LMFDB - Embedded newform 1000.2.v.c.507.1

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			507.1
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	1000.507
Dual form			1000.2.v.c.643.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$-1$	$-1$

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 $

$2$	1.39680	−	0.221232i	0.987688	−	0.156434i
$2$	1.39680	−	0.221232i	0.987688	−	0.156434i
$3$	2.65688	−	0.420808i	1.53395	−	0.242953i	0.668409	−	0.743794i	$-0.266976\pi$
$3$	2.65688	−	0.420808i	1.53395	−	0.242953i	0.865539	+	0.500841i	$0.166976\pi$
$4$	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	−0.593848	−	0.804577i	$-0.702392\pi$
$7$	0.557537	−	0.557537i	0.210729	−	0.210729i	0.804577	+	0.593848i	$0.202392\pi$
$8$	2.52015	−	1.28408i	0.891007	−	0.453990i
$9$	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	$0.121248\pi$
$12$	4.79360	−	2.44246i	1.38379	−	0.705078i
$13$	−2.87280	+	5.63818i	−0.796770	+	1.56375i	0.0288899	+	0.999583i	$0.490803\pi$
$13$	−2.87280	+	5.63818i	−0.796770	+	1.56375i	−0.825660	+	0.564167i	$0.809197\pi$
$14$	0.655423	−	0.902113i	0.175169	−	0.241100i
$15$		0			0
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$	−5.41695	−	0.857960i	−1.31380	−	0.208086i	−0.540082	−	0.841612i	$-0.681607\pi$
$17$	−5.41695	−	0.857960i	−1.31380	−	0.208086i	−0.773721	+	0.633526i	$0.781607\pi$
$18$	5.33776	−	2.71972i	1.25812	−	0.641045i
$19$	2.07533	+	2.85645i	0.476114	+	0.655315i	0.977752	−	0.209763i	$-0.0672691\pi$
$19$	2.07533	+	2.85645i	0.476114	+	0.655315i	−0.501638	+	0.865078i	$0.667269\pi$
$20$		0			0
$21$	1.24669	−	1.71592i	0.272050	−	0.374445i
$22$	−0.0978870	+	0.618034i	−0.0208696	+	0.131765i
$23$	−1.11507	+	0.568158i	−0.232509	+	0.118469i	−0.566364	−	0.824155i	$-0.691650\pi$
$23$	−1.11507	+	0.568158i	−0.232509	+	0.118469i	0.333855	+	0.942624i	$0.391650\pi$
$24$	6.15537	−	4.47214i	1.25646	−	0.912871i
$25$		0			0
$26$	−2.76538	+	8.51098i	−0.542336	+	1.66914i
$27$	2.96261	−	1.50953i	0.570155	−	0.290508i
$28$	0.715921	−	1.40507i	0.135296	−	0.265534i
$29$	−2.33927	−	1.69958i	−0.434391	−	0.315603i	0.349011	−	0.937118i	$-0.386517\pi$
$29$	−2.33927	−	1.69958i	−0.434391	−	0.315603i	−0.783402	+	0.621515i	$0.786517\pi$
$30$		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
$33$	−0.186192	+	1.17557i	−0.0324119	+	0.204641i
$34$	−7.75621			−1.33018
$35$		0			0
$36$	6.85410	−	4.97980i	1.14235	−	0.829966i
$37$	−4.58924	−	2.33833i	−0.754466	−	0.384420i	0.0340610	−	0.999420i	$-0.489156\pi$
$37$	−4.58924	−	2.33833i	−0.754466	−	0.384420i	−0.788527	+	0.615000i	$0.789156\pi$
$38$	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	$-0.289959\pi$
$42$	1.36176	−	2.67261i	0.210125	−	0.412393i
$43$	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
$47$	1.61803	−	0.256271i	0.236015	−	0.0373810i	−0.0373066	−	0.999304i	$-0.511878\pi$
$47$	1.61803	−	0.256271i	0.236015	−	0.0373810i	0.273321	+	0.961923i	$0.411878\pi$
$48$	7.60845	−	7.60845i	1.09819	−	1.09819i
$49$			6.37831i			0.911187i
$50$		0			0
$51$	−14.7532			−2.06586
$52$	−1.97980	+	12.4999i	−0.274548	+	1.73343i
$53$	−0.222164	−	1.40269i	−0.0305166	−	0.192674i	0.967721	−	0.252026i	$-0.0810967\pi$
$53$	−0.222164	−	1.40269i	−0.0305166	−	0.192674i	−0.998237	+	0.0593515i	$0.981097\pi$
$54$	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
$58$	−3.64349	−	1.85645i	−0.478414	−	0.243764i
$59$	10.7014	−	3.47709i	1.39320	−	0.452679i	0.486215	−	0.873839i	$-0.338377\pi$
$59$	10.7014	−	3.47709i	1.39320	−	0.452679i	0.906986	+	0.421160i	$0.138377\pi$
$60$		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
$63$	1.51634	−	2.97599i	0.191042	−	0.374940i
$64$	4.70228	−	6.47214i	0.587785	−	0.809017i
$65$		0			0
$66$			1.68323i			0.207191i
$67$	−6.22925	−	0.986616i	−0.761024	−	0.120534i	−0.236153	−	0.971716i	$-0.575887\pi$
$67$	−6.22925	−	0.986616i	−0.761024	−	0.120534i	−0.524871	+	0.851182i	$0.675887\pi$
$68$	−10.8339	+	1.71592i	−1.31380	+	0.208086i
$69$	−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
$73$	5.50380	+	10.8018i	0.644171	+	1.26426i	0.950024	+	0.312178i	$0.101059\pi$
$73$	5.50380	+	10.8018i	0.644171	+	1.26426i	−0.305852	+	0.952079i	$0.598941\pi$
$74$	−6.92757	−	2.25090i	−0.805314	−	0.261662i
$75$		0			0
$76$	5.71290	+	4.15067i	0.655315	+	0.476114i
$77$	0.158384	+	0.310847i	0.0180496	+	0.0354243i
$78$	−3.76580	+	23.7763i	−0.426393	+	2.69214i
$79$	10.5738	+	7.68233i	1.18965	+	0.864330i	0.993227	−	0.116190i	$-0.0370680\pi$
$79$	10.5738	+	7.68233i	1.18965	+	0.864330i	0.196421	+	0.980520i	$0.437068\pi$
$80$		0			0
$81$	−3.04508	+	2.21238i	−0.338343	+	0.245820i
$82$	−4.62064	−	9.06851i	−0.510264	−	1.00145i
$83$	−2.15693	+	13.6183i	−0.236754	+	1.49481i	0.527314	+	0.849671i	$0.323199\pi$
$83$	−2.15693	+	13.6183i	−0.236754	+	1.49481i	−0.764068	+	0.645136i	$0.776801\pi$
$84$	1.31085	−	4.03437i	0.143025	−	0.440186i
$85$		0			0
$86$	1.16308	−	1.60085i	0.125419	−	0.172624i
$87$	−6.93033	−	3.53118i	−0.743010	−	0.378582i
$88$	0.195774	+	1.23607i	0.0208696	+	0.131765i
$89$	−3.20347	−	1.04087i	−0.339567	−	0.110332i	0.134269	−	0.990945i	$-0.457131\pi$
$89$	−3.20347	−	1.04087i	−0.339567	−	0.110332i	−0.473837	+	0.880613i	$0.657131\pi$
$90$		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
$97$	−0.0445651	−	0.281373i	−0.00452490	−	0.0285691i	0.985323	−	0.170703i	$-0.0546038\pi$
$97$	−0.0445651	−	0.281373i	−0.00452490	−	0.0285691i	−0.989847	+	0.142134i	$0.954604\pi$
$98$	1.41108	+	8.90923i	0.142541	+	0.899968i
$99$			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	$0.867730\pi$
$102$	−20.6073	+	3.26388i	−2.04043	+	0.323172i
$103$	0.917847	+	5.79506i	0.0904381	+	0.571004i	0.990744	+	0.135746i	$0.0433430\pi$
$103$	0.917847	+	5.79506i	0.0904381	+	0.571004i	−0.900306	+	0.435258i	$0.856657\pi$
$104$			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	−0.841118	−	0.540851i	$-0.818102\pi$
$109$	−4.99614	−	15.3765i	−0.478544	−	1.47281i	0.362575	−	0.931955i	$-0.381898\pi$
$110$		0			0
$111$	−13.1770	−	4.28147i	−1.25071	−	0.406380i
$112$	0.493379	−	3.11507i	0.0466199	−	0.294347i
$113$	−7.09731	−	3.61626i	−0.667659	−	0.340189i	0.0870924	−	0.996200i	$-0.472242\pi$
$113$	−7.09731	−	3.61626i	−0.667659	−	0.340189i	−0.754751	+	0.656011i	$0.772242\pi$
$114$	10.8666	+	7.89504i	1.01775	+	0.739438i
$115$		0			0
$116$	−5.49994	−	1.78704i	−0.510657	−	0.165922i
$117$	−4.19328	+	26.4753i	−0.387669	+	2.44764i
$118$	14.1785	−	7.22429i	1.30523	−	0.665050i
$119$	−3.49849	+	2.54180i	−0.320706	+	0.233007i
$120$		0			0
$121$	8.74080	+	6.35056i	0.794618	+	0.577324i
$122$	6.71316	+	1.06326i	0.607781	+	0.0962630i
$123$	−8.78898	−	17.2493i	−0.792475	−	1.55532i
$124$	−16.2627	−	11.8156i	−1.46044	−	1.06107i
$125$		0			0
$126$	1.45965	−	4.49234i	0.130036	−	0.400209i
$127$	−3.75435	−	7.36833i	−0.333145	−	0.653833i	0.662293	−	0.749245i	$-0.269583\pi$
$127$	−3.75435	−	7.36833i	−0.333145	−	0.653833i	−0.995438	+	0.0954115i	$0.969583\pi$
$128$	5.13632	−	10.0806i	0.453990	−	0.891007i
$129$	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	$0.173771\pi$
$132$	0.372384	+	2.35114i	0.0324119	+	0.204641i
$133$	2.74965	+	0.435502i	0.238425	+	0.0377628i
$134$	−8.91930			−0.770510
$135$		0			0
$136$	−14.7532	+	4.79360i	−1.26508	+	0.411048i
$137$	−0.445169	+	0.873694i	−0.0380334	+	0.0746447i	−0.909241	−	0.416270i	$-0.863337\pi$
$137$	−0.445169	+	0.873694i	−0.0380334	+	0.0746447i	0.871208	+	0.490914i	$0.163337\pi$
$138$	−3.36646	+	3.36646i	−0.286572	+	0.286572i
$139$	−14.2326	−	4.62444i	−1.20719	−	0.392240i	−0.364789	−	0.931090i	$-0.618859\pi$
$139$	−14.2326	−	4.62444i	−1.20719	−	0.392240i	−0.842402	+	0.538850i	$0.818859\pi$
$140$		0			0
$141$	4.19107	−	1.36176i	0.352952	−	0.114681i
$142$	6.91815	−	13.5776i	0.580558	−	1.13941i
$143$	−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
$147$	2.68404	+	16.9464i	0.221376	+	1.39771i
$148$	−10.1744	−	1.61147i	−0.836332	−	0.132462i
$149$	21.0278			1.72267			0.861333	−	0.508042i	$-0.169630\pi$
$149$	21.0278			1.72267			0.861333	+	0.508042i	$0.169630\pi$
$150$		0			0
$151$			8.57286i			0.697649i	0.937188	+	0.348825i	$0.113419\pi$
$151$			8.57286i			0.697649i	−0.937188	+	0.348825i	$0.886581\pi$
$152$	8.89806	+	4.53379i	0.721728	+	0.367739i
$153$	−22.9466	+	3.63438i	−1.85512	+	0.293822i
$154$	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	−0.527120	−	0.849791i	$-0.676728\pi$
$157$	4.04306	−	4.04306i	0.322671	−	0.322671i	0.849791	+	0.527120i	$0.176728\pi$
$158$	16.4691	+	8.39144i	1.31021	+	0.667587i
$159$	−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
$163$	9.73221	+	4.95881i	0.762285	+	0.388404i	0.791500	−	0.611169i	$-0.209301\pi$
$163$	9.73221	+	4.95881i	0.762285	+	0.388404i	−0.0292144	+	0.999573i	$0.509301\pi$
$164$	−8.46036	−	11.6447i	−0.660643	−	0.909297i
$165$		0			0
$166$			19.4993i			1.51344i
$167$	−1.96683	+	12.4180i	−0.152198	+	0.960937i	0.786849	+	0.617146i	$0.211711\pi$
$167$	−1.96683	+	12.4180i	−0.152198	+	0.960937i	−0.939046	+	0.343791i	$0.888289\pi$
$168$	0.938463	−	5.92522i	0.0724040	−	0.457141i
$169$	−15.8949	−	21.8775i	−1.22269	−	1.68288i
$170$		0			0
$171$	12.1001	+	8.79125i	0.925320	+	0.672284i
$172$	1.27044	−	2.49338i	0.0968701	−	0.190118i
$173$	11.0743	−	5.64266i	0.841967	−	0.429004i	0.0208630	−	0.999782i	$-0.493359\pi$
$173$	11.0743	−	5.64266i	0.841967	−	0.429004i	0.821104	+	0.570779i	$0.193359\pi$
$174$	−10.4615	−	3.39915i	−0.793085	−	0.257689i
$175$		0			0
$176$	0.546915	+	1.68323i	0.0412253	+	0.126878i
$177$	26.9691	−	13.7414i	2.02712	−	1.03287i
$178$	−4.70489	−	0.745181i	−0.352646	−	0.0558537i
$179$	5.33119	−	7.33776i	0.398472	−	0.548450i	−0.561888	−	0.827214i	$-0.689925\pi$
$179$	5.33119	−	7.33776i	0.398472	−	0.548450i	0.960360	+	0.278764i	$0.0899247\pi$
$180$		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	$0.637925\pi$
$182$	3.20338	+	6.28698i	0.237450	+	0.466022i
$183$	12.7692	+	2.02244i	0.943925	+	0.149503i
$184$	−2.08059	+	2.86368i	−0.153383	+	0.211114i
$185$		0			0
$186$	−30.9335	−	22.4745i	−2.26816	−	1.64791i
$187$	1.10169	−	2.16219i	0.0805635	−	0.158115i
$188$	2.91930	−	1.48746i	0.212912	−	0.108484i
$189$	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	$0.634051\pi$
$192$	9.76985	−	19.1744i	0.705078	−	1.38379i
$193$	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
$197$	5.51120	−	0.872888i	0.392657	−	0.0621907i	0.0430155	−	0.999074i	$-0.486304\pi$
$197$	5.51120	−	0.872888i	0.392657	−	0.0621907i	0.349641	+	0.936884i	$0.386304\pi$
$198$	0.414656	+	2.61803i	0.0294683	+	0.186056i
$199$	−10.4853			−0.743281			−0.371640	−	0.928377i	$-0.621205\pi$
$199$	−10.4853			−0.743281			−0.371640	+	0.928377i	$0.621205\pi$
$200$		0			0
$201$	−16.9655			−1.19666
$202$	1.79506	+	11.3335i	0.126300	+	0.797425i
$203$	−2.25180	+	0.356650i	−0.158046	+	0.0250319i
$204$	−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
$208$	3.95959	+	24.9999i	0.274548	+	1.73343i
$209$	−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	$0.105193\pi$
$212$	−1.28949	−	2.53077i	−0.0885626	−	0.173814i
$213$	13.1591	−	25.8262i	0.901646	−	1.76958i
$214$	2.98281	+	2.16714i	0.203901	+	0.148143i
$215$		0			0
$216$	5.52786	−	7.60845i	0.376124	−	0.517690i
$217$	−7.82733	−	1.23973i	−0.531354	−	0.0841582i
$218$	−10.3804	−	20.3727i	−0.703049	−	1.37981i
$219$	19.1684	+	26.3831i	1.29528	+	1.78280i
$220$		0			0
$221$	20.3991	−	28.0770i	1.37219	−	1.88866i
$222$	−19.3529	−	3.06520i	−1.29888	−	0.205723i
$223$	−19.7149	+	10.0452i	−1.32021	+	0.672680i	−0.965035	−	0.262121i	$-0.915578\pi$
$223$	−19.7149	+	10.0452i	−1.32021	+	0.672680i	−0.355173	+	0.934801i	$0.615578\pi$
$224$		−	4.46029i		−	0.298016i
$225$		0			0
$226$	−10.7136	−	3.48105i	−0.712656	−	0.231556i
$227$	−1.39169	+	0.709101i	−0.0923697	+	0.0470647i	−0.499565	−	0.866276i	$-0.666507\pi$
$227$	−1.39169	+	0.709101i	−0.0923697	+	0.0470647i	0.407195	+	0.913341i	$0.366507\pi$
$228$	16.9251	+	8.62377i	1.12089	+	0.571123i
$229$	4.91602	+	3.57170i	0.324860	+	0.236024i	0.738246	−	0.674531i	$-0.235654\pi$
$229$	4.91602	+	3.57170i	0.324860	+	0.236024i	−0.413387	+	0.910556i	$0.635654\pi$
$230$		0			0
$231$	0.551615	+	0.759232i	0.0362936	+	0.0499538i
$232$	−8.07768	−	1.27938i	−0.530326	−	0.0839954i
$233$	2.47106	−	15.6017i	0.161885	−	1.02210i	−0.764254	−	0.644916i	$-0.776893\pi$
$233$	2.47106	−	15.6017i	0.161885	−	1.02210i	0.926138	−	0.377184i	$-0.123107\pi$
$234$			37.9085i			2.47815i
$235$		0			0
$236$	18.2063	−	13.2276i	1.18513	−	0.861046i
$237$	31.3261	+	15.9615i	2.03485	+	1.03681i
$238$	−4.32437	+	4.32437i	−0.280307	+	0.280307i
$239$	−0.321469	+	0.989378i	−0.0207941	+	0.0639976i	−0.960915	−	0.276843i	$-0.910712\pi$
$239$	−0.321469	+	0.989378i	−0.0207941	+	0.0639976i	0.940121	+	0.340841i	$0.110712\pi$
$240$		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	$0.996124\pi$
$242$	13.6141	+	6.93674i	0.875149	+	0.445911i
$243$	−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
$247$	−22.0672	+	3.49510i	−1.40410	+	0.222388i
$248$	−25.3298	−	12.9062i	−1.60844	−	0.819543i
$249$			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	$0.426442\pi$
$252$	1.04499	−	6.59783i	0.0658284	−	0.415624i
$253$	−0.0866228	−	0.546915i	−0.00544593	−	0.0343842i
$254$	−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	$0.754206\pi$
$258$	2.41652	−	4.74269i	0.150446	−	0.295267i
$259$	−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
$263$	−5.78283	+	11.3494i	−0.356584	+	0.699836i	−0.997713	−	0.0675976i	$-0.978467\pi$
$263$	−5.78283	+	11.3494i	−0.356584	+	0.699836i	0.641128	+	0.767434i	$0.278467\pi$
$264$	1.04029	+	3.20170i	0.0640257	+	0.197051i
$265$		0			0
$266$	3.93706			0.241397
$267$	−8.94923	−	1.41742i	−0.547684	−	0.0867446i
$268$	−12.4585	+	1.97323i	−0.761024	+	0.120534i
$269$	9.07519	−	6.59351i	0.553324	−	0.402013i	−0.275686	−	0.961248i	$-0.588905\pi$
$269$	9.07519	−	6.59351i	0.553324	−	0.402013i	0.829009	+	0.559235i	$0.188905\pi$
$270$		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	$0.307853\pi$
$272$	−19.5468	+	9.95959i	−1.18520	+	0.603889i
$273$	6.09319	+	11.9586i	0.368776	+	0.723765i
$274$	−0.428525	+	1.31886i	−0.0258881	+	0.0796755i
$275$		0			0
$276$	−3.95751	+	5.44705i	−0.238214	+	0.327874i
$277$	−3.95183	−	7.75589i	−0.237442	−	0.466006i	0.741280	−	0.671196i	$-0.234219\pi$
$277$	−3.95183	−	7.75589i	−0.237442	−	0.466006i	−0.978722	+	0.205189i	$0.934219\pi$
$278$	−20.9032	−	3.31073i	−1.25369	−	0.198565i
$279$	−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	$0.207675\pi$
$282$	5.55284	−	2.82931i	0.330667	−	0.168483i
$283$	1.16479	−	7.35420i	0.0692397	−	0.437162i	−0.928578	−	0.371137i	$-0.878968\pi$
$283$	1.16479	−	7.35420i	0.0692397	−	0.437162i	0.997818	−	0.0660254i	$-0.0210318\pi$
$284$	6.65948	−	20.4958i	0.395167	−	1.21620i
$285$		0			0
$286$	−3.20338	−	2.32739i	−0.189420	−	0.137621i
$287$	−5.05603	−	2.57617i	−0.298448	−	0.152067i
$288$	10.8789	−	21.3510i	0.641045	−	1.25812i
$289$	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	0.933631	−	0.358237i	$-0.116622\pi$
$293$	9.84915	+	9.84915i	0.575393	+	0.575393i	−0.358237	+	0.933631i	$0.616622\pi$
$294$	7.49815	+	23.0769i	0.437301	+	1.34587i
$295$		0			0
$296$	−14.5682			−0.846757
$297$	0.230146	+	1.45309i	0.0133544	+	0.0843165i
$298$	29.3717	−	4.65202i	1.70146	−	0.269484i
$299$		−	7.91919i		−	0.457978i
$300$		0			0
$301$		−	1.10323i		−	0.0635891i
$302$	1.89659	+	11.9746i	0.109136	+	0.689060i
$303$	3.41440	+	21.5577i	0.196152	+	1.23846i
$304$	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	0.135234	−	0.990814i	$-0.456821\pi$
$311$	−5.95620	−	1.93529i	−0.337745	−	0.109740i	−0.472979	+	0.881074i	$0.656821\pi$
$312$	7.53159	+	47.5526i	0.426393	+	2.69214i
$313$	−2.67107	−	1.36098i	−0.150978	−	0.0769270i	0.376869	−	0.926266i	$-0.377001\pi$
$313$	−2.67107	−	1.36098i	−0.150978	−	0.0769270i	−0.527847	+	0.849339i	$0.677001\pi$
$314$	4.75290	−	6.54180i	0.268222	−	0.369175i
$315$		0			0
$316$	24.8606	+	8.07768i	1.39852	+	0.454405i
$317$	1.82394	−	11.5159i	0.102443	−	0.646799i	−0.882021	−	0.471211i	$-0.843817\pi$
$317$	1.82394	−	11.5159i	0.102443	−	0.646799i	0.984464	−	0.175589i	$-0.0561828\pi$
$318$	−2.45276	−	4.81381i	−0.137544	−	0.269945i
$319$	1.03504	−	0.752000i	0.0579511	−	0.0421039i
$320$		0			0
$321$	5.67365	+	4.12215i	0.316672	+	0.230076i
$322$	−0.218302	+	1.37831i	−0.0121655	+	0.0768100i
$323$	−8.79125	−	17.2538i	−0.489158	−	0.960028i
$324$	−4.42477	+	6.09017i	−0.245820	+	0.338343i
$325$		0			0
$326$	14.6910	+	4.77340i	0.813660	+	0.264374i
$327$	−19.7447	−	38.7511i	−1.09188	−	2.14294i
$328$	−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	$0.555143\pi$
$332$	4.31386	+	27.2367i	0.236754	+	1.49481i
$333$	−21.5498	−	3.41315i	−1.18092	−	0.187039i
$334$			17.7807i			0.972915i
$335$		0			0
$336$		−	8.48398i		−	0.462839i
$337$	−9.93860	+	19.5056i	−0.541390	+	1.06254i	0.444599	+	0.895730i	$0.353346\pi$
$337$	−9.93860	+	19.5056i	−0.541390	+	1.06254i	−0.985989	+	0.166809i	$0.946654\pi$
$338$	−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
$342$	18.8464	+	9.60271i	1.01910	+	0.519255i
$343$	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
$347$	1.58341	+	9.99724i	0.0850017	+	0.536680i	0.993039	+	0.117790i	$0.0375808\pi$
$347$	1.58341	+	9.99724i	0.0850017	+	0.536680i	−0.908037	+	0.418890i	$0.862419\pi$
$348$	−15.3647	−	2.43352i	−0.823633	−	0.130451i
$349$	−17.7360			−0.949387			−0.474693	−	0.880151i	$-0.657441\pi$
$349$	−17.7360			−0.949387			−0.474693	+	0.880151i	$0.657441\pi$
$350$		0			0
$351$			21.0403i			1.12305i
$352$	1.13632	+	2.23015i	0.0605659	+	0.118867i
$353$	−22.2336	+	3.52146i	−1.18338	+	0.187428i	−0.716945	−	0.697130i	$-0.754460\pi$
$353$	−22.2336	+	3.52146i	−1.18338	+	0.187428i	−0.466430	+	0.884558i	$0.654460\pi$
$354$	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
$358$	5.82328	−	11.4288i	0.307770	−	0.604032i
$359$	3.80423	+	11.7082i	0.200779	+	0.617935i	0.999860	+	0.0167120i	$0.00531983\pi$
$359$	3.80423	+	11.7082i	0.200779	+	0.617935i	−0.799081	+	0.601223i	$0.794680\pi$
$360$		0			0
$361$	2.01902	−	6.21389i	0.106264	−	0.327047i
$362$	13.1161	+	13.1161i	0.689368	+	0.689368i
$363$	25.8956	+	13.1945i	1.35917	+	0.692530i
$364$	5.86537	+	8.07298i	0.307429	+	0.423139i
$365$		0			0
$366$	18.2835			0.955692
$367$	4.41991	−	27.9062i	0.230717	−	1.45669i	−0.551754	−	0.834007i	$-0.686041\pi$
$367$	4.41991	−	27.9062i	0.230717	−	1.45669i	0.782472	−	0.622686i	$-0.213959\pi$
$368$	−2.27263	+	4.46029i	−0.118469	+	0.232509i
$369$	−17.9193	−	24.6638i	−0.932843	−	1.28395i
$370$		0			0
$371$	−0.905915	−	0.658186i	−0.0470328	−	0.0341713i
$372$	−48.1801	−	24.5490i	−2.49802	−	1.27281i
$373$	6.97233	−	3.55258i	0.361014	−	0.183946i	−0.264070	−	0.964504i	$-0.585065\pi$
$373$	6.97233	−	3.55258i	0.361014	−	0.183946i	0.625084	+	0.780558i	$0.285065\pi$
$374$	1.06050	−	3.26388i	0.0548370	−	0.168771i
$375$		0			0
$376$	3.74861	−	2.72353i	0.193320	−	0.140455i
$377$	16.3028	−	8.30667i	0.839634	−	0.427815i
$378$	0.580002	−	3.66199i	0.0298321	−	0.188352i
$379$	−12.6090	+	17.3548i	−0.647682	+	0.891458i	−0.998996	−	0.0447999i	$-0.985735\pi$
$379$	−12.6090	+	17.3548i	−0.647682	+	0.891458i	0.351314	+	0.936258i	$0.385735\pi$
$380$		0			0
$381$	−13.0755	−	17.9969i	−0.669878	−	0.922008i
$382$	−23.3635	+	11.9043i	−1.19538	+	0.609077i
$383$	4.28247	+	0.678276i	0.218824	+	0.0346583i	0.264884	−	0.964280i	$-0.414666\pi$
$383$	4.28247	+	0.678276i	0.218824	+	0.0346583i	−0.0460597	+	0.998939i	$0.514666\pi$
$384$	9.40456	−	28.9443i	0.479925	−	1.47706i
$385$		0			0
$386$	13.2275	−	18.2060i	0.673260	−	0.926662i
$387$	2.69084	−	5.28106i	0.136783	−	0.268451i
$388$	−0.258666	−	0.507661i	−0.0131318	−	0.0257726i
$389$	2.91910	−	8.98407i	0.148004	−	0.455510i	−0.849381	−	0.527780i	$-0.823024\pi$
$389$	2.91910	−	8.98407i	0.148004	−	0.455510i	0.997385	+	0.0722702i	$0.0230244\pi$
$390$		0			0
$391$	6.52775	−	2.12099i	0.330123	−	0.107263i
$392$	8.19025	+	16.0743i	0.413670	+	0.811873i
$393$	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
$397$	34.6653	−	5.49045i	1.73980	−	0.275558i	0.795816	−	0.605539i	$-0.207042\pi$
$397$	34.6653	−	5.49045i	1.73980	−	0.275558i	0.943988	+	0.329981i	$0.107042\pi$
$398$	−14.6458	+	2.31967i	−0.734130	+	0.116275i
$399$	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	$0.581924\pi$
$402$	−23.6975	+	3.75331i	−1.18192	+	0.187198i
$403$	62.8179	−	9.94938i	3.12918	−	0.495614i
$404$	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
$408$	−37.1802	+	18.9443i	−1.84070	+	0.937881i
$409$	11.4621	−	3.72426i	0.566764	−	0.184153i	−0.0115985	−	0.999933i	$-0.503692\pi$
$409$	11.4621	−	3.72426i	0.566764	−	0.184153i	0.578362	+	0.815780i	$0.303692\pi$
$410$		0			0
$411$	−0.815103	+	2.50863i	−0.0402060	+	0.123741i
$412$	5.32739	+	10.4556i	0.262462	+	0.515110i
$413$	4.02781	−	7.90502i	0.198195	−	0.388980i
$414$	−4.40676	+	6.06538i	−0.216580	+	0.298097i
$415$		0			0
$416$	11.0615	+	34.0439i	0.542336	+	1.66914i
$417$	−39.7602	−	6.29739i	−1.94706	−	0.308385i
$418$	−1.96853	+	1.00302i	−0.0962841	+	0.0490592i
$419$	2.67537	+	3.68233i	0.130700	+	0.179894i	0.869352	−	0.494194i	$-0.164537\pi$
$419$	2.67537	+	3.68233i	0.130700	+	0.179894i	−0.738651	+	0.674088i	$0.764537\pi$
$420$		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	$0.941892\pi$
$422$	−0.104849	+	0.661988i	−0.00510395	+	0.0322251i
$423$	6.18317	−	3.15048i	0.300636	−	0.153182i
$424$	−2.36105	−	3.24971i	−0.114663	−	0.157820i
$425$		0			0
$426$	12.6671	−	38.9853i	0.613722	−	1.88884i
$427$	3.37646	−	1.72039i	0.163398	−	0.0832555i
$428$	4.64584	+	2.36717i	0.224565	+	0.114422i
$429$	−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	$0.622110\pi$
$432$	6.03810	−	11.8504i	0.290508	−	0.570155i
$433$	−2.99752	+	18.9256i	−0.144052	+	0.909505i	0.804746	+	0.593620i	$0.202302\pi$
$433$	−2.99752	+	18.9256i	−0.144052	+	0.909505i	−0.948797	+	0.315886i	$0.897698\pi$
$434$	−11.2075			−0.537977
$435$		0			0
$436$	−19.0065	−	26.1601i	−0.910244	−	1.25284i
$437$	−3.93706	−	2.00603i	−0.188335	−	0.0959617i
$438$	32.6112	+	32.6112i	1.55823	+	1.55823i
$439$	1.35681	−	4.17583i	0.0647569	−	0.199301i	−0.913443	−	0.406967i	$-0.866587\pi$
$439$	1.35681	−	4.17583i	0.0647569	−	0.199301i	0.978200	+	0.207665i	$0.0665865\pi$
$440$		0			0
$441$	8.34931	+	25.6965i	0.397586	+	1.22364i
$442$	22.2820	−	43.7309i	1.05985	−	2.08007i
$443$	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
$447$	55.8683	−	8.84867i	2.64248	−	0.418527i
$448$	−0.986758	−	6.23015i	−0.0466199	−	0.294347i
$449$		−	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
$452$	−15.7349	−	2.49216i	−0.740106	−	0.117221i
$453$	3.60753	+	22.7770i	0.169496	+	1.07016i
$454$	−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	$0.994078\pi$
$458$	7.65688	+	3.90137i	0.357782	+	0.182299i
$459$	−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
$463$	−11.5014	+	22.5727i	−0.534513	+	1.04904i	0.453001	+	0.891510i	$0.350353\pi$
$463$	−11.5014	+	22.5727i	−0.534513	+	1.04904i	−0.987514	+	0.157531i	$0.949647\pi$
$464$	−11.5660			−0.536936
$465$		0			0
$466$		−	22.3391i		−	1.03484i
$467$	12.6035	+	1.99620i	0.583220	+	0.0923730i	0.441071	−	0.897472i	$-0.354599\pi$
$467$	12.6035	+	1.99620i	0.583220	+	0.0923730i	0.142149	+	0.989845i	$0.454599\pi$
$468$	8.38655	+	52.9506i	0.387669	+	2.44764i
$469$	−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
$473$	0.281062	+	0.551615i	0.0129232	+	0.0253633i
$474$	47.2876	+	15.3647i	2.17199	+	0.705723i
$475$		0			0
$476$	−5.08361	+	6.99698i	−0.233007	+	0.320706i
$477$	−2.73119	−	5.36025i	−0.125052	−	0.245429i
$478$	−0.230146	+	1.45309i	−0.0105266	+	0.0664626i
$479$	21.3496	+	15.5114i	0.975487	+	0.708733i	0.956695	−	0.291091i	$-0.0940181\pi$
$479$	21.3496	+	15.5114i	0.975487	+	0.708733i	0.0187915	+	0.999823i	$0.494018\pi$
$480$		0			0
$481$	26.3679	−	19.1574i	1.20227	−	0.873502i
$482$	−5.92872	−	11.6358i	−0.270046	−	0.529995i
$483$	−0.415236	+	2.62169i	−0.0188939	+	0.119291i
$484$	20.5509	+	6.67738i	0.934130	+	0.303517i
$485$		0			0
$486$	−16.7082	+	22.9969i	−0.757900	+	1.04316i
$487$	−4.18515	−	2.13244i	−0.189647	−	0.0966302i	0.356589	−	0.934262i	$-0.383940\pi$
$487$	−4.18515	−	2.13244i	−0.189647	−	0.0966302i	−0.546236	+	0.837631i	$0.683940\pi$
$488$	13.4263	−	2.12652i	0.607781	−	0.0962630i
$489$	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
$497$	−1.32907	−	8.39144i	−0.0596171	−	0.376407i
$498$	8.20546	+	51.8072i	0.367695	+	2.32154i
$499$		−	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
$502$	10.1370	−	1.60555i	0.452438	−	0.0716591i
$503$	−6.73981	−	42.5535i	−0.300513	−	1.89737i	−0.425080	−	0.905156i	$-0.639754\pi$
$503$	−6.73981	−	42.5535i	−0.300513	−	1.89737i	0.124566	−	0.992211i	$-0.460246\pi$
$504$		−	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	$-0.981628\pi$
$509$	−5.06658	−	15.5933i	−0.224572	−	0.691163i	0.773762	−	0.633476i	$-0.218372\pi$
$510$		0			0
$511$	9.09098	+	2.95384i	0.402161	+	0.130670i
$512$	3.53971	−	22.3488i	0.156434	−	0.987688i
$513$	10.4603	+	5.32979i	0.461833	+	0.235316i
$514$	−0.484695	−	0.352151i	−0.0213790	−	0.0155327i
$515$		0			0
$516$	2.32617	−	7.15921i	0.102404	−	0.315167i
$517$	−0.113391	+	0.715921i	−0.00498692	+	0.0314862i
$518$	−5.11734	+	2.60741i	−0.224843	+	0.114563i
$519$	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	$0.728749\pi$
$522$	−17.1088	−	2.70977i	−0.748832	−	0.118603i
$523$	1.70869	+	3.35349i	0.0747158	+	0.146638i	0.925343	−	0.379132i	$-0.123777\pi$
$523$	1.70869	+	3.35349i	0.0747158	+	0.146638i	−0.850627	+	0.525770i	$0.823777\pi$
$524$	10.3939	−	14.3060i	0.454061	−	0.624962i
$525$		0			0
$526$	−5.56661	+	17.1323i	−0.242716	+	0.747002i
$527$	25.0258	+	49.1158i	1.09014	+	2.13952i
$528$	2.16140	+	4.24199i	0.0940629	+	0.184609i
$529$	−12.5985	+	17.3403i	−0.547760	+	0.753927i
$530$		0			0
$531$	38.5615	−	28.0166i	1.67343	−	1.21582i
$532$	5.49930	−	0.871004i	0.238425	−	0.0377628i
$533$	44.9799	+	7.12411i	1.94829	+	0.308580i
$534$	−12.8139			−0.554511
$535$		0			0
$536$	−16.9655	+	5.51243i	−0.732799	+	0.238101i
$537$	11.0765	−	21.7389i	0.477988	−	0.938103i
$538$	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	$0.308342\pi$
$542$	−7.02613	+	13.7895i	−0.301798	+	0.592312i
$543$	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
$547$	3.25968	+	20.5808i	0.139374	+	0.879971i	0.953961	+	0.299930i	$0.0969634\pi$
$547$	3.25968	+	20.5808i	0.139374	+	0.879971i	−0.814587	+	0.580041i	$0.803037\pi$
$548$	−0.306790	+	1.93700i	−0.0131054	+	0.0827443i
$549$	20.3589			0.868898
$550$		0			0
$551$		−	10.2092i		−	0.434926i
$552$	−4.32280	+	8.48398i	−0.183991	+	0.361102i
$553$	10.1785	−	1.61211i	0.432833	−	0.0685540i
$554$	−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	−0.259930	−	0.965627i	$-0.583700\pi$
$557$	16.6551	−	16.6551i	0.705697	−	0.705697i	0.965627	+	0.259930i	$0.0836995\pi$
$558$	−53.6493	−	27.3357i	−2.27116	−	1.15721i
$559$	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
$563$	−40.8947	−	20.8369i	−1.72350	−	0.878170i	−0.977130	−	0.212644i	$-0.931792\pi$
$563$	−40.8947	−	20.8369i	−1.72350	−	0.878170i	−0.746375	−	0.665525i	$-0.768208\pi$
$564$	7.13028	−	5.18045i	0.300239	−	0.218136i
$565$		0			0
$566$		−	10.5301i		−	0.442611i
$567$	−0.464261	+	2.93123i	−0.0194971	+	0.123100i
$568$	4.76766	−	30.1018i	0.200047	−	1.26304i
$569$	−23.0882	−	31.7781i	−0.967906	−	1.33221i	−0.943098	−	0.332516i	$-0.892103\pi$
$569$	−23.0882	−	31.7781i	−0.967906	−	1.33221i	−0.0248079	−	0.999692i	$-0.507897\pi$
$570$		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	$0.532402\pi$
$572$	−4.98938	−	2.54222i	−0.208616	−	0.106295i
$573$	−44.4400	+	22.6433i	−1.85651	+	0.945939i
$574$	−7.63220	−	2.47985i	−0.318562	−	0.103507i
$575$		0			0
$576$	10.4721	−	32.2299i	0.436339	−	1.34291i
$577$	−5.62119	+	2.86414i	−0.234013	+	0.119236i	−0.567066	−	0.823673i	$-0.691921\pi$
$577$	−5.62119	+	2.86414i	−0.234013	+	0.119236i	0.333052	+	0.942908i	$0.391921\pi$
$578$	18.2694	+	2.89359i	0.759906	+	0.120357i
$579$	25.1601	−	34.6299i	1.04562	−	1.43917i
$580$		0			0
$581$	6.39015	+	8.79529i	0.265108	+	0.364890i
$582$	−0.492012	−	0.965628i	−0.0203946	−	0.0400266i
$583$	0.620639	+	0.0982995i	0.0257042	+	0.00407115i
$584$	27.7408	+	20.1549i	1.14792	+	0.834014i
$585$		0			0
$586$	15.9363	+	11.5784i	0.658321	+	0.478298i
$587$	16.8133	−	32.9979i	0.693958	−	1.36197i	−0.227609	−	0.973753i	$-0.573091\pi$
$587$	16.8133	−	32.9979i	0.693958	−	1.36197i	0.921568	−	0.388218i	$-0.126909\pi$
$588$	15.5788	+	30.5751i	0.642458	+	1.26089i
$589$	10.9662	−	33.7506i	0.451856	−	1.39067i
$590$		0			0
$591$	14.2752	−	4.63831i	0.587205	−	0.190795i
$592$	−20.3488	+	3.22294i	−0.836332	+	0.132462i
$593$	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
$597$	−27.8580	+	4.41228i	−1.14015	+	0.180583i
$598$	−1.75198	−	11.0615i	−0.0716436	−	0.452340i
$599$	−1.55150			−0.0633926			−0.0316963	−	0.999498i	$-0.510091\pi$
$599$	−1.55150			−0.0633926			−0.0316963	+	0.999498i	$0.510091\pi$
$600$		0			0
$601$	13.6133			0.555299			0.277650	−	0.960682i	$-0.410445\pi$
$601$	13.6133			0.555299			0.277650	+	0.960682i	$0.410445\pi$
$602$	−0.244069	−	1.54099i	−0.00994752	−	0.0628062i
$603$	−26.3875	+	4.17937i	−1.07458	+	0.170197i
$604$	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	$0.508209\pi$
$607$	−25.2645	+	25.2645i	−1.02545	+	1.02545i	−0.999667	+	0.0257859i	$0.991791\pi$
$608$	19.7271	+	3.12447i	0.800041	+	0.126714i
$609$	−5.83268	+	1.89515i	−0.236352	+	0.0767954i
$610$		0			0
$611$	−3.20338	+	9.85898i	−0.129595	+	0.398852i
$612$	−41.4008	+	21.0948i	−1.67353	+	0.852705i
$613$	−16.7323	+	32.8390i	−0.675811	+	1.32635i	0.257148	+	0.966372i	$0.417217\pi$
$613$	−16.7323	+	32.8390i	−0.675811	+	1.32635i	−0.932959	+	0.359982i	$0.882783\pi$
$614$	−2.06236	−	1.49839i	−0.0832302	−	0.0604703i
$615$		0			0
$616$	0.798304	+	0.580002i	0.0321646	+	0.0233689i
$617$	−3.49115	−	0.552944i	−0.140548	−	0.0222607i	0.0857638	−	0.996316i	$-0.472667\pi$
$617$	−3.49115	−	0.552944i	−0.140548	−	0.0222607i	−0.226312	+	0.974055i	$0.572667\pi$
$618$	10.1333	+	19.8877i	0.407621	+	0.800001i
$619$	26.6760	+	36.7164i	1.07220	+	1.47576i	0.867830	+	0.496861i	$0.165514\pi$
$619$	26.6760	+	36.7164i	1.07220	+	1.47576i	0.204369	+	0.978894i	$0.434486\pi$
$620$		0			0
$621$	−2.44588	+	3.36646i	−0.0981497	+	0.135091i
$622$	−8.74779	−	1.38551i	−0.350754	−	0.0555540i
$623$	−2.36637	+	1.20573i	−0.0948068	+	0.0483065i
$624$	21.0403	+	64.7554i	0.842286	+	2.59229i
$625$		0			0
$626$	−4.03205	−	1.31009i	−0.161153	−	0.0523618i
$627$	−3.74437	+	1.90785i	−0.149536	+	0.0761923i
$628$	5.19160	−	10.1891i	0.207168	−	0.406589i
$629$	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	$0.885015\pi$
$632$	36.5123	+	5.78298i	1.45238	+	0.230035i
$633$	−0.199434	+	1.25918i	−0.00792679	+	0.0500478i
$634$		−	16.4890i		−	0.654862i
$635$		0			0
$636$	−4.49098	−	6.18131i	−0.178079	−	0.245105i
$637$	−35.9620	−	18.3236i	−1.42487	−	0.726007i
$638$	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	$0.994614\pi$
$642$	8.83692	+	4.50263i	0.348765	+	0.177705i
$643$	−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
$647$	44.1296	−	6.98945i	1.73492	−	0.274784i	0.792656	−	0.609669i	$-0.208698\pi$
$647$	44.1296	−	6.98945i	1.73492	−	0.274784i	0.942259	+	0.334885i	$0.108698\pi$
$648$	−4.83319	+	9.48566i	−0.189865	+	0.372632i
$649$			4.97864i			0.195429i
$650$		0			0
$651$	−21.3179			−0.835516
$652$	21.5765	+	3.41738i	0.845000	+	0.133835i
$653$	−0.00273094	−	0.0172425i	−0.000106870	−	0.000674750i	0.987635	−	0.156772i	$-0.0501087\pi$
$653$	−0.00273094	−	0.0172425i	−0.000106870	−	0.000674750i	−0.987742	+	0.156097i	$0.950109\pi$
$654$	−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
$658$	0.829312	−	1.62762i	0.0323299	−	0.0634511i
$659$	−36.7936	+	11.9550i	−1.43328	+	0.465700i	−0.919795	−	0.392400i	$-0.871645\pi$
$659$	−36.7936	+	11.9550i	−1.43328	+	0.465700i	−0.513482	+	0.858100i	$0.671645\pi$
$660$		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
$663$	42.3829	−	83.1812i	1.64602	−	3.23049i
$664$	12.0512	+	37.0899i	0.467678	+	1.43937i
$665$		0			0
$666$	−30.8559			−1.19564
$667$	3.57408	+	0.566079i	0.138389	+	0.0219187i
$668$	3.93365	+	24.8361i	0.152198	+	0.960937i
$669$	−48.1529	+	34.9852i	−1.86170	+	1.35260i
$670$		0			0
$671$	−1.24994	+	1.72039i	−0.0482533	+	0.0664149i
$672$	−1.87693	−	11.8504i	−0.0724040	−	0.457141i
$673$	−3.33103	−	6.53751i	−0.128402	−	0.252003i	0.817851	−	0.575429i	$-0.195165\pi$
$673$	−3.33103	−	6.53751i	−0.128402	−	0.252003i	−0.946253	+	0.323427i	$0.895165\pi$
$674$	−9.56701	+	29.4442i	−0.368507	+	1.13415i
$675$		0			0
$676$	−43.7549	−	31.7898i	−1.68288	−	1.22269i
$677$	−12.7398	−	25.0033i	−0.489631	−	0.960955i	−0.995171	−	0.0981518i	$-0.968707\pi$
$677$	−12.7398	−	25.0033i	−0.489631	−	0.960955i	0.505541	−	0.862803i	$-0.331293\pi$
$678$	−29.9295	−	4.74036i	−1.14943	−	0.182053i
$679$	−0.181722	−	0.132029i	−0.00697387	−	0.00506681i
$680$		0			0
$681$	−3.39915	+	2.46963i	−0.130256	+	0.0946364i
$682$	5.60375	−	2.85525i	0.214579	−	0.109333i
$683$	1.37281	−	8.66759i	0.0525292	−	0.331656i	−0.947403	−	0.320042i	$-0.896303\pi$
$683$	1.37281	−	8.66759i	0.0525292	−	0.331656i	0.999933	−	0.0116143i	$-0.00369703\pi$
$684$	28.4491	+	9.24367i	1.08778	+	0.353441i
$685$		0			0
$686$	12.0687	+	8.76846i	0.460787	+	0.334781i
$687$	14.5642	+	7.42085i	0.555661	+	0.283123i
$688$	0.875528	−	5.52786i	0.0333792	−	0.210748i
$689$	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
$697$	6.17458	+	38.9848i	0.233879	+	1.47665i
$698$	−24.7737	+	3.92377i	−0.937698	+	0.148517i
$699$		−	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	$-0.0650527\pi$
$702$	4.65478	+	29.3891i	0.175683	+	1.10922i
$703$	−2.84486	−	17.9618i	−0.107296	−	0.677441i
$704$	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	$-0.106839\pi$
$709$	−0.353547	−	1.08811i	−0.0132777	−	0.0408647i	−0.957476	+	0.288513i	$0.906839\pi$
$710$		0			0
$711$	52.6555	+	17.1088i	1.97474	+	0.641630i
$712$	−9.40977	+	1.49036i	−0.352646	+	0.0558537i
$713$	11.2075	+	5.71051i	0.419724	+	0.213860i
$714$	−9.66959	+	13.3091i	−0.361875	+	0.498079i
$715$		0			0
$716$	5.60555	−	17.2521i	0.209489	−	0.644741i
$717$	−0.437764	+	2.76393i	−0.0163486	+	0.103221i
$718$	7.90398	+	15.5124i	0.294974	+	0.578919i
$719$	−1.16479	+	0.846270i	−0.0434394	+	0.0315606i	−0.609293	−	0.792945i	$-0.708547\pi$
$719$	−1.16479	+	0.846270i	−0.0434394	+	0.0315606i	0.565854	+	0.824506i	$0.308547\pi$
$720$		0			0
$721$	3.74269	+	2.71922i	0.139385	+	0.101269i
$722$	1.44546	−	9.12625i	0.0537943	−	0.339644i
$723$	−11.2771	−	22.1326i	−0.419400	−	0.823119i
$724$	21.2223	+	15.4189i	0.788721	+	0.573039i
$725$		0			0
$726$	39.0901	+	12.7011i	1.45077	+	0.471383i
$727$	4.53561	+	8.90163i	0.168216	+	0.330143i	0.959690	−	0.281060i	$-0.0906859\pi$
$727$	4.53561	+	8.90163i	0.168216	+	0.330143i	−0.791474	+	0.611203i	$0.790686\pi$
$728$	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
$732$	25.5384	−	4.04488i	0.943925	−	0.149503i
$733$	−18.8528	−	2.98599i	−0.696344	−	0.110290i	−0.201779	−	0.979431i	$-0.564672\pi$
$733$	−18.8528	−	2.98599i	−0.696344	−	0.110290i	−0.494564	+	0.869141i	$0.664672\pi$
$734$		−	39.9573i		−	1.47485i
$735$		0			0
$736$	−2.18766	+	6.73292i	−0.0806382	+	0.248179i
$737$	1.26689	−	2.48642i	0.0466666	−	0.0915884i
$738$	−30.4862	−	30.4862i	−1.12221	−	1.12221i
$739$	30.4862	+	9.90557i	1.12145	+	0.364382i	0.810322	−	0.585985i	$-0.199292\pi$
$739$	30.4862	+	9.90557i	1.12145	+	0.364382i	0.311131	+	0.950367i	$0.399292\pi$
$740$		0			0
$741$	−57.1591	+	18.5721i	−2.09979	+	0.682263i
$742$	−1.41100	−	0.718938i	−0.0517993	−	0.0263931i
$743$	−27.7454	−	27.7454i	−1.01788	−	1.01788i	−0.999837	−	0.0180432i	$-0.994256\pi$
$743$	−27.7454	−	27.7454i	−1.01788	−	1.01788i	−0.0180432	−	0.999837i	$-0.505744\pi$
$744$	−72.7291	−	23.6311i	−2.66638	−	0.866359i
$745$		0			0
$746$	8.95303	−	6.50476i	0.327794	−	0.238156i
$747$	9.13691	+	57.6882i	0.334302	+	2.11070i
$748$	0.759232	−	4.79360i	0.0277603	−	0.175272i
$749$	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
$753$	19.2818	−	3.05393i	0.702667	−	0.111292i
$754$	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	−0.990126	−	0.140182i	$-0.955231\pi$
$757$	−23.3850	+	23.3850i	−0.849943	+	0.849943i	0.140182	+	0.990126i	$0.455231\pi$
$758$	−13.7729	+	27.0308i	−0.500253	+	0.981802i
$759$	−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
$763$	−11.3585	−	5.78745i	−0.411206	−	0.209520i
$764$	−30.0006	+	21.7967i	−1.08538	+	0.788577i
$765$		0			0
$766$	6.13182			0.221552
$767$	−11.1384	+	70.3253i	−0.402186	+	2.53930i
$768$	6.73292	−	42.5100i	0.242953	−	1.53395i
$769$	31.2607	+	43.0267i	1.12729	+	1.55158i	0.793114	+	0.609073i	$0.208458\pi$
$769$	31.2607	+	43.0267i	1.12729	+	1.55158i	0.334177	+	0.942510i	$0.391542\pi$
$770$		0			0
$771$	−0.921944	−	0.669832i	−0.0332030	−	0.0241234i
$772$	14.4484	−	28.3566i	0.520009	−	1.02057i
$773$	27.3771	−	13.9493i	0.984686	−	0.501722i	0.113957	−	0.993486i	$-0.463647\pi$
$773$	27.3771	−	13.9493i	0.984686	−	0.501722i	0.870729	+	0.491763i	$0.163647\pi$
$774$	2.59023	−	7.97190i	0.0931038	−	0.286544i
$775$		0			0
$776$	−0.473616	−	0.651876i	−0.0170018	−	0.0234010i
$777$	−9.73375	+	4.95959i	−0.349196	+	0.177924i
$778$	2.08985	−	13.1948i	0.0749246	−	0.473055i
$779$	14.9358	−	20.5574i	0.535130	−	0.736544i
$780$		0			0
$781$	2.80236	+	3.85712i	0.100276	+	0.138019i
$782$	8.64875	−	4.40676i	0.309279	−	0.157585i
$783$	−9.49589	−	1.50400i	−0.339355	−	0.0537486i
$784$	14.9963	+	20.6406i	0.535582	+	0.737165i
$785$		0			0
$786$	19.7705	−	27.2117i	0.705189	−	0.970609i
$787$	16.5654	−	32.5114i	0.590493	−	1.15891i	−0.381604	−	0.924326i	$-0.624628\pi$
$787$	16.5654	−	32.5114i	0.590493	−	1.15891i	0.972097	−	0.234581i	$-0.0753718\pi$
$788$	9.94345	−	5.06644i	0.354221	−	0.180484i
$789$	−10.5883	+	32.5875i	−0.376954	+	1.16015i
$790$		0			0
$791$	−5.97321	+	1.94081i	−0.212383	+	0.0690074i
$792$	2.40676	+	4.72353i	0.0855204	+	0.167843i
$793$	−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
$797$	−5.91196	+	0.936362i	−0.209412	+	0.0331677i	−0.260259	−	0.965539i	$-0.583808\pi$
$797$	−5.91196	+	0.936362i	−0.209412	+	0.0331677i	0.0508468	+	0.998706i	$0.483808\pi$
$798$	10.4603	−	1.65675i	0.370290	−	0.0586482i
$799$	−8.98468			−0.317855
$800$		0			0
$801$	−14.2685			−0.504151
$802$	−14.2394	+	2.25530i	−0.502812	+	0.0796376i
$803$	−5.29802	+	0.839124i	−0.186963	+	0.0296120i
$804$	−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
$808$	10.4189	+	20.4483i	0.366536	+	0.719368i
$809$	29.7722	−	9.67358i	1.04674	−	0.340105i	0.265349	−	0.964152i	$-0.414513\pi$
$809$	29.7722	−	9.67358i	1.04674	−	0.340105i	0.781387	+	0.624047i	$0.214513\pi$
$810$		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	$0.0645476\pi$
$812$	−4.06276	+	2.07008i	−0.142575	+	0.0726455i
$813$	−13.3645	+	26.2293i	−0.468713	+	0.919901i
$814$	1.89440	−	2.60741i	0.0663985	−	0.0913898i
$815$		0			0
$816$	−47.7424	+	34.6868i	−1.67132	+	1.21428i
$817$	4.87940	+	0.772821i	0.170709	+	0.0270376i
$818$	15.1863	−	7.73783i	0.530978	−	0.270547i
$819$	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	$0.0702149\pi$
$822$	−0.583549	+	3.68438i	−0.0203536	+	0.128508i
$823$	10.3867	−	5.29231i	0.362059	−	0.184478i	−0.263492	−	0.964662i	$-0.584874\pi$
$823$	10.3867	−	5.29231i	0.362059	−	0.184478i	0.625551	+	0.780183i	$0.284874\pi$
$824$	9.75442	+	13.4258i	0.339811	+	0.467710i
$825$		0			0
$826$	3.87721	−	11.9328i	0.134905	−	0.415196i
$827$	5.29276	−	2.69680i	0.184047	−	0.0937768i	−0.359539	−	0.933130i	$-0.617066\pi$
$827$	5.29276	−	2.69680i	0.184047	−	0.0937768i	0.543586	+	0.839353i	$0.317066\pi$
$828$	−4.81351	+	9.44705i	−0.167281	+	0.328308i
$829$	−30.1824	−	21.9288i	−1.04828	−	0.761619i	−0.0763946	−	0.997078i	$-0.524341\pi$
$829$	−30.1824	−	21.9288i	−1.04828	−	0.761619i	−0.971884	+	0.235458i	$0.924341\pi$
$830$		0			0
$831$	−13.7632	−	18.9435i	−0.477442	−	0.657142i
$832$	22.9824	+	45.1054i	0.796770	+	1.56375i
$833$	5.47233	−	34.5510i	0.189605	−	1.19712i
$834$	−56.9303			−1.97133
$835$		0			0
$836$	−2.52775	+	1.83652i	−0.0874241	+	0.0635173i
$837$	−29.7769	−	15.1721i	−1.02924	−	0.524425i
$838$	4.55161	+	4.55161i	0.157233	+	0.157233i
$839$	−13.8039	+	42.4840i	−0.476563	+	1.46671i	0.367276	+	0.930112i	$0.380290\pi$
$839$	−13.8039	+	42.4840i	−0.476563	+	1.46671i	−0.843839	+	0.536597i	$0.819710\pi$
$840$		0			0
$841$	−6.37789	−	19.6291i	−0.219927	−	0.676866i
$842$	−19.0986	+	37.4832i	−0.658183	+	1.29176i
$843$	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
$847$	8.41399	−	1.33264i	0.289108	−	0.0457902i
$848$	−4.01686	−	4.01686i	−0.137939	−	0.137939i
$849$		−	20.0294i		−	0.687406i
$850$		0			0
$851$	6.44588			0.220962
$852$	9.06863	−	57.2571i	0.310686	−	1.96160i
$853$	0.939165	+	5.92966i	0.0321564	+	0.203028i	0.998536	−	0.0540922i	$-0.0172265\pi$
$853$	0.939165	+	5.92966i	0.0321564	+	0.203028i	−0.966380	+	0.257120i	$0.917227\pi$
$854$	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	$0.721205\pi$
$858$	−9.49036	−	4.83558i	−0.323996	−	0.165084i
$859$	−30.1496	+	9.79621i	−1.02869	+	0.334242i	−0.774273	−	0.632852i	$-0.781884\pi$
$859$	−30.1496	+	9.79621i	−1.02869	+	0.334242i	−0.254419	+	0.967094i	$0.581884\pi$
$860$		0			0
$861$	−14.5173	−	4.71696i	−0.494749	−	0.160754i
$862$	22.0152	+	22.0152i	0.749841	+	0.749841i
$863$	4.66076	−	9.14726i	0.158654	−	0.311376i	−0.797972	−	0.602694i	$-0.794094\pi$
$863$	4.66076	−	9.14726i	0.158654	−	0.311376i	0.956626	+	0.291318i	$0.0940938\pi$
$864$	5.81234	−	17.8885i	0.197740	−	0.608581i
$865$		0			0
$866$			27.0984i			0.920843i
$867$	34.7504	+	5.50393i	1.18019	+	0.186923i
$868$	−15.6547	+	2.47946i	−0.531354	+	0.0841582i
$869$	−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
$873$	−0.547863	−	1.07524i	−0.0185424	−	0.0363914i
$874$	−5.94310	−	1.93103i	−0.201028	−	0.0653181i
$875$		0			0
$876$	52.7661	+	38.3368i	1.78280	+	1.29528i
$877$	−7.86511	−	15.4361i	−0.265586	−	0.521241i	0.719246	−	0.694756i	$-0.244488\pi$
$877$	−7.86511	−	15.4361i	−0.265586	−	0.521241i	−0.984831	+	0.173515i	$0.944488\pi$
$878$	0.971367	−	6.13297i	0.0327821	−	0.206978i
$879$	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	$0.484825\pi$
$882$	17.3472	+	34.0458i	0.584111	+	1.14638i
$883$	−2.63545	+	16.6396i	−0.0886900	+	0.559966i	0.902829	+	0.430001i	$0.141487\pi$
$883$	−2.63545	+	16.6396i	−0.0886900	+	0.559966i	−0.991519	+	0.129966i	$0.958513\pi$
$884$	21.4489	−	66.0130i	0.721405	−	2.22026i
$885$		0			0
$886$	0.665718	−	0.916282i	0.0223652	−	0.0307831i
$887$	−19.8108	−	10.0941i	−0.665183	−	0.338928i	0.0885846	−	0.996069i	$-0.471766\pi$
$887$	−19.8108	−	10.0941i	−0.665183	−	0.338928i	−0.753768	+	0.657141i	$0.771766\pi$
$888$	−38.7058	+	6.13039i	−1.29888	+	0.205723i
$889$	−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
$897$	−3.33246	−	21.0403i	−0.111267	−	0.702515i
$898$	−5.06579	−	31.9842i	−0.169048	−	1.06733i
$899$			29.0621i			0.969277i
$900$		0			0
$901$			7.78890i			0.259486i
$902$	4.44788	−	0.704474i	0.148098	−	0.0234564i
$903$	−0.464247	−	2.93114i	−0.0154492	−	0.0975423i
$904$	−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	0.433645	−	0.901084i	$-0.357227\pi$
$911$	7.69141	+	2.49909i	0.254828	+	0.0827985i	−0.178817	+	0.983882i	$0.557227\pi$
$912$	37.5233	+	5.94310i	1.24252	+	0.196796i
$913$	−5.43579	−	2.76967i	−0.179898	−	0.0916627i
$914$	−33.9401	−	24.6589i	−1.12264	−	0.815645i
$915$		0			0
$916$	11.5582	+	3.75550i	0.381895	+	0.124085i
$917$	1.09057	−	6.88557i	0.0360137	−	0.227382i
$918$	−22.9786	+	11.7082i	−0.758408	+	0.386428i
$919$	22.9679	−	16.6871i	0.757640	−	0.550458i	−0.140546	−	0.990074i	$-0.544886\pi$
$919$	22.9679	−	16.6871i	0.757640	−	0.550458i	0.898186	+	0.439617i	$0.144886\pi$
$920$		0			0
$921$	−3.92285	−	2.85011i	−0.129262	−	0.0939145i
$922$	27.1520	+	4.30046i	0.894204	+	0.141628i
$923$	30.9551	+	60.7529i	1.01890	+	1.99971i
$924$	1.51846	+	1.10323i	0.0499538	+	0.0362936i
$925$		0			0
$926$	−11.0713	+	34.0740i	−0.363826	+	1.11974i
$927$	11.2836	+	22.1453i	0.370602	+	0.727347i
$928$	−16.1554	+	2.55876i	−0.530326	+	0.0839954i
$929$	−8.36507	+	11.5135i	−0.274449	+	0.377747i	−0.923885	−	0.382669i	$-0.875005\pi$
$929$	−8.36507	+	11.5135i	−0.274449	+	0.377747i	0.649436	+	0.760416i	$0.275005\pi$
$930$		0			0
$931$	−18.2193	+	13.2371i	−0.597114	+	0.433829i
$932$	−4.94212	−	31.2033i	−0.161885	−	1.02210i
$933$	−16.6393	−	2.63540i	−0.544745	−	0.0862792i
$934$	18.0462			0.590490
$935$		0			0
$936$	23.4287	+	72.1062i	0.765791	+	2.35686i
$937$	−7.54279	+	14.8036i	−0.246412	+	0.483611i	−0.980774	−	0.195147i	$-0.937482\pi$
$937$	−7.54279	+	14.8036i	−0.246412	+	0.483611i	0.734362	+	0.678758i	$0.237482\pi$
$938$	−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	$0.695278\pi$
$942$	9.87502	−	19.3808i	0.321745	−	0.631461i
$943$	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
$947$	−2.96183	−	18.7002i	−0.0962464	−	0.607676i	−0.987916	−	0.154989i	$-0.950466\pi$
$947$	−2.96183	−	18.7002i	−0.0962464	−	0.607676i	0.891670	−	0.452687i	$-0.149534\pi$
$948$	69.4506	+	10.9999i	2.25565	+	0.357260i
$949$	−76.7139			−2.49024
$950$		0			0
$951$		−	31.3639i		−	1.01705i
$952$	−5.55284	+	10.8981i	−0.179968	+	0.353208i
$953$	20.4884	−	3.24504i	0.663683	−	0.105117i	0.184501	−	0.982832i	$-0.440933\pi$
$953$	20.4884	−	3.24504i	0.663683	−	0.105117i	0.479183	+	0.877715i	$0.340933\pi$
$954$	−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
$958$	33.2527	+	16.9431i	1.07435	+	0.547407i
$959$	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
$963$	9.84005	+	5.01376i	0.317091	+	0.161566i
$964$	−10.8555	−	14.9413i	−0.349631	−	0.481225i
$965$		0			0
$966$			3.75385i			0.120778i
$967$	4.24840	−	26.8233i	0.136619	−	0.862580i	−0.820238	−	0.572022i	$-0.806159\pi$
$967$	4.24840	−	26.8233i	0.136619	−	0.862580i	0.956857	−	0.290558i	$-0.0938408\pi$
$968$	30.1827	+	4.78048i	0.970110	+	0.153650i
$969$	−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	$0.862971\pi$
$972$	−18.2504	+	35.8185i	−0.585382	+	1.14888i
$973$	−10.5135	+	5.35688i	−0.337046	+	0.171734i
$974$	−6.31759	−	2.05271i	−0.202429	−	0.0657731i
$975$		0			0
$976$	18.2835	−	5.94066i	0.585239	−	0.190156i
$977$	38.5326	−	19.6333i	1.23277	−	0.628126i	0.288555	−	0.957463i	$-0.406825\pi$
$977$	38.5326	−	19.6333i	1.23277	−	0.628126i	0.944212	+	0.329337i	$0.106825\pi$
$978$	41.0409	+	6.50024i	1.31234	+	0.207855i
$979$	0.876013	−	1.20573i	0.0279975	−	0.0385352i
$980$		0			0
$981$	−40.2563	−	55.4081i	−1.28529	−	1.76904i
$982$	−17.7057	−	34.7494i	−0.565012	−	1.10890i
$983$	−59.3265	−	9.39639i	−1.89222	−	0.299698i	−0.901200	−	0.433405i	$-0.857312\pi$
$983$	−59.3265	−	9.39639i	−1.89222	−	0.299698i	−0.991021	+	0.133706i	$0.957312\pi$
$984$	−44.2990	−	32.1851i	−1.41220	−	1.02602i
$985$		0			0
$986$	18.1438	+	13.1823i	0.577818	+	0.419809i
$987$	1.57744	−	3.09591i	0.0502106	−	0.0985439i
$988$	−39.8142	+	20.2864i	−1.26666	+	0.645395i
$989$	−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	$0.659280\pi$
$992$	−56.1566	−	8.89433i	−1.78297	−	0.282395i
$993$	−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
$997$	−20.2230	+	3.20301i	−0.640468	+	0.101440i	−0.468218	−	0.883613i	$-0.655104\pi$
$997$	−20.2230	+	3.20301i	−0.640468	+	0.101440i	−0.172250	+	0.985053i	$0.555104\pi$
$998$	−7.91815	−	49.9932i	−0.250645	−	1.58251i
$999$	−17.1259			−0.541839

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.v.a.83.1	✓	8	25.17	odd	20
200.2.v.a.147.1	yes	8	40.19	odd	2
200.2.v.b.83.1	yes	8	200.67	even	20
200.2.v.b.147.1	yes	8	5.4	even	2
800.2.bp.a.47.1		8	20.19	odd	2
800.2.bp.a.783.1		8	200.117	odd	20
800.2.bp.b.47.1		8	40.29	even	2
800.2.bp.b.783.1		8	100.67	even	20
1000.2.v.a.107.1		8	25.6	even	5
1000.2.v.a.243.1		8	40.3	even	4
1000.2.v.b.107.1		8	200.131	odd	10
1000.2.v.b.243.1		8	5.3	odd	4
1000.2.v.c.507.1		8	1.1	even	1	trivial
1000.2.v.c.643.1		8	200.83	even	20	inner
1000.2.v.d.107.1		8	200.19	odd	10
1000.2.v.d.243.1		8	5.2	odd	4
1000.2.v.e.107.1		8	25.19	even	10
1000.2.v.e.243.1		8	40.27	even	4
1000.2.v.f.507.1		8	8.3	odd	2
1000.2.v.f.643.1		8	25.8	odd	20

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)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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