LMFDB - Embedded newform 980.2.x.n.863.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [112,4,0,0,0,0,0,-32,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			863.16
Character	$\chi$	$=$	980.863
Dual form			980.2.x.n.67.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.326252 - 1.37607i) q^{2} +(1.93300 + 0.517947i) q^{3} +(-1.78712 - 0.897890i) q^{4} +(-2.17870 + 0.503254i) q^{5} +(1.34338 - 2.49096i) q^{6} +(-1.81861 + 2.16626i) q^{8} +(0.870157 + 0.502386i) q^{9} +(-0.0182956 + 3.16222i) q^{10} +(4.92166 - 2.84152i) q^{11} +(-2.98945 - 2.66126i) q^{12} +(-4.82411 - 4.82411i) q^{13} +(-4.47209 - 0.155660i) q^{15} +(2.38759 + 3.20927i) q^{16} +(-3.65619 - 0.979673i) q^{17} +(0.975207 - 1.03349i) q^{18} +(0.564422 - 0.977608i) q^{19} +(4.34546 + 1.05686i) q^{20} +(-2.30442 - 7.69959i) q^{22} +(-1.26089 - 4.70570i) q^{23} +(-4.63738 + 3.24544i) q^{24} +(4.49347 - 2.19288i) q^{25} +(-8.21217 + 5.06442i) q^{26} +(-2.82336 - 2.82336i) q^{27} +0.781186i q^{29} +(-1.67323 + 6.10312i) q^{30} +(3.20202 - 1.84869i) q^{31} +(5.19513 - 2.23845i) q^{32} +(10.9853 - 2.94351i) q^{33} +(-2.54094 + 4.71154i) q^{34} +(-1.10399 - 1.67913i) q^{36} +(-0.889727 - 3.32051i) q^{37} +(-1.16111 - 1.09563i) q^{38} +(-6.82639 - 11.8236i) q^{39} +(2.87203 - 5.63484i) q^{40} -0.451387 q^{41} +(-0.613245 + 0.613245i) q^{43} +(-11.3470 + 0.659028i) q^{44} +(-2.14864 - 0.656638i) q^{45} +(-6.88673 + 0.199821i) q^{46} +(-4.14209 + 1.10987i) q^{47} +(2.95298 + 7.44018i) q^{48} +(-1.55154 - 6.89875i) q^{50} +(-6.56001 - 3.78742i) q^{51} +(4.28974 + 12.9528i) q^{52} +(0.544196 - 2.03097i) q^{53} +(-4.80626 + 2.96401i) q^{54} +(-9.29282 + 8.66767i) q^{55} +(1.59738 - 1.59738i) q^{57} +(1.07496 + 0.254864i) q^{58} +(4.63740 + 8.03221i) q^{59} +(7.85240 + 4.29363i) q^{60} +(-0.759742 + 1.31591i) q^{61} +(-1.49925 - 5.00933i) q^{62} +(-1.38533 - 7.87914i) q^{64} +(12.9380 + 8.08254i) q^{65} +(-0.466477 - 16.0769i) q^{66} +(-3.53578 + 13.1957i) q^{67} +(5.65441 + 5.03365i) q^{68} -9.74921i q^{69} -11.8314i q^{71} +(-2.67077 + 0.971341i) q^{72} +(-0.445622 + 1.66308i) q^{73} +(-4.85951 + 0.141001i) q^{74} +(9.82169 - 1.91146i) q^{75} +(-1.88647 + 1.24031i) q^{76} +(-18.4973 + 5.53607i) q^{78} +(-2.73105 + 4.73031i) q^{79} +(-6.81692 - 5.79048i) q^{80} +(-5.50237 - 9.53039i) q^{81} +(-0.147266 + 0.621139i) q^{82} +(0.968508 - 0.968508i) q^{83} +(8.45877 + 0.294423i) q^{85} +(0.643793 + 1.04394i) q^{86} +(-0.404613 + 1.51003i) q^{87} +(-2.79511 + 15.8292i) q^{88} +(8.16106 + 4.71179i) q^{89} +(-1.60458 + 2.74244i) q^{90} +(-1.97184 + 9.54179i) q^{92} +(7.14703 - 1.91504i) q^{93} +(0.175888 + 6.06189i) q^{94} +(-0.737723 + 2.41396i) q^{95} +(11.2016 - 1.63613i) q^{96} +(6.77428 - 6.77428i) q^{97} +5.71016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 4 q^{2} - 32 q^{8} - 32 q^{16} + 40 q^{22} - 32 q^{25} + 28 q^{30} + 64 q^{32} + 32 q^{36} + 8 q^{37} + 184 q^{46} - 24 q^{50} - 96 q^{53} - 16 q^{57} - 124 q^{58} - 8 q^{60} + 120 q^{65} + 80 q^{72}+ \cdots + 176 q^{93}+O(q^{100}) $ 112 * q + 4 * q^2 - 32 * q^8 - 32 * q^16 + 40 * q^22 - 32 * q^25 + 28 * q^30 + 64 * q^32 + 32 * q^36 + 8 * q^37 + 184 * q^46 - 24 * q^50 - 96 * q^53 - 16 * q^57 - 124 * q^58 - 8 * q^60 + 120 * q^65 + 80 * q^72 - 72 * q^78 + 72 * q^81 + 192 * q^85 - 104 * q^86 - 48 * q^88 - 304 * q^92 + 176 * q^93

Character values

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

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

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 $

$2$	0.326252	−	1.37607i	0.230695	−	0.973026i
$2$	0.326252	−	1.37607i	0.230695	−	0.973026i
$3$	1.93300	+	0.517947i	1.11602	+	0.299037i	0.769272	−	0.638922i	$-0.220619\pi$
$3$	1.93300	+	0.517947i	1.11602	+	0.299037i	0.346748	+	0.937958i	$0.387286\pi$
$4$	−1.78712	−	0.897890i	−0.893559	−	0.448945i
$5$	−2.17870	+	0.503254i	−0.974344	+	0.225062i
$5$	−2.17870	+	0.503254i	−0.974344	+	0.225062i
$6$	1.34338	−	2.49096i	0.548431	−	1.01693i
$7$		0			0
$7$		0			0
$8$	−1.81861	+	2.16626i	−0.642975	+	0.765887i
$9$	0.870157	+	0.502386i	0.290052	+	0.167462i
$10$	−0.0182956	+	3.16222i	−0.00578557	+	0.999983i
$11$	4.92166	−	2.84152i	1.48394	−	0.856751i	0.484104	−	0.875011i	$-0.339146\pi$
$11$	4.92166	−	2.84152i	1.48394	−	0.856751i	0.999833	+	0.0182593i	$0.00581245\pi$
$12$	−2.98945	−	2.66126i	−0.862979	−	0.768239i
$13$	−4.82411	−	4.82411i	−1.33797	−	1.33797i	−0.898027	−	0.439939i	$-0.855000\pi$
$13$	−4.82411	−	4.82411i	−1.33797	−	1.33797i	−0.439939	−	0.898027i	$-0.645000\pi$
$14$		0			0
$15$	−4.47209	−	0.155660i	−1.15469	−	0.0401912i
$16$	2.38759	+	3.20927i	0.596897	+	0.802318i
$17$	−3.65619	−	0.979673i	−0.886756	−	0.237606i	−0.213436	−	0.976957i	$-0.568466\pi$
$17$	−3.65619	−	0.979673i	−0.886756	−	0.237606i	−0.673320	+	0.739351i	$0.735132\pi$
$18$	0.975207	−	1.03349i	0.229858	−	0.243596i
$19$	0.564422	−	0.977608i	0.129487	−	0.224279i	−0.793991	−	0.607930i	$-0.792000\pi$
$19$	0.564422	−	0.977608i	0.129487	−	0.224279i	0.923478	+	0.383651i	$0.125333\pi$
$20$	4.34546	+	1.05686i	0.971675	+	0.236321i
$21$		0			0
$22$	−2.30442	−	7.69959i	−0.491304	−	1.64156i
$23$	−1.26089	−	4.70570i	−0.262914	−	0.981207i	−0.963515	−	0.267654i	$-0.913752\pi$
$23$	−1.26089	−	4.70570i	−0.262914	−	0.981207i	0.700601	−	0.713553i	$-0.252915\pi$
$24$	−4.63738	+	3.24544i	−0.946601	+	0.662472i
$25$	4.49347	−	2.19288i	0.898694	−	0.438576i
$26$	−8.21217	+	5.06442i	−1.61054	+	0.993214i
$27$	−2.82336	−	2.82336i	−0.543356	−	0.543356i
$28$		0			0
$29$			0.781186i			0.145063i	0.997366	+	0.0725313i	$0.0231077\pi$
$29$			0.781186i			0.145063i	−0.997366	+	0.0725313i	$0.976892\pi$
$30$	−1.67323	+	6.10312i	−0.305488	+	1.11427i
$31$	3.20202	−	1.84869i	0.575099	−	0.332034i	−0.184084	−	0.982911i	$-0.558932\pi$
$31$	3.20202	−	1.84869i	0.575099	−	0.332034i	0.759183	+	0.650877i	$0.225599\pi$
$32$	5.19513	−	2.23845i	0.918378	−	0.395705i
$33$	10.9853	−	2.94351i	1.91230	−	0.512400i
$34$	−2.54094	+	4.71154i	−0.435767	+	0.808023i
$35$		0			0
$36$	−1.10399	−	1.67913i	−0.183998	−	0.279855i
$37$	−0.889727	−	3.32051i	−0.146270	−	0.545888i	−0.999696	−	0.0246729i	$-0.992146\pi$
$37$	−0.889727	−	3.32051i	−0.146270	−	0.545888i	0.853425	−	0.521215i	$-0.174521\pi$
$38$	−1.16111	−	1.09563i	−0.188357	−	0.177735i
$39$	−6.82639	−	11.8236i	−1.09310	−	1.89330i
$40$	2.87203	−	5.63484i	0.454107	−	0.890947i
$41$	−0.451387			−0.0704948			−0.0352474	−	0.999379i	$-0.511222\pi$
$41$	−0.451387			−0.0704948			−0.0352474	+	0.999379i	$0.511222\pi$
$42$		0			0
$43$	−0.613245	+	0.613245i	−0.0935189	+	0.0935189i	−0.752319	−	0.658800i	$-0.771065\pi$
$43$	−0.613245	+	0.613245i	−0.0935189	+	0.0935189i	0.658800	+	0.752319i	$0.271065\pi$
$44$	−11.3470	+	0.659028i	−1.71062	+	0.0993522i
$45$	−2.14864	−	0.656638i	−0.320300	−	0.0978858i
$46$	−6.88673	+	0.199821i	−1.01539	+	0.0294620i
$47$	−4.14209	+	1.10987i	−0.604186	+	0.161891i	−0.547929	−	0.836525i	$-0.684583\pi$
$47$	−4.14209	+	1.10987i	−0.604186	+	0.161891i	−0.0562577	+	0.998416i	$0.517917\pi$
$48$	2.95298	+	7.44018i	0.426226	+	1.07390i
$49$		0			0
$50$	−1.55154	−	6.89875i	−0.219421	−	0.975630i
$51$	−6.56001	−	3.78742i	−0.918585	−	0.530345i
$52$	4.28974	+	12.9528i	0.594879	+	1.79623i
$53$	0.544196	−	2.03097i	0.0747511	−	0.278975i	−0.918426	−	0.395594i	$-0.870539\pi$
$53$	0.544196	−	2.03097i	0.0747511	−	0.278975i	0.993177	+	0.116619i	$0.0372055\pi$
$54$	−4.80626	+	2.96401i	−0.654050	+	0.403350i
$55$	−9.29282	+	8.66767i	−1.25304	+	1.16875i
$56$		0			0
$57$	1.59738	−	1.59738i	0.211578	−	0.211578i
$58$	1.07496	+	0.254864i	0.141150	+	0.0334652i
$59$	4.63740	+	8.03221i	0.603738	+	1.04570i	0.992250	+	0.124261i	$0.0396559\pi$
$59$	4.63740	+	8.03221i	0.603738	+	1.04570i	−0.388512	+	0.921444i	$0.627011\pi$
$60$	7.85240	+	4.29363i	1.01374	+	0.554305i
$61$	−0.759742	+	1.31591i	−0.0972751	+	0.168485i	−0.910556	−	0.413386i	$-0.864346\pi$
$61$	−0.759742	+	1.31591i	−0.0972751	+	0.168485i	0.813281	+	0.581871i	$0.197679\pi$
$62$	−1.49925	−	5.00933i	−0.190405	−	0.636185i
$63$		0			0
$64$	−1.38533	−	7.87914i	−0.173166	−	0.984893i
$65$	12.9380	+	8.08254i	1.60477	+	1.00252i
$66$	−0.466477	−	16.0769i	−0.0574194	−	1.97893i
$67$	−3.53578	+	13.1957i	−0.431965	+	1.61211i	0.316263	+	0.948672i	$0.397572\pi$
$67$	−3.53578	+	13.1957i	−0.431965	+	1.61211i	−0.748228	+	0.663442i	$0.769095\pi$
$68$	5.65441	+	5.03365i	0.685698	+	0.610420i
$69$		−	9.74921i		−	1.17367i
$70$		0			0
$71$		−	11.8314i		−	1.40413i	−0.712112	−	0.702066i	$-0.752261\pi$
$71$		−	11.8314i		−	1.40413i	0.712112	−	0.702066i	$-0.247739\pi$
$72$	−2.67077	+	0.971341i	−0.314753	+	0.114474i
$73$	−0.445622	+	1.66308i	−0.0521561	+	0.194649i	−0.987088	−	0.160177i	$-0.948793\pi$
$73$	−0.445622	+	1.66308i	−0.0521561	+	0.194649i	0.934932	+	0.354827i	$0.115460\pi$
$74$	−4.85951	+	0.141001i	−0.564907	+	0.0163910i
$75$	9.82169	−	1.91146i	1.13411	−	0.220717i
$76$	−1.88647	+	1.24031i	−0.216393	+	0.142274i
$77$		0			0
$78$	−18.4973	+	5.53607i	−2.09440	+	0.626837i
$79$	−2.73105	+	4.73031i	−0.307267	+	0.532201i	−0.977763	−	0.209711i	$-0.932748\pi$
$79$	−2.73105	+	4.73031i	−0.307267	+	0.532201i	0.670497	+	0.741912i	$0.266081\pi$
$80$	−6.81692	−	5.79048i	−0.762154	−	0.647395i
$81$	−5.50237	−	9.53039i	−0.611375	−	1.05893i
$82$	−0.147266	+	0.621139i	−0.0162628	+	0.0685933i
$83$	0.968508	−	0.968508i	0.106308	−	0.106308i	−0.651952	−	0.758260i	$-0.726050\pi$
$83$	0.968508	−	0.968508i	0.106308	−	0.106308i	0.758260	+	0.651952i	$0.226050\pi$
$84$		0			0
$85$	8.45877	+	0.294423i	0.917482	+	0.0319347i
$86$	0.643793	+	1.04394i	0.0694220	+	0.112571i
$87$	−0.404613	+	1.51003i	−0.0433790	+	0.161893i
$88$	−2.79511	+	15.8292i	−0.297960	+	1.68740i
$89$	8.16106	+	4.71179i	0.865071	+	0.499449i	0.865707	−	0.500551i	$-0.166869\pi$
$89$	8.16106	+	4.71179i	0.865071	+	0.499449i	−0.000636335		1.00000i	$0.500203\pi$
$90$	−1.60458	+	2.74244i	−0.169137	+	0.289079i
$91$		0			0
$92$	−1.97184	+	9.54179i	−0.205579	+	0.994800i
$93$	7.14703	−	1.91504i	0.741113	−	0.198581i
$94$	0.175888	+	6.06189i	0.0181415	+	0.625237i
$95$	−0.737723	+	2.41396i	−0.0756887	+	0.247667i
$96$	11.2016	−	1.63613i	1.14326	−	0.166986i
$97$	6.77428	−	6.77428i	0.687824	−	0.687824i	−0.273927	−	0.961751i	$-0.588323\pi$
$97$	6.77428	−	6.77428i	0.687824	−	0.687824i	0.961751	+	0.273927i	$0.0883225\pi$
$98$		0			0
$99$	5.71016			0.573893
$100$	−9.99933	−	0.115710i	−0.999933	−	0.0115710i
$101$	6.03052	+	10.4452i	0.600059	+	1.03933i	0.992811	+	0.119689i	$0.0381897\pi$
$101$	6.03052	+	10.4452i	0.600059	+	1.03933i	−0.392752	+	0.919644i	$0.628477\pi$
$102$	−7.35197	+	7.79135i	−0.727953	+	0.771459i
$103$	−2.83998	−	10.5989i	−0.279831	−	1.04434i	−0.952534	−	0.304432i	$-0.901533\pi$
$103$	−2.83998	−	10.5989i	−0.279831	−	1.04434i	0.672703	−	0.739913i	$-0.265133\pi$
$104$	19.2234	−	1.67709i	1.88501	−	0.164452i
$105$		0			0
$106$	−2.61720	−	1.41146i	−0.254205	−	0.137093i
$107$	9.51868	−	2.55052i	0.920205	−	0.246568i	0.232532	−	0.972589i	$-0.425299\pi$
$107$	9.51868	−	2.55052i	0.920205	−	0.246568i	0.687673	+	0.726021i	$0.258632\pi$
$108$	2.51062	+	7.58075i	0.241584	+	0.729458i
$109$	4.43091	−	2.55819i	0.424404	−	0.245030i	−0.272556	−	0.962140i	$-0.587869\pi$
$109$	4.43091	−	2.55819i	0.424404	−	0.245030i	0.696960	+	0.717110i	$0.254536\pi$
$110$	8.89549	+	15.6154i	0.848152	+	1.48887i
$111$		−	6.87938i		−	0.652962i
$112$		0			0
$113$	1.98553	+	1.98553i	0.186783	+	0.186783i	0.794304	−	0.607521i	$-0.207836\pi$
$113$	1.98553	+	1.98553i	0.186783	+	0.186783i	−0.607521	+	0.794304i	$0.707836\pi$
$114$	−1.67695	−	2.71925i	−0.157061	−	0.254681i
$115$	5.11526	+	9.61777i	0.477001	+	0.896862i
$116$	0.701419	−	1.39607i	0.0651251	−	0.129622i
$117$	−1.77417	−	6.62129i	−0.164022	−	0.612139i
$118$	12.5658	−	3.76084i	1.15678	−	0.346213i
$119$		0			0
$120$	8.47019	−	9.40462i	0.773219	−	0.858520i
$121$	10.6485	−	18.4437i	0.968046	−	1.67670i
$122$	1.56292	+	1.47478i	0.141500	+	0.133520i
$123$	−0.872533	−	0.233795i	−0.0786737	−	0.0210805i
$124$	−7.38230	+	0.428762i	−0.662950	+	0.0385039i
$125$	−8.68635	+	7.03898i	−0.776931	+	0.629586i
$126$		0			0
$127$	12.1710	+	12.1710i	1.08000	+	1.08000i	0.996509	+	0.0834907i	$0.0266069\pi$
$127$	12.1710	+	12.1710i	1.08000	+	1.08000i	0.0834907	+	0.996509i	$0.473393\pi$
$128$	−11.2942	−	0.664283i	−0.998275	−	0.0587149i
$129$	−1.50303	+	0.867776i	−0.132335	+	0.0764034i
$130$	15.3432	−	15.1667i	1.34569	−	1.33020i
$131$	2.79660	+	1.61462i	0.244340	+	0.141070i	0.617170	−	0.786830i	$-0.288279\pi$
$131$	2.79660	+	1.61462i	0.244340	+	0.141070i	−0.372830	+	0.927900i	$0.621612\pi$
$132$	−22.2751	−	4.60322i	−1.93880	−	0.400659i
$133$		0			0
$134$	17.0046	+	9.17061i	1.46898	+	0.792220i
$135$	7.57213	+	4.73039i	0.651705	+	0.407127i
$136$	8.77140	−	6.13860i	0.752141	−	0.526381i
$137$	14.5375	+	3.89530i	1.24202	+	0.332798i	0.819248	−	0.573439i	$-0.194391\pi$
$137$	14.5375	+	3.89530i	1.24202	+	0.332798i	0.422770	+	0.906237i	$0.361058\pi$
$138$	−13.4156	−	3.18070i	−1.14201	−	0.270759i
$139$	−7.49343			−0.635584			−0.317792	−	0.948160i	$-0.602941\pi$
$139$	−7.49343			−0.635584			−0.317792	+	0.948160i	$0.602941\pi$
$140$		0			0
$141$	−8.58153			−0.722696
$142$	−16.2808	−	3.86003i	−1.36626	−	0.323927i
$143$	−37.4504	−	10.0348i	−3.13176	−	0.839153i
$144$	0.465285	+	3.99206i	0.0387737	+	0.332672i
$145$	−0.393135	−	1.70197i	−0.0326480	−	0.141341i
$146$	2.14313	+	1.15579i	0.177367	+	0.0956539i
$147$		0			0
$148$	−1.39140	+	6.73302i	−0.114373	+	0.553451i
$149$	−3.75467	−	2.16776i	−0.307595	−	0.177590i	0.338255	−	0.941055i	$-0.390163\pi$
$149$	−3.75467	−	2.16776i	−0.307595	−	0.177590i	−0.645850	+	0.763465i	$0.723497\pi$
$150$	0.574051	−	14.1389i	0.0468710	−	1.15444i
$151$	−12.2708	+	7.08455i	−0.998584	+	0.576533i	−0.907829	−	0.419341i	$-0.862261\pi$
$151$	−12.2708	+	7.08455i	−0.998584	+	0.576533i	−0.0907547	+	0.995873i	$0.528928\pi$
$152$	1.09129	+	3.00057i	0.0885150	+	0.243378i
$153$	−2.68929	−	2.68929i	−0.217416	−	0.217416i
$154$		0			0
$155$	−6.04588	+	5.63916i	−0.485617	+	0.452948i
$156$	1.58323	+	27.2596i	0.126760	+	2.18252i
$157$	−4.82557	−	1.29301i	−0.385123	−	0.103193i	0.0610625	−	0.998134i	$-0.480551\pi$
$157$	−4.82557	−	1.29301i	−0.385123	−	0.103193i	−0.446185	+	0.894941i	$0.647218\pi$
$158$	5.61821	+	5.30138i	0.446961	+	0.421755i
$159$	2.10387	−	3.64400i	0.166847	−	0.288988i
$160$	−10.1921	+	7.49137i	−0.805758	+	0.592245i
$161$		0			0
$162$	−14.9096	+	4.46232i	−1.17141	+	0.350593i
$163$	−4.18245	−	15.6091i	−0.327595	−	1.22260i	−0.911678	−	0.410906i	$-0.865212\pi$
$163$	−4.18245	−	15.6091i	−0.327595	−	1.22260i	0.584083	−	0.811694i	$-0.301454\pi$
$164$	0.806683	+	0.405296i	0.0629913	+	0.0316483i
$165$	−22.4524	+	11.9415i	−1.74792	+	0.929641i
$166$	−1.01675	−	1.64871i	−0.0789154	−	0.127965i
$167$	5.33030	+	5.33030i	0.412471	+	0.412471i	0.882599	−	0.470127i	$-0.155792\pi$
$167$	5.33030	+	5.33030i	0.412471	+	0.412471i	−0.470127	+	0.882599i	$0.655792\pi$
$168$		0			0
$169$			33.5440i			2.58031i
$170$	3.16484	−	11.5438i	0.242732	−	0.885367i
$171$	0.982273	−	0.567115i	0.0751163	−	0.0433684i
$172$	1.64657	−	0.545315i	0.125550	−	0.0415799i
$173$	4.24379	−	1.13712i	0.322649	−	0.0864536i	−0.0938592	−	0.995585i	$-0.529920\pi$
$173$	4.24379	−	1.13712i	0.322649	−	0.0864536i	0.416508	+	0.909132i	$0.363254\pi$
$174$	1.94590	+	1.04943i	0.147518	+	0.0795568i
$175$		0			0
$176$	20.8701	+	9.01057i	1.57314	+	0.679197i
$177$	4.80385	+	17.9282i	0.361079	+	1.34757i
$178$	9.14630	−	9.69293i	0.685544	−	0.726516i
$179$	0.339543	+	0.588106i	0.0253787	+	0.0439571i	0.878436	−	0.477860i	$-0.158588\pi$
$179$	0.339543	+	0.588106i	0.0253787	+	0.0439571i	−0.853057	+	0.521818i	$0.825254\pi$
$180$	3.25029	+	3.10273i	0.242262	+	0.231264i
$181$	−7.86696			−0.584746			−0.292373	−	0.956304i	$-0.594445\pi$
$181$	−7.86696			−0.584746			−0.292373	+	0.956304i	$0.594445\pi$
$182$		0			0
$183$	−2.15016	+	2.15016i	−0.158944	+	0.158944i
$184$	12.4868	+	5.82642i	0.920541	+	0.429529i
$185$	3.60951	+	6.78663i	0.265376	+	0.498963i
$186$	−0.303489	−	10.4596i	−0.0222529	−	0.766934i
$187$	−20.7783	+	5.56753i	−1.51946	+	0.407138i
$188$	8.39895	+	1.73567i	0.612557	+	0.126587i
$189$		0			0
$190$	3.08109	+	1.80272i	0.223526	+	0.130783i
$191$	9.25179	+	5.34152i	0.669436	+	0.386499i	0.795863	−	0.605477i	$-0.207018\pi$
$191$	9.25179	+	5.34152i	0.669436	+	0.386499i	−0.126427	+	0.991976i	$0.540351\pi$
$192$	1.40313	−	15.9479i	0.101262	−	1.15094i
$193$	2.92066	−	10.9000i	0.210233	−	0.784602i	−0.777557	−	0.628813i	$-0.783541\pi$
$193$	2.92066	−	10.9000i	0.210233	−	0.784602i	0.987790	−	0.155789i	$-0.0497921\pi$
$194$	−7.11174	−	11.5320i	−0.510593	−	0.827949i
$195$	20.8229	+	22.3248i	1.49116	+	1.59871i
$196$		0			0
$197$	3.29596	−	3.29596i	0.234827	−	0.234827i	−0.579877	−	0.814704i	$-0.696899\pi$
$197$	3.29596	−	3.29596i	0.234827	−	0.234827i	0.814704	+	0.579877i	$0.196899\pi$
$198$	1.86295	−	7.85756i	0.132394	−	0.558412i
$199$	−4.78902	−	8.29482i	−0.339484	−	0.588004i	0.644851	−	0.764308i	$-0.276919\pi$
$199$	−4.78902	−	8.29482i	−0.339484	−	0.588004i	−0.984336	+	0.176304i	$0.943586\pi$
$200$	−3.42153	+	13.7220i	−0.241939	+	0.970292i
$201$	−13.6694	+	23.6760i	−0.964162	+	1.66998i
$202$	16.3407	−	4.89064i	1.14973	−	0.344104i
$203$		0			0
$204$	8.32283	+	12.6587i	0.582714	+	0.886289i
$205$	0.983438	−	0.227162i	0.0686863	−	0.0158657i
$206$	−15.5114	+	0.450069i	−1.08073	+	0.0313578i
$207$	1.26690	−	4.72815i	0.0880560	−	0.328629i
$208$	3.96390	−	26.9999i	0.274847	−	1.87210i
$209$		−	6.41528i		−	0.443754i
$210$		0			0
$211$		−	19.2356i		−	1.32424i	−0.749400	−	0.662118i	$-0.769658\pi$
$211$		−	19.2356i		−	1.32424i	0.749400	−	0.662118i	$-0.230342\pi$
$212$	−2.79613	+	3.14095i	−0.192039	+	0.215722i
$213$	6.12805	−	22.8702i	0.419887	−	1.56704i
$214$	−0.404197	−	13.9304i	−0.0276304	−	0.952266i
$215$	1.02746	−	1.64469i	0.0700721	−	0.112167i
$216$	11.2507	−	0.981536i	0.765514	−	0.0667850i
$217$		0			0
$218$	−2.07464	−	6.93184i	−0.140512	−	0.469483i
$219$	−1.72278	+	2.98394i	−0.116415	+	0.201636i
$220$	24.3900	−	7.14623i	1.64437	−	0.481799i
$221$	12.9118	+	22.3639i	0.868542	+	1.50436i
$222$	−9.46649	−	2.24441i	−0.635349	−	0.150635i
$223$	−6.67775	+	6.67775i	−0.447175	+	0.447175i	−0.894414	−	0.447239i	$-0.852407\pi$
$223$	−6.67775	+	6.67775i	−0.447175	+	0.447175i	0.447239	+	0.894414i	$0.352407\pi$
$224$		0			0
$225$	5.01170	+	0.349306i	0.334113	+	0.0232871i
$226$	3.38000	−	2.08443i	0.224834	−	0.138654i
$227$	7.06873	−	26.3809i	0.469168	−	1.75096i	−0.173520	−	0.984830i	$-0.555514\pi$
$227$	7.06873	−	26.3809i	0.469168	−	1.75096i	0.642688	−	0.766128i	$-0.277819\pi$
$228$	−4.28898	+	1.42044i	−0.284045	+	0.0940707i
$229$	−10.9593	−	6.32735i	−0.724210	−	0.418123i	0.0920901	−	0.995751i	$-0.470645\pi$
$229$	−10.9593	−	6.32735i	−0.724210	−	0.418123i	−0.816300	+	0.577628i	$0.803979\pi$
$230$	14.9036	−	3.90112i	0.982712	−	0.257232i
$231$		0			0
$232$	−1.69225	−	1.42067i	−0.111102	−	0.0932716i
$233$	−16.7399	+	4.48543i	−1.09666	+	0.293850i	−0.761406	−	0.648276i	$-0.775490\pi$
$233$	−16.7399	+	4.48543i	−1.09666	+	0.293850i	−0.335259	+	0.942126i	$0.608824\pi$
$234$	−9.69017	+	0.281164i	−0.633466	+	0.0183803i
$235$	8.46583	−	4.50260i	0.552250	−	0.293717i
$236$	−1.07554	−	18.5184i	−0.0700118	−	1.20544i
$237$	−7.72917	+	7.72917i	−0.502064	+	0.502064i
$238$		0			0
$239$	21.7639			1.40779			0.703893	−	0.710306i	$-0.251443\pi$
$239$	21.7639			1.40779			0.703893	+	0.710306i	$0.251443\pi$
$240$	−10.1780	−	14.7238i	−0.656985	−	0.950418i
$241$	10.4257	+	18.0579i	0.671579	+	1.16321i	0.977456	+	0.211138i	$0.0677171\pi$
$241$	10.4257	+	18.0579i	0.671579	+	1.16321i	−0.305877	+	0.952071i	$0.598950\pi$
$242$	−21.9057	−	20.6704i	−1.40815	−	1.32874i
$243$	−2.59961	−	9.70186i	−0.166765	−	0.622375i
$244$	2.53929	−	1.66953i	0.162562	−	0.106881i
$245$		0			0
$246$	−0.606383	+	1.12439i	−0.0386616	+	0.0716883i
$247$	−7.43892	+	1.99325i	−0.473327	+	0.126828i
$248$	−1.81849	+	10.2984i	−0.115474	+	0.653951i
$249$	2.37376	−	1.37049i	0.150431	−	0.0868515i
$250$	6.85216	+	14.2495i	0.433369	+	0.901217i
$251$		−	14.6586i		−	0.925243i	−0.886556	−	0.462621i	$-0.846909\pi$
$251$		−	14.6586i		−	0.925243i	0.886556	−	0.462621i	$-0.153091\pi$
$252$		0			0
$253$	−19.5770	−	19.5770i	−1.23080	−	1.23080i
$254$	20.7189	−	12.7773i	1.30002	−	0.801717i
$255$	16.1983	+	4.95031i	1.01438	+	0.310001i
$256$	−4.59885	+	15.3248i	−0.287428	+	0.957802i
$257$	−3.54821	−	13.2421i	−0.221331	−	0.826019i	−0.983841	−	0.179043i	$-0.942700\pi$
$257$	−3.54821	−	13.2421i	−0.221331	−	0.826019i	0.762510	−	0.646976i	$-0.223967\pi$
$258$	0.703750	+	2.35139i	0.0438136	+	0.146391i
$259$		0			0
$260$	−15.8646	−	26.0614i	−0.983880	−	1.61626i
$261$	−0.392456	+	0.679754i	−0.0242924	+	0.0420757i
$262$	3.13422	−	3.32154i	0.193633	−	0.205205i
$263$	22.2385	+	5.95878i	1.37128	+	0.367434i	0.867947	−	0.496657i	$-0.165439\pi$
$263$	22.2385	+	5.95878i	1.37128	+	0.367434i	0.503335	+	0.864091i	$0.332106\pi$
$264$	−13.6016	+	29.1502i	−0.837123	+	1.79407i
$265$	−0.163549	+	4.69874i	−0.0100467	+	0.288641i
$266$		0			0
$267$	13.3349	+	13.3349i	0.816083	+	0.816083i
$268$	18.1672	−	20.4076i	1.10974	−	1.24659i
$269$	26.1655	−	15.1067i	1.59534	−	0.921070i	0.602972	−	0.797762i	$-0.293983\pi$
$269$	26.1655	−	15.1067i	1.59534	−	0.921070i	0.992368	−	0.123308i	$-0.0393504\pi$
$270$	8.97976	−	8.87645i	0.546491	−	0.540204i
$271$	9.31890	+	5.38027i	0.566083	+	0.326828i	0.755583	−	0.655053i	$-0.227354\pi$
$271$	9.31890	+	5.38027i	0.566083	+	0.326828i	−0.189501	+	0.981881i	$0.560687\pi$
$272$	−5.58544	−	14.0728i	−0.338667	−	0.853287i
$273$		0			0
$274$	10.1031	−	18.7337i	0.610349	−	1.13174i
$275$	15.8842	−	23.5609i	0.957855	−	1.42078i
$276$	−8.75372	+	17.4230i	−0.526912	+	1.04874i
$277$	−31.1761	−	8.35362i	−1.87319	−	0.501920i	−0.999891	−	0.0147379i	$-0.995309\pi$
$277$	−31.1761	−	8.35362i	−1.87319	−	0.501920i	−0.873300	−	0.487182i	$-0.838025\pi$
$278$	−2.44475	+	10.3115i	−0.146626	+	0.618440i
$279$	3.71501			0.222412
$280$		0			0
$281$	1.05159			0.0627325			0.0313663	−	0.999508i	$-0.490014\pi$
$281$	1.05159			0.0627325			0.0313663	+	0.999508i	$0.490014\pi$
$282$	−2.79975	+	11.8088i	−0.166722	+	0.703202i
$283$	10.3831	+	2.78214i	0.617211	+	0.165381i	0.553860	−	0.832610i	$-0.313154\pi$
$283$	10.3831	+	2.78214i	0.617211	+	0.165381i	0.0633515	+	0.997991i	$0.479821\pi$
$284$	−10.6233	+	21.1442i	−0.630378	+	1.25468i
$285$	−2.67632	+	4.28410i	−0.158532	+	0.253768i
$286$	−26.0269	+	48.2604i	−1.53900	+	2.85370i
$287$		0			0
$288$	5.64514	+	0.662156i	0.332643	+	0.0390179i
$289$	−2.31446	−	1.33626i	−0.136145	−	0.0786033i
$290$	−2.47028	−	0.0142923i	−0.145060	−	0.000839270i
$291$	16.6034	−	9.58599i	0.973310	−	0.561941i
$292$	2.28965	−	2.57201i	0.133991	−	0.150515i
$293$	19.1160	+	19.1160i	1.11677	+	1.11677i	0.992213	+	0.124555i	$0.0397502\pi$
$293$	19.1160	+	19.1160i	1.11677	+	1.11677i	0.124555	+	0.992213i	$0.460250\pi$
$294$		0			0
$295$	−14.1457	−	15.1660i	−0.823597	−	0.882998i
$296$	8.81113	+	4.11132i	0.512137	+	0.238966i
$297$	−21.9183	−	5.87299i	−1.27183	−	0.340785i
$298$	−4.20795	+	4.45944i	−0.243760	+	0.258329i
$299$	−16.6182	+	28.7835i	−0.961053	+	1.66459i
$300$	−19.2688	−	5.40279i	−1.11249	−	0.311930i
$301$		0			0
$302$	5.74544	+	19.1968i	0.330613	+	1.10465i
$303$	6.24698	+	23.3140i	0.358879	+	1.33936i
$304$	4.48502	−	0.522740i	0.257233	−	0.0299812i
$305$	0.993014	−	3.24932i	0.0568598	−	0.186056i
$306$	−4.57802	+	2.82325i	−0.261708	+	0.161395i
$307$	−0.726484	−	0.726484i	−0.0414626	−	0.0414626i	0.686071	−	0.727534i	$-0.259334\pi$
$307$	−0.726484	−	0.726484i	−0.0414626	−	0.0414626i	−0.727534	+	0.686071i	$0.759334\pi$
$308$		0			0
$309$		−	21.9587i		−	1.24919i
$310$	5.78738	+	10.1593i	0.328701	+	0.577011i
$311$	11.5281	−	6.65573i	0.653697	−	0.377412i	−0.136174	−	0.990685i	$-0.543481\pi$
$311$	11.5281	−	6.65573i	0.653697	−	0.377412i	0.789871	+	0.613273i	$0.210147\pi$
$312$	38.0276	+	6.71488i	2.15289	+	0.380155i
$313$	21.0053	−	5.62834i	1.18729	−	0.318133i	0.389474	−	0.921037i	$-0.372657\pi$
$313$	21.0053	−	5.62834i	1.18729	−	0.318133i	0.797813	+	0.602905i	$0.205990\pi$
$314$	−3.35362	+	6.21847i	−0.189256	+	0.350928i
$315$		0			0
$316$	9.12800	−	6.00145i	0.513490	−	0.337608i
$317$	−3.99527	−	14.9105i	−0.224397	−	0.837460i	−0.982645	−	0.185494i	$-0.940611\pi$
$317$	−3.99527	−	14.9105i	−0.224397	−	0.837460i	0.758249	−	0.651966i	$-0.226055\pi$
$318$	−4.32800	−	4.08393i	−0.242702	−	0.229015i
$319$	2.21976	+	3.84473i	0.124283	+	0.215264i
$320$	6.98342	+	16.4691i	0.390385	+	0.920652i
$321$	19.7207			1.10070
$322$		0			0
$323$	−3.02137	+	3.02137i	−0.168114	+	0.168114i
$324$	1.27615	+	21.9725i	0.0708974	+	1.22069i
$325$	−32.2557	−	11.0983i	−1.78922	−	0.615624i
$326$	−22.8437	+	0.662819i	−1.26520	+	0.0367102i
$327$	9.88996	−	2.65001i	0.546916	−	0.146546i
$328$	0.820897	−	0.977820i	0.0453264	−	0.0539911i
$329$		0			0
$330$	9.10707	+	34.7920i	0.501328	+	1.91524i
$331$	−22.9196	−	13.2326i	−1.25977	−	0.727330i	−0.286743	−	0.958008i	$-0.592573\pi$
$331$	−22.9196	−	13.2326i	−1.25977	−	0.727330i	−0.973030	+	0.230677i	$0.925906\pi$
$332$	−2.60045	+	0.861225i	−0.142718	+	0.0472659i
$333$	0.893972	−	3.33635i	0.0489894	−	0.182831i
$334$	9.07387	−	5.59583i	0.496500	−	0.306190i
$335$	1.06262	−	30.5289i	0.0580570	−	1.66797i
$336$		0			0
$337$	−10.6349	+	10.6349i	−0.579322	+	0.579322i	−0.934717	−	0.355394i	$-0.884347\pi$
$337$	−10.6349	+	10.6349i	−0.579322	+	0.579322i	0.355394	+	0.934717i	$0.384347\pi$
$338$	46.1588	+	10.9438i	2.51071	+	0.595265i
$339$	2.80963	+	4.86642i	0.152598	+	0.264308i
$340$	−14.8525	−	8.12121i	−0.805488	−	0.440435i
$341$	10.5062	−	18.1972i	0.568941	−	0.985435i
$342$	−0.459920	−	1.53670i	−0.0248696	−	0.0830950i
$343$		0			0
$344$	−0.213193	−	2.44370i	−0.0114946	−	0.131755i
$345$	4.90633	+	21.2406i	0.264148	+	1.14356i
$346$	−0.180206	−	6.21072i	−0.00968796	−	0.333890i
$347$	1.35506	−	5.05713i	0.0727432	−	0.271481i	−0.919969	−	0.391991i	$-0.871786\pi$
$347$	1.35506	−	5.05713i	0.0727432	−	0.271481i	0.992712	+	0.120510i	$0.0384530\pi$
$348$	2.07894	−	2.33531i	0.111443	−	0.125186i
$349$			27.3545i			1.46426i	0.681168	+	0.732128i	$0.261473\pi$
$349$			27.3545i			1.46426i	−0.681168	+	0.732128i	$0.738527\pi$
$350$		0			0
$351$			27.2404i			1.45399i
$352$	19.2081	−	25.7790i	1.02379	−	1.37402i
$353$	3.87689	−	14.4688i	0.206346	−	0.770094i	−0.782689	−	0.622413i	$-0.786152\pi$
$353$	3.87689	−	14.4688i	0.206346	−	0.770094i	0.989035	−	0.147681i	$-0.0471810\pi$
$354$	26.2377	−	0.761296i	1.39452	−	0.0404624i
$355$	5.95421	+	25.7771i	0.316017	+	1.36811i
$356$	−10.3541	−	15.7483i	−0.548767	−	0.834656i
$357$		0			0
$358$	0.920050	−	0.275363i	0.0486262	−	0.0145534i
$359$	−11.9911	+	20.7692i	−0.632867	+	1.09616i	0.354095	+	0.935209i	$0.384789\pi$
$359$	−11.9911	+	20.7692i	−0.632867	+	1.09616i	−0.986963	+	0.160949i	$0.948545\pi$
$360$	5.32998	−	3.46034i	0.280915	−	0.182376i
$361$	8.86285	+	15.3509i	0.466466	+	0.807943i
$362$	−2.56661	+	10.8255i	−0.134898	+	0.568973i
$363$	30.1365	−	30.1365i	1.58175	−	1.58175i
$364$		0			0
$365$	0.133924	−	3.84762i	0.00700989	−	0.201394i
$366$	2.25727	+	3.66025i	0.117989	+	0.191325i
$367$	−3.50537	+	13.0822i	−0.182979	+	0.682887i	0.812075	+	0.583553i	$0.198338\pi$
$367$	−3.50537	+	13.0822i	−0.182979	+	0.682887i	−0.995054	+	0.0993339i	$0.968329\pi$
$368$	12.0914	−	15.2818i	0.630308	−	0.796620i
$369$	−0.392778	−	0.226770i	−0.0204472	−	0.0118052i
$370$	10.5165	−	2.75277i	0.546725	−	0.143110i
$371$		0			0
$372$	−14.4921	−	2.99484i	−0.751380	−	0.155275i
$373$	−17.7683	+	4.76101i	−0.920010	+	0.246516i	−0.687590	−	0.726100i	$-0.741331\pi$
$373$	−17.7683	+	4.76101i	−0.920010	+	0.246516i	−0.232420	+	0.972615i	$0.574664\pi$
$374$	0.882321	+	30.4087i	0.0456238	+	1.57240i
$375$	−20.4366	+	9.10730i	−1.05534	+	0.470299i
$376$	5.12858	−	10.9913i	0.264486	−	0.566831i
$377$	3.76852	−	3.76852i	0.194089	−	0.194089i
$378$		0			0
$379$	−27.8562			−1.43088			−0.715440	−	0.698675i	$-0.753774\pi$
$379$	−27.8562			−1.43088			−0.715440	+	0.698675i	$0.753774\pi$
$380$	3.48587	−	3.65165i	0.178821	−	0.187325i
$381$	17.2226	+	29.8304i	0.882341	+	1.52826i
$382$	10.3687	−	10.9884i	0.530509	−	0.562215i
$383$	−3.42176	−	12.7702i	−0.174844	−	0.652527i	−0.996578	−	0.0826556i	$-0.973660\pi$
$383$	−3.42176	−	12.7702i	−0.174844	−	0.652527i	0.821734	−	0.569871i	$-0.193007\pi$
$384$	−21.4876	−	7.13385i	−1.09654	−	0.364048i
$385$		0			0
$386$	−14.0463	−	7.57518i	−0.714938	−	0.385567i
$387$	−0.841705	+	0.225534i	−0.0427862	+	0.0114645i
$388$	−18.1890	+	6.02389i	−0.923407	+	0.305817i
$389$	14.5751	−	8.41493i	0.738986	−	0.426654i	−0.0827144	−	0.996573i	$-0.526359\pi$
$389$	14.5751	−	8.41493i	0.738986	−	0.426654i	0.821701	+	0.569919i	$0.193026\pi$
$390$	37.5139	−	21.3702i	1.89959	−	1.08212i
$391$			18.4402i			0.932561i
$392$		0			0
$393$	4.56955	+	4.56955i	0.230503	+	0.230503i
$394$	−3.46014	−	5.61077i	−0.174319	−	0.282666i
$395$	3.56959	−	11.6803i	0.179605	−	0.587702i
$396$	−10.2047	−	5.12709i	−0.512807	−	0.257646i
$397$	2.68943	+	10.0371i	0.134979	+	0.503748i	0.999998	+	0.00200883i	$0.000639432\pi$
$397$	2.68943	+	10.0371i	0.134979	+	0.503748i	−0.865019	+	0.501739i	$0.832694\pi$
$398$	−12.9767	+	3.88380i	−0.650461	+	0.194677i
$399$		0			0
$400$	17.7661	+	9.18508i	0.888305	+	0.459254i
$401$	−11.0986	+	19.2234i	−0.554239	+	0.959969i	0.443724	+	0.896164i	$0.353657\pi$
$401$	−11.0986	+	19.2234i	−0.554239	+	0.959969i	−0.997962	+	0.0638058i	$0.979676\pi$
$402$	28.1201	+	26.5343i	1.40250	+	1.32341i
$403$	−24.3651	−	6.52862i	−1.21371	−	0.325214i
$404$	−1.39865	−	24.0815i	−0.0695852	−	1.19810i
$405$	16.7842	+	17.9948i	0.834015	+	0.894168i
$406$		0			0
$407$	−13.8142	−	13.8142i	−0.684746	−	0.684746i
$408$	20.1346	−	7.32282i	0.996812	−	0.362534i
$409$	7.98006	−	4.60729i	0.394589	−	0.227816i	−0.289558	−	0.957161i	$-0.593508\pi$
$409$	7.98006	−	4.60729i	0.394589	−	0.227816i	0.684147	+	0.729345i	$0.260175\pi$
$410$	0.00825840	−	1.42739i	0.000407853	−	0.0704937i
$411$	26.0834	+	15.0593i	1.28660	+	0.742818i
$412$	−4.44130	+	21.4916i	−0.218807	+	1.05881i
$413$		0			0
$414$	−6.09292	−	3.28592i	−0.299451	−	0.161494i
$415$	−1.62268	+	2.59749i	−0.0796544	+	0.127506i
$416$	−35.8604	−	14.2634i	−1.75820	−	0.699318i
$417$	−14.4848	−	3.88120i	−0.709325	−	0.190063i
$418$	−8.82785	−	2.09300i	−0.431784	−	0.102372i
$419$	−18.5156			−0.904546			−0.452273	−	0.891880i	$-0.649387\pi$
$419$	−18.5156			−0.904546			−0.452273	+	0.891880i	$0.649387\pi$
$420$		0			0
$421$	25.5501			1.24524			0.622619	−	0.782525i	$-0.286069\pi$
$421$	25.5501			1.24524			0.622619	+	0.782525i	$0.286069\pi$
$422$	−26.4695	−	6.27567i	−1.28852	−	0.305495i
$423$	−4.16186	−	1.11517i	−0.202356	−	0.0542212i
$424$	3.40992	+	4.87240i	0.165600	+	0.236625i
$425$	−18.5773	+	3.61544i	−0.901131	+	0.175375i
$426$	−29.4716	−	15.8941i	−1.42790	−	0.770070i
$427$		0			0
$428$	−19.3011	−	3.98864i	−0.932953	−	0.192798i
$429$	−67.1943	−	38.7947i	−3.24417	−	1.87302i
$430$	−1.92800	−	1.95044i	−0.0929763	−	0.0940584i
$431$	9.02515	−	5.21067i	0.434726	−	0.250989i	−0.266632	−	0.963798i	$-0.585911\pi$
$431$	9.02515	−	5.21067i	0.434726	−	0.250989i	0.701358	+	0.712809i	$0.252577\pi$
$432$	2.31991	−	15.8020i	0.111617	−	0.760272i
$433$	−20.3802	−	20.3802i	−0.979412	−	0.979412i	0.0203805	−	0.999792i	$-0.493512\pi$
$433$	−20.3802	−	20.3802i	−0.979412	−	0.979412i	−0.999792	+	0.0203805i	$0.993512\pi$
$434$		0			0
$435$	0.121599	−	3.49354i	0.00583023	−	0.167502i
$436$	−10.2155	+	0.593315i	−0.489235	+	0.0284146i
$437$	−5.31201	−	1.42335i	−0.254108	−	0.0680880i
$438$	3.54404	+	3.34417i	0.169341	+	0.159791i
$439$	10.4182	−	18.0448i	0.497233	−	0.861233i	−0.502762	−	0.864425i	$-0.667683\pi$
$439$	10.4182	−	18.0448i	0.497233	−	0.861233i	0.999995	+	0.00319202i	$0.00101605\pi$
$440$	−1.87640	−	35.8937i	−0.0894537	−	1.71117i
$441$		0			0
$442$	34.9867	−	10.4712i	1.66415	−	0.498066i
$443$	6.91448	+	25.8052i	0.328517	+	1.22604i	0.910729	+	0.413004i	$0.135521\pi$
$443$	6.91448	+	25.8052i	0.328517	+	1.22604i	−0.582212	+	0.813037i	$0.697813\pi$
$444$	−6.17693	+	12.2943i	−0.293144	+	0.583460i
$445$	−20.1517	−	6.15850i	−0.955284	−	0.291941i
$446$	7.01040	+	11.3677i	0.331952	+	0.538274i
$447$	−6.13501	−	6.13501i	−0.290176	−	0.290176i
$448$		0			0
$449$		−	27.5815i		−	1.30165i	−0.759227	−	0.650826i	$-0.774423\pi$
$449$		−	27.5815i		−	1.30165i	0.759227	−	0.650826i	$-0.225577\pi$
$450$	2.11575	−	6.78247i	0.0997373	−	0.319729i
$451$	−2.22158	+	1.28263i	−0.104610	+	0.0603966i
$452$	−1.76559	−	5.33115i	−0.0830462	−	0.250756i
$453$	−27.3889	+	7.33884i	−1.28684	+	0.344809i
$454$	−33.9956	−	18.3339i	−1.59549	−	0.860451i
$455$		0			0
$456$	0.555326	+	6.36534i	0.0260055	+	0.298084i
$457$	0.356056	+	1.32882i	0.0166556	+	0.0621596i	0.973753	−	0.227605i	$-0.0730896\pi$
$457$	0.356056	+	1.32882i	0.0166556	+	0.0621596i	−0.957098	+	0.289765i	$0.906423\pi$
$458$	−12.2823	+	13.0164i	−0.573916	+	0.608216i
$459$	7.55678	+	13.0887i	0.352720	+	0.610929i
$460$	−0.505882	−	21.7810i	−0.0235869	−	1.01555i
$461$	17.6688			0.822918			0.411459	−	0.911428i	$-0.365019\pi$
$461$	17.6688			0.822918			0.411459	+	0.911428i	$0.365019\pi$
$462$		0			0
$463$	−5.55471	+	5.55471i	−0.258149	+	0.258149i	−0.824301	−	0.566152i	$-0.808432\pi$
$463$	−5.55471	+	5.55471i	−0.258149	+	0.258149i	0.566152	+	0.824301i	$0.308432\pi$
$464$	−2.50704	+	1.86515i	−0.116386	+	0.0865874i
$465$	−14.6075	+	7.76907i	−0.677406	+	0.360282i
$466$	0.710835	+	24.4985i	0.0329288	+	1.13487i
$467$	12.6645	−	3.39345i	0.586045	−	0.157030i	0.0463998	−	0.998923i	$-0.485225\pi$
$467$	12.6645	−	3.39345i	0.586045	−	0.157030i	0.539645	+	0.841893i	$0.318559\pi$
$468$	−2.77454	+	13.4261i	−0.128253	+	0.620619i
$469$		0			0
$470$	−3.43388	−	13.1185i	−0.158393	−	0.605113i
$471$	−8.65814	−	4.99878i	−0.398946	−	0.230332i
$472$	−25.8334	−	4.56165i	−1.18908	−	0.209967i
$473$	−1.27563	+	4.76073i	−0.0586537	+	0.218899i
$474$	8.11419	+	13.1575i	0.372697	+	0.604345i
$475$	0.392441	−	5.63057i	0.0180064	−	0.258348i
$476$		0			0
$477$	1.49387	−	1.49387i	0.0683994	−	0.0683994i
$478$	7.10051	−	29.9485i	0.324770	−	1.36981i
$479$	−1.27174	−	2.20272i	−0.0581072	−	0.100645i	0.835509	−	0.549477i	$-0.185173\pi$
$479$	−1.27174	−	2.20272i	−0.0581072	−	0.100645i	−0.893616	+	0.448833i	$0.851840\pi$
$480$	−23.5815	+	9.20187i	−1.07634	+	0.420006i
$481$	−11.7263	+	20.3106i	−0.534675	+	0.926085i
$482$	28.2502	−	8.45506i	1.28676	−	0.385117i
$483$		0			0
$484$	−35.5906	+	23.4000i	−1.61775	+	1.06364i
$485$	−11.3499	+	18.1683i	−0.515375	+	0.824981i
$486$	−14.1985	+	0.411976i	−0.644059	+	0.0186876i
$487$	−0.952635	+	3.55528i	−0.0431680	+	0.161105i	−0.984145	−	0.177365i	$-0.943243\pi$
$487$	−0.952635	+	3.55528i	−0.0431680	+	0.161105i	0.940977	+	0.338470i	$0.109909\pi$
$488$	−1.46893	−	4.03893i	−0.0664953	−	0.182834i
$489$		−	32.3388i		−	1.46241i
$490$		0			0
$491$			22.3410i			1.00823i	0.863635	+	0.504117i	$0.168182\pi$
$491$			22.3410i			1.00823i	−0.863635	+	0.504117i	$0.831818\pi$
$492$	1.34940	+	1.20126i	0.0608356	+	0.0541569i
$493$	0.765307	−	2.85616i	0.0344677	−	0.128635i
$494$	0.315884	+	10.8868i	0.0142123	+	0.489818i
$495$	−12.4407	+	2.87366i	−0.559169	+	0.129161i
$496$	13.5780	+	5.86225i	0.609672	+	0.263223i
$497$		0			0
$498$	−1.11144	−	3.71358i	−0.0498050	−	0.166410i
$499$	−4.97828	+	8.62263i	−0.222858	+	0.386002i	−0.955675	−	0.294424i	$-0.904872\pi$
$499$	−4.97828	+	8.62263i	−0.222858	+	0.386002i	0.732816	+	0.680426i	$0.238205\pi$
$500$	21.8438	−	4.78010i	0.976883	−	0.213773i
$501$	7.54268	+	13.0643i	0.336982	+	0.583670i
$502$	−20.1712	−	4.78240i	−0.900285	−	0.213449i
$503$	−8.22634	+	8.22634i	−0.366794	+	0.366794i	−0.866307	−	0.499512i	$-0.833513\pi$
$503$	−8.22634	+	8.22634i	−0.366794	+	0.366794i	0.499512	+	0.866307i	$0.333513\pi$
$504$		0			0
$505$	−18.3953	−	19.7220i	−0.818579	−	0.877618i
$506$	−33.3264	+	20.5522i	−1.48154	+	0.913659i
$507$	−17.3740	+	64.8407i	−0.771608	+	2.87968i
$508$	−10.8228	−	32.6792i	−0.480183	−	1.44990i
$509$	−28.4455	−	16.4230i	−1.26083	−	0.727938i	−0.287591	−	0.957753i	$-0.592854\pi$
$509$	−28.4455	−	16.4230i	−1.26083	−	0.727938i	−0.973234	+	0.229815i	$0.926188\pi$
$510$	12.0967	−	20.6749i	0.535651	−	0.915501i
$511$		0			0
$512$	19.5876	+	11.3281i	0.865658	+	0.500636i
$513$	−4.35371	+	1.16657i	−0.192221	+	0.0515055i
$514$	−19.3796	+	0.562307i	−0.854798	+	0.0248023i
$515$	11.5214	+	21.6627i	0.507694	+	0.954572i
$516$	3.46526	−	0.201261i	0.152550	−	0.00886004i
$517$	−17.2323	+	17.2323i	−0.757874	+	0.757874i
$518$		0			0
$519$	8.79222			0.385936
$520$	−41.0381	+	13.3281i	−1.79964	+	0.584477i
$521$	−0.899013	−	1.55714i	−0.0393865	−	0.0682194i	0.845660	−	0.533722i	$-0.179207\pi$
$521$	−0.899013	−	1.55714i	−0.0393865	−	0.0682194i	−0.885047	+	0.465502i	$0.845874\pi$
$522$	0.807347	+	0.761818i	0.0353366	+	0.0333438i
$523$	−6.64278	−	24.7912i	−0.290468	−	1.08404i	−0.944750	−	0.327792i	$-0.893696\pi$
$523$	−6.64278	−	24.7912i	−0.290468	−	1.08404i	0.654282	−	0.756251i	$-0.272971\pi$
$524$	−3.54811	−	5.39655i	−0.155000	−	0.235750i
$525$		0			0
$526$	15.4550	−	28.6575i	0.673871	−	1.24953i
$527$	−13.5183	+	3.62222i	−0.588866	+	0.157786i
$528$	35.6750	+	28.2271i	1.55256	+	1.22843i
$529$	−0.635213	+	0.366740i	−0.0276179	+	0.0159452i
$530$	6.41242	+	1.75803i	0.278538	+	0.0763639i
$531$			9.31904i			0.404412i
$532$		0			0
$533$	2.17754	+	2.17754i	0.0943198	+	0.0943198i
$534$	22.7003	−	13.9992i	0.982336	−	0.605803i
$535$	−19.4548	+	10.3471i	−0.841104	+	0.447345i
$536$	−22.1551	−	31.6572i	−0.956955	−	1.36738i
$537$	0.351731	+	1.31268i	0.0151783	+	0.0566462i
$538$	−12.2512	−	40.9341i	−0.528188	−	1.76479i
$539$		0			0
$540$	−9.28492	−	15.2527i	−0.399559	−	0.656372i
$541$	12.6660	−	21.9381i	0.544552	−	0.943192i	−0.454083	−	0.890959i	$-0.650033\pi$
$541$	12.6660	−	21.9381i	0.544552	−	0.943192i	0.998635	−	0.0522324i	$-0.0166336\pi$
$542$	10.4439	−	11.0681i	0.448605	−	0.475416i
$543$	−15.2069	−	4.07466i	−0.652589	−	0.174861i
$544$	−21.1873	+	3.09466i	−0.908399	+	0.132682i
$545$	−8.36620	+	7.80339i	−0.358369	+	0.334261i
$546$		0			0
$547$	−17.3594	−	17.3594i	−0.742233	−	0.742233i	0.230774	−	0.973007i	$-0.425874\pi$
$547$	−17.3594	−	17.3594i	−0.742233	−	0.742233i	−0.973007	+	0.230774i	$0.925874\pi$
$548$	−22.4826	−	20.0144i	−0.960409	−	0.854973i
$549$	−1.32219	+	0.763367i	−0.0564297	+	0.0325797i
$550$	−27.2391	−	29.5446i	−1.16148	−	1.25978i
$551$	0.763694	+	0.440919i	0.0325344	+	0.0187838i
$552$	21.1193	+	17.7300i	0.898897	+	0.754639i
$553$		0			0
$554$	−21.6664	+	40.1750i	−0.920518	+	1.70687i
$555$	3.46207	+	14.9881i	0.146957	+	0.636210i
$556$	13.3916	+	6.72827i	0.567932	+	0.285342i
$557$	27.1858	+	7.28440i	1.15190	+	0.308650i	0.783725	−	0.621108i	$-0.213317\pi$
$557$	27.1858	+	7.28440i	1.15190	+	0.308650i	0.368172	+	0.929758i	$0.379984\pi$
$558$	1.21203	−	5.11210i	0.0513094	−	0.216413i
$559$	5.91672			0.250250
$560$		0			0
$561$	−43.0482			−1.81750
$562$	0.343083	−	1.44706i	0.0144721	−	0.0610404i
$563$	23.6233	+	6.32985i	0.995605	+	0.266772i	0.719603	−	0.694386i	$-0.244324\pi$
$563$	23.6233	+	6.32985i	0.995605	+	0.266772i	0.276002	+	0.961157i	$0.410990\pi$
$564$	15.3362	+	7.70527i	0.645771	+	0.324451i
$565$	−5.32509	−	3.32664i	−0.224028	−	0.139953i
$566$	7.21592	−	13.3802i	0.303308	−	0.562410i
$567$		0			0
$568$	25.6299	+	21.5167i	1.07541	+	0.902822i
$569$	34.9968	+	20.2054i	1.46714	+	0.847055i	0.999324	−	0.0367696i	$-0.0117068\pi$
$569$	34.9968	+	20.2054i	1.46714	+	0.847055i	0.467818	+	0.883825i	$0.345040\pi$
$570$	5.02205	+	5.08050i	0.210350	+	0.212799i
$571$	13.5653	−	7.83192i	0.567690	−	0.327756i	−0.188536	−	0.982066i	$-0.560374\pi$
$571$	13.5653	−	7.83192i	0.567690	−	0.327756i	0.756226	+	0.654310i	$0.227041\pi$
$572$	57.9182	+	51.5598i	2.42168	+	2.15582i
$573$	15.1171	+	15.1171i	0.631526	+	0.631526i
$574$		0			0
$575$	−15.9848	−	18.3800i	−0.666612	−	0.766498i
$576$	2.75291	−	7.55206i	0.114705	−	0.314669i
$577$	−11.0044	−	2.94861i	−0.458118	−	0.122752i	0.0223775	−	0.999750i	$-0.492876\pi$
$577$	−11.0044	−	2.94861i	−0.458118	−	0.122752i	−0.480495	+	0.876997i	$0.659543\pi$
$578$	−2.59388	+	2.74890i	−0.107891	+	0.114339i
$579$	11.2913	−	19.5571i	0.469250	−	0.812764i
$580$	−0.825603	+	3.39461i	−0.0342813	+	0.140954i
$581$		0			0
$582$	−7.77406	−	25.9749i	−0.322245	−	1.07669i
$583$	−3.09269	−	11.5421i	−0.128086	−	0.478024i
$584$	−2.79225	−	3.98983i	−0.115544	−	0.165100i
$585$	7.19758	+	13.5330i	0.297583	+	0.559519i
$586$	32.5415	−	20.0682i	1.34428	−	0.829011i
$587$	10.0769	+	10.0769i	0.415916	+	0.415916i	0.883794	−	0.467877i	$-0.154981\pi$
$587$	10.0769	+	10.0769i	0.415916	+	0.415916i	−0.467877	+	0.883794i	$0.654981\pi$
$588$		0			0
$589$		−	4.17376i		−	0.171977i
$590$	−25.4845	+	14.5175i	−1.04918	+	0.597678i
$591$	8.07822	−	4.66396i	0.332294	−	0.191850i
$592$	8.53211	−	10.7834i	0.350667	−	0.443194i
$593$	10.7368	−	2.87691i	0.440907	−	0.118141i	−0.0315347	−	0.999503i	$-0.510039\pi$
$593$	10.7368	−	2.87691i	0.440907	−	0.118141i	0.472442	+	0.881362i	$0.343373\pi$
$594$	−15.2325	+	28.2449i	−0.624997	+	1.15890i
$595$		0			0
$596$	4.76363	+	7.24533i	0.195126	+	0.296780i
$597$	−4.96091	−	18.5144i	−0.203037	−	0.757743i
$598$	34.1863	+	32.2584i	1.39798	+	1.31914i
$599$	−5.65333	−	9.79185i	−0.230989	−	0.400084i	0.727111	−	0.686520i	$-0.240863\pi$
$599$	−5.65333	−	9.79185i	−0.230989	−	0.400084i	−0.958099	+	0.286436i	$0.907529\pi$
$600$	−13.7211	+	24.7525i	−0.560161	+	1.01052i
$601$	37.1086			1.51369			0.756846	−	0.653593i	$-0.226739\pi$
$601$	37.1086			1.51369			0.756846	+	0.653593i	$0.226739\pi$
$602$		0			0
$603$	−9.70602	+	9.70602i	−0.395260	+	0.395260i
$604$	28.2905	−	1.64310i	1.15113	−	0.0668570i
$605$	−13.9180	+	45.5423i	−0.565848	+	1.85156i
$606$	34.1198	−	0.989998i	1.38602	−	0.0402159i
$607$	−28.6075	+	7.66535i	−1.16114	+	0.311127i	−0.787422	−	0.616414i	$-0.788585\pi$
$607$	−28.6075	+	7.66535i	−1.16114	+	0.311127i	−0.373720	+	0.927541i	$0.621918\pi$
$608$	0.743923	−	6.34223i	0.0301700	−	0.257211i
$609$		0			0
$610$	−4.14731	−	2.42655i	−0.167920	−	0.0982482i
$611$	25.3360	+	14.6278i	1.02499	+	0.591776i
$612$	2.39139	+	7.22076i	0.0966663	+	0.291882i
$613$	−1.21113	+	4.51998i	−0.0489169	+	0.182560i	−0.986062	−	0.166381i	$-0.946792\pi$
$613$	−1.21113	+	4.51998i	−0.0489169	+	0.182560i	0.937145	+	0.348941i	$0.113459\pi$
$614$	−1.23671	+	0.762673i	−0.0499095	+	0.0307790i
$615$	2.01865	+	0.0702628i	0.0813997	+	0.00283327i
$616$		0			0
$617$	7.18275	−	7.18275i	0.289167	−	0.289167i	−0.547584	−	0.836751i	$-0.684452\pi$
$617$	7.18275	−	7.18275i	0.289167	−	0.289167i	0.836751	+	0.547584i	$0.184452\pi$
$618$	−30.2167	−	7.16409i	−1.21549	−	0.288182i
$619$	−16.0406	−	27.7831i	−0.644725	−	1.11670i	−0.984365	−	0.176141i	$-0.943639\pi$
$619$	−16.0406	−	27.7831i	−0.644725	−	1.11670i	0.339640	−	0.940556i	$-0.389695\pi$
$620$	15.8681	−	4.64931i	0.637276	−	0.186721i
$621$	−9.72596	+	16.8459i	−0.390289	+	0.676001i
$622$	−5.39767	−	18.0348i	−0.216427	−	0.723131i
$623$		0			0
$624$	21.6467	−	50.1377i	0.866562	−	2.00712i
$625$	15.3826	−	19.7073i	0.615303	−	0.788291i
$626$	−0.891959	−	30.7409i	−0.0356499	−	1.22865i
$627$	3.32277	−	12.4008i	0.132699	−	0.495238i
$628$	7.46290	+	6.64360i	0.297802	+	0.265108i
$629$			13.0120i			0.518824i
$630$		0			0
$631$			18.7069i			0.744710i	0.928090	+	0.372355i	$0.121450\pi$
$631$			18.7069i			0.744710i	−0.928090	+	0.372355i	$0.878550\pi$
$632$	−5.28036	−	14.5187i	−0.210041	−	0.577524i
$633$	9.96304	−	37.1826i	0.395995	−	1.47787i
$634$	−21.8214	+	0.633156i	−0.866638	+	0.0251458i
$635$	−32.6420	−	20.3918i	−1.29536	−	0.809225i
$636$	−7.03177	+	4.62323i	−0.278828	+	0.183323i
$637$		0			0
$638$	6.01481	−	1.80018i	0.238129	−	0.0712698i
$639$	5.94394	−	10.2952i	0.235139	−	0.407272i
$640$	24.9410	−	4.23657i	0.985878	−	0.167465i
$641$	14.8043	+	25.6419i	0.584736	+	1.01279i	0.994908	+	0.100785i	$0.0321353\pi$
$641$	14.8043	+	25.6419i	0.584736	+	1.01279i	−0.410172	+	0.912008i	$0.634531\pi$
$642$	6.43391	−	27.1370i	0.253926	−	1.07101i
$643$	−15.8819	+	15.8819i	−0.626323	+	0.626323i	−0.947141	−	0.320818i	$-0.896042\pi$
$643$	−15.8819	+	15.8819i	−0.626323	+	0.626323i	0.320818	+	0.947141i	$0.396042\pi$
$644$		0			0
$645$	2.83795	−	2.64703i	0.111744	−	0.104227i
$646$	3.17188	+	5.14334i	0.124796	+	0.202362i
$647$	−6.47181	+	24.1531i	−0.254433	+	0.949557i	0.713972	+	0.700174i	$0.246894\pi$
$647$	−6.47181	+	24.1531i	−0.254433	+	0.949557i	−0.968405	+	0.249383i	$0.919772\pi$
$648$	30.6519	+	5.41250i	1.20412	+	0.212623i
$649$	45.6474	+	26.3545i	1.79182	+	1.03451i
$650$	−25.7955	+	40.7651i	−1.01178	+	1.59894i
$651$		0			0
$652$	−6.54073	+	31.6507i	−0.256155	+	1.23954i
$653$	−39.9668	+	10.7091i	−1.56402	+	0.419079i	−0.933934	−	0.357445i	$-0.883648\pi$
$653$	−39.9668	+	10.7091i	−1.56402	+	0.419079i	−0.630088	+	0.776523i	$0.716981\pi$
$654$	−0.419964	−	14.4738i	−0.0164219	−	0.565971i
$655$	−6.90552	−	2.11037i	−0.269821	−	0.0824590i
$656$	−1.07773	−	1.44862i	−0.0420782	−	0.0565593i
$657$	−1.22327	+	1.22327i	−0.0477243	+	0.0477243i
$658$		0			0
$659$	−32.9086			−1.28194			−0.640968	−	0.767568i	$-0.721467\pi$
$659$	−32.9086			−1.28194			−0.640968	+	0.767568i	$0.721467\pi$
$660$	50.8473	−	1.18097i	1.97923	−	0.0459692i
$661$	−8.98502	−	15.5625i	−0.349477	−	0.605311i	0.636680	−	0.771128i	$-0.280307\pi$
$661$	−8.98502	−	15.5625i	−0.349477	−	0.605311i	−0.986157	+	0.165817i	$0.946974\pi$
$662$	−25.6865	+	27.2217i	−0.998335	+	1.05800i
$663$	13.3753	+	49.9171i	0.519452	+	1.93862i
$664$	0.336700	+	3.85937i	0.0130665	+	0.149773i
$665$		0			0
$666$	−4.29938	−	2.31866i	−0.166598	−	0.0898461i
$667$	3.67603	−	0.984989i	0.142336	−	0.0381389i
$668$	−4.73986	−	14.3119i	−0.183391	−	0.553744i
$669$	−16.3668	+	9.44939i	−0.632778	+	0.365335i
$670$	−41.6631	−	11.4224i	−1.60959	−	0.441284i
$671$			8.63530i			0.333362i
$672$		0			0
$673$	6.28219	+	6.28219i	0.242161	+	0.242161i	0.817744	−	0.575583i	$-0.195225\pi$
$673$	6.28219	+	6.28219i	0.242161	+	0.242161i	−0.575583	+	0.817744i	$0.695225\pi$
$674$	11.1647	+	18.1041i	0.430049	+	0.697343i
$675$	−18.8780	−	6.49541i	−0.726614	−	0.250008i
$676$	30.1189	−	59.9472i	1.15842	−	2.30566i
$677$	−7.03183	−	26.2432i	−0.270255	−	1.00861i	−0.958955	−	0.283560i	$-0.908485\pi$
$677$	−7.03183	−	26.2432i	−0.270255	−	1.00861i	0.688699	−	0.725047i	$-0.258182\pi$
$678$	7.61317	−	2.27856i	0.292382	−	0.0875075i
$679$		0			0
$680$	−16.0210	+	17.7884i	−0.614377	+	0.682155i
$681$	27.3278	−	47.3331i	1.04720	−	1.81381i
$682$	−21.6129	−	20.3941i	−0.827602	−	0.780929i
$683$	−21.7405	−	5.82534i	−0.831876	−	0.222900i	−0.182344	−	0.983235i	$-0.558368\pi$
$683$	−21.7405	−	5.82534i	−0.831876	−	0.222900i	−0.649532	+	0.760334i	$0.725035\pi$
$684$	−2.26465	+	0.131530i	−0.0865909	+	0.00502917i
$685$	−33.6331	−	1.17066i	−1.28505	−	0.0447287i
$686$		0			0
$687$	−17.9071	−	17.9071i	−0.683199	−	0.683199i
$688$	−3.43224	−	0.503894i	−0.130853	−	0.0192108i
$689$	−12.4229	+	7.17235i	−0.473274	+	0.273245i
$690$	30.8292	+	0.178368i	1.17365	+	0.00679034i
$691$	9.95579	+	5.74798i	0.378736	+	0.218663i	0.677268	−	0.735736i	$-0.263164\pi$
$691$	9.95579	+	5.74798i	0.378736	+	0.218663i	−0.298532	+	0.954400i	$0.596497\pi$
$692$	−8.60516	−	1.77829i	−0.327119	−	0.0676003i
$693$		0			0
$694$	−6.51686	−	3.51455i	−0.247377	−	0.133410i
$695$	16.3259	−	3.77110i	0.619278	−	0.143046i
$696$	−2.53529	−	3.62266i	−0.0960999	−	0.137316i
$697$	1.65036	+	0.442212i	0.0625118	+	0.0167500i
$698$	37.6417	+	8.92448i	1.42476	+	0.337797i
$699$	−34.6814			−1.31177
$700$		0			0
$701$	−2.54230			−0.0960214			−0.0480107	−	0.998847i	$-0.515288\pi$
$701$	−2.54230			−0.0960214			−0.0480107	+	0.998847i	$0.515288\pi$
$702$	37.4846	+	8.88725i	1.41477	+	0.335428i
$703$	−3.74834	−	1.00436i	−0.141371	−	0.0378803i
$704$	−29.2069	−	34.8420i	−1.10078	−	1.31316i
$705$	18.6966	−	4.31869i	0.704154	−	0.162651i
$706$	−18.6451	−	10.0553i	−0.701719	−	0.378437i
$707$		0			0
$708$	7.51251	−	36.3532i	0.282337	−	1.36624i
$709$	−8.79409	−	5.07727i	−0.330269	−	0.190681i	0.325692	−	0.945476i	$-0.394403\pi$
$709$	−8.79409	−	5.07727i	−0.330269	−	0.190681i	−0.655960	+	0.754795i	$0.727736\pi$
$710$	37.4136	+	0.216463i	1.40411	+	0.00812371i
$711$	−4.75288	+	2.74408i	−0.178247	+	0.102911i
$712$	−25.0487	+	9.11005i	−0.938740	+	0.341413i
$713$	−12.7368	−	12.7368i	−0.476995	−	0.476995i
$714$		0			0
$715$	86.6434	+	3.01579i	3.24028	+	0.112784i
$716$	−0.0787496	−	1.35589i	−0.00294301	−	0.0506719i
$717$	42.0696	+	11.2725i	1.57112	+	0.420980i
$718$	24.6677	+	23.2766i	0.920591	+	0.868675i
$719$	−18.7042	+	32.3967i	−0.697550	+	1.20819i	0.271763	+	0.962364i	$0.412393\pi$
$719$	−18.7042	+	32.3967i	−0.697550	+	1.20819i	−0.969313	+	0.245828i	$0.920940\pi$
$720$	−3.02273	−	8.46335i	−0.112651	−	0.315410i
$721$		0			0
$722$	24.0154	−	7.18761i	0.893761	−	0.267495i
$723$	10.7999	+	40.3059i	0.401654	+	1.49899i
$724$	14.0592	+	7.06366i	0.522505	+	0.262519i
$725$	1.71304	+	3.51024i	0.0636209	+	0.130367i
$726$	−31.6377	−	51.3019i	−1.17419	−	1.90399i
$727$	8.42845	+	8.42845i	0.312594	+	0.312594i	0.845914	−	0.533320i	$-0.179056\pi$
$727$	8.42845	+	8.42845i	0.312594	+	0.312594i	−0.533320	+	0.845914i	$0.679056\pi$
$728$		0			0
$729$			12.9141i			0.478298i
$730$	−5.25089	−	1.43958i	−0.194344	−	0.0532814i
$731$	2.84292	−	1.64136i	0.105149	−	0.0607079i
$732$	5.77319	−	1.91198i	0.213383	−	0.0706689i
$733$	−7.21528	+	1.93333i	−0.266503	+	0.0714092i	−0.389596	−	0.920986i	$-0.627385\pi$
$733$	−7.21528	+	1.93333i	−0.266503	+	0.0714092i	0.123093	+	0.992395i	$0.460719\pi$
$734$	16.8584	+	9.09173i	0.622254	+	0.335582i
$735$		0			0
$736$	−17.0839	−	21.6243i	−0.629723	−	0.797082i
$737$	20.0940	+	74.9919i	0.740172	+	2.76236i
$738$	−0.440196	+	0.466504i	−0.0162038	+	0.0171723i
$739$	1.19432	+	2.06863i	0.0439339	+	0.0760957i	0.887156	−	0.461469i	$-0.152678\pi$
$739$	1.19432	+	2.06863i	0.0439339	+	0.0760957i	−0.843222	+	0.537565i	$0.819344\pi$
$740$	−0.356968	−	15.3695i	−0.0131224	−	0.564992i
$741$	−15.4119			−0.566169
$742$		0			0
$743$	14.6605	−	14.6605i	0.537841	−	0.537841i	−0.385053	−	0.922894i	$-0.625817\pi$
$743$	14.6605	−	14.6605i	0.537841	−	0.537841i	0.922894	+	0.385053i	$0.125817\pi$
$744$	−8.84918	+	18.9650i	−0.324427	+	0.695291i
$745$	9.27124	+	2.83335i	0.339672	+	0.103806i
$746$	0.754508	+	26.0037i	0.0276245	+	0.952064i
$747$	1.32932	−	0.356190i	0.0486372	−	0.0130323i
$748$	42.1323	+	8.70679i	1.54051	+	0.318352i
$749$		0			0
$750$	5.86478	+	31.0934i	0.214151	+	1.13537i
$751$	0.704630	+	0.406818i	0.0257123	+	0.0148450i	0.512801	−	0.858507i	$-0.328608\pi$
$751$	0.704630	+	0.406818i	0.0257123	+	0.0148450i	−0.487089	+	0.873352i	$0.661941\pi$
$752$	−13.4515	−	10.6432i	−0.490525	−	0.388117i
$753$	7.59237	−	28.3351i	0.276681	−	1.03259i
$754$	−3.95625	−	6.41523i	−0.144078	−	0.233629i
$755$	23.1691	−	21.6104i	0.843209	−	0.786484i
$756$		0			0
$757$	11.0046	−	11.0046i	0.399968	−	0.399968i	−0.478254	−	0.878222i	$-0.658730\pi$
$757$	11.0046	−	11.0046i	0.399968	−	0.399968i	0.878222	+	0.478254i	$0.158730\pi$
$758$	−9.08816	+	38.3320i	−0.330097	+	1.39228i
$759$	−27.7026	−	47.9823i	−1.00554	−	1.74165i
$760$	−3.88763	−	5.98815i	−0.141019	−	0.217213i
$761$	−1.15696	+	2.00391i	−0.0419397	+	0.0726418i	−0.886233	−	0.463239i	$-0.846687\pi$
$761$	−1.15696	+	2.00391i	−0.0419397	+	0.0726418i	0.844294	+	0.535881i	$0.180020\pi$
$762$	46.6676	−	13.9672i	1.69059	−	0.505979i
$763$		0			0
$764$	−11.7379	−	17.8530i	−0.424664	−	0.645900i
$765$	7.21254	+	4.50576i	0.260770	+	0.162906i
$766$	−18.6890	+	0.542269i	−0.675261	+	0.0195930i
$767$	16.3769	−	61.1195i	0.591337	−	2.20690i
$768$	−16.8270	+	27.2410i	−0.607194	+	0.982975i
$769$		−	18.4165i		−	0.664117i	−0.943259	−	0.332059i	$-0.892257\pi$
$769$		−	18.4165i		−	0.664117i	0.943259	−	0.332059i	$-0.107743\pi$
$770$		0			0
$771$		−	27.4348i		−	0.988040i
$772$	−15.0066	+	16.8572i	−0.540099	+	0.606705i
$773$	−4.52774	+	16.8978i	−0.162852	+	0.607770i	0.835453	+	0.549562i	$0.185205\pi$
$773$	−4.52774	+	16.8978i	−0.162852	+	0.607770i	−0.998304	+	0.0582081i	$0.981461\pi$
$774$	0.0357418	+	1.23182i	0.00128471	+	0.0442769i
$775$	10.3342	−	15.3287i	0.371217	−	0.550622i
$776$	2.35506	+	26.9946i	0.0845419	+	0.969049i
$777$		0			0
$778$	−6.82435	−	22.8017i	−0.244665	−	0.817480i
$779$	−0.254773	+	0.441280i	−0.00912819	+	0.0158105i
$780$	−17.1679	−	58.5938i	−0.614709	−	2.09799i
$781$	−33.6193	−	58.2303i	−1.20299	−	2.08364i
$782$	25.3749	+	6.01616i	0.907406	+	0.215137i
$783$	2.20557	−	2.20557i	0.0788206	−	0.0788206i
$784$		0			0
$785$	11.1642	+	0.388591i	0.398467	+	0.0138694i
$786$	7.77884	−	4.79718i	0.277462	−	0.171110i
$787$	5.94282	−	22.1789i	0.211838	−	0.790592i	−0.775417	−	0.631449i	$-0.782460\pi$
$787$	5.94282	−	22.1789i	0.211838	−	0.790592i	0.987256	−	0.159143i	$-0.0508730\pi$
$788$	−8.84967	+	2.93086i	−0.315256	+	0.104408i
$789$	39.9007	+	23.0367i	1.42050	+	0.820127i
$790$	−14.9083	−	8.72272i	−0.530415	−	0.310341i
$791$		0			0
$792$	−10.3845	+	12.3697i	−0.368999	+	0.439537i
$793$	10.0132	−	2.68302i	0.355579	−	0.0952770i
$794$	14.6891	−	0.426211i	0.521298	−	0.0151257i
$795$	−2.74984	+	8.99797i	−0.0975267	+	0.319125i
$796$	1.11071	+	19.1238i	0.0393680	+	0.677827i
$797$	2.27256	−	2.27256i	0.0804981	−	0.0804981i	−0.665711	−	0.746209i	$-0.731872\pi$
$797$	2.27256	−	2.27256i	0.0804981	−	0.0804981i	0.746209	+	0.665711i	$0.231872\pi$
$798$		0			0
$799$	16.2316			0.574232
$800$	18.4355	−	21.4507i	0.651794	−	0.758396i
$801$	4.73427	+	8.20000i	0.167277	+	0.289733i
$802$	22.8317	+	21.5441i	0.806215	+	0.760749i
$803$	2.53249	+	9.45138i	0.0893697	+	0.333532i
$804$	45.6872	−	30.0383i	1.61126	−	1.05937i
$805$		0			0
$806$	−16.9330	+	31.3981i	−0.596440	+	1.10595i
$807$	58.4025	−	15.6489i	2.05587	−	0.550868i
$808$	−33.5941	−	5.93202i	−1.18183	−	0.208688i
$809$	9.03218	−	5.21473i	0.317555	−	0.183340i	−0.332747	−	0.943016i	$-0.607976\pi$
$809$	9.03218	−	5.21473i	0.317555	−	0.183340i	0.650302	+	0.759676i	$0.274642\pi$
$810$	30.2379	−	17.2254i	1.06245	−	0.605238i
$811$		−	13.6718i		−	0.480081i	−0.970763	−	0.240040i	$-0.922839\pi$
$811$		−	13.6718i		−	0.480081i	0.970763	−	0.240040i	$-0.0771607\pi$
$812$		0			0
$813$	15.2268	+	15.2268i	0.534026	+	0.534026i
$814$	−23.5162	+	14.5024i	−0.824243	+	0.508308i
$815$	16.9676	+	31.9028i	0.594351	+	1.11750i
$816$	−3.50772	−	30.0957i	−0.122795	−	1.05356i
$817$	0.253384	+	0.945642i	0.00886479	+	0.0330838i
$818$	−3.73643	−	12.4842i	−0.130641	−	0.436501i
$819$		0			0
$820$	−1.96149	−	0.477053i	−0.0684981	−	0.0166594i
$821$	15.7490	−	27.2781i	0.549645	−	0.952012i	−0.448654	−	0.893705i	$-0.648097\pi$
$821$	15.7490	−	27.2781i	0.549645	−	0.952012i	0.998299	−	0.0583068i	$-0.0185702\pi$
$822$	29.2323	−	30.9794i	1.01959	−	1.08053i
$823$	7.67895	+	2.05757i	0.267671	+	0.0717223i	0.390158	−	0.920748i	$-0.372420\pi$
$823$	7.67895	+	2.05757i	0.267671	+	0.0717223i	−0.122487	+	0.992470i	$0.539087\pi$
$824$	28.1248	+	13.1232i	0.979775	+	0.457168i
$825$	42.9076	−	37.3161i	1.49385	−	1.29918i
$826$		0			0
$827$	4.54203	+	4.54203i	0.157942	+	0.157942i	0.781654	−	0.623712i	$-0.214376\pi$
$827$	4.54203	+	4.54203i	0.157942	+	0.157942i	−0.623712	+	0.781654i	$0.714376\pi$
$828$	−6.50947	+	7.31223i	−0.226220	+	0.254118i
$829$	10.3234	−	5.96019i	0.358545	−	0.207006i	−0.309897	−	0.950770i	$-0.600295\pi$
$829$	10.3234	−	5.96019i	0.358545	−	0.207006i	0.668442	+	0.743764i	$0.266961\pi$
$830$	3.04492	+	3.08036i	0.105691	+	0.106921i
$831$	−55.9368	−	32.2951i	−1.94043	−	1.12031i
$832$	−31.3269	+	44.6928i	−1.08606	+	1.54944i
$833$		0			0
$834$	−10.0665	+	18.6658i	−0.348574	+	0.646345i
$835$	−14.2956	−	8.93064i	−0.494721	−	0.309057i
$836$	−5.76021	+	11.4649i	−0.199221	+	0.396521i
$837$	−14.2600	−	3.82095i	−0.492897	−	0.132071i
$838$	−6.04075	+	25.4787i	−0.208674	+	0.880146i
$839$	26.9117			0.929095			0.464548	−	0.885548i	$-0.346217\pi$
$839$	26.9117			0.929095			0.464548	+	0.885548i	$0.346217\pi$
$840$		0			0
$841$	28.3897			0.978957
$842$	8.33579	−	35.1587i	0.287270	−	1.21165i
$843$	2.03272	+	0.544667i	0.0700107	+	0.0187593i
$844$	−17.2715	+	34.3764i	−0.594509	+	1.18328i
$845$	−16.8812	−	73.0824i	−0.580730	−	2.51411i
$846$	−2.89236	+	5.36316i	−0.0994413	+	0.184389i
$847$		0			0
$848$	7.81725	−	3.10264i	0.268445	−	0.106545i
$849$	18.6296	+	10.7558i	0.639365	+	0.369138i
$850$	−1.08579	+	26.7431i	−0.0372423	+	0.917282i
$851$	−14.5035	+	8.37358i	−0.497173	+	0.287043i
$852$	−31.4865	+	35.3694i	−1.07871	+	1.21174i
$853$	17.1543	+	17.1543i	0.587353	+	0.587353i	0.936914	−	0.349561i	$-0.113669\pi$
$853$	17.1543	+	17.1543i	0.587353	+	0.587353i	−0.349561	+	0.936914i	$0.613669\pi$
$854$		0			0
$855$	−1.85467	+	1.72991i	−0.0634285	+	0.0591616i
$856$	−11.7857	+	25.2583i	−0.402825	+	0.863310i
$857$	35.4520	+	9.49933i	1.21102	+	0.324491i	0.807161	−	0.590331i	$-0.201003\pi$
$857$	35.4520	+	9.49933i	1.21102	+	0.324491i	0.403856	+	0.914823i	$0.367670\pi$
$858$	−75.3064	+	79.8070i	−2.57092	+	2.72457i
$859$	16.9027	−	29.2764i	0.576714	−	0.998897i	−0.419140	−	0.907922i	$-0.637668\pi$
$859$	16.9027	−	29.2764i	0.576714	−	0.998897i	0.995853	−	0.0909754i	$-0.0289985\pi$
$860$	−3.31295	+	2.01672i	−0.112970	+	0.0687695i
$861$		0			0
$862$	−4.22576	−	14.1192i	−0.143930	−	0.480902i
$863$	−8.34499	−	31.1439i	−0.284067	−	1.06015i	−0.949519	−	0.313710i	$-0.898428\pi$
$863$	−8.34499	−	31.1439i	−0.284067	−	1.06015i	0.665452	−	0.746441i	$-0.268239\pi$
$864$	−20.9877	−	8.34778i	−0.714015	−	0.283997i
$865$	−8.67368	+	4.61314i	−0.294914	+	0.156852i
$866$	−34.6937	+	21.3955i	−1.17894	+	0.727048i
$867$	−3.78176	−	3.78176i	−0.128435	−	0.128435i
$868$		0			0
$869$			31.0413i			1.05300i
$870$	−4.76767	−	1.30710i	−0.161639	−	0.0443149i
$871$	80.7146	−	46.6006i	2.73491	−	1.57900i
$872$	−2.51640	+	14.2508i	−0.0852160	+	0.482594i
$873$	9.29799	−	2.49139i	0.314689	−	0.0843208i
$874$	−3.69168	+	6.84531i	−0.124873	+	0.231546i
$875$		0			0
$876$	5.75806	−	3.78579i	0.194547	−	0.127910i
$877$	4.14155	+	15.4565i	0.139850	+	0.521928i	0.999931	+	0.0117699i	$0.00374657\pi$
$877$	4.14155	+	15.4565i	0.139850	+	0.521928i	−0.860080	+	0.510158i	$0.829587\pi$
$878$	−21.4319	−	20.2233i	−0.723293	−	0.682503i
$879$	27.0502	+	46.8523i	0.912380	+	1.58029i
$880$	−50.0043	−	9.12837i	−1.68565	−	0.307717i
$881$	−52.7104			−1.77586			−0.887929	−	0.459981i	$-0.847856\pi$
$881$	−52.7104			−1.77586			−0.887929	+	0.459981i	$0.847856\pi$
$882$		0			0
$883$	−5.34754	+	5.34754i	−0.179959	+	0.179959i	−0.791338	−	0.611379i	$-0.790615\pi$
$883$	−5.34754	+	5.34754i	−0.179959	+	0.179959i	0.611379	+	0.791338i	$0.290615\pi$
$884$	−2.99461	−	51.5603i	−0.100720	−	1.73416i
$885$	−19.4886	−	36.6426i	−0.655102	−	1.23173i
$886$	37.7655	−	1.09578i	1.26876	−	0.0368135i
$887$	44.6354	−	11.9600i	1.49871	−	0.401578i	0.586042	−	0.810281i	$-0.300685\pi$
$887$	44.6354	−	11.9600i	1.49871	−	0.401578i	0.912668	+	0.408703i	$0.134019\pi$
$888$	14.9025	+	12.5109i	0.500095	+	0.419838i
$889$		0			0
$890$	−15.0491	+	25.7209i	−0.504445	+	0.862167i
$891$	−54.1616	−	31.2702i	−1.81448	−	1.04759i
$892$	17.9298	−	5.93805i	0.600334	−	0.198820i
$893$	−1.25287	+	4.67578i	−0.0419258	+	0.156469i
$894$	−10.4437	+	6.44062i	−0.349291	+	0.215407i
$895$	−1.03573	−	1.11043i	−0.0346206	−	0.0371176i
$896$		0			0
$897$	−47.0313	+	47.0313i	−1.57033	+	1.57033i
$898$	−37.9540	−	8.99853i	−1.26654	−	0.300285i
$899$	1.44417	+	2.50137i	0.0481657	+	0.0834254i
$900$	−8.64286	−	5.12420i	−0.288095	−	0.170807i
$901$	−3.97937	+	6.89247i	−0.132572	+	0.229622i
$902$	1.04019	+	3.47550i	0.0346344	+	0.115721i
$903$		0			0
$904$	−7.91205	+	0.690264i	−0.263151	+	0.0229578i
$905$	17.1397	−	3.95907i	0.569744	−	0.131604i
$906$	1.16303	+	40.0833i	0.0386392	+	1.33168i
$907$	−15.4169	+	57.5368i	−0.511911	+	1.91048i	−0.112668	+	0.993633i	$0.535940\pi$
$907$	−15.4169	+	57.5368i	−0.511911	+	1.91048i	−0.399243	+	0.916845i	$0.630727\pi$
$908$	−36.3198	+	40.7988i	−1.20531	+	1.35396i
$909$			12.1186i			0.401948i
$910$		0			0
$911$			45.5865i			1.51035i	0.655524	+	0.755174i	$0.272448\pi$
$911$			45.5865i			1.51035i	−0.655524	+	0.755174i	$0.727552\pi$
$912$	8.94031	+	1.31254i	0.296043	+	0.0434626i
$913$	2.01463	−	7.51871i	0.0666746	−	0.248833i
$914$	1.94471	−	0.0564265i	0.0643252	−	0.00186642i
$915$	3.60247	−	5.76662i	0.119094	−	0.190639i
$916$	13.9043	+	21.1480i	0.459411	+	0.698748i
$917$		0			0
$918$	20.4764	−	6.12840i	0.675821	−	0.202267i
$919$	24.3756	−	42.2197i	0.804076	−	1.39270i	−0.112837	−	0.993613i	$-0.535994\pi$
$919$	24.3756	−	42.2197i	0.804076	−	1.39270i	0.916913	−	0.399087i	$-0.130673\pi$
$920$	−30.1372	−	6.40999i	−0.993594	−	0.211331i
$921$	−1.02802	−	1.78058i	−0.0338743	−	0.0586720i
$922$	5.76449	−	24.3135i	0.189843	−	0.800721i
$923$	−57.0761	+	57.0761i	−1.87868	+	1.87868i
$924$		0			0
$925$	−11.2794	−	12.9695i	−0.370865	−	0.426436i
$926$	5.83142	+	9.45589i	0.191632	+	0.310740i
$927$	2.85353	−	10.6495i	0.0937221	−	0.349776i
$928$	1.74864	+	4.05836i	0.0574020	+	0.133222i
$929$	−12.2678	−	7.08280i	−0.402493	−	0.232379i	0.285066	−	0.958508i	$-0.407984\pi$
$929$	−12.2678	−	7.08280i	−0.402493	−	0.232379i	−0.687559	+	0.726129i	$0.741318\pi$
$930$	5.92503	+	22.6356i	0.194290	+	0.742249i
$931$		0			0
$932$	33.9435	+	7.01455i	1.11186	+	0.229769i
$933$	25.7311	−	6.89463i	0.842398	−	0.225720i
$934$	−0.537782	−	18.5344i	−0.0175968	−	0.606463i
$935$	42.4678	−	22.5867i	1.38885	−	0.738665i
$936$	17.5699	+	8.19823i	0.574291	+	0.267968i
$937$	10.0190	−	10.0190i	0.327306	−	0.327306i	−0.524255	−	0.851561i	$-0.675656\pi$
$937$	10.0190	−	10.0190i	0.327306	−	0.327306i	0.851561	+	0.524255i	$0.175656\pi$
$938$		0			0
$939$	43.5184			1.42017
$940$	−19.1723	+	0.445292i	−0.625331	+	0.0145238i
$941$	−13.9028	−	24.0804i	−0.453219	−	0.784998i	0.545365	−	0.838199i	$-0.316391\pi$
$941$	−13.9028	−	24.0804i	−0.453219	−	0.784998i	−0.998584	+	0.0532008i	$0.983058\pi$
$942$	−9.70340	+	10.2833i	−0.316154	+	0.335049i
$943$	0.569149	+	2.12409i	0.0185341	+	0.0691700i
$944$	−14.7053	+	34.0603i	−0.478618	+	1.10857i
$945$		0			0
$946$	6.13491	+	3.30856i	0.199463	+	0.107570i
$947$	−28.0419	+	7.51380i	−0.911239	+	0.244166i	−0.683837	−	0.729635i	$-0.739690\pi$
$947$	−28.0419	+	7.51380i	−0.911239	+	0.244166i	−0.227402	+	0.973801i	$0.573023\pi$
$948$	20.7529	−	6.87300i	0.674022	−	0.223225i
$949$	10.1726	−	5.87317i	0.330217	−	0.190651i
$950$	−7.62000	−	2.37701i	−0.247225	−	0.0771204i
$951$		−	30.8915i		−	1.00172i
$952$		0			0
$953$	33.2622	+	33.2622i	1.07747	+	1.07747i	0.996736	+	0.0807336i	$0.0257263\pi$
$953$	33.2622	+	33.2622i	1.07747	+	1.07747i	0.0807336	+	0.996736i	$0.474274\pi$
$954$	−1.56828	−	2.54304i	−0.0507750	−	0.0823338i
$955$	−22.8450	−	6.98158i	−0.739247	−	0.225919i
$956$	−38.8946	−	19.5415i	−1.25794	−	0.632019i
$957$	2.29943	+	8.58159i	0.0743301	+	0.277404i
$958$	−3.44599	+	1.03136i	−0.111335	+	0.0333216i
$959$		0			0
$960$	4.96886	+	35.4519i	0.160369	+	1.14421i
$961$	−8.66472	+	15.0077i	−0.279507	+	0.484120i
$962$	24.1230	+	22.7626i	0.777758	+	0.733896i
$963$	9.56409	+	2.56269i	0.308198	+	0.0825815i
$964$	−2.41801	−	41.6327i	−0.0778790	−	1.34090i
$965$	−0.877752	+	25.2178i	−0.0282558	+	0.811788i
$966$		0			0
$967$	−8.70456	−	8.70456i	−0.279920	−	0.279920i	0.553157	−	0.833077i	$-0.313423\pi$
$967$	−8.70456	−	8.70456i	−0.279920	−	0.279920i	−0.833077	+	0.553157i	$0.813423\pi$
$968$	20.5884	+	56.6093i	0.661737	+	1.81949i
$969$	−7.40523	+	4.27541i	−0.237890	+	0.137346i
$970$	21.2979	+	21.5457i	0.683833	+	0.691792i
$971$	−43.9465	−	25.3725i	−1.41031	−	0.814243i	−0.414893	−	0.909870i	$-0.636181\pi$
$971$	−43.9465	−	25.3725i	−1.41031	−	0.814243i	−0.995417	+	0.0956276i	$0.969514\pi$
$972$	−4.06540	+	19.6725i	−0.130398	+	0.630997i
$973$		0			0
$974$	4.58151	+	2.47081i	0.146801	+	0.0791698i
$975$	−56.6020	−	38.1598i	−1.81271	−	1.22209i
$976$	−6.03707	+	0.703636i	−0.193242	+	0.0225228i
$977$	0.164491	+	0.0440753i	0.00526254	+	0.00141009i	0.261449	−	0.965217i	$-0.415800\pi$
$977$	0.164491	+	0.0440753i	0.00526254	+	0.00141009i	−0.256187	+	0.966627i	$0.582466\pi$
$978$	−44.5003	−	10.5506i	−1.42296	−	0.337371i
$979$	53.5546			1.71161
$980$		0			0
$981$	5.14078			0.164133
$982$	30.7427	+	7.28879i	0.981038	+	0.232595i
$983$	21.7109	+	5.81741i	0.692469	+	0.185546i	0.587855	−	0.808966i	$-0.299973\pi$
$983$	21.7109	+	5.81741i	0.692469	+	0.185546i	0.104614	+	0.994513i	$0.466639\pi$
$984$	2.09325	−	1.46495i	0.0667305	−	0.0467009i
$985$	−5.52220	+	8.83960i	−0.175952	+	0.281653i
$986$	−3.68059	−	1.98494i	−0.117214	−	0.0632135i
$987$		0			0
$988$	15.0840	+	3.11715i	0.479885	+	0.0991699i
$989$	3.65898	+	2.11251i	0.116349	+	0.0671740i
$990$	−0.104471	+	18.0568i	−0.00332030	+	0.573883i
$991$	−12.0154	+	6.93708i	−0.381681	+	0.220364i	−0.678549	−	0.734555i	$-0.737391\pi$
$991$	−12.0154	+	6.93708i	−0.381681	+	0.220364i	0.296869	+	0.954918i	$0.404058\pi$
$992$	12.4967	−	16.7717i	0.396771	−	0.532502i
$993$	−37.4498	−	37.4498i	−1.18843	−	1.18843i
$994$		0			0
$995$	14.6082	+	15.6618i	0.463112	+	0.496514i
$996$	−5.47275	+	0.317856i	−0.173411	+	0.0100716i
$997$	−15.2402	−	4.08361i	−0.482663	−	0.129329i	0.00927934	−	0.999957i	$-0.497046\pi$
$997$	−15.2402	−	4.08361i	−0.482663	−	0.129329i	−0.491942	+	0.870628i	$0.663713\pi$
$998$	10.2411	+	9.66359i	0.324178	+	0.305896i
$999$	−6.86297	+	11.8870i	−0.217135	+	0.376089i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.n.863.16		112
4.3	odd	2	inner	980.2.x.n.863.9		112
5.2	odd	4	inner	980.2.x.n.667.28		112
7.2	even	3		980.2.k.m.883.5	yes	56
7.3	odd	6	inner	980.2.x.n.263.22		112
7.4	even	3	inner	980.2.x.n.263.21		112
7.5	odd	6		980.2.k.m.883.6	yes	56
7.6	odd	2	inner	980.2.x.n.863.15		112
20.7	even	4	inner	980.2.x.n.667.21		112
28.3	even	6	inner	980.2.x.n.263.27		112
28.11	odd	6	inner	980.2.x.n.263.28		112
28.19	even	6		980.2.k.m.883.11	yes	56
28.23	odd	6		980.2.k.m.883.12	yes	56
28.27	even	2	inner	980.2.x.n.863.10		112
35.2	odd	12		980.2.k.m.687.12	yes	56
35.12	even	12		980.2.k.m.687.11	yes	56
35.17	even	12	inner	980.2.x.n.67.10		112
35.27	even	4	inner	980.2.x.n.667.27		112
35.32	odd	12	inner	980.2.x.n.67.9		112
140.27	odd	4	inner	980.2.x.n.667.22		112
140.47	odd	12		980.2.k.m.687.6	yes	56
140.67	even	12	inner	980.2.x.n.67.16		112
140.87	odd	12	inner	980.2.x.n.67.15		112
140.107	even	12		980.2.k.m.687.5	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.k.m.687.5	✓	56	140.107	even	12
980.2.k.m.687.6	yes	56	140.47	odd	12
980.2.k.m.687.11	yes	56	35.12	even	12
980.2.k.m.687.12	yes	56	35.2	odd	12
980.2.k.m.883.5	yes	56	7.2	even	3
980.2.k.m.883.6	yes	56	7.5	odd	6
980.2.k.m.883.11	yes	56	28.19	even	6
980.2.k.m.883.12	yes	56	28.23	odd	6
980.2.x.n.67.9		112	35.32	odd	12	inner
980.2.x.n.67.10		112	35.17	even	12	inner
980.2.x.n.67.15		112	140.87	odd	12	inner
980.2.x.n.67.16		112	140.67	even	12	inner
980.2.x.n.263.21		112	7.4	even	3	inner
980.2.x.n.263.22		112	7.3	odd	6	inner
980.2.x.n.263.27		112	28.3	even	6	inner
980.2.x.n.263.28		112	28.11	odd	6	inner
980.2.x.n.667.21		112	20.7	even	4	inner
980.2.x.n.667.22		112	140.27	odd	4	inner
980.2.x.n.667.27		112	35.27	even	4	inner
980.2.x.n.667.28		112	5.2	odd	4	inner
980.2.x.n.863.9		112	4.3	odd	2	inner
980.2.x.n.863.10		112	28.27	even	2	inner
980.2.x.n.863.15		112	7.6	odd	2	inner
980.2.x.n.863.16		112	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.326252 - 1.37607i) q^{2} +(1.93300 + 0.517947i) q^{3} +(-1.78712 - 0.897890i) q^{4} +(-2.17870 + 0.503254i) q^{5} +(1.34338 - 2.49096i) q^{6} +(-1.81861 + 2.16626i) q^{8} +(0.870157 + 0.502386i) q^{9} +(-0.0182956 + 3.16222i) q^{10} +(4.92166 - 2.84152i) q^{11} +(-2.98945 - 2.66126i) q^{12} +(-4.82411 - 4.82411i) q^{13} +(-4.47209 - 0.155660i) q^{15} +(2.38759 + 3.20927i) q^{16} +(-3.65619 - 0.979673i) q^{17} +(0.975207 - 1.03349i) q^{18} +(0.564422 - 0.977608i) q^{19} +(4.34546 + 1.05686i) q^{20} +(-2.30442 - 7.69959i) q^{22} +(-1.26089 - 4.70570i) q^{23} +(-4.63738 + 3.24544i) q^{24} +(4.49347 - 2.19288i) q^{25} +(-8.21217 + 5.06442i) q^{26} +(-2.82336 - 2.82336i) q^{27} +0.781186i q^{29} +(-1.67323 + 6.10312i) q^{30} +(3.20202 - 1.84869i) q^{31} +(5.19513 - 2.23845i) q^{32} +(10.9853 - 2.94351i) q^{33} +(-2.54094 + 4.71154i) q^{34} +(-1.10399 - 1.67913i) q^{36} +(-0.889727 - 3.32051i) q^{37} +(-1.16111 - 1.09563i) q^{38} +(-6.82639 - 11.8236i) q^{39} +(2.87203 - 5.63484i) q^{40} -0.451387 q^{41} +(-0.613245 + 0.613245i) q^{43} +(-11.3470 + 0.659028i) q^{44} +(-2.14864 - 0.656638i) q^{45} +(-6.88673 + 0.199821i) q^{46} +(-4.14209 + 1.10987i) q^{47} +(2.95298 + 7.44018i) q^{48} +(-1.55154 - 6.89875i) q^{50} +(-6.56001 - 3.78742i) q^{51} +(4.28974 + 12.9528i) q^{52} +(0.544196 - 2.03097i) q^{53} +(-4.80626 + 2.96401i) q^{54} +(-9.29282 + 8.66767i) q^{55} +(1.59738 - 1.59738i) q^{57} +(1.07496 + 0.254864i) q^{58} +(4.63740 + 8.03221i) q^{59} +(7.85240 + 4.29363i) q^{60} +(-0.759742 + 1.31591i) q^{61} +(-1.49925 - 5.00933i) q^{62} +(-1.38533 - 7.87914i) q^{64} +(12.9380 + 8.08254i) q^{65} +(-0.466477 - 16.0769i) q^{66} +(-3.53578 + 13.1957i) q^{67} +(5.65441 + 5.03365i) q^{68} -9.74921i q^{69} -11.8314i q^{71} +(-2.67077 + 0.971341i) q^{72} +(-0.445622 + 1.66308i) q^{73} +(-4.85951 + 0.141001i) q^{74} +(9.82169 - 1.91146i) q^{75} +(-1.88647 + 1.24031i) q^{76} +(-18.4973 + 5.53607i) q^{78} +(-2.73105 + 4.73031i) q^{79} +(-6.81692 - 5.79048i) q^{80} +(-5.50237 - 9.53039i) q^{81} +(-0.147266 + 0.621139i) q^{82} +(0.968508 - 0.968508i) q^{83} +(8.45877 + 0.294423i) q^{85} +(0.643793 + 1.04394i) q^{86} +(-0.404613 + 1.51003i) q^{87} +(-2.79511 + 15.8292i) q^{88} +(8.16106 + 4.71179i) q^{89} +(-1.60458 + 2.74244i) q^{90} +(-1.97184 + 9.54179i) q^{92} +(7.14703 - 1.91504i) q^{93} +(0.175888 + 6.06189i) q^{94} +(-0.737723 + 2.41396i) q^{95} +(11.2016 - 1.63613i) q^{96} +(6.77428 - 6.77428i) q^{97} +5.71016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 4 q^{2} - 32 q^{8} - 32 q^{16} + 40 q^{22} - 32 q^{25} + 28 q^{30} + 64 q^{32} + 32 q^{36} + 8 q^{37} + 184 q^{46} - 24 q^{50} - 96 q^{53} - 16 q^{57} - 124 q^{58} - 8 q^{60} + 120 q^{65} + 80 q^{72}+ \cdots + 176 q^{93}+O(q^{100}) \) 112 * q + 4 * q^2 - 32 * q^8 - 32 * q^16 + 40 * q^22 - 32 * q^25 + 28 * q^30 + 64 * q^32 + 32 * q^36 + 8 * q^37 + 184 * q^46 - 24 * q^50 - 96 * q^53 - 16 * q^57 - 124 * q^58 - 8 * q^60 + 120 * q^65 + 80 * q^72 - 72 * q^78 + 72 * q^81 + 192 * q^85 - 104 * q^86 - 48 * q^88 - 304 * q^92 + 176 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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