LMFDB - Embedded newform 980.2.x.l.667.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("980.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			667.4
Character	$\chi$	$=$	980.667
Dual form			980.2.x.l.263.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05861 + 0.937739i) q^{2} +(0.145273 - 0.542165i) q^{3} +(0.241290 - 1.98539i) q^{4} +(1.86388 + 1.23530i) q^{5} +(0.354623 + 0.710167i) q^{6} +(1.60635 + 2.32801i) q^{8} +(2.32524 + 1.34248i) q^{9} +O(q^{10})$	\(q+(-1.05861 + 0.937739i) q^{2} +(0.145273 - 0.542165i) q^{3} +(0.241290 - 1.98539i) q^{4} +(1.86388 + 1.23530i) q^{5} +(0.354623 + 0.710167i) q^{6} +(1.60635 + 2.32801i) q^{8} +(2.32524 + 1.34248i) q^{9} +(-3.13150 + 0.440142i) q^{10} +(-3.73254 + 2.15498i) q^{11} +(-1.04136 - 0.419242i) q^{12} +(-1.27735 + 1.27735i) q^{13} +(0.940505 - 0.831075i) q^{15} +(-3.88356 - 0.958111i) q^{16} +(0.130200 - 0.485914i) q^{17} +(-3.72040 + 0.759314i) q^{18} +(-4.08212 + 7.07044i) q^{19} +(2.90228 - 3.40246i) q^{20} +(1.93047 - 5.78142i) q^{22} +(-3.62985 + 0.972614i) q^{23} +(1.49553 - 0.532709i) q^{24} +(1.94809 + 4.60488i) q^{25} +(0.154388 - 2.55003i) q^{26} +(2.25631 - 2.25631i) q^{27} -3.36420i q^{29} +(-0.216292 + 1.76173i) q^{30} +(-0.130211 + 0.0751773i) q^{31} +(5.00961 - 2.62750i) q^{32} +(0.626120 + 2.33671i) q^{33} +(0.317830 + 0.636485i) q^{34} +(3.22640 - 4.29258i) q^{36} +(2.09567 - 0.561533i) q^{37} +(-2.30888 - 11.3128i) q^{38} +(0.506971 + 0.878099i) q^{39} +(0.118253 + 6.32345i) q^{40} -9.17384 q^{41} +(6.48688 + 6.48688i) q^{43} +(3.37786 + 7.93053i) q^{44} +(2.67560 + 5.37457i) q^{45} +(2.93052 - 4.43346i) q^{46} +(-1.96175 - 7.32135i) q^{47} +(-1.08363 + 1.96634i) q^{48} +(-6.38044 - 3.04796i) q^{50} +(-0.244531 - 0.141180i) q^{51} +(2.22783 + 2.84425i) q^{52} +(11.4470 + 3.06722i) q^{53} +(-0.272712 + 4.50438i) q^{54} +(-9.61904 - 0.594164i) q^{55} +(3.24033 + 3.24033i) q^{57} +(3.15475 + 3.56136i) q^{58} +(0.178676 + 0.309476i) q^{59} +(-1.42307 - 2.06780i) q^{60} +(-5.01582 + 8.68766i) q^{61} +(0.0673452 - 0.201687i) q^{62} +(-2.83929 + 7.47920i) q^{64} +(-3.95873 + 0.802921i) q^{65} +(-2.85404 - 1.88652i) q^{66} +(7.28570 + 1.95220i) q^{67} +(-0.933313 - 0.375745i) q^{68} +2.10927i q^{69} -2.69169i q^{71} +(0.609838 + 7.56967i) q^{72} +(-5.66210 - 1.51716i) q^{73} +(-1.69191 + 2.55963i) q^{74} +(2.77961 - 0.387221i) q^{75} +(13.0526 + 9.81064i) q^{76} +(-1.36011 - 0.454154i) q^{78} +(-4.58697 + 7.94486i) q^{79} +(-6.05493 - 6.58315i) q^{80} +(3.13192 + 5.42464i) q^{81} +(9.71147 - 8.60267i) q^{82} +(-4.83885 - 4.83885i) q^{83} +(0.842925 - 0.744849i) q^{85} +(-12.9501 - 0.784044i) q^{86} +(-1.82395 - 0.488727i) q^{87} +(-11.0126 - 5.22775i) q^{88} +(-1.03229 - 0.595991i) q^{89} +(-7.87235 - 3.18053i) q^{90} +(1.05517 + 7.44135i) q^{92} +(0.0218424 + 0.0815170i) q^{93} +(8.94224 + 5.91081i) q^{94} +(-16.3427 + 8.13582i) q^{95} +(-0.696781 - 3.09774i) q^{96} +(1.04890 + 1.04890i) q^{97} -11.5720 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 16 q^{6}+O(q^{10}) $ 72 * q + 16 * q^6	$ 72 q + 16 q^{6} - 16 q^{10} - 16 q^{12} + 8 q^{13} + 8 q^{16} - 20 q^{17} - 28 q^{18} - 40 q^{20} + 8 q^{22} + 20 q^{25} - 32 q^{26} + 4 q^{30} - 20 q^{37} - 36 q^{40} + 20 q^{45} - 16 q^{46} + 48 q^{48} + 80 q^{50} + 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} - 64 q^{61} - 80 q^{62} - 4 q^{65} + 32 q^{66} + 80 q^{68} - 80 q^{72} + 52 q^{73} - 16 q^{76} - 152 q^{78} - 20 q^{80} + 36 q^{81} + 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} + 32 q^{90} - 112 q^{92} - 32 q^{93} + 120 q^{96} - 40 q^{97}+O(q^{100}) $ 72 * q + 16 * q^6 - 16 * q^10 - 16 * q^12 + 8 * q^13 + 8 * q^16 - 20 * q^17 - 28 * q^18 - 40 * q^20 + 8 * q^22 + 20 * q^25 - 32 * q^26 + 4 * q^30 - 20 * q^37 - 36 * q^40 + 20 * q^45 - 16 * q^46 + 48 * q^48 + 80 * q^50 + 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 - 64 * q^61 - 80 * q^62 - 4 * q^65 + 32 * q^66 + 80 * q^68 - 80 * q^72 + 52 * q^73 - 16 * q^76 - 152 * q^78 - 20 * q^80 + 36 * q^81 + 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 + 32 * q^90 - 112 * q^92 - 32 * q^93 + 120 * q^96 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.05861	+	0.937739i	−0.748547	+	0.663082i
$2$	−1.05861	+	0.937739i	−0.748547	+	0.663082i
$3$	0.145273	−	0.542165i	0.0838732	−	0.313019i	−0.911225	−	0.411909i	$-0.864862\pi$
$3$	0.145273	−	0.542165i	0.0838732	−	0.313019i	0.995098	+	0.0988894i	$0.0315290\pi$
$4$	0.241290	−	1.98539i	0.120645	−	0.992696i
$5$	1.86388	+	1.23530i	0.833552	+	0.552441i
$5$	1.86388	+	1.23530i	0.833552	+	0.552441i
$6$	0.354623	+	0.710167i	0.144774	+	0.289924i
$7$		0			0
$7$		0			0
$8$	1.60635	+	2.32801i	0.567930	+	0.823077i
$9$	2.32524	+	1.34248i	0.775079	+	0.447492i
$10$	−3.13150	+	0.440142i	−0.990266	+	0.139185i
$11$	−3.73254	+	2.15498i	−1.12540	+	0.649751i	−0.942775	−	0.333431i	$-0.891794\pi$
$11$	−3.73254	+	2.15498i	−1.12540	+	0.649751i	−0.182628	+	0.983182i	$0.558460\pi$
$12$	−1.04136	−	0.419242i	−0.300614	−	0.121025i
$13$	−1.27735	+	1.27735i	−0.354273	+	0.354273i	−0.861697	−	0.507424i	$-0.830598\pi$
$13$	−1.27735	+	1.27735i	−0.354273	+	0.354273i	0.507424	+	0.861697i	$0.330598\pi$
$14$		0			0
$15$	0.940505	−	0.831075i	0.242837	−	0.214583i
$16$	−3.88356	−	0.958111i	−0.970890	−	0.239528i
$17$	0.130200	−	0.485914i	0.0315782	−	0.117851i	−0.948338	−	0.317263i	$-0.897236\pi$
$17$	0.130200	−	0.485914i	0.0315782	−	0.117851i	0.979916	+	0.199411i	$0.0639030\pi$
$18$	−3.72040	+	0.759314i	−0.876907	+	0.178972i
$19$	−4.08212	+	7.07044i	−0.936503	+	1.62207i	−0.164571	+	0.986365i	$0.552624\pi$
$19$	−4.08212	+	7.07044i	−0.936503	+	1.62207i	−0.771932	+	0.635705i	$0.780709\pi$
$20$	2.90228	−	3.40246i	0.648970	−	0.760814i
$21$		0			0
$22$	1.93047	−	5.78142i	0.411578	−	1.23260i
$23$	−3.62985	+	0.972614i	−0.756875	+	0.202804i	−0.616566	−	0.787304i	$-0.711476\pi$
$23$	−3.62985	+	0.972614i	−0.756875	+	0.202804i	−0.140310	+	0.990108i	$0.544810\pi$
$24$	1.49553	−	0.532709i	0.305273	−	0.108739i
$25$	1.94809	+	4.60488i	0.389618	+	0.920977i
$26$	0.154388	−	2.55003i	0.0302780	−	0.500102i
$27$	2.25631	−	2.25631i	0.434228	−	0.434228i
$28$		0			0
$29$		−	3.36420i		−	0.624717i	−0.949964	−	0.312359i	$-0.898881\pi$
$29$		−	3.36420i		−	0.624717i	0.949964	−	0.312359i	$-0.101119\pi$
$30$	−0.216292	+	1.76173i	−0.0394893	+	0.321646i
$31$	−0.130211	+	0.0751773i	−0.0233866	+	0.0135022i	−0.511648	−	0.859195i	$-0.670965\pi$
$31$	−0.130211	+	0.0751773i	−0.0233866	+	0.0135022i	0.488261	+	0.872698i	$0.337631\pi$
$32$	5.00961	−	2.62750i	0.885583	−	0.464481i
$33$	0.626120	+	2.33671i	0.108994	+	0.406769i
$34$	0.317830	+	0.636485i	0.0545074	+	0.109156i
$35$		0			0
$36$	3.22640	−	4.29258i	0.537733	−	0.715430i
$37$	2.09567	−	0.561533i	0.344526	−	0.0923154i	−0.0824071	−	0.996599i	$-0.526261\pi$
$37$	2.09567	−	0.561533i	0.344526	−	0.0923154i	0.426933	+	0.904283i	$0.359594\pi$
$38$	−2.30888	−	11.3128i	−0.374549	−	1.83517i
$39$	0.506971	+	0.878099i	0.0811803	+	0.140608i
$40$	0.118253	+	6.32345i	0.0186975	+	0.999825i
$41$	−9.17384			−1.43271			−0.716357	−	0.697734i	$-0.754192\pi$
$41$	−9.17384			−1.43271			−0.716357	+	0.697734i	$0.754192\pi$
$42$		0			0
$43$	6.48688	+	6.48688i	0.989241	+	0.989241i	0.999943	−	0.0107022i	$-0.00340667\pi$
$43$	6.48688	+	6.48688i	0.989241	+	0.989241i	−0.0107022	+	0.999943i	$0.503407\pi$
$44$	3.37786	+	7.93053i	0.509231	+	1.19557i
$45$	2.67560	+	5.37457i	0.398856	+	0.801194i
$46$	2.93052	−	4.43346i	0.432081	−	0.653679i
$47$	−1.96175	−	7.32135i	−0.286151	−	1.06793i	−0.947994	−	0.318287i	$-0.896892\pi$
$47$	−1.96175	−	7.32135i	−0.286151	−	1.06793i	0.661844	−	0.749642i	$-0.269774\pi$
$48$	−1.08363	+	1.96634i	−0.156408	+	0.283817i
$49$		0			0
$50$	−6.38044	−	3.04796i	−0.902330	−	0.431046i
$51$	−0.244531	−	0.141180i	−0.0342412	−	0.0197692i
$52$	2.22783	+	2.84425i	0.308944	+	0.394427i
$53$	11.4470	+	3.06722i	1.57237	+	0.421315i	0.936553	−	0.350526i	$-0.113997\pi$
$53$	11.4470	+	3.06722i	1.57237	+	0.421315i	0.635816	+	0.771841i	$0.280664\pi$
$54$	−0.272712	+	4.50438i	−0.0371114	+	0.612969i
$55$	−9.61904	−	0.594164i	−1.29703	−	0.0801171i
$56$		0			0
$57$	3.24033	+	3.24033i	0.429192	+	0.429192i
$58$	3.15475	+	3.56136i	0.414239	+	0.467630i
$59$	0.178676	+	0.309476i	0.0232616	+	0.0402903i	0.877422	−	0.479720i	$-0.159262\pi$
$59$	0.178676	+	0.309476i	0.0232616	+	0.0402903i	−0.854160	+	0.520010i	$0.825928\pi$
$60$	−1.42307	−	2.06780i	−0.183718	−	0.266952i
$61$	−5.01582	+	8.68766i	−0.642210	+	1.11234i	0.342728	+	0.939435i	$0.388649\pi$
$61$	−5.01582	+	8.68766i	−0.642210	+	1.11234i	−0.984938	+	0.172906i	$0.944684\pi$
$62$	0.0673452	−	0.201687i	0.00855285	−	0.0256143i
$63$		0			0
$64$	−2.83929	+	7.47920i	−0.354911	+	0.934900i
$65$	−3.95873	+	0.802921i	−0.491020	+	0.0995900i
$66$	−2.85404	−	1.88652i	−0.351308	−	0.232214i
$67$	7.28570	+	1.95220i	0.890090	+	0.238499i	0.674755	−	0.738041i	$-0.264249\pi$
$67$	7.28570	+	1.95220i	0.890090	+	0.238499i	0.215335	+	0.976540i	$0.430916\pi$
$68$	−0.933313	−	0.375745i	−0.113181	−	0.0455658i
$69$			2.10927i			0.253926i
$70$		0			0
$71$		−	2.69169i		−	0.319445i	−0.987162	−	0.159722i	$-0.948940\pi$
$71$		−	2.69169i		−	0.319445i	0.987162	−	0.159722i	$-0.0510599\pi$
$72$	0.609838	+	7.56967i	0.0718702	+	0.892094i
$73$	−5.66210	−	1.51716i	−0.662699	−	0.177570i	−0.0882353	−	0.996100i	$-0.528123\pi$
$73$	−5.66210	−	1.51716i	−0.662699	−	0.177570i	−0.574464	+	0.818530i	$0.694789\pi$
$74$	−1.69191	+	2.55963i	−0.196681	+	0.297551i
$75$	2.77961	−	0.387221i	0.320962	−	0.0447125i
$76$	13.0526	+	9.81064i	1.49724	+	1.12536i
$77$		0			0
$78$	−1.36011	−	0.454154i	−0.154002	−	0.0514228i
$79$	−4.58697	+	7.94486i	−0.516074	+	0.893866i	0.483752	+	0.875205i	$0.339274\pi$
$79$	−4.58697	+	7.94486i	−0.516074	+	0.893866i	−0.999826	+	0.0186612i	$0.994060\pi$
$80$	−6.05493	−	6.58315i	−0.676962	−	0.736018i
$81$	3.13192	+	5.42464i	0.347991	+	0.602737i
$82$	9.71147	−	8.60267i	1.07245	−	0.950006i
$83$	−4.83885	−	4.83885i	−0.531132	−	0.531132i	0.389777	−	0.920909i	$-0.372552\pi$
$83$	−4.83885	−	4.83885i	−0.531132	−	0.531132i	−0.920909	+	0.389777i	$0.872552\pi$
$84$		0			0
$85$	0.842925	−	0.744849i	0.0914281	−	0.0807902i
$86$	−12.9501	−	0.784044i	−1.39644	−	0.0845456i
$87$	−1.82395	−	0.488727i	−0.195548	−	0.0523970i
$88$	−11.0126	−	5.22775i	−1.17395	−	0.557280i
$89$	−1.03229	−	0.595991i	−0.109422	−	0.0631750i	0.444290	−	0.895883i	$-0.353456\pi$
$89$	−1.03229	−	0.595991i	−0.109422	−	0.0631750i	−0.553712	+	0.832708i	$0.686789\pi$
$90$	−7.87235	−	3.18053i	−0.829819	−	0.335257i
$91$		0			0
$92$	1.05517	+	7.44135i	0.110009	+	0.775814i
$93$	0.0218424	+	0.0815170i	0.00226495	+	0.00845292i
$94$	8.94224	+	5.91081i	0.922321	+	0.609654i
$95$	−16.3427	+	8.13582i	−1.67672	+	0.834717i
$96$	−0.696781	−	3.09774i	−0.0711149	−	0.316162i
$97$	1.04890	+	1.04890i	0.106500	+	0.106500i	0.758349	−	0.651849i	$-0.226006\pi$
$97$	1.04890	+	1.04890i	0.106500	+	0.106500i	−0.651849	+	0.758349i	$0.726006\pi$
$98$		0			0
$99$	−11.5720			−1.16303
$100$	9.61255	−	2.75660i	0.961255	−	0.275660i
$101$	7.61778	+	13.1944i	0.757997	+	1.31289i	0.943870	+	0.330316i	$0.107155\pi$
$101$	7.61778	+	13.1944i	0.757997	+	1.31289i	−0.185873	+	0.982574i	$0.559511\pi$
$102$	0.391252	−	0.0798524i	0.0387397	−	0.00790657i
$103$	1.92706	−	0.516355i	0.189879	−	0.0508779i	−0.162626	−	0.986688i	$-0.551997\pi$
$103$	1.92706	−	0.516355i	0.189879	−	0.0508779i	0.352505	+	0.935810i	$0.385330\pi$
$104$	−5.02556	−	0.921819i	−0.492797	−	0.0903918i
$105$		0			0
$106$	−14.9941	+	7.48734i	−1.45636	+	0.727235i
$107$	−0.706249	−	2.63576i	−0.0682757	−	0.254808i	0.923349	−	0.383962i	$-0.125441\pi$
$107$	−0.706249	−	2.63576i	−0.0682757	−	0.254808i	−0.991625	+	0.129154i	$0.958774\pi$
$108$	−3.93524	−	5.02409i	−0.378669	−	0.483444i
$109$	8.87425	−	5.12355i	0.849999	−	0.490747i	−0.0106518	−	0.999943i	$-0.503391\pi$
$109$	8.87425	−	5.12355i	0.849999	−	0.490747i	0.860650	+	0.509196i	$0.170057\pi$
$110$	10.7399	−	8.39116i	1.02401	−	0.800066i
$111$		−	1.21777i		−	0.115586i
$112$		0			0
$113$	8.33553	−	8.33553i	0.784141	−	0.784141i	−0.196386	−	0.980527i	$-0.562920\pi$
$113$	8.33553	−	8.33553i	0.784141	−	0.784141i	0.980527	+	0.196386i	$0.0629204\pi$
$114$	−6.46881	−	0.391645i	−0.605859	−	0.0366809i
$115$	−7.96706	−	2.67110i	−0.742932	−	0.249081i
$116$	−6.67926	−	0.811750i	−0.620154	−	0.0753691i
$117$	−4.68496	+	1.25533i	−0.433124	+	0.116055i
$118$	−0.479355	−	0.160061i	−0.0441282	−	0.0147348i
$119$		0			0
$120$	3.44553	+	0.854512i	0.314533	+	0.0780059i
$121$	3.78789	−	6.56082i	0.344354	−	0.596439i
$122$	−2.83698	−	13.9003i	−0.256848	−	1.25848i
$123$	−1.33271	+	4.97374i	−0.120166	+	0.448467i
$124$	0.117838	+	0.276659i	0.0105821	+	0.0248447i
$125$	−2.05739	+	10.9894i	−0.184019	+	0.982923i
$126$		0			0
$127$	−5.10188	+	5.10188i	−0.452719	+	0.452719i	−0.896256	−	0.443537i	$-0.853723\pi$
$127$	−5.10188	+	5.10188i	−0.452719	+	0.452719i	0.443537	+	0.896256i	$0.353723\pi$
$128$	−4.00785	−	10.5800i	−0.354247	−	0.935152i
$129$	4.45933	−	2.57459i	0.392622	−	0.226680i
$130$	3.43780	−	4.56223i	0.301515	−	0.400134i
$131$	−12.3192	−	7.11248i	−1.07633	−	0.621420i	−0.146427	−	0.989221i	$-0.546777\pi$
$131$	−12.3192	−	7.11248i	−1.07633	−	0.621420i	−0.929904	+	0.367801i	$0.880111\pi$
$132$	4.79036	−	0.679268i	0.416948	−	0.0591227i
$133$		0			0
$134$	−9.54334	+	4.76548i	−0.824419	+	0.411675i
$135$	6.99271	−	1.41828i	0.601837	−	0.122066i
$136$	1.34036	−	0.477439i	0.114935	−	0.0409401i
$137$	−2.90536	+	10.8430i	−0.248222	+	0.926377i	0.723514	+	0.690309i	$0.242525\pi$
$137$	−2.90536	+	10.8430i	−0.248222	+	0.926377i	−0.971737	+	0.236068i	$0.924141\pi$
$138$	−1.97795	−	2.23288i	−0.168374	−	0.190076i
$139$	12.9091			1.09493			0.547466	−	0.836828i	$-0.315592\pi$
$139$	12.9091			1.09493			0.547466	+	0.836828i	$0.315592\pi$
$140$		0			0
$141$	−4.25437			−0.358283
$142$	2.52410	+	2.84944i	0.211818	+	0.239120i
$143$	2.01509	−	7.52043i	0.168510	−	0.628890i
$144$	−7.74395	−	7.44142i	−0.645329	−	0.620118i
$145$	4.15579	−	6.27047i	0.345119	−	0.520734i
$146$	7.41663	−	3.70351i	0.613805	−	0.306504i
$147$		0			0
$148$	−0.609198	−	4.29621i	−0.0500757	−	0.353147i
$149$	1.81595	+	1.04844i	0.148769	+	0.0858916i	0.572537	−	0.819879i	$-0.305959\pi$
$149$	1.81595	+	1.04844i	0.148769	+	0.0858916i	−0.423768	+	0.905771i	$0.639293\pi$
$150$	−2.57940	+	3.01647i	−0.210607	+	0.246293i
$151$	9.34014	−	5.39253i	0.760090	−	0.438838i	−0.0692380	−	0.997600i	$-0.522057\pi$
$151$	9.34014	−	5.39253i	0.760090	−	0.438838i	0.829328	+	0.558762i	$0.188723\pi$
$152$	−23.0174	+	1.85436i	−1.86696	+	0.150408i
$153$	0.955075	−	0.955075i	0.0772132	−	0.0772132i
$154$		0			0
$155$	−0.335563	−	0.0207276i	−0.0269531	−	0.00166488i
$156$	1.86570	−	0.794658i	0.149375	−	0.0636236i
$157$	2.36123	−	8.81224i	0.188447	−	0.703293i	−0.805420	−	0.592705i	$-0.798060\pi$
$157$	2.36123	−	8.81224i	0.188447	−	0.703293i	0.993866	−	0.110588i	$-0.0352734\pi$
$158$	−2.59442	−	12.7118i	−0.206401	−	1.01130i
$159$	3.32588	−	5.76059i	0.263759	−	0.456844i
$160$	12.5831	+	1.29101i	0.994778	+	0.102063i
$161$		0			0
$162$	−8.40236	−	2.80563i	−0.660151	−	0.220431i
$163$	20.7209	−	5.55214i	1.62299	−	0.434878i	0.671108	−	0.741359i	$-0.265818\pi$
$163$	20.7209	−	5.55214i	1.62299	−	0.434878i	0.951877	+	0.306482i	$0.0991518\pi$
$164$	−2.21356	+	18.2137i	−0.172850	+	1.42225i
$165$	−1.71952	+	5.12879i	−0.133864	+	0.399276i
$166$	9.66001	+	0.584852i	0.749762	+	0.0453933i
$167$	2.09436	−	2.09436i	0.162067	−	0.162067i	−0.621415	−	0.783482i	$-0.713442\pi$
$167$	2.09436	−	2.09436i	0.162067	−	0.162067i	0.783482	+	0.621415i	$0.213442\pi$
$168$		0			0
$169$			9.73675i			0.748981i
$170$	−0.193851	+	1.57895i	−0.0148677	+	0.121100i
$171$	−18.9838	+	10.9603i	−1.45173	+	0.838155i
$172$	14.4442	−	11.3138i	1.10136	−	0.862668i
$173$	1.11058	+	4.14474i	0.0844359	+	0.315119i	0.995207	−	0.0977931i	$-0.0311783\pi$
$173$	1.11058	+	4.14474i	0.0844359	+	0.315119i	−0.910771	+	0.412912i	$0.864512\pi$
$174$	2.38915	−	1.19302i	0.181121	−	0.0904429i
$175$		0			0
$176$	16.5602	−	4.79281i	1.24828	−	0.361272i
$177$	0.193744	−	0.0519135i	0.0145627	−	0.00390206i
$178$	1.65167	−	0.337097i	0.123798	−	0.0252665i
$179$	0.791917	+	1.37164i	0.0591906	+	0.102521i	0.894102	−	0.447863i	$-0.147815\pi$
$179$	0.791917	+	1.37164i	0.0591906	+	0.102521i	−0.834912	+	0.550384i	$0.814481\pi$
$180$	11.3162	−	4.01529i	0.843461	−	0.299282i
$181$	−11.5907			−0.861530			−0.430765	−	0.902464i	$-0.641756\pi$
$181$	−11.5907			−0.861530			−0.430765	+	0.902464i	$0.641756\pi$
$182$		0			0
$183$	3.98148	+	3.98148i	0.294320	+	0.294320i
$184$	−8.09506	−	6.88797i	−0.596776	−	0.507788i
$185$	4.59973	+	1.54214i	0.338179	+	0.113380i
$186$	−0.0995642	−	0.0658118i	−0.00730040	−	0.00482556i
$187$	0.561158	+	2.09427i	0.0410360	+	0.153148i
$188$	−15.0091	+	2.12827i	−1.09465	+	0.155220i
$189$		0			0
$190$	9.67116	−	23.9378i	0.701619	−	1.73663i
$191$	4.35424	+	2.51392i	0.315062	+	0.181901i	0.649189	−	0.760627i	$-0.275108\pi$
$191$	4.35424	+	2.51392i	0.315062	+	0.181901i	−0.334128	+	0.942528i	$0.608442\pi$
$192$	3.64249	+	2.62589i	0.262874	+	0.189507i
$193$	−12.8208	−	3.43531i	−0.922859	−	0.247279i	−0.234052	−	0.972224i	$-0.575199\pi$
$193$	−12.8208	−	3.43531i	−0.922859	−	0.247279i	−0.688807	+	0.724945i	$0.741865\pi$
$194$	−2.09397	−	0.126777i	−0.150338	−	0.00910203i
$195$	−0.139780	+	2.26293i	−0.0100099	+	0.162052i
$196$		0			0
$197$	0.573982	+	0.573982i	0.0408945	+	0.0408945i	0.727258	−	0.686364i	$-0.240794\pi$
$197$	0.573982	+	0.573982i	0.0408945	+	0.0408945i	−0.686364	+	0.727258i	$0.740794\pi$
$198$	12.2502	−	10.8516i	0.870586	−	0.771187i
$199$	13.2467	+	22.9439i	0.939032	+	1.62645i	0.767282	+	0.641310i	$0.221609\pi$
$199$	13.2467	+	22.9439i	0.939032	+	1.62645i	0.171750	+	0.985141i	$0.445058\pi$
$200$	−7.59092	+	11.9322i	−0.536759	+	0.843735i
$201$	2.11683	−	3.66645i	0.149309	−	0.258612i
$202$	−20.4371	−	6.82415i	−1.43795	−	0.480145i
$203$		0			0
$204$	−0.339301	+	0.451425i	−0.0237558	+	0.0316060i
$205$	−17.0989	−	11.3324i	−1.19424	−	0.791490i
$206$	−1.55579	+	2.35370i	−0.108397	+	0.163990i
$207$	−9.74597	−	2.61142i	−0.677391	−	0.181507i
$208$	6.18451	−	3.73682i	0.428818	−	0.259102i
$209$		−	35.1876i		−	2.43398i
$210$		0			0
$211$		−	19.9593i		−	1.37405i	−0.726632	−	0.687027i	$-0.758915\pi$
$211$		−	19.9593i		−	1.37405i	0.726632	−	0.687027i	$-0.241085\pi$
$212$	8.85168	−	21.9867i	0.607936	−	1.51005i
$213$	−1.45934	−	0.391029i	−0.0999924	−	0.0267929i
$214$	3.21929	+	2.12795i	0.220066	+	0.145464i
$215$	4.07754	+	20.1040i	0.278086	+	1.37108i
$216$	8.87716	+	1.62830i	0.604014	+	0.110792i
$217$		0			0
$218$	−4.58977	+	13.7455i	−0.310859	+	0.930966i
$219$	−1.64510	+	2.84939i	−0.111165	+	0.192544i
$220$	−3.50063	+	18.9542i	−0.236012	+	1.27789i
$221$	0.454371	+	0.786994i	0.0305643	+	0.0529389i
$222$	1.14195	+	1.28914i	0.0766429	+	0.0865215i
$223$	11.8414	+	11.8414i	0.792957	+	0.792957i	0.981974	−	0.189017i	$-0.0605300\pi$
$223$	11.8414	+	11.8414i	0.792957	+	0.792957i	−0.189017	+	0.981974i	$0.560530\pi$
$224$		0			0
$225$	−1.65218	+	13.3227i	−0.110145	+	0.888181i
$226$	−1.00748	+	16.6406i	−0.0670168	+	1.10692i
$227$	25.9323	+	6.94854i	1.72119	+	0.461191i	0.978123	−	0.208030i	$-0.0667051\pi$
$227$	25.9323	+	6.94854i	1.72119	+	0.461191i	0.743064	+	0.669220i	$0.233372\pi$
$228$	7.21517	−	5.65146i	0.477837	−	0.374277i
$229$	−1.42734	−	0.824074i	−0.0943211	−	0.0544563i	0.452098	−	0.891969i	$-0.350676\pi$
$229$	−1.42734	−	0.824074i	−0.0943211	−	0.0544563i	−0.546419	+	0.837512i	$0.684009\pi$
$230$	10.9388	−	4.64339i	0.721281	−	0.306176i
$231$		0			0
$232$	7.83191	−	5.40408i	0.514190	−	0.354796i
$233$	−1.17366	−	4.38016i	−0.0768890	−	0.286954i	0.916766	−	0.399425i	$-0.130790\pi$
$233$	−1.17366	−	4.38016i	−0.0768890	−	0.286954i	−0.993655	+	0.112471i	$0.964123\pi$
$234$	3.78235	−	5.72217i	0.247260	−	0.374070i
$235$	5.38757	−	16.0695i	0.351446	−	1.04826i
$236$	0.657544	−	0.280068i	0.0428025	−	0.0182309i
$237$	3.64106	+	3.64106i	0.236513	+	0.236513i
$238$		0			0
$239$	17.0886			1.10537			0.552685	−	0.833390i	$-0.313603\pi$
$239$	17.0886			1.10537			0.552685	+	0.833390i	$0.313603\pi$
$240$	−4.44877	+	2.32642i	−0.287167	+	0.150170i
$241$	−2.31920	−	4.01698i	−0.149393	−	0.258756i	0.781610	−	0.623767i	$-0.214399\pi$
$241$	−2.31920	−	4.01698i	−0.149393	−	0.258756i	−0.931003	+	0.365011i	$0.881065\pi$
$242$	2.14246	+	10.4974i	0.137722	+	0.674797i
$243$	12.6426	−	3.38757i	0.811022	−	0.217313i
$244$	16.0381	+	12.0546i	1.02674	+	0.771717i
$245$		0			0
$246$	−3.25325	−	6.51496i	−0.207420	−	0.415378i
$247$	−3.81713	−	14.2457i	−0.242878	−	0.906434i
$248$	−0.384178	−	0.182372i	−0.0243953	−	0.0115806i
$249$	−3.32641	+	1.92050i	−0.210802	+	0.121707i
$250$	−8.12723	−	13.5627i	−0.514011	−	0.857783i
$251$		−	15.8297i		−	0.999160i	−0.866268	−	0.499580i	$-0.833488\pi$
$251$		−	15.8297i		−	0.999160i	0.866268	−	0.499580i	$-0.166512\pi$
$252$		0			0
$253$	11.4526	−	11.4526i	0.720017	−	0.720017i
$254$	0.616644	−	10.1851i	0.0386917	−	0.639071i
$255$	−0.281377	−	0.565211i	−0.0176205	−	0.0353949i
$256$	14.1640	+	7.44176i	0.885253	+	0.465110i
$257$	9.19252	−	2.46313i	0.573414	−	0.153646i	0.0395521	−	0.999218i	$-0.487407\pi$
$257$	9.19252	−	2.46313i	0.573414	−	0.153646i	0.533862	+	0.845572i	$0.320740\pi$
$258$	−2.30637	+	6.90717i	−0.143588	+	0.430021i
$259$		0			0
$260$	0.638908	+	8.05337i	0.0396234	+	0.499449i
$261$	4.51637	−	7.82257i	0.279556	−	0.484205i
$262$	19.7108	−	4.02287i	1.21774	−	0.248534i
$263$	4.20543	−	15.6949i	0.259318	−	0.967787i	−0.706319	−	0.707893i	$-0.749646\pi$
$263$	4.20543	−	15.6949i	0.259318	−	0.967787i	0.965637	−	0.259894i	$-0.0836876\pi$
$264$	−4.43413	+	5.21119i	−0.272902	+	0.320726i
$265$	17.5469	+	19.8574i	1.07790	+	1.21983i
$266$		0			0
$267$	−0.473089	+	0.473089i	−0.0289526	+	0.0289526i
$268$	5.63385	−	13.9939i	0.344142	−	0.854815i
$269$	14.7052	−	8.49004i	0.896590	−	0.517647i	0.0204980	−	0.999790i	$-0.493475\pi$
$269$	14.7052	−	8.49004i	0.896590	−	0.517647i	0.876092	+	0.482143i	$0.160141\pi$
$270$	−6.07255	+	8.05874i	−0.369563	+	0.490439i
$271$	9.32931	+	5.38628i	0.566715	+	0.327193i	0.755836	−	0.654761i	$-0.227231\pi$
$271$	9.32931	+	5.38628i	0.566715	+	0.327193i	−0.189121	+	0.981954i	$0.560564\pi$
$272$	−0.971200	+	1.76233i	−0.0588876	+	0.106857i
$273$		0			0
$274$	−7.09224	−	14.2029i	−0.428458	−	0.858028i
$275$	−17.1948	−	12.9898i	−1.03688	−	0.783315i
$276$	4.18773	+	0.508946i	0.252072	+	0.0306350i
$277$	5.23233	−	19.5273i	0.314380	−	1.17328i	−0.610184	−	0.792259i	$-0.708905\pi$
$277$	5.23233	−	19.5273i	0.314380	−	1.17328i	0.924565	−	0.381024i	$-0.124429\pi$
$278$	−13.6656	+	12.1053i	−0.819608	+	0.726030i
$279$	−0.403695			−0.0241686
$280$		0			0
$281$	−24.3209			−1.45086			−0.725430	−	0.688296i	$-0.758359\pi$
$281$	−24.3209			−1.45086			−0.725430	+	0.688296i	$0.758359\pi$
$282$	4.50370	−	3.98949i	0.268191	−	0.237571i
$283$	5.37505	−	20.0599i	0.319513	−	1.19244i	−0.600200	−	0.799850i	$-0.704912\pi$
$283$	5.37505	−	20.0599i	0.319513	−	1.19244i	0.919714	−	0.392590i	$-0.128421\pi$
$284$	−5.34406	−	0.649479i	−0.317112	−	0.0385395i
$285$	2.03681	+	10.0423i	0.120650	+	0.594857i
$286$	4.91901	+	9.85079i	0.290867	+	0.582490i
$287$		0			0
$288$	15.1759	+	0.615719i	0.894249	+	0.0362816i
$289$	14.5033	+	8.37347i	0.853134	+	0.492557i
$290$	1.48073	+	10.5350i	0.0869512	+	0.618636i
$291$	0.721055	−	0.416301i	0.0422690	−	0.0244040i
$292$	−4.37836	+	10.8754i	−0.256224	+	0.636436i
$293$	13.9330	−	13.9330i	0.813975	−	0.813975i	−0.171252	−	0.985227i	$-0.554781\pi$
$293$	13.9330	−	13.9330i	0.813975	−	0.813975i	0.985227	+	0.171252i	$0.0547812\pi$
$294$		0			0
$295$	−0.0492639	+	0.797544i	−0.00286826	+	0.0464348i
$296$	4.67363	+	3.97673i	0.271649	+	0.231142i
$297$	−3.55946	+	13.2841i	−0.206541	+	0.770821i
$298$	−2.90554	+	0.593005i	−0.168313	+	0.0343519i
$299$	3.39422	−	5.87896i	0.196293	−	0.339989i
$300$	−0.0980932	−	5.61205i	−0.00566341	−	0.324012i
$301$		0			0
$302$	−4.83073	+	14.4672i	−0.277978	+	0.832493i
$303$	8.26019	−	2.21331i	0.474535	−	0.127151i
$304$	22.6274	−	23.5473i	1.29777	−	1.35053i
$305$	−20.0807	+	9.99671i	−1.14982	+	0.572410i
$306$	−0.115436	+	1.90666i	−0.00659904	+	0.108996i
$307$	−18.4400	+	18.4400i	−1.05243	+	1.05243i	−0.0538811	+	0.998547i	$0.517159\pi$
$307$	−18.4400	+	18.4400i	−1.05243	+	1.05243i	−0.998547	+	0.0538811i	$0.982841\pi$
$308$		0			0
$309$		−	1.11980i		−	0.0637031i
$310$	0.374666	−	0.292729i	0.0212796	−	0.0166259i
$311$	−9.17669	+	5.29817i	−0.520362	+	0.300431i	−0.737083	−	0.675802i	$-0.763797\pi$
$311$	−9.17669	+	5.29817i	−0.520362	+	0.300431i	0.216720	+	0.976234i	$0.430464\pi$
$312$	−1.22985	+	2.59077i	−0.0696268	+	0.146673i
$313$	−6.16404	−	23.0045i	−0.348412	−	1.30029i	−0.888575	−	0.458731i	$-0.848304\pi$
$313$	−6.16404	−	23.0045i	−0.348412	−	1.30029i	0.540163	−	0.841560i	$-0.318362\pi$
$314$	5.76397	+	11.5429i	0.325280	+	0.651404i
$315$		0			0
$316$	14.6669	+	11.0239i	0.825076	+	0.620145i
$317$	−16.3939	+	4.39273i	−0.920774	+	0.246721i	−0.687916	−	0.725790i	$-0.741474\pi$
$317$	−16.3939	+	4.39273i	−0.920774	+	0.246721i	−0.232858	+	0.972511i	$0.574808\pi$
$318$	1.88114	+	9.21700i	0.105489	+	0.516863i
$319$	7.24980	+	12.5570i	0.405911	+	0.703058i
$320$	−14.5311	+	10.4330i	−0.812314	+	0.583220i
$321$	−1.53161			−0.0854864
$322$		0			0
$323$	2.90413	+	2.90413i	0.161590	+	0.161590i
$324$	11.5257	−	4.90917i	0.640318	−	0.272731i
$325$	−8.37044	−	3.39366i	−0.464309	−	0.188246i
$326$	−16.7288	+	25.3083i	−0.926521	+	1.40170i
$327$	−1.48862	−	5.55562i	−0.0823211	−	0.307226i
$328$	−14.7364	−	21.3568i	−0.813681	−	1.17923i
$329$		0			0
$330$	−2.98918	−	7.04183i	−0.164549	−	0.387640i
$331$	6.83169	+	3.94428i	0.375504	+	0.216797i	0.675860	−	0.737030i	$-0.263772\pi$
$331$	6.83169	+	3.94428i	0.375504	+	0.216797i	−0.300357	+	0.953827i	$0.597106\pi$
$332$	−10.7746	+	8.43944i	−0.591331	+	0.463174i
$333$	5.62677	+	1.50769i	0.308345	+	0.0826208i
$334$	−0.253137	+	4.18107i	−0.0138511	+	0.228778i
$335$	11.1681	+	12.6387i	0.610180	+	0.690524i
$336$		0			0
$337$	2.38503	+	2.38503i	0.129921	+	0.129921i	0.769077	−	0.639156i	$-0.220716\pi$
$337$	2.38503	+	2.38503i	0.129921	+	0.129921i	−0.639156	+	0.769077i	$0.720716\pi$
$338$	−9.13053	−	10.3074i	−0.496636	−	0.560647i
$339$	−3.30831	−	5.73016i	−0.179683	−	0.311220i
$340$	−1.27543	−	1.85326i	−0.0691697	−	0.100507i
$341$	0.324011	−	0.561204i	0.0175462	−	0.0303909i
$342$	9.81845	−	29.4045i	0.530921	−	1.59001i
$343$		0			0
$344$	−4.68136	+	25.5217i	−0.252402	+	1.37604i
$345$	−2.60557	+	3.93142i	−0.140279	+	0.211661i
$346$	−5.06236	−	3.34621i	−0.272154	−	0.179893i
$347$	−10.6362	−	2.84995i	−0.570979	−	0.152993i	−0.0382332	−	0.999269i	$-0.512173\pi$
$347$	−10.6362	−	2.84995i	−0.570979	−	0.152993i	−0.532745	+	0.846276i	$0.678840\pi$
$348$	−1.41042	+	3.50334i	−0.0756063	+	0.187799i
$349$			5.15739i			0.276069i	0.990427	+	0.138034i	$0.0440785\pi$
$349$			5.15739i			0.276069i	−0.990427	+	0.138034i	$0.955922\pi$
$350$		0			0
$351$			5.76421i			0.307671i
$352$	−13.0364	+	20.6029i	−0.694840	+	1.09814i
$353$	−28.8689	−	7.73541i	−1.53654	−	0.411714i	−0.611393	−	0.791327i	$-0.709391\pi$
$353$	−28.8689	−	7.73541i	−1.53654	−	0.411714i	−0.925145	+	0.379613i	$0.876057\pi$
$354$	−0.156417	+	0.236637i	−0.00831347	+	0.0125771i
$355$	3.32503	−	5.01698i	0.176474	−	0.266274i
$356$	−1.43236	+	1.90569i	−0.0759148	+	0.101001i
$357$		0			0
$358$	−2.12457	−	0.709414i	−0.112287	−	0.0374937i
$359$	−2.41304	+	4.17951i	−0.127356	+	0.220586i	−0.922651	−	0.385635i	$-0.873982\pi$
$359$	−2.41304	+	4.17951i	−0.127356	+	0.220586i	0.795296	+	0.606222i	$0.207316\pi$
$360$	−8.21411	+	14.8623i	−0.432922	+	0.783311i
$361$	−23.8274	−	41.2703i	−1.25407	−	2.17212i
$362$	12.2700	−	10.8691i	0.644896	−	0.571265i
$363$	−3.00677	−	3.00677i	−0.157815	−	0.157815i
$364$		0			0
$365$	−8.67934	−	9.82217i	−0.454297	−	0.514116i
$366$	−7.94841	−	0.481226i	−0.415470	−	0.0251541i
$367$	−3.82837	−	1.02581i	−0.199839	−	0.0535468i	0.157511	−	0.987517i	$-0.449653\pi$
$367$	−3.82837	−	1.02581i	−0.199839	−	0.0535468i	−0.357350	+	0.933970i	$0.616320\pi$
$368$	15.0286	−	0.299408i	0.783420	−	0.0156077i
$369$	−21.3314	−	12.3157i	−1.11047	−	0.641128i
$370$	−6.31542	+	2.68083i	−0.328323	+	0.139370i
$371$		0			0
$372$	0.167114	−	0.0236965i	0.00866443	−	0.00122861i
$373$	5.82714	+	21.7472i	0.301718	+	1.12603i	0.935734	+	0.352707i	$0.114739\pi$
$373$	5.82714	+	21.7472i	0.301718	+	1.12603i	−0.634016	+	0.773320i	$0.718595\pi$
$374$	−2.55793	−	1.69079i	−0.132267	−	0.0874285i
$375$	5.65919	+	2.71191i	0.292239	+	0.140042i
$376$	13.8929	−	16.3276i	0.716474	−	0.842033i
$377$	4.29727	+	4.29727i	0.221321	+	0.221321i
$378$		0			0
$379$	−12.6658			−0.650596			−0.325298	−	0.945612i	$-0.605465\pi$
$379$	−12.6658			−0.650596			−0.325298	+	0.945612i	$0.605465\pi$
$380$	12.2095	+	34.4097i	0.626332	+	1.76518i
$381$	2.02490	+	3.50723i	0.103739	+	0.179681i
$382$	−6.96682	+	1.42189i	−0.356454	+	0.0727502i
$383$	−33.2035	+	8.89684i	−1.69662	+	0.454607i	−0.972084	−	0.234632i	$-0.924611\pi$
$383$	−33.2035	+	8.89684i	−1.69662	+	0.454607i	−0.724533	+	0.689240i	$0.757945\pi$
$384$	−6.31836	+	0.635927i	−0.322432	+	0.0324520i
$385$		0			0
$386$	16.7936	−	8.38590i	0.854770	−	0.426831i
$387$	6.37506	+	23.7920i	0.324062	+	1.20942i
$388$	2.33557	−	1.82939i	0.118571	−	0.0928733i
$389$	17.0545	−	9.84643i	0.864698	−	0.499234i	−0.000884568	−	1.00000i	$-0.500282\pi$
$389$	17.0545	−	9.84643i	0.864698	−	0.499234i	0.865583	+	0.500766i	$0.166948\pi$
$390$	−1.97406	−	2.52663i	−0.0999607	−	0.127941i
$391$			1.89043i			0.0956031i
$392$		0			0
$393$	−5.64578	+	5.64578i	−0.284792	+	0.284792i
$394$	−1.14587	−	0.0693749i	−0.0577279	−	0.00349506i
$395$	−18.3638	+	9.14199i	−0.923983	+	0.459984i
$396$	−2.79222	+	22.9750i	−0.140314	+	1.15454i
$397$	4.86174	−	1.30270i	0.244004	−	0.0653806i	−0.134744	−	0.990880i	$-0.543021\pi$
$397$	4.86174	−	1.30270i	0.244004	−	0.0653806i	0.378748	+	0.925500i	$0.376355\pi$
$398$	−35.5384	−	11.8666i	−1.78138	−	0.594820i
$399$		0			0
$400$	−3.15352	−	19.7498i	−0.157676	−	0.987491i
$401$	−0.221054	+	0.382876i	−0.0110389	+	0.0191199i	−0.871492	−	0.490410i	$-0.836847\pi$
$401$	−0.221054	+	0.382876i	−0.0110389	+	0.0191199i	0.860453	+	0.509530i	$0.170181\pi$
$402$	1.19729	+	5.86636i	0.0597155	+	0.292587i
$403$	0.0702972	−	0.262353i	0.00350175	−	0.0130687i
$404$	28.0341	−	11.9406i	1.39475	−	0.594067i
$405$	−0.863521	+	13.9797i	−0.0429087	+	0.694657i
$406$		0			0
$407$	−6.61207	+	6.61207i	−0.327748	+	0.327748i
$408$	−0.0641330	−	0.796056i	−0.00317506	−	0.0394106i
$409$	−14.9736	+	8.64500i	−0.740396	+	0.427468i	−0.822213	−	0.569179i	$-0.807261\pi$
$409$	−14.9736	+	8.64500i	−0.740396	+	0.427468i	0.0818172	+	0.996647i	$0.473928\pi$
$410$	28.7279	−	4.03779i	1.41877	−	0.199412i
$411$	5.45661	+	3.15037i	0.269155	+	0.155396i
$412$	−0.560185	−	3.95056i	−0.0275983	−	0.194630i
$413$		0			0
$414$	12.7660	−	6.37471i	0.627413	−	0.313300i
$415$	−3.04162	−	14.9964i	−0.149307	−	0.736146i
$416$	−3.04279	+	9.75527i	−0.149185	+	0.478292i
$417$	1.87533	−	6.99884i	0.0918355	−	0.342735i
$418$	32.9968	+	37.2498i	1.61393	+	1.82195i
$419$	15.9655			0.779965			0.389982	−	0.920822i	$-0.372481\pi$
$419$	15.9655			0.779965			0.389982	+	0.920822i	$0.372481\pi$
$420$		0			0
$421$	−18.9207			−0.922137			−0.461069	−	0.887364i	$-0.652534\pi$
$421$	−18.9207			−0.922137			−0.461069	+	0.887364i	$0.652534\pi$
$422$	18.7166	+	21.1290i	0.911110	+	1.02854i
$423$	5.26721	−	19.6575i	0.256100	−	0.955779i
$424$	11.2474	+	31.5758i	0.546221	+	1.53346i
$425$	2.49122	−	0.347046i	0.120842	−	0.0168342i
$426$	1.91155	−	0.954535i	0.0926148	−	0.0462474i
$427$		0			0
$428$	−5.40342	+	0.766198i	−0.261184	+	0.0370356i
$429$	−3.78457	−	2.18503i	−0.182721	−	0.105494i
$430$	−23.1688	−	17.4585i	−1.11730	−	0.841924i
$431$	5.15786	−	2.97789i	0.248446	−	0.143440i	−0.370607	−	0.928790i	$-0.620850\pi$
$431$	5.15786	−	2.97789i	0.248446	−	0.143440i	0.619052	+	0.785350i	$0.287517\pi$
$432$	−10.9243	+	6.60073i	−0.525597	+	0.317578i
$433$	21.6247	−	21.6247i	1.03922	−	1.03922i	0.0400190	−	0.999199i	$-0.487258\pi$
$433$	21.6247	−	21.6247i	1.03922	−	1.03922i	0.999199	−	0.0400190i	$-0.0127418\pi$
$434$		0			0
$435$	−2.79591	−	3.16405i	−0.134053	−	0.151705i
$436$	−8.03098	−	18.8551i	−0.384614	−	0.902996i
$437$	7.94066	−	29.6349i	0.379853	−	1.41763i
$438$	−0.930479	−	4.55906i	−0.0444600	−	0.217840i
$439$	12.4127	−	21.4995i	0.592427	−	1.02611i	−0.401477	−	0.915869i	$-0.631503\pi$
$439$	12.4127	−	21.4995i	0.592427	−	1.02611i	0.993904	−	0.110245i	$-0.0351636\pi$
$440$	−14.0683	−	23.3477i	−0.670680	−	1.11306i
$441$		0			0
$442$	−1.21899	−	0.407034i	−0.0579817	−	0.0193606i
$443$	−29.9035	+	8.01262i	−1.42076	+	0.380691i	−0.885753	−	0.464158i	$-0.846357\pi$
$443$	−29.9035	+	8.01262i	−1.42076	+	0.380691i	−0.535005	+	0.844849i	$0.679690\pi$
$444$	−2.41776	−	0.293837i	−0.114742	−	0.0139449i
$445$	−1.18783	−	2.38604i	−0.0563087	−	0.113109i
$446$	−23.6395	−	1.43122i	−1.11936	−	0.0677702i
$447$	0.832236	−	0.832236i	0.0393634	−	0.0393634i
$448$		0			0
$449$		−	29.8132i		−	1.40697i	−0.710709	−	0.703487i	$-0.751626\pi$
$449$		−	29.8132i		−	1.40697i	0.710709	−	0.703487i	$-0.248374\pi$
$450$	−10.7442	−	15.6528i	−0.506487	−	0.737880i
$451$	34.2417	−	19.7695i	1.61238	−	0.930907i
$452$	−14.5380	−	18.5606i	−0.683811	−	0.873016i
$453$	−1.56678	−	5.84729i	−0.0736136	−	0.274730i
$454$	−33.9680	+	16.9620i	−1.59420	+	0.796065i
$455$		0			0
$456$	−2.33843	+	12.7486i	−0.109507	+	0.597008i
$457$	5.25982	−	1.40936i	0.246044	−	0.0659273i	−0.133689	−	0.991023i	$-0.542682\pi$
$457$	5.25982	−	1.40936i	0.246044	−	0.0659273i	0.379733	+	0.925096i	$0.376016\pi$
$458$	2.28375	−	0.466102i	0.106713	−	0.0217795i
$459$	−0.802602	−	1.39015i	−0.0374623	−	0.0648865i
$460$	−7.22555	+	15.1732i	−0.336893	+	0.707455i
$461$	−35.3477			−1.64631			−0.823153	−	0.567820i	$-0.807787\pi$
$461$	−35.3477			−1.64631			−0.823153	+	0.567820i	$0.807787\pi$
$462$		0			0
$463$	−17.1088	−	17.1088i	−0.795113	−	0.795113i	0.187208	−	0.982320i	$-0.440056\pi$
$463$	−17.1088	−	17.1088i	−0.795113	−	0.795113i	−0.982320	+	0.187208i	$0.940056\pi$
$464$	−3.22328	+	13.0651i	−0.149637	+	0.606531i
$465$	−0.0599860	+	0.178920i	−0.00278178	+	0.00829720i
$466$	5.34989	+	3.53627i	0.247829	+	0.163815i
$467$	3.78729	+	14.1344i	0.175255	+	0.654060i	0.996508	+	0.0834962i	$0.0266087\pi$
$467$	3.78729	+	14.1344i	0.175255	+	0.654060i	−0.821253	+	0.570564i	$0.806725\pi$
$468$	1.36189	+	9.60437i	0.0629533	+	0.443962i
$469$		0			0
$470$	9.36565	+	22.0633i	0.432005	+	1.01771i
$471$	−4.43467	−	2.56036i	−0.204339	−	0.117975i
$472$	−0.433448	+	0.913086i	−0.0199511	+	0.0420282i
$473$	−38.1917	−	10.2334i	−1.75605	−	0.470533i
$474$	−7.26882	−	0.440081i	−0.333868	−	0.0202136i
$475$	−40.5109	−	5.02385i	−1.85877	−	0.230510i
$476$		0			0
$477$	22.4994	+	22.4994i	1.03017	+	1.03017i
$478$	−18.0901	+	16.0246i	−0.827421	+	0.732950i
$479$	−17.6275	−	30.5318i	−0.805422	−	1.39503i	−0.916006	−	0.401165i	$-0.868605\pi$
$479$	−17.6275	−	30.5318i	−0.805422	−	1.39503i	0.110584	−	0.993867i	$-0.464728\pi$
$480$	2.52791	−	6.63455i	0.115383	−	0.302824i
$481$	−1.95963	+	3.39418i	−0.0893514	+	0.154761i
$482$	6.22200	+	2.07759i	0.283404	+	0.0946314i
$483$		0			0
$484$	−12.1118	−	9.10351i	−0.550537	−	0.413796i
$485$	0.659322	+	3.25073i	0.0299383	+	0.147608i
$486$	−10.2068	+	15.4415i	−0.462992	+	0.700442i
$487$	32.6903	+	8.75933i	1.48134	+	0.396923i	0.906802	−	0.421556i	$-0.138516\pi$
$487$	32.6903	+	8.75933i	1.48134	+	0.396923i	0.574536	+	0.818480i	$0.305183\pi$
$488$	−28.2821	+	2.27851i	−1.28027	+	0.103143i
$489$		−	12.0407i		−	0.544500i
$490$		0			0
$491$			2.82858i			0.127652i	0.997961	+	0.0638260i	$0.0203303\pi$
$491$			2.82858i			0.127652i	−0.997961	+	0.0638260i	$0.979670\pi$
$492$	9.55324	+	3.84606i	0.430693	+	0.173394i
$493$	−1.63471	−	0.438020i	−0.0736238	−	0.0197274i
$494$	17.3996	+	11.5011i	0.782846	+	0.517460i
$495$	−21.5689	−	14.2949i	−0.969450	−	0.642508i
$496$	0.577710	−	0.167199i	0.0259399	−	0.00750745i
$497$		0			0
$498$	1.72042	−	5.15235i	0.0770939	−	0.230883i
$499$	−7.99737	+	13.8519i	−0.358012	+	0.620094i	−0.987629	−	0.156811i	$-0.949879\pi$
$499$	−7.99737	+	13.8519i	−0.358012	+	0.620094i	0.629617	+	0.776906i	$0.283212\pi$
$500$	21.3219	+	6.73637i	0.953542	+	0.301260i
$501$	−0.831237	−	1.43974i	−0.0371369	−	0.0643230i
$502$	14.8441	+	16.7574i	0.662525	+	0.747918i
$503$	7.59472	+	7.59472i	0.338632	+	0.338632i	0.855852	−	0.517221i	$-0.173033\pi$
$503$	7.59472	+	7.59472i	0.338632	+	0.338632i	−0.517221	+	0.855852i	$0.673033\pi$
$504$		0			0
$505$	−2.10035	+	34.0029i	−0.0934642	+	1.51311i
$506$	−1.38423	+	22.8633i	−0.0615364	+	1.01640i
$507$	5.27893	+	1.41448i	0.234445	+	0.0628194i
$508$	8.89820	+	11.3603i	0.394794	+	0.504030i
$509$	14.8346	+	8.56476i	0.657532	+	0.379627i	0.791336	−	0.611381i	$-0.209386\pi$
$509$	14.8346	+	8.56476i	0.657532	+	0.379627i	−0.133804	+	0.991008i	$0.542719\pi$
$510$	0.827888	+	0.334477i	0.0366595	+	0.0148109i
$511$		0			0
$512$	−21.9726	+	5.40430i	−0.971059	+	0.238838i
$513$	6.74259	+	25.1637i	0.297693	+	1.11100i
$514$	−7.42148	+	11.2277i	−0.327348	+	0.495231i
$515$	4.22966	+	1.41807i	0.186381	+	0.0624876i
$516$	−4.03559	−	9.47474i	−0.177657	−	0.417102i
$517$	23.0997	+	23.0997i	1.01592	+	1.01592i
$518$		0			0
$519$	2.40847			0.105720
$520$	−8.22831	−	7.92621i	−0.360835	−	0.347587i
$521$	−8.24624	−	14.2829i	−0.361274	−	0.625745i	0.626897	−	0.779102i	$-0.284325\pi$
$521$	−8.24624	−	14.2829i	−0.361274	−	0.625745i	−0.988171	+	0.153357i	$0.950991\pi$
$522$	2.55449	+	12.5162i	0.111807	+	0.547819i
$523$	10.4187	−	2.79169i	0.455579	−	0.122072i	−0.0237299	−	0.999718i	$-0.507554\pi$
$523$	10.4187	−	2.79169i	0.455579	−	0.122072i	0.479308	+	0.877646i	$0.340888\pi$
$524$	−17.0936	+	22.7422i	−0.746735	+	0.993498i
$525$		0			0
$526$	10.2658	+	20.5583i	0.447611	+	0.896383i
$527$	0.0195762	+	0.0730594i	0.000852753	+	0.00318252i
$528$	−0.192744	−	9.67465i	−0.00838811	−	0.421035i
$529$	−7.68878	+	4.43912i	−0.334295	+	0.193005i
$530$	−37.1963	−	4.56668i	−1.61570	−	0.198364i
$531$			0.959474i			0.0416376i
$532$		0			0
$533$	11.7182	−	11.7182i	0.507572	−	0.507572i
$534$	0.0571804	−	0.944448i	0.00247444	−	0.0408703i
$535$	1.93958	−	5.78516i	0.0838553	−	0.250114i
$536$	7.15863	+	20.0971i	0.309206	+	0.868063i
$537$	0.858699	−	0.230088i	0.0370556	−	0.00992902i
$538$	−7.60554	+	22.7772i	−0.327898	+	0.981996i
$539$		0			0
$540$	−1.12857	−	14.2255i	−0.0485659	−	0.612168i
$541$	1.84800	−	3.20083i	0.0794517	−	0.137614i	−0.823562	−	0.567227i	$-0.808016\pi$
$541$	1.84800	−	3.20083i	0.0794517	−	0.137614i	0.903013	+	0.429612i	$0.141350\pi$
$542$	−14.9270	+	3.04652i	−0.641169	+	0.130859i
$543$	−1.68381	+	6.28408i	−0.0722593	+	0.269676i
$544$	−0.624488	−	2.77634i	−0.0267747	−	0.119035i
$545$	22.8696	+	1.41265i	0.979627	+	0.0605111i
$546$		0			0
$547$	2.39361	−	2.39361i	0.102343	−	0.102343i	−0.654081	−	0.756424i	$-0.726945\pi$
$547$	2.39361	−	2.39361i	0.102343	−	0.102343i	0.756424	+	0.654081i	$0.226945\pi$
$548$	20.8265	+	8.38459i	0.889664	+	0.358172i
$549$	−23.3259	+	13.4672i	−0.995527	+	0.574768i
$550$	30.3835	−	2.37311i	1.29556	−	0.101190i
$551$	23.7864	+	13.7331i	1.01334	+	0.585049i
$552$	−4.91041	+	3.38822i	−0.209001	+	0.144212i
$553$		0			0
$554$	12.7726	+	25.5783i	0.542655	+	1.08672i
$555$	1.50431	−	2.26978i	0.0638544	−	0.0963469i
$556$	3.11483	−	25.6295i	0.132098	−	1.08693i
$557$	−6.26666	+	23.3875i	−0.265527	+	0.990960i	0.696400	+	0.717654i	$0.254784\pi$
$557$	−6.26666	+	23.3875i	−0.265527	+	0.990960i	−0.961927	+	0.273307i	$0.911883\pi$
$558$	0.427354	−	0.378561i	0.0180913	−	0.0160257i
$559$	−16.5720			−0.700923
$560$		0			0
$561$	1.21696			0.0513802
$562$	25.7462	−	22.8066i	1.08604	−	0.962039i
$563$	−6.70044	+	25.0064i	−0.282390	+	1.05389i	0.668336	+	0.743860i	$0.267007\pi$
$563$	−6.70044	+	25.0064i	−0.282390	+	1.05389i	−0.950726	+	0.310033i	$0.899660\pi$
$564$	−1.02654	+	8.44659i	−0.0432250	+	0.355666i
$565$	25.8333	−	5.23957i	1.08681	−	0.220431i
$566$	13.1209	+	26.2760i	0.551515	+	1.10446i
$567$		0			0
$568$	6.26629	−	4.32379i	0.262928	−	0.181422i
$569$	15.1795	+	8.76388i	0.636357	+	0.367401i	0.783210	−	0.621758i	$-0.213581\pi$
$569$	15.1795	+	8.76388i	0.636357	+	0.367401i	−0.146853	+	0.989158i	$0.546914\pi$
$570$	−11.5733	−	8.72087i	−0.484751	−	0.365277i
$571$	8.75835	−	5.05663i	0.366525	−	0.211614i	−0.305414	−	0.952220i	$-0.598795\pi$
$571$	8.75835	−	5.05663i	0.366525	−	0.211614i	0.671939	+	0.740606i	$0.265462\pi$
$572$	−14.4448	−	5.81535i	−0.603966	−	0.243152i
$573$	1.99551	−	1.99551i	0.0833637	−	0.0833637i
$574$		0			0
$575$	−11.5500	−	14.8203i	−0.481670	−	0.618048i
$576$	−16.6427	+	13.5792i	−0.693445	+	0.565801i
$577$	0.938749	−	3.50346i	0.0390806	−	0.145851i	−0.943629	−	0.331006i	$-0.892612\pi$
$577$	0.938749	−	3.50346i	0.0390806	−	0.145851i	0.982709	+	0.185155i	$0.0592787\pi$
$578$	−23.2054	+	4.73609i	−0.965216	+	0.196995i
$579$	−3.72501	+	6.45192i	−0.154806	+	0.268132i
$580$	−11.4466	−	9.76387i	−0.475294	−	0.405423i
$581$		0			0
$582$	−0.372931	+	1.11686i	−0.0154585	+	0.0462954i
$583$	−49.3362	+	13.2196i	−2.04330	+	0.547500i
$584$	−5.56335	−	15.6185i	−0.230213	−	0.646299i
$585$	−10.2829	−	3.44752i	−0.425145	−	0.142538i
$586$	−1.68403	+	27.8151i	−0.0695666	+	1.14903i
$587$	4.54357	−	4.54357i	0.187533	−	0.187533i	−0.607096	−	0.794629i	$-0.707666\pi$
$587$	4.54357	−	4.54357i	0.187533	−	0.187533i	0.794629	+	0.607096i	$0.207666\pi$
$588$		0			0
$589$		−	1.22753i		−	0.0505795i
$590$	−0.695737	−	0.890481i	−0.0286430	−	0.0366605i
$591$	0.394577	−	0.227809i	0.0162307	−	0.00937082i
$592$	−8.67666	+	0.172862i	−0.356608	+	0.00710456i
$593$	3.15219	+	11.7641i	0.129445	+	0.483095i	0.999959	−	0.00904815i	$-0.00288015\pi$
$593$	3.15219	+	11.7641i	0.129445	+	0.483095i	−0.870514	+	0.492144i	$0.836213\pi$
$594$	−8.68895	−	17.4005i	−0.356512	−	0.713950i
$595$		0			0
$596$	2.51974	−	3.35240i	0.103212	−	0.137320i
$597$	14.3638	−	3.84876i	0.587870	−	0.157519i
$598$	1.91979	+	9.40638i	0.0785061	+	0.384656i
$599$	−2.68170	−	4.64483i	−0.109571	−	0.189783i	0.806025	−	0.591881i	$-0.201614\pi$
$599$	−2.68170	−	4.64483i	−0.109571	−	0.189783i	−0.915597	+	0.402098i	$0.868281\pi$
$600$	5.36648	+	5.84896i	0.219086	+	0.238783i
$601$	6.54295			0.266892			0.133446	−	0.991056i	$-0.457396\pi$
$601$	6.54295			0.266892			0.133446	+	0.991056i	$0.457396\pi$
$602$		0			0
$603$	14.3202	+	14.3202i	0.583164	+	0.583164i
$604$	−8.45261	−	19.8450i	−0.343932	−	0.807482i
$605$	15.1647	−	7.54941i	0.616534	−	0.306927i
$606$	−6.66877	+	10.0889i	−0.270900	+	0.409834i
$607$	10.3831	+	38.7502i	0.421436	+	1.57282i	0.771584	+	0.636127i	$0.219465\pi$
$607$	10.3831	+	38.7502i	0.421436	+	1.57282i	−0.350148	+	0.936694i	$0.613869\pi$
$608$	−1.87224	+	46.1460i	−0.0759294	+	1.87147i
$609$		0			0
$610$	11.8832	−	29.4130i	0.481138	−	1.19090i
$611$	11.8578	+	6.84609i	0.479714	+	0.276963i
$612$	−1.66575	−	2.12665i	−0.0673338	−	0.0859646i
$613$	45.3920	+	12.1628i	1.83337	+	0.491249i	0.998267	−	0.0588502i	$-0.0187434\pi$
$613$	45.3920	+	12.1628i	1.83337	+	0.491249i	0.835099	+	0.550099i	$0.185410\pi$
$614$	2.22877	−	36.8127i	0.0899460	−	1.48564i
$615$	−8.62804	+	7.62415i	−0.347916	+	0.307435i
$616$		0			0
$617$	−17.0146	−	17.0146i	−0.684981	−	0.684981i	0.276137	−	0.961118i	$-0.410945\pi$
$617$	−17.0146	−	17.0146i	−0.684981	−	0.684981i	−0.961118	+	0.276137i	$0.910945\pi$
$618$	1.05008	+	1.18542i	0.0422403	+	0.0476847i
$619$	3.86684	+	6.69757i	0.155422	+	0.269198i	0.933212	−	0.359325i	$-0.116993\pi$
$619$	3.86684	+	6.69757i	0.155422	+	0.269198i	−0.777791	+	0.628523i	$0.783660\pi$
$620$	−0.122121	+	0.661223i	−0.00490448	+	0.0265554i
$621$	−5.99555	+	10.3846i	−0.240593	+	0.416720i
$622$	4.74620	−	14.2140i	0.190305	−	0.569930i
$623$		0			0
$624$	−1.12753	−	3.89588i	−0.0451375	−	0.155960i
$625$	−17.4099	+	17.9414i	−0.696396	+	0.717658i
$626$	28.0975	+	18.5724i	1.12300	+	0.742303i
$627$	−19.0775	−	5.11180i	−0.761881	−	0.204145i
$628$	−16.9260	−	6.81428i	−0.675421	−	0.271919i
$629$		−	1.09143i		−	0.0435180i
$630$		0			0
$631$			11.7767i			0.468823i	0.972137	+	0.234411i	$0.0753163\pi$
$631$			11.7767i			0.468823i	−0.972137	+	0.234411i	$0.924684\pi$
$632$	−25.8640	+	2.08369i	−1.02881	+	0.0828848i
$633$	−10.8212	−	2.89954i	−0.430105	−	0.115246i
$634$	13.2354	−	20.0234i	0.525646	−	0.795230i
$635$	−15.8116	+	3.20695i	−0.627465	+	0.127264i
$636$	−10.6345	−	7.99314i	−0.421686	−	0.316949i
$637$		0			0
$638$	−19.4499	−	6.49451i	−0.770028	−	0.257120i
$639$	3.61353	−	6.25882i	0.142949	−	0.247595i
$640$	5.59932	−	24.6708i	0.221333	−	0.975198i
$641$	−7.29143	−	12.6291i	−0.287994	−	0.498821i	0.685337	−	0.728226i	$-0.259655\pi$
$641$	−7.29143	−	12.6291i	−0.287994	−	0.498821i	−0.973331	+	0.229406i	$0.926322\pi$
$642$	1.62138	−	1.43625i	0.0639906	−	0.0566845i
$643$	17.6813	+	17.6813i	0.697283	+	0.697283i	0.963824	−	0.266541i	$-0.0858807\pi$
$643$	17.6813	+	17.6813i	0.697283	+	0.697283i	−0.266541	+	0.963824i	$0.585881\pi$
$644$		0			0
$645$	11.4920	+	0.709858i	0.452498	+	0.0279506i
$646$	−5.79765	−	0.351011i	−0.228106	−	0.0138103i
$647$	−1.97977	−	0.530477i	−0.0778327	−	0.0208552i	0.219693	−	0.975569i	$-0.429495\pi$
$647$	−1.97977	−	0.530477i	−0.0778327	−	0.0208552i	−0.297525	+	0.954714i	$0.596161\pi$
$648$	−7.59768	+	16.0050i	−0.298465	+	0.628736i
$649$	−1.33383	−	0.770087i	−0.0523574	−	0.0302286i
$650$	12.0434	−	4.25675i	0.472379	−	0.166963i
$651$		0			0
$652$	−6.02343	−	42.4787i	−0.235896	−	1.66360i
$653$	−2.35798	−	8.80009i	−0.0922748	−	0.344374i	0.904317	−	0.426861i	$-0.140381\pi$
$653$	−2.35798	−	8.80009i	−0.0922748	−	0.344374i	−0.996592	+	0.0824864i	$0.973714\pi$
$654$	6.78559	+	4.48527i	0.265337	+	0.175388i
$655$	−14.1754	−	28.4746i	−0.553880	−	1.11260i
$656$	35.6271	+	8.78956i	1.39101	+	0.343175i
$657$	−11.1290	−	11.1290i	−0.434183	−	0.434183i
$658$		0			0
$659$	37.8341			1.47381			0.736904	−	0.675997i	$-0.236287\pi$
$659$	37.8341			1.47381			0.736904	+	0.675997i	$0.236287\pi$
$660$	9.76775	+	4.65144i	0.380209	+	0.181057i
$661$	6.67319	+	11.5583i	0.259557	+	0.449566i	0.966123	−	0.258081i	$-0.0830901\pi$
$661$	6.67319	+	11.5583i	0.259557	+	0.449566i	−0.706566	+	0.707647i	$0.749757\pi$
$662$	−10.9308	+	2.23091i	−0.424836	+	0.0867068i
$663$	0.492688	−	0.132015i	0.0191344	−	0.00512705i
$664$	3.49203	−	19.0378i	0.135517	−	0.738809i
$665$		0			0
$666$	−7.37035	+	3.68040i	−0.285595	+	0.142612i
$667$	3.27207	+	12.2115i	0.126695	+	0.472833i
$668$	−3.65278	−	4.66348i	−0.141330	−	0.180435i
$669$	8.14021	−	4.69975i	0.314719	−	0.181703i
$670$	−23.6744	−	2.90656i	−0.914622	−	0.112290i
$671$		−	43.2360i		−	1.66911i
$672$		0			0
$673$	−15.8055	+	15.8055i	−0.609258	+	0.609258i	−0.942752	−	0.333494i	$-0.891772\pi$
$673$	−15.8055	+	15.8055i	−0.609258	+	0.609258i	0.333494	+	0.942752i	$0.391772\pi$
$674$	−4.76135	−	0.288269i	−0.183400	−	0.0111037i
$675$	14.7856	+	5.99457i	0.569097	+	0.230731i
$676$	19.3313	+	2.34938i	0.743510	+	0.0903609i
$677$	38.7482	−	10.3826i	1.48922	−	0.399034i	0.579744	−	0.814799i	$-0.303153\pi$
$677$	38.7482	−	10.3826i	1.48922	−	0.399034i	0.909472	+	0.415765i	$0.136486\pi$
$678$	8.87559	+	2.96365i	0.340865	+	0.113818i
$679$		0			0
$680$	3.08805	+	0.765854i	0.118421	+	0.0293692i
$681$	7.53451	−	13.0502i	0.288723	−	0.500083i
$682$	0.183263	+	0.897932i	0.00701750	+	0.0343836i
$683$	3.88689	−	14.5061i	0.148728	−	0.555060i	−0.850833	−	0.525436i	$-0.823902\pi$
$683$	3.88689	−	14.5061i	0.148728	−	0.555060i	0.999561	−	0.0296241i	$-0.00943102\pi$
$684$	17.1799	+	40.3349i	0.656889	+	1.54224i
$685$	−18.8095	+	16.6210i	−0.718675	+	0.635055i
$686$		0			0
$687$	−0.654137	+	0.654137i	−0.0249569	+	0.0249569i
$688$	−18.9770	−	31.4073i	−0.723493	−	1.19739i
$689$	−18.5398	+	10.7039i	−0.706309	+	0.407788i
$690$	−0.928377	−	6.60517i	−0.0353427	−	0.251455i
$691$	−35.9465	−	20.7537i	−1.36747	−	0.789509i	−0.376865	−	0.926268i	$-0.622998\pi$
$691$	−35.9465	−	20.7537i	−1.36747	−	0.789509i	−0.990604	+	0.136760i	$0.956331\pi$
$692$	8.49691	−	1.20485i	0.323004	−	0.0458016i
$693$		0			0
$694$	13.9320	−	6.95697i	0.528851	−	0.264083i
$695$	24.0609	+	15.9465i	0.912683	+	0.604886i
$696$	−1.79214	−	5.03126i	−0.0679310	−	0.190709i
$697$	−1.19444	+	4.45770i	−0.0452425	+	0.168847i
$698$	−4.83629	−	5.45964i	−0.183056	−	0.206651i
$699$	−2.54527			−0.0962709
$700$		0			0
$701$	−3.56491			−0.134645			−0.0673224	−	0.997731i	$-0.521446\pi$
$701$	−3.56491			−0.134645			−0.0673224	+	0.997731i	$0.521446\pi$
$702$	−5.40532	−	6.10202i	−0.204011	−	0.230306i
$703$	−4.58449	+	17.1095i	−0.172907	+	0.645298i
$704$	−5.51978	−	34.0350i	−0.208035	−	1.28274i
$705$	−7.92963	−	5.25541i	−0.298647	−	0.197930i
$706$	37.8146	−	18.8828i	1.42317	−	0.710663i
$707$		0			0
$708$	−0.0563201	−	0.397184i	−0.00211664	−	0.0149271i
$709$	5.15413	+	2.97574i	0.193568	+	0.111756i	0.593652	−	0.804722i	$-0.297686\pi$
$709$	5.15413	+	2.97574i	0.193568	+	0.111756i	−0.400084	+	0.916478i	$0.631019\pi$
$710$	1.18472	+	8.42902i	0.0444619	+	0.316336i
$711$	−21.3316	+	12.3158i	−0.799996	+	0.461878i
$712$	−0.270737	−	3.36055i	−0.0101463	−	0.125942i
$713$	0.399527	−	0.399527i	0.0149624	−	0.0149624i
$714$		0			0
$715$	13.0458	−	11.5279i	0.487887	−	0.431120i
$716$	2.91432	−	1.24130i	0.108913	−	0.0463896i
$717$	2.48251	−	9.26484i	0.0927109	−	0.346002i
$718$	−1.36483	−	6.68726i	−0.0509351	−	0.249566i
$719$	3.25719	−	5.64161i	0.121473	−	0.210397i	−0.798876	−	0.601496i	$-0.794572\pi$
$719$	3.25719	−	5.64161i	0.121473	−	0.210397i	0.920349	+	0.391099i	$0.127905\pi$
$720$	−5.24143	−	23.4360i	−0.195337	−	0.873407i
$721$		0			0
$722$	63.9246	+	21.3451i	2.37903	+	0.794381i
$723$	−2.51478	+	0.673834i	−0.0935257	+	0.0250601i
$724$	−2.79672	+	23.0121i	−0.103939	+	0.855238i
$725$	15.4918	−	6.55377i	0.575350	−	0.243401i
$726$	6.00255	+	0.363417i	0.222776	+	0.0134877i
$727$	24.9567	−	24.9567i	0.925594	−	0.925594i	−0.0718237	−	0.997417i	$-0.522882\pi$
$727$	24.9567	−	24.9567i	0.925594	−	0.925594i	0.997417	+	0.0718237i	$0.0228819\pi$
$728$		0			0
$729$			11.4450i			0.423889i
$730$	18.3986	+	2.25884i	0.680964	+	0.0836035i
$731$	3.99666	−	2.30747i	0.147822	−	0.0853450i
$732$	8.86549	−	6.94411i	0.327678	−	0.256662i
$733$	−2.72380	−	10.1654i	−0.100606	−	0.375467i	0.897204	−	0.441617i	$-0.145595\pi$
$733$	−2.72380	−	10.1654i	−0.100606	−	0.375467i	−0.997810	+	0.0661503i	$0.978928\pi$
$734$	5.01468	−	2.50409i	0.185095	−	0.0924276i
$735$		0			0
$736$	−15.6286	+	14.4099i	−0.576077	+	0.531154i
$737$	−31.4011	+	8.41390i	−1.15667	+	0.309930i
$738$	34.1304	−	6.96582i	1.25636	−	0.256415i
$739$	14.3849	+	24.9154i	0.529157	+	0.916526i	0.999422	+	0.0340010i	$0.0108249\pi$
$739$	14.3849	+	24.9154i	0.529157	+	0.916526i	−0.470265	+	0.882525i	$0.655842\pi$
$740$	4.17162	−	8.76016i	0.153352	−	0.322030i
$741$	−8.27806			−0.304102
$742$		0			0
$743$	18.8941	+	18.8941i	0.693158	+	0.693158i	0.962926	−	0.269767i	$-0.0869467\pi$
$743$	18.8941	+	18.8941i	0.693158	+	0.693158i	−0.269767	+	0.962926i	$0.586947\pi$
$744$	−0.154686	+	0.181794i	−0.00567107	+	0.00666490i
$745$	2.08958	+	4.19740i	0.0765563	+	0.153781i
$746$	−26.5618	−	17.5573i	−0.972498	−	0.642820i
$747$	−4.75543	−	17.7475i	−0.173992	−	0.649347i
$748$	4.29335	−	0.608792i	0.156980	−	0.0222596i
$749$		0			0
$750$	−8.53391	+	2.43601i	−0.311614	+	0.0889503i
$751$	6.93125	+	4.00176i	0.252925	+	0.146026i	0.621103	−	0.783729i	$-0.286685\pi$
$751$	6.93125	+	4.00176i	0.252925	+	0.146026i	−0.368178	+	0.929755i	$0.620018\pi$
$752$	0.603903	+	30.3125i	0.0220221	+	1.10538i
$753$	−8.58229	−	2.29962i	−0.312756	−	0.0838028i
$754$	−8.57883	−	0.519394i	−0.312422	−	0.0189152i
$755$	24.0703	+	1.48681i	0.876007	+	0.0541106i
$756$		0			0
$757$	−6.84570	−	6.84570i	−0.248811	−	0.248811i	0.571672	−	0.820483i	$-0.306295\pi$
$757$	−6.84570	−	6.84570i	−0.248811	−	0.248811i	−0.820483	+	0.571672i	$0.806295\pi$
$758$	13.4080	−	11.8772i	0.487002	−	0.431398i
$759$	−4.54544	−	7.87293i	−0.164989	−	0.285769i
$760$	−45.1923	−	24.9770i	−1.63930	−	0.906010i
$761$	−1.13752	+	1.97025i	−0.0412352	+	0.0714215i	−0.885906	−	0.463864i	$-0.846463\pi$
$761$	−1.13752	+	1.97025i	−0.0412352	+	0.0714215i	0.844671	+	0.535285i	$0.179796\pi$
$762$	−5.43243	−	1.81394i	−0.196796	−	0.0657122i
$763$		0			0
$764$	6.04175	−	8.03828i	0.218583	−	0.290815i
$765$	2.95994	−	0.600344i	0.107017	−	0.0217055i
$766$	26.8064	−	40.5544i	0.968556	−	1.46529i
$767$	−0.623541	−	0.167077i	−0.0225148	−	0.00603281i
$768$	6.09231	−	6.59817i	0.219837	−	0.238091i
$769$		−	23.4892i		−	0.847041i	−0.905887	−	0.423520i	$-0.860794\pi$
$769$		−	23.4892i		−	0.847041i	0.905887	−	0.423520i	$-0.139206\pi$
$770$		0			0
$771$		−	5.34169i		−	0.192376i
$772$	−9.91397	+	24.6253i	−0.356812	+	0.886285i
$773$	49.5795	+	13.2848i	1.78325	+	0.477820i	0.991170	−	0.132598i	$-0.0423320\pi$
$773$	49.5795	+	13.2848i	1.78325	+	0.477820i	0.792079	+	0.610418i	$0.208999\pi$
$774$	−29.0594	−	19.2082i	−1.04452	−	0.690426i
$775$	−0.599845	−	0.453154i	−0.0215471	−	0.0162778i
$776$	−0.756956	+	4.12676i	−0.0271731	+	0.148142i
$777$		0			0
$778$	−8.82062	+	26.4162i	−0.316234	+	0.947066i
$779$	37.4487	−	64.8631i	1.34174	−	2.32396i
$780$	4.45907	+	0.823541i	0.159660	+	0.0294875i
$781$	5.80054	+	10.0468i	0.207560	+	0.359504i
$782$	−1.77273	−	2.00122i	−0.0633926	−	0.0715634i
$783$	−7.59070	−	7.59070i	−0.271270	−	0.271270i
$784$		0			0
$785$	15.2868	−	13.5081i	0.545608	−	0.482126i
$786$	0.682383	−	11.2709i	0.0243398	−	0.402020i
$787$	−49.5455	−	13.2757i	−1.76611	−	0.473227i	−0.778166	−	0.628058i	$-0.783850\pi$
$787$	−49.5455	−	13.2757i	−1.76611	−	0.473227i	−0.987941	+	0.154831i	$0.950517\pi$
$788$	1.27808	−	1.00108i	0.0455296	−	0.0356621i
$789$	−7.89828	−	4.56007i	−0.281186	−	0.162343i
$790$	10.8672	−	26.8982i	0.386638	−	0.956996i
$791$		0			0
$792$	−18.5887	−	26.9399i	−0.660522	−	0.957267i
$793$	−4.69022	−	17.5041i	−0.166555	−	0.621590i
$794$	−3.92507	+	5.93809i	−0.139296	+	0.210735i
$795$	13.3151	−	6.62860i	0.472237	−	0.235092i
$796$	48.7489	−	20.7637i	1.72786	−	0.735949i
$797$	1.76536	+	1.76536i	0.0625323	+	0.0625323i	0.737681	−	0.675149i	$-0.235921\pi$
$797$	1.76536	+	1.76536i	0.0625323	+	0.0625323i	−0.675149	+	0.737681i	$0.735921\pi$
$798$		0			0
$799$	−3.81297			−0.134893
$800$	21.8585	+	17.9501i	0.772815	+	0.634631i
$801$	−1.60021	−	2.77164i	−0.0565406	−	0.0979312i
$802$	−0.125029	−	0.612606i	−0.00441495	−	0.0216319i
$803$	24.4035	−	6.53889i	0.861179	−	0.230752i
$804$	−6.76857	−	5.08741i	−0.238709	−	0.179419i
$805$		0			0
$806$	0.171601	+	0.343648i	0.00604440	+	0.0121045i
$807$	−2.46674	−	9.20600i	−0.0868334	−	0.324067i
$808$	−18.4799	+	38.9291i	−0.650120	+	1.36952i
$809$	−21.5035	+	12.4151i	−0.756024	+	0.436491i	−0.827867	−	0.560925i	$-0.810446\pi$
$809$	−21.5035	+	12.4151i	−0.756024	+	0.436491i	0.0718421	+	0.997416i	$0.477112\pi$
$810$	−12.1952	−	15.6087i	−0.428495	−	0.548436i
$811$			25.4473i			0.893576i	0.894640	+	0.446788i	$0.147432\pi$
$811$			25.4473i			0.893576i	−0.894640	+	0.446788i	$0.852568\pi$
$812$		0			0
$813$	4.27555	−	4.27555i	0.149950	−	0.149950i
$814$	0.799174	−	13.2000i	0.0280110	−	0.462659i
$815$	45.4798	+	15.2479i	1.59309	+	0.534111i
$816$	0.814384	+	0.782569i	0.0285092	+	0.0273954i
$817$	−72.3454	+	19.3849i	−2.53104	+	0.678191i
$818$	7.74436	−	23.1930i	0.270775	−	0.810923i
$819$		0			0
$820$	−26.6251	+	31.2137i	−0.929788	+	1.09003i
$821$	27.9707	−	48.4466i	0.976183	−	1.69080i	0.300209	−	0.953874i	$-0.402944\pi$
$821$	27.9707	−	48.4466i	0.976183	−	1.69080i	0.675974	−	0.736925i	$-0.263723\pi$
$822$	−8.73062	+	1.78187i	−0.304515	+	0.0621500i
$823$	−11.6927	+	43.6378i	−0.407582	+	1.52112i	0.391661	+	0.920110i	$0.371901\pi$
$823$	−11.6927	+	43.6378i	−0.407582	+	1.52112i	−0.799243	+	0.601008i	$0.794766\pi$
$824$	4.29761	+	3.65678i	0.149714	+	0.127390i
$825$	−9.54055	+	7.43533i	−0.332159	+	0.258865i
$826$		0			0
$827$	5.59251	−	5.59251i	0.194471	−	0.194471i	−0.603154	−	0.797625i	$-0.706090\pi$
$827$	5.59251	−	5.59251i	0.194471	−	0.194471i	0.797625	+	0.603154i	$0.206090\pi$
$828$	−7.53630	+	18.7194i	−0.261905	+	0.650546i
$829$	29.2787	−	16.9041i	1.01689	−	0.587103i	0.103690	−	0.994610i	$-0.466935\pi$
$829$	29.2787	−	16.9041i	1.01689	−	0.587103i	0.913202	+	0.407507i	$0.133602\pi$
$830$	17.2826	+	13.0231i	0.599888	+	0.452037i
$831$	−9.82692	−	5.67358i	−0.340892	−	0.196814i
$832$	−5.92679	−	13.1803i	−0.205474	−	0.456946i
$833$		0			0
$834$	4.57785	+	9.16759i	0.158518	+	0.317448i
$835$	6.49080	−	1.31648i	0.224623	−	0.0455587i
$836$	−69.8611	−	8.49042i	−2.41620	−	0.293647i
$837$	−0.124173	+	0.463420i	−0.00429205	+	0.0160181i
$838$	−16.9011	+	14.9715i	−0.583840	+	0.517180i
$839$	10.7222			0.370170			0.185085	−	0.982722i	$-0.440744\pi$
$839$	10.7222			0.370170			0.185085	+	0.982722i	$0.440744\pi$
$840$		0			0
$841$	17.6821			0.609729
$842$	20.0295	−	17.7427i	0.690263	−	0.611453i
$843$	−3.53316	+	13.1859i	−0.121688	+	0.454147i
$844$	−39.6270	−	4.81598i	−1.36402	−	0.165773i
$845$	−12.0278	+	18.1481i	−0.413768	+	0.624314i
$846$	12.8577	+	25.7488i	0.442057	+	0.885261i
$847$		0			0
$848$	−41.5164	−	22.8792i	−1.42568	−	0.785676i
$849$	−10.0950	−	5.82832i	−0.346458	−	0.200028i
$850$	−2.31178	+	2.70350i	−0.0792934	+	0.0927292i
$851$	−7.06080	+	4.07655i	−0.242041	+	0.139742i
$852$	−1.12847	+	2.80301i	−0.0386608	+	0.0960296i
$853$	6.50453	−	6.50453i	0.222711	−	0.222711i	−0.586928	−	0.809639i	$-0.699663\pi$
$853$	6.50453	−	6.50453i	0.222711	−	0.222711i	0.809639	+	0.586928i	$0.199663\pi$
$854$		0			0
$855$	−48.9227	−	3.02194i	−1.67312	−	0.103348i
$856$	5.00160	−	5.87810i	0.170951	−	0.200909i
$857$	−6.34875	+	23.6939i	−0.216869	+	0.809367i	0.768631	+	0.639692i	$0.220938\pi$
$857$	−6.34875	+	23.6939i	−0.216869	+	0.809367i	−0.985500	+	0.169674i	$0.945728\pi$
$858$	6.05535	−	1.23586i	0.206726	−	0.0421917i
$859$	−7.68183	+	13.3053i	−0.262101	+	0.453972i	−0.966800	−	0.255534i	$-0.917749\pi$
$859$	−7.68183	+	13.3053i	−0.262101	+	0.453972i	0.704699	+	0.709506i	$0.251082\pi$
$860$	40.8982	−	3.24463i	1.39462	−	0.110641i
$861$		0			0
$862$	−2.66765	+	7.98915i	−0.0908607	+	0.272111i
$863$	50.5471	−	13.5441i	1.72064	−	0.461045i	0.742651	−	0.669679i	$-0.233568\pi$
$863$	50.5471	−	13.5441i	1.72064	−	0.461045i	0.977994	+	0.208634i	$0.0669016\pi$
$864$	5.37479	−	17.2317i	0.182854	−	0.586236i
$865$	−3.05000	+	9.09719i	−0.103703	+	0.309314i
$866$	−2.61369	+	43.1704i	−0.0888170	+	1.46699i
$867$	6.64673	−	6.64673i	0.225735	−	0.225735i
$868$		0			0
$869$		−	39.5393i		−	1.34128i
$870$	5.92682	+	0.727649i	0.200938	+	0.0246696i
$871$	−11.8000	+	6.81275i	−0.399829	+	0.230841i
$872$	26.1828	+	12.4292i	0.886662	+	0.420904i
$873$	1.03082	+	3.84707i	0.0348880	+	0.130204i
$874$	19.3838	+	38.8180i	0.655668	+	1.31304i
$875$		0			0
$876$	5.26022	+	3.95369i	0.177726	+	0.133583i
$877$	−27.7344	+	7.43141i	−0.936524	+	0.250941i	−0.694634	−	0.719363i	$-0.744434\pi$
$877$	−27.7344	+	7.43141i	−0.936524	+	0.250941i	−0.241890	+	0.970304i	$0.577767\pi$
$878$	7.02073	+	34.3994i	0.236938	+	1.16092i
$879$	−5.52991	−	9.57808i	−0.186519	−	0.323061i
$880$	36.7868	+	11.5236i	1.24008	+	0.388460i
$881$	−25.0247			−0.843102			−0.421551	−	0.906805i	$-0.638514\pi$
$881$	−25.0247			−0.843102			−0.421551	+	0.906805i	$0.638514\pi$
$882$		0			0
$883$	−12.6604	−	12.6604i	−0.426055	−	0.426055i	0.461227	−	0.887282i	$-0.347409\pi$
$883$	−12.6604	−	12.6604i	−0.426055	−	0.426055i	−0.887282	+	0.461227i	$0.847409\pi$
$884$	1.67213	−	0.712211i	0.0562397	−	0.0239542i
$885$	0.425244	+	0.142570i	0.0142944	+	0.00479245i
$886$	24.1422	−	36.5239i	0.811075	−	1.22704i
$887$	1.32625	+	4.94962i	0.0445310	+	0.166192i	0.984610	−	0.174764i	$-0.0559161\pi$
$887$	1.32625	+	4.94962i	0.0445310	+	0.166192i	−0.940079	+	0.340955i	$0.889249\pi$
$888$	2.83499	−	1.95617i	0.0951361	−	0.0656447i
$889$		0			0
$890$	3.49493	+	1.41199i	0.117150	+	0.0473301i
$891$	−23.3800	−	13.4984i	−0.783259	−	0.452215i
$892$	26.3670	−	20.6526i	0.882832	−	0.691499i
$893$	59.7733	+	16.0162i	2.00024	+	0.535962i
$894$	−0.100589	+	1.66143i	−0.00336420	+	0.0555665i
$895$	−0.218345	+	3.53482i	−0.00729845	+	0.118156i
$896$		0			0
$897$	−2.69428	−	2.69428i	−0.0899593	−	0.0899593i
$898$	27.9570	+	31.5604i	0.932938	+	1.05319i
$899$	0.252912	+	0.438056i	0.00843508	+	0.0146100i
$900$	26.0521	+	6.49486i	0.868405	+	0.216495i
$901$	2.98081	−	5.16291i	0.0993052	−	0.172002i
$902$	−17.7099	+	53.0378i	−0.589674	+	1.76597i
$903$		0			0
$904$	32.7950	+	6.01546i	1.09075	+	0.200071i
$905$	−21.6037	−	14.3180i	−0.718130	−	0.475945i
$906$	7.14183	+	4.72074i	0.237271	+	0.156836i
$907$	−22.7524	−	6.09648i	−0.755480	−	0.202430i	−0.139533	−	0.990217i	$-0.544560\pi$
$907$	−22.7524	−	6.09648i	−0.755480	−	0.202430i	−0.615948	+	0.787787i	$0.711227\pi$
$908$	20.0528	−	49.8091i	0.665475	−	1.65297i
$909$			40.9067i			1.35679i
$910$		0			0
$911$		−	36.8965i		−	1.22243i	−0.791463	−	0.611217i	$-0.790680\pi$
$911$		−	36.8965i		−	1.22243i	0.791463	−	0.611217i	$-0.209320\pi$
$912$	−9.47940	−	15.6886i	−0.313894	−	0.519501i
$913$	28.4888	+	7.63355i	0.942842	+	0.252634i
$914$	−4.24645	+	6.42430i	−0.140460	+	0.212497i
$915$	2.50269	+	12.3393i	0.0827364	+	0.407925i
$916$	−1.98051	+	2.63498i	−0.0654380	+	0.0870623i
$917$		0			0
$918$	2.15323	+	0.718986i	0.0710673	+	0.0237301i
$919$	−4.53453	+	7.85403i	−0.149580	+	0.259081i	−0.931072	−	0.364835i	$-0.881126\pi$
$919$	−4.53453	+	7.85403i	−0.149580	+	0.259081i	0.781492	+	0.623915i	$0.214459\pi$
$920$	−6.57952	−	22.8381i	−0.216920	−	0.752951i
$921$	7.31871	+	12.6764i	0.241160	+	0.417701i
$922$	37.4193	−	33.1469i	1.23234	−	1.09164i
$923$	3.43823	+	3.43823i	0.113171	+	0.113171i
$924$		0			0
$925$	6.66834	+	8.55639i	0.219254	+	0.281332i
$926$	34.1550	+	2.06787i	1.12240	+	0.0679545i
$927$	5.17407	+	1.38639i	0.169939	+	0.0455349i
$928$	−8.83946	−	16.8534i	−0.290169	−	0.553239i
$929$	−28.6658	−	16.5502i	−0.940496	−	0.542996i	−0.0503801	−	0.998730i	$-0.516043\pi$
$929$	−28.6658	−	16.5502i	−0.940496	−	0.542996i	−0.890116	+	0.455735i	$0.849377\pi$
$930$	−0.104278	−	0.245657i	−0.00341943	−	0.00805539i
$931$		0			0
$932$	−8.97952	+	1.27328i	−0.294134	+	0.0417078i
$933$	1.53936	+	5.74496i	0.0503963	+	0.188082i
$934$	−17.2636	−	11.4112i	−0.564882	−	0.373386i
$935$	−1.54111	+	4.59667i	−0.0503998	+	0.150327i
$936$	−10.4481	−	8.89014i	−0.341507	−	0.290583i
$937$	5.66479	+	5.66479i	0.185061	+	0.185061i	0.793557	−	0.608496i	$-0.208227\pi$
$937$	5.66479	+	5.66479i	0.185061	+	0.185061i	−0.608496	+	0.793557i	$0.708227\pi$
$938$		0			0
$939$	−13.3677			−0.436238
$940$	−30.6042	−	14.5738i	−0.998198	−	0.475346i
$941$	7.94113	+	13.7544i	0.258874	+	0.448382i	0.965940	−	0.258765i	$-0.0833154\pi$
$941$	7.94113	+	13.7544i	0.258874	+	0.448382i	−0.707067	+	0.707147i	$0.749982\pi$
$942$	7.09551	−	1.44815i	0.231184	−	0.0471834i
$943$	33.2996	−	8.92261i	1.08439	−	0.290560i
$944$	−0.397386	−	1.37306i	−0.0129338	−	0.0446893i
$945$		0			0
$946$	50.0262	−	24.9807i	1.62649	−	0.812191i
$947$	−6.42136	−	23.9649i	−0.208666	−	0.778753i	−0.988301	−	0.152518i	$-0.951262\pi$
$947$	−6.42136	−	23.9649i	−0.208666	−	0.778753i	0.779634	−	0.626235i	$-0.215405\pi$
$948$	8.10749	−	6.35038i	0.263319	−	0.206251i
$949$	9.17043	−	5.29455i	0.297685	−	0.171868i
$950$	47.5961	−	32.6704i	1.54422	−	1.05997i
$951$			9.52635i			0.308913i
$952$		0			0
$953$	−7.57040	+	7.57040i	−0.245229	+	0.245229i	−0.819009	−	0.573780i	$-0.805476\pi$
$953$	−7.57040	+	7.57040i	−0.245229	+	0.245229i	0.573780	+	0.819009i	$0.305476\pi$
$954$	−44.9165	−	2.71941i	−1.45422	−	0.0880441i
$955$	5.01034	+	10.0644i	0.162131	+	0.325677i
$956$	4.12331	−	33.9276i	0.133357	−	1.09730i
$957$	7.86118	−	2.10640i	0.254116	−	0.0680901i
$958$	47.2914	+	15.7911i	1.52792	+	0.510186i
$959$		0			0
$960$	3.54541	+	9.39389i	0.114428	+	0.303186i
$961$	−15.4887	+	26.8272i	−0.499635	+	0.865394i
$962$	−1.10838	−	5.43071i	−0.0357356	−	0.175093i
$963$	1.89625	−	7.07688i	0.0611057	−	0.228049i
$964$	−8.53487	+	3.63527i	−0.274890	+	0.117084i
$965$	−19.6527	−	22.2405i	−0.632644	−	0.715945i
$966$		0			0
$967$	5.93982	−	5.93982i	0.191012	−	0.191012i	−0.605121	−	0.796133i	$-0.706875\pi$
$967$	5.93982	−	5.93982i	0.191012	−	0.191012i	0.796133	+	0.605121i	$0.206875\pi$
$968$	21.3584	−	1.72070i	0.686484	−	0.0553055i
$969$	1.99641	−	1.15263i	0.0641340	−	0.0370278i
$970$	−3.74630	−	2.82297i	−0.120286	−	0.0906401i
$971$	16.8695	+	9.73962i	0.541368	+	0.312559i	0.745633	−	0.666356i	$-0.232147\pi$
$971$	16.8695	+	9.73962i	0.541368	+	0.312559i	−0.204265	+	0.978916i	$0.565480\pi$
$972$	−3.67512	−	25.9179i	−0.117880	−	0.831316i
$973$		0			0
$974$	−42.8201	+	21.3823i	−1.37204	+	0.685132i
$975$	−3.05592	+	4.04515i	−0.0978678	+	0.129549i
$976$	27.8030	−	28.9333i	0.889951	−	0.926132i
$977$	−9.16251	+	34.1950i	−0.293135	+	1.09399i	0.649553	+	0.760316i	$0.274956\pi$
$977$	−9.16251	+	34.1950i	−0.293135	+	1.09399i	−0.942687	+	0.333677i	$0.891711\pi$
$978$	11.2911	+	12.7464i	0.361048	+	0.407584i
$979$	5.13740			0.164192
$980$		0			0
$981$	27.5130			0.878422
$982$	−2.65247	−	2.99435i	−0.0846437	−	0.0955535i
$983$	−6.27502	+	23.4187i	−0.200142	+	0.746940i	0.790734	+	0.612160i	$0.209699\pi$
$983$	−6.27502	+	23.4187i	−0.200142	+	0.746940i	−0.990876	+	0.134780i	$0.956967\pi$
$984$	−13.7197	+	4.88699i	−0.437369	+	0.155792i
$985$	0.360795	+	1.77887i	0.0114959	+	0.0566795i
$986$	2.14127	−	1.06924i	0.0681918	−	0.0340517i
$987$		0			0
$988$	−29.2044	+	4.14115i	−0.929115	+	0.131747i
$989$	−29.8556	−	17.2372i	−0.949354	−	0.548110i
$990$	36.2378	−	5.09334i	1.15171	−	0.161877i
$991$	20.1148	−	11.6133i	0.638968	−	0.368908i	−0.145249	−	0.989395i	$-0.546398\pi$
$991$	20.1148	−	11.6133i	0.638968	−	0.368908i	0.784217	+	0.620487i	$0.213065\pi$
$992$	−0.454778	+	0.718739i	−0.0144392	+	0.0228200i
$993$	3.13091	−	3.13091i	0.0993563	−	0.0993563i
$994$		0			0
$995$	−3.65233	+	59.1282i	−0.115787	+	1.87449i
$996$	3.01032	+	7.06762i	0.0953856	+	0.223946i
$997$	−12.9371	+	48.2819i	−0.409722	+	1.52910i	0.385454	+	0.922727i	$0.374045\pi$
$997$	−12.9371	+	48.2819i	−0.409722	+	1.52910i	−0.795177	+	0.606378i	$0.792622\pi$
$998$	−4.52337	−	22.1631i	−0.143185	−	0.701561i
$999$	3.46149	−	5.99548i	0.109517	−	0.189689i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.l.667.4		72
4.3	odd	2	inner	980.2.x.l.667.2		72
5.3	odd	4	inner	980.2.x.l.863.13		72
7.2	even	3		980.2.k.l.687.17		36
7.3	odd	6		980.2.x.k.67.8		72
7.4	even	3	inner	980.2.x.l.67.8		72
7.5	odd	6		140.2.k.a.127.17	yes	36
7.6	odd	2		980.2.x.k.667.4		72
20.3	even	4	inner	980.2.x.l.863.8		72
28.3	even	6		980.2.x.k.67.13		72
28.11	odd	6	inner	980.2.x.l.67.13		72
28.19	even	6		140.2.k.a.127.11	yes	36
28.23	odd	6		980.2.k.l.687.11		36
28.27	even	2		980.2.x.k.667.2		72
35.3	even	12		980.2.x.k.263.2		72
35.12	even	12		700.2.k.b.43.8		36
35.13	even	4		980.2.x.k.863.13		72
35.18	odd	12	inner	980.2.x.l.263.2		72
35.19	odd	6		700.2.k.b.407.2		36
35.23	odd	12		980.2.k.l.883.11		36
35.33	even	12		140.2.k.a.43.11	✓	36
140.3	odd	12		980.2.x.k.263.4		72
140.19	even	6		700.2.k.b.407.8		36
140.23	even	12		980.2.k.l.883.17		36
140.47	odd	12		700.2.k.b.43.2		36
140.83	odd	4		980.2.x.k.863.8		72
140.103	odd	12		140.2.k.a.43.17	yes	36
140.123	even	12	inner	980.2.x.l.263.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.11	✓	36	35.33	even	12
140.2.k.a.43.17	yes	36	140.103	odd	12
140.2.k.a.127.11	yes	36	28.19	even	6
140.2.k.a.127.17	yes	36	7.5	odd	6
700.2.k.b.43.2		36	140.47	odd	12
700.2.k.b.43.8		36	35.12	even	12
700.2.k.b.407.2		36	35.19	odd	6
700.2.k.b.407.8		36	140.19	even	6
980.2.k.l.687.11		36	28.23	odd	6
980.2.k.l.687.17		36	7.2	even	3
980.2.k.l.883.11		36	35.23	odd	12
980.2.k.l.883.17		36	140.23	even	12
980.2.x.k.67.8		72	7.3	odd	6
980.2.x.k.67.13		72	28.3	even	6
980.2.x.k.263.2		72	35.3	even	12
980.2.x.k.263.4		72	140.3	odd	12
980.2.x.k.667.2		72	28.27	even	2
980.2.x.k.667.4		72	7.6	odd	2
980.2.x.k.863.8		72	140.83	odd	4
980.2.x.k.863.13		72	35.13	even	4
980.2.x.l.67.8		72	7.4	even	3	inner
980.2.x.l.67.13		72	28.11	odd	6	inner
980.2.x.l.263.2		72	35.18	odd	12	inner
980.2.x.l.263.4		72	140.123	even	12	inner
980.2.x.l.667.2		72	4.3	odd	2	inner
980.2.x.l.667.4		72	1.1	even	1	trivial
980.2.x.l.863.8		72	20.3	even	4	inner
980.2.x.l.863.13		72	5.3	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)

\(f(q)\)	\(=\)	\(q+(-1.05861 + 0.937739i) q^{2} +(0.145273 - 0.542165i) q^{3} +(0.241290 - 1.98539i) q^{4} +(1.86388 + 1.23530i) q^{5} +(0.354623 + 0.710167i) q^{6} +(1.60635 + 2.32801i) q^{8} +(2.32524 + 1.34248i) q^{9} +O(q^{10})\)	\(q+(-1.05861 + 0.937739i) q^{2} +(0.145273 - 0.542165i) q^{3} +(0.241290 - 1.98539i) q^{4} +(1.86388 + 1.23530i) q^{5} +(0.354623 + 0.710167i) q^{6} +(1.60635 + 2.32801i) q^{8} +(2.32524 + 1.34248i) q^{9} +(-3.13150 + 0.440142i) q^{10} +(-3.73254 + 2.15498i) q^{11} +(-1.04136 - 0.419242i) q^{12} +(-1.27735 + 1.27735i) q^{13} +(0.940505 - 0.831075i) q^{15} +(-3.88356 - 0.958111i) q^{16} +(0.130200 - 0.485914i) q^{17} +(-3.72040 + 0.759314i) q^{18} +(-4.08212 + 7.07044i) q^{19} +(2.90228 - 3.40246i) q^{20} +(1.93047 - 5.78142i) q^{22} +(-3.62985 + 0.972614i) q^{23} +(1.49553 - 0.532709i) q^{24} +(1.94809 + 4.60488i) q^{25} +(0.154388 - 2.55003i) q^{26} +(2.25631 - 2.25631i) q^{27} -3.36420i q^{29} +(-0.216292 + 1.76173i) q^{30} +(-0.130211 + 0.0751773i) q^{31} +(5.00961 - 2.62750i) q^{32} +(0.626120 + 2.33671i) q^{33} +(0.317830 + 0.636485i) q^{34} +(3.22640 - 4.29258i) q^{36} +(2.09567 - 0.561533i) q^{37} +(-2.30888 - 11.3128i) q^{38} +(0.506971 + 0.878099i) q^{39} +(0.118253 + 6.32345i) q^{40} -9.17384 q^{41} +(6.48688 + 6.48688i) q^{43} +(3.37786 + 7.93053i) q^{44} +(2.67560 + 5.37457i) q^{45} +(2.93052 - 4.43346i) q^{46} +(-1.96175 - 7.32135i) q^{47} +(-1.08363 + 1.96634i) q^{48} +(-6.38044 - 3.04796i) q^{50} +(-0.244531 - 0.141180i) q^{51} +(2.22783 + 2.84425i) q^{52} +(11.4470 + 3.06722i) q^{53} +(-0.272712 + 4.50438i) q^{54} +(-9.61904 - 0.594164i) q^{55} +(3.24033 + 3.24033i) q^{57} +(3.15475 + 3.56136i) q^{58} +(0.178676 + 0.309476i) q^{59} +(-1.42307 - 2.06780i) q^{60} +(-5.01582 + 8.68766i) q^{61} +(0.0673452 - 0.201687i) q^{62} +(-2.83929 + 7.47920i) q^{64} +(-3.95873 + 0.802921i) q^{65} +(-2.85404 - 1.88652i) q^{66} +(7.28570 + 1.95220i) q^{67} +(-0.933313 - 0.375745i) q^{68} +2.10927i q^{69} -2.69169i q^{71} +(0.609838 + 7.56967i) q^{72} +(-5.66210 - 1.51716i) q^{73} +(-1.69191 + 2.55963i) q^{74} +(2.77961 - 0.387221i) q^{75} +(13.0526 + 9.81064i) q^{76} +(-1.36011 - 0.454154i) q^{78} +(-4.58697 + 7.94486i) q^{79} +(-6.05493 - 6.58315i) q^{80} +(3.13192 + 5.42464i) q^{81} +(9.71147 - 8.60267i) q^{82} +(-4.83885 - 4.83885i) q^{83} +(0.842925 - 0.744849i) q^{85} +(-12.9501 - 0.784044i) q^{86} +(-1.82395 - 0.488727i) q^{87} +(-11.0126 - 5.22775i) q^{88} +(-1.03229 - 0.595991i) q^{89} +(-7.87235 - 3.18053i) q^{90} +(1.05517 + 7.44135i) q^{92} +(0.0218424 + 0.0815170i) q^{93} +(8.94224 + 5.91081i) q^{94} +(-16.3427 + 8.13582i) q^{95} +(-0.696781 - 3.09774i) q^{96} +(1.04890 + 1.04890i) q^{97} -11.5720 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 16 q^{6}+O(q^{10}) \) 72 * q + 16 * q^6	\( 72 q + 16 q^{6} - 16 q^{10} - 16 q^{12} + 8 q^{13} + 8 q^{16} - 20 q^{17} - 28 q^{18} - 40 q^{20} + 8 q^{22} + 20 q^{25} - 32 q^{26} + 4 q^{30} - 20 q^{37} - 36 q^{40} + 20 q^{45} - 16 q^{46} + 48 q^{48} + 80 q^{50} + 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} - 64 q^{61} - 80 q^{62} - 4 q^{65} + 32 q^{66} + 80 q^{68} - 80 q^{72} + 52 q^{73} - 16 q^{76} - 152 q^{78} - 20 q^{80} + 36 q^{81} + 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} + 32 q^{90} - 112 q^{92} - 32 q^{93} + 120 q^{96} - 40 q^{97}+O(q^{100}) \) 72 * q + 16 * q^6 - 16 * q^10 - 16 * q^12 + 8 * q^13 + 8 * q^16 - 20 * q^17 - 28 * q^18 - 40 * q^20 + 8 * q^22 + 20 * q^25 - 32 * q^26 + 4 * q^30 - 20 * q^37 - 36 * q^40 + 20 * q^45 - 16 * q^46 + 48 * q^48 + 80 * q^50 + 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 - 64 * q^61 - 80 * q^62 - 4 * q^65 + 32 * q^66 + 80 * q^68 - 80 * q^72 + 52 * q^73 - 16 * q^76 - 152 * q^78 - 20 * q^80 + 36 * q^81 + 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 + 32 * q^90 - 112 * q^92 - 32 * q^93 + 120 * q^96 - 40 * q^97

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