LMFDB - Embedded newform 980.2.x.k.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(67,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("980.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.4
Character	$\chi$	$=$	980.67
Dual form			980.2.x.k.863.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17392 - 0.788610i) q^{2} +(2.86329 - 0.767216i) q^{3} +(0.756188 + 1.85153i) q^{4} +(1.62505 + 1.53598i) q^{5} +(-3.96631 - 1.35737i) q^{6} +(0.572433 - 2.76990i) q^{8} +(5.01173 - 2.89352i) q^{9} +O(q^{10})$	\(q+(-1.17392 - 0.788610i) q^{2} +(2.86329 - 0.767216i) q^{3} +(0.756188 + 1.85153i) q^{4} +(1.62505 + 1.53598i) q^{5} +(-3.96631 - 1.35737i) q^{6} +(0.572433 - 2.76990i) q^{8} +(5.01173 - 2.89352i) q^{9} +(-0.696393 - 3.08465i) q^{10} +(0.186127 + 0.107460i) q^{11} +(3.58571 + 4.72132i) q^{12} +(4.29923 - 4.29923i) q^{13} +(5.83140 + 3.15118i) q^{15} +(-2.85636 + 2.80022i) q^{16} +(-2.74478 + 0.735462i) q^{17} +(-8.16524 - 0.555529i) q^{18} +(-0.438952 - 0.760287i) q^{19} +(-1.61507 + 4.17032i) q^{20} +(-0.133754 - 0.272931i) q^{22} +(-0.0330301 + 0.123270i) q^{23} +(-0.486067 - 8.37019i) q^{24} +(0.281556 + 4.99207i) q^{25} +(-8.43738 + 1.65655i) q^{26} +(5.84185 - 5.84185i) q^{27} +4.03098i q^{29} +(-4.36056 - 8.29795i) q^{30} +(-7.44914 - 4.30076i) q^{31} +(5.56142 - 1.03468i) q^{32} +(0.615379 + 0.164890i) q^{33} +(3.80215 + 1.30119i) q^{34} +(9.14726 + 7.09134i) q^{36} +(-0.473005 + 1.76528i) q^{37} +(-0.0842746 + 1.23868i) q^{38} +(9.01151 - 15.6084i) q^{39} +(5.18472 - 3.62197i) q^{40} +2.91481 q^{41} +(-2.06108 - 2.06108i) q^{43} +(-0.0582196 + 0.425880i) q^{44} +(12.5887 + 2.99578i) q^{45} +(0.135987 - 0.118661i) q^{46} +(6.67731 + 1.78918i) q^{47} +(-6.03021 + 10.2093i) q^{48} +(3.60627 - 6.08234i) q^{50} +(-7.29484 + 4.21168i) q^{51} +(11.2112 + 4.70915i) q^{52} +(-1.01543 - 3.78963i) q^{53} +(-11.4648 + 2.25094i) q^{54} +(0.137408 + 0.460514i) q^{55} +(-1.84015 - 1.84015i) q^{57} +(3.17887 - 4.73205i) q^{58} +(-5.24601 + 9.08635i) q^{59} +(-1.42488 + 13.1799i) q^{60} +(4.16343 + 7.21127i) q^{61} +(5.35309 + 10.9232i) q^{62} +(-7.34464 - 3.17116i) q^{64} +(13.5900 - 0.382938i) q^{65} +(-0.592373 - 0.678863i) q^{66} +(-0.203445 - 0.759268i) q^{67} +(-3.43730 - 4.52591i) q^{68} +0.378298i q^{69} -1.75036i q^{71} +(-5.14588 - 15.5383i) q^{72} +(1.53265 + 5.71993i) q^{73} +(1.94739 - 1.69928i) q^{74} +(4.63617 + 14.0777i) q^{75} +(1.07577 - 1.38765i) q^{76} +(-22.8877 + 11.2165i) q^{78} +(-6.20636 - 10.7497i) q^{79} +(-8.94278 + 0.163183i) q^{80} +(3.56437 - 6.17368i) q^{81} +(-3.42176 - 2.29865i) q^{82} +(5.30716 + 5.30716i) q^{83} +(-5.59005 - 3.02076i) q^{85} +(0.794160 + 4.04494i) q^{86} +(3.09263 + 11.5419i) q^{87} +(0.404198 - 0.454037i) q^{88} +(-11.0339 + 6.37043i) q^{89} +(-12.4156 - 13.4444i) q^{90} +(-0.253215 + 0.0320589i) q^{92} +(-24.6287 - 6.59923i) q^{93} +(-6.42768 - 7.36615i) q^{94} +(0.454465 - 1.90972i) q^{95} +(15.1301 - 7.22941i) q^{96} +(-2.58579 - 2.58579i) q^{97} +1.24375 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 16 q^{6}+O(q^{10}) $ 72 * q - 16 * q^6	$ 72 q - 16 q^{6} + 16 q^{10} + 16 q^{12} - 8 q^{13} + 8 q^{16} + 20 q^{17} - 28 q^{18} + 40 q^{20} + 8 q^{22} + 20 q^{25} + 32 q^{26} + 4 q^{30} - 20 q^{37} + 36 q^{40} - 20 q^{45} - 16 q^{46} - 48 q^{48} + 80 q^{50} - 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} + 64 q^{61} + 80 q^{62} - 4 q^{65} - 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 16 q^{76} - 152 q^{78} + 20 q^{80} + 36 q^{81} - 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} - 32 q^{90} - 112 q^{92} - 32 q^{93} - 120 q^{96} + 40 q^{97}+O(q^{100}) $ 72 * q - 16 * q^6 + 16 * q^10 + 16 * q^12 - 8 * q^13 + 8 * q^16 + 20 * q^17 - 28 * q^18 + 40 * q^20 + 8 * q^22 + 20 * q^25 + 32 * q^26 + 4 * q^30 - 20 * q^37 + 36 * q^40 - 20 * q^45 - 16 * q^46 - 48 * q^48 + 80 * q^50 - 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 + 64 * q^61 + 80 * q^62 - 4 * q^65 - 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 16 * q^76 - 152 * q^78 + 20 * q^80 + 36 * q^81 - 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 - 32 * q^90 - 112 * q^92 - 32 * q^93 - 120 * q^96 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.17392	−	0.788610i	−0.830089	−	0.557632i
$2$	−1.17392	−	0.788610i	−0.830089	−	0.557632i
$3$	2.86329	−	0.767216i	1.65312	−	0.442952i	0.692636	−	0.721287i	$-0.256449\pi$
$3$	2.86329	−	0.767216i	1.65312	−	0.442952i	0.960484	+	0.278335i	$0.0897824\pi$
$4$	0.756188	+	1.85153i	0.378094	+	0.925767i
$5$	1.62505	+	1.53598i	0.726743	+	0.686909i
$5$	1.62505	+	1.53598i	0.726743	+	0.686909i
$6$	−3.96631	−	1.35737i	−1.61924	−	0.554143i
$7$		0			0
$7$		0			0
$8$	0.572433	−	2.76990i	0.202386	−	0.979306i
$9$	5.01173	−	2.89352i	1.67058	−	0.964507i
$10$	−0.696393	−	3.08465i	−0.220219	−	0.975450i
$11$	0.186127	+	0.107460i	0.0561193	+	0.0324005i	0.527797	−	0.849370i	$-0.323018\pi$
$11$	0.186127	+	0.107460i	0.0561193	+	0.0324005i	−0.471678	+	0.881771i	$0.656351\pi$
$12$	3.58571	+	4.72132i	1.03511	+	1.36293i
$13$	4.29923	−	4.29923i	1.19239	−	1.19239i	0.215999	−	0.976394i	$-0.430699\pi$
$13$	4.29923	−	4.29923i	1.19239	−	1.19239i	0.976394	−	0.215999i	$-0.0693008\pi$
$14$		0			0
$15$	5.83140	+	3.15118i	1.50566	+	0.813631i
$16$	−2.85636	+	2.80022i	−0.714090	+	0.700054i
$17$	−2.74478	+	0.735462i	−0.665707	+	0.178376i	−0.575820	−	0.817576i	$-0.695317\pi$
$17$	−2.74478	+	0.735462i	−0.665707	+	0.178376i	−0.0898868	+	0.995952i	$0.528651\pi$
$18$	−8.16524	−	0.555529i	−1.92457	−	0.130939i
$19$	−0.438952	−	0.760287i	−0.100702	−	0.174422i	0.811272	−	0.584669i	$-0.198776\pi$
$19$	−0.438952	−	0.760287i	−0.100702	−	0.174422i	−0.911974	+	0.410247i	$0.865442\pi$
$20$	−1.61507	+	4.17032i	−0.361141	+	0.932511i
$21$		0			0
$22$	−0.133754	−	0.272931i	−0.0285164	−	0.0581891i
$23$	−0.0330301	+	0.123270i	−0.00688724	+	0.0257035i	−0.969284	−	0.245944i	$-0.920902\pi$
$23$	−0.0330301	+	0.123270i	−0.00688724	+	0.0257035i	0.962397	+	0.271648i	$0.0875686\pi$
$24$	−0.486067	−	8.37019i	−0.0992180	−	1.70856i
$25$	0.281556	+	4.99207i	0.0563112	+	0.998413i
$26$	−8.43738	+	1.65655i	−1.65471	+	0.324876i
$27$	5.84185	−	5.84185i	1.12426	−	1.12426i
$28$		0			0
$29$			4.03098i			0.748534i	0.927321	+	0.374267i	$0.122106\pi$
$29$			4.03098i			0.748534i	−0.927321	+	0.374267i	$0.877894\pi$
$30$	−4.36056	−	8.29795i	−0.796126	−	1.51499i
$31$	−7.44914	−	4.30076i	−1.33790	−	0.772440i	−0.351408	−	0.936222i	$-0.614297\pi$
$31$	−7.44914	−	4.30076i	−1.33790	−	0.772440i	−0.986496	+	0.163783i	$0.947630\pi$
$32$	5.56142	−	1.03468i	0.983130	−	0.182908i
$33$	0.615379	+	0.164890i	0.107124	+	0.0287037i
$34$	3.80215	+	1.30119i	0.652064	+	0.223152i
$35$		0			0
$36$	9.14726	+	7.09134i	1.52454	+	1.18189i
$37$	−0.473005	+	1.76528i	−0.0777615	+	0.290210i	−0.993845	−	0.110777i	$-0.964666\pi$
$37$	−0.473005	+	1.76528i	−0.0777615	+	0.290210i	0.916084	+	0.400987i	$0.131333\pi$
$38$	−0.0842746	+	1.23868i	−0.0136711	+	0.200940i
$39$	9.01151	−	15.6084i	1.44300	−	2.49934i
$40$	5.18472	−	3.62197i	0.819777	−	0.572683i
$41$	2.91481			0.455217			0.227608	−	0.973753i	$-0.426909\pi$
$41$	2.91481			0.455217			0.227608	+	0.973753i	$0.426909\pi$
$42$		0			0
$43$	−2.06108	−	2.06108i	−0.314312	−	0.314312i	0.532265	−	0.846578i	$-0.321341\pi$
$43$	−2.06108	−	2.06108i	−0.314312	−	0.314312i	−0.846578	+	0.532265i	$0.821341\pi$
$44$	−0.0582196	+	0.425880i	−0.00877694	+	0.0642038i
$45$	12.5887	+	2.99578i	1.87661	+	0.446585i
$46$	0.135987	−	0.118661i	0.0200501	−	0.0174957i
$47$	6.67731	+	1.78918i	0.973986	+	0.260979i	0.710510	−	0.703687i	$-0.248464\pi$
$47$	6.67731	+	1.78918i	0.973986	+	0.260979i	0.263476	+	0.964666i	$0.415131\pi$
$48$	−6.03021	+	10.2093i	−0.870386	+	1.47358i
$49$		0			0
$50$	3.60627	−	6.08234i	0.510004	−	0.860172i
$51$	−7.29484	+	4.21168i	−1.02148	+	0.589753i
$52$	11.2112	+	4.70915i	1.55471	+	0.653042i
$53$	−1.01543	−	3.78963i	−0.139480	−	0.520546i	−0.999939	−	0.0110266i	$-0.996490\pi$
$53$	−1.01543	−	3.78963i	−0.139480	−	0.520546i	0.860459	−	0.509519i	$-0.170177\pi$
$54$	−11.4648	+	2.25094i	−1.56016	+	0.306314i
$55$	0.137408	+	0.460514i	0.0185281	+	0.0620957i
$56$		0			0
$57$	−1.84015	−	1.84015i	−0.243734	−	0.243734i
$58$	3.17887	−	4.73205i	0.417406	−	0.621349i
$59$	−5.24601	+	9.08635i	−0.682972	+	1.18294i	0.291098	+	0.956693i	$0.405979\pi$
$59$	−5.24601	+	9.08635i	−0.682972	+	1.18294i	−0.974070	+	0.226249i	$0.927354\pi$
$60$	−1.42488	+	13.1799i	−0.183952	+	1.70152i
$61$	4.16343	+	7.21127i	0.533073	+	0.923309i	0.999254	+	0.0386198i	$0.0122961\pi$
$61$	4.16343	+	7.21127i	0.533073	+	0.923309i	−0.466181	+	0.884689i	$0.654371\pi$
$62$	5.35309	+	10.9232i	0.679843	+	1.38725i
$63$		0			0
$64$	−7.34464	−	3.17116i	−0.918080	−	0.396395i
$65$	13.5900	−	0.382938i	1.68563	−	0.0474976i
$66$	−0.592373	−	0.678863i	−0.0729161	−	0.0835622i
$67$	−0.203445	−	0.759268i	−0.0248548	−	0.0927593i	0.952384	−	0.304900i	$-0.0986231\pi$
$67$	−0.203445	−	0.759268i	−0.0248548	−	0.0927593i	−0.977239	+	0.212141i	$0.931956\pi$
$68$	−3.43730	−	4.52591i	−0.416834	−	0.548847i
$69$			0.378298i			0.0455418i
$70$		0			0
$71$		−	1.75036i		−	0.207729i	−0.994591	−	0.103865i	$-0.966879\pi$
$71$		−	1.75036i		−	0.207729i	0.994591	−	0.103865i	$-0.0331209\pi$
$72$	−5.14588	−	15.5383i	−0.606447	−	1.83121i
$73$	1.53265	+	5.71993i	0.179383	+	0.669467i	0.995763	+	0.0919523i	$0.0293107\pi$
$73$	1.53265	+	5.71993i	0.179383	+	0.669467i	−0.816380	+	0.577515i	$0.804023\pi$
$74$	1.94739	−	1.69928i	0.226379	−	0.197538i
$75$	4.63617	+	14.0777i	0.535339	+	1.62555i
$76$	1.07577	−	1.38765i	0.123399	−	0.159175i
$77$		0			0
$78$	−22.8877	+	11.2165i	−2.59153	+	1.27002i
$79$	−6.20636	−	10.7497i	−0.698270	−	1.20944i	−0.969066	−	0.246803i	$-0.920620\pi$
$79$	−6.20636	−	10.7497i	−0.698270	−	1.20944i	0.270795	−	0.962637i	$-0.412713\pi$
$80$	−8.94278	+	0.163183i	−0.999834	+	0.0182444i
$81$	3.56437	−	6.17368i	0.396041	−	0.685964i
$82$	−3.42176	−	2.29865i	−0.377870	−	0.253843i
$83$	5.30716	+	5.30716i	0.582537	+	0.582537i	0.935600	−	0.353063i	$-0.114860\pi$
$83$	5.30716	+	5.30716i	0.582537	+	0.582537i	−0.353063	+	0.935600i	$0.614860\pi$
$84$		0			0
$85$	−5.59005	−	3.02076i	−0.606326	−	0.327647i
$86$	0.794160	+	4.04494i	0.0856365	+	0.436177i
$87$	3.09263	+	11.5419i	0.331565	+	1.23742i
$88$	0.404198	−	0.454037i	0.0430877	−	0.0484005i
$89$	−11.0339	+	6.37043i	−1.16959	+	0.675264i	−0.953584	−	0.301127i	$-0.902637\pi$
$89$	−11.0339	+	6.37043i	−1.16959	+	0.675264i	−0.216008	+	0.976392i	$0.569304\pi$
$90$	−12.4156	−	13.4444i	−1.30872	−	1.41716i
$91$		0			0
$92$	−0.253215	+	0.0320589i	−0.0263995	+	0.00334237i
$93$	−24.6287	−	6.59923i	−2.55387	−	0.684308i
$94$	−6.42768	−	7.36615i	−0.662964	−	0.759761i
$95$	0.454465	−	1.90972i	0.0466271	−	0.195933i
$96$	15.1301	−	7.22941i	1.54421	−	0.737848i
$97$	−2.58579	−	2.58579i	−0.262547	−	0.262547i	0.563541	−	0.826088i	$-0.309439\pi$
$97$	−2.58579	−	2.58579i	−0.262547	−	0.262547i	−0.826088	+	0.563541i	$0.809439\pi$
$98$		0			0
$99$	1.24375			0.125002
$100$	−9.03007	+	4.29625i	−0.903007	+	0.429625i
$101$	7.59723	−	13.1588i	0.755952	−	1.30935i	−0.188947	−	0.981987i	$-0.560508\pi$
$101$	7.59723	−	13.1588i	0.755952	−	1.30935i	0.944900	−	0.327361i	$-0.106159\pi$
$102$	11.8850	+	0.808602i	1.17679	+	0.0800635i
$103$	−0.398628	+	1.48770i	−0.0392780	+	0.146587i	−0.982780	−	0.184779i	$-0.940843\pi$
$103$	−0.398628	+	1.48770i	−0.0392780	+	0.146587i	0.943502	+	0.331367i	$0.107510\pi$
$104$	−9.44740	−	14.3694i	−0.926394	−	1.40904i
$105$		0			0
$106$	−1.79651	+	5.24951i	−0.174492	+	0.509877i
$107$	13.2303	+	3.54506i	1.27903	+	0.342714i	0.833482	−	0.552546i	$-0.186344\pi$
$107$	13.2303	+	3.54506i	1.27903	+	0.342714i	0.445544	+	0.895260i	$0.353010\pi$
$108$	15.2339	+	6.39885i	1.46588	+	0.615729i
$109$	−10.4283	−	6.02078i	−0.998850	−	0.576686i	−0.0909422	−	0.995856i	$-0.528988\pi$
$109$	−10.4283	−	6.02078i	−0.998850	−	0.576686i	−0.907908	+	0.419170i	$0.862321\pi$
$110$	0.201859	−	0.648969i	0.0192465	−	0.0618768i
$111$			5.41740i			0.514197i
$112$		0			0
$113$	−3.14409	+	3.14409i	−0.295771	+	0.295771i	−0.839355	−	0.543584i	$-0.817067\pi$
$113$	−3.14409	+	3.14409i	−0.295771	+	0.295771i	0.543584	+	0.839355i	$0.317067\pi$
$114$	0.709032	+	3.61135i	0.0664070	+	0.338234i
$115$	−0.243015	+	0.149586i	−0.0226613	+	0.0139490i
$116$	−7.46349	+	3.04818i	−0.692968	+	0.283016i
$117$	9.10666	−	33.9865i	0.841911	−	3.14205i
$118$	13.3240	−	6.52961i	1.22657	−	0.601100i
$119$		0			0
$120$	12.0665	−	14.3485i	1.10152	−	1.30984i
$121$	−5.47690	−	9.48628i	−0.497900	−	0.862389i
$122$	0.799339	−	11.7488i	0.0723688	−	1.06369i
$123$	8.34594	−	2.23629i	0.752528	−	0.201639i
$124$	2.33006	−	17.0445i	0.209246	−	1.53064i
$125$	−7.21015	+	8.54481i	−0.644896	+	0.764271i
$126$		0			0
$127$	2.21268	−	2.21268i	0.196344	−	0.196344i	−0.602087	−	0.798431i	$-0.705664\pi$
$127$	2.21268	−	2.21268i	0.196344	−	0.196344i	0.798431	+	0.602087i	$0.205664\pi$
$128$	6.12123	+	9.51475i	0.541045	+	0.840993i
$129$	−7.48277	−	4.32018i	−0.658821	−	0.380370i
$130$	−16.2556	−	10.2677i	−1.42571	−	0.900533i
$131$	−3.21980	+	1.85895i	−0.281316	+	0.162418i	−0.634019	−	0.773318i	$-0.718596\pi$
$131$	−3.21980	+	1.85895i	−0.281316	+	0.162418i	0.352703	+	0.935735i	$0.385263\pi$
$132$	0.160042	+	1.26408i	0.0139299	+	0.110024i
$133$		0			0
$134$	−0.359937	+	1.05176i	−0.0310939	+	0.0908582i
$135$	18.4662	−	0.520340i	1.58932	−	0.0447838i
$136$	0.465949	+	8.02376i	0.0399548	+	0.688031i
$137$	−2.52662	+	0.677005i	−0.215863	+	0.0578404i	−0.365130	−	0.930957i	$-0.618975\pi$
$137$	−2.52662	+	0.677005i	−0.215863	+	0.0578404i	0.149267	+	0.988797i	$0.452309\pi$
$138$	0.298330	−	0.444093i	0.0253955	−	0.0378037i
$139$	10.9071			0.925130			0.462565	−	0.886585i	$-0.346929\pi$
$139$	10.9071			0.925130			0.462565	+	0.886585i	$0.346929\pi$
$140$		0			0
$141$	20.4918			1.72572
$142$	−1.38035	+	2.05478i	−0.115836	+	0.172434i
$143$	1.26220	−	0.338205i	0.105550	−	0.0282821i
$144$	−6.21281	+	22.2989i	−0.517734	+	1.85824i
$145$	−6.19148	+	6.55053i	−0.514175	+	0.543992i
$146$	2.71158	−	7.92342i	0.224412	−	0.655747i
$147$		0			0
$148$	−3.62615	+	0.459097i	−0.298068	+	0.0377376i
$149$	9.73603	−	5.62110i	0.797606	−	0.460498i	−0.0450271	−	0.998986i	$-0.514337\pi$
$149$	9.73603	−	5.62110i	0.797606	−	0.460498i	0.842634	+	0.538487i	$0.181004\pi$
$150$	5.65933	−	20.1823i	0.462082	−	1.64788i
$151$	−7.86444	−	4.54054i	−0.639999	−	0.369504i	0.144615	−	0.989488i	$-0.453806\pi$
$151$	−7.86444	−	4.54054i	−0.639999	−	0.369504i	−0.784614	+	0.619984i	$0.787139\pi$
$152$	−2.35719	+	0.780637i	−0.191193	+	0.0633180i
$153$	−11.6280	+	11.6280i	−0.940069	+	0.940069i
$154$		0			0
$155$	−5.49933	−	18.4306i	−0.441717	−	1.48038i
$156$	35.7139	+	4.88224i	2.85940	+	0.390892i
$157$	−20.2317	+	5.42108i	−1.61467	+	0.432649i	−0.949429	−	0.313981i	$-0.898337\pi$
$157$	−20.2317	+	5.42108i	−1.61467	+	0.432649i	−0.665240	+	0.746630i	$0.731671\pi$
$158$	−1.19156	+	17.5138i	−0.0947956	+	1.39332i
$159$	−5.81493	−	10.0717i	−0.461154	−	0.798742i
$160$	10.6268	+	6.86081i	0.840124	+	0.542394i
$161$		0			0
$162$	−9.05292	+	4.43652i	−0.711265	+	0.348566i
$163$	−4.11572	+	15.3601i	−0.322368	+	1.20309i	0.594563	+	0.804049i	$0.297325\pi$
$163$	−4.11572	+	15.3601i	−0.322368	+	1.20309i	−0.916931	+	0.399046i	$0.869341\pi$
$164$	2.20414	+	5.39687i	0.172115	+	0.421425i
$165$	0.746753	+	1.21316i	0.0581346	+	0.0944446i
$166$	−2.04492	−	10.4155i	−0.158716	−	0.808398i
$167$	−12.0570	+	12.0570i	−0.932995	+	0.932995i	−0.997892	−	0.0648970i	$-0.979328\pi$
$167$	−12.0570	+	12.0570i	−0.932995	+	0.932995i	0.0648970	+	0.997892i	$0.479328\pi$
$168$		0			0
$169$		−	23.9668i		−	1.84360i
$170$	4.18008	+	7.95450i	0.320598	+	0.610083i
$171$	−4.39981	−	2.54023i	−0.336462	−	0.194256i
$172$	2.25760	−	5.37473i	0.172140	−	0.409819i
$173$	0.438509	+	0.117498i	0.0333392	+	0.00893321i	0.275450	−	0.961315i	$-0.411173\pi$
$173$	0.438509	+	0.117498i	0.0333392	+	0.00893321i	−0.242111	+	0.970249i	$0.577840\pi$
$174$	5.47151	−	15.9881i	0.414794	−	1.21206i
$175$		0			0
$176$	−0.832556	+	0.214249i	−0.0627563	+	0.0161497i
$177$	−8.04964	+	30.0417i	−0.605048	+	2.25807i
$178$	17.9767	+	1.22306i	1.34741	+	0.0916724i
$179$	−2.42760	+	4.20473i	−0.181448	+	0.314276i	−0.942374	−	0.334562i	$-0.891412\pi$
$179$	−2.42760	+	4.20473i	−0.181448	+	0.314276i	0.760926	+	0.648839i	$0.224745\pi$
$180$	3.97261	+	25.5737i	0.296101	+	1.90615i
$181$	6.88269			0.511586			0.255793	−	0.966732i	$-0.417663\pi$
$181$	6.88269			0.511586			0.255793	+	0.966732i	$0.417663\pi$
$182$		0			0
$183$	17.4537	+	17.4537i	1.29022	+	1.29022i
$184$	0.322537	+	0.162054i	0.0237777	+	0.0119467i
$185$	−3.48008	+	2.14214i	−0.255861	+	0.157493i
$186$	23.7079	+	27.1694i	1.73835	+	1.99216i
$187$	−0.589909	−	0.158066i	−0.0431384	−	0.0115589i
$188$	1.73657	+	13.7162i	0.126653	+	1.00036i
$189$		0			0
$190$	−2.03953	+	1.88347i	−0.147963	+	0.136641i
$191$	−14.9328	+	8.62145i	−1.08050	+	0.623826i	−0.931031	−	0.364940i	$-0.881089\pi$
$191$	−14.9328	+	8.62145i	−1.08050	+	0.623826i	−0.149468	+	0.988767i	$0.547756\pi$
$192$	−23.4628	−	3.44502i	−1.69328	−	0.248623i
$193$	−5.24638	−	19.5798i	−0.377643	−	1.40938i	−0.849445	−	0.527678i	$-0.823063\pi$
$193$	−5.24638	−	19.5798i	−0.377643	−	1.40938i	0.471802	−	0.881705i	$-0.343604\pi$
$194$	0.996337	+	5.07470i	0.0715328	+	0.364342i
$195$	38.6182	−	11.5229i	2.76551	−	0.825172i
$196$		0			0
$197$	−12.9394	−	12.9394i	−0.921891	−	0.921891i	0.0752724	−	0.997163i	$-0.476017\pi$
$197$	−12.9394	−	12.9394i	−0.921891	−	0.921891i	−0.997163	+	0.0752724i	$0.976017\pi$
$198$	−1.46007	−	0.980837i	−0.103763	−	0.0697050i
$199$	10.9429	−	18.9536i	0.775720	−	1.34359i	−0.158669	−	0.987332i	$-0.550720\pi$
$199$	10.9429	−	18.9536i	0.775720	−	1.34359i	0.934389	−	0.356255i	$-0.115947\pi$
$200$	13.9887	+	2.07774i	0.989149	+	0.146919i
$201$	−1.16504	−	2.01792i	−0.0821759	−	0.142333i
$202$	−19.2957	+	9.45614i	−1.35764	+	0.665332i
$203$		0			0
$204$	−13.3143	−	10.3218i	−0.932190	−	0.722673i
$205$	4.73670	+	4.47708i	0.330826	+	0.312693i
$206$	1.64117	−	1.43208i	0.114346	−	0.0997778i
$207$	0.191146	+	0.713368i	0.0132856	+	0.0495825i
$208$	−0.241376	+	24.3189i	−0.0167364	+	1.68621i
$209$		−	0.188679i		−	0.0130512i
$210$		0			0
$211$			3.39701i			0.233860i	0.993140	+	0.116930i	$0.0373053\pi$
$211$			3.39701i			0.233860i	−0.993140	+	0.116930i	$0.962695\pi$
$212$	6.24877	−	4.74577i	0.429168	−	0.325941i
$213$	−1.34290	−	5.01178i	−0.0920141	−	0.343401i
$214$	−12.7357	−	14.5952i	−0.870597	−	0.997708i
$215$	−0.183583	−	6.51513i	−0.0125203	−	0.444328i
$216$	−12.8372	−	19.5254i	−0.873464	−	1.32853i
$217$		0			0
$218$	7.49397	+	15.2918i	0.507555	+	1.03569i
$219$	8.77684	+	15.2019i	0.593084	+	1.02725i
$220$	−0.748751	+	0.602651i	−0.0504808	+	0.0406307i
$221$	−8.63853	+	14.9624i	−0.581090	+	1.00648i
$222$	4.27222	−	6.35961i	0.286732	−	0.426829i
$223$	−19.7618	−	19.7618i	−1.32335	−	1.32335i	−0.911048	−	0.412300i	$-0.864725\pi$
$223$	−19.7618	−	19.7618i	−1.32335	−	1.32335i	−0.412300	−	0.911048i	$-0.635275\pi$
$224$		0			0
$225$	15.8557	+	24.2042i	1.05705	+	1.61361i
$226$	6.17039	−	1.21146i	0.410448	−	0.0805850i
$227$	5.40179	+	20.1598i	0.358530	+	1.33805i	0.875984	+	0.482340i	$0.160213\pi$
$227$	5.40179	+	20.1598i	0.358530	+	1.33805i	−0.517454	+	0.855711i	$0.673120\pi$
$228$	2.01560	−	4.79860i	0.133486	−	0.317795i
$229$	2.82162	−	1.62906i	0.186458	−	0.107652i	−0.403865	−	0.914818i	$-0.632334\pi$
$229$	2.82162	−	1.62906i	0.186458	−	0.107652i	0.590323	+	0.807167i	$0.299000\pi$
$230$	0.403246	+	0.0160417i	0.0265892	+	0.00105776i
$231$		0			0
$232$	11.1654	+	2.30746i	0.733043	+	0.151492i
$233$	−6.67321	−	1.78808i	−0.437176	−	0.117141i	0.0335166	−	0.999438i	$-0.489329\pi$
$233$	−6.67321	−	1.78808i	−0.437176	−	0.117141i	−0.470693	+	0.882297i	$0.655996\pi$
$234$	−37.4926	+	32.7159i	−2.45097	+	2.13871i
$235$	8.10280	+	13.1637i	0.528569	+	0.858704i
$236$	−20.7907	−	2.84217i	−1.35336	−	0.185010i
$237$	−26.0180	−	26.0180i	−1.69005	−	1.69005i
$238$		0			0
$239$	10.2770			0.664761			0.332380	−	0.943145i	$-0.392148\pi$
$239$	10.2770			0.664761			0.332380	+	0.943145i	$0.392148\pi$
$240$	−25.4806	+	7.32829i	−1.64476	+	0.473039i
$241$	−2.39425	+	4.14696i	−0.154227	+	0.267129i	−0.932777	−	0.360453i	$-0.882622\pi$
$241$	−2.39425	+	4.14696i	−0.154227	+	0.267129i	0.778550	+	0.627582i	$0.215955\pi$
$242$	−1.05151	+	15.4553i	−0.0675939	+	0.993504i
$243$	−0.945506	+	3.52868i	−0.0606542	+	0.226365i
$244$	−10.2036	+	13.1618i	−0.653218	+	0.842599i
$245$		0			0
$246$	−11.5611	−	3.95647i	−0.737106	−	0.252255i
$247$	−5.15581	−	1.38149i	−0.328056	−	0.0879023i
$248$	−16.1768	+	18.1714i	−1.02723	+	1.15389i
$249$	19.2677	+	11.1242i	1.22104	+	0.704968i
$250$	15.2027	−	4.34494i	0.961502	−	0.274798i
$251$			26.2656i			1.65787i	0.559347	+	0.828934i	$0.311052\pi$
$251$			26.2656i			1.65787i	−0.559347	+	0.828934i	$0.688948\pi$
$252$		0			0
$253$	−0.0193944	+	0.0193944i	−0.00121931	+	0.00121931i
$254$	−4.34246	+	0.852574i	−0.272470	+	0.0534952i
$255$	−18.3235	−	4.36052i	−1.14746	−	0.273067i
$256$	0.317582	−	15.9968i	0.0198489	−	0.999803i
$257$	−5.99909	+	22.3889i	−0.374213	+	1.39658i	0.480278	+	0.877116i	$0.340536\pi$
$257$	−5.99909	+	22.3889i	−0.374213	+	1.39658i	−0.854491	+	0.519466i	$0.826131\pi$
$258$	5.37725	+	10.9725i	0.334773	+	0.683121i
$259$		0			0
$260$	10.9856	+	24.8727i	0.681298	+	1.54254i
$261$	11.6637	+	20.2022i	0.721966	+	1.25048i
$262$	5.24579	+	0.356902i	0.324086	+	0.0220495i
$263$	5.75806	−	1.54287i	0.355057	−	0.0951373i	−0.0768816	−	0.997040i	$-0.524496\pi$
$263$	5.75806	−	1.54287i	0.355057	−	0.0951373i	0.431939	+	0.901903i	$0.357830\pi$
$264$	0.808992	−	1.61015i	0.0497900	−	0.0990977i
$265$	4.17066	−	7.71800i	0.256202	−	0.474113i
$266$		0			0
$267$	−26.7058	+	26.7058i	−1.63437	+	1.63437i
$268$	1.25197	−	0.950835i	0.0764761	−	0.0580815i
$269$	−0.0578535	−	0.0334017i	−0.00352739	−	0.00203654i	0.498235	−	0.867042i	$-0.333982\pi$
$269$	−0.0578535	−	0.0334017i	−0.00352739	−	0.00203654i	−0.501763	+	0.865005i	$0.667315\pi$
$270$	−22.0883	−	13.9518i	−1.34425	−	0.849080i
$271$	2.40782	−	1.39016i	0.146265	−	0.0844459i	−0.425082	−	0.905155i	$-0.639755\pi$
$271$	2.40782	−	1.39016i	0.146265	−	0.0844459i	0.571346	+	0.820709i	$0.306421\pi$
$272$	5.78063	−	9.78672i	0.350502	−	0.593407i
$273$		0			0
$274$	3.49994	+	1.19776i	0.211439	+	0.0723596i
$275$	−0.484043	+	0.959412i	−0.0291889	+	0.0578547i
$276$	−0.700432	+	0.286065i	−0.0421611	+	0.0172191i
$277$	−5.53275	+	1.48249i	−0.332430	+	0.0890745i	−0.421174	−	0.906980i	$-0.638382\pi$
$277$	−5.53275	+	1.48249i	−0.332430	+	0.0890745i	0.0887431	+	0.996055i	$0.471715\pi$
$278$	−12.8041	−	8.60147i	−0.767940	−	0.515882i
$279$	−49.7774			−2.98010
$280$		0			0
$281$	−22.9229			−1.36746			−0.683732	−	0.729734i	$-0.739644\pi$
$281$	−22.9229			−1.36746			−0.683732	+	0.729734i	$0.739644\pi$
$282$	−24.0557	−	16.1600i	−1.43250	−	0.962314i
$283$	−0.549214	+	0.147161i	−0.0326474	+	0.00874784i	−0.275106	−	0.961414i	$-0.588713\pi$
$283$	−0.549214	+	0.147161i	−0.0326474	+	0.00874784i	0.242458	+	0.970162i	$0.422046\pi$
$284$	3.24085	−	1.32360i	0.192309	−	0.0785411i
$285$	−0.163904	−	5.81676i	−0.00970886	−	0.344555i
$286$	−1.74843	−	0.598356i	−0.103387	−	0.0353815i
$287$		0			0
$288$	24.8785	−	21.2776i	1.46598	−	1.25380i
$289$	−7.72952	+	4.46264i	−0.454677	+	0.262508i
$290$	12.4341	−	2.80714i	0.730157	−	0.164841i
$291$	−9.38773	−	5.42001i	−0.550318	−	0.317726i
$292$	−9.43167	+	7.16310i	−0.551947	+	0.419188i
$293$	−1.43269	+	1.43269i	−0.0836989	+	0.0836989i	−0.747717	−	0.664018i	$-0.768850\pi$
$293$	−1.43269	+	1.43269i	−0.0836989	+	0.0836989i	0.664018	+	0.747717i	$0.268850\pi$
$294$		0			0
$295$	−22.4814	+	6.70801i	−1.30892	+	0.390555i
$296$	4.61887	+	2.32068i	0.268467	+	0.134887i
$297$	1.71509	−	0.459557i	0.0995196	−	0.0266662i
$298$	−15.8622	−	1.07920i	−0.918872	−	0.0625162i
$299$	0.387962	+	0.671970i	0.0224364	+	0.0388610i
$300$	−22.5596	+	19.2294i	−1.30248	+	1.11021i
$301$		0			0
$302$	5.65153	+	11.5322i	0.325209	+	0.663604i
$303$	11.6574	−	43.5061i	0.669702	−	2.49936i
$304$	3.38277	+	0.942493i	0.194015	+	0.0540557i
$305$	−4.31057	+	18.1136i	−0.246823	+	1.03718i
$306$	22.8204	−	4.48042i	1.30455	−	0.256128i
$307$	1.51038	−	1.51038i	0.0862017	−	0.0862017i	−0.662691	−	0.748893i	$-0.730586\pi$
$307$	1.51038	−	1.51038i	0.0862017	−	0.0862017i	0.748893	+	0.662691i	$0.230586\pi$
$308$		0			0
$309$			4.56555i			0.259725i
$310$	−8.07880	+	25.9730i	−0.458845	+	1.47517i
$311$	11.0383	+	6.37294i	0.625922	+	0.361376i	0.779171	−	0.626811i	$-0.215640\pi$
$311$	11.0383	+	6.37294i	0.625922	+	0.361376i	−0.153249	+	0.988188i	$0.548974\pi$
$312$	−38.0751	−	33.8957i	−2.15558	−	1.91897i
$313$	19.6676	+	5.26991i	1.11168	+	0.297873i	0.767511	−	0.641036i	$-0.221495\pi$
$313$	19.6676	+	5.26991i	1.11168	+	0.297873i	0.344166	+	0.938909i	$0.388162\pi$
$314$	28.0256	+	9.59103i	1.58158	+	0.541253i
$315$		0			0
$316$	15.2103	−	19.6201i	0.855648	−	1.10372i
$317$	2.55902	−	9.55038i	0.143729	−	0.536403i	−0.856080	−	0.516843i	$-0.827107\pi$
$317$	2.55902	−	9.55038i	0.143729	−	0.536403i	0.999809	−	0.0195596i	$-0.00622640\pi$
$318$	−1.11641	+	16.4092i	−0.0626052	+	0.920180i
$319$	−0.433170	+	0.750272i	−0.0242528	+	0.0420072i
$320$	−7.06456	−	16.4345i	−0.394921	−	0.918715i
$321$	40.6021			2.26619
$322$		0			0
$323$	1.76399	+	1.76399i	0.0981509	+	0.0981509i
$324$	14.1261	+	1.93110i	0.784784	+	0.107283i
$325$	22.6725	+	20.2516i	1.25765	+	1.12336i
$326$	16.9447	−	14.7859i	0.938478	−	0.818912i
$327$	−34.4785	−	9.23848i	−1.90666	−	0.510889i
$328$	1.66853	−	8.07372i	0.0921294	−	0.445797i
$329$		0			0
$330$	0.0800825	−	2.01306i	0.00440840	−	0.110815i
$331$	25.4182	−	14.6752i	1.39711	−	0.806621i	0.403020	−	0.915191i	$-0.367961\pi$
$331$	25.4182	−	14.6752i	1.39711	−	0.806621i	0.994089	+	0.108570i	$0.0346273\pi$
$332$	−5.81318	+	13.8396i	−0.319040	+	0.759547i
$333$	2.73730	+	10.2157i	0.150003	+	0.559819i
$334$	23.6622	−	4.64569i	1.29474	−	0.254201i
$335$	0.835609	−	1.54633i	0.0456542	−	0.0844852i
$336$		0			0
$337$	21.9434	+	21.9434i	1.19533	+	1.19533i	0.975549	+	0.219784i	$0.0705353\pi$
$337$	21.9434	+	21.9434i	1.19533	+	1.19533i	0.219784	+	0.975549i	$0.429465\pi$
$338$	−18.9005	+	28.1352i	−1.02805	+	1.53035i
$339$	−6.59025	+	11.4146i	−0.357933	+	0.619958i
$340$	1.36591	−	12.6344i	0.0740768	−	0.685198i
$341$	−0.924322	−	1.60097i	−0.0500548	−	0.0866975i
$342$	3.16179	+	6.45177i	0.170970	+	0.348872i
$343$		0			0
$344$	−6.88881	+	4.52915i	−0.371420	+	0.244195i
$345$	−0.581057	+	0.614753i	−0.0312831	+	0.0330972i
$346$	−0.422115	−	0.483746i	−0.0226930	−	0.0260063i
$347$	2.10261	+	7.84706i	0.112874	+	0.421252i	0.999119	−	0.0419646i	$-0.0133617\pi$
$347$	2.10261	+	7.84706i	0.112874	+	0.421252i	−0.886245	+	0.463217i	$0.846695\pi$
$348$	−19.0315	+	14.4539i	−1.02020	+	0.774811i
$349$		−	8.46417i		−	0.453076i	−0.974002	−	0.226538i	$-0.927259\pi$
$349$		−	8.46417i		−	0.453076i	0.974002	−	0.226538i	$-0.0727408\pi$
$350$		0			0
$351$		−	50.2309i		−	2.68113i
$352$	1.14632	+	0.405050i	0.0610988	+	0.0215892i
$353$	5.38289	+	20.0892i	0.286502	+	1.06924i	0.947735	+	0.319060i	$0.103367\pi$
$353$	5.38289	+	20.0892i	0.286502	+	1.06924i	−0.661232	+	0.750181i	$0.729966\pi$
$354$	33.1408	−	28.9186i	1.76141	−	1.53700i
$355$	2.68851	−	2.84441i	0.142691	−	0.150966i
$356$	−20.1388	−	15.6124i	−1.06735	−	0.827457i
$357$		0			0
$358$	6.16571	−	3.02160i	0.325868	−	0.159696i
$359$	−11.7824	−	20.4077i	−0.621851	−	1.07708i	−0.989141	−	0.146972i	$-0.953047\pi$
$359$	−11.7824	−	20.4077i	−0.621851	−	1.07708i	0.367289	−	0.930107i	$-0.380286\pi$
$360$	15.5042	−	33.1544i	0.817142	−	1.74739i
$361$	9.11464	−	15.7870i	0.479718	−	0.830896i
$362$	−8.07974	−	5.42776i	−0.424662	−	0.285277i
$363$	−22.9600	−	22.9600i	−1.20509	−	1.20509i
$364$		0			0
$365$	−6.29504	+	11.6493i	−0.329498	+	0.609751i
$366$	−6.72513	−	34.2535i	−0.351528	−	1.79046i
$367$	−1.38055	−	5.15227i	−0.0720639	−	0.268946i	0.920488	−	0.390772i	$-0.127792\pi$
$367$	−1.38055	−	5.15227i	−0.0720639	−	0.268946i	−0.992552	+	0.121826i	$0.961125\pi$
$368$	−0.250836	−	0.444594i	−0.0130758	−	0.0231761i
$369$	14.6082	−	8.43407i	0.760474	−	0.439060i
$370$	5.77466	+	0.229725i	0.300210	+	0.0119428i
$371$		0			0
$372$	−6.40519	−	50.5911i	−0.332094	−	2.62302i
$373$	31.1404	+	8.34406i	1.61239	+	0.432039i	0.948754	−	0.316016i	$-0.102345\pi$
$373$	31.1404	+	8.34406i	1.61239	+	0.432039i	0.663637	+	0.748055i	$0.269012\pi$
$374$	0.567856	+	0.650765i	0.0293631	+	0.0336503i
$375$	−14.0890	+	29.9980i	−0.727555	+	1.54909i
$376$	8.77815	−	17.4713i	0.452699	−	0.901012i
$377$	17.3301	+	17.3301i	0.892546	+	0.892546i
$378$		0			0
$379$	3.18566			0.163637			0.0818183	−	0.996647i	$-0.473927\pi$
$379$	3.18566			0.163637			0.0818183	+	0.996647i	$0.473927\pi$
$380$	3.87958	−	0.602651i	0.199018	−	0.0309153i
$381$	4.63794	−	8.03316i	0.237609	−	0.411551i
$382$	24.3289	+	1.65524i	1.24478	+	0.0846893i
$383$	7.29602	−	27.2291i	0.372809	−	1.39134i	−0.483711	−	0.875228i	$-0.660711\pi$
$383$	7.29602	−	27.2291i	0.372809	−	1.39134i	0.856520	−	0.516114i	$-0.172622\pi$
$384$	24.8267	+	22.5472i	1.26693	+	1.15061i
$385$		0			0
$386$	−9.28195	+	27.1225i	−0.472439	+	1.38050i
$387$	−16.2934	−	4.36579i	−0.828238	−	0.221926i
$388$	2.83234	−	6.74302i	0.143790	−	0.342325i
$389$	14.1562	+	8.17306i	0.717745	+	0.414391i	0.813922	−	0.580974i	$-0.197328\pi$
$389$	14.1562	+	8.17306i	0.717745	+	0.414391i	−0.0961769	+	0.995364i	$0.530661\pi$
$390$	−54.4219	−	16.9277i	−2.75576	−	0.857169i
$391$		−	0.362641i		−	0.0183395i
$392$		0			0
$393$	−7.79301	+	7.79301i	−0.393105	+	0.393105i
$394$	4.98569	+	25.3939i	0.251175	+	1.27933i
$395$	6.42570	−	27.0016i	0.323312	−	1.35860i
$396$	0.940512	+	2.30285i	0.0472625	+	0.115723i
$397$	−3.93142	+	14.6722i	−0.197312	+	0.736379i	0.794344	+	0.607468i	$0.207815\pi$
$397$	−3.93142	+	14.6722i	−0.197312	+	0.736379i	−0.991656	+	0.128911i	$0.958852\pi$
$398$	−27.7931	+	13.6204i	−1.39314	+	0.682730i
$399$		0			0
$400$	−14.7831	−	13.4707i	−0.739154	−	0.673536i
$401$	−11.8802	−	20.5772i	−0.593271	−	1.02758i	−0.993788	−	0.111287i	$-0.964503\pi$
$401$	−11.8802	−	20.5772i	−0.593271	−	1.02758i	0.400517	−	0.916289i	$-0.368830\pi$
$402$	−0.223677	+	3.28764i	−0.0111560	+	0.163973i
$403$	−50.5156	+	13.5356i	−2.51636	+	0.674256i
$404$	30.1089	+	4.11601i	1.49797	+	0.204779i
$405$	15.2749	−	4.55772i	0.759015	−	0.226475i
$406$		0			0
$407$	−0.277736	+	0.277736i	−0.0137669	+	0.0137669i
$408$	7.49010	+	22.6169i	0.370815	+	1.11970i
$409$	−19.5448	−	11.2842i	−0.966427	−	0.557967i	−0.0682817	−	0.997666i	$-0.521752\pi$
$409$	−19.5448	−	11.2842i	−0.966427	−	0.557967i	−0.898145	+	0.439699i	$0.855085\pi$
$410$	−2.02985	−	8.99115i	−0.100247	−	0.444041i
$411$	−6.71502	+	3.87692i	−0.331228	+	0.191234i
$412$	−3.05596	+	0.386907i	−0.150557	+	0.0190615i
$413$		0			0
$414$	0.338178	−	0.988179i	0.0166206	−	0.0485663i
$415$	0.472715	+	16.7761i	0.0232047	+	0.823505i
$416$	19.4615	−	28.3582i	0.954179	−	1.39037i
$417$	31.2302	−	8.36812i	1.52935	−	0.409789i
$418$	−0.148794	+	0.221495i	−0.00727778	+	0.0108337i
$419$	−12.4351			−0.607495			−0.303748	−	0.952753i	$-0.598238\pi$
$419$	−12.4351			−0.607495			−0.303748	+	0.952753i	$0.598238\pi$
$420$		0			0
$421$	−31.2799			−1.52449			−0.762244	−	0.647289i	$-0.775902\pi$
$421$	−31.2799			−1.52449			−0.762244	+	0.647289i	$0.775902\pi$
$422$	2.67892	−	3.98783i	0.130408	−	0.194124i
$423$	38.6419	−	10.3541i	1.87883	−	0.503432i
$424$	−11.0781	+	0.643321i	−0.538002	+	0.0312424i
$425$	−4.44428	−	13.4951i	−0.215579	−	0.654606i
$426$	−2.37588	+	6.94246i	−0.115112	+	0.336364i
$427$		0			0
$428$	3.44083	+	27.1772i	0.166319	+	1.31366i
$429$	3.35456	−	1.93676i	0.161960	−	0.0935075i
$430$	−4.92238	+	7.79303i	−0.237378	+	0.375813i
$431$	16.5660	+	9.56440i	0.797957	+	0.460701i	0.842756	−	0.538295i	$-0.180931\pi$
$431$	16.5660	+	9.56440i	0.797957	+	0.460701i	−0.0447992	+	0.998996i	$0.514265\pi$
$432$	−0.327984	+	33.0449i	−0.0157801	+	1.58987i
$433$	4.87478	−	4.87478i	0.234267	−	0.234267i	−0.580204	−	0.814471i	$-0.697027\pi$
$433$	4.87478	−	4.87478i	0.234267	−	0.234267i	0.814471	+	0.580204i	$0.197027\pi$
$434$		0			0
$435$	−12.7023	+	23.5063i	−0.609030	+	1.12704i
$436$	3.26193	−	23.8612i	0.156218	−	1.14274i
$437$	0.108219	−	0.0289972i	0.00517682	−	0.00138712i
$438$	1.68507	−	24.7674i	0.0805158	−	1.18343i
$439$	16.3920	+	28.3918i	0.782349	+	1.35507i	0.930570	+	0.366113i	$0.119312\pi$
$439$	16.3920	+	28.3918i	0.782349	+	1.35507i	−0.148222	+	0.988954i	$0.547355\pi$
$440$	1.35423	−	0.116993i	0.0645605	−	0.00557741i
$441$		0			0
$442$	21.9404	−	10.7522i	1.04360	−	0.511431i
$443$	−3.11619	+	11.6298i	−0.148055	+	0.552547i	0.851546	+	0.524280i	$0.175666\pi$
$443$	−3.11619	+	11.6298i	−0.148055	+	0.552547i	−0.999600	+	0.0282670i	$0.991001\pi$
$444$	−10.0305	+	4.09657i	−0.476027	+	0.194415i
$445$	−27.7155	−	6.59557i	−1.31384	−	0.312660i
$446$	7.61447	+	38.7832i	0.360555	+	1.83644i
$447$	23.5645	−	23.5645i	1.11456	−	1.11456i
$448$		0			0
$449$		−	5.52889i		−	0.260925i	−0.991453	−	0.130462i	$-0.958354\pi$
$449$		−	5.52889i		−	0.260925i	0.991453	−	0.130462i	$-0.0416462\pi$
$450$	0.474263	−	40.9178i	0.0223570	−	1.92889i
$451$	0.542523	+	0.313226i	0.0255464	+	0.0147492i
$452$	−8.19892	−	3.44387i	−0.385645	−	0.161986i
$453$	−26.0017	−	6.96714i	−1.22167	−	0.327345i
$454$	9.55691	−	27.9259i	0.448528	−	1.31063i
$455$		0			0
$456$	−6.15038	+	4.04366i	−0.288018	+	0.189362i
$457$	6.99093	−	26.0905i	0.327022	−	1.22046i	−0.585242	−	0.810859i	$-0.699000\pi$
$457$	6.99093	−	26.0905i	0.327022	−	1.22046i	0.912264	−	0.409603i	$-0.134333\pi$
$458$	−4.59706	−	0.312765i	−0.214806	−	0.0146145i
$459$	−11.7381	+	20.3310i	−0.547889	+	0.948972i
$460$	−0.460728	−	0.336835i	−0.0214816	−	0.0157050i
$461$	−8.24886			−0.384188			−0.192094	−	0.981377i	$-0.561528\pi$
$461$	−8.24886			−0.384188			−0.192094	+	0.981377i	$0.561528\pi$
$462$		0			0
$463$	15.4884	+	15.4884i	0.719806	+	0.719806i	0.968565	−	0.248759i	$-0.0800227\pi$
$463$	15.4884	+	15.4884i	0.719806	+	0.719806i	−0.248759	+	0.968565i	$0.580023\pi$
$464$	−11.2876	−	11.5139i	−0.524014	−	0.534520i
$465$	−29.8865	−	48.5531i	−1.38595	−	2.25159i
$466$	6.42373	+	7.36163i	0.297573	+	0.341021i
$467$	37.9505	+	10.1688i	1.75614	+	0.470556i	0.985919	−	0.167223i	$-0.0534799\pi$
$467$	37.9505	+	10.1688i	1.75614	+	0.470556i	0.770220	+	0.637779i	$0.220147\pi$
$468$	69.8135	−	8.83889i	3.22713	−	0.408578i
$469$		0			0
$470$	0.868953	−	21.8431i	0.0400818	−	1.00755i
$471$	−53.7702	+	31.0442i	−2.47760	+	1.43044i
$472$	22.1652	+	19.7322i	1.02024	+	0.908249i
$473$	−0.162138	−	0.605106i	−0.00745510	−	0.0278228i
$474$	10.0250	+	51.0611i	0.460466	+	2.34532i
$475$	3.67181	−	2.40534i	0.168474	−	0.110365i
$476$		0			0
$477$	−16.0544	−	16.0544i	−0.735082	−	0.735082i
$478$	−12.0643	−	8.10451i	−0.551810	−	0.370692i
$479$	1.93358	−	3.34906i	0.0883475	−	0.153022i	−0.818465	−	0.574556i	$-0.805175\pi$
$479$	1.93358	−	3.34906i	0.0883475	−	0.153022i	0.906813	+	0.421534i	$0.138508\pi$
$480$	35.6914	+	11.4914i	1.62908	+	0.524508i
$481$	5.55578	+	9.62290i	0.253322	+	0.438767i
$482$	6.08099	−	2.98008i	0.276982	−	0.135739i
$483$		0			0
$484$	13.4226	−	17.3141i	0.610118	−	0.787004i
$485$	−0.230319	−	8.17374i	−0.0104583	−	0.371151i
$486$	3.89270	−	3.39676i	0.176576	−	0.154080i
$487$	−0.115208	−	0.429962i	−0.00522057	−	0.0194834i	0.963266	−	0.268548i	$-0.0865437\pi$
$487$	−0.115208	−	0.429962i	−0.00522057	−	0.0194834i	−0.968487	+	0.249064i	$0.919877\pi$
$488$	22.3578	−	7.40430i	1.01209	−	0.335177i
$489$			47.1380i			2.13165i
$490$		0			0
$491$		−	40.4240i		−	1.82431i	−0.409844	−	0.912156i	$-0.634417\pi$
$491$		−	40.4240i		−	1.82431i	0.409844	−	0.912156i	$-0.365583\pi$
$492$	10.4517	+	13.7617i	0.471198	+	0.620427i
$493$	−2.96463	−	11.0641i	−0.133520	−	0.498304i
$494$	4.96306	+	5.68769i	0.223298	+	0.255901i
$495$	2.02116	+	1.91038i	0.0908443	+	0.0858650i
$496$	33.3205	−	8.57467i	1.49613	−	0.385014i
$497$		0			0
$498$	−13.8461	−	28.2536i	−0.620459	−	1.26608i
$499$	−15.8937	−	27.5287i	−0.711501	−	1.23236i	−0.964294	−	0.264835i	$-0.914683\pi$
$499$	−15.8937	−	27.5287i	−0.711501	−	1.23236i	0.252793	−	0.967520i	$-0.418651\pi$
$500$	−21.2732	−	6.88837i	−0.951368	−	0.308057i
$501$	−25.2723	+	43.7728i	−1.12908	+	1.95563i
$502$	20.7133	−	30.8337i	0.924479	−	1.37618i
$503$	6.28613	+	6.28613i	0.280285	+	0.280285i	0.833222	−	0.552938i	$-0.186493\pi$
$503$	6.28613	+	6.28613i	0.280285	+	0.280285i	−0.552938	+	0.833222i	$0.686493\pi$
$504$		0			0
$505$	32.5574	−	9.71448i	1.44879	−	0.432289i
$506$	0.0380621	−	0.00747289i	0.00169207	−	0.000332210i
$507$	−18.3877	−	68.6239i	−0.816627	−	3.04769i
$508$	5.77006	+	2.42365i	0.256005	+	0.107532i
$509$	−2.67962	+	1.54708i	−0.118772	+	0.0685730i	−0.558209	−	0.829700i	$-0.688511\pi$
$509$	−2.67962	+	1.54708i	−0.118772	+	0.0685730i	0.439437	+	0.898273i	$0.355178\pi$
$510$	18.0716	+	19.5690i	0.800224	+	0.866531i
$511$		0			0
$512$	−12.9881	+	18.5286i	−0.573998	+	0.818857i
$513$	−7.00577	−	1.87719i	−0.309312	−	0.0828800i
$514$	24.6986	−	21.5519i	1.08941	−	0.950614i
$515$	−2.93286	+	1.80530i	−0.129237	+	0.0795509i
$516$	2.34058	−	17.1215i	0.103038	−	0.753731i
$517$	1.05056	+	1.05056i	0.0462035	+	0.0462035i
$518$		0			0
$519$	1.34572			0.0590707
$520$	6.71865	−	37.8620i	0.294632	−	1.66036i
$521$	−2.55693	+	4.42873i	−0.112021	+	0.194026i	−0.916585	−	0.399840i	$-0.869066\pi$
$521$	−2.55693	+	4.42873i	−0.112021	+	0.194026i	0.804564	+	0.593866i	$0.202399\pi$
$522$	2.23932	−	32.9139i	0.0980125	−	1.44060i
$523$	6.56089	−	24.4856i	0.286888	−	1.07068i	−0.660561	−	0.750772i	$-0.729682\pi$
$523$	6.56089	−	24.4856i	0.286888	−	1.07068i	0.947449	−	0.319907i	$-0.103652\pi$
$524$	−5.87669	−	4.55586i	−0.256725	−	0.199024i
$525$		0			0
$526$	−7.97623	−	2.72966i	−0.347780	−	0.119019i
$527$	23.6093	+	6.32609i	1.02844	+	0.275569i
$528$	−2.21947	+	1.25221i	−0.0965902	+	0.0544954i
$529$	19.9045	+	11.4919i	0.865412	+	0.499646i
$530$	−10.9825	+	5.77131i	−0.477050	+	0.250690i
$531$			60.7177i			2.63493i
$532$		0			0
$533$	12.5314	−	12.5314i	0.542797	−	0.542797i
$534$	52.4110	−	10.2901i	2.26804	−	0.445295i
$535$	16.0548	+	26.0824i	0.694110	+	1.12764i
$536$	−2.21955	+	0.128892i	−0.0958700	+	0.00556728i
$537$	−3.72499	+	13.9019i	−0.160745	+	0.599909i
$538$	0.0415746	+	0.0848349i	0.00179241	+	0.00365749i
$539$		0			0
$540$	14.9274	+	33.7974i	0.642371	+	1.45441i
$541$	−0.501976	−	0.869449i	−0.0215817	−	0.0373805i	0.855033	−	0.518574i	$-0.173537\pi$
$541$	−0.501976	−	0.869449i	−0.0215817	−	0.0373805i	−0.876615	+	0.481193i	$0.840204\pi$
$542$	−3.92288	−	0.266897i	−0.168502	−	0.0114642i
$543$	19.7071	−	5.28051i	0.845713	−	0.226608i
$544$	−14.5039	+	6.93019i	−0.621850	+	0.297129i
$545$	−7.69870	−	25.8017i	−0.329776	−	1.10522i
$546$		0			0
$547$	11.1953	−	11.1953i	0.478676	−	0.478676i	−0.426032	−	0.904708i	$-0.640089\pi$
$547$	11.1953	−	11.1953i	0.478676	−	0.478676i	0.904708	+	0.426032i	$0.140089\pi$
$548$	−3.16409	−	4.16617i	−0.135163	−	0.177970i
$549$	41.7320	+	24.0940i	1.78108	+	1.02831i
$550$	1.32483	−	0.744554i	0.0564910	−	0.0317479i
$551$	3.06470	−	1.76940i	0.130561	−	0.0753792i
$552$	1.04785	+	0.216550i	0.0445993	+	0.00921700i
$553$		0			0
$554$	7.66412	+	2.62285i	0.325617	+	0.111434i
$555$	−8.32099	+	8.80353i	−0.353207	+	0.373689i
$556$	8.24783	+	20.1949i	0.349786	+	0.856455i
$557$	10.1973	−	2.73237i	0.432075	−	0.115774i	−0.0362252	−	0.999344i	$-0.511533\pi$
$557$	10.1973	−	2.73237i	0.432075	−	0.115774i	0.468300	+	0.883570i	$0.344867\pi$
$558$	58.4348	+	39.2550i	2.47374	+	1.66180i
$559$	−17.7221			−0.749567
$560$		0			0
$561$	−1.81035			−0.0764331
$562$	26.9097	+	18.0772i	1.13512	+	0.762541i
$563$	7.19675	−	1.92836i	0.303307	−	0.0812708i	−0.103956	−	0.994582i	$-0.533150\pi$
$563$	7.19675	−	1.92836i	0.303307	−	0.0812708i	0.407263	+	0.913311i	$0.366483\pi$
$564$	15.4956	+	37.9412i	0.652483	+	1.59761i
$565$	−9.93855	+	0.280048i	−0.418118	+	0.0117817i
$566$	0.760788	+	0.260360i	0.0319783	+	0.0109437i
$567$		0			0
$568$	−4.84831	−	1.00196i	−0.203430	−	0.0420414i
$569$	−23.6353	+	13.6458i	−0.990841	+	0.572063i	−0.905526	−	0.424291i	$-0.860523\pi$
$569$	−23.6353	+	13.6458i	−0.990841	+	0.572063i	−0.0853157	+	0.996354i	$0.527190\pi$
$570$	−4.39474	+	6.95768i	−0.184075	+	0.291425i
$571$	−5.57769	−	3.22028i	−0.233419	−	0.134765i	0.378729	−	0.925507i	$-0.376361\pi$
$571$	−5.57769	−	3.22028i	−0.233419	−	0.134765i	−0.612148	+	0.790743i	$0.709694\pi$
$572$	1.58066	+	2.08126i	0.0660906	+	0.0870217i
$573$	−36.1424	+	36.1424i	−1.50987	+	1.50987i
$574$		0			0
$575$	−0.624671	−	0.130181i	−0.0260506	−	0.00542892i
$576$	−45.9852	+	5.35889i	−1.91605	+	0.223287i
$577$	14.3060	−	3.83327i	0.595565	−	0.159581i	0.0515697	−	0.998669i	$-0.483578\pi$
$577$	14.3060	−	3.83327i	0.595565	−	0.159581i	0.543995	+	0.839088i	$0.316911\pi$
$578$	12.5931	+	0.856784i	0.523805	+	0.0356375i
$579$	−30.0438	−	52.0374i	−1.24858	−	2.16260i
$580$	−16.8105	−	6.51032i	−0.698016	−	0.270326i
$581$		0			0
$582$	6.74619	+	13.7659i	0.279639	+	0.570616i
$583$	0.218236	−	0.814469i	0.00903842	−	0.0337318i
$584$	16.7209	−	0.971005i	0.691918	−	0.0401805i
$585$	67.0012	−	41.2421i	2.77016	−	1.70515i
$586$	2.81171	−	0.552035i	0.116151	−	0.0228043i
$587$	15.0807	−	15.0807i	0.622447	−	0.622447i	−0.323710	−	0.946156i	$-0.604930\pi$
$587$	15.0807	−	15.0807i	0.622447	−	0.622447i	0.946156	+	0.323710i	$0.104930\pi$
$588$		0			0
$589$			7.55131i			0.311146i
$590$	31.6814	+	9.85440i	1.30430	+	0.405699i
$591$	−46.9764	−	27.1218i	−1.93235	−	1.11564i
$592$	−3.59209	−	6.36679i	−0.147634	−	0.261673i
$593$	−34.5845	−	9.26689i	−1.42022	−	0.380546i	−0.534655	−	0.845070i	$-0.679558\pi$
$593$	−34.5845	−	9.26689i	−1.42022	−	0.380546i	−0.885560	+	0.464525i	$0.846225\pi$
$594$	−2.37579	−	0.813053i	−0.0974800	−	0.0333600i
$595$		0			0
$596$	17.7699	+	13.7760i	0.727884	+	0.564286i
$597$	16.7911	−	62.6653i	0.687214	−	2.56472i
$598$	0.0744850	−	1.09479i	0.00304592	−	0.0447693i
$599$	11.1770	−	19.3591i	0.456680	−	0.790992i	−0.542103	−	0.840312i	$-0.682372\pi$
$599$	11.1770	−	19.3591i	0.456680	−	0.790992i	0.998783	+	0.0493194i	$0.0157052\pi$
$600$	41.6477	−	4.78316i	1.70026	−	0.195272i
$601$	−43.6119			−1.77897			−0.889483	−	0.456969i	$-0.848935\pi$
$601$	−43.6119			−1.77897			−0.889483	+	0.456969i	$0.848935\pi$
$602$		0			0
$603$	−3.21657	−	3.21657i	−0.130989	−	0.130989i
$604$	2.45997	−	17.9948i	0.100095	−	0.732197i
$605$	5.67046	−	23.8280i	0.230537	−	0.968748i
$606$	−47.9943	+	41.8796i	−1.94963	+	1.70124i
$607$	−23.0617	−	6.17935i	−0.936044	−	0.250812i	−0.241614	−	0.970373i	$-0.577677\pi$
$607$	−23.0617	−	6.17935i	−0.936044	−	0.250812i	−0.694430	+	0.719560i	$0.744343\pi$
$608$	−3.22785	−	3.77410i	−0.130907	−	0.153060i
$609$		0			0
$610$	19.3448	−	17.8646i	0.783250	−	0.723316i
$611$	36.3994	−	21.0152i	1.47256	−	0.850184i
$612$	−30.3226	−	12.7367i	−1.22572	−	0.514851i
$613$	−7.61342	−	28.4137i	−0.307503	−	1.14762i	−0.930769	−	0.365608i	$-0.880861\pi$
$613$	−7.61342	−	28.4137i	−0.307503	−	1.14762i	0.623266	−	0.782010i	$-0.285806\pi$
$614$	−2.96416	+	0.581966i	−0.119624	+	0.0234863i
$615$	16.9974	+	9.18509i	0.685403	+	0.370379i
$616$		0			0
$617$	12.8248	+	12.8248i	0.516307	+	0.516307i	0.916452	−	0.400145i	$-0.131040\pi$
$617$	12.8248	+	12.8248i	0.516307	+	0.516307i	−0.400145	+	0.916452i	$0.631040\pi$
$618$	3.60044	−	5.35960i	0.144831	−	0.215595i
$619$	−7.38068	+	12.7837i	−0.296655	+	0.513821i	−0.975368	−	0.220582i	$-0.929204\pi$
$619$	−7.38068	+	12.7837i	−0.296655	+	0.513821i	0.678714	+	0.734403i	$0.262538\pi$
$620$	29.9664	−	24.1192i	1.20348	−	0.968652i
$621$	0.527167	+	0.913080i	0.0211545	+	0.0366406i
$622$	−7.93229	−	16.1862i	−0.318056	−	0.649008i
$623$		0			0
$624$	17.9667	+	69.8173i	0.719245	+	2.79493i
$625$	−24.8415	+	2.81109i	−0.993658	+	0.112444i
$626$	−18.9323	−	21.6965i	−0.756687	−	0.867167i
$627$	−0.144758	−	0.540244i	−0.00578107	−	0.0215752i
$628$	−25.3363	−	33.3604i	−1.01103	−	1.33123i
$629$		−	5.19318i		−	0.207066i
$630$		0			0
$631$			31.4840i			1.25336i	0.779278	+	0.626678i	$0.215586\pi$
$631$			31.4840i			1.25336i	−0.779278	+	0.626678i	$0.784414\pi$
$632$	−33.3284	+	11.0375i	−1.32573	+	0.439047i
$633$	2.60624	+	9.72662i	0.103589	+	0.386598i
$634$	−10.5356	+	9.19334i	−0.418423	+	0.365114i
$635$	6.99434	−	0.197086i	0.277562	−	0.00782113i
$636$	14.2510	−	18.3827i	0.565089	−	0.728920i
$637$		0			0
$638$	1.10018	−	0.539159i	0.0435565	−	0.0213455i
$639$	−5.06470	−	8.77231i	−0.200356	−	0.347027i
$640$	−4.66715	+	24.8640i	−0.184485	+	0.982835i
$641$	11.4235	−	19.7861i	0.451201	−	0.781504i	−0.547260	−	0.836963i	$-0.684329\pi$
$641$	11.4235	−	19.7861i	0.451201	−	0.781504i	0.998461	+	0.0554593i	$0.0176623\pi$
$642$	−47.6638	−	32.0193i	−1.88114	−	1.26370i
$643$	−13.3643	−	13.3643i	−0.527038	−	0.527038i	0.392650	−	0.919688i	$-0.371558\pi$
$643$	−13.3643	−	13.3643i	−0.527038	−	0.527038i	−0.919688	+	0.392650i	$0.871558\pi$
$644$		0			0
$645$	−5.52416	−	18.5138i	−0.217514	−	0.728982i
$646$	−0.679686	−	3.46188i	−0.0267419	−	0.136206i
$647$	6.05981	+	22.6155i	0.238236	+	0.889108i	0.976663	+	0.214775i	$0.0689020\pi$
$647$	6.05981	+	22.6155i	0.238236	+	0.889108i	−0.738428	+	0.674333i	$0.764431\pi$
$648$	−15.0601	−	13.4070i	−0.591615	−	0.526675i
$649$	−1.95284	+	1.12747i	−0.0766557	+	0.0442572i
$650$	−10.6452	−	41.6536i	−0.417539	−	1.63379i
$651$		0			0
$652$	−31.5520	+	3.99471i	−1.23567	+	0.156445i
$653$	−21.3285	−	5.71494i	−0.834647	−	0.223643i	−0.183907	−	0.982944i	$-0.558875\pi$
$653$	−21.3285	−	5.71494i	−0.834647	−	0.223643i	−0.650740	+	0.759301i	$0.725541\pi$
$654$	33.1895	+	38.0353i	1.29781	+	1.48730i
$655$	−8.08764	−	1.92465i	−0.316010	−	0.0752024i
$656$	−8.32575	+	8.16210i	−0.325066	+	0.318676i
$657$	24.2320	+	24.2320i	0.945379	+	0.945379i
$658$		0			0
$659$	−23.8406			−0.928696			−0.464348	−	0.885653i	$-0.653711\pi$
$659$	−23.8406			−0.928696			−0.464348	+	0.885653i	$0.653711\pi$
$660$	−1.68153	+	2.30002i	−0.0654533	+	0.0895280i
$661$	−11.0124	+	19.0740i	−0.428331	+	0.741891i	−0.996725	−	0.0808656i	$-0.974232\pi$
$661$	−11.0124	+	19.0740i	−0.428331	+	0.741891i	0.568394	+	0.822756i	$0.307565\pi$
$662$	−41.4120	−	2.81750i	−1.60952	−	0.109505i
$663$	−13.2552	+	49.4692i	−0.514791	+	1.92122i
$664$	17.7383	−	11.6623i	0.688379	−	0.452585i
$665$		0			0
$666$	4.84286	−	14.1512i	0.187657	−	0.548346i
$667$	−0.496898	−	0.133143i	−0.0192400	−	0.00515533i
$668$	−31.4412	−	13.2065i	−1.21650	−	0.510976i
$669$	−71.7453	−	41.4222i	−2.77383	−	1.60147i
$670$	−2.20039	+	1.15630i	−0.0850086	+	0.0446720i
$671$			1.78961i			0.0690872i
$672$		0			0
$673$	15.2135	−	15.2135i	0.586437	−	0.586437i	−0.350227	−	0.936665i	$-0.613896\pi$
$673$	15.2135	−	15.2135i	0.586437	−	0.586437i	0.936665	+	0.350227i	$0.113896\pi$
$674$	−8.45506	−	43.0646i	−0.325677	−	1.65879i
$675$	30.8077	+	27.5181i	1.18579	+	1.05917i
$676$	44.3754	−	18.1234i	1.70674	−	0.697054i
$677$	−3.07519	+	11.4768i	−0.118189	+	0.441088i	−0.999506	−	0.0314382i	$-0.989991\pi$
$677$	−3.07519	+	11.4768i	−0.118189	+	0.441088i	0.881316	+	0.472527i	$0.156658\pi$
$678$	16.7381	−	8.20277i	0.642825	−	0.315026i
$679$		0			0
$680$	−11.5671	+	13.7547i	−0.443578	+	0.527467i
$681$	30.9338	+	53.5789i	1.18539	+	2.05315i
$682$	−0.177461	+	2.60835i	−0.00679533	+	0.0998787i
$683$	34.6511	−	9.28473i	1.32589	−	0.355270i	0.474707	−	0.880144i	$-0.342554\pi$
$683$	34.6511	−	9.28473i	1.32589	−	0.355270i	0.851180	+	0.524873i	$0.175887\pi$
$684$	1.37624	−	10.0673i	0.0526220	−	0.384933i
$685$	−5.14573	−	2.78066i	−0.196608	−	0.106243i
$686$		0			0
$687$	6.82927	−	6.82927i	0.260553	−	0.260553i
$688$	11.6587	+	0.115717i	0.444482	+	0.00441168i
$689$	−20.6581	−	11.9269i	−0.787009	−	0.454380i
$690$	1.16692	−	0.263444i	0.0444237	−	0.0100292i
$691$	−37.9496	+	21.9102i	−1.44367	+	0.833505i	−0.998092	−	0.0617372i	$-0.980336\pi$
$691$	−37.9496	+	21.9102i	−1.44367	+	0.833505i	−0.445580	+	0.895242i	$0.647003\pi$
$692$	0.114043	+	0.900764i	0.00433527	+	0.0342419i
$693$		0			0
$694$	3.71997	−	10.8700i	0.141208	−	0.412619i
$695$	17.7246	+	16.7531i	0.672332	+	0.635481i
$696$	33.7400	−	1.95932i	1.27891	−	0.0742680i
$697$	−8.00051	+	2.14373i	−0.303041	+	0.0811996i
$698$	−6.67493	+	9.93628i	−0.252650	+	0.376094i
$699$	−20.4792			−0.774593
$700$		0			0
$701$	38.4455			1.45207			0.726033	−	0.687660i	$-0.241362\pi$
$701$	38.4455			1.45207			0.726033	+	0.687660i	$0.241362\pi$
$702$	−39.6126	+	58.9672i	−1.49508	+	2.22557i
$703$	1.54974	−	0.415253i	0.0584497	−	0.0156616i
$704$	−1.02626	−	1.37949i	−0.0386786	−	0.0519916i
$705$	33.3001	+	31.4748i	1.25415	+	1.18541i
$706$	9.52347	−	27.8282i	0.358420	−	1.04733i
$707$		0			0
$708$	−61.7102	+	7.81296i	−2.31921	+	0.293629i
$709$	−33.8118	+	19.5213i	−1.26983	+	0.733137i	−0.974956	−	0.222400i	$-0.928611\pi$
$709$	−33.8118	+	19.5213i	−1.26983	+	0.733137i	−0.294874	+	0.955536i	$0.595278\pi$
$710$	−5.39923	+	1.21894i	−0.202630	+	0.0457459i
$711$	−62.2092	−	35.9165i	−2.33303	−	1.34697i
$712$	11.3293	+	34.2094i	0.424582	+	1.28205i
$713$	0.776200	−	0.776200i	0.0290689	−	0.0290689i
$714$		0			0
$715$	2.57061	+	1.38911i	0.0961352	+	0.0519496i
$716$	−9.62093	−	1.31522i	−0.359551	−	0.0491522i
$717$	29.4259	−	7.88464i	1.09893	−	0.294457i
$718$	−2.26211	+	33.2488i	−0.0844212	+	1.24083i
$719$	2.32924	+	4.03436i	0.0868659	+	0.150456i	0.906185	−	0.422882i	$-0.138982\pi$
$719$	2.32924	+	4.03436i	0.0868659	+	0.150456i	−0.819319	+	0.573338i	$0.805648\pi$
$720$	−44.3466	+	26.6940i	−1.65270	+	0.994825i
$721$		0			0
$722$	−23.1497	+	11.3448i	−0.861542	+	0.422211i
$723$	−3.67381	+	13.7108i	−0.136630	+	0.509912i
$724$	5.20460	+	12.7435i	0.193428	+	0.473610i
$725$	−20.1229	+	1.13495i	−0.747346	+	0.0421508i
$726$	8.84676	+	45.0597i	0.328334	+	1.67232i
$727$	8.55868	−	8.55868i	0.317424	−	0.317424i	−0.530353	−	0.847777i	$-0.677941\pi$
$727$	8.55868	−	8.55868i	0.317424	−	0.317424i	0.847777	+	0.530353i	$0.177941\pi$
$728$		0			0
$729$			32.2153i			1.19316i
$730$	16.5766	−	8.71100i	0.613528	−	0.322409i
$731$	7.17306	+	4.14137i	0.265305	+	0.153174i
$732$	−19.1179	+	45.5144i	−0.706617	+	1.68226i
$733$	1.07241	+	0.287351i	0.0396103	+	0.0106135i	0.278570	−	0.960416i	$-0.410140\pi$
$733$	1.07241	+	0.287351i	0.0396103	+	0.0106135i	−0.238959	+	0.971030i	$0.576806\pi$
$734$	−2.44248	+	7.13708i	−0.0901535	+	0.263434i
$735$		0			0
$736$	−0.0561491	+	0.719731i	−0.00206968	+	0.0265297i
$737$	0.0437245	−	0.163182i	0.00161061	−	0.00601089i
$738$	−23.8001	−	1.61926i	−0.876095	−	0.0596058i
$739$	−2.43294	+	4.21398i	−0.0894972	+	0.155014i	−0.907299	−	0.420487i	$-0.861859\pi$
$739$	−2.43294	+	4.21398i	−0.0894972	+	0.155014i	0.817802	+	0.575500i	$0.195193\pi$
$740$	−6.59783	−	4.82363i	−0.242541	−	0.177320i
$741$	−15.8225			−0.581253
$742$		0			0
$743$	−24.8474	−	24.8474i	−0.911564	−	0.911564i	0.0848314	−	0.996395i	$-0.472965\pi$
$743$	−24.8474	−	24.8474i	−0.911564	−	0.911564i	−0.996395	+	0.0848314i	$0.972965\pi$
$744$	−32.3774	+	64.4412i	−1.18701	+	2.36253i
$745$	24.4554	+	5.81975i	0.895976	+	0.213219i
$746$	−29.9763	−	34.3529i	−1.09751	−	1.25775i
$747$	41.9545	+	11.2417i	1.53503	+	0.411311i
$748$	−0.153418	−	1.21176i	−0.00560952	−	0.0443065i
$749$		0			0
$750$	40.1962	−	24.1046i	1.46776	−	0.880174i
$751$	−17.3437	+	10.0134i	−0.632882	+	0.365394i	−0.781867	−	0.623445i	$-0.785733\pi$
$751$	−17.3437	+	10.0134i	−0.632882	+	0.365394i	0.148986	+	0.988839i	$0.452399\pi$
$752$	−24.0829	+	13.5874i	−0.878212	+	0.495480i
$753$	20.1514	+	75.2059i	0.734356	+	2.74065i
$754$	−6.67750	−	34.0109i	−0.243180	−	1.23860i
$755$	−5.80593	−	19.4582i	−0.211299	−	0.708156i
$756$		0			0
$757$	10.7543	+	10.7543i	0.390871	+	0.390871i	0.874998	−	0.484127i	$-0.160863\pi$
$757$	10.7543	+	10.7543i	0.390871	+	0.390871i	−0.484127	+	0.874998i	$0.660863\pi$
$758$	−3.73972	−	2.51225i	−0.135833	−	0.0912489i
$759$	−0.0406520	+	0.0704114i	−0.00147557	+	0.00255577i
$760$	−5.02958	−	2.35201i	−0.182442	−	0.0853163i
$761$	−10.3017	−	17.8431i	−0.373437	−	0.646812i	0.616655	−	0.787234i	$-0.288488\pi$
$761$	−10.3017	−	17.8431i	−0.373437	−	0.646812i	−0.990092	+	0.140422i	$0.955154\pi$
$762$	−11.7796	+	5.77277i	−0.426730	+	0.209125i
$763$		0			0
$764$	−27.2549	−	21.1291i	−0.986048	−	0.764426i
$765$	−36.7564	+	1.03572i	−1.32893	+	0.0374466i
$766$	−30.0381	+	26.2111i	−1.08532	+	0.947047i
$767$	16.5105	+	61.6181i	0.596161	+	2.22490i
$768$	−11.3637	−	46.0473i	−0.410052	−	1.66159i
$769$			9.33534i			0.336641i	0.985732	+	0.168320i	$0.0538343\pi$
$769$			9.33534i			0.336641i	−0.985732	+	0.168320i	$0.946166\pi$
$770$		0			0
$771$			68.7086i			2.47448i
$772$	32.2854	−	24.5198i	1.16198	−	0.882488i
$773$	−3.79713	−	14.1711i	−0.136573	−	0.509698i	−0.999986	−	0.00520083i	$-0.998345\pi$
$773$	−3.79713	−	14.1711i	−0.136573	−	0.509698i	0.863413	−	0.504497i	$-0.168322\pi$
$774$	15.6842	+	17.9742i	0.563758	+	0.646070i
$775$	19.3723	−	38.3975i	0.695875	−	1.37928i
$776$	−8.64256	+	5.68218i	−0.310250	+	0.203978i
$777$		0			0
$778$	−10.1729	−	20.7582i	−0.364715	−	0.744218i
$779$	−1.27946	−	2.21609i	−0.0458414	−	0.0793997i
$780$	50.5377	+	62.7895i	1.80954	+	2.24822i
$781$	0.188094	−	0.325788i	0.00673052	−	0.0116576i
$782$	−0.285982	+	0.425712i	−0.0102267	+	0.0152234i
$783$	23.5484	+	23.5484i	0.841550	+	0.841550i
$784$		0			0
$785$	−41.2042	−	22.2660i	−1.47064	−	0.794706i
$786$	15.2940	−	3.00274i	0.545520	−	0.107104i
$787$	7.36321	+	27.4799i	0.262470	+	0.979551i	0.963781	+	0.266696i	$0.0859319\pi$
$787$	7.36321	+	27.4799i	0.262470	+	0.979551i	−0.701311	+	0.712856i	$0.747401\pi$
$788$	14.1731	−	33.7422i	0.504895	−	1.20202i
$789$	15.3033	−	8.83535i	0.544811	−	0.314547i
$790$	−28.8371	+	26.6305i	−1.02598	+	0.947469i
$791$		0			0
$792$	0.711966	−	3.44507i	0.0252986	−	0.122415i
$793$	48.9025	+	13.1034i	1.73658	+	0.465315i
$794$	16.1859	−	14.1237i	0.574415	−	0.501232i
$795$	6.02043	−	25.2987i	0.213523	−	0.897251i
$796$	43.3682	+	5.92862i	1.53714	+	0.210134i
$797$	−4.43257	−	4.43257i	−0.157010	−	0.157010i	0.624231	−	0.781240i	$-0.285413\pi$
$797$	−4.43257	−	4.43257i	−0.157010	−	0.157010i	−0.781240	+	0.624231i	$0.785413\pi$
$798$		0			0
$799$	−19.6436			−0.694941
$800$	6.73105	+	27.4717i	0.237979	+	0.971270i
$801$	−36.8660	+	63.8537i	−1.30260	+	2.25616i
$802$	−2.28089	+	33.5249i	−0.0805412	+	1.18381i
$803$	−0.329398	+	1.22933i	−0.0116242	+	0.0433821i
$804$	2.85525	−	3.68304i	0.100697	−	0.129891i
$805$		0			0
$806$	69.9757	+	23.9473i	2.46479	+	0.843509i
$807$	−0.191278	−	0.0512527i	−0.00673329	−	0.00180418i
$808$	−32.0995	−	28.5760i	−1.12926	−	1.00530i
$809$	−2.26376	−	1.30698i	−0.0795895	−	0.0459510i	0.459677	−	0.888086i	$-0.347965\pi$
$809$	−2.26376	−	1.30698i	−0.0795895	−	0.0459510i	−0.539267	+	0.842135i	$0.681298\pi$
$810$	−21.5258	−	6.69552i	−0.756340	−	0.235257i
$811$		−	20.5143i		−	0.720354i	−0.932884	−	0.360177i	$-0.882716\pi$
$811$		−	20.5143i		−	0.720354i	0.932884	−	0.360177i	$-0.117284\pi$
$812$		0			0
$813$	5.82774	−	5.82774i	0.204388	−	0.204388i
$814$	0.545066	−	0.107015i	0.0191045	−	0.00375088i
$815$	−30.2810	+	18.6392i	−1.06070	+	0.652903i
$816$	9.04308	−	32.4572i	0.316571	−	1.13623i
$817$	−0.662298	+	2.47173i	−0.0231709	+	0.0864748i
$818$	14.0452	+	28.6600i	0.491080	+	1.00207i
$819$		0			0
$820$	−4.70763	+	12.1557i	−0.164397	+	0.424495i
$821$	3.55951	+	6.16525i	0.124228	+	0.215169i	0.921431	−	0.388542i	$-0.127021\pi$
$821$	3.55951	+	6.16525i	0.124228	+	0.215169i	−0.797203	+	0.603711i	$0.793688\pi$
$822$	10.9403	+	0.744332i	0.381586	+	0.0259615i
$823$	21.7813	−	5.83627i	0.759247	−	0.203440i	0.141631	−	0.989919i	$-0.454765\pi$
$823$	21.7813	−	5.83627i	0.759247	−	0.203440i	0.617616	+	0.786480i	$0.288099\pi$
$824$	3.89258	+	1.95577i	0.135605	+	0.0681323i
$825$	−0.649880	+	3.11844i	−0.0226259	+	0.108570i
$826$		0			0
$827$	27.0197	−	27.0197i	0.939566	−	0.939566i	−0.0587089	−	0.998275i	$-0.518698\pi$
$827$	27.0197	−	27.0197i	0.939566	−	0.939566i	0.998275	+	0.0587089i	$0.0186984\pi$
$828$	−1.17628	+	0.893354i	−0.0408787	+	0.0310462i
$829$	−19.0572	−	11.0027i	−0.661884	−	0.382139i	0.131110	−	0.991368i	$-0.458146\pi$
$829$	−19.0572	−	11.0027i	−0.661884	−	0.382139i	−0.792995	+	0.609229i	$0.791479\pi$
$830$	12.6748	−	20.0666i	0.439950	−	0.696522i
$831$	−14.7045	+	8.48962i	−0.510092	+	0.294502i
$832$	−45.2099	+	17.9428i	−1.56737	+	0.622054i
$833$		0			0
$834$	−43.2611	−	14.8050i	−1.49801	−	0.512654i
$835$	−38.1123	+	1.07393i	−1.31893	+	0.0371648i
$836$	0.349346	−	0.142677i	0.0120824	−	0.00493459i
$837$	−68.6411	+	18.3923i	−2.37258	+	0.635732i
$838$	14.5979	+	9.80646i	0.504275	+	0.338758i
$839$	47.2741			1.63208			0.816041	−	0.577994i	$-0.196164\pi$
$839$	47.2741			1.63208			0.816041	+	0.577994i	$0.196164\pi$
$840$		0			0
$841$	12.7512			0.439697
$842$	36.7202	+	24.6676i	1.26546	+	0.850103i
$843$	−65.6348	+	17.5868i	−2.26058	+	0.605721i
$844$	−6.28968	+	2.56878i	−0.216500	+	0.0884210i
$845$	36.8124	−	38.9472i	1.26639	−	1.33982i
$846$	−53.5279	−	18.3185i	−1.84033	−	0.629804i
$847$		0			0
$848$	13.5122	+	7.98113i	0.464011	+	0.274073i
$849$	−1.45965	+	0.842732i	−0.0500952	+	0.0289225i
$850$	−5.42509	+	19.3470i	−0.186079	+	0.663595i
$851$	−0.201982	−	0.116614i	−0.00692386	−	0.00399749i
$852$	8.26399	−	6.27627i	0.283120	−	0.215022i
$853$	11.2255	−	11.2255i	0.384355	−	0.384355i	−0.488313	−	0.872668i	$-0.662388\pi$
$853$	11.2255	−	11.2255i	0.384355	−	0.384355i	0.872668	+	0.488313i	$0.162388\pi$
$854$		0			0
$855$	−3.24817	−	10.8860i	−0.111085	−	0.372294i
$856$	17.3929	−	34.6174i	0.594478	−	1.18320i
$857$	−4.56860	+	1.22415i	−0.156060	+	0.0418162i	−0.336003	−	0.941861i	$-0.609075\pi$
$857$	−4.56860	+	1.22415i	−0.156060	+	0.0418162i	0.179943	+	0.983677i	$0.442409\pi$
$858$	−5.46534	−	0.371839i	−0.186584	−	0.0126944i
$859$	2.80350	+	4.85581i	0.0956543	+	0.165678i	0.909881	−	0.414868i	$-0.136172\pi$
$859$	2.80350	+	4.85581i	0.0956543	+	0.165678i	−0.814227	+	0.580546i	$0.802839\pi$
$860$	11.9242	−	5.26657i	0.406610	−	0.179589i
$861$		0			0
$862$	−11.9046	−	24.2920i	−0.405474	−	0.827389i
$863$	12.9205	−	48.2200i	0.439819	−	1.64143i	−0.289445	−	0.957195i	$-0.593471\pi$
$863$	12.9205	−	48.2200i	0.439819	−	1.64143i	0.729264	−	0.684232i	$-0.239863\pi$
$864$	26.4445	−	38.5334i	0.899661	−	1.31093i
$865$	0.532123	+	0.864478i	0.0180927	+	0.0293931i
$866$	−9.56692	+	1.87831i	−0.325097	+	0.0638277i
$867$	−18.7080	+	18.7080i	−0.635358	+	0.635358i
$868$		0			0
$869$		−	2.66775i		−	0.0904971i
$870$	33.4488	−	17.5773i	1.13402	−	0.595927i
$871$	−4.13893	−	2.38961i	−0.140242	−	0.0809689i
$872$	−22.6464	+	25.4388i	−0.766905	+	0.861467i
$873$	−20.4413	−	5.47724i	−0.691834	−	0.185376i
$874$	−0.149908	−	0.0513022i	−0.00507072	−	0.00173532i
$875$		0			0
$876$	−21.5100	+	27.7461i	−0.726754	+	0.937455i
$877$	7.19083	−	26.8365i	0.242817	−	0.906206i	−0.731651	−	0.681679i	$-0.761250\pi$
$877$	7.19083	−	26.8365i	0.242817	−	0.906206i	0.974468	−	0.224526i	$-0.0720834\pi$
$878$	3.14711	−	46.2567i	0.106210	−	1.56109i
$879$	−3.00303	+	5.20140i	−0.101290	+	0.175439i
$880$	−1.68202	−	0.930621i	−0.0567010	−	0.0313712i
$881$	−3.05077			−0.102783			−0.0513915	−	0.998679i	$-0.516366\pi$
$881$	−3.05077			−0.102783			−0.0513915	+	0.998679i	$0.516366\pi$
$882$		0			0
$883$	15.9128	+	15.9128i	0.535509	+	0.535509i	0.922207	−	0.386697i	$-0.126384\pi$
$883$	15.9128	+	15.9128i	0.535509	+	0.535509i	−0.386697	+	0.922207i	$0.626384\pi$
$884$	−34.2357	−	4.68017i	−1.15147	−	0.157411i
$885$	−59.2243	+	36.4551i	−1.99080	+	1.22542i
$886$	12.8295	−	11.1950i	0.431016	−	0.376103i
$887$	37.7226	+	10.1077i	1.26660	+	0.339384i	0.828727	−	0.559653i	$-0.189066\pi$
$887$	37.7226	+	10.1077i	1.26660	+	0.339384i	0.437872	+	0.899037i	$0.355732\pi$
$888$	15.0056	+	3.10110i	0.503556	+	0.104066i
$889$		0			0
$890$	27.3345	+	29.5994i	0.916253	+	0.992174i
$891$	1.32685	−	0.766057i	0.0444511	−	0.0256639i
$892$	21.6460	−	51.5333i	0.724763	−	1.72546i
$893$	−1.57073	−	5.86203i	−0.0525624	−	0.196165i
$894$	−46.2460	+	9.07968i	−1.54670	+	0.303670i
$895$	−10.4033	+	3.10415i	−0.347745	+	0.103760i
$896$		0			0
$897$	1.62639	+	1.62639i	0.0543037	+	0.0543037i
$898$	−4.36014	+	6.49049i	−0.145500	+	0.216591i
$899$	17.3363	−	30.0273i	0.578197	−	1.00147i
$900$	−32.8250	+	47.6604i	−1.09417	+	1.58868i
$901$	5.57425	+	9.65489i	0.185705	+	0.321651i
$902$	−0.389867	−	0.795543i	−0.0129812	−	0.0264887i
$903$		0			0
$904$	6.90903	+	10.5086i	0.229791	+	0.349511i
$905$	11.1847	+	10.5716i	0.371792	+	0.351413i
$906$	25.0297	+	28.6841i	0.831555	+	0.952966i
$907$	−12.8014	−	47.7753i	−0.425062	−	1.58635i	−0.763788	−	0.645468i	$-0.776663\pi$
$907$	−12.8014	−	47.7753i	−0.425062	−	1.58635i	0.338726	−	0.940885i	$-0.390004\pi$
$908$	−33.2417	+	25.2462i	−1.10317	+	0.837824i
$909$		−	87.9310i		−	2.91649i
$910$		0			0
$911$		−	29.9032i		−	0.990736i	−0.868683	−	0.495368i	$-0.835033\pi$
$911$		−	29.9032i		−	0.990736i	0.868683	−	0.495368i	$-0.164967\pi$
$912$	10.4089	+	0.103313i	0.344675	+	0.00342104i
$913$	0.417495	+	1.55811i	0.0138171	+	0.0515660i
$914$	−28.7820	+	25.1151i	−0.952025	+	0.830734i
$915$	1.55462	+	55.1716i	0.0513942	+	1.82392i
$916$	5.14994	+	3.99245i	0.170159	+	0.131914i
$917$		0			0
$918$	29.8129	−	14.6103i	0.983973	−	0.482210i
$919$	23.0611	+	39.9429i	0.760714	+	1.31760i	0.942483	+	0.334254i	$0.108484\pi$
$919$	23.0611	+	39.9429i	0.760714	+	1.31760i	−0.181769	+	0.983341i	$0.558182\pi$
$920$	0.275228	+	0.758754i	0.00907399	+	0.0250154i
$921$	3.16586	−	5.48343i	0.104319	−	0.180685i
$922$	9.68352	+	6.50514i	0.318910	+	0.214235i
$923$	−7.52519	−	7.52519i	−0.247695	−	0.247695i
$924$		0			0
$925$	−8.94556	−	1.86425i	−0.294128	−	0.0612961i
$926$	−5.96787	−	30.3965i	−0.196116	−	0.998890i
$927$	2.30688	+	8.60938i	0.0757678	+	0.282769i
$928$	4.17078	+	22.4180i	0.136913	+	0.735906i
$929$	31.8393	−	18.3824i	1.04461	−	0.603108i	0.123477	−	0.992347i	$-0.460595\pi$
$929$	31.8393	−	18.3824i	1.04461	−	0.603108i	0.921137	+	0.389239i	$0.127262\pi$
$930$	−3.20505	+	80.5663i	−0.105098	+	2.64187i
$931$		0			0
$932$	−1.73551	−	13.7078i	−0.0568484	−	0.449014i
$933$	36.4951	+	9.77884i	1.19480	+	0.320145i
$934$	−36.5317	−	41.8655i	−1.19535	−	1.36988i
$935$	−0.715845	−	1.16295i	−0.0234106	−	0.0380326i
$936$	−88.9261	−	44.6795i	−2.90664	−	1.46039i
$937$	25.1593	+	25.1593i	0.821917	+	0.821917i	0.986383	−	0.164465i	$-0.0525899\pi$
$937$	25.1593	+	25.1593i	0.821917	+	0.821917i	−0.164465	+	0.986383i	$0.552590\pi$
$938$		0			0
$939$	60.3571			1.96968
$940$	−18.2458	+	24.9568i	−0.595112	+	0.814002i
$941$	12.8202	−	22.2052i	0.417926	−	0.723868i	−0.577805	−	0.816175i	$-0.696091\pi$
$941$	12.8202	−	22.2052i	0.417926	−	0.723868i	0.995731	+	0.0923065i	$0.0294240\pi$
$942$	87.6038	+	5.96020i	2.85429	+	0.194194i
$943$	−0.0962763	+	0.359308i	−0.00313519	+	0.0117007i
$944$	−10.4593	−	40.6438i	−0.340420	−	1.32284i
$945$		0			0
$946$	−0.286856	+	0.838211i	−0.00932649	+	0.0272526i
$947$	2.79497	+	0.748909i	0.0908242	+	0.0243363i	0.303945	−	0.952690i	$-0.401696\pi$
$947$	2.79497	+	0.748909i	0.0908242	+	0.0243363i	−0.213121	+	0.977026i	$0.568363\pi$
$948$	28.4987	−	67.8477i	0.925595	−	2.20359i
$949$	31.1805	+	18.0021i	1.01216	+	0.584372i
$950$	−6.20730	−	0.0719464i	−0.201391	−	0.00233425i
$951$		−	29.3088i		−	0.950404i
$952$		0			0
$953$	−29.4048	+	29.4048i	−0.952513	+	0.952513i	−0.998923	−	0.0464091i	$-0.985222\pi$
$953$	−29.4048	+	29.4048i	−0.952513	+	0.952513i	0.0464091	+	0.998923i	$0.485222\pi$
$954$	6.18597	+	31.5073i	0.200278	+	1.02009i
$955$	−37.5088	−	8.92614i	−1.21376	−	0.288843i
$956$	7.77131	+	19.0281i	0.251342	+	0.615414i
$957$	−0.664669	+	2.48058i	−0.0214857	+	0.0801857i
$958$	−4.91097	+	2.40669i	−0.158666	+	0.0777567i
$959$		0			0
$960$	−32.8367	−	41.6366i	−1.05980	−	1.34382i
$961$	21.4931	+	37.2272i	0.693326	+	1.20088i
$962$	1.06666	−	15.6779i	0.0343904	−	0.505475i
$963$	76.5646	−	20.5154i	2.46726	−	0.661100i
$964$	−9.48874	−	1.29715i	−0.305612	−	0.0417785i
$965$	21.5484	−	39.8763i	0.693668	−	1.28367i
$966$		0			0
$967$	−33.9934	+	33.9934i	−1.09315	+	1.09315i	−0.0979625	+	0.995190i	$0.531233\pi$
$967$	−33.9934	+	33.9934i	−1.09315	+	1.09315i	−0.995190	+	0.0979625i	$0.968767\pi$
$968$	−29.4112	+	9.74019i	−0.945310	+	0.313062i
$969$	6.40417	+	3.69745i	0.205731	+	0.118779i
$970$	−6.17552	+	9.77697i	−0.198284	+	0.313920i
$971$	−11.7604	+	6.78989i	−0.377410	+	0.217898i	−0.676691	−	0.736267i	$-0.736587\pi$
$971$	−11.7604	+	6.78989i	−0.377410	+	0.217898i	0.299281	+	0.954165i	$0.403253\pi$
$972$	−7.24844	+	0.917705i	−0.232494	+	0.0294354i
$973$		0			0
$974$	−0.203827	+	0.595596i	−0.00653104	+	0.0190841i
$975$	80.4553	+	40.5914i	2.57663	+	1.29997i
$976$	−32.0854	−	8.93949i	−1.02703	−	0.286146i
$977$	40.0832	−	10.7403i	1.28238	−	0.343611i	0.447616	−	0.894226i	$-0.352273\pi$
$977$	40.0832	−	10.7403i	1.28238	−	0.343611i	0.834759	+	0.550615i	$0.185607\pi$
$978$	37.1735	−	55.3364i	1.18868	−	1.76946i
$979$	−2.73827			−0.0875155
$980$		0			0
$981$	−69.6851			−2.22487
$982$	−31.8788	+	47.4547i	−1.01729	+	1.51434i
$983$	1.99250	−	0.533889i	0.0635509	−	0.0170284i	−0.226904	−	0.973917i	$-0.572860\pi$
$983$	1.99250	−	0.533889i	0.0635509	−	0.0170284i	0.290454	+	0.956889i	$0.406194\pi$
$984$	−1.41679	−	24.3975i	−0.0451657	−	0.777764i
$985$	−1.15252	−	40.9016i	−0.0367224	−	1.30323i
$986$	−5.24505	+	15.3264i	−0.167037	+	0.488092i
$987$		0			0
$988$	−1.34087	−	10.5908i	−0.0426589	−	0.336939i
$989$	0.322147	−	0.185992i	0.0102437	−	0.00591419i
$990$	−0.866141	−	3.83654i	−0.0275278	−	0.121933i
$991$	25.9485	+	14.9814i	0.824282	+	0.475899i	0.851891	−	0.523720i	$-0.175456\pi$
$991$	25.9485	+	14.9814i	0.824282	+	0.475899i	−0.0276091	+	0.999619i	$0.508789\pi$
$992$	−45.8777	−	16.2109i	−1.45662	−	0.514696i
$993$	61.5205	−	61.5205i	1.95229	−	1.95229i
$994$		0			0
$995$	46.8950	−	13.9925i	1.48667	−	0.443593i
$996$	−6.02686	+	44.0868i	−0.190968	+	1.39694i
$997$	56.5865	−	15.1623i	1.79211	−	0.480196i	0.799411	−	0.600784i	$-0.205145\pi$
$997$	56.5865	−	15.1623i	1.79211	−	0.480196i	0.992703	+	0.120588i	$0.0384781\pi$
$998$	−3.05144	+	44.8505i	−0.0965917	+	1.41972i
$999$	7.54927	+	13.0757i	0.238848	+	0.413697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.k.67.4		72
4.3	odd	2	inner	980.2.x.k.67.18		72
5.3	odd	4	inner	980.2.x.k.263.6		72
7.2	even	3	inner	980.2.x.k.667.10		72
7.3	odd	6		980.2.k.l.687.15		36
7.4	even	3		140.2.k.a.127.15	yes	36
7.5	odd	6		980.2.x.l.667.10		72
7.6	odd	2		980.2.x.l.67.4		72
20.3	even	4	inner	980.2.x.k.263.10		72
28.3	even	6		980.2.k.l.687.7		36
28.11	odd	6		140.2.k.a.127.7	yes	36
28.19	even	6		980.2.x.l.667.6		72
28.23	odd	6	inner	980.2.x.k.667.6		72
28.27	even	2		980.2.x.l.67.18		72
35.3	even	12		980.2.k.l.883.7		36
35.4	even	6		700.2.k.b.407.4		36
35.13	even	4		980.2.x.l.263.6		72
35.18	odd	12		140.2.k.a.43.7	✓	36
35.23	odd	12	inner	980.2.x.k.863.18		72
35.32	odd	12		700.2.k.b.43.12		36
35.33	even	12		980.2.x.l.863.18		72
140.3	odd	12		980.2.k.l.883.15		36
140.23	even	12	inner	980.2.x.k.863.4		72
140.39	odd	6		700.2.k.b.407.12		36
140.67	even	12		700.2.k.b.43.4		36
140.83	odd	4		980.2.x.l.263.10		72
140.103	odd	12		980.2.x.l.863.4		72
140.123	even	12		140.2.k.a.43.15	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.7	✓	36	35.18	odd	12
140.2.k.a.43.15	yes	36	140.123	even	12
140.2.k.a.127.7	yes	36	28.11	odd	6
140.2.k.a.127.15	yes	36	7.4	even	3
700.2.k.b.43.4		36	140.67	even	12
700.2.k.b.43.12		36	35.32	odd	12
700.2.k.b.407.4		36	35.4	even	6
700.2.k.b.407.12		36	140.39	odd	6
980.2.k.l.687.7		36	28.3	even	6
980.2.k.l.687.15		36	7.3	odd	6
980.2.k.l.883.7		36	35.3	even	12
980.2.k.l.883.15		36	140.3	odd	12
980.2.x.k.67.4		72	1.1	even	1	trivial
980.2.x.k.67.18		72	4.3	odd	2	inner
980.2.x.k.263.6		72	5.3	odd	4	inner
980.2.x.k.263.10		72	20.3	even	4	inner
980.2.x.k.667.6		72	28.23	odd	6	inner
980.2.x.k.667.10		72	7.2	even	3	inner
980.2.x.k.863.4		72	140.23	even	12	inner
980.2.x.k.863.18		72	35.23	odd	12	inner
980.2.x.l.67.4		72	7.6	odd	2
980.2.x.l.67.18		72	28.27	even	2
980.2.x.l.263.6		72	35.13	even	4
980.2.x.l.263.10		72	140.83	odd	4
980.2.x.l.667.6		72	28.19	even	6
980.2.x.l.667.10		72	7.5	odd	6
980.2.x.l.863.4		72	140.103	odd	12
980.2.x.l.863.18		72	35.33	even	12

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.17392 - 0.788610i) q^{2} +(2.86329 - 0.767216i) q^{3} +(0.756188 + 1.85153i) q^{4} +(1.62505 + 1.53598i) q^{5} +(-3.96631 - 1.35737i) q^{6} +(0.572433 - 2.76990i) q^{8} +(5.01173 - 2.89352i) q^{9} +O(q^{10})\)	\(q+(-1.17392 - 0.788610i) q^{2} +(2.86329 - 0.767216i) q^{3} +(0.756188 + 1.85153i) q^{4} +(1.62505 + 1.53598i) q^{5} +(-3.96631 - 1.35737i) q^{6} +(0.572433 - 2.76990i) q^{8} +(5.01173 - 2.89352i) q^{9} +(-0.696393 - 3.08465i) q^{10} +(0.186127 + 0.107460i) q^{11} +(3.58571 + 4.72132i) q^{12} +(4.29923 - 4.29923i) q^{13} +(5.83140 + 3.15118i) q^{15} +(-2.85636 + 2.80022i) q^{16} +(-2.74478 + 0.735462i) q^{17} +(-8.16524 - 0.555529i) q^{18} +(-0.438952 - 0.760287i) q^{19} +(-1.61507 + 4.17032i) q^{20} +(-0.133754 - 0.272931i) q^{22} +(-0.0330301 + 0.123270i) q^{23} +(-0.486067 - 8.37019i) q^{24} +(0.281556 + 4.99207i) q^{25} +(-8.43738 + 1.65655i) q^{26} +(5.84185 - 5.84185i) q^{27} +4.03098i q^{29} +(-4.36056 - 8.29795i) q^{30} +(-7.44914 - 4.30076i) q^{31} +(5.56142 - 1.03468i) q^{32} +(0.615379 + 0.164890i) q^{33} +(3.80215 + 1.30119i) q^{34} +(9.14726 + 7.09134i) q^{36} +(-0.473005 + 1.76528i) q^{37} +(-0.0842746 + 1.23868i) q^{38} +(9.01151 - 15.6084i) q^{39} +(5.18472 - 3.62197i) q^{40} +2.91481 q^{41} +(-2.06108 - 2.06108i) q^{43} +(-0.0582196 + 0.425880i) q^{44} +(12.5887 + 2.99578i) q^{45} +(0.135987 - 0.118661i) q^{46} +(6.67731 + 1.78918i) q^{47} +(-6.03021 + 10.2093i) q^{48} +(3.60627 - 6.08234i) q^{50} +(-7.29484 + 4.21168i) q^{51} +(11.2112 + 4.70915i) q^{52} +(-1.01543 - 3.78963i) q^{53} +(-11.4648 + 2.25094i) q^{54} +(0.137408 + 0.460514i) q^{55} +(-1.84015 - 1.84015i) q^{57} +(3.17887 - 4.73205i) q^{58} +(-5.24601 + 9.08635i) q^{59} +(-1.42488 + 13.1799i) q^{60} +(4.16343 + 7.21127i) q^{61} +(5.35309 + 10.9232i) q^{62} +(-7.34464 - 3.17116i) q^{64} +(13.5900 - 0.382938i) q^{65} +(-0.592373 - 0.678863i) q^{66} +(-0.203445 - 0.759268i) q^{67} +(-3.43730 - 4.52591i) q^{68} +0.378298i q^{69} -1.75036i q^{71} +(-5.14588 - 15.5383i) q^{72} +(1.53265 + 5.71993i) q^{73} +(1.94739 - 1.69928i) q^{74} +(4.63617 + 14.0777i) q^{75} +(1.07577 - 1.38765i) q^{76} +(-22.8877 + 11.2165i) q^{78} +(-6.20636 - 10.7497i) q^{79} +(-8.94278 + 0.163183i) q^{80} +(3.56437 - 6.17368i) q^{81} +(-3.42176 - 2.29865i) q^{82} +(5.30716 + 5.30716i) q^{83} +(-5.59005 - 3.02076i) q^{85} +(0.794160 + 4.04494i) q^{86} +(3.09263 + 11.5419i) q^{87} +(0.404198 - 0.454037i) q^{88} +(-11.0339 + 6.37043i) q^{89} +(-12.4156 - 13.4444i) q^{90} +(-0.253215 + 0.0320589i) q^{92} +(-24.6287 - 6.59923i) q^{93} +(-6.42768 - 7.36615i) q^{94} +(0.454465 - 1.90972i) q^{95} +(15.1301 - 7.22941i) q^{96} +(-2.58579 - 2.58579i) q^{97} +1.24375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 16 q^{6}+O(q^{10}) \) 72 * q - 16 * q^6	\( 72 q - 16 q^{6} + 16 q^{10} + 16 q^{12} - 8 q^{13} + 8 q^{16} + 20 q^{17} - 28 q^{18} + 40 q^{20} + 8 q^{22} + 20 q^{25} + 32 q^{26} + 4 q^{30} - 20 q^{37} + 36 q^{40} - 20 q^{45} - 16 q^{46} - 48 q^{48} + 80 q^{50} - 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} + 64 q^{61} + 80 q^{62} - 4 q^{65} - 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 16 q^{76} - 152 q^{78} + 20 q^{80} + 36 q^{81} - 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} - 32 q^{90} - 112 q^{92} - 32 q^{93} - 120 q^{96} + 40 q^{97}+O(q^{100}) \) 72 * q - 16 * q^6 + 16 * q^10 + 16 * q^12 - 8 * q^13 + 8 * q^16 + 20 * q^17 - 28 * q^18 + 40 * q^20 + 8 * q^22 + 20 * q^25 + 32 * q^26 + 4 * q^30 - 20 * q^37 + 36 * q^40 - 20 * q^45 - 16 * q^46 - 48 * q^48 + 80 * q^50 - 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 + 64 * q^61 + 80 * q^62 - 4 * q^65 - 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 16 * q^76 - 152 * q^78 + 20 * q^80 + 36 * q^81 - 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 - 32 * q^90 - 112 * q^92 - 32 * q^93 - 120 * q^96 + 40 * q^97

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