LMFDB - Embedded newform 740.2.be.a.51.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(51,740)] 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("740.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 0, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.be (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			51.19
Character	$\chi$	$=$	740.51
Dual form			740.2.be.a.711.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.994365 - 1.00560i) q^{2} +(-0.766676 - 1.32792i) q^{3} +(-0.0224764 + 1.99987i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-0.573007 + 2.09141i) q^{6} +(-3.13458 + 1.80975i) q^{7} +(2.03343 - 1.96600i) q^{8} +(0.324416 - 0.561906i) q^{9} +(0.700214 + 1.22870i) q^{10} +5.15947 q^{11} +(2.67291 - 1.50341i) q^{12} +(3.25613 + 0.872478i) q^{13} +(4.93681 + 1.35259i) q^{14} +(0.396861 + 1.48110i) q^{15} +(-3.99899 - 0.0899001i) q^{16} +(1.78801 + 6.67296i) q^{17} +(-0.887643 + 0.232505i) q^{18} +(2.05405 - 7.66583i) q^{19} +(0.539316 - 1.92591i) q^{20} +(4.80641 + 2.77498i) q^{21} +(-5.13039 - 5.18838i) q^{22} +(-4.81061 - 4.81061i) q^{23} +(-4.16968 - 1.19295i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.36042 - 4.14194i) q^{26} -5.59494 q^{27} +(-3.54882 - 6.30944i) q^{28} +(-0.412473 - 0.412473i) q^{29} +(1.09478 - 1.87184i) q^{30} +(-2.49979 + 2.49979i) q^{31} +(3.88605 + 4.11079i) q^{32} +(-3.95564 - 6.85136i) q^{33} +(4.93241 - 8.43339i) q^{34} +(3.49617 - 0.936796i) q^{35} +(1.11645 + 0.661422i) q^{36} +(1.00831 - 5.99861i) q^{37} +(-9.75127 + 5.55707i) q^{38} +(-1.33782 - 4.99280i) q^{39} +(-2.47298 + 1.37272i) q^{40} +(5.58614 - 3.22516i) q^{41} +(-1.98880 - 7.59269i) q^{42} +(0.0161262 + 0.0161262i) q^{43} +(-0.115966 + 10.3183i) q^{44} +(-0.458794 + 0.458794i) q^{45} +(-0.0540635 + 9.62107i) q^{46} -6.31272i q^{47} +(2.94655 + 5.37927i) q^{48} +(3.05039 - 5.28344i) q^{49} +(-0.358344 - 1.36806i) q^{50} +(7.49034 - 7.49034i) q^{51} +(-1.81803 + 6.49224i) q^{52} +(-0.796597 + 1.37975i) q^{53} +(5.56342 + 5.62629i) q^{54} +(-4.98366 - 1.33537i) q^{55} +(-2.81597 + 9.84259i) q^{56} +(-11.7544 + 3.14959i) q^{57} +(-0.00463554 + 0.824933i) q^{58} +(5.04561 - 1.35197i) q^{59} +(-2.97094 + 0.760381i) q^{60} +(1.98623 - 7.41272i) q^{61} +(4.99950 + 0.0280936i) q^{62} +2.34845i q^{63} +(0.269672 - 7.99545i) q^{64} +(-2.91937 - 1.68550i) q^{65} +(-2.95641 + 10.7906i) q^{66} +(-1.95347 - 3.38351i) q^{67} +(-13.3853 + 3.42582i) q^{68} +(-2.69993 + 10.0763i) q^{69} +(-4.41851 - 2.58424i) q^{70} +(-9.74493 + 5.62624i) q^{71} +(-0.445030 - 1.78040i) q^{72} -6.81535i q^{73} +(-7.03485 + 4.95085i) q^{74} -1.53335i q^{75} +(15.2845 + 4.28015i) q^{76} +(-16.1728 + 9.33735i) q^{77} +(-3.69050 + 6.30997i) q^{78} +(3.17179 - 11.8373i) q^{79} +(3.83946 + 1.12185i) q^{80} +(3.31626 + 5.74393i) q^{81} +(-8.79789 - 2.41046i) q^{82} +(3.39228 + 1.95853i) q^{83} +(-5.65765 + 9.54985i) q^{84} -6.90836i q^{85} +(0.000181233 - 0.0322519i) q^{86} +(-0.231499 + 0.863965i) q^{87} +(10.4914 - 10.1435i) q^{88} +(1.08737 - 0.291359i) q^{89} +(0.917574 + 0.00515611i) q^{90} +(-11.7856 + 3.15794i) q^{91} +(9.72874 - 9.51249i) q^{92} +(5.23605 + 1.40300i) q^{93} +(-6.34809 + 6.27715i) q^{94} +(-3.96813 + 6.87300i) q^{95} +(2.47947 - 8.31202i) q^{96} +(11.2735 - 11.2735i) q^{97} +(-8.34625 + 2.18618i) q^{98} +(1.67382 - 2.89913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) $ 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$1$	$-1$

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 $

$2$	−0.994365	−	1.00560i	−0.703122	−	0.711069i
$2$	−0.994365	−	1.00560i	−0.703122	−	0.711069i
$3$	−0.766676	−	1.32792i	−0.442640	−	0.766676i	0.555244	−	0.831687i	$-0.312625\pi$
$3$	−0.766676	−	1.32792i	−0.442640	−	0.766676i	−0.997885	+	0.0650117i	$0.979292\pi$
$4$	−0.0224764	+	1.99987i	−0.0112382	+	0.999937i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$6$	−0.573007	+	2.09141i	−0.233929	+	0.853815i
$7$	−3.13458	+	1.80975i	−1.18476	+	0.684021i	−0.957111	−	0.289722i	$-0.906437\pi$
$7$	−3.13458	+	1.80975i	−1.18476	+	0.684021i	−0.227649	+	0.973743i	$0.573104\pi$
$8$	2.03343	−	1.96600i	0.718926	−	0.695087i
$9$	0.324416	−	0.561906i	0.108139	−	0.187302i
$10$	0.700214	+	1.22870i	0.221427	+	0.388549i
$11$	5.15947			1.55564			0.777819	−	0.628489i	$-0.216326\pi$
$11$	5.15947			1.55564			0.777819	+	0.628489i	$0.216326\pi$
$12$	2.67291	−	1.50341i	0.771602	−	0.433996i
$13$	3.25613	+	0.872478i	0.903089	+	0.241982i	0.680342	−	0.732895i	$-0.261831\pi$
$13$	3.25613	+	0.872478i	0.903089	+	0.241982i	0.222746	+	0.974876i	$0.428498\pi$
$14$	4.93681	+	1.35259i	1.31942	+	0.361495i
$15$	0.396861	+	1.48110i	0.102469	+	0.382419i
$16$	−3.99899	−	0.0899001i	−0.999747	−	0.0224750i
$17$	1.78801	+	6.67296i	0.433657	+	1.61843i	0.744259	+	0.667891i	$0.232803\pi$
$17$	1.78801	+	6.67296i	0.433657	+	1.61843i	−0.310602	+	0.950540i	$0.600531\pi$
$18$	−0.887643	+	0.232505i	−0.209219	+	0.0548020i
$19$	2.05405	−	7.66583i	0.471232	−	1.75866i	−0.164120	−	0.986440i	$-0.552478\pi$
$19$	2.05405	−	7.66583i	0.471232	−	1.75866i	0.635352	−	0.772222i	$-0.280855\pi$
$20$	0.539316	−	1.92591i	0.120595	−	0.430647i
$21$	4.80641	+	2.77498i	1.04885	+	0.605551i
$22$	−5.13039	−	5.18838i	−1.09380	−	1.10617i
$23$	−4.81061	−	4.81061i	−1.00308	−	1.00308i	−0.999995	−	0.00308664i	$-0.999017\pi$
$23$	−4.81061	−	4.81061i	−1.00308	−	1.00308i	−0.00308664	−	0.999995i	$-0.500983\pi$
$24$	−4.16968	−	1.19295i	−0.851132	−	0.243510i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−2.36042	−	4.14194i	−0.462916	−	0.812301i
$27$	−5.59494			−1.07675
$28$	−3.54882	−	6.30944i	−0.670664	−	1.19237i
$29$	−0.412473	−	0.412473i	−0.0765943	−	0.0765943i	0.667772	−	0.744366i	$-0.267248\pi$
$29$	−0.412473	−	0.412473i	−0.0765943	−	0.0765943i	−0.744366	+	0.667772i	$0.767248\pi$
$30$	1.09478	−	1.87184i	0.199878	−	0.341750i
$31$	−2.49979	+	2.49979i	−0.448975	+	0.448975i	−0.895014	−	0.446039i	$-0.852834\pi$
$31$	−2.49979	+	2.49979i	−0.448975	+	0.448975i	0.446039	+	0.895014i	$0.352834\pi$
$32$	3.88605	+	4.11079i	0.686963	+	0.726692i
$33$	−3.95564	−	6.85136i	−0.688588	−	1.19267i
$34$	4.93241	−	8.43339i	0.845902	−	1.44632i
$35$	3.49617	−	0.936796i	0.590961	−	0.158347i
$36$	1.11645	+	0.661422i	0.186075	+	0.110237i
$37$	1.00831	−	5.99861i	0.165764	−	0.986165i
$37$	1.00831	−	5.99861i	0.165764	−	0.986165i
$38$	−9.75127	+	5.55707i	−1.58186	+	0.901476i
$39$	−1.33782	−	4.99280i	−0.214222	−	0.799487i
$40$	−2.47298	+	1.37272i	−0.391013	+	0.217046i
$41$	5.58614	−	3.22516i	0.872409	−	0.503685i	0.00426064	−	0.999991i	$-0.498644\pi$
$41$	5.58614	−	3.22516i	0.872409	−	0.503685i	0.868148	+	0.496306i	$0.165310\pi$
$42$	−1.98880	−	7.59269i	−0.306878	−	1.17158i
$43$	0.0161262	+	0.0161262i	0.00245923	+	0.00245923i	0.708335	−	0.705876i	$-0.249446\pi$
$43$	0.0161262	+	0.0161262i	0.00245923	+	0.00245923i	−0.705876	+	0.708335i	$0.749446\pi$
$44$	−0.115966	+	10.3183i	−0.0174826	+	1.55554i
$45$	−0.458794	+	0.458794i	−0.0683930	+	0.0683930i
$46$	−0.0540635	+	9.62107i	−0.00797124	+	1.41855i
$47$		−	6.31272i		−	0.920805i	−0.887710	−	0.460402i	$-0.847705\pi$
$47$		−	6.31272i		−	0.920805i	0.887710	−	0.460402i	$-0.152295\pi$
$48$	2.94655	+	5.37927i	0.425298	+	0.776430i
$49$	3.05039	−	5.28344i	0.435771	−	0.754777i
$50$	−0.358344	−	1.36806i	−0.0506774	−	0.193473i
$51$	7.49034	−	7.49034i	1.04886	−	1.04886i
$52$	−1.81803	+	6.49224i	−0.252116	+	0.900312i
$53$	−0.796597	+	1.37975i	−0.109421	+	0.189523i	−0.915536	−	0.402236i	$-0.868233\pi$
$53$	−0.796597	+	1.37975i	−0.109421	+	0.189523i	0.806115	+	0.591759i	$0.201566\pi$
$54$	5.56342	+	5.62629i	0.757085	+	0.765642i
$55$	−4.98366	−	1.33537i	−0.671997	−	0.180061i
$56$	−2.81597	+	9.84259i	−0.376300	+	1.31527i
$57$	−11.7544	+	3.14959i	−1.55691	+	0.417173i
$58$	−0.00463554	+	0.824933i	−0.000608676	+	0.108319i
$59$	5.04561	−	1.35197i	0.656882	−	0.176011i	0.0850436	−	0.996377i	$-0.472897\pi$
$59$	5.04561	−	1.35197i	0.656882	−	0.176011i	0.571839	+	0.820366i	$0.306230\pi$
$60$	−2.97094	+	0.760381i	−0.383547	+	0.0981648i
$61$	1.98623	−	7.41272i	0.254311	−	0.949102i	−0.714161	−	0.699981i	$-0.753192\pi$
$61$	1.98623	−	7.41272i	0.254311	−	0.949102i	0.968472	−	0.249121i	$-0.0801416\pi$
$62$	4.99950	+	0.0280936i	0.634937	+	0.00356789i
$63$			2.34845i			0.295877i
$64$	0.269672	−	7.99545i	0.0337090	−	0.999432i
$65$	−2.91937	−	1.68550i	−0.362103	−	0.209060i
$66$	−2.95641	+	10.7906i	−0.363909	+	1.32823i
$67$	−1.95347	−	3.38351i	−0.238655	−	0.413362i	0.721674	−	0.692233i	$-0.243373\pi$
$67$	−1.95347	−	3.38351i	−0.238655	−	0.413362i	−0.960328	+	0.278871i	$0.910040\pi$
$68$	−13.3853	+	3.42582i	−1.62320	+	0.415442i
$69$	−2.69993	+	10.0763i	−0.325034	+	1.21304i
$70$	−4.41851	−	2.58424i	−0.528113	−	0.308876i
$71$	−9.74493	+	5.62624i	−1.15651	+	0.667712i	−0.950465	−	0.310831i	$-0.899393\pi$
$71$	−9.74493	+	5.62624i	−1.15651	+	0.667712i	−0.206045	+	0.978543i	$0.566059\pi$
$72$	−0.445030	−	1.78040i	−0.0524473	−	0.209822i
$73$		−	6.81535i		−	0.797677i	−0.917021	−	0.398838i	$-0.869413\pi$
$73$		−	6.81535i		−	0.797677i	0.917021	−	0.398838i	$-0.130587\pi$
$74$	−7.03485	+	4.95085i	−0.817784	+	0.575525i
$75$		−	1.53335i		−	0.177056i
$76$	15.2845	+	4.28015i	1.75326	+	0.490967i
$77$	−16.1728	+	9.33735i	−1.84306	+	1.06409i
$78$	−3.69050	+	6.30997i	−0.417866	+	0.714464i
$79$	3.17179	−	11.8373i	0.356854	−	1.33180i	−0.521282	−	0.853385i	$-0.674546\pi$
$79$	3.17179	−	11.8373i	0.356854	−	1.33180i	0.878136	−	0.478412i	$-0.158787\pi$
$80$	3.83946	+	1.12185i	0.429265	+	0.125427i
$81$	3.31626	+	5.74393i	0.368473	+	0.638214i
$82$	−8.79789	−	2.41046i	−0.971565	−	0.266190i
$83$	3.39228	+	1.95853i	0.372351	+	0.214977i	0.674485	−	0.738288i	$-0.264366\pi$
$83$	3.39228	+	1.95853i	0.372351	+	0.214977i	−0.302134	+	0.953265i	$0.597699\pi$
$84$	−5.65765	+	9.54985i	−0.617300	+	1.04197i
$85$		−	6.90836i		−	0.749317i
$86$	0.000181233	−	0.0322519i	1.95428e−5	−	0.00347782i
$87$	−0.231499	+	0.863965i	−0.0248193	+	0.0926268i
$88$	10.4914	−	10.1435i	1.11839	−	1.08130i
$89$	1.08737	−	0.291359i	0.115261	−	0.0308840i	−0.200728	−	0.979647i	$-0.564331\pi$
$89$	1.08737	−	0.291359i	0.115261	−	0.0308840i	0.315988	+	0.948763i	$0.397664\pi$
$90$	0.917574	+	0.00515611i	0.0967208	+	0.000543502i
$91$	−11.7856	+	3.15794i	−1.23546	+	0.331042i
$92$	9.72874	−	9.51249i	1.01429	−	0.991746i
$93$	5.23605	+	1.40300i	0.542953	+	0.145484i
$94$	−6.34809	+	6.27715i	−0.654756	+	0.647438i
$95$	−3.96813	+	6.87300i	−0.407121	+	0.705155i
$96$	2.47947	−	8.31202i	0.253059	−	0.848341i
$97$	11.2735	−	11.2735i	1.14465	−	1.14465i	0.157060	−	0.987589i	$-0.449798\pi$
$97$	11.2735	−	11.2735i	1.14465	−	1.14465i	0.987589	−	0.157060i	$-0.0502015\pi$
$98$	−8.34625	+	2.18618i	−0.843099	+	0.220837i
$99$	1.67382	−	2.89913i	0.168225	−	0.291374i
$100$	−1.01940	+	1.72070i	−0.101940	+	0.172070i
$101$		−	4.40497i		−	0.438311i	−0.975690	−	0.219156i	$-0.929670\pi$
$101$		−	4.40497i		−	0.438311i	0.975690	−	0.219156i	$-0.0703303\pi$
$102$	−14.9804	−	0.0841794i	−1.48329	−	0.00833500i
$103$	0.555859	−	0.555859i	0.0547704	−	0.0547704i	−0.679191	−	0.733962i	$-0.737669\pi$
$103$	0.555859	−	0.555859i	0.0547704	−	0.0547704i	0.733962	+	0.679191i	$0.237669\pi$
$104$	8.33641	−	4.62744i	0.817452	−	0.453758i
$105$	−3.92442	−	3.92442i	−0.382984	−	0.382984i
$106$	2.17959	−	0.570911i	0.211700	−	0.0554518i
$107$	12.8840	−	7.43857i	1.24554	−	0.719114i	0.275324	−	0.961351i	$-0.411215\pi$
$107$	12.8840	−	7.43857i	1.24554	−	0.719114i	0.970217	+	0.242238i	$0.0778814\pi$
$108$	0.125754	−	11.1892i	0.0121007	−	1.07668i
$109$	1.00188	+	3.73906i	0.0959625	+	0.358137i	0.997164	−	0.0752641i	$-0.0239800\pi$
$109$	1.00188	+	3.73906i	0.0959625	+	0.358137i	−0.901201	+	0.433401i	$0.857313\pi$
$110$	3.61273	+	6.33943i	0.344460	+	0.604441i
$111$	−8.73873	+	3.26004i	−0.829443	+	0.309429i
$112$	12.6978	−	6.95538i	1.19983	−	0.657221i
$113$	−11.0210	+	2.95308i	−1.03677	+	0.277802i	−0.736775	−	0.676138i	$-0.763652\pi$
$113$	−11.0210	+	2.95308i	−1.03677	+	0.277802i	−0.299997	+	0.953940i	$0.596986\pi$
$114$	14.8554	+	8.68844i	1.39134	+	0.813747i
$115$	3.40162	+	5.89177i	0.317202	+	0.549411i
$116$	0.834165	−	0.815623i	0.0774503	−	0.0757287i
$117$	1.54659	−	1.54659i	0.142983	−	0.142983i
$118$	−6.37672	−	3.72953i	−0.587025	−	0.343331i
$119$	−17.6811	−	17.6811i	−1.62082	−	1.62082i
$120$	3.71884	+	2.23149i	0.339482	+	0.203706i
$121$	15.6201			1.42001
$122$	−9.42930	+	5.37359i	−0.853689	+	0.486502i
$123$	−8.56552	−	4.94530i	−0.772327	−	0.445903i
$124$	−4.94307	−	5.05545i	−0.443901	−	0.453993i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	2.36161	−	2.33522i	0.210389	−	0.208038i
$127$	15.7481	+	9.09219i	1.39742	+	0.806802i	0.994122	−	0.108267i	$-0.0345300\pi$
$127$	15.7481	+	9.09219i	1.39742	+	0.806802i	0.403299	+	0.915068i	$0.367863\pi$
$128$	−8.30841	+	7.67922i	−0.734366	+	0.678753i
$129$	0.00905077	−	0.0337779i	0.000796876	−	0.00297398i
$130$	1.20798	+	4.61173i	0.105946	+	0.404475i
$131$	2.77279	+	10.3482i	0.242260	+	0.904126i	0.974741	+	0.223339i	$0.0716956\pi$
$131$	2.77279	+	10.3482i	0.242260	+	0.904126i	−0.732481	+	0.680788i	$0.761638\pi$
$132$	13.7908	−	7.75678i	1.20033	−	0.675141i
$133$	7.43465	+	27.7465i	0.644666	+	2.40593i
$134$	−1.46001	+	5.32886i	−0.126125	+	0.460344i
$135$	5.40430	+	1.44808i	0.465128	+	0.124631i
$136$	16.7549	+	10.0538i	1.43672	+	0.862103i
$137$	−1.80173			−0.153932			−0.0769661	−	0.997034i	$-0.524523\pi$
$137$	−1.80173			−0.153932			−0.0769661	+	0.997034i	$0.524523\pi$
$138$	12.8175	−	7.30445i	1.09110	−	0.621796i
$139$	−4.22792	+	7.32297i	−0.358608	+	0.621126i	−0.987728	−	0.156181i	$-0.950082\pi$
$139$	−4.22792	+	7.32297i	−0.358608	+	0.621126i	0.629121	+	0.777307i	$0.283415\pi$
$140$	1.79489	+	7.01295i	0.151696	+	0.592703i
$141$	−8.38279	+	4.83981i	−0.705959	+	0.407585i
$142$	15.3478	+	4.20500i	1.28796	+	0.352876i
$143$	16.7999	+	4.50152i	1.40488	+	0.376436i
$144$	−1.34785	+	2.21789i	−0.112321	+	0.184824i
$145$	0.291663	+	0.505174i	0.0242213	+	0.0419524i
$146$	−6.85354	+	6.77695i	−0.567203	+	0.560864i
$147$	−9.35466			−0.771559
$148$	11.9738	+	2.15131i	0.984240	+	0.176837i
$149$	−15.8772			−1.30071			−0.650357	−	0.759629i	$-0.725381\pi$
$149$	−15.8772			−1.30071			−0.650357	+	0.759629i	$0.725381\pi$
$150$	−1.54194	+	1.52471i	−0.125899	+	0.124492i
$151$	−2.36835	−	4.10211i	−0.192734	−	0.333825i	0.753421	−	0.657538i	$-0.228402\pi$
$151$	−2.36835	−	4.10211i	−0.192734	−	0.333825i	−0.946155	+	0.323713i	$0.895069\pi$
$152$	−10.8943	−	19.6262i	−0.883642	−	1.59190i
$153$	4.32964	+	1.16012i	0.350031	+	0.0937904i
$154$	25.4713	+	6.97865i	2.05253	+	0.562356i
$155$	3.06160	−	1.76762i	0.245914	−	0.141978i
$156$	10.0150	−	2.56324i	0.801844	−	0.205224i
$157$	2.03691	−	3.52803i	0.162563	−	0.281568i	−0.773224	−	0.634133i	$-0.781357\pi$
$157$	2.03691	−	3.52803i	0.162563	−	0.281568i	0.935787	+	0.352565i	$0.114691\pi$
$158$	−15.0575	+	8.58100i	−1.19791	+	0.682668i
$159$	2.44293			0.193737
$160$	−2.68969	−	4.97650i	−0.212638	−	0.393427i
$161$	23.7853	+	6.37324i	1.87454	+	0.502282i
$162$	2.47854	−	9.04640i	0.194733	−	0.710752i
$163$	−1.34923	−	5.03540i	−0.105680	−	0.394403i	0.892742	−	0.450569i	$-0.148779\pi$
$163$	−1.34923	−	5.03540i	−0.105680	−	0.394403i	−0.998421	+	0.0561664i	$0.982112\pi$
$164$	6.32436	+	11.2441i	0.493849	+	0.878014i
$165$	2.04759	+	7.64170i	0.159405	+	0.594906i
$166$	−1.40366	−	5.35879i	−0.108945	−	0.415922i
$167$	2.55123	−	9.52132i	0.197420	−	0.736782i	−0.794207	−	0.607647i	$-0.792113\pi$
$167$	2.55123	−	9.52132i	0.197420	−	0.736782i	0.991627	−	0.129134i	$-0.0412199\pi$
$168$	15.2291	−	3.80668i	1.17495	−	0.293692i
$169$	−1.41715	−	0.818193i	−0.109012	−	0.0629379i
$170$	−6.94707	+	6.86943i	−0.532816	+	0.526861i
$171$	−3.64111	−	3.64111i	−0.278442	−	0.278442i
$172$	−0.0326129	+	0.0318880i	−0.00248671	+	0.00243143i
$173$	−5.62744	−	3.24900i	−0.427846	−	0.247017i	0.270582	−	0.962697i	$-0.412784\pi$
$173$	−5.62744	−	3.24900i	−0.427846	−	0.247017i	−0.698429	+	0.715680i	$0.746117\pi$
$174$	1.09900	−	0.626301i	0.0833150	−	0.0474797i
$175$	−3.61950			−0.273609
$176$	−20.6326	−	0.463836i	−1.55524	−	0.0349630i
$177$	−5.66365	−	5.66365i	−0.425706	−	0.425706i
$178$	−1.37423	−	0.803743i	−0.103003	−	0.0602431i
$179$	8.28910	−	8.28910i	0.619556	−	0.619556i	−0.325861	−	0.945418i	$-0.605654\pi$
$179$	8.28910	−	8.28910i	0.619556	−	0.619556i	0.945418	+	0.325861i	$0.105654\pi$
$180$	−0.907218	−	0.927843i	−0.0676201	−	0.0691573i
$181$	−0.575209	−	0.996291i	−0.0427549	−	0.0740537i	0.843856	−	0.536570i	$-0.180280\pi$
$181$	−0.575209	−	0.996291i	−0.0427549	−	0.0740537i	−0.886611	+	0.462516i	$0.846947\pi$
$182$	14.8948	+	8.71147i	1.10408	+	0.645737i
$183$	−11.3663	+	3.04559i	−0.840222	+	0.225137i
$184$	−19.2397	−	0.324368i	−1.41837	−	0.0239127i
$185$	−2.52650	+	5.53324i	−0.185752	+	0.406812i
$186$	−3.79569	−	6.66048i	−0.278313	−	0.488370i
$187$	9.22520	+	34.4289i	0.674613	+	2.51769i
$188$	12.6246	+	0.141887i	0.920747	+	0.0103482i
$189$	17.5378	−	10.1255i	1.27569	−	0.736518i
$190$	10.8573	−	2.84391i	0.787670	−	0.206319i
$191$	15.7049	+	15.7049i	1.13637	+	1.13637i	0.989097	+	0.147269i	$0.0470482\pi$
$191$	15.7049	+	15.7049i	1.13637	+	1.13637i	0.147269	+	0.989097i	$0.452952\pi$
$192$	−10.8241	+	5.77182i	−0.781161	+	0.416545i
$193$	14.1300	−	14.1300i	1.01710	−	1.01710i	0.0172478	−	0.999851i	$-0.494510\pi$
$193$	14.1300	−	14.1300i	1.01710	−	1.01710i	0.999851	−	0.0172478i	$-0.00549043\pi$
$194$	−22.5466	−	0.126696i	−1.61875	−	0.00909623i
$195$			5.16892i			0.370154i
$196$	10.4976	+	6.21916i	0.749832	+	0.444226i
$197$	8.87835	−	15.3777i	0.632556	−	1.09562i	−0.354471	−	0.935067i	$-0.615339\pi$
$197$	8.87835	−	15.3777i	0.632556	−	1.09562i	0.987027	−	0.160552i	$-0.0513275\pi$
$198$	−4.57976	+	1.19960i	−0.325470	+	0.0852520i
$199$	6.08558	−	6.08558i	0.431395	−	0.431395i	−0.457707	−	0.889103i	$-0.651329\pi$
$199$	6.08558	−	6.08558i	0.431395	−	0.431395i	0.889103	+	0.457707i	$0.151329\pi$
$200$	2.74400	−	0.685893i	0.194030	−	0.0485000i
$201$	−2.99536	+	5.18811i	−0.211276	+	0.365941i
$202$	−4.42966	+	4.38015i	−0.311670	+	0.308186i
$203$	2.03940	+	0.546457i	0.143138	+	0.0383537i
$204$	14.8114	+	15.1481i	1.03700	+	1.06058i
$205$	−6.23053	+	1.66947i	−0.435159	+	0.116601i
$206$	−1.11170	−	0.00624696i	−0.0774559	−	0.000435247i
$207$	−4.26375	+	1.14247i	−0.296351	+	0.0794071i
$208$	−12.9428	−	3.78176i	−0.897422	−	0.262218i
$209$	10.5978	−	39.5516i	0.733067	−	2.73584i
$210$	−0.0441042	+	7.84872i	−0.00304348	+	0.541613i
$211$			11.6429i			0.801531i	0.916181	+	0.400766i	$0.131256\pi$
$211$			11.6429i			0.801531i	−0.916181	+	0.400766i	$0.868744\pi$
$212$	−2.74141	−	1.62411i	−0.188281	−	0.111544i
$213$	14.9424	+	8.62700i	1.02384	+	0.591112i
$214$	−20.2916	−	5.55952i	−1.38711	−	0.380041i
$215$	−0.0114030	−	0.0197505i	−0.000777676	−	0.00134697i
$216$	−11.3769	+	10.9997i	−0.774102	+	0.748433i
$217$	3.31179	−	12.3598i	0.224819	−	0.839036i
$218$	2.76378	−	4.72548i	0.187187	−	0.320050i
$219$	−9.05026	+	5.22517i	−0.611560	+	0.353084i
$220$	2.78258	−	9.93668i	0.187602	−	0.669931i
$221$			23.2881i			1.56652i
$222$	11.9678	+	5.54602i	0.803225	+	0.372225i
$223$		−	6.94752i		−	0.465240i	−0.972568	−	0.232620i	$-0.925270\pi$
$223$		−	6.94752i		−	0.465240i	0.972568	−	0.232620i	$-0.0747298\pi$
$224$	−19.6206	−	5.85282i	−1.31096	−	0.391058i
$225$	0.561906	−	0.324416i	0.0374604	−	0.0216278i
$226$	13.9286	+	8.14635i	0.926514	+	0.541887i
$227$	−6.94686	+	25.9260i	−0.461079	+	1.72077i	0.208492	+	0.978024i	$0.433144\pi$
$227$	−6.94686	+	25.9260i	−0.461079	+	1.72077i	−0.669571	+	0.742748i	$0.733522\pi$
$228$	−6.03458	−	23.5781i	−0.399650	−	1.56150i
$229$	7.01555	+	12.1513i	0.463600	+	0.802979i	0.999137	−	0.0415326i	$-0.0132240\pi$
$229$	7.01555	+	12.1513i	0.463600	+	0.802979i	−0.535537	+	0.844512i	$0.679891\pi$
$230$	2.54234	−	9.27925i	0.167637	−	0.611856i
$231$	24.7985	+	14.3174i	1.63162	+	0.942018i
$232$	−1.64966	−	0.0278120i	−0.108305	−	0.00182595i
$233$		−	9.32897i		−	0.611161i	−0.952166	−	0.305580i	$-0.901150\pi$
$233$		−	9.32897i		−	0.611161i	0.952166	−	0.305580i	$-0.0988505\pi$
$234$	−3.09314	−	0.0173812i	−0.202205	−	0.00113625i
$235$	−1.63385	+	6.09762i	−0.106581	+	0.397765i
$236$	2.59036	+	10.1210i	0.168618	+	0.658819i
$237$	−18.1507	+	4.86346i	−1.17901	+	0.315916i
$238$	−0.198707	+	35.3616i	−0.0128803	+	2.29215i
$239$	−5.32391	+	1.42654i	−0.344375	+	0.0922750i	−0.426861	−	0.904317i	$-0.640381\pi$
$239$	−5.32391	+	1.42654i	−0.344375	+	0.0922750i	0.0824860	+	0.996592i	$0.473714\pi$
$240$	−1.45389	−	5.95860i	−0.0938482	−	0.384626i
$241$	−4.41407	−	1.18275i	−0.284335	−	0.0761873i	0.113833	−	0.993500i	$-0.463687\pi$
$241$	−4.41407	−	1.18275i	−0.284335	−	0.0761873i	−0.398168	+	0.917313i	$0.630354\pi$
$242$	−15.5321	−	15.7076i	−0.998439	−	1.00972i
$243$	−3.30743	+	5.72863i	−0.212171	+	0.367492i
$244$	14.7799	+	4.13883i	0.946184	+	0.264961i
$245$	−4.31391	+	4.31391i	−0.275606	+	0.275606i
$246$	3.54424	+	13.5309i	0.225972	+	0.862702i
$247$	13.3765	−	23.1689i	0.851129	−	1.47420i
$248$	−0.168555	+	9.99773i	−0.0107032	+	0.634857i
$249$		−	6.00624i		−	0.380630i
$250$	−0.00794674	+	1.41419i	−0.000502596	+	0.0894413i
$251$	−0.297081	+	0.297081i	−0.0187516	+	0.0187516i	−0.716420	−	0.697669i	$-0.754221\pi$
$251$	−0.297081	+	0.297081i	−0.0187516	+	0.0187516i	0.697669	+	0.716420i	$0.254221\pi$
$252$	−4.69661	−	0.0527848i	−0.295858	−	0.00332513i
$253$	−24.8202	−	24.8202i	−1.56043	−	1.56043i
$254$	−6.51626	−	24.8773i	−0.408866	−	1.56094i
$255$	−9.17376	+	5.29647i	−0.574483	+	0.331678i
$256$	15.9838	+	0.719019i	0.998990	+	0.0449387i
$257$	6.63713	+	24.7701i	0.414013	+	1.54512i	0.786804	+	0.617202i	$0.211734\pi$
$257$	6.63713	+	24.7701i	0.414013	+	1.54512i	−0.372792	+	0.927915i	$0.621599\pi$
$258$	−0.0429670	+	0.0244861i	−0.00267501	+	0.00152444i
$259$	7.69537	+	20.6279i	0.478167	+	1.28176i
$260$	3.43640	−	5.80048i	0.213116	−	0.359731i
$261$	−0.365584	+	0.0979580i	−0.0226291	+	0.00606345i
$262$	7.64902	−	13.0782i	0.472558	−	0.807975i
$263$	−13.8782	−	24.0377i	−0.855765	−	1.48223i	−0.875933	−	0.482432i	$-0.839753\pi$
$263$	−13.8782	−	24.0377i	−0.855765	−	1.48223i	0.0201679	−	0.999797i	$-0.493580\pi$
$264$	−21.5133	−	6.15498i	−1.32405	−	0.378813i
$265$	1.12656	−	1.12656i	0.0692039	−	0.0692039i
$266$	20.5092	−	35.0665i	1.25750	−	2.15006i
$267$	−1.22056	−	1.22056i	−0.0746971	−	0.0746971i
$268$	6.81051	−	3.83065i	0.416018	−	0.233994i
$269$	−19.2680			−1.17479			−0.587394	−	0.809301i	$-0.699846\pi$
$269$	−19.2680			−1.17479			−0.587394	+	0.809301i	$0.699846\pi$
$270$	−3.91766	−	6.87450i	−0.238421	−	0.418369i
$271$	2.45313	+	1.41632i	0.149017	+	0.0860350i	0.572655	−	0.819797i	$-0.305914\pi$
$271$	2.45313	+	1.41632i	0.149017	+	0.0860350i	−0.423638	+	0.905832i	$0.639247\pi$
$272$	−6.55035	−	26.8459i	−0.397174	−	1.62777i
$273$	13.2292	+	13.2292i	0.800668	+	0.800668i
$274$	1.79158	+	1.81183i	0.108233	+	0.109456i
$275$	4.46823	+	2.57973i	0.269444	+	0.155564i
$276$	−20.0906	−	5.62601i	−1.20931	−	0.338646i
$277$	1.17096	−	4.37008i	0.0703562	−	0.262573i	−0.921784	−	0.387704i	$-0.873268\pi$
$277$	1.17096	−	4.37008i	0.0703562	−	0.262573i	0.992140	+	0.125131i	$0.0399351\pi$
$278$	11.5681	−	3.03010i	0.693809	−	0.181733i
$279$	0.593673	+	2.21562i	0.0355423	+	0.132646i
$280$	5.26747	−	8.77839i	0.314792	−	0.524609i
$281$	3.71223	+	13.8542i	0.221453	+	0.826475i	0.983795	+	0.179299i	$0.0573831\pi$
$281$	3.71223	+	13.8542i	0.221453	+	0.826475i	−0.762341	+	0.647175i	$0.775950\pi$
$282$	13.2025	+	3.61723i	0.786197	+	0.215403i
$283$	9.36488	+	2.50931i	0.556684	+	0.149163i	0.526183	−	0.850372i	$-0.323623\pi$
$283$	9.36488	+	2.50931i	0.556684	+	0.149163i	0.0305018	+	0.999535i	$0.490289\pi$
$284$	−11.0327	−	19.6151i	−0.654672	−	1.16394i
$285$	12.1691			0.720833
$286$	−12.1785	−	21.3702i	−0.720129	−	1.26365i
$287$	−11.6735	+	20.2190i	−0.689063	+	1.19349i
$288$	3.57058	−	0.849987i	0.210398	−	0.0500859i
$289$	−26.6090	+	15.3627i	−1.56524	+	0.903689i
$290$	0.217986	−	0.795625i	0.0128006	−	0.0467207i
$291$	−23.6134	−	6.32719i	−1.38424	−	0.370907i
$292$	13.6298	+	0.153185i	0.797627	+	0.00896447i
$293$	9.78135	+	16.9418i	0.571433	+	0.989750i	0.996419	+	0.0845506i	$0.0269455\pi$
$293$	9.78135	+	16.9418i	0.571433	+	0.989750i	−0.424987	+	0.905200i	$0.639721\pi$
$294$	9.30194	+	9.40707i	0.542500	+	0.548632i
$295$	−5.22360			−0.304130
$296$	−9.74296	−	14.1801i	−0.566298	−	0.824201i
$297$	−28.8669			−1.67503
$298$	15.7878	+	15.9662i	0.914561	+	0.924898i
$299$	−11.4668	−	19.8611i	−0.663144	−	1.14860i
$300$	3.06651	+	0.0344643i	0.177045	+	0.00198980i
$301$	−0.0797334	−	0.0213645i	−0.00459576	−	0.00123143i
$302$	−1.77009	+	6.46062i	−0.101857	+	0.371767i
$303$	−5.84946	+	3.37719i	−0.336043	+	0.194014i
$304$	−8.90330	+	30.4709i	−0.510639	+	1.74763i
$305$	−3.83711	+	6.64607i	−0.219712	+	0.380553i
$306$	−3.13862	−	5.50748i	−0.179423	−	0.314842i
$307$	3.65607			0.208663			0.104331	−	0.994543i	$-0.466730\pi$
$307$	3.65607			0.208663			0.104331	+	0.994543i	$0.466730\pi$
$308$	−18.3100	−	32.5533i	−1.04331	−	1.85490i
$309$	−1.16430	−	0.311973i	−0.0662348	−	0.0177476i
$310$	−4.82187	−	1.32110i	−0.273864	−	0.0750335i
$311$	−1.53636	−	5.73379i	−0.0871192	−	0.325133i	0.908588	−	0.417694i	$-0.137161\pi$
$311$	−1.53636	−	5.73379i	−0.0871192	−	0.325133i	−0.995707	+	0.0925606i	$0.970495\pi$
$312$	−12.5362	−	7.52235i	−0.709723	−	0.425869i
$313$	−4.47183	−	16.6891i	−0.252763	−	0.943324i	−0.969321	−	0.245797i	$-0.920950\pi$
$313$	−4.47183	−	16.6891i	−0.252763	−	0.943324i	0.716558	−	0.697527i	$-0.245716\pi$
$314$	−5.57323	+	1.45983i	−0.314516	+	0.0823828i
$315$	0.607824	−	2.26843i	0.0342470	−	0.127812i
$316$	23.6017	+	6.60923i	1.32770	+	0.371798i
$317$	23.1657	+	13.3747i	1.30112	+	0.751201i	0.980596	−	0.196041i	$-0.0628084\pi$
$317$	23.1657	+	13.3747i	1.30112	+	0.751201i	0.320522	+	0.947241i	$0.396142\pi$
$318$	−2.42916	−	2.45662i	−0.136221	−	0.137760i
$319$	−2.12814	−	2.12814i	−0.119153	−	0.119153i
$320$	−2.32986	+	7.65322i	−0.130243	+	0.427828i
$321$	−19.7557	−	11.4059i	−1.10265	−	0.636618i
$322$	−17.2423	−	30.2559i	−0.960874	−	1.68609i
$323$	54.8265			3.05063
$324$	−11.5617	+	6.50299i	−0.642315	+	0.361277i
$325$	2.38365	+	2.38365i	0.132221	+	0.132221i
$326$	−3.72199	+	6.36381i	−0.206142	+	0.352459i
$327$	4.19706	−	4.19706i	0.232098	−	0.232098i
$328$	5.01835	−	17.5405i	0.277092	−	0.968512i
$329$	11.4244	+	19.7877i	0.629850	+	1.09093i
$330$	5.64847	−	9.65770i	0.310938	−	0.531639i
$331$	−14.9322	+	4.00108i	−0.820749	+	0.219919i	−0.644674	−	0.764458i	$-0.723007\pi$
$331$	−14.9322	+	4.00108i	−0.820749	+	0.219919i	−0.176075	+	0.984377i	$0.556340\pi$
$332$	−3.99307	+	6.74011i	−0.219148	+	0.369912i
$333$	−3.04354	−	2.51262i	−0.166785	−	0.137691i
$334$	−12.1115	+	6.90214i	−0.662713	+	0.377668i
$335$	1.01119	+	3.77382i	0.0552473	+	0.206186i
$336$	−18.9713	−	11.5292i	−1.03497	−	0.628971i
$337$	−26.7870	+	15.4655i	−1.45918	+	0.842459i	−0.998971	−	0.0453514i	$-0.985559\pi$
$337$	−26.7870	+	15.4655i	−1.45918	+	0.842459i	−0.460210	+	0.887810i	$0.652226\pi$
$338$	0.586388	+	2.23867i	0.0318953	+	0.121768i
$339$	12.3710	+	12.3710i	0.671901	+	0.671901i
$340$	13.8158	+	0.155275i	0.749269	+	0.00842098i
$341$	−12.8976	+	12.8976i	−0.698443	+	0.698443i
$342$	−0.0409202	+	7.28210i	−0.00221271	+	0.393771i
$343$		−	3.25469i		−	0.175737i
$344$	0.0644957	+	0.00108735i	0.00347738	+	5.86261e-5i
$345$	5.21587	−	9.03416i	0.280813	−	0.486383i
$346$	2.32852	+	8.88967i	0.125182	+	0.477911i
$347$	−15.2917	+	15.2917i	−0.820903	+	0.820903i	−0.986238	−	0.165334i	$-0.947130\pi$
$347$	−15.2917	+	15.2917i	−0.820903	+	0.820903i	0.165334	+	0.986238i	$0.447130\pi$
$348$	−1.72262	−	0.482387i	−0.0923420	−	0.0258587i
$349$	−2.13325	+	3.69489i	−0.114190	+	0.197783i	−0.917456	−	0.397838i	$-0.869761\pi$
$349$	−2.13325	+	3.69489i	−0.114190	+	0.197783i	0.803266	+	0.595621i	$0.203094\pi$
$350$	3.59911	+	3.63978i	0.192380	+	0.194555i
$351$	−18.2179	−	4.88147i	−0.972398	−	0.260553i
$352$	20.0499	+	21.2095i	1.06867	+	1.13047i
$353$	22.6620	−	6.07225i	1.20617	−	0.323194i	0.400915	−	0.916115i	$-0.368692\pi$
$353$	22.6620	−	6.07225i	1.20617	−	0.323194i	0.805260	+	0.592922i	$0.202026\pi$
$354$	−0.0636503	+	11.3271i	−0.00338298	+	0.602030i
$355$	10.8691	−	2.91235i	0.576870	−	0.154572i
$356$	0.558241	+	2.18115i	0.0295867	+	0.115600i
$357$	−9.92343	+	37.0347i	−0.525203	+	1.96009i
$358$	−16.5779	−	0.0931562i	−0.876171	−	0.00492346i
$359$			18.5437i			0.978701i	0.872087	+	0.489351i	$0.162766\pi$
$359$			18.5437i			0.978701i	−0.872087	+	0.489351i	$0.837234\pi$
$360$	−0.0309354	+	1.83492i	−0.00163044	+	0.0967086i
$361$	−38.0914	−	21.9921i	−2.00481	−	1.15748i
$362$	−0.429906	+	1.56911i	−0.0225954	+	0.0824705i
$363$	−11.9755	−	20.7422i	−0.628553	−	1.08869i
$364$	−6.05057	−	23.6406i	−0.317136	−	1.23911i
$365$	−1.76394	+	6.58313i	−0.0923290	+	0.344577i
$366$	14.3649	+	8.40157i	0.750866	+	0.439157i
$367$	3.68205	−	2.12583i	0.192202	−	0.110968i	−0.400811	−	0.916161i	$-0.631272\pi$
$367$	3.68205	−	2.12583i	0.192202	−	0.110968i	0.593013	+	0.805193i	$0.297938\pi$
$368$	18.8051	+	19.6701i	0.980284	+	1.02537i
$369$		−	4.18518i		−	0.217872i
$370$	8.07651	−	2.96140i	0.419878	−	0.153956i
$371$		−	5.76657i		−	0.299385i
$372$	−2.92350	+	10.4399i	−0.151576	+	0.541284i
$373$	−5.40517	+	3.12068i	−0.279869	+	0.161583i	−0.633364	−	0.773854i	$-0.718327\pi$
$373$	−5.40517	+	3.12068i	−0.279869	+	0.161583i	0.353495	+	0.935436i	$0.384993\pi$
$374$	25.4486	−	43.5118i	1.31592	−	2.24994i
$375$	−0.396861	+	1.48110i	−0.0204938	+	0.0764839i
$376$	−12.4108	−	12.8365i	−0.640039	−	0.661990i
$377$	−0.983193	−	1.70294i	−0.0506370	−	0.0877059i
$378$	−27.6212	−	7.56767i	−1.42068	−	0.389239i
$379$	−10.6125	−	6.12714i	−0.545128	−	0.314730i	0.202027	−	0.979380i	$-0.435247\pi$
$379$	−10.6125	−	6.12714i	−0.545128	−	0.314730i	−0.747155	+	0.664650i	$0.768581\pi$
$380$	−13.6559	−	8.09023i	−0.700535	−	0.415020i
$381$		−	27.8831i		−	1.42849i
$382$	0.176498	−	31.4093i	0.00903040	−	1.60704i
$383$	−8.15531	+	30.4360i	−0.416717	+	1.55521i	0.364655	+	0.931143i	$0.381187\pi$
$383$	−8.15531	+	30.4360i	−0.416717	+	1.55521i	−0.781372	+	0.624065i	$0.785480\pi$
$384$	16.5673	+	5.14544i	0.845444	+	0.262577i
$385$	18.0384	−	4.83337i	0.919320	−	0.246331i
$386$	−28.2595	−	0.158798i	−1.43837	−	0.00808263i
$387$	0.0142930	−	0.00382981i	0.000726556	−	0.000194680i
$388$	22.2922	+	22.7989i	1.13171	+	1.15744i
$389$	−0.832913	−	0.223178i	−0.0422303	−	0.0113156i	0.237642	−	0.971353i	$-0.423625\pi$
$389$	−0.832913	−	0.223178i	−0.0422303	−	0.0113156i	−0.279872	+	0.960037i	$0.590292\pi$
$390$	5.19789	−	5.13980i	0.263205	−	0.260264i
$391$	23.4996	−	40.7025i	1.18843	−	2.05841i
$392$	−4.18449	−	16.7406i	−0.211349	−	0.845527i
$393$	11.6158	−	11.6158i	0.585938	−	0.585938i
$394$	−24.2922	+	6.36300i	−1.22383	+	0.320563i
$395$	−6.12742	+	10.6130i	−0.308304	+	0.533998i
$396$	5.76028	+	3.41258i	0.289465	+	0.171489i
$397$		−	27.3686i		−	1.37359i	−0.726851	−	0.686795i	$-0.759017\pi$
$397$		−	27.3686i		−	1.37359i	0.726851	−	0.686795i	$-0.240983\pi$
$398$	−12.1710	−	0.0683922i	−0.610076	−	0.00342819i
$399$	31.1452	−	31.1452i	1.55921	−	1.55921i
$400$	−3.41828	−	2.07735i	−0.170914	−	0.103868i
$401$	−21.0596	−	21.0596i	−1.05167	−	1.05167i	−0.998591	−	0.0530753i	$-0.983098\pi$
$401$	−21.0596	−	21.0596i	−1.05167	−	1.05167i	−0.0530753	−	0.998591i	$-0.516902\pi$
$402$	8.19567	−	2.14674i	0.408763	−	0.107069i
$403$	−10.3207	+	5.95863i	−0.514108	+	0.296821i
$404$	8.80939	+	0.0990081i	0.438284	+	0.00492584i
$405$	−1.71662	−	6.40652i	−0.0852996	−	0.318343i
$406$	−1.47839	−	2.59421i	−0.0733714	−	0.128748i
$407$	5.20232	−	30.9496i	0.257869	−	1.53412i
$408$	0.505055	−	29.9571i	0.0250040	−	1.48310i
$409$	35.7839	−	9.58826i	1.76940	−	0.474109i	0.780813	−	0.624765i	$-0.214805\pi$
$409$	35.7839	−	9.58826i	1.76940	−	0.474109i	0.988586	+	0.150656i	$0.0481385\pi$
$410$	7.87424	+	4.60538i	0.388881	+	0.227444i
$411$	1.38134	+	2.39256i	0.0681367	+	0.118016i
$412$	1.09915	+	1.12414i	0.0541514	+	0.0553825i
$413$	−13.3691	+	13.3691i	−0.657852	+	0.657852i
$414$	5.38860	+	3.15161i	0.264835	+	0.154893i
$415$	−2.76978	−	2.76978i	−0.135963	−	0.135963i
$416$	9.06692	+	16.7758i	0.444542	+	0.822500i
$417$	12.9658			0.634937
$418$	−50.3113	+	28.6715i	−2.46081	+	1.40237i
$419$	4.89727	+	2.82744i	0.239247	+	0.138129i	0.614831	−	0.788659i	$-0.289224\pi$
$419$	4.89727	+	2.82744i	0.239247	+	0.138129i	−0.375584	+	0.926789i	$0.622558\pi$
$420$	7.93655	−	7.76014i	0.387264	−	0.378656i
$421$	11.8641	+	11.8641i	0.578220	+	0.578220i	0.934413	−	0.356192i	$-0.115925\pi$
$421$	11.8641	+	11.8641i	0.578220	+	0.578220i	−0.356192	+	0.934413i	$0.615925\pi$
$422$	11.7082	−	11.5773i	0.569944	−	0.563575i
$423$	−3.54715	−	2.04795i	−0.172469	−	0.0995747i
$424$	1.09276	+	4.37173i	0.0530691	+	0.212310i
$425$	−1.78801	+	6.67296i	−0.0867315	+	0.323686i
$426$	−6.18286	−	23.6045i	−0.299561	−	1.14364i
$427$	7.18917	+	26.8304i	0.347908	+	1.29841i
$428$	14.5866	+	25.9335i	0.705071	+	1.25354i
$429$	−6.90241	−	25.7602i	−0.333252	−	1.24371i
$430$	−0.00852247	+	0.0311061i	−0.000410990	+	0.00150007i
$431$	5.53673	+	1.48356i	0.266695	+	0.0714607i	0.389688	−	0.920947i	$-0.372583\pi$
$431$	5.53673	+	1.48356i	0.266695	+	0.0714607i	−0.122993	+	0.992407i	$0.539249\pi$
$432$	22.3741	+	0.502986i	1.07648	+	0.0241999i
$433$	−28.7218			−1.38028			−0.690142	−	0.723674i	$-0.742452\pi$
$433$	−28.7218			−1.38028			−0.690142	+	0.723674i	$0.742452\pi$
$434$	−15.7222	+	8.95978i	−0.754688	+	0.430083i
$435$	0.447221	−	0.774610i	0.0214426	−	0.0371397i
$436$	−7.50017	+	1.91959i	−0.359193	+	0.0919316i
$437$	−46.7586	+	26.9961i	−2.23677	+	1.29140i
$438$	14.2537	+	3.90524i	0.681068	+	0.186600i
$439$	11.8780	+	3.18270i	0.566905	+	0.151902i	0.530877	−	0.847449i	$-0.321863\pi$
$439$	11.8780	+	3.18270i	0.566905	+	0.151902i	0.0360283	+	0.999351i	$0.488529\pi$
$440$	−12.7593	+	7.08251i	−0.608274	+	0.337645i
$441$	−1.97920	−	3.42807i	−0.0942475	−	0.163241i
$442$	23.4185	−	23.1568i	1.11391	−	1.10146i
$443$	−10.6433			−0.505678			−0.252839	−	0.967508i	$-0.581364\pi$
$443$	−10.6433			−0.505678			−0.252839	+	0.967508i	$0.581364\pi$
$444$	−6.32325	−	17.5496i	−0.300088	−	0.832868i
$445$	−1.12573			−0.0533645
$446$	−6.98645	+	6.90837i	−0.330818	+	0.327121i
$447$	12.1727	+	21.0837i	0.575749	+	0.997226i
$448$	13.6245	+	25.5504i	0.643696	+	1.20714i
$449$	2.81488	+	0.754245i	0.132842	+	0.0355950i	0.324628	−	0.945842i	$-0.394761\pi$
$449$	2.81488	+	0.754245i	0.132842	+	0.0355950i	−0.191785	+	0.981437i	$0.561428\pi$
$450$	−0.884974	−	0.242466i	−0.0417181	−	0.0114300i
$451$	28.8215	−	16.6401i	1.35715	−	0.783552i
$452$	−5.65807	−	22.1071i	−0.266133	−	1.03983i
$453$	−3.63152	+	6.28997i	−0.170624	+	0.295529i
$454$	32.9790	−	18.7942i	1.54778	−	0.882054i
$455$	12.2013			0.572007
$456$	−17.7097	+	29.5137i	−0.829332	+	1.38210i
$457$	−25.8069	−	6.91494i	−1.20720	−	0.323467i	−0.401535	−	0.915844i	$-0.631523\pi$
$457$	−25.8069	−	6.91494i	−1.20720	−	0.323467i	−0.805661	+	0.592377i	$0.798190\pi$
$458$	5.24336	−	19.1377i	0.245006	−	0.894244i
$459$	−10.0038	−	37.3349i	−0.466939	−	1.74264i
$460$	−11.8593	+	6.67038i	−0.552941	+	0.311008i
$461$	1.75478	+	6.54893i	0.0817283	+	0.305014i	0.994675	−	0.103066i	$-0.0328652\pi$
$461$	1.75478	+	6.54893i	0.0817283	+	0.305014i	−0.912946	+	0.408080i	$0.866199\pi$
$462$	−10.2611	−	39.1742i	−0.477391	−	1.82255i
$463$	−5.02411	+	18.7502i	−0.233490	+	0.871398i	0.745333	+	0.666692i	$0.232290\pi$
$463$	−5.02411	+	18.7502i	−0.233490	+	0.871398i	−0.978824	+	0.204706i	$0.934376\pi$
$464$	1.61239	+	1.68656i	0.0748535	+	0.0782965i
$465$	−4.69451	−	2.71038i	−0.217703	−	0.125691i
$466$	−9.38124	+	9.27640i	−0.434578	+	0.429721i
$467$	13.0157	+	13.0157i	0.602294	+	0.602294i	0.940921	−	0.338627i	$-0.109962\pi$
$467$	13.0157	+	13.0157i	0.602294	+	0.602294i	−0.338627	+	0.940921i	$0.609962\pi$
$468$	3.05823	+	3.12775i	0.141367	+	0.144580i
$469$	12.2466	+	7.07059i	0.565497	+	0.326490i
$470$	7.75643	−	4.42025i	0.357777	−	0.203891i
$471$	−6.24660			−0.287828
$472$	7.60192	−	12.6688i	0.349907	−	0.583129i
$473$	0.0832027	+	0.0832027i	0.00382566	+	0.00382566i
$474$	22.9391	+	13.4163i	1.05363	+	0.616233i
$475$	5.61178	−	5.61178i	0.257486	−	0.257486i
$476$	35.7573	−	34.9625i	1.63893	−	1.60250i
$477$	0.516858	+	0.895225i	0.0236653	+	0.0409895i
$478$	6.72844	+	3.93524i	0.307752	+	0.179994i
$479$	2.53845	−	0.680175i	0.115985	−	0.0310780i	−0.200360	−	0.979722i	$-0.564211\pi$
$479$	2.53845	−	0.680175i	0.115985	−	0.0310780i	0.316344	+	0.948644i	$0.397544\pi$
$480$	−4.54629	+	7.38706i	−0.207509	+	0.337171i
$481$	8.51683	−	18.6525i	0.388334	−	0.850483i
$482$	3.19982	+	5.61488i	0.145748	+	0.255751i
$483$	−9.77242	−	36.4712i	−0.444660	−	1.65950i
$484$	−0.351084	+	31.2382i	−0.0159583	+	1.41992i
$485$	−13.8071	+	7.97156i	−0.626950	+	0.361970i
$486$	9.04952	−	2.37039i	0.410494	−	0.107523i
$487$	7.00849	+	7.00849i	0.317585	+	0.317585i	0.847839	−	0.530254i	$-0.177903\pi$
$487$	7.00849	+	7.00849i	0.317585	+	0.317585i	−0.530254	+	0.847839i	$0.677903\pi$
$488$	−10.5346	−	18.9782i	−0.476877	−	0.859102i
$489$	−5.65219	+	5.65219i	−0.255601	+	0.255601i
$490$	8.62768	+	0.0484814i	0.389759	+	0.00219017i
$491$			31.8586i			1.43776i	0.695136	+	0.718879i	$0.255344\pi$
$491$			31.8586i			1.43776i	−0.695136	+	0.718879i	$0.744656\pi$
$492$	10.0825	−	17.0188i	0.454554	−	0.767267i
$493$	2.01491	−	3.48993i	0.0907470	−	0.157178i
$494$	−36.5998	+	9.58680i	−1.64670	+	0.431330i
$495$	−2.36713	+	2.36713i	−0.106395	+	0.106395i
$496$	10.2214	−	9.77190i	0.458952	−	0.438771i
$497$	20.3642	−	35.2718i	0.913458	−	1.58216i
$498$	−6.03990	+	5.97240i	−0.270654	+	0.267629i
$499$	−29.7957	−	7.98372i	−1.33384	−	0.357400i	−0.479692	−	0.877437i	$-0.659252\pi$
$499$	−29.7957	−	7.98372i	−1.33384	−	0.357400i	−0.854144	+	0.520036i	$0.825918\pi$
$500$	1.43002	−	1.39823i	0.0639523	−	0.0625308i
$501$	−14.5995	+	3.91193i	−0.652259	+	0.174772i
$502$	0.594153	+	0.00333871i	0.0265183	+	0.000149014i
$503$	−5.23682	+	1.40320i	−0.233498	+	0.0625657i	−0.373671	−	0.927561i	$-0.621901\pi$
$503$	−5.23682	+	1.40320i	−0.233498	+	0.0625657i	0.140172	+	0.990127i	$0.455234\pi$
$504$	4.61706	+	4.77541i	0.205660	+	0.212714i
$505$	−1.14009	+	4.25488i	−0.0507334	+	0.189340i
$506$	−0.278939	+	49.6396i	−0.0124004	+	2.20675i
$507$			2.50915i			0.111435i
$508$	−18.5372	+	31.2899i	−0.822455	+	1.38827i
$509$	15.5728	+	8.99096i	0.690252	+	0.398517i	0.803707	−	0.595026i	$-0.202858\pi$
$509$	15.5728	+	8.99096i	0.690252	+	0.398517i	−0.113454	+	0.993543i	$0.536192\pi$
$510$	14.4482	+	3.95854i	0.639778	+	0.175287i
$511$	12.3341	+	21.3633i	0.545628	+	0.945056i
$512$	−15.1707	−	16.7884i	−0.670457	−	0.741948i
$513$	−11.4923	+	42.8899i	−0.507398	+	1.89364i
$514$	18.3092	−	31.3049i	0.807583	−	1.38080i
$515$	−0.680786	+	0.393052i	−0.0299990	+	0.0173199i
$516$	0.0673482	+	0.0188596i	0.00296484	+	0.000830248i
$517$		−	32.5703i		−	1.43244i
$518$	13.0915	−	28.2502i	0.575207	−	1.24124i
$519$			9.96373i			0.437359i
$520$	−9.25002	+	2.31214i	−0.405640	+	0.101394i
$521$	16.8973	−	9.75565i	0.740284	−	0.427403i	−0.0818888	−	0.996641i	$-0.526095\pi$
$521$	16.8973	−	9.75565i	0.740284	−	0.427403i	0.822172	+	0.569238i	$0.192762\pi$
$522$	0.462031	+	0.270227i	0.0202225	+	0.0118275i
$523$	5.58578	−	20.8464i	0.244249	−	0.911550i	−0.729510	−	0.683970i	$-0.760252\pi$
$523$	5.58578	−	20.8464i	0.244249	−	0.911550i	0.973759	−	0.227580i	$-0.0730813\pi$
$524$	−20.7574	+	5.31264i	−0.906792	+	0.232084i
$525$	2.77498	+	4.80641i	0.121110	+	0.209769i
$526$	−10.3724	+	37.8582i	−0.452259	+	1.65070i
$527$	−21.1507	−	12.2113i	−0.921337	−	0.531934i
$528$	15.2026	+	27.7541i	0.661609	+	1.20784i
$529$			23.2840i			1.01235i
$530$	−2.25308	−	0.0126607i	−0.0978676	−	0.000549946i
$531$	0.877201	−	3.27376i	0.0380673	−	0.142069i
$532$	−55.6566	+	14.2447i	−2.41302	+	0.617587i
$533$	21.0031	−	5.62776i	0.909745	−	0.243765i
$534$	−0.0137171	+	2.44108i	−0.000593598	+	0.105636i
$535$	−14.3702	+	3.85049i	−0.621278	+	0.166471i
$536$	−10.6242	−	3.03961i	−0.458897	−	0.131291i
$537$	−17.3623	−	4.65222i	−0.749240	−	0.200758i
$538$	19.1594	+	19.3759i	0.826019	+	0.835355i
$539$	15.7384	−	27.2597i	0.677901	−	1.17416i
$540$	−3.01744	+	10.7754i	−0.129850	+	0.463698i
$541$	−21.8678	+	21.8678i	−0.940170	+	0.940170i	−0.998309	−	0.0581388i	$-0.981483\pi$
$541$	−21.8678	+	21.8678i	−0.940170	+	0.940170i	0.0581388	+	0.998309i	$0.481483\pi$
$542$	−1.01506	−	3.87521i	−0.0436004	−	0.166455i
$543$	−0.881997	+	1.52766i	−0.0378501	+	0.0655583i
$544$	−20.4828	+	33.2816i	−0.878194	+	1.42694i
$545$		−	3.87096i		−	0.165814i
$546$	0.148675	−	26.4580i	0.00636270	−	1.13230i
$547$	−20.2030	+	20.2030i	−0.863817	+	0.863817i	−0.991779	−	0.127962i	$-0.959156\pi$
$547$	−20.2030	+	20.2030i	−0.863817	+	0.863817i	0.127962	+	0.991779i	$0.459156\pi$
$548$	0.0404965	−	3.60323i	0.00172992	−	0.153923i
$549$	−3.52089	−	3.52089i	−0.150268	−	0.150268i
$550$	−1.84886	−	7.05846i	−0.0788357	−	0.300974i
$551$	−4.00919	+	2.31471i	−0.170797	+	0.0986099i
$552$	14.3199	+	25.7975i	0.609495	+	1.09801i
$553$	11.4803	+	42.8450i	0.488191	+	1.82195i
$554$	−5.55893	+	3.16794i	−0.236176	+	0.134593i
$555$	9.28472	−	0.887206i	0.394114	−	0.0376598i
$556$	−14.5500	−	8.61990i	−0.617057	−	0.365565i
$557$	11.0449	−	2.95948i	0.467989	−	0.125397i	−0.0171156	−	0.999854i	$-0.505448\pi$
$557$	11.0449	−	2.95948i	0.467989	−	0.125397i	0.485104	+	0.874456i	$0.338782\pi$
$558$	1.63771	−	2.80013i	0.0693296	−	0.118539i
$559$	0.0384393	+	0.0665789i	0.00162581	+	0.00281599i
$560$	−14.0654	+	3.43193i	−0.594370	+	0.145026i
$561$	38.6462	−	38.6462i	1.63164	−	1.63164i
$562$	10.2406	−	17.5092i	0.431972	−	0.738581i
$563$	21.5073	+	21.5073i	0.906426	+	0.906426i	0.995982	−	0.0895560i	$-0.0285448\pi$
$563$	21.5073	+	21.5073i	0.906426	+	0.906426i	−0.0895560	+	0.995982i	$0.528545\pi$
$564$	−9.49059	−	16.8733i	−0.399626	−	0.710495i
$565$	11.4098			0.480015
$566$	−6.78874	−	11.9125i	−0.285352	−	0.500721i
$567$	−20.7902	−	12.0032i	−0.873104	−	0.504087i
$568$	−8.75443	+	30.5991i	−0.367328	+	1.28391i
$569$	24.2128	+	24.2128i	1.01506	+	1.01506i	0.999885	+	0.0151702i	$0.00482901\pi$
$569$	24.2128	+	24.2128i	1.01506	+	1.01506i	0.0151702	+	0.999885i	$0.495171\pi$
$570$	−12.1005	−	12.2373i	−0.506834	−	0.512562i
$571$	−14.9758	−	8.64627i	−0.626717	−	0.361835i	0.152763	−	0.988263i	$-0.451183\pi$
$571$	−14.9758	−	8.64627i	−0.626717	−	0.361835i	−0.779479	+	0.626428i	$0.784516\pi$
$572$	−9.38007	+	33.4965i	−0.392201	+	1.40056i
$573$	8.81430	−	32.8954i	0.368222	−	1.37423i
$574$	31.9400	−	8.36623i	1.33315	−	0.349200i
$575$	−1.76081	−	6.57142i	−0.0734307	−	0.274047i
$576$	−4.40521	−	2.74539i	−0.183550	−	0.114391i
$577$	7.86462	+	29.3512i	0.327409	+	1.22191i	0.911868	+	0.410483i	$0.134640\pi$
$577$	7.86462	+	29.3512i	0.327409	+	1.22191i	−0.584460	+	0.811423i	$0.698694\pi$
$578$	41.9079	+	11.4820i	1.74314	+	0.477586i
$579$	−29.5966	−	7.93040i	−1.22999	−	0.329576i
$580$	−1.01684	+	0.571934i	−0.0422220	+	0.0237483i
$581$	−14.1778			−0.588195
$582$	17.1177	+	30.0373i	0.709551	+	1.24508i
$583$	−4.11001	+	7.11875i	−0.170219	+	0.294829i
$584$	−13.3990	−	13.8585i	−0.554455	−	0.573471i
$585$	−1.89418	+	1.09361i	−0.0783148	+	0.0452151i
$586$	7.31049	−	26.6825i	0.301994	−	1.10224i
$587$	35.0866	+	9.40143i	1.44818	+	0.388039i	0.895390	−	0.445282i	$-0.146897\pi$
$587$	35.0866	+	9.40143i	1.44818	+	0.388039i	0.552790	+	0.833321i	$0.313563\pi$
$588$	0.210259	−	18.7081i	0.00867095	−	0.771510i
$589$	14.0283	+	24.2977i	0.578024	+	1.00117i
$590$	5.19416	+	5.25287i	0.213840	+	0.216257i
$591$	−27.2273			−1.11998
$592$	−4.57148	+	23.8977i	−0.187887	+	0.982191i
$593$	−34.2845			−1.40790			−0.703948	−	0.710252i	$-0.748581\pi$
$593$	−34.2845			−1.40790			−0.703948	+	0.710252i	$0.748581\pi$
$594$	28.7043	+	29.0287i	1.17775	+	1.19106i
$595$	12.5024	+	21.6548i	0.512549	+	0.887760i
$596$	0.356864	−	31.7525i	0.0146177	−	1.30063i
$597$	−12.7468	−	3.41551i	−0.521693	−	0.139787i
$598$	−8.57021	+	31.2803i	−0.350462	+	1.27915i
$599$	−5.52188	+	3.18806i	−0.225618	+	0.130261i	−0.608549	−	0.793516i	$-0.708248\pi$
$599$	−5.52188	+	3.18806i	−0.225618	+	0.130261i	0.382931	+	0.923777i	$0.374915\pi$
$600$	−3.01457	−	3.11796i	−0.123069	−	0.127290i
$601$	20.7688	−	35.9725i	0.847175	−	1.46735i	−0.0365439	−	0.999332i	$-0.511635\pi$
$601$	20.7688	−	35.9725i	0.847175	−	1.46735i	0.883719	−	0.468018i	$-0.155032\pi$
$602$	0.0577999	+	0.101424i	0.00235575	+	0.00413374i
$603$	−2.53495			−0.103231
$604$	8.25693	−	4.64421i	0.335970	−	0.188970i
$605$	−15.0878	−	4.04277i	−0.613408	−	0.164362i
$606$	9.21261	+	2.52408i	0.374237	+	0.102534i
$607$	3.11794	+	11.6363i	0.126553	+	0.472303i	0.999890	−	0.0148133i	$-0.00471540\pi$
$607$	3.11794	+	11.6363i	0.126553	+	0.472303i	−0.873337	+	0.487116i	$0.838049\pi$
$608$	39.4948	−	21.3460i	1.60173	−	0.865696i
$609$	−0.837910	−	3.12712i	−0.0339538	−	0.126717i
$610$	10.4988	−	2.75001i	0.425084	−	0.111345i
$611$	5.50771	−	20.5550i	0.222818	−	0.831568i
$612$	−2.41741	+	8.63265i	−0.0977182	+	0.348954i
$613$	−17.3115	−	9.99481i	−0.699206	−	0.403687i	0.107846	−	0.994168i	$-0.465605\pi$
$613$	−17.3115	−	9.99481i	−0.699206	−	0.403687i	−0.807052	+	0.590481i	$0.798938\pi$
$614$	−3.63547	−	3.67656i	−0.146716	−	0.148374i
$615$	6.99372	+	6.99372i	0.282014	+	0.282014i
$616$	−14.5289	+	50.7825i	−0.585387	+	2.04609i
$617$	−1.90373	−	1.09912i	−0.0766413	−	0.0442489i	0.461190	−	0.887302i	$-0.347423\pi$
$617$	−1.90373	−	1.09912i	−0.0766413	−	0.0442489i	−0.537831	+	0.843053i	$0.680756\pi$
$618$	0.844018	+	1.48104i	0.0339514	+	0.0595762i
$619$	−4.44435			−0.178633			−0.0893167	−	0.996003i	$-0.528468\pi$
$619$	−4.44435			−0.178633			−0.0893167	+	0.996003i	$0.528468\pi$
$620$	3.46620	+	6.16255i	0.139206	+	0.247494i
$621$	26.9151	+	26.9151i	1.08007	+	1.08007i
$622$	−4.23821	+	7.24645i	−0.169937	+	0.290556i
$623$	−2.88115	+	2.88115i	−0.115431	+	0.115431i
$624$	4.90106	+	20.0864i	0.196199	+	0.804100i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−12.3360	+	21.0920i	−0.493045	+	0.843004i
$627$	−60.6465	+	16.2502i	−2.42199	+	0.648970i
$628$	7.00983	+	4.15286i	0.279723	+	0.165717i
$629$	41.8314	−	3.99722i	1.66793	−	0.159380i
$630$	−2.88554	+	1.64442i	−0.114963	+	0.0655152i
$631$	8.06064	+	30.0827i	0.320889	+	1.19757i	0.918380	+	0.395699i	$0.129498\pi$
$631$	8.06064	+	30.0827i	0.320889	+	1.19757i	−0.597491	+	0.801875i	$0.703836\pi$
$632$	−16.8225	−	30.3060i	−0.669162	−	1.20551i
$633$	15.4609	−	8.92634i	0.614515	−	0.354790i
$634$	−9.58551	−	36.5949i	−0.380689	−	1.45337i
$635$	−12.8583	−	12.8583i	−0.510266	−	0.510266i
$636$	−0.0549083	+	4.88554i	−0.00217725	+	0.193724i
$637$	14.5422	−	14.5422i	0.576182	−	0.576182i
$638$	−0.0239169	+	4.25621i	−0.000946879	+	0.168505i
$639$			7.30098i			0.288822i
$640$	10.0128	−	5.26718i	0.395792	−	0.208204i
$641$	−16.6813	+	28.8929i	−0.658873	+	1.14120i	0.322034	+	0.946728i	$0.395633\pi$
$641$	−16.6813	+	28.8929i	−0.658873	+	1.14120i	−0.980908	+	0.194474i	$0.937700\pi$
$642$	8.17449	+	31.2080i	0.322622	+	1.23168i
$643$	12.3772	−	12.3772i	0.488109	−	0.488109i	−0.419600	−	0.907709i	$-0.637830\pi$
$643$	12.3772	−	12.3772i	0.488109	−	0.488109i	0.907709	+	0.419600i	$0.137830\pi$
$644$	−13.2803	+	47.4243i	−0.523316	+	1.86878i
$645$	−0.0174848	+	0.0302845i	−0.000688461	+	0.00119245i
$646$	−54.5176	−	55.1337i	−2.14496	−	2.16921i
$647$	27.2418	+	7.29941i	1.07098	+	0.286970i	0.750898	−	0.660419i	$-0.229621\pi$
$647$	27.2418	+	7.29941i	1.07098	+	0.286970i	0.320087	+	0.947388i	$0.396288\pi$
$648$	18.0360	+	5.16010i	0.708519	+	0.202708i
$649$	26.0326	−	6.97542i	1.02187	−	0.273809i
$650$	0.0267884	−	4.76723i	0.00105073	−	0.186986i
$651$	−18.9519	+	5.07814i	−0.742783	+	0.199028i
$652$	10.1005	−	2.58511i	0.395566	−	0.101241i
$653$	2.06145	−	7.69342i	0.0806706	−	0.301067i	−0.913789	−	0.406190i	$-0.866857\pi$
$653$	2.06145	−	7.69342i	0.0806706	−	0.301067i	0.994459	+	0.105123i	$0.0335237\pi$
$654$	−8.39399	−	0.0471682i	−0.328231	−	0.00184442i
$655$		−	10.7132i		−	0.418601i
$656$	−22.6289	+	12.3952i	−0.883508	+	0.483951i
$657$	−3.82959	−	2.21101i	−0.149406	−	0.0862599i
$658$	8.53853	−	31.1647i	0.332867	−	1.21493i
$659$	−22.1326	−	38.3348i	−0.862165	−	1.49331i	−0.869835	−	0.493343i	$-0.835775\pi$
$659$	−22.1326	−	38.3348i	−0.862165	−	1.49331i	0.00767007	−	0.999971i	$-0.497559\pi$
$660$	−15.3285	+	3.92316i	−0.596660	+	0.152709i
$661$	−7.96914	+	29.7412i	−0.309964	+	1.15680i	0.618624	+	0.785687i	$0.287690\pi$
$661$	−7.96914	+	29.7412i	−0.309964	+	1.15680i	−0.928588	+	0.371113i	$0.878976\pi$
$662$	18.8716	+	11.0374i	0.733465	+	0.428979i
$663$	30.9247	−	17.8544i	1.20102	−	0.693407i
$664$	10.7484	−	2.68669i	0.417120	−	0.104264i
$665$		−	28.7253i		−	1.11392i
$666$	0.499693	+	5.55906i	0.0193627	+	0.215409i
$667$			3.96850i			0.153661i
$668$	18.9841	+	5.31614i	0.734517	+	0.205688i
$669$	−9.22575	+	5.32649i	−0.356688	+	0.205934i
$670$	2.78947	−	4.76941i	0.107767	−	0.184258i
$671$	10.2479	−	38.2457i	0.395616	−	1.47646i
$672$	7.27059	+	30.5419i	0.280469	+	1.17818i
$673$	−18.5596	−	32.1462i	−0.715420	−	1.23914i	−0.962797	−	0.270225i	$-0.912902\pi$
$673$	−18.5596	−	32.1462i	−0.715420	−	1.23914i	0.247377	−	0.968919i	$-0.420431\pi$
$674$	42.1882	+	11.5588i	1.62503	+	0.445227i
$675$	−4.84536	−	2.79747i	−0.186498	−	0.107675i
$676$	1.66813	−	2.81573i	0.0641590	−	0.108297i
$677$		−	15.0143i		−	0.577045i	−0.957473	−	0.288523i	$-0.906836\pi$
$677$		−	15.0143i		−	0.577045i	0.957473	−	0.288523i	$-0.0931641\pi$
$678$	0.139030	−	24.7416i	0.00533943	−	0.950197i
$679$	−14.9354	+	55.7398i	−0.573170	+	2.13910i
$680$	−13.5818	−	14.0477i	−0.520840	−	0.538703i
$681$	39.7537	−	10.6520i	1.52337	−	0.408185i
$682$	25.7947	+	0.144948i	0.987731	+	0.00555034i
$683$	13.8732	−	3.71731i	0.530843	−	0.142239i	0.0165656	−	0.999863i	$-0.494727\pi$
$683$	13.8732	−	3.71731i	0.530843	−	0.142239i	0.514278	+	0.857624i	$0.328060\pi$
$684$	7.36359	−	7.19992i	0.281554	−	0.275296i
$685$	1.74034	+	0.466322i	0.0664949	+	0.0178173i
$686$	−3.27293	+	3.23635i	−0.124961	+	0.123565i
$687$	10.7573	−	18.6322i	0.410417	−	0.710862i
$688$	−0.0630389	−	0.0659384i	−0.00240333	−	0.00251388i
$689$	−3.79762	+	3.79762i	−0.144678	+	0.144678i
$690$	−14.2713	+	3.73815i	−0.543298	+	0.142309i
$691$	19.6985	−	34.1188i	0.749367	−	1.29794i	−0.198760	−	0.980048i	$-0.563691\pi$
$691$	19.6985	−	34.1188i	0.749367	−	1.29794i	0.948126	−	0.317893i	$-0.102975\pi$
$692$	6.62408	−	11.1811i	0.251810	−	0.425043i
$693$			12.1168i			0.460277i
$694$	30.5830	+	0.171855i	1.16091	+	0.00652351i
$695$	5.97918	−	5.97918i	0.226803	−	0.226803i
$696$	1.22782	+	2.21194i	0.0465404	+	0.0838433i
$697$	31.5095	+	31.5095i	1.19351	+	1.19351i
$698$	5.83683	−	1.52887i	0.220927	−	0.0578687i
$699$	−12.3881	+	7.15229i	−0.468562	+	0.270525i
$700$	0.0813535	−	7.23855i	0.00307487	−	0.273591i
$701$	−9.63810	−	35.9699i	−0.364026	−	1.35856i	−0.868736	−	0.495275i	$-0.835067\pi$
$701$	−9.63810	−	35.9699i	−0.364026	−	1.35856i	0.504710	−	0.863289i	$-0.331599\pi$
$702$	13.2064	+	23.1739i	0.498443	+	0.874643i
$703$	−43.9132	−	20.0510i	−1.65622	−	0.756237i
$704$	1.39136	−	41.2523i	0.0524389	−	1.55475i
$705$	9.34979	−	2.50527i	0.352134	−	0.0943539i
$706$	−28.6405	−	16.7509i	−1.07790	−	0.630429i
$707$	7.97191	+	13.8077i	0.299814	+	0.519294i
$708$	11.4539	−	11.1993i	0.430463	−	0.420895i
$709$	35.0525	−	35.0525i	1.31642	−	1.31642i	0.399836	−	0.916587i	$-0.369067\pi$
$709$	35.0525	−	35.0525i	1.31642	−	1.31642i	0.916587	−	0.399836i	$-0.130933\pi$
$710$	−13.7365	−	8.03402i	−0.515521	−	0.301511i
$711$	−5.62245	−	5.62245i	−0.210858	−	0.210858i
$712$	1.63827	−	2.73022i	0.0613968	−	0.102319i
$713$	24.0510			0.900718
$714$	47.1098	−	26.8470i	1.76304	−	1.00472i
$715$	−15.0624	−	8.69627i	−0.563301	−	0.325222i
$716$	16.3908	+	16.7635i	0.612555	+	0.626480i
$717$	5.97604	+	5.97604i	0.223179	+	0.223179i
$718$	18.6476	−	18.4392i	0.695924	−	0.688147i
$719$	34.3866	+	19.8531i	1.28240	+	0.740395i	0.977287	−	0.211920i	$-0.0679717\pi$
$719$	34.3866	+	19.8531i	1.28240	+	0.740395i	0.305115	+	0.952315i	$0.401305\pi$
$720$	1.87596	−	1.79347i	0.0699129	−	0.0668386i
$721$	−0.736418	+	2.74835i	−0.0274257	+	0.102354i
$722$	15.7614	+	60.1730i	0.586580	+	2.23941i
$723$	1.81356	+	6.76831i	0.0674472	+	0.251716i
$724$	2.00538	−	1.12795i	0.0745295	−	0.0419200i
$725$	−0.150976	−	0.563449i	−0.00560709	−	0.0209260i
$726$	−8.95041	+	32.6680i	−0.332181	+	1.21242i
$727$	−41.5491	−	11.1330i	−1.54097	−	0.412902i	−0.614391	−	0.789002i	$-0.710598\pi$
$727$	−41.5491	−	11.1330i	−1.54097	−	0.412902i	−0.926579	+	0.376100i	$0.877265\pi$
$728$	−17.7566	+	29.5919i	−0.658104	+	1.09675i
$729$	30.0404			1.11261
$730$	8.37402	−	4.77220i	0.309936	−	0.176627i
$731$	−0.0787758	+	0.136444i	−0.00291363	+	0.00504655i
$732$	−5.83533	−	22.7996i	−0.215680	−	0.842699i
$733$	13.0930	−	7.55923i	0.483600	−	0.279207i	−0.238316	−	0.971188i	$-0.576595\pi$
$733$	13.0930	−	7.55923i	0.483600	−	0.279207i	0.721915	+	0.691981i	$0.243262\pi$
$734$	−5.79905	−	1.58883i	−0.214047	−	0.0586448i
$735$	9.03590	+	2.42116i	0.333294	+	0.0893059i
$736$	1.08113	−	38.4697i	0.0398511	−	1.41801i
$737$	−10.0789	−	17.4571i	−0.371260	−	0.643041i
$738$	−4.20863	+	4.16160i	−0.154922	+	0.153190i
$739$	11.6177			0.427362			0.213681	−	0.976903i	$-0.431455\pi$
$739$	11.6177			0.427362			0.213681	+	0.976903i	$0.431455\pi$
$740$	−11.0090	−	5.17705i	−0.404699	−	0.190312i
$741$	−41.0219			−1.50698
$742$	−5.79888	+	5.73407i	−0.212884	+	0.210504i
$743$	17.8482	+	30.9139i	0.654786	+	1.13412i	0.981947	+	0.189154i	$0.0605745\pi$
$743$	17.8482	+	30.9139i	0.654786	+	1.13412i	−0.327162	+	0.944968i	$0.606092\pi$
$744$	13.4054	−	7.44119i	0.491467	−	0.272807i
$745$	15.3362	+	4.10933i	0.561876	+	0.150554i
$746$	8.51288	+	2.33237i	0.311679	+	0.0853941i
$747$	2.20102	−	1.27076i	0.0805312	−	0.0464947i
$748$	−69.0608	+	17.6754i	−2.52511	+	0.646277i
$749$	−26.9239	+	46.6336i	−0.983778	+	1.70395i
$750$	1.88403	−	1.07367i	0.0687950	−	0.0392050i
$751$	14.1730			0.517180			0.258590	−	0.965987i	$-0.416742\pi$
$751$	14.1730			0.517180			0.258590	+	0.965987i	$0.416742\pi$
$752$	−0.567514	+	25.2445i	−0.0206951	+	0.920572i
$753$	0.622265	+	0.166735i	0.0226766	+	0.00607618i
$754$	−0.734830	+	2.68205i	−0.0267609	+	0.0976744i
$755$	1.22595	+	4.57531i	0.0446169	+	0.166512i
$756$	19.8554	+	35.3010i	0.722135	+	1.28388i
$757$	12.0776	+	45.0744i	0.438970	+	1.63826i	0.731385	+	0.681965i	$0.238874\pi$
$757$	12.0776	+	45.0744i	0.438970	+	1.63826i	−0.292415	+	0.956291i	$0.594459\pi$
$758$	4.39124	+	16.7646i	0.159497	+	0.608917i
$759$	−13.9302	+	51.9883i	−0.505635	+	1.88706i
$760$	5.44342	+	21.7771i	0.197454	+	0.789939i
$761$	−13.7767	−	7.95398i	−0.499405	−	0.288332i	0.229063	−	0.973412i	$-0.426434\pi$
$761$	−13.7767	−	7.95398i	−0.499405	−	0.288332i	−0.728468	+	0.685080i	$0.759767\pi$
$762$	−28.0393	+	27.7259i	−1.01576	+	1.00440i
$763$	−9.90723	−	9.90723i	−0.358666	−	0.358666i
$764$	−31.7608	+	31.0548i	−1.14906	+	1.12352i
$765$	−3.88185	−	2.24119i	−0.140348	−	0.0810302i
$766$	38.7159	−	22.0635i	1.39886	−	0.797187i
$767$	17.6087			0.635814
$768$	−11.2996	−	21.7765i	−0.407740	−	0.785793i
$769$	7.90897	+	7.90897i	0.285205	+	0.285205i	0.835181	−	0.549976i	$-0.185363\pi$
$769$	7.90897	+	7.90897i	0.285205	+	0.285205i	−0.549976	+	0.835181i	$0.685363\pi$
$770$	−22.7972	−	13.3333i	−0.821553	−	0.480499i
$771$	27.8042	−	27.8042i	1.00135	−	1.00135i
$772$	27.9406	+	28.5758i	1.00560	+	1.02847i
$773$	11.0805	+	19.1920i	0.398539	+	0.690289i	0.993546	−	0.113431i	$-0.0361841\pi$
$773$	11.0805	+	19.1920i	0.398539	+	0.690289i	−0.595007	+	0.803720i	$0.702851\pi$
$774$	−0.0180638	−	0.0105649i	−0.000649288	−	0.000379747i
$775$	−3.41477	+	0.914986i	−0.122662	+	0.0328673i
$776$	0.760143	−	45.0875i	0.0272875	−	1.61855i
$777$	21.4924	−	26.0338i	0.771035	−	0.933956i
$778$	0.603790	+	1.05950i	0.0216469	+	0.0379849i
$779$	−13.2493	−	49.4471i	−0.474706	−	1.77163i
$780$	−10.3372	−	0.116179i	−0.370131	−	0.00415987i
$781$	−50.2786	+	29.0284i	−1.79911	+	1.03872i
$782$	−64.2977	+	16.8419i	−2.29928	+	0.602264i
$783$	2.30776	+	2.30776i	0.0824728	+	0.0824728i
$784$	−12.6735	+	20.8542i	−0.452624	+	0.744792i
$785$	−2.88063	+	2.88063i	−0.102814	+	0.102814i
$786$	−23.2312	−	0.130543i	−0.828628	−	0.00465630i
$787$		−	32.8130i		−	1.16966i	−0.811157	−	0.584828i	$-0.801162\pi$
$787$		−	32.8130i		−	1.16966i	0.811157	−	0.584828i	$-0.198838\pi$
$788$	30.5540	+	18.1012i	1.08844	+	0.644829i
$789$	−21.2801	+	36.8583i	−0.757593	+	1.31219i
$790$	16.7654	−	4.39144i	0.596485	−	0.156241i
$791$	29.2020	−	29.2020i	1.03830	−	1.03830i
$792$	−2.29612	−	9.18591i	−0.0815889	−	0.326407i
$793$	12.9349	−	22.4039i	0.459331	−	0.795584i
$794$	−27.5220	+	27.2144i	−0.976718	+	0.965802i
$795$	−2.35969	−	0.632276i	−0.0836894	−	0.0224245i
$796$	12.0336	+	12.3072i	0.426520	+	0.436216i
$797$	44.3682	−	11.8884i	1.57160	−	0.421110i	0.635289	−	0.772274i	$-0.280881\pi$
$797$	44.3682	−	11.8884i	1.57160	−	0.421110i	0.936314	+	0.351165i	$0.114214\pi$
$798$	−62.2894	−	0.350022i	−2.20502	−	0.0123906i
$799$	42.1245	−	11.2872i	1.49026	−	0.399314i
$800$	1.31002	+	5.50308i	0.0463163	+	0.194563i
$801$	0.189043	−	0.705520i	0.00667952	−	0.0249283i
$802$	−0.236676	+	42.1185i	−0.00835732	+	1.48726i
$803$		−	35.1636i		−	1.24090i
$804$	−10.3082	−	6.10695i	−0.363544	−	0.215376i
$805$	−21.3253	−	12.3122i	−0.751617	−	0.433946i
$806$	16.2545	+	4.45343i	0.572541	+	0.156865i
$807$	14.7723	+	25.5863i	0.520009	+	0.900681i
$808$	−8.66019	−	8.95721i	−0.304664	−	0.315113i
$809$	0.285439	−	1.06527i	0.0100355	−	0.0374531i	−0.960727	−	0.277497i	$-0.910495\pi$
$809$	0.285439	−	1.06527i	0.0100355	−	0.0374531i	0.970762	+	0.240044i	$0.0771618\pi$
$810$	−4.73547	+	8.09666i	−0.166387	+	0.284488i
$811$	1.39833	−	0.807328i	0.0491021	−	0.0283491i	−0.475248	−	0.879852i	$-0.657642\pi$
$811$	1.39833	−	0.807328i	0.0491021	−	0.0283491i	0.524350	+	0.851503i	$0.324308\pi$
$812$	−1.13868	+	4.06627i	−0.0399599	+	0.142698i
$813$		−	4.34342i		−	0.152330i
$814$	−36.2960	+	25.5437i	−1.27218	+	0.895308i
$815$			5.21303i			0.182604i
$816$	−30.6272	+	29.2804i	−1.07217	+	1.02502i
$817$	0.156745	−	0.0904968i	0.00548382	−	0.00316608i
$818$	−45.2242	−	26.4502i	−1.58123	−	0.924808i
$819$	−2.04897	+	7.64687i	−0.0715969	+	0.267203i
$820$	−3.19868	−	12.4978i	−0.111703	−	0.436442i
$821$	21.2571	+	36.8184i	0.741878	+	1.28497i	0.951639	+	0.307218i	$0.0993982\pi$
$821$	21.2571	+	36.8184i	0.741878	+	1.28497i	−0.209761	+	0.977753i	$0.567269\pi$
$822$	1.03240	−	3.76816i	0.0360092	−	0.131430i
$823$	−35.5920	−	20.5490i	−1.24066	−	0.716294i	−0.271430	−	0.962458i	$-0.587496\pi$
$823$	−35.5920	−	20.5490i	−1.24066	−	0.716294i	−0.969228	+	0.246164i	$0.920830\pi$
$824$	0.0374802	−	2.22312i	0.00130568	−	0.0774461i
$825$		−	7.91127i		−	0.275435i
$826$	26.7379	+	0.150248i	0.930329	+	0.00522778i
$827$	−6.08771	+	22.7196i	−0.211690	+	0.790039i	0.775615	+	0.631206i	$0.217440\pi$
$827$	−6.08771	+	22.7196i	−0.211690	+	0.790039i	−0.987305	+	0.158833i	$0.949227\pi$
$828$	−2.18896	−	8.55265i	−0.0760716	−	0.297225i
$829$	−1.51469	+	0.405859i	−0.0526073	+	0.0140961i	−0.285027	−	0.958520i	$-0.592002\pi$
$829$	−1.51469	+	0.405859i	−0.0526073	+	0.0140961i	0.232419	+	0.972616i	$0.425336\pi$
$830$	−0.0311279	+	5.53948i	−0.00108047	+	0.192278i
$831$	−6.70087	+	1.79549i	−0.232451	+	0.0622850i
$832$	7.85394	−	25.7990i	0.272287	−	0.894418i
$833$	40.7103	+	10.9083i	1.41053	+	0.377950i
$834$	−12.8927	−	13.0384i	−0.446438	−	0.451484i
$835$	−4.92860	+	8.53658i	−0.170561	+	0.295421i
$836$	78.8600	+	22.0833i	2.72743	+	0.763766i
$837$	13.9862	−	13.9862i	0.483433	−	0.483433i
$838$	−2.02639	−	7.73621i	−0.0700004	−	0.267243i
$839$	−22.3579	+	38.7249i	−0.771879	+	1.33693i	0.164653	+	0.986352i	$0.447350\pi$
$839$	−22.3579	+	38.7249i	−0.771879	+	1.33693i	−0.936532	+	0.350582i	$0.885984\pi$
$840$	−15.6954	−	0.264614i	−0.541544	−	0.00913005i
$841$		−	28.6597i		−	0.988267i
$842$	0.133333	−	23.7278i	0.00459497	−	0.817714i
$843$	15.5513	−	15.5513i	0.535614	−	0.535614i
$844$	−23.2844	−	0.261691i	−0.801481	−	0.00900778i
$845$	1.15710	+	1.15710i	0.0398054	+	0.0398054i
$846$	1.46774	+	5.60344i	0.0504619	+	0.192650i
$847$	−48.9624	+	28.2684i	−1.68237	+	0.971315i
$848$	3.30962	−	5.44598i	0.113653	−	0.187016i
$849$	−3.84766	−	14.3597i	−0.132051	−	0.492822i
$850$	8.48829	−	4.83733i	0.291146	−	0.165919i
$851$	−33.7075	+	24.0064i	−1.15548	+	0.822929i
$852$	−17.5888	+	29.6890i	−0.602581	+	1.01713i
$853$	4.22901	−	1.13316i	0.144798	−	0.0387986i	−0.185692	−	0.982608i	$-0.559453\pi$
$853$	4.22901	−	1.13316i	0.144798	−	0.0387986i	0.330490	+	0.943809i	$0.392786\pi$
$854$	19.8320	−	33.9086i	0.678638	−	1.16033i
$855$	2.57465	+	4.45943i	0.0880512	+	0.152509i
$856$	11.5744	−	40.4557i	0.395606	−	1.38275i
$857$	−12.8327	+	12.8327i	−0.438358	+	0.438358i	−0.891459	−	0.453101i	$-0.850318\pi$
$857$	−12.8327	+	12.8327i	−0.438358	+	0.438358i	0.453101	+	0.891459i	$0.350318\pi$
$858$	−19.0410	+	32.5561i	−0.650048	+	1.11145i
$859$	34.5265	+	34.5265i	1.17803	+	1.17803i	0.980245	+	0.197785i	$0.0633749\pi$
$859$	34.5265	+	34.5265i	1.17803	+	1.17803i	0.197785	+	0.980245i	$0.436625\pi$
$860$	0.0397548	−	0.0223606i	0.00135563	−	0.000762489i
$861$	35.7991			1.22003
$862$	−4.01366	−	7.04296i	−0.136706	−	0.239884i
$863$	21.2230	+	12.2531i	0.722440	+	0.417101i	0.815650	−	0.578545i	$-0.196379\pi$
$863$	21.2230	+	12.2531i	0.722440	+	0.417101i	−0.0932099	+	0.995646i	$0.529713\pi$
$864$	−21.7422	−	22.9996i	−0.739686	−	0.782464i
$865$	4.59479	+	4.59479i	0.156227	+	0.156227i
$866$	28.5600	+	28.8828i	0.970508	+	0.981476i
$867$	40.8010	+	23.5564i	1.38567	+	0.800019i
$868$	24.6436	+	6.90097i	0.836457	+	0.234234i
$869$	16.3647	−	61.0739i	0.555135	−	2.07179i
$870$	−1.22365	+	0.320518i	−0.0414857	+	0.0108666i
$871$	−3.40872	−	12.7215i	−0.115500	−	0.431052i
$872$	9.38825	+	5.63342i	0.317926	+	0.190772i
$873$	−2.67733	−	9.99194i	−0.0906140	−	0.338176i
$874$	73.6425	+	20.1766i	2.49099	+	0.682485i
$875$	3.49617	+	0.936796i	0.118192	+	0.0316695i
$876$	−10.2463	−	18.2168i	−0.346189	−	0.615489i
$877$	−2.26524			−0.0764919			−0.0382459	−	0.999268i	$-0.512177\pi$
$877$	−2.26524			−0.0764919			−0.0382459	+	0.999268i	$0.512177\pi$
$878$	−8.61052	−	15.1093i	−0.290591	−	0.509914i
$879$	14.9982	−	25.9777i	0.505878	−	0.876207i
$880$	19.8096	+	5.78815i	0.667780	+	0.195119i
$881$	36.6007	−	21.1314i	1.23311	−	0.711936i	0.265432	−	0.964129i	$-0.414485\pi$
$881$	36.6007	−	21.1314i	1.23311	−	0.711936i	0.967677	+	0.252194i	$0.0811520\pi$
$882$	−1.47923	+	5.39904i	−0.0498084	+	0.181795i
$883$	−7.81752	−	2.09470i	−0.263081	−	0.0704922i	0.124868	−	0.992173i	$-0.460149\pi$
$883$	−7.81752	−	2.09470i	−0.263081	−	0.0704922i	−0.387948	+	0.921681i	$0.626816\pi$
$884$	−46.5732	−	0.523432i	−1.56643	−	0.0176049i
$885$	4.00481	+	6.93653i	0.134620	+	0.233169i
$886$	10.5833	+	10.7029i	0.355553	+	0.359572i
$887$	−33.8163			−1.13544			−0.567719	−	0.823222i	$-0.692174\pi$
$887$	−33.8163			−1.13544			−0.567719	+	0.823222i	$0.692174\pi$
$888$	−11.3603	+	23.8094i	−0.381228	+	0.798992i
$889$	−65.8184			−2.20748
$890$	1.11938	+	1.13203i	0.0375218	+	0.0379458i
$891$	17.1101	+	29.6356i	0.573211	+	0.992830i
$892$	13.8942	+	0.156155i	0.465211	+	0.00522847i
$893$	−48.3923	−	12.9667i	−1.61939	−	0.433913i
$894$	9.09777	−	33.2058i	0.304275	−	1.11057i
$895$	−10.1520	+	5.86128i	−0.339345	+	0.195921i
$896$	12.1459	−	39.1073i	0.405766	−	1.30648i
$897$	−17.5827	+	30.4541i	−0.587069	+	1.01683i
$898$	−2.04055	−	3.58065i	−0.0680940	−	0.119488i
$899$	2.06219			0.0687779
$900$	0.636162	+	1.13103i	0.0212054	+	0.0377011i
$901$	−10.6313	−	2.84865i	−0.354181	−	0.0949025i
$902$	−45.3924	−	12.4367i	−1.51140	−	0.414096i
$903$	0.0327593	+	0.122259i	0.00109016	+	0.00406854i
$904$	−16.6047	+	27.6723i	−0.552266	+	0.920366i
$905$	0.297750	+	1.11122i	0.00989754	+	0.0369381i
$906$	9.93627	−	2.60266i	0.330111	−	0.0864677i
$907$	6.53912	−	24.4043i	0.217128	−	0.810332i	−0.768279	−	0.640115i	$-0.778887\pi$
$907$	6.53912	−	24.4043i	0.217128	−	0.810332i	0.985407	−	0.170217i	$-0.0544468\pi$
$908$	−51.6927	−	14.4756i	−1.71548	−	0.480389i
$909$	−2.47518	−	1.42905i	−0.0820966	−	0.0473985i
$910$	−12.1326	−	12.2697i	−0.402191	−	0.406736i
$911$	−24.6274	−	24.6274i	−0.815942	−	0.815942i	0.169575	−	0.985517i	$-0.445761\pi$
$911$	−24.6274	−	24.6274i	−0.815942	−	0.815942i	−0.985517	+	0.169575i	$0.945761\pi$
$912$	47.2889	−	11.5384i	1.56589	−	0.382076i
$913$	17.5023	+	10.1050i	0.579243	+	0.334426i
$914$	18.7078	+	32.8275i	0.618799	+	1.08584i
$915$	11.7673			0.389014
$916$	−24.4587	+	13.7571i	−0.808139	+	0.454547i
$917$	−27.4192	−	27.4192i	−0.905462	−	0.905462i
$918$	−27.5966	+	47.1844i	−0.910823	+	1.55732i
$919$	−6.33824	+	6.33824i	−0.209079	+	0.209079i	−0.803876	−	0.594797i	$-0.797233\pi$
$919$	−6.33824	+	6.33824i	−0.209079	+	0.209079i	0.594797	+	0.803876i	$0.297233\pi$
$920$	18.5002	+	5.29292i	0.609933	+	0.174502i
$921$	−2.80302	−	4.85497i	−0.0923627	−	0.159977i
$922$	4.84074	−	8.27664i	0.159421	−	0.272577i
$923$	−36.6395	+	9.81754i	−1.20601	+	0.323148i
$924$	−29.1904	+	49.2721i	−0.960295	+	1.62093i
$925$	3.87252	−	4.69080i	0.127328	−	0.154232i
$926$	23.8511	−	13.5923i	0.783796	−	0.446671i
$927$	−0.132011	−	0.492670i	−0.00433580	−	0.0161814i
$928$	0.0926990	−	3.29848i	0.00304299	−	0.108278i
$929$	−11.3695	+	6.56420i	−0.373022	+	0.215364i	−0.674778	−	0.738021i	$-0.735761\pi$
$929$	−11.3695	+	6.56420i	−0.373022	+	0.215364i	0.301756	+	0.953385i	$0.402427\pi$
$930$	1.94249	+	7.41592i	0.0636969	+	0.243178i
$931$	−34.2363	−	34.2363i	−1.12205	−	1.12205i
$932$	18.6568	+	0.209682i	0.611122	+	0.00686836i
$933$	−6.43612	+	6.43612i	−0.210709	+	0.210709i
$934$	0.146275	−	26.0310i	0.00478628	−	0.851759i
$935$		−	35.6434i		−	1.16567i
$936$	0.104283	−	6.18549i	0.00340860	−	0.202179i
$937$	20.2912	−	35.1454i	0.662884	−	1.14815i	−0.316970	−	0.948436i	$-0.602665\pi$
$937$	20.2912	−	35.1454i	0.662884	−	1.14815i	0.979854	−	0.199714i	$-0.0640013\pi$
$938$	−5.06741	−	19.3460i	−0.165457	−	0.631669i
$939$	−18.7334	+	18.7334i	−0.611341	+	0.611341i
$940$	−12.1577	−	3.40455i	−0.396542	−	0.111044i
$941$	−8.66526	+	15.0087i	−0.282480	+	0.489269i	−0.971995	−	0.235002i	$-0.924490\pi$
$941$	−8.66526	+	15.0087i	−0.282480	+	0.489269i	0.689515	+	0.724271i	$0.257824\pi$
$942$	6.21140	+	6.28160i	0.202378	+	0.204666i
$943$	−42.3877	−	11.3578i	−1.38033	−	0.369860i
$944$	−20.2989	+	4.95290i	−0.660672	+	0.161203i
$945$	−19.5609	+	5.24132i	−0.636315	+	0.170500i
$946$	0.000935065	−	0.166403i	3.04016e−5	−	0.00541022i
$947$	−10.8704	+	2.91273i	−0.353242	+	0.0946509i	−0.431077	−	0.902315i	$-0.641866\pi$
$947$	−10.8704	+	2.91273i	−0.353242	+	0.0946509i	0.0778344	+	0.996966i	$0.475199\pi$
$948$	−9.31835	−	36.4084i	−0.302646	−	1.18249i
$949$	5.94625	−	22.1917i	0.193023	−	0.720373i
$950$	−11.2234	−	0.0630674i	−0.364135	−	0.00204618i
$951$		−	41.0164i		−	1.33005i
$952$	−70.7142	−	1.19219i	−2.29186	−	0.0386391i
$953$	−34.6045	−	19.9789i	−1.12095	−	0.647180i	−0.179306	−	0.983793i	$-0.557385\pi$
$953$	−34.6045	−	19.9789i	−1.12095	−	0.647180i	−0.941643	+	0.336613i	$0.890718\pi$
$954$	0.386295	−	1.40994i	0.0125068	−	0.0456483i
$955$	−11.1050	−	19.2345i	−0.359350	−	0.622413i
$956$	−2.73323	−	10.6792i	−0.0883990	−	0.345390i
$957$	−1.19441	+	4.45760i	−0.0386098	+	0.144094i
$958$	−3.20813	−	1.87633i	−0.103650	−	0.0606215i
$959$	5.64767	−	3.26068i	0.182373	−	0.105293i
$960$	11.9491	−	2.77367i	0.385656	−	0.0895198i
$961$			18.5021i			0.596843i
$962$	−27.2259	+	9.98288i	−0.877798	+	0.321861i
$963$		−	9.65278i		−	0.311056i
$964$	2.46455	−	8.80099i	0.0793779	−	0.283461i
$965$	−17.3056	+	9.99141i	−0.557088	+	0.321635i
$966$	−26.9582	+	46.0928i	−0.867365	+	1.48301i
$967$	−2.57078	+	9.59429i	−0.0826708	+	0.308532i	−0.994863	−	0.101231i	$-0.967722\pi$
$967$	−2.57078	+	9.59429i	−0.0826708	+	0.308532i	0.912192	+	0.409763i	$0.134389\pi$
$968$	31.7623	−	30.7091i	1.02088	−	0.987028i
$969$	−42.0342	−	72.8053i	−1.35033	−	2.33884i
$970$	21.7456	+	5.95787i	0.698208	+	0.191296i
$971$	−40.3471	−	23.2944i	−1.29480	−	0.747553i	−0.315298	−	0.948993i	$-0.602105\pi$
$971$	−40.3471	−	23.2944i	−1.29480	−	0.747553i	−0.979501	+	0.201440i	$0.935438\pi$
$972$	−11.3822	−	6.74319i	−0.365084	−	0.216288i
$973$		−	30.6059i		−	0.981181i
$974$	0.0787642	−	14.0168i	0.00252377	−	0.449126i
$975$	1.33782	−	4.99280i	0.0428444	−	0.159897i
$976$	−8.60933	+	29.4648i	−0.275578	+	0.943147i
$977$	−13.1952	+	3.53565i	−0.422153	+	0.113116i	−0.463640	−	0.886024i	$-0.653457\pi$
$977$	−13.1952	+	3.53565i	−0.422153	+	0.113116i	0.0414875	+	0.999139i	$0.486790\pi$
$978$	11.3042	+	0.0635215i	0.361469	+	0.00203119i
$979$	5.61023	−	1.50326i	0.179304	−	0.0480443i
$980$	−8.53031	−	8.72424i	−0.272491	−	0.278685i
$981$	2.42603	+	0.650052i	0.0774570	+	0.0207546i
$982$	32.0371	−	31.6791i	1.02234	−	1.01092i
$983$	−13.2360	+	22.9255i	−0.422164	+	0.731209i	−0.996151	−	0.0876554i	$-0.972063\pi$
$983$	−13.2360	+	22.9255i	−0.422164	+	0.731209i	0.573987	+	0.818864i	$0.305396\pi$
$984$	−27.1399	+	6.78390i	−0.865187	+	0.216263i
$985$	−12.5559	+	12.5559i	−0.400064	+	0.400064i
$986$	−5.51304	+	1.44406i	−0.175571	+	0.0459882i
$987$	17.5177	−	30.3415i	0.557594	−	0.965782i
$988$	46.0341	+	27.2721i	1.46454	+	0.867643i
$989$		−	0.155154i		−	0.00493361i
$990$	4.73419	+	0.0266028i	0.150462	+	0.000845491i
$991$	8.10171	−	8.10171i	0.257359	−	0.257359i	−0.566620	−	0.823979i	$-0.691749\pi$
$991$	8.10171	−	8.10171i	0.257359	−	0.257359i	0.823979	+	0.566620i	$0.191749\pi$
$992$	−19.9904	−	0.561801i	−0.634696	−	0.0178372i
$993$	16.7613	+	16.7613i	0.531904	+	0.531904i
$994$	−55.7188	+	14.5947i	−1.76729	+	0.462917i
$995$	−7.45328	+	4.30316i	−0.236285	+	0.136419i
$996$	12.0117	+	0.134999i	0.380606	+	0.00427760i
$997$	11.1713	+	41.6919i	0.353799	+	1.32040i	0.881989	+	0.471270i	$0.156204\pi$
$997$	11.1713	+	41.6919i	0.353799	+	1.32040i	−0.528190	+	0.849126i	$0.677129\pi$
$998$	21.5993	+	37.9013i	0.683714	+	1.19975i
$999$	−5.64141	+	33.5619i	−0.178486	+	1.06185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.be.a.51.19	✓	304
4.3	odd	2	inner	740.2.be.a.51.32	yes	304
37.8	odd	12	inner	740.2.be.a.711.32	yes	304
148.119	even	12	inner	740.2.be.a.711.19	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.be.a.51.19	✓	304	1.1	even	1	trivial
740.2.be.a.51.32	yes	304	4.3	odd	2	inner
740.2.be.a.711.19	yes	304	148.119	even	12	inner
740.2.be.a.711.32	yes	304	37.8	odd	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.994365 - 1.00560i) q^{2} +(-0.766676 - 1.32792i) q^{3} +(-0.0224764 + 1.99987i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-0.573007 + 2.09141i) q^{6} +(-3.13458 + 1.80975i) q^{7} +(2.03343 - 1.96600i) q^{8} +(0.324416 - 0.561906i) q^{9} +(0.700214 + 1.22870i) q^{10} +5.15947 q^{11} +(2.67291 - 1.50341i) q^{12} +(3.25613 + 0.872478i) q^{13} +(4.93681 + 1.35259i) q^{14} +(0.396861 + 1.48110i) q^{15} +(-3.99899 - 0.0899001i) q^{16} +(1.78801 + 6.67296i) q^{17} +(-0.887643 + 0.232505i) q^{18} +(2.05405 - 7.66583i) q^{19} +(0.539316 - 1.92591i) q^{20} +(4.80641 + 2.77498i) q^{21} +(-5.13039 - 5.18838i) q^{22} +(-4.81061 - 4.81061i) q^{23} +(-4.16968 - 1.19295i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.36042 - 4.14194i) q^{26} -5.59494 q^{27} +(-3.54882 - 6.30944i) q^{28} +(-0.412473 - 0.412473i) q^{29} +(1.09478 - 1.87184i) q^{30} +(-2.49979 + 2.49979i) q^{31} +(3.88605 + 4.11079i) q^{32} +(-3.95564 - 6.85136i) q^{33} +(4.93241 - 8.43339i) q^{34} +(3.49617 - 0.936796i) q^{35} +(1.11645 + 0.661422i) q^{36} +(1.00831 - 5.99861i) q^{37} +(-9.75127 + 5.55707i) q^{38} +(-1.33782 - 4.99280i) q^{39} +(-2.47298 + 1.37272i) q^{40} +(5.58614 - 3.22516i) q^{41} +(-1.98880 - 7.59269i) q^{42} +(0.0161262 + 0.0161262i) q^{43} +(-0.115966 + 10.3183i) q^{44} +(-0.458794 + 0.458794i) q^{45} +(-0.0540635 + 9.62107i) q^{46} -6.31272i q^{47} +(2.94655 + 5.37927i) q^{48} +(3.05039 - 5.28344i) q^{49} +(-0.358344 - 1.36806i) q^{50} +(7.49034 - 7.49034i) q^{51} +(-1.81803 + 6.49224i) q^{52} +(-0.796597 + 1.37975i) q^{53} +(5.56342 + 5.62629i) q^{54} +(-4.98366 - 1.33537i) q^{55} +(-2.81597 + 9.84259i) q^{56} +(-11.7544 + 3.14959i) q^{57} +(-0.00463554 + 0.824933i) q^{58} +(5.04561 - 1.35197i) q^{59} +(-2.97094 + 0.760381i) q^{60} +(1.98623 - 7.41272i) q^{61} +(4.99950 + 0.0280936i) q^{62} +2.34845i q^{63} +(0.269672 - 7.99545i) q^{64} +(-2.91937 - 1.68550i) q^{65} +(-2.95641 + 10.7906i) q^{66} +(-1.95347 - 3.38351i) q^{67} +(-13.3853 + 3.42582i) q^{68} +(-2.69993 + 10.0763i) q^{69} +(-4.41851 - 2.58424i) q^{70} +(-9.74493 + 5.62624i) q^{71} +(-0.445030 - 1.78040i) q^{72} -6.81535i q^{73} +(-7.03485 + 4.95085i) q^{74} -1.53335i q^{75} +(15.2845 + 4.28015i) q^{76} +(-16.1728 + 9.33735i) q^{77} +(-3.69050 + 6.30997i) q^{78} +(3.17179 - 11.8373i) q^{79} +(3.83946 + 1.12185i) q^{80} +(3.31626 + 5.74393i) q^{81} +(-8.79789 - 2.41046i) q^{82} +(3.39228 + 1.95853i) q^{83} +(-5.65765 + 9.54985i) q^{84} -6.90836i q^{85} +(0.000181233 - 0.0322519i) q^{86} +(-0.231499 + 0.863965i) q^{87} +(10.4914 - 10.1435i) q^{88} +(1.08737 - 0.291359i) q^{89} +(0.917574 + 0.00515611i) q^{90} +(-11.7856 + 3.15794i) q^{91} +(9.72874 - 9.51249i) q^{92} +(5.23605 + 1.40300i) q^{93} +(-6.34809 + 6.27715i) q^{94} +(-3.96813 + 6.87300i) q^{95} +(2.47947 - 8.31202i) q^{96} +(11.2735 - 11.2735i) q^{97} +(-8.34625 + 2.18618i) q^{98} +(1.67382 - 2.89913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) \) 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more