LMFDB - Embedded newform 1000.2.t.b.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(101,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

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

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

chi := DirichletCharacter("1000.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.t (of order $10$, degree $4$, 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:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.6
Character	$\chi$	$=$	1000.101
Dual form			1000.2.t.b.901.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37312 + 0.338435i) q^{2} +(1.87526 - 2.58107i) q^{3} +(1.77092 - 0.929423i) q^{4} +(-1.70143 + 4.17877i) q^{6} -2.97769 q^{7} +(-2.11714 + 1.87555i) q^{8} +(-2.21828 - 6.82716i) q^{9} +O(q^{10})$	\(q+(-1.37312 + 0.338435i) q^{2} +(1.87526 - 2.58107i) q^{3} +(1.77092 - 0.929423i) q^{4} +(-1.70143 + 4.17877i) q^{6} -2.97769 q^{7} +(-2.11714 + 1.87555i) q^{8} +(-2.21828 - 6.82716i) q^{9} +(-0.263378 - 0.0855768i) q^{11} +(0.922031 - 6.31378i) q^{12} +(-4.19500 + 1.36304i) q^{13} +(4.08873 - 1.00775i) q^{14} +(2.27234 - 3.29188i) q^{16} +(-4.14580 + 3.01210i) q^{17} +(5.35651 + 8.62377i) q^{18} +(0.824879 + 1.13535i) q^{19} +(-5.58392 + 7.68561i) q^{21} +(0.390613 + 0.0283710i) q^{22} +(0.0998113 - 0.307187i) q^{23} +(0.870742 + 8.98164i) q^{24} +(5.29895 - 3.29135i) q^{26} +(-12.6785 - 4.11950i) q^{27} +(-5.27326 + 2.76753i) q^{28} +(-2.59226 + 3.56794i) q^{29} +(-3.04947 + 2.21557i) q^{31} +(-2.00612 + 5.28919i) q^{32} +(-0.714781 + 0.519319i) q^{33} +(4.67329 - 5.53907i) q^{34} +(-10.2737 - 10.0287i) q^{36} +(3.84202 - 1.24835i) q^{37} +(-1.51690 - 1.27980i) q^{38} +(-4.34861 + 13.3836i) q^{39} +(-1.97884 - 6.09023i) q^{41} +(5.06633 - 12.4431i) q^{42} -10.9079i q^{43} +(-0.545960 + 0.0932399i) q^{44} +(-0.0330901 + 0.455585i) q^{46} +(-2.30062 - 1.67150i) q^{47} +(-4.23533 - 12.0382i) q^{48} +1.86662 q^{49} +16.3491i q^{51} +(-6.16219 + 6.31278i) q^{52} +(-0.274854 + 0.378304i) q^{53} +(18.8033 + 1.36572i) q^{54} +(6.30419 - 5.58481i) q^{56} +4.47727 q^{57} +(2.35197 - 5.77652i) q^{58} +(5.09147 - 1.65432i) q^{59} +(-1.96419 - 0.638204i) q^{61} +(3.43747 - 4.07430i) q^{62} +(6.60534 + 20.3291i) q^{63} +(0.964603 - 7.94163i) q^{64} +(0.805726 - 0.954995i) q^{66} +(-0.908853 - 1.25093i) q^{67} +(-4.54239 + 9.18741i) q^{68} +(-0.605700 - 0.833675i) q^{69} +(7.81261 + 5.67620i) q^{71} +(17.5011 + 10.2936i) q^{72} +(2.77576 - 8.54291i) q^{73} +(-4.85308 + 3.01441i) q^{74} +(2.51602 + 1.24395i) q^{76} +(0.784258 + 0.254821i) q^{77} +(1.44168 - 19.8491i) q^{78} +(-4.49455 - 3.26548i) q^{79} +(-16.9856 + 12.3407i) q^{81} +(4.77833 + 7.69292i) q^{82} +(7.80599 + 10.7440i) q^{83} +(-2.74552 + 18.8005i) q^{84} +(3.69160 + 14.9778i) q^{86} +(4.34795 + 13.3816i) q^{87} +(0.718114 - 0.312802i) q^{88} +(-0.992059 + 3.05324i) q^{89} +(12.4914 - 4.05871i) q^{91} +(-0.108749 - 0.636773i) q^{92} +12.0257i q^{93} +(3.72473 + 1.51656i) q^{94} +(9.88976 + 15.0965i) q^{96} +(-13.3433 - 9.69449i) q^{97} +(-2.56310 + 0.631729i) q^{98} +1.98796i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$1$

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 $

$2$	−1.37312	+	0.338435i	−0.970943	+	0.239309i
$2$	−1.37312	+	0.338435i	−0.970943	+	0.239309i
$3$	1.87526	−	2.58107i	1.08268	−	1.49018i	0.226143	−	0.974094i	$-0.427388\pi$
$3$	1.87526	−	2.58107i	1.08268	−	1.49018i	0.856537	−	0.516086i	$-0.172612\pi$
$4$	1.77092	−	0.929423i	0.885462	−	0.464712i
$5$		0			0
$5$		0			0
$6$	−1.70143	+	4.17877i	−0.694606	+	1.70598i
$7$	−2.97769			−1.12546			−0.562730	−	0.826641i	$-0.690249\pi$
$7$	−2.97769			−1.12546			−0.562730	+	0.826641i	$0.690249\pi$
$8$	−2.11714	+	1.87555i	−0.748524	+	0.663108i
$9$	−2.21828	−	6.82716i	−0.739426	−	2.27572i
$10$		0			0
$11$	−0.263378	−	0.0855768i	−0.0794116	−	0.0258024i	0.269042	−	0.963129i	$-0.413293\pi$
$11$	−0.263378	−	0.0855768i	−0.0794116	−	0.0258024i	−0.348453	+	0.937326i	$0.613293\pi$
$12$	0.922031	−	6.31378i	0.266167	−	1.82263i
$13$	−4.19500	+	1.36304i	−1.16349	+	0.378039i	−0.826207	−	0.563366i	$-0.809506\pi$
$13$	−4.19500	+	1.36304i	−1.16349	+	0.378039i	−0.337278	+	0.941405i	$0.609506\pi$
$14$	4.08873	−	1.00775i	1.09276	−	0.269333i
$15$		0			0
$16$	2.27234	−	3.29188i	0.568086	−	0.822969i
$17$	−4.14580	+	3.01210i	−1.00551	+	0.730542i	−0.963262	−	0.268565i	$-0.913451\pi$
$17$	−4.14580	+	3.01210i	−1.00551	+	0.730542i	−0.0422436	+	0.999107i	$0.513451\pi$
$18$	5.35651	+	8.62377i	1.26254	+	2.03264i
$19$	0.824879	+	1.13535i	0.189240	+	0.260467i	0.893086	−	0.449886i	$-0.148535\pi$
$19$	0.824879	+	1.13535i	0.189240	+	0.260467i	−0.703846	+	0.710353i	$0.748535\pi$
$20$		0			0
$21$	−5.58392	+	7.68561i	−1.21851	+	1.67714i
$22$	0.390613	+	0.0283710i	0.0832789	+	0.00604872i
$23$	0.0998113	−	0.307187i	0.0208121	−	0.0640530i	−0.940111	−	0.340868i	$-0.889279\pi$
$23$	0.0998113	−	0.307187i	0.0208121	−	0.0640530i	0.960923	+	0.276815i	$0.0892790\pi$
$24$	0.870742	+	8.98164i	0.177739	+	1.83337i
$25$		0			0
$26$	5.29895	−	3.29135i	1.03921	−	0.645488i
$27$	−12.6785	−	4.11950i	−2.43998	−	0.792798i
$28$	−5.27326	+	2.76753i	−0.996552	+	0.523014i
$29$	−2.59226	+	3.56794i	−0.481371	+	0.662550i	−0.978768	−	0.204973i	$-0.934289\pi$
$29$	−2.59226	+	3.56794i	−0.481371	+	0.662550i	0.497397	+	0.867523i	$0.334289\pi$
$30$		0			0
$31$	−3.04947	+	2.21557i	−0.547702	+	0.397929i	−0.826937	−	0.562294i	$-0.809919\pi$
$31$	−3.04947	+	2.21557i	−0.547702	+	0.397929i	0.279236	+	0.960223i	$0.409919\pi$
$32$	−2.00612	+	5.28919i	−0.354635	+	0.935005i
$33$	−0.714781	+	0.519319i	−0.124427	+	0.0904018i
$34$	4.67329	−	5.53907i	0.801463	−	0.949942i
$35$		0			0
$36$	−10.2737	−	10.0287i	−1.71229	−	1.67144i
$37$	3.84202	−	1.24835i	0.631625	−	0.205227i	0.0243301	−	0.999704i	$-0.492255\pi$
$37$	3.84202	−	1.24835i	0.631625	−	0.205227i	0.607295	+	0.794477i	$0.292255\pi$
$38$	−1.51690	−	1.27980i	−0.246074	−	0.207612i
$39$	−4.34861	+	13.3836i	−0.696335	+	2.14310i
$40$		0			0
$41$	−1.97884	−	6.09023i	−0.309042	−	0.951135i	−0.978138	−	0.207958i	$-0.933318\pi$
$41$	−1.97884	−	6.09023i	−0.309042	−	0.951135i	0.669095	−	0.743177i	$-0.266682\pi$
$42$	5.06633	−	12.4431i	0.781752	−	1.92001i
$43$		−	10.9079i		−	1.66343i	−0.555199	−	0.831717i	$-0.687358\pi$
$43$		−	10.9079i		−	1.66343i	0.555199	−	0.831717i	$-0.312642\pi$
$44$	−0.545960	+	0.0932399i	−0.0823066	+	0.0140564i
$45$		0			0
$46$	−0.0330901	+	0.455585i	−0.00487887	+	0.0671724i
$47$	−2.30062	−	1.67150i	−0.335580	−	0.243813i	0.407214	−	0.913333i	$-0.366500\pi$
$47$	−2.30062	−	1.67150i	−0.335580	−	0.243813i	−0.742795	+	0.669519i	$0.766500\pi$
$48$	−4.23533	−	12.0382i	−0.611317	−	1.73756i
$49$	1.86662			0.266660
$50$		0			0
$51$			16.3491i			2.28933i
$52$	−6.16219	+	6.31278i	−0.854543	+	0.875424i
$53$	−0.274854	+	0.378304i	−0.0377541	+	0.0519641i	−0.827477	−	0.561500i	$-0.810224\pi$
$53$	−0.274854	+	0.378304i	−0.0377541	+	0.0519641i	0.789723	+	0.613464i	$0.210224\pi$
$54$	18.8033	+	1.36572i	2.55881	+	0.185852i
$55$		0			0
$56$	6.30419	−	5.58481i	0.842433	−	0.746302i
$57$	4.47727			0.593029
$58$	2.35197	−	5.77652i	0.308829	−	0.758495i
$59$	5.09147	−	1.65432i	0.662853	−	0.215374i	0.0417804	−	0.999127i	$-0.486697\pi$
$59$	5.09147	−	1.65432i	0.662853	−	0.215374i	0.621073	+	0.783753i	$0.286697\pi$
$60$		0			0
$61$	−1.96419	−	0.638204i	−0.251489	−	0.0817137i	0.180560	−	0.983564i	$-0.442209\pi$
$61$	−1.96419	−	0.638204i	−0.251489	−	0.0817137i	−0.432049	+	0.901850i	$0.642209\pi$
$62$	3.43747	−	4.07430i	0.436559	−	0.517436i
$63$	6.60534	+	20.3291i	0.832194	+	2.56123i
$64$	0.964603	−	7.94163i	0.120575	−	0.992704i
$65$		0			0
$66$	0.805726	−	0.954995i	0.0991780	−	0.117552i
$67$	−0.908853	−	1.25093i	−0.111034	−	0.152825i	0.749883	−	0.661570i	$-0.230110\pi$
$67$	−0.908853	−	1.25093i	−0.111034	−	0.152825i	−0.860917	+	0.508745i	$0.830110\pi$
$68$	−4.54239	+	9.18741i	−0.550845	+	1.11414i
$69$	−0.605700	−	0.833675i	−0.0729177	−	0.100363i
$70$		0			0
$71$	7.81261	+	5.67620i	0.927187	+	0.673640i	0.945302	−	0.326195i	$-0.105767\pi$
$71$	7.81261	+	5.67620i	0.927187	+	0.673640i	−0.0181158	+	0.999836i	$0.505767\pi$
$72$	17.5011	+	10.2936i	2.06253	+	1.21311i
$73$	2.77576	−	8.54291i	0.324878	−	0.999872i	−0.646618	−	0.762814i	$-0.723817\pi$
$73$	2.77576	−	8.54291i	0.324878	−	0.999872i	0.971496	−	0.237057i	$-0.0761829\pi$
$74$	−4.85308	+	3.01441i	−0.564159	+	0.350418i
$75$		0			0
$76$	2.51602	+	1.24395i	0.288607	+	0.142691i
$77$	0.784258	+	0.254821i	0.0893745	+	0.0290395i
$78$	1.44168	−	19.8491i	0.163238	−	2.24747i
$79$	−4.49455	−	3.26548i	−0.505677	−	0.367396i	0.305504	−	0.952191i	$-0.401175\pi$
$79$	−4.49455	−	3.26548i	−0.505677	−	0.367396i	−0.811181	+	0.584795i	$0.801175\pi$
$80$		0			0
$81$	−16.9856	+	12.3407i	−1.88729	+	1.37119i
$82$	4.77833	+	7.69292i	0.527678	+	0.849541i
$83$	7.80599	+	10.7440i	0.856819	+	1.17931i	0.982319	+	0.187217i	$0.0599466\pi$
$83$	7.80599	+	10.7440i	0.856819	+	1.17931i	−0.125500	+	0.992094i	$0.540053\pi$
$84$	−2.74552	+	18.8005i	−0.299561	+	2.05130i
$85$		0			0
$86$	3.69160	+	14.9778i	0.398075	+	1.61510i
$87$	4.34795	+	13.3816i	0.466149	+	1.43466i
$88$	0.718114	−	0.312802i	0.0765512	−	0.0333448i
$89$	−0.992059	+	3.05324i	−0.105158	+	0.323643i	−0.989768	−	0.142689i	$-0.954425\pi$
$89$	−0.992059	+	3.05324i	−0.105158	+	0.323643i	0.884610	+	0.466333i	$0.154425\pi$
$90$		0			0
$91$	12.4914	−	4.05871i	1.30946	−	0.425468i
$92$	−0.108749	−	0.636773i	−0.0113379	−	0.0663881i
$93$			12.0257i			1.24700i
$94$	3.72473	+	1.51656i	0.384176	+	0.156421i
$95$		0			0
$96$	9.88976	+	15.0965i	1.00937	+	1.54078i
$97$	−13.3433	−	9.69449i	−1.35481	−	0.984327i	−0.998756	−	0.0498611i	$-0.984122\pi$
$97$	−13.3433	−	9.69449i	−1.35481	−	0.984327i	−0.356053	−	0.934466i	$-0.615878\pi$
$98$	−2.56310	+	0.631729i	−0.258912	+	0.0638142i
$99$			1.98796i			0.199797i
$100$		0			0
$101$		−	19.4874i		−	1.93907i	−0.244946	−	0.969537i	$-0.578770\pi$
$101$		−	19.4874i		−	1.93907i	0.244946	−	0.969537i	$-0.421230\pi$
$102$	−5.53309	−	22.4492i	−0.547857	−	2.22281i
$103$	−5.71814	−	4.15447i	−0.563425	−	0.409352i	0.269286	−	0.963060i	$-0.413212\pi$
$103$	−5.71814	−	4.15447i	−0.563425	−	0.409352i	−0.832711	+	0.553708i	$0.813212\pi$
$104$	6.32498	−	10.7537i	0.620215	−	1.05449i
$105$		0			0
$106$	0.249377	−	0.612478i	0.0242216	−	0.0594891i
$107$			11.2557i			1.08813i	0.839044	+	0.544064i	$0.183115\pi$
$107$			11.2557i			1.08813i	−0.839044	+	0.544064i	$0.816885\pi$
$108$	−26.2814	+	4.48838i	−2.52893	+	0.431895i
$109$	−9.07913	+	2.94999i	−0.869623	+	0.282558i	−0.709642	−	0.704563i	$-0.751143\pi$
$109$	−9.07913	+	2.94999i	−0.869623	+	0.282558i	−0.159981	+	0.987120i	$0.551143\pi$
$110$		0			0
$111$	3.98270	−	12.2575i	0.378021	−	1.16343i
$112$	−6.76633	+	9.80218i	−0.639358	+	0.926219i
$113$	−3.26576	−	10.0510i	−0.307217	−	0.945517i	−0.978841	−	0.204624i	$-0.934403\pi$
$113$	−3.26576	−	10.0510i	−0.307217	−	0.945517i	0.671624	−	0.740892i	$-0.265597\pi$
$114$	−6.14783	+	1.51526i	−0.575797	+	0.141917i
$115$		0			0
$116$	−1.27457	+	8.72786i	−0.118341	+	0.810361i
$117$	18.6114	+	25.6164i	1.72062	+	2.36823i
$118$	−6.43133	+	3.99471i	−0.592052	+	0.367743i
$119$	12.3449	−	8.96910i	1.13166	−	0.822196i
$120$		0			0
$121$	−8.83714	−	6.42056i	−0.803377	−	0.583687i
$122$	2.91306	+	0.211582i	0.263736	+	0.0191557i
$123$	−19.4301	−	6.31323i	−1.75196	−	0.569245i
$124$	−3.34118	+	6.75786i	−0.300047	+	0.606874i
$125$		0			0
$126$	−15.9500	−	25.6789i	−1.42094	−	2.28766i
$127$	0.419412	−	1.29082i	0.0372168	−	0.114542i	−0.930722	−	0.365727i	$-0.880820\pi$
$127$	0.419412	−	1.29082i	0.0372168	−	0.114542i	0.967939	+	0.251185i	$0.0808204\pi$
$128$	1.36321	+	11.2313i	0.120491	+	0.992714i
$129$	−28.1540	−	20.4550i	−2.47882	−	1.80097i
$130$		0			0
$131$	−0.471129	−	0.648453i	−0.0411627	−	0.0566556i	0.787940	−	0.615753i	$-0.211148\pi$
$131$	−0.471129	−	0.648453i	−0.0411627	−	0.0566556i	−0.829102	+	0.559097i	$0.811148\pi$
$132$	−0.783156	+	1.58401i	−0.0681650	+	0.137870i
$133$	−2.45623	−	3.38071i	−0.212982	−	0.293145i
$134$	1.67132	+	1.41009i	0.144380	+	0.121813i
$135$		0			0
$136$	3.12791	−	14.1527i	0.268216	−	1.21359i
$137$	2.23985	+	6.89354i	0.191363	+	0.588955i	1.00000		0.000646705i	$0.000205853\pi$
$137$	2.23985	+	6.89354i	0.191363	+	0.588955i	−0.808637	+	0.588308i	$0.799794\pi$
$138$	1.11384	+	0.939747i	0.0948167	+	0.0799966i
$139$	−0.417329	−	0.135598i	−0.0353973	−	0.0115013i	0.291265	−	0.956642i	$-0.405924\pi$
$139$	−0.417329	−	0.135598i	−0.0353973	−	0.0115013i	−0.326662	+	0.945141i	$0.605924\pi$
$140$		0			0
$141$	−8.62851	+	2.80357i	−0.726652	+	0.236103i
$142$	−12.6487	−	5.15005i	−1.06145	−	0.432182i
$143$	1.22152			0.102148
$144$	−27.5148	−	8.21136i	−2.29290	−	0.684280i
$145$		0			0
$146$	−0.920239	+	12.6699i	−0.0761595	+	1.04856i
$147$	3.50039	−	4.81787i	0.288707	−	0.397372i
$148$	5.64369	−	5.78160i	0.463908	−	0.475244i
$149$			1.65547i			0.135621i	0.997698	+	0.0678107i	$0.0216014\pi$
$149$			1.65547i			0.135621i	−0.997698	+	0.0678107i	$0.978399\pi$
$150$		0			0
$151$	−14.0629			−1.14442			−0.572211	−	0.820107i	$-0.693914\pi$
$151$	−14.0629			−1.14442			−0.572211	+	0.820107i	$0.693914\pi$
$152$	−3.87579	−	0.856593i	−0.314368	−	0.0694788i
$153$	29.7606	+	21.6224i	2.40600	+	1.74806i
$154$	−1.16312	−	0.0844800i	−0.0937270	−	0.00680759i
$155$		0			0
$156$	4.73801	+	27.7431i	0.379345	+	2.22123i
$157$		−	9.56521i		−	0.763387i	−0.924289	−	0.381693i	$-0.875341\pi$
$157$		−	9.56521i		−	0.763387i	0.924289	−	0.381693i	$-0.124659\pi$
$158$	7.27672	+	2.96279i	0.578905	+	0.235707i
$159$	0.461007	+	1.41883i	0.0365603	+	0.112521i
$160$		0			0
$161$	−0.297207	+	0.914708i	−0.0234232	+	0.0720891i
$162$	19.1467	−	22.6938i	1.50431	−	1.78300i
$163$	5.22350	−	1.69722i	0.409136	−	0.132936i	−0.0972156	−	0.995263i	$-0.530994\pi$
$163$	5.22350	−	1.69722i	0.409136	−	0.132936i	0.506352	+	0.862327i	$0.330994\pi$
$164$	−9.16477	−	8.94616i	−0.715649	−	0.698578i
$165$		0			0
$166$	−14.3547	−	12.1110i	−1.11414	−	0.939999i
$167$	−9.73651	+	7.07399i	−0.753433	+	0.547401i	−0.896889	−	0.442255i	$-0.854179\pi$
$167$	−9.73651	+	7.07399i	−0.753433	+	0.547401i	0.143456	+	0.989657i	$0.454179\pi$
$168$	−2.59280	−	26.7445i	−0.200039	−	2.06338i
$169$	5.22297	−	3.79471i	0.401767	−	0.291901i
$170$		0			0
$171$	5.92139	−	8.15009i	0.452820	−	0.623253i
$172$	−10.1380	−	19.3170i	−0.773018	−	1.47291i
$173$	16.5363	+	5.37296i	1.25723	+	0.408498i	0.860506	−	0.509440i	$-0.170148\pi$
$173$	16.5363	+	5.37296i	1.25723	+	0.408498i	0.396722	+	0.917939i	$0.370148\pi$
$174$	−10.4991	−	16.9031i	−0.795931	−	1.28142i
$175$		0			0
$176$	−0.880195	+	0.672549i	−0.0663472	+	0.0506953i
$177$	5.27790	−	16.2437i	0.396711	−	1.22095i
$178$	0.328894	−	4.52822i	0.0246517	−	0.339404i
$179$	−12.5073	+	17.2148i	−0.934841	+	1.28670i	0.0231007	+	0.999733i	$0.492646\pi$
$179$	−12.5073	+	17.2148i	−0.934841	+	1.28670i	−0.957941	+	0.286964i	$0.907354\pi$
$180$		0			0
$181$	−4.82937	−	6.64706i	−0.358964	−	0.494072i	0.590896	−	0.806748i	$-0.298775\pi$
$181$	−4.82937	−	6.64706i	−0.358964	−	0.494072i	−0.949860	+	0.312676i	$0.898775\pi$
$182$	−15.7786	+	9.80062i	−1.16959	+	0.726470i
$183$	−5.33061	+	3.87291i	−0.394050	+	0.286294i
$184$	0.364831	+	0.837562i	0.0268957	+	0.0617459i
$185$		0			0
$186$	−4.06990	−	16.5127i	−0.298420	−	1.21077i
$187$	1.34968	−	0.438538i	0.0986985	−	0.0320691i
$188$	−5.62776	−	0.821848i	−0.410446	−	0.0599394i
$189$	37.7526	+	12.2666i	2.74610	+	0.892262i
$190$		0			0
$191$	−1.09517	−	3.37058i	−0.0792436	−	0.243887i	0.903585	−	0.428410i	$-0.140926\pi$
$191$	−1.09517	−	3.37058i	−0.0792436	−	0.243887i	−0.982828	+	0.184523i	$0.940926\pi$
$192$	−18.6890	−	17.3823i	−1.34876	−	1.25446i
$193$	13.3961			0.964273			0.482137	−	0.876096i	$-0.339861\pi$
$193$	13.3961			0.964273			0.482137	+	0.876096i	$0.339861\pi$
$194$	21.6030	+	8.79587i	1.55100	+	0.631507i
$195$		0			0
$196$	3.30564	−	1.73488i	0.236117	−	0.123920i
$197$	3.01790	−	4.15379i	0.215017	−	0.295945i	−0.687861	−	0.725842i	$-0.741450\pi$
$197$	3.01790	−	4.15379i	0.215017	−	0.295945i	0.902878	+	0.429897i	$0.141450\pi$
$198$	−0.672794	−	2.72971i	−0.0478134	−	0.193992i
$199$	−12.5552			−0.890012			−0.445006	−	0.895528i	$-0.646798\pi$
$199$	−12.5552			−0.890012			−0.445006	+	0.895528i	$0.646798\pi$
$200$		0			0
$201$	−4.93307			−0.347952
$202$	6.59523	+	26.7586i	0.464038	+	1.88273i
$203$	7.71894	−	10.6242i	0.541763	−	0.745673i
$204$	15.1952	+	28.9530i	1.06388	+	2.02711i
$205$		0			0
$206$	9.25771	+	3.76938i	0.645015	+	0.262625i
$207$	−2.31863			−0.161156
$208$	−5.04554	+	16.9067i	−0.349845	+	1.17227i
$209$	−0.120096	−	0.369617i	−0.00830719	−	0.0255669i
$210$		0			0
$211$	7.25107	+	2.35602i	0.499184	+	0.162195i	0.547778	−	0.836624i	$-0.315474\pi$
$211$	7.25107	+	2.35602i	0.499184	+	0.162195i	−0.0485936	+	0.998819i	$0.515474\pi$
$212$	−0.135141	+	0.925404i	−0.00928153	+	0.0635570i
$213$	29.3013	−	9.52057i	2.00769	−	0.652339i
$214$	−3.80931	−	15.4554i	−0.260399	−	1.05651i
$215$		0			0
$216$	34.5686	−	15.0576i	2.35209	−	1.02454i
$217$	9.08038	−	6.59728i	0.616416	−	0.447853i
$218$	11.4684	−	7.12338i	0.776736	−	0.482456i
$219$	−16.8446	−	23.1846i	−1.13825	−	1.56667i
$220$		0			0
$221$	13.2861	−	18.2867i	0.893717	−	1.23010i
$222$	−1.32037	+	18.1789i	−0.0886176	+	1.22009i
$223$	−5.96185	+	18.3487i	−0.399235	+	1.22872i	0.526379	+	0.850250i	$0.323549\pi$
$223$	−5.96185	+	18.3487i	−0.399235	+	1.22872i	−0.925614	+	0.378469i	$0.876451\pi$
$224$	5.97360	−	15.7495i	0.399128	−	1.05231i
$225$		0			0
$226$	7.88588	+	12.6960i	0.524561	+	0.844523i
$227$	22.9122	+	7.44462i	1.52073	+	0.494117i	0.945984	−	0.324212i	$-0.105099\pi$
$227$	22.9122	+	7.44462i	1.52073	+	0.494117i	0.574751	+	0.818329i	$0.305099\pi$
$228$	7.92890	−	4.16128i	0.525105	−	0.275587i
$229$	15.5176	−	21.3582i	1.02544	−	1.41139i	0.117113	−	0.993119i	$-0.462636\pi$
$229$	15.5176	−	21.3582i	1.02544	−	1.41139i	0.908322	−	0.418272i	$-0.137364\pi$
$230$		0			0
$231$	2.12840	−	1.54637i	0.140038	−	0.101744i
$232$	−1.20367	−	12.4158i	−0.0790248	−	0.815135i
$233$	−19.5668	+	14.2161i	−1.28186	+	0.931328i	−0.999608	−	0.0280108i	$-0.991083\pi$
$233$	−19.5668	+	14.2161i	−1.28186	+	0.931328i	−0.282256	+	0.959339i	$0.591083\pi$
$234$	−34.2251	−	28.8756i	−2.23737	−	1.88766i
$235$		0			0
$236$	7.47905	−	7.66181i	0.486845	−	0.498741i
$237$	−16.8569	+	5.47713i	−1.09497	+	0.355778i
$238$	−13.9156	+	16.4936i	−0.902014	+	1.06912i
$239$	−4.76280	+	14.6584i	−0.308080	+	0.948173i	0.670430	+	0.741973i	$0.266110\pi$
$239$	−4.76280	+	14.6584i	−0.308080	+	0.948173i	−0.978510	+	0.206200i	$0.933890\pi$
$240$		0			0
$241$	4.82186	+	14.8402i	0.310604	+	0.955940i	0.977526	+	0.210813i	$0.0676111\pi$
$241$	4.82186	+	14.8402i	0.310604	+	0.955940i	−0.666923	+	0.745127i	$0.732389\pi$
$242$	14.3074	+	5.82541i	0.919715	+	0.374472i
$243$			26.9901i			1.73141i
$244$	−4.07160	+	0.695353i	−0.260657	+	0.0445154i
$245$		0			0
$246$	28.8165	+	2.09301i	1.83728	+	0.133445i
$247$	−5.00790	−	3.63845i	−0.318645	−	0.231509i
$248$	2.30075	−	10.4101i	0.146098	−	0.661044i
$249$	42.3693			2.68505
$250$		0			0
$251$		−	2.59224i		−	0.163621i	−0.996648	−	0.0818104i	$-0.973930\pi$
$251$		−	2.59224i		−	0.163621i	0.996648	−	0.0818104i	$-0.0260702\pi$
$252$	30.5919	+	29.8622i	1.92711	+	1.88114i
$253$	−0.0525763	+	0.0723650i	−0.00330544	+	0.00454955i
$254$	−0.139046	+	1.91439i	−0.00872455	+	0.120120i
$255$		0			0
$256$	−5.67290	−	14.9606i	−0.354556	−	0.935035i
$257$	1.98944			0.124098			0.0620490	−	0.998073i	$-0.480236\pi$
$257$	1.98944			0.124098			0.0620490	+	0.998073i	$0.480236\pi$
$258$	45.5815	+	18.5590i	2.83778	+	1.15543i
$259$	−11.4403	+	3.71719i	−0.710868	+	0.230975i
$260$		0			0
$261$	30.1092	+	9.78308i	1.86371	+	0.605558i
$262$	0.866376	+	0.730959i	0.0535249	+	0.0451588i
$263$	−4.81097	−	14.8066i	−0.296657	−	0.913017i	−0.982660	−	0.185418i	$-0.940636\pi$
$263$	−4.81097	−	14.8066i	−0.296657	−	0.913017i	0.686003	−	0.727599i	$-0.259364\pi$
$264$	0.539285	−	2.44008i	0.0331907	−	0.150177i
$265$		0			0
$266$	4.51685	+	3.81085i	0.276946	+	0.233658i
$267$	6.02026	+	8.28618i	0.368434	+	0.507106i
$268$	−2.77215	−	1.37059i	−0.169336	−	0.0837222i
$269$	−0.776787	−	1.06916i	−0.0473616	−	0.0651876i	0.784679	−	0.619902i	$-0.212828\pi$
$269$	−0.776787	−	1.06916i	−0.0473616	−	0.0651876i	−0.832041	+	0.554714i	$0.812828\pi$
$270$		0			0
$271$	11.7169	+	8.51285i	0.711753	+	0.517119i	0.883739	−	0.467981i	$-0.155018\pi$
$271$	11.7169	+	8.51285i	0.711753	+	0.517119i	−0.171986	+	0.985099i	$0.555018\pi$
$272$	0.494775	+	20.4920i	0.0300001	+	1.24251i
$273$	12.9488	−	39.8523i	0.783697	−	2.41197i
$274$	−5.40859	−	8.70763i	−0.326745	−	0.526047i
$275$		0			0
$276$	−1.84749	−	0.913423i	−0.111206	−	0.0549816i
$277$	−12.1748	−	3.95585i	−0.731516	−	0.237684i	−0.0805069	−	0.996754i	$-0.525654\pi$
$277$	−12.1748	−	3.95585i	−0.731516	−	0.237684i	−0.651009	+	0.759070i	$0.725654\pi$
$278$	0.618934	+	0.0449545i	0.0371212	+	0.00269619i
$279$	21.8906	+	15.9045i	1.31056	+	0.952176i
$280$		0			0
$281$	−2.54841	+	1.85153i	−0.152025	+	0.110453i	−0.661198	−	0.750212i	$-0.729952\pi$
$281$	−2.54841	+	1.85153i	−0.152025	+	0.110453i	0.509172	+	0.860665i	$0.329952\pi$
$282$	10.8992	−	6.76983i	0.649036	−	0.403138i
$283$	−7.40638	−	10.1940i	−0.440264	−	0.605971i	0.530007	−	0.847993i	$-0.322189\pi$
$283$	−7.40638	−	10.1940i	−0.440264	−	0.605971i	−0.970271	+	0.242022i	$0.922189\pi$
$284$	19.1111	+	2.79089i	1.13404	+	0.165609i
$285$		0			0
$286$	−1.67729	+	0.413404i	−0.0991804	+	0.0244451i
$287$	5.89236	+	18.1348i	0.347815	+	1.07046i
$288$	40.5602	+	1.96321i	2.39003	+	0.115684i
$289$	2.86164	−	8.80721i	0.168332	−	0.518071i
$290$		0			0
$291$	−50.0443	+	16.2604i	−2.93365	+	0.953200i
$292$	−3.02432	−	17.7087i	−0.176985	−	1.03632i
$293$		−	9.19701i		−	0.537295i	−0.963239	−	0.268647i	$-0.913423\pi$
$293$		−	9.19701i		−	0.537295i	0.963239	−	0.268647i	$-0.0865766\pi$
$294$	−3.17593	+	7.80018i	−0.185224	+	0.454916i
$295$		0			0
$296$	−5.79278	+	9.84885i	−0.336698	+	0.572453i
$297$	2.98671	+	2.16997i	0.173307	+	0.125915i
$298$	−0.560268	−	2.27316i	−0.0324555	−	0.131681i
$299$			1.42470i			0.0823925i
$300$		0			0
$301$			32.4802i			1.87213i
$302$	19.3101	−	4.75937i	1.11117	−	0.273871i
$303$	−50.2984	−	36.5440i	−2.88957	−	2.09940i
$304$	5.61183	−	0.135496i	0.321861	−	0.00777126i
$305$		0			0
$306$	−48.1827	−	19.6181i	−2.75442	−	1.12149i
$307$		−	24.3699i		−	1.39087i	−0.718591	−	0.695433i	$-0.755213\pi$
$307$		−	24.3699i		−	1.39087i	0.718591	−	0.695433i	$-0.244787\pi$
$308$	1.62570	−	0.277639i	0.0926328	−	0.0158200i
$309$	−21.4459	+	6.96821i	−1.22002	+	0.396407i
$310$		0			0
$311$	7.74867	−	23.8479i	0.439387	−	1.35229i	−0.449138	−	0.893463i	$-0.648269\pi$
$311$	7.74867	−	23.8479i	0.439387	−	1.35229i	0.888524	−	0.458830i	$-0.151731\pi$
$312$	−15.8951	−	36.4912i	−0.899882	−	2.06590i
$313$	3.37148	+	10.3764i	0.190567	+	0.586506i	1.00000		0.000706882i	$-0.000225008\pi$
$313$	3.37148	+	10.3764i	0.190567	+	0.586506i	−0.809432	+	0.587213i	$0.800225\pi$
$314$	3.23720	+	13.1342i	0.182686	+	0.741205i
$315$		0			0
$316$	−10.9945	−	1.60558i	−0.618491	−	0.0903210i
$317$	0.505314	+	0.695505i	0.0283813	+	0.0390635i	0.822972	−	0.568082i	$-0.192314\pi$
$317$	0.505314	+	0.695505i	0.0283813	+	0.0390635i	−0.794591	+	0.607146i	$0.792314\pi$
$318$	−1.11320	−	1.79221i	−0.0624253	−	0.100502i
$319$	0.988078	−	0.717881i	0.0553218	−	0.0401936i
$320$		0			0
$321$	29.0517	+	21.1073i	1.62151	+	1.17809i
$322$	0.0985320	−	1.35659i	0.00549098	−	0.0755998i
$323$	−6.83957	−	2.22231i	−0.380564	−	0.123653i
$324$	−18.6104	+	37.6413i	−1.03391	+	2.09118i
$325$		0			0
$326$	−6.59811	+	4.09830i	−0.365435	+	0.226984i
$327$	−9.41157	+	28.9658i	−0.520461	+	1.60181i
$328$	15.6120	+	9.18249i	0.862031	+	0.507018i
$329$	6.85053	+	4.97720i	0.377682	+	0.274402i
$330$		0			0
$331$	−4.98309	−	6.85864i	−0.273895	−	0.376985i	0.649805	−	0.760101i	$-0.274851\pi$
$331$	−4.98309	−	6.85864i	−0.273895	−	0.376985i	−0.923700	+	0.383117i	$0.874851\pi$
$332$	23.8096	+	11.7718i	1.30672	+	0.646061i
$333$	−17.0453	−	23.4609i	−0.934079	−	1.28565i
$334$	10.9753	−	13.0086i	0.600543	−	0.711799i
$335$		0			0
$336$	12.6115	+	35.8460i	0.688013	+	1.95556i
$337$	−5.19430	−	15.9864i	−0.282951	−	0.870835i	−0.987005	−	0.160688i	$-0.948629\pi$
$337$	−5.19430	−	15.9864i	−0.282951	−	0.870835i	0.704054	−	0.710147i	$-0.251371\pi$
$338$	−5.88751	+	6.97823i	−0.320238	+	0.379566i
$339$	−32.0664	−	10.4190i	−1.74161	−	0.565883i
$340$		0			0
$341$	0.992767	−	0.322570i	0.0537613	−	0.0174681i
$342$	−5.37251	+	13.1951i	−0.290512	+	0.713508i
$343$	15.2856			0.825345
$344$	20.4583	+	23.0935i	1.10304	+	1.24512i
$345$		0			0
$346$	−24.5247	−	1.78128i	−1.31845	−	0.0957622i
$347$	10.3651	−	14.2663i	0.556427	−	0.765856i	−0.434440	−	0.900701i	$-0.643054\pi$
$347$	10.3651	−	14.2663i	0.556427	−	0.765856i	0.990867	+	0.134845i	$0.0430536\pi$
$348$	20.1371	+	19.6567i	1.07946	+	1.05371i
$349$		−	35.1956i		−	1.88398i	−0.335642	−	0.941990i	$-0.608953\pi$
$349$		−	35.1956i		−	1.88398i	0.335642	−	0.941990i	$-0.391047\pi$
$350$		0			0
$351$	58.8015			3.13859
$352$	0.981000	−	1.22138i	0.0522875	−	0.0650997i
$353$	−22.9889	−	16.7024i	−1.22358	−	0.888980i	−0.227184	−	0.973852i	$-0.572952\pi$
$353$	−22.9889	−	16.7024i	−1.22358	−	0.888980i	−0.996392	+	0.0848720i	$0.972952\pi$
$354$	−1.74977	+	24.0908i	−0.0929991	+	1.28041i
$355$		0			0
$356$	1.08089	+	6.32910i	0.0572873	+	0.335442i
$357$		−	48.6824i		−	2.57655i
$358$	11.3480	−	27.8710i	0.599758	−	1.47303i
$359$	−3.94315	−	12.1358i	−0.208112	−	0.640501i	−0.999571	−	0.0292801i	$-0.990679\pi$
$359$	−3.94315	−	12.1358i	−0.208112	−	0.640501i	0.791460	−	0.611221i	$-0.209321\pi$
$360$		0			0
$361$	5.26273	−	16.1970i	0.276986	−	0.852475i
$362$	8.88091	+	7.49279i	0.466770	+	0.393812i
$363$	−33.1438	+	10.7691i	−1.73960	+	0.565230i
$364$	18.3491	−	18.7975i	0.961753	−	0.985255i
$365$		0			0
$366$	6.00885	−	7.12204i	0.314087	−	0.372275i
$367$	17.2512	−	12.5338i	0.900507	−	0.654257i	−0.0380891	−	0.999274i	$-0.512127\pi$
$367$	17.2512	−	12.5338i	0.900507	−	0.654257i	0.938596	+	0.345018i	$0.112127\pi$
$368$	−0.784418	−	1.02660i	−0.0408906	−	0.0535153i
$369$	−37.1894	+	27.0197i	−1.93600	+	1.40659i
$370$		0			0
$371$	0.818430	−	1.12647i	0.0424908	−	0.0584835i
$372$	11.1769	+	21.2965i	0.579497	+	1.10417i
$373$	11.1964	+	3.63793i	0.579727	+	0.188365i	0.584178	−	0.811625i	$-0.301417\pi$
$373$	11.1964	+	3.63793i	0.579727	+	0.188365i	−0.00445132	+	0.999990i	$0.501417\pi$
$374$	−1.70486	+	1.05894i	−0.0881562	+	0.0547567i
$375$		0			0
$376$	8.00574	−	0.776131i	0.412864	−	0.0400259i
$377$	6.01130	−	18.5009i	0.309598	−	0.952844i
$378$	−55.9904	−	4.06670i	−2.87983	−	0.209168i
$379$	−10.7274	+	14.7650i	−0.551030	+	0.758428i	−0.990152	−	0.140000i	$-0.955290\pi$
$379$	−10.7274	+	14.7650i	−0.551030	+	0.758428i	0.439121	+	0.898428i	$0.355290\pi$
$380$		0			0
$381$	−2.54518	−	3.50315i	−0.130394	−	0.179472i
$382$	2.64452	+	4.25758i	0.135305	+	0.217836i
$383$	29.1018	−	21.1437i	1.48703	−	1.08039i	0.511830	−	0.859087i	$-0.328968\pi$
$383$	29.1018	−	21.1437i	1.48703	−	1.08039i	0.975204	−	0.221307i	$-0.0710324\pi$
$384$	31.5451	+	17.5430i	1.60978	+	0.895237i
$385$		0			0
$386$	−18.3945	+	4.53371i	−0.936255	+	0.230760i
$387$	−74.4697	+	24.1967i	−3.78551	+	1.22999i
$388$	−32.6403	−	4.76661i	−1.65706	−	0.241988i
$389$	−2.67533	−	0.869269i	−0.135645	−	0.0440737i	0.240408	−	0.970672i	$-0.422719\pi$
$389$	−2.67533	−	0.869269i	−0.135645	−	0.0440737i	−0.376053	+	0.926598i	$0.622719\pi$
$390$		0			0
$391$	0.511482	+	1.57418i	0.0258668	+	0.0796097i
$392$	−3.95190	+	3.50094i	−0.199601	+	0.176824i
$393$	−2.55719			−0.128993
$394$	−2.73816	+	6.72501i	−0.137947	+	0.338801i
$395$		0			0
$396$	1.84765	+	3.52052i	0.0928481	+	0.176913i
$397$	4.62715	−	6.36873i	0.232230	−	0.319637i	−0.676959	−	0.736021i	$-0.736703\pi$
$397$	4.62715	−	6.36873i	0.232230	−	0.319637i	0.909189	+	0.416383i	$0.136703\pi$
$398$	17.2398	−	4.24910i	0.864151	−	0.212988i
$399$	−13.3319			−0.667430
$400$		0			0
$401$	−6.74733			−0.336946			−0.168473	−	0.985706i	$-0.553884\pi$
$401$	−6.74733			−0.336946			−0.168473	+	0.985706i	$0.553884\pi$
$402$	6.77370	−	1.66952i	0.337841	−	0.0832681i
$403$	9.77264	−	13.4509i	0.486810	−	0.670037i
$404$	−18.1121	−	34.5108i	−0.901110	−	1.71698i
$405$		0			0
$406$	−7.00344	+	17.2007i	−0.347575	+	0.853655i
$407$	−1.11874			−0.0554537
$408$	−30.6635	−	34.6133i	−1.51807	−	1.71362i
$409$	8.52623	+	26.2411i	0.421595	+	1.29754i	0.906217	+	0.422813i	$0.138957\pi$
$409$	8.52623	+	26.2411i	0.421595	+	1.29754i	−0.484622	+	0.874724i	$0.661043\pi$
$410$		0			0
$411$	21.9930	+	7.14596i	1.08483	+	0.352484i
$412$	−13.9876	−	2.04268i	−0.689122	−	0.100636i
$413$	−15.1608	+	4.92605i	−0.746015	+	0.242395i
$414$	3.18375	−	0.784703i	0.156473	−	0.0385661i
$415$		0			0
$416$	1.20631	−	24.9226i	0.0591444	−	1.22193i
$417$	−1.13259	+	0.822872i	−0.0554630	+	0.0402962i
$418$	0.289997	+	0.466884i	0.0141842	+	0.0228360i
$419$	14.4072	+	19.8299i	0.703839	+	0.968752i	0.999908	+	0.0135851i	$0.00432441\pi$
$419$	14.4072	+	19.8299i	0.703839	+	0.968752i	−0.296068	+	0.955167i	$0.595676\pi$
$420$		0			0
$421$	15.9444	−	21.9456i	0.777084	−	1.06956i	−0.218514	−	0.975834i	$-0.570121\pi$
$421$	15.9444	−	21.9456i	0.777084	−	1.06956i	0.995598	−	0.0937303i	$-0.0298792\pi$
$422$	−10.7540	−	0.781083i	−0.523494	−	0.0380225i
$423$	−6.30817	+	19.4146i	−0.306714	+	0.943968i
$424$	−0.127624	−	1.31643i	−0.00619795	−	0.0639314i
$425$		0			0
$426$	−37.0121	+	22.9895i	−1.79324	+	1.11384i
$427$	5.84875	+	1.90037i	0.283041	+	0.0919655i
$428$	10.4613	+	19.9330i	0.505666	+	0.963496i
$429$	2.29066	−	3.15282i	0.110594	−	0.152220i
$430$		0			0
$431$	−6.94699	+	5.04728i	−0.334625	+	0.243119i	−0.742390	−	0.669968i	$-0.766308\pi$
$431$	−6.94699	+	5.04728i	−0.334625	+	0.243119i	0.407766	+	0.913087i	$0.366308\pi$
$432$	−42.3708	+	32.3752i	−2.03857	+	1.55765i
$433$	−23.6800	+	17.2045i	−1.13799	+	0.826797i	−0.986838	−	0.161714i	$-0.948298\pi$
$433$	−23.6800	+	17.2045i	−1.13799	+	0.826797i	−0.151150	+	0.988511i	$0.548298\pi$
$434$	−10.2357	+	12.1320i	−0.491330	+	0.582354i
$435$		0			0
$436$	−13.3367	+	13.6626i	−0.638710	+	0.654318i
$437$	0.431097	−	0.140072i	0.0206222	−	0.00670055i
$438$	30.9761	+	26.1344i	1.48009	+	1.24875i
$439$	−3.98757	+	12.2725i	−0.190317	+	0.585734i	−0.999999	−	0.00113362i	$-0.999639\pi$
$439$	−3.98757	+	12.2725i	−0.190317	+	0.585734i	0.809683	+	0.586868i	$0.199639\pi$
$440$		0			0
$441$	−4.14068	−	12.7437i	−0.197175	−	0.606843i
$442$	−12.0545	+	29.6063i	−0.573375	+	1.40823i
$443$			1.10768i			0.0526274i	0.999654	+	0.0263137i	$0.00837688\pi$
$443$			1.10768i			0.0526274i	−0.999654	+	0.0263137i	$0.991623\pi$
$444$	−4.33934	−	25.4087i	−0.205936	−	1.20584i
$445$		0			0
$446$	1.97651	−	27.2127i	0.0935906	−	1.28856i
$447$	4.27288	+	3.10443i	0.202100	+	0.146834i
$448$	−2.87229	+	23.6477i	−0.135703	+	1.11725i
$449$	6.01273			0.283758			0.141879	−	0.989884i	$-0.454686\pi$
$449$	6.01273			0.283758			0.141879	+	0.989884i	$0.454686\pi$
$450$		0			0
$451$			1.77338i			0.0835051i
$452$	−15.1250	−	14.7642i	−0.711422	−	0.694452i
$453$	−26.3715	+	36.2973i	−1.23904	+	1.70539i
$454$	−33.9807	−	2.46809i	−1.59479	−	0.115833i
$455$		0			0
$456$	−9.47903	+	8.39736i	−0.443896	+	0.393242i
$457$	36.8695			1.72468			0.862341	−	0.506328i	$-0.168997\pi$
$457$	36.8695			1.72468			0.862341	+	0.506328i	$0.168997\pi$
$458$	−14.0793	+	34.5791i	−0.657880	+	1.61578i
$459$	64.9710	−	21.1103i	3.03258	−	0.985347i
$460$		0			0
$461$	−32.4405	−	10.5406i	−1.51091	−	0.490923i	−0.567730	−	0.823215i	$-0.692178\pi$
$461$	−32.4405	−	10.5406i	−1.51091	−	0.490923i	−0.943177	+	0.332291i	$0.892178\pi$
$462$	−2.39920	+	2.84368i	−0.111621	+	0.132300i
$463$	12.9887	+	39.9752i	0.603637	+	1.85780i	0.505902	+	0.862591i	$0.331160\pi$
$463$	12.9887	+	39.9752i	0.603637	+	1.85780i	0.0977353	+	0.995212i	$0.468840\pi$
$464$	5.85471	+	16.6410i	0.271798	+	0.772538i
$465$		0			0
$466$	22.0564	−	26.1425i	1.02174	−	1.21103i
$467$	6.75711	+	9.30036i	0.312682	+	0.430370i	0.936215	−	0.351427i	$-0.114304\pi$
$467$	6.75711	+	9.30036i	0.312682	+	0.430370i	−0.623533	+	0.781797i	$0.714304\pi$
$468$	56.7678	+	28.0668i	2.62409	+	1.29739i
$469$	2.70628	+	3.72488i	0.124964	+	0.171999i
$470$		0			0
$471$	−24.6884	−	17.9372i	−1.13758	−	0.826503i
$472$	−7.67662	+	13.0518i	−0.353345	+	0.600756i
$473$	−0.933461	+	2.87290i	−0.0429206	+	0.132096i
$474$	21.2929	−	13.2257i	0.978015	−	0.607477i
$475$		0			0
$476$	13.5258	−	27.3572i	0.619954	−	1.25392i
$477$	3.19245	+	1.03729i	0.146172	+	0.0474942i
$478$	1.57900	−	21.7396i	0.0722216	−	0.994348i
$479$	−9.62460	−	6.99268i	−0.439759	−	0.319504i	0.345780	−	0.938316i	$-0.387614\pi$
$479$	−9.62460	−	6.99268i	−0.439759	−	0.319504i	−0.785539	+	0.618812i	$0.787614\pi$
$480$		0			0
$481$	−14.4158	+	10.4737i	−0.657302	+	0.477558i
$482$	−11.6434	−	18.7455i	−0.530344	−	0.853833i
$483$	1.80359	+	2.48242i	0.0820660	+	0.112954i
$484$	−21.6173	−	3.15688i	−0.982606	−	0.143494i
$485$		0			0
$486$	−9.13437	−	37.0606i	−0.414343	−	1.68110i
$487$	−6.75894	−	20.8019i	−0.306277	−	0.942622i	−0.979198	−	0.202908i	$-0.934961\pi$
$487$	−6.75894	−	20.8019i	−0.306277	−	0.942622i	0.672921	−	0.739714i	$-0.265039\pi$
$488$	5.35546	−	2.33277i	0.242430	−	0.105600i
$489$	5.41477	−	16.6649i	0.244864	−	0.753615i
$490$		0			0
$491$	3.07965	−	1.00064i	0.138983	−	0.0451582i	−0.238700	−	0.971093i	$-0.576721\pi$
$491$	3.07965	−	1.00064i	0.138983	−	0.0451582i	0.377682	+	0.925935i	$0.376721\pi$
$492$	−40.2770	+	6.87856i	−1.81583	+	0.310110i
$493$		−	22.6001i		−	1.01786i
$494$	8.10782	+	3.30119i	0.364788	+	0.148527i
$495$		0			0
$496$	0.363935	+	15.0730i	0.0163412	+	0.676799i
$497$	−23.2635	−	16.9019i	−1.04351	−	0.758155i
$498$	−58.1782	+	14.3392i	−2.60703	+	0.642556i
$499$		−	4.70824i		−	0.210770i	−0.994432	−	0.105385i	$-0.966393\pi$
$499$		−	4.70824i		−	0.210770i	0.994432	−	0.105385i	$-0.0336074\pi$
$500$		0			0
$501$			38.3961i			1.71541i
$502$	0.877304	+	3.55946i	0.0391560	+	0.158867i
$503$	10.4440	+	7.58802i	0.465676	+	0.338333i	0.795754	−	0.605621i	$-0.207075\pi$
$503$	10.4440	+	7.58802i	0.465676	+	0.338333i	−0.330078	+	0.943954i	$0.607075\pi$
$504$	−52.1128	−	30.6511i	−2.32129	−	1.36531i
$505$		0			0
$506$	0.0477028	−	0.117160i	0.00212065	−	0.00520838i
$507$		−	20.5969i		−	0.914740i
$508$	−0.456969	−	2.67575i	−0.0202747	−	0.118717i
$509$	−8.87419	+	2.88340i	−0.393342	+	0.127804i	−0.499008	−	0.866597i	$-0.666302\pi$
$509$	−8.87419	+	2.88340i	−0.393342	+	0.127804i	0.105667	+	0.994402i	$0.466302\pi$
$510$		0			0
$511$	−8.26534	+	25.4381i	−0.365637	+	1.12532i
$512$	12.8527	+	18.6228i	0.568017	+	0.823017i
$513$	−5.78117	−	17.7926i	−0.255245	−	0.785563i
$514$	−2.73175	+	0.673296i	−0.120492	+	0.0296978i
$515$		0			0
$516$	−68.8699	−	10.0574i	−3.03183	−	0.442752i
$517$	0.462892	+	0.637117i	0.0203580	+	0.0280204i
$518$	14.4510	−	8.97596i	0.634938	−	0.394381i
$519$	44.8777	−	32.6055i	1.96991	−	1.43122i
$520$		0			0
$521$	−14.6710	−	10.6591i	−0.642748	−	0.466984i	0.218045	−	0.975939i	$-0.430032\pi$
$521$	−14.6710	−	10.6591i	−0.642748	−	0.466984i	−0.860793	+	0.508955i	$0.830032\pi$
$522$	−44.6546	−	3.24336i	−1.95448	−	0.141958i
$523$	22.2349	+	7.22455i	0.972264	+	0.315908i	0.751729	−	0.659472i	$-0.229220\pi$
$523$	22.2349	+	7.22455i	0.972264	+	0.315908i	0.220534	+	0.975379i	$0.429220\pi$
$524$	−1.43702	−	0.710483i	−0.0627766	−	0.0310376i
$525$		0			0
$526$	11.6171	+	18.7031i	0.506531	+	0.815495i
$527$	5.96899	−	18.3707i	0.260013	−	0.800238i
$528$	0.0853046	+	3.53304i	0.00371240	+	0.153756i
$529$	18.5230	+	13.4577i	0.805347	+	0.585119i
$530$		0			0
$531$	−22.5886	−	31.0905i	−0.980262	−	1.34921i
$532$	−7.49191	−	3.70411i	−0.324816	−	0.160593i
$533$	16.6025	+	22.8513i	0.719132	+	0.989801i
$534$	−11.0709	−	9.34047i	−0.479084	−	0.404202i
$535$		0			0
$536$	4.27036	+	0.943796i	0.184451	+	0.0407658i
$537$	20.9783	+	64.5645i	0.905279	+	2.78616i
$538$	1.42846	+	1.20519i	0.0615854	+	0.0519594i
$539$	−0.491627	−	0.159739i	−0.0211759	−	0.00688046i
$540$		0			0
$541$	−1.23623	+	0.401675i	−0.0531496	+	0.0172694i	−0.335471	−	0.942050i	$-0.608896\pi$
$541$	−1.23623	+	0.401675i	−0.0531496	+	0.0172694i	0.282322	+	0.959320i	$0.408896\pi$
$542$	−18.9698	−	7.72376i	−0.814823	−	0.331764i
$543$	−26.2128			−1.12490
$544$	−7.61459	−	27.9706i	−0.326473	−	1.19923i
$545$		0			0
$546$	−4.29287	+	59.1044i	−0.183718	+	2.52943i
$547$	1.29680	−	1.78489i	0.0554470	−	0.0763163i	−0.780393	−	0.625289i	$-0.784981\pi$
$547$	1.29680	−	1.78489i	0.0554470	−	0.0763163i	0.835840	+	0.548973i	$0.184981\pi$
$548$	10.3736	+	10.1262i	0.443139	+	0.432569i
$549$			14.8256i			0.632739i
$550$		0			0
$551$	−6.18915			−0.263667
$552$	2.84596	+	0.628987i	0.121132	+	0.0267715i
$553$	13.3834	+	9.72359i	0.569119	+	0.413489i
$554$	18.0563	+	1.31147i	0.767140	+	0.0557190i
$555$		0			0
$556$	−0.865085	+	0.147741i	−0.0366878	+	0.00626560i
$557$			22.2912i			0.944509i	0.881462	+	0.472255i	$0.156560\pi$
$557$			22.2912i			0.944509i	−0.881462	+	0.472255i	$0.843440\pi$
$558$	−35.4411	−	14.4302i	−1.50034	−	0.610880i
$559$	14.8679	+	45.7586i	0.628844	+	1.93538i
$560$		0			0
$561$	1.39910	−	4.30599i	0.0590701	−	0.181799i
$562$	2.87265	−	3.40484i	0.121176	−	0.143624i
$563$	−20.1578	+	6.54968i	−0.849551	+	0.276036i	−0.701258	−	0.712907i	$-0.747378\pi$
$563$	−20.1578	+	6.54968i	−0.849551	+	0.276036i	−0.148293	+	0.988943i	$0.547378\pi$
$564$	−12.6747	+	12.9845i	−0.533702	+	0.546744i
$565$		0			0
$566$	13.6199	+	11.4910i	0.572486	+	0.483004i
$567$	50.5777	−	36.7469i	2.12406	−	1.54322i
$568$	−27.1864	+	2.63564i	−1.14072	+	0.110589i
$569$	−1.34832	+	0.979610i	−0.0565244	+	0.0410674i	−0.615689	−	0.787989i	$-0.711122\pi$
$569$	−1.34832	+	0.979610i	−0.0565244	+	0.0410674i	0.559164	+	0.829057i	$0.311122\pi$
$570$		0			0
$571$	−2.18726	+	3.01051i	−0.0915340	+	0.125986i	−0.852328	−	0.523008i	$-0.824810\pi$
$571$	−2.18726	+	3.01051i	−0.0915340	+	0.125986i	0.760794	+	0.648994i	$0.224810\pi$
$572$	2.16322	−	1.13531i	0.0904486	−	0.0474696i
$573$	−10.7534	−	3.49400i	−0.449231	−	0.145964i
$574$	−14.2284	−	22.9071i	−0.593881	−	0.956124i
$575$		0			0
$576$	−56.3585	+	11.0312i	−2.34827	+	0.459635i
$577$	−7.53910	+	23.2030i	−0.313857	+	0.965952i	0.662366	+	0.749181i	$0.269553\pi$
$577$	−7.53910	+	23.2030i	−0.313857	+	0.965952i	−0.976222	+	0.216771i	$0.930447\pi$
$578$	−0.948710	+	13.0618i	−0.0394611	+	0.543301i
$579$	25.1211	−	34.5763i	1.04400	−	1.43694i
$580$		0			0
$581$	−23.2438	−	31.9924i	−0.964315	−	1.32727i
$582$	63.2138	−	39.2642i	2.62030	−	1.62755i
$583$	0.104765	−	0.0761160i	0.00433891	−	0.00315240i
$584$	10.1460	+	23.2927i	0.419844	+	0.963857i
$585$		0			0
$586$	3.11258	+	12.6286i	0.128580	+	0.521683i
$587$	13.0862	−	4.25195i	0.540123	−	0.175497i	−0.0262350	−	0.999656i	$-0.508352\pi$
$587$	13.0862	−	4.25195i	0.540123	−	0.175497i	0.566358	+	0.824159i	$0.308352\pi$
$588$	1.72108	−	11.7854i	0.0709762	−	0.486023i
$589$	−5.03089	−	1.63464i	−0.207294	−	0.0673540i
$590$		0			0
$591$	−5.06187	−	15.5788i	−0.208217	−	0.640827i
$592$	4.62099	−	15.4841i	0.189922	−	0.636394i
$593$	−18.8934			−0.775861			−0.387930	−	0.921689i	$-0.626810\pi$
$593$	−18.8934			−0.775861			−0.387930	+	0.921689i	$0.626810\pi$
$594$	−4.83551	−	1.96883i	−0.198403	−	0.0807821i
$595$		0			0
$596$	1.53863	+	2.93171i	0.0630248	+	0.120088i
$597$	−23.5441	+	32.4057i	−0.963598	+	1.32628i
$598$	−0.482168	−	1.95629i	−0.0197173	−	0.0799985i
$599$	−33.9391			−1.38671			−0.693356	−	0.720595i	$-0.743869\pi$
$599$	−33.9391			−1.38671			−0.693356	+	0.720595i	$0.743869\pi$
$600$		0			0
$601$	13.3568			0.544836			0.272418	−	0.962179i	$-0.412177\pi$
$601$	13.3568			0.544836			0.272418	+	0.962179i	$0.412177\pi$
$602$	−10.9924	−	44.5993i	−0.448018	−	1.81773i
$603$	−6.52420	+	8.97979i	−0.265686	+	0.365685i
$604$	−24.9043	+	13.0704i	−1.01334	+	0.531826i
$605$		0			0
$606$	81.4336	+	33.1565i	3.30801	+	1.34689i
$607$	−22.7175			−0.922076			−0.461038	−	0.887380i	$-0.652523\pi$
$607$	−22.7175			−0.922076			−0.461038	+	0.887380i	$0.652523\pi$
$608$	−7.65987	+	2.08529i	−0.310649	+	0.0845697i
$609$	−12.9468	−	39.8462i	−0.524632	−	1.61465i
$610$		0			0
$611$	11.9294	+	3.87611i	0.482614	+	0.156811i
$612$	72.8002	+	10.6313i	2.94277	+	0.429747i
$613$	−28.4959	+	9.25887i	−1.15094	+	0.373962i	−0.821496	−	0.570214i	$-0.806860\pi$
$613$	−28.4959	+	9.25887i	−1.15094	+	0.373962i	−0.329441	+	0.944176i	$0.606860\pi$
$614$	8.24763	+	33.4629i	0.332847	+	1.35045i
$615$		0			0
$616$	−2.13832	+	0.931425i	−0.0861553	+	0.0375282i
$617$	19.6251	−	14.2585i	0.790077	−	0.574025i	−0.117909	−	0.993024i	$-0.537619\pi$
$617$	19.6251	−	14.2585i	0.790077	−	0.574025i	0.907986	+	0.419000i	$0.137619\pi$
$618$	27.0896	−	16.8262i	1.08970	−	0.676851i
$619$	20.9345	+	28.8138i	0.841428	+	1.15813i	0.985687	+	0.168586i	$0.0539201\pi$
$619$	20.9345	+	28.8138i	0.841428	+	1.15813i	−0.144259	+	0.989540i	$0.546080\pi$
$620$		0			0
$621$	−2.53092	+	3.48351i	−0.101562	+	0.139788i
$622$	−2.56889	+	35.3685i	−0.103003	+	1.41815i
$623$	2.95404	−	9.09160i	0.118351	−	0.364247i
$624$	34.1758	+	44.7273i	1.36813	+	1.79053i
$625$		0			0
$626$	−8.14117	−	13.1070i	−0.325387	−	0.523860i
$627$	−1.17922	−	0.383150i	−0.0470933	−	0.0153016i
$628$	−8.89013	−	16.9393i	−0.354755	−	0.675950i
$629$	−12.1681	+	16.7480i	−0.485175	+	0.667786i
$630$		0			0
$631$	−5.35186	+	3.88835i	−0.213054	+	0.154793i	−0.689194	−	0.724576i	$-0.742035\pi$
$631$	−5.35186	+	3.88835i	−0.213054	+	0.154793i	0.476140	+	0.879369i	$0.342035\pi$
$632$	15.6402	−	1.51627i	0.622134	−	0.0603140i
$633$	19.6786	−	14.2974i	0.782156	−	0.568270i
$634$	−0.929240	−	0.783997i	−0.0369049	−	0.0311365i
$635$		0			0
$636$	2.13511	+	2.08418i	0.0846625	+	0.0826430i
$637$	−7.83048	+	2.54428i	−0.310255	+	0.100808i
$638$	−1.11380	+	1.32014i	−0.0440956	+	0.0522647i
$639$	21.4217	−	65.9293i	0.847430	−	2.60812i
$640$		0			0
$641$	6.78939	+	20.8956i	0.268165	+	0.825327i	0.990947	+	0.134251i	$0.0428629\pi$
$641$	6.78939	+	20.8956i	0.268165	+	0.825327i	−0.722782	+	0.691076i	$0.757137\pi$
$642$	−47.0349	−	19.1508i	−1.85632	−	0.755820i
$643$		−	32.6614i		−	1.28804i	−0.765009	−	0.644019i	$-0.777266\pi$
$643$		−	32.6614i		−	1.28804i	0.765009	−	0.644019i	$-0.222734\pi$
$644$	0.323821	+	1.89611i	0.0127603	+	0.0747172i
$645$		0			0
$646$	10.1437	+	0.736756i	0.399097	+	0.0289873i
$647$	28.2564	+	20.5295i	1.11088	+	0.807098i	0.982801	−	0.184666i	$-0.0591205\pi$
$647$	28.2564	+	20.5295i	1.11088	+	0.807098i	0.128074	+	0.991765i	$0.459120\pi$
$648$	12.8152	−	57.9845i	0.503429	−	2.27785i
$649$	−1.48256			−0.0581954
$650$		0			0
$651$		−	35.8087i		−	1.40345i
$652$	7.67299	−	7.86049i	0.300498	−	0.307841i
$653$	−22.9581	+	31.5991i	−0.898420	+	1.23657i	0.0725499	+	0.997365i	$0.476886\pi$
$653$	−22.9581	+	31.5991i	−0.898420	+	1.23657i	−0.970969	+	0.239204i	$0.923114\pi$
$654$	3.12019	−	42.9588i	0.122009	−	1.67982i
$655$		0			0
$656$	−24.5449	−	7.32502i	−0.958317	−	0.285994i
$657$	−64.4812			−2.51565
$658$	−11.0911	−	4.51585i	−0.432375	−	0.176046i
$659$	40.4722	−	13.1502i	1.57657	−	0.512260i	0.615402	−	0.788213i	$-0.288994\pi$
$659$	40.4722	−	13.1502i	1.57657	−	0.512260i	0.961171	+	0.275953i	$0.0889936\pi$
$660$		0			0
$661$	−15.1858	−	4.93417i	−0.590660	−	0.191917i	−0.00158966	−	0.999999i	$-0.500506\pi$
$661$	−15.1858	−	4.93417i	−0.590660	−	0.191917i	−0.589071	+	0.808082i	$0.700506\pi$
$662$	9.16359	+	7.73129i	0.356153	+	0.300485i
$663$	−22.2844	−	68.5844i	−0.865455	−	2.66360i
$664$	−36.6774	−	8.10611i	−1.42336	−	0.314578i
$665$		0			0
$666$	31.3453	+	26.4459i	1.21461	+	1.02476i
$667$	0.837290	+	1.15243i	0.0324200	+	0.0446223i
$668$	−10.6679	+	21.5768i	−0.412753	+	0.834832i
$669$	36.1792	+	49.7964i	1.39877	+	1.92524i
$670$		0			0
$671$	0.462710	+	0.336178i	0.0178627	+	0.0129780i
$672$	−29.4486	−	44.9527i	−1.13600	−	1.73409i
$673$	2.74537	−	8.44939i	0.105826	−	0.325700i	−0.884097	−	0.467303i	$-0.845226\pi$
$673$	2.74537	−	8.44939i	0.105826	−	0.325700i	0.989924	+	0.141603i	$0.0452257\pi$
$674$	12.5427	+	20.1933i	0.483129	+	0.777818i
$675$		0			0
$676$	5.72259	−	11.5745i	0.220100	−	0.445173i
$677$	−22.4216	−	7.28520i	−0.861730	−	0.279993i	−0.155379	−	0.987855i	$-0.549660\pi$
$677$	−22.4216	−	7.28520i	−0.861730	−	0.279993i	−0.706351	+	0.707862i	$0.749660\pi$
$678$	47.5572	+	3.45418i	1.82642	+	0.132657i
$679$	39.7323	+	28.8672i	1.52478	+	1.10782i
$680$		0			0
$681$	62.1813	−	45.1773i	2.38279	−	1.73120i
$682$	−1.25402	+	0.778914i	−0.0480189	+	0.0298261i
$683$	15.1461	+	20.8468i	0.579548	+	0.797680i	0.993646	−	0.112553i	$-0.0359027\pi$
$683$	15.1461	+	20.8468i	0.579548	+	0.797680i	−0.414097	+	0.910233i	$0.635903\pi$
$684$	2.91144	−	19.9367i	0.111322	−	0.762298i
$685$		0			0
$686$	−20.9890	+	5.17317i	−0.801363	+	0.197513i
$687$	−26.0274	−	80.1042i	−0.993009	−	3.05617i
$688$	−35.9074	−	24.7864i	−1.36896	−	0.944974i
$689$	0.637371	−	1.96163i	0.0242819	−	0.0747320i
$690$		0			0
$691$	28.3342	−	9.20634i	1.07788	−	0.350225i	0.284330	−	0.958726i	$-0.408229\pi$
$691$	28.3342	−	9.20634i	1.07788	−	0.350225i	0.793553	+	0.608501i	$0.208229\pi$
$692$	34.2782	−	5.85409i	1.30306	−	0.222539i
$693$		−	5.91952i		−	0.224864i
$694$	−9.40431	+	23.0973i	−0.356983	+	0.876761i
$695$		0			0
$696$	−34.3031	−	20.1760i	−1.30026	−	0.764769i
$697$	26.5483	+	19.2885i	1.00559	+	0.730602i
$698$	11.9114	+	48.3279i	0.450854	+	1.82924i
$699$			77.1621i			2.91854i
$700$		0			0
$701$		−	5.84579i		−	0.220792i	−0.993888	−	0.110396i	$-0.964788\pi$
$701$		−	5.84579i		−	0.220792i	0.993888	−	0.110396i	$-0.0352120\pi$
$702$	−80.7415	+	19.9004i	−3.04739	+	0.751094i
$703$	4.58651	+	3.33230i	0.172984	+	0.125680i
$704$	−0.933675	+	2.00911i	−0.0351892	+	0.0757211i
$705$		0			0
$706$	37.2192	+	15.1542i	1.40076	+	0.570336i
$707$			58.0275i			2.18235i
$708$	−5.75052	−	33.6718i	−0.216118	−	1.26546i
$709$	18.5674	−	6.03290i	0.697312	−	0.226570i	0.0611529	−	0.998128i	$-0.480522\pi$
$709$	18.5674	−	6.03290i	0.697312	−	0.226570i	0.636159	+	0.771558i	$0.280522\pi$
$710$		0			0
$711$	−12.3238	+	37.9288i	−0.462179	+	1.42244i
$712$	−3.62619	−	8.32481i	−0.135897	−	0.311986i
$713$	0.376224	+	1.15790i	0.0140897	+	0.0433637i
$714$	16.4758	+	66.8468i	0.616591	+	2.50168i
$715$		0			0
$716$	−6.14963	+	42.1108i	−0.229822	+	1.57375i
$717$	28.9028	+	39.7814i	1.07940	+	1.48566i
$718$	9.52159	+	15.3294i	0.355342	+	0.572088i
$719$	−37.3747	+	27.1543i	−1.39384	+	1.01268i	−0.398408	+	0.917208i	$0.630437\pi$
$719$	−37.3747	+	27.1543i	−1.39384	+	1.01268i	−0.995432	+	0.0954761i	$0.969563\pi$
$720$		0			0
$721$	17.0268	+	12.3707i	0.634112	+	0.460709i
$722$	−1.74474	+	24.0216i	−0.0649324	+	0.893990i
$723$	47.3457	+	15.3836i	1.76081	+	0.572121i
$724$	−14.7304	−	7.28291i	−0.547450	−	0.270667i
$725$		0			0
$726$	41.8658	−	26.0043i	1.55379	−	0.965108i
$727$	2.22440	−	6.84600i	0.0824984	−	0.253904i	−0.901296	−	0.433204i	$-0.857383\pi$
$727$	2.22440	−	6.84600i	0.0824984	−	0.253904i	0.983795	+	0.179300i	$0.0573831\pi$
$728$	−18.8338	+	32.0212i	−0.698027	+	1.18678i
$729$	18.7064	+	13.5910i	0.692831	+	0.503371i
$730$		0			0
$731$	32.8556	+	45.2219i	1.21521	+	1.67259i
$732$	−5.84053	+	11.8130i	−0.215872	+	0.436622i
$733$	16.5038	+	22.7156i	0.609582	+	0.839018i	0.996543	−	0.0830781i	$-0.0264751\pi$
$733$	16.5038	+	22.7156i	0.609582	+	0.839018i	−0.386961	+	0.922096i	$0.626475\pi$
$734$	−19.4462	+	23.0488i	−0.717772	+	0.850746i
$735$		0			0
$736$	1.42454	+	1.14418i	0.0525092	+	0.0421749i
$737$	0.132322	+	0.407244i	0.00487413	+	0.0150010i
$738$	41.9211	−	49.6874i	1.54314	−	1.82902i
$739$	−37.8363	−	12.2937i	−1.39183	−	0.452233i	−0.485290	−	0.874353i	$-0.661286\pi$
$739$	−37.8363	−	12.2937i	−1.39183	−	0.452233i	−0.906540	+	0.422121i	$0.861286\pi$
$740$		0			0
$741$	−18.7822	+	6.10270i	−0.689980	+	0.224188i
$742$	−0.742566	+	1.82377i	−0.0272605	+	0.0669526i
$743$	20.8383			0.764482			0.382241	−	0.924063i	$-0.375152\pi$
$743$	20.8383			0.764482			0.382241	+	0.924063i	$0.375152\pi$
$744$	−22.5548	−	25.4601i	−0.826898	−	0.933411i
$745$		0			0
$746$	−16.6052	−	1.20607i	−0.607959	−	0.0441574i
$747$	56.0353	−	77.1260i	2.05022	−	2.82189i
$748$	1.98260	−	2.03104i	0.0724909	−	0.0742623i
$749$		−	33.5159i		−	1.22464i
$750$		0			0
$751$	−48.8753			−1.78348			−0.891742	−	0.452545i	$-0.850516\pi$
$751$	−48.8753			−1.78348			−0.891742	+	0.452545i	$0.850516\pi$
$752$	−10.7302	+	3.77514i	−0.391289	+	0.137665i
$753$	−6.69075	−	4.86111i	−0.243824	−	0.177149i
$754$	−1.99291	+	27.4384i	−0.0725774	+	0.999247i
$755$		0			0
$756$	78.2579	−	13.3650i	2.84621	−	0.486081i
$757$			18.6251i			0.676942i	0.940977	+	0.338471i	$0.109910\pi$
$757$			18.6251i			0.676942i	−0.940977	+	0.338471i	$0.890090\pi$
$758$	9.73305	−	23.9047i	0.353520	−	0.868257i
$759$	0.0881851	+	0.271406i	0.00320092	+	0.00985141i
$760$		0			0
$761$	12.5520	−	38.6311i	0.455009	−	1.40037i	−0.416115	−	0.909312i	$-0.636609\pi$
$761$	12.5520	−	38.6311i	0.455009	−	1.40037i	0.871124	−	0.491063i	$-0.163391\pi$
$762$	4.68043	+	3.94887i	0.169554	+	0.143052i
$763$	27.0348	−	8.78414i	0.978726	−	0.318007i
$764$	−5.07216	−	4.95117i	−0.183504	−	0.179127i
$765$		0			0
$766$	−32.8046	+	38.8820i	−1.18528	+	1.40486i
$767$	−19.1039	+	13.8798i	−0.689800	+	0.501169i
$768$	−49.2523	−	13.4127i	−1.77724	−	0.483990i
$769$	−14.8380	+	10.7804i	−0.535072	+	0.388753i	−0.822252	−	0.569124i	$-0.807282\pi$
$769$	−14.8380	+	10.7804i	−0.535072	+	0.388753i	0.287179	+	0.957877i	$0.407282\pi$
$770$		0			0
$771$	3.73071	−	5.13489i	0.134358	−	0.184928i
$772$	23.7235	−	12.4507i	0.853827	−	0.448109i
$773$	−30.8706	−	10.0305i	−1.11034	−	0.360770i	−0.304265	−	0.952588i	$-0.598411\pi$
$773$	−30.8706	−	10.0305i	−1.11034	−	0.360770i	−0.806072	+	0.591817i	$0.798411\pi$
$774$	94.0670	−	58.4281i	3.38117	−	2.10016i
$775$		0			0
$776$	46.4323	−	4.50147i	1.66682	−	0.161593i
$777$	−11.8592	+	36.4990i	−0.425448	+	1.30939i
$778$	3.96775	+	0.288186i	0.142251	+	0.0103320i
$779$	5.28223	−	7.27037i	0.189256	−	0.260488i
$780$		0			0
$781$	−1.57192	−	2.16357i	−0.0562478	−	0.0774185i
$782$	−1.23508	−	1.98844i	−0.0441665	−	0.0711064i
$783$	47.5641	−	34.5574i	1.69980	−	1.23498i
$784$	4.24160	−	6.14468i	0.151486	−	0.219453i
$785$		0			0
$786$	3.51133	−	0.865441i	0.125245	−	0.0308693i
$787$	−35.6398	+	11.5801i	−1.27042	+	0.412785i	−0.865197	−	0.501432i	$-0.832807\pi$
$787$	−35.6398	+	11.5801i	−1.27042	+	0.412785i	−0.405224	+	0.914217i	$0.632807\pi$
$788$	1.48385	−	10.1609i	0.0528600	−	0.361969i
$789$	−47.2388	−	15.3488i	−1.68174	−	0.546432i
$790$		0			0
$791$	9.72441	+	29.9287i	0.345760	+	1.06414i
$792$	−3.72852	−	4.20880i	−0.132487	−	0.149553i
$793$	9.10969			0.323495
$794$	−4.19824	+	10.3110i	−0.148990	+	0.365925i
$795$		0			0
$796$	−22.2342	+	11.6691i	−0.788072	+	0.413599i
$797$	32.0777	−	44.1511i	1.13625	−	1.56391i	0.360636	−	0.932707i	$-0.382560\pi$
$797$	32.0777	−	44.1511i	1.13625	−	1.56391i	0.775614	−	0.631207i	$-0.217440\pi$
$798$	18.3063	−	4.51198i	0.648037	−	0.159722i
$799$	14.5727			0.515544
$800$		0			0
$801$	23.0456			0.814277
$802$	9.26490	−	2.28353i	0.327155	−	0.0806342i
$803$	−1.46215	+	2.01248i	−0.0515981	+	0.0710187i
$804$	−8.73608	+	4.58491i	−0.308098	+	0.161697i
$805$		0			0
$806$	−8.86678	+	21.7771i	−0.312319	+	0.767066i
$807$	−4.21624			−0.148419
$808$	36.5497	+	41.2577i	1.28582	+	1.45144i
$809$	2.50898	+	7.72183i	0.0882109	+	0.271485i	0.985425	−	0.170111i	$-0.0544125\pi$
$809$	2.50898	+	7.72183i	0.0882109	+	0.271485i	−0.897214	+	0.441596i	$0.854413\pi$
$810$		0			0
$811$	1.71354	+	0.556763i	0.0601705	+	0.0195506i	0.338948	−	0.940805i	$-0.389929\pi$
$811$	1.71354	+	0.556763i	0.0601705	+	0.0195506i	−0.278777	+	0.960356i	$0.589929\pi$
$812$	3.79527	−	25.9888i	0.133188	−	0.912029i
$813$	43.9445	−	14.2784i	1.54120	−	0.500766i
$814$	1.53616	−	0.378619i	0.0538424	−	0.0132706i
$815$		0			0
$816$	53.8191	+	37.1507i	1.88405	+	1.30053i
$817$	12.3842	−	8.99767i	0.433269	−	0.314789i
$818$	−20.5884	−	33.1466i	−0.719858	−	1.15894i
$819$	−55.4188	−	76.2775i	−1.93649	−	2.66535i
$820$		0			0
$821$	−13.9783	+	19.2395i	−0.487848	+	0.671465i	−0.979989	−	0.199051i	$-0.936214\pi$
$821$	−13.9783	+	19.2395i	−0.487848	+	0.671465i	0.492142	+	0.870515i	$0.336214\pi$
$822$	−32.6175	−	2.36908i	−1.13767	−	0.0826310i
$823$	7.32692	−	22.5499i	0.255400	−	0.786042i	−0.738350	−	0.674418i	$-0.764395\pi$
$823$	7.32692	−	22.5499i	0.255400	−	0.786042i	0.993751	−	0.111624i	$-0.0356053\pi$
$824$	19.8980	−	1.92905i	0.693181	−	0.0672018i
$825$		0			0
$826$	19.1505	−	11.8950i	0.666331	−	0.413880i
$827$	8.41171	+	2.73313i	0.292504	+	0.0950402i	0.451593	−	0.892224i	$-0.350856\pi$
$827$	8.41171	+	2.73313i	0.292504	+	0.0950402i	−0.159089	+	0.987264i	$0.550856\pi$
$828$	−4.10611	+	2.15499i	−0.142697	+	0.0748909i
$829$	−4.69015	+	6.45543i	−0.162896	+	0.224206i	−0.882660	−	0.470012i	$-0.844250\pi$
$829$	−4.69015	+	6.45543i	−0.162896	+	0.224206i	0.719765	+	0.694218i	$0.244250\pi$
$830$		0			0
$831$	−33.0413	+	24.0059i	−1.14619	+	0.832755i
$832$	6.77825	+	34.6300i	0.234993	+	1.20058i
$833$	−7.73864	+	5.62245i	−0.268128	+	0.194806i
$834$	1.27669	−	1.51321i	0.0442082	−	0.0523982i
$835$		0			0
$836$	−0.556211	−	0.542943i	−0.0192370	−	0.0187781i
$837$	47.7898	−	15.5279i	1.65186	−	0.536721i
$838$	−26.4940	−	22.3529i	−0.915220	−	0.772168i
$839$	14.2160	−	43.7523i	0.490790	−	1.51050i	−0.332627	−	0.943058i	$-0.607935\pi$
$839$	14.2160	−	43.7523i	0.490790	−	1.51050i	0.823417	−	0.567437i	$-0.192065\pi$
$840$		0			0
$841$	2.95111	+	9.08258i	0.101762	+	0.313193i
$842$	−14.4665	+	35.5301i	−0.498548	+	1.22445i
$843$			10.0497i			0.346130i
$844$	15.0308	−	2.56699i	0.517383	−	0.0883594i
$845$		0			0
$846$	2.09133	−	28.7934i	0.0719014	−	0.989939i
$847$	26.3142	+	19.1184i	0.904168	+	0.656917i
$848$	0.620768	+	1.76442i	0.0213173	+	0.0605906i
$849$	−40.2003			−1.37967
$850$		0			0
$851$		−	1.30482i		−	0.0447287i
$852$	43.0417	−	44.0935i	1.47459	−	1.51062i
$853$	26.9220	−	37.0549i	0.921790	−	1.26874i	−0.0411867	−	0.999151i	$-0.513114\pi$
$853$	26.9220	−	37.0549i	0.921790	−	1.26874i	0.962977	−	0.269584i	$-0.0868862\pi$
$854$	−8.67419	−	0.630025i	−0.296825	−	0.0215590i
$855$		0			0
$856$	−21.1106	−	23.8299i	−0.721546	−	0.814489i
$857$	−46.7189			−1.59589			−0.797943	−	0.602733i	$-0.794078\pi$
$857$	−46.7189			−1.59589			−0.797943	+	0.602733i	$0.794078\pi$
$858$	−2.07833	+	5.10444i	−0.0709530	+	0.174263i
$859$	35.3436	−	11.4838i	1.20591	−	0.391824i	0.363978	−	0.931408i	$-0.381418\pi$
$859$	35.3436	−	11.4838i	1.20591	−	0.391824i	0.841932	+	0.539584i	$0.181418\pi$
$860$		0			0
$861$	57.8569	+	18.7988i	1.97176	+	0.640662i
$862$	7.83088	−	9.28163i	0.266721	−	0.316133i
$863$	15.4359	+	47.5068i	0.525444	+	1.61715i	0.763436	+	0.645883i	$0.223511\pi$
$863$	15.4359	+	47.5068i	0.525444	+	1.61715i	−0.237992	+	0.971267i	$0.576489\pi$
$864$	47.2234	−	58.7948i	1.60657	−	2.00024i
$865$		0			0
$866$	26.6929	−	31.6380i	0.907062	−	1.07510i
$867$	−17.3657	−	23.9019i	−0.589771	−	0.811750i
$868$	9.94899	−	20.1228i	0.337691	−	0.683012i
$869$	0.904318	+	1.24469i	0.0306769	+	0.0422231i
$870$		0			0
$871$	5.51771	+	4.00885i	0.186960	+	0.135835i
$872$	13.6890	−	23.2739i	0.463567	−	0.788155i
$873$	−36.5866	+	112.602i	−1.23827	+	3.81100i
$874$	−0.544543	+	0.338234i	−0.0184194	+	0.0114409i
$875$		0			0
$876$	−51.3787	−	25.4024i	−1.73593	−	0.858266i
$877$	−25.0044	−	8.12444i	−0.844340	−	0.274343i	−0.145267	−	0.989393i	$-0.546404\pi$
$877$	−25.0044	−	8.12444i	−0.844340	−	0.274343i	−0.699073	+	0.715050i	$0.746404\pi$
$878$	1.32199	−	18.2012i	0.0446149	−	0.614259i
$879$	−23.7381	−	17.2467i	−0.800666	−	0.581718i
$880$		0			0
$881$	−13.3185	+	9.67642i	−0.448710	+	0.326007i	−0.789086	−	0.614282i	$-0.789446\pi$
$881$	−13.3185	+	9.67642i	−0.448710	+	0.326007i	0.340376	+	0.940289i	$0.389446\pi$
$882$	9.99857	+	16.0973i	0.336669	+	0.542024i
$883$	3.71243	+	5.10972i	0.124933	+	0.171956i	0.866902	−	0.498479i	$-0.166108\pi$
$883$	3.71243	+	5.10972i	0.124933	+	0.171956i	−0.741969	+	0.670434i	$0.766108\pi$
$884$	6.53252	−	44.7327i	0.219712	−	1.50452i
$885$		0			0
$886$	−0.374877	−	1.52098i	−0.0125942	−	0.0510982i
$887$	8.52907	+	26.2498i	0.286378	+	0.881381i	0.985982	+	0.166850i	$0.0533597\pi$
$887$	8.52907	+	26.2498i	0.286378	+	0.881381i	−0.699604	+	0.714531i	$0.746640\pi$
$888$	14.5576	+	33.4207i	0.488522	+	1.12152i
$889$	−1.24888	+	3.84365i	−0.0418860	+	0.128912i
$890$		0			0
$891$	5.52971	−	1.79671i	0.185252	−	0.0601922i
$892$	6.49571	+	38.0352i	0.217493	+	1.27351i
$893$		−	3.99079i		−	0.133547i
$894$	−6.91783	−	2.81667i	−0.231367	−	0.0942035i
$895$		0			0
$896$	−4.05920	−	33.4432i	−0.135608	−	1.11726i
$897$	3.67725	+	2.67168i	0.122780	+	0.0892047i
$898$	−8.25621	+	2.03492i	−0.275513	+	0.0679060i
$899$		−	16.6237i		−	0.554431i
$900$		0			0
$901$		−	2.39626i		−	0.0798312i
$902$	−0.600172	−	2.43506i	−0.0199836	−	0.0810787i
$903$	83.8337	+	60.9087i	2.78981	+	2.02692i
$904$	25.7652	+	15.1543i	0.856939	+	0.504024i
$905$		0			0
$906$	23.9270	−	58.7656i	0.794923	−	1.95236i
$907$		−	15.5893i		−	0.517636i	−0.965926	−	0.258818i	$-0.916667\pi$
$907$		−	15.5893i		−	0.517636i	0.965926	−	0.258818i	$-0.0833329\pi$
$908$	47.4949	−	8.11126i	1.57617	−	0.269182i
$909$	−133.044	+	43.2286i	−4.41279	+	1.43380i
$910$		0			0
$911$	8.96903	−	27.6038i	0.297157	−	0.914556i	−0.685331	−	0.728232i	$-0.740342\pi$
$911$	8.96903	−	27.6038i	0.297157	−	0.914556i	0.982488	−	0.186324i	$-0.0596575\pi$
$912$	10.1739	−	14.7386i	0.336891	−	0.488044i
$913$	−1.13649	−	3.49776i	−0.0376123	−	0.115759i
$914$	−50.6263	+	12.4779i	−1.67457	+	0.412733i
$915$		0			0
$916$	7.62976	−	52.2462i	0.252094	−	1.72626i
$917$	1.40287	+	1.93089i	0.0463270	+	0.0637636i
$918$	−82.0685	+	50.9755i	−2.70867	+	1.68244i
$919$	−34.5740	+	25.1195i	−1.14049	+	0.828616i	−0.987188	−	0.159563i	$-0.948991\pi$
$919$	−34.5740	+	25.1195i	−1.14049	+	0.828616i	−0.153304	+	0.988179i	$0.548991\pi$
$920$		0			0
$921$	−62.9005	−	45.6999i	−2.07264	−	1.50586i
$922$	48.1121	+	3.49448i	1.58449	+	0.115085i
$923$	−40.5108	−	13.1628i	−1.33343	−	0.433258i
$924$	2.33199	−	4.71668i	0.0767170	−	0.155167i
$925$		0			0
$926$	−31.3641	−	50.4949i	−1.03069	−	1.65937i
$927$	−15.6788	+	48.2544i	−0.514959	+	1.58488i
$928$	−13.6711	−	20.8687i	−0.448776	−	0.685047i
$929$	7.83492	+	5.69240i	0.257055	+	0.186762i	0.708848	−	0.705361i	$-0.249215\pi$
$929$	7.83492	+	5.69240i	0.257055	+	0.186762i	−0.451792	+	0.892123i	$0.649215\pi$
$930$		0			0
$931$	1.53974	+	2.11926i	0.0504628	+	0.0694561i
$932$	−21.4385	+	43.3615i	−0.702242	+	1.42035i
$933$	−47.0224	−	64.7208i	−1.53945	−	2.11886i
$934$	−12.4259	−	10.4837i	−0.406588	−	0.343037i
$935$		0			0
$936$	−87.4478	−	19.3269i	−2.85832	−	0.631720i
$937$	−14.6482	−	45.0827i	−0.478537	−	1.47279i	−0.841127	−	0.540837i	$-0.818107\pi$
$937$	−14.6482	−	45.0827i	−0.478537	−	1.47279i	0.362590	−	0.931949i	$-0.381893\pi$
$938$	−4.97668	−	4.19881i	−0.162494	−	0.137096i
$939$	33.1045	+	10.7563i	1.08032	+	0.351018i
$940$		0			0
$941$	14.2417	−	4.62742i	0.464267	−	0.150850i	−0.0675373	−	0.997717i	$-0.521514\pi$
$941$	14.2417	−	4.62742i	0.464267	−	0.150850i	0.531804	+	0.846867i	$0.321514\pi$
$942$	39.9708	+	16.2745i	1.30232	+	0.530253i
$943$	−2.06835			−0.0673549
$944$	6.12377	−	20.5197i	0.199312	−	0.667859i
$945$		0			0
$946$	0.309467	−	4.26075i	0.0100617	−	0.138529i
$947$	−15.4226	+	21.2273i	−0.501166	+	0.689796i	−0.982398	−	0.186797i	$-0.940189\pi$
$947$	−15.4226	+	21.2273i	−0.501166	+	0.689796i	0.481233	+	0.876593i	$0.340189\pi$
$948$	−24.7617	+	25.3668i	−0.804222	+	0.823874i
$949$			39.6210i			1.28615i
$950$		0			0
$951$	2.74274			0.0889394
$952$	−9.31393	+	42.1424i	−0.301866	+	1.36584i
$953$	−24.1675	−	17.5587i	−0.782861	−	0.568782i	0.122975	−	0.992410i	$-0.460756\pi$
$953$	−24.1675	−	17.5587i	−0.782861	−	0.568782i	−0.905836	+	0.423628i	$0.860756\pi$
$954$	−4.73467	−	0.343889i	−0.153291	−	0.0111338i
$955$		0			0
$956$	5.18929	+	30.3856i	0.167834	+	0.982739i
$957$		−	3.89651i		−	0.125956i
$958$	15.5823	+	6.34450i	0.503441	+	0.204982i
$959$	−6.66957	−	20.5268i	−0.215371	−	0.662845i
$960$		0			0
$961$	−5.18900	+	15.9701i	−0.167387	+	0.515164i
$962$	16.2499	−	19.2604i	0.523919	−	0.620980i
$963$	76.8443	−	24.9682i	2.47627	−	0.804590i
$964$	22.3320	+	21.7993i	0.719264	+	0.702107i
$965$		0			0
$966$	−3.31668	−	2.79827i	−0.106712	−	0.0900329i
$967$	21.0745	−	15.3115i	0.677710	−	0.492385i	−0.194887	−	0.980826i	$-0.562434\pi$
$967$	21.0745	−	15.3115i	0.677710	−	0.492385i	0.872597	+	0.488440i	$0.162434\pi$
$968$	30.7516	−	2.98127i	0.988394	−	0.0958217i
$969$	−18.5619	+	13.4860i	−0.596294	+	0.433233i
$970$		0			0
$971$	−1.38452	+	1.90563i	−0.0444314	+	0.0611546i	−0.830655	−	0.556788i	$-0.812034\pi$
$971$	−1.38452	+	1.90563i	−0.0444314	+	0.0611546i	0.786223	+	0.617943i	$0.212034\pi$
$972$	25.0852	+	47.7973i	0.804608	+	1.53310i
$973$	1.24267	+	0.403769i	0.0398383	+	0.0129442i
$974$	16.3209	+	26.2760i	0.522956	+	0.841938i
$975$		0			0
$976$	−6.56421	+	5.01565i	−0.210115	+	0.160547i
$977$	−2.89960	+	8.92406i	−0.0927665	+	0.285506i	−0.986665	−	0.162763i	$-0.947959\pi$
$977$	−2.89960	+	8.92406i	−0.0927665	+	0.285506i	0.893899	+	0.448269i	$0.147959\pi$
$978$	−1.79514	+	24.7155i	−0.0574023	+	0.790315i
$979$	0.522574	−	0.719261i	0.0167015	−	0.0229877i
$980$		0			0
$981$	40.2801	+	55.4407i	1.28604	+	1.77009i
$982$	−3.89008	+	2.41626i	−0.124137	+	0.0771059i
$983$	−44.1807	+	32.0991i	−1.40914	+	1.02380i	−0.415698	+	0.909503i	$0.636463\pi$
$983$	−44.1807	+	32.0991i	−1.40914	+	1.02380i	−0.993446	+	0.114301i	$0.963537\pi$
$984$	52.9772	−	23.0762i	1.68885	−	0.735643i
$985$		0			0
$986$	7.64866	+	31.0327i	0.243583	+	0.988283i
$987$	25.6930	−	8.34816i	0.817817	−	0.265725i
$988$	−12.2503	−	1.78896i	−0.389733	−	0.0569145i
$989$	−3.35076	−	1.08873i	−0.106548	−	0.0346196i
$990$		0			0
$991$	19.1415	+	58.9116i	0.608051	+	1.87139i	0.474273	+	0.880378i	$0.342711\pi$
$991$	19.1415	+	58.9116i	0.608051	+	1.87139i	0.133778	+	0.991011i	$0.457289\pi$
$992$	−5.60096	−	20.5739i	−0.177831	−	0.653223i
$993$	−27.0472			−0.858316
$994$	37.6638	+	15.3352i	1.19462	+	0.486404i
$995$		0			0
$996$	75.0328	−	39.3790i	2.37751	−	1.24777i
$997$	−18.0845	+	24.8911i	−0.572741	+	0.788310i	−0.992876	−	0.119151i	$-0.961983\pi$
$997$	−18.0845	+	24.8911i	−0.572741	+	0.788310i	0.420135	+	0.907462i	$0.361983\pi$
$998$	1.59343	+	6.46498i	0.0504391	+	0.204645i
$999$	−53.8537			−1.70386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.t.b.101.6		224
5.2	odd	4		200.2.o.a.29.13	yes	112
5.3	odd	4		1000.2.o.a.149.16		112
5.4	even	2	inner	1000.2.t.b.101.51		224
8.5	even	2	inner	1000.2.t.b.101.40		224
20.7	even	4		800.2.be.a.529.28		112
25.6	even	5	inner	1000.2.t.b.901.40		224
25.8	odd	20		200.2.o.a.69.7	yes	112
25.17	odd	20		1000.2.o.a.349.22		112
25.19	even	10	inner	1000.2.t.b.901.17		224
40.13	odd	4		1000.2.o.a.149.22		112
40.27	even	4		800.2.be.a.529.1		112
40.29	even	2	inner	1000.2.t.b.101.17		224
40.37	odd	4		200.2.o.a.29.7	✓	112
100.83	even	20		800.2.be.a.369.1		112
200.69	even	10	inner	1000.2.t.b.901.51		224
200.83	even	20		800.2.be.a.369.28		112
200.117	odd	20		1000.2.o.a.349.16		112
200.133	odd	20		200.2.o.a.69.13	yes	112
200.181	even	10	inner	1000.2.t.b.901.6		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.7	✓	112	40.37	odd	4
200.2.o.a.29.13	yes	112	5.2	odd	4
200.2.o.a.69.7	yes	112	25.8	odd	20
200.2.o.a.69.13	yes	112	200.133	odd	20
800.2.be.a.369.1		112	100.83	even	20
800.2.be.a.369.28		112	200.83	even	20
800.2.be.a.529.1		112	40.27	even	4
800.2.be.a.529.28		112	20.7	even	4
1000.2.o.a.149.16		112	5.3	odd	4
1000.2.o.a.149.22		112	40.13	odd	4
1000.2.o.a.349.16		112	200.117	odd	20
1000.2.o.a.349.22		112	25.17	odd	20
1000.2.t.b.101.6		224	1.1	even	1	trivial
1000.2.t.b.101.17		224	40.29	even	2	inner
1000.2.t.b.101.40		224	8.5	even	2	inner
1000.2.t.b.101.51		224	5.4	even	2	inner
1000.2.t.b.901.6		224	200.181	even	10	inner
1000.2.t.b.901.17		224	25.19	even	10	inner
1000.2.t.b.901.40		224	25.6	even	5	inner
1000.2.t.b.901.51		224	200.69	even	10	inner

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.t (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.37312 + 0.338435i) q^{2} +(1.87526 - 2.58107i) q^{3} +(1.77092 - 0.929423i) q^{4} +(-1.70143 + 4.17877i) q^{6} -2.97769 q^{7} +(-2.11714 + 1.87555i) q^{8} +(-2.21828 - 6.82716i) q^{9} +O(q^{10})\)	\(q+(-1.37312 + 0.338435i) q^{2} +(1.87526 - 2.58107i) q^{3} +(1.77092 - 0.929423i) q^{4} +(-1.70143 + 4.17877i) q^{6} -2.97769 q^{7} +(-2.11714 + 1.87555i) q^{8} +(-2.21828 - 6.82716i) q^{9} +(-0.263378 - 0.0855768i) q^{11} +(0.922031 - 6.31378i) q^{12} +(-4.19500 + 1.36304i) q^{13} +(4.08873 - 1.00775i) q^{14} +(2.27234 - 3.29188i) q^{16} +(-4.14580 + 3.01210i) q^{17} +(5.35651 + 8.62377i) q^{18} +(0.824879 + 1.13535i) q^{19} +(-5.58392 + 7.68561i) q^{21} +(0.390613 + 0.0283710i) q^{22} +(0.0998113 - 0.307187i) q^{23} +(0.870742 + 8.98164i) q^{24} +(5.29895 - 3.29135i) q^{26} +(-12.6785 - 4.11950i) q^{27} +(-5.27326 + 2.76753i) q^{28} +(-2.59226 + 3.56794i) q^{29} +(-3.04947 + 2.21557i) q^{31} +(-2.00612 + 5.28919i) q^{32} +(-0.714781 + 0.519319i) q^{33} +(4.67329 - 5.53907i) q^{34} +(-10.2737 - 10.0287i) q^{36} +(3.84202 - 1.24835i) q^{37} +(-1.51690 - 1.27980i) q^{38} +(-4.34861 + 13.3836i) q^{39} +(-1.97884 - 6.09023i) q^{41} +(5.06633 - 12.4431i) q^{42} -10.9079i q^{43} +(-0.545960 + 0.0932399i) q^{44} +(-0.0330901 + 0.455585i) q^{46} +(-2.30062 - 1.67150i) q^{47} +(-4.23533 - 12.0382i) q^{48} +1.86662 q^{49} +16.3491i q^{51} +(-6.16219 + 6.31278i) q^{52} +(-0.274854 + 0.378304i) q^{53} +(18.8033 + 1.36572i) q^{54} +(6.30419 - 5.58481i) q^{56} +4.47727 q^{57} +(2.35197 - 5.77652i) q^{58} +(5.09147 - 1.65432i) q^{59} +(-1.96419 - 0.638204i) q^{61} +(3.43747 - 4.07430i) q^{62} +(6.60534 + 20.3291i) q^{63} +(0.964603 - 7.94163i) q^{64} +(0.805726 - 0.954995i) q^{66} +(-0.908853 - 1.25093i) q^{67} +(-4.54239 + 9.18741i) q^{68} +(-0.605700 - 0.833675i) q^{69} +(7.81261 + 5.67620i) q^{71} +(17.5011 + 10.2936i) q^{72} +(2.77576 - 8.54291i) q^{73} +(-4.85308 + 3.01441i) q^{74} +(2.51602 + 1.24395i) q^{76} +(0.784258 + 0.254821i) q^{77} +(1.44168 - 19.8491i) q^{78} +(-4.49455 - 3.26548i) q^{79} +(-16.9856 + 12.3407i) q^{81} +(4.77833 + 7.69292i) q^{82} +(7.80599 + 10.7440i) q^{83} +(-2.74552 + 18.8005i) q^{84} +(3.69160 + 14.9778i) q^{86} +(4.34795 + 13.3816i) q^{87} +(0.718114 - 0.312802i) q^{88} +(-0.992059 + 3.05324i) q^{89} +(12.4914 - 4.05871i) q^{91} +(-0.108749 - 0.636773i) q^{92} +12.0257i q^{93} +(3.72473 + 1.51656i) q^{94} +(9.88976 + 15.0965i) q^{96} +(-13.3433 - 9.69449i) q^{97} +(-2.56310 + 0.631729i) q^{98} +1.98796i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Introduction

L-functions

Modular forms

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Database

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