LMFDB - Embedded newform 980.2.x.n.667.2

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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			667.2
Character	$\chi$	$=$	980.667
Dual form			980.2.x.n.263.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41417 - 0.0109473i) q^{2} +(0.646443 - 2.41256i) q^{3} +(1.99976 + 0.0309628i) q^{4} +(0.0689030 - 2.23501i) q^{5} +(-0.940592 + 3.40469i) q^{6} +(-2.82766 - 0.0656787i) q^{8} +(-2.80447 - 1.61916i) q^{9} +O(q^{10})$	\(q+(-1.41417 - 0.0109473i) q^{2} +(0.646443 - 2.41256i) q^{3} +(1.99976 + 0.0309628i) q^{4} +(0.0689030 - 2.23501i) q^{5} +(-0.940592 + 3.40469i) q^{6} +(-2.82766 - 0.0656787i) q^{8} +(-2.80447 - 1.61916i) q^{9} +(-0.121908 + 3.15993i) q^{10} +(2.41093 - 1.39195i) q^{11} +(1.36743 - 4.80452i) q^{12} +(0.850111 - 0.850111i) q^{13} +(-5.34754 - 1.61104i) q^{15} +(3.99808 + 0.123836i) q^{16} +(-0.545228 + 2.03482i) q^{17} +(3.94828 + 2.32048i) q^{18} +(2.35869 - 4.08538i) q^{19} +(0.206991 - 4.46734i) q^{20} +(-3.42470 + 1.94206i) q^{22} +(-7.67188 + 2.05567i) q^{23} +(-1.98638 + 6.77945i) q^{24} +(-4.99050 - 0.307997i) q^{25} +(-1.21151 + 1.19290i) q^{26} +(-0.420915 + 0.420915i) q^{27} -9.15187i q^{29} +(7.54470 + 2.33682i) q^{30} +(8.84560 - 5.10701i) q^{31} +(-5.65262 - 0.218894i) q^{32} +(-1.79963 - 6.71632i) q^{33} +(0.793322 - 2.87161i) q^{34} +(-5.55814 - 3.32477i) q^{36} +(-7.20298 + 1.93003i) q^{37} +(-3.38032 + 5.75160i) q^{38} +(-1.50139 - 2.60049i) q^{39} +(-0.341627 + 6.31532i) q^{40} -8.44310 q^{41} +(4.72474 + 4.72474i) q^{43} +(4.86437 - 2.70892i) q^{44} +(-3.81208 + 6.15645i) q^{45} +(10.8719 - 2.82309i) q^{46} +(0.509705 + 1.90224i) q^{47} +(2.88330 - 9.56556i) q^{48} +(7.05406 + 0.490193i) q^{50} +(4.55666 + 2.63079i) q^{51} +(1.72634 - 1.67370i) q^{52} +(3.56281 + 0.954652i) q^{53} +(0.599854 - 0.590638i) q^{54} +(-2.94489 - 5.48435i) q^{55} +(-8.33145 - 8.33145i) q^{57} +(-0.100188 + 12.9423i) q^{58} +(5.07401 + 8.78844i) q^{59} +(-10.6439 - 3.38726i) q^{60} +(-2.80816 + 4.86388i) q^{61} +(-12.5651 + 7.12535i) q^{62} +(7.99137 + 0.371434i) q^{64} +(-1.84143 - 1.95858i) q^{65} +(2.47146 + 9.51772i) q^{66} +(3.28874 + 0.881215i) q^{67} +(-1.15333 + 4.05227i) q^{68} +19.8377i q^{69} +4.45800i q^{71} +(7.82377 + 4.76265i) q^{72} +(3.56653 + 0.955649i) q^{73} +(10.2074 - 2.65054i) q^{74} +(-3.96914 + 11.8408i) q^{75} +(4.84332 - 8.09674i) q^{76} +(2.09476 + 3.69398i) q^{78} +(-4.46895 + 7.74045i) q^{79} +(0.552255 - 8.92721i) q^{80} +(-4.11411 - 7.12584i) q^{81} +(11.9400 + 0.0924293i) q^{82} +(0.940405 + 0.940405i) q^{83} +(4.51026 + 1.35879i) q^{85} +(-6.62987 - 6.73331i) q^{86} +(-22.0794 - 5.91616i) q^{87} +(-6.90871 + 3.77762i) q^{88} +(4.46303 + 2.57673i) q^{89} +(5.45833 - 8.66455i) q^{90} +(-15.4056 + 3.87331i) q^{92} +(-6.60279 - 24.6419i) q^{93} +(-0.699986 - 2.69568i) q^{94} +(-8.96832 - 5.55319i) q^{95} +(-4.18219 + 13.4958i) q^{96} +(-1.28159 - 1.28159i) q^{97} -9.01518 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 4 q^{2} - 32 q^{8}+O(q^{10}) $ 112 * q + 4 * q^2 - 32 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.41417	−	0.0109473i	−0.999970	−	0.00774092i
$2$	−1.41417	−	0.0109473i	−0.999970	−	0.00774092i
$3$	0.646443	−	2.41256i	0.373224	−	1.39289i	−0.482698	−	0.875787i	$-0.660343\pi$
$3$	0.646443	−	2.41256i	0.373224	−	1.39289i	0.855922	−	0.517105i	$-0.172990\pi$
$4$	1.99976	+	0.0309628i	0.999880	+	0.0154814i
$5$	0.0689030	−	2.23501i	0.0308144	−	0.999525i
$5$	0.0689030	−	2.23501i	0.0308144	−	0.999525i
$6$	−0.940592	+	3.40469i	−0.383995	+	1.38996i
$7$		0			0
$7$		0			0
$8$	−2.82766	−	0.0656787i	−0.999730	−	0.0232209i
$9$	−2.80447	−	1.61916i	−0.934825	−	0.539721i
$10$	−0.121908	+	3.15993i	−0.0385507	+	0.999257i
$11$	2.41093	−	1.39195i	0.726922	−	0.419688i	−0.0903733	−	0.995908i	$-0.528806\pi$
$11$	2.41093	−	1.39195i	0.726922	−	0.419688i	0.817295	+	0.576220i	$0.195473\pi$
$12$	1.36743	−	4.80452i	0.394743	−	1.38695i
$13$	0.850111	−	0.850111i	0.235778	−	0.235778i	−0.579321	−	0.815099i	$-0.696682\pi$
$13$	0.850111	−	0.850111i	0.235778	−	0.235778i	0.815099	+	0.579321i	$0.196682\pi$
$14$		0			0
$15$	−5.34754	−	1.61104i	−1.38073	−	0.415968i
$16$	3.99808	+	0.123836i	0.999521	+	0.0309591i
$17$	−0.545228	+	2.03482i	−0.132237	+	0.493516i	−0.999994	−	0.00347314i	$-0.998894\pi$
$17$	−0.545228	+	2.03482i	−0.132237	+	0.493516i	0.867757	+	0.496989i	$0.165561\pi$
$18$	3.94828	+	2.32048i	0.930619	+	0.546942i
$19$	2.35869	−	4.08538i	0.541121	−	0.937250i	−0.457719	−	0.889097i	$-0.651333\pi$
$19$	2.35869	−	4.08538i	0.541121	−	0.937250i	0.998840	−	0.0481525i	$-0.0153333\pi$
$20$	0.206991	−	4.46734i	0.0462847	−	0.998928i
$21$		0			0
$22$	−3.42470	+	1.94206i	−0.730149	+	0.414049i
$23$	−7.67188	+	2.05567i	−1.59970	+	0.428638i	−0.944951	−	0.327211i	$-0.893891\pi$
$23$	−7.67188	+	2.05567i	−1.59970	+	0.428638i	−0.654747	+	0.755848i	$0.727225\pi$
$24$	−1.98638	+	6.77945i	−0.405468	+	1.38385i
$25$	−4.99050	−	0.307997i	−0.998101	−	0.0615994i
$26$	−1.21151	+	1.19290i	−0.237596	+	0.233946i
$27$	−0.420915	+	0.420915i	−0.0810051	+	0.0810051i
$28$		0			0
$29$		−	9.15187i		−	1.69946i	−0.527218	−	0.849730i	$-0.676765\pi$
$29$		−	9.15187i		−	1.69946i	0.527218	−	0.849730i	$-0.323235\pi$
$30$	7.54470	+	2.33682i	1.37747	+	0.426644i
$31$	8.84560	−	5.10701i	1.58872	−	0.917246i	0.595198	−	0.803579i	$-0.297073\pi$
$31$	8.84560	−	5.10701i	1.58872	−	0.917246i	0.993519	−	0.113668i	$-0.0362599\pi$
$32$	−5.65262	−	0.218894i	−0.999251	−	0.0386953i
$33$	−1.79963	−	6.71632i	−0.313276	−	1.16916i
$34$	0.793322	−	2.87161i	0.136054	−	0.492478i
$35$		0			0
$36$	−5.55814	−	3.32477i	−0.926357	−	0.554129i
$37$	−7.20298	+	1.93003i	−1.18416	+	0.317295i	−0.796576	−	0.604538i	$-0.793358\pi$
$37$	−7.20298	+	1.93003i	−1.18416	+	0.317295i	−0.387586	+	0.921834i	$0.626691\pi$
$38$	−3.38032	+	5.75160i	−0.548360	+	0.933033i
$39$	−1.50139	−	2.60049i	−0.240415	−	0.416412i
$40$	−0.341627	+	6.31532i	−0.0540159	+	0.998540i
$41$	−8.44310			−1.31859			−0.659295	−	0.751884i	$-0.729145\pi$
$41$	−8.44310			−1.31859			−0.659295	+	0.751884i	$0.729145\pi$
$42$		0			0
$43$	4.72474	+	4.72474i	0.720516	+	0.720516i	0.968710	−	0.248194i	$-0.0798371\pi$
$43$	4.72474	+	4.72474i	0.720516	+	0.720516i	−0.248194	+	0.968710i	$0.579837\pi$
$44$	4.86437	−	2.70892i	0.733332	−	0.408384i
$45$	−3.81208	+	6.15645i	−0.568271	+	0.917750i
$46$	10.8719	−	2.82309i	1.60297	−	0.416242i
$47$	0.509705	+	1.90224i	0.0743481	+	0.277471i	0.993085	−	0.117400i	$-0.0374560\pi$
$47$	0.509705	+	1.90224i	0.0743481	+	0.277471i	−0.918737	+	0.394871i	$0.870789\pi$
$48$	2.88330	−	9.56556i	0.416168	−	1.38067i
$49$		0			0
$50$	7.05406	+	0.490193i	0.997594	+	0.0693238i
$51$	4.55666	+	2.63079i	0.638060	+	0.368384i
$52$	1.72634	−	1.67370i	0.239400	−	0.232100i
$53$	3.56281	+	0.954652i	0.489390	+	0.131132i	0.495071	−	0.868852i	$-0.335142\pi$
$53$	3.56281	+	0.954652i	0.489390	+	0.131132i	−0.00568179	+	0.999984i	$0.501809\pi$
$54$	0.599854	−	0.590638i	0.0816297	−	0.0803756i
$55$	−2.94489	−	5.48435i	−0.397090	−	0.739509i
$56$		0			0
$57$	−8.33145	−	8.33145i	−1.10353	−	1.10353i
$58$	−0.100188	+	12.9423i	−0.0131554	+	1.69941i
$59$	5.07401	+	8.78844i	0.660580	+	1.14416i	0.980464	+	0.196701i	$0.0630227\pi$
$59$	5.07401	+	8.78844i	0.660580	+	1.14416i	−0.319884	+	0.947457i	$0.603644\pi$
$60$	−10.6439	−	3.38726i	−1.37412	−	0.437294i
$61$	−2.80816	+	4.86388i	−0.359548	+	0.622756i	−0.987885	−	0.155185i	$-0.950403\pi$
$61$	−2.80816	+	4.86388i	−0.359548	+	0.622756i	0.628337	+	0.777941i	$0.283736\pi$
$62$	−12.5651	+	7.12535i	−1.59577	+	0.904921i
$63$		0			0
$64$	7.99137	+	0.371434i	0.998922	+	0.0464293i
$65$	−1.84143	−	1.95858i	−0.228401	−	0.242932i
$66$	2.47146	+	9.51772i	0.304216	+	1.17155i
$67$	3.28874	+	0.881215i	0.401783	+	0.107658i	0.454051	−	0.890976i	$-0.349978\pi$
$67$	3.28874	+	0.881215i	0.401783	+	0.107658i	−0.0522678	+	0.998633i	$0.516645\pi$
$68$	−1.15333	+	4.05227i	−0.139862	+	0.491410i
$69$			19.8377i			2.38818i
$70$		0			0
$71$			4.45800i			0.529067i	0.964377	+	0.264533i	$0.0852180\pi$
$71$			4.45800i			0.529067i	−0.964377	+	0.264533i	$0.914782\pi$
$72$	7.82377	+	4.76265i	0.922040	+	0.561283i
$73$	3.56653	+	0.955649i	0.417431	+	0.111850i	0.461420	−	0.887182i	$-0.347340\pi$
$73$	3.56653	+	0.955649i	0.417431	+	0.111850i	−0.0439893	+	0.999032i	$0.514007\pi$
$74$	10.2074	−	2.65054i	1.18658	−	0.308119i
$75$	−3.96914	+	11.8408i	−0.458317	+	1.36726i
$76$	4.84332	−	8.09674i	0.555566	−	0.928760i
$77$		0			0
$78$	2.09476	+	3.69398i	0.237185	+	0.418260i
$79$	−4.46895	+	7.74045i	−0.502796	+	0.870868i	0.497199	+	0.867637i	$0.334362\pi$
$79$	−4.46895	+	7.74045i	−0.502796	+	0.870868i	−0.999995	+	0.00323158i	$0.998971\pi$
$80$	0.552255	−	8.92721i	0.0617439	−	0.998092i
$81$	−4.11411	−	7.12584i	−0.457123	−	0.791760i
$82$	11.9400	+	0.0924293i	1.31855	+	0.0102071i
$83$	0.940405	+	0.940405i	0.103223	+	0.103223i	0.756832	−	0.653609i	$-0.226746\pi$
$83$	0.940405	+	0.940405i	0.103223	+	0.103223i	−0.653609	+	0.756832i	$0.726746\pi$
$84$		0			0
$85$	4.51026	+	1.35879i	0.489207	+	0.147382i
$86$	−6.62987	−	6.73331i	−0.714917	−	0.726072i
$87$	−22.0794	−	5.91616i	−2.36716	−	0.634279i
$88$	−6.90871	+	3.77762i	−0.736471	+	0.402695i
$89$	4.46303	+	2.57673i	0.473080	+	0.273133i	0.717528	−	0.696529i	$-0.245273\pi$
$89$	4.46303	+	2.57673i	0.473080	+	0.273133i	−0.244448	+	0.969662i	$0.578607\pi$
$90$	5.45833	−	8.66455i	0.575358	−	0.913323i
$91$		0			0
$92$	−15.4056	+	3.87331i	−1.60614	+	0.403821i
$93$	−6.60279	−	24.6419i	−0.684677	−	2.55525i
$94$	−0.699986	−	2.69568i	−0.0721980	−	0.278038i
$95$	−8.96832	−	5.55319i	−0.920130	−	0.569745i
$96$	−4.18219	+	13.4958i	−0.426843	+	1.37741i
$97$	−1.28159	−	1.28159i	−0.130126	−	0.130126i	0.639044	−	0.769170i	$-0.279330\pi$
$97$	−1.28159	−	1.28159i	−0.130126	−	0.130126i	−0.769170	+	0.639044i	$0.779330\pi$
$98$		0			0
$99$	−9.01518			−0.906059
$100$	−9.97028	−	0.770440i	−0.997028	−	0.0770440i
$101$	−6.27596	−	10.8703i	−0.624481	−	1.08163i	−0.988641	−	0.150297i	$-0.951977\pi$
$101$	−6.27596	−	10.8703i	−0.624481	−	1.08163i	0.364160	−	0.931336i	$-0.381356\pi$
$102$	−6.41510	−	3.77027i	−0.635189	−	0.373312i
$103$	−2.06460	+	0.553208i	−0.203431	+	0.0545092i	−0.359096	−	0.933301i	$-0.616915\pi$
$103$	−2.06460	+	0.553208i	−0.203431	+	0.0545092i	0.155665	+	0.987810i	$0.450248\pi$
$104$	−2.45966	+	2.34799i	−0.241190	+	0.230240i
$105$		0			0
$106$	−5.02797	−	1.38904i	−0.488360	−	0.134916i
$107$	−2.60228	−	9.71185i	−0.251572	−	0.938880i	−0.969965	−	0.243243i	$-0.921789\pi$
$107$	−2.60228	−	9.71185i	−0.251572	−	0.938880i	0.718393	−	0.695637i	$-0.244878\pi$
$108$	−0.854762	+	0.828696i	−0.0822495	+	0.0797413i
$109$	5.20030	−	3.00240i	0.498099	−	0.287577i	−0.229829	−	0.973231i	$-0.573817\pi$
$109$	5.20030	−	3.00240i	0.498099	−	0.287577i	0.727928	+	0.685654i	$0.240483\pi$
$110$	4.10455	+	7.78804i	0.391353	+	0.742561i
$111$			18.6253i			1.76783i
$112$		0			0
$113$	2.55380	−	2.55380i	0.240241	−	0.240241i	−0.576709	−	0.816950i	$-0.695663\pi$
$113$	2.55380	−	2.55380i	0.240241	−	0.240241i	0.816950	+	0.576709i	$0.195663\pi$
$114$	11.6909	+	11.8733i	1.09495	+	1.11204i
$115$	4.06583	+	17.2883i	0.379141	+	1.61215i
$116$	0.283367	−	18.3016i	0.0263100	−	1.69926i
$117$	−3.76058	+	1.00765i	−0.347666	+	0.0931568i
$118$	−7.07931	−	12.4839i	−0.651703	−	1.14924i
$119$		0			0
$120$	15.0152	+	4.90669i	1.37070	+	0.447918i
$121$	−1.62496	+	2.81451i	−0.147723	+	0.255864i
$122$	4.02447	−	6.84762i	0.364358	−	0.619954i
$123$	−5.45798	+	20.3695i	−0.492130	+	1.83665i
$124$	17.8472	−	9.93891i	1.60273	−	0.892541i
$125$	−1.03224	+	11.1326i	−0.0923260	+	0.995729i
$126$		0			0
$127$	6.22515	−	6.22515i	0.552393	−	0.552393i	−0.374738	−	0.927131i	$-0.622267\pi$
$127$	6.22515	−	6.22515i	0.552393	−	0.552393i	0.927131	+	0.374738i	$0.122267\pi$
$128$	−11.2971	−	0.612756i	−0.998532	−	0.0541605i
$129$	14.4530	−	8.34444i	1.27251	−	0.734687i
$130$	2.58265	+	2.78992i	0.226514	+	0.244692i
$131$	−8.67385	−	5.00785i	−0.757838	−	0.437538i	0.0706810	−	0.997499i	$-0.477483\pi$
$131$	−8.67385	−	5.00785i	−0.757838	−	0.437538i	−0.828519	+	0.559961i	$0.810816\pi$
$132$	−3.39088	−	13.4867i	−0.295138	−	1.17387i
$133$		0			0
$134$	−4.64119	−	1.28219i	−0.400938	−	0.110765i
$135$	0.911745	+	0.969750i	0.0784705	+	0.0834628i
$136$	1.67537	−	5.71797i	0.143661	−	0.490312i
$137$	−3.63849	+	13.5790i	−0.310857	+	1.16014i	0.616927	+	0.787020i	$0.288377\pi$
$137$	−3.63849	+	13.5790i	−0.310857	+	1.16014i	−0.927785	+	0.373116i	$0.878289\pi$
$138$	0.217170	−	28.0540i	0.0184867	−	2.38811i
$139$	18.2497			1.54792			0.773960	−	0.633235i	$-0.218273\pi$
$139$	18.2497			1.54792			0.773960	+	0.633235i	$0.218273\pi$
$140$		0			0
$141$	4.91877			0.414235
$142$	0.0488031	−	6.30437i	0.00409547	−	0.529051i
$143$	0.866244	−	3.23287i	0.0724389	−	0.270346i
$144$	−11.0120	−	6.82085i	−0.917667	−	0.568404i
$145$	−20.4545	−	0.630591i	−1.69865	−	0.0523678i
$146$	−5.03322	−	1.39050i	−0.416552	−	0.115078i
$147$		0			0
$148$	−14.4640	+	3.63658i	−1.18893	+	0.298925i
$149$	−10.2804	−	5.93537i	−0.842200	−	0.486244i	0.0158115	−	0.999875i	$-0.494967\pi$
$149$	−10.2804	−	5.93537i	−0.842200	−	0.486244i	−0.858011	+	0.513631i	$0.828300\pi$
$150$	5.74267	−	16.7014i	0.468887	−	1.36367i
$151$	−6.36089	+	3.67246i	−0.517642	+	0.298861i	−0.735969	−	0.677015i	$-0.763273\pi$
$151$	−6.36089	+	3.67246i	−0.517642	+	0.298861i	0.218327	+	0.975876i	$0.429940\pi$
$152$	−6.93791	+	11.3972i	−0.562739	+	0.924432i
$153$	4.82378	−	4.82378i	0.389980	−	0.389980i
$154$		0			0
$155$	−10.8047	−	20.1219i	−0.867855	−	1.61623i
$156$	−2.92191	−	5.24685i	−0.233940	−	0.420084i
$157$	0.0850838	−	0.317537i	0.00679043	−	0.0253422i	−0.962447	−	0.271468i	$-0.912491\pi$
$157$	0.0850838	−	0.317537i	0.00679043	−	0.0253422i	0.969238	+	0.246126i	$0.0791576\pi$
$158$	6.40460	−	10.8974i	0.509522	−	0.866950i
$159$	4.60631	−	7.97836i	0.365304	−	0.632725i
$160$	−0.878711	+	12.6186i	−0.0694682	+	0.997584i
$161$		0			0
$162$	5.74004	+	10.1222i	0.450980	+	0.795275i
$163$	18.6149	−	4.98785i	1.45803	−	0.390678i	0.559222	−	0.829018i	$-0.311100\pi$
$163$	18.6149	−	4.98785i	1.45803	−	0.390678i	0.898809	+	0.438340i	$0.144433\pi$
$164$	−16.8842	−	0.261422i	−1.31843	−	0.0204136i
$165$	−15.1350	+	3.55941i	−1.17826	+	0.277100i
$166$	−1.31960	−	1.34019i	−0.102421	−	0.104019i
$167$	12.0798	−	12.0798i	0.934765	−	0.934765i	−0.0632340	−	0.997999i	$-0.520141\pi$
$167$	12.0798	−	12.0798i	0.934765	−	0.934765i	0.997999	+	0.0632340i	$0.0201415\pi$
$168$		0			0
$169$			11.5546i			0.888817i
$170$	−6.36341	−	1.97094i	−0.488051	−	0.151164i
$171$	−13.2298	+	7.63822i	−1.01171	+	0.584109i
$172$	9.30206	+	9.59464i	0.709275	+	0.731584i
$173$	−3.80222	−	14.1901i	−0.289077	−	1.07885i	−0.945808	−	0.324726i	$-0.894728\pi$
$173$	−3.80222	−	14.1901i	−0.289077	−	1.07885i	0.656731	−	0.754125i	$-0.271939\pi$
$174$	31.1593	+	8.60818i	2.36218	+	0.652584i
$175$		0			0
$176$	9.81146	−	5.26657i	0.739566	−	0.396982i
$177$	24.4827	−	6.56012i	1.84023	−	0.493088i
$178$	−6.28328	−	3.69280i	−0.470952	−	0.276787i
$179$	1.76716	+	3.06080i	0.132083	+	0.228775i	0.924480	−	0.381232i	$-0.124500\pi$
$179$	1.76716	+	3.06080i	0.132083	+	0.228775i	−0.792396	+	0.610007i	$0.791167\pi$
$180$	−7.81386	+	12.1934i	−0.582411	+	0.908842i
$181$	2.70410			0.200994			0.100497	−	0.994937i	$-0.467957\pi$
$181$	2.70410			0.200994			0.100497	+	0.994937i	$0.467957\pi$
$182$		0			0
$183$	9.91908	+	9.91908i	0.733240	+	0.733240i
$184$	21.8285	−	5.30888i	1.60922	−	0.391376i
$185$	3.81733	+	16.2317i	0.280655	+	1.19338i
$186$	9.06771	+	34.9202i	0.664876	+	2.56047i
$187$	1.51786	+	5.66473i	0.110997	+	0.414246i
$188$	0.960389	+	3.81982i	0.0700436	+	0.278589i
$189$		0			0
$190$	12.6219	+	7.95134i	0.915692	+	0.576851i
$191$	10.9962	+	6.34865i	0.795656	+	0.459372i	0.841950	−	0.539556i	$-0.181408\pi$
$191$	10.9962	+	6.34865i	0.795656	+	0.459372i	−0.0462938	+	0.998928i	$0.514741\pi$
$192$	6.06208	−	19.0395i	0.437493	−	1.37406i
$193$	−2.97021	−	0.795866i	−0.213801	−	0.0572877i	0.150329	−	0.988636i	$-0.451967\pi$
$193$	−2.97021	−	0.795866i	−0.213801	−	0.0572877i	−0.364129	+	0.931348i	$0.618633\pi$
$194$	1.79835	+	1.82641i	0.129114	+	0.131129i
$195$	−5.91556	+	3.17644i	−0.423622	+	0.227470i
$196$		0			0
$197$	−2.79190	−	2.79190i	−0.198915	−	0.198915i	0.600620	−	0.799535i	$-0.294920\pi$
$197$	−2.79190	−	2.79190i	−0.198915	−	0.198915i	−0.799535	+	0.600620i	$0.794920\pi$
$198$	12.7490	+	0.0986920i	0.906032	+	0.00701374i
$199$	−6.11266	−	10.5874i	−0.433315	−	0.750524i	0.563841	−	0.825883i	$-0.309323\pi$
$199$	−6.11266	−	10.5874i	−0.433315	−	0.750524i	−0.997156	+	0.0753593i	$0.975990\pi$
$200$	14.0912	+	1.19868i	0.996401	+	0.0847597i
$201$	4.25197	−	7.36462i	0.299911	−	0.519460i
$202$	8.75628	+	15.4411i	0.616090	+	1.08643i
$203$		0			0
$204$	9.03077	+	5.40203i	0.632281	+	0.378218i
$205$	−0.581755	+	18.8704i	−0.0406315	+	1.31796i
$206$	2.92575	−	0.759728i	0.203847	−	0.0529328i
$207$	24.8441	+	6.65695i	1.72678	+	0.462690i
$208$	3.50409	−	3.29354i	0.242965	−	0.228366i
$209$		−	13.1327i		−	0.908409i
$210$		0			0
$211$			9.27501i			0.638518i	0.947668	+	0.319259i	$0.103434\pi$
$211$			9.27501i			0.638518i	−0.947668	+	0.319259i	$0.896566\pi$
$212$	7.09521	+	2.01939i	0.487301	+	0.138692i
$213$	10.7552	+	2.88184i	0.736933	+	0.197461i
$214$	3.57375	+	13.7627i	0.244297	+	0.940799i
$215$	10.8854	−	10.2343i	0.742376	−	0.697972i
$216$	1.21785	−	1.16256i	0.0828643	−	0.0791023i
$217$		0			0
$218$	−7.38699	+	4.18897i	−0.500310	+	0.283713i
$219$	4.61112	−	7.98669i	0.311591	−	0.539691i
$220$	−5.71927	−	11.0586i	−0.385593	−	0.745568i
$221$	1.26632	+	2.19333i	0.0851817	+	0.147539i
$222$	0.203897	−	26.3393i	0.0136847	−	1.76778i
$223$	−7.89717	−	7.89717i	−0.528833	−	0.528833i	0.391391	−	0.920224i	$-0.371994\pi$
$223$	−7.89717	−	7.89717i	−0.528833	−	0.528833i	−0.920224	+	0.391391i	$0.871994\pi$
$224$		0			0
$225$	13.4970	+	8.94422i	0.899803	+	0.596281i
$226$	−3.63946	+	3.58355i	−0.242094	+	0.238374i
$227$	7.03559	+	1.88518i	0.466969	+	0.125124i	0.484628	−	0.874720i	$-0.338955\pi$
$227$	7.03559	+	1.88518i	0.466969	+	0.125124i	−0.0176596	+	0.999844i	$0.505622\pi$
$228$	−16.4029	−	16.9189i	−1.08631	−	1.12048i
$229$	10.2737	+	5.93153i	0.678906	+	0.391966i	0.799443	−	0.600742i	$-0.205128\pi$
$229$	10.2737	+	5.93153i	0.678906	+	0.391966i	−0.120537	+	0.992709i	$0.538462\pi$
$230$	−5.56052	−	24.4932i	−0.366650	−	1.61503i
$231$		0			0
$232$	−0.601083	+	25.8784i	−0.0394630	+	1.69900i
$233$	−1.47567	−	5.50726i	−0.0966741	−	0.360793i	0.900594	−	0.434662i	$-0.143132\pi$
$233$	−1.47567	−	5.50726i	−0.0966741	−	0.360793i	−0.997268	+	0.0738689i	$0.976465\pi$
$234$	5.32914	−	1.38381i	0.348377	−	0.0904628i
$235$	4.28665	−	1.00812i	0.279630	−	0.0657627i
$236$	9.87469	+	17.7319i	0.642787	+	1.15425i
$237$	15.7854	+	15.7854i	1.02537	+	1.02537i
$238$		0			0
$239$	−3.08431			−0.199507			−0.0997536	−	0.995012i	$-0.531805\pi$
$239$	−3.08431			−0.199507			−0.0997536	+	0.995012i	$0.531805\pi$
$240$	−21.1804	−	7.10328i	−1.36719	−	0.458515i
$241$	−11.3532	−	19.6644i	−0.731326	−	1.26669i	−0.956317	−	0.292332i	$-0.905569\pi$
$241$	−11.3532	−	19.6644i	−0.731326	−	1.26669i	0.224991	−	0.974361i	$-0.427765\pi$
$242$	2.32878	−	3.96240i	0.149699	−	0.254713i
$243$	−21.5760	+	5.78127i	−1.38410	+	0.370869i
$244$	−5.76625	+	9.63965i	−0.369146	+	0.617115i
$245$		0			0
$246$	7.94152	−	28.7462i	0.506333	−	1.83279i
$247$	−1.46787	−	5.47817i	−0.0933985	−	0.348568i
$248$	−25.3478	+	13.8599i	−1.60959	+	0.880108i
$249$	2.87670	−	1.66086i	0.182304	−	0.105253i
$250$	1.58163	−	15.7321i	0.100031	−	0.994984i
$251$			5.25443i			0.331657i	0.986155	+	0.165828i	$0.0530298\pi$
$251$			5.25443i			0.331657i	−0.986155	+	0.165828i	$0.946970\pi$
$252$		0			0
$253$	−15.6350	+	15.6350i	−0.982961	+	0.982961i
$254$	−8.87158	+	8.73528i	−0.556652	+	0.548100i
$255$	6.19380	−	10.0029i	0.387871	−	0.626406i
$256$	15.9693	+	0.990215i	0.998083	+	0.0618884i
$257$	25.9506	−	6.95345i	1.61876	−	0.433744i	0.668120	−	0.744053i	$-0.267099\pi$
$257$	25.9506	−	6.95345i	1.61876	−	0.433744i	0.950636	+	0.310309i	$0.100432\pi$
$258$	−20.5303	+	11.6422i	−1.27816	+	0.724814i
$259$		0			0
$260$	−3.62177	−	3.97370i	−0.224613	−	0.246439i
$261$	−14.8184	+	25.6662i	−0.917235	+	1.58870i
$262$	12.2115	+	7.17691i	0.754428	+	0.443391i
$263$	7.46169	−	27.8474i	0.460108	−	1.71715i	−0.212513	−	0.977158i	$-0.568165\pi$
$263$	7.46169	−	27.8474i	0.460108	−	1.71715i	0.672621	−	0.739987i	$-0.265169\pi$
$264$	4.64764	+	19.1097i	0.286042	+	1.17612i
$265$	2.37914	−	7.89712i	0.146149	−	0.485116i
$266$		0			0
$267$	9.10161	−	9.10161i	0.557010	−	0.557010i
$268$	6.54941	+	1.86405i	0.400069	+	0.113865i
$269$	10.3532	−	5.97740i	0.631243	−	0.364448i	−0.149990	−	0.988687i	$-0.547924\pi$
$269$	10.3532	−	5.97740i	0.631243	−	0.364448i	0.781233	+	0.624239i	$0.214591\pi$
$270$	−1.27875	−	1.38137i	−0.0778221	−	0.0840677i
$271$	9.73675	+	5.62151i	0.591465	+	0.341483i	0.765677	−	0.643226i	$-0.222404\pi$
$271$	9.73675	+	5.62151i	0.591465	+	0.341483i	−0.174211	+	0.984708i	$0.555738\pi$
$272$	−2.43185	+	8.06785i	−0.147453	+	0.489186i
$273$		0			0
$274$	5.29411	−	19.1633i	0.319829	−	1.15769i
$275$	−12.4605	+	6.20397i	−0.751394	+	0.374113i
$276$	−0.614231	+	39.6707i	−0.0369724	+	2.38790i
$277$	−1.94624	+	7.26348i	−0.116938	+	0.436420i	−0.999425	−	0.0339182i	$-0.989201\pi$
$277$	−1.94624	+	7.26348i	−0.116938	+	0.436420i	0.882486	+	0.470338i	$0.155868\pi$
$278$	−25.8082	−	0.199785i	−1.54787	−	0.0119823i
$279$	−33.0764			−1.98023
$280$		0			0
$281$	26.9008			1.60477			0.802383	−	0.596809i	$-0.203565\pi$
$281$	26.9008			1.60477			0.802383	+	0.596809i	$0.203565\pi$
$282$	−6.95599	−	0.0538474i	−0.414223	−	0.00320656i
$283$	3.21272	−	11.9900i	0.190977	−	0.712734i	−0.802295	−	0.596927i	$-0.796388\pi$
$283$	3.21272	−	11.9900i	0.190977	−	0.712734i	0.993272	−	0.115807i	$-0.0369453\pi$
$284$	−0.138032	+	8.91492i	−0.00819069	+	0.529003i
$285$	−19.1949	+	18.0468i	−1.13701	+	1.06900i
$286$	−1.26041	+	4.56234i	−0.0745295	+	0.269777i
$287$		0			0
$288$	15.4982	+	9.76640i	0.913240	+	0.575490i
$289$	10.8792	+	6.28112i	0.639954	+	0.369478i
$290$	28.9192	+	1.11569i	1.69820	+	0.0655153i
$291$	−3.92038	+	2.26343i	−0.229817	+	0.132685i
$292$	7.10262	+	2.02150i	0.415649	+	0.118299i
$293$	6.82973	−	6.82973i	0.398997	−	0.398997i	−0.478882	−	0.877879i	$-0.658958\pi$
$293$	6.82973	−	6.82973i	0.398997	−	0.398997i	0.877879	+	0.478882i	$0.158958\pi$
$294$		0			0
$295$	19.9918	−	10.7349i	1.16397	−	0.625009i
$296$	20.4944	−	4.98440i	1.19121	−	0.289712i
$297$	−0.428903	+	1.60069i	−0.0248875	+	0.0928813i
$298$	14.4732	+	8.50617i	0.838411	+	0.492749i
$299$	−4.77440	+	8.26950i	−0.276111	+	0.478238i
$300$	−8.30395	+	23.5558i	−0.479429	+	1.36000i
$301$		0			0
$302$	9.03559	−	5.12385i	0.519940	−	0.294845i
$303$	−30.2822	+	8.11410i	−1.73967	+	0.466143i
$304$	9.93617	−	16.0416i	0.569878	−	0.920048i
$305$	10.6773	+	6.61140i	0.611381	+	0.378568i
$306$	−6.87446	+	6.76885i	−0.392987	+	0.386949i
$307$	11.0402	−	11.0402i	0.630098	−	0.630098i	−0.317995	−	0.948092i	$-0.603009\pi$
$307$	11.0402	−	11.0402i	0.630098	−	0.630098i	0.948092	+	0.317995i	$0.103009\pi$
$308$		0			0
$309$			5.33858i			0.303701i
$310$	15.0594	+	28.5740i	0.855318	+	1.62290i
$311$	10.7343	−	6.19747i	0.608688	−	0.351426i	−0.163764	−	0.986500i	$-0.552363\pi$
$311$	10.7343	−	6.19747i	0.608688	−	0.351426i	0.772452	+	0.635073i	$0.219030\pi$
$312$	4.07464	+	7.45192i	0.230681	+	0.421882i
$313$	6.55721	+	24.4719i	0.370636	+	1.38323i	0.859618	+	0.510937i	$0.170702\pi$
$313$	6.55721	+	24.4719i	0.370636	+	1.38323i	−0.488982	+	0.872294i	$0.662632\pi$
$314$	−0.123799	+	0.448121i	−0.00698640	+	0.0252889i
$315$		0			0
$316$	−9.17649	+	15.3407i	−0.516218	+	0.862980i
$317$	9.05071	−	2.42513i	0.508339	−	0.136209i	0.00447129	−	0.999990i	$-0.498577\pi$
$317$	9.05071	−	2.42513i	0.508339	−	0.136209i	0.503867	+	0.863781i	$0.331910\pi$
$318$	−6.60145	+	11.2323i	−0.370191	+	0.629878i
$319$	−12.7389	−	22.0645i	−0.713244	−	1.23537i
$320$	1.38079	−	17.8352i	0.0771884	−	0.997017i
$321$	−25.1126			−1.40165
$322$		0			0
$323$	7.02697	+	7.02697i	0.390991	+	0.390991i
$324$	−8.00659	−	14.3774i	−0.444811	−	0.798742i
$325$	−4.50431	+	3.98065i	−0.249854	+	0.220807i
$326$	−26.3793	+	6.84989i	−1.46101	+	0.379380i
$327$	−3.88176	−	14.4869i	−0.214662	−	0.801128i
$328$	23.8743	+	0.554532i	1.31824	+	0.0306189i
$329$		0			0
$330$	21.4425	−	4.86793i	1.18037	−	0.267971i
$331$	−4.80323	−	2.77314i	−0.264009	−	0.152426i	0.362153	−	0.932119i	$-0.382042\pi$
$331$	−4.80323	−	2.77314i	−0.264009	−	0.152426i	−0.626162	+	0.779693i	$0.715375\pi$
$332$	1.85147	+	1.90970i	0.101612	+	0.104809i
$333$	23.3256	+	6.25008i	1.27824	+	0.342502i
$334$	−17.2152	+	16.9507i	−0.941973	+	0.927501i
$335$	2.19613	−	7.28963i	0.119987	−	0.398275i
$336$		0			0
$337$	−3.40876	−	3.40876i	−0.185687	−	0.185687i	0.608142	−	0.793829i	$-0.291915\pi$
$337$	−3.40876	−	3.40876i	−0.185687	−	0.185687i	−0.793829	+	0.608142i	$0.791915\pi$
$338$	0.126492	−	16.3402i	0.00688027	−	0.888791i
$339$	−4.51030	−	7.81207i	−0.244966	−	0.424293i
$340$	8.97738	+	2.85691i	0.486867	+	0.154938i
$341$	14.2174	−	24.6253i	0.769915	−	1.33353i
$342$	18.7928	−	10.6569i	1.01620	−	0.576260i
$343$		0			0
$344$	−13.0497	−	13.6703i	−0.703591	−	0.737053i
$345$	44.3375	+	1.36688i	2.38705	+	0.0735903i
$346$	5.22164	+	20.1088i	0.280717	+	1.08106i
$347$	−0.632213	−	0.169401i	−0.0339389	−	0.00909391i	0.241810	−	0.970324i	$-0.422259\pi$
$347$	−0.632213	−	0.169401i	−0.0339389	−	0.00909391i	−0.275749	+	0.961230i	$0.588926\pi$
$348$	−43.9704	−	12.5146i	−2.35706	−	0.670850i
$349$		−	9.05105i		−	0.484492i	−0.970215	−	0.242246i	$-0.922116\pi$
$349$		−	9.05105i		−	0.484492i	0.970215	−	0.242246i	$-0.0778841\pi$
$350$		0			0
$351$			0.715649i			0.0381985i
$352$	−13.9327	+	7.34042i	−0.742617	+	0.391246i
$353$	−14.0838	−	3.77374i	−0.749605	−	0.200856i	−0.136262	−	0.990673i	$-0.543509\pi$
$353$	−14.0838	−	3.77374i	−0.749605	−	0.200856i	−0.613343	+	0.789817i	$0.710176\pi$
$354$	−34.6945	+	9.00911i	−1.84399	+	0.478829i
$355$	9.96365	+	0.307169i	0.528816	+	0.0163029i
$356$	8.84521	+	5.29103i	0.468795	+	0.280424i
$357$		0			0
$358$	−2.46555	−	4.34785i	−0.130309	−	0.229791i
$359$	−7.26761	+	12.5879i	−0.383570	+	0.664362i	−0.991570	−	0.129575i	$-0.958639\pi$
$359$	−7.26761	+	12.5879i	−0.383570	+	0.664362i	0.608000	+	0.793937i	$0.291972\pi$
$360$	11.1836	−	17.1580i	0.589429	−	0.904306i
$361$	−1.62687	−	2.81781i	−0.0856245	−	0.148306i
$362$	−3.82406	−	0.0296026i	−0.200988	−	0.00155588i
$363$	5.73972	+	5.73972i	0.301257	+	0.301257i
$364$		0			0
$365$	2.38163	−	7.90537i	0.124660	−	0.413786i
$366$	−13.9187	−	14.1359i	−0.727542	−	0.738893i
$367$	9.12062	+	2.44386i	0.476092	+	0.127569i	0.488883	−	0.872350i	$-0.337405\pi$
$367$	9.12062	+	2.44386i	0.476092	+	0.127569i	−0.0127901	+	0.999918i	$0.504071\pi$
$368$	−30.9274	+	7.26870i	−1.61220	+	0.378907i
$369$	23.6785	+	13.6708i	1.23265	+	0.711672i
$370$	−5.22066	−	22.9962i	−0.271409	−	1.19551i
$371$		0			0
$372$	−12.4410	−	49.4824i	−0.645036	−	2.56554i
$373$	1.42310	+	5.31108i	0.0736853	+	0.274997i	0.992932	−	0.118685i	$-0.0378678\pi$
$373$	1.42310	+	5.31108i	0.0736853	+	0.274997i	−0.919247	+	0.393682i	$0.871201\pi$
$374$	−2.08450	−	8.02751i	−0.107787	−	0.415093i
$375$	26.1907	+	9.68692i	1.35248	+	0.500230i
$376$	−1.31634	−	5.41239i	−0.0678849	−	0.279123i
$377$	−7.78011	−	7.78011i	−0.400696	−	0.400696i
$378$		0			0
$379$	11.9123			0.611896			0.305948	−	0.952048i	$-0.401027\pi$
$379$	11.9123			0.611896			0.305948	+	0.952048i	$0.401027\pi$
$380$	−17.7625	−	11.3827i	−0.911199	−	0.583922i
$381$	−10.9943	−	19.0428i	−0.563257	−	0.975590i
$382$	−15.4810	−	9.09846i	−0.792076	−	0.465518i
$383$	8.58760	−	2.30104i	0.438806	−	0.117578i	−0.0326510	−	0.999467i	$-0.510395\pi$
$383$	8.58760	−	2.30104i	0.438806	−	0.117578i	0.471457	+	0.881889i	$0.343728\pi$
$384$	−8.78124	+	26.8588i	−0.448116	+	1.37063i
$385$		0			0
$386$	4.19168	+	1.15801i	0.213351	+	0.0589410i
$387$	−5.60028	−	20.9005i	−0.284678	−	1.06243i
$388$	−2.52319	−	2.60255i	−0.128095	−	0.132124i
$389$	−8.40368	+	4.85186i	−0.426083	+	0.245999i	−0.697677	−	0.716413i	$-0.745783\pi$
$389$	−8.40368	+	4.85186i	−0.426083	+	0.245999i	0.271593	+	0.962412i	$0.412449\pi$
$390$	8.40039	−	4.42728i	0.425370	−	0.224184i
$391$		−	16.7317i		−	0.846158i
$392$		0			0
$393$	−17.6889	+	17.6889i	−0.892286	+	0.892286i
$394$	3.91766	+	3.97879i	0.197369	+	0.200448i
$395$	16.9920	+	10.5215i	0.854961	+	0.529393i
$396$	−18.0282	−	0.279135i	−0.905951	−	0.0140271i
$397$	−31.3389	+	8.39722i	−1.57285	+	0.421444i	−0.936704	−	0.350122i	$-0.886140\pi$
$397$	−31.3389	+	8.39722i	−1.57285	+	0.421444i	−0.636148	+	0.771567i	$0.719473\pi$
$398$	8.52845	+	15.0394i	0.427492	+	0.753856i
$399$		0			0
$400$	−19.9143	−	1.84940i	−0.995715	−	0.0924702i
$401$	−17.0988	+	29.6159i	−0.853871	+	1.47895i	0.0238169	+	0.999716i	$0.492418\pi$
$401$	−17.0988	+	29.6159i	−0.853871	+	1.47895i	−0.877688	+	0.479232i	$0.840915\pi$
$402$	−6.09363	+	10.3683i	−0.303923	+	0.517123i
$403$	3.17822	−	11.8613i	0.158318	−	0.590852i
$404$	−12.2138	−	21.9323i	−0.607661	−	1.09117i
$405$	−16.2098	+	8.70406i	−0.805470	+	0.432508i
$406$		0			0
$407$	−14.6793	+	14.6793i	−0.727628	+	0.727628i
$408$	−12.7119	−	7.73826i	−0.629334	−	0.383101i
$409$	1.02295	−	0.590599i	0.0505815	−	0.0292032i	−0.474496	−	0.880258i	$-0.657370\pi$
$409$	1.02295	−	0.590599i	0.0505815	−	0.0292032i	0.525077	+	0.851054i	$0.324036\pi$
$410$	1.02928	−	26.6796i	0.0508326	−	1.31761i
$411$	30.4081	+	17.5562i	1.49992	+	0.865981i
$412$	−4.14583	+	1.04236i	−0.204250	+	0.0513532i
$413$		0			0
$414$	−35.0609	−	9.68604i	−1.72315	−	0.476043i
$415$	2.16661	−	2.03701i	0.106355	−	0.0999931i
$416$	−4.99144	+	4.61927i	−0.244725	+	0.226478i
$417$	11.7974	−	44.0285i	0.577721	−	2.15608i
$418$	−0.143768	+	18.5719i	−0.00703193	+	0.908382i
$419$	3.50746			0.171351			0.0856753	−	0.996323i	$-0.472695\pi$
$419$	3.50746			0.171351			0.0856753	+	0.996323i	$0.472695\pi$
$420$		0			0
$421$	−26.7845			−1.30539			−0.652697	−	0.757619i	$-0.726363\pi$
$421$	−26.7845			−1.30539			−0.652697	+	0.757619i	$0.726363\pi$
$422$	0.101536	−	13.1165i	0.00494272	−	0.638499i
$423$	1.65059	−	6.16009i	0.0802545	−	0.299514i
$424$	−10.0117	−	2.93344i	−0.486213	−	0.142460i
$425$	3.34768	−	9.98684i	0.162386	−	0.484433i
$426$	−15.1781	−	4.19316i	−0.735382	−	0.203159i
$427$		0			0
$428$	−4.90323	−	19.5019i	−0.237007	−	0.942662i
$429$	−7.23950	−	4.17973i	−0.349526	−	0.201799i
$430$	−15.5058	+	14.3539i	−0.747757	+	0.692204i
$431$	−32.5658	+	18.8019i	−1.56864	+	0.905655i	−0.572313	+	0.820035i	$0.693954\pi$
$431$	−32.5658	+	18.8019i	−1.56864	+	0.905655i	−0.996328	+	0.0856198i	$0.972713\pi$
$432$	−1.73498	+	1.63073i	−0.0834741	+	0.0784584i
$433$	28.0987	−	28.0987i	1.35034	−	1.35034i	0.465060	−	0.885279i	$-0.346033\pi$
$433$	28.0987	−	28.0987i	1.35034	−	1.35034i	0.885279	−	0.465060i	$-0.153967\pi$
$434$		0			0
$435$	−14.7440	+	48.9400i	−0.706921	+	2.34649i
$436$	10.4923	−	5.84306i	0.502491	−	0.279832i
$437$	−9.69741	+	36.1912i	−0.463890	+	1.73126i
$438$	−6.60834	+	11.2441i	−0.315759	+	0.537262i
$439$	8.35429	−	14.4701i	0.398728	−	0.690618i	−0.594841	−	0.803843i	$-0.702785\pi$
$439$	8.35429	−	14.4701i	0.398728	−	0.690618i	0.993569	+	0.113226i	$0.0361183\pi$
$440$	7.96697	+	15.7013i	0.379810	+	0.748530i
$441$		0			0
$442$	−1.76678	−	3.11560i	−0.0840371	−	0.148194i
$443$	12.3733	−	3.31541i	0.587872	−	0.157520i	0.0473913	−	0.998876i	$-0.484909\pi$
$443$	12.3733	−	3.31541i	0.587872	−	0.157520i	0.540480	+	0.841357i	$0.318243\pi$
$444$	−0.576690	+	37.2461i	−0.0273685	+	1.76762i
$445$	6.06653	−	9.79736i	0.287581	−	0.464439i
$446$	11.0815	+	11.2544i	0.524724	+	0.532911i
$447$	−20.9651	+	20.9651i	−0.991615	+	0.991615i
$448$		0			0
$449$		−	3.07224i		−	0.144988i	−0.997369	−	0.0724940i	$-0.976904\pi$
$449$		−	3.07224i		−	0.144988i	0.997369	−	0.0724940i	$-0.0230958\pi$
$450$	−18.9892	−	12.7964i	−0.895160	−	0.603229i
$451$	−20.3557	+	11.7524i	−0.958512	+	0.553397i
$452$	5.18606	−	5.02791i	0.243932	−	0.236493i
$453$	4.74807	+	17.7201i	0.223084	+	0.832561i
$454$	−9.92890	−	2.74299i	−0.465986	−	0.128735i
$455$		0			0
$456$	23.0113	+	24.1057i	1.07760	+	1.12885i
$457$	24.1677	−	6.47572i	1.13052	−	0.302922i	0.355386	−	0.934720i	$-0.384350\pi$
$457$	24.1677	−	6.47572i	1.13052	−	0.302922i	0.775133	+	0.631798i	$0.217683\pi$
$458$	−14.4638	−	8.50067i	−0.675851	−	0.397210i
$459$	−0.626991	−	1.08598i	−0.0292654	−	0.0506892i
$460$	7.59539	+	34.6984i	0.354137	+	1.61782i
$461$	2.14049			0.0996923			0.0498462	−	0.998757i	$-0.484127\pi$
$461$	2.14049			0.0996923			0.0498462	+	0.998757i	$0.484127\pi$
$462$		0			0
$463$	−15.0692	−	15.0692i	−0.700327	−	0.700327i	0.264154	−	0.964481i	$-0.414907\pi$
$463$	−15.0692	−	15.0692i	−0.700327	−	0.700327i	−0.964481	+	0.264154i	$0.914907\pi$
$464$	1.13333	−	36.5899i	0.0526137	−	1.69865i
$465$	−55.5298	+	13.0594i	−2.57513	+	0.605613i
$466$	2.02656	+	7.80437i	0.0938784	+	0.361530i
$467$	−5.02981	−	18.7715i	−0.232752	−	0.868641i	−0.979149	−	0.203141i	$-0.934885\pi$
$467$	−5.02981	−	18.7715i	−0.232752	−	0.868641i	0.746398	−	0.665500i	$-0.231782\pi$
$468$	−7.55146	+	1.89861i	−0.349067	+	0.0877633i
$469$		0			0
$470$	−6.07309	+	1.37873i	−0.280131	+	0.0635962i
$471$	−0.711075	−	0.410540i	−0.0327646	−	0.0189167i
$472$	−13.7704	−	25.1840i	−0.633833	−	1.15919i
$473$	17.9676	+	4.81440i	0.826151	+	0.221367i
$474$	−22.1504	−	22.4960i	−1.01740	−	1.03328i
$475$	−13.0294	+	19.6616i	−0.597828	+	0.902137i
$476$		0			0
$477$	−8.44607	−	8.44607i	−0.386719	−	0.386719i
$478$	4.36174	+	0.0337649i	0.199501	+	0.00154437i
$479$	−7.15682	−	12.3960i	−0.327003	−	0.566387i	0.654912	−	0.755705i	$-0.272706\pi$
$479$	−7.15682	−	12.3960i	−0.327003	−	0.566387i	−0.981916	+	0.189318i	$0.939372\pi$
$480$	29.8750	+	10.2771i	1.36360	+	0.469084i
$481$	−4.48259	+	7.76407i	−0.204388	+	0.354011i
$482$	15.8401	+	27.9331i	0.721498	+	1.27232i
$483$		0			0
$484$	−3.33667	+	5.57802i	−0.151667	+	0.253547i
$485$	−2.95266	+	2.77605i	−0.134073	+	0.126054i
$486$	30.5754	−	7.93951i	1.38693	−	0.360143i
$487$	−33.8536	−	9.07104i	−1.53405	−	0.411048i	−0.609714	−	0.792621i	$-0.708716\pi$
$487$	−33.8536	−	9.07104i	−1.53405	−	0.411048i	−0.924339	+	0.381573i	$0.875382\pi$
$488$	8.26000	−	13.5690i	0.373912	−	0.614239i
$489$		−	48.1339i		−	2.17669i
$490$		0			0
$491$		−	41.1970i		−	1.85920i	−0.368576	−	0.929598i	$-0.620155\pi$
$491$		−	41.1970i		−	1.85920i	0.368576	−	0.929598i	$-0.379845\pi$
$492$	−11.5454	+	40.5651i	−0.520505	+	1.82881i
$493$	18.6224	+	4.98986i	0.838711	+	0.224732i
$494$	2.01585	+	7.76314i	0.0906974	+	0.349280i
$495$	−0.621173	+	20.1490i	−0.0279196	+	0.905629i
$496$	35.9979	−	19.3228i	1.61635	−	0.867621i
$497$		0			0
$498$	−4.08633	+	2.31725i	−0.183113	+	0.103839i
$499$	16.6591	−	28.8545i	0.745766	−	1.29170i	−0.204070	−	0.978956i	$-0.565417\pi$
$499$	16.6591	−	28.8545i	0.745766	−	1.29170i	0.949836	−	0.312748i	$-0.101250\pi$
$500$	−2.40892	+	22.2305i	−0.107730	+	0.994180i
$501$	−21.3344	−	36.9522i	−0.953149	−	1.65090i
$502$	0.0575220	−	7.43067i	0.00256733	−	0.331647i
$503$	2.38397	+	2.38397i	0.106296	+	0.106296i	0.758255	−	0.651959i	$-0.226052\pi$
$503$	2.38397	+	2.38397i	0.106296	+	0.106296i	−0.651959	+	0.758255i	$0.726052\pi$
$504$		0			0
$505$	−24.7276	+	13.2778i	−1.10036	+	0.590855i
$506$	22.2817	−	21.9393i	0.990540	−	0.975322i
$507$	27.8762	+	7.46941i	1.23803	+	0.331728i
$508$	12.6416	−	12.2561i	0.560879	−	0.543775i
$509$	6.38129	+	3.68424i	0.282846	+	0.163301i	0.634711	−	0.772750i	$-0.281119\pi$
$509$	6.38129	+	3.68424i	0.282846	+	0.163301i	−0.351865	+	0.936051i	$0.614452\pi$
$510$	−8.86859	+	14.0780i	−0.392708	+	0.623384i
$511$		0			0
$512$	−22.5725	−	1.57515i	−0.997574	−	0.0696127i
$513$	0.726787	+	2.71240i	0.0320884	+	0.119756i
$514$	−36.7748	+	9.54928i	−1.62207	+	0.421201i
$515$	1.09417	+	4.65251i	0.0482147	+	0.205014i
$516$	29.1609	−	16.2394i	1.28374	−	0.714898i
$517$	3.87669	+	3.87669i	0.170497	+	0.170497i
$518$		0			0
$519$	−36.6923			−1.61061
$520$	5.07830	+	5.65914i	0.222698	+	0.248170i
$521$	17.6135	+	30.5075i	0.771663	+	1.33656i	0.936651	+	0.350264i	$0.113908\pi$
$521$	17.6135	+	30.5075i	0.771663	+	1.33656i	−0.164988	+	0.986296i	$0.552758\pi$
$522$	21.2367	−	36.1342i	0.929505	−	1.58155i
$523$	13.7791	−	3.69210i	0.602519	−	0.161444i	0.0553504	−	0.998467i	$-0.482372\pi$
$523$	13.7791	−	3.69210i	0.602519	−	0.161444i	0.547168	+	0.837023i	$0.315706\pi$
$524$	−17.1906	−	10.2831i	−0.750973	−	0.449218i
$525$		0			0
$526$	−10.8570	+	39.2993i	−0.473386	+	1.71353i
$527$	5.56897	+	20.7837i	0.242588	+	0.905352i
$528$	−6.36335	−	27.0753i	−0.276929	−	1.17830i
$529$	34.7134	−	20.0418i	1.50928	−	0.871382i
$530$	−3.45097	+	11.1418i	−0.149900	+	0.483971i
$531$		−	32.8626i		−	1.42612i
$532$		0			0
$533$	−7.17757	+	7.17757i	−0.310895	+	0.310895i
$534$	−12.9709	+	12.7716i	−0.561305	+	0.552681i
$535$	−21.8853	+	5.14694i	−0.946186	+	0.222522i
$536$	−9.24158	−	2.70778i	−0.399175	−	0.116958i
$537$	8.52673	−	2.28473i	0.367956	−	0.0985934i
$538$	−14.7066	+	8.33972i	−0.634045	+	0.359551i
$539$		0			0
$540$	1.79325	+	1.96750i	0.0771690	+	0.0846676i
$541$	−6.58238	+	11.4010i	−0.282999	+	0.490168i	−0.972122	−	0.234476i	$-0.924663\pi$
$541$	−6.58238	+	11.4010i	−0.282999	+	0.490168i	0.689123	+	0.724644i	$0.257996\pi$
$542$	−13.7079	−	8.05637i	−0.588804	−	0.346051i
$543$	1.74805	−	6.52380i	0.0750159	−	0.279963i
$544$	3.52737	−	11.3827i	0.151235	−	0.488029i
$545$	−6.35206	−	11.8296i	−0.272092	−	0.506724i
$546$		0			0
$547$	−21.6549	+	21.6549i	−0.925899	+	0.925899i	−0.997438	−	0.0715392i	$-0.977209\pi$
$547$	−21.6549	+	21.6549i	−0.925899	+	0.925899i	0.0715392	+	0.997438i	$0.477209\pi$
$548$	−7.69656	+	27.0422i	−0.328781	+	1.15518i
$549$	15.7508	−	9.09375i	0.672230	−	0.388112i
$550$	17.6891	−	8.63707i	0.754267	−	0.368286i
$551$	−37.3888	−	21.5865i	−1.59282	−	0.919614i
$552$	1.30292	−	56.0945i	0.0554558	−	2.38754i
$553$		0			0
$554$	2.83184	−	10.2505i	0.120313	−	0.435502i
$555$	41.6276	+	1.28334i	1.76699	+	0.0544746i
$556$	36.4950	+	0.565061i	1.54773	+	0.0239639i
$557$	−10.7916	+	40.2749i	−0.457256	+	1.70650i	0.224113	+	0.974563i	$0.428052\pi$
$557$	−10.7916	+	40.2749i	−0.457256	+	1.70650i	−0.681369	+	0.731940i	$0.738615\pi$
$558$	46.7756	+	0.362097i	1.98017	+	0.0153288i
$559$	8.03311			0.339764
$560$		0			0
$561$	14.6477			0.618426
$562$	−38.0423	−	0.294492i	−1.60472	−	0.0124224i
$563$	−9.49611	+	35.4400i	−0.400213	+	1.49362i	0.412503	+	0.910956i	$0.364655\pi$
$563$	−9.49611	+	35.4400i	−0.400213	+	1.49362i	−0.812716	+	0.582660i	$0.802012\pi$
$564$	9.83637	+	0.152299i	0.414186	+	0.00641294i
$565$	−5.53179	−	5.88372i	−0.232724	−	0.247530i
$566$	−4.67460	+	16.9208i	−0.196488	+	0.711235i
$567$		0			0
$568$	0.292795	−	12.6057i	0.0122854	−	0.528924i
$569$	7.21296	+	4.16440i	0.302383	+	0.174581i	0.643513	−	0.765435i	$-0.277476\pi$
$569$	7.21296	+	4.16440i	0.302383	+	0.174581i	−0.341130	+	0.940016i	$0.610810\pi$
$570$	27.3424	−	25.3111i	1.14525	−	1.06017i
$571$	7.95794	−	4.59452i	0.333030	−	0.192275i	−0.324156	−	0.946004i	$-0.605080\pi$
$571$	7.95794	−	4.59452i	0.333030	−	0.192275i	0.657185	+	0.753729i	$0.271747\pi$
$572$	1.83238	−	6.43814i	0.0766156	−	0.269192i
$573$	22.4249	−	22.4249i	0.936814	−	0.936814i
$574$		0			0
$575$	38.9197	−	7.89594i	1.62306	−	0.329283i
$576$	−21.8102	−	13.9810i	−0.908758	−	0.582543i
$577$	4.09647	−	15.2882i	0.170538	−	0.636457i	−0.826731	−	0.562598i	$-0.809802\pi$
$577$	4.09647	−	15.2882i	0.170538	−	0.636457i	0.997269	−	0.0738590i	$-0.0235315\pi$
$578$	−15.3163	−	9.00168i	−0.637075	−	0.374420i
$579$	−3.84015	+	6.65133i	−0.159591	+	0.276420i
$580$	−40.8846	−	1.89436i	−1.69764	−	0.0786590i
$581$		0			0
$582$	5.56887	−	3.15796i	0.230837	−	0.130902i
$583$	9.91850	−	2.65765i	0.410782	−	0.110069i
$584$	−10.0222	−	2.93650i	−0.414721	−	0.121513i
$585$	1.99298	+	8.47436i	0.0823995	+	0.350372i
$586$	−9.73318	+	9.58364i	−0.402074	+	0.395897i
$587$	−18.5622	+	18.5622i	−0.766145	+	0.766145i	−0.977425	−	0.211281i	$-0.932237\pi$
$587$	−18.5622	+	18.5622i	−0.766145	+	0.766145i	0.211281	+	0.977425i	$0.432237\pi$
$588$		0			0
$589$		−	48.1835i		−	1.98537i
$590$	−28.3894	+	14.9621i	−1.16877	+	0.615980i
$591$	−8.54042	+	4.93082i	−0.351306	+	0.202827i
$592$	−29.0371	+	6.82444i	−1.19342	+	0.280483i
$593$	0.139918	+	0.522182i	0.00574575	+	0.0214434i	0.968739	−	0.248081i	$-0.0798000\pi$
$593$	0.139918	+	0.522182i	0.00574575	+	0.0214434i	−0.962993	+	0.269525i	$0.913133\pi$
$594$	0.624065	−	2.25895i	0.0256057	−	0.0926858i
$595$		0			0
$596$	−20.3745	−	12.1876i	−0.834571	−	0.499224i
$597$	−29.4943	+	7.90298i	−1.20712	+	0.323447i
$598$	6.84235	−	11.6422i	0.279804	−	0.476086i
$599$	17.5455	+	30.3897i	0.716889	+	1.24169i	0.962226	+	0.272250i	$0.0877679\pi$
$599$	17.5455	+	30.3897i	0.716889	+	1.24169i	−0.245337	+	0.969438i	$0.578899\pi$
$600$	12.0011	−	33.2211i	0.489942	−	1.35624i
$601$	12.8741			0.525146			0.262573	−	0.964912i	$-0.415429\pi$
$601$	12.8741			0.525146			0.262573	+	0.964912i	$0.415429\pi$
$602$		0			0
$603$	−7.79635	−	7.79635i	−0.317492	−	0.317492i
$604$	−12.8340	+	7.14709i	−0.522207	+	0.290811i
$605$	6.17847	+	3.82571i	0.251191	+	0.155537i
$606$	42.9131	−	11.1432i	1.74323	−	0.452662i
$607$	5.84398	+	21.8100i	0.237200	+	0.885242i	0.977145	+	0.212574i	$0.0681848\pi$
$607$	5.84398	+	21.8100i	0.237200	+	0.885242i	−0.739945	+	0.672667i	$0.765149\pi$
$608$	−14.2271	+	22.5768i	−0.576983	+	0.915609i
$609$		0			0
$610$	−15.0272	−	9.46654i	−0.608432	−	0.383289i
$611$	2.05042	+	1.18381i	0.0829513	+	0.0478920i
$612$	9.79577	−	9.49705i	0.395970	−	0.383896i
$613$	−8.17180	−	2.18963i	−0.330056	−	0.0884382i	0.0899858	−	0.995943i	$-0.471318\pi$
$613$	−8.17180	−	2.18963i	−0.330056	−	0.0884382i	−0.420042	+	0.907505i	$0.637984\pi$
$614$	−15.7336	+	15.4919i	−0.634956	+	0.625201i
$615$	45.1498	+	13.6021i	1.82062	+	0.548492i
$616$		0			0
$617$	34.0313	+	34.0313i	1.37005	+	1.37005i	0.860359	+	0.509689i	$0.170240\pi$
$617$	34.0313	+	34.0313i	1.37005	+	1.37005i	0.509689	+	0.860359i	$0.329760\pi$
$618$	0.0584432	−	7.54967i	0.00235093	−	0.303692i
$619$	−4.68299	−	8.11118i	−0.188225	−	0.326016i	0.756433	−	0.654071i	$-0.226940\pi$
$619$	−4.68299	−	8.11118i	−0.188225	−	0.326016i	−0.944659	+	0.328055i	$0.893607\pi$
$620$	−20.9838	−	40.5735i	−0.842730	−	1.62947i
$621$	2.36395	−	4.09447i	0.0948619	−	0.164306i
$622$	−15.2480	+	8.64677i	−0.611390	+	0.346704i
$623$		0			0
$624$	−5.68066	−	10.5829i	−0.227408	−	0.423655i
$625$	24.8103	+	3.07412i	0.992411	+	0.122965i
$626$	−9.00512	−	34.6792i	−0.359917	−	1.38606i
$627$	−31.6835	−	8.48956i	−1.26532	−	0.339040i
$628$	0.179979	−	0.632364i	0.00718195	−	0.0252341i
$629$		−	15.7091i		−	0.626361i
$630$		0			0
$631$			33.8691i			1.34831i	0.738590	+	0.674155i	$0.235492\pi$
$631$			33.8691i			1.34831i	−0.738590	+	0.674155i	$0.764508\pi$
$632$	13.1451	−	21.5939i	0.522883	−	0.858958i
$633$	22.3765	+	5.99577i	0.889386	+	0.238310i
$634$	−12.8258	+	3.33047i	−0.509378	+	0.132270i
$635$	−13.4843	−	14.3422i	−0.535109	−	0.569152i
$636$	9.45854	−	15.8122i	0.375056	−	0.626994i
$637$		0			0
$638$	17.7735	+	31.3424i	0.703659	+	1.24086i
$639$	7.21823	−	12.5023i	0.285549	−	0.494585i
$640$	−2.14792	+	25.2069i	−0.0849039	+	0.996389i
$641$	−1.12253	−	1.94428i	−0.0443373	−	0.0767944i	0.843005	−	0.537906i	$-0.180784\pi$
$641$	−1.12253	−	1.94428i	−0.0443373	−	0.0767944i	−0.887342	+	0.461111i	$0.847451\pi$
$642$	35.5136	+	0.274916i	1.40161	+	0.0108501i
$643$	−21.5472	−	21.5472i	−0.849737	−	0.849737i	0.140363	−	0.990100i	$-0.455173\pi$
$643$	−21.5472	−	21.5472i	−0.849737	−	0.849737i	−0.990100	+	0.140363i	$0.955173\pi$
$644$		0			0
$645$	−17.6540	−	32.8775i	−0.695126	−	1.29455i
$646$	−9.86042	−	10.0143i	−0.387953	−	0.394006i
$647$	14.7661	+	3.95657i	0.580517	+	0.155549i	0.537115	−	0.843509i	$-0.319514\pi$
$647$	14.7661	+	3.95657i	0.580517	+	0.155549i	0.0434012	+	0.999058i	$0.486181\pi$
$648$	11.1653	+	20.4197i	0.438614	+	0.802162i
$649$	24.4661	+	14.1255i	0.960379	+	0.554475i
$650$	6.41345	−	5.58001i	0.251556	−	0.218866i
$651$		0			0
$652$	37.3798	−	9.39813i	1.46390	−	0.368059i
$653$	−7.66087	−	28.5907i	−0.299793	−	1.11884i	−0.937336	−	0.348427i	$-0.886716\pi$
$653$	−7.66087	−	28.5907i	−0.299793	−	1.11884i	0.637543	−	0.770415i	$-0.279951\pi$
$654$	5.33088	+	20.5295i	0.208454	+	0.802766i
$655$	−11.7902	+	19.0411i	−0.460682	+	0.743996i
$656$	−33.7562	−	1.04556i	−1.31796	−	0.0408223i
$657$	−8.45489	−	8.45489i	−0.329857	−	0.329857i
$658$		0			0
$659$	41.8771			1.63130			0.815650	−	0.578546i	$-0.196380\pi$
$659$	41.8771			1.63130			0.815650	+	0.578546i	$0.196380\pi$
$660$	−30.3766	+	6.64935i	−1.18241	+	0.258826i
$661$	−15.6144	−	27.0450i	−0.607332	−	1.05193i	−0.991678	−	0.128740i	$-0.958907\pi$
$661$	−15.6144	−	27.0450i	−0.607332	−	1.05193i	0.384347	−	0.923189i	$-0.374427\pi$
$662$	6.76223	+	3.97428i	0.262821	+	0.154465i
$663$	6.11013	−	1.63720i	0.237298	−	0.0635837i
$664$	−2.59739	−	2.72091i	−0.100798	−	0.105592i
$665$		0			0
$666$	−32.9180	−	9.09403i	−1.27555	−	0.352387i
$667$	18.8133	+	70.2121i	0.728453	+	2.71862i
$668$	24.5308	−	23.7827i	0.949124	−	0.920181i
$669$	−24.1574	+	13.9473i	−0.933981	+	0.539234i
$670$	−3.18550	+	10.2847i	−0.123067	+	0.397335i
$671$			15.6353i			0.603593i
$672$		0			0
$673$	15.7088	−	15.7088i	0.605529	−	0.605529i	−0.336246	−	0.941774i	$-0.609157\pi$
$673$	15.7088	−	15.7088i	0.605529	−	0.605529i	0.941774	+	0.336246i	$0.109157\pi$
$674$	4.78325	+	4.85789i	0.184244	+	0.187119i
$675$	2.23022	−	1.97094i	0.0858411	−	0.0758614i
$676$	−0.357763	+	23.1065i	−0.0137601	+	0.888711i
$677$	−9.56539	+	2.56304i	−0.367628	+	0.0985055i	−0.437903	−	0.899022i	$-0.644279\pi$
$677$	−9.56539	+	2.56304i	−0.367628	+	0.0985055i	0.0702757	+	0.997528i	$0.477612\pi$
$678$	6.29282	+	11.0970i	0.241674	+	0.426177i
$679$		0			0
$680$	−12.6643	−	4.13844i	−0.485653	−	0.158702i
$681$	9.09622	−	15.7551i	0.348568	−	0.603738i
$682$	−20.3754	+	34.6687i	−0.780215	+	1.32753i
$683$	2.04177	−	7.62000i	0.0781262	−	0.291571i	−0.915798	−	0.401640i	$-0.868440\pi$
$683$	2.04177	−	7.62000i	0.0781262	−	0.291571i	0.993924	+	0.110069i	$0.0351071\pi$
$684$	−26.6929	+	14.8650i	−1.02063	+	0.568377i
$685$	30.0985	+	9.06769i	1.15001	+	0.346459i
$686$		0			0
$687$	20.9515	−	20.9515i	0.799351	−	0.799351i
$688$	18.3048	+	19.4750i	0.697864	+	0.742477i
$689$	3.84034	−	2.21722i	0.146305	−	0.0844695i
$690$	−62.6858	−	2.41838i	−2.38641	−	0.0920661i
$691$	−34.4612	−	19.8962i	−1.31097	−	0.756886i	−0.328709	−	0.944431i	$-0.606614\pi$
$691$	−34.4612	−	19.8962i	−1.31097	−	0.756886i	−0.982256	+	0.187545i	$0.939947\pi$
$692$	−7.16416	−	28.4945i	−0.272341	−	1.08320i
$693$		0			0
$694$	0.892202	+	0.246483i	0.0338675	+	0.00935636i
$695$	1.25746	−	40.7882i	0.0476981	−	1.54718i
$696$	62.0446	+	18.1791i	2.35180	+	0.689076i
$697$	4.60342	−	17.1802i	0.174367	−	0.650746i
$698$	−0.0990848	+	12.7997i	−0.00375041	+	0.484477i
$699$	−14.2405			−0.538626
$700$		0			0
$701$	17.1754			0.648704			0.324352	−	0.945936i	$-0.394854\pi$
$701$	17.1754			0.648704			0.324352	+	0.945936i	$0.394854\pi$
$702$	0.00783443	−	1.01205i	0.000295692	−	0.0381974i
$703$	−9.10471	+	33.9792i	−0.343391	+	1.28155i
$704$	19.7836	−	10.2281i	0.745624	−	0.385485i
$705$	0.338918	−	10.9935i	0.0127644	−	0.414039i
$706$	19.8756	+	5.49090i	0.748028	+	0.206653i
$707$		0			0
$708$	49.1626	−	12.3606i	1.84764	−	0.464540i
$709$	−2.74131	−	1.58270i	−0.102952	−	0.0594395i	0.447640	−	0.894214i	$-0.352265\pi$
$709$	−2.74131	−	1.58270i	−0.102952	−	0.0594395i	−0.550592	+	0.834774i	$0.685598\pi$
$710$	−14.0869	−	0.543465i	−0.528674	−	0.0203959i
$711$	25.0661	−	14.4719i	0.940052	−	0.542739i
$712$	−12.4507	−	7.57926i	−0.466610	−	0.284045i
$713$	−57.3641	+	57.3641i	−2.14830	+	2.14830i
$714$		0			0
$715$	−7.16579	−	2.15881i	−0.267985	−	0.0807351i
$716$	3.43912	+	6.17559i	0.128526	+	0.230793i
$717$	−1.99383	+	7.44107i	−0.0744609	+	0.277892i
$718$	10.4154	−	17.7218i	0.388701	−	0.661373i
$719$	−13.6822	+	23.6982i	−0.510259	+	0.883794i	0.489671	+	0.871907i	$0.337117\pi$
$719$	−13.6822	+	23.6982i	−0.510259	+	0.883794i	−0.999929	+	0.0118865i	$0.996216\pi$
$720$	−16.0034	+	24.1419i	−0.596411	+	0.899717i
$721$		0			0
$722$	2.26982	+	4.00268i	0.0844739	+	0.148964i
$723$	−54.7806	+	14.6784i	−2.03731	+	0.545897i
$724$	5.40755	+	0.0837264i	0.200970	+	0.00311167i
$725$	−2.81875	+	45.6725i	−0.104686	+	1.69623i
$726$	−8.05411	−	8.17978i	−0.298916	−	0.303580i
$727$	2.54080	−	2.54080i	0.0942330	−	0.0942330i	−0.658419	−	0.752652i	$-0.728774\pi$
$727$	2.54080	−	2.54080i	0.0942330	−	0.0942330i	0.752652	+	0.658419i	$0.228774\pi$
$728$		0			0
$729$			31.1060i			1.15207i
$730$	−3.45457	+	11.1535i	−0.127859	+	0.412809i
$731$	−12.1901	+	7.03793i	−0.450865	+	0.260307i
$732$	19.5287	+	20.1429i	0.721800	+	0.744503i
$733$	4.04099	+	15.0812i	0.149257	+	0.557036i	0.999529	+	0.0306915i	$0.00977094\pi$
$733$	4.04099	+	15.0812i	0.149257	+	0.557036i	−0.850272	+	0.526344i	$0.823562\pi$
$734$	−12.8714	−	3.55589i	−0.475091	−	0.131250i
$735$		0			0
$736$	43.8162	−	9.94061i	1.61509	−	0.366416i
$737$	9.15552	−	2.45321i	0.337248	−	0.0903653i
$738$	−33.3357	−	19.5920i	−1.22711	−	0.721192i
$739$	21.8227	+	37.7981i	0.802763	+	1.39043i	0.917791	+	0.397064i	$0.129971\pi$
$739$	21.8227	+	37.7981i	0.802763	+	1.39043i	−0.115028	+	0.993362i	$0.536696\pi$
$740$	7.13116	+	32.5777i	0.262147	+	1.19758i
$741$	−14.1653			−0.520376
$742$		0			0
$743$	−10.8795	−	10.8795i	−0.399131	−	0.399131i	0.478795	−	0.877926i	$-0.341074\pi$
$743$	−10.8795	−	10.8795i	−0.399131	−	0.399131i	−0.877926	+	0.478795i	$0.841074\pi$
$744$	17.0520	+	70.1128i	0.625157	+	2.57046i
$745$	−13.9739	+	22.5677i	−0.511965	+	0.826817i
$746$	−1.95436	−	7.52635i	−0.0715543	−	0.275559i
$747$	−1.11467	−	4.16001i	−0.0407837	−	0.152207i
$748$	2.85996	+	11.3751i	0.104570	+	0.415915i
$749$		0			0
$750$	−36.9321	−	13.9857i	−1.34857	−	0.510685i
$751$	11.3380	+	6.54601i	0.413730	+	0.238867i	0.692391	−	0.721522i	$-0.256557\pi$
$751$	11.3380	+	6.54601i	0.413730	+	0.238867i	−0.278661	+	0.960389i	$0.589891\pi$
$752$	1.80228	+	7.66845i	0.0657222	+	0.279640i
$753$	12.6766	+	3.39669i	0.461962	+	0.123782i
$754$	10.9172	+	11.0876i	0.397582	+	0.403786i
$755$	7.76969	+	14.4697i	0.282768	+	0.526605i
$756$		0			0
$757$	5.79839	+	5.79839i	0.210746	+	0.210746i	0.804584	−	0.593838i	$-0.202388\pi$
$757$	5.79839	+	5.79839i	0.210746	+	0.210746i	−0.593838	+	0.804584i	$0.702388\pi$
$758$	−16.8461	−	0.130408i	−0.611877	−	0.00473664i
$759$	27.6131	+	47.8273i	1.00229	+	1.73602i
$760$	24.9947	+	16.2916i	0.906652	+	0.590958i
$761$	9.70058	−	16.8019i	0.351646	−	0.609068i	−0.634892	−	0.772601i	$-0.718956\pi$
$761$	9.70058	−	16.8019i	0.351646	−	0.609068i	0.986538	+	0.163533i	$0.0522889\pi$
$762$	15.3394	+	27.0501i	0.555688	+	0.979921i
$763$		0			0
$764$	21.7932	+	13.0363i	0.788449	+	0.471635i
$765$	−10.4488	−	11.1136i	−0.377778	−	0.401812i
$766$	−12.1695	+	3.16005i	−0.439703	+	0.114177i
$767$	11.7846	+	3.15768i	0.425518	+	0.114017i
$768$	12.7122	−	37.8868i	0.458713	−	1.36712i
$769$			21.2703i			0.767028i	0.923535	+	0.383514i	$0.125286\pi$
$769$			21.2703i			0.767028i	−0.923535	+	0.383514i	$0.874714\pi$
$770$		0			0
$771$		−	67.1024i		−	2.41664i
$772$	−5.91507	−	1.68351i	−0.212888	−	0.0605908i
$773$	38.1242	+	10.2153i	1.37123	+	0.367420i	0.867928	−	0.496689i	$-0.165451\pi$
$773$	38.1242	+	10.2153i	1.37123	+	0.367420i	0.503303	+	0.864110i	$0.332118\pi$
$774$	7.69095	+	29.6183i	0.276446	+	1.06461i
$775$	−45.7170	+	22.7621i	−1.64220	+	0.817640i
$776$	3.53973	+	3.70807i	0.127069	+	0.133112i
$777$		0			0
$778$	11.9374	−	6.76937i	0.427975	−	0.242694i
$779$	−19.9147	+	34.4932i	−0.713518	+	1.23585i
$780$	−11.9281	+	6.16896i	−0.427093	+	0.220884i
$781$	6.20530	+	10.7479i	0.222043	+	0.384590i
$782$	−0.183167	+	23.6615i	−0.00655005	+	0.846133i
$783$	3.85216	+	3.85216i	0.137665	+	0.137665i
$784$		0			0
$785$	−0.703835	−	0.212042i	−0.0251210	−	0.00756811i
$786$	25.2088	−	24.8215i	0.899167	−	0.885352i
$787$	5.94471	+	1.59288i	0.211906	+	0.0567800i	0.363210	−	0.931707i	$-0.381681\pi$
$787$	5.94471	+	1.59288i	0.211906	+	0.0567800i	−0.151304	+	0.988487i	$0.548347\pi$
$788$	−5.49668	−	5.66957i	−0.195811	−	0.201970i
$789$	−62.3600	−	36.0036i	−2.22007	−	1.28176i
$790$	−23.9144	−	15.0652i	−0.850838	−	0.535995i
$791$		0			0
$792$	25.4919	+	0.592105i	0.905815	+	0.0210395i
$793$	1.74759	+	6.52209i	0.0620587	+	0.231606i
$794$	44.4104	−	11.5320i	1.57607	−	0.409257i
$795$	−17.5143	−	10.8449i	−0.621168	−	0.384628i
$796$	−11.8960	−	21.3616i	−0.421644	−	0.757142i
$797$	22.2605	+	22.2605i	0.788508	+	0.788508i	0.981250	−	0.192741i	$-0.0617378\pi$
$797$	22.2605	+	22.2605i	0.788508	+	0.788508i	−0.192741	+	0.981250i	$0.561738\pi$
$798$		0			0
$799$	−4.14863			−0.146768
$800$	28.1420	+	2.83338i	0.994970	+	0.100175i
$801$	−8.34430	−	14.4528i	−0.294831	−	0.510663i
$802$	24.5048	−	41.6948i	0.865294	−	1.47229i
$803$	9.92886	−	2.66043i	0.350382	−	0.0938845i
$804$	8.73094	−	14.5958i	0.307917	−	0.514755i
$805$		0			0
$806$	−4.62439	+	16.7391i	−0.162887	+	0.589609i
$807$	−7.72810	−	28.8416i	−0.272042	−	1.01527i
$808$	17.0324	+	31.1497i	0.599196	+	1.09584i
$809$	9.83280	−	5.67697i	0.345703	−	0.199592i	−0.317088	−	0.948396i	$-0.602705\pi$
$809$	9.83280	−	5.67697i	0.345703	−	0.199592i	0.662791	+	0.748804i	$0.269372\pi$
$810$	23.0187	−	12.1316i	0.808794	−	0.426260i
$811$			15.7687i			0.553713i	0.960911	+	0.276857i	$0.0892927\pi$
$811$			15.7687i			0.553713i	−0.960911	+	0.276857i	$0.910707\pi$
$812$		0			0
$813$	19.8565	−	19.8565i	0.696397	−	0.696397i
$814$	20.9198	−	20.5984i	0.733239	−	0.721974i
$815$	−9.86525	−	41.9481i	−0.345565	−	1.46938i
$816$	17.8921	+	11.0824i	0.626349	+	0.387961i
$817$	30.4466	−	8.15813i	1.06519	−	0.285417i
$818$	−1.45309	+	0.824009i	−0.0508060	+	0.0288108i
$819$		0			0
$820$	−1.74765	+	37.7182i	−0.0610306	+	1.31718i
$821$	−22.6844	+	39.2906i	−0.791692	+	1.37125i	0.133226	+	0.991086i	$0.457466\pi$
$821$	−22.6844	+	39.2906i	−0.791692	+	1.37125i	−0.924918	+	0.380166i	$0.875867\pi$
$822$	−42.8101	−	25.1603i	−1.49317	−	0.877566i
$823$	−0.755780	+	2.82061i	−0.0263448	+	0.0983203i	−0.977846	−	0.209324i	$-0.932874\pi$
$823$	−0.755780	+	2.82061i	−0.0263448	+	0.0983203i	0.951502	+	0.307644i	$0.0995405\pi$
$824$	5.87433	−	1.42869i	0.204642	−	0.0497706i
$825$	6.91246	+	34.0721i	0.240661	+	1.18624i
$826$		0			0
$827$	−34.8943	+	34.8943i	−1.21339	+	1.21339i	−0.243489	+	0.969904i	$0.578292\pi$
$827$	−34.8943	+	34.8943i	−1.21339	+	1.21339i	−0.969904	+	0.243489i	$0.921708\pi$
$828$	49.4761	+	14.0815i	1.71941	+	0.489367i
$829$	−7.18791	+	4.14994i	−0.249647	+	0.144134i	−0.619602	−	0.784916i	$-0.712706\pi$
$829$	−7.18791	+	4.14994i	−0.249647	+	0.144134i	0.369956	+	0.929049i	$0.379373\pi$
$830$	−3.08625	+	2.85697i	−0.107125	+	0.0991668i
$831$	16.2654	+	9.39085i	0.564242	+	0.325765i
$832$	7.10931	−	6.47779i	0.246471	−	0.224577i
$833$		0			0
$834$	−17.1655	+	62.1346i	−0.594394	+	2.15155i
$835$	−26.1661	−	27.8308i	−0.905517	−	0.963125i
$836$	0.406625	−	26.2623i	0.0140634	−	0.908301i
$837$	−1.57363	+	5.87286i	−0.0543926	+	0.202996i
$838$	−4.96015	−	0.0383973i	−0.171345	−	0.00132641i
$839$	0.818867			0.0282704			0.0141352	−	0.999900i	$-0.495500\pi$
$839$	0.818867			0.0282704			0.0141352	+	0.999900i	$0.495500\pi$
$840$		0			0
$841$	−54.7568			−1.88816
$842$	37.8778	+	0.293218i	1.30536	+	0.0101050i
$843$	17.3898	−	64.8997i	0.598938	−	2.23527i
$844$	−0.287180	+	18.5478i	−0.00988514	+	0.638441i
$845$	25.8247	+	0.796148i	0.888395	+	0.0273883i
$846$	−2.40166	+	8.69336i	−0.0825706	+	0.298884i
$847$		0			0
$848$	14.1262	+	4.25798i	0.485095	+	0.146220i
$849$	−26.8498	−	15.5018i	−0.921484	−	0.532019i
$850$	−4.84352	+	14.0865i	−0.166132	+	0.483162i
$851$	51.2929	−	29.6140i	1.75830	−	1.01515i
$852$	21.4185	+	6.09600i	0.733787	+	0.208846i
$853$	−24.4303	+	24.4303i	−0.836477	+	0.836477i	−0.988393	−	0.151916i	$-0.951456\pi$
$853$	−24.4303	+	24.4303i	−0.836477	+	0.836477i	0.151916	+	0.988393i	$0.451456\pi$
$854$		0			0
$855$	16.1599	+	30.0950i	0.552657	+	1.02923i
$856$	6.72052	+	27.6328i	0.229703	+	0.944468i
$857$	−5.27702	+	19.6941i	−0.180259	+	0.672738i	0.815336	+	0.578988i	$0.196552\pi$
$857$	−5.27702	+	19.6941i	−0.180259	+	0.672738i	−0.995596	+	0.0937499i	$0.970115\pi$
$858$	10.1921	+	5.99010i	0.347954	+	0.204499i
$859$	5.83870	−	10.1129i	0.199214	−	0.345048i	−0.749060	−	0.662502i	$-0.769495\pi$
$859$	5.83870	−	10.1129i	0.199214	−	0.345048i	0.948274	+	0.317454i	$0.102828\pi$
$860$	22.0850	−	20.1291i	0.753093	−	0.686395i
$861$		0			0
$862$	46.2595	−	26.2326i	1.57560	−	0.893485i
$863$	42.0243	−	11.2604i	1.43052	−	0.383308i	0.541319	−	0.840818i	$-0.317925\pi$
$863$	42.0243	−	11.2604i	1.43052	−	0.383308i	0.889204	+	0.457510i	$0.151259\pi$
$864$	2.47141	−	2.28714i	0.0840790	−	0.0778099i
$865$	−31.9769	+	7.52024i	−1.08725	+	0.255696i
$866$	−40.0440	+	39.4288i	−1.36075	+	1.33985i
$867$	22.1864	−	22.1864i	0.753488	−	0.753488i
$868$		0			0
$869$			24.8822i			0.844071i
$870$	21.3863	−	69.0482i	0.725064	−	2.34095i
$871$	3.54492	−	2.04666i	0.120115	−	0.0693485i
$872$	−14.9019	+	8.14822i	−0.504642	+	0.275934i
$873$	1.51908	+	5.66928i	0.0514130	+	0.191876i
$874$	14.1100	−	51.0744i	0.477278	−	1.72762i
$875$		0			0
$876$	9.46842	−	15.8287i	0.319908	−	0.534802i
$877$	−2.15869	+	0.578418i	−0.0728936	+	0.0195318i	−0.295082	−	0.955472i	$-0.595347\pi$
$877$	−2.15869	+	0.578418i	−0.0728936	+	0.0195318i	0.222188	+	0.975004i	$0.428680\pi$
$878$	−11.9728	+	20.3717i	−0.404062	+	0.687511i
$879$	−12.0621	−	20.8922i	−0.406844	−	0.704675i
$880$	−11.0948	−	22.2915i	−0.374005	−	0.751448i
$881$	−11.1426			−0.375403			−0.187702	−	0.982226i	$-0.560104\pi$
$881$	−11.1426			−0.375403			−0.187702	+	0.982226i	$0.560104\pi$
$882$		0			0
$883$	13.0912	+	13.0912i	0.440554	+	0.440554i	0.892198	−	0.451644i	$-0.149162\pi$
$883$	13.0912	+	13.0912i	0.440554	+	0.440554i	−0.451644	+	0.892198i	$0.649162\pi$
$884$	2.46442	+	4.42533i	0.0828874	+	0.148840i
$885$	−12.9750	−	55.1710i	−0.436149	−	1.85455i
$886$	−17.5342	+	4.55310i	−0.589073	+	0.152964i
$887$	1.36658	+	5.10015i	0.0458853	+	0.171246i	0.985066	−	0.172177i	$-0.0550801\pi$
$887$	1.36658	+	5.10015i	0.0458853	+	0.171246i	−0.939181	+	0.343423i	$0.888413\pi$
$888$	1.22328	−	52.6660i	0.0410507	−	1.76736i
$889$		0			0
$890$	−8.68636	+	13.7887i	−0.291168	+	0.462199i
$891$	−19.8376	−	11.4533i	−0.664585	−	0.383699i
$892$	−15.5479	−	16.0370i	−0.520583	−	0.536957i
$893$	8.97362	+	2.40448i	0.300291	+	0.0804627i
$894$	29.8777	−	29.4187i	0.999261	−	0.983909i
$895$	6.96268	−	3.73871i	0.232737	−	0.124971i
$896$		0			0
$897$	16.8643	+	16.8643i	0.563082	+	0.563082i
$898$	−0.0336328	+	4.34467i	−0.00112234	+	0.144984i
$899$	−46.7387	−	80.9538i	−1.55882	−	2.69996i
$900$	26.7139	+	18.3042i	0.890464	+	0.610140i
$901$	−3.88509	+	6.72917i	−0.129431	+	0.224181i
$902$	28.9151	−	16.3970i	0.962767	−	0.545961i
$903$		0			0
$904$	−7.38901	+	7.05355i	−0.245755	+	0.234598i
$905$	0.186321	−	6.04368i	0.00619351	−	0.200899i
$906$	−6.52060	−	25.1112i	−0.216633	−	0.834263i
$907$	−10.1014	−	2.70666i	−0.335411	−	0.0898731i	0.0871827	−	0.996192i	$-0.472214\pi$
$907$	−10.1014	−	2.70666i	−0.335411	−	0.0898731i	−0.422594	+	0.906319i	$0.638880\pi$
$908$	14.0111	+	3.98775i	0.464976	+	0.132338i
$909$			40.6472i			1.34818i
$910$		0			0
$911$		−	0.169000i		−	0.00559921i	−0.999996	−	0.00279960i	$-0.999109\pi$
$911$		−	0.169000i		−	0.00559921i	0.999996	−	0.00279960i	$-0.000891143\pi$
$912$	−32.2781	−	34.3416i	−1.06883	−	1.13716i
$913$	3.57624	+	0.958252i	0.118356	+	0.0317135i
$914$	−34.2482	+	8.89321i	−1.13283	+	0.294161i
$915$	22.8527	−	21.4858i	0.755486	−	0.710297i
$916$	20.3613	+	12.1797i	0.672756	+	0.402430i
$917$		0			0
$918$	0.874784	+	1.54263i	0.0288722	+	0.0509142i
$919$	−8.49828	+	14.7195i	−0.280332	+	0.485550i	−0.971467	−	0.237176i	$-0.923778\pi$
$919$	−8.49828	+	14.7195i	−0.280332	+	0.485550i	0.691134	+	0.722726i	$0.257111\pi$
$920$	−10.3613	−	49.1527i	−0.341603	−	1.62052i
$921$	−19.4983	−	33.7720i	−0.642490	−	1.11283i
$922$	−3.02701	−	0.0234326i	−0.0996893	−	0.000771711i
$923$	3.78979	+	3.78979i	0.124743	+	0.124743i
$924$		0			0
$925$	36.5409	−	7.41334i	1.20146	−	0.243749i
$926$	21.1455	+	21.4755i	0.694885	+	0.705727i
$927$	6.68585	+	1.79147i	0.219592	+	0.0588395i
$928$	−2.00329	+	51.7320i	−0.0657612	+	1.69819i
$929$	−26.2847	−	15.1755i	−0.862374	−	0.497892i	0.00243225	−	0.999997i	$-0.499226\pi$
$929$	−26.2847	−	15.1755i	−0.862374	−	0.497892i	−0.864807	+	0.502105i	$0.832559\pi$
$930$	78.6716	−	17.8603i	2.57974	−	0.585661i
$931$		0			0
$932$	−2.78046	−	11.0589i	−0.0910770	−	0.362246i
$933$	−8.01262	−	29.9035i	−0.262322	−	0.978997i
$934$	6.90751	+	26.6012i	0.226021	+	0.870417i
$935$	12.7653	−	3.00211i	0.417470	−	0.0981794i
$936$	10.6998	−	2.60229i	0.349735	−	0.0850586i
$937$	−13.3701	−	13.3701i	−0.436781	−	0.436781i	0.454146	−	0.890927i	$-0.349944\pi$
$937$	−13.3701	−	13.3701i	−0.436781	−	0.436781i	−0.890927	+	0.454146i	$0.849944\pi$
$938$		0			0
$939$	63.2786			2.06502
$940$	8.60349	−	1.88328i	0.280615	−	0.0614258i
$941$	−15.1703	−	26.2757i	−0.494537	−	0.856563i	0.505443	−	0.862860i	$-0.331329\pi$
$941$	−15.1703	−	26.2757i	−0.494537	−	0.856563i	−0.999980	+	0.00629695i	$0.997996\pi$
$942$	1.00109	+	0.588358i	0.0326172	+	0.0191697i
$943$	64.7745	−	17.3563i	2.10935	−	0.565198i
$944$	19.1980	+	35.7653i	0.624841	+	1.16406i
$945$		0			0
$946$	−25.3566	−	7.00509i	−0.824413	−	0.227755i
$947$	−2.02470	−	7.55627i	−0.0657938	−	0.245546i	0.925195	−	0.379493i	$-0.123901\pi$
$947$	−2.02470	−	7.55627i	−0.0657938	−	0.245546i	−0.990988	+	0.133947i	$0.957235\pi$
$948$	31.0782	+	32.0557i	1.00937	+	1.04112i
$949$	3.84435	−	2.21954i	0.124793	−	0.0720493i
$950$	18.6410	−	27.6623i	0.604793	−	0.897482i
$951$		−	23.4031i		−	0.758897i
$952$		0			0
$953$	−4.36819	+	4.36819i	−0.141500	+	0.141500i	−0.774308	−	0.632809i	$-0.781902\pi$
$953$	−4.36819	+	4.36819i	−0.141500	+	0.141500i	0.632809	+	0.774308i	$0.281902\pi$
$954$	11.8517	+	12.0367i	0.383714	+	0.389701i
$955$	14.9469	−	24.1391i	0.483672	−	0.781123i
$956$	−6.16788	−	0.0954987i	−0.199483	−	0.00308865i
$957$	−61.4669	+	16.4700i	−1.98694	+	0.532400i
$958$	9.98527	+	17.6084i	0.322609	+	0.568901i
$959$		0			0
$960$	−42.1358	−	14.8607i	−1.35993	−	0.479626i
$961$	36.6631	−	63.5024i	1.18268	−	2.04846i
$962$	6.42414	−	10.9307i	0.207123	−	0.352418i
$963$	−8.42704	+	31.4502i	−0.271558	+	1.01347i
$964$	−22.0949	−	39.6755i	−0.711628	−	1.27786i
$965$	−1.98342	+	6.58361i	−0.0638487	+	0.211934i
$966$		0			0
$967$	−11.8371	+	11.8371i	−0.380654	+	0.380654i	−0.871338	−	0.490684i	$-0.836747\pi$
$967$	−11.8371	+	11.8371i	−0.380654	+	0.380654i	0.490684	+	0.871338i	$0.336747\pi$
$968$	4.77968	−	7.85175i	0.153625	−	0.252365i
$969$	21.4955	−	12.4104i	0.690536	−	0.398681i
$970$	4.20596	−	3.89349i	0.135045	−	0.125012i
$971$	42.9451	+	24.7944i	1.37817	+	0.795689i	0.991940	−	0.126712i	$-0.0404423\pi$
$971$	42.9451	+	24.7944i	1.37817	+	0.795689i	0.386234	+	0.922401i	$0.373776\pi$
$972$	−43.3258	+	10.8931i	−1.38968	+	0.349396i
$973$		0			0
$974$	47.7755	+	13.1986i	1.53082	+	0.422911i
$975$	6.69177	+	13.4402i	0.214308	+	0.430430i
$976$	−11.8296	+	19.0984i	−0.378656	+	0.611326i
$977$	−12.7675	+	47.6489i	−0.408468	+	1.52442i	0.389100	+	0.921195i	$0.372786\pi$
$977$	−12.7675	+	47.6489i	−0.408468	+	1.52442i	−0.797568	+	0.603229i	$0.793881\pi$
$978$	−0.526937	+	68.0696i	−0.0168496	+	2.17662i
$979$	14.3467			0.458523
$980$		0			0
$981$	−19.4455			−0.620847
$982$	−0.450997	+	58.2596i	−0.0143919	+	1.85914i
$983$	−8.01244	+	29.9028i	−0.255557	+	0.953752i	0.712222	+	0.701954i	$0.247689\pi$
$983$	−8.01244	+	29.9028i	−0.255557	+	0.953752i	−0.967780	+	0.251799i	$0.918978\pi$
$984$	16.7712	−	57.2396i	0.534646	−	1.82473i
$985$	−6.43228	+	6.04754i	−0.204949	+	0.192691i
$986$	−26.2806	−	7.26038i	−0.836946	−	0.231218i
$987$		0			0
$988$	−2.76577	−	11.0005i	−0.0879910	−	0.349972i
$989$	−45.9602	−	26.5351i	−1.46145	−	0.843768i
$990$	1.09902	−	28.4873i	0.0349292	−	0.905386i
$991$	23.4196	−	13.5213i	0.743948	−	0.429519i	−0.0795551	−	0.996830i	$-0.525350\pi$
$991$	23.4196	−	13.5213i	0.743948	−	0.429519i	0.823503	+	0.567312i	$0.192017\pi$
$992$	−51.1187	+	26.9317i	−1.62302	+	0.855083i
$993$	−9.79539	+	9.79539i	−0.310847	+	0.310847i
$994$		0			0
$995$	−24.0842	+	12.9323i	−0.763520	+	0.409983i
$996$	5.80414	−	3.23226i	0.183911	−	0.102418i
$997$	11.0937	−	41.4022i	0.351341	−	1.31122i	−0.533687	−	0.845682i	$-0.679194\pi$
$997$	11.0937	−	41.4022i	0.351341	−	1.31122i	0.885027	−	0.465539i	$-0.154139\pi$
$998$	−23.8748	+	40.6228i	−0.755742	+	1.28589i
$999$	2.21946	−	3.84422i	0.0702207	−	0.121626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.n.667.2		112
4.3	odd	2	inner	980.2.x.n.667.5		112
5.3	odd	4	inner	980.2.x.n.863.14		112
7.2	even	3		980.2.k.m.687.20	yes	56
7.3	odd	6	inner	980.2.x.n.67.20		112
7.4	even	3	inner	980.2.x.n.67.19		112
7.5	odd	6		980.2.k.m.687.19	✓	56
7.6	odd	2	inner	980.2.x.n.667.1		112
20.3	even	4	inner	980.2.x.n.863.19		112
28.3	even	6	inner	980.2.x.n.67.13		112
28.11	odd	6	inner	980.2.x.n.67.14		112
28.19	even	6		980.2.k.m.687.26	yes	56
28.23	odd	6		980.2.k.m.687.25	yes	56
28.27	even	2	inner	980.2.x.n.667.6		112
35.3	even	12	inner	980.2.x.n.263.6		112
35.13	even	4	inner	980.2.x.n.863.13		112
35.18	odd	12	inner	980.2.x.n.263.5		112
35.23	odd	12		980.2.k.m.883.25	yes	56
35.33	even	12		980.2.k.m.883.26	yes	56
140.3	odd	12	inner	980.2.x.n.263.1		112
140.23	even	12		980.2.k.m.883.20	yes	56
140.83	odd	4	inner	980.2.x.n.863.20		112
140.103	odd	12		980.2.k.m.883.19	yes	56
140.123	even	12	inner	980.2.x.n.263.2		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.k.m.687.19	✓	56	7.5	odd	6
980.2.k.m.687.20	yes	56	7.2	even	3
980.2.k.m.687.25	yes	56	28.23	odd	6
980.2.k.m.687.26	yes	56	28.19	even	6
980.2.k.m.883.19	yes	56	140.103	odd	12
980.2.k.m.883.20	yes	56	140.23	even	12
980.2.k.m.883.25	yes	56	35.23	odd	12
980.2.k.m.883.26	yes	56	35.33	even	12
980.2.x.n.67.13		112	28.3	even	6	inner
980.2.x.n.67.14		112	28.11	odd	6	inner
980.2.x.n.67.19		112	7.4	even	3	inner
980.2.x.n.67.20		112	7.3	odd	6	inner
980.2.x.n.263.1		112	140.3	odd	12	inner
980.2.x.n.263.2		112	140.123	even	12	inner
980.2.x.n.263.5		112	35.18	odd	12	inner
980.2.x.n.263.6		112	35.3	even	12	inner
980.2.x.n.667.1		112	7.6	odd	2	inner
980.2.x.n.667.2		112	1.1	even	1	trivial
980.2.x.n.667.5		112	4.3	odd	2	inner
980.2.x.n.667.6		112	28.27	even	2	inner
980.2.x.n.863.13		112	35.13	even	4	inner
980.2.x.n.863.14		112	5.3	odd	4	inner
980.2.x.n.863.19		112	20.3	even	4	inner
980.2.x.n.863.20		112	140.83	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.41417 - 0.0109473i) q^{2} +(0.646443 - 2.41256i) q^{3} +(1.99976 + 0.0309628i) q^{4} +(0.0689030 - 2.23501i) q^{5} +(-0.940592 + 3.40469i) q^{6} +(-2.82766 - 0.0656787i) q^{8} +(-2.80447 - 1.61916i) q^{9} +O(q^{10})\)	\(q+(-1.41417 - 0.0109473i) q^{2} +(0.646443 - 2.41256i) q^{3} +(1.99976 + 0.0309628i) q^{4} +(0.0689030 - 2.23501i) q^{5} +(-0.940592 + 3.40469i) q^{6} +(-2.82766 - 0.0656787i) q^{8} +(-2.80447 - 1.61916i) q^{9} +(-0.121908 + 3.15993i) q^{10} +(2.41093 - 1.39195i) q^{11} +(1.36743 - 4.80452i) q^{12} +(0.850111 - 0.850111i) q^{13} +(-5.34754 - 1.61104i) q^{15} +(3.99808 + 0.123836i) q^{16} +(-0.545228 + 2.03482i) q^{17} +(3.94828 + 2.32048i) q^{18} +(2.35869 - 4.08538i) q^{19} +(0.206991 - 4.46734i) q^{20} +(-3.42470 + 1.94206i) q^{22} +(-7.67188 + 2.05567i) q^{23} +(-1.98638 + 6.77945i) q^{24} +(-4.99050 - 0.307997i) q^{25} +(-1.21151 + 1.19290i) q^{26} +(-0.420915 + 0.420915i) q^{27} -9.15187i q^{29} +(7.54470 + 2.33682i) q^{30} +(8.84560 - 5.10701i) q^{31} +(-5.65262 - 0.218894i) q^{32} +(-1.79963 - 6.71632i) q^{33} +(0.793322 - 2.87161i) q^{34} +(-5.55814 - 3.32477i) q^{36} +(-7.20298 + 1.93003i) q^{37} +(-3.38032 + 5.75160i) q^{38} +(-1.50139 - 2.60049i) q^{39} +(-0.341627 + 6.31532i) q^{40} -8.44310 q^{41} +(4.72474 + 4.72474i) q^{43} +(4.86437 - 2.70892i) q^{44} +(-3.81208 + 6.15645i) q^{45} +(10.8719 - 2.82309i) q^{46} +(0.509705 + 1.90224i) q^{47} +(2.88330 - 9.56556i) q^{48} +(7.05406 + 0.490193i) q^{50} +(4.55666 + 2.63079i) q^{51} +(1.72634 - 1.67370i) q^{52} +(3.56281 + 0.954652i) q^{53} +(0.599854 - 0.590638i) q^{54} +(-2.94489 - 5.48435i) q^{55} +(-8.33145 - 8.33145i) q^{57} +(-0.100188 + 12.9423i) q^{58} +(5.07401 + 8.78844i) q^{59} +(-10.6439 - 3.38726i) q^{60} +(-2.80816 + 4.86388i) q^{61} +(-12.5651 + 7.12535i) q^{62} +(7.99137 + 0.371434i) q^{64} +(-1.84143 - 1.95858i) q^{65} +(2.47146 + 9.51772i) q^{66} +(3.28874 + 0.881215i) q^{67} +(-1.15333 + 4.05227i) q^{68} +19.8377i q^{69} +4.45800i q^{71} +(7.82377 + 4.76265i) q^{72} +(3.56653 + 0.955649i) q^{73} +(10.2074 - 2.65054i) q^{74} +(-3.96914 + 11.8408i) q^{75} +(4.84332 - 8.09674i) q^{76} +(2.09476 + 3.69398i) q^{78} +(-4.46895 + 7.74045i) q^{79} +(0.552255 - 8.92721i) q^{80} +(-4.11411 - 7.12584i) q^{81} +(11.9400 + 0.0924293i) q^{82} +(0.940405 + 0.940405i) q^{83} +(4.51026 + 1.35879i) q^{85} +(-6.62987 - 6.73331i) q^{86} +(-22.0794 - 5.91616i) q^{87} +(-6.90871 + 3.77762i) q^{88} +(4.46303 + 2.57673i) q^{89} +(5.45833 - 8.66455i) q^{90} +(-15.4056 + 3.87331i) q^{92} +(-6.60279 - 24.6419i) q^{93} +(-0.699986 - 2.69568i) q^{94} +(-8.96832 - 5.55319i) q^{95} +(-4.18219 + 13.4958i) q^{96} +(-1.28159 - 1.28159i) q^{97} -9.01518 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 4 q^{2} - 32 q^{8}+O(q^{10}) \) 112 * q + 4 * q^2 - 32 * q^8	\( 112 q + 4 q^{2} - 32 q^{8} - 32 q^{16} + 40 q^{22} - 32 q^{25} + 28 q^{30} + 64 q^{32} + 32 q^{36} + 8 q^{37} + 184 q^{46} - 24 q^{50} - 96 q^{53} - 16 q^{57} - 124 q^{58} - 8 q^{60} + 120 q^{65} + 80 q^{72} - 72 q^{78} + 72 q^{81} + 192 q^{85} - 104 q^{86} - 48 q^{88} - 304 q^{92} + 176 q^{93}+O(q^{100}) \) 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

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