i	0.516716	+	0.856157i	$0.327154\pi$
$570$		0			0
$571$	2.74000	+	1.13495i	0.114666	+	0.0474960i	0.439279	−	0.898351i	$-0.355234\pi$
$571$	2.74000	+	1.13495i	0.114666	+	0.0474960i	−0.324613	+	0.945847i	$0.605234\pi$
$572$	−1.05570	−	0.106619i	−0.0441411	−	0.00445797i
$573$		0			0
$574$	4.66419	+	5.15897i	0.194679	+	0.215331i
$575$	−2.83083			−0.118054
$576$		0			0
$577$	6.87235			0.286100			0.143050	−	0.989715i	$-0.454309\pi$
$577$	6.87235			0.286100			0.143050	+	0.989715i	$0.454309\pi$
$578$	−5.84855	−	6.46896i	−0.243267	−	0.269073i
$579$		0			0
$580$	−10.8751	−	1.09831i	−0.451562	−	0.0456049i
$581$	8.94478	+	3.70505i	0.371092	+	0.153711i
$582$		0			0
$583$	0.0572495	−	0.0572495i	0.00237103	−	0.00237103i
$584$	−0.344743	+	2.26601i	−0.0142656	+	0.0937684i
$585$		0			0
$586$	−1.53584	−	4.30920i	−0.0634449	−	0.178012i
$587$	38.8656	+	16.0987i	1.60415	+	0.664463i	0.991996	−	0.126272i	$-0.0403012\pi$
$587$	38.8656	+	16.0987i	1.60415	+	0.664463i	0.612159	+	0.790735i	$0.290301\pi$
$588$		0			0
$589$	−4.18013	−	10.0917i	−0.172239	−	0.415822i
$590$	−21.5367	−	1.08478i	−0.886653	−	0.0446595i
$591$		0			0
$592$	11.4948	−	17.0201i	0.472435	−	0.699521i
$593$	−3.82382			−0.157025			−0.0785126	−	0.996913i	$-0.525017\pi$
$593$	−3.82382			−0.157025			−0.0785126	+	0.996913i	$0.525017\pi$
$594$		0			0
$595$	−7.54743	+	3.12625i	−0.309415	+	0.128164i
$596$	−33.9462	−	18.2529i	−1.39049	−	0.747668i
$597$		0			0
$598$	−3.29641	−	9.24894i	−0.134800	−	0.378217i
$599$	24.3269	−	24.3269i	0.993971	−	0.993971i	−0.00601064	−	0.999982i	$-0.501913\pi$
$599$	24.3269	−	24.3269i	0.993971	−	0.993971i	0.999982	+	0.00601064i	$0.00191326\pi$
$600$		0			0
$601$	−11.3481	−	11.3481i	−0.462899	−	0.462899i	0.436706	−	0.899604i	$-0.356145\pi$
$601$	−11.3481	−	11.3481i	−0.462899	−	0.462899i	−0.899604	+	0.436706i	$0.856145\pi$
$602$	−0.874110	+	1.84224i	−0.0356261	+	0.0750842i
$603$		0			0
$604$	−6.53317	+	5.33460i	−0.265831	+	0.217062i
$605$	−8.10111	−	19.5578i	−0.329357	−	0.795138i
$606$		0			0
$607$			33.7633i			1.37041i	0.728349	+	0.685206i	$0.240288\pi$
$607$			33.7633i			1.37041i	−0.728349	+	0.685206i	$0.759712\pi$
$608$	−17.9888	−	13.5149i	−0.729541	−	0.548101i
$609$		0			0
$610$	−23.1032	−	25.5540i	−0.935422	−	1.03465i
$611$	−26.9998	+	11.1837i	−1.09229	+	0.452443i
$612$		0			0
$613$	−4.90460	+	11.8407i	−0.198095	+	0.478243i	−0.991445	−	0.130522i	$-0.958335\pi$
$613$	−4.90460	+	11.8407i	−0.198095	+	0.478243i	0.793351	+	0.608765i	$0.208335\pi$
$614$	38.6736	+	18.3499i	1.56074	+	0.740543i
$615$		0			0
$616$	−0.218010	+	0.360681i	−0.00878387	+	0.0145323i
$617$	−34.8951	−	34.8951i	−1.40482	−	1.40482i	−0.783760	−	0.621064i	$-0.786701\pi$
$617$	−34.8951	−	34.8951i	−1.40482	−	1.40482i	−0.621064	−	0.783760i	$-0.713299\pi$
$618$		0			0
$619$	4.75222	−	11.4729i	0.191008	−	0.461134i	−0.799142	−	0.601142i	$-0.794713\pi$
$619$	4.75222	−	11.4729i	0.191008	−	0.461134i	0.990150	+	0.140008i	$0.0447127\pi$
$620$	−9.33411	−	5.01896i	−0.374867	−	0.201566i
$621$		0			0
$622$	−38.9931	−	1.96403i	−1.56348	−	0.0787505i
$623$			8.31186i			0.333008i
$624$		0			0
$625$		−	16.9843i		−	0.679370i
$626$	−1.54128	+	30.5999i	−0.0616018	+	1.22302i
$627$		0			0
$628$	−2.02396	−	6.73209i	−0.0807647	−	0.268640i
$629$	−9.45739	+	22.8322i	−0.377091	+	0.910378i
$630$		0			0
$631$	−2.46865	−	2.46865i	−0.0982753	−	0.0982753i	0.656260	−	0.754535i	$-0.272138\pi$
$631$	−2.46865	−	2.46865i	−0.0982753	−	0.0982753i	−0.754535	+	0.656260i	$0.772138\pi$
$632$	28.8019	−	21.1955i	1.14568	−	0.843111i
$633$		0			0
$634$	−12.7954	+	26.9671i	−0.508169	+	1.07100i
$635$	12.5980	−	30.4143i	0.499937	−	1.20696i
$636$		0			0
$637$	−18.0162	+	7.46253i	−0.713826	+	0.295676i
$638$	0.503320	−	0.455048i	0.0199266	−	0.0180155i
$639$		0			0
$640$	−21.8121	+	0.882038i	−0.862197	+	0.0348656i
$641$		−	38.1577i		−	1.50714i	−0.657368	−	0.753570i	$-0.728330\pi$
$641$		−	38.1577i		−	1.50714i	0.657368	−	0.753570i	$-0.271670\pi$
$642$		0			0
$643$	1.23595	+	2.98384i	0.0487411	+	0.117671i	0.946375	−	0.323071i	$-0.104715\pi$
$643$	1.23595	+	2.98384i	0.0487411	+	0.117671i	−0.897634	+	0.440742i	$0.854715\pi$
$644$	−3.88021	−	0.391877i	−0.152902	−	0.0154421i
$645$		0			0
$646$	24.4603	+	11.6059i	0.962376	+	0.456630i
$647$	21.3045	+	21.3045i	0.837567	+	0.837567i	0.988538	−	0.150971i	$-0.0482401\pi$
$647$	21.3045	+	21.3045i	0.837567	+	0.837567i	−0.150971	+	0.988538i	$0.548240\pi$
$648$		0			0
$649$	0.946557	−	0.946557i	0.0371556	−	0.0371556i
$650$	−5.32796	+	1.89893i	−0.208980	+	0.0744823i
$651$		0			0
$652$	−34.5848	+	10.3977i	−1.35445	+	0.407205i
$653$	−13.2549	+	5.49034i	−0.518703	+	0.214854i	−0.626647	−	0.779303i	$-0.715573\pi$
$653$	−13.2549	+	5.49034i	−0.518703	+	0.214854i	0.107944	+	0.994157i	$0.465573\pi$
$654$		0			0
$655$	−24.9661			−0.975506
$656$	−12.3318	−	18.6553i	−0.481475	−	0.728365i
$657$		0			0
$658$	−0.583923	+	11.5930i	−0.0227637	+	0.451941i
$659$	−11.5078	−	27.7824i	−0.448282	−	1.08225i	−0.972965	−	0.230951i	$-0.925816\pi$
$659$	−11.5078	−	27.7824i	−0.448282	−	1.08225i	0.524683	−	0.851297i	$-0.324184\pi$
$660$		0			0
$661$	28.8418	+	11.9467i	1.12182	+	0.464671i	0.864991	−	0.501787i	$-0.167324\pi$
$661$	28.8418	+	11.9467i	1.12182	+	0.464671i	0.256824	+	0.966458i	$0.417324\pi$
$662$	−28.1458	+	10.0314i	−1.09392	+	0.389882i
$663$		0			0
$664$	−26.6423	−	16.1036i	−1.03392	−	0.624942i
$665$	4.77359	−	4.77359i	0.185112	−	0.185112i
$666$		0			0
$667$	5.80092	+	2.40282i	0.224612	+	0.0930375i
$668$	25.6021	−	20.9051i	0.990574	−	0.808844i
$669$		0			0
$670$	23.5394	−	21.2818i	0.909408	−	0.822190i
$671$	2.13853			0.0825569
$672$		0			0
$673$	−40.9502			−1.57851			−0.789257	−	0.614063i	$-0.789534\pi$
$673$	−40.9502			−1.57851			−0.789257	+	0.614063i	$0.789534\pi$
$674$	7.48603	−	6.76807i	0.288351	−	0.260696i
$675$		0			0
$676$	4.03593	+	4.94272i	0.155228	+	0.190104i
$677$	−38.6124	−	15.9938i	−1.48399	−	0.614690i	−0.513994	−	0.857794i	$-0.671834\pi$
$677$	−38.6124	−	15.9938i	−1.48399	−	0.614690i	−0.970000	+	0.243104i	$0.921834\pi$
$678$		0			0
$679$	3.68438	−	3.68438i	0.141394	−	0.141394i
$680$	25.5040	−	6.28780i	0.978035	−	0.241126i
$681$		0			0
$682$	0.619704	−	0.220868i	0.0237297	−	0.00845748i
$683$	19.6686	+	8.14698i	0.752596	+	0.311736i	0.725800	−	0.687905i	$-0.241470\pi$
$683$	19.6686	+	8.14698i	0.752596	+	0.311736i	0.0267959	+	0.999641i	$0.491470\pi$
$684$		0			0
$685$	0.585790	+	1.41422i	0.0223819	+	0.0540346i
$686$	−0.827691	+	16.4326i	−0.0316014	+	0.627401i
$687$		0			0
$688$	3.66960	−	5.43347i	0.139902	−	0.207149i
$689$	1.49698			0.0570302
$690$		0			0
$691$	−0.338658	+	0.140277i	−0.0128832	+	0.00533638i	−0.389116	−	0.921189i	$-0.627219\pi$
$691$	−0.338658	+	0.140277i	−0.0128832	+	0.00533638i	0.376233	+	0.926525i	$0.377219\pi$
$692$	13.0577	+	43.4327i	0.496381	+	1.65106i
$693$		0			0
$694$	−37.7951	+	13.4705i	−1.43468	+	0.511334i
$695$	−15.5201	+	15.5201i	−0.588712	+	0.588712i
$696$		0			0
$697$	19.0274	+	19.0274i	0.720716	+	0.720716i
$698$	−30.0617	−	14.2637i	−1.13785	−	0.539889i
$699$		0			0
$700$	−0.225745	+	2.23524i	−0.00853236	+	0.0844842i
$701$	−17.6750	−	42.6712i	−0.667575	−	1.61167i	−0.785655	−	0.618665i	$-0.787674\pi$
$701$	−17.6750	−	42.6712i	−0.667575	−	1.61167i	0.118080	−	0.993004i	$-0.462326\pi$
$702$		0			0
$703$		−	20.4224i		−	0.770247i
$704$	0.867452	−	1.04112i	0.0326933	−	0.0392386i
$705$		0			0
$706$	−21.0518	+	19.0328i	−0.792295	+	0.716309i
$707$	−4.04128	+	1.67395i	−0.151988	+	0.0629555i
$708$		0			0
$709$	5.95722	−	14.3820i	0.223728	−	0.540127i	−0.771663	−	0.636032i	$-0.780575\pi$
$709$	5.95722	−	14.3820i	0.223728	−	0.540127i	0.995390	+	0.0959051i	$0.0305745\pi$
$710$	−10.3013	+	21.7107i	−0.386601	+	0.814787i
$711$		0			0
$712$	4.01976	−	26.4221i	0.150647	−	0.990211i
$713$	4.30478	+	4.30478i	0.161215	+	0.161215i
$714$		0			0
$715$	−0.391743	+	0.945751i	−0.0146504	+	0.0353691i
$716$	4.47152	−	1.34433i	0.167109	−	0.0502401i
$717$		0			0
$718$	0.231137	−	4.58891i	0.00862596	−	0.171256i
$719$			26.6063i			0.992249i	0.868251	+	0.496124i	$0.165244\pi$
$719$			26.6063i			0.992249i	−0.868251	+	0.496124i	$0.834756\pi$
$720$		0			0
$721$			0.316346i			0.0117813i
$722$	4.49112	+	0.226212i	0.167142	+	0.00841873i
$723$		0			0
$724$	9.13551	−	16.9900i	0.339519	−	0.631427i
$725$	1.38417	−	3.34169i	0.0514068	−	0.124107i
$726$		0			0
$727$	32.3093	+	32.3093i	1.19828	+	1.19828i	0.974680	+	0.223604i	$0.0717823\pi$
$727$	32.3093	+	32.3093i	1.19828	+	1.19828i	0.223604	+	0.974680i	$0.428218\pi$
$728$	−7.56589	+	1.86530i	−0.280411	+	0.0691328i
$729$		0			0
$730$	1.99782	+	0.947929i	0.0739426	+	0.0350844i
$731$	−3.01917	+	7.28891i	−0.111668	+	0.269590i
$732$		0			0
$733$	−25.7622	+	10.6711i	−0.951549	+	0.394145i	−0.803813	−	0.594882i	$-0.797199\pi$
$733$	−25.7622	+	10.6711i	−0.951549	+	0.394145i	−0.147736	+	0.989027i	$0.547199\pi$
$734$	6.86060	+	7.58838i	0.253230	+	0.280092i
$735$		0			0
$736$	12.1451	+	3.12226i	0.447674	+	0.115088i
$737$			1.96993i			0.0725634i
$738$		0			0
$739$	9.64374	+	23.2821i	0.354751	+	0.856444i	0.996020	+	0.0891284i	$0.0284081\pi$
$739$	9.64374	+	23.2821i	0.354751	+	0.856444i	−0.641269	+	0.767316i	$0.721592\pi$
$740$	−12.5320	−	15.3477i	−0.460687	−	0.564193i
$741$		0			0
$742$	0.254884	−	0.537184i	0.00935708	−	0.0197207i
$743$	−12.1679	−	12.1679i	−0.446396	−	0.446396i	0.447759	−	0.894154i	$-0.352222\pi$
$743$	−12.1679	−	12.1679i	−0.446396	−	0.446396i	−0.894154	+	0.447759i	$0.852222\pi$
$744$		0			0
$745$	−26.2930	+	26.2930i	−0.963301	+	0.963301i
$746$	−8.51432	−	23.8892i	−0.311731	−	0.874645i
$747$		0			0
$748$	−0.772232	+	1.43617i	−0.0282356	+	0.0525117i
$749$	3.63419	−	1.50533i	0.132790	−	0.0550035i
$750$		0			0
$751$	21.0598			0.768485			0.384242	−	0.923232i	$-0.374463\pi$
$751$	21.0598			0.768485			0.384242	+	0.923232i	$0.374463\pi$
$752$	7.46276	−	36.5699i	0.272139	−	1.33357i
$753$		0			0
$754$	12.5298	+	0.631111i	0.456310	+	0.0229837i
$755$	3.11397	+	7.51778i	0.113329	+	0.273600i
$756$		0			0
$757$	−31.7664	−	13.1581i	−1.15457	−	0.478238i	−0.278505	−	0.960435i	$-0.589839\pi$
$757$	−31.7664	−	13.1581i	−1.15457	−	0.478238i	−0.876063	+	0.482197i	$0.839839\pi$
$758$	−10.5325	−	29.5517i	−0.382557	−	1.07337i
$759$		0			0
$760$	−17.4831	+	12.8659i	−0.634179	+	0.466696i
$761$	−15.4825	+	15.4825i	−0.561240	+	0.561240i	−0.929660	−	0.368419i	$-0.879899\pi$
$761$	−15.4825	+	15.4825i	−0.561240	+	0.561240i	0.368419	+	0.929660i	$0.379899\pi$
$762$		0			0
$763$	−10.3949	−	4.30571i	−0.376321	−	0.155877i
$764$	−0.489487	+	4.84672i	−0.0177090	+	0.175348i
$765$		0			0
$766$	2.45045	+	2.71040i	0.0885384	+	0.0979306i
$767$	24.7509			0.893701
$768$		0			0
$769$	16.8973			0.609333			0.304666	−	0.952459i	$-0.401455\pi$
$769$	16.8973			0.609333			0.304666	+	0.952459i	$0.401455\pi$
$770$	0.272679	+	0.301605i	0.00982666	+	0.0108691i
$771$		0			0
$772$	4.75461	−	47.0784i	0.171122	−	1.69439i
$773$	−28.9525	−	11.9925i	−1.04135	−	0.431341i	−0.204553	−	0.978856i	$-0.565574\pi$
$773$	−28.9525	−	11.9925i	−1.04135	−	0.431341i	−0.836796	+	0.547515i	$0.815574\pi$
$774$		0			0
$775$	2.47982	−	2.47982i	0.0890777	−	0.0890777i
$776$	−13.4939	+	9.93025i	−0.484403	+	0.356475i
$777$		0			0
$778$	2.53574	+	7.11468i	0.0909105	+	0.255074i
$779$	−20.5441	−	8.50964i	−0.736068	−	0.304889i
$780$		0			0
$781$	−0.570869	−	1.37820i	−0.0204273	−	0.0493159i
$782$	−15.0702	−	0.759065i	−0.538908	−	0.0271441i
$783$		0			0
$784$	4.97968	−	24.4020i	0.177846	−	0.871500i
$785$	−6.78198			−0.242059
$786$		0			0
$787$	17.7032	−	7.33292i	0.631052	−	0.261390i	−0.0441479	−	0.999025i	$-0.514057\pi$
$787$	17.7032	−	7.33292i	0.631052	−	0.261390i	0.675200	+	0.737635i	$0.264057\pi$
$788$	−3.44653	+	6.40976i	−0.122778	+	0.228338i
$789$		0			0
$790$	−11.5824	−	32.4975i	−0.412083	−	1.15621i
$791$	−7.84892	+	7.84892i	−0.279075	+	0.279075i
$792$		0			0
$793$	27.9594	+	27.9594i	0.992867	+	0.992867i
$794$	−10.3108	+	21.7306i	−0.365916	+	0.771191i
$795$		0			0
$796$	8.16391	+	9.99816i	0.289362	+	0.354375i
$797$	−2.51784	−	6.07859i	−0.0891863	−	0.215315i	0.872992	−	0.487734i	$-0.162176\pi$
$797$	−2.51784	−	6.07859i	−0.0891863	−	0.215315i	−0.962179	+	0.272419i	$0.912176\pi$
$798$		0			0
$799$			44.9111i			1.58884i
$800$	1.79861	−	6.99632i	0.0635905	−	0.247357i
$801$		0			0
$802$	−12.8171	−	14.1767i	−0.452586	−	0.500596i
$803$	−0.126822	+	0.0525315i	−0.00447546	+	0.00185379i
$804$		0			0
$805$	−1.43984	+	3.47609i	−0.0507478	+	0.122516i
$806$	10.9898	+	5.21444i	0.387098	+	0.183671i
$807$		0			0
$808$	13.6562	−	3.36681i	0.480423	−	0.118444i
$809$	−26.1388	−	26.1388i	−0.918990	−	0.918990i	0.0779658	−	0.996956i	$-0.475158\pi$
$809$	−26.1388	−	26.1388i	−0.918990	−	0.918990i	−0.996956	+	0.0779658i	$0.975158\pi$
$810$		0			0
$811$	0.0990278	−	0.239074i	0.00347734	−	0.00839503i	−0.922131	−	0.386877i	$-0.873554\pi$
$811$	0.0990278	−	0.239074i	0.00347734	−	0.00839503i	0.925609	+	0.378482i	$0.123554\pi$
$812$	2.35988	−	4.38883i	0.0828154	−	0.154018i
$813$		0			0
$814$	1.22845	+	0.0618756i	0.0430573	+	0.00216874i
$815$			34.8411i			1.22043i
$816$		0			0
$817$		−	6.51964i		−	0.228093i
$818$	−1.54025	+	30.5796i	−0.0538537	+	1.06919i
$819$		0			0
$820$	−20.6610	+	6.21158i	−0.721512	+	0.216918i
$821$	−18.4263	+	44.4851i	−0.643083	+	1.55254i	0.179416	+	0.983773i	$0.442579\pi$
$821$	−18.4263	+	44.4851i	−0.643083	+	1.55254i	−0.822499	+	0.568767i	$0.807421\pi$
$822$		0			0
$823$	19.9395	+	19.9395i	0.695048	+	0.695048i	0.963338	−	0.268290i	$-0.0864585\pi$
$823$	19.9395	+	19.9395i	0.695048	+	0.695048i	−0.268290	+	0.963338i	$0.586459\pi$
$824$	0.152991	−	1.00562i	0.00532968	−	0.0350323i
$825$		0			0
$826$	4.21423	−	8.88175i	0.146632	−	0.309036i
$827$	9.96943	−	24.0683i	0.346671	−	0.836938i	−0.650337	−	0.759645i	$-0.725372\pi$
$827$	9.96943	−	24.0683i	0.346671	−	0.836938i	0.997008	−	0.0772925i	$-0.0246275\pi$
$828$		0			0
$829$	−0.308480	+	0.127777i	−0.0107140	+	0.00443787i	−0.388034	−	0.921645i	$-0.626846\pi$
$829$	−0.308480	+	0.127777i	−0.0107140	+	0.00443787i	0.377320	+	0.926083i	$0.376846\pi$
$830$	−22.2785	+	20.1418i	−0.773298	+	0.699133i
$831$		0			0
$832$	24.9529	−	2.27052i	0.865087	−	0.0787160i
$833$			29.9679i			1.03832i
$834$		0			0
$835$	−12.2030	−	29.4605i	−0.422301	−	1.01952i
$836$	0.135401	−	1.34068i	0.00468293	−	0.0463686i
$837$		0			0
$838$	9.68278	+	4.59430i	0.334486	+	0.158707i
$839$	−38.2282	−	38.2282i	−1.31978	−	1.31978i	−0.913944	−	0.405841i	$-0.866979\pi$
$839$	−38.2282	−	38.2282i	−1.31978	−	1.31978i	−0.405841	−	0.913944i	$-0.633021\pi$
$840$		0			0
$841$	14.8332	−	14.8332i	0.511491	−	0.511491i
$842$	−15.4846	+	5.51885i	−0.533634	+	0.190192i
$843$		0			0
$844$	−2.29143	−	7.62175i	−0.0788742	−	0.262352i
$845$	5.68763	−	2.35589i	0.195660	−	0.0810452i
$846$		0			0
$847$	9.65084			0.331607
$848$	−1.07003	+	1.58436i	−0.0367449	+	0.0544071i
$849$		0			0
$850$	−0.437268	+	8.68134i	−0.0149982	+	0.297768i
$851$	4.35575	+	10.5157i	0.149313	+	0.360474i
$852$		0			0
$853$	5.42158	+	2.24569i	0.185631	+	0.0768911i	0.473563	−	0.880760i	$-0.342968\pi$
$853$	5.42158	+	2.24569i	0.185631	+	0.0768911i	−0.287932	+	0.957651i	$0.592968\pi$
$854$	14.7937	−	5.27259i	0.506229	−	0.180424i
$855$		0			0
$856$	−12.2805	+	3.02766i	−0.419740	+	0.103483i
$857$	16.3557	−	16.3557i	0.558701	−	0.558701i	−0.370236	−	0.928938i	$-0.620723\pi$
$857$	16.3557	−	16.3557i	0.558701	−	0.558701i	0.928938	+	0.370236i	$0.120723\pi$
$858$		0			0
$859$	30.2965	+	12.5492i	1.03370	+	0.428175i	0.834048	−	0.551691i	$-0.186017\pi$
$859$	30.2965	+	12.5492i	1.03370	+	0.428175i	0.199657	+	0.979866i	$0.436017\pi$
$860$	−4.00071	−	4.89958i	−0.136423	−	0.167074i
$861$		0			0
$862$	37.4914	−	33.8957i	1.27696	−	1.15449i
$863$	8.63755			0.294026			0.147013	−	0.989135i	$-0.453034\pi$
$863$	8.63755			0.294026			0.147013	+	0.989135i	$0.453034\pi$
$864$		0			0
$865$	43.7546			1.48770
$866$	−38.0498	+	34.4006i	−1.29298	+	1.16898i
$867$		0			0
$868$	3.74237	−	3.05580i	0.127024	−	0.103720i
$869$	1.97863	+	0.819575i	0.0671204	+	0.0278022i
$870$		0			0
$871$	−25.7552	+	25.7552i	−0.872681	+	0.872681i
$872$	30.9615	+	18.7144i	1.04849	+	0.633748i
$873$		0			0
$874$	11.7457	−	4.18626i	0.397303	−	0.141602i
$875$	9.84285	+	4.07704i	0.332749	+	0.137829i
$876$		0			0
$877$	15.3895	+	37.1535i	0.519666	+	1.25458i	0.938109	+	0.346341i	$0.112576\pi$
$877$	15.3895	+	37.1535i	0.519666	+	1.25458i	−0.418443	+	0.908243i	$0.637424\pi$
$878$	−0.447433	+	8.88317i	−0.0151001	+	0.299792i
$879$		0			0
$880$	−0.720943	−	1.09063i	−0.0243030	−	0.0367650i
$881$	6.48388			0.218447			0.109224	−	0.994017i	$-0.465164\pi$
$881$	6.48388			0.218447			0.109224	+	0.994017i	$0.465164\pi$
$882$		0			0
$883$	0.658325	−	0.272687i	0.0221544	−	0.00917665i	−0.371579	−	0.928401i	$-0.621183\pi$
$883$	0.658325	−	0.272687i	0.0221544	−	0.00917665i	0.393733	+	0.919225i	$0.371183\pi$
$884$	−28.8730	+	8.68048i	−0.971105	+	0.291956i
$885$		0			0
$886$	1.05335	−	0.375424i	0.0353880	−	0.0126126i
$887$	−8.84672	+	8.84672i	−0.297044	+	0.297044i	−0.839855	−	0.542811i	$-0.817360\pi$
$887$	−8.84672	+	8.84672i	−0.297044	+	0.297044i	0.542811	+	0.839855i	$0.317360\pi$
$888$		0			0
$889$	10.6123	+	10.6123i	0.355924	+	0.355924i
$890$	−23.2949	−	11.0530i	−0.780847	−	0.370498i
$891$		0			0
$892$	30.1042	+	3.04033i	1.00796	+	0.101798i
$893$	−14.2027	−	34.2883i	−0.475274	−	1.14741i
$894$		0			0
$895$		−	4.50466i		−	0.150574i
$896$	3.43386	−	9.34085i	0.114717	−	0.312056i
$897$		0			0
$898$	9.91775	−	8.96657i	0.330960	−	0.299218i
$899$	−7.18650	+	2.97675i	−0.239683	+	0.0992801i
$900$		0			0
$901$	0.880366	−	2.12539i	0.0293293	−	0.0708071i
$902$	0.574117	−	1.20999i	0.0191160	−	0.0402882i
$903$		0			0
$904$	28.7464	−	21.1546i	0.956090	−	0.703592i
$905$	−13.1595	−	13.1595i	−0.437438	−	0.437438i
$906$		0			0
$907$	−12.3164	+	29.7344i	−0.408958	+	0.987313i	0.576454	+	0.817130i	$0.304436\pi$
$907$	−12.3164	+	29.7344i	−0.408958	+	0.987313i	−0.985412	+	0.170183i	$0.945564\pi$
$908$	−9.02114	−	30.0061i	−0.299377	−	0.995788i
$909$		0			0
$910$	−0.378181	+	7.50827i	−0.0125366	+	0.248897i
$911$			8.91656i			0.295419i	0.989031	+	0.147709i	$0.0471901\pi$
$911$			8.91656i			0.295419i	−0.989031	+	0.147709i	$0.952810\pi$
$912$		0			0
$913$		−	1.86441i		−	0.0617029i
$914$	16.8001	+	0.846200i	0.555699	+	0.0279898i
$915$		0			0
$916$	−10.3364	−	5.55790i	−0.341525	−	0.183638i
$917$	4.35562	−	10.5154i	0.143835	−	0.347249i
$918$		0			0
$919$	−6.38230	−	6.38230i	−0.210533	−	0.210533i	0.593961	−	0.804494i	$-0.297563\pi$
$919$	−6.38230	−	6.38230i	−0.210533	−	0.210533i	−0.804494	+	0.593961i	$0.797563\pi$
$920$	6.25814	−	10.3536i	0.206325	−	0.341349i
$921$		0			0
$922$	−31.3052	−	14.8537i	−1.03098	−	0.489181i
$923$	10.5552	−	25.4824i	0.347427	−	0.838764i
$924$		0			0
$925$	6.05770	−	2.50918i	0.199176	−	0.0825013i
$926$	−2.83072	−	3.13101i	−0.0930233	−	0.102891i
$927$		0			0
$928$	−9.62420	+	12.8101i	−0.315930	+	0.420513i
$929$			16.9849i			0.557256i	0.960399	+	0.278628i	$0.0898797\pi$
$929$			16.9849i			0.557256i	−0.960399	+	0.278628i	$0.910120\pi$
$930$		0			0
$931$	−9.47702	−	22.8795i	−0.310597	−	0.749847i
$932$	47.0757	−	38.4392i	1.54202	−	1.25912i
$933$		0			0
$934$	23.3005	−	49.1073i	0.762416	−	1.60684i
$935$	1.11239	+	1.11239i	0.0363789	+	0.0363789i
$936$		0			0
$937$	25.3804	−	25.3804i	0.829140	−	0.829140i	−0.158258	−	0.987398i	$-0.550588\pi$
$937$	25.3804	−	25.3804i	0.829140	−	0.829140i	0.987398	+	0.158258i	$0.0505877\pi$
$938$	4.85692	+	13.6274i	0.158584	+	0.444950i
$939$		0			0
$940$	−31.7141	−	17.0527i	−1.03440	−	0.556198i
$941$	−38.0076	+	15.7433i	−1.23901	+	0.513216i	−0.903406	−	0.428786i	$-0.858942\pi$
$941$	−38.0076	+	15.7433i	−1.23901	+	0.513216i	−0.335607	+	0.942002i	$0.608942\pi$
$942$		0			0
$943$	12.3933			0.403582
$944$	−17.6918	+	26.1957i	−0.575817	+	0.852596i
$945$		0			0
$946$	0.392170	+	0.0197531i	0.0127506	+	0.000642229i
$947$	10.0319	+	24.2192i	0.325993	+	0.787017i	0.998882	+	0.0472735i	$0.0150532\pi$
$947$	10.0319	+	24.2192i	0.325993	+	0.787017i	−0.672889	+	0.739744i	$0.734947\pi$
$948$		0			0
$949$	−2.34490	−	0.971288i	−0.0761185	−	0.0315293i
$950$	−2.41154	−	6.76622i	−0.0782407	−	0.219525i
$951$		0			0
$952$	−1.80114	+	11.8390i	−0.0583751	+	0.383703i
$953$	−7.72678	+	7.72678i	−0.250295	+	0.250295i	−0.821092	−	0.570797i	$-0.806634\pi$
$953$	−7.72678	+	7.72678i	−0.250295	+	0.250295i	0.570797	+	0.821092i	$0.306634\pi$
$954$		0			0
$955$	4.34193	+	1.79849i	0.140502	+	0.0581977i
$956$	30.9067	+	3.12138i	0.999594	+	0.100953i
$957$		0			0
$958$	−37.7744	−	41.7815i	−1.22043	−	1.34990i
$959$	−0.697850			−0.0225348
$960$		0			0
$961$	23.4580			0.756710
$962$	15.2520	+	16.8700i	0.491745	+	0.543909i
$963$		0			0
$964$	51.1970	+	5.17057i	1.64894	+	0.166533i
$965$	−42.1752	−	17.4695i	−1.35767	−	0.562364i
$966$		0			0
$967$	−14.9131	+	14.9131i	−0.479574	+	0.479574i	−0.904995	−	0.425421i	$-0.860126\pi$
$967$	−14.9131	+	14.9131i	−0.479574	+	0.479574i	0.425421	+	0.904995i	$0.360126\pi$
$968$	−30.6785	−	4.66731i	−0.986046	−	0.150013i
$969$		0			0
$970$	5.42645	+	15.2253i	0.174233	+	0.488856i
$971$	8.02125	+	3.32251i	0.257414	+	0.106624i	0.507659	−	0.861558i	$-0.330511\pi$
$971$	8.02125	+	3.32251i	0.257414	+	0.106624i	−0.250245	+	0.968183i	$0.580511\pi$
$972$		0			0
$973$	−3.82922	−	9.24455i	−0.122759	−	0.296367i
$974$	−43.1282	−	2.17231i	−1.38192	−	0.0696052i
$975$		0			0
$976$	−49.5767	+	9.60629i	−1.58691	+	0.307490i
$977$	29.7718			0.952484			0.476242	−	0.879314i	$-0.341999\pi$
$977$	29.7718			0.952484			0.476242	+	0.879314i	$0.341999\pi$
$978$		0			0
$979$	1.47877	−	0.612526i	0.0472616	−	0.0195764i
$980$	−21.1619	−	11.3788i	−0.675992	−	0.363481i
$981$		0			0
$982$	−13.8434	−	38.8415i	−0.441762	−	1.23948i
$983$	23.9283	−	23.9283i	0.763194	−	0.763194i	−0.213704	−	0.976898i	$-0.568553\pi$
$983$	23.9283	−	23.9283i	0.763194	−	0.763194i	0.976898	+	0.213704i	$0.0685528\pi$
$984$		0			0
$985$	4.96467	+	4.96467i	0.158187	+	0.158187i
$986$	8.26480	−	17.4186i	0.263205	−	0.554721i
$987$		0			0
$988$	19.2986	−	15.7581i	0.613969	−	0.501331i
$989$	1.39053	+	3.35703i	0.0442161	+	0.106747i
$990$		0			0
$991$		−	44.7052i		−	1.42011i	−0.704148	−	0.710054i	$-0.748671\pi$
$991$		−	44.7052i		−	1.42011i	0.704148	−	0.710054i	$-0.251329\pi$
$992$	−13.3742	+	7.90403i	−0.424633	+	0.250953i
$993$		0			0
$994$	−7.34709	−	8.12647i	−0.233035	−	0.257756i
$995$	11.5050	−	4.76552i	0.364732	−	0.151077i
$996$		0			0
$997$	−10.1630	+	24.5356i	−0.321864	+	0.777049i	0.677281	+	0.735724i	$0.263158\pi$
$997$	−10.1630	+	24.5356i	−0.321864	+	0.777049i	−0.999146	+	0.0413253i	$0.986842\pi$
$998$	−15.7051	−	7.45176i	−0.497135	−	0.235881i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.a.107.9	✓	128
3.2	odd	2	inner	864.2.w.a.107.24	yes	128
32.3	odd	8	inner	864.2.w.a.323.24	yes	128
96.35	even	8	inner	864.2.w.a.323.9	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.a.107.9	✓	128	1.1	even	1	trivial
864.2.w.a.107.24	yes	128	3.2	odd	2	inner
864.2.w.a.323.9	yes	128	96.35	even	8	inner
864.2.w.a.323.24	yes	128	32.3	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.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.948429 - 1.04904i) q^{2} +(-0.200965 + 1.98988i) q^{4} +(1.78263 + 0.738390i) q^{5} +(-0.622002 + 0.622002i) q^{7} +(2.27806 - 1.67644i) q^{8} +O(q^{10})\)	\(q+(-0.948429 - 1.04904i) q^{2} +(-0.200965 + 1.98988i) q^{4} +(1.78263 + 0.738390i) q^{5} +(-0.622002 + 0.622002i) q^{7} +(2.27806 - 1.67644i) q^{8} +(-0.916100 - 2.57036i) q^{10} +(0.156498 + 0.0648236i) q^{11} +(1.19856 + 2.89359i) q^{13} +(1.24243 + 0.0625795i) q^{14} +(-3.91923 - 0.799791i) q^{16} +4.81317 q^{17} +(-3.67470 + 1.52211i) q^{19} +(-1.82755 + 3.39883i) q^{20} +(-0.0804248 - 0.225653i) q^{22} +(1.56750 - 1.56750i) q^{23} +(-0.902976 - 0.902976i) q^{25} +(1.89874 - 4.00171i) q^{26} +(-1.11271 - 1.36271i) q^{28} +(1.08392 + 2.61682i) q^{29} +2.74627i q^{31} +(2.87810 + 4.86997i) q^{32} +(-4.56495 - 5.04920i) q^{34} +(-1.56808 + 0.649520i) q^{35} +(-1.96490 + 4.74369i) q^{37} +(5.08195 + 2.41129i) q^{38} +(5.29881 - 1.30637i) q^{40} +(3.95321 + 3.95321i) q^{41} +(-0.627273 + 1.51437i) q^{43} +(-0.160442 + 0.298385i) q^{44} +(-3.13103 - 0.157706i) q^{46} +9.33089i q^{47} +6.22623i q^{49} +(-0.0908483 + 1.80367i) q^{50} +(-5.99876 + 1.80349i) q^{52} +(0.182908 - 0.441579i) q^{53} +(0.231113 + 0.231113i) q^{55} +(-0.374210 + 2.45971i) q^{56} +(1.71712 - 3.61895i) q^{58} +(3.02418 - 7.30102i) q^{59} +(11.6637 - 4.83126i) q^{61} +(2.88094 - 2.60464i) q^{62} +(2.37911 - 7.63805i) q^{64} +6.04322i q^{65} +(4.45039 + 10.7442i) q^{67} +(-0.967277 + 9.57761i) q^{68} +(2.16859 + 1.02895i) q^{70} +(-6.22714 - 6.22714i) q^{71} +(-0.573022 + 0.573022i) q^{73} +(6.83988 - 2.43779i) q^{74} +(-2.29033 - 7.61810i) q^{76} +(-0.137662 + 0.0570216i) q^{77} +12.6432 q^{79} +(-6.39598 - 4.31965i) q^{80} +(0.397731 - 7.89640i) q^{82} +(-4.21199 - 10.1686i) q^{83} +(8.58010 + 3.55400i) q^{85} +(2.18356 - 0.778239i) q^{86} +(0.465184 - 0.114687i) q^{88} +(6.68154 - 6.68154i) q^{89} +(-2.54533 - 1.05431i) q^{91} +(2.80412 + 3.43415i) q^{92} +(9.78847 - 8.84969i) q^{94} -7.67456 q^{95} -5.92342 q^{97} +(6.53155 - 5.90513i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

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