LMFDB - Embedded newform 980.2.x.n.667.5

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			667.5
Character	$\chi$	$=$	980.667
Dual form			980.2.x.n.263.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21923 + 0.716566i) q^{2} +(-0.646443 + 2.41256i) q^{3} +(0.973066 - 1.74732i) q^{4} +(0.0689030 - 2.23501i) q^{5} +(-0.940592 - 3.40469i) q^{6} +(0.0656787 + 2.82766i) q^{8} +(-2.80447 - 1.61916i) q^{9} +O(q^{10})$	\(q+(-1.21923 + 0.716566i) q^{2} +(-0.646443 + 2.41256i) q^{3} +(0.973066 - 1.74732i) q^{4} +(0.0689030 - 2.23501i) q^{5} +(-0.940592 - 3.40469i) q^{6} +(0.0656787 + 2.82766i) q^{8} +(-2.80447 - 1.61916i) q^{9} +(1.51752 + 2.77437i) q^{10} +(-2.41093 + 1.39195i) q^{11} +(3.58649 + 3.47712i) q^{12} +(0.850111 - 0.850111i) q^{13} +(5.34754 + 1.61104i) q^{15} +(-2.10629 - 3.40052i) q^{16} +(-0.545228 + 2.03482i) q^{17} +(4.57955 - 0.0354510i) q^{18} +(-2.35869 + 4.08538i) q^{19} +(-3.83823 - 2.29520i) q^{20} +(1.94206 - 3.42470i) q^{22} +(7.67188 - 2.05567i) q^{23} +(-6.86436 - 1.66947i) q^{24} +(-4.99050 - 0.307997i) q^{25} +(-0.427324 + 1.64565i) q^{26} +(0.420915 - 0.420915i) q^{27} -9.15187i q^{29} +(-7.67432 + 1.86764i) q^{30} +(-8.84560 + 5.10701i) q^{31} +(5.00476 + 2.63674i) 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} +(-0.0516427 - 6.67119i) q^{38} +(1.50139 + 2.60049i) q^{39} +(6.32437 + 0.0480423i) q^{40} -8.44310 q^{41} +(-4.72474 - 4.72474i) q^{43} +(0.0861972 + 5.56713i) q^{44} +(-3.81208 + 6.15645i) q^{45} +(-7.88080 + 8.00376i) q^{46} +(-0.509705 - 1.90224i) q^{47} +(9.56556 - 2.88330i) q^{48} +(6.30530 - 3.20051i) q^{50} +(-4.55666 - 2.63079i) q^{51} +(-0.658206 - 2.31263i) q^{52} +(3.56281 + 0.954652i) q^{53} +(-0.211581 + 0.814807i) q^{54} +(2.94489 + 5.48435i) q^{55} +(-8.33145 - 8.33145i) q^{57} +(6.55792 + 11.1583i) q^{58} +(-5.07401 - 8.78844i) q^{59} +(8.01851 - 7.77625i) q^{60} +(-2.80816 + 4.86388i) q^{61} +(7.12535 - 12.5651i) q^{62} +(-7.99137 + 0.371434i) q^{64} +(-1.84143 - 1.95858i) q^{65} +(7.00686 + 6.89921i) q^{66} +(-3.28874 - 0.881215i) q^{67} +(3.02495 + 2.93270i) q^{68} +19.8377i q^{69} -4.45800i q^{71} +(4.39426 - 8.03646i) q^{72} +(3.56653 + 0.955649i) q^{73} +(7.39912 - 7.51457i) q^{74} +(3.96914 - 11.8408i) q^{75} +(4.84332 + 8.09674i) q^{76} +(-3.69398 - 2.09476i) q^{78} +(4.46895 - 7.74045i) q^{79} +(-7.74532 + 4.47326i) q^{80} +(-4.11411 - 7.12584i) q^{81} +(10.2941 - 6.05004i) q^{82} +(-0.940405 - 0.940405i) q^{83} +(4.51026 + 1.35879i) q^{85} +(9.14616 + 2.37498i) q^{86} +(22.0794 + 5.91616i) q^{87} +(-4.09431 - 6.72587i) q^{88} +(4.46303 + 2.57673i) q^{89} +(0.236311 - 10.2378i) q^{90} +(3.87331 - 15.4056i) q^{92} +(-6.60279 - 24.6419i) q^{93} +(1.98453 + 1.95405i) q^{94} +(8.96832 + 5.55319i) q^{95} +(-9.59658 + 10.3698i) 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 $

$2$	−1.21923	+	0.716566i	−0.862129	+	0.506689i
$2$	−1.21923	+	0.716566i	−0.862129	+	0.506689i
$3$	−0.646443	+	2.41256i	−0.373224	+	1.39289i	0.482698	+	0.875787i	$0.339657\pi$
$3$	−0.646443	+	2.41256i	−0.373224	+	1.39289i	−0.855922	+	0.517105i	$0.827010\pi$
$4$	0.973066	−	1.74732i	0.486533	−	0.873662i
$5$	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
$8$	0.0656787	+	2.82766i	0.0232209	+	0.999730i
$9$	−2.80447	−	1.61916i	−0.934825	−	0.539721i
$10$	1.51752	+	2.77437i	0.479882	+	0.877333i
$11$	−2.41093	+	1.39195i	−0.726922	+	0.419688i	−0.817295	−	0.576220i	$-0.804527\pi$
$11$	−2.41093	+	1.39195i	−0.726922	+	0.419688i	0.0903733	+	0.995908i	$0.471194\pi$
$12$	3.58649	+	3.47712i	1.03533	+	1.00376i
$13$	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
$16$	−2.10629	−	3.40052i	−0.526572	−	0.850131i
$17$	−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	$0.165561\pi$
$18$	4.57955	−	0.0354510i	1.07941	−	0.00835588i
$19$	−2.35869	+	4.08538i	−0.541121	+	0.937250i	0.457719	+	0.889097i	$0.348667\pi$
$19$	−2.35869	+	4.08538i	−0.541121	+	0.937250i	−0.998840	+	0.0481525i	$0.984667\pi$
$20$	−3.83823	−	2.29520i	−0.858255	−	0.513223i
$21$		0			0
$22$	1.94206	−	3.42470i	0.414049	−	0.730149i
$23$	7.67188	−	2.05567i	1.59970	−	0.428638i	0.654747	−	0.755848i	$-0.272775\pi$
$23$	7.67188	−	2.05567i	1.59970	−	0.428638i	0.944951	+	0.327211i	$0.106109\pi$
$24$	−6.86436	−	1.66947i	−1.40118	−	0.340779i
$25$	−4.99050	−	0.307997i	−0.998101	−	0.0615994i
$26$	−0.427324	+	1.64565i	−0.0838051	+	0.322738i
$27$	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	$-0.323235\pi$
$30$	−7.67432	+	1.86764i	−1.40113	+	0.340982i
$31$	−8.84560	+	5.10701i	−1.58872	+	0.917246i	−0.595198	+	0.803579i	$0.702927\pi$
$31$	−8.84560	+	5.10701i	−1.58872	+	0.917246i	−0.993519	+	0.113668i	$0.963740\pi$
$32$	5.00476	+	2.63674i	0.884724	+	0.466114i
$33$	−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	$0.626691\pi$
$38$	−0.0516427	−	6.67119i	−0.00837756	−	1.08221i
$39$	1.50139	+	2.60049i	0.240415	+	0.416412i
$40$	6.32437	+	0.0480423i	0.999971	+	0.00759616i
$41$	−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	0.248194	−	0.968710i	$-0.420163\pi$
$43$	−4.72474	−	4.72474i	−0.720516	−	0.720516i	−0.968710	+	0.248194i	$0.920163\pi$
$44$	0.0861972	+	5.56713i	0.0129947	+	0.839276i
$45$	−3.81208	+	6.15645i	−0.568271	+	0.917750i
$46$	−7.88080	+	8.00376i	−1.16196	+	1.18009i
$47$	−0.509705	−	1.90224i	−0.0743481	−	0.277471i	0.918737	−	0.394871i	$-0.129211\pi$
$47$	−0.509705	−	1.90224i	−0.0743481	−	0.277471i	−0.993085	+	0.117400i	$0.962544\pi$
$48$	9.56556	−	2.88330i	1.38067	−	0.416168i
$49$		0			0
$50$	6.30530	−	3.20051i	0.891704	−	0.452620i
$51$	−4.55666	−	2.63079i	−0.638060	−	0.368384i
$52$	−0.658206	−	2.31263i	−0.0912768	−	0.320705i
$53$	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	$0.501809\pi$
$54$	−0.211581	+	0.814807i	−0.0287925	+	0.110881i
$55$	2.94489	+	5.48435i	0.397090	+	0.739509i
$56$		0			0
$57$	−8.33145	−	8.33145i	−1.10353	−	1.10353i
$58$	6.55792	+	11.1583i	0.861097	+	1.46515i
$59$	−5.07401	−	8.78844i	−0.660580	−	1.14416i	−0.980464	−	0.196701i	$-0.936977\pi$
$59$	−5.07401	−	8.78844i	−0.660580	−	1.14416i	0.319884	−	0.947457i	$-0.396356\pi$
$60$	8.01851	−	7.77625i	1.03519	−	1.00391i
$61$	−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	$0.283736\pi$
$62$	7.12535	−	12.5651i	0.904921	−	1.59577i
$63$		0			0
$64$	−7.99137	+	0.371434i	−0.998922	+	0.0464293i
$65$	−1.84143	−	1.95858i	−0.228401	−	0.242932i
$66$	7.00686	+	6.89921i	0.862485	+	0.849234i
$67$	−3.28874	−	0.881215i	−0.401783	−	0.107658i	0.0522678	−	0.998633i	$-0.483355\pi$
$67$	−3.28874	−	0.881215i	−0.401783	−	0.107658i	−0.454051	+	0.890976i	$0.650022\pi$
$68$	3.02495	+	2.93270i	0.366829	+	0.355642i
$69$			19.8377i			2.38818i
$70$		0			0
$71$		−	4.45800i		−	0.529067i	−0.964377	−	0.264533i	$-0.914782\pi$
$71$		−	4.45800i		−	0.529067i	0.964377	−	0.264533i	$-0.0852180\pi$
$72$	4.39426	−	8.03646i	0.517868	−	0.947106i
$73$	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	$0.514007\pi$
$74$	7.39912	−	7.51457i	0.860131	−	0.873551i
$75$	3.96914	−	11.8408i	0.458317	−	1.36726i
$76$	4.84332	+	8.09674i	0.555566	+	0.928760i
$77$		0			0
$78$	−3.69398	−	2.09476i	−0.418260	−	0.237185i
$79$	4.46895	−	7.74045i	0.502796	−	0.870868i	−0.497199	−	0.867637i	$-0.665638\pi$
$79$	4.46895	−	7.74045i	0.502796	−	0.870868i	0.999995	−	0.00323158i	$-0.00102865\pi$
$80$	−7.74532	+	4.47326i	−0.865953	+	0.500125i
$81$	−4.11411	−	7.12584i	−0.457123	−	0.791760i
$82$	10.2941	−	6.05004i	1.13680	−	0.668115i
$83$	−0.940405	−	0.940405i	−0.103223	−	0.103223i	0.653609	−	0.756832i	$-0.273254\pi$
$83$	−0.940405	−	0.940405i	−0.103223	−	0.103223i	−0.756832	+	0.653609i	$0.773254\pi$
$84$		0			0
$85$	4.51026	+	1.35879i	0.489207	+	0.147382i
$86$	9.14616	+	2.37498i	0.986255	+	0.256100i
$87$	22.0794	+	5.91616i	2.36716	+	0.634279i
$88$	−4.09431	−	6.72587i	−0.436455	−	0.716980i
$89$	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	$0.578607\pi$
$90$	0.236311	−	10.2378i	0.0249094	−	1.07916i
$91$		0			0
$92$	3.87331	−	15.4056i	0.403821	−	1.60614i
$93$	−6.60279	−	24.6419i	−0.684677	−	2.55525i
$94$	1.98453	+	1.95405i	0.204689	+	0.201544i
$95$	8.96832	+	5.55319i	0.920130	+	0.569745i
$96$	−9.59658	+	10.3698i	−0.979447	+	1.05836i
$97$	−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
$100$	−5.39426	+	8.42033i	−0.539426	+	0.842033i
$101$	−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	$-0.381356\pi$
$102$	7.44077	−	0.0576002i	0.736746	−	0.00570327i
$103$	2.06460	−	0.553208i	0.203431	−	0.0545092i	−0.155665	−	0.987810i	$-0.549752\pi$
$103$	2.06460	−	0.553208i	0.203431	−	0.0545092i	0.359096	+	0.933301i	$0.383085\pi$
$104$	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	$0.0782112\pi$
$107$	2.60228	+	9.71185i	0.251572	+	0.938880i	−0.718393	+	0.695637i	$0.755122\pi$
$108$	−0.325897	−	1.14505i	−0.0313595	−	0.110183i
$109$	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	$0.240483\pi$
$110$	−7.52041	−	4.57649i	−0.717043	−	0.436351i
$111$		−	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	$0.195663\pi$
$114$	16.1280	+	4.18795i	1.51053	+	0.392238i
$115$	−4.06583	−	17.2883i	−0.379141	−	1.61215i
$116$	−15.9913	−	8.90537i	−1.48475	−	0.826843i
$117$	−3.76058	+	1.00765i	−0.347666	+	0.0931568i
$118$	12.4839	+	7.07931i	1.14924	+	0.651703i
$119$		0			0
$120$	−4.20425	+	15.2269i	−0.383794	+	1.39002i
$121$	−1.62496	+	2.81451i	−0.147723	+	0.255864i
$122$	−0.0614837	−	7.94245i	−0.00556647	−	0.719075i
$123$	5.45798	−	20.3695i	0.492130	−	1.83665i
$124$	0.316254	+	20.4256i	0.0284005	+	1.83427i
$125$	−1.03224	+	11.1326i	−0.0923260	+	0.995729i
$126$		0			0
$127$	−6.22515	+	6.22515i	−0.552393	+	0.552393i	−0.927131	−	0.374738i	$-0.877733\pi$
$127$	−6.22515	+	6.22515i	−0.552393	+	0.552393i	0.374738	+	0.927131i	$0.377733\pi$
$128$	9.47720	−	6.17921i	0.837674	−	0.546170i
$129$	14.4530	−	8.34444i	1.27251	−	0.734687i
$130$	3.64858	+	1.06846i	0.320002	+	0.0937102i
$131$	8.67385	+	5.00785i	0.757838	+	0.437538i	0.828519	−	0.559961i	$-0.189184\pi$
$131$	8.67385	+	5.00785i	0.757838	+	0.437538i	−0.0706810	+	0.997499i	$0.522517\pi$
$132$	−13.4867	−	3.39088i	−1.17387	−	0.295138i
$133$		0			0
$134$	4.64119	−	1.28219i	0.400938	−	0.110765i
$135$	−0.911745	−	0.969750i	−0.0784705	−	0.0834628i
$136$	−5.78959	−	1.40808i	−0.496454	−	0.120742i
$137$	−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	$0.878289\pi$
$138$	−14.2151	−	24.1869i	−1.21007	−	2.05892i
$139$	−18.2497			−1.54792			−0.773960	−	0.633235i	$-0.781727\pi$
$139$	−18.2497			−1.54792			−0.773960	+	0.633235i	$0.781727\pi$
$140$		0			0
$141$	4.91877			0.414235
$142$	3.19445	+	5.43534i	0.268072	+	0.456124i
$143$	−0.866244	+	3.23287i	−0.0724389	+	0.270346i
$144$	0.401022	+	12.9471i	0.0334185	+	1.07893i
$145$	−20.4545	−	0.630591i	−1.69865	−	0.0523678i
$146$	−5.03322	+	1.39050i	−0.416552	+	0.115078i
$147$		0			0
$148$	−3.63658	+	14.4640i	−0.298925	+	1.18893i
$149$	−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	$0.828300\pi$
$150$	3.64539	+	17.2808i	0.297645	+	1.41097i
$151$	6.36089	−	3.67246i	0.517642	−	0.298861i	−0.218327	−	0.975876i	$-0.570060\pi$
$151$	6.36089	−	3.67246i	0.517642	−	0.298861i	0.735969	+	0.677015i	$0.236727\pi$
$152$	−11.7070	−	6.40127i	−0.949562	−	0.519212i
$153$	4.82378	−	4.82378i	0.389980	−	0.389980i
$154$		0			0
$155$	10.8047	+	20.1219i	0.867855	+	1.61623i
$156$	6.00486	−	0.0929746i	0.480773	−	0.00744393i
$157$	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	$0.0791576\pi$
$158$	0.0978460	+	12.6397i	0.00778421	+	1.00556i
$159$	−4.60631	+	7.97836i	−0.365304	+	0.632725i
$160$	6.23798	−	11.0040i	0.493155	−	0.869941i
$161$		0			0
$162$	10.1222	+	5.74004i	0.795275	+	0.450980i
$163$	−18.6149	+	4.98785i	−1.45803	+	0.390678i	−0.898809	−	0.438340i	$-0.855567\pi$
$163$	−18.6149	+	4.98785i	−1.45803	+	0.390678i	−0.559222	+	0.829018i	$0.688900\pi$
$164$	−8.21569	+	14.7528i	−0.641538	+	1.15200i
$165$	−15.1350	+	3.55941i	−1.17826	+	0.277100i
$166$	1.82044	+	0.472712i	0.141293	+	0.0366896i
$167$	−12.0798	+	12.0798i	−0.934765	+	0.934765i	−0.997999	−	0.0632340i	$-0.979859\pi$
$167$	−12.0798	+	12.0798i	−0.934765	+	0.934765i	0.0632340	+	0.997999i	$0.479859\pi$
$168$		0			0
$169$			11.5546i			0.888817i
$170$	−6.47274	+	1.57522i	−0.496436	+	0.120814i
$171$	13.2298	−	7.63822i	1.01171	−	0.584109i
$172$	−12.8531	+	3.65817i	−0.980043	+	0.278933i
$173$	−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
$178$	−7.28788	+	0.0564166i	−0.546250	+	0.00422860i
$179$	−1.76716	−	3.06080i	−0.132083	−	0.228775i	0.792396	−	0.610007i	$-0.208833\pi$
$179$	−1.76716	−	3.06080i	−0.132083	−	0.228775i	−0.924480	+	0.381232i	$0.875500\pi$
$180$	7.04792	+	12.6516i	0.525321	+	0.942992i
$181$	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
$184$	6.31664	+	21.5585i	0.465669	+	1.58931i
$185$	3.81733	+	16.2317i	0.280655	+	1.19338i
$186$	25.7079	+	25.3130i	1.88500	+	1.85604i
$187$	−1.51786	−	5.66473i	−0.110997	−	0.414246i
$188$	−3.81982	−	0.960389i	−0.278589	−	0.0700436i
$189$		0			0
$190$	−14.9137	−	0.344243i	−1.08195	−	0.0249740i
$191$	−10.9962	−	6.34865i	−0.795656	−	0.459372i	0.0462938	−	0.998928i	$-0.485259\pi$
$191$	−10.9962	−	6.34865i	−0.795656	−	0.459372i	−0.841950	+	0.539556i	$0.818592\pi$
$192$	4.26986	−	19.5198i	0.308151	−	1.40872i
$193$	−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	$0.618633\pi$
$194$	2.48090	+	0.644214i	0.178118	+	0.0462518i
$195$	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	$0.794920\pi$
$198$	−10.9916	+	6.45997i	−0.781140	+	0.459090i
$199$	6.11266	+	10.5874i	0.433315	+	0.750524i	0.997156	−	0.0753593i	$-0.0240104\pi$
$199$	6.11266	+	10.5874i	0.433315	+	0.750524i	−0.563841	+	0.825883i	$0.690677\pi$
$200$	0.543143	−	14.1317i	0.0384060	−	0.999262i
$201$	4.25197	−	7.36462i	0.299911	−	0.519460i
$202$	15.4411	+	8.75628i	1.08643	+	0.616090i
$203$		0			0
$204$	−9.03077	+	5.40203i	−0.632281	+	0.378218i
$205$	−0.581755	+	18.8704i	−0.0406315	+	1.31796i
$206$	−2.12082	+	2.15391i	−0.147765	+	0.150070i
$207$	−24.8441	−	6.65695i	−1.72678	−	0.462690i
$208$	−4.68140	−	1.10024i	−0.324597	−	0.0762882i
$209$		−	13.1327i		−	0.908409i
$210$		0			0
$211$		−	9.27501i		−	0.638518i	−0.947668	−	0.319259i	$-0.896566\pi$
$211$		−	9.27501i		−	0.638518i	0.947668	−	0.319259i	$-0.103434\pi$
$212$	5.13493	−	5.29645i	0.352669	−	0.363761i
$213$	10.7552	+	2.88184i	0.736933	+	0.197461i
$214$	−10.1320	−	9.97631i	−0.692608	−	0.681967i
$215$	−10.8854	+	10.2343i	−0.742376	+	0.697972i
$216$	1.21785	+	1.16256i	0.0828643	+	0.0791023i
$217$		0			0
$218$	−4.18897	+	7.38699i	−0.283713	+	0.500310i
$219$	−4.61112	+	7.98669i	−0.311591	+	0.539691i
$220$	12.4485	+	0.190941i	0.839278	+	0.0128732i
$221$	1.26632	+	2.19333i	0.0851817	+	0.147539i
$222$	13.3462	+	22.7086i	0.895741	+	1.52410i
$223$	7.89717	+	7.89717i	0.528833	+	0.528833i	0.920224	−	0.391391i	$-0.128006\pi$
$223$	7.89717	+	7.89717i	0.528833	+	0.528833i	−0.391391	+	0.920224i	$0.628006\pi$
$224$		0			0
$225$	13.4970	+	8.94422i	0.899803	+	0.596281i
$226$	−1.28371	+	4.94364i	−0.0853913	+	0.328846i
$227$	−7.03559	−	1.88518i	−0.466969	−	0.125124i	0.0176596	−	0.999844i	$-0.494378\pi$
$227$	−7.03559	−	1.88518i	−0.466969	−	0.125124i	−0.484628	+	0.874720i	$0.661045\pi$
$228$	−22.6648	+	6.45070i	−1.50101	+	0.427208i
$229$	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	$0.538462\pi$
$230$	17.3454	+	18.1651i	1.14372	+	1.19777i
$231$		0			0
$232$	25.8784	−	0.601083i	1.69900	−	0.0394630i
$233$	−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	$0.976465\pi$
$234$	3.86299	−	3.92326i	0.252531	−	0.256472i
$235$	−4.28665	+	1.00812i	−0.279630	+	0.0657627i
$236$	−20.2936	+	0.314211i	−1.32100	+	0.0204534i
$237$	15.7854	+	15.7854i	1.02537	+	1.02537i
$238$		0			0
$239$	3.08431			0.199507			0.0997536	−	0.995012i	$-0.468195\pi$
$239$	3.08431			0.199507			0.0997536	+	0.995012i	$0.468195\pi$
$240$	−5.78509	−	21.5777i	−0.373426	−	1.39284i
$241$	−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	$-0.427765\pi$
$242$	−0.0355778	−	4.59593i	−0.00228703	−	0.295438i
$243$	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
$248$	−15.0219	−	24.6770i	−0.953890	−	1.56699i
$249$	2.87670	−	1.66086i	0.182304	−	0.105253i
$250$	−6.71870	−	14.3129i	−0.424928	−	0.905227i
$251$		−	5.25443i		−	0.331657i	−0.986155	−	0.165828i	$-0.946970\pi$
$251$		−	5.25443i		−	0.331657i	0.986155	−	0.165828i	$-0.0530298\pi$
$252$		0			0
$253$	−15.6350	+	15.6350i	−0.982961	+	0.982961i
$254$	3.12919	−	12.0507i	0.196343	−	0.756125i
$255$	−6.19380	+	10.0029i	−0.387871	+	0.626406i
$256$	−7.12711	+	14.3250i	−0.445445	+	0.895310i
$257$	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	$0.100432\pi$
$258$	−11.6422	+	20.5303i	−0.724814	+	1.27816i
$259$		0			0
$260$	−5.21410	+	1.31175i	−0.323365	+	0.0813511i
$261$	−14.8184	+	25.6662i	−0.917235	+	1.58870i
$262$	−14.1639	+	0.109645i	−0.875050	+	0.00677390i
$263$	−7.46169	+	27.8474i	−0.460108	+	1.71715i	0.212513	+	0.977158i	$0.431835\pi$
$263$	−7.46169	+	27.8474i	−0.460108	+	1.71715i	−0.672621	+	0.739987i	$0.734831\pi$
$264$	18.8733	−	5.52987i	1.16157	−	0.340340i
$265$	2.37914	−	7.89712i	0.146149	−	0.485116i
$266$		0			0
$267$	−9.10161	+	9.10161i	−0.557010	+	0.557010i
$268$	−4.73993	+	4.88902i	−0.289537	+	0.298644i
$269$	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	$0.214591\pi$
$270$	1.80652	+	0.529027i	0.109941	+	0.0321955i
$271$	−9.73675	−	5.62151i	−0.591465	−	0.341483i	0.174211	−	0.984708i	$-0.444262\pi$
$271$	−9.73675	−	5.62151i	−0.591465	−	0.341483i	−0.765677	+	0.643226i	$0.777596\pi$
$272$	8.06785	−	2.43185i	0.489186	−	0.147453i
$273$		0			0
$274$	−5.29411	−	19.1633i	−0.319829	−	1.15769i
$275$	12.4605	−	6.20397i	0.751394	−	0.374113i
$276$	34.6630	+	19.3034i	2.08647	+	1.16193i
$277$	−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	$0.155868\pi$
$278$	22.2507	−	13.0771i	1.33451	−	0.784313i
$279$	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	$0.203565\pi$
$282$	−5.99714	+	3.52463i	−0.357124	+	0.209888i
$283$	−3.21272	+	11.9900i	−0.190977	+	0.712734i	0.802295	+	0.596927i	$0.203612\pi$
$283$	−3.21272	+	11.9900i	−0.190977	+	0.712734i	−0.993272	+	0.115807i	$0.963055\pi$
$284$	−7.78957	−	4.33792i	−0.462226	−	0.257408i
$285$	−19.1949	+	18.0468i	−1.13701	+	1.06900i
$286$	−1.26041	−	4.56234i	−0.0745295	−	0.269777i
$287$		0			0
$288$	−9.76640	−	15.4982i	−0.575490	−	0.913240i
$289$	10.8792	+	6.28112i	0.639954	+	0.369478i
$290$	25.3907	−	13.8882i	1.49099	−	0.815541i
$291$	3.92038	−	2.26343i	0.229817	−	0.132685i
$292$	5.14030	−	5.30198i	0.300813	−	0.310275i
$293$	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
$296$	−5.93057	−	20.2408i	−0.344707	−	1.17648i
$297$	−0.428903	+	1.60069i	−0.0248875	+	0.0928813i
$298$	16.7873	−	0.129953i	0.972460	−	0.00752796i
$299$	4.77440	−	8.26950i	0.276111	−	0.478238i
$300$	−16.8275	−	18.4572i	−0.971534	−	1.06563i
$301$		0			0
$302$	−5.12385	+	9.03559i	−0.294845	+	0.519940i
$303$	30.2822	−	8.11410i	1.73967	−	0.466143i
$304$	18.8605	−	0.584183i	1.08172	−	0.0335052i
$305$	10.6773	+	6.61140i	0.611381	+	0.378568i
$306$	−2.42476	+	9.33788i	−0.138614	+	0.533811i
$307$	−11.0402	+	11.0402i	−0.630098	+	0.630098i	−0.948092	−	0.317995i	$-0.896991\pi$
$307$	−11.0402	+	11.0402i	−0.630098	+	0.630098i	0.317995	+	0.948092i	$0.396991\pi$
$308$		0			0
$309$			5.33858i			0.303701i
$310$	−27.5921	−	16.7910i	−1.56713	−	0.953664i
$311$	−10.7343	+	6.19747i	−0.608688	+	0.351426i	−0.772452	−	0.635073i	$-0.780970\pi$
$311$	−10.7343	+	6.19747i	−0.608688	+	0.351426i	0.163764	+	0.986500i	$0.447637\pi$
$312$	−7.25471	+	4.41624i	−0.410717	+	0.250020i
$313$	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	$0.331910\pi$
$318$	−0.100853	−	13.0282i	−0.00565558	−	0.730586i
$319$	12.7389	+	22.0645i	0.713244	+	1.23537i
$320$	0.279529	+	17.8864i	0.0156261	+	0.999878i
$321$	−25.1126			−1.40165
$322$		0			0
$323$	−7.02697	−	7.02697i	−0.390991	−	0.390991i
$324$	−16.4545	+	0.254768i	−0.914137	+	0.0141538i
$325$	−4.50431	+	3.98065i	−0.249854	+	0.220807i
$326$	19.1218	−	19.4202i	1.05906	−	1.07558i
$327$	3.88176	+	14.4869i	0.214662	+	0.801128i
$328$	−0.554532	−	23.8743i	−0.0306189	−	1.31824i
$329$		0			0
$330$	15.9026	−	15.1850i	0.875408	−	0.835907i
$331$	4.80323	+	2.77314i	0.264009	+	0.152426i	0.626162	−	0.779693i	$-0.284625\pi$
$331$	4.80323	+	2.77314i	0.264009	+	0.152426i	−0.362153	+	0.932119i	$0.617958\pi$
$332$	−2.55827	+	0.728117i	−0.140403	+	0.0399606i
$333$	23.3256	+	6.25008i	1.27824	+	0.342502i
$334$	6.07214	−	23.3841i	0.332253	−	1.27952i
$335$	−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	$0.791915\pi$
$338$	−8.27965	−	14.0878i	−0.450354	−	0.766275i
$339$	4.51030	+	7.81207i	0.244966	+	0.424293i
$340$	6.76304	−	6.55870i	0.366777	−	0.355696i
$341$	14.2174	−	24.6253i	0.769915	−	1.33353i
$342$	−10.6569	+	18.7928i	−0.576260	+	1.01620i
$343$		0			0
$344$	13.0497	−	13.6703i	0.703591	−	0.737053i
$345$	44.3375	+	1.36688i	2.38705	+	0.0735903i
$346$	14.8039	+	14.5765i	0.795864	+	0.783637i
$347$	0.632213	+	0.169401i	0.0339389	+	0.00909391i	0.275749	−	0.961230i	$-0.411074\pi$
$347$	0.632213	+	0.169401i	0.0339389	+	0.00909391i	−0.241810	+	0.970324i	$0.577741\pi$
$348$	31.8222	−	32.8231i	1.70585	−	1.75950i
$349$		−	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
$352$	−15.7363	+	0.609378i	−0.838748	+	0.0324800i
$353$	−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	$0.710176\pi$
$354$	−25.1494	+	25.5418i	−1.33667	+	1.35753i
$355$	−9.96365	−	0.307169i	−0.528816	−	0.0163029i
$356$	8.84521	−	5.29103i	0.468795	−	0.280424i
$357$		0			0
$358$	4.34785	+	2.46555i	0.229791	+	0.130309i
$359$	7.26761	−	12.5879i	0.383570	−	0.664362i	−0.608000	−	0.793937i	$-0.708028\pi$
$359$	7.26761	−	12.5879i	0.383570	−	0.664362i	0.991570	+	0.129575i	$0.0413613\pi$
$360$	−17.6588	−	10.3749i	−0.930698	−	0.546807i
$361$	−1.62687	−	2.81781i	−0.0856245	−	0.148306i
$362$	−3.29693	+	1.93767i	−0.173283	+	0.101842i
$363$	−5.73972	−	5.73972i	−0.301257	−	0.301257i
$364$		0			0
$365$	2.38163	−	7.90537i	0.124660	−	0.413786i
$366$	19.2014	+	4.98601i	1.00367	+	0.260623i
$367$	−9.12062	−	2.44386i	−0.476092	−	0.127569i	0.0127901	−	0.999918i	$-0.495929\pi$
$367$	−9.12062	−	2.44386i	−0.476092	−	0.127569i	−0.488883	+	0.872350i	$0.662595\pi$
$368$	−23.1496	−	21.7586i	−1.20675	−	1.13424i
$369$	23.6785	+	13.6708i	1.23265	+	0.711672i
$370$	−16.2853	−	17.0549i	−0.846632	−	0.886640i
$371$		0			0
$372$	−49.4824	−	12.4410i	−2.56554	−	0.645036i
$373$	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	$0.871201\pi$
$374$	5.90978	+	5.81899i	0.305587	+	0.300893i
$375$	−26.1907	−	9.68692i	−1.35248	−	0.500230i
$376$	5.34543	−	1.56621i	0.275670	−	0.0807712i
$377$	−7.78011	−	7.78011i	−0.400696	−	0.400696i
$378$		0			0
$379$	−11.9123			−0.611896			−0.305948	−	0.952048i	$-0.598973\pi$
$379$	−11.9123			−0.611896			−0.305948	+	0.952048i	$0.598973\pi$
$380$	18.4300	−	10.2669i	0.945438	−	0.526683i
$381$	−10.9943	−	19.0428i	−0.563257	−	0.975590i
$382$	17.9562	−	0.139001i	0.918717	−	0.00711193i
$383$	−8.58760	+	2.30104i	−0.438806	+	0.117578i	−0.471457	−	0.881889i	$-0.656272\pi$
$383$	−8.58760	+	2.30104i	−0.438806	+	0.117578i	0.0326510	+	0.999467i	$0.489605\pi$
$384$	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
$388$	−3.48642	+	0.992281i	−0.176996	+	0.0503754i
$389$	−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	$0.412449\pi$
$390$	−4.93633	+	8.11172i	−0.249961	+	0.410753i
$391$			16.7317i			0.846158i
$392$		0			0
$393$	−17.6889	+	17.6889i	−0.892286	+	0.892286i
$394$	5.40456	+	1.40340i	0.272278	+	0.0707022i
$395$	−16.9920	−	10.5215i	−0.854961	−	0.529393i
$396$	8.77236	−	15.7524i	0.440828	−	0.791590i
$397$	−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	$0.719473\pi$
$398$	−15.0394	−	8.52845i	−0.753856	−	0.427492i
$399$		0			0
$400$	9.46408	+	17.6191i	0.473204	+	0.880953i
$401$	−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	$0.840915\pi$
$402$	0.0930953	+	12.0260i	0.00464317	+	0.599803i
$403$	−3.17822	+	11.8613i	−0.158318	+	0.590852i
$404$	−25.1008	+	0.388642i	−1.24881	+	0.0193357i
$405$	−16.2098	+	8.70406i	−0.805470	+	0.432508i
$406$		0			0
$407$	14.6793	−	14.6793i	0.727628	−	0.727628i
$408$	7.13971	−	13.0575i	0.353468	−	0.646442i
$409$	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	$0.324036\pi$
$410$	−12.8126	−	23.4243i	−0.632768	−	1.15684i
$411$	−30.4081	−	17.5562i	−1.49992	−	0.865981i
$412$	1.04236	−	4.14583i	0.0513532	−	0.204250i
$413$		0			0
$414$	35.0609	−	9.68604i	1.72315	−	0.476043i
$415$	−2.16661	+	2.03701i	−0.106355	+	0.0999931i
$416$	6.49612	−	2.01308i	0.318499	−	0.0986992i
$417$	11.7974	−	44.0285i	0.577721	−	2.15608i
$418$	9.41047	+	16.0119i	0.460281	+	0.783166i
$419$	−3.50746			−0.171351			−0.0856753	−	0.996323i	$-0.527305\pi$
$419$	−3.50746			−0.171351			−0.0856753	+	0.996323i	$0.527305\pi$
$420$		0			0
$421$	−26.7845			−1.30539			−0.652697	−	0.757619i	$-0.726363\pi$
$421$	−26.7845			−1.30539			−0.652697	+	0.757619i	$0.726363\pi$
$422$	6.64616	+	11.3084i	0.323530	+	0.550485i
$423$	−1.65059	+	6.16009i	−0.0802545	+	0.299514i
$424$	−2.46544	+	10.1371i	−0.119732	+	0.492303i
$425$	3.34768	−	9.98684i	0.162386	−	0.484433i
$426$	−15.1781	+	4.19316i	−0.735382	+	0.203159i
$427$		0			0
$428$	19.5019	+	4.90323i	0.942662	+	0.237007i
$429$	−7.23950	−	4.17973i	−0.349526	−	0.201799i
$430$	5.93829	−	20.2781i	0.286370	−	0.977895i
$431$	32.5658	−	18.8019i	1.56864	−	0.905655i	0.572313	−	0.820035i	$-0.306046\pi$
$431$	32.5658	−	18.8019i	1.56864	−	0.905655i	0.996328	−	0.0856198i	$-0.0272870\pi$
$432$	−2.31790	−	0.544763i	−0.111520	−	0.0262099i
$433$	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
$436$	−0.185925	−	12.0081i	−0.00890419	−	0.575086i
$437$	−9.69741	+	36.1912i	−0.463890	+	1.73126i
$438$	−0.100959	−	13.0418i	−0.00482400	−	0.623162i
$439$	−8.35429	+	14.4701i	−0.398728	+	0.690618i	−0.993569	−	0.113226i	$-0.963882\pi$
$439$	−8.35429	+	14.4701i	−0.398728	+	0.690618i	0.594841	+	0.803843i	$0.297215\pi$
$440$	−15.3145	+	8.68738i	−0.730089	+	0.414155i
$441$		0			0
$442$	−3.11560	−	1.76678i	−0.148194	−	0.0840371i
$443$	−12.3733	+	3.31541i	−0.587872	+	0.157520i	−0.540480	−	0.841357i	$-0.681757\pi$
$443$	−12.3733	+	3.31541i	−0.587872	+	0.157520i	−0.0473913	+	0.998876i	$0.515091\pi$
$444$	−32.5444	−	18.1236i	−1.54449	−	0.860108i
$445$	6.06653	−	9.79736i	0.287581	−	0.464439i
$446$	−15.2873	−	3.96965i	−0.723877	−	0.187969i
$447$	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	$-0.0230958\pi$
$450$	−22.8652	−	1.23357i	−1.07788	−	0.0581511i
$451$	20.3557	−	11.7524i	0.958512	−	0.553397i
$452$	−1.97730	−	6.94733i	−0.0930044	−	0.326775i
$453$	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	$0.217683\pi$
$458$	−16.7764	+	0.129869i	−0.783909	+	0.00606836i
$459$	0.626991	+	1.08598i	0.0292654	+	0.0506892i
$460$	−34.1647	−	9.71837i	−1.59294	−	0.453121i
$461$	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	0.964481	−	0.264154i	$-0.0850926\pi$
$463$	15.0692	+	15.0692i	0.700327	+	0.700327i	−0.264154	+	0.964481i	$0.585093\pi$
$464$	−31.1212	+	19.2765i	−1.44476	+	0.894887i
$465$	−55.5298	+	13.0594i	−2.57513	+	0.605613i
$466$	5.74550	+	5.65723i	0.266155	+	0.262066i
$467$	5.02981	+	18.7715i	0.232752	+	0.868641i	0.979149	+	0.203141i	$0.0651150\pi$
$467$	5.02981	+	18.7715i	0.232752	+	0.868641i	−0.746398	+	0.665500i	$0.768218\pi$
$468$	−1.89861	+	7.55146i	−0.0877633	+	0.349067i
$469$		0			0
$470$	4.50404	−	4.30081i	0.207756	−	0.198381i
$471$	0.711075	+	0.410540i	0.0327646	+	0.0189167i
$472$	24.5175	−	14.9248i	1.12851	−	0.686970i
$473$	17.9676	+	4.81440i	0.826151	+	0.221367i
$474$	−30.5573	−	7.93480i	−1.40354	−	0.364457i
$475$	13.0294	−	19.6616i	0.597828	−	0.902137i
$476$		0			0
$477$	−8.44607	−	8.44607i	−0.386719	−	0.386719i
$478$	−3.76049	+	2.21011i	−0.172001	+	0.101088i
$479$	7.15682	+	12.3960i	0.327003	+	0.566387i	0.981916	−	0.189318i	$-0.0606278\pi$
$479$	7.15682	+	12.3960i	0.327003	+	0.566387i	−0.654912	+	0.755705i	$0.727294\pi$
$480$	22.5153	+	22.1629i	1.02768	+	1.01159i
$481$	−4.48259	+	7.76407i	−0.204388	+	0.354011i
$482$	27.9331	+	15.8401i	1.27232	+	0.721498i
$483$		0			0
$484$	3.33667	+	5.57802i	0.151667	+	0.253547i
$485$	−2.95266	+	2.77605i	−0.134073	+	0.126054i
$486$	−22.1635	+	22.5094i	−1.00536	+	1.02105i
$487$	33.8536	+	9.07104i	1.53405	+	0.411048i	0.924339	−	0.381573i	$-0.124618\pi$
$487$	33.8536	+	9.07104i	1.53405	+	0.411048i	0.609714	+	0.792621i	$0.291284\pi$
$488$	−13.9379	−	7.62109i	−0.630937	−	0.344990i
$489$		−	48.1339i		−	2.17669i
$490$		0			0
$491$			41.1970i			1.85920i	0.368576	+	0.929598i	$0.379845\pi$
$491$			41.1970i			1.85920i	−0.368576	+	0.929598i	$0.620155\pi$
$492$	−30.2811	−	29.3577i	−1.36518	−	1.32355i
$493$	18.6224	+	4.98986i	0.838711	+	0.224732i
$494$	−5.71515	−	5.62735i	−0.257137	−	0.253186i
$495$	0.621173	−	20.1490i	0.0279196	−	0.905629i
$496$	35.9979	+	19.3228i	1.61635	+	0.867621i
$497$		0			0
$498$	−2.31725	+	4.08633i	−0.103839	+	0.183113i
$499$	−16.6591	+	28.8545i	−0.745766	+	1.29170i	0.204070	+	0.978956i	$0.434583\pi$
$499$	−16.6591	+	28.8545i	−0.745766	+	1.29170i	−0.949836	+	0.312748i	$0.898750\pi$
$500$	18.4478	+	12.6364i	0.825011	+	0.565117i
$501$	−21.3344	−	36.9522i	−0.953149	−	1.65090i
$502$	3.76515	+	6.40639i	0.168047	+	0.285931i
$503$	−2.38397	−	2.38397i	−0.106296	−	0.106296i	0.651959	−	0.758255i	$-0.273948\pi$
$503$	−2.38397	−	2.38397i	−0.106296	−	0.106296i	−0.758255	+	0.651959i	$0.773948\pi$
$504$		0			0
$505$	−24.7276	+	13.2778i	−1.10036	+	0.590855i
$506$	7.85919	−	30.2661i	0.349384	−	1.34549i
$507$	−27.8762	−	7.46941i	−1.23803	−	0.331728i
$508$	4.81988	+	16.9348i	0.213848	+	0.751362i
$509$	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	$0.614452\pi$
$510$	0.383955	−	16.6341i	0.0170018	−	0.736572i
$511$		0			0
$512$	−1.57515	−	22.5725i	−0.0696127	−	0.997574i
$513$	0.726787	+	2.71240i	0.0320884	+	0.119756i
$514$	−26.6573	+	27.0732i	−1.17580	+	1.19415i
$515$	−1.09417	−	4.65251i	−0.0482147	−	0.205014i
$516$	−0.516734	−	33.3737i	−0.0227479	−	1.46920i
$517$	3.87669	+	3.87669i	0.170497	+	0.170497i
$518$		0			0
$519$	36.6923			1.61061
$520$	5.41726	−	5.33558i	0.237563	−	0.233981i
$521$	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	$0.552758\pi$
$522$	−0.324443	−	41.9115i	−0.0142005	−	1.83441i
$523$	−13.7791	+	3.69210i	−0.602519	+	0.161444i	−0.547168	−	0.837023i	$-0.684294\pi$
$523$	−13.7791	+	3.69210i	−0.602519	+	0.161444i	−0.0553504	+	0.998467i	$0.517628\pi$
$524$	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
$528$	−19.0485	+	20.2662i	−0.828977	+	0.881972i
$529$	34.7134	−	20.0418i	1.50928	−	0.871382i
$530$	2.75808	+	11.3333i	0.119803	+	0.492285i
$531$			32.8626i			1.42612i
$532$		0			0
$533$	−7.17757	+	7.17757i	−0.310895	+	0.310895i
$534$	4.57509	−	17.6189i	0.197984	−	0.762445i
$535$	21.8853	−	5.14694i	0.946186	−	0.222522i
$536$	2.27578	−	9.35733i	0.0982988	−	0.404175i
$537$	8.52673	−	2.28473i	0.367956	−	0.0985934i
$538$	−8.33972	+	14.7066i	−0.359551	+	0.634045i
$539$		0			0
$540$	−2.58166	+	0.649485i	−0.111097	+	0.0279494i
$541$	−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	$0.257996\pi$
$542$	15.8996	−	0.123081i	0.682945	−	0.00528678i
$543$	−1.74805	+	6.52380i	−0.0750159	+	0.279963i
$544$	−8.09402	+	8.74615i	−0.347028	+	0.374988i
$545$	−6.35206	−	11.8296i	−0.272092	−	0.506724i
$546$		0			0
$547$	21.6549	−	21.6549i	0.925899	−	0.925899i	−0.0715392	−	0.997438i	$-0.522791\pi$
$547$	21.6549	−	21.6549i	0.925899	−	0.925899i	0.997438	+	0.0715392i	$0.0227911\pi$
$548$	20.1865	+	19.5709i	0.862324	+	0.836028i
$549$	15.7508	−	9.09375i	0.672230	−	0.388112i
$550$	−10.7467	+	16.4928i	−0.458239	+	0.703257i
$551$	37.3888	+	21.5865i	1.59282	+	0.919614i
$552$	−56.0945	+	1.30292i	−2.38754	+	0.0554558i
$553$		0			0
$554$	−2.83184	−	10.2505i	−0.120313	−	0.435502i
$555$	−41.6276	−	1.28334i	−1.76699	−	0.0544746i
$556$	−17.7582	+	31.8881i	−0.753114	+	1.35236i
$557$	−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	$0.738615\pi$
$558$	−40.3278	+	23.7014i	−1.70721	+	1.00336i
$559$	−8.03311			−0.339764
$560$		0			0
$561$	14.6477			0.618426
$562$	−32.7984	+	19.2762i	−1.38352	+	0.813117i
$563$	9.49611	−	35.4400i	0.400213	−	1.49362i	−0.412503	−	0.910956i	$-0.635345\pi$
$563$	9.49611	−	35.4400i	0.400213	−	1.49362i	0.812716	−	0.582660i	$-0.197988\pi$
$564$	4.78629	−	8.59469i	0.201539	−	0.361902i
$565$	−5.53179	−	5.88372i	−0.232724	−	0.247530i
$566$	−4.67460	−	16.9208i	−0.196488	−	0.711235i
$567$		0			0
$568$	12.6057	−	0.292795i	0.528924	−	0.0122854i
$569$	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	$0.610810\pi$
$570$	10.4714	−	35.7577i	0.438598	−	1.49772i
$571$	−7.95794	+	4.59452i	−0.333030	+	0.192275i	−0.657185	−	0.753729i	$-0.728253\pi$
$571$	−7.95794	+	4.59452i	−0.333030	+	0.192275i	0.324156	+	0.946004i	$0.394920\pi$
$572$	4.80595	+	4.65940i	0.200947	+	0.194819i
$573$	22.4249	−	22.4249i	0.936814	−	0.936814i
$574$		0			0
$575$	−38.9197	+	7.89594i	−1.62306	+	0.329283i
$576$	23.0130	+	11.8977i	0.958876	+	0.495736i
$577$	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	$-0.0235315\pi$
$578$	−17.7652	+	0.137523i	−0.738933	+	0.00572020i
$579$	3.84015	−	6.65133i	0.159591	−	0.276420i
$580$	−21.0054	+	35.1270i	−0.872202	+	1.45857i
$581$		0			0
$582$	−3.15796	+	5.56887i	−0.130902	+	0.230837i
$583$	−9.91850	+	2.65765i	−0.410782	+	0.110069i
$584$	−2.46801	+	10.1477i	−0.102127	+	0.419916i
$585$	1.99298	+	8.47436i	0.0823995	+	0.350372i
$586$	−3.43309	+	13.2210i	−0.141820	+	0.546155i
$587$	18.5622	−	18.5622i	0.766145	−	0.766145i	−0.211281	−	0.977425i	$-0.567763\pi$
$587$	18.5622	−	18.5622i	0.766145	−	0.766145i	0.977425	+	0.211281i	$0.0677634\pi$
$588$		0			0
$589$		−	48.1835i		−	1.98537i
$590$	16.6825	−	27.4138i	0.686806	−	1.12861i
$591$	8.54042	−	4.93082i	0.351306	−	0.202827i
$592$	21.7347	+	20.4287i	0.893289	+	0.839614i
$593$	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
$598$	0.104534	+	13.5036i	0.00427470	+	0.552205i
$599$	−17.5455	−	30.3897i	−0.716889	−	1.24169i	−0.962226	−	0.272250i	$-0.912232\pi$
$599$	−17.5455	−	30.3897i	−0.716889	−	1.24169i	0.245337	−	0.969438i	$-0.421101\pi$
$600$	33.7424	+	10.4457i	1.37753	+	0.426444i
$601$	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
$604$	−0.227419	−	14.6881i	−0.00925355	−	0.597650i
$605$	6.17847	+	3.82571i	0.251191	+	0.155537i
$606$	−31.1069	+	31.5922i	−1.26363	+	1.28335i
$607$	−5.84398	−	21.8100i	−0.237200	−	0.885242i	−0.977145	−	0.212574i	$-0.931815\pi$
$607$	−5.84398	−	21.8100i	−0.237200	−	0.885242i	0.739945	−	0.672667i	$-0.234851\pi$
$608$	−22.5768	+	14.2271i	−0.915609	+	0.576983i
$609$		0			0
$610$	−17.7557	−	0.409842i	−0.718905	−	0.0165940i
$611$	−2.05042	−	1.18381i	−0.0829513	−	0.0478920i
$612$	−3.73486	−	13.1226i	−0.150973	−	0.530449i
$613$	−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	$0.637984\pi$
$614$	5.54956	−	21.3716i	0.223962	−	0.862489i
$615$	−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	$0.329760\pi$
$618$	−3.82545	−	6.50898i	−0.153882	−	0.261830i
$619$	4.68299	+	8.11118i	0.188225	+	0.326016i	0.944659	−	0.328055i	$-0.106393\pi$
$619$	4.68299	+	8.11118i	0.188225	+	0.326016i	−0.756433	+	0.654071i	$0.773060\pi$
$620$	45.6731	+	0.700554i	1.83428	+	0.0281349i
$621$	2.36395	−	4.09447i	0.0948619	−	0.164306i
$622$	8.64677	−	15.2480i	0.346704	−	0.611390i
$623$		0			0
$624$	5.68066	−	10.5829i	0.227408	−	0.423655i
$625$	24.8103	+	3.07412i	0.992411	+	0.122965i
$626$	−25.5305	−	25.1382i	−1.02040	−	1.00473i
$627$	31.6835	+	8.48956i	1.26532	+	0.339040i
$628$	−0.472048	−	0.457654i	−0.0188368	−	0.0182624i
$629$		−	15.7091i		−	0.626361i
$630$		0			0
$631$		−	33.8691i		−	1.34831i	−0.738590	−	0.674155i	$-0.764508\pi$
$631$		−	33.8691i		−	1.34831i	0.738590	−	0.674155i	$-0.235492\pi$
$632$	22.1809	+	12.1283i	0.882309	+	0.482438i
$633$	22.3765	+	5.99577i	0.889386	+	0.238310i
$634$	−9.29717	+	9.44224i	−0.369238	+	0.374999i
$635$	13.4843	+	14.3422i	0.535109	+	0.569152i
$636$	9.45854	+	15.8122i	0.375056	+	0.626994i
$637$		0			0
$638$	−31.3424	−	17.7735i	−1.24086	−	0.703659i
$639$	−7.21823	+	12.5023i	−0.285549	+	0.494585i
$640$	−13.1576	−	21.6074i	−0.520099	−	0.854106i
$641$	−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	$0.847451\pi$
$642$	30.6182	−	17.9949i	1.20840	−	0.710201i
$643$	21.5472	+	21.5472i	0.849737	+	0.849737i	0.990100	−	0.140363i	$-0.0448269\pi$
$643$	21.5472	+	21.5472i	0.849737	+	0.849737i	−0.140363	+	0.990100i	$0.544827\pi$
$644$		0			0
$645$	−17.6540	−	32.8775i	−0.695126	−	1.29455i
$646$	13.6028	+	3.53224i	0.535196	+	0.138974i
$647$	−14.7661	−	3.95657i	−0.580517	−	0.155549i	−0.0434012	−	0.999058i	$-0.513819\pi$
$647$	−14.7661	−	3.95657i	−0.580517	−	0.155549i	−0.537115	+	0.843509i	$0.680486\pi$
$648$	19.8793	−	12.1013i	0.780932	−	0.475385i
$649$	24.4661	+	14.1255i	0.960379	+	0.554475i
$650$	2.63942	−	8.08099i	0.103526	−	0.316962i
$651$		0			0
$652$	−9.39813	+	37.3798i	−0.368059	+	1.46390i
$653$	−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	$-0.279951\pi$
$654$	−15.1136	−	14.8814i	−0.590989	−	0.581909i
$655$	11.7902	−	19.0411i	0.460682	−	0.743996i
$656$	17.7836	+	28.7110i	0.694333	+	1.12097i
$657$	−8.45489	−	8.45489i	−0.329857	−	0.329857i
$658$		0			0
$659$	−41.8771			−1.63130			−0.815650	−	0.578546i	$-0.803620\pi$
$659$	−41.8771			−1.63130			−0.815650	+	0.578546i	$0.803620\pi$
$660$	−8.50791	+	29.9093i	−0.331170	+	1.16422i
$661$	−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	$-0.374427\pi$
$662$	−7.84340	+	0.0607170i	−0.304842	+	0.00235983i
$663$	−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
$668$	9.35291	+	32.8618i	0.361875	+	1.27146i
$669$	−24.1574	+	13.9473i	−0.933981	+	0.539234i
$670$	−2.54591	−	10.4614i	−0.0983573	−	0.404161i
$671$		−	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	$0.109157\pi$
$674$	6.59868	+	1.71348i	0.254172	+	0.0660006i
$675$	−2.23022	+	1.97094i	−0.0858411	+	0.0758614i
$676$	20.1897	+	11.2434i	0.776526	+	0.432439i
$677$	−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	$0.477612\pi$
$678$	−11.0970	−	6.29282i	−0.426177	−	0.241674i
$679$		0			0
$680$	−3.54598	+	12.8428i	−0.135982	+	0.492497i
$681$	9.09622	−	15.7551i	0.348568	−	0.603738i
$682$	0.311285	+	40.2117i	0.0119197	+	1.53978i
$683$	−2.04177	+	7.62000i	−0.0781262	+	0.291571i	−0.993924	−	0.110069i	$-0.964893\pi$
$683$	−2.04177	+	7.62000i	−0.0781262	+	0.291571i	0.915798	+	0.401640i	$0.131560\pi$
$684$	−0.473001	−	30.5492i	−0.0180856	−	1.16808i
$685$	30.0985	+	9.06769i	1.15001	+	0.346459i
$686$		0			0
$687$	−20.9515	+	20.9515i	−0.799351	+	0.799351i
$688$	−6.11493	+	26.0182i	−0.233130	+	0.991936i
$689$	3.84034	−	2.21722i	0.146305	−	0.0844695i
$690$	−55.0372	+	30.1042i	−2.09523	+	1.14605i
$691$	34.4612	+	19.8962i	1.31097	+	0.756886i	0.982256	−	0.187545i	$-0.0600530\pi$
$691$	34.4612	+	19.8962i	1.31097	+	0.756886i	0.328709	+	0.944431i	$0.393386\pi$
$692$	−28.4945	−	7.16416i	−1.08320	−	0.272341i
$693$		0			0
$694$	−0.892202	+	0.246483i	−0.0338675	+	0.00935636i
$695$	−1.25746	+	40.7882i	−0.0476981	+	1.54718i
$696$	−15.2788	+	62.8218i	−0.579141	+	2.38125i
$697$	4.60342	−	17.1802i	0.174367	−	0.650746i
$698$	6.48568	+	11.0354i	0.245487	+	0.417694i
$699$	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	$0.394854\pi$
$702$	0.512810	+	0.872544i	0.0193548	+	0.0329320i
$703$	9.10471	−	33.9792i	0.343391	−	1.28155i
$704$	18.7496	−	12.0191i	0.706652	−	0.452986i
$705$	0.338918	−	10.9935i	0.0127644	−	0.414039i
$706$	19.8756	−	5.49090i	0.748028	−	0.206653i
$707$		0			0
$708$	12.3606	−	49.1626i	0.464540	−	1.84764i
$709$	−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	$0.685598\pi$
$710$	12.3681	−	6.76510i	0.464168	−	0.253890i
$711$	−25.0661	+	14.4719i	−0.940052	+	0.542739i
$712$	−6.99301	+	12.7892i	−0.262074	+	0.479295i
$713$	−57.3641	+	57.3641i	−2.14830	+	2.14830i
$714$		0			0
$715$	7.16579	+	2.15881i	0.267985	+	0.0807351i
$716$	−7.06778	+	0.109432i	−0.264135	+	0.00408967i
$717$	−1.99383	+	7.44107i	−0.0744609	+	0.277892i
$718$	0.159122	+	20.5553i	0.00593837	+	0.767116i
$719$	13.6822	−	23.6982i	0.510259	−	0.883794i	−0.489671	−	0.871907i	$-0.662883\pi$
$719$	13.6822	−	23.6982i	0.510259	−	0.883794i	0.999929	−	0.0118865i	$-0.00378368\pi$
$720$	28.9645	−	0.00419317i	1.07944	−	0.000156270i
$721$		0			0
$722$	4.00268	+	2.26982i	0.148964	+	0.0844739i
$723$	54.7806	−	14.6784i	2.03731	−	0.545897i
$724$	2.63127	−	4.72494i	0.0977903	−	0.175601i
$725$	−2.81875	+	45.6725i	−0.104686	+	1.69623i
$726$	11.1110	+	2.88517i	0.412366	+	0.107079i
$727$	−2.54080	+	2.54080i	−0.0942330	+	0.0942330i	−0.752652	−	0.658419i	$-0.771226\pi$
$727$	−2.54080	+	2.54080i	−0.0942330	+	0.0942330i	0.658419	+	0.752652i	$0.271226\pi$
$728$		0			0
$729$			31.1060i			1.15207i
$730$	2.76096	+	11.3451i	0.102188	+	0.419901i
$731$	12.1901	−	7.03793i	0.450865	−	0.260307i
$732$	−26.9838	+	7.67994i	−0.997349	+	0.283859i
$733$	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
$738$	−38.6656	+	0.299316i	−1.42330	+	0.0110180i
$739$	−21.8227	−	37.7981i	−0.802763	−	1.39043i	−0.917791	−	0.397064i	$-0.870029\pi$
$739$	−21.8227	−	37.7981i	−0.802763	−	1.39043i	0.115028	−	0.993362i	$-0.463304\pi$
$740$	32.0765	+	9.12439i	1.17916	+	0.335419i
$741$	−14.1653			−0.520376
$742$		0			0
$743$	10.8795	+	10.8795i	0.399131	+	0.399131i	0.877926	−	0.478795i	$-0.158926\pi$
$743$	10.8795	+	10.8795i	0.399131	+	0.399131i	−0.478795	+	0.877926i	$0.658926\pi$
$744$	69.2454	−	20.2889i	2.53866	−	0.743828i
$745$	−13.9739	+	22.5677i	−0.511965	+	0.826817i
$746$	−5.54083	−	5.45570i	−0.202864	−	0.199748i
$747$	1.11467	+	4.16001i	0.0407837	+	0.152207i
$748$	−11.3751	−	2.85996i	−0.415915	−	0.104570i
$749$		0			0
$750$	38.8740	−	6.95678i	1.41948	−	0.254026i
$751$	−11.3380	−	6.54601i	−0.413730	−	0.238867i	0.278661	−	0.960389i	$-0.410109\pi$
$751$	−11.3380	−	6.54601i	−0.413730	−	0.238867i	−0.692391	+	0.721522i	$0.743443\pi$
$752$	−5.39504	+	5.73994i	−0.196737	+	0.209314i
$753$	12.6766	+	3.39669i	0.461962	+	0.123782i
$754$	15.0607	+	3.91081i	0.548480	+	0.142423i
$755$	−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	$0.702388\pi$
$758$	14.5239	−	8.53598i	0.527533	−	0.310041i
$759$	−27.6131	−	47.8273i	−1.00229	−	1.73602i
$760$	−15.1135	+	25.7241i	−0.548225	+	0.933112i
$761$	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	$0.0522889\pi$
$762$	27.0501	+	15.3394i	0.979921	+	0.555688i
$763$		0			0
$764$	−21.7932	+	13.0363i	−0.788449	+	0.471635i
$765$	−10.4488	−	11.1136i	−0.377778	−	0.401812i
$766$	8.82145	−	8.95909i	0.318732	−	0.323705i
$767$	−11.7846	−	3.15768i	−0.425518	−	0.114017i
$768$	−29.9525	−	26.4548i	−1.08082	−	0.954607i
$769$			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
$772$	−4.28085	+	4.41550i	−0.154071	+	0.158917i
$773$	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	$0.332118\pi$
$774$	−21.8047	−	21.4697i	−0.783753	−	0.771712i
$775$	45.7170	−	22.7621i	1.64220	−	0.817640i
$776$	3.53973	−	3.70807i	0.127069	−	0.133112i
$777$		0			0
$778$	6.76937	−	11.9374i	0.242694	−	0.427975i
$779$	19.9147	−	34.4932i	0.713518	−	1.23585i
$780$	0.205954	−	13.4273i	0.00737433	−	0.480774i
$781$	6.20530	+	10.7479i	0.222043	+	0.384590i
$782$	−11.9894	−	20.3999i	−0.428739	−	0.729498i
$783$	−3.85216	−	3.85216i	−0.137665	−	0.137665i
$784$		0			0
$785$	−0.703835	−	0.212042i	−0.0251210	−	0.00756811i
$786$	8.89164	−	34.2422i	0.317154	−	1.22138i
$787$	−5.94471	−	1.59288i	−0.211906	−	0.0567800i	0.151304	−	0.988487i	$-0.451653\pi$
$787$	−5.94471	−	1.59288i	−0.211906	−	0.0567800i	−0.363210	+	0.931707i	$0.618319\pi$
$788$	−7.59505	+	2.16165i	−0.270563	+	0.0770057i
$789$	−62.3600	−	36.0036i	−2.22007	−	1.28176i
$790$	28.2566	+	0.652228i	1.00532	+	0.0232052i
$791$		0			0
$792$	0.592105	+	25.4919i	0.0210395	+	0.905815i
$793$	1.74759	+	6.52209i	0.0620587	+	0.231606i
$794$	32.1923	−	32.6946i	1.14246	−	1.16029i
$795$	17.5143	+	10.8449i	0.621168	+	0.384628i
$796$	24.4477	−	0.378530i	0.866527	−	0.0134166i
$797$	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
$800$	−24.1642	−	14.7001i	−0.854332	−	0.519728i
$801$	−8.34430	−	14.4528i	−0.294831	−	0.510663i
$802$	−0.374371	−	48.3611i	−0.0132195	−	1.70769i
$803$	−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
$808$	30.3253	−	18.4602i	1.06684	−	0.649429i
$809$	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	$0.269372\pi$
$810$	13.5265	−	22.2277i	0.475272	−	0.781001i
$811$		−	15.7687i		−	0.553713i	−0.960911	−	0.276857i	$-0.910707\pi$
$811$		−	15.7687i		−	0.553713i	0.960911	−	0.276857i	$-0.0892927\pi$
$812$		0			0
$813$	19.8565	−	19.8565i	0.696397	−	0.696397i
$814$	−7.37884	+	28.4163i	−0.258628	+	0.995990i
$815$	9.86525	+	41.9481i	0.345565	+	1.46938i
$816$	0.651574	+	21.0362i	0.0228097	+	0.736415i
$817$	30.4466	−	8.15813i	1.06519	−	0.285417i
$818$	−0.824009	+	1.45309i	−0.0288108	+	0.0508060i
$819$		0			0
$820$	32.4066	+	19.3786i	1.13169	+	0.676731i
$821$	−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	$0.875867\pi$
$822$	49.6548	−	0.384386i	1.73191	−	0.0134070i
$823$	0.755780	−	2.82061i	0.0263448	−	0.0983203i	−0.951502	−	0.307644i	$-0.900460\pi$
$823$	0.755780	−	2.82061i	0.0263448	−	0.0983203i	0.977846	+	0.209324i	$0.0671262\pi$
$824$	1.69989	+	5.80166i	0.0592183	+	0.202110i
$825$	6.91246	+	34.0721i	0.240661	+	1.18624i
$826$		0			0
$827$	34.8943	−	34.8943i	1.21339	−	1.21339i	0.243489	−	0.969904i	$-0.421708\pi$
$827$	34.8943	−	34.8943i	1.21339	−	1.21339i	0.969904	−	0.243489i	$-0.0782921\pi$
$828$	−35.8068	+	36.9330i	−1.24437	+	1.28351i
$829$	−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	$0.379373\pi$
$830$	1.18195	−	4.03612i	0.0410260	−	0.140096i
$831$	−16.2654	−	9.39085i	−0.564242	−	0.325765i
$832$	−6.47779	+	7.10931i	−0.224577	+	0.246471i
$833$		0			0
$834$	17.1655	+	62.1346i	0.594394	+	2.15155i
$835$	26.1661	+	27.8308i	0.905517	+	0.963125i
$836$	−22.9471	−	12.7790i	−0.793643	−	0.441971i
$837$	−1.57363	+	5.87286i	−0.0543926	+	0.202996i
$838$	4.27641	−	2.51333i	0.147726	−	0.0868214i
$839$	−0.818867			−0.0282704			−0.0141352	−	0.999900i	$-0.504500\pi$
$839$	−0.818867			−0.0282704			−0.0141352	+	0.999900i	$0.504500\pi$
$840$		0			0
$841$	−54.7568			−1.88816
$842$	32.6565	−	19.1928i	1.12542	−	0.661429i
$843$	−17.3898	+	64.8997i	−0.598938	+	2.23527i
$844$	−16.2065	−	9.02519i	−0.557849	−	0.310660i
$845$	25.8247	+	0.796148i	0.888395	+	0.0273883i
$846$	−2.40166	−	8.69336i	−0.0825706	−	0.298884i
$847$		0			0
$848$	−4.25798	−	14.1262i	−0.146220	−	0.485095i
$849$	−26.8498	−	15.5018i	−0.921484	−	0.532019i
$850$	3.07463	+	14.5751i	0.105459	+	0.499923i
$851$	−51.2929	+	29.6140i	−1.75830	+	1.01515i
$852$	15.5010	−	15.9886i	0.531056	−	0.547759i
$853$	−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
$856$	−27.2909	+	7.99624i	−0.932785	+	0.273306i
$857$	−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	$0.970115\pi$
$858$	11.8217	−	0.0915136i	0.403586	−	0.00312422i
$859$	−5.83870	+	10.1129i	−0.199214	+	0.345048i	−0.948274	−	0.317454i	$-0.897172\pi$
$859$	−5.83870	+	10.1129i	−0.199214	+	0.345048i	0.749060	+	0.662502i	$0.230505\pi$
$860$	7.29042	+	28.9789i	0.248601	+	0.988172i
$861$		0			0
$862$	−26.2326	+	46.2595i	−0.893485	+	1.57560i
$863$	−42.0243	+	11.2604i	−1.43052	+	0.383308i	−0.889204	−	0.457510i	$-0.848741\pi$
$863$	−42.0243	+	11.2604i	−1.43052	+	0.383308i	−0.541319	+	0.840818i	$0.682075\pi$
$864$	3.21642	−	0.996733i	0.109425	−	0.0339096i
$865$	−31.9769	+	7.52024i	−1.08725	+	0.255696i
$866$	−14.1243	+	54.3936i	−0.479965	+	1.84837i
$867$	−22.1864	+	22.1864i	−0.753488	+	0.753488i
$868$		0			0
$869$			24.8822i			0.844071i
$870$	17.0924	+	70.2344i	0.579485	+	2.38117i
$871$	−3.54492	+	2.04666i	−0.120115	+	0.0693485i
$872$	8.83132	+	14.5075i	0.299066	+	0.491287i
$873$	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	$0.428680\pi$
$878$	−0.182914	−	23.6288i	−0.00617305	−	0.797433i
$879$	12.0621	+	20.8922i	0.406844	+	0.704675i
$880$	12.4468	−	21.5658i	0.419583	−	0.726982i
$881$	−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	0.451644	−	0.892198i	$-0.350838\pi$
$883$	−13.0912	−	13.0912i	−0.440554	−	0.440554i	−0.892198	+	0.451644i	$0.850838\pi$
$884$	5.06466	−	0.0784174i	0.170343	−	0.00263746i
$885$	−12.9750	−	55.1710i	−0.436149	−	1.85455i
$886$	12.7102	−	12.9085i	0.427008	−	0.433670i
$887$	−1.36658	−	5.10015i	−0.0458853	−	0.171246i	0.939181	−	0.343423i	$-0.111587\pi$
$887$	−1.36658	−	5.10015i	−0.0458853	−	0.171246i	−0.985066	+	0.172177i	$0.944920\pi$
$888$	52.6660	−	1.22328i	1.76736	−	0.0410507i
$889$		0			0
$890$	−0.376065	+	16.2923i	−0.0126057	+	0.546121i
$891$	19.8376	+	11.4533i	0.664585	+	0.383699i
$892$	21.4834	−	6.11445i	0.719317	−	0.204727i
$893$	8.97362	+	2.40448i	0.300291	+	0.0804627i
$894$	−10.5385	+	40.5842i	−0.352460	+	1.35734i
$895$	−6.96268	+	3.73871i	−0.232737	+	0.124971i
$896$		0			0
$897$	16.8643	+	16.8643i	0.563082	+	0.563082i
$898$	2.20146	+	3.74578i	0.0734638	+	0.124998i
$899$	46.7387	+	80.9538i	1.55882	+	2.69996i
$900$	28.7620	−	14.8804i	0.958732	−	0.496014i
$901$	−3.88509	+	6.72917i	−0.129431	+	0.224181i
$902$	−16.3970	+	28.9151i	−0.545961	+	0.962767i
$903$		0			0
$904$	7.38901	+	7.05355i	0.245755	+	0.234598i
$905$	0.186321	−	6.04368i	0.00619351	−	0.200899i
$906$	−18.4866	−	18.2026i	−0.614177	−	0.604741i
$907$	10.1014	+	2.70666i	0.335411	+	0.0898731i	0.422594	−	0.906319i	$-0.361120\pi$
$907$	10.1014	+	2.70666i	0.335411	+	0.0898731i	−0.0871827	+	0.996192i	$0.527786\pi$
$908$	−10.1401	+	10.4591i	−0.336512	+	0.347096i
$909$			40.6472i			1.34818i
$910$		0			0
$911$			0.169000i			0.00559921i	0.999996	+	0.00279960i	$0.000891143\pi$
$911$			0.169000i			0.00559921i	−0.999996	+	0.00279960i	$0.999109\pi$
$912$	−10.7829	+	45.8797i	−0.357056	+	1.51923i
$913$	3.57624	+	0.958252i	0.118356	+	0.0317135i
$914$	−24.8258	+	25.2132i	−0.821166	+	0.833979i
$915$	−22.8527	+	21.4858i	−0.755486	+	0.710297i
$916$	20.3613	−	12.1797i	0.672756	−	0.402430i
$917$		0			0
$918$	−1.54263	−	0.874784i	−0.0509142	−	0.0288722i
$919$	8.49828	−	14.7195i	0.280332	−	0.485550i	−0.691134	−	0.722726i	$-0.742889\pi$
$919$	8.49828	−	14.7195i	0.280332	−	0.485550i	0.971467	+	0.237176i	$0.0762220\pi$
$920$	48.6186	−	12.6323i	1.60291	−	0.416474i
$921$	−19.4983	−	33.7720i	−0.642490	−	1.11283i
$922$	−2.60975	+	1.53380i	−0.0859476	+	0.0505130i
$923$	−3.78979	−	3.78979i	−0.124743	−	0.124743i
$924$		0			0
$925$	36.5409	−	7.41334i	1.20146	−	0.243749i
$926$	−29.1711	−	7.57483i	−0.958620	−	0.248924i
$927$	−6.68585	−	1.79147i	−0.219592	−	0.0588395i
$928$	24.1311	−	45.8029i	0.792143	−	1.50355i
$929$	−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	$0.832559\pi$
$930$	58.3460	−	55.7132i	1.91324	−	1.82691i
$931$		0			0
$932$	−11.0589	−	2.78046i	−0.362246	−	0.0910770i
$933$	−8.01262	−	29.9035i	−0.262322	−	0.978997i
$934$	−19.5835	−	19.2827i	−0.640793	−	0.630948i
$935$	−12.7653	+	3.00211i	−0.417470	+	0.0981794i
$936$	−3.09627	−	10.5675i	−0.101205	−	0.345409i
$937$	−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
$940$	−2.40967	+	8.47114i	−0.0785948	+	0.276298i
$941$	−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	$0.997996\pi$
$942$	−1.16115	+	0.00898861i	−0.0378322	+	0.000292865i
$943$	−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	0.990988	−	0.133947i	$-0.0427652\pi$
$947$	2.02470	+	7.55627i	0.0657938	+	0.245546i	−0.925195	+	0.379493i	$0.876099\pi$
$948$	42.9423	−	12.2220i	1.39470	−	0.396951i
$949$	3.84435	−	2.21954i	0.124793	−	0.0720493i
$950$	−1.79699	+	33.3085i	−0.0583019	+	1.08067i
$951$			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	$0.281902\pi$
$954$	16.3499	+	4.24557i	0.529348	+	0.137455i
$955$	−14.9469	+	24.1391i	−0.483672	+	0.781123i
$956$	3.00123	−	5.38929i	0.0970668	−	0.174302i
$957$	−61.4669	+	16.4700i	−1.98694	+	0.532400i
$958$	−17.6084	−	9.98527i	−0.568901	−	0.322609i
$959$		0			0
$960$	−43.3326	−	10.8881i	−1.39855	−	0.351413i
$961$	36.6631	−	63.5024i	1.18268	−	2.04846i
$962$	−0.0981447	−	12.6783i	−0.00316431	−	0.408765i
$963$	8.42704	−	31.4502i	0.271558	−	1.01347i
$964$	−45.4075	+	0.703055i	−1.46248	+	0.0226439i
$965$	−1.98342	+	6.58361i	−0.0638487	+	0.211934i
$966$		0			0
$967$	11.8371	−	11.8371i	0.380654	−	0.380654i	−0.490684	−	0.871338i	$-0.663253\pi$
$967$	11.8371	−	11.8371i	0.380654	−	0.380654i	0.871338	+	0.490684i	$0.163253\pi$
$968$	−8.06520	−	4.40998i	−0.259225	−	0.141742i
$969$	21.4955	−	12.4104i	0.690536	−	0.398681i
$970$	1.61076	−	5.50044i	0.0517185	−	0.176608i
$971$	−42.9451	−	24.7944i	−1.37817	−	0.795689i	−0.386234	−	0.922401i	$-0.626224\pi$
$971$	−42.9451	−	24.7944i	−1.37817	−	0.795689i	−0.991940	+	0.126712i	$0.959558\pi$
$972$	10.8931	−	43.3258i	0.349396	−	1.38968i
$973$		0			0
$974$	−47.7755	+	13.1986i	−1.53082	+	0.422911i
$975$	−6.69177	−	13.4402i	−0.214308	−	0.430430i
$976$	22.4545	−	0.695505i	0.718752	−	0.0222626i
$977$	−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	$0.793881\pi$
$978$	34.4911	+	58.6865i	1.10290	+	1.87659i
$979$	−14.3467			−0.458523
$980$		0			0
$981$	−19.4455			−0.620847
$982$	−29.5204	−	50.2288i	−0.942033	−	1.60287i
$983$	8.01244	−	29.9028i	0.255557	−	0.953752i	−0.712222	−	0.701954i	$-0.752311\pi$
$983$	8.01244	−	29.9028i	0.255557	−	0.953752i	0.967780	−	0.251799i	$-0.0810221\pi$
$984$	57.9565	+	14.0955i	1.84759	+	0.449348i
$985$	−6.43228	+	6.04754i	−0.204949	+	0.192691i
$986$	−26.2806	+	7.26038i	−0.836946	+	0.231218i
$987$		0			0
$988$	11.0005	+	2.76577i	0.349972	+	0.0879910i
$989$	−45.9602	−	26.5351i	−1.46145	−	0.843768i
$990$	13.6807	+	25.0114i	0.434802	+	0.794916i
$991$	−23.4196	+	13.5213i	−0.743948	+	0.429519i	−0.823503	−	0.567312i	$-0.807983\pi$
$991$	−23.4196	+	13.5213i	−0.743948	+	0.429519i	0.0795551	+	0.996830i	$0.474650\pi$
$992$	−57.7360	+	2.23579i	−1.83312	+	0.0709863i
$993$	−9.79539	+	9.79539i	−0.310847	+	0.310847i
$994$		0			0
$995$	24.0842	−	12.9323i	0.763520	−	0.409983i
$996$	−0.102850	−	6.64266i	−0.00325892	−	0.210481i
$997$	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	$-0.154139\pi$
$998$	−0.364746	−	47.1178i	−0.0115458	−	1.49149i
$999$	−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.667.5		112
4.3	odd	2	inner	980.2.x.n.667.2		112
5.3	odd	4	inner	980.2.x.n.863.19		112
7.2	even	3		980.2.k.m.687.25	yes	56
7.3	odd	6	inner	980.2.x.n.67.13		112
7.4	even	3	inner	980.2.x.n.67.14		112
7.5	odd	6		980.2.k.m.687.26	yes	56
7.6	odd	2	inner	980.2.x.n.667.6		112
20.3	even	4	inner	980.2.x.n.863.14		112
28.3	even	6	inner	980.2.x.n.67.20		112
28.11	odd	6	inner	980.2.x.n.67.19		112
28.19	even	6		980.2.k.m.687.19	✓	56
28.23	odd	6		980.2.k.m.687.20	yes	56
28.27	even	2	inner	980.2.x.n.667.1		112
35.3	even	12	inner	980.2.x.n.263.1		112
35.13	even	4	inner	980.2.x.n.863.20		112
35.18	odd	12	inner	980.2.x.n.263.2		112
35.23	odd	12		980.2.k.m.883.20	yes	56
35.33	even	12		980.2.k.m.883.19	yes	56
140.3	odd	12	inner	980.2.x.n.263.6		112
140.23	even	12		980.2.k.m.883.25	yes	56
140.83	odd	4	inner	980.2.x.n.863.13		112
140.103	odd	12		980.2.k.m.883.26	yes	56
140.123	even	12	inner	980.2.x.n.263.5		112

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

\(f(q)\)	\(=\)	\(q+(-1.21923 + 0.716566i) q^{2} +(-0.646443 + 2.41256i) q^{3} +(0.973066 - 1.74732i) q^{4} +(0.0689030 - 2.23501i) q^{5} +(-0.940592 - 3.40469i) q^{6} +(0.0656787 + 2.82766i) q^{8} +(-2.80447 - 1.61916i) q^{9} +O(q^{10})\)	\(q+(-1.21923 + 0.716566i) q^{2} +(-0.646443 + 2.41256i) q^{3} +(0.973066 - 1.74732i) q^{4} +(0.0689030 - 2.23501i) q^{5} +(-0.940592 - 3.40469i) q^{6} +(0.0656787 + 2.82766i) q^{8} +(-2.80447 - 1.61916i) q^{9} +(1.51752 + 2.77437i) q^{10} +(-2.41093 + 1.39195i) q^{11} +(3.58649 + 3.47712i) q^{12} +(0.850111 - 0.850111i) q^{13} +(5.34754 + 1.61104i) q^{15} +(-2.10629 - 3.40052i) q^{16} +(-0.545228 + 2.03482i) q^{17} +(4.57955 - 0.0354510i) q^{18} +(-2.35869 + 4.08538i) q^{19} +(-3.83823 - 2.29520i) q^{20} +(1.94206 - 3.42470i) q^{22} +(7.67188 - 2.05567i) q^{23} +(-6.86436 - 1.66947i) q^{24} +(-4.99050 - 0.307997i) q^{25} +(-0.427324 + 1.64565i) q^{26} +(0.420915 - 0.420915i) q^{27} -9.15187i q^{29} +(-7.67432 + 1.86764i) q^{30} +(-8.84560 + 5.10701i) q^{31} +(5.00476 + 2.63674i) 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} +(-0.0516427 - 6.67119i) q^{38} +(1.50139 + 2.60049i) q^{39} +(6.32437 + 0.0480423i) q^{40} -8.44310 q^{41} +(-4.72474 - 4.72474i) q^{43} +(0.0861972 + 5.56713i) q^{44} +(-3.81208 + 6.15645i) q^{45} +(-7.88080 + 8.00376i) q^{46} +(-0.509705 - 1.90224i) q^{47} +(9.56556 - 2.88330i) q^{48} +(6.30530 - 3.20051i) q^{50} +(-4.55666 - 2.63079i) q^{51} +(-0.658206 - 2.31263i) q^{52} +(3.56281 + 0.954652i) q^{53} +(-0.211581 + 0.814807i) q^{54} +(2.94489 + 5.48435i) q^{55} +(-8.33145 - 8.33145i) q^{57} +(6.55792 + 11.1583i) q^{58} +(-5.07401 - 8.78844i) q^{59} +(8.01851 - 7.77625i) q^{60} +(-2.80816 + 4.86388i) q^{61} +(7.12535 - 12.5651i) q^{62} +(-7.99137 + 0.371434i) q^{64} +(-1.84143 - 1.95858i) q^{65} +(7.00686 + 6.89921i) q^{66} +(-3.28874 - 0.881215i) q^{67} +(3.02495 + 2.93270i) q^{68} +19.8377i q^{69} -4.45800i q^{71} +(4.39426 - 8.03646i) q^{72} +(3.56653 + 0.955649i) q^{73} +(7.39912 - 7.51457i) q^{74} +(3.96914 - 11.8408i) q^{75} +(4.84332 + 8.09674i) q^{76} +(-3.69398 - 2.09476i) q^{78} +(4.46895 - 7.74045i) q^{79} +(-7.74532 + 4.47326i) q^{80} +(-4.11411 - 7.12584i) q^{81} +(10.2941 - 6.05004i) q^{82} +(-0.940405 - 0.940405i) q^{83} +(4.51026 + 1.35879i) q^{85} +(9.14616 + 2.37498i) q^{86} +(22.0794 + 5.91616i) q^{87} +(-4.09431 - 6.72587i) q^{88} +(4.46303 + 2.57673i) q^{89} +(0.236311 - 10.2378i) q^{90} +(3.87331 - 15.4056i) q^{92} +(-6.60279 - 24.6419i) q^{93} +(1.98453 + 1.95405i) q^{94} +(8.96832 + 5.55319i) q^{95} +(-9.59658 + 10.3698i) 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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