LMFDB - Embedded newform 1000.2.t.b.101.17

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			101.17
Character	$\chi$	$=$	1000.101
Dual form			1000.2.t.b.901.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.911952 - 1.08090i) q^{2} +(1.87526 - 2.58107i) q^{3} +(-0.336688 + 1.97146i) q^{4} +(-4.50002 + 0.326846i) q^{6} +2.97769 q^{7} +(2.43799 - 1.43395i) q^{8} +(-2.21828 - 6.82716i) q^{9} +O(q^{10})$	\(q+(-0.911952 - 1.08090i) q^{2} +(1.87526 - 2.58107i) q^{3} +(-0.336688 + 1.97146i) q^{4} +(-4.50002 + 0.326846i) q^{6} +2.97769 q^{7} +(2.43799 - 1.43395i) q^{8} +(-2.21828 - 6.82716i) q^{9} +(0.263378 + 0.0855768i) q^{11} +(4.45709 + 4.56600i) q^{12} +(-4.19500 + 1.36304i) q^{13} +(-2.71551 - 3.21858i) q^{14} +(-3.77328 - 1.32753i) 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} +(-0.147688 - 0.362728i) 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} +(-1.00255 + 5.87038i) 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} +(-7.03655 - 1.73431i) q^{34} +(14.2063 - 2.07461i) q^{36} +(3.84202 - 1.24835i) q^{37} +(-0.474948 + 1.92699i) q^{38} +(-4.34861 + 13.3836i) q^{39} +(-1.97884 - 6.09023i) q^{41} +(-13.3996 + 0.973245i) q^{42} -10.9079i q^{43} +(-0.257387 + 0.490426i) q^{44} +(0.423062 - 0.172254i) q^{46} +(2.30062 + 1.67150i) q^{47} +(-10.5023 + 7.24963i) q^{48} +1.86662 q^{49} -16.3491i q^{51} +(-1.27476 - 8.72919i) q^{52} +(-0.274854 + 0.378304i) q^{53} +(7.10942 + 17.4610i) q^{54} +(7.25957 - 4.26984i) q^{56} -4.47727 q^{57} +(-6.22060 + 0.451815i) q^{58} +(-5.09147 + 1.65432i) q^{59} +(1.96419 + 0.638204i) q^{61} +(5.17578 + 1.27568i) q^{62} +(-6.60534 - 20.3291i) q^{63} +(3.88759 - 6.99190i) q^{64} +(-1.21318 - 0.299013i) 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} +(-15.1979 - 13.4636i) 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} +(18.4321 - 7.50482i) 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} +(13.2718 + 13.5961i) q^{84} +(-11.7903 + 9.94745i) q^{86} +(-4.34795 - 13.3816i) q^{87} +(0.764826 - 0.169035i) q^{88} +(-0.992059 + 3.05324i) q^{89} +(-12.4914 + 4.05871i) q^{91} +(-0.572001 - 0.300200i) q^{92} +12.0257i q^{93} +(-0.291332 - 4.01107i) q^{94} +(17.4137 + 4.74064i) q^{96} +(13.3433 + 9.69449i) q^{97} +(-1.70227 - 2.01763i) 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 $

$2$	−0.911952	−	1.08090i	−0.644847	−	0.764312i
$2$	−0.911952	−	1.08090i	−0.644847	−	0.764312i
$3$	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	$-0.172612\pi$
$4$	−0.336688	+	1.97146i	−0.168344	+	0.985728i
$5$		0			0
$5$		0			0
$6$	−4.50002	+	0.326846i	−1.83712	+	0.133434i
$7$	2.97769			1.12546			0.562730	−	0.826641i	$-0.309751\pi$
$7$	2.97769			1.12546			0.562730	+	0.826641i	$0.309751\pi$
$8$	2.43799	−	1.43395i	0.861960	−	0.506977i
$9$	−2.21828	−	6.82716i	−0.739426	−	2.27572i
$10$		0			0
$11$	0.263378	+	0.0855768i	0.0794116	+	0.0258024i	0.348453	−	0.937326i	$-0.386707\pi$
$11$	0.263378	+	0.0855768i	0.0794116	+	0.0258024i	−0.269042	+	0.963129i	$0.586707\pi$
$12$	4.45709	+	4.56600i	1.28665	+	1.31809i
$13$	−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	$0.609506\pi$
$14$	−2.71551	−	3.21858i	−0.725750	−	0.860202i
$15$		0			0
$16$	−3.77328	−	1.32753i	−0.943320	−	0.331883i
$17$	4.14580	−	3.01210i	1.00551	−	0.730542i	0.0422436	−	0.999107i	$-0.486549\pi$
$17$	4.14580	−	3.01210i	1.00551	−	0.730542i	0.963262	+	0.268565i	$0.0865495\pi$
$18$	−5.35651	+	8.62377i	−1.26254	+	2.03264i
$19$	−0.824879	−	1.13535i	−0.189240	−	0.260467i	0.703846	−	0.710353i	$-0.251465\pi$
$19$	−0.824879	−	1.13535i	−0.189240	−	0.260467i	−0.893086	+	0.449886i	$0.851465\pi$
$20$		0			0
$21$	5.58392	−	7.68561i	1.21851	−	1.67714i
$22$	−0.147688	−	0.362728i	−0.0314873	−	0.0773338i
$23$	−0.0998113	+	0.307187i	−0.0208121	+	0.0640530i	−0.960923	−	0.276815i	$-0.910721\pi$
$23$	−0.0998113	+	0.307187i	−0.0208121	+	0.0640530i	0.940111	+	0.340868i	$0.110721\pi$
$24$	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
$28$	−1.00255	+	5.87038i	−0.189465	+	1.10940i
$29$	2.59226	−	3.56794i	0.481371	−	0.662550i	−0.497397	−	0.867523i	$-0.665711\pi$
$29$	2.59226	−	3.56794i	0.481371	−	0.662550i	0.978768	+	0.204973i	$0.0657107\pi$
$30$		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
$34$	−7.03655	−	1.73431i	−1.20676	−	0.297431i
$35$		0			0
$36$	14.2063	−	2.07461i	2.36772	−	0.345769i
$37$	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	$0.292255\pi$
$38$	−0.474948	+	1.92699i	−0.0770467	+	0.312600i
$39$	−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	$-0.266682\pi$
$42$	−13.3996	+	0.973245i	−2.06761	+	0.150175i
$43$		−	10.9079i		−	1.66343i	−0.555199	−	0.831717i	$-0.687358\pi$
$43$		−	10.9079i		−	1.66343i	0.555199	−	0.831717i	$-0.312642\pi$
$44$	−0.257387	+	0.490426i	−0.0388026	+	0.0739345i
$45$		0			0
$46$	0.423062	−	0.172254i	0.0623771	−	0.0253975i
$47$	2.30062	+	1.67150i	0.335580	+	0.243813i	0.742795	−	0.669519i	$-0.233500\pi$
$47$	2.30062	+	1.67150i	0.335580	+	0.243813i	−0.407214	+	0.913333i	$0.633500\pi$
$48$	−10.5023	+	7.24963i	−1.51588	+	1.04639i
$49$	1.86662			0.266660
$50$		0			0
$51$		−	16.3491i		−	2.28933i
$52$	−1.27476	−	8.72919i	−0.176778	−	1.21052i
$53$	−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	$0.210224\pi$
$54$	7.10942	+	17.4610i	0.967470	+	2.37614i
$55$		0			0
$56$	7.25957	−	4.26984i	0.970101	−	0.570582i
$57$	−4.47727			−0.593029
$58$	−6.22060	+	0.451815i	−0.816805	+	0.0593263i
$59$	−5.09147	+	1.65432i	−0.662853	+	0.215374i	−0.621073	−	0.783753i	$-0.713303\pi$
$59$	−5.09147	+	1.65432i	−0.662853	+	0.215374i	−0.0417804	+	0.999127i	$0.513303\pi$
$60$		0			0
$61$	1.96419	+	0.638204i	0.251489	+	0.0817137i	0.432049	−	0.901850i	$-0.357791\pi$
$61$	1.96419	+	0.638204i	0.251489	+	0.0817137i	−0.180560	+	0.983564i	$0.557791\pi$
$62$	5.17578	+	1.27568i	0.657325	+	0.162012i
$63$	−6.60534	−	20.3291i	−0.832194	−	2.56123i
$64$	3.88759	−	6.99190i	0.485949	−	0.873987i
$65$		0			0
$66$	−1.21318	−	0.299013i	−0.149332	−	0.0368060i
$67$	−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	$0.505767\pi$
$72$	−15.1979	−	13.4636i	−1.79109	−	1.58671i
$73$	−2.77576	+	8.54291i	−0.324878	+	0.999872i	0.646618	+	0.762814i	$0.276183\pi$
$73$	−2.77576	+	8.54291i	−0.324878	+	0.999872i	−0.971496	+	0.237057i	$0.923817\pi$
$74$	−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
$78$	18.4321	−	7.50482i	2.08702	−	0.849754i
$79$	−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	$0.540053\pi$
$84$	13.2718	+	13.5961i	1.44807	+	1.48346i
$85$		0			0
$86$	−11.7903	+	9.94745i	−1.27138	+	1.07266i
$87$	−4.34795	−	13.3816i	−0.466149	−	1.43466i
$88$	0.764826	−	0.169035i	0.0815308	−	0.0180192i
$89$	−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
$92$	−0.572001	−	0.300200i	−0.0596353	−	0.0312980i
$93$			12.0257i			1.24700i
$94$	−0.291332	−	4.01107i	−0.0300486	−	0.413710i
$95$		0			0
$96$	17.4137	+	4.74064i	1.77728	+	0.483840i
$97$	13.3433	+	9.69449i	1.35481	+	0.984327i	0.998756	+	0.0498611i	$0.0158779\pi$
$97$	13.3433	+	9.69449i	1.35481	+	0.984327i	0.356053	+	0.934466i	$0.384122\pi$
$98$	−1.70227	−	2.01763i	−0.171955	−	0.203811i
$99$		−	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	$0.578770\pi$
$102$	−17.6717	+	14.9096i	−1.74976	+	1.47627i
$103$	5.71814	+	4.15447i	0.563425	+	0.409352i	0.832711	−	0.553708i	$-0.186788\pi$
$103$	5.71814	+	4.15447i	0.563425	+	0.409352i	−0.269286	+	0.963060i	$0.586788\pi$
$104$	−8.27286	+	9.33849i	−0.811220	+	0.915714i
$105$		0			0
$106$	0.659563	−	0.0479054i	0.0640624	−	0.00465299i
$107$			11.2557i			1.08813i	0.839044	+	0.544064i	$0.183115\pi$
$107$			11.2557i			1.08813i	−0.839044	+	0.544064i	$0.816885\pi$
$108$	12.3901	−	23.6081i	1.19224	−	2.27169i
$109$	9.07913	−	2.94999i	0.869623	−	0.282558i	0.159981	−	0.987120i	$-0.448857\pi$
$109$	9.07913	−	2.94999i	0.869623	−	0.282558i	0.709642	+	0.704563i	$0.248857\pi$
$110$		0			0
$111$	3.98270	−	12.2575i	0.378021	−	1.16343i
$112$	−11.2357	−	3.95298i	−1.06167	−	0.373521i
$113$	3.26576	+	10.0510i	0.307217	+	0.945517i	0.978841	+	0.204624i	$0.0655972\pi$
$113$	3.26576	+	10.0510i	0.307217	+	0.945517i	−0.671624	+	0.740892i	$0.734403\pi$
$114$	4.08305	+	4.83948i	0.382413	+	0.453259i
$115$		0			0
$116$	6.16125	+	6.31181i	0.572058	+	0.586037i
$117$	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
$122$	−1.10141	−	2.70511i	−0.0997172	−	0.244909i
$123$	−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	$-0.919180\pi$
$127$	−0.419412	+	1.29082i	−0.0372168	+	0.114542i	0.930722	+	0.365727i	$0.119180\pi$
$128$	−11.1028	+	2.17417i	−0.981361	+	0.192171i
$129$	−28.1540	−	20.4550i	−2.47882	−	1.80097i
$130$		0			0
$131$	0.471129	+	0.648453i	0.0411627	+	0.0566556i	0.829102	−	0.559097i	$-0.188852\pi$
$131$	0.471129	+	0.648453i	0.0411627	+	0.0566556i	−0.787940	+	0.615753i	$0.788852\pi$
$132$	0.783156	+	1.58401i	0.0681650	+	0.137870i
$133$	−2.45623	−	3.38071i	−0.212982	−	0.293145i
$134$	−0.523299	+	2.12317i	−0.0452061	+	0.183414i
$135$		0			0
$136$	5.78824	−	13.2883i	0.496337	−	1.13947i
$137$	−2.23985	−	6.89354i	−0.191363	−	0.588955i	−1.00000		0.000646705i	$-0.999794\pi$
$137$	−2.23985	−	6.89354i	−0.191363	−	0.588955i	0.808637	−	0.588308i	$-0.200206\pi$
$138$	0.348750	−	1.41497i	0.0296875	−	0.120450i
$139$	0.417329	+	0.135598i	0.0353973	+	0.0115013i	0.326662	−	0.945141i	$-0.394076\pi$
$139$	0.417329	+	0.135598i	0.0353973	+	0.0115013i	−0.291265	+	0.956642i	$0.594076\pi$
$140$		0			0
$141$	8.62851	−	2.80357i	0.726652	−	0.236103i
$142$	−0.989327	−	13.6211i	−0.0830225	−	1.14305i
$143$	−1.22152			−0.102148
$144$	−0.693091	+	28.7056i	−0.0577576	+	2.39214i
$145$		0			0
$146$	11.7654	−	4.79040i	0.973710	−	0.396456i
$147$	3.50039	−	4.81787i	0.288707	−	0.397372i
$148$	1.16750	+	7.99469i	0.0959680	+	0.657159i
$149$		−	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	$0.693914\pi$
$152$	−3.63908	−	1.58514i	−0.295168	−	0.128572i
$153$	−29.7606	−	21.6224i	−2.40600	−	1.74806i
$154$	−0.439770	−	1.08009i	−0.0354377	−	0.0870361i
$155$		0			0
$156$	−24.9211	−	13.0792i	−1.99529	−	1.04717i
$157$		−	9.56521i		−	0.763387i	−0.924289	−	0.381693i	$-0.875341\pi$
$157$		−	9.56521i		−	0.763387i	0.924289	−	0.381693i	$-0.124659\pi$
$158$	0.569154	+	7.83613i	0.0452795	+	0.623409i
$159$	0.461007	+	1.41883i	0.0365603	+	0.112521i
$160$		0			0
$161$	−0.297207	+	0.914708i	−0.0234232	+	0.0720891i
$162$	28.8291	+	7.10554i	2.26503	+	0.558264i
$163$	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	$0.330994\pi$
$164$	12.6729	−	1.85068i	0.989586	−	0.144514i
$165$		0			0
$166$	4.49453	−	18.2355i	0.348843	−	1.41535i
$167$	9.73651	−	7.07399i	0.753433	−	0.547401i	−0.143456	−	0.989657i	$-0.545821\pi$
$167$	9.73651	−	7.07399i	0.753433	−	0.547401i	0.896889	+	0.442255i	$0.145821\pi$
$168$	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
$172$	21.5044	+	3.67255i	1.63969	+	0.280030i
$173$	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
$178$	4.20496	−	1.71209i	0.315175	−	0.128327i
$179$	12.5073	−	17.2148i	0.934841	−	1.28670i	−0.0231007	−	0.999733i	$-0.507354\pi$
$179$	12.5073	−	17.2148i	0.934841	−	1.28670i	0.957941	−	0.286964i	$-0.0926462\pi$
$180$		0			0
$181$	4.82937	+	6.64706i	0.358964	+	0.494072i	0.949860	−	0.312676i	$-0.101225\pi$
$181$	4.82937	+	6.64706i	0.358964	+	0.494072i	−0.590896	+	0.806748i	$0.701225\pi$
$182$	15.7786	+	9.80062i	1.16959	+	0.726470i
$183$	5.33061	−	3.87291i	0.394050	−	0.286294i
$184$	0.197152	+	0.892044i	0.0145342	+	0.0657624i
$185$		0			0
$186$	12.9985	−	10.9668i	0.953099	−	0.804127i
$187$	1.34968	−	0.438538i	0.0986985	−	0.0320691i
$188$	−4.06988	+	3.97280i	−0.296827	+	0.289746i
$189$	−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	$0.940926\pi$
$192$	−10.7563	−	23.1457i	−0.776271	−	1.67040i
$193$	−13.3961			−0.964273			−0.482137	−	0.876096i	$-0.660139\pi$
$193$	−13.3961			−0.964273			−0.482137	+	0.876096i	$0.660139\pi$
$194$	−1.68969	−	23.2637i	−0.121313	−	1.67024i
$195$		0			0
$196$	−0.628469	+	3.67996i	−0.0448907	+	0.262854i
$197$	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	$0.141450\pi$
$198$	−2.14878	+	1.81292i	−0.152707	+	0.128839i
$199$	−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
$202$	21.0640	−	17.7716i	1.48206	−	1.25041i
$203$	7.71894	−	10.6242i	0.541763	−	0.745673i
$204$	32.2315	+	5.50454i	2.25665	+	0.385395i
$205$		0			0
$206$	−0.724099	−	9.96941i	−0.0504504	−	0.694601i
$207$	2.31863			0.161156
$208$	17.6384	+	0.425876i	1.22300	+	0.0295292i
$209$	−0.120096	−	0.369617i	−0.00830719	−	0.0255669i
$210$		0			0
$211$	−7.25107	−	2.35602i	−0.499184	−	0.162195i	0.0485936	−	0.998819i	$-0.484526\pi$
$211$	−7.25107	−	2.35602i	−0.499184	−	0.162195i	−0.547778	+	0.836624i	$0.684526\pi$
$212$	−0.653270	−	0.669234i	−0.0448668	−	0.0459632i
$213$	29.3013	−	9.52057i	2.00769	−	0.652339i
$214$	12.1663	−	10.2646i	0.831668	−	0.701676i
$215$		0			0
$216$	−36.8172	+	8.13701i	−2.50509	+	0.553653i
$217$	−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
$222$	−16.8812	+	6.87334i	−1.13299	+	0.461309i
$223$	5.96185	−	18.3487i	0.399235	−	1.22872i	−0.526379	−	0.850250i	$-0.676451\pi$
$223$	5.96185	−	18.3487i	0.399235	−	1.22872i	0.925614	−	0.378469i	$-0.123549\pi$
$224$	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	$0.305099\pi$
$228$	1.50744	−	8.82674i	0.0998330	−	0.584565i
$229$	−15.5176	+	21.3582i	−1.02544	+	1.41139i	−0.117113	+	0.993119i	$0.537364\pi$
$229$	−15.5176	+	21.3582i	−1.02544	+	1.41139i	−0.908322	+	0.418272i	$0.862636\pi$
$230$		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	$-0.408917\pi$
$233$	19.5668	−	14.2161i	1.28186	−	0.931328i	0.999608	+	0.0280108i	$0.00891727\pi$
$234$	10.7160	−	43.4779i	0.700529	−	2.84224i
$235$		0			0
$236$	−1.54718	−	10.5946i	−0.100713	−	0.689650i
$237$	−16.8569	+	5.47713i	−1.09497	+	0.355778i
$238$	−20.9527	−	5.16422i	−1.35816	−	0.334747i
$239$	−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	$0.732389\pi$
$242$	1.11907	+	15.4073i	0.0719362	+	0.990419i
$243$			26.9901i			1.73141i
$244$	−1.91951	+	3.65744i	−0.122884	+	0.234144i
$245$		0			0
$246$	10.8954	+	26.7594i	0.694663	+	1.70612i
$247$	5.00790	+	3.63845i	0.318645	+	0.231509i
$248$	−4.25758	+	9.77433i	−0.270356	+	0.620670i
$249$	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	$0.973930\pi$
$252$	42.3019	−	6.17755i	2.66477	−	0.389149i
$253$	−0.0525763	+	0.0723650i	−0.00330544	+	0.00454955i
$254$	1.77773	−	0.723821i	0.111545	−	0.0454166i
$255$		0			0
$256$	12.4753	+	10.0183i	0.779707	+	0.626145i
$257$	−1.98944			−0.124098			−0.0620490	−	0.998073i	$-0.519764\pi$
$257$	−1.98944			−0.124098			−0.0620490	+	0.998073i	$0.519764\pi$
$258$	3.56519	+	49.0856i	0.221959	+	3.05594i
$259$	11.4403	−	3.71719i	0.710868	−	0.230975i
$260$		0			0
$261$	−30.1092	−	9.78308i	−1.86371	−	0.605558i
$262$	0.271266	−	1.10060i	0.0167589	−	0.0679954i
$263$	4.81097	+	14.8066i	0.296657	+	0.913017i	0.982660	+	0.185418i	$0.0593638\pi$
$263$	4.81097	+	14.8066i	0.296657	+	0.913017i	−0.686003	+	0.727599i	$0.740636\pi$
$264$	0.997954	−	2.29105i	0.0614198	−	0.141005i
$265$		0			0
$266$	−1.41425	+	5.73798i	−0.0867130	+	0.351818i
$267$	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	$-0.187172\pi$
$269$	0.776787	+	1.06916i	0.0473616	+	0.0651876i	−0.784679	+	0.619902i	$0.787172\pi$
$270$		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	$0.555018\pi$
$272$	−19.6420	+	5.86182i	−1.19097	+	0.355425i
$273$	−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	$0.725654\pi$
$278$	−0.234015	−	0.574749i	−0.0140353	−	0.0344712i
$279$	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	$0.922189\pi$
$284$	−13.8208	+	13.4911i	−0.820113	+	0.800550i
$285$		0			0
$286$	1.11397	+	1.32034i	0.0658702	+	0.0780733i
$287$	−5.89236	−	18.1348i	−0.347815	−	1.07046i
$288$	31.6600	−	25.4290i	1.86558	−	1.49842i
$289$	2.86164	−	8.80721i	0.168332	−	0.518071i
$290$		0			0
$291$	50.0443	−	16.2604i	2.93365	−	0.953200i
$292$	−15.9074	−	8.34859i	−0.930910	−	0.488564i
$293$		−	9.19701i		−	0.537295i	−0.963239	−	0.268647i	$-0.913423\pi$
$293$		−	9.19701i		−	0.537295i	0.963239	−	0.268647i	$-0.0865766\pi$
$294$	−8.39983	+	0.610097i	−0.489888	+	0.0355816i
$295$		0			0
$296$	7.57675	−	8.55272i	0.440390	−	0.497117i
$297$	−2.98671	−	2.16997i	−0.173307	−	0.125915i
$298$	−1.78940	+	1.50971i	−0.103657	+	0.0874551i
$299$		−	1.42470i		−	0.0823925i
$300$		0			0
$301$		−	32.4802i		−	1.87213i
$302$	12.8247	+	15.2006i	0.737977	+	0.874695i
$303$	50.2984	+	36.5440i	2.88957	+	2.09940i
$304$	1.60529	+	5.37904i	0.0920695	+	0.308509i
$305$		0			0
$306$	3.76865	+	51.8868i	0.215439	+	2.96617i
$307$		−	24.3699i		−	1.39087i	−0.718591	−	0.695433i	$-0.755213\pi$
$307$		−	24.3699i		−	1.39087i	0.718591	−	0.695433i	$-0.244787\pi$
$308$	−0.766419	+	1.46034i	−0.0436708	+	0.0832104i
$309$	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	$-0.151731\pi$
$312$	8.58956	+	38.8649i	0.486288	+	2.20029i
$313$	−3.37148	−	10.3764i	−0.190567	−	0.586506i	0.809432	−	0.587213i	$-0.199775\pi$
$313$	−3.37148	−	10.3764i	−0.190567	−	0.586506i	−1.00000		0.000706882i	$0.999775\pi$
$314$	−10.3390	+	8.72301i	−0.583465	+	0.492268i
$315$		0			0
$316$	7.95102	−	7.76137i	0.447280	−	0.436611i
$317$	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
$322$	1.25975	−	0.512919i	0.0702029	−	0.0285839i
$323$	−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
$328$	−13.5575	−	12.0104i	−0.748585	−	0.663163i
$329$	6.85053	+	4.97720i	0.377682	+	0.274402i
$330$		0			0
$331$	4.98309	+	6.85864i	0.273895	+	0.376985i	0.923700	−	0.383117i	$-0.125149\pi$
$331$	4.98309	+	6.85864i	0.273895	+	0.376985i	−0.649805	+	0.760101i	$0.725149\pi$
$332$	−23.8096	+	11.7718i	−1.30672	+	0.646061i
$333$	−17.0453	−	23.4609i	−0.934079	−	1.28565i
$334$	−16.5255	−	4.07305i	−0.904235	−	0.222868i
$335$		0			0
$336$	−31.2726	+	21.5871i	−1.70606	+	1.17767i
$337$	5.19430	+	15.9864i	0.282951	+	0.870835i	0.987005	+	0.160688i	$0.0513713\pi$
$337$	5.19430	+	15.9864i	0.282951	+	0.870835i	−0.704054	+	0.710147i	$0.748629\pi$
$338$	−8.86479	−	2.18491i	−0.482181	−	0.118844i
$339$	32.0664	+	10.4190i	1.74161	+	0.565883i
$340$		0			0
$341$	−0.992767	+	0.322570i	−0.0537613	+	0.0174681i
$342$	14.2095	−	1.03206i	0.768359	−	0.0558076i
$343$	−15.2856			−0.825345
$344$	−15.6413	−	26.5933i	−0.843323	−	1.43381i
$345$		0			0
$346$	−9.27264	−	22.7739i	−0.498500	−	1.22433i
$347$	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	$0.0430536\pi$
$348$	27.8451	−	4.06636i	1.49266	−	0.217980i
$349$			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
$352$	0.0757370	+	1.56473i	0.00403679	+	0.0834006i
$353$	22.9889	+	16.7024i	1.22358	+	0.888980i	0.996392	−	0.0848720i	$-0.0270481\pi$
$353$	22.9889	+	16.7024i	1.22358	+	0.888980i	0.227184	+	0.973852i	$0.427048\pi$
$354$	22.3710	−	9.10860i	1.18901	−	0.484117i
$355$		0			0
$356$	−5.68532	−	2.98379i	−0.301321	−	0.158141i
$357$		−	48.6824i		−	2.57655i
$358$	−30.0136	+	2.17995i	−1.58627	+	0.115214i
$359$	−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
$362$	2.78065	−	11.2819i	0.146148	−	0.592961i
$363$	−33.1438	+	10.7691i	−1.73960	+	0.565230i
$364$	−3.79585	−	25.9928i	−0.198956	−	1.36239i
$365$		0			0
$366$	−9.04749	−	2.22994i	−0.472920	−	0.116561i
$367$	−17.2512	+	12.5338i	−0.900507	+	0.654257i	−0.938596	−	0.345018i	$-0.887873\pi$
$367$	−17.2512	+	12.5338i	−0.900507	+	0.654257i	0.0380891	+	0.999274i	$0.487873\pi$
$368$	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
$372$	−23.7081	−	4.04890i	−1.22921	−	0.209926i
$373$	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
$378$	21.1696	+	51.9933i	1.08885	+	2.67425i
$379$	10.7274	−	14.7650i	0.551030	−	0.758428i	−0.439121	−	0.898428i	$-0.644710\pi$
$379$	10.7274	−	14.7650i	0.551030	−	0.758428i	0.990152	+	0.140000i	$0.0447102\pi$
$380$		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	$0.671032\pi$
$383$	−29.1018	+	21.1437i	−1.48703	+	1.08039i	−0.975204	+	0.221307i	$0.928968\pi$
$384$	−15.2090	+	32.7343i	−0.776130	+	1.67047i
$385$		0			0
$386$	12.2166	+	14.4799i	0.621809	+	0.737005i
$387$	−74.4697	+	24.1967i	−3.78551	+	1.22999i
$388$	−23.6048	+	23.0418i	−1.19835	+	1.16977i
$389$	2.67533	+	0.869269i	0.135645	+	0.0440737i	0.376053	−	0.926598i	$-0.377281\pi$
$389$	2.67533	+	0.869269i	0.135645	+	0.0440737i	−0.240408	+	0.970672i	$0.577281\pi$
$390$		0			0
$391$	0.511482	+	1.57418i	0.0258668	+	0.0796097i
$392$	4.55080	−	2.67663i	0.229850	−	0.135190i
$393$	2.55719			0.128993
$394$	−7.24201	+	0.526002i	−0.364847	+	0.0264996i
$395$		0			0
$396$	3.91917	+	0.669323i	0.196946	+	0.0336347i
$397$	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	$0.136703\pi$
$398$	11.4497	+	13.5709i	0.573922	+	0.680246i
$399$	−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	$0.553884\pi$
$402$	4.49872	+	5.33215i	0.224376	+	0.265943i
$403$	9.77264	−	13.4509i	0.486810	−	0.670037i
$404$	−38.4187	−	6.56120i	−1.91140	−	0.326432i
$405$		0			0
$406$	−18.5230	+	1.34536i	−0.919281	+	0.0667693i
$407$	1.11874			0.0554537
$408$	−23.4437	−	39.8589i	−1.16064	−	1.97331i
$409$	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
$412$	−10.1156	+	9.87430i	−0.498359	+	0.486472i
$413$	−15.1608	+	4.92605i	−0.746015	+	0.242395i
$414$	−2.11447	−	2.50620i	−0.103921	−	0.123173i
$415$		0			0
$416$	−15.6251	−	19.4537i	−0.766081	−	0.953798i
$417$	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	$-0.995676\pi$
$419$	−14.4072	−	19.8299i	−0.703839	−	0.968752i	0.296068	−	0.955167i	$-0.404324\pi$
$420$		0			0
$421$	−15.9444	+	21.9456i	−0.777084	+	1.06956i	0.218514	+	0.975834i	$0.429879\pi$
$421$	−15.9444	+	21.9456i	−0.777084	+	1.06956i	−0.995598	+	0.0937303i	$0.970121\pi$
$422$	4.06601	+	9.98625i	0.197930	+	0.486123i
$423$	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
$428$	−22.1901	−	3.78966i	−1.07260	−	0.183180i
$429$	−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	0.151150	−	0.988511i	$-0.451702\pi$
$433$	23.6800	−	17.2045i	1.13799	−	0.826797i	0.986838	+	0.161714i	$0.0517022\pi$
$434$	15.4119	+	3.79858i	0.739793	+	0.182338i
$435$		0			0
$436$	2.75894	+	18.8923i	0.132129	+	0.904779i
$437$	0.431097	−	0.140072i	0.0206222	−	0.00670055i
$438$	9.69875	−	39.3505i	0.463424	−	1.88024i
$439$	−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
$442$	31.8823	−	2.31568i	1.51649	−	0.110146i
$443$			1.10768i			0.0526274i	0.999654	+	0.0263137i	$0.00837688\pi$
$443$			1.10768i			0.0526274i	−0.999654	+	0.0263137i	$0.991623\pi$
$444$	22.8242	+	11.9787i	1.08319	+	0.568483i
$445$		0			0
$446$	−25.2700	+	10.2890i	−1.19657	+	0.487196i
$447$	−4.27288	−	3.10443i	−0.202100	−	0.146834i
$448$	11.5760	−	20.8197i	0.546916	−	0.983637i
$449$	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
$452$	−20.9146	+	3.05426i	−0.983741	+	0.143660i
$453$	−26.3715	+	36.2973i	−1.23904	+	1.70539i
$454$	−12.8479	−	31.5549i	−0.602983	−	1.48095i
$455$		0			0
$456$	−10.9155	+	6.42017i	−0.511167	+	0.300652i
$457$	−36.8695			−1.72468			−0.862341	−	0.506328i	$-0.831003\pi$
$457$	−36.8695			−1.72468			−0.862341	+	0.506328i	$0.831003\pi$
$458$	37.2374	−	2.70463i	1.73999	−	0.126379i
$459$	−64.9710	+	21.1103i	−3.03258	+	0.985347i
$460$		0			0
$461$	32.4405	+	10.5406i	1.51091	+	0.490923i	0.943177	−	0.332291i	$-0.107822\pi$
$461$	32.4405	+	10.5406i	1.51091	+	0.490923i	0.567730	+	0.823215i	$0.307822\pi$
$462$	−3.61246	−	0.890367i	−0.168067	−	0.0414236i
$463$	−12.9887	−	39.9752i	−0.603637	−	1.85780i	−0.505902	−	0.862591i	$-0.668840\pi$
$463$	−12.9887	−	39.9752i	−0.603637	−	1.85780i	−0.0977353	−	0.995212i	$-0.531160\pi$
$464$	−14.5179	+	10.0215i	−0.673976	+	0.465238i
$465$		0			0
$466$	−33.2102	−	8.18534i	−1.53843	−	0.379179i
$467$	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
$472$	−10.0408	+	11.3341i	−0.462163	+	0.521695i
$473$	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
$478$	20.1877	−	8.21964i	0.923364	−	0.375957i
$479$	−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
$484$	15.6332	−	15.2603i	0.710601	−	0.693651i
$485$		0			0
$486$	29.1735	−	24.6136i	1.32334	−	1.11650i
$487$	6.75894	+	20.8019i	0.306277	+	0.942622i	0.979198	+	0.202908i	$0.0650393\pi$
$487$	6.75894	+	20.8019i	0.306277	+	0.942622i	−0.672921	+	0.739714i	$0.734961\pi$
$488$	5.70383	−	1.26061i	0.258200	−	0.0570651i
$489$	5.41477	−	16.6649i	0.244864	−	0.753615i
$490$		0			0
$491$	−3.07965	+	1.00064i	−0.138983	+	0.0451582i	−0.377682	−	0.925935i	$-0.623279\pi$
$491$	−3.07965	+	1.00064i	−0.138983	+	0.0451582i	0.238700	+	0.971093i	$0.423279\pi$
$492$	18.9882	−	36.1801i	0.856053	−	1.63112i
$493$		−	22.6001i		−	1.01786i
$494$	−0.634160	−	8.73112i	−0.0285322	−	0.392832i
$495$		0			0
$496$	14.4478	−	4.31170i	0.648724	−	0.193601i
$497$	23.2635	+	16.9019i	1.04351	+	0.758155i
$498$	−38.6388	−	45.7970i	−1.73144	−	2.05221i
$499$			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
$502$	2.80195	−	2.36400i	0.125057	−	0.105510i
$503$	−10.4440	−	7.58802i	−0.465676	−	0.338333i	0.330078	−	0.943954i	$-0.392925\pi$
$503$	−10.4440	−	7.58802i	−0.465676	−	0.338333i	−0.795754	+	0.605621i	$0.792925\pi$
$504$	−45.2546	−	40.0905i	−2.01580	−	1.78577i
$505$		0			0
$506$	0.126166	−	0.00916373i	0.00560878	−	0.000407377i
$507$		−	20.5969i		−	0.914740i
$508$	−2.40358	−	1.26146i	−0.106642	−	0.0559681i
$509$	8.87419	−	2.88340i	0.393342	−	0.127804i	−0.105667	−	0.994402i	$-0.533698\pi$
$509$	8.87419	−	2.88340i	0.393342	−	0.127804i	0.499008	+	0.866597i	$0.333698\pi$
$510$		0			0
$511$	−8.26534	+	25.4381i	−0.365637	+	1.12532i
$512$	−0.548087	−	22.6208i	−0.0242223	−	0.999707i
$513$	5.78117	+	17.7926i	0.255245	+	0.785563i
$514$	1.81428	+	2.15039i	0.0800243	+	0.0948495i
$515$		0			0
$516$	49.8054	−	48.6173i	2.19256	−	2.14026i
$517$	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	$0.830032\pi$
$522$	16.8836	+	41.4668i	0.738977	+	1.81495i
$523$	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
$528$	−3.38648	+	1.01064i	−0.147378	+	0.0439825i
$529$	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
$534$	3.46634	−	14.0639i	0.150003	−	0.608604i
$535$		0			0
$536$	−4.00954	−	1.74651i	−0.173186	−	0.0754376i
$537$	−20.9783	−	64.5645i	−0.905279	−	2.78616i
$538$	0.447258	−	1.81465i	0.0192827	−	0.0782350i
$539$	0.491627	+	0.159739i	0.0211759	+	0.00688046i
$540$		0			0
$541$	1.23623	−	0.401675i	0.0531496	−	0.0172694i	−0.282322	−	0.959320i	$-0.591104\pi$
$541$	1.23623	−	0.401675i	0.0531496	−	0.0172694i	0.335471	+	0.942050i	$0.391104\pi$
$542$	−1.48374	−	20.4281i	−0.0637320	−	0.877464i
$543$	26.2128			1.12490
$544$	24.2485	+	15.8853i	1.03965	+	0.681076i
$545$		0			0
$546$	54.8850	−	22.3470i	2.34886	−	0.956364i
$547$	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	$0.184981\pi$
$548$	14.3444	−	2.09479i	0.612764	−	0.0894848i
$549$		−	14.8256i		−	0.632739i
$550$		0			0
$551$	−6.18915			−0.263667
$552$	2.67214	+	1.16395i	0.113734	+	0.0495410i
$553$	−13.3834	−	9.72359i	−0.569119	−	0.413489i
$554$	6.82700	+	16.7673i	0.290051	+	0.712376i
$555$		0			0
$556$	−0.407836	+	0.777091i	−0.0172961	+	0.0329560i
$557$			22.2912i			0.944509i	0.881462	+	0.472255i	$0.156560\pi$
$557$			22.2912i			0.944509i	−0.881462	+	0.472255i	$0.843440\pi$
$558$	−2.77206	−	38.1657i	−0.117350	−	1.61568i
$559$	14.8679	+	45.7586i	0.628844	+	1.93538i
$560$		0			0
$561$	1.39910	−	4.30599i	0.0590701	−	0.181799i
$562$	4.32534	+	1.06607i	0.182453	+	0.0449695i
$563$	−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	$0.547378\pi$
$564$	2.62200	+	17.9547i	0.110406	+	0.756028i
$565$		0			0
$566$	−4.26444	+	17.3020i	−0.179248	+	0.727258i
$567$	−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	−0.760794	−	0.648994i	$-0.775190\pi$
$571$	2.18726	−	3.01051i	0.0915340	−	0.125986i	0.852328	+	0.523008i	$0.175190\pi$
$572$	0.411271	−	2.40817i	0.0171961	−	0.100691i
$573$	−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	$-0.730447\pi$
$577$	7.53910	−	23.2030i	0.313857	−	0.965952i	0.976222	−	0.216771i	$-0.0695526\pi$
$578$	−12.1294	+	4.93861i	−0.504516	+	0.205419i
$579$	−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
$584$	5.48280	+	24.8078i	0.226880	+	1.02655i
$585$		0			0
$586$	−9.94104	+	8.38722i	−0.410661	+	0.346473i
$587$	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	$0.308352\pi$
$588$	8.31969	+	8.52299i	0.343098	+	0.351482i
$589$	5.03089	+	1.63464i	0.207294	+	0.0673540i
$590$		0			0
$591$	−5.06187	−	15.5788i	−0.208217	−	0.640827i
$592$	−16.1543	−	0.390041i	−0.663936	−	0.0160306i
$593$	18.8934			0.775861			0.387930	−	0.921689i	$-0.373190\pi$
$593$	18.8934			0.775861			0.387930	+	0.921689i	$0.373190\pi$
$594$	0.378213	+	5.20725i	0.0155183	+	0.213656i
$595$		0			0
$596$	3.26369	+	0.557378i	0.133686	+	0.0228311i
$597$	−23.5441	+	32.4057i	−0.963598	+	1.32628i
$598$	−1.53996	+	1.29926i	−0.0629735	+	0.0531306i
$599$	−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	$0.412177\pi$
$602$	−35.1079	+	29.6204i	−1.43089	+	1.20724i
$603$	−6.52420	+	8.97979i	−0.265686	+	0.365685i
$604$	4.73481	−	27.7244i	0.192657	−	1.12809i
$605$		0			0
$606$	−6.36939	−	87.6939i	−0.258739	−	3.56232i
$607$	22.7175			0.922076			0.461038	−	0.887380i	$-0.347477\pi$
$607$	22.7175			0.922076			0.461038	+	0.887380i	$0.347477\pi$
$608$	4.35026	−	6.64058i	0.176426	−	0.269311i
$609$	−12.9468	−	39.8462i	−0.524632	−	1.61465i
$610$		0			0
$611$	−11.9294	−	3.87611i	−0.482614	−	0.156811i
$612$	52.6476	−	51.3918i	2.12815	−	2.07739i
$613$	−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	$0.606860\pi$
$614$	−26.3415	+	22.2242i	−1.06306	+	0.896896i
$615$		0			0
$616$	2.27741	−	0.503333i	0.0917596	−	0.0202799i
$617$	−19.6251	+	14.2585i	−0.790077	+	0.574025i	−0.907986	−	0.419000i	$-0.862381\pi$
$617$	−19.6251	+	14.2585i	−0.790077	+	0.574025i	0.117909	+	0.993024i	$0.462381\pi$
$618$	−27.0896	−	16.8262i	−1.08970	−	0.676851i
$619$	−20.9345	−	28.8138i	−0.841428	−	1.15813i	−0.985687	−	0.168586i	$-0.946080\pi$
$619$	−20.9345	−	28.8138i	−0.841428	−	1.15813i	0.144259	−	0.989540i	$-0.453920\pi$
$620$		0			0
$621$	2.53092	−	3.48351i	0.101562	−	0.139788i
$622$	−32.8436	+	13.3726i	−1.31691	+	0.536194i
$623$	−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
$628$	18.8574	+	3.22049i	0.752492	+	0.128512i
$629$	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
$634$	0.290949	−	1.18046i	0.0115551	−	0.0468821i
$635$		0			0
$636$	−2.95239	+	0.431151i	−0.117070	+	0.0170962i
$637$	−7.83048	+	2.54428i	−0.310255	+	0.100808i
$638$	−1.67704	−	0.413341i	−0.0663945	−	0.0163643i
$639$	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	$0.757137\pi$
$642$	−3.67887	−	50.6508i	−0.145193	−	1.99903i
$643$		−	32.6614i		−	1.28804i	−0.765009	−	0.644019i	$-0.777266\pi$
$643$		−	32.6614i		−	1.28804i	0.765009	−	0.644019i	$-0.222734\pi$
$644$	−1.70324	−	0.893902i	−0.0671171	−	0.0352247i
$645$		0			0
$646$	3.83526	+	9.41953i	0.150896	+	0.370606i
$647$	−28.2564	−	20.5295i	−1.11088	−	0.807098i	−0.128074	−	0.991765i	$-0.540880\pi$
$647$	−28.2564	−	20.5295i	−1.11088	−	0.807098i	−0.982801	+	0.184666i	$0.940880\pi$
$648$	−23.7147	+	54.4430i	−0.931602	+	2.13872i
$649$	−1.48256			−0.0581954
$650$		0			0
$651$			35.8087i			1.40345i
$652$	1.58730	+	10.8693i	0.0621635	+	0.425676i
$653$	−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	$0.923114\pi$
$654$	−39.8921	+	16.2425i	−1.55990	+	0.635131i
$655$		0			0
$656$	−0.618279	+	25.6071i	−0.0241397	+	0.999791i
$657$	64.4812			2.51565
$658$	−0.867497	−	11.9437i	−0.0338185	−	0.465614i
$659$	−40.4722	+	13.1502i	−1.57657	+	0.512260i	−0.961171	−	0.275953i	$-0.911006\pi$
$659$	−40.4722	+	13.1502i	−1.57657	+	0.512260i	−0.615402	+	0.788213i	$0.711006\pi$
$660$		0			0
$661$	15.1858	+	4.93417i	0.590660	+	0.191917i	0.589071	−	0.808082i	$-0.299494\pi$
$661$	15.1858	+	4.93417i	0.590660	+	0.191917i	0.00158966	+	0.999999i	$0.499494\pi$
$662$	2.86916	−	11.6410i	0.111513	−	0.452439i
$663$	22.2844	+	68.5844i	0.865455	+	2.66360i
$664$	34.4373	+	15.0005i	1.33643	+	0.582131i
$665$		0			0
$666$	−9.81436	+	39.8195i	−0.380299	+	1.54298i
$667$	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
$672$	51.8527	+	14.1162i	2.00026	+	0.544542i
$673$	−2.74537	+	8.44939i	−0.105826	+	0.325700i	−0.989924	−	0.141603i	$-0.954774\pi$
$673$	−2.74537	+	8.44939i	−0.105826	+	0.325700i	0.884097	+	0.467303i	$0.154774\pi$
$674$	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	$0.749660\pi$
$678$	−17.9811	−	44.1622i	−0.690560	−	1.69604i
$679$	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	$0.635903\pi$
$684$	−14.0739	−	14.4178i	−0.538129	−	0.551279i
$685$		0			0
$686$	13.9397	+	16.5222i	0.532221	+	0.630821i
$687$	26.0274	+	80.1042i	0.993009	+	3.05617i
$688$	−14.4806	+	41.1585i	−0.552066	+	1.56915i
$689$	0.637371	−	1.96163i	0.0242819	−	0.0747320i
$690$		0			0
$691$	−28.3342	+	9.20634i	−1.07788	+	0.350225i	−0.793553	−	0.608501i	$-0.791771\pi$
$691$	−28.3342	+	9.20634i	−1.07788	+	0.350225i	−0.284330	+	0.958726i	$0.591771\pi$
$692$	−16.1601	+	30.7915i	−0.614315	+	1.17052i
$693$		−	5.91952i		−	0.224864i
$694$	−24.8729	+	1.80657i	−0.944163	+	0.0685766i
$695$		0			0
$696$	−29.7887	−	26.3895i	−1.12914	−	1.00029i
$697$	−26.5483	−	19.2885i	−1.00559	−	0.730602i
$698$	38.0429	−	32.0967i	1.43995	−	1.21488i
$699$		−	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	$0.964788\pi$
$702$	−53.6241	−	63.5585i	−2.02391	−	2.39886i
$703$	−4.58651	−	3.33230i	−0.172984	−	0.125680i
$704$	1.62225	−	1.50883i	0.0611409	−	0.0568660i
$705$		0			0
$706$	−2.91113	−	40.0805i	−0.109562	−	1.50845i
$707$			58.0275i			2.18235i
$708$	−30.2468	−	15.8742i	−1.13674	−	0.596590i
$709$	−18.5674	+	6.03290i	−0.697312	+	0.226570i	−0.636159	−	0.771558i	$-0.719478\pi$
$709$	−18.5674	+	6.03290i	−0.697312	+	0.226570i	−0.0611529	+	0.998128i	$0.519478\pi$
$710$		0			0
$711$	−12.3238	+	37.9288i	−0.462179	+	1.42244i
$712$	1.95956	+	8.86633i	0.0734375	+	0.332280i
$713$	−0.376224	−	1.15790i	−0.0140897	−	0.0433637i
$714$	−52.6208	+	44.3960i	−1.96928	+	1.66148i
$715$		0			0
$716$	29.7272	+	30.4537i	1.11096	+	1.13811i
$717$	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
$722$	−22.3067	+	9.08242i	−0.830170	+	0.338013i
$723$	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	$-0.942617\pi$
$727$	−2.22440	+	6.84600i	−0.0824984	+	0.253904i	0.901296	+	0.433204i	$0.142617\pi$
$728$	−24.6340	+	27.8071i	−0.912996	+	1.03060i
$729$	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	$0.626475\pi$
$734$	29.2800	+	7.21668i	1.08075	+	0.266372i
$735$		0			0
$736$	−1.82500	+	0.0883347i	−0.0672706	+	0.00325606i
$737$	−0.132322	−	0.407244i	−0.00487413	−	0.0150010i
$738$	63.1204	+	15.5574i	2.32350	+	0.572674i
$739$	37.8363	+	12.2937i	1.39183	+	0.452233i	0.906540	−	0.422121i	$-0.138714\pi$
$739$	37.8363	+	12.2937i	1.39183	+	0.452233i	0.485290	+	0.874353i	$0.338714\pi$
$740$		0			0
$741$	18.7822	−	6.10270i	0.689980	−	0.224188i
$742$	1.96397	−	0.142647i	0.0720997	−	0.00523675i
$743$	−20.8383			−0.764482			−0.382241	−	0.924063i	$-0.624848\pi$
$743$	−20.8383			−0.764482			−0.382241	+	0.924063i	$0.624848\pi$
$744$	17.2442	+	29.3185i	0.632202	+	1.07487i
$745$		0			0
$746$	−6.27833	−	15.4198i	−0.229866	−	0.564558i
$747$	56.0353	−	77.1260i	2.05022	−	2.82189i
$748$	0.410137	+	2.80849i	0.0149961	+	0.102689i
$749$			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	$0.850516\pi$
$752$	−6.46192	−	9.36119i	−0.235642	−	0.341368i
$753$	6.69075	+	4.86111i	0.243824	+	0.177149i
$754$	25.4796	−	10.3743i	0.927913	−	0.377809i
$755$		0			0
$756$	36.8939	−	70.2977i	1.34182	−	2.55670i
$757$			18.6251i			0.676942i	0.940977	+	0.338471i	$0.109910\pi$
$757$			18.6251i			0.676942i	−0.940977	+	0.338471i	$0.890090\pi$
$758$	−25.7424	+	1.86972i	−0.935005	+	0.0679114i
$759$	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	$-0.163391\pi$
$762$	1.46546	−	5.94579i	0.0530882	−	0.215393i
$763$	27.0348	−	8.78414i	0.978726	−	0.318007i
$764$	7.01369	−	1.02424i	0.253746	−	0.0370557i
$765$		0			0
$766$	49.3937	+	12.1741i	1.78467	+	0.439869i
$767$	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
$772$	4.51032	−	26.4099i	0.162330	−	0.950511i
$773$	−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
$778$	−1.50018	−	3.68450i	−0.0537842	−	0.132096i
$779$	−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
$784$	−7.04328	−	2.47800i	−0.251546	−	0.0885000i
$785$		0			0
$786$	−2.33203	−	2.76406i	−0.0831809	−	0.0985909i
$787$	−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	$0.632807\pi$
$788$	7.17292	+	7.34820i	0.255525	+	0.261769i
$789$	47.2388	+	15.3488i	1.68174	+	0.546432i
$790$		0			0
$791$	9.72441	+	29.9287i	0.345760	+	1.06414i
$792$	−2.85063	−	4.84662i	−0.101293	−	0.172217i
$793$	−9.10969			−0.323495
$794$	−11.1037	+	0.806485i	−0.394056	+	0.0286211i
$795$		0			0
$796$	4.22718	−	24.7520i	0.149828	−	0.877310i
$797$	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	$-0.217440\pi$
$798$	12.1581	+	14.4105i	0.430390	+	0.510125i
$799$	14.5727			0.515544
$800$		0			0
$801$	23.0456			0.814277
$802$	6.15324	+	7.29319i	0.217278	+	0.257531i
$803$	−1.46215	+	2.01248i	−0.0515981	+	0.0710187i
$804$	1.66091	−	9.72532i	0.0585756	−	0.342986i
$805$		0			0
$806$	−23.4512	+	1.70331i	−0.826035	+	0.0599967i
$807$	4.21624			0.148419
$808$	27.9440	+	47.5102i	0.983065	+	1.67140i
$809$	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	0.278777	−	0.960356i	$-0.410071\pi$
$811$	−1.71354	−	0.556763i	−0.0601705	−	0.0195506i	−0.338948	+	0.940805i	$0.610071\pi$
$812$	18.3463	+	18.7946i	0.643828	+	0.659561i
$813$	43.9445	−	14.2784i	1.54120	−	0.500766i
$814$	−1.02023	−	1.20924i	−0.0357591	−	0.0423839i
$815$		0			0
$816$	−21.7039	+	61.6896i	−0.759789	+	2.15957i
$817$	−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	$-0.663786\pi$
$821$	13.9783	−	19.2395i	0.487848	−	0.671465i	0.979989	+	0.199051i	$0.0637858\pi$
$822$	12.3325	+	30.2890i	0.430145	+	1.05645i
$823$	−7.32692	+	22.5499i	−0.255400	+	0.786042i	0.738350	+	0.674418i	$0.235605\pi$
$823$	−7.32692	+	22.5499i	−0.255400	+	0.786042i	−0.993751	+	0.111624i	$0.964395\pi$
$824$	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	$0.550856\pi$
$828$	−0.780655	+	4.57107i	−0.0271296	+	0.158856i
$829$	4.69015	−	6.45543i	0.162896	−	0.224206i	−0.719765	−	0.694218i	$-0.755750\pi$
$829$	4.69015	−	6.45543i	0.162896	−	0.224206i	0.882660	+	0.470012i	$0.155750\pi$
$830$		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
$834$	−1.92231	−	0.473793i	−0.0665640	−	0.0164061i
$835$		0			0
$836$	0.769118	−	0.112318i	0.0266005	−	0.00388459i
$837$	47.7898	−	15.5279i	1.65186	−	0.536721i
$838$	−8.29539	+	33.6566i	−0.286559	+	1.16265i
$839$	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
$842$	38.2616	−	2.77902i	1.31858	−	0.0957713i
$843$			10.0497i			0.346130i
$844$	7.08613	−	13.5019i	0.243915	−	0.464756i
$845$		0			0
$846$	−26.7379	+	10.8866i	−0.919269	+	0.374290i
$847$	−26.3142	−	19.1184i	−0.904168	−	0.656917i
$848$	1.53931	−	1.06257i	0.0528603	−	0.0364888i
$849$	−40.2003			−1.37967
$850$		0			0
$851$			1.30482i			0.0447287i
$852$	8.90398	+	60.9717i	0.305045	+	2.08886i
$853$	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	$-0.0868862\pi$
$854$	−3.27966	−	8.05496i	−0.112228	−	0.275635i
$855$		0			0
$856$	16.1400	+	27.4412i	0.551655	+	0.937922i
$857$	46.7189			1.59589			0.797943	−	0.602733i	$-0.205922\pi$
$857$	46.7189			1.59589			0.797943	+	0.602733i	$0.205922\pi$
$858$	5.49685	−	0.399248i	0.187659	−	0.0136301i
$859$	−35.3436	+	11.4838i	−1.20591	+	0.391824i	−0.841932	−	0.539584i	$-0.818582\pi$
$859$	−35.3436	+	11.4838i	−1.20591	+	0.391824i	−0.363978	+	0.931408i	$0.618582\pi$
$860$		0			0
$861$	−57.8569	−	18.7988i	−1.97176	−	0.640662i
$862$	11.7909	+	2.90612i	0.401600	+	0.0989828i
$863$	−15.4359	−	47.5068i	−0.525444	−	1.61715i	−0.763436	−	0.645883i	$-0.776489\pi$
$863$	−15.4359	−	47.5068i	−0.525444	−	1.61715i	0.237992	−	0.971267i	$-0.423511\pi$
$864$	−3.64583	−	75.3232i	−0.124034	−	2.56255i
$865$		0			0
$866$	−40.1914	−	9.90601i	−1.36576	−	0.336620i
$867$	−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
$872$	17.9047	−	20.2110i	0.606330	−	0.684432i
$873$	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	$0.746404\pi$
$878$	16.9018	−	6.88175i	0.570408	−	0.232248i
$879$	−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	$0.766108\pi$
$884$	−31.5781	−	32.3498i	−1.06209	−	1.08804i
$885$		0			0
$886$	1.19729	−	1.01015i	0.0402237	−	0.0339366i
$887$	−8.52907	−	26.2498i	−0.286378	−	0.881381i	−0.985982	−	0.166850i	$-0.946640\pi$
$887$	−8.52907	−	26.2498i	−0.286378	−	0.881381i	0.699604	−	0.714531i	$-0.253360\pi$
$888$	−7.86681	−	35.5946i	−0.263993	−	1.19448i
$889$	−1.24888	+	3.84365i	−0.0418860	+	0.128912i
$890$		0			0
$891$	−5.52971	+	1.79671i	−0.185252	+	0.0601922i
$892$	34.1664	+	17.9313i	1.14397	+	0.600385i
$893$		−	3.99079i		−	0.133547i
$894$	0.541083	+	7.44964i	0.0180965	+	0.249153i
$895$		0			0
$896$	−33.0608	+	6.47400i	−1.10448	+	0.216281i
$897$	−3.67725	−	2.67168i	−0.122780	−	0.0892047i
$898$	−5.48332	−	6.49916i	−0.182981	−	0.216880i
$899$			16.6237i			0.554431i
$900$		0			0
$901$			2.39626i			0.0798312i
$902$	−1.91684	+	1.61724i	−0.0638239	+	0.0538480i
$903$	−83.8337	−	60.9087i	−2.78981	−	2.02692i
$904$	22.3745	+	19.8213i	0.744164	+	0.659245i
$905$		0			0
$906$	63.2833	−	4.59640i	2.10245	−	0.152705i
$907$		−	15.5893i		−	0.517636i	−0.965926	−	0.258818i	$-0.916667\pi$
$907$		−	15.5893i		−	0.517636i	0.965926	−	0.258818i	$-0.0833329\pi$
$908$	−22.3910	+	42.6639i	−0.743072	+	1.41585i
$909$	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	$-0.0596575\pi$
$912$	16.8940	+	5.94372i	0.559416	+	0.196816i
$913$	1.13649	+	3.49776i	0.0376123	+	0.115759i
$914$	33.6232	+	39.8522i	1.11216	+	1.31819i
$915$		0			0
$916$	−36.8822	−	37.7834i	−1.21862	−	1.24840i
$917$	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
$922$	−18.1909	−	44.6775i	−0.599086	−	1.47137i
$923$	−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
$928$	24.0719	+	6.55323i	0.790198	+	0.215120i
$929$	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
$934$	3.89060	−	15.7852i	0.127304	−	0.516509i
$935$		0			0
$936$	82.1068	+	35.7647i	2.68375	+	1.16901i
$937$	14.6482	+	45.0827i	0.478537	+	1.47279i	0.841127	+	0.540837i	$0.181893\pi$
$937$	14.6482	+	45.0827i	0.478537	+	1.47279i	−0.362590	+	0.931949i	$0.618107\pi$
$938$	−1.55822	+	6.32212i	−0.0508777	+	0.206425i
$939$	−33.1045	−	10.7563i	−1.08032	−	0.351018i
$940$		0			0
$941$	−14.2417	+	4.62742i	−0.464267	+	0.150850i	−0.531804	−	0.846867i	$-0.678486\pi$
$941$	−14.2417	+	4.62742i	−0.464267	+	0.150850i	0.0675373	+	0.997717i	$0.478486\pi$
$942$	3.12635	+	43.0436i	0.101862	+	1.40244i
$943$	2.06835			0.0673549
$944$	21.4077	+	0.516885i	0.696762	+	0.0168232i
$945$		0			0
$946$	−3.95658	+	1.61097i	−0.128640	+	0.0523770i
$947$	−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	$0.340189\pi$
$948$	−5.12241	−	35.0767i	−0.166368	−	1.13924i
$949$		−	39.6210i		−	1.28615i
$950$		0			0
$951$	2.74274			0.0889394
$952$	17.2356	−	39.5685i	0.558607	−	1.28242i
$953$	24.1675	+	17.5587i	0.782861	+	0.568782i	0.905836	−	0.423628i	$-0.139244\pi$
$953$	24.1675	+	17.5587i	0.782861	+	0.568782i	−0.122975	+	0.992410i	$0.539244\pi$
$954$	−1.79015	−	4.39667i	−0.0579583	−	0.142347i
$955$		0			0
$956$	−27.2948	−	14.3250i	−0.882777	−	0.463303i
$957$		−	3.89651i		−	0.125956i
$958$	1.21878	+	16.7802i	0.0393771	+	0.542144i
$959$	−6.66957	−	20.5268i	−0.215371	−	0.662845i
$960$		0			0
$961$	−5.18900	+	15.9701i	−0.167387	+	0.515164i
$962$	24.4675	+	6.03052i	0.788862	+	0.194432i
$963$	76.8443	−	24.9682i	2.47627	−	0.804590i
$964$	−30.8802	+	4.50958i	−0.994585	+	0.145244i
$965$		0			0
$966$	1.03847	−	4.21334i	0.0334121	−	0.135562i
$967$	−21.0745	+	15.3115i	−0.677710	+	0.492385i	−0.872597	−	0.488440i	$-0.837566\pi$
$967$	−21.0745	+	15.3115i	−0.677710	+	0.492385i	0.194887	+	0.980826i	$0.437566\pi$
$968$	−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	$-0.787966\pi$
$971$	1.38452	−	1.90563i	0.0444314	−	0.0611546i	0.830655	+	0.556788i	$0.187966\pi$
$972$	−53.2097	−	9.08724i	−1.70670	−	0.291473i
$973$	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	$-0.852041\pi$
$977$	2.89960	−	8.92406i	0.0927665	−	0.285506i	0.986665	+	0.162763i	$0.0520406\pi$
$978$	−22.9511	+	9.34480i	−0.733896	+	0.298814i
$979$	−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	$-0.363537\pi$
$983$	44.1807	−	32.0991i	1.40914	−	1.02380i	0.993446	−	0.114301i	$-0.0364628\pi$
$984$	−56.4233	+	12.4702i	−1.79871	+	0.397535i
$985$		0			0
$986$	−24.4285	+	20.6102i	−0.777961	+	0.656363i
$987$	25.6930	−	8.34816i	0.817817	−	0.265725i
$988$	−8.85914	+	8.64782i	−0.281847	+	0.275124i
$989$	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	$0.457289\pi$
$992$	−17.8362	−	11.6845i	−0.566299	−	0.370984i
$993$	27.0472			0.858316
$994$	−2.94591	−	40.5593i	−0.0934385	−	1.28646i
$995$		0			0
$996$	−14.2653	+	83.5292i	−0.452012	+	2.64673i
$997$	−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	$0.361983\pi$
$998$	5.08913	−	4.29368i	0.161094	−	0.135914i
$999$	−53.8537			−1.70386

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.7	✓	112	5.3	odd	4
200.2.o.a.29.13	yes	112	40.13	odd	4
200.2.o.a.69.7	yes	112	200.117	odd	20
200.2.o.a.69.13	yes	112	25.17	odd	20
800.2.be.a.369.1		112	200.67	even	20
800.2.be.a.369.28		112	100.67	even	20
800.2.be.a.529.1		112	20.3	even	4
800.2.be.a.529.28		112	40.3	even	4
1000.2.o.a.149.16		112	40.37	odd	4
1000.2.o.a.149.22		112	5.2	odd	4
1000.2.o.a.349.16		112	25.8	odd	20
1000.2.o.a.349.22		112	200.133	odd	20
1000.2.t.b.101.6		224	40.29	even	2	inner
1000.2.t.b.101.17		224	1.1	even	1	trivial
1000.2.t.b.101.40		224	5.4	even	2	inner
1000.2.t.b.101.51		224	8.5	even	2	inner
1000.2.t.b.901.6		224	25.19	even	10	inner
1000.2.t.b.901.17		224	200.181	even	10	inner
1000.2.t.b.901.40		224	200.69	even	10	inner
1000.2.t.b.901.51		224	25.6	even	5	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)

\(f(q)\)	\(=\)	\(q+(-0.911952 - 1.08090i) q^{2} +(1.87526 - 2.58107i) q^{3} +(-0.336688 + 1.97146i) q^{4} +(-4.50002 + 0.326846i) q^{6} +2.97769 q^{7} +(2.43799 - 1.43395i) q^{8} +(-2.21828 - 6.82716i) q^{9} +O(q^{10})\)	\(q+(-0.911952 - 1.08090i) q^{2} +(1.87526 - 2.58107i) q^{3} +(-0.336688 + 1.97146i) q^{4} +(-4.50002 + 0.326846i) q^{6} +2.97769 q^{7} +(2.43799 - 1.43395i) q^{8} +(-2.21828 - 6.82716i) q^{9} +(0.263378 + 0.0855768i) q^{11} +(4.45709 + 4.56600i) q^{12} +(-4.19500 + 1.36304i) q^{13} +(-2.71551 - 3.21858i) q^{14} +(-3.77328 - 1.32753i) 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} +(-0.147688 - 0.362728i) 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} +(-1.00255 + 5.87038i) 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} +(-7.03655 - 1.73431i) q^{34} +(14.2063 - 2.07461i) q^{36} +(3.84202 - 1.24835i) q^{37} +(-0.474948 + 1.92699i) q^{38} +(-4.34861 + 13.3836i) q^{39} +(-1.97884 - 6.09023i) q^{41} +(-13.3996 + 0.973245i) q^{42} -10.9079i q^{43} +(-0.257387 + 0.490426i) q^{44} +(0.423062 - 0.172254i) q^{46} +(2.30062 + 1.67150i) q^{47} +(-10.5023 + 7.24963i) q^{48} +1.86662 q^{49} -16.3491i q^{51} +(-1.27476 - 8.72919i) q^{52} +(-0.274854 + 0.378304i) q^{53} +(7.10942 + 17.4610i) q^{54} +(7.25957 - 4.26984i) q^{56} -4.47727 q^{57} +(-6.22060 + 0.451815i) q^{58} +(-5.09147 + 1.65432i) q^{59} +(1.96419 + 0.638204i) q^{61} +(5.17578 + 1.27568i) q^{62} +(-6.60534 - 20.3291i) q^{63} +(3.88759 - 6.99190i) q^{64} +(-1.21318 - 0.299013i) 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} +(-15.1979 - 13.4636i) 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} +(18.4321 - 7.50482i) 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} +(13.2718 + 13.5961i) q^{84} +(-11.7903 + 9.94745i) q^{86} +(-4.34795 - 13.3816i) q^{87} +(0.764826 - 0.169035i) q^{88} +(-0.992059 + 3.05324i) q^{89} +(-12.4914 + 4.05871i) q^{91} +(-0.572001 - 0.300200i) q^{92} +12.0257i q^{93} +(-0.291332 - 4.01107i) q^{94} +(17.4137 + 4.74064i) q^{96} +(13.3433 + 9.69449i) q^{97} +(-1.70227 - 2.01763i) 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

Varieties

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Database

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