LMFDB - Embedded newform 1000.2.v.e.243.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1000.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-0.420808 - 2.65688i) q^{3} +2.00000i q^{4} +(2.23607 - 3.07768i) q^{6} +(-0.557537 - 0.557537i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-4.02874 + 1.30902i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	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	−0.743794	−	0.668409i	$-0.766976\pi$
$3$	−0.420808	−	2.65688i	−0.242953	−	1.53395i	0.500841	−	0.865539i	$-0.333024\pi$
$4$			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	$-0.297608\pi$
$7$	−0.557537	−	0.557537i	−0.210729	−	0.210729i	−0.804577	+	0.593848i	$0.797608\pi$
$8$	−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	−0.969551	−	0.244890i	$-0.921248\pi$
$11$	−0.136729	+	0.420808i	−0.0412253	+	0.126878i	0.928326	+	0.371768i	$0.121248\pi$
$12$	5.31375	−	0.841616i	1.53395	−	0.242953i
$13$	−5.63818	−	2.87280i	−1.56375	−	0.796770i	−0.564167	−	0.825660i	$-0.690803\pi$
$13$	−5.63818	−	2.87280i	−1.56375	−	0.796770i	−0.999583	+	0.0288899i	$0.990803\pi$
$14$		−	1.11507i		−	0.298016i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	0.857960	−	5.41695i	0.208086	−	1.31380i	−0.633526	−	0.773721i	$-0.718393\pi$
$17$	0.857960	−	5.41695i	0.208086	−	1.31380i	0.841612	−	0.540082i	$-0.181607\pi$
$18$	−5.33776	−	2.71972i	−1.25812	−	0.641045i
$19$	−2.07533	−	2.85645i	−0.476114	−	0.655315i	0.501638	−	0.865078i	$-0.332731\pi$
$19$	−2.07533	−	2.85645i	−0.476114	−	0.655315i	−0.977752	+	0.209763i	$0.932731\pi$
$20$		0			0
$21$	−1.24669	+	1.71592i	−0.272050	+	0.374445i
$22$	−0.557537	+	0.284079i	−0.118867	+	0.0605659i
$23$	−0.568158	−	1.11507i	−0.118469	−	0.232509i	0.824155	−	0.566364i	$-0.191650\pi$
$23$	−0.568158	−	1.11507i	−0.118469	−	0.232509i	−0.942624	+	0.333855i	$0.891650\pi$
$24$	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	0.349011	−	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	$0.158343\pi$
$31$	5.90778	+	8.13136i	1.06107	+	1.46044i	0.182267	+	0.983249i	$0.441657\pi$
$32$	−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	$-0.989156\pi$
$37$	−2.33833	+	4.58924i	−0.384420	+	0.754466i	0.615000	+	0.788527i	$0.289156\pi$
$38$	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	−0.960330	−	0.278867i	$-0.910041\pi$
$41$	−2.22394	−	6.84458i	−0.347321	−	1.06894i	0.613009	−	0.790076i	$-0.289959\pi$
$42$	−2.96261	+	0.469231i	−0.457141	+	0.0724040i
$43$	−0.989378	−	0.989378i	−0.150879	−	0.150879i	0.627632	−	0.778510i	$-0.284024\pi$
$43$	−0.989378	−	0.989378i	−0.150879	−	0.150879i	−0.778510	+	0.627632i	$0.784024\pi$
$44$	−0.841616	−	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	$-0.0881222\pi$
$47$	−0.256271	−	1.61803i	−0.0373810	−	0.236015i	−0.999304	+	0.0373066i	$0.988122\pi$
$48$	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	$-0.518903\pi$
$53$	1.40269	−	0.222164i	0.192674	−	0.0305166i	0.252026	+	0.967721i	$0.418903\pi$
$54$	−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	−0.906986	−	0.421160i	$-0.861623\pi$
$59$	−10.7014	+	3.47709i	−1.39320	+	0.452679i	−0.486215	+	0.873839i	$0.661623\pi$
$60$		0			0
$61$	−4.57086	−	1.48516i	−0.585239	−	0.190156i	0.00140712	−	0.999999i	$-0.499552\pi$
$61$	−4.57086	−	1.48516i	−0.585239	−	0.190156i	−0.586646	+	0.809843i	$0.699552\pi$
$62$	−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	−0.851182	−	0.524871i	$-0.824113\pi$
$67$	0.986616	−	6.22925i	0.120534	−	0.761024i	0.971716	−	0.236153i	$-0.0758865\pi$
$68$	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	$0.420815\pi$
$71$	−6.33354	+	8.71737i	−0.751653	+	1.03456i	−0.997863	+	0.0653452i	$0.979185\pi$
$72$	5.43945	−	10.6755i	0.641045	−	1.25812i
$73$	10.8018	−	5.50380i	1.26426	−	0.644171i	0.312178	−	0.950024i	$-0.398941\pi$
$73$	10.8018	−	5.50380i	1.26426	−	0.644171i	0.952079	+	0.305852i	$0.0989413\pi$
$74$	−6.92757	+	2.25090i	−0.805314	+	0.261662i
$75$		0			0
$76$	5.71290	−	4.15067i	0.655315	−	0.476114i
$77$	0.310847	−	0.158384i	0.0354243	−	0.0180496i
$78$	−21.4489	+	10.9288i	−2.42861	+	1.23744i
$79$	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
$83$	13.6183	+	2.15693i	1.49481	+	0.236754i	0.849671	−	0.527314i	$-0.176801\pi$
$83$	13.6183	+	2.15693i	1.49481	+	0.236754i	0.645136	+	0.764068i	$0.276801\pi$
$84$	−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	0.473837	−	0.880613i	$-0.342869\pi$
$89$	3.20347	+	1.04087i	0.339567	+	0.110332i	−0.134269	+	0.990945i	$0.542869\pi$
$90$		0			0
$91$	1.54180	+	4.74518i	0.161625	+	0.497430i
$92$	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	$-0.545396\pi$
$97$	0.281373	−	0.0445651i	0.0285691	−	0.00452490i	0.170703	+	0.985323i	$0.445396\pi$
$98$	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	$-0.867730\pi$
$101$		−	8.11392i		−	0.807365i	0.914899	−	0.403683i	$-0.132270\pi$
$102$	−14.7532	−	14.7532i	−1.46078	−	1.46078i
$103$	−5.79506	+	0.917847i	−0.571004	+	0.0904381i	−0.435258	−	0.900306i	$-0.643343\pi$
$103$	−5.79506	+	0.917847i	−0.571004	+	0.0904381i	−0.135746	+	0.990744i	$0.543343\pi$
$104$	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	$-0.790220\pi$
$107$	−1.84348	+	1.84348i	−0.178216	+	0.178216i	0.612362	+	0.790578i	$0.290220\pi$
$108$	−5.92522	+	3.01905i	−0.570155	+	0.290508i
$109$	−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
$112$	2.23015	+	2.23015i	0.210729	+	0.210729i
$113$	−3.61626	+	7.09731i	−0.340189	+	0.667659i	−0.996200	−	0.0870924i	$-0.972242\pi$
$113$	−3.61626	+	7.09731i	−0.340189	+	0.667659i	0.656011	+	0.754751i	$0.272242\pi$
$114$	−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	$-0.769583\pi$
$127$	−7.36833	+	3.75435i	−0.653833	+	0.333145i	0.0954115	+	0.995438i	$0.469583\pi$
$128$	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	−0.229689	−	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
$133$	−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	$-0.363337\pi$
$137$	−0.873694	−	0.445169i	−0.0746447	−	0.0380334i	−0.490914	+	0.871208i	$0.663337\pi$
$138$	−4.70228	−	0.744768i	−0.400285	−	0.0633989i
$139$	14.2326	+	4.62444i	1.20719	+	0.392240i	0.842402	−	0.538850i	$-0.181141\pi$
$139$	14.2326	+	4.62444i	1.20719	+	0.392240i	0.364789	+	0.931090i	$0.381141\pi$
$140$		0			0
$141$	−4.19107	+	1.36176i	−0.352952	+	0.114681i
$142$	−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	$-0.886581\pi$
$151$		−	8.57286i		−	0.697649i	0.937188	−	0.348825i	$-0.113419\pi$
$152$	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	$-0.323272\pi$
$157$	−4.04306	−	4.04306i	−0.322671	−	0.322671i	−0.849791	+	0.527120i	$0.823272\pi$
$158$	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	$-0.709301\pi$
$163$	4.95881	−	9.73221i	0.388404	−	0.762285i	0.999573	+	0.0292144i	$0.00930056\pi$
$164$	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	$-0.288289\pi$
$167$	12.4180	+	1.96683i	0.960937	+	0.152198i	0.343791	+	0.939046i	$0.388289\pi$
$168$	−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	0.999782	+	0.0208630i	$0.00664138\pi$
$173$	5.64266	+	11.0743i	0.429004	+	0.841967i	−0.570779	+	0.821104i	$0.693359\pi$
$174$	−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	−0.960360	−	0.278764i	$-0.910075\pi$
$179$	−5.33119	+	7.33776i	−0.398472	+	0.548450i	0.561888	+	0.827214i	$0.310075\pi$
$180$		0			0
$181$	−7.70946	−	10.6112i	−0.573039	−	0.788721i	0.419871	−	0.907584i	$-0.362075\pi$
$181$	−7.70946	−	10.6112i	−0.573039	−	0.788721i	−0.992911	+	0.118863i	$0.962075\pi$
$182$	−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	0.408795	−	0.912626i	$-0.365949\pi$
$191$	17.6339	−	5.72960i	1.27594	−	0.414580i	0.867150	+	0.498047i	$0.165949\pi$
$192$	−21.2550	+	3.36646i	−1.53395	+	0.242953i
$193$	−11.2519	−	11.2519i	−0.809933	−	0.809933i	0.174691	−	0.984623i	$-0.444107\pi$
$193$	−11.2519	−	11.2519i	−0.809933	−	0.809933i	−0.984623	+	0.174691i	$0.944107\pi$
$194$	0.325938	+	0.236808i	0.0234010	+	0.0170018i
$195$		0			0
$196$	12.7566			0.911187
$197$	−0.872888	−	5.51120i	−0.0621907	−	0.392657i	−0.999074	−	0.0430155i	$-0.986304\pi$
$197$	−0.872888	−	5.51120i	−0.0621907	−	0.392657i	0.936884	−	0.349641i	$-0.113696\pi$
$198$	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	−0.955971	−	0.293461i	$-0.905193\pi$
$211$	−0.146453	+	0.450735i	−0.0100822	+	0.0310299i	0.945889	+	0.324491i	$0.105193\pi$
$212$	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	−0.934801	−	0.355173i	$-0.884422\pi$
$223$	−10.0452	−	19.7149i	−0.672680	−	1.32021i	0.262121	−	0.965035i	$-0.415578\pi$
$224$			4.46029i			0.298016i
$225$		0			0
$226$	−10.7136	+	3.48105i	−0.712656	+	0.231556i
$227$	−0.709101	−	1.39169i	−0.0470647	−	0.0923697i	0.866276	−	0.499565i	$-0.166507\pi$
$227$	−0.709101	−	1.39169i	−0.0470647	−	0.0923697i	−0.913341	+	0.407195i	$0.866507\pi$
$228$	−13.4318	−	13.4318i	−0.889545	−	0.889545i
$229$	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
$233$	−15.6017	−	2.47106i	−1.02210	−	0.161885i	−0.377184	−	0.926138i	$-0.623107\pi$
$233$	−15.6017	−	2.47106i	−1.02210	−	0.161885i	−0.644916	+	0.764254i	$0.723107\pi$
$234$	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	−0.960915	−	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	$0.996124\pi$
$242$	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	$-0.745794\pi$
$257$	0.299558	−	0.299558i	0.0186859	−	0.0186859i	0.716388	+	0.697702i	$0.245794\pi$
$258$	−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	$-0.478467\pi$
$263$	−11.3494	−	5.78283i	−0.699836	−	0.356584i	−0.767434	+	0.641128i	$0.778467\pi$
$264$	−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	−0.275686	−	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	−0.567650	−	0.823270i	$-0.692147\pi$
$271$	6.43240	−	8.85343i	0.390740	−	0.537808i	0.958390	+	0.285462i	$0.0921472\pi$
$272$	−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	$-0.734219\pi$
$277$	−7.75589	+	3.95183i	−0.466006	+	0.237442i	0.205189	+	0.978722i	$0.434219\pi$
$278$	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	−0.331857	−	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
$283$	−7.35420	−	1.16479i	−0.437162	−	0.0692397i	−0.0660254	−	0.997818i	$-0.521032\pi$
$283$	−7.35420	−	1.16479i	−0.437162	−	0.0692397i	−0.371137	+	0.928578i	$0.621032\pi$
$284$	−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	$-0.883378\pi$
$293$	−9.84915	+	9.84915i	−0.575393	+	0.575393i	0.358237	+	0.933631i	$0.383378\pi$
$294$	−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	$-0.733619\pi$
$307$	1.27461	−	1.27461i	0.0727458	−	0.0727458i	0.742544	+	0.669798i	$0.233619\pi$
$308$	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	0.472979	−	0.881074i	$-0.343179\pi$
$311$	5.95620	+	1.93529i	0.337745	+	0.109740i	−0.135234	+	0.990814i	$0.543179\pi$
$312$	−21.8575	−	42.8978i	−1.23744	−	2.42861i
$313$	−1.36098	+	2.67107i	−0.0769270	+	0.150978i	−0.926266	−	0.376869i	$-0.877001\pi$
$313$	−1.36098	+	2.67107i	−0.0769270	+	0.150978i	0.849339	+	0.527847i	$0.177001\pi$
$314$		−	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	$-0.556183\pi$
$317$	−11.5159	−	1.82394i	−0.646799	−	0.102443i	−0.471211	+	0.882021i	$0.656183\pi$
$318$	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	−0.990087	−	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
$333$	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	$-0.553346\pi$
$337$	−19.5056	−	9.93860i	−1.06254	−	0.541390i	−0.895730	+	0.444599i	$0.853346\pi$
$338$	−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	$-0.637581\pi$
$347$	−9.99724	+	1.58341i	−0.536680	+	0.0850017i	−0.117790	+	0.993039i	$0.537581\pi$
$348$	−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	0.884558	+	0.466430i	$0.154460\pi$
$353$	3.52146	+	22.2336i	0.187428	+	1.18338i	−0.697130	+	0.716945i	$0.745540\pi$
$354$	−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	0.999860	+	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
$362$	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	$-0.713959\pi$
$367$	−27.9062	−	4.41991i	−1.45669	−	0.230717i	−0.834007	+	0.551754i	$0.813959\pi$
$368$	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	$-0.0850649\pi$
$373$	3.55258	+	6.97233i	0.183946	+	0.361014i	−0.780558	+	0.625084i	$0.785065\pi$
$374$	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	−0.351314	−	0.936258i	$-0.614265\pi$
$379$	12.6090	−	17.3548i	0.647682	−	0.891458i	0.998996	+	0.0447999i	$0.0142650\pi$
$380$		0			0
$381$	13.0755	+	17.9969i	0.669878	+	0.922008i
$382$	23.3635	+	11.9043i	1.19538	+	0.609077i
$383$	−0.678276	+	4.28247i	−0.0346583	+	0.218824i	−0.998939	−	0.0460597i	$-0.985334\pi$
$383$	−0.678276	+	4.28247i	−0.0346583	+	0.218824i	0.964280	+	0.264884i	$0.0853336\pi$
$384$	−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	−0.849381	−	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
$392$	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	−0.605539	−	0.795816i	$-0.707042\pi$
$397$	−5.49045	−	34.6653i	−0.275558	−	1.73980i	0.329981	−	0.943988i	$-0.392958\pi$
$398$	−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	−0.578362	−	0.815780i	$-0.696308\pi$
$409$	−11.4621	+	3.72426i	−0.566764	+	0.184153i	0.0115985	+	0.999933i	$0.496308\pi$
$410$		0			0
$411$	−0.815103	+	2.50863i	−0.0402060	+	0.123741i
$412$	−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	0.738651	−	0.674088i	$-0.235463\pi$
$419$	−2.67537	−	3.68233i	−0.130700	−	0.179894i	−0.869352	+	0.494194i	$0.835463\pi$
$420$		0			0
$421$	17.4848	−	24.0657i	0.852155	−	1.17289i	−0.131229	−	0.991352i	$-0.541892\pi$
$421$	17.4848	−	24.0657i	0.852155	−	1.17289i	0.983384	−	0.181538i	$-0.0581076\pi$
$422$	−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	0.374280	−	0.927316i	$-0.377890\pi$
$431$	−12.9402	−	17.8107i	−0.623308	−	0.857910i	−0.997589	+	0.0694055i	$0.977890\pi$
$432$	−6.03810	−	11.8504i	−0.290508	−	0.570155i
$433$	18.9256	+	2.99752i	0.909505	+	0.144052i	0.593620	−	0.804746i	$-0.297698\pi$
$433$	18.9256	+	2.99752i	0.909505	+	0.144052i	0.315886	+	0.948797i	$0.397698\pi$
$434$	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	−0.913443	−	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
$442$	−48.4761	+	7.67786i	−2.30577	+	0.365199i
$443$	−0.566293	−	0.566293i	−0.0269054	−	0.0269054i	0.693526	−	0.720432i	$-0.256056\pi$
$443$	−0.566293	−	0.566293i	−0.0269054	−	0.0269054i	−0.720432	+	0.693526i	$0.756056\pi$
$444$	−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	$0.181695\pi$
$449$			22.8981i			1.08063i	−0.841463	+	0.540315i	$0.818305\pi$
$450$		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	$-0.505922\pi$
$457$	20.9761	−	20.9761i	0.981222	−	0.981222i	0.999827	+	0.0186046i	$0.00592238\pi$
$458$	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	−0.154977	−	0.987918i	$-0.549530\pi$
$461$	−18.4873	−	6.00689i	−0.861039	−	0.279769i	−0.706062	+	0.708150i	$0.749530\pi$
$462$	0.207618	−	1.31085i	0.00965925	−	0.0609861i
$463$	−22.5727	−	11.5014i	−1.04904	−	0.534513i	−0.157531	−	0.987514i	$-0.550353\pi$
$463$	−22.5727	−	11.5014i	−1.04904	−	0.534513i	−0.891510	+	0.453001i	$0.850353\pi$
$464$	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	0.897472	+	0.441071i	$0.145401\pi$
$467$	−1.99620	+	12.6035i	−0.0923730	+	0.583220i	−0.989845	+	0.142149i	$0.954599\pi$
$468$	−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	0.956695	−	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
$483$	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	$-0.883940\pi$
$487$	−2.13244	+	4.18515i	−0.0966302	+	0.189647i	0.837631	+	0.546236i	$0.183940\pi$
$488$	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	−0.936780	−	0.349918i	$-0.886209\pi$
$491$	−8.52185	−	26.2276i	−0.384586	−	1.18363i	0.552194	−	0.833715i	$-0.313791\pi$
$492$	−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	$0.295760\pi$
$499$			35.7912i			1.60223i	−0.598508	+	0.801117i	$0.704240\pi$
$500$		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	$-0.139754\pi$
$503$	42.5535	−	6.73981i	1.89737	−	0.300513i	0.992211	+	0.124566i	$0.0397540\pi$
$504$	−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	−0.998335	−	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
$512$	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	0.512421	−	0.858734i	$-0.328749\pi$
$521$	−3.33109	−	2.42018i	−0.145937	−	0.106030i	−0.658358	+	0.752705i	$0.728749\pi$
$522$	7.86406	+	15.4341i	0.344200	+	0.675531i
$523$	3.35349	−	1.70869i	0.146638	−	0.0747158i	−0.379132	−	0.925343i	$-0.623777\pi$
$523$	3.35349	−	1.70869i	0.146638	−	0.0747158i	0.525770	+	0.850627i	$0.323777\pi$
$524$	10.3939	+	14.3060i	0.454061	+	0.624962i
$525$		0			0
$526$	−5.56661	−	17.1323i	−0.242716	−	0.747002i
$527$	49.1158	−	25.0258i	2.13952	−	1.09014i
$528$	−4.70228	−	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	−0.566384	−	0.824142i	$-0.691658\pi$
$541$	−12.5643	+	4.08238i	−0.540180	+	0.175515i	0.0262040	+	0.999657i	$0.491658\pi$
$542$	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	$-0.696963\pi$
$547$	−20.5808	+	3.25968i	−0.879971	+	0.139374i	−0.299930	+	0.953961i	$0.596963\pi$
$548$	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	$-0.416300\pi$
$557$	−16.6551	−	16.6551i	−0.705697	−	0.705697i	−0.965627	+	0.259930i	$0.916300\pi$
$558$	−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	−0.212644	+	0.977130i	$0.568208\pi$
$563$	−20.8369	+	40.8947i	−0.878170	+	1.72350i	−0.665525	+	0.746375i	$0.731792\pi$
$564$	−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	0.943098	+	0.332516i	$0.107897\pi$
$569$	23.0882	+	31.7781i	0.967906	+	1.33221i	0.0248079	+	0.999692i	$0.492103\pi$
$570$		0			0
$571$	19.4298	+	14.1166i	0.813111	+	0.590760i	0.914731	−	0.404063i	$-0.132402\pi$
$571$	19.4298	+	14.1166i	0.813111	+	0.590760i	−0.101620	+	0.994823i	$0.532402\pi$
$572$	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	$-0.191921\pi$
$577$	−2.86414	−	5.62119i	−0.119236	−	0.234013i	−0.942908	+	0.333052i	$0.891921\pi$
$578$	−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	$-0.0730909\pi$
$587$	32.9979	+	16.8133i	1.36197	+	0.693958i	0.388218	+	0.921568i	$0.373091\pi$
$588$	−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	$-0.409047\pi$
$593$	−16.5004	−	16.5004i	−0.677590	−	0.677590i	−0.959454	+	0.281864i	$0.909047\pi$
$594$	−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	0.999667	+	0.0257859i	$0.00820882\pi$
$607$	25.2645	+	25.2645i	1.02545	+	1.02545i	0.0257859	+	0.999667i	$0.491791\pi$
$608$	−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	$-0.617217\pi$
$613$	−32.8390	−	16.7323i	−1.32635	−	0.675811i	−0.966372	+	0.257148i	$0.917217\pi$
$614$	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	$-0.927333\pi$
$617$	0.552944	−	3.49115i	0.0222607	−	0.140548i	0.996316	+	0.0857638i	$0.0273330\pi$
$618$	−10.1333	+	19.8877i	−0.407621	+	0.800001i
$619$	−26.6760	−	36.7164i	−1.07220	−	1.47576i	−0.867830	−	0.496861i	$-0.834486\pi$
$619$	−26.6760	−	36.7164i	−1.07220	−	1.47576i	−0.204369	−	0.978894i	$-0.565514\pi$
$620$		0			0
$621$	2.44588	−	3.36646i	0.0981497	−	0.135091i
$622$	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	0.935461	−	0.353431i	$-0.114985\pi$
$631$	7.79351	+	10.7268i	0.310255	+	0.427029i	−0.625206	+	0.780460i	$0.714985\pi$
$632$	−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	0.818846	−	0.574014i	$-0.194614\pi$
$641$	−4.58284	−	14.1045i	−0.181011	−	0.557095i	−0.999857	+	0.0169186i	$0.994614\pi$
$642$	1.55150	+	9.79580i	0.0612329	+	0.386609i
$643$	23.8113	+	23.8113i	0.939027	+	0.939027i	0.998245	−	0.0592183i	$-0.0188608\pi$
$643$	23.8113	+	23.8113i	0.939027	+	0.939027i	−0.0592183	+	0.998245i	$0.518861\pi$
$644$	−1.87693	−	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	−0.609669	−	0.792656i	$-0.708698\pi$
$647$	−6.98945	−	44.1296i	−0.274784	−	1.73492i	0.334885	−	0.942259i	$-0.391302\pi$
$648$	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	$-0.549891\pi$
$653$	0.0172425	−	0.00273094i	0.000674750	−	0.000106870i	0.156772	+	0.987635i	$0.449891\pi$
$654$	−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	0.513482	−	0.858100i	$-0.328355\pi$
$659$	36.7936	−	11.9550i	1.43328	−	0.465700i	0.919795	+	0.392400i	$0.128355\pi$
$660$		0			0
$661$	−2.89246	−	0.939818i	−0.112504	−	0.0365547i	0.252224	−	0.967669i	$-0.418838\pi$
$661$	−2.89246	−	0.939818i	−0.112504	−	0.0365547i	−0.364728	+	0.931114i	$0.618838\pi$
$662$	−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	$-0.695165\pi$
$673$	−6.53751	+	3.33103i	−0.252003	+	0.128402i	0.323427	+	0.946253i	$0.395165\pi$
$674$	−9.56701	−	29.4442i	−0.368507	−	1.13415i
$675$		0			0
$676$	−43.7549	+	31.7898i	−1.68288	+	1.22269i
$677$	−25.0033	+	12.7398i	−0.960955	+	0.489631i	−0.862803	−	0.505541i	$-0.831293\pi$
$677$	−25.0033	+	12.7398i	−0.960955	+	0.489631i	−0.0981518	+	0.995171i	$0.531293\pi$
$678$	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	$-0.503697\pi$
$683$	−8.66759	−	1.37281i	−0.331656	−	0.0525292i	−0.320042	+	0.947403i	$0.603697\pi$
$684$	−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	−0.963487	−	0.267755i	$-0.913718\pi$
$691$	−8.97413	−	27.6195i	−0.341392	−	1.05070i	0.622095	−	0.782942i	$-0.286282\pi$
$692$	−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	$0.0650527\pi$
$701$			10.7467i			0.405899i	−0.979189	+	0.202949i	$0.934947\pi$
$702$	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	0.944198	−	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
$712$	−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	−0.609293	−	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
$722$	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	$-0.590686\pi$
$727$	8.90163	−	4.53561i	0.330143	−	0.168216i	0.611203	+	0.791474i	$0.290686\pi$
$728$	−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	−0.869141	−	0.494564i	$-0.835328\pi$
$733$	2.98599	−	18.8528i	0.110290	−	0.696344i	0.979431	−	0.201779i	$-0.0646724\pi$
$734$	−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	−0.311131	−	0.950367i	$-0.600708\pi$
$739$	−30.4862	−	9.90557i	−1.12145	−	0.364382i	−0.810322	+	0.585985i	$0.800708\pi$
$740$		0			0
$741$	57.1591	−	18.5721i	2.09979	−	0.682263i
$742$	−0.247729	−	1.56410i	−0.00909443	−	0.0574200i
$743$	27.7454	−	27.7454i	1.01788	−	1.01788i	0.0180432	−	0.999837i	$-0.494256\pi$
$743$	27.7454	−	27.7454i	1.01788	−	1.01788i	0.999837	−	0.0180432i	$-0.00574364\pi$
$744$			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	$0.0782963\pi$
$751$			13.3460i			0.487004i	−0.969900	+	0.243502i	$0.921704\pi$
$752$	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	$-0.0447689\pi$
$757$	23.3850	+	23.3850i	0.849943	+	0.849943i	−0.140182	+	0.990126i	$0.544769\pi$
$758$	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	0.760464	+	0.649380i	$0.224971\pi$
$761$	−6.52304	+	20.0758i	−0.236460	+	0.727749i	−0.996924	+	0.0783693i	$0.975029\pi$
$762$	−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	−0.793114	−	0.609073i	$-0.791542\pi$
$769$	−31.2607	−	43.0267i	−1.12729	−	1.55158i	−0.334177	−	0.942510i	$-0.608458\pi$
$770$		0			0
$771$	−0.921944	−	0.669832i	−0.0332030	−	0.0241234i
$772$	22.5039	−	22.5039i	0.809933	−	0.809933i
$773$	13.9493	+	27.3771i	0.501722	+	0.984686i	0.993486	+	0.113957i	$0.0363525\pi$
$773$	13.9493	+	27.3771i	0.501722	+	0.984686i	−0.491763	+	0.870729i	$0.663647\pi$
$774$	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	$-0.124628\pi$
$787$	32.5114	+	16.5654i	1.15891	+	0.590493i	0.234581	+	0.972097i	$0.424628\pi$
$788$	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	$-0.0161920\pi$
$797$	0.936362	+	5.91196i	0.0331677	+	0.209412i	−0.965539	+	0.260259i	$0.916192\pi$
$798$	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	−0.781387	−	0.624047i	$-0.785487\pi$
$809$	−29.7722	+	9.67358i	−1.04674	+	0.340105i	−0.265349	+	0.964152i	$0.585487\pi$
$810$		0			0
$811$	1.95623	−	6.02066i	0.0686926	−	0.211414i	−0.910817	−	0.412809i	$-0.864548\pi$
$811$	1.95623	−	6.02066i	0.0686926	−	0.211414i	0.979510	+	0.201395i	$0.0645476\pi$
$812$	−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	−0.975769	−	0.218802i	$-0.929785\pi$
$821$	−13.3566	+	18.3837i	−0.466147	+	0.641596i	0.509622	+	0.860398i	$0.329785\pi$
$822$	−3.32373	+	1.69353i	−0.115928	+	0.0590685i
$823$	5.29231	+	10.3867i	0.184478	+	0.362059i	0.964662	−	0.263492i	$-0.0848743\pi$
$823$	5.29231	+	10.3867i	0.184478	+	0.362059i	−0.780183	+	0.625551i	$0.784874\pi$
$824$	9.75442	−	13.4258i	0.339811	−	0.467710i
$825$		0			0
$826$	3.87721	+	11.9328i	0.134905	+	0.415196i
$827$	2.69680	+	5.29276i	0.0937768	+	0.184047i	0.933130	−	0.359539i	$-0.117066\pi$
$827$	2.69680	+	5.29276i	0.0937768	+	0.184047i	−0.839353	+	0.543586i	$0.817066\pi$
$828$	−7.49722	+	7.49722i	−0.260546	+	0.260546i
$829$	−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
$833$	−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	0.367276	+	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
$842$	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	$-0.582773\pi$
$853$	−5.92966	+	0.939165i	−0.203028	+	0.0321564i	0.0540922	+	0.998536i	$0.482773\pi$
$854$	−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	$-0.778795\pi$
$857$	−3.74007	+	3.74007i	−0.127758	+	0.127758i	0.640336	+	0.768095i	$0.278795\pi$
$858$	−1.66623	−	10.5201i	−0.0568841	−	0.359152i
$859$	30.1496	−	9.79621i	1.02869	−	0.334242i	0.254419	−	0.967094i	$-0.418116\pi$
$859$	30.1496	−	9.79621i	1.02869	−	0.334242i	0.774273	+	0.632852i	$0.218116\pi$
$860$		0			0
$861$	14.5173	+	4.71696i	0.494749	+	0.160754i
$862$	4.87046	−	30.7509i	0.165889	−	1.04738i
$863$	9.14726	+	4.66076i	0.311376	+	0.158654i	0.602694	−	0.797972i	$-0.294094\pi$
$863$	9.14726	+	4.66076i	0.311376	+	0.158654i	−0.291318	+	0.956626i	$0.594094\pi$
$864$	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	$-0.744488\pi$
$877$	−15.4361	+	7.86511i	−0.521241	+	0.265586i	0.173515	+	0.984831i	$0.444488\pi$
$878$	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	−0.935250	−	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
$883$	16.6396	+	2.63545i	0.559966	+	0.0886900i	0.430001	−	0.902829i	$-0.358513\pi$
$883$	16.6396	+	2.63545i	0.559966	+	0.0886900i	0.129966	+	0.991519i	$0.458513\pi$
$884$	−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	$-0.971766\pi$
$887$	−10.0941	+	19.8108i	−0.338928	+	0.665183i	0.657141	+	0.753768i	$0.271766\pi$
$888$	−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	$-0.850264\pi$
$907$	−13.1949	+	13.1949i	−0.438131	+	0.438131i	0.453252	+	0.891383i	$0.350264\pi$
$908$	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	0.178817	−	0.983882i	$-0.442773\pi$
$911$	−7.69141	−	2.49909i	−0.254828	−	0.0827985i	−0.433645	+	0.901084i	$0.642773\pi$
$912$	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	−0.140546	−	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
$922$	−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	−0.649436	−	0.760416i	$-0.724995\pi$
$929$	8.36507	−	11.5135i	0.274449	−	0.377747i	0.923885	+	0.382669i	$0.124995\pi$
$930$		0			0
$931$	−18.2193	+	13.2371i	−0.597114	+	0.433829i
$932$	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	$-0.437482\pi$
$937$	−14.8036	−	7.54279i	−0.483611	−	0.246412i	−0.678758	+	0.734362i	$0.737482\pi$
$938$	−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	0.575720	−	0.817647i	$-0.304722\pi$
$941$	46.6912	−	15.1709i	1.52209	−	0.494556i	0.946368	+	0.323090i	$0.104722\pi$
$942$	−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	$-0.450466\pi$
$947$	18.7002	−	2.96183i	0.607676	−	0.0962464i	0.452687	+	0.891670i	$0.350466\pi$
$948$	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	−0.982832	−	0.184501i	$-0.940933\pi$
$953$	−3.24504	−	20.4884i	−0.105117	−	0.663683i	0.877715	−	0.479183i	$-0.159067\pi$
$954$	−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	$-0.593841\pi$
$967$	−26.8233	−	4.24840i	−0.862580	−	0.136619i	−0.572022	+	0.820238i	$0.693841\pi$
$968$	−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	$0.862971\pi$
$972$	−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	0.957463	+	0.288555i	$0.0931748\pi$
$977$	19.6333	+	38.5326i	0.628126	+	1.23277i	−0.329337	+	0.944212i	$0.606825\pi$
$978$	−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	−0.133706	−	0.991021i	$-0.542688\pi$
$983$	9.39639	−	59.3265i	0.299698	−	1.89222i	0.433405	−	0.901200i	$-0.357312\pi$
$984$	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	0.479770	−	0.877394i	$-0.340720\pi$
$991$	43.5569	−	14.1525i	1.38363	−	0.449569i	0.903862	+	0.427825i	$0.140720\pi$
$992$	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	0.985053	+	0.172250i	$0.0551038\pi$
$997$	3.20301	+	20.2230i	0.101440	+	0.640468i	−0.883613	+	0.468218i	$0.844896\pi$
$998$	−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.e.243.1		8
5.2	odd	4		200.2.v.a.147.1	yes	8
5.3	odd	4		1000.2.v.f.507.1		8
5.4	even	2		1000.2.v.a.243.1		8
8.3	odd	2		1000.2.v.d.243.1		8
20.7	even	4		800.2.bp.b.47.1		8
25.6	even	5		200.2.v.b.83.1	yes	8
25.8	odd	20		1000.2.v.b.107.1		8
25.17	odd	20		1000.2.v.d.107.1		8
25.19	even	10		1000.2.v.c.643.1		8
40.3	even	4		1000.2.v.c.507.1		8
40.19	odd	2		1000.2.v.b.243.1		8
40.27	even	4		200.2.v.b.147.1	yes	8
40.37	odd	4		800.2.bp.a.47.1		8
100.31	odd	10		800.2.bp.a.783.1		8
200.19	odd	10		1000.2.v.f.643.1		8
200.67	even	20	inner	1000.2.v.e.107.1		8
200.83	even	20		1000.2.v.a.107.1		8
200.131	odd	10		200.2.v.a.83.1	✓	8
200.181	even	10		800.2.bp.b.783.1		8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-0.420808 - 2.65688i) q^{3} +2.00000i q^{4} +(2.23607 - 3.07768i) q^{6} +(-0.557537 - 0.557537i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-4.02874 + 1.30902i) q^{9} +O(q^{10})\)	\(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

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Database

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