LMFDB - Embedded newform 867.2.h.k.733.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(688,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("867.688");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.h (of order $8$, degree $4$, not 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8x^{14} + 32x^{12} + 296x^{10} + 1057x^{8} + 1184x^{6} + 512x^{4} - 512x^{2} + 256 $ x^16 - 8x^14 + 32x^12 + 296x^10 + 1057x^8 + 1184x^6 + 512x^4 - 512*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			733.2
Root			$-2.83302 + 1.17347i$ of defining polynomial
Character	$\chi$	$=$	867.733
Dual form			867.2.h.k.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16830 - 1.16830i) q^{2} +(0.923880 - 0.382683i) q^{3} +0.729840i q^{4} +(-1.55616 - 3.75690i) q^{5} +(-1.52645 - 0.632278i) q^{6} +(0.352980 - 0.852170i) q^{7} +(-1.48392 + 1.48392i) q^{8} +(0.707107 - 0.707107i) q^{9} +(-2.57112 + 6.20723i) q^{10} +(-2.09735 - 0.868752i) q^{11} +(0.279298 + 0.674285i) q^{12} -3.57461i q^{13} +(-1.40798 + 0.583202i) q^{14} +(-2.87540 - 2.87540i) q^{15} +4.92701 q^{16} -1.65222 q^{18} +(1.22318 + 1.22318i) q^{19} +(2.74194 - 1.13575i) q^{20} -0.922382i q^{21} +(1.43537 + 3.46530i) q^{22} +(-4.71048 - 1.95114i) q^{23} +(-0.803094 + 1.93884i) q^{24} +(-8.15712 + 8.15712i) q^{25} +(-4.17620 + 4.17620i) q^{26} +(0.382683 - 0.923880i) q^{27} +(0.621948 + 0.257619i) q^{28} +(0.843328 + 2.03597i) q^{29} +6.71866i q^{30} +(3.81828 - 1.58158i) q^{31} +(-2.78837 - 2.78837i) q^{32} -2.27016 q^{33} -3.75081 q^{35} +(0.516075 + 0.516075i) q^{36} +(5.50127 - 2.27870i) q^{37} -2.85808i q^{38} +(-1.36794 - 3.30250i) q^{39} +(7.88417 + 3.26573i) q^{40} +(1.93259 - 4.66568i) q^{41} +(-1.07762 + 1.07762i) q^{42} +(-3.69920 + 3.69920i) q^{43} +(0.634051 - 1.53073i) q^{44} +(-3.75690 - 1.55616i) q^{45} +(3.22373 + 7.78276i) q^{46} +6.96130i q^{47} +(4.55197 - 1.88549i) q^{48} +(4.34815 + 4.34815i) q^{49} +19.0599 q^{50} +2.60889 q^{52} +(-1.90604 - 1.90604i) q^{53} +(-1.52645 + 0.632278i) q^{54} +9.23146i q^{55} +(0.740760 + 1.78835i) q^{56} +(1.59816 + 0.661981i) q^{57} +(1.39337 - 3.36388i) q^{58} +(5.23146 - 5.23146i) q^{59} +(2.09859 - 2.09859i) q^{60} +(1.48873 - 3.59411i) q^{61} +(-6.30864 - 2.61313i) q^{62} +(-0.352980 - 0.852170i) q^{63} -3.33873i q^{64} +(-13.4294 + 5.56265i) q^{65} +(2.65222 + 2.65222i) q^{66} -12.0419 q^{67} -5.09859 q^{69} +(4.38206 + 4.38206i) q^{70} +(1.40798 - 0.583202i) q^{71} +2.09859i q^{72} +(0.445835 + 1.07634i) q^{73} +(-9.08933 - 3.76492i) q^{74} +(-4.41460 + 10.6578i) q^{75} +(-0.892728 + 0.892728i) q^{76} +(-1.48065 + 1.48065i) q^{77} +(-2.26015 + 5.45647i) q^{78} +(-10.9791 - 4.54769i) q^{79} +(-7.66721 - 18.5103i) q^{80} -1.00000i q^{81} +(-7.70875 + 3.19307i) q^{82} +(4.51494 + 4.51494i) q^{83} +0.673192 q^{84} +8.64354 q^{86} +(1.55827 + 1.55827i) q^{87} +(4.40148 - 1.82315i) q^{88} +10.3597i q^{89} +(2.57112 + 6.20723i) q^{90} +(-3.04617 - 1.26177i) q^{91} +(1.42402 - 3.43790i) q^{92} +(2.92238 - 2.92238i) q^{93} +(8.13287 - 8.13287i) q^{94} +(2.69190 - 6.49883i) q^{95} +(-3.64318 - 1.50906i) q^{96} +(5.53723 + 13.3680i) q^{97} -10.1599i q^{98} +(-2.09735 + 0.868752i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 32 q^{8} - 8 q^{15} - 24 q^{16} - 8 q^{18} - 32 q^{25} - 40 q^{26} - 16 q^{32} - 24 q^{33} + 16 q^{35} - 48 q^{42} - 48 q^{43} - 32 q^{49} + 120 q^{50} - 32 q^{52} - 16 q^{53} - 56 q^{59}+ \cdots + 48 q^{94}+O(q^{100}) $ 16 * q + 8 * q^2 - 32 * q^8 - 8 * q^15 - 24 * q^16 - 8 * q^18 - 32 * q^25 - 40 * q^26 - 16 * q^32 - 24 * q^33 + 16 * q^35 - 48 * q^42 - 48 * q^43 - 32 * q^49 + 120 * q^50 - 32 * q^52 - 16 * q^53 - 56 * q^59 - 24 * q^60 + 24 * q^66 - 16 * q^67 - 24 * q^69 + 64 * q^70 + 64 * q^76 + 40 * q^77 - 16 * q^83 - 96 * q^84 - 16 * q^86 - 8 * q^87 + 16 * q^93 + 48 * q^94

Character values

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

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−1.16830	−	1.16830i	−0.826111	−	0.826111i	0.160865	−	0.986976i	$-0.448572\pi$
$2$	−1.16830	−	1.16830i	−0.826111	−	0.826111i	−0.986976	+	0.160865i	$0.948572\pi$
$3$	0.923880	−	0.382683i	0.533402	−	0.220942i
$3$	0.923880	−	0.382683i	0.533402	−	0.220942i
$4$			0.729840i			0.364920i
$5$	−1.55616	−	3.75690i	−0.695935	−	1.68014i	−0.732466	−	0.680803i	$-0.761631\pi$
$5$	−1.55616	−	3.75690i	−0.695935	−	1.68014i	0.0365315	−	0.999333i	$-0.488369\pi$
$6$	−1.52645	−	0.632278i	−0.623173	−	0.258127i
$7$	0.352980	−	0.852170i	0.133414	−	0.322090i	−0.843028	−	0.537870i	$-0.819229\pi$
$7$	0.352980	−	0.852170i	0.133414	−	0.322090i	0.976442	+	0.215780i	$0.0692293\pi$
$8$	−1.48392	+	1.48392i	−0.524647	+	0.524647i
$9$	0.707107	−	0.707107i	0.235702	−	0.235702i
$10$	−2.57112	+	6.20723i	−0.813059	+	1.96290i
$11$	−2.09735	−	0.868752i	−0.632376	−	0.261939i	0.0433862	−	0.999058i	$-0.486185\pi$
$11$	−2.09735	−	0.868752i	−0.632376	−	0.261939i	−0.675762	+	0.737120i	$0.736185\pi$
$12$	0.279298	+	0.674285i	0.0806263	+	0.194649i
$13$		−	3.57461i		−	0.991417i	−0.868489	−	0.495709i	$-0.834908\pi$
$13$		−	3.57461i		−	0.991417i	0.868489	−	0.495709i	$-0.165092\pi$
$14$	−1.40798	+	0.583202i	−0.376297	+	0.155867i
$15$	−2.87540	−	2.87540i	−0.742426	−	0.742426i
$16$	4.92701			1.23175
$17$		0			0
$17$		0			0
$18$	−1.65222			−0.389433
$19$	1.22318	+	1.22318i	0.280617	+	0.280617i	0.833355	−	0.552738i	$-0.186417\pi$
$19$	1.22318	+	1.22318i	0.280617	+	0.280617i	−0.552738	+	0.833355i	$0.686417\pi$
$20$	2.74194	−	1.13575i	0.613115	−	0.253961i
$21$		−	0.922382i		−	0.201280i
$22$	1.43537	+	3.46530i	0.306022	+	0.738804i
$23$	−4.71048	−	1.95114i	−0.982203	−	0.406842i	−0.166962	−	0.985963i	$-0.553396\pi$
$23$	−4.71048	−	1.95114i	−0.982203	−	0.406842i	−0.815241	+	0.579122i	$0.803396\pi$
$24$	−0.803094	+	1.93884i	−0.163931	+	0.395764i
$25$	−8.15712	+	8.15712i	−1.63142	+	1.63142i
$26$	−4.17620	+	4.17620i	−0.819021	+	0.819021i
$27$	0.382683	−	0.923880i	0.0736475	−	0.177801i
$28$	0.621948	+	0.257619i	0.117537	+	0.0486855i
$29$	0.843328	+	2.03597i	0.156602	+	0.378071i	0.982635	−	0.185552i	$-0.0594072\pi$
$29$	0.843328	+	2.03597i	0.156602	+	0.378071i	−0.826032	+	0.563623i	$0.809407\pi$
$30$			6.71866i			1.22665i
$31$	3.81828	−	1.58158i	0.685783	−	0.284061i	−0.0124592	−	0.999922i	$-0.503966\pi$
$31$	3.81828	−	1.58158i	0.685783	−	0.284061i	0.698242	+	0.715862i	$0.253966\pi$
$32$	−2.78837	−	2.78837i	−0.492919	−	0.492919i
$33$	−2.27016			−0.395184
$34$		0			0
$35$	−3.75081			−0.634003
$36$	0.516075	+	0.516075i	0.0860125	+	0.0860125i
$37$	5.50127	−	2.27870i	0.904403	−	0.374616i	0.118492	−	0.992955i	$-0.462194\pi$
$37$	5.50127	−	2.27870i	0.904403	−	0.374616i	0.785912	+	0.618339i	$0.212194\pi$
$38$		−	2.85808i		−	0.463642i
$39$	−1.36794	−	3.30250i	−0.219046	−	0.528824i
$40$	7.88417	+	3.26573i	1.24660	+	0.516358i
$41$	1.93259	−	4.66568i	0.301820	−	0.728657i	−0.698100	−	0.716000i	$-0.745971\pi$
$41$	1.93259	−	4.66568i	0.301820	−	0.728657i	0.999920	−	0.0126571i	$-0.00402900\pi$
$42$	−1.07762	+	1.07762i	−0.166280	+	0.166280i
$43$	−3.69920	+	3.69920i	−0.564123	+	0.564123i	−0.930476	−	0.366353i	$-0.880606\pi$
$43$	−3.69920	+	3.69920i	−0.564123	+	0.564123i	0.366353	+	0.930476i	$0.380606\pi$
$44$	0.634051	−	1.53073i	0.0955867	−	0.230767i
$45$	−3.75690	−	1.55616i	−0.560045	−	0.231978i
$46$	3.22373	+	7.78276i	0.475312	+	1.14751i
$47$			6.96130i			1.01541i	0.861531	+	0.507705i	$0.169506\pi$
$47$			6.96130i			1.01541i	−0.861531	+	0.507705i	$0.830494\pi$
$48$	4.55197	−	1.88549i	0.657020	−	0.272147i
$49$	4.34815	+	4.34815i	0.621164	+	0.621164i
$50$	19.0599			2.69548
$51$		0			0
$52$	2.60889			0.361788
$53$	−1.90604	−	1.90604i	−0.261815	−	0.261815i	0.563976	−	0.825791i	$-0.309271\pi$
$53$	−1.90604	−	1.90604i	−0.261815	−	0.261815i	−0.825791	+	0.563976i	$0.809271\pi$
$54$	−1.52645	+	0.632278i	−0.207724	+	0.0860422i
$55$			9.23146i			1.24477i
$56$	0.740760	+	1.78835i	0.0989882	+	0.238979i
$57$	1.59816	+	0.661981i	0.211682	+	0.0876816i
$58$	1.39337	−	3.36388i	0.182958	−	0.441700i
$59$	5.23146	−	5.23146i	0.681078	−	0.681078i	−0.279165	−	0.960243i	$-0.590058\pi$
$59$	5.23146	−	5.23146i	0.681078	−	0.681078i	0.960243	+	0.279165i	$0.0900577\pi$
$60$	2.09859	−	2.09859i	0.270926	−	0.270926i
$61$	1.48873	−	3.59411i	0.190612	−	0.460178i	−0.799463	−	0.600715i	$-0.794883\pi$
$61$	1.48873	−	3.59411i	0.190612	−	0.460178i	0.990075	+	0.140537i	$0.0448828\pi$
$62$	−6.30864	−	2.61313i	−0.801199	−	0.331867i
$63$	−0.352980	−	0.852170i	−0.0444714	−	0.107363i
$64$		−	3.33873i		−	0.417341i
$65$	−13.4294	+	5.56265i	−1.66572	+	0.689962i
$66$	2.65222	+	2.65222i	0.326466	+	0.326466i
$67$	−12.0419			−1.47116			−0.735578	−	0.677440i	$-0.763090\pi$
$67$	−12.0419			−1.47116			−0.735578	+	0.677440i	$0.763090\pi$
$68$		0			0
$69$	−5.09859			−0.613798
$70$	4.38206	+	4.38206i	0.523757	+	0.523757i
$71$	1.40798	−	0.583202i	0.167096	−	0.0692134i	−0.297567	−	0.954701i	$-0.596175\pi$
$71$	1.40798	−	0.583202i	0.167096	−	0.0692134i	0.464663	+	0.885487i	$0.346175\pi$
$72$			2.09859i			0.247321i
$73$	0.445835	+	1.07634i	0.0521810	+	0.125976i	0.947820	−	0.318805i	$-0.103281\pi$
$73$	0.445835	+	1.07634i	0.0521810	+	0.125976i	−0.895639	+	0.444781i	$0.853281\pi$
$74$	−9.08933	−	3.76492i	−1.05661	−	0.437663i
$75$	−4.41460	+	10.6578i	−0.509754	+	1.23066i
$76$	−0.892728	+	0.892728i	−0.102403	+	0.102403i
$77$	−1.48065	+	1.48065i	−0.168736	+	0.168736i
$78$	−2.26015	+	5.45647i	−0.255911	+	0.617824i
$79$	−10.9791	−	4.54769i	−1.23524	−	0.511655i	−0.333019	−	0.942920i	$-0.608067\pi$
$79$	−10.9791	−	4.54769i	−1.23524	−	0.511655i	−0.902225	+	0.431265i	$0.858067\pi$
$80$	−7.66721	−	18.5103i	−0.857220	−	2.06951i
$81$		−	1.00000i		−	0.111111i
$82$	−7.70875	+	3.19307i	−0.851289	+	0.352615i
$83$	4.51494	+	4.51494i	0.495579	+	0.495579i	0.910058	−	0.414480i	$-0.136036\pi$
$83$	4.51494	+	4.51494i	0.495579	+	0.495579i	−0.414480	+	0.910058i	$0.636036\pi$
$84$	0.673192			0.0734513
$85$		0			0
$86$	8.64354			0.932057
$87$	1.55827	+	1.55827i	0.167064	+	0.167064i
$88$	4.40148	−	1.82315i	0.469199	−	0.194349i
$89$			10.3597i			1.09813i	0.835781	+	0.549063i	$0.185015\pi$
$89$			10.3597i			1.09813i	−0.835781	+	0.549063i	$0.814985\pi$
$90$	2.57112	+	6.20723i	0.271020	+	0.654300i
$91$	−3.04617	−	1.26177i	−0.319326	−	0.132269i
$92$	1.42402	−	3.43790i	0.148465	−	0.358426i
$93$	2.92238	−	2.92238i	0.303037	−	0.303037i
$94$	8.13287	−	8.13287i	0.838842	−	0.838842i
$95$	2.69190	−	6.49883i	0.276184	−	0.666766i
$96$	−3.64318	−	1.50906i	−0.371831	−	0.154017i
$97$	5.53723	+	13.3680i	0.562220	+	1.35732i	0.907987	+	0.418999i	$0.137619\pi$
$97$	5.53723	+	13.3680i	0.562220	+	1.35732i	−0.345767	+	0.938321i	$0.612381\pi$
$98$		−	10.1599i		−	1.02630i
$99$	−2.09735	+	0.868752i	−0.210792	+	0.0873129i
$100$	−5.95339	−	5.95339i	−0.595339	−	0.595339i
$101$	−0.265746			−0.0264427			−0.0132213	−	0.999913i	$-0.504209\pi$
$101$	−0.265746			−0.0264427			−0.0132213	+	0.999913i	$0.504209\pi$
$102$		0			0
$103$	−3.03429			−0.298977			−0.149489	−	0.988763i	$-0.547763\pi$
$103$	−3.03429			−0.298977			−0.149489	+	0.988763i	$0.547763\pi$
$104$	5.30445	+	5.30445i	0.520144	+	0.520144i
$105$	−3.46530	+	1.43537i	−0.338178	+	0.140078i
$106$			4.45366i			0.432577i
$107$	−7.52066	−	18.1565i	−0.727050	−	1.75525i	−0.652185	−	0.758060i	$-0.726147\pi$
$107$	−7.52066	−	18.1565i	−0.727050	−	1.75525i	−0.0748654	−	0.997194i	$-0.523853\pi$
$108$	0.674285	+	0.279298i	0.0648831	+	0.0268754i
$109$	−0.273863	+	0.661164i	−0.0262313	+	0.0633280i	−0.936452	−	0.350795i	$-0.885912\pi$
$109$	−0.273863	+	0.661164i	−0.0262313	+	0.0633280i	0.910221	+	0.414123i	$0.135912\pi$
$110$	10.7851	−	10.7851i	1.02832	−	1.02832i
$111$	4.21049	−	4.21049i	0.399642	−	0.399642i
$112$	1.73914	−	4.19865i	0.164333	−	0.396736i
$113$	10.8903	+	4.51092i	1.02447	+	0.424351i	0.830715	−	0.556698i	$-0.187932\pi$
$113$	10.8903	+	4.51092i	1.02447	+	0.424351i	0.193759	+	0.981049i	$0.437932\pi$
$114$	−1.09374	−	2.64052i	−0.102438	−	0.247308i
$115$			20.7331i			1.93337i
$116$	−1.48594	+	0.615495i	−0.137966	+	0.0571473i
$117$	−2.52763	−	2.52763i	−0.233679	−	0.233679i
$118$	−12.2238			−1.12529
$119$		0			0
$120$	8.53377			0.779023
$121$	−4.13401	−	4.13401i	−0.375819	−	0.375819i
$122$	−5.93826	+	2.45971i	−0.537625	+	0.222692i
$123$		−	5.05010i		−	0.455352i
$124$	1.15430	+	2.78673i	0.103659	+	0.250256i
$125$	24.5547	+	10.1709i	2.19624	+	0.909713i
$126$	−0.583202	+	1.40798i	−0.0519558	+	0.125432i
$127$	−1.98731	+	1.98731i	−0.176345	+	0.176345i	−0.789760	−	0.613415i	$-0.789795\pi$
$127$	−1.98731	+	1.98731i	−0.176345	+	0.176345i	0.613415	+	0.789760i	$0.289795\pi$
$128$	−9.47738	+	9.47738i	−0.837690	+	0.837690i
$129$	−2.00199	+	4.83324i	−0.176266	+	0.425543i
$130$	22.1884	+	9.19074i	1.94605	+	0.806081i
$131$	−3.03354	−	7.32361i	−0.265041	−	0.639866i	0.734195	−	0.678939i	$-0.237560\pi$
$131$	−3.03354	−	7.32361i	−0.265041	−	0.639866i	−0.999236	+	0.0390722i	$0.987560\pi$
$132$		−	1.65685i		−	0.144211i
$133$	1.47412	−	0.610600i	0.127822	−	0.0529457i
$134$	14.0686	+	14.0686i	1.21534	+	1.21534i
$135$	−4.06644			−0.349983
$136$		0			0
$137$	−0.103218			−0.00881851			−0.00440926	−	0.999990i	$-0.501404\pi$
$137$	−0.103218			−0.00881851			−0.00440926	+	0.999990i	$0.501404\pi$
$138$	5.95667	+	5.95667i	0.507065	+	0.507065i
$139$	−13.3467	+	5.52838i	−1.13205	+	0.468911i	−0.868478	−	0.495728i	$-0.834901\pi$
$139$	−13.3467	+	5.52838i	−1.13205	+	0.468911i	−0.263574	+	0.964639i	$0.584901\pi$
$140$		−	2.73749i		−	0.231360i
$141$	2.66397	+	6.43140i	0.224347	+	0.541622i
$142$	−2.32629	−	0.963580i	−0.195218	−	0.0808619i
$143$	−3.10545	+	7.49721i	−0.259691	+	0.626948i
$144$	3.48392	−	3.48392i	0.290327	−	0.290327i
$145$	6.33660	−	6.33660i	0.526226	−	0.526226i
$146$	0.736619	−	1.77836i	0.0609630	−	0.147178i
$147$	5.68113	+	2.35320i	0.468572	+	0.194089i
$148$	1.66309	+	4.01505i	0.136705	+	0.330035i
$149$		−	3.59557i		−	0.294561i	−0.989095	−	0.147280i	$-0.952948\pi$
$149$		−	3.59557i		−	0.294561i	0.989095	−	0.147280i	$-0.0470520\pi$
$150$	17.6090	−	7.29390i	1.43777	−	0.595545i
$151$	−5.36573	−	5.36573i	−0.436657	−	0.436657i	0.454229	−	0.890885i	$-0.349915\pi$
$151$	−5.36573	−	5.36573i	−0.436657	−	0.436657i	−0.890885	+	0.454229i	$0.849915\pi$
$152$	−3.63022			−0.294450
$153$		0			0
$154$	3.45968			0.278789
$155$	−11.8837	−	11.8837i	−0.954520	−	0.954520i
$156$	2.41030	−	0.998380i	0.192979	−	0.0799343i
$157$		−	18.9569i		−	1.51292i	−0.654038	−	0.756462i	$-0.726926\pi$
$157$		−	18.9569i		−	1.51292i	0.654038	−	0.756462i	$-0.273074\pi$
$158$	7.51379	+	18.1399i	0.597765	+	1.44313i
$159$	−2.49037	−	1.03154i	−0.197499	−	0.0818068i
$160$	−6.13648	+	14.8148i	−0.485131	+	1.17121i
$161$	−3.32541	+	3.32541i	−0.262079	+	0.262079i
$162$	−1.16830	+	1.16830i	−0.0917902	+	0.0917902i
$163$	5.14060	−	12.4105i	0.402643	−	0.972067i	−0.584379	−	0.811481i	$-0.698662\pi$
$163$	5.14060	−	12.4105i	0.402643	−	0.972067i	0.987022	−	0.160586i	$-0.0513383\pi$
$164$	3.40520	+	1.41048i	0.265902	+	0.110140i
$165$	3.53273	+	8.52876i	0.275022	+	0.663963i
$166$		−	10.5496i		−	0.818806i
$167$	1.97460	−	0.817904i	0.152799	−	0.0632913i	−0.304973	−	0.952361i	$-0.598648\pi$
$167$	1.97460	−	0.817904i	0.152799	−	0.0632913i	0.457772	+	0.889070i	$0.348648\pi$
$168$	1.36875	+	1.36875i	0.105601	+	0.105601i
$169$	0.222197			0.0170921
$170$		0			0
$171$	1.72984			0.132284
$172$	−2.69983	−	2.69983i	−0.205860	−	0.205860i
$173$	−4.87804	+	2.02055i	−0.370870	+	0.153619i	−0.560331	−	0.828269i	$-0.689326\pi$
$173$	−4.87804	+	2.02055i	−0.370870	+	0.153619i	0.189461	+	0.981888i	$0.439326\pi$
$174$		−	3.64104i		−	0.276027i
$175$	4.07195	+	9.83056i	0.307810	+	0.743120i
$176$	−10.3337	−	4.28036i	−0.778931	−	0.322644i
$177$	2.83125	−	6.83523i	0.212809	−	0.513767i
$178$	12.1032	−	12.1032i	0.907175	−	0.907175i
$179$	−5.49860	+	5.49860i	−0.410985	+	0.410985i	−0.882081	−	0.471097i	$-0.843858\pi$
$179$	−5.49860	+	5.49860i	−0.410985	+	0.410985i	0.471097	+	0.882081i	$0.343858\pi$
$180$	1.13575	−	2.74194i	0.0846536	−	0.204372i
$181$	−0.846119	−	0.350474i	−0.0628915	−	0.0260505i	0.351016	−	0.936369i	$-0.385836\pi$
$181$	−0.846119	−	0.350474i	−0.0628915	−	0.0260505i	−0.413907	+	0.910319i	$0.635836\pi$
$182$	2.08472	+	5.03296i	0.154530	+	0.373067i
$183$		−	3.89023i		−	0.287574i
$184$	9.88535	−	4.09465i	0.728758	−	0.301861i
$185$	−17.1217	−	17.1217i	−1.25881	−	1.25881i
$186$	−6.82843			−0.500685
$187$		0			0
$188$	−5.08064			−0.370544
$189$	−0.652223	−	0.652223i	−0.0474422	−	0.0474422i
$190$	−10.7375	+	4.44763i	−0.778982	+	0.322665i
$191$		−	19.1658i		−	1.38679i	−0.720560	−	0.693393i	$-0.756115\pi$
$191$		−	19.1658i		−	1.38679i	0.720560	−	0.693393i	$-0.243885\pi$
$192$	−1.27768	−	3.08459i	−0.0922084	−	0.222611i
$193$	4.35274	+	1.80296i	0.313317	+	0.129780i	0.533800	−	0.845611i	$-0.320763\pi$
$193$	4.35274	+	1.80296i	0.313317	+	0.129780i	−0.220483	+	0.975391i	$0.570763\pi$
$194$	9.14873	−	22.0870i	0.656841	−	1.58575i
$195$	−10.2784	+	10.2784i	−0.736054	+	0.736054i
$196$	−3.17345	+	3.17345i	−0.226675	+	0.226675i
$197$	5.70002	−	13.7611i	0.406109	−	0.980435i	−0.580042	−	0.814587i	$-0.696964\pi$
$197$	5.70002	−	13.7611i	0.406109	−	0.980435i	0.986151	−	0.165848i	$-0.0530362\pi$
$198$	3.46530	+	1.43537i	0.246268	+	0.102007i
$199$	−7.18821	−	17.3539i	−0.509559	−	1.23018i	−0.944138	−	0.329550i	$-0.893103\pi$
$199$	−7.18821	−	17.3539i	−0.509559	−	1.23018i	0.434579	−	0.900634i	$-0.356897\pi$
$200$		−	24.2091i		−	1.71184i
$201$	−11.1253	+	4.60825i	−0.784718	+	0.325041i
$202$	0.310470	+	0.310470i	0.0218446	+	0.0218446i
$203$	2.03268			0.142666
$204$		0			0
$205$	−20.5359			−1.43429
$206$	3.54495	+	3.54495i	0.246988	+	0.246988i
$207$	−4.71048	+	1.95114i	−0.327401	+	0.135614i
$208$		−	17.6121i		−	1.22118i
$209$	−1.50280	−	3.62809i	−0.103951	−	0.250960i
$210$	5.72544	+	2.37156i	0.395093	+	0.163653i
$211$	2.25043	−	5.43302i	0.154926	−	0.374025i	−0.827291	−	0.561774i	$-0.810119\pi$
$211$	2.25043	−	5.43302i	0.154926	−	0.374025i	0.982217	+	0.187749i	$0.0601192\pi$
$212$	1.39111	−	1.39111i	0.0955417	−	0.0955417i
$213$	1.07762	−	1.07762i	0.0738371	−	0.0738371i
$214$	−12.4258	+	29.9986i	−0.849411	+	2.05066i
$215$	19.6541	+	8.14098i	1.34040	+	0.555210i
$216$	0.803094	+	1.93884i	0.0546436	+	0.131921i
$217$		−	3.81209i		−	0.258781i
$218$	1.09239	−	0.452483i	0.0739860	−	0.0306460i
$219$	0.823796	+	0.823796i	0.0556670	+	0.0556670i
$220$	−6.73749			−0.454242
$221$		0			0
$222$	−9.83822			−0.660298
$223$	−3.94839	−	3.94839i	−0.264404	−	0.264404i	0.562437	−	0.826840i	$-0.309864\pi$
$223$	−3.94839	−	3.94839i	−0.264404	−	0.264404i	−0.826840	+	0.562437i	$0.809864\pi$
$224$	−3.36041	+	1.39193i	−0.224527	+	0.0930020i
$225$			11.5359i			0.769060i
$226$	−7.45304	−	17.9932i	−0.495769	−	1.19689i
$227$	−25.4343	−	10.5352i	−1.68813	−	0.699248i	−0.688472	−	0.725263i	$-0.741718\pi$
$227$	−25.4343	−	10.5352i	−1.68813	−	0.699248i	−0.999662	+	0.0260154i	$0.991718\pi$
$228$	−0.483141	+	1.16640i	−0.0319968	+	0.0772470i
$229$	2.52451	−	2.52451i	0.166824	−	0.166824i	−0.618758	−	0.785582i	$-0.712364\pi$
$229$	2.52451	−	2.52451i	0.166824	−	0.166824i	0.785582	+	0.618758i	$0.212364\pi$
$230$	24.2224	−	24.2224i	1.59718	−	1.59718i
$231$	−0.801322	+	1.93456i	−0.0527231	+	0.127285i
$232$	−4.27267	−	1.76980i	−0.280514	−	0.116193i
$233$	−0.524614	−	1.26653i	−0.0343686	−	0.0829731i	0.905763	−	0.423784i	$-0.139298\pi$
$233$	−0.524614	−	1.26653i	−0.0343686	−	0.0829731i	−0.940132	+	0.340811i	$0.889298\pi$
$234$			5.90604i			0.386090i
$235$	26.1529	−	10.8329i	1.70603	−	0.706659i
$236$	3.81813	+	3.81813i	0.248539	+	0.248539i
$237$	−11.8837			−0.771928
$238$		0			0
$239$	21.6121			1.39797			0.698986	−	0.715135i	$-0.253635\pi$
$239$	21.6121			1.39797			0.698986	+	0.715135i	$0.253635\pi$
$240$	−14.1672	−	14.1672i	−0.914486	−	0.914486i
$241$	0.980980	−	0.406335i	0.0631905	−	0.0261744i	−0.350864	−	0.936426i	$-0.614112\pi$
$241$	0.980980	−	0.406335i	0.0631905	−	0.0261744i	0.414055	+	0.910252i	$0.364112\pi$
$242$			9.65952i			0.620937i
$243$	−0.382683	−	0.923880i	−0.0245492	−	0.0592669i
$244$	2.62312	+	1.08653i	0.167928	+	0.0695582i
$245$	9.56914	−	23.1020i	0.611350	−	1.47593i
$246$	−5.90002	+	5.90002i	−0.376172	+	0.376172i
$247$	4.37239	−	4.37239i	0.278209	−	0.278209i
$248$	−3.31909	+	8.01298i	−0.210762	+	0.508825i
$249$	5.89905	+	2.44347i	0.373837	+	0.154848i
$250$	−16.8046	−	40.5699i	−1.06282	−	2.56586i
$251$			7.29715i			0.460592i	0.973121	+	0.230296i	$0.0739695\pi$
$251$			7.29715i			0.460592i	−0.973121	+	0.230296i	$0.926031\pi$
$252$	0.621948	−	0.257619i	0.0391791	−	0.0162285i
$253$	8.18448	+	8.18448i	0.514554	+	0.514554i
$254$	4.64354			0.291361
$255$		0			0
$256$	15.4673			0.966708
$257$	−15.9501	−	15.9501i	−0.994941	−	0.994941i	0.00504619	−	0.999987i	$-0.498394\pi$
$257$	−15.9501	−	15.9501i	−0.994941	−	0.994941i	−0.999987	+	0.00504619i	$0.998394\pi$
$258$	7.98559	−	3.30774i	0.497161	−	0.205931i
$259$		−	5.49236i		−	0.341278i
$260$	−4.05985	−	9.80134i	−0.251781	−	0.607853i
$261$	2.03597	+	0.843328i	0.126024	+	0.0522007i
$262$	−5.01208	+	12.1002i	−0.309647	+	0.747555i
$263$	3.00463	−	3.00463i	0.185274	−	0.185274i	−0.608376	−	0.793649i	$-0.708179\pi$
$263$	3.00463	−	3.00463i	0.185274	−	0.185274i	0.793649	+	0.608376i	$0.208179\pi$
$264$	3.36875	−	3.36875i	0.207332	−	0.207332i
$265$	−4.19471	+	10.1269i	−0.257679	+	0.622092i
$266$	−2.43557	−	1.00885i	−0.149335	−	0.0618564i
$267$	3.96449	+	9.57112i	0.242623	+	0.585743i
$268$		−	8.78869i		−	0.536855i
$269$	10.9330	−	4.52860i	0.666597	−	0.276114i	−0.0236145	−	0.999721i	$-0.507517\pi$
$269$	10.9330	−	4.52860i	0.666597	−	0.276114i	0.690212	+	0.723608i	$0.257517\pi$
$270$	4.75081	+	4.75081i	0.289125	+	0.289125i
$271$	11.8045			0.717070			0.358535	−	0.933516i	$-0.383276\pi$
$271$	11.8045			0.717070			0.358535	+	0.933516i	$0.383276\pi$
$272$		0			0
$273$	−3.29715			−0.199553
$274$	0.120589	+	0.120589i	0.00728508	+	0.00728508i
$275$	24.1949	−	10.0218i	1.45901	−	0.604340i
$276$		−	3.72115i		−	0.223987i
$277$	−3.99044	−	9.63378i	−0.239762	−	0.578838i	0.757496	−	0.652840i	$-0.226423\pi$
$277$	−3.99044	−	9.63378i	−0.239762	−	0.578838i	−0.997258	+	0.0740024i	$0.976423\pi$
$278$	22.0517	+	9.13412i	1.32257	+	0.547828i
$279$	1.58158	−	3.81828i	0.0946868	−	0.228594i
$280$	5.56592	−	5.56592i	0.332627	−	0.332627i
$281$	−3.86573	+	3.86573i	−0.230610	+	0.230610i	−0.812947	−	0.582337i	$-0.802138\pi$
$281$	−3.86573	+	3.86573i	−0.230610	+	0.230610i	0.582337	+	0.812947i	$0.302138\pi$
$282$	4.40148	−	10.6261i	0.262104	−	0.632776i
$283$	−16.2949	−	6.74958i	−0.968633	−	0.401221i	−0.158430	−	0.987370i	$-0.550643\pi$
$283$	−16.2949	−	6.74958i	−0.968633	−	0.401221i	−0.810203	+	0.586149i	$0.800643\pi$
$284$	0.425645	+	1.02760i	0.0252574	+	0.0609767i
$285$		−	7.03429i		−	0.416675i
$286$	12.3871	−	5.13089i	0.732463	−	0.303396i
$287$	−3.29379	−	3.29379i	−0.194426	−	0.194426i
$288$	−3.94335			−0.232364
$289$		0			0
$290$	−14.8061			−0.869442
$291$	10.2315	+	10.2315i	0.599779	+	0.599779i
$292$	−0.785557	+	0.325388i	−0.0459713	+	0.0190419i
$293$		−	8.25845i		−	0.482464i	−0.970467	−	0.241232i	$-0.922449\pi$
$293$		−	8.25845i		−	0.482464i	0.970467	−	0.241232i	$-0.0775515\pi$
$294$	−3.88801	−	9.38649i	−0.226753	−	0.547431i
$295$	−27.7950	−	11.5131i	−1.61829	−	0.670317i
$296$	−4.78205	+	11.5449i	−0.277951	+	0.671033i
$297$	−1.60525	+	1.60525i	−0.0931458	+	0.0931458i
$298$	−4.20070	+	4.20070i	−0.243340	+	0.243340i
$299$	−6.97457	+	16.8381i	−0.403350	+	0.973773i
$300$	−7.77848	−	3.22195i	−0.449091	−	0.186020i
$301$	1.84660	+	4.45809i	0.106436	+	0.256960i
$302$			12.5375i			0.721454i
$303$	−0.245517	+	0.101697i	−0.0141046	+	0.00584231i
$304$	6.02663	+	6.02663i	0.345651	+	0.345651i
$305$	−15.8194			−0.905815
$306$		0			0
$307$	−9.94601			−0.567649			−0.283824	−	0.958876i	$-0.591603\pi$
$307$	−9.94601			−0.567649			−0.283824	+	0.958876i	$0.591603\pi$
$308$	−1.08064	−	1.08064i	−0.0615751	−	0.0615751i
$309$	−2.80331	+	1.16117i	−0.159475	+	0.0660567i
$310$			27.7674i			1.57708i
$311$	6.34739	+	15.3240i	0.359927	+	0.868942i	0.995309	+	0.0967437i	$0.0308427\pi$
$311$	6.34739	+	15.3240i	0.359927	+	0.868942i	−0.635382	+	0.772198i	$0.719157\pi$
$312$	6.93059	+	2.87075i	0.392368	+	0.162524i
$313$	−7.88772	+	19.0426i	−0.445840	+	1.07635i	0.528025	+	0.849229i	$0.322933\pi$
$313$	−7.88772	+	19.0426i	−0.445840	+	1.07635i	−0.973866	+	0.227125i	$0.927067\pi$
$314$	−22.1473	+	22.1473i	−1.24984	+	1.24984i
$315$	−2.65222	+	2.65222i	−0.149436	+	0.149436i
$316$	3.31909	−	8.01298i	0.186713	−	0.450766i
$317$	−3.94314	−	1.63330i	−0.221469	−	0.0917354i	0.269190	−	0.963087i	$-0.413244\pi$
$317$	−3.94314	−	1.63330i	−0.221469	−	0.0917354i	−0.490659	+	0.871352i	$0.663244\pi$
$318$	1.70434	+	4.11464i	0.0955747	+	0.230738i
$319$		−	5.00280i		−	0.280103i
$320$	−12.5433	+	5.19559i	−0.701190	+	0.290443i
$321$	−13.8964	−	13.8964i	−0.775620	−	0.775620i
$322$	7.77015			0.433014
$323$		0			0
$324$	0.729840			0.0405467
$325$	29.1585	+	29.1585i	1.61742	+	1.61742i
$326$	−20.5049	+	8.49342i	−1.13566	+	0.470407i
$327$			0.715639i			0.0395749i
$328$	4.05571	+	9.79134i	0.223939	+	0.540636i
$329$	5.93221	+	2.45720i	0.327053	+	0.135470i
$330$	5.83685	−	14.0914i	0.321308	−	0.775706i
$331$	20.2307	−	20.2307i	1.11198	−	1.11198i	0.119097	−	0.992883i	$-0.462000\pi$
$331$	20.2307	−	20.2307i	1.11198	−	1.11198i	0.992883	−	0.119097i	$-0.0379999\pi$
$332$	−3.29518	+	3.29518i	−0.180847	+	0.180847i
$333$	2.27870	−	5.50127i	0.124872	−	0.301468i
$334$	−3.26247	−	1.35136i	−0.178515	−	0.0739431i
$335$	18.7392	+	45.2403i	1.02383	+	2.47174i
$336$		−	4.54459i		−	0.247928i
$337$	−28.9514	+	11.9921i	−1.57709	+	0.653250i	−0.987948	−	0.154783i	$-0.950532\pi$
$337$	−28.9514	+	11.9921i	−1.57709	+	0.653250i	−0.589137	+	0.808033i	$0.700532\pi$
$338$	−0.259592	−	0.259592i	−0.0141199	−	0.0141199i
$339$	11.7876			0.640214
$340$		0			0
$341$	−9.38228			−0.508079
$342$	−2.02097	−	2.02097i	−0.109281	−	0.109281i
$343$	11.2054	−	4.64141i	0.605033	−	0.250613i
$344$		−	10.9787i		−	0.591930i
$345$	7.93421	+	19.1549i	0.427163	+	1.03126i
$346$	8.05960	+	3.33840i	0.433287	+	0.179473i
$347$	−4.60594	+	11.1197i	−0.247260	+	0.596938i	−0.997969	−	0.0636944i	$-0.979712\pi$
$347$	−4.60594	+	11.1197i	−0.247260	+	0.596938i	0.750710	+	0.660632i	$0.229712\pi$
$348$	−1.13729	+	1.13729i	−0.0609650	+	0.0609650i
$349$	23.5829	−	23.5829i	1.26236	−	1.26236i	0.312418	−	0.949945i	$-0.398861\pi$
$349$	23.5829	−	23.5829i	1.26236	−	1.26236i	0.949945	−	0.312418i	$-0.101139\pi$
$350$	6.72777	−	16.2423i	0.359614	−	0.868186i
$351$	−3.30250	−	1.36794i	−0.176275	−	0.0730154i
$352$	3.42580	+	8.27060i	0.182596	+	0.440825i
$353$			6.56570i			0.349457i	0.984617	+	0.174729i	$0.0559048\pi$
$353$			6.56570i			0.349457i	−0.984617	+	0.174729i	$0.944095\pi$
$354$	−11.2933	+	4.67785i	−0.600233	+	0.248625i
$355$	−4.38206	−	4.38206i	−0.232576	−	0.232576i
$356$	−7.56093			−0.400728
$357$		0			0
$358$	12.8480			0.679038
$359$	15.2388	+	15.2388i	0.804271	+	0.804271i	0.983760	−	0.179489i	$-0.0574445\pi$
$359$	15.2388	+	15.2388i	0.804271	+	0.804271i	−0.179489	+	0.983760i	$0.557445\pi$
$360$	7.88417	−	3.26573i	0.415533	−	0.172119i
$361$		−	16.0077i		−	0.842508i
$362$	0.579061	+	1.39798i	0.0304348	+	0.0734761i
$363$	−5.40135	−	2.23731i	−0.283497	−	0.117428i
$364$	0.920888	−	2.22322i	0.0482676	−	0.116528i
$365$	3.34991	−	3.34991i	0.175342	−	0.175342i
$366$	−4.54495	+	4.54495i	−0.237568	+	0.237568i
$367$	13.6099	−	32.8572i	0.710431	−	1.71513i	0.0115096	−	0.999934i	$-0.496336\pi$
$367$	13.6099	−	32.8572i	0.710431	−	1.71513i	0.698921	−	0.715198i	$-0.253664\pi$
$368$	−23.2086	−	9.61332i	−1.20983	−	0.501129i
$369$	−1.93259	−	4.66568i	−0.100607	−	0.242886i
$370$			40.0065i			2.07984i
$371$	−2.29707	+	0.951478i	−0.119258	+	0.0493983i
$372$	2.13287	+	2.13287i	0.110584	+	0.110584i
$373$	35.8452			1.85599			0.927997	−	0.372588i	$-0.121529\pi$
$373$	35.8452			1.85599			0.927997	+	0.372588i	$0.121529\pi$
$374$		0			0
$375$	26.5778			1.37247
$376$	−10.3300	−	10.3300i	−0.532731	−	0.532731i
$377$	7.27781	−	3.01457i	0.374826	−	0.155258i
$378$			1.52398i			0.0783851i
$379$	8.38866	+	20.2520i	0.430897	+	1.04028i	0.978999	+	0.203865i	$0.0653504\pi$
$379$	8.38866	+	20.2520i	0.430897	+	1.04028i	−0.548102	+	0.836411i	$0.684650\pi$
$380$	4.74311	+	1.96466i	0.243316	+	0.100785i
$381$	−1.07552	+	2.59654i	−0.0551007	+	0.133025i
$382$	−22.3913	+	22.3913i	−1.14564	+	1.14564i
$383$	−24.2615	+	24.2615i	−1.23970	+	1.23970i	−0.279581	+	0.960122i	$0.590196\pi$
$383$	−24.2615	+	24.2615i	−1.23970	+	1.23970i	−0.960122	+	0.279581i	$0.909804\pi$
$384$	−5.12912	+	12.3828i	−0.261744	+	0.631906i
$385$	7.86678	+	3.25853i	0.400928	+	0.166070i
$386$	−2.97890	−	7.19169i	−0.151622	−	0.366047i
$387$			5.23146i			0.265930i
$388$	−9.75654	+	4.04129i	−0.495313	+	0.205165i
$389$	24.1800	+	24.1800i	1.22597	+	1.22597i	0.965474	+	0.260499i	$0.0838870\pi$
$389$	24.1800	+	24.1800i	1.22597	+	1.22597i	0.260499	+	0.965474i	$0.416113\pi$
$390$	24.0166			1.21613
$391$		0			0
$392$	−12.9047			−0.651783
$393$	−5.60525	−	5.60525i	−0.282747	−	0.282747i
$394$	−22.7363	+	9.41770i	−1.14544	+	0.474457i
$395$			48.3242i			2.43146i
$396$	−0.634051	−	1.53073i	−0.0318622	−	0.0769223i
$397$	0.212822	+	0.0881539i	0.0106812	+	0.00442432i	0.388018	−	0.921652i	$-0.373160\pi$
$397$	0.212822	+	0.0881539i	0.0106812	+	0.00442432i	−0.377336	+	0.926076i	$0.623160\pi$
$398$	−11.8765	+	28.6725i	−0.595317	+	1.43722i
$399$	1.12824	−	1.12824i	0.0564827	−	0.0564827i
$400$	−40.1902	+	40.1902i	−2.00951	+	2.00951i
$401$	0.232195	−	0.560569i	0.0115953	−	0.0279935i	−0.917976	−	0.396636i	$-0.870177\pi$
$401$	0.232195	−	0.560569i	0.0115953	−	0.0279935i	0.929571	+	0.368643i	$0.120177\pi$
$402$	18.3815	+	7.61386i	0.916785	+	0.379745i
$403$	−5.65353	−	13.6488i	−0.281622	−	0.679897i
$404$		−	0.193952i		−	0.00964947i
$405$	−3.75690	+	1.55616i	−0.186682	+	0.0773261i
$406$	−2.37477	−	2.37477i	−0.117858	−	0.117858i
$407$	−13.5177			−0.670049
$408$		0			0
$409$	−1.50925			−0.0746278			−0.0373139	−	0.999304i	$-0.511880\pi$
$409$	−1.50925			−0.0746278			−0.0373139	+	0.999304i	$0.511880\pi$
$410$	23.9921	+	23.9921i	1.18488	+	1.18488i
$411$	−0.0953611	+	0.0394998i	−0.00470381	+	0.00194838i
$412$		−	2.21454i		−	0.109103i
$413$	−2.61149	−	6.30470i	−0.128503	−	0.310234i
$414$	7.78276	+	3.22373i	0.382502	+	0.158437i
$415$	9.93620	−	23.9881i	0.487749	−	1.17753i
$416$	−9.96732	+	9.96732i	−0.488688	+	0.488688i
$417$	−10.2151	+	10.2151i	−0.500237	+	0.500237i
$418$	−2.48297	+	5.99441i	−0.121446	+	0.293196i
$419$	11.1972	+	4.63804i	0.547020	+	0.226583i	0.639039	−	0.769174i	$-0.279332\pi$
$419$	11.1972	+	4.63804i	0.547020	+	0.226583i	−0.0920195	+	0.995757i	$0.529332\pi$
$420$	−1.04759	−	2.52911i	−0.0511173	−	0.123408i
$421$			17.8730i			0.871078i	0.900170	+	0.435539i	$0.143442\pi$
$421$			17.8730i			0.871078i	−0.900170	+	0.435539i	$0.856558\pi$
$422$	−8.97656	+	3.71821i	−0.436972	+	0.181000i
$423$	4.92238	+	4.92238i	0.239334	+	0.239334i
$424$	5.65685			0.274721
$425$		0			0
$426$	−2.51796			−0.121995
$427$	−2.53730	−	2.53730i	−0.122788	−	0.122788i
$428$	13.2513	−	5.48888i	0.640528	−	0.265315i
$429$			8.11492i			0.391792i
$430$	−13.4507	−	32.4729i	−0.648651	−	1.56598i
$431$	10.2884	+	4.26161i	0.495576	+	0.205274i	0.616451	−	0.787393i	$-0.288570\pi$
$431$	10.2884	+	4.26161i	0.495576	+	0.205274i	−0.120875	+	0.992668i	$0.538570\pi$
$432$	1.88549	−	4.55197i	0.0907155	−	0.219007i
$433$	20.5897	−	20.5897i	0.989475	−	0.989475i	−0.0104697	−	0.999945i	$-0.503333\pi$
$433$	20.5897	−	20.5897i	0.989475	−	0.989475i	0.999945	+	0.0104697i	$0.00333268\pi$
$434$	−4.45366	+	4.45366i	−0.213782	+	0.213782i
$435$	3.42934	−	8.27916i	0.164424	−	0.396955i
$436$	−0.482544	−	0.199876i	−0.0231097	−	0.00957234i
$437$	−3.37517	−	8.14838i	−0.161456	−	0.389790i
$438$		−	1.92488i		−	0.0919742i
$439$	−20.8758	+	8.64704i	−0.996347	+	0.412700i	−0.820456	−	0.571709i	$-0.806281\pi$
$439$	−20.8758	+	8.64704i	−0.996347	+	0.412700i	−0.175891	+	0.984410i	$0.556281\pi$
$440$	−13.6988	−	13.6988i	−0.653064	−	0.653064i
$441$	6.14921			0.292820
$442$		0			0
$443$	32.1976			1.52975			0.764877	−	0.644176i	$-0.222800\pi$
$443$	32.1976			1.52975			0.764877	+	0.644176i	$0.222800\pi$
$444$	3.07299	+	3.07299i	0.145837	+	0.145837i
$445$	38.9203	−	16.1213i	1.84500	−	0.764224i
$446$			9.22579i			0.436854i
$447$	−1.37597	−	3.32188i	−0.0650810	−	0.157119i
$448$	−2.84517	−	1.17851i	−0.134422	−	0.0556792i
$449$	−0.428720	+	1.03502i	−0.0202325	+	0.0488457i	−0.933673	−	0.358127i	$-0.883416\pi$
$449$	−0.428720	+	1.03502i	−0.0202325	+	0.0488457i	0.913440	+	0.406973i	$0.133416\pi$
$450$	13.4774	−	13.4774i	0.635330	−	0.635330i
$451$	−8.10665	+	8.10665i	−0.381727	+	0.381727i
$452$	−3.29225	+	7.94819i	−0.154854	+	0.373851i
$453$	−7.01066	−	2.90391i	−0.329389	−	0.136438i
$454$	17.4065	+	42.0231i	0.816930	+	1.97224i
$455$			13.4077i			0.628561i
$456$	−3.35389	+	1.38923i	−0.157060	+	0.0650564i
$457$	−28.3405	−	28.3405i	−1.32571	−	1.32571i	−0.909072	−	0.416639i	$-0.863208\pi$
$457$	−28.3405	−	28.3405i	−1.32571	−	1.32571i	−0.416639	−	0.909072i	$-0.636792\pi$
$458$	−5.89875			−0.275631
$459$		0			0
$460$	−15.1318			−0.705526
$461$	3.53267	+	3.53267i	0.164533	+	0.164533i	0.784571	−	0.620039i	$-0.212883\pi$
$461$	3.53267	+	3.53267i	0.164533	+	0.164533i	−0.620039	+	0.784571i	$0.712883\pi$
$462$	3.19633	−	1.32396i	0.148707	−	0.0615963i
$463$			39.0452i			1.81458i	0.420502	+	0.907292i	$0.361854\pi$
$463$			39.0452i			1.81458i	−0.420502	+	0.907292i	$0.638146\pi$
$464$	4.15509	+	10.0313i	0.192895	+	0.465690i
$465$	−15.5268	−	6.43140i	−0.720037	−	0.298249i
$466$	−0.866779	+	2.09259i	−0.0401528	+	0.0969374i
$467$	−7.44173	+	7.44173i	−0.344362	+	0.344362i	−0.858004	−	0.513642i	$-0.828296\pi$
$467$	−7.44173	+	7.44173i	−0.344362	+	0.344362i	0.513642	+	0.858004i	$0.328296\pi$
$468$	1.84476	−	1.84476i	0.0852743	−	0.0852743i
$469$	−4.25057	+	10.2618i	−0.196273	+	0.473845i
$470$	−43.2104	−	17.8983i	−1.99315	−	0.825589i
$471$	−7.25449	−	17.5139i	−0.334269	−	0.806997i
$472$			15.5262i			0.714651i
$473$	10.9722	−	4.54484i	0.504503	−	0.208972i
$474$	13.8837	+	13.8837i	0.637699	+	0.637699i
$475$	−19.9553			−0.915611
$476$		0			0
$477$	−2.69555			−0.123421
$478$	−25.2494	−	25.2494i	−1.15488	−	1.15488i
$479$	−23.9876	+	9.93598i	−1.09602	+	0.453986i	−0.856102	−	0.516807i	$-0.827121\pi$
$479$	−23.9876	+	9.93598i	−1.09602	+	0.453986i	−0.239918	+	0.970793i	$0.577121\pi$
$480$			16.0354i			0.731912i
$481$	−8.14546	−	19.6649i	−0.371401	−	0.896641i
$482$	−1.62080	−	0.671356i	−0.0738253	−	0.0305794i
$483$	−1.79970	+	4.34486i	−0.0818893	+	0.197698i
$484$	3.01717	−	3.01717i	0.137144	−	0.137144i
$485$	41.6056	−	41.6056i	1.88921	−	1.88921i
$486$	−0.632278	+	1.52645i	−0.0286807	+	0.0692414i
$487$	−23.5964	−	9.77394i	−1.06925	−	0.442900i	−0.222527	−	0.974927i	$-0.571430\pi$
$487$	−23.5964	−	9.77394i	−1.06925	−	0.442900i	−0.846727	+	0.532027i	$0.821430\pi$
$488$	3.12422	+	7.54254i	0.141427	+	0.341435i
$489$		−	13.4330i		−	0.607463i
$490$	−38.1696	+	15.8104i	−1.72433	+	0.714239i
$491$	1.77317	+	1.77317i	0.0800221	+	0.0800221i	0.745985	−	0.665963i	$-0.231979\pi$
$491$	1.77317	+	1.77317i	0.0800221	+	0.0800221i	−0.665963	+	0.745985i	$0.731979\pi$
$492$	3.68577			0.166167
$493$		0			0
$494$	−10.2165			−0.459663
$495$	6.52763	+	6.52763i	0.293395	+	0.293395i
$496$	18.8127	−	7.79248i	0.844715	−	0.349893i
$497$		−	1.40569i		−	0.0630540i
$498$	−4.03715	−	9.74654i	−0.180909	−	0.436753i
$499$	14.0680	+	5.82714i	0.629768	+	0.260859i	0.674655	−	0.738134i	$-0.264293\pi$
$499$	14.0680	+	5.82714i	0.629768	+	0.260859i	−0.0448864	+	0.998992i	$0.514293\pi$
$500$	−7.42313	+	17.9210i	−0.331973	+	0.801453i
$501$	1.51129	−	1.51129i	0.0675195	−	0.0675195i
$502$	8.52525	−	8.52525i	0.380501	−	0.380501i
$503$	−14.9625	+	36.1228i	−0.667147	+	1.61064i	0.119214	+	0.992869i	$0.461962\pi$
$503$	−14.9625	+	36.1228i	−0.667147	+	1.61064i	−0.786361	+	0.617767i	$0.788038\pi$
$504$	1.78835	+	0.740760i	0.0796596	+	0.0329961i
$505$	0.413542	+	0.998380i	0.0184024	+	0.0444273i
$506$		−	19.1238i		−	0.850158i
$507$	0.205283	−	0.0850310i	0.00911694	−	0.00377636i
$508$	−1.45042	−	1.45042i	−0.0643519	−	0.0643519i
$509$	31.9138			1.41455			0.707277	−	0.706937i	$-0.249924\pi$
$509$	31.9138			1.41455			0.707277	+	0.706937i	$0.249924\pi$
$510$		0			0
$511$	1.07460			0.0475374
$512$	0.884296	+	0.884296i	0.0390807	+	0.0390807i
$513$	1.59816	−	0.661981i	0.0705607	−	0.0292272i
$514$			37.2690i			1.64386i
$515$	4.72183	+	11.3995i	0.208069	+	0.502322i
$516$	−3.52749	−	1.46114i	−0.155289	−	0.0643229i
$517$	6.04765	−	14.6003i	0.265975	−	0.642121i
$518$	−6.41671	+	6.41671i	−0.281934	+	0.281934i
$519$	−3.73349	+	3.73349i	−0.163882	+	0.163882i
$520$	11.6737	−	28.1828i	0.511926	−	1.23590i
$521$	4.46286	+	1.84858i	0.195521	+	0.0809876i	0.478296	−	0.878199i	$-0.341255\pi$
$521$	4.46286	+	1.84858i	0.195521	+	0.0809876i	−0.282774	+	0.959186i	$0.591255\pi$
$522$	−1.39337	−	3.36388i	−0.0609860	−	0.147233i
$523$		−	36.5734i		−	1.59924i	−0.600503	−	0.799622i	$-0.705033\pi$
$523$		−	36.5734i		−	1.59924i	0.600503	−	0.799622i	$-0.294967\pi$
$524$	5.34506	−	2.21400i	0.233500	−	0.0967189i
$525$	7.52398	+	7.52398i	0.328373	+	0.328373i
$526$	−7.02061			−0.306113
$527$		0			0
$528$	−11.1851			−0.486769
$529$	2.11820	+	2.11820i	0.0920956	+	0.0920956i
$530$	16.7319	−	6.93059i	0.726789	−	0.301046i
$531$		−	7.39840i		−	0.321063i
$532$	0.445641	+	1.07587i	0.0193210	+	0.0466449i
$533$	−16.6780	−	6.90824i	−0.722403	−	0.299229i
$534$	6.55021	−	15.8136i	0.283455	−	0.684322i
$535$	−56.5087	+	56.5087i	−2.44309	+	2.44309i
$536$	17.8693	−	17.8693i	0.771838	−	0.771838i
$537$	−2.97582	+	7.18427i	−0.128416	+	0.310024i
$538$	−18.0638	−	7.48226i	−0.778784	−	0.322583i
$539$	−5.34214	−	12.8971i	−0.230102	−	0.555516i
$540$		−	2.96785i		−	0.127716i
$541$	−10.1896	+	4.22067i	−0.438085	+	0.181461i	−0.590815	−	0.806807i	$-0.701194\pi$
$541$	−10.1896	+	4.22067i	−0.438085	+	0.181461i	0.152730	+	0.988268i	$0.451194\pi$
$542$	−13.7911	−	13.7911i	−0.592379	−	0.592379i
$543$	−0.915833			−0.0393021
$544$		0			0
$545$	2.91010			0.124655
$546$	3.85206	+	3.85206i	0.164853	+	0.164853i
$547$	−24.8307	+	10.2852i	−1.06169	+	0.439765i	−0.844050	−	0.536265i	$-0.819835\pi$
$547$	−24.8307	+	10.2852i	−1.06169	+	0.439765i	−0.217636	+	0.976030i	$0.569835\pi$
$548$		−	0.0753327i		−	0.00321805i
$549$	−1.48873	−	3.59411i	−0.0635373	−	0.153393i
$550$	−39.9753	−	16.5583i	−1.70455	−	0.706049i
$551$	−1.45882	+	3.52191i	−0.0621480	+	0.150038i
$552$	7.56592	−	7.56592i	0.322027	−	0.322027i
$553$	−7.75081	+	7.75081i	−0.329598	+	0.329598i
$554$	−6.59310	+	15.9172i	−0.280114	+	0.676255i
$555$	−22.3706	−	9.26619i	−0.949578	−	0.393328i
$556$	−4.03484	−	9.74096i	−0.171115	−	0.413109i
$557$			34.9146i			1.47938i	0.672948	+	0.739690i	$0.265028\pi$
$557$			34.9146i			1.47938i	−0.672948	+	0.739690i	$0.734972\pi$
$558$	−6.30864	+	2.61313i	−0.267066	+	0.110622i
$559$	13.2232	+	13.2232i	0.559281	+	0.559281i
$560$	−18.4803			−0.780935
$561$		0			0
$562$	9.03266			0.381020
$563$	−5.59557	−	5.59557i	−0.235825	−	0.235825i	0.579294	−	0.815119i	$-0.303328\pi$
$563$	−5.59557	−	5.59557i	−0.235825	−	0.235825i	−0.815119	+	0.579294i	$0.803328\pi$
$564$	−4.69390	+	1.94428i	−0.197649	+	0.0818688i
$565$		−	47.9335i		−	2.01658i
$566$	11.1518	+	26.9229i	0.468746	+	1.13165i
$567$	−0.852170	−	0.352980i	−0.0357878	−	0.0148238i
$568$	−1.22390	+	2.95476i	−0.0513537	+	0.123979i
$569$	12.2298	−	12.2298i	0.512702	−	0.512702i	−0.402651	−	0.915353i	$-0.631911\pi$
$569$	12.2298	−	12.2298i	0.512702	−	0.512702i	0.915353	+	0.402651i	$0.131911\pi$
$570$	−8.21814	+	8.21814i	−0.344220	+	0.344220i
$571$	−7.41605	+	17.9039i	−0.310352	+	0.749256i	0.689340	+	0.724438i	$0.257901\pi$
$571$	−7.41605	+	17.9039i	−0.310352	+	0.749256i	−0.999692	+	0.0248178i	$0.992099\pi$
$572$	−5.47177	−	2.26648i	−0.228786	−	0.0947663i
$573$	−7.33442	−	17.7069i	−0.306400	−	0.739715i
$574$			7.69626i			0.321236i
$575$	54.3396	−	22.5082i	2.26612	−	0.938658i
$576$	−2.36084	−	2.36084i	−0.0983683	−	0.0983683i
$577$	2.89714			0.120610			0.0603048	−	0.998180i	$-0.480793\pi$
$577$	2.89714			0.120610			0.0603048	+	0.998180i	$0.480793\pi$
$578$		0			0
$579$	4.71137			0.195798
$580$	4.62470	+	4.62470i	0.192030	+	0.192030i
$581$	5.44118	−	2.25381i	0.225738	−	0.0935038i
$582$		−	23.9068i		−	0.990968i
$583$	2.34177	+	5.65353i	0.0969862	+	0.234145i
$584$	−2.25879	−	0.935623i	−0.0934696	−	0.0387164i
$585$	−5.56265	+	13.4294i	−0.229987	+	0.555238i
$586$	−9.64833	+	9.64833i	−0.398569	+	0.398569i
$587$	8.70909	−	8.70909i	0.359463	−	0.359463i	−0.504152	−	0.863615i	$-0.668195\pi$
$587$	8.70909	−	8.70909i	0.359463	−	0.359463i	0.863615	+	0.504152i	$0.168195\pi$
$588$	−1.71746	+	4.14632i	−0.0708269	+	0.170991i
$589$	6.60501	+	2.73588i	0.272155	+	0.112730i
$590$	19.0222	+	45.9236i	0.783131	+	1.89064i
$591$		−	14.8949i		−	0.612693i
$592$	27.1048	−	11.2272i	1.11400	−	0.461435i
$593$	−30.5302	−	30.5302i	−1.25373	−	1.25373i	−0.954037	−	0.299690i	$-0.903117\pi$
$593$	−30.5302	−	30.5302i	−1.25373	−	1.25373i	−0.299690	−	0.954037i	$-0.596883\pi$
$594$	3.75081			0.153898
$595$		0			0
$596$	2.62420			0.107491
$597$	−13.2821	−	13.2821i	−0.543599	−	0.543599i
$598$	27.8203	−	11.5235i	1.13766	−	0.471233i
$599$			6.70607i			0.274003i	0.990571	+	0.137001i	$0.0437464\pi$
$599$			6.70607i			0.274003i	−0.990571	+	0.137001i	$0.956254\pi$
$600$	−9.26442	−	22.3663i	−0.378218	−	0.913100i
$601$	29.4156	+	12.1844i	1.19989	+	0.497010i	0.890963	−	0.454076i	$-0.150030\pi$
$601$	29.4156	+	12.1844i	1.19989	+	0.497010i	0.308926	+	0.951086i	$0.400030\pi$
$602$	3.05100	−	7.36577i	0.124349	−	0.300206i
$603$	−8.51494	+	8.51494i	−0.346755	+	0.346755i
$604$	3.91612	−	3.91612i	0.159345	−	0.159345i
$605$	−9.09788	+	21.9642i	−0.369882	+	0.892973i
$606$	0.405649	+	0.168025i	0.0164784	+	0.00682556i
$607$	10.6833	+	25.7918i	0.433622	+	1.04685i	0.978110	+	0.208087i	$0.0667237\pi$
$607$	10.6833	+	25.7918i	0.433622	+	1.04685i	−0.544489	+	0.838768i	$0.683276\pi$
$608$		−	6.82137i		−	0.276643i
$609$	1.87795	−	0.777871i	0.0760983	−	0.0315209i
$610$	18.4818	+	18.4818i	0.748304	+	0.748304i
$611$	24.8839			1.00669
$612$		0			0
$613$	−5.84314			−0.236002			−0.118001	−	0.993013i	$-0.537649\pi$
$613$	−5.84314			−0.236002			−0.118001	+	0.993013i	$0.537649\pi$
$614$	11.6199	+	11.6199i	0.468941	+	0.468941i
$615$	−18.9727	+	7.85875i	−0.765053	+	0.316895i
$616$		−	4.39435i		−	0.177053i
$617$	−14.1792	−	34.2317i	−0.570835	−	1.37812i	−0.900845	−	0.434140i	$-0.857052\pi$
$617$	−14.1792	−	34.2317i	−0.570835	−	1.37812i	0.330010	−	0.943977i	$-0.392948\pi$
$618$	4.63170	+	1.91851i	0.186314	+	0.0771739i
$619$	6.18744	−	14.9378i	0.248694	−	0.600401i	−0.749399	−	0.662118i	$-0.769658\pi$
$619$	6.18744	−	14.9378i	0.248694	−	0.600401i	0.998094	+	0.0617170i	$0.0196576\pi$
$620$	8.67319	−	8.67319i	0.348324	−	0.348324i
$621$	−3.60525	+	3.60525i	−0.144674	+	0.144674i
$622$	10.4873	−	25.3186i	0.420503	−	1.01518i
$623$	8.82823	+	3.65677i	0.353696	+	0.146505i
$624$	−6.73987	−	16.2715i	−0.269811	−	0.651381i
$625$		−	50.3976i		−	2.01590i
$626$	31.4627	−	13.0323i	1.25750	−	0.520874i
$627$	−2.77682	−	2.77682i	−0.110895	−	0.110895i
$628$	13.8355			0.552097
$629$		0			0
$630$	6.19717			0.246901
$631$	−22.3920	−	22.3920i	−0.891410	−	0.891410i	0.103246	−	0.994656i	$-0.467077\pi$
$631$	−22.3920	−	22.3920i	−0.891410	−	0.891410i	−0.994656	+	0.103246i	$0.967077\pi$
$632$	23.0406	−	9.54372i	0.916505	−	0.379629i
$633$		−	5.88066i		−	0.233735i
$634$	2.69858	+	6.51495i	0.107174	+	0.258742i
$635$	10.5587	+	4.37355i	0.419008	+	0.173559i
$636$	0.752862	−	1.81757i	0.0298529	−	0.0720714i
$637$	15.5429	−	15.5429i	0.615833	−	0.615833i
$638$	−5.84476	+	5.84476i	−0.231396	+	0.231396i
$639$	0.583202	−	1.40798i	0.0230711	−	0.0556986i
$640$	50.3538	+	20.8572i	1.99041	+	0.824455i
$641$	−6.09588	−	14.7167i	−0.240773	−	0.581277i	0.756587	−	0.653893i	$-0.226865\pi$
$641$	−6.09588	−	14.7167i	−0.240773	−	0.581277i	−0.997360	+	0.0726161i	$0.976865\pi$
$642$			32.4702i			1.28150i
$643$	15.4161	−	6.38557i	0.607953	−	0.251822i	−0.0574003	−	0.998351i	$-0.518281\pi$
$643$	15.4161	−	6.38557i	0.607953	−	0.251822i	0.665353	+	0.746529i	$0.268281\pi$
$644$	−2.42702	−	2.42702i	−0.0956381	−	0.0956381i
$645$	21.2734			0.837639
$646$		0			0
$647$	−8.35044			−0.328290			−0.164145	−	0.986436i	$-0.552486\pi$
$647$	−8.35044			−0.328290			−0.164145	+	0.986436i	$0.552486\pi$
$648$	1.48392	+	1.48392i	0.0582941	+	0.0582941i
$649$	−15.5171	+	6.42738i	−0.609098	+	0.252297i
$650$		−	68.1316i		−	2.67234i
$651$	−1.45882	−	3.52191i	−0.0571758	−	0.138035i
$652$	9.05770	+	3.75182i	0.354727	+	0.146933i
$653$	−10.9821	+	26.5132i	−0.429764	+	1.03754i	0.549598	+	0.835429i	$0.314781\pi$
$653$	−10.9821	+	26.5132i	−0.429764	+	1.03754i	−0.979362	+	0.202113i	$0.935219\pi$
$654$	0.836079	−	0.836079i	0.0326933	−	0.0326933i
$655$	−22.7934	+	22.7934i	−0.890611	+	0.890611i
$656$	9.52189	−	22.9879i	0.371767	−	0.897526i
$657$	1.07634	+	0.445835i	0.0419921	+	0.0173937i
$658$	−4.05985	−	9.80134i	−0.158269	−	0.382096i
$659$			40.3690i			1.57255i	0.617876	+	0.786276i	$0.287993\pi$
$659$			40.3690i			1.57255i	−0.617876	+	0.786276i	$0.712007\pi$
$660$	−6.22463	+	2.57833i	−0.242293	+	0.100361i
$661$	27.9099	+	27.9099i	1.08557	+	1.08557i	0.995979	+	0.0895910i	$0.0285560\pi$
$661$	27.9099	+	27.9099i	1.08557	+	1.08557i	0.0895910	+	0.995979i	$0.471444\pi$
$662$	−47.2710			−1.83724
$663$		0			0
$664$	−13.3997			−0.520007
$665$	−4.58792	−	4.58792i	−0.177912	−	0.177912i
$666$	−9.08933	+	3.76492i	−0.352204	+	0.145888i
$667$		−	11.2359i		−	0.435055i
$668$	0.596940	+	1.44114i	0.0230963	+	0.0557594i
$669$	−5.15882	−	2.13685i	−0.199452	−	0.0826155i
$670$	30.9613	−	74.7471i	1.19614	−	2.88773i
$671$	−6.24478	+	6.24478i	−0.241077	+	0.241077i
$672$	−2.57194	+	2.57194i	−0.0992149	+	0.0992149i
$673$	−8.26810	+	19.9610i	−0.318712	+	0.769438i	0.680611	+	0.732645i	$0.261714\pi$
$673$	−8.26810	+	19.9610i	−0.318712	+	0.769438i	−0.999323	+	0.0367934i	$0.988286\pi$
$674$	47.8342	+	19.8136i	1.84251	+	0.763191i
$675$	4.41460	+	10.6578i	0.169918	+	0.410218i
$676$			0.162168i			0.00623724i
$677$	−2.31970	+	0.960853i	−0.0891535	+	0.0369286i	−0.426814	−	0.904339i	$-0.640364\pi$
$677$	−2.31970	+	0.960853i	−0.0891535	+	0.0369286i	0.337661	+	0.941268i	$0.390364\pi$
$678$	−13.7714	−	13.7714i	−0.528888	−	0.528888i
$679$	13.3464			0.512187
$680$		0			0
$681$	−27.5299			−1.05495
$682$	10.9613	+	10.9613i	0.419730	+	0.419730i
$683$	17.3157	−	7.17238i	0.662566	−	0.274444i	−0.0259521	−	0.999663i	$-0.508262\pi$
$683$	17.3157	−	7.17238i	0.662566	−	0.274444i	0.688518	+	0.725220i	$0.258262\pi$
$684$			1.26251i			0.0482732i
$685$	0.160624	+	0.387780i	0.00613711	+	0.0148163i
$686$	−18.5138	−	7.66865i	−0.706859	−	0.292790i
$687$	1.36625	−	3.29843i	0.0521258	−	0.125843i
$688$	−18.2260	+	18.2260i	−0.694860	+	0.694860i
$689$	−6.81336	+	6.81336i	−0.259568	+	0.259568i
$690$	13.1091	−	31.6481i	0.499054	−	1.20482i
$691$	35.6342	+	14.7602i	1.35559	+	0.561504i	0.937843	−	0.347060i	$-0.112820\pi$
$691$	35.6342	+	14.7602i	1.35559	+	0.561504i	0.417747	+	0.908563i	$0.362820\pi$
$692$	−1.47468	−	3.56019i	−0.0560588	−	0.135338i
$693$			2.09396i			0.0795428i
$694$	18.3723	−	7.61004i	0.697401	−	0.288873i
$695$	41.5391	+	41.5391i	1.57567	+	1.57567i
$696$	−4.62470			−0.175299
$697$		0			0
$698$	−55.1037			−2.08570
$699$	−0.969360	−	0.969360i	−0.0366646	−	0.0366646i
$700$	−7.17474	+	2.97187i	−0.271180	+	0.112326i
$701$		−	28.7827i		−	1.08711i	−0.839375	−	0.543553i	$-0.817079\pi$
$701$		−	28.7827i		−	1.08711i	0.839375	−	0.543553i	$-0.182921\pi$
$702$	2.26015	+	5.45647i	0.0853037	+	0.205941i
$703$	9.51632	+	3.94179i	0.358915	+	0.148667i
$704$	−2.90053	+	7.00250i	−0.109318	+	0.263917i
$705$	20.0166	−	20.0166i	0.753867	−	0.753867i
$706$	7.67070	−	7.67070i	0.288690	−	0.288690i
$707$	−0.0938031	+	0.226461i	−0.00352783	+	0.00851693i
$708$	4.98863	+	2.06636i	0.187484	+	0.0776585i
$709$	−1.96924	−	4.75418i	−0.0739565	−	0.178547i	0.882578	−	0.470166i	$-0.155806\pi$
$709$	−1.96924	−	4.75418i	−0.0739565	−	0.178547i	−0.956534	+	0.291619i	$0.905806\pi$
$710$			10.2391i			0.384267i
$711$	−10.9791	+	4.54769i	−0.411748	+	0.170552i
$712$	−15.3730	−	15.3730i	−0.576128	−	0.576128i
$713$	−21.0718			−0.789146
$714$		0			0
$715$	32.9988			1.23409
$716$	−4.01310	−	4.01310i	−0.149977	−	0.149977i
$717$	19.9670	−	8.27060i	0.745681	−	0.308871i
$718$		−	35.6068i		−	1.32883i
$719$	12.0554	+	29.1042i	0.449589	+	1.08540i	0.972476	+	0.233003i	$0.0748551\pi$
$719$	12.0554	+	29.1042i	0.449589	+	1.08540i	−0.522887	+	0.852402i	$0.675145\pi$
$720$	−18.5103	−	7.66721i	−0.689838	−	0.285740i
$721$	−1.07104	+	2.58573i	−0.0398878	+	0.0962976i
$722$	−18.7017	+	18.7017i	−0.696005	+	0.696005i
$723$	0.750810	−	0.750810i	0.0279229	−	0.0279229i
$724$	0.255790	−	0.617532i	0.00950636	−	0.0229504i
$725$	−23.4868	−	9.72856i	−0.872278	−	0.361309i
$726$	3.69654	+	8.92423i	0.137191	+	0.331209i
$727$		−	31.2775i		−	1.16002i	−0.814610	−	0.580010i	$-0.803049\pi$
$727$		−	31.2775i		−	1.16002i	0.814610	−	0.580010i	$-0.196951\pi$
$728$	6.39266	−	2.64793i	0.236928	−	0.0981386i
$729$	−0.707107	−	0.707107i	−0.0261891	−	0.0261891i
$730$	−7.82739			−0.289705
$731$		0			0
$732$	2.83925			0.104942
$733$	13.3044	+	13.3044i	0.491411	+	0.491411i	0.908751	−	0.417340i	$-0.137037\pi$
$733$	13.3044	+	13.3044i	0.491411	+	0.491411i	−0.417340	+	0.908751i	$0.637037\pi$
$734$	−54.2874	+	22.4866i	−2.00379	+	0.829995i
$735$		−	25.0054i		−	0.922337i
$736$	7.69405	+	18.5751i	0.283606	+	0.684686i
$737$	25.2562	+	10.4615i	0.930324	+	0.385353i
$738$	−3.19307	+	7.70875i	−0.117538	+	0.283763i
$739$	−4.91271	+	4.91271i	−0.180717	+	0.180717i	−0.791668	−	0.610951i	$-0.790787\pi$
$739$	−4.91271	+	4.91271i	−0.180717	+	0.180717i	0.610951	+	0.791668i	$0.290787\pi$
$740$	12.4961	−	12.4961i	0.459366	−	0.459366i
$741$	2.36632	−	5.71281i	0.0869290	−	0.209865i
$742$	3.79527	+	1.57205i	0.139329	+	0.0577119i
$743$	−12.9945	−	31.3716i	−0.476723	−	1.15091i	−0.961137	−	0.276072i	$-0.910967\pi$
$743$	−12.9945	−	31.3716i	−0.476723	−	1.15091i	0.484414	−	0.874839i	$-0.339033\pi$
$744$			8.67319i			0.317975i
$745$	−13.5082	+	5.59528i	−0.494902	+	0.204995i
$746$	−41.8779	−	41.8779i	−1.53326	−	1.53326i
$747$	6.38508			0.233618
$748$		0			0
$749$	−18.1271			−0.662349
$750$	−31.0508	−	31.0508i	−1.13382	−	1.13382i
$751$	−6.38871	+	2.64629i	−0.233127	+	0.0965645i	−0.496189	−	0.868215i	$-0.665268\pi$
$751$	−6.38871	+	2.64629i	−0.233127	+	0.0965645i	0.263062	+	0.964779i	$0.415268\pi$
$752$			34.2984i			1.25073i
$753$	2.79250	+	6.74169i	0.101764	+	0.245681i
$754$	−12.0246	−	4.98073i	−0.437909	−	0.181388i
$755$	−11.8086	+	28.5084i	−0.429758	+	1.03753i
$756$	0.476019	−	0.476019i	0.0173126	−	0.0173126i
$757$	1.31639	−	1.31639i	0.0478452	−	0.0478452i	−0.682779	−	0.730625i	$-0.739229\pi$
$757$	1.31639	−	1.31639i	0.0478452	−	0.0478452i	0.730625	+	0.682779i	$0.239229\pi$
$758$	13.8599	−	33.4609i	0.503416	−	1.21535i
$759$	10.6935	+	4.42941i	0.388151	+	0.160777i
$760$	5.64920	+	13.6384i	0.204918	+	0.494715i
$761$		−	49.2335i		−	1.78471i	−0.451330	−	0.892357i	$-0.649050\pi$
$761$		−	49.2335i		−	1.78471i	0.451330	−	0.892357i	$-0.350950\pi$
$762$	4.29007	−	1.77700i	0.155413	−	0.0643741i
$763$	0.466756	+	0.466756i	0.0168977	+	0.0168977i
$764$	13.9880			0.506066
$765$		0			0
$766$	56.6893			2.04827
$767$	−18.7004	−	18.7004i	−0.675232	−	0.675232i
$768$	14.2900	−	5.91909i	0.515644	−	0.213587i
$769$			50.9303i			1.83659i	0.395895	+	0.918296i	$0.370435\pi$
$769$			50.9303i			1.83659i	−0.395895	+	0.918296i	$0.629565\pi$
$770$	−5.38381	−	12.9977i	−0.194019	−	0.468403i
$771$	−20.8398	−	8.63214i	−0.750528	−	0.310879i
$772$	−1.31587	+	3.17680i	−0.0473594	+	0.114336i
$773$	−2.06202	+	2.06202i	−0.0741658	+	0.0741658i	−0.743217	−	0.669051i	$-0.766701\pi$
$773$	−2.06202	+	2.06202i	−0.0741658	+	0.0741658i	0.669051	+	0.743217i	$0.266701\pi$
$774$	6.11190	−	6.11190i	0.219688	−	0.219688i
$775$	−18.2450	+	44.0473i	−0.655379	+	1.58222i
$776$	−28.0540	−	11.6203i	−1.00708	−	0.417146i
$777$	−2.10183	−	5.07428i	−0.0754029	−	0.182039i
$778$		−	56.4988i		−	2.02558i
$779$	8.07089	−	3.34307i	0.289170	−	0.119778i
$780$	−7.50162	−	7.50162i	−0.268601	−	0.268601i
$781$	−3.45968			−0.123797
$782$		0			0
$783$	2.20372			0.0787546
$784$	21.4234	+	21.4234i	0.765121	+	0.765121i
$785$	−71.2191	+	29.4999i	−2.54192	+	1.05290i
$786$			13.0972i			0.467161i
$787$	19.4760	+	47.0192i	0.694243	+	1.67605i	0.736051	+	0.676926i	$0.236688\pi$
$787$	19.4760	+	47.0192i	0.694243	+	1.67605i	−0.0418077	+	0.999126i	$0.513312\pi$
$788$	10.0434	+	4.16010i	0.357781	+	0.148198i
$789$	1.62609	−	3.92574i	0.0578905	−	0.139760i
$790$	56.4571	−	56.4571i	2.00865	−	2.00865i
$791$	7.68814	−	7.68814i	0.273359	−	0.273359i
$792$	1.82315	−	4.40148i	0.0647829	−	0.156400i
$793$	−12.8475	−	5.32161i	−0.456228	−	0.188976i
$794$	−0.145650	−	0.351630i	−0.00516892	−	0.0124789i
$795$			10.9613i			0.388757i
$796$	12.6656	−	5.24625i	0.448919	−	0.185948i
$797$	9.62096	+	9.62096i	0.340792	+	0.340792i	0.856665	−	0.515873i	$-0.172532\pi$
$797$	9.62096	+	9.62096i	0.340792	+	0.340792i	−0.515873	+	0.856665i	$0.672532\pi$
$798$	−2.63624			−0.0933220
$799$		0			0
$800$	45.4901			1.60832
$801$	7.32541	+	7.32541i	0.258831	+	0.258831i
$802$	−0.926185	+	0.383638i	−0.0327047	+	0.0135467i
$803$		−	2.64479i		−	0.0933326i
$804$	−3.36329	−	8.11969i	−0.118614	−	0.286360i
$805$	17.6681	+	7.31837i	0.622719	+	0.257939i
$806$	−9.34089	+	22.5509i	−0.329019	+	0.794322i
$807$	8.36776	−	8.36776i	0.294559	−	0.294559i
$808$	0.394347	−	0.394347i	0.0138731	−	0.0138731i
$809$	6.65627	−	16.0697i	0.234022	−	0.564979i	−0.762621	−	0.646845i	$-0.776088\pi$
$809$	6.65627	−	16.0697i	0.234022	−	0.564979i	0.996643	+	0.0818660i	$0.0260879\pi$
$810$	6.20723	+	2.57112i	0.218100	+	0.0903399i
$811$	−12.6012	−	30.4221i	−0.442489	−	1.06826i	−0.975073	−	0.221886i	$-0.928779\pi$
$811$	−12.6012	−	30.4221i	−0.442489	−	1.06826i	0.532583	−	0.846378i	$-0.321221\pi$
$812$			1.48353i			0.0520617i
$813$	10.9059	−	4.51737i	0.382486	−	0.158431i
$814$	15.7927	+	15.7927i	0.553536	+	0.553536i
$815$	−54.6246			−1.91342
$816$		0			0
$817$	−9.04959			−0.316605
$818$	1.76326	+	1.76326i	0.0616509	+	0.0616509i
$819$	−3.04617	+	1.26177i	−0.106442	+	0.0440897i
$820$		−	14.9879i		−	0.523401i
$821$	−16.7374	−	40.4076i	−0.584138	−	1.41023i	−0.889031	−	0.457847i	$-0.848621\pi$
$821$	−16.7374	−	40.4076i	−0.584138	−	1.41023i	0.304893	−	0.952387i	$-0.401379\pi$
$822$	0.157558	+	0.0652625i	0.00549546	+	0.00227629i
$823$	−0.640622	+	1.54660i	−0.0223307	+	0.0539110i	−0.934652	−	0.355565i	$-0.884288\pi$
$823$	−0.640622	+	1.54660i	−0.0223307	+	0.0539110i	0.912321	+	0.409476i	$0.134288\pi$
$824$	4.50265	−	4.50265i	0.156857	−	0.156857i
$825$	18.5180	−	18.5180i	0.644713	−	0.644713i
$826$	−4.31477	+	10.4168i	−0.150130	+	0.362446i
$827$	2.09735	+	0.868752i	0.0729321	+	0.0302095i	0.418851	−	0.908055i	$-0.362433\pi$
$827$	2.09735	+	0.868752i	0.0729321	+	0.0302095i	−0.345919	+	0.938264i	$0.612433\pi$
$828$	−1.42402	−	3.43790i	−0.0494883	−	0.119475i
$829$		−	19.2597i		−	0.668918i	−0.942410	−	0.334459i	$-0.891446\pi$
$829$		−	19.2597i		−	0.668918i	0.942410	−	0.334459i	$-0.108554\pi$
$830$	−39.6337	+	16.4168i	−1.37571	+	0.569836i
$831$	−7.37338	−	7.37338i	−0.255780	−	0.255780i
$832$	−11.9346			−0.413760
$833$		0			0
$834$	23.8686			0.826502
$835$	−6.14556	−	6.14556i	−0.212676	−	0.212676i
$836$	2.64793	−	1.09681i	0.0915804	−	0.0379338i
$837$		−	4.13287i		−	0.142853i
$838$	−7.66307	−	18.5003i	−0.264716	−	0.639082i
$839$	13.6789	+	5.66598i	0.472248	+	0.195611i	0.606098	−	0.795390i	$-0.292734\pi$
$839$	13.6789	+	5.66598i	0.472248	+	0.195611i	−0.133850	+	0.991002i	$0.542734\pi$
$840$	3.01225	−	7.27222i	0.103933	−	0.250916i
$841$	17.0721	−	17.0721i	0.588693	−	0.588693i
$842$	20.8810	−	20.8810i	0.719608	−	0.719608i
$843$	−2.09212	+	5.05082i	−0.0720564	+	0.173960i
$844$	3.96524	+	1.64246i	0.136489	+	0.0565357i
$845$	−0.345773	−	0.834771i	−0.0118950	−	0.0287170i
$846$		−	11.5016i		−	0.395434i
$847$	−4.98211	+	2.06366i	−0.171187	+	0.0709081i
$848$	−9.39111	−	9.39111i	−0.322492	−	0.322492i
$849$	−17.6375			−0.605318
$850$		0			0
$851$	−30.3597			−1.04072
$852$	0.786489	+	0.786489i	0.0269447	+	0.0269447i
$853$	5.87376	−	2.43299i	0.201114	−	0.0833040i	−0.279853	−	0.960043i	$-0.590286\pi$
$853$	5.87376	−	2.43299i	0.201114	−	0.0833040i	0.480967	+	0.876739i	$0.340286\pi$
$854$			5.92864i			0.202874i
$855$	−2.69190	−	6.49883i	−0.0920612	−	0.222255i
$856$	38.1030	+	15.7828i	1.30233	+	0.539444i
$857$	15.6254	−	37.7231i	0.533754	−	1.28859i	−0.395267	−	0.918566i	$-0.629348\pi$
$857$	15.6254	−	37.7231i	0.533754	−	1.28859i	0.929020	−	0.370029i	$-0.120652\pi$
$858$	9.48065	−	9.48065i	0.323664	−	0.323664i
$859$	15.6599	−	15.6599i	0.534308	−	0.534308i	−0.387543	−	0.921851i	$-0.626676\pi$
$859$	15.6599	−	15.6599i	0.534308	−	0.534308i	0.921851	+	0.387543i	$0.126676\pi$
$860$	−5.94161	+	14.3443i	−0.202607	+	0.489137i
$861$	−4.30354	−	1.78259i	−0.146664	−	0.0607504i
$862$	−7.04112	−	16.9988i	−0.239822	−	0.578980i
$863$		−	17.3423i		−	0.590339i	−0.955445	−	0.295170i	$-0.904624\pi$
$863$		−	17.3423i		−	0.590339i	0.955445	−	0.295170i	$-0.0953762\pi$
$864$	−3.64318	+	1.50906i	−0.123944	+	0.0513391i
$865$	15.1820	+	15.1820i	0.516203	+	0.516203i
$866$	−48.1097			−1.63483
$867$		0			0
$868$	2.78222			0.0944346
$869$	19.0762	+	19.0762i	0.647117	+	0.647117i
$870$	−13.6790	+	5.66604i	−0.463762	+	0.192097i
$871$			43.0452i			1.45853i
$872$	−0.574725	−	1.38751i	−0.0194627	−	0.0469870i
$873$	13.3680	+	5.53723i	0.452440	+	0.187407i
$874$	−5.57653	+	13.4629i	−0.188629	+	0.455391i
$875$	17.3347	−	17.3347i	0.586019	−	0.586019i
$876$	−0.601239	+	0.601239i	−0.0203140	+	0.0203140i
$877$	11.5687	−	27.9294i	0.390649	−	0.943110i	−0.599150	−	0.800637i	$-0.704495\pi$
$877$	11.5687	−	27.9294i	0.390649	−	0.943110i	0.989799	−	0.142473i	$-0.0455053\pi$
$878$	34.4915	+	14.2868i	1.16403	+	0.482157i
$879$	−3.16037	−	7.62982i	−0.106597	−	0.257347i
$880$			45.4835i			1.53325i
$881$	−9.76049	+	4.04293i	−0.328839	+	0.136210i	−0.540994	−	0.841026i	$-0.681952\pi$
$881$	−9.76049	+	4.04293i	−0.328839	+	0.136210i	0.212155	+	0.977236i	$0.431952\pi$
$882$	−7.18411	−	7.18411i	−0.241902	−	0.241902i
$883$	−13.9150			−0.468276			−0.234138	−	0.972203i	$-0.575227\pi$
$883$	−13.9150			−0.468276			−0.234138	+	0.972203i	$0.575227\pi$
$884$		0			0
$885$	−30.0851			−1.01130
$886$	−37.6164	−	37.6164i	−1.26375	−	1.26375i
$887$	33.2268	−	13.7630i	1.11565	−	0.462116i	0.252767	−	0.967527i	$-0.418659\pi$
$887$	33.2268	−	13.7630i	1.11565	−	0.462116i	0.862878	+	0.505412i	$0.168659\pi$
$888$			12.4961i			0.419342i
$889$	0.992044	+	2.39501i	0.0332721	+	0.0803259i
$890$	−64.3051	−	26.6360i	−2.15551	−	0.892842i
$891$	−0.868752	+	2.09735i	−0.0291043	+	0.0702640i
$892$	2.88170	−	2.88170i	0.0964863	−	0.0964863i
$893$	−8.51494	+	8.51494i	−0.284941	+	0.284941i
$894$	−2.27340	+	5.48848i	−0.0760340	+	0.183562i
$895$	29.2144	+	12.1010i	0.976528	+	0.404491i
$896$	4.73101	+	11.4217i	0.158052	+	0.381571i
$897$			18.2254i			0.608530i
$898$	1.71009	−	0.708341i	0.0570663	−	0.0236376i
$899$	6.44012	+	6.44012i	0.214790	+	0.214790i
$900$	−8.41937			−0.280646
$901$		0			0
$902$	18.9420			0.630698
$903$	3.41208	+	3.41208i	0.113547	+	0.113547i
$904$	−22.8543	+	9.46655i	−0.760122	+	0.314853i
$905$			3.72418i			0.123796i
$906$	4.79791	+	11.5832i	0.159400	+	0.384825i
$907$	−36.2016	−	14.9952i	−1.20205	−	0.497907i	−0.310391	−	0.950609i	$-0.600460\pi$
$907$	−36.2016	−	14.9952i	−1.20205	−	0.497907i	−0.891662	+	0.452702i	$0.850460\pi$
$908$	7.68904	−	18.5630i	0.255170	−	0.616034i
$909$	−0.187911	+	0.187911i	−0.00623260	+	0.00623260i
$910$	15.6641	−	15.6641i	0.519261	−	0.519261i
$911$	3.79931	−	9.17234i	0.125877	−	0.303893i	−0.848361	−	0.529419i	$-0.822410\pi$
$911$	3.79931	−	9.17234i	0.125877	−	0.303893i	0.974237	+	0.225526i	$0.0724100\pi$
$912$	7.87418	+	3.26159i	0.260740	+	0.108002i
$913$	−5.54706	−	13.3918i	−0.183581	−	0.443203i
$914$			66.2202i			2.19037i
$915$	−14.6152	+	6.05382i	−0.483164	+	0.200133i
$916$	1.84249	+	1.84249i	0.0608775	+	0.0608775i
$917$	−7.31174			−0.241455
$918$		0			0
$919$	42.8795			1.41446			0.707232	−	0.706982i	$-0.249944\pi$
$919$	42.8795			1.41446			0.707232	+	0.706982i	$0.249944\pi$
$920$	−30.7663	−	30.7663i	−1.01434	−	1.01434i
$921$	−9.18892	+	3.80617i	−0.302785	+	0.125418i
$922$		−	8.25442i		−	0.271845i
$923$	−2.08472	−	5.03296i	−0.0686193	−	0.165662i
$924$	−1.41192	−	0.584837i	−0.0464488	−	0.0192397i
$925$	−26.2869	+	63.4621i	−0.864307	+	2.08662i
$926$	45.6164	−	45.6164i	1.49905	−	1.49905i
$927$	−2.14556	+	2.14556i	−0.0704696	+	0.0704696i
$928$	3.32554	−	8.02856i	0.109166	−	0.263551i
$929$	16.7798	+	6.95043i	0.550529	+	0.228036i	0.640568	−	0.767902i	$-0.278699\pi$
$929$	16.7798	+	6.95043i	0.550529	+	0.228036i	−0.0900390	+	0.995938i	$0.528699\pi$
$930$	10.6261	+	25.6537i	0.348444	+	0.841218i
$931$			10.6372i			0.348619i
$932$	0.924365	−	0.382884i	0.0302786	−	0.0125418i
$933$	11.7284	+	11.7284i	0.383972	+	0.383972i
$934$	17.3883			0.568963
$935$		0			0
$936$	7.50162			0.245198
$937$	1.13309	+	1.13309i	0.0370165	+	0.0370165i	0.725373	−	0.688356i	$-0.241667\pi$
$937$	1.13309	+	1.13309i	0.0370165	+	0.0370165i	−0.688356	+	0.725373i	$0.741667\pi$
$938$	16.9548	−	7.02289i	0.553592	−	0.229305i
$939$			20.6116i			0.672634i
$940$	7.90628	+	19.0874i	0.257874	+	0.622564i
$941$	29.8916	+	12.3815i	0.974437	+	0.403625i	0.812362	−	0.583153i	$-0.198181\pi$
$941$	29.8916	+	12.3815i	0.974437	+	0.403625i	0.162075	+	0.986778i	$0.448181\pi$
$942$	−11.9860	+	28.9368i	−0.390526	+	0.942813i
$943$	−18.2068	+	18.2068i	−0.592896	+	0.592896i
$944$	25.7755	−	25.7755i	0.838920	−	0.838920i
$945$	−1.43537	+	3.46530i	−0.0466927	+	0.112726i
$946$	−18.1286	−	7.50909i	−0.589410	−	0.244142i
$947$	9.63669	+	23.2650i	0.313150	+	0.756012i	0.999585	+	0.0288200i	$0.00917496\pi$
$947$	9.63669	+	23.2650i	0.313150	+	0.756012i	−0.686434	+	0.727192i	$0.740825\pi$
$948$		−	8.67319i		−	0.281692i
$949$	3.84749	−	1.59368i	0.124895	−	0.0517332i
$950$	23.3137	+	23.3137i	0.756397	+	0.756397i
$951$	−4.26802			−0.138400
$952$		0			0
$953$	54.0658			1.75136			0.875681	−	0.482889i	$-0.160413\pi$
$953$	54.0658			1.75136			0.875681	+	0.482889i	$0.160413\pi$
$954$	3.14921	+	3.14921i	0.101959	+	0.101959i
$955$	−72.0038	+	29.8250i	−2.32999	+	0.965113i
$956$			15.7734i			0.510148i
$957$	−1.91449	−	4.62199i	−0.0618867	−	0.149408i
$958$	39.6328	+	16.4164i	1.28048	+	0.530391i
$959$	−0.0364340	+	0.0879594i	−0.00117651	+	0.00284036i
$960$	−9.60021	+	9.60021i	−0.309845	+	0.309845i
$961$	−9.84248	+	9.84248i	−0.317499	+	0.317499i
$962$	−13.4581	+	32.4908i	−0.433907	+	1.04754i
$963$	−18.1565	−	7.52066i	−0.585085	−	0.242350i
$964$	0.296560	+	0.715959i	0.00955155	+	0.0230595i
$965$		−	19.1585i		−	0.616733i
$966$	7.17868	−	2.97351i	0.230970	−	0.0956711i
$967$	1.53792	+	1.53792i	0.0494563	+	0.0494563i	0.731402	−	0.681946i	$-0.238866\pi$
$967$	1.53792	+	1.53792i	0.0494563	+	0.0494563i	−0.681946	+	0.731402i	$0.738866\pi$
$968$	12.2691			0.394345
$969$		0			0
$970$	−97.2154			−3.12140
$971$	33.5508	+	33.5508i	1.07670	+	1.07670i	0.996803	+	0.0798947i	$0.0254584\pi$
$971$	33.5508	+	33.5508i	1.07670	+	1.07670i	0.0798947	+	0.996803i	$0.474542\pi$
$972$	0.674285	−	0.279298i	0.0216277	−	0.00895848i
$973$			13.3251i			0.427182i
$974$	16.1487	+	38.9865i	0.517439	+	1.24921i
$975$	38.0974	+	15.7805i	1.22009	+	0.505379i
$976$	7.33498	−	17.7082i	0.234787	−	0.566826i
$977$	14.7238	−	14.7238i	0.471057	−	0.471057i	−0.431200	−	0.902256i	$-0.641910\pi$
$977$	14.7238	−	14.7238i	0.471057	−	0.471057i	0.902256	+	0.431200i	$0.141910\pi$
$978$	−15.6938	+	15.6938i	−0.501832	+	0.501832i
$979$	9.00002	−	21.7280i	0.287642	−	0.694429i
$980$	16.8607	+	6.98395i	0.538597	+	0.223094i
$981$	0.273863	+	0.661164i	0.00874377	+	0.0211093i
$982$		−	4.14319i		−	0.132214i
$983$	−2.24538	+	0.930068i	−0.0716166	+	0.0296646i	−0.418204	−	0.908353i	$-0.637340\pi$
$983$	−2.24538	+	0.930068i	−0.0716166	+	0.0296646i	0.346588	+	0.938018i	$0.387340\pi$
$984$	7.49397	+	7.49397i	0.238899	+	0.238899i
$985$	−60.5690			−1.92989
$986$		0			0
$987$	6.42098			0.204382
$988$	3.19115	+	3.19115i	0.101524	+	0.101524i
$989$	24.6427	−	10.2073i	0.783592	−	0.324574i
$990$		−	15.2524i		−	0.484754i
$991$	−13.9977	−	33.7934i	−0.444651	−	1.07348i	−0.974298	−	0.225264i	$-0.927676\pi$
$991$	−13.9977	−	33.7934i	−0.444651	−	1.07348i	0.529647	−	0.848218i	$-0.322324\pi$
$992$	−15.0568	−	6.23673i	−0.478054	−	0.198016i
$993$	10.9488	−	26.4327i	0.347449	−	0.838816i
$994$	−1.64227	+	1.64227i	−0.0520896	+	0.0520896i
$995$	−54.0107	+	54.0107i	−1.71226	+	1.71226i
$996$	−1.78334	+	4.30536i	−0.0565073	+	0.136421i
$997$	−19.1344	−	7.92571i	−0.605991	−	0.251010i	0.0585222	−	0.998286i	$-0.481361\pi$
$997$	−19.1344	−	7.92571i	−0.605991	−	0.251010i	−0.664513	+	0.747276i	$0.731361\pi$
$998$	−9.62773	−	23.2434i	−0.304760	−	0.735757i
$999$		−	5.95453i		−	0.188393i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.k.733.2		16
17.2	even	8		867.2.h.i.688.4		16
17.3	odd	16		867.2.a.l.1.2		4
17.4	even	4		867.2.h.i.712.3		16
17.5	odd	16		867.2.d.f.577.6		8
17.6	odd	16		51.2.e.a.4.2	✓	8
17.7	odd	16		867.2.e.g.829.3		8
17.8	even	8	inner	867.2.h.k.757.1		16
17.9	even	8	inner	867.2.h.k.757.2		16
17.10	odd	16		51.2.e.a.13.3	yes	8
17.11	odd	16		867.2.e.g.616.2		8
17.12	odd	16		867.2.d.f.577.5		8
17.13	even	4		867.2.h.i.712.4		16
17.14	odd	16		867.2.a.k.1.2		4
17.15	even	8		867.2.h.i.688.3		16
17.16	even	2	inner	867.2.h.k.733.1		16
51.14	even	16		2601.2.a.bf.1.3		4
51.20	even	16		2601.2.a.be.1.3		4
51.23	even	16		153.2.f.b.55.3		8
51.44	even	16		153.2.f.b.64.2		8
68.23	even	16		816.2.bd.e.769.1		8
68.27	even	16		816.2.bd.e.625.1		8
204.23	odd	16		2448.2.be.x.1585.4		8
204.95	odd	16		2448.2.be.x.1441.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.e.a.4.2	✓	8	17.6	odd	16
51.2.e.a.13.3	yes	8	17.10	odd	16
153.2.f.b.55.3		8	51.23	even	16
153.2.f.b.64.2		8	51.44	even	16
816.2.bd.e.625.1		8	68.27	even	16
816.2.bd.e.769.1		8	68.23	even	16
867.2.a.k.1.2		4	17.14	odd	16
867.2.a.l.1.2		4	17.3	odd	16
867.2.d.f.577.5		8	17.12	odd	16
867.2.d.f.577.6		8	17.5	odd	16
867.2.e.g.616.2		8	17.11	odd	16
867.2.e.g.829.3		8	17.7	odd	16
867.2.h.i.688.3		16	17.15	even	8
867.2.h.i.688.4		16	17.2	even	8
867.2.h.i.712.3		16	17.4	even	4
867.2.h.i.712.4		16	17.13	even	4
867.2.h.k.733.1		16	17.16	even	2	inner
867.2.h.k.733.2		16	1.1	even	1	trivial
867.2.h.k.757.1		16	17.8	even	8	inner
867.2.h.k.757.2		16	17.9	even	8	inner
2448.2.be.x.1441.4		8	204.95	odd	16
2448.2.be.x.1585.4		8	204.23	odd	16
2601.2.a.be.1.3		4	51.20	even	16
2601.2.a.bf.1.3		4	51.14	even	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.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.16830 - 1.16830i) q^{2} +(0.923880 - 0.382683i) q^{3} +0.729840i q^{4} +(-1.55616 - 3.75690i) q^{5} +(-1.52645 - 0.632278i) q^{6} +(0.352980 - 0.852170i) q^{7} +(-1.48392 + 1.48392i) q^{8} +(0.707107 - 0.707107i) q^{9} +(-2.57112 + 6.20723i) q^{10} +(-2.09735 - 0.868752i) q^{11} +(0.279298 + 0.674285i) q^{12} -3.57461i q^{13} +(-1.40798 + 0.583202i) q^{14} +(-2.87540 - 2.87540i) q^{15} +4.92701 q^{16} -1.65222 q^{18} +(1.22318 + 1.22318i) q^{19} +(2.74194 - 1.13575i) q^{20} -0.922382i q^{21} +(1.43537 + 3.46530i) q^{22} +(-4.71048 - 1.95114i) q^{23} +(-0.803094 + 1.93884i) q^{24} +(-8.15712 + 8.15712i) q^{25} +(-4.17620 + 4.17620i) q^{26} +(0.382683 - 0.923880i) q^{27} +(0.621948 + 0.257619i) q^{28} +(0.843328 + 2.03597i) q^{29} +6.71866i q^{30} +(3.81828 - 1.58158i) q^{31} +(-2.78837 - 2.78837i) q^{32} -2.27016 q^{33} -3.75081 q^{35} +(0.516075 + 0.516075i) q^{36} +(5.50127 - 2.27870i) q^{37} -2.85808i q^{38} +(-1.36794 - 3.30250i) q^{39} +(7.88417 + 3.26573i) q^{40} +(1.93259 - 4.66568i) q^{41} +(-1.07762 + 1.07762i) q^{42} +(-3.69920 + 3.69920i) q^{43} +(0.634051 - 1.53073i) q^{44} +(-3.75690 - 1.55616i) q^{45} +(3.22373 + 7.78276i) q^{46} +6.96130i q^{47} +(4.55197 - 1.88549i) q^{48} +(4.34815 + 4.34815i) q^{49} +19.0599 q^{50} +2.60889 q^{52} +(-1.90604 - 1.90604i) q^{53} +(-1.52645 + 0.632278i) q^{54} +9.23146i q^{55} +(0.740760 + 1.78835i) q^{56} +(1.59816 + 0.661981i) q^{57} +(1.39337 - 3.36388i) q^{58} +(5.23146 - 5.23146i) q^{59} +(2.09859 - 2.09859i) q^{60} +(1.48873 - 3.59411i) q^{61} +(-6.30864 - 2.61313i) q^{62} +(-0.352980 - 0.852170i) q^{63} -3.33873i q^{64} +(-13.4294 + 5.56265i) q^{65} +(2.65222 + 2.65222i) q^{66} -12.0419 q^{67} -5.09859 q^{69} +(4.38206 + 4.38206i) q^{70} +(1.40798 - 0.583202i) q^{71} +2.09859i q^{72} +(0.445835 + 1.07634i) q^{73} +(-9.08933 - 3.76492i) q^{74} +(-4.41460 + 10.6578i) q^{75} +(-0.892728 + 0.892728i) q^{76} +(-1.48065 + 1.48065i) q^{77} +(-2.26015 + 5.45647i) q^{78} +(-10.9791 - 4.54769i) q^{79} +(-7.66721 - 18.5103i) q^{80} -1.00000i q^{81} +(-7.70875 + 3.19307i) q^{82} +(4.51494 + 4.51494i) q^{83} +0.673192 q^{84} +8.64354 q^{86} +(1.55827 + 1.55827i) q^{87} +(4.40148 - 1.82315i) q^{88} +10.3597i q^{89} +(2.57112 + 6.20723i) q^{90} +(-3.04617 - 1.26177i) q^{91} +(1.42402 - 3.43790i) q^{92} +(2.92238 - 2.92238i) q^{93} +(8.13287 - 8.13287i) q^{94} +(2.69190 - 6.49883i) q^{95} +(-3.64318 - 1.50906i) q^{96} +(5.53723 + 13.3680i) q^{97} -10.1599i q^{98} +(-2.09735 + 0.868752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 32 q^{8} - 8 q^{15} - 24 q^{16} - 8 q^{18} - 32 q^{25} - 40 q^{26} - 16 q^{32} - 24 q^{33} + 16 q^{35} - 48 q^{42} - 48 q^{43} - 32 q^{49} + 120 q^{50} - 32 q^{52} - 16 q^{53} - 56 q^{59}+ \cdots + 48 q^{94}+O(q^{100}) \) 16 * q + 8 * q^2 - 32 * q^8 - 8 * q^15 - 24 * q^16 - 8 * q^18 - 32 * q^25 - 40 * q^26 - 16 * q^32 - 24 * q^33 + 16 * q^35 - 48 * q^42 - 48 * q^43 - 32 * q^49 + 120 * q^50 - 32 * q^52 - 16 * q^53 - 56 * q^59 - 24 * q^60 + 24 * q^66 - 16 * q^67 - 24 * q^69 + 64 * q^70 + 64 * q^76 + 40 * q^77 - 16 * q^83 - 96 * q^84 - 16 * q^86 - 8 * q^87 + 16 * q^93 + 48 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more