LMFDB - Embedded newform 920.2.bv.a.217.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.1
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.05677 + 0.664961i) q^{3} +(2.09365 - 0.785246i) q^{5} +(-1.51231 + 0.825782i) q^{7} +(6.17280 - 2.81902i) q^{9} +O(q^{10})$	\(q+(-3.05677 + 0.664961i) q^{3} +(2.09365 - 0.785246i) q^{5} +(-1.51231 + 0.825782i) q^{7} +(6.17280 - 2.81902i) q^{9} +(1.45186 + 1.25805i) q^{11} +(-1.50762 + 2.76100i) q^{13} +(-5.87767 + 3.79252i) q^{15} +(-5.05315 - 3.78274i) q^{17} +(0.770911 - 5.36180i) q^{19} +(4.07367 - 3.52985i) q^{21} +(3.96387 + 2.69959i) q^{23} +(3.76678 - 3.28807i) q^{25} +(-9.48141 + 7.09770i) q^{27} +(7.28588 - 1.04755i) q^{29} +(-4.63948 + 2.98161i) q^{31} +(-5.27457 - 2.88013i) q^{33} +(-2.51781 + 2.91644i) q^{35} +(6.47586 + 2.41537i) q^{37} +(2.77250 - 9.44228i) q^{39} +(-2.27727 + 4.98653i) q^{41} +(-1.26199 - 5.80129i) q^{43} +(10.7101 - 10.7492i) q^{45} +(9.54867 + 9.54867i) q^{47} +(-2.17933 + 3.39110i) q^{49} +(17.9617 + 8.20283i) q^{51} +(2.20497 + 4.03809i) q^{53} +(4.02757 + 1.49384i) q^{55} +(1.20889 + 16.9024i) q^{57} +(1.46023 + 4.97307i) q^{59} +(6.07716 + 9.45625i) q^{61} +(-7.00727 + 9.36062i) q^{63} +(-0.988371 + 6.96444i) q^{65} +(10.4532 + 0.747626i) q^{67} +(-13.9118 - 5.61621i) q^{69} +(0.656006 + 0.757071i) q^{71} +(2.00670 + 2.68064i) q^{73} +(-9.32775 + 12.5556i) q^{75} +(-3.23453 - 0.703630i) q^{77} +(6.98390 - 2.05066i) q^{79} +(10.9311 - 12.6152i) q^{81} +(5.02643 - 13.4764i) q^{83} +(-13.5499 - 3.95178i) q^{85} +(-21.5747 + 8.04695i) q^{87} +(2.34825 + 1.50913i) q^{89} -5.42045i q^{91} +(12.1992 - 12.1992i) q^{93} +(-2.59632 - 11.8311i) q^{95} +(0.180676 + 0.484412i) q^{97} +(12.5085 + 3.67283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * q	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.05677	+	0.664961i	−1.76483	+	0.383915i	−0.973718	−	0.227757i	$-0.926861\pi$
$3$	−3.05677	+	0.664961i	−1.76483	+	0.383915i	−0.791112	+	0.611672i	$0.790497\pi$
$4$		0			0
$5$	2.09365	−	0.785246i	0.936311	−	0.351173i
$5$	2.09365	−	0.785246i	0.936311	−	0.351173i
$6$		0			0
$7$	−1.51231	+	0.825782i	−0.571598	+	0.312116i	−0.738928	−	0.673785i	$-0.764668\pi$
$7$	−1.51231	+	0.825782i	−0.571598	+	0.312116i	0.167329	+	0.985901i	$0.446486\pi$
$8$		0			0
$9$	6.17280	−	2.81902i	2.05760	−	0.939675i
$10$		0			0
$11$	1.45186	+	1.25805i	0.437753	+	0.379315i	0.845672	−	0.533703i	$-0.179200\pi$
$11$	1.45186	+	1.25805i	0.437753	+	0.379315i	−0.407919	+	0.913018i	$0.633745\pi$
$12$		0			0
$13$	−1.50762	+	2.76100i	−0.418139	+	0.765765i	−0.998830	−	0.0483594i	$-0.984601\pi$
$13$	−1.50762	+	2.76100i	−0.418139	+	0.765765i	0.580691	+	0.814124i	$0.302783\pi$
$14$		0			0
$15$	−5.87767	+	3.79252i	−1.51761	+	0.979224i
$16$		0			0
$17$	−5.05315	−	3.78274i	−1.22557	−	0.917449i	−0.227160	−	0.973857i	$-0.572944\pi$
$17$	−5.05315	−	3.78274i	−1.22557	−	0.917449i	−0.998408	+	0.0564088i	$0.982035\pi$
$18$		0			0
$19$	0.770911	−	5.36180i	0.176859	−	1.23008i	−0.687116	−	0.726548i	$-0.741124\pi$
$19$	0.770911	−	5.36180i	0.176859	−	1.23008i	0.863975	−	0.503534i	$-0.167967\pi$
$20$		0			0
$21$	4.07367	−	3.52985i	0.888948	−	0.770277i
$22$		0			0
$23$	3.96387	+	2.69959i	0.826523	+	0.562903i
$23$	3.96387	+	2.69959i	0.826523	+	0.562903i
$24$		0			0
$25$	3.76678	−	3.28807i	0.753355	−	0.657614i
$26$		0			0
$27$	−9.48141	+	7.09770i	−1.82470	+	1.36595i
$28$		0			0
$29$	7.28588	−	1.04755i	1.35295	−	0.194525i	0.572586	−	0.819845i	$-0.305940\pi$
$29$	7.28588	−	1.04755i	1.35295	−	0.194525i	0.780369	+	0.625320i	$0.215031\pi$
$30$		0			0
$31$	−4.63948	+	2.98161i	−0.833275	+	0.535513i	−0.886317	−	0.463079i	$-0.846745\pi$
$31$	−4.63948	+	2.98161i	−0.833275	+	0.535513i	0.0530422	+	0.998592i	$0.483108\pi$
$32$		0			0
$33$	−5.27457	−	2.88013i	−0.918185	−	0.501367i
$34$		0			0
$35$	−2.51781	+	2.91644i	−0.425587	+	0.492968i
$36$		0			0
$37$	6.47586	+	2.41537i	1.06463	+	0.397085i	0.819899	−	0.572507i	$-0.194029\pi$
$37$	6.47586	+	2.41537i	1.06463	+	0.397085i	0.244726	+	0.969592i	$0.421302\pi$
$38$		0			0
$39$	2.77250	−	9.44228i	0.443956	−	1.51197i
$40$		0			0
$41$	−2.27727	+	4.98653i	−0.355650	+	0.778764i	0.644253	+	0.764813i	$0.277168\pi$
$41$	−2.27727	+	4.98653i	−0.355650	+	0.778764i	−0.999903	+	0.0139519i	$0.995559\pi$
$42$		0			0
$43$	−1.26199	−	5.80129i	−0.192452	−	0.884688i	−0.967517	−	0.252806i	$-0.918646\pi$
$43$	−1.26199	−	5.80129i	−0.192452	−	0.884688i	0.775065	−	0.631882i	$-0.217717\pi$
$44$		0			0
$45$	10.7101	−	10.7492i	1.59657	−	1.60240i
$46$		0			0
$47$	9.54867	+	9.54867i	1.39282	+	1.39282i	0.818947	+	0.573868i	$0.194558\pi$
$47$	9.54867	+	9.54867i	1.39282	+	1.39282i	0.573868	+	0.818947i	$0.305442\pi$
$48$		0			0
$49$	−2.17933	+	3.39110i	−0.311333	+	0.484443i
$50$		0			0
$51$	17.9617	+	8.20283i	2.51514	+	1.14863i
$52$		0			0
$53$	2.20497	+	4.03809i	0.302875	+	0.554675i	0.984147	−	0.177356i	$-0.0567544\pi$
$53$	2.20497	+	4.03809i	0.302875	+	0.554675i	−0.681271	+	0.732031i	$0.738573\pi$
$54$		0			0
$55$	4.02757	+	1.49384i	0.543078	+	0.201430i
$56$		0			0
$57$	1.20889	+	16.9024i	0.160121	+	2.23878i
$58$		0			0
$59$	1.46023	+	4.97307i	0.190105	+	0.647439i	0.998287	+	0.0585059i	$0.0186336\pi$
$59$	1.46023	+	4.97307i	0.190105	+	0.647439i	−0.808182	+	0.588933i	$0.799548\pi$
$60$		0			0
$61$	6.07716	+	9.45625i	0.778101	+	1.21075i	0.973199	+	0.229965i	$0.0738611\pi$
$61$	6.07716	+	9.45625i	0.778101	+	1.21075i	−0.195098	+	0.980784i	$0.562502\pi$
$62$		0			0
$63$	−7.00727	+	9.36062i	−0.882834	+	1.17933i
$64$		0			0
$65$	−0.988371	+	6.96444i	−0.122592	+	0.863833i
$66$		0			0
$67$	10.4532	+	0.747626i	1.27706	+	0.0913370i	0.693335	−	0.720616i	$-0.256141\pi$
$67$	10.4532	+	0.747626i	1.27706	+	0.0913370i	0.583723	+	0.811953i	$0.301595\pi$
$68$		0			0
$69$	−13.9118	−	5.61621i	−1.67478	−	0.676112i
$70$		0			0
$71$	0.656006	+	0.757071i	0.0778536	+	0.0898478i	0.793340	−	0.608779i	$-0.208340\pi$
$71$	0.656006	+	0.757071i	0.0778536	+	0.0898478i	−0.715486	+	0.698627i	$0.753795\pi$
$72$		0			0
$73$	2.00670	+	2.68064i	0.234866	+	0.313745i	0.902454	−	0.430787i	$-0.141764\pi$
$73$	2.00670	+	2.68064i	0.234866	+	0.313745i	−0.667587	+	0.744531i	$0.732673\pi$
$74$		0			0
$75$	−9.32775	+	12.5556i	−1.07708	+	1.44980i
$76$		0			0
$77$	−3.23453	−	0.703630i	−0.368609	−	0.0801861i
$78$		0			0
$79$	6.98390	−	2.05066i	0.785750	−	0.230717i	0.135843	−	0.990730i	$-0.456626\pi$
$79$	6.98390	−	2.05066i	0.785750	−	0.230717i	0.649907	+	0.760013i	$0.274808\pi$
$80$		0			0
$81$	10.9311	−	12.6152i	1.21457	−	1.40169i
$82$		0			0
$83$	5.02643	−	13.4764i	0.551722	−	1.47922i	−0.299334	−	0.954148i	$-0.596764\pi$
$83$	5.02643	−	13.4764i	0.551722	−	1.47922i	0.851056	−	0.525075i	$-0.175963\pi$
$84$		0			0
$85$	−13.5499	−	3.95178i	−1.46970	−	0.428631i
$86$		0			0
$87$	−21.5747	+	8.04695i	−2.31305	+	0.862724i
$88$		0			0
$89$	2.34825	+	1.50913i	0.248914	+	0.159967i	0.659149	−	0.752013i	$-0.270917\pi$
$89$	2.34825	+	1.50913i	0.248914	+	0.159967i	−0.410235	+	0.911980i	$0.634553\pi$
$90$		0			0
$91$		−	5.42045i		−	0.568218i
$92$		0			0
$93$	12.1992	−	12.1992i	1.26500	−	1.26500i
$94$		0			0
$95$	−2.59632	−	11.8311i	−0.266376	−	1.21385i
$96$		0			0
$97$	0.180676	+	0.484412i	0.0183449	+	0.0491846i	0.945799	−	0.324752i	$-0.105281\pi$
$97$	0.180676	+	0.484412i	0.0183449	+	0.0491846i	−0.927454	+	0.373936i	$0.878008\pi$
$98$		0			0
$99$	12.5085	+	3.67283i	1.25715	+	0.369134i
$100$		0			0
$101$	2.74223	+	6.00465i	0.272862	+	0.597485i	0.995607	−	0.0936297i	$-0.0298470\pi$
$101$	2.74223	+	6.00465i	0.272862	+	0.597485i	−0.722745	+	0.691115i	$0.757120\pi$
$102$		0			0
$103$	−9.91160	+	0.708892i	−0.976619	+	0.0698492i	−0.550515	−	0.834825i	$-0.685569\pi$
$103$	−9.91160	+	0.708892i	−0.976619	+	0.0698492i	−0.426104	+	0.904674i	$0.640114\pi$
$104$		0			0
$105$	5.75705	−	10.5891i	0.561831	−	1.03339i
$106$		0			0
$107$	0.654783	−	3.00999i	0.0633003	−	0.290987i	−0.934604	−	0.355689i	$-0.884246\pi$
$107$	0.654783	−	3.00999i	0.0633003	−	0.290987i	0.997905	+	0.0647024i	$0.0206098\pi$
$108$		0			0
$109$	−0.477630	−	3.32199i	−0.0457487	−	0.318189i	−0.999826	−	0.0186300i	$-0.994070\pi$
$109$	−0.477630	−	3.32199i	−0.0457487	−	0.318189i	0.954078	−	0.299559i	$-0.0968395\pi$
$110$		0			0
$111$	−21.4014	−	3.07705i	−2.03133	−	0.292061i
$112$		0			0
$113$	−0.0659640	+	0.922298i	−0.00620537	+	0.0867625i	−0.999611	−	0.0278904i	$-0.991121\pi$
$113$	−0.0659640	+	0.922298i	−0.00620537	+	0.0867625i	0.993406	+	0.114653i	$0.0365756\pi$
$114$		0			0
$115$	10.4188	+	2.53939i	0.971559	+	0.236799i
$116$		0			0
$117$	−1.52292	+	21.2932i	−0.140794	+	1.96855i
$118$		0			0
$119$	10.7656	+	1.54786i	0.986883	+	0.141892i
$120$		0			0
$121$	−1.04024	−	7.23502i	−0.0945671	−	0.657729i
$122$		0			0
$123$	3.64526	−	16.7570i	0.328682	−	1.51093i
$124$		0			0
$125$	5.30438	−	9.84193i	0.474438	−	0.880289i
$126$		0			0
$127$	1.96810	−	0.140761i	0.174641	−	0.0124905i	0.0162551	−	0.999868i	$-0.494826\pi$
$127$	1.96810	−	0.140761i	0.174641	−	0.0124905i	0.158386	+	0.987377i	$0.449371\pi$
$128$		0			0
$129$	7.71526	+	16.8941i	0.679291	+	1.48744i
$130$		0			0
$131$	9.99845	+	2.93581i	0.873568	+	0.256503i	0.687632	−	0.726059i	$-0.258650\pi$
$131$	9.99845	+	2.93581i	0.873568	+	0.256503i	0.185936	+	0.982562i	$0.440468\pi$
$132$		0			0
$133$	3.26183	+	8.74530i	0.282836	+	0.758313i
$134$		0			0
$135$	−14.2774	+	22.3054i	−1.22880	+	1.91974i
$136$		0			0
$137$	−11.3411	+	11.3411i	−0.968939	+	0.968939i	−0.999532	−	0.0305931i	$-0.990260\pi$
$137$	−11.3411	+	11.3411i	−0.968939	+	0.968939i	0.0305931	+	0.999532i	$0.490260\pi$
$138$		0			0
$139$			4.09450i			0.347291i	0.984808	+	0.173645i	$0.0555547\pi$
$139$			4.09450i			0.347291i	−0.984808	+	0.173645i	$0.944445\pi$
$140$		0			0
$141$	−35.5376	−	22.8386i	−2.99281	−	1.92336i
$142$		0			0
$143$	−5.66233	+	2.11194i	−0.473508	+	0.176609i
$144$		0			0
$145$	14.4315	−	7.91442i	1.19847	−	0.657257i
$146$		0			0
$147$	4.40677	−	11.8150i	0.363464	−	0.974485i
$148$		0			0
$149$	7.62118	−	8.79531i	0.624351	−	0.720540i	−0.352176	−	0.935934i	$-0.614558\pi$
$149$	7.62118	−	8.79531i	0.624351	−	0.720540i	0.976527	+	0.215394i	$0.0691036\pi$
$150$		0			0
$151$	−5.53501	+	1.62523i	−0.450433	+	0.132259i	−0.499078	−	0.866557i	$-0.666328\pi$
$151$	−5.53501	+	1.62523i	−0.450433	+	0.132259i	0.0486450	+	0.998816i	$0.484510\pi$
$152$		0			0
$153$	−41.8557	−	9.10515i	−3.38383	−	0.736108i
$154$		0			0
$155$	−7.37216	+	9.88560i	−0.592146	+	0.794030i
$156$		0			0
$157$	4.25536	+	5.68450i	0.339615	+	0.453672i	0.937539	−	0.347880i	$-0.113099\pi$
$157$	4.25536	+	5.68450i	0.339615	+	0.453672i	−0.597924	+	0.801553i	$0.704008\pi$
$158$		0			0
$159$	−9.42526	−	10.8773i	−0.747472	−	0.862628i
$160$		0			0
$161$	−8.22385	−	0.809313i	−0.648130	−	0.0637828i
$162$		0			0
$163$	17.0911	+	1.22238i	1.33868	+	0.0957442i	0.722231	−	0.691652i	$-0.243117\pi$
$163$	17.0911	+	1.22238i	1.33868	+	0.0957442i	0.616447	+	0.787396i	$0.288571\pi$
$164$		0			0
$165$	−13.3047	−	1.88817i	−1.03577	−	0.146993i
$166$		0			0
$167$	4.55834	−	6.08923i	0.352735	−	0.471199i	−0.588720	−	0.808337i	$-0.700368\pi$
$167$	4.55834	−	6.08923i	0.352735	−	0.471199i	0.941455	+	0.337138i	$0.109459\pi$
$168$		0			0
$169$	1.67811	+	2.61119i	0.129086	+	0.200861i
$170$		0			0
$171$	−10.3564	−	35.2706i	−0.791972	−	2.69721i
$172$		0			0
$173$	−0.168826	−	2.36050i	−0.0128356	−	0.179466i	−0.999825	−	0.0186829i	$-0.994053\pi$
$173$	−0.168826	−	2.36050i	−0.0128356	−	0.179466i	0.986990	−	0.160783i	$-0.0514019\pi$
$174$		0			0
$175$	−2.98129	+	8.08311i	−0.225365	+	0.611025i
$176$		0			0
$177$	−7.77048	−	14.2306i	−0.584065	−	1.06964i
$178$		0			0
$179$	−17.1544	−	7.83416i	−1.28218	−	0.585553i	−0.346385	−	0.938092i	$-0.612591\pi$
$179$	−17.1544	−	7.83416i	−1.28218	−	0.585553i	−0.935797	+	0.352540i	$0.885318\pi$
$180$		0			0
$181$	1.63260	−	2.54038i	0.121350	−	0.188825i	−0.775264	−	0.631638i	$-0.782383\pi$
$181$	1.63260	−	2.54038i	0.121350	−	0.188825i	0.896614	+	0.442813i	$0.146019\pi$
$182$		0			0
$183$	−24.8646	−	24.8646i	−1.83804	−	1.83804i
$184$		0			0
$185$	15.4549	−	0.0281942i	1.13627	−	0.00207288i
$186$		0			0
$187$	−2.57762	−	11.8491i	−0.188494	−	0.866492i
$188$		0			0
$189$	8.47766	−	18.5635i	0.616659	−	1.35029i
$190$		0			0
$191$	−2.60478	+	8.87108i	−0.188476	+	0.641889i	0.809986	+	0.586449i	$0.199474\pi$
$191$	−2.60478	+	8.87108i	−0.188476	+	0.641889i	−0.998462	+	0.0554402i	$0.982344\pi$
$192$		0			0
$193$	20.4030	+	7.60993i	1.46864	+	0.547775i	0.951371	−	0.308047i	$-0.0996754\pi$
$193$	20.4030	+	7.60993i	1.46864	+	0.547775i	0.517270	+	0.855822i	$0.326948\pi$
$194$		0			0
$195$	−1.60985	−	21.9460i	−0.115284	−	1.57158i
$196$		0			0
$197$	−19.4318	−	10.6106i	−1.38446	−	0.755971i	−0.397599	−	0.917559i	$-0.630157\pi$
$197$	−19.4318	−	10.6106i	−1.38446	−	0.755971i	−0.986858	+	0.161588i	$0.948338\pi$
$198$		0			0
$199$	17.0559	−	10.9612i	1.20906	−	0.777018i	0.228562	−	0.973529i	$-0.426597\pi$
$199$	17.0559	−	10.9612i	1.20906	−	0.777018i	0.980502	+	0.196511i	$0.0629611\pi$
$200$		0			0
$201$	−32.4501	+	4.66562i	−2.28886	+	0.329088i
$202$		0			0
$203$	−10.1534	+	7.60077i	−0.712632	+	0.533470i
$204$		0			0
$205$	−0.852165	+	12.2283i	−0.0595178	+	0.854060i
$206$		0			0
$207$	32.0784	+	5.48978i	2.22960	+	0.381566i
$208$		0			0
$209$	7.86465	−	6.81476i	0.544009	−	0.471387i
$210$		0			0
$211$	−2.54227	+	17.6818i	−0.175017	+	1.21727i	0.693075	+	0.720865i	$0.256255\pi$
$211$	−2.54227	+	17.6818i	−0.175017	+	1.21727i	−0.868092	+	0.496403i	$0.834654\pi$
$212$		0			0
$213$	−2.50868	−	1.87798i	−0.171892	−	0.128677i
$214$		0			0
$215$	−7.19762	−	11.1549i	−0.490874	−	0.760759i
$216$		0			0
$217$	4.55415	−	8.34031i	0.309156	−	0.566177i
$218$		0			0
$219$	−7.91654	−	6.85972i	−0.534950	−	0.463537i
$220$		0			0
$221$	18.0624	−	8.24882i	1.21501	−	0.554875i
$222$		0			0
$223$	−18.1161	+	9.89213i	−1.21314	+	0.662426i	−0.952949	−	0.303131i	$-0.901968\pi$
$223$	−18.1161	+	9.89213i	−1.21314	+	0.662426i	−0.260193	+	0.965557i	$0.583786\pi$
$224$		0			0
$225$	13.9824	−	30.9152i	0.932161	−	2.06102i
$226$		0			0
$227$	−20.2020	+	4.39467i	−1.34085	+	0.291685i	−0.825068	−	0.565034i	$-0.808863\pi$
$227$	−20.2020	+	4.39467i	−1.34085	+	0.291685i	−0.515785	+	0.856718i	$0.672499\pi$
$228$		0			0
$229$	−14.5868			−0.963926			−0.481963	−	0.876192i	$-0.660076\pi$
$229$	−14.5868			−0.963926			−0.481963	+	0.876192i	$0.660076\pi$
$230$		0			0
$231$	10.3551			0.681317
$232$		0			0
$233$	−9.66715	+	2.10296i	−0.633316	+	0.137769i	−0.517752	−	0.855531i	$-0.673231\pi$
$233$	−9.66715	+	2.10296i	−0.633316	+	0.137769i	−0.115564	+	0.993300i	$0.536867\pi$
$234$		0			0
$235$	27.4897	+	12.4935i	1.79323	+	0.814989i
$236$		0			0
$237$	−19.9846	+	10.9124i	−1.29814	+	0.708838i
$238$		0			0
$239$	−11.2003	+	5.11498i	−0.724484	+	0.330861i	−0.743296	−	0.668962i	$-0.766739\pi$
$239$	−11.2003	+	5.11498i	−0.724484	+	0.330861i	0.0188123	+	0.999823i	$0.494012\pi$
$240$		0			0
$241$	−9.04934	−	7.84130i	−0.582919	−	0.505103i	0.312743	−	0.949838i	$-0.398752\pi$
$241$	−9.04934	−	7.84130i	−0.582919	−	0.505103i	−0.895662	+	0.444735i	$0.853298\pi$
$242$		0			0
$243$	−7.99703	+	14.6455i	−0.513010	+	0.939508i
$244$		0			0
$245$	−1.89991	+	8.81111i	−0.121381	+	0.562921i
$246$		0			0
$247$	13.6417	+	10.2121i	0.868002	+	0.649778i
$248$		0			0
$249$	−6.40340	+	44.5366i	−0.405799	+	2.82239i
$250$		0			0
$251$	17.1589	−	14.8683i	1.08306	−	0.938478i	0.0847408	−	0.996403i	$-0.472994\pi$
$251$	17.1589	−	14.8683i	1.08306	−	0.938478i	0.998321	+	0.0579247i	$0.0184483\pi$
$252$		0			0
$253$	2.35879	+	8.90615i	0.148296	+	0.559925i
$254$		0			0
$255$	44.0468	+	3.06954i	2.75832	+	0.192222i
$256$		0			0
$257$	−19.6543	+	14.7130i	−1.22600	+	0.917774i	−0.998431	−	0.0559877i	$-0.982169\pi$
$257$	−19.6543	+	14.7130i	−1.22600	+	0.917774i	−0.227571	+	0.973762i	$0.573078\pi$
$258$		0			0
$259$	−11.7881	+	1.69487i	−0.732475	+	0.105314i
$260$		0			0
$261$	42.0212	−	27.0054i	2.60105	−	1.67159i
$262$		0			0
$263$	−6.92667	−	3.78225i	−0.427116	−	0.233223i	0.251287	−	0.967913i	$-0.419146\pi$
$263$	−6.92667	−	3.78225i	−0.427116	−	0.233223i	−0.678404	+	0.734689i	$0.737328\pi$
$264$		0			0
$265$	7.78734	+	6.72293i	0.478372	+	0.412986i
$266$		0			0
$267$	−8.18158	−	3.05157i	−0.500705	−	0.186753i
$268$		0			0
$269$	0.551450	−	1.87807i	0.0336225	−	0.114508i	−0.940972	−	0.338484i	$-0.890086\pi$
$269$	0.551450	−	1.87807i	0.0336225	−	0.114508i	0.974595	+	0.223977i	$0.0719039\pi$
$270$		0			0
$271$	7.01905	−	15.3696i	0.426377	−	0.933636i	−0.567523	−	0.823357i	$-0.692098\pi$
$271$	7.01905	−	15.3696i	0.426377	−	0.933636i	0.993901	−	0.110279i	$-0.0351743\pi$
$272$		0			0
$273$	3.60439	+	16.5691i	0.218148	+	1.00281i
$274$		0			0
$275$	9.60538	−	0.0350461i	0.579226	−	0.00211336i
$276$		0			0
$277$	−1.45811	−	1.45811i	−0.0876093	−	0.0876093i	0.661944	−	0.749553i	$-0.269732\pi$
$277$	−1.45811	−	1.45811i	−0.0876093	−	0.0876093i	−0.749553	+	0.661944i	$0.769732\pi$
$278$		0			0
$279$	−20.2333	+	31.4837i	−1.21134	+	1.88488i
$280$		0			0
$281$	−11.4650	−	5.23589i	−0.683944	−	0.312347i	0.0429687	−	0.999076i	$-0.486318\pi$
$281$	−11.4650	−	5.23589i	−0.683944	−	0.312347i	−0.726913	+	0.686730i	$0.759046\pi$
$282$		0			0
$283$	0.275963	+	0.505389i	0.0164043	+	0.0300422i	0.885753	−	0.464158i	$-0.153643\pi$
$283$	0.275963	+	0.505389i	0.0164043	+	0.0300422i	−0.869348	+	0.494200i	$0.835461\pi$
$284$		0			0
$285$	15.8036	+	34.4386i	0.936123	+	2.03997i
$286$		0			0
$287$	−0.673852	−	9.42169i	−0.0397762	−	0.556145i
$288$		0			0
$289$	6.43573	+	21.9181i	0.378572	+	1.28930i
$290$		0			0
$291$	−0.874401	−	1.36060i	−0.0512583	−	0.0797595i
$292$		0			0
$293$	1.33037	−	1.77717i	0.0777210	−	0.103823i	−0.759996	−	0.649928i	$-0.774799\pi$
$293$	1.33037	−	1.77717i	0.0777210	−	0.103823i	0.837717	+	0.546105i	$0.183890\pi$
$294$		0			0
$295$	6.96230	+	9.26526i	0.405361	+	0.539444i
$296$		0			0
$297$	−22.6949	−	1.62317i	−1.31689	−	0.0941861i
$298$		0			0
$299$	−13.4296	+	6.87430i	−0.776653	+	0.397551i
$300$		0			0
$301$	6.69912	+	7.73120i	0.386131	+	0.445619i
$302$		0			0
$303$	−12.3753	−	16.5314i	−0.710940	−	0.949704i
$304$		0			0
$305$	20.1490	+	15.0260i	1.15373	+	0.860389i
$306$		0			0
$307$	26.6125	+	5.78920i	1.51886	+	0.330407i	0.893189	−	0.449681i	$-0.148462\pi$
$307$	26.6125	+	5.78920i	1.51886	+	0.330407i	0.625669	+	0.780089i	$0.284826\pi$
$308$		0			0
$309$	29.8262	−	8.75775i	1.69675	−	0.498211i
$310$		0			0
$311$	−15.0375	+	17.3542i	−0.852697	+	0.984064i	−0.999987	−	0.00502896i	$-0.998399\pi$
$311$	−15.0375	+	17.3542i	−0.852697	+	0.984064i	0.147291	+	0.989093i	$0.452945\pi$
$312$		0			0
$313$	8.23991	−	22.0921i	0.465747	−	1.24872i	−0.465733	−	0.884925i	$-0.654209\pi$
$313$	8.23991	−	22.0921i	0.465747	−	1.24872i	0.931480	−	0.363792i	$-0.118518\pi$
$314$		0			0
$315$	−7.32041	+	25.1003i	−0.412459	+	1.41424i
$316$		0			0
$317$	32.7688	−	12.2221i	1.84048	−	0.686463i	0.854533	−	0.519397i	$-0.173844\pi$
$317$	32.7688	−	12.2221i	1.84048	−	0.686463i	0.985946	−	0.167066i	$-0.0534292\pi$
$318$		0			0
$319$	11.8960	+	7.64507i	0.666046	+	0.428042i
$320$		0			0
$321$			9.63627i			0.537844i
$322$		0			0
$323$	−24.1778	+	24.1778i	−1.34529	+	1.34529i
$324$		0			0
$325$	3.39950	+	15.3573i	0.188570	+	0.851867i
$326$		0			0
$327$	3.66900	+	9.83697i	0.202896	+	0.543986i
$328$		0			0
$329$	−22.3256	−	6.55540i	−1.23085	−	0.361411i
$330$		0			0
$331$	8.45926	+	18.5232i	0.464963	+	1.01813i	0.986328	+	0.164793i	$0.0526956\pi$
$331$	8.45926	+	18.5232i	0.464963	+	1.01813i	−0.521365	+	0.853334i	$0.674577\pi$
$332$		0			0
$333$	46.7832	−	3.34600i	2.56371	−	0.183360i
$334$		0			0
$335$	22.4724	−	6.64305i	1.22780	−	0.362948i
$336$		0			0
$337$	4.52759	−	20.8130i	0.246634	−	1.13376i	−0.672588	−	0.740017i	$-0.734817\pi$
$337$	4.52759	−	20.8130i	0.246634	−	1.13376i	0.919222	−	0.393740i	$-0.128819\pi$
$338$		0			0
$339$	−0.411655	−	2.86312i	−0.0223580	−	0.155503i
$340$		0			0
$341$	−10.4869	−	1.50779i	−0.567897	−	0.0816512i
$342$		0			0
$343$	1.35596	−	18.9588i	0.0732151	−	1.02368i
$344$		0			0
$345$	−33.5365	−	0.834240i	−1.80555	−	0.0449140i
$346$		0			0
$347$	−0.396629	+	5.54560i	−0.0212922	+	0.297703i	0.975637	+	0.219392i	$0.0704073\pi$
$347$	−0.396629	+	5.54560i	−0.0212922	+	0.297703i	−0.996929	+	0.0783113i	$0.975047\pi$
$348$		0			0
$349$	24.0727	+	3.46113i	1.28858	+	0.185270i	0.752329	−	0.658787i	$-0.228930\pi$
$349$	24.0727	+	3.46113i	1.28858	+	0.185270i	0.536253	+	0.844057i	$0.319839\pi$
$350$		0			0
$351$	−5.30238	−	36.8789i	−0.283020	−	1.96845i
$352$		0			0
$353$	4.53721	−	20.8572i	0.241491	−	1.11012i	−0.683447	−	0.730000i	$-0.739520\pi$
$353$	4.53721	−	20.8572i	0.241491	−	1.11012i	0.924938	−	0.380117i	$-0.124116\pi$
$354$		0			0
$355$	1.96794	+	1.06992i	0.104447	+	0.0567854i
$356$		0			0
$357$	−33.9374	+	2.42725i	−1.79616	+	0.128464i
$358$		0			0
$359$	−11.1278	−	24.3665i	−0.587302	−	1.28601i	−0.937059	−	0.349172i	$-0.886463\pi$
$359$	−11.1278	−	24.3665i	−0.587302	−	1.28601i	0.349756	−	0.936841i	$-0.386264\pi$
$360$		0			0
$361$	−9.92426	−	2.91403i	−0.522329	−	0.153370i
$362$		0			0
$363$	7.99077	+	21.4241i	0.419407	+	1.12447i
$364$		0			0
$365$	6.30629	+	4.03657i	0.330086	+	0.211284i
$366$		0			0
$367$	16.4936	−	16.4936i	0.860959	−	0.860959i	−0.130491	−	0.991450i	$-0.541655\pi$
$367$	16.4936	−	16.4936i	0.860959	−	0.860959i	0.991450	+	0.130491i	$0.0416553\pi$
$368$		0			0
$369$			37.2005i			1.93658i
$370$		0			0
$371$	−6.66917	−	4.28602i	−0.346246	−	0.222519i
$372$		0			0
$373$	17.0946	−	6.37597i	0.885127	−	0.330135i	0.134541	−	0.990908i	$-0.457044\pi$
$373$	17.0946	−	6.37597i	0.885127	−	0.330135i	0.750586	+	0.660773i	$0.229771\pi$
$374$		0			0
$375$	−9.66981	+	33.6118i	−0.499347	+	1.73570i
$376$		0			0
$377$	−8.09206	+	21.6957i	−0.416763	+	1.11738i
$378$		0			0
$379$	−12.8502	+	14.8299i	−0.660069	+	0.761760i	−0.982788	−	0.184735i	$-0.940857\pi$
$379$	−12.8502	+	14.8299i	−0.660069	+	0.761760i	0.322720	+	0.946495i	$0.395403\pi$
$380$		0			0
$381$	−5.92244	+	1.73899i	−0.303416	+	0.0890909i
$382$		0			0
$383$	−5.38357	−	1.17112i	−0.275088	−	0.0598417i	0.0729051	−	0.997339i	$-0.476773\pi$
$383$	−5.38357	−	1.17112i	−0.275088	−	0.0598417i	−0.347993	+	0.937497i	$0.613137\pi$
$384$		0			0
$385$	−7.32452	+	1.06675i	−0.373292	+	0.0543665i
$386$		0			0
$387$	−24.1440	−	32.2526i	−1.22731	−	1.63949i
$388$		0			0
$389$	−23.8953	−	27.5767i	−1.21154	−	1.39819i	−0.892863	−	0.450329i	$-0.851307\pi$
$389$	−23.8953	−	27.5767i	−1.21154	−	1.39819i	−0.318678	−	0.947863i	$-0.603239\pi$
$390$		0			0
$391$	−9.81817	−	28.6357i	−0.496526	−	1.44817i
$392$		0			0
$393$	−32.5152	−	2.32553i	−1.64017	−	0.117308i
$394$		0			0
$395$	13.0116	−	9.77745i	0.654685	−	0.491957i
$396$		0			0
$397$	6.03277	−	8.05883i	0.302776	−	0.404461i	−0.623189	−	0.782071i	$-0.714163\pi$
$397$	6.03277	−	8.05883i	0.302776	−	0.404461i	0.925965	+	0.377610i	$0.123254\pi$
$398$		0			0
$399$	−15.7859	−	24.5634i	−0.790286	−	1.22971i
$400$		0			0
$401$	6.36318	+	21.6710i	0.317762	+	1.08220i	0.951244	+	0.308440i	$0.0998070\pi$
$401$	6.36318	+	21.6710i	0.317762	+	1.08220i	−0.633482	+	0.773758i	$0.718375\pi$
$402$		0			0
$403$	−1.23766	−	17.3048i	−0.0616523	−	0.862012i
$404$		0			0
$405$	12.9799	−	34.9954i	0.644979	−	1.73894i
$406$		0			0
$407$	6.36342	+	11.6537i	0.315423	+	0.577654i
$408$		0			0
$409$	16.8911	+	7.71390i	0.835210	+	0.381428i	0.786655	−	0.617393i	$-0.211811\pi$
$409$	16.8911	+	7.71390i	0.835210	+	0.381428i	0.0485552	+	0.998821i	$0.484538\pi$
$410$		0			0
$411$	27.1259	−	42.2087i	1.33802	−	2.08200i
$412$		0			0
$413$	−6.31498	−	6.31498i	−0.310740	−	0.310740i
$414$		0			0
$415$	−0.0586725	−	32.1618i	−0.00288012	−	1.57876i
$416$		0			0
$417$	−2.72268	−	12.5160i	−0.133330	−	0.612909i
$418$		0			0
$419$	1.20239	−	2.63286i	0.0587404	−	0.128624i	−0.877985	−	0.478687i	$-0.841113\pi$
$419$	1.20239	−	2.63286i	0.0587404	−	0.128624i	0.936726	+	0.350064i	$0.113840\pi$
$420$		0			0
$421$	−4.53171	+	15.4336i	−0.220862	+	0.752186i	0.772281	+	0.635281i	$0.219116\pi$
$421$	−4.53171	+	15.4336i	−0.220862	+	0.752186i	−0.993143	+	0.116906i	$0.962703\pi$
$422$		0			0
$423$	85.8600	+	32.0241i	4.17465	+	1.55707i
$424$		0			0
$425$	−31.4720	+	2.36637i	−1.52661	+	0.114786i
$426$		0			0
$427$	−16.9993	−	9.28234i	−0.822656	−	0.449204i
$428$		0			0
$429$	15.9041	−	10.2210i	0.767858	−	0.493472i
$430$		0			0
$431$	−3.94203	+	0.566779i	−0.189881	+	0.0273008i	−0.236599	−	0.971607i	$-0.576033\pi$
$431$	−3.94203	+	0.566779i	−0.189881	+	0.0273008i	0.0467182	+	0.998908i	$0.485124\pi$
$432$		0			0
$433$	−24.5878	+	18.4062i	−1.18162	+	0.884547i	−0.995194	−	0.0979231i	$-0.968780\pi$
$433$	−24.5878	+	18.4062i	−1.18162	+	0.884547i	−0.186422	+	0.982470i	$0.559689\pi$
$434$		0			0
$435$	−38.8512	+	33.7890i	−1.86277	+	1.62006i
$436$		0			0
$437$	17.5304	−	19.1723i	0.838594	−	0.917137i
$438$		0			0
$439$	0.575113	−	0.498338i	0.0274486	−	0.0237844i	−0.641028	−	0.767517i	$-0.721492\pi$
$439$	0.575113	−	0.498338i	0.0274486	−	0.0237844i	0.668477	+	0.743733i	$0.266946\pi$
$440$		0			0
$441$	−3.89297	+	27.0762i	−0.185379	+	1.28934i
$442$		0			0
$443$	15.9961	+	11.9745i	0.759996	+	0.568926i	0.907459	−	0.420142i	$-0.138020\pi$
$443$	15.9961	+	11.9745i	0.759996	+	0.568926i	−0.147462	+	0.989068i	$0.547111\pi$
$444$		0			0
$445$	6.10146	+	1.31564i	0.289237	+	0.0623672i
$446$		0			0
$447$	−17.4477	+	31.9531i	−0.825248	+	1.51133i
$448$		0			0
$449$	−15.1480	−	13.1259i	−0.714881	−	0.619447i	0.219547	−	0.975602i	$-0.429542\pi$
$449$	−15.1480	−	13.1259i	−0.714881	−	0.619447i	−0.934427	+	0.356155i	$0.884088\pi$
$450$		0			0
$451$	−9.57956	+	4.37484i	−0.451084	+	0.206003i
$452$		0			0
$453$	15.8386	−	8.64852i	0.744161	−	0.406343i
$454$		0			0
$455$	−4.25639	−	11.3486i	−0.199543	−	0.532029i
$456$		0			0
$457$	−30.0118	+	6.52866i	−1.40389	+	0.305398i	−0.849821	−	0.527072i	$-0.823290\pi$
$457$	−30.0118	+	6.52866i	−1.40389	+	0.305398i	−0.554070	+	0.832470i	$0.686926\pi$
$458$		0			0
$459$	74.7597			3.48948
$460$		0			0
$461$	−12.2575			−0.570891			−0.285445	−	0.958395i	$-0.592142\pi$
$461$	−12.2575			−0.570891			−0.285445	+	0.958395i	$0.592142\pi$
$462$		0			0
$463$	35.3814	−	7.69675i	1.64431	−	0.357698i	0.707278	−	0.706935i	$-0.249923\pi$
$463$	35.3814	−	7.69675i	1.64431	−	0.357698i	0.937034	+	0.349237i	$0.113559\pi$
$464$		0			0
$465$	15.9615	−	35.1202i	0.740197	−	1.62866i
$466$		0			0
$467$	16.9599	−	9.26079i	0.784809	−	0.428538i	−0.0362774	−	0.999342i	$-0.511550\pi$
$467$	16.9599	−	9.26079i	0.784809	−	0.428538i	0.821087	+	0.570803i	$0.193368\pi$
$468$		0			0
$469$	−16.4258	+	7.50140i	−0.758472	+	0.346383i
$470$		0			0
$471$	−16.7876	−	14.5466i	−0.773534	−	0.670271i
$472$		0			0
$473$	5.46605	−	10.0103i	0.251329	−	0.460275i
$474$		0			0
$475$	−14.7261	−	22.7315i	−0.675681	−	1.04299i
$476$		0			0
$477$	24.9943	+	18.7105i	1.14441	+	0.856695i
$478$		0			0
$479$	−1.55843	+	10.8391i	−0.0712067	+	0.495253i	0.922743	+	0.385416i	$0.125942\pi$
$479$	−1.55843	+	10.8391i	−0.0712067	+	0.495253i	−0.993950	+	0.109837i	$0.964967\pi$
$480$		0			0
$481$	−16.4320	+	14.2384i	−0.749235	+	0.649216i
$482$		0			0
$483$	25.6766	−	2.99465i	1.16833	−	0.136261i
$484$		0			0
$485$	0.758656	+	0.872315i	0.0344488	+	0.0396098i
$486$		0			0
$487$	−9.53029	+	7.13428i	−0.431858	+	0.323285i	−0.792995	−	0.609228i	$-0.791480\pi$
$487$	−9.53029	+	7.13428i	−0.431858	+	0.323285i	0.361137	+	0.932513i	$0.382389\pi$
$488$		0			0
$489$	−53.0565	+	7.62837i	−2.39930	+	0.344967i
$490$		0			0
$491$	15.1757	−	9.75284i	0.684871	−	0.440140i	−0.151388	−	0.988474i	$-0.548374\pi$
$491$	15.1757	−	9.75284i	0.684871	−	0.440140i	0.836259	+	0.548335i	$0.184738\pi$
$492$		0			0
$493$	−40.7792	−	22.2671i	−1.83660	−	1.00286i
$494$		0			0
$495$	29.0726	−	2.13263i	1.30672	−	0.0958546i
$496$		0			0
$497$	−1.61726	−	0.603206i	−0.0725439	−	0.0270575i
$498$		0			0
$499$	−1.48616	+	5.06140i	−0.0665297	+	0.226579i	−0.986046	−	0.166472i	$-0.946762\pi$
$499$	−1.48616	+	5.06140i	−0.0665297	+	0.226579i	0.919516	+	0.393052i	$0.128581\pi$
$500$		0			0
$501$	−9.88473	+	21.6445i	−0.441617	+	0.967006i
$502$		0			0
$503$	2.82881	+	13.0038i	0.126131	+	0.579813i	0.996216	+	0.0869119i	$0.0276999\pi$
$503$	2.82881	+	13.0038i	0.126131	+	0.579813i	−0.870085	+	0.492901i	$0.835936\pi$
$504$		0			0
$505$	10.4564	+	10.4183i	0.465305	+	0.463610i
$506$		0			0
$507$	−6.86595	−	6.86595i	−0.304928	−	0.304928i
$508$		0			0
$509$	−16.9745	+	26.4128i	−0.752381	+	1.17073i	0.228008	+	0.973659i	$0.426779\pi$
$509$	−16.9745	+	26.4128i	−0.752381	+	1.17073i	−0.980390	+	0.197069i	$0.936858\pi$
$510$		0			0
$511$	−5.24836	−	2.39685i	−0.232174	−	0.106030i
$512$		0			0
$513$	30.7471	+	56.3092i	1.35752	+	2.48611i
$514$		0			0
$515$	−20.1948	+	9.26723i	−0.889890	+	0.408363i
$516$		0			0
$517$	1.85069	+	25.8760i	0.0813932	+	1.13803i
$518$		0			0
$519$	2.08571	+	7.10326i	0.0915523	+	0.311799i
$520$		0			0
$521$	11.5722	+	18.0067i	0.506988	+	0.788889i	0.996543	−	0.0830840i	$-0.0264770\pi$
$521$	11.5722	+	18.0067i	0.506988	+	0.788889i	−0.489555	+	0.871973i	$0.662841\pi$
$522$		0			0
$523$	−3.31174	+	4.42396i	−0.144812	+	0.193446i	−0.867083	−	0.498164i	$-0.834008\pi$
$523$	−3.31174	+	4.42396i	−0.144812	+	0.193446i	0.722270	+	0.691611i	$0.243099\pi$
$524$		0			0
$525$	3.73820	−	26.6907i	0.163148	−	1.16488i
$526$		0			0
$527$	34.7226	+	2.48341i	1.51254	+	0.108179i
$528$		0			0
$529$	8.42447	+	21.4016i	0.366281	+	0.930504i
$530$		0			0
$531$	23.0329	+	26.5814i	0.999543	+	1.15353i
$532$		0			0
$533$	−10.3346	−	13.8053i	−0.447639	−	0.597976i
$534$		0			0
$535$	−0.992694	−	6.81605i	−0.0429179	−	0.294683i
$536$		0			0
$537$	57.6466	+	12.5403i	2.48764	+	0.541152i
$538$		0			0
$539$	−7.43025	+	2.18172i	−0.320044	+	0.0939733i
$540$		0			0
$541$	1.85456	−	2.14028i	0.0797339	−	0.0920178i	−0.714481	−	0.699655i	$-0.753337\pi$
$541$	1.85456	−	2.14028i	0.0797339	−	0.0920178i	0.794215	+	0.607637i	$0.207883\pi$
$542$		0			0
$543$	−3.30124	+	8.85098i	−0.141670	+	0.379832i
$544$		0			0
$545$	−3.60857	−	6.58004i	−0.154574	−	0.281858i
$546$		0			0
$547$	5.92424	−	2.20963i	0.253302	−	0.0944769i	−0.219606	−	0.975589i	$-0.570477\pi$
$547$	5.92424	−	2.20963i	0.253302	−	0.0944769i	0.472908	+	0.881112i	$0.343204\pi$
$548$		0			0
$549$	64.1705	+	41.2399i	2.73873	+	1.76008i
$550$		0			0
$551$		−	39.8730i		−	1.69865i
$552$		0			0
$553$	−8.86840	+	8.86840i	−0.377123	+	0.377123i
$554$		0			0
$555$	−47.2233	+	10.3631i	−2.00452	+	0.439888i
$556$		0			0
$557$	−7.17907	−	19.2478i	−0.304187	−	0.815557i	−0.995652	−	0.0931472i	$-0.970307\pi$
$557$	−7.17907	−	19.2478i	−0.304187	−	0.815557i	0.691465	−	0.722410i	$-0.256965\pi$
$558$		0			0
$559$	17.9200	+	5.26178i	0.757935	+	0.222550i
$560$		0			0
$561$	15.7584	+	34.5060i	0.665319	+	1.45685i
$562$		0			0
$563$	−6.29581	+	0.450285i	−0.265337	+	0.0189773i	−0.203374	−	0.979101i	$-0.565191\pi$
$563$	−6.29581	+	0.450285i	−0.265337	+	0.0189773i	−0.0619631	+	0.998078i	$0.519736\pi$
$564$		0			0
$565$	0.586125	+	1.98277i	0.0246585	+	0.0834158i
$566$		0			0
$567$	−6.11381	+	28.1047i	−0.256756	+	1.18029i
$568$		0			0
$569$	−4.38561	−	30.5026i	−0.183854	−	1.27873i	−0.847544	−	0.530725i	$-0.821920\pi$
$569$	−4.38561	−	30.5026i	−0.183854	−	1.27873i	0.663690	−	0.748008i	$-0.268990\pi$
$570$		0			0
$571$	−8.39612	−	1.20718i	−0.351367	−	0.0505189i	−0.0356281	−	0.999365i	$-0.511343\pi$
$571$	−8.39612	−	1.20718i	−0.351367	−	0.0505189i	−0.315739	+	0.948846i	$0.602252\pi$
$572$		0			0
$573$	2.06332	−	28.8490i	0.0861964	−	1.20518i
$574$		0			0
$575$	23.8074	−	2.86473i	0.992838	−	0.119467i
$576$		0			0
$577$	0.828421	−	11.5828i	0.0344876	−	0.482200i	−0.950631	−	0.310324i	$-0.899563\pi$
$577$	0.828421	−	11.5828i	0.0344876	−	0.482200i	0.985119	−	0.171876i	$-0.0549829\pi$
$578$		0			0
$579$	−67.4277	−	9.69465i	−2.80220	−	0.402896i
$580$		0			0
$581$	3.52705	+	24.5311i	0.146327	+	1.01772i
$582$		0			0
$583$	−1.87880	+	8.63671i	−0.0778120	+	0.357696i
$584$		0			0
$585$	13.5319	+	45.7764i	0.559476	+	1.89262i
$586$		0			0
$587$	−18.8858	+	1.35074i	−0.779500	+	0.0557510i	−0.455418	−	0.890278i	$-0.650510\pi$
$587$	−18.8858	+	1.35074i	−0.779500	+	0.0557510i	−0.324083	+	0.946029i	$0.605056\pi$
$588$		0			0
$589$	12.4102	+	27.1745i	0.511353	+	1.11971i
$590$		0			0
$591$	66.4542	+	19.5127i	2.73356	+	0.802646i
$592$		0			0
$593$	−14.1529	−	37.9455i	−0.581191	−	1.55823i	−0.811029	−	0.585006i	$-0.801092\pi$
$593$	−14.1529	−	37.9455i	−0.581191	−	1.55823i	0.229838	−	0.973229i	$-0.426180\pi$
$594$		0			0
$595$	23.7550	−	5.21298i	0.973858	−	0.213711i
$596$		0			0
$597$	−44.8474	+	44.8474i	−1.83548	+	1.83548i
$598$		0			0
$599$		−	29.0930i		−	1.18871i	−0.804203	−	0.594354i	$-0.797408\pi$
$599$		−	29.0930i		−	1.18871i	0.804203	−	0.594354i	$-0.202592\pi$
$600$		0			0
$601$	31.8441	+	20.4650i	1.29895	+	0.834784i	0.993097	−	0.117295i	$-0.0374224\pi$
$601$	31.8441	+	20.4650i	1.29895	+	0.834784i	0.305852	+	0.952079i	$0.401059\pi$
$602$		0			0
$603$	66.6329	−	24.8528i	2.71350	−	1.01208i
$604$		0			0
$605$	−7.85917	−	14.3308i	−0.319521	−	0.582629i
$606$		0			0
$607$	8.90931	−	23.8868i	0.361618	−	0.969535i	−0.620986	−	0.783822i	$-0.713268\pi$
$607$	8.90931	−	23.8868i	0.361618	−	0.969535i	0.982604	−	0.185713i	$-0.0594596\pi$
$608$		0			0
$609$	25.9826	−	29.9855i	1.05287	−	1.21507i
$610$		0			0
$611$	−40.7597	+	11.9681i	−1.64896	+	0.484178i
$612$		0			0
$613$	6.03300	+	1.31240i	0.243671	+	0.0530073i	0.332742	−	0.943018i	$-0.392026\pi$
$613$	6.03300	+	1.31240i	0.243671	+	0.0530073i	−0.0890712	+	0.996025i	$0.528390\pi$
$614$		0			0
$615$	−5.52645	−	37.9458i	−0.222848	−	1.53012i
$616$		0			0
$617$	−17.5620	−	23.4601i	−0.707019	−	0.944466i	0.292913	−	0.956139i	$-0.405375\pi$
$617$	−17.5620	−	23.4601i	−0.707019	−	0.944466i	−0.999932	+	0.0116726i	$0.996284\pi$
$618$		0			0
$619$	−18.1850	−	20.9866i	−0.730916	−	0.843522i	0.261658	−	0.965161i	$-0.415731\pi$
$619$	−18.1850	−	20.9866i	−0.730916	−	0.843522i	−0.992574	+	0.121638i	$0.961185\pi$
$620$		0			0
$621$	−56.7439	+	2.53843i	−2.27705	+	0.101864i
$622$		0			0
$623$	−4.79749	−	0.343123i	−0.192207	−	0.0137469i
$624$		0			0
$625$	3.37721	−	24.7708i	0.135088	−	0.990834i
$626$		0			0
$627$	−19.5089	+	26.0609i	−0.779111	+	1.04077i
$628$		0			0
$629$	−23.5868	−	36.7017i	−0.940466	−	1.46339i
$630$		0			0
$631$	1.02906	+	3.50467i	0.0409664	+	0.139519i	0.977437	−	0.211228i	$-0.0677461\pi$
$631$	1.02906	+	3.50467i	0.0409664	+	0.139519i	−0.936471	+	0.350746i	$0.885928\pi$
$632$		0			0
$633$	−3.98660	−	55.7399i	−0.158453	−	2.21546i
$634$		0			0
$635$	4.00999	−	1.84015i	0.159132	−	0.0730241i
$636$		0			0
$637$	−6.07724	−	11.1296i	−0.240789	−	0.440972i
$638$		0			0
$639$	6.18360	+	2.82395i	0.244619	+	0.111714i
$640$		0			0
$641$	8.49387	−	13.2167i	0.335488	−	0.522029i	−0.631993	−	0.774974i	$-0.717763\pi$
$641$	8.49387	−	13.2167i	0.335488	−	0.522029i	0.967481	+	0.252945i	$0.0813992\pi$
$642$		0			0
$643$	−19.0340	−	19.0340i	−0.750627	−	0.750627i	0.223969	−	0.974596i	$-0.428098\pi$
$643$	−19.0340	−	19.0340i	−0.750627	−	0.750627i	−0.974596	+	0.223969i	$0.928098\pi$
$644$		0			0
$645$	29.4191	+	29.3119i	1.15838	+	1.15416i
$646$		0			0
$647$	5.44321	+	25.0220i	0.213995	+	0.983718i	0.951326	+	0.308186i	$0.0997220\pi$
$647$	5.44321	+	25.0220i	0.213995	+	0.983718i	−0.737331	+	0.675531i	$0.763914\pi$
$648$		0			0
$649$	−4.13631	+	9.05725i	−0.162364	+	0.355528i
$650$		0			0
$651$	−8.37504	+	28.5228i	−0.328244	+	1.11790i
$652$		0			0
$653$	10.9420	+	4.08116i	0.428194	+	0.159708i	0.554316	−	0.832307i	$-0.312980\pi$
$653$	10.9420	+	4.08116i	0.428194	+	0.159708i	−0.126121	+	0.992015i	$0.540253\pi$
$654$		0			0
$655$	23.2386	−	1.70468i	0.908008	−	0.0666072i
$656$		0			0
$657$	19.9437	+	10.8901i	0.778079	+	0.424863i
$658$		0			0
$659$	1.49965	−	0.963767i	0.0584181	−	0.0375430i	−0.511106	−	0.859518i	$-0.670764\pi$
$659$	1.49965	−	0.963767i	0.0584181	−	0.0375430i	0.569524	+	0.821975i	$0.307128\pi$
$660$		0			0
$661$	−12.2920	+	1.76732i	−0.478102	+	0.0687406i	−0.377153	−	0.926151i	$-0.623097\pi$
$661$	−12.2920	+	1.76732i	−0.478102	+	0.0687406i	−0.100949	+	0.994892i	$0.532188\pi$
$662$		0			0
$663$	−49.7275	+	37.2256i	−1.93126	+	1.44572i
$664$		0			0
$665$	13.6964	+	15.7483i	0.531122	+	0.610692i
$666$		0			0
$667$	31.7082	+	15.5165i	1.22775	+	0.600802i
$668$		0			0
$669$	48.7989	−	42.2845i	1.88667	−	1.63481i
$670$		0			0
$671$	−3.07319	+	21.3745i	−0.118639	+	0.825154i
$672$		0			0
$673$	−4.62280	−	3.46059i	−0.178196	−	0.133396i	0.506457	−	0.862266i	$-0.330955\pi$
$673$	−4.62280	−	3.46059i	−0.178196	−	0.133396i	−0.684652	+	0.728870i	$0.740046\pi$
$674$		0			0
$675$	−12.3766	+	57.9110i	−0.476377	+	2.22899i
$676$		0			0
$677$	−23.0509	+	42.2147i	−0.885920	+	1.62244i	−0.107935	+	0.994158i	$0.534424\pi$
$677$	−23.0509	+	42.2147i	−0.885920	+	1.62244i	−0.777985	+	0.628283i	$0.783758\pi$
$678$		0			0
$679$	−0.673257	−	0.583380i	−0.0258372	−	0.0223881i
$680$		0			0
$681$	58.8306	−	26.8670i	2.25439	−	1.02955i
$682$		0			0
$683$	−22.0467	+	12.0384i	−0.843593	+	0.460637i	−0.842074	−	0.539362i	$-0.818665\pi$
$683$	−22.0467	+	12.0384i	−0.843593	+	0.460637i	−0.00151900	+	0.999999i	$0.500484\pi$
$684$		0			0
$685$	−14.8388	+	32.6500i	−0.566963	+	1.24749i
$686$		0			0
$687$	44.5887	−	9.69968i	1.70117	−	0.370066i
$688$		0			0
$689$	−14.4735			−0.551395
$690$		0			0
$691$	−44.3203			−1.68602			−0.843012	−	0.537895i	$-0.819220\pi$
$691$	−44.3203			−1.68602			−0.843012	+	0.537895i	$0.819220\pi$
$692$		0			0
$693$	−21.9497	+	4.77486i	−0.833800	+	0.181382i
$694$		0			0
$695$	3.21519	+	8.57246i	0.121959	+	0.325172i
$696$		0			0
$697$	30.3701	−	16.5833i	1.15035	−	0.628138i
$698$		0			0
$699$	28.1519	−	12.8566i	1.06480	−	0.486279i
$700$		0			0
$701$	28.5070	+	24.7014i	1.07669	+	0.932960i	0.997954	−	0.0639351i	$-0.0203651\pi$
$701$	28.5070	+	24.7014i	1.07669	+	0.932960i	0.0787394	+	0.996895i	$0.474911\pi$
$702$		0			0
$703$	17.9431	−	32.8603i	0.676736	−	1.23935i
$704$		0			0
$705$	−92.3374	−	19.9104i	−3.47763	−	0.749870i
$706$		0			0
$707$	−9.10564	−	6.81639i	−0.342453	−	0.256357i
$708$		0			0
$709$	−0.436052	+	3.03281i	−0.0163763	+	0.113899i	−0.996370	−	0.0851294i	$-0.972870\pi$
$709$	−0.436052	+	3.03281i	−0.0163763	+	0.113899i	0.979994	+	0.199029i	$0.0637787\pi$
$710$		0			0
$711$	37.3294	−	32.3461i	1.39996	−	1.21307i
$712$		0			0
$713$	−26.4394	−	0.705960i	−0.990163	−	0.0264384i
$714$		0			0
$715$	−10.1966	+	8.86800i	−0.381330	+	0.331644i
$716$		0			0
$717$	30.8354	−	23.0831i	1.15157	−	0.862053i
$718$		0			0
$719$	−26.1120	+	3.75435i	−0.973815	+	0.140013i	−0.610813	−	0.791775i	$-0.709157\pi$
$719$	−26.1120	+	3.75435i	−0.973815	+	0.140013i	−0.363002	+	0.931788i	$0.618248\pi$
$720$		0			0
$721$	14.4040	−	9.25689i	0.536433	−	0.344745i
$722$		0			0
$723$	32.8760	+	17.9516i	1.22267	+	0.667628i
$724$		0			0
$725$	23.9999	−	27.9024i	0.891333	−	1.03627i
$726$		0			0
$727$	13.8486	+	5.16526i	0.513616	+	0.191569i	0.592889	−	0.805284i	$-0.297987\pi$
$727$	13.8486	+	5.16526i	0.513616	+	0.191569i	−0.0792733	+	0.996853i	$0.525260\pi$
$728$		0			0
$729$	0.598199	−	2.03728i	0.0221555	−	0.0754548i
$730$		0			0
$731$	−15.5677	+	34.0885i	−0.575793	+	1.26081i
$732$		0			0
$733$	−2.68142	−	12.3263i	−0.0990406	−	0.455283i	−0.999781	−	0.0209247i	$-0.993339\pi$
$733$	−2.68142	−	12.3263i	−0.0990406	−	0.455283i	0.900740	−	0.434358i	$-0.143025\pi$
$734$		0			0
$735$	−0.0514394	−	28.1969i	−0.00189737	−	1.04006i
$736$		0			0
$737$	14.2360	+	14.2360i	0.524391	+	0.524391i
$738$		0			0
$739$	−13.7749	+	21.4341i	−0.506717	+	0.788466i	−0.996519	−	0.0833671i	$-0.973433\pi$
$739$	−13.7749	+	21.4341i	−0.506717	+	0.788466i	0.489802	+	0.871834i	$0.337069\pi$
$740$		0			0
$741$	−48.4903	−	22.1448i	−1.78133	−	0.813508i
$742$		0			0
$743$	5.61584	+	10.2846i	0.206025	+	0.377307i	0.960177	−	0.279393i	$-0.0901334\pi$
$743$	5.61584	+	10.2846i	0.206025	+	0.377307i	−0.754151	+	0.656701i	$0.771952\pi$
$744$		0			0
$745$	9.04963	−	24.3988i	0.331553	−	0.893904i
$746$		0			0
$747$	−6.96308	−	97.3566i	−0.254766	−	3.56209i
$748$		0			0
$749$	1.49536	+	5.09274i	0.0546394	+	0.186085i
$750$		0			0
$751$	17.7120	+	27.5605i	0.646322	+	1.00570i	0.997588	+	0.0694203i	$0.0221150\pi$
$751$	17.7120	+	27.5605i	0.646322	+	1.00570i	−0.351266	+	0.936276i	$0.614249\pi$
$752$		0			0
$753$	−42.5641	+	56.8590i	−1.55112	+	2.07206i
$754$		0			0
$755$	−10.3122	+	7.74901i	−0.375299	+	0.282015i
$756$		0			0
$757$	−40.9407	−	2.92814i	−1.48802	−	0.106425i	−0.696493	−	0.717564i	$-0.745257\pi$
$757$	−40.9407	−	2.92814i	−1.48802	−	0.106425i	−0.791523	+	0.611139i	$0.790712\pi$
$758$		0			0
$759$	−13.1325	−	25.6556i	−0.476680	−	0.931240i
$760$		0			0
$761$	14.1333	+	16.3107i	0.512333	+	0.591264i	0.951695	−	0.307046i	$-0.0993407\pi$
$761$	14.1333	+	16.3107i	0.512333	+	0.591264i	−0.439361	+	0.898310i	$0.644795\pi$
$762$		0			0
$763$	3.46556	+	4.62945i	0.125462	+	0.167597i
$764$		0			0
$765$	−94.7812	+	13.8040i	−3.42682	+	0.499085i
$766$		0			0
$767$	−15.9321	−	3.46583i	−0.575276	−	0.125144i
$768$		0			0
$769$	39.9667	−	11.7353i	1.44124	−	0.423185i	0.534603	−	0.845103i	$-0.320461\pi$
$769$	39.9667	−	11.7353i	1.44124	−	0.423185i	0.906634	+	0.421918i	$0.138643\pi$
$770$		0			0
$771$	50.2952	−	58.0438i	1.81134	−	2.09040i
$772$		0			0
$773$	−13.2230	+	35.4524i	−0.475600	+	1.27513i	0.448774	+	0.893645i	$0.351861\pi$
$773$	−13.2230	+	35.4524i	−0.475600	+	1.27513i	−0.924374	+	0.381487i	$0.875412\pi$
$774$		0			0
$775$	−7.67213	+	26.4860i	−0.275591	+	0.951405i
$776$		0			0
$777$	34.9064	−	13.0194i	1.25226	−	0.467069i
$778$		0			0
$779$	24.9812	+	16.0544i	0.895044	+	0.575210i
$780$		0			0
$781$			1.92445i			0.0688622i
$782$		0			0
$783$	−61.6453	+	61.6453i	−2.20302	+	2.20302i
$784$		0			0
$785$	13.3730	+	8.55986i	0.477302	+	0.305515i
$786$		0			0
$787$	18.7370	+	50.2358i	0.667902	+	1.79071i	0.610013	+	0.792391i	$0.291164\pi$
$787$	18.7370	+	50.2358i	0.667902	+	1.79071i	0.0578891	+	0.998323i	$0.481563\pi$
$788$		0			0
$789$	23.6883	+	6.95551i	0.843326	+	0.247623i
$790$		0			0
$791$	−0.661859	−	1.44927i	−0.0235330	−	0.0515301i
$792$		0			0
$793$	−35.2708	+	2.52262i	−1.25250	+	0.0895808i
$794$		0			0
$795$	−28.2746	−	15.3722i	−1.00280	−	0.545196i
$796$		0			0
$797$	2.65168	−	12.1896i	0.0939275	−	0.431778i	−0.906036	−	0.423201i	$-0.860906\pi$
$797$	2.65168	−	12.1896i	0.0939275	−	0.431778i	0.999963	−	0.00857642i	$-0.00272999\pi$
$798$		0			0
$799$	−12.1307	−	84.3709i	−0.429153	−	2.98483i
$800$		0			0
$801$	18.7496	+	2.69578i	0.662483	+	0.0952507i
$802$		0			0
$803$	−0.458912	+	6.41643i	−0.0161947	+	0.226431i
$804$		0			0
$805$	−17.8534	+	4.76333i	−0.629250	+	0.167885i
$806$		0			0
$807$	−0.436818	+	6.10752i	−0.0153767	+	0.214995i
$808$		0			0
$809$	17.7784	+	2.55614i	0.625054	+	0.0898693i	0.447562	−	0.894253i	$-0.352292\pi$
$809$	17.7784	+	2.55614i	0.625054	+	0.0898693i	0.177492	+	0.984122i	$0.443201\pi$
$810$		0			0
$811$	−1.76877	−	12.3021i	−0.0621100	−	0.431985i	−0.997023	−	0.0771072i	$-0.975432\pi$
$811$	−1.76877	−	12.3021i	−0.0621100	−	0.431985i	0.934913	−	0.354878i	$-0.115477\pi$
$812$		0			0
$813$	−11.2355	+	51.6488i	−0.394046	+	1.81140i
$814$		0			0
$815$	36.7427	−	10.8615i	1.28704	−	0.380461i
$816$		0			0
$817$	−32.0783	+	2.29428i	−1.12228	+	0.0802668i
$818$		0			0
$819$	−15.2804	−	33.4594i	−0.533940	−	1.16917i
$820$		0			0
$821$	−35.8750	−	10.5338i	−1.25205	−	0.367634i	−0.412517	−	0.910950i	$-0.635350\pi$
$821$	−35.8750	−	10.5338i	−1.25205	−	0.367634i	−0.839528	+	0.543316i	$0.817168\pi$
$822$		0			0
$823$	2.36365	+	6.33719i	0.0823916	+	0.220901i	0.971613	−	0.236577i	$-0.0760256\pi$
$823$	2.36365	+	6.33719i	0.0823916	+	0.220901i	−0.889221	+	0.457478i	$0.848753\pi$
$824$		0			0
$825$	−29.3382	+	6.49433i	−1.02142	+	0.226104i
$826$		0			0
$827$	−24.3816	+	24.3816i	−0.847832	+	0.847832i	−0.989862	−	0.142030i	$-0.954637\pi$
$827$	−24.3816	+	24.3816i	−0.847832	+	0.847832i	0.142030	+	0.989862i	$0.454637\pi$
$828$		0			0
$829$		−	21.1473i		−	0.734477i	−0.930127	−	0.367239i	$-0.880303\pi$
$829$		−	21.1473i		−	0.734477i	0.930127	−	0.367239i	$-0.119697\pi$
$830$		0			0
$831$	5.42670	+	3.48753i	0.188250	+	0.120981i
$832$		0			0
$833$	23.8401	−	8.89190i	0.826011	−	0.308086i
$834$		0			0
$835$	4.76205	−	16.3282i	0.164797	−	0.565060i
$836$		0			0
$837$	22.8262	−	61.1995i	0.788990	−	2.11536i
$838$		0			0
$839$	−4.75121	+	5.48319i	−0.164030	+	0.189301i	−0.831814	−	0.555054i	$-0.812698\pi$
$839$	−4.75121	+	5.48319i	−0.164030	+	0.189301i	0.667784	+	0.744355i	$0.267243\pi$
$840$		0			0
$841$	24.1614	−	7.09443i	0.833152	−	0.244636i
$842$		0			0
$843$	38.5276	+	8.38116i	1.32696	+	0.288662i
$844$		0			0
$845$	5.56382	+	4.14920i	0.191401	+	0.142737i
$846$		0			0
$847$	7.54771	+	10.0826i	0.259342	+	0.346441i
$848$		0			0
$849$	−1.17962	−	1.36135i	−0.0404845	−	0.0467216i
$850$		0			0
$851$	19.1490	+	27.0564i	0.656418	+	0.927480i
$852$		0			0
$853$	−25.8114	−	1.84607i	−0.883766	−	0.0632082i	−0.377926	−	0.925836i	$-0.623363\pi$
$853$	−25.8114	−	1.84607i	−0.883766	−	0.0632082i	−0.505840	+	0.862627i	$0.668817\pi$
$854$		0			0
$855$	−49.3788	−	65.7121i	−1.68872	−	2.24731i
$856$		0			0
$857$	27.8704	−	37.2305i	0.952034	−	1.27177i	−0.0103133	−	0.999947i	$-0.503283\pi$
$857$	27.8704	−	37.2305i	0.952034	−	1.27177i	0.962348	−	0.271822i	$-0.0876262\pi$
$858$		0			0
$859$	−11.1146	−	17.2946i	−0.379225	−	0.590086i	0.598206	−	0.801343i	$-0.295881\pi$
$859$	−11.1146	−	17.2946i	−0.379225	−	0.590086i	−0.977431	+	0.211257i	$0.932244\pi$
$860$		0			0
$861$	8.32487	+	28.3519i	0.283711	+	0.966230i
$862$		0			0
$863$	3.19910	+	44.7293i	0.108899	+	1.52260i	0.698911	+	0.715209i	$0.253668\pi$
$863$	3.19910	+	44.7293i	0.108899	+	1.52260i	−0.590012	+	0.807394i	$0.700877\pi$
$864$		0			0
$865$	−2.20704	−	4.80951i	−0.0750416	−	0.163528i
$866$		0			0
$867$	−34.2472	−	62.7191i	−1.16310	−	2.13005i
$868$		0			0
$869$	12.7195	+	5.80879i	0.431479	+	0.197050i
$870$		0			0
$871$	−17.8236	+	27.7341i	−0.603931	+	0.939734i
$872$		0			0
$873$	2.48085	+	2.48085i	0.0839640	+	0.0839640i
$874$		0			0
$875$	0.105432	+	19.2643i	0.00356425	+	0.651252i
$876$		0			0
$877$	−5.88792	−	27.0663i	−0.198821	−	0.913965i	−0.963114	−	0.269095i	$-0.913275\pi$
$877$	−5.88792	−	27.0663i	−0.198821	−	0.913965i	0.764293	−	0.644870i	$-0.223088\pi$
$878$		0			0
$879$	−2.88490	+	6.31704i	−0.0973051	+	0.213068i
$880$		0			0
$881$	10.3668	−	35.3061i	0.349266	−	1.18949i	−0.578297	−	0.815826i	$-0.696282\pi$
$881$	10.3668	−	35.3061i	0.349266	−	1.18949i	0.927563	−	0.373666i	$-0.121899\pi$
$882$		0			0
$883$	−52.9974	−	19.7670i	−1.78350	−	0.665212i	−0.998982	−	0.0451110i	$-0.985636\pi$
$883$	−52.9974	−	19.7670i	−1.78350	−	0.665212i	−0.784522	−	0.620101i	$-0.787091\pi$
$884$		0			0
$885$	−27.4432	−	23.6922i	−0.922493	−	0.796403i
$886$		0			0
$887$	−39.2288	−	21.4206i	−1.31717	−	0.719232i	−0.341797	−	0.939774i	$-0.611036\pi$
$887$	−39.2288	−	21.4206i	−1.31717	−	0.719232i	−0.975377	+	0.220542i	$0.929217\pi$
$888$		0			0
$889$	−2.86013	+	1.83810i	−0.0959258	+	0.0616478i
$890$		0			0
$891$	31.7410	−	4.56366i	1.06336	−	0.152888i
$892$		0			0
$893$	58.5592	−	43.8369i	1.95961	−	1.46695i
$894$		0			0
$895$	−42.0672	−	2.93158i	−1.40615	−	0.0979919i
$896$		0			0
$897$	36.4801	−	29.9433i	1.21803	−	0.999778i
$898$		0			0
$899$	−30.6793	+	26.5838i	−1.02321	+	0.886618i
$900$		0			0
$901$	4.13303	−	28.7459i	0.137691	−	0.957664i
$902$		0			0
$903$	−25.6187	−	19.1779i	−0.852535	−	0.638200i
$904$		0			0
$905$	1.42328	−	6.60067i	0.0473115	−	0.219414i
$906$		0			0
$907$	10.0669	−	18.4361i	0.334265	−	0.612160i	−0.655446	−	0.755242i	$-0.727519\pi$
$907$	10.0669	−	18.4361i	0.334265	−	0.612160i	0.989711	+	0.143082i	$0.0457013\pi$
$908$		0			0
$909$	33.8545	+	29.3351i	1.12288	+	0.972985i
$910$		0			0
$911$	−14.1956	+	6.48293i	−0.470323	+	0.214789i	−0.636454	−	0.771314i	$-0.719600\pi$
$911$	−14.1956	+	6.48293i	−0.470323	+	0.214789i	0.166132	+	0.986104i	$0.446872\pi$
$912$		0			0
$913$	24.2516	−	13.2424i	0.802610	−	0.438258i
$914$		0			0
$915$	−71.5826	−	32.5330i	−2.36645	−	1.07551i
$916$		0			0
$917$	−17.5451	+	3.81669i	−0.579389	+	0.126038i
$918$		0			0
$919$	0.0967353			0.00319100			0.00159550	−	0.999999i	$-0.499492\pi$
$919$	0.0967353			0.00319100			0.00159550	+	0.999999i	$0.499492\pi$
$920$		0			0
$921$	−85.1981			−2.80737
$922$		0			0
$923$	−3.07929	+	0.669858i	−0.101356	+	0.0220486i
$924$		0			0
$925$	32.3350	−	12.1949i	1.06317	−	0.400967i
$926$		0			0
$927$	−59.1840	+	32.3169i	−1.94386	+	1.06143i
$928$		0			0
$929$	−15.9407	+	7.27987i	−0.522997	+	0.238845i	−0.659378	−	0.751812i	$-0.729180\pi$
$929$	−15.9407	+	7.27987i	−0.522997	+	0.238845i	0.136381	+	0.990657i	$0.456453\pi$
$930$		0			0
$931$	16.5024	+	14.2994i	0.540843	+	0.468643i
$932$		0			0
$933$	34.4263	−	63.0471i	1.12707	−	2.06407i
$934$		0			0
$935$	−14.7011	−	22.7839i	−0.480777	−	0.745112i
$936$		0			0
$937$	12.8821	+	9.64339i	0.420838	+	0.315036i	0.788625	−	0.614875i	$-0.210793\pi$
$937$	12.8821	+	9.64339i	0.420838	+	0.315036i	−0.367787	+	0.929910i	$0.619884\pi$
$938$		0			0
$939$	−10.4972	+	73.0097i	−0.342563	+	2.38258i
$940$		0			0
$941$	41.7677	−	36.1919i	1.36159	−	1.17982i	0.396459	−	0.918052i	$-0.370239\pi$
$941$	41.7677	−	36.1919i	1.36159	−	1.17982i	0.965130	−	0.261772i	$-0.0843067\pi$
$942$		0			0
$943$	−22.4883	+	13.6182i	−0.732321	+	0.443471i
$944$		0			0
$945$	3.17238	−	45.5226i	0.103197	−	1.48085i
$946$		0			0
$947$	0.165568	−	0.123943i	0.00538023	−	0.00402759i	−0.596584	−	0.802551i	$-0.703476\pi$
$947$	0.165568	−	0.123943i	0.00538023	−	0.00402759i	0.601964	+	0.798523i	$0.294385\pi$
$948$		0			0
$949$	−10.4266	+	1.49912i	−0.338461	+	0.0486634i
$950$		0			0
$951$	−92.0396	+	59.1502i	−2.98459	+	1.91808i
$952$		0			0
$953$	27.6804	+	15.1146i	0.896655	+	0.489610i	0.860335	−	0.509730i	$-0.170255\pi$
$953$	27.6804	+	15.1146i	0.896655	+	0.489610i	0.0363200	+	0.999340i	$0.488436\pi$
$954$		0			0
$955$	1.51247	+	20.6184i	0.0489423	+	0.667195i
$956$		0			0
$957$	−41.4470	−	15.4589i	−1.33979	−	0.499716i
$958$		0			0
$959$	7.78597	−	26.5166i	0.251422	−	0.856265i
$960$		0			0
$961$	−0.243119	+	0.532355i	−0.00784253	+	0.0171728i
$962$		0			0
$963$	−4.44339	−	20.4259i	−0.143186	−	0.658216i
$964$		0			0
$965$	48.6925	−	0.0888293i	1.56747	−	0.00285952i
$966$		0			0
$967$	23.7519	+	23.7519i	0.763810	+	0.763810i	0.977009	−	0.213199i	$-0.0683883\pi$
$967$	23.7519	+	23.7519i	0.763810	+	0.763810i	−0.213199	+	0.977009i	$0.568388\pi$
$968$		0			0
$969$	57.8288	−	89.9834i	1.85773	−	2.89068i
$970$		0			0
$971$	−26.4870	−	12.0962i	−0.850008	−	0.388186i	−0.0577200	−	0.998333i	$-0.518383\pi$
$971$	−26.4870	−	12.0962i	−0.850008	−	0.388186i	−0.792288	+	0.610147i	$0.791110\pi$
$972$		0			0
$973$	−3.38116	−	6.19214i	−0.108395	−	0.198511i
$974$		0			0
$975$	−20.6035	−	44.6831i	−0.659839	−	1.43101i
$976$		0			0
$977$	4.40633	+	61.6086i	0.140971	+	1.97103i	0.224328	+	0.974514i	$0.427981\pi$
$977$	4.40633	+	61.6086i	0.140971	+	1.97103i	−0.0833565	+	0.996520i	$0.526564\pi$
$978$		0			0
$979$	1.51078	+	5.14525i	0.0482848	+	0.164443i
$980$		0			0
$981$	−12.3131	−	19.1595i	−0.393127	−	0.611717i
$982$		0			0
$983$	−5.59556	+	7.47479i	−0.178471	+	0.238409i	−0.880852	−	0.473392i	$-0.843029\pi$
$983$	−5.59556	+	7.47479i	−0.178471	+	0.238409i	0.702381	+	0.711801i	$0.252120\pi$
$984$		0			0
$985$	−49.0154	−	6.95610i	−1.56176	−	0.221640i
$986$		0			0
$987$	72.6035	+	5.19271i	2.31100	+	0.165286i
$988$		0			0
$989$	10.6587	−	26.4024i	0.338927	−	0.839547i
$990$		0			0
$991$	−9.65051	−	11.1373i	−0.306558	−	0.353787i	0.581477	−	0.813563i	$-0.302475\pi$
$991$	−9.65051	−	11.1373i	−0.306558	−	0.353787i	−0.888035	+	0.459776i	$0.847930\pi$
$992$		0			0
$993$	−38.1752	−	50.9962i	−1.21145	−	1.61831i
$994$		0			0
$995$	27.1020	−	36.3421i	0.859192	−	1.15212i
$996$		0			0
$997$	29.5176	+	6.42117i	0.934833	+	0.203360i	0.654085	−	0.756421i	$-0.273054\pi$
$997$	29.5176	+	6.42117i	0.934833	+	0.203360i	0.280748	+	0.959781i	$0.409417\pi$
$998$		0			0
$999$	−78.5439	+	23.0626i	−2.48502	+	0.729668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.1	yes	720
5.3	odd	4	inner	920.2.bv.a.33.1	✓	720
23.7	odd	22	inner	920.2.bv.a.697.1	yes	720
115.53	even	44	inner	920.2.bv.a.513.1	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.1	✓	720	5.3	odd	4	inner
920.2.bv.a.217.1	yes	720	1.1	even	1	trivial
920.2.bv.a.513.1	yes	720	115.53	even	44	inner
920.2.bv.a.697.1	yes	720	23.7	odd	22	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.05677 + 0.664961i) q^{3} +(2.09365 - 0.785246i) q^{5} +(-1.51231 + 0.825782i) q^{7} +(6.17280 - 2.81902i) q^{9} +O(q^{10})\)	\(q+(-3.05677 + 0.664961i) q^{3} +(2.09365 - 0.785246i) q^{5} +(-1.51231 + 0.825782i) q^{7} +(6.17280 - 2.81902i) q^{9} +(1.45186 + 1.25805i) q^{11} +(-1.50762 + 2.76100i) q^{13} +(-5.87767 + 3.79252i) q^{15} +(-5.05315 - 3.78274i) q^{17} +(0.770911 - 5.36180i) q^{19} +(4.07367 - 3.52985i) q^{21} +(3.96387 + 2.69959i) q^{23} +(3.76678 - 3.28807i) q^{25} +(-9.48141 + 7.09770i) q^{27} +(7.28588 - 1.04755i) q^{29} +(-4.63948 + 2.98161i) q^{31} +(-5.27457 - 2.88013i) q^{33} +(-2.51781 + 2.91644i) q^{35} +(6.47586 + 2.41537i) q^{37} +(2.77250 - 9.44228i) q^{39} +(-2.27727 + 4.98653i) q^{41} +(-1.26199 - 5.80129i) q^{43} +(10.7101 - 10.7492i) q^{45} +(9.54867 + 9.54867i) q^{47} +(-2.17933 + 3.39110i) q^{49} +(17.9617 + 8.20283i) q^{51} +(2.20497 + 4.03809i) q^{53} +(4.02757 + 1.49384i) q^{55} +(1.20889 + 16.9024i) q^{57} +(1.46023 + 4.97307i) q^{59} +(6.07716 + 9.45625i) q^{61} +(-7.00727 + 9.36062i) q^{63} +(-0.988371 + 6.96444i) q^{65} +(10.4532 + 0.747626i) q^{67} +(-13.9118 - 5.61621i) q^{69} +(0.656006 + 0.757071i) q^{71} +(2.00670 + 2.68064i) q^{73} +(-9.32775 + 12.5556i) q^{75} +(-3.23453 - 0.703630i) q^{77} +(6.98390 - 2.05066i) q^{79} +(10.9311 - 12.6152i) q^{81} +(5.02643 - 13.4764i) q^{83} +(-13.5499 - 3.95178i) q^{85} +(-21.5747 + 8.04695i) q^{87} +(2.34825 + 1.50913i) q^{89} -5.42045i q^{91} +(12.1992 - 12.1992i) q^{93} +(-2.59632 - 11.8311i) q^{95} +(0.180676 + 0.484412i) q^{97} +(12.5085 + 3.67283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * q	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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