LMFDB - Embedded newform 968.2.k.g.403.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(403,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("968.403");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.k (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			403.6
Character	$\chi$	$=$	968.403
Dual form			968.2.k.g.723.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.468639 + 1.33431i) q^{2} +(0.127999 - 0.393941i) q^{3} +(-1.56076 + 1.25062i) q^{4} +(1.55513 + 2.14046i) q^{5} +(0.585623 - 0.0138256i) q^{6} +(1.01687 + 3.12960i) q^{7} +(-2.40014 - 1.49644i) q^{8} +(2.28825 + 1.66251i) q^{9} +(-2.12723 + 3.07813i) q^{10} +(0.292893 + 0.774923i) q^{12} +(1.10272 + 0.801172i) q^{13} +(-3.69931 + 2.82347i) q^{14} +(1.04227 - 0.338654i) q^{15} +(0.871917 - 3.90381i) q^{16} +(-3.22705 - 4.44165i) q^{17} +(-1.14594 + 3.83234i) q^{18} +(2.16281 + 0.702738i) q^{19} +(-5.10408 - 1.39586i) q^{20} +1.36303 q^{21} +6.38741i q^{23} +(-0.896724 + 0.753968i) q^{24} +(-0.618034 + 1.90211i) q^{25} +(-0.552234 + 1.84683i) q^{26} +(1.95314 - 1.41904i) q^{27} +(-5.50101 - 3.61283i) q^{28} +(-2.03374 - 6.25920i) q^{29} +(0.940315 + 1.23200i) q^{30} +(0.644157 - 0.886607i) q^{31} +(5.61750 - 0.666071i) q^{32} +(4.41421 - 6.38741i) q^{34} +(-5.11741 + 7.04351i) q^{35} +(-5.65055 + 0.266949i) q^{36} +(4.60080 - 1.49489i) q^{37} +(0.0759050 + 3.21518i) q^{38} +(0.456761 - 0.331856i) q^{39} +(-0.529464 - 7.46456i) q^{40} +(-9.54709 - 3.10204i) q^{41} +(0.638771 + 1.81871i) q^{42} +6.43215i q^{43} +7.48331i q^{45} +(-8.52277 + 2.99339i) q^{46} +(-1.42627 - 0.843168i) q^{48} +(-3.09726 + 2.25029i) q^{49} +(-2.82764 + 0.0667558i) q^{50} +(-2.16281 + 0.702738i) q^{51} +(-2.72303 + 0.128644i) q^{52} +(4.39858 - 6.05413i) q^{53} +(2.80875 + 1.94107i) q^{54} +(2.24264 - 9.03316i) q^{56} +(0.553674 - 0.762067i) q^{57} +(7.39862 - 5.64694i) q^{58} +(1.00203 + 3.08393i) q^{59} +(-1.20320 + 1.83203i) q^{60} +(-5.32440 + 3.86840i) q^{61} +(1.48488 + 0.444006i) q^{62} +(-2.87614 + 8.85185i) q^{63} +(3.52132 + 7.18333i) q^{64} +3.60625i q^{65} -6.07107 q^{67} +(10.5914 + 2.89653i) q^{68} +(2.51626 + 0.817582i) q^{69} +(-11.7964 - 3.52734i) q^{70} +(3.75442 + 5.16752i) q^{71} +(-3.00426 - 7.41447i) q^{72} +(-0.895864 + 0.291084i) q^{73} +(4.15075 + 5.43832i) q^{74} +(0.670212 + 0.486937i) q^{75} +(-4.25447 + 1.60804i) q^{76} +(0.656854 + 0.453939i) q^{78} +(-7.52983 - 5.47074i) q^{79} +(9.71190 - 4.20465i) q^{80} +(2.31308 + 7.11893i) q^{81} +(-0.335061 - 14.1925i) q^{82} +(-2.67338 - 3.67959i) q^{83} +(-2.12736 + 1.70463i) q^{84} +(4.48868 - 13.8147i) q^{85} +(-8.58247 + 3.01435i) q^{86} -2.72607 q^{87} -10.6569 q^{89} +(-9.98505 + 3.50697i) q^{90} +(-1.38603 + 4.26576i) q^{91} +(-7.98820 - 9.96919i) q^{92} +(-0.266819 - 0.367244i) q^{93} +(1.85927 + 5.72225i) q^{95} +(0.456643 - 2.29822i) q^{96} +(-6.05572 - 4.39974i) q^{97} +(-4.45408 - 3.07813i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} + 32 q^{12} + 8 q^{14} + 24 q^{16} + 16 q^{25} - 24 q^{26} + 8 q^{27} + 96 q^{34} + 16 q^{36} + 8 q^{38} + 24 q^{42} - 24 q^{48} - 8 q^{49} - 64 q^{56} - 16 q^{58} + 8 q^{59} - 56 q^{60}+ \cdots + 8 q^{97}+O(q^{100}) $ 32 * q + 8 * q^3 + 32 * q^12 + 8 * q^14 + 24 * q^16 + 16 * q^25 - 24 * q^26 + 8 * q^27 + 96 * q^34 + 16 * q^36 + 8 * q^38 + 24 * q^42 - 24 * q^48 - 8 * q^49 - 64 * q^56 - 16 * q^58 + 8 * q^59 - 56 * q^60 + 32 * q^67 + 56 * q^70 - 16 * q^75 - 160 * q^78 - 56 * q^80 + 8 * q^81 + 8 * q^82 - 64 * q^86 - 160 * q^89 - 32 * q^91 + 56 * q^92 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.468639	+	1.33431i	0.331378	+	0.943498i
$2$	0.468639	+	1.33431i	0.331378	+	0.943498i
$3$	0.127999	−	0.393941i	0.0739003	−	0.227442i	−0.907283	−	0.420521i	$-0.861847\pi$
$3$	0.127999	−	0.393941i	0.0739003	−	0.227442i	0.981183	+	0.193079i	$0.0618474\pi$
$4$	−1.56076	+	1.25062i	−0.780378	+	0.625308i
$5$	1.55513	+	2.14046i	0.695477	+	0.957242i	0.999989	+	0.00473329i	$0.00150666\pi$
$5$	1.55513	+	2.14046i	0.695477	+	0.957242i	−0.304512	+	0.952509i	$0.598493\pi$
$6$	0.585623	−	0.0138256i	0.239080	−	0.00564427i
$7$	1.01687	+	3.12960i	0.384340	+	1.18288i	0.936958	+	0.349443i	$0.113629\pi$
$7$	1.01687	+	3.12960i	0.384340	+	1.18288i	−0.552617	+	0.833435i	$0.686371\pi$
$8$	−2.40014	−	1.49644i	−0.848577	−	0.529072i
$9$	2.28825	+	1.66251i	0.762749	+	0.554169i
$10$	−2.12723	+	3.07813i	−0.672691	+	0.973390i
$11$		0			0
$11$		0			0
$12$	0.292893	+	0.774923i	0.0845510	+	0.223701i
$13$	1.10272	+	0.801172i	0.305839	+	0.222205i	0.730109	−	0.683331i	$-0.239469\pi$
$13$	1.10272	+	0.801172i	0.305839	+	0.222205i	−0.424270	+	0.905536i	$0.639469\pi$
$14$	−3.69931	+	2.82347i	−0.988682	+	0.754604i
$15$	1.04227	−	0.338654i	0.269113	−	0.0874400i
$16$	0.871917	−	3.90381i	0.217979	−	0.975953i
$17$	−3.22705	−	4.44165i	−0.782675	−	1.07726i	−0.994982	−	0.100056i	$-0.968098\pi$
$17$	−3.22705	−	4.44165i	−0.782675	−	1.07726i	0.212307	−	0.977203i	$-0.431902\pi$
$18$	−1.14594	+	3.83234i	−0.270100	+	0.903291i
$19$	2.16281	+	0.702738i	0.496182	+	0.161219i	0.546409	−	0.837519i	$-0.315994\pi$
$19$	2.16281	+	0.702738i	0.496182	+	0.161219i	−0.0502270	+	0.998738i	$0.515994\pi$
$20$	−5.10408	−	1.39586i	−1.14131	−	0.312123i
$21$	1.36303			0.297439
$22$		0			0
$23$			6.38741i			1.33187i	0.746011	+	0.665933i	$0.231967\pi$
$23$			6.38741i			1.33187i	−0.746011	+	0.665933i	$0.768033\pi$
$24$	−0.896724	+	0.753968i	−0.183043	+	0.153903i
$25$	−0.618034	+	1.90211i	−0.123607	+	0.380423i
$26$	−0.552234	+	1.84683i	−0.108302	+	0.362192i
$27$	1.95314	−	1.41904i	0.375882	−	0.273094i
$28$	−5.50101	−	3.61283i	−1.03959	−	0.682761i
$29$	−2.03374	−	6.25920i	−0.377656	−	1.16230i	−0.941669	−	0.336539i	$-0.890743\pi$
$29$	−2.03374	−	6.25920i	−0.377656	−	1.16230i	0.564014	−	0.825765i	$-0.309257\pi$
$30$	0.940315	+	1.23200i	0.171677	+	0.224932i
$31$	0.644157	−	0.886607i	0.115694	−	0.159239i	−0.747243	−	0.664551i	$-0.768623\pi$
$31$	0.644157	−	0.886607i	0.115694	−	0.159239i	0.862937	+	0.505312i	$0.168623\pi$
$32$	5.61750	−	0.666071i	0.993044	−	0.117746i
$33$		0			0
$34$	4.41421	−	6.38741i	0.757031	−	1.09543i
$35$	−5.11741	+	7.04351i	−0.865001	+	1.19057i
$36$	−5.65055	+	0.266949i	−0.941759	+	0.0444915i
$37$	4.60080	−	1.49489i	0.756366	−	0.245758i	0.0946479	−	0.995511i	$-0.469827\pi$
$37$	4.60080	−	1.49489i	0.756366	−	0.245758i	0.661718	+	0.749753i	$0.269827\pi$
$38$	0.0759050	+	3.21518i	0.0123134	+	0.521571i
$39$	0.456761	−	0.331856i	0.0731403	−	0.0531395i
$40$	−0.529464	−	7.46456i	−0.0837156	−	1.18025i
$41$	−9.54709	−	3.10204i	−1.49100	−	0.484457i	−0.553625	−	0.832766i	$-0.686756\pi$
$41$	−9.54709	−	3.10204i	−1.49100	−	0.484457i	−0.937380	+	0.348309i	$0.886756\pi$
$42$	0.638771	+	1.81871i	0.0985645	+	0.280633i
$43$			6.43215i			0.980894i	0.871471	+	0.490447i	$0.163166\pi$
$43$			6.43215i			0.980894i	−0.871471	+	0.490447i	$0.836834\pi$
$44$		0			0
$45$			7.48331i			1.11555i
$46$	−8.52277	+	2.99339i	−1.25661	+	0.441351i
$47$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$47$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$48$	−1.42627	−	0.843168i	−0.205864	−	0.121701i
$49$	−3.09726	+	2.25029i	−0.442466	+	0.321470i
$50$	−2.82764	+	0.0667558i	−0.399889	+	0.00944070i
$51$	−2.16281	+	0.702738i	−0.302853	+	0.0984031i
$52$	−2.72303	+	0.128644i	−0.377617	+	0.0178397i
$53$	4.39858	−	6.05413i	0.604192	−	0.831599i	−0.391892	−	0.920011i	$-0.628179\pi$
$53$	4.39858	−	6.05413i	0.604192	−	0.831599i	0.996084	+	0.0884126i	$0.0281794\pi$
$54$	2.80875	+	1.94107i	0.382223	+	0.264147i
$55$		0			0
$56$	2.24264	−	9.03316i	0.299685	−	1.20711i
$57$	0.553674	−	0.762067i	0.0733359	−	0.100938i
$58$	7.39862	−	5.64694i	0.971486	−	0.741479i
$59$	1.00203	+	3.08393i	0.130453	+	0.401494i	0.994855	−	0.101308i	$-0.0323026\pi$
$59$	1.00203	+	3.08393i	0.130453	+	0.401494i	−0.864402	+	0.502802i	$0.832303\pi$
$60$	−1.20320	+	1.83203i	−0.155333	+	0.236515i
$61$	−5.32440	+	3.86840i	−0.681719	+	0.495298i	−0.873928	−	0.486056i	$-0.838435\pi$
$61$	−5.32440	+	3.86840i	−0.681719	+	0.495298i	0.192209	+	0.981354i	$0.438435\pi$
$62$	1.48488	+	0.444006i	0.188580	+	0.0563889i
$63$	−2.87614	+	8.85185i	−0.362360	+	1.11523i
$64$	3.52132	+	7.18333i	0.440165	+	0.897917i
$65$			3.60625i			0.447300i
$66$		0			0
$67$	−6.07107			−0.741699			−0.370849	−	0.928693i	$-0.620933\pi$
$67$	−6.07107			−0.741699			−0.370849	+	0.928693i	$0.620933\pi$
$68$	10.5914	+	2.89653i	1.28440	+	0.351256i
$69$	2.51626	+	0.817582i	0.302922	+	0.0984253i
$70$	−11.7964	−	3.52734i	−1.40994	−	0.421598i
$71$	3.75442	+	5.16752i	0.445568	+	0.613272i	0.971438	−	0.237293i	$-0.0762601\pi$
$71$	3.75442	+	5.16752i	0.445568	+	0.613272i	−0.525870	+	0.850565i	$0.676260\pi$
$72$	−3.00426	−	7.41447i	−0.354055	−	0.873804i
$73$	−0.895864	+	0.291084i	−0.104853	+	0.0340688i	−0.360974	−	0.932576i	$-0.617556\pi$
$73$	−0.895864	+	0.291084i	−0.104853	+	0.0340688i	0.256121	+	0.966645i	$0.417556\pi$
$74$	4.15075	+	5.43832i	0.482515	+	0.632191i
$75$	0.670212	+	0.486937i	0.0773894	+	0.0562267i
$76$	−4.25447	+	1.60804i	−0.488021	+	0.184455i
$77$		0			0
$78$	0.656854	+	0.453939i	0.0743741	+	0.0513985i
$79$	−7.52983	−	5.47074i	−0.847172	−	0.615507i	0.0771926	−	0.997016i	$-0.475404\pi$
$79$	−7.52983	−	5.47074i	−0.847172	−	0.615507i	−0.924365	+	0.381509i	$0.875404\pi$
$80$	9.71190	−	4.20465i	1.08582	−	0.470094i
$81$	2.31308	+	7.11893i	0.257009	+	0.790992i
$82$	−0.335061	−	14.1925i	−0.0370013	−	1.56730i
$83$	−2.67338	−	3.67959i	−0.293441	−	0.403887i	0.636687	−	0.771122i	$-0.280304\pi$
$83$	−2.67338	−	3.67959i	−0.293441	−	0.403887i	−0.930128	+	0.367235i	$0.880304\pi$
$84$	−2.12736	+	1.70463i	−0.232115	+	0.185991i
$85$	4.48868	−	13.8147i	0.486865	−	1.49842i
$86$	−8.58247	+	3.01435i	−0.925472	+	0.325046i
$87$	−2.72607			−0.292265
$88$		0			0
$89$	−10.6569			−1.12962			−0.564812	−	0.825220i	$-0.691051\pi$
$89$	−10.6569			−1.12962			−0.564812	+	0.825220i	$0.691051\pi$
$90$	−9.98505	+	3.50697i	−1.05252	+	0.369667i
$91$	−1.38603	+	4.26576i	−0.145295	+	0.447173i
$92$	−7.98820	−	9.96919i	−0.832827	−	1.03936i
$93$	−0.266819	−	0.367244i	−0.0276678	−	0.0380815i
$94$		0			0
$95$	1.85927	+	5.72225i	0.190757	+	0.587090i
$96$	0.456643	−	2.29822i	0.0466059	−	0.234561i
$97$	−6.05572	−	4.39974i	−0.614865	−	0.446726i	0.236259	−	0.971690i	$-0.424079\pi$
$97$	−6.05572	−	4.39974i	−0.614865	−	0.446726i	−0.851124	+	0.524964i	$0.824079\pi$
$98$	−4.45408	−	3.07813i	−0.449930	−	0.310938i
$99$		0			0
$100$	−1.41421	−	3.74166i	−0.141421	−	0.374166i
$101$	13.9569	+	10.1403i	1.38877	+	1.00900i	0.995999	+	0.0893619i	$0.0284828\pi$
$101$	13.9569	+	10.1403i	1.38877	+	1.00900i	0.392769	+	0.919637i	$0.371517\pi$
$102$	−1.95124	−	2.55652i	−0.193202	−	0.253133i
$103$	17.1821	−	5.58280i	1.69300	−	0.550090i	0.705640	−	0.708571i	$-0.250660\pi$
$103$	17.1821	−	5.58280i	1.69300	−	0.550090i	0.987362	+	0.158481i	$0.0506597\pi$
$104$	−1.44777	−	3.57308i	−0.141965	−	0.350369i
$105$	2.11970	+	2.91752i	0.206862	+	0.284721i
$106$	10.1394	+	3.03187i	0.984827	+	0.294481i
$107$	8.28015	+	2.69038i	0.800472	+	0.260089i	0.680557	−	0.732695i	$-0.261738\pi$
$107$	8.28015	+	2.69038i	0.800472	+	0.260089i	0.119915	+	0.992784i	$0.461738\pi$
$108$	−1.27370	+	4.65740i	−0.122562	+	0.448159i
$109$	2.72607			0.261110			0.130555	−	0.991441i	$-0.458324\pi$
$109$	2.72607			0.261110			0.130555	+	0.991441i	$0.458324\pi$
$110$		0			0
$111$		−	2.00378i		−	0.190191i
$112$	13.1040	−	1.24091i	1.23821	−	0.117255i
$113$	1.90712	−	5.86951i	0.179407	−	0.552157i	−0.820400	−	0.571789i	$-0.806249\pi$
$113$	1.90712	−	5.86951i	0.179407	−	0.552157i	0.999807	+	0.0196319i	$0.00624944\pi$
$114$	1.27631	+	0.381638i	0.119537	+	0.0357437i
$115$	−13.6720	+	9.93327i	−1.27492	+	0.926283i
$116$	11.0020	+	7.22566i	1.02151	+	0.670886i
$117$	1.19134	+	3.66656i	0.110139	+	0.338973i
$118$	−3.64533	+	2.78227i	−0.335580	+	0.256129i
$119$	10.6191	−	14.6160i	0.973453	−	1.33984i
$120$	−3.00836	−	0.746879i	−0.274625	−	0.0681804i
$121$		0			0
$122$	−7.65685	−	5.29150i	−0.693219	−	0.479070i
$123$	−2.44404	+	3.36393i	−0.220371	+	0.303315i
$124$	0.103432	+	2.18937i	0.00928850	+	0.196611i
$125$	7.54878	−	2.45275i	0.675183	−	0.219380i
$126$	−13.1590	+	0.310661i	−1.17229	+	0.0276759i
$127$	−0.456761	+	0.331856i	−0.0405310	+	0.0294475i	−0.607866	−	0.794039i	$-0.707974\pi$
$127$	−0.456761	+	0.331856i	−0.0405310	+	0.0294475i	0.567335	+	0.823487i	$0.307974\pi$
$128$	−7.93455	+	8.06492i	−0.701322	+	0.712845i
$129$	2.53389	+	0.823309i	0.223096	+	0.0724883i
$130$	−4.81185	+	1.69003i	−0.422027	+	0.148225i
$131$		−	6.82233i		−	0.596070i	−0.954555	−	0.298035i	$-0.903669\pi$
$131$		−	6.82233i		−	0.596070i	0.954555	−	0.298035i	$-0.0963311\pi$
$132$		0			0
$133$			7.48331i			0.648886i
$134$	−2.84514	−	8.10067i	−0.245782	−	0.699792i
$135$	6.07479	+	1.97382i	0.522834	+	0.169879i
$136$	1.09869	+	15.4897i	0.0942118	+	1.32823i
$137$	7.00354	−	5.08837i	0.598353	−	0.434729i	−0.246941	−	0.969031i	$-0.579425\pi$
$137$	7.00354	−	5.08837i	0.598353	−	0.434729i	0.845294	+	0.534302i	$0.179425\pi$
$138$	0.0883096	+	3.74062i	0.00751741	+	0.318422i
$139$	18.7231	−	6.08350i	1.58807	−	0.515996i	0.623952	−	0.781462i	$-0.285526\pi$
$139$	18.7231	−	6.08350i	1.58807	−	0.515996i	0.964120	+	0.265466i	$0.0855259\pi$
$140$	−0.821703	−	17.3931i	−0.0694465	−	1.46999i
$141$		0			0
$142$	−5.13560	+	7.43126i	−0.430970	+	0.623617i
$143$		0			0
$144$	8.48528	−	7.48331i	0.707107	−	0.623610i
$145$	10.2348	−	14.0870i	0.849956	−	1.16986i
$146$	−0.808232	−	1.05895i	−0.0668897	−	0.0876389i
$147$	0.490035	+	1.50817i	0.0404174	+	0.124392i
$148$	−5.31119	+	8.08699i	−0.436577	+	0.664746i
$149$	17.0759	−	12.4064i	1.39891	−	1.01637i	0.404093	−	0.914718i	$-0.367587\pi$
$149$	17.0759	−	12.4064i	1.39891	−	1.01637i	0.994820	−	0.101652i	$-0.0324127\pi$
$150$	−0.335637	+	1.12247i	−0.0274047	+	0.0916490i
$151$	−4.06748	+	12.5184i	−0.331007	+	1.01873i	0.637649	+	0.770327i	$0.279907\pi$
$151$	−4.06748	+	12.5184i	−0.331007	+	1.01873i	−0.968656	+	0.248407i	$0.920093\pi$
$152$	−4.13943	−	4.92318i	−0.335752	−	0.399323i
$153$		−	15.5286i		−	1.25541i
$154$		0			0
$155$	2.89949			0.232893
$156$	−0.297867	+	1.08918i	−0.0238485	+	0.0872041i
$157$	−0.431722	−	0.140275i	−0.0344552	−	0.0111952i	0.291739	−	0.956498i	$-0.405766\pi$
$157$	−0.431722	−	0.140275i	−0.0344552	−	0.0111952i	−0.326194	+	0.945303i	$0.605766\pi$
$158$	3.77089	−	12.6109i	0.299996	−	1.00327i
$159$	−1.82195	−	2.50770i	−0.144490	−	0.198874i
$160$	10.1617	+	10.9882i	0.803350	+	0.868693i
$161$	−19.9900	+	6.49516i	−1.57544	+	0.511890i
$162$	−8.41484	+	6.42256i	−0.661132	+	0.504604i
$163$	10.3784	+	7.54036i	0.812900	+	0.590607i	0.914670	−	0.404201i	$-0.132451\pi$
$163$	10.3784	+	7.54036i	0.812900	+	0.590607i	−0.101770	+	0.994808i	$0.532451\pi$
$164$	18.7801	−	7.09822i	1.46648	−	0.554278i
$165$		0			0
$166$	3.65685	−	5.29150i	0.283827	−	0.410700i
$167$	−17.7219	−	12.8757i	−1.37136	−	0.996351i	−0.997630	−	0.0688128i	$-0.978079\pi$
$167$	−17.7219	−	12.8757i	−1.37136	−	0.996351i	−0.373729	−	0.927538i	$-0.621921\pi$
$168$	−3.27147	−	2.03970i	−0.252400	−	0.157366i
$169$	−3.44311	−	10.5968i	−0.264855	−	0.815139i
$170$	20.5367	−	0.484836i	1.57509	−	0.0371852i
$171$	3.78072	+	5.20372i	0.289119	+	0.397938i
$172$	−8.04415	−	10.0390i	−0.613361	−	0.765468i
$173$	1.68480	−	5.18529i	0.128093	−	0.394231i	−0.866359	−	0.499422i	$-0.833546\pi$
$173$	1.68480	−	5.18529i	0.128093	−	0.394231i	0.994452	+	0.105192i	$0.0335456\pi$
$174$	−1.27754	−	3.63742i	−0.0968502	−	0.275752i
$175$	−6.58132			−0.497501
$176$		0			0
$177$	1.34315			0.100957
$178$	−4.99421	−	14.2195i	−0.374332	−	1.06580i
$179$	3.00609	−	9.25180i	0.224686	−	0.691512i	−0.773637	−	0.633629i	$-0.781565\pi$
$179$	3.00609	−	9.25180i	0.224686	−	0.691512i	0.998323	−	0.0578837i	$-0.0184352\pi$
$180$	−9.35876	−	11.6796i	−0.697560	−	0.870548i
$181$	−1.55513	−	2.14046i	−0.115592	−	0.159099i	0.747300	−	0.664486i	$-0.231350\pi$
$181$	−1.55513	−	2.14046i	−0.115592	−	0.159099i	−0.862893	+	0.505387i	$0.831350\pi$
$182$	−6.34138	+	0.149709i	−0.470054	+	0.0110972i
$183$	0.842402	+	2.59265i	0.0622721	+	0.191654i
$184$	9.55839	−	15.3307i	0.704654	−	1.13019i
$185$	10.3546	+	7.52306i	0.761285	+	0.553106i
$186$	0.364976	−	0.528123i	0.0267613	−	0.0387239i
$187$		0			0
$188$		0			0
$189$	6.42711	+	4.66957i	0.467504	+	0.339661i
$190$	−6.76392	+	5.16251i	−0.490706	+	0.374528i
$191$	−16.1398	+	5.24415i	−1.16784	+	0.379453i	−0.827835	−	0.560972i	$-0.810428\pi$
$191$	−16.1398	+	5.24415i	−1.16784	+	0.379453i	−0.340002	+	0.940425i	$0.610428\pi$
$192$	3.28053	−	0.467732i	0.236752	−	0.0337557i
$193$	7.56145	+	10.4074i	0.544285	+	0.749144i	0.989223	−	0.146417i	$-0.0467743\pi$
$193$	7.56145	+	10.4074i	0.544285	+	0.749144i	−0.444938	+	0.895561i	$0.646774\pi$
$194$	3.03266	−	10.1421i	0.217732	−	0.728159i
$195$	1.42065	+	0.461597i	0.101735	+	0.0330556i
$196$	2.01982	−	7.38565i	0.144273	−	0.527546i
$197$	10.4366			0.743574			0.371787	−	0.928318i	$-0.378745\pi$
$197$	10.4366			0.743574			0.371787	+	0.928318i	$0.378745\pi$
$198$		0			0
$199$			21.1660i			1.50042i	0.661200	+	0.750209i	$0.270047\pi$
$199$			21.1660i			1.50042i	−0.661200	+	0.750209i	$0.729953\pi$
$200$	4.32977	−	3.64048i	0.306161	−	0.257421i
$201$	−0.777091	+	2.39164i	−0.0548118	+	0.168693i
$202$	−6.98954	+	23.3750i	−0.491782	+	1.64466i
$203$	17.5208	−	12.7296i	1.22972	−	0.893441i
$204$	2.49676	−	3.80164i	0.174808	−	0.266168i
$205$	−8.20722	−	25.2592i	−0.573217	−	1.76418i
$206$	15.5014	+	20.3099i	1.08003	+	1.41506i
$207$	−10.6191	+	14.6160i	−0.738080	+	1.01588i
$208$	4.08910	−	3.60625i	0.283528	−	0.250049i
$209$		0			0
$210$	−2.89949	+	4.19560i	−0.200084	+	0.289524i
$211$	5.34675	−	7.35917i	0.368086	−	0.506626i	−0.584294	−	0.811542i	$-0.698628\pi$
$211$	5.34675	−	7.35917i	0.368086	−	0.506626i	0.952379	+	0.304916i	$0.0986284\pi$
$212$	0.706280	+	14.9500i	0.0485075	+	1.02677i
$213$	2.51626	−	0.817582i	0.172411	−	0.0560198i
$214$	0.290597	+	12.3091i	0.0198648	+	0.841432i
$215$	−13.7678	+	10.0029i	−0.938953	+	0.682189i
$216$	−6.81131	+	0.483129i	−0.463451	+	0.0328728i
$217$	3.42975	+	1.11439i	0.232827	+	0.0756499i
$218$	1.27754	+	3.63742i	0.0865260	+	0.246357i
$219$			0.390175i			0.0263656i
$220$		0			0
$221$		−	7.48331i		−	0.503382i
$222$	2.67367	−	0.939051i	0.179445	−	0.0630250i
$223$	−3.99025	−	1.29651i	−0.267207	−	0.0868208i	0.172349	−	0.985036i	$-0.444864\pi$
$223$	−3.99025	−	1.29651i	−0.267207	−	0.0868208i	−0.439556	+	0.898215i	$0.644864\pi$
$224$	7.79680	+	16.9032i	0.520946	+	1.12940i
$225$	−4.57649	+	3.32502i	−0.305099	+	0.221668i
$226$	8.72549	−	0.205994i	0.580411	−	0.0137025i
$227$	12.6058	−	4.09586i	0.836674	−	0.271852i	0.140820	−	0.990035i	$-0.455026\pi$
$227$	12.6058	−	4.09586i	0.836674	−	0.271852i	0.695854	+	0.718183i	$0.255026\pi$
$228$	0.0889034	+	1.88183i	0.00588777	+	0.124628i
$229$	−5.95372	+	8.19459i	−0.393433	+	0.541514i	−0.959081	−	0.283133i	$-0.908626\pi$
$229$	−5.95372	+	8.19459i	−0.393433	+	0.541514i	0.565648	+	0.824647i	$0.308626\pi$
$230$	−19.6613	−	13.5875i	−1.29643	−	0.895934i
$231$		0			0
$232$	−4.48528	+	18.0663i	−0.294473	+	1.18611i
$233$	4.88807	−	6.72785i	0.320228	−	0.440756i	−0.618309	−	0.785935i	$-0.712182\pi$
$233$	4.88807	−	6.72785i	0.320228	−	0.440756i	0.938537	+	0.345179i	$0.112182\pi$
$234$	−4.33401	+	3.30790i	−0.283323	+	0.216244i
$235$		0			0
$236$	−5.42074	−	3.56011i	−0.352860	−	0.231744i
$237$	−3.11896	+	2.26606i	−0.202598	+	0.147196i
$238$	24.4787	+	7.31957i	1.58672	+	0.474457i
$239$	−1.68480	+	5.18529i	−0.108981	+	0.335409i	−0.990644	−	0.136470i	$-0.956424\pi$
$239$	−1.68480	+	5.18529i	−0.108981	+	0.335409i	0.881663	+	0.471879i	$0.156424\pi$
$240$	−0.413268	−	4.36410i	−0.0266764	−	0.281701i
$241$		−	4.54822i		−	0.292977i	−0.989212	−	0.146488i	$-0.953203\pi$
$241$		−	4.54822i		−	0.292977i	0.989212	−	0.146488i	$-0.0467971\pi$
$242$		0			0
$243$	10.3431			0.663513
$244$	3.47220	−	12.6964i	0.222285	−	0.812804i
$245$	−9.63331	−	3.13005i	−0.615450	−	0.199972i
$246$	−5.63389	−	1.68463i	−0.359203	−	0.107408i
$247$	1.82195	+	2.50770i	0.115928	+	0.159561i
$248$	−2.87282	+	1.16403i	−0.182424	+	0.0739162i
$249$	−1.79173	+	0.582168i	−0.113546	+	0.0368934i
$250$	6.81037	+	8.92294i	0.430725	+	0.564336i
$251$	−14.8974	−	10.8236i	−0.940316	−	0.683180i	0.00818049	−	0.999967i	$-0.497396\pi$
$251$	−14.8974	−	10.8236i	−0.940316	−	0.683180i	−0.948497	+	0.316787i	$0.897396\pi$
$252$	−6.58132	−	17.4125i	−0.414584	−	1.09689i
$253$		0			0
$254$	−0.656854	−	0.453939i	−0.0412147	−	0.0284827i
$255$	−4.86763	−	3.53654i	−0.304823	−	0.221467i
$256$	−14.4795	−	6.80761i	−0.904970	−	0.425475i
$257$	2.00406	+	6.16787i	0.125010	+	0.384741i	0.993903	−	0.110259i	$-0.0351680\pi$
$257$	2.00406	+	6.16787i	0.125010	+	0.384741i	−0.868893	+	0.495000i	$0.835168\pi$
$258$	0.0889282	+	3.76682i	0.00553643	+	0.234512i
$259$	9.35682	+	12.8786i	0.581404	+	0.800234i
$260$	−4.51004	−	5.62848i	−0.279701	−	0.349063i
$261$	5.75228	−	17.7037i	0.356057	−	1.09583i
$262$	9.10309	−	3.19721i	0.562391	−	0.197524i
$263$	−19.1794			−1.18265			−0.591325	−	0.806433i	$-0.701395\pi$
$263$	−19.1794			−1.18265			−0.591325	+	0.806433i	$0.701395\pi$
$264$		0			0
$265$	19.7990			1.21624
$266$	−9.98505	+	3.50697i	−0.612223	+	0.215026i
$267$	−1.36407	+	4.19817i	−0.0834795	+	0.256924i
$268$	9.47545	−	7.59258i	0.578805	−	0.463790i
$269$	8.04249	+	11.0695i	0.490359	+	0.674921i	0.980454	−	0.196748i	$-0.0630380\pi$
$269$	8.04249	+	11.0695i	0.490359	+	0.674921i	−0.490095	+	0.871669i	$0.663038\pi$
$270$	0.213198	+	9.03064i	0.0129748	+	0.549587i
$271$	3.89301	+	11.9815i	0.236483	+	0.727821i	0.996921	+	0.0784104i	$0.0249844\pi$
$271$	3.89301	+	11.9815i	0.236483	+	0.727821i	−0.760438	+	0.649411i	$0.775016\pi$
$272$	−20.1531	+	8.72505i	−1.22196	+	0.529034i
$273$	1.50304	+	1.09203i	0.0909684	+	0.0660924i
$274$	10.0716	+	6.96028i	0.608447	+	0.420486i
$275$		0			0
$276$	−4.94975	+	1.87083i	−0.297940	+	0.112611i
$277$	3.11896	+	2.26606i	0.187400	+	0.136154i	0.677530	−	0.735495i	$-0.263051\pi$
$277$	3.11896	+	2.26606i	0.187400	+	0.136154i	−0.490130	+	0.871650i	$0.663051\pi$
$278$	16.8916	+	22.1314i	1.01309	+	1.32735i
$279$	2.94798	−	0.957857i	0.176491	−	0.0573454i
$280$	22.8227	−	9.24749i	1.36392	−	0.552643i
$281$	3.78072	+	5.20372i	0.225539	+	0.310428i	0.906758	−	0.421652i	$-0.138550\pi$
$281$	3.78072	+	5.20372i	0.225539	+	0.310428i	−0.681219	+	0.732080i	$0.738550\pi$
$282$		0			0
$283$	1.79173	+	0.582168i	0.106507	+	0.0346063i	0.361786	−	0.932261i	$-0.382167\pi$
$283$	1.79173	+	0.582168i	0.106507	+	0.0346063i	−0.255279	+	0.966868i	$0.582167\pi$
$284$	−12.3223	−	3.36990i	−0.731196	−	0.199966i
$285$	2.49221			0.147626
$286$		0			0
$287$		−	33.0329i		−	1.94987i
$288$	13.9616	+	7.81501i	0.822694	+	0.460504i
$289$	−4.06114	+	12.4989i	−0.238891	+	0.735230i
$290$	23.5929	+	7.05468i	1.38542	+	0.414265i
$291$	−2.50836	+	1.82243i	−0.147043	+	0.106833i
$292$	1.03419	−	1.57469i	0.0605214	−	0.0921519i
$293$	4.48868	+	13.8147i	0.262231	+	0.807065i	0.992318	+	0.123711i	$0.0394795\pi$
$293$	4.48868	+	13.8147i	0.262231	+	0.807065i	−0.730087	+	0.683354i	$0.760520\pi$
$294$	−1.78272	+	1.36065i	−0.103970	+	0.0793544i
$295$	−5.04274	+	6.94074i	−0.293600	+	0.404105i
$296$	−13.2796	−	3.29688i	−0.771859	−	0.191627i
$297$		0			0
$298$	24.5563	+	16.9704i	1.42251	+	0.983070i
$299$	−5.11741	+	7.04351i	−0.295948	+	0.407337i
$300$	−1.65501	+	0.0781875i	−0.0955520	+	0.00451416i
$301$	−20.1301	+	6.54066i	−1.16028	+	0.376997i
$302$	−18.6096	+	0.439341i	−1.07086	+	0.0252812i
$303$	5.78116	−	4.20026i	0.332119	−	0.241298i
$304$	4.62915	−	7.83046i	0.265500	−	0.449108i
$305$	−16.5603	−	5.38077i	−0.948240	−	0.308102i
$306$	20.7199	−	7.27730i	1.18448	−	0.416015i
$307$			22.3509i			1.27563i	0.770188	+	0.637817i	$0.220162\pi$
$307$			22.3509i			1.27563i	−0.770188	+	0.637817i	$0.779838\pi$
$308$		0			0
$309$		−	7.48331i		−	0.425711i
$310$	1.35882	+	3.86882i	0.0771755	+	0.219734i
$311$	−14.2341	−	4.62494i	−0.807142	−	0.262256i	−0.123755	−	0.992313i	$-0.539494\pi$
$311$	−14.2341	−	4.62494i	−0.807142	−	0.262256i	−0.683387	+	0.730056i	$0.739494\pi$
$312$	−1.59289	+	0.112984i	−0.0901798	+	0.00639649i
$313$	−6.33333	+	4.60143i	−0.357981	+	0.260088i	−0.752209	−	0.658924i	$-0.771012\pi$
$313$	−6.33333	+	4.60143i	−0.357981	+	0.260088i	0.394228	+	0.919012i	$0.371012\pi$
$314$	−0.0151515	−	0.641788i	−0.000855051	−	0.0362182i
$315$	−23.4198	+	7.60955i	−1.31956	+	0.428750i
$316$	18.5940	−	0.878437i	1.04600	−	0.0494159i
$317$	9.06398	−	12.4755i	0.509084	−	0.700694i	−0.474681	−	0.880158i	$-0.657436\pi$
$317$	9.06398	−	12.4755i	0.509084	−	0.700694i	0.983765	+	0.179464i	$0.0574364\pi$
$318$	2.49221	−	3.60625i	0.139756	−	0.202229i
$319$		0			0
$320$	−9.89949	+	18.7083i	−0.553399	+	1.04583i
$321$	2.11970	−	2.91752i	0.118310	−	0.162840i
$322$	−18.0346	−	23.6290i	−1.00503	−	1.31679i
$323$	−3.85816	−	11.8742i	−0.214674	−	0.660699i
$324$	−12.5132	−	8.21813i	−0.695178	−	0.456563i
$325$	−2.20544	+	1.60234i	−0.122336	+	0.0888820i
$326$	−5.19744	+	17.3817i	−0.287859	+	0.962684i
$327$	0.348934	−	1.07391i	0.0192961	−	0.0593873i
$328$	18.2723	+	21.7320i	1.00892	+	1.19995i
$329$		0			0
$330$		0			0
$331$	−18.0711			−0.993276			−0.496638	−	0.867958i	$-0.665432\pi$
$331$	−18.0711			−0.993276			−0.496638	+	0.867958i	$0.665432\pi$
$332$	8.77424	+	2.39957i	0.481549	+	0.131693i
$333$	13.0130	+	4.22819i	0.713109	+	0.231703i
$334$	8.87498	−	29.6805i	0.485618	−	1.62404i
$335$	−9.44132	−	12.9949i	−0.515835	−	0.709985i
$336$	1.18845	−	5.32103i	0.0648355	−	0.290286i
$337$	18.1983	−	5.91299i	0.991325	−	0.322101i	0.231931	−	0.972732i	$-0.425496\pi$
$337$	18.1983	−	5.91299i	0.991325	−	0.322101i	0.759394	+	0.650631i	$0.225496\pi$
$338$	12.5258	−	9.56024i	0.681315	−	0.520008i
$339$	−2.06813	−	1.50258i	−0.112325	−	0.0816092i
$340$	10.2712	+	27.1750i	0.557034	+	1.47377i
$341$		0			0
$342$	−5.17157	+	7.48331i	−0.279647	+	0.404651i
$343$	8.44335	+	6.13446i	0.455898	+	0.331230i
$344$	9.62534	−	15.4381i	0.518964	−	0.832364i
$345$	2.16312	+	6.65740i	0.116458	+	0.358422i
$346$	7.70834	−	0.181981i	0.414403	−	0.00978336i
$347$	−2.44404	−	3.36393i	−0.131203	−	0.180585i	0.738361	−	0.674406i	$-0.235600\pi$
$347$	−2.44404	−	3.36393i	−0.131203	−	0.180585i	−0.869564	+	0.493820i	$0.835600\pi$
$348$	4.25473	−	3.40927i	0.228077	−	0.182756i
$349$	−4.48868	+	13.8147i	−0.240273	+	0.739485i	0.756105	+	0.654451i	$0.227100\pi$
$349$	−4.48868	+	13.8147i	−0.240273	+	0.739485i	−0.996378	+	0.0850347i	$0.972900\pi$
$350$	−3.08426	−	8.78150i	−0.164861	−	0.469391i
$351$	3.29066			0.175642
$352$		0			0
$353$	1.82843			0.0973174			0.0486587	−	0.998815i	$-0.484505\pi$
$353$	1.82843			0.0973174			0.0486587	+	0.998815i	$0.484505\pi$
$354$	0.629450	+	1.79217i	0.0334549	+	0.0952528i
$355$	−5.22223	+	16.0724i	−0.277167	+	0.853033i
$356$	16.6327	−	13.3276i	0.881534	−	0.706363i
$357$	−4.39858	−	6.05413i	−0.232798	−	0.320418i
$358$	13.7535	−	0.324698i	0.726896	−	0.0171608i
$359$	−1.01687	−	3.12960i	−0.0536683	−	0.165174i	0.920630	−	0.390437i	$-0.127676\pi$
$359$	−1.01687	−	3.12960i	−0.0536683	−	0.165174i	−0.974298	+	0.225263i	$0.927676\pi$
$360$	11.1983	−	17.9610i	0.590205	−	0.946627i
$361$	−11.1874	−	8.12815i	−0.588812	−	0.427797i
$362$	2.12723	−	3.07813i	0.111805	−	0.161783i
$363$		0			0
$364$	−3.17157	−	8.39119i	−0.166236	−	0.439818i
$365$	−2.01624	−	1.46488i	−0.105535	−	0.0766756i
$366$	−3.06461	+	2.33904i	−0.160190	+	0.122263i
$367$	−21.1723	+	6.87931i	−1.10519	+	0.359097i	−0.804097	−	0.594498i	$-0.797351\pi$
$367$	−21.1723	+	6.87931i	−1.10519	+	0.359097i	−0.301090	+	0.953596i	$0.597351\pi$
$368$	24.9353	+	5.56929i	1.29984	+	0.290319i
$369$	−16.6889	−	22.9703i	−0.868791	−	1.19579i
$370$	−5.18551	+	17.3418i	−0.269582	+	0.901558i
$371$	23.4198	+	7.60955i	1.21590	+	0.395068i
$372$	0.875721	+	0.239491i	0.0454040	+	0.0124170i
$373$	0.233860			0.0121088			0.00605440	−	0.999982i	$-0.498073\pi$
$373$	0.233860			0.0121088			0.00605440	+	0.999982i	$0.498073\pi$
$374$		0			0
$375$		−	3.28772i		−	0.169777i
$376$		0			0
$377$	2.77206	−	8.53151i	0.142768	−	0.439395i
$378$	−3.21865	+	10.7641i	−0.165550	+	0.553645i
$379$	13.0018	−	9.44634i	0.667856	−	0.485226i	−0.201451	−	0.979499i	$-0.564566\pi$
$379$	13.0018	−	9.44634i	0.667856	−	0.485226i	0.869307	+	0.494273i	$0.164566\pi$
$380$	−10.0582	−	6.60580i	−0.515975	−	0.338870i
$381$	0.0722667	+	0.222414i	0.00370233	+	0.0113946i
$382$	−14.5610	−	19.0779i	−0.745008	−	0.976110i
$383$	−4.28806	+	5.90201i	−0.219110	+	0.301579i	−0.904395	−	0.426696i	$-0.859677\pi$
$383$	−4.28806	+	5.90201i	−0.219110	+	0.301579i	0.685285	+	0.728275i	$0.259677\pi$
$384$	2.16148	+	4.15804i	0.110303	+	0.212189i
$385$		0			0
$386$	−10.3431	+	14.9666i	−0.526452	+	0.761781i
$387$	−10.6935	+	14.7183i	−0.543581	+	0.748175i
$388$	14.9539	−	0.706466i	0.759168	−	0.0358654i
$389$	−30.9845	+	10.0675i	−1.57098	+	0.510441i	−0.959712	−	0.280986i	$-0.909339\pi$
$389$	−30.9845	+	10.0675i	−1.57098	+	0.510441i	−0.611264	+	0.791427i	$0.709339\pi$
$390$	0.0498585	+	2.11190i	0.00252468	+	0.106940i
$391$	28.3707	−	20.6125i	1.43477	−	1.04242i
$392$	10.8013	−	0.766140i	0.545548	−	0.0386959i
$393$	−2.68759	−	0.873251i	−0.135571	−	0.0440497i
$394$	4.89097	+	13.9256i	0.246404	+	0.701561i
$395$		−	24.6250i		−	1.23902i
$396$		0			0
$397$		−	22.4499i		−	1.12673i	−0.826208	−	0.563365i	$-0.809506\pi$
$397$		−	22.4499i		−	1.12673i	0.826208	−	0.563365i	$-0.190494\pi$
$398$	−28.2420	+	9.91921i	−1.41564	+	0.497205i
$399$	2.94798	+	0.957857i	0.147584	+	0.0479528i
$400$	6.88662	+	4.07117i	0.344331	+	0.203559i
$401$	3.90628	−	2.83808i	0.195070	−	0.141727i	−0.485963	−	0.873979i	$-0.661531\pi$
$401$	3.90628	−	2.83808i	0.195070	−	0.141727i	0.681033	+	0.732253i	$0.261531\pi$
$402$	−3.55536	+	0.0839360i	−0.177325	+	0.00418635i
$403$	1.42065	−	0.461597i	0.0707675	−	0.0229938i
$404$	−34.4650	+	1.62823i	−1.71470	+	0.0810075i
$405$	−11.6406	+	16.0219i	−0.578427	+	0.796136i
$406$	25.1961	+	17.4125i	1.25046	+	0.864169i
$407$		0			0
$408$	6.24264	+	1.54985i	0.309057	+	0.0767288i
$409$	−1.10735	+	1.52413i	−0.0547549	+	0.0753636i	−0.835516	−	0.549466i	$-0.814831\pi$
$409$	−1.10735	+	1.52413i	−0.0547549	+	0.0753636i	0.780762	+	0.624829i	$0.214831\pi$
$410$	29.8574	−	22.7884i	1.47455	−	1.12544i
$411$	−1.10807	−	3.41029i	−0.0546570	−	0.168217i
$412$	−19.8351	+	30.2016i	−0.977206	+	1.48793i
$413$	−8.63255	+	6.27192i	−0.424780	+	0.308621i
$414$	−24.4787	−	7.31957i	−1.20306	−	0.359737i
$415$	3.71854	−	11.4445i	0.182536	−	0.561788i
$416$	6.72816	+	3.76610i	0.329875	+	0.184648i
$417$		−	8.15447i		−	0.399326i
$418$		0			0
$419$	16.1421			0.788595			0.394297	−	0.918983i	$-0.370988\pi$
$419$	16.1421			0.788595			0.394297	+	0.918983i	$0.370988\pi$
$420$	−6.95703	−	1.90260i	−0.339468	−	0.0928374i
$421$	7.11706	+	2.31247i	0.346864	+	0.112703i	0.477268	−	0.878758i	$-0.341627\pi$
$421$	7.11706	+	2.31247i	0.346864	+	0.112703i	−0.130403	+	0.991461i	$0.541627\pi$
$422$	12.3251	+	3.68542i	0.599976	+	0.179404i
$423$		0			0
$424$	−19.6169	+	7.94852i	−0.952679	+	0.386014i
$425$	10.4430	−	3.39312i	0.506558	−	0.164591i
$426$	2.27012	+	2.97431i	0.109988	+	0.144106i
$427$	−17.5208	−	12.7296i	−0.847889	−	0.616028i
$428$	−16.2879	+	6.15626i	−0.787307	+	0.297574i
$429$		0			0
$430$	−19.7990	−	13.6827i	−0.954792	−	0.659838i
$431$	1.74868	+	1.27049i	0.0842308	+	0.0611972i	0.629104	−	0.777321i	$-0.283422\pi$
$431$	1.74868	+	1.27049i	0.0842308	+	0.0611972i	−0.544873	+	0.838519i	$0.683422\pi$
$432$	−3.83669	−	8.86198i	−0.184593	−	0.426372i
$433$	−5.35933	−	16.4943i	−0.257553	−	0.792666i	−0.993316	−	0.115427i	$-0.963176\pi$
$433$	−5.35933	−	16.4943i	−0.257553	−	0.792666i	0.735763	−	0.677239i	$-0.236824\pi$
$434$	0.120369	+	5.09859i	0.00577790	+	0.244740i
$435$	−4.23940	−	5.83504i	−0.203264	−	0.279769i
$436$	−4.25473	+	3.40927i	−0.203765	+	0.163274i
$437$	−4.48868	+	13.8147i	−0.214723	+	0.660848i
$438$	−0.520614	+	0.182851i	−0.0248759	+	0.00873697i
$439$	34.5035			1.64676			0.823380	−	0.567490i	$-0.192085\pi$
$439$	34.5035			1.64676			0.823380	+	0.567490i	$0.192085\pi$
$440$		0			0
$441$	−10.8284			−0.515639
$442$	9.98505	−	3.50697i	0.474940	−	0.166810i
$443$	8.16244	−	25.1214i	0.387809	−	1.19355i	−0.546612	−	0.837386i	$-0.684083\pi$
$443$	8.16244	−	25.1214i	0.387809	−	1.19355i	0.934422	−	0.356169i	$-0.115917\pi$
$444$	2.50597	+	3.12742i	0.118928	+	0.148421i
$445$	−16.5728	−	22.8105i	−0.785628	−	1.08132i
$446$	−0.140040	−	5.93182i	−0.00663110	−	0.280880i
$447$	−2.70167	−	8.31489i	−0.127785	−	0.393281i
$448$	−18.9002	+	18.3248i	−0.892953	+	0.865768i
$449$	−12.9205	−	9.38726i	−0.609754	−	0.443012i	0.239574	−	0.970878i	$-0.422992\pi$
$449$	−12.9205	−	9.38726i	−0.609754	−	0.443012i	−0.849328	+	0.527866i	$0.822992\pi$
$450$	−6.58132	−	4.54822i	−0.310246	−	0.214405i
$451$		0			0
$452$	4.36396	+	11.5460i	0.205263	+	0.543076i
$453$	4.41087	+	3.20469i	0.207241	+	0.150569i
$454$	11.3727	+	14.9005i	0.533746	+	0.699315i
$455$	−11.2861	+	3.66709i	−0.529102	+	0.171916i
$456$	−2.46928	+	1.00052i	−0.115635	+	0.0468539i
$457$	−13.3669	−	18.3979i	−0.625276	−	0.860619i	0.372447	−	0.928053i	$-0.378519\pi$
$457$	−13.3669	−	18.3979i	−0.625276	−	0.860619i	−0.997724	+	0.0674344i	$0.978519\pi$
$458$	−13.7242	−	4.10379i	−0.641292	−	0.191758i
$459$	−12.6058	−	4.09586i	−0.588386	−	0.191178i
$460$	8.91591	−	32.6018i	0.415706	−	1.52007i
$461$	−3.85525			−0.179557			−0.0897783	−	0.995962i	$-0.528616\pi$
$461$	−3.85525			−0.179557			−0.0897783	+	0.995962i	$0.528616\pi$
$462$		0			0
$463$		−	22.2619i		−	1.03460i	−0.855804	−	0.517300i	$-0.826937\pi$
$463$		−	22.2619i		−	1.03460i	0.855804	−	0.517300i	$-0.173063\pi$
$464$	−26.2080	+	2.48183i	−1.21668	+	0.115216i
$465$	0.371133	−	1.14223i	0.0172109	−	0.0529696i
$466$	11.2678	+	3.36926i	0.521969	+	0.156078i
$467$	−29.1821	+	21.2020i	−1.35039	+	0.981113i	−0.351395	+	0.936227i	$0.614292\pi$
$467$	−29.1821	+	21.2020i	−1.35039	+	0.981113i	−0.998992	+	0.0448861i	$0.985708\pi$
$468$	−6.44484	−	4.23269i	−0.297913	−	0.195656i
$469$	−6.17348	−	19.0000i	−0.285065	−	0.877339i
$470$		0			0
$471$	−0.110520	+	0.152118i	−0.00509249	+	0.00700921i
$472$	2.20992	−	8.90135i	0.101720	−	0.409718i
$473$		0			0
$474$	−4.48528	−	3.09969i	−0.206016	−	0.142373i
$475$	−2.67338	+	3.67959i	−0.122663	+	0.168831i
$476$	1.70511	+	36.0924i	0.0781536	+	1.65429i
$477$	20.1301	−	6.54066i	0.921693	−	0.299476i
$478$	−7.70834	+	0.181981i	−0.352571	+	0.00832362i
$479$	−22.1327	+	16.0804i	−1.01127	+	0.734731i	−0.964475	−	0.264173i	$-0.914901\pi$
$479$	−22.1327	+	16.0804i	−1.01127	+	0.734731i	−0.0467954	+	0.998904i	$0.514901\pi$
$480$	5.62938	−	2.59661i	0.256945	−	0.118519i
$481$	6.27105	+	2.03759i	0.285935	+	0.0929059i
$482$	6.06872	−	2.13147i	0.276423	−	0.0970858i
$483$			8.70626i			0.396149i
$484$		0			0
$485$		−	19.8042i		−	0.899262i
$486$	4.84720	+	13.8009i	0.219873	+	0.626023i
$487$	25.3414	+	8.23392i	1.14833	+	0.373115i	0.820514	−	0.571627i	$-0.193688\pi$
$487$	25.3414	+	8.23392i	1.14833	+	0.373115i	0.327816	+	0.944742i	$0.393688\pi$
$488$	18.5681	−	1.31704i	0.840539	−	0.0596198i
$489$	4.29888	−	3.12332i	0.194402	−	0.141241i
$490$	−0.338087	−	14.3207i	−0.0152732	−	0.646942i
$491$	−24.4694	+	7.95058i	−1.10429	+	0.358805i	−0.803751	−	0.594966i	$-0.797166\pi$
$491$	−24.4694	+	7.95058i	−1.10429	+	0.358805i	−0.300536	+	0.953770i	$0.597166\pi$
$492$	−0.392439	−	8.30682i	−0.0176925	−	0.374500i
$493$	−21.2382	+	29.2319i	−0.956522	+	1.31654i
$494$	−2.49221	+	3.60625i	−0.112130	+	0.162253i
$495$		0			0
$496$	−2.89949	−	3.28772i	−0.130191	−	0.147623i
$497$	−12.3545	+	17.0045i	−0.554176	+	0.762758i
$498$	−1.61646	−	2.11789i	−0.0724355	−	0.0949049i
$499$	5.71227	+	17.5805i	0.255716	+	0.787013i	0.993688	+	0.112182i	$0.0357838\pi$
$499$	5.71227	+	17.5805i	0.255716	+	0.787013i	−0.737972	+	0.674832i	$0.764216\pi$
$500$	−8.71435	+	13.2688i	−0.389718	+	0.593397i
$501$	−7.34064	+	5.33328i	−0.327955	+	0.238274i
$502$	7.46052	−	24.9501i	0.332979	−	1.11358i
$503$	1.19134	−	3.66656i	0.0531191	−	0.163484i	−0.920978	−	0.389615i	$-0.872608\pi$
$503$	1.19134	−	3.66656i	0.0531191	−	0.163484i	0.974097	+	0.226132i	$0.0726080\pi$
$504$	20.1494	−	16.9417i	0.897526	−	0.754642i
$505$			45.6438i			2.03112i
$506$		0			0
$507$	−4.61522			−0.204969
$508$	0.297867	−	1.08918i	0.0132157	−	0.0483245i
$509$	−33.9325	−	11.0253i	−1.50403	−	0.488689i	−0.562840	−	0.826566i	$-0.690291\pi$
$509$	−33.9325	−	11.0253i	−1.50403	−	0.488689i	−0.941190	+	0.337877i	$0.890291\pi$
$510$	2.43768	−	8.15228i	0.107942	−	0.360989i
$511$	−1.82195	−	2.50770i	−0.0805984	−	0.110934i
$512$	2.29778	−	22.5104i	0.101549	−	0.994831i
$513$	5.22148	−	1.69656i	0.230534	−	0.0749050i
$514$	−7.29066	+	5.56454i	−0.321577	+	0.245441i
$515$	38.6702	+	28.0955i	1.70401	+	1.23804i
$516$	−4.98442	+	1.88393i	−0.219427	+	0.0829356i
$517$		0			0
$518$	−12.7990	+	18.5203i	−0.562355	+	0.813733i
$519$	−1.82704	−	1.32743i	−0.0801983	−	0.0582675i
$520$	5.39655	−	8.65550i	0.236654	−	0.379569i
$521$	−6.21517	−	19.1283i	−0.272291	−	0.838027i	−0.989923	−	0.141604i	$-0.954774\pi$
$521$	−6.21517	−	19.1283i	−0.272291	−	0.838027i	0.717632	−	0.696422i	$-0.245226\pi$
$522$	26.3179	−	0.621322i	1.15190	−	0.0271945i
$523$	−10.0055	−	13.7714i	−0.437509	−	0.602180i	0.532147	−	0.846652i	$-0.321385\pi$
$523$	−10.0055	−	13.7714i	−0.437509	−	0.602180i	−0.969656	+	0.244472i	$0.921385\pi$
$524$	8.53211	+	10.6480i	0.372727	+	0.465160i
$525$	−0.842402	+	2.59265i	−0.0367654	+	0.113152i
$526$	−8.98819	−	25.5912i	−0.391904	−	1.11583i
$527$	−6.01673			−0.262093
$528$		0			0
$529$	−17.7990			−0.773869
$530$	9.27857	+	26.4180i	0.403035	+	1.14752i
$531$	−2.83417	+	8.72268i	−0.122993	+	0.378532i
$532$	−9.35876	−	11.6796i	−0.405754	−	0.506376i
$533$	−8.04249	−	11.0695i	−0.348359	−	0.479475i
$534$	−6.24090	+	0.147337i	−0.270070	+	0.00637590i
$535$	7.11808	+	21.9072i	0.307742	+	0.947131i
$536$	14.5714	+	9.08500i	0.629389	+	0.392412i
$537$	−3.25988	−	2.36844i	−0.140674	−	0.102206i
$538$	−11.0011	+	15.9188i	−0.474293	+	0.686307i
$539$		0			0
$540$	−11.9497	+	4.51658i	−0.514235	+	0.194363i
$541$	−13.9569	−	10.1403i	−0.600056	−	0.435966i	0.245843	−	0.969310i	$-0.420935\pi$
$541$	−13.9569	−	10.1403i	−0.600056	−	0.435966i	−0.845899	+	0.533344i	$0.820935\pi$
$542$	−14.1625	+	10.8094i	−0.608333	+	0.464305i
$543$	−1.04227	+	0.338654i	−0.0447280	+	0.0145330i
$544$	−21.0864	−	22.8016i	−0.904073	−	0.977609i
$545$	4.23940	+	5.83504i	0.181596	+	0.249946i
$546$	−0.752714	+	2.51729i	−0.0322132	+	0.107730i
$547$	−39.2379	−	12.7492i	−1.67769	−	0.545115i	−0.693231	−	0.720715i	$-0.743813\pi$
$547$	−39.2379	−	12.7492i	−1.67769	−	0.545115i	−0.984462	+	0.175600i	$0.943813\pi$
$548$	−4.56722	+	16.7004i	−0.195102	+	0.713408i
$549$	−18.6148			−0.794459
$550$		0			0
$551$		−	14.9666i		−	0.637600i
$552$	−4.81590	−	5.72775i	−0.204978	−	0.243789i
$553$	9.46439	−	29.1284i	0.402467	−	1.23867i
$554$	−1.56195	+	5.22361i	−0.0663610	+	0.221930i
$555$	4.28902	−	3.11615i	0.182059	−	0.132273i
$556$	−21.6141	+	32.9103i	−0.916640	+	1.39571i
$557$	7.36482	+	22.6666i	0.312057	+	0.960414i	0.976949	+	0.213474i	$0.0684778\pi$
$557$	7.36482	+	22.6666i	0.312057	+	0.960414i	−0.664891	+	0.746940i	$0.731522\pi$
$558$	2.65961	+	3.48463i	0.112590	+	0.147516i
$559$	−5.15326	+	7.09285i	−0.217960	+	0.299996i
$560$	23.0346	+	26.1188i	0.973390	+	1.10372i
$561$		0			0
$562$	−5.17157	+	7.48331i	−0.218150	+	0.315665i
$563$	6.91278	−	9.51462i	0.291339	−	0.400994i	−0.638110	−	0.769946i	$-0.720283\pi$
$563$	6.91278	−	9.51462i	0.291339	−	0.400994i	0.929448	+	0.368952i	$0.120283\pi$
$564$		0			0
$565$	15.5293	−	5.04577i	0.653322	−	0.212277i
$566$	0.0628817	+	2.66354i	0.00264312	+	0.111957i
$567$	−19.9273	+	14.4780i	−0.836868	+	0.608020i
$568$	−1.27824	−	18.0210i	−0.0536337	−	0.756146i
$569$	−2.53389	−	0.823309i	−0.106226	−	0.0345149i	0.255422	−	0.966830i	$-0.417786\pi$
$569$	−2.53389	−	0.823309i	−0.106226	−	0.0345149i	−0.361648	+	0.932315i	$0.617786\pi$
$570$	1.16795	+	3.32538i	0.0489199	+	0.139285i
$571$			21.9607i			0.919028i	0.888170	+	0.459514i	$0.151976\pi$
$571$			21.9607i			0.919028i	−0.888170	+	0.459514i	$0.848024\pi$
$572$		0			0
$573$			7.02938i			0.293656i
$574$	44.0761	−	15.4805i	1.83970	−	0.646144i
$575$	−12.1496	−	3.94764i	−0.506672	−	0.164628i
$576$	−3.88470	+	22.2915i	−0.161862	+	0.928811i
$577$	25.5871	−	18.5901i	1.06521	−	0.773917i	0.0901613	−	0.995927i	$-0.471262\pi$
$577$	25.5871	−	18.5901i	1.06521	−	0.773917i	0.975044	+	0.222010i	$0.0712618\pi$
$578$	−18.5806	+	0.438657i	−0.772851	+	0.0182457i
$579$	5.06777	−	1.64662i	0.210609	−	0.0684311i
$580$	1.64341	+	34.7862i	0.0682387	+	1.44442i
$581$	8.79716	−	12.1083i	0.364968	−	0.502335i
$582$	−3.60720	−	2.49287i	−0.149523	−	0.103333i
$583$		0			0
$584$	2.58579	+	0.641967i	0.107001	+	0.0265648i
$585$	−5.99542	+	8.25199i	−0.247880	+	0.341178i
$586$	−16.3295	+	12.4634i	−0.674567	+	0.514858i
$587$	−9.35835	−	28.8021i	−0.386261	−	1.18879i	−0.935562	−	0.353163i	$-0.885106\pi$
$587$	−9.35835	−	28.8021i	−0.386261	−	1.18879i	0.549301	−	0.835625i	$-0.314894\pi$
$588$	−2.65097	−	1.74104i	−0.109324	−	0.0717994i
$589$	2.01624	−	1.46488i	0.0830777	−	0.0603595i
$590$	−11.6243	−	3.47587i	−0.478565	−	0.143099i
$591$	1.33587	−	4.11138i	0.0549503	−	0.169120i
$592$	−1.82425	−	19.2641i	−0.0749764	−	0.791748i
$593$		−	1.88393i		−	0.0773639i	−0.999252	−	0.0386819i	$-0.987684\pi$
$593$		−	1.88393i		−	0.0773639i	0.999252	−	0.0386819i	$-0.0123159\pi$
$594$		0			0
$595$	47.7990			1.95957
$596$	−11.1357	+	40.7187i	−0.456136	+	1.66790i
$597$	8.33815	+	2.70923i	0.341258	+	0.110881i
$598$	−11.7964	−	3.52734i	−0.482392	−	0.144244i
$599$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$599$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$600$	−0.879927	−	2.17165i	−0.0359229	−	0.0886572i
$601$	−31.1752	+	10.1294i	−1.27166	+	0.413188i	−0.865636	−	0.500674i	$-0.833085\pi$
$601$	−31.1752	+	10.1294i	−1.27166	+	0.413188i	−0.406025	+	0.913862i	$0.633085\pi$
$602$	−18.1610	−	23.7945i	−0.740186	−	0.969792i
$603$	−13.8921	−	10.0932i	−0.565730	−	0.411027i
$604$	−9.30739	−	24.6250i	−0.378712	−	1.00198i
$605$		0			0
$606$	8.31371	+	5.74544i	0.337721	+	0.233393i
$607$	23.5030	+	17.0759i	0.953958	+	0.693091i	0.951740	−	0.306906i	$-0.0992938\pi$
$607$	23.5030	+	17.0759i	0.953958	+	0.693091i	0.00221844	+	0.999998i	$0.499294\pi$
$608$	12.6176	+	2.50705i	0.511713	+	0.101674i
$609$	−2.77206	−	8.53151i	−0.112329	−	0.345714i
$610$	−0.581193	−	24.6182i	−0.0235318	−	0.996760i
$611$		0			0
$612$	19.4203	+	24.2363i	0.785019	+	0.979696i
$613$	−8.27949	+	25.4816i	−0.334405	+	1.02919i	0.632609	+	0.774471i	$0.281984\pi$
$613$	−8.27949	+	25.4816i	−0.334405	+	1.02919i	−0.967014	+	0.254722i	$0.918016\pi$
$614$	−29.8230	+	10.4745i	−1.20356	+	0.422716i
$615$	−11.0011			−0.443609
$616$		0			0
$617$	33.1127			1.33307			0.666534	−	0.745475i	$-0.267777\pi$
$617$	33.1127			1.33307			0.666534	+	0.745475i	$0.267777\pi$
$618$	9.98505	−	3.50697i	0.401657	−	0.141071i
$619$	9.74235	−	29.9839i	0.391578	−	1.20515i	−0.540016	−	0.841655i	$-0.681582\pi$
$619$	9.74235	−	29.9839i	0.391578	−	1.20515i	0.931595	−	0.363499i	$-0.118418\pi$
$620$	−4.52540	+	3.62616i	−0.181745	+	0.145630i
$621$	9.06398	+	12.4755i	0.363725	+	0.500625i
$622$	−0.499555	−	21.1601i	−0.0200303	−	0.848443i
$623$	−10.8366	−	33.3517i	−0.434160	−	1.33621i
$624$	−0.897247	−	2.07246i	−0.0359186	−	0.0829648i
$625$	25.0795	+	18.2213i	1.00318	+	0.728854i
$626$	−9.10777	−	6.29420i	−0.364020	−	0.251567i
$627$		0			0
$628$	0.849242	−	0.320983i	0.0338885	−	0.0128086i
$629$	−21.4868	−	15.6111i	−0.856734	−	0.622454i
$630$	−21.1289	−	27.6831i	−0.841796	−	1.10292i
$631$	11.1073	−	3.60898i	0.442175	−	0.143671i	−0.0794640	−	0.996838i	$-0.525321\pi$
$631$	11.1073	−	3.60898i	0.442175	−	0.143671i	0.521639	+	0.853166i	$0.325321\pi$
$632$	9.88599	+	24.3985i	0.393243	+	0.970520i
$633$	−2.21470	−	3.04827i	−0.0880263	−	0.121158i
$634$	20.8939	+	6.24764i	0.829803	+	0.248126i
$635$	−1.42065	−	0.461597i	−0.0563767	−	0.0183179i
$636$	5.97980	+	1.63535i	0.237114	+	0.0648457i
$637$	−5.21828			−0.206756
$638$		0			0
$639$			18.0663i			0.714693i
$640$	−29.6019	−	4.44155i	−1.17012	−	0.175568i
$641$	−5.50929	+	16.9558i	−0.217604	+	0.669715i	0.781355	+	0.624087i	$0.214529\pi$
$641$	−5.50929	+	16.9558i	−0.217604	+	0.669715i	−0.998958	+	0.0456283i	$0.985471\pi$
$642$	4.88624	+	1.46107i	0.192845	+	0.0576639i
$643$	−0.497726	+	0.361619i	−0.0196284	+	0.0142609i	−0.597556	−	0.801827i	$-0.703862\pi$
$643$	−0.497726	+	0.361619i	−0.0196284	+	0.0142609i	0.577928	+	0.816088i	$0.303862\pi$
$644$	23.0766	−	35.1372i	0.909346	−	1.38460i
$645$	2.17827	+	6.70403i	0.0857694	+	0.263971i
$646$	14.0358	−	10.7127i	0.552230	−	0.421485i
$647$	13.8399	−	19.0490i	0.544103	−	0.748893i	−0.445095	−	0.895484i	$-0.646830\pi$
$647$	13.8399	−	19.0490i	0.544103	−	0.748893i	0.989197	+	0.146590i	$0.0468299\pi$
$648$	5.10135	−	20.5478i	0.200400	−	0.807193i
$649$		0			0
$650$	−3.17157	−	2.19181i	−0.124399	−	0.0859699i
$651$	0.878009	−	1.20848i	0.0344119	−	0.0473639i
$652$	−25.6283	+	1.21076i	−1.00368	+	0.0474168i
$653$	−34.7959	+	11.3059i	−1.36167	+	0.442433i	−0.896600	−	0.442841i	$-0.853970\pi$
$653$	−34.7959	+	11.3059i	−1.36167	+	0.442433i	−0.465069	+	0.885274i	$0.653970\pi$
$654$	1.59645	−	0.0376895i	0.0624261	−	0.00147378i
$655$	14.6029	−	10.6096i	0.570583	−	0.414553i
$656$	−20.4340	+	34.5653i	−0.797816	+	1.34955i
$657$	−2.53389	−	0.823309i	−0.0988563	−	0.0321204i
$658$		0			0
$659$		−	10.9804i		−	0.427735i	−0.976863	−	0.213867i	$-0.931394\pi$
$659$		−	10.9804i		−	0.427735i	0.976863	−	0.213867i	$-0.0686060\pi$
$660$		0			0
$661$			12.3209i			0.479227i	0.970868	+	0.239613i	$0.0770207\pi$
$661$			12.3209i			0.479227i	−0.970868	+	0.239613i	$0.922979\pi$
$662$	−8.46880	−	24.1124i	−0.329149	−	0.937154i
$663$	−2.94798	−	0.957857i	−0.114490	−	0.0372001i
$664$	0.910183	+	12.8321i	0.0353220	+	0.497981i
$665$	−16.0177	+	11.6376i	−0.621141	+	0.451285i
$666$	0.456700	+	19.3449i	0.0176968	+	0.749598i
$667$	39.9801	−	12.9903i	1.54804	−	0.502987i
$668$	43.7620	−	2.06745i	1.69320	−	0.0799920i
$669$	−1.02150	+	1.40597i	−0.0394933	+	0.0543579i
$670$	12.9146	−	18.6875i	0.498934	−	0.721962i
$671$		0			0
$672$	7.65685	−	0.907878i	0.295370	−	0.0350222i
$673$	−22.4944	+	30.9608i	−0.867094	+	1.19345i	0.112738	+	0.993625i	$0.464038\pi$
$673$	−22.4944	+	30.9608i	−0.867094	+	1.19345i	−0.979831	+	0.199827i	$0.935962\pi$
$674$	16.4182	+	21.5111i	0.632405	+	0.828577i
$675$	1.49207	+	4.59211i	0.0574296	+	0.176750i
$676$	18.6264	+	12.2330i	0.716399	+	0.470500i
$677$	2.01624	−	1.46488i	0.0774904	−	0.0563001i	−0.548366	−	0.836239i	$-0.684750\pi$
$677$	2.01624	−	1.46488i	0.0774904	−	0.0563001i	0.625856	+	0.779939i	$0.284750\pi$
$678$	1.03570	−	3.46369i	0.0397760	−	0.133022i
$679$	7.61155	−	23.4259i	0.292105	−	0.899005i
$680$	−31.4464	+	26.4402i	−1.20591	+	1.01394i
$681$		−	5.49019i		−	0.210384i
$682$		0			0
$683$	−36.4264			−1.39382			−0.696909	−	0.717160i	$-0.745442\pi$
$683$	−36.4264			−1.39382			−0.696909	+	0.717160i	$0.745442\pi$
$684$	−12.4086	−	3.39350i	−0.474456	−	0.129754i
$685$	21.7829	+	7.07769i	0.832281	+	0.270425i
$686$	−4.22837	+	14.1409i	−0.161440	+	0.539901i
$687$	2.46611	+	3.39431i	0.0940880	+	0.129501i
$688$	25.1099	+	5.60831i	0.957307	+	0.213815i
$689$	9.70080	−	3.15198i	0.369571	−	0.120081i
$690$	−7.86930	+	6.00618i	−0.299579	+	0.228651i
$691$	7.08485	+	5.14745i	0.269520	+	0.195818i	0.714334	−	0.699805i	$-0.246730\pi$
$691$	7.08485	+	5.14745i	0.269520	+	0.195818i	−0.444813	+	0.895623i	$0.646730\pi$
$692$	3.85525	+	10.2000i	0.146554	+	0.387747i
$693$		0			0
$694$	3.34315	−	4.83756i	0.126904	−	0.183631i
$695$	42.1384	+	30.6153i	1.59840	+	1.16131i
$696$	6.54294	+	4.07941i	0.248010	+	0.154629i
$697$	17.0308	+	52.4153i	0.645086	+	1.98537i
$698$	−20.5367	+	0.484836i	−0.777324	+	0.0183513i
$699$	−2.02471	−	2.78677i	−0.0765814	−	0.105405i
$700$	10.2718	−	8.23070i	0.388239	−	0.311091i
$701$	8.06269	−	24.8144i	0.304523	−	0.937227i	−0.675331	−	0.737515i	$-0.735999\pi$
$701$	8.06269	−	24.8144i	0.304523	−	0.937227i	0.979855	−	0.199712i	$-0.0640007\pi$
$702$	1.54213	+	4.39075i	0.0582039	+	0.165718i
$703$	11.0011			0.414916
$704$		0			0
$705$		0			0
$706$	0.856871	+	2.43968i	0.0322488	+	0.0918188i
$707$	−17.5428	+	53.9911i	−0.659763	+	2.03054i
$708$	−2.09632	+	1.67976i	−0.0787846	+	0.0631292i
$709$	27.1919	+	37.4265i	1.02122	+	1.40558i	0.911349	+	0.411636i	$0.135042\pi$
$709$	27.1919	+	37.4265i	1.02122	+	1.40558i	0.109867	+	0.993946i	$0.464958\pi$
$710$	−23.8928	+	0.564070i	−0.896682	+	0.0211692i
$711$	−8.13495	−	25.0368i	−0.305085	−	0.938954i
$712$	25.5779	+	15.9474i	0.958573	+	0.597653i
$713$	5.66312	+	4.11450i	0.212085	+	0.154089i
$714$	6.01673	−	8.70626i	0.225170	−	0.325824i
$715$		0			0
$716$	6.87868	+	18.1993i	0.257068	+	0.680139i
$717$	1.82704	+	1.32743i	0.0682322	+	0.0495736i
$718$	3.69931	−	2.82347i	0.138057	−	0.105371i
$719$	4.85369	−	1.57706i	0.181012	−	0.0588144i	−0.217108	−	0.976147i	$-0.569663\pi$
$719$	4.85369	−	1.57706i	0.181012	−	0.0588144i	0.398121	+	0.917333i	$0.369663\pi$
$720$	29.2135	+	6.52483i	1.08872	+	0.243166i
$721$	34.9439	+	48.0961i	1.30138	+	1.79119i
$722$	5.60259	−	18.7366i	0.208507	−	0.697306i
$723$	−1.79173	−	0.582168i	−0.0666351	−	0.0216510i
$724$	5.10408	+	1.39586i	0.189691	+	0.0518766i
$725$	13.1626			0.488848
$726$		0			0
$727$			8.57922i			0.318186i	0.987264	+	0.159093i	$0.0508569\pi$
$727$			8.57922i			0.318186i	−0.987264	+	0.159093i	$0.949143\pi$
$728$	9.71011	−	8.16429i	0.359881	−	0.302589i
$729$	−5.61532	+	17.2822i	−0.207975	+	0.640081i
$730$	1.00972	−	3.37679i	0.0373714	−	0.124980i
$731$	28.5694	−	20.7569i	1.05668	−	0.767721i
$732$	−4.55719	−	2.99297i	−0.168439	−	0.110623i
$733$	8.48389	+	26.1107i	0.313360	+	0.964421i	0.976424	+	0.215860i	$0.0692553\pi$
$733$	8.48389	+	26.1107i	0.313360	+	0.964421i	−0.663065	+	0.748562i	$0.730745\pi$
$734$	−19.1013	−	25.0265i	−0.705042	−	0.923745i
$735$	−2.46611	+	3.39431i	−0.0909638	+	0.125201i
$736$	4.25447	+	35.8813i	0.156822	+	1.32260i
$737$		0			0
$738$	22.8284	−	33.0329i	0.840326	−	1.21596i
$739$	28.0311	−	38.5815i	1.03114	−	1.41924i	0.127053	−	0.991896i	$-0.459448\pi$
$739$	28.0311	−	38.5815i	1.03114	−	1.41924i	0.904088	−	0.427347i	$-0.140552\pi$
$740$	−25.5695	+	1.20798i	−0.939952	+	0.0444061i
$741$	1.22109	−	0.396757i	0.0448580	−	0.0145752i
$742$	0.821932	+	34.8153i	0.0301741	+	1.27811i
$743$	20.3841	−	14.8099i	0.747819	−	0.543322i	−0.147331	−	0.989087i	$-0.547068\pi$
$743$	20.3841	−	14.8099i	0.747819	−	0.543322i	0.895150	+	0.445765i	$0.147068\pi$
$744$	0.0908417	+	1.28072i	0.00333042	+	0.0469533i
$745$	53.1106	+	17.2567i	1.94582	+	0.632236i
$746$	0.109596	+	0.312041i	0.00401258	+	0.0114246i
$747$		−	12.8643i		−	0.470680i
$748$		0			0
$749$			28.6493i			1.04682i
$750$	4.38683	−	1.54075i	0.160184	−	0.0562603i
$751$	−6.93823	−	2.25437i	−0.253180	−	0.0822630i	0.179678	−	0.983726i	$-0.442495\pi$
$751$	−6.93823	−	2.25437i	−0.253180	−	0.0822630i	−0.432857	+	0.901463i	$0.642495\pi$
$752$		0			0
$753$	−6.17071	+	4.48328i	−0.224873	+	0.163380i
$754$	12.6828	−	0.299419i	0.461879	−	0.0109042i
$755$	−33.1206	+	10.7615i	−1.20538	+	0.391652i
$756$	−15.8710	+	0.749793i	−0.577223	+	0.0272697i
$757$	16.8397	−	23.1778i	0.612048	−	0.842411i	−0.384696	−	0.923043i	$-0.625694\pi$
$757$	16.8397	−	23.1778i	0.612048	−	0.842411i	0.996744	+	0.0806320i	$0.0256939\pi$
$758$	18.6975	+	12.9214i	0.679122	+	0.469328i
$759$		0			0
$760$	4.10051	−	16.5165i	0.148741	−	0.599116i
$761$	−4.33440	+	5.96579i	−0.157122	+	0.216260i	−0.880319	−	0.474382i	$-0.842672\pi$
$761$	−4.33440	+	5.96579i	−0.157122	+	0.216260i	0.723197	+	0.690641i	$0.242672\pi$
$762$	−0.262902	+	0.200658i	−0.00952392	+	0.00726906i
$763$	2.77206	+	8.53151i	0.100355	+	0.308861i
$764$	18.6319	−	28.3696i	0.674079	−	1.02637i
$765$	33.2383	−	24.1490i	1.20173	−	0.873110i
$766$	−9.88465	−	2.95569i	−0.357147	−	0.106793i
$767$	−1.36580	+	4.20351i	−0.0493163	+	0.151780i
$768$	−4.53516	+	4.83270i	−0.163648	+	0.174385i
$769$			2.82590i			0.101905i	0.998701	+	0.0509523i	$0.0162256\pi$
$769$			2.82590i			0.101905i	−0.998701	+	0.0509523i	$0.983774\pi$
$770$		0			0
$771$	2.68629			0.0967444
$772$	−24.8173	−	6.78700i	−0.893194	−	0.244270i
$773$	−8.33815	−	2.70923i	−0.299902	−	0.0974442i	0.155201	−	0.987883i	$-0.450398\pi$
$773$	−8.33815	−	2.70923i	−0.299902	−	0.0974442i	−0.455103	+	0.890439i	$0.650398\pi$
$774$	−24.6502	−	7.37084i	−0.886033	−	0.264939i
$775$	1.28831	+	1.77321i	0.0462776	+	0.0636957i
$776$	7.95061	+	19.6220i	0.285410	+	0.704389i
$777$	6.27105	−	2.03759i	0.224973	−	0.0730980i
$778$	−27.9536	−	36.6248i	−1.00219	−	1.31306i
$779$	−18.4686	−	13.4182i	−0.661706	−	0.480757i
$780$	−2.79457	+	1.05625i	−0.100062	+	0.0378197i
$781$		0			0
$782$	40.7990	+	28.1954i	1.45897	+	1.00826i
$783$	−12.8542	−	9.33914i	−0.459373	−	0.333754i
$784$	6.08417	+	14.0532i	0.217292	+	0.501900i
$785$	−0.371133	−	1.14223i	−0.0132463	−	0.0407679i
$786$	−0.0943226	−	3.99531i	−0.00336438	−	0.142508i
$787$	−19.3623	−	26.6499i	−0.690191	−	0.949967i	0.309808	−	0.950799i	$-0.399735\pi$
$787$	−19.3623	−	26.6499i	−0.690191	−	0.949967i	−1.00000		0.000832032i	$0.999735\pi$
$788$	−16.2889	+	13.0521i	−0.580269	+	0.464963i
$789$	−2.45494	+	7.55553i	−0.0873981	+	0.268984i
$790$	32.8574	−	11.5402i	1.16901	−	0.410583i
$791$	20.3085			0.722088
$792$		0			0
$793$	−8.97056			−0.318554
$794$	29.9551	−	10.5209i	1.06307	−	0.373373i
$795$	2.53425	−	7.79962i	0.0898806	−	0.276624i
$796$	−26.4706	−	33.0350i	−0.938224	−	1.17089i
$797$	−25.9036	−	35.6533i	−0.917554	−	1.26290i	−0.964520	−	0.264008i	$-0.914955\pi$
$797$	−25.9036	−	35.6533i	−0.917554	−	1.26290i	0.0469667	−	0.998896i	$-0.485045\pi$
$798$	0.103461	+	4.38240i	0.00366249	+	0.155135i
$799$		0			0
$800$	−2.20487	+	11.0968i	−0.0779538	+	0.392330i
$801$	−24.3855	−	17.7171i	−0.861619	−	0.626003i
$802$	5.61750	+	3.88215i	0.198361	+	0.137083i
$803$		0			0
$804$	−1.77817	−	4.70461i	−0.0627114	−	0.165919i
$805$	−44.9898	−	32.6870i	−1.58568	−	1.15207i
$806$	1.28168	+	1.67926i	0.0451454	+	0.0591494i
$807$	5.39017	−	1.75137i	0.189743	−	0.0616512i
$808$	−18.3242	−	45.2239i	−0.644643	−	1.59097i
$809$	−0.553674	−	0.762067i	−0.0194661	−	0.0267929i	0.799173	−	0.601101i	$-0.205271\pi$
$809$	−0.553674	−	0.762067i	−0.0194661	−	0.0267929i	−0.818639	+	0.574308i	$0.805271\pi$
$810$	−26.8334	−	8.02367i	−0.942831	−	0.281923i
$811$	−5.37518	−	1.74650i	−0.188748	−	0.0613280i	0.213118	−	0.977027i	$-0.431638\pi$
$811$	−5.37518	−	1.74650i	−0.188748	−	0.0613280i	−0.401866	+	0.915699i	$0.631638\pi$
$812$	−11.4258	+	41.7795i	−0.400967	+	1.46617i
$813$	5.21828			0.183013
$814$		0			0
$815$			33.9408i			1.18890i
$816$	0.857571	+	9.05592i	0.0300210	+	0.317021i
$817$	−4.52012	+	13.9115i	−0.158139	+	0.486702i
$818$	−2.55261	−	0.763276i	−0.0892500	−	0.0266873i
$819$	−10.2634	+	7.45682i	−0.358633	+	0.260562i
$820$	44.3991	+	29.1594i	1.55048	+	1.01829i
$821$	6.59468	+	20.2963i	0.230156	+	0.708347i	0.997727	+	0.0673836i	$0.0214651\pi$
$821$	6.59468	+	20.2963i	0.230156	+	0.708347i	−0.767571	+	0.640964i	$0.778535\pi$
$822$	4.03109	−	3.07670i	0.140600	−	0.107312i
$823$	−21.1277	+	29.0798i	−0.736466	+	1.01366i	0.262348	+	0.964973i	$0.415503\pi$
$823$	−21.1277	+	29.0798i	−0.736466	+	1.01366i	−0.998814	+	0.0486850i	$0.984497\pi$
$824$	−49.5937	−	12.3125i	−1.72768	−	0.428927i
$825$		0			0
$826$	−12.4142	−	8.57922i	−0.431946	−	0.298509i
$827$	29.8265	−	41.0526i	1.03717	−	1.42754i	0.137741	−	0.990468i	$-0.456016\pi$
$827$	29.8265	−	41.0526i	1.03717	−	1.42754i	0.899427	−	0.437071i	$-0.143984\pi$
$828$	−1.70511	−	36.0924i	−0.0592567	−	1.25430i
$829$	39.8284	−	12.9410i	1.38330	−	0.449461i	0.479546	−	0.877517i	$-0.340801\pi$
$829$	39.8284	−	12.9410i	1.38330	−	0.449461i	0.903752	+	0.428056i	$0.140801\pi$
$830$	17.0131	−	0.401651i	0.590535	−	0.0139415i
$831$	1.29192	−	0.938631i	0.0448160	−	0.0325608i
$832$	−1.87206	+	10.7424i	−0.0649019	+	0.372425i
$833$	19.9900	+	6.49516i	0.692614	+	0.225044i
$834$	10.8806	−	3.82150i	0.376763	−	0.132328i
$835$		−	57.9563i		−	2.00566i
$836$		0			0
$837$		−	2.64575i		−	0.0914505i
$838$	7.56483	+	21.5386i	0.261323	+	0.744038i
$839$	−51.7251	−	16.8065i	−1.78575	−	0.580225i	−0.786449	−	0.617655i	$-0.788083\pi$
$839$	−51.7251	−	16.8065i	−1.78575	−	0.580225i	−0.999299	+	0.0374297i	$0.988083\pi$
$840$	−0.721678	−	10.1745i	−0.0249003	−	0.351052i
$841$	−11.5800	+	8.41339i	−0.399311	+	0.290117i
$842$	0.249777	+	10.5801i	0.00860789	+	0.364613i
$843$	2.53389	−	0.823309i	0.0872716	−	0.0283563i
$844$	0.858528	+	18.1726i	0.0295517	+	0.625527i
$845$	17.3275	−	23.8493i	0.596084	−	0.820440i
$846$		0			0
$847$		0			0
$848$	−19.7990	−	22.4499i	−0.679900	−	0.770934i
$849$	0.458679	−	0.631317i	0.0157418	−	0.0216667i
$850$	9.42144	+	12.3440i	0.323153	+	0.423395i
$851$	9.54847	+	29.3872i	0.327317	+	1.00738i
$852$	−2.90478	+	4.42292i	−0.0995163	+	0.151527i
$853$	−47.0060	+	34.1519i	−1.60946	+	1.16934i	−0.744284	+	0.667863i	$0.767209\pi$
$853$	−47.0060	+	34.1519i	−1.60946	+	1.16934i	−0.865172	+	0.501475i	$0.832791\pi$
$854$	8.77427	−	29.3437i	0.300250	−	1.00412i
$855$	−5.25881	+	16.1850i	−0.179848	+	0.553514i
$856$	−15.8475	−	18.8480i	−0.541656	−	0.644213i
$857$		−	21.9607i		−	0.750165i	−0.926992	−	0.375082i	$-0.877614\pi$
$857$		−	21.9607i		−	0.750165i	0.926992	−	0.375082i	$-0.122386\pi$
$858$		0			0
$859$	−49.2426			−1.68014			−0.840069	−	0.542480i	$-0.817485\pi$
$859$	−49.2426			−1.68014			−0.840069	+	0.542480i	$0.817485\pi$
$860$	8.97836	−	32.8302i	0.306160	−	1.11950i
$861$	−13.0130	−	4.22819i	−0.443482	−	0.144096i
$862$	−0.875725	+	2.92867i	−0.0298273	+	0.0997510i
$863$	8.79716	+	12.1083i	0.299459	+	0.412170i	0.932058	−	0.362310i	$-0.118012\pi$
$863$	8.79716	+	12.1083i	0.299459	+	0.412170i	−0.632599	+	0.774480i	$0.718012\pi$
$864$	10.0266	−	9.27239i	0.341111	−	0.315453i
$865$	13.7190	−	4.45757i	0.466460	−	0.151562i
$866$	19.4969	−	14.8809i	0.662532	−	0.505672i
$867$	4.40401	+	3.19970i	0.149568	+	0.108667i
$868$	−6.74668	+	2.55000i	−0.228997	+	0.0865528i
$869$		0			0
$870$	5.79899	−	8.39119i	0.196604	−	0.284488i
$871$	−6.69468	−	4.86397i	−0.226841	−	0.164809i
$872$	−6.54294	−	4.07941i	−0.221572	−	0.138146i
$873$	−6.54238	−	20.1354i	−0.221426	−	0.681479i
$874$	−20.5367	+	0.484836i	−0.694663	+	0.0163998i
$875$	15.3522	+	21.1305i	0.519000	+	0.714343i
$876$	−0.487960	−	0.608969i	−0.0164866	−	0.0205751i
$877$	−9.04962	+	27.8519i	−0.305584	+	0.940491i	0.673875	+	0.738846i	$0.264629\pi$
$877$	−9.04962	+	27.8519i	−0.305584	+	0.940491i	−0.979459	+	0.201645i	$0.935371\pi$
$878$	16.1697	+	46.0383i	0.545699	+	1.55372i
$879$	6.01673			0.202939
$880$		0			0
$881$	6.51472			0.219486			0.109743	−	0.993960i	$-0.464997\pi$
$881$	6.51472			0.219486			0.109743	+	0.993960i	$0.464997\pi$
$882$	−5.07462	−	14.4485i	−0.170871	−	0.486505i
$883$	−1.34211	+	4.13058i	−0.0451655	+	0.139005i	−0.971096	−	0.238688i	$-0.923283\pi$
$883$	−1.34211	+	4.13058i	−0.0451655	+	0.139005i	0.925931	+	0.377693i	$0.123283\pi$
$884$	9.35876	+	11.6796i	0.314769	+	0.392828i
$885$	2.08877	+	2.87495i	0.0702133	+	0.0966403i
$886$	37.3449	−	0.881651i	1.25463	−	0.0296196i
$887$	−14.3807	−	44.2592i	−0.482857	−	1.48608i	−0.835061	−	0.550157i	$-0.814568\pi$
$887$	−14.3807	−	44.2592i	−0.482857	−	1.48608i	0.352205	−	0.935923i	$-0.385432\pi$
$888$	−2.99855	+	4.80936i	−0.100625	+	0.161392i
$889$	−1.50304	−	1.09203i	−0.0504105	−	0.0366254i
$890$	22.6696	−	32.8032i	0.759888	−	1.09956i
$891$		0			0
$892$	7.84924	−	2.96673i	0.262812	−	0.0993336i
$893$		0			0
$894$	9.82852	−	7.50154i	0.328715	−	0.250889i
$895$	24.4780	−	7.95338i	0.818208	−	0.265852i
$896$	−33.3084	−	16.6310i	−1.11275	−	0.555603i
$897$	2.11970	+	2.91752i	0.0707748	+	0.0974131i
$898$	6.47047	−	21.6391i	0.215923	−	0.722106i
$899$	−6.85950	−	2.22879i	−0.228777	−	0.0743342i
$900$	2.98447	−	10.9130i	0.0994822	−	0.363766i
$901$	−41.0848			−1.36873
$902$		0			0
$903$			8.76725i			0.291756i
$904$	−13.3607	+	11.2337i	−0.444372	+	0.373629i
$905$	2.16312	−	6.65740i	0.0719045	−	0.221299i
$906$	−2.20893	+	7.38730i	−0.0733869	+	0.245427i
$907$	27.1140	−	19.6995i	0.900305	−	0.654110i	−0.0382395	−	0.999269i	$-0.512175\pi$
$907$	27.1140	−	19.6995i	0.900305	−	0.654110i	0.938544	+	0.345159i	$0.112175\pi$
$908$	−14.5522	+	22.1576i	−0.482931	+	0.735326i
$909$	15.0786	+	46.4071i	0.500125	+	1.53923i
$910$	−10.1821	−	13.3406i	−0.337535	−	0.442238i
$911$	26.3915	−	36.3248i	0.874389	−	1.20349i	−0.103554	−	0.994624i	$-0.533022\pi$
$911$	26.3915	−	36.3248i	0.874389	−	1.20349i	0.977943	−	0.208870i	$-0.0669784\pi$
$912$	−2.49221	−	2.82590i	−0.0825253	−	0.0935749i
$913$		0			0
$914$	18.2843	−	26.4575i	0.604790	−	0.875137i
$915$	−4.23940	+	5.83504i	−0.140150	+	0.192900i
$916$	−0.955988	−	20.2356i	−0.0315867	−	0.668602i
$917$	21.3512	−	6.93741i	0.705078	−	0.229094i
$918$	−0.442407	−	18.7394i	−0.0146016	−	0.618494i
$919$	−19.0921	+	13.8713i	−0.629792	+	0.457571i	−0.856328	−	0.516432i	$-0.827260\pi$
$919$	−19.0921	+	13.8713i	−0.629792	+	0.457571i	0.226536	+	0.974003i	$0.427260\pi$
$920$	47.6792	−	3.38190i	1.57194	−	0.111498i
$921$	8.80493	+	2.86090i	0.290132	+	0.0942697i
$922$	−1.80672	−	5.14408i	−0.0595010	−	0.169411i
$923$			8.70626i			0.286570i
$924$		0			0
$925$			9.67513i			0.318116i
$926$	29.7043	−	10.4328i	0.976142	−	0.342843i
$927$	48.5983	+	15.7905i	1.59618	+	0.518629i
$928$	−15.5936	−	33.8065i	−0.511885	−	1.10975i
$929$	−27.8992	+	20.2699i	−0.915342	+	0.665035i	−0.942360	−	0.334600i	$-0.891399\pi$
$929$	−27.8992	+	20.2699i	−0.915342	+	0.665035i	0.0270180	+	0.999635i	$0.491399\pi$
$930$	1.69801	−	0.0400872i	0.0556800	−	0.00131451i
$931$	−8.28015	+	2.69038i	−0.271371	+	0.0881737i
$932$	0.784878	+	16.6136i	0.0257095	+	0.544198i
$933$	−3.64390	+	5.01540i	−0.119296	+	0.164197i
$934$	−41.9659	−	29.0018i	−1.37317	−	0.948969i
$935$		0			0
$936$	2.62742	−	10.5830i	0.0858798	−	0.345916i
$937$	12.8132	−	17.6359i	0.418589	−	0.576139i	−0.546698	−	0.837330i	$-0.684115\pi$
$937$	12.8132	−	17.6359i	0.418589	−	0.576139i	0.965287	+	0.261191i	$0.0841154\pi$
$938$	22.4588	−	17.1415i	0.733304	−	0.559689i
$939$	1.00203	+	3.08393i	0.0327000	+	0.100640i
$940$		0			0
$941$	11.9407	−	8.67543i	0.389256	−	0.282811i	−0.375895	−	0.926662i	$-0.622665\pi$
$941$	11.9407	−	8.67543i	0.389256	−	0.282811i	0.765151	+	0.643851i	$0.222665\pi$
$942$	−0.254766	−	0.0761794i	−0.00830072	−	0.00248206i
$943$	19.8140	−	60.9812i	0.645232	−	1.98582i
$944$	12.9128	−	1.22281i	0.420276	−	0.0397990i
$945$			21.0188i			0.683741i
$946$		0			0
$947$	24.4142			0.793355			0.396678	−	0.917958i	$-0.370163\pi$
$947$	24.4142			0.793355			0.396678	+	0.917958i	$0.370163\pi$
$948$	2.03397	−	7.43738i	0.0660601	−	0.241555i
$949$	−1.22109	−	0.396757i	−0.0396384	−	0.0128793i
$950$	−6.16255	−	1.84271i	−0.199939	−	0.0597854i
$951$	−3.75442	−	5.16752i	−0.121746	−	0.167568i
$952$	−47.3593	+	19.1894i	−1.53492	+	0.621933i
$953$	34.7586	−	11.2938i	1.12594	−	0.365841i	0.313909	−	0.949453i	$-0.398361\pi$
$953$	34.7586	−	11.2938i	1.12594	−	0.365841i	0.812032	+	0.583612i	$0.198361\pi$
$954$	18.1610	+	23.7945i	0.587983	+	0.770376i
$955$	−36.3245	−	26.3913i	−1.17543	−	0.854001i
$956$	−3.85525	−	10.2000i	−0.124688	−	0.329892i
$957$		0			0
$958$	−31.8284	−	21.9960i	−1.02833	−	0.710659i
$959$	23.0463	+	16.7441i	0.744203	+	0.540695i
$960$	6.10283	+	6.29445i	0.196968	+	0.203153i
$961$	9.20839	+	28.3405i	0.297045	+	0.914210i
$962$	0.220086	+	9.32240i	0.00709586	+	0.300566i
$963$	14.4742	+	19.9221i	0.466425	+	0.641980i
$964$	5.68808	+	7.09866i	0.183201	+	0.228632i
$965$	−10.5176	+	32.3699i	−0.338574	+	1.04202i
$966$	−11.6168	+	4.08009i	−0.373766	+	0.131275i
$967$	−3.85525			−0.123976			−0.0619882	−	0.998077i	$-0.519744\pi$
$967$	−3.85525			−0.123976			−0.0619882	+	0.998077i	$0.519744\pi$
$968$		0			0
$969$	−5.17157			−0.166135
$970$	26.4249	−	9.28101i	0.848452	−	0.297995i
$971$	10.1483	−	31.2333i	0.325675	−	1.00232i	−0.645460	−	0.763794i	$-0.723334\pi$
$971$	10.1483	−	31.2333i	0.325675	−	1.00232i	0.971135	−	0.238530i	$-0.0766656\pi$
$972$	−16.1431	+	12.9353i	−0.517791	+	0.414900i
$973$	38.0779	+	52.4097i	1.22072	+	1.68018i
$974$	0.889372	+	37.6720i	0.0284973	+	1.20709i
$975$	0.348934	+	1.07391i	0.0111748	+	0.0343926i
$976$	10.4591	+	24.1584i	0.334787	+	0.773291i
$977$	36.9134	+	26.8191i	1.18096	+	0.858020i	0.992280	−	0.124018i	$-0.0395782\pi$
$977$	36.9134	+	26.8191i	1.18096	+	0.858020i	0.188683	+	0.982038i	$0.439578\pi$
$978$	6.18209	+	4.27232i	0.197681	+	0.136614i
$979$		0			0
$980$	18.9497	−	7.16233i	0.605327	−	0.228792i
$981$	6.23792	+	4.53211i	0.199161	+	0.144699i
$982$	−22.0758	−	28.9237i	−0.704467	−	0.922993i
$983$	−17.0033	+	5.52470i	−0.542320	+	0.176210i	−0.567351	−	0.823476i	$-0.692032\pi$
$983$	−17.0033	+	5.52470i	−0.542320	+	0.176210i	0.0250308	+	0.999687i	$0.492032\pi$
$984$	10.8999	−	4.41653i	0.347478	−	0.140794i
$985$	16.2302	+	22.3390i	0.517139	+	0.711780i
$986$	−48.9574	−	14.6391i	−1.55912	−	0.466205i
$987$		0			0
$988$	−5.97980	−	1.63535i	−0.190243	−	0.0520273i
$989$	−41.0848			−1.30642
$990$		0			0
$991$			29.9333i			0.950861i	0.879753	+	0.475431i	$0.157708\pi$
$991$			29.9333i			0.950861i	−0.879753	+	0.475431i	$0.842292\pi$
$992$	3.02801	−	5.40957i	0.0961395	−	0.171754i
$993$	−2.31308	+	7.11893i	−0.0734033	+	0.225912i
$994$	−28.4791	−	8.51576i	−0.903302	−	0.270103i
$995$	−45.3050	+	32.9160i	−1.43626	+	1.04351i
$996$	2.06838	−	3.14939i	0.0655392	−	0.0997921i
$997$	−17.1846	−	52.8887i	−0.544241	−	1.67500i	−0.722788	−	0.691070i	$-0.757140\pi$
$997$	−17.1846	−	52.8887i	−0.544241	−	1.67500i	0.178547	−	0.983931i	$-0.442860\pi$
$998$	−20.7809	+	15.8608i	−0.657807	+	0.502066i
$999$	6.86469	−	9.44844i	0.217189	−	0.298935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.k.g.403.6		32
8.3	odd	2	inner	968.2.k.g.403.1		32
11.2	odd	10	inner	968.2.k.g.699.4		32
11.3	even	5	inner	968.2.k.g.723.8		32
11.4	even	5	inner	968.2.k.g.475.2		32
11.5	even	5		88.2.g.b.43.1	✓	8
11.6	odd	10		88.2.g.b.43.8	yes	8
11.7	odd	10	inner	968.2.k.g.475.7		32
11.8	odd	10	inner	968.2.k.g.723.1		32
11.9	even	5	inner	968.2.k.g.699.5		32
11.10	odd	2	inner	968.2.k.g.403.3		32
33.5	odd	10		792.2.h.g.307.8		8
33.17	even	10		792.2.h.g.307.1		8
44.27	odd	10		352.2.g.b.175.1		8
44.39	even	10		352.2.g.b.175.2		8
88.3	odd	10	inner	968.2.k.g.723.3		32
88.5	even	10		352.2.g.b.175.4		8
88.19	even	10	inner	968.2.k.g.723.6		32
88.27	odd	10		88.2.g.b.43.7	yes	8
88.35	even	10	inner	968.2.k.g.699.2		32
88.43	even	2	inner	968.2.k.g.403.8		32
88.51	even	10	inner	968.2.k.g.475.5		32
88.59	odd	10	inner	968.2.k.g.475.4		32
88.61	odd	10		352.2.g.b.175.3		8
88.75	odd	10	inner	968.2.k.g.699.7		32
88.83	even	10		88.2.g.b.43.2	yes	8
132.71	even	10		3168.2.h.g.2287.5		8
132.83	odd	10		3168.2.h.g.2287.8		8
176.5	even	20		2816.2.e.o.2815.7		16
176.27	odd	20		2816.2.e.o.2815.12		16
176.61	odd	20		2816.2.e.o.2815.10		16
176.83	even	20		2816.2.e.o.2815.5		16
176.93	even	20		2816.2.e.o.2815.9		16
176.115	odd	20		2816.2.e.o.2815.6		16
176.149	odd	20		2816.2.e.o.2815.8		16
176.171	even	20		2816.2.e.o.2815.11		16
264.5	odd	10		3168.2.h.g.2287.4		8
264.83	odd	10		792.2.h.g.307.7		8
264.149	even	10		3168.2.h.g.2287.1		8
264.203	even	10		792.2.h.g.307.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.g.b.43.1	✓	8	11.5	even	5
88.2.g.b.43.2	yes	8	88.83	even	10
88.2.g.b.43.7	yes	8	88.27	odd	10
88.2.g.b.43.8	yes	8	11.6	odd	10
352.2.g.b.175.1		8	44.27	odd	10
352.2.g.b.175.2		8	44.39	even	10
352.2.g.b.175.3		8	88.61	odd	10
352.2.g.b.175.4		8	88.5	even	10
792.2.h.g.307.1		8	33.17	even	10
792.2.h.g.307.2		8	264.203	even	10
792.2.h.g.307.7		8	264.83	odd	10
792.2.h.g.307.8		8	33.5	odd	10
968.2.k.g.403.1		32	8.3	odd	2	inner
968.2.k.g.403.3		32	11.10	odd	2	inner
968.2.k.g.403.6		32	1.1	even	1	trivial
968.2.k.g.403.8		32	88.43	even	2	inner
968.2.k.g.475.2		32	11.4	even	5	inner
968.2.k.g.475.4		32	88.59	odd	10	inner
968.2.k.g.475.5		32	88.51	even	10	inner
968.2.k.g.475.7		32	11.7	odd	10	inner
968.2.k.g.699.2		32	88.35	even	10	inner
968.2.k.g.699.4		32	11.2	odd	10	inner
968.2.k.g.699.5		32	11.9	even	5	inner
968.2.k.g.699.7		32	88.75	odd	10	inner
968.2.k.g.723.1		32	11.8	odd	10	inner
968.2.k.g.723.3		32	88.3	odd	10	inner
968.2.k.g.723.6		32	88.19	even	10	inner
968.2.k.g.723.8		32	11.3	even	5	inner
2816.2.e.o.2815.5		16	176.83	even	20
2816.2.e.o.2815.6		16	176.115	odd	20
2816.2.e.o.2815.7		16	176.5	even	20
2816.2.e.o.2815.8		16	176.149	odd	20
2816.2.e.o.2815.9		16	176.93	even	20
2816.2.e.o.2815.10		16	176.61	odd	20
2816.2.e.o.2815.11		16	176.171	even	20
2816.2.e.o.2815.12		16	176.27	odd	20
3168.2.h.g.2287.1		8	264.149	even	10
3168.2.h.g.2287.4		8	264.5	odd	10
3168.2.h.g.2287.5		8	132.71	even	10
3168.2.h.g.2287.8		8	132.83	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.k (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.468639 + 1.33431i) q^{2} +(0.127999 - 0.393941i) q^{3} +(-1.56076 + 1.25062i) q^{4} +(1.55513 + 2.14046i) q^{5} +(0.585623 - 0.0138256i) q^{6} +(1.01687 + 3.12960i) q^{7} +(-2.40014 - 1.49644i) q^{8} +(2.28825 + 1.66251i) q^{9} +(-2.12723 + 3.07813i) q^{10} +(0.292893 + 0.774923i) q^{12} +(1.10272 + 0.801172i) q^{13} +(-3.69931 + 2.82347i) q^{14} +(1.04227 - 0.338654i) q^{15} +(0.871917 - 3.90381i) q^{16} +(-3.22705 - 4.44165i) q^{17} +(-1.14594 + 3.83234i) q^{18} +(2.16281 + 0.702738i) q^{19} +(-5.10408 - 1.39586i) q^{20} +1.36303 q^{21} +6.38741i q^{23} +(-0.896724 + 0.753968i) q^{24} +(-0.618034 + 1.90211i) q^{25} +(-0.552234 + 1.84683i) q^{26} +(1.95314 - 1.41904i) q^{27} +(-5.50101 - 3.61283i) q^{28} +(-2.03374 - 6.25920i) q^{29} +(0.940315 + 1.23200i) q^{30} +(0.644157 - 0.886607i) q^{31} +(5.61750 - 0.666071i) q^{32} +(4.41421 - 6.38741i) q^{34} +(-5.11741 + 7.04351i) q^{35} +(-5.65055 + 0.266949i) q^{36} +(4.60080 - 1.49489i) q^{37} +(0.0759050 + 3.21518i) q^{38} +(0.456761 - 0.331856i) q^{39} +(-0.529464 - 7.46456i) q^{40} +(-9.54709 - 3.10204i) q^{41} +(0.638771 + 1.81871i) q^{42} +6.43215i q^{43} +7.48331i q^{45} +(-8.52277 + 2.99339i) q^{46} +(-1.42627 - 0.843168i) q^{48} +(-3.09726 + 2.25029i) q^{49} +(-2.82764 + 0.0667558i) q^{50} +(-2.16281 + 0.702738i) q^{51} +(-2.72303 + 0.128644i) q^{52} +(4.39858 - 6.05413i) q^{53} +(2.80875 + 1.94107i) q^{54} +(2.24264 - 9.03316i) q^{56} +(0.553674 - 0.762067i) q^{57} +(7.39862 - 5.64694i) q^{58} +(1.00203 + 3.08393i) q^{59} +(-1.20320 + 1.83203i) q^{60} +(-5.32440 + 3.86840i) q^{61} +(1.48488 + 0.444006i) q^{62} +(-2.87614 + 8.85185i) q^{63} +(3.52132 + 7.18333i) q^{64} +3.60625i q^{65} -6.07107 q^{67} +(10.5914 + 2.89653i) q^{68} +(2.51626 + 0.817582i) q^{69} +(-11.7964 - 3.52734i) q^{70} +(3.75442 + 5.16752i) q^{71} +(-3.00426 - 7.41447i) q^{72} +(-0.895864 + 0.291084i) q^{73} +(4.15075 + 5.43832i) q^{74} +(0.670212 + 0.486937i) q^{75} +(-4.25447 + 1.60804i) q^{76} +(0.656854 + 0.453939i) q^{78} +(-7.52983 - 5.47074i) q^{79} +(9.71190 - 4.20465i) q^{80} +(2.31308 + 7.11893i) q^{81} +(-0.335061 - 14.1925i) q^{82} +(-2.67338 - 3.67959i) q^{83} +(-2.12736 + 1.70463i) q^{84} +(4.48868 - 13.8147i) q^{85} +(-8.58247 + 3.01435i) q^{86} -2.72607 q^{87} -10.6569 q^{89} +(-9.98505 + 3.50697i) q^{90} +(-1.38603 + 4.26576i) q^{91} +(-7.98820 - 9.96919i) q^{92} +(-0.266819 - 0.367244i) q^{93} +(1.85927 + 5.72225i) q^{95} +(0.456643 - 2.29822i) q^{96} +(-6.05572 - 4.39974i) q^{97} +(-4.45408 - 3.07813i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} + 32 q^{12} + 8 q^{14} + 24 q^{16} + 16 q^{25} - 24 q^{26} + 8 q^{27} + 96 q^{34} + 16 q^{36} + 8 q^{38} + 24 q^{42} - 24 q^{48} - 8 q^{49} - 64 q^{56} - 16 q^{58} + 8 q^{59} - 56 q^{60}+ \cdots + 8 q^{97}+O(q^{100}) \) 32 * q + 8 * q^3 + 32 * q^12 + 8 * q^14 + 24 * q^16 + 16 * q^25 - 24 * q^26 + 8 * q^27 + 96 * q^34 + 16 * q^36 + 8 * q^38 + 24 * q^42 - 24 * q^48 - 8 * q^49 - 64 * q^56 - 16 * q^58 + 8 * q^59 - 56 * q^60 + 32 * q^67 + 56 * q^70 - 16 * q^75 - 160 * q^78 - 56 * q^80 + 8 * q^81 + 8 * q^82 - 64 * q^86 - 160 * q^89 - 32 * q^91 + 56 * q^92 + 8 * q^97

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