LMFDB - Embedded newform 230.2.j.a.219.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(9,230)] 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("230.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.j (of order $22$, degree $10$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			219.11
Character	$\chi$	$=$	230.219
Dual form			230.2.j.a.209.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.540641 + 0.841254i) q^{2} +(2.16151 + 0.310778i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-1.74640 + 1.39646i) q^{5} +(0.907157 + 1.98640i) q^{6} +(-0.282303 + 0.244617i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(1.69707 + 0.498303i) q^{9} +(-2.11895 - 0.714183i) q^{10} +(4.60733 + 2.96095i) q^{11} +(-1.18062 + 1.83708i) q^{12} +(-3.65165 - 3.16417i) q^{13} +(-0.358409 - 0.105238i) q^{14} +(-4.20885 + 2.47571i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(5.87094 - 2.68117i) q^{17} +(0.498303 + 1.69707i) q^{18} +(0.895578 - 1.96104i) q^{19} +(-0.544781 - 2.16869i) q^{20} +(-0.686222 + 0.441008i) q^{21} +5.47675i q^{22} +(-0.710740 - 4.74287i) q^{23} -2.18374 q^{24} +(1.09982 - 4.87754i) q^{25} +(0.687640 - 4.78264i) q^{26} +(-2.44583 - 1.11697i) q^{27} +(-0.105238 - 0.358409i) q^{28} +(-2.68040 - 5.86927i) q^{29} +(-4.35818 - 2.20224i) q^{30} +(1.32802 + 9.23656i) q^{31} +(0.281733 - 0.959493i) q^{32} +(9.03860 + 7.83199i) q^{33} +(5.42961 + 3.48940i) q^{34} +(0.151417 - 0.821422i) q^{35} +(-1.15826 + 1.33670i) q^{36} +(-1.00097 + 3.40899i) q^{37} +(2.13392 - 0.306811i) q^{38} +(-6.90972 - 7.97424i) q^{39} +(1.52989 - 1.63078i) q^{40} +(-7.81585 + 2.29494i) q^{41} +(-0.742000 - 0.338860i) q^{42} +(-1.08417 - 0.155879i) q^{43} +(-4.60733 + 2.96095i) q^{44} +(-3.65961 + 1.49964i) q^{45} +(3.60570 - 3.16210i) q^{46} -3.02265i q^{47} +(-1.18062 - 1.83708i) q^{48} +(-0.976346 + 6.79064i) q^{49} +(4.69786 - 1.71177i) q^{50} +(13.5233 - 3.97081i) q^{51} +(4.39518 - 2.00721i) q^{52} +(2.40632 - 2.08509i) q^{53} +(-0.382658 - 2.66145i) q^{54} +(-12.1811 + 1.26293i) q^{55} +(0.244617 - 0.282303i) q^{56} +(2.54525 - 3.96049i) q^{57} +(3.48841 - 5.42807i) q^{58} +(0.366229 - 0.422651i) q^{59} +(-0.503567 - 4.85695i) q^{60} +(0.459593 + 3.19654i) q^{61} +(-7.05231 + 6.11086i) q^{62} +(-0.600980 + 0.274458i) q^{63} +(0.959493 - 0.281733i) q^{64} +(10.7959 + 0.426540i) q^{65} +(-1.70205 + 11.8380i) q^{66} +(-3.28419 - 5.11029i) q^{67} +6.45419i q^{68} +(-0.0622909 - 10.4727i) q^{69} +(0.772887 - 0.316714i) q^{70} +(9.50897 - 6.11104i) q^{71} +(-1.75071 - 0.251714i) q^{72} +(-2.75739 - 1.25926i) q^{73} +(-3.40899 + 1.00097i) q^{74} +(3.89311 - 10.2011i) q^{75} +(1.41179 + 1.62929i) q^{76} +(-2.02496 + 0.291146i) q^{77} +(2.97268 - 10.1240i) q^{78} +(0.359389 - 0.414757i) q^{79} +(2.19902 + 0.405356i) q^{80} +(-9.40336 - 6.04317i) q^{81} +(-6.15620 - 5.33438i) q^{82} +(0.880203 - 2.99770i) q^{83} +(-0.116088 - 0.807411i) q^{84} +(-6.50887 + 12.8809i) q^{85} +(-0.455010 - 0.996332i) q^{86} +(-3.96968 - 13.5195i) q^{87} +(-4.98183 - 2.27512i) q^{88} +(-2.05531 + 14.2950i) q^{89} +(-3.24011 - 2.26789i) q^{90} +1.80488 q^{91} +(4.60952 + 1.32375i) q^{92} +20.3776i q^{93} +(2.54282 - 1.63417i) q^{94} +(1.17447 + 4.67540i) q^{95} +(0.907157 - 1.98640i) q^{96} +(0.880494 + 2.99869i) q^{97} +(-6.24050 + 2.84994i) q^{98} +(6.34349 + 7.32078i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41}+ \cdots + 188 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$3$	2.16151	+	0.310778i	1.24795	+	0.179428i	0.734450	−	0.678663i	$-0.237440\pi$
$3$	2.16151	+	0.310778i	1.24795	+	0.179428i	0.513498	+	0.858091i	$0.328349\pi$
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	−1.74640	+	1.39646i	−0.781014	+	0.624514i
$5$	−1.74640	+	1.39646i	−0.781014	+	0.624514i
$6$	0.907157	+	1.98640i	0.370345	+	0.810943i
$7$	−0.282303	+	0.244617i	−0.106700	+	0.0924565i	−0.706577	−	0.707636i	$-0.749762\pi$
$7$	−0.282303	+	0.244617i	−0.106700	+	0.0924565i	0.599877	+	0.800092i	$0.295216\pi$
$8$	−0.989821	+	0.142315i	−0.349955	+	0.0503159i
$9$	1.69707	+	0.498303i	0.565688	+	0.166101i
$10$	−2.11895	−	0.714183i	−0.670070	−	0.225845i
$11$	4.60733	+	2.96095i	1.38916	+	0.892761i	0.999601	−	0.0282391i	$-0.00898997\pi$
$11$	4.60733	+	2.96095i	1.38916	+	0.892761i	0.389562	+	0.921000i	$0.372626\pi$
$12$	−1.18062	+	1.83708i	−0.340815	+	0.530318i
$13$	−3.65165	−	3.16417i	−1.01279	−	0.877583i	−0.0202811	−	0.999794i	$-0.506456\pi$
$13$	−3.65165	−	3.16417i	−1.01279	−	0.877583i	−0.992504	+	0.122211i	$0.961002\pi$
$14$	−0.358409	−	0.105238i	−0.0957889	−	0.0281262i
$15$	−4.20885	+	2.47571i	−1.08672	+	0.639226i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	5.87094	−	2.68117i	1.42391	−	0.650278i	0.453394	−	0.891310i	$-0.350213\pi$
$17$	5.87094	−	2.68117i	1.42391	−	0.650278i	0.970517	+	0.241032i	$0.0774858\pi$
$18$	0.498303	+	1.69707i	0.117451	+	0.400002i
$19$	0.895578	−	1.96104i	0.205460	−	0.449894i	−0.778649	−	0.627459i	$-0.784095\pi$
$19$	0.895578	−	1.96104i	0.205460	−	0.449894i	0.984109	+	0.177565i	$0.0568221\pi$
$20$	−0.544781	−	2.16869i	−0.121817	−	0.484934i
$21$	−0.686222	+	0.441008i	−0.149746	+	0.0962359i
$22$			5.47675i			1.16765i
$23$	−0.710740	−	4.74287i	−0.148200	−	0.988957i
$23$	−0.710740	−	4.74287i	−0.148200	−	0.988957i
$24$	−2.18374			−0.445754
$25$	1.09982	−	4.87754i	0.219964	−	0.975508i
$26$	0.687640	−	4.78264i	0.134857	−	0.937954i
$27$	−2.44583	−	1.11697i	−0.470700	−	0.214962i
$28$	−0.105238	−	0.358409i	−0.0198882	−	0.0677330i
$29$	−2.68040	−	5.86927i	−0.497739	−	1.08990i	−0.977198	−	0.212331i	$-0.931894\pi$
$29$	−2.68040	−	5.86927i	−0.497739	−	1.08990i	0.479459	−	0.877564i	$-0.340833\pi$
$30$	−4.35818	−	2.20224i	−0.795690	−	0.402072i
$31$	1.32802	+	9.23656i	0.238519	+	1.65894i	0.659380	+	0.751810i	$0.270819\pi$
$31$	1.32802	+	9.23656i	0.238519	+	1.65894i	−0.420861	+	0.907125i	$0.638272\pi$
$32$	0.281733	−	0.959493i	0.0498038	−	0.169616i
$33$	9.03860	+	7.83199i	1.57342	+	1.36337i
$34$	5.42961	+	3.48940i	0.931170	+	0.598427i
$35$	0.151417	−	0.821422i	0.0255941	−	0.138846i
$36$	−1.15826	+	1.33670i	−0.193043	+	0.222784i
$37$	−1.00097	+	3.40899i	−0.164558	+	0.560434i	0.835384	+	0.549667i	$0.185245\pi$
$37$	−1.00097	+	3.40899i	−0.164558	+	0.560434i	−0.999942	+	0.0107668i	$0.996573\pi$
$38$	2.13392	−	0.306811i	0.346168	−	0.0497714i
$39$	−6.90972	−	7.97424i	−1.10644	−	1.27690i
$40$	1.52989	−	1.63078i	0.241896	−	0.257849i
$41$	−7.81585	+	2.29494i	−1.22063	+	0.358410i	−0.827707	−	0.561161i	$-0.810355\pi$
$41$	−7.81585	+	2.29494i	−1.22063	+	0.358410i	−0.392925	+	0.919571i	$0.628537\pi$
$42$	−0.742000	−	0.338860i	−0.114493	−	0.0522872i
$43$	−1.08417	−	0.155879i	−0.165334	−	0.0237714i	0.0591508	−	0.998249i	$-0.481161\pi$
$43$	−1.08417	−	0.155879i	−0.165334	−	0.0237714i	−0.224484	+	0.974478i	$0.572070\pi$
$44$	−4.60733	+	2.96095i	−0.694582	+	0.446381i
$45$	−3.65961	+	1.49964i	−0.545543	+	0.223553i
$46$	3.60570	−	3.16210i	0.531632	−	0.466227i
$47$		−	3.02265i		−	0.440899i	−0.975398	−	0.220450i	$-0.929248\pi$
$47$		−	3.02265i		−	0.440899i	0.975398	−	0.220450i	$-0.0707525\pi$
$48$	−1.18062	−	1.83708i	−0.170407	−	0.265159i
$49$	−0.976346	+	6.79064i	−0.139478	+	0.970091i
$50$	4.69786	−	1.71177i	0.664377	−	0.242081i
$51$	13.5233	−	3.97081i	1.89365	−	0.556025i
$52$	4.39518	−	2.00721i	0.609502	−	0.278350i
$53$	2.40632	−	2.08509i	0.330533	−	0.286409i	−0.473744	−	0.880662i	$-0.657098\pi$
$53$	2.40632	−	2.08509i	0.330533	−	0.286409i	0.804278	+	0.594254i	$0.202552\pi$
$54$	−0.382658	−	2.66145i	−0.0520732	−	0.362177i
$55$	−12.1811	+	1.26293i	−1.64250	+	0.170294i
$56$	0.244617	−	0.282303i	0.0326883	−	0.0377243i
$57$	2.54525	−	3.96049i	0.337127	−	0.524579i
$58$	3.48841	−	5.42807i	0.458050	−	0.712740i
$59$	0.366229	−	0.422651i	0.0476790	−	0.0550245i	−0.731409	−	0.681939i	$-0.761137\pi$
$59$	0.366229	−	0.422651i	0.0476790	−	0.0550245i	0.779088	+	0.626914i	$0.215682\pi$
$60$	−0.503567	−	4.85695i	−0.0650103	−	0.627030i
$61$	0.459593	+	3.19654i	0.0588448	+	0.409275i	0.997859	+	0.0653971i	$0.0208314\pi$
$61$	0.459593	+	3.19654i	0.0588448	+	0.409275i	−0.939014	+	0.343878i	$0.888259\pi$
$62$	−7.05231	+	6.11086i	−0.895644	+	0.776080i
$63$	−0.600980	+	0.274458i	−0.0757163	+	0.0345785i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	10.7959	+	0.426540i	1.33906	+	0.0529058i
$66$	−1.70205	+	11.8380i	−0.209508	+	1.45716i
$67$	−3.28419	−	5.11029i	−0.401227	−	0.624322i	0.580580	−	0.814203i	$-0.302826\pi$
$67$	−3.28419	−	5.11029i	−0.401227	−	0.624322i	−0.981807	+	0.189882i	$0.939190\pi$
$68$			6.45419i			0.782685i
$69$	−0.0622909	−	10.4727i	−0.00749894	−	1.26076i
$70$	0.772887	−	0.316714i	0.0923776	−	0.0378546i
$71$	9.50897	−	6.11104i	1.12851	−	0.725248i	0.163259	−	0.986583i	$-0.447799\pi$
$71$	9.50897	−	6.11104i	1.12851	−	0.725248i	0.965248	+	0.261336i	$0.0841629\pi$
$72$	−1.75071	−	0.251714i	−0.206323	−	0.0296647i
$73$	−2.75739	−	1.25926i	−0.322728	−	0.147385i	0.247463	−	0.968897i	$-0.420403\pi$
$73$	−2.75739	−	1.25926i	−0.322728	−	0.147385i	−0.570190	+	0.821513i	$0.693131\pi$
$74$	−3.40899	+	1.00097i	−0.396287	+	0.116360i
$75$	3.89311	−	10.2011i	0.449537	−	1.17792i
$76$	1.41179	+	1.62929i	0.161943	+	0.186893i
$77$	−2.02496	+	0.291146i	−0.230766	+	0.0331791i
$78$	2.97268	−	10.1240i	0.336590	−	1.14632i
$79$	0.359389	−	0.414757i	0.0404344	−	0.0466638i	−0.735172	−	0.677880i	$-0.762899\pi$
$79$	0.359389	−	0.414757i	0.0404344	−	0.0466638i	0.775607	+	0.631217i	$0.217444\pi$
$80$	2.19902	+	0.405356i	0.245858	+	0.0453202i
$81$	−9.40336	−	6.04317i	−1.04482	−	0.671464i
$82$	−6.15620	−	5.33438i	−0.679838	−	0.589083i
$83$	0.880203	−	2.99770i	0.0966148	−	0.329040i	−0.896976	−	0.442080i	$-0.854241\pi$
$83$	0.880203	−	2.99770i	0.0966148	−	0.329040i	0.993590	+	0.113040i	$0.0360589\pi$
$84$	−0.116088	−	0.807411i	−0.0126663	−	0.0880958i
$85$	−6.50887	+	12.8809i	−0.705986	+	1.39713i
$86$	−0.455010	−	0.996332i	−0.0490650	−	0.107437i
$87$	−3.96968	−	13.5195i	−0.425595	−	1.44944i
$88$	−4.98183	−	2.27512i	−0.531064	−	0.242529i
$89$	−2.05531	+	14.2950i	−0.217862	+	1.51526i	0.528046	+	0.849216i	$0.322925\pi$
$89$	−2.05531	+	14.2950i	−0.217862	+	1.51526i	−0.745908	+	0.666049i	$0.767984\pi$
$90$	−3.24011	−	2.26789i	−0.341538	−	0.239057i
$91$	1.80488			0.189203
$92$	4.60952	+	1.32375i	0.480576	+	0.138010i
$93$			20.3776i			2.11306i
$94$	2.54282	−	1.63417i	0.262272	−	0.168552i
$95$	1.17447	+	4.67540i	0.120498	+	0.479686i
$96$	0.907157	−	1.98640i	0.0925864	−	0.202736i
$97$	0.880494	+	2.99869i	0.0894006	+	0.304471i	0.992039	−	0.125929i	$-0.0401910\pi$
$97$	0.880494	+	2.99869i	0.0894006	+	0.304471i	−0.902639	+	0.430399i	$0.858373\pi$
$98$	−6.24050	+	2.84994i	−0.630386	+	0.287888i
$99$	6.34349	+	7.32078i	0.637545	+	0.735766i
$100$	3.97988	+	3.02664i	0.397988	+	0.302664i
$101$	5.89709	+	1.73154i	0.586783	+	0.172295i	0.561630	−	0.827389i	$-0.310175\pi$
$101$	5.89709	+	1.73154i	0.586783	+	0.172295i	0.0251529	+	0.999684i	$0.491993\pi$
$102$	10.6517	+	9.22977i	1.05468	+	0.913884i
$103$	−7.96252	+	12.3899i	−0.784570	+	1.22081i	0.186602	+	0.982436i	$0.440253\pi$
$103$	−7.96252	+	12.3899i	−0.784570	+	1.22081i	−0.971172	+	0.238379i	$0.923384\pi$
$104$	4.06479	+	2.61228i	0.398585	+	0.256155i
$105$	0.582569	−	1.72846i	0.0568530	−	0.168680i
$106$	3.05504	+	0.897041i	0.296732	+	0.0871283i
$107$	−9.43649	+	1.35676i	−0.912260	+	0.131163i	−0.582433	−	0.812878i	$-0.697899\pi$
$107$	−9.43649	+	1.35676i	−0.912260	+	0.131163i	−0.329827	+	0.944042i	$0.606990\pi$
$108$	2.03207	−	1.76080i	0.195536	−	0.169433i
$109$	−2.44737	−	5.35899i	−0.234415	−	0.513298i	0.755467	−	0.655186i	$-0.227410\pi$
$109$	−2.44737	−	5.35899i	−0.234415	−	0.513298i	−0.989883	+	0.141888i	$0.954683\pi$
$110$	−7.64804	−	9.56459i	−0.729212	−	0.911948i
$111$	−3.22304	+	7.05748i	−0.305918	+	0.669866i
$112$	0.369738	+	0.0531603i	0.0349370	+	0.00502318i
$113$	4.12614	+	6.42039i	0.388154	+	0.603980i	0.979258	−	0.202615i	$-0.0649441\pi$
$113$	4.12614	+	6.42039i	0.388154	+	0.603980i	−0.591104	+	0.806595i	$0.701308\pi$
$114$	4.70784			0.440930
$115$	7.86445	+	7.29043i	0.733364	+	0.679836i
$116$	6.45235			0.599086
$117$	−4.62037	−	7.18944i	−0.427153	−	0.664664i
$118$	0.553555	+	0.0795892i	0.0509589	+	0.00732678i
$119$	−1.00152	+	2.19303i	−0.0918095	+	0.201035i
$120$	3.81368	−	3.04949i	0.348140	−	0.278379i
$121$	7.89071	+	17.2783i	0.717338	+	1.57075i
$122$	−2.44062	+	2.11481i	−0.220964	+	0.191466i
$123$	−17.6073	+	2.53154i	−1.58759	+	0.228262i
$124$	−8.95355	−	2.62900i	−0.804052	−	0.236091i
$125$	4.89054	+	10.0540i	0.437423	+	0.899256i
$126$	−0.555803	−	0.357193i	−0.0495149	−	0.0318213i
$127$	3.19512	−	4.97171i	0.283521	−	0.441167i	−0.670059	−	0.742308i	$-0.733731\pi$
$127$	3.19512	−	4.97171i	0.283521	−	0.441167i	0.953580	+	0.301141i	$0.0973674\pi$
$128$	0.755750	+	0.654861i	0.0667995	+	0.0578821i
$129$	−2.29499	−	0.673870i	−0.202063	−	0.0593309i
$130$	5.47786	+	9.31266i	0.480440	+	0.816775i
$131$	−8.32754	−	9.61050i	−0.727581	−	0.839673i	0.264616	−	0.964354i	$-0.414755\pi$
$131$	−8.32754	−	9.61050i	−0.727581	−	0.839673i	−0.992197	+	0.124681i	$0.960209\pi$
$132$	−10.8790	+	4.96827i	−0.946895	+	0.432433i
$133$	0.226880	+	0.772681i	0.0196730	+	0.0670000i
$134$	2.52349	−	5.52567i	0.217996	−	0.477345i
$135$	5.83120	−	1.46481i	0.501870	−	0.126071i
$136$	−5.42961	+	3.48940i	−0.465585	+	0.299213i
$137$			4.70032i			0.401576i	0.979635	+	0.200788i	$0.0643502\pi$
$137$			4.70032i			0.401576i	−0.979635	+	0.200788i	$0.935650\pi$
$138$	8.77648	−	5.71435i	0.747104	−	0.486437i
$139$	−10.7013			−0.907676			−0.453838	−	0.891084i	$-0.649945\pi$
$139$	−10.7013			−0.907676			−0.453838	+	0.891084i	$0.649945\pi$
$140$	0.684291	+	0.478965i	0.0578332	+	0.0404799i
$141$	0.939375	−	6.53350i	0.0791097	−	0.550220i
$142$	10.2819	+	4.69558i	0.862836	+	0.394044i
$143$	−7.45540	−	25.3908i	−0.623452	−	2.12328i
$144$	−0.734749	−	1.60888i	−0.0612291	−	0.134073i
$145$	12.8772	+	6.50702i	1.06940	+	0.540378i
$146$	−0.431402	−	3.00047i	−0.0357031	−	0.248320i
$147$	−4.22077	+	14.3746i	−0.348123	+	1.18560i
$148$	−2.68511	−	2.32666i	−0.220714	−	0.191250i
$149$	15.3295	+	9.85165i	1.25584	+	0.807079i	0.987709	−	0.156304i	$-0.0499580\pi$
$149$	15.3295	+	9.85165i	1.25584	+	0.807079i	0.268130	+	0.963383i	$0.413594\pi$
$150$	10.6864	−	2.24001i	0.872545	−	0.182896i
$151$	−10.5609	+	12.1879i	−0.859435	+	0.991840i	0.140564	+	0.990072i	$0.455108\pi$
$151$	−10.5609	+	12.1879i	−0.859435	+	0.991840i	−0.999998	+	0.00176869i	$0.999437\pi$
$152$	−0.607377	+	2.06854i	−0.0492648	+	0.167780i
$153$	11.2994	−	1.62461i	0.913502	−	0.131342i
$154$	−1.33970	−	1.54610i	−0.107956	−	0.124588i
$155$	−15.2177	−	14.2762i	−1.22231	−	1.14669i
$156$	10.1240	−	2.97268i	0.810571	−	0.238005i
$157$	2.83255	+	1.29358i	0.226062	+	0.103239i	0.525226	−	0.850963i	$-0.323981\pi$
$157$	2.83255	+	1.29358i	0.226062	+	0.103239i	−0.299165	+	0.954202i	$0.596708\pi$
$158$	0.543216	+	0.0781026i	0.0432159	+	0.00621351i
$159$	5.84928	−	3.75911i	0.463878	−	0.298116i
$160$	0.847872	+	2.06908i	0.0670302	+	0.163576i
$161$	1.36083	+	1.16507i	0.107248	+	0.0918202i
$162$		−	11.1778i		−	0.878210i
$163$	−6.13815	−	9.55114i	−0.480777	−	0.748103i	0.513132	−	0.858310i	$-0.328485\pi$
$163$	−6.13815	−	9.55114i	−0.480777	−	0.748103i	−0.993909	+	0.110207i	$0.964849\pi$
$164$	1.15927	−	8.06290i	0.0905238	−	0.629607i
$165$	−26.7220	−	1.05578i	−2.08031	−	0.0821921i
$166$	2.99770	−	0.880203i	0.232666	−	0.0683170i
$167$	18.2486	−	8.33388i	1.41212	−	0.644895i	0.444150	−	0.895952i	$-0.353506\pi$
$167$	18.2486	−	8.33388i	1.41212	−	0.644895i	0.967972	+	0.251057i	$0.0807783\pi$
$168$	0.616475	−	0.534179i	0.0475621	−	0.0412128i
$169$	1.47246	+	10.2412i	0.113266	+	0.787786i
$170$	−14.3551	+	1.48833i	−1.10098	+	0.114150i
$171$	2.49705	−	2.88175i	0.190954	−	0.220373i
$172$	0.592171	−	0.921437i	0.0451526	−	0.0702589i
$173$	−7.23710	+	11.2611i	−0.550226	+	0.856169i	−0.999303	−	0.0373244i	$-0.988117\pi$
$173$	−7.23710	+	11.2611i	−0.550226	+	0.856169i	0.449077	+	0.893493i	$0.351753\pi$
$174$	9.22715	−	10.6487i	0.699508	−	0.807276i
$175$	0.882646	+	1.64598i	0.0667217	+	0.124424i
$176$	−0.779423	−	5.42100i	−0.0587512	−	0.408623i
$177$	0.922959	−	0.799748i	0.0693738	−	0.0601128i
$178$	−13.1369	+	5.99941i	−0.984651	+	0.449675i
$179$	0.220709	−	0.0648060i	0.0164966	−	0.00484383i	−0.273474	−	0.961879i	$-0.588173\pi$
$179$	0.220709	−	0.0648060i	0.0164966	−	0.00484383i	0.289970	+	0.957036i	$0.406355\pi$
$180$	0.156137	−	3.95187i	0.0116378	−	0.294555i
$181$	2.10117	−	14.6140i	0.156179	−	1.08625i	−0.749415	−	0.662101i	$-0.769665\pi$
$181$	2.10117	−	14.6140i	0.156179	−	1.08625i	0.905594	−	0.424146i	$-0.139426\pi$
$182$	0.975792	+	1.51836i	0.0723305	+	0.112549i
$183$			7.05218i			0.521312i
$184$	1.37849	+	4.59345i	0.101623	+	0.338634i
$185$	−3.01241	−	7.35126i	−0.221477	−	0.540475i
$186$	−17.1428	+	11.0170i	−1.25697	+	0.807804i
$187$	34.9882	+	5.03054i	2.55859	+	0.367869i
$188$	2.74950	+	1.25566i	0.200528	+	0.0915781i
$189$	0.963696	−	0.282967i	0.0700985	−	0.0205828i
$190$	−3.29823	+	3.51574i	−0.239279	+	0.255059i
$191$	−11.0984	−	12.8083i	−0.803056	−	0.926775i	0.195489	−	0.980706i	$-0.437371\pi$
$191$	−11.0984	−	12.8083i	−0.803056	−	0.926775i	−0.998545	+	0.0539304i	$0.982825\pi$
$192$	2.16151	−	0.310778i	0.155994	−	0.0224285i
$193$	1.09473	−	3.72829i	0.0788001	−	0.268368i	−0.910664	−	0.413148i	$-0.864429\pi$
$193$	1.09473	−	3.72829i	0.0788001	−	0.268368i	0.989464	+	0.144780i	$0.0462474\pi$
$194$	−2.04663	+	2.36193i	−0.146939	+	0.169577i
$195$	23.2028	+	4.27709i	1.66159	+	0.306289i
$196$	−5.77139	−	3.70905i	−0.412242	−	0.264932i
$197$	−5.68740	−	4.92816i	−0.405211	−	0.351117i	0.428284	−	0.903644i	$-0.359118\pi$
$197$	−5.68740	−	4.92816i	−0.405211	−	0.351117i	−0.833495	+	0.552527i	$0.813664\pi$
$198$	−2.72908	+	9.29440i	−0.193947	+	0.660524i
$199$	0.168690	+	1.17326i	0.0119581	+	0.0831704i	0.994927	−	0.100604i	$-0.0320775\pi$
$199$	0.168690	+	1.17326i	0.0119581	+	0.0831704i	−0.982968	+	0.183774i	$0.941168\pi$
$200$	−0.394480	+	4.98441i	−0.0278940	+	0.352451i
$201$	−5.51063	−	12.0666i	−0.388690	−	0.851113i
$202$	1.73154	+	5.89709i	0.121831	+	0.414918i
$203$	2.19241	+	1.00124i	0.153877	+	0.0702732i
$204$	−2.00582	+	13.9508i	−0.140436	+	0.976751i
$205$	10.4448	−	14.9224i	0.729498	−	1.04222i
$206$	−14.7279			−1.02614
$207$	1.15722	−	8.40313i	0.0804321	−	0.584058i
$208$			4.83182i			0.335027i
$209$	9.93278	−	6.38341i	0.687065	−	0.441550i
$210$	1.76903	−	0.444385i	0.122075	−	0.0306655i
$211$	−1.51354	+	3.31419i	−0.104196	+	0.228158i	−0.954548	−	0.298056i	$-0.903662\pi$
$211$	−1.51354	+	3.31419i	−0.104196	+	0.228158i	0.850352	+	0.526214i	$0.176389\pi$
$212$	0.897041	+	3.05504i	0.0616090	+	0.209821i
$213$	22.4529	−	10.2539i	1.53845	−	0.702586i
$214$	−6.24313	−	7.20496i	−0.426772	−	0.492521i
$215$	2.11106	−	1.24176i	0.143973	−	0.0846874i
$216$	2.57990	+	0.757526i	0.175540	+	0.0515431i
$217$	−2.63432	−	2.28265i	−0.178829	−	0.154957i
$218$	3.18512	−	4.95614i	0.215724	−	0.335672i
$219$	−5.56877	−	3.57883i	−0.376302	−	0.241835i
$220$	3.91140	−	11.6049i	0.263707	−	0.782405i
$221$	−29.9223	−	8.78597i	−2.01279	−	0.591008i
$222$	−7.67964	+	1.10417i	−0.515424	+	0.0741067i
$223$	−13.1958	+	11.4343i	−0.883659	+	0.765695i	−0.973121	−	0.230295i	$-0.926031\pi$
$223$	−13.1958	+	11.4343i	−0.883659	+	0.765695i	0.0894614	+	0.995990i	$0.471485\pi$
$224$	0.155174	+	0.339784i	0.0103680	+	0.0227028i
$225$	4.29696	−	7.72946i	0.286464	−	0.515297i
$226$	−3.17042	+	6.94225i	−0.210893	+	0.461792i
$227$	19.6997	+	2.83239i	1.30752	+	0.187992i	0.760614	−	0.649204i	$-0.224898\pi$
$227$	19.6997	+	2.83239i	1.30752	+	0.187992i	0.546902	+	0.837197i	$0.315807\pi$
$228$	2.54525	+	3.96049i	0.168563	+	0.262290i
$229$	−17.5337			−1.15866			−0.579330	−	0.815093i	$-0.696686\pi$
$229$	−17.5337			−1.15866			−0.579330	+	0.815093i	$0.696686\pi$
$230$	−1.88126	+	10.5575i	−0.124047	+	0.696141i
$231$	−4.46746			−0.293937
$232$	3.48841	+	5.42807i	0.229025	+	0.356370i
$233$	19.6380	+	2.82352i	1.28653	+	0.184975i	0.751429	−	0.659814i	$-0.229365\pi$
$233$	19.6380	+	2.82352i	1.28653	+	0.184975i	0.535100	+	0.844789i	$0.320274\pi$
$234$	3.55018	−	7.77380i	0.232082	−	0.508189i
$235$	4.22100	+	5.27876i	0.275348	+	0.344348i
$236$	0.232320	+	0.508709i	0.0151227	+	0.0331142i
$237$	0.905719	−	0.784810i	0.0588328	−	0.0509789i
$238$	−2.38636	+	0.343107i	−0.154685	+	0.0222403i
$239$	8.79581	+	2.58268i	0.568953	+	0.167060i	0.553542	−	0.832821i	$-0.313276\pi$
$239$	8.79581	+	2.58268i	0.568953	+	0.167060i	0.0154116	+	0.999881i	$0.495094\pi$
$240$	4.62723	+	1.55959i	0.298686	+	0.100671i
$241$	−19.6148	−	12.6057i	−1.26350	−	0.812002i	−0.274740	−	0.961518i	$-0.588592\pi$
$241$	−19.6148	−	12.6057i	−1.26350	−	0.812002i	−0.988759	+	0.149517i	$0.952228\pi$
$242$	−10.2693	+	15.9794i	−0.660139	+	1.02720i
$243$	−12.3512	−	10.7023i	−0.792328	−	0.686556i
$244$	−3.09859	−	0.909829i	−0.198367	−	0.0582459i
$245$	−7.77774	−	13.2226i	−0.496901	−	0.844760i
$246$	−11.6489	−	13.4435i	−0.742705	−	0.857128i
$247$	−9.47541	+	4.32728i	−0.602906	+	0.275338i
$248$	−2.62900	−	8.95355i	−0.166942	−	0.568551i
$249$	2.83419	−	6.20600i	0.179609	−	0.393289i
$250$	−5.81392	+	9.54978i	−0.367705	+	0.603981i
$251$	7.14975	−	4.59487i	0.451288	−	0.290025i	−0.295186	−	0.955440i	$-0.595382\pi$
$251$	7.14975	−	4.59487i	0.451288	−	0.290025i	0.746474	+	0.665415i	$0.231745\pi$
$252$		−	0.660685i		−	0.0416192i
$253$	10.7688	−	23.9565i	0.677029	−	1.50613i
$254$	5.90988			0.370819
$255$	−18.0721	+	25.8194i	−1.13172	+	1.61687i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−20.8775	−	9.53443i	−1.30230	−	0.594741i	−0.361081	−	0.932534i	$-0.617592\pi$
$257$	−20.8775	−	9.53443i	−1.30230	−	0.594741i	−0.941220	+	0.337793i	$0.890320\pi$
$258$	−0.673870	−	2.29499i	−0.0419533	−	0.142880i
$259$	−0.551319	−	1.20722i	−0.0342573	−	0.0750130i
$260$	−4.87276	+	9.64307i	−0.302196	+	0.598038i
$261$	−1.62415	−	11.2962i	−0.100532	−	0.699216i
$262$	3.58266	−	12.2014i	0.221337	−	0.753805i
$263$	1.34791	+	1.16797i	0.0831156	+	0.0720201i	0.695428	−	0.718596i	$-0.255215\pi$
$263$	1.34791	+	1.16797i	0.0831156	+	0.0720201i	−0.612312	+	0.790616i	$0.709760\pi$
$264$	−10.0612	−	6.46595i	−0.619225	−	0.397951i
$265$	−1.29066	+	7.00171i	−0.0792847	+	0.430112i
$266$	−0.527361	+	0.608607i	−0.0323345	+	0.0373161i
$267$	−8.88513	+	30.2600i	−0.543761	+	1.85188i
$268$	6.01279	−	0.864508i	0.367289	−	0.0528082i
$269$	17.8905	+	20.6467i	1.09080	+	1.25885i	0.963707	+	0.266960i	$0.0860193\pi$
$269$	17.8905	+	20.6467i	1.09080	+	1.25885i	0.127093	+	0.991891i	$0.459435\pi$
$270$	4.38486	+	4.11358i	0.266854	+	0.250345i
$271$	15.6117	−	4.58401i	0.948344	−	0.278459i	0.229247	−	0.973368i	$-0.426374\pi$
$271$	15.6117	−	4.58401i	0.948344	−	0.278459i	0.719097	+	0.694910i	$0.244556\pi$
$272$	−5.87094	−	2.68117i	−0.355978	−	0.162570i
$273$	3.90127	+	0.560918i	0.236116	+	0.0339483i
$274$	−3.95416	+	2.54119i	−0.238880	+	0.153519i
$275$	19.5094	−	19.2159i	1.17646	−	1.15876i
$276$	9.55214	+	4.29384i	0.574971	+	0.258459i
$277$		−	1.03669i		−	0.0622889i	−0.999515	−	0.0311445i	$-0.990085\pi$
$277$		−	1.03669i		−	0.0622889i	0.999515	−	0.0311445i	$-0.00991520\pi$
$278$	−5.78558	−	9.00254i	−0.346996	−	0.539936i
$279$	−2.34888	+	16.3368i	−0.140624	+	0.978059i
$280$	−0.0329751	+	0.834610i	−0.00197064	+	0.0498775i
$281$	25.0281	−	7.34891i	1.49305	−	0.438399i	0.569537	−	0.821965i	$-0.307122\pi$
$281$	25.0281	−	7.34891i	1.49305	−	0.438399i	0.923513	+	0.383566i	$0.125304\pi$
$282$	6.00419	−	2.74202i	0.357544	−	0.163285i
$283$	10.9840	−	9.51770i	0.652932	−	0.565768i	−0.264143	−	0.964483i	$-0.585089\pi$
$283$	10.9840	−	9.51770i	0.652932	−	0.565768i	0.917075	+	0.398715i	$0.130544\pi$
$284$	1.60863	+	11.1883i	0.0954548	+	0.663902i
$285$	1.08562	+	10.4709i	0.0643067	+	0.620244i
$286$	17.3294	−	19.9992i	1.02471	−	1.18258i
$287$	1.64506	−	2.55976i	0.0971046	−	0.151098i
$288$	0.956237	−	1.48793i	0.0563468	−	0.0876773i
$289$	16.1466	−	18.6342i	0.949800	−	1.09613i
$290$	1.48791	+	14.3510i	0.0873728	+	0.842718i
$291$	0.971270	+	6.75533i	0.0569369	+	0.396005i
$292$	2.29092	−	1.98509i	0.134066	−	0.116169i
$293$	−25.4826	+	11.6375i	−1.48871	+	0.679871i	−0.983130	−	0.182908i	$-0.941449\pi$
$293$	−25.4826	+	11.6375i	−1.48871	+	0.679871i	−0.505580	+	0.862779i	$0.668722\pi$
$294$	−14.3746	+	4.22077i	−0.838344	+	0.246160i
$295$	−0.0493688	+	1.24954i	−0.00287437	+	0.0727511i
$296$	0.505631	−	3.51674i	0.0293892	−	0.204406i
$297$	−7.96145	−	12.3883i	−0.461970	−	0.718840i
$298$			18.2222i			1.05558i
$299$	−12.4119	+	19.5682i	−0.717798	+	1.13166i
$300$	7.66195	+	7.77897i	0.442363	+	0.449119i
$301$	0.344194	−	0.221200i	0.0198390	−	0.0127497i
$302$	−15.9628	−	2.29510i	−0.918556	−	0.132068i
$303$	12.2085	+	5.57544i	0.701360	+	0.320300i
$304$	−2.06854	+	0.607377i	−0.118639	+	0.0348355i
$305$	−5.26646	−	4.94063i	−0.301556	−	0.282900i
$306$	7.47562	+	8.62733i	0.427353	+	0.493191i
$307$	−21.3279	+	3.06649i	−1.21725	+	0.175014i	−0.720856	−	0.693085i	$-0.756251\pi$
$307$	−21.3279	+	3.06649i	−1.21725	+	0.175014i	−0.496391	+	0.868099i	$0.665342\pi$
$308$	0.576365	−	1.96292i	0.0328414	−	0.111848i
$309$	−21.0616	+	24.3064i	−1.19815	+	1.38274i
$310$	3.78260	−	20.5202i	0.214837	−	1.16547i
$311$	4.34824	+	2.79445i	0.246566	+	0.158458i	0.658087	−	0.752942i	$-0.271366\pi$
$311$	4.34824	+	2.79445i	0.246566	+	0.158458i	−0.411521	+	0.911400i	$0.635002\pi$
$312$	7.97424	+	6.90972i	0.451453	+	0.391186i
$313$	0.388840	−	1.32427i	0.0219785	−	0.0748520i	−0.947774	−	0.318944i	$-0.896672\pi$
$313$	0.388840	−	1.32427i	0.0219785	−	0.0748520i	0.969752	+	0.244092i	$0.0784899\pi$
$314$	0.443161	+	3.08225i	0.0250090	+	0.173942i
$315$	0.666282	−	1.31856i	0.0375407	−	0.0742922i
$316$	0.227980	+	0.499207i	0.0128249	+	0.0280826i
$317$	−4.54324	−	15.4729i	−0.255174	−	0.869043i	−0.983051	−	0.183335i	$-0.941311\pi$
$317$	−4.54324	−	15.4729i	−0.255174	−	0.869043i	0.727877	−	0.685708i	$-0.240507\pi$
$318$	6.32472	+	2.88840i	0.354673	+	0.161974i
$319$	5.02911	−	34.9782i	0.281576	−	1.95840i
$320$	−1.28223	+	1.83191i	−0.0716789	+	0.102407i
$321$	−20.8187			−1.16199
$322$	−0.244397	+	1.77469i	−0.0136197	+	0.0988994i
$323$		−	13.9143i		−	0.774215i
$324$	9.40336	−	6.04317i	0.522409	−	0.335732i
$325$	−19.4495	+	14.3310i	−1.07887	+	0.794943i
$326$	4.71640	−	10.3275i	0.261217	−	0.571986i
$327$	−3.62455	−	12.3441i	−0.200438	−	0.682630i
$328$	7.40970	−	3.38389i	0.409132	−	0.186844i
$329$	0.739392	+	0.853304i	0.0407640	+	0.0470442i
$330$	−13.5588	−	23.0508i	−0.746390	−	1.26890i
$331$	11.1676	+	3.27910i	0.613826	+	0.180236i	0.573844	−	0.818965i	$-0.305452\pi$
$331$	11.1676	+	3.27910i	0.613826	+	0.180236i	0.0399825	+	0.999200i	$0.487270\pi$
$332$	2.36115	+	2.04595i	0.129585	+	0.112286i
$333$	−3.39742	+	5.28649i	−0.186177	+	0.289698i
$334$	16.8769	+	10.8461i	0.923461	+	0.593472i
$335$	12.8718	+	4.33839i	0.703262	+	0.237032i
$336$	0.782672	+	0.229813i	0.0426982	+	0.0125373i
$337$	29.9730	−	4.30946i	1.63273	−	0.234751i	0.735889	−	0.677102i	$-0.236764\pi$
$337$	29.9730	−	4.30946i	1.63273	−	0.234751i	0.896842	+	0.442350i	$0.145855\pi$
$338$	−7.81938	+	6.77553i	−0.425318	+	0.368540i
$339$	6.92337	+	15.1601i	0.376026	+	0.823382i
$340$	−9.01299	−	11.2716i	−0.488798	−	0.611288i
$341$	−21.2304	+	46.4881i	−1.14969	+	2.51747i
$342$	3.77429	+	0.542660i	0.204090	+	0.0293437i
$343$	−2.79914	−	4.35554i	−0.151139	−	0.235177i
$344$	1.09531			0.0590554
$345$	14.7334	+	18.2024i	0.793219	+	0.979987i
$346$	−13.3861			−0.719644
$347$	−10.0910	−	15.7019i	−0.541714	−	0.842924i	0.457207	−	0.889360i	$-0.348850\pi$
$347$	−10.0910	−	15.7019i	−0.541714	−	0.842924i	−0.998921	+	0.0464365i	$0.985213\pi$
$348$	13.9468	+	2.00525i	0.747629	+	0.107493i
$349$	8.46325	−	18.5319i	0.453027	−	0.991991i	−0.535995	−	0.844221i	$-0.680063\pi$
$349$	8.46325	−	18.5319i	0.453027	−	0.991991i	0.989022	−	0.147770i	$-0.0472095\pi$
$350$	−0.907491	+	1.63241i	−0.0485074	+	0.0872561i
$351$	5.39702	+	11.8178i	0.288072	+	0.630789i
$352$	4.13905	−	3.58651i	0.220612	−	0.191161i
$353$	31.6328	−	4.54811i	1.68364	−	0.242071i	0.766963	−	0.641692i	$-0.221767\pi$
$353$	31.6328	−	4.54811i	1.68364	−	0.242071i	0.916681	+	0.399620i	$0.130858\pi$
$354$	1.17178	+	0.344066i	0.0622794	+	0.0182869i
$355$	−8.07266	+	23.9512i	−0.428452	+	1.27120i
$356$	−12.1494	−	7.80792i	−0.643915	−	0.413819i
$357$	−2.84635	+	4.42901i	−0.150645	+	0.234408i
$358$	0.173843	+	0.150635i	0.00918786	+	0.00796133i
$359$	17.3419	+	5.09205i	0.915272	+	0.268748i	0.705258	−	0.708950i	$-0.250831\pi$
$359$	17.3419	+	5.09205i	0.915272	+	0.268748i	0.210014	+	0.977698i	$0.432649\pi$
$360$	3.40894	−	2.00519i	0.179667	−	0.105683i
$361$	9.39873	+	10.8467i	0.494670	+	0.570879i
$362$	13.4300	−	6.13328i	0.705866	−	0.322358i
$363$	11.6862	+	39.7994i	0.613364	+	2.08893i
$364$	−0.749775	+	1.64178i	−0.0392989	+	0.0860525i
$365$	6.57399	−	1.65140i	0.344098	−	0.0864384i
$366$	−5.93267	+	3.81270i	−0.310106	+	0.199293i
$367$			33.4560i			1.74639i	0.487372	+	0.873195i	$0.337956\pi$
$367$			33.4560i			1.74639i	−0.487372	+	0.873195i	$0.662044\pi$
$368$	−3.11899	+	3.64306i	−0.162589	+	0.189908i
$369$	−14.4076			−0.750029
$370$	4.55564	−	6.50859i	0.236837	−	0.338366i
$371$	−0.169263	+	1.17725i	−0.00878771	+	0.0611199i
$372$	−18.5362	−	8.46518i	−0.961055	−	0.438899i
$373$	8.53013	+	29.0510i	0.441673	+	1.50420i	0.816631	+	0.577160i	$0.195839\pi$
$373$	8.53013	+	29.0510i	0.441673	+	1.50420i	−0.374958	+	0.927042i	$0.622343\pi$
$374$	14.6841	+	32.1536i	0.759295	+	1.66263i
$375$	7.44640	+	23.2517i	0.384530	+	1.20071i
$376$	0.430168	+	2.99189i	0.0221842	+	0.154295i
$377$	−8.78347	+	29.9138i	−0.452372	+	1.54064i
$378$	0.759060	+	0.657729i	0.0390418	+	0.0338299i
$379$	−4.57371	−	2.93935i	−0.234936	−	0.150984i	0.417876	−	0.908504i	$-0.362775\pi$
$379$	−4.57371	−	2.93935i	−0.234936	−	0.150984i	−0.652812	+	0.757520i	$0.726411\pi$
$380$	−4.74079	−	0.873893i	−0.243197	−	0.0448298i
$381$	8.45139	−	9.75342i	0.432978	−	0.499683i
$382$	4.77475	−	16.2613i	0.244297	−	0.832000i
$383$	−17.5654	+	2.52552i	−0.897550	+	0.129048i	−0.575622	−	0.817716i	$-0.695240\pi$
$383$	−17.5654	+	2.52552i	−0.897550	+	0.129048i	−0.321928	+	0.946764i	$0.604331\pi$
$384$	1.43004	+	1.65036i	0.0729766	+	0.0842195i
$385$	3.12982	−	3.33623i	0.159510	−	0.170030i
$386$	3.72829	−	1.09473i	0.189765	−	0.0557201i
$387$	−1.76222	−	0.804781i	−0.0895789	−	0.0409093i
$388$	−3.09347	−	0.444774i	−0.157047	−	0.0225800i
$389$	7.29476	−	4.68806i	0.369859	−	0.237694i	−0.342487	−	0.939523i	$-0.611269\pi$
$389$	7.29476	−	4.68806i	0.369859	−	0.237694i	0.712346	+	0.701829i	$0.247633\pi$
$390$	8.94627	+	21.8318i	0.453012	+	1.10550i
$391$	−16.8891	−	25.9395i	−0.854121	−	1.31182i
$392$		−	6.86047i		−	0.346506i
$393$	−15.0133	−	23.3612i	−0.757323	−	1.17842i
$394$	1.07099	−	7.44891i	0.0539558	−	0.375271i
$395$	−0.0484467	+	1.22620i	−0.00243762	+	0.0616969i
$396$	−9.29440	+	2.72908i	−0.467061	+	0.137142i
$397$	−22.7493	+	10.3892i	−1.14175	+	0.521421i	−0.894295	−	0.447478i	$-0.852322\pi$
$397$	−22.7493	+	10.3892i	−1.14175	+	0.521421i	−0.247457	+	0.968899i	$0.579595\pi$
$398$	−0.895811	+	0.776225i	−0.0449029	+	0.0389086i
$399$	0.250270	+	1.74067i	0.0125292	+	0.0871424i
$400$	−4.40643	+	2.36292i	−0.220321	+	0.118146i
$401$	4.71541	−	5.44187i	0.235476	−	0.271754i	−0.625696	−	0.780067i	$-0.715185\pi$
$401$	4.71541	−	5.44187i	0.235476	−	0.271754i	0.861173	+	0.508313i	$0.169731\pi$
$402$	7.17180	−	11.1595i	0.357697	−	0.556587i
$403$	24.3766	−	37.9307i	1.21429	−	1.88947i
$404$	−4.02481	+	4.64488i	−0.200242	+	0.231091i
$405$	24.8610	−	2.57759i	1.23536	−	0.128081i
$406$	0.343009	+	2.38568i	0.0170233	+	0.118399i
$407$	−14.7056	+	12.7425i	−0.728932	+	0.631623i
$408$	−12.8206	+	5.85496i	−0.634714	+	0.289864i
$409$	−7.14898	+	2.09913i	−0.353494	+	0.103795i	−0.453658	−	0.891176i	$-0.649881\pi$
$409$	−7.14898	+	2.09913i	−0.353494	+	0.103795i	0.100164	+	0.994971i	$0.468063\pi$
$410$	18.2004	+	0.719091i	0.898854	+	0.0355134i
$411$	−1.46076	+	10.1598i	−0.0720539	+	0.501146i
$412$	−7.96252	−	12.3899i	−0.392285	−	0.610407i
$413$			0.208901i			0.0102794i
$414$	7.69480	−	3.56956i	0.378179	−	0.175434i
$415$	2.64896	+	6.46434i	0.130033	+	0.317322i
$416$	−4.06479	+	2.61228i	−0.199293	+	0.128078i
$417$	−23.1311	−	3.32574i	−1.13273	−	0.162862i
$418$	10.7401	+	4.90486i	0.525317	+	0.239904i
$419$	−11.7860	+	3.46067i	−0.575782	+	0.169065i	−0.556643	−	0.830752i	$-0.687911\pi$
$419$	−11.7860	+	3.46067i	−0.575782	+	0.169065i	−0.0191394	+	0.999817i	$0.506093\pi$
$420$	1.33025	+	1.24795i	0.0649096	+	0.0608937i
$421$	−10.2417	−	11.8195i	−0.499148	−	0.576047i	0.449139	−	0.893462i	$-0.351731\pi$
$421$	−10.2417	−	11.8195i	−0.499148	−	0.576047i	−0.948287	+	0.317414i	$0.897185\pi$
$422$	−3.60636	+	0.518516i	−0.175555	+	0.0252409i
$423$	1.50620	−	5.12964i	0.0732339	−	0.249412i
$424$	−2.08509	+	2.40632i	−0.101261	+	0.116861i
$425$	−6.62052	−	31.5845i	−0.321142	−	1.53207i
$426$	20.7651	+	13.3449i	1.00607	+	0.646563i
$427$	−0.911671	−	0.789968i	−0.0441189	−	0.0382292i
$428$	2.68591	−	9.14735i	0.129828	−	0.442154i
$429$	−8.22403	−	57.1994i	−0.397060	−	2.76161i
$430$	2.18596	+	1.10459i	0.105417	+	0.0532682i
$431$	6.93910	+	15.1945i	0.334245	+	0.731894i	0.999897	−	0.0143685i	$-0.00457379\pi$
$431$	6.93910	+	15.1945i	0.334245	+	0.731894i	−0.665652	+	0.746262i	$0.731847\pi$
$432$	0.757526	+	2.57990i	0.0364465	+	0.124125i
$433$	−1.42576	−	0.651124i	−0.0685178	−	0.0312910i	0.380861	−	0.924632i	$-0.375628\pi$
$433$	−1.42576	−	0.651124i	−0.0685178	−	0.0312910i	−0.449379	+	0.893341i	$0.648355\pi$
$434$	0.496068	−	3.45023i	0.0238120	−	0.165616i
$435$	25.8120	+	18.0669i	1.23759	+	0.866244i
$436$	5.89138			0.282146
$437$	−9.93750	−	2.85382i	−0.475375	−	0.136517i
$438$		−	6.61961i		−	0.316297i
$439$	22.0370	−	14.1623i	1.05177	−	0.675930i	0.103898	−	0.994588i	$-0.466869\pi$
$439$	22.0370	−	14.1623i	1.05177	−	0.675930i	0.947870	+	0.318658i	$0.103232\pi$
$440$	11.8774	−	2.98363i	0.566231	−	0.142239i
$441$	−5.04072	+	11.0376i	−0.240034	+	0.525602i
$442$	−8.78597	−	29.9223i	−0.417906	−	1.42326i
$443$	−26.1730	+	11.9528i	−1.24352	+	0.567896i	−0.924981	−	0.380014i	$-0.875919\pi$
$443$	−26.1730	+	11.9528i	−1.24352	+	0.567896i	−0.318538	+	0.947910i	$0.603192\pi$
$444$	−5.08081	−	5.86357i	−0.241125	−	0.278273i
$445$	−16.3729	−	27.8349i	−0.776151	−	1.31950i
$446$	−16.7533	−	4.91922i	−0.793293	−	0.232932i
$447$	30.0731	+	26.0585i	1.42241	+	1.23253i
$448$	−0.201951	+	0.314242i	−0.00954129	+	0.0148465i
$449$	6.57925	+	4.22823i	0.310494	+	0.199542i	0.686602	−	0.727033i	$-0.259102\pi$
$449$	6.57925	+	4.22823i	0.310494	+	0.199542i	−0.376108	+	0.926576i	$0.622738\pi$
$450$	8.82555	−	0.564026i	0.416040	−	0.0265884i
$451$	−42.8055	−	12.5688i	−2.01563	−	0.591843i
$452$	−7.55425	+	1.08614i	−0.355322	+	0.0510876i
$453$	−26.6153	+	23.0623i	−1.25049	+	1.08356i
$454$	8.26771	+	18.1038i	0.388023	+	0.849652i
$455$	−3.15204	+	2.52044i	−0.147770	+	0.118160i
$456$	−1.95571	+	4.28240i	−0.0915844	+	0.200542i
$457$	10.5987	+	1.52387i	0.495788	+	0.0712835i	0.385673	−	0.922635i	$-0.373969\pi$
$457$	10.5987	+	1.52387i	0.495788	+	0.0712835i	0.110114	+	0.993919i	$0.464878\pi$
$458$	−9.47943	−	14.7503i	−0.442945	−	0.689236i
$459$	−17.3541			−0.810020
$460$	−9.89862	+	4.12520i	−0.461526	+	0.192338i
$461$	8.31279			0.387165			0.193583	−	0.981084i	$-0.437989\pi$
$461$	8.31279			0.387165			0.193583	+	0.981084i	$0.437989\pi$
$462$	−2.41529	−	3.75827i	−0.112370	−	0.174850i
$463$	0.481902	+	0.0692870i	0.0223959	+	0.00322004i	0.153504	−	0.988148i	$-0.450944\pi$
$463$	0.481902	+	0.0692870i	0.0223959	+	0.00322004i	−0.131108	+	0.991368i	$0.541853\pi$
$464$	−2.68040	+	5.86927i	−0.124435	+	0.272474i
$465$	−28.4565	−	35.5875i	−1.31964	−	1.65033i
$466$	8.24182	+	18.0471i	0.381795	+	0.836014i
$467$	17.7016	−	15.3385i	0.819130	−	0.709780i	−0.140794	−	0.990039i	$-0.544966\pi$
$467$	17.7016	−	15.3385i	0.819130	−	0.709780i	0.959925	+	0.280259i	$0.0904202\pi$
$468$	8.45911	−	1.21624i	0.391023	−	0.0562206i
$469$	2.17720	+	0.639283i	0.100534	+	0.0295194i
$470$	−2.15873	+	6.40485i	−0.0995748	+	0.295434i
$471$	5.72056	+	3.67638i	0.263590	+	0.169399i
$472$	−0.302352	+	0.470469i	−0.0139169	+	0.0216551i
$473$	−4.53356	−	3.92835i	−0.208453	−	0.180626i
$474$	1.14989	+	0.337639i	0.0528164	+	0.0155083i
$475$	−8.58009	−	6.52501i	−0.393681	−	0.299388i
$476$	−1.57880	−	1.82204i	−0.0723643	−	0.0835129i
$477$	5.12268	−	2.33945i	0.234552	−	0.107116i
$478$	2.58268	+	8.79581i	0.118129	+	0.402311i
$479$	14.3577	−	31.4389i	0.656019	−	1.43648i	−0.230168	−	0.973151i	$-0.573927\pi$
$479$	14.3577	−	31.4389i	0.656019	−	1.43648i	0.886186	−	0.463329i	$-0.153345\pi$
$480$	1.18966	+	4.73585i	0.0543002	+	0.216161i
$481$	14.4418	−	9.28119i	0.658490	−	0.423186i
$482$		−	23.3161i		−	1.06202i
$483$	2.57937	+	2.94122i	0.117366	+	0.133830i
$484$	−18.9948			−0.863399
$485$	−5.72523	−	4.00733i	−0.259969	−	0.181964i
$486$	2.32584	−	16.1766i	0.105502	−	0.733785i
$487$	6.93232	+	3.16588i	0.314133	+	0.143460i	0.566242	−	0.824239i	$-0.308397\pi$
$487$	6.93232	+	3.16588i	0.314133	+	0.143460i	−0.252109	+	0.967699i	$0.581124\pi$
$488$	−0.909829	−	3.09859i	−0.0411860	−	0.140267i
$489$	−10.2994	−	22.5525i	−0.465754	−	1.01986i
$490$	6.91859	−	13.6917i	0.312550	−	0.618529i
$491$	−0.0699236	−	0.486329i	−0.00315561	−	0.0219477i	0.988183	−	0.153280i	$-0.0489836\pi$
$491$	−0.0699236	−	0.486329i	−0.00315561	−	0.0219477i	−0.991338	+	0.131332i	$0.958075\pi$
$492$	5.01155	−	17.0678i	0.225938	−	0.769475i
$493$	−31.4730	−	27.2715i	−1.41747	−	1.22825i
$494$	−8.76313	−	5.63172i	−0.394272	−	0.253383i
$495$	−21.3014	−	3.92660i	−0.957428	−	0.176487i
$496$	6.11086	−	7.05231i	0.274386	−	0.316658i
$497$	−1.18955	+	4.05122i	−0.0533584	+	0.181722i
$498$	6.75310	−	0.970949i	0.302614	−	0.0435093i
$499$	−17.0604	−	19.6888i	−0.763729	−	0.881391i	0.232094	−	0.972693i	$-0.425442\pi$
$499$	−17.0604	−	19.6888i	−0.763729	−	0.881391i	−0.995823	+	0.0913027i	$0.970897\pi$
$500$	−11.1770	+	0.272018i	−0.499852	+	0.0121650i
$501$	42.0346	−	12.3425i	1.87797	−	0.551421i
$502$	7.73089	+	3.53058i	0.345047	+	0.157578i
$503$	2.43086	+	0.349505i	0.108387	+	0.0155837i	0.196295	−	0.980545i	$-0.437109\pi$
$503$	2.43086	+	0.349505i	0.108387	+	0.0155837i	−0.0879080	+	0.996129i	$0.528018\pi$
$504$	0.555803	−	0.357193i	0.0247574	−	0.0159106i
$505$	−12.7167	+	5.21107i	−0.565886	+	0.231889i
$506$	25.9755	−	3.89255i	1.15475	−	0.173045i
$507$			22.5941i			1.00344i
$508$	3.19512	+	4.97171i	0.141761	+	0.220584i
$509$	0.855526	−	5.95031i	0.0379205	−	0.263743i	−0.962037	−	0.272918i	$-0.912011\pi$
$509$	0.855526	−	5.95031i	0.0379205	−	0.263743i	0.999958	+	0.00917468i	$0.00292043\pi$
$510$	−31.4911	−	1.24420i	−1.39445	−	0.0550942i
$511$	1.08645	−	0.319011i	0.0480619	−	0.0141122i
$512$	−0.909632	+	0.415415i	−0.0402004	+	0.0183589i
$513$	−4.38086	+	3.79604i	−0.193420	+	0.167599i
$514$	−3.26635	−	22.7180i	−0.144072	−	1.00205i
$515$	−3.39624	−	32.7570i	−0.149656	−	1.44345i
$516$	1.56635	−	1.80766i	0.0689546	−	0.0795778i
$517$	8.94994	−	13.9264i	0.393618	−	0.612481i
$518$	0.717513	−	1.11647i	0.0315257	−	0.0490550i
$519$	−19.1428	+	22.0919i	−0.840275	+	0.969729i
$520$	−10.7467	+	1.11421i	−0.471273	+	0.0488615i
$521$	3.73931	+	26.0074i	0.163822	+	1.13941i	0.891346	+	0.453324i	$0.149762\pi$
$521$	3.73931	+	26.0074i	0.163822	+	1.13941i	−0.727524	+	0.686083i	$0.759329\pi$
$522$	8.62488	−	7.47350i	0.377501	−	0.327106i
$523$	−1.87398	+	0.855816i	−0.0819433	+	0.0374222i	−0.455965	−	0.889998i	$-0.650706\pi$
$523$	−1.87398	+	0.855816i	−0.0819433	+	0.0374222i	0.374022	+	0.927420i	$0.377979\pi$
$524$	12.2014	−	3.58266i	0.533021	−	0.156509i
$525$	1.39631	+	3.83211i	0.0609401	+	0.167247i
$526$	−0.253824	+	1.76538i	−0.0110673	+	0.0769744i
$527$	32.5615	+	50.6666i	1.41840	+	2.20707i
$528$		−	11.9598i		−	0.520483i
$529$	−21.9897	+	6.74190i	−0.956074	+	0.293126i
$530$	−6.58800	+	2.69964i	−0.286164	+	0.117265i
$531$	0.832123	−	0.534773i	0.0361111	−	0.0232072i
$532$	−0.797105	−	0.114606i	−0.0345589	−	0.00496882i
$533$	35.8023	+	16.3504i	1.55077	+	0.708214i
$534$	−30.2600	+	8.88513i	−1.30948	+	0.384497i
$535$	14.5852	−	15.5471i	0.630574	−	0.672159i
$536$	3.97803	+	4.59089i	0.171825	+	0.198296i
$537$	0.497205	−	0.0714873i	0.0214560	−	0.00308490i
$538$	−7.69679	+	26.2129i	−0.331832	+	1.13012i
$539$	−24.6051	+	28.3958i	−1.05982	+	1.22309i
$540$	−1.08993	+	5.91275i	−0.0469030	+	0.254444i
$541$	5.42995	+	3.48962i	0.233452	+	0.150030i	0.652137	−	0.758101i	$-0.273873\pi$
$541$	5.42995	+	3.48962i	0.233452	+	0.150030i	−0.418685	+	0.908131i	$0.637509\pi$
$542$	12.2966	+	10.6551i	0.528186	+	0.457676i
$543$	9.08340	−	30.9352i	0.389806	−	1.32756i
$544$	−0.918527	−	6.38849i	−0.0393815	−	0.273904i
$545$	11.7577	+	5.94129i	0.503643	+	0.254497i
$546$	1.63731	+	3.58521i	0.0700704	+	0.153433i
$547$	−7.16300	−	24.3949i	−0.306268	−	1.04305i	−0.958514	−	0.285045i	$-0.907991\pi$
$547$	−7.16300	−	24.3949i	−0.306268	−	1.04305i	0.652247	−	0.758007i	$-0.273827\pi$
$548$	−4.27557	−	1.95259i	−0.182643	−	0.0834103i
$549$	−0.812886	+	5.65375i	−0.0346931	+	0.241296i
$550$	26.7131	+	6.02344i	1.13905	+	0.256840i
$551$	−13.9104			−0.592603
$552$	1.55207	+	10.3572i	0.0660605	+	0.440831i
$553$			0.204999i			0.00871746i
$554$	0.872123	−	0.560479i	0.0370530	−	0.0238125i
$555$	−4.22674	−	16.8260i	−0.179415	−	0.714225i
$556$	4.44550	−	9.73428i	0.188531	−	0.412825i
$557$	9.86536	+	33.5983i	0.418009	+	1.42361i	0.852403	+	0.522885i	$0.175144\pi$
$557$	9.86536	+	33.5983i	0.418009	+	1.42361i	−0.434394	+	0.900723i	$0.643038\pi$
$558$	−15.0133	+	6.85634i	−0.635563	+	0.290252i
$559$	3.46576	+	3.99970i	0.146586	+	0.169169i
$560$	−0.719947	+	0.423484i	−0.0304233	+	0.0178955i
$561$	74.0639	+	21.7471i	3.12698	+	0.918164i
$562$	19.7135	+	17.0818i	0.831564	+	0.720554i
$563$	−17.8264	+	27.7385i	−0.751295	+	1.16904i	0.229369	+	0.973340i	$0.426334\pi$
$563$	−17.8264	+	27.7385i	−0.751295	+	1.16904i	−0.980664	+	0.195699i	$0.937303\pi$
$564$	5.55285	+	3.56860i	0.233817	+	0.150265i
$565$	−16.1717	−	5.45060i	−0.680348	−	0.229309i
$566$	13.9452	+	4.09468i	0.586161	+	0.172112i
$567$	4.13286	−	0.594215i	0.173564	−	0.0249547i
$568$	−8.54249	+	7.40211i	−0.358435	+	0.310586i
$569$	10.5105	+	23.0147i	0.440621	+	0.964826i	0.991484	+	0.130230i	$0.0415715\pi$
$569$	10.5105	+	23.0147i	0.440621	+	0.964826i	−0.550863	+	0.834596i	$0.685701\pi$
$570$	−8.22177	+	6.57429i	−0.344372	+	0.275367i
$571$	−2.81701	+	6.16840i	−0.117888	+	0.258139i	−0.959373	−	0.282142i	$-0.908955\pi$
$571$	−2.81701	+	6.16840i	−0.117888	+	0.258139i	0.841484	+	0.540282i	$0.181682\pi$
$572$	26.1933	+	3.76603i	1.09520	+	0.157466i
$573$	−20.0089	−	31.1344i	−0.835883	−	1.30066i
$574$	3.04279			0.127004
$575$	−23.9152	−	1.74965i	−0.997334	−	0.0729654i
$576$	1.76871			0.0736963
$577$	4.30453	+	6.69798i	0.179200	+	0.278840i	0.919220	−	0.393744i	$-0.128820\pi$
$577$	4.30453	+	6.69798i	0.179200	+	0.278840i	−0.740020	+	0.672585i	$0.765184\pi$
$578$	24.4056	+	3.50899i	1.01514	+	0.145955i
$579$	3.52493	−	7.71853i	0.146491	−	0.320771i
$580$	−11.2684	+	9.01043i	−0.467894	+	0.374138i
$581$	0.484803	+	1.06157i	0.0201130	+	0.0440414i
$582$	−5.15784	+	4.46929i	−0.213799	+	0.185258i
$583$	17.2606	−	2.48169i	0.714859	−	0.102781i
$584$	2.90853	+	0.854021i	0.120356	+	0.0353397i
$585$	18.1087	+	6.10348i	0.748704	+	0.252348i
$586$	−23.5670	−	15.1456i	−0.973546	−	0.625660i
$587$	16.0448	−	24.9662i	0.662240	−	1.03047i	−0.333893	−	0.942611i	$-0.608362\pi$
$587$	16.0448	−	24.9662i	0.662240	−	1.03047i	0.996133	−	0.0878548i	$-0.0280012\pi$
$588$	−11.3222	−	9.81077i	−0.466921	−	0.404589i
$589$	19.3026	+	5.66776i	0.795351	+	0.233536i
$590$	−1.07787	+	0.634021i	−0.0443752	+	0.0261022i
$591$	−10.7618	−	12.4198i	−0.442682	−	0.510882i
$592$	3.23184	−	1.47593i	0.132828	−	0.0606603i
$593$	8.22674	+	28.0177i	0.337832	+	1.15055i	0.936826	+	0.349796i	$0.113749\pi$
$593$	8.22674	+	28.0177i	0.337832	+	1.15055i	−0.598994	+	0.800753i	$0.704433\pi$
$594$	6.11738	−	13.3952i	0.250999	−	0.549612i
$595$	−1.31341	−	5.22849i	−0.0538446	−	0.214347i
$596$	−15.3295	+	9.85165i	−0.627919	+	0.403539i
$597$			2.58845i			0.105938i
$598$	−23.1722	+	0.137827i	−0.947582	+	0.00563617i
$599$	31.4528			1.28513			0.642563	−	0.766233i	$-0.277871\pi$
$599$	31.4528			1.28513			0.642563	+	0.766233i	$0.277871\pi$
$600$	−2.40172	+	10.6513i	−0.0980498	+	0.434836i
$601$	−4.89337	+	34.0342i	−0.199605	+	1.38828i	0.605828	+	0.795595i	$0.292842\pi$
$601$	−4.89337	+	34.0342i	−0.199605	+	1.38828i	−0.805433	+	0.592687i	$0.798067\pi$
$602$	0.372170	+	0.169964i	0.0151685	+	0.00692724i
$603$	−3.02700	−	10.3090i	−0.123269	−	0.419816i
$604$	−6.69938	−	14.6696i	−0.272594	−	0.596897i
$605$	−37.9087	−	19.1557i	−1.54121	−	0.778790i
$606$	1.91006	+	13.2848i	0.0775909	+	0.539656i
$607$	0.204335	−	0.695901i	0.00829370	−	0.0282457i	−0.955242	−	0.295825i	$-0.904406\pi$
$607$	0.204335	−	0.695901i	0.00829370	−	0.0282457i	0.963536	+	0.267579i	$0.0862237\pi$
$608$	−1.62929	−	1.41179i	−0.0660766	−	0.0572557i
$609$	4.42775	+	2.84554i	0.179421	+	0.115307i
$610$	1.30906	−	7.10153i	0.0530023	−	0.287533i
$611$	−9.56420	+	11.0377i	−0.386926	+	0.446536i
$612$	−3.21614	+	10.9532i	−0.130005	+	0.442756i
$613$	−2.74961	+	0.395334i	−0.111056	+	0.0159674i	−0.197619	−	0.980279i	$-0.563321\pi$
$613$	−2.74961	+	0.395334i	−0.111056	+	0.0159674i	0.0865629	+	0.996246i	$0.472412\pi$
$614$	−14.1104	−	16.2843i	−0.569450	−	0.657181i
$615$	27.2141	−	29.0089i	1.09738	−	1.16975i
$616$	1.96292	−	0.576365i	0.0790882	−	0.0232224i
$617$	15.6368	+	7.14111i	0.629516	+	0.287490i	0.704510	−	0.709694i	$-0.251167\pi$
$617$	15.6368	+	7.14111i	0.629516	+	0.287490i	−0.0749946	+	0.997184i	$0.523894\pi$
$618$	−31.8346	−	4.57712i	−1.28057	−	0.184119i
$619$	−38.1368	+	24.5090i	−1.53285	+	0.985102i	−0.543520	+	0.839396i	$0.682909\pi$
$619$	−38.1368	+	24.5090i	−1.53285	+	0.985102i	−0.989328	+	0.145706i	$0.953455\pi$
$620$	19.3078	−	7.91195i	0.775418	−	0.317752i
$621$	−3.55931	+	12.3941i	−0.142830	+	0.497360i
$622$			5.16876i			0.207249i
$623$	−2.91657	−	4.53827i	−0.116850	−	0.181822i
$624$	−1.50163	+	10.4440i	−0.0601132	+	0.418096i
$625$	−22.5808	−	10.7288i	−0.903231	−	0.429154i
$626$	1.32427	−	0.388840i	0.0529284	−	0.0155412i
$627$	23.4536	−	10.7109i	0.936648	−	0.427753i
$628$	−2.35336	+	2.03920i	−0.0939095	+	0.0813730i
$629$	3.26344	+	22.6977i	0.130122	+	0.905017i
$630$	1.46946	−	0.152353i	0.0585446	−	0.00606989i
$631$	5.81601	−	6.71203i	0.231532	−	0.267202i	−0.628081	−	0.778148i	$-0.716159\pi$
$631$	5.81601	−	6.71203i	0.231532	−	0.267202i	0.859613	+	0.510946i	$0.170705\pi$
$632$	−0.296705	+	0.461681i	−0.0118023	+	0.0183647i
$633$	−4.30151	+	6.69328i	−0.170970	+	0.266034i
$634$	10.5603	−	12.1873i	0.419405	−	0.484019i
$635$	1.36281	+	13.1444i	0.0540815	+	0.521621i
$636$	0.989523	+	6.88228i	0.0392371	+	0.272900i
$637$	25.0520	−	21.7077i	0.992597	−	0.860090i
$638$	32.1445	−	14.6799i	1.27261	−	0.581183i
$639$	19.1825	−	5.63249i	0.758848	−	0.222818i
$640$	−2.23432	−	0.0882773i	−0.0883194	−	0.00348947i
$641$	6.68039	−	46.4631i	0.263860	−	1.83518i	−0.239247	−	0.970959i	$-0.576900\pi$
$641$	6.68039	−	46.4631i	0.263860	−	1.83518i	0.503106	−	0.864225i	$-0.332190\pi$
$642$	−11.2555	−	17.5138i	−0.444217	−	0.691216i
$643$			20.4313i			0.805731i	0.915259	+	0.402866i	$0.131986\pi$
$643$			20.4313i			0.805731i	−0.915259	+	0.402866i	$0.868014\pi$
$644$	−1.62509	+	0.753869i	−0.0640376	+	0.0297066i
$645$	4.94900	−	2.02801i	0.194867	−	0.0798527i
$646$	11.7055	−	7.52266i	0.460547	−	0.295975i
$647$	−31.3128	−	4.50211i	−1.23103	−	0.176996i	−0.504065	−	0.863666i	$-0.668163\pi$
$647$	−31.3128	−	4.50211i	−1.23103	−	0.176996i	−0.726970	+	0.686670i	$0.759072\pi$
$648$	10.1677	+	4.64342i	0.399424	+	0.182411i
$649$	2.93879	−	0.862907i	0.115358	−	0.0338720i
$650$	−22.5713	−	8.61405i	−0.885317	−	0.337871i
$651$	−4.98471	−	5.75267i	−0.195366	−	0.225465i
$652$	11.2379	−	1.61577i	0.440110	−	0.0632783i
$653$	−0.00274616	+	0.00935256i	−0.000107466	+	0.000365994i	−0.959547	−	0.281550i	$-0.909152\pi$
$653$	−0.00274616	+	0.00935256i	−0.000107466	+	0.000365994i	0.959439	+	0.281916i	$0.0909698\pi$
$654$	8.42493	−	9.72289i	0.329441	−	0.380195i
$655$	27.9639	+	5.15472i	1.09264	+	0.201411i
$656$	6.85270	+	4.40396i	0.267553	+	0.171946i
$657$	−4.05197	−	3.51105i	−0.158082	−	0.136979i
$658$	−0.318099	+	1.08335i	−0.0124008	+	0.0422333i
$659$	0.0895145	+	0.622587i	0.00348699	+	0.0242526i	0.991491	−	0.130178i	$-0.0415548\pi$
$659$	0.0895145	+	0.622587i	0.00348699	+	0.0242526i	−0.988004	+	0.154430i	$0.950646\pi$
$660$	12.0611	−	23.8686i	0.469478	−	0.929085i
$661$	7.38866	+	16.1789i	0.287385	+	0.629286i	0.997174	−	0.0751287i	$-0.0239367\pi$
$661$	7.38866	+	16.1789i	0.287385	+	0.629286i	−0.709788	+	0.704415i	$0.751209\pi$
$662$	3.27910	+	11.1676i	0.127446	+	0.434041i
$663$	−61.9468	−	28.2902i	−2.40581	−	1.09870i
$664$	−0.444627	+	3.09245i	−0.0172549	+	0.120010i
$665$	−1.47524	−	1.03258i	−0.0572073	−	0.0400418i
$666$	−6.28406			−0.243502
$667$	−25.9321	+	16.8843i	−1.00410	+	0.653764i
$668$			20.0616i			0.776205i
$669$	−32.0765	+	20.6143i	−1.24015	+	0.796995i
$670$	3.30933	+	13.1740i	0.127851	+	0.508954i
$671$	−7.34730	+	16.0883i	−0.283639	+	0.621084i
$672$	0.229813	+	0.782672i	0.00886524	+	0.0301922i
$673$	38.3097	−	17.4954i	1.47673	−	0.674400i	0.495742	−	0.868470i	$-0.334896\pi$
$673$	38.3097	−	17.4954i	1.47673	−	0.674400i	0.980988	+	0.194070i	$0.0621690\pi$
$674$	19.8300	+	22.8850i	0.763822	+	0.881497i
$675$	−8.13806	+	10.7012i	−0.313234	+	0.411888i
$676$	−9.92742	−	2.91495i	−0.381824	−	0.112114i
$677$	−24.7596	−	21.4543i	−0.951590	−	0.824557i	0.0329967	−	0.999455i	$-0.489495\pi$
$677$	−24.7596	−	21.4543i	−0.951590	−	0.824557i	−0.984587	+	0.174898i	$0.944040\pi$
$678$	−9.01040	+	14.0205i	−0.346042	+	0.538452i
$679$	−0.982096	−	0.631155i	−0.0376894	−	0.0242215i
$680$	4.60947	−	13.6761i	0.176765	−	0.524454i
$681$	41.7009	+	12.2445i	1.59798	+	0.469210i
$682$	−50.5863	+	7.27321i	−1.93705	+	0.278506i
$683$	−23.2285	+	20.1276i	−0.888812	+	0.770160i	−0.974081	−	0.226198i	$-0.927370\pi$
$683$	−23.2285	+	20.1276i	−0.888812	+	0.770160i	0.0852691	+	0.996358i	$0.472825\pi$
$684$	1.58402	+	3.46852i	0.0605665	+	0.132622i
$685$	−6.56380	−	8.20864i	−0.250790	−	0.313636i
$686$	2.15079	−	4.70957i	0.0821174	−	0.179812i
$687$	−37.8993	−	5.44909i	−1.44595	−	0.207896i
$688$	0.592171	+	0.921437i	0.0225763	+	0.0351294i
$689$	−15.3846			−0.586107
$690$	−7.34740	+	22.2355i	−0.279711	+	0.846491i
$691$	47.2507			1.79750			0.898751	−	0.438459i	$-0.144476\pi$
$691$	47.2507			1.79750			0.898751	+	0.438459i	$0.144476\pi$
$692$	−7.23710	−	11.2611i	−0.275113	−	0.428084i
$693$	−3.58157	−	0.514952i	−0.136053	−	0.0195614i
$694$	7.75369	−	16.9782i	0.294326	−	0.644484i
$695$	18.6888	−	14.9440i	0.708907	−	0.566856i
$696$	5.85330	+	12.8169i	0.221869	+	0.485825i
$697$	−39.7333	+	34.4291i	−1.50500	+	1.30409i
$698$	20.1656	−	2.89938i	0.763280	−	0.109743i
$699$	41.5703	+	12.2061i	1.57233	+	0.461679i
$700$	−1.86390	+	0.119119i	−0.0704488	+	0.00450226i
$701$	−1.42163	−	0.913629i	−0.0536944	−	0.0345073i	0.513518	−	0.858079i	$-0.328342\pi$
$701$	−1.42163	−	0.913629i	−0.0536944	−	0.0345073i	−0.567213	+	0.823571i	$0.691978\pi$
$702$	−7.02394	+	10.9295i	−0.265101	+	0.412506i
$703$	5.78872	+	5.01596i	0.218326	+	0.189180i
$704$	5.25490	+	1.54298i	0.198052	+	0.0581532i
$705$	7.48322	+	12.7219i	0.281834	+	0.479134i
$706$	20.9281	+	24.1523i	0.787639	+	0.908984i
$707$	−2.08833	+	0.953709i	−0.0785398	+	0.0358679i
$708$	0.344066	+	1.17178i	0.0129308	+	0.0440382i
$709$	1.46496	−	3.20781i	0.0550176	−	0.120472i	−0.880127	−	0.474739i	$-0.842542\pi$
$709$	1.46496	−	3.20781i	0.0550176	−	0.120472i	0.935144	+	0.354267i	$0.115270\pi$
$710$	−24.5134	+	6.15784i	−0.919972	+	0.231100i
$711$	0.816580	−	0.524784i	0.0306242	−	0.0196810i
$712$		−	14.4420i		−	0.541236i
$713$	42.8640	−	12.8634i	1.60527	−	0.481739i
$714$	−5.26477			−0.197029
$715$	48.4772	+	33.9313i	1.81294	+	1.26896i
$716$	−0.0327362	+	0.227685i	−0.00122341	+	0.00850900i
$717$	18.2096	+	8.31604i	0.680049	+	0.310568i
$718$	5.09205	+	17.3419i	0.190034	+	0.647195i
$719$	−7.94653	−	17.4005i	−0.296356	−	0.648928i	0.701618	−	0.712553i	$-0.252461\pi$
$719$	−7.94653	−	17.4005i	−0.296356	−	0.648928i	−0.997974	+	0.0636247i	$0.979734\pi$
$720$	3.52989	+	1.78369i	0.131551	+	0.0664744i
$721$	−0.782941	−	5.44548i	−0.0291583	−	0.202800i
$722$	−4.04350	+	13.7709i	−0.150483	+	0.512499i
$723$	−38.4800	−	33.3431i	−1.43109	−	1.24004i
$724$	12.4205	+	7.98215i	0.461603	+	0.296654i
$725$	−31.5755	+	6.61864i	−1.17269	+	0.245810i
$726$	−27.1634	+	31.3482i	−1.00813	+	1.16344i
$727$	3.39073	−	11.5478i	0.125755	−	0.428283i	−0.872414	−	0.488768i	$-0.837446\pi$
$727$	3.39073	−	11.5478i	0.125755	−	0.428283i	0.998169	+	0.0604847i	$0.0192647\pi$
$728$	−1.78651	+	0.256861i	−0.0662125	+	0.00951991i
$729$	−1.41142	−	1.62886i	−0.0522747	−	0.0603282i
$730$	4.94342	+	4.63758i	0.182964	+	0.171644i
$731$	−6.78300	+	1.99167i	−0.250878	+	0.0736645i
$732$	−6.41489	−	2.92958i	−0.237101	−	0.108280i
$733$	5.12744	+	0.737214i	0.189386	+	0.0272296i	0.236355	−	0.971667i	$-0.424047\pi$
$733$	5.12744	+	0.737214i	0.189386	+	0.0272296i	−0.0469690	+	0.998896i	$0.514956\pi$
$734$	−28.1450	+	18.0877i	−1.03885	+	0.667628i
$735$	−12.7024	−	30.9979i	−0.468534	−	1.14338i
$736$	−4.75099	−	0.654271i	−0.175124	−	0.0241168i
$737$		−	33.2691i		−	1.22548i
$738$	−7.78933	−	12.1204i	−0.286729	−	0.446159i
$739$	−3.76944	+	26.2170i	−0.138661	+	0.964410i	0.795091	+	0.606490i	$0.207423\pi$
$739$	−3.76944	+	26.2170i	−0.138661	+	0.964410i	−0.933752	+	0.357920i	$0.883486\pi$
$740$	7.93834	+	0.313641i	0.291819	+	0.0115297i
$741$	−21.8260	+	6.40870i	−0.801799	+	0.235429i
$742$	−1.08188	+	0.494077i	−0.0397170	+	0.0181381i
$743$	35.0534	−	30.3740i	1.28599	−	1.11431i	0.298873	−	0.954293i	$-0.403389\pi$
$743$	35.0534	−	30.3740i	1.28599	−	1.11431i	0.987114	−	0.160020i	$-0.0511560\pi$
$744$	−2.90004	−	20.1702i	−0.106321	−	0.739476i
$745$	−40.5288	+	4.20201i	−1.48486	+	0.153950i
$746$	−19.8275	+	22.8821i	−0.725936	+	0.837775i
$747$	2.98752	−	4.64868i	0.109308	−	0.170086i
$748$	−19.1106	+	29.7366i	−0.698751	+	1.08728i
$749$	2.33206	−	2.69134i	0.0852117	−	0.0983395i
$750$	−15.5347	+	18.8351i	−0.567248	+	0.687761i
$751$	3.28497	+	22.8475i	0.119870	+	0.833717i	0.957697	+	0.287780i	$0.0929171\pi$
$751$	3.28497	+	22.8475i	0.119870	+	0.833717i	−0.837826	+	0.545937i	$0.816174\pi$
$752$	−2.28437	+	1.97942i	−0.0833024	+	0.0721819i
$753$	16.8822	−	7.70986i	0.615223	−	0.280963i
$754$	−29.9138	+	8.78347i	−1.08940	+	0.319875i
$755$	1.42364	−	36.0328i	0.0518117	−	1.31137i
$756$	−0.142938	+	0.994157i	−0.00519861	+	0.0361571i
$757$	5.15483	+	8.02108i	0.187356	+	0.291531i	0.922207	−	0.386698i	$-0.126384\pi$
$757$	5.15483	+	8.02108i	0.187356	+	0.291531i	−0.734851	+	0.678229i	$0.762748\pi$
$758$		−	5.43678i		−	0.197473i
$759$	30.7220	−	48.4354i	1.11514	−	1.75810i
$760$	−1.82790	−	4.46066i	−0.0663048	−	0.161805i
$761$	−5.07810	+	3.26350i	−0.184081	+	0.118302i	−0.629436	−	0.777053i	$-0.716714\pi$
$761$	−5.07810	+	3.26350i	−0.184081	+	0.118302i	0.445355	+	0.895354i	$0.353078\pi$
$762$	12.7743	+	1.83666i	0.462763	+	0.0665352i
$763$	2.00180	+	0.914191i	0.0724700	+	0.0330959i
$764$	16.2613	−	4.77475i	0.588313	−	0.172744i
$765$	−17.4646	+	18.6163i	−0.631433	+	0.673075i
$766$	−11.6212	−	13.4115i	−0.419890	−	0.484579i
$767$	−2.67468	+	0.384561i	−0.0965771	+	0.0138857i
$768$	−0.615230	+	2.09528i	−0.0222002	+	0.0756069i
$769$	15.2893	−	17.6448i	0.551345	−	0.636286i	−0.409851	−	0.912153i	$-0.634419\pi$
$769$	15.2893	−	17.6448i	0.551345	−	0.636286i	0.961196	+	0.275866i	$0.0889647\pi$
$770$	4.49872	+	0.829272i	0.162123	+	0.0298849i
$771$	−42.1638	−	27.0970i	−1.51849	−	0.975876i
$772$	2.93661	+	2.54459i	0.105691	+	0.0915817i
$773$	−12.5851	+	42.8610i	−0.452656	+	1.54160i	0.345066	+	0.938578i	$0.387856\pi$
$773$	−12.5851	+	42.8610i	−0.452656	+	1.54160i	−0.797722	+	0.603025i	$0.793962\pi$
$774$	−0.275706	−	1.91757i	−0.00991003	−	0.0689258i
$775$	46.5123	+	3.68111i	1.67077	+	0.132229i
$776$	−1.29829	−	2.84286i	−0.0466059	−	0.102053i
$777$	−0.816504	−	2.78076i	−0.0292919	−	0.0997591i
$778$	7.88769	+	3.60219i	0.282788	+	0.129145i
$779$	−2.49923	+	17.3825i	−0.0895442	+	0.622793i
$780$	−13.5294	+	19.3293i	−0.484429	+	0.692098i
$781$	61.9055			2.21515
$782$	12.6907	−	28.2320i	0.453820	−	1.00957i
$783$			17.3492i			0.620009i
$784$	5.77139	−	3.70905i	0.206121	−	0.132466i
$785$	−6.75319	+	1.69642i	−0.241032	+	0.0605478i
$786$	11.5359	−	25.2600i	0.411471	−	0.900996i
$787$	0.667647	+	2.27380i	0.0237991	+	0.0810522i	0.970536	−	0.240955i	$-0.0774606\pi$
$787$	0.667647	+	2.27380i	0.0237991	+	0.0810522i	−0.946737	+	0.322007i	$0.895642\pi$
$788$	6.84545	−	3.12621i	0.243859	−	0.111367i
$789$	2.55054	+	2.94348i	0.0908016	+	0.104791i
$790$	−1.05774	+	0.622178i	−0.0376326	+	0.0221361i
$791$	−2.73536	−	0.803173i	−0.0972581	−	0.0285576i
$792$	−7.32078	−	6.34349i	−0.260133	−	0.225406i
$793$	8.43612	−	13.1269i	0.299576	−	0.466149i
$794$	−21.0392	−	13.5210i	−0.746652	−	0.479844i
$795$	−4.96576	+	14.7332i	−0.176117	+	0.522531i
$796$	−1.13731	−	0.333945i	−0.0403110	−	0.0118364i
$797$	23.8925	−	3.43522i	0.846314	−	0.121682i	0.294503	−	0.955651i	$-0.404846\pi$
$797$	23.8925	−	3.43522i	0.846314	−	0.121682i	0.551811	+	0.833969i	$0.313937\pi$
$798$	−1.32904	+	1.15162i	−0.0470474	+	0.0407668i
$799$	−8.10424	−	17.7458i	−0.286707	−	0.627802i
$800$	−4.37011	−	2.42943i	−0.154507	−	0.0858934i
$801$	−10.6112	+	23.2353i	−0.374929	+	0.820980i
$802$	7.12734	+	1.02476i	0.251675	+	0.0361854i
$803$	−8.97560	−	13.9663i	−0.316742	−	0.492860i
$804$	13.2654			0.467834
$805$	−4.00352	−	0.134333i	−0.141106	−	0.00473462i
$806$	45.0884			1.58817
$807$	32.2539	+	50.1880i	1.13539	+	1.76670i
$808$	−6.08349	−	0.874674i	−0.214017	−	0.0307709i
$809$	−19.2231	+	42.0927i	−0.675848	+	1.47990i	0.191135	+	0.981564i	$0.438783\pi$
$809$	−19.2231	+	42.0927i	−0.675848	+	1.47990i	−0.866983	+	0.498337i	$0.833944\pi$
$810$	15.6093	+	19.5209i	0.548455	+	0.685894i
$811$	−2.78537	−	6.09912i	−0.0978077	−	0.214169i	0.854403	−	0.519611i	$-0.173923\pi$
$811$	−2.78537	−	6.09912i	−0.0978077	−	0.214169i	−0.952211	+	0.305442i	$0.901196\pi$
$812$	−1.82152	+	1.57835i	−0.0639228	+	0.0553894i
$813$	35.1695	−	5.05661i	1.23345	−	0.177343i
$814$	−18.6702	−	5.48205i	−0.654389	−	0.192146i
$815$	24.0574	+	8.10846i	0.842694	+	0.284027i
$816$	−11.8568	−	7.61993i	−0.415072	−	0.266751i
$817$	−1.27664	+	1.98649i	−0.0446640	+	0.0694985i
$818$	−5.63093	−	4.87923i	−0.196881	−	0.170598i
$819$	3.06300	+	0.899378i	0.107030	+	0.0314268i
$820$	9.23494	+	15.6999i	0.322498	+	0.548265i
$821$	−22.6840	−	26.1787i	−0.791677	−	0.913644i	0.206217	−	0.978506i	$-0.433885\pi$
$821$	−22.6840	−	26.1787i	−0.791677	−	0.913644i	−0.997894	+	0.0648621i	$0.979339\pi$
$822$	−9.33671	+	4.26393i	−0.325655	+	0.148722i
$823$	−2.25147	−	7.66780i	−0.0784813	−	0.267283i	0.910900	−	0.412628i	$-0.135389\pi$
$823$	−2.25147	−	7.66780i	−0.0784813	−	0.267283i	−0.989381	+	0.145345i	$0.953571\pi$
$824$	6.11820	−	13.3970i	0.213138	−	0.466706i
$825$	48.1417	−	35.4723i	1.67608	−	1.23499i
$826$	−0.175739	+	0.112941i	−0.00611474	+	0.00392971i
$827$		−	17.7674i		−	0.617834i	−0.951089	−	0.308917i	$-0.900034\pi$
$827$		−	17.7674i		−	0.617834i	0.951089	−	0.308917i	$-0.0999665\pi$
$828$	7.16303	+	4.54343i	0.248933	+	0.157895i
$829$	−51.2244			−1.77910			−0.889549	−	0.456840i	$-0.848981\pi$
$829$	−51.2244			−1.77910			−0.889549	+	0.456840i	$0.848981\pi$
$830$	−4.00601	+	5.72334i	−0.139051	+	0.198660i
$831$	0.322182	−	2.24083i	0.0111764	−	0.0777334i
$832$	−4.39518	−	2.00721i	−0.152376	−	0.0695876i
$833$	12.4748	+	42.4851i	0.432225	+	1.47202i
$834$	−9.70780	−	21.2571i	−0.336154	−	0.736074i
$835$	−20.2315	+	40.0377i	−0.700141	+	1.38556i
$836$	1.68033	+	11.6869i	0.0581154	+	0.404201i
$837$	7.06889	−	24.0744i	0.244337	−	0.832134i
$838$	−9.28328	−	8.04401i	−0.320686	−	0.277876i
$839$	14.3814	+	9.24235i	0.496500	+	0.319081i	0.764815	−	0.644250i	$-0.222830\pi$
$839$	14.3814	+	9.24235i	0.496500	+	0.319081i	−0.268315	+	0.963331i	$0.586467\pi$
$840$	−0.330655	+	1.79377i	−0.0114087	+	0.0618910i
$841$	−8.27277	+	9.54728i	−0.285268	+	0.329217i
$842$	4.40614	−	15.0059i	0.151846	−	0.517139i
$843$	56.3824	−	8.10656i	1.94191	−	0.279205i
$844$	−2.38595	−	2.75353i	−0.0821277	−	0.0947804i
$845$	−16.8729	−	15.8290i	−0.580446	−	0.544535i
$846$	5.12964	−	1.50620i	0.176361	−	0.0517842i
$847$	−6.45412	−	2.94750i	−0.221766	−	0.101277i
$848$	−3.15161	−	0.453133i	−0.108227	−	0.0155606i
$849$	26.6999	−	17.1590i	0.916340	−	0.588896i
$850$	22.9913	−	22.6454i	0.788594	−	0.776731i
$851$	16.8798	+	2.32456i	0.578633	+	0.0796850i
$852$			24.6835i			0.845643i
$853$	11.4285	+	17.7830i	0.391303	+	0.608879i	0.979886	−	0.199557i	$-0.0639504\pi$
$853$	11.4285	+	17.7830i	0.391303	+	0.608879i	−0.588583	+	0.808437i	$0.700314\pi$
$854$	0.171676	−	1.19404i	0.00587465	−	0.0408591i
$855$	−0.336610	+	8.51970i	−0.0115118	+	0.291368i
$856$	9.14735	−	2.68591i	0.312650	−	0.0918024i
$857$	−43.3671	+	19.8051i	−1.48139	+	0.676528i	−0.981832	−	0.189752i	$-0.939232\pi$
$857$	−43.3671	+	19.8051i	−1.48139	+	0.676528i	−0.499558	+	0.866280i	$0.666504\pi$
$858$	43.6729	−	37.8428i	1.49097	−	1.29193i
$859$	−0.882625	−	6.13879i	−0.0301148	−	0.209453i	0.969208	−	0.246243i	$-0.0791960\pi$
$859$	−0.882625	−	6.13879i	−0.0301148	−	0.209453i	−0.999323	+	0.0367896i	$0.988287\pi$
$860$	0.252578	+	2.43614i	0.00861284	+	0.0830716i
$861$	4.35132	−	5.02170i	0.148293	−	0.171139i
$862$	−9.03087	+	14.0523i	−0.307593	+	0.478624i
$863$	−6.81093	+	10.5980i	−0.231847	+	0.360761i	−0.937611	−	0.347686i	$-0.886967\pi$
$863$	−6.81093	+	10.5980i	−0.231847	+	0.360761i	0.705764	+	0.708447i	$0.250604\pi$
$864$	−1.76080	+	2.03207i	−0.0599036	+	0.0691324i
$865$	−3.08683	−	29.7727i	−0.104955	−	1.01230i
$866$	−0.223065	−	1.55145i	−0.00758006	−	0.0527205i
$867$	40.6921	−	35.2599i	1.38198	−	1.19749i
$868$	3.17071	−	1.44801i	0.107621	−	0.0491488i
$869$	2.88390	−	0.846789i	0.0978295	−	0.0287253i
$870$	−1.24385	+	31.4822i	−0.0421704	+	1.06735i
$871$	−4.17715	+	29.0527i	−0.141537	+	0.984414i
$872$	3.18512	+	4.95614i	0.107862	+	0.167836i
$873$			5.52772i			0.187085i
$874$	−2.97183	−	9.90285i	−0.100524	−	0.334969i
$875$	−3.83999	−	1.64196i	−0.129815	−	0.0555084i
$876$	5.56877	−	3.57883i	0.188151	−	0.120917i
$877$	−6.53730	−	0.939922i	−0.220749	−	0.0317389i	0.0310528	−	0.999518i	$-0.490114\pi$
$877$	−6.53730	−	0.939922i	−0.220749	−	0.0317389i	−0.251802	+	0.967779i	$0.581023\pi$
$878$	23.8282	+	10.8820i	0.804162	+	0.367248i
$879$	−58.6976	+	17.2352i	−1.97982	+	0.581328i
$880$	8.93137	+	8.37881i	0.301077	+	0.282449i
$881$	−24.6736	−	28.4749i	−0.831275	−	0.959343i	0.168377	−	0.985723i	$-0.446148\pi$
$881$	−24.6736	−	28.4749i	−0.831275	−	0.959343i	−0.999652	+	0.0263799i	$0.991602\pi$
$882$	−12.0107	+	1.72687i	−0.404420	+	0.0581469i
$883$	14.0066	−	47.7021i	0.471359	−	1.60530i	−0.290037	−	0.957015i	$-0.593668\pi$
$883$	14.0066	−	47.7021i	0.471359	−	1.60530i	0.761396	−	0.648287i	$-0.224514\pi$
$884$	20.4222	−	23.5684i	0.686872	−	0.792692i
$885$	−0.495041	+	2.68555i	−0.0166406	+	0.0902738i
$886$	−24.2056	−	15.5560i	−0.813202	−	0.522613i
$887$	−39.6841	−	34.3865i	−1.33246	−	1.15459i	−0.975384	−	0.220511i	$-0.929227\pi$
$887$	−39.6841	−	34.3865i	−1.33246	−	1.15459i	−0.357078	−	0.934074i	$-0.616227\pi$
$888$	2.18585	−	7.44433i	0.0733524	−	0.249815i
$889$	0.314171	+	2.18511i	0.0105370	+	0.0732861i
$890$	14.5643	−	28.8224i	0.488197	−	0.966130i
$891$	−25.4309	−	55.6858i	−0.851966	−	1.86555i
$892$	−4.91922	−	16.7533i	−0.164708	−	0.560943i
$893$	−5.92755	−	2.70702i	−0.198358	−	0.0905871i
$894$	−5.66305	+	39.3874i	−0.189401	+	1.31731i
$895$	−0.294947	+	0.421387i	−0.00985900	+	0.0140854i
$896$	−0.373540			−0.0124791
$897$	−32.9098	+	38.4396i	−1.09883	+	1.28346i
$898$			7.82077i			0.260982i
$899$	50.6522	−	32.5522i	1.68935	−	1.08568i
$900$	5.24594	+	7.11959i	0.174865	+	0.237320i
$901$	8.53688	−	18.6932i	0.284405	−	0.622759i
$902$	−12.5688	−	42.8055i	−0.418496	−	1.42527i
$903$	0.812722	−	0.371158i	0.0270457	−	0.0123514i
$904$	−4.99786	−	5.76783i	−0.166226	−	0.191835i
$905$	16.7383	+	28.4560i	0.556399	+	0.945909i
$906$	−33.7905	−	9.92179i	−1.12261	−	0.329629i
$907$	−16.7289	−	14.4957i	−0.555475	−	0.481322i	0.331299	−	0.943526i	$-0.392513\pi$
$907$	−16.7289	−	14.4957i	−0.555475	−	0.481322i	−0.886774	+	0.462204i	$0.847059\pi$
$908$	−10.7600	+	16.7429i	−0.357083	+	0.555632i
$909$	9.14492	+	5.87708i	0.303318	+	0.194931i
$910$	−3.82445	−	1.28902i	−0.126779	−	0.0427305i
$911$	−14.8197	−	4.35147i	−0.491000	−	0.144171i	0.0268545	−	0.999639i	$-0.491451\pi$
$911$	−14.8197	−	4.35147i	−0.491000	−	0.144171i	−0.517854	+	0.855469i	$0.673269\pi$
$912$	−4.65992	+	0.669996i	−0.154305	+	0.0221858i
$913$	12.9314	−	11.2051i	0.427968	−	0.370836i
$914$	4.44815	+	9.74009i	0.147132	+	0.322173i
$915$	−9.84806	−	12.3159i	−0.325567	−	0.407152i
$916$	7.28376	−	15.9492i	0.240662	−	0.526977i
$917$	4.70178	+	0.676014i	0.155266	+	0.0223239i
$918$	−9.38234	−	14.5992i	−0.309663	−	0.481846i
$919$	30.1785			0.995495			0.497748	−	0.867322i	$-0.334161\pi$
$919$	30.1785			0.995495			0.497748	+	0.867322i	$0.334161\pi$
$920$	−8.82194	−	6.09700i	−0.290851	−	0.201012i
$921$	−47.0535			−1.55046
$922$	4.49424	+	6.99317i	0.148010	+	0.230308i
$923$	−54.0598	−	7.77263i	−1.77940	−	0.255839i
$924$	1.85585	−	4.06374i	0.0610530	−	0.133687i
$925$	15.5266	+	8.63154i	0.510511	+	0.283803i
$926$	0.202248	+	0.442861i	0.00664627	+	0.0145533i
$927$	−19.6868	+	17.0588i	−0.646601	+	0.560283i
$928$	−6.38668	+	0.918266i	−0.209653	+	0.0301435i
$929$	−12.9840	−	3.81246i	−0.425993	−	0.125083i	0.0617068	−	0.998094i	$-0.480346\pi$
$929$	−12.9840	−	3.81246i	−0.425993	−	0.125083i	−0.487699	+	0.873012i	$0.662164\pi$
$930$	14.5534	−	43.1792i	0.477224	−	1.41590i
$931$	12.4423	+	7.99620i	0.407781	+	0.262065i
$932$	−10.7263	+	16.6904i	−0.351351	+	0.546713i
$933$	8.53032	+	7.39156i	0.279270	+	0.241989i
$934$	22.4737	+	6.59888i	0.735363	+	0.215922i
$935$	−68.1282	+	40.0741i	−2.22803	+	1.31056i
$936$	5.59650	+	6.45871i	0.182927	+	0.211110i
$937$	−5.63296	+	2.57248i	−0.184021	+	0.0840394i	−0.505295	−	0.862947i	$-0.668616\pi$
$937$	−5.63296	+	2.57248i	−0.184021	+	0.0840394i	0.321274	+	0.946986i	$0.395889\pi$
$938$	0.639283	+	2.17720i	0.0208733	+	0.0710881i
$939$	1.25203	−	2.74157i	0.0408586	−	0.0894679i
$940$	−6.55520	+	1.64668i	−0.213807	+	0.0537089i
$941$	−19.1661	+	12.3173i	−0.624796	+	0.401532i	−0.814380	−	0.580333i	$-0.802923\pi$
$941$	−19.1661	+	12.3173i	−0.624796	+	0.401532i	0.189584	+	0.981865i	$0.439286\pi$
$942$			6.80005i			0.221557i
$943$	16.4397	+	35.4385i	0.535349	+	1.15404i
$944$	−0.559247			−0.0182020
$945$	−1.28785	+	1.83993i	−0.0418937	+	0.0598530i
$946$	0.853712	−	5.93770i	0.0277566	−	0.193051i
$947$	−2.35318	−	1.07466i	−0.0764682	−	0.0349219i	0.376814	−	0.926289i	$-0.377020\pi$
$947$	−2.35318	−	1.07466i	−0.0764682	−	0.0349219i	−0.453282	+	0.891367i	$0.649747\pi$
$948$	0.337639	+	1.14989i	0.0109660	+	0.0373468i
$949$	6.08450	+	13.3232i	0.197511	+	0.432489i
$950$	0.850446	−	10.7457i	0.0275921	−	0.348637i
$951$	−5.01164	−	34.8567i	−0.162513	−	1.13031i
$952$	0.679229	−	2.31324i	0.0220139	−	0.0749726i
$953$	−10.0785	−	8.73311i	−0.326476	−	0.282893i	0.476164	−	0.879356i	$-0.342027\pi$
$953$	−10.0785	−	8.73311i	−0.326476	−	0.282893i	−0.802641	+	0.596463i	$0.796572\pi$
$954$	4.73760	+	3.04467i	0.153386	+	0.0985749i
$955$	37.2685	+	6.86990i	1.20598	+	0.222305i
$956$	−6.00320	+	6.92806i	−0.194157	+	0.224070i
$957$	21.7409	−	74.0429i	0.702785	−	2.39347i
$958$	34.2104	−	4.91872i	1.10529	−	0.158917i
$959$	−1.14978	−	1.32692i	−0.0371283	−	0.0428483i
$960$	−3.34087	+	3.56120i	−0.107826	+	0.114937i
$961$	−53.8061	+	15.7989i	−1.73568	+	0.509642i
$962$	15.6157	+	7.13143i	0.503469	+	0.229927i
$963$	−16.6904	−	2.39972i	−0.537841	−	0.0773299i
$964$	19.6148	−	12.6057i	0.631750	−	0.406001i
$965$	3.29457	+	8.03982i	0.106056	+	0.258811i
$966$	−1.07980	+	3.76005i	−0.0347420	+	0.120978i
$967$		−	17.0664i		−	0.548819i	−0.961613	−	0.274410i	$-0.911518\pi$
$967$		−	17.0664i		−	0.548819i	0.961613	−	0.274410i	$-0.0884824\pi$
$968$	−10.2693	−	15.9794i	−0.330069	−	0.513598i
$969$	4.32428	−	30.0760i	0.138916	−	0.966181i
$970$	0.275892	−	6.98290i	0.00885834	−	0.224207i
$971$	7.13353	−	2.09459i	0.228926	−	0.0672187i	−0.165258	−	0.986250i	$-0.552846\pi$
$971$	7.13353	−	2.09459i	0.228926	−	0.0672187i	0.394184	+	0.919032i	$0.371027\pi$
$972$	14.8661	−	6.78910i	0.476829	−	0.217760i
$973$	3.02102	−	2.61773i	0.0968494	−	0.0839205i
$974$	1.08458	+	7.54344i	0.0347523	+	0.241707i
$975$	−46.4942	+	24.9322i	−1.48900	+	0.798469i
$976$	2.11481	−	2.44062i	0.0676935	−	0.0781225i
$977$	−24.8760	+	38.7078i	−0.795853	+	1.23837i	0.171562	+	0.985173i	$0.445119\pi$
$977$	−24.8760	+	38.7078i	−0.795853	+	1.23837i	−0.967415	+	0.253198i	$0.918518\pi$
$978$	13.4041	−	20.8572i	0.428616	−	0.666939i
$979$	−51.7962	+	59.7760i	−1.65541	+	1.91045i
$980$	15.2587	−	1.58202i	0.487421	−	0.0505356i
$981$	−1.48294	−	10.3141i	−0.0473467	−	0.329303i
$982$	0.371322	−	0.321753i	0.0118494	−	0.0102675i
$983$	−9.23524	+	4.21759i	−0.294558	+	0.134520i	−0.557213	−	0.830370i	$-0.688129\pi$
$983$	−9.23524	+	4.21759i	−0.294558	+	0.134520i	0.262655	+	0.964890i	$0.415402\pi$
$984$	17.0678	−	5.01155i	0.544101	−	0.159762i
$985$	16.8144	+	0.664332i	0.535753	+	0.0211674i
$986$	5.92666	−	41.2208i	0.188743	−	1.31274i
$987$	1.33302	+	2.07421i	0.0424303	+	0.0660229i
$988$		−	10.4168i		−	0.331401i
$989$	0.0312437	+	5.25285i	0.000993492	+	0.167031i
$990$	−8.21315	−	20.0428i	−0.261031	−	0.637001i
$991$	−17.9593	+	11.5417i	−0.570495	+	0.366635i	−0.793861	−	0.608100i	$-0.791932\pi$
$991$	−17.9593	+	11.5417i	−0.570495	+	0.366635i	0.223365	+	0.974735i	$0.428296\pi$
$992$	9.23656	+	1.32802i	0.293261	+	0.0421646i
$993$	23.1198	+	10.5585i	0.733685	+	0.335063i
$994$	−4.05122	+	1.18955i	−0.128497	+	0.0377301i
$995$	−1.93301	−	1.81342i	−0.0612805	−	0.0574892i
$996$	4.46781	+	5.15613i	0.141568	+	0.163378i
$997$	0.841451	−	0.120982i	0.0266490	−	0.00383155i	−0.128977	−	0.991648i	$-0.541169\pi$
$997$	0.841451	−	0.120982i	0.0266490	−	0.00383155i	0.155626	+	0.987816i	$0.450260\pi$
$998$	7.33969	−	24.9967i	0.232334	−	0.791257i
$999$	6.25595	−	7.21975i	0.197929	−	0.228423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.j.a.219.11	yes	120
5.4	even	2	inner	230.2.j.a.219.2	yes	120
23.2	even	11	inner	230.2.j.a.209.2	✓	120
115.94	even	22	inner	230.2.j.a.209.11	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.j.a.209.2	✓	120	23.2	even	11	inner
230.2.j.a.209.11	yes	120	115.94	even	22	inner
230.2.j.a.219.2	yes	120	5.4	even	2	inner
230.2.j.a.219.11	yes	120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 + 0.841254i) q^{2} +(2.16151 + 0.310778i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-1.74640 + 1.39646i) q^{5} +(0.907157 + 1.98640i) q^{6} +(-0.282303 + 0.244617i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(1.69707 + 0.498303i) q^{9} +(-2.11895 - 0.714183i) q^{10} +(4.60733 + 2.96095i) q^{11} +(-1.18062 + 1.83708i) q^{12} +(-3.65165 - 3.16417i) q^{13} +(-0.358409 - 0.105238i) q^{14} +(-4.20885 + 2.47571i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(5.87094 - 2.68117i) q^{17} +(0.498303 + 1.69707i) q^{18} +(0.895578 - 1.96104i) q^{19} +(-0.544781 - 2.16869i) q^{20} +(-0.686222 + 0.441008i) q^{21} +5.47675i q^{22} +(-0.710740 - 4.74287i) q^{23} -2.18374 q^{24} +(1.09982 - 4.87754i) q^{25} +(0.687640 - 4.78264i) q^{26} +(-2.44583 - 1.11697i) q^{27} +(-0.105238 - 0.358409i) q^{28} +(-2.68040 - 5.86927i) q^{29} +(-4.35818 - 2.20224i) q^{30} +(1.32802 + 9.23656i) q^{31} +(0.281733 - 0.959493i) q^{32} +(9.03860 + 7.83199i) q^{33} +(5.42961 + 3.48940i) q^{34} +(0.151417 - 0.821422i) q^{35} +(-1.15826 + 1.33670i) q^{36} +(-1.00097 + 3.40899i) q^{37} +(2.13392 - 0.306811i) q^{38} +(-6.90972 - 7.97424i) q^{39} +(1.52989 - 1.63078i) q^{40} +(-7.81585 + 2.29494i) q^{41} +(-0.742000 - 0.338860i) q^{42} +(-1.08417 - 0.155879i) q^{43} +(-4.60733 + 2.96095i) q^{44} +(-3.65961 + 1.49964i) q^{45} +(3.60570 - 3.16210i) q^{46} -3.02265i q^{47} +(-1.18062 - 1.83708i) q^{48} +(-0.976346 + 6.79064i) q^{49} +(4.69786 - 1.71177i) q^{50} +(13.5233 - 3.97081i) q^{51} +(4.39518 - 2.00721i) q^{52} +(2.40632 - 2.08509i) q^{53} +(-0.382658 - 2.66145i) q^{54} +(-12.1811 + 1.26293i) q^{55} +(0.244617 - 0.282303i) q^{56} +(2.54525 - 3.96049i) q^{57} +(3.48841 - 5.42807i) q^{58} +(0.366229 - 0.422651i) q^{59} +(-0.503567 - 4.85695i) q^{60} +(0.459593 + 3.19654i) q^{61} +(-7.05231 + 6.11086i) q^{62} +(-0.600980 + 0.274458i) q^{63} +(0.959493 - 0.281733i) q^{64} +(10.7959 + 0.426540i) q^{65} +(-1.70205 + 11.8380i) q^{66} +(-3.28419 - 5.11029i) q^{67} +6.45419i q^{68} +(-0.0622909 - 10.4727i) q^{69} +(0.772887 - 0.316714i) q^{70} +(9.50897 - 6.11104i) q^{71} +(-1.75071 - 0.251714i) q^{72} +(-2.75739 - 1.25926i) q^{73} +(-3.40899 + 1.00097i) q^{74} +(3.89311 - 10.2011i) q^{75} +(1.41179 + 1.62929i) q^{76} +(-2.02496 + 0.291146i) q^{77} +(2.97268 - 10.1240i) q^{78} +(0.359389 - 0.414757i) q^{79} +(2.19902 + 0.405356i) q^{80} +(-9.40336 - 6.04317i) q^{81} +(-6.15620 - 5.33438i) q^{82} +(0.880203 - 2.99770i) q^{83} +(-0.116088 - 0.807411i) q^{84} +(-6.50887 + 12.8809i) q^{85} +(-0.455010 - 0.996332i) q^{86} +(-3.96968 - 13.5195i) q^{87} +(-4.98183 - 2.27512i) q^{88} +(-2.05531 + 14.2950i) q^{89} +(-3.24011 - 2.26789i) q^{90} +1.80488 q^{91} +(4.60952 + 1.32375i) q^{92} +20.3776i q^{93} +(2.54282 - 1.63417i) q^{94} +(1.17447 + 4.67540i) q^{95} +(0.907157 - 1.98640i) q^{96} +(0.880494 + 2.99869i) q^{97} +(-6.24050 + 2.84994i) q^{98} +(6.34349 + 7.32078i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41}+ \cdots + 188 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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