LMFDB - Embedded newform 1000.2.v.b.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(43,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 10, 19]))

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

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

chi := DirichletCharacter("1000.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.v (of order $20$, degree $8$, 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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.1
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	1000.107
Dual form			1000.2.v.b.243.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.221232 + 1.39680i) q^{2} +(0.420808 - 2.65688i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(3.61803 + 1.17557i) q^{6} +(-0.557537 + 0.557537i) q^{7} +(1.28408 - 2.52015i) q^{8} +(-4.02874 - 1.30902i) q^{9} +O(q^{10})$	\(q+(-0.221232 + 1.39680i) q^{2} +(0.420808 - 2.65688i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(3.61803 + 1.17557i) q^{6} +(-0.557537 + 0.557537i) q^{7} +(1.28408 - 2.52015i) q^{8} +(-4.02874 - 1.30902i) q^{9} +(-0.136729 - 0.420808i) q^{11} +(-2.44246 + 4.79360i) q^{12} +(-5.63818 + 2.87280i) q^{13} +(-0.655423 - 0.902113i) q^{14} +(3.23607 + 2.35114i) q^{16} +(-0.857960 - 5.41695i) q^{17} +(2.71972 - 5.33776i) q^{18} +(-2.07533 + 2.85645i) q^{19} +(1.24669 + 1.71592i) q^{21} +(0.618034 - 0.0978870i) q^{22} +(-0.568158 + 1.11507i) q^{23} +(-6.15537 - 4.47214i) q^{24} +(-2.76538 - 8.51098i) q^{26} +(-1.50953 + 2.96261i) q^{27} +(1.40507 - 0.715921i) q^{28} +(2.33927 - 1.69958i) q^{29} +(-5.90778 + 8.13136i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-1.17557 + 0.186192i) q^{33} +7.75621 q^{34} +(6.85410 + 4.97980i) q^{36} +(-2.33833 - 4.58924i) q^{37} +(-3.53077 - 3.53077i) q^{38} +(5.26007 + 16.1888i) q^{39} +(-2.22394 + 6.84458i) q^{41} +(-2.67261 + 1.36176i) q^{42} +(0.989378 - 0.989378i) q^{43} +0.884927i q^{44} +(-1.43184 - 1.04029i) q^{46} +(-0.256271 + 1.61803i) q^{47} +(7.60845 - 7.60845i) q^{48} +6.37831i q^{49} -14.7532 q^{51} +(12.4999 - 1.97980i) q^{52} +(1.40269 + 0.222164i) q^{53} +(-3.80423 - 2.76393i) q^{54} +(0.689153 + 2.12099i) q^{56} +(6.71592 + 6.71592i) q^{57} +(1.85645 + 3.64349i) q^{58} +(-10.7014 - 3.47709i) q^{59} +(4.57086 - 1.48516i) q^{61} +(-10.0509 - 10.0509i) q^{62} +(2.97599 - 1.51634i) q^{63} +(-4.70228 - 6.47214i) q^{64} -1.68323i q^{66} +(-0.986616 - 6.22925i) q^{67} +(-1.71592 + 10.8339i) q^{68} +(2.72353 + 1.97876i) q^{69} +(6.33354 + 8.71737i) q^{71} +(-8.47214 + 8.47214i) q^{72} +(-10.8018 - 5.50380i) q^{73} +(6.92757 - 2.25090i) q^{74} +(5.71290 - 4.15067i) q^{76} +(0.310847 + 0.158384i) q^{77} +(-23.7763 + 3.76580i) q^{78} +(-10.5738 + 7.68233i) q^{79} +(-3.04508 - 2.21238i) q^{81} +(-9.06851 - 4.62064i) q^{82} +(-13.6183 + 2.15693i) q^{83} +(-1.31085 - 4.03437i) q^{84} +(1.16308 + 1.60085i) q^{86} +(-3.53118 - 6.93033i) q^{87} +(-1.23607 - 0.195774i) q^{88} +(3.20347 - 1.04087i) q^{89} +(1.54180 - 4.74518i) q^{91} +(1.76985 - 1.76985i) q^{92} +(19.1180 + 19.1180i) q^{93} +(-2.20338 - 0.715921i) q^{94} +(8.94427 + 12.3107i) q^{96} +(-0.281373 - 0.0445651i) q^{97} +(-8.90923 - 1.41108i) q^{98} +1.87431i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 20 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 + 20 * q^6 - 4 * q^7 + 4 * q^8	$ 8 q - 2 q^{2} + 20 q^{6} - 4 q^{7} + 4 q^{8} - 4 q^{11} - 20 q^{12} - 12 q^{13} - 20 q^{14} + 8 q^{16} - 10 q^{17} - 6 q^{18} + 10 q^{19} - 20 q^{21} - 4 q^{22} + 8 q^{23} - 4 q^{26} - 12 q^{28} + 10 q^{29} + 10 q^{31} - 32 q^{32} + 20 q^{34} + 28 q^{36} - 14 q^{37} + 8 q^{38} + 30 q^{39} + 16 q^{41} - 20 q^{42} + 20 q^{43} - 24 q^{46} - 24 q^{47} - 20 q^{51} + 36 q^{52} + 28 q^{53} - 24 q^{56} + 60 q^{57} - 10 q^{58} - 10 q^{59} - 10 q^{61} - 20 q^{62} + 18 q^{63} + 10 q^{67} - 20 q^{68} - 40 q^{69} + 20 q^{71} - 32 q^{72} + 10 q^{73} + 10 q^{74} - 4 q^{76} + 32 q^{77} - 60 q^{78} - 30 q^{79} - 2 q^{81} - 24 q^{82} - 40 q^{84} + 20 q^{86} - 20 q^{87} + 8 q^{88} + 10 q^{89} - 8 q^{91} + 16 q^{92} + 80 q^{93} + 20 q^{94} - 30 q^{97} + 22 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 20 * q^6 - 4 * q^7 + 4 * q^8 - 4 * q^11 - 20 * q^12 - 12 * q^13 - 20 * q^14 + 8 * q^16 - 10 * q^17 - 6 * q^18 + 10 * q^19 - 20 * q^21 - 4 * q^22 + 8 * q^23 - 4 * q^26 - 12 * q^28 + 10 * q^29 + 10 * q^31 - 32 * q^32 + 20 * q^34 + 28 * q^36 - 14 * q^37 + 8 * q^38 + 30 * q^39 + 16 * q^41 - 20 * q^42 + 20 * q^43 - 24 * q^46 - 24 * q^47 - 20 * q^51 + 36 * q^52 + 28 * q^53 - 24 * q^56 + 60 * q^57 - 10 * q^58 - 10 * q^59 - 10 * q^61 - 20 * q^62 + 18 * q^63 + 10 * q^67 - 20 * q^68 - 40 * q^69 + 20 * q^71 - 32 * q^72 + 10 * q^73 + 10 * q^74 - 4 * q^76 + 32 * q^77 - 60 * q^78 - 30 * q^79 - 2 * q^81 - 24 * q^82 - 40 * q^84 + 20 * q^86 - 20 * q^87 + 8 * q^88 + 10 * q^89 - 8 * q^91 + 16 * q^92 + 80 * q^93 + 20 * q^94 - 30 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$	$-1$

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 $

$2$	−0.221232	+	1.39680i	−0.156434	+	0.987688i
$2$	−0.221232	+	1.39680i	−0.156434	+	0.987688i
$3$	0.420808	−	2.65688i	0.242953	−	1.53395i	−0.500841	−	0.865539i	$-0.666976\pi$
$3$	0.420808	−	2.65688i	0.242953	−	1.53395i	0.743794	−	0.668409i	$-0.233024\pi$
$4$	−1.90211	−	0.618034i	−0.951057	−	0.309017i
$5$		0			0
$5$		0			0
$6$	3.61803	+	1.17557i	1.47706	+	0.479925i
$7$	−0.557537	+	0.557537i	−0.210729	+	0.210729i	−0.804577	−	0.593848i	$-0.797608\pi$
$7$	−0.557537	+	0.557537i	−0.210729	+	0.210729i	0.593848	+	0.804577i	$0.297608\pi$
$8$	1.28408	−	2.52015i	0.453990	−	0.891007i
$9$	−4.02874	−	1.30902i	−1.34291	−	0.436339i
$10$		0			0
$11$	−0.136729	−	0.420808i	−0.0412253	−	0.126878i	0.928326	−	0.371768i	$-0.121248\pi$
$11$	−0.136729	−	0.420808i	−0.0412253	−	0.126878i	−0.969551	+	0.244890i	$0.921248\pi$
$12$	−2.44246	+	4.79360i	−0.705078	+	1.38379i
$13$	−5.63818	+	2.87280i	−1.56375	+	0.796770i	−0.999583	−	0.0288899i	$-0.990803\pi$
$13$	−5.63818	+	2.87280i	−1.56375	+	0.796770i	−0.564167	+	0.825660i	$0.690803\pi$
$14$	−0.655423	−	0.902113i	−0.175169	−	0.241100i
$15$		0			0
$16$	3.23607	+	2.35114i	0.809017	+	0.587785i
$17$	−0.857960	−	5.41695i	−0.208086	−	1.31380i	−0.841612	−	0.540082i	$-0.818393\pi$
$17$	−0.857960	−	5.41695i	−0.208086	−	1.31380i	0.633526	−	0.773721i	$-0.281607\pi$
$18$	2.71972	−	5.33776i	0.641045	−	1.25812i
$19$	−2.07533	+	2.85645i	−0.476114	+	0.655315i	−0.977752	−	0.209763i	$-0.932731\pi$
$19$	−2.07533	+	2.85645i	−0.476114	+	0.655315i	0.501638	+	0.865078i	$0.332731\pi$
$20$		0			0
$21$	1.24669	+	1.71592i	0.272050	+	0.374445i
$22$	0.618034	−	0.0978870i	0.131765	−	0.0208696i
$23$	−0.568158	+	1.11507i	−0.118469	+	0.232509i	−0.942624	−	0.333855i	$-0.891650\pi$
$23$	−0.568158	+	1.11507i	−0.118469	+	0.232509i	0.824155	+	0.566364i	$0.191650\pi$
$24$	−6.15537	−	4.47214i	−1.25646	−	0.912871i
$25$		0			0
$26$	−2.76538	−	8.51098i	−0.542336	−	1.66914i
$27$	−1.50953	+	2.96261i	−0.290508	+	0.570155i
$28$	1.40507	−	0.715921i	0.265534	−	0.135296i
$29$	2.33927	−	1.69958i	0.434391	−	0.315603i	−0.349011	−	0.937118i	$-0.613483\pi$
$29$	2.33927	−	1.69958i	0.434391	−	0.315603i	0.783402	+	0.621515i	$0.213483\pi$
$30$		0			0
$31$	−5.90778	+	8.13136i	−1.06107	+	1.46044i	−0.182267	+	0.983249i	$0.558343\pi$
$31$	−5.90778	+	8.13136i	−1.06107	+	1.46044i	−0.878802	+	0.477186i	$0.841657\pi$
$32$	−4.00000	+	4.00000i	−0.707107	+	0.707107i
$33$	−1.17557	+	0.186192i	−0.204641	+	0.0324119i
$34$	7.75621			1.33018
$35$		0			0
$36$	6.85410	+	4.97980i	1.14235	+	0.829966i
$37$	−2.33833	−	4.58924i	−0.384420	−	0.754466i	0.615000	−	0.788527i	$-0.289156\pi$
$37$	−2.33833	−	4.58924i	−0.384420	−	0.754466i	−0.999420	+	0.0340610i	$0.989156\pi$
$38$	−3.53077	−	3.53077i	−0.572766	−	0.572766i
$39$	5.26007	+	16.1888i	0.842286	+	2.59229i
$40$		0			0
$41$	−2.22394	+	6.84458i	−0.347321	+	1.06894i	0.613009	+	0.790076i	$0.289959\pi$
$41$	−2.22394	+	6.84458i	−0.347321	+	1.06894i	−0.960330	+	0.278867i	$0.910041\pi$
$42$	−2.67261	+	1.36176i	−0.412393	+	0.210125i
$43$	0.989378	−	0.989378i	0.150879	−	0.150879i	−0.627632	−	0.778510i	$-0.715976\pi$
$43$	0.989378	−	0.989378i	0.150879	−	0.150879i	0.778510	+	0.627632i	$0.215976\pi$
$44$			0.884927i			0.133408i
$45$		0			0
$46$	−1.43184	−	1.04029i	−0.211114	−	0.153383i
$47$	−0.256271	+	1.61803i	−0.0373810	+	0.236015i	−0.999304	−	0.0373066i	$-0.988122\pi$
$47$	−0.256271	+	1.61803i	−0.0373810	+	0.236015i	0.961923	+	0.273321i	$0.0881222\pi$
$48$	7.60845	−	7.60845i	1.09819	−	1.09819i
$49$			6.37831i			0.911187i
$50$		0			0
$51$	−14.7532			−2.06586
$52$	12.4999	−	1.97980i	1.73343	−	0.274548i
$53$	1.40269	+	0.222164i	0.192674	+	0.0305166i	0.252026	−	0.967721i	$-0.418903\pi$
$53$	1.40269	+	0.222164i	0.192674	+	0.0305166i	−0.0593515	+	0.998237i	$0.518903\pi$
$54$	−3.80423	−	2.76393i	−0.517690	−	0.376124i
$55$		0			0
$56$	0.689153	+	2.12099i	0.0920919	+	0.283430i
$57$	6.71592	+	6.71592i	0.889545	+	0.889545i
$58$	1.85645	+	3.64349i	0.243764	+	0.478414i
$59$	−10.7014	−	3.47709i	−1.39320	−	0.452679i	−0.486215	−	0.873839i	$-0.661623\pi$
$59$	−10.7014	−	3.47709i	−1.39320	−	0.452679i	−0.906986	+	0.421160i	$0.861623\pi$
$60$		0			0
$61$	4.57086	−	1.48516i	0.585239	−	0.190156i	−0.00140712	−	0.999999i	$-0.500448\pi$
$61$	4.57086	−	1.48516i	0.585239	−	0.190156i	0.586646	+	0.809843i	$0.300448\pi$
$62$	−10.0509	−	10.0509i	−1.27647	−	1.27647i
$63$	2.97599	−	1.51634i	0.374940	−	0.191042i
$64$	−4.70228	−	6.47214i	−0.587785	−	0.809017i
$65$		0			0
$66$		−	1.68323i		−	0.207191i
$67$	−0.986616	−	6.22925i	−0.120534	−	0.761024i	−0.971716	−	0.236153i	$-0.924113\pi$
$67$	−0.986616	−	6.22925i	−0.120534	−	0.761024i	0.851182	−	0.524871i	$-0.175887\pi$
$68$	−1.71592	+	10.8339i	−0.208086	+	1.31380i
$69$	2.72353	+	1.97876i	0.327874	+	0.238214i
$70$		0			0
$71$	6.33354	+	8.71737i	0.751653	+	1.03456i	0.997863	+	0.0653452i	$0.0208149\pi$
$71$	6.33354	+	8.71737i	0.751653	+	1.03456i	−0.246210	+	0.969217i	$0.579185\pi$
$72$	−8.47214	+	8.47214i	−0.998451	+	0.998451i
$73$	−10.8018	−	5.50380i	−1.26426	−	0.644171i	−0.312178	−	0.950024i	$-0.601059\pi$
$73$	−10.8018	−	5.50380i	−1.26426	−	0.644171i	−0.952079	+	0.305852i	$0.901059\pi$
$74$	6.92757	−	2.25090i	0.805314	−	0.261662i
$75$		0			0
$76$	5.71290	−	4.15067i	0.655315	−	0.476114i
$77$	0.310847	+	0.158384i	0.0354243	+	0.0180496i
$78$	−23.7763	+	3.76580i	−2.69214	+	0.426393i
$79$	−10.5738	+	7.68233i	−1.18965	+	0.864330i	−0.993227	−	0.116190i	$-0.962932\pi$
$79$	−10.5738	+	7.68233i	−1.18965	+	0.864330i	−0.196421	+	0.980520i	$0.562932\pi$
$80$		0			0
$81$	−3.04508	−	2.21238i	−0.338343	−	0.245820i
$82$	−9.06851	−	4.62064i	−1.00145	−	0.510264i
$83$	−13.6183	+	2.15693i	−1.49481	+	0.236754i	−0.849671	−	0.527314i	$-0.823199\pi$
$83$	−13.6183	+	2.15693i	−1.49481	+	0.236754i	−0.645136	+	0.764068i	$0.723199\pi$
$84$	−1.31085	−	4.03437i	−0.143025	−	0.440186i
$85$		0			0
$86$	1.16308	+	1.60085i	0.125419	+	0.172624i
$87$	−3.53118	−	6.93033i	−0.378582	−	0.743010i
$88$	−1.23607	−	0.195774i	−0.131765	−	0.0208696i
$89$	3.20347	−	1.04087i	0.339567	−	0.110332i	−0.134269	−	0.990945i	$-0.542869\pi$
$89$	3.20347	−	1.04087i	0.339567	−	0.110332i	0.473837	+	0.880613i	$0.342869\pi$
$90$		0			0
$91$	1.54180	−	4.74518i	0.161625	−	0.497430i
$92$	1.76985	−	1.76985i	0.184520	−	0.184520i
$93$	19.1180	+	19.1180i	1.98244	+	1.98244i
$94$	−2.20338	−	0.715921i	−0.227261	−	0.0738416i
$95$		0			0
$96$	8.94427	+	12.3107i	0.912871	+	1.25646i
$97$	−0.281373	−	0.0445651i	−0.0285691	−	0.00452490i	0.142134	−	0.989847i	$-0.454604\pi$
$97$	−0.281373	−	0.0445651i	−0.0285691	−	0.00452490i	−0.170703	+	0.985323i	$0.554604\pi$
$98$	−8.90923	−	1.41108i	−0.899968	−	0.142541i
$99$			1.87431i			0.188375i
$100$		0			0
$101$		−	8.11392i		−	0.807365i	−0.914899	−	0.403683i	$-0.867730\pi$
$101$		−	8.11392i		−	0.807365i	0.914899	−	0.403683i	$-0.132270\pi$
$102$	3.26388	−	20.6073i	0.323172	−	2.04043i
$103$	−5.79506	−	0.917847i	−0.571004	−	0.0904381i	−0.135746	−	0.990744i	$-0.543343\pi$
$103$	−5.79506	−	0.917847i	−0.571004	−	0.0904381i	−0.435258	+	0.900306i	$0.643343\pi$
$104$			17.8979i			1.75504i
$105$		0			0
$106$	−0.620639	+	1.91013i	−0.0602818	+	0.185528i
$107$	1.84348	+	1.84348i	0.178216	+	0.178216i	0.790578	−	0.612362i	$-0.209780\pi$
$107$	1.84348	+	1.84348i	0.178216	+	0.178216i	−0.612362	+	0.790578i	$0.709780\pi$
$108$	4.70228	−	4.70228i	0.452477	−	0.452477i
$109$	4.99614	−	15.3765i	0.478544	−	1.47281i	−0.362575	−	0.931955i	$-0.618102\pi$
$109$	4.99614	−	15.3765i	0.478544	−	1.47281i	0.841118	−	0.540851i	$-0.181898\pi$
$110$		0			0
$111$	−13.1770	+	4.28147i	−1.25071	+	0.406380i
$112$	−3.11507	+	0.493379i	−0.294347	+	0.0466199i
$113$	3.61626	+	7.09731i	0.340189	+	0.667659i	0.996200	−	0.0870924i	$-0.0277576\pi$
$113$	3.61626	+	7.09731i	0.340189	+	0.667659i	−0.656011	+	0.754751i	$0.727758\pi$
$114$	−10.8666	+	7.89504i	−1.01775	+	0.739438i
$115$		0			0
$116$	−5.49994	+	1.78704i	−0.510657	+	0.165922i
$117$	26.4753	−	4.19328i	2.44764	−	0.387669i
$118$	7.22429	−	14.1785i	0.665050	−	1.30523i
$119$	3.49849	+	2.54180i	0.320706	+	0.233007i
$120$		0			0
$121$	8.74080	−	6.35056i	0.794618	−	0.577324i
$122$	1.06326	+	6.71316i	0.0962630	+	0.607781i
$123$	17.2493	+	8.78898i	1.55532	+	0.792475i
$124$	16.2627	−	11.8156i	1.46044	−	1.06107i
$125$		0			0
$126$	1.45965	+	4.49234i	0.130036	+	0.400209i
$127$	−7.36833	−	3.75435i	−0.653833	−	0.333145i	0.0954115	−	0.995438i	$-0.469583\pi$
$127$	−7.36833	−	3.75435i	−0.653833	−	0.333145i	−0.749245	+	0.662293i	$0.769583\pi$
$128$	10.0806	−	5.13632i	0.891007	−	0.453990i
$129$	−2.21232	−	3.04499i	−0.194784	−	0.268097i
$130$		0			0
$131$	7.15302	+	5.19697i	0.624962	+	0.454061i	0.854651	−	0.519203i	$-0.173771\pi$
$131$	7.15302	+	5.19697i	0.624962	+	0.454061i	−0.229689	+	0.973264i	$0.573771\pi$
$132$	2.35114	+	0.372384i	0.204641	+	0.0324119i
$133$	−0.435502	−	2.74965i	−0.0377628	−	0.238425i
$134$	8.91930			0.770510
$135$		0			0
$136$	−14.7532	−	4.79360i	−1.26508	−	0.411048i
$137$	0.873694	−	0.445169i	0.0746447	−	0.0380334i	−0.416270	−	0.909241i	$-0.636663\pi$
$137$	0.873694	−	0.445169i	0.0746447	−	0.0380334i	0.490914	+	0.871208i	$0.336663\pi$
$138$	−3.36646	+	3.36646i	−0.286572	+	0.286572i
$139$	14.2326	−	4.62444i	1.20719	−	0.392240i	0.364789	−	0.931090i	$-0.381141\pi$
$139$	14.2326	−	4.62444i	1.20719	−	0.392240i	0.842402	+	0.538850i	$0.181141\pi$
$140$		0			0
$141$	4.19107	+	1.36176i	0.352952	+	0.114681i
$142$	−13.5776	+	6.91815i	−1.13941	+	0.580558i
$143$	1.97980	+	1.97980i	0.165559	+	0.165559i
$144$	−9.95959	−	13.7082i	−0.829966	−	1.14235i
$145$		0			0
$146$	10.0774	−	13.8704i	0.834014	−	1.14792i
$147$	16.9464	+	2.68404i	1.39771	+	0.221376i
$148$	1.61147	+	10.1744i	0.132462	+	0.836332i
$149$	−21.0278			−1.72267			−0.861333	−	0.508042i	$-0.830370\pi$
$149$	−21.0278			−1.72267			−0.861333	+	0.508042i	$0.830370\pi$
$150$		0			0
$151$		−	8.57286i		−	0.697649i	−0.937188	−	0.348825i	$-0.886581\pi$
$151$		−	8.57286i		−	0.697649i	0.937188	−	0.348825i	$-0.113419\pi$
$152$	4.53379	+	8.89806i	0.367739	+	0.721728i
$153$	−3.63438	+	22.9466i	−0.293822	+	1.85512i
$154$	−0.290001	+	0.399152i	−0.0233689	+	0.0321646i
$155$		0			0
$156$		−	34.0439i		−	2.72569i
$157$	−4.04306	+	4.04306i	−0.322671	+	0.322671i	−0.849791	−	0.527120i	$-0.823272\pi$
$157$	−4.04306	+	4.04306i	−0.322671	+	0.322671i	0.527120	+	0.849791i	$0.323272\pi$
$158$	−8.39144	−	16.4691i	−0.667587	−	1.31021i
$159$	1.18053	−	3.63328i	0.0936217	−	0.288138i
$160$		0			0
$161$	−0.304925	−	0.938463i	−0.0240315	−	0.0739612i
$162$	3.76393	−	3.76393i	0.295722	−	0.295722i
$163$	−4.95881	−	9.73221i	−0.388404	−	0.762285i	0.611169	−	0.791500i	$-0.290699\pi$
$163$	−4.95881	−	9.73221i	−0.388404	−	0.762285i	−0.999573	+	0.0292144i	$0.990699\pi$
$164$	8.46036	−	11.6447i	0.660643	−	0.909297i
$165$		0			0
$166$		−	19.4993i		−	1.51344i
$167$	12.4180	−	1.96683i	0.960937	−	0.152198i	0.343791	−	0.939046i	$-0.388289\pi$
$167$	12.4180	−	1.96683i	0.960937	−	0.152198i	0.617146	+	0.786849i	$0.288289\pi$
$168$	5.92522	−	0.938463i	0.457141	−	0.0724040i
$169$	15.8949	−	21.8775i	1.22269	−	1.68288i
$170$		0			0
$171$	12.1001	−	8.79125i	0.925320	−	0.672284i
$172$	−2.49338	+	1.27044i	−0.190118	+	0.0968701i
$173$	5.64266	−	11.0743i	0.429004	−	0.841967i	−0.570779	−	0.821104i	$-0.693359\pi$
$173$	5.64266	−	11.0743i	0.429004	−	0.841967i	0.999782	−	0.0208630i	$-0.00664138\pi$
$174$	10.4615	−	3.39915i	0.793085	−	0.257689i
$175$		0			0
$176$	0.546915	−	1.68323i	0.0412253	−	0.126878i
$177$	−13.7414	+	26.9691i	−1.03287	+	2.02712i
$178$	0.745181	+	4.70489i	0.0558537	+	0.352646i
$179$	−5.33119	−	7.33776i	−0.398472	−	0.548450i	0.561888	−	0.827214i	$-0.310075\pi$
$179$	−5.33119	−	7.33776i	−0.398472	−	0.548450i	−0.960360	+	0.278764i	$0.910075\pi$
$180$		0			0
$181$	7.70946	−	10.6112i	0.573039	−	0.788721i	−0.419871	−	0.907584i	$-0.637925\pi$
$181$	7.70946	−	10.6112i	0.573039	−	0.788721i	0.992911	+	0.118863i	$0.0379248\pi$
$182$	6.28698	+	3.20338i	0.466022	+	0.237450i
$183$	−2.02244	−	12.7692i	−0.149503	−	0.943925i
$184$	2.08059	+	2.86368i	0.153383	+	0.211114i
$185$		0			0
$186$	−30.9335	+	22.4745i	−2.26816	+	1.64791i
$187$	−2.16219	+	1.10169i	−0.158115	+	0.0805635i
$188$	1.48746	−	2.91930i	0.108484	−	0.212912i
$189$	−0.810148	−	2.49338i	−0.0589296	−	0.181367i
$190$		0			0
$191$	−17.6339	−	5.72960i	−1.27594	−	0.414580i	−0.408795	−	0.912626i	$-0.634051\pi$
$191$	−17.6339	−	5.72960i	−1.27594	−	0.414580i	−0.867150	+	0.498047i	$0.834051\pi$
$192$	−19.1744	+	9.76985i	−1.38379	+	0.705078i
$193$	11.2519	−	11.2519i	0.809933	−	0.809933i	−0.174691	−	0.984623i	$-0.555893\pi$
$193$	11.2519	−	11.2519i	0.809933	−	0.809933i	0.984623	+	0.174691i	$0.0558926\pi$
$194$	0.124497	−	0.383163i	0.00893839	−	0.0275095i
$195$		0			0
$196$	3.94201	−	12.1323i	0.281572	−	0.866590i
$197$	−0.872888	+	5.51120i	−0.0621907	+	0.392657i	0.936884	+	0.349641i	$0.113696\pi$
$197$	−0.872888	+	5.51120i	−0.0621907	+	0.392657i	−0.999074	+	0.0430155i	$0.986304\pi$
$198$	−2.61803	−	0.414656i	−0.186056	−	0.0294683i
$199$	10.4853			0.743281			0.371640	−	0.928377i	$-0.378795\pi$
$199$	10.4853			0.743281			0.371640	+	0.928377i	$0.378795\pi$
$200$		0			0
$201$	−16.9655			−1.19666
$202$	11.3335	+	1.79506i	0.797425	+	0.126300i
$203$	−0.356650	+	2.25180i	−0.0250319	+	0.158046i
$204$	28.0622	+	9.11798i	1.96475	+	0.638386i
$205$		0			0
$206$	2.56410	−	7.89149i	0.178649	−	0.549826i
$207$	3.74861	−	3.74861i	0.260546	−	0.260546i
$208$	−24.9999	−	3.95959i	−1.73343	−	0.274548i
$209$	1.48577	+	0.482758i	0.102773	+	0.0333930i
$210$		0			0
$211$	−0.146453	−	0.450735i	−0.0100822	−	0.0310299i	0.945889	−	0.324491i	$-0.105193\pi$
$211$	−0.146453	−	0.450735i	−0.0100822	−	0.0310299i	−0.955971	+	0.293461i	$0.905193\pi$
$212$	−2.53077	−	1.28949i	−0.173814	−	0.0885626i
$213$	25.8262	−	13.1591i	1.76958	−	0.901646i
$214$	−2.98281	+	2.16714i	−0.203901	+	0.148143i
$215$		0			0
$216$	5.52786	+	7.60845i	0.376124	+	0.517690i
$217$	−1.23973	−	7.82733i	−0.0841582	−	0.531354i
$218$	20.3727	+	10.3804i	1.37981	+	0.703049i
$219$	−19.1684	+	26.3831i	−1.29528	+	1.78280i
$220$		0			0
$221$	20.3991	+	28.0770i	1.37219	+	1.88866i
$222$	−3.06520	−	19.3529i	−0.205723	−	1.29888i
$223$	−10.0452	+	19.7149i	−0.672680	+	1.32021i	0.262121	+	0.965035i	$0.415578\pi$
$223$	−10.0452	+	19.7149i	−0.672680	+	1.32021i	−0.934801	+	0.355173i	$0.884422\pi$
$224$		−	4.46029i		−	0.298016i
$225$		0			0
$226$	−10.7136	+	3.48105i	−0.712656	+	0.231556i
$227$	0.709101	−	1.39169i	0.0470647	−	0.0923697i	−0.866276	−	0.499565i	$-0.833493\pi$
$227$	0.709101	−	1.39169i	0.0470647	−	0.0923697i	0.913341	+	0.407195i	$0.133493\pi$
$228$	−8.62377	−	16.9251i	−0.571123	−	1.12089i
$229$	−4.91602	+	3.57170i	−0.324860	+	0.236024i	−0.738246	−	0.674531i	$-0.764346\pi$
$229$	−4.91602	+	3.57170i	−0.324860	+	0.236024i	0.413387	+	0.910556i	$0.364346\pi$
$230$		0			0
$231$	0.551615	−	0.759232i	0.0362936	−	0.0499538i
$232$	−1.27938	−	8.07768i	−0.0839954	−	0.530326i
$233$	15.6017	−	2.47106i	1.02210	−	0.161885i	0.377184	−	0.926138i	$-0.376893\pi$
$233$	15.6017	−	2.47106i	1.02210	−	0.161885i	0.644916	+	0.764254i	$0.276893\pi$
$234$			37.9085i			2.47815i
$235$		0			0
$236$	18.2063	+	13.2276i	1.18513	+	0.861046i
$237$	15.9615	+	31.3261i	1.03681	+	2.03485i
$238$	−4.32437	+	4.32437i	−0.280307	+	0.280307i
$239$	0.321469	+	0.989378i	0.0207941	+	0.0639976i	0.960915	−	0.276843i	$-0.0892883\pi$
$239$	0.321469	+	0.989378i	0.0207941	+	0.0639976i	−0.940121	+	0.340841i	$0.889288\pi$
$240$		0			0
$241$	−2.85353	+	8.78225i	−0.183812	+	0.565714i	−0.999926	−	0.0121764i	$-0.996124\pi$
$241$	−2.85353	+	8.78225i	−0.183812	+	0.565714i	0.816114	+	0.577891i	$0.196124\pi$
$242$	6.93674	+	13.6141i	0.445911	+	0.875149i
$243$	−14.2128	+	14.2128i	−0.911755	+	0.911755i
$244$	−9.61218			−0.615357
$245$		0			0
$246$	−16.0926	+	22.1495i	−1.02602	+	1.41220i
$247$	3.49510	−	22.0672i	0.222388	−	1.40410i
$248$	12.9062	+	25.3298i	0.819543	+	1.60844i
$249$			37.0899i			2.35048i
$250$		0			0
$251$	7.25731			0.458077			0.229039	−	0.973417i	$-0.426442\pi$
$251$	7.25731			0.458077			0.229039	+	0.973417i	$0.426442\pi$
$252$	−6.59783	+	1.04499i	−0.415624	+	0.0658284i
$253$	0.546915	+	0.0866228i	0.0343842	+	0.00544593i
$254$	6.87419	−	9.46151i	0.431325	−	0.593668i
$255$		0			0
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$	−0.299558	−	0.299558i	−0.0186859	−	0.0186859i	0.697702	−	0.716388i	$-0.254206\pi$
$257$	−0.299558	−	0.299558i	−0.0186859	−	0.0186859i	−0.716388	+	0.697702i	$0.754206\pi$
$258$	4.74269	−	2.41652i	0.295267	−	0.150446i
$259$	3.86237	+	1.25496i	0.239996	+	0.0779795i
$260$		0			0
$261$	−11.6491	+	3.78501i	−0.721059	+	0.234286i
$262$	−8.84162	+	8.84162i	−0.546237	+	0.546237i
$263$	−11.3494	+	5.78283i	−0.699836	+	0.356584i	−0.767434	−	0.641128i	$-0.778467\pi$
$263$	−11.3494	+	5.78283i	−0.699836	+	0.356584i	0.0675976	+	0.997713i	$0.478467\pi$
$264$	−1.04029	+	3.20170i	−0.0640257	+	0.197051i
$265$		0			0
$266$	3.93706			0.241397
$267$	−1.41742	−	8.94923i	−0.0867446	−	0.547684i
$268$	−1.97323	+	12.4585i	−0.120534	+	0.761024i
$269$	−9.07519	−	6.59351i	−0.553324	−	0.402013i	0.275686	−	0.961248i	$-0.411095\pi$
$269$	−9.07519	−	6.59351i	−0.553324	−	0.402013i	−0.829009	+	0.559235i	$0.811095\pi$
$270$		0			0
$271$	−6.43240	−	8.85343i	−0.390740	−	0.537808i	0.567650	−	0.823270i	$-0.307853\pi$
$271$	−6.43240	−	8.85343i	−0.390740	−	0.537808i	−0.958390	+	0.285462i	$0.907853\pi$
$272$	9.95959	−	19.5468i	0.603889	−	1.18520i
$273$	−11.9586	−	6.09319i	−0.723765	−	0.368776i
$274$	0.428525	+	1.31886i	0.0258881	+	0.0796755i
$275$		0			0
$276$	−3.95751	−	5.44705i	−0.238214	−	0.327874i
$277$	−7.75589	−	3.95183i	−0.466006	−	0.237442i	0.205189	−	0.978722i	$-0.434219\pi$
$277$	−7.75589	−	3.95183i	−0.466006	−	0.237442i	−0.671196	+	0.741280i	$0.734219\pi$
$278$	3.31073	+	20.9032i	0.198565	+	1.25369i
$279$	34.4450	−	25.0258i	2.06217	−	1.49825i
$280$		0			0
$281$	7.75715	+	5.63590i	0.462753	+	0.336209i	0.794610	−	0.607120i	$-0.207675\pi$
$281$	7.75715	+	5.63590i	0.462753	+	0.336209i	−0.331857	+	0.943330i	$0.607675\pi$
$282$	−2.82931	+	5.55284i	−0.168483	+	0.330667i
$283$	7.35420	−	1.16479i	0.437162	−	0.0692397i	0.0660254	−	0.997818i	$-0.478968\pi$
$283$	7.35420	−	1.16479i	0.437162	−	0.0692397i	0.371137	+	0.928578i	$0.378968\pi$
$284$	−6.65948	−	20.4958i	−0.395167	−	1.21620i
$285$		0			0
$286$	−3.20338	+	2.32739i	−0.189420	+	0.137621i
$287$	−2.57617	−	5.05603i	−0.152067	−	0.298448i
$288$	21.3510	−	10.8789i	1.25812	−	0.641045i
$289$	−12.4393	+	4.04177i	−0.731722	+	0.237751i
$290$		0			0
$291$	−0.236808	+	0.728820i	−0.0138819	+	0.0427242i
$292$	17.1447	+	17.1447i	1.00332	+	1.00332i
$293$	−9.84915	−	9.84915i	−0.575393	−	0.575393i	0.358237	−	0.933631i	$-0.383378\pi$
$293$	−9.84915	−	9.84915i	−0.575393	−	0.575393i	−0.933631	+	0.358237i	$0.883378\pi$
$294$	−7.49815	+	23.0769i	−0.437301	+	1.34587i
$295$		0			0
$296$	−14.5682			−0.846757
$297$	1.45309	+	0.230146i	0.0843165	+	0.0133544i
$298$	4.65202	−	29.3717i	0.269484	−	1.70146i
$299$		−	7.91919i		−	0.457978i
$300$		0			0
$301$			1.10323i			0.0635891i
$302$	11.9746	+	1.89659i	0.689060	+	0.109136i
$303$	−21.5577	−	3.41440i	−1.23846	−	0.196152i
$304$	−13.4318	+	4.36427i	−0.770369	+	0.250308i
$305$		0			0
$306$	−31.2478	−	10.1530i	−1.78632	−	0.580409i
$307$	−1.27461	−	1.27461i	−0.0727458	−	0.0727458i	0.669798	−	0.742544i	$-0.266381\pi$
$307$	−1.27461	−	1.27461i	−0.0727458	−	0.0727458i	−0.742544	+	0.669798i	$0.766381\pi$
$308$	−0.493379	−	0.493379i	−0.0281129	−	0.0281129i
$309$	−4.87721	+	15.0105i	−0.277455	+	0.853918i
$310$		0			0
$311$	−5.95620	+	1.93529i	−0.337745	+	0.109740i	−0.472979	−	0.881074i	$-0.656821\pi$
$311$	−5.95620	+	1.93529i	−0.337745	+	0.109740i	0.135234	+	0.990814i	$0.456821\pi$
$312$	47.5526	+	7.53159i	2.69214	+	0.426393i
$313$	1.36098	+	2.67107i	0.0769270	+	0.150978i	0.926266	−	0.376869i	$-0.122999\pi$
$313$	1.36098	+	2.67107i	0.0769270	+	0.150978i	−0.849339	+	0.527847i	$0.822999\pi$
$314$	−4.75290	−	6.54180i	−0.268222	−	0.369175i
$315$		0			0
$316$	24.8606	−	8.07768i	1.39852	−	0.454405i
$317$	−11.5159	+	1.82394i	−0.646799	+	0.102443i	−0.471211	−	0.882021i	$-0.656183\pi$
$317$	−11.5159	+	1.82394i	−0.646799	+	0.102443i	−0.175589	+	0.984464i	$0.556183\pi$
$318$	4.81381	+	2.45276i	0.269945	+	0.137544i
$319$	−1.03504	−	0.752000i	−0.0579511	−	0.0421039i
$320$		0			0
$321$	5.67365	−	4.12215i	0.316672	−	0.230076i
$322$	1.37831	−	0.218302i	0.0768100	−	0.0121655i
$323$	17.2538	+	8.79125i	0.960028	+	0.489158i
$324$	4.42477	+	6.09017i	0.245820	+	0.338343i
$325$		0			0
$326$	14.6910	−	4.77340i	0.813660	−	0.264374i
$327$	−38.7511	−	19.7447i	−2.14294	−	1.09188i
$328$	14.3936	+	14.3936i	0.794755	+	0.794755i
$329$	−0.759232	−	1.04499i	−0.0418578	−	0.0576124i
$330$		0			0
$331$	−21.1491	−	15.3657i	−1.16246	−	0.844576i	−0.172373	−	0.985032i	$-0.555143\pi$
$331$	−21.1491	−	15.3657i	−1.16246	−	0.844576i	−0.990087	+	0.140455i	$0.955143\pi$
$332$	27.2367	+	4.31386i	1.49481	+	0.236754i
$333$	3.41315	+	21.5498i	0.187039	+	1.18092i
$334$			17.7807i			0.972915i
$335$		0			0
$336$			8.48398i			0.462839i
$337$	19.5056	−	9.93860i	1.06254	−	0.541390i	0.166809	−	0.985989i	$-0.446654\pi$
$337$	19.5056	−	9.93860i	1.06254	−	0.541390i	0.895730	+	0.444599i	$0.146654\pi$
$338$	27.0420	+	27.0420i	1.47089	+	1.47089i
$339$	20.3784	−	6.62135i	1.10680	−	0.359622i
$340$		0			0
$341$	4.22950	+	1.37425i	0.229040	+	0.0744198i
$342$	9.60271	+	18.8464i	0.519255	+	1.01910i
$343$	−7.45889	−	7.45889i	−0.402742	−	0.402742i
$344$	−1.22294	−	3.76382i	−0.0659365	−	0.202932i
$345$		0			0
$346$	14.2203	+	10.3317i	0.764490	+	0.555434i
$347$	9.99724	+	1.58341i	0.536680	+	0.0850017i	0.418890	−	0.908037i	$-0.362419\pi$
$347$	9.99724	+	1.58341i	0.536680	+	0.0850017i	0.117790	+	0.993039i	$0.462419\pi$
$348$	2.43352	+	15.3647i	0.130451	+	0.823633i
$349$	17.7360			0.949387			0.474693	−	0.880151i	$-0.342559\pi$
$349$	17.7360			0.949387			0.474693	+	0.880151i	$0.342559\pi$
$350$		0			0
$351$		−	21.0403i		−	1.12305i
$352$	2.23015	+	1.13632i	0.118867	+	0.0605659i
$353$	−3.52146	+	22.2336i	−0.187428	+	1.18338i	0.697130	+	0.716945i	$0.254460\pi$
$353$	−3.52146	+	22.2336i	−0.187428	+	1.18338i	−0.884558	+	0.466430i	$0.845540\pi$
$354$	−34.6304	−	25.1605i	−1.84059	−	1.33726i
$355$		0			0
$356$	−6.73665			−0.357042
$357$	8.22545	−	8.22545i	0.435337	−	0.435337i
$358$	11.4288	−	5.82328i	0.604032	−	0.307770i
$359$	−3.80423	+	11.7082i	−0.200779	+	0.617935i	0.799081	+	0.601223i	$0.205320\pi$
$359$	−3.80423	+	11.7082i	−0.200779	+	0.617935i	−0.999860	+	0.0167120i	$0.994680\pi$
$360$		0			0
$361$	2.01902	+	6.21389i	0.106264	+	0.327047i
$362$	13.1161	+	13.1161i	0.689368	+	0.689368i
$363$	−13.1945	−	25.8956i	−0.692530	−	1.35917i
$364$	−5.86537	+	8.07298i	−0.307429	+	0.423139i
$365$		0			0
$366$	18.2835			0.955692
$367$	−27.9062	+	4.41991i	−1.45669	+	0.230717i	−0.834007	−	0.551754i	$-0.813959\pi$
$367$	−27.9062	+	4.41991i	−1.45669	+	0.230717i	−0.622686	+	0.782472i	$0.713959\pi$
$368$	−4.46029	+	2.27263i	−0.232509	+	0.118469i
$369$	17.9193	−	24.6638i	0.932843	−	1.28395i
$370$		0			0
$371$	−0.905915	+	0.658186i	−0.0470328	+	0.0341713i
$372$	−24.5490	−	48.1801i	−1.27281	−	2.49802i
$373$	3.55258	−	6.97233i	0.183946	−	0.361014i	−0.780558	−	0.625084i	$-0.785065\pi$
$373$	3.55258	−	6.97233i	0.183946	−	0.361014i	0.964504	+	0.264070i	$0.0850649\pi$
$374$	−1.06050	−	3.26388i	−0.0548370	−	0.168771i
$375$		0			0
$376$	3.74861	+	2.72353i	0.193320	+	0.140455i
$377$	−8.30667	+	16.3028i	−0.427815	+	0.839634i
$378$	3.66199	−	0.580002i	0.188352	−	0.0298321i
$379$	12.6090	+	17.3548i	0.647682	+	0.891458i	0.998996	−	0.0447999i	$-0.0142650\pi$
$379$	12.6090	+	17.3548i	0.647682	+	0.891458i	−0.351314	+	0.936258i	$0.614265\pi$
$380$		0			0
$381$	−13.0755	+	17.9969i	−0.669878	+	0.922008i
$382$	11.9043	−	23.3635i	0.609077	−	1.19538i
$383$	−0.678276	−	4.28247i	−0.0346583	−	0.218824i	0.964280	−	0.264884i	$-0.0853336\pi$
$383$	−0.678276	−	4.28247i	−0.0346583	−	0.218824i	−0.998939	+	0.0460597i	$0.985334\pi$
$384$	−9.40456	−	28.9443i	−0.479925	−	1.47706i
$385$		0			0
$386$	13.2275	+	18.2060i	0.673260	+	0.926662i
$387$	−5.28106	+	2.69084i	−0.268451	+	0.136783i
$388$	0.507661	+	0.258666i	0.0257726	+	0.0131318i
$389$	−2.91910	−	8.98407i	−0.148004	−	0.455510i	0.849381	−	0.527780i	$-0.176976\pi$
$389$	−2.91910	−	8.98407i	−0.148004	−	0.455510i	−0.997385	+	0.0722702i	$0.976976\pi$
$390$		0			0
$391$	6.52775	+	2.12099i	0.330123	+	0.107263i
$392$	16.0743	+	8.19025i	0.811873	+	0.413670i
$393$	16.8178	−	16.8178i	0.848343	−	0.848343i
$394$	−7.50494	−	2.43850i	−0.378094	−	0.122850i
$395$		0			0
$396$	1.15838	−	3.56514i	0.0582110	−	0.179155i
$397$	−5.49045	+	34.6653i	−0.275558	+	1.73980i	0.329981	+	0.943988i	$0.392958\pi$
$397$	−5.49045	+	34.6653i	−0.275558	+	1.73980i	−0.605539	+	0.795816i	$0.707042\pi$
$398$	−2.31967	+	14.6458i	−0.116275	+	0.734130i
$399$	−7.48874			−0.374906
$400$		0			0
$401$	−10.1943			−0.509079			−0.254540	−	0.967062i	$-0.581924\pi$
$401$	−10.1943			−0.509079			−0.254540	+	0.967062i	$0.581924\pi$
$402$	3.75331	−	23.6975i	0.187198	−	1.18192i
$403$	9.94938	−	62.8179i	0.495614	−	3.12918i
$404$	−5.01468	+	15.4336i	−0.249490	+	0.767850i
$405$		0			0
$406$	−3.06642	−	0.996340i	−0.152184	−	0.0494475i
$407$	−1.61147	+	1.61147i	−0.0798776	+	0.0798776i
$408$	−18.9443	+	37.1802i	−0.937881	+	1.84070i
$409$	−11.4621	−	3.72426i	−0.566764	−	0.184153i	0.0115985	−	0.999933i	$-0.496308\pi$
$409$	−11.4621	−	3.72426i	−0.566764	−	0.184153i	−0.578362	+	0.815780i	$0.696308\pi$
$410$		0			0
$411$	−0.815103	−	2.50863i	−0.0402060	−	0.123741i
$412$	10.4556	+	5.32739i	0.515110	+	0.262462i
$413$	7.90502	−	4.02781i	0.388980	−	0.198195i
$414$	4.40676	+	6.06538i	0.216580	+	0.298097i
$415$		0			0
$416$	11.0615	−	34.0439i	0.542336	−	1.66914i
$417$	−6.29739	−	39.7602i	−0.308385	−	1.94706i
$418$	−1.00302	+	1.96853i	−0.0490592	+	0.0962841i
$419$	−2.67537	+	3.68233i	−0.130700	+	0.179894i	−0.869352	−	0.494194i	$-0.835463\pi$
$419$	−2.67537	+	3.68233i	−0.130700	+	0.179894i	0.738651	+	0.674088i	$0.235463\pi$
$420$		0			0
$421$	−17.4848	−	24.0657i	−0.852155	−	1.17289i	−0.983384	−	0.181538i	$-0.941892\pi$
$421$	−17.4848	−	24.0657i	−0.852155	−	1.17289i	0.131229	−	0.991352i	$-0.458108\pi$
$422$	0.661988	−	0.104849i	0.0322251	−	0.00510395i
$423$	3.15048	−	6.18317i	0.153182	−	0.300636i
$424$	2.36105	−	3.24971i	0.114663	−	0.157820i
$425$		0			0
$426$	12.6671	+	38.9853i	0.613722	+	1.88884i
$427$	−1.72039	+	3.37646i	−0.0832555	+	0.163398i
$428$	−2.36717	−	4.64584i	−0.114422	−	0.224565i
$429$	6.09319	−	4.42696i	0.294182	−	0.213736i
$430$		0			0
$431$	12.9402	−	17.8107i	0.623308	−	0.857910i	−0.374280	−	0.927316i	$-0.622110\pi$
$431$	12.9402	−	17.8107i	0.623308	−	0.857910i	0.997589	+	0.0694055i	$0.0221102\pi$
$432$	−11.8504	+	6.03810i	−0.570155	+	0.290508i
$433$	−18.9256	+	2.99752i	−0.909505	+	0.144052i	−0.593620	−	0.804746i	$-0.702302\pi$
$433$	−18.9256	+	2.99752i	−0.909505	+	0.144052i	−0.315886	+	0.948797i	$0.602302\pi$
$434$	11.2075			0.537977
$435$		0			0
$436$	−19.0065	+	26.1601i	−0.910244	+	1.25284i
$437$	−2.00603	−	3.93706i	−0.0959617	−	0.188335i
$438$	−32.6112	−	32.6112i	−1.55823	−	1.55823i
$439$	−1.35681	−	4.17583i	−0.0647569	−	0.199301i	0.913443	−	0.406967i	$-0.133413\pi$
$439$	−1.35681	−	4.17583i	−0.0647569	−	0.199301i	−0.978200	+	0.207665i	$0.933413\pi$
$440$		0			0
$441$	8.34931	−	25.6965i	0.397586	−	1.22364i
$442$	−43.7309	+	22.2820i	−2.08007	+	1.05985i
$443$	0.566293	−	0.566293i	0.0269054	−	0.0269054i	−0.693526	−	0.720432i	$-0.743944\pi$
$443$	0.566293	−	0.566293i	0.0269054	−	0.0269054i	0.720432	+	0.693526i	$0.243944\pi$
$444$	27.7103			1.31507
$445$		0			0
$446$	−25.3155	−	18.3928i	−1.19872	−	0.870924i
$447$	−8.84867	+	55.8683i	−0.418527	+	2.64248i
$448$	6.23015	+	0.986758i	0.294347	+	0.0466199i
$449$		−	22.8981i		−	1.08063i	−0.841463	−	0.540315i	$-0.818305\pi$
$449$		−	22.8981i		−	1.08063i	0.841463	−	0.540315i	$-0.181695\pi$
$450$		0			0
$451$	3.18433			0.149944
$452$	−2.49216	−	15.7349i	−0.117221	−	0.740106i
$453$	−22.7770	−	3.60753i	−1.07016	−	0.169496i
$454$	1.78704	+	1.29836i	0.0838699	+	0.0609351i
$455$		0			0
$456$	25.5489	−	8.30133i	1.19644	−	0.388746i
$457$	−20.9761	−	20.9761i	−0.981222	−	0.981222i	0.0186046	−	0.999827i	$-0.494078\pi$
$457$	−20.9761	−	20.9761i	−0.981222	−	0.981222i	−0.999827	+	0.0186046i	$0.994078\pi$
$458$	−3.90137	−	7.65688i	−0.182299	−	0.357782i
$459$	17.3434	+	5.63522i	0.809522	+	0.263030i
$460$		0			0
$461$	18.4873	−	6.00689i	0.861039	−	0.279769i	0.154977	−	0.987918i	$-0.450470\pi$
$461$	18.4873	−	6.00689i	0.861039	−	0.279769i	0.706062	+	0.708150i	$0.250470\pi$
$462$	0.938463	+	0.938463i	0.0436612	+	0.0436612i
$463$	−22.5727	+	11.5014i	−1.04904	+	0.534513i	−0.891510	−	0.453001i	$-0.850353\pi$
$463$	−22.5727	+	11.5014i	−1.04904	+	0.534513i	−0.157531	+	0.987514i	$0.550353\pi$
$464$	11.5660			0.536936
$465$		0			0
$466$			22.3391i			1.03484i
$467$	1.99620	+	12.6035i	0.0923730	+	0.583220i	0.989845	+	0.142149i	$0.0454013\pi$
$467$	1.99620	+	12.6035i	0.0923730	+	0.583220i	−0.897472	+	0.441071i	$0.854599\pi$
$468$	−52.9506	−	8.38655i	−2.44764	−	0.387669i
$469$	4.02311	+	2.92296i	0.185770	+	0.134970i
$470$		0			0
$471$	9.04055	+	12.4432i	0.416567	+	0.573355i
$472$	−22.5042	+	22.5042i	−1.03584	+	1.03584i
$473$	−0.551615	−	0.281062i	−0.0253633	−	0.0129232i
$474$	−47.2876	+	15.3647i	−2.17199	+	0.705723i
$475$		0			0
$476$	−5.08361	−	6.99698i	−0.233007	−	0.320706i
$477$	−5.36025	−	2.73119i	−0.245429	−	0.125052i
$478$	−1.45309	+	0.230146i	−0.0664626	+	0.0105266i
$479$	−21.3496	+	15.5114i	−0.975487	+	0.708733i	−0.956695	−	0.291091i	$-0.905982\pi$
$479$	−21.3496	+	15.5114i	−0.975487	+	0.708733i	−0.0187915	+	0.999823i	$0.505982\pi$
$480$		0			0
$481$	26.3679	+	19.1574i	1.20227	+	0.873502i
$482$	−11.6358	−	5.92872i	−0.529995	−	0.270046i
$483$	−2.62169	+	0.415236i	−0.119291	+	0.0188939i
$484$	−20.5509	+	6.67738i	−0.934130	+	0.303517i
$485$		0			0
$486$	−16.7082	−	22.9969i	−0.757900	−	1.04316i
$487$	−2.13244	−	4.18515i	−0.0966302	−	0.189647i	0.837631	−	0.546236i	$-0.183940\pi$
$487$	−2.13244	−	4.18515i	−0.0966302	−	0.189647i	−0.934262	+	0.356589i	$0.883940\pi$
$488$	2.12652	−	13.4263i	0.0962630	−	0.607781i
$489$	−27.9440	+	9.07955i	−1.26367	+	0.410591i
$490$		0			0
$491$	−8.52185	+	26.2276i	−0.384586	+	1.18363i	0.552194	+	0.833715i	$0.313791\pi$
$491$	−8.52185	+	26.2276i	−0.384586	+	1.18363i	−0.936780	+	0.349918i	$0.886209\pi$
$492$	−27.3783	−	27.3783i	−1.23431	−	1.23431i
$493$	−11.2135	−	11.2135i	−0.505031	−	0.505031i
$494$	30.0503	+	9.76393i	1.35203	+	0.439300i
$495$		0			0
$496$	−38.2360	+	12.4236i	−1.71685	+	0.557837i
$497$	−8.39144	−	1.32907i	−0.376407	−	0.0596171i
$498$	−51.8072	−	8.20546i	−2.32154	−	0.367695i
$499$		−	35.7912i		−	1.60223i	−0.598508	−	0.801117i	$-0.704240\pi$
$499$		−	35.7912i		−	1.60223i	0.598508	−	0.801117i	$-0.295760\pi$
$500$		0			0
$501$		−	33.8209i		−	1.51100i
$502$	−1.60555	+	10.1370i	−0.0716591	+	0.452438i
$503$	42.5535	+	6.73981i	1.89737	+	0.300513i	0.992211	−	0.124566i	$-0.0397540\pi$
$503$	42.5535	+	6.73981i	1.89737	+	0.300513i	0.905156	+	0.425080i	$0.139754\pi$
$504$		−	9.44705i		−	0.420805i
$505$		0			0
$506$	−0.241990	+	0.744768i	−0.0107578	+	0.0331090i
$507$	−51.4370	−	51.4370i	−2.28440	−	2.28440i
$508$	11.6951	+	11.6951i	0.518885	+	0.518885i
$509$	5.06658	−	15.5933i	0.224572	−	0.691163i	−0.773762	−	0.633476i	$-0.781628\pi$
$509$	5.06658	−	15.5933i	0.224572	−	0.691163i	0.998335	−	0.0576867i	$-0.0183724\pi$
$510$		0			0
$511$	9.09098	−	2.95384i	0.402161	−	0.130670i
$512$	−22.3488	+	3.53971i	−0.987688	+	0.156434i
$513$	−5.32979	−	10.4603i	−0.235316	−	0.461833i
$514$	0.484695	−	0.352151i	0.0213790	−	0.0155327i
$515$		0			0
$516$	2.32617	+	7.15921i	0.102404	+	0.315167i
$517$	0.715921	−	0.113391i	0.0314862	−	0.00498692i
$518$	−2.60741	+	5.11734i	−0.114563	+	0.224843i
$519$	−27.0487	−	19.6520i	−1.18731	−	0.862628i
$520$		0			0
$521$	−3.33109	+	2.42018i	−0.145937	+	0.106030i	−0.658358	−	0.752705i	$-0.728749\pi$
$521$	−3.33109	+	2.42018i	−0.145937	+	0.106030i	0.512421	+	0.858734i	$0.328749\pi$
$522$	−2.70977	−	17.1088i	−0.118603	−	0.748832i
$523$	−3.35349	−	1.70869i	−0.146638	−	0.0747158i	0.379132	−	0.925343i	$-0.376223\pi$
$523$	−3.35349	−	1.70869i	−0.146638	−	0.0747158i	−0.525770	+	0.850627i	$0.676223\pi$
$524$	−10.3939	−	14.3060i	−0.454061	−	0.624962i
$525$		0			0
$526$	−5.56661	−	17.1323i	−0.242716	−	0.747002i
$527$	49.1158	+	25.0258i	2.13952	+	1.09014i
$528$	−4.24199	−	2.16140i	−0.184609	−	0.0940629i
$529$	12.5985	+	17.3403i	0.547760	+	0.753927i
$530$		0			0
$531$	38.5615	+	28.0166i	1.67343	+	1.21582i
$532$	−0.871004	+	5.49930i	−0.0377628	+	0.238425i
$533$	−7.12411	−	44.9799i	−0.308580	−	1.94829i
$534$	12.8139			0.554511
$535$		0			0
$536$	−16.9655	−	5.51243i	−0.732799	−	0.238101i
$537$	−21.7389	+	11.0765i	−0.938103	+	0.477988i
$538$	11.2175	−	11.2175i	0.483623	−	0.483623i
$539$	2.68404	−	0.872098i	0.115610	−	0.0375639i
$540$		0			0
$541$	12.5643	+	4.08238i	0.540180	+	0.175515i	0.566384	−	0.824142i	$-0.308342\pi$
$541$	12.5643	+	4.08238i	0.540180	+	0.175515i	−0.0262040	+	0.999657i	$0.508342\pi$
$542$	13.7895	−	7.02613i	0.592312	−	0.301798i
$543$	−24.9483	−	24.9483i	−1.07064	−	1.07064i
$544$	25.0996	+	18.2360i	1.07614	+	0.781860i
$545$		0			0
$546$	11.1566	−	15.3557i	0.477458	−	0.657164i
$547$	20.5808	+	3.25968i	0.879971	+	0.139374i	0.580041	−	0.814587i	$-0.303037\pi$
$547$	20.5808	+	3.25968i	0.879971	+	0.139374i	0.299930	+	0.953961i	$0.403037\pi$
$548$	−1.93700	+	0.306790i	−0.0827443	+	0.0131054i
$549$	−20.3589			−0.868898
$550$		0			0
$551$			10.2092i			0.434926i
$552$	8.48398	−	4.32280i	0.361102	−	0.183991i
$553$	1.61211	−	10.1785i	0.0685540	−	0.432833i
$554$	7.23577	−	9.95918i	0.307418	−	0.423125i
$555$		0			0
$556$	−29.9300			−1.26932
$557$	−16.6551	+	16.6551i	−0.705697	+	0.705697i	−0.965627	−	0.259930i	$-0.916300\pi$
$557$	−16.6551	+	16.6551i	−0.705697	+	0.705697i	0.259930	+	0.965627i	$0.416300\pi$
$558$	27.3357	+	53.6493i	1.15721	+	2.27116i
$559$	−2.73601	+	8.42058i	−0.115721	+	0.356152i
$560$		0			0
$561$	2.01719	+	6.20826i	0.0851657	+	0.262113i
$562$	−9.58836	+	9.58836i	−0.404461	+	0.404461i
$563$	20.8369	+	40.8947i	0.878170	+	1.72350i	0.665525	+	0.746375i	$0.268208\pi$
$563$	20.8369	+	40.8947i	0.878170	+	1.72350i	0.212644	+	0.977130i	$0.431792\pi$
$564$	−7.13028	−	5.18045i	−0.300239	−	0.218136i
$565$		0			0
$566$			10.5301i			0.442611i
$567$	2.93123	−	0.464261i	0.123100	−	0.0194971i
$568$	30.1018	−	4.76766i	1.26304	−	0.200047i
$569$	23.0882	−	31.7781i	0.967906	−	1.33221i	0.0248079	−	0.999692i	$-0.492103\pi$
$569$	23.0882	−	31.7781i	0.967906	−	1.33221i	0.943098	−	0.332516i	$-0.107897\pi$
$570$		0			0
$571$	19.4298	−	14.1166i	0.813111	−	0.590760i	−0.101620	−	0.994823i	$-0.532402\pi$
$571$	19.4298	−	14.1166i	0.813111	−	0.590760i	0.914731	+	0.404063i	$0.132402\pi$
$572$	−2.54222	−	4.98938i	−0.106295	−	0.208616i
$573$	−22.6433	+	44.4400i	−0.945939	+	1.85651i
$574$	7.63220	−	2.47985i	0.318562	−	0.103507i
$575$		0			0
$576$	10.4721	+	32.2299i	0.436339	+	1.34291i
$577$	2.86414	−	5.62119i	0.119236	−	0.234013i	−0.823673	−	0.567066i	$-0.808079\pi$
$577$	2.86414	−	5.62119i	0.119236	−	0.234013i	0.942908	+	0.333052i	$0.108079\pi$
$578$	−2.89359	−	18.2694i	−0.120357	−	0.759906i
$579$	−25.1601	−	34.6299i	−1.04562	−	1.43917i
$580$		0			0
$581$	6.39015	−	8.79529i	0.265108	−	0.364890i
$582$	−0.965628	−	0.492012i	−0.0400266	−	0.0203946i
$583$	−0.0982995	−	0.620639i	−0.00407115	−	0.0257042i
$584$	−27.7408	+	20.1549i	−1.14792	+	0.834014i
$585$		0			0
$586$	15.9363	−	11.5784i	0.658321	−	0.478298i
$587$	−32.9979	+	16.8133i	−1.36197	+	0.693958i	−0.973753	−	0.227609i	$-0.926909\pi$
$587$	−32.9979	+	16.8133i	−1.36197	+	0.693958i	−0.388218	+	0.921568i	$0.626909\pi$
$588$	−30.5751	−	15.5788i	−1.26089	−	0.642458i
$589$	−10.9662	−	33.7506i	−0.451856	−	1.39067i
$590$		0			0
$591$	14.2752	+	4.63831i	0.587205	+	0.190795i
$592$	3.22294	−	20.3488i	0.132462	−	0.836332i
$593$	16.5004	−	16.5004i	0.677590	−	0.677590i	−0.281864	−	0.959454i	$-0.590953\pi$
$593$	16.5004	−	16.5004i	0.677590	−	0.677590i	0.959454	+	0.281864i	$0.0909527\pi$
$594$	−0.642937	+	1.97876i	−0.0263800	+	0.0811894i
$595$		0			0
$596$	39.9973	+	12.9959i	1.63835	+	0.532333i
$597$	4.41228	−	27.8580i	0.180583	−	1.14015i
$598$	11.0615	+	1.75198i	0.452340	+	0.0716436i
$599$	1.55150			0.0633926			0.0316963	−	0.999498i	$-0.489909\pi$
$599$	1.55150			0.0633926			0.0316963	+	0.999498i	$0.489909\pi$
$600$		0			0
$601$	13.6133			0.555299			0.277650	−	0.960682i	$-0.410445\pi$
$601$	13.6133			0.555299			0.277650	+	0.960682i	$0.410445\pi$
$602$	−1.54099	−	0.244069i	−0.0628062	−	0.00994752i
$603$	−4.17937	+	26.3875i	−0.170197	+	1.07458i
$604$	−5.29832	+	16.3065i	−0.215585	+	0.663504i
$605$		0			0
$606$	9.53849	−	29.3564i	0.387474	−	1.19252i
$607$	25.2645	−	25.2645i	1.02545	−	1.02545i	0.0257859	−	0.999667i	$-0.491791\pi$
$607$	25.2645	−	25.2645i	1.02545	−	1.02545i	0.999667	−	0.0257859i	$-0.00820882\pi$
$608$	−3.12447	−	19.7271i	−0.126714	−	0.800041i
$609$	5.83268	+	1.89515i	0.236352	+	0.0767954i
$610$		0			0
$611$	−3.20338	−	9.85898i	−0.129595	−	0.398852i
$612$	21.0948	−	41.4008i	0.852705	−	1.67353i
$613$	−32.8390	+	16.7323i	−1.32635	+	0.675811i	−0.966372	−	0.257148i	$-0.917217\pi$
$613$	−32.8390	+	16.7323i	−1.32635	+	0.675811i	−0.359982	+	0.932959i	$0.617217\pi$
$614$	2.06236	−	1.49839i	0.0832302	−	0.0604703i
$615$		0			0
$616$	0.798304	−	0.580002i	0.0321646	−	0.0233689i
$617$	−0.552944	−	3.49115i	−0.0222607	−	0.140548i	0.974055	−	0.226312i	$-0.0726670\pi$
$617$	−0.552944	−	3.49115i	−0.0222607	−	0.140548i	−0.996316	+	0.0857638i	$0.972667\pi$
$618$	−19.8877	−	10.1333i	−0.800001	−	0.407621i
$619$	−26.6760	+	36.7164i	−1.07220	+	1.47576i	−0.204369	+	0.978894i	$0.565514\pi$
$619$	−26.6760	+	36.7164i	−1.07220	+	1.47576i	−0.867830	+	0.496861i	$0.834486\pi$
$620$		0			0
$621$	−2.44588	−	3.36646i	−0.0981497	−	0.135091i
$622$	−1.38551	−	8.74779i	−0.0555540	−	0.350754i
$623$	−1.20573	+	2.36637i	−0.0483065	+	0.0948068i
$624$	−21.0403	+	64.7554i	−0.842286	+	2.59229i
$625$		0			0
$626$	−4.03205	+	1.31009i	−0.161153	+	0.0523618i
$627$	1.90785	−	3.74437i	0.0761923	−	0.149536i
$628$	10.1891	−	5.19160i	0.406589	−	0.207168i
$629$	−22.8535	+	16.6040i	−0.911227	+	0.662046i
$630$		0			0
$631$	−7.79351	+	10.7268i	−0.310255	+	0.427029i	−0.935461	−	0.353431i	$-0.885015\pi$
$631$	−7.79351	+	10.7268i	−0.310255	+	0.427029i	0.625206	+	0.780460i	$0.285015\pi$
$632$	5.78298	+	36.5123i	0.230035	+	1.45238i
$633$	−1.25918	+	0.199434i	−0.0500478	+	0.00792679i
$634$		−	16.4890i		−	0.654862i
$635$		0			0
$636$	−4.49098	+	6.18131i	−0.178079	+	0.245105i
$637$	−18.3236	−	35.9620i	−0.726007	−	1.42487i
$638$	1.27938	−	1.27938i	0.0506511	−	0.0506511i
$639$	−14.1050	−	43.4107i	−0.557985	−	1.71730i
$640$		0			0
$641$	−4.58284	+	14.1045i	−0.181011	+	0.557095i	−0.999857	−	0.0169186i	$-0.994614\pi$
$641$	−4.58284	+	14.1045i	−0.181011	+	0.557095i	0.818846	+	0.574014i	$0.194614\pi$
$642$	4.50263	+	8.83692i	0.177705	+	0.348765i
$643$	−23.8113	+	23.8113i	−0.939027	+	0.939027i	−0.998245	−	0.0592183i	$-0.981139\pi$
$643$	−23.8113	+	23.8113i	−0.939027	+	0.939027i	0.0592183	+	0.998245i	$0.481139\pi$
$644$			1.97352i			0.0777674i
$645$		0			0
$646$	−16.0967	+	22.1553i	−0.633318	+	0.871687i
$647$	−6.98945	+	44.1296i	−0.274784	+	1.73492i	0.334885	+	0.942259i	$0.391302\pi$
$647$	−6.98945	+	44.1296i	−0.274784	+	1.73492i	−0.609669	+	0.792656i	$0.708698\pi$
$648$	−9.48566	+	4.83319i	−0.372632	+	0.189865i
$649$			4.97864i			0.195429i
$650$		0			0
$651$	−21.3179			−0.835516
$652$	3.41738	+	21.5765i	0.133835	+	0.845000i
$653$	0.0172425	+	0.00273094i	0.000674750	+	0.000106870i	0.156772	−	0.987635i	$-0.449891\pi$
$653$	0.0172425	+	0.00273094i	0.000674750	+	0.000106870i	−0.156097	+	0.987742i	$0.549891\pi$
$654$	36.1524	−	49.7595i	1.41367	−	1.94575i
$655$		0			0
$656$	−23.2894	+	16.9207i	−0.909297	+	0.660643i
$657$	36.3132	+	36.3132i	1.41671	+	1.41671i
$658$	1.62762	−	0.829312i	0.0634511	−	0.0323299i
$659$	36.7936	+	11.9550i	1.43328	+	0.465700i	0.919795	−	0.392400i	$-0.128355\pi$
$659$	36.7936	+	11.9550i	1.43328	+	0.465700i	0.513482	+	0.858100i	$0.328355\pi$
$660$		0			0
$661$	2.89246	−	0.939818i	0.112504	−	0.0365547i	−0.252224	−	0.967669i	$-0.581162\pi$
$661$	2.89246	−	0.939818i	0.112504	−	0.0365547i	0.364728	+	0.931114i	$0.381162\pi$
$662$	26.1417	−	26.1417i	1.01603	−	1.01603i
$663$	83.1812	−	42.3829i	3.23049	−	1.64602i
$664$	−12.0512	+	37.0899i	−0.467678	+	1.43937i
$665$		0			0
$666$	−30.8559			−1.19564
$667$	0.566079	+	3.57408i	0.0219187	+	0.138389i
$668$	−24.8361	−	3.93365i	−0.960937	−	0.152198i
$669$	48.1529	+	34.9852i	1.86170	+	1.35260i
$670$		0			0
$671$	−1.24994	−	1.72039i	−0.0482533	−	0.0664149i
$672$	−11.8504	−	1.87693i	−0.457141	−	0.0724040i
$673$	6.53751	+	3.33103i	0.252003	+	0.128402i	0.575429	−	0.817851i	$-0.304835\pi$
$673$	6.53751	+	3.33103i	0.252003	+	0.128402i	−0.323427	+	0.946253i	$0.604835\pi$
$674$	9.56701	+	29.4442i	0.368507	+	1.13415i
$675$		0			0
$676$	−43.7549	+	31.7898i	−1.68288	+	1.22269i
$677$	−25.0033	−	12.7398i	−0.960955	−	0.489631i	−0.0981518	−	0.995171i	$-0.531293\pi$
$677$	−25.0033	−	12.7398i	−0.960955	−	0.489631i	−0.862803	+	0.505541i	$0.831293\pi$
$678$	4.74036	+	29.9295i	0.182053	+	1.14943i
$679$	0.181722	−	0.132029i	0.00697387	−	0.00506681i
$680$		0			0
$681$	−3.39915	−	2.46963i	−0.130256	−	0.0946364i
$682$	−2.85525	+	5.60375i	−0.109333	+	0.214579i
$683$	8.66759	−	1.37281i	0.331656	−	0.0525292i	0.0116143	−	0.999933i	$-0.496303\pi$
$683$	8.66759	−	1.37281i	0.331656	−	0.0525292i	0.320042	+	0.947403i	$0.396303\pi$
$684$	−28.4491	+	9.24367i	−1.08778	+	0.353441i
$685$		0			0
$686$	12.0687	−	8.76846i	0.460787	−	0.334781i
$687$	7.42085	+	14.5642i	0.283123	+	0.555661i
$688$	5.52786	−	0.875528i	0.210748	−	0.0333792i
$689$	−8.54685	+	2.77704i	−0.325609	+	0.105797i
$690$		0			0
$691$	−8.97413	+	27.6195i	−0.341392	+	1.05070i	0.622095	+	0.782942i	$0.286282\pi$
$691$	−8.97413	+	27.6195i	−0.341392	+	1.05070i	−0.963487	+	0.267755i	$0.913718\pi$
$692$	−17.5773	+	17.5773i	−0.668189	+	0.668189i
$693$	−1.04499	−	1.04499i	−0.0396960	−	0.0396960i
$694$	−4.42341	+	13.6139i	−0.167910	+	0.516775i
$695$		0			0
$696$	−21.9998			−0.833899
$697$	38.9848	+	6.17458i	1.47665	+	0.233879i
$698$	−3.92377	+	24.7737i	−0.148517	+	0.937698i
$699$		−	42.4915i		−	1.60718i
$700$		0			0
$701$			10.7467i			0.405899i	0.979189	+	0.202949i	$0.0650527\pi$
$701$			10.7467i			0.405899i	−0.979189	+	0.202949i	$0.934947\pi$
$702$	29.3891	+	4.65478i	1.10922	+	0.175683i
$703$	17.9618	+	2.84486i	0.677441	+	0.107296i
$704$	−2.08059	+	2.86368i	−0.0784151	+	0.107929i
$705$		0			0
$706$	−30.2769	−	9.83756i	−1.13949	−	0.370241i
$707$	4.52381	+	4.52381i	0.170135	+	0.170135i
$708$	42.8055	−	42.8055i	1.60873	−	1.60873i
$709$	0.353547	−	1.08811i	0.0132777	−	0.0408647i	−0.944198	−	0.329378i	$-0.893161\pi$
$709$	0.353547	−	1.08811i	0.0132777	−	0.0408647i	0.957476	+	0.288513i	$0.0931610\pi$
$710$		0			0
$711$	52.6555	−	17.1088i	1.97474	−	0.641630i
$712$	1.49036	−	9.40977i	0.0558537	−	0.352646i
$713$	−5.71051	−	11.2075i	−0.213860	−	0.419724i
$714$	9.66959	+	13.3091i	0.361875	+	0.498079i
$715$		0			0
$716$	5.60555	+	17.2521i	0.209489	+	0.644741i
$717$	2.76393	−	0.437764i	0.103221	−	0.0163486i
$718$	−15.5124	−	7.90398i	−0.578919	−	0.294974i
$719$	1.16479	+	0.846270i	0.0434394	+	0.0315606i	0.609293	−	0.792945i	$-0.291453\pi$
$719$	1.16479	+	0.846270i	0.0434394	+	0.0315606i	−0.565854	+	0.824506i	$0.691453\pi$
$720$		0			0
$721$	3.74269	−	2.71922i	0.139385	−	0.101269i
$722$	−9.12625	+	1.44546i	−0.339644	+	0.0537943i
$723$	22.1326	+	11.2771i	0.823119	+	0.419400i
$724$	−21.2223	+	15.4189i	−0.788721	+	0.573039i
$725$		0			0
$726$	39.0901	−	12.7011i	1.45077	−	0.471383i
$727$	8.90163	+	4.53561i	0.330143	+	0.168216i	0.611203	−	0.791474i	$-0.290686\pi$
$727$	8.90163	+	4.53561i	0.330143	+	0.168216i	−0.281060	+	0.959690i	$0.590686\pi$
$728$	−9.97876	−	9.97876i	−0.369837	−	0.369837i
$729$	25.1437	+	34.6074i	0.931250	+	1.28176i
$730$		0			0
$731$	−6.20826	−	4.51057i	−0.229621	−	0.166829i
$732$	−4.04488	+	25.5384i	−0.149503	+	0.943925i
$733$	2.98599	+	18.8528i	0.110290	+	0.696344i	0.979431	+	0.201779i	$0.0646724\pi$
$733$	2.98599	+	18.8528i	0.110290	+	0.696344i	−0.869141	+	0.494564i	$0.835328\pi$
$734$		−	39.9573i		−	1.47485i
$735$		0			0
$736$	−2.18766	−	6.73292i	−0.0806382	−	0.248179i
$737$	−2.48642	+	1.26689i	−0.0915884	+	0.0466666i
$738$	30.4862	+	30.4862i	1.12221	+	1.12221i
$739$	−30.4862	+	9.90557i	−1.12145	+	0.364382i	−0.810322	−	0.585985i	$-0.800708\pi$
$739$	−30.4862	+	9.90557i	−1.12145	+	0.364382i	−0.311131	+	0.950367i	$0.600708\pi$
$740$		0			0
$741$	−57.1591	−	18.5721i	−2.09979	−	0.682263i
$742$	−0.718938	−	1.41100i	−0.0263931	−	0.0517993i
$743$	27.7454	+	27.7454i	1.01788	+	1.01788i	0.999837	+	0.0180432i	$0.00574364\pi$
$743$	27.7454	+	27.7454i	1.01788	+	1.01788i	0.0180432	+	0.999837i	$0.494256\pi$
$744$	72.7291	−	23.6311i	2.66638	−	0.866359i
$745$		0			0
$746$	8.95303	+	6.50476i	0.327794	+	0.238156i
$747$	57.6882	+	9.13691i	2.11070	+	0.334302i
$748$	4.79360	−	0.759232i	0.175272	−	0.0277603i
$749$	−2.05562			−0.0751105
$750$		0			0
$751$			13.3460i			0.487004i	0.969900	+	0.243502i	$0.0782963\pi$
$751$			13.3460i			0.487004i	−0.969900	+	0.243502i	$0.921704\pi$
$752$	−4.63354	+	4.63354i	−0.168968	+	0.168968i
$753$	3.05393	−	19.2818i	0.111292	−	0.702667i
$754$	−20.9340	−	15.2095i	−0.762372	−	0.553896i
$755$		0			0
$756$			5.24339i			0.190700i
$757$	23.3850	−	23.3850i	0.849943	−	0.849943i	−0.140182	−	0.990126i	$-0.544769\pi$
$757$	23.3850	−	23.3850i	0.849943	−	0.849943i	0.990126	+	0.140182i	$0.0447689\pi$
$758$	−27.0308	+	13.7729i	−0.981802	+	0.500253i
$759$	0.460292	−	1.41663i	0.0167075	−	0.0514205i
$760$		0			0
$761$	−6.52304	−	20.0758i	−0.236460	−	0.727749i	−0.996924	−	0.0783693i	$-0.975029\pi$
$761$	−6.52304	−	20.0758i	−0.236460	−	0.727749i	0.760464	−	0.649380i	$-0.224971\pi$
$762$	−22.2454	−	22.2454i	−0.805864	−	0.805864i
$763$	5.78745	+	11.3585i	0.209520	+	0.411206i
$764$	30.0006	+	21.7967i	1.08538	+	0.788577i
$765$		0			0
$766$	6.13182			0.221552
$767$	70.3253	−	11.1384i	2.53930	−	0.402186i
$768$	42.5100	−	6.73292i	1.53395	−	0.242953i
$769$	−31.2607	+	43.0267i	−1.12729	+	1.55158i	−0.334177	+	0.942510i	$0.608458\pi$
$769$	−31.2607	+	43.0267i	−1.12729	+	1.55158i	−0.793114	+	0.609073i	$0.791542\pi$
$770$		0			0
$771$	−0.921944	+	0.669832i	−0.0332030	+	0.0241234i
$772$	−28.3566	+	14.4484i	−1.02057	+	0.520009i
$773$	13.9493	−	27.3771i	0.501722	−	0.984686i	−0.491763	−	0.870729i	$-0.663647\pi$
$773$	13.9493	−	27.3771i	0.501722	−	0.984686i	0.993486	−	0.113957i	$-0.0363525\pi$
$774$	−2.59023	−	7.97190i	−0.0931038	−	0.286544i
$775$		0			0
$776$	−0.473616	+	0.651876i	−0.0170018	+	0.0234010i
$777$	4.95959	−	9.73375i	0.177924	−	0.349196i
$778$	13.1948	−	2.08985i	0.473055	−	0.0749246i
$779$	−14.9358	−	20.5574i	−0.535130	−	0.736544i
$780$		0			0
$781$	2.80236	−	3.85712i	0.100276	−	0.138019i
$782$	−4.40676	+	8.64875i	−0.157585	+	0.309279i
$783$	1.50400	+	9.49589i	0.0537486	+	0.339355i
$784$	−14.9963	+	20.6406i	−0.535582	+	0.737165i
$785$		0			0
$786$	19.7705	+	27.2117i	0.705189	+	0.970609i
$787$	−32.5114	+	16.5654i	−1.15891	+	0.590493i	−0.924326	−	0.381604i	$-0.875372\pi$
$787$	−32.5114	+	16.5654i	−1.15891	+	0.590493i	−0.234581	+	0.972097i	$0.575372\pi$
$788$	5.06644	−	9.94345i	0.180484	−	0.354221i
$789$	10.5883	+	32.5875i	0.376954	+	1.16015i
$790$		0			0
$791$	−5.97321	−	1.94081i	−0.212383	−	0.0690074i
$792$	4.72353	+	2.40676i	0.167843	+	0.0855204i
$793$	−21.5048	+	21.5048i	−0.763657	+	0.763657i
$794$	−47.2060	−	15.3381i	−1.67528	−	0.544330i
$795$		0			0
$796$	−19.9442	−	6.48025i	−0.706902	−	0.229686i
$797$	0.936362	−	5.91196i	0.0331677	−	0.209412i	−0.965539	−	0.260259i	$-0.916192\pi$
$797$	0.936362	−	5.91196i	0.0331677	−	0.209412i	0.998706	+	0.0508468i	$0.0161920\pi$
$798$	1.65675	−	10.4603i	0.0586482	−	0.370290i
$799$	8.98468			0.317855
$800$		0			0
$801$	−14.2685			−0.504151
$802$	2.25530	−	14.2394i	0.0796376	−	0.502812i
$803$	−0.839124	+	5.29802i	−0.0296120	+	0.186963i
$804$	32.2703	+	10.4853i	1.13809	+	0.369787i
$805$		0			0
$806$	85.5431	+	27.7946i	3.01313	+	0.979025i
$807$	−21.3370	+	21.3370i	−0.751099	+	0.751099i
$808$	−20.4483	−	10.4189i	−0.719368	−	0.366536i
$809$	−29.7722	−	9.67358i	−1.04674	−	0.340105i	−0.265349	−	0.964152i	$-0.585487\pi$
$809$	−29.7722	−	9.67358i	−1.04674	−	0.340105i	−0.781387	+	0.624047i	$0.785487\pi$
$810$		0			0
$811$	1.95623	+	6.02066i	0.0686926	+	0.211414i	0.979510	−	0.201395i	$-0.0645476\pi$
$811$	1.95623	+	6.02066i	0.0686926	+	0.211414i	−0.910817	+	0.412809i	$0.864548\pi$
$812$	2.07008	−	4.06276i	0.0726455	−	0.142575i
$813$	−26.2293	+	13.3645i	−0.919901	+	0.468713i
$814$	−1.89440	−	2.60741i	−0.0663985	−	0.0913898i
$815$		0			0
$816$	−47.7424	−	34.6868i	−1.67132	−	1.21428i
$817$	0.772821	+	4.87940i	0.0270376	+	0.170709i
$818$	7.73783	−	15.1863i	0.270547	−	0.530978i
$819$	−12.4230	+	17.0989i	−0.434096	+	0.597482i
$820$		0			0
$821$	13.3566	+	18.3837i	0.466147	+	0.641596i	0.975769	−	0.218802i	$-0.0702149\pi$
$821$	13.3566	+	18.3837i	0.466147	+	0.641596i	−0.509622	+	0.860398i	$0.670215\pi$
$822$	3.68438	−	0.583549i	0.128508	−	0.0203536i
$823$	5.29231	−	10.3867i	0.184478	−	0.362059i	−0.780183	−	0.625551i	$-0.784874\pi$
$823$	5.29231	−	10.3867i	0.184478	−	0.362059i	0.964662	+	0.263492i	$0.0848743\pi$
$824$	−9.75442	+	13.4258i	−0.339811	+	0.467710i
$825$		0			0
$826$	3.87721	+	11.9328i	0.134905	+	0.415196i
$827$	−2.69680	+	5.29276i	−0.0937768	+	0.184047i	−0.933130	−	0.359539i	$-0.882934\pi$
$827$	−2.69680	+	5.29276i	−0.0937768	+	0.184047i	0.839353	+	0.543586i	$0.182934\pi$
$828$	−9.44705	+	4.81351i	−0.328308	+	0.167281i
$829$	30.1824	−	21.9288i	1.04828	−	0.761619i	0.0763946	−	0.997078i	$-0.475659\pi$
$829$	30.1824	−	21.9288i	1.04828	−	0.761619i	0.971884	+	0.235458i	$0.0756591\pi$
$830$		0			0
$831$	−13.7632	+	18.9435i	−0.477442	+	0.657142i
$832$	45.1054	+	22.9824i	1.56375	+	0.796770i
$833$	34.5510	−	5.47233i	1.19712	−	0.189605i
$834$	56.9303			1.97133
$835$		0			0
$836$	−2.52775	−	1.83652i	−0.0874241	−	0.0635173i
$837$	−15.1721	−	29.7769i	−0.524425	−	1.02924i
$838$	−4.55161	−	4.55161i	−0.157233	−	0.157233i
$839$	13.8039	+	42.4840i	0.476563	+	1.46671i	0.843839	+	0.536597i	$0.180290\pi$
$839$	13.8039	+	42.4840i	0.476563	+	1.46671i	−0.367276	+	0.930112i	$0.619710\pi$
$840$		0			0
$841$	−6.37789	+	19.6291i	−0.219927	+	0.676866i
$842$	37.4832	−	19.0986i	1.29176	−	0.658183i
$843$	18.2381	−	18.2381i	0.628155	−	0.628155i
$844$			0.947862i			0.0326268i
$845$		0			0
$846$	7.93969	+	5.76852i	0.272972	+	0.198326i
$847$	−1.33264	+	8.41399i	−0.0457902	+	0.289108i
$848$	4.01686	+	4.01686i	0.137939	+	0.137939i
$849$		−	20.0294i		−	0.687406i
$850$		0			0
$851$	6.44588			0.220962
$852$	−57.2571	+	9.06863i	−1.96160	+	0.310686i
$853$	−5.92966	−	0.939165i	−0.203028	−	0.0321564i	0.0540922	−	0.998536i	$-0.482773\pi$
$853$	−5.92966	−	0.939165i	−0.203028	−	0.0321564i	−0.257120	+	0.966380i	$0.582773\pi$
$854$	−4.33564	−	3.15002i	−0.148362	−	0.107792i
$855$		0			0
$856$	7.01302	−	2.27867i	0.239700	−	0.0778832i
$857$	3.74007	+	3.74007i	0.127758	+	0.127758i	0.768095	−	0.640336i	$-0.221205\pi$
$857$	3.74007	+	3.74007i	0.127758	+	0.127758i	−0.640336	+	0.768095i	$0.721205\pi$
$858$	4.83558	+	9.49036i	0.165084	+	0.323996i
$859$	30.1496	+	9.79621i	1.02869	+	0.334242i	0.774273	−	0.632852i	$-0.218116\pi$
$859$	30.1496	+	9.79621i	1.02869	+	0.334242i	0.254419	+	0.967094i	$0.418116\pi$
$860$		0			0
$861$	−14.5173	+	4.71696i	−0.494749	+	0.160754i
$862$	22.0152	+	22.0152i	0.749841	+	0.749841i
$863$	9.14726	−	4.66076i	0.311376	−	0.158654i	−0.291318	−	0.956626i	$-0.594094\pi$
$863$	9.14726	−	4.66076i	0.311376	−	0.158654i	0.602694	+	0.797972i	$0.294094\pi$
$864$	−5.81234	−	17.8885i	−0.197740	−	0.608581i
$865$		0			0
$866$		−	27.0984i		−	0.920843i
$867$	5.50393	+	34.7504i	0.186923	+	1.18019i
$868$	−2.47946	+	15.6547i	−0.0841582	+	0.531354i
$869$	4.67853	+	3.39915i	0.158708	+	0.115308i
$870$		0			0
$871$	23.4581	+	32.2873i	0.794847	+	1.09401i
$872$	−32.3357	−	32.3357i	−1.09503	−	1.09503i
$873$	1.07524	+	0.547863i	0.0363914	+	0.0185424i
$874$	5.94310	−	1.93103i	0.201028	−	0.0653181i
$875$		0			0
$876$	52.7661	−	38.3368i	1.78280	−	1.29528i
$877$	−15.4361	−	7.86511i	−0.521241	−	0.265586i	0.173515	−	0.984831i	$-0.444488\pi$
$877$	−15.4361	−	7.86511i	−0.521241	−	0.265586i	−0.694756	+	0.719246i	$0.744488\pi$
$878$	6.13297	−	0.971367i	0.206978	−	0.0327821i
$879$	−30.3126	+	22.0234i	−1.02242	+	0.742830i
$880$		0			0
$881$	−26.3453	−	19.1410i	−0.887595	−	0.644876i	0.0476546	−	0.998864i	$-0.484825\pi$
$881$	−26.3453	−	19.1410i	−0.887595	−	0.644876i	−0.935250	+	0.353988i	$0.884825\pi$
$882$	34.0458	+	17.3472i	1.14638	+	0.584111i
$883$	−16.6396	+	2.63545i	−0.559966	+	0.0886900i	−0.430001	−	0.902829i	$-0.641487\pi$
$883$	−16.6396	+	2.63545i	−0.559966	+	0.0886900i	−0.129966	+	0.991519i	$0.541487\pi$
$884$	−21.4489	−	66.0130i	−0.721405	−	2.22026i
$885$		0			0
$886$	0.665718	+	0.916282i	0.0223652	+	0.0307831i
$887$	−10.0941	−	19.8108i	−0.338928	−	0.665183i	0.657141	−	0.753768i	$-0.271766\pi$
$887$	−10.0941	−	19.8108i	−0.338928	−	0.665183i	−0.996069	+	0.0885846i	$0.971766\pi$
$888$	−6.13039	+	38.7058i	−0.205723	+	1.29888i
$889$	6.20130	−	2.01492i	0.207985	−	0.0675784i
$890$		0			0
$891$	−0.514638	+	1.58389i	−0.0172410	+	0.0530624i
$892$	31.2917	−	31.2917i	1.04772	−	1.04772i
$893$	−4.08999	−	4.08999i	−0.136866	−	0.136866i
$894$	−76.0793	−	24.7197i	−2.54447	−	0.826749i
$895$		0			0
$896$	−2.75661	+	8.48398i	−0.0920919	+	0.283430i
$897$	−21.0403	−	3.33246i	−0.702515	−	0.111267i
$898$	31.9842	+	5.06579i	1.06733	+	0.169048i
$899$			29.0621i			0.969277i
$900$		0			0
$901$		−	7.78890i		−	0.259486i
$902$	−0.704474	+	4.44788i	−0.0234564	+	0.148098i
$903$	2.93114	+	0.464247i	0.0975423	+	0.0154492i
$904$	22.5298			0.749331
$905$		0			0
$906$	10.0780	−	31.0169i	0.334819	−	1.03047i
$907$	13.1949	+	13.1949i	0.438131	+	0.438131i	0.891383	−	0.453252i	$-0.149736\pi$
$907$	13.1949	+	13.1949i	0.438131	+	0.438131i	−0.453252	+	0.891383i	$0.649736\pi$
$908$	−2.20890	+	2.20890i	−0.0733050	+	0.0733050i
$909$	−10.6213	+	32.6889i	−0.352285	+	1.08422i
$910$		0			0
$911$	7.69141	−	2.49909i	0.254828	−	0.0827985i	−0.178817	−	0.983882i	$-0.557227\pi$
$911$	7.69141	−	2.49909i	0.254828	−	0.0827985i	0.433645	+	0.901084i	$0.357227\pi$
$912$	5.94310	+	37.5233i	0.196796	+	1.24252i
$913$	2.76967	+	5.43579i	0.0916627	+	0.179898i
$914$	33.9401	−	24.6589i	1.12264	−	0.815645i
$915$		0			0
$916$	11.5582	−	3.75550i	0.381895	−	0.124085i
$917$	−6.88557	+	1.09057i	−0.227382	+	0.0360137i
$918$	−11.7082	+	22.9786i	−0.386428	+	0.758408i
$919$	−22.9679	−	16.6871i	−0.757640	−	0.550458i	0.140546	−	0.990074i	$-0.455114\pi$
$919$	−22.9679	−	16.6871i	−0.757640	−	0.550458i	−0.898186	+	0.439617i	$0.855114\pi$
$920$		0			0
$921$	−3.92285	+	2.85011i	−0.129262	+	0.0939145i
$922$	4.30046	+	27.1520i	0.141628	+	0.894204i
$923$	−60.7529	−	30.9551i	−1.99971	−	1.01890i
$924$	−1.51846	+	1.10323i	−0.0499538	+	0.0362936i
$925$		0			0
$926$	−11.0713	−	34.0740i	−0.363826	−	1.11974i
$927$	22.1453	+	11.2836i	0.727347	+	0.370602i
$928$	−2.55876	+	16.1554i	−0.0839954	+	0.530326i
$929$	8.36507	+	11.5135i	0.274449	+	0.377747i	0.923885	−	0.382669i	$-0.124995\pi$
$929$	8.36507	+	11.5135i	0.274449	+	0.377747i	−0.649436	+	0.760416i	$0.724995\pi$
$930$		0			0
$931$	−18.2193	−	13.2371i	−0.597114	−	0.433829i
$932$	−31.2033	−	4.94212i	−1.02210	−	0.161885i
$933$	2.63540	+	16.6393i	0.0862792	+	0.544745i
$934$	−18.0462			−0.590490
$935$		0			0
$936$	23.4287	−	72.1062i	0.765791	−	2.35686i
$937$	14.8036	−	7.54279i	0.483611	−	0.246412i	−0.195147	−	0.980774i	$-0.562518\pi$
$937$	14.8036	−	7.54279i	0.483611	−	0.246412i	0.678758	+	0.734362i	$0.262518\pi$
$938$	−4.97283	+	4.97283i	−0.162369	+	0.162369i
$939$	7.66941	−	2.49194i	0.250282	−	0.0813215i
$940$		0			0
$941$	−46.6912	−	15.1709i	−1.52209	−	0.494556i	−0.575720	−	0.817647i	$-0.695278\pi$
$941$	−46.6912	−	15.1709i	−1.52209	−	0.494556i	−0.946368	+	0.323090i	$0.895278\pi$
$942$	−19.3808	+	9.87502i	−0.631461	+	0.321745i
$943$	−6.36865	−	6.36865i	−0.207392	−	0.207392i
$944$	−26.4553	−	36.4126i	−0.861046	−	1.18513i
$945$		0			0
$946$	0.514622	−	0.708317i	0.0167318	−	0.0230294i
$947$	−18.7002	−	2.96183i	−0.607676	−	0.0962464i	−0.154989	−	0.987916i	$-0.549534\pi$
$947$	−18.7002	−	2.96183i	−0.607676	−	0.0962464i	−0.452687	+	0.891670i	$0.649534\pi$
$948$	−10.9999	−	69.4506i	−0.357260	−	2.25565i
$949$	76.7139			2.49024
$950$		0			0
$951$			31.3639i			1.01705i
$952$	10.8981	−	5.55284i	0.353208	−	0.179968i
$953$	3.24504	−	20.4884i	0.105117	−	0.663683i	−0.877715	−	0.479183i	$-0.840933\pi$
$953$	3.24504	−	20.4884i	0.105117	−	0.663683i	0.982832	−	0.184501i	$-0.0590668\pi$
$954$	5.00078	−	6.88299i	0.161906	−	0.222845i
$955$		0			0
$956$		−	2.08059i		−	0.0672910i
$957$	−2.43352	+	2.43352i	−0.0786647	+	0.0786647i
$958$	−16.9431	−	33.2527i	−0.547407	−	1.07435i
$959$	−0.238918	+	0.735315i	−0.00771507	+	0.0237445i
$960$		0			0
$961$	−21.6376	−	66.5938i	−0.697989	−	2.14819i
$962$	−32.5925	+	32.5925i	−1.05082	+	1.05082i
$963$	−5.01376	−	9.84005i	−0.161566	−	0.317091i
$964$	10.8555	−	14.9413i	0.349631	−	0.481225i
$965$		0			0
$966$		−	3.75385i		−	0.120778i
$967$	−26.8233	+	4.24840i	−0.862580	+	0.136619i	−0.572022	−	0.820238i	$-0.693841\pi$
$967$	−26.8233	+	4.24840i	−0.862580	+	0.136619i	−0.290558	+	0.956857i	$0.593841\pi$
$968$	−4.78048	−	30.1827i	−0.153650	−	0.970110i
$969$	30.6178	−	42.1418i	0.983586	−	1.35379i
$970$		0			0
$971$	−24.7010	+	17.9463i	−0.792692	+	0.575924i	−0.908761	−	0.417317i	$-0.862971\pi$
$971$	−24.7010	+	17.9463i	−0.792692	+	0.575924i	0.116069	+	0.993241i	$0.462971\pi$
$972$	35.8185	−	18.2504i	1.14888	−	0.585382i
$973$	−5.35688	+	10.5135i	−0.171734	+	0.337046i
$974$	6.31759	−	2.05271i	0.202429	−	0.0657731i
$975$		0			0
$976$	18.2835	+	5.94066i	0.585239	+	0.190156i
$977$	−19.6333	+	38.5326i	−0.628126	+	1.23277i	0.329337	+	0.944212i	$0.393175\pi$
$977$	−19.6333	+	38.5326i	−0.628126	+	1.23277i	−0.957463	+	0.288555i	$0.906825\pi$
$978$	−6.50024	−	41.0409i	−0.207855	−	1.31234i
$979$	−0.876013	−	1.20573i	−0.0279975	−	0.0385352i
$980$		0			0
$981$	−40.2563	+	55.4081i	−1.28529	+	1.76904i
$982$	−34.7494	−	17.7057i	−1.10890	−	0.565012i
$983$	9.39639	+	59.3265i	0.299698	+	1.89222i	0.433405	+	0.901200i	$0.357312\pi$
$983$	9.39639	+	59.3265i	0.299698	+	1.89222i	−0.133706	+	0.991021i	$0.542688\pi$
$984$	44.2990	−	32.1851i	1.41220	−	1.02602i
$985$		0			0
$986$	18.1438	−	13.1823i	0.577818	−	0.419809i
$987$	−3.09591	+	1.57744i	−0.0985439	+	0.0502106i
$988$	−20.2864	+	39.8142i	−0.645395	+	1.26666i
$989$	0.541106	+	1.66535i	0.0172062	+	0.0529551i
$990$		0			0
$991$	−43.5569	−	14.1525i	−1.38363	−	0.449569i	−0.479770	−	0.877394i	$-0.659280\pi$
$991$	−43.5569	−	14.1525i	−1.38363	−	0.449569i	−0.903862	+	0.427825i	$0.859280\pi$
$992$	−8.89433	−	56.1566i	−0.282395	−	1.78297i
$993$	−49.7245	+	49.7245i	−1.57796	+	1.57796i
$994$	3.71290	−	11.4271i	0.117766	−	0.362447i
$995$		0			0
$996$	22.9228	−	70.5491i	0.726337	−	2.23543i
$997$	3.20301	−	20.2230i	0.101440	−	0.640468i	−0.883613	−	0.468218i	$-0.844896\pi$
$997$	3.20301	−	20.2230i	0.101440	−	0.640468i	0.985053	−	0.172250i	$-0.0551038\pi$
$998$	49.9932	+	7.91815i	1.58251	+	0.250645i
$999$	17.1259			0.541839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.v.b.107.1		8
5.2	odd	4		200.2.v.b.83.1	yes	8
5.3	odd	4		1000.2.v.c.643.1		8
5.4	even	2		1000.2.v.d.107.1		8
8.3	odd	2		1000.2.v.a.107.1		8
20.7	even	4		800.2.bp.a.783.1		8
25.3	odd	20		1000.2.v.a.243.1		8
25.4	even	10		200.2.v.a.147.1	yes	8
25.21	even	5		1000.2.v.f.507.1		8
25.22	odd	20		1000.2.v.e.243.1		8
40.3	even	4		1000.2.v.f.643.1		8
40.19	odd	2		1000.2.v.e.107.1		8
40.27	even	4		200.2.v.a.83.1	✓	8
40.37	odd	4		800.2.bp.b.783.1		8
100.79	odd	10		800.2.bp.b.47.1		8
200.3	even	20	inner	1000.2.v.b.243.1		8
200.29	even	10		800.2.bp.a.47.1		8
200.147	even	20		1000.2.v.d.243.1		8
200.171	odd	10		1000.2.v.c.507.1		8
200.179	odd	10		200.2.v.b.147.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.v.a.83.1	✓	8	40.27	even	4
200.2.v.a.147.1	yes	8	25.4	even	10
200.2.v.b.83.1	yes	8	5.2	odd	4
200.2.v.b.147.1	yes	8	200.179	odd	10
800.2.bp.a.47.1		8	200.29	even	10
800.2.bp.a.783.1		8	20.7	even	4
800.2.bp.b.47.1		8	100.79	odd	10
800.2.bp.b.783.1		8	40.37	odd	4
1000.2.v.a.107.1		8	8.3	odd	2
1000.2.v.a.243.1		8	25.3	odd	20
1000.2.v.b.107.1		8	1.1	even	1	trivial
1000.2.v.b.243.1		8	200.3	even	20	inner
1000.2.v.c.507.1		8	200.171	odd	10
1000.2.v.c.643.1		8	5.3	odd	4
1000.2.v.d.107.1		8	5.4	even	2
1000.2.v.d.243.1		8	200.147	even	20
1000.2.v.e.107.1		8	40.19	odd	2
1000.2.v.e.243.1		8	25.22	odd	20
1000.2.v.f.507.1		8	25.21	even	5
1000.2.v.f.643.1		8	40.3	even	4

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.v (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.221232 + 1.39680i) q^{2} +(0.420808 - 2.65688i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(3.61803 + 1.17557i) q^{6} +(-0.557537 + 0.557537i) q^{7} +(1.28408 - 2.52015i) q^{8} +(-4.02874 - 1.30902i) q^{9} +O(q^{10})\)	\(q+(-0.221232 + 1.39680i) q^{2} +(0.420808 - 2.65688i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(3.61803 + 1.17557i) q^{6} +(-0.557537 + 0.557537i) q^{7} +(1.28408 - 2.52015i) q^{8} +(-4.02874 - 1.30902i) q^{9} +(-0.136729 - 0.420808i) q^{11} +(-2.44246 + 4.79360i) q^{12} +(-5.63818 + 2.87280i) q^{13} +(-0.655423 - 0.902113i) q^{14} +(3.23607 + 2.35114i) q^{16} +(-0.857960 - 5.41695i) q^{17} +(2.71972 - 5.33776i) q^{18} +(-2.07533 + 2.85645i) q^{19} +(1.24669 + 1.71592i) q^{21} +(0.618034 - 0.0978870i) q^{22} +(-0.568158 + 1.11507i) q^{23} +(-6.15537 - 4.47214i) q^{24} +(-2.76538 - 8.51098i) q^{26} +(-1.50953 + 2.96261i) q^{27} +(1.40507 - 0.715921i) q^{28} +(2.33927 - 1.69958i) q^{29} +(-5.90778 + 8.13136i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-1.17557 + 0.186192i) q^{33} +7.75621 q^{34} +(6.85410 + 4.97980i) q^{36} +(-2.33833 - 4.58924i) q^{37} +(-3.53077 - 3.53077i) q^{38} +(5.26007 + 16.1888i) q^{39} +(-2.22394 + 6.84458i) q^{41} +(-2.67261 + 1.36176i) q^{42} +(0.989378 - 0.989378i) q^{43} +0.884927i q^{44} +(-1.43184 - 1.04029i) q^{46} +(-0.256271 + 1.61803i) q^{47} +(7.60845 - 7.60845i) q^{48} +6.37831i q^{49} -14.7532 q^{51} +(12.4999 - 1.97980i) q^{52} +(1.40269 + 0.222164i) q^{53} +(-3.80423 - 2.76393i) q^{54} +(0.689153 + 2.12099i) q^{56} +(6.71592 + 6.71592i) q^{57} +(1.85645 + 3.64349i) q^{58} +(-10.7014 - 3.47709i) q^{59} +(4.57086 - 1.48516i) q^{61} +(-10.0509 - 10.0509i) q^{62} +(2.97599 - 1.51634i) q^{63} +(-4.70228 - 6.47214i) q^{64} -1.68323i q^{66} +(-0.986616 - 6.22925i) q^{67} +(-1.71592 + 10.8339i) q^{68} +(2.72353 + 1.97876i) q^{69} +(6.33354 + 8.71737i) q^{71} +(-8.47214 + 8.47214i) q^{72} +(-10.8018 - 5.50380i) q^{73} +(6.92757 - 2.25090i) q^{74} +(5.71290 - 4.15067i) q^{76} +(0.310847 + 0.158384i) q^{77} +(-23.7763 + 3.76580i) q^{78} +(-10.5738 + 7.68233i) q^{79} +(-3.04508 - 2.21238i) q^{81} +(-9.06851 - 4.62064i) q^{82} +(-13.6183 + 2.15693i) q^{83} +(-1.31085 - 4.03437i) q^{84} +(1.16308 + 1.60085i) q^{86} +(-3.53118 - 6.93033i) q^{87} +(-1.23607 - 0.195774i) q^{88} +(3.20347 - 1.04087i) q^{89} +(1.54180 - 4.74518i) q^{91} +(1.76985 - 1.76985i) q^{92} +(19.1180 + 19.1180i) q^{93} +(-2.20338 - 0.715921i) q^{94} +(8.94427 + 12.3107i) q^{96} +(-0.281373 - 0.0445651i) q^{97} +(-8.90923 - 1.41108i) q^{98} +1.87431i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 20 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 + 20 * q^6 - 4 * q^7 + 4 * q^8	\( 8 q - 2 q^{2} + 20 q^{6} - 4 q^{7} + 4 q^{8} - 4 q^{11} - 20 q^{12} - 12 q^{13} - 20 q^{14} + 8 q^{16} - 10 q^{17} - 6 q^{18} + 10 q^{19} - 20 q^{21} - 4 q^{22} + 8 q^{23} - 4 q^{26} - 12 q^{28} + 10 q^{29} + 10 q^{31} - 32 q^{32} + 20 q^{34} + 28 q^{36} - 14 q^{37} + 8 q^{38} + 30 q^{39} + 16 q^{41} - 20 q^{42} + 20 q^{43} - 24 q^{46} - 24 q^{47} - 20 q^{51} + 36 q^{52} + 28 q^{53} - 24 q^{56} + 60 q^{57} - 10 q^{58} - 10 q^{59} - 10 q^{61} - 20 q^{62} + 18 q^{63} + 10 q^{67} - 20 q^{68} - 40 q^{69} + 20 q^{71} - 32 q^{72} + 10 q^{73} + 10 q^{74} - 4 q^{76} + 32 q^{77} - 60 q^{78} - 30 q^{79} - 2 q^{81} - 24 q^{82} - 40 q^{84} + 20 q^{86} - 20 q^{87} + 8 q^{88} + 10 q^{89} - 8 q^{91} + 16 q^{92} + 80 q^{93} + 20 q^{94} - 30 q^{97} + 22 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 20 * q^6 - 4 * q^7 + 4 * q^8 - 4 * q^11 - 20 * q^12 - 12 * q^13 - 20 * q^14 + 8 * q^16 - 10 * q^17 - 6 * q^18 + 10 * q^19 - 20 * q^21 - 4 * q^22 + 8 * q^23 - 4 * q^26 - 12 * q^28 + 10 * q^29 + 10 * q^31 - 32 * q^32 + 20 * q^34 + 28 * q^36 - 14 * q^37 + 8 * q^38 + 30 * q^39 + 16 * q^41 - 20 * q^42 + 20 * q^43 - 24 * q^46 - 24 * q^47 - 20 * q^51 + 36 * q^52 + 28 * q^53 - 24 * q^56 + 60 * q^57 - 10 * q^58 - 10 * q^59 - 10 * q^61 - 20 * q^62 + 18 * q^63 + 10 * q^67 - 20 * q^68 - 40 * q^69 + 20 * q^71 - 32 * q^72 + 10 * q^73 + 10 * q^74 - 4 * q^76 + 32 * q^77 - 60 * q^78 - 30 * q^79 - 2 * q^81 - 24 * q^82 - 40 * q^84 + 20 * q^86 - 20 * q^87 + 8 * q^88 + 10 * q^89 - 8 * q^91 + 16 * q^92 + 80 * q^93 + 20 * q^94 - 30 * q^97 + 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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