LMFDB - Embedded newform 819.2.dt.a.337.46

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			337.46
Character	$\chi$	$=$	819.337
Dual form			819.2.dt.a.610.46

$q$-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} +(3.60551 + 0.0177493i) 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} +(-6.07978 + 1.42696i) 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} +(-3.51481 + 6.01921i) 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} +(6.01448 + 3.51205i) 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} +(-1.17637 + 1.10502i) 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	−0.418777	−	0.908089i	$-0.637541\pi$
$2$	0.223818	−	0.129221i	0.158263	−	0.0913734i	0.577040	+	0.816716i	$0.304208\pi$
$3$	−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	0.825022	−	0.565101i	$-0.191163\pi$
$5$	1.67289	+	0.965845i	0.748140	+	0.431939i	−0.0768812	+	0.997040i	$0.524496\pi$
$6$	−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	0.0219531	−	0.999759i	$-0.493012\pi$
$11$	2.98080	−	1.72097i	0.898746	−	0.518891i	0.876793	+	0.480868i	$0.159678\pi$
$12$	0.951524	−	3.21037i	0.274681	−	0.926754i
$13$	3.60551	+	0.0177493i	0.999988	+	0.00492278i
$13$	3.60551	+	0.0177493i	0.999988	+	0.00492278i
$14$	−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	$0.183366\pi$
$19$			4.74880i			1.08945i	−0.838615	+	0.544725i	$0.816634\pi$
$20$	−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	−0.0319612	−	0.999489i	$-0.510175\pi$
$31$	−5.08629	−	2.93657i	−0.913525	−	0.527424i	−0.881564	+	0.472065i	$0.843509\pi$
$32$	−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	$0.187149\pi$
$37$			6.74764i			1.10931i	−0.832082	+	0.554653i	$0.812851\pi$
$38$	0.613647	+	1.06287i	0.0995467	+	0.172420i
$39$	−6.07978	+	1.42696i	−0.973545	+	0.228497i
$40$	−0.981791	+	1.70051i	−0.155235	+	0.268874i
$41$	−10.5297	−	6.07930i	−1.64446	−	0.949427i	−0.979222	−	0.202792i	$-0.934999\pi$
$41$	−10.5297	−	6.07930i	−1.64446	−	0.949427i	−0.665234	−	0.746635i	$-0.731668\pi$
$42$	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	−0.317751	−	0.948174i	$-0.602928\pi$
$47$	2.36188	−	1.36363i	0.344516	−	0.198906i	0.662267	+	0.749268i	$0.269594\pi$
$48$	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
$52$	−3.51481	+	6.01921i	−0.487417	+	0.834714i
$53$	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	0.282582	−	0.959243i	$-0.408809\pi$
$59$	−3.12512	−	1.80429i	−0.406856	−	0.234898i	−0.689438	+	0.724345i	$0.742142\pi$
$60$	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
$65$	6.01448	+	3.51205i	0.746005	+	0.435617i
$66$	−0.437833	+	1.47722i	−0.0538935	+	0.181833i
$67$	4.33801	+	2.50455i	0.529972	+	0.305980i	0.741005	−	0.671499i	$-0.234349\pi$
$67$	4.33801	+	2.50455i	0.529972	+	0.305980i	−0.211033	+	0.977479i	$0.567683\pi$
$68$	−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	$0.0615902\pi$
$71$			3.24047i			0.384573i	−0.981339	+	0.192286i	$0.938410\pi$
$72$	1.38357	+	2.71760i	0.163055	+	0.320272i
$73$		−	16.8138i		−	1.96791i	−0.178429	−	0.983953i	$-0.557101\pi$
$73$		−	16.8138i		−	1.96791i	0.178429	−	0.983953i	$-0.442899\pi$
$74$	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
$78$	−1.17637	+	1.10502i	−0.133198	+	0.125119i
$79$	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	−0.850817	−	0.525462i	$-0.823893\pi$
$83$	−7.48114	+	4.31924i	−0.821162	+	0.474098i	0.0296549	+	0.999560i	$0.490559\pi$
$84$	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	$0.285750\pi$
$89$			14.7529i			1.56380i	−0.623403	+	0.781901i	$0.714250\pi$
$90$	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	−0.626531	−	0.779396i	$-0.715526\pi$
$97$	−2.60817	+	1.50583i	−0.264820	+	0.152894i	0.361711	+	0.932290i	$0.382193\pi$
$98$		−	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	$-0.154983\pi$
$104$	−0.0180424	+	3.66503i	−0.00176920	+	0.359386i
$105$	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	$0.205860\pi$
$109$			12.5822i			1.20516i	−0.798060	+	0.602578i	$0.794140\pi$
$110$	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
$117$	9.66335	−	4.86001i	0.893377	−	0.449308i
$118$	−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
$130$	1.79998	+	0.00886103i	0.157869	+	0.000777164i
$131$	−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	−0.712370	−	0.701804i	$-0.752378\pi$
$137$	−5.39324	+	3.11379i	−0.460776	+	0.266029i	0.251595	+	0.967833i	$0.419045\pi$
$138$	−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	$-0.985693\pi$
$149$	−18.7663	−	10.8347i	−1.53740	−	0.887616i	−0.538407	−	0.842685i	$-0.680974\pi$
$150$	0.544448	+	0.161369i	0.0444540	+	0.0131758i
$151$	5.27423	−	3.04508i	0.429211	−	0.247805i	−0.269800	−	0.962917i	$-0.586957\pi$
$151$	5.27423	−	3.04508i	0.429211	−	0.247805i	0.699010	+	0.715111i	$0.253624\pi$
$152$	−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
$156$	3.48771	−	11.5581i	0.279240	−	0.925390i
$157$	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	$-0.960717\pi$
$163$		−	3.14320i		−	0.246195i	0.992395	−	0.123097i	$-0.0392827\pi$
$164$	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	0.731725	−	0.681600i	$-0.238716\pi$
$167$	6.55581	+	3.78500i	0.507304	+	0.292892i	−0.224421	+	0.974492i	$0.572049\pi$
$168$	1.21174	+	1.27732i	0.0934878	+	0.0985478i
$169$	12.9994	+	0.127991i	0.999952	+	0.00984545i
$170$	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	$0.406941\pi$
$182$	−0.469882	+	0.804684i	−0.0348299	+	0.0596472i
$183$	−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	0.607661	−	0.794196i	$-0.292108\pi$
$193$	3.10771	+	1.79423i	0.223698	+	0.129152i	−0.383964	+	0.923348i	$0.625441\pi$
$194$	−0.389171	+	0.674064i	−0.0279409	+	0.0483950i
$195$	−11.5491	−	3.48497i	−0.827045	−	0.249564i
$196$	0.966604	+	1.67421i	0.0690431	+	0.119586i
$197$			3.36090i			0.239454i	0.992807	+	0.119727i	$0.0382020\pi$
$197$			3.36090i			0.239454i	−0.992807	+	0.119727i	$0.961798\pi$
$198$	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
$221$	21.9848	+	0.108228i	1.47886	+	0.00728020i
$222$	−2.07881	−	2.19132i	−0.139521	−	0.147072i
$223$	1.07274	−	0.619347i	0.0718360	−	0.0414745i	−0.463652	−	0.886018i	$-0.653461\pi$
$223$	1.07274	−	0.619347i	0.0718360	−	0.0414745i	0.535488	+	0.844543i	$0.320128\pi$
$224$	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	−0.837442	−	0.546526i	$-0.815950\pi$
$227$	−11.7949	+	6.80981i	−0.782857	+	0.451983i	0.0545849	+	0.998509i	$0.482616\pi$
$228$	15.2454	+	4.51860i	1.00965	+	0.299252i
$229$	−2.21762	−	1.28034i	−0.146544	−	0.0846073i	0.424935	−	0.905224i	$-0.360297\pi$
$229$	−2.21762	−	1.28034i	−0.146544	−	0.0846073i	−0.571479	+	0.820616i	$0.693630\pi$
$230$	−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	$0.375699\pi$
$234$	1.53482	−	2.33647i	0.100334	−	0.152740i
$235$	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	0.301844	−	0.953357i	$-0.402398\pi$
$239$	−5.76436	−	3.32806i	−0.372866	−	0.215274i	−0.674710	+	0.738083i	$0.735731\pi$
$240$	2.81279	+	11.7245i	0.181565	+	0.756816i
$241$	−21.8758	+	12.6300i	−1.40914	+	0.813570i	−0.995306	−	0.0967801i	$-0.969146\pi$
$241$	−21.8758	+	12.6300i	−1.40914	+	0.813570i	−0.413839	+	0.910350i	$0.635812\pi$
$242$		−	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
$247$	−0.0842882	+	17.1218i	−0.00536313	+	1.08944i
$248$	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	$-0.778723\pi$
$271$		−	21.0883i		−	1.28102i	0.767949	−	0.640511i	$-0.221277\pi$
$272$	−10.9869	−	19.0299i	−0.666180	−	1.15386i
$273$	4.55177	−	4.27568i	0.275485	−	0.258776i
$274$	−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	−0.273332	−	0.961920i	$-0.588126\pi$
$281$	7.09160	−	4.09434i	0.423049	−	0.244248i	0.696381	+	0.717672i	$0.254792\pi$
$282$	−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
$286$	1.61730	−	2.76967i	0.0956331	−	0.163774i
$287$	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	0.886019	−	0.463648i	$-0.153460\pi$
$293$	15.8762	+	9.16613i	0.927498	+	0.535491i	0.0414787	+	0.999139i	$0.486793\pi$
$294$	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
$299$	−15.0060	+	25.6982i	−0.867819	+	1.48616i
$300$	−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	$-0.598020\pi$
$307$		−	33.3944i		−	1.90592i	0.303096	−	0.952960i	$-0.401980\pi$
$308$	−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	$0.241570\pi$
$312$	−1.45052	−	6.18016i	−0.0821197	−	0.349883i
$313$	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	0.440868	−	0.897572i	$-0.354671\pi$
$317$	25.6139	−	14.7882i	1.43862	−	0.830589i	0.997754	+	0.0669829i	$0.0213373\pi$
$318$	−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	−0.850600	−	0.525813i	$-0.823761\pi$
$331$	−14.9283	+	8.61885i	−0.820533	+	0.473735i	0.0300675	+	0.999548i	$0.490428\pi$
$332$		−	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	$0.132600\pi$
$338$	2.92603	−	1.65115i	0.159155	−	0.0898108i
$339$	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	−0.347964	−	0.937508i	$-0.613127\pi$
$349$	5.41690	−	3.12745i	0.289960	−	0.167408i	0.637924	+	0.770100i	$0.279793\pi$
$350$	0.327854			0.0175245
$351$	−14.3118	+	12.0901i	−0.763909	+	0.645324i
$352$	−10.2032			−0.543831
$353$	−4.94671	+	2.85598i	−0.263287	+	0.152009i	−0.625833	−	0.779957i	$-0.715241\pi$
$353$	−4.94671	+	2.85598i	−0.263287	+	0.152009i	0.362546	+	0.931966i	$0.381907\pi$
$354$	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	$-0.788146\pi$
$359$		−	23.3999i		−	1.23500i	0.786571	−	0.617499i	$-0.211854\pi$
$360$	−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
$364$	0.0343132	−	6.97019i	0.00179850	−	0.365337i
$365$	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	$-0.755566\pi$
$379$		−	27.0462i		−	1.38927i	0.719362	−	0.694635i	$-0.244434\pi$
$380$	−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	0.708341	−	0.705870i	$-0.249444\pi$
$383$	8.83036	+	5.09821i	0.451211	+	0.260507i	−0.257131	+	0.966377i	$0.582777\pi$
$384$	−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	$0.734300\pi$
$390$	−3.03522	+	0.712386i	−0.153694	+	0.0360730i
$391$	−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	$-0.930275\pi$
$397$		−	8.65938i		−	0.434602i	0.976105	−	0.217301i	$-0.0697253\pi$
$398$	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	0.823668	−	0.567072i	$-0.191924\pi$
$401$	14.9067	+	8.60637i	0.744404	+	0.429782i	−0.0792646	+	0.996854i	$0.525257\pi$
$402$	−2.18039	+	0.523089i	−0.108748	+	0.0260893i
$403$	−18.2865	−	10.6781i	−0.910917	−	0.531914i
$404$	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	0.282445	−	0.959283i	$-0.408854\pi$
$409$	−8.23301	−	4.75333i	−0.407096	−	0.235037i	−0.689541	+	0.724246i	$0.742188\pi$
$410$	−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
$416$	−9.22982	−	5.38960i	−0.452529	−	0.264247i
$417$	−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	0.331418	−	0.943484i	$-0.392473\pi$
$421$	26.9653	−	15.5684i	1.31421	−	0.758758i	0.982790	+	0.184726i	$0.0591396\pi$
$422$			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
$429$	−15.6669	+	14.7166i	−0.756404	+	0.710525i
$430$	0.496058	+	0.859198i	0.0239221	+	0.0414342i
$431$		−	5.23250i		−	0.252041i	−0.992028	−	0.126020i	$-0.959780\pi$
$431$		−	5.23250i		−	0.252041i	0.992028	−	0.126020i	$-0.0402205\pi$
$432$	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	$0.0779847\pi$
$449$			10.2792i			0.485105i	−0.970138	+	0.242553i	$0.922015\pi$
$450$	−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
$455$	−6.96472	−	0.0342862i	−0.326511	−	0.00160736i
$456$	8.13027	−	1.95050i	0.380735	−	0.0913407i
$457$	−8.45024	+	4.87875i	−0.395285	+	0.228218i	−0.684448	−	0.729062i	$-0.739957\pi$
$457$	−8.45024	+	4.87875i	−0.395285	+	0.228218i	0.289162	+	0.957280i	$0.406623\pi$
$458$	−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	−0.641091	−	0.767465i	$-0.721518\pi$
$461$	−6.37671	+	3.68160i	−0.296993	+	0.171469i	0.344098	+	0.938934i	$0.388185\pi$
$462$	−0.359433	−	1.49822i	−0.0167224	−	0.0697037i
$463$	−20.0590	−	11.5810i	−0.932219	−	0.538217i	−0.0447061	−	0.999000i	$-0.514235\pi$
$463$	−20.0590	−	11.5810i	−0.932219	−	0.538217i	−0.887513	+	0.460783i	$0.847568\pi$
$464$	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	$0.438351\pi$
$468$	−1.20398	+	20.8761i	−0.0556539	+	0.965000i
$469$	−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	−0.0556457	−	0.998451i	$-0.517722\pi$
$479$	17.0977	−	9.87138i	0.781215	−	0.451035i	0.836861	+	0.547416i	$0.184388\pi$
$480$	6.82603	+	7.19548i	0.311564	+	0.328427i
$481$	−0.119766	+	24.3287i	−0.00546087	+	1.10929i
$482$	−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	$0.124894\pi$
$487$			16.8765i			0.764749i	−0.924007	+	0.382375i	$0.875106\pi$
$488$	−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	0.831960	−	0.554835i	$-0.187219\pi$
$499$	17.1433	+	9.89768i	0.767439	+	0.443081i	−0.0645215	+	0.997916i	$0.520552\pi$
$500$	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
$507$	−21.9460	+	5.03702i	−0.974658	+	0.223702i
$508$	−15.1617	+	26.2608i	−0.672690	+	1.16513i
$509$	38.9102	+	22.4648i	1.72466	+	0.995735i	0.908462	+	0.417966i	$0.137257\pi$
$509$	38.9102	+	22.4648i	1.72466	+	0.995735i	0.816201	+	0.577768i	$0.196076\pi$
$510$	−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
$520$	−3.57004	+	6.11378i	−0.156556	+	0.268107i
$521$	−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
$533$	−37.8568	−	22.1059i	−1.63976	−	0.957511i
$534$	−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	$-0.951066\pi$
$541$		−	7.12325i		−	0.306252i	0.988207	−	0.153126i	$-0.0489341\pi$
$542$	−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
$546$	0.466258	−	1.54516i	0.0199540	−	0.0661267i
$547$	−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	$-0.760464\pi$
$557$		−	32.2616i		−	1.36697i	0.729966	−	0.683483i	$-0.239536\pi$
$558$	−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	$0.100931\pi$
$572$	−0.118104	+	23.9910i	−0.00493817	+	1.00311i
$573$	−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	$0.103137\pi$
$577$			15.2952i			0.636747i	−0.947965	+	0.318373i	$0.896863\pi$
$578$	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
$585$	20.8598	+	1.20303i	0.862445	+	0.0497393i
$586$	4.73784			0.195719
$587$	−12.2491	+	7.07204i	−0.505576	+	0.291894i	−0.731013	−	0.682363i	$-0.760952\pi$
$587$	−12.2491	+	7.07204i	−0.505576	+	0.291894i	0.225437	+	0.974258i	$0.427619\pi$
$588$	−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	$0.00123212\pi$
$593$			0.188520i			0.00774161i	−0.999993	+	0.00387080i	$0.998768\pi$
$594$	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
$598$	−0.0378606	+	7.69081i	−0.00154824	+	0.314501i
$599$	−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	$0.190399\pi$
$613$			27.8844i			1.12624i	−0.826375	+	0.563121i	$0.809601\pi$
$614$	−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	−0.226589	−	0.973990i	$-0.572758\pi$
$617$	−29.3947	−	16.9710i	−1.18338	−	0.683227i	−0.956795	+	0.290763i	$0.906091\pi$
$618$	1.79554	+	7.48434i	0.0722273	+	0.301064i
$619$	−0.181637	+	0.104868i	−0.00730062	+	0.00421501i	−0.503646	−	0.863910i	$-0.668008\pi$
$619$	−0.181637	+	0.104868i	−0.00730062	+	0.00421501i	0.496345	+	0.868125i	$0.334675\pi$
$620$	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
$624$	15.4083	+	16.4032i	0.616825	+	0.656654i
$625$	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	$-0.741680\pi$
$631$		−	36.4409i		−	1.45069i	0.688386	−	0.725345i	$-0.258320\pi$
$632$	−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
$637$	1.81813	−	3.11359i	0.0720367	−	0.123365i
$638$	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	0.320684	−	0.947186i	$-0.396087\pi$
$643$	−8.60281	−	4.96683i	−0.339262	−	0.195873i	−0.659945	+	0.751314i	$0.729421\pi$
$644$	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
$650$	−1.02080	−	0.596079i	−0.0400391	−	0.0233801i
$651$	−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	−0.315799	−	0.948826i	$-0.602272\pi$
$661$	−33.3048	−	19.2285i	−1.29541	−	0.747903i	−0.979607	+	0.200923i	$0.935606\pi$
$662$	−2.22748	+	3.85811i	−0.0865735	+	0.149950i
$663$	−37.0719	+	8.70102i	−1.43975	+	0.337919i
$664$	−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	$-0.750724\pi$
$683$		−	36.8753i		−	1.41099i	0.708713	−	0.705497i	$-0.249276\pi$
$684$	−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
$689$	13.9370	+	0.0686099i	0.530959	+	0.00261383i
$690$	2.02808	−	6.84258i	0.0772075	−	0.260492i
$691$	9.14528	−	5.28003i	0.347903	−	0.200862i	−0.315858	−	0.948806i	$-0.602292\pi$
$691$	9.14528	−	5.28003i	0.347903	−	0.200862i	0.663761	+	0.747944i	$0.268959\pi$
$692$	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	$0.846467\pi$
$702$	−1.64094	+	4.55539i	−0.0619334	+	0.171932i
$703$	−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	−0.351548	−	0.936170i	$-0.614344\pi$
$709$	7.54679	−	4.35714i	0.283426	−	0.163636i	0.634973	+	0.772534i	$0.281011\pi$
$710$			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
$715$	23.9721	+	0.118011i	0.896507	+	0.00441336i
$716$	−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	0.968759	−	0.248005i	$-0.0797751\pi$
$733$	33.5273	+	19.3570i	1.23836	+	0.714967i	0.269600	+	0.962972i	$0.413108\pi$
$734$	−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	$-0.945185\pi$
$739$		−	9.31654i		−	0.342714i	0.985209	−	0.171357i	$-0.0548152\pi$
$740$	−12.5991	−	21.8222i	−0.463150	−	0.802200i
$741$	−6.77637	−	28.8717i	−0.248936	−	1.06063i
$742$	−0.499504	+	0.865166i	−0.0183374	+	0.0317612i
$743$	−4.08990	−	2.36130i	−0.150044	−	0.0866278i	0.423098	−	0.906084i	$-0.360942\pi$
$743$	−4.08990	−	2.36130i	−0.150044	−	0.0866278i	−0.573142	+	0.819456i	$0.694276\pi$
$744$	−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
$754$	5.10863	+	2.98310i	0.186045	+	0.108638i
$755$	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	0.199700	−	0.979857i	$-0.436003\pi$
$761$	−15.1457	−	8.74437i	−0.549031	−	0.316983i	−0.748731	+	0.662874i	$0.769337\pi$
$762$	−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
$767$	−11.2356	−	6.56085i	−0.405695	−	0.236898i
$768$	5.37487	−	18.1344i	0.193949	−	0.654369i
$769$	3.42010	+	1.97459i	0.123332	+	0.0712057i	0.560397	−	0.828224i	$-0.310649\pi$
$769$	3.42010	+	1.97459i	0.123332	+	0.0712057i	−0.437065	+	0.899430i	$0.643982\pi$
$770$	−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	$0.0696896\pi$
$773$			12.0771i			0.434383i	−0.976129	+	0.217192i	$0.930310\pi$
$774$	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
$780$	16.9979	−	15.9669i	0.608623	−	0.571707i
$781$	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	$0.0761655\pi$
$787$	46.6394	+	26.9273i	1.66251	+	0.959853i	0.691006	+	0.722849i	$0.257168\pi$
$788$	−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
$806$	−5.47270	−	0.0269412i	−0.192768	−	0.000948965i
$807$	−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	$-0.758093\pi$
$811$		−	39.2371i		−	1.37780i	0.724855	−	0.688901i	$-0.241907\pi$
$812$	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
$819$	−5.93870	+	9.04056i	−0.207515	+	0.315903i
$820$	45.4045			1.58560
$821$	1.68295	−	0.971650i	0.0587352	−	0.0339108i	−0.470345	−	0.882483i	$-0.655870\pi$
$821$	1.68295	−	0.971650i	0.0587352	−	0.0339108i	0.529080	+	0.848572i	$0.322537\pi$
$822$	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	$-0.954117\pi$
$827$		−	8.26190i		−	0.287294i	0.989629	−	0.143647i	$-0.0458830\pi$
$828$	−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
$832$	23.2241	+	0.114329i	0.805151	+	0.00396363i
$833$	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	−0.114122	−	0.993467i	$-0.536406\pi$
$839$	19.9625	−	11.5254i	0.689184	−	0.397900i	0.803306	+	0.595566i	$0.203072\pi$
$840$	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	−0.425932	−	0.904755i	$-0.640054\pi$
$853$	4.22449	−	2.43901i	0.144644	−	0.0835101i	0.570575	+	0.821245i	$0.306720\pi$
$854$	−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	$0.531326\pi$
$858$	−1.60483	+	5.31834i	−0.0547880	+	0.181565i
$859$	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	$0.187961\pi$
$863$			32.7125i			1.11355i	−0.830664	+	0.556774i	$0.812039\pi$
$864$	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
$871$	15.5963	+	9.10718i	0.528460	+	0.308585i
$872$	−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	0.680814	−	0.732456i	$-0.261626\pi$
$877$	11.4576	+	6.61505i	0.386895	+	0.223374i	−0.293919	+	0.955830i	$0.594959\pi$
$878$	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	$0.447722\pi$
$884$	−21.4318	+	36.7025i	−0.720830	+	1.23444i
$885$	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
$897$	14.8903	−	49.3458i	0.497172	−	1.64761i
$898$	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
$923$	−0.0575162	+	11.6835i	−0.00189317	+	0.384568i
$924$	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	−0.907203	−	0.420693i	$-0.861787\pi$
$929$	−30.3720	+	17.5353i	−0.996474	+	0.575315i	−0.0892711	+	0.996007i	$0.528454\pi$
$930$	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
$936$	4.94024	+	9.82289i	0.161477	+	0.321071i
$937$	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	−0.468447	−	0.883492i	$-0.655186\pi$
$941$	−45.0257	−	25.9956i	−1.46780	−	0.847433i	−0.999350	+	0.0360591i	$0.988520\pi$
$942$	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	−0.343952	−	0.938987i	$-0.611766\pi$
$947$	9.14767	−	5.28141i	0.297259	−	0.171623i	0.641211	+	0.767365i	$0.278432\pi$
$948$	15.0132	−	3.60176i	0.487606	−	0.116980i
$949$	0.298434	−	60.6223i	0.00968757	−	1.96788i
$950$	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	0.975971	−	0.217901i	$-0.0699210\pi$
$967$	39.6559	+	22.8954i	1.27525	+	0.736265i	0.299278	+	0.954166i	$0.403254\pi$
$968$	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
$975$	5.42401	+	5.77425i	0.173707	+	0.184924i
$976$	18.6613	−	32.3224i	0.597335	−	1.03461i
$977$	24.3218	+	14.0422i	0.778122	+	0.449249i	0.835764	−	0.549088i	$-0.185025\pi$
$977$	24.3218	+	14.0422i	0.778122	+	0.449249i	−0.0576422	+	0.998337i	$0.518358\pi$
$978$	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	−0.329196	−	0.944261i	$-0.606778\pi$
$983$	10.1571	−	5.86418i	0.323960	−	0.187038i	0.653156	+	0.757223i	$0.273444\pi$
$984$	−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
$988$	−28.5840	−	16.6912i	−0.909379	−	0.531016i
$989$	−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.337.46	yes	168
9.7	even	3	inner	819.2.dt.a.610.39	yes	168
13.12	even	2	inner	819.2.dt.a.337.39	✓	168
117.25	even	6	inner	819.2.dt.a.610.46	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.dt.a.337.39	✓	168	13.12	even	2	inner
819.2.dt.a.337.46	yes	168	1.1	even	1	trivial
819.2.dt.a.610.39	yes	168	9.7	even	3	inner
819.2.dt.a.610.46	yes	168	117.25	even	6	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} +(3.60551 + 0.0177493i) 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} +(-6.07978 + 1.42696i) 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} +(-3.51481 + 6.01921i) 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} +(6.01448 + 3.51205i) 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} +(-1.17637 + 1.10502i) 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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