LMFDB - Embedded newform 140.2.s.b.19.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [140,2,Mod(19,140)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("140.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(140, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.s (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.15
Character	$\chi$	$=$	140.19
Dual form			140.2.s.b.59.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38503 - 0.285823i) q^{2} +(-2.24836 + 1.29809i) q^{3} +(1.83661 - 0.791746i) q^{4} +(0.316513 + 2.21355i) q^{5} +(-2.74302 + 2.44053i) q^{6} +(2.57589 + 0.603960i) q^{7} +(2.31746 - 1.62154i) q^{8} +(1.87009 - 3.23909i) q^{9} +(1.07106 + 2.97537i) q^{10} +(-3.12008 + 1.80138i) q^{11} +(-3.10161 + 4.16422i) q^{12} +0.818282 q^{13} +(3.74031 + 0.100253i) q^{14} +(-3.58504 - 4.56601i) q^{15} +(2.74628 - 2.90826i) q^{16} +(-3.69814 - 6.40537i) q^{17} +(1.66432 - 5.02075i) q^{18} +(1.65329 - 2.86358i) q^{19} +(2.33388 + 3.81484i) q^{20} +(-6.57554 + 1.98583i) q^{21} +(-3.80652 + 3.38675i) q^{22} +(1.26758 - 2.19550i) q^{23} +(-3.10559 + 6.65408i) q^{24} +(-4.79964 + 1.40124i) q^{25} +(1.13334 - 0.233884i) q^{26} +1.92166i q^{27} +(5.20910 - 0.930214i) q^{28} -2.04334 q^{29} +(-6.27045 - 5.29937i) q^{30} +(0.955727 + 1.65537i) q^{31} +(2.97243 - 4.81297i) q^{32} +(4.67671 - 8.10030i) q^{33} +(-6.95283 - 7.81461i) q^{34} +(-0.521593 + 5.89304i) q^{35} +(0.870092 - 7.42959i) q^{36} +(6.20697 + 3.58360i) q^{37} +(1.47138 - 4.43869i) q^{38} +(-1.83980 + 1.06221i) q^{39} +(4.32286 + 4.61658i) q^{40} +2.65824i q^{41} +(-8.53972 + 4.62987i) q^{42} -2.39696 q^{43} +(-4.30413 + 5.77873i) q^{44} +(7.76182 + 3.11433i) q^{45} +(1.12810 - 3.40314i) q^{46} +(1.15593 + 0.667376i) q^{47} +(-2.39944 + 10.1037i) q^{48} +(6.27046 + 3.11147i) q^{49} +(-6.24713 + 3.31260i) q^{50} +(16.6295 + 9.60106i) q^{51} +(1.50287 - 0.647871i) q^{52} +(-1.56838 + 0.905503i) q^{53} +(0.549253 + 2.66155i) q^{54} +(-4.97499 - 6.33630i) q^{55} +(6.94888 - 2.77725i) q^{56} +8.58450i q^{57} +(-2.83009 + 0.584034i) q^{58} +(-0.955727 - 1.65537i) q^{59} +(-10.1994 - 5.54755i) q^{60} +(-8.46625 - 4.88799i) q^{61} +(1.79685 + 2.01956i) q^{62} +(6.77344 - 7.21411i) q^{63} +(2.74124 - 7.51569i) q^{64} +(0.258997 + 1.81131i) q^{65} +(4.16213 - 12.5559i) q^{66} +(-4.63112 - 8.02134i) q^{67} +(-11.8635 - 8.83618i) q^{68} +6.58172i q^{69} +(0.961944 + 8.31112i) q^{70} +1.38422i q^{71} +(-0.918444 - 10.5389i) q^{72} +(3.69814 + 6.40537i) q^{73} +(9.62111 + 3.18929i) q^{74} +(8.97240 - 9.38087i) q^{75} +(0.769222 - 6.56827i) q^{76} +(-9.12495 + 2.75576i) q^{77} +(-2.24457 + 1.99704i) q^{78} +(-6.70979 - 3.87390i) q^{79} +(7.30682 + 5.15853i) q^{80} +(3.11579 + 5.39670i) q^{81} +(0.759784 + 3.68173i) q^{82} +10.4973i q^{83} +(-10.5044 + 8.85335i) q^{84} +(13.0081 - 10.2134i) q^{85} +(-3.31986 + 0.685105i) q^{86} +(4.59418 - 2.65245i) q^{87} +(-4.30966 + 9.23393i) q^{88} +(-9.19133 - 5.30662i) q^{89} +(11.6405 + 2.09494i) q^{90} +(2.10781 + 0.494210i) q^{91} +(0.589761 - 5.03589i) q^{92} +(-4.29764 - 2.48125i) q^{93} +(1.79175 + 0.593945i) q^{94} +(6.86198 + 2.75329i) q^{95} +(-0.435416 + 14.6798i) q^{96} +7.32005 q^{97} +(9.57411 + 2.51724i) q^{98} +13.4750i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{4} - 6 q^{5} + 4 q^{9} - 12 q^{10} + 22 q^{14} + 18 q^{16} - 52 q^{21} - 48 q^{24} - 26 q^{25} - 18 q^{26} - 26 q^{30} - 28 q^{36} + 42 q^{40} - 26 q^{44} + 36 q^{45} - 22 q^{46} + 36 q^{50}+ \cdots + 60 q^{96}+O(q^{100}) $ 32 * q + 6 * q^4 - 6 * q^5 + 4 * q^9 - 12 * q^10 + 22 * q^14 + 18 * q^16 - 52 * q^21 - 48 * q^24 - 26 * q^25 - 18 * q^26 - 26 * q^30 - 28 * q^36 + 42 * q^40 - 26 * q^44 + 36 * q^45 - 22 * q^46 + 36 * q^50 + 48 * q^54 - 16 * q^56 + 4 * q^60 + 36 * q^61 + 36 * q^64 - 4 * q^65 - 24 * q^66 + 26 * q^70 + 14 * q^74 + 72 * q^80 + 72 * q^81 + 56 * q^84 + 20 * q^85 + 8 * q^86 - 108 * q^89 + 30 * q^94 + 60 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.38503	−	0.285823i	0.979363	−	0.202107i
$2$	1.38503	−	0.285823i	0.979363	−	0.202107i
$3$	−2.24836	+	1.29809i	−1.29809	+	0.749454i	−0.980075	−	0.198630i	$-0.936351\pi$
$3$	−2.24836	+	1.29809i	−1.29809	+	0.749454i	−0.318019	+	0.948084i	$0.603017\pi$
$4$	1.83661	−	0.791746i	0.918305	−	0.395873i
$5$	0.316513	+	2.21355i	0.141549	+	0.989931i
$5$	0.316513	+	2.21355i	0.141549	+	0.989931i
$6$	−2.74302	+	2.44053i	−1.11983	+	0.996342i
$7$	2.57589	+	0.603960i	0.973597	+	0.228275i
$7$	2.57589	+	0.603960i	0.973597	+	0.228275i
$8$	2.31746	−	1.62154i	0.819346	−	0.573300i
$9$	1.87009	−	3.23909i	0.623364	−	1.07970i
$10$	1.07106	+	2.97537i	0.338700	+	0.940894i
$11$	−3.12008	+	1.80138i	−0.940738	+	0.543136i	−0.890192	−	0.455586i	$-0.849430\pi$
$11$	−3.12008	+	1.80138i	−0.940738	+	0.543136i	−0.0505467	+	0.998722i	$0.516096\pi$
$12$	−3.10161	+	4.16422i	−0.895357	+	1.20211i
$13$	0.818282			0.226951			0.113475	−	0.993541i	$-0.463802\pi$
$13$	0.818282			0.226951			0.113475	+	0.993541i	$0.463802\pi$
$14$	3.74031	+	0.100253i	0.999641	+	0.0267937i
$15$	−3.58504	−	4.56601i	−0.925652	−	1.17894i
$16$	2.74628	−	2.90826i	0.686569	−	0.727064i
$17$	−3.69814	−	6.40537i	−0.896931	−	1.55353i	−0.831396	−	0.555680i	$-0.812458\pi$
$17$	−3.69814	−	6.40537i	−0.896931	−	1.55353i	−0.0655347	−	0.997850i	$-0.520875\pi$
$18$	1.66432	−	5.02075i	0.392285	−	1.18340i
$19$	1.65329	−	2.86358i	0.379291	−	0.656951i	−0.611668	−	0.791114i	$-0.709501\pi$
$19$	1.65329	−	2.86358i	0.379291	−	0.656951i	0.990959	+	0.134163i	$0.0428346\pi$
$20$	2.33388	+	3.81484i	0.521872	+	0.853024i
$21$	−6.57554	+	1.98583i	−1.43490	+	0.433344i
$22$	−3.80652	+	3.38675i	−0.811553	+	0.722057i
$23$	1.26758	−	2.19550i	0.264308	−	0.457794i	−0.703074	−	0.711116i	$-0.748190\pi$
$23$	1.26758	−	2.19550i	0.264308	−	0.457794i	0.967382	+	0.253322i	$0.0815232\pi$
$24$	−3.10559	+	6.65408i	−0.633925	+	1.35826i
$25$	−4.79964	+	1.40124i	−0.959928	+	0.280248i
$26$	1.13334	−	0.233884i	0.222267	−	0.0458684i
$27$			1.92166i			0.369823i
$28$	5.20910	−	0.930214i	0.984427	−	0.175794i
$29$	−2.04334			−0.379439			−0.189720	−	0.981838i	$-0.560758\pi$
$29$	−2.04334			−0.379439			−0.189720	+	0.981838i	$0.560758\pi$
$30$	−6.27045	−	5.29937i	−1.14482	−	0.967528i
$31$	0.955727	+	1.65537i	0.171654	+	0.297313i	0.938998	−	0.343922i	$-0.111756\pi$
$31$	0.955727	+	1.65537i	0.171654	+	0.297313i	−0.767345	+	0.641235i	$0.778422\pi$
$32$	2.97243	−	4.81297i	0.525456	−	0.850821i
$33$	4.67671	−	8.10030i	0.814111	−	1.41008i
$34$	−6.95283	−	7.81461i	−1.19240	−	1.34019i
$35$	−0.521593	+	5.89304i	−0.0881653	+	0.996106i
$36$	0.870092	−	7.42959i	0.145015	−	1.23827i
$37$	6.20697	+	3.58360i	1.02042	+	0.589140i	0.914226	−	0.405206i	$-0.132800\pi$
$37$	6.20697	+	3.58360i	1.02042	+	0.589140i	0.106195	+	0.994345i	$0.466133\pi$
$38$	1.47138	−	4.43869i	0.238689	−	0.720051i
$39$	−1.83980	+	1.06221i	−0.294603	+	0.170089i
$40$	4.32286	+	4.61658i	0.683505	+	0.729946i
$41$			2.65824i			0.415147i	0.978219	+	0.207573i	$0.0665566\pi$
$41$			2.65824i			0.415147i	−0.978219	+	0.207573i	$0.933443\pi$
$42$	−8.53972	+	4.62987i	−1.31771	+	0.714405i
$43$	−2.39696			−0.365533			−0.182766	−	0.983156i	$-0.558505\pi$
$43$	−2.39696			−0.365533			−0.182766	+	0.983156i	$0.558505\pi$
$44$	−4.30413	+	5.77873i	−0.648872	+	0.871177i
$45$	7.76182	+	3.11433i	1.15706	+	0.464257i
$46$	1.12810	−	3.40314i	0.166330	−	0.501766i
$47$	1.15593	+	0.667376i	0.168610	+	0.0973468i	0.581930	−	0.813239i	$-0.302298\pi$
$47$	1.15593	+	0.667376i	0.168610	+	0.0973468i	−0.413320	+	0.910586i	$0.635631\pi$
$48$	−2.39944	+	10.1037i	−0.346330	+	1.45835i
$49$	6.27046	+	3.11147i	0.895781	+	0.444496i
$50$	−6.24713	+	3.31260i	−0.883478	+	0.468472i
$51$	16.6295	+	9.60106i	2.32860	+	1.34442i
$52$	1.50287	−	0.647871i	0.208410	−	0.0898436i
$53$	−1.56838	+	0.905503i	−0.215433	+	0.124380i	−0.603834	−	0.797110i	$-0.706361\pi$
$53$	−1.56838	+	0.905503i	−0.215433	+	0.124380i	0.388401	+	0.921491i	$0.373028\pi$
$54$	0.549253	+	2.66155i	0.0747439	+	0.362191i
$55$	−4.97499	−	6.33630i	−0.670827	−	0.854386i
$56$	6.94888	−	2.77725i	0.928583	−	0.371126i
$57$			8.58450i			1.13705i
$58$	−2.83009	+	0.584034i	−0.371609	+	0.0766874i
$59$	−0.955727	−	1.65537i	−0.124425	−	0.215510i	0.797083	−	0.603870i	$-0.206375\pi$
$59$	−0.955727	−	1.65537i	−0.124425	−	0.215510i	−0.921508	+	0.388359i	$0.873042\pi$
$60$	−10.1994	−	5.54755i	−1.31674	−	0.716185i
$61$	−8.46625	−	4.88799i	−1.08399	−	0.625843i	−0.152021	−	0.988377i	$-0.548578\pi$
$61$	−8.46625	−	4.88799i	−1.08399	−	0.625843i	−0.931970	+	0.362534i	$0.881912\pi$
$62$	1.79685	+	2.01956i	0.228200	+	0.256485i
$63$	6.77344	−	7.21411i	0.853374	−	0.908892i
$64$	2.74124	−	7.51569i	0.342655	−	0.939461i
$65$	0.258997	+	1.81131i	0.0321246	+	0.224666i
$66$	4.16213	−	12.5559i	0.512323	−	1.54552i
$67$	−4.63112	−	8.02134i	−0.565782	−	0.979963i	−0.996976	−	0.0777041i	$-0.975241\pi$
$67$	−4.63112	−	8.02134i	−0.565782	−	0.979963i	0.431195	−	0.902259i	$-0.358092\pi$
$68$	−11.8635	−	8.83618i	−1.43866	−	1.07154i
$69$			6.58172i			0.792346i
$70$	0.961944	+	8.31112i	0.114974	+	0.993368i
$71$			1.38422i			0.164277i	0.996621	+	0.0821385i	$0.0261750\pi$
$71$			1.38422i			0.164277i	−0.996621	+	0.0821385i	$0.973825\pi$
$72$	−0.918444	−	10.5389i	−0.108240	−	1.24202i
$73$	3.69814	+	6.40537i	0.432835	+	0.749692i	0.997116	−	0.0758908i	$-0.0241800\pi$
$73$	3.69814	+	6.40537i	0.432835	+	0.749692i	−0.564281	+	0.825583i	$0.690847\pi$
$74$	9.62111	+	3.18929i	1.11843	+	0.370748i
$75$	8.97240	−	9.38087i	1.03604	−	1.08321i
$76$	0.769222	−	6.56827i	0.0882358	−	0.753433i
$77$	−9.12495	+	2.75576i	−1.03988	+	0.314048i
$78$	−2.24457	+	1.99704i	−0.254147	+	0.226121i
$79$	−6.70979	−	3.87390i	−0.754910	−	0.435848i	0.0725552	−	0.997364i	$-0.476885\pi$
$79$	−6.70979	−	3.87390i	−0.754910	−	0.435848i	−0.827465	+	0.561517i	$0.810218\pi$
$80$	7.30682	+	5.15853i	0.816927	+	0.576741i
$81$	3.11579	+	5.39670i	0.346199	+	0.599634i
$82$	0.759784	+	3.68173i	0.0839041	+	0.406579i
$83$			10.4973i			1.15223i	0.817370	+	0.576113i	$0.195431\pi$
$83$			10.4973i			1.15223i	−0.817370	+	0.576113i	$0.804569\pi$
$84$	−10.5044	+	8.85335i	−1.14613	+	0.965980i
$85$	13.0081	−	10.2134i	1.41093	−	1.10780i
$86$	−3.31986	+	0.685105i	−0.357989	+	0.0738768i
$87$	4.59418	−	2.65245i	0.492547	−	0.284372i
$88$	−4.30966	+	9.23393i	−0.459411	+	0.984341i
$89$	−9.19133	−	5.30662i	−0.974279	−	0.562500i	−0.0737410	−	0.997277i	$-0.523494\pi$
$89$	−9.19133	−	5.30662i	−0.974279	−	0.562500i	−0.900538	+	0.434777i	$0.856827\pi$
$90$	11.6405	+	2.09494i	1.22702	+	0.220826i
$91$	2.10781	+	0.494210i	0.220958	+	0.0518073i
$92$	0.589761	−	5.03589i	0.0614868	−	0.525027i
$93$	−4.29764	−	2.48125i	−0.445645	−	0.257293i
$94$	1.79175	+	0.593945i	0.184805	+	0.0612607i
$95$	6.86198	+	2.75329i	0.704025	+	0.282481i
$96$	−0.435416	+	14.6798i	−0.0444395	+	1.49825i
$97$	7.32005			0.743239			0.371619	−	0.928385i	$-0.378803\pi$
$97$	7.32005			0.743239			0.371619	+	0.928385i	$0.378803\pi$
$98$	9.57411	+	2.51724i	0.967131	+	0.254280i
$99$			13.4750i			1.35428i
$100$	−7.70564	+	6.37362i	−0.770564	+	0.637362i
$101$	−5.50608	+	3.17894i	−0.547875	+	0.316316i	−0.748265	−	0.663400i	$-0.769113\pi$
$101$	−5.50608	+	3.17894i	−0.547875	+	0.316316i	0.200389	+	0.979716i	$0.435779\pi$
$102$	25.7766	+	8.54465i	2.55226	+	0.846047i
$103$	0.885144	+	0.511038i	0.0872158	+	0.0503541i	0.542974	−	0.839750i	$-0.317298\pi$
$103$	0.885144	+	0.511038i	0.0872158	+	0.0503541i	−0.455758	+	0.890104i	$0.650632\pi$
$104$	1.89634	−	1.32687i	0.185951	−	0.130111i
$105$	−6.47699	−	13.9268i	−0.632089	−	1.35911i
$106$	−1.91343	+	1.70243i	−0.185849	+	0.165354i
$107$	−3.62578	+	6.28003i	−0.350517	+	0.607114i	−0.986340	−	0.164721i	$-0.947328\pi$
$107$	−3.62578	+	6.28003i	−0.350517	+	0.607114i	0.635823	+	0.771835i	$0.280661\pi$
$108$	1.52146	+	3.52933i	0.146403	+	0.339610i
$109$	3.98588	+	6.90375i	0.381778	+	0.661259i	0.991316	−	0.131498i	$-0.0419786\pi$
$109$	3.98588	+	6.90375i	0.381778	+	0.661259i	−0.609538	+	0.792756i	$0.708645\pi$
$110$	−8.70156	−	7.35399i	−0.829661	−	0.701175i
$111$	−18.6074			−1.76613
$112$	8.83059	−	5.83272i	0.834413	−	0.551140i
$113$			7.61610i			0.716462i	0.933633	+	0.358231i	$0.116620\pi$
$113$			7.61610i			0.716462i	−0.933633	+	0.358231i	$0.883380\pi$
$114$	2.45365	+	11.8898i	0.229805	+	1.11358i
$115$	5.26107	+	2.11094i	0.490597	+	0.196846i
$116$	−3.75282	+	1.61781i	−0.348441	+	0.150210i
$117$	1.53026	−	2.65049i	0.141473	−	0.245038i
$118$	−1.79685	−	2.01956i	−0.165414	−	0.185916i
$119$	−5.65744	−	18.7331i	−0.518616	−	1.71726i
$120$	−15.7121	−	4.76828i	−1.43431	−	0.435283i
$121$	0.989917	−	1.71459i	0.0899925	−	0.155872i
$122$	−13.1231	−	4.35016i	−1.18811	−	0.393845i
$123$	−3.45064	−	5.97668i	−0.311134	−	0.538899i
$124$	3.06593	+	2.28357i	0.275328	+	0.205071i
$125$	−4.62086	−	10.1807i	−0.413303	−	0.910594i
$126$	7.31946	−	11.9277i	0.652069	−	1.06261i
$127$	−8.78136			−0.779220			−0.389610	−	0.920980i	$-0.627390\pi$
$127$	−8.78136			−0.779220			−0.389610	+	0.920980i	$0.627390\pi$
$128$	1.64855	−	11.1930i	0.145712	−	0.989327i
$129$	5.38923	−	3.11147i	0.474495	−	0.273950i
$130$	0.876433	+	2.43469i	0.0768682	+	0.213537i
$131$	−6.69467	+	11.5955i	−0.584916	+	1.01310i	0.409970	+	0.912099i	$0.365539\pi$
$131$	−6.69467	+	11.5955i	−0.584916	+	1.01310i	−0.994886	+	0.101005i	$0.967794\pi$
$132$	2.17592	−	18.5799i	0.189389	−	1.61717i
$133$	5.98819	−	6.37777i	0.519242	−	0.553023i
$134$	−8.70692	−	9.78611i	−0.752164	−	0.845391i
$135$	−4.25369	+	0.608229i	−0.366099	+	0.0523481i
$136$	−18.9568	−	8.84752i	−1.62553	−	0.758668i
$137$	−4.52425	+	2.61208i	−0.386533	+	0.223165i	−0.680657	−	0.732602i	$-0.738306\pi$
$137$	−4.52425	+	2.61208i	−0.386533	+	0.223165i	0.294124	+	0.955767i	$0.404972\pi$
$138$	1.88121	+	9.11588i	0.160139	+	0.775995i
$139$	21.9442			1.86128			0.930641	−	0.365933i	$-0.119250\pi$
$139$	21.9442			1.86128			0.930641	+	0.365933i	$0.119250\pi$
$140$	3.70783	+	11.2362i	0.313369	+	0.949632i
$141$	−3.46527			−0.291828
$142$	0.395643	+	1.91719i	0.0332016	+	0.160887i
$143$	−2.55310	+	1.47403i	−0.213501	+	0.123265i
$144$	−4.28433	−	14.3342i	−0.357027	−	1.19451i
$145$	−0.646745	−	4.52305i	−0.0537092	−	0.375619i
$146$	6.95283	+	7.81461i	0.575421	+	0.646742i
$147$	−18.1373	+	1.14392i	−1.49594	+	0.0943492i
$148$	14.2371	+	1.66733i	1.17028	+	0.137054i
$149$	11.9749	−	20.7411i	0.981019	−	1.69917i	0.322575	−	0.946544i	$-0.395452\pi$
$149$	11.9749	−	20.7411i	0.981019	−	1.69917i	0.658444	−	0.752630i	$-0.271215\pi$
$150$	9.74576	−	15.5573i	0.795738	−	1.27025i
$151$	6.06876	−	3.50380i	0.493869	−	0.285135i	−0.232309	−	0.972642i	$-0.574628\pi$
$151$	6.06876	−	3.50380i	0.493869	−	0.285135i	0.726178	+	0.687507i	$0.241295\pi$
$152$	−0.811968	−	9.31711i	−0.0658593	−	0.755717i
$153$	−27.6635			−2.23646
$154$	−11.8507	+	6.42492i	−0.954953	+	0.517735i
$155$	−3.36174	+	2.63950i	−0.270022	+	0.212010i
$156$	−2.53799	+	3.40751i	−0.203202	+	0.272819i
$157$	−3.21277	−	5.56468i	−0.256407	−	0.444110i	0.708870	−	0.705340i	$-0.249205\pi$
$157$	−3.21277	−	5.56468i	−0.256407	−	0.444110i	−0.965277	+	0.261229i	$0.915872\pi$
$158$	−10.4005	−	3.44765i	−0.827419	−	0.274280i
$159$	2.35085	−	4.07180i	0.186435	−	0.322915i
$160$	11.5946	+	5.05626i	0.916632	+	0.399733i
$161$	4.59114	−	4.88982i	0.361832	−	0.385372i
$162$	5.85796	+	6.58403i	0.460245	+	0.517290i
$163$	−9.23950	+	16.0033i	−0.723693	+	1.25347i	0.235816	+	0.971798i	$0.424224\pi$
$163$	−9.23950	+	16.0033i	−0.723693	+	1.25347i	−0.959510	+	0.281676i	$0.909110\pi$
$164$	2.10465	+	4.88214i	0.164345	+	0.381231i
$165$	19.4107	+	7.78830i	1.51112	+	0.606318i
$166$	3.00036	+	14.5390i	0.232873	+	1.12845i
$167$			1.82894i			0.141527i	0.997493	+	0.0707637i	$0.0225436\pi$
$167$			1.82894i			0.141527i	−0.997493	+	0.0707637i	$0.977456\pi$
$168$	−12.0185	+	15.2646i	−0.927245	+	1.17769i
$169$	−12.3304			−0.948493
$170$	15.0974	−	17.8639i	1.15792	−	1.37010i
$171$	−6.18361	−	10.7103i	−0.472873	−	0.819039i
$172$	−4.40228	+	1.89778i	−0.335671	+	0.144704i
$173$	−7.62476	+	13.2065i	−0.579700	+	1.00407i	0.415814	+	0.909450i	$0.363497\pi$
$173$	−7.62476	+	13.2065i	−0.579700	+	1.00407i	−0.995514	+	0.0946193i	$0.969837\pi$
$174$	5.60494	−	4.98684i	0.424909	−	0.378051i
$175$	−13.2097	+	0.710651i	−0.998556	+	0.0537201i
$176$	−3.32973	+	14.0211i	−0.250988	+	1.05688i
$177$	4.29764	+	2.48125i	0.323031	+	0.186502i
$178$	−14.2470	−	4.72273i	−1.06786	−	0.353983i
$179$	−10.8572	+	6.26844i	−0.811509	+	0.468525i	−0.847480	−	0.530828i	$-0.821881\pi$
$179$	−10.8572	+	6.26844i	−0.811509	+	0.468525i	0.0359707	+	0.999353i	$0.488548\pi$
$180$	16.7212	−	0.425568i	1.24632	−	0.0317200i
$181$		−	8.01839i		−	0.596002i	−0.954566	−	0.298001i	$-0.903680\pi$
$181$		−	8.01839i		−	0.596002i	0.954566	−	0.298001i	$-0.0963199\pi$
$182$	3.06063	+	0.0820350i	0.226869	+	0.00608084i
$183$	25.3803			1.87616
$184$	−0.622535	−	7.14341i	−0.0458939	−	0.526619i
$185$	−5.96790	+	14.8737i	−0.438769	+	1.09354i
$186$	−6.66156	−	2.20823i	−0.488449	−	0.161915i
$187$	23.0770	+	13.3235i	1.68755	+	0.974310i
$188$	2.65139	+	0.310508i	0.193372	+	0.0226461i
$189$	−1.16060	+	4.94998i	−0.0844215	+	0.360058i
$190$	10.2910	+	1.85207i	0.746587	+	0.134363i
$191$	5.85379	+	3.37969i	0.423565	+	0.244546i	0.696602	−	0.717458i	$-0.254695\pi$
$191$	5.85379	+	3.37969i	0.423565	+	0.244546i	−0.273036	+	0.962004i	$0.588028\pi$
$192$	3.59276	+	20.4564i	0.259285	+	1.47631i
$193$	2.04384	−	1.18001i	0.147119	−	0.0849392i	−0.424634	−	0.905365i	$-0.639597\pi$
$193$	2.04384	−	1.18001i	0.147119	−	0.0849392i	0.571753	+	0.820426i	$0.306264\pi$
$194$	10.1385	−	2.09224i	0.727901	−	0.150214i
$195$	−2.93357	−	3.73628i	−0.210077	−	0.267561i
$196$	13.9799	+	0.749953i	0.998564	+	0.0535681i
$197$		−	20.3205i		−	1.44777i	−0.689918	−	0.723887i	$-0.742353\pi$
$197$		−	20.3205i		−	1.44777i	0.689918	−	0.723887i	$-0.257647\pi$
$198$	3.85145	+	18.6632i	0.273711	+	1.32634i
$199$	5.72909	+	9.92308i	0.406125	+	0.703429i	0.994452	−	0.105195i	$-0.0335465\pi$
$199$	5.72909	+	9.92308i	0.406125	+	0.703429i	−0.588327	+	0.808623i	$0.700213\pi$
$200$	−8.85081	+	11.0301i	−0.625847	+	0.779946i
$201$	20.8249	+	12.0233i	1.46888	+	0.848056i
$202$	−6.71746	+	5.97668i	−0.472639	+	0.420518i
$203$	−5.26343	−	1.23410i	−0.369421	−	0.0866166i
$204$	38.1436	+	4.46706i	2.67058	+	0.312757i
$205$	−5.88415	+	0.841366i	−0.410967	+	0.0587636i
$206$	1.37202	+	0.454808i	0.0955929	+	0.0316880i
$207$	−4.74097	−	8.21159i	−0.329520	−	0.570745i
$208$	2.24723	−	2.37978i	0.155817	−	0.165008i
$209$			11.9128i			0.824026i
$210$	−12.9514	−	17.4377i	−0.893732	−	1.20332i
$211$		−	22.0647i		−	1.51900i	−0.650510	−	0.759498i	$-0.725445\pi$
$211$		−	22.0647i		−	1.51900i	0.650510	−	0.759498i	$-0.274555\pi$
$212$	−2.16357	+	2.90481i	−0.148595	+	0.199503i
$213$	−1.79685	−	3.11224i	−0.123118	−	0.213247i
$214$	−3.22683	+	9.73436i	−0.220582	+	0.665427i
$215$	−0.758668	−	5.30579i	−0.0517408	−	0.361852i
$216$	3.11603	+	4.45336i	0.212019	+	0.303013i
$217$	1.46208	+	4.84127i	0.0992522	+	0.328647i
$218$	7.49381	+	8.42263i	0.507545	+	0.570453i
$219$	−16.6295	−	9.60106i	−1.12372	−	0.648780i
$220$	−14.1539	−	7.69838i	−0.954253	−	0.519025i
$221$	−3.02612	−	5.24140i	−0.203559	−	0.352575i
$222$	−25.7718	+	5.31841i	−1.72969	+	0.356948i
$223$		−	23.5776i		−	1.57887i	−0.613833	−	0.789436i	$-0.710373\pi$
$223$		−	23.5776i		−	1.57887i	0.613833	−	0.789436i	$-0.289627\pi$
$224$	10.5635	−	10.6025i	0.705804	−	0.708408i
$225$	−4.43703	+	18.1669i	−0.295802	+	1.21113i
$226$	2.17685	+	10.5485i	0.144802	+	0.701677i
$227$	18.1231	−	10.4634i	1.20287	−	0.694478i	0.241678	−	0.970356i	$-0.422302\pi$
$227$	18.1231	−	10.4634i	1.20287	−	0.694478i	0.961192	+	0.275879i	$0.0889689\pi$
$228$	6.79674	+	15.7664i	0.450125	+	1.04415i
$229$	4.48735	+	2.59077i	0.296533	+	0.171203i	0.640884	−	0.767638i	$-0.278568\pi$
$229$	4.48735	+	2.59077i	0.296533	+	0.171203i	−0.344352	+	0.938841i	$0.611901\pi$
$230$	7.89009	+	1.41998i	0.520257	+	0.0936306i
$231$	16.9390	−	18.0410i	1.11450	−	1.18701i
$232$	−4.73536	+	3.31335i	−0.310892	+	0.217532i
$233$	17.9868	+	10.3847i	1.17836	+	0.680324i	0.955634	−	0.294558i	$-0.0951724\pi$
$233$	17.9868	+	10.3847i	1.17836	+	0.680324i	0.222722	+	0.974882i	$0.428506\pi$
$234$	1.36189	−	4.10839i	0.0890294	−	0.268574i
$235$	−1.11141	+	2.76995i	−0.0725002	+	0.180691i
$236$	−3.06593	−	2.28357i	−0.199575	−	0.148648i
$237$	20.1147			1.30659
$238$	−13.1901	−	24.3288i	−0.854984	−	1.57700i
$239$			21.1286i			1.36670i	0.730092	+	0.683349i	$0.239477\pi$
$239$			21.1286i			1.36670i	−0.730092	+	0.683349i	$0.760523\pi$
$240$	−23.1246	−	2.11332i	−1.49269	−	0.136415i
$241$	1.57448	−	0.909029i	0.101421	−	0.0585557i	−0.448431	−	0.893817i	$-0.648017\pi$
$241$	1.57448	−	0.909029i	0.101421	−	0.0585557i	0.549853	+	0.835262i	$0.314684\pi$
$242$	0.880996	−	2.65769i	0.0566326	−	0.170843i
$243$	−19.0035	−	10.9716i	−1.21907	−	0.703832i
$244$	−19.4192	−	2.27422i	−1.24319	−	0.145592i
$245$	−4.90273	+	14.8648i	−0.313224	+	0.949679i
$246$	−6.48750	−	7.29160i	−0.413628	−	0.464896i
$247$	1.35286	−	2.34322i	0.0860803	−	0.149095i
$248$	4.89910	+	2.28650i	0.311093	+	0.145193i
$249$	−13.6264	−	23.6017i	−0.863540	−	1.49570i
$250$	−9.30992	−	12.7799i	−0.588811	−	0.808271i
$251$	14.0187			0.884856			0.442428	−	0.896804i	$-0.354117\pi$
$251$	14.0187			0.884856			0.442428	+	0.896804i	$0.354117\pi$
$252$	6.72844	−	18.6123i	0.423852	−	1.17247i
$253$			9.13352i			0.574220i
$254$	−12.1624	+	2.50991i	−0.763140	+	0.157486i
$255$	−15.9890	+	39.8492i	−1.00127	+	2.49546i
$256$	−0.915918	−	15.9738i	−0.0572449	−	0.998360i
$257$	8.93624	−	15.4780i	0.557427	−	0.965492i	−0.440283	−	0.897859i	$-0.645122\pi$
$257$	8.93624	−	15.4780i	0.557427	−	0.965492i	0.997710	−	0.0676333i	$-0.0215448\pi$
$258$	6.57491	−	5.84985i	0.409336	−	0.364196i
$259$	13.8242	+	12.9797i	0.858991	+	0.806521i
$260$	1.90977	+	3.12161i	0.118439	+	0.193594i
$261$	−3.82124	+	6.61858i	−0.236529	+	0.409680i
$262$	−5.95805	+	17.9736i	−0.368090	+	1.11041i
$263$	10.9482	+	18.9629i	0.675097	+	1.16930i	0.976440	+	0.215787i	$0.0692317\pi$
$263$	10.9482	+	18.9629i	0.675097	+	1.16930i	−0.301343	+	0.953516i	$0.597435\pi$
$264$	−2.29684	−	26.3556i	−0.141361	−	1.62207i
$265$	−2.50079	−	3.18508i	−0.153622	−	0.195658i
$266$	6.47091	−	10.5450i	0.396757	−	0.646553i
$267$	27.5539			1.68627
$268$	−14.8564	−	11.0654i	−0.907501	−	0.675928i
$269$	2.49661	−	1.44142i	0.152221	−	0.0878847i	−0.421955	−	0.906617i	$-0.638656\pi$
$269$	2.49661	−	1.44142i	0.152221	−	0.0878847i	0.574176	+	0.818732i	$0.305323\pi$
$270$	−5.71764	+	2.05822i	−0.347964	+	0.125259i
$271$	−8.47793	+	14.6842i	−0.514997	+	0.892002i	0.484851	+	0.874597i	$0.338874\pi$
$271$	−8.47793	+	14.6842i	−0.514997	+	0.892002i	−0.999849	+	0.0174049i	$0.994460\pi$
$272$	−28.7846	−	6.83578i	−1.74532	−	0.414480i
$273$	−5.38065	+	1.62497i	−0.325652	+	0.0983476i
$274$	−5.51963	+	4.91094i	−0.333453	+	0.296681i
$275$	12.4511	−	13.0179i	0.750829	−	0.785010i
$276$	5.21105	+	12.0881i	0.313668	+	0.727616i
$277$	−23.2541	+	13.4258i	−1.39720	+	0.806677i	−0.994099	−	0.108477i	$-0.965403\pi$
$277$	−23.2541	+	13.4258i	−1.39720	+	0.806677i	−0.403106	+	0.915153i	$0.632069\pi$
$278$	30.3933	−	6.27215i	1.82287	−	0.376179i
$279$	7.14919			0.428011
$280$	8.34701	+	14.5027i	0.498829	+	0.866700i
$281$	24.9497			1.48838			0.744188	−	0.667971i	$-0.232837\pi$
$281$	24.9497			1.48838			0.744188	+	0.667971i	$0.232837\pi$
$282$	−4.79950	+	0.990452i	−0.285806	+	0.0589806i
$283$	−8.52014	+	4.91910i	−0.506470	+	0.292410i	−0.731381	−	0.681969i	$-0.761124\pi$
$283$	−8.52014	+	4.91910i	−0.506470	+	0.292410i	0.224912	+	0.974379i	$0.427791\pi$
$284$	1.09595	+	2.54228i	0.0650328	+	0.150857i
$285$	−19.0023	+	2.71711i	−1.12560	+	0.160948i
$286$	−3.11481	+	2.77132i	−0.184183	+	0.163871i
$287$	−1.60547	+	6.84733i	−0.0947678	+	0.404185i
$288$	−10.0309	−	18.6287i	−0.591079	−	1.09770i
$289$	−18.8525	+	32.6535i	−1.10897	+	1.92079i
$290$	−2.18855	−	6.07970i	−0.128516	−	0.357012i
$291$	−16.4581	+	9.50211i	−0.964793	+	0.557024i
$292$	11.8635	+	8.83618i	0.694257	+	0.517098i
$293$	23.4039			1.36727			0.683636	−	0.729823i	$-0.260398\pi$
$293$	23.4039			1.36727			0.683636	+	0.729823i	$0.260398\pi$
$294$	−24.7937	+	6.76841i	−1.44600	+	0.394742i
$295$	3.36174	−	2.63950i	0.195728	−	0.153678i
$296$	20.1953	−	1.75999i	1.17383	−	0.102297i
$297$	−3.46163	−	5.99571i	−0.200864	−	0.347907i
$298$	10.6573	−	32.1497i	0.617358	−	1.86238i
$299$	1.03723	−	1.79654i	0.0599848	−	0.103897i
$300$	9.05153	−	24.3329i	0.522591	−	1.40486i
$301$	−6.17431	−	1.44767i	−0.355881	−	0.0834421i
$302$	7.40395	−	6.58746i	0.426049	−	0.379066i
$303$	8.25311	−	14.2948i	0.474129	−	0.821215i
$304$	−3.78764	−	12.6724i	−0.217236	−	0.726811i
$305$	8.14015	−	20.2876i	0.466104	−	1.16166i
$306$	−38.3147	+	7.90685i	−2.19031	+	0.452004i
$307$		−	2.18529i		−	0.124721i	−0.998054	−	0.0623606i	$-0.980137\pi$
$307$		−	2.18529i		−	0.124721i	0.998054	−	0.0623606i	$-0.0198629\pi$
$308$	−14.5771	+	12.2859i	−0.830608	+	0.700053i
$309$	−2.65350			−0.150952
$310$	−3.90168	+	4.61664i	−0.221601	+	0.262208i
$311$	−14.4501	−	25.0282i	−0.819388	−	1.41922i	−0.906134	−	0.422991i	$-0.860980\pi$
$311$	−14.4501	−	25.0282i	−0.819388	−	1.41922i	0.0867457	−	0.996230i	$-0.472353\pi$
$312$	−2.54125	+	5.44492i	−0.143870	+	0.308258i
$313$	3.17652	−	5.50189i	0.179548	−	0.310985i	−0.762178	−	0.647367i	$-0.775870\pi$
$313$	3.17652	−	5.50189i	0.179548	−	0.310985i	0.941726	+	0.336382i	$0.109203\pi$
$314$	−6.04030	−	6.78897i	−0.340874	−	0.383124i
$315$	18.1127	+	12.7100i	1.02053	+	0.716129i
$316$	−15.3904	−	1.80240i	−0.865778	−	0.101393i
$317$	−16.2839	−	9.40153i	−0.914597	−	0.528043i	−0.0326894	−	0.999466i	$-0.510407\pi$
$317$	−16.2839	−	9.40153i	−0.914597	−	0.528043i	−0.881907	+	0.471423i	$0.843741\pi$
$318$	2.09219	−	6.31149i	0.117324	−	0.353931i
$319$	6.37538	−	3.68083i	0.356953	−	0.206087i
$320$	17.5040	+	3.68907i	0.978504	+	0.206225i
$321$		−	18.8264i		−	1.05079i
$322$	4.96124	−	8.08480i	0.276479	−	0.450548i
$323$	−24.4564			−1.36079
$324$	9.99530	+	7.44473i	0.555295	+	0.413596i
$325$	−3.92746	+	1.14661i	−0.217856	+	0.0636024i
$326$	−8.22287	+	24.8059i	−0.455423	+	1.37387i
$327$	−17.9234	−	10.3481i	−0.991167	−	0.572250i
$328$	4.31042	+	6.16035i	0.238003	+	0.340149i
$329$	2.57448	+	2.41723i	0.141936	+	0.133266i
$330$	29.1104	+	5.23900i	1.60248	+	0.288398i
$331$	−11.3353	−	6.54441i	−0.623042	−	0.359713i	0.155010	−	0.987913i	$-0.450459\pi$
$331$	−11.3353	−	6.54441i	−0.623042	−	0.359713i	−0.778052	+	0.628199i	$0.783792\pi$
$332$	8.31117	+	19.2794i	0.456135	+	1.05809i
$333$	23.2152	−	13.4033i	1.27219	−	0.734497i
$334$	0.522752	+	2.53313i	0.0286037	+	0.138607i
$335$	16.2899	−	12.7901i	0.890010	−	0.698798i
$336$	−12.2830	+	24.5770i	−0.670091	+	1.34079i
$337$		−	11.7319i		−	0.639079i	−0.947573	−	0.319539i	$-0.896472\pi$
$337$		−	11.7319i		−	0.639079i	0.947573	−	0.319539i	$-0.103528\pi$
$338$	−17.0780	+	3.52431i	−0.928920	+	0.191697i
$339$	−9.88640	−	17.1238i	−0.536956	−	0.930035i
$340$	15.8044	−	29.0572i	0.857115	−	1.57585i
$341$	−5.96388	−	3.44325i	−0.322962	−	0.186462i
$342$	−11.6257	−	13.0667i	−0.628648	−	0.706566i
$343$	14.2729	+	11.8019i	0.770661	+	0.637245i
$344$	−5.55485	+	3.88675i	−0.299498	+	0.209560i
$345$	−14.5690	+	2.08320i	−0.784369	+	0.112156i
$346$	−6.78580	+	20.4707i	−0.364807	+	1.10051i
$347$	2.20585	+	3.82065i	0.118416	+	0.205103i	0.919140	−	0.393930i	$-0.128885\pi$
$347$	2.20585	+	3.82065i	0.118416	+	0.205103i	−0.800724	+	0.599034i	$0.795552\pi$
$348$	6.33765	−	8.50894i	0.339734	−	0.456127i
$349$			18.3479i			0.982142i	0.871120	+	0.491071i	$0.163394\pi$
$349$			18.3479i			0.982142i	−0.871120	+	0.491071i	$0.836606\pi$
$350$	−18.0926	+	4.75989i	−0.967092	+	0.254427i
$351$			1.57246i			0.0839316i
$352$	−0.604231	+	20.3713i	−0.0322056	+	1.08579i
$353$	−5.87406	−	10.1742i	−0.312645	−	0.541516i	0.666289	−	0.745693i	$-0.267882\pi$
$353$	−5.87406	−	10.1742i	−0.312645	−	0.541516i	−0.978934	+	0.204177i	$0.934548\pi$
$354$	6.66156	+	2.20823i	0.354058	+	0.117366i
$355$	−3.06405	+	0.438125i	−0.162623	+	0.0232533i
$356$	−21.0824	−	2.46899i	−1.11736	−	0.130856i
$357$	37.0373	+	34.7749i	1.96022	+	1.84048i
$358$	−13.2459	+	11.7852i	−0.700070	+	0.622868i
$359$	−0.171388	−	0.0989510i	−0.00904552	−	0.00522243i	0.495470	−	0.868625i	$-0.334996\pi$
$359$	−0.171388	−	0.0989510i	−0.00904552	−	0.00522243i	−0.504516	+	0.863402i	$0.668329\pi$
$360$	23.0377	−	5.36872i	1.21419	−	0.282957i
$361$	4.03326	+	6.98581i	0.212277	+	0.367674i
$362$	−2.29184	−	11.1057i	−0.120456	−	0.583703i
$363$			5.14002i			0.269781i
$364$	4.26251	−	0.761178i	0.223416	−	0.0398966i
$365$	−13.0081	+	10.2134i	−0.680876	+	0.534595i
$366$	35.1524	−	7.25426i	1.83745	−	0.379186i
$367$	−6.51964	+	3.76412i	−0.340323	+	0.196485i	−0.660415	−	0.750901i	$-0.729619\pi$
$367$	−6.51964	+	3.76412i	−0.340323	+	0.196485i	0.320092	+	0.947386i	$0.396286\pi$
$368$	−2.90398	−	9.71590i	−0.151380	−	0.506476i
$369$	8.61028	+	4.97115i	0.448233	+	0.258787i
$370$	−4.01446	+	22.3063i	−0.208702	+	1.15965i
$371$	−4.58686	+	1.38524i	−0.238138	+	0.0719182i
$372$	−9.85761	−	1.15444i	−0.511093	−	0.0598550i
$373$	−26.9674	−	15.5696i	−1.39632	−	0.806164i	−0.402312	−	0.915503i	$-0.631793\pi$
$373$	−26.9674	−	15.5696i	−1.39632	−	0.806164i	−0.994005	+	0.109339i	$0.965127\pi$
$374$	35.7704	+	11.8575i	1.84964	+	0.613137i
$375$	23.6049	+	16.8917i	1.21895	+	0.872284i
$376$	3.76100	−	0.327763i	0.193959	−	0.0169031i
$377$	−1.67203			−0.0861140
$378$	−0.192651	+	7.18760i	−0.00990891	+	0.369690i
$379$		−	16.3396i		−	0.839307i	−0.907684	−	0.419654i	$-0.862152\pi$
$379$		−	16.3396i		−	0.839307i	0.907684	−	0.419654i	$-0.137848\pi$
$380$	14.7827	−	0.376232i	0.758336	−	0.0193003i
$381$	19.7437	−	11.3990i	1.01150	−	0.583990i
$382$	9.07366	+	3.00782i	0.464249	+	0.153893i
$383$	7.66318	+	4.42434i	0.391570	+	0.226073i	0.682840	−	0.730568i	$-0.260744\pi$
$383$	7.66318	+	4.42434i	0.391570	+	0.226073i	−0.291270	+	0.956641i	$0.594078\pi$
$384$	10.8230	+	27.3058i	0.552307	+	1.39344i
$385$	−8.98818	−	19.3263i	−0.458080	−	0.984961i
$386$	2.49351	−	2.21853i	0.126916	−	0.112920i
$387$	−4.48253	+	7.76397i	−0.227860	+	0.394665i
$388$	13.4441	−	5.79562i	0.682520	−	0.294228i
$389$	−4.67264	−	8.09325i	−0.236912	−	0.410344i	0.722915	−	0.690937i	$-0.242802\pi$
$389$	−4.67264	−	8.09325i	−0.236912	−	0.410344i	−0.959827	+	0.280594i	$0.909469\pi$
$390$	−5.13100	−	4.33638i	−0.259818	−	0.219581i
$391$	−18.7507			−0.948263
$392$	19.5769	−	2.95707i	0.988784	−	0.149354i
$393$		−	34.7612i		−	1.75347i
$394$	−5.80806	−	28.1445i	−0.292606	−	1.41790i
$395$	6.45134	−	16.0786i	0.324602	−	0.809003i
$396$	10.6687	+	24.7483i	0.536125	+	1.24365i
$397$	−10.1513	+	17.5826i	−0.509480	+	0.882446i	0.490459	+	0.871464i	$0.336829\pi$
$397$	−10.1513	+	17.5826i	−0.509480	+	0.882446i	−0.999940	+	0.0109817i	$0.996504\pi$
$398$	10.7712	+	12.1063i	0.539912	+	0.606831i
$399$	−5.18470	+	22.1128i	−0.259559	+	1.10702i
$400$	−9.10598	+	17.8068i	−0.455299	+	0.890339i
$401$	5.54334	−	9.60135i	0.276821	−	0.479469i	−0.693772	−	0.720195i	$-0.744052\pi$
$401$	5.54334	−	9.60135i	0.276821	−	0.479469i	0.970593	+	0.240726i	$0.0773857\pi$
$402$	32.2796	+	10.7003i	1.60996	+	0.533684i
$403$	0.782054	+	1.35456i	0.0389569	+	0.0674753i
$404$	−7.59561	+	10.1979i	−0.377896	+	0.507363i
$405$	−10.9597	+	8.60509i	−0.544592	+	0.427590i
$406$	−7.64274	−	0.204851i	−0.379303	−	0.0101666i
$407$	−25.8216			−1.27993
$408$	54.1067	−	4.71530i	2.67868	−	0.233442i
$409$	5.09812	−	2.94340i	0.252086	−	0.145542i	−0.368633	−	0.929575i	$-0.620174\pi$
$409$	5.09812	−	2.94340i	0.252086	−	0.145542i	0.620719	+	0.784033i	$0.286841\pi$
$410$	−7.90923	+	2.84714i	−0.390609	+	0.140610i
$411$	6.78145	−	11.7458i	0.334504	−	0.579378i
$412$	2.03028	+	0.237769i	0.100025	+	0.0117140i
$413$	−1.46208	−	4.84127i	−0.0719441	−	0.238223i
$414$	−8.91343	−	10.0182i	−0.438071	−	0.492369i
$415$	−23.2363	+	3.32252i	−1.14062	+	0.163096i
$416$	2.43229	−	3.93837i	0.119253	−	0.193094i
$417$	−49.3385	+	28.4856i	−2.41612	+	1.39495i
$418$	3.40495	+	16.4996i	0.166542	+	0.807020i
$419$	−16.7262			−0.817126			−0.408563	−	0.912730i	$-0.633970\pi$
$419$	−16.7262			−0.817126			−0.408563	+	0.912730i	$0.633970\pi$
$420$	−22.9222	−	20.4499i	−1.11849	−	0.997855i
$421$	−1.18823			−0.0579109			−0.0289555	−	0.999581i	$-0.509218\pi$
$421$	−1.18823			−0.0579109			−0.0289555	+	0.999581i	$0.509218\pi$
$422$	−6.30659	−	30.5602i	−0.307000	−	1.48765i
$423$	4.32339	−	2.49611i	0.210210	−	0.121365i
$424$	−2.16635	+	4.64165i	−0.105207	+	0.225418i
$425$	26.7252	+	25.5615i	1.29636	+	1.23991i
$426$	−3.37824	−	3.79696i	−0.163676	−	0.183963i
$427$	−18.8560	−	17.7042i	−0.912506	−	0.856767i
$428$	−1.68696	+	14.4047i	−0.0815421	+	0.696276i
$429$	3.82687	−	6.62833i	0.184763	−	0.320019i
$430$	−2.56729	−	7.13183i	−0.123806	−	0.343928i
$431$	20.8669	−	12.0475i	1.00512	−	0.580307i	0.0953622	−	0.995443i	$-0.469599\pi$
$431$	20.8669	−	12.0475i	1.00512	−	0.580307i	0.909760	+	0.415135i	$0.136266\pi$
$432$	5.58867	+	5.27740i	0.268885	+	0.253909i
$433$	14.9805			0.719916			0.359958	−	0.932968i	$-0.382791\pi$
$433$	14.9805			0.719916			0.359958	+	0.932968i	$0.382791\pi$
$434$	3.40876	+	6.28741i	0.163626	+	0.301805i
$435$	7.32546	+	9.32992i	0.351229	+	0.447335i
$436$	12.7865	+	9.52369i	0.612363	+	0.456102i
$437$	−4.19134	−	7.25962i	−0.200499	−	0.347275i
$438$	−25.7766	−	8.54465i	−1.23165	−	0.408279i
$439$	−8.66266	+	15.0042i	−0.413446	+	0.716110i	−0.995264	−	0.0972091i	$-0.969008\pi$
$439$	−8.66266	+	15.0042i	−0.413446	+	0.716110i	0.581818	+	0.813319i	$0.302342\pi$
$440$	−21.8039	−	6.61699i	−1.03946	−	0.315453i
$441$	21.8047	−	14.4919i	1.03832	−	0.690090i
$442$	−5.68938	−	6.39456i	−0.270616	−	0.304158i
$443$	12.6162	−	21.8520i	0.599416	−	1.03822i	−0.393492	−	0.919328i	$-0.628733\pi$
$443$	12.6162	−	21.8520i	0.599416	−	1.03822i	0.992907	−	0.118890i	$-0.0379336\pi$
$444$	−34.1745	+	14.7323i	−1.62185	+	0.699164i
$445$	8.83730	−	22.0251i	0.418928	−	1.04409i
$446$	−6.73901	−	32.6556i	−0.319101	−	1.54629i
$447$			62.1779i			2.94091i
$448$	11.6003	−	17.7040i	0.548064	−	0.836436i
$449$	7.06145			0.333251			0.166625	−	0.986020i	$-0.446713\pi$
$449$	7.06145			0.333251			0.166625	+	0.986020i	$0.446713\pi$
$450$	−0.952888	+	26.4299i	−0.0449196	+	1.24592i
$451$	−4.78848	−	8.29390i	−0.225481	−	0.390544i
$452$	6.03001	+	13.9878i	0.283628	+	0.657931i
$453$	−9.09653	+	15.7556i	−0.427392	+	0.740265i
$454$	22.1103	−	19.6720i	1.03769	−	0.923255i
$455$	−0.426810	+	4.82217i	−0.0200092	+	0.226067i
$456$	13.9201	+	19.8942i	0.651867	+	0.931633i
$457$	16.3519	+	9.44078i	0.764910	+	0.441621i	0.831056	−	0.556189i	$-0.187737\pi$
$457$	16.3519	+	9.44078i	0.764910	+	0.441621i	−0.0661459	+	0.997810i	$0.521070\pi$
$458$	6.95562	+	2.30571i	0.325015	+	0.107739i
$459$	12.3089	−	7.10656i	0.574531	−	0.331706i
$460$	11.3339	−	0.288456i	0.528444	−	0.0134493i
$461$			34.6087i			1.61189i	0.591992	+	0.805944i	$0.298342\pi$
$461$			34.6087i			1.61189i	−0.591992	+	0.805944i	$0.701658\pi$
$462$	18.3044	−	29.8288i	0.851600	−	1.38776i
$463$	−15.0235			−0.698202			−0.349101	−	0.937085i	$-0.613513\pi$
$463$	−15.0235			−0.698202			−0.349101	+	0.937085i	$0.613513\pi$
$464$	−5.61159	+	5.94257i	−0.260511	+	0.275877i
$465$	4.13211	−	10.2984i	0.191622	−	0.477577i
$466$	27.8804	+	9.24206i	1.29154	+	0.428130i
$467$	−22.0309	−	12.7195i	−1.01947	−	0.588590i	−0.105518	−	0.994417i	$-0.533650\pi$
$467$	−22.0309	−	12.7195i	−1.01947	−	0.588590i	−0.913950	+	0.405828i	$0.866983\pi$
$468$	0.711981	−	6.07950i	0.0329113	−	0.281025i
$469$	−7.08472	−	23.4591i	−0.327142	−	1.08324i
$470$	−0.747616	+	4.15412i	−0.0344850	+	0.191615i
$471$	14.4470	+	8.34096i	0.665681	+	0.384331i
$472$	−4.89910	−	2.28650i	−0.225499	−	0.105245i
$473$	7.47869	−	4.31782i	0.343871	−	0.198534i
$474$	27.8595	−	5.74925i	1.27963	−	0.264072i
$475$	−3.92264	+	16.0608i	−0.179983	+	0.736921i
$476$	−25.2223	−	29.9261i	−1.15606	−	1.37166i
$477$			6.77350i			0.310137i
$478$	6.03905	+	29.2638i	0.276220	+	1.33849i
$479$	10.2844	+	17.8131i	0.469905	+	0.813900i	0.999408	−	0.0344084i	$-0.0109547\pi$
$479$	10.2844	+	17.8131i	0.469905	+	0.813900i	−0.529502	+	0.848308i	$0.677621\pi$
$480$	−32.6323	+	3.68253i	−1.48945	+	0.168084i
$481$	5.07906	+	2.93239i	0.231585	+	0.133706i
$482$	1.92089	−	1.70906i	0.0874939	−	0.0778453i
$483$	−3.97510	+	16.9538i	−0.180873	+	0.771426i
$484$	0.460576	−	3.93279i	0.0209353	−	0.178763i
$485$	2.31689	+	16.2033i	0.105205	+	0.735755i
$486$	−29.4563	−	9.76443i	−1.33616	−	0.442924i
$487$	−14.5295	−	25.1658i	−0.658394	−	1.14037i	−0.981031	−	0.193849i	$-0.937903\pi$
$487$	−14.5295	−	25.1658i	−0.658394	−	1.14037i	0.322638	−	0.946522i	$-0.395430\pi$
$488$	−27.5462	+	2.40060i	−1.24696	+	0.108670i
$489$		−	47.9749i		−	2.16950i
$490$	−2.54172	+	21.9895i	−0.114823	+	0.993386i
$491$		−	9.51815i		−	0.429548i	−0.976664	−	0.214774i	$-0.931098\pi$
$491$		−	9.51815i		−	0.429548i	0.976664	−	0.214774i	$-0.0689015\pi$
$492$	−11.0695	−	8.24481i	−0.499051	−	0.371705i
$493$	7.55657	+	13.0884i	0.340331	+	0.589470i
$494$	1.20400	−	3.63210i	0.0541706	−	0.163416i
$495$	−29.8276	+	4.26500i	−1.34065	+	0.191698i
$496$	7.43893	+	1.76660i	0.334018	+	0.0793226i
$497$	−0.836015	+	3.56561i	−0.0375004	+	0.159940i
$498$	−25.6189	−	28.7943i	−1.14801	−	1.29030i
$499$	17.4855	+	10.0953i	0.782760	+	0.451927i	0.837407	−	0.546579i	$-0.184070\pi$
$499$	17.4855	+	10.0953i	0.782760	+	0.451927i	−0.0546477	+	0.998506i	$0.517404\pi$
$500$	−16.5473	−	15.0395i	−0.740017	−	0.672588i
$501$	−2.37413	−	4.11211i	−0.106068	−	0.183716i
$502$	19.4164	−	4.00688i	0.866595	−	0.178836i
$503$		−	13.3134i		−	0.593616i	−0.954937	−	0.296808i	$-0.904078\pi$
$503$		−	13.3134i		−	0.593616i	0.954937	−	0.296808i	$-0.0959221\pi$
$504$	3.99925	−	27.7018i	0.178141	−	1.23394i
$505$	−8.77949	−	11.1818i	−0.390682	−	0.497585i
$506$	2.61057	+	12.6502i	0.116054	+	0.562370i
$507$	27.7233	−	16.0060i	1.23123	−	0.710853i
$508$	−16.1279	+	6.95261i	−0.715562	+	0.308472i
$509$	12.4294	+	7.17613i	0.550925	+	0.318077i	0.749495	−	0.662010i	$-0.230296\pi$
$509$	12.4294	+	7.17613i	0.550925	+	0.318077i	−0.198570	+	0.980087i	$0.563630\pi$
$510$	−10.7554	+	59.7624i	−0.476258	+	2.64632i
$511$	5.65744	+	18.7331i	0.250270	+	0.828703i
$512$	−5.83424	−	21.8623i	−0.257839	−	0.966188i
$513$	5.50282	+	3.17706i	0.242956	+	0.140270i
$514$	7.95298	−	23.9917i	0.350791	−	1.05823i
$515$	−0.851050	+	2.12106i	−0.0375018	+	0.0934652i
$516$	7.43442	−	9.98147i	0.327282	−	0.439410i
$517$	−4.80879			−0.211490
$518$	22.8568	+	14.0260i	1.00427	+	0.616269i
$519$		−	39.5906i		−	1.73783i
$520$	3.53732	+	3.77767i	0.155122	+	0.165662i
$521$	−31.9571	+	18.4505i	−1.40007	+	0.808330i	−0.994399	−	0.105690i	$-0.966295\pi$
$521$	−31.9571	+	18.4505i	−1.40007	+	0.808330i	−0.405669	+	0.914020i	$0.632961\pi$
$522$	−3.40079	+	10.2591i	−0.148848	+	0.449030i
$523$	15.7185	+	9.07509i	0.687323	+	0.396826i	0.802608	−	0.596506i	$-0.203445\pi$
$523$	15.7185	+	9.07509i	0.687323	+	0.396826i	−0.115285	+	0.993332i	$0.536778\pi$
$524$	−3.11481	+	26.5969i	−0.136071	+	1.16189i
$525$	28.7776	−	18.7452i	1.25596	−	0.818106i
$526$	20.5837	+	23.1349i	0.897490	+	1.00873i
$527$	7.06883	−	12.2436i	0.307923	−	0.533338i
$528$	−10.7142	−	35.8467i	−0.466276	−	1.56003i
$529$	8.28651	+	14.3526i	0.360283	+	0.624028i
$530$	−4.37404	−	3.69665i	−0.189996	−	0.160572i
$531$	−7.14919			−0.310248
$532$	5.94841	−	16.4546i	0.257896	−	0.713397i
$533$			2.17519i			0.0942178i
$534$	38.1630	−	7.87554i	1.65147	−	0.340808i
$535$	−15.0488	−	6.03814i	−0.650616	−	0.261052i
$536$	−23.7393	−	11.0796i	−1.02538	−	0.478566i
$537$	16.2740	−	28.1874i	0.702276	−	1.21638i
$538$	3.04588	−	2.70999i	0.131317	−	0.116836i
$539$	−25.1693	+	1.58743i	−1.08412	+	0.0683756i
$540$	−7.33081	+	4.48492i	−0.315468	+	0.193000i
$541$	9.37629	−	16.2402i	0.403118	−	0.698221i	−0.590982	−	0.806685i	$-0.701260\pi$
$541$	9.37629	−	16.2402i	0.403118	−	0.698221i	0.994100	+	0.108463i	$0.0345930\pi$
$542$	−7.54509	+	22.7612i	−0.324090	+	0.977678i
$543$	10.4086	+	18.0283i	0.446677	+	0.773667i
$544$	−41.8213	−	1.24046i	−1.79307	−	0.0531842i
$545$	−14.0202	+	11.0081i	−0.600561	+	0.471535i
$546$	−6.98790	+	3.78854i	−0.299055	+	0.162135i
$547$	34.1580			1.46049			0.730246	−	0.683185i	$-0.239406\pi$
$547$	34.1580			1.46049			0.730246	+	0.683185i	$0.239406\pi$
$548$	−6.24119	+	8.37943i	−0.266610	+	0.357952i
$549$	−31.6653	+	18.2820i	−1.35144	+	0.780256i
$550$	13.5243	−	21.5890i	0.576678	−	0.920558i
$551$	−3.37824	+	5.85128i	−0.143918	+	0.249273i
$552$	10.6725	+	15.2529i	0.454252	+	0.649206i
$553$	−14.9440	−	14.0312i	−0.635485	−	0.596667i
$554$	−28.3702	+	25.2416i	−1.20534	+	1.07241i
$555$	−5.88948	−	41.1884i	−0.249994	−	1.74835i
$556$	40.3029	−	17.3742i	1.70923	−	0.736831i
$557$	35.0192	−	20.2183i	1.48381	−	0.856679i	0.483980	−	0.875079i	$-0.339191\pi$
$557$	35.0192	−	20.2183i	1.48381	−	0.856679i	0.999831	+	0.0184005i	$0.00585738\pi$
$558$	9.90183	−	2.04340i	0.419178	−	0.0865041i
$559$	−1.96139			−0.0829579
$560$	15.7060	+	17.7009i	0.663701	+	0.747998i
$561$	−69.1805			−2.92080
$562$	34.5561	−	7.13120i	1.45766	−	0.300811i
$563$	−0.276201	+	0.159465i	−0.0116405	+	0.00672065i	−0.505809	−	0.862646i	$-0.668806\pi$
$563$	−0.276201	+	0.159465i	−0.0116405	+	0.00672065i	0.494168	+	0.869366i	$0.335473\pi$
$564$	−6.36435	+	2.74361i	−0.267987	+	0.115527i
$565$	−16.8586	+	2.41059i	−0.709248	+	0.101414i
$566$	−10.3946	+	9.24835i	−0.436920	+	0.388737i
$567$	4.76655	+	15.7831i	0.200176	+	0.662830i
$568$	2.24457	+	3.20788i	0.0941800	+	0.134600i
$569$	−15.3058	+	26.5104i	−0.641651	+	1.11137i	0.343413	+	0.939184i	$0.388417\pi$
$569$	−15.3058	+	26.5104i	−0.641651	+	1.11137i	−0.985064	+	0.172188i	$0.944916\pi$
$570$	−25.5421	+	9.19455i	−1.06984	+	0.385117i
$571$	7.35081	−	4.24399i	0.307622	−	0.177606i	−0.338240	−	0.941060i	$-0.609832\pi$
$571$	7.35081	−	4.24399i	0.307622	−	0.177606i	0.645862	+	0.763454i	$0.276498\pi$
$572$	−3.52200	+	4.72864i	−0.147262	+	0.197714i
$573$	−17.5486			−0.733103
$574$	−0.266495	+	9.94264i	−0.0111233	+	0.414998i
$575$	−3.00748	+	12.3138i	−0.125421	+	0.513521i
$576$	−19.2177	−	22.9342i	−0.800735	−	0.955591i
$577$	−1.68251	−	2.91419i	−0.0700438	−	0.121319i	0.828876	−	0.559432i	$-0.188981\pi$
$577$	−1.68251	−	2.91419i	−0.0700438	−	0.121319i	−0.898920	+	0.438112i	$0.855647\pi$
$578$	−16.7781	+	50.6145i	−0.697879	+	2.10529i
$579$	−3.06354	+	5.30620i	−0.127316	+	0.220518i
$580$	−4.76892	−	7.79502i	−0.198019	−	0.323671i
$581$	−6.33993	+	27.0399i	−0.263025	+	1.12180i
$582$	−20.0791	+	17.8648i	−0.832305	+	0.740520i
$583$	3.26230	−	5.65048i	0.135111	−	0.234019i
$584$	18.9568	+	8.84752i	0.784439	+	0.366113i
$585$	6.35136	+	2.54840i	0.262596	+	0.105364i
$586$	32.4151	−	6.68938i	1.33906	−	0.276336i
$587$		−	2.02359i		−	0.0835225i	−0.999128	−	0.0417613i	$-0.986703\pi$
$587$		−	2.02359i		−	0.0835225i	0.999128	−	0.0417613i	$-0.0132969\pi$
$588$	−32.4054	+	16.4610i	−1.33638	+	0.678842i
$589$	6.32038			0.260427
$590$	3.90168	−	4.61664i	0.160630	−	0.190064i
$591$	26.3779	+	45.6878i	1.08504	+	1.87935i
$592$	27.4681	−	8.20992i	1.12893	−	0.337426i
$593$	−13.4129	+	23.2318i	−0.550802	+	0.954016i	0.447415	+	0.894326i	$0.352345\pi$
$593$	−13.4129	+	23.2318i	−0.550802	+	0.954016i	−0.998217	+	0.0596901i	$0.980989\pi$
$594$	−6.50817	−	7.31483i	−0.267033	−	0.300131i
$595$	39.6760	−	18.4523i	1.62656	−	0.756471i
$596$	5.57151	−	47.5743i	0.228218	−	1.94872i
$597$	−25.7622	−	14.8738i	−1.05438	−	0.608744i
$598$	0.923107	−	2.78473i	0.0377487	−	0.113876i
$599$	32.0964	−	18.5309i	1.31143	−	0.757152i	0.329093	−	0.944297i	$-0.393257\pi$
$599$	32.0964	−	18.5309i	1.31143	−	0.757152i	0.982332	+	0.187146i	$0.0599237\pi$
$600$	5.58175	−	36.2889i	0.227874	−	1.48149i
$601$			1.27911i			0.0521761i	0.999660	+	0.0260880i	$0.00830503\pi$
$601$			1.27911i			0.0521761i	−0.999660	+	0.0260880i	$0.991695\pi$
$602$	−8.96537	−	0.240301i	−0.365401	−	0.00979396i
$603$	−34.6425			−1.41075
$604$	8.37184	−	11.2400i	0.340645	−	0.457351i
$605$	4.10865	+	1.64855i	0.167040	+	0.0670229i
$606$	7.34501	−	22.1576i	0.298371	−	0.900093i
$607$	19.5800	+	11.3045i	0.794727	+	0.458836i	0.841624	−	0.540064i	$-0.181600\pi$
$607$	19.5800	+	11.3045i	0.794727	+	0.458836i	−0.0468970	+	0.998900i	$0.514933\pi$
$608$	−8.86805	−	16.4690i	−0.359647	−	0.667907i
$609$	13.4361	−	4.05773i	0.544458	−	0.164428i
$610$	5.47568	−	30.4256i	0.221704	−	1.23190i
$611$	0.945877	+	0.546102i	0.0382661	+	0.0220929i
$612$	−50.8070	+	21.9024i	−2.05375	+	0.885353i
$613$	2.61492	−	1.50973i	0.105616	−	0.0609773i	−0.446262	−	0.894903i	$-0.647245\pi$
$613$	2.61492	−	1.50973i	0.105616	−	0.0609773i	0.551877	+	0.833925i	$0.313912\pi$
$614$	−0.624606	−	3.02669i	−0.0252071	−	0.122147i
$615$	12.1375	−	9.52987i	0.489432	−	0.384281i
$616$	−16.6781	+	21.1828i	−0.671982	+	0.853479i
$617$			14.3344i			0.577081i	0.957468	+	0.288540i	$0.0931700\pi$
$617$			14.3344i			0.577081i	−0.957468	+	0.288540i	$0.906830\pi$
$618$	−3.67517	+	0.758431i	−0.147837	+	0.0305086i
$619$	10.8987	+	18.8771i	0.438055	+	0.758733i	0.997539	−	0.0701078i	$-0.0223343\pi$
$619$	10.8987	+	18.8771i	0.438055	+	0.758733i	−0.559485	+	0.828841i	$0.689001\pi$
$620$	−4.08440	+	7.50938i	−0.164034	+	0.301584i
$621$	4.21901	+	2.43584i	0.169303	+	0.0977471i
$622$	−27.1674	−	30.5347i	−1.08931	−	1.22433i
$623$	−20.4709	−	19.2205i	−0.820150	−	0.770052i
$624$	−1.96342	+	8.26771i	−0.0785997	+	0.330973i
$625$	21.0731	−	13.4509i	0.842923	−	0.538035i
$626$	2.82701	−	8.52821i	0.112990	−	0.340856i
$627$	−15.4639	−	26.7843i	−0.617570	−	1.06966i
$628$	−10.3064	−	7.67646i	−0.411271	−	0.306324i
$629$		−	53.0106i		−	2.11367i
$630$	28.7194	+	12.4267i	1.14421	+	0.495093i
$631$			15.1512i			0.603160i	0.953441	+	0.301580i	$0.0975140\pi$
$631$			15.1512i			0.603160i	−0.953441	+	0.301580i	$0.902486\pi$
$632$	−21.8313	+	1.90256i	−0.868404	+	0.0756797i
$633$	28.6420	+	49.6094i	1.13842	+	1.97180i
$634$	−25.2409	−	8.36708i	−1.00244	−	0.332299i
$635$	−2.77942	−	19.4380i	−0.110298	−	0.771374i
$636$	1.09378	−	9.33959i	0.0433710	−	0.370339i
$637$	5.13101	+	2.54606i	0.203298	+	0.100879i
$638$	7.77803	−	6.92029i	0.307935	−	0.273977i
$639$	4.48363	+	2.58863i	0.177370	+	0.102404i
$640$	25.2980	+	0.106426i	0.999991	+	0.00420687i
$641$	−14.9960	−	25.9739i	−0.592308	−	1.02591i	−0.993921	−	0.110098i	$-0.964884\pi$
$641$	−14.9960	−	25.9739i	−0.592308	−	1.02591i	0.401613	−	0.915809i	$-0.368450\pi$
$642$	−5.38101	−	26.0751i	−0.212372	−	1.02910i
$643$		−	1.63196i		−	0.0643583i	−0.999482	−	0.0321792i	$-0.989755\pi$
$643$		−	1.63196i		−	0.0643583i	0.999482	−	0.0321792i	$-0.0102447\pi$
$644$	4.56063	−	12.6157i	0.179714	−	0.497129i
$645$	8.59318	+	10.9445i	0.338356	+	0.430940i
$646$	−33.8728	+	6.99020i	−1.33271	+	0.275026i
$647$	28.3765	−	16.3832i	1.11560	−	0.644090i	0.175323	−	0.984511i	$-0.443903\pi$
$647$	28.3765	−	16.3832i	1.11560	−	0.644090i	0.940273	+	0.340421i	$0.110570\pi$
$648$	15.9717	+	7.45428i	0.627426	+	0.292832i
$649$	5.96388	+	3.44325i	0.234103	+	0.135159i
$650$	−5.11192	+	2.71064i	−0.200506	+	0.106320i
$651$	−9.57170	−	8.98703i	−0.375145	−	0.352229i
$652$	−4.29883	+	36.7071i	−0.168355	+	1.43756i
$653$	−19.5109	−	11.2646i	−0.763521	−	0.440819i	0.0670377	−	0.997750i	$-0.478645\pi$
$653$	−19.5109	−	11.2646i	−0.763521	−	0.440819i	−0.830558	+	0.556932i	$0.811979\pi$
$654$	−27.7822	−	9.20948i	−1.08637	−	0.360119i
$655$	−27.7862	−	11.1489i	−1.08570	−	0.435623i
$656$	7.73083	+	7.30025i	0.301838	+	0.285027i
$657$	27.6635			1.07925
$658$	4.25663	+	2.61208i	0.165941	+	0.101830i
$659$		−	19.2525i		−	0.749969i	−0.927031	−	0.374985i	$-0.877648\pi$
$659$		−	19.2525i		−	0.749969i	0.927031	−	0.374985i	$-0.122352\pi$
$660$	41.8162	−	1.06426i	1.62769	−	0.0414262i
$661$	30.1079	−	17.3828i	1.17106	−	0.676113i	0.217132	−	0.976142i	$-0.430330\pi$
$661$	30.1079	−	17.3828i	1.17106	−	0.676113i	0.953930	+	0.300030i	$0.0969966\pi$
$662$	−17.5702	−	5.82433i	−0.682885	−	0.226369i
$663$	13.6077	+	7.85638i	0.528477	+	0.305117i
$664$	17.0217	+	24.3270i	0.660570	+	0.944071i
$665$	16.0129	+	11.2365i	0.620953	+	0.435734i
$666$	28.3228	−	25.1994i	1.09749	−	0.976458i
$667$	−2.59009	+	4.48617i	−0.100289	+	0.173705i
$668$	1.44805	+	3.35904i	0.0560268	+	0.129965i
$669$	30.6059	+	53.0110i	1.18329	+	2.04952i
$670$	18.9062	−	22.3707i	0.730411	−	0.864255i
$671$	35.2205			1.35967
$672$	−9.98759	+	37.5506i	−0.385280	+	1.44855i
$673$			42.6368i			1.64353i	0.569827	+	0.821764i	$0.307010\pi$
$673$			42.6368i			1.64353i	−0.569827	+	0.821764i	$0.692990\pi$
$674$	−3.35325	−	16.2491i	−0.129162	−	0.625890i
$675$	−2.69270	−	9.22326i	−0.103642	−	0.355003i
$676$	−22.6462	+	9.76255i	−0.871007	+	0.375483i
$677$	0.892648	−	1.54611i	0.0343073	−	0.0594219i	−0.848362	−	0.529417i	$-0.822411\pi$
$677$	0.892648	−	1.54611i	0.0343073	−	0.0594219i	0.882669	+	0.469995i	$0.155744\pi$
$678$	−18.5873	−	20.8911i	−0.713842	−	0.802319i
$679$	18.8557	+	4.42102i	0.723615	+	0.169663i
$680$	13.5844	−	44.7623i	0.520937	−	1.71656i
$681$	−27.1648	+	47.0509i	−1.04096	+	1.80299i
$682$	−9.24431	−	3.06439i	−0.353983	−	0.117341i
$683$	−4.30263	−	7.45237i	−0.164636	−	0.285157i	0.771890	−	0.635756i	$-0.219311\pi$
$683$	−4.30263	−	7.45237i	−0.164636	−	0.285157i	−0.936526	+	0.350599i	$0.885978\pi$
$684$	−19.8367	−	14.7749i	−0.758477	−	0.564931i
$685$	−7.21396	−	9.18792i	−0.275631	−	0.351052i
$686$	23.1416	+	12.2665i	0.883549	+	0.468338i
$687$	−13.4523			−0.513236
$688$	−6.58271	+	6.97097i	−0.250963	+	0.265766i
$689$	−1.28338	+	0.740957i	−0.0488927	+	0.0282282i
$690$	−19.5831	+	7.04945i	−0.745514	+	0.268368i
$691$	−20.1511	+	34.9027i	−0.766583	+	1.32776i	0.172822	+	0.984953i	$0.444711\pi$
$691$	−20.1511	+	34.9027i	−0.766583	+	1.32776i	−0.939405	+	0.342808i	$0.888622\pi$
$692$	−3.54755	+	30.2920i	−0.134858	+	1.15153i
$693$	−8.13834	+	34.7101i	−0.309150	+	1.31853i
$694$	4.14720	+	4.66123i	0.157426	+	0.176938i
$695$	6.94562	+	48.5746i	0.263463	+	1.84254i
$696$	6.34578	−	13.5966i	0.240536	−	0.515377i
$697$	17.0270	−	9.83053i	0.644943	−	0.372358i
$698$	5.24425	+	25.4124i	0.198498	+	0.961874i
$699$	−53.9212			−2.03949
$700$	−23.6983	+	11.7639i	−0.895713	+	0.444633i
$701$	37.3051			1.40899			0.704497	−	0.709707i	$-0.251172\pi$
$701$	37.3051			1.40899			0.704497	+	0.709707i	$0.251172\pi$
$702$	0.449444	+	2.17790i	0.0169632	+	0.0821995i
$703$	20.5239	−	11.8495i	0.774072	−	0.446911i
$704$	4.98570	+	28.3875i	0.187906	+	1.06990i
$705$	−1.09680	−	7.67055i	−0.0413080	−	0.288890i
$706$	−11.0438	−	12.4126i	−0.415637	−	0.467154i
$707$	−16.1030	+	4.86315i	−0.605617	+	0.182898i
$708$	9.85761	+	1.15444i	0.370472	+	0.0433866i
$709$	4.02866	−	6.97784i	0.151299	−	0.262058i	−0.780406	−	0.625273i	$-0.784988\pi$
$709$	4.02866	−	6.97784i	0.151299	−	0.262058i	0.931705	+	0.363215i	$0.118321\pi$
$710$	−4.11858	+	1.48259i	−0.154567	+	0.0556407i
$711$	−25.0958	+	14.4891i	−0.941168	+	0.543383i
$712$	−29.9054	+	2.60620i	−1.12075	+	0.0976714i
$713$	4.84582			0.181477
$714$	61.2371	+	37.5782i	2.29174	+	1.40633i
$715$	−4.07095	−	5.18488i	−0.152245	−	0.193903i
$716$	−14.9775	+	20.1089i	−0.559737	+	0.751503i
$717$	−27.4269	−	47.5049i	−1.02428	−	1.77410i
$718$	−0.265660	−	0.0880634i	−0.00991434	−	0.00328650i
$719$	5.87241	−	10.1713i	0.219004	−	0.379326i	−0.735500	−	0.677525i	$-0.763053\pi$
$719$	5.87241	−	10.1713i	0.219004	−	0.379326i	0.954504	+	0.298199i	$0.0963859\pi$
$720$	30.3734	−	14.0205i	1.13195	−	0.522515i
$721$	1.97139	+	1.85097i	0.0734184	+	0.0689338i
$722$	7.58289	+	8.52275i	0.282206	+	0.317184i
$723$	−2.36001	+	4.08766i	−0.0877697	+	0.152022i
$724$	−6.34853	−	14.7267i	−0.235941	−	0.547312i
$725$	9.80731	−	2.86321i	0.364234	−	0.106337i
$726$	1.46913	+	7.11908i	0.0545247	+	0.264214i
$727$			33.3549i			1.23706i	0.785760	+	0.618532i	$0.212272\pi$
$727$			33.3549i			1.23706i	−0.785760	+	0.618532i	$0.787728\pi$
$728$	5.68614	−	2.27258i	0.210742	−	0.0842273i
$729$	38.2742			1.41756
$730$	−15.0974	+	17.8639i	−0.558780	+	0.661172i
$731$	8.86429	+	15.3534i	0.327857	+	0.567866i
$732$	46.6137	−	20.0947i	1.72289	−	0.742722i
$733$	5.75003	−	9.95934i	0.212382	−	0.367856i	−0.740077	−	0.672522i	$-0.765211\pi$
$733$	5.75003	−	9.95934i	0.212382	−	0.367856i	0.952460	+	0.304665i	$0.0985445\pi$
$734$	−7.95403	+	7.07688i	−0.293588	+	0.261212i
$735$	−8.27282	−	39.7857i	−0.305148	−	1.46752i
$736$	−6.79912	−	12.6268i	−0.250619	−	0.465429i
$737$	28.8989	+	16.6848i	1.06451	+	0.614593i
$738$	13.3463	+	4.42417i	0.491286	+	0.162856i
$739$	−9.70301	+	5.60203i	−0.356931	+	0.206074i	−0.667734	−	0.744400i	$-0.732735\pi$
$739$	−9.70301	+	5.60203i	−0.356931	+	0.206074i	0.310803	+	0.950474i	$0.399402\pi$
$740$	0.815503	+	32.0423i	0.0299785	+	1.17790i
$741$			7.02455i			0.258053i
$742$	−5.95700	+	3.22963i	−0.218688	+	0.118564i
$743$	43.7950			1.60668			0.803341	−	0.595520i	$-0.203054\pi$
$743$	43.7950			1.60668			0.803341	+	0.595520i	$0.203054\pi$
$744$	−13.9830	+	1.21859i	−0.512643	+	0.0446759i
$745$	49.7016	+	19.9422i	1.82093	+	0.730625i
$746$	−41.8007	−	13.8565i	−1.53043	−	0.507322i
$747$	34.0017	+	19.6309i	1.24406	+	0.718256i
$748$	52.9322	+	6.19898i	1.93539	+	0.226657i
$749$	−13.1325	+	13.9869i	−0.479852	+	0.511069i
$750$	37.5216	+	16.6487i	1.37009	+	0.607924i
$751$	−44.5322	−	25.7107i	−1.62500	−	0.938196i	−0.985554	−	0.169364i	$-0.945829\pi$
$751$	−44.5322	−	25.7107i	−1.62500	−	0.938196i	−0.639450	−	0.768832i	$-0.720838\pi$
$752$	5.11541	−	1.52894i	0.186540	−	0.0557547i
$753$	−31.5192	+	18.1976i	−1.14862	+	0.663159i
$754$	−2.31581	+	0.477905i	−0.0843369	+	0.0174043i
$755$	9.67670	+	12.3245i	0.352171	+	0.448536i
$756$	1.78755	+	10.0101i	0.0650126	+	0.364064i
$757$		−	18.1453i		−	0.659502i	−0.944068	−	0.329751i	$-0.893035\pi$
$757$		−	18.1453i		−	0.659502i	0.944068	−	0.329751i	$-0.106965\pi$
$758$	−4.67022	−	22.6308i	−0.169630	−	0.821987i
$759$	−11.8562	−	20.5355i	−0.430352	−	0.745391i
$760$	20.3669	−	4.74632i	0.738786	−	0.172167i
$761$	−28.4860	−	16.4464i	−1.03262	−	0.596181i	−0.114883	−	0.993379i	$-0.536649\pi$
$761$	−28.4860	−	16.4464i	−1.03262	−	0.596181i	−0.917733	+	0.397198i	$0.869983\pi$
$762$	24.0875	−	21.4312i	0.872598	−	0.776370i
$763$	6.09762	+	20.1906i	0.220749	+	0.730950i
$764$	13.4270	+	1.57246i	0.485771	+	0.0568895i
$765$	−8.75585	−	61.2346i	−0.316568	−	2.21394i
$766$	11.8783	+	3.93753i	0.429181	+	0.142269i
$767$	−0.782054	−	1.35456i	−0.0282383	−	0.0489102i
$768$	22.7948	+	34.7259i	0.822535	+	1.25306i
$769$			20.8502i			0.751876i	0.926645	+	0.375938i	$0.122679\pi$
$769$			20.8502i			0.751876i	−0.926645	+	0.375938i	$0.877321\pi$
$770$	−17.9728	−	24.1985i	−0.647694	−	0.872053i
$771$			46.4003i			1.67107i
$772$	2.81947	−	3.78543i	0.101475	−	0.136241i
$773$	−4.34380	−	7.52368i	−0.156236	−	0.270608i	0.777273	−	0.629164i	$-0.216603\pi$
$773$	−4.34380	−	7.52368i	−0.156236	−	0.270608i	−0.933508	+	0.358556i	$0.883269\pi$
$774$	−3.98932	+	12.0345i	−0.143393	+	0.432572i
$775$	−6.90671	−	6.60597i	−0.248096	−	0.237293i
$776$	16.9639	−	11.8697i	0.608970	−	0.426099i
$777$	−47.9306	−	11.2381i	−1.71950	−	0.403165i
$778$	−8.78497	−	9.87384i	−0.314957	−	0.353994i
$779$	7.61208	+	4.39484i	0.272731	+	0.157461i
$780$	−8.34601	−	4.53946i	−0.298835	−	0.162539i
$781$	−2.49351	−	4.31888i	−0.0892247	−	0.154542i
$782$	−25.9703	+	5.35937i	−0.928694	+	0.191651i
$783$		−	3.92660i		−	0.140325i
$784$	26.2694	−	9.69115i	0.938193	−	0.346113i
$785$	11.3008	−	8.87294i	0.403344	−	0.316689i
$786$	−9.93555	−	48.1453i	−0.354389	−	1.71729i
$787$	−32.2270	+	18.6062i	−1.14877	+	0.663241i	−0.948586	−	0.316518i	$-0.897486\pi$
$787$	−32.2270	+	18.6062i	−1.14877	+	0.663241i	−0.200180	+	0.979759i	$0.564153\pi$
$788$	−16.0887	−	37.3208i	−0.573135	−	1.32950i
$789$	−49.2312	−	28.4237i	−1.75268	−	1.01191i
$790$	4.33966	−	24.1133i	0.154398	−	0.857912i
$791$	−4.59982	+	19.6183i	−0.163551	+	0.697545i
$792$	21.8501	+	31.2277i	0.776411	+	1.10963i
$793$	−6.92778	−	3.99976i	−0.246013	−	0.142036i
$794$	−9.03437	+	27.2539i	−0.320618	+	0.967205i
$795$	9.75722	+	3.91496i	0.346053	+	0.138849i
$796$	18.3787	+	13.6889i	0.651415	+	0.485189i
$797$	21.3900			0.757671			0.378835	−	0.925464i	$-0.376325\pi$
$797$	21.3900			0.757671			0.378835	+	0.925464i	$0.376325\pi$
$798$	−0.860619	+	32.1087i	−0.0304656	+	1.13664i
$799$		−	9.87221i		−	0.349254i
$800$	−7.52247	+	27.2656i	−0.265959	+	0.963984i
$801$	−34.3773	+	19.8477i	−1.21466	+	0.701285i
$802$	4.93341	−	14.8826i	0.174205	−	0.525522i
$803$	−23.0770	−	13.3235i	−0.814368	−	0.470176i
$804$	47.7666	+	5.59403i	1.68460	+	0.197286i
$805$	12.2770	+	8.61503i	0.432709	+	0.303640i
$806$	1.47033	+	1.65257i	0.0517902	+	0.0582094i
$807$	−3.74219	+	6.48166i	−0.131731	+	0.228165i
$808$	−7.60536	+	16.2954i	−0.267556	+	0.573269i
$809$	−12.1707	−	21.0803i	−0.427900	−	0.741144i	0.568787	−	0.822485i	$-0.307413\pi$
$809$	−12.1707	−	21.0803i	−0.427900	−	0.741144i	−0.996686	+	0.0813411i	$0.974080\pi$
$810$	−12.7200	+	15.0508i	−0.446934	+	0.528832i
$811$	31.3778			1.10183			0.550913	−	0.834563i	$-0.314280\pi$
$811$	31.3778			1.10183			0.550913	+	0.834563i	$0.314280\pi$
$812$	−10.6440	+	1.90075i	−0.373530	+	0.0667031i
$813$		−	44.0206i		−	1.54387i
$814$	−35.7637	+	7.38041i	−1.25352	+	0.258683i
$815$	−38.3485	−	15.3869i	−1.34329	−	0.538979i
$816$	73.5917	−	21.9958i	2.57622	−	0.770006i
$817$	−3.96287	+	6.86389i	−0.138643	+	0.240137i
$818$	6.21976	−	5.53386i	0.217469	−	0.193487i
$819$	5.54259	−	5.90317i	0.193674	−	0.206274i
$820$	−10.1407	+	6.20401i	−0.354130	+	0.216653i
$821$	−0.0785681	+	0.136084i	−0.00274204	+	0.00474936i	−0.867393	−	0.497623i	$-0.834206\pi$
$821$	−0.0785681	+	0.136084i	−0.00274204	+	0.00474936i	0.864651	+	0.502373i	$0.167539\pi$
$822$	6.03528	−	18.2066i	0.210505	−	0.635027i
$823$	−9.34753	−	16.1904i	−0.325835	−	0.564362i	0.655846	−	0.754894i	$-0.272312\pi$
$823$	−9.34753	−	16.1904i	−0.325835	−	0.564362i	−0.981681	+	0.190532i	$0.938979\pi$
$824$	2.87995	−	0.250982i	0.100328	−	0.00874338i
$825$	−11.0961	+	45.4317i	−0.386316	+	1.58173i
$826$	−3.40876	−	6.28741i	−0.118606	−	0.218767i
$827$	35.2960			1.22736			0.613681	−	0.789554i	$-0.289688\pi$
$827$	35.2960			1.22736			0.613681	+	0.789554i	$0.289688\pi$
$828$	−15.2088	−	11.3279i	−0.528542	−	0.393670i
$829$	−14.2590	+	8.23245i	−0.495237	+	0.285925i	−0.726744	−	0.686908i	$-0.758967\pi$
$829$	−14.2590	+	8.23245i	−0.495237	+	0.285925i	0.231508	+	0.972833i	$0.425634\pi$
$830$	−31.2333	+	11.2432i	−1.08412	+	0.390259i
$831$	34.8558	−	60.3720i	1.20913	−	2.09428i
$832$	2.24311	−	6.14996i	0.0777659	−	0.213211i
$833$	−3.25893	−	51.6713i	−0.112915	−	1.79030i
$834$	−60.1934	+	53.5555i	−2.08433	+	1.85447i
$835$	−4.04845	+	0.578882i	−0.140102	+	0.0200330i
$836$	9.43191	+	21.8792i	0.326209	+	0.756707i
$837$	−3.18105	+	1.83658i	−0.109953	+	0.0634814i
$838$	−23.1662	+	4.78072i	−0.800264	+	0.165147i
$839$	−54.8000			−1.89191			−0.945953	−	0.324303i	$-0.894870\pi$
$839$	−54.8000			−1.89191			−0.945953	+	0.324303i	$0.894870\pi$
$840$	−37.5929	−	21.7721i	−1.29708	−	0.751208i
$841$	−24.8248			−0.856026
$842$	−1.64574	+	0.339624i	−0.0567158	+	0.0117042i
$843$	−56.0960	+	32.3871i	−1.93205	+	1.11547i
$844$	−17.4696	−	40.5243i	−0.601329	−	1.39490i
$845$	−3.90274	−	27.2940i	−0.134258	−	0.938943i
$846$	5.27458	−	4.69291i	0.181344	−	0.161346i
$847$	3.58546	−	3.81872i	0.123198	−	0.131213i
$848$	−1.67376	+	7.04801i	−0.0574773	+	0.242030i
$849$	12.7709	−	22.1199i	0.438297	−	0.759152i
$850$	44.3212	+	27.7647i	1.52021	+	0.952322i
$851$	15.7356	−	9.08496i	0.539410	−	0.311428i
$852$	−5.76422	−	4.29332i	−0.197479	−	0.147087i
$853$	−38.9225			−1.33268			−0.666340	−	0.745648i	$-0.732140\pi$
$853$	−38.9225			−1.33268			−0.666340	+	0.745648i	$0.732140\pi$
$854$	−31.1764	−	19.1314i	−1.06683	−	0.654662i
$855$	21.7507	−	17.0777i	0.743858	−	0.584046i
$856$	1.78070	+	20.4331i	0.0608631	+	0.698388i
$857$	−14.6766	−	25.4206i	−0.501342	−	0.868350i	−0.999999	−	0.00155047i	$-0.999506\pi$
$857$	−14.6766	−	25.4206i	−0.501342	−	0.868350i	0.498657	−	0.866800i	$-0.333827\pi$
$858$	3.40580	−	10.2742i	0.116272	−	0.350757i
$859$	23.6874	−	41.0277i	0.808202	−	1.39985i	−0.105905	−	0.994376i	$-0.533774\pi$
$859$	23.6874	−	41.0277i	0.808202	−	1.39985i	0.914108	−	0.405471i	$-0.132893\pi$
$860$	−5.59422	−	9.14400i	−0.190761	−	0.311808i
$861$	−5.27880	−	17.4793i	−0.179901	−	0.595694i
$862$	25.4578	−	22.6504i	0.867095	−	0.771474i
$863$	−11.8505	+	20.5257i	−0.403397	+	0.698704i	−0.994133	−	0.108161i	$-0.965504\pi$
$863$	−11.8505	+	20.5257i	−0.403397	+	0.698704i	0.590737	+	0.806865i	$0.298837\pi$
$864$	9.24887	+	5.71198i	0.314653	+	0.194326i
$865$	−31.6466	−	12.6978i	−1.07602	−	0.431738i
$866$	20.7484	−	4.28176i	0.705060	−	0.145500i
$867$		−	97.8892i		−	3.32449i
$868$	6.51832	+	7.73394i	0.221246	+	0.262507i
$869$	27.9134			0.946897
$870$	12.8127	+	10.8284i	0.434390	+	0.367118i
$871$	−3.78957	−	6.56372i	−0.128405	−	0.222403i
$872$	20.4318	+	9.53591i	0.691908	+	0.322927i
$873$	13.6892	−	23.7103i	0.463308	−	0.802474i
$874$	−7.88009	−	8.85680i	−0.266548	−	0.299586i
$875$	−5.75409	−	29.0153i	−0.194524	−	0.980898i
$876$	−38.1436	−	4.46706i	−1.28875	−	0.150928i
$877$	28.7555	+	16.6020i	0.971004	+	0.560610i	0.899542	−	0.436834i	$-0.143900\pi$
$877$	28.7555	+	16.6020i	0.971004	+	0.560610i	0.0714621	+	0.997443i	$0.477234\pi$
$878$	−7.70951	+	23.2572i	−0.260183	+	0.784893i
$879$	−52.6205	+	30.3805i	−1.77485	+	1.02471i
$880$	−32.0903	−	2.93268i	−1.08176	−	0.0988607i
$881$		−	19.2043i		−	0.647008i	−0.946227	−	0.323504i	$-0.895139\pi$
$881$		−	19.2043i		−	0.647008i	0.946227	−	0.323504i	$-0.104861\pi$
$882$	26.0580	−	26.3040i	0.877420	−	0.885700i
$883$	−8.57526			−0.288581			−0.144290	−	0.989535i	$-0.546090\pi$
$883$	−8.57526			−0.288581			−0.144290	+	0.989535i	$0.546090\pi$
$884$	−9.70767	−	7.23049i	−0.326504	−	0.243188i
$885$	−4.13211	+	10.2984i	−0.138899	+	0.346177i
$886$	11.2281	−	33.8716i	0.377214	−	1.13794i
$887$	−12.7746	−	7.37543i	−0.428930	−	0.247643i	0.269961	−	0.962871i	$-0.412989\pi$
$887$	−12.7746	−	7.37543i	−0.428930	−	0.247643i	−0.698891	+	0.715229i	$0.746323\pi$
$888$	−43.1219	+	30.1725i	−1.44707	+	1.01252i
$889$	−22.6199	−	5.30359i	−0.758646	−	0.177877i
$890$	5.94464	−	33.0313i	0.199265	−	1.10721i
$891$	−19.4430	−	11.2254i	−0.651365	−	0.376066i
$892$	−18.6674	−	43.3028i	−0.625032	−	1.44989i
$893$	3.82218	−	2.20673i	0.127904	−	0.0738455i
$894$	17.7719	+	86.1182i	0.594380	+	2.88022i
$895$	−17.3120	−	22.0491i	−0.578676	−	0.737019i
$896$	11.0066	−	27.8362i	0.367704	−	0.929943i
$897$			5.38571i			0.179824i
$898$	9.78032	−	2.01832i	0.326373	−	0.0673524i
$899$	−1.95288	−	3.38248i	−0.0651321	−	0.112812i
$900$	6.23450	+	36.8786i	0.207817	+	1.22929i
$901$	11.6002	+	6.69736i	0.386457	+	0.223121i
$902$	−9.00277	−	10.1186i	−0.299760	−	0.336914i
$903$	15.7613	−	4.75995i	0.524503	−	0.158401i
$904$	12.3498	+	17.6500i	0.410747	+	0.587030i
$905$	17.7491	−	2.53793i	0.590001	−	0.0843635i
$906$	−8.09563	+	24.4220i	−0.268959	+	0.811367i
$907$	23.7946	+	41.2134i	0.790085	+	1.36847i	0.925914	+	0.377736i	$0.123297\pi$
$907$	23.7946	+	41.2134i	0.790085	+	1.36847i	−0.135828	+	0.990732i	$0.543369\pi$
$908$	25.0007	−	33.5660i	0.829678	−	1.11393i
$909$			23.7796i			0.788720i
$910$	0.787142	+	6.80084i	0.0260935	+	0.225446i
$911$			34.7074i			1.14991i	0.818186	+	0.574954i	$0.194980\pi$
$911$			34.7074i			1.14991i	−0.818186	+	0.574954i	$0.805020\pi$
$912$	24.9659	+	23.5754i	0.826705	+	0.780660i
$913$	−18.9095	−	32.7523i	−0.625814	−	1.08394i
$914$	25.3463	+	8.40200i	0.838380	+	0.277914i
$915$	8.03319	+	56.1806i	0.265569	+	1.85727i
$916$	10.2928	+	1.20540i	0.340082	+	0.0398276i
$917$	−24.2480	+	25.8255i	−0.800739	+	0.852833i
$918$	15.0170	−	13.3610i	0.495635	−	0.440977i
$919$	44.9270	+	25.9386i	1.48200	+	0.855635i	0.999792	−	0.0204194i	$-0.00650013\pi$
$919$	44.9270	+	25.9386i	1.48200	+	0.855635i	0.482212	+	0.876055i	$0.339833\pi$
$920$	15.6153	−	3.63900i	0.514821	−	0.119974i
$921$	2.83671	+	4.91333i	0.0934729	+	0.161900i
$922$	9.89195	+	47.9340i	0.325774	+	1.57862i
$923$			1.13269i			0.0372828i
$924$	16.8264	−	46.5456i	0.553549	−	1.53124i
$925$	−34.8127	−	8.50253i	−1.14463	−	0.279562i
$926$	−20.8080	+	4.29406i	−0.683794	+	0.141112i
$927$	3.31060	−	1.91138i	0.108734	−	0.0627778i
$928$	−6.07369	+	9.83454i	−0.199379	+	0.322835i
$929$	37.9198	+	21.8930i	1.24411	+	0.718286i	0.969928	−	0.243393i	$-0.0782603\pi$
$929$	37.9198	+	21.8930i	1.24411	+	0.718286i	0.274180	+	0.961678i	$0.411594\pi$
$930$	2.77957	−	15.4446i	0.0911457	−	0.506450i
$931$	19.2769	−	12.8118i	0.631774	−	0.419891i
$932$	41.2568	+	4.83166i	1.35141	+	0.158266i
$933$	64.9780	+	37.5151i	2.12728	+	1.22819i
$934$	−34.1489	−	11.3200i	−1.11739	−	0.370402i
$935$	−22.1881	+	55.2992i	−0.725629	+	1.80848i
$936$	−0.751546	−	8.62379i	−0.0245651	−	0.281877i
$937$	−14.2224			−0.464624			−0.232312	−	0.972641i	$-0.574629\pi$
$937$	−14.2224			−0.464624			−0.232312	+	0.972641i	$0.574629\pi$
$938$	−16.5177	−	30.4666i	−0.539322	−	0.994771i
$939$			16.4937i			0.538251i
$940$	0.151872	+	5.96726i	0.00495351	+	0.194631i
$941$	4.80070	−	2.77169i	0.156498	−	0.0903544i	−0.419706	−	0.907660i	$-0.637867\pi$
$941$	4.80070	−	2.77169i	0.156498	−	0.0903544i	0.576204	+	0.817306i	$0.304533\pi$
$942$	22.3935	+	7.42320i	0.729619	+	0.241861i
$943$	5.83617	+	3.36951i	0.190052	+	0.109726i
$944$	−7.43893	−	1.76660i	−0.242116	−	0.0574979i
$945$	−11.3244	−	1.00232i	−0.368383	−	0.0326056i
$946$	9.12407	−	8.11789i	0.296649	−	0.263935i
$947$	−29.7881	+	51.5945i	−0.967983	+	1.67660i	−0.266607	+	0.963805i	$0.585902\pi$
$947$	−29.7881	+	51.5945i	−0.967983	+	1.67660i	−0.701377	+	0.712791i	$0.747431\pi$
$948$	36.9429	−	15.9257i	1.19985	−	0.517244i
$949$	3.02612	+	5.24140i	0.0982321	+	0.170143i
$950$	−0.842419	+	23.3659i	−0.0273317	+	0.758089i
$951$	48.8163			1.58298
$952$	−43.4872	−	34.2394i	−1.40943	−	1.10971i
$953$			12.2577i			0.397065i	0.980094	+	0.198532i	$0.0636175\pi$
$953$			12.2577i			0.397065i	−0.980094	+	0.198532i	$0.936383\pi$
$954$	1.93602	+	9.38149i	0.0626809	+	0.303737i
$955$	−5.62832	+	14.0274i	−0.182128	+	0.453916i
$956$	16.7285	+	38.8051i	0.541039	+	1.25505i
$957$	−9.55612	+	16.5517i	−0.308906	+	0.535040i
$958$	19.3355	+	21.7321i	0.624703	+	0.702133i
$959$	−13.2316	+	3.99597i	−0.427270	+	0.129037i
$960$	−44.1442	+	14.4275i	−1.42475	+	0.465645i
$961$	13.6732	−	23.6826i	0.441070	−	0.763956i
$962$	7.87279	+	2.60974i	0.253829	+	0.0841414i
$963$	13.5611	+	23.4885i	0.437000	+	0.756906i
$964$	2.17200	−	2.91612i	0.0699553	−	0.0939220i
$965$	3.25893	+	4.15067i	0.104909	+	0.133615i
$966$	−0.659836	+	24.6177i	−0.0212299	+	0.792062i
$967$	−53.4551			−1.71900			−0.859499	−	0.511137i	$-0.829225\pi$
$967$	−53.4551			−1.71900			−0.859499	+	0.511137i	$0.829225\pi$
$968$	−0.486170	−	5.57867i	−0.0156261	−	0.179305i
$969$	54.9869	−	31.7467i	1.76643	−	1.01985i
$970$	7.84025	+	21.7799i	0.251735	+	0.699309i
$971$	11.1284	−	19.2749i	0.357126	−	0.618561i	−0.630353	−	0.776308i	$-0.717090\pi$
$971$	11.1284	−	19.2749i	0.357126	−	0.618561i	0.987479	+	0.157748i	$0.0504232\pi$
$972$	−43.5887	−	5.10475i	−1.39811	−	0.163735i
$973$	56.5259	+	13.2534i	1.81214	+	0.424885i
$974$	−27.3167	−	30.7025i	−0.875284	−	0.983772i
$975$	7.34195	−	7.67620i	0.235131	−	0.245835i
$976$	−37.4662	+	11.1982i	−1.19926	+	0.358447i
$977$	−27.5351	+	15.8974i	−0.880926	+	0.508603i	−0.870964	−	0.491347i	$-0.836505\pi$
$977$	−27.5351	+	15.8974i	−0.880926	+	0.508603i	−0.00996251	+	0.999950i	$0.503171\pi$
$978$	−13.7123	−	66.4466i	−0.438472	−	2.12473i
$979$	38.2369			1.22206
$980$	2.76476	+	31.1826i	0.0883170	+	0.996092i
$981$	29.8158			0.951947
$982$	−2.72051	−	13.1829i	−0.0868148	−	0.420684i
$983$	17.8275	−	10.2927i	0.568609	−	0.328287i	−0.187985	−	0.982172i	$-0.560195\pi$
$983$	17.8275	−	10.2927i	0.568609	−	0.328287i	0.756594	+	0.653885i	$0.226862\pi$
$984$	−17.6881	−	8.25538i	−0.563877	−	0.263172i
$985$	44.9805	−	6.43170i	1.43320	−	0.204931i
$986$	14.2070	+	15.9679i	0.452444	+	0.508522i
$987$	−8.92616	−	2.09288i	−0.284123	−	0.0666172i
$988$	0.629440	−	5.37470i	0.0200252	−	0.170992i
$989$	−3.03832	+	5.26253i	−0.0966131	+	0.167339i
$990$	−40.0930	+	14.4325i	−1.27424	+	0.458696i
$991$	−32.2836	+	18.6390i	−1.02552	+	0.592086i	−0.915699	−	0.401865i	$-0.868362\pi$
$991$	−32.2836	+	18.6390i	−1.02552	+	0.592086i	−0.109824	+	0.993951i	$0.535029\pi$
$992$	10.8081	+	0.320577i	0.343156	+	0.0101783i
$993$	33.9810			1.07836
$994$	−0.138772	+	5.17743i	−0.00440158	+	0.164218i
$995$	−20.1519	+	15.8224i	−0.638859	+	0.501605i
$996$	−43.7130	−	32.5584i	−1.38510	−	1.03165i
$997$	6.32111	+	10.9485i	0.200191	+	0.346742i	0.948590	−	0.316508i	$-0.102510\pi$
$997$	6.32111	+	10.9485i	0.200191	+	0.346742i	−0.748399	+	0.663249i	$0.769177\pi$
$998$	27.1034	+	8.98449i	0.857944	+	0.284399i
$999$	−6.88644	+	11.9277i	−0.217877	+	0.377375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.s.b.19.15	yes	32
4.3	odd	2	inner	140.2.s.b.19.10	yes	32
5.2	odd	4		700.2.p.e.551.10		32
5.3	odd	4		700.2.p.e.551.7		32
5.4	even	2	inner	140.2.s.b.19.2	✓	32
7.2	even	3		980.2.c.d.979.5		32
7.3	odd	6	inner	140.2.s.b.59.7	yes	32
7.4	even	3		980.2.s.e.619.7		32
7.5	odd	6		980.2.c.d.979.6		32
7.6	odd	2		980.2.s.e.19.15		32
20.3	even	4		700.2.p.e.551.15		32
20.7	even	4		700.2.p.e.551.2		32
20.19	odd	2	inner	140.2.s.b.19.7	yes	32
28.3	even	6	inner	140.2.s.b.59.2	yes	32
28.11	odd	6		980.2.s.e.619.2		32
28.19	even	6		980.2.c.d.979.25		32
28.23	odd	6		980.2.c.d.979.26		32
28.27	even	2		980.2.s.e.19.10		32
35.3	even	12		700.2.p.e.451.15		32
35.4	even	6		980.2.s.e.619.10		32
35.9	even	6		980.2.c.d.979.28		32
35.17	even	12		700.2.p.e.451.2		32
35.19	odd	6		980.2.c.d.979.27		32
35.24	odd	6	inner	140.2.s.b.59.10	yes	32
35.34	odd	2		980.2.s.e.19.2		32
140.3	odd	12		700.2.p.e.451.7		32
140.19	even	6		980.2.c.d.979.8		32
140.39	odd	6		980.2.s.e.619.15		32
140.59	even	6	inner	140.2.s.b.59.15	yes	32
140.79	odd	6		980.2.c.d.979.7		32
140.87	odd	12		700.2.p.e.451.10		32
140.139	even	2		980.2.s.e.19.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.2	✓	32	5.4	even	2	inner
140.2.s.b.19.7	yes	32	20.19	odd	2	inner
140.2.s.b.19.10	yes	32	4.3	odd	2	inner
140.2.s.b.19.15	yes	32	1.1	even	1	trivial
140.2.s.b.59.2	yes	32	28.3	even	6	inner
140.2.s.b.59.7	yes	32	7.3	odd	6	inner
140.2.s.b.59.10	yes	32	35.24	odd	6	inner
140.2.s.b.59.15	yes	32	140.59	even	6	inner
700.2.p.e.451.2		32	35.17	even	12
700.2.p.e.451.7		32	140.3	odd	12
700.2.p.e.451.10		32	140.87	odd	12
700.2.p.e.451.15		32	35.3	even	12
700.2.p.e.551.2		32	20.7	even	4
700.2.p.e.551.7		32	5.3	odd	4
700.2.p.e.551.10		32	5.2	odd	4
700.2.p.e.551.15		32	20.3	even	4
980.2.c.d.979.5		32	7.2	even	3
980.2.c.d.979.6		32	7.5	odd	6
980.2.c.d.979.7		32	140.79	odd	6
980.2.c.d.979.8		32	140.19	even	6
980.2.c.d.979.25		32	28.19	even	6
980.2.c.d.979.26		32	28.23	odd	6
980.2.c.d.979.27		32	35.19	odd	6
980.2.c.d.979.28		32	35.9	even	6
980.2.s.e.19.2		32	35.34	odd	2
980.2.s.e.19.7		32	140.139	even	2
980.2.s.e.19.10		32	28.27	even	2
980.2.s.e.19.15		32	7.6	odd	2
980.2.s.e.619.2		32	28.11	odd	6
980.2.s.e.619.7		32	7.4	even	3
980.2.s.e.619.10		32	35.4	even	6
980.2.s.e.619.15		32	140.39	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38503 - 0.285823i) q^{2} +(-2.24836 + 1.29809i) q^{3} +(1.83661 - 0.791746i) q^{4} +(0.316513 + 2.21355i) q^{5} +(-2.74302 + 2.44053i) q^{6} +(2.57589 + 0.603960i) q^{7} +(2.31746 - 1.62154i) q^{8} +(1.87009 - 3.23909i) q^{9} +(1.07106 + 2.97537i) q^{10} +(-3.12008 + 1.80138i) q^{11} +(-3.10161 + 4.16422i) q^{12} +0.818282 q^{13} +(3.74031 + 0.100253i) q^{14} +(-3.58504 - 4.56601i) q^{15} +(2.74628 - 2.90826i) q^{16} +(-3.69814 - 6.40537i) q^{17} +(1.66432 - 5.02075i) q^{18} +(1.65329 - 2.86358i) q^{19} +(2.33388 + 3.81484i) q^{20} +(-6.57554 + 1.98583i) q^{21} +(-3.80652 + 3.38675i) q^{22} +(1.26758 - 2.19550i) q^{23} +(-3.10559 + 6.65408i) q^{24} +(-4.79964 + 1.40124i) q^{25} +(1.13334 - 0.233884i) q^{26} +1.92166i q^{27} +(5.20910 - 0.930214i) q^{28} -2.04334 q^{29} +(-6.27045 - 5.29937i) q^{30} +(0.955727 + 1.65537i) q^{31} +(2.97243 - 4.81297i) q^{32} +(4.67671 - 8.10030i) q^{33} +(-6.95283 - 7.81461i) q^{34} +(-0.521593 + 5.89304i) q^{35} +(0.870092 - 7.42959i) q^{36} +(6.20697 + 3.58360i) q^{37} +(1.47138 - 4.43869i) q^{38} +(-1.83980 + 1.06221i) q^{39} +(4.32286 + 4.61658i) q^{40} +2.65824i q^{41} +(-8.53972 + 4.62987i) q^{42} -2.39696 q^{43} +(-4.30413 + 5.77873i) q^{44} +(7.76182 + 3.11433i) q^{45} +(1.12810 - 3.40314i) q^{46} +(1.15593 + 0.667376i) q^{47} +(-2.39944 + 10.1037i) q^{48} +(6.27046 + 3.11147i) q^{49} +(-6.24713 + 3.31260i) q^{50} +(16.6295 + 9.60106i) q^{51} +(1.50287 - 0.647871i) q^{52} +(-1.56838 + 0.905503i) q^{53} +(0.549253 + 2.66155i) q^{54} +(-4.97499 - 6.33630i) q^{55} +(6.94888 - 2.77725i) q^{56} +8.58450i q^{57} +(-2.83009 + 0.584034i) q^{58} +(-0.955727 - 1.65537i) q^{59} +(-10.1994 - 5.54755i) q^{60} +(-8.46625 - 4.88799i) q^{61} +(1.79685 + 2.01956i) q^{62} +(6.77344 - 7.21411i) q^{63} +(2.74124 - 7.51569i) q^{64} +(0.258997 + 1.81131i) q^{65} +(4.16213 - 12.5559i) q^{66} +(-4.63112 - 8.02134i) q^{67} +(-11.8635 - 8.83618i) q^{68} +6.58172i q^{69} +(0.961944 + 8.31112i) q^{70} +1.38422i q^{71} +(-0.918444 - 10.5389i) q^{72} +(3.69814 + 6.40537i) q^{73} +(9.62111 + 3.18929i) q^{74} +(8.97240 - 9.38087i) q^{75} +(0.769222 - 6.56827i) q^{76} +(-9.12495 + 2.75576i) q^{77} +(-2.24457 + 1.99704i) q^{78} +(-6.70979 - 3.87390i) q^{79} +(7.30682 + 5.15853i) q^{80} +(3.11579 + 5.39670i) q^{81} +(0.759784 + 3.68173i) q^{82} +10.4973i q^{83} +(-10.5044 + 8.85335i) q^{84} +(13.0081 - 10.2134i) q^{85} +(-3.31986 + 0.685105i) q^{86} +(4.59418 - 2.65245i) q^{87} +(-4.30966 + 9.23393i) q^{88} +(-9.19133 - 5.30662i) q^{89} +(11.6405 + 2.09494i) q^{90} +(2.10781 + 0.494210i) q^{91} +(0.589761 - 5.03589i) q^{92} +(-4.29764 - 2.48125i) q^{93} +(1.79175 + 0.593945i) q^{94} +(6.86198 + 2.75329i) q^{95} +(-0.435416 + 14.6798i) q^{96} +7.32005 q^{97} +(9.57411 + 2.51724i) q^{98} +13.4750i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{4} - 6 q^{5} + 4 q^{9} - 12 q^{10} + 22 q^{14} + 18 q^{16} - 52 q^{21} - 48 q^{24} - 26 q^{25} - 18 q^{26} - 26 q^{30} - 28 q^{36} + 42 q^{40} - 26 q^{44} + 36 q^{45} - 22 q^{46} + 36 q^{50}+ \cdots + 60 q^{96}+O(q^{100}) \) 32 * q + 6 * q^4 - 6 * q^5 + 4 * q^9 - 12 * q^10 + 22 * q^14 + 18 * q^16 - 52 * q^21 - 48 * q^24 - 26 * q^25 - 18 * q^26 - 26 * q^30 - 28 * q^36 + 42 * q^40 - 26 * q^44 + 36 * q^45 - 22 * q^46 + 36 * q^50 + 48 * q^54 - 16 * q^56 + 4 * q^60 + 36 * q^61 + 36 * q^64 - 4 * q^65 - 24 * q^66 + 26 * q^70 + 14 * q^74 + 72 * q^80 + 72 * q^81 + 56 * q^84 + 20 * q^85 + 8 * q^86 - 108 * q^89 + 30 * q^94 + 60 * q^96

Introduction

L-functions

Modular forms

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