LMFDB - Embedded newform 867.2.i.h.827.2

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			827.2
Character	$\chi$	$=$	867.827
Dual form			867.2.i.h.65.2

$q$-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} +(-0.802099 + 1.53513i) q^{3} +(0.192538 + 0.192538i) q^{4} +(0.0781694 - 0.116989i) q^{5} +(-1.46076 - 1.74623i) q^{6} +(1.47102 - 0.982905i) q^{7} +(-2.75940 + 1.14298i) q^{8} +(-1.71327 - 2.46266i) q^{9} +(0.102748 + 0.153773i) q^{10} +(-0.710485 + 3.57185i) q^{11} +(-0.450006 + 0.141137i) q^{12} +(-0.0825311 + 0.0825311i) q^{13} +(0.453674 + 2.28077i) q^{14} +(0.116894 + 0.213837i) q^{15} -3.38128i q^{16} +(3.85237 - 0.841809i) q^{18} +(-6.20278 - 2.56928i) q^{19} +(0.0375753 - 0.00747420i) q^{20} +(0.328986 + 3.04660i) q^{21} +(-3.98016 - 2.65946i) q^{22} +(-6.15884 - 1.22507i) q^{23} +(0.458684 - 5.15283i) q^{24} +(1.90584 + 4.60111i) q^{25} +(-0.0587094 - 0.141737i) q^{26} +(5.15473 - 0.654807i) q^{27} +(0.472474 + 0.0939809i) q^{28} +(-3.27292 - 2.18690i) q^{29} +(-0.318476 + 0.0343905i) q^{30} +(-8.78185 + 1.74682i) q^{31} +(-1.41268 - 0.585150i) q^{32} +(-4.91339 - 3.95567i) q^{33} -0.248926i q^{35} +(0.144285 - 0.804026i) q^{36} +(-0.0726522 - 0.365247i) q^{37} +(6.24010 - 6.24010i) q^{38} +(-0.0604982 - 0.192895i) q^{39} +(-0.0819847 + 0.412165i) q^{40} +(2.44315 + 3.65643i) q^{41} +(-3.86518 - 1.13296i) q^{42} +(1.94823 - 0.806985i) q^{43} +(-0.824512 + 0.550921i) q^{44} +(-0.422029 + 0.00792913i) q^{45} +(4.58563 - 6.86288i) q^{46} +(-2.11141 - 2.11141i) q^{47} +(5.19072 + 2.71212i) q^{48} +(-1.48098 + 3.57541i) q^{49} -6.54610 q^{50} -0.0317807 q^{52} +(-2.45113 + 5.91755i) q^{53} +(-1.79769 + 6.58912i) q^{54} +(0.362328 + 0.362328i) q^{55} +(-2.93569 + 4.39357i) q^{56} +(8.91943 - 7.46129i) q^{57} +(4.30201 - 2.87451i) q^{58} +(8.83540 - 3.65974i) q^{59} +(-0.0186653 + 0.0636782i) q^{60} +(2.20784 + 3.30427i) q^{61} +(2.29606 - 11.5431i) q^{62} +(-4.94082 - 1.93864i) q^{63} +(6.20303 - 6.20303i) q^{64} +(0.00320381 + 0.0161066i) q^{65} +(7.27511 - 3.97693i) q^{66} -5.81844i q^{67} +(6.82064 - 8.47201i) q^{69} +(0.302288 + 0.125212i) q^{70} +(12.7462 - 2.53537i) q^{71} +(7.54238 + 4.83722i) q^{72} +(3.71467 + 2.48206i) q^{73} +(0.480089 + 0.0954957i) q^{74} +(-8.59199 - 0.764823i) q^{75} +(-0.699588 - 1.68895i) q^{76} +(2.46565 + 5.95260i) q^{77} +(0.264676 + 0.0235604i) q^{78} +(-2.39893 - 0.477177i) q^{79} +(-0.395572 - 0.264312i) q^{80} +(-3.12939 + 8.43842i) q^{81} +(-5.66918 + 1.12767i) q^{82} +(-5.11813 - 2.12000i) q^{83} +(-0.523244 + 0.649928i) q^{84} +2.77180i q^{86} +(5.98239 - 3.27027i) q^{87} +(-2.12204 - 10.6682i) q^{88} +(-2.89760 + 2.89760i) q^{89} +(0.202655 - 0.516488i) q^{90} +(-0.0402848 + 0.202525i) q^{91} +(-0.949937 - 1.42168i) q^{92} +(4.36231 - 14.8824i) q^{93} +(3.62608 - 1.50197i) q^{94} +(-0.785444 + 0.524817i) q^{95} +(2.03139 - 1.69930i) q^{96} +(2.54849 - 3.81409i) q^{97} +(-3.59692 - 3.59692i) q^{98} +(10.0135 - 4.36987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} - 16 q^{4} + 8 q^{6} + 16 q^{7} - 8 q^{9} + 16 q^{10} - 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} + 16 q^{22} - 16 q^{24} + 16 q^{25} + 8 q^{27} - 32 q^{28} - 8 q^{30}+ \cdots + 64 q^{99}+O(q^{100}) $ 32 * q + 8 * q^3 - 16 * q^4 + 8 * q^6 + 16 * q^7 - 8 * q^9 + 16 * q^10 - 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 + 16 * q^22 - 16 * q^24 + 16 * q^25 + 8 * q^27 - 32 * q^28 - 8 * q^30 - 16 * q^31 + 8 * q^36 - 16 * q^37 + 24 * q^39 - 16 * q^40 - 56 * q^42 + 16 * q^43 + 40 * q^45 + 32 * q^46 + 64 * q^48 - 48 * q^49 - 96 * q^52 + 24 * q^54 - 48 * q^55 - 8 * q^57 + 48 * q^58 + 32 * q^60 + 32 * q^61 - 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 - 48 * q^73 - 88 * q^75 + 48 * q^76 - 96 * q^78 - 16 * q^79 + 48 * q^81 - 112 * q^82 - 56 * q^87 - 16 * q^88 + 88 * q^90 - 16 * q^91 - 72 * q^93 - 48 * q^94 + 112 * q^96 + 16 * q^97 + 64 * q^99

Character values

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

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{7}{16}\right)$

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	0.640216	+	0.768195i	$0.278845\pi$
$2$	−0.503008	+	1.21437i	−0.355681	+	0.858689i	−0.995897	+	0.0904942i	$0.971155\pi$
$3$	−0.802099	+	1.53513i	−0.463092	+	0.886310i
$3$	−0.802099	+	1.53513i	−0.463092	+	0.886310i
$4$	0.192538	+	0.192538i	0.0962690	+	0.0962690i
$5$	0.0781694	−	0.116989i	0.0349584	−	0.0523190i	−0.813579	−	0.581455i	$-0.802484\pi$
$5$	0.0781694	−	0.116989i	0.0349584	−	0.0523190i	0.848537	+	0.529136i	$0.177484\pi$
$6$	−1.46076	−	1.74623i	−0.596352	−	0.712895i
$7$	1.47102	−	0.982905i	0.555994	−	0.371503i	−0.245601	−	0.969371i	$-0.578985\pi$
$7$	1.47102	−	0.982905i	0.555994	−	0.371503i	0.801595	+	0.597868i	$0.203985\pi$
$8$	−2.75940	+	1.14298i	−0.975595	+	0.404105i
$9$	−1.71327	−	2.46266i	−0.571091	−	0.820887i
$10$	0.102748	+	0.153773i	0.0324917	+	0.0486272i
$11$	−0.710485	+	3.57185i	−0.214219	+	1.07695i	0.712636	+	0.701534i	$0.247501\pi$
$11$	−0.710485	+	3.57185i	−0.214219	+	1.07695i	−0.926855	+	0.375419i	$0.877499\pi$
$12$	−0.450006	+	0.141137i	−0.129906	+	0.0407427i
$13$	−0.0825311	+	0.0825311i	−0.0228900	+	0.0228900i	−0.718459	−	0.695569i	$-0.755152\pi$
$13$	−0.0825311	+	0.0825311i	−0.0228900	+	0.0228900i	0.695569	+	0.718459i	$0.255152\pi$
$14$	0.453674	+	2.28077i	0.121249	+	0.609562i
$15$	0.116894	+	0.213837i	0.0301819	+	0.0552125i
$16$		−	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	$-0.654809\pi$
$19$	−6.20278	−	2.56928i	−1.42302	−	0.589432i	−0.955616	+	0.294614i	$0.904809\pi$
$20$	0.0375753	−	0.00747420i	0.00840210	−	0.00167128i
$21$	0.328986	+	3.04660i	0.0717906	+	0.664823i
$22$	−3.98016	−	2.65946i	−0.848574	−	0.566999i
$23$	−6.15884	−	1.22507i	−1.28421	−	0.255444i	−0.494633	−	0.869102i	$-0.664698\pi$
$23$	−6.15884	−	1.22507i	−1.28421	−	0.255444i	−0.789573	+	0.613657i	$0.789698\pi$
$24$	0.458684	−	5.15283i	0.0936284	−	1.05182i
$25$	1.90584	+	4.60111i	0.381168	+	0.920222i
$26$	−0.0587094	−	0.141737i	−0.0115139	−	0.0277969i
$27$	5.15473	−	0.654807i	0.992028	−	0.126018i
$28$	0.472474	+	0.0939809i	0.0892891	+	0.0177607i
$29$	−3.27292	−	2.18690i	−0.607766	−	0.406097i	0.213253	−	0.976997i	$-0.431594\pi$
$29$	−3.27292	−	2.18690i	−0.607766	−	0.406097i	−0.821019	+	0.570900i	$0.806594\pi$
$30$	−0.318476	+	0.0343905i	−0.0581455	+	0.00627881i
$31$	−8.78185	+	1.74682i	−1.57727	+	0.313738i	−0.904618	−	0.426224i	$-0.859844\pi$
$31$	−8.78185	+	1.74682i	−1.57727	+	0.313738i	−0.672649	+	0.739962i	$0.734844\pi$
$32$	−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
$36$	0.144285	−	0.804026i	0.0240475	−	0.134004i
$37$	−0.0726522	−	0.365247i	−0.0119439	−	0.0600462i	0.974354	−	0.225022i	$-0.0722454\pi$
$37$	−0.0726522	−	0.365247i	−0.0119439	−	0.0600462i	−0.986298	+	0.164976i	$0.947245\pi$
$38$	6.24010	−	6.24010i	1.01228	−	1.01228i
$39$	−0.0604982	−	0.192895i	−0.00968747	−	0.0308878i
$40$	−0.0819847	+	0.412165i	−0.0129629	+	0.0651690i
$41$	2.44315	+	3.65643i	0.381556	+	0.571039i	0.971688	−	0.236268i	$-0.0759243\pi$
$41$	2.44315	+	3.65643i	0.381556	+	0.571039i	−0.590132	+	0.807307i	$0.700924\pi$
$42$	−3.86518	−	1.13296i	−0.596410	−	0.174819i
$43$	1.94823	−	0.806985i	0.297103	−	0.123064i	−0.229153	−	0.973390i	$-0.573596\pi$
$43$	1.94823	−	0.806985i	0.297103	−	0.123064i	0.526256	+	0.850326i	$0.323596\pi$
$44$	−0.824512	+	0.550921i	−0.124300	+	0.0830545i
$45$	−0.422029	+	0.00792913i	−0.0629124	+	0.00118201i
$46$	4.58563	−	6.86288i	0.676114	−	1.01188i
$47$	−2.11141	−	2.11141i	−0.307980	−	0.307980i	0.536145	−	0.844126i	$-0.319880\pi$
$47$	−2.11141	−	2.11141i	−0.307980	−	0.307980i	−0.844126	+	0.536145i	$0.819880\pi$
$48$	5.19072	+	2.71212i	0.749215	+	0.391461i
$49$	−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	0.661341	+	0.750085i	$0.269988\pi$
$53$	−2.45113	+	5.91755i	−0.336688	+	0.812837i	−0.998029	+	0.0627519i	$0.980012\pi$
$54$	−1.79769	+	6.58912i	−0.244635	+	0.896665i
$55$	0.362328	+	0.362328i	0.0488563	+	0.0488563i
$56$	−2.93569	+	4.39357i	−0.392298	+	0.587116i
$57$	8.91943	−	7.46129i	1.18141	−	0.988272i
$58$	4.30201	−	2.87451i	0.564881	−	0.377442i
$59$	8.83540	−	3.65974i	1.15027	−	0.476458i	0.275647	−	0.961259i	$-0.411108\pi$
$59$	8.83540	−	3.65974i	1.15027	−	0.476458i	0.874624	+	0.484801i	$0.161108\pi$
$60$	−0.0186653	+	0.0636782i	−0.00240967	+	0.00822083i
$61$	2.20784	+	3.30427i	0.282685	+	0.423068i	0.945454	−	0.325756i	$-0.105619\pi$
$61$	2.20784	+	3.30427i	0.282685	+	0.423068i	−0.662769	+	0.748824i	$0.730619\pi$
$62$	2.29606	−	11.5431i	0.291600	−	1.46597i
$63$	−4.94082	−	1.93864i	−0.622485	−	0.244246i
$64$	6.20303	−	6.20303i	0.775378	−	0.775378i
$65$	0.00320381	+	0.0161066i	0.000397383	+	0.00199778i
$66$	7.27511	−	3.97693i	0.895505	−	0.489527i
$67$		−	5.81844i		−	0.710836i	−0.934707	−	0.355418i	$-0.884339\pi$
$67$		−	5.81844i		−	0.710836i	0.934707	−	0.355418i	$-0.115661\pi$
$68$		0			0
$69$	6.82064	−	8.47201i	0.821109	−	1.01991i
$70$	0.302288	+	0.125212i	0.0361303	+	0.0149657i
$71$	12.7462	−	2.53537i	1.51269	−	0.300893i	0.632143	−	0.774851i	$-0.282175\pi$
$71$	12.7462	−	2.53537i	1.51269	−	0.300893i	0.880547	+	0.473959i	$0.157175\pi$
$72$	7.54238	+	4.83722i	0.888878	+	0.570072i
$73$	3.71467	+	2.48206i	0.434769	+	0.290504i	0.753631	−	0.657298i	$-0.228301\pi$
$73$	3.71467	+	2.48206i	0.434769	+	0.290504i	−0.318862	+	0.947801i	$0.603301\pi$
$74$	0.480089	+	0.0954957i	0.0558093	+	0.0111012i
$75$	−8.59199	−	0.764823i	−0.992118	−	0.0883142i
$76$	−0.699588	−	1.68895i	−0.0802482	−	0.193736i
$77$	2.46565	+	5.95260i	0.280987	+	0.678362i
$78$	0.264676	+	0.0235604i	0.0299687	+	0.00266769i
$79$	−2.39893	−	0.477177i	−0.269901	−	0.0536866i	0.0582845	−	0.998300i	$-0.481437\pi$
$79$	−2.39893	−	0.477177i	−0.269901	−	0.0536866i	−0.328185	+	0.944613i	$0.606437\pi$
$80$	−0.395572	−	0.264312i	−0.0442262	−	0.0295510i
$81$	−3.12939	+	8.43842i	−0.347710	+	0.937602i
$82$	−5.66918	+	1.12767i	−0.626057	+	0.124530i
$83$	−5.11813	−	2.12000i	−0.561788	−	0.232700i	0.0836731	−	0.996493i	$-0.473335\pi$
$83$	−5.11813	−	2.12000i	−0.561788	−	0.232700i	−0.645461	+	0.763793i	$0.723335\pi$
$84$	−0.523244	+	0.649928i	−0.0570906	+	0.0709130i
$85$		0			0
$86$			2.77180i			0.298890i
$87$	5.98239	−	3.27027i	0.641379	−	0.350609i
$88$	−2.12204	−	10.6682i	−0.226210	−	1.13724i
$89$	−2.89760	+	2.89760i	−0.307145	+	0.307145i	−0.843801	−	0.536656i	$-0.819687\pi$
$89$	−2.89760	+	2.89760i	−0.307145	+	0.307145i	0.536656	+	0.843801i	$0.319687\pi$
$90$	0.202655	−	0.516488i	0.0213617	−	0.0544426i
$91$	−0.0402848	+	0.202525i	−0.00422299	+	0.0212304i
$92$	−0.949937	−	1.42168i	−0.0990378	−	0.148221i
$93$	4.36231	−	14.8824i	0.452351	−	1.54324i
$94$	3.62608	−	1.50197i	0.374002	−	0.154917i
$95$	−0.785444	+	0.524817i	−0.0805849	+	0.0538451i
$96$	2.03139	−	1.69930i	0.207328	−	0.173434i
$97$	2.54849	−	3.81409i	0.258760	−	0.387262i	−0.679229	−	0.733926i	$-0.737686\pi$
$97$	2.54849	−	3.81409i	0.258760	−	0.387262i	0.937989	+	0.346664i	$0.112686\pi$
$98$	−3.59692	−	3.59692i	−0.363344	−	0.363344i
$99$	10.0135	−	4.36987i	1.00639	−	0.439189i
$100$	−0.518941	+	1.25283i	−0.0518941	+	0.125283i
$101$	5.06729			0.504214			0.252107	−	0.967699i	$-0.418877\pi$
$101$	5.06729			0.504214			0.252107	+	0.967699i	$0.418877\pi$
$102$		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
$105$	0.382135	+	0.199663i	0.0372925	+	0.0194851i
$106$	−5.95315	−	5.95315i	−0.578221	−	0.578221i
$107$	−0.756986	+	1.13291i	−0.0731806	+	0.109522i	−0.866255	−	0.499603i	$-0.833479\pi$
$107$	−0.756986	+	1.13291i	−0.0731806	+	0.109522i	0.793074	+	0.609125i	$0.208479\pi$
$108$	1.11856	+	0.866406i	0.107633	+	0.0833699i
$109$	−9.54382	+	6.37698i	−0.914132	+	0.610804i	−0.921165	−	0.389171i	$-0.872761\pi$
$109$	−9.54382	+	6.37698i	−0.914132	+	0.610804i	0.00703284	+	0.999975i	$0.497761\pi$
$110$	−0.622254	+	0.257746i	−0.0593296	+	0.0245751i
$111$	0.618977	+	0.181434i	0.0587507	+	0.0172209i
$112$	−3.32347	−	4.97393i	−0.314039	−	0.469992i
$113$	−2.64375	+	13.2910i	−0.248703	+	1.25031i	0.631373	+	0.775479i	$0.282492\pi$
$113$	−2.64375	+	13.2910i	−0.248703	+	1.25031i	−0.880076	+	0.474834i	$0.842508\pi$
$114$	4.57421	+	14.5846i	0.428414	+	1.36597i
$115$	−0.624752	+	0.624752i	−0.0582584	+	0.0582584i
$116$	−0.209101	−	1.05122i	−0.0194146	−	0.0976035i
$117$	0.344645	+	0.0618477i	0.0318624	+	0.00571782i
$118$			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
$122$	−5.12316	+	1.01906i	−0.463829	+	0.0922614i
$123$	−7.57276	+	0.817741i	−0.682813	+	0.0737332i
$124$	−2.02717	−	1.35451i	−0.182045	−	0.121639i
$125$	1.37724	+	0.273951i	0.123184	+	0.0245029i
$126$	4.83950	−	5.02483i	0.431137	−	0.447647i
$127$	3.78439	+	9.13631i	0.335810	+	0.810717i	0.998109	+	0.0614768i	$0.0195810\pi$
$127$	3.78439	+	9.13631i	0.335810	+	0.810717i	−0.662299	+	0.749240i	$0.730419\pi$
$128$	3.24229	+	7.82759i	0.286581	+	0.691867i
$129$	−0.323847	+	3.63808i	−0.0285131	+	0.320315i
$130$	−0.0211709	−	0.00421116i	−0.00185681	−	0.000369343i
$131$	10.8334	+	7.23868i	0.946523	+	0.632446i	0.930056	−	0.367418i	$-0.119758\pi$
$131$	10.8334	+	7.23868i	0.946523	+	0.632446i	0.0164667	+	0.999864i	$0.494758\pi$
$132$	−0.184398	−	1.70763i	−0.0160497	−	0.148630i
$133$	−11.6498	+	2.31728i	−1.01016	+	0.200934i
$134$	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	$-0.0437163\pi$
$138$	6.85731	+	12.5443i	0.583733	+	1.06784i
$139$	−0.993879	−	4.99657i	−0.0842997	−	0.423803i	−0.999771	−	0.0214191i	$-0.993182\pi$
$139$	−0.993879	−	4.99657i	−0.0842997	−	0.423803i	0.915471	−	0.402384i	$-0.131818\pi$
$140$	0.0479277	−	0.0479277i	0.00405063	−	0.00405063i
$141$	4.93485	−	1.54773i	0.415589	−	0.130343i
$142$	−3.33255	+	16.7539i	−0.279661	+	1.40595i
$143$	−0.236152	−	0.353426i	−0.0197480	−	0.0295550i
$144$	−8.32694	+	5.79306i	−0.693912	+	0.482755i
$145$	−0.511685	+	0.211947i	−0.0424931	+	0.0176012i
$146$	−4.88265	+	3.26248i	−0.404091	+	0.270005i
$147$	−4.30084	−	5.14134i	−0.354727	−	0.424051i
$148$	0.0563356	−	0.0843122i	0.00463076	−	0.00693042i
$149$	15.7137	+	15.7137i	1.28731	+	1.28731i	0.936412	+	0.350902i	$0.114125\pi$
$149$	15.7137	+	15.7137i	1.28731	+	1.28731i	0.350902	+	0.936412i	$0.385875\pi$
$150$	5.25062	−	10.0491i	0.428711	−	0.820509i
$151$	−1.57857	+	3.81101i	−0.128462	+	0.310135i	−0.975004	−	0.222187i	$-0.928681\pi$
$151$	−1.57857	+	3.81101i	−0.128462	+	0.310135i	0.846542	+	0.532322i	$0.178681\pi$
$152$	20.0526			1.62648
$153$		0			0
$154$	−8.46890			−0.682443
$155$	−0.482114	+	1.16393i	−0.0387243	+	0.0934887i
$156$	0.0254913	−	0.0487877i	0.00204094	−	0.00390614i
$157$	−9.87094	−	9.87094i	−0.787787	−	0.787787i	0.193344	−	0.981131i	$-0.438067\pi$
$157$	−9.87094	−	9.87094i	−0.787787	−	0.787787i	−0.981131	+	0.193344i	$0.938067\pi$
$158$	1.78615	−	2.67316i	0.142098	−	0.212665i
$159$	−7.11818	−	8.50927i	−0.564508	−	0.674829i
$160$	−0.178884	+	0.119526i	−0.0141420	+	0.00944940i
$161$	−10.2639	+	4.25145i	−0.808909	+	0.335061i
$162$	−8.67325	−	8.04483i	−0.681435	−	0.632061i
$163$	−6.19697	−	9.27442i	−0.485384	−	0.726429i	0.505250	−	0.862973i	$-0.331400\pi$
$163$	−6.19697	−	9.27442i	−0.485384	−	0.726429i	−0.990634	+	0.136544i	$0.956400\pi$
$164$	−0.233603	+	1.17440i	−0.0182413	+	0.0917053i
$165$	−0.846845	+	0.265599i	−0.0659268	+	0.0206769i
$166$	5.14893	−	5.14893i	0.399634	−	0.399634i
$167$	−0.409682	−	2.05961i	−0.0317021	−	0.159377i	0.961692	−	0.274134i	$-0.0883912\pi$
$167$	−0.409682	−	2.05961i	−0.0317021	−	0.159377i	−0.993394	+	0.114757i	$0.963391\pi$
$168$	−4.39001	−	8.03076i	−0.338697	−	0.619587i
$169$			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
$173$	−12.0778	+	2.40243i	−0.918260	+	0.182653i	−0.631524	−	0.775356i	$-0.717570\pi$
$173$	−12.0778	+	2.40243i	−0.918260	+	0.182653i	−0.286736	+	0.958010i	$0.592570\pi$
$174$	0.962121	+	8.90980i	0.0729382	+	0.675450i
$175$	7.32598	+	4.89506i	0.553792	+	0.370032i
$176$	12.0774	+	2.40235i	0.910369	+	0.181084i
$177$	−1.46867	+	16.4990i	−0.110392	+	1.24014i
$178$	−2.06124	−	4.97628i	−0.154497	−	0.372988i
$179$	−7.07462	−	17.0796i	−0.528782	−	1.27659i	−0.932322	−	0.361630i	$-0.882220\pi$
$179$	−7.07462	−	17.0796i	−0.528782	−	1.27659i	0.403540	−	0.914962i	$-0.367780\pi$
$180$	−0.0827833	−	0.0797299i	−0.00617030	−	0.00594272i
$181$	2.08780	+	0.415290i	0.155185	+	0.0308683i	0.272071	−	0.962277i	$-0.412291\pi$
$181$	2.08780	+	0.415290i	0.155185	+	0.0308683i	−0.116886	+	0.993145i	$0.537291\pi$
$182$	−0.225677	−	0.150792i	−0.0167283	−	0.0111775i
$183$	−6.84340	+	0.738981i	−0.505879	+	0.0546271i
$184$	18.3949	−	3.65898i	1.35609	−	0.269743i
$185$	−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
$189$	6.93910	−	6.02984i	0.504745	−	0.438606i
$190$	−0.242237	−	1.21781i	−0.0175737	−	0.0883490i
$191$	−12.2604	+	12.2604i	−0.887130	+	0.887130i	−0.994247	−	0.107116i	$-0.965838\pi$
$191$	−12.2604	+	12.2604i	−0.887130	+	0.887130i	0.107116	+	0.994247i	$0.465838\pi$
$192$	4.54703	+	14.4979i	0.328154	+	1.04630i
$193$	−3.16756	+	15.9244i	−0.228006	+	1.14626i	0.681898	+	0.731447i	$0.261155\pi$
$193$	−3.16756	+	15.9244i	−0.228006	+	1.14626i	−0.909904	+	0.414818i	$0.863845\pi$
$194$	3.34980	+	5.01333i	0.240501	+	0.359936i
$195$	−0.0272956	−	0.00800084i	−0.00195468	−	0.000572952i
$196$	−0.973548	+	0.403257i	−0.0695391	+	0.0288040i
$197$	−6.52782	+	4.36175i	−0.465088	+	0.310762i	−0.765944	−	0.642908i	$-0.777728\pi$
$197$	−6.52782	+	4.36175i	−0.465088	+	0.310762i	0.300855	+	0.953670i	$0.402728\pi$
$198$	0.269763	+	14.3582i	0.0191712	+	1.02039i
$199$	−7.11102	+	10.6424i	−0.504087	+	0.754419i	−0.993026	−	0.117899i	$-0.962384\pi$
$199$	−7.11102	+	10.6424i	−0.504087	+	0.754419i	0.488939	+	0.872318i	$0.337384\pi$
$200$	−10.5180	−	10.5180i	−0.743732	−	0.743732i
$201$	8.93209	+	4.66697i	0.630021	+	0.329183i
$202$	−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
$207$	7.53484	+	17.2660i	0.523708	+	1.20007i
$208$	0.279061	+	0.279061i	0.0193494	+	0.0193494i
$209$	13.5840	−	20.3300i	0.939628	−	1.40625i
$210$	−0.434682	+	0.363620i	−0.0299959	+	0.0250922i
$211$	4.25722	−	2.84458i	0.293079	−	0.195829i	−0.400334	−	0.916369i	$-0.631106\pi$
$211$	4.25722	−	2.84458i	0.293079	−	0.195829i	0.693413	+	0.720540i	$0.256106\pi$
$212$	−1.61129	+	0.667417i	−0.110664	+	0.0458384i
$213$	−6.33155	+	21.6007i	−0.433831	+	1.48005i
$214$	−0.995000	−	1.48912i	−0.0680168	−	0.101794i
$215$	0.0578841	−	0.291003i	0.00394766	−	0.0198462i
$216$	−13.4755	+	7.69863i	−0.916893	+	0.523825i
$217$	−11.2013	+	11.2013i	−0.760395	+	0.760395i
$218$	−2.94339	−	14.7974i	−0.199351	−	1.00221i
$219$	−6.78984	+	3.71166i	−0.458815	+	0.250810i
$220$			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	$-0.372987\pi$
$223$	0.174491	+	0.0722764i	0.0116848	+	0.00483999i	−0.376833	+	0.926281i	$0.622987\pi$
$224$	−2.65322	+	0.527759i	−0.177276	+	0.0352624i
$225$	8.06574	−	12.5764i	0.537716	−	0.838426i
$226$	−14.8104	−	9.89597i	−0.985171	−	0.658270i
$227$	2.08928	+	0.415583i	0.138670	+	0.0275832i	0.263937	−	0.964540i	$-0.414979\pi$
$227$	2.08928	+	0.415583i	0.138670	+	0.0275832i	−0.125267	+	0.992123i	$0.539979\pi$
$228$	3.15391	+	0.280748i	0.208873	+	0.0185930i
$229$	6.61427	+	15.9683i	0.437084	+	1.05521i	0.976951	+	0.213463i	$0.0684743\pi$
$229$	6.61427	+	15.9683i	0.437084	+	1.05521i	−0.539868	+	0.841750i	$0.681526\pi$
$230$	−0.444424	−	1.07293i	−0.0293045	−	0.0707472i
$231$	−11.1157	−	0.989476i	−0.731362	−	0.0651028i
$232$	11.5309	+	2.29363i	0.757039	+	0.150584i
$233$	−8.14185	−	5.44021i	−0.533390	−	0.356400i	0.259521	−	0.965738i	$-0.416435\pi$
$233$	−8.14185	−	5.44021i	−0.533390	−	0.356400i	−0.792911	+	0.609337i	$0.791435\pi$
$234$	−0.248465	+	0.387416i	−0.0162427	+	0.0253262i
$235$	−0.412058	+	0.0819634i	−0.0268797	+	0.00534670i
$236$	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	$0.741537\pi$
$240$	0.723043	−	0.395251i	0.0466722	−	0.0255133i
$241$	−0.0791082	−	0.397704i	−0.00509581	−	0.0256184i	0.978154	−	0.207883i	$-0.0666573\pi$
$241$	−0.0791082	−	0.397704i	−0.00509581	−	0.0256184i	−0.983250	+	0.182265i	$0.941657\pi$
$242$	2.10322	−	2.10322i	0.135200	−	0.135200i
$243$	−10.4440	−	11.5725i	−0.669985	−	0.742375i
$244$	−0.211104	+	1.06129i	−0.0135145	+	0.0679421i
$245$	0.302515	+	0.452746i	0.0193270	+	0.0289249i
$246$	2.81612	−	9.60746i	0.179549	−	0.612549i
$247$	0.723968	−	0.299877i	0.0460650	−	0.0190807i
$248$	22.2360	−	14.8577i	1.41199	−	0.943462i
$249$	7.35974	−	6.15657i	0.466404	−	0.390157i
$250$	−1.02544	+	1.53468i	−0.0648547	+	0.0970619i
$251$	0.749951	+	0.749951i	0.0473365	+	0.0473365i	0.730379	−	0.683042i	$-0.239344\pi$
$251$	0.749951	+	0.749951i	0.0473365	+	0.0473365i	−0.683042	+	0.730379i	$0.739344\pi$
$252$	−0.578034	−	1.32456i	−0.0364127	−	0.0834392i
$253$	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	−0.478757	−	0.877947i	$-0.658913\pi$
$257$	7.70425	−	18.5997i	0.480578	−	1.16022i	0.959335	−	0.282270i	$-0.0910874\pi$
$258$	−4.25508	−	2.22326i	−0.264910	−	0.138414i
$259$	−0.465876	−	0.465876i	−0.0289481	−	0.0289481i
$260$	−0.00248428	+	0.00371799i	−0.000154069	+	0.000230580i
$261$	0.221828	+	11.8068i	0.0137308	+	0.730826i
$262$	−14.2397	+	9.51469i	−0.879734	+	0.587820i
$263$	−5.10116	+	2.11297i	−0.314551	+	0.130291i	−0.534373	−	0.845249i	$-0.679452\pi$
$263$	−5.10116	+	2.11297i	−0.314551	+	0.130291i	0.219822	+	0.975540i	$0.429452\pi$
$264$	18.0792	+	5.29936i	1.11270	+	0.326153i
$265$	0.500683	+	0.749325i	0.0307567	+	0.0460307i
$266$	3.04589	−	15.3127i	0.186756	−	0.938884i
$267$	−2.12404	−	6.77237i	−0.129989	−	0.414462i
$268$	1.12027	−	1.12027i	0.0684314	−	0.0684314i
$269$	1.78305	+	8.96401i	0.108715	+	0.546545i	0.996303	+	0.0859079i	$0.0273791\pi$
$269$	1.78305	+	8.96401i	0.108715	+	0.546545i	−0.887588	+	0.460637i	$0.847621\pi$
$270$	0.630328	+	0.725377i	0.0383605	+	0.0441451i
$271$			2.64822i			0.160868i	0.996760	+	0.0804339i	$0.0256306\pi$
$271$			2.64822i			0.160868i	−0.996760	+	0.0804339i	$0.974369\pi$
$272$		0			0
$273$	−0.278591	−	0.224288i	−0.0168611	−	0.0135745i
$274$	3.89196	+	1.61210i	0.235122	+	0.0973906i
$275$	−17.7885	+	3.53836i	−1.07269	+	0.213371i
$276$	2.94442	−	0.317951i	0.177233	−	0.0191384i
$277$	17.2028	+	11.4945i	1.03362	+	0.690640i	0.952023	−	0.306026i	$-0.0989995\pi$
$277$	17.2028	+	11.4945i	1.03362	+	0.690640i	0.0815922	+	0.996666i	$0.473999\pi$
$278$	6.56761	+	1.30638i	0.393899	+	0.0783514i
$279$	19.3475	+	18.6339i	1.15831	+	1.11558i
$280$	0.284517	+	0.686886i	0.0170032	+	0.0410493i
$281$	−3.93729	−	9.50546i	−0.234879	−	0.567048i	0.761860	−	0.647742i	$-0.224286\pi$
$281$	−3.93729	−	9.50546i	−0.234879	−	0.567048i	−0.996739	+	0.0806938i	$0.974286\pi$
$282$	−0.602748	+	6.77125i	−0.0358931	+	0.403222i
$283$	−12.5960	−	2.50549i	−0.748753	−	0.148936i	−0.194058	−	0.980990i	$-0.562165\pi$
$283$	−12.5960	−	2.50549i	−0.748753	−	0.148936i	−0.554695	+	0.832054i	$0.687165\pi$
$284$	2.94227	+	1.96596i	0.174592	+	0.116659i
$285$	−0.175660	−	1.62672i	−0.0104052	−	0.0963584i
$286$	0.547976	−	0.108999i	0.0324025	−	0.00644525i
$287$	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
$291$	3.81099	+	6.97155i	0.223404	+	0.408680i
$292$	0.237324	+	1.19311i	0.0138883	+	0.0698213i
$293$	0.797696	−	0.797696i	0.0466019	−	0.0466019i	−0.683422	−	0.730024i	$-0.739509\pi$
$293$	0.797696	−	0.797696i	0.0466019	−	0.0466019i	0.730024	+	0.683422i	$0.239509\pi$
$294$	8.40685	−	2.63667i	0.490297	−	0.153774i
$295$	0.262509	−	1.31972i	0.0152839	−	0.0768372i
$296$	0.617947	+	0.924822i	0.0359174	+	0.0537542i
$297$	−1.32348	+	18.8771i	−0.0767964	+	1.09536i
$298$	−26.9863	+	11.1781i	−1.56327	+	0.647530i
$299$	0.609402	−	0.407189i	0.0352426	−	0.0235484i
$300$	−1.50703	−	1.80154i	−0.0870082	−	0.104012i
$301$	2.07270	−	3.10202i	0.119469	−	0.178797i
$302$	−3.83394	−	3.83394i	−0.220618	−	0.220618i
$303$	−4.06447	+	7.77896i	−0.233497	+	0.446890i
$304$	−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
$309$	12.8143	−	24.5253i	0.728981	−	1.39519i
$310$	−1.17093	−	1.17093i	−0.0665042	−	0.0665042i
$311$	−16.3199	+	24.4244i	−0.925415	+	1.38498i	−0.00249223	+	0.999997i	$0.500793\pi$
$311$	−16.3199	+	24.4244i	−0.925415	+	1.38498i	−0.922923	+	0.384985i	$0.874207\pi$
$312$	0.387413	+	0.463125i	0.0219330	+	0.0262193i
$313$	14.8171	−	9.90044i	0.837509	−	0.559606i	−0.0612125	−	0.998125i	$-0.519497\pi$
$313$	14.8171	−	9.90044i	0.837509	−	0.559606i	0.898722	+	0.438519i	$0.144497\pi$
$314$	16.9521	−	7.02180i	0.956664	−	0.396263i
$315$	−0.613020	+	0.426478i	−0.0345398	+	0.0240293i
$316$	−0.370010	−	0.553759i	−0.0208147	−	0.0311514i
$317$	2.75488	−	13.8497i	0.154729	−	0.777877i	−0.823006	−	0.568033i	$-0.807704\pi$
$317$	2.75488	−	13.8497i	0.154729	−	0.777877i	0.977735	−	0.209844i	$-0.0672955\pi$
$318$	13.9139	−	4.36387i	0.780253	−	0.244713i
$319$	10.1366	−	10.1366i	0.567542	−	0.567542i
$320$	−0.240798	−	1.21057i	−0.0134610	−	0.0676730i
$321$	−1.13199	−	2.07078i	−0.0631815	−	0.115580i
$322$		−	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
$326$	14.3797	−	2.86030i	0.796418	−	0.158417i
$327$	−2.13442	−	19.7660i	−0.118034	−	1.09306i
$328$	−10.9209	−	7.29708i	−0.603003	−	0.402914i
$329$	−5.18123	−	1.03061i	−0.285651	−	0.0568194i
$330$	0.103435	−	1.16198i	0.00569389	−	0.0639649i
$331$	−2.76796	−	6.68245i	−0.152141	−	0.367301i	0.829372	−	0.558697i	$-0.188698\pi$
$331$	−2.76796	−	6.68245i	−0.152141	−	0.367301i	−0.981513	+	0.191396i	$0.938698\pi$
$332$	−0.577254	−	1.39362i	−0.0316810	−	0.0764846i
$333$	−0.775006	+	0.804686i	−0.0424701	+	0.0440965i
$334$	2.70720	+	0.538496i	0.148131	+	0.0294652i
$335$	−0.680692	−	0.454824i	−0.0371902	−	0.0248497i
$336$	10.3014	−	1.11239i	0.561988	−	0.0606860i
$337$	−13.1112	+	2.60797i	−0.714210	+	0.142065i	−0.538804	−	0.842431i	$-0.681124\pi$
$337$	−13.1112	+	2.60797i	−0.714210	+	0.142065i	−0.175406	+	0.984496i	$0.556124\pi$
$338$	−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
$342$	−26.0582	−	4.67625i	−1.40907	−	0.252862i
$343$	3.75178	+	18.8615i	0.202577	+	1.01842i
$344$	−4.45359	+	4.45359i	−0.240121	+	0.240121i
$345$	−0.457965	−	1.46019i	−0.0246560	−	0.0786140i
$346$	3.15781	−	15.8754i	0.169765	−	0.853466i
$347$	−18.5966	−	27.8318i	−0.998320	−	1.49409i	−0.864214	−	0.503124i	$-0.832184\pi$
$347$	−18.5966	−	27.8318i	−0.998320	−	1.49409i	−0.134106	−	0.990967i	$-0.542816\pi$
$348$	1.78149	+	0.522186i	0.0954977	+	0.0279921i
$349$	25.7122	−	10.6503i	1.37634	−	0.570099i	0.432840	−	0.901471i	$-0.357511\pi$
$349$	25.7122	−	10.6503i	1.37634	−	0.570099i	0.943500	+	0.331372i	$0.107511\pi$
$350$	−9.62945	+	6.43419i	−0.514715	+	0.343922i
$351$	−0.371384	+	0.479468i	−0.0198230	+	0.0255921i
$352$	3.09375	−	4.63013i	0.164898	−	0.246787i
$353$	5.10785	+	5.10785i	0.271864	+	0.271864i	0.829850	−	0.557986i	$-0.188426\pi$
$353$	5.10785	+	5.10785i	0.271864	+	0.271864i	−0.557986	+	0.829850i	$0.688426\pi$
$354$	−19.2971	−	10.0826i	−1.02563	−	0.535886i
$355$	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	0.355942	+	0.934508i	$0.384160\pi$
$359$	−10.5450	+	25.4579i	−0.556544	+	1.34362i	−0.912486	+	0.409108i	$0.865840\pi$
$360$	1.15548	−	0.504251i	0.0608993	−	0.0265763i
$361$	18.4383	+	18.4383i	0.970437	+	0.970437i
$362$	−1.55450	+	2.32647i	−0.0817026	+	0.122277i
$363$	3.00628	−	2.51481i	0.157789	−	0.131994i
$364$	−0.0467501	+	0.0312374i	−0.00245037	+	0.00163729i
$365$	0.580747	−	0.240553i	0.0303977	−	0.0125911i
$366$	2.54489	−	8.68213i	0.133024	−	0.453822i
$367$	6.24111	+	9.34048i	0.325783	+	0.487569i	0.957820	−	0.287370i	$-0.0927808\pi$
$367$	6.24111	+	9.34048i	0.325783	+	0.487569i	−0.632037	+	0.774939i	$0.717781\pi$
$368$	−4.14230	+	20.8247i	−0.215932	+	1.08556i
$369$	4.81876	−	12.2811i	0.250855	−	0.639329i
$370$	0.0487002	−	0.0487002i	0.00253180	−	0.00253180i
$371$	2.21072	+	11.1141i	0.114775	+	0.577013i
$372$	3.70534	−	2.02552i	0.192113	−	0.105018i
$373$			5.50325i			0.284948i	0.989799	+	0.142474i	$0.0455057\pi$
$373$			5.50325i			0.284948i	−0.989799	+	0.142474i	$0.954494\pi$
$374$		0			0
$375$	−1.52524	+	1.89452i	−0.0787630	+	0.0978326i
$376$	8.23951	+	3.41292i	0.424920	+	0.176008i
$377$	0.450605	−	0.0896309i	0.0232073	−	0.00461623i
$378$	3.83203	+	11.4597i	0.197098	+	0.589423i
$379$	4.37931	+	2.92616i	0.224950	+	0.150307i	0.662939	−	0.748674i	$-0.269309\pi$
$379$	4.37931	+	2.92616i	0.224950	+	0.150307i	−0.437989	+	0.898981i	$0.644309\pi$
$380$	−0.252275	−	0.0501806i	−0.0129414	−	0.00257421i
$381$	−17.0609	−	1.51869i	−0.874057	−	0.0778049i
$382$	−8.72156	−	21.0557i	−0.446234	−	1.07730i
$383$	8.09691	+	19.5477i	0.413733	+	0.998840i	0.984127	+	0.177468i	$0.0567907\pi$
$383$	8.09691	+	19.5477i	0.413733	+	0.998840i	−0.570394	+	0.821372i	$0.693209\pi$
$384$	−14.6170	−	1.30115i	−0.745922	−	0.0663989i
$385$	0.889126	+	0.176858i	0.0453140	+	0.00901352i
$386$	−17.7448	−	11.8567i	−0.903188	−	0.603491i
$387$	−5.32519	−	3.41525i	−0.270694	−	0.173607i
$388$	1.22504	−	0.243675i	0.0621919	−	0.0123707i
$389$	11.5459	+	4.78245i	0.585398	+	0.242480i	0.655669	−	0.755048i	$-0.272387\pi$
$389$	11.5459	+	4.78245i	0.585398	+	0.242480i	−0.0702713	+	0.997528i	$0.522387\pi$
$390$	0.0234459	−	0.0291224i	0.00118723	−	0.00147467i
$391$		0			0
$392$		−	11.5587i		−	0.583804i
$393$	−19.8018	+	10.8247i	−0.998871	+	0.546032i
$394$	−2.01323	−	10.1212i	−0.101425	−	0.509898i
$395$	−0.243347	+	0.243347i	−0.0122441	+	0.0122441i
$396$	2.76934	+	1.08661i	0.139165	+	0.0546044i
$397$	7.58893	−	38.1521i	0.380877	−	1.91480i	−0.0224569	−	0.999748i	$-0.507149\pi$
$397$	7.58893	−	38.1521i	0.380877	−	1.91480i	0.403334	−	0.915053i	$-0.367851\pi$
$398$	−9.34689	−	13.9886i	−0.468517	−	0.701186i
$399$	5.78693	−	19.7427i	0.289709	−	0.988369i
$400$	15.5576	−	6.44418i	0.777881	−	0.322209i
$401$	22.6390	−	15.1269i	1.13054	−	0.755401i	0.157837	−	0.987465i	$-0.449548\pi$
$401$	22.6390	−	15.1269i	1.13054	−	0.755401i	0.972701	+	0.232064i	$0.0745478\pi$
$402$	−10.1603	+	8.49933i	−0.506752	+	0.423908i
$403$	0.580609	−	0.868943i	0.0289222	−	0.0432851i
$404$	0.975645	+	0.975645i	0.0485401	+	0.0485401i
$405$	0.742578	+	1.02573i	0.0368990	+	0.0509689i
$406$	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
$411$	4.91998	+	2.57066i	0.242685	+	0.126801i
$412$	−3.07598	−	3.07598i	−0.151543	−	0.151543i
$413$	9.39988	−	14.0679i	0.462538	−	0.692237i
$414$	−24.7574	+	0.465145i	−1.21676	+	0.0228606i
$415$	−0.648098	+	0.433045i	−0.0318139	+	0.0212573i
$416$	0.164883	−	0.0682967i	0.00808405	−	0.00334852i
$417$	8.46759	+	2.48201i	0.414660	+	0.121544i
$418$	17.8552	+	26.7222i	0.873326	+	1.30703i
$419$	−1.82223	+	9.16095i	−0.0890216	+	0.447542i	0.910406	+	0.413716i	$0.135769\pi$
$419$	−1.82223	+	9.16095i	−0.0890216	+	0.447542i	−0.999428	+	0.0338260i	$0.989231\pi$
$420$	0.0351327	+	0.112018i	0.00171430	+	0.00546593i
$421$	−9.40617	+	9.40617i	−0.458429	+	0.458429i	−0.898139	−	0.439711i	$-0.855081\pi$
$421$	−9.40617	+	9.40617i	−0.458429	+	0.458429i	0.439711	+	0.898139i	$0.355081\pi$
$422$	1.31296	+	6.60069i	0.0639138	+	0.321316i
$423$	−1.58226	+	8.81709i	−0.0769320	+	0.428702i
$424$		−	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
$428$	−0.363877	+	0.0723795i	−0.0175886	+	0.00349860i
$429$	0.731973	−	0.0790418i	0.0353400	−	0.00381617i
$430$	0.324269	+	0.216670i	0.0156376	+	0.0104487i
$431$	−14.3298	−	2.85038i	−0.690243	−	0.137298i	−0.162508	−	0.986707i	$-0.551958\pi$
$431$	−14.3298	−	2.85038i	−0.690243	−	0.137298i	−0.527734	+	0.849409i	$0.676958\pi$
$432$	−2.21409	−	17.4296i	−0.106525	−	0.838581i
$433$	−6.82738	−	16.4827i	−0.328103	−	0.792110i	−0.998733	−	0.0503185i	$-0.983976\pi$
$433$	−6.82738	−	16.4827i	−0.328103	−	0.792110i	0.670631	−	0.741792i	$-0.266024\pi$
$434$	−7.96819	−	19.2369i	−0.382485	−	0.923401i
$435$	0.0850552	−	0.955507i	0.00407809	−	0.0458131i
$436$	−3.06536	−	0.609738i	−0.146804	−	0.0292011i
$437$	35.0544	+	23.4226i	1.67688	+	1.12045i
$438$	−1.09198	−	10.1124i	−0.0521768	−	0.483187i
$439$	25.8533	−	5.14255i	1.23391	−	0.245440i	0.465299	−	0.885154i	$-0.345947\pi$
$439$	25.8533	−	5.14255i	1.23391	−	0.245440i	0.768614	+	0.639713i	$0.220947\pi$
$440$	−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	$-0.0737831\pi$
$444$	0.0842438	+	0.154109i	0.00399803	+	0.00731371i
$445$	0.112483	+	0.565491i	0.00533221	+	0.0268068i
$446$	−0.175541	+	0.175541i	−0.00831208	+	0.00831208i
$447$	−36.7265	+	11.5187i	−1.73710	+	0.544814i
$448$	3.02780	−	15.2218i	0.143050	−	0.719161i
$449$	0.587080	+	0.878627i	0.0277060	+	0.0414650i	0.845064	−	0.534665i	$-0.179562\pi$
$449$	0.587080	+	0.878627i	0.0277060	+	0.0414650i	−0.817358	+	0.576130i	$0.804562\pi$
$450$	11.2153	+	16.1208i	0.528692	+	0.759942i
$451$	−14.7960	+	6.12872i	−0.696718	+	0.288590i
$452$	−3.06805	+	2.05000i	−0.144309	+	0.0964240i
$453$	−4.58424	−	5.48012i	−0.215386	−	0.257479i
$454$	−1.55560	+	2.32811i	−0.0730077	+	0.109264i
$455$	0.0205441	+	0.0205441i	0.000963124	+	0.000963124i
$456$	−16.0842	+	30.7834i	−0.753210	+	1.44157i
$457$	8.19942	−	19.7952i	0.383553	−	0.925978i	−0.607720	−	0.794151i	$-0.707916\pi$
$457$	8.19942	−	19.7952i	0.383553	−	0.925978i	0.991273	−	0.131827i	$-0.0420843\pi$
$458$	−22.7184			−1.06156
$459$		0			0
$460$	−0.240577			−0.0112169
$461$	−9.42954	+	22.7649i	−0.439177	+	1.06027i	0.537056	+	0.843547i	$0.319536\pi$
$461$	−9.42954	+	22.7649i	−0.439177	+	1.06027i	−0.976233	+	0.216721i	$0.930464\pi$
$462$	6.79290	−	13.0009i	0.316034	−	0.604856i
$463$	13.6466	+	13.6466i	0.634213	+	0.634213i	0.949122	−	0.314909i	$-0.101974\pi$
$463$	13.6466	+	13.6466i	0.634213	+	0.634213i	−0.314909	+	0.949122i	$0.601974\pi$
$464$	−7.39451	+	11.0667i	−0.343281	+	0.513757i
$465$	−1.40008	−	1.67369i	−0.0649271	−	0.0776156i
$466$	10.7018	−	7.15074i	0.495753	−	0.331252i
$467$	−11.4980	+	4.76264i	−0.532066	+	0.220389i	−0.632508	−	0.774554i	$-0.717974\pi$
$467$	−11.4980	+	4.76264i	−0.532066	+	0.220389i	0.100442	+	0.994943i	$0.467974\pi$
$468$	0.0544491	+	0.0782652i	0.00251691	+	0.00361781i
$469$	−5.71897	−	8.55905i	−0.264078	−	0.395220i
$470$	0.107735	−	0.541619i	0.00496943	−	0.0249830i
$471$	23.0707	−	7.23574i	1.06304	−	0.333405i
$472$	−20.1974	+	20.1974i	−0.929660	+	0.929660i
$473$	1.49824	+	7.53215i	0.0688890	+	0.346329i
$474$	2.67099	+	4.88612i	0.122683	+	0.224427i
$475$		−	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
$479$	22.2629	−	4.42837i	1.01722	−	0.202337i	0.341801	−	0.939772i	$-0.388963\pi$
$479$	22.2629	−	4.42837i	1.01722	−	0.202337i	0.675418	+	0.737435i	$0.263963\pi$
$480$	−0.0400064	−	0.370483i	−0.00182604	−	0.0169102i
$481$	0.0361403	+	0.0241482i	0.00164786	+	0.00110106i
$482$	0.522751	+	0.103982i	0.0238107	+	0.00473624i
$483$	1.70613	−	19.1665i	0.0776314	−	0.872108i
$484$	−0.235795	−	0.569259i	−0.0107179	−	0.0258754i
$485$	−0.246991	−	0.596290i	−0.0112153	−	0.0270761i
$486$	19.3067	−	6.86185i	0.875770	−	0.311260i
$487$	−22.5436	−	4.48421i	−1.02155	−	0.203199i	−0.344228	−	0.938886i	$-0.611859\pi$
$487$	−22.5436	−	4.48421i	−1.02155	−	0.203199i	−0.677322	+	0.735687i	$0.736859\pi$
$488$	−9.86902	−	6.59427i	−0.446750	−	0.298509i
$489$	19.2081	−	2.07417i	0.868619	−	0.0937974i
$490$	−0.701969	+	0.139630i	−0.0317117	+	0.00630785i
$491$	18.8224	+	7.79649i	0.849443	+	0.351851i	0.764570	−	0.644541i	$-0.222951\pi$
$491$	18.8224	+	7.79649i	0.849443	+	0.351851i	0.0848732	+	0.996392i	$0.472951\pi$
$492$	−1.61549	−	1.30060i	−0.0728319	−	0.0586355i
$493$		0			0
$494$			1.03001i			0.0463421i
$495$	0.271524	−	1.51306i	0.0122041	−	0.0680069i
$496$	5.90648	+	29.6939i	0.265209	+	1.33329i
$497$	16.2578	−	16.2578i	0.729264	−	0.729264i
$498$	3.77434	+	12.0342i	0.169132	+	0.539267i
$499$	0.210533	−	1.05842i	0.00942477	−	0.0473815i	−0.975787	−	0.218724i	$-0.929811\pi$
$499$	0.210533	−	1.05842i	0.00942477	−	0.0473815i	0.985211	+	0.171343i	$0.0548105\pi$
$500$	0.212426	+	0.317918i	0.00949997	+	0.0142177i
$501$	3.49038	+	1.02309i	0.155939	+	0.0457085i
$502$	−1.28795	+	0.533486i	−0.0574840	+	0.0238106i
$503$	−7.80319	+	5.21393i	−0.347927	+	0.232478i	−0.717238	−	0.696829i	$-0.754594\pi$
$503$	−7.80319	+	5.21393i	−0.347927	+	0.232478i	0.369311	+	0.929306i	$0.379594\pi$
$504$	15.8495	−	0.297783i	0.705994	−	0.0132643i
$505$	0.396107	−	0.592815i	0.0176265	−	0.0263799i
$506$	21.2552	+	21.2552i	0.944907	+	0.944907i
$507$	−19.9358	−	10.4164i	−0.885381	−	0.462607i
$508$	−1.03045	+	2.48772i	−0.0457188	+	0.110375i
$509$	−7.99190			−0.354235			−0.177117	−	0.984190i	$-0.556677\pi$
$509$	−7.99190			−0.354235			−0.177117	+	0.984190i	$0.556677\pi$
$510$		0			0
$511$	7.90399			0.349652
$512$	−9.70803	+	23.4372i	−0.429038	+	1.03579i
$513$	−33.6560	−	9.18230i	−1.48595	−	0.405408i
$514$	18.7116	+	18.7116i	0.825334	+	0.825334i
$515$	−1.24883	+	1.86901i	−0.0550301	+	0.0823584i
$516$	−0.762822	+	0.638116i	−0.0335814	+	0.0280915i
$517$	9.04174	−	6.04150i	0.397655	−	0.265705i
$518$	0.800085	−	0.331406i	0.0351537	−	0.0145611i
$519$	5.99957	−	20.4681i	0.263352	−	0.898449i
$520$	−0.0272501	−	0.0407827i	−0.00119500	−	0.00178844i
$521$	0.307543	−	1.54613i	0.0134737	−	0.0677370i	−0.973463	−	0.228842i	$-0.926506\pi$
$521$	0.307543	−	1.54613i	0.0134737	−	0.0677370i	0.986937	+	0.161105i	$0.0515059\pi$
$522$	−14.4495	−	5.66956i	−0.632435	−	0.248150i
$523$	24.2095	−	24.2095i	1.05861	−	1.05861i	0.0604341	−	0.998172i	$-0.480751\pi$
$523$	24.2095	−	24.2095i	1.05861	−	1.05861i	0.998172	−	0.0604341i	$-0.0192485\pi$
$524$	0.692129	+	3.47957i	0.0302358	+	0.152006i
$525$	−13.3907	+	7.32004i	−0.584420	+	0.319473i
$526$		−	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
$530$	−1.16181	+	0.231097i	−0.0504656	+	0.0100382i
$531$	−24.1502	−	15.4884i	−1.04803	−	0.672141i
$532$	−2.68919	−	1.79686i	−0.116591	−	0.0779037i
$533$	−0.503405	−	0.100134i	−0.0218049	−	0.00433727i
$534$	9.29257	+	0.827186i	0.402129	+	0.0357958i
$535$	0.0733645	+	0.177118i	0.00317183	+	0.00765746i
$536$	6.65037	+	16.0554i	0.287252	+	0.693488i
$537$	31.8941	+	2.83908i	1.37633	+	0.122515i
$538$	−11.7825	−	2.34369i	−0.507980	−	0.101043i
$539$	−11.7186	−	7.83012i	−0.504756	−	0.337267i
$540$	0.188797	−	0.0631321i	0.00812451	−	0.00271677i
$541$	2.97344	−	0.591454i	0.127838	−	0.0254286i	−0.130756	−	0.991415i	$-0.541741\pi$
$541$	2.97344	−	0.591454i	0.127838	−	0.0254286i	0.258595	+	0.965986i	$0.416741\pi$
$542$	−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
$546$	0.412502	−	0.225494i	0.0176535	−	0.00965024i
$547$	−0.339058	−	1.70456i	−0.0144971	−	0.0728817i	0.972860	−	0.231396i	$-0.0743295\pi$
$547$	−0.339058	−	1.70456i	−0.0144971	−	0.0728817i	−0.987357	+	0.158515i	$0.949329\pi$
$548$	0.617069	−	0.617069i	0.0263599	−	0.0263599i
$549$	4.35465	−	11.0983i	0.185852	−	0.473663i
$550$	4.65090	−	23.3817i	0.198315	−	0.996998i
$551$	14.6825	+	21.9739i	0.625495	+	0.936119i
$552$	−9.13753	+	31.1735i	−0.388919	+	1.32683i
$553$	−3.99789	+	1.65598i	−0.170008	+	0.0704195i
$554$	−22.6118	+	15.1087i	−0.960681	+	0.641907i
$555$	0.0696108	−	0.0582308i	0.00295481	−	0.00247176i
$556$	0.770669	−	1.15339i	0.0326837	−	0.0489146i
$557$	−29.9311	−	29.9311i	−1.26822	−	1.26822i	−0.947006	−	0.321217i	$-0.895908\pi$
$557$	−29.9311	−	29.9311i	−1.26822	−	1.26822i	−0.321217	−	0.947006i	$-0.604092\pi$
$558$	−32.3604	+	14.1220i	−1.36993	+	0.597833i
$559$	−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	−0.510550	−	0.859848i	$-0.670558\pi$
$563$	10.8784	−	26.2627i	0.458468	−	1.10684i	0.969018	−	0.246991i	$-0.0794420\pi$
$564$	1.24814	+	0.652148i	0.0525563	+	0.0274604i
$565$	1.34824	+	1.34824i	0.0567208	+	0.0567208i
$566$	9.37847	−	14.0359i	0.394207	−	0.589972i
$567$	3.69077	+	15.4890i	0.154998	+	0.650476i
$568$	−32.2739	+	21.5647i	−1.35418	+	0.904835i
$569$	19.2820	−	7.98685i	0.808342	−	0.334826i	0.0600499	−	0.998195i	$-0.480874\pi$
$569$	19.2820	−	7.98685i	0.808342	−	0.334826i	0.748292	+	0.663369i	$0.230874\pi$
$570$	2.06379	+	0.604936i	0.0864428	+	0.0253380i
$571$	3.48855	+	5.22099i	0.145991	+	0.218492i	0.897257	−	0.441508i	$-0.145556\pi$
$571$	3.48855	+	5.22099i	0.145991	+	0.218492i	−0.751266	+	0.660000i	$0.770556\pi$
$572$	0.0225797	−	0.113516i	0.000944106	−	0.00474634i
$573$	−8.98729	−	28.6554i	−0.375449	−	1.19710i
$574$	−7.23109	+	7.23109i	−0.301820	+	0.301820i
$575$	−6.10109	−	30.6723i	−0.254433	−	1.27912i
$576$	−25.9034	−	4.64846i	−1.07931	−	0.193686i
$577$			36.1978i			1.50693i	0.657485	+	0.753467i	$0.271620\pi$
$577$			36.1978i			1.50693i	−0.657485	+	0.753467i	$0.728380\pi$
$578$		0			0
$579$	−21.9054	−	17.6356i	−0.910358	−	0.732911i
$580$	−0.139326	−	0.0577109i	−0.00578522	−	0.00239632i
$581$	−9.61264	+	1.91207i	−0.398799	+	0.0793261i
$582$	−10.3830	+	1.12120i	−0.430389	+	0.0464754i
$583$	−19.3951	−	12.9594i	−0.803262	−	0.536723i
$584$	−13.0872	−	2.60321i	−0.541553	−	0.107722i
$585$	0.0341761	−	0.0354849i	0.00141301	−	0.00146712i
$586$	0.567450	+	1.36995i	0.0234412	+	0.0565919i
$587$	−2.98442	−	7.20502i	−0.123180	−	0.297383i	0.850246	−	0.526386i	$-0.176453\pi$
$587$	−2.98442	−	7.20502i	−0.123180	−	0.297383i	−0.973426	+	0.229003i	$0.926453\pi$
$588$	0.161829	−	1.81798i	0.00667371	−	0.0749722i
$589$	58.9600	+	11.7279i	2.42940	+	0.483238i
$590$	1.47059	+	0.982614i	0.0605431	+	0.0404536i
$591$	−1.45991	−	13.5196i	−0.0600528	−	0.556124i
$592$	−1.23500	+	0.245657i	−0.0507583	+	0.0100964i
$593$	−28.0114	−	11.6027i	−1.15029	−	0.476465i	−0.275659	−	0.961256i	$-0.588896\pi$
$593$	−28.0114	−	11.6027i	−1.15029	−	0.476465i	−0.874630	+	0.484790i	$0.838896\pi$
$594$	−22.2581	−	11.1026i	−0.913261	−	0.455543i
$595$		0			0
$596$			6.05095i			0.247857i
$597$	−10.6338	−	19.4526i	−0.435211	−	0.796143i
$598$	0.187944	+	0.944859i	0.00768561	+	0.0386381i
$599$	17.7610	−	17.7610i	0.725695	−	0.725695i	−0.244064	−	0.969759i	$-0.578481\pi$
$599$	17.7610	−	17.7610i	0.725695	−	0.725695i	0.969759	+	0.244064i	$0.0784808\pi$
$600$	24.5829	−	7.71003i	1.00359	−	0.314761i
$601$	−5.94298	+	29.8774i	−0.242419	+	1.21872i	0.647307	+	0.762229i	$0.275895\pi$
$601$	−5.94298	+	29.8774i	−0.242419	+	1.21872i	−0.889726	+	0.456494i	$0.849105\pi$
$602$	2.72441	+	4.07737i	0.111039	+	0.166181i
$603$	−14.3288	+	9.96858i	−0.583516	+	0.405952i
$604$	−1.03770	+	0.429829i	−0.0422233	+	0.0174895i
$605$	−0.264733	+	0.176889i	−0.0107629	+	0.00719155i
$606$	−7.40207	−	8.84865i	−0.300689	−	0.359452i
$607$	−12.1073	+	18.1199i	−0.491421	+	0.735464i	−0.991442	−	0.130550i	$-0.958326\pi$
$607$	−12.1073	+	18.1199i	−0.491421	+	0.735464i	0.500020	+	0.866014i	$0.333326\pi$
$608$	7.25911	+	7.25911i	0.294396	+	0.294396i
$609$	5.58586	−	10.6907i	0.226350	−	0.433211i
$610$	−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
$615$	−0.496292	+	0.949850i	−0.0200124	+	0.0383017i
$616$	−13.6074	−	13.6074i	−0.548258	−	0.548258i
$617$	−13.1285	+	19.6482i	−0.528534	+	0.791007i	−0.995648	−	0.0931902i	$-0.970294\pi$
$617$	−13.1285	+	19.6482i	−0.528534	+	0.791007i	0.467115	+	0.884197i	$0.345294\pi$
$618$	23.3370	+	27.8977i	0.938753	+	1.12221i
$619$	33.2074	−	22.1885i	1.33472	−	0.891831i	0.335973	−	0.941872i	$-0.390935\pi$
$619$	33.2074	−	22.1885i	1.33472	−	0.891831i	0.998747	+	0.0500404i	$0.0159350\pi$
$620$	−0.316925	+	0.131275i	−0.0127280	+	0.00527211i
$621$	−32.5493	−	2.28205i	−1.30616	−	0.0915754i
$622$	−21.4512	−	32.1040i	−0.860116	−	1.28725i
$623$	−1.41437	+	7.11050i	−0.0566654	+	0.284876i
$624$	−0.652230	+	0.204561i	−0.0261101	+	0.00818901i
$625$	−17.4680	+	17.4680i	−0.698719	+	0.698719i
$626$	4.56969	+	22.9734i	0.182642	+	0.918201i
$627$	20.3135	+	37.1600i	0.811242	+	1.48403i
$628$		−	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	$-0.554007\pi$
$631$	−24.7481	−	10.2510i	−0.985205	−	0.408085i	−0.816351	+	0.577556i	$0.804007\pi$
$632$	7.16501	−	1.42521i	0.285009	−	0.0566917i
$633$	0.952104	+	8.81704i	0.0378428	+	0.350446i
$634$	15.4329	+	10.3120i	0.612920	+	0.409540i
$635$	1.36467	+	0.271450i	0.0541552	+	0.0107721i
$636$	0.267838	−	3.00888i	0.0106205	−	0.119310i
$637$	−0.172855	−	0.417310i	−0.00684878	−	0.0165344i
$638$	7.21080	+	17.4084i	0.285478	+	0.689206i
$639$	−28.0814	−	27.0457i	−1.11088	−	1.06991i
$640$	1.16919	+	0.232566i	0.0462162	+	0.00919297i
$641$	−35.4034	−	23.6558i	−1.39835	−	0.934349i	−0.999852	−	0.0171805i	$-0.994531\pi$
$641$	−35.4034	−	23.6558i	−1.39835	−	0.934349i	−0.398500	−	0.917168i	$-0.630469\pi$
$642$	3.08409	−	0.333034i	0.121719	−	0.0131438i
$643$	25.2906	−	5.03062i	0.997365	−	0.198388i	0.330692	−	0.943739i	$-0.392718\pi$
$643$	25.2906	−	5.03062i	0.997365	−	0.198388i	0.666673	+	0.745351i	$0.267718\pi$
$644$	−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	$0.729712\pi$
$648$	−1.00972	−	26.8618i	−0.0396656	−	1.05523i
$649$	6.79463	+	34.1589i	0.266712	+	1.34085i
$650$	0.540257	−	0.540257i	0.0211906	−	0.0211906i
$651$	−8.21096	−	26.1801i	−0.321813	−	1.02608i
$652$	0.592526	−	2.97883i	0.0232051	−	0.116660i
$653$	19.0588	+	28.5236i	0.745830	+	1.11621i	0.989242	+	0.146290i	$0.0467333\pi$
$653$	19.0588	+	28.5236i	0.745830	+	1.11621i	−0.243412	+	0.969923i	$0.578267\pi$
$654$	25.0769	+	7.35049i	0.980584	+	0.287427i
$655$	1.69369	−	0.701548i	0.0661778	−	0.0274118i
$656$	12.3634	−	8.26097i	0.482710	−	0.322537i
$657$	−0.251769	−	13.4004i	−0.00982243	−	0.522800i
$658$	3.85774	−	5.77352i	0.150391	−	0.225075i
$659$	−24.7106	−	24.7106i	−0.962589	−	0.962589i	0.0367361	−	0.999325i	$-0.488304\pi$
$659$	−24.7106	−	24.7106i	−0.962589	−	0.962589i	−0.999325	+	0.0367361i	$0.988304\pi$
$660$	−0.214188	−	0.111912i	−0.00833724	−	0.00435616i
$661$	4.65040	−	11.2271i	0.180880	−	0.436682i	−0.807269	−	0.590184i	$-0.799055\pi$
$661$	4.65040	−	11.2271i	0.180880	−	0.436682i	0.988148	+	0.153502i	$0.0490552\pi$
$662$	9.50727			0.369510
$663$		0			0
$664$	16.5461			0.642113
$665$	−0.639559	+	1.54403i	−0.0248011	+	0.0598750i
$666$	−0.587351	−	1.34591i	−0.0227594	−	0.0521528i
$667$	17.4783	+	17.4783i	0.676762	+	0.676762i
$668$	0.317674	−	0.475432i	0.0122912	−	0.0183950i
$669$	−0.250913	+	0.209894i	−0.00970085	+	0.00811496i
$670$	0.894718	−	0.597832i	0.0345660	−	0.0230962i
$671$	−13.3710	+	5.53844i	−0.516181	+	0.213809i
$672$	1.31797	−	4.49637i	0.0508417	−	0.173451i
$673$	22.5244	+	33.7102i	0.868252	+	1.29943i	0.952982	+	0.303027i	$0.0979973\pi$
$673$	22.5244	+	33.7102i	0.868252	+	1.29943i	−0.0847298	+	0.996404i	$0.527003\pi$
$674$	3.42798	−	17.2336i	0.132041	−	0.663814i
$675$	12.8369	+	22.4695i	0.494094	+	0.864852i
$676$	−2.50037	+	2.50037i	−0.0961681	+	0.0961681i
$677$	1.33713	+	6.72222i	0.0513902	+	0.258356i	0.997936	−	0.0642128i	$-0.0204537\pi$
$677$	1.33713	+	6.72222i	0.0513902	+	0.258356i	−0.946546	+	0.322569i	$0.895454\pi$
$678$	27.0710	−	14.7984i	1.03966	−	0.568327i
$679$		−	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
$683$	9.68496	−	1.92646i	0.370585	−	0.0737139i	−0.00628472	−	0.999980i	$-0.502001\pi$
$683$	9.68496	−	1.92646i	0.370585	−	0.0737139i	0.376870	+	0.926266i	$0.377001\pi$
$684$	−2.96073	+	4.61649i	−0.113206	+	0.176516i
$685$	−0.374940	−	0.250527i	−0.0143257	−	0.00957213i
$686$	−24.7920	−	4.93143i	−0.946562	−	0.188283i
$687$	−29.8187	−	2.65434i	−1.13766	−	0.101269i
$688$	−2.72864	−	6.58752i	−0.104028	−	0.251147i
$689$	−0.286087	−	0.690676i	−0.0108991	−	0.0263127i
$690$	2.00357	+	0.178349i	0.0762746	+	0.00678965i
$691$	−13.6051	−	2.70622i	−0.517563	−	0.102950i	−0.0706044	−	0.997504i	$-0.522493\pi$
$691$	−13.6051	−	2.70622i	−0.517563	−	0.102950i	−0.446958	+	0.894555i	$0.647493\pi$
$692$	−2.78800	−	1.86288i	−0.105984	−	0.0708161i
$693$	10.4349	−	16.2705i	0.396389	−	0.618065i
$694$	43.1524	−	8.58354i	1.63804	−	0.325827i
$695$	−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
$699$	14.8820	−	8.13525i	0.562890	−	0.307703i
$700$	0.468044	+	2.35301i	0.0176904	+	0.0889356i
$701$	−7.15325	+	7.15325i	−0.270175	+	0.270175i	−0.829170	−	0.558996i	$-0.811187\pi$
$701$	−7.15325	+	7.15325i	−0.270175	+	0.270175i	0.558996	+	0.829170i	$0.311187\pi$
$702$	−0.395442	−	0.692173i	−0.0149250	−	0.0261244i
$703$	−0.487775	+	2.45221i	−0.0183968	+	0.0924869i
$704$	17.7491	+	26.5634i	0.668945	+	1.00115i
$705$	0.204687	−	0.698307i	0.00770894	−	0.0262998i
$706$	−8.77211	+	3.63353i	−0.330143	+	0.136750i
$707$	7.45408	−	4.98066i	0.280340	−	0.187317i
$708$	−3.45946	+	2.89391i	−0.130014	+	0.108760i
$709$	−25.0275	+	37.4563i	−0.939929	+	1.40670i	−0.0265247	+	0.999648i	$0.508444\pi$
$709$	−25.0275	+	37.4563i	−0.939929	+	1.40670i	−0.913404	+	0.407054i	$0.866556\pi$
$710$	1.69951	+	1.69951i	0.0637814	+	0.0637814i
$711$	2.93490	+	6.72528i	0.110067	+	0.252218i
$712$	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
$717$	−34.4433	−	17.9965i	−1.28631	−	0.672090i
$718$	−25.6111	−	25.6111i	−0.955796	−	0.955796i
$719$	15.9794	−	23.9148i	0.595929	−	0.891871i	−0.403807	−	0.914844i	$-0.632313\pi$
$719$	15.9794	−	23.9148i	0.595929	−	0.891871i	0.999736	+	0.0229732i	$0.00731323\pi$
$720$	0.0268106	+	1.42700i	0.000999172	+	0.0531811i
$721$	−23.5010	+	15.7029i	−0.875222	+	0.584805i
$722$	−31.6655	+	13.1163i	−1.17847	+	0.488138i
$723$	0.673981	+	0.197556i	0.0250656	+	0.00734719i
$724$	0.322022	+	0.481940i	0.0119679	+	0.0179112i
$725$	3.82448	−	19.2269i	0.142038	−	0.714071i
$726$	1.54173	+	4.91571i	0.0572190	+	0.182439i
$727$	−1.86673	+	1.86673i	−0.0692331	+	0.0692331i	−0.740876	−	0.671642i	$-0.765589\pi$
$727$	−1.86673	+	1.86673i	−0.0692331	+	0.0692331i	0.671642	+	0.740876i	$0.265589\pi$
$728$	−0.120321	−	0.604893i	−0.00445938	−	0.0224188i
$729$	26.1425	−	6.75071i	0.968239	−	0.250026i
$730$			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	$-0.178484\pi$
$733$	28.9600	+	11.9956i	1.06966	+	0.443068i	0.222790	+	0.974866i	$0.428484\pi$
$734$	−14.4821	+	2.88067i	−0.534545	+	0.106328i
$735$	−0.937673	+	0.101254i	−0.0345866	+	0.00373482i
$736$	7.98360	+	5.33447i	0.294279	+	0.196631i
$737$	20.7826	+	4.13391i	0.765537	+	0.152275i
$738$	12.4899	+	12.0293i	0.459761	+	0.442803i
$739$	1.82751	+	4.41201i	0.0672262	+	0.162298i	0.953922	−	0.300055i	$-0.0970051\pi$
$739$	1.82751	+	4.41201i	0.0672262	+	0.162298i	−0.886696	+	0.462354i	$0.847005\pi$
$740$	−0.00545986	−	0.0131813i	−0.000200708	−	0.000484553i
$741$	−0.120342	+	1.35192i	−0.00442088	+	0.0496640i
$742$	−14.6086	−	2.90583i	−0.536298	−	0.106676i
$743$	17.5085	+	11.6988i	0.642325	+	0.429188i	0.833615	−	0.552346i	$-0.186267\pi$
$743$	17.5085	+	11.6988i	0.642325	+	0.429188i	−0.191290	+	0.981534i	$0.561267\pi$
$744$	4.97297	+	46.0526i	0.182318	+	1.68837i
$745$	3.06665	−	0.609995i	0.112353	−	0.0223485i
$746$	−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
$750$	−1.53344	−	2.80516i	−0.0559933	−	0.102430i
$751$	−4.52121	−	22.7296i	−0.164981	−	0.829416i	−0.971286	−	0.237916i	$-0.923536\pi$
$751$	−4.52121	−	22.7296i	−0.164981	−	0.829416i	0.806305	−	0.591500i	$-0.201464\pi$
$752$	−7.13925	+	7.13925i	−0.260342	+	0.260342i
$753$	−1.75281	+	0.549740i	−0.0638759	+	0.0200336i
$754$	−0.117813	+	0.592286i	−0.00429050	+	0.0215698i
$755$	0.322449	+	0.482579i	0.0117351	+	0.0175629i
$756$	2.49701	+	0.175067i	0.0908155	+	0.00636711i
$757$	−23.7983	+	9.85760i	−0.864965	+	0.358280i	−0.770647	−	0.637262i	$-0.780067\pi$
$757$	−23.7983	+	9.85760i	−0.864965	+	0.358280i	−0.0943180	+	0.995542i	$0.530067\pi$
$758$	−5.75627	+	3.84622i	−0.209077	+	0.139701i
$759$	25.4148	+	30.3815i	0.922498	+	1.10278i
$760$	1.56750	−	2.34593i	0.0568591	−	0.0850957i
$761$	15.9336	+	15.9336i	0.577594	+	0.577594i	0.934240	−	0.356646i	$-0.116080\pi$
$761$	15.9336	+	15.9336i	0.577594	+	0.577594i	−0.356646	+	0.934240i	$0.616080\pi$
$762$	10.4260	−	19.9543i	0.377695	−	0.722870i
$763$	−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
$768$	−5.14012	+	9.83764i	−0.185478	+	0.354985i
$769$	10.2112	+	10.2112i	0.368226	+	0.368226i	0.866830	−	0.498604i	$-0.166154\pi$
$769$	10.2112	+	10.2112i	0.368226	+	0.368226i	−0.498604	+	0.866830i	$0.666154\pi$
$770$	−0.662009	+	0.990766i	−0.0238571	+	0.0357047i
$771$	22.3735	+	26.7459i	0.805761	+	0.963229i
$772$	−3.67593	+	2.45618i	−0.132300	+	0.0883998i
$773$	−2.24744	+	0.930920i	−0.0808348	+	0.0334829i	−0.422734	−	0.906254i	$-0.638930\pi$
$773$	−2.24744	+	0.930920i	−0.0808348	+	0.0334829i	0.341900	+	0.939736i	$0.388930\pi$
$774$	6.82599	−	4.74884i	0.245355	−	0.170694i
$775$	−24.7741	−	37.0771i	−0.889912	−	1.33185i
$776$	−2.67288	+	13.4375i	−0.0959507	+	0.482377i
$777$	1.08886	−	0.341503i	0.0390626	−	0.0122514i
$778$	−11.6153	+	11.6153i	−0.416429	+	0.416429i
$779$	−5.75994	−	28.9572i	−0.206371	−	1.03750i
$780$	−0.00371497	−	0.00679590i	−0.000133017	−	0.000243332i
$781$			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
$785$	−1.92639	+	0.383184i	−0.0687559	+	0.0136764i
$786$	−3.18464	−	29.4916i	−0.113592	−	1.05193i
$787$	26.3671	+	17.6179i	0.939884	+	0.628010i	0.928264	−	0.371922i	$-0.121301\pi$
$787$	26.3671	+	17.6179i	0.939884	+	0.628010i	0.0116199	+	0.999932i	$0.496301\pi$
$788$	−2.09666	−	0.417051i	−0.0746903	−	0.0148568i
$789$	0.847945	−	9.52578i	0.0301876	−	0.339127i
$790$	−0.173108	−	0.417919i	−0.00615889	−	0.0148689i
$791$	9.17479	+	22.1499i	0.326218	+	0.787560i
$792$	−22.6366	+	23.5035i	−0.804356	+	0.835159i
$793$	−0.454920	−	0.0904893i	−0.0161547	−	0.00321337i
$794$	42.5135	+	28.4066i	1.50875	+	1.00811i
$795$	−1.55191	+	0.167583i	−0.0550407	+	0.00594354i
$796$	−3.41820	+	0.679923i	−0.121155	+	0.0240992i
$797$	−41.8726	−	17.3442i	−1.48320	−	0.614363i	−0.513377	−	0.858163i	$-0.671606\pi$
$797$	−41.8726	−	17.3442i	−1.48320	−	0.614363i	−0.969825	+	0.243800i	$0.921606\pi$
$798$	21.0640	+	16.9582i	0.745658	+	0.600314i
$799$		0			0
$800$		−	7.61508i		−	0.269234i
$801$	12.1002	+	2.17142i	0.427539	+	0.0767235i
$802$	6.98204	+	35.1011i	0.246544	+	1.23946i
$803$	−11.5048	+	11.5048i	−0.405995	+	0.405995i
$804$	0.821198	+	2.61833i	0.0289614	+	0.0923415i
$805$	−0.304951	+	1.53309i	−0.0107481	+	0.0540345i
$806$	0.763166	+	1.14216i	0.0268814	+	0.0402308i
$807$	−15.1911	−	4.45280i	−0.534753	−	0.156746i
$808$	−13.9827	+	5.79181i	−0.491908	+	0.203755i
$809$	−20.9122	+	13.9731i	−0.735233	+	0.491267i	−0.865936	−	0.500155i	$-0.833276\pi$
$809$	−20.9122	+	13.9731i	−0.735233	+	0.491267i	0.130703	+	0.991422i	$0.458276\pi$
$810$	−1.61914	+	0.385814i	−0.0568907	+	0.0135561i
$811$	−12.9298	+	19.3507i	−0.454025	+	0.679496i	−0.985902	−	0.167325i	$-0.946487\pi$
$811$	−12.9298	+	19.3507i	−0.454025	+	0.679496i	0.531877	+	0.846822i	$0.321487\pi$
$812$	−1.34084	−	1.34084i	−0.0470544	−	0.0470544i
$813$	−4.06537	−	2.12413i	−0.142579	−	0.0744966i
$814$	−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
$819$	0.567770	−	0.247773i	0.0198395	−	0.00865790i
$820$	0.119131	+	0.119131i	0.00416024	+	0.00416024i
$821$	−24.0120	+	35.9365i	−0.838025	+	1.25419i	0.126965	+	0.991907i	$0.459476\pi$
$821$	−24.0120	+	35.9365i	−0.838025	+	1.25419i	−0.964990	+	0.262286i	$0.915524\pi$
$822$	−5.59653	+	4.68161i	−0.195201	+	0.163290i
$823$	14.0236	−	9.37028i	0.488833	−	0.326627i	−0.286608	−	0.958048i	$-0.592528\pi$
$823$	14.0236	−	9.37028i	0.488833	−	0.326627i	0.775441	+	0.631420i	$0.217528\pi$
$824$	44.0841	−	18.2602i	1.53574	−	0.636125i
$825$	8.83631	−	30.1459i	0.307641	−	1.04955i
$826$	12.3554	+	18.4912i	0.429900	+	0.643391i
$827$	−4.32515	+	21.7440i	−0.150400	+	0.756114i	0.829793	+	0.558071i	$0.188458\pi$
$827$	−4.32515	+	21.7440i	−0.150400	+	0.756114i	−0.980193	+	0.198042i	$0.936542\pi$
$828$	−1.87362	+	4.77510i	−0.0651127	+	0.165946i
$829$	19.3451	−	19.3451i	0.671883	−	0.671883i	−0.286267	−	0.958150i	$-0.592415\pi$
$829$	19.3451	−	19.3451i	0.671883	−	0.671883i	0.958150	+	0.286267i	$0.0924145\pi$
$830$	−0.199878	−	1.00486i	−0.00693787	−	0.0348790i
$831$	−31.4440	+	17.1888i	−1.09078	+	0.596274i
$832$			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
$836$	6.52973	−	1.29884i	0.225836	−	0.0449215i
$837$	−44.1242	+	14.7548i	−1.52516	+	0.510000i
$838$	−10.2082	−	6.82089i	−0.352636	−	0.235624i
$839$	24.3543	+	4.84436i	0.840802	+	0.167246i	0.596661	−	0.802494i	$-0.296494\pi$
$839$	24.3543	+	4.84436i	0.840802	+	0.167246i	0.244142	+	0.969740i	$0.421494\pi$
$840$	−1.28267	−	0.114178i	−0.0442564	−	0.00393952i
$841$	−5.16832	−	12.4774i	−0.178218	−	0.430256i
$842$	−6.69119	−	16.1539i	−0.230593	−	0.556702i
$843$	17.7502	+	1.58005i	0.611351	+	0.0544199i
$844$	1.36737	+	0.271986i	0.0470667	+	0.00936215i
$845$	1.51926	+	1.01514i	0.0522641	+	0.0349218i
$846$	−9.91131	−	6.35651i	−0.340758	−	0.218541i
$847$	−3.92654	+	0.781037i	−0.134917	+	0.0268367i
$848$	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
$852$	−5.37801	+	2.93989i	−0.184248	+	0.100719i
$853$	−5.82018	−	29.2600i	−0.199279	−	1.00184i	−0.942858	−	0.333196i	$-0.891873\pi$
$853$	−5.82018	−	29.2600i	−0.199279	−	1.00184i	0.743578	−	0.668649i	$-0.233127\pi$
$854$	−6.53464	+	6.53464i	−0.223611	+	0.223611i
$855$	2.63813	+	1.03513i	0.0902220	+	0.0354006i
$856$	0.793933	−	3.99137i	0.0271361	−	0.136422i
$857$	−18.9054	−	28.2940i	−0.645798	−	0.966505i	−0.999515	−	0.0311521i	$-0.990082\pi$
$857$	−18.9054	−	28.2940i	−0.645798	−	0.966505i	0.353717	−	0.935353i	$-0.384918\pi$
$858$	−0.272203	+	0.928644i	−0.00929284	+	0.0317034i
$859$	18.2111	−	7.54327i	0.621354	−	0.257373i	−0.0497206	−	0.998763i	$-0.515833\pi$
$859$	18.2111	−	7.54327i	0.621354	−	0.257373i	0.671074	+	0.741390i	$0.265833\pi$
$860$	0.0671740	−	0.0448842i	0.00229061	−	0.00153054i
$861$	−10.3359	+	8.64622i	−0.352247	+	0.294662i
$862$	10.6694	−	15.9679i	0.363402	−	0.543869i
$863$	4.36492	+	4.36492i	0.148584	+	0.148584i	0.777485	−	0.628901i	$-0.216495\pi$
$863$	4.36492	+	4.36492i	0.148584	+	0.148584i	−0.628901	+	0.777485i	$0.716495\pi$
$864$	−7.66513	−	2.09126i	−0.260773	−	0.0711460i
$865$	−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
$870$	1.11755	+	0.583916i	0.0378887	+	0.0197966i
$871$	0.480203	+	0.480203i	0.0162710	+	0.0162710i
$872$	19.0465	−	28.5050i	0.644994	−	0.965302i
$873$	−13.7591	+	0.258507i	−0.465674	+	0.00874913i
$874$	−46.0763	+	30.7872i	−1.55855	+	1.04139i
$875$	2.29522	−	0.950712i	0.0775927	−	0.0321399i
$876$	−2.02194	−	0.592666i	−0.0683149	−	0.0200243i
$877$	−5.29644	−	7.92668i	−0.178848	−	0.267665i	0.731204	−	0.682159i	$-0.238959\pi$
$877$	−5.29644	−	7.92668i	−0.178848	−	0.267665i	−0.910052	+	0.414494i	$0.863959\pi$
$878$	−6.75949	+	33.9822i	−0.228122	+	1.14685i
$879$	0.584739	+	1.86440i	0.0197228	+	0.0628847i
$880$	1.22513	−	1.22513i	0.0412992	−	0.0412992i
$881$	−8.39169	−	42.1879i	−0.282723	−	1.42135i	−0.817294	−	0.576222i	$-0.804527\pi$
$881$	−8.39169	−	42.1879i	−0.282723	−	1.42135i	0.534570	−	0.845124i	$-0.320473\pi$
$882$	−2.69548	+	15.0205i	−0.0907617	+	0.505767i
$883$			41.3162i			1.39040i	0.718816	+	0.695200i	$0.244684\pi$
$883$			41.3162i			1.39040i	−0.718816	+	0.695200i	$0.755316\pi$
$884$		0			0
$885$	1.81539	+	1.46153i	0.0610237	+	0.0491289i
$886$	11.7434	+	4.86427i	0.394527	+	0.163418i
$887$	14.5578	−	2.89572i	0.488801	−	0.0972287i	0.0554646	−	0.998461i	$-0.482336\pi$
$887$	14.5578	−	2.89572i	0.488801	−	0.0972287i	0.433337	+	0.901232i	$0.357336\pi$
$888$	−1.91538	+	0.206831i	−0.0642760	+	0.00694081i
$889$	14.5470	+	9.72002i	0.487892	+	0.325999i
$890$	−0.743294	−	0.147850i	−0.0249153	−	0.00495596i
$891$	−27.9174	−	17.1731i	−0.935267	−	0.575319i
$892$	0.0196801	+	0.0475120i	0.000658939	+	0.00159082i
$893$	7.67180	+	18.5214i	0.256727	+	0.619794i
$894$	4.48582	−	50.3935i	0.150028	−	1.68541i
$895$	−2.55114	−	0.507454i	−0.0852754	−	0.0169623i
$896$	12.4632	+	8.32768i	0.416368	+	0.278208i
$897$	0.136289	+	1.26212i	0.00455057	+	0.0421410i
$898$	−1.36228	+	0.270975i	−0.0454600	+	0.00904256i
$899$	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
$903$	3.09950	+	5.67001i	0.103145	+	0.188686i
$904$	−7.89621	−	39.6970i	−0.262624	−	1.32030i
$905$	0.211787	−	0.211787i	0.00704002	−	0.00704002i
$906$	8.96080	−	2.81041i	0.297703	−	0.0933696i
$907$	−3.33756	+	16.7791i	−0.110822	+	0.557140i	0.884982	+	0.465626i	$0.154171\pi$
$907$	−3.33756	+	16.7791i	−0.110822	+	0.557140i	−0.995804	+	0.0915140i	$0.970829\pi$
$908$	0.322250	+	0.482281i	0.0106942	+	0.0160050i
$909$	−8.68165	−	12.4790i	−0.287952	−	0.413902i
$910$	−0.0352820	+	0.0146143i	−0.00116959	+	0.000484459i
$911$	−45.9977	+	30.7347i	−1.52397	+	1.01829i	−0.539653	+	0.841887i	$0.681445\pi$
$911$	−45.9977	+	30.7347i	−1.52397	+	1.01829i	−0.984319	+	0.176398i	$0.943555\pi$
$912$	−25.2287	−	30.1591i	−0.835406	−	0.998667i
$913$	11.2087	−	16.7750i	0.370953	−	0.555171i
$914$	19.9143	+	19.9143i	0.658705	+	0.658705i
$915$	−0.448492	+	0.858366i	−0.0148267	+	0.0283767i
$916$	−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
$921$	15.7062	−	30.0601i	0.517538	−	0.990514i
$922$	−22.9019	−	22.9019i	−0.754233	−	0.754233i
$923$	−0.842708	+	1.26120i	−0.0277381	+	0.0415130i
$924$	−1.94969	−	2.33071i	−0.0641401	−	0.0766748i
$925$	1.54208	−	1.03038i	0.0507032	−	0.0338788i
$926$	−23.4364	+	9.70769i	−0.770169	+	0.319014i
$927$	27.3712	+	39.3434i	0.898989	+	1.29221i
$928$	3.34392	+	5.00453i	0.109770	+	0.164282i
$929$	6.98713	−	35.1267i	0.229240	−	1.15247i	−0.679038	−	0.734103i	$-0.737603\pi$
$929$	6.98713	−	35.1267i	0.229240	−	1.15247i	0.908278	−	0.418366i	$-0.137397\pi$
$930$	2.73673	−	0.858331i	0.0897410	−	0.0281458i
$931$	18.3724	−	18.3724i	0.602132	−	0.602132i
$932$	−0.520168	−	2.61506i	−0.0170387	−	0.0856592i
$933$	−24.4046	−	44.6440i	−0.798971	−	1.46158i
$934$		−	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	$-0.482143\pi$
$937$	−18.6808	−	7.73785i	−0.610276	−	0.252785i	−0.666347	+	0.745642i	$0.732143\pi$
$938$	13.2705	−	2.63967i	0.433298	−	0.0861884i
$939$	3.31375	+	30.6873i	0.108140	+	1.00144i
$940$	−0.0951179	−	0.0635557i	−0.00310240	−	0.00207296i
$941$	−7.61499	−	1.51472i	−0.248242	−	0.0493783i	0.0694010	−	0.997589i	$-0.477891\pi$
$941$	−7.61499	−	1.51472i	−0.248242	−	0.0493783i	−0.317643	+	0.948211i	$0.602891\pi$
$942$	−2.81788	+	31.6560i	−0.0918116	+	1.03141i
$943$	−10.5676	−	25.5124i	−0.344128	−	0.830798i
$944$	−12.3746	−	29.8749i	−0.402759	−	0.972347i
$945$	−0.162998	−	1.28315i	−0.00530234	−	0.0417407i
$946$	−9.90043	−	1.96932i	−0.321891	−	0.0640281i
$947$	2.99573	+	2.00168i	0.0973480	+	0.0650459i	0.603291	−	0.797521i	$-0.293856\pi$
$947$	2.99573	+	2.00168i	0.0973480	+	0.0650459i	−0.505943	+	0.862567i	$0.668856\pi$
$948$	1.14688	−	0.123845i	0.0372489	−	0.00402231i
$949$	−0.511424	+	0.101728i	−0.0166015	+	0.00330225i
$950$	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	$-0.118954\pi$
$954$	−4.46121	+	24.8600i	−0.144437	+	0.804871i
$955$	0.475940	+	2.39271i	0.0154011	+	0.0774264i
$956$	−4.31991	+	4.31991i	−0.139716	+	0.139716i
$957$	7.43050	+	23.6917i	0.240194	+	0.765843i
$958$	−5.82076	+	29.2629i	−0.188060	+	0.945442i
$959$	−3.15013	−	4.71450i	−0.101723	−	0.152239i
$960$	2.05153	+	0.601342i	0.0662129	+	0.0194082i
$961$	45.4292	−	18.8174i	1.46546	−	0.607013i
$962$	−0.0475037	+	0.0317410i	−0.00153158	+	0.00102337i
$963$	4.08689	−	0.0767851i	0.131698	−	0.00247436i
$964$	0.0613417	−	0.0918044i	0.00197568	−	0.00295682i
$965$	1.61537	+	1.61537i	0.0520007	+	0.0520007i
$966$	22.4171	+	11.7128i	0.721257	+	0.376853i
$967$	8.59605	−	20.7527i	0.276430	−	0.667362i	−0.723301	−	0.690533i	$-0.757376\pi$
$967$	8.59605	−	20.7527i	0.276430	−	0.667362i	0.999732	+	0.0231709i	$0.00737619\pi$
$968$	6.75869			0.217233
$969$		0			0
$970$	0.848355			0.0272390
$971$	13.1165	−	31.6660i	0.420928	−	1.01621i	−0.561147	−	0.827716i	$-0.689640\pi$
$971$	13.1165	−	31.6660i	0.420928	−	1.01621i	0.982075	−	0.188493i	$-0.0603603\pi$
$972$	0.217270	−	4.23901i	0.00696893	−	0.135966i
$973$	−6.37317	−	6.37317i	−0.204314	−	0.204314i
$974$	16.7851	−	25.1207i	0.537830	−	0.804920i
$975$	0.772229	−	0.645985i	0.0247311	−	0.0206881i
$976$	11.1726	−	7.46532i	0.357628	−	0.238959i
$977$	26.0166	−	10.7764i	0.832345	−	0.344769i	0.0745143	−	0.997220i	$-0.476259\pi$
$977$	26.0166	−	10.7764i	0.832345	−	0.344769i	0.757831	+	0.652451i	$0.226259\pi$
$978$	−7.14301	+	24.3690i	−0.228408	+	0.779235i
$979$	−8.29109	−	12.4085i	−0.264985	−	0.396577i
$980$	−0.0289251	+	0.145416i	−0.000923980	+	0.00464516i
$981$	32.0555	+	12.5777i	1.02345	+	0.401574i
$982$	−18.9356	+	18.9356i	−0.604261	+	0.604261i
$983$	8.14020	+	40.9235i	0.259632	+	1.30526i	0.861946	+	0.506999i	$0.169245\pi$
$983$	8.14020	+	40.9235i	0.259632	+	1.30526i	−0.602314	+	0.798259i	$0.705755\pi$
$984$	19.9616	−	10.9120i	0.636353	−	0.347862i
$985$			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
$989$	−12.9875	+	2.58337i	−0.412977	+	0.0821463i
$990$	1.70083	+	1.09081i	0.0540560	+	0.0346682i
$991$	−8.43842	−	5.63837i	−0.268055	−	0.179109i	0.414277	−	0.910151i	$-0.364034\pi$
$991$	−8.43842	−	5.63837i	−0.268055	−	0.179109i	−0.682333	+	0.731042i	$0.739034\pi$
$992$	13.4281	+	2.67101i	0.426341	+	0.0848046i
$993$	12.4786	+	1.11080i	0.395998	+	0.0352500i
$994$	11.5652	+	27.9208i	0.366826	+	0.885595i
$995$	0.689176	+	1.66382i	0.0218483	+	0.0527466i
$996$	2.60240	+	0.231655i	0.0824603	+	0.00734027i
$997$	39.1586	+	7.78912i	1.24016	+	0.246684i	0.771234	−	0.636552i	$-0.219640\pi$
$997$	39.1586	+	7.78912i	1.24016	+	0.246684i	0.468930	+	0.883235i	$0.344640\pi$
$998$	1.17942	+	0.788061i	0.0373338	+	0.0249456i
$999$	−0.613668	−	1.83518i	−0.0194156	−	0.0580624i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.11.2	✓	32	17.16	even	2
51.2.i.a.11.3	yes	32	51.50	odd	2
51.2.i.a.14.2	yes	32	51.20	even	16
51.2.i.a.14.3	yes	32	17.3	odd	16
816.2.cj.c.65.1		32	204.71	odd	16
816.2.cj.c.65.4		32	68.3	even	16
816.2.cj.c.113.1		32	68.67	odd	2
816.2.cj.c.113.4		32	204.203	even	2
867.2.i.b.158.2		32	17.6	odd	16
867.2.i.b.158.3		32	51.23	even	16
867.2.i.b.653.2		32	51.8	odd	8
867.2.i.b.653.3		32	17.8	even	8
867.2.i.c.224.2		32	17.5	odd	16
867.2.i.c.224.3		32	51.5	even	16
867.2.i.c.329.2		32	51.47	odd	4
867.2.i.c.329.3		32	17.13	even	4
867.2.i.d.224.2		32	17.12	odd	16
867.2.i.d.224.3		32	51.29	even	16
867.2.i.d.329.2		32	51.38	odd	4
867.2.i.d.329.3		32	17.4	even	4
867.2.i.f.131.2		32	51.44	even	16
867.2.i.f.131.3		32	17.10	odd	16
867.2.i.f.503.2		32	17.15	even	8
867.2.i.f.503.3		32	51.32	odd	8
867.2.i.g.131.2		32	51.41	even	16
867.2.i.g.131.3		32	17.7	odd	16
867.2.i.g.503.2		32	17.2	even	8
867.2.i.g.503.3		32	51.2	odd	8
867.2.i.h.65.2		32	51.14	even	16	inner
867.2.i.h.65.3		32	17.14	odd	16	inner
867.2.i.h.827.2		32	1.1	even	1	trivial
867.2.i.h.827.3		32	3.2	odd	2	inner
867.2.i.i.158.2		32	17.11	odd	16
867.2.i.i.158.3		32	51.11	even	16
867.2.i.i.653.2		32	51.26	odd	8
867.2.i.i.653.3		32	17.9	even	8

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} +(-0.802099 + 1.53513i) q^{3} +(0.192538 + 0.192538i) q^{4} +(0.0781694 - 0.116989i) q^{5} +(-1.46076 - 1.74623i) q^{6} +(1.47102 - 0.982905i) q^{7} +(-2.75940 + 1.14298i) q^{8} +(-1.71327 - 2.46266i) q^{9} +(0.102748 + 0.153773i) q^{10} +(-0.710485 + 3.57185i) q^{11} +(-0.450006 + 0.141137i) q^{12} +(-0.0825311 + 0.0825311i) q^{13} +(0.453674 + 2.28077i) q^{14} +(0.116894 + 0.213837i) q^{15} -3.38128i q^{16} +(3.85237 - 0.841809i) q^{18} +(-6.20278 - 2.56928i) q^{19} +(0.0375753 - 0.00747420i) q^{20} +(0.328986 + 3.04660i) q^{21} +(-3.98016 - 2.65946i) q^{22} +(-6.15884 - 1.22507i) q^{23} +(0.458684 - 5.15283i) q^{24} +(1.90584 + 4.60111i) q^{25} +(-0.0587094 - 0.141737i) q^{26} +(5.15473 - 0.654807i) q^{27} +(0.472474 + 0.0939809i) q^{28} +(-3.27292 - 2.18690i) q^{29} +(-0.318476 + 0.0343905i) q^{30} +(-8.78185 + 1.74682i) q^{31} +(-1.41268 - 0.585150i) q^{32} +(-4.91339 - 3.95567i) q^{33} -0.248926i q^{35} +(0.144285 - 0.804026i) q^{36} +(-0.0726522 - 0.365247i) q^{37} +(6.24010 - 6.24010i) q^{38} +(-0.0604982 - 0.192895i) q^{39} +(-0.0819847 + 0.412165i) q^{40} +(2.44315 + 3.65643i) q^{41} +(-3.86518 - 1.13296i) q^{42} +(1.94823 - 0.806985i) q^{43} +(-0.824512 + 0.550921i) q^{44} +(-0.422029 + 0.00792913i) q^{45} +(4.58563 - 6.86288i) q^{46} +(-2.11141 - 2.11141i) q^{47} +(5.19072 + 2.71212i) q^{48} +(-1.48098 + 3.57541i) q^{49} -6.54610 q^{50} -0.0317807 q^{52} +(-2.45113 + 5.91755i) q^{53} +(-1.79769 + 6.58912i) q^{54} +(0.362328 + 0.362328i) q^{55} +(-2.93569 + 4.39357i) q^{56} +(8.91943 - 7.46129i) q^{57} +(4.30201 - 2.87451i) q^{58} +(8.83540 - 3.65974i) q^{59} +(-0.0186653 + 0.0636782i) q^{60} +(2.20784 + 3.30427i) q^{61} +(2.29606 - 11.5431i) q^{62} +(-4.94082 - 1.93864i) q^{63} +(6.20303 - 6.20303i) q^{64} +(0.00320381 + 0.0161066i) q^{65} +(7.27511 - 3.97693i) q^{66} -5.81844i q^{67} +(6.82064 - 8.47201i) q^{69} +(0.302288 + 0.125212i) q^{70} +(12.7462 - 2.53537i) q^{71} +(7.54238 + 4.83722i) q^{72} +(3.71467 + 2.48206i) q^{73} +(0.480089 + 0.0954957i) q^{74} +(-8.59199 - 0.764823i) q^{75} +(-0.699588 - 1.68895i) q^{76} +(2.46565 + 5.95260i) q^{77} +(0.264676 + 0.0235604i) q^{78} +(-2.39893 - 0.477177i) q^{79} +(-0.395572 - 0.264312i) q^{80} +(-3.12939 + 8.43842i) q^{81} +(-5.66918 + 1.12767i) q^{82} +(-5.11813 - 2.12000i) q^{83} +(-0.523244 + 0.649928i) q^{84} +2.77180i q^{86} +(5.98239 - 3.27027i) q^{87} +(-2.12204 - 10.6682i) q^{88} +(-2.89760 + 2.89760i) q^{89} +(0.202655 - 0.516488i) q^{90} +(-0.0402848 + 0.202525i) q^{91} +(-0.949937 - 1.42168i) q^{92} +(4.36231 - 14.8824i) q^{93} +(3.62608 - 1.50197i) q^{94} +(-0.785444 + 0.524817i) q^{95} +(2.03139 - 1.69930i) q^{96} +(2.54849 - 3.81409i) q^{97} +(-3.59692 - 3.59692i) q^{98} +(10.0135 - 4.36987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} - 16 q^{4} + 8 q^{6} + 16 q^{7} - 8 q^{9} + 16 q^{10} - 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} + 16 q^{22} - 16 q^{24} + 16 q^{25} + 8 q^{27} - 32 q^{28} - 8 q^{30}+ \cdots + 64 q^{99}+O(q^{100}) \) 32 * q + 8 * q^3 - 16 * q^4 + 8 * q^6 + 16 * q^7 - 8 * q^9 + 16 * q^10 - 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 + 16 * q^22 - 16 * q^24 + 16 * q^25 + 8 * q^27 - 32 * q^28 - 8 * q^30 - 16 * q^31 + 8 * q^36 - 16 * q^37 + 24 * q^39 - 16 * q^40 - 56 * q^42 + 16 * q^43 + 40 * q^45 + 32 * q^46 + 64 * q^48 - 48 * q^49 - 96 * q^52 + 24 * q^54 - 48 * q^55 - 8 * q^57 + 48 * q^58 + 32 * q^60 + 32 * q^61 - 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 - 48 * q^73 - 88 * q^75 + 48 * q^76 - 96 * q^78 - 16 * q^79 + 48 * q^81 - 112 * q^82 - 56 * q^87 - 16 * q^88 + 88 * q^90 - 16 * q^91 - 72 * q^93 - 48 * q^94 + 112 * q^96 + 16 * q^97 + 64 * q^99

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