LMFDB - Embedded newform 819.2.dt.a.337.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(337,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("819.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dt (of order $6$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			337.39
Character	$\chi$	$=$	819.337
Dual form			819.2.dt.a.610.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.223818 + 0.129221i) q^{2} +(-1.68426 + 0.404065i) q^{3} +(-0.966604 + 1.67421i) q^{4} +(-1.67289 - 0.965845i) q^{5} +(0.324754 - 0.308080i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.01651i q^{8} +(2.67346 - 1.36110i) q^{9} +O(q^{10})$	\(q+(-0.223818 + 0.129221i) q^{2} +(-1.68426 + 0.404065i) q^{3} +(-0.966604 + 1.67421i) q^{4} +(-1.67289 - 0.965845i) q^{5} +(0.324754 - 0.308080i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.01651i q^{8} +(2.67346 - 1.36110i) q^{9} +0.499232 q^{10} +(-2.98080 + 1.72097i) q^{11} +(0.951524 - 3.21037i) q^{12} +(-1.81813 - 3.11359i) q^{13} +(-0.129221 + 0.223818i) q^{14} +(3.20785 + 0.950777i) q^{15} +(-1.80185 - 3.12090i) q^{16} +6.09757 q^{17} +(-0.422486 + 0.650108i) q^{18} -4.74880i q^{19} +(3.23405 - 1.86718i) q^{20} +(-1.25658 + 1.19206i) q^{21} +(0.444772 - 0.770368i) q^{22} +(-4.12678 + 7.14779i) q^{23} +(0.410736 + 1.71207i) q^{24} +(-0.634287 - 1.09862i) q^{25} +(0.809271 + 0.461936i) q^{26} +(-3.95283 + 3.37270i) q^{27} +1.93321i q^{28} +(3.17431 + 5.49806i) q^{29} +(-0.840836 + 0.201722i) q^{30} +(5.08629 + 2.93657i) q^{31} +(2.56722 + 1.48219i) q^{32} +(4.32507 - 4.10300i) q^{33} +(-1.36475 + 0.787937i) q^{34} -1.93169 q^{35} +(-0.305416 + 5.79157i) q^{36} -6.74764i q^{37} +(0.613647 + 1.06287i) q^{38} +(4.32029 + 4.50945i) q^{39} +(-0.981791 + 1.70051i) q^{40} +(10.5297 + 6.07930i) q^{41} +(0.127205 - 0.429182i) q^{42} +(0.993644 + 1.72104i) q^{43} -6.65398i q^{44} +(-5.78703 - 0.305176i) q^{45} -2.13307i q^{46} +(-2.36188 + 1.36363i) q^{47} +(4.29583 + 4.52834i) q^{48} +(0.500000 - 0.866025i) q^{49} +(0.283930 + 0.163927i) q^{50} +(-10.2699 + 2.46381i) q^{51} +(6.97019 - 0.0343132i) q^{52} +3.86549 q^{53} +(0.448891 - 1.26566i) q^{54} +6.64875 q^{55} +(-0.508255 - 0.880323i) q^{56} +(1.91882 + 7.99822i) q^{57} +(-1.42093 - 0.820377i) q^{58} +(3.12512 + 1.80429i) q^{59} +(-4.69252 + 4.45158i) q^{60} +(5.17837 + 8.96921i) q^{61} -1.51787 q^{62} +(1.63474 - 2.51548i) q^{63} +6.44129 q^{64} +(0.0342862 + 6.96472i) q^{65} +(-0.437833 + 1.47722i) q^{66} +(-4.33801 - 2.50455i) q^{67} +(-5.89393 + 10.2086i) q^{68} +(4.06240 - 13.7062i) q^{69} +(0.432347 - 0.249616i) q^{70} -3.24047i q^{71} +(-1.38357 - 2.71760i) q^{72} +16.8138i q^{73} +(0.871940 + 1.51024i) q^{74} +(1.51222 + 1.59406i) q^{75} +(7.95048 + 4.59021i) q^{76} +(-1.72097 + 2.98080i) q^{77} +(-1.54968 - 0.451023i) q^{78} +(2.30545 + 3.99316i) q^{79} +6.96124i q^{80} +(5.29481 - 7.27770i) q^{81} -3.14230 q^{82} +(7.48114 - 4.31924i) q^{83} +(-0.781141 - 3.25602i) q^{84} +(-10.2006 - 5.88931i) q^{85} +(-0.444791 - 0.256800i) q^{86} +(-7.56793 - 7.97754i) q^{87} +(1.74938 + 3.03002i) q^{88} -14.7529i q^{89} +(1.33468 - 0.679504i) q^{90} +(-3.13134 - 1.78738i) q^{91} +(-7.97792 - 13.8182i) q^{92} +(-9.75320 - 2.89076i) q^{93} +(0.352421 - 0.610412i) q^{94} +(-4.58661 + 7.94424i) q^{95} +(-4.92277 - 1.45906i) q^{96} +(2.60817 - 1.50583i) q^{97} +0.258443i q^{98} +(-5.62666 + 8.65812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 84 q^{4} - 8 q^{9}+O(q^{10}) $ 168 * q + 84 * q^4 - 8 * q^9	$ 168 q + 84 q^{4} - 8 q^{9} - 24 q^{12} + 8 q^{14} - 84 q^{16} - 32 q^{23} + 84 q^{25} - 8 q^{26} + 48 q^{27} + 4 q^{29} + 80 q^{30} - 32 q^{35} + 4 q^{36} + 24 q^{38} + 24 q^{39} + 4 q^{48} + 84 q^{49} + 64 q^{51} + 18 q^{52} - 48 q^{53} - 24 q^{56} + 24 q^{62} - 240 q^{64} - 22 q^{65} - 132 q^{66} - 156 q^{68} - 52 q^{69} + 84 q^{74} - 60 q^{75} - 16 q^{77} - 148 q^{78} + 12 q^{79} - 8 q^{81} - 24 q^{82} + 88 q^{87} + 24 q^{88} - 164 q^{90} + 12 q^{91} + 128 q^{92} - 60 q^{94} - 96 q^{95}+O(q^{100}) $ 168 * q + 84 * q^4 - 8 * q^9 - 24 * q^12 + 8 * q^14 - 84 * q^16 - 32 * q^23 + 84 * q^25 - 8 * q^26 + 48 * q^27 + 4 * q^29 + 80 * q^30 - 32 * q^35 + 4 * q^36 + 24 * q^38 + 24 * q^39 + 4 * q^48 + 84 * q^49 + 64 * q^51 + 18 * q^52 - 48 * q^53 - 24 * q^56 + 24 * q^62 - 240 * q^64 - 22 * q^65 - 132 * q^66 - 156 * q^68 - 52 * q^69 + 84 * q^74 - 60 * q^75 - 16 * q^77 - 148 * q^78 + 12 * q^79 - 8 * q^81 - 24 * q^82 + 88 * q^87 + 24 * q^88 - 164 * q^90 + 12 * q^91 + 128 * q^92 - 60 * q^94 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.223818	+	0.129221i	−0.158263	+	0.0913734i	−0.577040	−	0.816716i	$-0.695792\pi$
$2$	−0.223818	+	0.129221i	−0.158263	+	0.0913734i	0.418777	+	0.908089i	$0.362459\pi$
$3$	−1.68426	+	0.404065i	−0.972408	+	0.233287i
$3$	−1.68426	+	0.404065i	−0.972408	+	0.233287i
$4$	−0.966604	+	1.67421i	−0.483302	+	0.837103i
$5$	−1.67289	−	0.965845i	−0.748140	−	0.431939i	0.0768812	−	0.997040i	$-0.475504\pi$
$5$	−1.67289	−	0.965845i	−0.748140	−	0.431939i	−0.825022	+	0.565101i	$0.808837\pi$
$6$	0.324754	−	0.308080i	0.132580	−	0.125773i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$		−	1.01651i		−	0.359390i
$9$	2.67346	−	1.36110i	0.891154	−	0.453700i
$10$	0.499232			0.157871
$11$	−2.98080	+	1.72097i	−0.898746	+	0.518891i	−0.876793	−	0.480868i	$-0.840322\pi$
$11$	−2.98080	+	1.72097i	−0.898746	+	0.518891i	−0.0219531	+	0.999759i	$0.506988\pi$
$12$	0.951524	−	3.21037i	0.274681	−	0.926754i
$13$	−1.81813	−	3.11359i	−0.504257	−	0.863554i
$13$	−1.81813	−	3.11359i	−0.504257	−	0.863554i
$14$	−0.129221	+	0.223818i	−0.0345359	+	0.0598179i
$15$	3.20785	+	0.950777i	0.828263	+	0.245490i
$16$	−1.80185	−	3.12090i	−0.450463	−	0.780225i
$17$	6.09757			1.47888			0.739439	−	0.673223i	$-0.235091\pi$
$17$	6.09757			1.47888			0.739439	+	0.673223i	$0.235091\pi$
$18$	−0.422486	+	0.650108i	−0.0995809	+	0.153232i
$19$		−	4.74880i		−	1.08945i	−0.838615	−	0.544725i	$-0.816634\pi$
$19$		−	4.74880i		−	1.08945i	0.838615	−	0.544725i	$-0.183366\pi$
$20$	3.23405	−	1.86718i	0.723155	−	0.417514i
$21$	−1.25658	+	1.19206i	−0.274208	+	0.260129i
$22$	0.444772	−	0.770368i	0.0948257	−	0.164243i
$23$	−4.12678	+	7.14779i	−0.860493	+	1.49042i	0.0109617	+	0.999940i	$0.496511\pi$
$23$	−4.12678	+	7.14779i	−0.860493	+	1.49042i	−0.871454	+	0.490477i	$0.836823\pi$
$24$	0.410736	+	1.71207i	0.0838411	+	0.349474i
$25$	−0.634287	−	1.09862i	−0.126857	−	0.219723i
$26$	0.809271	+	0.461936i	0.158711	+	0.0905932i
$27$	−3.95283	+	3.37270i	−0.760723	+	0.649076i
$28$			1.93321i			0.365342i
$29$	3.17431	+	5.49806i	0.589454	+	1.02096i	0.994304	+	0.106581i	$0.0339904\pi$
$29$	3.17431	+	5.49806i	0.589454	+	1.02096i	−0.404850	+	0.914383i	$0.632676\pi$
$30$	−0.840836	+	0.201722i	−0.153515	+	0.0368292i
$31$	5.08629	+	2.93657i	0.913525	+	0.527424i	0.881564	−	0.472065i	$-0.156491\pi$
$31$	5.08629	+	2.93657i	0.913525	+	0.527424i	0.0319612	+	0.999489i	$0.489825\pi$
$32$	2.56722	+	1.48219i	0.453825	+	0.262016i
$33$	4.32507	−	4.10300i	0.752897	−	0.714240i
$34$	−1.36475	+	0.787937i	−0.234052	+	0.135130i
$35$	−1.93169			−0.326515
$36$	−0.305416	+	5.79157i	−0.0509027	+	0.965262i
$37$		−	6.74764i		−	1.10931i	−0.832082	−	0.554653i	$-0.812851\pi$
$37$		−	6.74764i		−	1.10931i	0.832082	−	0.554653i	$-0.187149\pi$
$38$	0.613647	+	1.06287i	0.0995467	+	0.172420i
$39$	4.32029	+	4.50945i	0.691799	+	0.722090i
$40$	−0.981791	+	1.70051i	−0.155235	+	0.268874i
$41$	10.5297	+	6.07930i	1.64446	+	0.949427i	0.979222	+	0.202792i	$0.0650014\pi$
$41$	10.5297	+	6.07930i	1.64446	+	0.949427i	0.665234	+	0.746635i	$0.268332\pi$
$42$	0.127205	−	0.429182i	0.0196282	−	0.0662242i
$43$	0.993644	+	1.72104i	0.151529	+	0.262456i	0.931790	−	0.362998i	$-0.118247\pi$
$43$	0.993644	+	1.72104i	0.151529	+	0.262456i	−0.780261	+	0.625455i	$0.784914\pi$
$44$		−	6.65398i		−	1.00312i
$45$	−5.78703	−	0.305176i	−0.862679	−	0.0454930i
$46$		−	2.13307i		−	0.314504i
$47$	−2.36188	+	1.36363i	−0.344516	+	0.198906i	−0.662267	−	0.749268i	$-0.730406\pi$
$47$	−2.36188	+	1.36363i	−0.344516	+	0.198906i	0.317751	+	0.948174i	$0.397072\pi$
$48$	4.29583	+	4.52834i	0.620050	+	0.653610i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	0.283930	+	0.163927i	0.0401537	+	0.0231828i
$51$	−10.2699	+	2.46381i	−1.43807	+	0.345003i
$52$	6.97019	−	0.0343132i	0.966592	−	0.00475838i
$53$	3.86549			0.530965			0.265483	−	0.964116i	$-0.414469\pi$
$53$	3.86549			0.530965			0.265483	+	0.964116i	$0.414469\pi$
$54$	0.448891	−	1.26566i	0.0610863	−	0.172235i
$55$	6.64875			0.896518
$56$	−0.508255	−	0.880323i	−0.0679184	−	0.117638i
$57$	1.91882	+	7.99822i	0.254155	+	1.05939i
$58$	−1.42093	−	0.820377i	−0.186578	−	0.107721i
$59$	3.12512	+	1.80429i	0.406856	+	0.234898i	0.689438	−	0.724345i	$-0.257858\pi$
$59$	3.12512	+	1.80429i	0.406856	+	0.234898i	−0.282582	+	0.959243i	$0.591191\pi$
$60$	−4.69252	+	4.45158i	−0.605801	+	0.574696i
$61$	5.17837	+	8.96921i	0.663023	+	1.14839i	0.979817	+	0.199895i	$0.0640602\pi$
$61$	5.17837	+	8.96921i	0.663023	+	1.14839i	−0.316794	+	0.948494i	$0.602606\pi$
$62$	−1.51787			−0.192770
$63$	1.63474	−	2.51548i	0.205957	−	0.316921i
$64$	6.44129			0.805161
$65$	0.0342862	+	6.96472i	0.00425268	+	0.863868i
$66$	−0.437833	+	1.47722i	−0.0538935	+	0.181833i
$67$	−4.33801	−	2.50455i	−0.529972	−	0.305980i	0.211033	−	0.977479i	$-0.432317\pi$
$67$	−4.33801	−	2.50455i	−0.529972	−	0.305980i	−0.741005	+	0.671499i	$0.765651\pi$
$68$	−5.89393	+	10.2086i	−0.714745	+	1.23797i
$69$	4.06240	−	13.7062i	0.489055	−	1.65003i
$70$	0.432347	−	0.249616i	0.0516754	−	0.0298348i
$71$		−	3.24047i		−	0.384573i	−0.981339	−	0.192286i	$-0.938410\pi$
$71$		−	3.24047i		−	0.384573i	0.981339	−	0.192286i	$-0.0615902\pi$
$72$	−1.38357	−	2.71760i	−0.163055	−	0.320272i
$73$			16.8138i			1.96791i	0.178429	+	0.983953i	$0.442899\pi$
$73$			16.8138i			1.96791i	−0.178429	+	0.983953i	$0.557101\pi$
$74$	0.871940	+	1.51024i	0.101361	+	0.175562i
$75$	1.51222	+	1.59406i	0.174616	+	0.184067i
$76$	7.95048	+	4.59021i	0.911983	+	0.526533i
$77$	−1.72097	+	2.98080i	−0.196123	+	0.339694i
$78$	−1.54968	−	0.451023i	−0.175466	−	0.0510683i
$79$	2.30545	+	3.99316i	0.259384	+	0.449265i	0.966077	−	0.258254i	$-0.0831473\pi$
$79$	2.30545	+	3.99316i	0.259384	+	0.449265i	−0.706693	+	0.707520i	$0.749814\pi$
$80$			6.96124i			0.778290i
$81$	5.29481	−	7.27770i	0.588312	−	0.808634i
$82$	−3.14230			−0.347009
$83$	7.48114	−	4.31924i	0.821162	−	0.474098i	−0.0296549	−	0.999560i	$-0.509441\pi$
$83$	7.48114	−	4.31924i	0.821162	−	0.474098i	0.850817	+	0.525462i	$0.176107\pi$
$84$	−0.781141	−	3.25602i	−0.0852295	−	0.355261i
$85$	−10.2006	−	5.88931i	−1.10641	−	0.638785i
$86$	−0.444791	−	0.256800i	−0.0479631	−	0.0276915i
$87$	−7.56793	−	7.97754i	−0.811367	−	0.855282i
$88$	1.74938	+	3.03002i	0.186485	+	0.323001i
$89$		−	14.7529i		−	1.56380i	−0.623403	−	0.781901i	$-0.714250\pi$
$89$		−	14.7529i		−	1.56380i	0.623403	−	0.781901i	$-0.285750\pi$
$90$	1.33468	−	0.679504i	0.140687	−	0.0716260i
$91$	−3.13134	−	1.78738i	−0.328253	−	0.187369i
$92$	−7.97792	−	13.8182i	−0.831755	−	1.44064i
$93$	−9.75320	−	2.89076i	−1.01136	−	0.299758i
$94$	0.352421	−	0.610412i	0.0363495	−	0.0629591i
$95$	−4.58661	+	7.94424i	−0.470576	+	0.815062i
$96$	−4.92277	−	1.45906i	−0.502428	−	0.148915i
$97$	2.60817	−	1.50583i	0.264820	−	0.152894i	−0.361711	−	0.932290i	$-0.617807\pi$
$97$	2.60817	−	1.50583i	0.264820	−	0.152894i	0.626531	+	0.779396i	$0.284474\pi$
$98$			0.258443i			0.0261067i
$99$	−5.62666	+	8.65812i	−0.565501	+	0.870174i
$100$	2.45242			0.245242
$101$	−3.04648	−	5.27666i	−0.303136	−	0.525047i	0.673709	−	0.738997i	$-0.264700\pi$
$101$	−3.04648	−	5.27666i	−0.303136	−	0.525047i	−0.976845	+	0.213950i	$0.931367\pi$
$102$	1.98021	−	1.87854i	0.196070	−	0.186003i
$103$	8.59706	−	14.8905i	0.847093	−	1.46721i	−0.0366974	−	0.999326i	$-0.511684\pi$
$103$	8.59706	−	14.8905i	0.847093	−	1.46721i	0.883791	−	0.467882i	$-0.154983\pi$
$104$	−3.16499	+	1.84814i	−0.310353	+	0.181225i
$105$	3.25347	−	0.780528i	0.317506	−	0.0761717i
$106$	−0.865166	+	0.499504i	−0.0840323	+	0.0485161i
$107$	1.61973			0.156585			0.0782925	−	0.996930i	$-0.475053\pi$
$107$	1.61973			0.156585			0.0782925	+	0.996930i	$0.475053\pi$
$108$	−1.82577	−	9.87792i	−0.175685	−	0.950504i
$109$		−	12.5822i		−	1.20516i	−0.798060	−	0.602578i	$-0.794140\pi$
$109$		−	12.5822i		−	1.20516i	0.798060	−	0.602578i	$-0.205860\pi$
$110$	−1.48811	+	0.859162i	−0.141886	+	0.0819178i
$111$	2.72648	+	11.3648i	0.258786	+	1.07870i
$112$	−3.12090	−	1.80185i	−0.294897	−	0.170259i
$113$	−1.03636	+	1.79503i	−0.0974925	+	0.168862i	−0.910646	−	0.413187i	$-0.864416\pi$
$113$	−1.03636	+	1.79503i	−0.0974925	+	0.168862i	0.813154	+	0.582049i	$0.197749\pi$
$114$	−1.46301	−	1.54219i	−0.137023	−	0.144440i
$115$	13.8073	−	7.97165i	1.28754	−	0.743361i
$116$	−12.2732			−1.13954
$117$	−9.09859	−	5.84941i	−0.841165	−	0.540778i
$118$	−0.932611			−0.0858538
$119$	5.28065	−	3.04879i	0.484077	−	0.279482i
$120$	0.966474	−	3.26081i	0.0882266	−	0.297670i
$121$	0.423463	−	0.733459i	0.0384966	−	0.0666781i
$122$	−2.31803	−	1.33831i	−0.209864	−	0.121165i
$123$	−20.1911	−	5.98446i	−1.82057	−	0.539600i
$124$	−9.83285	+	5.67700i	−0.883016	+	0.509810i
$125$			12.1089i			1.08306i
$126$	−0.0408299	+	0.774253i	−0.00363742	+	0.0689759i
$127$	15.6855			1.39186			0.695932	−	0.718108i	$-0.254992\pi$
$127$	15.6855			1.39186			0.695932	+	0.718108i	$0.254992\pi$
$128$	−6.57612	+	3.79672i	−0.581252	+	0.335586i
$129$	−2.36897	−	2.49719i	−0.208576	−	0.219865i
$130$	−0.907665	−	1.55440i	−0.0796075	−	0.136330i
$131$	−6.92206	+	11.9894i	−0.604783	+	1.04751i	0.387303	+	0.921953i	$0.373407\pi$
$131$	−6.92206	+	11.9894i	−0.604783	+	1.04751i	−0.992086	+	0.125562i	$0.959927\pi$
$132$	2.68864	+	11.2070i	0.234016	+	0.975446i
$133$	−2.37440	−	4.11259i	−0.205887	−	0.356606i
$134$	1.29457			0.111834
$135$	9.87017	−	1.82434i	0.849489	−	0.157014i
$136$		−	6.19824i		−	0.531495i
$137$	5.39324	−	3.11379i	0.460776	−	0.266029i	−0.251595	−	0.967833i	$-0.580955\pi$
$137$	5.39324	−	3.11379i	0.460776	−	0.266029i	0.712370	+	0.701804i	$0.247622\pi$
$138$	0.861899	+	3.59265i	0.0733698	+	0.305827i
$139$	2.42444	−	4.19926i	0.205638	−	0.356176i	−0.744698	−	0.667402i	$-0.767406\pi$
$139$	2.42444	−	4.19926i	0.205638	−	0.356176i	0.950336	+	0.311226i	$0.100740\pi$
$140$	1.86718	−	3.23405i	0.157805	−	0.273327i
$141$	3.42703	−	3.25107i	0.288608	−	0.273789i
$142$	0.418738	+	0.725275i	0.0351397	+	0.0608637i
$143$	10.7779	+	6.15206i	0.901290	+	0.514461i
$144$	−9.06504	−	5.89111i	−0.755420	−	0.490926i
$145$		−	12.2636i		−	1.01843i
$146$	−2.17270	−	3.76323i	−0.179814	−	0.311447i
$147$	−0.492200	+	1.66064i	−0.0405959	+	0.136968i
$148$	11.2969	+	6.52230i	0.928603	+	0.536129i
$149$	18.7663	+	10.8347i	1.53740	+	0.887616i	0.998990	+	0.0449311i	$0.0143068\pi$
$149$	18.7663	+	10.8347i	1.53740	+	0.887616i	0.538407	+	0.842685i	$0.319026\pi$
$150$	−0.544448	−	0.161369i	−0.0444540	−	0.0131758i
$151$	−5.27423	+	3.04508i	−0.429211	+	0.247805i	−0.699010	−	0.715111i	$-0.746376\pi$
$151$	−5.27423	+	3.04508i	−0.429211	+	0.247805i	0.269800	+	0.962917i	$0.413043\pi$
$152$	−4.82720			−0.391538
$153$	16.3016	−	8.29941i	1.31791	−	0.670967i
$154$		−	0.889544i		−	0.0716815i
$155$	−5.67255	−	9.82514i	−0.455630	−	0.789174i
$156$	−11.7258	+	2.87420i	−0.938812	+	0.230120i
$157$	10.1558	−	17.5904i	0.810522	−	1.40387i	−0.101977	−	0.994787i	$-0.532517\pi$
$157$	10.1558	−	17.5904i	0.810522	−	1.40387i	0.912499	−	0.409078i	$-0.134150\pi$
$158$	−1.03200	−	0.595827i	−0.0821018	−	0.0474015i
$159$	−6.51048	+	1.56191i	−0.516315	+	0.123867i
$160$	−2.86312	−	4.95907i	−0.226350	−	0.392049i
$161$			8.25355i			0.650471i
$162$	−0.244639	+	2.31308i	−0.0192207	+	0.181733i
$163$			3.14320i			0.246195i	0.992395	+	0.123097i	$0.0392827\pi$
$163$			3.14320i			0.246195i	−0.992395	+	0.123097i	$0.960717\pi$
$164$	−20.3560	+	11.7525i	−1.58954	+	0.917719i
$165$	−11.1982	+	2.68653i	−0.871781	+	0.209146i
$166$	−1.11628	+	1.93345i	−0.0866399	+	0.150065i
$167$	−6.55581	−	3.78500i	−0.507304	−	0.292892i	0.224421	−	0.974492i	$-0.427951\pi$
$167$	−6.55581	−	3.78500i	−0.507304	−	0.292892i	−0.731725	+	0.681600i	$0.761284\pi$
$168$	1.21174	+	1.27732i	0.0934878	+	0.0985478i
$169$	−6.38884	+	11.3218i	−0.491449	+	0.870906i
$170$	3.04410			0.233472
$171$	−6.46360	−	12.6958i	−0.494284	−	0.970869i
$172$	−3.84184			−0.292938
$173$	−9.31810	−	16.1394i	−0.708442	−	1.22706i	−0.965435	−	0.260644i	$-0.916065\pi$
$173$	−9.31810	−	16.1394i	−0.708442	−	1.22706i	0.256993	−	0.966413i	$-0.417268\pi$
$174$	2.72471	+	0.807579i	0.206560	+	0.0612224i
$175$	−1.09862	−	0.634287i	−0.0830476	−	0.0479476i
$176$	10.7419	+	6.20186i	0.809704	+	0.467483i
$177$	−5.99257	−	1.77614i	−0.450429	−	0.133503i
$178$	1.90639	+	3.30196i	0.142890	+	0.247492i
$179$	1.99466			0.149088			0.0745440	−	0.997218i	$-0.476250\pi$
$179$	1.99466			0.149088			0.0745440	+	0.997218i	$0.476250\pi$
$180$	6.10469	−	9.39370i	0.455017	−	0.700165i
$181$	7.75481			0.576410			0.288205	−	0.957569i	$-0.406941\pi$
$181$	7.75481			0.576410			0.288205	+	0.957569i	$0.406941\pi$
$182$	0.931818	−	0.00458719i	0.0690709	−	0.000340025i
$183$	−12.3459	−	13.0141i	−0.912633	−	0.962028i
$184$	7.26579	+	4.19491i	0.535641	+	0.309253i
$185$	−6.51718	+	11.2881i	−0.479152	+	0.829916i
$186$	2.55649	−	0.613319i	0.187451	−	0.0449707i
$187$	−18.1757	+	10.4937i	−1.32914	+	0.767377i
$188$		−	5.27237i		−	0.384527i
$189$	−1.73691	+	4.89726i	−0.126341	+	0.356223i
$190$		−	2.37075i		−	0.171992i
$191$	0.110128	+	0.190747i	0.00796856	+	0.0138020i	0.869982	−	0.493083i	$-0.164130\pi$
$191$	0.110128	+	0.190747i	0.00796856	+	0.0138020i	−0.862014	+	0.506885i	$0.830797\pi$
$192$	−10.8488	+	2.60270i	−0.782945	+	0.187834i
$193$	−3.10771	−	1.79423i	−0.223698	−	0.129152i	0.383964	−	0.923348i	$-0.374559\pi$
$193$	−3.10771	−	1.79423i	−0.223698	−	0.129152i	−0.607661	+	0.794196i	$0.707892\pi$
$194$	−0.389171	+	0.674064i	−0.0279409	+	0.0483950i
$195$	−2.87195	−	11.7166i	−0.205664	−	0.839040i
$196$	0.966604	+	1.67421i	0.0690431	+	0.119586i
$197$		−	3.36090i		−	0.239454i	−0.992807	−	0.119727i	$-0.961798\pi$
$197$		−	3.36090i		−	0.239454i	0.992807	−	0.119727i	$-0.0382020\pi$
$198$	0.140534	−	2.66493i	0.00998731	−	0.189388i
$199$	4.82625			0.342124			0.171062	−	0.985260i	$-0.445280\pi$
$199$	4.82625			0.342124			0.171062	+	0.985260i	$0.445280\pi$
$200$	−1.11675	+	0.644758i	−0.0789665	+	0.0455913i
$201$	8.31834	+	2.46548i	0.586730	+	0.173901i
$202$	1.36371	+	0.787341i	0.0959506	+	0.0553971i
$203$	5.49806	+	3.17431i	0.385888	+	0.222793i
$204$	5.80198	−	19.5755i	0.406220	−	1.37056i
$205$	−11.7433	−	20.3400i	−0.820189	−	1.42061i
$206$			4.44370i			0.309607i
$207$	−1.30393	+	24.7263i	−0.0906295	+	1.71860i
$208$	−6.44120	+	11.2844i	−0.446617	+	0.782433i
$209$	8.17254	+	14.1553i	0.565306	+	0.979140i
$210$	−0.627324	+	0.595114i	−0.0432895	+	0.0410668i
$211$	−12.8147	+	22.1958i	−0.882202	+	1.52802i	−0.0333147	+	0.999445i	$0.510606\pi$
$211$	−12.8147	+	22.1958i	−0.882202	+	1.52802i	−0.848887	+	0.528574i	$0.822727\pi$
$212$	−3.73639	+	6.47162i	−0.256617	+	0.444473i
$213$	1.30936	+	5.45779i	0.0897158	+	0.373962i
$214$	−0.362524	+	0.209303i	−0.0247816	+	0.0143077i
$215$		−	3.83882i		−	0.261806i
$216$	3.42838	+	4.01809i	0.233272	+	0.273397i
$217$	5.87314			0.398695
$218$	1.62589	+	2.81612i	0.110119	+	0.190732i
$219$	−6.79386	−	28.3188i	−0.459087	−	1.91361i
$220$	−6.42671	+	11.1314i	−0.433289	+	0.750478i
$221$	−11.0861	−	18.9853i	−0.745735	−	1.27709i
$222$	−2.07881	−	2.19132i	−0.139521	−	0.147072i
$223$	−1.07274	+	0.619347i	−0.0718360	+	0.0414745i	−0.535488	−	0.844543i	$-0.679872\pi$
$223$	−1.07274	+	0.619347i	−0.0718360	+	0.0414745i	0.463652	+	0.886018i	$0.346539\pi$
$224$	2.96437			0.198065
$225$	−3.19107	−	2.07378i	−0.212738	−	0.138252i
$226$		−	0.535680i		−	0.0356329i
$227$	11.7949	−	6.80981i	0.782857	−	0.451983i	−0.0545849	−	0.998509i	$-0.517384\pi$
$227$	11.7949	−	6.80981i	0.782857	−	0.451983i	0.837442	+	0.546526i	$0.184050\pi$
$228$	−15.2454	−	4.51860i	−1.00965	−	0.299252i
$229$	2.21762	+	1.28034i	0.146544	+	0.0846073i	0.571479	−	0.820616i	$-0.306370\pi$
$229$	2.21762	+	1.28034i	0.146544	+	0.0846073i	−0.424935	+	0.905224i	$0.639703\pi$
$230$	−2.06022	+	3.56840i	−0.135847	+	0.235293i
$231$	1.69412	−	5.71583i	0.111465	−	0.376074i
$232$	5.58883	−	3.22671i	0.366925	−	0.211844i
$233$	11.6209			0.761308			0.380654	−	0.924718i	$-0.375699\pi$
$233$	11.6209			0.761308			0.380654	+	0.924718i	$0.375699\pi$
$234$	2.79230	+	0.133470i	0.182538	+	0.00872521i
$235$	5.26823			0.343662
$236$	−6.04151	+	3.48807i	−0.393269	+	0.227054i
$237$	−5.49647	−	5.79397i	−0.357034	−	0.376358i
$238$	−0.787937	+	1.36475i	−0.0510744	+	0.0884634i
$239$	5.76436	+	3.32806i	0.372866	+	0.215274i	0.674710	−	0.738083i	$-0.264269\pi$
$239$	5.76436	+	3.32806i	0.372866	+	0.215274i	−0.301844	+	0.953357i	$0.597602\pi$
$240$	−2.81279	−	11.7245i	−0.181565	−	0.756816i
$241$	21.8758	−	12.6300i	1.40914	−	0.813570i	0.413839	−	0.910350i	$-0.364188\pi$
$241$	21.8758	−	12.6300i	1.40914	−	0.813570i	0.995306	+	0.0967801i	$0.0308544\pi$
$242$			0.218882i			0.0140703i
$243$	−5.97718	+	14.3970i	−0.383436	+	0.923567i
$244$	−20.0217			−1.28176
$245$	−1.67289	+	0.965845i	−0.106877	+	0.0617056i
$246$	5.29245	−	1.26969i	0.337435	−	0.0809527i
$247$	−14.7858	+	8.63392i	−0.940799	+	0.549363i
$248$	2.98505	−	5.17026i	0.189551	−	0.328312i
$249$	−10.8549	+	10.2976i	−0.687904	+	0.652583i
$250$	−1.56473	−	2.71020i	−0.0989625	−	0.171408i
$251$	9.10322			0.574590			0.287295	−	0.957842i	$-0.407244\pi$
$251$	9.10322			0.574590			0.287295	+	0.957842i	$0.407244\pi$
$252$	2.63129	+	5.16836i	0.165756	+	0.325576i
$253$		−	28.4082i		−	1.78601i
$254$	−3.51070	+	2.02690i	−0.220281	+	0.127179i
$255$	19.5601	+	5.79743i	1.22490	+	0.363049i
$256$	−5.46005	+	9.45709i	−0.341253	+	0.591068i
$257$	−2.17182	+	3.76170i	−0.135474	+	0.234648i	−0.925779	−	0.378066i	$-0.876589\pi$
$257$	−2.17182	+	3.76170i	−0.135474	+	0.234648i	0.790304	+	0.612715i	$0.209922\pi$
$258$	0.852908	+	0.252794i	0.0530997	+	0.0157383i
$259$	−3.37382	−	5.84363i	−0.209639	−	0.363105i
$260$	−11.6935	−	6.67472i	−0.725202	−	0.413949i
$261$	15.9698	+	10.3783i	0.988506	+	0.642401i
$262$		−	3.57791i		−	0.221044i
$263$	−2.07104	−	3.58715i	−0.127706	−	0.221193i	0.795082	−	0.606503i	$-0.207428\pi$
$263$	−2.07104	−	3.58715i	−0.127706	−	0.221193i	−0.922787	+	0.385310i	$0.874095\pi$
$264$	−4.17073	−	4.39647i	−0.256691	−	0.270584i
$265$	−6.46654	−	3.73346i	−0.397237	−	0.229345i
$266$	1.06287	+	0.613647i	0.0651686	+	0.0376251i
$267$	5.96112	+	24.8477i	0.364814	+	1.52065i
$268$	8.38627	−	4.84182i	0.512273	−	0.295761i
$269$	13.4826			0.822051			0.411025	−	0.911624i	$-0.365171\pi$
$269$	13.4826			0.822051			0.411025	+	0.911624i	$0.365171\pi$
$270$	−1.97338	+	1.68376i	−0.120096	+	0.102470i
$271$			21.0883i			1.28102i	0.767949	+	0.640511i	$0.221277\pi$
$271$			21.0883i			1.28102i	−0.767949	+	0.640511i	$0.778723\pi$
$272$	−10.9869	−	19.0299i	−0.666180	−	1.15386i
$273$	5.99620	+	1.74515i	0.362907	+	0.105622i
$274$	−0.804736	+	1.39384i	−0.0486159	+	0.0842052i
$275$	3.78137	+	2.18317i	0.228025	+	0.131650i
$276$	19.0203	+	20.0498i	1.14489	+	1.20685i
$277$	4.94102	+	8.55810i	0.296877	+	0.514207i	0.975420	−	0.220355i	$-0.0707214\pi$
$277$	4.94102	+	8.55810i	0.296877	+	0.514207i	−0.678543	+	0.734561i	$0.737388\pi$
$278$			1.25316i			0.0751595i
$279$	17.5950	+	0.927864i	1.05338	+	0.0555497i
$280$			1.96358i			0.117346i
$281$	−7.09160	+	4.09434i	−0.423049	+	0.244248i	−0.696381	−	0.717672i	$-0.745208\pi$
$281$	−7.09160	+	4.09434i	−0.423049	+	0.244248i	0.273332	+	0.961920i	$0.411874\pi$
$282$	−0.346923	+	1.17049i	−0.0206590	+	0.0697018i
$283$	16.2323	−	28.1152i	0.964913	−	1.67128i	0.255063	−	0.966924i	$-0.417904\pi$
$283$	16.2323	−	28.1152i	0.964913	−	1.67128i	0.709849	−	0.704354i	$-0.248763\pi$
$284$	5.42521	+	3.13225i	0.321927	+	0.185865i
$285$	4.51505	−	15.2335i	0.267449	−	0.902352i
$286$	−3.20726	+	0.0157888i	−0.189649	+	0.000933613i
$287$	12.1586			0.717699
$288$	8.88077	+	0.468324i	0.523305	+	0.0275962i
$289$	20.1804			1.18708
$290$	1.58471	+	2.74481i	0.0930576	+	0.161181i
$291$	−3.78439	+	3.59008i	−0.221845	+	0.210454i
$292$	−28.1498	−	16.2523i	−1.64734	−	0.951092i
$293$	−15.8762	−	9.16613i	−0.927498	−	0.535491i	−0.0414787	−	0.999139i	$-0.513207\pi$
$293$	−15.8762	−	9.16613i	−0.927498	−	0.535491i	−0.886019	+	0.463648i	$0.846540\pi$
$294$	−0.104428	−	0.435285i	−0.00609035	−	0.0253863i
$295$	−3.48533	−	6.03676i	−0.202924	−	0.351474i
$296$	−6.85904			−0.398674
$297$	5.97832	−	16.8561i	0.346897	−	0.978088i
$298$	−5.60032			−0.324418
$299$	29.7583	−	0.146495i	1.72096	−	0.00847204i
$300$	−4.13050	+	0.990935i	−0.238475	+	0.0572116i
$301$	1.72104	+	0.993644i	0.0991992	+	0.0572727i
$302$	0.786979	−	1.36309i	0.0452856	−	0.0784369i
$303$	7.26318	+	7.65629i	0.417259	+	0.439842i
$304$	−14.8205	+	8.55664i	−0.850016	+	0.490757i
$305$		−	20.0060i		−	1.14554i
$306$	−2.57614	+	3.96408i	−0.147268	+	0.226611i
$307$			33.3944i			1.90592i	0.303096	+	0.952960i	$0.401980\pi$
$307$			33.3944i			1.90592i	−0.303096	+	0.952960i	$0.598020\pi$
$308$	−3.32699	−	5.76251i	−0.189573	−	0.328350i
$309$	−8.46294	+	28.5533i	−0.481440	+	1.62434i
$310$	2.53924	+	1.46603i	0.144219	+	0.0832649i
$311$	−4.11163	+	7.12154i	−0.233149	+	0.403826i	−0.958733	−	0.284308i	$-0.908236\pi$
$311$	−4.11163	+	7.12154i	−0.233149	+	0.403826i	0.725584	+	0.688133i	$0.241570\pi$
$312$	4.58390	−	4.39161i	0.259512	−	0.248626i
$313$	2.82982	+	4.90139i	0.159951	+	0.277043i	0.934851	−	0.355041i	$-0.115533\pi$
$313$	2.82982	+	4.90139i	0.159951	+	0.277043i	−0.774900	+	0.632084i	$0.782200\pi$
$314$			5.24939i			0.296240i
$315$	−5.16430	+	2.62922i	−0.290975	+	0.148140i
$316$	−8.91383			−0.501442
$317$	−25.6139	+	14.7882i	−1.43862	+	0.830589i	−0.997754	−	0.0669829i	$-0.978663\pi$
$317$	−25.6139	+	14.7882i	−1.43862	+	0.830589i	−0.440868	+	0.897572i	$0.645329\pi$
$318$	1.25533	−	1.19088i	0.0703955	−	0.0667811i
$319$	−18.9240	−	10.9258i	−1.05954	−	0.611725i
$320$	−10.7756	−	6.22129i	−0.602374	−	0.347781i
$321$	−2.72804	+	0.654475i	−0.152264	+	0.0365292i
$322$	−1.06654	−	1.84729i	−0.0594357	−	0.102946i
$323$		−	28.9562i		−	1.61116i
$324$	7.06639	+	15.8993i	0.392577	+	0.883292i
$325$	−2.26743	+	3.97233i	−0.125774	+	0.220345i
$326$	−0.406169	−	0.703506i	−0.0224956	−	0.0389636i
$327$	5.08402	+	21.1917i	0.281147	+	1.17190i
$328$	6.17966	−	10.7035i	0.341215	−	0.591001i
$329$	−1.36363	+	2.36188i	−0.0751795	+	0.130215i
$330$	2.15921	−	2.04835i	0.118861	−	0.112758i
$331$	14.9283	−	8.61885i	0.820533	−	0.473735i	−0.0300675	−	0.999548i	$-0.509572\pi$
$331$	14.9283	−	8.61885i	0.820533	−	0.473735i	0.850600	+	0.525813i	$0.176239\pi$
$332$			16.7000i			0.916530i
$333$	−9.18422	−	18.0396i	−0.503292	−	0.988563i
$334$	1.95641			0.107050
$335$	4.83802	+	8.37969i	0.264329	+	0.457832i
$336$	5.98447	+	1.77374i	0.326480	+	0.0967656i
$337$	1.96094	−	3.39645i	0.106819	−	0.185016i	−0.807661	−	0.589647i	$-0.799267\pi$
$337$	1.96094	−	3.39645i	0.106819	−	0.185016i	0.914480	+	0.404631i	$0.132600\pi$
$338$	−0.0330783	−	3.35959i	−0.00179922	−	0.182738i
$339$	1.02019	−	3.44205i	0.0554092	−	0.186946i
$340$	19.7198	−	11.3853i	1.06946	−	0.617452i
$341$	−20.2150			−1.09470
$342$	3.08723	+	2.00630i	0.166939	+	0.108488i
$343$		−	1.00000i		−	0.0539949i
$344$	1.74946	−	1.01005i	0.0943243	−	0.0544582i
$345$	−20.0340	+	19.0054i	−1.07860	+	1.02322i
$346$	4.17112	+	2.40820i	0.224241	+	0.129465i
$347$	−2.26690	+	3.92638i	−0.121693	+	0.210779i	−0.920436	−	0.390894i	$-0.872166\pi$
$347$	−2.26690	+	3.92638i	−0.121693	+	0.210779i	0.798742	+	0.601673i	$0.205499\pi$
$348$	20.6712	−	4.95916i	1.10809	−	0.265839i
$349$	−5.41690	+	3.12745i	−0.289960	+	0.167408i	−0.637924	−	0.770100i	$-0.720207\pi$
$349$	−5.41690	+	3.12745i	−0.289960	+	0.167408i	0.347964	+	0.937508i	$0.386873\pi$
$350$	0.327854			0.0175245
$351$	17.6879	+	6.17550i	0.944112	+	0.329624i
$352$	−10.2032			−0.543831
$353$	4.94671	−	2.85598i	0.263287	−	0.152009i	−0.362546	−	0.931966i	$-0.618093\pi$
$353$	4.94671	−	2.85598i	0.263287	−	0.152009i	0.625833	+	0.779957i	$0.284759\pi$
$354$	1.57076	−	0.376835i	0.0834850	−	0.0200286i
$355$	−3.12979	+	5.42095i	−0.166112	+	0.287714i
$356$	24.6994	+	14.2602i	1.30906	+	0.755788i
$357$	−7.66208	+	7.26867i	−0.405520	+	0.384699i
$358$	−0.446442	+	0.257753i	−0.0235952	+	0.0136227i
$359$			23.3999i			1.23500i	0.786571	+	0.617499i	$0.211854\pi$
$359$			23.3999i			1.23500i	−0.786571	+	0.617499i	$0.788146\pi$
$360$	−0.310215	+	5.88257i	−0.0163498	+	0.310039i
$361$	−3.55114			−0.186902
$362$	−1.73567	+	1.00209i	−0.0912246	+	0.0526686i
$363$	−0.416857	+	1.40644i	−0.0218793	+	0.0738191i
$364$	6.01921	−	3.51481i	0.315492	−	0.184226i
$365$	16.2395	−	28.1277i	0.850015	−	1.47227i
$366$	4.44493	+	1.31744i	0.232340	+	0.0688635i
$367$	−13.5207	−	23.4186i	−0.705775	−	1.22244i	−0.966411	−	0.257001i	$-0.917266\pi$
$367$	−13.5207	−	23.4186i	−0.705775	−	1.22244i	0.260636	−	0.965437i	$-0.416068\pi$
$368$	29.7434			1.55048
$369$	36.4252	+	1.92087i	1.89622	+	0.0999963i
$370$		−	3.36864i		−	0.175127i
$371$	3.34761	−	1.93274i	0.173799	−	0.100343i
$372$	14.2672	−	13.5347i	0.739720	−	0.701739i
$373$	14.1465	−	24.5025i	0.732479	−	1.26869i	−0.223341	−	0.974740i	$-0.571696\pi$
$373$	14.1465	−	24.5025i	0.732479	−	1.26869i	0.955820	−	0.293951i	$-0.0949703\pi$
$374$	2.71203	−	4.69737i	0.140236	−	0.242895i
$375$	−4.89280	−	20.3946i	−0.252663	−	1.05317i
$376$	1.38615	+	2.40088i	0.0714850	+	0.123816i
$377$	11.3474	−	19.8796i	0.584421	−	1.02385i
$378$	−0.244080	−	1.32054i	−0.0125541	−	0.0679213i
$379$			27.0462i			1.38927i	0.719362	+	0.694635i	$0.244434\pi$
$379$			27.0462i			1.38927i	−0.719362	+	0.694635i	$0.755566\pi$
$380$	−8.86687	−	15.3579i	−0.454861	−	0.787842i
$381$	−26.4185	+	6.33796i	−1.35346	+	0.324703i
$382$	−0.0492971	−	0.0284617i	−0.00252226	−	0.00145623i
$383$	−8.83036	−	5.09821i	−0.451211	−	0.260507i	0.257131	−	0.966377i	$-0.417223\pi$
$383$	−8.83036	−	5.09821i	−0.451211	−	0.260507i	−0.708341	+	0.705870i	$0.750556\pi$
$384$	9.54177	−	9.05185i	0.486926	−	0.461925i
$385$	5.75799	−	3.32438i	0.293454	−	0.169426i
$386$	0.927414			0.0472042
$387$	4.99898	+	3.24869i	0.254113	+	0.165140i
$388$			5.82216i			0.295576i
$389$	6.03780	+	10.4578i	0.306128	+	0.530230i	0.977512	−	0.210880i	$-0.0676330\pi$
$389$	6.03780	+	10.4578i	0.306128	+	0.530230i	−0.671383	+	0.741110i	$0.734300\pi$
$390$	2.15682	+	2.25126i	0.109215	+	0.113997i
$391$	−25.1633	+	43.5841i	−1.27256	+	2.20414i
$392$	−0.880323	−	0.508255i	−0.0444630	−	0.0256707i
$393$	6.81407	−	22.9902i	0.343724	−	1.15970i
$394$	0.434300	+	0.752230i	0.0218797	+	0.0378968i
$395$		−	8.90683i		−	0.448151i
$396$	−9.05673	−	17.7892i	−0.455118	−	0.893939i
$397$			8.65938i			0.434602i	0.976105	+	0.217301i	$0.0697253\pi$
$397$			8.65938i			0.434602i	−0.976105	+	0.217301i	$0.930275\pi$
$398$	−1.08020	+	0.623656i	−0.0541457	+	0.0312610i
$399$	5.66086	+	5.96725i	0.283398	+	0.298736i
$400$	−2.28578	+	3.95909i	−0.114289	+	0.197955i
$401$	−14.9067	−	8.60637i	−0.744404	−	0.429782i	0.0792646	−	0.996854i	$-0.474743\pi$
$401$	−14.9067	−	8.60637i	−0.744404	−	0.429782i	−0.823668	+	0.567072i	$0.808076\pi$
$402$	−2.18039	+	0.523089i	−0.108748	+	0.0260893i
$403$	−0.104244	−	21.1757i	−0.00519279	−	1.05483i
$404$	11.7790			0.586025
$405$	−15.8868	+	7.06085i	−0.789421	+	0.350856i
$406$	−1.64075			−0.0814293
$407$	11.6125	+	20.1134i	0.575609	+	0.996984i
$408$	2.50449	+	10.4394i	0.123991	+	0.516830i
$409$	8.23301	+	4.75333i	0.407096	+	0.235037i	0.689541	−	0.724246i	$-0.257812\pi$
$409$	8.23301	+	4.75333i	0.407096	+	0.235037i	−0.282445	+	0.959283i	$0.591146\pi$
$410$	5.25674	+	3.03498i	0.259612	+	0.149887i
$411$	−7.82545	+	7.42365i	−0.386001	+	0.366182i
$412$	16.6199	+	28.7865i	0.818804	+	1.41821i
$413$	3.60858			0.177567
$414$	−2.90333	−	5.70269i	−0.142691	−	0.280272i
$415$	−16.6869			−0.819126
$416$	−0.0526156	−	10.6881i	−0.00257969	−	0.524025i
$417$	−2.38662	+	8.05227i	−0.116873	+	0.394321i
$418$	−3.65833	−	2.11214i	−0.178935	−	0.103308i
$419$	14.1720	−	24.5467i	0.692350	−	1.19919i	−0.278716	−	0.960374i	$-0.589909\pi$
$419$	14.1720	−	24.5467i	0.692350	−	1.19919i	0.971066	−	0.238812i	$-0.0767579\pi$
$420$	−1.83805	+	6.20144i	−0.0896876	+	0.302599i
$421$	−26.9653	+	15.5684i	−1.31421	+	0.758758i	−0.982790	−	0.184726i	$-0.940860\pi$
$421$	−26.9653	+	15.5684i	−1.31421	+	0.758758i	−0.331418	+	0.943484i	$0.607527\pi$
$422$		−	6.62375i		−	0.322439i
$423$	−4.45836	+	6.86038i	−0.216773	+	0.333563i
$424$		−	3.92930i		−	0.190824i
$425$	−3.86761	−	6.69889i	−0.187607	−	0.324944i
$426$	−0.998321	−	1.05235i	−0.0483688	−	0.0509867i
$427$	8.96921	+	5.17837i	0.434050	+	0.250599i
$428$	−1.56563	+	2.71176i	−0.0756778	+	0.131078i
$429$	−20.6385	−	6.00671i	−0.996438	−	0.290007i
$430$	0.496058	+	0.859198i	0.0239221	+	0.0414342i
$431$			5.23250i			0.252041i	0.992028	+	0.126020i	$0.0402205\pi$
$431$			5.23250i			0.252041i	−0.992028	+	0.126020i	$0.959780\pi$
$432$	17.6483	+	6.25929i	0.849103	+	0.301150i
$433$	17.0043			0.817173			0.408587	−	0.912720i	$-0.366022\pi$
$433$	17.0043			0.817173			0.408587	+	0.912720i	$0.366022\pi$
$434$	−1.31452	+	0.758936i	−0.0630988	+	0.0364301i
$435$	4.95527	+	20.6550i	0.237587	+	0.990332i
$436$	21.0652	+	12.1620i	1.00884	+	0.582454i
$437$	33.9434	+	19.5973i	1.62374	+	0.937464i
$438$	5.17999	+	5.46035i	0.247509	+	0.260905i
$439$	2.56555	+	4.44366i	0.122447	+	0.212084i	0.920732	−	0.390195i	$-0.127593\pi$
$439$	2.56555	+	4.44366i	0.122447	+	0.212084i	−0.798285	+	0.602280i	$0.794259\pi$
$440$		−	6.75852i		−	0.322200i
$441$	0.157984	−	2.99584i	0.00752306	−	0.142659i
$442$	4.93459	+	2.81669i	0.234715	+	0.133976i
$443$	4.28447	+	7.42091i	0.203561	+	0.352578i	0.949673	−	0.313242i	$-0.101415\pi$
$443$	4.28447	+	7.42091i	0.203561	+	0.352578i	−0.746112	+	0.665820i	$0.768082\pi$
$444$	−21.6624	−	6.42054i	−1.02805	−	0.304705i
$445$	−14.2490	+	24.6800i	−0.675467	+	1.16994i
$446$	0.160066	−	0.277242i	0.00757933	−	0.0131278i
$447$	−35.9853	−	10.6657i	−1.70205	−	0.504471i
$448$	5.57832	−	3.22064i	0.263551	−	0.152161i
$449$		−	10.2792i		−	0.485105i	−0.970138	−	0.242553i	$-0.922015\pi$
$449$		−	10.2792i		−	0.485105i	0.970138	−	0.242553i	$-0.0779847\pi$
$450$	0.982196	+	0.0517957i	0.0463012	+	0.00244167i
$451$	−41.8491			−1.97060
$452$	−2.00350	−	3.47016i	−0.0942366	−	0.163223i
$453$	7.65277	−	7.25984i	0.359558	−	0.341097i
$454$	−1.75995	+	3.04832i	−0.0825983	+	0.143065i
$455$	3.51205	+	6.01448i	0.164648	+	0.281963i
$456$	8.13027	−	1.95050i	0.380735	−	0.0913407i
$457$	8.45024	−	4.87875i	0.395285	−	0.228218i	−0.289162	−	0.957280i	$-0.593377\pi$
$457$	8.45024	−	4.87875i	0.395285	−	0.228218i	0.684448	+	0.729062i	$0.260043\pi$
$458$	−0.661790			−0.0309234
$459$	−24.1027	+	20.5653i	−1.12502	+	0.959905i
$460$			30.8217i			1.43707i
$461$	6.37671	−	3.68160i	0.296993	−	0.171469i	−0.344098	−	0.938934i	$-0.611815\pi$
$461$	6.37671	−	3.68160i	0.296993	−	0.171469i	0.641091	+	0.767465i	$0.278482\pi$
$462$	0.359433	+	1.49822i	0.0167224	+	0.0697037i
$463$	20.0590	+	11.5810i	0.932219	+	0.538217i	0.887513	−	0.460783i	$-0.152432\pi$
$463$	20.0590	+	11.5810i	0.932219	+	0.538217i	0.0447061	+	0.999000i	$0.485765\pi$
$464$	11.4393	−	19.8134i	0.531055	−	0.919814i
$465$	13.5240	+	14.2560i	0.627162	+	0.661107i
$466$	−2.60096	+	1.50166i	−0.120487	+	0.0695632i
$467$	8.31848			0.384933			0.192467	−	0.981303i	$-0.438351\pi$
$467$	8.31848			0.384933			0.192467	+	0.981303i	$0.438351\pi$
$468$	18.5879	−	9.57887i	0.859224	−	0.442783i
$469$	−5.00910			−0.231299
$470$	−1.17913	+	0.680769i	−0.0543890	+	0.0314015i
$471$	−9.99737	+	33.7304i	−0.460655	+	1.55421i
$472$	1.83408	−	3.17671i	0.0844202	−	0.146220i
$473$	−5.92372	−	3.42006i	−0.272373	−	0.157255i
$474$	1.97891	+	0.586532i	0.0908946	+	0.0269403i
$475$	−5.21712	+	3.01210i	−0.239378	+	0.138205i
$476$			11.7879i			0.540296i
$477$	10.3342	−	5.26131i	0.473172	−	0.240899i
$478$	−1.72023			−0.0786813
$479$	−17.0977	+	9.87138i	−0.781215	+	0.451035i	−0.836861	−	0.547416i	$-0.815612\pi$
$479$	−17.0977	+	9.87138i	−0.781215	+	0.451035i	0.0556457	+	0.998451i	$0.482278\pi$
$480$	6.82603	+	7.19548i	0.311564	+	0.328427i
$481$	−21.0094	+	12.2681i	−0.957945	+	0.559375i
$482$	−3.26413	+	5.65365i	−0.148677	+	0.257517i
$483$	−3.33497	−	13.9011i	−0.151746	−	0.632523i
$484$	0.818642	+	1.41793i	0.0372110	+	0.0644513i
$485$	−5.81759			−0.264163
$486$	−0.522600	−	3.99469i	−0.0237056	−	0.181203i
$487$		−	16.8765i		−	0.764749i	−0.924007	−	0.382375i	$-0.875106\pi$
$487$		−	16.8765i		−	0.764749i	0.924007	−	0.382375i	$-0.124894\pi$
$488$	9.11728	−	5.26387i	0.412720	−	0.238284i
$489$	−1.27006	−	5.29397i	−0.0574340	−	0.239402i
$490$	0.249616	−	0.432347i	0.0112765	−	0.0195315i
$491$	−10.9647	+	18.9913i	−0.494828	+	0.857067i	−0.999982	−	0.00596169i	$-0.998102\pi$
$491$	−10.9647	+	18.9913i	−0.494828	+	0.857067i	0.505154	+	0.863029i	$0.331436\pi$
$492$	29.5360	−	28.0195i	1.33159	−	1.26322i
$493$	19.3556	+	33.5248i	0.871731	+	1.50988i
$494$	2.19364	−	3.84307i	0.0986968	−	0.172908i
$495$	17.7752	−	9.04962i	0.798936	−	0.406750i
$496$		−	21.1651i		−	0.950340i
$497$	−1.62023	−	2.80633i	−0.0726774	−	0.125881i
$498$	1.09886	−	3.70748i	0.0492412	−	0.166136i
$499$	−17.1433	−	9.89768i	−0.767439	−	0.443081i	0.0645215	−	0.997916i	$-0.479448\pi$
$499$	−17.1433	−	9.89768i	−0.767439	−	0.443081i	−0.831960	+	0.554835i	$0.812781\pi$
$500$	−20.2729	−	11.7045i	−0.906630	−	0.523443i
$501$	12.5711	+	3.72595i	0.561634	+	0.166463i
$502$	−2.03747	+	1.17633i	−0.0909366	+	0.0525022i
$503$	−28.5879			−1.27467			−0.637335	−	0.770587i	$-0.719963\pi$
$503$	−28.5879			−1.27467			−0.637335	+	0.770587i	$0.719963\pi$
$504$	−2.55701	−	1.66173i	−0.113898	−	0.0740191i
$505$			11.7697i			0.523745i
$506$	3.67095	+	6.35827i	0.163194	+	0.282660i
$507$	6.18574	−	21.6503i	0.274718	−	0.961525i
$508$	−15.1617	+	26.2608i	−0.672690	+	1.16513i
$509$	−38.9102	−	22.4648i	−1.72466	−	0.995735i	−0.908462	−	0.417966i	$-0.862743\pi$
$509$	−38.9102	−	22.4648i	−1.72466	−	0.995735i	−0.816201	−	0.577768i	$-0.803924\pi$
$510$	−5.12706	+	1.23001i	−0.227030	+	0.0544659i
$511$	8.40690	+	14.5612i	0.371899	+	0.644148i
$512$		−	18.0091i		−	0.795898i
$513$	16.0163	+	18.7712i	0.707136	+	0.828770i
$514$		−	1.12258i		−	0.0495149i
$515$	−28.7639	+	16.6069i	−1.26749	+	0.731785i
$516$	6.47066	−	1.55235i	0.284855	−	0.0683385i
$517$	4.69354	−	8.12945i	0.206422	−	0.357533i
$518$	1.51024	+	0.871940i	0.0663563	+	0.0383108i
$519$	22.2155	+	23.4179i	0.975151	+	1.02793i
$520$	7.07971	−	0.0348523i	0.310466	−	0.00152837i
$521$	−19.1758			−0.840108			−0.420054	−	0.907499i	$-0.637989\pi$
$521$	−19.1758			−0.840108			−0.420054	+	0.907499i	$0.637989\pi$
$522$	−4.91543	−	0.259213i	−0.215143	−	0.0113455i
$523$	35.7614			1.56374			0.781869	−	0.623442i	$-0.214266\pi$
$523$	35.7614			1.56374			0.781869	+	0.623442i	$0.214266\pi$
$524$	−13.3818	−	23.1779i	−0.584585	−	1.01253i
$525$	2.10665	+	0.624391i	0.0919417	+	0.0272507i
$526$	0.927073	+	0.535246i	0.0404223	+	0.0233378i
$527$	31.0140	+	17.9060i	1.35099	+	0.779996i
$528$	−20.5982	−	6.10511i	−0.896420	−	0.265691i
$529$	−22.5606	−	39.0761i	−0.980895	−	1.69896i
$530$	1.92977			0.0838240
$531$	10.8107	+	0.570098i	0.469145	+	0.0247402i
$532$	9.18042			0.398022
$533$	−0.215807	−	43.8379i	−0.00934765	−	1.89883i
$534$	−4.54506	−	4.79106i	−0.196684	−	0.207329i
$535$	−2.70963	−	1.56441i	−0.117148	−	0.0676351i
$536$	−2.54590	+	4.40963i	−0.109966	+	0.190467i
$537$	−3.35953	+	0.805973i	−0.144974	+	0.0347803i
$538$	−3.01766	+	1.74225i	−0.130100	+	0.0751135i
$539$			3.44194i			0.148255i
$540$	−6.48623	+	18.2881i	−0.279123	+	0.786995i
$541$			7.12325i			0.306252i	0.988207	+	0.153126i	$0.0489341\pi$
$541$			7.12325i			0.306252i	−0.988207	+	0.153126i	$0.951066\pi$
$542$	−2.72506	−	4.71994i	−0.117051	−	0.202739i
$543$	−13.0611	+	3.13345i	−0.560506	+	0.134469i
$544$	15.6538	+	9.03773i	0.671152	+	0.387490i
$545$	−12.1525	+	21.0487i	−0.520554	+	0.901626i
$546$	−1.56757	+	0.384241i	−0.0670858	+	0.0164440i
$547$	−15.7879	−	27.3454i	−0.675041	−	1.16920i	−0.976457	−	0.215712i	$-0.930793\pi$
$547$	−15.7879	−	27.3454i	−0.675041	−	1.16920i	0.301416	−	0.953493i	$-0.402541\pi$
$548$			12.0392i			0.514289i
$549$	26.0522	+	16.9306i	1.11188	+	0.722579i
$550$	−1.12845			−0.0481173
$551$	26.1092	−	15.0742i	1.11229	−	0.642181i
$552$	−13.9325	−	4.12946i	−0.593007	−	0.175762i
$553$	3.99316	+	2.30545i	0.169806	+	0.0980378i
$554$	−2.21178	−	1.27697i	−0.0939696	−	0.0542533i
$555$	6.41550	−	21.6454i	0.272323	−	0.918797i
$556$	4.68695	+	8.11803i	0.198771	+	0.344281i
$557$			32.2616i			1.36697i	0.729966	+	0.683483i	$0.239536\pi$
$557$			32.2616i			1.36697i	−0.729966	+	0.683483i	$0.760464\pi$
$558$	−4.05797	+	2.06598i	−0.171788	+	0.0874597i
$559$	3.55204	−	6.22287i	0.150235	−	0.263199i
$560$	3.48062	+	6.02861i	0.147083	+	0.254755i
$561$	26.3724	−	25.0183i	1.11344	−	1.05627i
$562$	1.05815	−	1.83277i	0.0446354	−	0.0773109i
$563$	16.5256	−	28.6231i	0.696469	−	1.20632i	−0.273214	−	0.961953i	$-0.588087\pi$
$563$	16.5256	−	28.6231i	0.696469	−	1.20632i	0.969683	−	0.244366i	$-0.0785800\pi$
$564$	2.13038	+	8.88004i	0.0897052	+	0.373917i
$565$	3.46744	−	2.00193i	0.145876	−	0.0842216i
$566$			8.39027i			0.352669i
$567$	0.946590	−	8.95008i	0.0397530	−	0.375868i
$568$	−3.29396			−0.138212
$569$	−3.44096	−	5.95991i	−0.144252	−	0.249853i	0.784841	−	0.619697i	$-0.212744\pi$
$569$	−3.44096	−	5.95991i	−0.144252	−	0.249853i	−0.929094	+	0.369844i	$0.879411\pi$
$570$	0.957938	+	3.99296i	0.0401236	+	0.167247i
$571$	4.89983	−	8.48675i	0.205051	−	0.355159i	−0.745098	−	0.666955i	$-0.767597\pi$
$571$	4.89983	−	8.48675i	0.205051	−	0.355159i	0.950149	+	0.311796i	$0.100931\pi$
$572$	−20.7177	+	12.0978i	−0.866252	+	0.505833i
$573$	−0.262558	−	0.276768i	−0.0109685	−	0.0115622i
$574$	−2.72131	+	1.57115i	−0.113585	+	0.0655786i
$575$	10.4702			0.436639
$576$	17.2206	−	8.76724i	0.717523	−	0.365302i
$577$		−	15.2952i		−	0.636747i	−0.947965	−	0.318373i	$-0.896863\pi$
$577$		−	15.2952i		−	0.636747i	0.947965	−	0.318373i	$-0.103137\pi$
$578$	−4.51673	+	2.60774i	−0.187871	+	0.108468i
$579$	5.95917	+	1.76624i	0.247655	+	0.0734026i
$580$	20.5317	+	11.8540i	0.852533	+	0.492210i
$581$	4.31924	−	7.48114i	0.179192	−	0.310370i
$582$	0.383100	−	1.29255i	0.0158800	−	0.0535779i
$583$	−11.5223	+	6.65238i	−0.477203	+	0.275513i
$584$	17.0914			0.707246
$585$	9.57135	+	18.5733i	0.395727	+	0.767910i
$586$	4.73784			0.195719
$587$	12.2491	−	7.07204i	0.505576	−	0.291894i	−0.225437	−	0.974258i	$-0.572381\pi$
$587$	12.2491	−	7.07204i	0.505576	−	0.291894i	0.731013	+	0.682363i	$0.239048\pi$
$588$	−2.30450	−	2.42923i	−0.0950360	−	0.100180i
$589$	13.9452	−	24.1538i	0.574602	−	0.995240i
$590$	1.56016	+	0.900758i	0.0642307	+	0.0370836i
$591$	1.35802	+	5.66063i	0.0558615	+	0.232847i
$592$	−21.0587	+	12.1583i	−0.865508	+	0.499701i
$593$		−	0.188520i		−	0.00774161i	−0.999993	−	0.00387080i	$-0.998768\pi$
$593$		−	0.188520i		−	0.00774161i	0.999993	−	0.00387080i	$-0.00123212\pi$
$594$	0.840108	+	4.54522i	0.0344701	+	0.186493i
$595$	−11.7786			−0.482876
$596$	−36.2792	+	20.9458i	−1.48605	+	0.857973i
$597$	−8.12867	+	1.95012i	−0.332684	+	0.0798131i
$598$	−6.64151	+	3.87819i	−0.271591	+	0.158591i
$599$	−4.39585	+	7.61384i	−0.179610	+	0.311093i	−0.941747	−	0.336322i	$-0.890817\pi$
$599$	−4.39585	+	7.61384i	−0.179610	+	0.311093i	0.762137	+	0.647416i	$0.224150\pi$
$600$	1.62038	−	1.53718i	0.0661518	−	0.0627552i
$601$	−7.90667	−	13.6948i	−0.322520	−	0.558621i	0.658487	−	0.752592i	$-0.271197\pi$
$601$	−7.90667	−	13.6948i	−0.322520	−	0.558621i	−0.981007	+	0.193971i	$0.937863\pi$
$602$	−0.513600			−0.0209328
$603$	−15.0065	−	0.791359i	−0.611110	−	0.0322266i
$604$		−	11.7735i		−	0.479058i
$605$	−1.41682	+	0.817999i	−0.0576018	+	0.0332564i
$606$	−2.61499	−	0.775058i	−0.106227	−	0.0314846i
$607$	−11.3801	+	19.7110i	−0.461905	+	0.800043i	−0.999056	−	0.0434431i	$-0.986167\pi$
$607$	−11.3801	+	19.7110i	−0.461905	+	0.800043i	0.537151	+	0.843486i	$0.319501\pi$
$608$	7.03861	−	12.1912i	0.285453	−	0.494420i
$609$	−10.5428	−	3.12479i	−0.427215	−	0.126623i
$610$	2.58521	+	4.47771i	0.104672	+	0.181297i
$611$	8.53999	+	4.87467i	0.345491	+	0.197208i
$612$	−1.86230	+	35.3145i	−0.0752789	+	1.42751i
$613$		−	27.8844i		−	1.12624i	−0.826375	−	0.563121i	$-0.809601\pi$
$613$		−	27.8844i		−	1.12624i	0.826375	−	0.563121i	$-0.190399\pi$
$614$	−4.31528	−	7.47428i	−0.174150	−	0.301637i
$615$	27.9975	+	29.5128i	1.12897	+	1.19007i
$616$	3.03002	+	1.74938i	0.122083	+	0.0704845i
$617$	29.3947	+	16.9710i	1.18338	+	0.683227i	0.956795	−	0.290763i	$-0.0939091\pi$
$617$	29.3947	+	16.9710i	1.18338	+	0.683227i	0.226589	+	0.973990i	$0.427242\pi$
$618$	−1.79554	−	7.48434i	−0.0722273	−	0.301064i
$619$	0.181637	−	0.104868i	0.00730062	−	0.00421501i	−0.496345	−	0.868125i	$-0.665325\pi$
$619$	0.181637	−	0.104868i	0.00730062	−	0.00421501i	0.503646	+	0.863910i	$0.331992\pi$
$620$	21.9324			0.880827
$621$	−7.79487	−	42.1724i	−0.312797	−	1.69232i
$622$		−	2.12524i		−	0.0852144i
$623$	−7.37644	−	12.7764i	−0.295531	−	0.511874i
$624$	6.28902	−	21.6085i	0.251762	−	0.865034i
$625$	8.52393	−	14.7639i	0.340957	−	0.590555i
$626$	−1.26673	−	0.731346i	−0.0506287	−	0.0292305i
$627$	−19.4843	−	20.5389i	−0.778129	−	0.820244i
$628$	19.6333	+	34.0059i	0.783453	+	1.35698i
$629$		−	41.1442i		−	1.64053i
$630$	0.816112	−	1.25581i	0.0325147	−	0.0500325i
$631$			36.4409i			1.45069i	0.688386	+	0.725345i	$0.258320\pi$
$631$			36.4409i			1.45069i	−0.688386	+	0.725345i	$0.741680\pi$
$632$	4.05908	−	2.34351i	0.161462	−	0.0932199i
$633$	12.6148	−	42.5614i	0.501393	−	1.69166i
$634$	3.82191	−	6.61974i	0.151787	−	0.262904i
$635$	−26.2402	−	15.1498i	−1.04131	−	0.601200i
$636$	3.67810	−	12.4096i	0.145846	−	0.492074i
$637$	−3.60551	+	0.0177493i	−0.142855	+	0.000703255i
$638$	5.64737			0.223582
$639$	−4.41060	−	8.66327i	−0.174481	−	0.342714i
$640$	14.6682			0.579811
$641$	−10.8403	−	18.7759i	−0.428165	−	0.741603i	0.568545	−	0.822652i	$-0.307506\pi$
$641$	−10.8403	−	18.7759i	−0.428165	−	0.741603i	−0.996710	+	0.0810487i	$0.974173\pi$
$642$	0.526013	−	0.499005i	0.0207601	−	0.0196941i
$643$	8.60281	+	4.96683i	0.339262	+	0.195873i	0.659945	−	0.751314i	$-0.270579\pi$
$643$	8.60281	+	4.96683i	0.339262	+	0.195873i	−0.320684	+	0.947186i	$0.603913\pi$
$644$	−13.8182	−	7.97792i	−0.544512	−	0.314374i
$645$	1.55113	+	6.46558i	0.0610758	+	0.254582i
$646$	3.74176	+	6.48092i	0.147218	+	0.254988i
$647$	−0.588921			−0.0231529			−0.0115764	−	0.999933i	$-0.503685\pi$
$647$	−0.588921			−0.0231529			−0.0115764	+	0.999933i	$0.503685\pi$
$648$	−7.39785	−	5.38223i	−0.290615	−	0.211434i
$649$	−12.4205			−0.487547
$650$	−0.00581919	−	1.18208i	−0.000228247	−	0.0463650i
$651$	−9.89190	+	2.37313i	−0.387694	+	0.0930103i
$652$	−5.26237	−	3.03823i	−0.206090	−	0.118986i
$653$	−6.71413	+	11.6292i	−0.262744	+	0.455086i	−0.966970	−	0.254890i	$-0.917961\pi$
$653$	−6.71413	+	11.6292i	−0.262744	+	0.455086i	0.704226	+	0.709976i	$0.251294\pi$
$654$	−3.87632	−	4.08612i	−0.151576	−	0.159780i
$655$	23.1597	−	13.3713i	0.904925	−	0.522459i
$656$		−	43.8160i		−	1.71073i
$657$	22.8853	+	44.9511i	0.892839	+	1.75371i
$658$		−	0.704843i		−	0.0274776i
$659$	23.4932	+	40.6914i	0.915164	+	1.58511i	0.806661	+	0.591014i	$0.201272\pi$
$659$	23.4932	+	40.6914i	0.915164	+	1.58511i	0.108503	+	0.994096i	$0.465394\pi$
$660$	6.32645	−	21.3450i	0.246257	−	0.830851i
$661$	33.3048	+	19.2285i	1.29541	+	0.747903i	0.979607	−	0.200923i	$-0.0643942\pi$
$661$	33.3048	+	19.2285i	1.29541	+	0.747903i	0.315799	+	0.948826i	$0.397728\pi$
$662$	−2.22748	+	3.85811i	−0.0865735	+	0.149950i
$663$	26.3433	+	27.4967i	1.02309	+	1.06788i
$664$	−4.39055	−	7.60465i	−0.170386	−	0.295118i
$665$			9.17322i			0.355722i
$666$	4.38669	+	2.85079i	0.169981	+	0.110466i
$667$	−52.3986			−2.02888
$668$	12.6737	−	7.31719i	0.490362	−	0.283111i
$669$	1.55652	−	1.47660i	0.0601784	−	0.0570886i
$670$	−2.16567	−	1.25035i	−0.0836672	−	0.0483053i
$671$	−30.8714	−	17.8236i	−1.19178	−	0.688074i
$672$	−4.99277	+	1.19780i	−0.192600	+	0.0462061i
$673$	12.8786	+	22.3064i	0.496433	+	0.859848i	0.999992	−	0.00411342i	$-0.00130935\pi$
$673$	12.8786	+	22.3064i	0.496433	+	0.859848i	−0.503558	+	0.863961i	$0.667976\pi$
$674$			1.01358i			0.0390417i
$675$	6.21253	+	2.20339i	0.239121	+	0.0848086i
$676$	−12.7795	−	21.6399i	−0.491520	−	0.832304i
$677$	−2.99900	−	5.19443i	−0.115261	−	0.199638i	0.802623	−	0.596487i	$-0.203437\pi$
$677$	−2.99900	−	5.19443i	−0.115261	−	0.199638i	−0.917884	+	0.396849i	$0.870104\pi$
$678$	0.216449	+	0.902224i	0.00831268	+	0.0346497i
$679$	1.50583	−	2.60817i	0.0577885	−	0.100093i
$680$	−5.98654	+	10.3690i	−0.229573	+	0.397633i
$681$	−17.1141	+	16.2354i	−0.655815	+	0.622142i
$682$	4.52448	−	2.61221i	0.173251	−	0.100027i
$683$			36.8753i			1.41099i	0.708713	+	0.705497i	$0.249276\pi$
$683$			36.8753i			1.41099i	−0.708713	+	0.705497i	$0.750724\pi$
$684$	27.5031	+	1.45036i	1.05161	+	0.0554560i
$685$	−12.0297			−0.459633
$686$	0.129221	+	0.223818i	0.00493370	+	0.00854541i
$687$	−4.25238	−	1.26037i	−0.162239	−	0.0480860i
$688$	3.58080	−	6.20213i	0.136517	−	0.236454i
$689$	−7.02794	−	12.0355i	−0.267743	−	0.458517i
$690$	2.02808	−	6.84258i	0.0772075	−	0.260492i
$691$	−9.14528	+	5.28003i	−0.347903	+	0.200862i	−0.663761	−	0.747944i	$-0.731041\pi$
$691$	−9.14528	+	5.28003i	−0.347903	+	0.200862i	0.315858	+	0.948806i	$0.397708\pi$
$692$	36.0276			1.36956
$693$	−0.543772	+	10.3115i	−0.0206562	+	0.391701i
$694$		−	1.17173i		−	0.0444781i
$695$	−8.11166	+	4.68327i	−0.307693	+	0.177647i
$696$	−8.10924	+	7.69287i	−0.307380	+	0.291598i
$697$	64.2053	+	37.0690i	2.43195	+	1.40409i
$698$	0.808266	−	1.39996i	0.0305933	−	0.0529892i
$699$	−19.5725	+	4.69558i	−0.740302	+	0.177603i
$700$	2.12385	−	1.22621i	0.0802741	−	0.0463463i
$701$	−46.9116			−1.77183			−0.885913	−	0.463852i	$-0.846467\pi$
$701$	−46.9116			−1.77183			−0.885913	+	0.463852i	$0.846467\pi$
$702$	−4.75689	+	0.903472i	−0.179537	+	0.0340993i
$703$	−32.0432			−1.20853
$704$	−19.2002	+	11.0853i	−0.723636	+	0.417791i
$705$	−8.87307	+	2.12871i	−0.334179	+	0.0801718i
$706$	−0.738108	+	1.27844i	−0.0277791	+	0.0481148i
$707$	−5.27666	−	3.04648i	−0.198449	−	0.114575i
$708$	8.76606	−	8.31597i	0.329449	−	0.312533i
$709$	−7.54679	+	4.35714i	−0.283426	+	0.163636i	−0.634973	−	0.772534i	$-0.718989\pi$
$709$	−7.54679	+	4.35714i	−0.283426	+	0.163636i	0.351548	+	0.936170i	$0.385656\pi$
$710$		−	1.61774i		−	0.0607128i
$711$	11.5986	+	7.53761i	0.434983	+	0.282683i
$712$	−14.9964			−0.562015
$713$	−41.9800	+	24.2372i	−1.57216	+	0.907688i
$714$	0.775644	−	2.61697i	0.0290278	−	0.0979375i
$715$	−12.0883	−	20.7015i	−0.452076	−	0.774191i
$716$	−1.92805	+	3.33948i	−0.0720545	+	0.124802i
$717$	−11.0534	−	3.27614i	−0.412798	−	0.122350i
$718$	−3.02377	−	5.23732i	−0.112846	−	0.195455i
$719$	−19.5540			−0.729242			−0.364621	−	0.931156i	$-0.618801\pi$
$719$	−19.5540			−0.729242			−0.364621	+	0.931156i	$0.618801\pi$
$720$	9.47495	+	18.6106i	0.353110	+	0.693577i
$721$		−	17.1941i		−	0.640342i
$722$	0.794810	−	0.458884i	0.0295798	−	0.0170779i
$723$	−31.7412	+	30.1115i	−1.18047	+	1.11986i
$724$	−7.49583	+	12.9832i	−0.278580	+	0.482515i
$725$	4.02684	−	6.97469i	0.149553	−	0.259034i
$726$	−0.0884425	−	0.368654i	−0.00328241	−	0.0136820i
$727$	−17.2609	−	29.8967i	−0.640171	−	1.10881i	−0.985394	−	0.170288i	$-0.945530\pi$
$727$	−17.2609	−	29.8967i	−0.640171	−	1.10881i	0.345224	−	0.938520i	$-0.387803\pi$
$728$	−1.81689	+	3.18303i	−0.0673385	+	0.117971i
$729$	4.24980	−	26.6634i	0.157400	−	0.987535i
$730$			8.39398i			0.310675i
$731$	6.05882	+	10.4942i	0.224093	+	0.388141i
$732$	33.7218	−	8.09008i	1.24639	−	0.299018i
$733$	−33.5273	−	19.3570i	−1.23836	−	0.714967i	−0.269600	−	0.962972i	$-0.586892\pi$
$733$	−33.5273	−	19.3570i	−1.23836	−	0.714967i	−0.968759	+	0.248005i	$0.920225\pi$
$734$	6.05236	+	3.49433i	0.223397	+	0.128978i
$735$	2.42732	−	2.30269i	0.0895331	−	0.0849360i
$736$	−21.1887	+	12.2333i	−0.781026	+	0.450925i
$737$	17.2410			0.635081
$738$	−8.40083	+	4.27699i	−0.309239	+	0.157438i
$739$			9.31654i			0.342714i	0.985209	+	0.171357i	$0.0548152\pi$
$739$			9.31654i			0.342714i	−0.985209	+	0.171357i	$0.945185\pi$
$740$	−12.5991	−	21.8222i	−0.463150	−	0.802200i
$741$	21.4145	−	20.5162i	0.786681	−	0.753681i
$742$	−0.499504	+	0.865166i	−0.0183374	+	0.0317612i
$743$	4.08990	+	2.36130i	0.150044	+	0.0866278i	0.573142	−	0.819456i	$-0.305724\pi$
$743$	4.08990	+	2.36130i	0.150044	+	0.0866278i	−0.423098	+	0.906084i	$0.639058\pi$
$744$	−2.93848	+	9.91422i	−0.107730	+	0.363473i
$745$	−20.9294	−	36.2507i	−0.766792	−	1.32812i
$746$			7.31214i			0.267716i
$747$	14.1216	−	21.7299i	0.516684	−	0.795056i
$748$		−	40.5731i		−	1.48350i
$749$	1.40272	−	0.809864i	0.0512544	−	0.0295918i
$750$	3.73052	+	3.93243i	0.136219	+	0.143592i
$751$	−4.48720	+	7.77207i	−0.163740	+	0.283607i	−0.936207	−	0.351448i	$-0.885689\pi$
$751$	−4.48720	+	7.77207i	−0.163740	+	0.283607i	0.772467	+	0.635055i	$0.219023\pi$
$752$	8.51152	+	4.91413i	0.310383	+	0.179200i
$753$	−15.3322	+	3.67829i	−0.558736	+	0.134044i
$754$	0.0291223	+	5.91575i	0.00106057	+	0.215439i
$755$	11.7643			0.428147
$756$	−6.52013	−	7.64165i	−0.237135	−	0.277924i
$757$	−40.5523			−1.47390			−0.736948	−	0.675949i	$-0.763734\pi$
$757$	−40.5523			−1.47390			−0.736948	+	0.675949i	$0.763734\pi$
$758$	−3.49495	−	6.05343i	−0.126942	−	0.219870i
$759$	11.4788	+	47.8468i	0.416652	+	1.73673i
$760$	8.07539	+	4.66233i	0.292925	+	0.169121i
$761$	15.1457	+	8.74437i	0.549031	+	0.316983i	0.748731	−	0.662874i	$-0.230663\pi$
$761$	15.1457	+	8.74437i	0.549031	+	0.316983i	−0.199700	+	0.979857i	$0.563997\pi$
$762$	5.09393	−	4.83238i	0.184534	−	0.175059i
$763$	−6.29110	−	10.8965i	−0.227753	−	0.394480i
$764$	−0.425799			−0.0154049
$765$	−35.2868	−	1.86084i	−1.27580	−	0.0672786i
$766$	2.63519			0.0952134
$767$	−0.0640499	−	13.0108i	−0.00231271	−	0.469791i
$768$	5.37487	−	18.1344i	0.193949	−	0.654369i
$769$	−3.42010	−	1.97459i	−0.123332	−	0.0712057i	0.437065	−	0.899430i	$-0.356018\pi$
$769$	−3.42010	−	1.97459i	−0.123332	−	0.0712057i	−0.560397	+	0.828224i	$0.689351\pi$
$770$	−0.859162	+	1.48811i	−0.0309620	+	0.0536278i
$771$	2.13794	−	7.21323i	0.0769959	−	0.259778i
$772$	6.00784	−	3.46863i	0.216227	−	0.124839i
$773$		−	12.0771i		−	0.434383i	−0.976129	−	0.217192i	$-0.930310\pi$
$773$		−	12.0771i		−	0.434383i	0.976129	−	0.217192i	$-0.0696896\pi$
$774$	−1.53866	−	0.0811408i	−0.0553061	−	0.00291654i
$775$		−	7.45051i		−	0.267630i
$776$	−1.53069	−	2.65123i	−0.0549486	−	0.0951737i
$777$	8.04360	+	8.47895i	0.288562	+	0.304181i
$778$	−2.70274	−	1.56043i	−0.0968978	−	0.0559440i
$779$	28.8694	−	50.0033i	1.03435	−	1.79155i
$780$	22.3920	+	6.51703i	0.801761	+	0.233347i
$781$	5.57674	+	9.65920i	0.199551	+	0.345633i
$782$		−	13.0066i		−	0.465114i
$783$	−31.0908	−	11.0269i	−1.11110	−	0.394071i
$784$	−3.60370			−0.128704
$785$	−33.9792	+	19.6179i	−1.21277	+	0.700192i
$786$	1.44571	+	6.02614i	0.0515667	+	0.214945i
$787$	−46.6394	−	26.9273i	−1.66251	−	0.959853i	−0.971509	−	0.237004i	$-0.923834\pi$
$787$	−46.6394	−	26.9273i	−1.66251	−	0.959853i	−0.691006	−	0.722849i	$-0.742832\pi$
$788$	5.62684	+	3.24866i	0.200448	+	0.115729i
$789$	4.93761	+	5.20486i	0.175784	+	0.185298i
$790$	1.15095	+	1.99351i	0.0409491	+	0.0709259i
$791$			2.07272i			0.0736974i
$792$	8.80106	+	5.71955i	0.312732	+	0.203235i
$793$	18.5115	−	32.4305i	0.657362	−	1.15164i
$794$	−1.11898	−	1.93813i	−0.0397110	−	0.0687815i
$795$	12.3999	+	3.67522i	0.439779	+	0.130346i
$796$	−4.66508	+	8.08015i	−0.165349	+	0.286393i
$797$	3.66955	−	6.35584i	0.129982	−	0.225136i	−0.793687	−	0.608326i	$-0.791841\pi$
$797$	3.66955	−	6.35584i	0.129982	−	0.225136i	0.923669	+	0.383190i	$0.125175\pi$
$798$	−2.03810	−	0.604074i	−0.0721480	−	0.0213840i
$799$	−14.4017	+	8.31485i	−0.509497	+	0.294158i
$800$		−	3.76052i		−	0.132955i
$801$	−20.0801	−	39.4413i	−0.709497	−	1.39359i
$802$	4.44851			0.157082
$803$	−28.9360	−	50.1186i	−1.02113	−	1.76865i
$804$	−12.1683	+	11.5435i	−0.429141	+	0.407107i
$805$	7.97165	−	13.8073i	0.280964	−	0.486644i
$806$	2.75968	+	4.72603i	0.0972056	+	0.166467i
$807$	−22.7083	+	5.44786i	−0.799369	+	0.191774i
$808$	−5.36377	+	3.09678i	−0.188697	+	0.108944i
$809$	−5.77487			−0.203034			−0.101517	−	0.994834i	$-0.532370\pi$
$809$	−5.77487			−0.203034			−0.101517	+	0.994834i	$0.532370\pi$
$810$	2.64334	−	3.63326i	0.0928774	−	0.127660i
$811$			39.2371i			1.37780i	0.724855	+	0.688901i	$0.241907\pi$
$811$			39.2371i			1.37780i	−0.724855	+	0.688901i	$0.758093\pi$
$812$	−10.6289	+	6.13659i	−0.373001	+	0.215352i
$813$	−8.52103	−	35.5181i	−0.298846	−	1.24568i
$814$	−5.19817	−	3.00116i	−0.182196	−	0.105191i
$815$	3.03585	−	5.25824i	0.106341	−	0.184188i
$816$	26.1942	+	27.6119i	0.916979	+	0.966609i
$817$	8.17289	−	4.71862i	0.285933	−	0.165084i
$818$	−2.45693			−0.0859045
$819$	−10.8043	−	0.516439i	−0.377533	−	0.0180458i
$820$	45.4045			1.58560
$821$	−1.68295	+	0.971650i	−0.0587352	+	0.0339108i	−0.529080	−	0.848572i	$-0.677463\pi$
$821$	−1.68295	+	0.971650i	−0.0587352	+	0.0339108i	0.470345	+	0.882483i	$0.344130\pi$
$822$	0.792182	−	2.67276i	0.0276305	−	0.0932233i
$823$	19.0681	−	33.0269i	0.664672	−	1.15125i	−0.314702	−	0.949190i	$-0.601905\pi$
$823$	19.0681	−	33.0269i	0.664672	−	1.15125i	0.979374	−	0.202055i	$-0.0647620\pi$
$824$	−15.1364	−	8.73899i	−0.527301	−	0.304437i
$825$	−7.25095	−	2.14912i	−0.252446	−	0.0748226i
$826$	−0.807665	+	0.466306i	−0.0281023	+	0.0162249i
$827$			8.26190i			0.287294i	0.989629	+	0.143647i	$0.0458830\pi$
$827$			8.26190i			0.287294i	−0.989629	+	0.143647i	$0.954117\pi$
$828$	−40.1366	−	26.0836i	−1.39484	−	0.906467i
$829$	−18.4945			−0.642341			−0.321171	−	0.947021i	$-0.604076\pi$
$829$	−18.4945			−0.642341			−0.321171	+	0.947021i	$0.604076\pi$
$830$	3.73482	−	2.15630i	0.129638	−	0.0748463i
$831$	−11.7800	−	12.4176i	−0.408643	−	0.430761i
$832$	−11.7111	−	20.0555i	−0.406008	−	0.695300i
$833$	3.04879	−	5.28065i	0.105634	−	0.182964i
$834$	−0.506357	−	2.11065i	−0.0175337	−	0.0730857i
$835$	7.31145	+	12.6638i	0.253023	+	0.438249i
$836$	−31.5984			−1.09285
$837$	−30.0094	+	5.54675i	−1.03728	+	0.191724i
$838$			7.32533i			0.253049i
$839$	−19.9625	+	11.5254i	−0.689184	+	0.397900i	−0.803306	−	0.595566i	$-0.796928\pi$
$839$	−19.9625	+	11.5254i	−0.689184	+	0.397900i	0.114122	+	0.993467i	$0.463594\pi$
$840$	−0.793414	−	3.30718i	−0.0273754	−	0.114109i
$841$	−5.65245	+	9.79033i	−0.194912	+	0.337598i
$842$	4.02355	−	6.96899i	0.138661	−	0.240167i
$843$	10.2897	−	9.76139i	0.354397	−	0.336200i
$844$	−24.7735	−	42.9090i	−0.852740	−	1.47699i
$845$	21.6229	−	12.7695i	0.743851	−	0.439284i
$846$	0.111354	−	2.11159i	0.00382843	−	0.0725981i
$847$		−	0.846926i		−	0.0291007i
$848$	−6.96504	−	12.0638i	−0.239180	−	0.414272i
$849$	−15.9791	+	53.9123i	−0.548402	+	1.85027i
$850$	1.73128	+	0.999556i	0.0593825	+	0.0342845i
$851$	48.2307	+	27.8460i	1.65333	+	0.954549i
$852$	−10.4031	−	3.08338i	−0.356404	−	0.105635i
$853$	−4.22449	+	2.43901i	−0.144644	+	0.0835101i	−0.570575	−	0.821245i	$-0.693280\pi$
$853$	−4.22449	+	2.43901i	−0.144644	+	0.0835101i	0.425932	+	0.904755i	$0.359946\pi$
$854$	−2.67663			−0.0915923
$855$	−1.44922	+	27.4815i	−0.0495624	+	0.939846i
$856$		−	1.64647i		−	0.0562751i
$857$	23.7916	+	41.2083i	0.812707	+	1.40765i	0.910963	+	0.412489i	$0.135340\pi$
$857$	23.7916	+	41.2083i	0.812707	+	1.40765i	−0.0982553	+	0.995161i	$0.531326\pi$
$858$	5.39548	−	1.32253i	0.184199	−	0.0451505i
$859$	10.1436	−	17.5692i	0.346094	−	0.599452i	−0.639458	−	0.768826i	$-0.720841\pi$
$859$	10.1436	−	17.5692i	0.346094	−	0.599452i	0.985552	+	0.169374i	$0.0541746\pi$
$860$	6.42699	+	3.71062i	0.219158	+	0.126531i
$861$	−20.4782	+	4.91286i	−0.697896	+	0.167430i
$862$	−0.676151	−	1.17113i	−0.0230298	−	0.0398888i
$863$		−	32.7125i		−	1.11355i	−0.830664	−	0.556774i	$-0.812039\pi$
$863$		−	32.7125i		−	1.11355i	0.830664	−	0.556774i	$-0.187961\pi$
$864$	−15.1468	+	2.79963i	−0.515303	+	0.0952453i
$865$			35.9994i			1.22401i
$866$	−3.80586	+	2.19732i	−0.129329	+	0.0746679i
$867$	−33.9890	+	8.15418i	−1.15433	+	0.276930i
$868$	−5.67700	+	9.83285i	−0.192690	+	0.333749i
$869$	−13.7442	−	7.93522i	−0.466240	−	0.269184i
$870$	−3.77815	−	3.98264i	−0.128091	−	0.135024i
$871$	0.0889083	+	18.0604i	0.00301254	+	0.611952i
$872$	−12.7899			−0.433122
$873$	4.92327	−	7.57577i	0.166628	−	0.256401i
$874$	−10.1295			−0.342637
$875$	6.05447	+	10.4867i	0.204678	+	0.354513i
$876$	53.9785	+	15.9987i	1.82376	+	0.540547i
$877$	−11.4576	−	6.61505i	−0.386895	−	0.223374i	0.293919	−	0.955830i	$-0.405041\pi$
$877$	−11.4576	−	6.61505i	−0.386895	−	0.223374i	−0.680814	+	0.732456i	$0.738374\pi$
$878$	−1.14843	−	0.663047i	−0.0387577	−	0.0223768i
$879$	30.4434	+	9.02314i	1.02683	+	0.304343i
$880$	−11.9801	−	20.7501i	−0.403848	−	0.699486i
$881$	1.28236			0.0432039			0.0216019	−	0.999767i	$-0.493123\pi$
$881$	1.28236			0.0432039			0.0216019	+	0.999767i	$0.493123\pi$
$882$	0.351767	+	0.690938i	0.0118446	+	0.0232651i
$883$	9.71689			0.327000			0.163500	−	0.986543i	$-0.447722\pi$
$883$	9.71689			0.327000			0.163500	+	0.986543i	$0.447722\pi$
$884$	42.5013	−	0.209227i	1.42947	−	0.00703706i
$885$	8.30944	+	8.75918i	0.279319	+	0.294437i
$886$	−1.91788	−	1.10729i	−0.0644325	−	0.0372001i
$887$	3.62152	−	6.27265i	0.121599	−	0.210615i	−0.798800	−	0.601597i	$-0.794531\pi$
$887$	3.62152	−	6.27265i	0.121599	−	0.210615i	0.920398	+	0.390982i	$0.127865\pi$
$888$	11.5524	−	2.77150i	0.387673	−	0.0930054i
$889$	13.5840	−	7.84275i	0.455594	−	0.263037i
$890$		−	7.36510i		−	0.246879i
$891$	−3.25810	+	30.8056i	−0.109151	+	1.03203i
$892$		−	2.39465i		−	0.0801789i
$893$	6.47563	+	11.2161i	0.216699	+	0.375333i
$894$	9.43240	−	2.26289i	0.315467	−	0.0756825i
$895$	−3.33686	−	1.92653i	−0.111539	−	0.0643970i
$896$	−3.79672	+	6.57612i	−0.126840	+	0.219693i
$897$	−50.0614	+	12.2710i	−1.67150	+	0.409717i
$898$	1.32829	+	2.30067i	0.0443257	+	0.0767744i
$899$			37.2863i			1.24357i
$900$	6.55644	−	3.33798i	0.218548	−	0.111266i
$901$	23.5701			0.785233
$902$	9.36659	−	5.40780i	0.311873	−	0.180060i
$903$	−3.30018	−	0.978142i	−0.109823	−	0.0325505i
$904$	1.82466	+	1.05347i	0.0606874	+	0.0350379i
$905$	−12.9730	−	7.48994i	−0.431236	−	0.248974i
$906$	−0.774702	+	2.61378i	−0.0257377	+	0.0868372i
$907$	15.2639	+	26.4378i	0.506828	+	0.877852i	0.999969	+	0.00790224i	$0.00251539\pi$
$907$	15.2639	+	26.4378i	0.506828	+	0.877852i	−0.493141	+	0.869949i	$0.664151\pi$
$908$			26.3295i			0.873776i
$909$	−15.3267	−	9.96039i	−0.508355	−	0.330365i
$910$	−1.56326	−	0.892318i	−0.0518216	−	0.0295800i
$911$	1.48687	+	2.57534i	0.0492623	+	0.0853248i	0.889605	−	0.456731i	$-0.150980\pi$
$911$	1.48687	+	2.57534i	0.0492623	+	0.0853248i	−0.840343	+	0.542055i	$0.817646\pi$
$912$	21.5042	−	20.4001i	0.712076	−	0.675514i
$913$	−14.8666	+	25.7496i	−0.492011	+	0.852188i
$914$	−1.26088	+	2.18390i	−0.0417061	+	0.0722371i
$915$	8.08373	+	33.6954i	0.267240	+	1.11393i
$916$	−4.28711	+	2.47516i	−0.141650	+	0.0817817i
$917$			13.8441i			0.457173i
$918$	2.73714	−	7.71746i	0.0903392	−	0.254714i
$919$	−27.1150			−0.894443			−0.447221	−	0.894423i	$-0.647586\pi$
$919$	−27.1150			−0.894443			−0.447221	+	0.894423i	$0.647586\pi$
$920$	−8.10326	−	14.0353i	−0.267157	−	0.462729i
$921$	−13.4935	−	56.2449i	−0.444626	−	1.85333i
$922$	−0.951482	+	1.64802i	−0.0313354	+	0.0542745i
$923$	−10.0895	+	5.89157i	−0.332099	+	0.193924i
$924$	7.93194	+	8.36125i	0.260942	+	0.275065i
$925$	−7.41307	+	4.27994i	−0.243740	+	0.140724i
$926$	−5.98608			−0.196715
$927$	2.71640	−	51.5108i	0.0892182	−	1.69184i
$928$			18.8196i			0.617785i
$929$	30.3720	−	17.5353i	0.996474	−	0.575315i	0.0892711	−	0.996007i	$-0.471546\pi$
$929$	30.3720	−	17.5353i	0.996474	−	0.575315i	0.907203	+	0.420693i	$0.138213\pi$
$930$	−4.86911	−	1.44316i	−0.159664	−	0.0473230i
$931$	−4.11259	−	2.37440i	−0.134785	−	0.0778179i
$932$	−11.2328	+	19.4557i	−0.367941	+	0.637293i
$933$	4.04748	−	13.6559i	0.132509	−	0.447074i
$934$	−1.86183	+	1.07493i	−0.0609208	+	0.0351727i
$935$	40.5413			1.32584
$936$	−5.94598	+	9.24881i	−0.194350	+	0.302307i
$937$	1.25208			0.0409036			0.0204518	−	0.999791i	$-0.493490\pi$
$937$	1.25208			0.0409036			0.0204518	+	0.999791i	$0.493490\pi$
$938$	1.12113	−	0.647284i	0.0366061	−	0.0211346i
$939$	−6.74663	−	7.11178i	−0.220168	−	0.232084i
$940$	−5.09229	+	8.82011i	−0.166092	+	0.287680i
$941$	45.0257	+	25.9956i	1.46780	+	0.847433i	0.999350	−	0.0360591i	$-0.0114804\pi$
$941$	45.0257	+	25.9956i	1.46780	+	0.847433i	0.468447	+	0.883492i	$0.344814\pi$
$942$	−2.12110	−	8.84134i	−0.0691090	−	0.288067i
$943$	−86.9071	+	50.1758i	−2.83008	+	1.63395i
$944$		−	13.0043i		−	0.423252i
$945$	7.63565	−	6.51501i	0.248388	−	0.211933i
$946$	1.76778			0.0574755
$947$	−9.14767	+	5.28141i	−0.297259	+	0.171623i	−0.641211	−	0.767365i	$-0.721568\pi$
$947$	−9.14767	+	5.28141i	−0.297259	+	0.171623i	0.343952	+	0.938987i	$0.388234\pi$
$948$	15.0132	−	3.60176i	0.487606	−	0.116980i
$949$	52.3512	−	30.5696i	1.69939	−	0.992331i
$950$	0.778457	−	1.34833i	0.0252565	−	0.0437455i
$951$	37.1651	−	35.2569i	1.20516	−	1.14328i
$952$	−3.09912	−	5.36783i	−0.100443	−	0.173972i
$953$	−19.8711			−0.643688			−0.321844	−	0.946793i	$-0.604303\pi$
$953$	−19.8711			−0.643688			−0.321844	+	0.946793i	$0.604303\pi$
$954$	−1.63311	+	2.51298i	−0.0528740	+	0.0813608i
$955$		−	0.425465i		−	0.0137677i
$956$	−11.1437	+	6.43383i	−0.360413	+	0.208085i
$957$	36.2876	+	10.7553i	1.17301	+	0.347670i
$958$	2.55119	−	4.41879i	0.0824251	−	0.142764i
$959$	3.11379	−	5.39324i	0.100549	−	0.174157i
$960$	20.6627	+	6.12423i	0.666885	+	0.197659i
$961$	1.74690	+	3.02572i	0.0563517	+	0.0976040i
$962$	3.11698	−	5.46067i	0.100495	−	0.176059i
$963$	4.33028	−	2.20461i	0.139541	−	0.0710426i
$964$			48.8328i			1.57280i
$965$	3.46591	+	6.00312i	0.111571	+	0.193247i
$966$	2.54275	+	2.68038i	0.0818117	+	0.0862397i
$967$	−39.6559	−	22.8954i	−1.27525	−	0.736265i	−0.299278	−	0.954166i	$-0.596746\pi$
$967$	−39.6559	−	22.8954i	−1.27525	−	0.736265i	−0.975971	+	0.217901i	$0.930079\pi$
$968$	−0.745568	−	0.430454i	−0.0239635	−	0.0138353i
$969$	11.7002	+	48.7697i	0.375864	+	1.56671i
$970$	1.30208	−	0.751758i	0.0418074	−	0.0241375i
$971$	9.76398			0.313341			0.156671	−	0.987651i	$-0.449924\pi$
$971$	9.76398			0.313341			0.156671	+	0.987651i	$0.449924\pi$
$972$	−18.3260	−	23.9232i	−0.587806	−	0.767337i
$973$		−	4.84888i		−	0.155448i
$974$	2.18081	+	3.77728i	0.0698777	+	0.121032i
$975$	2.21386	−	7.60662i	0.0709001	−	0.243607i
$976$	18.6613	−	32.3224i	0.597335	−	1.03461i
$977$	−24.3218	−	14.0422i	−0.778122	−	0.449249i	0.0576422	−	0.998337i	$-0.481642\pi$
$977$	−24.3218	−	14.0422i	−0.778122	−	0.449249i	−0.835764	+	0.549088i	$0.814975\pi$
$978$	0.968356	+	1.02077i	0.0309646	+	0.0326406i
$979$	25.3892	+	43.9754i	0.811443	+	1.40546i
$980$		−	3.73436i		−	0.119290i
$981$	−17.1256	−	33.6381i	−0.546780	−	1.07398i
$982$		−	5.66748i		−	0.180856i
$983$	−10.1571	+	5.86418i	−0.323960	+	0.187038i	−0.653156	−	0.757223i	$-0.726556\pi$
$983$	−10.1571	+	5.86418i	−0.323960	+	0.187038i	0.329196	+	0.944261i	$0.393222\pi$
$984$	−6.08326	+	20.5244i	−0.193927	+	0.654295i
$985$	−3.24611	+	5.62242i	−0.103430	+	0.179145i
$986$	−8.66425	−	5.00231i	−0.275926	−	0.159306i
$987$	1.34236	−	4.52902i	0.0427278	−	0.144160i
$988$	−0.162947	−	33.1001i	−0.00518402	−	1.05305i
$989$	−16.4022			−0.521559
$990$	−2.80901	+	4.32241i	−0.0892761	+	0.137375i
$991$	39.0712			1.24114			0.620569	−	0.784152i	$-0.286902\pi$
$991$	39.0712			1.24114			0.620569	+	0.784152i	$0.286902\pi$
$992$	8.70509	+	15.0777i	0.276387	+	0.478716i
$993$	−21.6605	+	20.5484i	−0.687376	+	0.652083i
$994$	0.725275	+	0.418738i	0.0230043	+	0.0132816i
$995$	−8.07381	−	4.66141i	−0.255957	−	0.147777i
$996$	−6.74787	−	28.1271i	−0.213814	−	0.891241i
$997$	5.22665	+	9.05283i	0.165530	+	0.286706i	0.936843	−	0.349749i	$-0.113733\pi$
$997$	5.22665	+	9.05283i	0.165530	+	0.286706i	−0.771313	+	0.636455i	$0.780400\pi$
$998$	5.11597			0.161943
$999$	22.7578	+	26.6723i	0.720024	+	0.843875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dt.a.337.39	✓	168
9.7	even	3	inner	819.2.dt.a.610.46	yes	168
13.12	even	2	inner	819.2.dt.a.337.46	yes	168
117.25	even	6	inner	819.2.dt.a.610.39	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.dt.a.337.39	✓	168	1.1	even	1	trivial
819.2.dt.a.337.46	yes	168	13.12	even	2	inner
819.2.dt.a.610.39	yes	168	117.25	even	6	inner
819.2.dt.a.610.46	yes	168	9.7	even	3	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.223818 + 0.129221i) q^{2} +(-1.68426 + 0.404065i) q^{3} +(-0.966604 + 1.67421i) q^{4} +(-1.67289 - 0.965845i) q^{5} +(0.324754 - 0.308080i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.01651i q^{8} +(2.67346 - 1.36110i) q^{9} +O(q^{10})\)	\(q+(-0.223818 + 0.129221i) q^{2} +(-1.68426 + 0.404065i) q^{3} +(-0.966604 + 1.67421i) q^{4} +(-1.67289 - 0.965845i) q^{5} +(0.324754 - 0.308080i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.01651i q^{8} +(2.67346 - 1.36110i) q^{9} +0.499232 q^{10} +(-2.98080 + 1.72097i) q^{11} +(0.951524 - 3.21037i) q^{12} +(-1.81813 - 3.11359i) q^{13} +(-0.129221 + 0.223818i) q^{14} +(3.20785 + 0.950777i) q^{15} +(-1.80185 - 3.12090i) q^{16} +6.09757 q^{17} +(-0.422486 + 0.650108i) q^{18} -4.74880i q^{19} +(3.23405 - 1.86718i) q^{20} +(-1.25658 + 1.19206i) q^{21} +(0.444772 - 0.770368i) q^{22} +(-4.12678 + 7.14779i) q^{23} +(0.410736 + 1.71207i) q^{24} +(-0.634287 - 1.09862i) q^{25} +(0.809271 + 0.461936i) q^{26} +(-3.95283 + 3.37270i) q^{27} +1.93321i q^{28} +(3.17431 + 5.49806i) q^{29} +(-0.840836 + 0.201722i) q^{30} +(5.08629 + 2.93657i) q^{31} +(2.56722 + 1.48219i) q^{32} +(4.32507 - 4.10300i) q^{33} +(-1.36475 + 0.787937i) q^{34} -1.93169 q^{35} +(-0.305416 + 5.79157i) q^{36} -6.74764i q^{37} +(0.613647 + 1.06287i) q^{38} +(4.32029 + 4.50945i) q^{39} +(-0.981791 + 1.70051i) q^{40} +(10.5297 + 6.07930i) q^{41} +(0.127205 - 0.429182i) q^{42} +(0.993644 + 1.72104i) q^{43} -6.65398i q^{44} +(-5.78703 - 0.305176i) q^{45} -2.13307i q^{46} +(-2.36188 + 1.36363i) q^{47} +(4.29583 + 4.52834i) q^{48} +(0.500000 - 0.866025i) q^{49} +(0.283930 + 0.163927i) q^{50} +(-10.2699 + 2.46381i) q^{51} +(6.97019 - 0.0343132i) q^{52} +3.86549 q^{53} +(0.448891 - 1.26566i) q^{54} +6.64875 q^{55} +(-0.508255 - 0.880323i) q^{56} +(1.91882 + 7.99822i) q^{57} +(-1.42093 - 0.820377i) q^{58} +(3.12512 + 1.80429i) q^{59} +(-4.69252 + 4.45158i) q^{60} +(5.17837 + 8.96921i) q^{61} -1.51787 q^{62} +(1.63474 - 2.51548i) q^{63} +6.44129 q^{64} +(0.0342862 + 6.96472i) q^{65} +(-0.437833 + 1.47722i) q^{66} +(-4.33801 - 2.50455i) q^{67} +(-5.89393 + 10.2086i) q^{68} +(4.06240 - 13.7062i) q^{69} +(0.432347 - 0.249616i) q^{70} -3.24047i q^{71} +(-1.38357 - 2.71760i) q^{72} +16.8138i q^{73} +(0.871940 + 1.51024i) q^{74} +(1.51222 + 1.59406i) q^{75} +(7.95048 + 4.59021i) q^{76} +(-1.72097 + 2.98080i) q^{77} +(-1.54968 - 0.451023i) q^{78} +(2.30545 + 3.99316i) q^{79} +6.96124i q^{80} +(5.29481 - 7.27770i) q^{81} -3.14230 q^{82} +(7.48114 - 4.31924i) q^{83} +(-0.781141 - 3.25602i) q^{84} +(-10.2006 - 5.88931i) q^{85} +(-0.444791 - 0.256800i) q^{86} +(-7.56793 - 7.97754i) q^{87} +(1.74938 + 3.03002i) q^{88} -14.7529i q^{89} +(1.33468 - 0.679504i) q^{90} +(-3.13134 - 1.78738i) q^{91} +(-7.97792 - 13.8182i) q^{92} +(-9.75320 - 2.89076i) q^{93} +(0.352421 - 0.610412i) q^{94} +(-4.58661 + 7.94424i) q^{95} +(-4.92277 - 1.45906i) q^{96} +(2.60817 - 1.50583i) q^{97} +0.258443i q^{98} +(-5.62666 + 8.65812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 84 q^{4} - 8 q^{9}+O(q^{10}) \) 168 * q + 84 * q^4 - 8 * q^9	\( 168 q + 84 q^{4} - 8 q^{9} - 24 q^{12} + 8 q^{14} - 84 q^{16} - 32 q^{23} + 84 q^{25} - 8 q^{26} + 48 q^{27} + 4 q^{29} + 80 q^{30} - 32 q^{35} + 4 q^{36} + 24 q^{38} + 24 q^{39} + 4 q^{48} + 84 q^{49} + 64 q^{51} + 18 q^{52} - 48 q^{53} - 24 q^{56} + 24 q^{62} - 240 q^{64} - 22 q^{65} - 132 q^{66} - 156 q^{68} - 52 q^{69} + 84 q^{74} - 60 q^{75} - 16 q^{77} - 148 q^{78} + 12 q^{79} - 8 q^{81} - 24 q^{82} + 88 q^{87} + 24 q^{88} - 164 q^{90} + 12 q^{91} + 128 q^{92} - 60 q^{94} - 96 q^{95}+O(q^{100}) \) 168 * q + 84 * q^4 - 8 * q^9 - 24 * q^12 + 8 * q^14 - 84 * q^16 - 32 * q^23 + 84 * q^25 - 8 * q^26 + 48 * q^27 + 4 * q^29 + 80 * q^30 - 32 * q^35 + 4 * q^36 + 24 * q^38 + 24 * q^39 + 4 * q^48 + 84 * q^49 + 64 * q^51 + 18 * q^52 - 48 * q^53 - 24 * q^56 + 24 * q^62 - 240 * q^64 - 22 * q^65 - 132 * q^66 - 156 * q^68 - 52 * q^69 + 84 * q^74 - 60 * q^75 - 16 * q^77 - 148 * q^78 + 12 * q^79 - 8 * q^81 - 24 * q^82 + 88 * q^87 + 24 * q^88 - 164 * q^90 + 12 * q^91 + 128 * q^92 - 60 * q^94 - 96 * q^95

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