LMFDB - Embedded newform 1000.2.t.b.901.6

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			901.6
Character	$\chi$	$=$	1000.901
Dual form			1000.2.t.b.101.6

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$1$

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	0.856537	+	0.516086i	$0.172612\pi$
$3$	1.87526	+	2.58107i	1.08268	+	1.49018i	0.226143	+	0.974094i	$0.427388\pi$
$4$	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	−0.348453	−	0.937326i	$-0.613293\pi$
$11$	−0.263378	+	0.0855768i	−0.0794116	+	0.0258024i	0.269042	+	0.963129i	$0.413293\pi$
$12$	0.922031	+	6.31378i	0.266167	+	1.82263i
$13$	−4.19500	−	1.36304i	−1.16349	−	0.378039i	−0.337278	−	0.941405i	$-0.609506\pi$
$13$	−4.19500	−	1.36304i	−1.16349	−	0.378039i	−0.826207	+	0.563366i	$0.809506\pi$
$14$	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	−0.0422436	−	0.999107i	$-0.513451\pi$
$17$	−4.14580	−	3.01210i	−1.00551	−	0.730542i	−0.963262	+	0.268565i	$0.913451\pi$
$18$	5.35651	−	8.62377i	1.26254	−	2.03264i
$19$	0.824879	−	1.13535i	0.189240	−	0.260467i	−0.703846	−	0.710353i	$-0.748535\pi$
$19$	0.824879	−	1.13535i	0.189240	−	0.260467i	0.893086	+	0.449886i	$0.148535\pi$
$20$		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	0.960923	−	0.276815i	$-0.0892790\pi$
$23$	0.0998113	+	0.307187i	0.0208121	+	0.0640530i	−0.940111	+	0.340868i	$0.889279\pi$
$24$	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	0.497397	−	0.867523i	$-0.334289\pi$
$29$	−2.59226	−	3.56794i	−0.481371	−	0.662550i	−0.978768	+	0.204973i	$0.934289\pi$
$30$		0			0
$31$	−3.04947	−	2.21557i	−0.547702	−	0.397929i	0.279236	−	0.960223i	$-0.409919\pi$
$31$	−3.04947	−	2.21557i	−0.547702	−	0.397929i	−0.826937	+	0.562294i	$0.809919\pi$
$32$	−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	0.607295	−	0.794477i	$-0.292255\pi$
$37$	3.84202	+	1.24835i	0.631625	+	0.205227i	0.0243301	+	0.999704i	$0.492255\pi$
$38$	−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	0.669095	+	0.743177i	$0.266682\pi$
$41$	−1.97884	+	6.09023i	−0.309042	+	0.951135i	−0.978138	+	0.207958i	$0.933318\pi$
$42$	5.06633	+	12.4431i	0.781752	+	1.92001i
$43$			10.9079i			1.66343i	0.555199	+	0.831717i	$0.312642\pi$
$43$			10.9079i			1.66343i	−0.555199	+	0.831717i	$0.687358\pi$
$44$	−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	−0.742795	−	0.669519i	$-0.766500\pi$
$47$	−2.30062	+	1.67150i	−0.335580	+	0.243813i	0.407214	+	0.913333i	$0.366500\pi$
$48$	−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	0.789723	−	0.613464i	$-0.210224\pi$
$53$	−0.274854	−	0.378304i	−0.0377541	−	0.0519641i	−0.827477	+	0.561500i	$0.810224\pi$
$54$	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	0.621073	−	0.783753i	$-0.286697\pi$
$59$	5.09147	+	1.65432i	0.662853	+	0.215374i	0.0417804	+	0.999127i	$0.486697\pi$
$60$		0			0
$61$	−1.96419	+	0.638204i	−0.251489	+	0.0817137i	−0.432049	−	0.901850i	$-0.642209\pi$
$61$	−1.96419	+	0.638204i	−0.251489	+	0.0817137i	0.180560	+	0.983564i	$0.442209\pi$
$62$	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	−0.860917	−	0.508745i	$-0.830110\pi$
$67$	−0.908853	+	1.25093i	−0.111034	+	0.152825i	0.749883	+	0.661570i	$0.230110\pi$
$68$	−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	−0.0181158	−	0.999836i	$-0.505767\pi$
$71$	7.81261	−	5.67620i	0.927187	−	0.673640i	0.945302	+	0.326195i	$0.105767\pi$
$72$	17.5011	−	10.2936i	2.06253	−	1.21311i
$73$	2.77576	+	8.54291i	0.324878	+	0.999872i	0.971496	+	0.237057i	$0.0761829\pi$
$73$	2.77576	+	8.54291i	0.324878	+	0.999872i	−0.646618	+	0.762814i	$0.723817\pi$
$74$	−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	−0.811181	−	0.584795i	$-0.801175\pi$
$79$	−4.49455	+	3.26548i	−0.505677	+	0.367396i	0.305504	+	0.952191i	$0.401175\pi$
$80$		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	−0.125500	−	0.992094i	$-0.540053\pi$
$83$	7.80599	−	10.7440i	0.856819	−	1.17931i	0.982319	−	0.187217i	$-0.0599466\pi$
$84$	−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	0.884610	−	0.466333i	$-0.154425\pi$
$89$	−0.992059	−	3.05324i	−0.105158	−	0.323643i	−0.989768	+	0.142689i	$0.954425\pi$
$90$		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	−0.356053	+	0.934466i	$0.615878\pi$
$97$	−13.3433	+	9.69449i	−1.35481	+	0.984327i	−0.998756	+	0.0498611i	$0.984122\pi$
$98$	−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	$0.421230\pi$
$101$			19.4874i			1.93907i	−0.244946	+	0.969537i	$0.578770\pi$
$102$	−5.53309	+	22.4492i	−0.547857	+	2.22281i
$103$	−5.71814	+	4.15447i	−0.563425	+	0.409352i	−0.832711	−	0.553708i	$-0.813212\pi$
$103$	−5.71814	+	4.15447i	−0.563425	+	0.409352i	0.269286	+	0.963060i	$0.413212\pi$
$104$	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	$-0.816885\pi$
$107$		−	11.2557i		−	1.08813i	0.839044	−	0.544064i	$-0.183115\pi$
$108$	−26.2814	−	4.48838i	−2.52893	−	0.431895i
$109$	−9.07913	−	2.94999i	−0.869623	−	0.282558i	−0.159981	−	0.987120i	$-0.551143\pi$
$109$	−9.07913	−	2.94999i	−0.869623	−	0.282558i	−0.709642	+	0.704563i	$0.751143\pi$
$110$		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	0.671624	+	0.740892i	$0.265597\pi$
$113$	−3.26576	+	10.0510i	−0.307217	+	0.945517i	−0.978841	+	0.204624i	$0.934403\pi$
$114$	−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	0.967939	−	0.251185i	$-0.0808204\pi$
$127$	0.419412	+	1.29082i	0.0372168	+	0.114542i	−0.930722	+	0.365727i	$0.880820\pi$
$128$	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	−0.829102	−	0.559097i	$-0.811148\pi$
$131$	−0.471129	+	0.648453i	−0.0411627	+	0.0566556i	0.787940	+	0.615753i	$0.211148\pi$
$132$	−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	−0.808637	−	0.588308i	$-0.799794\pi$
$137$	2.23985	−	6.89354i	0.191363	−	0.588955i	1.00000		0.000646705i	$-0.000205853\pi$
$138$	1.11384	−	0.939747i	0.0948167	−	0.0799966i
$139$	−0.417329	+	0.135598i	−0.0353973	+	0.0115013i	−0.326662	−	0.945141i	$-0.605924\pi$
$139$	−0.417329	+	0.135598i	−0.0353973	+	0.0115013i	0.291265	+	0.956642i	$0.405924\pi$
$140$		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	$-0.978399\pi$
$149$		−	1.65547i		−	0.135621i	0.997698	−	0.0678107i	$-0.0216014\pi$
$150$		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	$0.124659\pi$
$157$			9.56521i			0.763387i	−0.924289	+	0.381693i	$0.875341\pi$
$158$	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	0.506352	−	0.862327i	$-0.330994\pi$
$163$	5.22350	+	1.69722i	0.409136	+	0.132936i	−0.0972156	+	0.995263i	$0.530994\pi$
$164$	−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	0.143456	−	0.989657i	$-0.454179\pi$
$167$	−9.73651	−	7.07399i	−0.753433	−	0.547401i	−0.896889	+	0.442255i	$0.854179\pi$
$168$	−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	0.396722	−	0.917939i	$-0.370148\pi$
$173$	16.5363	−	5.37296i	1.25723	−	0.408498i	0.860506	+	0.509440i	$0.170148\pi$
$174$	−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	−0.957941	−	0.286964i	$-0.907354\pi$
$179$	−12.5073	−	17.2148i	−0.934841	−	1.28670i	0.0231007	−	0.999733i	$-0.492646\pi$
$180$		0			0
$181$	−4.82937	+	6.64706i	−0.358964	+	0.494072i	−0.949860	−	0.312676i	$-0.898775\pi$
$181$	−4.82937	+	6.64706i	−0.358964	+	0.494072i	0.590896	+	0.806748i	$0.298775\pi$
$182$	−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	−0.982828	−	0.184523i	$-0.940926\pi$
$191$	−1.09517	+	3.37058i	−0.0792436	+	0.243887i	0.903585	+	0.428410i	$0.140926\pi$
$192$	−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	0.902878	−	0.429897i	$-0.141450\pi$
$197$	3.01790	+	4.15379i	0.215017	+	0.295945i	−0.687861	+	0.725842i	$0.741450\pi$
$198$	−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	−0.0485936	−	0.998819i	$-0.515474\pi$
$211$	7.25107	−	2.35602i	0.499184	−	0.162195i	0.547778	+	0.836624i	$0.315474\pi$
$212$	−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	−0.925614	−	0.378469i	$-0.876451\pi$
$223$	−5.96185	−	18.3487i	−0.399235	−	1.22872i	0.526379	−	0.850250i	$-0.323549\pi$
$224$	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	0.574751	−	0.818329i	$-0.305099\pi$
$227$	22.9122	−	7.44462i	1.52073	−	0.494117i	0.945984	+	0.324212i	$0.105099\pi$
$228$	7.92890	+	4.16128i	0.525105	+	0.275587i
$229$	15.5176	+	21.3582i	1.02544	+	1.41139i	0.908322	+	0.418272i	$0.137364\pi$
$229$	15.5176	+	21.3582i	1.02544	+	1.41139i	0.117113	+	0.993119i	$0.462636\pi$
$230$		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	−0.282256	−	0.959339i	$-0.591083\pi$
$233$	−19.5668	−	14.2161i	−1.28186	−	0.931328i	−0.999608	+	0.0280108i	$0.991083\pi$
$234$	−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	−0.978510	−	0.206200i	$-0.933890\pi$
$239$	−4.76280	−	14.6584i	−0.308080	−	0.948173i	0.670430	−	0.741973i	$-0.266110\pi$
$240$		0			0
$241$	4.82186	−	14.8402i	0.310604	−	0.955940i	−0.666923	−	0.745127i	$-0.732389\pi$
$241$	4.82186	−	14.8402i	0.310604	−	0.955940i	0.977526	−	0.210813i	$-0.0676111\pi$
$242$	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	$0.0260702\pi$
$251$			2.59224i			0.163621i	−0.996648	+	0.0818104i	$0.973930\pi$
$252$	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	0.686003	+	0.727599i	$0.259364\pi$
$263$	−4.81097	+	14.8066i	−0.296657	+	0.913017i	−0.982660	+	0.185418i	$0.940636\pi$
$264$	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	−0.832041	−	0.554714i	$-0.812828\pi$
$269$	−0.776787	+	1.06916i	−0.0473616	+	0.0651876i	0.784679	+	0.619902i	$0.212828\pi$
$270$		0			0
$271$	11.7169	−	8.51285i	0.711753	−	0.517119i	−0.171986	−	0.985099i	$-0.555018\pi$
$271$	11.7169	−	8.51285i	0.711753	−	0.517119i	0.883739	+	0.467981i	$0.155018\pi$
$272$	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	−0.651009	−	0.759070i	$-0.725654\pi$
$277$	−12.1748	+	3.95585i	−0.731516	+	0.237684i	−0.0805069	+	0.996754i	$0.525654\pi$
$278$	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	0.509172	−	0.860665i	$-0.329952\pi$
$281$	−2.54841	−	1.85153i	−0.152025	−	0.110453i	−0.661198	+	0.750212i	$0.729952\pi$
$282$	10.8992	+	6.76983i	0.649036	+	0.403138i
$283$	−7.40638	+	10.1940i	−0.440264	+	0.605971i	−0.970271	−	0.242022i	$-0.922189\pi$
$283$	−7.40638	+	10.1940i	−0.440264	+	0.605971i	0.530007	+	0.847993i	$0.322189\pi$
$284$	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	$0.0865766\pi$
$293$			9.19701i			0.537295i	−0.963239	+	0.268647i	$0.913423\pi$
$294$	−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	$0.244787\pi$
$307$			24.3699i			1.39087i	−0.718591	+	0.695433i	$0.755213\pi$
$308$	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	0.888524	+	0.458830i	$0.151731\pi$
$311$	7.74867	+	23.8479i	0.439387	+	1.35229i	−0.449138	+	0.893463i	$0.648269\pi$
$312$	−15.8951	+	36.4912i	−0.899882	+	2.06590i
$313$	3.37148	−	10.3764i	0.190567	−	0.586506i	−0.809432	−	0.587213i	$-0.800225\pi$
$313$	3.37148	−	10.3764i	0.190567	−	0.586506i	1.00000		0.000706882i	$0.000225008\pi$
$314$	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	−0.794591	−	0.607146i	$-0.792314\pi$
$317$	0.505314	−	0.695505i	0.0283813	−	0.0390635i	0.822972	+	0.568082i	$0.192314\pi$
$318$	−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	−0.923700	−	0.383117i	$-0.874851\pi$
$331$	−4.98309	+	6.85864i	−0.273895	+	0.376985i	0.649805	+	0.760101i	$0.274851\pi$
$332$	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	0.704054	+	0.710147i	$0.251371\pi$
$337$	−5.19430	+	15.9864i	−0.282951	+	0.870835i	−0.987005	+	0.160688i	$0.948629\pi$
$338$	−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	0.990867	−	0.134845i	$-0.0430536\pi$
$347$	10.3651	+	14.2663i	0.556427	+	0.765856i	−0.434440	+	0.900701i	$0.643054\pi$
$348$	20.1371	−	19.6567i	1.07946	−	1.05371i
$349$			35.1956i			1.88398i	0.335642	+	0.941990i	$0.391047\pi$
$349$			35.1956i			1.88398i	−0.335642	+	0.941990i	$0.608953\pi$
$350$		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	−0.996392	−	0.0848720i	$-0.972952\pi$
$353$	−22.9889	+	16.7024i	−1.22358	+	0.888980i	−0.227184	+	0.973852i	$0.572952\pi$
$354$	−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	0.791460	+	0.611221i	$0.209321\pi$
$359$	−3.94315	+	12.1358i	−0.208112	+	0.640501i	−0.999571	+	0.0292801i	$0.990679\pi$
$360$		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	0.938596	−	0.345018i	$-0.112127\pi$
$367$	17.2512	+	12.5338i	0.900507	+	0.654257i	−0.0380891	+	0.999274i	$0.512127\pi$
$368$	−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	−0.00445132	−	0.999990i	$-0.501417\pi$
$373$	11.1964	−	3.63793i	0.579727	−	0.188365i	0.584178	+	0.811625i	$0.301417\pi$
$374$	−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	0.439121	−	0.898428i	$-0.355290\pi$
$379$	−10.7274	−	14.7650i	−0.551030	−	0.758428i	−0.990152	+	0.140000i	$0.955290\pi$
$380$		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	0.975204	+	0.221307i	$0.0710324\pi$
$383$	29.1018	+	21.1437i	1.48703	+	1.08039i	0.511830	+	0.859087i	$0.328968\pi$
$384$	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	−0.376053	−	0.926598i	$-0.622719\pi$
$389$	−2.67533	+	0.869269i	−0.135645	+	0.0440737i	0.240408	+	0.970672i	$0.422719\pi$
$390$		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	0.909189	−	0.416383i	$-0.136703\pi$
$397$	4.62715	+	6.36873i	0.232230	+	0.319637i	−0.676959	+	0.736021i	$0.736703\pi$
$398$	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	−0.484622	−	0.874724i	$-0.661043\pi$
$409$	8.52623	−	26.2411i	0.421595	−	1.29754i	0.906217	−	0.422813i	$-0.138957\pi$
$410$		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	−0.296068	−	0.955167i	$-0.595676\pi$
$419$	14.4072	−	19.8299i	0.703839	−	0.968752i	0.999908	−	0.0135851i	$-0.00432441\pi$
$420$		0			0
$421$	15.9444	+	21.9456i	0.777084	+	1.06956i	0.995598	+	0.0937303i	$0.0298792\pi$
$421$	15.9444	+	21.9456i	0.777084	+	1.06956i	−0.218514	+	0.975834i	$0.570121\pi$
$422$	−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	0.407766	−	0.913087i	$-0.366308\pi$
$431$	−6.94699	−	5.04728i	−0.334625	−	0.243119i	−0.742390	+	0.669968i	$0.766308\pi$
$432$	−42.3708	−	32.3752i	−2.03857	−	1.55765i
$433$	−23.6800	−	17.2045i	−1.13799	−	0.826797i	−0.151150	−	0.988511i	$-0.548298\pi$
$433$	−23.6800	−	17.2045i	−1.13799	−	0.826797i	−0.986838	+	0.161714i	$0.948298\pi$
$434$	−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	0.809683	−	0.586868i	$-0.199639\pi$
$439$	−3.98757	−	12.2725i	−0.190317	−	0.585734i	−0.999999	+	0.00113362i	$0.999639\pi$
$440$		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	$-0.991623\pi$
$443$		−	1.10768i		−	0.0526274i	0.999654	−	0.0263137i	$-0.00837688\pi$
$444$	−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	−0.943177	−	0.332291i	$-0.892178\pi$
$461$	−32.4405	+	10.5406i	−1.51091	+	0.490923i	−0.567730	+	0.823215i	$0.692178\pi$
$462$	−2.39920	−	2.84368i	−0.111621	−	0.132300i
$463$	12.9887	−	39.9752i	0.603637	−	1.85780i	0.0977353	−	0.995212i	$-0.468840\pi$
$463$	12.9887	−	39.9752i	0.603637	−	1.85780i	0.505902	−	0.862591i	$-0.331160\pi$
$464$	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	−0.623533	−	0.781797i	$-0.714304\pi$
$467$	6.75711	−	9.30036i	0.312682	−	0.430370i	0.936215	+	0.351427i	$0.114304\pi$
$468$	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	−0.785539	−	0.618812i	$-0.787614\pi$
$479$	−9.62460	+	6.99268i	−0.439759	+	0.319504i	0.345780	+	0.938316i	$0.387614\pi$
$480$		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	0.672921	+	0.739714i	$0.265039\pi$
$487$	−6.75894	+	20.8019i	−0.306277	+	0.942622i	−0.979198	+	0.202908i	$0.934961\pi$
$488$	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	0.377682	−	0.925935i	$-0.376721\pi$
$491$	3.07965	+	1.00064i	0.138983	+	0.0451582i	−0.238700	+	0.971093i	$0.576721\pi$
$492$	−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	$0.0336074\pi$
$499$			4.70824i			0.210770i	−0.994432	+	0.105385i	$0.966393\pi$
$500$		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	−0.330078	−	0.943954i	$-0.607075\pi$
$503$	10.4440	−	7.58802i	0.465676	−	0.338333i	0.795754	+	0.605621i	$0.207075\pi$
$504$	−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	0.105667	−	0.994402i	$-0.466302\pi$
$509$	−8.87419	−	2.88340i	−0.393342	−	0.127804i	−0.499008	+	0.866597i	$0.666302\pi$
$510$		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	−0.860793	−	0.508955i	$-0.830032\pi$
$521$	−14.6710	+	10.6591i	−0.642748	+	0.466984i	0.218045	+	0.975939i	$0.430032\pi$
$522$	−44.6546	+	3.24336i	−1.95448	+	0.141958i
$523$	22.2349	−	7.22455i	0.972264	−	0.315908i	0.220534	−	0.975379i	$-0.429220\pi$
$523$	22.2349	−	7.22455i	0.972264	−	0.315908i	0.751729	+	0.659472i	$0.229220\pi$
$524$	−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	0.282322	−	0.959320i	$-0.408896\pi$
$541$	−1.23623	−	0.401675i	−0.0531496	−	0.0172694i	−0.335471	+	0.942050i	$0.608896\pi$
$542$	−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	0.835840	−	0.548973i	$-0.184981\pi$
$547$	1.29680	+	1.78489i	0.0554470	+	0.0763163i	−0.780393	+	0.625289i	$0.784981\pi$
$548$	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	$-0.843440\pi$
$557$		−	22.2912i		−	0.944509i	0.881462	−	0.472255i	$-0.156560\pi$
$558$	−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	−0.148293	−	0.988943i	$-0.547378\pi$
$563$	−20.1578	−	6.54968i	−0.849551	−	0.276036i	−0.701258	+	0.712907i	$0.747378\pi$
$564$	−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	0.559164	−	0.829057i	$-0.311122\pi$
$569$	−1.34832	−	0.979610i	−0.0565244	−	0.0410674i	−0.615689	+	0.787989i	$0.711122\pi$
$570$		0			0
$571$	−2.18726	−	3.01051i	−0.0915340	−	0.125986i	0.760794	−	0.648994i	$-0.224810\pi$
$571$	−2.18726	−	3.01051i	−0.0915340	−	0.125986i	−0.852328	+	0.523008i	$0.824810\pi$
$572$	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	−0.976222	−	0.216771i	$-0.930447\pi$
$577$	−7.53910	−	23.2030i	−0.313857	−	0.965952i	0.662366	−	0.749181i	$-0.269553\pi$
$578$	−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	0.566358	−	0.824159i	$-0.308352\pi$
$587$	13.0862	+	4.25195i	0.540123	+	0.175497i	−0.0262350	+	0.999656i	$0.508352\pi$
$588$	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	−0.329441	−	0.944176i	$-0.606860\pi$
$613$	−28.4959	−	9.25887i	−1.15094	−	0.373962i	−0.821496	+	0.570214i	$0.806860\pi$
$614$	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	0.907986	−	0.419000i	$-0.137619\pi$
$617$	19.6251	+	14.2585i	0.790077	+	0.574025i	−0.117909	+	0.993024i	$0.537619\pi$
$618$	27.0896	+	16.8262i	1.08970	+	0.676851i
$619$	20.9345	−	28.8138i	0.841428	−	1.15813i	−0.144259	−	0.989540i	$-0.546080\pi$
$619$	20.9345	−	28.8138i	0.841428	−	1.15813i	0.985687	−	0.168586i	$-0.0539201\pi$
$620$		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	0.476140	−	0.879369i	$-0.342035\pi$
$631$	−5.35186	−	3.88835i	−0.213054	−	0.154793i	−0.689194	+	0.724576i	$0.742035\pi$
$632$	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	−0.722782	−	0.691076i	$-0.757137\pi$
$641$	6.78939	−	20.8956i	0.268165	−	0.825327i	0.990947	−	0.134251i	$-0.0428629\pi$
$642$	−47.0349	+	19.1508i	−1.85632	+	0.755820i
$643$			32.6614i			1.28804i	0.765009	+	0.644019i	$0.222734\pi$
$643$			32.6614i			1.28804i	−0.765009	+	0.644019i	$0.777266\pi$
$644$	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	0.128074	−	0.991765i	$-0.459120\pi$
$647$	28.2564	−	20.5295i	1.11088	−	0.807098i	0.982801	+	0.184666i	$0.0591205\pi$
$648$	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	−0.970969	−	0.239204i	$-0.923114\pi$
$653$	−22.9581	−	31.5991i	−0.898420	−	1.23657i	0.0725499	−	0.997365i	$-0.476886\pi$
$654$	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	0.961171	−	0.275953i	$-0.0889936\pi$
$659$	40.4722	+	13.1502i	1.57657	+	0.512260i	0.615402	+	0.788213i	$0.288994\pi$
$660$		0			0
$661$	−15.1858	+	4.93417i	−0.590660	+	0.191917i	−0.589071	−	0.808082i	$-0.700506\pi$
$661$	−15.1858	+	4.93417i	−0.590660	+	0.191917i	−0.00158966	+	0.999999i	$0.500506\pi$
$662$	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	0.989924	−	0.141603i	$-0.0452257\pi$
$673$	2.74537	+	8.44939i	0.105826	+	0.325700i	−0.884097	+	0.467303i	$0.845226\pi$
$674$	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	−0.706351	−	0.707862i	$-0.749660\pi$
$677$	−22.4216	+	7.28520i	−0.861730	+	0.279993i	−0.155379	+	0.987855i	$0.549660\pi$
$678$	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	−0.414097	−	0.910233i	$-0.635903\pi$
$683$	15.1461	−	20.8468i	0.579548	−	0.797680i	0.993646	+	0.112553i	$0.0359027\pi$
$684$	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	0.793553	−	0.608501i	$-0.208229\pi$
$691$	28.3342	+	9.20634i	1.07788	+	0.350225i	0.284330	+	0.958726i	$0.408229\pi$
$692$	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	$0.0352120\pi$
$701$			5.84579i			0.220792i	−0.993888	+	0.110396i	$0.964788\pi$
$702$	−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	0.636159	−	0.771558i	$-0.280522\pi$
$709$	18.5674	+	6.03290i	0.697312	+	0.226570i	0.0611529	+	0.998128i	$0.480522\pi$
$710$		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	−0.995432	−	0.0954761i	$-0.969563\pi$
$719$	−37.3747	−	27.1543i	−1.39384	−	1.01268i	−0.398408	−	0.917208i	$-0.630437\pi$
$720$		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	0.983795	−	0.179300i	$-0.0573831\pi$
$727$	2.22440	+	6.84600i	0.0824984	+	0.253904i	−0.901296	+	0.433204i	$0.857383\pi$
$728$	−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	−0.386961	−	0.922096i	$-0.626475\pi$
$733$	16.5038	−	22.7156i	0.609582	−	0.839018i	0.996543	+	0.0830781i	$0.0264751\pi$
$734$	−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	−0.906540	−	0.422121i	$-0.861286\pi$
$739$	−37.8363	+	12.2937i	−1.39183	+	0.452233i	−0.485290	+	0.874353i	$0.661286\pi$
$740$		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	$-0.890090\pi$
$757$		−	18.6251i		−	0.676942i	0.940977	−	0.338471i	$-0.109910\pi$
$758$	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	0.871124	+	0.491063i	$0.163391\pi$
$761$	12.5520	+	38.6311i	0.455009	+	1.40037i	−0.416115	+	0.909312i	$0.636609\pi$
$762$	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	0.287179	−	0.957877i	$-0.407282\pi$
$769$	−14.8380	−	10.7804i	−0.535072	−	0.388753i	−0.822252	+	0.569124i	$0.807282\pi$
$770$		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	−0.806072	−	0.591817i	$-0.798411\pi$
$773$	−30.8706	+	10.0305i	−1.11034	+	0.360770i	−0.304265	+	0.952588i	$0.598411\pi$
$774$	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	−0.405224	−	0.914217i	$-0.632807\pi$
$787$	−35.6398	−	11.5801i	−1.27042	−	0.412785i	−0.865197	+	0.501432i	$0.832807\pi$
$788$	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	0.775614	+	0.631207i	$0.217440\pi$
$797$	32.0777	+	44.1511i	1.13625	+	1.56391i	0.360636	+	0.932707i	$0.382560\pi$
$798$	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	−0.897214	−	0.441596i	$-0.854413\pi$
$809$	2.50898	−	7.72183i	0.0882109	−	0.271485i	0.985425	+	0.170111i	$0.0544125\pi$
$810$		0			0
$811$	1.71354	−	0.556763i	0.0601705	−	0.0195506i	−0.278777	−	0.960356i	$-0.589929\pi$
$811$	1.71354	−	0.556763i	0.0601705	−	0.0195506i	0.338948	+	0.940805i	$0.389929\pi$
$812$	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	0.492142	−	0.870515i	$-0.336214\pi$
$821$	−13.9783	−	19.2395i	−0.487848	−	0.671465i	−0.979989	+	0.199051i	$0.936214\pi$
$822$	−32.6175	+	2.36908i	−1.13767	+	0.0826310i
$823$	7.32692	+	22.5499i	0.255400	+	0.786042i	0.993751	+	0.111624i	$0.0356053\pi$
$823$	7.32692	+	22.5499i	0.255400	+	0.786042i	−0.738350	+	0.674418i	$0.764395\pi$
$824$	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	−0.159089	−	0.987264i	$-0.550856\pi$
$827$	8.41171	−	2.73313i	0.292504	−	0.0950402i	0.451593	+	0.892224i	$0.350856\pi$
$828$	−4.10611	−	2.15499i	−0.142697	−	0.0748909i
$829$	−4.69015	−	6.45543i	−0.162896	−	0.224206i	0.719765	−	0.694218i	$-0.244250\pi$
$829$	−4.69015	−	6.45543i	−0.162896	−	0.224206i	−0.882660	+	0.470012i	$0.844250\pi$
$830$		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	0.823417	+	0.567437i	$0.192065\pi$
$839$	14.2160	+	43.7523i	0.490790	+	1.51050i	−0.332627	+	0.943058i	$0.607935\pi$
$840$		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	0.962977	+	0.269584i	$0.0868862\pi$
$853$	26.9220	+	37.0549i	0.921790	+	1.26874i	−0.0411867	+	0.999151i	$0.513114\pi$
$854$	−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	0.841932	−	0.539584i	$-0.181418\pi$
$859$	35.3436	+	11.4838i	1.20591	+	0.391824i	0.363978	+	0.931408i	$0.381418\pi$
$860$		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	−0.237992	−	0.971267i	$-0.576489\pi$
$863$	15.4359	−	47.5068i	0.525444	−	1.61715i	0.763436	−	0.645883i	$-0.223511\pi$
$864$	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	−0.699073	−	0.715050i	$-0.746404\pi$
$877$	−25.0044	+	8.12444i	−0.844340	+	0.274343i	−0.145267	+	0.989393i	$0.546404\pi$
$878$	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	0.340376	−	0.940289i	$-0.389446\pi$
$881$	−13.3185	−	9.67642i	−0.448710	−	0.326007i	−0.789086	+	0.614282i	$0.789446\pi$
$882$	9.99857	−	16.0973i	0.336669	−	0.542024i
$883$	3.71243	−	5.10972i	0.124933	−	0.171956i	−0.741969	−	0.670434i	$-0.766108\pi$
$883$	3.71243	−	5.10972i	0.124933	−	0.171956i	0.866902	+	0.498479i	$0.166108\pi$
$884$	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	−0.699604	−	0.714531i	$-0.746640\pi$
$887$	8.52907	−	26.2498i	0.286378	−	0.881381i	0.985982	−	0.166850i	$-0.0533597\pi$
$888$	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	$0.0833329\pi$
$907$			15.5893i			0.517636i	−0.965926	+	0.258818i	$0.916667\pi$
$908$	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	0.982488	+	0.186324i	$0.0596575\pi$
$911$	8.96903	+	27.6038i	0.297157	+	0.914556i	−0.685331	+	0.728232i	$0.740342\pi$
$912$	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	−0.153304	−	0.988179i	$-0.548991\pi$
$919$	−34.5740	−	25.1195i	−1.14049	−	0.828616i	−0.987188	+	0.159563i	$0.948991\pi$
$920$		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	−0.451792	−	0.892123i	$-0.649215\pi$
$929$	7.83492	−	5.69240i	0.257055	−	0.186762i	0.708848	+	0.705361i	$0.249215\pi$
$930$		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	0.362590	+	0.931949i	$0.381893\pi$
$937$	−14.6482	+	45.0827i	−0.478537	+	1.47279i	−0.841127	+	0.540837i	$0.818107\pi$
$938$	−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	0.531804	−	0.846867i	$-0.321514\pi$
$941$	14.2417	+	4.62742i	0.464267	+	0.150850i	−0.0675373	+	0.997717i	$0.521514\pi$
$942$	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	0.481233	−	0.876593i	$-0.340189\pi$
$947$	−15.4226	−	21.2273i	−0.501166	−	0.689796i	−0.982398	+	0.186797i	$0.940189\pi$
$948$	−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	−0.905836	−	0.423628i	$-0.860756\pi$
$953$	−24.1675	+	17.5587i	−0.782861	+	0.568782i	0.122975	+	0.992410i	$0.460756\pi$
$954$	−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	0.872597	−	0.488440i	$-0.162434\pi$
$967$	21.0745	+	15.3115i	0.677710	+	0.492385i	−0.194887	+	0.980826i	$0.562434\pi$
$968$	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	0.786223	−	0.617943i	$-0.212034\pi$
$971$	−1.38452	−	1.90563i	−0.0444314	−	0.0611546i	−0.830655	+	0.556788i	$0.812034\pi$
$972$	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	0.893899	−	0.448269i	$-0.147959\pi$
$977$	−2.89960	−	8.92406i	−0.0927665	−	0.285506i	−0.986665	+	0.162763i	$0.947959\pi$
$978$	−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	−0.993446	−	0.114301i	$-0.963537\pi$
$983$	−44.1807	−	32.0991i	−1.40914	−	1.02380i	−0.415698	−	0.909503i	$-0.636463\pi$
$984$	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	0.133778	−	0.991011i	$-0.457289\pi$
$991$	19.1415	−	58.9116i	0.608051	−	1.87139i	0.474273	−	0.880378i	$-0.342711\pi$
$992$	−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	0.420135	−	0.907462i	$-0.361983\pi$
$997$	−18.0845	−	24.8911i	−0.572741	−	0.788310i	−0.992876	+	0.119151i	$0.961983\pi$
$998$	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.901.6		224
5.2	odd	4		1000.2.o.a.349.16		112
5.3	odd	4		200.2.o.a.69.13	yes	112
5.4	even	2	inner	1000.2.t.b.901.51		224
8.5	even	2	inner	1000.2.t.b.901.40		224
20.3	even	4		800.2.be.a.369.28		112
25.3	odd	20		1000.2.o.a.149.22		112
25.4	even	10	inner	1000.2.t.b.101.17		224
25.21	even	5	inner	1000.2.t.b.101.40		224
25.22	odd	20		200.2.o.a.29.7	✓	112
40.3	even	4		800.2.be.a.369.1		112
40.13	odd	4		200.2.o.a.69.7	yes	112
40.29	even	2	inner	1000.2.t.b.901.17		224
40.37	odd	4		1000.2.o.a.349.22		112
100.47	even	20		800.2.be.a.529.1		112
200.21	even	10	inner	1000.2.t.b.101.6		224
200.29	even	10	inner	1000.2.t.b.101.51		224
200.53	odd	20		1000.2.o.a.149.16		112
200.147	even	20		800.2.be.a.529.28		112
200.197	odd	20		200.2.o.a.29.13	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.7	✓	112	25.22	odd	20
200.2.o.a.29.13	yes	112	200.197	odd	20
200.2.o.a.69.7	yes	112	40.13	odd	4
200.2.o.a.69.13	yes	112	5.3	odd	4
800.2.be.a.369.1		112	40.3	even	4
800.2.be.a.369.28		112	20.3	even	4
800.2.be.a.529.1		112	100.47	even	20
800.2.be.a.529.28		112	200.147	even	20
1000.2.o.a.149.16		112	200.53	odd	20
1000.2.o.a.149.22		112	25.3	odd	20
1000.2.o.a.349.16		112	5.2	odd	4
1000.2.o.a.349.22		112	40.37	odd	4
1000.2.t.b.101.6		224	200.21	even	10	inner
1000.2.t.b.101.17		224	25.4	even	10	inner
1000.2.t.b.101.40		224	25.21	even	5	inner
1000.2.t.b.101.51		224	200.29	even	10	inner
1000.2.t.b.901.6		224	1.1	even	1	trivial
1000.2.t.b.901.17		224	40.29	even	2	inner
1000.2.t.b.901.40		224	8.5	even	2	inner
1000.2.t.b.901.51		224	5.4	even	2	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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