LMFDB - Embedded newform 230.2.l.a.7.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] 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("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.3
Character	$\chi$	$=$	230.7
Dual form			230.2.l.a.33.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.997452 + 0.0713392i) q^{2} +(-0.293712 + 1.35017i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.12582 - 0.693460i) q^{5} +(0.196644 - 1.36769i) q^{6} +(-0.324076 + 0.593501i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(0.992195 + 0.453120i) q^{9} +(2.16988 + 0.540039i) q^{10} +(-2.95294 + 2.55874i) q^{11} +(-0.0985729 + 1.37823i) q^{12} +(-5.45538 + 2.97886i) q^{13} +(0.280911 - 0.615108i) q^{14} +(1.56067 - 2.66655i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-3.47136 - 4.63719i) q^{17} +(-1.02199 - 0.381184i) q^{18} +(-0.740929 - 5.15327i) q^{19} +(-2.20287 - 0.383866i) q^{20} +(-0.706144 - 0.611878i) q^{21} +(2.76288 - 2.76288i) q^{22} +(-0.889192 + 4.71268i) q^{23} -1.38175i q^{24} +(4.03823 + 2.94834i) q^{25} +(5.22897 - 3.36046i) q^{26} +(-3.38737 + 4.52499i) q^{27} +(-0.236314 + 0.633581i) q^{28} +(-7.94969 - 1.14299i) q^{29} +(-1.36646 + 2.77109i) q^{30} +(7.58954 + 4.87750i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(-2.58743 - 4.73852i) q^{33} +(3.79333 + 4.37773i) q^{34} +(1.10050 - 1.03694i) q^{35} +(1.04658 + 0.307304i) q^{36} +(0.301897 + 0.809417i) q^{37} +(1.10667 + 5.08728i) q^{38} +(-2.41967 - 8.24064i) q^{39} +(2.22464 + 0.225736i) q^{40} +(-0.603651 - 1.32181i) q^{41} +(0.747996 + 0.559943i) q^{42} +(3.56804 + 0.776180i) q^{43} +(-2.55874 + 2.95294i) q^{44} +(-1.79501 - 1.65130i) q^{45} +(0.550727 - 4.76411i) q^{46} +(4.53479 + 4.53479i) q^{47} +(0.0985729 + 1.37823i) q^{48} +(3.53727 + 5.50410i) q^{49} +(-4.23827 - 2.65275i) q^{50} +(7.28059 - 3.32493i) q^{51} +(-4.97592 + 3.72493i) q^{52} +(8.86106 + 4.83850i) q^{53} +(3.05593 - 4.75512i) q^{54} +(8.05181 - 3.39167i) q^{55} +(0.190512 - 0.648825i) q^{56} +(7.17543 + 0.513197i) q^{57} +(8.01097 + 0.572956i) q^{58} +(2.82083 - 9.60688i) q^{59} +(1.16530 - 2.86151i) q^{60} +(-4.29089 + 6.67676i) q^{61} +(-7.91816 - 4.32364i) q^{62} +(-0.590475 + 0.442024i) q^{63} +(0.909632 - 0.415415i) q^{64} +(13.6629 - 2.54944i) q^{65} +(2.91887 + 4.54186i) q^{66} +(-0.416288 - 5.82046i) q^{67} +(-4.09596 - 4.09596i) q^{68} +(-6.10177 - 2.58473i) q^{69} +(-1.02372 + 1.11281i) q^{70} +(-4.01533 + 4.63394i) q^{71} +(-1.06584 - 0.231859i) q^{72} +(-9.91495 - 7.42224i) q^{73} +(-0.358871 - 0.785817i) q^{74} +(-5.16685 + 4.58634i) q^{75} +(-1.46677 - 4.99537i) q^{76} +(-0.561636 - 2.58180i) q^{77} +(3.00139 + 8.04703i) q^{78} +(5.43844 + 1.59687i) q^{79} +(-2.23508 - 0.0664569i) q^{80} +(-2.97171 - 3.42954i) q^{81} +(0.696409 + 1.27538i) q^{82} +(6.58215 - 2.45502i) q^{83} +(-0.786036 - 0.505155i) q^{84} +(4.16378 + 12.2651i) q^{85} +(-3.61432 - 0.519661i) q^{86} +(3.87816 - 10.3977i) q^{87} +(2.34156 - 3.12796i) q^{88} +(-6.82908 + 4.38878i) q^{89} +(1.90824 + 1.51904i) q^{90} -4.20316i q^{91} +(-0.209457 + 4.79126i) q^{92} +(-8.81462 + 8.81462i) q^{93} +(-4.84674 - 4.19973i) q^{94} +(-1.99851 + 11.4687i) q^{95} +(-0.196644 - 1.36769i) q^{96} +(-3.10002 - 1.15625i) q^{97} +(-3.92091 - 5.23773i) q^{98} +(-4.08931 + 1.20073i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

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

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$3$	−0.293712	+	1.35017i	−0.169575	+	0.779523i	0.811261	+	0.584685i	$0.198782\pi$
$3$	−0.293712	+	1.35017i	−0.169575	+	0.779523i	−0.980835	+	0.194838i	$0.937582\pi$
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	−2.12582	−	0.693460i	−0.950696	−	0.310125i
$5$	−2.12582	−	0.693460i	−0.950696	−	0.310125i
$6$	0.196644	−	1.36769i	0.0802794	−	0.558356i
$7$	−0.324076	+	0.593501i	−0.122489	+	0.224322i	−0.931727	−	0.363158i	$-0.881698\pi$
$7$	−0.324076	+	0.593501i	−0.122489	+	0.224322i	0.809238	+	0.587481i	$0.199880\pi$
$8$	−0.977147	+	0.212565i	−0.345474	+	0.0751532i
$9$	0.992195	+	0.453120i	0.330732	+	0.151040i
$10$	2.16988	+	0.540039i	0.686175	+	0.170775i
$11$	−2.95294	+	2.55874i	−0.890345	+	0.771489i	−0.974364	−	0.224975i	$-0.927770\pi$
$11$	−2.95294	+	2.55874i	−0.890345	+	0.771489i	0.0840190	+	0.996464i	$0.473224\pi$
$12$	−0.0985729	+	1.37823i	−0.0284556	+	0.397861i
$13$	−5.45538	+	2.97886i	−1.51305	+	0.826188i	−0.999492	−	0.0318659i	$-0.989855\pi$
$13$	−5.45538	+	2.97886i	−1.51305	+	0.826188i	−0.513559	+	0.858054i	$0.671673\pi$
$14$	0.280911	−	0.615108i	0.0750765	−	0.164395i
$15$	1.56067	−	2.66655i	0.402963	−	0.688500i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	−3.47136	−	4.63719i	−0.841928	−	1.12468i	−0.990734	−	0.135817i	$-0.956634\pi$
$17$	−3.47136	−	4.63719i	−0.841928	−	1.12468i	0.148806	−	0.988866i	$-0.452457\pi$
$18$	−1.02199	−	0.381184i	−0.240886	−	0.0898458i
$19$	−0.740929	−	5.15327i	−0.169981	−	1.18224i	−0.878919	−	0.476971i	$-0.841735\pi$
$19$	−0.740929	−	5.15327i	−0.169981	−	1.18224i	0.708938	−	0.705270i	$-0.249174\pi$
$20$	−2.20287	−	0.383866i	−0.492577	−	0.0858350i
$21$	−0.706144	−	0.611878i	−0.154093	−	0.133523i
$22$	2.76288	−	2.76288i	0.589048	−	0.589048i
$23$	−0.889192	+	4.71268i	−0.185409	+	0.982661i
$23$	−0.889192	+	4.71268i	−0.185409	+	0.982661i
$24$		−	1.38175i		−	0.282049i
$25$	4.03823	+	2.94834i	0.807645	+	0.589668i
$26$	5.22897	−	3.36046i	1.02549	−	0.659040i
$27$	−3.38737	+	4.52499i	−0.651899	+	0.870835i
$28$	−0.236314	+	0.633581i	−0.0446591	+	0.119736i
$29$	−7.94969	−	1.14299i	−1.47622	−	0.212248i	−0.643288	−	0.765624i	$-0.722430\pi$
$29$	−7.94969	−	1.14299i	−1.47622	−	0.212248i	−0.832932	+	0.553376i	$0.813339\pi$
$30$	−1.36646	+	2.77109i	−0.249481	+	0.505930i
$31$	7.58954	+	4.87750i	1.36312	+	0.876025i	0.998480	−	0.0551221i	$-0.0175548\pi$
$31$	7.58954	+	4.87750i	1.36312	+	0.876025i	0.364643	+	0.931148i	$0.381191\pi$
$32$	−0.936950	+	0.349464i	−0.165631	+	0.0617771i
$33$	−2.58743	−	4.73852i	−0.450413	−	0.824870i
$34$	3.79333	+	4.37773i	0.650550	+	0.750775i
$35$	1.10050	−	1.03694i	0.186018	−	0.175275i
$36$	1.04658	+	0.307304i	0.174430	+	0.0512174i
$37$	0.301897	+	0.809417i	0.0496315	+	0.133067i	0.959400	−	0.282048i	$-0.0910138\pi$
$37$	0.301897	+	0.809417i	0.0496315	+	0.133067i	−0.909769	+	0.415116i	$0.863741\pi$
$38$	1.10667	+	5.08728i	0.179526	+	0.825266i
$39$	−2.41967	−	8.24064i	−0.387457	−	1.31956i
$40$	2.22464	+	0.225736i	0.351747	+	0.0356921i
$41$	−0.603651	−	1.32181i	−0.0942744	−	0.206432i	0.856620	−	0.515948i	$-0.172560\pi$
$41$	−0.603651	−	1.32181i	−0.0942744	−	0.206432i	−0.950894	+	0.309516i	$0.899833\pi$
$42$	0.747996	+	0.559943i	0.115418	+	0.0864010i
$43$	3.56804	+	0.776180i	0.544121	+	0.118366i	0.476221	−	0.879326i	$-0.342006\pi$
$43$	3.56804	+	0.776180i	0.544121	+	0.118366i	0.0679005	+	0.997692i	$0.478370\pi$
$44$	−2.55874	+	2.95294i	−0.385744	+	0.445173i
$45$	−1.79501	−	1.65130i	−0.267584	−	0.246161i
$46$	0.550727	−	4.76411i	0.0812003	−	0.702429i
$47$	4.53479	+	4.53479i	0.661467	+	0.661467i	0.955726	−	0.294259i	$-0.0950728\pi$
$47$	4.53479	+	4.53479i	0.661467	+	0.661467i	−0.294259	+	0.955726i	$0.595073\pi$
$48$	0.0985729	+	1.37823i	0.0142278	+	0.198930i
$49$	3.53727	+	5.50410i	0.505324	+	0.786299i
$50$	−4.23827	−	2.65275i	−0.599382	−	0.375155i
$51$	7.28059	−	3.32493i	1.01949	−	0.465584i
$52$	−4.97592	+	3.72493i	−0.690036	+	0.516554i
$53$	8.86106	+	4.83850i	1.21716	+	0.664620i	0.953906	−	0.300107i	$-0.0970224\pi$
$53$	8.86106	+	4.83850i	1.21716	+	0.664620i	0.263254	+	0.964726i	$0.415204\pi$
$54$	3.05593	−	4.75512i	0.415859	−	0.647089i
$55$	8.05181	−	3.39167i	1.08571	−	0.457333i
$56$	0.190512	−	0.648825i	0.0254583	−	0.0867029i
$57$	7.17543	+	0.513197i	0.950409	+	0.0679746i
$58$	8.01097	+	0.572956i	1.05189	+	0.0752328i
$59$	2.82083	−	9.60688i	0.367241	−	1.25071i	−0.544087	−	0.839029i	$-0.683124\pi$
$59$	2.82083	−	9.60688i	0.367241	−	1.25071i	0.911328	−	0.411681i	$-0.135058\pi$
$60$	1.16530	−	2.86151i	0.150439	−	0.369420i
$61$	−4.29089	+	6.67676i	−0.549393	+	0.854871i	−0.999269	−	0.0382192i	$-0.987832\pi$
$61$	−4.29089	+	6.67676i	−0.549393	+	0.854871i	0.449877	+	0.893091i	$0.351468\pi$
$62$	−7.91816	−	4.32364i	−1.00561	−	0.549103i
$63$	−0.590475	+	0.442024i	−0.0743928	+	0.0556898i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	13.6629	−	2.54944i	1.69467	−	0.316219i
$66$	2.91887	+	4.54186i	0.359289	+	0.559064i
$67$	−0.416288	−	5.82046i	−0.0508576	−	0.711083i	−0.957363	−	0.288888i	$-0.906714\pi$
$67$	−0.416288	−	5.82046i	−0.0508576	−	0.711083i	0.906505	−	0.422195i	$-0.138740\pi$
$68$	−4.09596	−	4.09596i	−0.496709	−	0.496709i
$69$	−6.10177	−	2.58473i	−0.734566	−	0.311165i
$70$	−1.02372	+	1.11281i	−0.122358	+	0.133006i
$71$	−4.01533	+	4.63394i	−0.476532	+	0.549948i	−0.942217	−	0.335003i	$-0.891263\pi$
$71$	−4.01533	+	4.63394i	−0.476532	+	0.549948i	0.465685	+	0.884951i	$0.345808\pi$
$72$	−1.06584	−	0.231859i	−0.125610	−	0.0273248i
$73$	−9.91495	−	7.42224i	−1.16046	−	0.868707i	−0.167347	−	0.985898i	$-0.553520\pi$
$73$	−9.91495	−	7.42224i	−1.16046	−	0.868707i	−0.993109	+	0.117191i	$0.962611\pi$
$74$	−0.358871	−	0.785817i	−0.0417179	−	0.0913494i
$75$	−5.16685	+	4.58634i	−0.596616	+	0.529585i
$76$	−1.46677	−	4.99537i	−0.168251	−	0.573009i
$77$	−0.561636	−	2.58180i	−0.0640044	−	0.294224i
$78$	3.00139	+	8.04703i	0.339840	+	0.911146i
$79$	5.43844	+	1.59687i	0.611872	+	0.179662i	0.572964	−	0.819581i	$-0.305794\pi$
$79$	5.43844	+	1.59687i	0.611872	+	0.179662i	0.0389088	+	0.999243i	$0.487612\pi$
$80$	−2.23508	−	0.0664569i	−0.249890	−	0.00743011i
$81$	−2.97171	−	3.42954i	−0.330190	−	0.381060i
$82$	0.696409	+	1.27538i	0.0769055	+	0.140842i
$83$	6.58215	−	2.45502i	0.722485	−	0.269473i	0.0387968	−	0.999247i	$-0.487647\pi$
$83$	6.58215	−	2.45502i	0.722485	−	0.269473i	0.683688	+	0.729774i	$0.260375\pi$
$84$	−0.786036	−	0.505155i	−0.0857636	−	0.0551169i
$85$	4.16378	+	12.2651i	0.451625	+	1.33033i
$86$	−3.61432	−	0.519661i	−0.389742	−	0.0560365i
$87$	3.87816	−	10.3977i	0.415782	−	1.11475i
$88$	2.34156	−	3.12796i	0.249611	−	0.333441i
$89$	−6.82908	+	4.38878i	−0.723881	+	0.465210i	−0.849985	−	0.526807i	$-0.823389\pi$
$89$	−6.82908	+	4.38878i	−0.723881	+	0.465210i	0.126104	+	0.992017i	$0.459753\pi$
$90$	1.90824	+	1.51904i	0.201146	+	0.160121i
$91$		−	4.20316i		−	0.440610i
$92$	−0.209457	+	4.79126i	−0.0218374	+	0.499523i
$93$	−8.81462	+	8.81462i	−0.914033	+	0.914033i
$94$	−4.84674	−	4.19973i	−0.499903	−	0.433169i
$95$	−1.99851	+	11.4687i	−0.205042	+	1.17667i
$96$	−0.196644	−	1.36769i	−0.0200699	−	0.139589i
$97$	−3.10002	−	1.15625i	−0.314760	−	0.117399i	0.187119	−	0.982337i	$-0.440085\pi$
$97$	−3.10002	−	1.15625i	−0.314760	−	0.117399i	−0.501879	+	0.864938i	$0.667358\pi$
$98$	−3.92091	−	5.23773i	−0.396072	−	0.529090i
$99$	−4.08931	+	1.20073i	−0.410991	+	0.120678i
$100$	4.41672	+	2.34363i	0.441672	+	0.234363i
$101$	−2.55404	+	5.59257i	−0.254137	+	0.556482i	−0.993101	−	0.117263i	$-0.962588\pi$
$101$	−2.55404	+	5.59257i	−0.254137	+	0.556482i	0.738964	+	0.673745i	$0.235315\pi$
$102$	−7.02484	+	3.83585i	−0.695563	+	0.379806i
$103$	−0.189662	+	2.65182i	−0.0186879	+	0.261291i	0.979515	+	0.201370i	$0.0645395\pi$
$103$	−0.189662	+	2.65182i	−0.0186879	+	0.261291i	−0.998203	+	0.0599211i	$0.980915\pi$
$104$	4.69751	−	4.07041i	0.460629	−	0.399137i
$105$	1.07682	+	1.79042i	0.105087	+	0.174728i
$106$	−9.18365	−	4.19403i	−0.891995	−	0.407361i
$107$	3.65471	−	0.795033i	0.353314	−	0.0768587i	−0.0324057	−	0.999475i	$-0.510317\pi$
$107$	3.65471	−	0.795033i	0.353314	−	0.0768587i	0.385720	+	0.922616i	$0.373953\pi$
$108$	−2.70892	+	4.96101i	−0.260665	+	0.477373i
$109$	−0.217674	+	1.51396i	−0.0208494	+	0.145011i	−0.997587	−	0.0694272i	$-0.977883\pi$
$109$	−0.217674	+	1.51396i	−0.0208494	+	0.145011i	0.976738	+	0.214438i	$0.0687919\pi$
$110$	−7.78933	+	3.95744i	−0.742684	+	0.377327i
$111$	−1.18152	+	0.169877i	−0.112145	+	0.0161241i
$112$	−0.143740	+	0.660763i	−0.0135822	+	0.0624362i
$113$	−12.6237	+	0.902862i	−1.18753	+	0.0849341i	−0.651089	−	0.759001i	$-0.725688\pi$
$113$	−12.6237	+	0.902862i	−1.18753	+	0.0849341i	−0.536445	+	0.843936i	$0.680233\pi$
$114$	−7.19376			−0.673757
$115$	5.15831	−	9.40169i	0.481015	−	0.876712i
$116$	−8.03143			−0.745700
$117$	−6.76259	+	0.483670i	−0.625202	+	0.0447153i
$118$	−2.12830	+	9.78364i	−0.195926	+	0.900657i
$119$	3.87716	−	0.557452i	0.355419	−	0.0511015i
$120$	−0.958188	+	2.93735i	−0.0874702	+	0.268142i
$121$	0.607259	−	4.22358i	0.0552053	−	0.383962i
$122$	3.80365	−	6.96586i	0.344366	−	0.630659i
$123$	1.96197	−	0.426801i	0.176905	−	0.0384833i
$124$	8.20643	+	3.74775i	0.736960	+	0.336558i
$125$	−6.53999	−	9.06800i	−0.584954	−	0.811066i
$126$	0.557436	−	0.483021i	0.0496604	−	0.0430310i
$127$	−0.168822	+	2.36044i	−0.0149805	+	0.209455i	0.984449	+	0.175673i	$0.0562100\pi$
$127$	−0.168822	+	2.36044i	−0.0149805	+	0.209455i	−0.999429	+	0.0337828i	$0.989245\pi$
$128$	−0.877679	+	0.479249i	−0.0775766	+	0.0423600i
$129$	−2.09595	+	4.58950i	−0.184539	+	0.404083i
$130$	−13.4462	+	3.51765i	−1.17931	+	0.308518i
$131$	5.51871	−	1.62044i	0.482172	−	0.141579i	−0.0316081	−	0.999500i	$-0.510063\pi$
$131$	5.51871	−	1.62044i	0.482172	−	0.141579i	0.513780	+	0.857922i	$0.328245\pi$
$132$	−3.23545	−	4.32206i	−0.281610	−	0.376187i
$133$	3.29859	+	1.23031i	0.286024	+	0.106681i
$134$	0.830454	+	5.77594i	0.0717403	+	0.498965i
$135$	10.3388	−	7.27032i	0.889825	−	0.625730i
$136$	4.37773	+	3.79333i	0.375387	+	0.325275i
$137$	2.78731	−	2.78731i	0.238136	−	0.238136i	−0.577942	−	0.816078i	$-0.696144\pi$
$137$	2.78731	−	2.78731i	0.238136	−	0.238136i	0.816078	+	0.577942i	$0.196144\pi$
$138$	6.27061	+	2.14285i	0.533790	+	0.182412i
$139$			10.7390i			0.910868i	0.890269	+	0.455434i	$0.150516\pi$
$139$			10.7390i			0.910868i	−0.890269	+	0.455434i	$0.849484\pi$
$140$	0.941723	−	1.18301i	0.0795901	−	0.0999822i
$141$	−7.45467	+	4.79083i	−0.627797	+	0.403460i
$142$	3.67452	−	4.90858i	0.308359	−	0.411919i
$143$	8.48729	−	22.7553i	0.709743	−	1.90289i
$144$	1.07966	+	0.155232i	0.0899719	+	0.0129360i
$145$	16.1070	+	7.94258i	1.33761	+	0.659596i
$146$	10.4192	+	6.69600i	0.862298	+	0.554165i
$147$	−8.47042	+	3.15930i	−0.698628	+	0.260575i
$148$	0.414016	+	0.758214i	0.0340319	+	0.0623248i
$149$	8.19158	+	9.45359i	0.671081	+	0.774468i	0.984545	−	0.175132i	$-0.0560351\pi$
$149$	8.19158	+	9.45359i	0.671081	+	0.774468i	−0.313464	+	0.949600i	$0.601490\pi$
$150$	4.82650	−	4.94325i	0.394082	−	0.403615i
$151$	−12.2539	−	3.59807i	−0.997209	−	0.292807i	−0.257899	−	0.966172i	$-0.583030\pi$
$151$	−12.2539	−	3.59807i	−0.997209	−	0.292807i	−0.739310	+	0.673365i	$0.764848\pi$
$152$	1.81940	+	4.87801i	0.147573	+	0.395659i
$153$	−1.34306	−	6.17394i	−0.108580	−	0.499134i
$154$	0.744389	+	2.53516i	0.0599846	+	0.204289i
$155$	−12.7517	−	15.6317i	−1.02424	−	1.25557i
$156$	−3.56781	−	7.81241i	−0.285653	−	0.625493i
$157$	−10.3877	−	7.77616i	−0.829031	−	0.620605i	0.0981696	−	0.995170i	$-0.468701\pi$
$157$	−10.3877	−	7.77616i	−0.829031	−	0.620605i	−0.927201	+	0.374565i	$0.877792\pi$
$158$	−5.53850	−	1.20483i	−0.440620	−	0.0958509i
$159$	−9.13542	+	10.5428i	−0.724486	+	0.836101i
$160$	2.23413	−	0.0931612i	0.176623	−	0.00736504i
$161$	−2.50881	−	2.05500i	−0.197722	−	0.161957i
$162$	3.20880	+	3.20880i	0.252107	+	0.252107i
$163$	0.397622	+	5.55948i	0.0311442	+	0.435452i	0.988971	+	0.148107i	$0.0473181\pi$
$163$	0.397622	+	5.55948i	0.0311442	+	0.435452i	−0.957827	+	0.287345i	$0.907227\pi$
$164$	−0.785619	−	1.22245i	−0.0613466	−	0.0954571i
$165$	2.21443	+	11.8675i	0.172393	+	0.923884i
$166$	−6.39024	+	2.91833i	−0.495979	+	0.226506i
$167$	−7.03622	+	5.26725i	−0.544479	+	0.407592i	−0.835800	−	0.549033i	$-0.814996\pi$
$167$	−7.03622	+	5.26725i	−0.544479	+	0.407592i	0.291321	+	0.956625i	$0.405905\pi$
$168$	0.820071	+	0.447792i	0.0632698	+	0.0345479i
$169$	13.8592	−	21.5654i	1.06610	−	1.65888i
$170$	−5.02815	−	11.9368i	−0.385641	−	0.915510i
$171$	1.59991	−	5.44878i	0.122348	−	0.416679i
$172$	3.64219	+	0.260494i	0.277714	+	0.0198625i
$173$	20.7134	+	1.48145i	1.57481	+	0.112633i	0.831199	−	0.555975i	$-0.187655\pi$
$173$	20.7134	+	1.48145i	1.57481	+	0.112633i	0.743615	+	0.668608i	$0.233110\pi$
$174$	−3.12651	+	10.6479i	−0.237020	+	0.807216i
$175$	−3.05854	+	1.44121i	−0.231204	+	0.108945i
$176$	−2.11245	+	3.28703i	−0.159232	+	0.247769i
$177$	12.1424	+	6.63027i	0.912682	+	0.498362i
$178$	6.49859	−	4.86478i	0.487090	−	0.364631i
$179$	−19.6913	+	8.99270i	−1.47179	+	0.672146i	−0.980079	−	0.198609i	$-0.936357\pi$
$179$	−19.6913	+	8.99270i	−1.47179	+	0.672146i	−0.491716	+	0.870756i	$0.663630\pi$
$180$	−2.01174	−	1.37904i	−0.149946	−	0.102787i
$181$	−6.16120	−	9.58702i	−0.457958	−	0.712597i	0.533096	−	0.846055i	$-0.321028\pi$
$181$	−6.16120	−	9.58702i	−0.457958	−	0.712597i	−0.991055	+	0.133457i	$0.957392\pi$
$182$	0.299850	+	4.19245i	0.0222263	+	0.310765i
$183$	−7.75449	−	7.75449i	−0.573229	−	0.573229i
$184$	−0.132881	−	4.79399i	−0.00979613	−	0.353418i
$185$	−0.0804806	−	1.93003i	−0.00591705	−	0.141899i
$186$	8.16333	−	9.42098i	0.598564	−	0.690780i
$187$	22.1161	+	4.81106i	1.61729	+	0.351819i
$188$	5.13400	+	3.84326i	0.374435	+	0.280299i
$189$	−1.58782	−	3.47685i	−0.115497	−	0.252904i
$190$	1.17524	−	11.5821i	0.0852611	−	0.840253i
$191$	3.98172	+	13.5605i	0.288107	+	0.981202i	0.968637	+	0.248482i	$0.0799315\pi$
$191$	3.98172	+	13.5605i	0.288107	+	0.981202i	−0.680530	+	0.732720i	$0.738250\pi$
$192$	0.293712	+	1.35017i	0.0211969	+	0.0974403i
$193$	−4.55192	−	12.2042i	−0.327655	−	0.878476i	−0.991441	−	0.130554i	$-0.958324\pi$
$193$	−4.55192	−	12.2042i	−0.327655	−	0.878476i	0.663787	−	0.747922i	$-0.268948\pi$
$194$	3.17461	+	0.932150i	0.227924	+	0.0669245i
$195$	−0.570768	+	19.1961i	−0.0408735	+	1.37466i
$196$	4.28458	+	4.94467i	0.306041	+	0.353190i
$197$	−4.24528	−	7.77465i	−0.302464	−	0.553921i	0.681603	−	0.731723i	$-0.261283\pi$
$197$	−4.24528	−	7.77465i	−0.302464	−	0.553921i	−0.984066	+	0.177802i	$0.943102\pi$
$198$	3.99323	−	1.48940i	0.283787	−	0.105847i
$199$	−8.54887	−	5.49403i	−0.606013	−	0.389461i	0.201347	−	0.979520i	$-0.435468\pi$
$199$	−8.54887	−	5.49403i	−0.606013	−	0.389461i	−0.807360	+	0.590059i	$0.799105\pi$
$200$	−4.57266	−	2.02258i	−0.323336	−	0.143018i
$201$	7.98090	+	1.14748i	0.562929	+	0.0809370i
$202$	2.14856	−	5.76053i	0.151172	−	0.405309i
$203$	3.25467	−	4.34773i	0.228433	−	0.305151i
$204$	6.73330	−	4.32723i	0.471425	−	0.302966i
$205$	0.366630	+	3.22854i	0.0256066	+	0.225491i
$206$		−	2.65859i		−	0.185233i
$207$	−3.01766	+	4.27299i	−0.209742	+	0.296993i
$208$	−4.39516	+	4.39516i	−0.304749	+	0.304749i
$209$	15.3738	+	13.3215i	1.06343	+	0.921465i
$210$	−1.20181	−	1.70904i	−0.0829326	−	0.117935i
$211$	2.29354	+	15.9519i	0.157893	+	1.09817i	0.902506	+	0.430677i	$0.141725\pi$
$211$	2.29354	+	15.9519i	0.157893	+	1.09817i	−0.744613	+	0.667497i	$0.767366\pi$
$212$	9.45945	+	3.52819i	0.649678	+	0.242317i
$213$	−5.07727	−	6.78244i	−0.347889	−	0.464725i
$214$	−3.58868	+	1.05373i	−0.245317	+	0.0720316i
$215$	−7.04677	−	4.12431i	−0.480586	−	0.281276i
$216$	2.34810	−	5.14162i	0.159768	−	0.349843i
$217$	−5.35439	+	2.92372i	−0.363480	+	0.198475i
$218$	0.109115	−	1.52563i	0.00739020	−	0.103328i
$219$	12.9334	−	11.2069i	0.873961	−	0.757292i
$220$	7.48717	−	4.50304i	0.504785	−	0.303595i
$221$	32.7511	+	14.9569i	2.20308	+	1.00611i
$222$	1.16639	−	0.253734i	0.0782833	−	0.0170295i
$223$	7.79475	−	14.2750i	0.521975	−	0.955926i	−0.475132	−	0.879915i	$-0.657600\pi$
$223$	7.79475	−	14.2750i	0.521975	−	0.955926i	0.997107	−	0.0760114i	$-0.0242185\pi$
$224$	0.0962357	−	0.669334i	0.00643002	−	0.0447218i
$225$	2.67076	+	4.75514i	0.178050	+	0.317009i
$226$	12.5271	−	1.80112i	0.833289	−	0.119809i
$227$	1.03600	−	4.76243i	0.0687620	−	0.316094i	−0.929900	−	0.367813i	$-0.880107\pi$
$227$	1.03600	−	4.76243i	0.0687620	−	0.316094i	0.998662	+	0.0517195i	$0.0164702\pi$
$228$	7.17543	−	0.513197i	0.475204	−	0.0339873i
$229$	−14.2072			−0.938839			−0.469420	−	0.882975i	$-0.655537\pi$
$229$	−14.2072			−0.938839			−0.469420	+	0.882975i	$0.655537\pi$
$230$	−4.47446	+	9.74573i	−0.295037	+	0.642614i
$231$	3.65084			0.240207
$232$	8.01097	−	0.572956i	0.525946	−	0.0376164i
$233$	−3.36267	+	15.4579i	−0.220296	+	1.01268i	0.725576	+	0.688142i	$0.241573\pi$
$233$	−3.36267	+	15.4579i	−0.220296	+	1.01268i	−0.945872	+	0.324541i	$0.894790\pi$
$234$	6.71086	−	0.964875i	0.438702	−	0.0630759i
$235$	−6.49545	−	12.7848i	−0.423717	−	0.833991i
$236$	1.42492	−	9.91054i	0.0927545	−	0.645121i
$237$	−3.75339	+	6.87382i	−0.243809	+	0.446502i
$238$	−3.82752	+	0.832625i	−0.248101	+	0.0539711i
$239$	9.90756	+	4.52463i	0.640867	+	0.292674i	0.709220	−	0.704987i	$-0.249047\pi$
$239$	9.90756	+	4.52463i	0.640867	+	0.292674i	−0.0683534	+	0.997661i	$0.521775\pi$
$240$	0.746199	−	2.99823i	0.0481669	−	0.193535i
$241$	−9.27791	+	8.03936i	−0.597643	+	0.517860i	−0.900318	−	0.435233i	$-0.856666\pi$
$241$	−9.27791	+	8.03936i	−0.597643	+	0.517860i	0.302675	+	0.953094i	$0.402120\pi$
$242$	−0.304405	+	4.25614i	−0.0195679	+	0.273595i
$243$	−9.37972	+	5.12172i	−0.601709	+	0.328558i
$244$	−3.29702	+	7.21946i	−0.211070	+	0.462178i
$245$	−3.70273	−	14.1537i	−0.236559	−	0.904245i
$246$	−1.92653	+	0.565679i	−0.122831	+	0.0360664i
$247$	19.3929	+	25.9059i	1.23394	+	1.64836i
$248$	−8.45289	−	3.15276i	−0.536759	−	0.200201i
$249$	1.38144	+	9.60811i	0.0875451	+	0.608890i
$250$	7.17023	+	8.57833i	0.453485	+	0.542541i
$251$	−3.57725	−	3.09970i	−0.225794	−	0.195651i	0.534616	−	0.845095i	$-0.320456\pi$
$251$	−3.57725	−	3.09970i	−0.225794	−	0.195651i	−0.760410	+	0.649444i	$0.775002\pi$
$252$	−0.521558	+	0.521558i	−0.0328551	+	0.0328551i
$253$	−9.43278	−	16.1915i	−0.593034	−	1.01795i
$254$		−	2.36647i		−	0.148486i
$255$	−17.7829	+	2.01942i	−1.11361	+	0.126461i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	4.58415	−	6.12371i	0.285951	−	0.381986i	−0.634448	−	0.772965i	$-0.718773\pi$
$257$	4.58415	−	6.12371i	0.285951	−	0.381986i	0.920400	+	0.390979i	$0.127864\pi$
$258$	1.76320	−	4.72733i	0.109772	−	0.294311i
$259$	−0.578227	−	0.0831366i	−0.0359293	−	0.00516585i
$260$	13.1610	−	4.46793i	0.816210	−	0.277089i
$261$	−7.36973	−	4.73624i	−0.456175	−	0.293166i
$262$	−5.38905	+	2.01001i	−0.332937	+	0.124179i
$263$	9.30221	+	17.0357i	0.573599	+	1.05047i	0.989971	+	0.141274i	$0.0451197\pi$
$263$	9.30221	+	17.0357i	0.573599	+	1.05047i	−0.416372	+	0.909194i	$0.636698\pi$
$264$	3.53554	+	4.08023i	0.217597	+	0.251121i
$265$	−15.4817	−	16.4306i	−0.951034	−	1.00932i
$266$	−3.37796	−	0.991857i	−0.207116	−	0.0608147i
$267$	−3.91983	−	10.5095i	−0.239890	−	0.643170i
$268$	−1.24039	−	5.70198i	−0.0757688	−	0.348304i
$269$	1.91055	+	6.50675i	0.116488	+	0.396723i	0.997009	−	0.0772846i	$-0.0246250\pi$
$269$	1.91055	+	6.50675i	0.116488	+	0.396723i	−0.880521	+	0.474008i	$0.842807\pi$
$270$	−9.79384	+	7.98936i	−0.596034	+	0.486217i
$271$	−3.83102	−	8.38876i	−0.232718	−	0.509581i	0.756861	−	0.653576i	$-0.226732\pi$
$271$	−3.83102	−	8.38876i	−0.232718	−	0.509581i	−0.989578	+	0.143996i	$0.954005\pi$
$272$	−4.63719	−	3.47136i	−0.281171	−	0.210482i
$273$	5.67499	+	1.23452i	0.343466	+	0.0747164i
$274$	−2.58137	+	2.97906i	−0.155946	+	0.179971i
$275$	−19.4687	+	1.62648i	−1.17401	+	0.0980807i
$276$	−6.40750	−	1.69005i	−0.385686	−	0.101729i
$277$	−4.69324	−	4.69324i	−0.281990	−	0.281990i	0.551912	−	0.833902i	$-0.313898\pi$
$277$	−4.69324	−	4.69324i	−0.281990	−	0.281990i	−0.833902	+	0.551912i	$0.813898\pi$
$278$	−0.766110	−	10.7116i	−0.0459482	−	0.642440i
$279$	5.32021	+	8.27841i	0.318513	+	0.495616i
$280$	−0.854929	+	1.24717i	−0.0510918	+	0.0745329i
$281$	−3.90494	+	1.78333i	−0.232949	+	0.106384i	−0.528470	−	0.848952i	$-0.677234\pi$
$281$	−3.90494	+	1.78333i	−0.232949	+	0.106384i	0.295521	+	0.955336i	$0.404507\pi$
$282$	7.09390	−	5.31043i	0.422436	−	0.316232i
$283$	2.37622	+	1.29752i	0.141252	+	0.0771293i	0.548321	−	0.836268i	$-0.315267\pi$
$283$	2.37622	+	1.29752i	0.141252	+	0.0771293i	−0.407069	+	0.913397i	$0.633449\pi$
$284$	−3.31498	+	5.15822i	−0.196708	+	0.306084i
$285$	−14.8978	−	6.06684i	−0.882469	−	0.359368i
$286$	−6.84232	+	23.3028i	−0.404595	+	1.37792i
$287$	0.980125	+	0.0700999i	0.0578549	+	0.00413787i
$288$	−1.08799	−	0.0778143i	−0.0641102	−	0.00458525i
$289$	−4.66376	+	15.8833i	−0.274339	+	0.934312i
$290$	−16.6326	−	6.77329i	−0.976698	−	0.397741i
$291$	2.47165	−	3.84596i	0.144891	−	0.225454i
$292$	−10.8703	−	5.93564i	−0.636137	−	0.347357i
$293$	15.3392	−	11.4828i	0.896128	−	0.670833i	−0.0485542	−	0.998821i	$-0.515461\pi$
$293$	15.3392	−	11.4828i	0.896128	−	0.670833i	0.944682	+	0.327988i	$0.106370\pi$
$294$	8.22346	−	3.75553i	0.479602	−	0.219027i
$295$	−12.6586	+	18.4664i	−0.737011	+	1.07515i
$296$	−0.467051	−	0.726746i	−0.0271468	−	0.0422413i
$297$	−1.57558	−	22.0294i	−0.0914242	−	1.27828i
$298$	−8.84512	−	8.84512i	−0.512384	−	0.512384i
$299$	−9.18755	−	28.3582i	−0.531330	−	1.64000i
$300$	−4.46155	+	5.27498i	−0.257588	+	0.304551i
$301$	−1.61698	+	1.86610i	−0.0932012	+	0.107560i
$302$	12.4794	+	2.71472i	0.718107	+	0.156215i
$303$	−6.80079	−	5.09100i	−0.390695	−	0.292471i
$304$	−2.16276	−	4.73578i	−0.124043	−	0.271616i
$305$	13.7517	−	11.2180i	0.787422	−	0.642343i
$306$	1.78008	+	6.06240i	0.101760	+	0.346564i
$307$	4.32217	+	19.8687i	0.246680	+	1.13397i	0.919170	+	0.393862i	$0.128861\pi$
$307$	4.32217	+	19.8687i	0.246680	+	1.13397i	−0.672490	+	0.740106i	$0.734775\pi$
$308$	−0.923348	−	2.47559i	−0.0526127	−	0.141060i
$309$	−3.52471	−	1.03495i	−0.200514	−	0.0588761i
$310$	13.8343	+	14.6822i	0.785737	+	0.833894i
$311$	−0.577829	−	0.666850i	−0.0327657	−	0.0378136i	0.739130	−	0.673563i	$-0.235237\pi$
$311$	−0.577829	−	0.666850i	−0.0327657	−	0.0378136i	−0.771896	+	0.635749i	$0.780691\pi$
$312$	4.11605	+	7.53798i	0.233025	+	0.426754i
$313$	18.5624	−	6.92340i	1.04921	−	0.391334i	0.235052	−	0.971983i	$-0.424474\pi$
$313$	18.5624	−	6.92340i	1.04921	−	0.391334i	0.814154	+	0.580649i	$0.197201\pi$
$314$	10.9160	+	7.01529i	0.616026	+	0.395896i
$315$	1.56177	−	0.530193i	0.0879957	−	0.0298730i
$316$	5.61034	+	0.806646i	0.315606	+	0.0453774i
$317$	0.208778	−	0.559756i	0.0117261	−	0.0314390i	−0.930955	−	0.365134i	$-0.881023\pi$
$317$	0.208778	−	0.559756i	0.0117261	−	0.0314390i	0.942681	+	0.333695i	$0.108296\pi$
$318$	8.36002	−	11.1677i	0.468807	−	0.626253i
$319$	26.3996	−	16.9660i	1.47809	−	0.949912i
$320$	−2.22179	+	0.252305i	−0.124202	+	0.0141043i
$321$			5.16800i			0.288449i
$322$	2.64902	+	1.87079i	0.147624	+	0.104255i
$323$	−21.3247	+	21.3247i	−1.18654	+	1.18654i
$324$	−3.42954	−	2.97171i	−0.190530	−	0.165095i
$325$	−30.8128	−	4.05501i	−1.70919	−	0.224931i
$326$	−0.793218	−	5.51695i	−0.0439323	−	0.305556i
$327$	−1.98017	−	0.738564i	−0.109504	−	0.0408427i
$328$	0.870826	+	1.16329i	0.0480833	+	0.0642318i
$329$	−4.16102	+	1.22179i	−0.229404	+	0.0673592i
$330$	−3.05541	−	11.6793i	−0.168195	−	0.642924i
$331$	−11.0245	+	24.1402i	−0.605959	+	1.32687i	0.319344	+	0.947639i	$0.396537\pi$
$331$	−11.0245	+	24.1402i	−0.605959	+	1.32687i	−0.925304	+	0.379227i	$0.876190\pi$
$332$	6.16577	−	3.36677i	0.338391	−	0.184775i
$333$	−0.0672226	+	0.939895i	−0.00368378	+	0.0515059i
$334$	6.64253	−	5.75579i	0.363463	−	0.314943i
$335$	−3.15130	+	12.6619i	−0.172174	+	0.691796i
$336$	−0.849926	−	0.388148i	−0.0463673	−	0.0211752i
$337$	0.126918	−	0.0276093i	0.00691365	−	0.00150397i	−0.209107	−	0.977893i	$-0.567056\pi$
$337$	0.126918	−	0.0276093i	0.00691365	−	0.00150397i	0.216021	+	0.976389i	$0.430692\pi$
$338$	−12.2855	+	22.4992i	−0.668242	+	1.22379i
$339$	2.48870	−	17.3093i	0.135168	−	0.940112i
$340$	5.86690	+	11.5477i	0.318177	+	0.626261i
$341$	−34.8917	+	5.01667i	−1.88949	+	0.271668i
$342$	−1.20712	+	5.54904i	−0.0652735	+	0.300057i
$343$	−9.13449	+	0.653312i	−0.493216	+	0.0352755i
$344$	−3.65149			−0.196875
$345$	11.1788	+	9.72601i	0.601849	+	0.523631i
$346$	−20.7664			−1.11641
$347$	10.2051	−	0.729882i	0.547837	−	0.0391821i	0.205322	−	0.978694i	$-0.434176\pi$
$347$	10.2051	−	0.729882i	0.547837	−	0.0391821i	0.342515	+	0.939512i	$0.388721\pi$
$348$	2.35893	−	10.8438i	0.126452	−	0.581290i
$349$	13.2652	−	1.90725i	0.710072	−	0.102093i	0.222191	−	0.975003i	$-0.428679\pi$
$349$	13.2652	−	1.90725i	0.710072	−	0.102093i	0.487881	+	0.872910i	$0.337770\pi$
$350$	2.94793	−	1.65573i	0.157574	−	0.0885023i
$351$	5.00005	−	34.7761i	0.266883	−	1.85621i
$352$	1.87257	−	3.42936i	0.0998083	−	0.182785i
$353$	16.9651	−	3.69053i	0.902961	−	0.196427i	0.262965	−	0.964805i	$-0.415300\pi$
$353$	16.9651	−	3.69053i	0.902961	−	0.196427i	0.639996	+	0.768378i	$0.278936\pi$
$354$	−12.5845	−	5.74715i	−0.668859	−	0.305457i
$355$	11.7493	−	7.06646i	0.623590	−	0.375049i
$356$	−6.13498	+	5.31599i	−0.325153	+	0.281747i
$357$	−0.386113	+	5.39857i	−0.0204353	+	0.285723i
$358$	18.9996	−	10.3745i	1.00416	−	0.548312i
$359$	0.355602	−	0.778660i	0.0187680	−	0.0410961i	−0.900016	−	0.435857i	$-0.856445\pi$
$359$	0.355602	−	0.778660i	0.0187680	−	0.0410961i	0.918784	+	0.394761i	$0.129173\pi$
$360$	2.10500	+	1.23201i	0.110943	+	0.0649325i
$361$	−7.77687	+	2.28349i	−0.409309	+	0.120184i
$362$	6.82943	+	9.12305i	0.358947	+	0.479497i
$363$	5.52420	+	2.06042i	0.289945	+	0.108144i
$364$	−0.598171	−	4.16037i	−0.0313527	−	0.218063i
$365$	15.9304	+	22.6540i	0.833834	+	1.18576i
$366$	8.28793	+	7.18154i	0.433217	+	0.375385i
$367$	−18.4177	+	18.4177i	−0.961398	+	0.961398i	−0.999282	−	0.0378842i	$-0.987938\pi$
$367$	−18.4177	+	18.4177i	−0.961398	+	0.961398i	0.0378842	+	0.999282i	$0.487938\pi$
$368$	0.474542	+	4.77230i	0.0247372	+	0.248773i
$369$		−	1.58502i		−	0.0825129i
$370$	0.217962	+	1.91937i	0.0113313	+	0.0997833i
$371$	−5.74332	+	3.69100i	−0.298178	+	0.191627i
$372$	−7.47044	+	9.97935i	−0.387325	+	0.517405i
$373$	0.0116625	−	0.0312684i	0.000603862	−	0.00161902i	−0.936647	−	0.350274i	$-0.886089\pi$
$373$	0.0116625	−	0.0312684i	0.000603862	−	0.00161902i	0.937251	+	0.348655i	$0.113361\pi$
$374$	−22.4029	−	3.22106i	−1.15843	−	0.166557i
$375$	14.1642	−	6.16674i	0.731438	−	0.318449i
$376$	−5.39509	−	3.46722i	−0.278231	−	0.178808i
$377$	46.7734	−	17.4456i	2.40895	−	0.898493i
$378$	1.83181	+	3.35472i	0.0942183	+	0.172548i
$379$	−1.00552	−	1.16043i	−0.0516500	−	0.0596073i	0.729337	−	0.684155i	$-0.239829\pi$
$379$	−1.00552	−	1.16043i	−0.0516500	−	0.0596073i	−0.780987	+	0.624548i	$0.785283\pi$
$380$	−0.345992	+	11.6364i	−0.0177490	+	0.596936i
$381$	−3.13742	−	0.921229i	−0.160735	−	0.0471960i
$382$	−4.93897	−	13.2419i	−0.252699	−	0.677513i
$383$	2.82993	+	13.0090i	0.144603	+	0.664727i	0.991187	+	0.132472i	$0.0422915\pi$
$383$	2.82993	+	13.0090i	0.144603	+	0.664727i	−0.846584	+	0.532255i	$0.821345\pi$
$384$	−0.389284	−	1.32578i	−0.0198656	−	0.0676559i
$385$	−0.596437	+	5.87792i	−0.0303972	+	0.299566i
$386$	5.41096	+	11.8484i	0.275411	+	0.603065i
$387$	3.18849	+	2.38688i	0.162080	+	0.121332i
$388$	−3.23302	−	0.703301i	−0.164132	−	0.0357047i
$389$	−7.09896	+	8.19264i	−0.359932	+	0.415383i	−0.906617	−	0.421955i	$-0.861344\pi$
$389$	−7.09896	+	8.19264i	−0.359932	+	0.415383i	0.546685	+	0.837338i	$0.315889\pi$
$390$	−0.800118	−	19.1879i	−0.0405156	−	0.971616i
$391$	24.9403	−	12.2360i	1.26128	−	0.618803i
$392$	−4.62641	−	4.62641i	−0.233669	−	0.233669i
$393$	0.566962	+	7.92716i	0.0285994	+	0.399872i
$394$	4.78910	+	7.45199i	0.241271	+	0.375426i
$395$	−10.4538	−	7.16600i	−0.525987	−	0.360561i
$396$	−3.87681	+	1.77048i	−0.194817	+	0.0889699i
$397$	−26.9875	+	20.2026i	−1.35446	+	1.01394i	−0.357675	+	0.933846i	$0.616430\pi$
$397$	−26.9875	+	20.2026i	−1.35446	+	1.01394i	−0.996788	+	0.0800914i	$0.974479\pi$
$398$	8.91903	+	4.87016i	0.447070	+	0.244119i
$399$	−2.62997	+	4.09231i	−0.131663	+	0.204872i
$400$	4.70529	+	1.69121i	0.235265	+	0.0845607i
$401$	7.99637	−	27.2331i	0.399320	−	1.35996i	−0.477286	−	0.878748i	$-0.658379\pi$
$401$	7.99637	−	27.2331i	0.399320	−	1.35996i	0.876606	−	0.481210i	$-0.159802\pi$
$402$	−8.04243	−	0.575206i	−0.401120	−	0.0286887i
$403$	−55.9333	−	4.00043i	−2.78624	−	0.199276i
$404$	−1.73214	+	5.89912i	−0.0861772	+	0.293492i
$405$	3.93908	+	9.35135i	0.195735	+	0.464672i
$406$	−2.93622	+	4.56884i	−0.145722	+	0.226748i
$407$	−2.96257	−	1.61769i	−0.146849	−	0.0801857i
$408$	−6.40744	+	4.79655i	−0.317216	+	0.237465i
$409$	−15.9120	+	7.26675i	−0.786796	+	0.359318i	−0.767954	−	0.640505i	$-0.778725\pi$
$409$	−15.9120	+	7.26675i	−0.786796	+	0.359318i	−0.0188417	+	0.999822i	$0.505998\pi$
$410$	−0.596018	−	3.19416i	−0.0294352	−	0.157748i
$411$	2.94469	+	4.58202i	0.145251	+	0.226014i
$412$	0.189662	+	2.65182i	0.00934396	+	0.130646i
$413$	4.78753	+	4.78753i	0.235579	+	0.235579i
$414$	2.70514	−	4.47738i	0.132951	−	0.220051i
$415$	−15.6949	+	0.654465i	−0.770434	+	0.0321264i
$416$	4.07041	−	4.69751i	0.199568	−	0.230314i
$417$	−14.4995	−	3.15417i	−0.710043	−	0.154460i
$418$	−16.2850	−	12.1908i	−0.796524	−	0.596270i
$419$	13.7438	+	30.0947i	0.671429	+	1.47022i	0.871476	+	0.490437i	$0.163163\pi$
$419$	13.7438	+	30.0947i	0.671429	+	1.47022i	−0.200048	+	0.979786i	$0.564110\pi$
$420$	1.32067	+	1.61895i	0.0644420	+	0.0789968i
$421$	−10.0658	−	34.2810i	−0.490577	−	1.67075i	−0.717277	−	0.696789i	$-0.754612\pi$
$421$	−10.0658	−	34.2810i	−0.490577	−	1.67075i	0.226699	−	0.973965i	$-0.427207\pi$
$422$	−3.42569	−	15.7476i	−0.166760	−	0.766582i
$423$	2.44459	+	6.55420i	0.118860	+	0.318676i
$424$	−9.68705	−	2.84438i	−0.470445	−	0.138135i
$425$	−0.346103	−	28.9608i	−0.0167885	−	1.40480i
$426$	5.54819	+	6.40295i	0.268811	+	0.310224i
$427$	−2.57209	−	4.71043i	−0.124472	−	0.227954i
$428$	3.50436	−	1.30706i	0.169390	−	0.0631791i
$429$	28.2308	+	18.1428i	1.36300	+	0.875944i
$430$	7.32304	+	3.61109i	0.353148	+	0.174142i
$431$	−6.94987	−	0.999241i	−0.334763	−	0.0481317i	−0.0271165	−	0.999632i	$-0.508632\pi$
$431$	−6.94987	−	0.999241i	−0.334763	−	0.0481317i	−0.307647	+	0.951501i	$0.599542\pi$
$432$	−1.97532	+	5.29603i	−0.0950375	+	0.254805i
$433$	21.1046	−	28.1925i	1.01422	−	1.35484i	0.0805360	−	0.996752i	$-0.474337\pi$
$433$	21.1046	−	28.1925i	1.01422	−	1.35484i	0.933687	−	0.358091i	$-0.116572\pi$
$434$	5.13218	−	3.29825i	0.246352	−	0.158321i
$435$	−15.4547	+	19.4144i	−0.740995	+	0.930849i
$436$			1.52952i			0.0732509i
$437$	24.9445	+	1.09049i	1.19326	+	0.0521651i
$438$	−12.1010	+	12.1010i	−0.578208	+	0.578208i
$439$	−28.3482	−	24.5638i	−1.35298	−	1.17237i	−0.968436	−	0.249262i	$-0.919812\pi$
$439$	−28.3482	−	24.5638i	−1.35298	−	1.17237i	−0.384547	−	0.923105i	$-0.625643\pi$
$440$	−7.14685	+	5.02570i	−0.340713	+	0.239591i
$441$	1.01564	+	7.06395i	0.0483639	+	0.336378i
$442$	−33.7347	−	12.5824i	−1.60460	−	0.598484i
$443$	13.0332	+	17.4103i	0.619226	+	0.827188i	0.995037	−	0.0995077i	$-0.0317268\pi$
$443$	13.0332	+	17.4103i	0.619226	+	0.827188i	−0.375811	+	0.926696i	$0.622636\pi$
$444$	−1.14532	+	0.336297i	−0.0543545	+	0.0159599i
$445$	17.5608	−	4.59407i	0.832464	−	0.217780i
$446$	−6.75652	+	14.7947i	−0.319931	+	0.700550i
$447$	−15.1700	+	8.28342i	−0.717514	+	0.391792i
$448$	−0.0482408	+	0.674494i	−0.00227916	+	0.0318668i
$449$	13.3091	−	11.5324i	0.628094	−	0.544246i	−0.281597	−	0.959533i	$-0.590864\pi$
$449$	13.3091	−	11.5324i	0.628094	−	0.544246i	0.909691	+	0.415286i	$0.136319\pi$
$450$	−3.00318	−	4.55249i	−0.141571	−	0.214606i
$451$	5.16471	+	2.35864i	0.243197	+	0.111064i
$452$	−12.3667	+	2.69021i	−0.581679	+	0.126537i
$453$	8.45714	−	15.4881i	0.397351	−	0.727694i
$454$	−0.693616	+	4.82421i	−0.0325530	+	0.226411i
$455$	−2.91472	+	8.93516i	−0.136644	+	0.418887i
$456$	−7.12053	+	1.02378i	−0.333450	+	0.0479428i
$457$	−5.83849	+	26.8391i	−0.273113	+	1.25548i	0.612281	+	0.790640i	$0.290252\pi$
$457$	−5.83849	+	26.8391i	−0.273113	+	1.25548i	−0.885394	+	0.464841i	$0.846112\pi$
$458$	14.1710	−	1.01353i	0.662168	−	0.0473592i
$459$	32.7420			1.52827
$460$	3.76781	−	10.0401i	0.175675	−	0.468122i
$461$	23.0791			1.07490			0.537451	−	0.843295i	$-0.319387\pi$
$461$	23.0791			1.07490			0.537451	+	0.843295i	$0.319387\pi$
$462$	−3.64154	+	0.260448i	−0.169420	+	0.0121171i
$463$	−0.444460	+	2.04315i	−0.0206558	+	0.0949531i	−0.986321	−	0.164838i	$-0.947290\pi$
$463$	−0.444460	+	2.04315i	−0.0206558	+	0.0949531i	0.965665	+	0.259791i	$0.0836536\pi$
$464$	−7.94969	+	1.14299i	−0.369055	+	0.0530621i
$465$	24.8509	−	12.6257i	1.15243	−	0.585503i
$466$	2.25134	−	15.6584i	0.104291	−	0.725363i
$467$	12.1723	−	22.2920i	0.563269	−	1.03155i	−0.428504	−	0.903540i	$-0.640959\pi$
$467$	12.1723	−	22.2920i	0.563269	−	1.03155i	0.991773	−	0.128010i	$-0.0408589\pi$
$468$	−6.62492	+	1.44116i	−0.306237	+	0.0666178i
$469$	3.58936	+	1.63921i	0.165741	+	0.0756915i
$470$	7.39096	+	12.2889i	0.340920	+	0.566844i
$471$	13.5502	−	11.7413i	0.624359	−	0.541010i
$472$	−0.714280	+	9.98695i	−0.0328774	+	0.459686i
$473$	−12.5223	+	6.83767i	−0.575774	+	0.314396i
$474$	3.25345	−	7.12407i	0.149436	−	0.327219i
$475$	12.2016	−	22.9946i	0.559846	−	1.05506i
$476$	3.75837	−	1.10356i	0.172264	−	0.0505814i
$477$	6.59948	+	8.81587i	0.302169	+	0.403651i
$478$	−10.2051	−	3.80630i	−0.466770	−	0.174096i
$479$	−1.57973	−	10.9873i	−0.0721798	−	0.502021i	−0.993555	−	0.113348i	$-0.963843\pi$
$479$	−1.57973	−	10.9873i	−0.0721798	−	0.502021i	0.921376	−	0.388673i	$-0.127067\pi$
$480$	−0.530406	+	3.04382i	−0.0242096	+	0.138931i
$481$	−4.05811	−	3.51637i	−0.185034	−	0.160333i
$482$	8.68075	−	8.68075i	0.395397	−	0.395397i
$483$	3.51148	−	2.78375i	0.159778	−	0.126665i
$484$		−	4.26701i		−	0.193955i
$485$	5.78828	+	4.60772i	0.262832	+	0.209226i
$486$	8.99044	−	5.77781i	0.407815	−	0.262087i
$487$	3.82413	−	5.10844i	0.173288	−	0.231486i	−0.705486	−	0.708724i	$-0.749271\pi$
$487$	3.82413	−	5.10844i	0.173288	−	0.231486i	0.878774	+	0.477238i	$0.158362\pi$
$488$	2.77359	−	7.43627i	0.125554	−	0.336624i
$489$	−7.62305	−	1.09603i	−0.344726	−	0.0495641i
$490$	4.70300	+	13.8535i	0.212460	+	0.625836i
$491$	9.22863	+	5.93088i	0.416482	+	0.267657i	0.732056	−	0.681244i	$-0.238561\pi$
$491$	9.22863	+	5.93088i	0.416482	+	0.267657i	−0.315574	+	0.948901i	$0.602197\pi$
$492$	1.88126	−	0.701674i	0.0848138	−	0.0316339i
$493$	22.2959	+	40.8319i	1.00416	+	1.83898i
$494$	−21.1916	−	24.4565i	−0.953457	−	1.10035i
$495$	9.52580	+	0.283236i	0.428153	+	0.0127305i
$496$	8.65627	+	2.54171i	0.388678	+	0.114126i
$497$	−1.44898	−	3.88486i	−0.0649955	−	0.174260i
$498$	−2.06335	−	9.48508i	−0.0924611	−	0.425037i
$499$	3.05762	+	10.4133i	0.136878	+	0.466163i	0.999191	−	0.0402119i	$-0.0128033\pi$
$499$	3.05762	+	10.4133i	0.136878	+	0.466163i	−0.862313	+	0.506375i	$0.830985\pi$
$500$	−7.76393	−	8.04496i	−0.347214	−	0.359781i
$501$	−5.04507	−	11.0472i	−0.225397	−	0.493551i
$502$	3.78926	+	2.83661i	0.169123	+	0.126604i
$503$	−26.2694	−	5.71457i	−1.17130	−	0.254800i	−0.415492	−	0.909597i	$-0.636390\pi$
$503$	−26.2694	−	5.71457i	−1.17130	−	0.254800i	−0.755805	+	0.654797i	$0.772754\pi$
$504$	0.483021	−	0.557436i	0.0215155	−	0.0248302i
$505$	9.30766	−	10.1177i	0.414185	−	0.450231i
$506$	10.5638	+	15.4773i	0.469620	+	0.688050i
$507$	25.0464	+	25.0464i	1.11235	+	1.11235i
$508$	0.168822	+	2.36044i	0.00749027	+	0.104728i
$509$	−7.74865	−	12.0571i	−0.343453	−	0.534423i	0.625961	−	0.779854i	$-0.284707\pi$
$509$	−7.74865	−	12.0571i	−0.343453	−	0.534423i	−0.969414	+	0.245431i	$0.921071\pi$
$510$	17.5936	−	3.28289i	0.779056	−	0.145369i
$511$	7.61831	−	3.47916i	0.337014	−	0.153909i
$512$	−0.800541	+	0.599278i	−0.0353793	+	0.0264846i
$513$	25.8283	+	14.1033i	1.14035	+	0.622677i
$514$	−4.13561	+	6.43513i	−0.182414	+	0.283842i
$515$	2.24212	−	5.50577i	0.0987994	−	0.242613i
$516$	−1.42147	+	4.84107i	−0.0625766	+	0.213116i
$517$	−24.9943	−	1.78763i	−1.09925	−	0.0786198i
$518$	0.582685	+	0.0416745i	0.0256017	+	0.00183107i
$519$	−8.08401	+	27.5316i	−0.354849	+	1.20850i
$520$	−12.8087	+	5.39544i	−0.561700	+	0.236606i
$521$	8.84745	−	13.7669i	0.387614	−	0.603139i	−0.591536	−	0.806279i	$-0.701478\pi$
$521$	8.84745	−	13.7669i	0.387614	−	0.603139i	0.979150	+	0.203140i	$0.0651146\pi$
$522$	7.68883	+	4.19842i	0.336531	+	0.183760i
$523$	12.4251	−	9.30135i	0.543314	−	0.406720i	−0.292062	−	0.956399i	$-0.594341\pi$
$523$	12.4251	−	9.30135i	0.543314	−	0.406720i	0.835375	+	0.549680i	$0.185250\pi$
$524$	5.23193	−	2.38934i	0.228558	−	0.104379i
$525$	−1.04755	−	4.55286i	−0.0457187	−	0.198703i
$526$	−10.4938	−	16.3287i	−0.457553	−	0.711966i
$527$	−3.72810	−	52.1257i	−0.162399	−	2.27063i
$528$	−3.81761	−	3.81761i	−0.166140	−	0.166140i
$529$	−21.4187	−	8.38095i	−0.931247	−	0.364389i
$530$	16.6144	+	15.2843i	0.721684	+	0.663906i
$531$	7.15189	−	8.25373i	0.310366	−	0.358181i
$532$	3.44011	+	0.748349i	0.149148	+	0.0324451i
$533$	7.23064	+	5.41279i	0.313194	+	0.234454i
$534$	4.65958	+	10.2031i	0.201640	+	0.441530i
$535$	−8.32057	−	0.844295i	−0.359730	−	0.0365021i
$536$	1.64400	+	5.59896i	0.0710101	+	0.241838i
$537$	−6.35814	−	29.2279i	−0.274374	−	1.26128i
$538$	−2.36987	−	6.35387i	−0.102172	−	0.273935i
$539$	−24.5289	−	7.20233i	−1.05653	−	0.310226i
$540$	9.19893	−	8.66769i	0.395859	−	0.372998i
$541$	4.92446	+	5.68313i	0.211719	+	0.244337i	0.851669	−	0.524080i	$-0.175591\pi$
$541$	4.92446	+	5.68313i	0.211719	+	0.244337i	−0.639950	+	0.768416i	$0.721045\pi$
$542$	4.41970	+	8.09408i	0.189843	+	0.347671i
$543$	14.7538	−	5.50286i	0.633144	−	0.236151i
$544$	4.87302	+	3.13170i	0.208929	+	0.134270i
$545$	1.51260	−	3.06745i	0.0647928	−	0.131395i
$546$	−5.74860	−	0.826524i	−0.246017	−	0.0353719i
$547$	−0.162285	+	0.435103i	−0.00693881	+	0.0186037i	−0.940373	−	0.340145i	$-0.889524\pi$
$547$	−0.162285	+	0.435103i	−0.00693881	+	0.0186037i	0.933434	+	0.358749i	$0.116797\pi$
$548$	2.36227	−	3.15562i	0.100911	−	0.134801i
$549$	−7.28278	+	4.68036i	−0.310822	+	0.199753i
$550$	19.3031	−	3.01122i	0.823085	−	0.128399i
$551$			41.8138i			1.78133i
$552$	6.51175	+	1.22864i	0.277158	+	0.0522944i
$553$	−2.71021	+	2.71021i	−0.115250	+	0.115250i
$554$	5.01610	+	4.34647i	0.213114	+	0.184664i
$555$	2.62951	+	0.458210i	0.111616	+	0.0194499i
$556$	1.52832	+	10.6297i	0.0648150	+	0.450798i
$557$	−19.6132	−	7.31535i	−0.831038	−	0.309961i	−0.102300	−	0.994754i	$-0.532620\pi$
$557$	−19.6132	−	7.31535i	−0.831038	−	0.309961i	−0.728738	+	0.684792i	$0.759893\pi$
$558$	−5.89723	−	7.87778i	−0.249650	−	0.333493i
$559$	−21.7772	+	6.39435i	−0.921076	+	0.270452i
$560$	0.763779	−	1.30499i	0.0322755	−	0.0551457i
$561$	−12.9915	+	28.4475i	−0.548502	+	1.20105i
$562$	3.76777	−	2.05736i	0.158934	−	0.0867844i
$563$	−2.36016	+	32.9993i	−0.0994687	+	1.39075i	0.665361	+	0.746522i	$0.268278\pi$
$563$	−2.36016	+	32.9993i	−0.0994687	+	1.39075i	−0.764830	+	0.644232i	$0.777177\pi$
$564$	−6.69699	+	5.80297i	−0.281994	+	0.244349i
$565$	27.4617	+	6.83468i	1.15532	+	0.287537i
$566$	−2.46273	−	1.12469i	−0.103516	−	0.0472744i
$567$	2.99850	−	0.652283i	0.125925	−	0.0273933i
$568$	2.93855	−	5.38156i	0.123299	−	0.225805i
$569$	−4.10345	+	28.5401i	−0.172026	+	1.19646i	0.702571	+	0.711613i	$0.252035\pi$
$569$	−4.10345	+	28.5401i	−0.172026	+	1.19646i	−0.874597	+	0.484851i	$0.838874\pi$
$570$	15.2926	+	4.98858i	0.640538	+	0.208949i
$571$	37.5317	−	5.39624i	1.57065	−	0.225826i	0.698700	−	0.715415i	$-0.253762\pi$
$571$	37.5317	−	5.39624i	1.57065	−	0.225826i	0.871953	+	0.489589i	$0.162853\pi$
$572$	5.16249	−	23.7316i	0.215854	−	0.992267i
$573$	−19.4785	+	1.39313i	−0.813725	+	0.0581988i
$574$	−0.982628			−0.0410141
$575$	−17.4853	+	16.4092i	−0.729189	+	0.684312i
$576$	1.09077			0.0454486
$577$	9.85791	−	0.705051i	0.410390	−	0.0293517i	0.135382	−	0.990794i	$-0.456774\pi$
$577$	9.85791	−	0.705051i	0.410390	−	0.0293517i	0.275008	+	0.961442i	$0.411319\pi$
$578$	3.51878	−	16.1755i	0.146362	−	0.672814i
$579$	17.8147	−	2.56137i	0.740354	−	0.106447i
$580$	17.0734	+	5.56948i	0.708934	+	0.231260i
$581$	−0.676064	+	4.70213i	−0.0280479	+	0.195077i
$582$	−2.19099	+	4.01249i	−0.0908193	+	0.166323i
$583$	−38.5467	+	8.38531i	−1.59644	+	0.347284i
$584$	11.2661	+	5.14504i	0.466193	+	0.212903i
$585$	14.7115	+	3.66139i	0.608244	+	0.151380i
$586$	−14.4810	+	12.5478i	−0.598204	+	0.518347i
$587$	−3.04303	+	42.5472i	−0.125599	+	1.75611i	0.410414	+	0.911899i	$0.365384\pi$
$587$	−3.04303	+	42.5472i	−0.125599	+	1.75611i	−0.536013	+	0.844210i	$0.680070\pi$
$588$	−7.93459	+	4.33261i	−0.327217	+	0.178674i
$589$	19.5118	−	42.7249i	0.803969	−	1.76045i
$590$	11.3089	−	19.3224i	0.465582	−	0.795490i
$591$	11.7440	−	3.44835i	0.483084	−	0.141846i
$592$	0.517707	+	0.691576i	0.0212776	+	0.0284236i
$593$	7.90076	+	2.94683i	0.324445	+	0.121012i	0.506409	−	0.862293i	$-0.330973\pi$
$593$	7.90076	+	2.94683i	0.324445	+	0.121012i	−0.181964	+	0.983305i	$0.558245\pi$
$594$	3.14312	+	21.8609i	0.128964	+	0.896964i
$595$	−8.62872	−	1.50361i	−0.353743	−	0.0616422i
$596$	9.45359	+	8.19158i	0.387234	+	0.335540i
$597$	9.92879	−	9.92879i	0.406358	−	0.406358i
$598$	11.1872	+	27.6306i	0.457478	+	1.12990i
$599$		−	38.4922i		−	1.57275i	−0.617750	−	0.786374i	$-0.711956\pi$
$599$		−	38.4922i		−	1.57275i	0.617750	−	0.786374i	$-0.288044\pi$
$600$	4.07387	−	5.57982i	0.166315	−	0.227795i
$601$	17.0101	−	10.9318i	0.693858	−	0.445915i	−0.145597	−	0.989344i	$-0.546510\pi$
$601$	17.0101	−	10.9318i	0.693858	−	0.445915i	0.839456	+	0.543428i	$0.182874\pi$
$602$	1.47974	−	1.97670i	0.0603095	−	0.0805641i
$603$	2.22433	−	5.96367i	0.0905818	−	0.242859i
$604$	−12.6412	−	1.81754i	−0.514365	−	0.0739545i
$605$	−4.21980	+	8.55746i	−0.171559	+	0.347910i
$606$	7.14665	+	4.59287i	0.290313	+	0.186573i
$607$	−12.9609	+	4.83416i	−0.526066	+	0.196213i	−0.598444	−	0.801165i	$-0.704214\pi$
$607$	−12.9609	+	4.83416i	−0.526066	+	0.196213i	0.0723776	+	0.997377i	$0.476941\pi$
$608$	2.49510	+	4.56943i	0.101190	+	0.185315i
$609$	4.91425	+	5.67135i	0.199136	+	0.229815i
$610$	−12.9164	+	12.1705i	−0.522970	+	0.492769i
$611$	−38.2475	−	11.2305i	−1.54733	−	0.454337i
$612$	−2.20803	−	5.91996i	−0.0892544	−	0.239300i
$613$	4.09602	+	18.8291i	0.165437	+	0.760500i	0.982844	+	0.184440i	$0.0590471\pi$
$613$	4.09602	+	18.8291i	0.165437	+	0.760500i	−0.817407	+	0.576060i	$0.804589\pi$
$614$	−5.72858	−	19.5098i	−0.231187	−	0.787350i
$615$	−4.46677	−	0.453247i	−0.180118	−	0.0182767i
$616$	1.09760	+	2.40341i	0.0442237	+	0.0968363i
$617$	−27.7063	−	20.7407i	−1.11541	−	0.834988i	−0.127785	−	0.991802i	$-0.540787\pi$
$617$	−27.7063	−	20.7407i	−1.11541	−	0.834988i	−0.987628	+	0.156814i	$0.949878\pi$
$618$	3.58956	+	0.780861i	0.144393	+	0.0314108i
$619$	10.8820	−	12.5585i	0.437383	−	0.504767i	−0.493671	−	0.869649i	$-0.664345\pi$
$619$	10.8820	−	12.5585i	0.437383	−	0.504767i	0.931054	+	0.364882i	$0.118891\pi$
$620$	−14.8465	−	13.6579i	−0.596249	−	0.548514i
$621$	−18.3128	−	19.9872i	−0.734868	−	0.802057i
$622$	0.623929	+	0.623929i	0.0250173	+	0.0250173i
$623$	−0.391606	−	5.47537i	−0.0156894	−	0.219366i
$624$	−4.64331	−	7.22514i	−0.185881	−	0.289237i
$625$	7.61455	+	23.8122i	0.304582	+	0.952486i
$626$	−18.0211	+	8.22998i	−0.720270	+	0.328936i
$627$	−22.5018	+	16.8446i	−0.898634	+	0.672709i
$628$	−11.3887	−	6.21868i	−0.454457	−	0.248152i
$629$	2.70543	−	4.20973i	0.107872	−	0.167853i
$630$	−1.51997	+	0.640257i	−0.0605569	+	0.0255085i
$631$	11.5001	−	39.1659i	0.457813	−	1.55917i	−0.330446	−	0.943825i	$-0.607199\pi$
$631$	11.5001	−	39.1659i	0.457813	−	1.55917i	0.788259	−	0.615343i	$-0.210983\pi$
$632$	−5.65359	−	0.404353i	−0.224888	−	0.0160843i
$633$	−22.2114	−	1.58859i	−0.882826	−	0.0631409i
$634$	−0.168314	+	0.573223i	−0.00668459	+	0.0227656i
$635$	1.99576	−	4.90080i	0.0791992	−	0.194482i
$636$	−7.54203	+	11.7356i	−0.299061	+	0.465348i
$637$	−35.6931	−	19.4899i	−1.41421	−	0.772218i
$638$	−25.1220	+	18.8061i	−0.994589	+	0.744540i
$639$	−6.08373	+	2.77835i	−0.240669	+	0.109910i
$640$	2.19813	−	0.410162i	0.0868886	−	0.0162131i
$641$	16.1214	+	25.0853i	0.636755	+	0.990811i	0.998290	+	0.0584521i	$0.0186165\pi$
$641$	16.1214	+	25.0853i	0.636755	+	0.990811i	−0.361535	+	0.932359i	$0.617747\pi$
$642$	−0.368681	−	5.15483i	−0.0145507	−	0.203445i
$643$	15.0124	+	15.0124i	0.592031	+	0.592031i	0.938180	−	0.346149i	$-0.112511\pi$
$643$	15.0124	+	15.0124i	0.592031	+	0.592031i	−0.346149	+	0.938180i	$0.612511\pi$
$644$	−2.77574	−	1.67704i	−0.109379	−	0.0660848i
$645$	7.63826	−	8.30299i	0.300756	−	0.326930i
$646$	19.7491	−	22.7916i	0.777016	−	0.896725i
$647$	−40.5675	−	8.82492i	−1.59487	−	0.346943i	−0.674589	−	0.738194i	$-0.735679\pi$
$647$	−40.5675	−	8.82492i	−1.59487	−	0.346943i	−0.920284	+	0.391250i	$0.872043\pi$
$648$	3.63280	+	2.71948i	0.142710	+	0.106831i
$649$	16.2517	+	35.5863i	0.637937	+	1.39689i
$650$	31.0236	+	1.84652i	1.21684	+	0.0724263i
$651$	−2.37488	−	8.08809i	−0.0930788	−	0.316997i
$652$	1.18477	+	5.44631i	0.0463992	+	0.213294i
$653$	1.28395	+	3.44241i	0.0502450	+	0.134712i	0.959648	−	0.281204i	$-0.0907337\pi$
$653$	1.28395	+	3.44241i	0.0502450	+	0.134712i	−0.909403	+	0.415916i	$0.863461\pi$
$654$	2.02781	+	0.595419i	0.0792937	+	0.0232827i
$655$	−12.8555	−	0.382240i	−0.502306	−	0.0149354i
$656$	−0.951595	−	1.09820i	−0.0371536	−	0.0428775i
$657$	−6.47440	−	11.8570i	−0.252590	−	0.462585i
$658$	4.06326	−	1.51552i	0.158402	−	0.0590810i
$659$	1.74793	+	1.12333i	0.0680897	+	0.0437586i	0.574243	−	0.818685i	$-0.305297\pi$
$659$	1.74793	+	1.12333i	0.0680897	+	0.0437586i	−0.506153	+	0.862444i	$0.668933\pi$
$660$	3.88081	+	11.4316i	0.151061	+	0.444973i
$661$	19.0113	+	2.73341i	0.739453	+	0.106317i	0.501740	−	0.865018i	$-0.332693\pi$
$661$	19.0113	+	2.73341i	0.739453	+	0.106317i	0.237713	+	0.971336i	$0.423602\pi$
$662$	9.27423	−	24.8652i	0.360453	−	0.966412i
$663$	−29.8139	+	39.8267i	−1.15788	+	1.54674i
$664$	−5.90988	+	3.79805i	−0.229348	+	0.147393i
$665$	−6.15904	−	4.90286i	−0.238837	−	0.190125i
$666$		−	0.942296i		−	0.0365132i
$667$	12.4553	−	36.4480i	0.482273	−	1.41127i
$668$	−6.21499	+	6.21499i	−0.240465	+	0.240465i
$669$	16.9843	+	14.7170i	0.656652	+	0.568992i
$670$	2.23998	−	12.8545i	0.0865381	−	0.496612i
$671$	−4.41333	−	30.6954i	−0.170375	−	1.18498i
$672$	0.875451	+	0.326526i	0.0337713	+	0.0125960i
$673$	7.88296	+	10.5304i	0.303866	+	0.405917i	0.926319	−	0.376740i	$-0.122955\pi$
$673$	7.88296	+	10.5304i	0.303866	+	0.405917i	−0.622453	+	0.782657i	$0.713864\pi$
$674$	−0.124625	+	0.0365931i	−0.00480036	+	0.00140951i
$675$	−27.0202	+	8.28583i	−1.04001	+	0.318922i
$676$	10.6491	−	23.3183i	0.409581	−	0.896857i
$677$	−19.2786	+	10.5269i	−0.740938	+	0.404583i	−0.804932	−	0.593367i	$-0.797798\pi$
$677$	−19.2786	+	10.5269i	−0.740938	+	0.404583i	0.0639936	+	0.997950i	$0.479616\pi$
$678$	−1.24753	+	17.4427i	−0.0479111	+	0.669884i
$679$	1.69088	−	1.46516i	0.0648900	−	0.0562275i
$680$	−6.67575	−	11.0997i	−0.256003	−	0.425655i
$681$	6.12582	+	2.79757i	0.234742	+	0.107203i
$682$	34.4450	−	7.49304i	1.31897	−	0.286923i
$683$	3.43302	−	6.28711i	0.131361	−	0.240570i	−0.803717	−	0.595012i	$-0.797147\pi$
$683$	3.43302	−	6.28711i	0.131361	−	0.240570i	0.935078	+	0.354442i	$0.115329\pi$
$684$	0.808180	−	5.62101i	0.0309015	−	0.214925i
$685$	−7.85822	+	3.99244i	−0.300247	+	0.152543i
$686$	9.06461	−	1.30329i	0.346088	−	0.0497600i
$687$	4.17283	−	19.1822i	0.159203	−	0.731846i
$688$	3.64219	−	0.260494i	0.138857	−	0.00993125i
$689$	−62.7537			−2.39073
$690$	−11.8442	−	8.90374i	−0.450901	−	0.338960i
$691$	−29.2883			−1.11418			−0.557090	−	0.830452i	$-0.688082\pi$
$691$	−29.2883			−1.11418			−0.557090	+	0.830452i	$0.688082\pi$
$692$	20.7134	−	1.48145i	0.787407	−	0.0563165i
$693$	0.612614	−	2.81614i	0.0232713	−	0.106976i
$694$	−10.1270	+	1.45604i	−0.384416	+	0.0552707i
$695$	7.44705	−	22.8291i	0.282483	−	0.865959i
$696$	−1.57933	+	10.9845i	−0.0598643	+	0.416366i
$697$	−4.03400	+	7.38772i	−0.152799	+	0.279830i
$698$	−13.0954	+	2.84873i	−0.495668	+	0.107826i
$699$	−19.8832	−	9.08037i	−0.752053	−	0.343451i
$700$	−2.82230	+	1.86181i	−0.106673	+	0.0703698i
$701$	10.3014	−	8.92624i	0.389080	−	0.337140i	−0.438253	−	0.898852i	$-0.644403\pi$
$701$	10.3014	−	8.92624i	0.389080	−	0.337140i	0.827333	+	0.561712i	$0.189857\pi$
$702$	−2.50641	+	35.0442i	−0.0945983	+	1.32266i
$703$	3.94746	−	2.15548i	0.148881	−	0.0812953i
$704$	−1.62315	+	3.55421i	−0.0611748	+	0.133954i
$705$	19.1695	−	5.01492i	0.721967	−	0.188873i
$706$	−16.6586	+	4.89140i	−0.626954	+	0.184090i
$707$	−2.49149	−	3.32825i	−0.0937023	−	0.125172i
$708$	12.9624	+	4.83474i	0.487158	+	0.181701i
$709$	3.42866	+	23.8468i	0.128766	+	0.895587i	0.947122	+	0.320875i	$0.103977\pi$
$709$	3.42866	+	23.8468i	0.128766	+	0.895587i	−0.818356	+	0.574712i	$0.805114\pi$
$710$	−11.2153	+	7.88664i	−0.420902	+	0.295980i
$711$	4.67242	+	4.04868i	0.175229	+	0.151837i
$712$	5.74011	−	5.74011i	0.215120	−	0.215120i
$713$	−29.7347	+	31.4300i	−1.11357	+	1.17706i
$714$		−	5.41236i		−	0.202553i
$715$	−33.8224	+	42.4881i	−1.26488	+	1.58897i
$716$	−18.2110	+	11.7035i	−0.680579	+	0.437381i
$717$	−9.01900	+	12.0480i	−0.336821	+	0.449940i
$718$	−0.299147	+	0.802045i	−0.0111641	+	0.0299321i
$719$	37.3531	+	5.37056i	1.39303	+	0.200288i	0.797634	−	0.603141i	$-0.206084\pi$
$719$	37.3531	+	5.37056i	1.39303	+	0.200288i	0.595400	+	0.803429i	$0.296994\pi$
$720$	−2.18752	−	1.07870i	−0.0815242	−	0.0402007i
$721$	−1.51239	−	0.971956i	−0.0563244	−	0.0361975i
$722$	7.59415	−	2.83247i	0.282625	−	0.105414i
$723$	−8.12949	−	14.8880i	−0.302339	−	0.553692i
$724$	−7.46286	−	8.61260i	−0.277355	−	0.320085i
$725$	−28.7327	−	28.0541i	−1.06711	−	1.04190i
$726$	−5.65711	−	1.66108i	−0.209955	−	0.0616484i
$727$	−5.44774	−	14.6060i	−0.202046	−	0.541705i	0.795924	−	0.605397i	$-0.206985\pi$
$727$	−5.44774	−	14.6060i	−0.202046	−	0.541705i	−0.997970	+	0.0636913i	$0.979713\pi$
$728$	0.893445	+	4.10710i	0.0331133	+	0.152219i
$729$	−7.99571	−	27.2309i	−0.296138	−	1.00855i
$730$	−17.5059	−	21.4598i	−0.647923	−	0.794262i
$731$	−8.78665	−	19.2401i	−0.324986	−	0.711620i
$732$	−8.77914	−	6.57198i	−0.324486	−	0.242908i
$733$	−21.9592	−	4.77692i	−0.811080	−	0.176440i	−0.212146	−	0.977238i	$-0.568045\pi$
$733$	−21.9592	−	4.77692i	−0.811080	−	0.176440i	−0.598934	+	0.800798i	$0.704409\pi$
$734$	17.0569	−	19.6847i	0.629582	−	0.726576i
$735$	20.1974	−	0.842216i	0.744994	−	0.0310656i
$736$	−0.813785	−	4.72628i	−0.0299965	−	0.174213i
$737$	16.1223	+	16.1223i	0.593873	+	0.593873i
$738$	0.113074	+	1.58098i	0.00416231	+	0.0581968i
$739$	−2.00965	−	3.12708i	−0.0739262	−	0.115031i	0.802322	−	0.596891i	$-0.203598\pi$
$739$	−2.00965	−	3.12708i	−0.0739262	−	0.115031i	−0.876248	+	0.481860i	$0.839961\pi$
$740$	−0.354333	−	1.89893i	−0.0130255	−	0.0698060i
$741$	−40.6735	+	18.5749i	−1.49418	+	0.682368i
$742$	5.46537	−	4.09132i	0.200640	−	0.150197i
$743$	−0.0284225	−	0.0155199i	−0.00104272	−	0.000569369i	0.478728	−	0.877964i	$-0.341098\pi$
$743$	−0.0284225	−	0.0155199i	−0.00104272	−	0.000569369i	−0.479770	+	0.877394i	$0.659280\pi$
$744$	6.73949	−	10.4869i	0.247082	−	0.384467i
$745$	−10.8582	−	25.7772i	−0.397812	−	0.944402i
$746$	−0.00940214	+	0.0320208i	−0.000344237	+	0.00117236i
$747$	7.64320	+	0.546653i	0.279650	+	0.0200010i
$748$	22.5756	+	1.61464i	0.825448	+	0.0590372i
$749$	−0.712551	+	2.42672i	−0.0260360	+	0.0886706i
$750$	−13.6882	+	7.16149i	−0.499823	+	0.261501i
$751$	−27.3719	+	42.5916i	−0.998816	+	1.55419i	−0.177178	+	0.984179i	$0.556697\pi$
$751$	−27.3719	+	42.5916i	−0.998816	+	1.55419i	−0.821638	+	0.570009i	$0.806940\pi$
$752$	5.62870	+	3.07350i	0.205257	+	0.112079i
$753$	5.23581	−	3.91948i	0.190804	−	0.142834i
$754$	−45.4097	+	20.7379i	−1.65372	+	0.755230i
$755$	23.5545	+	16.1464i	0.857236	+	0.587629i
$756$	−2.06647	−	3.21549i	−0.0751568	−	0.116946i
$757$	3.15757	+	44.1485i	0.114764	+	1.60461i	0.650021	+	0.759917i	$0.274760\pi$
$757$	3.15757	+	44.1485i	0.114764	+	1.60461i	−0.535257	+	0.844689i	$0.679785\pi$
$758$	1.08574	+	1.08574i	0.0394359	+	0.0394359i
$759$	24.6318	−	7.98026i	0.894078	−	0.289665i
$760$	−0.485022	−	11.6315i	−0.0175936	−	0.421917i
$761$	−15.1473	+	17.4809i	−0.549088	+	0.633681i	−0.960670	−	0.277692i	$-0.910431\pi$
$761$	−15.1473	+	17.4809i	−0.549088	+	0.633681i	0.411583	+	0.911372i	$0.364976\pi$
$762$	3.19515	+	0.695061i	0.115748	+	0.0251794i
$763$	−0.827991	−	0.619827i	−0.0299753	−	0.0224392i
$764$	5.87105	+	12.8558i	0.212407	+	0.465106i
$765$	−1.42628	+	14.0561i	−0.0515672	+	0.508198i
$766$	−3.75077	−	12.7739i	−0.135521	−	0.461541i
$767$	13.2289	+	60.8121i	0.477667	+	2.19580i
$768$	0.482872	+	1.29463i	0.0174242	+	0.0467160i
$769$	6.70935	+	1.97004i	0.241945	+	0.0710416i	0.400457	−	0.916316i	$-0.368851\pi$
$769$	6.70935	+	1.97004i	0.241945	+	0.0710416i	−0.158512	+	0.987357i	$0.550670\pi$
$770$	0.175591	−	5.90549i	0.00632787	−	0.212819i
$771$	6.92164	+	7.98800i	0.249277	+	0.287681i
$772$	−6.24243	−	11.4322i	−0.224670	−	0.411452i
$773$	−30.2219	+	11.2722i	−1.08701	+	0.405433i	−0.828163	−	0.560487i	$-0.810614\pi$
$773$	−30.2219	+	11.2722i	−1.08701	+	0.405433i	−0.258843	+	0.965919i	$0.583341\pi$
$774$	−3.35065	−	2.15333i	−0.120436	−	0.0773998i
$775$	16.2677	+	42.0730i	0.584355	+	1.51131i
$776$	3.27496	+	0.470868i	0.117564	+	0.0169032i
$777$	0.282081	−	0.756289i	0.0101196	−	0.0271317i
$778$	6.49642	−	8.67820i	0.232908	−	0.311128i
$779$	−6.36439	+	4.09014i	−0.228028	+	0.146545i
$780$	2.16693	+	19.0819i	0.0775884	+	0.683242i
$781$		−	23.9579i		−	0.857283i
$782$	−24.0038	+	13.9841i	−0.858375	+	0.500070i
$783$	32.1005	−	32.1005i	1.14718	−	1.14718i
$784$	4.94467	+	4.28458i	0.176595	+	0.153021i
$785$	16.6900	+	23.7342i	0.595692	+	0.847110i
$786$	−1.13103	−	7.86652i	−0.0403427	−	0.280589i
$787$	21.1438	+	7.88623i	0.753695	+	0.281114i	0.696799	−	0.717266i	$-0.254607\pi$
$787$	21.1438	+	7.88623i	0.753695	+	0.281114i	0.0568960	+	0.998380i	$0.481880\pi$
$788$	−5.30852	−	7.09135i	−0.189108	−	0.252619i
$789$	−25.7334	+	7.55599i	−0.916132	+	0.269001i
$790$	10.9384	+	6.40198i	0.389170	+	0.227772i
$791$	3.55518	−	7.78475i	0.126408	−	0.276794i
$792$	3.74063	−	2.04254i	0.132917	−	0.0725784i
$793$	3.51930	−	49.2063i	0.124974	−	1.74737i
$794$	25.4775	−	22.0764i	0.904162	−	0.783461i
$795$	26.7313	−	16.0771i	0.948061	−	0.570197i
$796$	−9.24374	−	4.22147i	−0.327636	−	0.149626i
$797$	−1.76920	+	0.384867i	−0.0626684	+	0.0136327i	−0.243790	−	0.969828i	$-0.578391\pi$
$797$	−1.76920	+	0.384867i	−0.0626684	+	0.0136327i	0.181122	+	0.983461i	$0.442027\pi$
$798$	2.33133	−	4.26950i	0.0825280	−	0.151139i
$799$	5.28681	−	36.7705i	0.187034	−	1.30085i
$800$	−4.81396	−	1.35123i	−0.170199	−	0.0477733i
$801$	−8.76443	+	1.26013i	−0.309676	+	0.0445247i
$802$	−6.03321	+	27.7342i	−0.213040	+	0.979329i
$803$	48.2698	−	3.45233i	1.70341	−	0.121830i
$804$	8.06297			0.284359
$805$	3.90823	+	6.10833i	0.137747	+	0.215290i
$806$	56.0762			1.97520
$807$	−9.34639	+	0.668467i	−0.329008	+	0.0235311i
$808$	1.30689	−	6.00766i	0.0459761	−	0.211349i
$809$	17.5210	−	2.51914i	0.616005	−	0.0885681i	0.172753	−	0.984965i	$-0.444734\pi$
$809$	17.5210	−	2.51914i	0.616005	−	0.0885681i	0.443252	+	0.896397i	$0.353825\pi$
$810$	−4.59616	−	9.04652i	−0.161493	−	0.317862i
$811$	−7.05851	+	49.0930i	−0.247858	+	1.72389i	0.362689	+	0.931910i	$0.381859\pi$
$811$	−7.05851	+	49.0930i	−0.247858	+	1.72389i	−0.610547	+	0.791980i	$0.709050\pi$
$812$	2.60280	−	4.76667i	0.0913403	−	0.167277i
$813$	12.4515	−	2.70866i	0.436693	−	0.0949967i
$814$	3.07043	+	1.40222i	0.107618	+	0.0491477i
$815$	3.01000	−	12.0942i	0.105436	−	0.423641i
$816$	6.04893	−	5.24143i	0.211755	−	0.183487i
$817$	1.35620	−	18.9622i	0.0474475	−	0.663403i
$818$	15.3530	−	8.38338i	0.536806	−	0.293118i
$819$	1.90454	−	4.17035i	0.0665499	−	0.145724i
$820$	0.822368	+	3.14350i	0.0287183	+	0.109776i
$821$	16.9342	−	4.97234i	0.591009	−	0.173536i	0.0274659	−	0.999623i	$-0.491256\pi$
$821$	16.9342	−	4.97234i	0.591009	−	0.173536i	0.563543	+	0.826087i	$0.309438\pi$
$822$	−3.26406	−	4.36028i	−0.113847	−	0.152082i
$823$	25.2523	+	9.41863i	0.880241	+	0.328313i	0.748630	−	0.662988i	$-0.230712\pi$
$823$	25.2523	+	9.41863i	0.880241	+	0.328313i	0.131611	+	0.991301i	$0.457985\pi$
$824$	−0.378357	−	2.63153i	−0.0131807	−	0.0916737i
$825$	3.52216	−	26.7638i	0.122626	−	0.931796i
$826$	−5.11687	−	4.43379i	−0.178039	−	0.154271i
$827$	7.60159	−	7.60159i	0.264333	−	0.264333i	−0.562479	−	0.826812i	$-0.690152\pi$
$827$	7.60159	−	7.60159i	0.264333	−	0.264333i	0.826812	+	0.562479i	$0.190152\pi$
$828$	−2.37884	+	4.65895i	−0.0826703	+	0.161910i
$829$		−	26.4541i		−	0.918790i	−0.888232	−	0.459395i	$-0.848066\pi$
$829$		−	26.4541i		−	0.918790i	0.888232	−	0.459395i	$-0.151934\pi$
$830$	15.6083	−	1.77246i	0.541770	−	0.0615230i
$831$	7.71516	−	4.95823i	0.267636	−	0.171999i
$832$	−3.72493	+	4.97592i	−0.129139	+	0.172509i
$833$	13.2444	−	35.5097i	0.458892	−	1.23034i
$834$	14.6876	+	2.11175i	0.508588	+	0.0731240i
$835$	18.6104	−	6.31789i	0.644038	−	0.218640i
$836$	17.1132	+	10.9980i	0.591871	+	0.380372i
$837$	−47.7792	+	17.8207i	−1.65149	+	0.615975i
$838$	−15.8557	−	29.0376i	−0.547727	−	1.00309i
$839$	−2.43822	−	2.81386i	−0.0841768	−	0.0971452i	0.712099	−	0.702079i	$-0.247745\pi$
$839$	−2.43822	−	2.81386i	−0.0841768	−	0.0971452i	−0.796275	+	0.604934i	$0.793199\pi$
$840$	−1.43280	−	1.52061i	−0.0494362	−	0.0524661i
$841$	34.0658	+	10.0026i	1.17468	+	0.344918i
$842$	12.4857	+	33.4756i	0.430287	+	1.15364i
$843$	−1.26087	−	5.79613i	−0.0434267	−	0.199629i
$844$	4.54038	+	15.4631i	0.156286	+	0.532262i
$845$	−44.4170	+	36.2333i	−1.52799	+	1.24647i
$846$	−2.90593	−	6.36311i	−0.0999081	−	0.218768i
$847$	2.30990	+	1.72917i	0.0793691	+	0.0594150i
$848$	9.86529	+	2.14606i	0.338775	+	0.0736961i
$849$	−2.44980	+	2.82722i	−0.0840768	+	0.0970298i
$850$	2.41126	+	28.8623i	0.0827055	+	0.989969i
$851$	−4.08297	+	0.703016i	−0.139962	+	0.0240991i
$852$	−5.99083	−	5.99083i	−0.205243	−	0.205243i
$853$	2.49634	+	34.9034i	0.0854732	+	1.19507i	0.841399	+	0.540414i	$0.181732\pi$
$853$	2.49634	+	34.9034i	0.0854732	+	1.19507i	−0.755926	+	0.654657i	$0.772813\pi$
$854$	2.90157	+	4.51494i	0.0992898	+	0.154498i
$855$	−7.17963	+	10.4737i	−0.245538	+	0.358192i
$856$	−3.40219	+	1.55373i	−0.116284	+	0.0531053i
$857$	19.2810	−	14.4336i	0.658625	−	0.493041i	−0.216912	−	0.976191i	$-0.569598\pi$
$857$	19.2810	−	14.4336i	0.658625	−	0.493041i	0.875537	+	0.483150i	$0.160508\pi$
$858$	−29.4532	−	16.0826i	−1.00551	−	0.549052i
$859$	10.2753	−	15.9887i	0.350588	−	0.545526i	−0.620512	−	0.784197i	$-0.713075\pi$
$859$	10.2753	−	15.9887i	0.350588	−	0.545526i	0.971101	+	0.238671i	$0.0767116\pi$
$860$	−7.56199	−	3.07947i	−0.257862	−	0.105009i
$861$	−0.382522	+	1.30275i	−0.0130363	+	0.0443976i
$862$	7.00345	+	0.500897i	0.238538	+	0.0170606i
$863$	−5.04209	−	0.360617i	−0.171635	−	0.0122755i	−0.0147427	−	0.999891i	$-0.504693\pi$
$863$	−5.04209	−	0.360617i	−0.171635	−	0.0122755i	−0.156892	+	0.987616i	$0.550147\pi$
$864$	1.59247	−	5.42345i	0.0541769	−	0.184510i
$865$	−43.0057	−	17.5132i	−1.46224	−	0.595468i
$866$	−19.0396	+	29.6262i	−0.646992	+	1.00674i
$867$	−20.0754	−	10.9620i	−0.681797	−	0.372289i
$868$	−4.88381	+	3.65597i	−0.165767	+	0.124092i
$869$	−20.1454	+	9.20008i	−0.683385	+	0.312091i
$870$	14.0303	−	20.4674i	0.475672	−	0.693911i
$871$	19.6094	+	30.5128i	0.664439	+	1.03389i
$872$	−0.109115	−	1.52563i	−0.00369510	−	0.0516642i
$873$	−2.55191	−	2.55191i	−0.0863690	−	0.0863690i
$874$	−24.9588	+	0.691814i	−0.844243	+	0.0234010i
$875$	7.50132	−	0.942770i	0.253591	−	0.0318715i
$876$	11.2069	−	12.9334i	0.378646	−	0.436981i
$877$	34.0686	+	7.41117i	1.15041	+	0.250257i	0.747041	−	0.664778i	$-0.231474\pi$
$877$	34.0686	+	7.41117i	1.15041	+	0.250257i	0.403374	+	0.915035i	$0.367838\pi$
$878$	30.0283	+	22.4789i	1.01341	+	0.758626i
$879$	10.9985	+	24.0833i	0.370969	+	0.812308i
$880$	6.77011	−	5.52274i	0.228220	−	0.186172i
$881$	−10.7539	−	36.6243i	−0.362307	−	1.23391i	−0.915998	−	0.401183i	$-0.868599\pi$
$881$	−10.7539	−	36.6243i	−0.362307	−	1.23391i	0.553690	−	0.832723i	$-0.313219\pi$
$882$	−1.51699	−	6.97349i	−0.0510797	−	0.234810i
$883$	−1.49129	−	3.99832i	−0.0501861	−	0.134554i	0.909438	−	0.415839i	$-0.136512\pi$
$883$	−1.49129	−	3.99832i	−0.0501861	−	0.134554i	−0.959624	+	0.281285i	$0.909239\pi$
$884$	34.5464	+	10.1437i	1.16192	+	0.341171i
$885$	−21.2148	−	22.5151i	−0.713128	−	0.756836i
$886$	−14.2420	−	16.4362i	−0.478470	−	0.552184i
$887$	9.73989	+	17.8373i	0.327034	+	0.598917i	0.988529	−	0.151032i	$-0.0482597\pi$
$887$	9.73989	+	17.8373i	0.327034	+	0.598917i	−0.661495	+	0.749949i	$0.730078\pi$
$888$	1.11841	−	0.417146i	0.0375314	−	0.0139985i
$889$	−1.34621	−	0.865159i	−0.0451506	−	0.0290165i
$890$	−17.1884	+	5.83514i	−0.576155	+	0.195594i
$891$	17.5506	+	2.52339i	0.587967	+	0.0845369i
$892$	5.68386	−	15.2390i	0.190310	−	0.510240i
$893$	20.0090	−	26.7290i	0.669577	−	0.894450i
$894$	14.5404	−	9.34453i	0.486303	−	0.312528i
$895$	48.0962	−	5.46177i	1.60768	−	0.182567i
$896$		−	0.676217i		−	0.0225908i
$897$	40.9870	−	4.07562i	1.36852	−	0.136081i
$898$	−12.4524	+	12.4524i	−0.415544	+	0.415544i
$899$	−54.7595	−	47.4494i	−1.82633	−	1.58253i
$900$	3.32030	+	4.32665i	0.110677	+	0.144222i
$901$	−8.32283	−	57.8866i	−0.277274	−	1.92848i
$902$	−5.31982	−	1.98419i	−0.177131	−	0.0660663i
$903$	−2.04463	−	2.73130i	−0.0680409	−	0.0908920i
$904$	12.1432	−	3.56558i	0.403878	−	0.118589i
$905$	6.44940	+	24.6528i	0.214385	+	0.819488i
$906$	−7.33068	+	16.0520i	−0.243546	+	0.533291i
$907$	36.1471	−	19.7378i	1.20024	−	0.655383i	0.250412	−	0.968139i	$-0.419434\pi$
$907$	36.1471	−	19.7378i	1.20024	−	0.655383i	0.949833	+	0.312756i	$0.101252\pi$
$908$	0.347694	−	4.86140i	0.0115386	−	0.161331i
$909$	−5.06822	+	4.39164i	−0.168102	+	0.145661i
$910$	2.26987	−	9.12032i	0.0752454	−	0.302336i
$911$	46.4880	+	21.2304i	1.54022	+	0.703393i	0.991194	−	0.132415i	$-0.0422731\pi$
$911$	46.4880	+	21.2304i	1.54022	+	0.703393i	0.549022	+	0.835808i	$0.315000\pi$
$912$	7.02936	−	1.52914i	0.232765	−	0.0506350i
$913$	−13.1550	+	24.0915i	−0.435366	+	0.797313i
$914$	3.90894	−	27.1872i	0.129296	−	0.899274i
$915$	11.1072	+	21.8621i	0.367194	+	0.722738i
$916$	−14.0626	+	2.02190i	−0.464641	+	0.0668054i
$917$	−0.826750	+	3.80051i	−0.0273017	+	0.125504i
$918$	−32.6586	+	2.33579i	−1.07789	+	0.0770925i
$919$	55.9704			1.84629			0.923146	−	0.384448i	$-0.125608\pi$
$919$	55.9704			1.84629			0.923146	+	0.384448i	$0.125608\pi$
$920$	−3.04196	+	10.2833i	−0.100290	+	0.339031i
$921$	−28.0957			−0.925784
$922$	−23.0203	+	1.64645i	−0.758134	+	0.0542228i
$923$	8.10130	−	37.2411i	0.266657	−	1.22580i
$924$	3.61368	−	0.519568i	0.118881	−	0.0170925i
$925$	−1.16731	+	4.15870i	−0.0383809	+	0.136737i
$926$	0.297571	−	2.06965i	0.00977878	−	0.0680129i
$927$	−1.38977	+	2.54518i	−0.0456462	+	0.0835947i
$928$	7.84789	−	1.70720i	0.257620	−	0.0560417i
$929$	16.7331	+	7.64176i	0.548996	+	0.250718i	0.670547	−	0.741867i	$-0.266059\pi$
$929$	16.7331	+	7.64176i	0.548996	+	0.250718i	−0.121551	+	0.992585i	$0.538787\pi$
$930$	−23.8868	+	14.3664i	−0.783281	+	0.471092i
$931$	25.7432	−	22.3066i	0.843700	−	0.731071i
$932$	−1.12855	+	15.7792i	−0.0369668	+	0.516863i
$933$	1.07008	−	0.584307i	0.0350328	−	0.0191294i
$934$	−10.5510	+	23.1035i	−0.345240	+	0.755971i
$935$	−43.6785	−	25.5641i	−1.42844	−	0.836034i
$936$	6.50523	−	1.91011i	0.212630	−	0.0624339i
$937$	16.3280	+	21.8117i	0.533413	+	0.712556i	0.983597	−	0.180379i	$-0.0577326\pi$
$937$	16.3280	+	21.8117i	0.533413	+	0.712556i	−0.450184	+	0.892936i	$0.648642\pi$
$938$	−3.69716	−	1.37897i	−0.120716	−	0.0450249i
$939$	3.89580	+	27.0959i	0.127135	+	0.884240i
$940$	−8.24881	−	11.7303i	−0.269047	−	0.382601i
$941$	−22.9066	−	19.8487i	−0.746733	−	0.647048i	0.195997	−	0.980605i	$-0.437206\pi$
$941$	−22.9066	−	19.8487i	−0.746733	−	0.647048i	−0.942730	+	0.333556i	$0.891751\pi$
$942$	−12.6780	+	12.6780i	−0.413072	+	0.413072i
$943$	6.76603	−	1.66947i	0.220332	−	0.0543654i
$944$		−	10.0125i		−	0.325878i
$945$	0.964374	+	8.49225i	0.0313711	+	0.276253i
$946$	12.0026	−	7.71358i	0.390237	−	0.250790i
$947$	17.2690	−	23.0687i	0.561168	−	0.749633i	−0.426791	−	0.904350i	$-0.640356\pi$
$947$	17.2690	−	23.0687i	0.561168	−	0.749633i	0.987959	+	0.154718i	$0.0494468\pi$
$948$	−2.73694	+	7.33801i	−0.0888916	+	0.238328i
$949$	76.1997	+	10.9559i	2.47355	+	0.355642i
$950$	−10.5301	+	23.8065i	−0.341641	+	0.772383i
$951$	0.694446	+	0.446294i	0.0225190	+	0.0144721i
$952$	−3.67006	+	1.36886i	−0.118947	+	0.0443651i
$953$	−17.1015	−	31.3191i	−0.553973	−	1.01453i	−0.993230	−	0.116164i	$-0.962940\pi$
$953$	−17.1015	−	31.3191i	−0.553973	−	1.01453i	0.439257	−	0.898361i	$-0.355242\pi$
$954$	−7.21158	−	8.32260i	−0.233483	−	0.269454i
$955$	0.939234	−	31.5883i	0.0303929	−	1.02217i
$956$	10.4506	+	3.06858i	0.337998	+	0.0992451i
$957$	15.1531	+	40.6271i	0.489831	+	1.31329i
$958$	2.35953	+	10.8466i	0.0762329	+	0.350437i
$959$	0.750972	+	2.55758i	0.0242501	+	0.0825884i
$960$	0.311911	−	3.07390i	0.0100669	−	0.0992098i
$961$	20.9333	+	45.8375i	0.675267	+	1.47863i
$962$	4.29862	+	3.21791i	0.138593	+	0.103750i
$963$	3.98643	+	0.867195i	0.128461	+	0.0279450i
$964$	−8.03936	+	9.27791i	−0.258930	+	0.298821i
$965$	1.21347	+	29.1005i	0.0390628	+	0.936777i
$966$	−3.30394	+	3.02717i	−0.106303	+	0.0973975i
$967$	19.0473	+	19.0473i	0.612521	+	0.612521i	0.943602	−	0.331081i	$-0.107413\pi$
$967$	19.0473	+	19.0473i	0.612521	+	0.612521i	−0.331081	+	0.943602i	$0.607413\pi$
$968$	0.304405	+	4.25614i	0.00978395	+	0.136797i
$969$	−22.5287	−	35.0553i	−0.723726	−	1.12614i
$970$	−6.10224	−	4.18305i	−0.195931	−	0.134310i
$971$	−12.7822	+	5.83743i	−0.410200	+	0.187332i	−0.609817	−	0.792542i	$-0.708757\pi$
$971$	−12.7822	+	5.83743i	−0.410200	+	0.187332i	0.199618	+	0.979874i	$0.436030\pi$
$972$	−8.55535	+	6.40446i	−0.274413	+	0.205423i
$973$	−6.37360	−	3.48025i	−0.204328	−	0.111572i
$974$	−3.44996	+	5.36824i	−0.110544	+	0.172009i
$975$	14.5251	−	40.4116i	0.465174	−	1.29421i
$976$	−2.23602	+	7.61519i	−0.0715733	+	0.243756i
$977$	−5.30060	−	0.379106i	−0.169581	−	0.0121287i	−0.0137096	−	0.999906i	$-0.504364\pi$
$977$	−5.30060	−	0.379106i	−0.169581	−	0.0121287i	−0.155872	+	0.987777i	$0.549819\pi$
$978$	7.68182	+	0.549414i	0.245637	+	0.0175683i
$979$	8.93613	−	30.4337i	0.285600	−	0.972664i
$980$	−5.67932	−	13.4827i	−0.181419	−	0.430688i
$981$	−0.901979	+	1.40351i	−0.0287980	+	0.0448105i
$982$	−9.62822	−	5.25741i	−0.307249	−	0.167771i
$983$	−31.6807	+	23.7159i	−1.01046	+	0.756419i	−0.970085	−	0.242766i	$-0.921945\pi$
$983$	−31.6807	+	23.7159i	−1.01046	+	0.756419i	−0.0403725	+	0.999185i	$0.512854\pi$
$984$	−1.82641	+	0.834094i	−0.0582239	+	0.0265900i
$985$	3.63330	+	19.4714i	0.115766	+	0.620412i
$986$	−25.1520	−	39.1373i	−0.801004	−	1.24639i
$987$	−0.427480	−	5.97695i	−0.0136068	−	0.190248i
$988$	22.8824	+	22.8824i	0.727985	+	0.727985i
$989$	−6.83056	+	16.1249i	−0.217199	+	0.512741i
$990$	−9.52174	+	0.397048i	−0.302621	+	0.0126190i
$991$	−10.5655	+	12.1932i	−0.335623	+	0.387330i	−0.898326	−	0.439329i	$-0.855216\pi$
$991$	−10.5655	+	12.1932i	−0.335623	+	0.387330i	0.562703	+	0.826659i	$0.309762\pi$
$992$	−8.81553	−	1.91770i	−0.279893	−	0.0608871i
$993$	−29.3554	−	21.9752i	−0.931567	−	0.697362i
$994$	1.72243	+	3.77159i	0.0546321	+	0.119628i
$995$	14.3635	+	17.6076i	0.455353	+	0.558199i
$996$	2.73475	+	9.31372i	0.0866540	+	0.295116i
$997$	−3.13312	−	14.4027i	−0.0992269	−	0.456139i	−0.999772	−	0.0213751i	$-0.993196\pi$
$997$	−3.13312	−	14.4027i	−0.0992269	−	0.456139i	0.900545	−	0.434764i	$-0.143168\pi$
$998$	−3.79271	−	10.1686i	−0.120056	−	0.321883i
$999$	−4.68524	−	1.37571i	−0.148234	−	0.0435256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.7.3	✓	240
5.3	odd	4	inner	230.2.l.a.53.9	yes	240
23.10	odd	22	inner	230.2.l.a.217.9	yes	240
115.33	even	44	inner	230.2.l.a.33.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.3	✓	240	1.1	even	1	trivial
230.2.l.a.33.3	yes	240	115.33	even	44	inner
230.2.l.a.53.9	yes	240	5.3	odd	4	inner
230.2.l.a.217.9	yes	240	23.10	odd	22	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(-0.293712 + 1.35017i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.12582 - 0.693460i) q^{5} +(0.196644 - 1.36769i) q^{6} +(-0.324076 + 0.593501i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(0.992195 + 0.453120i) q^{9} +(2.16988 + 0.540039i) q^{10} +(-2.95294 + 2.55874i) q^{11} +(-0.0985729 + 1.37823i) q^{12} +(-5.45538 + 2.97886i) q^{13} +(0.280911 - 0.615108i) q^{14} +(1.56067 - 2.66655i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-3.47136 - 4.63719i) q^{17} +(-1.02199 - 0.381184i) q^{18} +(-0.740929 - 5.15327i) q^{19} +(-2.20287 - 0.383866i) q^{20} +(-0.706144 - 0.611878i) q^{21} +(2.76288 - 2.76288i) q^{22} +(-0.889192 + 4.71268i) q^{23} -1.38175i q^{24} +(4.03823 + 2.94834i) q^{25} +(5.22897 - 3.36046i) q^{26} +(-3.38737 + 4.52499i) q^{27} +(-0.236314 + 0.633581i) q^{28} +(-7.94969 - 1.14299i) q^{29} +(-1.36646 + 2.77109i) q^{30} +(7.58954 + 4.87750i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(-2.58743 - 4.73852i) q^{33} +(3.79333 + 4.37773i) q^{34} +(1.10050 - 1.03694i) q^{35} +(1.04658 + 0.307304i) q^{36} +(0.301897 + 0.809417i) q^{37} +(1.10667 + 5.08728i) q^{38} +(-2.41967 - 8.24064i) q^{39} +(2.22464 + 0.225736i) q^{40} +(-0.603651 - 1.32181i) q^{41} +(0.747996 + 0.559943i) q^{42} +(3.56804 + 0.776180i) q^{43} +(-2.55874 + 2.95294i) q^{44} +(-1.79501 - 1.65130i) q^{45} +(0.550727 - 4.76411i) q^{46} +(4.53479 + 4.53479i) q^{47} +(0.0985729 + 1.37823i) q^{48} +(3.53727 + 5.50410i) q^{49} +(-4.23827 - 2.65275i) q^{50} +(7.28059 - 3.32493i) q^{51} +(-4.97592 + 3.72493i) q^{52} +(8.86106 + 4.83850i) q^{53} +(3.05593 - 4.75512i) q^{54} +(8.05181 - 3.39167i) q^{55} +(0.190512 - 0.648825i) q^{56} +(7.17543 + 0.513197i) q^{57} +(8.01097 + 0.572956i) q^{58} +(2.82083 - 9.60688i) q^{59} +(1.16530 - 2.86151i) q^{60} +(-4.29089 + 6.67676i) q^{61} +(-7.91816 - 4.32364i) q^{62} +(-0.590475 + 0.442024i) q^{63} +(0.909632 - 0.415415i) q^{64} +(13.6629 - 2.54944i) q^{65} +(2.91887 + 4.54186i) q^{66} +(-0.416288 - 5.82046i) q^{67} +(-4.09596 - 4.09596i) q^{68} +(-6.10177 - 2.58473i) q^{69} +(-1.02372 + 1.11281i) q^{70} +(-4.01533 + 4.63394i) q^{71} +(-1.06584 - 0.231859i) q^{72} +(-9.91495 - 7.42224i) q^{73} +(-0.358871 - 0.785817i) q^{74} +(-5.16685 + 4.58634i) q^{75} +(-1.46677 - 4.99537i) q^{76} +(-0.561636 - 2.58180i) q^{77} +(3.00139 + 8.04703i) q^{78} +(5.43844 + 1.59687i) q^{79} +(-2.23508 - 0.0664569i) q^{80} +(-2.97171 - 3.42954i) q^{81} +(0.696409 + 1.27538i) q^{82} +(6.58215 - 2.45502i) q^{83} +(-0.786036 - 0.505155i) q^{84} +(4.16378 + 12.2651i) q^{85} +(-3.61432 - 0.519661i) q^{86} +(3.87816 - 10.3977i) q^{87} +(2.34156 - 3.12796i) q^{88} +(-6.82908 + 4.38878i) q^{89} +(1.90824 + 1.51904i) q^{90} -4.20316i q^{91} +(-0.209457 + 4.79126i) q^{92} +(-8.81462 + 8.81462i) q^{93} +(-4.84674 - 4.19973i) q^{94} +(-1.99851 + 11.4687i) q^{95} +(-0.196644 - 1.36769i) q^{96} +(-3.10002 - 1.15625i) q^{97} +(-3.92091 - 5.23773i) q^{98} +(-4.08931 + 1.20073i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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