LMFDB - Embedded newform 1000.2.v.d.243.1

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			243.1
Root			$-0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	1000.243
Dual form			1000.2.v.d.107.1

$q$-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 $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$-1$	$-1$

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	−0.743794	−	0.668409i	$-0.766976\pi$
$3$	−0.420808	−	2.65688i	−0.242953	−	1.53395i	0.500841	−	0.865539i	$-0.333024\pi$
$4$	−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	$-0.202392\pi$
$7$	0.557537	+	0.557537i	0.210729	+	0.210729i	−0.593848	+	0.804577i	$0.702392\pi$
$8$	−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	−0.969551	−	0.244890i	$-0.921248\pi$
$11$	−0.136729	+	0.420808i	−0.0412253	+	0.126878i	0.928326	+	0.371768i	$0.121248\pi$
$12$	2.44246	+	4.79360i	0.705078	+	1.38379i
$13$	5.63818	+	2.87280i	1.56375	+	0.796770i	0.999583	−	0.0288899i	$-0.00919723\pi$
$13$	5.63818	+	2.87280i	1.56375	+	0.796770i	0.564167	+	0.825660i	$0.309197\pi$
$14$	−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	−0.633526	−	0.773721i	$-0.718393\pi$
$17$	0.857960	−	5.41695i	0.208086	−	1.31380i	0.841612	−	0.540082i	$-0.181607\pi$
$18$	−2.71972	−	5.33776i	−0.641045	−	1.25812i
$19$	−2.07533	−	2.85645i	−0.476114	−	0.655315i	0.501638	−	0.865078i	$-0.332731\pi$
$19$	−2.07533	−	2.85645i	−0.476114	−	0.655315i	−0.977752	+	0.209763i	$0.932731\pi$
$20$		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	$-0.108350\pi$
$23$	0.568158	+	1.11507i	0.118469	+	0.232509i	−0.824155	+	0.566364i	$0.808350\pi$
$24$	−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	0.783402	−	0.621515i	$-0.213483\pi$
$29$	2.33927	+	1.69958i	0.434391	+	0.315603i	−0.349011	+	0.937118i	$0.613483\pi$
$30$		0			0
$31$	−5.90778	−	8.13136i	−1.06107	−	1.46044i	−0.878802	−	0.477186i	$-0.841657\pi$
$31$	−5.90778	−	8.13136i	−1.06107	−	1.46044i	−0.182267	−	0.983249i	$-0.558343\pi$
$32$	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	$-0.710844\pi$
$37$	2.33833	−	4.58924i	0.384420	−	0.754466i	0.999420	+	0.0340610i	$0.0108441\pi$
$38$	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	−0.960330	−	0.278867i	$-0.910041\pi$
$41$	−2.22394	−	6.84458i	−0.347321	−	1.06894i	0.613009	−	0.790076i	$-0.289959\pi$
$42$	2.67261	+	1.36176i	0.412393	+	0.210125i
$43$	−0.989378	−	0.989378i	−0.150879	−	0.150879i	0.627632	−	0.778510i	$-0.284024\pi$
$43$	−0.989378	−	0.989378i	−0.150879	−	0.150879i	−0.778510	+	0.627632i	$0.784024\pi$
$44$		−	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	$-0.0118778\pi$
$47$	0.256271	+	1.61803i	0.0373810	+	0.236015i	−0.961923	+	0.273321i	$0.911878\pi$
$48$	−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	$-0.581097\pi$
$53$	−1.40269	+	0.222164i	−0.192674	+	0.0305166i	0.0593515	+	0.998237i	$0.481097\pi$
$54$	−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	−0.906986	−	0.421160i	$-0.861623\pi$
$59$	−10.7014	+	3.47709i	−1.39320	+	0.452679i	−0.486215	+	0.873839i	$0.661623\pi$
$60$		0			0
$61$	4.57086	+	1.48516i	0.585239	+	0.190156i	0.586646	−	0.809843i	$-0.300448\pi$
$61$	4.57086	+	1.48516i	0.585239	+	0.190156i	−0.00140712	+	0.999999i	$0.500448\pi$
$62$	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	−0.851182	−	0.524871i	$-0.824113\pi$
$67$	0.986616	−	6.22925i	0.120534	−	0.761024i	0.971716	−	0.236153i	$-0.0758865\pi$
$68$	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	−0.246210	−	0.969217i	$-0.579185\pi$
$71$	6.33354	−	8.71737i	0.751653	−	1.03456i	0.997863	−	0.0653452i	$-0.0208149\pi$
$72$	8.47214	+	8.47214i	0.998451	+	0.998451i
$73$	10.8018	−	5.50380i	1.26426	−	0.644171i	0.312178	−	0.950024i	$-0.398941\pi$
$73$	10.8018	−	5.50380i	1.26426	−	0.644171i	0.952079	+	0.305852i	$0.0989413\pi$
$74$	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	−0.196421	−	0.980520i	$-0.562932\pi$
$79$	−10.5738	−	7.68233i	−1.18965	−	0.864330i	−0.993227	+	0.116190i	$0.962932\pi$
$80$		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	$-0.176801\pi$
$83$	13.6183	+	2.15693i	1.49481	+	0.236754i	0.645136	+	0.764068i	$0.276801\pi$
$84$	−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	0.473837	−	0.880613i	$-0.342869\pi$
$89$	3.20347	+	1.04087i	0.339567	+	0.110332i	−0.134269	+	0.990945i	$0.542869\pi$
$90$		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	$-0.545396\pi$
$97$	0.281373	−	0.0445651i	0.0285691	−	0.00452490i	0.170703	+	0.985323i	$0.445396\pi$
$98$	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	$0.132270\pi$
$101$			8.11392i			0.807365i	−0.914899	+	0.403683i	$0.867730\pi$
$102$	−3.26388	−	20.6073i	−0.323172	−	2.04043i
$103$	5.79506	−	0.917847i	0.571004	−	0.0904381i	0.135746	−	0.990744i	$-0.456657\pi$
$103$	5.79506	−	0.917847i	0.571004	−	0.0904381i	0.435258	+	0.900306i	$0.356657\pi$
$104$		−	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	$-0.790220\pi$
$107$	−1.84348	+	1.84348i	−0.178216	+	0.178216i	0.612362	+	0.790578i	$0.290220\pi$
$108$	−4.70228	−	4.70228i	−0.452477	−	0.452477i
$109$	4.99614	+	15.3765i	0.478544	+	1.47281i	0.841118	+	0.540851i	$0.181898\pi$
$109$	4.99614	+	15.3765i	0.478544	+	1.47281i	−0.362575	+	0.931955i	$0.618102\pi$
$110$		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	$-0.972242\pi$
$113$	−3.61626	+	7.09731i	−0.340189	+	0.667659i	0.656011	+	0.754751i	$0.272242\pi$
$114$	−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	$-0.530417\pi$
$127$	7.36833	−	3.75435i	0.653833	−	0.333145i	0.749245	+	0.662293i	$0.230417\pi$
$128$	−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	−0.229689	−	0.973264i	$-0.573771\pi$
$131$	7.15302	−	5.19697i	0.624962	−	0.454061i	0.854651	+	0.519203i	$0.173771\pi$
$132$	−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	$-0.363337\pi$
$137$	−0.873694	−	0.445169i	−0.0746447	−	0.0380334i	−0.490914	+	0.871208i	$0.663337\pi$
$138$	3.36646	+	3.36646i	0.286572	+	0.286572i
$139$	14.2326	+	4.62444i	1.20719	+	0.392240i	0.842402	−	0.538850i	$-0.181141\pi$
$139$	14.2326	+	4.62444i	1.20719	+	0.392240i	0.364789	+	0.931090i	$0.381141\pi$
$140$		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	$0.113419\pi$
$151$			8.57286i			0.697649i	−0.937188	+	0.348825i	$0.886581\pi$
$152$	−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	$-0.176728\pi$
$157$	4.04306	+	4.04306i	0.322671	+	0.322671i	−0.527120	+	0.849791i	$0.676728\pi$
$158$	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	$-0.709301\pi$
$163$	4.95881	−	9.73221i	0.388404	−	0.762285i	0.999573	+	0.0292144i	$0.00930056\pi$
$164$	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	$-0.611711\pi$
$167$	−12.4180	−	1.96683i	−0.960937	−	0.152198i	−0.617146	+	0.786849i	$0.711711\pi$
$168$	−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	−0.999782	−	0.0208630i	$-0.993359\pi$
$173$	−5.64266	−	11.0743i	−0.429004	−	0.841967i	0.570779	−	0.821104i	$-0.306641\pi$
$174$	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	−0.960360	−	0.278764i	$-0.910075\pi$
$179$	−5.33119	+	7.33776i	−0.398472	+	0.548450i	0.561888	+	0.827214i	$0.310075\pi$
$180$		0			0
$181$	7.70946	+	10.6112i	0.573039	+	0.788721i	0.992911	−	0.118863i	$-0.0379248\pi$
$181$	7.70946	+	10.6112i	0.573039	+	0.788721i	−0.419871	+	0.907584i	$0.637925\pi$
$182$	−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	−0.867150	−	0.498047i	$-0.834051\pi$
$191$	−17.6339	+	5.72960i	−1.27594	+	0.414580i	−0.408795	+	0.912626i	$0.634051\pi$
$192$	19.1744	+	9.76985i	1.38379	+	0.705078i
$193$	−11.2519	−	11.2519i	−0.809933	−	0.809933i	0.174691	−	0.984623i	$-0.444107\pi$
$193$	−11.2519	−	11.2519i	−0.809933	−	0.809933i	−0.984623	+	0.174691i	$0.944107\pi$
$194$	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	0.999074	+	0.0430155i	$0.0136965\pi$
$197$	0.872888	+	5.51120i	0.0621907	+	0.392657i	−0.936884	+	0.349641i	$0.886304\pi$
$198$	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	−0.955971	−	0.293461i	$-0.905193\pi$
$211$	−0.146453	+	0.450735i	−0.0100822	+	0.0310299i	0.945889	+	0.324491i	$0.105193\pi$
$212$	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	0.934801	+	0.355173i	$0.115578\pi$
$223$	10.0452	+	19.7149i	0.672680	+	1.32021i	−0.262121	+	0.965035i	$0.584422\pi$
$224$			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	$-0.166507\pi$
$227$	−0.709101	−	1.39169i	−0.0470647	−	0.0923697i	−0.913341	+	0.407195i	$0.866507\pi$
$228$	8.62377	−	16.9251i	0.571123	−	1.12089i
$229$	−4.91602	−	3.57170i	−0.324860	−	0.236024i	0.413387	−	0.910556i	$-0.364346\pi$
$229$	−4.91602	−	3.57170i	−0.324860	−	0.236024i	−0.738246	+	0.674531i	$0.764346\pi$
$230$		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	$-0.623107\pi$
$233$	−15.6017	−	2.47106i	−1.02210	−	0.161885i	−0.644916	+	0.764254i	$0.723107\pi$
$234$		−	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	−0.940121	−	0.340841i	$-0.889288\pi$
$239$	0.321469	−	0.989378i	0.0207941	−	0.0639976i	0.960915	+	0.276843i	$0.0892883\pi$
$240$		0			0
$241$	−2.85353	−	8.78225i	−0.183812	−	0.565714i	0.816114	−	0.577891i	$-0.196124\pi$
$241$	−2.85353	−	8.78225i	−0.183812	−	0.565714i	−0.999926	+	0.0121764i	$0.996124\pi$
$242$	−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	$-0.745794\pi$
$257$	0.299558	−	0.299558i	0.0186859	−	0.0186859i	0.716388	+	0.697702i	$0.245794\pi$
$258$	−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	$-0.221533\pi$
$263$	11.3494	+	5.78283i	0.699836	+	0.356584i	−0.0675976	+	0.997713i	$0.521533\pi$
$264$	−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	−0.829009	−	0.559235i	$-0.811095\pi$
$269$	−9.07519	+	6.59351i	−0.553324	+	0.402013i	0.275686	+	0.961248i	$0.411095\pi$
$270$		0			0
$271$	−6.43240	+	8.85343i	−0.390740	+	0.537808i	−0.958390	−	0.285462i	$-0.907853\pi$
$271$	−6.43240	+	8.85343i	−0.390740	+	0.537808i	0.567650	+	0.823270i	$0.307853\pi$
$272$	−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	$-0.565781\pi$
$277$	7.75589	−	3.95183i	0.466006	−	0.237442i	0.671196	+	0.741280i	$0.265781\pi$
$278$	−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	−0.331857	−	0.943330i	$-0.607675\pi$
$281$	7.75715	−	5.63590i	0.462753	−	0.336209i	0.794610	+	0.607120i	$0.207675\pi$
$282$	2.82931	+	5.55284i	0.168483	+	0.330667i
$283$	−7.35420	−	1.16479i	−0.437162	−	0.0692397i	−0.0660254	−	0.997818i	$-0.521032\pi$
$283$	−7.35420	−	1.16479i	−0.437162	−	0.0692397i	−0.371137	+	0.928578i	$0.621032\pi$
$284$	−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	$-0.616622\pi$
$293$	9.84915	−	9.84915i	0.575393	−	0.575393i	0.933631	+	0.358237i	$0.116622\pi$
$294$	−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	$-0.733619\pi$
$307$	1.27461	−	1.27461i	0.0727458	−	0.0727458i	0.742544	+	0.669798i	$0.233619\pi$
$308$	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	0.135234	−	0.990814i	$-0.456821\pi$
$311$	−5.95620	−	1.93529i	−0.337745	−	0.109740i	−0.472979	+	0.881074i	$0.656821\pi$
$312$	−47.5526	+	7.53159i	−2.69214	+	0.426393i
$313$	−1.36098	+	2.67107i	−0.0769270	+	0.150978i	−0.926266	−	0.376869i	$-0.877001\pi$
$313$	−1.36098	+	2.67107i	−0.0769270	+	0.150978i	0.849339	+	0.527847i	$0.177001\pi$
$314$	−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	$-0.343817\pi$
$317$	11.5159	+	1.82394i	0.646799	+	0.102443i	0.175589	+	0.984464i	$0.443817\pi$
$318$	−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	−0.990087	−	0.140455i	$-0.955143\pi$
$331$	−21.1491	+	15.3657i	−1.16246	+	0.844576i	−0.172373	+	0.985032i	$0.555143\pi$
$332$	−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	$-0.553346\pi$
$337$	−19.5056	−	9.93860i	−1.06254	−	0.541390i	−0.895730	+	0.444599i	$0.853346\pi$
$338$	−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	$-0.637581\pi$
$347$	−9.99724	+	1.58341i	−0.536680	+	0.0850017i	−0.117790	+	0.993039i	$0.537581\pi$
$348$	−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	0.884558	+	0.466430i	$0.154460\pi$
$353$	3.52146	+	22.2336i	0.187428	+	1.18338i	−0.697130	+	0.716945i	$0.745540\pi$
$354$	−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	−0.999860	−	0.0167120i	$-0.994680\pi$
$359$	−3.80423	−	11.7082i	−0.200779	−	0.617935i	0.799081	−	0.601223i	$-0.205320\pi$
$360$		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	$-0.186041\pi$
$367$	27.9062	+	4.41991i	1.45669	+	0.230717i	0.622686	+	0.782472i	$0.286041\pi$
$368$	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	$-0.214935\pi$
$373$	−3.55258	−	6.97233i	−0.183946	−	0.361014i	−0.964504	+	0.264070i	$0.914935\pi$
$374$	−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	−0.351314	−	0.936258i	$-0.614265\pi$
$379$	12.6090	−	17.3548i	0.647682	−	0.891458i	0.998996	+	0.0447999i	$0.0142650\pi$
$380$		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	$-0.914666\pi$
$383$	0.678276	−	4.28247i	0.0346583	−	0.218824i	0.998939	+	0.0460597i	$0.0146664\pi$
$384$	−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	−0.997385	−	0.0722702i	$-0.976976\pi$
$389$	−2.91910	+	8.98407i	−0.148004	+	0.455510i	0.849381	+	0.527780i	$0.176976\pi$
$390$		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	0.605539	+	0.795816i	$0.292958\pi$
$397$	5.49045	+	34.6653i	0.275558	+	1.73980i	−0.329981	+	0.943988i	$0.607042\pi$
$398$	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	−0.578362	−	0.815780i	$-0.696308\pi$
$409$	−11.4621	+	3.72426i	−0.566764	+	0.184153i	0.0115985	+	0.999933i	$0.496308\pi$
$410$		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	0.738651	−	0.674088i	$-0.235463\pi$
$419$	−2.67537	−	3.68233i	−0.130700	−	0.179894i	−0.869352	+	0.494194i	$0.835463\pi$
$420$		0			0
$421$	−17.4848	+	24.0657i	−0.852155	+	1.17289i	0.131229	+	0.991352i	$0.458108\pi$
$421$	−17.4848	+	24.0657i	−0.852155	+	1.17289i	−0.983384	+	0.181538i	$0.941892\pi$
$422$	−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	0.997589	−	0.0694055i	$-0.0221102\pi$
$431$	12.9402	+	17.8107i	0.623308	+	0.857910i	−0.374280	+	0.927316i	$0.622110\pi$
$432$	11.8504	+	6.03810i	0.570155	+	0.290508i
$433$	18.9256	+	2.99752i	0.909505	+	0.144052i	0.593620	−	0.804746i	$-0.297698\pi$
$433$	18.9256	+	2.99752i	0.909505	+	0.144052i	0.315886	+	0.948797i	$0.397698\pi$
$434$	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	−0.978200	−	0.207665i	$-0.933413\pi$
$439$	−1.35681	+	4.17583i	−0.0647569	+	0.199301i	0.913443	+	0.406967i	$0.133413\pi$
$440$		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	$-0.256056\pi$
$443$	−0.566293	−	0.566293i	−0.0269054	−	0.0269054i	−0.720432	+	0.693526i	$0.756056\pi$
$444$	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	$0.181695\pi$
$449$			22.8981i			1.08063i	−0.841463	+	0.540315i	$0.818305\pi$
$450$		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	$-0.505922\pi$
$457$	20.9761	−	20.9761i	0.981222	−	0.981222i	0.999827	+	0.0186046i	$0.00592238\pi$
$458$	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	0.706062	−	0.708150i	$-0.250470\pi$
$461$	18.4873	+	6.00689i	0.861039	+	0.279769i	0.154977	+	0.987918i	$0.450470\pi$
$462$	−0.938463	+	0.938463i	−0.0436612	+	0.0436612i
$463$	22.5727	+	11.5014i	1.04904	+	0.534513i	0.891510	−	0.453001i	$-0.149647\pi$
$463$	22.5727	+	11.5014i	1.04904	+	0.534513i	0.157531	+	0.987514i	$0.449647\pi$
$464$	11.5660			0.536936
$465$		0			0
$466$		−	22.3391i		−	1.03484i
$467$	−1.99620	+	12.6035i	−0.0923730	+	0.583220i	0.897472	+	0.441071i	$0.145401\pi$
$467$	−1.99620	+	12.6035i	−0.0923730	+	0.583220i	−0.989845	+	0.142149i	$0.954599\pi$
$468$	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	−0.0187915	−	0.999823i	$-0.505982\pi$
$479$	−21.3496	−	15.5114i	−0.975487	−	0.708733i	−0.956695	+	0.291091i	$0.905982\pi$
$480$		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	$-0.816060\pi$
$487$	2.13244	−	4.18515i	0.0966302	−	0.189647i	0.934262	+	0.356589i	$0.116060\pi$
$488$	−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	−0.936780	−	0.349918i	$-0.886209\pi$
$491$	−8.52185	−	26.2276i	−0.384586	−	1.18363i	0.552194	−	0.833715i	$-0.313791\pi$
$492$	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	$0.295760\pi$
$499$			35.7912i			1.60223i	−0.598508	+	0.801117i	$0.704240\pi$
$500$		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	$-0.960246\pi$
$503$	−42.5535	+	6.73981i	−1.89737	+	0.300513i	−0.905156	+	0.425080i	$0.860246\pi$
$504$			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	0.998335	+	0.0576867i	$0.0183724\pi$
$509$	5.06658	+	15.5933i	0.224572	+	0.691163i	−0.773762	+	0.633476i	$0.781628\pi$
$510$		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	0.512421	−	0.858734i	$-0.328749\pi$
$521$	−3.33109	−	2.42018i	−0.145937	−	0.106030i	−0.658358	+	0.752705i	$0.728749\pi$
$522$	2.70977	−	17.1088i	0.118603	−	0.748832i
$523$	3.35349	−	1.70869i	0.146638	−	0.0747158i	−0.379132	−	0.925343i	$-0.623777\pi$
$523$	3.35349	−	1.70869i	0.146638	−	0.0747158i	0.525770	+	0.850627i	$0.323777\pi$
$524$	−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	−0.0262040	−	0.999657i	$-0.508342\pi$
$541$	12.5643	−	4.08238i	0.540180	−	0.175515i	0.566384	+	0.824142i	$0.308342\pi$
$542$	−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	$-0.696963\pi$
$547$	−20.5808	+	3.25968i	−0.879971	+	0.139374i	−0.299930	+	0.953961i	$0.596963\pi$
$548$	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	$-0.0836995\pi$
$557$	16.6551	+	16.6551i	0.705697	+	0.705697i	−0.259930	+	0.965627i	$0.583700\pi$
$558$	−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	−0.212644	+	0.977130i	$0.568208\pi$
$563$	−20.8369	+	40.8947i	−0.878170	+	1.72350i	−0.665525	+	0.746375i	$0.731792\pi$
$564$	−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	0.943098	+	0.332516i	$0.107897\pi$
$569$	23.0882	+	31.7781i	0.967906	+	1.33221i	0.0248079	+	0.999692i	$0.492103\pi$
$570$		0			0
$571$	19.4298	+	14.1166i	0.813111	+	0.590760i	0.914731	−	0.404063i	$-0.132402\pi$
$571$	19.4298	+	14.1166i	0.813111	+	0.590760i	−0.101620	+	0.994823i	$0.532402\pi$
$572$	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	$-0.191921\pi$
$577$	−2.86414	−	5.62119i	−0.119236	−	0.234013i	−0.942908	+	0.333052i	$0.891921\pi$
$578$	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	$-0.0730909\pi$
$587$	32.9979	+	16.8133i	1.36197	+	0.693958i	0.388218	+	0.921568i	$0.373091\pi$
$588$	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	$-0.409047\pi$
$593$	−16.5004	−	16.5004i	−0.677590	−	0.677590i	−0.959454	+	0.281864i	$0.909047\pi$
$594$	−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	−0.999667	−	0.0257859i	$-0.991791\pi$
$607$	−25.2645	−	25.2645i	−1.02545	−	1.02545i	−0.0257859	−	0.999667i	$-0.508209\pi$
$608$	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	$-0.0827828\pi$
$613$	32.8390	+	16.7323i	1.32635	+	0.675811i	0.359982	+	0.932959i	$0.382783\pi$
$614$	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	$-0.927333\pi$
$617$	0.552944	−	3.49115i	0.0222607	−	0.140548i	0.996316	+	0.0857638i	$0.0273330\pi$
$618$	19.8877	−	10.1333i	0.800001	−	0.407621i
$619$	−26.6760	−	36.7164i	−1.07220	−	1.47576i	−0.867830	−	0.496861i	$-0.834486\pi$
$619$	−26.6760	−	36.7164i	−1.07220	−	1.47576i	−0.204369	−	0.978894i	$-0.565514\pi$
$620$		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	0.625206	−	0.780460i	$-0.285015\pi$
$631$	−7.79351	−	10.7268i	−0.310255	−	0.427029i	−0.935461	+	0.353431i	$0.885015\pi$
$632$	−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	0.818846	−	0.574014i	$-0.194614\pi$
$641$	−4.58284	−	14.1045i	−0.181011	−	0.557095i	−0.999857	+	0.0169186i	$0.994614\pi$
$642$	−4.50263	+	8.83692i	−0.177705	+	0.348765i
$643$	23.8113	+	23.8113i	0.939027	+	0.939027i	0.998245	−	0.0592183i	$-0.0188608\pi$
$643$	23.8113	+	23.8113i	0.939027	+	0.939027i	−0.0592183	+	0.998245i	$0.518861\pi$
$644$		−	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	0.609669	+	0.792656i	$0.291302\pi$
$647$	6.98945	+	44.1296i	0.274784	+	1.73492i	−0.334885	+	0.942259i	$0.608698\pi$
$648$	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	$-0.550109\pi$
$653$	−0.0172425	+	0.00273094i	−0.000674750	+	0.000106870i	0.156097	+	0.987742i	$0.450109\pi$
$654$	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	0.513482	−	0.858100i	$-0.328355\pi$
$659$	36.7936	−	11.9550i	1.43328	−	0.465700i	0.919795	+	0.392400i	$0.128355\pi$
$660$		0			0
$661$	2.89246	+	0.939818i	0.112504	+	0.0365547i	0.364728	−	0.931114i	$-0.381162\pi$
$661$	2.89246	+	0.939818i	0.112504	+	0.0365547i	−0.252224	+	0.967669i	$0.581162\pi$
$662$	−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	$-0.695165\pi$
$673$	−6.53751	+	3.33103i	−0.252003	+	0.128402i	0.323427	+	0.946253i	$0.395165\pi$
$674$	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	$-0.468707\pi$
$677$	25.0033	−	12.7398i	0.960955	−	0.489631i	0.862803	+	0.505541i	$0.168707\pi$
$678$	−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	$-0.503697\pi$
$683$	−8.66759	−	1.37281i	−0.331656	−	0.0525292i	−0.320042	+	0.947403i	$0.603697\pi$
$684$	−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	−0.963487	−	0.267755i	$-0.913718\pi$
$691$	−8.97413	−	27.6195i	−0.341392	−	1.05070i	0.622095	−	0.782942i	$-0.286282\pi$
$692$	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	$-0.934947\pi$
$701$		−	10.7467i		−	0.405899i	0.979189	−	0.202949i	$-0.0650527\pi$
$702$	−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	0.957476	−	0.288513i	$-0.0931610\pi$
$709$	0.353547	+	1.08811i	0.0132777	+	0.0408647i	−0.944198	+	0.329378i	$0.893161\pi$
$710$		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	−0.565854	−	0.824506i	$-0.691453\pi$
$719$	1.16479	−	0.846270i	0.0434394	−	0.0315606i	0.609293	+	0.792945i	$0.291453\pi$
$720$		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	$-0.709314\pi$
$727$	−8.90163	+	4.53561i	−0.330143	+	0.168216i	0.281060	+	0.959690i	$0.409314\pi$
$728$	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	0.869141	+	0.494564i	$0.164672\pi$
$733$	−2.98599	+	18.8528i	−0.110290	+	0.696344i	−0.979431	+	0.201779i	$0.935328\pi$
$734$			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	−0.311131	−	0.950367i	$-0.600708\pi$
$739$	−30.4862	−	9.90557i	−1.12145	−	0.364382i	−0.810322	+	0.585985i	$0.800708\pi$
$740$		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	−0.0180432	+	0.999837i	$0.505744\pi$
$743$	−27.7454	+	27.7454i	−1.01788	+	1.01788i	−0.999837	+	0.0180432i	$0.994256\pi$
$744$	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	$-0.921704\pi$
$751$		−	13.3460i		−	0.487004i	0.969900	−	0.243502i	$-0.0782963\pi$
$752$	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	$-0.455231\pi$
$757$	−23.3850	−	23.3850i	−0.849943	−	0.849943i	−0.990126	+	0.140182i	$0.955231\pi$
$758$	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	0.760464	+	0.649380i	$0.224971\pi$
$761$	−6.52304	+	20.0758i	−0.236460	+	0.727749i	−0.996924	+	0.0783693i	$0.975029\pi$
$762$	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	−0.793114	−	0.609073i	$-0.791542\pi$
$769$	−31.2607	−	43.0267i	−1.12729	−	1.55158i	−0.334177	−	0.942510i	$-0.608458\pi$
$770$		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	−0.993486	−	0.113957i	$-0.963647\pi$
$773$	−13.9493	−	27.3771i	−0.501722	−	0.984686i	0.491763	−	0.870729i	$-0.336353\pi$
$774$	−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	$-0.124628\pi$
$787$	32.5114	+	16.5654i	1.15891	+	0.590493i	0.234581	+	0.972097i	$0.424628\pi$
$788$	−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	$-0.0838080\pi$
$797$	−0.936362	−	5.91196i	−0.0331677	−	0.209412i	−0.998706	+	0.0508468i	$0.983808\pi$
$798$	−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	−0.781387	−	0.624047i	$-0.785487\pi$
$809$	−29.7722	+	9.67358i	−1.04674	+	0.340105i	−0.265349	+	0.964152i	$0.585487\pi$
$810$		0			0
$811$	1.95623	−	6.02066i	0.0686926	−	0.211414i	−0.910817	−	0.412809i	$-0.864548\pi$
$811$	1.95623	−	6.02066i	0.0686926	−	0.211414i	0.979510	+	0.201395i	$0.0645476\pi$
$812$	−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	−0.509622	−	0.860398i	$-0.670215\pi$
$821$	13.3566	−	18.3837i	0.466147	−	0.641596i	0.975769	+	0.218802i	$0.0702149\pi$
$822$	−3.68438	−	0.583549i	−0.128508	−	0.0203536i
$823$	−5.29231	−	10.3867i	−0.184478	−	0.362059i	0.780183	−	0.625551i	$-0.215126\pi$
$823$	−5.29231	−	10.3867i	−0.184478	−	0.362059i	−0.964662	+	0.263492i	$0.915126\pi$
$824$	−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	$-0.117066\pi$
$827$	2.69680	+	5.29276i	0.0937768	+	0.184047i	−0.839353	+	0.543586i	$0.817066\pi$
$828$	9.44705	+	4.81351i	0.328308	+	0.167281i
$829$	30.1824	+	21.9288i	1.04828	+	0.761619i	0.971884	−	0.235458i	$-0.0756591\pi$
$829$	30.1824	+	21.9288i	1.04828	+	0.761619i	0.0763946	+	0.997078i	$0.475659\pi$
$830$		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	−0.367276	−	0.930112i	$-0.619710\pi$
$839$	13.8039	−	42.4840i	0.476563	−	1.46671i	0.843839	−	0.536597i	$-0.180290\pi$
$840$		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	$-0.517227\pi$
$853$	5.92966	−	0.939165i	0.203028	−	0.0321564i	0.257120	+	0.966380i	$0.417227\pi$
$854$	−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	$-0.778795\pi$
$857$	−3.74007	+	3.74007i	−0.127758	+	0.127758i	0.640336	+	0.768095i	$0.278795\pi$
$858$	−4.83558	+	9.49036i	−0.165084	+	0.323996i
$859$	30.1496	−	9.79621i	1.02869	−	0.334242i	0.254419	−	0.967094i	$-0.418116\pi$
$859$	30.1496	−	9.79621i	1.02869	−	0.334242i	0.774273	+	0.632852i	$0.218116\pi$
$860$		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	$-0.405906\pi$
$863$	−9.14726	−	4.66076i	−0.311376	−	0.158654i	−0.602694	+	0.797972i	$0.705906\pi$
$864$	−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	$-0.555512\pi$
$877$	15.4361	−	7.86511i	0.521241	−	0.265586i	0.694756	+	0.719246i	$0.255512\pi$
$878$	−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	−0.935250	−	0.353988i	$-0.884825\pi$
$881$	−26.3453	+	19.1410i	−0.887595	+	0.644876i	0.0476546	+	0.998864i	$0.484825\pi$
$882$	−34.0458	+	17.3472i	−1.14638	+	0.584111i
$883$	16.6396	+	2.63545i	0.559966	+	0.0886900i	0.430001	−	0.902829i	$-0.358513\pi$
$883$	16.6396	+	2.63545i	0.559966	+	0.0886900i	0.129966	+	0.991519i	$0.458513\pi$
$884$	−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	$-0.728234\pi$
$887$	10.0941	−	19.8108i	0.338928	−	0.665183i	0.996069	+	0.0885846i	$0.0282344\pi$
$888$	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	$-0.850264\pi$
$907$	−13.1949	+	13.1949i	−0.438131	+	0.438131i	0.453252	+	0.891383i	$0.350264\pi$
$908$	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	0.433645	−	0.901084i	$-0.357227\pi$
$911$	7.69141	+	2.49909i	0.254828	+	0.0827985i	−0.178817	+	0.983882i	$0.557227\pi$
$912$	−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	−0.898186	−	0.439617i	$-0.855114\pi$
$919$	−22.9679	+	16.6871i	−0.757640	+	0.550458i	0.140546	+	0.990074i	$0.455114\pi$
$920$		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	−0.649436	−	0.760416i	$-0.724995\pi$
$929$	8.36507	−	11.5135i	0.274449	−	0.377747i	0.923885	+	0.382669i	$0.124995\pi$
$930$		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	$-0.437482\pi$
$937$	−14.8036	−	7.54279i	−0.483611	−	0.246412i	−0.678758	+	0.734362i	$0.737482\pi$
$938$	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	−0.946368	−	0.323090i	$-0.895278\pi$
$941$	−46.6912	+	15.1709i	−1.52209	+	0.494556i	−0.575720	+	0.817647i	$0.695278\pi$
$942$	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	$-0.450466\pi$
$947$	18.7002	−	2.96183i	0.607676	−	0.0962464i	0.452687	+	0.891670i	$0.350466\pi$
$948$	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	−0.982832	−	0.184501i	$-0.940933\pi$
$953$	−3.24504	−	20.4884i	−0.105117	−	0.663683i	0.877715	−	0.479183i	$-0.159067\pi$
$954$	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	$-0.306159\pi$
$967$	26.8233	+	4.24840i	0.862580	+	0.136619i	0.290558	+	0.956857i	$0.406159\pi$
$968$	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	0.116069	−	0.993241i	$-0.462971\pi$
$971$	−24.7010	−	17.9463i	−0.792692	−	0.575924i	−0.908761	+	0.417317i	$0.862971\pi$
$972$	−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	0.957463	+	0.288555i	$0.0931748\pi$
$977$	19.6333	+	38.5326i	0.628126	+	1.23277i	−0.329337	+	0.944212i	$0.606825\pi$
$978$	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	0.133706	+	0.991021i	$0.457312\pi$
$983$	−9.39639	+	59.3265i	−0.299698	+	1.89222i	−0.433405	+	0.901200i	$0.642688\pi$
$984$	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	−0.903862	−	0.427825i	$-0.859280\pi$
$991$	−43.5569	+	14.1525i	−1.38363	+	0.449569i	−0.479770	+	0.877394i	$0.659280\pi$
$992$	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	−0.985053	−	0.172250i	$-0.944896\pi$
$997$	−3.20301	−	20.2230i	−0.101440	−	0.640468i	0.883613	−	0.468218i	$-0.155104\pi$
$998$	−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.d.243.1		8
5.2	odd	4		200.2.v.b.147.1	yes	8
5.3	odd	4		1000.2.v.c.507.1		8
5.4	even	2		1000.2.v.b.243.1		8
8.3	odd	2		1000.2.v.e.243.1		8
20.7	even	4		800.2.bp.a.47.1		8
25.6	even	5		200.2.v.a.83.1	✓	8
25.8	odd	20		1000.2.v.a.107.1		8
25.17	odd	20		1000.2.v.e.107.1		8
25.19	even	10		1000.2.v.f.643.1		8
40.3	even	4		1000.2.v.f.507.1		8
40.19	odd	2		1000.2.v.a.243.1		8
40.27	even	4		200.2.v.a.147.1	yes	8
40.37	odd	4		800.2.bp.b.47.1		8
100.31	odd	10		800.2.bp.b.783.1		8
200.19	odd	10		1000.2.v.c.643.1		8
200.67	even	20	inner	1000.2.v.d.107.1		8
200.83	even	20		1000.2.v.b.107.1		8
200.131	odd	10		200.2.v.b.83.1	yes	8
200.181	even	10		800.2.bp.a.783.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.v.a.83.1	✓	8	25.6	even	5
200.2.v.a.147.1	yes	8	40.27	even	4
200.2.v.b.83.1	yes	8	200.131	odd	10
200.2.v.b.147.1	yes	8	5.2	odd	4
800.2.bp.a.47.1		8	20.7	even	4
800.2.bp.a.783.1		8	200.181	even	10
800.2.bp.b.47.1		8	40.37	odd	4
800.2.bp.b.783.1		8	100.31	odd	10
1000.2.v.a.107.1		8	25.8	odd	20
1000.2.v.a.243.1		8	40.19	odd	2
1000.2.v.b.107.1		8	200.83	even	20
1000.2.v.b.243.1		8	5.4	even	2
1000.2.v.c.507.1		8	5.3	odd	4
1000.2.v.c.643.1		8	200.19	odd	10
1000.2.v.d.107.1		8	200.67	even	20	inner
1000.2.v.d.243.1		8	1.1	even	1	trivial
1000.2.v.e.107.1		8	25.17	odd	20
1000.2.v.e.243.1		8	8.3	odd	2
1000.2.v.f.507.1		8	40.3	even	4
1000.2.v.f.643.1		8	25.19	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
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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