LMFDB - Embedded newform 867.2.i.d.224.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(65,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 9]))

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

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

chi := DirichletCharacter("867.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.i (of order $16$, degree $8$, 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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			224.2
Character	$\chi$	$=$	867.224
Dual form			867.2.i.d.329.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.503008 - 1.21437i) q^{2} +(1.11133 + 1.32851i) q^{3} +(0.192538 - 0.192538i) q^{4} +(0.116989 - 0.0781694i) q^{5} +(1.05430 - 2.01782i) q^{6} +(0.982905 - 1.47102i) q^{7} +(-2.75940 - 1.14298i) q^{8} +(-0.529896 + 2.95283i) q^{9} +(-0.153773 - 0.102748i) q^{10} +(3.57185 - 0.710485i) q^{11} +(0.469762 + 0.0418163i) q^{12} +(-0.0825311 - 0.0825311i) q^{13} +(-2.28077 - 0.453674i) q^{14} +(0.233862 + 0.0685492i) q^{15} +3.38128i q^{16} +(3.85237 - 0.841809i) q^{18} +(6.20278 - 2.56928i) q^{19} +(0.00747420 - 0.0375753i) q^{20} +(3.04660 - 0.328986i) q^{21} +(-2.65946 - 3.98016i) q^{22} +(-1.22507 - 6.15884i) q^{23} +(-1.54813 - 4.93613i) q^{24} +(-1.90584 + 4.60111i) q^{25} +(-0.0587094 + 0.141737i) q^{26} +(-4.51176 + 2.57759i) q^{27} +(-0.0939809 - 0.472474i) q^{28} +(2.18690 + 3.27292i) q^{29} +(-0.0343905 - 0.318476i) q^{30} +(1.74682 - 8.78185i) q^{31} +(-1.41268 + 0.585150i) q^{32} +(4.91339 + 3.95567i) q^{33} -0.248926i q^{35} +(0.466507 + 0.670557i) q^{36} +(-0.365247 - 0.0726522i) q^{37} +(-6.24010 - 6.24010i) q^{38} +(0.0179245 - 0.201363i) q^{39} +(-0.412165 + 0.0819847i) q^{40} +(3.65643 + 2.44315i) q^{41} +(-1.93198 - 3.53422i) q^{42} +(-1.94823 - 0.806985i) q^{43} +(0.550921 - 0.824512i) q^{44} +(0.168829 + 0.386870i) q^{45} +(-6.86288 + 4.58563i) q^{46} +(2.11141 - 2.11141i) q^{47} +(-4.49207 + 3.75771i) q^{48} +(1.48098 + 3.57541i) q^{49} +6.54610 q^{50} -0.0317807 q^{52} +(-2.45113 - 5.91755i) q^{53} +(5.39960 + 4.18240i) q^{54} +(0.362328 - 0.362328i) q^{55} +(-4.39357 + 2.93569i) q^{56} +(10.3066 + 5.38517i) q^{57} +(2.87451 - 4.30201i) q^{58} +(8.83540 + 3.65974i) q^{59} +(0.0582256 - 0.0318290i) q^{60} +(-3.30427 - 2.20784i) q^{61} +(-11.5431 + 2.29606i) q^{62} +(3.82284 + 3.68184i) q^{63} +(6.20303 + 6.20303i) q^{64} +(-0.0161066 - 0.00320381i) q^{65} +(2.33217 - 7.95640i) q^{66} +5.81844i q^{67} +(6.82064 - 8.47201i) q^{69} +(-0.302288 + 0.125212i) q^{70} +(2.53537 - 12.7462i) q^{71} +(4.83722 - 7.54238i) q^{72} +(2.48206 + 3.71467i) q^{73} +(0.0954957 + 0.480089i) q^{74} +(-8.23065 + 2.58141i) q^{75} +(0.699588 - 1.68895i) q^{76} +(2.46565 - 5.95260i) q^{77} +(-0.253545 + 0.0795203i) q^{78} +(0.477177 + 2.39893i) q^{79} +(0.264312 + 0.395572i) q^{80} +(-8.43842 - 3.12939i) q^{81} +(1.12767 - 5.66918i) q^{82} +(-5.11813 + 2.12000i) q^{83} +(0.523244 - 0.649928i) q^{84} +2.77180i q^{86} +(-1.91776 + 6.54262i) q^{87} +(-10.6682 - 2.12204i) q^{88} +(2.89760 + 2.89760i) q^{89} +(0.384880 - 0.399620i) q^{90} +(-0.202525 + 0.0402848i) q^{91} +(-1.42168 - 0.949937i) q^{92} +(13.6081 - 7.43885i) q^{93} +(-3.62608 - 1.50197i) q^{94} +(0.524817 - 0.785444i) q^{95} +(-2.34733 - 1.22647i) q^{96} +(-3.81409 + 2.54849i) q^{97} +(3.59692 - 3.59692i) q^{98} +(0.205233 + 10.9235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{4} + 8 q^{9} + 32 q^{10} + 24 q^{12} - 16 q^{13} - 16 q^{15} + 16 q^{18} + 16 q^{19} + 16 q^{21} - 48 q^{22} + 8 q^{24} - 16 q^{25} - 48 q^{27} - 64 q^{28} - 8 q^{30} + 16 q^{31} - 8 q^{36}+ \cdots + 96 q^{97}+O(q^{100}) $ 32 * q - 16 * q^4 + 8 * q^9 + 32 * q^10 + 24 * q^12 - 16 * q^13 - 16 * q^15 + 16 * q^18 + 16 * q^19 + 16 * q^21 - 48 * q^22 + 8 * q^24 - 16 * q^25 - 48 * q^27 - 64 * q^28 - 8 * q^30 + 16 * q^31 - 8 * q^36 - 32 * q^37 + 8 * q^39 - 64 * q^40 + 56 * q^42 - 16 * q^43 + 24 * q^45 - 80 * q^46 - 72 * q^48 + 48 * q^49 - 96 * q^52 + 48 * q^54 - 48 * q^55 + 24 * q^57 - 32 * q^58 - 32 * q^60 + 64 * q^61 - 16 * q^63 + 16 * q^64 - 72 * q^66 + 80 * q^69 - 48 * q^70 + 64 * q^72 - 48 * q^76 - 16 * q^78 - 32 * q^79 + 48 * q^81 + 48 * q^82 + 56 * q^87 - 80 * q^88 + 104 * q^90 + 80 * q^91 + 72 * q^93 + 48 * q^94 + 72 * q^96 + 96 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{1}{16}\right)$

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 $

$2$	−0.503008	−	1.21437i	−0.355681	−	0.858689i	−0.995897	−	0.0904942i	$-0.971155\pi$
$2$	−0.503008	−	1.21437i	−0.355681	−	0.858689i	0.640216	−	0.768195i	$-0.278845\pi$
$3$	1.11133	+	1.32851i	0.641626	+	0.767018i
$3$	1.11133	+	1.32851i	0.641626	+	0.767018i
$4$	0.192538	−	0.192538i	0.0962690	−	0.0962690i
$5$	0.116989	−	0.0781694i	0.0523190	−	0.0349584i	−0.529136	−	0.848537i	$-0.677484\pi$
$5$	0.116989	−	0.0781694i	0.0523190	−	0.0349584i	0.581455	+	0.813579i	$0.302484\pi$
$6$	1.05430	−	2.01782i	0.430416	−	0.823770i
$7$	0.982905	−	1.47102i	0.371503	−	0.555994i	−0.597868	−	0.801595i	$-0.703985\pi$
$7$	0.982905	−	1.47102i	0.371503	−	0.555994i	0.969371	+	0.245601i	$0.0789853\pi$
$8$	−2.75940	−	1.14298i	−0.975595	−	0.404105i
$9$	−0.529896	+	2.95283i	−0.176632	+	0.984277i
$10$	−0.153773	−	0.102748i	−0.0486272	−	0.0324917i
$11$	3.57185	−	0.710485i	1.07695	−	0.214219i	0.375419	−	0.926855i	$-0.377499\pi$
$11$	3.57185	−	0.710485i	1.07695	−	0.214219i	0.701534	+	0.712636i	$0.252499\pi$
$12$	0.469762	+	0.0418163i	0.135609	+	0.0120713i
$13$	−0.0825311	−	0.0825311i	−0.0228900	−	0.0228900i	0.695569	−	0.718459i	$-0.255152\pi$
$13$	−0.0825311	−	0.0825311i	−0.0228900	−	0.0228900i	−0.718459	+	0.695569i	$0.755152\pi$
$14$	−2.28077	−	0.453674i	−0.609562	−	0.121249i
$15$	0.233862	+	0.0685492i	0.0603829	+	0.0176993i
$16$			3.38128i			0.845320i
$17$		0			0
$17$		0			0
$18$	3.85237	−	0.841809i	0.908012	−	0.198416i
$19$	6.20278	−	2.56928i	1.42302	−	0.589432i	0.467399	−	0.884046i	$-0.345191\pi$
$19$	6.20278	−	2.56928i	1.42302	−	0.589432i	0.955616	+	0.294614i	$0.0951910\pi$
$20$	0.00747420	−	0.0375753i	0.00167128	−	0.00840210i
$21$	3.04660	−	0.328986i	0.664823	−	0.0717906i
$22$	−2.65946	−	3.98016i	−0.566999	−	0.848574i
$23$	−1.22507	−	6.15884i	−0.255444	−	1.28421i	−0.869102	−	0.494633i	$-0.835302\pi$
$23$	−1.22507	−	6.15884i	−0.255444	−	1.28421i	0.613657	−	0.789573i	$-0.289698\pi$
$24$	−1.54813	−	4.93613i	−0.316012	−	1.00758i
$25$	−1.90584	+	4.60111i	−0.381168	+	0.920222i
$26$	−0.0587094	+	0.141737i	−0.0115139	+	0.0277969i
$27$	−4.51176	+	2.57759i	−0.868289	+	0.496058i
$28$	−0.0939809	−	0.472474i	−0.0177607	−	0.0892891i
$29$	2.18690	+	3.27292i	0.406097	+	0.607766i	0.976997	−	0.213253i	$-0.0684058\pi$
$29$	2.18690	+	3.27292i	0.406097	+	0.607766i	−0.570900	+	0.821019i	$0.693406\pi$
$30$	−0.0343905	−	0.318476i	−0.00627881	−	0.0581455i
$31$	1.74682	−	8.78185i	0.313738	−	1.57727i	−0.426224	−	0.904618i	$-0.640156\pi$
$31$	1.74682	−	8.78185i	0.313738	−	1.57727i	0.739962	−	0.672649i	$-0.234844\pi$
$32$	−1.41268	+	0.585150i	−0.249728	+	0.103441i
$33$	4.91339	+	3.95567i	0.855311	+	0.688593i
$34$		0			0
$35$		−	0.248926i		−	0.0420762i
$36$	0.466507	+	0.670557i	0.0777511	+	0.111760i
$37$	−0.365247	−	0.0726522i	−0.0600462	−	0.0119439i	0.164976	−	0.986298i	$-0.447245\pi$
$37$	−0.365247	−	0.0726522i	−0.0600462	−	0.0119439i	−0.225022	+	0.974354i	$0.572245\pi$
$38$	−6.24010	−	6.24010i	−1.01228	−	1.01228i
$39$	0.0179245	−	0.201363i	0.00287022	−	0.0322439i
$40$	−0.412165	+	0.0819847i	−0.0651690	+	0.0129629i
$41$	3.65643	+	2.44315i	0.571039	+	0.381556i	0.807307	−	0.590132i	$-0.200924\pi$
$41$	3.65643	+	2.44315i	0.571039	+	0.381556i	−0.236268	+	0.971688i	$0.575924\pi$
$42$	−1.93198	−	3.53422i	−0.298110	−	0.545341i
$43$	−1.94823	−	0.806985i	−0.297103	−	0.123064i	0.229153	−	0.973390i	$-0.426404\pi$
$43$	−1.94823	−	0.806985i	−0.297103	−	0.123064i	−0.526256	+	0.850326i	$0.676404\pi$
$44$	0.550921	−	0.824512i	0.0830545	−	0.124300i
$45$	0.168829	+	0.386870i	0.0251676	+	0.0576711i
$46$	−6.86288	+	4.58563i	−1.01188	+	0.676114i
$47$	2.11141	−	2.11141i	0.307980	−	0.307980i	−0.536145	−	0.844126i	$-0.680120\pi$
$47$	2.11141	−	2.11141i	0.307980	−	0.307980i	0.844126	+	0.536145i	$0.180120\pi$
$48$	−4.49207	+	3.75771i	−0.648375	+	0.542379i
$49$	1.48098	+	3.57541i	0.211569	+	0.510773i
$50$	6.54610			0.925758
$51$		0			0
$52$	−0.0317807			−0.00440720
$53$	−2.45113	−	5.91755i	−0.336688	−	0.812837i	−0.998029	−	0.0627519i	$-0.980012\pi$
$53$	−2.45113	−	5.91755i	−0.336688	−	0.812837i	0.661341	−	0.750085i	$-0.269988\pi$
$54$	5.39960	+	4.18240i	0.734793	+	0.569152i
$55$	0.362328	−	0.362328i	0.0488563	−	0.0488563i
$56$	−4.39357	+	2.93569i	−0.587116	+	0.392298i
$57$	10.3066	+	5.38517i	1.36515	+	0.713283i
$58$	2.87451	−	4.30201i	0.377442	−	0.564881i
$59$	8.83540	+	3.65974i	1.15027	+	0.476458i	0.874624	−	0.484801i	$-0.161108\pi$
$59$	8.83540	+	3.65974i	1.15027	+	0.476458i	0.275647	+	0.961259i	$0.411108\pi$
$60$	0.0582256	−	0.0318290i	0.00751690	−	0.00410910i
$61$	−3.30427	−	2.20784i	−0.423068	−	0.282685i	0.325756	−	0.945454i	$-0.394381\pi$
$61$	−3.30427	−	2.20784i	−0.423068	−	0.282685i	−0.748824	+	0.662769i	$0.769381\pi$
$62$	−11.5431	+	2.29606i	−1.46597	+	0.291600i
$63$	3.82284	+	3.68184i	0.481632	+	0.463868i
$64$	6.20303	+	6.20303i	0.775378	+	0.775378i
$65$	−0.0161066	−	0.00320381i	−0.00199778	−	0.000397383i
$66$	2.33217	−	7.95640i	0.287070	−	0.979365i
$67$			5.81844i			0.710836i	0.934707	+	0.355418i	$0.115661\pi$
$67$			5.81844i			0.710836i	−0.934707	+	0.355418i	$0.884339\pi$
$68$		0			0
$69$	6.82064	−	8.47201i	0.821109	−	1.01991i
$70$	−0.302288	+	0.125212i	−0.0361303	+	0.0149657i
$71$	2.53537	−	12.7462i	0.300893	−	1.51269i	−0.473959	−	0.880547i	$-0.657175\pi$
$71$	2.53537	−	12.7462i	0.300893	−	1.51269i	0.774851	−	0.632143i	$-0.217825\pi$
$72$	4.83722	−	7.54238i	0.570072	−	0.888878i
$73$	2.48206	+	3.71467i	0.290504	+	0.434769i	0.947801	−	0.318862i	$-0.103301\pi$
$73$	2.48206	+	3.71467i	0.290504	+	0.434769i	−0.657298	+	0.753631i	$0.728301\pi$
$74$	0.0954957	+	0.480089i	0.0111012	+	0.0558093i
$75$	−8.23065	+	2.58141i	−0.950394	+	0.298075i
$76$	0.699588	−	1.68895i	0.0802482	−	0.193736i
$77$	2.46565	−	5.95260i	0.280987	−	0.678362i
$78$	−0.253545	+	0.0795203i	−0.0287083	+	0.00900390i
$79$	0.477177	+	2.39893i	0.0536866	+	0.269901i	0.998300	−	0.0582845i	$-0.0185630\pi$
$79$	0.477177	+	2.39893i	0.0536866	+	0.269901i	−0.944613	+	0.328185i	$0.893563\pi$
$80$	0.264312	+	0.395572i	0.0295510	+	0.0442262i
$81$	−8.43842	−	3.12939i	−0.937602	−	0.347710i
$82$	1.12767	−	5.66918i	0.124530	−	0.626057i
$83$	−5.11813	+	2.12000i	−0.561788	+	0.232700i	−0.645461	−	0.763793i	$-0.723335\pi$
$83$	−5.11813	+	2.12000i	−0.561788	+	0.232700i	0.0836731	+	0.996493i	$0.473335\pi$
$84$	0.523244	−	0.649928i	0.0570906	−	0.0709130i
$85$		0			0
$86$			2.77180i			0.298890i
$87$	−1.91776	+	6.54262i	−0.205605	+	0.701442i
$88$	−10.6682	−	2.12204i	−1.13724	−	0.226210i
$89$	2.89760	+	2.89760i	0.307145	+	0.307145i	0.843801	−	0.536656i	$-0.180313\pi$
$89$	2.89760	+	2.89760i	0.307145	+	0.307145i	−0.536656	+	0.843801i	$0.680313\pi$
$90$	0.384880	−	0.399620i	0.0405699	−	0.0421236i
$91$	−0.202525	+	0.0402848i	−0.0212304	+	0.00422299i
$92$	−1.42168	−	0.949937i	−0.148221	−	0.0990378i
$93$	13.6081	−	7.43885i	1.41109	−	0.771373i
$94$	−3.62608	−	1.50197i	−0.374002	−	0.154917i
$95$	0.524817	−	0.785444i	0.0538451	−	0.0805849i
$96$	−2.34733	−	1.22647i	−0.239573	−	0.125176i
$97$	−3.81409	+	2.54849i	−0.387262	+	0.258760i	−0.733926	−	0.679229i	$-0.762314\pi$
$97$	−3.81409	+	2.54849i	−0.387262	+	0.258760i	0.346664	+	0.937989i	$0.387314\pi$
$98$	3.59692	−	3.59692i	0.363344	−	0.363344i
$99$	0.205233	+	10.9235i	0.0206267	+	1.09786i
$100$	0.518941	+	1.25283i	0.0518941	+	0.125283i
$101$	−5.06729			−0.504214			−0.252107	−	0.967699i	$-0.581123\pi$
$101$	−5.06729			−0.504214			−0.252107	+	0.967699i	$0.581123\pi$
$102$		0			0
$103$	−15.9760			−1.57416			−0.787080	−	0.616851i	$-0.788408\pi$
$103$	−15.9760			−1.57416			−0.787080	+	0.616851i	$0.788408\pi$
$104$	0.133405	+	0.322068i	0.0130814	+	0.0315813i
$105$	0.330701	−	0.276639i	0.0322732	−	0.0269972i
$106$	−5.95315	+	5.95315i	−0.578221	+	0.578221i
$107$	−1.13291	+	0.756986i	−0.109522	+	0.0731806i	−0.609125	−	0.793074i	$-0.708479\pi$
$107$	−1.13291	+	0.756986i	−0.109522	+	0.0731806i	0.499603	+	0.866255i	$0.333479\pi$
$108$	−0.372402	+	1.36497i	−0.0358344	+	0.131344i
$109$	−6.37698	+	9.54382i	−0.610804	+	0.914132i	−0.999975	−	0.00703284i	$-0.997761\pi$
$109$	−6.37698	+	9.54382i	−0.610804	+	0.914132i	0.389171	+	0.921165i	$0.372761\pi$
$110$	−0.622254	−	0.257746i	−0.0593296	−	0.0245751i
$111$	−0.309390	−	0.565976i	−0.0293660	−	0.0537201i
$112$	4.97393	+	3.32347i	0.469992	+	0.314039i
$113$	13.2910	−	2.64375i	1.25031	−	0.248703i	0.474834	−	0.880076i	$-0.342508\pi$
$113$	13.2910	−	2.64375i	1.25031	−	0.248703i	0.775479	+	0.631373i	$0.217508\pi$
$114$	1.35525	−	15.2249i	0.126931	−	1.42594i
$115$	−0.624752	−	0.624752i	−0.0582584	−	0.0582584i
$116$	1.05122	+	0.209101i	0.0976035	+	0.0194146i
$117$	0.287433	−	0.199968i	0.0265732	−	0.0184870i
$118$		−	12.5703i		−	1.15719i
$119$		0			0
$120$	−0.566968	−	0.456454i	−0.0517569	−	0.0416684i
$121$	2.09064	−	0.865970i	0.190058	−	0.0787246i
$122$	−1.01906	+	5.12316i	−0.0922614	+	0.463829i
$123$	0.817741	+	7.57276i	0.0737332	+	0.682813i
$124$	−1.35451	−	2.02717i	−0.121639	−	0.182045i
$125$	0.273951	+	1.37724i	0.0245029	+	0.123184i
$126$	2.54819	−	6.49433i	0.227011	−	0.578561i
$127$	−3.78439	+	9.13631i	−0.335810	+	0.810717i	0.662299	+	0.749240i	$0.269581\pi$
$127$	−3.78439	+	9.13631i	−0.335810	+	0.810717i	−0.998109	+	0.0614768i	$0.980419\pi$
$128$	3.24229	−	7.82759i	0.286581	−	0.691867i
$129$	−1.09304	−	3.48508i	−0.0962367	−	0.306844i
$130$	0.00421116	+	0.0211709i	0.000369343	+	0.00185681i
$131$	−7.23868	−	10.8334i	−0.632446	−	0.946523i	−0.999864	−	0.0164667i	$-0.994758\pi$
$131$	−7.23868	−	10.8334i	−0.632446	−	0.946523i	0.367418	−	0.930056i	$-0.380242\pi$
$132$	1.70763	−	0.184398i	0.148630	−	0.0160497i
$133$	2.31728	−	11.6498i	0.200934	−	1.01016i
$134$	7.06574	−	2.92672i	0.610387	−	0.252830i
$135$	−0.326337	+	0.654231i	−0.0280866	+	0.0563073i
$136$		0			0
$137$		−	3.20492i		−	0.273815i	−0.990584	−	0.136907i	$-0.956284\pi$
$137$		−	3.20492i		−	0.273815i	0.990584	−	0.136907i	$-0.0437163\pi$
$138$	−13.7190	−	4.02129i	−1.16784	−	0.342315i
$139$	−4.99657	−	0.993879i	−0.423803	−	0.0842997i	−0.0214191	−	0.999771i	$-0.506818\pi$
$139$	−4.99657	−	0.993879i	−0.423803	−	0.0842997i	−0.402384	+	0.915471i	$0.631818\pi$
$140$	−0.0479277	−	0.0479277i	−0.00405063	−	0.00405063i
$141$	5.15150	+	0.458565i	0.433834	+	0.0386181i
$142$	−16.7539	+	3.33255i	−1.40595	+	0.279661i
$143$	−0.353426	−	0.236152i	−0.0295550	−	0.0197480i
$144$	−9.98434	−	1.79173i	−0.832029	−	0.149311i
$145$	0.511685	+	0.211947i	0.0424931	+	0.0176012i
$146$	3.26248	−	4.88265i	0.270005	−	0.404091i
$147$	−3.10412	+	5.94096i	−0.256024	+	0.490003i
$148$	−0.0843122	+	0.0563356i	−0.00693042	+	0.00463076i
$149$	−15.7137	+	15.7137i	−1.28731	+	1.28731i	−0.350902	+	0.936412i	$0.614125\pi$
$149$	−15.7137	+	15.7137i	−1.28731	+	1.28731i	−0.936412	+	0.350902i	$0.885875\pi$
$150$	7.27487	+	8.69658i	0.593990	+	0.710073i
$151$	1.57857	+	3.81101i	0.128462	+	0.310135i	0.975004	−	0.222187i	$-0.0713195\pi$
$151$	1.57857	+	3.81101i	0.128462	+	0.310135i	−0.846542	+	0.532322i	$0.821319\pi$
$152$	−20.0526			−1.62648
$153$		0			0
$154$	−8.46890			−0.682443
$155$	−0.482114	−	1.16393i	−0.0387243	−	0.0934887i
$156$	−0.0353189	−	0.0422212i	−0.00282777	−	0.00338040i
$157$	−9.87094	+	9.87094i	−0.787787	+	0.787787i	−0.981131	−	0.193344i	$-0.938067\pi$
$157$	−9.87094	+	9.87094i	−0.787787	+	0.787787i	0.193344	+	0.981131i	$0.438067\pi$
$158$	2.67316	−	1.78615i	0.212665	−	0.142098i
$159$	5.13753	−	9.83270i	0.407433	−	0.779784i
$160$	−0.119526	+	0.178884i	−0.00944940	+	0.0141420i
$161$	−10.2639	−	4.25145i	−0.808909	−	0.335061i
$162$	0.444363	+	11.8215i	0.0349125	+	0.928782i
$163$	9.27442	+	6.19697i	0.726429	+	0.485384i	0.862973	−	0.505250i	$-0.168600\pi$
$163$	9.27442	+	6.19697i	0.726429	+	0.485384i	−0.136544	+	0.990634i	$0.543600\pi$
$164$	1.17440	−	0.233603i	0.0917053	−	0.0182413i
$165$	0.884023	+	0.0786920i	0.0688211	+	0.00612617i
$166$	5.14893	+	5.14893i	0.399634	+	0.399634i
$167$	2.05961	+	0.409682i	0.159377	+	0.0317021i	0.274134	−	0.961692i	$-0.411609\pi$
$167$	2.05961	+	0.409682i	0.159377	+	0.0317021i	−0.114757	+	0.993394i	$0.536609\pi$
$168$	−8.78281	−	2.57440i	−0.677609	−	0.198619i
$169$		−	12.9864i		−	0.998952i
$170$		0			0
$171$	4.29981	+	19.6772i	0.328815	+	1.50475i
$172$	−0.530484	+	0.219734i	−0.0404490	+	0.0167545i
$173$	−2.40243	+	12.0778i	−0.182653	+	0.918260i	0.775356	+	0.631524i	$0.217570\pi$
$173$	−2.40243	+	12.0778i	−0.182653	+	0.918260i	−0.958010	+	0.286736i	$0.907430\pi$
$174$	8.90980	−	0.962121i	0.675450	−	0.0729382i
$175$	4.89506	+	7.32598i	0.370032	+	0.553792i
$176$	2.40235	+	12.0774i	0.181084	+	0.910369i
$177$	4.95702	+	15.8051i	0.372592	+	1.18799i
$178$	2.06124	−	4.97628i	0.154497	−	0.372988i
$179$	−7.07462	+	17.0796i	−0.528782	+	1.27659i	0.403540	+	0.914962i	$0.367780\pi$
$179$	−7.07462	+	17.0796i	−0.528782	+	1.27659i	−0.932322	+	0.361630i	$0.882220\pi$
$180$	0.106993	+	0.0419811i	0.00797479	+	0.00312908i
$181$	−0.415290	−	2.08780i	−0.0308683	−	0.155185i	0.962277	−	0.272071i	$-0.0877087\pi$
$181$	−0.415290	−	2.08780i	−0.0308683	−	0.155185i	−0.993145	+	0.116886i	$0.962709\pi$
$182$	0.150792	+	0.225677i	0.0111775	+	0.0167283i
$183$	−0.738981	−	6.84340i	−0.0546271	−	0.505879i
$184$	−3.65898	+	18.3949i	−0.269743	+	1.35609i
$185$	−0.0484090	+	0.0200517i	−0.00355910	+	0.00147423i
$186$	−15.8785	−	12.7834i	−1.16427	−	0.937328i
$187$		0			0
$188$		−	0.813051i		−	0.0592979i
$189$	−0.642943	+	9.17043i	−0.0467672	+	0.667050i
$190$	−1.21781	−	0.242237i	−0.0883490	−	0.0175737i
$191$	12.2604	+	12.2604i	0.887130	+	0.887130i	0.994247	−	0.107116i	$-0.0341617\pi$
$191$	12.2604	+	12.2604i	0.887130	+	0.887130i	−0.107116	+	0.994247i	$0.534162\pi$
$192$	−1.34720	+	15.1344i	−0.0972259	+	1.09223i
$193$	−15.9244	+	3.16756i	−1.14626	+	0.228006i	−0.731447	−	0.681898i	$-0.761155\pi$
$193$	−15.9244	+	3.16756i	−1.14626	+	0.228006i	−0.414818	+	0.909904i	$0.636155\pi$
$194$	5.01333	+	3.34980i	0.359936	+	0.240501i
$195$	−0.0136435	−	0.0249583i	−0.000977028	−	0.00178730i
$196$	0.973548	+	0.403257i	0.0695391	+	0.0288040i
$197$	4.36175	−	6.52782i	0.310762	−	0.465088i	−0.642908	−	0.765944i	$-0.722272\pi$
$197$	4.36175	−	6.52782i	0.310762	−	0.465088i	0.953670	+	0.300855i	$0.0972722\pi$
$198$	13.1620	−	5.74386i	0.935382	−	0.408199i
$199$	10.6424	−	7.11102i	0.754419	−	0.504087i	−0.117899	−	0.993026i	$-0.537616\pi$
$199$	10.6424	−	7.11102i	0.754419	−	0.504087i	0.872318	+	0.488939i	$0.162616\pi$
$200$	10.5180	−	10.5180i	0.743732	−	0.743732i
$201$	−7.72988	+	6.46620i	−0.545224	+	0.456091i
$202$	2.54889	+	6.15356i	0.179339	+	0.432963i
$203$	6.96405			0.488780
$204$		0			0
$205$	0.618741			0.0432147
$206$	8.03605	+	19.4007i	0.559898	+	1.35171i
$207$	18.8352	−	0.353877i	1.30913	−	0.0245962i
$208$	0.279061	−	0.279061i	0.0193494	−	0.0193494i
$209$	20.3300	−	13.5840i	1.40625	−	0.939628i
$210$	−0.502287	−	0.262442i	−0.0346611	−	0.0181102i
$211$	2.84458	−	4.25722i	0.195829	−	0.293079i	−0.720540	−	0.693413i	$-0.756106\pi$
$211$	2.84458	−	4.25722i	0.195829	−	0.293079i	0.916369	+	0.400334i	$0.131106\pi$
$212$	−1.61129	−	0.667417i	−0.110664	−	0.0458384i
$213$	19.7511	−	10.7969i	1.35332	−	0.739792i
$214$	1.48912	+	0.995000i	0.101794	+	0.0680168i
$215$	−0.291003	+	0.0578841i	−0.0198462	+	0.00394766i
$216$	15.3959	−	1.95575i	1.04756	−	0.133072i
$217$	−11.2013	−	11.2013i	−0.760395	−	0.760395i
$218$	14.7974	+	2.94339i	1.00221	+	0.199351i
$219$	−2.17660	+	7.42568i	−0.147081	+	0.501781i
$220$		−	0.139524i		−	0.00940669i
$221$		0			0
$222$	−0.531678	+	0.660405i	−0.0356839	+	0.0443235i
$223$	−0.174491	+	0.0722764i	−0.0116848	+	0.00483999i	−0.388518	−	0.921441i	$-0.627013\pi$
$223$	−0.174491	+	0.0722764i	−0.0116848	+	0.00483999i	0.376833	+	0.926281i	$0.377013\pi$
$224$	−0.527759	+	2.65322i	−0.0352624	+	0.177276i
$225$	−12.5764	−	8.06574i	−0.838426	−	0.537716i
$226$	−9.89597	−	14.8104i	−0.658270	−	0.985171i
$227$	0.415583	+	2.08928i	0.0275832	+	0.138670i	0.992123	−	0.125267i	$-0.0399788\pi$
$227$	0.415583	+	2.08928i	0.0275832	+	0.138670i	−0.964540	+	0.263937i	$0.914979\pi$
$228$	3.02127	−	0.947572i	0.200088	−	0.0627545i
$229$	−6.61427	+	15.9683i	−0.437084	+	1.05521i	0.539868	+	0.841750i	$0.318474\pi$
$229$	−6.61427	+	15.9683i	−0.437084	+	1.05521i	−0.976951	+	0.213463i	$0.931526\pi$
$230$	−0.444424	+	1.07293i	−0.0293045	+	0.0707472i
$231$	10.6483	−	3.33965i	0.700604	−	0.219733i
$232$	−2.29363	−	11.5309i	−0.150584	−	0.757039i
$233$	5.44021	+	8.14185i	0.356400	+	0.533390i	0.965738	−	0.259521i	$-0.0835645\pi$
$233$	5.44021	+	8.14185i	0.356400	+	0.533390i	−0.609337	+	0.792911i	$0.708565\pi$
$234$	−0.387416	−	0.248465i	−0.0253262	−	0.0162427i
$235$	0.0819634	−	0.412058i	0.00534670	−	0.0268797i
$236$	2.40579	−	0.996510i	0.156603	−	0.0648673i
$237$	−2.65671	+	3.29993i	−0.172572	+	0.214354i
$238$		0			0
$239$			22.4367i			1.45131i	0.688059	+	0.725654i	$0.258463\pi$
$239$			22.4367i			1.45131i	−0.688059	+	0.725654i	$0.741537\pi$
$240$	−0.231784	+	0.790753i	−0.0149616	+	0.0510429i
$241$	−0.397704	−	0.0791082i	−0.0256184	−	0.00509581i	0.182265	−	0.983250i	$-0.441657\pi$
$241$	−0.397704	−	0.0791082i	−0.0256184	−	0.00509581i	−0.207883	+	0.978154i	$0.566657\pi$
$242$	−2.10322	−	2.10322i	−0.135200	−	0.135200i
$243$	−5.22043	−	14.6883i	−0.334891	−	0.942257i
$244$	−1.06129	+	0.211104i	−0.0679421	+	0.0135145i
$245$	0.452746	+	0.302515i	0.0289249	+	0.0193270i
$246$	8.78480	−	4.80220i	0.560098	−	0.306177i
$247$	−0.723968	−	0.299877i	−0.0460650	−	0.0190807i
$248$	−14.8577	+	22.2360i	−0.943462	+	1.41199i
$249$	−8.50438	−	4.44349i	−0.538943	−	0.281595i
$250$	1.53468	−	1.02544i	0.0970619	−	0.0648547i
$251$	−0.749951	+	0.749951i	−0.0473365	+	0.0473365i	−0.730379	−	0.683042i	$-0.760656\pi$
$251$	−0.749951	+	0.749951i	−0.0473365	+	0.0473365i	0.683042	+	0.730379i	$0.260656\pi$
$252$	1.44493	−	0.0271476i	0.0910223	−	0.00171014i
$253$	−8.75152	−	21.1280i	−0.550203	−	1.32831i
$254$	12.9984			0.815594
$255$		0			0
$256$	6.40833			0.400521
$257$	7.70425	+	18.5997i	0.480578	+	1.16022i	0.959335	+	0.282270i	$0.0910874\pi$
$257$	7.70425	+	18.5997i	0.480578	+	1.16022i	−0.478757	+	0.877947i	$0.658913\pi$
$258$	−3.68237	+	3.08038i	−0.229254	+	0.191776i
$259$	−0.465876	+	0.465876i	−0.0289481	+	0.0289481i
$260$	−0.00371799	+	0.00248428i	−0.000230580	+	0.000154069i
$261$	−10.8232	+	4.72323i	−0.669940	+	0.292360i
$262$	−9.51469	+	14.2397i	−0.587820	+	0.879734i
$263$	−5.10116	−	2.11297i	−0.314551	−	0.130291i	0.219822	−	0.975540i	$-0.429452\pi$
$263$	−5.10116	−	2.11297i	−0.314551	−	0.130291i	−0.534373	+	0.845249i	$0.679452\pi$
$264$	−9.03675	−	16.5312i	−0.556173	−	1.01742i
$265$	−0.749325	−	0.500683i	−0.0460307	−	0.0307567i
$266$	−15.3127	+	3.04589i	−0.938884	+	0.186756i
$267$	−0.629315	+	7.06969i	−0.0385134	+	0.432658i
$268$	1.12027	+	1.12027i	0.0684314	+	0.0684314i
$269$	−8.96401	−	1.78305i	−0.546545	−	0.108715i	−0.0859079	−	0.996303i	$-0.527379\pi$
$269$	−8.96401	−	1.78305i	−0.546545	−	0.108715i	−0.460637	+	0.887588i	$0.652379\pi$
$270$	0.958628	+	0.0672099i	0.0583403	+	0.00409026i
$271$		−	2.64822i		−	0.160868i	−0.996760	−	0.0804339i	$-0.974369\pi$
$271$		−	2.64822i		−	0.160868i	0.996760	−	0.0804339i	$-0.0256306\pi$
$272$		0			0
$273$	−0.278591	−	0.224288i	−0.0168611	−	0.0135745i
$274$	−3.89196	+	1.61210i	−0.235122	+	0.0973906i
$275$	−3.53836	+	17.7885i	−0.213371	+	1.07269i
$276$	−0.317951	−	2.94442i	−0.0191384	−	0.177233i
$277$	11.4945	+	17.2028i	0.690640	+	1.03362i	0.996666	+	0.0815922i	$0.0260005\pi$
$277$	11.4945	+	17.2028i	0.690640	+	1.03362i	−0.306026	+	0.952023i	$0.598999\pi$
$278$	1.30638	+	6.56761i	0.0783514	+	0.393899i
$279$	25.0057	+	9.81153i	1.49705	+	0.587401i
$280$	−0.284517	+	0.686886i	−0.0170032	+	0.0410493i
$281$	−3.93729	+	9.50546i	−0.234879	+	0.567048i	−0.996739	−	0.0806938i	$-0.974286\pi$
$281$	−3.93729	+	9.50546i	−0.234879	+	0.567048i	0.761860	+	0.647742i	$0.224286\pi$
$282$	−2.03438	−	6.48648i	−0.121145	−	0.386264i
$283$	2.50549	+	12.5960i	0.148936	+	0.748753i	0.980990	+	0.194058i	$0.0621650\pi$
$283$	2.50549	+	12.5960i	0.148936	+	0.748753i	−0.832054	+	0.554695i	$0.812835\pi$
$284$	−1.96596	−	2.94227i	−0.116659	−	0.174592i
$285$	1.62672	−	0.175660i	0.0963584	−	0.0104052i
$286$	−0.108999	+	0.547976i	−0.00644525	+	0.0324025i
$287$	7.18785	−	2.97730i	0.424285	−	0.175745i
$288$	−0.979277	−	4.48146i	−0.0577044	−	0.264073i
$289$		0			0
$290$		−	0.727985i		−	0.0427488i
$291$	−7.62441	−	2.23485i	−0.446951	−	0.131009i
$292$	1.19311	+	0.237324i	0.0698213	+	0.0138883i
$293$	−0.797696	−	0.797696i	−0.0466019	−	0.0466019i	0.683422	−	0.730024i	$-0.260491\pi$
$293$	−0.797696	−	0.797696i	−0.0466019	−	0.0466019i	−0.730024	+	0.683422i	$0.760491\pi$
$294$	8.77592	+	0.781196i	0.511822	+	0.0455603i
$295$	1.31972	−	0.262509i	0.0768372	−	0.0152839i
$296$	0.924822	+	0.617947i	0.0537542	+	0.0359174i
$297$	−14.2840	+	12.4123i	−0.828842	+	0.720235i
$298$	26.9863	+	11.1781i	1.56327	+	0.647530i
$299$	−0.407189	+	0.609402i	−0.0235484	+	0.0352426i
$300$	−1.08769	+	2.08173i	−0.0627980	+	0.120189i
$301$	−3.10202	+	2.07270i	−0.178797	+	0.119469i
$302$	3.83394	−	3.83394i	0.220618	−	0.220618i
$303$	−5.63142	−	6.73196i	−0.323517	−	0.386741i
$304$	8.68744	+	20.9733i	0.498259	+	1.20290i
$305$	−0.559148			−0.0320167
$306$		0			0
$307$	−19.5814			−1.11757			−0.558785	−	0.829312i	$-0.688732\pi$
$307$	−19.5814			−1.11757			−0.558785	+	0.829312i	$0.688732\pi$
$308$	−0.671371	−	1.62083i	−0.0382549	−	0.0923555i
$309$	−17.7546	−	21.2243i	−1.01002	−	1.20741i
$310$	−1.17093	+	1.17093i	−0.0665042	+	0.0665042i
$311$	−24.4244	+	16.3199i	−1.38498	+	0.925415i	−0.384985	+	0.922923i	$0.625793\pi$
$311$	−24.4244	+	16.3199i	−1.38498	+	0.925415i	−0.999997	+	0.00249223i	$0.999207\pi$
$312$	−0.279615	+	0.535153i	−0.0158301	+	0.0302971i
$313$	9.90044	−	14.8171i	0.559606	−	0.837509i	−0.438519	−	0.898722i	$-0.644497\pi$
$313$	9.90044	−	14.8171i	0.559606	−	0.837509i	0.998125	+	0.0612125i	$0.0194967\pi$
$314$	16.9521	+	7.02180i	0.956664	+	0.396263i
$315$	0.735036	+	0.131905i	0.0414146	+	0.00743200i
$316$	0.553759	+	0.370010i	0.0311514	+	0.0208147i
$317$	−13.8497	+	2.75488i	−0.777877	+	0.154729i	−0.568033	−	0.823006i	$-0.692296\pi$
$317$	−13.8497	+	2.75488i	−0.777877	+	0.154729i	−0.209844	+	0.977735i	$0.567296\pi$
$318$	−14.5247	−	1.29293i	−0.814507	−	0.0725040i
$319$	10.1366	+	10.1366i	0.567542	+	0.567542i
$320$	1.21057	+	0.240798i	0.0676730	+	0.0134610i
$321$	−2.26470	−	0.663825i	−0.126403	−	0.0370511i
$322$			14.6027i			0.813775i
$323$		0			0
$324$	−2.22724	+	1.02219i	−0.123736	+	0.0567883i
$325$	0.537026	−	0.222443i	0.0297888	−	0.0123389i
$326$	2.86030	−	14.3797i	0.158417	−	0.796418i
$327$	−19.7660	+	2.13442i	−1.09306	+	0.118034i
$328$	−7.29708	−	10.9209i	−0.402914	−	0.603003i
$329$	−1.03061	−	5.18123i	−0.0568194	−	0.285651i
$330$	−0.349110	−	1.11311i	−0.0192179	−	0.0612749i
$331$	2.76796	−	6.68245i	0.152141	−	0.367301i	−0.829372	−	0.558697i	$-0.811302\pi$
$331$	2.76796	−	6.68245i	0.152141	−	0.367301i	0.981513	+	0.191396i	$0.0613015\pi$
$332$	−0.577254	+	1.39362i	−0.0316810	+	0.0764846i
$333$	0.408072	−	1.04001i	0.0223622	−	0.0569924i
$334$	−0.538496	−	2.70720i	−0.0294652	−	0.148131i
$335$	0.454824	+	0.680692i	0.0248497	+	0.0371902i
$336$	1.11239	+	10.3014i	0.0606860	+	0.561988i
$337$	2.60797	−	13.1112i	0.142065	−	0.714210i	−0.842431	−	0.538804i	$-0.818876\pi$
$337$	2.60797	−	13.1112i	0.142065	−	0.714210i	0.984496	−	0.175406i	$-0.0561238\pi$
$338$	−15.7703	+	6.53226i	−0.857789	+	0.355308i
$339$	18.2829	+	14.7192i	0.992993	+	0.799438i
$340$		0			0
$341$		−	32.6085i		−	1.76585i
$342$	21.7326	−	15.1194i	1.17516	−	0.817561i
$343$	18.8615	+	3.75178i	1.01842	+	0.202577i
$344$	4.45359	+	4.45359i	0.240121	+	0.240121i
$345$	0.135686	−	1.52430i	0.00730511	−	0.0820653i
$346$	15.8754	−	3.15781i	0.853466	−	0.169765i
$347$	−27.8318	−	18.5966i	−1.49409	−	0.998320i	−0.990967	−	0.134106i	$-0.957184\pi$
$347$	−27.8318	−	18.5966i	−1.49409	−	0.998320i	−0.503124	−	0.864214i	$-0.667816\pi$
$348$	0.890460	+	1.62894i	0.0477337	+	0.0873205i
$349$	−25.7122	−	10.6503i	−1.37634	−	0.570099i	−0.432840	−	0.901471i	$-0.642489\pi$
$349$	−25.7122	−	10.6503i	−1.37634	−	0.570099i	−0.943500	+	0.331372i	$0.892489\pi$
$350$	6.43419	−	9.62945i	0.343922	−	0.514715i
$351$	0.585093	+	0.159629i	0.0312299	+	0.00852039i
$352$	−4.63013	+	3.09375i	−0.246787	+	0.164898i
$353$	−5.10785	+	5.10785i	−0.271864	+	0.271864i	−0.829850	−	0.557986i	$-0.811574\pi$
$353$	−5.10785	+	5.10785i	−0.271864	+	0.271864i	0.557986	+	0.829850i	$0.311574\pi$
$354$	16.6998	−	13.9698i	0.887586	−	0.742484i
$355$	−0.699750	−	1.68935i	−0.0371389	−	0.0896611i
$356$	1.11580			0.0591371
$357$		0			0
$358$	24.2996			1.28427
$359$	−10.5450	−	25.4579i	−0.556544	−	1.34362i	−0.912486	−	0.409108i	$-0.865840\pi$
$359$	−10.5450	−	25.4579i	−0.556544	−	1.34362i	0.355942	−	0.934508i	$-0.384160\pi$
$360$	−0.0236823	−	1.26050i	−0.00124817	−	0.0664340i
$361$	18.4383	−	18.4383i	0.970437	−	0.970437i
$362$	−2.32647	+	1.55450i	−0.122277	+	0.0817026i
$363$	3.47384	+	1.81506i	0.182329	+	0.0952660i
$364$	−0.0312374	+	0.0467501i	−0.00163729	+	0.00245037i
$365$	0.580747	+	0.240553i	0.0303977	+	0.0125911i
$366$	−7.93870	+	4.33968i	−0.414963	+	0.226839i
$367$	−9.34048	−	6.24111i	−0.487569	−	0.325783i	0.287370	−	0.957820i	$-0.407219\pi$
$367$	−9.34048	−	6.24111i	−0.487569	−	0.325783i	−0.774939	+	0.632037i	$0.782219\pi$
$368$	20.8247	−	4.14230i	1.08556	−	0.215932i
$369$	−9.15174	+	9.50221i	−0.476420	+	0.494665i
$370$	0.0487002	+	0.0487002i	0.00253180	+	0.00253180i
$371$	−11.1141	−	2.21072i	−0.577013	−	0.114775i
$372$	1.18781	−	4.05234i	0.0615853	−	0.210104i
$373$		−	5.50325i		−	0.284948i	−0.989799	−	0.142474i	$-0.954494\pi$
$373$		−	5.50325i		−	0.284948i	0.989799	−	0.142474i	$-0.0455057\pi$
$374$		0			0
$375$	−1.52524	+	1.89452i	−0.0787630	+	0.0978326i
$376$	−8.23951	+	3.41292i	−0.424920	+	0.176008i
$377$	0.0896309	−	0.450605i	0.00461623	−	0.0232073i
$378$	11.4597	−	3.83203i	0.589423	−	0.197098i
$379$	2.92616	+	4.37931i	0.150307	+	0.224950i	0.898981	−	0.437989i	$-0.144309\pi$
$379$	2.92616	+	4.37931i	0.150307	+	0.224950i	−0.748674	+	0.662939i	$0.769309\pi$
$380$	−0.0501806	−	0.252275i	−0.00257421	−	0.0129414i
$381$	−16.3434	+	5.12584i	−0.837298	+	0.262605i
$382$	8.72156	−	21.0557i	0.446234	−	1.07730i
$383$	8.09691	−	19.5477i	0.413733	−	0.998840i	−0.570394	−	0.821372i	$-0.693209\pi$
$383$	8.09691	−	19.5477i	0.413733	−	0.998840i	0.984127	−	0.177468i	$-0.0567907\pi$
$384$	14.0023	−	4.39159i	0.714552	−	0.224108i
$385$	−0.176858	−	0.889126i	−0.00901352	−	0.0453140i
$386$	11.8567	+	17.7448i	0.603491	+	0.903188i
$387$	3.41525	−	5.32519i	0.173607	−	0.270694i
$388$	−0.243675	+	1.22504i	−0.0123707	+	0.0621919i
$389$	11.5459	−	4.78245i	0.585398	−	0.242480i	−0.0702713	−	0.997528i	$-0.522387\pi$
$389$	11.5459	−	4.78245i	0.585398	−	0.242480i	0.655669	+	0.755048i	$0.272387\pi$
$390$	−0.0234459	+	0.0291224i	−0.00118723	+	0.00147467i
$391$		0			0
$392$		−	11.5587i		−	0.583804i
$393$	6.34783	−	21.6562i	0.320206	−	1.09241i
$394$	−10.1212	−	2.01323i	−0.509898	−	0.101425i
$395$	0.243347	+	0.243347i	0.0122441	+	0.0122441i
$396$	2.14271	+	2.06368i	0.107675	+	0.103704i
$397$	38.1521	−	7.58893i	1.91480	−	0.380877i	0.915053	−	0.403334i	$-0.132149\pi$
$397$	38.1521	−	7.58893i	1.91480	−	0.380877i	0.999748	+	0.0224569i	$0.00714887\pi$
$398$	−13.9886	−	9.34689i	−0.701186	−	0.468517i
$399$	18.0521	−	9.86819i	0.903738	−	0.494027i
$400$	−15.5576	−	6.44418i	−0.777881	−	0.322209i
$401$	−15.1269	+	22.6390i	−0.755401	+	1.13054i	0.232064	+	0.972701i	$0.425452\pi$
$401$	−15.1269	+	22.6390i	−0.755401	+	1.13054i	−0.987465	+	0.157837i	$0.949548\pi$
$402$	11.7406	+	6.13437i	0.585565	+	0.305955i
$403$	−0.868943	+	0.580609i	−0.0432851	+	0.0289222i
$404$	−0.975645	+	0.975645i	−0.0485401	+	0.0485401i
$405$	−1.23182	+	0.293523i	−0.0612098	+	0.0145853i
$406$	−3.50297	−	8.45693i	−0.173850	−	0.419710i
$407$	−1.35623			−0.0672256
$408$		0			0
$409$	28.2231			1.39554			0.697770	−	0.716322i	$-0.254176\pi$
$409$	28.2231			1.39554			0.697770	+	0.716322i	$0.254176\pi$
$410$	−0.311232	−	0.751380i	−0.0153706	−	0.0371080i
$411$	4.25778	−	3.56172i	0.210021	−	0.175687i
$412$	−3.07598	+	3.07598i	−0.151543	+	0.151543i
$413$	14.0679	−	9.39988i	0.692237	−	0.462538i
$414$	−9.90398	−	22.6948i	−0.486754	−	1.11539i
$415$	−0.433045	+	0.648098i	−0.0212573	+	0.0318139i
$416$	0.164883	+	0.0682967i	0.00808405	+	0.00334852i
$417$	−4.23245	−	7.74253i	−0.207264	−	0.379154i
$418$	−26.7222	−	17.8552i	−1.30703	−	0.873326i
$419$	9.16095	−	1.82223i	0.447542	−	0.0890216i	0.0338260	−	0.999428i	$-0.489231\pi$
$419$	9.16095	−	1.82223i	0.447542	−	0.0890216i	0.413716	+	0.910406i	$0.364231\pi$
$420$	0.0104092	−	0.116936i	0.000507915	−	0.00570589i
$421$	−9.40617	−	9.40617i	−0.458429	−	0.458429i	0.439711	−	0.898139i	$-0.355081\pi$
$421$	−9.40617	−	9.40617i	−0.458429	−	0.458429i	−0.898139	+	0.439711i	$0.855081\pi$
$422$	−6.60069	−	1.31296i	−0.321316	−	0.0639138i
$423$	5.11580	+	7.35345i	0.248739	+	0.357537i
$424$			19.1305i			0.929057i
$425$		0			0
$426$	−23.0464	−	18.5542i	−1.11660	−	0.898952i
$427$	−6.49556	+	2.69055i	−0.314342	+	0.130205i
$428$	−0.0723795	+	0.363877i	−0.00349860	+	0.0175886i
$429$	−0.0790418	−	0.731973i	−0.00381617	−	0.0353400i
$430$	0.216670	+	0.324269i	0.0104487	+	0.0156376i
$431$	−2.85038	−	14.3298i	−0.137298	−	0.690243i	−0.986707	−	0.162508i	$-0.948042\pi$
$431$	−2.85038	−	14.3298i	−0.137298	−	0.690243i	0.849409	−	0.527734i	$-0.176958\pi$
$432$	−8.71556	−	15.2555i	−0.419327	−	0.733982i
$433$	6.82738	−	16.4827i	0.328103	−	0.792110i	−0.670631	−	0.741792i	$-0.733976\pi$
$433$	6.82738	−	16.4827i	0.328103	−	0.792110i	0.998733	−	0.0503185i	$-0.0160236\pi$
$434$	−7.96819	+	19.2369i	−0.382485	+	0.923401i
$435$	0.287076	+	0.915323i	0.0137642	+	0.0438864i
$436$	0.609738	+	3.06536i	0.0292011	+	0.146804i
$437$	−23.4226	−	35.0544i	−1.12045	−	1.67688i
$438$	10.1124	−	1.09198i	0.483187	−	0.0521768i
$439$	−5.14255	+	25.8533i	−0.245440	+	1.23391i	0.639713	+	0.768614i	$0.279053\pi$
$439$	−5.14255	+	25.8533i	−0.245440	+	1.23391i	−0.885154	+	0.465299i	$0.845947\pi$
$440$	−1.41394	+	0.585674i	−0.0674070	+	0.0279209i
$441$	−11.3424	+	2.47850i	−0.540112	+	0.118024i
$442$		0			0
$443$		−	9.67036i		−	0.459453i	−0.973255	−	0.229726i	$-0.926217\pi$
$443$		−	9.67036i		−	0.459453i	0.973255	−	0.229726i	$-0.0737831\pi$
$444$	−0.168541	−	0.0494025i	−0.00799861	−	0.00234454i
$445$	0.565491	+	0.112483i	0.0268068	+	0.00533221i
$446$	0.175541	+	0.175541i	0.00831208	+	0.00831208i
$447$	−38.3389	−	3.41277i	−1.81337	−	0.161418i
$448$	15.2218	−	3.02780i	0.719161	−	0.143050i
$449$	0.878627	+	0.587080i	0.0414650	+	0.0277060i	0.576130	−	0.817358i	$-0.304562\pi$
$449$	0.878627	+	0.587080i	0.0414650	+	0.0277060i	−0.534665	+	0.845064i	$0.679562\pi$
$450$	−3.46875	+	19.3295i	−0.163519	+	0.911202i
$451$	14.7960	+	6.12872i	0.696718	+	0.288590i
$452$	2.05000	−	3.06805i	0.0964240	−	0.144309i
$453$	−3.30866	+	6.33243i	−0.155455	+	0.297524i
$454$	2.32811	−	1.55560i	0.109264	−	0.0730077i
$455$	−0.0205441	+	0.0205441i	−0.000963124	+	0.000963124i
$456$	−22.2850	−	26.6401i	−1.04359	−	1.24754i
$457$	−8.19942	−	19.7952i	−0.383553	−	0.925978i	−0.991273	−	0.131827i	$-0.957916\pi$
$457$	−8.19942	−	19.7952i	−0.383553	−	0.925978i	0.607720	−	0.794151i	$-0.292084\pi$
$458$	22.7184			1.06156
$459$		0			0
$460$	−0.240577			−0.0112169
$461$	−9.42954	−	22.7649i	−0.439177	−	1.06027i	−0.976233	−	0.216721i	$-0.930464\pi$
$461$	−9.42954	−	22.7649i	−0.439177	−	1.06027i	0.537056	−	0.843547i	$-0.319536\pi$
$462$	−9.41173	−	11.2510i	−0.437873	−	0.523446i
$463$	13.6466	−	13.6466i	0.634213	−	0.634213i	−0.314909	−	0.949122i	$-0.601974\pi$
$463$	13.6466	−	13.6466i	0.634213	−	0.634213i	0.949122	+	0.314909i	$0.101974\pi$
$464$	−11.0667	+	7.39451i	−0.513757	+	0.343281i
$465$	1.01050	−	1.93400i	0.0468610	−	0.0896870i
$466$	7.15074	−	10.7018i	0.331252	−	0.495753i
$467$	−11.4980	−	4.76264i	−0.532066	−	0.220389i	0.100442	−	0.994943i	$-0.467974\pi$
$467$	−11.4980	−	4.76264i	−0.532066	−	0.220389i	−0.632508	+	0.774554i	$0.717974\pi$
$468$	0.0168405	−	0.0938432i	0.000778452	−	0.00433790i
$469$	8.55905	+	5.71897i	0.395220	+	0.264078i
$470$	−0.541619	+	0.107735i	−0.0249830	+	0.00496943i
$471$	−24.0835	−	2.14382i	−1.10971	−	0.0987818i
$472$	−20.1974	−	20.1974i	−0.929660	−	0.929660i
$473$	−7.53215	−	1.49824i	−0.346329	−	0.0688890i
$474$	5.34369	+	1.56633i	0.245444	+	0.0719440i
$475$			33.4363i			1.53416i
$476$		0			0
$477$	18.7724	−	4.10208i	0.859527	−	0.187821i
$478$	27.2464	−	11.2858i	1.24622	−	0.516202i
$479$	4.42837	−	22.2629i	0.202337	−	1.01722i	−0.737435	−	0.675418i	$-0.763963\pi$
$479$	4.42837	−	22.2629i	0.202337	−	1.01722i	0.939772	−	0.341801i	$-0.111037\pi$
$480$	−0.370483	+	0.0400064i	−0.0169102	+	0.00182604i
$481$	0.0241482	+	0.0361403i	0.00110106	+	0.00164786i
$482$	0.103982	+	0.522751i	0.00473624	+	0.0238107i
$483$	−5.75846	−	18.3605i	−0.262019	−	0.835431i
$484$	0.235795	−	0.569259i	0.0107179	−	0.0258754i
$485$	−0.246991	+	0.596290i	−0.0112153	+	0.0270761i
$486$	−15.2111	+	13.7279i	−0.689992	+	0.622709i
$487$	4.48421	+	22.5436i	0.203199	+	1.02155i	0.938886	+	0.344228i	$0.111859\pi$
$487$	4.48421	+	22.5436i	0.203199	+	1.02155i	−0.735687	+	0.677322i	$0.763141\pi$
$488$	6.59427	+	9.86902i	0.298509	+	0.446750i
$489$	2.07417	+	19.2081i	0.0937974	+	0.868619i
$490$	0.139630	−	0.701969i	0.00630785	−	0.0317117i
$491$	18.8224	−	7.79649i	0.849443	−	0.351851i	0.0848732	−	0.996392i	$-0.472951\pi$
$491$	18.8224	−	7.79649i	0.849443	−	0.351851i	0.764570	+	0.644541i	$0.222951\pi$
$492$	1.61549	+	1.30060i	0.0728319	+	0.0586355i
$493$		0			0
$494$			1.03001i			0.0463421i
$495$	0.877897	+	1.26189i	0.0394585	+	0.0567177i
$496$	29.6939	+	5.90648i	1.33329	+	0.265209i
$497$	−16.2578	−	16.2578i	−0.729264	−	0.729264i
$498$	−1.11827	+	12.5626i	−0.0501108	+	0.562942i
$499$	1.05842	−	0.210533i	0.0473815	−	0.00942477i	−0.171343	−	0.985211i	$-0.554811\pi$
$499$	1.05842	−	0.210533i	0.0473815	−	0.00942477i	0.218724	+	0.975787i	$0.429811\pi$
$500$	0.317918	+	0.212426i	0.0142177	+	0.00949997i
$501$	1.74464	+	3.19151i	0.0779446	+	0.142586i
$502$	1.28795	+	0.533486i	0.0574840	+	0.0238106i
$503$	5.21393	−	7.80319i	0.232478	−	0.347927i	−0.696829	−	0.717238i	$-0.745406\pi$
$503$	5.21393	−	7.80319i	0.232478	−	0.347927i	0.929306	+	0.369311i	$0.120406\pi$
$504$	−6.34046	−	14.5291i	−0.282427	−	0.647177i
$505$	−0.592815	+	0.396107i	−0.0263799	+	0.0176265i
$506$	−21.2552	+	21.2552i	−0.944907	+	0.944907i
$507$	17.2526	−	14.4321i	0.766214	−	0.640954i
$508$	1.03045	+	2.48772i	0.0457188	+	0.110375i
$509$	7.99190			0.354235			0.177117	−	0.984190i	$-0.443323\pi$
$509$	7.99190			0.354235			0.177117	+	0.984190i	$0.443323\pi$
$510$		0			0
$511$	7.90399			0.349652
$512$	−9.70803	−	23.4372i	−0.429038	−	1.03579i
$513$	−21.3629	+	27.5802i	−0.943197	+	1.21770i
$514$	18.7116	−	18.7116i	0.825334	−	0.825334i
$515$	−1.86901	+	1.24883i	−0.0823584	+	0.0550301i
$516$	−0.881462	−	0.460559i	−0.0388042	−	0.0202750i
$517$	6.04150	−	9.04174i	0.265705	−	0.397655i
$518$	0.800085	+	0.331406i	0.0351537	+	0.0145611i
$519$	−18.7154	+	10.2308i	−0.821517	+	0.449081i
$520$	0.0407827	+	0.0272501i	0.00178844	+	0.00119500i
$521$	−1.54613	+	0.307543i	−0.0677370	+	0.0134737i	−0.228842	−	0.973463i	$-0.573494\pi$
$521$	−1.54613	+	0.307543i	−0.0677370	+	0.0134737i	0.161105	+	0.986937i	$0.448494\pi$
$522$	11.1799	+	10.7676i	0.489331	+	0.471283i
$523$	24.2095	+	24.2095i	1.05861	+	1.05861i	0.998172	+	0.0604341i	$0.0192485\pi$
$523$	24.2095	+	24.2095i	1.05861	+	1.05861i	0.0604341	+	0.998172i	$0.480751\pi$
$524$	−3.47957	−	0.692129i	−0.152006	−	0.0302358i
$525$	−4.29264	+	14.6447i	−0.187346	+	0.639149i
$526$			7.25753i			0.316443i
$527$		0			0
$528$	−13.3752	+	16.6135i	−0.582081	+	0.723011i
$529$	−15.1812	+	6.28827i	−0.660054	+	0.273403i
$530$	−0.231097	+	1.16181i	−0.0100382	+	0.0504656i
$531$	−15.4884	+	24.1502i	−0.672141	+	1.04803i
$532$	−1.79686	−	2.68919i	−0.0779037	−	0.116591i
$533$	−0.100134	−	0.503405i	−0.00433727	−	0.0218049i
$534$	8.90177	−	2.79189i	0.385217	−	0.120817i
$535$	−0.0733645	+	0.177118i	−0.00317183	+	0.00765746i
$536$	6.65037	−	16.0554i	0.287252	−	0.693488i
$537$	−30.5528	+	9.58237i	−1.31845	+	0.413510i
$538$	2.34369	+	11.7825i	0.101043	+	0.507980i
$539$	7.83012	+	11.7186i	0.337267	+	0.504756i
$540$	0.0631321	+	0.188797i	0.00271677	+	0.00812451i
$541$	−0.591454	+	2.97344i	−0.0254286	+	0.127838i	−0.991415	−	0.130756i	$-0.958259\pi$
$541$	−0.591454	+	2.97344i	−0.0254286	+	0.127838i	0.965986	+	0.258595i	$0.0832594\pi$
$542$	−3.21592	+	1.33208i	−0.138135	+	0.0572176i
$543$	2.31215	−	2.87196i	0.0992239	−	0.123247i
$544$		0			0
$545$			1.61500i			0.0691792i
$546$	−0.132235	+	0.451131i	−0.00565912	+	0.0193066i
$547$	−1.70456	−	0.339058i	−0.0728817	−	0.0144971i	0.158515	−	0.987357i	$-0.449329\pi$
$547$	−1.70456	−	0.339058i	−0.0728817	−	0.0144971i	−0.231396	+	0.972860i	$0.574329\pi$
$548$	−0.617069	−	0.617069i	−0.0263599	−	0.0263599i
$549$	8.27030	−	8.58701i	0.352968	−	0.366485i
$550$	23.3817	−	4.65090i	0.996998	−	0.198315i
$551$	21.9739	+	14.6825i	0.936119	+	0.625495i
$552$	−28.5042	+	15.5818i	−1.21322	+	0.663206i
$553$	3.99789	+	1.65598i	0.170008	+	0.0704195i
$554$	15.1087	−	22.6118i	0.641907	−	0.960681i
$555$	−0.0804372	−	0.0420280i	−0.00341437	−	0.00178399i
$556$	−1.15339	+	0.770669i	−0.0489146	+	0.0326837i
$557$	29.9311	−	29.9311i	1.26822	−	1.26822i	0.321217	−	0.947006i	$-0.395908\pi$
$557$	29.9311	−	29.9311i	1.26822	−	1.26822i	0.947006	−	0.321217i	$-0.104092\pi$
$558$	−0.663247	−	35.3014i	−0.0280775	−	1.49443i
$559$	0.0941886	+	0.227391i	0.00398375	+	0.00961763i
$560$	0.841688			0.0355678
$561$		0			0
$562$	13.5236			0.570460
$563$	10.8784	+	26.2627i	0.458468	+	1.10684i	0.969018	+	0.246991i	$0.0794420\pi$
$563$	10.8784	+	26.2627i	0.458468	+	1.10684i	−0.510550	+	0.859848i	$0.670558\pi$
$564$	1.08015	−	0.903567i	0.0454825	−	0.0380471i
$565$	1.34824	−	1.34824i	0.0567208	−	0.0567208i
$566$	14.0359	−	9.37847i	0.589972	−	0.394207i
$567$	−12.8976	+	9.33720i	−0.541646	+	0.392126i
$568$	−21.5647	+	32.2739i	−0.904835	+	1.35418i
$569$	19.2820	+	7.98685i	0.808342	+	0.334826i	0.748292	−	0.663369i	$-0.230874\pi$
$569$	19.2820	+	7.98685i	0.808342	+	0.334826i	0.0600499	+	0.998195i	$0.480874\pi$
$570$	−1.03157	−	1.88708i	−0.0432077	−	0.0790410i
$571$	−5.22099	−	3.48855i	−0.218492	−	0.145991i	0.441508	−	0.897257i	$-0.354444\pi$
$571$	−5.22099	−	3.48855i	−0.218492	−	0.145991i	−0.660000	+	0.751266i	$0.729444\pi$
$572$	−0.113516	+	0.0225797i	−0.00474634	+	0.000944106i
$573$	−2.66277	+	29.9134i	−0.111239	+	1.24965i
$574$	−7.23109	−	7.23109i	−0.301820	−	0.301820i
$575$	30.6723	+	6.10109i	1.27912	+	0.254433i
$576$	−21.6034	+	15.0295i	−0.900144	+	0.626230i
$577$		−	36.1978i		−	1.50693i	−0.657485	−	0.753467i	$-0.728380\pi$
$577$		−	36.1978i		−	1.50693i	0.657485	−	0.753467i	$-0.271620\pi$
$578$		0			0
$579$	−21.9054	−	17.6356i	−0.910358	−	0.732911i
$580$	0.139326	−	0.0577109i	0.00578522	−	0.00239632i
$581$	−1.91207	+	9.61264i	−0.0793261	+	0.398799i
$582$	1.12120	+	10.3830i	0.0464754	+	0.430389i
$583$	−12.9594	−	19.3951i	−0.536723	−	0.803262i
$584$	−2.60321	−	13.0872i	−0.107722	−	0.541553i
$585$	0.0179951	−	0.0458624i	0.000744007	−	0.00189618i
$586$	−0.567450	+	1.36995i	−0.0234412	+	0.0565919i
$587$	−2.98442	+	7.20502i	−0.123180	+	0.297383i	−0.973426	−	0.229003i	$-0.926453\pi$
$587$	−2.98442	+	7.20502i	−0.123180	+	0.297383i	0.850246	+	0.526386i	$0.176453\pi$
$588$	0.546200	+	1.74152i	0.0225249	+	0.0718192i
$589$	−11.7279	−	58.9600i	−0.483238	−	2.42940i
$590$	−0.982614	−	1.47059i	−0.0404536	−	0.0605431i
$591$	13.5196	−	1.45991i	0.556124	−	0.0600528i
$592$	0.245657	−	1.23500i	0.0100964	−	0.0507583i
$593$	−28.0114	+	11.6027i	−1.15029	+	0.476465i	−0.874630	−	0.484790i	$-0.838896\pi$
$593$	−28.0114	+	11.6027i	−1.15029	+	0.476465i	−0.275659	+	0.961256i	$0.588896\pi$
$594$	22.2581	+	11.1026i	0.913261	+	0.455543i
$595$		0			0
$596$			6.05095i			0.247857i
$597$	21.2743	+	6.23588i	0.870698	+	0.255218i
$598$	0.944859	+	0.187944i	0.0386381	+	0.00768561i
$599$	−17.7610	−	17.7610i	−0.725695	−	0.725695i	0.244064	−	0.969759i	$-0.421519\pi$
$599$	−17.7610	−	17.7610i	−0.725695	−	0.725695i	−0.969759	+	0.244064i	$0.921519\pi$
$600$	25.6621	+	2.28434i	1.04765	+	0.0932577i
$601$	−29.8774	+	5.94298i	−1.21872	+	0.242419i	−0.762229	−	0.647307i	$-0.775895\pi$
$601$	−29.8774	+	5.94298i	−1.21872	+	0.242419i	−0.456494	+	0.889726i	$0.650895\pi$
$602$	4.07737	+	2.72441i	0.166181	+	0.111039i
$603$	−17.1809	−	3.08317i	−0.699659	−	0.125556i
$604$	1.03770	+	0.429829i	0.0422233	+	0.0174895i
$605$	0.176889	−	0.264733i	0.00719155	−	0.0107629i
$606$	−5.34243	+	10.2249i	−0.217021	+	0.415356i
$607$	18.1199	−	12.1073i	0.735464	−	0.491421i	−0.130550	−	0.991442i	$-0.541674\pi$
$607$	18.1199	−	12.1073i	0.735464	−	0.491421i	0.866014	+	0.500020i	$0.166674\pi$
$608$	−7.25911	+	7.25911i	−0.294396	+	0.294396i
$609$	7.73935	+	9.25183i	0.313614	+	0.374903i
$610$	0.281256	+	0.679012i	0.0113877	+	0.0274924i
$611$	−0.348513			−0.0140993
$612$		0			0
$613$	17.5623			0.709337			0.354668	−	0.934992i	$-0.384594\pi$
$613$	17.5623			0.709337			0.354668	+	0.934992i	$0.384594\pi$
$614$	9.84962	+	23.7791i	0.397498	+	0.959646i
$615$	0.687625	+	0.822006i	0.0277277	+	0.0331465i
$616$	−13.6074	+	13.6074i	−0.548258	+	0.548258i
$617$	−19.6482	+	13.1285i	−0.791007	+	0.528534i	−0.884197	−	0.467115i	$-0.845294\pi$
$617$	−19.6482	+	13.1285i	−0.791007	+	0.528534i	0.0931902	+	0.995648i	$0.470294\pi$
$618$	−16.8434	+	32.2366i	−0.677543	+	1.29675i
$619$	22.1885	−	33.2074i	0.891831	−	1.33472i	−0.0500404	−	0.998747i	$-0.515935\pi$
$619$	22.1885	−	33.2074i	0.891831	−	1.33472i	0.941872	−	0.335973i	$-0.109065\pi$
$620$	−0.316925	−	0.131275i	−0.0127280	−	0.00527211i
$621$	21.4022	+	24.6295i	0.858840	+	0.988347i
$622$	32.1040	+	21.4512i	1.28725	+	0.860116i
$623$	7.11050	−	1.41437i	0.284876	−	0.0566654i
$624$	0.680864	+	0.0606077i	0.0272564	+	0.00242625i
$625$	−17.4680	−	17.4680i	−0.698719	−	0.698719i
$626$	−22.9734	−	4.56969i	−0.918201	−	0.182642i
$627$	40.6399	+	11.9123i	1.62300	+	0.475731i
$628$			3.80106i			0.151679i
$629$		0			0
$630$	−0.209548	−	0.958955i	−0.00834859	−	0.0382057i
$631$	24.7481	−	10.2510i	0.985205	−	0.408085i	0.168854	−	0.985641i	$-0.445993\pi$
$631$	24.7481	−	10.2510i	0.985205	−	0.408085i	0.816351	+	0.577556i	$0.195993\pi$
$632$	1.42521	−	7.16501i	0.0566917	−	0.285009i
$633$	8.81704	−	0.952104i	0.350446	−	0.0378428i
$634$	10.3120	+	15.4329i	0.409540	+	0.612920i
$635$	0.271450	+	1.36467i	0.0107721	+	0.0541552i
$636$	−0.903997	−	2.88234i	−0.0358458	−	0.114292i
$637$	0.172855	−	0.417310i	0.00684878	−	0.0165344i
$638$	7.21080	−	17.4084i	0.285478	−	0.689206i
$639$	36.2938	+	14.2407i	1.43576	+	0.563352i
$640$	−0.232566	−	1.16919i	−0.00919297	−	0.0462162i
$641$	23.6558	+	35.4034i	0.934349	+	1.39835i	0.917168	+	0.398500i	$0.130469\pi$
$641$	23.6558	+	35.4034i	0.934349	+	1.39835i	0.0171805	+	0.999852i	$0.494531\pi$
$642$	0.333034	+	3.08409i	0.0131438	+	0.121719i
$643$	−5.03062	+	25.2906i	−0.198388	+	0.997365i	0.745351	+	0.666673i	$0.232282\pi$
$643$	−5.03062	+	25.2906i	−0.198388	+	0.997365i	−0.943739	+	0.330692i	$0.892718\pi$
$644$	−2.79475	+	1.15763i	−0.110129	+	0.0456168i
$645$	−0.400300	−	0.322273i	−0.0157618	−	0.0126895i
$646$		0			0
$647$			38.1903i			1.50142i	0.660634	+	0.750709i	$0.270288\pi$
$647$			38.1903i			1.50142i	−0.660634	+	0.750709i	$0.729712\pi$
$648$	19.7081	+	18.2802i	0.774209	+	0.718113i
$649$	34.1589	+	6.79463i	1.34085	+	0.266712i
$650$	−0.540257	−	0.540257i	−0.0211906	−	0.0211906i
$651$	2.43275	−	27.3295i	0.0953472	−	1.07113i
$652$	2.97883	−	0.592526i	0.116660	−	0.0232051i
$653$	28.5236	+	19.0588i	1.11621	+	0.745830i	0.969923	−	0.243412i	$-0.0782667\pi$
$653$	28.5236	+	19.0588i	1.11621	+	0.745830i	0.146290	+	0.989242i	$0.453267\pi$
$654$	12.5345	+	22.9296i	0.490136	+	0.896619i
$655$	−1.69369	−	0.701548i	−0.0661778	−	0.0274118i
$656$	−8.26097	+	12.3634i	−0.322537	+	0.482710i
$657$	−12.2840	+	5.36072i	−0.479246	+	0.209142i
$658$	−5.77352	+	3.85774i	−0.225075	+	0.150391i
$659$	24.7106	−	24.7106i	0.962589	−	0.962589i	−0.0367361	−	0.999325i	$-0.511696\pi$
$659$	24.7106	−	24.7106i	0.962589	−	0.962589i	0.999325	+	0.0367361i	$0.0116961\pi$
$660$	0.185359	−	0.155057i	0.00721510	−	0.00603558i
$661$	−4.65040	−	11.2271i	−0.180880	−	0.436682i	0.807269	−	0.590184i	$-0.200945\pi$
$661$	−4.65040	−	11.2271i	−0.180880	−	0.436682i	−0.988148	+	0.153502i	$0.950945\pi$
$662$	−9.50727			−0.369510
$663$		0			0
$664$	16.5461			0.642113
$665$	−0.639559	−	1.54403i	−0.0248011	−	0.0598750i
$666$	−1.46823	+	0.0275852i	−0.0568926	+	0.00106890i
$667$	17.4783	−	17.4783i	0.676762	−	0.676762i
$668$	0.475432	−	0.317674i	0.0183950	−	0.0122912i
$669$	−0.289937	−	0.151490i	−0.0112096	−	0.00585696i
$670$	0.597832	−	0.894718i	0.0230962	−	0.0345660i
$671$	−13.3710	−	5.53844i	−0.516181	−	0.213809i
$672$	−4.11136	+	2.24747i	−0.158599	+	0.0866980i
$673$	−33.7102	−	22.5244i	−1.29943	−	0.868252i	−0.303027	−	0.952982i	$-0.597997\pi$
$673$	−33.7102	−	22.5244i	−1.29943	−	0.868252i	−0.996404	+	0.0847298i	$0.972997\pi$
$674$	−17.2336	+	3.42798i	−0.663814	+	0.132041i
$675$	−3.26107	−	25.6716i	−0.125519	−	0.988100i
$676$	−2.50037	−	2.50037i	−0.0961681	−	0.0961681i
$677$	−6.72222	−	1.33713i	−0.258356	−	0.0513902i	0.0642128	−	0.997936i	$-0.479546\pi$
$677$	−6.72222	−	1.33713i	−0.258356	−	0.0513902i	−0.322569	+	0.946546i	$0.604546\pi$
$678$	8.67810	−	29.6061i	0.333280	−	1.13702i
$679$			8.11552i			0.311445i
$680$		0			0
$681$	−2.31378	+	2.87398i	−0.0886644	+	0.110131i
$682$	−39.5988	+	16.4024i	−1.51632	+	0.628079i
$683$	1.92646	−	9.68496i	0.0737139	−	0.370585i	−0.926266	−	0.376870i	$-0.877001\pi$
$683$	1.92646	−	9.68496i	0.0737139	−	0.370585i	0.999980	+	0.00628472i	$0.00200050\pi$
$684$	4.61649	+	2.96073i	0.176516	+	0.113206i
$685$	−0.250527	−	0.374940i	−0.00957213	−	0.0143257i
$686$	−4.93143	−	24.7920i	−0.188283	−	0.946562i
$687$	−28.5647	+	8.95885i	−1.08981	+	0.341801i
$688$	2.72864	−	6.58752i	0.104028	−	0.251147i
$689$	−0.286087	+	0.690676i	−0.0108991	+	0.0263127i
$690$	−1.91931	+	0.601960i	−0.0730669	+	0.0229162i
$691$	2.70622	+	13.6051i	0.102950	+	0.517563i	0.997504	+	0.0706044i	$0.0224928\pi$
$691$	2.70622	+	13.6051i	0.102950	+	0.517563i	−0.894555	+	0.446958i	$0.852507\pi$
$692$	1.86288	+	2.78800i	0.0708161	+	0.105984i
$693$	16.2705	+	10.4349i	0.618065	+	0.396389i
$694$	−8.58354	+	43.1524i	−0.325827	+	1.63804i
$695$	−0.662233	+	0.274306i	−0.0251199	+	0.0104050i
$696$	12.7699	−	15.8617i	0.484044	−	0.601237i
$697$		0			0
$698$			36.5813i			1.38462i
$699$	−4.77070	+	16.2757i	−0.180444	+	0.615602i
$700$	2.35301	+	0.468044i	0.0889356	+	0.0176904i
$701$	7.15325	+	7.15325i	0.270175	+	0.270175i	0.829170	−	0.558996i	$-0.188813\pi$
$701$	7.15325	+	7.15325i	0.270175	+	0.270175i	−0.558996	+	0.829170i	$0.688813\pi$
$702$	−0.100457	−	0.790814i	−0.00379152	−	0.0298473i
$703$	−2.45221	+	0.487775i	−0.0924869	+	0.0183968i
$704$	26.5634	+	17.7491i	1.00115	+	0.668945i
$705$	0.638513	−	0.349042i	0.0240478	−	0.0131457i
$706$	8.77211	+	3.63353i	0.330143	+	0.136750i
$707$	−4.98066	+	7.45408i	−0.187317	+	0.280340i
$708$	3.99750	+	2.08867i	0.150235	+	0.0784971i
$709$	37.4563	−	25.0275i	1.40670	−	0.939929i	0.407054	−	0.913404i	$-0.366556\pi$
$709$	37.4563	−	25.0275i	1.40670	−	0.939929i	0.999648	−	0.0265247i	$-0.00844407\pi$
$710$	−1.69951	+	1.69951i	−0.0637814	+	0.0637814i
$711$	−7.33648	+	0.137839i	−0.275140	+	0.00516936i
$712$	−4.68374	−	11.3075i	−0.175531	−	0.423768i
$713$	−56.2259			−2.10568
$714$		0			0
$715$	−0.0598067			−0.00223664
$716$	1.92635	+	4.65061i	0.0719909	+	0.173801i
$717$	−29.8074	+	24.9345i	−1.11318	+	0.931197i
$718$	−25.6111	+	25.6111i	−0.955796	+	0.955796i
$719$	23.9148	−	15.9794i	0.891871	−	0.595929i	−0.0229732	−	0.999736i	$-0.507313\pi$
$719$	23.9148	−	15.9794i	0.891871	−	0.595929i	0.914844	+	0.403807i	$0.132313\pi$
$720$	−1.30811	+	0.570858i	−0.0487505	+	0.0212746i
$721$	−15.7029	+	23.5010i	−0.584805	+	0.875222i
$722$	−31.6655	−	13.1163i	−1.17847	−	0.488138i
$723$	−0.336883	−	0.616270i	−0.0125288	−	0.0229193i
$724$	−0.481940	−	0.322022i	−0.0179112	−	0.0119679i
$725$	−19.2269	+	3.82448i	−0.714071	+	0.142038i
$726$	0.456786	−	5.13151i	0.0169529	−	0.190448i
$727$	−1.86673	−	1.86673i	−0.0692331	−	0.0692331i	0.671642	−	0.740876i	$-0.265589\pi$
$727$	−1.86673	−	1.86673i	−0.0692331	−	0.0692331i	−0.740876	+	0.671642i	$0.765589\pi$
$728$	0.604893	+	0.120321i	0.0224188	+	0.00445938i
$729$	13.7120	−	23.2590i	0.507853	−	0.861444i
$730$		−	0.826242i		−	0.0305806i
$731$		0			0
$732$	−1.45990	−	1.17533i	−0.0539593	−	0.0434415i
$733$	−28.9600	+	11.9956i	−1.06966	+	0.443068i	−0.846871	−	0.531798i	$-0.821516\pi$
$733$	−28.9600	+	11.9956i	−1.06966	+	0.443068i	−0.222790	+	0.974866i	$0.571516\pi$
$734$	−2.88067	+	14.4821i	−0.106328	+	0.534545i
$735$	0.101254	+	0.937673i	0.00373482	+	0.0345866i
$736$	5.33447	+	7.98360i	0.196631	+	0.294279i
$737$	4.13391	+	20.7826i	0.152275	+	0.765537i
$738$	16.1426	+	6.33390i	0.594217	+	0.233154i
$739$	−1.82751	+	4.41201i	−0.0672262	+	0.162298i	−0.953922	−	0.300055i	$-0.902995\pi$
$739$	−1.82751	+	4.41201i	−0.0672262	+	0.162298i	0.886696	+	0.462354i	$0.152995\pi$
$740$	−0.00545986	+	0.0131813i	−0.000200708	+	0.000484553i
$741$	−0.406175	−	1.29506i	−0.0149212	−	0.0475753i
$742$	2.90583	+	14.6086i	0.106676	+	0.536298i
$743$	−11.6988	−	17.5085i	−0.429188	−	0.642325i	0.552346	−	0.833615i	$-0.313733\pi$
$743$	−11.6988	−	17.5085i	−0.429188	−	0.642325i	−0.981534	+	0.191290i	$0.938733\pi$
$744$	−46.0526	+	4.97297i	−1.68837	+	0.182318i
$745$	−0.609995	+	3.06665i	−0.0223485	+	0.112353i
$746$	−6.68298	+	2.76818i	−0.244681	+	0.101350i
$747$	−3.54792	−	16.2364i	−0.129812	−	0.594058i
$748$		0			0
$749$			2.41058i			0.0880806i
$750$	3.06785	+	0.899244i	0.112022	+	0.0328357i
$751$	−22.7296	−	4.52121i	−0.829416	−	0.164981i	−0.237916	−	0.971286i	$-0.576464\pi$
$751$	−22.7296	−	4.52121i	−0.829416	−	0.164981i	−0.591500	+	0.806305i	$0.701464\pi$
$752$	7.13925	+	7.13925i	0.260342	+	0.260342i
$753$	−1.82976	−	0.162878i	−0.0666802	−	0.00593559i
$754$	−0.592286	+	0.117813i	−0.0215698	+	0.00429050i
$755$	0.482579	+	0.322449i	0.0175629	+	0.0117351i
$756$	1.64186	+	1.88945i	0.0597140	+	0.0687185i
$757$	23.7983	+	9.85760i	0.864965	+	0.358280i	0.770647	−	0.637262i	$-0.219933\pi$
$757$	23.7983	+	9.85760i	0.864965	+	0.358280i	0.0943180	+	0.995542i	$0.469933\pi$
$758$	3.84622	−	5.75627i	0.139701	−	0.209077i
$759$	18.3431	−	35.1067i	0.665811	−	1.27429i
$760$	−2.34593	+	1.56750i	−0.0850957	+	0.0568591i
$761$	−15.9336	+	15.9336i	−0.577594	+	0.577594i	−0.934240	−	0.356646i	$-0.883920\pi$
$761$	−15.9336	+	15.9336i	−0.577594	+	0.577594i	0.356646	+	0.934240i	$0.383920\pi$
$762$	14.4455	+	17.2686i	0.523307	+	0.625575i
$763$	7.77120	+	18.7613i	0.281336	+	0.679206i
$764$	4.72118			0.170806
$765$		0			0
$766$	−27.8109			−1.00485
$767$	−0.427153	−	1.03124i	−0.0154236	−	0.0372359i
$768$	7.12176	+	8.51355i	0.256984	+	0.307206i
$769$	10.2112	−	10.2112i	0.368226	−	0.368226i	−0.498604	−	0.866830i	$-0.666154\pi$
$769$	10.2112	−	10.2112i	0.368226	−	0.368226i	0.866830	+	0.498604i	$0.166154\pi$
$770$	−0.990766	+	0.662009i	−0.0357047	+	0.0238571i
$771$	−16.1480	+	30.9056i	−0.581556	+	1.11304i
$772$	−2.45618	+	3.67593i	−0.0883998	+	0.132300i
$773$	−2.24744	−	0.930920i	−0.0808348	−	0.0334829i	0.341900	−	0.939736i	$-0.388930\pi$
$773$	−2.24744	−	0.930920i	−0.0808348	−	0.0334829i	−0.422734	+	0.906254i	$0.638930\pi$
$774$	−8.18464	−	1.46876i	−0.294191	−	0.0527936i
$775$	37.0771	+	24.7741i	1.33185	+	0.889912i
$776$	13.4375	−	2.67288i	0.482377	−	0.0959507i
$777$	−1.13666	−	0.101181i	−0.0407776	−	0.00362985i
$778$	−11.6153	−	11.6153i	−0.416429	−	0.416429i
$779$	28.9572	+	5.75994i	1.03750	+	0.206371i
$780$	−0.00743231	−	0.00217855i	−0.000266119	−	7.80045e-5i
$781$		−	47.3287i		−	1.69355i
$782$		0			0
$783$	−18.3030	−	9.12973i	−0.654097	−	0.326270i
$784$	−12.0895	+	5.00762i	−0.431766	+	0.178844i
$785$	−0.383184	+	1.92639i	−0.0136764	+	0.0687559i
$786$	−29.4916	+	3.18464i	−1.05193	+	0.113592i
$787$	17.6179	+	26.3671i	0.628010	+	0.939884i	0.999932	+	0.0116199i	$0.00369882\pi$
$787$	17.6179	+	26.3671i	0.628010	+	0.939884i	−0.371922	+	0.928264i	$0.621301\pi$
$788$	−0.417051	−	2.09666i	−0.0148568	−	0.0746903i
$789$	−2.86196	−	9.12516i	−0.101888	−	0.324864i
$790$	0.173108	−	0.417919i	0.00615889	−	0.0148689i
$791$	9.17479	−	22.1499i	0.326218	−	0.787560i
$792$	11.9191	−	30.3770i	0.423526	−	1.07940i
$793$	0.0904893	+	0.454920i	0.00321337	+	0.0161547i
$794$	−28.4066	−	42.5135i	−1.00811	−	1.50875i
$795$	−0.167583	−	1.55191i	−0.00594354	−	0.0550407i
$796$	0.679923	−	3.41820i	0.0240992	−	0.121155i
$797$	−41.8726	+	17.3442i	−1.48320	+	0.614363i	−0.969825	−	0.243800i	$-0.921606\pi$
$797$	−41.8726	+	17.3442i	−1.48320	+	0.614363i	−0.513377	+	0.858163i	$0.671606\pi$
$798$	−21.0640	−	16.9582i	−0.745658	−	0.600314i
$799$		0			0
$800$		−	7.61508i		−	0.269234i
$801$	−10.0916	+	7.02070i	−0.356568	+	0.248064i
$802$	35.1011	+	6.98204i	1.23946	+	0.246544i
$803$	11.5048	+	11.5048i	0.405995	+	0.405995i
$804$	−0.243306	+	2.73328i	−0.00858072	+	0.0963955i
$805$	−1.53309	+	0.304951i	−0.0540345	+	0.0107481i
$806$	1.14216	+	0.763166i	0.0402308	+	0.0268814i
$807$	−7.59315	−	13.8904i	−0.267292	−	0.488964i
$808$	13.9827	+	5.79181i	0.491908	+	0.203755i
$809$	13.9731	−	20.9122i	0.491267	−	0.735233i	−0.500155	−	0.865936i	$-0.666724\pi$
$809$	13.9731	−	20.9122i	0.491267	−	0.735233i	0.991422	+	0.130703i	$0.0417236\pi$
$810$	0.976062	+	1.34824i	0.0342953	+	0.0473724i
$811$	19.3507	−	12.9298i	0.679496	−	0.454025i	−0.167325	−	0.985902i	$-0.553513\pi$
$811$	19.3507	−	12.9298i	0.679496	−	0.454025i	0.846822	+	0.531877i	$0.178513\pi$
$812$	1.34084	−	1.34084i	0.0470544	−	0.0470544i
$813$	3.51819	−	2.94304i	0.123388	−	0.103217i
$814$	0.682192	+	1.64696i	0.0239108	+	0.0577259i
$815$	1.56942			0.0549743
$816$		0			0
$817$	−14.1578			−0.495320
$818$	−14.1964	−	34.2732i	−0.496367	−	1.19834i
$819$	−0.0116368	−	0.619369i	−0.000406622	−	0.0216425i
$820$	0.119131	−	0.119131i	0.00416024	−	0.00416024i
$821$	−35.9365	+	24.0120i	−1.25419	+	0.838025i	−0.991907	−	0.126965i	$-0.959476\pi$
$821$	−35.9365	+	24.0120i	−1.25419	+	0.838025i	−0.262286	+	0.964990i	$0.584476\pi$
$822$	−6.46694	−	3.37894i	−0.225560	−	0.117854i
$823$	9.37028	−	14.0236i	0.326627	−	0.488833i	−0.631420	−	0.775441i	$-0.717528\pi$
$823$	9.37028	−	14.0236i	0.326627	−	0.488833i	0.958048	+	0.286608i	$0.0925278\pi$
$824$	44.0841	+	18.2602i	1.53574	+	0.636125i
$825$	−27.5646	+	15.0682i	−0.959676	+	0.524606i
$826$	−18.4912	−	12.3554i	−0.643391	−	0.429900i
$827$	21.7440	−	4.32515i	0.756114	−	0.150400i	0.198042	−	0.980193i	$-0.436542\pi$
$827$	21.7440	−	4.32515i	0.756114	−	0.150400i	0.558071	+	0.829793i	$0.311542\pi$
$828$	3.55835	−	3.69462i	0.123661	−	0.128397i
$829$	19.3451	+	19.3451i	0.671883	+	0.671883i	0.958150	−	0.286267i	$-0.0924145\pi$
$829$	19.3451	+	19.3451i	0.671883	+	0.671883i	−0.286267	+	0.958150i	$0.592415\pi$
$830$	1.00486	+	0.199878i	0.0348790	+	0.00693787i
$831$	−10.0799	+	34.3886i	−0.349669	+	1.19293i
$832$		−	1.02389i		−	0.0354968i
$833$		0			0
$834$	−7.27334	+	9.03431i	−0.251855	+	0.312833i
$835$	0.272976	−	0.113070i	0.00944672	−	0.00391296i
$836$	1.29884	−	6.52973i	0.0449215	−	0.225836i
$837$	14.7548	+	44.1242i	0.510000	+	1.52516i
$838$	−6.82089	−	10.2082i	−0.235624	−	0.352636i
$839$	4.84436	+	24.3543i	0.167246	+	0.840802i	0.969740	+	0.244142i	$0.0785062\pi$
$839$	4.84436	+	24.3543i	0.167246	+	0.840802i	−0.802494	+	0.596661i	$0.796494\pi$
$840$	−1.22873	+	0.385371i	−0.0423952	+	0.0132966i
$841$	5.16832	−	12.4774i	0.178218	−	0.430256i
$842$	−6.69119	+	16.1539i	−0.230593	+	0.556702i
$843$	−17.0037	+	5.33295i	−0.585640	+	0.183676i
$844$	−0.271986	−	1.36737i	−0.00936215	−	0.0470667i
$845$	−1.01514	−	1.51926i	−0.0349218	−	0.0522641i
$846$	6.35651	−	9.91131i	0.218541	−	0.340758i
$847$	0.781037	−	3.92654i	0.0268367	−	0.134917i
$848$	20.0089	−	8.28795i	0.687107	−	0.284609i
$849$	−13.9495	+	17.3269i	−0.478745	+	0.594656i
$850$		0			0
$851$			2.33850i			0.0801628i
$852$	1.72402	−	5.88164i	0.0590638	−	0.201502i
$853$	−29.2600	−	5.82018i	−1.00184	−	0.199279i	−0.333196	−	0.942858i	$-0.608127\pi$
$853$	−29.2600	−	5.82018i	−1.00184	−	0.199279i	−0.668649	+	0.743578i	$0.733127\pi$
$854$	6.53464	+	6.53464i	0.223611	+	0.223611i
$855$	2.04119	+	1.96590i	0.0698071	+	0.0672323i
$856$	3.99137	−	0.793933i	0.136422	−	0.0271361i
$857$	−28.2940	−	18.9054i	−0.966505	−	0.645798i	−0.0311521	−	0.999515i	$-0.509918\pi$
$857$	−28.2940	−	18.9054i	−0.966505	−	0.645798i	−0.935353	+	0.353717i	$0.884918\pi$
$858$	−0.849127	+	0.464174i	−0.0289887	+	0.0158467i
$859$	−18.2111	−	7.54327i	−0.621354	−	0.257373i	0.0497206	−	0.998763i	$-0.484167\pi$
$859$	−18.2111	−	7.54327i	−0.621354	−	0.257373i	−0.671074	+	0.741390i	$0.734167\pi$
$860$	−0.0448842	+	0.0671740i	−0.00153054	+	0.00229061i
$861$	11.9435	+	6.24039i	0.407032	+	0.212672i
$862$	−15.9679	+	10.6694i	−0.543869	+	0.363402i
$863$	−4.36492	+	4.36492i	−0.148584	+	0.148584i	−0.777485	−	0.628901i	$-0.783505\pi$
$863$	−4.36492	+	4.36492i	−0.148584	+	0.148584i	0.628901	+	0.777485i	$0.283505\pi$
$864$	4.86539	−	6.28136i	0.165524	−	0.213696i
$865$	0.663059	+	1.60077i	0.0225447	+	0.0544277i
$866$	−23.4504			−0.796876
$867$		0			0
$868$	−4.31336			−0.146405
$869$	3.40880	+	8.22958i	0.115636	+	0.279169i
$870$	0.967138	−	0.809031i	0.0327891	−	0.0274287i
$871$	0.480203	−	0.480203i	0.0162710	−	0.0162710i
$872$	28.5050	−	19.0465i	0.965302	−	0.644994i
$873$	−5.50419	−	12.6128i	−0.186289	−	0.426878i
$874$	−30.7872	+	46.0763i	−1.04139	+	1.55855i
$875$	2.29522	+	0.950712i	0.0775927	+	0.0321399i
$876$	1.01065	+	1.84880i	0.0341466	+	0.0624652i
$877$	7.92668	+	5.29644i	0.267665	+	0.178848i	0.682159	−	0.731204i	$-0.261041\pi$
$877$	7.92668	+	5.29644i	0.267665	+	0.178848i	−0.414494	+	0.910052i	$0.636041\pi$
$878$	33.9822	−	6.75949i	1.14685	−	0.228122i
$879$	0.173247	−	1.94625i	0.00584349	−	0.0656455i
$880$	1.22513	+	1.22513i	0.0412992	+	0.0412992i
$881$	42.1879	+	8.39169i	1.42135	+	0.282723i	0.845124	−	0.534570i	$-0.179527\pi$
$881$	42.1879	+	8.39169i	1.42135	+	0.282723i	0.576222	+	0.817294i	$0.304527\pi$
$882$	8.71511	+	12.5271i	0.293453	+	0.421809i
$883$		−	41.3162i		−	1.39040i	−0.718816	−	0.695200i	$-0.755316\pi$
$883$		−	41.3162i		−	1.39040i	0.718816	−	0.695200i	$-0.244684\pi$
$884$		0			0
$885$	1.81539	+	1.46153i	0.0610237	+	0.0491289i
$886$	−11.7434	+	4.86427i	−0.394527	+	0.163418i
$887$	2.89572	−	14.5578i	0.0972287	−	0.488801i	−0.901232	−	0.433337i	$-0.857336\pi$
$887$	2.89572	−	14.5578i	0.0972287	−	0.488801i	0.998461	−	0.0554646i	$-0.0176640\pi$
$888$	0.206831	+	1.91538i	0.00694081	+	0.0642760i
$889$	9.72002	+	14.5470i	0.325999	+	0.487892i
$890$	−0.147850	−	0.743294i	−0.00495596	−	0.0249153i
$891$	−32.3641	−	5.18233i	−1.08424	−	0.173614i
$892$	−0.0196801	+	0.0475120i	−0.000658939	+	0.00159082i
$893$	7.67180	−	18.5214i	0.256727	−	0.619794i
$894$	15.1404	+	48.2742i	0.506371	+	1.61453i
$895$	0.507454	+	2.55114i	0.0169623	+	0.0852754i
$896$	−8.32768	−	12.4632i	−0.278208	−	0.416368i
$897$	−1.26212	+	0.136289i	−0.0421410	+	0.00455057i
$898$	0.270975	−	1.36228i	0.00904256	−	0.0454600i
$899$	32.5624	−	13.4878i	1.08602	−	0.449843i
$900$	−3.97439	+	0.868473i	−0.132480	+	0.0289491i
$901$		0			0
$902$		−	21.0507i		−	0.700910i
$903$	−6.20098	−	1.81762i	−0.206356	−	0.0604866i
$904$	−39.6970	−	7.89621i	−1.32030	−	0.262624i
$905$	−0.211787	−	0.211787i	−0.00704002	−	0.00704002i
$906$	9.35420	+	0.832672i	0.310772	+	0.0276637i
$907$	−16.7791	+	3.33756i	−0.557140	+	0.110822i	−0.465626	−	0.884982i	$-0.654171\pi$
$907$	−16.7791	+	3.33756i	−0.557140	+	0.110822i	−0.0915140	+	0.995804i	$0.529171\pi$
$908$	0.482281	+	0.322250i	0.0160050	+	0.0106942i
$909$	2.68514	−	14.9628i	0.0890603	−	0.496286i
$910$	0.0352820	+	0.0146143i	0.00116959	+	0.000484459i
$911$	30.7347	−	45.9977i	1.01829	−	1.52397i	0.176398	−	0.984319i	$-0.443555\pi$
$911$	30.7347	−	45.9977i	1.01829	−	1.52397i	0.841887	−	0.539653i	$-0.181445\pi$
$912$	−18.2088	+	34.8497i	−0.602952	+	1.15399i
$913$	−16.7750	+	11.2087i	−0.555171	+	0.370953i
$914$	−19.9143	+	19.9143i	−0.658705	+	0.658705i
$915$	−0.621397	−	0.742835i	−0.0205427	−	0.0245574i
$916$	1.80100	+	4.34800i	0.0595067	+	0.143662i
$917$	−23.0511			−0.761216
$918$		0			0
$919$	−57.0283			−1.88119			−0.940595	−	0.339530i	$-0.889732\pi$
$919$	−57.0283			−1.88119			−0.940595	+	0.339530i	$0.889732\pi$
$920$	1.00986	+	2.43802i	0.0332941	+	0.0803791i
$921$	−21.7614	−	26.0142i	−0.717063	−	0.857196i
$922$	−22.9019	+	22.9019i	−0.754233	+	0.754233i
$923$	−1.26120	+	0.842708i	−0.0415130	+	0.0277381i
$924$	1.40718	−	2.69320i	0.0462929	−	0.0885999i
$925$	1.03038	−	1.54208i	0.0338788	−	0.0507032i
$926$	−23.4364	−	9.70769i	−0.770169	−	0.319014i
$927$	8.46561	−	47.1743i	0.278047	−	1.54941i
$928$	−5.00453	−	3.34392i	−0.164282	−	0.109770i
$929$	−35.1267	+	6.98713i	−1.15247	+	0.229240i	−0.734103	−	0.679038i	$-0.762397\pi$
$929$	−35.1267	+	6.98713i	−1.15247	+	0.229240i	−0.418366	+	0.908278i	$0.637397\pi$
$930$	−2.85688	−	0.254308i	−0.0936808	−	0.00833907i
$931$	18.3724	+	18.3724i	0.602132	+	0.602132i
$932$	2.61506	+	0.520168i	0.0856592	+	0.0170387i
$933$	−48.8247	−	14.3114i	−1.59845	−	0.468535i
$934$			16.3585i			0.535267i
$935$		0			0
$936$	−1.02170	+	0.223259i	−0.0333954	+	0.00729746i
$937$	18.6808	−	7.73785i	0.610276	−	0.252785i	−0.0560704	−	0.998427i	$-0.517857\pi$
$937$	18.6808	−	7.73785i	0.610276	−	0.252785i	0.666347	+	0.745642i	$0.267857\pi$
$938$	2.63967	−	13.2705i	0.0861884	−	0.433298i
$939$	30.6873	−	3.31375i	1.00144	−	0.108140i
$940$	−0.0635557	−	0.0951179i	−0.00207296	−	0.00310240i
$941$	−1.51472	−	7.61499i	−0.0493783	−	0.248242i	0.948211	−	0.317643i	$-0.102891\pi$
$941$	−1.51472	−	7.61499i	−0.0493783	−	0.248242i	−0.997589	+	0.0694010i	$0.977891\pi$
$942$	9.51083	+	30.3247i	0.309880	+	0.988031i
$943$	10.5676	−	25.5124i	0.344128	−	0.830798i
$944$	−12.3746	+	29.8749i	−0.402759	+	0.972347i
$945$	0.641629	+	1.12310i	0.0208722	+	0.0365343i
$946$	1.96932	+	9.90043i	0.0640281	+	0.321891i
$947$	−2.00168	−	2.99573i	−0.0650459	−	0.0973480i	0.797521	−	0.603291i	$-0.206144\pi$
$947$	−2.00168	−	2.99573i	−0.0650459	−	0.0973480i	−0.862567	+	0.505943i	$0.831144\pi$
$948$	0.123845	+	1.14688i	0.00402231	+	0.0372489i
$949$	0.101728	−	0.511424i	0.00330225	−	0.0166015i
$950$	40.6040	−	16.8187i	1.31737	−	0.545672i
$951$	−19.0515	−	15.3379i	−0.617786	−	0.497367i
$952$		0			0
$953$		−	22.5397i		−	0.730132i	−0.930982	−	0.365066i	$-0.881046\pi$
$953$		−	22.5397i		−	0.730132i	0.930982	−	0.365066i	$-0.118954\pi$
$954$	−14.4241	−	20.7332i	−0.466997	−	0.671262i
$955$	2.39271	+	0.475940i	0.0774264	+	0.0154011i
$956$	4.31991	+	4.31991i	0.139716	+	0.139716i
$957$	−2.20152	+	24.7318i	−0.0711650	+	0.799465i
$958$	−29.2629	+	5.82076i	−0.945442	+	0.188060i
$959$	−4.71450	−	3.15013i	−0.152239	−	0.101723i
$960$	1.02544	+	1.87587i	0.0330959	+	0.0605433i
$961$	−45.4292	−	18.8174i	−1.46546	−	0.607013i
$962$	0.0317410	−	0.0475037i	0.00102337	−	0.00153158i
$963$	−1.63493	−	3.74641i	−0.0526848	−	0.120727i
$964$	−0.0918044	+	0.0613417i	−0.00295682	+	0.00197568i
$965$	−1.61537	+	1.61537i	−0.0520007	+	0.0520007i
$966$	−19.3999	+	16.2284i	−0.624180	+	0.522140i
$967$	−8.59605	−	20.7527i	−0.276430	−	0.667362i	0.723301	−	0.690533i	$-0.242624\pi$
$967$	−8.59605	−	20.7527i	−0.276430	−	0.667362i	−0.999732	+	0.0231709i	$0.992624\pi$
$968$	−6.75869			−0.217233
$969$		0			0
$970$	0.848355			0.0272390
$971$	13.1165	+	31.6660i	0.420928	+	1.01621i	0.982075	+	0.188493i	$0.0603603\pi$
$971$	13.1165	+	31.6660i	0.420928	+	1.01621i	−0.561147	+	0.827716i	$0.689640\pi$
$972$	−3.83319	−	1.82293i	−0.122950	−	0.0584705i
$973$	−6.37317	+	6.37317i	−0.204314	+	0.204314i
$974$	25.1207	−	16.7851i	0.804920	−	0.537830i
$975$	0.892331	+	0.466238i	0.0285775	+	0.0149316i
$976$	7.46532	−	11.1726i	0.238959	−	0.357628i
$977$	26.0166	+	10.7764i	0.832345	+	0.344769i	0.757831	−	0.652451i	$-0.226259\pi$
$977$	26.0166	+	10.7764i	0.832345	+	0.344769i	0.0745143	+	0.997220i	$0.476259\pi$
$978$	22.2824	−	12.1806i	0.712512	−	0.389494i
$979$	12.4085	+	8.29109i	0.396577	+	0.264985i
$980$	0.145416	−	0.0289251i	0.00464516	−	0.000923980i
$981$	−24.8022	−	23.8874i	−0.791872	−	0.762665i
$982$	−18.9356	−	18.9356i	−0.604261	−	0.604261i
$983$	−40.9235	−	8.14020i	−1.30526	−	0.259632i	−0.506999	−	0.861946i	$-0.669245\pi$
$983$	−40.9235	−	8.14020i	−1.30526	−	0.259632i	−0.798259	+	0.602314i	$0.794245\pi$
$984$	6.39905	−	21.8309i	0.203994	−	0.695945i
$985$		−	1.10464i		−	0.0351967i
$986$		0			0
$987$	5.73799	−	7.12723i	0.182642	−	0.226862i
$988$	−0.197129	+	0.0816535i	−0.00627151	+	0.00259774i
$989$	−2.58337	+	12.9875i	−0.0821463	+	0.412977i
$990$	1.09081	−	1.70083i	0.0346682	−	0.0540560i
$991$	−5.63837	−	8.43842i	−0.179109	−	0.268055i	0.731042	−	0.682333i	$-0.239034\pi$
$991$	−5.63837	−	8.43842i	−0.179109	−	0.268055i	−0.910151	+	0.414277i	$0.864034\pi$
$992$	2.67101	+	13.4281i	0.0848046	+	0.426341i
$993$	11.9538	−	3.74913i	0.379344	−	0.118975i
$994$	−11.5652	+	27.9208i	−0.366826	+	0.885595i
$995$	0.689176	−	1.66382i	0.0218483	−	0.0527466i
$996$	−2.49296	+	0.781875i	−0.0789923	+	0.0247747i
$997$	−7.78912	−	39.1586i	−0.246684	−	1.24016i	−0.883235	−	0.468930i	$-0.844640\pi$
$997$	−7.78912	−	39.1586i	−0.246684	−	1.24016i	0.636552	−	0.771234i	$-0.280360\pi$
$998$	−0.788061	−	1.17942i	−0.0249456	−	0.0373338i
$999$	1.83518	−	0.613668i	0.0580624	−	0.0194156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.i.d.224.2		32
3.2	odd	2	inner	867.2.i.d.224.3		32
17.2	even	8		867.2.i.g.131.3		32
17.3	odd	16		867.2.i.g.503.2		32
17.4	even	4		867.2.i.h.65.3		32
17.5	odd	16		867.2.i.i.653.3		32
17.6	odd	16	inner	867.2.i.d.329.3		32
17.7	odd	16		51.2.i.a.11.2	✓	32
17.8	even	8		867.2.i.i.158.2		32
17.9	even	8		867.2.i.b.158.2		32
17.10	odd	16		867.2.i.h.827.2		32
17.11	odd	16		867.2.i.c.329.3		32
17.12	odd	16		867.2.i.b.653.3		32
17.13	even	4		51.2.i.a.14.3	yes	32
17.14	odd	16		867.2.i.f.503.2		32
17.15	even	8		867.2.i.f.131.3		32
17.16	even	2		867.2.i.c.224.2		32
51.2	odd	8		867.2.i.g.131.2		32
51.5	even	16		867.2.i.i.653.2		32
51.8	odd	8		867.2.i.i.158.3		32
51.11	even	16		867.2.i.c.329.2		32
51.14	even	16		867.2.i.f.503.3		32
51.20	even	16		867.2.i.g.503.3		32
51.23	even	16	inner	867.2.i.d.329.2		32
51.26	odd	8		867.2.i.b.158.3		32
51.29	even	16		867.2.i.b.653.2		32
51.32	odd	8		867.2.i.f.131.2		32
51.38	odd	4		867.2.i.h.65.2		32
51.41	even	16		51.2.i.a.11.3	yes	32
51.44	even	16		867.2.i.h.827.3		32
51.47	odd	4		51.2.i.a.14.2	yes	32
51.50	odd	2		867.2.i.c.224.3		32
68.7	even	16		816.2.cj.c.113.1		32
68.47	odd	4		816.2.cj.c.65.4		32
204.47	even	4		816.2.cj.c.65.1		32
204.143	odd	16		816.2.cj.c.113.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.11.2	✓	32	17.7	odd	16
51.2.i.a.11.3	yes	32	51.41	even	16
51.2.i.a.14.2	yes	32	51.47	odd	4
51.2.i.a.14.3	yes	32	17.13	even	4
816.2.cj.c.65.1		32	204.47	even	4
816.2.cj.c.65.4		32	68.47	odd	4
816.2.cj.c.113.1		32	68.7	even	16
816.2.cj.c.113.4		32	204.143	odd	16
867.2.i.b.158.2		32	17.9	even	8
867.2.i.b.158.3		32	51.26	odd	8
867.2.i.b.653.2		32	51.29	even	16
867.2.i.b.653.3		32	17.12	odd	16
867.2.i.c.224.2		32	17.16	even	2
867.2.i.c.224.3		32	51.50	odd	2
867.2.i.c.329.2		32	51.11	even	16
867.2.i.c.329.3		32	17.11	odd	16
867.2.i.d.224.2		32	1.1	even	1	trivial
867.2.i.d.224.3		32	3.2	odd	2	inner
867.2.i.d.329.2		32	51.23	even	16	inner
867.2.i.d.329.3		32	17.6	odd	16	inner
867.2.i.f.131.2		32	51.32	odd	8
867.2.i.f.131.3		32	17.15	even	8
867.2.i.f.503.2		32	17.14	odd	16
867.2.i.f.503.3		32	51.14	even	16
867.2.i.g.131.2		32	51.2	odd	8
867.2.i.g.131.3		32	17.2	even	8
867.2.i.g.503.2		32	17.3	odd	16
867.2.i.g.503.3		32	51.20	even	16
867.2.i.h.65.2		32	51.38	odd	4
867.2.i.h.65.3		32	17.4	even	4
867.2.i.h.827.2		32	17.10	odd	16
867.2.i.h.827.3		32	51.44	even	16
867.2.i.i.158.2		32	17.8	even	8
867.2.i.i.158.3		32	51.8	odd	8
867.2.i.i.653.2		32	51.5	even	16
867.2.i.i.653.3		32	17.5	odd	16

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.503008 - 1.21437i) q^{2} +(1.11133 + 1.32851i) q^{3} +(0.192538 - 0.192538i) q^{4} +(0.116989 - 0.0781694i) q^{5} +(1.05430 - 2.01782i) q^{6} +(0.982905 - 1.47102i) q^{7} +(-2.75940 - 1.14298i) q^{8} +(-0.529896 + 2.95283i) q^{9} +(-0.153773 - 0.102748i) q^{10} +(3.57185 - 0.710485i) q^{11} +(0.469762 + 0.0418163i) q^{12} +(-0.0825311 - 0.0825311i) q^{13} +(-2.28077 - 0.453674i) q^{14} +(0.233862 + 0.0685492i) q^{15} +3.38128i q^{16} +(3.85237 - 0.841809i) q^{18} +(6.20278 - 2.56928i) q^{19} +(0.00747420 - 0.0375753i) q^{20} +(3.04660 - 0.328986i) q^{21} +(-2.65946 - 3.98016i) q^{22} +(-1.22507 - 6.15884i) q^{23} +(-1.54813 - 4.93613i) q^{24} +(-1.90584 + 4.60111i) q^{25} +(-0.0587094 + 0.141737i) q^{26} +(-4.51176 + 2.57759i) q^{27} +(-0.0939809 - 0.472474i) q^{28} +(2.18690 + 3.27292i) q^{29} +(-0.0343905 - 0.318476i) q^{30} +(1.74682 - 8.78185i) q^{31} +(-1.41268 + 0.585150i) q^{32} +(4.91339 + 3.95567i) q^{33} -0.248926i q^{35} +(0.466507 + 0.670557i) q^{36} +(-0.365247 - 0.0726522i) q^{37} +(-6.24010 - 6.24010i) q^{38} +(0.0179245 - 0.201363i) q^{39} +(-0.412165 + 0.0819847i) q^{40} +(3.65643 + 2.44315i) q^{41} +(-1.93198 - 3.53422i) q^{42} +(-1.94823 - 0.806985i) q^{43} +(0.550921 - 0.824512i) q^{44} +(0.168829 + 0.386870i) q^{45} +(-6.86288 + 4.58563i) q^{46} +(2.11141 - 2.11141i) q^{47} +(-4.49207 + 3.75771i) q^{48} +(1.48098 + 3.57541i) q^{49} +6.54610 q^{50} -0.0317807 q^{52} +(-2.45113 - 5.91755i) q^{53} +(5.39960 + 4.18240i) q^{54} +(0.362328 - 0.362328i) q^{55} +(-4.39357 + 2.93569i) q^{56} +(10.3066 + 5.38517i) q^{57} +(2.87451 - 4.30201i) q^{58} +(8.83540 + 3.65974i) q^{59} +(0.0582256 - 0.0318290i) q^{60} +(-3.30427 - 2.20784i) q^{61} +(-11.5431 + 2.29606i) q^{62} +(3.82284 + 3.68184i) q^{63} +(6.20303 + 6.20303i) q^{64} +(-0.0161066 - 0.00320381i) q^{65} +(2.33217 - 7.95640i) q^{66} +5.81844i q^{67} +(6.82064 - 8.47201i) q^{69} +(-0.302288 + 0.125212i) q^{70} +(2.53537 - 12.7462i) q^{71} +(4.83722 - 7.54238i) q^{72} +(2.48206 + 3.71467i) q^{73} +(0.0954957 + 0.480089i) q^{74} +(-8.23065 + 2.58141i) q^{75} +(0.699588 - 1.68895i) q^{76} +(2.46565 - 5.95260i) q^{77} +(-0.253545 + 0.0795203i) q^{78} +(0.477177 + 2.39893i) q^{79} +(0.264312 + 0.395572i) q^{80} +(-8.43842 - 3.12939i) q^{81} +(1.12767 - 5.66918i) q^{82} +(-5.11813 + 2.12000i) q^{83} +(0.523244 - 0.649928i) q^{84} +2.77180i q^{86} +(-1.91776 + 6.54262i) q^{87} +(-10.6682 - 2.12204i) q^{88} +(2.89760 + 2.89760i) q^{89} +(0.384880 - 0.399620i) q^{90} +(-0.202525 + 0.0402848i) q^{91} +(-1.42168 - 0.949937i) q^{92} +(13.6081 - 7.43885i) q^{93} +(-3.62608 - 1.50197i) q^{94} +(0.524817 - 0.785444i) q^{95} +(-2.34733 - 1.22647i) q^{96} +(-3.81409 + 2.54849i) q^{97} +(3.59692 - 3.59692i) q^{98} +(0.205233 + 10.9235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{4} + 8 q^{9} + 32 q^{10} + 24 q^{12} - 16 q^{13} - 16 q^{15} + 16 q^{18} + 16 q^{19} + 16 q^{21} - 48 q^{22} + 8 q^{24} - 16 q^{25} - 48 q^{27} - 64 q^{28} - 8 q^{30} + 16 q^{31} - 8 q^{36}+ \cdots + 96 q^{97}+O(q^{100}) \) 32 * q - 16 * q^4 + 8 * q^9 + 32 * q^10 + 24 * q^12 - 16 * q^13 - 16 * q^15 + 16 * q^18 + 16 * q^19 + 16 * q^21 - 48 * q^22 + 8 * q^24 - 16 * q^25 - 48 * q^27 - 64 * q^28 - 8 * q^30 + 16 * q^31 - 8 * q^36 - 32 * q^37 + 8 * q^39 - 64 * q^40 + 56 * q^42 - 16 * q^43 + 24 * q^45 - 80 * q^46 - 72 * q^48 + 48 * q^49 - 96 * q^52 + 48 * q^54 - 48 * q^55 + 24 * q^57 - 32 * q^58 - 32 * q^60 + 64 * q^61 - 16 * q^63 + 16 * q^64 - 72 * q^66 + 80 * q^69 - 48 * q^70 + 64 * q^72 - 48 * q^76 - 16 * q^78 - 32 * q^79 + 48 * q^81 + 48 * q^82 + 56 * q^87 - 80 * q^88 + 104 * q^90 + 80 * q^91 + 72 * q^93 + 48 * q^94 + 72 * q^96 + 96 * q^97

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