LMFDB - Embedded newform 867.2.i.h.158.1

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 = [32,0,8,-16,0,8,16,0,-8,16] 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			158.1
Character	$\chi$	$=$	867.158
Dual form			867.2.i.h.653.1

$q$-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} +(-1.10321 + 1.33527i) q^{3} +(1.51674 - 1.51674i) q^{4} +(-2.03727 - 0.405238i) q^{5} +(1.03475 - 3.37109i) q^{6} +(-0.388855 - 1.95490i) q^{7} +(-0.112963 + 0.272718i) q^{8} +(-0.565877 - 2.94615i) q^{9} +(4.14772 - 0.825033i) q^{10} +(1.30817 - 1.95782i) q^{11} +(0.351977 + 3.69852i) q^{12} +(-4.24491 - 4.24491i) q^{13} +(2.25451 + 3.37411i) q^{14} +(2.78862 - 2.27324i) q^{15} +3.68900i q^{16} +(3.35977 + 5.10067i) q^{18} +(1.93477 + 4.67096i) q^{19} +(-3.70464 + 2.47536i) q^{20} +(3.03931 + 1.63744i) q^{21} +(-0.935240 + 4.70177i) q^{22} +(-0.734889 - 0.491037i) q^{23} +(-0.239529 - 0.451700i) q^{24} +(-0.633157 - 0.262262i) q^{25} +(11.2917 + 4.67719i) q^{26} +(4.55817 + 2.49461i) q^{27} +(-3.55487 - 2.37529i) q^{28} +(0.0116792 - 0.0587151i) q^{29} +(-3.47415 + 6.44850i) q^{30} +(-2.44942 + 1.63665i) q^{31} +(-3.10008 - 7.48426i) q^{32} +(1.17103 + 3.90663i) q^{33} +4.14024i q^{35} +(-5.32682 - 3.61024i) q^{36} +(1.52979 + 2.28949i) q^{37} +(-7.27842 - 7.27842i) q^{38} +(10.3511 - 0.985083i) q^{39} +(0.340652 - 0.509822i) q^{40} +(-3.25313 + 0.647088i) q^{41} +(-6.99253 - 0.711965i) q^{42} +(-2.53831 + 6.12803i) q^{43} +(-0.985341 - 4.95364i) q^{44} +(-0.0410472 + 6.23140i) q^{45} +(1.76486 + 0.351053i) q^{46} +(5.76615 - 5.76615i) q^{47} +(-4.92580 - 4.06972i) q^{48} +(2.79671 - 1.15844i) q^{49} +1.39527 q^{50} -12.8768 q^{52} +(1.75216 - 0.725770i) q^{53} +(-10.5173 - 1.14089i) q^{54} +(-3.45848 + 3.45848i) q^{55} +(0.577063 + 0.114785i) q^{56} +(-8.37143 - 2.56958i) q^{57} +(0.0237779 + 0.119540i) q^{58} +(-3.54618 + 8.56124i) q^{59} +(0.781708 - 7.67751i) q^{60} +(-5.30616 + 1.05546i) q^{61} +(3.33210 - 4.98684i) q^{62} +(-5.53939 + 2.25186i) q^{63} +(6.44515 + 6.44515i) q^{64} +(6.92782 + 10.3682i) q^{65} +(-5.24636 - 6.43581i) q^{66} -7.09503i q^{67} +(1.46640 - 0.439558i) q^{69} +(-3.22572 - 7.78759i) q^{70} +(0.742386 - 0.496046i) q^{71} +(0.867389 + 0.178482i) q^{72} +(0.551496 - 2.77256i) q^{73} +(-4.66124 - 3.11454i) q^{74} +(1.04869 - 0.556105i) q^{75} +(10.0192 + 4.15007i) q^{76} +(-4.33604 - 1.79604i) q^{77} +(-18.7024 + 9.91759i) q^{78} +(3.30560 + 2.20873i) q^{79} +(1.49492 - 7.51548i) q^{80} +(-8.35957 + 3.33431i) q^{81} +(5.61482 - 3.75170i) q^{82} +(1.44855 + 3.49712i) q^{83} +(7.09339 - 2.12627i) q^{84} -13.5041i q^{86} +(0.0655159 + 0.0803696i) q^{87} +(0.386156 + 0.577923i) q^{88} +(2.00979 + 2.00979i) q^{89} +(-4.77777 - 11.7529i) q^{90} +(-6.64775 + 9.94906i) q^{91} +(-1.85941 + 0.369859i) q^{92} +(0.516848 - 5.07620i) q^{93} +(-6.35335 + 15.3383i) q^{94} +(-2.04880 - 10.3000i) q^{95} +(13.4135 + 4.11723i) q^{96} +(-18.4735 - 3.67461i) q^{97} +(-4.35792 + 4.35792i) q^{98} +(-6.50828 - 2.74618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} - 16 q^{4} + 8 q^{6} + 16 q^{7} - 8 q^{9} + 16 q^{10} - 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} + 16 q^{22} - 16 q^{24} + 16 q^{25} + 8 q^{27} - 32 q^{28} - 8 q^{30}+ \cdots + 64 q^{99}+O(q^{100}) $ 32 * q + 8 * q^3 - 16 * q^4 + 8 * q^6 + 16 * q^7 - 8 * q^9 + 16 * q^10 - 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 + 16 * q^22 - 16 * q^24 + 16 * q^25 + 8 * q^27 - 32 * q^28 - 8 * q^30 - 16 * q^31 + 8 * q^36 - 16 * q^37 + 24 * q^39 - 16 * q^40 - 56 * q^42 + 16 * q^43 + 40 * q^45 + 32 * q^46 + 64 * q^48 - 48 * q^49 - 96 * q^52 + 24 * q^54 - 48 * q^55 - 8 * q^57 + 48 * q^58 + 32 * q^60 + 32 * q^61 - 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 - 48 * q^73 - 88 * q^75 + 48 * q^76 - 96 * q^78 - 16 * q^79 + 48 * q^81 - 112 * q^82 - 56 * q^87 - 16 * q^88 + 88 * q^90 - 16 * q^91 - 72 * q^93 - 48 * q^94 + 112 * q^96 + 16 * q^97 + 64 * q^99

Character values

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

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{5}{16}\right)$

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	−0.930665	−	0.365874i	$-0.880770\pi$
$2$	−1.88095	+	0.779115i	−1.33003	+	0.550917i	−0.399367	+	0.916791i	$0.630770\pi$
$3$	−1.10321	+	1.33527i	−0.636936	+	0.770917i
$3$	−1.10321	+	1.33527i	−0.636936	+	0.770917i
$4$	1.51674	−	1.51674i	0.758368	−	0.758368i
$5$	−2.03727	−	0.405238i	−0.911094	−	0.181228i	−0.282777	−	0.959186i	$-0.591256\pi$
$5$	−2.03727	−	0.405238i	−0.911094	−	0.181228i	−0.628316	+	0.777958i	$0.716256\pi$
$6$	1.03475	−	3.37109i	0.422433	−	1.37624i
$7$	−0.388855	−	1.95490i	−0.146973	−	0.738885i	−0.982031	−	0.188722i	$-0.939566\pi$
$7$	−0.388855	−	1.95490i	−0.146973	−	0.738885i	0.835057	−	0.550163i	$-0.185434\pi$
$8$	−0.112963	+	0.272718i	−0.0399386	+	0.0964202i
$9$	−0.565877	−	2.94615i	−0.188626	−	0.982049i
$10$	4.14772	−	0.825033i	1.31163	−	0.260898i
$11$	1.30817	−	1.95782i	0.394429	−	0.590304i	−0.580106	−	0.814541i	$-0.696989\pi$
$11$	1.30817	−	1.95782i	0.394429	−	0.590304i	0.974535	+	0.224237i	$0.0719889\pi$
$12$	0.351977	+	3.69852i	0.101607	+	1.06767i
$13$	−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	$-0.563089\pi$
$14$	2.25451	+	3.37411i	0.602543	+	0.901770i
$15$	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	$0.0719244\pi$
$19$	1.93477	+	4.67096i	0.443868	+	1.07159i	−0.530712	+	0.847552i	$0.678076\pi$
$20$	−3.70464	+	2.47536i	−0.828382	+	0.553507i
$21$	3.03931	+	1.63744i	0.663231	+	0.357318i
$22$	−0.935240	+	4.70177i	−0.199394	+	1.00242i
$23$	−0.734889	−	0.491037i	−0.153235	−	0.102388i	0.476589	−	0.879126i	$-0.341873\pi$
$23$	−0.734889	−	0.491037i	−0.153235	−	0.102388i	−0.629824	+	0.776738i	$0.716873\pi$
$24$	−0.239529	−	0.451700i	−0.0488937	−	0.0922028i
$25$	−0.633157	−	0.262262i	−0.126631	−	0.0524525i
$26$	11.2917	+	4.67719i	2.21449	+	0.917273i
$27$	4.55817	+	2.49461i	0.877221	+	0.480087i
$28$	−3.55487	−	2.37529i	−0.671806	−	0.448887i
$29$	0.0116792	−	0.0587151i	0.00216877	−	0.0109031i	−0.979686	−	0.200539i	$-0.935731\pi$
$29$	0.0116792	−	0.0587151i	0.00216877	−	0.0109031i	0.981855	+	0.189636i	$0.0607307\pi$
$30$	−3.47415	+	6.44850i	−0.634290	+	1.17733i
$31$	−2.44942	+	1.63665i	−0.439930	+	0.293952i	−0.755741	−	0.654870i	$-0.772723\pi$
$31$	−2.44942	+	1.63665i	−0.439930	+	0.293952i	0.315812	+	0.948822i	$0.397723\pi$
$32$	−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
$37$	1.52979	+	2.28949i	0.251496	+	0.376390i	0.935640	−	0.352957i	$-0.114824\pi$
$37$	1.52979	+	2.28949i	0.251496	+	0.376390i	−0.684144	+	0.729347i	$0.739824\pi$
$38$	−7.27842	−	7.27842i	−1.18072	−	1.18072i
$39$	10.3511	−	0.985083i	1.65750	−	0.157740i
$40$	0.340652	−	0.509822i	0.0538618	−	0.0806099i
$41$	−3.25313	+	0.647088i	−0.508054	+	0.101058i	−0.442460	−	0.896788i	$-0.645894\pi$
$41$	−3.25313	+	0.647088i	−0.508054	+	0.101058i	−0.0655937	+	0.997846i	$0.520894\pi$
$42$	−6.99253	−	0.711965i	−1.07897	−	0.109859i
$43$	−2.53831	+	6.12803i	−0.387089	+	0.934515i	0.603465	+	0.797390i	$0.293786\pi$
$43$	−2.53831	+	6.12803i	−0.387089	+	0.934515i	−0.990554	+	0.137126i	$0.956214\pi$
$44$	−0.985341	−	4.95364i	−0.148546	−	0.746790i
$45$	−0.0410472	+	6.23140i	−0.00611895	+	0.928923i
$46$	1.76486	+	0.351053i	0.260215	+	0.0517599i
$47$	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	$0.0472576\pi$
$48$	−4.92580	−	4.06972i	−0.710978	−	0.587414i
$49$	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	−0.259084	−	0.965855i	$-0.583421\pi$
$53$	1.75216	−	0.725770i	0.240678	−	0.0996922i	0.499762	+	0.866163i	$0.333421\pi$
$54$	−10.5173	−	1.14089i	−1.43122	−	0.155256i
$55$	−3.45848	+	3.45848i	−0.466341	+	0.466341i
$56$	0.577063	+	0.114785i	0.0771133	+	0.0153388i
$57$	−8.37143	−	2.56958i	−1.10882	−	0.340350i
$58$	0.0237779	+	0.119540i	0.00312219	+	0.0156963i
$59$	−3.54618	+	8.56124i	−0.461674	+	1.11458i	0.506036	+	0.862512i	$0.331110\pi$
$59$	−3.54618	+	8.56124i	−0.461674	+	1.11458i	−0.967710	+	0.252067i	$0.918890\pi$
$60$	0.781708	−	7.67751i	0.100918	−	0.991162i
$61$	−5.30616	+	1.05546i	−0.679385	+	0.135138i	−0.522708	−	0.852512i	$-0.675078\pi$
$61$	−5.30616	+	1.05546i	−0.679385	+	0.135138i	−0.156677	+	0.987650i	$0.550078\pi$
$62$	3.33210	−	4.98684i	0.423177	−	0.633330i
$63$	−5.53939	+	2.25186i	−0.697898	+	0.283708i
$64$	6.44515	+	6.44515i	0.805644	+	0.805644i
$65$	6.92782	+	10.3682i	0.859291	+	1.28602i
$66$	−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
$71$	0.742386	−	0.496046i	0.0881050	−	0.0588699i	−0.510737	−	0.859737i	$-0.670628\pi$
$71$	0.742386	−	0.496046i	0.0881050	−	0.0588699i	0.598842	+	0.800867i	$0.295628\pi$
$72$	0.867389	+	0.178482i	0.102223	+	0.0210343i
$73$	0.551496	−	2.77256i	0.0645477	−	0.324503i	−0.934998	−	0.354654i	$-0.884599\pi$
$73$	0.551496	−	2.77256i	0.0645477	−	0.324503i	0.999545	+	0.0301507i	$0.00959872\pi$
$74$	−4.66124	−	3.11454i	−0.541858	−	0.362058i
$75$	1.04869	−	0.556105i	0.121093	−	0.0642135i
$76$	10.0192	+	4.15007i	1.14928	+	0.476046i
$77$	−4.33604	−	1.79604i	−0.494137	−	0.204678i
$78$	−18.7024	+	9.91759i	−2.11763	+	1.12295i
$79$	3.30560	+	2.20873i	0.371909	+	0.248502i	0.727452	−	0.686158i	$-0.240704\pi$
$79$	3.30560	+	2.20873i	0.371909	+	0.248502i	−0.355543	+	0.934660i	$0.615704\pi$
$80$	1.49492	−	7.51548i	0.167137	−	0.840256i
$81$	−8.35957	+	3.33431i	−0.928841	+	0.370479i
$82$	5.61482	−	3.75170i	0.620053	−	0.414306i
$83$	1.44855	+	3.49712i	0.159000	+	0.383859i	0.983223	−	0.182405i	$-0.0583882\pi$
$83$	1.44855	+	3.49712i	0.159000	+	0.383859i	−0.824224	+	0.566264i	$0.808388\pi$
$84$	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
$88$	0.386156	+	0.577923i	0.0411643	+	0.0616068i
$89$	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	$0.701867\pi$
$90$	−4.77777	−	11.7529i	−0.503621	−	1.23887i
$91$	−6.64775	+	9.94906i	−0.696873	+	1.04294i
$92$	−1.85941	+	0.369859i	−0.193856	+	0.0385604i
$93$	0.516848	−	5.07620i	0.0535947	−	0.526377i
$94$	−6.35335	+	15.3383i	−0.655298	+	1.58203i
$95$	−2.04880	−	10.3000i	−0.210203	−	1.05676i
$96$	13.4135	+	4.11723i	1.36901	+	0.420213i
$97$	−18.4735	−	3.67461i	−1.87570	−	0.373100i	−0.880758	−	0.473566i	$-0.842967\pi$
$97$	−18.4735	−	3.67461i	−1.87570	−	0.373100i	−0.994940	+	0.100466i	$0.967967\pi$
$98$	−4.35792	+	4.35792i	−0.440216	+	0.440216i
$99$	−6.50828	−	2.74618i	−0.654107	−	0.276002i
$100$	−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
$105$	−5.52833	−	4.56754i	−0.539510	−	0.445746i
$106$	−2.73027	+	2.73027i	−0.265188	+	0.265188i
$107$	−3.93543	−	0.782805i	−0.380452	−	0.0756766i	0.00115968	−	0.999999i	$-0.499631\pi$
$107$	−3.93543	−	0.782805i	−0.380452	−	0.0756766i	−0.381612	+	0.924323i	$0.624631\pi$
$108$	10.6972	−	3.12988i	1.02934	−	0.301173i
$109$	2.89730	+	14.5657i	0.277511	+	1.39514i	0.828200	+	0.560433i	$0.189365\pi$
$109$	2.89730	+	14.5657i	0.277511	+	1.39514i	−0.550689	+	0.834711i	$0.685635\pi$
$110$	3.81067	−	9.19977i	0.363333	−	0.877163i
$111$	−4.74476	−	0.483102i	−0.450352	−	0.0458540i
$112$	7.21164	−	1.43449i	0.681436	−	0.135546i
$113$	−3.69755	+	5.53377i	−0.347836	+	0.520573i	−0.963597	−	0.267360i	$-0.913849\pi$
$113$	−3.69755	+	5.53377i	−0.347836	+	0.520573i	0.615761	+	0.787933i	$0.288849\pi$
$114$	17.7482	−	1.68905i	1.66227	−	0.158194i
$115$	1.29818	+	1.29818i	0.121056	+	0.121056i
$116$	−0.0713412	−	0.106770i	−0.00662386	−	0.00991331i
$117$	−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
$122$	9.15830	−	6.11938i	0.829153	−	0.554023i
$123$	2.72484	−	5.05767i	0.245690	−	0.456035i
$124$	−1.23276	+	6.19750i	−0.110705	+	0.556552i
$125$	9.81919	+	6.56097i	0.878255	+	0.586831i
$126$	8.66486	−	8.55146i	0.771927	−	0.761824i
$127$	3.25107	+	1.34664i	0.288486	+	0.119495i	0.522234	−	0.852803i	$-0.325099\pi$
$127$	3.25107	+	1.34664i	0.288486	+	0.119495i	−0.233748	+	0.972297i	$0.575099\pi$
$128$	−2.17601	−	0.901332i	−0.192334	−	0.0796672i
$129$	−5.38227	−	10.1498i	−0.473883	−	0.893640i
$130$	−21.1089	−	14.1045i	−1.85137	−	1.23705i
$131$	−4.01054	+	20.1623i	−0.350402	+	1.76159i	0.256237	+	0.966614i	$0.417517\pi$
$131$	−4.01054	+	20.1623i	−0.350402	+	1.76159i	−0.606640	+	0.794977i	$0.707483\pi$
$132$	7.70147	+	4.14919i	0.670327	+	0.361141i
$133$	8.37893	−	5.59862i	0.726546	−	0.485462i
$134$	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
$139$	0.0563146	+	0.0842808i	0.00477654	+	0.00714860i	0.833850	−	0.551991i	$-0.186132\pi$
$139$	0.0563146	+	0.0842808i	0.00477654	+	0.00714860i	−0.829074	+	0.559139i	$0.811132\pi$
$140$	6.27966	+	6.27966i	0.530728	+	0.530728i
$141$	1.33811	+	14.0606i	0.112689	+	1.18412i
$142$	−1.00991	+	1.51144i	−0.0847500	+	0.126837i
$143$	−13.8638	+	2.75769i	−1.15935	+	0.230610i
$144$	10.8683	−	2.08752i	0.905695	−	0.173960i
$145$	−0.0475872	+	0.114886i	−0.00395190	+	0.00954073i
$146$	1.12280	+	5.64471i	0.0929239	+	0.467160i
$147$	−1.53853	+	5.01235i	−0.126895	+	0.413412i
$148$	5.79285	+	1.15227i	0.476169	+	0.0947159i
$149$	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	$0.0572163\pi$
$150$	−1.53927	+	1.86306i	−0.125681	+	0.152118i
$151$	4.63104	−	1.91824i	0.376869	−	0.156104i	−0.186205	−	0.982511i	$-0.559619\pi$
$151$	4.63104	−	1.91824i	0.376869	−	0.156104i	0.563074	+	0.826407i	$0.309619\pi$
$152$	−1.49241			−0.121050
$153$		0			0
$154$	9.55519			0.769979
$155$	5.65337	−	2.34170i	0.454089	−	0.188090i
$156$	14.2058	−	17.1940i	1.13737	−	1.37662i
$157$	−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	$0.408846\pi$
$158$	−7.93852	−	1.57907i	−0.631555	−	0.125624i
$159$	−0.963899	+	3.14028i	−0.0764422	+	0.249040i
$160$	3.28279	+	16.5037i	0.259527	+	1.30473i
$161$	−0.674165	+	1.62758i	−0.0531317	+	0.128271i
$162$	13.1261	−	12.7847i	1.03128	−	1.00446i
$163$	11.3986	−	2.26731i	0.892803	−	0.177590i	0.272690	−	0.962102i	$-0.412087\pi$
$163$	11.3986	−	2.26731i	0.892803	−	0.177590i	0.620113	+	0.784512i	$0.287087\pi$
$164$	−3.95268	+	5.91560i	−0.308652	+	0.461931i
$165$	−0.802581	−	8.43340i	−0.0624809	−	0.656539i
$166$	−5.44932	−	5.44932i	−0.422949	−	0.422949i
$167$	−8.95841	−	13.4072i	−0.693223	−	1.03748i	−0.996419	−	0.0845529i	$-0.973054\pi$
$167$	−8.95841	−	13.4072i	−0.693223	−	1.03748i	0.303196	−	0.952928i	$-0.401946\pi$
$168$	−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
$173$	15.1405	−	10.1166i	1.15111	−	0.769149i	0.174607	−	0.984638i	$-0.444134\pi$
$173$	15.1405	−	10.1166i	1.15111	−	0.769149i	0.976506	+	0.215489i	$0.0691345\pi$
$174$	−0.185849	−	0.100127i	−0.0140892	−	0.00759059i
$175$	−0.266492	+	1.33974i	−0.0201449	+	0.101275i
$176$	7.22239	+	4.82584i	0.544408	+	0.363762i
$177$	−7.51938	−	14.1799i	−0.565191	−	1.06583i
$178$	−5.34616	−	2.21445i	−0.400712	−	0.165980i
$179$	−17.7630	−	7.35767i	−1.32767	−	0.549938i	−0.397679	−	0.917525i	$-0.630184\pi$
$179$	−17.7630	−	7.35767i	−1.32767	−	0.549938i	−0.929989	+	0.367587i	$0.880184\pi$
$180$	9.38914	+	9.51366i	0.699825	+	0.709106i
$181$	−2.91194	−	1.94570i	−0.216443	−	0.144623i	0.442623	−	0.896708i	$-0.354048\pi$
$181$	−2.91194	−	1.94570i	−0.216443	−	0.144623i	−0.659066	+	0.752085i	$0.729048\pi$
$182$	4.75262	−	23.8930i	0.352288	−	1.77107i
$183$	4.44446	−	8.24954i	0.328544	−	0.609823i
$184$	0.216930	−	0.144948i	0.0159923	−	0.0106857i
$185$	−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
$190$	11.8786	+	17.7776i	0.861764	+	1.28972i
$191$	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	$0.649210\pi$
$192$	−15.7163	+	1.49568i	−1.13423	+	0.107941i
$193$	5.97920	−	8.94851i	0.430392	−	0.644128i	−0.551365	−	0.834264i	$-0.685893\pi$
$193$	5.97920	−	8.94851i	0.430392	−	0.644128i	0.981758	+	0.190136i	$0.0608930\pi$
$194$	37.6106	−	7.48122i	2.70029	−	0.537120i
$195$	−21.4872	−	2.18778i	−1.53873	−	0.156670i
$196$	2.48483	−	5.99892i	0.177488	−	0.428494i
$197$	4.95440	+	24.9075i	0.352987	+	1.77458i	0.594408	+	0.804163i	$0.297386\pi$
$197$	4.95440	+	24.9075i	0.352987	+	1.77458i	−0.241422	+	0.970420i	$0.577614\pi$
$198$	14.3813	+	0.0947319i	1.02204	+	0.00673231i
$199$	23.7232	+	4.71884i	1.68169	+	0.334510i	0.941276	−	0.337637i	$-0.109628\pi$
$199$	23.7232	+	4.71884i	1.68169	+	0.334510i	0.740418	+	0.672147i	$0.234628\pi$
$200$	0.143047	−	0.143047i	0.0101150	−	0.0101150i
$201$	9.47376	+	7.82727i	0.668227	+	0.552093i
$202$	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
$207$	−1.03081	+	2.44296i	−0.0716463	+	0.169797i
$208$	15.6595	−	15.6595i	1.08579	−	1.08579i
$209$	11.6759	+	2.32248i	0.807639	+	0.160649i
$210$	13.9571	+	4.28410i	0.963134	+	0.295631i
$211$	−2.14574	−	10.7873i	−0.147719	−	0.742631i	−0.981639	−	0.190747i	$-0.938909\pi$
$211$	−2.14574	−	10.7873i	−0.147719	−	0.742631i	0.833921	−	0.551884i	$-0.186091\pi$
$212$	1.55677	−	3.75837i	0.106919	−	0.258126i
$213$	−0.156649	+	1.53852i	−0.0107334	+	0.105418i
$214$	8.01223	−	1.59373i	0.547705	−	0.108945i
$215$	7.65453	−	11.4558i	0.522034	−	0.781280i
$216$	−1.19523	+	0.961294i	−0.0813251	+	0.0654078i
$217$	4.15197	+	4.15197i	0.281854	+	0.281854i
$218$	−16.7980	−	25.1401i	−1.13771	−	1.70270i
$219$	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	0.998795	−	0.0490833i	$-0.0156300\pi$
$223$	3.85027	+	9.29537i	0.257833	+	0.622464i	−0.740962	+	0.671547i	$0.765630\pi$
$224$	−13.4255	+	8.97065i	−0.897031	+	0.599377i
$225$	−0.414374	+	2.01378i	−0.0276249	+	0.134252i
$226$	2.64346	−	13.2895i	0.175840	−	0.884008i
$227$	−1.50999	−	1.00895i	−0.100222	−	0.0669661i	0.504449	−	0.863441i	$-0.331695\pi$
$227$	−1.50999	−	1.00895i	−0.100222	−	0.0669661i	−0.604671	+	0.796475i	$0.706695\pi$
$228$	−16.5946	+	8.79987i	−1.09901	+	0.582786i
$229$	1.66699	+	0.690491i	0.110158	+	0.0456290i	0.437082	−	0.899422i	$-0.356012\pi$
$229$	1.66699	+	0.690491i	0.110158	+	0.0456290i	−0.326924	+	0.945051i	$0.606012\pi$
$230$	−3.45324	−	1.43038i	−0.227700	−	0.0943163i
$231$	7.18174	−	3.80836i	0.472523	−	0.250572i
$232$	0.0146933	+	0.00981777i	0.000964664	+	0.000644568i
$233$	−0.271493	+	1.36489i	−0.0177861	+	0.0894166i	−0.988659	−	0.150179i	$-0.952015\pi$
$233$	−0.271493	+	1.36489i	−0.0177861	+	0.0894166i	0.970873	+	0.239596i	$0.0770149\pi$
$234$	7.38996	−	35.9138i	0.483097	−	2.34776i
$235$	−14.0839	+	9.41054i	−0.918730	+	0.613876i
$236$	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
$241$	9.62530	+	14.4053i	0.620020	+	0.927925i	0.999996	+	0.00292882i	$0.000932274\pi$
$241$	9.62530	+	14.4053i	0.620020	+	0.927925i	−0.379976	+	0.924996i	$0.624068\pi$
$242$	−7.85403	−	7.85403i	−0.504876	−	0.504876i
$243$	4.77012	−	14.8407i	0.306003	−	0.952031i
$244$	−6.44719	+	9.64891i	−0.412739	+	0.617708i
$245$	−6.16709	+	1.22671i	−0.394001	+	0.0783717i
$246$	−1.18477	+	11.6362i	−0.0755383	+	0.741896i
$247$	11.6149	−	28.0408i	0.739036	−	1.78419i
$248$	−0.169649	−	0.852883i	−0.0107727	−	0.0541581i
$249$	−6.26764	−	1.92383i	−0.397196	−	0.121918i
$250$	−23.5811	−	4.69058i	−1.49140	−	0.296658i
$251$	−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	$0.497338\pi$
$252$	−4.98632	+	11.8173i	−0.314109	+	0.744418i
$253$	−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	−0.833124	−	0.553086i	$-0.813450\pi$
$257$	−16.5305	+	6.84714i	−1.03114	+	0.427113i	−0.198017	+	0.980199i	$0.563450\pi$
$258$	18.0316	+	14.8978i	1.12260	+	0.927499i
$259$	3.88088	−	3.88088i	0.241146	−	0.241146i
$260$	26.2335	+	5.21818i	1.62694	+	0.323618i
$261$	−0.179592	−	0.00118300i	−0.0111165	−	7.32259e-5i
$262$	−8.16515	−	41.0490i	−0.504445	−	2.53601i
$263$	2.97552	−	7.18354i	0.183478	−	0.442956i	−0.805201	−	0.593003i	$-0.797942\pi$
$263$	2.97552	−	7.18354i	0.183478	−	0.442956i	0.988679	+	0.150047i	$0.0479424\pi$
$264$	−1.19769	−	0.121946i	−0.0737127	−	0.00750528i
$265$	−3.86374	+	0.768545i	−0.237347	+	0.0472113i
$266$	−11.3984	+	17.0589i	−0.698879	+	1.04595i
$267$	−4.90081	+	0.466396i	−0.299925	+	0.0285429i
$268$	−10.7613	−	10.7613i	−0.657350	−	0.657350i
$269$	6.79874	+	10.1750i	0.414527	+	0.620383i	0.978705	−	0.205270i	$-0.0658071\pi$
$269$	6.79874	+	10.1750i	0.414527	+	0.620383i	−0.564179	+	0.825653i	$0.690807\pi$
$270$	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
$275$	−1.34174	+	0.896522i	−0.0809099	+	0.0540623i
$276$	1.55745	−	2.89083i	0.0937472	−	0.174008i
$277$	−3.28766	+	16.5282i	−0.197536	+	0.993081i	0.747038	+	0.664782i	$0.231475\pi$
$277$	−3.28766	+	16.5282i	−0.197536	+	0.993081i	−0.944574	+	0.328299i	$0.893525\pi$
$278$	−0.171589	−	0.114652i	−0.0102912	−	0.00687639i
$279$	6.20789	+	6.29022i	0.371657	+	0.376586i
$280$	−1.12912	−	0.467695i	−0.0674776	−	0.0279501i
$281$	4.14660	+	1.71758i	0.247365	+	0.102462i	0.502921	−	0.864332i	$-0.332259\pi$
$281$	4.14660	+	1.71758i	0.247365	+	0.102462i	−0.255556	+	0.966794i	$0.582259\pi$
$282$	−13.4717	−	25.4048i	−0.802230	−	1.51283i
$283$	−4.58733	−	3.06516i	−0.272688	−	0.182205i	0.411706	−	0.911317i	$-0.364933\pi$
$283$	−4.58733	−	3.06516i	−0.272688	−	0.182205i	−0.684394	+	0.729112i	$0.739933\pi$
$284$	0.373632	−	1.87837i	0.0221710	−	0.111461i
$285$	16.0135	+	8.62735i	0.948561	+	0.511040i
$286$	23.9286	−	15.9886i	1.41493	−	0.945425i
$287$	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
$292$	−3.36876	−	5.04171i	−0.197142	−	0.295044i
$293$	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	$0.499320\pi$
$294$	−1.01131	−	10.6267i	−0.0589806	−	0.619759i
$295$	10.6939	−	16.0045i	0.622621	−	0.931818i
$296$	−0.797195	+	0.158572i	−0.0463360	+	0.00921681i
$297$	10.8469	−	5.66069i	0.629398	−	0.328467i
$298$	−10.8283	+	26.1419i	−0.627269	+	1.51436i
$299$	1.03513	+	5.20395i	0.0598631	+	0.300952i
$300$	0.747125	−	2.43405i	0.0431353	−	0.140530i
$301$	12.9667	+	2.57925i	0.747391	+	0.148665i
$302$	−7.21623	+	7.21623i	−0.415247	+	0.415247i
$303$	3.84325	−	4.65169i	0.220789	−	0.267233i
$304$	−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
$309$	4.20119	−	5.08492i	0.238997	−	0.289271i
$310$	−8.80924	+	8.80924i	−0.500331	+	0.500331i
$311$	−28.4123	−	5.65155i	−1.61111	−	0.320470i	−0.694268	−	0.719717i	$-0.744272\pi$
$311$	−28.4123	−	5.65155i	−1.61111	−	0.320470i	−0.916844	+	0.399247i	$0.869272\pi$
$312$	−0.900645	+	2.93421i	−0.0509890	+	0.166117i
$313$	2.17257	+	10.9222i	0.122801	+	0.617361i	0.992344	+	0.123504i	$0.0394133\pi$
$313$	2.17257	+	10.9222i	0.122801	+	0.617361i	−0.869543	+	0.493857i	$0.835587\pi$
$314$	9.34394	−	22.5583i	0.527309	−	1.27304i
$315$	12.1978	−	2.34287i	0.687266	−	0.132006i
$316$	8.36379	−	1.66366i	0.470500	−	0.0935882i
$317$	−6.07417	+	9.09064i	−0.341159	+	0.510581i	−0.961888	−	0.273445i	$-0.911837\pi$
$317$	−6.07417	+	9.09064i	−0.341159	+	0.510581i	0.620728	+	0.784026i	$0.286837\pi$
$318$	−0.633593	−	6.65770i	−0.0355301	−	0.373345i
$319$	−0.0996751	−	0.0996751i	−0.00558074	−	0.00558074i
$320$	−10.5187	−	15.7423i	−0.588012	−	0.880022i
$321$	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
$326$	−19.6736	+	13.1455i	−1.08962	+	0.728061i
$327$	−22.6455	−	12.2003i	−1.25230	−	0.674679i
$328$	0.191012	−	0.960283i	0.0105469	−	0.0530228i
$329$	−13.5145	−	9.03009i	−0.745077	−	0.497845i
$330$	8.08020	+	15.2375i	0.444800	+	0.838796i
$331$	10.9585	+	4.53916i	0.602334	+	0.249495i	0.662947	−	0.748666i	$-0.269305\pi$
$331$	10.9585	+	4.53916i	0.602334	+	0.249495i	−0.0606127	+	0.998161i	$0.519305\pi$
$332$	7.50129	+	3.10713i	0.411687	+	0.170526i
$333$	5.87951	−	5.80256i	0.322195	−	0.317978i
$334$	27.2961	+	18.2386i	1.49357	+	0.997974i
$335$	−2.87517	+	14.4545i	−0.157087	+	0.789732i
$336$	−6.04050	+	11.2120i	−0.329536	+	0.611665i
$337$	−19.3446	+	12.9256i	−1.05377	+	0.704103i	−0.956671	−	0.291172i	$-0.905955\pi$
$337$	−19.3446	+	12.9256i	−1.05377	+	0.704103i	−0.0970945	+	0.995275i	$0.530955\pi$
$338$	−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
$343$	−11.1037	−	16.6179i	−0.599543	−	0.897280i
$344$	−1.38448	−	1.38448i	−0.0746464	−	0.0746464i
$345$	−3.16557	+	0.301258i	−0.170429	+	0.0162192i
$346$	−20.5966	+	30.8250i	−1.10728	+	1.65716i
$347$	28.6483	−	5.69850i	1.53792	−	0.305912i	0.647863	−	0.761757i	$-0.275663\pi$
$347$	28.6483	−	5.69850i	1.53792	−	0.305912i	0.890059	+	0.455845i	$0.150663\pi$
$348$	0.221270	+	0.0225292i	0.0118613	+	0.00120769i
$349$	−4.16097	+	10.0455i	−0.222732	+	0.537722i	−0.995259	−	0.0972594i	$-0.968992\pi$
$349$	−4.16097	+	10.0455i	−0.222732	+	0.537722i	0.772527	+	0.634982i	$0.218992\pi$
$350$	−0.542557	−	2.72762i	−0.0290009	−	0.145797i
$351$	−8.75965	−	29.9384i	−0.467556	−	1.59800i
$352$	−18.7082	−	3.72130i	−0.997153	−	0.198346i
$353$	−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	$0.486734\pi$
$354$	25.1913	+	20.8132i	1.33890	+	1.10621i
$355$	−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	−0.00240862	−	0.999997i	$-0.500767\pi$
$359$	13.3198	−	5.51725i	0.702993	−	0.291189i	0.705402	+	0.708808i	$0.250767\pi$
$360$	−1.69478	−	0.715114i	−0.0893226	−	0.0376898i
$361$	−4.63947	+	4.63947i	−0.244183	+	0.244183i
$362$	6.99314	+	1.39102i	0.367551	+	0.0731104i
$363$	−9.03347	−	2.77280i	−0.474134	−	0.145534i
$364$	5.00722	+	25.1730i	0.262449	+	1.31942i
$365$	−2.24709	+	5.42495i	−0.117618	+	0.283955i
$366$	−1.93247	+	18.9797i	−0.101012	+	0.992085i
$367$	−34.1345	+	6.78978i	−1.78181	+	0.354424i	−0.972490	−	0.232947i	$-0.925163\pi$
$367$	−34.1345	+	6.78978i	−1.78181	+	0.354424i	−0.809318	+	0.587370i	$0.800163\pi$
$368$	1.81143	−	2.71100i	0.0944276	−	0.141321i
$369$	3.74729	+	9.21803i	0.195076	+	0.479871i
$370$	8.23406	+	8.23406i	0.428068	+	0.428068i
$371$	−2.10015	−	3.14309i	−0.109034	−	0.163181i
$372$	−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
$377$	−0.298818	+	0.199664i	−0.0153899	+	0.0102832i
$378$	1.85936	+	21.0039i	0.0956351	+	1.08032i
$379$	2.74737	−	13.8119i	0.141123	−	0.709472i	−0.843825	−	0.536619i	$-0.819701\pi$
$379$	2.74737	−	13.8119i	0.141123	−	0.709472i	0.984948	−	0.172853i	$-0.0552986\pi$
$380$	−18.7299	−	12.5149i	−0.960825	−	0.642003i
$381$	−5.38472	+	2.85543i	−0.275868	+	0.146288i
$382$	−16.1886	−	6.70552i	−0.828279	−	0.343084i
$383$	−15.0509	−	6.23429i	−0.769065	−	0.318557i	−0.0365717	−	0.999331i	$-0.511644\pi$
$383$	−15.0509	−	6.23429i	−0.769065	−	0.318557i	−0.732494	+	0.680774i	$0.761644\pi$
$384$	3.60410	−	1.91120i	0.183921	−	0.0975304i
$385$	8.10584	+	5.41615i	0.413112	+	0.276032i
$386$	−4.27466	+	21.4902i	−0.217575	+	1.09382i
$387$	19.4904	+	4.01053i	0.990755	+	0.203867i
$388$	−33.5928	+	22.4460i	−1.70542	+	1.13952i
$389$	1.24058	+	2.99501i	0.0628997	+	0.151853i	0.952204	−	0.305462i	$-0.0988110\pi$
$389$	1.24058	+	2.99501i	0.0628997	+	0.151853i	−0.889304	+	0.457316i	$0.848811\pi$
$390$	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
$394$	−28.7248	−	42.9896i	−1.44713	−	2.16579i
$395$	−5.83933	−	5.83933i	−0.293809	−	0.293809i
$396$	−14.0366	+	5.70611i	−0.705365	+	0.286743i
$397$	9.87912	−	14.7851i	0.495819	−	0.742045i	−0.496190	−	0.868214i	$-0.665268\pi$
$397$	9.87912	−	14.7851i	0.495819	−	0.742045i	0.992009	+	0.126169i	$0.0402681\pi$
$398$	−48.2987	+	9.60721i	−2.42099	+	0.481566i
$399$	−1.76802	+	17.3645i	−0.0885118	+	0.869315i
$400$	0.967485	−	2.33572i	0.0483743	−	0.116786i
$401$	−2.86708	−	14.4138i	−0.143175	−	0.719791i	−0.983955	−	0.178414i	$-0.942903\pi$
$401$	−2.86708	−	14.4138i	−0.143175	−	0.719791i	0.840780	−	0.541377i	$-0.182097\pi$
$402$	−23.9180	−	7.34155i	−1.19292	−	0.366163i
$403$	17.3450	+	3.45014i	0.864018	+	0.171864i
$404$	−5.28388	+	5.28388i	−0.262883	+	0.262883i
$405$	18.3819	−	3.40528i	0.913402	−	0.169210i
$406$	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
$411$	−17.8988	−	14.7881i	−0.882881	−	0.729441i
$412$	−5.77599	+	5.77599i	−0.284562	+	0.284562i
$413$	18.1154	+	3.60337i	0.891399	+	0.177310i
$414$	0.0355587	−	5.39820i	0.00174761	−	0.265307i
$415$	−1.53393	−	7.71158i	−0.0752976	−	0.378547i
$416$	−18.6104	+	44.9296i	−0.912452	+	2.20285i
$417$	−0.174664	−	0.0177839i	−0.00855333	−	0.000870883i
$418$	−23.7712	+	4.72840i	−1.16269	+	0.231273i
$419$	5.48388	−	8.20720i	0.267905	−	0.400948i	−0.672987	−	0.739654i	$-0.734989\pi$
$419$	5.48388	−	8.20720i	0.267905	−	0.400948i	0.940892	+	0.338706i	$0.109989\pi$
$420$	−15.3128	+	1.45727i	−0.747187	+	0.0711075i
$421$	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	$0.731721\pi$
$422$	12.4406	+	18.6187i	0.605599	+	0.906343i
$423$	−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
$428$	−7.15631	+	4.78170i	−0.345914	+	0.231132i
$429$	11.6124	−	21.5542i	0.560652	−	1.04065i
$430$	−5.47239	+	27.5115i	−0.263902	+	1.32672i
$431$	17.1107	+	11.4330i	0.824191	+	0.550707i	0.894629	−	0.446809i	$-0.147440\pi$
$431$	17.1107	+	11.4330i	0.824191	+	0.550707i	−0.0704381	+	0.997516i	$0.522440\pi$
$432$	−9.20261	+	16.8151i	−0.442761	+	0.809017i
$433$	−8.90305	−	3.68777i	−0.427853	−	0.177223i	0.158356	−	0.987382i	$-0.449381\pi$
$433$	−8.90305	−	3.68777i	−0.427853	−	0.177223i	−0.586210	+	0.810159i	$0.699381\pi$
$434$	−11.0445	−	4.57479i	−0.530153	−	0.219597i
$435$	−0.100905	−	0.190284i	−0.00483800	−	0.00912342i
$436$	26.4868	+	17.6979i	1.26849	+	0.847577i
$437$	0.871769	−	4.38268i	0.0417024	−	0.209652i
$438$	−8.77589	−	4.72804i	−0.419328	−	0.225914i
$439$	32.3786	−	21.6347i	1.54534	−	1.03257i	0.567465	−	0.823398i	$-0.307924\pi$
$439$	32.3786	−	21.6347i	1.54534	−	1.03257i	0.977880	−	0.209168i	$-0.0670757\pi$
$440$	−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
$445$	−3.28003	−	4.90892i	−0.155489	−	0.232705i
$446$	−14.4843	−	14.4843i	−0.685852	−	0.685852i
$447$	2.28060	+	23.9642i	0.107869	+	1.13347i
$448$	10.0934	−	15.1059i	0.476870	−	0.713686i
$449$	−20.7822	+	4.13384i	−0.980774	+	0.195088i	−0.659341	−	0.751844i	$-0.729165\pi$
$449$	−20.7822	+	4.13384i	−0.980774	+	0.195088i	−0.321433	+	0.946932i	$0.604165\pi$
$450$	−0.789550	−	4.11067i	−0.0372198	−	0.193779i
$451$	−2.98877	+	7.21554i	−0.140736	+	0.339766i
$452$	2.78507	+	14.0015i	0.130998	+	0.658574i
$453$	−2.54763	+	8.29989i	−0.119698	+	0.389963i
$454$	3.62631	+	0.721317i	0.170191	+	0.0338531i
$455$	17.5750	−	17.5750i	0.823927	−	0.823927i
$456$	1.64643	−	1.99277i	0.0771014	−	0.0933199i
$457$	−12.9893	+	5.38033i	−0.607612	+	0.251681i	−0.665207	−	0.746659i	$-0.731657\pi$
$457$	−12.9893	+	5.38033i	−0.607612	+	0.251681i	0.0575953	+	0.998340i	$0.481657\pi$
$458$	−3.67350			−0.171651
$459$		0			0
$460$	3.93799			0.183610
$461$	−23.3686	+	9.67958i	−1.08838	+	0.450823i	−0.853443	−	0.521187i	$-0.825489\pi$
$461$	−23.3686	+	9.67958i	−1.08838	+	0.450823i	−0.234940	+	0.972010i	$0.575489\pi$
$462$	−10.5413	+	12.7587i	−0.490427	+	0.593590i
$463$	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	$0.246107\pi$
$464$	0.216600	+	0.0430844i	0.0100554	+	0.00200014i
$465$	−3.11003	+	10.1321i	−0.144224	+	0.469866i
$466$	−0.552739	−	2.77880i	−0.0256051	−	0.128726i
$467$	−5.76357	+	13.9145i	−0.266706	+	0.643886i	−0.999324	−	0.0367542i	$-0.988298\pi$
$467$	−5.76357	+	13.9145i	−0.266706	+	0.643886i	0.732618	+	0.680640i	$0.238298\pi$
$468$	7.28670	+	37.9370i	0.336828	+	1.75364i
$469$	−13.8701	+	2.75894i	−0.640462	+	0.127396i
$470$	19.1591	−	28.6737i	0.883745	−	1.32262i
$471$	−1.96797	−	20.6791i	−0.0906792	−	0.952843i
$472$	−1.93421	−	1.93421i	−0.0890293	−	0.0890293i
$473$	8.67701	+	12.9861i	0.398969	+	0.597100i
$474$	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
$479$	−8.39525	+	5.60953i	−0.383589	+	0.256306i	−0.732382	−	0.680894i	$-0.761592\pi$
$479$	−8.39525	+	5.60953i	−0.383589	+	0.256306i	0.348793	+	0.937200i	$0.386592\pi$
$480$	−25.6584	−	13.8236i	−1.17114	−	0.630956i
$481$	3.22487	−	16.2125i	0.147042	−	0.739228i
$482$	−29.3281	−	19.5964i	−1.33586	−	0.892591i
$483$	−1.42951	−	2.69574i	−0.0650450	−	0.122661i
$484$	10.8115	+	4.47827i	0.491432	+	0.203558i
$485$	36.1464	+	14.9723i	1.64132	+	0.679858i
$486$	2.59025	+	31.6310i	0.117496	+	1.43481i
$487$	3.66950	+	2.45188i	0.166281	+	0.111105i	0.635926	−	0.771750i	$-0.280618\pi$
$487$	3.66950	+	2.45188i	0.166281	+	0.111105i	−0.469645	+	0.882855i	$0.655618\pi$
$488$	0.311559	−	1.56631i	0.0141036	−	0.0709036i
$489$	−9.54747	+	17.7214i	−0.431752	+	0.801390i
$490$	10.6442	−	7.11225i	0.480858	−	0.321299i
$491$	−14.6134	−	35.2798i	−0.659492	−	1.59216i	−0.798589	−	0.601877i	$-0.794420\pi$
$491$	−14.6134	−	35.2798i	−0.659492	−	1.59216i	0.139096	−	0.990279i	$-0.455580\pi$
$492$	−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
$496$	−6.03761	−	9.03592i	−0.271097	−	0.405725i
$497$	−1.25840	−	1.25840i	−0.0564471	−	0.0564471i
$498$	13.2880	−	1.26458i	0.595450	−	0.0566672i
$499$	7.24621	−	10.8447i	0.324385	−	0.485477i	−0.633056	−	0.774106i	$-0.718200\pi$
$499$	7.24621	−	10.8447i	0.324385	−	0.485477i	0.957441	+	0.288630i	$0.0931996\pi$
$500$	24.8444	−	4.94186i	1.11108	−	0.221007i
$501$	27.7852	+	2.82903i	1.24135	+	0.126392i
$502$	17.3098	−	41.7895i	0.772573	−	1.86516i
$503$	0.728223	+	3.66103i	0.0324699	+	0.163237i	0.993618	−	0.112795i	$-0.0359804\pi$
$503$	0.728223	+	3.66103i	0.0324699	+	0.163237i	−0.961148	+	0.276032i	$0.910980\pi$
$504$	0.0116268	−	1.76507i	0.000517897	−	0.0786223i
$505$	7.09726	+	1.41173i	0.315824	+	0.0628213i
$506$	2.99604	−	2.99604i	0.133190	−	0.133190i
$507$	−30.7627	−	25.4163i	−1.36622	−	1.12878i
$508$	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
$513$	−2.83317	+	26.1175i	−0.125088	+	1.15312i
$514$	25.7582	−	25.7582i	1.13615	−	1.13615i
$515$	7.75825	+	1.54321i	0.341870	+	0.0680021i
$516$	−23.5581	−	7.23107i	−1.03709	−	0.318330i
$517$	−3.74596	−	18.8322i	−0.164747	−	0.828239i
$518$	−4.27608	+	10.3234i	−0.187880	+	0.453583i
$519$	−3.19478	+	31.3773i	−0.140235	+	1.37731i
$520$	−3.61019	+	0.718111i	−0.158317	+	0.0314912i
$521$	−9.04943	+	13.5434i	−0.396463	+	0.593348i	−0.974972	−	0.222328i	$-0.928635\pi$
$521$	−9.04943	+	13.5434i	−0.396463	+	0.593348i	0.578509	+	0.815676i	$0.303635\pi$
$522$	0.338726	−	0.137698i	0.0148256	−	0.00602687i
$523$	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	$0.622324\pi$
$524$	24.4980	+	36.6639i	1.07020	+	1.60167i
$525$	−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
$530$	6.66871	−	4.45589i	0.289670	−	0.193551i
$531$	27.2294	+	5.60297i	1.18165	+	0.243148i
$532$	4.21700	−	21.2003i	0.182830	−	0.919148i
$533$	16.5561	+	11.0624i	0.717124	+	0.479167i
$534$	8.85480	−	4.69556i	0.383185	−	0.203197i
$535$	7.70029	+	3.18957i	0.332913	+	0.137897i
$536$	1.93494	+	0.801478i	0.0835766	+	0.0346186i
$537$	29.4207	−	15.6013i	1.26960	−	0.673247i
$538$	−20.7156	−	13.8417i	−0.893113	−	0.596759i
$539$	1.39057	−	6.99088i	0.0598962	−	0.301119i
$540$	−23.0614	+	2.04150i	−0.992405	+	0.0878521i
$541$	−23.5252	+	15.7191i	−1.01143	+	0.675815i	−0.946710	−	0.322089i	$-0.895615\pi$
$541$	−23.5252	+	15.7191i	−1.01143	+	0.675815i	−0.0647190	+	0.997904i	$0.520615\pi$
$542$	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
$547$	17.7662	+	26.5890i	0.759629	+	1.13687i	0.986631	+	0.162971i	$0.0521078\pi$
$547$	17.7662	+	26.5890i	0.759629	+	1.13687i	−0.227001	+	0.973894i	$0.572892\pi$
$548$	20.3313	+	20.3313i	0.868510	+	0.868510i
$549$	6.11218	+	15.0355i	0.260861	+	0.641698i
$550$	1.82525	−	2.73168i	0.0778290	−	0.116479i
$551$	0.296852	−	0.0590476i	0.0126463	−	0.00251551i
$552$	−0.0457739	+	0.449566i	−0.00194827	+	0.0191348i
$553$	3.03246	−	7.32101i	0.128953	−	0.311321i
$554$	−6.69342	−	33.6501i	−0.284376	−	1.42966i
$555$	9.47057	+	2.90696i	0.402003	+	0.123394i
$556$	0.213246	+	0.0424173i	0.00904365	+	0.00179889i
$557$	−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	$0.296493\pi$
$558$	−16.5775	−	6.99492i	−0.701783	−	0.296119i
$559$	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	−0.598082	−	0.801435i	$-0.704070\pi$
$563$	−10.7792	+	4.46490i	−0.454290	+	0.188173i	0.143792	+	0.989608i	$0.454070\pi$
$564$	23.3558	+	19.2967i	0.983456	+	0.812537i
$565$	9.77538	−	9.77538i	0.411253	−	0.411253i
$566$	11.0166	+	2.19135i	0.463064	+	0.0921092i
$567$	9.76892	+	15.0456i	0.410256	+	0.631856i
$568$	0.0514182	+	0.258497i	0.00215746	+	0.0108463i
$569$	16.5175	−	39.8769i	0.692452	−	1.67173i	−0.0473304	−	0.998879i	$-0.515071\pi$
$569$	16.5175	−	39.8769i	0.692452	−	1.67173i	0.739782	−	0.672847i	$-0.234929\pi$
$570$	−36.8424	−	3.75121i	−1.54316	−	0.157121i
$571$	9.09986	−	1.81007i	0.380817	−	0.0757493i	−0.000969942	−	1.00000i	$-0.500309\pi$
$571$	9.09986	−	1.81007i	0.380817	−	0.0757493i	0.381787	+	0.924250i	$0.375309\pi$
$572$	−16.8451	+	25.2105i	−0.704329	+	1.05410i
$573$	−14.8400	+	1.41228i	−0.619950	+	0.0589988i
$574$	−9.51757	−	9.51757i	−0.397256	−	0.397256i
$575$	0.336520	+	0.503637i	0.0140338	+	0.0210031i
$576$	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
$581$	6.27326	−	4.19166i	0.260259	−	0.173899i
$582$	−31.5028	+	58.4736i	−1.30583	+	2.42381i
$583$	0.871206	−	4.37985i	0.0360817	−	0.181395i
$584$	0.693826	+	0.463600i	0.0287107	+	0.0191839i
$585$	26.6260	−	26.2775i	1.10085	−	1.08644i
$586$	−45.6302	−	18.9006i	−1.88497	−	0.780778i
$587$	26.6989	+	11.0590i	1.10198	+	0.456455i	0.858169	−	0.513367i	$-0.171602\pi$
$587$	26.6989	+	11.0590i	1.10198	+	0.456455i	0.243812	+	0.969823i	$0.421602\pi$
$588$	5.26888	+	9.93595i	0.217285	+	0.409752i
$589$	−12.3838	−	8.27460i	−0.510266	−	0.340949i
$590$	−7.64527	+	38.4354i	−0.314751	+	1.58236i
$591$	−38.7239	−	20.8626i	−1.59289	−	0.858173i
$592$	−8.44594	+	5.64340i	−0.347126	+	0.231942i
$593$	15.8785	+	38.3341i	0.652052	+	1.57419i	0.809795	+	0.586712i	$0.199578\pi$
$593$	15.8785	+	38.3341i	0.652052	+	1.57419i	−0.157744	+	0.987480i	$0.550422\pi$
$594$	−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
$598$	−6.00150	−	8.98188i	−0.245419	−	0.367296i
$599$	−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	$0.968417\pi$
$600$	0.0331958	+	0.348816i	0.00135521	+	0.0142404i
$601$	3.23917	−	4.84775i	0.132128	−	0.197744i	−0.759506	−	0.650500i	$-0.774559\pi$
$601$	3.23917	−	4.84775i	0.132128	−	0.197744i	0.891634	+	0.452756i	$0.149559\pi$
$602$	−26.3993	+	5.25115i	−1.07596	+	0.214021i
$603$	−20.9030	+	4.01491i	−0.851236	+	0.163500i
$604$	4.11461	−	9.93354i	0.167421	−	0.404190i
$605$	−2.21083	−	11.1146i	−0.0898830	−	0.451873i
$606$	−3.60476	+	11.7439i	−0.146434	+	0.477065i
$607$	−32.9476	−	6.55369i	−1.33730	−	0.266006i	−0.525927	−	0.850530i	$-0.676281\pi$
$607$	−32.9476	−	6.55369i	−1.33730	−	0.266006i	−0.811377	+	0.584524i	$0.801281\pi$
$608$	28.9607	−	28.9607i	1.17451	−	1.17451i
$609$	0.131639	−	0.159329i	0.00533427	−	0.00645635i
$610$	−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
$615$	−7.60078	+	9.19962i	−0.306493	+	0.370964i
$616$	0.979626	−	0.979626i	0.0394702	−	0.0394702i
$617$	−33.4612	−	6.65584i	−1.34710	−	0.267954i	−0.531737	−	0.846910i	$-0.678460\pi$
$617$	−33.4612	−	6.65584i	−1.34710	−	0.267954i	−0.815359	+	0.578956i	$0.803460\pi$
$618$	−3.94049	+	12.8377i	−0.158510	+	0.516407i
$619$	2.31092	+	11.6178i	0.0928839	+	0.466959i	0.999032	+	0.0439976i	$0.0140094\pi$
$619$	2.31092	+	11.6178i	0.0928839	+	0.466959i	−0.906148	+	0.422961i	$0.860991\pi$
$620$	5.02292	−	12.1264i	0.201725	−	0.487008i
$621$	−2.12480	−	4.07149i	−0.0852655	−	0.163383i
$622$	57.8452	−	11.5061i	2.31938	−	0.461354i
$623$	3.14743	−	4.71046i	0.126099	−	0.188721i
$624$	3.63397	+	38.1852i	0.145475	+	1.52863i
$625$	−14.9226	−	14.9226i	−0.596903	−	0.596903i
$626$	−12.5962	−	18.8515i	−0.503444	−	0.753457i
$627$	−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	$-0.897710\pi$
$631$	−12.5910	−	30.3974i	−0.501240	−	1.21010i	0.447568	−	0.894250i	$-0.352290\pi$
$632$	−0.975771	+	0.651990i	−0.0388141	+	0.0259348i
$633$	16.7712	+	9.03552i	0.666594	+	0.359130i
$634$	4.34256	−	21.8315i	0.172465	−	0.867040i
$635$	−6.07759	−	4.06092i	−0.241182	−	0.161153i
$636$	3.30100	+	6.22496i	0.130893	+	0.246836i
$637$	−16.7893	−	6.95434i	−0.665215	−	0.275541i
$638$	0.265142	+	0.109825i	0.0104971	+	0.00434803i
$639$	−1.88152	−	1.90648i	−0.0744319	−	0.0754190i
$640$	4.06785	+	2.71805i	0.160796	+	0.107441i
$641$	4.61604	−	23.2064i	0.182322	−	0.916597i	−0.775962	−	0.630780i	$-0.782735\pi$
$641$	4.61604	−	23.2064i	0.182322	−	0.916597i	0.958284	−	0.285817i	$-0.0922649\pi$
$642$	−6.71108	+	12.4567i	−0.264865	+	0.491626i
$643$	37.0269	−	24.7406i	1.46020	−	0.975672i	0.464253	−	0.885703i	$-0.346323\pi$
$643$	37.0269	−	24.7406i	1.46020	−	0.975672i	0.995945	−	0.0899696i	$-0.0286770\pi$
$644$	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
$649$	12.1223	+	18.1424i	0.475843	+	0.712150i
$650$	−5.92280	−	5.92280i	−0.232311	−	0.232311i
$651$	−10.1245	+	0.963515i	−0.396809	+	0.0377631i
$652$	13.8497	−	20.7275i	0.542395	−	0.811752i
$653$	19.1428	−	3.80775i	0.749117	−	0.149009i	0.194255	−	0.980951i	$-0.437771\pi$
$653$	19.1428	−	3.80775i	0.749117	−	0.149009i	0.554862	+	0.831943i	$0.312771\pi$
$654$	52.1004	+	5.30476i	2.03729	+	0.207432i
$655$	16.3411	−	39.4508i	0.638498	−	1.54147i
$656$	−2.38711	−	12.0008i	−0.0932009	−	0.468552i
$657$	−8.48044	−	0.0558619i	−0.330853	−	0.00217938i
$658$	32.4555	+	6.45581i	1.26525	+	0.251673i
$659$	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	$0.165344\pi$
$660$	−14.0085	−	11.5739i	−0.545282	−	0.450515i
$661$	3.15244	−	1.30578i	0.122616	−	0.0507890i	−0.320532	−	0.947238i	$-0.603862\pi$
$661$	3.15244	−	1.30578i	0.122616	−	0.0507890i	0.443148	+	0.896449i	$0.353862\pi$
$662$	−24.1489			−0.938575
$663$		0			0
$664$	−1.11736			−0.0433620
$665$	−19.3389	+	8.01043i	−0.749930	+	0.310631i
$666$	−6.53820	+	15.4951i	−0.253350	+	0.600424i
$667$	−0.0374142	+	0.0374142i	−0.00144868	+	0.00144868i
$668$	−33.9228	−	6.74765i	−1.31251	−	0.261075i
$669$	−16.6594	−	5.11356i	−0.644091	−	0.197702i
$670$	−5.85363	−	29.4282i	−0.226146	−	1.13691i
$671$	−4.87497	+	11.7692i	−0.188196	+	0.454346i
$672$	2.83289	−	27.8231i	0.109281	−	1.07330i
$673$	−10.7113	+	2.13061i	−0.412890	+	0.0821289i	−0.397165	−	0.917747i	$-0.630006\pi$
$673$	−10.7113	+	2.13061i	−0.412890	+	0.0821289i	−0.0157255	+	0.999876i	$0.505006\pi$
$674$	26.3156	−	39.3841i	1.01364	−	1.51702i
$675$	−2.23180	−	2.77492i	−0.0859019	−	0.106807i
$676$	34.9435	+	34.9435i	1.34398	+	1.34398i
$677$	8.78236	+	13.1437i	0.337533	+	0.505154i	0.960945	−	0.276739i	$-0.0892539\pi$
$677$	8.78236	+	13.1437i	0.337533	+	0.505154i	−0.623412	+	0.781894i	$0.714254\pi$
$678$	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
$683$	−23.8160	+	15.9134i	−0.911295	+	0.608908i	−0.920369	−	0.391051i	$-0.872112\pi$
$683$	−23.8160	+	15.9134i	−0.911295	+	0.608908i	0.00907414	+	0.999959i	$0.497112\pi$
$684$	6.55711	−	31.8663i	0.250717	−	1.21844i
$685$	5.43206	−	27.3088i	0.207549	−	1.04342i
$686$	33.8327	+	22.6063i	1.29174	+	0.863112i
$687$	−2.76103	+	1.46413i	−0.105340	+	0.0558600i
$688$	−22.6063	−	9.36383i	−0.861857	−	0.356993i
$689$	−10.5186	−	4.35695i	−0.400727	−	0.165987i
$690$	5.71956	−	3.03299i	0.217740	−	0.115464i
$691$	19.3217	+	12.9103i	0.735032	+	0.491133i	0.865869	−	0.500271i	$-0.166766\pi$
$691$	19.3217	+	12.9103i	0.735032	+	0.491133i	−0.130837	+	0.991404i	$0.541766\pi$
$692$	7.62001	−	38.3084i	0.289669	−	1.45627i
$693$	−2.83775	+	13.7909i	−0.107797	+	0.523874i
$694$	−49.4462	+	33.0389i	−1.87695	+	1.25414i
$695$	−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
$700$	1.62784	+	2.43624i	0.0615266	+	0.0920811i
$701$	−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	$0.865402\pi$
$702$	39.8019	+	49.4879i	1.50223	+	1.86780i
$703$	−7.73433	+	11.5752i	−0.291706	+	0.436568i
$704$	21.0498	−	4.18706i	0.793344	−	0.157806i
$705$	2.97181	−	29.1875i	0.111925	−	1.09926i
$706$	19.8211	−	47.8524i	0.745977	−	1.80095i
$707$	1.35466	+	6.81034i	0.0509472	+	0.256129i
$708$	−32.9121	−	10.1023i	−1.23691	−	0.379666i
$709$	19.7635	+	3.93121i	0.742235	+	0.147640i	0.551702	−	0.834041i	$-0.313978\pi$
$709$	19.7635	+	3.93121i	0.742235	+	0.147640i	0.190533	+	0.981681i	$0.438978\pi$
$710$	2.66995	−	2.66995i	0.100202	−	0.100202i
$711$	4.63669	−	10.9887i	0.173889	−	0.412107i
$712$	−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
$717$	−10.6960	−	8.83706i	−0.399448	−	0.330026i
$718$	−20.7553	+	20.7553i	−0.774582	+	0.774582i
$719$	−25.0780	−	4.98832i	−0.935252	−	0.186033i	−0.296138	−	0.955145i	$-0.595699\pi$
$719$	−25.0780	−	4.98832i	−0.935252	−	0.186033i	−0.639114	+	0.769112i	$0.720699\pi$
$720$	−22.9876	−	0.151423i	−0.856699	−	0.00564320i
$721$	1.48082	+	7.44460i	0.0551488	+	0.277252i
$722$	5.11193	−	12.3413i	0.190246	−	0.459295i
$723$	−29.8536	−	3.03963i	−1.11027	−	0.113045i
$724$	−7.36776	+	1.46554i	−0.273821	+	0.0544663i
$725$	−0.0227935	+	0.0341129i	−0.000846530	+	0.00126692i
$726$	19.1518	−	1.82262i	0.710791	−	0.0676438i
$727$	−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	$0.903056\pi$
$728$	−1.96233	−	2.93684i	−0.0727288	−	0.108846i
$729$	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	$0.226407\pi$
$733$	18.5044	+	44.6736i	0.683476	+	1.65006i	−0.0740508	+	0.997254i	$0.523593\pi$
$734$	58.9153	−	39.3659i	2.17460	−	1.45302i
$735$	5.16558	−	9.58803i	0.190535	−	0.353660i
$736$	−1.39683	+	7.02235i	−0.0514879	+	0.258847i
$737$	−13.8908	−	9.28151i	−0.511673	−	0.341889i
$738$	−14.2304	−	14.4191i	−0.523827	−	0.530774i
$739$	18.8828	+	7.82153i	0.694617	+	0.287720i	0.701922	−	0.712254i	$-0.252325\pi$
$739$	18.8828	+	7.82153i	0.694617	+	0.287720i	−0.00730558	+	0.999973i	$0.502325\pi$
$740$	−11.3346	−	4.69496i	−0.416669	−	0.172590i
$741$	24.6283	+	46.4437i	0.904744	+	1.70615i
$742$	6.39910	+	4.27574i	0.234918	+	0.156968i
$743$	9.42343	−	47.3748i	0.345712	−	1.73801i	−0.281861	−	0.959455i	$-0.590952\pi$
$743$	9.42343	−	47.3748i	0.345712	−	1.73801i	0.627573	−	0.778558i	$-0.284048\pi$
$744$	1.32598	+	0.714378i	0.0486129	+	0.0261904i
$745$	−24.0038	+	16.0389i	−0.879433	+	0.587618i
$746$	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
$751$	−6.36250	−	9.52215i	−0.232171	−	0.347468i	0.697031	−	0.717041i	$-0.254504\pi$
$751$	−6.36250	−	9.52215i	−0.232171	−	0.347468i	−0.929202	+	0.369573i	$0.879504\pi$
$752$	21.2713	+	21.2713i	0.775686	+	0.775686i
$753$	−3.64568	−	38.3083i	−0.132856	−	1.39603i
$754$	0.406500	−	0.608370i	0.0148039	−	0.0221555i
$755$	−10.2120	+	2.03130i	−0.371653	+	0.0739264i
$756$	−10.2783	−	19.6950i	−0.373818	−	0.716299i
$757$	−13.3441	+	32.2155i	−0.484999	+	1.17089i	0.472207	+	0.881488i	$0.343457\pi$
$757$	−13.3441	+	32.2155i	−0.484999	+	1.17089i	−0.957207	+	0.289405i	$0.906543\pi$
$758$	5.59343	+	28.1201i	0.203163	+	1.02137i
$759$	1.05773	−	3.44596i	0.0383930	−	0.125080i
$760$	3.04044	+	0.604781i	0.110288	+	0.0219377i
$761$	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	$0.0881789\pi$
$762$	7.90368	−	9.56624i	0.286320	−	0.346548i
$763$	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
$768$	14.8209	−	17.9386i	0.534805	−	0.647303i
$769$	−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	$0.275363\pi$
$770$	−19.4665	−	3.87212i	−0.701523	−	0.139542i
$771$	9.09372	−	29.6264i	0.327502	−	1.06697i
$772$	−4.50366	−	22.6414i	−0.162090	−	0.814882i
$773$	−10.5772	+	25.5356i	−0.380436	+	0.918453i	0.611446	+	0.791286i	$0.290588\pi$
$773$	−10.5772	+	25.5356i	−0.380436	+	0.918453i	−0.991881	+	0.127167i	$0.959412\pi$
$774$	−39.7852	+	7.64168i	−1.43005	+	0.274675i
$775$	1.98010	−	0.393867i	0.0711274	−	0.0141481i
$776$	3.08896	−	4.62295i	0.110887	−	0.165954i
$777$	0.900604	+	9.46341i	0.0323090	+	0.339498i
$778$	−4.66692	−	4.66692i	−0.167317	−	0.167317i
$779$	−9.31659	−	13.9433i	−0.333802	−	0.499569i
$780$	−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
$785$	20.7133	−	13.8402i	0.739289	−	0.493977i
$786$	63.8192	+	34.3828i	2.27636	+	1.22639i
$787$	−6.32596	+	31.8028i	−0.225496	+	1.13365i	0.687659	+	0.726034i	$0.258638\pi$
$787$	−6.32596	+	31.8028i	−0.225496	+	1.13365i	−0.913155	+	0.407612i	$0.866362\pi$
$788$	45.2926	+	30.2635i	1.61348	+	1.07809i
$789$	6.30933	+	11.8980i	0.224618	+	0.423581i
$790$	15.5330	+	6.43398i	0.552639	+	0.228911i
$791$	12.2558	+	5.07652i	0.435766	+	0.180500i
$792$	1.48413	−	1.46470i	0.0527362	−	0.0520460i
$793$	27.0045	+	18.0439i	0.958960	+	0.640756i
$794$	−7.06280	+	35.5071i	−0.250649	+	1.26010i
$795$	3.23628	−	6.00698i	0.114779	−	0.213046i
$796$	43.1391	−	28.8246i	1.52903	−	1.02166i
$797$	−12.9695	−	31.3112i	−0.459404	−	1.10910i	−0.968639	−	0.248472i	$-0.920072\pi$
$797$	−12.9695	−	31.3112i	−0.459404	−	1.10910i	0.509235	−	0.860627i	$-0.329928\pi$
$798$	−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
$802$	16.6228	+	24.8778i	0.586973	+	0.878467i
$803$	−4.70671	−	4.70671i	−0.166096	−	0.166096i
$804$	26.2411	−	2.49729i	0.925452	−	0.0880725i
$805$	2.03301	−	3.04262i	0.0716542	−	0.107238i
$806$	−35.3132	+	7.02423i	−1.24385	+	0.247418i
$807$	−21.0868	−	2.14702i	−0.742291	−	0.0755785i
$808$	0.393532	−	0.950071i	0.0138444	−	0.0334234i
$809$	3.43987	+	17.2934i	0.120939	+	0.608004i	0.992952	+	0.118520i	$0.0378149\pi$
$809$	3.43987	+	17.2934i	0.120939	+	0.608004i	−0.872012	+	0.489484i	$0.837185\pi$
$810$	−31.9222	+	20.7267i	−1.12163	+	0.728263i
$811$	2.34514	+	0.466478i	0.0823490	+	0.0163802i	0.236093	−	0.971730i	$-0.424133\pi$
$811$	2.34514	+	0.466478i	0.0823490	+	0.0163802i	−0.153744	+	0.988111i	$0.549133\pi$
$812$	−0.180983	+	0.180983i	−0.00635126	+	0.00635126i
$813$	1.79941	+	1.48668i	0.0631080	+	0.0521402i
$814$	−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
$819$	33.0732	+	13.9553i	1.15567	+	0.487638i
$820$	10.4499	−	10.4499i	0.364926	−	0.364926i
$821$	45.7670	+	9.10361i	1.59728	+	0.317718i	0.911882	−	0.410453i	$-0.134629\pi$
$821$	45.7670	+	9.10361i	1.59728	+	0.317718i	0.685396	+	0.728171i	$0.259629\pi$
$822$	45.1883	+	13.8704i	1.57612	+	0.483786i
$823$	9.41661	+	47.3405i	0.328242	+	1.65019i	0.694368	+	0.719620i	$0.255684\pi$
$823$	9.41661	+	47.3405i	0.328242	+	1.65019i	−0.366125	+	0.930566i	$0.619316\pi$
$824$	0.430183	−	1.03855i	0.0149861	−	0.0361797i
$825$	0.283118	−	2.78063i	0.00985690	−	0.0968091i
$826$	−36.8815	+	7.33619i	−1.28327	+	0.255259i
$827$	17.9442	−	26.8554i	0.623982	−	0.933855i	−0.375992	−	0.926623i	$-0.622698\pi$
$827$	17.9442	−	26.8554i	0.623982	−	0.933855i	0.999974	−	0.00723238i	$-0.00230216\pi$
$828$	2.14185	+	5.26879i	0.0744346	+	0.183103i
$829$	−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	$0.771617\pi$
$830$	8.89345	+	13.3100i	0.308696	+	0.461996i
$831$	−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
$836$	21.2319	−	14.1867i	0.734319	−	0.490656i
$837$	−15.2477	+	1.34979i	−0.527038	+	0.0466557i
$838$	−3.92054	+	19.7099i	−0.135433	+	0.680867i
$839$	15.4135	+	10.2990i	0.532134	+	0.355561i	0.792425	−	0.609970i	$-0.208818\pi$
$839$	15.4135	+	10.2990i	0.532134	+	0.355561i	−0.260291	+	0.965530i	$0.583818\pi$
$840$	1.87015	−	0.991708i	0.0645262	−	0.0342172i
$841$	26.7892	+	11.0964i	0.923765	+	0.382636i
$842$	−4.43018	−	1.83504i	−0.152674	−	0.0632396i
$843$	−6.86797	+	3.64197i	−0.236545	+	0.125436i
$844$	−19.6161	−	13.1070i	−0.675213	−	0.451163i
$845$	9.33610	−	46.9357i	0.321172	−	1.61464i
$846$	48.7842	+	10.0383i	1.67724	+	0.345123i
$847$	9.04157	−	6.04138i	0.310672	−	0.207584i
$848$	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
$853$	−20.6014	−	30.8322i	−0.705378	−	1.05567i	−0.995130	−	0.0985712i	$-0.968573\pi$
$853$	−20.6014	−	30.8322i	−0.705378	−	1.05567i	0.289752	−	0.957102i	$-0.406427\pi$
$854$	−15.5241	−	15.5241i	−0.531222	−	0.531222i
$855$	−29.1860	+	11.8646i	−0.998142	+	0.405762i
$856$	0.658043	−	0.984832i	0.0224915	−	0.0336609i
$857$	48.2422	−	9.59597i	1.64792	−	0.327792i	0.718139	−	0.695900i	$-0.244994\pi$
$857$	48.2422	−	9.59597i	1.64792	−	0.327792i	0.929783	+	0.368108i	$0.119994\pi$
$858$	−5.04913	+	49.5898i	−0.172375	+	1.69297i
$859$	−10.7823	+	26.0307i	−0.367887	+	0.888157i	0.626209	+	0.779655i	$0.284605\pi$
$859$	−10.7823	+	26.0307i	−0.367887	+	0.888157i	−0.994096	+	0.108502i	$0.965395\pi$
$860$	−5.76554	−	28.9853i	−0.196603	−	0.988392i
$861$	−10.9468	−	3.36009i	−0.373067	−	0.114512i
$862$	−41.0919	−	8.17368i	−1.39959	−	0.278397i
$863$	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	$0.211031\pi$
$864$	4.53958	−	41.8480i	0.154440	−	1.42370i
$865$	−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
$870$	0.338049	+	0.279298i	0.0114609	+	0.00946909i
$871$	−30.1178	+	30.1178i	−1.02050	+	1.02050i
$872$	−4.29962	−	0.855247i	−0.145603	−	0.0289623i
$873$	−0.372207	+	56.5050i	−0.0125973	+	1.91240i
$874$	1.77486	+	8.92281i	0.0600354	+	0.301818i
$875$	9.00784	−	21.7469i	0.304521	−	0.735178i
$876$	10.4485	+	1.06384i	0.353021	+	0.0359439i
$877$	−23.3238	+	4.63939i	−0.787588	+	0.156661i	−0.572469	−	0.819927i	$-0.694014\pi$
$877$	−23.3238	+	4.63939i	−0.787588	+	0.156661i	−0.215120	+	0.976588i	$0.569014\pi$
$878$	−44.0465	+	65.9203i	−1.48650	+	2.22470i
$879$	−41.8290	+	3.98074i	−1.41086	+	0.134267i
$880$	−12.7583	−	12.7583i	−0.430083	−	0.430083i
$881$	−10.9801	−	16.4329i	−0.369930	−	0.553639i	0.599071	−	0.800696i	$-0.295537\pi$
$881$	−10.9801	−	16.4329i	−0.369930	−	0.553639i	−0.969001	+	0.247056i	$0.920537\pi$
$882$	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
$887$	3.55045	−	2.37234i	0.119213	−	0.0796553i	−0.494535	−	0.869158i	$-0.664661\pi$
$887$	3.55045	−	2.37234i	0.119213	−	0.0796553i	0.613747	+	0.789503i	$0.289661\pi$
$888$	0.667734	−	1.23941i	0.0224077	−	0.0415917i
$889$	1.36835	−	6.87918i	0.0458931	−	0.230720i
$890$	9.99419	+	6.67790i	0.335006	+	0.223844i
$891$	−4.40777	+	20.7284i	−0.147666	+	0.694426i
$892$	19.9385	+	8.25878i	0.667589	+	0.276525i
$893$	38.0897	+	15.7773i	1.27462	+	0.527966i
$894$	−22.9606	−	43.2986i	−0.767916	−	1.44812i
$895$	33.2064	+	22.1878i	1.10997	+	0.741656i
$896$	−0.915867	+	4.60437i	−0.0305970	+	0.153821i
$897$	−8.09062	−	4.35885i	−0.270138	−	0.145538i
$898$	35.8696	−	23.9673i	1.19698	−	0.799799i
$899$	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
$904$	−1.09147	−	1.63350i	−0.0363017	−	0.0543293i
$905$	5.14393	+	5.14393i	0.170990	+	0.170990i
$906$	−1.67461	−	17.5966i	−0.0556353	−	0.584607i
$907$	−30.0777	+	45.0145i	−0.998715	+	1.49468i	−0.134910	+	0.990858i	$0.543074\pi$
$907$	−30.0777	+	45.0145i	−0.998715	+	1.49468i	−0.863806	+	0.503825i	$0.831926\pi$
$908$	−3.82057	+	0.759958i	−0.126790	+	0.0252201i
$909$	1.97136	+	10.2635i	0.0653857	+	0.340420i
$910$	−19.3647	+	46.7505i	−0.641934	+	1.54977i
$911$	−10.7023	−	53.8041i	−0.354583	−	1.78261i	−0.586577	−	0.809893i	$-0.699525\pi$
$911$	−10.7023	−	53.8041i	−0.354583	−	1.78261i	0.231994	−	0.972717i	$-0.425475\pi$
$912$	9.47920	−	30.8822i	0.313888	−	1.02261i
$913$	8.74168	+	1.73883i	0.289307	+	0.0575468i
$914$	20.2402	−	20.2402i	0.669488	−	0.669488i
$915$	−12.3976	+	15.0054i	−0.409851	+	0.496065i
$916$	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
$921$	23.7978	−	28.8037i	0.784164	−	0.949115i
$922$	36.4136	−	36.4136i	1.19922	−	1.19922i
$923$	−5.25704	−	1.04569i	−0.173037	−	0.0344193i
$924$	5.11652	−	16.6691i	0.168321	−	0.548372i
$925$	−0.368150	−	1.85082i	−0.0121047	−	0.0608544i
$926$	−0.410037	+	0.989916i	−0.0134746	+	0.0325307i
$927$	2.15495	+	11.2194i	0.0707780	+	0.368494i
$928$	−0.475645	+	0.0946117i	−0.0156138	+	0.00310578i
$929$	−4.95694	+	7.41858i	−0.162632	+	0.243396i	−0.903831	−	0.427889i	$-0.859257\pi$
$929$	−4.95694	+	7.41858i	−0.162632	+	0.243396i	0.741199	+	0.671285i	$0.234257\pi$
$930$	−2.04429	−	21.4811i	−0.0670349	−	0.704393i
$931$	10.8220	+	10.8220i	0.354677	+	0.354677i
$932$	1.65839	+	2.48195i	0.0543223	+	0.0812991i
$933$	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	0.999781	−	0.0209128i	$-0.00665724\pi$
$937$	8.51098	+	20.5473i	0.278042	+	0.671252i	−0.721740	+	0.692165i	$0.756657\pi$
$938$	23.9394	−	15.9958i	0.781650	−	0.522282i
$939$	−16.9809	−	9.14851i	−0.554150	−	0.298550i
$940$	−7.08820	+	35.6348i	−0.231192	+	1.16228i
$941$	−33.0806	−	22.1038i	−1.07840	−	0.720563i	−0.116286	−	0.993216i	$-0.537099\pi$
$941$	−33.0806	−	22.1038i	−1.07840	−	0.720563i	−0.962112	+	0.272653i	$0.912099\pi$
$942$	19.8130	+	37.3631i	0.645544	+	1.21735i
$943$	2.70843	+	1.12187i	0.0881987	+	0.0365331i
$944$	−31.5824	−	13.0819i	−1.02792	−	0.425778i
$945$	−10.3283	+	18.8719i	−0.335979	+	0.613904i
$946$	−26.4386	−	17.6657i	−0.859594	−	0.574363i
$947$	−1.22705	+	6.16877i	−0.0398736	+	0.200458i	−0.995587	−	0.0938399i	$-0.970086\pi$
$947$	−1.22705	+	6.16877i	−0.0398736	+	0.200458i	0.955714	+	0.294298i	$0.0950858\pi$
$948$	−7.00554	+	13.0033i	−0.227529	+	0.422326i
$949$	−14.1103	+	9.42821i	−0.458040	+	0.306053i
$950$	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
$955$	−9.93218	−	14.8646i	−0.321398	−	0.481006i
$956$	12.1496	+	12.1496i	0.392946	+	0.392946i
$957$	0.243055	−	0.0231308i	0.00785685	−	0.000747713i
$958$	11.4206	−	17.0921i	0.368982	−	0.552221i
$959$	26.2048	−	5.21246i	0.846197	−	0.168319i
$960$	32.6245	+	3.32176i	1.05295	+	0.107209i
$961$	−8.54214	+	20.6226i	−0.275553	+	0.665244i
$962$	6.56560	+	33.0075i	0.211683	+	1.06420i
$963$	−0.0792916	+	12.0373i	−0.00255513	+	0.387897i
$964$	36.4480	+	7.24997i	1.17391	+	0.233506i
$965$	−15.8075	+	15.8075i	−0.508862	+	0.508862i
$966$	4.78913	+	3.95681i	0.154088	+	0.127308i
$967$	−30.2049	+	12.5113i	−0.971323	+	0.402335i	−0.811204	−	0.584763i	$-0.801188\pi$
$967$	−30.2049	+	12.5113i	−0.971323	+	0.402335i	−0.160119	+	0.987098i	$0.551188\pi$
$968$	−1.61044			−0.0517614
$969$		0			0
$970$	−79.6546			−2.55755
$971$	−22.2614	+	9.22099i	−0.714403	+	0.295916i	−0.710125	−	0.704075i	$-0.751362\pi$
$971$	−22.2614	+	9.22099i	−0.714403	+	0.295916i	−0.00427801	+	0.999991i	$0.501362\pi$
$972$	−15.2744	−	29.7444i	−0.489927	−	0.954053i
$973$	0.142863	−	0.142863i	0.00457997	−	0.00457997i
$974$	−8.81244	−	1.75290i	−0.282369	−	0.0561667i
$975$	−6.81223	−	2.09099i	−0.218166	−	0.0669653i
$976$	−3.89360	−	19.5744i	−0.124631	−	0.626562i
$977$	16.3952	−	39.5815i	0.524529	−	1.26633i	−0.410534	−	0.911845i	$-0.634658\pi$
$977$	16.3952	−	39.5815i	0.524529	−	1.26633i	0.935063	−	0.354481i	$-0.115342\pi$
$978$	4.15129	−	40.7717i	0.132744	−	1.30373i
$979$	6.56395	−	1.30565i	0.209785	−	0.0417288i
$980$	−7.49325	+	11.2144i	−0.239363	+	0.358232i
$981$	41.2733	−	16.7783i	1.31775	−	0.535690i
$982$	54.9740	+	54.9740i	1.75429	+	1.75429i
$983$	−20.8744	−	31.2407i	−0.665790	−	0.996425i	−0.998572	−	0.0534211i	$-0.982987\pi$
$983$	−20.8744	−	31.2407i	−0.665790	−	0.996425i	0.332782	−	0.943004i	$-0.392013\pi$
$984$	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
$989$	4.87446	−	3.25701i	0.154999	−	0.103567i
$990$	−29.2602	−	6.02085i	−0.929951	−	0.191355i
$991$	2.99298	−	15.0467i	0.0950750	−	0.477974i	−0.903685	−	0.428197i	$-0.859149\pi$
$991$	2.99298	−	15.0467i	0.0950750	−	0.477974i	0.998760	−	0.0497773i	$-0.0158511\pi$
$992$	19.8425	+	13.2584i	0.630001	+	0.420953i
$993$	−18.1505	+	9.62491i	−0.575988	+	0.305437i
$994$	3.34743	+	1.38655i	0.106174	+	0.0439788i
$995$	−46.4183	−	19.2271i	−1.47156	−	0.609539i
$996$	−12.4243	+	6.58842i	−0.393679	+	0.208762i
$997$	−31.0246	−	20.7300i	−0.982558	−	0.656524i	−0.0430578	−	0.999073i	$-0.513710\pi$
$997$	−31.0246	−	20.7300i	−0.982558	−	0.656524i	−0.939500	+	0.342548i	$0.888710\pi$
$998$	−5.18048	+	26.0440i	−0.163985	+	0.824409i
$999$	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.h.158.1		32
3.2	odd	2	inner	867.2.i.h.158.4		32
17.2	even	8		867.2.i.b.224.1		32
17.3	odd	16		867.2.i.g.827.1		32
17.4	even	4		867.2.i.c.131.4		32
17.5	odd	16		867.2.i.i.329.4		32
17.6	odd	16		867.2.i.c.503.1		32
17.7	odd	16	inner	867.2.i.h.653.4		32
17.8	even	8		867.2.i.g.65.4		32
17.9	even	8		867.2.i.f.65.4		32
17.10	odd	16		51.2.i.a.41.4	yes	32
17.11	odd	16		867.2.i.d.503.1		32
17.12	odd	16		867.2.i.b.329.4		32
17.13	even	4		867.2.i.d.131.4		32
17.14	odd	16		867.2.i.f.827.1		32
17.15	even	8		867.2.i.i.224.1		32
17.16	even	2		51.2.i.a.5.1	✓	32
51.2	odd	8		867.2.i.b.224.4		32
51.5	even	16		867.2.i.i.329.1		32
51.8	odd	8		867.2.i.g.65.1		32
51.11	even	16		867.2.i.d.503.4		32
51.14	even	16		867.2.i.f.827.4		32
51.20	even	16		867.2.i.g.827.4		32
51.23	even	16		867.2.i.c.503.4		32
51.26	odd	8		867.2.i.f.65.1		32
51.29	even	16		867.2.i.b.329.1		32
51.32	odd	8		867.2.i.i.224.4		32
51.38	odd	4		867.2.i.c.131.1		32
51.41	even	16	inner	867.2.i.h.653.1		32
51.44	even	16		51.2.i.a.41.1	yes	32
51.47	odd	4		867.2.i.d.131.1		32
51.50	odd	2		51.2.i.a.5.4	yes	32
68.27	even	16		816.2.cj.c.449.4		32
68.67	odd	2		816.2.cj.c.209.2		32
204.95	odd	16		816.2.cj.c.449.2		32
204.203	even	2		816.2.cj.c.209.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.5.1	✓	32	17.16	even	2
51.2.i.a.5.4	yes	32	51.50	odd	2
51.2.i.a.41.1	yes	32	51.44	even	16
51.2.i.a.41.4	yes	32	17.10	odd	16
816.2.cj.c.209.2		32	68.67	odd	2
816.2.cj.c.209.4		32	204.203	even	2
816.2.cj.c.449.2		32	204.95	odd	16
816.2.cj.c.449.4		32	68.27	even	16
867.2.i.b.224.1		32	17.2	even	8
867.2.i.b.224.4		32	51.2	odd	8
867.2.i.b.329.1		32	51.29	even	16
867.2.i.b.329.4		32	17.12	odd	16
867.2.i.c.131.1		32	51.38	odd	4
867.2.i.c.131.4		32	17.4	even	4
867.2.i.c.503.1		32	17.6	odd	16
867.2.i.c.503.4		32	51.23	even	16
867.2.i.d.131.1		32	51.47	odd	4
867.2.i.d.131.4		32	17.13	even	4
867.2.i.d.503.1		32	17.11	odd	16
867.2.i.d.503.4		32	51.11	even	16
867.2.i.f.65.1		32	51.26	odd	8
867.2.i.f.65.4		32	17.9	even	8
867.2.i.f.827.1		32	17.14	odd	16
867.2.i.f.827.4		32	51.14	even	16
867.2.i.g.65.1		32	51.8	odd	8
867.2.i.g.65.4		32	17.8	even	8
867.2.i.g.827.1		32	17.3	odd	16
867.2.i.g.827.4		32	51.20	even	16
867.2.i.h.158.1		32	1.1	even	1	trivial
867.2.i.h.158.4		32	3.2	odd	2	inner
867.2.i.h.653.1		32	51.41	even	16	inner
867.2.i.h.653.4		32	17.7	odd	16	inner
867.2.i.i.224.1		32	17.15	even	8
867.2.i.i.224.4		32	51.32	odd	8
867.2.i.i.329.1		32	51.5	even	16
867.2.i.i.329.4		32	17.5	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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} +(-1.10321 + 1.33527i) q^{3} +(1.51674 - 1.51674i) q^{4} +(-2.03727 - 0.405238i) q^{5} +(1.03475 - 3.37109i) q^{6} +(-0.388855 - 1.95490i) q^{7} +(-0.112963 + 0.272718i) q^{8} +(-0.565877 - 2.94615i) q^{9} +(4.14772 - 0.825033i) q^{10} +(1.30817 - 1.95782i) q^{11} +(0.351977 + 3.69852i) q^{12} +(-4.24491 - 4.24491i) q^{13} +(2.25451 + 3.37411i) q^{14} +(2.78862 - 2.27324i) q^{15} +3.68900i q^{16} +(3.35977 + 5.10067i) q^{18} +(1.93477 + 4.67096i) q^{19} +(-3.70464 + 2.47536i) q^{20} +(3.03931 + 1.63744i) q^{21} +(-0.935240 + 4.70177i) q^{22} +(-0.734889 - 0.491037i) q^{23} +(-0.239529 - 0.451700i) q^{24} +(-0.633157 - 0.262262i) q^{25} +(11.2917 + 4.67719i) q^{26} +(4.55817 + 2.49461i) q^{27} +(-3.55487 - 2.37529i) q^{28} +(0.0116792 - 0.0587151i) q^{29} +(-3.47415 + 6.44850i) q^{30} +(-2.44942 + 1.63665i) q^{31} +(-3.10008 - 7.48426i) q^{32} +(1.17103 + 3.90663i) q^{33} +4.14024i q^{35} +(-5.32682 - 3.61024i) q^{36} +(1.52979 + 2.28949i) q^{37} +(-7.27842 - 7.27842i) q^{38} +(10.3511 - 0.985083i) q^{39} +(0.340652 - 0.509822i) q^{40} +(-3.25313 + 0.647088i) q^{41} +(-6.99253 - 0.711965i) q^{42} +(-2.53831 + 6.12803i) q^{43} +(-0.985341 - 4.95364i) q^{44} +(-0.0410472 + 6.23140i) q^{45} +(1.76486 + 0.351053i) q^{46} +(5.76615 - 5.76615i) q^{47} +(-4.92580 - 4.06972i) q^{48} +(2.79671 - 1.15844i) q^{49} +1.39527 q^{50} -12.8768 q^{52} +(1.75216 - 0.725770i) q^{53} +(-10.5173 - 1.14089i) q^{54} +(-3.45848 + 3.45848i) q^{55} +(0.577063 + 0.114785i) q^{56} +(-8.37143 - 2.56958i) q^{57} +(0.0237779 + 0.119540i) q^{58} +(-3.54618 + 8.56124i) q^{59} +(0.781708 - 7.67751i) q^{60} +(-5.30616 + 1.05546i) q^{61} +(3.33210 - 4.98684i) q^{62} +(-5.53939 + 2.25186i) q^{63} +(6.44515 + 6.44515i) q^{64} +(6.92782 + 10.3682i) q^{65} +(-5.24636 - 6.43581i) q^{66} -7.09503i q^{67} +(1.46640 - 0.439558i) q^{69} +(-3.22572 - 7.78759i) q^{70} +(0.742386 - 0.496046i) q^{71} +(0.867389 + 0.178482i) q^{72} +(0.551496 - 2.77256i) q^{73} +(-4.66124 - 3.11454i) q^{74} +(1.04869 - 0.556105i) q^{75} +(10.0192 + 4.15007i) q^{76} +(-4.33604 - 1.79604i) q^{77} +(-18.7024 + 9.91759i) q^{78} +(3.30560 + 2.20873i) q^{79} +(1.49492 - 7.51548i) q^{80} +(-8.35957 + 3.33431i) q^{81} +(5.61482 - 3.75170i) q^{82} +(1.44855 + 3.49712i) q^{83} +(7.09339 - 2.12627i) q^{84} -13.5041i q^{86} +(0.0655159 + 0.0803696i) q^{87} +(0.386156 + 0.577923i) q^{88} +(2.00979 + 2.00979i) q^{89} +(-4.77777 - 11.7529i) q^{90} +(-6.64775 + 9.94906i) q^{91} +(-1.85941 + 0.369859i) q^{92} +(0.516848 - 5.07620i) q^{93} +(-6.35335 + 15.3383i) q^{94} +(-2.04880 - 10.3000i) q^{95} +(13.4135 + 4.11723i) q^{96} +(-18.4735 - 3.67461i) q^{97} +(-4.35792 + 4.35792i) q^{98} +(-6.50828 - 2.74618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} - 16 q^{4} + 8 q^{6} + 16 q^{7} - 8 q^{9} + 16 q^{10} - 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} + 16 q^{22} - 16 q^{24} + 16 q^{25} + 8 q^{27} - 32 q^{28} - 8 q^{30}+ \cdots + 64 q^{99}+O(q^{100}) \) 32 * q + 8 * q^3 - 16 * q^4 + 8 * q^6 + 16 * q^7 - 8 * q^9 + 16 * q^10 - 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 + 16 * q^22 - 16 * q^24 + 16 * q^25 + 8 * q^27 - 32 * q^28 - 8 * q^30 - 16 * q^31 + 8 * q^36 - 16 * q^37 + 24 * q^39 - 16 * q^40 - 56 * q^42 + 16 * q^43 + 40 * q^45 + 32 * q^46 + 64 * q^48 - 48 * q^49 - 96 * q^52 + 24 * q^54 - 48 * q^55 - 8 * q^57 + 48 * q^58 + 32 * q^60 + 32 * q^61 - 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 - 48 * q^73 - 88 * q^75 + 48 * q^76 - 96 * q^78 - 16 * q^79 + 48 * q^81 - 112 * q^82 - 56 * q^87 - 16 * q^88 + 88 * q^90 - 16 * q^91 - 72 * q^93 - 48 * q^94 + 112 * q^96 + 16 * q^97 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more