LMFDB - Embedded newform 288.2.v.c.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			181.2
Character	$\chi$	$=$	288.181
Dual form			288.2.v.c.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14926 + 0.824131i) q^{2} +(0.641617 - 1.89429i) q^{4} +(-0.549515 + 1.32665i) q^{5} +(0.197478 + 0.197478i) q^{7} +(0.823754 + 2.70581i) q^{8} +O(q^{10})$	\(q+(-1.14926 + 0.824131i) q^{2} +(0.641617 - 1.89429i) q^{4} +(-0.549515 + 1.32665i) q^{5} +(0.197478 + 0.197478i) q^{7} +(0.823754 + 2.70581i) q^{8} +(-0.461792 - 1.97754i) q^{10} +(0.658433 + 0.272732i) q^{11} +(0.906224 + 2.18782i) q^{13} +(-0.389702 - 0.0642066i) q^{14} +(-3.17666 - 2.43081i) q^{16} +4.76970i q^{17} +(1.97066 + 4.75760i) q^{19} +(2.16047 + 1.89214i) q^{20} +(-0.981481 + 0.229194i) q^{22} +(2.40435 - 2.40435i) q^{23} +(2.07751 + 2.07751i) q^{25} +(-2.84454 - 1.76753i) q^{26} +(0.500785 - 0.247375i) q^{28} +(-6.15869 + 2.55101i) q^{29} -4.22524 q^{31} +(5.65413 + 0.175669i) q^{32} +(-3.93086 - 5.48165i) q^{34} +(-0.370500 + 0.153466i) q^{35} +(-3.16327 + 7.63680i) q^{37} +(-6.18570 - 3.84366i) q^{38} +(-4.04232 - 0.394055i) q^{40} +(-0.581135 + 0.581135i) q^{41} +(7.48124 + 3.09883i) q^{43} +(0.939095 - 1.07227i) q^{44} +(-0.781734 + 4.74473i) q^{46} -11.1004i q^{47} -6.92201i q^{49} +(-4.09975 - 0.675469i) q^{50} +(4.72581 - 0.312908i) q^{52} +(5.34257 + 2.21296i) q^{53} +(-0.723637 + 0.723637i) q^{55} +(-0.371665 + 0.697011i) q^{56} +(4.97559 - 8.00735i) q^{58} +(5.69609 - 13.7516i) q^{59} +(-4.01893 + 1.66470i) q^{61} +(4.85591 - 3.48215i) q^{62} +(-6.64286 + 4.45785i) q^{64} -3.40044 q^{65} +(2.28719 - 0.947386i) q^{67} +(9.03520 + 3.06032i) q^{68} +(0.299326 - 0.481714i) q^{70} +(6.50799 + 6.50799i) q^{71} +(7.33562 - 7.33562i) q^{73} +(-2.65829 - 11.3837i) q^{74} +(10.2767 - 0.680446i) q^{76} +(0.0761674 + 0.183884i) q^{77} -9.45819i q^{79} +(4.97045 - 2.87853i) q^{80} +(0.188946 - 1.14681i) q^{82} +(-0.902594 - 2.17905i) q^{83} +(-6.32771 - 2.62102i) q^{85} +(-11.1518 + 2.60414i) q^{86} +(-0.195575 + 2.00626i) q^{88} +(-6.06214 - 6.06214i) q^{89} +(-0.253086 + 0.611005i) q^{91} +(-3.01186 - 6.09720i) q^{92} +(9.14821 + 12.7573i) q^{94} -7.39456 q^{95} +5.92830 q^{97} +(5.70464 + 7.95521i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 8 q^{16} - 24 q^{22} - 40 q^{28} + 48 q^{31} - 40 q^{34} - 72 q^{40} + 16 q^{43} - 32 q^{46} - 8 q^{52} + 32 q^{55} - 32 q^{58} - 32 q^{61} + 72 q^{64} + 16 q^{67} + 120 q^{70} + 72 q^{76} + 120 q^{82} + 128 q^{88} - 48 q^{91} + 80 q^{94}+O(q^{100}) $ 32 * q - 8 * q^10 - 8 * q^16 - 24 * q^22 - 40 * q^28 + 48 * q^31 - 40 * q^34 - 72 * q^40 + 16 * q^43 - 32 * q^46 - 8 * q^52 + 32 * q^55 - 32 * q^58 - 32 * q^61 + 72 * q^64 + 16 * q^67 + 120 * q^70 + 72 * q^76 + 120 * q^82 + 128 * q^88 - 48 * q^91 + 80 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$1$

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 $

$2$	−1.14926	+	0.824131i	−0.812653	+	0.582748i
$2$	−1.14926	+	0.824131i	−0.812653	+	0.582748i
$3$		0			0
$3$		0			0
$4$	0.641617	−	1.89429i	0.320808	−	0.947144i
$5$	−0.549515	+	1.32665i	−0.245750	+	0.593294i	−0.997835	−	0.0657731i	$-0.979049\pi$
$5$	−0.549515	+	1.32665i	−0.245750	+	0.593294i	0.752084	+	0.659067i	$0.229049\pi$
$6$		0			0
$7$	0.197478	+	0.197478i	0.0746396	+	0.0746396i	0.743441	−	0.668801i	$-0.233192\pi$
$7$	0.197478	+	0.197478i	0.0746396	+	0.0746396i	−0.668801	+	0.743441i	$0.733192\pi$
$8$	0.823754	+	2.70581i	0.291241	+	0.956650i
$9$		0			0
$10$	−0.461792	−	1.97754i	−0.146031	−	0.625353i
$11$	0.658433	+	0.272732i	0.198525	+	0.0822318i	0.479731	−	0.877416i	$-0.340734\pi$
$11$	0.658433	+	0.272732i	0.198525	+	0.0822318i	−0.281206	+	0.959648i	$0.590734\pi$
$12$		0			0
$13$	0.906224	+	2.18782i	0.251341	+	0.606792i	0.998313	−	0.0580644i	$-0.0184929\pi$
$13$	0.906224	+	2.18782i	0.251341	+	0.606792i	−0.746972	+	0.664856i	$0.768493\pi$
$14$	−0.389702	−	0.0642066i	−0.104152	−	0.0171599i
$15$		0			0
$16$	−3.17666	−	2.43081i	−0.794164	−	0.607704i
$17$			4.76970i			1.15682i	0.815745	+	0.578412i	$0.196327\pi$
$17$			4.76970i			1.15682i	−0.815745	+	0.578412i	$0.803673\pi$
$18$		0			0
$19$	1.97066	+	4.75760i	0.452101	+	1.09147i	0.971522	+	0.236950i	$0.0761476\pi$
$19$	1.97066	+	4.75760i	0.452101	+	1.09147i	−0.519421	+	0.854518i	$0.673852\pi$
$20$	2.16047	+	1.89214i	0.483096	+	0.423095i
$21$		0			0
$22$	−0.981481	+	0.229194i	−0.209252	+	0.0488643i
$23$	2.40435	−	2.40435i	0.501341	−	0.501341i	−0.410514	−	0.911855i	$-0.634651\pi$
$23$	2.40435	−	2.40435i	0.501341	−	0.501341i	0.911855	+	0.410514i	$0.134651\pi$
$24$		0			0
$25$	2.07751	+	2.07751i	0.415502	+	0.415502i
$26$	−2.84454	−	1.76753i	−0.557860	−	0.346642i
$27$		0			0
$28$	0.500785	−	0.247375i	0.0946394	−	0.0467494i
$29$	−6.15869	+	2.55101i	−1.14364	+	0.473711i	−0.872396	−	0.488800i	$-0.837435\pi$
$29$	−6.15869	+	2.55101i	−1.14364	+	0.473711i	−0.271244	+	0.962511i	$0.587435\pi$
$30$		0			0
$31$	−4.22524			−0.758875			−0.379437	−	0.925217i	$-0.623882\pi$
$31$	−4.22524			−0.758875			−0.379437	+	0.925217i	$0.623882\pi$
$32$	5.65413	+	0.175669i	0.999518	+	0.0310541i
$33$		0			0
$34$	−3.93086	−	5.48165i	−0.674137	−	0.940095i
$35$	−0.370500	+	0.153466i	−0.0626259	+	0.0259405i
$36$		0			0
$37$	−3.16327	+	7.63680i	−0.520038	+	1.25548i	0.417841	+	0.908520i	$0.362787\pi$
$37$	−3.16327	+	7.63680i	−0.520038	+	1.25548i	−0.937879	+	0.346963i	$0.887213\pi$
$38$	−6.18570	−	3.84366i	−1.00345	−	0.623523i
$39$		0			0
$40$	−4.04232	−	0.394055i	−0.639147	−	0.0623055i
$41$	−0.581135	+	0.581135i	−0.0907580	+	0.0907580i	−0.751028	−	0.660270i	$-0.770442\pi$
$41$	−0.581135	+	0.581135i	−0.0907580	+	0.0907580i	0.660270	+	0.751028i	$0.270442\pi$
$42$		0			0
$43$	7.48124	+	3.09883i	1.14088	+	0.472567i	0.871465	−	0.490458i	$-0.163170\pi$
$43$	7.48124	+	3.09883i	1.14088	+	0.472567i	0.269413	+	0.963025i	$0.413170\pi$
$44$	0.939095	−	1.07227i	0.141574	−	0.161651i
$45$		0			0
$46$	−0.781734	+	4.74473i	−0.115260	+	0.699572i
$47$		−	11.1004i		−	1.61917i	−0.587006	−	0.809583i	$-0.699694\pi$
$47$		−	11.1004i		−	1.61917i	0.587006	−	0.809583i	$-0.300306\pi$
$48$		0			0
$49$		−	6.92201i		−	0.988858i
$50$	−4.09975	−	0.675469i	−0.579792	−	0.0955257i
$51$		0			0
$52$	4.72581	−	0.312908i	0.655352	−	0.0433926i
$53$	5.34257	+	2.21296i	0.733858	+	0.303974i	0.718136	−	0.695902i	$-0.244995\pi$
$53$	5.34257	+	2.21296i	0.733858	+	0.303974i	0.0157218	+	0.999876i	$0.494995\pi$
$54$		0			0
$55$	−0.723637	+	0.723637i	−0.0975753	+	0.0975753i
$56$	−0.371665	+	0.697011i	−0.0496658	+	0.0931420i
$57$		0			0
$58$	4.97559	−	8.00735i	0.653327	−	1.05142i
$59$	5.69609	−	13.7516i	0.741567	−	1.79030i	0.142183	−	0.989840i	$-0.454588\pi$
$59$	5.69609	−	13.7516i	0.741567	−	1.79030i	0.599384	−	0.800461i	$-0.295412\pi$
$60$		0			0
$61$	−4.01893	+	1.66470i	−0.514571	+	0.213142i	−0.624830	−	0.780760i	$-0.714832\pi$
$61$	−4.01893	+	1.66470i	−0.514571	+	0.213142i	0.110259	+	0.993903i	$0.464832\pi$
$62$	4.85591	−	3.48215i	0.616702	−	0.442233i
$63$		0			0
$64$	−6.64286	+	4.45785i	−0.830357	+	0.557231i
$65$	−3.40044			−0.421773
$66$		0			0
$67$	2.28719	−	0.947386i	0.279425	−	0.115742i	−0.238570	−	0.971125i	$-0.576679\pi$
$67$	2.28719	−	0.947386i	0.279425	−	0.115742i	0.517995	+	0.855384i	$0.326679\pi$
$68$	9.03520	+	3.06032i	1.09568	+	0.371119i
$69$		0			0
$70$	0.299326	−	0.481714i	0.0357763	−	0.0575758i
$71$	6.50799	+	6.50799i	0.772356	+	0.772356i	0.978518	−	0.206162i	$-0.0660974\pi$
$71$	6.50799	+	6.50799i	0.772356	+	0.772356i	−0.206162	+	0.978518i	$0.566097\pi$
$72$		0			0
$73$	7.33562	−	7.33562i	0.858570	−	0.858570i	−0.132600	−	0.991170i	$-0.542333\pi$
$73$	7.33562	−	7.33562i	0.858570	−	0.858570i	0.991170	+	0.132600i	$0.0423325\pi$
$74$	−2.65829	−	11.3837i	−0.309020	−	1.32332i
$75$		0			0
$76$	10.2767	−	0.680446i	1.17882	−	0.0780525i
$77$	0.0761674	+	0.183884i	0.00868008	+	0.0209556i
$78$		0			0
$79$		−	9.45819i		−	1.06413i	−0.846704	−	0.532065i	$-0.821416\pi$
$79$		−	9.45819i		−	1.06413i	0.846704	−	0.532065i	$-0.178584\pi$
$80$	4.97045	−	2.87853i	0.555713	−	0.321829i
$81$		0			0
$82$	0.188946	−	1.14681i	0.0208656	−	0.126644i
$83$	−0.902594	−	2.17905i	−0.0990726	−	0.239182i	0.866570	−	0.499055i	$-0.166319\pi$
$83$	−0.902594	−	2.17905i	−0.0990726	−	0.239182i	−0.965643	+	0.259873i	$0.916319\pi$
$84$		0			0
$85$	−6.32771	−	2.62102i	−0.686336	−	0.284290i
$86$	−11.1518	+	2.60414i	−1.20253	+	0.280812i
$87$		0			0
$88$	−0.195575	+	2.00626i	−0.0208484	+	0.213868i
$89$	−6.06214	−	6.06214i	−0.642585	−	0.642585i	0.308605	−	0.951190i	$-0.400138\pi$
$89$	−6.06214	−	6.06214i	−0.642585	−	0.642585i	−0.951190	+	0.308605i	$0.900138\pi$
$90$		0			0
$91$	−0.253086	+	0.611005i	−0.0265307	+	0.0640507i
$92$	−3.01186	−	6.09720i	−0.314008	−	0.635677i
$93$		0			0
$94$	9.14821	+	12.7573i	0.943566	+	1.31582i
$95$	−7.39456			−0.758665
$96$		0			0
$97$	5.92830			0.601928			0.300964	−	0.953636i	$-0.402692\pi$
$97$	5.92830			0.601928			0.300964	+	0.953636i	$0.402692\pi$
$98$	5.70464	+	7.95521i	0.576255	+	0.803598i
$99$		0			0
$100$	5.26837	−	2.60244i	0.526837	−	0.260244i
$101$	0.311082	−	0.751019i	0.0309539	−	0.0747292i	−0.907647	−	0.419735i	$-0.862123\pi$
$101$	0.311082	−	0.751019i	0.0309539	−	0.0747292i	0.938601	+	0.345006i	$0.112123\pi$
$102$		0			0
$103$	−11.4922	−	11.4922i	−1.13236	−	1.13236i	−0.989784	−	0.142577i	$-0.954461\pi$
$103$	−11.4922	−	11.4922i	−1.13236	−	1.13236i	−0.142577	−	0.989784i	$-0.545539\pi$
$104$	−5.17332	+	4.25430i	−0.507286	+	0.417168i
$105$		0			0
$106$	−7.96379	+	1.85969i	−0.773512	+	0.180629i
$107$	8.12637	+	3.36605i	0.785606	+	0.325409i	0.739176	−	0.673513i	$-0.235215\pi$
$107$	8.12637	+	3.36605i	0.785606	+	0.325409i	0.0464307	+	0.998922i	$0.485215\pi$
$108$		0			0
$109$	1.04348	+	2.51918i	0.0999473	+	0.241294i	0.965942	−	0.258759i	$-0.0833137\pi$
$109$	1.04348	+	2.51918i	0.0999473	+	0.241294i	−0.865995	+	0.500053i	$0.833314\pi$
$110$	0.235279	−	1.42802i	0.0224330	−	0.136157i
$111$		0			0
$112$	−0.147287	−	1.10735i	−0.0139173	−	0.104635i
$113$			17.8114i			1.67555i	0.546012	+	0.837777i	$0.316145\pi$
$113$			17.8114i			1.67555i	−0.546012	+	0.837777i	$0.683855\pi$
$114$		0			0
$115$	1.86849	+	4.51094i	0.174238	+	0.420647i
$116$	0.880834	+	13.3031i	0.0817834	+	1.23516i
$117$		0			0
$118$	4.78678	+	20.4985i	0.440659	+	1.88704i
$119$	−0.941911	+	0.941911i	−0.0863448	+	0.0863448i
$120$		0			0
$121$	−7.41902	−	7.41902i	−0.674457	−	0.674457i
$122$	3.24689	−	5.22530i	0.293959	−	0.473076i
$123$		0			0
$124$	−2.71098	+	8.00382i	−0.243453	+	0.718764i
$125$	−10.5310	+	4.36207i	−0.941919	+	0.390156i
$126$		0			0
$127$	−14.2836			−1.26746			−0.633732	−	0.773552i	$-0.718478\pi$
$127$	−14.2836			−1.26746			−0.633732	+	0.773552i	$0.718478\pi$
$128$	3.96055	−	10.5978i	0.350066	−	0.936725i
$129$		0			0
$130$	3.90801	−	2.80241i	0.342755	−	0.245788i
$131$	−17.4764	+	7.23898i	−1.52692	+	0.632473i	−0.978964	−	0.204032i	$-0.934595\pi$
$131$	−17.4764	+	7.23898i	−1.52692	+	0.632473i	−0.547960	+	0.836504i	$0.684595\pi$
$132$		0			0
$133$	−0.550358	+	1.32868i	−0.0477221	+	0.115211i
$134$	−1.84782	+	2.97374i	−0.159627	+	0.256892i
$135$		0			0
$136$	−12.9059	+	3.92906i	−1.10667	+	0.336914i
$137$	9.34478	−	9.34478i	0.798378	−	0.798378i	−0.184461	−	0.982840i	$-0.559054\pi$
$137$	9.34478	−	9.34478i	0.798378	−	0.798378i	0.982840	+	0.184461i	$0.0590541\pi$
$138$		0			0
$139$	−1.05367	−	0.436446i	−0.0893714	−	0.0370188i	0.337550	−	0.941308i	$-0.390402\pi$
$139$	−1.05367	−	0.436446i	−0.0893714	−	0.0370188i	−0.426921	+	0.904289i	$0.640402\pi$
$140$	0.0529900	+	0.800300i	0.00447847	+	0.0676377i
$141$		0			0
$142$	−12.8428	−	2.11596i	−1.07775	−	0.177568i
$143$			1.68769i			0.141132i
$144$		0			0
$145$		−	9.57222i		−	0.794929i
$146$	−2.38506	+	14.4761i	−0.197389	+	1.19805i
$147$		0			0
$148$	12.4367	+	10.8920i	1.02229	+	0.895320i
$149$	16.7758	+	6.94875i	1.37432	+	0.569264i	0.942957	−	0.332913i	$-0.108032\pi$
$149$	16.7758	+	6.94875i	1.37432	+	0.569264i	0.431366	+	0.902177i	$0.358032\pi$
$150$		0			0
$151$	2.15407	−	2.15407i	0.175296	−	0.175296i	−0.614006	−	0.789302i	$-0.710443\pi$
$151$	2.15407	−	2.15407i	0.175296	−	0.175296i	0.789302	+	0.614006i	$0.210443\pi$
$152$	−11.2498	+	9.25134i	−0.912482	+	0.750382i
$153$		0			0
$154$	−0.239081	−	0.148560i	−0.0192657	−	0.0119713i
$155$	2.32183	−	5.60539i	0.186494	−	0.450236i
$156$		0			0
$157$	−13.3749	+	5.54008i	−1.06744	+	0.442146i	−0.846085	−	0.533048i	$-0.821046\pi$
$157$	−13.3749	+	5.54008i	−1.06744	+	0.442146i	−0.221351	+	0.975194i	$0.571046\pi$
$158$	7.79479	+	10.8700i	0.620120	+	0.864768i
$159$		0			0
$160$	−3.34007	+	7.40449i	−0.264056	+	0.585376i
$161$	0.949610			0.0748398
$162$		0			0
$163$	8.55073	−	3.54183i	0.669745	−	0.277417i	−0.0217879	−	0.999763i	$-0.506936\pi$
$163$	8.55073	−	3.54183i	0.669745	−	0.277417i	0.691533	+	0.722345i	$0.256936\pi$
$164$	0.727971	+	1.47370i	0.0568450	+	0.115077i
$165$		0			0
$166$	2.83314	+	1.76045i	0.219895	+	0.136638i
$167$	12.2164	+	12.2164i	0.945333	+	0.945333i	0.998581	−	0.0532484i	$-0.0169575\pi$
$167$	12.2164	+	12.2164i	0.945333	+	0.945333i	−0.0532484	+	0.998581i	$0.516958\pi$
$168$		0			0
$169$	5.22708	−	5.22708i	0.402083	−	0.402083i
$170$	9.43227	−	2.20261i	0.723422	−	0.168933i
$171$		0			0
$172$	10.6702	−	12.1834i	0.813592	−	0.928972i
$173$	−4.14975	−	10.0184i	−0.315500	−	0.761684i	−0.999482	−	0.0321850i	$-0.989753\pi$
$173$	−4.14975	−	10.0184i	−0.315500	−	0.761684i	0.683982	−	0.729499i	$-0.260247\pi$
$174$		0			0
$175$			0.820525i			0.0620258i
$176$	−1.42865	−	2.46690i	−0.107689	−	0.185950i
$177$		0			0
$178$	11.9630	+	1.97100i	0.896664	+	0.147733i
$179$	7.57201	+	18.2805i	0.565959	+	1.36635i	0.904935	+	0.425550i	$0.139920\pi$
$179$	7.57201	+	18.2805i	0.565959	+	1.36635i	−0.338976	+	0.940795i	$0.610080\pi$
$180$		0			0
$181$	4.25731	+	1.76344i	0.316443	+	0.131075i	0.535251	−	0.844693i	$-0.320217\pi$
$181$	4.25731	+	1.76344i	0.316443	+	0.131075i	−0.218808	+	0.975768i	$0.570217\pi$
$182$	−0.212685	−	0.910782i	−0.0157652	−	0.0675117i
$183$		0			0
$184$	8.48631	+	4.52513i	0.625619	+	0.333597i
$185$	−8.39307	−	8.39307i	−0.617071	−	0.617071i
$186$		0			0
$187$	−1.30085	+	3.14053i	−0.0951277	+	0.229658i
$188$	−21.0274	−	7.12223i	−1.53358	−	0.519442i
$189$		0			0
$190$	8.49830	−	6.09408i	0.616531	−	0.442111i
$191$	−16.2465			−1.17555			−0.587776	−	0.809023i	$-0.699997\pi$
$191$	−16.2465			−1.17555			−0.587776	+	0.809023i	$0.699997\pi$
$192$		0			0
$193$	3.56175			0.256381			0.128190	−	0.991750i	$-0.459083\pi$
$193$	3.56175			0.256381			0.128190	+	0.991750i	$0.459083\pi$
$194$	−6.81318	+	4.88570i	−0.489158	+	0.350772i
$195$		0			0
$196$	−13.1123	−	4.44128i	−0.936591	−	0.317234i
$197$	6.70549	−	16.1885i	0.477746	−	1.15338i	−0.482917	−	0.875666i	$-0.660423\pi$
$197$	6.70549	−	16.1885i	0.477746	−	1.15338i	0.960663	−	0.277715i	$-0.0895772\pi$
$198$		0			0
$199$	−5.07666	−	5.07666i	−0.359875	−	0.359875i	0.503892	−	0.863767i	$-0.331901\pi$
$199$	−5.07666	−	5.07666i	−0.359875	−	0.359875i	−0.863767	+	0.503892i	$0.831901\pi$
$200$	−3.91000	+	7.33272i	−0.276479	+	0.518501i
$201$		0			0
$202$	0.261422	+	1.11949i	0.0183936	+	0.0787672i
$203$	−1.71997	−	0.712436i	−0.120718	−	0.0500032i
$204$		0			0
$205$	−0.451618	−	1.09030i	−0.0315424	−	0.0761500i
$206$	22.6787	+	3.73650i	1.58010	+	0.260334i
$207$		0			0
$208$	2.43942	−	9.15281i	0.169143	−	0.634633i
$209$			3.67002i			0.253861i
$210$		0			0
$211$	−1.77896	−	4.29479i	−0.122469	−	0.295665i	0.850741	−	0.525585i	$-0.176154\pi$
$211$	−1.77896	−	4.29479i	−0.122469	−	0.295665i	−0.973210	+	0.229920i	$0.926154\pi$
$212$	7.61987	−	8.70049i	0.523335	−	0.597552i
$213$		0			0
$214$	−12.1134	+	2.82871i	−0.828056	+	0.193367i
$215$	−8.22210	+	8.22210i	−0.560742	+	0.560742i
$216$		0			0
$217$	−0.834390	−	0.834390i	−0.0566421	−	0.0566421i
$218$	−3.27537	−	2.03524i	−0.221836	−	0.137844i
$219$		0			0
$220$	0.906480	+	1.83508i	0.0611149	+	0.123721i
$221$	−10.4352	+	4.32242i	−0.701951	+	0.290758i
$222$		0			0
$223$	23.2291			1.55553			0.777766	−	0.628554i	$-0.216353\pi$
$223$	23.2291			1.55553			0.777766	+	0.628554i	$0.216353\pi$
$224$	1.08187	+	1.15125i	0.0722857	+	0.0769214i
$225$		0			0
$226$	−14.6789	−	20.4700i	−0.976427	−	1.36164i
$227$	−13.1469	+	5.44563i	−0.872591	+	0.361439i	−0.773619	−	0.633651i	$-0.781556\pi$
$227$	−13.1469	+	5.44563i	−0.872591	+	0.361439i	−0.0989722	+	0.995090i	$0.531556\pi$
$228$		0			0
$229$	0.698819	−	1.68710i	0.0461793	−	0.111487i	−0.899107	−	0.437730i	$-0.855783\pi$
$229$	0.698819	−	1.68710i	0.0461793	−	0.111487i	0.945286	+	0.326243i	$0.105783\pi$
$230$	−5.86500	−	3.64438i	−0.386726	−	0.240303i
$231$		0			0
$232$	−11.9758	−	14.5629i	−0.786250	−	0.956099i
$233$	19.5389	−	19.5389i	1.28003	−	1.28003i	0.339387	−	0.940647i	$-0.389780\pi$
$233$	19.5389	−	19.5389i	1.28003	−	1.28003i	0.940647	−	0.339387i	$-0.110220\pi$
$234$		0			0
$235$	14.7263	+	6.09985i	0.960641	+	0.397910i
$236$	−22.3947	−	19.6133i	−1.45777	−	1.27672i
$237$		0			0
$238$	0.306247	−	1.85876i	0.0198510	−	0.120486i
$239$		−	16.5111i		−	1.06801i	−0.845480	−	0.534007i	$-0.820685\pi$
$239$		−	16.5111i		−	1.06801i	0.845480	−	0.534007i	$-0.179315\pi$
$240$		0			0
$241$			15.9379i			1.02665i	0.858194	+	0.513326i	$0.171587\pi$
$241$			15.9379i			1.02665i	−0.858194	+	0.513326i	$0.828413\pi$
$242$	14.6407	+	2.41217i	0.941137	+	0.155060i
$243$		0			0
$244$	0.574799	+	8.68111i	0.0367978	+	0.555751i
$245$	9.18305	+	3.80374i	0.586683	+	0.243012i
$246$		0			0
$247$	−8.62290	+	8.62290i	−0.548662	+	0.548662i
$248$	−3.48056	−	11.4327i	−0.221015	−	0.725978i
$249$		0			0
$250$	8.50795	−	13.6921i	0.538090	−	0.865963i
$251$	−2.37460	+	5.73279i	−0.149883	+	0.361850i	−0.980933	−	0.194349i	$-0.937741\pi$
$251$	−2.37460	+	5.73279i	−0.149883	+	0.361850i	0.831049	+	0.556199i	$0.187741\pi$
$252$		0			0
$253$	2.23884	−	0.927360i	0.140755	−	0.0583026i
$254$	16.4156	−	11.7716i	1.03001	−	0.738613i
$255$		0			0
$256$	4.18228	+	15.4437i	0.261393	+	0.965233i
$257$	10.3907			0.648153			0.324076	−	0.946031i	$-0.394947\pi$
$257$	10.3907			0.648153			0.324076	+	0.946031i	$0.394947\pi$
$258$		0			0
$259$	−2.13277	+	0.883424i	−0.132524	+	0.0548933i
$260$	−2.18178	+	6.44142i	−0.135308	+	0.399480i
$261$		0			0
$262$	14.1192	−	22.7224i	0.872287	−	1.40379i
$263$	6.12958	+	6.12958i	0.377966	+	0.377966i	0.870368	−	0.492402i	$-0.163881\pi$
$263$	6.12958	+	6.12958i	0.377966	+	0.377966i	−0.492402	+	0.870368i	$0.663881\pi$
$264$		0			0
$265$	−5.87164	+	5.87164i	−0.360692	+	0.360692i
$266$	−0.462501	−	1.98057i	−0.0283577	−	0.121437i
$267$		0			0
$268$	−0.327121	−	4.94046i	−0.0199821	−	0.301787i
$269$	−8.84106	−	21.3442i	−0.539049	−	1.30138i	−0.925388	−	0.379022i	$-0.876260\pi$
$269$	−8.84106	−	21.3442i	−0.539049	−	1.30138i	0.386339	−	0.922357i	$-0.373740\pi$
$270$		0			0
$271$			2.17168i			0.131920i	0.997822	+	0.0659602i	$0.0210110\pi$
$271$			2.17168i			0.131920i	−0.997822	+	0.0659602i	$0.978989\pi$
$272$	11.5943	−	15.1517i	0.703006	−	0.918707i
$273$		0			0
$274$	−3.03830	+	18.4409i	−0.183550	+	1.11406i
$275$	0.801299	+	1.93451i	0.0483201	+	0.116655i
$276$		0			0
$277$	9.75823	+	4.04199i	0.586315	+	0.242860i	0.656064	−	0.754705i	$-0.272220\pi$
$277$	9.75823	+	4.04199i	0.586315	+	0.242860i	−0.0697493	+	0.997565i	$0.522220\pi$
$278$	1.57064	−	0.366773i	0.0942006	−	0.0219976i
$279$		0			0
$280$	−0.720451	−	0.876086i	−0.0430552	−	0.0523561i
$281$	−2.72202	−	2.72202i	−0.162382	−	0.162382i	0.621239	−	0.783621i	$-0.286630\pi$
$281$	−2.72202	−	2.72202i	−0.162382	−	0.162382i	−0.783621	+	0.621239i	$0.786630\pi$
$282$		0			0
$283$	−6.42704	+	15.5163i	−0.382048	+	0.922346i	0.609521	+	0.792770i	$0.291362\pi$
$283$	−6.42704	+	15.5163i	−0.382048	+	0.922346i	−0.991569	+	0.129576i	$0.958638\pi$
$284$	16.5036	−	8.15237i	0.979311	−	0.483754i
$285$		0			0
$286$	−1.39088	−	1.93960i	−0.0822442	−	0.114691i
$287$	−0.229522			−0.0135483
$288$		0			0
$289$	−5.75008			−0.338240
$290$	7.88876	+	11.0010i	0.463244	+	0.646001i
$291$		0			0
$292$	−9.18913	−	18.6024i	−0.537753	−	1.08863i
$293$	6.26393	−	15.1225i	0.365943	−	0.883464i	−0.628463	−	0.777839i	$-0.716316\pi$
$293$	6.26393	−	15.1225i	0.365943	−	0.883464i	0.994406	−	0.105625i	$-0.0336843\pi$
$294$		0			0
$295$	15.1134	+	15.1134i	0.879935	+	0.879935i
$296$	−23.2695	−	2.26837i	−1.35251	−	0.131846i
$297$		0			0
$298$	−25.0065	+	5.83947i	−1.44859	+	0.338272i
$299$	7.43915	+	3.08140i	0.430217	+	0.178202i
$300$		0			0
$301$	0.865428	+	2.08933i	0.0498824	+	0.120427i
$302$	−0.700361	+	4.25084i	−0.0403013	+	0.244608i
$303$		0			0
$304$	5.30473	−	19.9036i	0.304247	−	1.14155i
$305$		−	6.24647i		−	0.357672i
$306$		0			0
$307$	1.79868	+	4.34240i	0.102656	+	0.247834i	0.966860	−	0.255309i	$-0.0821771\pi$
$307$	1.79868	+	4.34240i	0.102656	+	0.247834i	−0.864203	+	0.503143i	$0.832177\pi$
$308$	0.397200	−	0.0262997i	0.0226326	−	0.00149856i
$309$		0			0
$310$	1.95118	+	8.35557i	0.110820	+	0.474564i
$311$	1.50351	−	1.50351i	0.0852560	−	0.0852560i	−0.663193	−	0.748449i	$-0.730799\pi$
$311$	1.50351	−	1.50351i	0.0852560	−	0.0852560i	0.748449	+	0.663193i	$0.230799\pi$
$312$		0			0
$313$	13.7776	+	13.7776i	0.778756	+	0.778756i	0.979619	−	0.200863i	$-0.0643746\pi$
$313$	13.7776	+	13.7776i	0.778756	+	0.778756i	−0.200863	+	0.979619i	$0.564375\pi$
$314$	10.8056	−	17.3897i	0.609794	−	0.981358i
$315$		0			0
$316$	−17.9165	−	6.06854i	−1.00788	−	0.341382i
$317$	4.26285	−	1.76573i	0.239425	−	0.0991732i	−0.259745	−	0.965677i	$-0.583638\pi$
$317$	4.26285	−	1.76573i	0.239425	−	0.0991732i	0.499170	+	0.866504i	$0.333638\pi$
$318$		0			0
$319$	−4.75083			−0.265995
$320$	−2.26364	−	11.2624i	−0.126541	−	0.629586i
$321$		0			0
$322$	−1.09135	+	0.782603i	−0.0608187	+	0.0436128i
$323$	−22.6923	+	9.39948i	−1.26264	+	0.523001i
$324$		0			0
$325$	−2.66253	+	6.42791i	−0.147690	+	0.356556i
$326$	−6.90812	+	11.1174i	−0.382605	+	0.615737i
$327$		0			0
$328$	−2.05115	−	1.09373i	−0.113256	−	0.0603912i
$329$	2.19209	−	2.19209i	0.120854	−	0.120854i
$330$		0			0
$331$	−25.0582	−	10.3794i	−1.37732	−	0.570505i	−0.433558	−	0.901126i	$-0.642742\pi$
$331$	−25.0582	−	10.3794i	−1.37732	−	0.570505i	−0.943764	+	0.330621i	$0.892742\pi$
$332$	−4.70688	+	0.311655i	−0.258323	+	0.0171043i
$333$		0			0
$334$	−24.1078	−	3.97196i	−1.31912	−	0.217336i
$335$			3.55490i			0.194225i
$336$		0			0
$337$			13.8768i			0.755918i	0.925822	+	0.377959i	$0.123374\pi$
$337$			13.8768i			0.755918i	−0.925822	+	0.377959i	$0.876626\pi$
$338$	−1.69950	+	10.3151i	−0.0924406	+	0.561067i
$339$		0			0
$340$	−9.02494	+	10.3048i	−0.489446	+	0.558857i
$341$	−2.78204	−	1.15236i	−0.150656	−	0.0624036i
$342$		0			0
$343$	2.74929	−	2.74929i	0.148448	−	0.148448i
$344$	−2.22216	+	22.7955i	−0.119811	+	1.22905i
$345$		0			0
$346$	13.0256	+	8.09384i	0.700262	+	0.435127i
$347$	8.38549	−	20.2444i	0.450156	−	1.08677i	−0.522106	−	0.852881i	$-0.674853\pi$
$347$	8.38549	−	20.2444i	0.450156	−	1.08677i	0.972262	−	0.233893i	$-0.0751466\pi$
$348$		0			0
$349$	19.7956	−	8.19962i	1.05964	−	0.438915i	0.216313	−	0.976324i	$-0.430597\pi$
$349$	19.7956	−	8.19962i	1.05964	−	0.438915i	0.843322	+	0.537409i	$0.180597\pi$
$350$	−0.676220	−	0.943000i	−0.0361455	−	0.0504055i
$351$		0			0
$352$	3.67495	+	1.65773i	0.195876	+	0.0883572i
$353$	2.44302			0.130029			0.0650143	−	0.997884i	$-0.479291\pi$
$353$	2.44302			0.130029			0.0650143	+	0.997884i	$0.479291\pi$
$354$		0			0
$355$	−12.2100	+	5.05756i	−0.648041	+	0.268427i
$356$	−15.3730	+	7.59387i	−0.814768	+	0.402474i
$357$		0			0
$358$	−23.7677	−	14.7687i	−1.25616	−	0.780553i
$359$	12.2454	+	12.2454i	0.646286	+	0.646286i	0.952093	−	0.305808i	$-0.0989264\pi$
$359$	12.2454	+	12.2454i	0.646286	+	0.646286i	−0.305808	+	0.952093i	$0.598926\pi$
$360$		0			0
$361$	−5.31621	+	5.31621i	−0.279801	+	0.279801i
$362$	−6.34608	+	1.48193i	−0.333542	+	0.0778883i
$363$		0			0
$364$	0.995034	+	0.871449i	0.0521540	+	0.0456764i
$365$	5.70074	+	13.7628i	0.298390	+	0.720378i
$366$		0			0
$367$			29.9743i			1.56465i	0.622873	+	0.782323i	$0.285966\pi$
$367$			29.9743i			1.56465i	−0.622873	+	0.782323i	$0.714034\pi$
$368$	−13.4823	+	1.79326i	−0.702814	+	0.0934802i
$369$		0			0
$370$	16.5628	+	2.72887i	0.861061	+	0.141867i
$371$	0.618027	+	1.49205i	0.0320864	+	0.0774634i
$372$		0			0
$373$	−4.87833	−	2.02067i	−0.252590	−	0.104626i	0.252796	−	0.967520i	$-0.418650\pi$
$373$	−4.87833	−	2.02067i	−0.252590	−	0.104626i	−0.505386	+	0.862893i	$0.668650\pi$
$374$	−1.09319	−	4.68137i	−0.0565274	−	0.242068i
$375$		0			0
$376$	30.0357	−	9.14403i	1.54897	−	0.471567i
$377$	−11.1623	−	11.1623i	−0.574888	−	0.574888i
$378$		0			0
$379$	13.1597	−	31.7704i	0.675970	−	1.63194i	−0.0953165	−	0.995447i	$-0.530386\pi$
$379$	13.1597	−	31.7704i	0.675970	−	1.63194i	0.771286	−	0.636488i	$-0.219614\pi$
$380$	−4.74447	+	14.0074i	−0.243386	+	0.718565i
$381$		0			0
$382$	18.6715	−	13.3892i	0.955316	−	0.685052i
$383$	−30.0647			−1.53624			−0.768118	−	0.640309i	$-0.778806\pi$
$383$	−30.0647			−1.53624			−0.768118	+	0.640309i	$0.778806\pi$
$384$		0			0
$385$	−0.285805			−0.0145660
$386$	−4.09339	+	2.93535i	−0.208348	+	0.149405i
$387$		0			0
$388$	3.80370	−	11.2299i	0.193103	−	0.570112i
$389$	−6.46585	+	15.6099i	−0.327832	+	0.791455i	0.670921	+	0.741529i	$0.265899\pi$
$389$	−6.46585	+	15.6099i	−0.327832	+	0.791455i	−0.998753	+	0.0499268i	$0.984101\pi$
$390$		0			0
$391$	11.4680	+	11.4680i	0.579963	+	0.579963i
$392$	18.7297	−	5.70203i	0.945991	−	0.287996i
$393$		0			0
$394$	5.63505	+	24.1310i	0.283890	+	1.21570i
$395$	12.5477	+	5.19742i	0.631342	+	0.261510i
$396$		0			0
$397$	2.22883	+	5.38088i	0.111862	+	0.270059i	0.969890	−	0.243545i	$-0.0783103\pi$
$397$	2.22883	+	5.38088i	0.111862	+	0.270059i	−0.858028	+	0.513603i	$0.828310\pi$
$398$	10.0182	+	1.65059i	0.502169	+	0.0827366i
$399$		0			0
$400$	−1.54949	−	11.6496i	−0.0774747	−	0.582479i
$401$			23.8287i			1.18995i	0.803745	+	0.594974i	$0.202838\pi$
$401$			23.8287i			1.18995i	−0.803745	+	0.594974i	$0.797162\pi$
$402$		0			0
$403$	−3.82901	−	9.24405i	−0.190737	−	0.460479i
$404$	−1.22305	−	1.07115i	−0.0608491	−	0.0532915i
$405$		0			0
$406$	2.56384	−	0.598705i	0.127241	−	0.0297132i
$407$	−4.16560	+	4.16560i	−0.206481	+	0.206481i
$408$		0			0
$409$	−6.76143	−	6.76143i	−0.334331	−	0.334331i	0.519898	−	0.854229i	$-0.325970\pi$
$409$	−6.76143	−	6.76143i	−0.334331	−	0.334331i	−0.854229	+	0.519898i	$0.825970\pi$
$410$	1.41758	+	0.880853i	0.0700093	+	0.0435022i
$411$		0			0
$412$	−29.1431	+	14.3960i	−1.43578	+	0.709238i
$413$	3.84048	−	1.59078i	0.188978	−	0.0782771i
$414$		0			0
$415$	3.38682			0.166253
$416$	4.73957	+	12.5294i	0.232377	+	0.614304i
$417$		0			0
$418$	−3.02458	−	4.21783i	−0.147937	−	0.206301i
$419$	12.3331	−	5.10855i	0.602513	−	0.249569i	−0.0605105	−	0.998168i	$-0.519273\pi$
$419$	12.3331	−	5.10855i	0.602513	−	0.249569i	0.663024	+	0.748598i	$0.269273\pi$
$420$		0			0
$421$	13.8841	−	33.5191i	0.676669	−	1.63362i	−0.0933745	−	0.995631i	$-0.529765\pi$
$421$	13.8841	−	33.5191i	0.676669	−	1.63362i	0.770043	−	0.637992i	$-0.220235\pi$
$422$	5.58396	+	3.46975i	0.271823	+	0.168905i
$423$		0			0
$424$	−1.58691	+	16.2789i	−0.0770671	+	0.790575i
$425$	−9.90912	+	9.90912i	−0.480663	+	0.480663i
$426$		0			0
$427$	−1.12239	−	0.464909i	−0.0543162	−	0.0224985i
$428$	11.5903	−	13.2340i	0.560238	−	0.639688i
$429$		0			0
$430$	2.67328	−	16.2254i	0.128917	−	0.782461i
$431$			9.57641i			0.461280i	0.973039	+	0.230640i	$0.0740819\pi$
$431$			9.57641i			0.461280i	−0.973039	+	0.230640i	$0.925918\pi$
$432$		0			0
$433$		−	11.6546i		−	0.560084i	−0.959988	−	0.280042i	$-0.909652\pi$
$433$		−	11.6546i		−	0.560084i	0.959988	−	0.280042i	$-0.0903484\pi$
$434$	1.64658	+	0.271288i	0.0790385	+	0.0130223i
$435$		0			0
$436$	5.44158	−	0.360301i	0.260604	−	0.0172553i
$437$	16.1771	+	6.70076i	0.773854	+	0.320541i
$438$		0			0
$439$	17.6901	−	17.6901i	0.844303	−	0.844303i	−0.145112	−	0.989415i	$-0.546354\pi$
$439$	17.6901	−	17.6901i	0.844303	−	0.844303i	0.989415	+	0.145112i	$0.0463542\pi$
$440$	−2.55413	−	1.36193i	−0.121763	−	0.0649274i
$441$		0			0
$442$	8.43062	−	13.5676i	0.401004	−	0.645346i
$443$	−2.97406	+	7.18001i	−0.141302	+	0.341132i	−0.978649	−	0.205539i	$-0.934105\pi$
$443$	−2.97406	+	7.18001i	−0.141302	+	0.341132i	0.837347	+	0.546671i	$0.184105\pi$
$444$		0			0
$445$	11.3735	−	4.71108i	0.539158	−	0.223326i
$446$	−26.6963	+	19.1438i	−1.26411	+	0.906484i
$447$		0			0
$448$	−2.19214	−	0.431491i	−0.103569	−	0.0203860i
$449$	−18.7087			−0.882919			−0.441460	−	0.897281i	$-0.645539\pi$
$449$	−18.7087			−0.882919			−0.441460	+	0.897281i	$0.645539\pi$
$450$		0			0
$451$	−0.541132	+	0.224144i	−0.0254809	+	0.0105545i
$452$	33.7399	+	11.4281i	1.58699	+	0.537532i
$453$		0			0
$454$	10.6214	−	17.0932i	0.498485	−	0.802226i
$455$	−0.671512	−	0.671512i	−0.0314810	−	0.0314810i
$456$		0			0
$457$	−25.6052	+	25.6052i	−1.19776	+	1.19776i	−0.222924	+	0.974836i	$0.571560\pi$
$457$	−25.6052	+	25.6052i	−1.19776	+	1.19776i	−0.974836	+	0.222924i	$0.928440\pi$
$458$	0.587262	+	2.51484i	0.0274410	+	0.117511i
$459$		0			0
$460$	9.74388	−	0.645168i	0.454311	−	0.0300811i
$461$	4.42470	+	10.6822i	0.206079	+	0.497518i	0.992799	−	0.119791i	$-0.0382226\pi$
$461$	4.42470	+	10.6822i	0.206079	+	0.497518i	−0.786720	+	0.617310i	$0.788223\pi$
$462$		0			0
$463$		−	26.6186i		−	1.23707i	−0.785757	−	0.618535i	$-0.787726\pi$
$463$		−	26.6186i		−	1.23707i	0.785757	−	0.618535i	$-0.212274\pi$
$464$	25.7651	+	6.86694i	1.19611	+	0.318790i
$465$		0			0
$466$	−6.35274	+	38.5579i	−0.294285	+	1.78616i
$467$	−3.21259	−	7.75587i	−0.148661	−	0.358899i	0.831954	−	0.554845i	$-0.187222\pi$
$467$	−3.21259	−	7.75587i	−0.148661	−	0.358899i	−0.980615	+	0.195946i	$0.937222\pi$
$468$		0			0
$469$	0.638757	+	0.264582i	0.0294951	+	0.0122173i
$470$	−21.9515	+	5.12609i	−1.01255	+	0.236449i
$471$		0			0
$472$	41.9014	+	4.08464i	1.92867	+	0.188011i
$473$	4.08075	+	4.08075i	0.187633	+	0.187633i
$474$		0			0
$475$	−5.78989	+	13.9780i	−0.265659	+	0.641356i
$476$	1.17990	+	2.38860i	0.0540808	+	0.109481i
$477$		0			0
$478$	13.6073	+	18.9756i	0.622384	+	0.867925i
$479$	38.7324			1.76973			0.884865	−	0.465847i	$-0.154250\pi$
$479$	38.7324			1.76973			0.884865	+	0.465847i	$0.154250\pi$
$480$		0			0
$481$	−19.5746			−0.892523
$482$	−13.1349	−	18.3169i	−0.598280	−	0.834311i
$483$		0			0
$484$	−18.8139	+	9.29360i	−0.855179	+	0.422436i
$485$	−3.25769	+	7.86475i	−0.147924	+	0.357120i
$486$		0			0
$487$	10.6582	+	10.6582i	0.482967	+	0.482967i	0.906078	−	0.423111i	$-0.139062\pi$
$487$	10.6582	+	10.6582i	0.482967	+	0.482967i	−0.423111	+	0.906078i	$0.639062\pi$
$488$	−7.81496	−	9.50318i	−0.353767	−	0.430189i
$489$		0			0
$490$	−13.6885	+	3.19653i	−0.618385	+	0.144404i
$491$	−26.8161	−	11.1076i	−1.21020	−	0.501279i	−0.315915	−	0.948787i	$-0.602312\pi$
$491$	−26.8161	−	11.1076i	−1.21020	−	0.501279i	−0.894280	+	0.447508i	$0.852312\pi$
$492$		0			0
$493$	−12.1676	−	29.3751i	−0.548000	−	1.32299i
$494$	2.80359	−	17.0164i	0.126140	−	0.765604i
$495$		0			0
$496$	13.4221	+	10.2708i	0.602671	+	0.461171i
$497$			2.57036i			0.115297i
$498$		0			0
$499$	−10.5140	−	25.3831i	−0.470673	−	1.13631i	−0.963867	−	0.266386i	$-0.914171\pi$
$499$	−10.5140	−	25.3831i	−0.470673	−	1.13631i	0.493194	−	0.869920i	$-0.335829\pi$
$500$	1.50617	+	22.7475i	0.0673580	+	1.01730i
$501$		0			0
$502$	−1.99553	−	8.54547i	−0.0890646	−	0.381403i
$503$	0.101263	−	0.101263i	0.00451509	−	0.00451509i	−0.704846	−	0.709361i	$-0.748984\pi$
$503$	0.101263	−	0.101263i	0.00451509	−	0.00451509i	0.709361	+	0.704846i	$0.248984\pi$
$504$		0			0
$505$	0.825392	+	0.825392i	0.0367295	+	0.0367295i
$506$	−1.80876	+	2.91088i	−0.0804091	+	0.129404i
$507$		0			0
$508$	−9.16460	+	27.0573i	−0.406613	+	1.20047i
$509$	−29.1676	+	12.0816i	−1.29283	+	0.535508i	−0.919828	−	0.392322i	$-0.871672\pi$
$509$	−29.1676	+	12.0816i	−1.29283	+	0.535508i	−0.373003	+	0.927830i	$0.621672\pi$
$510$		0			0
$511$	2.89725			0.128167
$512$	−17.5342	−	14.3022i	−0.774909	−	0.632073i
$513$		0			0
$514$	−11.9416	+	8.56328i	−0.526723	+	0.377710i
$515$	21.5612	−	8.93095i	0.950101	−	0.393545i
$516$		0			0
$517$	3.02744	−	7.30890i	0.133147	−	0.321445i
$518$	1.72306	−	2.77297i	0.0757071	−	0.121837i
$519$		0			0
$520$	−2.80113	−	9.20097i	−0.122838	−	0.403489i
$521$	−9.59061	+	9.59061i	−0.420172	+	0.420172i	−0.885263	−	0.465091i	$-0.846022\pi$
$521$	−9.59061	+	9.59061i	−0.420172	+	0.420172i	0.465091	+	0.885263i	$0.346022\pi$
$522$		0			0
$523$	−25.5093	−	10.5663i	−1.11544	−	0.462032i	−0.252634	−	0.967562i	$-0.581297\pi$
$523$	−25.5093	−	10.5663i	−1.11544	−	0.462032i	−0.862809	+	0.505530i	$0.831297\pi$
$524$	2.49953	+	37.7501i	0.109193	+	1.64912i
$525$		0			0
$526$	−12.0961	−	1.99293i	−0.527414	−	0.0868960i
$527$		−	20.1531i		−	0.877884i
$528$		0			0
$529$			11.4382i			0.497314i
$530$	1.90907	−	11.5871i	0.0829245	−	0.503310i
$531$		0			0
$532$	2.16379	+	1.89504i	0.0938121	+	0.0821605i
$533$	−1.79806	−	0.744779i	−0.0778824	−	0.0322600i
$534$		0			0
$535$	−8.93112	+	8.93112i	−0.386126	+	0.386126i
$536$	4.44753	+	5.40830i	0.192104	+	0.233603i
$537$		0			0
$538$	27.7511	+	17.2439i	1.19644	+	0.743439i
$539$	1.88785	−	4.55768i	0.0813156	−	0.196313i
$540$		0			0
$541$	15.2727	−	6.32616i	0.656625	−	0.271983i	−0.0293928	−	0.999568i	$-0.509357\pi$
$541$	15.2727	−	6.32616i	0.656625	−	0.271983i	0.686017	+	0.727585i	$0.259357\pi$
$542$	−1.78975	−	2.49584i	−0.0768764	−	0.107205i
$543$		0			0
$544$	−0.837888	+	26.9685i	−0.0359241	+	1.15627i
$545$	−3.91547			−0.167720
$546$		0			0
$547$	−25.8087	+	10.6903i	−1.10350	+	0.457085i	−0.858695	−	0.512487i	$-0.828724\pi$
$547$	−25.8087	+	10.6903i	−1.10350	+	0.457085i	−0.244807	+	0.969572i	$0.578724\pi$
$548$	−11.7059	−	23.6975i	−0.500053	−	1.01231i
$549$		0			0
$550$	−2.51519	−	1.56288i	−0.107248	−	0.0666416i
$551$	−24.2734	−	24.2734i	−1.03408	−	1.03408i
$552$		0			0
$553$	1.86778	−	1.86778i	0.0794262	−	0.0794262i
$554$	−14.5459	+	3.39674i	−0.617997	+	0.144314i
$555$		0			0
$556$	−1.50281	+	1.71593i	−0.0637333	+	0.0727716i
$557$	−4.23730	−	10.2297i	−0.179540	−	0.433448i	0.808330	−	0.588729i	$-0.200372\pi$
$557$	−4.23730	−	10.2297i	−0.179540	−	0.433448i	−0.987870	+	0.155281i	$0.950372\pi$
$558$		0			0
$559$			19.1758i			0.811051i
$560$	1.55000	+	0.413108i	0.0654994	+	0.0174570i
$561$		0			0
$562$	5.37162	+	0.885020i	0.226588	+	0.0373323i
$563$	−1.13872	−	2.74912i	−0.0479915	−	0.115862i	0.898066	−	0.439861i	$-0.144972\pi$
$563$	−1.13872	−	2.74912i	−0.0479915	−	0.115862i	−0.946057	+	0.323999i	$0.894972\pi$
$564$		0			0
$565$	−23.6294	−	9.78762i	−0.994097	−	0.411768i
$566$	−5.40105	−	23.1290i	−0.227023	−	0.972185i
$567$		0			0
$568$	−12.2484	+	22.9704i	−0.513932	+	0.963816i
$569$	23.0118	+	23.0118i	0.964707	+	0.964707i	0.999398	−	0.0346915i	$-0.0110449\pi$
$569$	23.0118	+	23.0118i	0.964707	+	0.964707i	−0.0346915	+	0.999398i	$0.511045\pi$
$570$		0			0
$571$	15.9468	−	38.4989i	0.667351	−	1.61113i	−0.118674	−	0.992933i	$-0.537864\pi$
$571$	15.9468	−	38.4989i	0.667351	−	1.61113i	0.786025	−	0.618194i	$-0.212136\pi$
$572$	3.19697	+	1.08285i	0.133672	+	0.0452762i
$573$		0			0
$574$	0.263782	−	0.189156i	0.0110100	−	0.00789524i
$575$	9.99012			0.416617
$576$		0			0
$577$	−30.5299			−1.27098			−0.635488	−	0.772111i	$-0.719201\pi$
$577$	−30.5299			−1.27098			−0.635488	+	0.772111i	$0.719201\pi$
$578$	6.60837	−	4.73882i	0.274872	−	0.197109i
$579$		0			0
$580$	−18.1325	−	6.14169i	−0.752913	−	0.255020i
$581$	0.252073	−	0.608557i	0.0104577	−	0.0252472i
$582$		0			0
$583$	2.91418	+	2.91418i	0.120693	+	0.120693i
$584$	25.8916	+	13.8061i	1.07140	+	0.571300i
$585$		0			0
$586$	5.26398	+	22.5420i	0.217453	+	0.931202i
$587$	10.8951	+	4.51289i	0.449688	+	0.186267i	0.596022	−	0.802968i	$-0.296747\pi$
$587$	10.8951	+	4.51289i	0.449688	+	0.186267i	−0.146333	+	0.989235i	$0.546747\pi$
$588$		0			0
$589$	−8.32651	−	20.1020i	−0.343088	−	0.828288i
$590$	−29.8247	−	4.91387i	−1.22786	−	0.202301i
$591$		0			0
$592$	28.6123	−	16.5702i	1.17596	−	0.681030i
$593$		−	23.5969i		−	0.969009i	−0.874789	−	0.484505i	$-0.839000\pi$
$593$		−	23.5969i		−	0.969009i	0.874789	−	0.484505i	$-0.161000\pi$
$594$		0			0
$595$	−0.731988	−	1.76718i	−0.0300086	−	0.0724471i
$596$	23.9265	−	27.3197i	0.980069	−	1.11906i
$597$		0			0
$598$	−11.0890	+	2.58949i	−0.453464	+	0.105892i
$599$	29.8629	−	29.8629i	1.22017	−	1.22017i	0.252594	−	0.967572i	$-0.418716\pi$
$599$	29.8629	−	29.8629i	1.22017	−	1.22017i	0.967572	−	0.252594i	$-0.0812837\pi$
$600$		0			0
$601$	6.21081	+	6.21081i	0.253344	+	0.253344i	0.822340	−	0.568996i	$-0.192668\pi$
$601$	6.21081	+	6.21081i	0.253344	+	0.253344i	−0.568996	+	0.822340i	$0.692668\pi$
$602$	−2.71648	−	1.68796i	−0.110716	−	0.0687963i
$603$		0			0
$604$	−2.69834	−	5.46252i	−0.109794	−	0.222267i
$605$	13.9193	−	5.76555i	0.565899	−	0.234403i
$606$		0			0
$607$	32.4865			1.31859			0.659293	−	0.751886i	$-0.270856\pi$
$607$	32.4865			1.31859			0.659293	+	0.751886i	$0.270856\pi$
$608$	10.3066	+	27.2462i	0.417988	+	1.10498i
$609$		0			0
$610$	5.14791	+	7.17884i	0.208433	+	0.290663i
$611$	24.2857	−	10.0595i	0.982496	−	0.406963i
$612$		0			0
$613$	−6.25645	+	15.1044i	−0.252696	+	0.610061i	−0.998420	−	0.0561936i	$-0.982104\pi$
$613$	−6.25645	+	15.1044i	−0.252696	+	0.610061i	0.745724	+	0.666255i	$0.232104\pi$
$614$	−5.64587	−	3.50822i	−0.227849	−	0.141580i
$615$		0			0
$616$	−0.434814	+	0.357570i	−0.0175192	+	0.0144069i
$617$	−6.54203	+	6.54203i	−0.263372	+	0.263372i	−0.826423	−	0.563050i	$-0.809628\pi$
$617$	−6.54203	+	6.54203i	−0.263372	+	0.263372i	0.563050	+	0.826423i	$0.309628\pi$
$618$		0			0
$619$	−11.5343	−	4.77767i	−0.463603	−	0.192031i	0.138641	−	0.990343i	$-0.455727\pi$
$619$	−11.5343	−	4.77767i	−0.463603	−	0.192031i	−0.602244	+	0.798312i	$0.705727\pi$
$620$	−9.12850	−	7.99473i	−0.366610	−	0.321076i
$621$		0			0
$622$	−0.488840	+	2.96701i	−0.0196007	+	0.118966i
$623$		−	2.39427i		−	0.0959246i
$624$		0			0
$625$		−	1.67767i		−	0.0671066i
$626$	−27.1887	−	4.47956i	−1.08668	−	0.179039i
$627$		0			0
$628$	1.91292	+	28.8906i	0.0763339	+	1.15286i
$629$	−36.4253	−	15.0879i	−1.45237	−	0.601592i
$630$		0			0
$631$	−4.46066	+	4.46066i	−0.177576	+	0.177576i	−0.790298	−	0.612722i	$-0.790074\pi$
$631$	−4.46066	+	4.46066i	−0.177576	+	0.177576i	0.612722	+	0.790298i	$0.290074\pi$
$632$	25.5921	−	7.79122i	1.01800	−	0.309918i
$633$		0			0
$634$	−3.44395	+	5.54243i	−0.136777	+	0.220118i
$635$	7.84905	−	18.9493i	0.311480	−	0.751979i
$636$		0			0
$637$	15.1441	−	6.27289i	0.600031	−	0.248541i
$638$	5.45996	−	3.91530i	0.216162	−	0.155008i
$639$		0			0
$640$	11.8832	+	11.0779i	0.469724	+	0.437893i
$641$	2.87009			0.113362			0.0566808	−	0.998392i	$-0.481948\pi$
$641$	2.87009			0.113362			0.0566808	+	0.998392i	$0.481948\pi$
$642$		0			0
$643$	−0.482951	+	0.200045i	−0.0190457	+	0.00788899i	−0.392186	−	0.919886i	$-0.628281\pi$
$643$	−0.482951	+	0.200045i	−0.0190457	+	0.00788899i	0.373140	+	0.927775i	$0.378281\pi$
$644$	0.609286	−	1.79884i	0.0240092	−	0.0708840i
$645$		0			0
$646$	18.3331	−	29.5039i	0.721306	−	1.16082i
$647$	−7.92956	−	7.92956i	−0.311743	−	0.311743i	0.533841	−	0.845585i	$-0.320748\pi$
$647$	−7.92956	−	7.92956i	−0.311743	−	0.311743i	−0.845585	+	0.533841i	$0.820748\pi$
$648$		0			0
$649$	7.50099	−	7.50099i	0.294439	−	0.294439i
$650$	−2.23749	−	9.58164i	−0.0877616	−	0.375823i
$651$		0			0
$652$	−1.22295	−	18.4700i	−0.0478944	−	0.723343i
$653$	10.8968	+	26.3073i	0.426426	+	1.02948i	0.980412	+	0.196958i	$0.0631062\pi$
$653$	10.8968	+	26.3073i	0.426426	+	1.02948i	−0.553986	+	0.832526i	$0.686894\pi$
$654$		0			0
$655$		−	27.1630i		−	1.06135i
$656$	3.25870	−	0.433434i	0.127231	−	0.0169228i
$657$		0			0
$658$	−0.712722	+	4.32586i	−0.0277848	+	0.168640i
$659$	−12.3853	−	29.9008i	−0.482463	−	1.16477i	−0.958436	−	0.285308i	$-0.907904\pi$
$659$	−12.3853	−	29.9008i	−0.482463	−	1.16477i	0.475973	−	0.879460i	$-0.342096\pi$
$660$		0			0
$661$	24.3791	+	10.0982i	0.948238	+	0.392773i	0.802568	−	0.596560i	$-0.203466\pi$
$661$	24.3791	+	10.0982i	0.948238	+	0.392773i	0.145670	+	0.989333i	$0.453466\pi$
$662$	37.3525	−	8.72250i	1.45174	−	0.339009i
$663$		0			0
$664$	5.15260	−	4.23726i	0.199960	−	0.164437i
$665$	−1.46026	−	1.46026i	−0.0566265	−	0.0566265i
$666$		0			0
$667$	−8.67411	+	20.9411i	−0.335863	+	0.810844i
$668$	30.9796	−	15.3031i	1.19864	−	0.592096i
$669$		0			0
$670$	−2.92970	−	4.08551i	−0.113184	−	0.157837i
$671$	−3.10021			−0.119682
$672$		0			0
$673$	15.6075			0.601627			0.300813	−	0.953683i	$-0.402742\pi$
$673$	15.6075			0.601627			0.300813	+	0.953683i	$0.402742\pi$
$674$	−11.4363	−	15.9481i	−0.440510	−	0.614299i
$675$		0			0
$676$	−6.54781	−	13.2554i	−0.251839	−	0.509822i
$677$	−12.1504	+	29.3336i	−0.466977	+	1.12738i	0.498499	+	0.866891i	$0.333885\pi$
$677$	−12.1504	+	29.3336i	−0.466977	+	1.12738i	−0.965476	+	0.260492i	$0.916115\pi$
$678$		0			0
$679$	1.17071	+	1.17071i	0.0449276	+	0.0449276i
$680$	1.87953	−	19.2807i	0.0720765	−	0.739380i
$681$		0			0
$682$	4.14699	−	0.968399i	0.158796	−	0.0370819i
$683$	−3.56870	−	1.47820i	−0.136552	−	0.0565618i	0.313361	−	0.949634i	$-0.398545\pi$
$683$	−3.56870	−	1.47820i	−0.136552	−	0.0565618i	−0.449913	+	0.893072i	$0.648545\pi$
$684$		0			0
$685$	7.26212	+	17.5323i	0.277471	+	0.669875i
$686$	−0.893885	+	5.42543i	−0.0341287	+	0.207144i
$687$		0			0
$688$	−16.2326	−	28.0294i	−0.618863	−	1.06861i
$689$			13.6940i			0.521700i
$690$		0			0
$691$	−5.84545	−	14.1122i	−0.222371	−	0.536852i	0.772840	−	0.634601i	$-0.218836\pi$
$691$	−5.84545	−	14.1122i	−0.222371	−	0.536852i	−0.995211	+	0.0977495i	$0.968836\pi$
$692$	−21.6403	+	1.43286i	−0.822639	+	0.0544691i
$693$		0			0
$694$	7.04686	+	30.1768i	0.267495	+	1.14550i
$695$	1.15802	−	1.15802i	0.0439261	−	0.0439261i
$696$		0			0
$697$	−2.77184	−	2.77184i	−0.104991	−	0.104991i
$698$	−15.9928	+	25.7377i	−0.605338	+	0.974187i
$699$		0			0
$700$	1.55431	+	0.526462i	0.0587474	+	0.0198984i
$701$	26.6321	−	11.0314i	1.00588	−	0.416649i	0.181930	−	0.983312i	$-0.441766\pi$
$701$	26.6321	−	11.0314i	1.00588	−	0.416649i	0.823950	+	0.566662i	$0.191766\pi$
$702$		0			0
$703$	−42.5666			−1.60543
$704$	−5.58968	+	1.12348i	−0.210669	+	0.0423426i
$705$		0			0
$706$	−2.80767	+	2.01337i	−0.105668	+	0.0757740i
$707$	0.209741	−	0.0868778i	0.00788814	−	0.00326737i
$708$		0			0
$709$	12.8177	−	30.9446i	0.481377	−	1.16215i	−0.477578	−	0.878589i	$-0.658485\pi$
$709$	12.8177	−	30.9446i	0.481377	−	1.16215i	0.958955	−	0.283558i	$-0.0915148\pi$
$710$	9.86446	−	15.8751i	0.370206	−	0.595783i
$711$		0			0
$712$	11.4093	−	21.3967i	0.427582	−	0.801876i
$713$	−10.1589	+	10.1589i	−0.380455	+	0.380455i
$714$		0			0
$715$	−2.23896	−	0.927410i	−0.0837325	−	0.0346832i
$716$	39.4868	−	2.61453i	1.47569	−	0.0977094i
$717$		0			0
$718$	−24.1649	−	3.98138i	−0.901828	−	0.148584i
$719$			10.1508i			0.378560i	0.981923	+	0.189280i	$0.0606154\pi$
$719$			10.1508i			0.378560i	−0.981923	+	0.189280i	$0.939385\pi$
$720$		0			0
$721$		−	4.53891i		−	0.169038i
$722$	1.72848	−	10.4910i	0.0643273	−	0.390434i
$723$		0			0
$724$	6.07202	−	6.93312i	0.225665	−	0.257667i
$725$	−18.0945	−	7.49499i	−0.672013	−	0.278357i
$726$		0			0
$727$	1.86676	−	1.86676i	0.0692343	−	0.0692343i	−0.671642	−	0.740876i	$-0.734411\pi$
$727$	1.86676	−	1.86676i	0.0692343	−	0.0692343i	0.740876	+	0.671642i	$0.234411\pi$
$728$	−1.86175	−	0.181487i	−0.0690009	−	0.00672637i
$729$		0			0
$730$	−17.8940	−	11.1189i	−0.662287	−	0.411531i
$731$	−14.7805	+	35.6833i	−0.546677	+	1.31979i
$732$		0			0
$733$	−13.2921	+	5.50576i	−0.490954	+	0.203360i	−0.614405	−	0.788991i	$-0.710604\pi$
$733$	−13.2921	+	5.50576i	−0.490954	+	0.203360i	0.123451	+	0.992351i	$0.460604\pi$
$734$	−24.7028	−	34.4484i	−0.911795	−	1.27151i
$735$		0			0
$736$	14.0168	−	13.1721i	0.516668	−	0.485530i
$737$	1.76435			0.0649905
$738$		0			0
$739$	30.9403	−	12.8159i	1.13816	−	0.471440i	0.267610	−	0.963527i	$-0.413766\pi$
$739$	30.9403	−	12.8159i	1.13816	−	0.471440i	0.870546	+	0.492088i	$0.163766\pi$
$740$	−21.2840	+	10.5138i	−0.782416	+	0.386493i
$741$		0			0
$742$	−1.93992	−	1.20542i	−0.0712167	−	0.0442525i
$743$	−16.0447	−	16.0447i	−0.588622	−	0.588622i	0.348636	−	0.937258i	$-0.386645\pi$
$743$	−16.0447	−	16.0447i	−0.588622	−	0.588622i	−0.937258	+	0.348636i	$0.886645\pi$
$744$		0			0
$745$	−18.4370	+	18.4370i	−0.675481	+	0.675481i
$746$	7.27179	−	1.69810i	0.266239	−	0.0621718i
$747$		0			0
$748$	5.11443	+	4.47921i	0.187002	+	0.163776i
$749$	0.940057	+	2.26950i	0.0343489	+	0.0829257i
$750$		0			0
$751$			47.4378i			1.73103i	0.500883	+	0.865515i	$0.333009\pi$
$751$			47.4378i			1.73103i	−0.500883	+	0.865515i	$0.666991\pi$
$752$	−26.9831	+	35.2623i	−0.983973	+	1.28588i
$753$		0			0
$754$	22.0276	+	3.62924i	0.802199	+	0.132169i
$755$	1.67400	+	4.04139i	0.0609230	+	0.147081i
$756$		0			0
$757$	26.9413	+	11.1595i	0.979199	+	0.405598i	0.814129	−	0.580684i	$-0.197215\pi$
$757$	26.9413	+	11.1595i	0.979199	+	0.405598i	0.165070	+	0.986282i	$0.447215\pi$
$758$	11.0590	+	47.3579i	0.401679	+	1.72012i
$759$		0			0
$760$	−6.09129	−	20.0083i	−0.220954	−	0.725777i
$761$	−0.136516	−	0.136516i	−0.00494872	−	0.00494872i	0.704628	−	0.709577i	$-0.251114\pi$
$761$	−0.136516	−	0.136516i	−0.00494872	−	0.00494872i	−0.709577	+	0.704628i	$0.751114\pi$
$762$		0			0
$763$	−0.291419	+	0.703547i	−0.0105501	+	0.0254701i
$764$	−10.4240	+	30.7755i	−0.377127	+	1.11342i
$765$		0			0
$766$	34.5523	−	24.7773i	1.24843	−	0.895239i
$767$	35.2479			1.27273
$768$		0			0
$769$	24.0921			0.868783			0.434392	−	0.900724i	$-0.356963\pi$
$769$	24.0921			0.868783			0.434392	+	0.900724i	$0.356963\pi$
$770$	0.328465	−	0.235540i	0.0118371	−	0.00848829i
$771$		0			0
$772$	2.28528	−	6.74698i	0.0822490	−	0.242829i
$773$	−2.08372	+	5.03054i	−0.0749462	+	0.180936i	−0.956913	−	0.290376i	$-0.906220\pi$
$773$	−2.08372	+	5.03054i	−0.0749462	+	0.180936i	0.881966	+	0.471312i	$0.156220\pi$
$774$		0			0
$775$	−8.77798	−	8.77798i	−0.315314	−	0.315314i
$776$	4.88346	+	16.0409i	0.175306	+	0.575834i
$777$		0			0
$778$	−5.43366	−	23.2687i	−0.194806	−	0.834222i
$779$	−3.91003	−	1.61959i	−0.140091	−	0.0580277i
$780$		0			0
$781$	2.51014	+	6.06001i	0.0898198	+	0.216844i
$782$	−22.6309	−	3.72864i	−0.809281	−	0.133336i
$783$		0			0
$784$	−16.8261	+	21.9888i	−0.600933	+	0.785315i
$785$		−	20.7881i		−	0.741961i
$786$		0			0
$787$	5.70122	+	13.7640i	0.203227	+	0.490633i	0.992328	−	0.123630i	$-0.0394536\pi$
$787$	5.70122	+	13.7640i	0.203227	+	0.490633i	−0.789102	+	0.614263i	$0.789454\pi$
$788$	−26.3633	−	23.0889i	−0.939153	−	0.822509i
$789$		0			0
$790$	−18.7039	+	4.36772i	−0.665456	+	0.155396i
$791$	−3.51735	+	3.51735i	−0.125063	+	0.125063i
$792$		0			0
$793$	−7.28410	−	7.28410i	−0.258666	−	0.258666i
$794$	−6.99607	−	4.34720i	−0.248281	−	0.154276i
$795$		0			0
$796$	−12.8739	+	6.35938i	−0.456304	+	0.225402i
$797$	−8.78924	+	3.64062i	−0.311331	+	0.128958i	−0.532878	−	0.846192i	$-0.678889\pi$
$797$	−8.78924	+	3.64062i	−0.311331	+	0.128958i	0.221547	+	0.975150i	$0.428889\pi$
$798$		0			0
$799$	52.9458			1.87309
$800$	11.3816	+	12.1115i	0.402399	+	0.428205i
$801$		0			0
$802$	−19.6379	−	27.3855i	−0.693440	−	0.967014i
$803$	6.83068	−	2.82936i	0.241049	−	0.0998459i
$804$		0			0
$805$	−0.521825	+	1.25980i	−0.0183919	+	0.0444020i
$806$	12.0189	+	7.46825i	0.423346	+	0.263058i
$807$		0			0
$808$	2.28837	+	0.223076i	0.0805047	+	0.00784779i
$809$	−23.4048	+	23.4048i	−0.822867	+	0.822867i	−0.986518	−	0.163651i	$-0.947673\pi$
$809$	−23.4048	+	23.4048i	−0.822867	+	0.822867i	0.163651	+	0.986518i	$0.447673\pi$
$810$		0			0
$811$	40.9058	+	16.9438i	1.43640	+	0.594976i	0.958922	−	0.283669i	$-0.0915518\pi$
$811$	40.9058	+	16.9438i	1.43640	+	0.594976i	0.477476	+	0.878645i	$0.341552\pi$
$812$	−2.45312	+	2.80101i	−0.0860877	+	0.0982963i
$813$		0			0
$814$	1.35438	−	8.22038i	0.0474709	−	0.288124i
$815$			13.2901i			0.465531i
$816$		0			0
$817$			41.6995i			1.45888i
$818$	13.3430	+	2.19837i	0.466526	+	0.0768641i
$819$		0			0
$820$	−2.35511	+	0.155938i	−0.0822441	+	0.00544560i
$821$	−25.3281	−	10.4912i	−0.883956	−	0.366147i	−0.105927	−	0.994374i	$-0.533781\pi$
$821$	−25.3281	−	10.4912i	−0.883956	−	0.366147i	−0.778030	+	0.628227i	$0.783781\pi$
$822$		0			0
$823$	9.48009	−	9.48009i	0.330455	−	0.330455i	−0.522304	−	0.852759i	$-0.674927\pi$
$823$	9.48009	−	9.48009i	0.330455	−	0.330455i	0.852759	+	0.522304i	$0.174927\pi$
$824$	21.6290	−	40.5625i	0.753483	−	1.41306i
$825$		0			0
$826$	−3.10272	+	4.99328i	−0.107957	+	0.173739i
$827$	−12.9127	+	31.1740i	−0.449019	+	1.08403i	0.523672	+	0.851920i	$0.324562\pi$
$827$	−12.9127	+	31.1740i	−0.449019	+	1.08403i	−0.972690	+	0.232107i	$0.925438\pi$
$828$		0			0
$829$	−29.8748	+	12.3745i	−1.03759	+	0.429785i	−0.835447	−	0.549570i	$-0.814791\pi$
$829$	−29.8748	+	12.3745i	−1.03759	+	0.429785i	−0.202146	+	0.979355i	$0.564791\pi$
$830$	−3.89235	+	2.79118i	−0.135106	+	0.0968834i
$831$		0			0
$832$	−15.7729	−	10.4936i	−0.546826	−	0.363799i
$833$	33.0159			1.14393
$834$		0			0
$835$	−22.9199	+	9.49374i	−0.793176	+	0.328544i
$836$	6.95208	+	2.35475i	0.240443	+	0.0814407i
$837$		0			0
$838$	−9.96392	+	16.0352i	−0.344198	+	0.553927i
$839$	−9.14661	−	9.14661i	−0.315776	−	0.315776i	0.531366	−	0.847142i	$-0.321679\pi$
$839$	−9.14661	−	9.14661i	−0.315776	−	0.315776i	−0.847142	+	0.531366i	$0.821679\pi$
$840$		0			0
$841$	10.9157	−	10.9157i	0.376403	−	0.376403i
$842$	11.6677	+	49.9646i	0.402095	+	1.72190i
$843$		0			0
$844$	−9.27698	+	0.614254i	−0.319327	+	0.0211435i
$845$	4.06213	+	9.80684i	0.139741	+	0.337366i
$846$		0			0
$847$		−	2.93018i		−	0.100682i
$848$	−11.5922	−	20.0166i	−0.398078	−	0.687373i
$849$		0			0
$850$	3.22179	−	19.5546i	0.110506	−	0.670717i
$851$	10.7559	+	25.9671i	0.368709	+	0.890141i
$852$		0			0
$853$	−34.3154	−	14.2139i	−1.17494	−	0.486675i	−0.292115	−	0.956383i	$-0.594359\pi$
$853$	−34.3154	−	14.2139i	−1.17494	−	0.486675i	−0.882822	+	0.469708i	$0.844359\pi$
$854$	1.67307	−	0.390692i	0.0572512	−	0.0133692i
$855$		0			0
$856$	−2.41379	+	24.7613i	−0.0825015	+	0.846322i
$857$	32.7384	+	32.7384i	1.11832	+	1.11832i	0.991988	+	0.126335i	$0.0403216\pi$
$857$	32.7384	+	32.7384i	1.11832	+	1.11832i	0.126335	+	0.991988i	$0.459678\pi$
$858$		0			0
$859$	−18.2754	+	44.1207i	−0.623548	+	1.50538i	0.223961	+	0.974598i	$0.428101\pi$
$859$	−18.2754	+	44.1207i	−0.623548	+	1.50538i	−0.847509	+	0.530780i	$0.821899\pi$
$860$	10.2996	+	20.8505i	0.351213	+	0.710995i
$861$		0			0
$862$	−7.89222	−	11.0058i	−0.268810	−	0.374860i
$863$	−0.661247			−0.0225091			−0.0112546	−	0.999937i	$-0.503583\pi$
$863$	−0.661247			−0.0225091			−0.0112546	+	0.999937i	$0.503583\pi$
$864$		0			0
$865$	15.5712			0.529437
$866$	9.60491	+	13.3942i	0.326388	+	0.455154i
$867$		0			0
$868$	−2.11593	+	1.04522i	−0.0718195	+	0.0354770i
$869$	2.57955	−	6.22759i	0.0875053	−	0.211257i
$870$		0			0
$871$	4.14542	+	4.14542i	0.140462	+	0.140462i
$872$	−5.95687	+	4.89865i	−0.201725	+	0.165889i
$873$		0			0
$874$	−24.1140	+	5.63108i	−0.815670	+	0.190474i
$875$	−2.94105	−	1.21822i	−0.0994255	−	0.0411834i
$876$		0			0
$877$	13.9001	+	33.5578i	0.469372	+	1.13317i	0.964438	+	0.264310i	$0.0851441\pi$
$877$	13.9001	+	33.5578i	0.469372	+	1.13317i	−0.495065	+	0.868856i	$0.664856\pi$
$878$	−5.75165	+	34.9096i	−0.194109	+	1.17814i
$879$		0			0
$880$	4.05778	−	0.539719i	0.136788	−	0.0181939i
$881$		−	56.5397i		−	1.90487i	−0.304739	−	0.952436i	$-0.598569\pi$
$881$		−	56.5397i		−	1.90487i	0.304739	−	0.952436i	$-0.401431\pi$
$882$		0			0
$883$	13.0913	+	31.6051i	0.440556	+	1.06360i	0.975754	+	0.218870i	$0.0702372\pi$
$883$	13.0913	+	31.6051i	0.440556	+	1.06360i	−0.535198	+	0.844727i	$0.679763\pi$
$884$	1.49248	+	22.5407i	0.0501975	+	0.758126i
$885$		0			0
$886$	−2.49929	−	10.7027i	−0.0839652	−	0.359566i
$887$	−7.53591	+	7.53591i	−0.253031	+	0.253031i	−0.822212	−	0.569181i	$-0.807260\pi$
$887$	−7.53591	+	7.53591i	−0.253031	+	0.253031i	0.569181	+	0.822212i	$0.307260\pi$
$888$		0			0
$889$	−2.82069	−	2.82069i	−0.0946030	−	0.0946030i
$890$	−9.18866	+	14.7876i	−0.308005	+	0.495680i
$891$		0			0
$892$	14.9042	−	44.0025i	0.499028	−	1.47331i
$893$	52.8114	−	21.8752i	1.76727	−	0.732026i
$894$		0			0
$895$	−28.4126			−0.949729
$896$	2.87496	−	1.31072i	0.0960456	−	0.0437879i
$897$		0			0
$898$	21.5013	−	15.4184i	0.717507	−	0.514520i
$899$	26.0219	−	10.7786i	0.867880	−	0.359487i
$900$		0			0
$901$	−10.5552	+	25.4825i	−0.351644	+	0.848944i
$902$	0.437180	−	0.703565i	0.0145565	−	0.0234262i
$903$		0			0
$904$	−48.1943	+	14.6722i	−1.60292	+	0.487990i
$905$	−4.67891	+	4.67891i	−0.155532	+	0.155532i
$906$		0			0
$907$	−29.8888	−	12.3803i	−0.992441	−	0.411083i	−0.173421	−	0.984848i	$-0.555482\pi$
$907$	−29.8888	−	12.3803i	−0.992441	−	0.411083i	−0.819020	+	0.573765i	$0.805482\pi$
$908$	1.88031	+	28.3980i	0.0624003	+	0.942422i
$909$		0			0
$910$	1.32516	+	0.218331i	0.0439286	+	0.00723760i
$911$			45.8749i			1.51990i	0.649979	+	0.759952i	$0.274778\pi$
$911$			45.8749i			1.51990i	−0.649979	+	0.759952i	$0.725222\pi$
$912$		0			0
$913$		−	1.68093i		−	0.0556306i
$914$	8.32510	−	50.5292i	0.275370	−	1.67136i
$915$		0			0
$916$	−2.74748	−	2.40624i	−0.0907792	−	0.0795043i
$917$	−4.88075	−	2.02167i	−0.161177	−	0.0667615i
$918$		0			0
$919$	−17.8634	+	17.8634i	−0.589260	+	0.589260i	−0.937431	−	0.348171i	$-0.886803\pi$
$919$	−17.8634	+	17.8634i	−0.589260	+	0.589260i	0.348171	+	0.937431i	$0.386803\pi$
$920$	−10.6666	+	8.77170i	−0.351667	+	0.289194i
$921$		0			0
$922$	−13.8887	−	8.63011i	−0.457399	−	0.284217i
$923$	−8.34060	+	20.1360i	−0.274534	+	0.662784i
$924$		0			0
$925$	−22.4373	+	9.29382i	−0.737733	+	0.305579i
$926$	21.9372	+	30.5918i	0.720901	+	1.00531i
$927$		0			0
$928$	−35.2701	+	13.3419i	−1.15780	+	0.437968i
$929$	−49.0074			−1.60788			−0.803940	−	0.594710i	$-0.797267\pi$
$929$	−49.0074			−1.60788			−0.803940	+	0.594710i	$0.797267\pi$
$930$		0			0
$931$	32.9321	−	13.6409i	1.07931	−	0.447064i
$932$	−24.4758	−	49.5487i	−0.801731	−	1.62302i
$933$		0			0
$934$	10.0840	+	6.26596i	0.329958	+	0.205028i
$935$	−3.45154	−	3.45154i	−0.112877	−	0.112877i
$936$		0			0
$937$	12.0021	−	12.0021i	0.392093	−	0.392093i	−0.483340	−	0.875433i	$-0.660576\pi$
$937$	12.0021	−	12.0021i	0.392093	−	0.392093i	0.875433	+	0.483340i	$0.160576\pi$
$938$	−0.952151	+	0.222345i	−0.0310888	+	0.00725982i
$939$		0			0
$940$	21.0035	−	23.9822i	0.685060	−	0.782212i
$941$	5.60243	+	13.5255i	0.182634	+	0.440918i	0.988508	−	0.151170i	$-0.0483040\pi$
$941$	5.60243	+	13.5255i	0.182634	+	0.440918i	−0.805874	+	0.592087i	$0.798304\pi$
$942$		0			0
$943$			2.79450i			0.0910014i
$944$	−51.5220	+	29.8379i	−1.67690	+	0.971140i
$945$		0			0
$946$	−8.05292	−	1.32679i	−0.261823	−	0.0431376i
$947$	−14.7344	−	35.5719i	−0.478803	−	1.15593i	−0.960171	−	0.279414i	$-0.909860\pi$
$947$	−14.7344	−	35.5719i	−0.478803	−	1.15593i	0.481368	−	0.876519i	$-0.340140\pi$
$948$		0			0
$949$	22.6967	+	9.40129i	0.736767	+	0.305179i
$950$	−4.86562	−	20.8361i	−0.157861	−	0.676012i
$951$		0			0
$952$	−3.32454	−	1.77273i	−0.107749	−	0.0574546i
$953$	19.5054	+	19.5054i	0.631843	+	0.631843i	0.948530	−	0.316687i	$-0.102571\pi$
$953$	19.5054	+	19.5054i	0.631843	+	0.631843i	−0.316687	+	0.948530i	$0.602571\pi$
$954$		0			0
$955$	8.92767	−	21.5533i	0.288893	−	0.697448i
$956$	−31.2768	−	10.5938i	−1.01156	−	0.342628i
$957$		0			0
$958$	−44.5138	+	31.9206i	−1.43818	+	1.03131i
$959$	3.69077			0.119181
$960$		0			0
$961$	−13.1474			−0.424109
$962$	22.4964	−	16.1320i	0.725311	−	0.520117i
$963$		0			0
$964$	30.1910	+	10.2260i	0.972387	+	0.329359i
$965$	−1.95723	+	4.72518i	−0.0630056	+	0.152109i
$966$		0			0
$967$	−3.89581	−	3.89581i	−0.125281	−	0.125281i	0.641686	−	0.766967i	$-0.278235\pi$
$967$	−3.89581	−	3.89581i	−0.125281	−	0.125281i	−0.766967	+	0.641686i	$0.778235\pi$
$968$	13.9630	−	26.1859i	0.448789	−	0.841648i
$969$		0			0
$970$	−2.73764	−	11.7234i	−0.0879004	−	0.376417i
$971$	−37.9034	−	15.7001i	−1.21638	−	0.503840i	−0.320121	−	0.947377i	$-0.603723\pi$
$971$	−37.9034	−	15.7001i	−1.21638	−	0.503840i	−0.896256	+	0.443537i	$0.853723\pi$
$972$		0			0
$973$	−0.121889	−	0.294265i	−0.00390757	−	0.00943371i
$974$	−21.0328	−	3.46532i	−0.673933	−	0.111036i
$975$		0			0
$976$	16.8133	+	4.48111i	0.538181	+	0.143437i
$977$		−	18.6668i		−	0.597203i	−0.954378	−	0.298601i	$-0.903480\pi$
$977$		−	18.6668i		−	0.597203i	0.954378	−	0.298601i	$-0.0965201\pi$
$978$		0			0
$979$	−2.33817	−	5.64485i	−0.0747284	−	0.180410i
$980$	13.0974	−	14.9548i	0.418381	−	0.477713i
$981$		0			0
$982$	39.9729	−	9.33443i	1.27559	−	0.297874i
$983$	−39.1656	+	39.1656i	−1.24919	+	1.24919i	−0.293108	+	0.956079i	$0.594690\pi$
$983$	−39.1656	+	39.1656i	−1.24919	+	1.24919i	−0.956079	+	0.293108i	$0.905310\pi$
$984$		0			0
$985$	17.7916	+	17.7916i	0.566888	+	0.566888i
$986$	38.1927	+	23.7321i	1.21630	+	0.755784i
$987$		0			0
$988$	10.8017	+	21.8669i	0.343647	+	0.695677i
$989$	25.4381	−	10.5368i	0.808886	−	0.335052i
$990$		0			0
$991$	6.95147			0.220821			0.110410	−	0.993886i	$-0.464783\pi$
$991$	6.95147			0.220821			0.110410	+	0.993886i	$0.464783\pi$
$992$	−23.8900	−	0.742242i	−0.758509	−	0.0235662i
$993$		0			0
$994$	−2.11832	−	2.95403i	−0.0671889	−	0.0936961i
$995$	9.52462	−	3.94523i	0.301951	−	0.125072i
$996$		0			0
$997$	−13.9165	+	33.5973i	−0.440739	+	1.06404i	0.534951	+	0.844883i	$0.320330\pi$
$997$	−13.9165	+	33.5973i	−0.440739	+	1.06404i	−0.975690	+	0.219155i	$0.929670\pi$
$998$	33.0024	+	20.5070i	1.04467	+	0.649137i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.c.181.2	✓	32
3.2	odd	2	inner	288.2.v.c.181.7	yes	32
4.3	odd	2		1152.2.v.d.433.3		32
12.11	even	2		1152.2.v.d.433.6		32
32.3	odd	8		1152.2.v.d.721.3		32
32.29	even	8	inner	288.2.v.c.253.2	yes	32
96.29	odd	8	inner	288.2.v.c.253.7	yes	32
96.35	even	8		1152.2.v.d.721.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.v.c.181.2	✓	32	1.1	even	1	trivial
288.2.v.c.181.7	yes	32	3.2	odd	2	inner
288.2.v.c.253.2	yes	32	32.29	even	8	inner
288.2.v.c.253.7	yes	32	96.29	odd	8	inner
1152.2.v.d.433.3		32	4.3	odd	2
1152.2.v.d.433.6		32	12.11	even	2
1152.2.v.d.721.3		32	32.3	odd	8
1152.2.v.d.721.6		32	96.35	even	8

Overview	Random
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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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14926 + 0.824131i) q^{2} +(0.641617 - 1.89429i) q^{4} +(-0.549515 + 1.32665i) q^{5} +(0.197478 + 0.197478i) q^{7} +(0.823754 + 2.70581i) q^{8} +O(q^{10})\)	\(q+(-1.14926 + 0.824131i) q^{2} +(0.641617 - 1.89429i) q^{4} +(-0.549515 + 1.32665i) q^{5} +(0.197478 + 0.197478i) q^{7} +(0.823754 + 2.70581i) q^{8} +(-0.461792 - 1.97754i) q^{10} +(0.658433 + 0.272732i) q^{11} +(0.906224 + 2.18782i) q^{13} +(-0.389702 - 0.0642066i) q^{14} +(-3.17666 - 2.43081i) q^{16} +4.76970i q^{17} +(1.97066 + 4.75760i) q^{19} +(2.16047 + 1.89214i) q^{20} +(-0.981481 + 0.229194i) q^{22} +(2.40435 - 2.40435i) q^{23} +(2.07751 + 2.07751i) q^{25} +(-2.84454 - 1.76753i) q^{26} +(0.500785 - 0.247375i) q^{28} +(-6.15869 + 2.55101i) q^{29} -4.22524 q^{31} +(5.65413 + 0.175669i) q^{32} +(-3.93086 - 5.48165i) q^{34} +(-0.370500 + 0.153466i) q^{35} +(-3.16327 + 7.63680i) q^{37} +(-6.18570 - 3.84366i) q^{38} +(-4.04232 - 0.394055i) q^{40} +(-0.581135 + 0.581135i) q^{41} +(7.48124 + 3.09883i) q^{43} +(0.939095 - 1.07227i) q^{44} +(-0.781734 + 4.74473i) q^{46} -11.1004i q^{47} -6.92201i q^{49} +(-4.09975 - 0.675469i) q^{50} +(4.72581 - 0.312908i) q^{52} +(5.34257 + 2.21296i) q^{53} +(-0.723637 + 0.723637i) q^{55} +(-0.371665 + 0.697011i) q^{56} +(4.97559 - 8.00735i) q^{58} +(5.69609 - 13.7516i) q^{59} +(-4.01893 + 1.66470i) q^{61} +(4.85591 - 3.48215i) q^{62} +(-6.64286 + 4.45785i) q^{64} -3.40044 q^{65} +(2.28719 - 0.947386i) q^{67} +(9.03520 + 3.06032i) q^{68} +(0.299326 - 0.481714i) q^{70} +(6.50799 + 6.50799i) q^{71} +(7.33562 - 7.33562i) q^{73} +(-2.65829 - 11.3837i) q^{74} +(10.2767 - 0.680446i) q^{76} +(0.0761674 + 0.183884i) q^{77} -9.45819i q^{79} +(4.97045 - 2.87853i) q^{80} +(0.188946 - 1.14681i) q^{82} +(-0.902594 - 2.17905i) q^{83} +(-6.32771 - 2.62102i) q^{85} +(-11.1518 + 2.60414i) q^{86} +(-0.195575 + 2.00626i) q^{88} +(-6.06214 - 6.06214i) q^{89} +(-0.253086 + 0.611005i) q^{91} +(-3.01186 - 6.09720i) q^{92} +(9.14821 + 12.7573i) q^{94} -7.39456 q^{95} +5.92830 q^{97} +(5.70464 + 7.95521i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 8 q^{16} - 24 q^{22} - 40 q^{28} + 48 q^{31} - 40 q^{34} - 72 q^{40} + 16 q^{43} - 32 q^{46} - 8 q^{52} + 32 q^{55} - 32 q^{58} - 32 q^{61} + 72 q^{64} + 16 q^{67} + 120 q^{70} + 72 q^{76} + 120 q^{82} + 128 q^{88} - 48 q^{91} + 80 q^{94}+O(q^{100}) \) 32 * q - 8 * q^10 - 8 * q^16 - 24 * q^22 - 40 * q^28 + 48 * q^31 - 40 * q^34 - 72 * q^40 + 16 * q^43 - 32 * q^46 - 8 * q^52 + 32 * q^55 - 32 * q^58 - 32 * q^61 + 72 * q^64 + 16 * q^67 + 120 * q^70 + 72 * q^76 + 120 * q^82 + 128 * q^88 - 48 * q^91 + 80 * q^94

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