LMFDB - Embedded newform 867.2.h.i.712.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(688,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [16,-8,0,0,0,0,0,32,0,0,0,0,0,0,8,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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			712.3
Root			$2.83302 - 1.17347i$ of defining polynomial
Character	$\chi$	$=$	867.712
Dual form			867.2.h.i.688.3

$q$-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} +(-0.382683 - 0.923880i) q^{3} +0.729840i q^{4} +(-3.75690 + 1.55616i) q^{5} +(0.632278 - 1.52645i) q^{6} +(0.852170 + 0.352980i) q^{7} +(1.48392 - 1.48392i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-6.20723 - 2.57112i) q^{10} +(0.868752 - 2.09735i) q^{11} +(0.674285 - 0.279298i) q^{12} -3.57461i q^{13} +(0.583202 + 1.40798i) q^{14} +(2.87540 + 2.87540i) q^{15} +4.92701 q^{16} -1.65222 q^{18} +(-1.22318 - 1.22318i) q^{19} +(-1.13575 - 2.74194i) q^{20} -0.922382i q^{21} +(3.46530 - 1.43537i) q^{22} +(1.95114 - 4.71048i) q^{23} +(-1.93884 - 0.803094i) q^{24} +(8.15712 - 8.15712i) q^{25} +(4.17620 - 4.17620i) q^{26} +(0.923880 + 0.382683i) q^{27} +(-0.257619 + 0.621948i) q^{28} +(2.03597 - 0.843328i) q^{29} +6.71866i q^{30} +(-1.58158 - 3.81828i) q^{31} +(2.78837 + 2.78837i) q^{32} -2.27016 q^{33} -3.75081 q^{35} +(-0.516075 - 0.516075i) q^{36} +(-2.27870 - 5.50127i) q^{37} -2.85808i q^{38} +(-3.30250 + 1.36794i) q^{39} +(-3.26573 + 7.88417i) q^{40} +(4.66568 + 1.93259i) q^{41} +(1.07762 - 1.07762i) q^{42} +(3.69920 - 3.69920i) q^{43} +(1.53073 + 0.634051i) q^{44} +(1.55616 - 3.75690i) q^{45} +(7.78276 - 3.22373i) q^{46} +6.96130i q^{47} +(-1.88549 - 4.55197i) q^{48} +(-4.34815 - 4.34815i) q^{49} +19.0599 q^{50} +2.60889 q^{52} +(1.90604 + 1.90604i) q^{53} +(0.632278 + 1.52645i) q^{54} +9.23146i q^{55} +(1.78835 - 0.740760i) q^{56} +(-0.661981 + 1.59816i) q^{57} +(3.36388 + 1.39337i) q^{58} +(-5.23146 + 5.23146i) q^{59} +(-2.09859 + 2.09859i) q^{60} +(3.59411 + 1.48873i) q^{61} +(2.61313 - 6.30864i) q^{62} +(-0.852170 + 0.352980i) q^{63} -3.33873i q^{64} +(5.56265 + 13.4294i) q^{65} +(-2.65222 - 2.65222i) q^{66} -12.0419 q^{67} -5.09859 q^{69} +(-4.38206 - 4.38206i) q^{70} +(-0.583202 - 1.40798i) q^{71} +2.09859i q^{72} +(1.07634 - 0.445835i) q^{73} +(3.76492 - 9.08933i) q^{74} +(-10.6578 - 4.41460i) q^{75} +(0.892728 - 0.892728i) q^{76} +(1.48065 - 1.48065i) q^{77} +(-5.45647 - 2.26015i) q^{78} +(4.54769 - 10.9791i) q^{79} +(-18.5103 + 7.66721i) q^{80} -1.00000i q^{81} +(3.19307 + 7.70875i) q^{82} +(-4.51494 - 4.51494i) q^{83} +0.673192 q^{84} +8.64354 q^{86} +(-1.55827 - 1.55827i) q^{87} +(-1.82315 - 4.40148i) q^{88} +10.3597i q^{89} +(6.20723 - 2.57112i) q^{90} +(1.26177 - 3.04617i) q^{91} +(3.43790 + 1.42402i) q^{92} +(-2.92238 + 2.92238i) q^{93} +(-8.13287 + 8.13287i) q^{94} +(6.49883 + 2.69190i) q^{95} +(1.50906 - 3.64318i) q^{96} +(13.3680 - 5.53723i) q^{97} -10.1599i q^{98} +(0.868752 + 2.09735i) 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 $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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	0.986976	−	0.160865i	$-0.0514284\pi$
$2$	1.16830	+	1.16830i	0.826111	+	0.826111i	−0.160865	+	0.986976i	$0.551428\pi$
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$4$			0.729840i			0.364920i
$5$	−3.75690	+	1.55616i	−1.68014	+	0.695935i	−0.999333	−	0.0365315i	$-0.988369\pi$
$5$	−3.75690	+	1.55616i	−1.68014	+	0.695935i	−0.680803	+	0.732466i	$0.738369\pi$
$6$	0.632278	−	1.52645i	0.258127	−	0.623173i
$7$	0.852170	+	0.352980i	0.322090	+	0.133414i	0.537870	−	0.843028i	$-0.319229\pi$
$7$	0.852170	+	0.352980i	0.322090	+	0.133414i	−0.215780	+	0.976442i	$0.569229\pi$
$8$	1.48392	−	1.48392i	0.524647	−	0.524647i
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$	−6.20723	−	2.57112i	−1.96290	−	0.813059i
$11$	0.868752	−	2.09735i	0.261939	−	0.632376i	−0.737120	−	0.675762i	$-0.763815\pi$
$11$	0.868752	−	2.09735i	0.261939	−	0.632376i	0.999058	+	0.0433862i	$0.0138146\pi$
$12$	0.674285	−	0.279298i	0.194649	−	0.0806263i
$13$		−	3.57461i		−	0.991417i	−0.868489	−	0.495709i	$-0.834908\pi$
$13$		−	3.57461i		−	0.991417i	0.868489	−	0.495709i	$-0.165092\pi$
$14$	0.583202	+	1.40798i	0.155867	+	0.376297i
$15$	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	0.552738	−	0.833355i	$-0.313583\pi$
$19$	−1.22318	−	1.22318i	−0.280617	−	0.280617i	−0.833355	+	0.552738i	$0.813583\pi$
$20$	−1.13575	−	2.74194i	−0.253961	−	0.613115i
$21$		−	0.922382i		−	0.201280i
$22$	3.46530	−	1.43537i	0.738804	−	0.306022i
$23$	1.95114	−	4.71048i	0.406842	−	0.982203i	−0.579122	−	0.815241i	$-0.696604\pi$
$23$	1.95114	−	4.71048i	0.406842	−	0.982203i	0.985963	−	0.166962i	$-0.0533956\pi$
$24$	−1.93884	−	0.803094i	−0.395764	−	0.163931i
$25$	8.15712	−	8.15712i	1.63142	−	1.63142i
$26$	4.17620	−	4.17620i	0.819021	−	0.819021i
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$	−0.257619	+	0.621948i	−0.0486855	+	0.117537i
$29$	2.03597	−	0.843328i	0.378071	−	0.156602i	−0.185552	−	0.982635i	$-0.559407\pi$
$29$	2.03597	−	0.843328i	0.378071	−	0.156602i	0.563623	+	0.826032i	$0.309407\pi$
$30$			6.71866i			1.22665i
$31$	−1.58158	−	3.81828i	−0.284061	−	0.685783i	0.715862	−	0.698242i	$-0.246034\pi$
$31$	−1.58158	−	3.81828i	−0.284061	−	0.685783i	−0.999922	+	0.0124592i	$0.996034\pi$
$32$	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
$37$	−2.27870	−	5.50127i	−0.374616	−	0.904403i	−0.992955	−	0.118492i	$-0.962194\pi$
$37$	−2.27870	−	5.50127i	−0.374616	−	0.904403i	0.618339	−	0.785912i	$-0.287806\pi$
$38$		−	2.85808i		−	0.463642i
$39$	−3.30250	+	1.36794i	−0.528824	+	0.219046i
$40$	−3.26573	+	7.88417i	−0.516358	+	1.24660i
$41$	4.66568	+	1.93259i	0.728657	+	0.301820i	0.716000	−	0.698100i	$-0.245971\pi$
$41$	4.66568	+	1.93259i	0.728657	+	0.301820i	0.0126571	+	0.999920i	$0.495971\pi$
$42$	1.07762	−	1.07762i	0.166280	−	0.166280i
$43$	3.69920	−	3.69920i	0.564123	−	0.564123i	−0.366353	−	0.930476i	$-0.619394\pi$
$43$	3.69920	−	3.69920i	0.564123	−	0.564123i	0.930476	+	0.366353i	$0.119394\pi$
$44$	1.53073	+	0.634051i	0.230767	+	0.0955867i
$45$	1.55616	−	3.75690i	0.231978	−	0.560045i
$46$	7.78276	−	3.22373i	1.14751	−	0.475312i
$47$			6.96130i			1.01541i	0.861531	+	0.507705i	$0.169506\pi$
$47$			6.96130i			1.01541i	−0.861531	+	0.507705i	$0.830494\pi$
$48$	−1.88549	−	4.55197i	−0.272147	−	0.657020i
$49$	−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	0.825791	−	0.563976i	$-0.190729\pi$
$53$	1.90604	+	1.90604i	0.261815	+	0.261815i	−0.563976	+	0.825791i	$0.690729\pi$
$54$	0.632278	+	1.52645i	0.0860422	+	0.207724i
$55$			9.23146i			1.24477i
$56$	1.78835	−	0.740760i	0.238979	−	0.0989882i
$57$	−0.661981	+	1.59816i	−0.0876816	+	0.211682i
$58$	3.36388	+	1.39337i	0.441700	+	0.182958i
$59$	−5.23146	+	5.23146i	−0.681078	+	0.681078i	−0.960243	−	0.279165i	$-0.909942\pi$
$59$	−5.23146	+	5.23146i	−0.681078	+	0.681078i	0.279165	+	0.960243i	$0.409942\pi$
$60$	−2.09859	+	2.09859i	−0.270926	+	0.270926i
$61$	3.59411	+	1.48873i	0.460178	+	0.190612i	0.600715	−	0.799463i	$-0.294883\pi$
$61$	3.59411	+	1.48873i	0.460178	+	0.190612i	−0.140537	+	0.990075i	$0.544883\pi$
$62$	2.61313	−	6.30864i	0.331867	−	0.801199i
$63$	−0.852170	+	0.352980i	−0.107363	+	0.0444714i
$64$		−	3.33873i		−	0.417341i
$65$	5.56265	+	13.4294i	0.689962	+	1.66572i
$66$	−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
$71$	−0.583202	−	1.40798i	−0.0692134	−	0.167096i	0.885487	−	0.464663i	$-0.153825\pi$
$71$	−0.583202	−	1.40798i	−0.0692134	−	0.167096i	−0.954701	+	0.297567i	$0.903825\pi$
$72$			2.09859i			0.247321i
$73$	1.07634	−	0.445835i	0.125976	−	0.0521810i	−0.318805	−	0.947820i	$-0.603281\pi$
$73$	1.07634	−	0.445835i	0.125976	−	0.0521810i	0.444781	+	0.895639i	$0.353281\pi$
$74$	3.76492	−	9.08933i	0.437663	−	1.05661i
$75$	−10.6578	−	4.41460i	−1.23066	−	0.509754i
$76$	0.892728	−	0.892728i	0.102403	−	0.102403i
$77$	1.48065	−	1.48065i	0.168736	−	0.168736i
$78$	−5.45647	−	2.26015i	−0.617824	−	0.255911i
$79$	4.54769	−	10.9791i	0.511655	−	1.23524i	−0.431265	−	0.902225i	$-0.641933\pi$
$79$	4.54769	−	10.9791i	0.511655	−	1.23524i	0.942920	−	0.333019i	$-0.108067\pi$
$80$	−18.5103	+	7.66721i	−2.06951	+	0.857220i
$81$		−	1.00000i		−	0.111111i
$82$	3.19307	+	7.70875i	0.352615	+	0.851289i
$83$	−4.51494	−	4.51494i	−0.495579	−	0.495579i	0.414480	−	0.910058i	$-0.363964\pi$
$83$	−4.51494	−	4.51494i	−0.495579	−	0.495579i	−0.910058	+	0.414480i	$0.863964\pi$
$84$	0.673192			0.0734513
$85$		0			0
$86$	8.64354			0.932057
$87$	−1.55827	−	1.55827i	−0.167064	−	0.167064i
$88$	−1.82315	−	4.40148i	−0.194349	−	0.469199i
$89$			10.3597i			1.09813i	0.835781	+	0.549063i	$0.185015\pi$
$89$			10.3597i			1.09813i	−0.835781	+	0.549063i	$0.814985\pi$
$90$	6.20723	−	2.57112i	0.654300	−	0.271020i
$91$	1.26177	−	3.04617i	0.132269	−	0.319326i
$92$	3.43790	+	1.42402i	0.358426	+	0.148465i
$93$	−2.92238	+	2.92238i	−0.303037	+	0.303037i
$94$	−8.13287	+	8.13287i	−0.838842	+	0.838842i
$95$	6.49883	+	2.69190i	0.666766	+	0.276184i
$96$	1.50906	−	3.64318i	0.154017	−	0.371831i
$97$	13.3680	−	5.53723i	1.35732	−	0.562220i	0.418999	−	0.907987i	$-0.362381\pi$
$97$	13.3680	−	5.53723i	1.35732	−	0.562220i	0.938321	+	0.345767i	$0.112381\pi$
$98$		−	10.1599i		−	1.02630i
$99$	0.868752	+	2.09735i	0.0873129	+	0.210792i
$100$	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
$105$	1.43537	+	3.46530i	0.140078	+	0.338178i
$106$			4.45366i			0.432577i
$107$	−18.1565	+	7.52066i	−1.75525	+	0.727050i	−0.758060	+	0.652185i	$0.773853\pi$
$107$	−18.1565	+	7.52066i	−1.75525	+	0.727050i	−0.997194	+	0.0748654i	$0.976147\pi$
$108$	−0.279298	+	0.674285i	−0.0268754	+	0.0648831i
$109$	−0.661164	−	0.273863i	−0.0633280	−	0.0262313i	0.350795	−	0.936452i	$-0.385912\pi$
$109$	−0.661164	−	0.273863i	−0.0633280	−	0.0262313i	−0.414123	+	0.910221i	$0.635912\pi$
$110$	−10.7851	+	10.7851i	−1.02832	+	1.02832i
$111$	−4.21049	+	4.21049i	−0.399642	+	0.399642i
$112$	4.19865	+	1.73914i	0.396736	+	0.164333i
$113$	−4.51092	+	10.8903i	−0.424351	+	1.02447i	0.556698	+	0.830715i	$0.312068\pi$
$113$	−4.51092	+	10.8903i	−0.424351	+	1.02447i	−0.981049	+	0.193759i	$0.937932\pi$
$114$	−2.64052	+	1.09374i	−0.247308	+	0.102438i
$115$			20.7331i			1.93337i
$116$	0.615495	+	1.48594i	0.0571473	+	0.137966i
$117$	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
$122$	2.45971	+	5.93826i	0.222692	+	0.537625i
$123$		−	5.05010i		−	0.455352i
$124$	2.78673	−	1.15430i	0.250256	−	0.103659i
$125$	−10.1709	+	24.5547i	−0.909713	+	2.19624i
$126$	−1.40798	−	0.583202i	−0.125432	−	0.0519558i
$127$	1.98731	−	1.98731i	0.176345	−	0.176345i	−0.613415	−	0.789760i	$-0.710205\pi$
$127$	1.98731	−	1.98731i	0.176345	−	0.176345i	0.789760	+	0.613415i	$0.210205\pi$
$128$	9.47738	−	9.47738i	0.837690	−	0.837690i
$129$	−4.83324	−	2.00199i	−0.425543	−	0.176266i
$130$	−9.19074	+	22.1884i	−0.806081	+	1.94605i
$131$	−7.32361	+	3.03354i	−0.639866	+	0.265041i	−0.678939	−	0.734195i	$-0.737560\pi$
$131$	−7.32361	+	3.03354i	−0.639866	+	0.265041i	0.0390722	+	0.999236i	$0.487560\pi$
$132$		−	1.65685i		−	0.144211i
$133$	−0.610600	−	1.47412i	−0.0529457	−	0.127822i
$134$	−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
$139$	5.52838	+	13.3467i	0.468911	+	1.13205i	0.964639	+	0.263574i	$0.0849014\pi$
$139$	5.52838	+	13.3467i	0.468911	+	1.13205i	−0.495728	+	0.868478i	$0.665099\pi$
$140$		−	2.73749i		−	0.231360i
$141$	6.43140	−	2.66397i	0.541622	−	0.224347i
$142$	0.963580	−	2.32629i	0.0808619	−	0.195218i
$143$	−7.49721	−	3.10545i	−0.626948	−	0.259691i
$144$	−3.48392	+	3.48392i	−0.290327	+	0.290327i
$145$	−6.33660	+	6.33660i	−0.526226	+	0.526226i
$146$	1.77836	+	0.736619i	0.147178	+	0.0609630i
$147$	−2.35320	+	5.68113i	−0.194089	+	0.468572i
$148$	4.01505	−	1.66309i	0.330035	−	0.136705i
$149$		−	3.59557i		−	0.294561i	−0.989095	−	0.147280i	$-0.952948\pi$
$149$		−	3.59557i		−	0.294561i	0.989095	−	0.147280i	$-0.0470520\pi$
$150$	−7.29390	−	17.6090i	−0.595545	−	1.43777i
$151$	5.36573	+	5.36573i	0.436657	+	0.436657i	0.890885	−	0.454229i	$-0.150085\pi$
$151$	5.36573	+	5.36573i	0.436657	+	0.436657i	−0.454229	+	0.890885i	$0.650085\pi$
$152$	−3.63022			−0.294450
$153$		0			0
$154$	3.45968			0.278789
$155$	11.8837	+	11.8837i	0.954520	+	0.954520i
$156$	−0.998380	−	2.41030i	−0.0799343	−	0.192979i
$157$		−	18.9569i		−	1.51292i	−0.654038	−	0.756462i	$-0.726926\pi$
$157$		−	18.9569i		−	1.51292i	0.654038	−	0.756462i	$-0.273074\pi$
$158$	18.1399	−	7.51379i	1.44313	−	0.597765i
$159$	1.03154	−	2.49037i	0.0818068	−	0.197499i
$160$	−14.8148	−	6.13648i	−1.17121	−	0.485131i
$161$	3.32541	−	3.32541i	0.262079	−	0.262079i
$162$	1.16830	−	1.16830i	0.0917902	−	0.0917902i
$163$	12.4105	+	5.14060i	0.972067	+	0.402643i	0.811481	−	0.584379i	$-0.198662\pi$
$163$	12.4105	+	5.14060i	0.972067	+	0.402643i	0.160586	+	0.987022i	$0.448662\pi$
$164$	−1.41048	+	3.40520i	−0.110140	+	0.265902i
$165$	8.52876	−	3.53273i	0.663963	−	0.275022i
$166$		−	10.5496i		−	0.818806i
$167$	−0.817904	−	1.97460i	−0.0632913	−	0.152799i	0.889070	−	0.457772i	$-0.151352\pi$
$167$	−0.817904	−	1.97460i	−0.0632913	−	0.152799i	−0.952361	+	0.304973i	$0.901352\pi$
$168$	−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
$173$	2.02055	+	4.87804i	0.153619	+	0.370870i	0.981888	−	0.189461i	$-0.0606740\pi$
$173$	2.02055	+	4.87804i	0.153619	+	0.370870i	−0.828269	+	0.560331i	$0.810674\pi$
$174$		−	3.64104i		−	0.276027i
$175$	9.83056	−	4.07195i	0.743120	−	0.307810i
$176$	4.28036	−	10.3337i	0.322644	−	0.778931i
$177$	6.83523	+	2.83125i	0.513767	+	0.212809i
$178$	−12.1032	+	12.1032i	−0.907175	+	0.907175i
$179$	5.49860	−	5.49860i	0.410985	−	0.410985i	−0.471097	−	0.882081i	$-0.656142\pi$
$179$	5.49860	−	5.49860i	0.410985	−	0.410985i	0.882081	+	0.471097i	$0.156142\pi$
$180$	2.74194	+	1.13575i	0.204372	+	0.0846536i
$181$	0.350474	−	0.846119i	0.0260505	−	0.0628915i	−0.910319	−	0.413907i	$-0.864164\pi$
$181$	0.350474	−	0.846119i	0.0260505	−	0.0628915i	0.936369	+	0.351016i	$0.114164\pi$
$182$	5.03296	−	2.08472i	0.373067	−	0.154530i
$183$		−	3.89023i		−	0.287574i
$184$	−4.09465	−	9.88535i	−0.301861	−	0.728758i
$185$	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
$190$	4.44763	+	10.7375i	0.322665	+	0.778982i
$191$		−	19.1658i		−	1.38679i	−0.720560	−	0.693393i	$-0.756115\pi$
$191$		−	19.1658i		−	1.38679i	0.720560	−	0.693393i	$-0.243885\pi$
$192$	−3.08459	+	1.27768i	−0.222611	+	0.0922084i
$193$	−1.80296	+	4.35274i	−0.129780	+	0.313317i	−0.975391	−	0.220483i	$-0.929237\pi$
$193$	−1.80296	+	4.35274i	−0.129780	+	0.313317i	0.845611	+	0.533800i	$0.179237\pi$
$194$	22.0870	+	9.14873i	1.58575	+	0.656841i
$195$	10.2784	−	10.2784i	0.736054	−	0.736054i
$196$	3.17345	−	3.17345i	0.226675	−	0.226675i
$197$	13.7611	+	5.70002i	0.980435	+	0.406109i	0.814587	−	0.580042i	$-0.196964\pi$
$197$	13.7611	+	5.70002i	0.980435	+	0.406109i	0.165848	+	0.986151i	$0.446964\pi$
$198$	−1.43537	+	3.46530i	−0.102007	+	0.246268i
$199$	−17.3539	+	7.18821i	−1.23018	+	0.509559i	−0.900634	−	0.434579i	$-0.856897\pi$
$199$	−17.3539	+	7.18821i	−1.23018	+	0.509559i	−0.329550	+	0.944138i	$0.606897\pi$
$200$		−	24.2091i		−	1.71184i
$201$	4.60825	+	11.1253i	0.325041	+	0.784718i
$202$	−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
$207$	1.95114	+	4.71048i	0.135614	+	0.327401i
$208$		−	17.6121i		−	1.22118i
$209$	−3.62809	+	1.50280i	−0.250960	+	0.103951i
$210$	−2.37156	+	5.72544i	−0.163653	+	0.395093i
$211$	5.43302	+	2.25043i	0.374025	+	0.154926i	0.561774	−	0.827291i	$-0.310119\pi$
$211$	5.43302	+	2.25043i	0.374025	+	0.154926i	−0.187749	+	0.982217i	$0.560119\pi$
$212$	−1.39111	+	1.39111i	−0.0955417	+	0.0955417i
$213$	−1.07762	+	1.07762i	−0.0738371	+	0.0738371i
$214$	−29.9986	−	12.4258i	−2.05066	−	0.849411i
$215$	−8.14098	+	19.6541i	−0.555210	+	1.34040i
$216$	1.93884	−	0.803094i	0.131921	−	0.0546436i
$217$		−	3.81209i		−	0.258781i
$218$	−0.452483	−	1.09239i	−0.0306460	−	0.0739860i
$219$	−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	0.826840	−	0.562437i	$-0.190136\pi$
$223$	3.94839	+	3.94839i	0.264404	+	0.264404i	−0.562437	+	0.826840i	$0.690136\pi$
$224$	1.39193	+	3.36041i	0.0930020	+	0.224527i
$225$			11.5359i			0.769060i
$226$	−17.9932	+	7.45304i	−1.19689	+	0.495769i
$227$	10.5352	−	25.4343i	0.699248	−	1.68813i	−0.0260154	−	0.999662i	$-0.508282\pi$
$227$	10.5352	−	25.4343i	0.699248	−	1.68813i	0.725263	−	0.688472i	$-0.241718\pi$
$228$	−1.16640	−	0.483141i	−0.0772470	−	0.0319968i
$229$	−2.52451	+	2.52451i	−0.166824	+	0.166824i	−0.785582	−	0.618758i	$-0.787636\pi$
$229$	−2.52451	+	2.52451i	−0.166824	+	0.166824i	0.618758	+	0.785582i	$0.287636\pi$
$230$	−24.2224	+	24.2224i	−1.59718	+	1.59718i
$231$	−1.93456	−	0.801322i	−0.127285	−	0.0527231i
$232$	1.76980	−	4.27267i	0.116193	−	0.280514i
$233$	−1.26653	+	0.524614i	−0.0829731	+	0.0343686i	−0.423784	−	0.905763i	$-0.639298\pi$
$233$	−1.26653	+	0.524614i	−0.0829731	+	0.0343686i	0.340811	+	0.940132i	$0.389298\pi$
$234$			5.90604i			0.386090i
$235$	−10.8329	−	26.1529i	−0.706659	−	1.70603i
$236$	−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
$241$	−0.406335	−	0.980980i	−0.0261744	−	0.0631905i	0.910252	−	0.414055i	$-0.135888\pi$
$241$	−0.406335	−	0.980980i	−0.0261744	−	0.0631905i	−0.936426	+	0.350864i	$0.885888\pi$
$242$			9.65952i			0.620937i
$243$	−0.923880	+	0.382683i	−0.0592669	+	0.0245492i
$244$	−1.08653	+	2.62312i	−0.0695582	+	0.167928i
$245$	23.1020	+	9.56914i	1.47593	+	0.611350i
$246$	5.90002	−	5.90002i	0.376172	−	0.376172i
$247$	−4.37239	+	4.37239i	−0.278209	+	0.278209i
$248$	−8.01298	−	3.31909i	−0.508825	−	0.210762i
$249$	−2.44347	+	5.89905i	−0.154848	+	0.373837i
$250$	−40.5699	+	16.8046i	−2.56586	+	1.06282i
$251$			7.29715i			0.460592i	0.973121	+	0.230296i	$0.0739695\pi$
$251$			7.29715i			0.460592i	−0.973121	+	0.230296i	$0.926031\pi$
$252$	−0.257619	−	0.621948i	−0.0162285	−	0.0391791i
$253$	−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	0.999987	−	0.00504619i	$-0.00160626\pi$
$257$	15.9501	+	15.9501i	0.994941	+	0.994941i	−0.00504619	+	0.999987i	$0.501606\pi$
$258$	−3.30774	−	7.98559i	−0.205931	−	0.497161i
$259$		−	5.49236i		−	0.341278i
$260$	−9.80134	+	4.05985i	−0.607853	+	0.251781i
$261$	−0.843328	+	2.03597i	−0.0522007	+	0.126024i
$262$	−12.1002	−	5.01208i	−0.747555	−	0.309647i
$263$	−3.00463	+	3.00463i	−0.185274	+	0.185274i	−0.793649	−	0.608376i	$-0.791821\pi$
$263$	−3.00463	+	3.00463i	−0.185274	+	0.185274i	0.608376	+	0.793649i	$0.291821\pi$
$264$	−3.36875	+	3.36875i	−0.207332	+	0.207332i
$265$	−10.1269	−	4.19471i	−0.622092	−	0.257679i
$266$	1.00885	−	2.43557i	0.0618564	−	0.149335i
$267$	9.57112	−	3.96449i	0.585743	−	0.242623i
$268$		−	8.78869i		−	0.536855i
$269$	−4.52860	−	10.9330i	−0.276114	−	0.666597i	0.723608	−	0.690212i	$-0.242483\pi$
$269$	−4.52860	−	10.9330i	−0.276114	−	0.666597i	−0.999721	+	0.0236145i	$0.992483\pi$
$270$	−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
$275$	−10.0218	−	24.1949i	−0.604340	−	1.45901i
$276$		−	3.72115i		−	0.223987i
$277$	−9.63378	+	3.99044i	−0.578838	+	0.239762i	−0.652840	−	0.757496i	$-0.726423\pi$
$277$	−9.63378	+	3.99044i	−0.578838	+	0.239762i	0.0740024	+	0.997258i	$0.476423\pi$
$278$	−9.13412	+	22.0517i	−0.547828	+	1.32257i
$279$	3.81828	+	1.58158i	0.228594	+	0.0946868i
$280$	−5.56592	+	5.56592i	−0.332627	+	0.332627i
$281$	3.86573	−	3.86573i	0.230610	−	0.230610i	−0.582337	−	0.812947i	$-0.697862\pi$
$281$	3.86573	−	3.86573i	0.230610	−	0.230610i	0.812947	+	0.582337i	$0.197862\pi$
$282$	10.6261	+	4.40148i	0.632776	+	0.262104i
$283$	6.74958	−	16.2949i	0.401221	−	0.968633i	−0.586149	−	0.810203i	$-0.699357\pi$
$283$	6.74958	−	16.2949i	0.401221	−	0.968633i	0.987370	−	0.158430i	$-0.0506433\pi$
$284$	1.02760	−	0.425645i	0.0609767	−	0.0252574i
$285$		−	7.03429i		−	0.416675i
$286$	−5.13089	−	12.3871i	−0.303396	−	0.732463i
$287$	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
$292$	0.325388	+	0.785557i	0.0190419	+	0.0459713i
$293$		−	8.25845i		−	0.482464i	−0.970467	−	0.241232i	$-0.922449\pi$
$293$		−	8.25845i		−	0.482464i	0.970467	−	0.241232i	$-0.0775515\pi$
$294$	−9.38649	+	3.88801i	−0.547431	+	0.226753i
$295$	11.5131	−	27.7950i	0.670317	−	1.61829i
$296$	−11.5449	−	4.78205i	−0.671033	−	0.277951i
$297$	1.60525	−	1.60525i	0.0931458	−	0.0931458i
$298$	4.20070	−	4.20070i	0.243340	−	0.243340i
$299$	−16.8381	−	6.97457i	−0.973773	−	0.403350i
$300$	3.22195	−	7.77848i	0.186020	−	0.449091i
$301$	4.45809	−	1.84660i	0.256960	−	0.106436i
$302$			12.5375i			0.721454i
$303$	0.101697	+	0.245517i	0.00584231	+	0.0141046i
$304$	−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
$309$	1.16117	+	2.80331i	0.0660567	+	0.159475i
$310$			27.7674i			1.57708i
$311$	15.3240	−	6.34739i	0.868942	−	0.359927i	0.0967437	−	0.995309i	$-0.469157\pi$
$311$	15.3240	−	6.34739i	0.868942	−	0.359927i	0.772198	+	0.635382i	$0.219157\pi$
$312$	−2.87075	+	6.93059i	−0.162524	+	0.392368i
$313$	−19.0426	−	7.88772i	−1.07635	−	0.445840i	−0.227125	−	0.973866i	$-0.572933\pi$
$313$	−19.0426	−	7.88772i	−1.07635	−	0.445840i	−0.849229	+	0.528025i	$0.822933\pi$
$314$	22.1473	−	22.1473i	1.24984	−	1.24984i
$315$	2.65222	−	2.65222i	0.149436	−	0.149436i
$316$	8.01298	+	3.31909i	0.450766	+	0.186713i
$317$	1.63330	−	3.94314i	0.0917354	−	0.221469i	−0.871352	−	0.490659i	$-0.836756\pi$
$317$	1.63330	−	3.94314i	0.0917354	−	0.221469i	0.963087	+	0.269190i	$0.0867561\pi$
$318$	4.11464	−	1.70434i	0.230738	−	0.0955747i
$319$		−	5.00280i		−	0.280103i
$320$	5.19559	+	12.5433i	0.290443	+	0.701190i
$321$	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
$326$	8.49342	+	20.5049i	0.470407	+	1.13566i
$327$			0.715639i			0.0395749i
$328$	9.79134	−	4.05571i	0.540636	−	0.223939i
$329$	−2.45720	+	5.93221i	−0.135470	+	0.327053i
$330$	14.0914	+	5.83685i	0.775706	+	0.321308i
$331$	−20.2307	+	20.2307i	−1.11198	+	1.11198i	−0.119097	+	0.992883i	$0.538000\pi$
$331$	−20.2307	+	20.2307i	−1.11198	+	1.11198i	−0.992883	+	0.119097i	$0.962000\pi$
$332$	3.29518	−	3.29518i	0.180847	−	0.180847i
$333$	5.50127	+	2.27870i	0.301468	+	0.124872i
$334$	1.35136	−	3.26247i	0.0739431	−	0.178515i
$335$	45.2403	−	18.7392i	2.47174	−	1.02383i
$336$		−	4.54459i		−	0.247928i
$337$	11.9921	+	28.9514i	0.653250	+	1.57709i	0.808033	+	0.589137i	$0.200532\pi$
$337$	11.9921	+	28.9514i	0.653250	+	1.57709i	−0.154783	+	0.987948i	$0.549468\pi$
$338$	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
$343$	−4.64141	−	11.2054i	−0.250613	−	0.605033i
$344$		−	10.9787i		−	0.591930i
$345$	19.1549	−	7.93421i	1.03126	−	0.427163i
$346$	−3.33840	+	8.05960i	−0.179473	+	0.433287i
$347$	−11.1197	−	4.60594i	−0.596938	−	0.247260i	0.0636944	−	0.997969i	$-0.479712\pi$
$347$	−11.1197	−	4.60594i	−0.596938	−	0.247260i	−0.660632	+	0.750710i	$0.729712\pi$
$348$	1.13729	−	1.13729i	0.0609650	−	0.0609650i
$349$	−23.5829	+	23.5829i	−1.26236	+	1.26236i	−0.312418	+	0.949945i	$0.601139\pi$
$349$	−23.5829	+	23.5829i	−1.26236	+	1.26236i	−0.949945	+	0.312418i	$0.898861\pi$
$350$	16.2423	+	6.72777i	0.868186	+	0.359614i
$351$	1.36794	−	3.30250i	0.0730154	−	0.176275i
$352$	8.27060	−	3.42580i	0.440825	−	0.182596i
$353$			6.56570i			0.349457i	0.984617	+	0.174729i	$0.0559048\pi$
$353$			6.56570i			0.349457i	−0.984617	+	0.174729i	$0.944095\pi$
$354$	4.67785	+	11.2933i	0.248625	+	0.600233i
$355$	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	0.179489	−	0.983760i	$-0.442555\pi$
$359$	−15.2388	−	15.2388i	−0.804271	−	0.804271i	−0.983760	+	0.179489i	$0.942555\pi$
$360$	−3.26573	−	7.88417i	−0.172119	−	0.415533i
$361$		−	16.0077i		−	0.842508i
$362$	1.39798	−	0.579061i	0.0734761	−	0.0304348i
$363$	2.23731	−	5.40135i	0.117428	−	0.283497i
$364$	2.22322	+	0.920888i	0.116528	+	0.0482676i
$365$	−3.34991	+	3.34991i	−0.175342	+	0.175342i
$366$	4.54495	−	4.54495i	0.237568	−	0.237568i
$367$	32.8572	+	13.6099i	1.71513	+	0.710431i	0.999934	+	0.0115096i	$0.00366371\pi$
$367$	32.8572	+	13.6099i	1.71513	+	0.710431i	0.715198	+	0.698921i	$0.246336\pi$
$368$	9.61332	−	23.2086i	0.501129	−	1.20983i
$369$	−4.66568	+	1.93259i	−0.242886	+	0.100607i
$370$			40.0065i			2.07984i
$371$	0.951478	+	2.29707i	0.0493983	+	0.119258i
$372$	−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
$377$	−3.01457	−	7.27781i	−0.155258	−	0.374826i
$378$			1.52398i			0.0783851i
$379$	20.2520	−	8.38866i	1.04028	−	0.430897i	0.203865	−	0.978999i	$-0.434650\pi$
$379$	20.2520	−	8.38866i	1.04028	−	0.430897i	0.836411	+	0.548102i	$0.184650\pi$
$380$	−1.96466	+	4.74311i	−0.100785	+	0.243316i
$381$	−2.59654	−	1.07552i	−0.133025	−	0.0551007i
$382$	22.3913	−	22.3913i	1.14564	−	1.14564i
$383$	24.2615	−	24.2615i	1.23970	−	1.23970i	0.279581	−	0.960122i	$-0.409804\pi$
$383$	24.2615	−	24.2615i	1.23970	−	1.23970i	0.960122	−	0.279581i	$-0.0901957\pi$
$384$	−12.3828	−	5.12912i	−0.631906	−	0.261744i
$385$	−3.25853	+	7.86678i	−0.166070	+	0.400928i
$386$	−7.19169	+	2.97890i	−0.366047	+	0.151622i
$387$			5.23146i			0.265930i
$388$	4.04129	+	9.75654i	0.205165	+	0.495313i
$389$	−24.1800	−	24.1800i	−1.22597	−	1.22597i	−0.965474	−	0.260499i	$-0.916113\pi$
$389$	−24.1800	−	24.1800i	−1.22597	−	1.22597i	−0.260499	−	0.965474i	$-0.583887\pi$
$390$	24.0166			1.21613
$391$		0			0
$392$	−12.9047			−0.651783
$393$	5.60525	+	5.60525i	0.282747	+	0.282747i
$394$	9.41770	+	22.7363i	0.474457	+	1.14544i
$395$			48.3242i			2.43146i
$396$	−1.53073	+	0.634051i	−0.0769223	+	0.0318622i
$397$	−0.0881539	+	0.212822i	−0.00442432	+	0.0106812i	−0.926076	−	0.377336i	$-0.876840\pi$
$397$	−0.0881539	+	0.212822i	−0.00442432	+	0.0106812i	0.921652	+	0.388018i	$0.126840\pi$
$398$	−28.6725	−	11.8765i	−1.43722	−	0.595317i
$399$	−1.12824	+	1.12824i	−0.0564827	+	0.0564827i
$400$	40.1902	−	40.1902i	2.00951	−	2.00951i
$401$	0.560569	+	0.232195i	0.0279935	+	0.0115953i	0.396636	−	0.917976i	$-0.370177\pi$
$401$	0.560569	+	0.232195i	0.0279935	+	0.0115953i	−0.368643	+	0.929571i	$0.620177\pi$
$402$	−7.61386	+	18.3815i	−0.379745	+	0.916785i
$403$	−13.6488	+	5.65353i	−0.679897	+	0.281622i
$404$		−	0.193952i		−	0.00964947i
$405$	1.55616	+	3.75690i	0.0773261	+	0.186682i
$406$	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
$411$	0.0394998	+	0.0953611i	0.00194838	+	0.00470381i
$412$		−	2.21454i		−	0.109103i
$413$	−6.30470	+	2.61149i	−0.310234	+	0.128503i
$414$	−3.22373	+	7.78276i	−0.158437	+	0.382502i
$415$	23.9881	+	9.93620i	1.17753	+	0.487749i
$416$	9.96732	−	9.96732i	0.488688	−	0.488688i
$417$	10.2151	−	10.2151i	0.500237	−	0.500237i
$418$	−5.99441	−	2.48297i	−0.293196	−	0.121446i
$419$	−4.63804	+	11.1972i	−0.226583	+	0.547020i	−0.995757	−	0.0920195i	$-0.970668\pi$
$419$	−4.63804	+	11.1972i	−0.226583	+	0.547020i	0.769174	+	0.639039i	$0.220668\pi$
$420$	−2.52911	+	1.04759i	−0.123408	+	0.0511173i
$421$			17.8730i			0.871078i	0.900170	+	0.435539i	$0.143442\pi$
$421$			17.8730i			0.871078i	−0.900170	+	0.435539i	$0.856558\pi$
$422$	3.71821	+	8.97656i	0.181000	+	0.436972i
$423$	−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
$428$	−5.48888	−	13.2513i	−0.265315	−	0.640528i
$429$			8.11492i			0.391792i
$430$	−32.4729	+	13.4507i	−1.56598	+	0.648651i
$431$	−4.26161	+	10.2884i	−0.205274	+	0.495576i	−0.992668	−	0.120875i	$-0.961430\pi$
$431$	−4.26161	+	10.2884i	−0.205274	+	0.495576i	0.787393	+	0.616451i	$0.211430\pi$
$432$	4.55197	+	1.88549i	0.219007	+	0.0907155i
$433$	−20.5897	+	20.5897i	−0.989475	+	0.989475i	−0.999945	−	0.0104697i	$-0.996667\pi$
$433$	−20.5897	+	20.5897i	−0.989475	+	0.989475i	0.0104697	+	0.999945i	$0.496667\pi$
$434$	4.45366	−	4.45366i	0.213782	−	0.213782i
$435$	8.27916	+	3.42934i	0.396955	+	0.164424i
$436$	0.199876	−	0.482544i	0.00957234	−	0.0231097i
$437$	−8.14838	+	3.37517i	−0.389790	+	0.161456i
$438$		−	1.92488i		−	0.0919742i
$439$	8.64704	+	20.8758i	0.412700	+	0.996347i	0.984410	+	0.175891i	$0.0562806\pi$
$439$	8.64704	+	20.8758i	0.412700	+	0.996347i	−0.571709	+	0.820456i	$0.693719\pi$
$440$	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
$445$	−16.1213	−	38.9203i	−0.764224	−	1.84500i
$446$			9.22579i			0.436854i
$447$	−3.32188	+	1.37597i	−0.157119	+	0.0650810i
$448$	1.17851	−	2.84517i	0.0556792	−	0.134422i
$449$	−1.03502	−	0.428720i	−0.0488457	−	0.0202325i	0.358127	−	0.933673i	$-0.383416\pi$
$449$	−1.03502	−	0.428720i	−0.0488457	−	0.0202325i	−0.406973	+	0.913440i	$0.633416\pi$
$450$	−13.4774	+	13.4774i	−0.635330	+	0.635330i
$451$	8.10665	−	8.10665i	0.381727	−	0.381727i
$452$	−7.94819	−	3.29225i	−0.373851	−	0.154854i
$453$	2.90391	−	7.01066i	0.136438	−	0.329389i
$454$	42.0231	−	17.4065i	1.97224	−	0.816930i
$455$			13.4077i			0.628561i
$456$	1.38923	+	3.35389i	0.0650564	+	0.157060i
$457$	28.3405	+	28.3405i	1.32571	+	1.32571i	0.909072	+	0.416639i	$0.136792\pi$
$457$	28.3405	+	28.3405i	1.32571	+	1.32571i	0.416639	+	0.909072i	$0.363208\pi$
$458$	−5.89875			−0.275631
$459$		0			0
$460$	−15.1318			−0.705526
$461$	−3.53267	−	3.53267i	−0.164533	−	0.164533i	0.620039	−	0.784571i	$-0.287117\pi$
$461$	−3.53267	−	3.53267i	−0.164533	−	0.164533i	−0.784571	+	0.620039i	$0.787117\pi$
$462$	−1.32396	−	3.19633i	−0.0615963	−	0.148707i
$463$			39.0452i			1.81458i	0.420502	+	0.907292i	$0.361854\pi$
$463$			39.0452i			1.81458i	−0.420502	+	0.907292i	$0.638146\pi$
$464$	10.0313	−	4.15509i	0.465690	−	0.192895i
$465$	6.43140	−	15.5268i	0.298249	−	0.720037i
$466$	−2.09259	−	0.866779i	−0.0969374	−	0.0401528i
$467$	7.44173	−	7.44173i	0.344362	−	0.344362i	−0.513642	−	0.858004i	$-0.671704\pi$
$467$	7.44173	−	7.44173i	0.344362	−	0.344362i	0.858004	+	0.513642i	$0.171704\pi$
$468$	−1.84476	+	1.84476i	−0.0852743	+	0.0852743i
$469$	−10.2618	−	4.25057i	−0.473845	−	0.196273i
$470$	17.8983	−	43.2104i	0.825589	−	1.99315i
$471$	−17.5139	+	7.25449i	−0.806997	+	0.334269i
$472$			15.5262i			0.714651i
$473$	−4.54484	−	10.9722i	−0.208972	−	0.504503i
$474$	−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
$479$	9.93598	+	23.9876i	0.453986	+	1.09602i	0.970793	+	0.239918i	$0.0771206\pi$
$479$	9.93598	+	23.9876i	0.453986	+	1.09602i	−0.516807	+	0.856102i	$0.672879\pi$
$480$			16.0354i			0.731912i
$481$	−19.6649	+	8.14546i	−0.896641	+	0.371401i
$482$	0.671356	−	1.62080i	0.0305794	−	0.0738253i
$483$	−4.34486	−	1.79970i	−0.197698	−	0.0818893i
$484$	−3.01717	+	3.01717i	−0.137144	+	0.137144i
$485$	−41.6056	+	41.6056i	−1.88921	+	1.88921i
$486$	−1.52645	−	0.632278i	−0.0692414	−	0.0286807i
$487$	9.77394	−	23.5964i	0.442900	−	1.06925i	−0.532027	−	0.846727i	$-0.678570\pi$
$487$	9.77394	−	23.5964i	0.442900	−	1.06925i	0.974927	−	0.222527i	$-0.0714304\pi$
$488$	7.54254	−	3.12422i	0.341435	−	0.141427i
$489$		−	13.4330i		−	0.607463i
$490$	15.8104	+	38.1696i	0.714239	+	1.72433i
$491$	−1.77317	−	1.77317i	−0.0800221	−	0.0800221i	0.665963	−	0.745985i	$-0.268021\pi$
$491$	−1.77317	−	1.77317i	−0.0800221	−	0.0800221i	−0.745985	+	0.665963i	$0.768021\pi$
$492$	3.68577			0.166167
$493$		0			0
$494$	−10.2165			−0.459663
$495$	−6.52763	−	6.52763i	−0.293395	−	0.293395i
$496$	−7.79248	−	18.8127i	−0.349893	−	0.844715i
$497$		−	1.40569i		−	0.0630540i
$498$	−9.74654	+	4.03715i	−0.436753	+	0.180909i
$499$	−5.82714	+	14.0680i	−0.260859	+	0.629768i	−0.998992	−	0.0448864i	$-0.985707\pi$
$499$	−5.82714	+	14.0680i	−0.260859	+	0.629768i	0.738134	+	0.674655i	$0.235707\pi$
$500$	−17.9210	−	7.42313i	−0.801453	−	0.331973i
$501$	−1.51129	+	1.51129i	−0.0675195	+	0.0675195i
$502$	−8.52525	+	8.52525i	−0.380501	+	0.380501i
$503$	−36.1228	−	14.9625i	−1.61064	−	0.667147i	−0.617767	−	0.786361i	$-0.711962\pi$
$503$	−36.1228	−	14.9625i	−1.61064	−	0.667147i	−0.992869	+	0.119214i	$0.961962\pi$
$504$	−0.740760	+	1.78835i	−0.0329961	+	0.0796596i
$505$	0.998380	−	0.413542i	0.0444273	−	0.0184024i
$506$		−	19.1238i		−	0.850158i
$507$	−0.0850310	−	0.205283i	−0.00377636	−	0.00911694i
$508$	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
$513$	−0.661981	−	1.59816i	−0.0292272	−	0.0705607i
$514$			37.2690i			1.64386i
$515$	11.3995	−	4.72183i	0.502322	−	0.208069i
$516$	1.46114	−	3.52749i	0.0643229	−	0.155289i
$517$	14.6003	+	6.04765i	0.642121	+	0.265975i
$518$	6.41671	−	6.41671i	0.281934	−	0.281934i
$519$	3.73349	−	3.73349i	0.163882	−	0.163882i
$520$	28.1828	+	11.6737i	1.23590	+	0.511926i
$521$	−1.84858	+	4.46286i	−0.0809876	+	0.195521i	−0.959186	−	0.282774i	$-0.908745\pi$
$521$	−1.84858	+	4.46286i	−0.0809876	+	0.195521i	0.878199	+	0.478296i	$0.158745\pi$
$522$	−3.36388	+	1.39337i	−0.147233	+	0.0609860i
$523$		−	36.5734i		−	1.59924i	−0.600503	−	0.799622i	$-0.705033\pi$
$523$		−	36.5734i		−	1.59924i	0.600503	−	0.799622i	$-0.294967\pi$
$524$	−2.21400	−	5.34506i	−0.0967189	−	0.233500i
$525$	−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
$530$	−6.93059	−	16.7319i	−0.301046	−	0.726789i
$531$		−	7.39840i		−	0.321063i
$532$	1.07587	−	0.445641i	0.0466449	−	0.0193210i
$533$	6.90824	−	16.6780i	0.299229	−	0.722403i
$534$	15.8136	+	6.55021i	0.684322	+	0.283455i
$535$	56.5087	−	56.5087i	2.44309	−	2.44309i
$536$	−17.8693	+	17.8693i	−0.771838	+	0.771838i
$537$	−7.18427	−	2.97582i	−0.310024	−	0.128416i
$538$	7.48226	−	18.0638i	0.322583	−	0.778784i
$539$	−12.8971	+	5.34214i	−0.555516	+	0.230102i
$540$		−	2.96785i		−	0.127716i
$541$	4.22067	+	10.1896i	0.181461	+	0.438085i	0.988268	−	0.152730i	$-0.0488065\pi$
$541$	4.22067	+	10.1896i	0.181461	+	0.438085i	−0.806807	+	0.590815i	$0.798806\pi$
$542$	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
$547$	10.2852	+	24.8307i	0.439765	+	1.06169i	0.976030	+	0.217636i	$0.0698347\pi$
$547$	10.2852	+	24.8307i	0.439765	+	1.06169i	−0.536265	+	0.844050i	$0.680165\pi$
$548$		−	0.0753327i		−	0.00321805i
$549$	−3.59411	+	1.48873i	−0.153393	+	0.0635373i
$550$	16.5583	−	39.9753i	0.706049	−	1.70455i
$551$	−3.52191	−	1.45882i	−0.150038	−	0.0621480i
$552$	−7.56592	+	7.56592i	−0.322027	+	0.322027i
$553$	7.75081	−	7.75081i	0.329598	−	0.329598i
$554$	−15.9172	−	6.59310i	−0.676255	−	0.280114i
$555$	9.26619	−	22.3706i	0.393328	−	0.949578i
$556$	−9.74096	+	4.03484i	−0.413109	+	0.171115i
$557$			34.9146i			1.47938i	0.672948	+	0.739690i	$0.265028\pi$
$557$			34.9146i			1.47938i	−0.672948	+	0.739690i	$0.734972\pi$
$558$	2.61313	+	6.30864i	0.110622	+	0.267066i
$559$	−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	0.815119	−	0.579294i	$-0.196672\pi$
$563$	5.59557	+	5.59557i	0.235825	+	0.235825i	−0.579294	+	0.815119i	$0.696672\pi$
$564$	1.94428	+	4.69390i	0.0818688	+	0.197649i
$565$		−	47.9335i		−	2.01658i
$566$	26.9229	−	11.1518i	1.13165	−	0.468746i
$567$	0.352980	−	0.852170i	0.0148238	−	0.0357878i
$568$	−2.95476	−	1.22390i	−0.123979	−	0.0513537i
$569$	−12.2298	+	12.2298i	−0.512702	+	0.512702i	−0.915353	−	0.402651i	$-0.868089\pi$
$569$	−12.2298	+	12.2298i	−0.512702	+	0.512702i	0.402651	+	0.915353i	$0.368089\pi$
$570$	8.21814	−	8.21814i	0.344220	−	0.344220i
$571$	−17.9039	−	7.41605i	−0.749256	−	0.310352i	−0.0248178	−	0.999692i	$-0.507901\pi$
$571$	−17.9039	−	7.41605i	−0.749256	−	0.310352i	−0.724438	+	0.689340i	$0.757901\pi$
$572$	2.26648	−	5.47177i	0.0947663	−	0.228786i
$573$	−17.7069	+	7.33442i	−0.739715	+	0.306400i
$574$			7.69626i			0.321236i
$575$	−22.5082	−	54.3396i	−0.938658	−	2.26612i
$576$	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
$581$	−2.25381	−	5.44118i	−0.0935038	−	0.225738i
$582$		−	23.9068i		−	0.990968i
$583$	5.65353	−	2.34177i	0.234145	−	0.0969862i
$584$	0.935623	−	2.25879i	0.0387164	−	0.0934696i
$585$	−13.4294	−	5.56265i	−0.555238	−	0.229987i
$586$	9.64833	−	9.64833i	0.398569	−	0.398569i
$587$	−8.70909	+	8.70909i	−0.359463	+	0.359463i	−0.863615	−	0.504152i	$-0.831805\pi$
$587$	−8.70909	+	8.70909i	−0.359463	+	0.359463i	0.504152	+	0.863615i	$0.331805\pi$
$588$	−4.14632	−	1.71746i	−0.170991	−	0.0708269i
$589$	−2.73588	+	6.60501i	−0.112730	+	0.272155i
$590$	45.9236	−	19.0222i	1.89064	−	0.783131i
$591$		−	14.8949i		−	0.612693i
$592$	−11.2272	−	27.1048i	−0.461435	−	1.11400i
$593$	30.5302	+	30.5302i	1.25373	+	1.25373i	0.954037	+	0.299690i	$0.0968833\pi$
$593$	30.5302	+	30.5302i	1.25373	+	1.25373i	0.299690	+	0.954037i	$0.403117\pi$
$594$	3.75081			0.153898
$595$		0			0
$596$	2.62420			0.107491
$597$	13.2821	+	13.2821i	0.543599	+	0.543599i
$598$	−11.5235	−	27.8203i	−0.471233	−	1.13766i
$599$			6.70607i			0.274003i	0.990571	+	0.137001i	$0.0437464\pi$
$599$			6.70607i			0.274003i	−0.990571	+	0.137001i	$0.956254\pi$
$600$	−22.3663	+	9.26442i	−0.913100	+	0.378218i
$601$	−12.1844	+	29.4156i	−0.497010	+	1.19989i	0.454076	+	0.890963i	$0.349970\pi$
$601$	−12.1844	+	29.4156i	−0.497010	+	1.19989i	−0.951086	+	0.308926i	$0.900030\pi$
$602$	7.36577	+	3.05100i	0.300206	+	0.124349i
$603$	8.51494	−	8.51494i	0.346755	−	0.346755i
$604$	−3.91612	+	3.91612i	−0.159345	+	0.159345i
$605$	−21.9642	−	9.09788i	−0.892973	−	0.369882i
$606$	−0.168025	+	0.405649i	−0.00682556	+	0.0164784i
$607$	25.7918	−	10.6833i	1.04685	−	0.433622i	0.208087	−	0.978110i	$-0.433276\pi$
$607$	25.7918	−	10.6833i	1.04685	−	0.433622i	0.838768	+	0.544489i	$0.183276\pi$
$608$		−	6.82137i		−	0.276643i
$609$	−0.777871	−	1.87795i	−0.0315209	−	0.0760983i
$610$	−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
$615$	7.85875	+	18.9727i	0.316895	+	0.765053i
$616$		−	4.39435i		−	0.177053i
$617$	−34.2317	+	14.1792i	−1.37812	+	0.570835i	−0.943977	−	0.330010i	$-0.892948\pi$
$617$	−34.2317	+	14.1792i	−1.37812	+	0.570835i	−0.434140	+	0.900845i	$0.642948\pi$
$618$	−1.91851	+	4.63170i	−0.0771739	+	0.186314i
$619$	14.9378	+	6.18744i	0.600401	+	0.248694i	0.662118	−	0.749399i	$-0.269658\pi$
$619$	14.9378	+	6.18744i	0.600401	+	0.248694i	−0.0617170	+	0.998094i	$0.519658\pi$
$620$	−8.67319	+	8.67319i	−0.348324	+	0.348324i
$621$	3.60525	−	3.60525i	0.144674	−	0.144674i
$622$	25.3186	+	10.4873i	1.01518	+	0.420503i
$623$	−3.65677	+	8.82823i	−0.146505	+	0.353696i
$624$	−16.2715	+	6.73987i	−0.651381	+	0.269811i
$625$		−	50.3976i		−	2.01590i
$626$	−13.0323	−	31.4627i	−0.520874	−	1.25750i
$627$	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	0.994656	−	0.103246i	$-0.0329228\pi$
$631$	22.3920	+	22.3920i	0.891410	+	0.891410i	−0.103246	+	0.994656i	$0.532923\pi$
$632$	−9.54372	−	23.0406i	−0.379629	−	0.916505i
$633$		−	5.88066i		−	0.233735i
$634$	6.51495	−	2.69858i	0.258742	−	0.107174i
$635$	−4.37355	+	10.5587i	−0.173559	+	0.419008i
$636$	1.81757	+	0.752862i	0.0720714	+	0.0298529i
$637$	−15.5429	+	15.5429i	−0.615833	+	0.615833i
$638$	5.84476	−	5.84476i	0.231396	−	0.231396i
$639$	1.40798	+	0.583202i	0.0556986	+	0.0230711i
$640$	−20.8572	+	50.3538i	−0.824455	+	1.99041i
$641$	−14.7167	+	6.09588i	−0.581277	+	0.240773i	−0.653893	−	0.756587i	$-0.726865\pi$
$641$	−14.7167	+	6.09588i	−0.581277	+	0.240773i	0.0726161	+	0.997360i	$0.476865\pi$
$642$			32.4702i			1.28150i
$643$	−6.38557	−	15.4161i	−0.251822	−	0.607953i	0.746529	−	0.665353i	$-0.231719\pi$
$643$	−6.38557	−	15.4161i	−0.251822	−	0.607953i	−0.998351	+	0.0574003i	$0.981719\pi$
$644$	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
$649$	6.42738	+	15.5171i	0.252297	+	0.609098i
$650$		−	68.1316i		−	2.67234i
$651$	−3.52191	+	1.45882i	−0.138035	+	0.0571758i
$652$	−3.75182	+	9.05770i	−0.146933	+	0.354727i
$653$	−26.5132	−	10.9821i	−1.03754	−	0.429764i	−0.202113	−	0.979362i	$-0.564781\pi$
$653$	−26.5132	−	10.9821i	−1.03754	−	0.429764i	−0.835429	+	0.549598i	$0.814781\pi$
$654$	−0.836079	+	0.836079i	−0.0326933	+	0.0326933i
$655$	22.7934	−	22.7934i	0.890611	−	0.890611i
$656$	22.9879	+	9.52189i	0.897526	+	0.371767i
$657$	−0.445835	+	1.07634i	−0.0173937	+	0.0419921i
$658$	−9.80134	+	4.05985i	−0.382096	+	0.158269i
$659$			40.3690i			1.57255i	0.617876	+	0.786276i	$0.287993\pi$
$659$			40.3690i			1.57255i	−0.617876	+	0.786276i	$0.712007\pi$
$660$	2.57833	+	6.22463i	0.100361	+	0.242293i
$661$	−27.9099	−	27.9099i	−1.08557	−	1.08557i	−0.995979	−	0.0895910i	$-0.971444\pi$
$661$	−27.9099	−	27.9099i	−1.08557	−	1.08557i	−0.0895910	−	0.995979i	$-0.528556\pi$
$662$	−47.2710			−1.83724
$663$		0			0
$664$	−13.3997			−0.520007
$665$	4.58792	+	4.58792i	0.177912	+	0.177912i
$666$	3.76492	+	9.08933i	0.145888	+	0.352204i
$667$		−	11.2359i		−	0.435055i
$668$	1.44114	−	0.596940i	0.0557594	−	0.0230963i
$669$	2.13685	−	5.15882i	0.0826155	−	0.199452i
$670$	74.7471	+	30.9613i	2.88773	+	1.19614i
$671$	6.24478	−	6.24478i	0.241077	−	0.241077i
$672$	2.57194	−	2.57194i	0.0992149	−	0.0992149i
$673$	−19.9610	−	8.26810i	−0.769438	−	0.318712i	−0.0367934	−	0.999323i	$-0.511714\pi$
$673$	−19.9610	−	8.26810i	−0.769438	−	0.318712i	−0.732645	+	0.680611i	$0.761714\pi$
$674$	−19.8136	+	47.8342i	−0.763191	+	1.84251i
$675$	10.6578	−	4.41460i	0.410218	−	0.169918i
$676$			0.162168i			0.00623724i
$677$	0.960853	+	2.31970i	0.0369286	+	0.0891535i	0.941268	−	0.337661i	$-0.109636\pi$
$677$	0.960853	+	2.31970i	0.0369286	+	0.0891535i	−0.904339	+	0.426814i	$0.859636\pi$
$678$	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
$683$	−7.17238	−	17.3157i	−0.274444	−	0.662566i	0.725220	−	0.688518i	$-0.241738\pi$
$683$	−7.17238	−	17.3157i	−0.274444	−	0.662566i	−0.999663	+	0.0259521i	$0.991738\pi$
$684$			1.26251i			0.0482732i
$685$	0.387780	−	0.160624i	0.0148163	−	0.00613711i
$686$	7.66865	−	18.5138i	0.292790	−	0.706859i
$687$	3.29843	+	1.36625i	0.125843	+	0.0521258i
$688$	18.2260	−	18.2260i	0.694860	−	0.694860i
$689$	6.81336	−	6.81336i	0.259568	−	0.259568i
$690$	31.6481	+	13.1091i	1.20482	+	0.499054i
$691$	−14.7602	+	35.6342i	−0.561504	+	1.35559i	0.347060	+	0.937843i	$0.387180\pi$
$691$	−14.7602	+	35.6342i	−0.561504	+	1.35559i	−0.908563	+	0.417747i	$0.862820\pi$
$692$	−3.56019	+	1.47468i	−0.135338	+	0.0560588i
$693$			2.09396i			0.0795428i
$694$	−7.61004	−	18.3723i	−0.288873	−	0.697401i
$695$	−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
$700$	2.97187	+	7.17474i	0.112326	+	0.271180i
$701$		−	28.7827i		−	1.08711i	−0.839375	−	0.543553i	$-0.817079\pi$
$701$		−	28.7827i		−	1.08711i	0.839375	−	0.543553i	$-0.182921\pi$
$702$	5.45647	−	2.26015i	0.205941	−	0.0853037i
$703$	−3.94179	+	9.51632i	−0.148667	+	0.358915i
$704$	−7.00250	−	2.90053i	−0.263917	−	0.109318i
$705$	−20.0166	+	20.0166i	−0.753867	+	0.753867i
$706$	−7.67070	+	7.67070i	−0.288690	+	0.288690i
$707$	−0.226461	−	0.0938031i	−0.00851693	−	0.00352783i
$708$	−2.06636	+	4.98863i	−0.0776585	+	0.187484i
$709$	−4.75418	+	1.96924i	−0.178547	+	0.0739565i	−0.470166	−	0.882578i	$-0.655806\pi$
$709$	−4.75418	+	1.96924i	−0.178547	+	0.0739565i	0.291619	+	0.956534i	$0.405806\pi$
$710$			10.2391i			0.384267i
$711$	4.54769	+	10.9791i	0.170552	+	0.411748i
$712$	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
$717$	−8.27060	−	19.9670i	−0.308871	−	0.745681i
$718$		−	35.6068i		−	1.32883i
$719$	29.1042	−	12.0554i	1.08540	−	0.449589i	0.233003	−	0.972476i	$-0.425145\pi$
$719$	29.1042	−	12.0554i	1.08540	−	0.449589i	0.852402	+	0.522887i	$0.175145\pi$
$720$	7.66721	−	18.5103i	0.285740	−	0.689838i
$721$	−2.58573	−	1.07104i	−0.0962976	−	0.0398878i
$722$	18.7017	−	18.7017i	0.696005	−	0.696005i
$723$	−0.750810	+	0.750810i	−0.0279229	+	0.0279229i
$724$	0.617532	+	0.255790i	0.0229504	+	0.00950636i
$725$	9.72856	−	23.4868i	0.361309	−	0.872278i
$726$	8.92423	−	3.69654i	0.331209	−	0.137191i
$727$		−	31.2775i		−	1.16002i	−0.814610	−	0.580010i	$-0.803049\pi$
$727$		−	31.2775i		−	1.16002i	0.814610	−	0.580010i	$-0.196951\pi$
$728$	−2.64793	−	6.39266i	−0.0981386	−	0.236928i
$729$	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	0.417340	−	0.908751i	$-0.362963\pi$
$733$	−13.3044	−	13.3044i	−0.491411	−	0.491411i	−0.908751	+	0.417340i	$0.862963\pi$
$734$	22.4866	+	54.2874i	0.829995	+	2.00379i
$735$		−	25.0054i		−	0.922337i
$736$	18.5751	−	7.69405i	0.684686	−	0.283606i
$737$	−10.4615	+	25.2562i	−0.385353	+	0.930324i
$738$	−7.70875	−	3.19307i	−0.283763	−	0.117538i
$739$	4.91271	−	4.91271i	0.180717	−	0.180717i	−0.610951	−	0.791668i	$-0.709213\pi$
$739$	4.91271	−	4.91271i	0.180717	−	0.180717i	0.791668	+	0.610951i	$0.209213\pi$
$740$	−12.4961	+	12.4961i	−0.459366	+	0.459366i
$741$	5.71281	+	2.36632i	0.209865	+	0.0869290i
$742$	−1.57205	+	3.79527i	−0.0577119	+	0.139329i
$743$	−31.3716	+	12.9945i	−1.15091	+	0.476723i	−0.874839	−	0.484414i	$-0.839033\pi$
$743$	−31.3716	+	12.9945i	−1.15091	+	0.476723i	−0.276072	+	0.961137i	$0.589033\pi$
$744$			8.67319i			0.317975i
$745$	5.59528	+	13.5082i	0.204995	+	0.494902i
$746$	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
$751$	2.64629	+	6.38871i	0.0965645	+	0.233127i	0.964779	−	0.263062i	$-0.0847323\pi$
$751$	2.64629	+	6.38871i	0.0965645	+	0.233127i	−0.868215	+	0.496189i	$0.834732\pi$
$752$			34.2984i			1.25073i
$753$	6.74169	−	2.79250i	0.245681	−	0.101764i
$754$	4.98073	−	12.0246i	0.181388	−	0.437909i
$755$	−28.5084	−	11.8086i	−1.03753	−	0.429758i
$756$	−0.476019	+	0.476019i	−0.0173126	+	0.0173126i
$757$	−1.31639	+	1.31639i	−0.0478452	+	0.0478452i	−0.730625	−	0.682779i	$-0.760771\pi$
$757$	−1.31639	+	1.31639i	−0.0478452	+	0.0478452i	0.682779	+	0.730625i	$0.260771\pi$
$758$	33.4609	+	13.8599i	1.21535	+	0.503416i
$759$	−4.42941	+	10.6935i	−0.160777	+	0.388151i
$760$	13.6384	−	5.64920i	0.494715	−	0.204918i
$761$		−	49.2335i		−	1.78471i	−0.451330	−	0.892357i	$-0.649050\pi$
$761$		−	49.2335i		−	1.78471i	0.451330	−	0.892357i	$-0.350950\pi$
$762$	−1.77700	−	4.29007i	−0.0643741	−	0.155413i
$763$	−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
$768$	−5.91909	−	14.2900i	−0.213587	−	0.515644i
$769$			50.9303i			1.83659i	0.395895	+	0.918296i	$0.370435\pi$
$769$			50.9303i			1.83659i	−0.395895	+	0.918296i	$0.629565\pi$
$770$	−12.9977	+	5.38381i	−0.468403	+	0.194019i
$771$	8.63214	−	20.8398i	0.310879	−	0.750528i
$772$	−3.17680	−	1.31587i	−0.114336	−	0.0473594i
$773$	2.06202	−	2.06202i	0.0741658	−	0.0741658i	−0.669051	−	0.743217i	$-0.733299\pi$
$773$	2.06202	−	2.06202i	0.0741658	−	0.0741658i	0.743217	+	0.669051i	$0.233299\pi$
$774$	−6.11190	+	6.11190i	−0.219688	+	0.219688i
$775$	−44.0473	−	18.2450i	−1.58222	−	0.655379i
$776$	11.6203	−	28.0540i	0.417146	−	1.00708i
$777$	−5.07428	+	2.10183i	−0.182039	+	0.0754029i
$778$		−	56.4988i		−	2.02558i
$779$	−3.34307	−	8.07089i	−0.119778	−	0.289170i
$780$	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
$785$	29.4999	+	71.2191i	1.05290	+	2.54192i
$786$			13.0972i			0.467161i
$787$	47.0192	−	19.4760i	1.67605	−	0.694243i	0.676926	−	0.736051i	$-0.263312\pi$
$787$	47.0192	−	19.4760i	1.67605	−	0.694243i	0.999126	+	0.0418077i	$0.0133117\pi$
$788$	−4.16010	+	10.0434i	−0.148198	+	0.357781i
$789$	3.92574	+	1.62609i	0.139760	+	0.0578905i
$790$	−56.4571	+	56.4571i	−2.00865	+	2.00865i
$791$	−7.68814	+	7.68814i	−0.273359	+	0.273359i
$792$	4.40148	+	1.82315i	0.156400	+	0.0647829i
$793$	5.32161	−	12.8475i	0.188976	−	0.456228i
$794$	−0.351630	+	0.145650i	−0.0124789	+	0.00516892i
$795$			10.9613i			0.388757i
$796$	−5.24625	−	12.6656i	−0.185948	−	0.448919i
$797$	−9.62096	−	9.62096i	−0.340792	−	0.340792i	0.515873	−	0.856665i	$-0.327468\pi$
$797$	−9.62096	−	9.62096i	−0.340792	−	0.340792i	−0.856665	+	0.515873i	$0.827468\pi$
$798$	−2.63624			−0.0933220
$799$		0			0
$800$	45.4901			1.60832
$801$	−7.32541	−	7.32541i	−0.258831	−	0.258831i
$802$	0.383638	+	0.926185i	0.0135467	+	0.0327047i
$803$		−	2.64479i		−	0.0933326i
$804$	−8.11969	+	3.36329i	−0.286360	+	0.118614i
$805$	−7.31837	+	17.6681i	−0.257939	+	0.622719i
$806$	−22.5509	−	9.34089i	−0.794322	−	0.329019i
$807$	−8.36776	+	8.36776i	−0.294559	+	0.294559i
$808$	−0.394347	+	0.394347i	−0.0138731	+	0.0138731i
$809$	16.0697	+	6.65627i	0.564979	+	0.234022i	0.646845	−	0.762621i	$-0.276088\pi$
$809$	16.0697	+	6.65627i	0.564979	+	0.234022i	−0.0818660	+	0.996643i	$0.526088\pi$
$810$	−2.57112	+	6.20723i	−0.0903399	+	0.218100i
$811$	−30.4221	+	12.6012i	−1.06826	+	0.442489i	−0.846378	−	0.532583i	$-0.821221\pi$
$811$	−30.4221	+	12.6012i	−1.06826	+	0.442489i	−0.221886	+	0.975073i	$0.571221\pi$
$812$			1.48353i			0.0520617i
$813$	−4.51737	−	10.9059i	−0.158431	−	0.382486i
$814$	−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
$819$	1.26177	+	3.04617i	0.0440897	+	0.106442i
$820$		−	14.9879i		−	0.523401i
$821$	−40.4076	+	16.7374i	−1.41023	+	0.584138i	−0.952387	−	0.304893i	$-0.901379\pi$
$821$	−40.4076	+	16.7374i	−1.41023	+	0.584138i	−0.457847	+	0.889031i	$0.651379\pi$
$822$	−0.0652625	+	0.157558i	−0.00227629	+	0.00549546i
$823$	−1.54660	−	0.640622i	−0.0539110	−	0.0223307i	0.355565	−	0.934652i	$-0.384288\pi$
$823$	−1.54660	−	0.640622i	−0.0539110	−	0.0223307i	−0.409476	+	0.912321i	$0.634288\pi$
$824$	−4.50265	+	4.50265i	−0.156857	+	0.156857i
$825$	−18.5180	+	18.5180i	−0.644713	+	0.644713i
$826$	−10.4168	−	4.31477i	−0.362446	−	0.150130i
$827$	−0.868752	+	2.09735i	−0.0302095	+	0.0729321i	−0.938264	−	0.345919i	$-0.887567\pi$
$827$	−0.868752	+	2.09735i	−0.0302095	+	0.0729321i	0.908055	+	0.418851i	$0.137567\pi$
$828$	−3.43790	+	1.42402i	−0.119475	+	0.0494883i
$829$		−	19.2597i		−	0.668918i	−0.942410	−	0.334459i	$-0.891446\pi$
$829$		−	19.2597i		−	0.668918i	0.942410	−	0.334459i	$-0.108554\pi$
$830$	16.4168	+	39.6337i	0.569836	+	1.37571i
$831$	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
$836$	−1.09681	−	2.64793i	−0.0379338	−	0.0915804i
$837$		−	4.13287i		−	0.142853i
$838$	−18.5003	+	7.66307i	−0.639082	+	0.264716i
$839$	−5.66598	+	13.6789i	−0.195611	+	0.472248i	−0.991002	−	0.133850i	$-0.957266\pi$
$839$	−5.66598	+	13.6789i	−0.195611	+	0.472248i	0.795390	+	0.606098i	$0.207266\pi$
$840$	7.27222	+	3.01225i	0.250916	+	0.103933i
$841$	−17.0721	+	17.0721i	−0.588693	+	0.588693i
$842$	−20.8810	+	20.8810i	−0.719608	+	0.719608i
$843$	−5.05082	−	2.09212i	−0.173960	−	0.0720564i
$844$	−1.64246	+	3.96524i	−0.0565357	+	0.136489i
$845$	−0.834771	+	0.345773i	−0.0287170	+	0.0118950i
$846$		−	11.5016i		−	0.395434i
$847$	2.06366	+	4.98211i	0.0709081	+	0.171187i
$848$	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
$853$	−2.43299	−	5.87376i	−0.0833040	−	0.201114i	0.876739	−	0.480967i	$-0.159714\pi$
$853$	−2.43299	−	5.87376i	−0.0833040	−	0.201114i	−0.960043	+	0.279853i	$0.909714\pi$
$854$			5.92864i			0.202874i
$855$	−6.49883	+	2.69190i	−0.222255	+	0.0920612i
$856$	−15.7828	+	38.1030i	−0.539444	+	1.30233i
$857$	37.7231	+	15.6254i	1.28859	+	0.533754i	0.918566	−	0.395267i	$-0.129348\pi$
$857$	37.7231	+	15.6254i	1.28859	+	0.533754i	0.370029	+	0.929020i	$0.379348\pi$
$858$	−9.48065	+	9.48065i	−0.323664	+	0.323664i
$859$	−15.6599	+	15.6599i	−0.534308	+	0.534308i	−0.921851	−	0.387543i	$-0.873324\pi$
$859$	−15.6599	+	15.6599i	−0.534308	+	0.534308i	0.387543	+	0.921851i	$0.373324\pi$
$860$	−14.3443	−	5.94161i	−0.489137	−	0.202607i
$861$	1.78259	−	4.30354i	0.0607504	−	0.146664i
$862$	−16.9988	+	7.04112i	−0.578980	+	0.239822i
$863$		−	17.3423i		−	0.590339i	−0.955445	−	0.295170i	$-0.904624\pi$
$863$		−	17.3423i		−	0.590339i	0.955445	−	0.295170i	$-0.0953762\pi$
$864$	1.50906	+	3.64318i	0.0513391	+	0.123944i
$865$	−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
$870$	5.66604	+	13.6790i	0.192097	+	0.463762i
$871$			43.0452i			1.45853i
$872$	−1.38751	+	0.574725i	−0.0469870	+	0.0194627i
$873$	−5.53723	+	13.3680i	−0.187407	+	0.452440i
$874$	−13.4629	−	5.57653i	−0.455391	−	0.188629i
$875$	−17.3347	+	17.3347i	−0.586019	+	0.586019i
$876$	0.601239	−	0.601239i	0.0203140	−	0.0203140i
$877$	27.9294	+	11.5687i	0.943110	+	0.390649i	0.800637	−	0.599150i	$-0.204495\pi$
$877$	27.9294	+	11.5687i	0.943110	+	0.390649i	0.142473	+	0.989799i	$0.454495\pi$
$878$	−14.2868	+	34.4915i	−0.482157	+	1.16403i
$879$	−7.62982	+	3.16037i	−0.257347	+	0.106597i
$880$			45.4835i			1.53325i
$881$	4.04293	+	9.76049i	0.136210	+	0.328839i	0.977236	−	0.212155i	$-0.0680481\pi$
$881$	4.04293	+	9.76049i	0.136210	+	0.328839i	−0.841026	+	0.540994i	$0.818048\pi$
$882$	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
$887$	−13.7630	−	33.2268i	−0.462116	−	1.11565i	−0.967527	−	0.252767i	$-0.918659\pi$
$887$	−13.7630	−	33.2268i	−0.462116	−	1.11565i	0.505412	−	0.862878i	$-0.331341\pi$
$888$			12.4961i			0.419342i
$889$	2.39501	−	0.992044i	0.0803259	−	0.0332721i
$890$	26.6360	−	64.3051i	0.892842	−	2.15551i
$891$	−2.09735	−	0.868752i	−0.0702640	−	0.0291043i
$892$	−2.88170	+	2.88170i	−0.0964863	+	0.0964863i
$893$	8.51494	−	8.51494i	0.284941	−	0.284941i
$894$	−5.48848	−	2.27340i	−0.183562	−	0.0760340i
$895$	−12.1010	+	29.2144i	−0.404491	+	0.976528i
$896$	11.4217	−	4.73101i	0.381571	−	0.158052i
$897$			18.2254i			0.608530i
$898$	−0.708341	−	1.71009i	−0.0236376	−	0.0570663i
$899$	−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
$904$	9.46655	+	22.8543i	0.314853	+	0.760122i
$905$			3.72418i			0.123796i
$906$	11.5832	−	4.79791i	0.384825	−	0.159400i
$907$	14.9952	−	36.2016i	0.497907	−	1.20205i	−0.452702	−	0.891662i	$-0.649540\pi$
$907$	14.9952	−	36.2016i	0.497907	−	1.20205i	0.950609	−	0.310391i	$-0.100460\pi$
$908$	18.5630	+	7.68904i	0.616034	+	0.255170i
$909$	0.187911	−	0.187911i	0.00623260	−	0.00623260i
$910$	−15.6641	+	15.6641i	−0.519261	+	0.519261i
$911$	9.17234	+	3.79931i	0.303893	+	0.125877i	0.529419	−	0.848361i	$-0.322410\pi$
$911$	9.17234	+	3.79931i	0.303893	+	0.125877i	−0.225526	+	0.974237i	$0.572410\pi$
$912$	−3.26159	+	7.87418i	−0.108002	+	0.260740i
$913$	−13.3918	+	5.54706i	−0.443203	+	0.183581i
$914$			66.2202i			2.19037i
$915$	6.05382	+	14.6152i	0.200133	+	0.483164i
$916$	−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
$921$	3.80617	+	9.18892i	0.125418	+	0.302785i
$922$		−	8.25442i		−	0.271845i
$923$	−5.03296	+	2.08472i	−0.165662	+	0.0686193i
$924$	0.584837	−	1.41192i	0.0192397	−	0.0464488i
$925$	−63.4621	−	26.2869i	−2.08662	−	0.864307i
$926$	−45.6164	+	45.6164i	−1.49905	+	1.49905i
$927$	2.14556	−	2.14556i	0.0704696	−	0.0704696i
$928$	8.02856	+	3.32554i	0.263551	+	0.109166i
$929$	−6.95043	+	16.7798i	−0.228036	+	0.550529i	−0.995938	−	0.0900390i	$-0.971301\pi$
$929$	−6.95043	+	16.7798i	−0.228036	+	0.550529i	0.767902	+	0.640568i	$0.221301\pi$
$930$	25.6537	−	10.6261i	0.841218	−	0.348444i
$931$			10.6372i			0.348619i
$932$	−0.382884	−	0.924365i	−0.0125418	−	0.0302786i
$933$	−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	0.688356	−	0.725373i	$-0.258333\pi$
$937$	−1.13309	−	1.13309i	−0.0370165	−	0.0370165i	−0.725373	+	0.688356i	$0.758333\pi$
$938$	−7.02289	−	16.9548i	−0.229305	−	0.553592i
$939$			20.6116i			0.672634i
$940$	19.0874	−	7.90628i	0.622564	−	0.257874i
$941$	−12.3815	+	29.8916i	−0.403625	+	0.974437i	0.583153	+	0.812362i	$0.301819\pi$
$941$	−12.3815	+	29.8916i	−0.403625	+	0.974437i	−0.986778	+	0.162075i	$0.948181\pi$
$942$	−28.9368	−	11.9860i	−0.942813	−	0.390526i
$943$	18.2068	−	18.2068i	0.592896	−	0.592896i
$944$	−25.7755	+	25.7755i	−0.838920	+	0.838920i
$945$	−3.46530	−	1.43537i	−0.112726	−	0.0466927i
$946$	7.50909	−	18.1286i	0.244142	−	0.589410i
$947$	23.2650	−	9.63669i	0.756012	−	0.313150i	0.0288200	−	0.999585i	$-0.490825\pi$
$947$	23.2650	−	9.63669i	0.756012	−	0.313150i	0.727192	+	0.686434i	$0.240825\pi$
$948$		−	8.67319i		−	0.281692i
$949$	−1.59368	−	3.84749i	−0.0517332	−	0.124895i
$950$	−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
$955$	29.8250	+	72.0038i	0.965113	+	2.32999i
$956$			15.7734i			0.510148i
$957$	−4.62199	+	1.91449i	−0.149408	+	0.0618867i
$958$	−16.4164	+	39.6328i	−0.530391	+	1.28048i
$959$	−0.0879594	−	0.0364340i	−0.00284036	−	0.00117651i
$960$	9.60021	−	9.60021i	0.309845	−	0.309845i
$961$	9.84248	−	9.84248i	0.317499	−	0.317499i
$962$	−32.4908	−	13.4581i	−1.04754	−	0.433907i
$963$	7.52066	−	18.1565i	0.242350	−	0.585085i
$964$	0.715959	−	0.296560i	0.0230595	−	0.00955155i
$965$		−	19.1585i		−	0.616733i
$966$	−2.97351	−	7.17868i	−0.0956711	−	0.230970i
$967$	−1.53792	−	1.53792i	−0.0494563	−	0.0494563i	0.681946	−	0.731402i	$-0.261134\pi$
$967$	−1.53792	−	1.53792i	−0.0494563	−	0.0494563i	−0.731402	+	0.681946i	$0.761134\pi$
$968$	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	$-0.974542\pi$
$971$	−33.5508	−	33.5508i	−1.07670	−	1.07670i	−0.0798947	−	0.996803i	$-0.525458\pi$
$972$	−0.279298	−	0.674285i	−0.00895848	−	0.0216277i
$973$			13.3251i			0.427182i
$974$	38.9865	−	16.1487i	1.24921	−	0.517439i
$975$	−15.7805	+	38.0974i	−0.505379	+	1.22009i
$976$	17.7082	+	7.33498i	0.566826	+	0.234787i
$977$	−14.7238	+	14.7238i	−0.471057	+	0.471057i	−0.902256	−	0.431200i	$-0.858090\pi$
$977$	−14.7238	+	14.7238i	−0.471057	+	0.471057i	0.431200	+	0.902256i	$0.358090\pi$
$978$	15.6938	−	15.6938i	0.501832	−	0.501832i
$979$	21.7280	+	9.00002i	0.694429	+	0.287642i
$980$	−6.98395	+	16.8607i	−0.223094	+	0.538597i
$981$	0.661164	−	0.273863i	0.0211093	−	0.00874377i
$982$		−	4.14319i		−	0.132214i
$983$	0.930068	+	2.24538i	0.0296646	+	0.0716166i	0.938018	−	0.346588i	$-0.112660\pi$
$983$	0.930068	+	2.24538i	0.0296646	+	0.0716166i	−0.908353	+	0.418204i	$0.862660\pi$
$984$	−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
$989$	−10.2073	−	24.6427i	−0.324574	−	0.783592i
$990$		−	15.2524i		−	0.484754i
$991$	−33.7934	+	13.9977i	−1.07348	+	0.444651i	−0.848218	−	0.529647i	$-0.822324\pi$
$991$	−33.7934	+	13.9977i	−1.07348	+	0.444651i	−0.225264	+	0.974298i	$0.572324\pi$
$992$	6.23673	−	15.0568i	0.198016	−	0.478054i
$993$	26.4327	+	10.9488i	0.838816	+	0.347449i
$994$	1.64227	−	1.64227i	0.0520896	−	0.0520896i
$995$	54.0107	−	54.0107i	1.71226	−	1.71226i
$996$	−4.30536	−	1.78334i	−0.136421	−	0.0565073i
$997$	7.92571	−	19.1344i	0.251010	−	0.605991i	−0.747276	−	0.664513i	$-0.768639\pi$
$997$	7.92571	−	19.1344i	0.251010	−	0.605991i	0.998286	+	0.0585222i	$0.0186388\pi$
$998$	−23.2434	+	9.62773i	−0.735757	+	0.304760i
$999$		−	5.95453i		−	0.188393i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.e.a.4.2	✓	8	17.10	odd	16
51.2.e.a.13.3	yes	8	17.11	odd	16
153.2.f.b.55.3		8	51.44	even	16
153.2.f.b.64.2		8	51.11	even	16
816.2.bd.e.625.1		8	68.11	even	16
816.2.bd.e.769.1		8	68.27	even	16
867.2.a.k.1.2		4	17.12	odd	16
867.2.a.l.1.2		4	17.5	odd	16
867.2.d.f.577.5		8	17.3	odd	16
867.2.d.f.577.6		8	17.14	odd	16
867.2.e.g.616.2		8	17.7	odd	16
867.2.e.g.829.3		8	17.6	odd	16
867.2.h.i.688.3		16	17.8	even	8	inner
867.2.h.i.688.4		16	17.9	even	8	inner
867.2.h.i.712.3		16	1.1	even	1	trivial
867.2.h.i.712.4		16	17.16	even	2	inner
867.2.h.k.733.1		16	17.4	even	4
867.2.h.k.733.2		16	17.13	even	4
867.2.h.k.757.1		16	17.2	even	8
867.2.h.k.757.2		16	17.15	even	8
2448.2.be.x.1441.4		8	204.11	odd	16
2448.2.be.x.1585.4		8	204.95	odd	16
2601.2.a.be.1.3		4	51.5	even	16
2601.2.a.bf.1.3		4	51.29	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 $\F_{q}$
Belyi maps

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

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Database

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