LMFDB - Embedded newform 1000.2.v.a.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1000.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(0.420808 - 2.65688i) q^{3} -2.00000i q^{4} +(2.23607 + 3.07768i) q^{6} +(0.557537 - 0.557537i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-4.02874 - 1.30902i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(0.420808 - 2.65688i) q^{3} -2.00000i q^{4} +(2.23607 + 3.07768i) q^{6} +(0.557537 - 0.557537i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-4.02874 - 1.30902i) q^{9} +(-0.136729 - 0.420808i) q^{11} +(-5.31375 - 0.841616i) q^{12} +(5.63818 - 2.87280i) q^{13} +1.11507i q^{14} -4.00000 q^{16} +(-0.857960 - 5.41695i) q^{17} +(5.33776 - 2.71972i) q^{18} +(-2.07533 + 2.85645i) q^{19} +(-1.24669 - 1.71592i) q^{21} +(0.557537 + 0.284079i) 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} +(-1.11507 - 1.11507i) 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} +(6.27491 + 4.55899i) q^{34} +(-2.61803 + 8.05748i) q^{36} +(2.33833 + 4.58924i) q^{37} +(-0.781118 - 4.93179i) q^{38} +(-5.26007 - 16.1888i) q^{39} +(-2.22394 + 6.84458i) q^{41} +(2.96261 + 0.469231i) q^{42} +(0.989378 - 0.989378i) q^{43} +(-0.841616 + 0.273457i) q^{44} +(0.546915 + 1.68323i) q^{46} +(0.256271 - 1.61803i) q^{47} +(-1.68323 + 10.6275i) q^{48} +6.37831i q^{49} -14.7532 q^{51} +(-5.74559 - 11.2764i) q^{52} +(-1.40269 - 0.222164i) q^{53} +(-1.45309 - 4.47214i) q^{54} +2.23015 q^{56} +(6.71592 + 6.71592i) q^{57} +(0.639690 - 4.03884i) q^{58} +(-10.7014 - 3.47709i) q^{59} +(-4.57086 + 1.48516i) q^{61} +(2.22358 + 14.0391i) q^{62} +(-2.97599 + 1.51634i) q^{63} +8.00000i q^{64} +(0.989378 - 1.36176i) q^{66} +(-0.986616 - 6.22925i) q^{67} +(-10.8339 + 1.71592i) q^{68} +(-2.72353 - 1.97876i) q^{69} +(-6.33354 - 8.71737i) q^{71} +(-5.43945 - 10.6755i) 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} +(21.4489 + 10.9288i) q^{78} +(10.5738 - 7.68233i) q^{79} +(-3.04508 - 2.21238i) q^{81} +(-4.62064 - 9.06851i) q^{82} +(-13.6183 + 2.15693i) q^{83} +(-3.43184 + 2.49338i) q^{84} +1.97876i q^{86} +(3.53118 + 6.93033i) q^{87} +(0.568158 - 1.11507i) q^{88} +(3.20347 - 1.04087i) q^{89} +(1.54180 - 4.74518i) q^{91} +(-2.23015 - 1.13632i) q^{92} +(-19.1180 - 19.1180i) q^{93} +(1.36176 + 1.87431i) q^{94} +(-8.94427 - 12.3107i) q^{96} +(-0.281373 - 0.0445651i) q^{97} +(-6.37831 - 6.37831i) q^{98} +1.87431i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 4 q^{7} + 16 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 4 * q^7 + 16 * q^8	$ 8 q - 8 q^{2} + 4 q^{7} + 16 q^{8} - 4 q^{11} + 12 q^{13} - 32 q^{16} - 10 q^{17} + 6 q^{18} + 10 q^{19} + 20 q^{21} + 4 q^{22} - 8 q^{23} - 4 q^{26} - 8 q^{28} - 10 q^{29} - 10 q^{31} + 32 q^{32} + 20 q^{34} - 12 q^{36} + 14 q^{37} - 8 q^{38} - 30 q^{39} + 16 q^{41} + 20 q^{43} + 16 q^{46} + 24 q^{47} - 20 q^{51} - 16 q^{52} - 28 q^{53} + 16 q^{56} + 60 q^{57} - 10 q^{59} + 10 q^{61} + 20 q^{62} - 18 q^{63} + 20 q^{66} + 10 q^{67} - 20 q^{68} + 40 q^{69} - 20 q^{71} + 12 q^{72} + 10 q^{73} - 10 q^{74} - 4 q^{76} - 32 q^{77} + 40 q^{78} + 30 q^{79} - 2 q^{81} - 56 q^{82} - 40 q^{84} + 20 q^{87} - 8 q^{88} + 10 q^{89} - 8 q^{91} - 16 q^{92} - 80 q^{93} - 20 q^{94} - 30 q^{97} + 8 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 4 * q^7 + 16 * q^8 - 4 * q^11 + 12 * q^13 - 32 * q^16 - 10 * q^17 + 6 * q^18 + 10 * q^19 + 20 * q^21 + 4 * q^22 - 8 * q^23 - 4 * q^26 - 8 * q^28 - 10 * q^29 - 10 * q^31 + 32 * q^32 + 20 * q^34 - 12 * q^36 + 14 * q^37 - 8 * q^38 - 30 * q^39 + 16 * q^41 + 20 * q^43 + 16 * q^46 + 24 * q^47 - 20 * q^51 - 16 * q^52 - 28 * q^53 + 16 * q^56 + 60 * q^57 - 10 * q^59 + 10 * q^61 + 20 * q^62 - 18 * q^63 + 20 * q^66 + 10 * q^67 - 20 * q^68 + 40 * q^69 - 20 * q^71 + 12 * q^72 + 10 * q^73 - 10 * q^74 - 4 * q^76 - 32 * q^77 + 40 * q^78 + 30 * q^79 - 2 * q^81 - 56 * q^82 - 40 * q^84 + 20 * q^87 - 8 * q^88 + 10 * q^89 - 8 * q^91 - 16 * q^92 - 80 * q^93 - 20 * q^94 - 30 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	0.420808	−	2.65688i	0.242953	−	1.53395i	−0.500841	−	0.865539i	$-0.666976\pi$
$3$	0.420808	−	2.65688i	0.242953	−	1.53395i	0.743794	−	0.668409i	$-0.233024\pi$
$4$		−	2.00000i		−	1.00000i
$5$		0			0
$5$		0			0
$6$	2.23607	+	3.07768i	0.912871	+	1.25646i
$7$	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	$0.202392\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−4.02874	−	1.30902i	−1.34291	−	0.436339i
$10$		0			0
$11$	−0.136729	−	0.420808i	−0.0412253	−	0.126878i	0.928326	−	0.371768i	$-0.121248\pi$
$11$	−0.136729	−	0.420808i	−0.0412253	−	0.126878i	−0.969551	+	0.244890i	$0.921248\pi$
$12$	−5.31375	−	0.841616i	−1.53395	−	0.242953i
$13$	5.63818	−	2.87280i	1.56375	−	0.796770i	0.564167	−	0.825660i	$-0.309197\pi$
$13$	5.63818	−	2.87280i	1.56375	−	0.796770i	0.999583	+	0.0288899i	$0.00919723\pi$
$14$			1.11507i			0.298016i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	−0.857960	−	5.41695i	−0.208086	−	1.31380i	−0.841612	−	0.540082i	$-0.818393\pi$
$17$	−0.857960	−	5.41695i	−0.208086	−	1.31380i	0.633526	−	0.773721i	$-0.281607\pi$
$18$	5.33776	−	2.71972i	1.25812	−	0.641045i
$19$	−2.07533	+	2.85645i	−0.476114	+	0.655315i	−0.977752	−	0.209763i	$-0.932731\pi$
$19$	−2.07533	+	2.85645i	−0.476114	+	0.655315i	0.501638	+	0.865078i	$0.332731\pi$
$20$		0			0
$21$	−1.24669	−	1.71592i	−0.272050	−	0.374445i
$22$	0.557537	+	0.284079i	0.118867	+	0.0605659i
$23$	0.568158	−	1.11507i	0.118469	−	0.232509i	−0.824155	−	0.566364i	$-0.808350\pi$
$23$	0.568158	−	1.11507i	0.118469	−	0.232509i	0.942624	+	0.333855i	$0.108350\pi$
$24$	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
$28$	−1.11507	−	1.11507i	−0.210729	−	0.210729i
$29$	−2.33927	+	1.69958i	−0.434391	+	0.315603i	−0.783402	−	0.621515i	$-0.786517\pi$
$29$	−2.33927	+	1.69958i	−0.434391	+	0.315603i	0.349011	+	0.937118i	$0.386517\pi$
$30$		0			0
$31$	5.90778	−	8.13136i	1.06107	−	1.46044i	0.182267	−	0.983249i	$-0.441657\pi$
$31$	5.90778	−	8.13136i	1.06107	−	1.46044i	0.878802	−	0.477186i	$-0.158343\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	−1.17557	+	0.186192i	−0.204641	+	0.0324119i
$34$	6.27491	+	4.55899i	1.07614	+	0.781860i
$35$		0			0
$36$	−2.61803	+	8.05748i	−0.436339	+	1.34291i
$37$	2.33833	+	4.58924i	0.384420	+	0.754466i	0.999420	−	0.0340610i	$-0.0108441\pi$
$37$	2.33833	+	4.58924i	0.384420	+	0.754466i	−0.615000	+	0.788527i	$0.710844\pi$
$38$	−0.781118	−	4.93179i	−0.126714	−	0.800041i
$39$	−5.26007	−	16.1888i	−0.842286	−	2.59229i
$40$		0			0
$41$	−2.22394	+	6.84458i	−0.347321	+	1.06894i	0.613009	+	0.790076i	$0.289959\pi$
$41$	−2.22394	+	6.84458i	−0.347321	+	1.06894i	−0.960330	+	0.278867i	$0.910041\pi$
$42$	2.96261	+	0.469231i	0.457141	+	0.0724040i
$43$	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	$0.215976\pi$
$44$	−0.841616	+	0.273457i	−0.126878	+	0.0412253i
$45$		0			0
$46$	0.546915	+	1.68323i	0.0806382	+	0.248179i
$47$	0.256271	−	1.61803i	0.0373810	−	0.236015i	−0.961923	−	0.273321i	$-0.911878\pi$
$47$	0.256271	−	1.61803i	0.0373810	−	0.236015i	0.999304	+	0.0373066i	$0.0118778\pi$
$48$	−1.68323	+	10.6275i	−0.242953	+	1.53395i
$49$			6.37831i			0.911187i
$50$		0			0
$51$	−14.7532			−2.06586
$52$	−5.74559	−	11.2764i	−0.796770	−	1.56375i
$53$	−1.40269	−	0.222164i	−0.192674	−	0.0305166i	0.0593515	−	0.998237i	$-0.481097\pi$
$53$	−1.40269	−	0.222164i	−0.192674	−	0.0305166i	−0.252026	+	0.967721i	$0.581097\pi$
$54$	−1.45309	−	4.47214i	−0.197740	−	0.608581i
$55$		0			0
$56$	2.23015			0.298016
$57$	6.71592	+	6.71592i	0.889545	+	0.889545i
$58$	0.639690	−	4.03884i	0.0839954	−	0.530326i
$59$	−10.7014	−	3.47709i	−1.39320	−	0.452679i	−0.486215	−	0.873839i	$-0.661623\pi$
$59$	−10.7014	−	3.47709i	−1.39320	−	0.452679i	−0.906986	+	0.421160i	$0.861623\pi$
$60$		0			0
$61$	−4.57086	+	1.48516i	−0.585239	+	0.190156i	−0.586646	−	0.809843i	$-0.699552\pi$
$61$	−4.57086	+	1.48516i	−0.585239	+	0.190156i	0.00140712	+	0.999999i	$0.499552\pi$
$62$	2.22358	+	14.0391i	0.282395	+	1.78297i
$63$	−2.97599	+	1.51634i	−0.374940	+	0.191042i
$64$			8.00000i			1.00000i
$65$		0			0
$66$	0.989378	−	1.36176i	0.121784	−	0.167621i
$67$	−0.986616	−	6.22925i	−0.120534	−	0.761024i	−0.971716	−	0.236153i	$-0.924113\pi$
$67$	−0.986616	−	6.22925i	−0.120534	−	0.761024i	0.851182	−	0.524871i	$-0.175887\pi$
$68$	−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	−0.997863	−	0.0653452i	$-0.979185\pi$
$71$	−6.33354	−	8.71737i	−0.751653	−	1.03456i	0.246210	−	0.969217i	$-0.420815\pi$
$72$	−5.43945	−	10.6755i	−0.641045	−	1.25812i
$73$	−10.8018	−	5.50380i	−1.26426	−	0.644171i	−0.312178	−	0.950024i	$-0.601059\pi$
$73$	−10.8018	−	5.50380i	−1.26426	−	0.644171i	−0.952079	+	0.305852i	$0.901059\pi$
$74$	−6.92757	−	2.25090i	−0.805314	−	0.261662i
$75$		0			0
$76$	5.71290	+	4.15067i	0.655315	+	0.476114i
$77$	−0.310847	−	0.158384i	−0.0354243	−	0.0180496i
$78$	21.4489	+	10.9288i	2.42861	+	1.23744i
$79$	10.5738	−	7.68233i	1.18965	−	0.864330i	0.196421	−	0.980520i	$-0.437068\pi$
$79$	10.5738	−	7.68233i	1.18965	−	0.864330i	0.993227	+	0.116190i	$0.0370680\pi$
$80$		0			0
$81$	−3.04508	−	2.21238i	−0.338343	−	0.245820i
$82$	−4.62064	−	9.06851i	−0.510264	−	1.00145i
$83$	−13.6183	+	2.15693i	−1.49481	+	0.236754i	−0.849671	−	0.527314i	$-0.823199\pi$
$83$	−13.6183	+	2.15693i	−1.49481	+	0.236754i	−0.645136	+	0.764068i	$0.723199\pi$
$84$	−3.43184	+	2.49338i	−0.374445	+	0.272050i
$85$		0			0
$86$			1.97876i			0.213375i
$87$	3.53118	+	6.93033i	0.378582	+	0.743010i
$88$	0.568158	−	1.11507i	0.0605659	−	0.118867i
$89$	3.20347	−	1.04087i	0.339567	−	0.110332i	−0.134269	−	0.990945i	$-0.542869\pi$
$89$	3.20347	−	1.04087i	0.339567	−	0.110332i	0.473837	+	0.880613i	$0.342869\pi$
$90$		0			0
$91$	1.54180	−	4.74518i	0.161625	−	0.497430i
$92$	−2.23015	−	1.13632i	−0.232509	−	0.118469i
$93$	−19.1180	−	19.1180i	−1.98244	−	1.98244i
$94$	1.36176	+	1.87431i	0.140455	+	0.193320i
$95$		0			0
$96$	−8.94427	−	12.3107i	−0.912871	−	1.25646i
$97$	−0.281373	−	0.0445651i	−0.0285691	−	0.00452490i	0.142134	−	0.989847i	$-0.454604\pi$
$97$	−0.281373	−	0.0445651i	−0.0285691	−	0.00452490i	−0.170703	+	0.985323i	$0.554604\pi$
$98$	−6.37831	−	6.37831i	−0.644306	−	0.644306i
$99$			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	$0.867730\pi$
$102$	14.7532	−	14.7532i	1.46078	−	1.46078i
$103$	5.79506	+	0.917847i	0.571004	+	0.0904381i	0.435258	−	0.900306i	$-0.356657\pi$
$103$	5.79506	+	0.917847i	0.571004	+	0.0904381i	0.135746	+	0.990744i	$0.456657\pi$
$104$	17.0220	+	5.53077i	1.66914	+	0.542336i
$105$		0			0
$106$	1.62485	−	1.18053i	0.157820	−	0.114663i
$107$	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	$0.709780\pi$
$108$	5.92522	+	3.01905i	0.570155	+	0.290508i
$109$	−4.99614	+	15.3765i	−0.478544	+	1.47281i	0.362575	+	0.931955i	$0.381898\pi$
$109$	−4.99614	+	15.3765i	−0.478544	+	1.47281i	−0.841118	+	0.540851i	$0.818102\pi$
$110$		0			0
$111$	13.1770	−	4.28147i	1.25071	−	0.406380i
$112$	−2.23015	+	2.23015i	−0.210729	+	0.210729i
$113$	3.61626	+	7.09731i	0.340189	+	0.667659i	0.996200	−	0.0870924i	$-0.0277576\pi$
$113$	3.61626	+	7.09731i	0.340189	+	0.667659i	−0.656011	+	0.754751i	$0.727758\pi$
$114$	−13.4318			−1.25801
$115$		0			0
$116$	3.39915	+	4.67853i	0.315603	+	0.434391i
$117$	−26.4753	+	4.19328i	−2.44764	+	0.387669i
$118$	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
$122$	3.08570	−	6.05603i	0.279366	−	0.548287i
$123$	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	0.749245	−	0.662293i	$-0.230417\pi$
$127$	7.36833	+	3.75435i	0.653833	+	0.333145i	−0.0954115	+	0.995438i	$0.530417\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	−2.21232	−	3.04499i	−0.194784	−	0.268097i
$130$		0			0
$131$	7.15302	+	5.19697i	0.624962	+	0.454061i	0.854651	−	0.519203i	$-0.173771\pi$
$131$	7.15302	+	5.19697i	0.624962	+	0.454061i	−0.229689	+	0.973264i	$0.573771\pi$
$132$	0.372384	+	2.35114i	0.0324119	+	0.204641i
$133$	0.435502	+	2.74965i	0.0377628	+	0.238425i
$134$	7.21586	+	5.24263i	0.623356	+	0.452894i
$135$		0			0
$136$	9.11798	−	12.5498i	0.781860	−	1.07614i
$137$	0.873694	−	0.445169i	0.0746447	−	0.0380334i	−0.416270	−	0.909241i	$-0.636663\pi$
$137$	0.873694	−	0.445169i	0.0746447	−	0.0380334i	0.490914	+	0.871208i	$0.336663\pi$
$138$	4.70228	−	0.744768i	0.400285	−	0.0633989i
$139$	14.2326	−	4.62444i	1.20719	−	0.392240i	0.364789	−	0.931090i	$-0.381141\pi$
$139$	14.2326	−	4.62444i	1.20719	−	0.392240i	0.842402	+	0.538850i	$0.181141\pi$
$140$		0			0
$141$	−4.19107	−	1.36176i	−0.352952	−	0.114681i
$142$	15.0509	+	2.38383i	1.26304	+	0.200047i
$143$	−1.97980	−	1.97980i	−0.165559	−	0.165559i
$144$	16.1150	+	5.23607i	1.34291	+	0.436339i
$145$		0			0
$146$	16.3056	−	5.29802i	1.34946	−	0.438467i
$147$	16.9464	+	2.68404i	1.39771	+	0.221376i
$148$	9.17848	−	4.67667i	0.754466	−	0.384420i
$149$	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	$0.886581\pi$
$152$	−9.86357	+	1.56224i	−0.800041	+	0.126714i
$153$	−3.63438	+	22.9466i	−0.293822	+	1.85512i
$154$	0.469231	−	0.152463i	0.0378117	−	0.0122858i
$155$		0			0
$156$	−32.3777	+	10.5201i	−2.59229	+	0.842286i
$157$	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	$0.176728\pi$
$158$	−2.89149	+	18.2562i	−0.230035	+	1.45238i
$159$	−1.18053	+	3.63328i	−0.0936217	+	0.288138i
$160$		0			0
$161$	−0.304925	−	0.938463i	−0.0240315	−	0.0739612i
$162$	5.25747	−	0.832701i	0.413066	−	0.0654232i
$163$	−4.95881	−	9.73221i	−0.388404	−	0.762285i	0.611169	−	0.791500i	$-0.290699\pi$
$163$	−4.95881	−	9.73221i	−0.388404	−	0.762285i	−0.999573	+	0.0292144i	$0.990699\pi$
$164$	13.6892	+	4.44788i	1.06894	+	0.347321i
$165$		0			0
$166$	11.4614	−	15.7753i	0.889577	−	1.22440i
$167$	−12.4180	+	1.96683i	−0.960937	+	0.152198i	−0.617146	−	0.786849i	$-0.711711\pi$
$167$	−12.4180	+	1.96683i	−0.960937	+	0.152198i	−0.343791	+	0.939046i	$0.611711\pi$
$168$	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
$172$	−1.97876	−	1.97876i	−0.150879	−	0.150879i
$173$	−5.64266	+	11.0743i	−0.429004	+	0.841967i	0.570779	+	0.821104i	$0.306641\pi$
$173$	−5.64266	+	11.0743i	−0.429004	+	0.841967i	−0.999782	+	0.0208630i	$0.993359\pi$
$174$	−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
$178$	−2.16260	+	4.24434i	−0.162094	+	0.318127i
$179$	−5.33119	−	7.33776i	−0.398472	−	0.548450i	0.561888	−	0.827214i	$-0.310075\pi$
$179$	−5.33119	−	7.33776i	−0.398472	−	0.548450i	−0.960360	+	0.278764i	$0.910075\pi$
$180$		0			0
$181$	−7.70946	+	10.6112i	−0.573039	+	0.788721i	−0.992911	−	0.118863i	$-0.962075\pi$
$181$	−7.70946	+	10.6112i	−0.573039	+	0.788721i	0.419871	+	0.907584i	$0.362075\pi$
$182$	3.20338	+	6.28698i	0.237450	+	0.466022i
$183$	2.02244	+	12.7692i	0.149503	+	0.943925i
$184$	3.36646	−	1.09383i	0.248179	−	0.0806382i
$185$		0			0
$186$	38.2360			2.80360
$187$	−2.16219	+	1.10169i	−0.158115	+	0.0805635i
$188$	−3.23607	−	0.512543i	−0.236015	−	0.0373810i
$189$	0.810148	+	2.49338i	0.0589296	+	0.181367i
$190$		0			0
$191$	17.6339	+	5.72960i	1.27594	+	0.414580i	0.867150	−	0.498047i	$-0.165949\pi$
$191$	17.6339	+	5.72960i	1.27594	+	0.414580i	0.408795	+	0.912626i	$0.365949\pi$
$192$	21.2550	+	3.36646i	1.53395	+	0.242953i
$193$	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	$0.0558926\pi$
$194$	0.325938	−	0.236808i	0.0234010	−	0.0170018i
$195$		0			0
$196$	12.7566			0.911187
$197$	0.872888	−	5.51120i	0.0621907	−	0.392657i	−0.936884	−	0.349641i	$-0.886304\pi$
$197$	0.872888	−	5.51120i	0.0621907	−	0.392657i	0.999074	−	0.0430155i	$-0.0136965\pi$
$198$	−1.87431	−	1.87431i	−0.133201	−	0.133201i
$199$	−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
$202$	−8.11392	−	8.11392i	−0.570893	−	0.570893i
$203$	−0.356650	+	2.25180i	−0.0250319	+	0.158046i
$204$			29.5064i			2.06586i
$205$		0			0
$206$	−6.71290	+	4.87721i	−0.467710	+	0.339811i
$207$	−3.74861	+	3.74861i	−0.260546	+	0.260546i
$208$	−22.5527	+	11.4912i	−1.56375	+	0.796770i
$209$	1.48577	+	0.482758i	0.102773	+	0.0333930i
$210$		0			0
$211$	−0.146453	−	0.450735i	−0.0100822	−	0.0310299i	0.945889	−	0.324491i	$-0.105193\pi$
$211$	−0.146453	−	0.450735i	−0.0100822	−	0.0310299i	−0.955971	+	0.293461i	$0.905193\pi$
$212$	−0.444328	+	2.80538i	−0.0305166	+	0.192674i
$213$	−25.8262	+	13.1591i	−1.76958	+	0.901646i
$214$	−3.68696			−0.252035
$215$		0			0
$216$	−8.94427	+	2.90617i	−0.608581	+	0.197740i
$217$	−1.23973	−	7.82733i	−0.0841582	−	0.531354i
$218$	−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
$222$	−8.89555	+	17.4585i	−0.597030	+	1.17174i
$223$	10.0452	−	19.7149i	0.672680	−	1.32021i	−0.262121	−	0.965035i	$-0.584422\pi$
$223$	10.0452	−	19.7149i	0.672680	−	1.32021i	0.934801	−	0.355173i	$-0.115578\pi$
$224$		−	4.46029i		−	0.298016i
$225$		0			0
$226$	−10.7136	−	3.48105i	−0.712656	−	0.231556i
$227$	0.709101	−	1.39169i	0.0470647	−	0.0923697i	−0.866276	−	0.499565i	$-0.833493\pi$
$227$	0.709101	−	1.39169i	0.0470647	−	0.0923697i	0.913341	+	0.407195i	$0.133493\pi$
$228$	13.4318	−	13.4318i	0.889545	−	0.889545i
$229$	4.91602	−	3.57170i	0.324860	−	0.236024i	−0.413387	−	0.910556i	$-0.635654\pi$
$229$	4.91602	−	3.57170i	0.324860	−	0.236024i	0.738246	+	0.674531i	$0.235654\pi$
$230$		0			0
$231$	−0.551615	+	0.759232i	−0.0362936	+	0.0499538i
$232$	−8.07768	−	1.27938i	−0.530326	−	0.0839954i
$233$	15.6017	−	2.47106i	1.02210	−	0.161885i	0.377184	−	0.926138i	$-0.376893\pi$
$233$	15.6017	−	2.47106i	1.02210	−	0.161885i	0.644916	+	0.764254i	$0.276893\pi$
$234$	22.2820	−	30.6686i	1.45662	−	2.00487i
$235$		0			0
$236$	−6.95418	+	21.4028i	−0.452679	+	1.39320i
$237$	−15.9615	−	31.3261i	−1.03681	−	2.03485i
$238$	6.04029	−	0.956689i	0.391534	−	0.0620129i
$239$	−0.321469	−	0.989378i	−0.0207941	−	0.0639976i	0.940121	−	0.340841i	$-0.110712\pi$
$239$	−0.321469	−	0.989378i	−0.0207941	−	0.0639976i	−0.960915	+	0.276843i	$0.910712\pi$
$240$		0			0
$241$	−2.85353	+	8.78225i	−0.183812	+	0.565714i	−0.999926	−	0.0121764i	$-0.996124\pi$
$241$	−2.85353	+	8.78225i	−0.183812	+	0.565714i	0.816114	+	0.577891i	$0.196124\pi$
$242$	−2.39024	+	15.0914i	−0.153650	+	0.970110i
$243$	−14.2128	+	14.2128i	−0.911755	+	0.911755i
$244$	2.97033	+	9.14173i	0.190156	+	0.585239i
$245$		0			0
$246$	−26.0383	+	8.46036i	−1.66014	+	0.539413i
$247$	−3.49510	+	22.0672i	−0.222388	+	1.40410i
$248$	28.0783	−	4.44716i	1.78297	−	0.282395i
$249$			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	$0.426442\pi$
$252$	3.03269	+	5.95199i	0.191042	+	0.374940i
$253$	−0.546915	−	0.0866228i	−0.0343842	−	0.00544593i
$254$	−11.1227	+	3.61398i	−0.697899	+	0.226761i
$255$		0			0
$256$	16.0000			1.00000
$257$	−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	$0.754206\pi$
$258$	5.25731	+	0.832676i	0.327306	+	0.0518402i
$259$	3.86237	+	1.25496i	0.239996	+	0.0779795i
$260$		0			0
$261$	11.6491	−	3.78501i	0.721059	−	0.234286i
$262$	−12.3500	+	1.95605i	−0.762985	+	0.120845i
$263$	11.3494	−	5.78283i	0.699836	−	0.356584i	−0.0675976	−	0.997713i	$-0.521533\pi$
$263$	11.3494	−	5.78283i	0.699836	−	0.356584i	0.767434	+	0.641128i	$0.221533\pi$
$264$	−2.72353	−	1.97876i	−0.167621	−	0.121784i
$265$		0			0
$266$	−3.18515	−	2.31415i	−0.195294	−	0.141890i
$267$	−1.41742	−	8.94923i	−0.0867446	−	0.547684i
$268$	−12.4585	+	1.97323i	−0.761024	+	0.120534i
$269$	9.07519	+	6.59351i	0.553324	+	0.402013i	0.829009	−	0.559235i	$-0.188905\pi$
$269$	9.07519	+	6.59351i	0.553324	+	0.402013i	−0.275686	+	0.961248i	$0.588905\pi$
$270$		0			0
$271$	6.43240	+	8.85343i	0.390740	+	0.537808i	0.958390	−	0.285462i	$-0.0921472\pi$
$271$	6.43240	+	8.85343i	0.390740	+	0.537808i	−0.567650	+	0.823270i	$0.692147\pi$
$272$	3.43184	+	21.6678i	0.208086	+	1.31380i
$273$	−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	0.671196	−	0.741280i	$-0.265781\pi$
$277$	7.75589	+	3.95183i	0.466006	+	0.237442i	−0.205189	+	0.978722i	$0.565781\pi$
$278$	−9.60812	+	18.8570i	−0.576257	+	1.13097i
$279$	−34.4450	+	25.0258i	−2.06217	+	1.49825i
$280$		0			0
$281$	7.75715	+	5.63590i	0.462753	+	0.336209i	0.794610	−	0.607120i	$-0.207675\pi$
$281$	7.75715	+	5.63590i	0.462753	+	0.336209i	−0.331857	+	0.943330i	$0.607675\pi$
$282$	5.55284	−	2.82931i	0.330667	−	0.168483i
$283$	7.35420	−	1.16479i	0.437162	−	0.0692397i	0.0660254	−	0.997818i	$-0.478968\pi$
$283$	7.35420	−	1.16479i	0.437162	−	0.0692397i	0.371137	+	0.928578i	$0.378968\pi$
$284$	−17.4347	+	12.6671i	−1.03456	+	0.751653i
$285$		0			0
$286$	3.95959			0.234136
$287$	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
$292$	−11.0076	+	21.6036i	−0.644171	+	1.26426i
$293$	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	$0.616622\pi$
$294$	−19.6304	+	14.2623i	−1.14487	+	0.831796i
$295$		0			0
$296$	−4.50181	+	13.8551i	−0.261662	+	0.805314i
$297$	1.45309	+	0.230146i	0.0843165	+	0.0133544i
$298$	−21.0278	+	21.0278i	−1.21811	+	1.21811i
$299$		−	7.91919i		−	0.457978i
$300$		0			0
$301$		−	1.10323i		−	0.0635891i
$302$	−8.57286	−	8.57286i	−0.493313	−	0.493313i
$303$	21.5577	+	3.41440i	1.23846	+	0.196152i
$304$	8.30133	−	11.4258i	0.476114	−	0.655315i
$305$		0			0
$306$	−19.3122	−	26.5809i	−1.10400	−	1.51953i
$307$	−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	$0.766381\pi$
$308$	−0.316769	+	0.621694i	−0.0180496	+	0.0354243i
$309$	4.87721	−	15.0105i	0.277455	−	0.853918i
$310$		0			0
$311$	5.95620	−	1.93529i	0.337745	−	0.109740i	−0.135234	−	0.990814i	$-0.543179\pi$
$311$	5.95620	−	1.93529i	0.337745	−	0.109740i	0.472979	+	0.881074i	$0.343179\pi$
$312$	21.8575	−	42.8978i	1.23744	−	2.42861i
$313$	1.36098	+	2.67107i	0.0769270	+	0.150978i	0.926266	−	0.376869i	$-0.122999\pi$
$313$	1.36098	+	2.67107i	0.0769270	+	0.150978i	−0.849339	+	0.527847i	$0.822999\pi$
$314$			8.08611i			0.456326i
$315$		0			0
$316$	−15.3647	−	21.1477i	−0.864330	−	1.18965i
$317$	11.5159	−	1.82394i	0.646799	−	0.102443i	0.175589	−	0.984464i	$-0.443817\pi$
$317$	11.5159	−	1.82394i	0.646799	−	0.102443i	0.471211	+	0.882021i	$0.343817\pi$
$318$	−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
$322$	1.24339	+	0.633538i	0.0692913	+	0.0353057i
$323$	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
$328$	−18.1370	+	9.24128i	−1.00145	+	0.510264i
$329$	−0.759232	−	1.04499i	−0.0418578	−	0.0576124i
$330$		0			0
$331$	−21.1491	−	15.3657i	−1.16246	−	0.844576i	−0.172373	−	0.985032i	$-0.555143\pi$
$331$	−21.1491	−	15.3657i	−1.16246	−	0.844576i	−0.990087	+	0.140455i	$0.955143\pi$
$332$	4.31386	+	27.2367i	0.236754	+	1.49481i
$333$	−3.41315	−	21.5498i	−0.187039	−	1.18092i
$334$	10.4512	−	14.3849i	0.571865	−	0.787105i
$335$		0			0
$336$	4.98676	+	6.86368i	0.272050	+	0.374445i
$337$	19.5056	−	9.93860i	1.06254	−	0.541390i	0.166809	−	0.985989i	$-0.446654\pi$
$337$	19.5056	−	9.93860i	1.06254	−	0.541390i	0.895730	+	0.444599i	$0.146654\pi$
$338$	5.98256	+	37.7724i	0.325408	+	2.05455i
$339$	20.3784	−	6.62135i	1.10680	−	0.359622i
$340$		0			0
$341$	−4.22950	−	1.37425i	−0.229040	−	0.0744198i
$342$	−3.30887	+	20.8914i	−0.178923	+	1.12968i
$343$	7.45889	+	7.45889i	0.402742	+	0.402742i
$344$	3.95751			0.213375
$345$		0			0
$346$	−5.43168	−	16.7170i	−0.292009	−	0.898712i
$347$	9.99724	+	1.58341i	0.536680	+	0.0850017i	0.418890	−	0.908037i	$-0.362419\pi$
$347$	9.99724	+	1.58341i	0.536680	+	0.0850017i	0.117790	+	0.993039i	$0.462419\pi$
$348$	13.8607	−	7.06236i	0.743010	−	0.378582i
$349$	−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
$352$	−2.23015	−	1.13632i	−0.118867	−	0.0605659i
$353$	−3.52146	+	22.2336i	−0.187428	+	1.18338i	0.697130	+	0.716945i	$0.254460\pi$
$353$	−3.52146	+	22.2336i	−0.187428	+	1.18338i	−0.884558	+	0.466430i	$0.845540\pi$
$354$	−13.2276	−	40.7105i	−0.703041	−	2.16374i
$355$		0			0
$356$	−2.08174	−	6.40694i	−0.110332	−	0.339567i
$357$	−8.22545	+	8.22545i	−0.435337	+	0.435337i
$358$	12.6689	+	2.00656i	0.669575	+	0.106050i
$359$	3.80423	−	11.7082i	0.200779	−	0.617935i	−0.799081	−	0.601223i	$-0.794680\pi$
$359$	3.80423	−	11.7082i	0.200779	−	0.617935i	0.999860	−	0.0167120i	$-0.00531983\pi$
$360$		0			0
$361$	2.01902	+	6.21389i	0.106264	+	0.327047i
$362$	−2.90170	−	18.3206i	−0.152510	−	0.962910i
$363$	−13.1945	−	25.8956i	−0.692530	−	1.35917i
$364$	−9.49036	−	3.08361i	−0.497430	−	0.161625i
$365$		0			0
$366$	−14.7916	−	10.7467i	−0.773171	−	0.561741i
$367$	27.9062	−	4.41991i	1.45669	−	0.230717i	0.622686	−	0.782472i	$-0.286041\pi$
$367$	27.9062	−	4.41991i	1.45669	−	0.230717i	0.834007	+	0.551754i	$0.186041\pi$
$368$	−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
$372$	−38.2360	+	38.2360i	−1.98244	+	1.98244i
$373$	−3.55258	+	6.97233i	−0.183946	+	0.361014i	−0.964504	−	0.264070i	$-0.914935\pi$
$373$	−3.55258	+	6.97233i	−0.183946	+	0.361014i	0.780558	+	0.625084i	$0.214935\pi$
$374$	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
$378$	−3.30353	−	1.68323i	−0.169915	−	0.0865761i
$379$	12.6090	+	17.3548i	0.647682	+	0.891458i	0.998996	−	0.0447999i	$-0.0142650\pi$
$379$	12.6090	+	17.3548i	0.647682	+	0.891458i	−0.351314	+	0.936258i	$0.614265\pi$
$380$		0			0
$381$	13.0755	−	17.9969i	0.669878	−	0.922008i
$382$	−23.3635	+	11.9043i	−1.19538	+	0.609077i
$383$	0.678276	+	4.28247i	0.0346583	+	0.218824i	0.998939	−	0.0460597i	$-0.0146664\pi$
$383$	0.678276	+	4.28247i	0.0346583	+	0.218824i	−0.964280	+	0.264884i	$0.914666\pi$
$384$	−24.6215	+	17.8885i	−1.25646	+	0.912871i
$385$		0			0
$386$			22.5039i			1.14542i
$387$	−5.28106	+	2.69084i	−0.268451	+	0.136783i
$388$	−0.0891302	+	0.562746i	−0.00452490	+	0.0285691i
$389$	2.91910	+	8.98407i	0.148004	+	0.455510i	0.997385	−	0.0722702i	$-0.0230244\pi$
$389$	2.91910	+	8.98407i	0.148004	+	0.455510i	−0.849381	+	0.527780i	$0.823024\pi$
$390$		0			0
$391$	−6.52775	−	2.12099i	−0.330123	−	0.107263i
$392$	−12.7566	+	12.7566i	−0.644306	+	0.644306i
$393$	16.8178	−	16.8178i	0.848343	−	0.848343i
$394$	4.63831	+	6.38409i	0.233675	+	0.321626i
$395$		0			0
$396$	3.74861			0.188375
$397$	5.49045	−	34.6653i	0.275558	−	1.73980i	−0.329981	−	0.943988i	$-0.607042\pi$
$397$	5.49045	−	34.6653i	0.275558	−	1.73980i	0.605539	−	0.795816i	$-0.292958\pi$
$398$	10.4853	−	10.4853i	0.525579	−	0.525579i
$399$	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	$0.581924\pi$
$402$	16.9655	−	16.9655i	0.846163	−	0.846163i
$403$	9.94938	−	62.8179i	0.495614	−	3.12918i
$404$	16.2278			0.807365
$405$		0			0
$406$	−1.89515	−	2.60845i	−0.0940548	−	0.129455i
$407$	1.61147	−	1.61147i	0.0798776	−	0.0798776i
$408$	−29.5064	−	29.5064i	−1.46078	−	1.46078i
$409$	−11.4621	−	3.72426i	−0.566764	−	0.184153i	0.0115985	−	0.999933i	$-0.496308\pi$
$409$	−11.4621	−	3.72426i	−0.566764	−	0.184153i	−0.578362	+	0.815780i	$0.696308\pi$
$410$		0			0
$411$	−0.815103	−	2.50863i	−0.0402060	−	0.123741i
$412$	1.83569	−	11.5901i	0.0904381	−	0.571004i
$413$	−7.90502	+	4.02781i	−0.388980	+	0.198195i
$414$		−	7.49722i		−	0.368468i
$415$		0			0
$416$	11.0615	−	34.0439i	0.542336	−	1.66914i
$417$	−6.29739	−	39.7602i	−0.308385	−	1.94706i
$418$	−1.96853	+	1.00302i	−0.0962841	+	0.0490592i
$419$	−2.67537	+	3.68233i	−0.130700	+	0.179894i	−0.869352	−	0.494194i	$-0.835463\pi$
$419$	−2.67537	+	3.68233i	−0.130700	+	0.179894i	0.738651	+	0.674088i	$0.235463\pi$
$420$		0			0
$421$	17.4848	+	24.0657i	0.852155	+	1.17289i	0.983384	+	0.181538i	$0.0581076\pi$
$421$	17.4848	+	24.0657i	0.852155	+	1.17289i	−0.131229	+	0.991352i	$0.541892\pi$
$422$	0.597188	+	0.304282i	0.0290707	+	0.0148122i
$423$	−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
$428$	3.68696	−	3.68696i	0.178216	−	0.178216i
$429$	−6.09319	+	4.42696i	−0.294182	+	0.213736i
$430$		0			0
$431$	−12.9402	+	17.8107i	−0.623308	+	0.857910i	−0.997589	−	0.0694055i	$-0.977890\pi$
$431$	−12.9402	+	17.8107i	−0.623308	+	0.857910i	0.374280	+	0.927316i	$0.377890\pi$
$432$	6.03810	−	11.8504i	0.290508	−	0.570155i
$433$	−18.9256	+	2.99752i	−0.909505	+	0.144052i	−0.593620	−	0.804746i	$-0.702302\pi$
$433$	−18.9256	+	2.99752i	−0.909505	+	0.144052i	−0.315886	+	0.948797i	$0.602302\pi$
$434$	9.06706	+	6.58761i	0.435233	+	0.316215i
$435$		0			0
$436$	30.7531	+	9.99228i	1.47281	+	0.478544i
$437$	2.00603	+	3.93706i	0.0959617	+	0.188335i
$438$	−7.21464	−	45.5515i	−0.344729	−	2.17653i
$439$	1.35681	+	4.17583i	0.0647569	+	0.199301i	0.978200	−	0.207665i	$-0.0665865\pi$
$439$	1.35681	+	4.17583i	0.0647569	+	0.199301i	−0.913443	+	0.406967i	$0.866587\pi$
$440$		0			0
$441$	8.34931	−	25.6965i	0.397586	−	1.22364i
$442$	48.4761	+	7.67786i	2.30577	+	0.365199i
$443$	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	$0.243944\pi$
$444$	−8.56295	−	26.3540i	−0.406380	−	1.25071i
$445$		0			0
$446$	9.66966	+	29.7602i	0.457872	+	1.40918i
$447$	8.84867	−	55.8683i	0.418527	−	2.64248i
$448$	4.46029	+	4.46029i	0.210729	+	0.210729i
$449$		−	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
$452$	14.1946	−	7.23252i	0.667659	−	0.340189i
$453$	22.7770	+	3.60753i	1.07016	+	0.169496i
$454$	0.682589	+	2.10079i	0.0320355	+	0.0985950i
$455$		0			0
$456$			26.8637i			1.25801i
$457$	−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	$0.994078\pi$
$458$	−1.34432	+	8.48771i	−0.0628160	+	0.396605i
$459$	17.3434	+	5.63522i	0.809522	+	0.263030i
$460$		0			0
$461$	−18.4873	+	6.00689i	−0.861039	+	0.279769i	−0.706062	−	0.708150i	$-0.749530\pi$
$461$	−18.4873	+	6.00689i	−0.861039	+	0.279769i	−0.154977	+	0.987918i	$0.549530\pi$
$462$	−0.207618	−	1.31085i	−0.00965925	−	0.0609861i
$463$	22.5727	−	11.5014i	1.04904	−	0.534513i	0.157531	−	0.987514i	$-0.449647\pi$
$463$	22.5727	−	11.5014i	1.04904	−	0.534513i	0.891510	+	0.453001i	$0.149647\pi$
$464$	9.35706	−	6.79830i	0.434391	−	0.315603i
$465$		0			0
$466$	−13.1306	+	18.0727i	−0.608264	+	0.837203i
$467$	1.99620	+	12.6035i	0.0923730	+	0.583220i	0.989845	+	0.142149i	$0.0454013\pi$
$467$	1.99620	+	12.6035i	0.0923730	+	0.583220i	−0.897472	+	0.441071i	$0.854599\pi$
$468$	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
$472$	−14.4486	−	28.3570i	−0.665050	−	1.30523i
$473$	−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
$478$	1.31085	+	0.667910i	0.0599567	+	0.0305495i
$479$	21.3496	−	15.5114i	0.975487	−	0.708733i	0.0187915	−	0.999823i	$-0.494018\pi$
$479$	21.3496	−	15.5114i	0.975487	−	0.708733i	0.956695	+	0.291091i	$0.0940181\pi$
$480$		0			0
$481$	26.3679	+	19.1574i	1.20227	+	0.873502i
$482$	−5.92872	−	11.6358i	−0.270046	−	0.529995i
$483$	−2.62169	+	0.415236i	−0.119291	+	0.0188939i
$484$	−12.7011	−	17.4816i	−0.577324	−	0.794618i
$485$		0			0
$486$		−	28.4257i		−	1.28942i
$487$	2.13244	+	4.18515i	0.0966302	+	0.189647i	0.934262	−	0.356589i	$-0.116060\pi$
$487$	2.13244	+	4.18515i	0.0966302	+	0.189647i	−0.837631	+	0.546236i	$0.816060\pi$
$488$	−12.1121	−	6.17140i	−0.548287	−	0.279366i
$489$	−27.9440	+	9.07955i	−1.26367	+	0.410591i
$490$		0			0
$491$	−8.52185	+	26.2276i	−0.384586	+	1.18363i	0.552194	+	0.833715i	$0.313791\pi$
$491$	−8.52185	+	26.2276i	−0.384586	+	1.18363i	−0.936780	+	0.349918i	$0.886209\pi$
$492$	17.5780	−	34.4987i	0.792475	−	1.55532i
$493$	11.2135	+	11.2135i	0.505031	+	0.505031i
$494$	−18.5721	−	25.5623i	−0.835598	−	1.15010i
$495$		0			0
$496$	−23.6311	+	32.5254i	−1.06107	+	1.46044i
$497$	−8.39144	−	1.32907i	−0.376407	−	0.0596171i
$498$	−37.0899	−	37.0899i	−1.66204	−	1.66204i
$499$		−	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
$502$	−7.25731	+	7.25731i	−0.323910	+	0.323910i
$503$	−42.5535	−	6.73981i	−1.89737	−	0.300513i	−0.905156	−	0.425080i	$-0.860246\pi$
$503$	−42.5535	−	6.73981i	−1.89737	−	0.300513i	−0.992211	+	0.124566i	$0.960246\pi$
$504$	−8.98468	−	2.91930i	−0.400209	−	0.130036i
$505$		0			0
$506$	0.633538	−	0.460292i	0.0281642	−	0.0204625i
$507$	−51.4370	−	51.4370i	−2.28440	−	2.28440i
$508$	7.50870	−	14.7367i	0.333145	−	0.653833i
$509$	−5.06658	+	15.5933i	−0.224572	+	0.691163i	0.773762	+	0.633476i	$0.218372\pi$
$509$	−5.06658	+	15.5933i	−0.224572	+	0.691163i	−0.998335	+	0.0576867i	$0.981628\pi$
$510$		0			0
$511$	−9.09098	+	2.95384i	−0.402161	+	0.130670i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−5.32979	−	10.4603i	−0.235316	−	0.461833i
$514$	0.599116			0.0264259
$515$		0			0
$516$	−6.08999	+	4.42463i	−0.268097	+	0.194784i
$517$	−0.715921	+	0.113391i	−0.0314862	+	0.00498692i
$518$	−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	−0.658358	−	0.752705i	$-0.728749\pi$
$521$	−3.33109	+	2.42018i	−0.145937	+	0.106030i	0.512421	+	0.858734i	$0.328749\pi$
$522$	−7.86406	+	15.4341i	−0.344200	+	0.675531i
$523$	−3.35349	−	1.70869i	−0.146638	−	0.0747158i	0.379132	−	0.925343i	$-0.376223\pi$
$523$	−3.35349	−	1.70869i	−0.146638	−	0.0747158i	−0.525770	+	0.850627i	$0.676223\pi$
$524$	10.3939	−	14.3060i	0.454061	−	0.624962i
$525$		0			0
$526$	−5.56661	+	17.1323i	−0.242716	+	0.747002i
$527$	−49.1158	−	25.0258i	−2.13952	−	1.09014i
$528$	4.70228	−	0.744768i	0.204641	−	0.0324119i
$529$	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
$533$	7.12411	+	44.9799i	0.308580	+	1.94829i
$534$	10.3666	+	7.53181i	0.448609	+	0.325933i
$535$		0			0
$536$	10.4853	−	14.4317i	0.452894	−	0.623356i
$537$	−21.7389	+	11.0765i	−0.938103	+	0.477988i
$538$	−15.6687	+	2.48168i	−0.675525	+	0.106993i
$539$	2.68404	−	0.872098i	0.115610	−	0.0375639i
$540$		0			0
$541$	−12.5643	−	4.08238i	−0.540180	−	0.175515i	0.0262040	−	0.999657i	$-0.491658\pi$
$541$	−12.5643	−	4.08238i	−0.540180	−	0.175515i	−0.566384	+	0.824142i	$0.691658\pi$
$542$	−15.2858	−	2.42104i	−0.656583	−	0.103992i
$543$	24.9483	+	24.9483i	1.07064	+	1.07064i
$544$	−25.0996	−	18.2360i	−1.07614	−	0.781860i
$545$		0			0
$546$	18.0517	−	5.86537i	0.772543	−	0.251014i
$547$	20.5808	+	3.25968i	0.879971	+	0.139374i	0.580041	−	0.814587i	$-0.303037\pi$
$547$	20.5808	+	3.25968i	0.879971	+	0.139374i	0.299930	+	0.953961i	$0.403037\pi$
$548$	−0.890339	−	1.74739i	−0.0380334	−	0.0746447i
$549$	20.3589			0.868898
$550$		0			0
$551$		−	10.2092i		−	0.434926i
$552$	−1.48954	−	9.40456i	−0.0633989	−	0.400285i
$553$	1.61211	−	10.1785i	0.0685540	−	0.432833i
$554$	−11.7077	+	3.80407i	−0.497413	+	0.161619i
$555$		0			0
$556$	−9.24888	−	28.4651i	−0.392240	−	1.20719i
$557$	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	$0.0836995\pi$
$558$	9.41924	−	59.4708i	0.398748	−	2.51760i
$559$	2.73601	−	8.42058i	0.115721	−	0.356152i
$560$		0			0
$561$	2.01719	+	6.20826i	0.0851657	+	0.262113i
$562$	−13.3930	+	2.12125i	−0.564952	+	0.0894795i
$563$	20.8369	+	40.8947i	0.878170	+	1.72350i	0.665525	+	0.746375i	$0.268208\pi$
$563$	20.8369	+	40.8947i	0.878170	+	1.72350i	0.212644	+	0.977130i	$0.431792\pi$
$564$	−2.72353	+	8.38215i	−0.114681	+	0.352952i
$565$		0			0
$566$	−6.18941	+	8.51899i	−0.260160	+	0.358080i
$567$	−2.93123	+	0.464261i	−0.123100	+	0.0194971i
$568$	4.76766	−	30.1018i	0.200047	−	1.26304i
$569$	23.0882	−	31.7781i	0.967906	−	1.33221i	0.0248079	−	0.999692i	$-0.492103\pi$
$569$	23.0882	−	31.7781i	0.967906	−	1.33221i	0.943098	−	0.332516i	$-0.107897\pi$
$570$		0			0
$571$	19.4298	−	14.1166i	0.813111	−	0.590760i	−0.101620	−	0.994823i	$-0.532402\pi$
$571$	19.4298	−	14.1166i	0.813111	−	0.590760i	0.914731	+	0.404063i	$0.132402\pi$
$572$	−3.95959	+	3.95959i	−0.165559	+	0.165559i
$573$	22.6433	−	44.4400i	0.945939	−	1.85651i
$574$	−7.63220	−	2.47985i	−0.318562	−	0.103507i
$575$		0			0
$576$	10.4721	−	32.2299i	0.436339	−	1.34291i
$577$	2.86414	−	5.62119i	0.119236	−	0.234013i	−0.823673	−	0.567066i	$-0.808079\pi$
$577$	2.86414	−	5.62119i	0.119236	−	0.234013i	0.942908	+	0.333052i	$0.108079\pi$
$578$	8.39751	−	16.4811i	0.349291	−	0.685521i
$579$	−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
$583$	0.0982995	+	0.620639i	0.00407115	+	0.0257042i
$584$	−10.5960	−	32.6112i	−0.438467	−	1.34946i
$585$		0			0
$586$	−19.6983			−0.813729
$587$	−32.9979	+	16.8133i	−1.36197	+	0.693958i	−0.973753	−	0.227609i	$-0.926909\pi$
$587$	−32.9979	+	16.8133i	−1.36197	+	0.693958i	−0.388218	+	0.921568i	$0.626909\pi$
$588$	5.36808	−	33.8927i	0.221376	−	1.39771i
$589$	10.9662	+	33.7506i	0.451856	+	1.39067i
$590$		0			0
$591$	−14.2752	−	4.63831i	−0.587205	−	0.190795i
$592$	−9.35333	−	18.3570i	−0.384420	−	0.754466i
$593$	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	$0.0909527\pi$
$594$	−1.68323	+	1.22294i	−0.0690638	+	0.0501778i
$595$		0			0
$596$		−	42.0556i		−	1.72267i
$597$	−4.41228	+	27.8580i	−0.180583	+	1.14015i
$598$	7.91919	+	7.91919i	0.323840	+	0.323840i
$599$	−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	$0.410445\pi$
$602$	1.10323	+	1.10323i	0.0449643	+	0.0449643i
$603$	−4.17937	+	26.3875i	−0.170197	+	1.07458i
$604$	17.1457			0.697649
$605$		0			0
$606$	−24.9721	+	18.1433i	−1.01442	+	0.737020i
$607$	−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	$0.991791\pi$
$608$	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
$612$	45.8931	+	7.26876i	1.85512	+	0.293822i
$613$	32.8390	−	16.7323i	1.32635	−	0.675811i	0.359982	−	0.932959i	$-0.382783\pi$
$613$	32.8390	−	16.7323i	1.32635	−	0.675811i	0.966372	+	0.257148i	$0.0827828\pi$
$614$	2.54922			0.102878
$615$		0			0
$616$	−0.304925	−	0.938463i	−0.0122858	−	0.0378117i
$617$	−0.552944	−	3.49115i	−0.0222607	−	0.140548i	0.974055	−	0.226312i	$-0.0726670\pi$
$617$	−0.552944	−	3.49115i	−0.0222607	−	0.140548i	−0.996316	+	0.0857638i	$0.972667\pi$
$618$	10.1333	+	19.8877i	0.407621	+	0.800001i
$619$	−26.6760	+	36.7164i	−1.07220	+	1.47576i	−0.204369	+	0.978894i	$0.565514\pi$
$619$	−26.6760	+	36.7164i	−1.07220	+	1.47576i	−0.867830	+	0.496861i	$0.834486\pi$
$620$		0			0
$621$	2.44588	+	3.36646i	0.0981497	+	0.135091i
$622$	−4.02092	+	7.89149i	−0.161224	+	0.316420i
$623$	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
$628$	−8.08611	−	8.08611i	−0.322671	−	0.322671i
$629$	22.8535	−	16.6040i	0.911227	−	0.662046i
$630$		0			0
$631$	7.79351	−	10.7268i	0.310255	−	0.427029i	−0.625206	−	0.780460i	$-0.714985\pi$
$631$	7.79351	−	10.7268i	0.310255	−	0.427029i	0.935461	+	0.353431i	$0.114985\pi$
$632$	36.5123	+	5.78298i	1.45238	+	0.230035i
$633$	−1.25918	+	0.199434i	−0.0500478	+	0.00792679i
$634$	−9.69199	+	13.3399i	−0.384918	+	0.529794i
$635$		0			0
$636$	7.26657	+	2.36105i	0.288138	+	0.0936217i
$637$	18.3236	+	35.9620i	0.726007	+	1.42487i
$638$	−1.78704	+	0.283039i	−0.0707496	+	0.0112056i
$639$	14.1050	+	43.4107i	0.557985	+	1.71730i
$640$		0			0
$641$	−4.58284	+	14.1045i	−0.181011	+	0.557095i	−0.999857	−	0.0169186i	$-0.994614\pi$
$641$	−4.58284	+	14.1045i	−0.181011	+	0.557095i	0.818846	+	0.574014i	$0.194614\pi$
$642$	−1.55150	+	9.79580i	−0.0612329	+	0.386609i
$643$	−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	$0.481139\pi$
$644$	−1.87693	+	0.609850i	−0.0739612	+	0.0240315i
$645$		0			0
$646$	−26.0451	+	8.46255i	−1.02473	+	0.332955i
$647$	6.98945	−	44.1296i	0.274784	−	1.73492i	−0.334885	−	0.942259i	$-0.608698\pi$
$647$	6.98945	−	44.1296i	0.274784	−	1.73492i	0.609669	−	0.792656i	$-0.291302\pi$
$648$	−1.66540	−	10.5149i	−0.0654232	−	0.413066i
$649$			4.97864i			0.195429i
$650$		0			0
$651$	−21.3179			−0.835516
$652$	−19.4644	+	9.91762i	−0.762285	+	0.388404i
$653$	−0.0172425	−	0.00273094i	−0.000674750	−	0.000106870i	0.156097	−	0.987742i	$-0.450109\pi$
$653$	−0.0172425	−	0.00273094i	−0.000674750	−	0.000106870i	−0.156772	+	0.987635i	$0.550109\pi$
$654$	−58.4958	+	19.0065i	−2.28737	+	0.743211i
$655$		0			0
$656$	8.89575	−	27.3783i	0.347321	−	1.06894i
$657$	36.3132	+	36.3132i	1.41671	+	1.41671i
$658$	1.80423	+	0.285761i	0.0703361	+	0.0111401i
$659$	36.7936	+	11.9550i	1.43328	+	0.465700i	0.919795	−	0.392400i	$-0.128355\pi$
$659$	36.7936	+	11.9550i	1.43328	+	0.465700i	0.513482	+	0.858100i	$0.328355\pi$
$660$		0			0
$661$	−2.89246	+	0.939818i	−0.112504	+	0.0365547i	−0.364728	−	0.931114i	$-0.618838\pi$
$661$	−2.89246	+	0.939818i	−0.112504	+	0.0365547i	0.252224	+	0.967669i	$0.418838\pi$
$662$	36.5148	−	5.78338i	1.41919	−	0.224777i
$663$	−83.1812	+	42.3829i	−3.23049	+	1.64602i
$664$	−31.5505	−	22.9228i	−1.22440	−	0.889577i
$665$		0			0
$666$	24.9629	+	18.1366i	0.967293	+	0.702780i
$667$	0.566079	+	3.57408i	0.0219187	+	0.138389i
$668$	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
$672$	−11.8504	−	1.87693i	−0.457141	−	0.0724040i
$673$	6.53751	+	3.33103i	0.252003	+	0.128402i	0.575429	−	0.817851i	$-0.304835\pi$
$673$	6.53751	+	3.33103i	0.252003	+	0.128402i	−0.323427	+	0.946253i	$0.604835\pi$
$674$	−9.56701	+	29.4442i	−0.368507	+	1.13415i
$675$		0			0
$676$	−43.7549	−	31.7898i	−1.68288	−	1.22269i
$677$	25.0033	+	12.7398i	0.960955	+	0.489631i	0.862803	−	0.505541i	$-0.168707\pi$
$677$	25.0033	+	12.7398i	0.960955	+	0.489631i	0.0981518	+	0.995171i	$0.468707\pi$
$678$	−13.7571	+	26.9998i	−0.528337	+	1.03692i
$679$	−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
$683$	8.66759	−	1.37281i	0.331656	−	0.0525292i	0.0116143	−	0.999933i	$-0.496303\pi$
$683$	8.66759	−	1.37281i	0.331656	−	0.0525292i	0.320042	+	0.947403i	$0.396303\pi$
$684$	−17.5825	−	24.2002i	−0.672284	−	0.925320i
$685$		0			0
$686$	−14.9178			−0.569564
$687$	−7.42085	−	14.5642i	−0.283123	−	0.555661i
$688$	−3.95751	+	3.95751i	−0.150879	+	0.150879i
$689$	−8.54685	+	2.77704i	−0.325609	+	0.105797i
$690$		0			0
$691$	−8.97413	+	27.6195i	−0.341392	+	1.05070i	0.622095	+	0.782942i	$0.286282\pi$
$691$	−8.97413	+	27.6195i	−0.341392	+	1.05070i	−0.963487	+	0.267755i	$0.913718\pi$
$692$	22.1487	+	11.2853i	0.841967	+	0.429004i
$693$	1.04499	+	1.04499i	0.0396960	+	0.0396960i
$694$	−11.5806	+	8.41383i	−0.439595	+	0.319385i
$695$		0			0
$696$	−6.79830	+	20.9230i	−0.257689	+	0.793085i
$697$	38.9848	+	6.17458i	1.47665	+	0.233879i
$698$	17.7360	−	17.7360i	0.671318	−	0.671318i
$699$		−	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	$-0.0650527\pi$
$702$	−21.0403	−	21.0403i	−0.794115	−	0.794115i
$703$	−17.9618	−	2.84486i	−0.677441	−	0.107296i
$704$	3.36646	−	1.09383i	0.126878	−	0.0412253i
$705$		0			0
$706$	−18.7121	−	25.7551i	−0.704241	−	0.969305i
$707$	4.52381	+	4.52381i	0.170135	+	0.170135i
$708$	53.9381	+	27.4828i	2.02712	+	1.03287i
$709$	−0.353547	+	1.08811i	−0.0132777	+	0.0408647i	−0.957476	−	0.288513i	$-0.906839\pi$
$709$	−0.353547	+	1.08811i	−0.0132777	+	0.0408647i	0.944198	+	0.329378i	$0.106839\pi$
$710$		0			0
$711$	−52.6555	+	17.1088i	−1.97474	+	0.641630i
$712$	8.48868	+	4.32520i	0.318127	+	0.162094i
$713$	−5.71051	−	11.2075i	−0.213860	−	0.419724i
$714$		−	16.4509i		−	0.615659i
$715$		0			0
$716$	−14.6755	+	10.6624i	−0.548450	+	0.398472i
$717$	−2.76393	+	0.437764i	−0.103221	+	0.0163486i
$718$	7.90398	+	15.5124i	0.294974	+	0.578919i
$719$	−1.16479	−	0.846270i	−0.0434394	−	0.0315606i	0.565854	−	0.824506i	$-0.308547\pi$
$719$	−1.16479	−	0.846270i	−0.0434394	−	0.0315606i	−0.609293	+	0.792945i	$0.708547\pi$
$720$		0			0
$721$	3.74269	−	2.71922i	0.139385	−	0.101269i
$722$	−8.23291	−	4.19488i	−0.306397	−	0.156117i
$723$	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	0.281060	−	0.959690i	$-0.409314\pi$
$727$	−8.90163	−	4.53561i	−0.330143	−	0.168216i	−0.611203	+	0.791474i	$0.709314\pi$
$728$	12.5740	−	6.40676i	0.466022	−	0.237450i
$729$	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
$733$	−2.98599	−	18.8528i	−0.110290	−	0.696344i	−0.979431	−	0.201779i	$-0.935328\pi$
$733$	−2.98599	−	18.8528i	−0.110290	−	0.696344i	0.869141	−	0.494564i	$-0.164672\pi$
$734$	−23.4863	+	32.3261i	−0.866895	+	1.19318i
$735$		0			0
$736$	−2.18766	−	6.73292i	−0.0806382	−	0.248179i
$737$	−2.48642	+	1.26689i	−0.0915884	+	0.0466666i
$738$	6.74451	+	42.5832i	0.248269	+	1.56751i
$739$	−30.4862	+	9.90557i	−1.12145	+	0.364382i	−0.810322	−	0.585985i	$-0.800708\pi$
$739$	−30.4862	+	9.90557i	−1.12145	+	0.364382i	−0.311131	+	0.950367i	$0.600708\pi$
$740$		0			0
$741$	57.1591	+	18.5721i	2.09979	+	0.682263i
$742$	0.247729	−	1.56410i	0.00909443	−	0.0574200i
$743$	−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	$-0.505744\pi$
$744$		−	76.4719i		−	2.80360i
$745$		0			0
$746$	−3.41975	−	10.5249i	−0.125206	−	0.385345i
$747$	57.6882	+	9.13691i	2.11070	+	0.334302i
$748$	2.20338	+	4.32437i	0.0805635	+	0.158115i
$749$	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	$-0.0782963\pi$
$752$	−1.02509	+	6.47214i	−0.0373810	+	0.236015i
$753$	3.05393	−	19.2818i	0.111292	−	0.702667i
$754$	−7.99609	−	24.6094i	−0.291200	−	0.896222i
$755$		0			0
$756$	4.98676	−	1.62030i	0.181367	−	0.0589296i
$757$	−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	$0.455231\pi$
$758$	−29.9639	−	4.74581i	−1.08834	−	0.172376i
$759$	−0.460292	+	1.41663i	−0.0167075	+	0.0514205i
$760$		0			0
$761$	−6.52304	−	20.0758i	−0.236460	−	0.727749i	−0.996924	−	0.0783693i	$-0.975029\pi$
$761$	−6.52304	−	20.0758i	−0.236460	−	0.727749i	0.760464	−	0.649380i	$-0.224971\pi$
$762$	4.92138	+	31.0724i	0.178283	+	1.12563i
$763$	5.78745	+	11.3585i	0.209520	+	0.411206i
$764$	11.4592	−	35.2678i	0.414580	−	1.27594i
$765$		0			0
$766$	−4.96075	−	3.60419i	−0.179239	−	0.130225i
$767$	−70.3253	+	11.1384i	−2.53930	+	0.402186i
$768$	6.73292	−	42.5100i	0.242953	−	1.53395i
$769$	−31.2607	+	43.0267i	−1.12729	+	1.55158i	−0.334177	+	0.942510i	$0.608458\pi$
$769$	−31.2607	+	43.0267i	−1.12729	+	1.55158i	−0.793114	+	0.609073i	$0.791542\pi$
$770$		0			0
$771$	−0.921944	+	0.669832i	−0.0332030	+	0.0241234i
$772$	−22.5039	−	22.5039i	−0.809933	−	0.809933i
$773$	−13.9493	+	27.3771i	−0.501722	+	0.984686i	0.491763	+	0.870729i	$0.336353\pi$
$773$	−13.9493	+	27.3771i	−0.501722	+	0.984686i	−0.993486	+	0.113957i	$0.963647\pi$
$774$	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
$778$	−11.9032	−	6.06497i	−0.426749	−	0.217440i
$779$	−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
$783$	−1.50400	−	9.49589i	−0.0537486	−	0.339355i
$784$		−	25.5132i		−	0.911187i
$785$		0			0
$786$			33.6355i			1.19974i
$787$	−32.5114	+	16.5654i	−1.15891	+	0.590493i	−0.924326	−	0.381604i	$-0.875372\pi$
$787$	−32.5114	+	16.5654i	−1.15891	+	0.590493i	−0.234581	+	0.972097i	$0.575372\pi$
$788$	−11.0224	−	1.74578i	−0.392657	−	0.0621907i
$789$	−10.5883	−	32.5875i	−0.376954	−	1.16015i
$790$		0			0
$791$	5.97321	+	1.94081i	0.212383	+	0.0690074i
$792$	−3.74861	+	3.74861i	−0.133201	+	0.133201i
$793$	−21.5048	+	21.5048i	−0.763657	+	0.763657i
$794$	29.1749	+	40.1558i	1.03538	+	1.42508i
$795$		0			0
$796$			20.9705i			0.743281i
$797$	−0.936362	+	5.91196i	−0.0331677	+	0.209412i	−0.998706	−	0.0508468i	$-0.983808\pi$
$797$	−0.936362	+	5.91196i	−0.0331677	+	0.209412i	0.965539	+	0.260259i	$0.0838080\pi$
$798$	−7.48874	+	7.48874i	−0.265099	+	0.265099i
$799$	−8.98468			−0.317855
$800$		0			0
$801$	−14.2685			−0.504151
$802$	10.1943	−	10.1943i	0.359973	−	0.359973i
$803$	−0.839124	+	5.29802i	−0.0296120	+	0.186963i
$804$			33.9310i			1.19666i
$805$		0			0
$806$	52.8686	+	72.7673i	1.86222	+	2.56312i
$807$	21.3370	−	21.3370i	0.751099	−	0.751099i
$808$	−16.2278	+	16.2278i	−0.570893	+	0.570893i
$809$	−29.7722	−	9.67358i	−1.04674	−	0.340105i	−0.265349	−	0.964152i	$-0.585487\pi$
$809$	−29.7722	−	9.67358i	−1.04674	−	0.340105i	−0.781387	+	0.624047i	$0.785487\pi$
$810$		0			0
$811$	1.95623	+	6.02066i	0.0686926	+	0.211414i	0.979510	−	0.201395i	$-0.0645476\pi$
$811$	1.95623	+	6.02066i	0.0686926	+	0.211414i	−0.910817	+	0.412809i	$0.864548\pi$
$812$	4.50360	+	0.713301i	0.158046	+	0.0250319i
$813$	26.2293	−	13.3645i	0.919901	−	0.468713i
$814$			3.22294i			0.112964i
$815$		0			0
$816$	59.0128			2.06586
$817$	0.772821	+	4.87940i	0.0270376	+	0.170709i
$818$	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	$-0.329785\pi$
$821$	−13.3566	−	18.3837i	−0.466147	−	0.641596i	−0.975769	+	0.218802i	$0.929785\pi$
$822$	3.32373	+	1.69353i	0.115928	+	0.0590685i
$823$	−5.29231	+	10.3867i	−0.184478	+	0.362059i	−0.964662	−	0.263492i	$-0.915126\pi$
$823$	−5.29231	+	10.3867i	−0.184478	+	0.362059i	0.780183	+	0.625551i	$0.215126\pi$
$824$	9.75442	+	13.4258i	0.339811	+	0.467710i
$825$		0			0
$826$	3.87721	−	11.9328i	0.134905	−	0.415196i
$827$	−2.69680	+	5.29276i	−0.0937768	+	0.184047i	−0.933130	−	0.359539i	$-0.882934\pi$
$827$	−2.69680	+	5.29276i	−0.0937768	+	0.184047i	0.839353	+	0.543586i	$0.182934\pi$
$828$	7.49722	+	7.49722i	0.260546	+	0.260546i
$829$	−30.1824	+	21.9288i	−1.04828	+	0.761619i	−0.971884	−	0.235458i	$-0.924341\pi$
$829$	−30.1824	+	21.9288i	−1.04828	+	0.761619i	−0.0763946	+	0.997078i	$0.524341\pi$
$830$		0			0
$831$	13.7632	−	18.9435i	0.477442	−	0.657142i
$832$	22.9824	+	45.1054i	0.796770	+	1.56375i
$833$	34.5510	−	5.47233i	1.19712	−	0.189605i
$834$	46.0575	+	33.4628i	1.59484	+	1.15872i
$835$		0			0
$836$	0.965515	−	2.97155i	0.0333930	−	0.102773i
$837$	15.1721	+	29.7769i	0.524425	+	1.02924i
$838$	−1.00696	−	6.35771i	−0.0347849	−	0.219623i
$839$	−13.8039	−	42.4840i	−0.476563	−	1.46671i	−0.843839	−	0.536597i	$-0.819710\pi$
$839$	−13.8039	−	42.4840i	−0.476563	−	1.46671i	0.367276	−	0.930112i	$-0.380290\pi$
$840$		0			0
$841$	−6.37789	+	19.6291i	−0.219927	+	0.676866i
$842$	−41.5504	−	6.58094i	−1.43192	−	0.226794i
$843$	18.2381	−	18.2381i	0.628155	−	0.628155i
$844$	−0.901470	+	0.292906i	−0.0310299	+	0.0100822i
$845$		0			0
$846$	−3.03269	−	9.33366i	−0.104266	−	0.320898i
$847$	1.33264	−	8.41399i	0.0457902	−	0.289108i
$848$	5.61076	+	0.888657i	0.192674	+	0.0305166i
$849$		−	20.0294i		−	0.687406i
$850$		0			0
$851$	6.44588			0.220962
$852$	26.3182	+	51.6524i	0.901646	+	1.76958i
$853$	5.92966	+	0.939165i	0.203028	+	0.0321564i	0.257120	−	0.966380i	$-0.417227\pi$
$853$	5.92966	+	0.939165i	0.203028	+	0.0321564i	−0.0540922	+	0.998536i	$0.517227\pi$
$854$	−1.65607	−	5.09685i	−0.0566694	−	0.174411i
$855$		0			0
$856$			7.37392i			0.252035i
$857$	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	$0.721205\pi$
$858$	1.66623	−	10.5201i	0.0568841	−	0.359152i
$859$	30.1496	+	9.79621i	1.02869	+	0.334242i	0.774273	−	0.632852i	$-0.218116\pi$
$859$	30.1496	+	9.79621i	1.02869	+	0.334242i	0.254419	+	0.967094i	$0.418116\pi$
$860$		0			0
$861$	14.5173	−	4.71696i	0.494749	−	0.160754i
$862$	−4.87046	−	30.7509i	−0.165889	−	1.04738i
$863$	−9.14726	+	4.66076i	−0.311376	+	0.158654i	−0.602694	−	0.797972i	$-0.705906\pi$
$863$	−9.14726	+	4.66076i	−0.311376	+	0.158654i	0.291318	+	0.956626i	$0.405906\pi$
$864$	5.81234	+	17.8885i	0.197740	+	0.608581i
$865$		0			0
$866$	15.9281	−	21.9231i	0.541258	−	0.744977i
$867$	5.50393	+	34.7504i	0.186923	+	1.18019i
$868$	−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
$872$	−40.7454	+	20.7608i	−1.37981	+	0.703049i
$873$	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	0.694756	−	0.719246i	$-0.255512\pi$
$877$	15.4361	+	7.86511i	0.521241	+	0.265586i	−0.173515	+	0.984831i	$0.555512\pi$
$878$	−5.53263	−	2.81902i	−0.186717	−	0.0951372i
$879$	30.3126	−	22.0234i	1.02242	−	0.742830i
$880$		0			0
$881$	−26.3453	−	19.1410i	−0.887595	−	0.644876i	0.0476546	−	0.998864i	$-0.484825\pi$
$881$	−26.3453	−	19.1410i	−0.887595	−	0.644876i	−0.935250	+	0.353988i	$0.884825\pi$
$882$	17.3472	+	34.0458i	0.584111	+	1.14638i
$883$	−16.6396	+	2.63545i	−0.559966	+	0.0886900i	−0.430001	−	0.902829i	$-0.641487\pi$
$883$	−16.6396	+	2.63545i	−0.559966	+	0.0886900i	−0.129966	+	0.991519i	$0.541487\pi$
$884$	−56.1540	+	40.7983i	−1.88866	+	1.37219i
$885$		0			0
$886$			1.13259i			0.0380500i
$887$	10.0941	+	19.8108i	0.338928	+	0.665183i	0.996069	−	0.0885846i	$-0.0282344\pi$
$887$	10.0941	+	19.8108i	0.338928	+	0.665183i	−0.657141	+	0.753768i	$0.728234\pi$
$888$	34.9170	+	17.7911i	1.17174	+	0.597030i
$889$	6.20130	−	2.01492i	0.207985	−	0.0675784i
$890$		0			0
$891$	−0.514638	+	1.58389i	−0.0172410	+	0.0530624i
$892$	−39.4298	−	20.0905i	−1.32021	−	0.672680i
$893$	4.08999	+	4.08999i	0.136866	+	0.136866i
$894$	47.0196	+	64.7169i	1.57257	+	2.16446i
$895$		0			0
$896$	−8.92058			−0.298016
$897$	−21.0403	−	3.33246i	−0.702515	−	0.111267i
$898$	22.8981	+	22.8981i	0.764120	+	0.764120i
$899$			29.0621i			0.969277i
$900$		0			0
$901$			7.78890i			0.259486i
$902$	−3.18433	+	3.18433i	−0.106026	+	0.106026i
$903$	−2.93114	−	0.464247i	−0.0975423	−	0.0154492i
$904$	−6.96210	+	21.4271i	−0.231556	+	0.712656i
$905$		0			0
$906$	−26.3845	+	19.1695i	−0.876568	+	0.636864i
$907$	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	$0.649736\pi$
$908$	−2.78338	−	1.41820i	−0.0923697	−	0.0470647i
$909$	10.6213	−	32.6889i	0.352285	−	1.08422i
$910$		0			0
$911$	−7.69141	+	2.49909i	−0.254828	+	0.0827985i	−0.433645	−	0.901084i	$-0.642773\pi$
$911$	−7.69141	+	2.49909i	−0.254828	+	0.0827985i	0.178817	+	0.983882i	$0.442773\pi$
$912$	−26.8637	−	26.8637i	−0.889545	−	0.889545i
$913$	2.76967	+	5.43579i	0.0916627	+	0.179898i
$914$	41.9523			1.38766
$915$		0			0
$916$	−7.14339	−	9.83203i	−0.236024	−	0.324860i
$917$	6.88557	−	1.09057i	0.227382	−	0.0360137i
$918$	−22.9786	+	11.7082i	−0.758408	+	0.386428i
$919$	22.9679	+	16.6871i	0.757640	+	0.550458i	0.898186	−	0.439617i	$-0.144886\pi$
$919$	22.9679	+	16.6871i	0.757640	+	0.550458i	−0.140546	+	0.990074i	$0.544886\pi$
$920$		0			0
$921$	−3.92285	+	2.85011i	−0.129262	+	0.0939145i
$922$	12.4804	−	24.4942i	0.411020	−	0.806673i
$923$	−60.7529	−	30.9551i	−1.99971	−	1.01890i
$924$	1.51846	+	1.10323i	0.0499538	+	0.0362936i
$925$		0			0
$926$	−11.0713	+	34.0740i	−0.363826	+	1.11974i
$927$	−22.1453	−	11.2836i	−0.727347	−	0.370602i
$928$	−2.55876	+	16.1554i	−0.0839954	+	0.530326i
$929$	8.36507	+	11.5135i	0.274449	+	0.377747i	0.923885	−	0.382669i	$-0.124995\pi$
$929$	8.36507	+	11.5135i	0.274449	+	0.377747i	−0.649436	+	0.760416i	$0.724995\pi$
$930$		0			0
$931$	−18.2193	−	13.2371i	−0.597114	−	0.433829i
$932$	−4.94212	−	31.2033i	−0.161885	−	1.02210i
$933$	−2.63540	−	16.6393i	−0.0862792	−	0.544745i
$934$	−14.5997	−	10.6073i	−0.477717	−	0.347081i
$935$		0			0
$936$	−61.3372	−	44.5641i	−2.00487	−	1.45662i
$937$	14.8036	−	7.54279i	0.483611	−	0.246412i	−0.195147	−	0.980774i	$-0.562518\pi$
$937$	14.8036	−	7.54279i	0.483611	−	0.246412i	0.678758	+	0.734362i	$0.262518\pi$
$938$	6.94607	−	1.10015i	0.226797	−	0.0359211i
$939$	7.66941	−	2.49194i	0.250282	−	0.0813215i
$940$		0			0
$941$	46.6912	+	15.1709i	1.52209	+	0.494556i	0.946368	−	0.323090i	$-0.104722\pi$
$941$	46.6912	+	15.1709i	1.52209	+	0.494556i	0.575720	+	0.817647i	$0.304722\pi$
$942$	21.4838	+	3.40270i	0.699980	+	0.110866i
$943$	6.36865	+	6.36865i	0.207392	+	0.207392i
$944$	42.8055	+	13.9084i	1.39320	+	0.452679i
$945$		0			0
$946$	0.832676	−	0.270553i	0.0270726	−	0.00879643i
$947$	−18.7002	−	2.96183i	−0.607676	−	0.0962464i	−0.154989	−	0.987916i	$-0.549534\pi$
$947$	−18.7002	−	2.96183i	−0.607676	−	0.0962464i	−0.452687	+	0.891670i	$0.649534\pi$
$948$	−62.6523	+	31.9229i	−2.03485	+	1.03681i
$949$	−76.7139			−2.49024
$950$		0			0
$951$		−	31.3639i		−	1.01705i
$952$	−1.91338	−	12.0806i	−0.0620129	−	0.391534i
$953$	3.24504	−	20.4884i	0.105117	−	0.663683i	−0.877715	−	0.479183i	$-0.840933\pi$
$953$	3.24504	−	20.4884i	0.105117	−	0.663683i	0.982832	−	0.184501i	$-0.0590668\pi$
$954$	−8.09144	+	2.62907i	−0.261970	+	0.0851192i
$955$		0			0
$956$	−1.97876	+	0.642937i	−0.0639976	+	0.0207941i
$957$	2.43352	−	2.43352i	0.0786647	−	0.0786647i
$958$	−5.83820	+	36.8610i	−0.188624	+	1.19092i
$959$	0.238918	−	0.735315i	0.00771507	−	0.0237445i
$960$		0			0
$961$	−21.6376	−	66.5938i	−0.697989	−	2.14819i
$962$	−45.5253	+	7.21050i	−1.46779	+	0.232476i
$963$	−5.01376	−	9.84005i	−0.161566	−	0.317091i
$964$	17.5645	+	5.70705i	0.565714	+	0.183812i
$965$		0			0
$966$	2.20646	−	3.03693i	0.0709916	−	0.0977116i
$967$	26.8233	−	4.24840i	0.862580	−	0.136619i	0.290558	−	0.956857i	$-0.406159\pi$
$967$	26.8233	−	4.24840i	0.862580	−	0.136619i	0.572022	+	0.820238i	$0.306159\pi$
$968$	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	−0.908761	−	0.417317i	$-0.862971\pi$
$971$	−24.7010	+	17.9463i	−0.792692	+	0.575924i	0.116069	+	0.993241i	$0.462971\pi$
$972$	28.4257	+	28.4257i	0.911755	+	0.911755i
$973$	5.35688	−	10.5135i	0.171734	−	0.337046i
$974$	−6.31759	−	2.05271i	−0.202429	−	0.0657731i
$975$		0			0
$976$	18.2835	−	5.94066i	0.585239	−	0.190156i
$977$	−19.6333	+	38.5326i	−0.628126	+	1.23277i	0.329337	+	0.944212i	$0.393175\pi$
$977$	−19.6333	+	38.5326i	−0.628126	+	1.23277i	−0.957463	+	0.288555i	$0.906825\pi$
$978$	18.8644	−	37.0235i	0.603218	−	1.18388i
$979$	−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
$983$	−9.39639	−	59.3265i	−0.299698	−	1.89222i	−0.433405	−	0.901200i	$-0.642688\pi$
$983$	−9.39639	−	59.3265i	−0.299698	−	1.89222i	0.133706	−	0.991021i	$-0.457312\pi$
$984$	16.9207	+	52.0766i	0.539413	+	1.66014i
$985$		0			0
$986$	−22.4270			−0.714222
$987$	−3.09591	+	1.57744i	−0.0985439	+	0.0502106i
$988$	44.1344	+	6.99020i	1.40410	+	0.222388i
$989$	−0.541106	−	1.66535i	−0.0172062	−	0.0529551i
$990$		0			0
$991$	43.5569	+	14.1525i	1.38363	+	0.449569i	0.903862	−	0.427825i	$-0.140720\pi$
$991$	43.5569	+	14.1525i	1.38363	+	0.449569i	0.479770	+	0.877394i	$0.340720\pi$
$992$	−8.89433	−	56.1566i	−0.282395	−	1.78297i
$993$	−49.7245	+	49.7245i	−1.57796	+	1.57796i
$994$	9.72051	−	7.06236i	0.308316	−	0.224005i
$995$		0			0
$996$	74.1797			2.35048
$997$	−3.20301	+	20.2230i	−0.101440	+	0.640468i	0.883613	+	0.468218i	$0.155104\pi$
$997$	−3.20301	+	20.2230i	−0.101440	+	0.640468i	−0.985053	+	0.172250i	$0.944896\pi$
$998$	35.7912	+	35.7912i	1.13295	+	1.13295i
$999$	−17.1259			−0.541839

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(0.420808 - 2.65688i) q^{3} -2.00000i q^{4} +(2.23607 + 3.07768i) q^{6} +(0.557537 - 0.557537i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-4.02874 - 1.30902i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(0.420808 - 2.65688i) q^{3} -2.00000i q^{4} +(2.23607 + 3.07768i) q^{6} +(0.557537 - 0.557537i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-4.02874 - 1.30902i) q^{9} +(-0.136729 - 0.420808i) q^{11} +(-5.31375 - 0.841616i) q^{12} +(5.63818 - 2.87280i) q^{13} +1.11507i q^{14} -4.00000 q^{16} +(-0.857960 - 5.41695i) q^{17} +(5.33776 - 2.71972i) q^{18} +(-2.07533 + 2.85645i) q^{19} +(-1.24669 - 1.71592i) q^{21} +(0.557537 + 0.284079i) 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} +(-1.11507 - 1.11507i) 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} +(6.27491 + 4.55899i) q^{34} +(-2.61803 + 8.05748i) q^{36} +(2.33833 + 4.58924i) q^{37} +(-0.781118 - 4.93179i) q^{38} +(-5.26007 - 16.1888i) q^{39} +(-2.22394 + 6.84458i) q^{41} +(2.96261 + 0.469231i) q^{42} +(0.989378 - 0.989378i) q^{43} +(-0.841616 + 0.273457i) q^{44} +(0.546915 + 1.68323i) q^{46} +(0.256271 - 1.61803i) q^{47} +(-1.68323 + 10.6275i) q^{48} +6.37831i q^{49} -14.7532 q^{51} +(-5.74559 - 11.2764i) q^{52} +(-1.40269 - 0.222164i) q^{53} +(-1.45309 - 4.47214i) q^{54} +2.23015 q^{56} +(6.71592 + 6.71592i) q^{57} +(0.639690 - 4.03884i) q^{58} +(-10.7014 - 3.47709i) q^{59} +(-4.57086 + 1.48516i) q^{61} +(2.22358 + 14.0391i) q^{62} +(-2.97599 + 1.51634i) q^{63} +8.00000i q^{64} +(0.989378 - 1.36176i) q^{66} +(-0.986616 - 6.22925i) q^{67} +(-10.8339 + 1.71592i) q^{68} +(-2.72353 - 1.97876i) q^{69} +(-6.33354 - 8.71737i) q^{71} +(-5.43945 - 10.6755i) 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} +(21.4489 + 10.9288i) q^{78} +(10.5738 - 7.68233i) q^{79} +(-3.04508 - 2.21238i) q^{81} +(-4.62064 - 9.06851i) q^{82} +(-13.6183 + 2.15693i) q^{83} +(-3.43184 + 2.49338i) q^{84} +1.97876i q^{86} +(3.53118 + 6.93033i) q^{87} +(0.568158 - 1.11507i) q^{88} +(3.20347 - 1.04087i) q^{89} +(1.54180 - 4.74518i) q^{91} +(-2.23015 - 1.13632i) q^{92} +(-19.1180 - 19.1180i) q^{93} +(1.36176 + 1.87431i) q^{94} +(-8.94427 - 12.3107i) q^{96} +(-0.281373 - 0.0445651i) q^{97} +(-6.37831 - 6.37831i) q^{98} +1.87431i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 4 q^{7} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 4 * q^7 + 16 * q^8	\( 8 q - 8 q^{2} + 4 q^{7} + 16 q^{8} - 4 q^{11} + 12 q^{13} - 32 q^{16} - 10 q^{17} + 6 q^{18} + 10 q^{19} + 20 q^{21} + 4 q^{22} - 8 q^{23} - 4 q^{26} - 8 q^{28} - 10 q^{29} - 10 q^{31} + 32 q^{32} + 20 q^{34} - 12 q^{36} + 14 q^{37} - 8 q^{38} - 30 q^{39} + 16 q^{41} + 20 q^{43} + 16 q^{46} + 24 q^{47} - 20 q^{51} - 16 q^{52} - 28 q^{53} + 16 q^{56} + 60 q^{57} - 10 q^{59} + 10 q^{61} + 20 q^{62} - 18 q^{63} + 20 q^{66} + 10 q^{67} - 20 q^{68} + 40 q^{69} - 20 q^{71} + 12 q^{72} + 10 q^{73} - 10 q^{74} - 4 q^{76} - 32 q^{77} + 40 q^{78} + 30 q^{79} - 2 q^{81} - 56 q^{82} - 40 q^{84} + 20 q^{87} - 8 q^{88} + 10 q^{89} - 8 q^{91} - 16 q^{92} - 80 q^{93} - 20 q^{94} - 30 q^{97} + 8 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 4 * q^7 + 16 * q^8 - 4 * q^11 + 12 * q^13 - 32 * q^16 - 10 * q^17 + 6 * q^18 + 10 * q^19 + 20 * q^21 + 4 * q^22 - 8 * q^23 - 4 * q^26 - 8 * q^28 - 10 * q^29 - 10 * q^31 + 32 * q^32 + 20 * q^34 - 12 * q^36 + 14 * q^37 - 8 * q^38 - 30 * q^39 + 16 * q^41 + 20 * q^43 + 16 * q^46 + 24 * q^47 - 20 * q^51 - 16 * q^52 - 28 * q^53 + 16 * q^56 + 60 * q^57 - 10 * q^59 + 10 * q^61 + 20 * q^62 - 18 * q^63 + 20 * q^66 + 10 * q^67 - 20 * q^68 + 40 * q^69 - 20 * q^71 + 12 * q^72 + 10 * q^73 - 10 * q^74 - 4 * q^76 - 32 * q^77 + 40 * q^78 + 30 * q^79 - 2 * q^81 - 56 * q^82 - 40 * q^84 + 20 * q^87 - 8 * q^88 + 10 * q^89 - 8 * q^91 - 16 * q^92 - 80 * q^93 - 20 * q^94 - 30 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more