LMFDB - Embedded newform 975.2.bt.k.68.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(68,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("975.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bt (of order $12$, degree $4$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			68.11
Character	$\chi$	$=$	975.68
Dual form			975.2.bt.k.932.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.646049 - 2.41109i) q^{2} +(-0.163899 + 1.72428i) q^{3} +(-3.66392 - 2.11536i) q^{4} +(4.05150 + 1.50914i) q^{6} +(0.0914428 + 0.341269i) q^{7} +(-3.93732 + 3.93732i) q^{8} +(-2.94627 - 0.565216i) q^{9} +O(q^{10})$	\(q+(0.646049 - 2.41109i) q^{2} +(-0.163899 + 1.72428i) q^{3} +(-3.66392 - 2.11536i) q^{4} +(4.05150 + 1.50914i) q^{6} +(0.0914428 + 0.341269i) q^{7} +(-3.93732 + 3.93732i) q^{8} +(-2.94627 - 0.565216i) q^{9} +(-1.70372 + 0.983646i) q^{11} +(4.24799 - 5.97091i) q^{12} +(1.22537 - 3.39094i) q^{13} +0.881907 q^{14} +(2.71879 + 4.70909i) q^{16} +(-4.76464 + 1.27668i) q^{17} +(-3.26622 + 6.73857i) q^{18} +(-2.77722 - 1.60343i) q^{19} +(-0.603431 + 0.101739i) q^{21} +(1.27097 + 4.74331i) q^{22} +(-5.37848 - 1.44116i) q^{23} +(-6.14371 - 7.43436i) q^{24} +(-7.38421 - 5.14518i) q^{26} +(1.45748 - 4.98756i) q^{27} +(0.386869 - 1.44382i) q^{28} +(3.72058 + 6.44424i) q^{29} +2.20686 q^{31} +(2.35355 - 0.630632i) q^{32} +(-1.41684 - 3.09891i) q^{33} +12.3128i q^{34} +(9.59926 + 8.30334i) q^{36} +(-9.21595 - 2.46941i) q^{37} +(-5.66024 + 5.66024i) q^{38} +(5.64609 + 2.66865i) q^{39} +(-8.32418 + 4.80597i) q^{41} +(-0.144544 + 1.52065i) q^{42} +(-8.46282 + 2.26761i) q^{43} +8.32307 q^{44} +(-6.94952 + 12.0369i) q^{46} +(-3.89520 - 3.89520i) q^{47} +(-8.56539 + 3.91614i) q^{48} +(5.95407 - 3.43759i) q^{49} +(-1.42043 - 8.42481i) q^{51} +(-11.6627 + 9.83202i) q^{52} +(4.34456 - 4.34456i) q^{53} +(-11.0838 - 6.73632i) q^{54} +(-1.70372 - 0.983646i) q^{56} +(3.21995 - 4.52591i) q^{57} +(17.9413 - 4.80736i) q^{58} +(-3.72058 + 6.44424i) q^{59} +(0.730725 - 1.26565i) q^{61} +(1.42574 - 5.32094i) q^{62} +(-0.0765249 - 1.05716i) q^{63} +4.79314i q^{64} +(-8.38711 + 1.41408i) q^{66} +(6.94026 + 1.85964i) q^{67} +(20.1579 + 5.40129i) q^{68} +(3.36649 - 9.03779i) q^{69} +(11.7316 + 6.77326i) q^{71} +(13.8259 - 9.37498i) q^{72} +(-2.66523 - 2.66523i) q^{73} +(-11.9079 + 20.6251i) q^{74} +(6.78367 + 11.7497i) q^{76} +(-0.491481 - 0.491481i) q^{77} +(10.0820 - 11.8891i) q^{78} -4.66831i q^{79} +(8.36106 + 3.33056i) q^{81} +(6.20978 + 23.1752i) q^{82} +(6.24568 - 6.24568i) q^{83} +(2.42613 + 0.903711i) q^{84} +21.8696i q^{86} +(-11.7215 + 5.35912i) q^{87} +(2.83518 - 10.5810i) q^{88} +(-4.80597 - 8.32418i) q^{89} +(1.26927 + 0.108103i) q^{91} +(16.6577 + 16.6577i) q^{92} +(-0.361703 + 3.80524i) q^{93} +(-11.9081 + 6.87517i) q^{94} +(0.701640 + 4.16154i) q^{96} +(-4.03580 - 15.0618i) q^{97} +(-4.44170 - 16.5766i) q^{98} +(5.57561 - 1.93512i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 28 q^{6}+O(q^{10}) $ 48 * q - 28 * q^6	$ 48 q - 28 q^{6} + 40 q^{16} + 48 q^{31} + 76 q^{36} - 120 q^{46} - 32 q^{51} - 88 q^{61} - 8 q^{66} - 40 q^{76} + 32 q^{81} + 184 q^{91} + 88 q^{96}+O(q^{100}) $ 48 * q - 28 * q^6 + 40 * q^16 + 48 * q^31 + 76 * q^36 - 120 * q^46 - 32 * q^51 - 88 * q^61 - 8 * q^66 - 40 * q^76 + 32 * q^81 + 184 * q^91 + 88 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.646049	−	2.41109i	0.456826	−	1.70490i	−0.225839	−	0.974165i	$-0.572512\pi$
$2$	0.646049	−	2.41109i	0.456826	−	1.70490i	0.682664	−	0.730732i	$-0.260821\pi$
$3$	−0.163899	+	1.72428i	−0.0946272	+	0.995513i
$3$	−0.163899	+	1.72428i	−0.0946272	+	0.995513i
$4$	−3.66392	−	2.11536i	−1.83196	−	1.05768i
$5$		0			0
$5$		0			0
$6$	4.05150	+	1.50914i	1.65402	+	0.616105i
$7$	0.0914428	+	0.341269i	0.0345621	+	0.128988i	0.981051	−	0.193748i	$-0.0620643\pi$
$7$	0.0914428	+	0.341269i	0.0345621	+	0.128988i	−0.946489	+	0.322735i	$0.895398\pi$
$8$	−3.93732	+	3.93732i	−1.39205	+	1.39205i
$9$	−2.94627	−	0.565216i	−0.982091	−	0.188405i
$10$		0			0
$11$	−1.70372	+	0.983646i	−0.513692	+	0.296580i	−0.734350	−	0.678771i	$-0.762513\pi$
$11$	−1.70372	+	0.983646i	−0.513692	+	0.296580i	0.220658	+	0.975351i	$0.429180\pi$
$12$	4.24799	−	5.97091i	1.22629	−	1.72365i
$13$	1.22537	−	3.39094i	0.339856	−	0.940478i
$13$	1.22537	−	3.39094i	0.339856	−	0.940478i
$14$	0.881907			0.235699
$15$		0			0
$16$	2.71879	+	4.70909i	0.679698	+	1.17727i
$17$	−4.76464	+	1.27668i	−1.15559	+	0.309641i	−0.785205	−	0.619236i	$-0.787442\pi$
$17$	−4.76464	+	1.27668i	−1.15559	+	0.309641i	−0.370389	+	0.928877i	$0.620776\pi$
$18$	−3.26622	+	6.73857i	−0.769856	+	1.58830i
$19$	−2.77722	−	1.60343i	−0.637139	−	0.367852i	0.146373	−	0.989230i	$-0.453240\pi$
$19$	−2.77722	−	1.60343i	−0.637139	−	0.367852i	−0.783512	+	0.621377i	$0.786573\pi$
$20$		0			0
$21$	−0.603431	+	0.101739i	−0.131679	+	0.0222013i
$22$	1.27097	+	4.74331i	0.270971	+	1.01128i
$23$	−5.37848	−	1.44116i	−1.12149	−	0.300502i	−0.350004	−	0.936748i	$-0.613820\pi$
$23$	−5.37848	−	1.44116i	−1.12149	−	0.300502i	−0.771486	+	0.636246i	$0.780486\pi$
$24$	−6.14371	−	7.43436i	−1.25408	−	1.51753i
$25$		0			0
$26$	−7.38421	−	5.14518i	−1.44816	−	1.00905i
$27$	1.45748	−	4.98756i	0.280492	−	0.959856i
$28$	0.386869	−	1.44382i	0.0731115	−	0.272856i
$29$	3.72058	+	6.44424i	0.690895	+	1.19666i	0.971545	+	0.236855i	$0.0761166\pi$
$29$	3.72058	+	6.44424i	0.690895	+	1.19666i	−0.280650	+	0.959810i	$0.590550\pi$
$30$		0			0
$31$	2.20686			0.396364			0.198182	−	0.980165i	$-0.436496\pi$
$31$	2.20686			0.396364			0.198182	+	0.980165i	$0.436496\pi$
$32$	2.35355	−	0.630632i	0.416053	−	0.111481i
$33$	−1.41684	−	3.09891i	−0.246640	−	0.539452i
$34$			12.3128i			2.11162i
$35$		0			0
$36$	9.59926	+	8.30334i	1.59988	+	1.38389i
$37$	−9.21595	−	2.46941i	−1.51509	−	0.405968i	−0.596970	−	0.802263i	$-0.703629\pi$
$37$	−9.21595	−	2.46941i	−1.51509	−	0.405968i	−0.918123	+	0.396295i	$0.870296\pi$
$38$	−5.66024	+	5.66024i	−0.918211	+	0.918211i
$39$	5.64609	+	2.66865i	0.904098	+	0.427325i
$40$		0			0
$41$	−8.32418	+	4.80597i	−1.30002	+	0.750566i	−0.980407	−	0.196983i	$-0.936886\pi$
$41$	−8.32418	+	4.80597i	−1.30002	+	0.750566i	−0.319611	+	0.947549i	$0.603552\pi$
$42$	−0.144544	+	1.52065i	−0.0223036	+	0.234642i
$43$	−8.46282	+	2.26761i	−1.29057	+	0.345807i	−0.837876	−	0.545860i	$-0.816203\pi$
$43$	−8.46282	+	2.26761i	−1.29057	+	0.345807i	−0.452692	+	0.891667i	$0.649536\pi$
$44$	8.32307			1.25475
$45$		0			0
$46$	−6.94952	+	12.0369i	−1.02465	+	1.77475i
$47$	−3.89520	−	3.89520i	−0.568173	−	0.568173i	0.363443	−	0.931616i	$-0.381601\pi$
$47$	−3.89520	−	3.89520i	−0.568173	−	0.568173i	−0.931616	+	0.363443i	$0.881601\pi$
$48$	−8.56539	+	3.91614i	−1.23631	+	0.565246i
$49$	5.95407	−	3.43759i	0.850582	−	0.491084i
$50$		0			0
$51$	−1.42043	−	8.42481i	−0.198900	−	1.17971i
$52$	−11.6627	+	9.83202i	−1.61733	+	1.36346i
$53$	4.34456	−	4.34456i	0.596771	−	0.596771i	−0.342681	−	0.939452i	$-0.611335\pi$
$53$	4.34456	−	4.34456i	0.596771	−	0.596771i	0.939452	+	0.342681i	$0.111335\pi$
$54$	−11.0838	−	6.73632i	−1.50832	−	0.916698i
$55$		0			0
$56$	−1.70372	−	0.983646i	−0.227670	−	0.131445i
$57$	3.21995	−	4.52591i	0.426492	−	0.599471i
$58$	17.9413	−	4.80736i	2.35581	−	0.631237i
$59$	−3.72058	+	6.44424i	−0.484379	+	0.838968i	−0.999839	−	0.0179451i	$-0.994288\pi$
$59$	−3.72058	+	6.44424i	−0.484379	+	0.838968i	0.515460	+	0.856913i	$0.327621\pi$
$60$		0			0
$61$	0.730725	−	1.26565i	0.0935598	−	0.162050i	−0.815447	−	0.578832i	$-0.803509\pi$
$61$	0.730725	−	1.26565i	0.0935598	−	0.162050i	0.909007	+	0.416782i	$0.136842\pi$
$62$	1.42574	−	5.32094i	0.181069	−	0.675760i
$63$	−0.0765249	−	1.05716i	−0.00964123	−	0.133189i
$64$			4.79314i			0.599142i
$65$		0			0
$66$	−8.38711	+	1.41408i	−1.03238	+	0.174061i
$67$	6.94026	+	1.85964i	0.847888	+	0.227191i	0.656502	−	0.754324i	$-0.272035\pi$
$67$	6.94026	+	1.85964i	0.847888	+	0.227191i	0.191386	+	0.981515i	$0.438702\pi$
$68$	20.1579	+	5.40129i	2.44450	+	0.655002i
$69$	3.36649	−	9.03779i	0.405277	−	1.08802i
$70$		0			0
$71$	11.7316	+	6.77326i	1.39229	+	0.803838i	0.993568	−	0.113235i	$-0.0361212\pi$
$71$	11.7316	+	6.77326i	1.39229	+	0.803838i	0.398720	+	0.917073i	$0.369455\pi$
$72$	13.8259	−	9.37498i	1.62939	−	1.10485i
$73$	−2.66523	−	2.66523i	−0.311941	−	0.311941i	0.533720	−	0.845661i	$-0.320794\pi$
$73$	−2.66523	−	2.66523i	−0.311941	−	0.311941i	−0.845661	+	0.533720i	$0.820794\pi$
$74$	−11.9079	+	20.6251i	−1.38427	+	2.39762i
$75$		0			0
$76$	6.78367	+	11.7497i	0.778141	+	1.34778i
$77$	−0.491481	−	0.491481i	−0.0560095	−	0.0560095i
$78$	10.0820	−	11.8891i	1.14156	−	1.34618i
$79$		−	4.66831i		−	0.525226i	−0.964901	−	0.262613i	$-0.915416\pi$
$79$		−	4.66831i		−	0.525226i	0.964901	−	0.262613i	$-0.0845843\pi$
$80$		0			0
$81$	8.36106	+	3.33056i	0.929007	+	0.370062i
$82$	6.20978	+	23.1752i	0.685756	+	2.55928i
$83$	6.24568	−	6.24568i	0.685552	−	0.685552i	−0.275693	−	0.961246i	$-0.588907\pi$
$83$	6.24568	−	6.24568i	0.685552	−	0.685552i	0.961246	+	0.275693i	$0.0889075\pi$
$84$	2.42613	+	0.903711i	0.264713	+	0.0986030i
$85$		0			0
$86$			21.8696i			2.35826i
$87$	−11.7215	+	5.35912i	−1.25667	+	0.574558i
$88$	2.83518	−	10.5810i	0.302231	−	1.12794i
$89$	−4.80597	−	8.32418i	−0.509432	−	0.882361i	−0.999940	−	0.0109250i	$-0.996522\pi$
$89$	−4.80597	−	8.32418i	−0.509432	−	0.882361i	0.490509	−	0.871436i	$-0.336811\pi$
$90$		0			0
$91$	1.26927	+	0.108103i	0.133056	+	0.0113323i
$92$	16.6577	+	16.6577i	1.73669	+	1.73669i
$93$	−0.361703	+	3.80524i	−0.0375068	+	0.394585i
$94$	−11.9081	+	6.87517i	−1.22823	+	0.709120i
$95$		0			0
$96$	0.701640	+	4.16154i	0.0716108	+	0.424735i
$97$	−4.03580	−	15.0618i	−0.409774	−	1.52930i	−0.795079	−	0.606506i	$-0.792570\pi$
$97$	−4.03580	−	15.0618i	−0.409774	−	1.52930i	0.385305	−	0.922789i	$-0.374096\pi$
$98$	−4.44170	−	16.5766i	−0.448679	−	1.67449i
$99$	5.57561	−	1.93512i	0.560370	−	0.194487i
$100$		0			0
$101$	−1.70372	+	0.983646i	−0.169527	+	0.0978764i	−0.582363	−	0.812929i	$-0.697872\pi$
$101$	−1.70372	+	0.983646i	−0.169527	+	0.0978764i	0.412836	+	0.910805i	$0.364538\pi$
$102$	−21.2306	−	2.01805i	−2.10215	−	0.199817i
$103$	6.49672	+	6.49672i	0.640141	+	0.640141i	0.950590	−	0.310449i	$-0.100479\pi$
$103$	6.49672	+	6.49672i	0.640141	+	0.640141i	−0.310449	+	0.950590i	$0.600479\pi$
$104$	8.52655	+	18.1759i	0.836097	+	1.78229i
$105$		0			0
$106$	−7.66831	−	13.2819i	−0.744812	−	1.29005i
$107$	−4.75524	+	17.7468i	−0.459706	+	1.71565i	0.214165	+	0.976798i	$0.431297\pi$
$107$	−4.75524	+	17.7468i	−0.459706	+	1.71565i	−0.673871	+	0.738849i	$0.735370\pi$
$108$	−15.8906	+	15.1909i	−1.52907	+	1.46174i
$109$		−	12.2546i		−	1.17378i	−0.809668	−	0.586888i	$-0.800353\pi$
$109$		−	12.2546i		−	1.17378i	0.809668	−	0.586888i	$-0.199647\pi$
$110$		0			0
$111$	5.76843	−	15.4861i	0.547516	−	1.46988i
$112$	−1.35845	+	1.35845i	−0.128362	+	0.128362i
$113$	−3.32950	−	12.4258i	−0.313213	−	1.16893i	−0.925642	−	0.378400i	$-0.876474\pi$
$113$	−3.32950	−	12.4258i	−0.313213	−	1.16893i	0.612429	−	0.790525i	$-0.290192\pi$
$114$	−8.83212	−	10.6875i	−0.827203	−	1.00098i
$115$		0			0
$116$		−	31.4815i		−	2.92299i
$117$	−5.52688	+	9.29804i	−0.510960	+	0.859604i
$118$	13.1339	+	13.1339i	1.20908	+	1.20908i
$119$	−0.871384	−	1.50928i	−0.0798796	−	0.138356i
$120$		0			0
$121$	−3.56488	+	6.17456i	−0.324080	+	0.561323i
$122$	−2.57952	−	2.57952i	−0.233539	−	0.233539i
$123$	−6.92250	−	15.1409i	−0.624181	−	1.36521i
$124$	−8.08575	−	4.66831i	−0.726122	−	0.419227i
$125$		0			0
$126$	−2.59834	−	0.498468i	−0.231478	−	0.0444070i
$127$	0.341269	+	0.0914428i	0.0302827	+	0.00811424i	0.273929	−	0.961750i	$-0.411677\pi$
$127$	0.341269	+	0.0914428i	0.0302827	+	0.00811424i	−0.243646	+	0.969864i	$0.578343\pi$
$128$	16.2638	+	4.35787i	1.43753	+	0.385185i
$129$	−2.52294	−	14.9639i	−0.222132	−	1.31750i
$130$		0			0
$131$			7.23769i			0.632360i	0.948699	+	0.316180i	$0.102400\pi$
$131$			7.23769i			0.632360i	−0.948699	+	0.316180i	$0.897600\pi$
$132$	−1.36414	+	14.3513i	−0.118734	+	1.24912i
$133$	0.293244	−	1.09440i	0.0254275	−	0.0948968i
$134$	8.96750	−	15.5322i	0.774674	−	1.34178i
$135$		0			0
$136$	13.7332	−	23.7866i	1.17761	−	2.03968i
$137$	−7.36162	+	1.97254i	−0.628945	+	0.168525i	−0.559191	−	0.829039i	$-0.688888\pi$
$137$	−7.36162	+	1.97254i	−0.628945	+	0.168525i	−0.0697543	+	0.997564i	$0.522222\pi$
$138$	−19.6160	−	13.9557i	−1.66982	−	1.18799i
$139$	2.23978	+	1.29314i	0.189976	+	0.109683i	0.591971	−	0.805959i	$-0.298350\pi$
$139$	2.23978	+	1.29314i	0.189976	+	0.109683i	−0.401995	+	0.915642i	$0.631683\pi$
$140$		0			0
$141$	7.35482	−	6.07798i	0.619388	−	0.511859i
$142$	23.9101	−	23.9101i	2.00649	−	2.00649i
$143$	1.24780	+	6.98256i	0.104346	+	0.583911i
$144$	−5.34866	−	15.4110i	−0.445722	−	1.28425i
$145$		0			0
$146$	−8.14796	+	4.70423i	−0.674330	+	0.389325i
$147$	4.95149	+	10.8299i	0.408392	+	0.893235i
$148$	28.5428	+	28.5428i	2.34620	+	2.34620i
$149$	0.101739	−	0.176217i	0.00833480	−	0.0144363i	−0.861828	−	0.507201i	$-0.830680\pi$
$149$	0.101739	−	0.176217i	0.00833480	−	0.0144363i	0.870163	+	0.492764i	$0.164014\pi$
$150$		0			0
$151$	8.46145			0.688583			0.344292	−	0.938863i	$-0.388119\pi$
$151$	8.46145			0.688583			0.344292	+	0.938863i	$0.388119\pi$
$152$	17.2480	−	4.62159i	1.39900	−	0.374861i
$153$	14.7595	−	1.06840i	1.19324	−	0.0863753i
$154$	−1.50253	+	0.867484i	−0.121077	+	0.0699038i
$155$		0			0
$156$	−15.0416	−	21.7212i	−1.20430	−	1.73909i
$157$	−2.16557	+	2.16557i	−0.172832	+	0.172832i	−0.788222	−	0.615391i	$-0.788998\pi$
$157$	−2.16557	+	2.16557i	−0.172832	+	0.172832i	0.615391	+	0.788222i	$0.288998\pi$
$158$	−11.2557	−	3.01596i	−0.895456	−	0.239937i
$159$	6.77916	+	8.20330i	0.537622	+	0.650564i
$160$		0			0
$161$		−	1.96729i		−	0.155044i
$162$	13.4319	−	18.0076i	1.05531	−	1.41481i
$163$	9.82790	−	2.63338i	0.769780	−	0.206262i	0.147506	−	0.989061i	$-0.452875\pi$
$163$	9.82790	−	2.63338i	0.769780	−	0.206262i	0.622274	+	0.782799i	$0.286209\pi$
$164$	40.6655			3.17544
$165$		0			0
$166$	−11.0239	−	19.0939i	−0.855618	−	1.48197i
$167$	2.70242	−	10.0856i	0.209120	−	0.780445i	−0.779035	−	0.626981i	$-0.784290\pi$
$167$	2.70242	−	10.0856i	0.209120	−	0.780445i	0.988154	−	0.153464i	$-0.0490430\pi$
$168$	1.97532	−	2.77648i	0.152399	−	0.214210i
$169$	−9.99695	−	8.31029i	−0.768996	−	0.639253i
$170$		0			0
$171$	7.27618	+	6.29388i	0.556423	+	0.481305i
$172$	35.8039	+	9.59362i	2.73002	+	0.731506i
$173$	0.313537	+	1.17014i	0.0238378	+	0.0889639i	0.976820	−	0.214063i	$-0.0686696\pi$
$173$	0.313537	+	1.17014i	0.0238378	+	0.0889639i	−0.952982	+	0.303026i	$0.902003\pi$
$174$	5.34866	+	31.7237i	0.405481	+	2.40497i
$175$		0			0
$176$	−9.26415	−	5.34866i	−0.698312	−	0.403170i
$177$	−10.5019	−	7.47153i	−0.789368	−	0.561594i
$178$	−23.1752	+	6.20978i	−1.73706	+	0.465443i
$179$	−13.1290	−	22.7402i	−0.981310	−	1.69968i	−0.657306	−	0.753624i	$-0.728304\pi$
$179$	−13.1290	−	22.7402i	−0.981310	−	1.69968i	−0.324005	−	0.946055i	$-0.605029\pi$
$180$		0			0
$181$	19.3844			1.44083			0.720414	−	0.693544i	$-0.243952\pi$
$181$	19.3844			1.44083			0.720414	+	0.693544i	$0.243952\pi$
$182$	1.08066	−	2.99049i	0.0801038	−	0.221670i
$183$	2.06257	+	1.46741i	0.152470	+	0.108474i
$184$	26.8511	−	15.5025i	1.97949	−	1.14286i
$185$		0			0
$186$	8.94110	+	3.33047i	0.655593	+	0.244202i
$187$	6.86183	−	6.86183i	0.501787	−	0.501787i
$188$	6.03192	+	22.5114i	0.439923	+	1.64181i
$189$	1.83538	+	0.0413171i	0.133504	+	0.00300537i
$190$		0			0
$191$	−17.8052	−	10.2798i	−1.28834	−	0.743823i	−0.309981	−	0.950743i	$-0.600323\pi$
$191$	−17.8052	−	10.2798i	−1.28834	−	0.743823i	−0.978358	+	0.206919i	$0.933656\pi$
$192$	−8.26471	−	0.785591i	−0.596454	−	0.0566952i
$193$	4.21869	−	15.7444i	0.303668	−	1.13330i	−0.630418	−	0.776256i	$-0.717117\pi$
$193$	4.21869	−	15.7444i	0.303668	−	1.13330i	0.934086	−	0.357048i	$-0.116217\pi$
$194$	−38.9227			−2.79449
$195$		0			0
$196$	−29.0870			−2.07764
$197$	5.61557	−	20.9576i	0.400093	−	1.49317i	−0.412836	−	0.910805i	$-0.635462\pi$
$197$	5.61557	−	20.9576i	0.400093	−	1.49317i	0.812929	−	0.582362i	$-0.197871\pi$
$198$	−1.06362	−	14.6935i	−0.0755883	−	1.04422i
$199$	14.9059	+	8.60590i	1.05665	+	0.610056i	0.924503	−	0.381174i	$-0.124480\pi$
$199$	14.9059	+	8.60590i	1.05665	+	0.610056i	0.132145	+	0.991230i	$0.457814\pi$
$200$		0			0
$201$	−4.34404	+	11.6622i	−0.306405	+	0.822585i
$202$	1.27097	+	4.74331i	0.0894249	+	0.333738i
$203$	−1.85900	+	1.85900i	−0.130476	+	0.130476i
$204$	−12.6172	+	33.8725i	−0.883379	+	2.37155i
$205$		0			0
$206$	19.8614	−	11.4670i	1.38381	−	0.798941i
$207$	15.0319	+	7.28605i	1.04479	+	0.506415i
$208$	19.2998	−	3.44891i	1.33820	−	0.239139i
$209$	6.30883			0.436391
$210$		0			0
$211$	−4.70686	−	8.15252i	−0.324034	−	0.561243i	0.657283	−	0.753644i	$-0.271706\pi$
$211$	−4.70686	−	8.15252i	−0.324034	−	0.561243i	−0.981316	+	0.192401i	$0.938372\pi$
$212$	−25.1084	+	6.72778i	−1.72445	+	0.462066i
$213$	−13.6018	+	19.1185i	−0.931979	+	1.30998i
$214$	39.7169	+	22.9306i	2.71499	+	1.56750i
$215$		0			0
$216$	13.8990	+	25.3762i	0.945710	+	1.72663i
$217$	0.201802	+	0.753134i	0.0136992	+	0.0511261i
$218$	−29.5469	−	7.91707i	−2.00117	−	0.536211i
$219$	5.03242	−	4.15876i	0.340060	−	0.281023i
$220$		0			0
$221$	−1.50928	+	17.7210i	−0.101525	+	1.19204i
$222$	−33.6118	−	23.9130i	−2.25587	−	1.60494i
$223$	−3.83400	+	14.3087i	−0.256744	+	0.958180i	0.710369	+	0.703830i	$0.248528\pi$
$223$	−3.83400	+	14.3087i	−0.256744	+	0.958180i	−0.967112	+	0.254350i	$0.918138\pi$
$224$	0.430430	+	0.745527i	0.0287593	+	0.0498126i
$225$		0			0
$226$	−32.1108			−2.13598
$227$	−17.8619	+	4.78607i	−1.18553	+	0.317663i	−0.797119	−	0.603822i	$-0.793644\pi$
$227$	−17.8619	+	4.78607i	−1.18553	+	0.317663i	−0.388414	+	0.921485i	$0.626977\pi$
$228$	−21.3715	+	9.77119i	−1.41537	+	0.647113i
$229$		−	2.66338i		−	0.176001i	−0.996120	−	0.0880004i	$-0.971952\pi$
$229$		−	2.66338i		−	0.176001i	0.996120	−	0.0880004i	$-0.0280477\pi$
$230$		0			0
$231$	0.928004	−	0.766898i	0.0610582	−	0.0504582i
$232$	−40.0221	−	10.7239i	−2.62758	−	0.704058i
$233$	−10.5060	+	10.5060i	−0.688270	+	0.688270i	−0.961850	−	0.273579i	$-0.911792\pi$
$233$	−10.5060	+	10.5060i	−0.688270	+	0.688270i	0.273579	+	0.961850i	$0.411792\pi$
$234$	18.8478	+	19.3328i	1.23212	+	1.26382i
$235$		0			0
$236$	27.2638	−	15.7408i	1.77472	−	1.02464i
$237$	8.04947	+	0.765133i	0.522869	+	0.0497007i
$238$	−4.20197	+	1.12591i	−0.272373	+	0.0729821i
$239$	0.406957			0.0263238			0.0131619	−	0.999913i	$-0.495810\pi$
$239$	0.406957			0.0263238			0.0131619	+	0.999913i	$0.495810\pi$
$240$		0			0
$241$	−12.0887	+	20.9383i	−0.778705	+	1.34876i	0.153984	+	0.988073i	$0.450790\pi$
$241$	−12.0887	+	20.9383i	−0.778705	+	1.34876i	−0.932689	+	0.360683i	$0.882544\pi$
$242$	12.5843	+	12.5843i	0.808950	+	0.808950i
$243$	−7.11319	+	13.8709i	−0.456311	+	0.889820i
$244$	−5.35463	+	3.09150i	−0.342795	+	0.197913i
$245$		0			0
$246$	−40.9783	+	6.90900i	−2.61268	+	0.440501i
$247$	−8.84026	+	7.45261i	−0.562492	+	0.474198i
$248$	−8.68911	+	8.68911i	−0.551759	+	0.551759i
$249$	9.74563	+	11.7929i	0.617604	+	0.747348i
$250$		0			0
$251$	11.5372	+	6.66100i	0.728221	+	0.420438i	0.817771	−	0.575544i	$-0.195210\pi$
$251$	11.5372	+	6.66100i	0.728221	+	0.420438i	−0.0895502	+	0.995982i	$0.528543\pi$
$252$	−1.95589	+	4.03521i	−0.123210	+	0.254195i
$253$	10.5810	−	2.83518i	0.665224	−	0.178246i
$254$	0.440953	−	0.763754i	0.0276679	−	0.0479222i
$255$		0			0
$256$	16.2213	−	28.0960i	1.01383	−	1.75600i
$257$	−0.0154174	+	0.0575384i	−0.000961709	+	0.00358915i	−0.966405	−	0.257024i	$-0.917258\pi$
$257$	−0.0154174	+	0.0575384i	−0.000961709	+	0.00358915i	0.965443	+	0.260613i	$0.0839247\pi$
$258$	−37.7093	−	3.58441i	−2.34768	−	0.223155i
$259$		−	3.37093i		−	0.209459i
$260$		0			0
$261$	−7.31947	−	21.0894i	−0.453064	−	1.30540i
$262$	17.4507	+	4.67590i	1.07811	+	0.288878i
$263$	−12.0687	−	3.23380i	−0.744189	−	0.199405i	−0.133250	−	0.991082i	$-0.542541\pi$
$263$	−12.0687	−	3.23380i	−0.744189	−	0.199405i	−0.610939	+	0.791678i	$0.709208\pi$
$264$	17.7800	+	6.62286i	1.09428	+	0.407609i
$265$		0			0
$266$	−2.44925	−	1.41408i	−0.150173	−	0.0867026i
$267$	15.1409	−	6.92250i	0.926608	−	0.423650i
$268$	−21.4947	−	21.4947i	−1.31300	−	1.31300i
$269$	−4.60249	+	7.97174i	−0.280619	+	0.486046i	−0.971537	−	0.236887i	$-0.923873\pi$
$269$	−4.60249	+	7.97174i	−0.280619	+	0.486046i	0.690919	+	0.722933i	$0.257206\pi$
$270$		0			0
$271$	1.16831	+	2.02358i	0.0709699	+	0.122923i	0.899327	−	0.437277i	$-0.144057\pi$
$271$	1.16831	+	2.02358i	0.0709699	+	0.122923i	−0.828357	+	0.560201i	$0.810724\pi$
$272$	−18.9661	−	18.9661i	−1.14999	−	1.14999i
$273$	−0.394433	+	2.17087i	−0.0238721	+	0.131387i
$274$			19.0239i			1.14927i
$275$		0			0
$276$	−31.4527	+	25.9923i	−1.89323	+	1.56456i
$277$	−0.659016	−	2.45948i	−0.0395964	−	0.147776i	0.943297	−	0.331949i	$-0.107706\pi$
$277$	−0.659016	−	2.45948i	−0.0395964	−	0.147776i	−0.982894	+	0.184173i	$0.941039\pi$
$278$	4.56488	−	4.56488i	0.273783	−	0.273783i
$279$	−6.50202	−	1.24735i	−0.389266	−	0.0746771i
$280$		0			0
$281$			9.40846i			0.561261i	0.959816	+	0.280631i	$0.0905436\pi$
$281$			9.40846i			0.561261i	−0.959816	+	0.280631i	$0.909456\pi$
$282$	−9.90298	−	21.6598i	−0.589714	−	1.28982i
$283$	2.63338	−	9.82790i	0.156538	−	0.584208i	−0.842431	−	0.538805i	$-0.818876\pi$
$283$	2.63338	−	9.82790i	0.156538	−	0.584208i	0.998969	−	0.0454032i	$-0.0144572\pi$
$284$	−28.6558	−	49.6333i	−1.70041	−	2.94519i
$285$		0			0
$286$	17.6417	+	1.50253i	1.04318	+	0.0888462i
$287$	−2.40132	−	2.40132i	−0.141745	−	0.141745i
$288$	−7.29065	+	0.527751i	−0.429605	+	0.0310980i
$289$	6.34943	−	3.66584i	0.373496	−	0.215638i
$290$		0			0
$291$	26.6322	−	4.49023i	1.56121	−	0.263222i
$292$	4.12724	+	15.4031i	0.241529	+	0.901397i
$293$	2.53794	+	9.47174i	0.148268	+	0.553345i	0.999588	+	0.0286978i	$0.00913603\pi$
$293$	2.53794	+	9.47174i	0.148268	+	0.553345i	−0.851320	+	0.524647i	$0.824197\pi$
$294$	29.3108	−	4.94183i	1.70944	−	0.288213i
$295$		0			0
$296$	46.0090	−	26.5633i	2.67422	−	1.54396i
$297$	2.42285	+	9.93107i	0.140588	+	0.576259i
$298$	−0.359147	−	0.359147i	−0.0208048	−	0.0208048i
$299$	−11.4775	+	16.4721i	−0.663760	+	0.952609i
$300$		0			0
$301$	−1.54773	−	2.68074i	−0.0892096	−	0.154516i
$302$	5.46651	−	20.4013i	0.314562	−	1.17396i
$303$	−1.41684	−	3.09891i	−0.0813954	−	0.178028i
$304$		−	17.4376i		−	1.00011i
$305$		0			0
$306$	6.95937	−	36.2768i	0.397840	−	2.07380i
$307$	−10.7245	+	10.7245i	−0.612080	+	0.612080i	−0.943488	−	0.331408i	$-0.892476\pi$
$307$	−10.7245	+	10.7245i	−0.612080	+	0.612080i	0.331408	+	0.943488i	$0.392476\pi$
$308$	0.761085	+	2.84041i	0.0433668	+	0.161847i
$309$	−12.2670	+	10.1373i	−0.697843	+	0.576694i
$310$		0			0
$311$			30.3961i			1.72361i	0.507242	+	0.861803i	$0.330665\pi$
$311$			30.3961i			1.72361i	−0.507242	+	0.861803i	$0.669335\pi$
$312$	−32.7378	+	11.7231i	−1.85341	+	0.663692i
$313$	−8.61061	−	8.61061i	−0.486701	−	0.486701i	0.420563	−	0.907263i	$-0.361833\pi$
$313$	−8.61061	−	8.61061i	−0.486701	−	0.486701i	−0.907263	+	0.420563i	$0.861833\pi$
$314$	3.82232	+	6.62045i	0.215706	+	0.373614i
$315$		0			0
$316$	−9.87517	+	17.1043i	−0.555522	+	0.962192i
$317$	14.0361	+	14.0361i	0.788344	+	0.788344i	0.981223	−	0.192878i	$-0.0617823\pi$
$317$	14.0361	+	14.0361i	0.788344	+	0.788344i	−0.192878	+	0.981223i	$0.561782\pi$
$318$	24.1585	−	11.0454i	1.35474	−	0.619396i
$319$	−12.6777	−	7.31947i	−0.709815	−	0.409812i
$320$		0			0
$321$	−29.8210	−	11.1080i	−1.66445	−	0.619990i
$322$	−4.74331	−	1.27097i	−0.264335	−	0.0708282i
$323$	15.2795	+	4.09414i	0.850176	+	0.227804i
$324$	−23.5889	−	29.8896i	−1.31049	−	1.66053i
$325$		0			0
$326$		−	25.3972i		−	1.40662i
$327$	21.1303	+	2.00852i	1.16851	+	0.111071i
$328$	13.8523	−	51.6976i	0.764866	−	2.85452i
$329$	0.973123	−	1.68550i	0.0536500	−	0.0929245i
$330$		0			0
$331$	11.9615	−	20.7178i	0.657461	−	1.13876i	−0.323810	−	0.946122i	$-0.604964\pi$
$331$	11.9615	−	20.7178i	0.657461	−	1.13876i	0.981271	−	0.192633i	$-0.0617028\pi$
$332$	−36.0955	+	9.67176i	−1.98100	+	0.530807i
$333$	25.7570	+	12.4846i	1.41147	+	0.684149i
$334$	−22.5713	−	13.0316i	−1.23505	−	0.713055i
$335$		0			0
$336$	−2.11970	−	2.56500i	−0.115639	−	0.139932i
$337$	−16.0550	+	16.0550i	−0.874569	+	0.874569i	−0.992966	−	0.118397i	$-0.962224\pi$
$337$	−16.0550	+	16.0550i	−0.874569	+	0.874569i	0.118397	+	0.992966i	$0.462224\pi$
$338$	−26.4954	+	18.7347i	−1.44116	+	1.01903i
$339$	21.9713	−	3.70439i	1.19332	−	0.201195i
$340$		0			0
$341$	−3.75988	+	2.17077i	−0.203609	+	0.117554i
$342$	19.8759	−	13.4774i	1.07476	−	0.728772i
$343$	3.46638	+	3.46638i	0.187167	+	0.187167i
$344$	24.3925	−	42.2491i	1.31516	−	2.27792i
$345$		0			0
$346$	3.02386			0.162564
$347$	16.2505	−	4.35431i	0.872373	−	0.233752i	0.205259	−	0.978708i	$-0.434196\pi$
$347$	16.2505	−	4.35431i	0.872373	−	0.233752i	0.667114	+	0.744956i	$0.267530\pi$
$348$	54.2829	+	5.15980i	2.90987	+	0.276594i
$349$	−21.0348	+	12.1444i	−1.12597	+	0.650077i	−0.942918	−	0.333026i	$-0.891930\pi$
$349$	−21.0348	+	12.1444i	−1.12597	+	0.650077i	−0.183050	+	0.983104i	$0.558597\pi$
$350$		0			0
$351$	−15.1266	−	11.0538i	−0.807396	−	0.590009i
$352$	−3.38948	+	3.38948i	−0.180660	+	0.180660i
$353$	16.0203	+	4.29264i	0.852677	+	0.228474i	0.658582	−	0.752509i	$-0.271156\pi$
$353$	16.0203	+	4.29264i	0.852677	+	0.228474i	0.194095	+	0.980983i	$0.437823\pi$
$354$	−24.7992	+	20.4939i	−1.31806	+	1.08924i
$355$		0			0
$356$			40.6655i			2.15526i
$357$	2.74524	−	1.25514i	0.145294	−	0.0664290i
$358$	−63.3105	+	16.9640i	−3.34607	+	0.896576i
$359$	24.6977			1.30350			0.651748	−	0.758435i	$-0.274036\pi$
$359$	24.6977			1.30350			0.651748	+	0.758435i	$0.274036\pi$
$360$		0			0
$361$	−4.35802	−	7.54831i	−0.229369	−	0.397280i
$362$	12.5232	−	46.7374i	0.658207	−	2.45646i
$363$	−10.0624	−	7.15885i	−0.528138	−	0.375742i
$364$	−4.42184	−	3.08106i	−0.231767	−	0.161491i
$365$		0			0
$366$	4.87059	−	4.02503i	0.254590	−	0.210392i
$367$	−17.1094	−	4.58446i	−0.893105	−	0.239307i	−0.217052	−	0.976160i	$-0.569644\pi$
$367$	−17.1094	−	4.58446i	−0.893105	−	0.239307i	−0.676053	+	0.736853i	$0.736311\pi$
$368$	−7.83642	−	29.2459i	−0.408502	−	1.52455i
$369$	27.2417	−	9.45474i	1.41815	−	0.492194i
$370$		0			0
$371$	1.87994	+	1.08539i	0.0976017	+	0.0563504i
$372$	9.37472	−	13.1770i	0.486057	−	0.683194i
$373$	6.41520	−	1.71895i	0.332167	−	0.0890038i	−0.0888811	−	0.996042i	$-0.528329\pi$
$373$	6.41520	−	1.71895i	0.332167	−	0.0890038i	0.421048	+	0.907038i	$0.361662\pi$
$374$	−12.1114	−	20.9776i	−0.626265	−	1.08472i
$375$		0			0
$376$	30.6732			1.58185
$377$	26.4111	−	4.71972i	1.36024	−	0.243078i
$378$	1.28536	−	4.39856i	0.0661119	−	0.226238i
$379$	18.9858	−	10.9615i	0.975235	−	0.563052i	0.0744065	−	0.997228i	$-0.476294\pi$
$379$	18.9858	−	10.9615i	0.975235	−	0.563052i	0.900828	+	0.434176i	$0.142960\pi$
$380$		0			0
$381$	−0.213607	+	0.573456i	−0.0109434	+	0.0293790i
$382$	−36.2886	+	36.2886i	−1.85669	+	1.85669i
$383$	3.82293	+	14.2674i	0.195343	+	0.729028i	0.992178	+	0.124832i	$0.0398391\pi$
$383$	3.82293	+	14.2674i	0.195343	+	0.729028i	−0.796835	+	0.604196i	$0.793494\pi$
$384$	−10.1798	+	27.3290i	−0.519486	+	1.39463i
$385$		0			0
$386$	−35.2355	−	20.3433i	−1.79344	−	1.03544i
$387$	26.2155	−	1.89767i	1.33261	−	0.0964640i
$388$	−17.0744	+	63.7224i	−0.866820	+	3.23501i
$389$	−32.3424			−1.63982			−0.819912	−	0.572490i	$-0.805978\pi$
$389$	−32.3424			−1.63982			−0.819912	+	0.572490i	$0.805978\pi$
$390$		0			0
$391$	27.4664			1.38903
$392$	−9.90821	+	36.9780i	−0.500440	+	1.86767i
$393$	−12.4798	−	1.18625i	−0.629522	−	0.0598384i
$394$	−46.9027	−	27.0793i	−2.36292	−	1.36423i
$395$		0			0
$396$	−24.5220	−	4.70433i	−1.23228	−	0.236402i
$397$	−5.21314	−	19.4557i	−0.261640	−	0.976454i	−0.964275	−	0.264904i	$-0.914660\pi$
$397$	−5.21314	−	19.4557i	−0.261640	−	0.976454i	0.702635	−	0.711551i	$-0.252007\pi$
$398$	30.3795	−	30.3795i	1.52279	−	1.52279i
$399$	1.83899	+	0.685007i	0.0920648	+	0.0342932i
$400$		0			0
$401$	14.2398	−	8.22133i	0.711100	−	0.410554i	−0.100368	−	0.994950i	$-0.532002\pi$
$401$	14.2398	−	8.22133i	0.711100	−	0.410554i	0.811468	+	0.584397i	$0.198669\pi$
$402$	25.3120	+	18.0082i	1.26245	+	0.898167i
$403$	2.70421	−	7.48333i	0.134707	−	0.372771i
$404$	8.32307			0.414088
$405$		0			0
$406$	3.28121	+	5.68322i	0.162844	+	0.282053i
$407$	18.1305	−	4.85804i	0.898694	−	0.240804i
$408$	38.7639	+	27.5785i	1.91910	+	1.36534i
$409$	−11.0421	−	6.37517i	−0.545998	−	0.315232i	0.201508	−	0.979487i	$-0.435416\pi$
$409$	−11.0421	−	6.37517i	−0.545998	−	0.315232i	−0.747506	+	0.664255i	$0.768749\pi$
$410$		0			0
$411$	−2.19464	−	13.0168i	−0.108254	−	0.642070i
$412$	−10.0605	−	37.5464i	−0.495646	−	1.84978i
$413$	−2.53944	−	0.680441i	−0.124958	−	0.0334823i
$414$	27.2786	−	31.5361i	1.34067	−	1.54991i
$415$		0			0
$416$	0.745527	−	8.75350i	0.0365525	−	0.429176i
$417$	−2.59683	+	3.65006i	−0.127167	+	0.178744i
$418$	4.07582	−	15.2111i	0.199355	−	0.744002i
$419$	−3.72058	−	6.44424i	−0.181762	−	0.314822i	0.760718	−	0.649082i	$-0.224847\pi$
$419$	−3.72058	−	6.44424i	−0.181762	−	0.314822i	−0.942481	+	0.334260i	$0.891513\pi$
$420$		0			0
$421$	−20.3023			−0.989474			−0.494737	−	0.869043i	$-0.664736\pi$
$421$	−20.3023			−0.989474			−0.494737	+	0.869043i	$0.664736\pi$
$422$	−22.6973	+	6.08173i	−1.10489	+	0.296054i
$423$	9.27469	+	13.6779i	0.450951	+	0.665044i
$424$			34.2118i			1.66147i
$425$		0			0
$426$	37.3089	+	45.1466i	1.80762	+	2.18736i
$427$	0.498748	+	0.133639i	0.0241361	+	0.00646725i
$428$	54.9637	−	54.9637i	2.65677	−	2.65677i
$429$	−12.2444	+	1.00711i	−0.591164	+	0.0486239i
$430$		0			0
$431$	11.5372	−	6.66100i	0.555727	−	0.320849i	−0.195702	−	0.980663i	$-0.562698\pi$
$431$	11.5372	−	6.66100i	0.555727	−	0.320849i	0.751429	+	0.659815i	$0.229365\pi$
$432$	27.4494	−	6.69674i	1.32066	−	0.322197i
$433$	4.89265	−	1.31098i	0.235126	−	0.0630017i	−0.139332	−	0.990246i	$-0.544496\pi$
$433$	4.89265	−	1.31098i	0.235126	−	0.0630017i	0.374458	+	0.927244i	$0.377829\pi$
$434$	1.94625			0.0934228
$435$		0			0
$436$	−25.9229	+	44.8998i	−1.24148	+	2.15031i
$437$	12.6264	+	12.6264i	0.604004	+	0.604004i
$438$	−6.77596	−	14.8204i	−0.323768	−	0.708145i
$439$	19.1692	−	11.0673i	0.914897	−	0.528216i	0.0328932	−	0.999459i	$-0.489528\pi$
$439$	19.1692	−	11.0673i	0.914897	−	0.528216i	0.882003	+	0.471243i	$0.156195\pi$
$440$		0			0
$441$	−19.4853	+	6.76274i	−0.927872	+	0.322035i
$442$	41.7518	+	15.0876i	1.98593	+	0.717646i
$443$	−14.4854	+	14.4854i	−0.688224	+	0.688224i	−0.961839	−	0.273616i	$-0.911780\pi$
$443$	−14.4854	+	14.4854i	−0.688224	+	0.688224i	0.273616	+	0.961839i	$0.411780\pi$
$444$	−53.8939	+	44.5376i	−2.55769	+	2.11366i
$445$		0			0
$446$	32.0225	+	18.4882i	1.51631	+	0.875443i
$447$	0.287173	+	0.204309i	0.0135828	+	0.00966346i
$448$	−1.63575	+	0.438298i	−0.0772820	+	0.0207076i
$449$	−0.101739	+	0.176217i	−0.00480137	+	0.00831621i	−0.868416	−	0.495836i	$-0.834862\pi$
$449$	−0.101739	+	0.176217i	−0.00480137	+	0.00831621i	0.863615	+	0.504152i	$0.168195\pi$
$450$		0			0
$451$	9.45474	−	16.3761i	0.445206	−	0.771120i
$452$	−14.0862	+	52.5704i	−0.662558	+	2.47270i
$453$	−1.38682	+	14.5899i	−0.0651587	+	0.685493i
$454$			46.1586i			2.16633i
$455$		0			0
$456$	5.14198	+	30.4979i	0.240795	+	1.42819i
$457$	−14.2218	−	3.81072i	−0.665268	−	0.178258i	−0.0896455	−	0.995974i	$-0.528573\pi$
$457$	−14.2218	−	3.81072i	−0.665268	−	0.178258i	−0.575622	+	0.817716i	$0.695240\pi$
$458$	−6.42163	−	1.72067i	−0.300063	−	0.0804017i
$459$	−0.576849	+	25.6247i	−0.0269250	+	1.19606i
$460$		0			0
$461$	14.3978	+	8.31255i	0.670570	+	0.387154i	0.796293	−	0.604911i	$-0.206792\pi$
$461$	14.3978	+	8.31255i	0.670570	+	0.387154i	−0.125722	+	0.992065i	$0.540125\pi$
$462$	−1.24952	−	2.73295i	−0.0581330	−	0.127149i
$463$	9.22555	+	9.22555i	0.428748	+	0.428748i	0.888202	−	0.459454i	$-0.151955\pi$
$463$	9.22555	+	9.22555i	0.428748	+	0.428748i	−0.459454	+	0.888202i	$0.651955\pi$
$464$	−20.2310	+	35.0411i	−0.939200	+	1.62674i
$465$		0			0
$466$	18.5435	+	32.1183i	0.859010	+	1.48785i
$467$	14.3818	+	14.3818i	0.665508	+	0.665508i	0.956673	−	0.291165i	$-0.0940428\pi$
$467$	14.3818	+	14.3818i	0.665508	+	0.665508i	−0.291165	+	0.956673i	$0.594043\pi$
$468$	39.9188	−	22.3759i	1.84525	−	1.03433i
$469$			2.53855i			0.117219i
$470$		0			0
$471$	−3.37912	−	4.08899i	−0.155701	−	0.188411i
$472$	−10.7239	−	40.0221i	−0.493607	−	1.84217i
$473$	12.1878	−	12.1878i	0.560395	−	0.560395i
$474$	7.04516	−	18.9137i	0.323595	−	0.868734i
$475$		0			0
$476$			7.37317i			0.337949i
$477$	−15.2559	+	10.3446i	−0.698518	+	0.473649i
$478$	0.262914	−	0.981208i	0.0120254	−	0.0448794i
$479$	−0.214001	−	0.370661i	−0.00977797	−	0.0169359i	0.861095	−	0.508444i	$-0.169779\pi$
$479$	−0.214001	−	0.370661i	−0.00977797	−	0.0169359i	−0.870873	+	0.491508i	$0.836446\pi$
$480$		0			0
$481$	−19.6665	+	28.2248i	−0.896717	+	1.28694i
$482$	42.6742	+	42.6742i	1.94376	+	1.94376i
$483$	3.39216	+	0.322438i	0.154349	+	0.0146714i
$484$	26.1229	−	15.0820i	1.18740	−	0.685547i
$485$		0			0
$486$	28.8486	+	26.1118i	1.30860	+	1.18446i
$487$	8.36485	+	31.2180i	0.379047	+	1.41462i	0.847340	+	0.531051i	$0.178203\pi$
$487$	8.36485	+	31.2180i	0.379047	+	1.41462i	−0.468293	+	0.883573i	$0.655131\pi$
$488$	2.10618	+	7.86038i	0.0953424	+	0.355823i
$489$	2.92989	+	17.3776i	0.132494	+	0.785844i
$490$		0			0
$491$	−35.9811	+	20.7737i	−1.62380	+	0.937503i	−0.637913	+	0.770108i	$0.720202\pi$
$491$	−35.9811	+	20.7737i	−1.62380	+	0.937503i	−0.985890	+	0.167395i	$0.946465\pi$
$492$	−6.66503	+	70.1186i	−0.300483	+	3.16119i
$493$	−25.9545	−	25.9545i	−1.16893	−	1.16893i
$494$	12.2577	+	26.1294i	0.551498	+	1.17562i
$495$		0			0
$496$	6.00000	+	10.3923i	0.269408	+	0.466628i
$497$	−1.23873	+	4.62301i	−0.0555647	+	0.207370i
$498$	34.7300	−	15.8787i	1.55629	−	0.711543i
$499$			13.7503i			0.615550i	0.951459	+	0.307775i	$0.0995844\pi$
$499$			13.7503i			0.615550i	−0.951459	+	0.307775i	$0.900416\pi$
$500$		0			0
$501$	16.9474	+	6.31275i	0.757155	+	0.282033i
$502$	23.5138	−	23.5138i	1.04947	−	1.04947i
$503$	−3.92574	−	14.6510i	−0.175040	−	0.653258i	−0.996545	−	0.0830565i	$-0.973532\pi$
$503$	−3.92574	−	14.6510i	−0.175040	−	0.653258i	0.821505	−	0.570201i	$-0.193135\pi$
$504$	4.46367	+	3.86106i	0.198828	+	0.171985i
$505$		0			0
$506$		−	27.3435i		−	1.21557i
$507$	15.9678	−	15.8755i	0.709153	−	0.705055i
$508$	−1.05695	−	1.05695i	−0.0468944	−	0.0468944i
$509$	−11.4775	−	19.8796i	−0.508731	−	0.881147i	−0.999949	−	0.0101108i	$-0.996782\pi$
$509$	−11.4775	−	19.8796i	−0.508731	−	0.881147i	0.491218	−	0.871037i	$-0.336552\pi$
$510$		0			0
$511$	0.665844	−	1.15328i	0.0294552	−	0.0510179i
$512$	−33.4505	−	33.4505i	−1.47832	−	1.47832i
$513$	−12.0450	+	11.5146i	−0.531798	+	0.508382i
$514$	0.128770	+	0.0743453i	0.00567979	+	0.00327923i
$515$		0			0
$516$	−22.4103	+	60.1635i	−0.986558	+	2.64855i
$517$	10.4678	+	2.80485i	0.460375	+	0.123357i
$518$	−8.12761	−	2.17779i	−0.357107	−	0.0956865i
$519$	−2.06903	+	0.348841i	−0.0908204	+	0.0153124i
$520$		0			0
$521$		−	24.2908i		−	1.06420i	−0.846682	−	0.532099i	$-0.821403\pi$
$521$		−	24.2908i		−	1.06420i	0.846682	−	0.532099i	$-0.178597\pi$
$522$	−55.5772	+	4.02309i	−2.43255	+	0.176086i
$523$	3.83400	−	14.3087i	0.167649	−	0.625675i	−0.830038	−	0.557706i	$-0.811682\pi$
$523$	3.83400	−	14.3087i	0.167649	−	0.625675i	0.997687	−	0.0679686i	$-0.0216518\pi$
$524$	15.3103	−	26.5183i	0.668835	−	1.15846i
$525$		0			0
$526$	−15.5940	+	27.0095i	−0.679929	+	1.17767i
$527$	−10.5149	+	2.81746i	−0.458036	+	0.122730i
$528$	10.7410	−	15.0973i	0.467441	−	0.657027i
$529$	6.93248	+	4.00247i	0.301412	+	0.174020i
$530$		0			0
$531$	14.6042	−	16.8836i	0.633770	−	0.732684i
$532$	−3.38948	+	3.38948i	−0.146953	+	0.146953i
$533$	6.09657	+	34.1159i	0.264072	+	1.47772i
$534$	−6.90900	−	40.9783i	−0.298981	−	1.77331i
$535$		0			0
$536$	−34.6480	+	20.0040i	−1.49657	+	0.864043i
$537$	41.3622	−	18.9110i	1.78491	−	0.816071i
$538$	16.2471	+	16.2471i	0.700464	+	0.700464i
$539$	−6.76274	+	11.7134i	−0.291292	+	0.504532i
$540$		0			0
$541$	−36.4187			−1.56576			−0.782880	−	0.622172i	$-0.786250\pi$
$541$	−36.4187			−1.56576			−0.782880	+	0.622172i	$0.786250\pi$
$542$	5.63381	−	1.50957i	0.241993	−	0.0648418i
$543$	−3.17708	+	33.4240i	−0.136342	+	1.43436i
$544$	−10.4087	+	6.00946i	−0.446269	+	0.257654i
$545$		0			0
$546$	4.97932	+	2.35350i	0.213095	+	0.100720i
$547$	3.89510	−	3.89510i	0.166542	−	0.166542i	−0.618915	−	0.785458i	$-0.712428\pi$
$547$	3.89510	−	3.89510i	0.166542	−	0.166542i	0.785458	+	0.618915i	$0.212428\pi$
$548$	31.1450	+	8.34527i	1.33045	+	0.356492i
$549$	−2.86828	+	3.31594i	−0.122415	+	0.141521i
$550$		0			0
$551$		−	23.8628i		−	1.01659i
$552$	22.3297	+	48.8396i	0.950416	+	2.07875i
$553$	1.59315	−	0.426884i	0.0677477	−	0.0181529i
$554$	−6.35578			−0.270031
$555$		0			0
$556$	−5.47091	−	9.47590i	−0.232018	−	0.401868i
$557$	4.68326	−	17.4782i	0.198436	−	0.740574i	−0.792914	−	0.609333i	$-0.791437\pi$
$557$	4.68326	−	17.4782i	0.198436	−	0.740574i	0.991350	−	0.131241i	$-0.0418962\pi$
$558$	−7.20810	+	14.8711i	−0.305143	+	0.629543i
$559$	−2.68074	+	31.4756i	−0.113383	+	1.33127i
$560$		0			0
$561$	10.7071	+	12.9564i	0.452052	+	0.547018i
$562$	22.6846	+	6.07832i	0.956893	+	0.256399i
$563$	0.187009	+	0.697927i	0.00788149	+	0.0294141i	0.969755	−	0.244082i	$-0.0784866\pi$
$563$	0.187009	+	0.697927i	0.00788149	+	0.0294141i	−0.961873	+	0.273496i	$0.911820\pi$
$564$	−39.8046	+	6.71110i	−1.67608	+	0.282588i
$565$		0			0
$566$	−21.9946	−	12.6986i	−0.924503	−	0.533762i
$567$	−0.372059	+	3.15793i	−0.0156250	+	0.132621i
$568$	−72.8596	+	19.5227i	−3.05712	+	0.819153i
$569$	−7.85864	−	13.6116i	−0.329452	−	0.570627i	0.652952	−	0.757400i	$-0.273530\pi$
$569$	−7.85864	−	13.6116i	−0.329452	−	0.570627i	−0.982403	+	0.186773i	$0.940197\pi$
$570$		0			0
$571$	16.9229			0.708201			0.354101	−	0.935207i	$-0.384787\pi$
$571$	16.9229			0.708201			0.354101	+	0.935207i	$0.384787\pi$
$572$	10.1988	−	28.2230i	0.426434	−	1.18006i
$573$	20.6436	−	29.0163i	0.862397	−	1.21217i
$574$	−7.34115	+	4.23842i	−0.306414	+	0.176908i
$575$		0			0
$576$	2.70916	−	14.1219i	0.112882	−	0.588413i
$577$	−4.94608	+	4.94608i	−0.205908	+	0.205908i	−0.802526	−	0.596618i	$-0.796511\pi$
$577$	−4.94608	+	4.94608i	−0.205908	+	0.205908i	0.596618	+	0.802526i	$0.296511\pi$
$578$	−4.73663	−	17.6773i	−0.197018	−	0.735281i
$579$	26.4562	+	9.85468i	1.09948	+	0.409546i
$580$		0			0
$581$	2.70258	+	1.56034i	0.112122	+	0.0647336i
$582$	6.37940	−	67.1136i	0.264434	−	2.78195i
$583$	−3.12842	+	11.6754i	−0.129566	+	0.483547i
$584$	20.9877			0.868476
$585$		0			0
$586$	24.4768			1.01113
$587$	7.43905	−	27.7629i	0.307043	−	1.14590i	−0.624130	−	0.781320i	$-0.714547\pi$
$587$	7.43905	−	27.7629i	0.307043	−	1.14590i	0.931173	−	0.364578i	$-0.118787\pi$
$588$	4.76733	−	50.1540i	0.196601	−	2.06832i
$589$	−6.12895	−	3.53855i	−0.252539	−	0.145803i
$590$		0			0
$591$	35.2164	+	13.1177i	1.44861	+	0.539592i
$592$	−13.4276	−	50.1125i	−0.551872	−	2.05961i
$593$	−0.187921	+	0.187921i	−0.00771699	+	0.00771699i	−0.710955	−	0.703238i	$-0.751737\pi$
$593$	−0.187921	+	0.187921i	−0.00771699	+	0.00771699i	0.703238	+	0.710955i	$0.251737\pi$
$594$	25.5100	+	0.574267i	1.04669	+	0.0235625i
$595$		0			0
$596$	−0.745527	+	0.430430i	−0.0305380	+	0.0176311i
$597$	−17.2820	+	24.2913i	−0.707306	+	0.994179i
$598$	32.3008	+	38.3150i	1.32088	+	1.56682i
$599$	−4.56606			−0.186564			−0.0932822	−	0.995640i	$-0.529736\pi$
$599$	−4.56606			−0.186564			−0.0932822	+	0.995640i	$0.529736\pi$
$600$		0			0
$601$	21.3299	+	36.9445i	0.870065	+	1.50700i	0.861928	+	0.507030i	$0.169257\pi$
$601$	21.3299	+	36.9445i	0.870065	+	1.50700i	0.00813719	+	0.999967i	$0.497410\pi$
$602$	−7.46342	+	1.99982i	−0.304186	+	0.0815064i
$603$	−19.3968	−	9.40175i	−0.789900	−	0.382869i
$604$	−31.0020	−	17.8990i	−1.26146	−	0.728302i
$605$		0			0
$606$	−8.38711	+	1.41408i	−0.340703	+	0.0574429i
$607$	−6.77517	−	25.2853i	−0.274996	−	1.02630i	−0.955844	−	0.293874i	$-0.905055\pi$
$607$	−6.77517	−	25.2853i	−0.274996	−	1.02630i	0.680848	−	0.732424i	$-0.261611\pi$
$608$	−7.54751	−	2.02235i	−0.306092	−	0.0820171i
$609$	−2.90074	−	3.51012i	−0.117544	−	0.142237i
$610$		0			0
$611$	−17.9814	+	8.43533i	−0.727451	+	0.341257i
$612$	−56.3377	−	27.3072i	−2.27732	−	1.10383i
$613$	−0.0870784	+	0.324981i	−0.00351706	+	0.0131259i	−0.967662	−	0.252250i	$-0.918829\pi$
$613$	−0.0870784	+	0.324981i	−0.00351706	+	0.0131259i	0.964145	+	0.265376i	$0.0854961\pi$
$614$	18.9292	+	32.7863i	0.763919	+	1.32315i
$615$		0			0
$616$	3.87024			0.155936
$617$	4.49603	−	1.20471i	0.181003	−	0.0484997i	−0.167179	−	0.985927i	$-0.553466\pi$
$617$	4.49603	−	1.20471i	0.181003	−	0.0484997i	0.348182	+	0.937427i	$0.386799\pi$
$618$	16.5170	+	36.1260i	0.664410	+	1.45320i
$619$			17.0343i			0.684667i	0.939579	+	0.342333i	$0.111217\pi$
$619$			17.0343i			0.684667i	−0.939579	+	0.342333i	$0.888783\pi$
$620$		0			0
$621$	−15.0269	+	24.7250i	−0.603008	+	0.992180i
$622$	73.2878	+	19.6374i	2.93857	+	0.787388i
$623$	2.40132	−	2.40132i	0.0962067	−	0.0962067i
$624$	2.78366	+	33.8434i	0.111436	+	1.35482i
$625$		0			0
$626$	−26.3238	+	15.1981i	−1.05211	+	0.607437i
$627$	−1.03401	+	10.8782i	−0.0412945	+	0.434433i
$628$	12.5155	−	3.35351i	0.499421	−	0.133819i
$629$	47.0633			1.87654
$630$		0			0
$631$	−0.293139	+	0.507731i	−0.0116697	+	0.0202125i	−0.871801	−	0.489860i	$-0.837048\pi$
$631$	−0.293139	+	0.507731i	−0.0116697	+	0.0202125i	0.860132	+	0.510072i	$0.170381\pi$
$632$	18.3806	+	18.3806i	0.731142	+	0.731142i
$633$	14.8287	−	6.77975i	0.589387	−	0.269471i
$634$	42.9102	−	24.7742i	1.70418	−	0.983910i
$635$		0			0
$636$	−7.48531	−	44.3966i	−0.296812	−	1.76044i
$637$	−4.36072	−	24.4022i	−0.172778	−	0.966851i
$638$	−25.8383	+	25.8383i	−1.02295	+	1.02295i
$639$	−30.7362	−	26.5868i	−1.21591	−	1.05176i
$640$		0			0
$641$	−26.6945	−	15.4121i	−1.05437	−	0.608740i	−0.130500	−	0.991448i	$-0.541658\pi$
$641$	−26.6945	−	15.4121i	−1.05437	−	0.608740i	−0.923869	+	0.382708i	$0.874991\pi$
$642$	−46.0483	+	64.7248i	−1.81738	+	2.55448i
$643$	−32.8112	+	8.79173i	−1.29395	+	0.346712i	−0.839158	−	0.543887i	$-0.816952\pi$
$643$	−32.8112	+	8.79173i	−1.29395	+	0.346712i	−0.454789	+	0.890599i	$0.650285\pi$
$644$	−4.16154	+	7.20799i	−0.163987	+	0.284035i
$645$		0			0
$646$	19.7427	−	34.1953i	0.776764	−	1.34540i
$647$	−8.16893	+	30.4869i	−0.321154	+	1.19856i	0.596968	+	0.802265i	$0.296372\pi$
$647$	−8.16893	+	30.4869i	−0.321154	+	1.19856i	−0.918122	+	0.396298i	$0.870295\pi$
$648$	−46.0336	+	19.8067i	−1.80837	+	0.778080i
$649$		−	14.6389i		−	0.574629i
$650$		0			0
$651$	−1.33169	+	0.224524i	−0.0521930	+	0.00879980i
$652$	−41.5791	−	11.1411i	−1.62836	−	0.436319i
$653$	−11.0712	−	2.96652i	−0.433249	−	0.116089i	0.0356017	−	0.999366i	$-0.488665\pi$
$653$	−11.0712	−	2.96652i	−0.433249	−	0.116089i	−0.468851	+	0.883277i	$0.655332\pi$
$654$	18.4939	−	49.6495i	0.723170	−	1.94145i
$655$		0			0
$656$	−45.2634	−	26.1329i	−1.76724	−	1.02032i
$657$	6.34606	+	9.35891i	0.247583	+	0.365126i
$658$	−3.43520	−	3.43520i	−0.133918	−	0.133918i
$659$	2.52294	−	4.36985i	0.0982796	−	0.170225i	−0.812693	−	0.582692i	$-0.801999\pi$
$659$	2.52294	−	4.36985i	0.0982796	−	0.170225i	0.910973	+	0.412467i	$0.135333\pi$
$660$		0			0
$661$	−3.37517	−	5.84597i	−0.131279	−	0.227382i	0.792891	−	0.609364i	$-0.208575\pi$
$661$	−3.37517	−	5.84597i	−0.131279	−	0.227382i	−0.924170	+	0.381982i	$0.875242\pi$
$662$	−42.2249	−	42.2249i	−1.64112	−	1.64112i
$663$	−30.3086	−	5.50688i	−1.17709	−	0.213869i
$664$			49.1824i			1.90865i
$665$		0			0
$666$	46.7416	−	54.0367i	1.81120	−	2.09388i
$667$	−10.7239	−	40.0221i	−0.415231	−	1.54966i
$668$	−31.2361	+	31.2361i	−1.20856	+	1.20856i
$669$	−24.0438	−	8.95606i	−0.929586	−	0.346261i
$670$		0			0
$671$			2.87510i			0.110992i
$672$	−1.35604	+	0.619991i	−0.0523105	+	0.0239167i
$673$	−2.30980	+	8.62030i	−0.0890363	+	0.332288i	−0.996048	−	0.0888176i	$-0.971691\pi$
$673$	−2.30980	+	8.62030i	−0.0890363	+	0.332288i	0.907012	+	0.421106i	$0.138358\pi$
$674$	28.3376	+	49.0822i	1.09152	+	1.89058i
$675$		0			0
$676$	19.0487	+	51.5954i	0.732643	+	1.98444i
$677$	−14.5784	−	14.5784i	−0.560293	−	0.560293i	0.369098	−	0.929391i	$-0.379667\pi$
$677$	−14.5784	−	14.5784i	−0.560293	−	0.560293i	−0.929391	+	0.369098i	$0.879667\pi$
$678$	5.26294	−	55.3680i	0.202122	−	2.12640i
$679$	4.77109	−	2.75459i	0.183098	−	0.105711i
$680$		0			0
$681$	−5.32498	−	31.5833i	−0.204054	−	1.21027i
$682$	2.80485	+	10.4678i	0.107403	+	0.400834i
$683$	−3.89171	−	14.5241i	−0.148912	−	0.555748i	−0.999550	−	0.0299958i	$-0.990451\pi$
$683$	−3.89171	−	14.5241i	−0.148912	−	0.555748i	0.850638	−	0.525752i	$-0.176216\pi$
$684$	−13.3455	−	38.4520i	−0.510277	−	1.47025i
$685$		0			0
$686$	10.5972	−	6.11830i	0.404604	−	0.233598i
$687$	4.59240	+	0.436525i	0.175211	+	0.0166545i
$688$	−33.6870	−	33.6870i	−1.28431	−	1.28431i
$689$	−9.40846	−	20.0558i	−0.358434	−	0.764065i
$690$		0			0
$691$	−18.0435	−	31.2522i	−0.686407	−	1.18889i	−0.972993	−	0.230836i	$-0.925854\pi$
$691$	−18.0435	−	31.2522i	−0.686407	−	1.18889i	0.286586	−	0.958055i	$-0.407480\pi$
$692$	1.32649	−	4.95053i	0.0504256	−	0.188191i
$693$	1.17025	+	1.72583i	0.0444540	+	0.0655589i
$694$		−	41.9945i		−	1.59409i
$695$		0			0
$696$	25.0506	−	67.2517i	0.949540	−	2.54917i
$697$	33.5260	−	33.5260i	1.26989	−	1.26989i
$698$	15.6918	+	58.5627i	0.593944	+	2.21663i
$699$	−16.3933	−	19.8372i	−0.620053	−	0.750311i
$700$		0			0
$701$		−	7.01316i		−	0.264883i	−0.991191	−	0.132442i	$-0.957718\pi$
$701$		−	7.01316i		−	0.264883i	0.991191	−	0.132442i	$-0.0422817\pi$
$702$	−36.4242	+	29.3302i	−1.37474	+	1.10700i
$703$	21.6352	+	21.6352i	0.815988	+	0.815988i
$704$	−4.71475	−	8.16619i	−0.177694	−	0.307775i
$705$		0			0
$706$	20.6999	−	35.8532i	0.779050	−	1.34935i
$707$	−0.491481	−	0.491481i	−0.0184841	−	0.0184841i
$708$	22.6729	+	49.5903i	0.852102	+	1.86372i
$709$	−8.95178	−	5.16831i	−0.336191	−	0.194100i	0.322395	−	0.946605i	$-0.395512\pi$
$709$	−8.95178	−	5.16831i	−0.336191	−	0.194100i	−0.658586	+	0.752505i	$0.728845\pi$
$710$		0			0
$711$	−2.63860	+	13.7541i	−0.0989554	+	0.515820i
$712$	51.6976	+	13.8523i	1.93745	+	0.519138i
$713$	−11.8695	−	3.18044i	−0.444518	−	0.119108i
$714$	−1.25269	−	7.42990i	−0.0468807	−	0.278057i
$715$		0			0
$716$			111.091i			4.15165i
$717$	−0.0666999	+	0.701707i	−0.00249095	+	0.0262057i
$718$	15.9560	−	59.5484i	0.595471	−	2.22233i
$719$	−7.85864	+	13.6116i	−0.293078	+	0.507626i	−0.974536	−	0.224231i	$-0.928013\pi$
$719$	−7.85864	+	13.6116i	−0.293078	+	0.507626i	0.681458	+	0.731857i	$0.261346\pi$
$720$		0			0
$721$	−1.62305	+	2.81121i	−0.0604456	+	0.104695i
$722$	−21.0151	+	5.63099i	−0.782103	+	0.209564i
$723$	−34.1222	−	24.2761i	−1.26902	−	0.902839i
$724$	−71.0226	−	41.0049i	−2.63954	−	1.52394i
$725$		0			0
$726$	−23.7614	+	19.6363i	−0.881869	+	0.728771i
$727$	−36.9805	+	36.9805i	−1.37153	+	1.37153i	−0.513351	+	0.858178i	$0.671596\pi$
$727$	−36.9805	+	36.9805i	−1.37153	+	1.37153i	−0.858178	+	0.513351i	$0.828404\pi$
$728$	−5.42317	+	4.57190i	−0.200996	+	0.169446i
$729$	−22.7515	−	14.5385i	−0.842648	−	0.538465i
$730$		0			0
$731$	37.4273	−	21.6086i	1.38430	−	0.799224i
$732$	−4.45299	−	9.73957i	−0.164587	−	0.359985i
$733$	−10.1096	−	10.1096i	−0.373406	−	0.373406i	0.495310	−	0.868716i	$-0.335054\pi$
$733$	−10.1096	−	10.1096i	−0.373406	−	0.373406i	−0.868716	+	0.495310i	$0.835054\pi$
$734$	−22.1071	+	38.2906i	−0.815987	+	1.41333i
$735$		0			0
$736$	−13.5673			−0.500099
$737$	−13.6535	+	3.65845i	−0.502934	+	0.134761i
$738$	−5.19672	−	71.7904i	−0.191294	−	2.64264i
$739$	−36.7515	+	21.2185i	−1.35193	+	0.780535i	−0.988519	−	0.151095i	$-0.951720\pi$
$739$	−36.7515	+	21.2185i	−1.35193	+	0.780535i	−0.363408	+	0.931630i	$0.618387\pi$
$740$		0			0
$741$	−11.4015	−	16.4645i	−0.418843	−	0.604840i
$742$	3.83149	−	3.83149i	0.140659	−	0.140659i
$743$	−8.44766	−	2.26354i	−0.309915	−	0.0830414i	0.100510	−	0.994936i	$-0.467953\pi$
$743$	−8.44766	−	2.26354i	−0.309915	−	0.0830414i	−0.410424	+	0.911895i	$0.634619\pi$
$744$	−13.5583	−	16.4066i	−0.497072	−	0.601495i
$745$		0			0
$746$		−	16.5781i		−	0.606969i
$747$	−21.9316	+	14.8713i	−0.802436	+	0.544113i
$748$	−39.6564	+	10.6259i	−1.44998	+	0.388522i
$749$	−6.49126			−0.237186
$750$		0			0
$751$	−14.6084	−	25.3024i	−0.533067	−	0.923299i	−0.999254	−	0.0386129i	$-0.987706\pi$
$751$	−14.6084	−	25.3024i	−0.533067	−	0.923299i	0.466187	−	0.884686i	$-0.345627\pi$
$752$	7.75259	−	28.9331i	0.282708	−	1.05508i
$753$	−13.3764	+	18.8016i	−0.487461	+	0.685168i
$754$	5.68322	−	66.7287i	0.206971	−	2.43011i
$755$		0			0
$756$	−6.63727	−	4.03387i	−0.241395	−	0.146710i
$757$	2.45948	+	0.659016i	0.0893913	+	0.0239523i	0.303237	−	0.952915i	$-0.401932\pi$
$757$	2.45948	+	0.659016i	0.0893913	+	0.0239523i	−0.213846	+	0.976867i	$0.568599\pi$
$758$	−14.1633	−	52.8580i	−0.514433	−	1.91989i
$759$	3.15442	+	18.7093i	0.114498	+	0.679106i
$760$		0			0
$761$	34.2956	+	19.8006i	1.24321	+	0.717770i	0.969747	−	0.244112i	$-0.0784964\pi$
$761$	34.2956	+	19.8006i	1.24321	+	0.717770i	0.273466	+	0.961882i	$0.411830\pi$
$762$	1.24465	+	0.885505i	0.0450890	+	0.0320785i
$763$	4.18211	−	1.12059i	0.151403	−	0.0405682i
$764$	43.4912	+	75.3289i	1.57346	+	2.72531i
$765$		0			0
$766$	36.8697			1.33216
$767$	17.2929	+	20.5128i	0.624412	+	0.740675i
$768$	45.7868	+	32.5749i	1.65219	+	1.17545i
$769$	17.3089	−	9.99329i	0.624174	−	0.360367i	−0.154318	−	0.988021i	$-0.549318\pi$
$769$	17.3089	−	9.99329i	0.624174	−	0.360367i	0.778492	+	0.627654i	$0.215985\pi$
$770$		0			0
$771$	−0.0966854	−	0.0360143i	−0.00348204	−	0.00129702i
$772$	−48.7619	+	48.7619i	−1.75498	+	1.75498i
$773$	−13.2377	−	49.4038i	−0.476127	−	1.77693i	−0.617064	−	0.786913i	$-0.711678\pi$
$773$	−13.2377	−	49.4038i	−0.476127	−	1.77693i	0.140937	−	0.990019i	$-0.454988\pi$
$774$	12.3610	−	64.4338i	0.444308	−	2.31603i
$775$		0			0
$776$	75.1934	+	43.4129i	2.69928	+	1.55843i
$777$	5.81242	+	0.552493i	0.208520	+	0.0198206i
$778$	−20.8948	+	77.9803i	−0.749114	+	2.79573i
$779$	30.8241			1.10439
$780$		0			0
$781$	−26.6500			−0.953610
$782$	17.7446	−	66.2239i	0.634547	−	2.36816i
$783$	37.5637	−	9.16427i	1.34242	−	0.327504i
$784$	32.3758	+	18.6922i	1.15628	+	0.667578i
$785$		0			0
$786$	−10.9227	+	29.3235i	−0.389600	+	1.04593i
$787$	−7.16422	−	26.7372i	−0.255377	−	0.953080i	−0.967880	−	0.251411i	$-0.919105\pi$
$787$	−7.16422	−	26.7372i	−0.255377	−	0.953080i	0.712503	−	0.701669i	$-0.247561\pi$
$788$	−64.9079	+	64.9079i	−2.31225	+	2.31225i
$789$	7.55403	−	20.2798i	0.268931	−	0.721980i
$790$		0			0
$791$	3.93610	−	2.27251i	0.139952	−	0.0808011i
$792$	−14.3338	+	29.5721i	−0.509329	+	1.05080i
$793$	−3.39635	−	4.02874i	−0.120608	−	0.143065i
$794$	−50.2774			−1.78428
$795$		0			0
$796$	−36.4092	−	63.0626i	−1.29049	−	2.23519i
$797$	−51.8738	+	13.8995i	−1.83746	+	0.492347i	−0.998644	−	0.0520611i	$-0.983421\pi$
$797$	−51.8738	+	13.8995i	−1.83746	+	0.492347i	−0.838820	+	0.544408i	$0.816754\pi$
$798$	2.83969	−	3.99143i	0.100524	−	0.141295i
$799$	23.5321	+	13.5863i	0.832507	+	0.480648i
$800$		0			0
$801$	9.45474	+	27.2417i	0.334067	+	0.962539i
$802$	−10.6228	−	39.6447i	−0.375103	−	1.39990i
$803$	7.16245	+	1.91917i	0.252757	+	0.0677261i
$804$	40.5859	−	33.5399i	1.43135	−	1.18286i
$805$		0			0
$806$	−16.2959	−	11.3547i	−0.573999	−	0.399952i
$807$	−12.9912	−	9.24254i	−0.457311	−	0.325353i
$808$	2.83518	−	10.5810i	0.0997412	−	0.372239i
$809$	13.8517	+	23.9919i	0.487001	+	0.843511i	0.999888	−	0.0149454i	$-0.00475743\pi$
$809$	13.8517	+	23.9919i	0.487001	+	0.843511i	−0.512887	+	0.858456i	$0.671424\pi$
$810$		0			0
$811$	29.8030			1.04653			0.523263	−	0.852171i	$-0.324715\pi$
$811$	29.8030			1.04653			0.523263	+	0.852171i	$0.324715\pi$
$812$	10.7437	−	2.87876i	0.377029	−	0.101025i
$813$	−3.68069	+	1.68283i	−0.129088	+	0.0590195i
$814$		−	46.8527i		−	1.64219i
$815$		0			0
$816$	35.8113	−	29.5943i	1.25365	−	1.03601i
$817$	27.1391	+	7.27190i	0.949477	+	0.254411i
$818$	−22.5049	+	22.5049i	−0.786864	+	0.786864i
$819$	−3.67853	−	1.03591i	−0.128538	−	0.0361978i
$820$		0			0
$821$	−40.7216	+	23.5106i	−1.42119	+	0.820526i	−0.996401	−	0.0847647i	$-0.972986\pi$
$821$	−40.7216	+	23.5106i	−1.42119	+	0.820526i	−0.424792	+	0.905291i	$0.639653\pi$
$822$	−32.8024	−	3.11800i	−1.14412	−	0.108753i
$823$	21.8889	−	5.86511i	0.762999	−	0.204445i	0.143722	−	0.989618i	$-0.454093\pi$
$823$	21.8889	−	5.86511i	0.762999	−	0.204445i	0.619276	+	0.785173i	$0.287426\pi$
$824$	−51.1593			−1.78222
$825$		0			0
$826$	−3.28121	+	5.68322i	−0.114168	+	0.197744i
$827$	−16.1144	−	16.1144i	−0.560352	−	0.560352i	0.369055	−	0.929407i	$-0.379681\pi$
$827$	−16.1144	−	16.1144i	−0.560352	−	0.560352i	−0.929407	+	0.369055i	$0.879681\pi$
$828$	−39.6630	−	58.4934i	−1.37838	−	2.03279i
$829$	−37.8221	+	21.8366i	−1.31362	+	0.758417i	−0.982693	−	0.185240i	$-0.940694\pi$
$829$	−37.8221	+	21.8366i	−1.31362	+	0.758417i	−0.330924	+	0.943657i	$0.607360\pi$
$830$		0			0
$831$	4.34884	−	0.733220i	0.150860	−	0.0254351i
$832$	16.2532	+	5.87335i	0.563480	+	0.203622i
$833$	−23.9803	+	23.9803i	−0.830868	+	0.830868i
$834$	7.12295	+	8.61931i	0.246647	+	0.298462i
$835$		0			0
$836$	−23.1150	−	13.3455i	−0.799450	−	0.461563i
$837$	3.21646	−	11.0069i	0.111177	−	0.380452i
$838$	−17.9413	+	4.80736i	−0.619772	+	0.166067i
$839$	−18.2402	+	31.5930i	−0.629722	+	1.09071i	0.357885	+	0.933766i	$0.383498\pi$
$839$	−18.2402	+	31.5930i	−0.629722	+	1.09071i	−0.987607	+	0.156946i	$0.949835\pi$
$840$		0			0
$841$	−13.1855	+	22.8379i	−0.454671	+	0.787514i
$842$	−13.1163	+	48.9507i	−0.452017	+	1.68695i
$843$	−16.2228	−	1.54204i	−0.558743	−	0.0531106i
$844$			39.8269i			1.37090i
$845$		0			0
$846$	38.9706	−	13.5255i	1.33984	−	0.465015i
$847$	−2.43317	−	0.651966i	−0.0836047	−	0.0224018i
$848$	32.2709	+	8.64695i	1.10819	+	0.296937i
$849$	16.5144	+	6.15146i	0.566774	+	0.211118i
$850$		0			0
$851$	46.0090	+	26.5633i	1.57717	+	0.910578i
$852$	90.2783	−	41.2757i	3.09288	−	1.41408i
$853$	−9.49464	−	9.49464i	−0.325090	−	0.325090i	0.525626	−	0.850716i	$-0.323831\pi$
$853$	−9.49464	−	9.49464i	−0.325090	−	0.325090i	−0.850716	+	0.525626i	$0.823831\pi$
$854$	0.644432	−	1.11619i	0.0220520	−	0.0381952i
$855$		0			0
$856$	−51.1519	−	88.5976i	−1.74833	−	3.02820i
$857$	−11.6856	−	11.6856i	−0.399172	−	0.399172i	0.478769	−	0.877941i	$-0.341083\pi$
$857$	−11.6856	−	11.6856i	−0.399172	−	0.399172i	−0.877941	+	0.478769i	$0.841083\pi$
$858$	−5.48223	+	30.1729i	−0.187160	+	1.03009i
$859$			45.2461i			1.54378i	0.635758	+	0.771889i	$0.280688\pi$
$859$			45.2461i			1.54378i	−0.635758	+	0.771889i	$0.719312\pi$
$860$		0			0
$861$	4.53411	−	3.74696i	0.154522	−	0.127696i
$862$	−8.60666	−	32.1205i	−0.293144	−	1.09403i
$863$	−0.626558	+	0.626558i	−0.0213283	+	0.0213283i	−0.717690	−	0.696362i	$-0.754801\pi$
$863$	−0.626558	+	0.626558i	−0.0213283	+	0.0213283i	0.696362	+	0.717690i	$0.254801\pi$
$864$	0.284941	−	12.6576i	0.00969391	−	0.430620i
$865$		0			0
$866$		−	12.6436i		−	0.429646i
$867$	5.28027	+	11.5490i	0.179327	+	0.392225i
$868$	0.853767	−	3.18630i	0.0289787	−	0.108150i
$869$	4.59197	+	7.95352i	0.155772	+	0.269805i
$870$		0			0
$871$	14.8103	−	21.2553i	0.501828	−	0.720208i
$872$	48.2502	+	48.2502i	1.63396	+	1.63396i
$873$	3.37740	+	46.6573i	0.114308	+	1.57911i
$874$	38.6007	−	22.2861i	1.30569	−	0.753840i
$875$		0			0
$876$	−27.2357	+	4.59197i	−0.920208	+	0.155148i
$877$	0.659016	+	2.45948i	0.0222534	+	0.0830507i	0.976160	−	0.217054i	$-0.0696449\pi$
$877$	0.659016	+	2.45948i	0.0222534	+	0.0830507i	−0.953906	+	0.300105i	$0.902978\pi$
$878$	−14.3001	−	53.3687i	−0.482605	−	1.80111i
$879$	−16.7479	+	2.82371i	−0.564892	+	0.0952415i
$880$		0			0
$881$	−39.5465	+	22.8322i	−1.33236	+	0.769236i	−0.985660	−	0.168742i	$-0.946030\pi$
$881$	−39.5465	+	22.8322i	−1.33236	+	0.769236i	−0.346696	+	0.937978i	$0.612696\pi$
$882$	3.71708	+	51.3499i	0.125161	+	1.72904i
$883$	−12.4421	−	12.4421i	−0.418710	−	0.418710i	0.466049	−	0.884759i	$-0.345677\pi$
$883$	−12.4421	−	12.4421i	−0.418710	−	0.418710i	−0.884759	+	0.466049i	$0.845677\pi$
$884$	43.0162	−	61.7356i	1.44679	−	2.07639i
$885$		0			0
$886$	25.5673	+	44.2839i	0.858952	+	1.48775i
$887$	10.3522	−	38.6349i	0.347593	−	1.29723i	−0.541961	−	0.840404i	$-0.682318\pi$
$887$	10.3522	−	38.6349i	0.347593	−	1.29723i	0.889554	−	0.456831i	$-0.151016\pi$
$888$	38.2617	+	83.6860i	1.28398	+	2.80832i
$889$			0.124826i			0.00418655i
$890$		0			0
$891$	−17.5210	+	2.54997i	−0.586977	+	0.0854271i
$892$	44.3155	−	44.3155i	1.48379	−	1.48379i
$893$	4.57215	+	17.0635i	0.153001	+	0.571009i
$894$	0.678134	−	0.560406i	0.0226802	−	0.0187428i
$895$		0			0
$896$			5.94882i			0.198736i
$897$	−26.5214	−	22.4902i	−0.885524	−	0.750925i
$898$	0.359147	+	0.359147i	0.0119849	+	0.0119849i
$899$	8.21081	+	14.2215i	0.273846	+	0.474315i
$900$		0			0
$901$	−15.1536	+	26.2469i	−0.504841	+	0.874409i
$902$	−33.3760	−	33.3760i	−1.11130	−	1.11130i
$903$	4.87602	−	2.22934i	0.162264	−	0.0741879i
$904$	62.0338	+	35.8152i	2.06321	+	1.19120i
$905$		0			0
$906$	34.2816	+	12.7695i	1.13893	+	0.424240i
$907$	−4.28071	−	1.14701i	−0.142139	−	0.0380859i	0.187048	−	0.982351i	$-0.440108\pi$
$907$	−4.28071	−	1.14701i	−0.142139	−	0.0380859i	−0.329187	+	0.944265i	$0.606775\pi$
$908$	75.5686	+	20.2486i	2.50783	+	0.671972i
$909$	5.57561	−	1.93512i	0.184931	−	0.0641838i
$910$		0			0
$911$		−	53.3301i		−	1.76690i	−0.468522	−	0.883452i	$-0.655213\pi$
$911$		−	53.3301i		−	1.76690i	0.468522	−	0.883452i	$-0.344787\pi$
$912$	30.0673	+	2.85801i	0.995626	+	0.0946380i
$913$	−4.49738	+	16.7844i	−0.148842	+	0.555484i
$914$	−18.3760	+	31.8281i	−0.607823	+	1.05278i
$915$		0			0
$916$	−5.63401	+	9.75838i	−0.186153	+	0.322426i
$917$	−2.47000	+	0.661834i	−0.0815666	+	0.0218557i
$918$	61.4106	+	17.9456i	2.02685	+	0.592294i
$919$	39.3836	+	22.7381i	1.29914	+	0.750062i	0.980256	−	0.197731i	$-0.0633571\pi$
$919$	39.3836	+	22.7381i	1.29914	+	0.750062i	0.318889	+	0.947792i	$0.396690\pi$
$920$		0			0
$921$	−16.7343	−	20.2498i	−0.551414	−	0.667253i
$922$	29.3439	−	29.3439i	0.966391	−	0.966391i
$923$	37.3433	−	31.4815i	1.22917	−	1.03623i
$924$	−5.02240	+	0.846782i	−0.165225	+	0.0278571i
$925$		0			0
$926$	28.2038	−	16.2835i	0.926833	−	0.535108i
$927$	−15.4691	−	22.8132i	−0.508071	−	0.749283i
$928$	12.8205	+	12.8205i	0.420854	+	0.420854i
$929$	−23.3071	+	40.3692i	−0.764682	+	1.32447i	0.175732	+	0.984438i	$0.443771\pi$
$929$	−23.3071	+	40.3692i	−0.764682	+	1.32447i	−0.940414	+	0.340031i	$0.889563\pi$
$930$		0			0
$931$	−22.0477			−0.722585
$932$	60.7171	−	16.2691i	1.98885	−	0.532912i
$933$	−52.4114	−	4.98190i	−1.71587	−	0.163100i
$934$	43.9670	−	25.3844i	1.43864	−	0.830601i
$935$		0			0
$936$	−14.8483	−	58.3704i	−0.485331	−	1.90790i
$937$	−24.6656	+	24.6656i	−0.805789	+	0.805789i	−0.983994	−	0.178204i	$-0.942971\pi$
$937$	−24.6656	+	24.6656i	−0.805789	+	0.805789i	0.178204	+	0.983994i	$0.442971\pi$
$938$	6.12067	+	1.64003i	0.199847	+	0.0535488i
$939$	16.2584	−	13.4358i	0.530572	−	0.438462i
$940$		0			0
$941$		−	39.0792i		−	1.27395i	−0.770886	−	0.636973i	$-0.780186\pi$
$941$		−	39.0792i		−	1.27395i	0.770886	−	0.636973i	$-0.219814\pi$
$942$	−12.0420	+	5.50566i	−0.392349	+	0.179384i
$943$	51.6976	−	13.8523i	1.68350	−	0.451094i
$944$	−40.4620			−1.31693
$945$		0			0
$946$	−21.5119	−	37.2598i	−0.699413	−	1.21142i
$947$	4.54962	−	16.9794i	0.147843	−	0.551757i	−0.851770	−	0.523917i	$-0.824470\pi$
$947$	4.54962	−	16.9794i	0.147843	−	0.551757i	0.999612	−	0.0278403i	$-0.00886300\pi$
$948$	−27.8741	−	19.8309i	−0.905307	−	0.644079i
$949$	−12.3035	+	5.77174i	−0.399389	+	0.187359i
$950$		0			0
$951$	−26.5026	+	21.9016i	−0.859406	+	0.710208i
$952$	9.37343	+	2.51160i	0.303795	+	0.0814015i
$953$	9.72120	+	36.2800i	0.314901	+	1.17523i	0.924082	+	0.382194i	$0.124832\pi$
$953$	9.72120	+	36.2800i	0.314901	+	1.17523i	−0.609181	+	0.793031i	$0.708502\pi$
$954$	15.0858	+	43.4664i	0.488421	+	1.40728i
$955$		0			0
$956$	−1.49105	−	0.860861i	−0.0482242	−	0.0278422i
$957$	14.6987	−	20.6602i	0.475141	−	0.667850i
$958$	−1.03195	+	0.276511i	−0.0333408	+	0.00893365i
$959$	−1.34633	−	2.33192i	−0.0434754	−	0.0753016i
$960$		0			0
$961$	−26.1298			−0.842896
$962$	55.3470	+	65.6524i	1.78446	+	2.11672i
$963$	24.0410	−	49.5992i	0.774710	−	1.59831i
$964$	88.5843	−	51.1442i	2.85311	−	1.64724i
$965$		0			0
$966$	2.96893	−	7.97048i	0.0955237	−	0.256446i
$967$	5.33045	−	5.33045i	0.171416	−	0.171416i	−0.616185	−	0.787601i	$-0.711323\pi$
$967$	5.33045	−	5.33045i	0.171416	−	0.171416i	0.787601	+	0.616185i	$0.211323\pi$
$968$	−10.2751	−	38.3473i	−0.330255	−	1.23253i
$969$	−9.56374	+	25.6751i	−0.307232	+	0.824805i
$970$		0			0
$971$	−24.4621	−	14.1232i	−0.785027	−	0.453235i	0.0531822	−	0.998585i	$-0.483064\pi$
$971$	−24.4621	−	14.1232i	−0.785027	−	0.453235i	−0.838209	+	0.545350i	$0.816397\pi$
$972$	55.4042	−	35.7749i	1.77709	−	1.14748i
$973$	−0.236496	+	0.882617i	−0.00758173	+	0.0282954i
$974$	80.6735			2.58495
$975$		0			0
$976$	7.94677			0.254370
$977$	−12.5727	+	46.9219i	−0.402236	+	1.50116i	0.406861	+	0.913490i	$0.366623\pi$
$977$	−12.5727	+	46.9219i	−0.402236	+	1.50116i	−0.809097	+	0.587675i	$0.800043\pi$
$978$	43.7919	+	4.16258i	1.40031	+	0.133105i
$979$	16.3761	+	9.45474i	0.523382	+	0.302175i
$980$		0			0
$981$	−6.92649	+	36.1054i	−0.221146	+	1.15276i
$982$	26.8416	+	100.174i	0.856551	+	3.19669i
$983$	14.3925	−	14.3925i	0.459049	−	0.459049i	−0.439294	−	0.898343i	$-0.644772\pi$
$983$	14.3925	−	14.3925i	0.459049	−	0.459049i	0.898343	+	0.439294i	$0.144772\pi$
$984$	86.8706	+	32.3584i	2.76933	+	1.03155i
$985$		0			0
$986$	−79.3464	+	45.8106i	−2.52690	+	1.45891i
$987$	2.74677	+	1.95419i	0.0874308	+	0.0622025i
$988$	48.1549	−	8.60538i	1.53201	−	0.273774i
$989$	48.7850			1.55127
$990$		0			0
$991$	−15.4015	−	26.6762i	−0.489245	−	0.847397i	0.510678	−	0.859772i	$-0.329394\pi$
$991$	−15.4015	−	26.6762i	−0.489245	−	0.847397i	−0.999923	+	0.0123746i	$0.996061\pi$
$992$	5.19396	−	1.39172i	0.164908	−	0.0441871i
$993$	33.7629	+	24.0205i	1.07143	+	0.762268i
$994$	10.3462	+	5.97338i	0.328162	+	0.189464i
$995$		0			0
$996$	−10.7608	−	63.8239i	−0.340969	−	2.02234i
$997$	9.52327	+	35.5413i	0.301605	+	1.12561i	0.935829	+	0.352456i	$0.114653\pi$
$997$	9.52327	+	35.5413i	0.301605	+	1.12561i	−0.634223	+	0.773150i	$0.718680\pi$
$998$	33.1533	+	8.88340i	1.04945	+	0.281199i
$999$	−25.7484	+	42.3660i	−0.814643	+	1.34040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bt.k.68.11	yes	48
3.2	odd	2	inner	975.2.bt.k.68.1	✓	48
5.2	odd	4	inner	975.2.bt.k.107.12	yes	48
5.3	odd	4	inner	975.2.bt.k.107.1	yes	48
5.4	even	2	inner	975.2.bt.k.68.2	yes	48
13.9	even	3	inner	975.2.bt.k.893.2	yes	48
15.2	even	4	inner	975.2.bt.k.107.2	yes	48
15.8	even	4	inner	975.2.bt.k.107.11	yes	48
15.14	odd	2	inner	975.2.bt.k.68.12	yes	48
39.35	odd	6	inner	975.2.bt.k.893.12	yes	48
65.9	even	6	inner	975.2.bt.k.893.11	yes	48
65.22	odd	12	inner	975.2.bt.k.932.1	yes	48
65.48	odd	12	inner	975.2.bt.k.932.12	yes	48
195.74	odd	6	inner	975.2.bt.k.893.1	yes	48
195.113	even	12	inner	975.2.bt.k.932.2	yes	48
195.152	even	12	inner	975.2.bt.k.932.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.bt.k.68.1	✓	48	3.2	odd	2	inner
975.2.bt.k.68.2	yes	48	5.4	even	2	inner
975.2.bt.k.68.11	yes	48	1.1	even	1	trivial
975.2.bt.k.68.12	yes	48	15.14	odd	2	inner
975.2.bt.k.107.1	yes	48	5.3	odd	4	inner
975.2.bt.k.107.2	yes	48	15.2	even	4	inner
975.2.bt.k.107.11	yes	48	15.8	even	4	inner
975.2.bt.k.107.12	yes	48	5.2	odd	4	inner
975.2.bt.k.893.1	yes	48	195.74	odd	6	inner
975.2.bt.k.893.2	yes	48	13.9	even	3	inner
975.2.bt.k.893.11	yes	48	65.9	even	6	inner
975.2.bt.k.893.12	yes	48	39.35	odd	6	inner
975.2.bt.k.932.1	yes	48	65.22	odd	12	inner
975.2.bt.k.932.2	yes	48	195.113	even	12	inner
975.2.bt.k.932.11	yes	48	195.152	even	12	inner
975.2.bt.k.932.12	yes	48	65.48	odd	12	inner

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.646049 - 2.41109i) q^{2} +(-0.163899 + 1.72428i) q^{3} +(-3.66392 - 2.11536i) q^{4} +(4.05150 + 1.50914i) q^{6} +(0.0914428 + 0.341269i) q^{7} +(-3.93732 + 3.93732i) q^{8} +(-2.94627 - 0.565216i) q^{9} +O(q^{10})\)	\(q+(0.646049 - 2.41109i) q^{2} +(-0.163899 + 1.72428i) q^{3} +(-3.66392 - 2.11536i) q^{4} +(4.05150 + 1.50914i) q^{6} +(0.0914428 + 0.341269i) q^{7} +(-3.93732 + 3.93732i) q^{8} +(-2.94627 - 0.565216i) q^{9} +(-1.70372 + 0.983646i) q^{11} +(4.24799 - 5.97091i) q^{12} +(1.22537 - 3.39094i) q^{13} +0.881907 q^{14} +(2.71879 + 4.70909i) q^{16} +(-4.76464 + 1.27668i) q^{17} +(-3.26622 + 6.73857i) q^{18} +(-2.77722 - 1.60343i) q^{19} +(-0.603431 + 0.101739i) q^{21} +(1.27097 + 4.74331i) q^{22} +(-5.37848 - 1.44116i) q^{23} +(-6.14371 - 7.43436i) q^{24} +(-7.38421 - 5.14518i) q^{26} +(1.45748 - 4.98756i) q^{27} +(0.386869 - 1.44382i) q^{28} +(3.72058 + 6.44424i) q^{29} +2.20686 q^{31} +(2.35355 - 0.630632i) q^{32} +(-1.41684 - 3.09891i) q^{33} +12.3128i q^{34} +(9.59926 + 8.30334i) q^{36} +(-9.21595 - 2.46941i) q^{37} +(-5.66024 + 5.66024i) q^{38} +(5.64609 + 2.66865i) q^{39} +(-8.32418 + 4.80597i) q^{41} +(-0.144544 + 1.52065i) q^{42} +(-8.46282 + 2.26761i) q^{43} +8.32307 q^{44} +(-6.94952 + 12.0369i) q^{46} +(-3.89520 - 3.89520i) q^{47} +(-8.56539 + 3.91614i) q^{48} +(5.95407 - 3.43759i) q^{49} +(-1.42043 - 8.42481i) q^{51} +(-11.6627 + 9.83202i) q^{52} +(4.34456 - 4.34456i) q^{53} +(-11.0838 - 6.73632i) q^{54} +(-1.70372 - 0.983646i) q^{56} +(3.21995 - 4.52591i) q^{57} +(17.9413 - 4.80736i) q^{58} +(-3.72058 + 6.44424i) q^{59} +(0.730725 - 1.26565i) q^{61} +(1.42574 - 5.32094i) q^{62} +(-0.0765249 - 1.05716i) q^{63} +4.79314i q^{64} +(-8.38711 + 1.41408i) q^{66} +(6.94026 + 1.85964i) q^{67} +(20.1579 + 5.40129i) q^{68} +(3.36649 - 9.03779i) q^{69} +(11.7316 + 6.77326i) q^{71} +(13.8259 - 9.37498i) q^{72} +(-2.66523 - 2.66523i) q^{73} +(-11.9079 + 20.6251i) q^{74} +(6.78367 + 11.7497i) q^{76} +(-0.491481 - 0.491481i) q^{77} +(10.0820 - 11.8891i) q^{78} -4.66831i q^{79} +(8.36106 + 3.33056i) q^{81} +(6.20978 + 23.1752i) q^{82} +(6.24568 - 6.24568i) q^{83} +(2.42613 + 0.903711i) q^{84} +21.8696i q^{86} +(-11.7215 + 5.35912i) q^{87} +(2.83518 - 10.5810i) q^{88} +(-4.80597 - 8.32418i) q^{89} +(1.26927 + 0.108103i) q^{91} +(16.6577 + 16.6577i) q^{92} +(-0.361703 + 3.80524i) q^{93} +(-11.9081 + 6.87517i) q^{94} +(0.701640 + 4.16154i) q^{96} +(-4.03580 - 15.0618i) q^{97} +(-4.44170 - 16.5766i) q^{98} +(5.57561 - 1.93512i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 28 q^{6}+O(q^{10}) \) 48 * q - 28 * q^6	\( 48 q - 28 q^{6} + 40 q^{16} + 48 q^{31} + 76 q^{36} - 120 q^{46} - 32 q^{51} - 88 q^{61} - 8 q^{66} - 40 q^{76} + 32 q^{81} + 184 q^{91} + 88 q^{96}+O(q^{100}) \) 48 * q - 28 * q^6 + 40 * q^16 + 48 * q^31 + 76 * q^36 - 120 * q^46 - 32 * q^51 - 88 * q^61 - 8 * q^66 - 40 * q^76 + 32 * q^81 + 184 * q^91 + 88 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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