LMFDB - Embedded newform 384.2.v.a.157.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			157.30
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35188 + 0.415224i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.65518 + 1.12267i) q^{4} +(-0.677180 + 0.361960i) q^{5} +(0.545732 - 1.30467i) q^{6} +(0.993614 + 4.99523i) q^{7} +(1.77145 + 2.20499i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(1.35188 + 0.415224i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.65518 + 1.12267i) q^{4} +(-0.677180 + 0.361960i) q^{5} +(0.545732 - 1.30467i) q^{6} +(0.993614 + 4.99523i) q^{7} +(1.77145 + 2.20499i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-1.06576 + 0.208147i) q^{10} +(0.499964 - 0.609207i) q^{11} +(1.27950 - 1.53717i) q^{12} +(-0.998498 + 1.86806i) q^{13} +(-0.730889 + 7.16555i) q^{14} +(0.293842 + 0.709398i) q^{15} +(1.47923 + 3.71643i) q^{16} +(2.93770 - 7.09224i) q^{17} +(-1.24490 - 0.670985i) q^{18} +(-2.01785 - 6.65195i) q^{19} +(-1.52722 - 0.161139i) q^{20} +(5.06857 - 0.499211i) q^{21} +(0.928850 - 0.615981i) q^{22} +(4.69047 - 3.13407i) q^{23} +(2.36800 - 1.54679i) q^{24} +(-2.45029 + 3.66712i) q^{25} +(-2.12551 + 2.11080i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(-3.96338 + 9.38350i) q^{28} +(-2.70120 + 2.21682i) q^{29} +(0.102682 + 1.08103i) q^{30} +(3.85963 - 3.85963i) q^{31} +(0.456601 + 5.63840i) q^{32} +(-0.557269 - 0.557269i) q^{33} +(6.91630 - 8.36808i) q^{34} +(-2.48093 - 3.02303i) q^{35} +(-1.40435 - 1.42401i) q^{36} +(-10.9951 - 3.33533i) q^{37} +(0.0341523 - 9.83051i) q^{38} +(1.76119 + 1.17679i) q^{39} +(-1.99771 - 0.851978i) q^{40} +(4.07285 + 6.09545i) q^{41} +(7.05940 + 1.42972i) q^{42} +(-0.587363 - 5.96360i) q^{43} +(1.51147 - 0.447054i) q^{44} +(0.734783 - 0.222894i) q^{45} +(7.64231 - 2.28931i) q^{46} +(1.54022 + 0.637982i) q^{47} +(3.84353 - 1.10784i) q^{48} +(-17.4979 + 7.24788i) q^{49} +(-4.83519 + 3.94010i) q^{50} +(-6.77015 - 3.61872i) q^{51} +(-3.74990 + 1.97099i) q^{52} +(-4.60384 - 3.77827i) q^{53} +(-0.789775 + 1.17314i) q^{54} +(-0.118057 + 0.593510i) q^{55} +(-9.25428 + 11.0397i) q^{56} +(-6.81770 + 1.35612i) q^{57} +(-4.57218 + 1.87528i) q^{58} +(1.77696 + 3.32445i) q^{59} +(-0.310057 + 1.50407i) q^{60} +(6.20404 + 0.611045i) q^{61} +(6.82039 - 3.61516i) q^{62} -5.09310i q^{63} +(-1.72392 + 7.81205i) q^{64} -1.62643i q^{65} +(-0.521971 - 0.984754i) q^{66} +(5.97888 + 0.588869i) q^{67} +(12.8247 - 8.44086i) q^{68} +(-2.65923 - 4.97508i) q^{69} +(-2.09870 - 5.11692i) q^{70} +(-7.18146 + 1.42848i) q^{71} +(-1.30724 - 2.50821i) q^{72} +(1.07502 - 5.40450i) q^{73} +(-13.4792 - 9.07440i) q^{74} +(3.40929 + 2.79794i) q^{75} +(4.12803 - 13.2755i) q^{76} +(3.53990 + 1.89212i) q^{77} +(1.89230 + 2.32217i) q^{78} +(1.18623 - 0.491353i) q^{79} +(-2.34691 - 1.98127i) q^{80} +(0.923880 + 0.382683i) q^{81} +(2.97504 + 9.93147i) q^{82} +(2.28080 - 0.691874i) q^{83} +(8.94984 + 4.86404i) q^{84} +(0.577756 + 5.86606i) q^{85} +(1.68218 - 8.30598i) q^{86} +(1.94138 + 2.90548i) q^{87} +(2.22895 + 0.0232317i) q^{88} +(1.08832 + 0.727195i) q^{89} +(1.08589 + 0.00377251i) q^{90} +(-10.3235 - 3.13160i) q^{91} +(11.2821 + 0.0783914i) q^{92} +(-3.46274 - 4.21936i) q^{93} +(1.81730 + 1.50201i) q^{94} +(3.77419 + 3.77419i) q^{95} +(5.65600 + 0.0982574i) q^{96} +(-6.78129 + 6.78129i) q^{97} +(-26.6647 + 2.53274i) q^{98} +(-0.609207 + 0.499964i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{27}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	1.35188	+	0.415224i	0.955926	+	0.293607i
$2$	1.35188	+	0.415224i	0.955926	+	0.293607i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$4$	1.65518	+	1.12267i	0.827589	+	0.561334i
$5$	−0.677180	+	0.361960i	−0.302844	+	0.161874i	−0.615819	−	0.787888i	$-0.711175\pi$
$5$	−0.677180	+	0.361960i	−0.302844	+	0.161874i	0.312974	+	0.949762i	$0.398675\pi$
$6$	0.545732	−	1.30467i	0.222794	−	0.532631i
$7$	0.993614	+	4.99523i	0.375551	+	1.88802i	0.453828	+	0.891089i	$0.350058\pi$
$7$	0.993614	+	4.99523i	0.375551	+	1.88802i	−0.0782769	+	0.996932i	$0.524942\pi$
$8$	1.77145	+	2.20499i	0.626302	+	0.779580i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	−1.06576	+	0.208147i	−0.337024	+	0.0658219i
$11$	0.499964	−	0.609207i	0.150745	−	0.183683i	−0.692163	−	0.721741i	$-0.743342\pi$
$11$	0.499964	−	0.609207i	0.150745	−	0.183683i	0.842908	+	0.538058i	$0.180842\pi$
$12$	1.27950	−	1.53717i	0.369359	−	0.443742i
$13$	−0.998498	+	1.86806i	−0.276933	+	0.518106i	−0.981483	−	0.191549i	$-0.938649\pi$
$13$	−0.998498	+	1.86806i	−0.276933	+	0.518106i	0.704550	+	0.709655i	$0.251149\pi$
$14$	−0.730889	+	7.16555i	−0.195338	+	1.91507i
$15$	0.293842	+	0.709398i	0.0758697	+	0.183166i
$16$	1.47923	+	3.71643i	0.369808	+	0.929108i
$17$	2.93770	−	7.09224i	0.712498	−	1.72012i	0.0188335	−	0.999823i	$-0.494005\pi$
$17$	2.93770	−	7.09224i	0.712498	−	1.72012i	0.693664	−	0.720299i	$-0.255995\pi$
$18$	−1.24490	−	0.670985i	−0.293426	−	0.158153i
$19$	−2.01785	−	6.65195i	−0.462926	−	1.52606i	−0.808974	−	0.587844i	$-0.799977\pi$
$19$	−2.01785	−	6.65195i	−0.462926	−	1.52606i	0.346048	−	0.938217i	$-0.387523\pi$
$20$	−1.52722	−	0.161139i	−0.341496	−	0.0360319i
$21$	5.06857	−	0.499211i	1.10605	−	0.108937i
$22$	0.928850	−	0.615981i	0.198031	−	0.131328i
$23$	4.69047	−	3.13407i	0.978031	−	0.653499i	0.0396902	−	0.999212i	$-0.487363\pi$
$23$	4.69047	−	3.13407i	0.978031	−	0.653499i	0.938340	+	0.345713i	$0.112363\pi$
$24$	2.36800	−	1.54679i	0.483366	−	0.315738i
$25$	−2.45029	+	3.66712i	−0.490059	+	0.733425i
$26$	−2.12551	+	2.11080i	−0.416848	+	0.413961i
$27$	−0.290285	+	0.956940i	−0.0558653	+	0.184163i
$28$	−3.96338	+	9.38350i	−0.749009	+	1.77332i
$29$	−2.70120	+	2.21682i	−0.501600	+	0.411652i	−0.850875	−	0.525368i	$-0.823928\pi$
$29$	−2.70120	+	2.21682i	−0.501600	+	0.411652i	0.349275	+	0.937020i	$0.386428\pi$
$30$	0.102682	+	1.08103i	0.0187470	+	0.197369i
$31$	3.85963	−	3.85963i	0.693211	−	0.693211i	−0.269726	−	0.962937i	$-0.586933\pi$
$31$	3.85963	−	3.85963i	0.693211	−	0.693211i	0.962937	+	0.269726i	$0.0869332\pi$
$32$	0.456601	+	5.63840i	0.0807164	+	0.996737i
$33$	−0.557269	−	0.557269i	−0.0970081	−	0.0970081i
$34$	6.91630	−	8.36808i	1.18614	−	1.43511i
$35$	−2.48093	−	3.02303i	−0.419354	−	0.510985i
$36$	−1.40435	−	1.42401i	−0.234059	−	0.237334i
$37$	−10.9951	−	3.33533i	−1.80758	−	0.548324i	−0.808396	−	0.588640i	$-0.799664\pi$
$37$	−10.9951	−	3.33533i	−1.80758	−	0.548324i	−0.999187	+	0.0403155i	$0.987164\pi$
$38$	0.0341523	−	9.83051i	0.00554024	−	1.59472i
$39$	1.76119	+	1.17679i	0.282017	+	0.188437i
$40$	−1.99771	−	0.851978i	−0.315866	−	0.134710i
$41$	4.07285	+	6.09545i	0.636072	+	0.951949i	0.999791	+	0.0204400i	$0.00650672\pi$
$41$	4.07285	+	6.09545i	0.636072	+	0.951949i	−0.363719	+	0.931509i	$0.618493\pi$
$42$	7.05940	+	1.42972i	1.08929	+	0.220610i
$43$	−0.587363	−	5.96360i	−0.0895720	−	0.909440i	−0.930010	−	0.367533i	$-0.880202\pi$
$43$	−0.587363	−	5.96360i	−0.0895720	−	0.909440i	0.840438	−	0.541907i	$-0.182298\pi$
$44$	1.51147	−	0.447054i	0.227862	−	0.0673959i
$45$	0.734783	−	0.222894i	0.109535	−	0.0332271i
$46$	7.64231	−	2.28931i	1.12680	−	0.337540i
$47$	1.54022	+	0.637982i	0.224665	+	0.0930592i	0.492177	−	0.870495i	$-0.336201\pi$
$47$	1.54022	+	0.637982i	0.224665	+	0.0930592i	−0.267512	+	0.963555i	$0.586201\pi$
$48$	3.84353	−	1.10784i	0.554765	−	0.159902i
$49$	−17.4979	+	7.24788i	−2.49971	+	1.03541i
$50$	−4.83519	+	3.94010i	−0.683799	+	0.557215i
$51$	−6.77015	−	3.61872i	−0.948010	−	0.506722i
$52$	−3.74990	+	1.97099i	−0.520018	+	0.273327i
$53$	−4.60384	−	3.77827i	−0.632386	−	0.518986i	0.262701	−	0.964877i	$-0.415387\pi$
$53$	−4.60384	−	3.77827i	−0.632386	−	0.518986i	−0.895087	+	0.445892i	$0.852887\pi$
$54$	−0.789775	+	1.17314i	−0.107475	+	0.159644i
$55$	−0.118057	+	0.593510i	−0.0159187	+	0.0800289i
$56$	−9.25428	+	11.0397i	−1.23666	+	1.47524i
$57$	−6.81770	+	1.35612i	−0.903026	+	0.179623i
$58$	−4.57218	+	1.87528i	−0.600357	+	0.246236i
$59$	1.77696	+	3.32445i	0.231340	+	0.432807i	0.970629	−	0.240581i	$-0.0773381\pi$
$59$	1.77696	+	3.32445i	0.231340	+	0.432807i	−0.739289	+	0.673389i	$0.764838\pi$
$60$	−0.310057	+	1.50407i	−0.0400282	+	0.194174i
$61$	6.20404	+	0.611045i	0.794346	+	0.0782363i	0.487046	−	0.873376i	$-0.338074\pi$
$61$	6.20404	+	0.611045i	0.794346	+	0.0782363i	0.307300	+	0.951613i	$0.400574\pi$
$62$	6.82039	−	3.61516i	0.866190	−	0.459126i
$63$		−	5.09310i		−	0.641670i
$64$	−1.72392	+	7.81205i	−0.215491	+	0.976506i
$65$		−	1.62643i		−	0.201734i
$66$	−0.521971	−	0.984754i	−0.0642502	−	0.121215i
$67$	5.97888	+	0.588869i	0.730437	+	0.0719418i	0.456397	−	0.889776i	$-0.349140\pi$
$67$	5.97888	+	0.588869i	0.730437	+	0.0719418i	0.274040	+	0.961718i	$0.411640\pi$
$68$	12.8247	−	8.44086i	1.55522	−	1.02360i
$69$	−2.65923	−	4.97508i	−0.320134	−	0.598929i
$70$	−2.09870	−	5.11692i	−0.250843	−	0.611589i
$71$	−7.18146	+	1.42848i	−0.852283	+	0.169530i	−0.601855	−	0.798606i	$-0.705571\pi$
$71$	−7.18146	+	1.42848i	−0.852283	+	0.169530i	−0.250428	+	0.968135i	$0.580571\pi$
$72$	−1.30724	−	2.50821i	−0.154060	−	0.295595i
$73$	1.07502	−	5.40450i	0.125822	−	0.632549i	−0.865480	−	0.500943i	$-0.832987\pi$
$73$	1.07502	−	5.40450i	0.125822	−	0.632549i	0.991302	−	0.131606i	$-0.0420134\pi$
$74$	−13.4792	−	9.07440i	−1.56692	−	1.05488i
$75$	3.40929	+	2.79794i	0.393671	+	0.323078i
$76$	4.12803	−	13.2755i	0.473518	−	1.52281i
$77$	3.53990	+	1.89212i	0.403410	+	0.215627i
$78$	1.89230	+	2.32217i	0.214260	+	0.262934i
$79$	1.18623	−	0.491353i	0.133461	−	0.0552816i	−0.314953	−	0.949107i	$-0.601989\pi$
$79$	1.18623	−	0.491353i	0.133461	−	0.0552816i	0.448415	+	0.893826i	$0.351989\pi$
$80$	−2.34691	−	1.98127i	−0.262392	−	0.221513i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	2.97504	+	9.93147i	0.328538	+	1.09675i
$83$	2.28080	−	0.691874i	0.250350	−	0.0759430i	−0.162615	−	0.986690i	$-0.551993\pi$
$83$	2.28080	−	0.691874i	0.250350	−	0.0759430i	0.412966	+	0.910747i	$0.364493\pi$
$84$	8.94984	+	4.86404i	0.976508	+	0.530710i
$85$	0.577756	+	5.86606i	0.0626665	+	0.636263i
$86$	1.68218	−	8.30598i	0.181394	−	0.895657i
$87$	1.94138	+	2.90548i	0.208138	+	0.311500i
$88$	2.22895	+	0.0232317i	0.237607	+	0.00247650i
$89$	1.08832	+	0.727195i	0.115362	+	0.0770825i	0.611913	−	0.790925i	$-0.290400\pi$
$89$	1.08832	+	0.727195i	0.115362	+	0.0770825i	−0.496551	+	0.868008i	$0.665400\pi$
$90$	1.08589	+	0.00377251i	0.114463	+	0.000397658i
$91$	−10.3235	−	3.13160i	−1.08220	−	0.328281i
$92$	11.2821	+	0.0783914i	1.17624	+	0.00817287i
$93$	−3.46274	−	4.21936i	−0.359069	−	0.437527i
$94$	1.81730	+	1.50201i	0.187440	+	0.154921i
$95$	3.77419	+	3.77419i	0.387223	+	0.387223i
$96$	5.65600	+	0.0982574i	0.577263	+	0.0100284i
$97$	−6.78129	+	6.78129i	−0.688536	+	0.688536i	−0.961908	−	0.273372i	$-0.911861\pi$
$97$	−6.78129	+	6.78129i	−0.688536	+	0.688536i	0.273372	+	0.961908i	$0.411861\pi$
$98$	−26.6647	+	2.53274i	−2.69354	+	0.255845i
$99$	−0.609207	+	0.499964i	−0.0612276	+	0.0502482i
$100$	−8.17264	+	3.31888i	−0.817264	+	0.331888i
$101$	3.91970	−	12.9215i	0.390024	−	1.28574i	−0.513828	−	0.857893i	$-0.671773\pi$
$101$	3.91970	−	12.9215i	0.390024	−	1.28574i	0.903852	−	0.427845i	$-0.140727\pi$
$102$	−7.64987	−	7.70321i	−0.757450	−	0.762731i
$103$	0.317801	−	0.475622i	0.0313138	−	0.0468644i	−0.815482	−	0.578782i	$-0.803528\pi$
$103$	0.317801	−	0.475622i	0.0313138	−	0.0468644i	0.846796	+	0.531917i	$0.178528\pi$
$104$	−5.88783	+	1.10750i	−0.577349	+	0.108599i
$105$	−3.25164	+	2.17268i	−0.317328	+	0.212032i
$106$	−4.65503	−	7.01941i	−0.452136	−	0.681785i
$107$	11.7471	−	1.15699i	1.13564	−	0.111850i	0.487322	−	0.873222i	$-0.337974\pi$
$107$	11.7471	−	1.15699i	1.13564	−	0.111850i	0.648315	+	0.761372i	$0.275474\pi$
$108$	−1.55480	+	1.25801i	−0.149611	+	0.121052i
$109$	2.46456	+	8.12458i	0.236062	+	0.778194i	0.992296	+	0.123892i	$0.0395375\pi$
$109$	2.46456	+	8.12458i	0.236062	+	0.778194i	−0.756233	+	0.654302i	$0.772963\pi$
$110$	−0.406038	+	0.753337i	−0.0387142	+	0.0718278i
$111$	−4.39697	+	10.6152i	−0.417342	+	1.00755i
$112$	−17.0947	+	11.0818i	−1.61529	+	1.04713i
$113$	−6.92255	−	16.7125i	−0.651219	−	1.57218i	−0.811011	−	0.585031i	$-0.801082\pi$
$113$	−6.92255	−	16.7125i	−0.651219	−	1.57218i	0.159791	−	0.987151i	$-0.448918\pi$
$114$	−9.77983	−	0.997547i	−0.915965	−	0.0934288i
$115$	−2.04188	+	3.82010i	−0.190407	+	0.356226i
$116$	−6.95972	+	0.636678i	−0.646193	+	0.0591141i
$117$	1.34375	−	1.63737i	0.124230	−	0.151375i
$118$	1.02185	+	5.23211i	0.0940688	+	0.481655i
$119$	38.3464	+	7.62756i	3.51520	+	0.699218i
$120$	−1.04369	+	1.90458i	−0.0952750	+	0.173864i
$121$	2.02482	+	10.1795i	0.184075	+	0.925407i
$122$	8.13343	+	3.40213i	0.736366	+	0.308014i
$123$	6.46530	−	3.45578i	0.582957	−	0.311597i
$124$	10.7215	−	2.05530i	0.962816	−	0.184571i
$125$	0.708248	−	7.19096i	0.0633476	−	0.643179i
$126$	2.11477	−	6.88527i	0.188399	−	0.613389i
$127$	−4.18716			−0.371550			−0.185775	−	0.982592i	$-0.559480\pi$
$127$	−4.18716			−0.371550			−0.185775	+	0.982592i	$0.559480\pi$
$128$	−5.57429	+	9.84517i	−0.492702	+	0.870198i
$129$	−5.99245			−0.527606
$130$	0.675331	−	2.19874i	0.0592305	−	0.192842i
$131$	1.33105	−	13.5143i	0.116294	−	1.18075i	−0.743007	−	0.669284i	$-0.766601\pi$
$131$	1.33105	−	13.5143i	0.116294	−	1.18075i	0.859301	−	0.511470i	$-0.170899\pi$
$132$	−0.296752	−	1.54801i	−0.0258289	−	0.134737i
$133$	31.2231	−	16.6891i	2.70738	−	1.44713i
$134$	7.83824	+	3.27866i	0.677121	+	0.283233i
$135$	−0.149799	−	0.753093i	−0.0128927	−	0.0648159i
$136$	20.8423	−	6.08596i	1.78721	−	0.521867i
$137$	−17.3319	−	3.44753i	−1.48077	−	0.294543i	−0.612432	−	0.790523i	$-0.709809\pi$
$137$	−17.3319	−	3.44753i	−1.48077	−	0.294543i	−0.868334	+	0.495981i	$0.834809\pi$
$138$	−1.52921	−	7.82990i	−0.130175	−	0.666525i
$139$	−7.28154	+	8.87258i	−0.617612	+	0.752563i	−0.984052	−	0.177879i	$-0.943076\pi$
$139$	−7.28154	+	8.87258i	−0.617612	+	0.752563i	0.366440	+	0.930442i	$0.380576\pi$
$140$	−0.712533	−	7.78891i	−0.0602201	−	0.658283i
$141$	0.785878	−	1.47027i	0.0661829	−	0.123819i
$142$	−10.3016	−	1.05077i	−0.864494	−	0.0881788i
$143$	0.638822	+	1.54225i	0.0534210	+	0.128970i
$144$	−0.725770	−	3.93361i	−0.0604808	−	0.327801i
$145$	1.02680	−	2.47891i	0.0852710	−	0.205862i
$146$	3.69738	−	6.85989i	0.305998	−	0.567728i
$147$	5.49789	+	18.1241i	0.453458	+	1.49485i
$148$	−14.4544	−	17.8644i	−1.18814	−	1.46844i
$149$	4.45647	−	0.438924i	0.365088	−	0.0359581i	0.0861901	−	0.996279i	$-0.472531\pi$
$149$	4.45647	−	0.438924i	0.365088	−	0.0359581i	0.278898	+	0.960321i	$0.410031\pi$
$150$	3.44720	+	5.19810i	0.281463	+	0.424423i
$151$	1.42745	−	0.953789i	0.116164	−	0.0776183i	−0.496131	−	0.868248i	$-0.665246\pi$
$151$	1.42745	−	0.953789i	0.116164	−	0.0776183i	0.612295	+	0.790629i	$0.290246\pi$
$152$	11.0929	−	16.2329i	0.899756	−	1.31666i
$153$	−4.26488	+	6.38285i	−0.344795	+	0.516023i
$154$	3.99989	+	4.02778i	0.322320	+	0.324567i
$155$	−1.21663	+	4.01070i	−0.0977223	+	0.322147i
$156$	1.59394	+	3.92503i	0.127618	+	0.314254i
$157$	−11.6591	+	9.56838i	−0.930498	+	0.763640i	−0.971873	−	0.235504i	$-0.924326\pi$
$157$	−11.6591	+	9.56838i	−0.930498	+	0.763640i	0.0413758	+	0.999144i	$0.486826\pi$
$158$	1.80767	−	0.171701i	0.143810	−	0.0136598i
$159$	−4.21133	+	4.21133i	−0.333980	+	0.333980i
$160$	−2.35008	−	3.65294i	−0.185790	−	0.288790i
$161$	20.3159	+	20.3159i	1.60112	+	1.60112i
$162$	1.09008	+	0.900960i	0.0856446	+	0.0707861i
$163$	2.42206	+	2.95129i	0.189710	+	0.231162i	0.859176	−	0.511681i	$-0.170977\pi$
$163$	2.42206	+	2.95129i	0.189710	+	0.231162i	−0.669466	+	0.742843i	$0.733477\pi$
$164$	−0.101873	+	14.6615i	−0.00795492	+	1.14487i
$165$	0.579081	+	0.175662i	0.0450814	+	0.0136753i
$166$	3.37066	+	0.0117101i	0.261614	+	0.000908876i
$167$	−3.91867	−	2.61837i	−0.303235	−	0.202615i	0.394638	−	0.918837i	$-0.370870\pi$
$167$	−3.91867	−	2.61837i	−0.303235	−	0.202615i	−0.697873	+	0.716221i	$0.745870\pi$
$168$	10.0795	+	10.2918i	0.777649	+	0.794030i
$169$	4.72977	+	7.07860i	0.363829	+	0.544508i
$170$	−1.65467	+	8.17013i	−0.126907	+	0.626620i
$171$	0.681343	+	6.91779i	0.0521036	+	0.529017i
$172$	5.72295	−	10.5302i	0.436371	−	0.802923i
$173$	−17.4179	+	5.28367i	−1.32426	+	0.401710i	−0.871707	−	0.490028i	$-0.836987\pi$
$173$	−17.4179	+	5.28367i	−1.32426	+	0.401710i	−0.452553	+	0.891738i	$0.649487\pi$
$174$	1.41809	+	4.73397i	0.107505	+	0.358882i
$175$	−20.7528	−	8.59609i	−1.56876	−	0.649803i
$176$	3.00364	+	0.956921i	0.226408	+	0.0721306i
$177$	3.48262	−	1.44255i	0.261770	−	0.108429i
$178$	1.16934	+	1.43498i	0.0876456	+	0.107556i
$179$	−8.72961	−	4.66607i	−0.652481	−	0.348759i	0.111717	−	0.993740i	$-0.464365\pi$
$179$	−8.72961	−	4.66607i	−0.652481	−	0.348759i	−0.764198	+	0.644981i	$0.776865\pi$
$180$	1.46643	+	0.455988i	0.109302	+	0.0339874i
$181$	4.11545	+	3.37746i	0.305899	+	0.251045i	0.774801	−	0.632205i	$-0.217850\pi$
$181$	4.11545	+	3.37746i	0.305899	+	0.251045i	−0.468902	+	0.883250i	$0.655350\pi$
$182$	−12.6559	−	8.52013i	−0.938115	−	0.631554i
$183$	1.21621	−	6.11428i	0.0899045	−	0.451980i
$184$	15.2195	+	4.79057i	1.12200	+	0.353165i
$185$	8.65292	−	1.72117i	0.636175	−	0.126543i
$186$	−2.92924	−	7.14189i	−0.214782	−	0.523669i
$187$	−2.85190	−	5.33553i	−0.208552	−	0.390173i
$188$	1.83310	+	2.78513i	0.133693	+	0.203127i
$189$	−5.06857	−	0.499211i	−0.368684	−	0.0363122i
$190$	3.53513	+	6.66939i	0.256465	+	0.483849i
$191$			5.48968i			0.397219i	0.980079	+	0.198610i	$0.0636426\pi$
$191$			5.48968i			0.397219i	−0.980079	+	0.198610i	$0.936357\pi$
$192$	7.60546	+	2.48134i	0.548877	+	0.179075i
$193$			16.8051i			1.20966i	0.796355	+	0.604830i	$0.206759\pi$
$193$			16.8051i			1.20966i	−0.796355	+	0.604830i	$0.793241\pi$
$194$	−11.9833	+	6.35177i	−0.860349	+	0.456030i
$195$	−1.61860	−	0.159418i	−0.115910	−	0.0114162i
$196$	−37.0992	−	7.64783i	−2.64994	−	0.546274i
$197$	6.66536	+	12.4700i	0.474887	+	0.888452i	0.999315	+	0.0369970i	$0.0117792\pi$
$197$	6.66536	+	12.4700i	0.474887	+	0.888452i	−0.524428	+	0.851455i	$0.675721\pi$
$198$	−1.03117	+	0.422935i	−0.0732823	+	0.0300567i
$199$	10.6411	−	2.11666i	0.754331	−	0.150046i	0.197077	−	0.980388i	$-0.436855\pi$
$199$	10.6411	−	2.11666i	0.754331	−	0.150046i	0.557254	+	0.830342i	$0.311855\pi$
$200$	−12.4265	+	1.09327i	−0.878688	+	0.0773056i
$201$	1.17207	−	5.89238i	0.0826712	−	0.415616i
$202$	10.6643	−	15.8408i	0.750337	−	1.11456i
$203$	−13.7575	−	11.2905i	−0.965585	−	0.792435i
$204$	−7.14318	−	13.5903i	−0.500123	−	0.951508i
$205$	−4.96436	−	2.65351i	−0.346726	−	0.185329i
$206$	0.627119	−	0.511027i	0.0436934	−	0.0356050i
$207$	−5.21177	+	2.15879i	−0.362243	+	0.150046i
$208$	−8.41952	−	0.947556i	−0.583789	−	0.0657012i
$209$	−5.06126	−	2.09644i	−0.350095	−	0.145014i
$210$	−5.29799	+	1.58705i	−0.365596	+	0.109517i
$211$	6.14446	−	1.86390i	0.423002	−	0.128316i	−0.0716047	−	0.997433i	$-0.522812\pi$
$211$	6.14446	−	1.86390i	0.423002	−	0.128316i	0.494607	+	0.869117i	$0.335312\pi$
$212$	−3.37843	−	11.4223i	−0.232031	−	0.784487i
$213$	0.717697	+	7.28690i	0.0491758	+	0.499290i
$214$	16.3612	+	3.31357i	1.11843	+	0.226511i
$215$	2.55634	+	3.82583i	0.174341	+	0.260919i
$216$	−2.62426	+	1.05510i	−0.178559	+	0.0717904i
$217$	23.1148	+	15.4448i	1.56913	+	1.04846i
$218$	−0.0417131	+	12.0068i	−0.00282517	+	0.813205i
$219$	−5.27311	−	1.59958i	−0.356324	−	0.108090i
$220$	−0.861720	+	0.849827i	−0.0580971	+	0.0572953i
$221$	10.3154	+	12.5694i	0.693891	+	0.845508i
$222$	−10.3519	+	12.5248i	−0.694773	+	0.840612i
$223$	5.60341	+	5.60341i	0.375232	+	0.375232i	0.869379	−	0.494146i	$-0.164519\pi$
$223$	5.60341	+	5.60341i	0.375232	+	0.375232i	−0.494146	+	0.869379i	$0.664519\pi$
$224$	−27.7114	+	7.88322i	−1.85155	+	0.526720i
$225$	3.11863	−	3.11863i	0.207909	−	0.207909i
$226$	−2.41905	−	25.4678i	−0.160913	−	1.69409i
$227$	−6.69423	+	5.49381i	−0.444312	+	0.364637i	−0.829786	−	0.558081i	$-0.811538\pi$
$227$	−6.69423	+	5.49381i	−0.444312	+	0.364637i	0.385475	+	0.922718i	$0.374038\pi$
$228$	−12.8070	−	5.40938i	−0.848163	−	0.358245i
$229$	−1.38163	+	4.55463i	−0.0913009	+	0.300979i	−0.990684	−	0.136183i	$-0.956516\pi$
$229$	−1.38163	+	4.55463i	−0.0913009	+	0.300979i	0.899383	+	0.437162i	$0.144016\pi$
$230$	−4.34658	+	4.31649i	−0.286605	+	0.284621i
$231$	2.22998	−	3.33740i	0.146722	−	0.219585i
$232$	−9.67309	−	2.02912i	−0.635069	−	0.133218i
$233$	−0.808077	+	0.539940i	−0.0529389	+	0.0353726i	−0.581758	−	0.813362i	$-0.697635\pi$
$233$	−0.808077	+	0.539940i	−0.0529389	+	0.0353726i	0.528819	+	0.848735i	$0.322635\pi$
$234$	2.49647	−	1.65557i	0.163199	−	0.108228i
$235$	−1.27393	+	0.125471i	−0.0831023	+	0.00818486i
$236$	−0.791076	+	7.49750i	−0.0514946	+	0.488046i
$237$	−0.372716	−	1.22868i	−0.0242105	−	0.0798114i
$238$	48.6727	+	26.2339i	3.15498	+	1.70049i
$239$	−0.524823	+	1.26704i	−0.0339480	+	0.0819577i	−0.939944	−	0.341328i	$-0.889123\pi$
$239$	−0.524823	+	1.26704i	−0.0339480	+	0.0819577i	0.905996	+	0.423286i	$0.139123\pi$
$240$	−2.20177	+	2.14141i	−0.142123	+	0.138227i
$241$	1.01378	+	2.44748i	0.0653032	+	0.157656i	0.953162	−	0.302460i	$-0.0978079\pi$
$241$	1.01378	+	2.44748i	0.0653032	+	0.157656i	−0.887859	+	0.460116i	$0.847808\pi$
$242$	−1.48943	+	14.6022i	−0.0957444	+	0.938666i
$243$	0.471397	−	0.881921i	0.0302401	−	0.0565753i
$244$	9.58280	+	7.97647i	0.613476	+	0.510641i
$245$	9.22581	−	11.2417i	0.589416	−	0.718205i
$246$	10.1753	−	1.98726i	0.648751	−	0.126703i
$247$	14.4410	+	2.87250i	0.918861	+	0.182773i
$248$	15.3476	+	1.67329i	0.974573	+	0.106254i
$249$	−0.464984	−	2.33763i	−0.0294672	−	0.148142i
$250$	3.94332	−	9.42726i	0.249398	−	0.596232i
$251$	2.77948	−	1.48566i	0.175439	−	0.0937743i	−0.381339	−	0.924435i	$-0.624537\pi$
$251$	2.77948	−	1.48566i	0.175439	−	0.0937743i	0.556779	+	0.830661i	$0.312037\pi$
$252$	5.71786	−	8.42999i	0.360191	−	0.531039i
$253$	0.435764	−	4.42439i	0.0273963	−	0.278159i
$254$	−5.66055	−	1.73861i	−0.355174	−	0.109090i
$255$	5.89444			0.369124
$256$	−11.6237	+	10.9949i	−0.726484	+	0.687184i
$257$	−0.290600			−0.0181271			−0.00906355	−	0.999959i	$-0.502885\pi$
$257$	−0.290600			−0.0181271			−0.00906355	+	0.999959i	$0.502885\pi$
$258$	−8.10110	−	2.48821i	−0.504352	−	0.154909i
$259$	5.73585	−	58.2371i	0.356409	−	3.61868i
$260$	1.82594	−	2.69203i	0.113240	−	0.166953i
$261$	3.08178	−	1.64724i	0.190757	−	0.101962i
$262$	7.41089	−	17.7171i	0.457846	−	1.09457i
$263$	6.06627	+	30.4972i	0.374062	+	1.88054i	0.466018	+	0.884775i	$0.345688\pi$
$263$	6.06627	+	30.4972i	0.374062	+	1.88054i	−0.0919552	+	0.995763i	$0.529312\pi$
$264$	0.241596	−	2.21594i	0.0148692	−	0.136382i
$265$	4.48521	+	0.892164i	0.275524	+	0.0548052i
$266$	49.1397	−	9.59714i	3.01295	−	0.588438i
$267$	0.830367	−	1.01181i	0.0508177	−	0.0619215i
$268$	9.23502	+	7.68699i	0.564119	+	0.469557i
$269$	1.18619	−	2.21921i	0.0723236	−	0.135308i	−0.843161	−	0.537662i	$-0.819308\pi$
$269$	1.18619	−	2.21921i	0.0723236	−	0.135308i	0.915484	+	0.402354i	$0.131808\pi$
$270$	0.110190	−	1.08029i	0.00670598	−	0.0657446i
$271$	−0.152262	−	0.367594i	−0.00924928	−	0.0223297i	0.919187	−	0.393820i	$-0.128847\pi$
$271$	−0.152262	−	0.367594i	−0.00924928	−	0.0223297i	−0.928437	+	0.371491i	$0.878847\pi$
$272$	30.7034	+	0.426694i	1.86167	+	0.0258721i
$273$	−4.12840	+	9.96685i	−0.249862	+	0.603221i
$274$	−21.9992	−	11.8573i	−1.32902	−	0.716325i
$275$	1.00898	+	3.32616i	0.0608438	+	0.200575i
$276$	1.18385	−	11.2201i	0.0712595	−	0.675369i
$277$	2.96594	−	0.292120i	0.178206	−	0.0175518i	−0.00852043	−	0.999964i	$-0.502712\pi$
$277$	2.96594	−	0.292120i	0.178206	−	0.0175518i	0.186727	+	0.982412i	$0.440212\pi$
$278$	−13.5279	+	8.97123i	−0.811350	+	0.538059i
$279$	−4.53845	+	3.03249i	−0.271710	+	0.181551i
$280$	2.27088	−	10.8256i	0.135711	−	0.646951i
$281$	9.62914	−	14.4110i	0.574426	−	0.859690i	−0.424528	−	0.905415i	$-0.639560\pi$
$281$	9.62914	−	14.4110i	0.574426	−	0.859690i	0.998954	+	0.0457251i	$0.0145598\pi$
$282$	1.67291	−	1.66132i	0.0996202	−	0.0989304i
$283$	−5.91964	+	19.5144i	−0.351886	+	1.16001i	0.585192	+	0.810894i	$0.301019\pi$
$283$	−5.91964	+	19.5144i	−0.351886	+	1.16001i	−0.937079	+	0.349119i	$0.886481\pi$
$284$	−13.4903	−	5.69800i	−0.800503	−	0.338114i
$285$	4.12595	−	3.38608i	0.244400	−	0.200574i
$286$	0.223233	+	2.35020i	0.0132001	+	0.138970i
$287$	−26.4013	+	26.4013i	−1.55842	+	1.55842i
$288$	0.652169	−	5.61913i	0.0384294	−	0.331111i
$289$	−29.6490	−	29.6490i	−1.74406	−	1.74406i
$290$	2.41741	−	2.92485i	0.141955	−	0.171753i
$291$	6.08396	+	7.41332i	0.356648	+	0.434577i
$292$	7.84682	−	7.73853i	0.459200	−	0.452863i
$293$	6.64055	+	2.01439i	0.387945	+	0.117682i	0.478231	−	0.878234i	$-0.341278\pi$
$293$	6.64055	+	2.01439i	0.387945	+	0.117682i	−0.0902859	+	0.995916i	$0.528778\pi$
$294$	−0.0930525	+	26.7845i	−0.00542693	+	1.56211i
$295$	−2.40664	−	1.60807i	−0.140120	−	0.0936253i
$296$	−12.1229	−	30.1524i	−0.704631	−	1.75257i
$297$	0.437843	+	0.655279i	0.0254062	+	0.0380231i
$298$	6.20688	+	1.25706i	0.359555	+	0.0728194i
$299$	1.17120	+	11.8914i	0.0677325	+	0.687699i
$300$	2.50184	+	8.45859i	0.144444	+	0.488357i
$301$	29.2060	−	8.85953i	1.68340	−	0.510655i
$302$	2.32578	−	0.696703i	0.133833	−	0.0400907i
$303$	−12.4751	−	5.16735i	−0.716675	−	0.296857i
$304$	21.7366	−	17.3390i	1.24668	−	0.994458i
$305$	−4.42243	+	1.83183i	−0.253228	+	0.104890i
$306$	−8.41594	+	6.85799i	−0.481107	+	0.392045i
$307$	9.80183	+	5.23919i	0.559420	+	0.299016i	0.726770	−	0.686881i	$-0.241021\pi$
$307$	9.80183	+	5.23919i	0.559420	+	0.299016i	−0.167349	+	0.985898i	$0.553521\pi$
$308$	3.73495	+	7.10593i	0.212819	+	0.404898i
$309$	−0.442182	−	0.362889i	−0.0251549	−	0.0206441i
$310$	−3.31008	+	4.91683i	−0.188000	+	0.279257i
$311$	1.58001	−	7.94327i	0.0895944	−	0.450422i	−0.909781	−	0.415088i	$-0.863751\pi$
$311$	1.58001	−	7.94327i	0.0895944	−	0.450422i	0.999376	−	0.0353333i	$-0.0112493\pi$
$312$	0.525058	+	5.96803i	0.0297256	+	0.337873i
$313$	16.4669	−	3.27547i	0.930763	−	0.185140i	0.293652	−	0.955912i	$-0.405129\pi$
$313$	16.4669	−	3.27547i	0.930763	−	0.185140i	0.637111	+	0.770772i	$0.280129\pi$
$314$	−19.7348	+	8.09420i	−1.11370	+	0.456782i
$315$	1.84350	+	3.44894i	0.103869	+	0.194326i
$316$	2.51505	+	0.518467i	0.141483	+	0.0291660i
$317$	−15.7361	−	1.54987i	−0.883830	−	0.0870496i	−0.354091	−	0.935211i	$-0.615210\pi$
$317$	−15.7361	−	1.54987i	−0.883830	−	0.0870496i	−0.529738	+	0.848161i	$0.677710\pi$
$318$	−7.44188	+	3.94459i	−0.417320	+	0.221201i
$319$			2.75392i			0.154190i
$320$	−1.66024	−	5.91416i	−0.0928105	−	0.330611i
$321$		−	11.8040i		−	0.658833i
$322$	19.0291	+	35.9004i	1.06045	+	2.00065i
$323$	−53.1050	−	5.23039i	−2.95484	−	0.291027i
$324$	1.09956	+	1.67062i	0.0610866	+	0.0928122i
$325$	−4.40379	−	8.23890i	−0.244278	−	0.457012i
$326$	2.04890	+	4.99549i	0.113478	+	0.276675i
$327$	8.32703	−	1.65635i	0.460486	−	0.0915963i
$328$	−6.22552	+	19.7783i	−0.343747	+	1.09208i
$329$	−1.65648	+	8.32769i	−0.0913247	+	0.459120i
$330$	0.709911	+	0.477923i	0.0390793	+	0.0263088i
$331$	10.3267	+	8.47492i	0.567608	+	0.465824i	0.873894	−	0.486116i	$-0.161587\pi$
$331$	10.3267	+	8.47492i	0.567608	+	0.465824i	−0.306287	+	0.951939i	$0.599087\pi$
$332$	4.55188	+	1.41541i	0.249817	+	0.0776806i
$333$	10.1331	+	5.41628i	0.555293	+	0.296810i
$334$	−4.21037	−	5.16685i	−0.230381	−	0.282718i
$335$	−4.26193	+	1.76535i	−0.232854	+	0.0964513i
$336$	9.35288	+	18.0986i	0.510242	+	0.987357i
$337$	−6.12692	−	2.53785i	−0.333755	−	0.138246i	0.209512	−	0.977806i	$-0.432813\pi$
$337$	−6.12692	−	2.53785i	−0.333755	−	0.138246i	−0.543266	+	0.839560i	$0.682813\pi$
$338$	3.45490	+	11.5334i	0.187922	+	0.627332i
$339$	−17.3106	+	5.25111i	−0.940182	+	0.285201i
$340$	−5.62935	+	10.3580i	−0.305294	+	0.561742i
$341$	−0.421641	−	4.28099i	−0.0228331	−	0.231829i
$342$	−1.95133	+	9.63496i	−0.105516	+	0.520999i
$343$	−33.7841	−	50.5614i	−1.82417	−	2.73006i
$344$	12.1092	−	11.8593i	0.652882	−	0.639413i
$345$	3.60156	+	2.40649i	0.193902	+	0.129561i
$346$	−25.7409	−	0.0894268i	−1.38384	−	0.00480761i
$347$	−11.2146	−	3.40190i	−0.602030	−	0.182624i	−0.0254658	−	0.999676i	$-0.508107\pi$
$347$	−11.2146	−	3.40190i	−0.602030	−	0.182624i	−0.576564	+	0.817052i	$0.695607\pi$
$348$	−0.0485590	+	6.98861i	−0.00260304	+	0.374629i
$349$	−12.3551	−	15.0547i	−0.661353	−	0.805861i	0.329014	−	0.944325i	$-0.393284\pi$
$349$	−12.3551	−	15.0547i	−0.661353	−	0.805861i	−0.990368	+	0.138464i	$0.955784\pi$
$350$	−24.4861	−	20.2380i	−1.30883	−	1.08176i
$351$	−1.49777	−	1.49777i	−0.0799451	−	0.0799451i
$352$	3.66324	+	2.54083i	0.195251	+	0.135427i
$353$	−3.87761	+	3.87761i	−0.206384	+	0.206384i	−0.802729	−	0.596344i	$-0.796619\pi$
$353$	−3.87761	+	3.87761i	−0.206384	+	0.206384i	0.596344	+	0.802729i	$0.296619\pi$
$354$	5.30708	−	0.504091i	0.282068	−	0.0267922i
$355$	4.34609	−	3.56674i	0.230667	−	0.189303i
$356$	0.984972	+	2.42546i	0.0522034	+	0.128549i
$357$	11.3494	−	37.4141i	0.600676	−	1.98016i
$358$	−9.86395	−	9.93273i	−0.521326	−	0.524961i
$359$	−12.6279	+	18.8989i	−0.666473	+	0.997448i	0.332057	+	0.943259i	$0.392257\pi$
$359$	−12.6279	+	18.8989i	−0.666473	+	0.997448i	−0.998531	+	0.0541886i	$0.982743\pi$
$360$	1.79311	+	1.22534i	0.0945052	+	0.0645811i
$361$	−24.3788	+	16.2894i	−1.28309	+	0.857335i
$362$	4.16121	+	6.27477i	0.218708	+	0.329795i
$363$	10.3289	−	1.01731i	0.542128	−	0.0533949i
$364$	−13.5715	−	16.7732i	−0.711340	−	0.879156i
$365$	1.22823	+	4.04894i	0.0642886	+	0.211931i
$366$	4.18296	−	7.76079i	0.218647	−	0.405663i
$367$	0.771364	−	1.86224i	0.0402649	−	0.0972080i	−0.902468	−	0.430757i	$-0.858246\pi$
$367$	0.771364	−	1.86224i	0.0402649	−	0.0972080i	0.942733	+	0.333550i	$0.108246\pi$
$368$	18.5859	+	12.7958i	0.968855	+	0.667027i
$369$	−2.80543	−	6.77290i	−0.146045	−	0.352583i
$370$	12.4124	+	1.26607i	0.645290	+	0.0658199i
$371$	14.2989	−	26.7514i	0.742363	−	1.38886i
$372$	−0.994512	−	10.8713i	−0.0515630	−	0.563651i
$373$	−11.1742	+	13.6158i	−0.578578	+	0.705000i	−0.977249	−	0.212094i	$-0.931972\pi$
$373$	−11.1742	+	13.6158i	−0.578578	+	0.705000i	0.398671	+	0.917094i	$0.369472\pi$
$374$	−1.64000	−	8.39720i	−0.0848024	−	0.434209i
$375$	−7.08691	−	1.40967i	−0.365967	−	0.0727953i
$376$	1.32169	+	4.52633i	0.0681610	+	0.233427i
$377$	−1.44400	−	7.25948i	−0.0743698	−	0.373882i
$378$	−6.64484	−	2.77947i	−0.341773	−	0.142960i
$379$	−8.81705	+	4.71281i	−0.452902	+	0.242081i	−0.682043	−	0.731312i	$-0.738908\pi$
$379$	−8.81705	+	4.71281i	−0.452902	+	0.242081i	0.229141	+	0.973393i	$0.426408\pi$
$380$	2.00979	+	10.4841i	0.103100	+	0.537824i
$381$	−0.410413	+	4.16699i	−0.0210261	+	0.213482i
$382$	−2.27944	+	7.42140i	−0.116626	+	0.379712i
$383$	28.6087			1.46184			0.730919	−	0.682464i	$-0.239092\pi$
$383$	28.6087			1.46184			0.730919	+	0.682464i	$0.239092\pi$
$384$	9.25138	+	6.51244i	0.472108	+	0.332337i
$385$	−3.08203			−0.157075
$386$	−6.97789	+	22.7186i	−0.355165	+	1.15635i
$387$	−0.587363	+	5.96360i	−0.0298573	+	0.303147i
$388$	−18.8374	+	3.61111i	−0.956324	+	0.183326i
$389$	3.42394	−	1.83013i	0.173600	−	0.0927914i	−0.382308	−	0.924035i	$-0.624871\pi$
$389$	3.42394	−	1.83013i	0.173600	−	0.0927914i	0.555908	+	0.831244i	$0.312371\pi$
$390$	−2.12196	−	0.887594i	−0.107450	−	0.0449451i
$391$	−8.44839	−	42.4729i	−0.427253	−	2.14795i
$392$	−46.9782	−	25.7434i	−2.37276	−	1.30024i
$393$	−13.3188	−	2.64927i	−0.671845	−	0.133638i
$394$	3.83295	+	19.6256i	0.193101	+	0.988725i
$395$	−0.625442	+	0.762104i	−0.0314694	+	0.0383456i
$396$	−1.56964	+	0.143591i	−0.0788774	+	0.00721574i
$397$	10.7886	−	20.1840i	0.541462	−	1.01300i	−0.451239	−	0.892403i	$-0.649018\pi$
$397$	10.7886	−	20.1840i	0.541462	−	1.01300i	0.992701	−	0.120602i	$-0.0384823\pi$
$398$	15.2645	+	1.55698i	0.765139	+	0.0780445i
$399$	−13.5483	−	32.7085i	−0.678264	−	1.63748i
$400$	−17.2532	−	3.68182i	−0.862659	−	0.184091i
$401$	6.05517	−	14.6185i	0.302381	−	0.730012i	−0.697529	−	0.716557i	$-0.745717\pi$
$401$	6.05517	−	14.6185i	0.302381	−	0.730012i	0.999909	−	0.0134549i	$-0.00428295\pi$
$402$	4.03115	−	7.47914i	0.201056	−	0.373025i
$403$	3.35618	+	11.0639i	0.167183	+	0.551130i
$404$	20.9944	−	16.9869i	1.04451	−	0.845129i
$405$	−0.764149	+	0.0752621i	−0.0379709	+	0.00373981i
$406$	−13.9104	−	20.9758i	−0.690363	−	1.04101i
$407$	−7.52905	+	5.03075i	−0.373201	+	0.249365i
$408$	−4.01376	−	21.3385i	−0.198711	−	1.05641i
$409$	13.0631	−	19.5503i	0.645927	−	0.966699i	−0.353583	−	0.935403i	$-0.615037\pi$
$409$	13.0631	−	19.5503i	0.645927	−	0.966699i	0.999510	−	0.0312954i	$-0.00996328\pi$
$410$	−5.60944	−	5.64855i	−0.277030	−	0.278962i
$411$	−5.12976	+	16.9105i	−0.253032	+	0.834136i
$412$	1.05998	−	0.430455i	0.0522216	−	0.0212070i
$413$	−14.8408	+	12.1795i	−0.730269	+	0.599316i
$414$	−7.94209	+	0.754377i	−0.390332	+	0.0370756i
$415$	−1.29408	+	1.29408i	−0.0635240	+	0.0635240i
$416$	−10.9888	−	4.77697i	−0.538769	−	0.234210i
$417$	8.11614	+	8.11614i	0.397449	+	0.397449i
$418$	−5.97175	−	4.93570i	−0.292088	−	0.241413i
$419$	−8.10632	−	9.87758i	−0.396020	−	0.482551i	0.536382	−	0.843975i	$-0.319791\pi$
$419$	−8.10632	−	9.87758i	−0.396020	−	0.482551i	−0.932402	+	0.361424i	$0.882291\pi$
$420$	−7.82125	−	0.0543444i	−0.381638	−	0.00265174i
$421$	13.6995	+	4.15569i	0.667671	+	0.202536i	0.605883	−	0.795554i	$-0.292820\pi$
$421$	13.6995	+	4.15569i	0.667671	+	0.202536i	0.0617877	+	0.998089i	$0.480320\pi$
$422$	9.08054	+	0.0315468i	0.442034	+	0.00153567i
$423$	−1.38617	−	0.926206i	−0.0673977	−	0.0450337i
$424$	0.175564	−	16.8444i	0.00852614	−	0.818037i
$425$	18.8099	+	28.1510i	0.912414	+	1.36552i
$426$	−2.05545	+	10.1490i	−0.0995868	+	0.491723i
$427$	3.11211	+	31.5978i	0.150606	+	1.52912i
$428$	20.7425	+	11.2731i	1.00263	+	0.544905i
$429$	1.59744	−	0.484579i	0.0771252	−	0.0233957i
$430$	1.86730	+	6.23353i	0.0900490	+	0.300607i
$431$	5.27871	+	2.18651i	0.254267	+	0.105321i	0.506176	−	0.862430i	$-0.331059\pi$
$431$	5.27871	+	2.18651i	0.254267	+	0.105321i	−0.251910	+	0.967751i	$0.581059\pi$
$432$	−3.98580	+	0.336715i	−0.191767	+	0.0162002i
$433$	2.51812	−	1.04304i	0.121013	−	0.0501253i	−0.321355	−	0.946959i	$-0.604138\pi$
$433$	2.51812	−	1.04304i	0.121013	−	0.0501253i	0.442368	+	0.896833i	$0.354138\pi$
$434$	24.8354	+	30.4774i	1.19214	+	1.46296i
$435$	−2.36633	−	1.26483i	−0.113457	−	0.0606440i
$436$	−5.04191	+	16.2145i	−0.241464	+	0.776535i
$437$	−30.3123	−	24.8767i	−1.45003	−	1.19001i
$438$	−6.46445	−	4.35197i	−0.308883	−	0.207945i
$439$	−0.912831	+	4.58911i	−0.0435670	+	0.219026i	−0.996436	−	0.0843572i	$-0.973116\pi$
$439$	−0.912831	+	4.58911i	−0.0435670	+	0.219026i	0.952869	+	0.303383i	$0.0981163\pi$
$440$	−1.51781	+	0.791061i	−0.0723589	+	0.0377124i
$441$	18.5757	−	3.69494i	0.884558	−	0.175950i
$442$	8.72615	+	21.2756i	0.415061	+	1.01197i
$443$	−11.3780	−	21.2867i	−0.540585	−	1.01136i	−0.992837	−	0.119474i	$-0.961879\pi$
$443$	−11.3780	−	21.2867i	−0.540585	−	1.01136i	0.452252	−	0.891890i	$-0.350621\pi$
$444$	−19.1952	+	12.6338i	−0.910962	+	0.599572i
$445$	−1.00021	−	0.0985118i	−0.0474144	−	0.00466991i
$446$	5.24849	+	9.90183i	0.248523	+	0.468865i
$447$		−	4.47804i		−	0.211804i
$448$	−40.7359	−	0.849247i	−1.92459	−	0.0401231i
$449$		−	24.2506i		−	1.14446i	−0.820094	−	0.572229i	$-0.806079\pi$
$449$		−	24.2506i		−	1.14446i	0.820094	−	0.572229i	$-0.193921\pi$
$450$	5.51096	−	2.92110i	0.259789	−	0.137702i
$451$	5.74966	+	0.566293i	0.270741	+	0.0266657i
$452$	7.30455	−	35.4339i	0.343577	−	1.66667i
$453$	−0.809282	−	1.51406i	−0.0380234	−	0.0711368i
$454$	−11.3310	+	4.64739i	−0.531789	+	0.218113i
$455$	8.12439	−	1.61604i	0.380877	−	0.0757612i
$456$	−15.0675	−	12.6306i	−0.705598	−	0.591483i
$457$	−0.869794	+	4.37275i	−0.0406872	+	0.204549i	−0.995782	−	0.0917524i	$-0.970753\pi$
$457$	−0.869794	+	4.37275i	−0.0406872	+	0.204549i	0.955095	+	0.296301i	$0.0957532\pi$
$458$	−3.75900	+	5.58365i	−0.175647	+	0.260907i
$459$	5.93408	+	4.86998i	0.276979	+	0.227311i
$460$	−7.66838	+	4.03058i	−0.357540	+	0.187927i
$461$	−7.65902	−	4.09383i	−0.356716	−	0.190669i	0.283298	−	0.959032i	$-0.408571\pi$
$461$	−7.65902	−	4.09383i	−0.356716	−	0.190669i	−0.640014	+	0.768363i	$0.721071\pi$
$462$	4.40044	−	3.58583i	0.204727	−	0.166828i
$463$	−16.1135	+	6.67444i	−0.748859	+	0.310187i	−0.724276	−	0.689510i	$-0.757826\pi$
$463$	−16.1135	+	6.67444i	−0.748859	+	0.310187i	−0.0245830	+	0.999698i	$0.507826\pi$
$464$	−12.2344	−	6.75963i	−0.567965	−	0.313808i
$465$	3.87214	+	1.60389i	0.179566	+	0.0743787i
$466$	−1.31662	+	0.394403i	−0.0609913	+	0.0182704i
$467$	5.90560	−	1.79144i	0.273279	−	0.0828982i	−0.150671	−	0.988584i	$-0.548143\pi$
$467$	5.90560	−	1.79144i	0.273279	−	0.0828982i	0.423950	+	0.905686i	$0.360643\pi$
$468$	4.06237	−	1.20155i	0.187783	−	0.0555415i
$469$	2.99917	+	30.4510i	0.138489	+	1.40610i
$470$	−1.77431	−	0.359344i	−0.0818428	−	0.0165753i
$471$	8.37951	+	12.5408i	0.386107	+	0.577851i
$472$	−4.18258	+	9.80727i	−0.192519	+	0.451416i
$473$	−3.92673	−	2.62376i	−0.180551	−	0.120640i
$474$	0.00630827	−	1.81579i	0.000289749	−	0.0834022i
$475$	29.3378	+	8.89953i	1.34611	+	0.408338i
$476$	54.9068	+	55.6752i	2.51665	+	2.55187i
$477$	3.77827	+	4.60384i	0.172995	+	0.210795i
$478$	−1.23560	+	1.49497i	−0.0565151	+	0.0683781i
$479$	−22.6735	−	22.6735i	−1.03598	−	1.03598i	−0.999328	−	0.0366516i	$-0.988331\pi$
$479$	−22.6735	−	22.6735i	−1.03598	−	1.03598i	−0.0366516	−	0.999328i	$-0.511669\pi$
$480$	−3.86570	+	1.98071i	−0.176444	+	0.0904066i
$481$	17.2092	−	17.2092i	0.784670	−	0.784670i
$482$	0.354260	+	3.72965i	0.0161361	+	0.169881i
$483$	22.2094	−	18.2268i	1.01056	−	0.829348i
$484$	−8.07673	+	19.1221i	−0.367124	+	0.869184i
$485$	2.13760	−	7.04672i	0.0970633	−	0.319975i
$486$	1.00347	−	0.996520i	0.0455182	−	0.0452031i
$487$	−11.3070	+	16.9221i	−0.512369	+	0.766814i	−0.993979	−	0.109572i	$-0.965052\pi$
$487$	−11.3070	+	16.9221i	−0.512369	+	0.766814i	0.481610	+	0.876386i	$0.340052\pi$
$488$	9.64281	+	14.7623i	0.436510	+	0.668256i
$489$	3.17448	−	2.12112i	0.143555	−	0.0959203i
$490$	17.1400	−	11.3667i	0.774308	−	0.513494i
$491$	−12.1068	+	1.19242i	−0.546372	+	0.0538130i	−0.367438	−	0.930048i	$-0.619765\pi$
$491$	−12.1068	+	1.19242i	−0.546372	+	0.0538130i	−0.178934	+	0.983861i	$0.557265\pi$
$492$	14.5809	+	1.53846i	0.657359	+	0.0693592i
$493$	7.78688	+	25.6699i	0.350703	+	1.15611i
$494$	18.3299	+	9.87954i	0.824700	+	0.444502i
$495$	0.231576	−	0.559074i	0.0104086	−	0.0251285i
$496$	20.0534	+	8.63477i	0.900423	+	0.387713i
$497$	−14.2712	−	34.4537i	−0.640151	−	1.54546i
$498$	0.342036	−	3.35328i	0.0153270	−	0.150264i
$499$	−7.52891	+	14.0856i	−0.337040	+	0.630558i	−0.992161	−	0.124966i	$-0.960118\pi$
$499$	−7.52891	+	14.0856i	−0.337040	+	0.630558i	0.655121	+	0.755524i	$0.272618\pi$
$500$	9.24534	−	11.1072i	0.413464	−	0.496729i
$501$	−2.98986	+	3.64315i	−0.133577	+	0.162764i
$502$	4.37442	−	0.854338i	0.195240	−	0.0381310i
$503$	−17.0551	−	3.39248i	−0.760451	−	0.151263i	−0.200392	−	0.979716i	$-0.564222\pi$
$503$	−17.0551	−	3.39248i	−0.760451	−	0.151263i	−0.560059	+	0.828453i	$0.689222\pi$
$504$	11.2302	−	9.02217i	0.500233	−	0.401879i
$505$	2.02273	+	10.1690i	0.0900104	+	0.452513i
$506$	2.42621	−	5.80032i	0.107858	−	0.257856i
$507$	7.50812	−	4.01317i	0.333447	−	0.178231i
$508$	−6.93049	−	4.70079i	−0.307491	−	0.208564i
$509$	−3.07661	+	31.2374i	−0.136369	+	1.38457i	0.646751	+	0.762701i	$0.276127\pi$
$509$	−3.07661	+	31.2374i	−0.136369	+	1.38457i	−0.783119	+	0.621871i	$0.786373\pi$
$510$	7.96860	+	2.44751i	0.352855	+	0.108378i
$511$	28.0649			1.24152
$512$	−20.2793	+	10.0374i	−0.896227	+	0.443596i
$513$	6.95127			0.306906
$514$	−0.392857	−	0.120664i	−0.0173282	−	0.00532225i
$515$	−0.0430519	+	0.437113i	−0.00189709	+	0.0192615i
$516$	−9.91858	−	6.72754i	−0.436641	−	0.296163i
$517$	1.15872	−	0.619348i	0.0509604	−	0.0272389i
$518$	31.9356	−	76.3481i	1.40317	−	3.35454i
$519$	3.55097	+	17.8519i	0.155870	+	0.783613i
$520$	3.58625	−	2.88114i	0.157268	−	0.126346i
$521$	−4.57228	−	0.909484i	−0.200315	−	0.0398452i	0.0939127	−	0.995580i	$-0.470063\pi$
$521$	−4.57228	−	0.909484i	−0.200315	−	0.0398452i	−0.294228	+	0.955735i	$0.595063\pi$
$522$	4.85018	−	0.947255i	0.212286	−	0.0414602i
$523$	−12.4717	+	15.1968i	−0.545349	+	0.664510i	−0.970637	−	0.240548i	$-0.922673\pi$
$523$	−12.4717	+	15.1968i	−0.545349	+	0.664510i	0.425288	+	0.905058i	$0.360173\pi$
$524$	17.3752	−	20.8743i	0.759041	−	0.911899i
$525$	−10.5888	+	19.8103i	−0.462134	+	0.864592i
$526$	−4.46227	+	43.7475i	−0.194564	+	1.90748i
$527$	−16.0350	−	38.7119i	−0.698495	−	1.68632i
$528$	1.24672	−	2.89538i	0.0542566	−	0.126005i
$529$	3.37638	−	8.15131i	0.146799	−	0.354405i
$530$	5.69304	+	3.06847i	0.247290	+	0.133286i
$531$	−1.09425	−	3.60724i	−0.0474862	−	0.156541i
$532$	70.4161	+	7.42973i	3.05292	+	0.322120i
$533$	−15.4534	+	1.52202i	−0.669360	+	0.0659262i
$534$	1.54269	−	1.02306i	0.0667585	−	0.0442719i
$535$	−7.53613	+	5.03548i	−0.325815	+	0.217703i
$536$	9.29285	+	14.2265i	0.401390	+	0.614492i
$537$	−5.49926	+	8.23022i	−0.237310	+	0.355160i
$538$	2.52507	−	2.50758i	0.108863	−	0.108110i
$539$	−4.33287	+	14.2836i	−0.186630	+	0.615236i
$540$	0.597528	−	1.41468i	0.0257135	−	0.0608780i
$541$	−10.6789	+	8.76392i	−0.459120	+	0.376790i	−0.835334	−	0.549743i	$-0.814726\pi$
$541$	−10.6789	+	8.76392i	−0.459120	+	0.376790i	0.376214	+	0.926533i	$0.377226\pi$
$542$	−0.0532074	−	0.560167i	−0.00228545	−	0.0240612i
$543$	3.76459	−	3.76459i	0.161554	−	0.161554i
$544$	41.3302	+	13.3256i	1.77202	+	0.571331i
$545$	−4.60973	−	4.60973i	−0.197459	−	0.197459i
$546$	−9.71959	+	11.7598i	−0.415960	+	0.503273i
$547$	−19.1721	−	23.3612i	−0.819739	−	0.998854i	−0.999884	−	0.0152144i	$-0.995157\pi$
$547$	−19.1721	−	23.3612i	−0.819739	−	0.998854i	0.180146	−	0.983640i	$-0.442343\pi$
$548$	−24.8170	−	25.1643i	−1.06013	−	1.07496i
$549$	−5.96563	−	1.80965i	−0.254607	−	0.0772341i
$550$	−0.0170771	+	4.91554i	−0.000728172	+	0.209599i
$551$	20.1967	+	13.4950i	0.860410	+	0.574908i
$552$	6.25927	−	14.6767i	0.266412	−	0.624681i
$553$	3.63308	+	5.43729i	0.154494	+	0.231217i
$554$	4.13090	+	0.836617i	0.175505	+	0.0355444i
$555$	−0.864750	−	8.77996i	−0.0367066	−	0.372688i
$556$	−22.0132	+	6.51096i	−0.933568	+	0.276126i
$557$	23.9326	−	7.25988i	1.01406	−	0.307611i	0.260840	−	0.965382i	$-0.416000\pi$
$557$	23.9326	−	7.25988i	1.01406	−	0.307611i	0.753218	+	0.657771i	$0.228500\pi$
$558$	−7.39462	+	2.21511i	−0.313039	+	0.0937730i
$559$	11.7268	+	4.85741i	0.495992	+	0.205447i
$560$	7.56499	−	13.6920i	0.319679	−	0.578592i
$561$	−5.58938	+	2.31520i	−0.235984	+	0.0977476i
$562$	19.0013	−	15.4838i	0.801520	−	0.653144i
$563$	24.3598	+	13.0206i	1.02664	+	0.548752i	0.896639	−	0.442762i	$-0.146001\pi$
$563$	24.3598	+	13.0206i	1.02664	+	0.548752i	0.130003	+	0.991514i	$0.458501\pi$
$564$	2.95140	−	1.55129i	0.124276	−	0.0653210i
$565$	10.7371	+	8.81170i	0.451713	+	0.370711i
$566$	−16.1055	+	23.9233i	−0.676966	+	1.00557i
$567$	−0.993614	+	4.99523i	−0.0417279	+	0.209780i
$568$	−15.8714	−	13.3045i	−0.665949	−	0.558246i
$569$	31.7737	−	6.32019i	1.33202	−	0.264956i	0.522799	−	0.852456i	$-0.324888\pi$
$569$	31.7737	−	6.32019i	1.33202	−	0.264956i	0.809224	+	0.587500i	$0.199888\pi$
$570$	6.98378	−	2.86439i	0.292518	−	0.119976i
$571$	−8.49593	−	15.8948i	−0.355544	−	0.665175i	0.639033	−	0.769179i	$-0.279335\pi$
$571$	−8.49593	−	15.8948i	−0.355544	−	0.665175i	−0.994577	+	0.104004i	$0.966835\pi$
$572$	−0.674073	+	3.26989i	−0.0281844	+	0.136721i
$573$	5.46324	+	0.538082i	0.228230	+	0.0224787i
$574$	−46.6540	+	24.7291i	−1.94730	+	1.03217i
$575$			24.8799i			1.03756i
$576$	3.21485	−	7.32562i	0.133952	−	0.305234i
$577$			34.7874i			1.44822i	0.689685	+	0.724109i	$0.257749\pi$
$577$			34.7874i			1.44822i	−0.689685	+	0.724109i	$0.742251\pi$
$578$	−27.7710	−	52.3929i	−1.15512	−	2.17926i
$579$	16.7242	+	1.64719i	0.695034	+	0.0684549i
$580$	4.48253	−	2.95029i	0.186127	−	0.122504i
$581$	5.72231	+	10.7057i	0.237401	+	0.444147i
$582$	5.14661	+	12.5481i	0.213334	+	0.520138i
$583$	−4.60350	+	0.915693i	−0.190658	+	0.0379241i
$584$	13.8212	−	7.20340i	0.571926	−	0.298079i
$585$	−0.317300	+	1.59518i	−0.0131188	+	0.0659525i
$586$	8.14083	+	5.48054i	0.336295	+	0.226399i
$587$	19.9533	+	16.3753i	0.823563	+	0.675881i	0.948672	−	0.316262i	$-0.102428\pi$
$587$	19.9533	+	16.3753i	0.823563	+	0.675881i	−0.125109	+	0.992143i	$0.539928\pi$
$588$	−11.2474	+	36.1709i	−0.463833	+	1.49166i
$589$	−33.4622	−	17.8859i	−1.37879	−	0.736977i
$590$	−2.58579	−	3.17321i	−0.106455	−	0.130639i
$591$	13.0633	−	5.41099i	0.537352	−	0.222578i
$592$	−3.86880	−	45.7963i	−0.159007	−	1.88221i
$593$	14.0374	+	5.81449i	0.576448	+	0.238773i	0.651808	−	0.758384i	$-0.274011\pi$
$593$	14.0374	+	5.81449i	0.576448	+	0.238773i	−0.0753602	+	0.997156i	$0.524011\pi$
$594$	0.319826	+	1.06766i	0.0131226	+	0.0438068i
$595$	−28.7283	+	8.71463i	−1.17774	+	0.357265i
$596$	7.86902	+	4.27664i	0.322328	+	0.175178i
$597$	−1.06345	−	10.7974i	−0.0435240	−	0.441907i
$598$	−3.35427	+	16.5621i	−0.137166	+	0.677276i
$599$	14.0022	+	20.9558i	0.572116	+	0.856232i	0.998840	−	0.0481495i	$-0.0153324\pi$
$599$	14.0022	+	20.9558i	0.572116	+	0.856232i	−0.426724	+	0.904382i	$0.640332\pi$
$600$	−0.130011	+	12.4739i	−0.00530767	+	0.509243i
$601$	−23.3352	−	15.5921i	−0.951862	−	0.636014i	−0.0203765	−	0.999792i	$-0.506487\pi$
$601$	−23.3352	−	15.5921i	−0.951862	−	0.636014i	−0.931485	+	0.363779i	$0.881487\pi$
$602$	43.1617	+	0.149949i	1.75914	+	0.00611146i
$603$	−5.74912	−	1.74398i	−0.234122	−	0.0710202i
$604$	3.43347	+	0.0238568i	0.139706	+	0.000970719i
$605$	−5.05574	−	6.16043i	−0.205545	−	0.250457i
$606$	−14.7193	−	12.1656i	−0.597929	−	0.494194i
$607$	−5.04016	−	5.04016i	−0.204574	−	0.204574i	0.597383	−	0.801956i	$-0.296207\pi$
$607$	−5.04016	−	5.04016i	−0.204574	−	0.204574i	−0.801956	+	0.597383i	$0.796207\pi$
$608$	36.5850	−	14.4147i	1.48372	−	0.584593i
$609$	−12.5846	+	12.5846i	−0.509952	+	0.509952i
$610$	−6.73923	+	0.640124i	−0.272863	+	0.0259179i
$611$	−2.72970	+	2.24020i	−0.110432	+	0.0906290i
$612$	−14.2250	+	5.77671i	−0.575010	+	0.233510i
$613$	−2.29617	+	7.56945i	−0.0927413	+	0.305727i	−0.991023	−	0.133694i	$-0.957316\pi$
$613$	−2.29617	+	7.56945i	−0.0927413	+	0.305727i	0.898281	+	0.439421i	$0.144816\pi$
$614$	11.0755	+	11.1527i	0.446971	+	0.450087i
$615$	−3.12732	+	4.68037i	−0.126106	+	0.188731i
$616$	2.09867	+	11.1572i	0.0845579	+	0.449538i
$617$	36.2977	−	24.2534i	1.46129	−	0.976404i	0.465473	−	0.885062i	$-0.345884\pi$
$617$	36.2977	−	24.2534i	1.46129	−	0.976404i	0.995820	−	0.0913418i	$-0.0291156\pi$
$618$	−0.447098	−	0.674189i	−0.0179849	−	0.0271198i
$619$	37.7754	−	3.72055i	1.51832	−	0.149542i	0.695784	−	0.718251i	$-0.255057\pi$
$619$	37.7754	−	3.72055i	1.51832	−	0.149542i	0.822538	+	0.568710i	$0.192557\pi$
$620$	−6.51643	+	5.27255i	−0.261706	+	0.211751i
$621$	1.63755	+	5.39827i	0.0657125	+	0.216625i
$622$	5.43423	−	10.0823i	0.217893	−	0.404264i
$623$	−2.55113	+	6.15898i	−0.102209	+	0.246754i
$624$	−1.76825	+	8.28610i	−0.0707867	+	0.331710i
$625$	−6.31573	−	15.2475i	−0.252629	−	0.609900i
$626$	23.6214	+	2.40939i	0.944099	+	0.0962985i
$627$	−2.58244	+	4.83140i	−0.103133	+	0.192948i
$628$	−30.0400	+	2.74807i	−1.19873	+	0.109660i
$629$	−55.9553	+	68.1817i	−2.23108	+	2.71858i
$630$	1.06011	+	5.42804i	0.0422359	+	0.216258i
$631$	39.6663	+	7.89012i	1.57909	+	0.314101i	0.905284	−	0.424807i	$-0.139658\pi$
$631$	39.6663	+	7.89012i	1.57909	+	0.314101i	0.673806	+	0.738908i	$0.264658\pi$
$632$	3.18478	+	1.74522i	0.126684	+	0.0694210i
$633$	−1.25266	−	6.29757i	−0.0497890	−	0.250306i
$634$	−20.6299	−	8.62927i	−0.819318	−	0.342712i
$635$	2.83546	−	1.51559i	0.112522	−	0.0601442i
$636$	−11.6984	+	2.24258i	−0.463873	+	0.0889241i
$637$	3.93219	−	39.9242i	0.155799	−	1.58185i
$638$	−1.14349	+	3.72298i	−0.0452713	+	0.147394i
$639$	7.32215			0.289660
$640$	0.211240	−	8.68462i	0.00835001	−	0.343290i
$641$	37.1568			1.46760			0.733802	−	0.679363i	$-0.237744\pi$
$641$	37.1568			1.46760			0.733802	+	0.679363i	$0.237744\pi$
$642$	4.90128	−	15.9576i	0.193438	−	0.629796i
$643$	−0.963874	+	9.78638i	−0.0380115	+	0.385937i	0.957291	+	0.289125i	$0.0933645\pi$
$643$	−0.963874	+	9.78638i	−0.0380115	+	0.385937i	−0.995303	+	0.0968117i	$0.969136\pi$
$644$	10.8185	+	56.4346i	0.426307	+	2.22383i
$645$	4.05797	−	2.16903i	0.159782	−	0.0854055i
$646$	−69.6201	−	29.1213i	−2.73916	−	1.14576i
$647$	−6.88255	−	34.6009i	−0.270581	−	1.36030i	−0.841926	−	0.539593i	$-0.818578\pi$
$647$	−6.88255	−	34.6009i	−0.270581	−	1.36030i	0.571345	−	0.820710i	$-0.306422\pi$
$648$	0.792796	+	2.71505i	0.0311440	+	0.106657i
$649$	2.91370	+	0.579570i	0.114373	+	0.0227501i
$650$	−2.53242	−	12.9666i	−0.0993296	−	0.508592i
$651$	17.6361	−	21.4896i	0.691212	−	0.842244i
$652$	0.695624	+	7.60407i	0.0272427	+	0.297798i
$653$	−17.2998	+	32.3656i	−0.676992	+	1.26656i	0.275296	+	0.961360i	$0.411224\pi$
$653$	−17.2998	+	32.3656i	−0.676992	+	1.26656i	−0.952287	+	0.305203i	$0.901276\pi$
$654$	11.9449	+	1.21839i	0.467084	+	0.0476427i
$655$	3.99030	+	9.63343i	0.155914	+	0.376409i
$656$	−16.6286	+	24.1530i	−0.649239	+	0.943018i
$657$	−2.10873	+	5.09093i	−0.0822695	+	0.198616i
$658$	−5.69722	+	10.5703i	−0.222101	+	0.412071i
$659$	12.3651	+	40.7622i	0.481675	+	1.58787i	0.775068	+	0.631877i	$0.217715\pi$
$659$	12.3651	+	40.7622i	0.481675	+	1.58787i	−0.293394	+	0.955992i	$0.594785\pi$
$660$	0.761272	+	0.940868i	0.0296325	+	0.0366232i
$661$	4.00766	−	0.394720i	0.155880	−	0.0153528i	−0.0197762	−	0.999804i	$-0.506295\pi$
$661$	4.00766	−	0.394720i	0.155880	−	0.0153528i	0.175656	+	0.984452i	$0.443795\pi$
$662$	10.4415	+	15.7450i	0.405822	+	0.611947i
$663$	13.5199	−	9.03374i	0.525071	−	0.350841i
$664$	5.56590	+	3.80351i	0.215999	+	0.147605i
$665$	−15.1029	+	22.6030i	−0.585664	+	0.876508i
$666$	11.4499	+	11.5297i	0.443673	+	0.446766i
$667$	−5.72223	+	18.8637i	−0.221566	+	0.730404i
$668$	−3.54653	−	8.73323i	−0.137219	−	0.337899i
$669$	6.12566	−	5.02720i	0.236832	−	0.194363i
$670$	−6.49465	+	0.616893i	−0.250910	+	0.0238326i
$671$	3.47405	−	3.47405i	0.134114	−	0.134114i
$672$	5.12906	+	28.3507i	0.197858	+	1.09365i
$673$	−6.58939	−	6.58939i	−0.254002	−	0.254002i	0.568607	−	0.822609i	$-0.307483\pi$
$673$	−6.58939	−	6.58939i	−0.254002	−	0.254002i	−0.822609	+	0.568607i	$0.807483\pi$
$674$	−7.22911	−	5.97493i	−0.278455	−	0.230146i
$675$	−2.79794	−	3.40929i	−0.107693	−	0.131224i
$676$	−0.118304	+	17.0263i	−0.00455016	+	0.654858i
$677$	−29.7149	−	9.01391i	−1.14204	−	0.346433i	−0.338078	−	0.941118i	$-0.609777\pi$
$677$	−29.7149	−	9.01391i	−1.14204	−	0.346433i	−0.803959	+	0.594685i	$0.797277\pi$
$678$	−25.5823	−	0.0888757i	−0.982481	−	0.00341325i
$679$	−40.6121	−	27.1362i	−1.55855	−	1.04139i
$680$	−11.9111	+	11.6654i	−0.456770	+	0.447347i
$681$	4.81121	+	7.20049i	0.184366	+	0.275923i
$682$	1.20756	−	5.96248i	0.0462399	−	0.228315i
$683$	1.97622	+	20.0649i	0.0756181	+	0.767763i	0.955974	+	0.293450i	$0.0948035\pi$
$683$	1.97622	+	20.0649i	0.0756181	+	0.767763i	−0.880356	+	0.474313i	$0.842696\pi$
$684$	−6.63864	+	12.2151i	−0.253835	+	0.467056i
$685$	12.9847	−	3.93887i	0.496120	−	0.150496i
$686$	−24.6778	−	82.3811i	−0.942204	−	3.14533i
$687$	4.39728	+	1.82141i	0.167767	+	0.0694912i
$688$	21.2945	−	11.0044i	0.811844	−	0.419541i
$689$	11.6550	−	4.82764i	0.444018	−	0.183918i
$690$	3.86966	+	4.74874i	0.147316	+	0.180782i
$691$	33.1510	+	17.7196i	1.26112	+	0.674084i	0.960133	−	0.279543i	$-0.0901830\pi$
$691$	33.1510	+	17.7196i	1.26112	+	0.674084i	0.300990	+	0.953627i	$0.402683\pi$
$692$	−34.7616	−	10.8091i	−1.32144	−	0.410901i
$693$	−3.10275	−	2.54636i	−0.117864	−	0.0967283i
$694$	−13.7482	−	9.25553i	−0.521876	−	0.351335i
$695$	1.71939	−	8.64397i	0.0652203	−	0.327884i
$696$	−2.96748	+	9.42762i	−0.112482	+	0.357353i
$697$	55.1952	−	10.9790i	2.09067	−	0.415859i
$698$	−10.4516	−	25.4824i	−0.395598	−	0.964522i
$699$	0.458134	+	0.857109i	0.0173282	+	0.0324189i
$700$	−24.6990	−	37.5265i	−0.933535	−	1.41837i
$701$	−36.6431	−	3.60903i	−1.38399	−	0.136311i	−0.621552	−	0.783373i	$-0.713498\pi$
$701$	−36.6431	−	3.60903i	−1.38399	−	0.136311i	−0.762438	+	0.647061i	$0.775998\pi$
$702$	−1.40290	−	2.64672i	−0.0529491	−	0.0998941i
$703$			79.8690i			3.01231i
$704$	3.89726	+	4.95597i	0.146883	+	0.186785i
$705$			1.28010i			0.0482113i
$706$	−6.85215	+	3.63200i	−0.257884	+	0.136692i
$707$	68.4406	+	6.74081i	2.57397	+	0.253514i
$708$	7.38386	+	1.52215i	0.277502	+	0.0572059i
$709$	20.6480	+	38.6296i	0.775451	+	1.45077i	0.889327	+	0.457271i	$0.151173\pi$
$709$	20.6480	+	38.6296i	0.775451	+	1.45077i	−0.113876	+	0.993495i	$0.536327\pi$
$710$	7.35640	−	3.01722i	0.276081	−	0.113234i
$711$	−1.25930	+	0.250490i	−0.0472273	+	0.00939410i
$712$	0.324458	+	3.68793i	0.0121596	+	0.138211i
$713$	6.00713	−	30.1999i	0.224969	−	1.13099i
$714$	30.8783	−	45.8669i	1.15559	−	1.71653i
$715$	−0.990832	−	0.813155i	−0.0370550	−	0.0304103i
$716$	−9.21061	−	17.5236i	−0.344217	−	0.654889i
$717$	1.20949	+	0.646487i	0.0451693	+	0.0241435i
$718$	−24.9187	+	20.3058i	−0.929957	+	0.757805i
$719$	16.8051	−	6.96088i	0.626723	−	0.259597i	−0.0466372	−	0.998912i	$-0.514850\pi$
$719$	16.8051	−	6.96088i	0.626723	−	0.259597i	0.673360	+	0.739315i	$0.264850\pi$
$720$	1.91529	+	2.40106i	0.0713785	+	0.0894822i
$721$	2.69161	+	1.11490i	0.100241	+	0.0415212i
$722$	−39.7210	+	11.8987i	−1.47826	+	0.442824i
$723$	2.53506	−	0.769002i	0.0942799	−	0.0285995i
$724$	3.02004	+	10.2106i	0.112239	+	0.379474i
$725$	−1.51061	−	15.3375i	−0.0561026	−	0.569620i
$726$	14.3859	+	2.91353i	0.533911	+	0.108131i
$727$	−8.46832	−	12.6737i	−0.314073	−	0.470043i	0.640527	−	0.767936i	$-0.278716\pi$
$727$	−8.46832	−	12.6737i	−0.314073	−	0.470043i	−0.954599	+	0.297893i	$0.903716\pi$
$728$	−11.3824	−	28.3107i	−0.421862	−	1.04926i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	−0.0207880	+	5.98369i	−0.000769398	+	0.221466i
$731$	−44.0208	−	13.3536i	−1.62817	−	0.493899i
$732$	8.87734	−	8.75483i	0.328116	−	0.323588i
$733$	−29.3758	−	35.7946i	−1.08502	−	1.32210i	−0.943206	−	0.332209i	$-0.892206\pi$
$733$	−29.3758	−	35.7946i	−1.08502	−	1.32210i	−0.141815	−	0.989893i	$-0.545294\pi$
$734$	1.81604	−	2.19724i	0.0670312	−	0.0811016i
$735$	−10.2833	−	10.2833i	−0.379304	−	0.379304i
$736$	19.8128	+	25.0157i	0.730310	+	0.922091i
$737$	3.34797	−	3.34797i	0.123324	−	0.123324i
$738$	−0.980342	−	10.3210i	−0.0360869	−	0.379923i
$739$	20.7246	−	17.0083i	0.762368	−	0.625659i	−0.170715	−	0.985320i	$-0.554608\pi$
$739$	20.7246	−	17.0083i	0.762368	−	0.625659i	0.933083	+	0.359661i	$0.117108\pi$
$740$	16.2544	+	6.86551i	0.597525	+	0.252381i
$741$	4.27414	−	14.0899i	0.157014	−	0.517607i
$742$	30.4383	−	30.2275i	1.11742	−	1.10969i
$743$	−10.8375	+	16.2194i	−0.397588	+	0.595033i	−0.975213	−	0.221270i	$-0.928980\pi$
$743$	−10.8375	+	16.2194i	−0.397588	+	0.595033i	0.577624	+	0.816303i	$0.303980\pi$
$744$	3.16956	−	15.1097i	0.116202	−	0.553948i
$745$	−2.85896	+	1.91030i	−0.104744	+	0.0699879i
$746$	−20.7598	+	13.7672i	−0.760071	+	0.504053i
$747$	−2.37195	+	0.233617i	−0.0867853	+	0.00854760i
$748$	1.26962	−	12.0330i	0.0464221	−	0.439970i
$749$	17.4515	+	57.5300i	0.637665	+	2.10210i
$750$	−8.99535	−	4.84837i	−0.328464	−	0.177037i
$751$	13.1802	−	31.8197i	0.480951	−	1.16112i	−0.478207	−	0.878247i	$-0.658713\pi$
$751$	13.1802	−	31.8197i	0.480951	−	1.16112i	0.959158	−	0.282871i	$-0.0912869\pi$
$752$	−0.0926652	+	6.66786i	−0.00337915	+	0.243152i
$753$	−1.20607	−	2.91172i	−0.0439518	−	0.106109i
$754$	1.06219	−	10.4136i	0.0386826	−	0.379239i
$755$	−0.621405	+	1.16257i	−0.0226152	+	0.0423101i
$756$	−7.82894	−	6.51661i	−0.284736	−	0.237007i
$757$	−5.63821	+	6.87017i	−0.204924	+	0.249701i	−0.865323	−	0.501214i	$-0.832887\pi$
$757$	−5.63821	+	6.87017i	−0.204924	+	0.249701i	0.660399	+	0.750915i	$0.270387\pi$
$758$	−13.8765	+	2.71013i	−0.504017	+	0.0984362i
$759$	−4.36037	−	0.867332i	−0.158272	−	0.0314822i
$760$	−1.63624	+	15.0078i	−0.0593527	+	0.544391i
$761$	−3.32901	−	16.7360i	−0.120676	−	0.606681i	−0.993036	−	0.117815i	$-0.962411\pi$
$761$	−3.32901	−	16.7360i	−0.120676	−	0.606681i	0.872359	−	0.488866i	$-0.162589\pi$
$762$	−2.28507	+	5.46288i	−0.0827792	+	0.197899i
$763$	−38.1354	+	20.3838i	−1.38059	+	0.737942i
$764$	−6.16308	+	9.08640i	−0.222973	+	0.328734i
$765$	0.577756	−	5.86606i	0.0208888	−	0.212088i
$766$	38.6757	+	11.8790i	1.39741	+	0.429206i
$767$	−7.98456			−0.288306
$768$	9.80267	+	12.6455i	0.353723	+	0.456304i
$769$	−7.95660			−0.286923			−0.143461	−	0.989656i	$-0.545823\pi$
$769$	−7.95660			−0.286923			−0.143461	+	0.989656i	$0.545823\pi$
$770$	−4.16654	−	1.27973i	−0.150152	−	0.0461183i
$771$	−0.0284837	+	0.289200i	−0.00102582	+	0.0104153i
$772$	−18.8666	+	27.8155i	−0.679023	+	1.00110i
$773$	−12.8736	+	6.88106i	−0.463030	+	0.247495i	−0.686379	−	0.727244i	$-0.740801\pi$
$773$	−12.8736	+	6.88106i	−0.463030	+	0.247495i	0.223349	+	0.974738i	$0.428301\pi$
$774$	−3.27027	+	7.81820i	−0.117548	+	0.281020i
$775$	4.69652	+	23.6110i	0.168704	+	0.848132i
$776$	−26.9654	−	2.93993i	−0.968001	−	0.105537i
$777$	−57.3945	−	11.4165i	−2.05901	−	0.409564i
$778$	5.38868	−	1.05243i	0.193193	−	0.0377313i
$779$	32.3282	−	39.3920i	1.15828	−	1.41137i
$780$	−2.50009	−	2.08101i	−0.0895177	−	0.0745122i
$781$	−2.72023	+	5.08919i	−0.0973374	+	0.182105i
$782$	6.21452	−	60.9264i	0.222231	−	2.17872i
$783$	−1.33724	−	3.22839i	−0.0477892	−	0.115373i
$784$	−52.8198	−	54.3086i	−1.88642	−	1.93959i
$785$	4.43194	−	10.6996i	0.158183	−	0.381887i
$786$	−16.9054	−	9.11179i	−0.602997	−	0.325007i
$787$	−12.0467	−	39.7125i	−0.429417	−	1.41560i	−0.858723	−	0.512439i	$-0.828742\pi$
$787$	−12.0467	−	39.7125i	−0.429417	−	1.41560i	0.429306	−	0.903159i	$-0.358758\pi$
$788$	−2.96732	+	28.1231i	−0.105706	+	1.00184i
$789$	30.9450	−	3.04781i	1.10167	−	0.108505i
$790$	−1.16197	+	0.770577i	−0.0413410	+	0.0274159i
$791$	76.6046	−	51.1856i	2.72375	−	1.81995i
$792$	−2.18159	−	0.457633i	−0.0775195	−	0.0162613i
$793$	−7.33619	+	10.9794i	−0.260516	+	0.389889i
$794$	22.9657	−	22.8067i	0.815024	−	0.809380i
$795$	1.32750	−	4.37617i	0.0470814	−	0.155207i
$796$	19.9893	+	8.44303i	0.708502	+	0.299255i
$797$	−35.9888	+	29.5352i	−1.27479	+	1.04619i	−0.278471	+	0.960445i	$0.589828\pi$
$797$	−35.9888	+	29.5352i	−1.27479	+	1.04619i	−0.996317	+	0.0857465i	$0.972672\pi$
$798$	−4.73440	−	49.8437i	−0.167596	−	1.76445i
$799$	9.04944	−	9.04944i	0.320146	−	0.320146i
$800$	−21.7955	−	12.1413i	−0.770587	−	0.429260i
$801$	−0.925543	−	0.925543i	−0.0327025	−	0.0327025i
$802$	14.2558	−	17.2482i	0.503390	−	0.609056i
$803$	−2.75499	−	3.35697i	−0.0972215	−	0.118465i
$804$	8.55516	−	8.43709i	0.301717	−	0.297553i
$805$	−21.1111	−	6.40399i	−0.744069	−	0.225711i
$806$	−0.0568039	+	16.3506i	−0.00200083	+	0.575926i
$807$	−2.09226	−	1.39800i	−0.0736511	−	0.0492121i
$808$	35.4353	−	14.2469i	1.24661	−	0.501206i
$809$	−12.1389	−	18.1672i	−0.426782	−	0.638724i	0.554300	−	0.832317i	$-0.312986\pi$
$809$	−12.1389	−	18.1672i	−0.426782	−	0.638724i	−0.981082	+	0.193592i	$0.937986\pi$
$810$	−1.06429	−	0.215547i	−0.0373954	−	0.00757356i
$811$	−1.98181	−	20.1216i	−0.0695907	−	0.706566i	−0.965163	−	0.261650i	$-0.915733\pi$
$811$	−1.98181	−	20.1216i	−0.0695907	−	0.706566i	0.895572	−	0.444916i	$-0.146767\pi$
$812$	−10.0956	−	34.1328i	−0.354287	−	1.19783i
$813$	−0.380748	+	0.115499i	−0.0133534	+	0.00405072i
$814$	−12.2673	+	3.67475i	−0.429968	+	0.128800i
$815$	−2.70842	−	1.12186i	−0.0948717	−	0.0392972i
$816$	3.43410	−	30.5137i	0.120217	−	1.06819i
$817$	−38.4843	+	15.9407i	−1.34640	+	0.557696i
$818$	25.7775	−	21.0056i	0.901289	−	0.734443i
$819$	9.51420	+	5.08545i	0.332453	+	0.177700i
$820$	−5.23790	−	9.96536i	−0.182915	−	0.348005i
$821$	10.4348	+	8.56365i	0.364178	+	0.298873i	0.798631	−	0.601821i	$-0.205558\pi$
$821$	10.4348	+	8.56365i	0.364178	+	0.298873i	−0.434452	+	0.900695i	$0.643058\pi$
$822$	−13.9565	+	20.7311i	−0.486789	+	0.723080i
$823$	6.33941	−	31.8704i	0.220978	−	1.11093i	−0.697841	−	0.716252i	$-0.745856\pi$
$823$	6.33941	−	31.8704i	0.220978	−	1.11093i	0.918819	−	0.394678i	$-0.129144\pi$
$824$	1.61171	−	0.141796i	0.0561465	−	0.00493968i
$825$	3.40905	−	0.678101i	0.118688	−	0.0236085i
$826$	−25.1203	+	10.3031i	−0.874047	+	0.358490i
$827$	−11.0409	−	20.6561i	−0.383930	−	0.718282i	0.613518	−	0.789681i	$-0.289754\pi$
$827$	−11.0409	−	20.6561i	−0.383930	−	0.718282i	−0.997448	+	0.0713987i	$0.977254\pi$
$828$	−11.0500	−	2.27791i	−0.384014	−	0.0791629i
$829$	−6.97782	−	0.687255i	−0.242350	−	0.0238693i	−0.0238869	−	0.999715i	$-0.507604\pi$
$829$	−6.97782	−	0.687255i	−0.242350	−	0.0238693i	−0.218463	+	0.975845i	$0.570104\pi$
$830$	−2.28678	+	1.21212i	−0.0793754	+	0.0420732i
$831$		−	2.98029i		−	0.103385i
$832$	−12.8720	−	11.0207i	−0.446257	−	0.382074i
$833$			145.392i			5.03753i
$834$	7.60207	+	14.3421i	0.263238	+	0.496626i
$835$	3.60139	+	0.354706i	0.124631	+	0.0122751i
$836$	−6.02369	−	9.15211i	−0.208334	−	0.316532i
$837$	2.57305	+	4.81383i	0.0889375	+	0.166390i
$838$	−6.85740	−	16.7193i	−0.236885	−	0.577558i
$839$	−19.7664	+	3.93179i	−0.682413	+	0.135740i	−0.524111	−	0.851650i	$-0.675602\pi$
$839$	−19.7664	+	3.93179i	−0.682413	+	0.135740i	−0.158303	+	0.987391i	$0.550602\pi$
$840$	−10.5508	−	3.32103i	−0.364039	−	0.114587i
$841$	−3.27542	+	16.4667i	−0.112946	+	0.567816i
$842$	16.7945	+	11.3063i	0.578778	+	0.389642i
$843$	−13.3978	−	10.9953i	−0.461445	−	0.378698i
$844$	12.2627	+	3.81310i	0.422101	+	0.131252i
$845$	−5.76508	−	3.08150i	−0.198325	−	0.106007i
$846$	−1.48935	−	1.82769i	−0.0512050	−	0.0628373i
$847$	−48.8370	+	20.2289i	−1.67806	+	0.695074i
$848$	7.23154	−	22.6988i	0.248332	−	0.779480i
$849$	18.8402	+	7.80389i	0.646596	+	0.267829i
$850$	13.7398	+	45.8672i	0.471272	+	1.57323i
$851$	−62.0253	+	18.8152i	−2.12620	+	0.644976i
$852$	−6.99285	+	12.8669i	−0.239571	+	0.440811i
$853$	−1.15133	−	11.6897i	−0.0394208	−	0.400246i	−0.994566	−	0.104108i	$-0.966801\pi$
$853$	−1.15133	−	11.6897i	−0.0394208	−	0.400246i	0.955145	−	0.296138i	$-0.0956988\pi$
$854$	−8.91294	+	44.0088i	−0.304994	+	1.50595i
$855$	−2.96536	−	4.43797i	−0.101413	−	0.151776i
$856$	23.3606	+	23.8527i	0.798449	+	0.815268i
$857$	−21.6500	−	14.4660i	−0.739549	−	0.494151i	0.127832	−	0.991796i	$-0.459198\pi$
$857$	−21.6500	−	14.4660i	−0.739549	−	0.494151i	−0.867381	+	0.497645i	$0.834198\pi$
$858$	2.36076	+	0.00820156i	0.0805952	+	0.000279997i
$859$	38.1306	+	11.5668i	1.30100	+	0.394654i	0.863402	−	0.504516i	$-0.168329\pi$
$859$	38.1306	+	11.5668i	1.30100	+	0.394654i	0.437599	+	0.899170i	$0.355829\pi$
$860$	−0.0639408	+	9.20235i	−0.00218036	+	0.313797i
$861$	23.6864	+	28.8620i	0.807231	+	0.983614i
$862$	6.22831	+	5.14776i	0.212137	+	0.175333i
$863$	−20.4536	−	20.4536i	−0.696248	−	0.696248i	0.267351	−	0.963599i	$-0.413852\pi$
$863$	−20.4536	−	20.4536i	−0.696248	−	0.696248i	−0.963599	+	0.267351i	$0.913852\pi$
$864$	−5.52815	−	1.19980i	−0.188072	−	0.0408180i
$865$	9.88259	−	9.88259i	0.336018	−	0.336018i
$866$	3.83730	−	0.364485i	0.130397	−	0.0123857i
$867$	−32.4123	+	26.6001i	−1.10078	+	0.903387i
$868$	20.9197	+	51.5141i	0.710061	+	1.74850i
$869$	0.293737	−	0.968320i	0.00996433	−	0.0328480i
$870$	−2.67382	−	2.69246i	−0.0906509	−	0.0912829i
$871$	−7.06994	+	10.5809i	−0.239556	+	0.358521i
$872$	−13.5487	+	19.8266i	−0.458818	+	0.671414i
$873$	7.97396	−	5.32803i	0.269878	−	0.180326i
$874$	−30.6493	−	46.2168i	−1.03673	−	1.56331i
$875$	36.6243	−	3.60717i	1.23813	−	0.121945i
$876$	−6.93214	−	8.56754i	−0.234215	−	0.289470i
$877$	6.15598	+	20.2935i	0.207873	+	0.685264i	0.997434	+	0.0715927i	$0.0228082\pi$
$877$	6.15598	+	20.2935i	0.207873	+	0.685264i	−0.789561	+	0.613672i	$0.789692\pi$
$878$	−3.13955	+	5.82491i	−0.105955	+	0.196581i
$879$	2.65558	−	6.41113i	0.0895704	−	0.216242i
$880$	−2.38037	+	0.439191i	−0.0802424	+	0.0148051i
$881$	0.392124	+	0.946671i	0.0132110	+	0.0318942i	0.930347	−	0.366679i	$-0.119505\pi$
$881$	0.392124	+	0.946671i	0.0132110	+	0.0318942i	−0.917136	+	0.398574i	$0.869505\pi$
$882$	26.6464	+	2.71795i	0.897232	+	0.0915180i
$883$	10.7958	−	20.1976i	0.363308	−	0.679702i	−0.632156	−	0.774841i	$-0.717830\pi$
$883$	10.7958	−	20.1976i	0.363308	−	0.679702i	0.995464	+	0.0951394i	$0.0303297\pi$
$884$	2.96263	+	32.3854i	0.0996440	+	1.08924i
$885$	−1.83622	+	2.23744i	−0.0617237	+	0.0752106i
$886$	−6.54298	−	33.5016i	−0.219816	−	1.12551i
$887$	−38.4294	−	7.64409i	−1.29033	−	0.256663i	−0.498227	−	0.867046i	$-0.666016\pi$
$887$	−38.4294	−	7.64409i	−1.29033	−	0.256663i	−0.792106	+	0.610383i	$0.791016\pi$
$888$	−31.1955	+	9.10910i	−1.04685	+	0.305681i
$889$	−4.16042	−	20.9158i	−0.139536	−	0.701494i
$890$	−1.31126	−	0.548486i	−0.0439535	−	0.0183853i
$891$	0.695040	−	0.371506i	0.0232847	−	0.0124459i
$892$	2.98388	+	15.5654i	0.0999076	+	0.521169i
$893$	1.13589	−	11.5328i	0.0380110	−	0.385932i
$894$	1.85939	−	6.05378i	0.0621872	−	0.202469i
$895$	7.60045			0.254055
$896$	−54.7176	−	18.0626i	−1.82799	−	0.603429i
$897$	11.9490			0.398964
$898$	10.0694	−	32.7840i	0.336022	−	1.09402i
$899$	−1.86954	+	18.9817i	−0.0623526	+	0.633076i
$900$	8.66308	−	1.66070i	0.288769	−	0.0553568i
$901$	−40.3211	+	21.5521i	−1.34329	+	0.718004i
$902$	7.53774	+	3.15296i	0.250979	+	0.104982i
$903$	−5.95418	−	29.9337i	−0.198143	−	0.996131i
$904$	24.5879	−	44.8696i	0.817782	−	1.49234i
$905$	−4.00941	−	0.797521i	−0.133277	−	0.0265105i
$906$	−0.465382	−	2.38287i	−0.0154613	−	0.0791655i
$907$	10.6384	−	12.9629i	0.353241	−	0.430426i	−0.565827	−	0.824524i	$-0.691443\pi$
$907$	10.6384	−	12.9629i	0.353241	−	0.430426i	0.919068	+	0.394098i	$0.128943\pi$
$908$	−17.2479	+	1.57784i	−0.572391	+	0.0523626i
$909$	−6.36524	+	11.9085i	−0.211122	+	0.394981i
$910$	11.6543	+	1.18874i	0.386335	+	0.0394063i
$911$	2.54621	+	6.14711i	0.0843598	+	0.203663i	0.960430	−	0.278520i	$-0.0898440\pi$
$911$	2.54621	+	6.14711i	0.0843598	+	0.203663i	−0.876070	+	0.482183i	$0.839844\pi$
$912$	−15.1249	−	23.3315i	−0.500836	−	0.772583i
$913$	0.718823	−	1.73539i	0.0237896	−	0.0574331i
$914$	−2.99153	+	5.55029i	−0.0989510	+	0.183587i
$915$	1.38954	+	4.58069i	0.0459366	+	0.151433i
$916$	−7.40019	+	5.98762i	−0.244509	+	0.197836i
$917$	68.8298	−	6.77915i	2.27296	−	0.223867i
$918$	6.00006	+	9.04761i	0.198031	+	0.298616i
$919$	−22.7291	+	15.1871i	−0.749764	+	0.500976i	−0.870779	−	0.491675i	$-0.836385\pi$
$919$	−22.7291	+	15.1871i	−0.749764	+	0.500976i	0.121015	+	0.992651i	$0.461385\pi$
$920$	−12.0404	+	2.26479i	−0.396959	+	0.0746678i
$921$	6.17471	−	9.24110i	0.203464	−	0.304505i
$922$	−8.65425	−	8.71459i	−0.285013	−	0.287000i
$923$	4.50219	−	14.8417i	0.148191	−	0.488521i
$924$	7.43780	−	3.02047i	0.244686	−	0.0993660i
$925$	39.1723	−	32.1478i	1.28798	−	1.05701i
$926$	−24.5550	+	2.33235i	−0.806927	+	0.0766458i
$927$	−0.404483	+	0.404483i	−0.0132850	+	0.0132850i
$928$	−13.7327	−	14.2182i	−0.450797	−	0.466736i
$929$	−13.7244	−	13.7244i	−0.450282	−	0.450282i	0.445166	−	0.895448i	$-0.353145\pi$
$929$	−13.7244	−	13.7244i	−0.450282	−	0.450282i	−0.895448	+	0.445166i	$0.853145\pi$
$930$	4.56871	+	3.77608i	0.149814	+	0.123823i
$931$	83.5207	+	101.770i	2.73728	+	3.33539i
$932$	−1.94369	−	0.0135053i	−0.0636675	−	0.000442382i
$933$	−7.75015	−	2.35098i	−0.253729	−	0.0769677i
$934$	8.72753	+	0.0303204i	0.285574	+	0.000992115i
$935$	3.86250	+	2.58084i	0.126317	+	0.0844026i
$936$	5.99076	+	0.0624397i	0.195814	+	0.00204091i
$937$	−20.1522	−	30.1599i	−0.658344	−	0.985281i	−0.998983	−	0.0450870i	$-0.985644\pi$
$937$	−20.1522	−	30.1599i	−0.658344	−	0.985281i	0.340639	−	0.940194i	$-0.389356\pi$
$938$	−8.58947	+	42.4116i	−0.280456	+	1.38479i
$939$	−1.64566	−	16.7086i	−0.0537040	−	0.545266i
$940$	−2.24945	−	1.22253i	−0.0733690	−	0.0398744i
$941$	58.3359	−	17.6960i	1.90169	−	0.576873i	0.918142	−	0.396251i	$-0.129689\pi$
$941$	58.3359	−	17.6960i	1.90169	−	0.576873i	0.983553	−	0.180622i	$-0.0578111\pi$
$942$	6.12088	+	20.4331i	0.199429	+	0.665747i
$943$	38.2071	+	15.8259i	1.24420	+	0.515363i
$944$	−9.72658	+	11.5216i	−0.316573	+	0.374996i
$945$	3.61303	−	1.49657i	0.117532	−	0.0486833i
$946$	−4.21903	−	5.17748i	−0.137173	−	0.168334i
$947$	−8.78432	−	4.69532i	−0.285452	−	0.152577i	0.322457	−	0.946584i	$-0.395491\pi$
$947$	−8.78432	−	4.69532i	−0.285452	−	0.152577i	−0.607909	+	0.794007i	$0.707991\pi$
$948$	0.762489	−	2.45212i	0.0247645	−	0.0796412i
$949$	9.02252	+	7.40459i	0.292883	+	0.240363i
$950$	35.9660	+	24.2129i	1.16689	+	0.785570i
$951$	−3.08482	+	15.5085i	−0.100032	+	0.502896i
$952$	51.1100	+	98.0650i	1.65648	+	3.17831i
$953$	−47.4089	+	9.43022i	−1.53572	+	0.305475i	−0.889236	−	0.457449i	$-0.848763\pi$
$953$	−47.4089	+	9.43022i	−1.53572	+	0.305475i	−0.646489	+	0.762923i	$0.723763\pi$
$954$	3.19616	+	7.79268i	0.103480	+	0.252297i
$955$	−1.98705	−	3.71750i	−0.0642993	−	0.120295i
$956$	−2.29114	+	1.50797i	−0.0741006	+	0.0487712i
$957$	2.74066	+	0.269931i	0.0885928	+	0.00872563i
$958$	−21.2374	−	40.0665i	−0.686149	−	1.29449i
$959$		−	90.0025i		−	2.90633i
$960$	−6.04841	+	1.07256i	−0.195212	+	0.0346168i
$961$			1.20646i			0.0389180i
$962$	30.4104	−	16.1191i	0.980472	−	0.519702i
$963$	−11.7471	−	1.15699i	−0.378546	−	0.0372835i
$964$	−1.06972	+	5.18915i	−0.0344534	+	0.167131i
$965$	−6.08279	−	11.3801i	−0.195812	−	0.366338i
$966$	37.5928	−	15.4186i	1.20953	−	0.496087i
$967$	30.4957	−	6.06598i	0.980677	−	0.195069i	0.321379	−	0.946951i	$-0.395854\pi$
$967$	30.4957	−	6.06598i	0.980677	−	0.195069i	0.659298	+	0.751882i	$0.270854\pi$
$968$	−18.8587	+	22.4971i	−0.606142	+	0.723086i
$969$	−10.4104	+	52.3367i	−0.334431	+	1.68130i
$970$	5.81575	−	8.63876i	0.186732	−	0.277374i
$971$	21.0340	+	17.2621i	0.675012	+	0.553968i	0.908238	−	0.418454i	$-0.137428\pi$
$971$	21.0340	+	17.2621i	0.675012	+	0.553968i	−0.233225	+	0.972423i	$0.574928\pi$
$972$	1.77035	−	0.930515i	0.0567840	−	0.0298463i
$973$	−51.5557	−	27.5571i	−1.65280	−	0.883440i
$974$	−22.3122	+	18.1818i	−0.714929	+	0.582582i
$975$	−8.63088	+	3.57503i	−0.276409	+	0.114492i
$976$	6.90632	+	23.9608i	0.221066	+	0.766966i
$977$	13.4246	+	5.56066i	0.429492	+	0.177901i	0.586948	−	0.809625i	$-0.300329\pi$
$977$	13.4246	+	5.56066i	0.429492	+	0.177901i	−0.157456	+	0.987526i	$0.550329\pi$
$978$	5.17226	−	1.54939i	0.165391	−	0.0495439i
$979$	0.987135	−	0.299444i	0.0315490	−	0.00957027i
$980$	27.8911	−	8.24947i	0.890947	−	0.263520i
$981$	−0.832182	−	8.44928i	−0.0265695	−	0.269765i
$982$	−16.8621	−	3.41502i	−0.538092	−	0.108978i
$983$	−17.1838	−	25.7174i	−0.548078	−	0.820257i	0.449243	−	0.893410i	$-0.351694\pi$
$983$	−17.1838	−	25.7174i	−0.548078	−	0.820257i	−0.997321	+	0.0731529i	$0.976694\pi$
$984$	19.0729	+	8.13416i	0.608022	+	0.259308i
$985$	−9.02730	−	6.03185i	−0.287634	−	0.192191i
$986$	−0.131794	+	37.9360i	−0.00419718	+	1.20813i
$987$	8.12522	+	2.46476i	0.258629	+	0.0784542i
$988$	20.6776	+	20.9670i	0.657843	+	0.667049i
$989$	−21.4454	−	26.1312i	−0.681922	−	0.830925i
$990$	0.545205	−	0.659648i	0.0173277	−	0.0209650i
$991$	21.3998	+	21.3998i	0.679786	+	0.679786i	0.959952	−	0.280165i	$-0.0903893\pi$
$991$	21.3998	+	21.3998i	0.679786	+	0.679786i	−0.280165	+	0.959952i	$0.590389\pi$
$992$	23.5245	+	19.9998i	0.746902	+	0.634995i
$993$	9.44630	−	9.44630i	0.299769	−	0.299769i
$994$	−4.98700	−	52.5032i	−0.158178	−	1.66530i
$995$	−6.43983	+	5.28503i	−0.204156	+	0.167547i
$996$	1.85475	−	4.39123i	0.0587702	−	0.139141i
$997$	9.19930	−	30.3260i	0.291345	−	0.960435i	−0.682051	−	0.731305i	$-0.738912\pi$
$997$	9.19930	−	30.3260i	0.291345	−	0.960435i	0.973396	−	0.229130i	$-0.0735882\pi$
$998$	−16.0269	+	15.9159i	−0.507322	+	0.503809i
$999$	6.38342	−	9.55346i	0.201962	−	0.302258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.30	✓	512
128.53	even	32	inner	384.2.v.a.181.30	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.30	✓	512	1.1	even	1	trivial
384.2.v.a.181.30	yes	512	128.53	even	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35188 + 0.415224i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.65518 + 1.12267i) q^{4} +(-0.677180 + 0.361960i) q^{5} +(0.545732 - 1.30467i) q^{6} +(0.993614 + 4.99523i) q^{7} +(1.77145 + 2.20499i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(1.35188 + 0.415224i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.65518 + 1.12267i) q^{4} +(-0.677180 + 0.361960i) q^{5} +(0.545732 - 1.30467i) q^{6} +(0.993614 + 4.99523i) q^{7} +(1.77145 + 2.20499i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-1.06576 + 0.208147i) q^{10} +(0.499964 - 0.609207i) q^{11} +(1.27950 - 1.53717i) q^{12} +(-0.998498 + 1.86806i) q^{13} +(-0.730889 + 7.16555i) q^{14} +(0.293842 + 0.709398i) q^{15} +(1.47923 + 3.71643i) q^{16} +(2.93770 - 7.09224i) q^{17} +(-1.24490 - 0.670985i) q^{18} +(-2.01785 - 6.65195i) q^{19} +(-1.52722 - 0.161139i) q^{20} +(5.06857 - 0.499211i) q^{21} +(0.928850 - 0.615981i) q^{22} +(4.69047 - 3.13407i) q^{23} +(2.36800 - 1.54679i) q^{24} +(-2.45029 + 3.66712i) q^{25} +(-2.12551 + 2.11080i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(-3.96338 + 9.38350i) q^{28} +(-2.70120 + 2.21682i) q^{29} +(0.102682 + 1.08103i) q^{30} +(3.85963 - 3.85963i) q^{31} +(0.456601 + 5.63840i) q^{32} +(-0.557269 - 0.557269i) q^{33} +(6.91630 - 8.36808i) q^{34} +(-2.48093 - 3.02303i) q^{35} +(-1.40435 - 1.42401i) q^{36} +(-10.9951 - 3.33533i) q^{37} +(0.0341523 - 9.83051i) q^{38} +(1.76119 + 1.17679i) q^{39} +(-1.99771 - 0.851978i) q^{40} +(4.07285 + 6.09545i) q^{41} +(7.05940 + 1.42972i) q^{42} +(-0.587363 - 5.96360i) q^{43} +(1.51147 - 0.447054i) q^{44} +(0.734783 - 0.222894i) q^{45} +(7.64231 - 2.28931i) q^{46} +(1.54022 + 0.637982i) q^{47} +(3.84353 - 1.10784i) q^{48} +(-17.4979 + 7.24788i) q^{49} +(-4.83519 + 3.94010i) q^{50} +(-6.77015 - 3.61872i) q^{51} +(-3.74990 + 1.97099i) q^{52} +(-4.60384 - 3.77827i) q^{53} +(-0.789775 + 1.17314i) q^{54} +(-0.118057 + 0.593510i) q^{55} +(-9.25428 + 11.0397i) q^{56} +(-6.81770 + 1.35612i) q^{57} +(-4.57218 + 1.87528i) q^{58} +(1.77696 + 3.32445i) q^{59} +(-0.310057 + 1.50407i) q^{60} +(6.20404 + 0.611045i) q^{61} +(6.82039 - 3.61516i) q^{62} -5.09310i q^{63} +(-1.72392 + 7.81205i) q^{64} -1.62643i q^{65} +(-0.521971 - 0.984754i) q^{66} +(5.97888 + 0.588869i) q^{67} +(12.8247 - 8.44086i) q^{68} +(-2.65923 - 4.97508i) q^{69} +(-2.09870 - 5.11692i) q^{70} +(-7.18146 + 1.42848i) q^{71} +(-1.30724 - 2.50821i) q^{72} +(1.07502 - 5.40450i) q^{73} +(-13.4792 - 9.07440i) q^{74} +(3.40929 + 2.79794i) q^{75} +(4.12803 - 13.2755i) q^{76} +(3.53990 + 1.89212i) q^{77} +(1.89230 + 2.32217i) q^{78} +(1.18623 - 0.491353i) q^{79} +(-2.34691 - 1.98127i) q^{80} +(0.923880 + 0.382683i) q^{81} +(2.97504 + 9.93147i) q^{82} +(2.28080 - 0.691874i) q^{83} +(8.94984 + 4.86404i) q^{84} +(0.577756 + 5.86606i) q^{85} +(1.68218 - 8.30598i) q^{86} +(1.94138 + 2.90548i) q^{87} +(2.22895 + 0.0232317i) q^{88} +(1.08832 + 0.727195i) q^{89} +(1.08589 + 0.00377251i) q^{90} +(-10.3235 - 3.13160i) q^{91} +(11.2821 + 0.0783914i) q^{92} +(-3.46274 - 4.21936i) q^{93} +(1.81730 + 1.50201i) q^{94} +(3.77419 + 3.77419i) q^{95} +(5.65600 + 0.0982574i) q^{96} +(-6.78129 + 6.78129i) q^{97} +(-26.6647 + 2.53274i) q^{98} +(-0.609207 + 0.499964i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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