LMFDB - Embedded newform 867.2.i.h.158.4

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 = [32,0,8,-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			158.4
Character	$\chi$	$=$	867.158
Dual form			867.2.i.h.653.4

$q$-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} +(1.65580 - 0.508244i) q^{3} +(1.51674 - 1.51674i) q^{4} +(2.03727 + 0.405238i) q^{5} +(2.71850 - 2.24604i) q^{6} +(-0.388855 - 1.95490i) q^{7} +(0.112963 - 0.272718i) q^{8} +(2.48338 - 1.68311i) q^{9} +(4.14772 - 0.825033i) q^{10} +(-1.30817 + 1.95782i) q^{11} +(1.74055 - 3.28229i) q^{12} +(-4.24491 - 4.24491i) q^{13} +(-2.25451 - 3.37411i) q^{14} +(3.57928 - 0.364435i) q^{15} +3.68900i q^{16} +(3.35977 - 5.10067i) q^{18} +(1.93477 + 4.67096i) q^{19} +(3.70464 - 2.47536i) q^{20} +(-1.63744 - 3.03931i) q^{21} +(-0.935240 + 4.70177i) q^{22} +(0.734889 + 0.491037i) q^{23} +(0.0484381 - 0.508980i) q^{24} +(-0.633157 - 0.262262i) q^{25} +(-11.2917 - 4.67719i) q^{26} +(3.25656 - 4.04905i) q^{27} +(-3.55487 - 2.37529i) q^{28} +(-0.0116792 + 0.0587151i) q^{29} +(6.44850 - 3.47415i) q^{30} +(-2.44942 + 1.63665i) q^{31} +(3.10008 + 7.48426i) q^{32} +(-1.17103 + 3.90663i) q^{33} -4.14024i q^{35} +(1.21380 - 6.31945i) q^{36} +(1.52979 + 2.28949i) q^{37} +(7.27842 + 7.27842i) q^{38} +(-9.18620 - 4.87129i) q^{39} +(0.340652 - 0.509822i) q^{40} +(3.25313 - 0.647088i) q^{41} +(-5.44790 - 4.44103i) q^{42} +(-2.53831 + 6.12803i) q^{43} +(0.985341 + 4.95364i) q^{44} +(5.74136 - 2.42258i) q^{45} +(1.76486 + 0.351053i) q^{46} +(-5.76615 + 5.76615i) q^{47} +(1.87491 + 6.10826i) q^{48} +(2.79671 - 1.15844i) q^{49} -1.39527 q^{50} -12.8768 q^{52} +(-1.75216 + 0.725770i) q^{53} +(2.97074 - 10.1533i) q^{54} +(-3.45848 + 3.45848i) q^{55} +(-0.577063 - 0.114785i) q^{56} +(5.57759 + 6.75086i) q^{57} +(0.0237779 + 0.119540i) q^{58} +(3.54618 - 8.56124i) q^{59} +(4.87607 - 5.98157i) q^{60} +(-5.30616 + 1.05546i) q^{61} +(-3.33210 + 4.98684i) q^{62} +(-4.25598 - 4.20028i) q^{63} +(6.44515 + 6.44515i) q^{64} +(-6.92782 - 10.3682i) q^{65} +(0.841072 + 8.26054i) q^{66} -7.09503i q^{67} +(1.46640 + 0.439558i) q^{69} +(-3.22572 - 7.78759i) q^{70} +(-0.742386 + 0.496046i) q^{71} +(-0.178482 - 0.867389i) q^{72} +(0.551496 - 2.77256i) q^{73} +(4.66124 + 3.11454i) q^{74} +(-1.18168 - 0.112457i) q^{75} +(10.0192 + 4.15007i) q^{76} +(4.33604 + 1.79604i) q^{77} +(-21.0741 - 2.00556i) q^{78} +(3.30560 + 2.20873i) q^{79} +(-1.49492 + 7.51548i) q^{80} +(3.33431 - 8.35957i) q^{81} +(5.61482 - 3.75170i) q^{82} +(-1.44855 - 3.49712i) q^{83} +(-7.09339 - 2.12627i) q^{84} +13.5041i q^{86} +(0.0105032 + 0.103157i) q^{87} +(0.386156 + 0.577923i) q^{88} +(-2.00979 - 2.00979i) q^{89} +(8.91174 - 9.02992i) q^{90} +(-6.64775 + 9.94906i) q^{91} +(1.85941 - 0.369859i) q^{92} +(-3.22395 + 3.95488i) q^{93} +(-6.35335 + 15.3383i) q^{94} +(2.04880 + 10.3000i) q^{95} +(8.93695 + 10.8169i) q^{96} +(-18.4735 - 3.67461i) q^{97} +(4.35792 - 4.35792i) q^{98} +(0.0465302 + 7.06379i) 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	0.399367	−	0.916791i	$-0.369230\pi$
$2$	1.88095	−	0.779115i	1.33003	−	0.550917i	0.930665	+	0.365874i	$0.119230\pi$
$3$	1.65580	−	0.508244i	0.955979	−	0.293435i
$3$	1.65580	−	0.508244i	0.955979	−	0.293435i
$4$	1.51674	−	1.51674i	0.758368	−	0.758368i
$5$	2.03727	+	0.405238i	0.911094	+	0.181228i	0.628316	−	0.777958i	$-0.283744\pi$
$5$	2.03727	+	0.405238i	0.911094	+	0.181228i	0.282777	+	0.959186i	$0.408744\pi$
$6$	2.71850	−	2.24604i	1.10982	−	0.916943i
$7$	−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
$9$	2.48338	−	1.68311i	0.827792	−	0.561035i
$10$	4.14772	−	0.825033i	1.31163	−	0.260898i
$11$	−1.30817	+	1.95782i	−0.394429	+	0.590304i	−0.974535	−	0.224237i	$-0.928011\pi$
$11$	−1.30817	+	1.95782i	−0.394429	+	0.590304i	0.580106	+	0.814541i	$0.303011\pi$
$12$	1.74055	−	3.28229i	0.502453	−	0.947516i
$13$	−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
$15$	3.57928	−	0.364435i	0.924165	−	0.0940966i
$16$			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
$21$	−1.63744	−	3.03931i	−0.357318	−	0.663231i
$22$	−0.935240	+	4.70177i	−0.199394	+	1.00242i
$23$	0.734889	+	0.491037i	0.153235	+	0.102388i	0.629824	−	0.776738i	$-0.283127\pi$
$23$	0.734889	+	0.491037i	0.153235	+	0.102388i	−0.476589	+	0.879126i	$0.658127\pi$
$24$	0.0484381	−	0.508980i	0.00988738	−	0.103895i
$25$	−0.633157	−	0.262262i	−0.126631	−	0.0524525i
$26$	−11.2917	−	4.67719i	−2.21449	−	0.917273i
$27$	3.25656	−	4.04905i	0.626725	−	0.779241i
$28$	−3.55487	−	2.37529i	−0.671806	−	0.448887i
$29$	−0.0116792	+	0.0587151i	−0.00216877	+	0.0109031i	−0.981855	−	0.189636i	$-0.939269\pi$
$29$	−0.0116792	+	0.0587151i	−0.00216877	+	0.0109031i	0.979686	+	0.200539i	$0.0642693\pi$
$30$	6.44850	−	3.47415i	1.17733	−	0.634290i
$31$	−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
$36$	1.21380	−	6.31945i	0.202300	−	1.05324i
$37$	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
$39$	−9.18620	−	4.87129i	−1.47097	−	0.780031i
$40$	0.340652	−	0.509822i	0.0538618	−	0.0806099i
$41$	3.25313	−	0.647088i	0.508054	−	0.101058i	0.0655937	−	0.997846i	$-0.479106\pi$
$41$	3.25313	−	0.647088i	0.508054	−	0.101058i	0.442460	+	0.896788i	$0.354106\pi$
$42$	−5.44790	−	4.44103i	−0.840630	−	0.685266i
$43$	−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
$45$	5.74136	−	2.42258i	0.855871	−	0.361137i
$46$	1.76486	+	0.351053i	0.260215	+	0.0517599i
$47$	−5.76615	+	5.76615i	−0.841080	+	0.841080i	−0.988999	−	0.147919i	$-0.952742\pi$
$47$	−5.76615	+	5.76615i	−0.841080	+	0.841080i	0.147919	+	0.988999i	$0.452742\pi$
$48$	1.87491	+	6.10826i	0.270620	+	0.881652i
$49$	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	$0.416579\pi$
$54$	2.97074	−	10.1533i	0.404267	−	1.38169i
$55$	−3.45848	+	3.45848i	−0.466341	+	0.466341i
$56$	−0.577063	−	0.114785i	−0.0771133	−	0.0153388i
$57$	5.57759	+	6.75086i	0.738770	+	0.894173i
$58$	0.0237779	+	0.119540i	0.00312219	+	0.0156963i
$59$	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	$-0.0811102\pi$
$60$	4.87607	−	5.98157i	0.629498	−	0.772217i
$61$	−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
$63$	−4.25598	−	4.20028i	−0.536203	−	0.529186i
$64$	6.44515	+	6.44515i	0.805644	+	0.805644i
$65$	−6.92782	−	10.3682i	−0.859291	−	1.28602i
$66$	0.841072	+	8.26054i	0.103529	+	1.01680i
$67$		−	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	−0.598842	−	0.800867i	$-0.704372\pi$
$71$	−0.742386	+	0.496046i	−0.0881050	+	0.0588699i	0.510737	+	0.859737i	$0.329372\pi$
$72$	−0.178482	−	0.867389i	−0.0210343	−	0.102223i
$73$	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
$75$	−1.18168	−	0.112457i	−0.136448	−	0.0129854i
$76$	10.0192	+	4.15007i	1.14928	+	0.476046i
$77$	4.33604	+	1.79604i	0.494137	+	0.204678i
$78$	−21.0741	−	2.00556i	−2.38617	−	0.227084i
$79$	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
$81$	3.33431	−	8.35957i	0.370479	−	0.928841i
$82$	5.61482	−	3.75170i	0.620053	−	0.414306i
$83$	−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
$87$	0.0105032	+	0.103157i	0.00112606	+	0.0110596i
$88$	0.386156	+	0.577923i	0.0411643	+	0.0616068i
$89$	−2.00979	−	2.00979i	−0.213037	−	0.213037i	0.592519	−	0.805556i	$-0.298133\pi$
$89$	−2.00979	−	2.00979i	−0.213037	−	0.213037i	−0.805556	+	0.592519i	$0.798133\pi$
$90$	8.91174	−	9.02992i	0.939380	−	0.951837i
$91$	−6.64775	+	9.94906i	−0.696873	+	1.04294i
$92$	1.85941	−	0.369859i	0.193856	−	0.0385604i
$93$	−3.22395	+	3.95488i	−0.334308	+	0.410102i
$94$	−6.35335	+	15.3383i	−0.655298	+	1.58203i
$95$	2.04880	+	10.3000i	0.210203	+	1.05676i
$96$	8.93695	+	10.8169i	0.912124	+	1.10399i
$97$	−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
$99$	0.0465302	+	7.06379i	0.00467646	+	0.709937i
$100$	−1.35812	+	0.562550i	−0.135812	+	0.0562550i
$101$	3.48372			0.346643			0.173321	−	0.984865i	$-0.444550\pi$
$101$	3.48372			0.346643			0.173321	+	0.984865i	$0.444550\pi$
$102$		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
$105$	−2.10425	−	6.85543i	−0.205354	−	0.669022i
$106$	−2.73027	+	2.73027i	−0.265188	+	0.265188i
$107$	3.93543	+	0.782805i	0.380452	+	0.0756766i	0.381612	−	0.924323i	$-0.375369\pi$
$107$	3.93543	+	0.782805i	0.380452	+	0.0756766i	−0.00115968	+	0.999999i	$0.500369\pi$
$108$	−1.20201	−	11.0807i	−0.115663	−	1.06624i
$109$	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
$111$	3.69665	+	3.01345i	0.350871	+	0.286024i
$112$	7.21164	−	1.43449i	0.681436	−	0.135546i
$113$	3.69755	−	5.53377i	0.347836	−	0.520573i	−0.615761	−	0.787933i	$-0.711151\pi$
$113$	3.69755	−	5.53377i	0.347836	−	0.520573i	0.963597	+	0.267360i	$0.0861513\pi$
$114$	15.7509	+	8.35243i	1.47520	+	0.782277i
$115$	1.29818	+	1.29818i	0.121056	+	0.121056i
$116$	0.0713412	+	0.106770i	0.00662386	+	0.00991331i
$117$	−17.6864	−	3.39708i	−1.63510	−	0.314060i
$118$		−	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
$123$	5.05767	−	2.72484i	0.456035	−	0.245690i
$124$	−1.23276	+	6.19750i	−0.110705	+	0.556552i
$125$	−9.81919	−	6.56097i	−0.878255	−	0.586831i
$126$	−11.2778	−	4.58462i	−1.00471	−	0.408430i
$127$	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
$129$	−1.08841	+	11.4369i	−0.0958296	+	1.00696i
$130$	−21.1089	−	14.1045i	−1.85137	−	1.23705i
$131$	4.01054	−	20.1623i	0.350402	−	1.76159i	−0.256237	−	0.966614i	$-0.582483\pi$
$131$	4.01054	−	20.1623i	0.350402	−	1.76159i	0.606640	−	0.794977i	$-0.292517\pi$
$132$	4.14919	+	7.70147i	0.361141	+	0.670327i
$133$	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	$-0.805928\pi$
$137$		−	13.4046i		−	1.14524i	0.819822	−	0.572618i	$-0.194072\pi$
$138$	3.10069	−	0.315706i	0.263948	−	0.0268746i
$139$	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
$141$	−6.61701	+	12.4782i	−0.557253	+	1.05086i
$142$	−1.00991	+	1.51144i	−0.0847500	+	0.126837i
$143$	13.8638	−	2.75769i	1.15935	−	0.230610i
$144$	6.20897	+	9.16117i	0.517415	+	0.763431i
$145$	−0.0475872	+	0.114886i	−0.00395190	+	0.00954073i
$146$	−1.12280	−	5.64471i	−0.0929239	−	0.467160i
$147$	4.04204	−	3.33955i	0.333382	−	0.275442i
$148$	5.79285	+	1.15227i	0.476169	+	0.0947159i
$149$	−9.82755	+	9.82755i	−0.805104	+	0.805104i	−0.983888	−	0.178784i	$-0.942784\pi$
$149$	−9.82755	+	9.82755i	−0.805104	+	0.805104i	0.178784	+	0.983888i	$0.442784\pi$
$150$	−2.31029	+	0.709137i	−0.188635	+	0.0579008i
$151$	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
$156$	−21.3215	+	6.54457i	−1.70709	+	0.523985i
$157$	−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
$159$	−2.53237	+	2.09226i	−0.200830	+	0.165927i
$160$	3.28279	+	16.5037i	0.259527	+	1.30473i
$161$	0.674165	−	1.62758i	0.0531317	−	0.128271i
$162$	−0.241386	−	18.3217i	−0.0189651	−	1.43949i
$163$	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
$165$	−3.96881	+	7.48431i	−0.308971	+	0.582653i
$166$	−5.44932	−	5.44932i	−0.422949	−	0.422949i
$167$	8.95841	+	13.4072i	0.693223	+	1.03748i	0.996419	+	0.0845529i	$0.0269462\pi$
$167$	8.95841	+	13.4072i	0.693223	+	1.03748i	−0.303196	+	0.952928i	$0.598054\pi$
$168$	−1.01384	+	0.103227i	−0.0782196	+	0.00796417i
$169$			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	−0.976506	−	0.215489i	$-0.930866\pi$
$173$	−15.1405	+	10.1166i	−1.15111	+	0.769149i	−0.174607	+	0.984638i	$0.555866\pi$
$174$	0.100127	+	0.185849i	0.00759059	+	0.0140892i
$175$	−0.266492	+	1.33974i	−0.0201449	+	0.101275i
$176$	−7.22239	−	4.82584i	−0.544408	−	0.363762i
$177$	1.52058	−	15.9781i	0.114294	−	1.20099i
$178$	−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	$0.369816\pi$
$180$	5.03372	−	12.3825i	0.375191	−	0.922940i
$181$	−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
$183$	−8.24954	+	4.44446i	−0.609823	+	0.328544i
$184$	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
$189$	−9.18184	−	4.79177i	−0.667881	−	0.348550i
$190$	11.8786	+	17.7776i	0.861764	+	1.28972i
$191$	−6.08578	−	6.08578i	−0.440352	−	0.440352i	0.451778	−	0.892130i	$-0.350790\pi$
$191$	−6.08578	−	6.08578i	−0.440352	−	0.440352i	−0.892130	+	0.451778i	$0.850790\pi$
$192$	13.9476	+	7.39620i	1.00658	+	0.533775i
$193$	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
$195$	−16.7407	−	13.6467i	−1.19883	−	0.977262i
$196$	2.48483	−	5.99892i	0.177488	−	0.428494i
$197$	−4.95440	−	24.9075i	−0.352987	−	1.77458i	−0.594408	−	0.804163i	$-0.702614\pi$
$197$	−4.95440	−	24.9075i	−0.352987	−	1.77458i	0.241422	−	0.970420i	$-0.422386\pi$
$198$	5.59102	+	13.2504i	0.397337	+	0.941663i
$199$	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
$201$	−3.60601	−	11.7480i	−0.254348	−	0.828638i
$202$	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
$207$	2.65147	−	0.0174656i	0.184290	−	0.00121394i
$208$	15.6595	−	15.6595i	1.08579	−	1.08579i
$209$	−11.6759	−	2.32248i	−0.807639	−	0.160649i
$210$	−9.29916	−	11.2553i	−0.641703	−	0.776687i
$211$	−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
$213$	−0.977133	+	1.19867i	−0.0669520	+	0.0821314i
$214$	8.01223	−	1.59373i	0.547705	−	0.108945i
$215$	−7.65453	+	11.4558i	−0.522034	+	0.781280i
$216$	−0.736377	−	1.34551i	−0.0501041	−	0.0915507i
$217$	4.15197	+	4.15197i	0.281854	+	0.281854i
$218$	16.7980	+	25.1401i	1.13771	+	1.70270i
$219$	−0.495966	−	4.87110i	−0.0335143	−	0.329159i
$220$			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
$225$	−2.01378	+	0.414374i	−0.134252	+	0.0276249i
$226$	2.64346	−	13.2895i	0.175840	−	0.884008i
$227$	1.50999	+	1.00895i	0.100222	+	0.0669661i	0.604671	−	0.796475i	$-0.293305\pi$
$227$	1.50999	+	1.00895i	0.100222	+	0.0669661i	−0.504449	+	0.863441i	$0.668305\pi$
$228$	18.6990	+	1.77953i	1.23837	+	0.117852i
$229$	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
$231$	8.09245	+	0.770135i	0.532444	+	0.0506711i
$232$	0.0146933	+	0.00981777i	0.000964664	+	0.000644568i
$233$	0.271493	−	1.36489i	0.0177861	−	0.0894166i	−0.970873	−	0.239596i	$-0.922985\pi$
$233$	0.271493	−	1.36489i	0.0177861	−	0.0894166i	0.988659	+	0.150179i	$0.0479851\pi$
$234$	−35.9138	+	7.38996i	−2.34776	+	0.483097i
$235$	−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	$-0.916583\pi$
$239$		−	8.01035i		−	0.518146i	0.965858	−	0.259073i	$-0.0834171\pi$
$240$	1.34440	+	13.2039i	0.0867806	+	0.852311i
$241$	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
$243$	1.27227	−	15.5365i	0.0816163	−	0.996664i
$244$	−6.44719	+	9.64891i	−0.412739	+	0.617708i
$245$	6.16709	−	1.22671i	0.394001	−	0.0783717i
$246$	7.39026	−	9.06578i	0.471186	−	0.578013i
$247$	11.6149	−	28.0408i	0.739036	−	1.78419i
$248$	0.169649	+	0.852883i	0.0107727	+	0.0541581i
$249$	−4.17591	−	5.05433i	−0.264638	−	0.320305i
$250$	−23.5811	−	4.69058i	−1.49140	−	0.296658i
$251$	15.7099	−	15.7099i	0.991603	−	0.991603i	−0.00836189	−	0.999965i	$-0.502662\pi$
$251$	15.7099	−	15.7099i	0.991603	−	0.991603i	0.999965	+	0.00836189i	$0.00266170\pi$
$252$	−12.8259	+	0.0844862i	−0.807957	+	0.00532213i
$253$	−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	$0.186550\pi$
$258$	6.86340	+	22.3602i	0.427297	+	1.39209i
$259$	3.88088	−	3.88088i	0.241146	−	0.241146i
$260$	−26.2335	−	5.21818i	−1.62694	−	0.323618i
$261$	0.0698200	+	0.165469i	0.00432175	+	0.0102423i
$262$	−8.16515	−	41.0490i	−0.504445	−	2.53601i
$263$	−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	$0.202058\pi$
$264$	0.933124	+	0.760666i	0.0574298	+	0.0468157i
$265$	−3.86374	+	0.768545i	−0.237347	+	0.0472113i
$266$	11.3984	−	17.0589i	0.698879	−	1.04595i
$267$	−4.34928	−	2.30635i	−0.266172	−	0.141147i
$268$	−10.7613	−	10.7613i	−0.657350	−	0.657350i
$269$	−6.79874	−	10.1750i	−0.414527	−	0.620383i	0.564179	−	0.825653i	$-0.309193\pi$
$269$	−6.79874	−	10.1750i	−0.414527	−	0.620383i	−0.978705	+	0.205270i	$0.934193\pi$
$270$	10.1667	−	19.4811i	0.618725	−	1.18558i
$271$		−	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
$276$	2.89083	−	1.55745i	0.174008	−	0.0937472i
$277$	−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
$279$	−3.32818	+	8.18706i	−0.199253	+	0.490147i
$280$	−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	$0.667741\pi$
$282$	−2.72428	+	28.6263i	−0.162229	+	1.70467i
$283$	−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
$285$	8.62735	+	16.0135i	0.511040	+	0.948561i
$286$	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
$291$	−32.4561	+	3.30461i	−1.90261	+	0.193720i
$292$	−3.36876	−	5.04171i	−0.197142	−	0.295044i
$293$	−17.1538	−	17.1538i	−1.00214	−	1.00214i	−0.999998	−	0.00213730i	$-0.999320\pi$
$293$	−17.1538	−	17.1538i	−1.00214	−	1.00214i	−0.00213730	−	0.999998i	$-0.500680\pi$
$294$	5.00097	−	9.43074i	0.291663	−	0.550012i
$295$	10.6939	−	16.0045i	0.622621	−	0.931818i
$296$	0.797195	−	0.158572i	0.0463360	−	0.00921681i
$297$	3.66717	+	11.6726i	0.212791	+	0.677313i
$298$	−10.8283	+	26.1419i	−0.627269	+	1.51436i
$299$	−1.03513	−	5.20395i	−0.0598631	−	0.300952i
$300$	−1.96286	+	1.62173i	−0.113326	+	0.0936304i
$301$	12.9667	+	2.57925i	0.747391	+	0.148665i
$302$	7.21623	−	7.21623i	0.415247	−	0.415247i
$303$	5.76835	−	1.77058i	0.331383	−	0.101717i
$304$	−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
$309$	−6.30558	+	1.93548i	−0.358712	+	0.110106i
$310$	−8.80924	+	8.80924i	−0.500331	+	0.500331i
$311$	28.4123	+	5.65155i	1.61111	+	0.320470i	0.916844	−	0.399247i	$-0.130728\pi$
$311$	28.4123	+	5.65155i	1.61111	+	0.320470i	0.694268	+	0.719717i	$0.255728\pi$
$312$	−2.36619	+	1.95496i	−0.133959	+	0.110678i
$313$	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
$315$	−6.96846	−	10.2818i	−0.392628	−	0.579313i
$316$	8.36379	−	1.66366i	0.470500	−	0.0935882i
$317$	6.07417	−	9.09064i	0.341159	−	0.510581i	−0.620728	−	0.784026i	$-0.713163\pi$
$317$	6.07417	−	9.09064i	0.341159	−	0.510581i	0.961888	+	0.273445i	$0.0881630\pi$
$318$	−3.13315	+	5.90844i	−0.175699	+	0.331329i
$319$	−0.0996751	−	0.0996751i	−0.00558074	−	0.00558074i
$320$	10.5187	+	15.7423i	0.588012	+	0.880022i
$321$	6.91415	−	0.703985i	0.385910	−	0.0392926i
$322$		−	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
$327$	12.2003	+	22.6455i	0.674679	+	1.25230i
$328$	0.191012	−	0.960283i	0.0105469	−	0.0530228i
$329$	13.5145	+	9.03009i	0.745077	+	0.497845i
$330$	−1.63399	+	17.1698i	−0.0899485	+	0.945164i
$331$	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
$333$	7.65250	+	3.11087i	0.419355	+	0.170475i
$334$	27.2961	+	18.2386i	1.49357	+	0.997974i
$335$	2.87517	−	14.4545i	0.157087	−	0.789732i
$336$	11.2120	−	6.04050i	0.611665	−	0.329536i
$337$	−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
$342$	30.3254	+	5.82471i	1.63981	+	0.314964i
$343$	−11.1037	−	16.6179i	−0.599543	−	0.897280i
$344$	1.38448	+	1.38448i	0.0746464	+	0.0746464i
$345$	2.80932	+	1.48974i	0.151249	+	0.0802048i
$346$	−20.5966	+	30.8250i	−1.10728	+	1.65716i
$347$	−28.6483	+	5.69850i	−1.53792	+	0.305912i	−0.890059	−	0.455845i	$-0.849337\pi$
$347$	−28.6483	+	5.69850i	−1.53792	+	0.305912i	−0.647863	+	0.761757i	$0.724337\pi$
$348$	0.172392	+	0.140531i	0.00924118	+	0.00753324i
$349$	−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
$351$	−31.0117	+	3.36408i	−1.65528	+	0.179561i
$352$	−18.7082	−	3.72130i	−0.997153	−	0.198346i
$353$	17.9892	−	17.9892i	0.957468	−	0.957468i	−0.0416640	−	0.999132i	$-0.513266\pi$
$353$	17.9892	−	17.9892i	0.957468	−	0.957468i	0.999132	+	0.0416640i	$0.0132659\pi$
$354$	−9.58860	−	31.2386i	−0.509629	−	1.66032i
$355$	−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	$0.499233\pi$
$360$	−0.0121166	−	1.83943i	−0.000638601	−	0.0969465i
$361$	−4.63947	+	4.63947i	−0.244183	+	0.244183i
$362$	−6.99314	−	1.39102i	−0.367551	−	0.0731104i
$363$	6.01869	+	7.28474i	0.315899	+	0.382349i
$364$	5.00722	+	25.1730i	0.262449	+	1.31942i
$365$	2.24709	−	5.42495i	0.117618	−	0.283955i
$366$	−12.0542	+	14.7871i	−0.630084	+	0.772936i
$367$	−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
$369$	6.98963	−	7.08232i	0.363866	−	0.368691i
$370$	8.23406	+	8.23406i	0.428068	+	0.428068i
$371$	2.10015	+	3.14309i	0.109034	+	0.163181i
$372$	1.10863	+	10.8884i	0.0574800	+	0.564537i
$373$		−	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
$378$	−21.0039	−	1.85936i	−1.08032	−	0.0956351i
$379$	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
$381$	6.06756	+	0.577431i	0.310851	+	0.0295827i
$382$	−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	$0.488356\pi$
$384$	4.06114	+	0.386486i	0.207244	+	0.0197228i
$385$	8.10584	+	5.41615i	0.413112	+	0.276032i
$386$	4.27466	−	21.4902i	0.217575	−	1.09382i
$387$	4.01053	+	19.4904i	0.203867	+	0.990755i
$388$	−33.5928	+	22.4460i	−1.70542	+	1.13952i
$389$	−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
$393$	−3.60672	−	35.4232i	−0.181935	−	1.78686i
$394$	−28.7248	−	42.9896i	−1.44713	−	2.16579i
$395$	5.83933	+	5.83933i	0.293809	+	0.293809i
$396$	10.7845	+	10.6433i	0.541940	+	0.534847i
$397$	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
$399$	11.0284	−	13.5288i	0.552111	−	0.677286i
$400$	0.967485	−	2.33572i	0.0483743	−	0.116786i
$401$	2.86708	+	14.4138i	0.143175	+	0.719791i	0.983955	+	0.178414i	$0.0570967\pi$
$401$	2.86708	+	14.4138i	0.143175	+	0.719791i	−0.840780	+	0.541377i	$0.817903\pi$
$402$	−15.9357	−	19.2879i	−0.794802	−	0.961991i
$403$	17.3450	+	3.45014i	0.864018	+	0.171864i
$404$	5.28388	−	5.28388i	0.262883	−	0.262883i
$405$	10.1805	−	15.6795i	0.505873	−	0.779120i
$406$	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
$411$	−6.81283	−	22.1955i	−0.336052	−	1.09482i
$412$	−5.77599	+	5.77599i	−0.284562	+	0.284562i
$413$	−18.1154	−	3.60337i	−0.891399	−	0.177310i
$414$	4.97368	−	2.09865i	0.244443	−	0.103143i
$415$	−1.53393	−	7.71158i	−0.0752976	−	0.378547i
$416$	18.6104	−	44.9296i	0.912452	−	2.20285i
$417$	0.136081	+	0.110931i	0.00666392	+	0.00543231i
$418$	−23.7712	+	4.72840i	−1.16269	+	0.231273i
$419$	−5.48388	+	8.20720i	−0.267905	+	0.400948i	−0.940892	−	0.338706i	$-0.890011\pi$
$419$	−5.48388	+	8.20720i	−0.267905	+	0.400948i	0.672987	+	0.739654i	$0.265011\pi$
$420$	−13.5895	−	7.20629i	−0.663099	−	0.351631i
$421$	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
$423$	−4.61449	+	24.0246i	−0.224364	+	1.16811i
$424$			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
$429$	21.5542	−	11.6124i	1.04065	−	0.560652i
$430$	−5.47239	+	27.5115i	−0.263902	+	1.32672i
$431$	−17.1107	−	11.4330i	−0.824191	−	0.550707i	0.0704381	−	0.997516i	$-0.477560\pi$
$431$	−17.1107	−	11.4330i	−0.824191	−	0.550707i	−0.894629	+	0.446809i	$0.852560\pi$
$432$	14.9370	+	12.0134i	0.718655	+	0.577997i
$433$	−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
$435$	−0.0204051	+	0.214414i	−0.000978351	+	0.0102804i
$436$	26.4868	+	17.6979i	1.26849	+	0.847577i
$437$	−0.871769	+	4.38268i	−0.0417024	+	0.209652i
$438$	−4.72804	−	8.77589i	−0.225914	−	0.419328i
$439$	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	$-0.899109\pi$
$443$		−	13.1202i		−	0.623358i	0.950187	−	0.311679i	$-0.100891\pi$
$444$	10.1775	−	1.03625i	0.483001	−	0.0491781i
$445$	−3.28003	−	4.90892i	−0.155489	−	0.232705i
$446$	14.4843	+	14.4843i	0.685852	+	0.685852i
$447$	−11.2777	+	21.2673i	−0.533417	+	1.00591i
$448$	10.0934	−	15.1059i	0.476870	−	0.713686i
$449$	20.7822	−	4.13384i	0.980774	−	0.195088i	0.321433	−	0.946932i	$-0.395835\pi$
$449$	20.7822	−	4.13384i	0.980774	−	0.195088i	0.659341	+	0.751844i	$0.270835\pi$
$450$	−3.46498	+	2.34838i	−0.163341	+	0.110704i
$451$	−2.98877	+	7.21554i	−0.140736	+	0.339766i
$452$	−2.78507	−	14.0015i	−0.130998	−	0.658574i
$453$	6.69317	−	5.52993i	0.314472	−	0.259819i
$454$	3.62631	+	0.721317i	0.170191	+	0.0338531i
$455$	−17.5750	+	17.5750i	−0.823927	+	0.823927i
$456$	2.47114	−	0.758509i	0.115722	−	0.0355204i
$457$	−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	0.234940	−	0.972010i	$-0.424511\pi$
$461$	23.3686	−	9.67958i	1.08838	−	0.450823i	0.853443	+	0.521187i	$0.174511\pi$
$462$	15.8215	−	4.85637i	0.736084	−	0.225939i
$463$	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
$465$	−8.17071	+	6.75069i	−0.378908	+	0.313056i
$466$	−0.552739	−	2.77880i	−0.0256051	−	0.128726i
$467$	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	$0.0117019\pi$
$468$	−31.9780	+	21.6731i	−1.47818	+	1.00184i
$469$	−13.8701	+	2.75894i	−0.640462	+	0.127396i
$470$	−19.1591	+	28.6737i	−0.883745	+	1.32262i
$471$	−9.73171	+	18.3519i	−0.448414	+	0.845610i
$472$	−1.93421	−	1.93421i	−0.0890293	−	0.0890293i
$473$	−8.67701	−	12.9861i	−0.398969	−	0.597100i
$474$	13.9472	−	1.42007i	0.640616	−	0.0652262i
$475$		−	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	−0.348793	−	0.937200i	$-0.613408\pi$
$479$	8.39525	−	5.60953i	0.383589	−	0.256306i	0.732382	+	0.680894i	$0.238408\pi$
$480$	13.8236	+	25.6584i	0.630956	+	1.17114i
$481$	3.22487	−	16.2125i	0.147042	−	0.739228i
$482$	29.3281	+	19.5964i	1.33586	+	0.892591i
$483$	0.289079	−	3.03759i	0.0131535	−	0.138215i
$484$	10.8115	+	4.47827i	0.491432	+	0.203558i
$485$	−36.1464	−	14.9723i	−1.64132	−	0.679858i
$486$	−9.71160	−	30.2145i	−0.440527	−	1.37056i
$487$	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
$489$	17.7214	−	9.54747i	0.801390	−	0.431752i
$490$	10.6442	−	7.11225i	0.480858	−	0.321299i
$491$	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
$495$	−2.76772	+	14.4097i	−0.124400	+	0.647667i
$496$	−6.03761	−	9.03592i	−0.271097	−	0.405725i
$497$	1.25840	+	1.25840i	0.0564471	+	0.0564471i
$498$	−11.7926	−	6.25342i	−0.528438	−	0.280222i
$499$	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
$501$	21.6475	+	17.6467i	0.967139	+	0.788394i
$502$	17.3098	−	41.7895i	0.772573	−	1.86516i
$503$	−0.728223	−	3.66103i	−0.0324699	−	0.163237i	0.961148	−	0.276032i	$-0.0890196\pi$
$503$	−0.728223	−	3.66103i	−0.0324699	−	0.163237i	−0.993618	+	0.112795i	$0.964020\pi$
$504$	−1.62626	+	0.686204i	−0.0724394	+	0.0305659i
$505$	7.09726	+	1.41173i	0.315824	+	0.0628213i
$506$	−2.99604	+	2.99604i	−0.133190	+	0.133190i
$507$	11.7092	+	38.1474i	0.520025	+	1.69418i
$508$	6.97351	−	2.88852i	0.309400	−	0.128158i
$509$	−40.1261			−1.77856			−0.889279	−	0.457364i	$-0.848793\pi$
$509$	−40.1261			−1.77856			−0.889279	+	0.457364i	$0.848793\pi$
$510$		0			0
$511$	−5.63453			−0.249257
$512$	−29.6215	+	12.2696i	−1.30910	+	0.542246i
$513$	25.2137	+	7.37724i	1.11321	+	0.325713i
$514$	25.7582	−	25.7582i	1.13615	−	1.13615i
$515$	−7.75825	−	1.54321i	−0.341870	−	0.0680021i
$516$	15.6959	+	18.9976i	0.690974	+	0.836322i
$517$	−3.74596	−	18.8322i	−0.164747	−	0.828239i
$518$	4.27608	−	10.3234i	0.187880	−	0.453583i
$519$	−19.9281	+	24.4462i	−0.874745	+	1.07307i
$520$	−3.61019	+	0.718111i	−0.158317	+	0.0314912i
$521$	9.04943	−	13.5434i	0.396463	−	0.593348i	−0.578509	−	0.815676i	$-0.696365\pi$
$521$	9.04943	−	13.5434i	0.396463	−	0.593348i	0.974972	+	0.222328i	$0.0713654\pi$
$522$	0.260247	+	0.256841i	0.0113907	+	0.0112416i
$523$	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
$525$	0.239659	+	2.35380i	0.0104596	+	0.102728i
$526$			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
$531$	−5.60297	−	27.2294i	−0.243148	−	1.18165i
$532$	4.21700	−	21.2003i	0.182830	−	0.919148i
$533$	−16.5561	−	11.0624i	−0.717124	−	0.479167i
$534$	−9.97769	−	0.949546i	−0.431777	−	0.0410909i
$535$	7.70029	+	3.18957i	0.332913	+	0.137897i
$536$	−1.93494	−	0.801478i	−0.0835766	−	0.0346186i
$537$	33.1515	+	3.15493i	1.43059	+	0.136145i
$538$	−20.7156	−	13.8417i	−0.893113	−	0.596759i
$539$	−1.39057	+	6.99088i	−0.0598962	+	0.301119i
$540$	2.04150	−	23.0614i	0.0878521	−	0.992405i
$541$	−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
$546$	4.27408	+	41.9777i	0.182914	+	1.79648i
$547$	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
$549$	−11.4007	+	11.5519i	−0.486572	+	0.493025i
$550$	1.82525	−	2.73168i	0.0778290	−	0.116479i
$551$	−0.296852	+	0.0590476i	−0.0126463	+	0.00251551i
$552$	0.285524	−	0.350259i	0.0121527	−	0.0149080i
$553$	3.03246	−	7.32101i	0.128953	−	0.311321i
$554$	6.69342	+	33.6501i	0.284376	+	1.42966i
$555$	6.30991	+	7.63722i	0.267841	+	0.324182i
$556$	0.213246	+	0.0424173i	0.00904365	+	0.00179889i
$557$	4.85771	−	4.85771i	0.205828	−	0.205828i	−0.596664	−	0.802491i	$-0.703507\pi$
$557$	4.85771	−	4.85771i	0.205828	−	0.205828i	0.802491	+	0.596664i	$0.203507\pi$
$558$	0.118519	+	17.9925i	0.00501731	+	0.761683i
$559$	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	$0.295930\pi$
$564$	8.88994	+	28.9625i	0.374334	+	1.21954i
$565$	9.77538	−	9.77538i	0.411253	−	0.411253i
$566$	−11.0166	−	2.19135i	−0.463064	−	0.0921092i
$567$	−17.6387	−	3.26761i	−0.740757	−	0.137227i
$568$	0.0514182	+	0.258497i	0.00215746	+	0.0108463i
$569$	−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	$0.765071\pi$
$570$	28.7040	+	23.3990i	1.20228	+	0.980075i
$571$	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
$573$	−13.1699	−	6.98380i	−0.550182	−	0.291753i
$574$	−9.51757	−	9.51757i	−0.397256	−	0.397256i
$575$	−0.336520	−	0.503637i	−0.0140338	−	0.0210031i
$576$	26.8536	+	5.15787i	1.11890	+	0.214911i
$577$			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
$582$	−58.4736	+	31.5028i	−2.42381	+	1.30583i
$583$	0.871206	−	4.37985i	0.0360817	−	0.181395i
$584$	−0.693826	−	0.463600i	−0.0287107	−	0.0191839i
$585$	−34.6552	−	14.0879i	−1.43282	−	0.582465i
$586$	−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	$0.828398\pi$
$588$	1.06548	−	11.1959i	0.0439398	−	0.461712i
$589$	−12.3838	−	8.27460i	−0.510266	−	0.340949i
$590$	7.64527	−	38.4354i	0.314751	−	1.58236i
$591$	−20.8626	−	38.7239i	−0.858173	−	1.59289i
$592$	−8.44594	+	5.64340i	−0.347126	+	0.231942i
$593$	−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
$597$	41.6793	−	4.24370i	1.70582	−	0.173683i
$598$	−6.00150	−	8.98188i	−0.245419	−	0.367296i
$599$	21.9297	+	21.9297i	0.896025	+	0.896025i	0.995082	−	0.0990569i	$-0.0315826\pi$
$599$	21.9297	+	21.9297i	0.896025	+	0.896025i	−0.0990569	+	0.995082i	$0.531583\pi$
$600$	−0.164155	+	0.309561i	−0.00670160	+	0.0126378i
$601$	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
$603$	−11.9417	−	17.6196i	−0.486303	−	0.717526i
$604$	4.11461	−	9.93354i	0.167421	−	0.404190i
$605$	2.21083	+	11.1146i	0.0898830	+	0.451873i
$606$	9.47050	−	7.82458i	0.384713	−	0.317852i
$607$	−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
$609$	0.197577	−	0.0606457i	0.00800623	−	0.00245749i
$610$	−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
$615$	11.4080	−	3.50166i	0.460016	−	0.141201i
$616$	0.979626	−	0.979626i	0.0394702	−	0.0394702i
$617$	33.4612	+	6.65584i	1.34710	+	0.267954i	0.815359	−	0.578956i	$-0.196540\pi$
$617$	33.4612	+	6.65584i	1.34710	+	0.267954i	0.531737	+	0.846910i	$0.321540\pi$
$618$	−10.3525	+	8.55331i	−0.416439	+	0.344064i
$619$	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
$621$	4.38144	−	1.37651i	0.175821	−	0.0552376i
$622$	57.8452	−	11.5061i	2.31938	−	0.461354i
$623$	−3.14743	+	4.71046i	−0.126099	+	0.188721i
$624$	17.9702	−	33.8879i	0.719384	−	1.35660i
$625$	−14.9226	−	14.9226i	−0.596903	−	0.596903i
$626$	12.5962	+	18.8515i	0.503444	+	0.753457i
$627$	−20.5134	+	2.08863i	−0.819226	+	0.0834119i
$628$			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
$633$	−9.03552	−	16.7712i	−0.359130	−	0.666594i
$634$	4.34256	−	21.8315i	0.172465	−	0.867040i
$635$	6.07759	+	4.06092i	0.241182	+	0.161153i
$636$	−0.667534	+	7.01435i	−0.0264695	+	0.278137i
$637$	−16.7893	−	6.95434i	−0.665215	−	0.275541i
$638$	−0.265142	−	0.109825i	−0.0104971	−	0.00434803i
$639$	−1.00872	+	2.48138i	−0.0399045	+	0.0981620i
$640$	4.06785	+	2.71805i	0.160796	+	0.107441i
$641$	−4.61604	+	23.2064i	−0.182322	+	0.916597i	0.775962	+	0.630780i	$0.217265\pi$
$641$	−4.61604	+	23.2064i	−0.182322	+	0.916597i	−0.958284	+	0.285817i	$0.907735\pi$
$642$	12.4567	−	6.71108i	0.491626	−	0.264865i
$643$	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	$0.245478\pi$
$647$			35.4575i			1.39398i	−0.717081	+	0.696990i	$0.754522\pi$
$648$	−1.90315	−	1.85365i	−0.0747626	−	0.0728182i
$649$	12.1223	+	18.1424i	0.475843	+	0.712150i
$650$	5.92280	+	5.92280i	0.232311	+	0.232311i
$651$	8.98507	+	4.76464i	0.352153	+	0.186741i
$652$	13.8497	−	20.7275i	0.542395	−	0.811752i
$653$	−19.1428	+	3.80775i	−0.749117	+	0.149009i	−0.554862	−	0.831943i	$-0.687229\pi$
$653$	−19.1428	+	3.80775i	−0.749117	+	0.149009i	−0.194255	+	0.980951i	$0.562229\pi$
$654$	40.5916	+	33.0895i	1.58726	+	1.29390i
$655$	16.3411	−	39.4508i	0.638498	−	1.54147i
$656$	2.38711	+	12.0008i	0.0932009	+	0.468552i
$657$	−3.29693	−	7.81352i	−0.128626	−	0.304835i
$658$	32.4555	+	6.45581i	1.26525	+	0.251673i
$659$	−9.54185	+	9.54185i	−0.371698	+	0.371698i	−0.868095	−	0.496398i	$-0.834656\pi$
$659$	−9.54185	+	9.54185i	−0.371698	+	0.371698i	0.496398	+	0.868095i	$0.334656\pi$
$660$	5.33209	+	17.3714i	0.207551	+	0.676179i
$661$	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
$666$	16.8177	−	0.110781i	0.651673	−	0.00429266i
$667$	−0.0374142	+	0.0374142i	−0.00144868	+	0.00144868i
$668$	33.9228	+	6.74765i	1.31251	+	0.261075i
$669$	11.0996	+	13.4344i	0.429136	+	0.519405i
$670$	−5.85363	−	29.4282i	−0.226146	−	1.13691i
$671$	4.87497	−	11.7692i	0.188196	−	0.454346i
$672$	17.6708	−	21.6771i	0.681665	−	0.836212i
$673$	−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
$675$	−3.12383	+	1.70962i	−0.120236	+	0.0658031i
$676$	34.9435	+	34.9435i	1.34398	+	1.34398i
$677$	−8.78236	−	13.1437i	−0.337533	−	0.505154i	0.623412	−	0.781894i	$-0.285746\pi$
$677$	−8.78236	−	13.1437i	−0.337533	−	0.505154i	−0.960945	+	0.276739i	$0.910746\pi$
$678$	−2.37729	−	23.3484i	−0.0912992	−	0.896690i
$679$			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	−0.00907414	−	0.999959i	$-0.502888\pi$
$683$	23.8160	−	15.9134i	0.911295	−	0.608908i	0.920369	+	0.391051i	$0.127888\pi$
$684$	31.8663	−	6.55711i	1.21844	−	0.250717i
$685$	5.43206	−	27.3088i	0.207549	−	1.04342i
$686$	−33.8327	−	22.6063i	−1.29174	−	0.863112i
$687$	3.11115	+	0.296079i	0.118698	+	0.0112961i
$688$	−22.6063	−	9.36383i	−0.861857	−	0.356993i
$689$	10.5186	+	4.35695i	0.400727	+	0.165987i
$690$	6.44486	+	0.613338i	0.245352	+	0.0233494i
$691$	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
$693$	13.7909	−	2.83775i	0.523874	−	0.107797i
$694$	−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
$699$	−0.244156	−	2.39797i	−0.00923484	−	0.0906995i
$700$	1.62784	+	2.43624i	0.0615266	+	0.0920811i
$701$	13.2794	+	13.2794i	0.501558	+	0.501558i	0.911922	−	0.410364i	$-0.134598\pi$
$701$	13.2794	+	13.2794i	0.501558	+	0.501558i	−0.410364	+	0.911922i	$0.634598\pi$
$702$	−55.7104	+	30.4893i	−2.10265	+	1.15075i
$703$	−7.73433	+	11.5752i	−0.291706	+	0.436568i
$704$	−21.0498	+	4.18706i	−0.793344	+	0.157806i
$705$	−18.5373	+	22.7400i	−0.698154	+	0.856440i
$706$	19.8211	−	47.8524i	0.745977	−	1.80095i
$707$	−1.35466	−	6.81034i	−0.0509472	−	0.256129i
$708$	−21.9282	−	26.5408i	−0.824112	−	0.997466i
$709$	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
$711$	11.9266	−	0.0785621i	0.447282	−	0.00294631i
$712$	−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
$717$	−4.07121	−	13.2636i	−0.152042	−	0.495337i
$718$	−20.7553	+	20.7553i	−0.774582	+	0.774582i
$719$	25.0780	+	4.98832i	0.935252	+	0.186033i	0.639114	−	0.769112i	$-0.279301\pi$
$719$	25.0780	+	4.98832i	0.935252	+	0.186033i	0.296138	+	0.955145i	$0.404301\pi$
$720$	8.93689	+	21.1799i	0.333058	+	0.789327i
$721$	1.48082	+	7.44460i	0.0551488	+	0.277252i
$722$	−5.11193	+	12.3413i	−0.190246	+	0.459295i
$723$	23.2590	+	18.9603i	0.865012	+	0.705142i
$724$	−7.36776	+	1.46554i	−0.273821	+	0.0544663i
$725$	0.0227935	−	0.0341129i	0.000846530	−	0.00126692i
$726$	16.9965	+	9.01297i	0.630799	+	0.334503i
$727$	−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
$729$	−5.78968	−	26.3719i	−0.214432	−	0.976739i
$730$		−	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
$735$	9.58803	−	5.16558i	0.353660	−	0.190535i
$736$	−1.39683	+	7.02235i	−0.0514879	+	0.258847i
$737$	13.8908	+	9.28151i	0.511673	+	0.341889i
$738$	7.62920	−	18.7672i	0.280835	−	0.690831i
$739$	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
$741$	4.98039	−	52.3332i	0.182959	−	1.92251i
$742$	6.39910	+	4.27574i	0.234918	+	0.156968i
$743$	−9.42343	+	47.3748i	−0.345712	+	1.73801i	0.281861	+	0.959455i	$0.409048\pi$
$743$	−9.42343	+	47.3748i	−0.345712	+	1.73801i	−0.627573	+	0.778558i	$0.715952\pi$
$744$	0.714378	+	1.32598i	0.0261904	+	0.0486129i
$745$	−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
$750$	−41.4297	+	4.21829i	−1.51280	+	0.154030i
$751$	−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
$753$	18.0281	−	33.9971i	0.656981	−	1.23892i
$754$	0.406500	−	0.608370i	0.0148039	−	0.0221555i
$755$	10.2120	−	2.03130i	0.371653	−	0.0739264i
$756$	−21.1943	+	6.65859i	−0.770829	+	0.242171i
$757$	−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
$759$	−2.77888	+	2.29592i	−0.100867	+	0.0833367i
$760$	3.04044	+	0.604781i	0.110288	+	0.0219377i
$761$	−18.9898	+	18.9898i	−0.688381	+	0.688381i	−0.961874	−	0.273493i	$-0.911821\pi$
$761$	−18.9898	+	18.9898i	−0.688381	+	0.688381i	0.273493	+	0.961874i	$0.411821\pi$
$762$	11.8627	−	3.64121i	0.429739	−	0.131907i
$763$	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
$768$	−22.2448	+	6.82798i	−0.802691	+	0.246383i
$769$	−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
$771$	23.8912	−	19.7390i	0.860420	−	0.710884i
$772$	−4.50366	−	22.6414i	−0.162090	−	0.814882i
$773$	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	$-0.0405883\pi$
$774$	22.7289	+	33.5359i	0.816973	+	1.20542i
$775$	1.98010	−	0.393867i	0.0711274	−	0.0141481i
$776$	−3.08896	+	4.62295i	−0.110887	+	0.165954i
$777$	4.45354	−	8.39840i	0.159770	−	0.301291i
$778$	−4.66692	−	4.66692i	−0.167317	−	0.167317i
$779$	9.31659	+	13.9433i	0.333802	+	0.499569i
$780$	−46.0897	+	4.69276i	−1.65028	+	0.168028i
$781$		−	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
$786$	−34.3828	−	63.8192i	−1.22639	−	2.27636i
$787$	−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
$789$	−1.27589	+	13.4068i	−0.0454228	+	0.477295i
$790$	15.5330	+	6.43398i	0.552639	+	0.228911i
$791$	−12.2558	−	5.07652i	−0.435766	−	0.180500i
$792$	1.93167	+	0.785259i	0.0686391	+	0.0279030i
$793$	27.0045	+	18.0439i	0.958960	+	0.640756i
$794$	7.06280	−	35.5071i	0.250649	−	1.26010i
$795$	−6.00698	+	3.23628i	−0.213046	+	0.114779i
$796$	43.1391	−	28.8246i	1.52903	−	1.02166i
$797$	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
$801$	−8.37374	−	1.60837i	−0.295872	−	0.0568291i
$802$	16.6228	+	24.8778i	0.586973	+	0.878467i
$803$	4.70671	+	4.70671i	0.166096	+	0.166096i
$804$	−23.2879	−	12.3492i	−0.821303	−	0.435524i
$805$	2.03301	−	3.04262i	0.0716542	−	0.107238i
$806$	35.3132	−	7.02423i	1.24385	−	0.247418i
$807$	−16.4288	−	13.3925i	−0.578321	−	0.471437i
$808$	0.393532	−	0.950071i	0.0138444	−	0.0334234i
$809$	−3.43987	−	17.2934i	−0.120939	−	0.608004i	−0.992952	−	0.118520i	$-0.962185\pi$
$809$	−3.43987	−	17.2934i	−0.120939	−	0.608004i	0.872012	−	0.489484i	$-0.162815\pi$
$810$	6.93289	−	37.4241i	0.243597	−	1.31495i
$811$	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
$813$	−0.684911	−	2.23137i	−0.0240209	−	0.0782574i
$814$	−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
$819$	0.236453	+	35.8961i	0.00826233	+	1.25431i
$820$	10.4499	−	10.4499i	0.364926	−	0.364926i
$821$	−45.7670	−	9.10361i	−1.59728	−	0.317718i	−0.685396	−	0.728171i	$-0.740371\pi$
$821$	−45.7670	−	9.10361i	−1.59728	−	0.317718i	−0.911882	+	0.410453i	$0.865371\pi$
$822$	−30.1074	−	36.4406i	−1.05012	−	1.27101i
$823$	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
$825$	1.76601	−	2.16640i	0.0614845	−	0.0754242i
$826$	−36.8815	+	7.33619i	−1.28327	+	0.255259i
$827$	−17.9442	+	26.8554i	−0.623982	+	0.933855i	0.375992	+	0.926623i	$0.377302\pi$
$827$	−17.9442	+	26.8554i	−0.623982	+	0.933855i	−0.999974	+	0.00723238i	$0.997698\pi$
$828$	3.99509	−	4.04807i	0.138839	−	0.140680i
$829$	−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
$831$	2.95662	+	29.0383i	0.102564	+	1.00733i
$832$		−	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
$837$	−1.34979	+	15.2477i	−0.0466557	+	0.527038i
$838$	−3.92054	+	19.7099i	−0.135433	+	0.680867i
$839$	−15.4135	−	10.2990i	−0.532134	−	0.355561i	0.260291	−	0.965530i	$-0.416182\pi$
$839$	−15.4135	−	10.2990i	−0.532134	−	0.355561i	−0.792425	+	0.609970i	$0.791182\pi$
$840$	−2.10730	−	0.200545i	−0.0727087	−	0.00691947i
$841$	26.7892	+	11.0964i	0.923765	+	0.382636i
$842$	4.43018	+	1.83504i	0.152674	+	0.0632396i
$843$	−7.73890	−	0.736488i	−0.266542	−	0.0253660i
$844$	−19.6161	−	13.1070i	−0.675213	−	0.451163i
$845$	−9.33610	+	46.9357i	−0.321172	+	1.61464i
$846$	10.0383	+	48.7842i	0.345123	+	1.67724i
$847$	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
$852$	0.336011	+	3.30012i	0.0115116	+	0.113060i
$853$	−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
$855$	22.4240	+	22.1305i	0.766884	+	0.756847i
$856$	0.658043	−	0.984832i	0.0224915	−	0.0336609i
$857$	−48.2422	+	9.59597i	−1.64792	+	0.327792i	−0.929783	−	0.368108i	$-0.880006\pi$
$857$	−48.2422	+	9.59597i	−1.64792	+	0.327792i	−0.718139	+	0.695900i	$0.755006\pi$
$858$	31.4950	−	38.6356i	1.07522	−	1.31900i
$859$	−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
$861$	−7.29349	−	8.82770i	−0.248562	−	0.300847i
$862$	−41.0919	−	8.17368i	−1.39959	−	0.278397i
$863$	−5.07346	+	5.07346i	−0.172702	+	0.172702i	−0.788166	−	0.615463i	$-0.788969\pi$
$863$	−5.07346	+	5.07346i	−0.172702	+	0.172702i	0.615463	+	0.788166i	$0.288969\pi$
$864$	40.3997	+	11.8205i	1.37443	+	0.402142i
$865$	−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
$870$	0.128672	+	0.419200i	0.00436239	+	0.0142122i
$871$	−30.1178	+	30.1178i	−1.02050	+	1.02050i
$872$	4.29962	+	0.855247i	0.145603	+	0.0289623i
$873$	−52.0614	+	21.9674i	−1.76201	+	0.743484i
$874$	1.77486	+	8.92281i	0.0600354	+	0.301818i
$875$	−9.00784	+	21.7469i	−0.304521	+	0.735178i
$876$	−8.14043	−	6.63593i	−0.275040	−	0.224207i
$877$	−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
$879$	−37.1216	−	19.6850i	−1.25208	−	0.663959i
$880$	−12.7583	−	12.7583i	−0.430083	−	0.430083i
$881$	10.9801	+	16.4329i	0.369930	+	0.553639i	0.969001	−	0.247056i	$-0.0794633\pi$
$881$	10.9801	+	16.4329i	0.369930	+	0.553639i	−0.599071	+	0.800696i	$0.704463\pi$
$882$	3.48751	−	18.1572i	0.117431	−	0.611384i
$883$			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	−0.613747	−	0.789503i	$-0.710339\pi$
$887$	−3.55045	+	2.37234i	−0.119213	+	0.0796553i	0.494535	+	0.869158i	$0.335339\pi$
$888$	1.23941	−	0.667734i	0.0415917	−	0.0224077i
$889$	1.36835	−	6.87918i	0.0458931	−	0.230720i
$890$	−9.99419	−	6.67790i	−0.335006	−	0.223844i
$891$	12.0046	+	17.4637i	0.402171	+	0.585057i
$892$	19.9385	+	8.25878i	0.667589	+	0.276525i
$893$	−38.0897	−	15.7773i	−1.27462	−	0.527966i
$894$	−4.64313	+	48.7893i	−0.155290	+	1.63176i
$895$	33.2064	+	22.1878i	1.10997	+	0.741656i
$896$	0.915867	−	4.60437i	0.0305970	−	0.153821i
$897$	−4.35885	−	8.09062i	−0.145538	−	0.270138i
$898$	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
$903$	22.7813	−	2.31954i	0.758113	−	0.0771896i
$904$	−1.09147	−	1.63350i	−0.0363017	−	0.0543293i
$905$	−5.14393	−	5.14393i	−0.170990	−	0.170990i
$906$	8.28106	−	15.6163i	0.275120	−	0.518816i
$907$	−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
$909$	8.65138	−	5.86346i	0.286948	−	0.194479i
$910$	−19.3647	+	46.7505i	−0.641934	+	1.54977i
$911$	10.7023	+	53.8041i	0.354583	+	1.78261i	0.586577	+	0.809893i	$0.300475\pi$
$911$	10.7023	+	53.8041i	0.354583	+	1.78261i	−0.231994	+	0.972717i	$0.574525\pi$
$912$	−24.9039	+	20.5757i	−0.824651	+	0.681331i
$913$	8.74168	+	1.73883i	0.289307	+	0.0575468i
$914$	−20.2402	+	20.2402i	−0.669488	+	0.669488i
$915$	−18.6076	+	5.71154i	−0.615147	+	0.188818i
$916$	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
$921$	−35.7182	+	10.9636i	−1.17695	+	0.361262i
$922$	36.4136	−	36.4136i	1.19922	−	1.19922i
$923$	5.25704	+	1.04569i	0.173037	+	0.0344193i
$924$	13.4422	−	11.1060i	0.442216	−	0.365362i
$925$	−0.368150	−	1.85082i	−0.0121047	−	0.0608544i
$926$	0.410037	−	0.989916i	0.0134746	−	0.0325307i
$927$	−9.45711	+	6.40955i	−0.310612	+	0.210517i
$928$	−0.475645	+	0.0946117i	−0.0156138	+	0.00310578i
$929$	4.95694	−	7.41858i	0.162632	−	0.243396i	−0.741199	−	0.671285i	$-0.765743\pi$
$929$	4.95694	−	7.41858i	0.162632	−	0.243396i	0.903831	+	0.427889i	$0.140743\pi$
$930$	−10.1091	+	19.0636i	−0.331492	+	0.625121i
$931$	10.8220	+	10.8220i	0.354677	+	0.354677i
$932$	−1.65839	−	2.48195i	−0.0543223	−	0.0812991i
$933$	49.9175	−	5.08250i	1.63423	−	0.166394i
$934$		−	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
$939$	9.14851	+	16.9809i	0.298550	+	0.554150i
$940$	−7.08820	+	35.6348i	−0.231192	+	1.16228i
$941$	33.0806	+	22.1038i	1.07840	+	0.720563i	0.962112	−	0.272653i	$-0.0879012\pi$
$941$	33.0806	+	22.1038i	1.07840	+	0.720563i	0.116286	+	0.993216i	$0.462901\pi$
$942$	−4.00663	+	42.1011i	−0.130543	+	1.37173i
$943$	2.70843	+	1.12187i	0.0881987	+	0.0365331i
$944$	31.5824	+	13.0819i	1.02792	+	0.425778i
$945$	−16.7641	−	13.4829i	−0.545335	−	0.438600i
$946$	−26.4386	−	17.6657i	−0.859594	−	0.574363i
$947$	1.22705	−	6.16877i	0.0398736	−	0.200458i	−0.955714	−	0.294298i	$-0.904914\pi$
$947$	1.22705	−	6.16877i	0.0398736	−	0.200458i	0.995587	+	0.0938399i	$0.0299142\pi$
$948$	13.0033	−	7.00554i	0.422326	−	0.227529i
$949$	−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	$0.263255\pi$
$953$			45.4373i			1.47186i	−0.677058	+	0.735930i	$0.736745\pi$
$954$	−2.18496	+	11.3756i	−0.0707406	+	0.368300i
$955$	−9.93218	−	14.8646i	−0.321398	−	0.481006i
$956$	−12.1496	−	12.1496i	−0.392946	−	0.392946i
$957$	−0.215702	−	0.114383i	−0.00697265	−	0.00369748i
$958$	11.4206	−	17.0921i	0.368982	−	0.552221i
$959$	−26.2048	+	5.21246i	−0.846197	+	0.168319i
$960$	25.4178	+	20.7201i	0.820356	+	0.668740i
$961$	−8.54214	+	20.6226i	−0.275553	+	0.665244i
$962$	−6.56560	−	33.0075i	−0.211683	−	1.06420i
$963$	11.0907	−	4.67974i	0.357392	−	0.150802i
$964$	36.4480	+	7.24997i	1.17391	+	0.233506i
$965$	15.8075	−	15.8075i	0.508862	−	0.508862i
$966$	−1.82289	−	5.93878i	−0.0586506	−	0.191077i
$967$	−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	0.00427801	−	0.999991i	$-0.498638\pi$
$971$	22.2614	−	9.22099i	0.714403	−	0.295916i	0.710125	+	0.704075i	$0.248638\pi$
$972$	−21.6350	−	25.4944i	−0.693943	−	0.817733i
$973$	0.142863	−	0.142863i	0.00457997	−	0.00457997i
$974$	8.81244	+	1.75290i	0.282369	+	0.0561667i
$975$	4.53875	+	5.49349i	0.145356	+	0.175932i
$976$	−3.89360	−	19.5744i	−0.124631	−	0.626562i
$977$	−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	$0.884658\pi$
$978$	25.8945	−	31.7653i	0.828015	−	1.01574i
$979$	6.56395	−	1.30565i	0.209785	−	0.0417288i
$980$	7.49325	−	11.2144i	0.239363	−	0.358232i
$981$	31.7107	+	31.2957i	1.01245	+	0.999195i
$982$	54.9740	+	54.9740i	1.75429	+	1.75429i
$983$	20.8744	+	31.2407i	0.665790	+	0.996425i	0.998572	+	0.0534211i	$0.0170126\pi$
$983$	20.8744	+	31.2407i	0.665790	+	0.996425i	−0.332782	+	0.943004i	$0.607987\pi$
$984$	−0.171779	−	1.68712i	−0.00547612	−	0.0537835i
$985$		−	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
$990$	6.02085	+	29.2602i	0.191355	+	0.929951i
$991$	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
$993$	20.4522	+	1.94637i	0.649030	+	0.0617662i
$994$	3.34743	+	1.38655i	0.106174	+	0.0439788i
$995$	46.4183	+	19.2271i	1.47156	+	0.609539i
$996$	−13.9998	−	1.33232i	−0.443602	−	0.0422163i
$997$	−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
$999$	14.2521	+	1.26166i	0.450917	+	0.0399172i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.88095 - 0.779115i) q^{2} +(1.65580 - 0.508244i) q^{3} +(1.51674 - 1.51674i) q^{4} +(2.03727 + 0.405238i) q^{5} +(2.71850 - 2.24604i) q^{6} +(-0.388855 - 1.95490i) q^{7} +(0.112963 - 0.272718i) q^{8} +(2.48338 - 1.68311i) q^{9} +(4.14772 - 0.825033i) q^{10} +(-1.30817 + 1.95782i) q^{11} +(1.74055 - 3.28229i) q^{12} +(-4.24491 - 4.24491i) q^{13} +(-2.25451 - 3.37411i) q^{14} +(3.57928 - 0.364435i) q^{15} +3.68900i q^{16} +(3.35977 - 5.10067i) q^{18} +(1.93477 + 4.67096i) q^{19} +(3.70464 - 2.47536i) q^{20} +(-1.63744 - 3.03931i) q^{21} +(-0.935240 + 4.70177i) q^{22} +(0.734889 + 0.491037i) q^{23} +(0.0484381 - 0.508980i) q^{24} +(-0.633157 - 0.262262i) q^{25} +(-11.2917 - 4.67719i) q^{26} +(3.25656 - 4.04905i) q^{27} +(-3.55487 - 2.37529i) q^{28} +(-0.0116792 + 0.0587151i) q^{29} +(6.44850 - 3.47415i) q^{30} +(-2.44942 + 1.63665i) q^{31} +(3.10008 + 7.48426i) q^{32} +(-1.17103 + 3.90663i) q^{33} -4.14024i q^{35} +(1.21380 - 6.31945i) q^{36} +(1.52979 + 2.28949i) q^{37} +(7.27842 + 7.27842i) q^{38} +(-9.18620 - 4.87129i) q^{39} +(0.340652 - 0.509822i) q^{40} +(3.25313 - 0.647088i) q^{41} +(-5.44790 - 4.44103i) q^{42} +(-2.53831 + 6.12803i) q^{43} +(0.985341 + 4.95364i) q^{44} +(5.74136 - 2.42258i) q^{45} +(1.76486 + 0.351053i) q^{46} +(-5.76615 + 5.76615i) q^{47} +(1.87491 + 6.10826i) q^{48} +(2.79671 - 1.15844i) q^{49} -1.39527 q^{50} -12.8768 q^{52} +(-1.75216 + 0.725770i) q^{53} +(2.97074 - 10.1533i) q^{54} +(-3.45848 + 3.45848i) q^{55} +(-0.577063 - 0.114785i) q^{56} +(5.57759 + 6.75086i) q^{57} +(0.0237779 + 0.119540i) q^{58} +(3.54618 - 8.56124i) q^{59} +(4.87607 - 5.98157i) q^{60} +(-5.30616 + 1.05546i) q^{61} +(-3.33210 + 4.98684i) q^{62} +(-4.25598 - 4.20028i) q^{63} +(6.44515 + 6.44515i) q^{64} +(-6.92782 - 10.3682i) q^{65} +(0.841072 + 8.26054i) q^{66} -7.09503i q^{67} +(1.46640 + 0.439558i) q^{69} +(-3.22572 - 7.78759i) q^{70} +(-0.742386 + 0.496046i) q^{71} +(-0.178482 - 0.867389i) q^{72} +(0.551496 - 2.77256i) q^{73} +(4.66124 + 3.11454i) q^{74} +(-1.18168 - 0.112457i) q^{75} +(10.0192 + 4.15007i) q^{76} +(4.33604 + 1.79604i) q^{77} +(-21.0741 - 2.00556i) q^{78} +(3.30560 + 2.20873i) q^{79} +(-1.49492 + 7.51548i) q^{80} +(3.33431 - 8.35957i) q^{81} +(5.61482 - 3.75170i) q^{82} +(-1.44855 - 3.49712i) q^{83} +(-7.09339 - 2.12627i) q^{84} +13.5041i q^{86} +(0.0105032 + 0.103157i) q^{87} +(0.386156 + 0.577923i) q^{88} +(-2.00979 - 2.00979i) q^{89} +(8.91174 - 9.02992i) q^{90} +(-6.64775 + 9.94906i) q^{91} +(1.85941 - 0.369859i) q^{92} +(-3.22395 + 3.95488i) q^{93} +(-6.35335 + 15.3383i) q^{94} +(2.04880 + 10.3000i) q^{95} +(8.93695 + 10.8169i) q^{96} +(-18.4735 - 3.67461i) q^{97} +(4.35792 - 4.35792i) q^{98} +(0.0465302 + 7.06379i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} - 16 q^{4} + 8 q^{6} + 16 q^{7} - 8 q^{9} + 16 q^{10} - 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} + 16 q^{22} - 16 q^{24} + 16 q^{25} + 8 q^{27} - 32 q^{28} - 8 q^{30}+ \cdots + 64 q^{99}+O(q^{100}) \) 32 * q + 8 * q^3 - 16 * q^4 + 8 * q^6 + 16 * q^7 - 8 * q^9 + 16 * q^10 - 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 + 16 * q^22 - 16 * q^24 + 16 * q^25 + 8 * q^27 - 32 * q^28 - 8 * q^30 - 16 * q^31 + 8 * q^36 - 16 * q^37 + 24 * q^39 - 16 * q^40 - 56 * q^42 + 16 * q^43 + 40 * q^45 + 32 * q^46 + 64 * q^48 - 48 * q^49 - 96 * q^52 + 24 * q^54 - 48 * q^55 - 8 * q^57 + 48 * q^58 + 32 * q^60 + 32 * q^61 - 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 - 48 * q^73 - 88 * q^75 + 48 * q^76 - 96 * q^78 - 16 * q^79 + 48 * q^81 - 112 * q^82 - 56 * q^87 - 16 * q^88 + 88 * q^90 - 16 * q^91 - 72 * q^93 - 48 * q^94 + 112 * q^96 + 16 * q^97 + 64 * q^99

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