LMFDB - Embedded newform 867.2.i.d.131.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(65,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.65"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [32,0,0,-16,0,0,0,0,8,32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			131.4
Character	$\chi$	$=$	867.131
Dual form			867.2.i.d.503.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.88095 - 0.779115i) q^{2} +(-1.33527 - 1.10321i) q^{3} +(1.51674 - 1.51674i) q^{4} +(0.405238 - 2.03727i) q^{5} +(-3.37109 - 1.03475i) q^{6} +(-1.95490 + 0.388855i) q^{7} +(0.112963 - 0.272718i) q^{8} +(0.565877 + 2.94615i) q^{9} +(-0.825033 - 4.14772i) q^{10} +(-1.95782 - 1.30817i) q^{11} +(-3.69852 + 0.351977i) q^{12} +(-4.24491 - 4.24491i) q^{13} +(-3.37411 + 2.25451i) q^{14} +(-2.78862 + 2.27324i) q^{15} +3.68900i q^{16} +(3.35977 + 5.10067i) q^{18} +(-1.93477 - 4.67096i) q^{19} +(-2.47536 - 3.70464i) q^{20} +(3.03931 + 1.63744i) q^{21} +(-4.70177 - 0.935240i) q^{22} +(-0.491037 + 0.734889i) q^{23} +(-0.451700 + 0.239529i) q^{24} +(0.633157 + 0.262262i) q^{25} +(-11.2917 - 4.67719i) q^{26} +(2.49461 - 4.55817i) q^{27} +(-2.37529 + 3.55487i) q^{28} +(0.0587151 + 0.0116792i) q^{29} +(-3.47415 + 6.44850i) q^{30} +(-1.63665 - 2.44942i) q^{31} +(3.10008 + 7.48426i) q^{32} +(1.17103 + 3.90663i) q^{33} +4.14024i q^{35} +(5.32682 + 3.61024i) q^{36} +(-2.28949 + 1.52979i) q^{37} +(-7.27842 - 7.27842i) q^{38} +(0.985083 + 10.3511i) q^{39} +(-0.509822 - 0.340652i) q^{40} +(0.647088 + 3.25313i) q^{41} +(6.99253 + 0.711965i) q^{42} +(2.53831 - 6.12803i) q^{43} +(-4.95364 + 0.985341i) q^{44} +(6.23140 + 0.0410472i) q^{45} +(-0.351053 + 1.76486i) q^{46} +(5.76615 - 5.76615i) q^{47} +(4.06972 - 4.92580i) q^{48} +(-2.79671 + 1.15844i) q^{49} +1.39527 q^{50} -12.8768 q^{52} +(-1.75216 + 0.725770i) q^{53} +(1.14089 - 10.5173i) q^{54} +(-3.45848 + 3.45848i) q^{55} +(-0.114785 + 0.577063i) q^{56} +(-2.56958 + 8.37143i) q^{57} +(0.119540 - 0.0237779i) q^{58} +(3.54618 - 8.56124i) q^{59} +(-0.781708 + 7.67751i) q^{60} +(1.05546 + 5.30616i) q^{61} +(-4.98684 - 3.33210i) q^{62} +(-2.25186 - 5.53939i) q^{63} +(6.44515 + 6.44515i) q^{64} +(-10.3682 + 6.92782i) q^{65} +(5.24636 + 6.43581i) q^{66} -7.09503i q^{67} +(1.46640 - 0.439558i) q^{69} +(3.22572 + 7.78759i) q^{70} +(0.496046 + 0.742386i) q^{71} +(0.867389 + 0.178482i) q^{72} +(2.77256 + 0.551496i) q^{73} +(-3.11454 + 4.66124i) q^{74} +(-0.556105 - 1.04869i) q^{75} +(-10.0192 - 4.15007i) q^{76} +(4.33604 + 1.79604i) q^{77} +(9.91759 + 18.7024i) q^{78} +(2.20873 - 3.30560i) q^{79} +(7.51548 + 1.49492i) q^{80} +(-8.35957 + 3.33431i) q^{81} +(3.75170 + 5.61482i) q^{82} +(-1.44855 - 3.49712i) q^{83} +(7.09339 - 2.12627i) q^{84} -13.5041i q^{86} +(-0.0655159 - 0.0803696i) q^{87} +(-0.577923 + 0.386156i) q^{88} +(2.00979 + 2.00979i) q^{89} +(11.7529 - 4.77777i) q^{90} +(9.94906 + 6.64775i) q^{91} +(0.369859 + 1.85941i) q^{92} +(-0.516848 + 5.07620i) q^{93} +(6.35335 - 15.3383i) q^{94} +(-10.3000 + 2.04880i) q^{95} +(4.11723 - 13.4135i) q^{96} +(3.67461 - 18.4735i) q^{97} +(-4.35792 + 4.35792i) q^{98} +(2.74618 - 6.50828i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{4} + 8 q^{9} + 32 q^{10} + 24 q^{12} - 16 q^{13} - 16 q^{15} + 16 q^{18} + 16 q^{19} + 16 q^{21} - 48 q^{22} + 8 q^{24} - 16 q^{25} - 48 q^{27} - 64 q^{28} - 8 q^{30} + 16 q^{31} - 8 q^{36}+ \cdots + 96 q^{97}+O(q^{100}) $ 32 * q - 16 * q^4 + 8 * q^9 + 32 * q^10 + 24 * q^12 - 16 * q^13 - 16 * q^15 + 16 * q^18 + 16 * q^19 + 16 * q^21 - 48 * q^22 + 8 * q^24 - 16 * q^25 - 48 * q^27 - 64 * q^28 - 8 * q^30 + 16 * q^31 - 8 * q^36 - 32 * q^37 + 8 * q^39 - 64 * q^40 + 56 * q^42 - 16 * q^43 + 24 * q^45 - 80 * q^46 - 72 * q^48 + 48 * q^49 - 96 * q^52 + 48 * q^54 - 48 * q^55 + 24 * q^57 - 32 * q^58 - 32 * q^60 + 64 * q^61 - 16 * q^63 + 16 * q^64 - 72 * q^66 + 80 * q^69 - 48 * q^70 + 64 * q^72 - 48 * q^76 - 16 * q^78 - 32 * q^79 + 48 * q^81 + 48 * q^82 + 56 * q^87 - 80 * q^88 + 104 * q^90 + 80 * q^91 + 72 * q^93 + 48 * q^94 + 72 * q^96 + 96 * q^97

Character values

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

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{13}{16}\right)$

Coefficient data

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

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

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

$2$	1.88095	−	0.779115i	1.33003	−	0.550917i	0.399367	−	0.916791i	$-0.369230\pi$
$2$	1.88095	−	0.779115i	1.33003	−	0.550917i	0.930665	+	0.365874i	$0.119230\pi$
$3$	−1.33527	−	1.10321i	−0.770917	−	0.636936i
$3$	−1.33527	−	1.10321i	−0.770917	−	0.636936i
$4$	1.51674	−	1.51674i	0.758368	−	0.758368i
$5$	0.405238	−	2.03727i	0.181228	−	0.911094i	−0.777958	−	0.628316i	$-0.783744\pi$
$5$	0.405238	−	2.03727i	0.181228	−	0.911094i	0.959186	−	0.282777i	$-0.0912557\pi$
$6$	−3.37109	−	1.03475i	−1.37624	−	0.422433i
$7$	−1.95490	+	0.388855i	−0.738885	+	0.146973i	−0.550163	−	0.835057i	$-0.685434\pi$
$7$	−1.95490	+	0.388855i	−0.738885	+	0.146973i	−0.188722	+	0.982031i	$0.560434\pi$
$8$	0.112963	−	0.272718i	0.0399386	−	0.0964202i
$9$	0.565877	+	2.94615i	0.188626	+	0.982049i
$10$	−0.825033	−	4.14772i	−0.260898	−	1.31163i
$11$	−1.95782	−	1.30817i	−0.590304	−	0.394429i	0.224237	−	0.974535i	$-0.428011\pi$
$11$	−1.95782	−	1.30817i	−0.590304	−	0.394429i	−0.814541	+	0.580106i	$0.803011\pi$
$12$	−3.69852	+	0.351977i	−1.06767	+	0.101607i
$13$	−4.24491	−	4.24491i	−1.17733	−	1.17733i	−0.980423	−	0.196905i	$-0.936911\pi$
$13$	−4.24491	−	4.24491i	−1.17733	−	1.17733i	−0.196905	−	0.980423i	$-0.563089\pi$
$14$	−3.37411	+	2.25451i	−0.901770	+	0.602543i
$15$	−2.78862	+	2.27324i	−0.720020	+	0.586947i
$16$			3.68900i			0.922250i
$17$		0			0
$17$		0			0
$18$	3.35977	+	5.10067i	0.791906	+	1.20224i
$19$	−1.93477	−	4.67096i	−0.443868	−	1.07159i	−0.974580	−	0.224039i	$-0.928076\pi$
$19$	−1.93477	−	4.67096i	−0.443868	−	1.07159i	0.530712	−	0.847552i	$-0.321924\pi$
$20$	−2.47536	−	3.70464i	−0.553507	−	0.828382i
$21$	3.03931	+	1.63744i	0.663231	+	0.357318i
$22$	−4.70177	−	0.935240i	−1.00242	−	0.199394i
$23$	−0.491037	+	0.734889i	−0.102388	+	0.153235i	−0.879126	−	0.476589i	$-0.841873\pi$
$23$	−0.491037	+	0.734889i	−0.102388	+	0.153235i	0.776738	+	0.629824i	$0.216873\pi$
$24$	−0.451700	+	0.239529i	−0.0922028	+	0.0488937i
$25$	0.633157	+	0.262262i	0.126631	+	0.0524525i
$26$	−11.2917	−	4.67719i	−2.21449	−	0.917273i
$27$	2.49461	−	4.55817i	0.480087	−	0.877221i
$28$	−2.37529	+	3.55487i	−0.448887	+	0.671806i
$29$	0.0587151	+	0.0116792i	0.0109031	+	0.00216877i	0.200539	−	0.979686i	$-0.435731\pi$
$29$	0.0587151	+	0.0116792i	0.0109031	+	0.00216877i	−0.189636	+	0.981855i	$0.560731\pi$
$30$	−3.47415	+	6.44850i	−0.634290	+	1.17733i
$31$	−1.63665	−	2.44942i	−0.293952	−	0.439930i	0.654870	−	0.755741i	$-0.272723\pi$
$31$	−1.63665	−	2.44942i	−0.293952	−	0.439930i	−0.948822	+	0.315812i	$0.897723\pi$
$32$	3.10008	+	7.48426i	0.548022	+	1.32304i
$33$	1.17103	+	3.90663i	0.203850	+	0.680057i
$34$		0			0
$35$			4.14024i			0.699829i
$36$	5.32682	+	3.61024i	0.887803	+	0.601707i
$37$	−2.28949	+	1.52979i	−0.376390	+	0.251496i	−0.729347	−	0.684144i	$-0.760176\pi$
$37$	−2.28949	+	1.52979i	−0.376390	+	0.251496i	0.352957	+	0.935640i	$0.385176\pi$
$38$	−7.27842	−	7.27842i	−1.18072	−	1.18072i
$39$	0.985083	+	10.3511i	0.157740	+	1.65750i
$40$	−0.509822	−	0.340652i	−0.0806099	−	0.0538618i
$41$	0.647088	+	3.25313i	0.101058	+	0.508054i	0.997846	+	0.0655937i	$0.0208941\pi$
$41$	0.647088	+	3.25313i	0.101058	+	0.508054i	−0.896788	+	0.442460i	$0.854106\pi$
$42$	6.99253	+	0.711965i	1.07897	+	0.109859i
$43$	2.53831	−	6.12803i	0.387089	−	0.934515i	−0.603465	−	0.797390i	$-0.706214\pi$
$43$	2.53831	−	6.12803i	0.387089	−	0.934515i	0.990554	−	0.137126i	$-0.0437864\pi$
$44$	−4.95364	+	0.985341i	−0.746790	+	0.148546i
$45$	6.23140	+	0.0410472i	0.928923	+	0.00611895i
$46$	−0.351053	+	1.76486i	−0.0517599	+	0.260215i
$47$	5.76615	−	5.76615i	0.841080	−	0.841080i	−0.147919	−	0.988999i	$-0.547258\pi$
$47$	5.76615	−	5.76615i	0.841080	−	0.841080i	0.988999	+	0.147919i	$0.0472576\pi$
$48$	4.06972	−	4.92580i	0.587414	−	0.710978i
$49$	−2.79671	+	1.15844i	−0.399530	+	0.165491i
$50$	1.39527			0.197321
$51$		0			0
$52$	−12.8768			−1.78570
$53$	−1.75216	+	0.725770i	−0.240678	+	0.0996922i	−0.499762	−	0.866163i	$-0.666579\pi$
$53$	−1.75216	+	0.725770i	−0.240678	+	0.0996922i	0.259084	+	0.965855i	$0.416579\pi$
$54$	1.14089	−	10.5173i	0.155256	−	1.43122i
$55$	−3.45848	+	3.45848i	−0.466341	+	0.466341i
$56$	−0.114785	+	0.577063i	−0.0153388	+	0.0771133i
$57$	−2.56958	+	8.37143i	−0.340350	+	1.10882i
$58$	0.119540	−	0.0237779i	0.0156963	−	0.00312219i
$59$	3.54618	−	8.56124i	0.461674	−	1.11458i	−0.506036	−	0.862512i	$-0.668890\pi$
$59$	3.54618	−	8.56124i	0.461674	−	1.11458i	0.967710	−	0.252067i	$-0.0811102\pi$
$60$	−0.781708	+	7.67751i	−0.100918	+	0.991162i
$61$	1.05546	+	5.30616i	0.135138	+	0.679385i	0.987650	+	0.156677i	$0.0500781\pi$
$61$	1.05546	+	5.30616i	0.135138	+	0.679385i	−0.852512	+	0.522708i	$0.824922\pi$
$62$	−4.98684	−	3.33210i	−0.633330	−	0.423177i
$63$	−2.25186	−	5.53939i	−0.283708	−	0.697898i
$64$	6.44515	+	6.44515i	0.805644	+	0.805644i
$65$	−10.3682	+	6.92782i	−1.28602	+	0.859291i
$66$	5.24636	+	6.43581i	0.645782	+	0.792194i
$67$		−	7.09503i		−	0.866796i	−0.901203	−	0.433398i	$-0.857315\pi$
$67$		−	7.09503i		−	0.866796i	0.901203	−	0.433398i	$-0.142685\pi$
$68$		0			0
$69$	1.46640	−	0.439558i	0.176534	−	0.0529166i
$70$	3.22572	+	7.78759i	0.385548	+	0.930795i
$71$	0.496046	+	0.742386i	0.0588699	+	0.0881050i	0.859737	−	0.510737i	$-0.170628\pi$
$71$	0.496046	+	0.742386i	0.0588699	+	0.0881050i	−0.800867	+	0.598842i	$0.795628\pi$
$72$	0.867389	+	0.178482i	0.102223	+	0.0210343i
$73$	2.77256	+	0.551496i	0.324503	+	0.0645477i	0.354654	−	0.934998i	$-0.384599\pi$
$73$	2.77256	+	0.551496i	0.324503	+	0.0645477i	−0.0301507	+	0.999545i	$0.509599\pi$
$74$	−3.11454	+	4.66124i	−0.362058	+	0.541858i
$75$	−0.556105	−	1.04869i	−0.0642135	−	0.121093i
$76$	−10.0192	−	4.15007i	−1.14928	−	0.476046i
$77$	4.33604	+	1.79604i	0.494137	+	0.204678i
$78$	9.91759	+	18.7024i	1.12295	+	2.11763i
$79$	2.20873	−	3.30560i	0.248502	−	0.371909i	−0.686158	−	0.727452i	$-0.740704\pi$
$79$	2.20873	−	3.30560i	0.248502	−	0.371909i	0.934660	+	0.355543i	$0.115704\pi$
$80$	7.51548	+	1.49492i	0.840256	+	0.167137i
$81$	−8.35957	+	3.33431i	−0.928841	+	0.370479i
$82$	3.75170	+	5.61482i	0.414306	+	0.620053i
$83$	−1.44855	−	3.49712i	−0.159000	−	0.383859i	0.824224	−	0.566264i	$-0.191612\pi$
$83$	−1.44855	−	3.49712i	−0.159000	−	0.383859i	−0.983223	+	0.182405i	$0.941612\pi$
$84$	7.09339	−	2.12627i	0.773952	−	0.231995i
$85$		0			0
$86$		−	13.5041i		−	1.45619i
$87$	−0.0655159	−	0.0803696i	−0.00702404	−	0.00861653i
$88$	−0.577923	+	0.386156i	−0.0616068	+	0.0411643i
$89$	2.00979	+	2.00979i	0.213037	+	0.213037i	0.805556	−	0.592519i	$-0.201867\pi$
$89$	2.00979	+	2.00979i	0.213037	+	0.213037i	−0.592519	+	0.805556i	$0.701867\pi$
$90$	11.7529	−	4.77777i	1.23887	−	0.503621i
$91$	9.94906	+	6.64775i	1.04294	+	0.696873i
$92$	0.369859	+	1.85941i	0.0385604	+	0.193856i
$93$	−0.516848	+	5.07620i	−0.0535947	+	0.526377i
$94$	6.35335	−	15.3383i	0.655298	−	1.58203i
$95$	−10.3000	+	2.04880i	−1.05676	+	0.210203i
$96$	4.11723	−	13.4135i	0.420213	−	1.36901i
$97$	3.67461	−	18.4735i	0.373100	−	1.87570i	−0.100466	−	0.994940i	$-0.532033\pi$
$97$	3.67461	−	18.4735i	0.373100	−	1.87570i	0.473566	−	0.880758i	$-0.342967\pi$
$98$	−4.35792	+	4.35792i	−0.440216	+	0.440216i
$99$	2.74618	−	6.50828i	0.276002	−	0.654107i
$100$	1.35812	−	0.562550i	0.135812	−	0.0562550i
$101$	−3.48372			−0.346643			−0.173321	−	0.984865i	$-0.555450\pi$
$101$	−3.48372			−0.346643			−0.173321	+	0.984865i	$0.555450\pi$
$102$		0			0
$103$	−3.80817			−0.375230			−0.187615	−	0.982243i	$-0.560076\pi$
$103$	−3.80817			−0.375230			−0.187615	+	0.982243i	$0.560076\pi$
$104$	−1.63718	+	0.678143i	−0.160539	+	0.0664974i
$105$	4.56754	−	5.52833i	0.445746	−	0.539510i
$106$	−2.73027	+	2.73027i	−0.265188	+	0.265188i
$107$	0.782805	−	3.93543i	0.0756766	−	0.380452i	−0.924323	−	0.381612i	$-0.875369\pi$
$107$	0.782805	−	3.93543i	0.0756766	−	0.380452i	0.999999	+	0.00115968i	$0.000369137\pi$
$108$	−3.12988	−	10.6972i	−0.301173	−	1.02934i
$109$	14.5657	−	2.89730i	1.39514	−	0.277511i	0.560433	−	0.828200i	$-0.310635\pi$
$109$	14.5657	−	2.89730i	1.39514	−	0.277511i	0.834711	+	0.550689i	$0.185635\pi$
$110$	−3.81067	+	9.19977i	−0.363333	+	0.877163i
$111$	4.74476	+	0.483102i	0.450352	+	0.0458540i
$112$	−1.43449	−	7.21164i	−0.135546	−	0.681436i
$113$	5.53377	+	3.69755i	0.520573	+	0.347836i	0.787933	−	0.615761i	$-0.211151\pi$
$113$	5.53377	+	3.69755i	0.520573	+	0.347836i	−0.267360	+	0.963597i	$0.586151\pi$
$114$	1.68905	+	17.7482i	0.158194	+	1.66227i
$115$	1.29818	+	1.29818i	0.121056	+	0.121056i
$116$	0.106770	−	0.0713412i	0.00991331	−	0.00662386i
$117$	10.1040	−	14.9082i	0.934119	−	1.37827i
$118$		−	18.8661i		−	1.73677i
$119$		0			0
$120$	0.304939	+	1.01730i	0.0278370	+	0.0928663i
$121$	−2.08778	−	5.04035i	−0.189798	−	0.458214i
$122$	6.11938	+	9.15830i	0.554023	+	0.829153i
$123$	2.72484	−	5.05767i	0.245690	−	0.456035i
$124$	−6.19750	−	1.23276i	−0.556552	−	0.110705i
$125$	6.56097	−	9.81919i	0.586831	−	0.878255i
$126$	−8.55146	−	8.66486i	−0.761824	−	0.771927i
$127$	−3.25107	−	1.34664i	−0.288486	−	0.119495i	0.233748	−	0.972297i	$-0.424901\pi$
$127$	−3.25107	−	1.34664i	−0.288486	−	0.119495i	−0.522234	+	0.852803i	$0.674901\pi$
$128$	2.17601	+	0.901332i	0.192334	+	0.0796672i
$129$	−10.1498	+	5.38227i	−0.893640	+	0.473883i
$130$	−14.1045	+	21.1089i	−1.23705	+	1.85137i
$131$	−20.1623	−	4.01054i	−1.76159	−	0.350402i	−0.794977	−	0.606640i	$-0.792517\pi$
$131$	−20.1623	−	4.01054i	−1.76159	−	0.350402i	−0.966614	+	0.256237i	$0.917517\pi$
$132$	7.70147	+	4.14919i	0.670327	+	0.361141i
$133$	5.59862	+	8.37893i	0.485462	+	0.726546i
$134$	−5.52784	−	13.3454i	−0.477533	−	1.15287i
$135$	−8.27531	−	6.92933i	−0.712225	−	0.596381i
$136$		0			0
$137$			13.4046i			1.14524i	0.819822	+	0.572618i	$0.194072\pi$
$137$			13.4046i			1.14524i	−0.819822	+	0.572618i	$0.805928\pi$
$138$	2.41575	−	1.96928i	0.205643	−	0.167636i
$139$	−0.0842808	+	0.0563146i	−0.00714860	+	0.00477654i	−0.559139	−	0.829074i	$-0.688868\pi$
$139$	−0.0842808	+	0.0563146i	−0.00714860	+	0.00477654i	0.551991	+	0.833850i	$0.313868\pi$
$140$	6.27966	+	6.27966i	0.530728	+	0.530728i
$141$	−14.0606	+	1.33811i	−1.18412	+	0.112689i
$142$	1.51144	+	1.00991i	0.126837	+	0.0847500i
$143$	2.75769	+	13.8638i	0.230610	+	1.15935i
$144$	−10.8683	+	2.08752i	−0.905695	+	0.173960i
$145$	0.0475872	−	0.114886i	0.00395190	−	0.00954073i
$146$	5.64471	−	1.12280i	0.467160	−	0.0929239i
$147$	5.01235	+	1.53853i	0.413412	+	0.126895i
$148$	−1.15227	+	5.79285i	−0.0947159	+	0.476169i
$149$	9.82755	−	9.82755i	0.805104	−	0.805104i	−0.178784	−	0.983888i	$-0.557216\pi$
$149$	9.82755	−	9.82755i	0.805104	−	0.805104i	0.983888	+	0.178784i	$0.0572163\pi$
$150$	−1.86306	−	1.53927i	−0.152118	−	0.125681i
$151$	−4.63104	+	1.91824i	−0.376869	+	0.156104i	−0.563074	−	0.826407i	$-0.690381\pi$
$151$	−4.63104	+	1.91824i	−0.376869	+	0.156104i	0.186205	+	0.982511i	$0.440381\pi$
$152$	−1.49241			−0.121050
$153$		0			0
$154$	9.55519			0.769979
$155$	−5.65337	+	2.34170i	−0.454089	+	0.188090i
$156$	17.1940	+	14.2058i	1.37662	+	1.13737i
$157$	−8.48035	+	8.48035i	−0.676806	+	0.676806i	−0.959276	−	0.282470i	$-0.908846\pi$
$157$	−8.48035	+	8.48035i	−0.676806	+	0.676806i	0.282470	+	0.959276i	$0.408846\pi$
$158$	1.57907	−	7.93852i	0.125624	−	0.631555i
$159$	3.14028	+	0.963899i	0.249040	+	0.0764422i
$160$	16.5037	−	3.28279i	1.30473	−	0.259527i
$161$	0.674165	−	1.62758i	0.0531317	−	0.128271i
$162$	−13.1261	+	12.7847i	−1.03128	+	1.00446i
$163$	−2.26731	−	11.3986i	−0.177590	−	0.892803i	−0.962102	−	0.272690i	$-0.912087\pi$
$163$	−2.26731	−	11.3986i	−0.177590	−	0.892803i	0.784512	−	0.620113i	$-0.212913\pi$
$164$	5.91560	+	3.95268i	0.461931	+	0.308652i
$165$	8.43340	−	0.802581i	0.656539	−	0.0624809i
$166$	−5.44932	−	5.44932i	−0.422949	−	0.422949i
$167$	13.4072	−	8.95841i	1.03748	−	0.693223i	0.0845529	−	0.996419i	$-0.473054\pi$
$167$	13.4072	−	8.95841i	1.03748	−	0.693223i	0.952928	+	0.303196i	$0.0980538\pi$
$168$	0.789888	−	0.643902i	0.0609412	−	0.0496781i
$169$			23.0386i			1.77220i
$170$		0			0
$171$	12.6665	−	8.34332i	0.968630	−	0.638029i
$172$	−5.44465	−	13.1446i	−0.415151	−	1.00226i
$173$	10.1166	+	15.1405i	0.769149	+	1.15111i	0.984638	+	0.174607i	$0.0558655\pi$
$173$	10.1166	+	15.1405i	0.769149	+	1.15111i	−0.215489	+	0.976506i	$0.569134\pi$
$174$	−0.185849	−	0.100127i	−0.0140892	−	0.00759059i
$175$	−1.33974	−	0.266492i	−0.101275	−	0.0201449i
$176$	4.82584	−	7.22239i	0.363762	−	0.544408i
$177$	−14.1799	+	7.51938i	−1.06583	+	0.565191i
$178$	5.34616	+	2.21445i	0.400712	+	0.165980i
$179$	17.7630	+	7.35767i	1.32767	+	0.549938i	0.929989	−	0.367587i	$-0.119816\pi$
$179$	17.7630	+	7.35767i	1.32767	+	0.549938i	0.397679	+	0.917525i	$0.369816\pi$
$180$	9.51366	−	9.38914i	0.709106	−	0.699825i
$181$	−1.94570	+	2.91194i	−0.144623	+	0.216443i	−0.896708	−	0.442623i	$-0.854048\pi$
$181$	−1.94570	+	2.91194i	−0.144623	+	0.216443i	0.752085	+	0.659066i	$0.229048\pi$
$182$	23.8930	+	4.75262i	1.77107	+	0.352288i
$183$	4.44446	−	8.24954i	0.328544	−	0.609823i
$184$	0.144948	+	0.216930i	0.0106857	+	0.0159923i
$185$	2.18880	+	5.28424i	0.160924	+	0.388505i
$186$	2.98278	+	9.95076i	0.218708	+	0.729625i
$187$		0			0
$188$		−	17.4915i		−	1.27570i
$189$	−3.10425	+	9.88083i	−0.225801	+	0.718725i
$190$	−17.7776	+	11.8786i	−1.28972	+	0.861764i
$191$	6.08578	+	6.08578i	0.440352	+	0.440352i	0.892130	−	0.451778i	$-0.149210\pi$
$191$	6.08578	+	6.08578i	0.440352	+	0.440352i	−0.451778	+	0.892130i	$0.649210\pi$
$192$	−1.49568	−	15.7163i	−0.107941	−	1.13423i
$193$	−8.94851	−	5.97920i	−0.644128	−	0.430392i	0.190136	−	0.981758i	$-0.439107\pi$
$193$	−8.94851	−	5.97920i	−0.644128	−	0.430392i	−0.834264	+	0.551365i	$0.814107\pi$
$194$	−7.48122	−	37.6106i	−0.537120	−	2.70029i
$195$	21.4872	+	2.18778i	1.53873	+	0.156670i
$196$	−2.48483	+	5.99892i	−0.177488	+	0.428494i
$197$	24.9075	−	4.95440i	1.77458	−	0.352987i	0.804163	−	0.594408i	$-0.202614\pi$
$197$	24.9075	−	4.95440i	1.77458	−	0.352987i	0.970420	+	0.241422i	$0.0776136\pi$
$198$	0.0947319	−	14.3813i	0.00673231	−	1.02204i
$199$	−4.71884	+	23.7232i	−0.334510	+	1.68169i	0.337637	+	0.941276i	$0.390372\pi$
$199$	−4.71884	+	23.7232i	−0.334510	+	1.68169i	−0.672147	+	0.740418i	$0.734628\pi$
$200$	0.143047	−	0.143047i	0.0101150	−	0.0101150i
$201$	−7.82727	+	9.47376i	−0.552093	+	0.668227i
$202$	−6.55269	+	2.71422i	−0.461046	+	0.190972i
$203$	−0.119324			−0.00837490
$204$		0			0
$205$	6.88972			0.481199
$206$	−7.16297	+	2.96700i	−0.499068	+	0.206721i
$207$	−2.44296	−	1.03081i	−0.169797	−	0.0716463i
$208$	15.6595	−	15.6595i	1.08579	−	1.08579i
$209$	−2.32248	+	11.6759i	−0.160649	+	0.807639i
$210$	4.28410	−	13.9571i	0.295631	−	0.963134i
$211$	−10.7873	+	2.14574i	−0.742631	+	0.147719i	−0.551884	−	0.833921i	$-0.686091\pi$
$211$	−10.7873	+	2.14574i	−0.742631	+	0.147719i	−0.190747	+	0.981639i	$0.561091\pi$
$212$	−1.55677	+	3.75837i	−0.106919	+	0.258126i
$213$	0.156649	−	1.53852i	0.0107334	−	0.105418i
$214$	−1.59373	−	8.01223i	−0.108945	−	0.547705i
$215$	−11.4558	−	7.65453i	−0.781280	−	0.522034i
$216$	−0.961294	−	1.19523i	−0.0654078	−	0.0813251i
$217$	4.15197	+	4.15197i	0.281854	+	0.281854i
$218$	25.1401	−	16.7980i	1.70270	−	1.13771i
$219$	−3.09369	−	3.79509i	−0.209052	−	0.256449i
$220$			10.4912i			0.707316i
$221$		0			0
$222$	9.30104	−	2.78802i	0.624245	−	0.187120i
$223$	−3.85027	−	9.29537i	−0.257833	−	0.622464i	0.740962	−	0.671547i	$-0.234370\pi$
$223$	−3.85027	−	9.29537i	−0.257833	−	0.622464i	−0.998795	+	0.0490833i	$0.984370\pi$
$224$	−8.97065	−	13.4255i	−0.599377	−	0.897031i
$225$	−0.414374	+	2.01378i	−0.0276249	+	0.134252i
$226$	13.2895	+	2.64346i	0.884008	+	0.175840i
$227$	−1.00895	+	1.50999i	−0.0669661	+	0.100222i	−0.863441	−	0.504449i	$-0.831695\pi$
$227$	−1.00895	+	1.50999i	−0.0669661	+	0.100222i	0.796475	+	0.604671i	$0.206695\pi$
$228$	8.79987	+	16.5946i	0.582786	+	1.09901i
$229$	−1.66699	−	0.690491i	−0.110158	−	0.0456290i	0.326924	−	0.945051i	$-0.393988\pi$
$229$	−1.66699	−	0.690491i	−0.110158	−	0.0456290i	−0.437082	+	0.899422i	$0.643988\pi$
$230$	3.45324	+	1.43038i	0.227700	+	0.0943163i
$231$	−3.80836	−	7.18174i	−0.250572	−	0.472523i
$232$	0.00981777	−	0.0146933i	0.000644568	−	0.000964664i
$233$	−1.36489	−	0.271493i	−0.0894166	−	0.0177861i	0.150179	−	0.988659i	$-0.452015\pi$
$233$	−1.36489	−	0.271493i	−0.0894166	−	0.0177861i	−0.239596	+	0.970873i	$0.577015\pi$
$234$	7.38996	−	35.9138i	0.483097	−	2.34776i
$235$	−9.41054	−	14.0839i	−0.613876	−	0.918730i
$236$	−7.60652	−	18.3638i	−0.495143	−	1.19538i
$237$	−6.59600	+	1.97718i	−0.428456	+	0.128431i
$238$		0			0
$239$			8.01035i			0.518146i	0.965858	+	0.259073i	$0.0834171\pi$
$239$			8.01035i			0.518146i	−0.965858	+	0.259073i	$0.916583\pi$
$240$	−8.38597	−	10.2872i	−0.541312	−	0.664038i
$241$	−14.4053	+	9.62530i	−0.927925	+	0.620020i	−0.924996	−	0.379976i	$-0.875932\pi$
$241$	−14.4053	+	9.62530i	−0.927925	+	0.620020i	−0.00292882	+	0.999996i	$0.500932\pi$
$242$	−7.85403	−	7.85403i	−0.504876	−	0.504876i
$243$	14.8407	+	4.77012i	0.952031	+	0.306003i
$244$	9.64891	+	6.44719i	0.617708	+	0.412739i
$245$	1.22671	+	6.16709i	0.0783717	+	0.394001i
$246$	1.18477	−	11.6362i	0.0755383	−	0.741896i
$247$	−11.6149	+	28.0408i	−0.739036	+	1.78419i
$248$	−0.852883	+	0.169649i	−0.0541581	+	0.0107727i
$249$	−1.92383	+	6.26764i	−0.121918	+	0.397196i
$250$	4.69058	−	23.5811i	0.296658	−	1.49140i
$251$	−15.7099	+	15.7099i	−0.991603	+	0.991603i	−0.999965	−	0.00836189i	$-0.997338\pi$
$251$	−15.7099	+	15.7099i	−0.991603	+	0.991603i	0.00836189	+	0.999965i	$0.497338\pi$
$252$	−11.8173	−	4.98632i	−0.744418	−	0.314109i
$253$	1.92272	−	0.796417i	0.120880	−	0.0500703i
$254$	−7.16429			−0.449527
$255$		0			0
$256$	−13.4344			−0.839653
$257$	16.5305	−	6.84714i	1.03114	−	0.427113i	0.198017	−	0.980199i	$-0.436550\pi$
$257$	16.5305	−	6.84714i	1.03114	−	0.427113i	0.833124	+	0.553086i	$0.186550\pi$
$258$	−14.8978	+	18.0316i	−0.927499	+	1.12260i
$259$	3.88088	−	3.88088i	0.241146	−	0.241146i
$260$	−5.21818	+	26.2335i	−0.323618	+	1.62694i
$261$	−0.00118300	+	0.179592i	−7.32259e−5	+	0.0111165i
$262$	−41.0490	+	8.16515i	−2.53601	+	0.504445i
$263$	−2.97552	+	7.18354i	−0.183478	+	0.442956i	−0.988679	−	0.150047i	$-0.952058\pi$
$263$	−2.97552	+	7.18354i	−0.183478	+	0.442956i	0.805201	+	0.593003i	$0.202058\pi$
$264$	1.19769	+	0.121946i	0.0737127	+	0.00750528i
$265$	0.768545	+	3.86374i	0.0472113	+	0.237347i
$266$	17.0589	+	11.3984i	1.04595	+	0.698879i
$267$	−0.466396	−	4.90081i	−0.0285429	−	0.299925i
$268$	−10.7613	−	10.7613i	−0.657350	−	0.657350i
$269$	−10.1750	+	6.79874i	−0.620383	+	0.414527i	−0.825653	−	0.564179i	$-0.809193\pi$
$269$	−10.1750	+	6.79874i	−0.620383	+	0.414527i	0.205270	+	0.978705i	$0.434193\pi$
$270$	−20.9642	−	6.58630i	−1.27584	−	0.400829i
$271$		−	1.34760i		−	0.0818610i	−0.999162	−	0.0409305i	$-0.986968\pi$
$271$		−	1.34760i		−	0.0818610i	0.999162	−	0.0409305i	$-0.0130322\pi$
$272$		0			0
$273$	−5.95082	−	19.8524i	−0.360160	−	1.20152i
$274$	10.4437	+	25.2134i	0.630930	+	1.52320i
$275$	−0.896522	−	1.34174i	−0.0540623	−	0.0809099i
$276$	1.55745	−	2.89083i	0.0937472	−	0.174008i
$277$	−16.5282	−	3.28766i	−0.993081	−	0.197536i	−0.328299	−	0.944574i	$-0.606475\pi$
$277$	−16.5282	−	3.28766i	−0.993081	−	0.197536i	−0.664782	+	0.747038i	$0.731475\pi$
$278$	−0.114652	+	0.171589i	−0.00687639	+	0.0102912i
$279$	6.29022	−	6.20789i	0.376586	−	0.371657i
$280$	1.12912	+	0.467695i	0.0674776	+	0.0279501i
$281$	−4.14660	−	1.71758i	−0.247365	−	0.102462i	0.255556	−	0.966794i	$-0.417741\pi$
$281$	−4.14660	−	1.71758i	−0.247365	−	0.102462i	−0.502921	+	0.864332i	$0.667741\pi$
$282$	−25.4048	+	13.4717i	−1.51283	+	0.802230i
$283$	−3.06516	+	4.58733i	−0.182205	+	0.272688i	−0.911317	−	0.411706i	$-0.864933\pi$
$283$	−3.06516	+	4.58733i	−0.182205	+	0.272688i	0.729112	+	0.684394i	$0.239933\pi$
$284$	1.87837	+	0.373632i	0.111461	+	0.0221710i
$285$	16.0135	+	8.62735i	0.948561	+	0.511040i
$286$	15.9886	+	23.9286i	0.945425	+	1.41493i
$287$	−2.52999	−	6.10794i	−0.149341	−	0.360540i
$288$	−20.2955	+	13.3685i	−1.19592	+	0.787744i
$289$		0			0
$290$		−	0.253170i		−	0.0148666i
$291$	−25.2866	+	20.6132i	−1.48233	+	1.20837i
$292$	5.04171	−	3.36876i	0.295044	−	0.197142i
$293$	17.1538	+	17.1538i	1.00214	+	1.00214i	0.999998	+	0.00213730i	$0.000680326\pi$
$293$	17.1538	+	17.1538i	1.00214	+	1.00214i	0.00213730	+	0.999998i	$0.499320\pi$
$294$	10.6267	−	1.01131i	0.619759	−	0.0589806i
$295$	−16.0045	−	10.6939i	−0.931818	−	0.622621i
$296$	0.158572	+	0.797195i	0.00921681	+	0.0463360i
$297$	−10.8469	+	5.66069i	−0.629398	+	0.328467i
$298$	10.8283	−	26.1419i	0.627269	−	1.51436i
$299$	5.20395	−	1.03513i	0.300952	−	0.0598631i
$300$	−2.43405	−	0.747125i	−0.140530	−	0.0431353i
$301$	−2.57925	+	12.9667i	−0.148665	+	0.747391i
$302$	−7.21623	+	7.21623i	−0.415247	+	0.415247i
$303$	4.65169	+	3.84325i	0.267233	+	0.220789i
$304$	17.2312	−	7.13738i	0.988275	−	0.409357i
$305$	11.2378			0.643474
$306$		0			0
$307$	−21.5715			−1.23115			−0.615575	−	0.788078i	$-0.711076\pi$
$307$	−21.5715			−1.23115			−0.615575	+	0.788078i	$0.711076\pi$
$308$	9.30075	−	3.85250i	0.529959	−	0.219516i
$309$	5.08492	+	4.20119i	0.289271	+	0.238997i
$310$	−8.80924	+	8.80924i	−0.500331	+	0.500331i
$311$	5.65155	−	28.4123i	0.320470	−	1.61111i	−0.399247	−	0.916844i	$-0.630728\pi$
$311$	5.65155	−	28.4123i	0.320470	−	1.61111i	0.719717	−	0.694268i	$-0.244272\pi$
$312$	2.93421	+	0.900645i	0.166117	+	0.0509890i
$313$	10.9222	−	2.17257i	0.617361	−	0.122801i	0.123504	−	0.992344i	$-0.460587\pi$
$313$	10.9222	−	2.17257i	0.617361	−	0.122801i	0.493857	+	0.869543i	$0.335587\pi$
$314$	−9.34394	+	22.5583i	−0.527309	+	1.27304i
$315$	−12.1978	+	2.34287i	−0.687266	+	0.132006i
$316$	−1.66366	−	8.36379i	−0.0935882	−	0.470500i
$317$	9.09064	+	6.07417i	0.510581	+	0.341159i	0.784026	−	0.620728i	$-0.213163\pi$
$317$	9.09064	+	6.07417i	0.510581	+	0.341159i	−0.273445	+	0.961888i	$0.588163\pi$
$318$	6.65770	−	0.633593i	0.373345	−	0.0355301i
$319$	−0.0996751	−	0.0996751i	−0.00558074	−	0.00558074i
$320$	15.7423	−	10.5187i	0.880022	−	0.588012i
$321$	−5.38684	+	4.39125i	−0.300664	+	0.245096i
$322$		−	3.58665i		−	0.199876i
$323$		0			0
$324$	−7.62198	+	17.7365i	−0.423444	+	0.985363i
$325$	−1.57442	−	3.80098i	−0.0873329	−	0.210840i
$326$	−13.1455	−	19.6736i	−0.728061	−	1.08962i
$327$	−22.6455	−	12.2003i	−1.25230	−	0.674679i
$328$	0.960283	+	0.191012i	0.0530228	+	0.0105469i
$329$	−9.03009	+	13.5145i	−0.497845	+	0.745077i
$330$	15.2375	−	8.08020i	0.838796	−	0.444800i
$331$	−10.9585	−	4.53916i	−0.602334	−	0.249495i	0.0606127	−	0.998161i	$-0.480695\pi$
$331$	−10.9585	−	4.53916i	−0.602334	−	0.249495i	−0.662947	+	0.748666i	$0.730695\pi$
$332$	−7.50129	−	3.10713i	−0.411687	−	0.170526i
$333$	−5.80256	−	5.87951i	−0.317978	−	0.322195i
$334$	18.2386	−	27.2961i	0.997974	−	1.49357i
$335$	−14.4545	−	2.87517i	−0.789732	−	0.157087i
$336$	−6.04050	+	11.2120i	−0.329536	+	0.611665i
$337$	−12.9256	−	19.3446i	−0.704103	−	1.05377i	−0.995275	−	0.0970945i	$-0.969045\pi$
$337$	−12.9256	−	19.3446i	−0.704103	−	1.05377i	0.291172	−	0.956671i	$-0.405955\pi$
$338$	17.9497	+	43.3344i	0.976335	+	2.35708i
$339$	−3.30991	−	11.0421i	−0.179769	−	0.599724i
$340$		0			0
$341$			6.93655i			0.375635i
$342$	17.3246	−	25.5620i	0.936808	−	1.38223i
$343$	16.6179	−	11.1037i	0.897280	−	0.599543i
$344$	−1.38448	−	1.38448i	−0.0746464	−	0.0746464i
$345$	−0.301258	−	3.16557i	−0.0162192	−	0.170429i
$346$	30.8250	+	20.5966i	1.65716	+	1.10728i
$347$	−5.69850	−	28.6483i	−0.305912	−	1.53792i	−0.761757	−	0.647863i	$-0.775663\pi$
$347$	−5.69850	−	28.6483i	−0.305912	−	1.53792i	0.455845	−	0.890059i	$-0.349337\pi$
$348$	−0.221270	−	0.0225292i	−0.0118613	−	0.00120769i
$349$	4.16097	−	10.0455i	0.222732	−	0.537722i	−0.772527	−	0.634982i	$-0.781008\pi$
$349$	4.16097	−	10.0455i	0.222732	−	0.537722i	0.995259	+	0.0972594i	$0.0310076\pi$
$350$	−2.72762	+	0.542557i	−0.145797	+	0.0290009i
$351$	−29.9384	+	8.75965i	−1.59800	+	0.467556i
$352$	3.72130	−	18.7082i	0.198346	−	0.997153i
$353$	−17.9892	+	17.9892i	−0.957468	+	0.957468i	−0.999132	−	0.0416640i	$-0.986734\pi$
$353$	−17.9892	+	17.9892i	−0.957468	+	0.957468i	0.0416640	+	0.999132i	$0.486734\pi$
$354$	−20.8132	+	25.1913i	−1.10621	+	1.33890i
$355$	1.71345	−	0.709736i	0.0909407	−	0.0376689i
$356$	6.09664			0.323121
$357$		0			0
$358$	39.1437			2.06881
$359$	−13.3198	+	5.51725i	−0.702993	+	0.291189i	−0.705402	−	0.708808i	$-0.749233\pi$
$359$	−13.3198	+	5.51725i	−0.702993	+	0.291189i	0.00240862	+	0.999997i	$0.499233\pi$
$360$	0.715114	−	1.69478i	0.0376898	−	0.0893226i
$361$	−4.63947	+	4.63947i	−0.244183	+	0.244183i
$362$	−1.39102	+	6.99314i	−0.0731104	+	0.367551i
$363$	−2.77280	+	9.03347i	−0.145534	+	0.474134i
$364$	25.1730	−	5.00722i	1.31942	−	0.262449i
$365$	2.24709	−	5.42495i	0.117618	−	0.283955i
$366$	1.93247	−	18.9797i	0.101012	−	0.992085i
$367$	6.78978	+	34.1345i	0.354424	+	1.78181i	0.587370	+	0.809318i	$0.300163\pi$
$367$	6.78978	+	34.1345i	0.354424	+	1.78181i	−0.232947	+	0.972490i	$0.574837\pi$
$368$	−2.71100	−	1.81143i	−0.141321	−	0.0944276i
$369$	−9.21803	+	3.74729i	−0.479871	+	0.195076i
$370$	8.23406	+	8.23406i	0.428068	+	0.428068i
$371$	3.14309	−	2.10015i	0.163181	−	0.109034i
$372$	6.91533	+	8.48318i	0.358543	+	0.439832i
$373$		−	28.1519i		−	1.45765i	−0.684699	−	0.728826i	$-0.740066\pi$
$373$		−	28.1519i		−	1.45765i	0.684699	−	0.728826i	$-0.259934\pi$
$374$		0			0
$375$	−19.5932	+	5.87314i	−1.01179	+	0.303288i
$376$	−0.921168	−	2.22390i	−0.0475056	−	0.114689i
$377$	−0.199664	−	0.298818i	−0.0102832	−	0.0153899i
$378$	1.85936	+	21.0039i	0.0956351	+	1.08032i
$379$	13.8119	+	2.74737i	0.709472	+	0.141123i	0.536619	−	0.843825i	$-0.319701\pi$
$379$	13.8119	+	2.74737i	0.709472	+	0.141123i	0.172853	+	0.984948i	$0.444701\pi$
$380$	−12.5149	+	18.7299i	−0.642003	+	0.960825i
$381$	2.85543	+	5.38472i	0.146288	+	0.275868i
$382$	16.1886	+	6.70552i	0.828279	+	0.343084i
$383$	15.0509	+	6.23429i	0.769065	+	0.318557i	0.732494	−	0.680774i	$-0.238356\pi$
$383$	15.0509	+	6.23429i	0.769065	+	0.318557i	0.0365717	+	0.999331i	$0.488356\pi$
$384$	−1.91120	−	3.60410i	−0.0975304	−	0.183921i
$385$	5.41615	−	8.10584i	0.276032	−	0.413112i
$386$	−21.4902	−	4.27466i	−1.09382	−	0.217575i
$387$	19.4904	+	4.01053i	0.990755	+	0.203867i
$388$	−22.4460	−	33.5928i	−1.13952	−	1.70542i
$389$	−1.24058	−	2.99501i	−0.0628997	−	0.151853i	0.889304	−	0.457316i	$-0.151189\pi$
$389$	−1.24058	−	2.99501i	−0.0628997	−	0.151853i	−0.952204	+	0.305462i	$0.901189\pi$
$390$	42.1208	−	12.6259i	2.13287	−	0.639335i
$391$		0			0
$392$			0.893573i			0.0451322i
$393$	22.4977	+	27.5983i	1.13486	+	1.39215i
$394$	42.9896	−	28.7248i	2.16579	−	1.44713i
$395$	−5.83933	−	5.83933i	−0.293809	−	0.293809i
$396$	−5.70611	−	14.0366i	−0.286743	−	0.705365i
$397$	−14.7851	−	9.87912i	−0.742045	−	0.495819i	0.126169	−	0.992009i	$-0.459732\pi$
$397$	−14.7851	−	9.87912i	−0.742045	−	0.495819i	−0.868214	+	0.496190i	$0.834732\pi$
$398$	9.60721	+	48.2987i	0.481566	+	2.42099i
$399$	1.76802	−	17.3645i	0.0885118	−	0.869315i
$400$	−0.967485	+	2.33572i	−0.0483743	+	0.116786i
$401$	−14.4138	+	2.86708i	−0.719791	+	0.143175i	−0.541377	−	0.840780i	$-0.682097\pi$
$401$	−14.4138	+	2.86708i	−0.719791	+	0.143175i	−0.178414	+	0.983955i	$0.557097\pi$
$402$	−7.34155	+	23.9180i	−0.366163	+	1.19292i
$403$	−3.45014	+	17.3450i	−0.171864	+	0.864018i
$404$	−5.28388	+	5.28388i	−0.262883	+	0.262883i
$405$	3.40528	+	18.3819i	0.169210	+	0.913402i
$406$	−0.224442	+	0.0929671i	−0.0111389	+	0.00461388i
$407$	6.48364			0.321382
$408$		0			0
$409$	−3.98334			−0.196964			−0.0984819	−	0.995139i	$-0.531399\pi$
$409$	−3.98334			−0.196964			−0.0984819	+	0.995139i	$0.531399\pi$
$410$	12.9592	−	5.36788i	0.640010	−	0.265101i
$411$	14.7881	−	17.8988i	0.729441	−	0.882881i
$412$	−5.77599	+	5.77599i	−0.284562	+	0.284562i
$413$	−3.60337	+	18.1154i	−0.177310	+	0.891399i
$414$	−5.39820	−	0.0355587i	−0.265307	−	0.00174761i
$415$	−7.71158	+	1.53393i	−0.378547	+	0.0752976i
$416$	18.6104	−	44.9296i	0.912452	−	2.20285i
$417$	0.174664	+	0.0177839i	0.00855333	+	0.000870883i
$418$	4.72840	+	23.7712i	0.231273	+	1.16269i
$419$	−8.20720	−	5.48388i	−0.400948	−	0.267905i	0.338706	−	0.940892i	$-0.390011\pi$
$419$	−8.20720	−	5.48388i	−0.400948	−	0.267905i	−0.739654	+	0.672987i	$0.765011\pi$
$420$	−1.45727	−	15.3128i	−0.0711075	−	0.747187i
$421$	1.66544	+	1.66544i	0.0811686	+	0.0811686i	0.746525	−	0.665357i	$-0.231721\pi$
$421$	1.66544	+	1.66544i	0.0811686	+	0.0811686i	−0.665357	+	0.746525i	$0.731721\pi$
$422$	−18.6187	+	12.4406i	−0.906343	+	0.605599i
$423$	20.2509	+	13.7250i	0.984631	+	0.667333i
$424$			0.559831i			0.0271878i
$425$		0			0
$426$	−0.904037	−	3.01593i	−0.0438007	−	0.146122i
$427$	−4.12665	−	9.96262i	−0.199703	−	0.482125i
$428$	−4.78170	−	7.15631i	−0.231132	−	0.345914i
$429$	11.6124	−	21.5542i	0.560652	−	1.04065i
$430$	−27.5115	−	5.47239i	−1.32672	−	0.263902i
$431$	11.4330	−	17.1107i	0.550707	−	0.824191i	−0.446809	−	0.894629i	$-0.647440\pi$
$431$	11.4330	−	17.1107i	0.550707	−	0.824191i	0.997516	+	0.0704381i	$0.0224397\pi$
$432$	16.8151	+	9.20261i	0.809017	+	0.442761i
$433$	8.90305	+	3.68777i	0.427853	+	0.177223i	0.586210	−	0.810159i	$-0.300619\pi$
$433$	8.90305	+	3.68777i	0.427853	+	0.177223i	−0.158356	+	0.987382i	$0.550619\pi$
$434$	11.0445	+	4.57479i	0.530153	+	0.219597i
$435$	−0.190284	+	0.100905i	−0.00912342	+	0.00483800i
$436$	17.6979	−	26.4868i	0.847577	−	1.26849i
$437$	4.38268	+	0.871769i	0.209652	+	0.0417024i
$438$	−8.77589	−	4.72804i	−0.419328	−	0.225914i
$439$	21.6347	+	32.3786i	1.03257	+	1.54534i	0.823398	+	0.567465i	$0.192076\pi$
$439$	21.6347	+	32.3786i	1.03257	+	1.54534i	0.209168	+	0.977880i	$0.432924\pi$
$440$	0.552506	+	1.33387i	0.0263397	+	0.0635897i
$441$	−4.99552	−	7.58399i	−0.237882	−	0.361142i
$442$		0			0
$443$			13.1202i			0.623358i	0.950187	+	0.311679i	$0.100891\pi$
$443$			13.1202i			0.623358i	−0.950187	+	0.311679i	$0.899109\pi$
$444$	7.92929	−	6.46381i	0.376307	−	0.306759i
$445$	4.90892	−	3.28003i	0.232705	−	0.155489i
$446$	−14.4843	−	14.4843i	−0.685852	−	0.685852i
$447$	−23.9642	+	2.28060i	−1.13347	+	0.107869i
$448$	−15.1059	−	10.0934i	−0.713686	−	0.476870i
$449$	4.13384	+	20.7822i	0.195088	+	0.980774i	0.946932	+	0.321433i	$0.104165\pi$
$449$	4.13384	+	20.7822i	0.195088	+	0.980774i	−0.751844	+	0.659341i	$0.770835\pi$
$450$	0.789550	+	4.11067i	0.0372198	+	0.193779i
$451$	2.98877	−	7.21554i	0.140736	−	0.339766i
$452$	14.0015	−	2.78507i	0.658574	−	0.130998i
$453$	8.29989	+	2.54763i	0.389963	+	0.119698i
$454$	−0.721317	+	3.62631i	−0.0338531	+	0.170191i
$455$	17.5750	−	17.5750i	0.823927	−	0.823927i
$456$	1.99277	+	1.64643i	0.0933199	+	0.0771014i
$457$	12.9893	−	5.38033i	0.607612	−	0.251681i	−0.0575953	−	0.998340i	$-0.518343\pi$
$457$	12.9893	−	5.38033i	0.607612	−	0.251681i	0.665207	+	0.746659i	$0.268343\pi$
$458$	−3.67350			−0.171651
$459$		0			0
$460$	3.93799			0.183610
$461$	23.3686	−	9.67958i	1.08838	−	0.450823i	0.234940	−	0.972010i	$-0.424511\pi$
$461$	23.3686	−	9.67958i	1.08838	−	0.450823i	0.853443	+	0.521187i	$0.174511\pi$
$462$	−12.7587	−	10.5413i	−0.593590	−	0.490427i
$463$	0.372140	−	0.372140i	0.0172948	−	0.0172948i	−0.698406	−	0.715701i	$-0.746107\pi$
$463$	0.372140	−	0.372140i	0.0172948	−	0.0172948i	0.715701	+	0.698406i	$0.246107\pi$
$464$	−0.0430844	+	0.216600i	−0.00200014	+	0.0100554i
$465$	10.1321	+	3.11003i	0.469866	+	0.144224i
$466$	−2.77880	+	0.552739i	−0.128726	+	0.0256051i
$467$	5.76357	−	13.9145i	0.266706	−	0.643886i	−0.732618	−	0.680640i	$-0.761702\pi$
$467$	5.76357	−	13.9145i	0.266706	−	0.643886i	0.999324	+	0.0367542i	$0.0117019\pi$
$468$	−7.28670	−	37.9370i	−0.336828	−	1.75364i
$469$	2.75894	+	13.8701i	0.127396	+	0.640462i
$470$	−28.6737	−	19.1591i	−1.32262	−	0.883745i
$471$	20.6791	−	1.96797i	0.952843	−	0.0906792i
$472$	−1.93421	−	1.93421i	−0.0890293	−	0.0890293i
$473$	−12.9861	+	8.67701i	−0.597100	+	0.398969i
$474$	−10.8663	+	8.85801i	−0.499106	+	0.406862i
$475$		−	3.46487i		−	0.158979i
$476$		0			0
$477$	−3.12973	−	4.75144i	−0.143301	−	0.217553i
$478$	6.24098	+	15.0671i	0.285456	+	0.689151i
$479$	−5.60953	−	8.39525i	−0.256306	−	0.383589i	0.680894	−	0.732382i	$-0.261592\pi$
$479$	−5.60953	−	8.39525i	−0.256306	−	0.383589i	−0.937200	+	0.348793i	$0.886592\pi$
$480$	−25.6584	−	13.8236i	−1.17114	−	0.630956i
$481$	16.2125	+	3.22487i	0.739228	+	0.147042i
$482$	−19.5964	+	29.3281i	−0.892591	+	1.33586i
$483$	−2.69574	+	1.42951i	−0.122661	+	0.0650450i
$484$	−10.8115	−	4.47827i	−0.491432	−	0.203558i
$485$	−36.1464	−	14.9723i	−1.64132	−	0.679858i
$486$	31.6310	−	2.59025i	1.43481	−	0.117496i
$487$	2.45188	−	3.66950i	0.111105	−	0.166281i	−0.771750	−	0.635926i	$-0.780618\pi$
$487$	2.45188	−	3.66950i	0.111105	−	0.166281i	0.882855	+	0.469645i	$0.155618\pi$
$488$	1.56631	+	0.311559i	0.0709036	+	0.0141036i
$489$	−9.54747	+	17.7214i	−0.431752	+	0.801390i
$490$	7.11225	+	10.6442i	0.321299	+	0.480858i
$491$	14.6134	+	35.2798i	0.659492	+	1.59216i	0.798589	+	0.601877i	$0.205580\pi$
$491$	14.6134	+	35.2798i	0.659492	+	1.59216i	−0.139096	+	0.990279i	$0.544420\pi$
$492$	−3.53830	−	11.8040i	−0.159519	−	0.532166i
$493$		0			0
$494$			61.7926i			2.78018i
$495$	−12.1463	−	8.23211i	−0.545933	−	0.370006i
$496$	9.03592	−	6.03761i	0.405725	−	0.271097i
$497$	−1.25840	−	1.25840i	−0.0564471	−	0.0564471i
$498$	1.26458	+	13.2880i	0.0566672	+	0.595450i
$499$	−10.8447	−	7.24621i	−0.485477	−	0.324385i	0.288630	−	0.957441i	$-0.406800\pi$
$499$	−10.8447	−	7.24621i	−0.485477	−	0.324385i	−0.774106	+	0.633056i	$0.781800\pi$
$500$	−4.94186	−	24.8444i	−0.221007	−	1.11108i
$501$	−27.7852	−	2.82903i	−1.24135	−	0.126392i
$502$	−17.3098	+	41.7895i	−0.772573	+	1.86516i
$503$	3.66103	−	0.728223i	0.163237	−	0.0324699i	−0.112795	−	0.993618i	$-0.535980\pi$
$503$	3.66103	−	0.728223i	0.163237	−	0.0324699i	0.276032	+	0.961148i	$0.410980\pi$
$504$	−1.76507	−	0.0116268i	−0.0786223	−	0.000517897i
$505$	−1.41173	+	7.09726i	−0.0628213	+	0.315824i
$506$	2.99604	−	2.99604i	0.133190	−	0.133190i
$507$	25.4163	−	30.7627i	1.12878	−	1.36622i
$508$	−6.97351	+	2.88852i	−0.309400	+	0.128158i
$509$	40.1261			1.77856			0.889279	−	0.457364i	$-0.151207\pi$
$509$	40.1261			1.77856			0.889279	+	0.457364i	$0.151207\pi$
$510$		0			0
$511$	−5.63453			−0.249257
$512$	−29.6215	+	12.2696i	−1.30910	+	0.542246i
$513$	−26.1175	−	2.83317i	−1.15312	−	0.125088i
$514$	25.7582	−	25.7582i	1.13615	−	1.13615i
$515$	−1.54321	+	7.75825i	−0.0680021	+	0.341870i
$516$	−7.23107	+	23.5581i	−0.318330	+	1.03709i
$517$	−18.8322	+	3.74596i	−0.828239	+	0.164747i
$518$	4.27608	−	10.3234i	0.187880	−	0.453583i
$519$	3.19478	−	31.3773i	0.140235	−	1.37731i
$520$	0.718111	+	3.61019i	0.0314912	+	0.158317i
$521$	13.5434	+	9.04943i	0.593348	+	0.396463i	0.815676	−	0.578509i	$-0.196365\pi$
$521$	13.5434	+	9.04943i	0.593348	+	0.396463i	−0.222328	+	0.974972i	$0.571365\pi$
$522$	0.137698	+	0.338726i	0.00602687	+	0.0148256i
$523$	12.6275	+	12.6275i	0.552161	+	0.552161i	0.927064	−	0.374903i	$-0.122324\pi$
$523$	12.6275	+	12.6275i	0.552161	+	0.552161i	−0.374903	+	0.927064i	$0.622324\pi$
$524$	−36.6639	+	24.4980i	−1.60167	+	1.07020i
$525$	1.49492	+	1.83385i	0.0652437	+	0.0800358i
$526$			15.8301i			0.690227i
$527$		0			0
$528$	−14.4116	+	4.31992i	−0.627183	+	0.188000i
$529$	8.50277	+	20.5275i	0.369686	+	0.892501i
$530$	4.45589	+	6.66871i	0.193551	+	0.289670i
$531$	27.2294	+	5.60297i	1.18165	+	0.243148i
$532$	21.2003	+	4.21700i	0.919148	+	0.182830i
$533$	11.0624	−	16.5561i	0.479167	−	0.717124i
$534$	−4.69556	−	8.85480i	−0.203197	−	0.383185i
$535$	−7.70029	−	3.18957i	−0.332913	−	0.137897i
$536$	−1.93494	−	0.801478i	−0.0835766	−	0.0346186i
$537$	−15.6013	−	29.4207i	−0.673247	−	1.26960i
$538$	−13.8417	+	20.7156i	−0.596759	+	0.893113i
$539$	6.99088	+	1.39057i	0.301119	+	0.0598962i
$540$	−23.0614	+	2.04150i	−0.992405	+	0.0878521i
$541$	−15.7191	−	23.5252i	−0.675815	−	1.01143i	−0.997904	−	0.0647190i	$-0.979385\pi$
$541$	−15.7191	−	23.5252i	−0.675815	−	1.01143i	0.322089	−	0.946710i	$-0.395615\pi$
$542$	−1.04994	−	2.53477i	−0.0450986	−	0.108878i
$543$	5.81049	−	1.74172i	0.249352	−	0.0747442i
$544$		0			0
$545$		−	30.8484i		−	1.32140i
$546$	−26.6605	−	32.7049i	−1.14096	−	1.39964i
$547$	−26.5890	+	17.7662i	−1.13687	+	0.759629i	−0.973894	−	0.227001i	$-0.927108\pi$
$547$	−26.5890	+	17.7662i	−1.13687	+	0.759629i	−0.162971	+	0.986631i	$0.552108\pi$
$548$	20.3313	+	20.3313i	0.868510	+	0.868510i
$549$	−15.0355	+	6.11218i	−0.641698	+	0.260861i
$550$	−2.73168	−	1.82525i	−0.116479	−	0.0778290i
$551$	−0.0590476	−	0.296852i	−0.00251551	−	0.0126463i
$552$	0.0457739	−	0.449566i	0.00194827	−	0.0191348i
$553$	−3.03246	+	7.32101i	−0.128953	+	0.311321i
$554$	−33.6501	+	6.69342i	−1.42966	+	0.284376i
$555$	2.90696	−	9.47057i	0.123394	−	0.402003i
$556$	−0.0424173	+	0.213246i	−0.00179889	+	0.00904365i
$557$	−4.85771	+	4.85771i	−0.205828	+	0.205828i	−0.802491	−	0.596664i	$-0.796493\pi$
$557$	−4.85771	+	4.85771i	−0.205828	+	0.205828i	0.596664	+	0.802491i	$0.296493\pi$
$558$	6.99492	−	16.5775i	0.296119	−	0.701783i
$559$	−36.7879	+	15.2380i	−1.55596	+	0.644500i
$560$	−15.2734			−0.645417
$561$		0			0
$562$	−9.13772			−0.385452
$563$	10.7792	−	4.46490i	0.454290	−	0.188173i	−0.143792	−	0.989608i	$-0.545930\pi$
$563$	10.7792	−	4.46490i	0.454290	−	0.188173i	0.598082	+	0.801435i	$0.295930\pi$
$564$	−19.2967	+	23.3558i	−0.812537	+	0.983456i
$565$	9.77538	−	9.77538i	0.411253	−	0.411253i
$566$	−2.19135	+	11.0166i	−0.0921092	+	0.463064i
$567$	15.0456	−	9.76892i	0.631856	−	0.410256i
$568$	0.258497	−	0.0514182i	0.0108463	−	0.00215746i
$569$	−16.5175	+	39.8769i	−0.692452	+	1.67173i	0.0473304	+	0.998879i	$0.484929\pi$
$569$	−16.5175	+	39.8769i	−0.692452	+	1.67173i	−0.739782	+	0.672847i	$0.765071\pi$
$570$	36.8424	+	3.75121i	1.54316	+	0.157121i
$571$	−1.81007	−	9.09986i	−0.0757493	−	0.380817i	0.924250	−	0.381787i	$-0.124691\pi$
$571$	−1.81007	−	9.09986i	−0.0757493	−	0.380817i	−1.00000		0.000969942i	$0.999691\pi$
$572$	25.2105	+	16.8451i	1.05410	+	0.704329i
$573$	−1.41228	−	14.8400i	−0.0589988	−	0.619950i
$574$	−9.51757	−	9.51757i	−0.397256	−	0.397256i
$575$	−0.503637	+	0.336520i	−0.0210031	+	0.0140338i
$576$	−15.3412	+	22.6355i	−0.639217	+	0.943147i
$577$			16.0098i			0.666496i	0.942839	+	0.333248i	$0.108145\pi$
$577$			16.0098i			0.666496i	−0.942839	+	0.333248i	$0.891855\pi$
$578$		0			0
$579$	5.35236	+	17.8559i	0.222437	+	0.742065i
$580$	−0.102074	−	0.246428i	−0.00423839	−	0.0102324i
$581$	4.19166	+	6.27326i	0.173899	+	0.260259i
$582$	−31.5028	+	58.4736i	−1.30583	+	2.42381i
$583$	4.37985	+	0.871206i	0.181395	+	0.0360817i
$584$	0.463600	−	0.693826i	0.0191839	−	0.0287107i
$585$	−26.2775	−	26.6260i	−1.08644	−	1.10085i
$586$	45.6302	+	18.9006i	1.88497	+	0.780778i
$587$	−26.6989	−	11.0590i	−1.10198	−	0.456455i	−0.243812	−	0.969823i	$-0.578398\pi$
$587$	−26.6989	−	11.0590i	−1.10198	−	0.456455i	−0.858169	+	0.513367i	$0.828398\pi$
$588$	9.93595	−	5.26888i	0.409752	−	0.217285i
$589$	−8.27460	+	12.3838i	−0.340949	+	0.510266i
$590$	−38.4354	−	7.64527i	−1.58236	−	0.314751i
$591$	−38.7239	−	20.8626i	−1.59289	−	0.858173i
$592$	−5.64340	−	8.44594i	−0.231942	−	0.347126i
$593$	−15.8785	−	38.3341i	−0.652052	−	1.57419i	−0.809795	−	0.586712i	$-0.800422\pi$
$593$	−15.8785	−	38.3341i	−0.652052	−	1.57419i	0.157744	−	0.987480i	$-0.449578\pi$
$594$	−15.9921	+	19.0984i	−0.656162	+	0.783618i
$595$		0			0
$596$		−	29.8116i		−	1.22113i
$597$	32.4725	−	26.4710i	1.32901	−	1.08339i
$598$	8.98188	−	6.00150i	0.367296	−	0.245419i
$599$	−21.9297	−	21.9297i	−0.896025	−	0.896025i	0.0990569	−	0.995082i	$-0.468417\pi$
$599$	−21.9297	−	21.9297i	−0.896025	−	0.896025i	−0.995082	+	0.0990569i	$0.968417\pi$
$600$	−0.348816	+	0.0331958i	−0.0142404	+	0.00135521i
$601$	−4.84775	−	3.23917i	−0.197744	−	0.132128i	0.452756	−	0.891634i	$-0.350441\pi$
$601$	−4.84775	−	3.23917i	−0.197744	−	0.132128i	−0.650500	+	0.759506i	$0.725441\pi$
$602$	5.25115	+	26.3993i	0.214021	+	1.07596i
$603$	20.9030	−	4.01491i	0.851236	−	0.163500i
$604$	−4.11461	+	9.93354i	−0.167421	+	0.404190i
$605$	−11.1146	+	2.21083i	−0.451873	+	0.0898830i
$606$	11.7439	+	3.60476i	0.477065	+	0.146434i
$607$	6.55369	−	32.9476i	0.266006	−	1.33730i	−0.584524	−	0.811377i	$-0.698719\pi$
$607$	6.55369	−	32.9476i	0.266006	−	1.33730i	0.850530	−	0.525927i	$-0.176281\pi$
$608$	28.9607	−	28.9607i	1.17451	−	1.17451i
$609$	0.159329	+	0.131639i	0.00645635	+	0.00533427i
$610$	21.1377	−	8.75552i	0.855841	−	0.354501i
$611$	−48.9537			−1.98045
$612$		0			0
$613$	38.7828			1.56642			0.783210	−	0.621757i	$-0.213581\pi$
$613$	38.7828			1.56642			0.783210	+	0.621757i	$0.213581\pi$
$614$	−40.5749	+	16.8067i	−1.63747	+	0.678262i
$615$	−9.19962	−	7.60078i	−0.370964	−	0.306493i
$616$	0.979626	−	0.979626i	0.0394702	−	0.0394702i
$617$	6.65584	−	33.4612i	0.267954	−	1.34710i	−0.578956	−	0.815359i	$-0.696540\pi$
$617$	6.65584	−	33.4612i	0.267954	−	1.34710i	0.846910	−	0.531737i	$-0.178460\pi$
$618$	12.8377	+	3.94049i	0.516407	+	0.158510i
$619$	11.6178	−	2.31092i	0.466959	−	0.0928839i	0.0439976	−	0.999032i	$-0.485991\pi$
$619$	11.6178	−	2.31092i	0.466959	−	0.0928839i	0.422961	+	0.906148i	$0.360991\pi$
$620$	−5.02292	+	12.1264i	−0.201725	+	0.487008i
$621$	2.12480	+	4.07149i	0.0852655	+	0.163383i
$622$	−11.5061	−	57.8452i	−0.461354	−	2.31938i
$623$	−4.71046	−	3.14743i	−0.188721	−	0.126099i
$624$	−38.1852	+	3.63397i	−1.52863	+	0.145475i
$625$	−14.9226	−	14.9226i	−0.596903	−	0.596903i
$626$	18.8515	−	12.5962i	0.753457	−	0.503444i
$627$	15.9820	−	13.0283i	0.638261	−	0.520299i
$628$			25.7249i			1.02654i
$629$		0			0
$630$	−21.1180	+	13.9103i	−0.841362	+	0.554198i
$631$	12.5910	+	30.3974i	0.501240	+	1.21010i	0.948809	+	0.315851i	$0.102290\pi$
$631$	12.5910	+	30.3974i	0.501240	+	1.21010i	−0.447568	+	0.894250i	$0.647710\pi$
$632$	−0.651990	−	0.975771i	−0.0259348	−	0.0388141i
$633$	16.7712	+	9.03552i	0.666594	+	0.359130i
$634$	21.8315	+	4.34256i	0.867040	+	0.172465i
$635$	−4.06092	+	6.07759i	−0.161153	+	0.241182i
$636$	6.22496	−	3.30100i	0.246836	−	0.130893i
$637$	16.7893	+	6.95434i	0.665215	+	0.275541i
$638$	−0.265142	−	0.109825i	−0.0104971	−	0.00434803i
$639$	−1.90648	+	1.88152i	−0.0754190	+	0.0744319i
$640$	2.71805	−	4.06785i	0.107441	−	0.160796i
$641$	23.2064	+	4.61604i	0.916597	+	0.182322i	0.630780	−	0.775962i	$-0.282735\pi$
$641$	23.2064	+	4.61604i	0.916597	+	0.182322i	0.285817	+	0.958284i	$0.407735\pi$
$642$	−6.71108	+	12.4567i	−0.264865	+	0.491626i
$643$	24.7406	+	37.0269i	0.975672	+	1.46020i	0.885703	+	0.464253i	$0.153677\pi$
$643$	24.7406	+	37.0269i	0.975672	+	1.46020i	0.0899696	+	0.995945i	$0.471323\pi$
$644$	−1.44608	−	3.49114i	−0.0569834	−	0.137570i
$645$	6.85205	+	22.8589i	0.269799	+	0.900070i
$646$		0			0
$647$		−	35.4575i		−	1.39398i	−0.717081	−	0.696990i	$-0.754522\pi$
$647$		−	35.4575i		−	1.39398i	0.717081	−	0.696990i	$-0.245478\pi$
$648$	−0.0349984	+	2.65646i	−0.00137487	+	0.104355i
$649$	−18.1424	+	12.1223i	−0.712150	+	0.475843i
$650$	−5.92280	−	5.92280i	−0.232311	−	0.232311i
$651$	−0.963515	−	10.1245i	−0.0377631	−	0.396809i
$652$	−20.7275	−	13.8497i	−0.811752	−	0.542395i
$653$	−3.80775	−	19.1428i	−0.149009	−	0.749117i	−0.980951	−	0.194255i	$-0.937771\pi$
$653$	−3.80775	−	19.1428i	−0.149009	−	0.749117i	0.831943	−	0.554862i	$-0.187229\pi$
$654$	−52.1004	−	5.30476i	−2.03729	−	0.207432i
$655$	−16.3411	+	39.4508i	−0.638498	+	1.54147i
$656$	−12.0008	+	2.38711i	−0.468552	+	0.0932009i
$657$	−0.0558619	+	8.48044i	−0.00217938	+	0.330853i
$658$	−6.45581	+	32.4555i	−0.251673	+	1.26525i
$659$	9.54185	−	9.54185i	0.371698	−	0.371698i	−0.496398	−	0.868095i	$-0.665344\pi$
$659$	9.54185	−	9.54185i	0.371698	−	0.371698i	0.868095	+	0.496398i	$0.165344\pi$
$660$	11.5739	−	14.0085i	0.450515	−	0.545282i
$661$	−3.15244	+	1.30578i	−0.122616	+	0.0507890i	−0.443148	−	0.896449i	$-0.646138\pi$
$661$	−3.15244	+	1.30578i	−0.122616	+	0.0507890i	0.320532	+	0.947238i	$0.396138\pi$
$662$	−24.1489			−0.938575
$663$		0			0
$664$	−1.11736			−0.0433620
$665$	19.3389	−	8.01043i	0.749930	−	0.310631i
$666$	−15.4951	−	6.53820i	−0.600424	−	0.253350i
$667$	−0.0374142	+	0.0374142i	−0.00144868	+	0.00144868i
$668$	6.74765	−	33.9228i	0.261075	−	1.31251i
$669$	−5.11356	+	16.6594i	−0.197702	+	0.644091i
$670$	−29.4282	+	5.85363i	−1.13691	+	0.226146i
$671$	4.87497	−	11.7692i	0.188196	−	0.454346i
$672$	−2.83289	+	27.8231i	−0.109281	+	1.07330i
$673$	2.13061	+	10.7113i	0.0821289	+	0.412890i	0.999876	+	0.0157255i	$0.00500577\pi$
$673$	2.13061	+	10.7113i	0.0821289	+	0.412890i	−0.917747	+	0.397165i	$0.869994\pi$
$674$	−39.3841	−	26.3156i	−1.51702	−	1.01364i
$675$	2.77492	−	2.23180i	0.106807	−	0.0859019i
$676$	34.9435	+	34.9435i	1.34398	+	1.34398i
$677$	−13.1437	+	8.78236i	−0.505154	+	0.337533i	−0.781894	−	0.623412i	$-0.785746\pi$
$677$	−13.1437	+	8.78236i	−0.505154	+	0.337533i	0.276739	+	0.960945i	$0.410746\pi$
$678$	−14.8288	−	18.1908i	−0.569498	−	0.698614i
$679$			37.5428i			1.44076i
$680$		0			0
$681$	3.01305	−	0.903171i	0.115460	−	0.0346096i
$682$	5.40437	+	13.0473i	0.206944	+	0.499607i
$683$	−15.9134	−	23.8160i	−0.608908	−	0.911295i	0.391051	−	0.920369i	$-0.372112\pi$
$683$	−15.9134	−	23.8160i	−0.608908	−	0.911295i	−0.999959	+	0.00907414i	$0.997112\pi$
$684$	6.55711	−	31.8663i	0.250717	−	1.21844i
$685$	27.3088	+	5.43206i	1.04342	+	0.207549i
$686$	22.6063	−	33.8327i	0.863112	−	1.29174i
$687$	1.46413	+	2.76103i	0.0558600	+	0.105340i
$688$	22.6063	+	9.36383i	0.861857	+	0.356993i
$689$	10.5186	+	4.35695i	0.400727	+	0.165987i
$690$	−3.03299	−	5.71956i	−0.115464	−	0.217740i
$691$	12.9103	−	19.3217i	0.491133	−	0.735032i	−0.500271	−	0.865869i	$-0.666766\pi$
$691$	12.9103	−	19.3217i	0.491133	−	0.735032i	0.991404	+	0.130837i	$0.0417664\pi$
$692$	38.3084	+	7.62001i	1.45627	+	0.289669i
$693$	−2.83775	+	13.7909i	−0.107797	+	0.523874i
$694$	−33.0389	−	49.4462i	−1.25414	−	1.87695i
$695$	0.0805742	+	0.194523i	0.00305635	+	0.00737869i
$696$	−0.0293191	+	0.00878851i	−0.00111134	+	0.000333127i
$697$		0			0
$698$		−	22.1369i		−	0.837895i
$699$	1.52297	+	1.86826i	0.0576042	+	0.0706642i
$700$	−2.43624	+	1.62784i	−0.0920811	+	0.0615266i
$701$	−13.2794	−	13.2794i	−0.501558	−	0.501558i	0.410364	−	0.911922i	$-0.365402\pi$
$701$	−13.2794	−	13.2794i	−0.501558	−	0.501558i	−0.911922	+	0.410364i	$0.865402\pi$
$702$	−49.4879	+	39.8019i	−1.86780	+	1.50223i
$703$	11.5752	+	7.73433i	0.436568	+	0.291706i
$704$	−4.18706	−	21.0498i	−0.157806	−	0.793344i
$705$	−2.97181	+	29.1875i	−0.111925	+	1.09926i
$706$	−19.8211	+	47.8524i	−0.745977	+	1.80095i
$707$	6.81034	−	1.35466i	0.256129	−	0.0509472i
$708$	−10.1023	+	32.9121i	−0.379666	+	1.23691i
$709$	−3.93121	+	19.7635i	−0.147640	+	0.742235i	0.834041	+	0.551702i	$0.186022\pi$
$709$	−3.93121	+	19.7635i	−0.147640	+	0.742235i	−0.981681	+	0.190533i	$0.938978\pi$
$710$	2.66995	−	2.66995i	0.100202	−	0.100202i
$711$	10.9887	+	4.63669i	0.412107	+	0.173889i
$712$	0.775137	−	0.321072i	0.0290495	−	0.0120327i
$713$	2.60371			0.0975097
$714$		0			0
$715$	29.3619			1.09807
$716$	38.1014	−	15.7821i	1.42392	−	0.589806i
$717$	8.83706	−	10.6960i	0.330026	−	0.399448i
$718$	−20.7553	+	20.7553i	−0.774582	+	0.774582i
$719$	4.98832	−	25.0780i	0.186033	−	0.935252i	−0.769112	−	0.639114i	$-0.779301\pi$
$719$	4.98832	−	25.0780i	0.186033	−	0.935252i	0.955145	−	0.296138i	$-0.0956988\pi$
$720$	−0.151423	+	22.9876i	−0.00564320	+	0.856699i
$721$	7.44460	−	1.48082i	0.277252	−	0.0551488i
$722$	−5.11193	+	12.3413i	−0.190246	+	0.459295i
$723$	29.8536	+	3.03963i	1.11027	+	0.113045i
$724$	1.46554	+	7.36776i	0.0544663	+	0.273821i
$725$	0.0341129	+	0.0227935i	0.00126692	+	0.000846530i
$726$	1.82262	+	19.1518i	0.0676438	+	0.710791i
$727$	−17.6366	−	17.6366i	−0.654107	−	0.654107i	0.299872	−	0.953979i	$-0.403056\pi$
$727$	−17.6366	−	17.6366i	−0.654107	−	0.654107i	−0.953979	+	0.299872i	$0.903056\pi$
$728$	2.93684	−	1.96233i	0.108846	−	0.0727288i
$729$	−14.5539	−	22.7417i	−0.539032	−	0.842285i
$730$		−	11.9548i		−	0.442467i
$731$		0			0
$732$	−5.77129	−	19.2535i	−0.213313	−	0.711628i
$733$	−18.5044	−	44.6736i	−0.683476	−	1.65006i	−0.757527	−	0.652804i	$-0.773593\pi$
$733$	−18.5044	−	44.6736i	−0.683476	−	1.65006i	0.0740508	−	0.997254i	$-0.476407\pi$
$734$	39.3659	+	58.9153i	1.45302	+	2.17460i
$735$	5.16558	−	9.58803i	0.190535	−	0.353660i
$736$	−7.02235	−	1.39683i	−0.258847	−	0.0514879i
$737$	−9.28151	+	13.8908i	−0.341889	+	0.511673i
$738$	−14.4191	+	14.2304i	−0.530774	+	0.523827i
$739$	−18.8828	−	7.82153i	−0.694617	−	0.287720i	0.00730558	−	0.999973i	$-0.497675\pi$
$739$	−18.8828	−	7.82153i	−0.694617	−	0.287720i	−0.701922	+	0.712254i	$0.747675\pi$
$740$	11.3346	+	4.69496i	0.416669	+	0.172590i
$741$	46.4437	−	24.6283i	1.70615	−	0.904744i
$742$	4.27574	−	6.39910i	0.156968	−	0.234918i
$743$	47.3748	+	9.42343i	1.73801	+	0.345712i	0.959455	−	0.281861i	$-0.0909516\pi$
$743$	47.3748	+	9.42343i	1.73801	+	0.345712i	0.778558	+	0.627573i	$0.215952\pi$
$744$	1.32598	+	0.714378i	0.0486129	+	0.0261904i
$745$	−16.0389	−	24.0038i	−0.587618	−	0.879433i
$746$	−21.9336	−	52.9523i	−0.803045	−	1.93872i
$747$	9.48333	−	6.24660i	0.346977	−	0.228551i
$748$		0			0
$749$			7.99778i			0.292233i
$750$	−32.2780	+	26.3125i	−1.17863	+	0.960795i
$751$	9.52215	−	6.36250i	0.347468	−	0.232171i	−0.369573	−	0.929202i	$-0.620496\pi$
$751$	9.52215	−	6.36250i	0.347468	−	0.232171i	0.717041	+	0.697031i	$0.245496\pi$
$752$	21.2713	+	21.2713i	0.775686	+	0.775686i
$753$	38.3083	−	3.64568i	1.39603	−	0.132856i
$754$	−0.608370	−	0.406500i	−0.0221555	−	0.0148039i
$755$	2.03130	+	10.2120i	0.0739264	+	0.371653i
$756$	10.2783	+	19.6950i	0.373818	+	0.716299i
$757$	13.3441	−	32.2155i	0.484999	−	1.17089i	−0.472207	−	0.881488i	$-0.656543\pi$
$757$	13.3441	−	32.2155i	0.484999	−	1.17089i	0.957207	−	0.289405i	$-0.0934574\pi$
$758$	28.1201	−	5.59343i	1.02137	−	0.203163i
$759$	−3.44596	−	1.05773i	−0.125080	−	0.0383930i
$760$	−0.604781	+	3.04044i	−0.0219377	+	0.110288i
$761$	18.9898	−	18.9898i	0.688381	−	0.688381i	−0.273493	−	0.961874i	$-0.588179\pi$
$761$	18.9898	−	18.9898i	0.688381	−	0.688381i	0.961874	+	0.273493i	$0.0881789\pi$
$762$	9.56624	+	7.90368i	0.346548	+	0.286320i
$763$	−27.3480	+	11.3279i	−0.990063	+	0.410098i
$764$	18.4611			0.667898
$765$		0			0
$766$	33.1672			1.19838
$767$	−51.3950	+	21.2885i	−1.85576	+	0.768683i
$768$	17.9386	+	14.8209i	0.647303	+	0.534805i
$769$	−3.12150	+	3.12150i	−0.112564	+	0.112564i	−0.761145	−	0.648581i	$-0.775363\pi$
$769$	−3.12150	+	3.12150i	−0.112564	+	0.112564i	0.648581	+	0.761145i	$0.275363\pi$
$770$	3.87212	−	19.4665i	0.139542	−	0.701523i
$771$	−29.6264	−	9.09372i	−1.06697	−	0.327502i
$772$	−22.6414	+	4.50366i	−0.814882	+	0.162090i
$773$	10.5772	−	25.5356i	0.380436	−	0.918453i	−0.611446	−	0.791286i	$-0.709412\pi$
$773$	10.5772	−	25.5356i	0.380436	−	0.918453i	0.991881	−	0.127167i	$-0.0405883\pi$
$774$	39.7852	−	7.64168i	1.43005	−	0.274675i
$775$	−0.393867	−	1.98010i	−0.0141481	−	0.0711274i
$776$	−4.62295	−	3.08896i	−0.165954	−	0.110887i
$777$	−9.46341	+	0.900604i	−0.339498	+	0.0323090i
$778$	−4.66692	−	4.66692i	−0.167317	−	0.167317i
$779$	13.9433	−	9.31659i	0.499569	−	0.333802i
$780$	35.9086	−	29.2721i	1.28574	−	1.04811i
$781$		−	2.10237i		−	0.0752287i
$782$		0			0
$783$	0.199707	−	0.238499i	0.00713694	−	0.00852325i
$784$	−4.27347	−	10.3171i	−0.152624	−	0.368467i
$785$	13.8402	+	20.7133i	0.493977	+	0.739289i
$786$	63.8192	+	34.3828i	2.27636	+	1.22639i
$787$	−31.8028	−	6.32596i	−1.13365	−	0.225496i	−0.407612	−	0.913155i	$-0.633638\pi$
$787$	−31.8028	−	6.32596i	−1.13365	−	0.225496i	−0.726034	+	0.687659i	$0.758638\pi$
$788$	30.2635	−	45.2926i	1.07809	−	1.61348i
$789$	11.8980	−	6.30933i	0.423581	−	0.224618i
$790$	−15.5330	−	6.43398i	−0.552639	−	0.228911i
$791$	−12.2558	−	5.07652i	−0.435766	−	0.180500i
$792$	−1.46470	−	1.48413i	−0.0520460	−	0.0527362i
$793$	18.0439	−	27.0045i	0.640756	−	0.958960i
$794$	−35.5071	−	7.06280i	−1.26010	−	0.250649i
$795$	3.23628	−	6.00698i	0.114779	−	0.213046i
$796$	28.8246	+	43.1391i	1.02166	+	1.52903i
$797$	12.9695	+	31.3112i	0.459404	+	1.10910i	0.968639	+	0.248472i	$0.0799283\pi$
$797$	12.9695	+	31.3112i	0.459404	+	1.10910i	−0.509235	+	0.860627i	$0.670072\pi$
$798$	−10.2034	−	34.0393i	−0.361197	−	1.20498i
$799$		0			0
$800$			5.55174i			0.196284i
$801$	−4.78384	+	7.05842i	−0.169029	+	0.249397i
$802$	−24.8778	+	16.6228i	−0.878467	+	0.586973i
$803$	−4.70671	−	4.70671i	−0.166096	−	0.166096i
$804$	2.49729	+	26.2411i	0.0880725	+	0.925452i
$805$	−3.04262	−	2.03301i	−0.107238	−	0.0716542i
$806$	7.02423	+	35.3132i	0.247418	+	1.24385i
$807$	21.0868	+	2.14702i	0.742291	+	0.0755785i
$808$	−0.393532	+	0.950071i	−0.0138444	+	0.0334234i
$809$	17.2934	−	3.43987i	0.608004	−	0.120939i	0.118520	−	0.992952i	$-0.462185\pi$
$809$	17.2934	−	3.43987i	0.608004	−	0.120939i	0.489484	+	0.872012i	$0.337185\pi$
$810$	20.7267	+	31.9222i	0.728263	+	1.12163i
$811$	−0.466478	+	2.34514i	−0.0163802	+	0.0823490i	−0.988111	−	0.153744i	$-0.950867\pi$
$811$	−0.466478	+	2.34514i	−0.0163802	+	0.0823490i	0.971730	+	0.236093i	$0.0758670\pi$
$812$	−0.180983	+	0.180983i	−0.00635126	+	0.00635126i
$813$	−1.48668	+	1.79941i	−0.0521402	+	0.0631080i
$814$	12.1954	−	5.05150i	0.427448	−	0.177055i
$815$	−24.1407			−0.845612
$816$		0			0
$817$	−33.5348			−1.17323
$818$	−7.49247	+	3.10348i	−0.261968	+	0.108511i
$819$	−13.9553	+	33.0732i	−0.487638	+	1.15567i
$820$	10.4499	−	10.4499i	0.364926	−	0.364926i
$821$	−9.10361	+	45.7670i	−0.317718	+	1.59728i	0.410453	+	0.911882i	$0.365371\pi$
$821$	−9.10361	+	45.7670i	−0.317718	+	1.59728i	−0.728171	+	0.685396i	$0.759629\pi$
$822$	13.8704	−	45.1883i	0.483786	−	1.57612i
$823$	47.3405	−	9.41661i	1.65019	−	0.328242i	0.719620	−	0.694368i	$-0.244316\pi$
$823$	47.3405	−	9.41661i	1.65019	−	0.328242i	0.930566	+	0.366125i	$0.119316\pi$
$824$	−0.430183	+	1.03855i	−0.0149861	+	0.0361797i
$825$	−0.283118	+	2.78063i	−0.00985690	+	0.0968091i
$826$	7.33619	+	36.8815i	0.255259	+	1.28327i
$827$	−26.8554	−	17.9442i	−0.933855	−	0.623982i	−0.00723238	−	0.999974i	$-0.502302\pi$
$827$	−26.8554	−	17.9442i	−0.933855	−	0.623982i	−0.926623	+	0.375992i	$0.877302\pi$
$828$	−5.26879	+	2.14185i	−0.183103	+	0.0744346i
$829$	−2.76317	−	2.76317i	−0.0959688	−	0.0959688i	0.657492	−	0.753461i	$-0.271617\pi$
$829$	−2.76317	−	2.76317i	−0.0959688	−	0.0959688i	−0.753461	+	0.657492i	$0.771617\pi$
$830$	−13.3100	+	8.89345i	−0.461996	+	0.308696i
$831$	18.4426	+	22.6239i	0.639765	+	0.784813i
$832$		−	54.7182i		−	1.89701i
$833$		0			0
$834$	0.342390	−	0.102633i	0.0118560	−	0.00355387i
$835$	−12.8176	−	30.9444i	−0.443570	−	1.07087i
$836$	14.1867	+	21.2319i	0.490656	+	0.734319i
$837$	−15.2477	+	1.34979i	−0.527038	+	0.0466557i
$838$	−19.7099	−	3.92054i	−0.680867	−	0.135433i
$839$	10.2990	−	15.4135i	0.355561	−	0.532134i	−0.609970	−	0.792425i	$-0.708818\pi$
$839$	10.2990	−	15.4135i	0.355561	−	0.532134i	0.965530	+	0.260291i	$0.0838184\pi$
$840$	−0.991708	−	1.87015i	−0.0342172	−	0.0645262i
$841$	−26.7892	−	11.0964i	−0.923765	−	0.382636i
$842$	4.43018	+	1.83504i	0.152674	+	0.0632396i
$843$	3.64197	+	6.86797i	0.125436	+	0.236545i
$844$	−13.1070	+	19.6161i	−0.451163	+	0.675213i
$845$	46.9357	+	9.33610i	1.61464	+	0.321172i
$846$	48.7842	+	10.0383i	1.67724	+	0.345123i
$847$	6.04138	+	9.04157i	0.207584	+	0.310672i
$848$	−2.67737	−	6.46373i	−0.0919411	−	0.221965i
$849$	9.15357	−	2.74382i	0.314150	−	0.0941675i
$850$		0			0
$851$		−	2.43371i		−	0.0834264i
$852$	−2.09594	−	2.57113i	−0.0718057	−	0.0880855i
$853$	30.8322	−	20.6014i	1.05567	−	0.705378i	0.0985712	−	0.995130i	$-0.468573\pi$
$853$	30.8322	−	20.6014i	1.05567	−	0.705378i	0.957102	+	0.289752i	$0.0935728\pi$
$854$	−15.5241	−	15.5241i	−0.531222	−	0.531222i
$855$	−11.8646	−	29.1860i	−0.405762	−	0.998142i
$856$	−0.984832	−	0.658043i	−0.0336609	−	0.0224915i
$857$	−9.59597	−	48.2422i	−0.327792	−	1.64792i	−0.695900	−	0.718139i	$-0.744994\pi$
$857$	−9.59597	−	48.2422i	−0.327792	−	1.64792i	0.368108	−	0.929783i	$-0.380006\pi$
$858$	5.04913	−	49.5898i	0.172375	−	1.69297i
$859$	10.7823	−	26.0307i	0.367887	−	0.888157i	−0.626209	−	0.779655i	$-0.715395\pi$
$859$	10.7823	−	26.0307i	0.367887	−	0.888157i	0.994096	−	0.108502i	$-0.0346055\pi$
$860$	−28.9853	+	5.76554i	−0.988392	+	0.196603i
$861$	−3.36009	+	10.9468i	−0.114512	+	0.373067i
$862$	8.17368	−	41.0919i	0.278397	−	1.39959i
$863$	5.07346	−	5.07346i	0.172702	−	0.172702i	−0.615463	−	0.788166i	$-0.711031\pi$
$863$	5.07346	−	5.07346i	0.172702	−	0.172702i	0.788166	+	0.615463i	$0.211031\pi$
$864$	41.8480	+	4.53958i	1.42370	+	0.154440i
$865$	34.9449	−	14.4747i	1.18816	−	0.492153i
$866$	19.6194			0.666694
$867$		0			0
$868$	12.5949			0.427498
$869$	−8.64858	+	3.58236i	−0.293383	+	0.121523i
$870$	−0.279298	+	0.338049i	−0.00946909	+	0.0114609i
$871$	−30.1178	+	30.1178i	−1.02050	+	1.02050i
$872$	0.855247	−	4.29962i	0.0289623	−	0.145603i
$873$	56.5050	+	0.372207i	1.91240	+	0.0125973i
$874$	8.92281	−	1.77486i	0.301818	−	0.0600354i
$875$	−9.00784	+	21.7469i	−0.304521	+	0.735178i
$876$	−10.4485	−	1.06384i	−0.353021	−	0.0359439i
$877$	4.63939	+	23.3238i	0.156661	+	0.787588i	0.976588	+	0.215120i	$0.0690141\pi$
$877$	4.63939	+	23.3238i	0.156661	+	0.787588i	−0.819927	+	0.572469i	$0.805986\pi$
$878$	65.9203	+	44.0465i	2.22470	+	1.48650i
$879$	−3.98074	−	41.8290i	−0.134267	−	1.41086i
$880$	−12.7583	−	12.7583i	−0.430083	−	0.430083i
$881$	16.4329	−	10.9801i	0.553639	−	0.369930i	−0.247056	−	0.969001i	$-0.579463\pi$
$881$	16.4329	−	10.9801i	0.553639	−	0.369930i	0.800696	+	0.599071i	$0.204463\pi$
$882$	−15.3051	−	10.3730i	−0.515350	−	0.349278i
$883$			1.29910i			0.0437182i	0.999761	+	0.0218591i	$0.00695852\pi$
$883$			1.29910i			0.0437182i	−0.999761	+	0.0218591i	$0.993041\pi$
$884$		0			0
$885$	9.57275	+	31.9354i	0.321785	+	1.07350i
$886$	10.2221	+	24.6784i	0.343419	+	0.829087i
$887$	2.37234	+	3.55045i	0.0796553	+	0.119213i	0.869158	−	0.494535i	$-0.164661\pi$
$887$	2.37234	+	3.55045i	0.0796553	+	0.119213i	−0.789503	+	0.613747i	$0.789661\pi$
$888$	0.667734	−	1.23941i	0.0224077	−	0.0415917i
$889$	6.87918	+	1.36835i	0.230720	+	0.0458931i
$890$	6.67790	−	9.99419i	0.223844	−	0.335006i
$891$	20.7284	+	4.40777i	0.694426	+	0.147666i
$892$	−19.9385	−	8.25878i	−0.667589	−	0.276525i
$893$	−38.0897	−	15.7773i	−1.27462	−	0.527966i
$894$	−43.2986	+	22.9606i	−1.44812	+	0.767916i
$895$	22.1878	−	33.2064i	0.741656	−	1.10997i
$896$	−4.60437	−	0.915867i	−0.153821	−	0.0305970i
$897$	−8.09062	−	4.35885i	−0.270138	−	0.145538i
$898$	23.9673	+	35.8696i	0.799799	+	1.19698i
$899$	−0.0674890	−	0.162933i	−0.00225089	−	0.00543412i
$900$	2.42588	+	3.68287i	0.0808627	+	0.122762i
$901$		0			0
$902$		−	15.9007i		−	0.529434i
$903$	17.7490	−	14.4686i	0.590648	−	0.481486i
$904$	1.63350	−	1.09147i	0.0543293	−	0.0363017i
$905$	5.14393	+	5.14393i	0.170990	+	0.170990i
$906$	17.5966	−	1.67461i	0.584607	−	0.0556353i
$907$	45.0145	+	30.0777i	1.49468	+	0.998715i	0.990858	+	0.134910i	$0.0430744\pi$
$907$	45.0145	+	30.0777i	1.49468	+	0.998715i	0.503825	+	0.863806i	$0.331926\pi$
$908$	0.759958	+	3.82057i	0.0252201	+	0.126790i
$909$	−1.97136	−	10.2635i	−0.0653857	−	0.340420i
$910$	19.3647	−	46.7505i	0.641934	−	1.54977i
$911$	−53.8041	+	10.7023i	−1.78261	+	0.354583i	−0.972717	−	0.231994i	$-0.925475\pi$
$911$	−53.8041	+	10.7023i	−1.78261	+	0.354583i	−0.809893	+	0.586577i	$0.800475\pi$
$912$	−30.8822	−	9.47920i	−1.02261	−	0.313888i
$913$	−1.73883	+	8.74168i	−0.0575468	+	0.289307i
$914$	20.2402	−	20.2402i	0.669488	−	0.669488i
$915$	−15.0054	−	12.3976i	−0.496065	−	0.409851i
$916$	−3.57568	+	1.48110i	−0.118144	+	0.0489368i
$917$	40.9750			1.35311
$918$		0			0
$919$	8.09126			0.266906			0.133453	−	0.991055i	$-0.457393\pi$
$919$	8.09126			0.266906			0.133453	+	0.991055i	$0.457393\pi$
$920$	0.500682	−	0.207389i	0.0165070	−	0.00683743i
$921$	28.8037	+	23.7978i	0.949115	+	0.784164i
$922$	36.4136	−	36.4136i	1.19922	−	1.19922i
$923$	1.04569	−	5.25704i	0.0344193	−	0.173037i
$924$	−16.6691	−	5.11652i	−0.548372	−	0.168321i
$925$	−1.85082	+	0.368150i	−0.0608544	+	0.0121047i
$926$	0.410037	−	0.989916i	0.0134746	−	0.0325307i
$927$	−2.15495	−	11.2194i	−0.0707780	−	0.368494i
$928$	0.0946117	+	0.475645i	0.00310578	+	0.0156138i
$929$	7.41858	+	4.95694i	0.243396	+	0.162632i	0.671285	−	0.741199i	$-0.265743\pi$
$929$	7.41858	+	4.95694i	0.243396	+	0.162632i	−0.427889	+	0.903831i	$0.640743\pi$
$930$	21.4811	−	2.04429i	0.704393	−	0.0670349i
$931$	10.8220	+	10.8220i	0.354677	+	0.354677i
$932$	−2.48195	+	1.65839i	−0.0812991	+	0.0543223i
$933$	−38.8909	+	31.7031i	−1.27323	+	1.03791i
$934$		−	30.6629i		−	1.00332i
$935$		0			0
$936$	−2.92435	−	4.43963i	−0.0955854	−	0.145114i
$937$	−8.51098	−	20.5473i	−0.278042	−	0.671252i	0.721740	−	0.692165i	$-0.243343\pi$
$937$	−8.51098	−	20.5473i	−0.278042	−	0.671252i	−0.999781	+	0.0209128i	$0.993343\pi$
$938$	15.9958	+	23.9394i	0.522282	+	0.781650i
$939$	−16.9809	−	9.14851i	−0.554150	−	0.298550i
$940$	−35.6348	−	7.08820i	−1.16228	−	0.231192i
$941$	−22.1038	+	33.0806i	−0.720563	+	1.07840i	0.272653	+	0.962112i	$0.412099\pi$
$941$	−22.1038	+	33.0806i	−0.720563	+	1.07840i	−0.993216	+	0.116286i	$0.962901\pi$
$942$	37.3631	−	19.8130i	1.21735	−	0.645544i
$943$	−2.70843	−	1.12187i	−0.0881987	−	0.0365331i
$944$	31.5824	+	13.0819i	1.02792	+	0.425778i
$945$	18.8719	+	10.3283i	0.613904	+	0.335979i
$946$	−17.6657	+	26.4386i	−0.574363	+	0.859594i
$947$	−6.16877	−	1.22705i	−0.200458	−	0.0398736i	0.0938399	−	0.995587i	$-0.470086\pi$
$947$	−6.16877	−	1.22705i	−0.200458	−	0.0398736i	−0.294298	+	0.955714i	$0.595086\pi$
$948$	−7.00554	+	13.0033i	−0.227529	+	0.422326i
$949$	−9.42821	−	14.1103i	−0.306053	−	0.458040i
$950$	−2.69953	−	6.51724i	−0.0875843	−	0.211447i
$951$	−5.43738	−	18.1395i	−0.176319	−	0.588213i
$952$		0			0
$953$		−	45.4373i		−	1.47186i	−0.677058	−	0.735930i	$-0.736745\pi$
$953$		−	45.4373i		−	1.47186i	0.677058	−	0.735930i	$-0.263255\pi$
$954$	−9.58878	−	6.49879i	−0.310448	−	0.210406i
$955$	14.8646	−	9.93218i	0.481006	−	0.321398i
$956$	12.1496	+	12.1496i	0.392946	+	0.392946i
$957$	0.0231308	+	0.243055i	0.000747713	+	0.00785685i
$958$	−17.0921	−	11.4206i	−0.552221	−	0.368982i
$959$	−5.21246	−	26.2048i	−0.168319	−	0.846197i
$960$	−32.6245	−	3.32176i	−1.05295	−	0.107209i
$961$	8.54214	−	20.6226i	0.275553	−	0.665244i
$962$	33.0075	−	6.56560i	1.06420	−	0.211683i
$963$	12.0373	+	0.0792916i	0.387897	+	0.00255513i
$964$	−7.24997	+	36.4480i	−0.233506	+	1.17391i
$965$	−15.8075	+	15.8075i	−0.508862	+	0.508862i
$966$	−3.95681	+	4.78913i	−0.127308	+	0.154088i
$967$	30.2049	−	12.5113i	0.971323	−	0.402335i	0.160119	−	0.987098i	$-0.448812\pi$
$967$	30.2049	−	12.5113i	0.971323	−	0.402335i	0.811204	+	0.584763i	$0.198812\pi$
$968$	−1.61044			−0.0517614
$969$		0			0
$970$	−79.6546			−2.55755
$971$	22.2614	−	9.22099i	0.714403	−	0.295916i	0.00427801	−	0.999991i	$-0.498638\pi$
$971$	22.2614	−	9.22099i	0.714403	−	0.295916i	0.710125	+	0.704075i	$0.248638\pi$
$972$	29.7444	−	15.2744i	0.954053	−	0.489927i
$973$	0.142863	−	0.142863i	0.00457997	−	0.00457997i
$974$	1.75290	−	8.81244i	0.0561667	−	0.282369i
$975$	−2.09099	+	6.81223i	−0.0669653	+	0.218166i
$976$	−19.5744	+	3.89360i	−0.626562	+	0.124631i
$977$	−16.3952	+	39.5815i	−0.524529	+	1.26633i	0.410534	+	0.911845i	$0.365342\pi$
$977$	−16.3952	+	39.5815i	−0.524529	+	1.26633i	−0.935063	+	0.354481i	$0.884658\pi$
$978$	−4.15129	+	40.7717i	−0.132744	+	1.30373i
$979$	−1.30565	−	6.56395i	−0.0417288	−	0.209785i
$980$	11.2144	+	7.49325i	0.358232	+	0.239363i
$981$	16.7783	+	41.2733i	0.535690	+	1.31775i
$982$	54.9740	+	54.9740i	1.75429	+	1.75429i
$983$	31.2407	−	20.8744i	0.996425	−	0.665790i	0.0534211	−	0.998572i	$-0.482987\pi$
$983$	31.2407	−	20.8744i	0.996425	−	0.665790i	0.943004	+	0.332782i	$0.107987\pi$
$984$	−1.07151	−	1.31444i	−0.0341585	−	0.0419029i
$985$		−	52.7509i		−	1.68078i
$986$		0			0
$987$	26.9668	−	8.08340i	0.858363	−	0.257298i
$988$	24.9138	+	60.1471i	0.792612	+	1.91354i
$989$	3.25701	+	4.87446i	0.103567	+	0.154999i
$990$	−29.2602	−	6.02085i	−0.929951	−	0.191355i
$991$	15.0467	+	2.99298i	0.477974	+	0.0950750i	0.428197	−	0.903685i	$-0.359149\pi$
$991$	15.0467	+	2.99298i	0.477974	+	0.0950750i	0.0497773	+	0.998760i	$0.484149\pi$
$992$	13.2584	−	19.8425i	0.420953	−	0.630001i
$993$	9.62491	+	18.1505i	0.305437	+	0.575988i
$994$	−3.34743	−	1.38655i	−0.106174	−	0.0439788i
$995$	46.4183	+	19.2271i	1.47156	+	0.609539i
$996$	6.58842	+	12.4243i	0.208762	+	0.393679i
$997$	−20.7300	+	31.0246i	−0.656524	+	0.982558i	0.342548	+	0.939500i	$0.388710\pi$
$997$	−20.7300	+	31.0246i	−0.656524	+	0.982558i	−0.999073	+	0.0430578i	$0.986290\pi$
$998$	−26.0440	−	5.18048i	−0.824409	−	0.163985i
$999$	1.26166	+	14.2521i	0.0399172	+	0.450917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.i.d.131.4		32
3.2	odd	2	inner	867.2.i.d.131.1		32
17.2	even	8		867.2.i.f.65.4		32
17.3	odd	16		867.2.i.i.329.4		32
17.4	even	4		867.2.i.h.158.1		32
17.5	odd	16		867.2.i.f.827.1		32
17.6	odd	16		51.2.i.a.41.4	yes	32
17.7	odd	16		867.2.i.c.503.1		32
17.8	even	8		867.2.i.b.224.1		32
17.9	even	8		867.2.i.i.224.1		32
17.10	odd	16	inner	867.2.i.d.503.1		32
17.11	odd	16		867.2.i.h.653.4		32
17.12	odd	16		867.2.i.g.827.1		32
17.13	even	4		51.2.i.a.5.1	✓	32
17.14	odd	16		867.2.i.b.329.4		32
17.15	even	8		867.2.i.g.65.4		32
17.16	even	2		867.2.i.c.131.4		32
51.2	odd	8		867.2.i.f.65.1		32
51.5	even	16		867.2.i.f.827.4		32
51.8	odd	8		867.2.i.b.224.4		32
51.11	even	16		867.2.i.h.653.1		32
51.14	even	16		867.2.i.b.329.1		32
51.20	even	16		867.2.i.i.329.1		32
51.23	even	16		51.2.i.a.41.1	yes	32
51.26	odd	8		867.2.i.i.224.4		32
51.29	even	16		867.2.i.g.827.4		32
51.32	odd	8		867.2.i.g.65.1		32
51.38	odd	4		867.2.i.h.158.4		32
51.41	even	16		867.2.i.c.503.4		32
51.44	even	16	inner	867.2.i.d.503.4		32
51.47	odd	4		51.2.i.a.5.4	yes	32
51.50	odd	2		867.2.i.c.131.1		32
68.23	even	16		816.2.cj.c.449.4		32
68.47	odd	4		816.2.cj.c.209.2		32
204.23	odd	16		816.2.cj.c.449.2		32
204.47	even	4		816.2.cj.c.209.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.5.1	✓	32	17.13	even	4
51.2.i.a.5.4	yes	32	51.47	odd	4
51.2.i.a.41.1	yes	32	51.23	even	16
51.2.i.a.41.4	yes	32	17.6	odd	16
816.2.cj.c.209.2		32	68.47	odd	4
816.2.cj.c.209.4		32	204.47	even	4
816.2.cj.c.449.2		32	204.23	odd	16
816.2.cj.c.449.4		32	68.23	even	16
867.2.i.b.224.1		32	17.8	even	8
867.2.i.b.224.4		32	51.8	odd	8
867.2.i.b.329.1		32	51.14	even	16
867.2.i.b.329.4		32	17.14	odd	16
867.2.i.c.131.1		32	51.50	odd	2
867.2.i.c.131.4		32	17.16	even	2
867.2.i.c.503.1		32	17.7	odd	16
867.2.i.c.503.4		32	51.41	even	16
867.2.i.d.131.1		32	3.2	odd	2	inner
867.2.i.d.131.4		32	1.1	even	1	trivial
867.2.i.d.503.1		32	17.10	odd	16	inner
867.2.i.d.503.4		32	51.44	even	16	inner
867.2.i.f.65.1		32	51.2	odd	8
867.2.i.f.65.4		32	17.2	even	8
867.2.i.f.827.1		32	17.5	odd	16
867.2.i.f.827.4		32	51.5	even	16
867.2.i.g.65.1		32	51.32	odd	8
867.2.i.g.65.4		32	17.15	even	8
867.2.i.g.827.1		32	17.12	odd	16
867.2.i.g.827.4		32	51.29	even	16
867.2.i.h.158.1		32	17.4	even	4
867.2.i.h.158.4		32	51.38	odd	4
867.2.i.h.653.1		32	51.11	even	16
867.2.i.h.653.4		32	17.11	odd	16
867.2.i.i.224.1		32	17.9	even	8
867.2.i.i.224.4		32	51.26	odd	8
867.2.i.i.329.1		32	51.20	even	16
867.2.i.i.329.4		32	17.3	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.88095 - 0.779115i) q^{2} +(-1.33527 - 1.10321i) q^{3} +(1.51674 - 1.51674i) q^{4} +(0.405238 - 2.03727i) q^{5} +(-3.37109 - 1.03475i) q^{6} +(-1.95490 + 0.388855i) q^{7} +(0.112963 - 0.272718i) q^{8} +(0.565877 + 2.94615i) q^{9} +(-0.825033 - 4.14772i) q^{10} +(-1.95782 - 1.30817i) q^{11} +(-3.69852 + 0.351977i) q^{12} +(-4.24491 - 4.24491i) q^{13} +(-3.37411 + 2.25451i) q^{14} +(-2.78862 + 2.27324i) q^{15} +3.68900i q^{16} +(3.35977 + 5.10067i) q^{18} +(-1.93477 - 4.67096i) q^{19} +(-2.47536 - 3.70464i) q^{20} +(3.03931 + 1.63744i) q^{21} +(-4.70177 - 0.935240i) q^{22} +(-0.491037 + 0.734889i) q^{23} +(-0.451700 + 0.239529i) q^{24} +(0.633157 + 0.262262i) q^{25} +(-11.2917 - 4.67719i) q^{26} +(2.49461 - 4.55817i) q^{27} +(-2.37529 + 3.55487i) q^{28} +(0.0587151 + 0.0116792i) q^{29} +(-3.47415 + 6.44850i) q^{30} +(-1.63665 - 2.44942i) q^{31} +(3.10008 + 7.48426i) q^{32} +(1.17103 + 3.90663i) q^{33} +4.14024i q^{35} +(5.32682 + 3.61024i) q^{36} +(-2.28949 + 1.52979i) q^{37} +(-7.27842 - 7.27842i) q^{38} +(0.985083 + 10.3511i) q^{39} +(-0.509822 - 0.340652i) q^{40} +(0.647088 + 3.25313i) q^{41} +(6.99253 + 0.711965i) q^{42} +(2.53831 - 6.12803i) q^{43} +(-4.95364 + 0.985341i) q^{44} +(6.23140 + 0.0410472i) q^{45} +(-0.351053 + 1.76486i) q^{46} +(5.76615 - 5.76615i) q^{47} +(4.06972 - 4.92580i) q^{48} +(-2.79671 + 1.15844i) q^{49} +1.39527 q^{50} -12.8768 q^{52} +(-1.75216 + 0.725770i) q^{53} +(1.14089 - 10.5173i) q^{54} +(-3.45848 + 3.45848i) q^{55} +(-0.114785 + 0.577063i) q^{56} +(-2.56958 + 8.37143i) q^{57} +(0.119540 - 0.0237779i) q^{58} +(3.54618 - 8.56124i) q^{59} +(-0.781708 + 7.67751i) q^{60} +(1.05546 + 5.30616i) q^{61} +(-4.98684 - 3.33210i) q^{62} +(-2.25186 - 5.53939i) q^{63} +(6.44515 + 6.44515i) q^{64} +(-10.3682 + 6.92782i) q^{65} +(5.24636 + 6.43581i) q^{66} -7.09503i q^{67} +(1.46640 - 0.439558i) q^{69} +(3.22572 + 7.78759i) q^{70} +(0.496046 + 0.742386i) q^{71} +(0.867389 + 0.178482i) q^{72} +(2.77256 + 0.551496i) q^{73} +(-3.11454 + 4.66124i) q^{74} +(-0.556105 - 1.04869i) q^{75} +(-10.0192 - 4.15007i) q^{76} +(4.33604 + 1.79604i) q^{77} +(9.91759 + 18.7024i) q^{78} +(2.20873 - 3.30560i) q^{79} +(7.51548 + 1.49492i) q^{80} +(-8.35957 + 3.33431i) q^{81} +(3.75170 + 5.61482i) q^{82} +(-1.44855 - 3.49712i) q^{83} +(7.09339 - 2.12627i) q^{84} -13.5041i q^{86} +(-0.0655159 - 0.0803696i) q^{87} +(-0.577923 + 0.386156i) q^{88} +(2.00979 + 2.00979i) q^{89} +(11.7529 - 4.77777i) q^{90} +(9.94906 + 6.64775i) q^{91} +(0.369859 + 1.85941i) q^{92} +(-0.516848 + 5.07620i) q^{93} +(6.35335 - 15.3383i) q^{94} +(-10.3000 + 2.04880i) q^{95} +(4.11723 - 13.4135i) q^{96} +(3.67461 - 18.4735i) q^{97} +(-4.35792 + 4.35792i) q^{98} +(2.74618 - 6.50828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{4} + 8 q^{9} + 32 q^{10} + 24 q^{12} - 16 q^{13} - 16 q^{15} + 16 q^{18} + 16 q^{19} + 16 q^{21} - 48 q^{22} + 8 q^{24} - 16 q^{25} - 48 q^{27} - 64 q^{28} - 8 q^{30} + 16 q^{31} - 8 q^{36}+ \cdots + 96 q^{97}+O(q^{100}) \) 32 * q - 16 * q^4 + 8 * q^9 + 32 * q^10 + 24 * q^12 - 16 * q^13 - 16 * q^15 + 16 * q^18 + 16 * q^19 + 16 * q^21 - 48 * q^22 + 8 * q^24 - 16 * q^25 - 48 * q^27 - 64 * q^28 - 8 * q^30 + 16 * q^31 - 8 * q^36 - 32 * q^37 + 8 * q^39 - 64 * q^40 + 56 * q^42 - 16 * q^43 + 24 * q^45 - 80 * q^46 - 72 * q^48 + 48 * q^49 - 96 * q^52 + 48 * q^54 - 48 * q^55 + 24 * q^57 - 32 * q^58 - 32 * q^60 + 64 * q^61 - 16 * q^63 + 16 * q^64 - 72 * q^66 + 80 * q^69 - 48 * q^70 + 64 * q^72 - 48 * q^76 - 16 * q^78 - 32 * q^79 + 48 * q^81 + 48 * q^82 + 56 * q^87 - 80 * q^88 + 104 * q^90 + 80 * q^91 + 72 * q^93 + 48 * q^94 + 72 * q^96 + 96 * q^97

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