LMFDB - Embedded newform 1000.2.t.b.101.40

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			101.40
Character	$\chi$	$=$	1000.101
Dual form			1000.2.t.b.901.40

$q$-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	$0.572612\pi$
$3$	−1.87526	+	2.58107i	−1.08268	+	1.49018i	−0.856537	+	0.516086i	$0.827388\pi$
$4$	−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	$-0.690249\pi$
$7$	−2.97769			−1.12546			−0.562730	+	0.826641i	$0.690249\pi$
$8$	−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	0.337278	−	0.941405i	$-0.390494\pi$
$13$	4.19500	−	1.36304i	1.16349	−	0.378039i	0.826207	+	0.563366i	$0.190494\pi$
$14$	−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	−0.963262	−	0.268565i	$-0.913451\pi$
$17$	−4.14580	+	3.01210i	−1.00551	+	0.730542i	−0.0422436	+	0.999107i	$0.513451\pi$
$18$	5.35651	−	8.62377i	1.26254	−	2.03264i
$19$	−0.824879	−	1.13535i	−0.189240	−	0.260467i	0.703846	−	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	−0.940111	−	0.340868i	$-0.889279\pi$
$23$	0.0998113	−	0.307187i	0.0208121	−	0.0640530i	0.960923	+	0.276815i	$0.0892790\pi$
$24$	0.870742	−	8.98164i	0.177739	−	1.83337i
$25$		0			0
$26$	5.29895	+	3.29135i	1.03921	+	0.645488i
$27$	12.6785	+	4.11950i	2.43998	+	0.792798i
$28$	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	−0.607295	−	0.794477i	$-0.707745\pi$
$37$	−3.84202	+	1.24835i	−0.631625	+	0.205227i	−0.0243301	+	0.999704i	$0.507745\pi$
$38$	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	$0.312642\pi$
$43$			10.9079i			1.66343i	−0.555199	+	0.831717i	$0.687358\pi$
$44$	−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	0.407214	−	0.913333i	$-0.366500\pi$
$47$	−2.30062	−	1.67150i	−0.335580	−	0.243813i	−0.742795	+	0.669519i	$0.766500\pi$
$48$	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	−0.789723	−	0.613464i	$-0.789776\pi$
$53$	0.274854	−	0.378304i	0.0377541	−	0.0519641i	0.827477	+	0.561500i	$0.189776\pi$
$54$	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	0.860917	−	0.508745i	$-0.169890\pi$
$67$	0.908853	+	1.25093i	0.111034	+	0.152825i	−0.749883	+	0.661570i	$0.769890\pi$
$68$	−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	$-0.723817\pi$
$73$	2.77576	−	8.54291i	0.324878	−	0.999872i	0.971496	−	0.237057i	$-0.0761829\pi$
$74$	−4.85308	−	3.01441i	−0.564159	−	0.350418i
$75$		0			0
$76$	2.51602	−	1.24395i	0.288607	−	0.142691i
$77$	−0.784258	−	0.254821i	−0.0893745	−	0.0290395i
$78$	−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	$-0.940053\pi$
$83$	−7.80599	−	10.7440i	−0.856819	−	1.17931i	0.125500	−	0.992094i	$-0.459947\pi$
$84$	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	$-0.984122\pi$
$97$	−13.3433	−	9.69449i	−1.35481	−	0.984327i	−0.356053	−	0.934466i	$-0.615878\pi$
$98$	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	0.269286	−	0.963060i	$-0.413212\pi$
$103$	−5.71814	−	4.15447i	−0.563425	−	0.409352i	−0.832711	+	0.553708i	$0.813212\pi$
$104$	−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	$-0.816885\pi$
$107$		−	11.2557i		−	1.08813i	0.839044	−	0.544064i	$-0.183115\pi$
$108$	−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	$-0.934403\pi$
$113$	−3.26576	−	10.0510i	−0.307217	−	0.945517i	0.671624	−	0.740892i	$-0.265597\pi$
$114$	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	−0.930722	−	0.365727i	$-0.880820\pi$
$127$	0.419412	−	1.29082i	0.0372168	−	0.114542i	0.967939	+	0.251185i	$0.0808204\pi$
$128$	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	$0.000205853\pi$
$137$	2.23985	+	6.89354i	0.191363	+	0.588955i	−0.808637	+	0.588308i	$0.799794\pi$
$138$	−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	$0.124659\pi$
$157$			9.56521i			0.763387i	−0.924289	+	0.381693i	$0.875341\pi$
$158$	−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	−0.506352	−	0.862327i	$-0.669006\pi$
$163$	−5.22350	+	1.69722i	−0.409136	+	0.132936i	0.0972156	+	0.995263i	$0.469006\pi$
$164$	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	−0.896889	−	0.442255i	$-0.854179\pi$
$167$	−9.73651	+	7.07399i	−0.753433	+	0.547401i	0.143456	+	0.989657i	$0.454179\pi$
$168$	−2.59280	+	26.7445i	−0.200039	+	2.06338i
$169$	5.22297	−	3.79471i	0.401767	−	0.291901i
$170$		0			0
$171$	−5.92139	+	8.15009i	−0.452820	+	0.623253i
$172$	−21.5044	−	3.67255i	−1.63969	−	0.280030i
$173$	−16.5363	−	5.37296i	−1.25723	−	0.408498i	−0.396722	−	0.917939i	$-0.629852\pi$
$173$	−16.5363	−	5.37296i	−1.25723	−	0.408498i	−0.860506	+	0.509440i	$0.829852\pi$
$174$	−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	$-0.339861\pi$
$193$	13.3961			0.964273			0.482137	+	0.876096i	$0.339861\pi$
$194$	−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	−0.902878	−	0.429897i	$-0.858550\pi$
$197$	−3.01790	+	4.15379i	−0.215017	+	0.295945i	0.687861	+	0.725842i	$0.258550\pi$
$198$	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	$0.323549\pi$
$223$	−5.96185	+	18.3487i	−0.399235	+	1.22872i	−0.925614	+	0.378469i	$0.876451\pi$
$224$	5.97360	+	15.7495i	0.399128	+	1.05231i
$225$		0			0
$226$	7.88588	−	12.6960i	0.524561	−	0.844523i
$227$	−22.9122	−	7.44462i	−1.52073	−	0.494117i	−0.574751	−	0.818329i	$-0.694901\pi$
$227$	−22.9122	−	7.44462i	−1.52073	−	0.494117i	−0.945984	+	0.324212i	$0.894901\pi$
$228$	−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	−0.999608	−	0.0280108i	$-0.991083\pi$
$233$	−19.5668	+	14.2161i	−1.28186	+	0.931328i	−0.282256	+	0.959339i	$0.591083\pi$
$234$	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	$-0.480236\pi$
$257$	1.98944			0.124098			0.0620490	+	0.998073i	$0.480236\pi$
$258$	−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	$-0.940636\pi$
$263$	−4.81097	−	14.8066i	−0.296657	−	0.913017i	0.686003	−	0.727599i	$-0.259364\pi$
$264$	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	0.651009	−	0.759070i	$-0.274346\pi$
$277$	12.1748	+	3.95585i	0.731516	+	0.237684i	0.0805069	+	0.996754i	$0.474346\pi$
$278$	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	0.970271	−	0.242022i	$-0.0778107\pi$
$283$	7.40638	+	10.1940i	0.440264	+	0.605971i	−0.530007	+	0.847993i	$0.677811\pi$
$284$	−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	$0.0865766\pi$
$293$			9.19701i			0.537295i	−0.963239	+	0.268647i	$0.913423\pi$
$294$	−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	$0.244787\pi$
$307$			24.3699i			1.39087i	−0.718591	+	0.695433i	$0.755213\pi$
$308$	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	1.00000		0.000706882i	$-0.000225008\pi$
$313$	3.37148	+	10.3764i	0.190567	+	0.586506i	−0.809432	+	0.587213i	$0.800225\pi$
$314$	−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	0.794591	−	0.607146i	$-0.207686\pi$
$317$	−0.505314	−	0.695505i	−0.0283813	−	0.0390635i	−0.822972	+	0.568082i	$0.807686\pi$
$318$	−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	$-0.948629\pi$
$337$	−5.19430	−	15.9864i	−0.282951	−	0.870835i	0.704054	−	0.710147i	$-0.251371\pi$
$338$	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	−0.990867	−	0.134845i	$-0.956946\pi$
$347$	−10.3651	+	14.2663i	−0.556427	+	0.765856i	0.434440	+	0.900701i	$0.356946\pi$
$348$	−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	−0.227184	−	0.973852i	$-0.572952\pi$
$353$	−22.9889	−	16.7024i	−1.22358	−	0.888980i	−0.996392	+	0.0848720i	$0.972952\pi$
$354$	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	−0.0380891	−	0.999274i	$-0.512127\pi$
$367$	17.2512	−	12.5338i	0.900507	−	0.654257i	0.938596	+	0.345018i	$0.112127\pi$
$368$	−0.784418	+	1.02660i	−0.0408906	+	0.0535153i
$369$	−37.1894	+	27.0197i	−1.93600	+	1.40659i
$370$		0			0
$371$	−0.818430	+	1.12647i	−0.0424908	+	0.0584835i
$372$	23.7081	+	4.04890i	1.22921	+	0.209926i
$373$	−11.1964	−	3.63793i	−0.579727	−	0.188365i	0.00445132	−	0.999990i	$-0.498583\pi$
$373$	−11.1964	−	3.63793i	−0.579727	−	0.188365i	−0.584178	+	0.811625i	$0.698583\pi$
$374$	−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	$-0.328968\pi$
$383$	29.1018	−	21.1437i	1.48703	−	1.08039i	0.975204	−	0.221307i	$-0.0710324\pi$
$384$	−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	−0.909189	−	0.416383i	$-0.863297\pi$
$397$	−4.62715	+	6.36873i	−0.232230	+	0.319637i	0.676959	+	0.736021i	$0.263297\pi$
$398$	−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	−0.986838	−	0.161714i	$-0.948298\pi$
$433$	−23.6800	+	17.2045i	−1.13799	+	0.826797i	−0.151150	+	0.988511i	$0.548298\pi$
$434$	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	$-0.991623\pi$
$443$		−	1.10768i		−	0.0526274i	0.999654	−	0.0263137i	$-0.00837688\pi$
$444$	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	$-0.168997\pi$
$457$	36.8695			1.72468			0.862341	+	0.506328i	$0.168997\pi$
$458$	−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	$0.331160\pi$
$463$	12.9887	+	39.9752i	0.603637	+	1.85780i	0.0977353	+	0.995212i	$0.468840\pi$
$464$	−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	0.623533	−	0.781797i	$-0.285696\pi$
$467$	−6.75711	−	9.30036i	−0.312682	−	0.430370i	−0.936215	+	0.351427i	$0.885696\pi$
$468$	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	$-0.934961\pi$
$487$	−6.75894	−	20.8019i	−0.306277	−	0.942622i	0.672921	−	0.739714i	$-0.265039\pi$
$488$	−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	0.795754	−	0.605621i	$-0.207075\pi$
$503$	10.4440	+	7.58802i	0.465676	+	0.338333i	−0.330078	+	0.943954i	$0.607075\pi$
$504$	−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	−0.220534	−	0.975379i	$-0.570780\pi$
$523$	−22.2349	−	7.22455i	−0.972264	−	0.315908i	−0.751729	+	0.659472i	$0.770780\pi$
$524$	−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	−0.835840	−	0.548973i	$-0.815019\pi$
$547$	−1.29680	+	1.78489i	−0.0554470	+	0.0763163i	0.780393	+	0.625289i	$0.215019\pi$
$548$	−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	$-0.843440\pi$
$557$		−	22.2912i		−	0.944509i	0.881462	−	0.472255i	$-0.156560\pi$
$558$	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	0.148293	−	0.988943i	$-0.452622\pi$
$563$	20.1578	−	6.54968i	0.849551	−	0.276036i	0.701258	+	0.712907i	$0.252622\pi$
$564$	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	$0.269553\pi$
$577$	−7.53910	+	23.2030i	−0.313857	+	0.965952i	−0.976222	+	0.216771i	$0.930447\pi$
$578$	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	−0.566358	−	0.824159i	$-0.691648\pi$
$587$	−13.0862	+	4.25195i	−0.540123	+	0.175497i	0.0262350	+	0.999656i	$0.491648\pi$
$588$	−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	$-0.626810\pi$
$593$	−18.8934			−0.775861			−0.387930	+	0.921689i	$0.626810\pi$
$594$	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	$-0.652523\pi$
$607$	−22.7175			−0.922076			−0.461038	+	0.887380i	$0.652523\pi$
$608$	−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	0.329441	−	0.944176i	$-0.393140\pi$
$613$	28.4959	−	9.25887i	1.15094	−	0.373962i	0.821496	+	0.570214i	$0.193140\pi$
$614$	−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	−0.117909	−	0.993024i	$-0.537619\pi$
$617$	19.6251	−	14.2585i	0.790077	−	0.574025i	0.907986	+	0.419000i	$0.137619\pi$
$618$	27.0896	+	16.8262i	1.08970	+	0.676851i
$619$	−20.9345	−	28.8138i	−0.841428	−	1.15813i	−0.985687	−	0.168586i	$-0.946080\pi$
$619$	−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	$0.222734\pi$
$643$			32.6614i			1.28804i	−0.765009	+	0.644019i	$0.777266\pi$
$644$	−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	0.982801	−	0.184666i	$-0.0591205\pi$
$647$	28.2564	+	20.5295i	1.11088	+	0.807098i	0.128074	+	0.991765i	$0.459120\pi$
$648$	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	$-0.523114\pi$
$653$	22.9581	−	31.5991i	0.898420	−	1.23657i	0.970969	−	0.239204i	$-0.0768863\pi$
$654$	−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	−0.884097	−	0.467303i	$-0.845226\pi$
$673$	2.74537	−	8.44939i	0.105826	−	0.325700i	0.989924	+	0.141603i	$0.0452257\pi$
$674$	12.5427	−	20.1933i	0.483129	−	0.777818i
$675$		0			0
$676$	5.72259	+	11.5745i	0.220100	+	0.445173i
$677$	22.4216	+	7.28520i	0.861730	+	0.279993i	0.706351	−	0.707862i	$-0.250340\pi$
$677$	22.4216	+	7.28520i	0.861730	+	0.279993i	0.155379	+	0.987855i	$0.450340\pi$
$678$	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	0.414097	−	0.910233i	$-0.364097\pi$
$683$	−15.1461	−	20.8468i	−0.579548	−	0.797680i	−0.993646	+	0.112553i	$0.964097\pi$
$684$	−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	−0.901296	−	0.433204i	$-0.857383\pi$
$727$	2.22440	−	6.84600i	0.0824984	−	0.253904i	0.983795	+	0.179300i	$0.0573831\pi$
$728$	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	0.386961	−	0.922096i	$-0.373525\pi$
$733$	−16.5038	−	22.7156i	−0.609582	−	0.839018i	−0.996543	+	0.0830781i	$0.973525\pi$
$734$	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	$-0.375152\pi$
$743$	20.8383			0.764482			0.382241	+	0.924063i	$0.375152\pi$
$744$	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	$-0.890090\pi$
$757$		−	18.6251i		−	0.676942i	0.940977	−	0.338471i	$-0.109910\pi$
$758$	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	0.806072	−	0.591817i	$-0.201589\pi$
$773$	30.8706	+	10.0305i	1.11034	+	0.360770i	0.304265	+	0.952588i	$0.401589\pi$
$774$	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	0.405224	−	0.914217i	$-0.367193\pi$
$787$	35.6398	−	11.5801i	1.27042	−	0.412785i	0.865197	+	0.501432i	$0.167193\pi$
$788$	−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	$0.617440\pi$
$797$	−32.0777	+	44.1511i	−1.13625	+	1.56391i	−0.775614	+	0.631207i	$0.782560\pi$
$798$	−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	$-0.764395\pi$
$823$	7.32692	−	22.5499i	0.255400	−	0.786042i	0.993751	−	0.111624i	$-0.0356053\pi$
$824$	19.8980	+	1.92905i	0.693181	+	0.0672018i
$825$		0			0
$826$	19.1505	+	11.8950i	0.666331	+	0.413880i
$827$	−8.41171	−	2.73313i	−0.292504	−	0.0950402i	0.159089	−	0.987264i	$-0.449144\pi$
$827$	−8.41171	−	2.73313i	−0.292504	−	0.0950402i	−0.451593	+	0.892224i	$0.649144\pi$
$828$	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	$0.486886\pi$
$853$	−26.9220	+	37.0549i	−0.921790	+	1.26874i	−0.962977	+	0.269584i	$0.913114\pi$
$854$	−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	$-0.794078\pi$
$857$	−46.7189			−1.59589			−0.797943	+	0.602733i	$0.794078\pi$
$858$	−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	$0.223511\pi$
$863$	15.4359	+	47.5068i	0.525444	+	1.61715i	−0.237992	+	0.971267i	$0.576489\pi$
$864$	−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	0.699073	−	0.715050i	$-0.253596\pi$
$877$	25.0044	+	8.12444i	0.844340	+	0.274343i	0.145267	+	0.989393i	$0.453596\pi$
$878$	−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	0.741969	−	0.670434i	$-0.233892\pi$
$883$	−3.71243	−	5.10972i	−0.124933	−	0.171956i	−0.866902	+	0.498479i	$0.833892\pi$
$884$	−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	$0.0533597\pi$
$887$	8.52907	+	26.2498i	0.286378	+	0.881381i	−0.699604	+	0.714531i	$0.746640\pi$
$888$	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	$0.0833329\pi$
$907$			15.5893i			0.517636i	−0.965926	+	0.258818i	$0.916667\pi$
$908$	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	$-0.818107\pi$
$937$	−14.6482	−	45.0827i	−0.478537	−	1.47279i	0.362590	−	0.931949i	$-0.381893\pi$
$938$	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	−0.481233	−	0.876593i	$-0.659811\pi$
$947$	15.4226	−	21.2273i	0.501166	−	0.689796i	0.982398	+	0.186797i	$0.0598108\pi$
$948$	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	0.122975	−	0.992410i	$-0.460756\pi$
$953$	−24.1675	−	17.5587i	−0.782861	−	0.568782i	−0.905836	+	0.423628i	$0.860756\pi$
$954$	−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	−0.194887	−	0.980826i	$-0.562434\pi$
$967$	21.0745	−	15.3115i	0.677710	−	0.492385i	0.872597	+	0.488440i	$0.162434\pi$
$968$	30.7516	+	2.98127i	0.988394	+	0.0958217i
$969$	−18.5619	+	13.4860i	−0.596294	+	0.433233i
$970$		0			0
$971$	1.38452	−	1.90563i	0.0444314	−	0.0611546i	−0.786223	−	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	−0.986665	−	0.162763i	$-0.947959\pi$
$977$	−2.89960	+	8.92406i	−0.0927665	+	0.285506i	0.893899	+	0.448269i	$0.147959\pi$
$978$	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	$0.636463\pi$
$983$	−44.1807	+	32.0991i	−1.40914	+	1.02380i	−0.993446	+	0.114301i	$0.963537\pi$
$984$	−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	−0.420135	−	0.907462i	$-0.638017\pi$
$997$	18.0845	−	24.8911i	0.572741	−	0.788310i	0.992876	+	0.119151i	$0.0380173\pi$
$998$	−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.101.40		224
5.2	odd	4		200.2.o.a.29.7	✓	112
5.3	odd	4		1000.2.o.a.149.22		112
5.4	even	2	inner	1000.2.t.b.101.17		224
8.5	even	2	inner	1000.2.t.b.101.6		224
20.7	even	4		800.2.be.a.529.1		112
25.6	even	5	inner	1000.2.t.b.901.6		224
25.8	odd	20		200.2.o.a.69.13	yes	112
25.17	odd	20		1000.2.o.a.349.16		112
25.19	even	10	inner	1000.2.t.b.901.51		224
40.13	odd	4		1000.2.o.a.149.16		112
40.27	even	4		800.2.be.a.529.28		112
40.29	even	2	inner	1000.2.t.b.101.51		224
40.37	odd	4		200.2.o.a.29.13	yes	112
100.83	even	20		800.2.be.a.369.28		112
200.69	even	10	inner	1000.2.t.b.901.17		224
200.83	even	20		800.2.be.a.369.1		112
200.117	odd	20		1000.2.o.a.349.22		112
200.133	odd	20		200.2.o.a.69.7	yes	112
200.181	even	10	inner	1000.2.t.b.901.40		224

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.t (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.911952 + 1.08090i) q^{2} +(-1.87526 + 2.58107i) q^{3} +(-0.336688 + 1.97146i) q^{4} +(-4.50002 + 0.326846i) q^{6} -2.97769 q^{7} +(-2.43799 + 1.43395i) q^{8} +(-2.21828 - 6.82716i) q^{9} +O(q^{10})\)	\(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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Representations

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Database

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