LMFDB - Embedded newform 230.2.l.a.217.9

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			217.9
Character	$\chi$	$=$	230.217
Dual form			230.2.l.a.53.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0713392 - 0.997452i) q^{2} +(-1.35017 + 0.293712i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.868035 - 2.06071i) q^{5} +(0.196644 + 1.36769i) q^{6} +(0.593501 - 0.324076i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(-0.992195 + 0.453120i) q^{9} +(-2.11738 + 0.718814i) q^{10} +(-2.95294 - 2.55874i) q^{11} +(1.37823 - 0.0985729i) q^{12} +(-2.97886 + 5.45538i) q^{13} +(-0.280911 - 0.615108i) q^{14} +(1.77725 + 2.52736i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-4.63719 - 3.47136i) q^{17} +(0.381184 + 1.02199i) q^{18} +(0.740929 - 5.15327i) q^{19} +(0.565930 + 2.16327i) q^{20} +(-0.706144 + 0.611878i) q^{21} +(-2.76288 + 2.76288i) q^{22} +(-4.71268 + 0.889192i) q^{23} -1.38175i q^{24} +(-3.49303 + 3.57753i) q^{25} +(5.22897 + 3.36046i) q^{26} +(4.52499 - 3.38737i) q^{27} +(-0.633581 + 0.236314i) q^{28} +(7.94969 - 1.14299i) q^{29} +(2.64771 - 1.59242i) q^{30} +(7.58954 - 4.87750i) q^{31} +(0.349464 - 0.936950i) q^{32} +(4.73852 + 2.58743i) q^{33} +(-3.79333 + 4.37773i) q^{34} +(-1.18301 - 0.941723i) q^{35} +(1.04658 - 0.307304i) q^{36} +(0.809417 + 0.301897i) q^{37} +(-5.08728 - 1.10667i) q^{38} +(2.41967 - 8.24064i) q^{39} +(2.19813 - 0.410162i) q^{40} +(-0.603651 + 1.32181i) q^{41} +(0.559943 + 0.747996i) q^{42} +(-0.776180 - 3.56804i) 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} +(-1.37823 - 0.0985729i) q^{48} +(-3.53727 + 5.50410i) q^{49} +(3.31923 + 3.73935i) q^{50} +(7.28059 + 3.32493i) q^{51} +(3.72493 - 4.97592i) q^{52} +(-4.83850 - 8.86106i) q^{53} +(-3.05593 - 4.75512i) q^{54} +(-2.70956 + 8.30622i) q^{55} +(0.190512 + 0.648825i) q^{56} +(0.513197 + 7.17543i) q^{57} +(-0.572956 - 8.01097i) q^{58} +(-2.82083 - 9.60688i) q^{59} +(-1.39948 - 2.75456i) q^{60} +(-4.29089 - 6.67676i) q^{61} +(-4.32364 - 7.91816i) q^{62} +(-0.442024 + 0.590475i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(13.8277 + 1.40311i) q^{65} +(2.91887 - 4.54186i) q^{66} +(-5.82046 - 0.416288i) 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} +(-0.231859 - 1.06584i) q^{72} +(7.42224 + 9.91495i) q^{73} +(0.358871 - 0.785817i) q^{74} +(3.66543 - 5.85623i) q^{75} +(-1.46677 + 4.99537i) q^{76} +(-2.58180 - 0.561636i) q^{77} +(-8.04703 - 3.00139i) q^{78} +(-5.43844 + 1.59687i) q^{79} +(-0.252305 - 2.22179i) q^{80} +(-2.97171 + 3.42954i) q^{81} +(1.27538 + 0.696409i) q^{82} +(2.45502 - 6.58215i) q^{83} +(0.786036 - 0.505155i) q^{84} +(-3.12821 + 12.5692i) q^{85} +(-3.61432 + 0.519661i) q^{86} +(-10.3977 + 3.87816i) q^{87} +(3.12796 - 2.34156i) q^{88} +(6.82908 + 4.38878i) q^{89} +(1.77515 - 1.67263i) q^{90} +4.20316i q^{91} +(4.79126 - 0.209457i) q^{92} +(-8.81462 + 8.81462i) q^{93} +(4.84674 - 4.19973i) q^{94} +(-11.2625 + 2.94638i) q^{95} +(-0.196644 + 1.36769i) q^{96} +(-1.15625 - 3.10002i) q^{97} +(5.23773 + 3.92091i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$3$	−1.35017	+	0.293712i	−0.779523	+	0.169575i	−0.584685	−	0.811261i	$-0.698782\pi$
$3$	−1.35017	+	0.293712i	−0.779523	+	0.169575i	−0.194838	+	0.980835i	$0.562418\pi$
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	−0.868035	−	2.06071i	−0.388197	−	0.921576i
$5$	−0.868035	−	2.06071i	−0.388197	−	0.921576i
$6$	0.196644	+	1.36769i	0.0802794	+	0.558356i
$7$	0.593501	−	0.324076i	0.224322	−	0.122489i	−0.363158	−	0.931727i	$-0.618302\pi$
$7$	0.593501	−	0.324076i	0.224322	−	0.122489i	0.587481	+	0.809238i	$0.300120\pi$
$8$	−0.212565	+	0.977147i	−0.0751532	+	0.345474i
$9$	−0.992195	+	0.453120i	−0.330732	+	0.151040i
$10$	−2.11738	+	0.718814i	−0.669575	+	0.227309i
$11$	−2.95294	−	2.55874i	−0.890345	−	0.771489i	0.0840190	−	0.996464i	$-0.473224\pi$
$11$	−2.95294	−	2.55874i	−0.890345	−	0.771489i	−0.974364	+	0.224975i	$0.927770\pi$
$12$	1.37823	−	0.0985729i	0.397861	−	0.0284556i
$13$	−2.97886	+	5.45538i	−0.826188	+	1.51305i	0.0318659	+	0.999492i	$0.489855\pi$
$13$	−2.97886	+	5.45538i	−0.826188	+	1.51305i	−0.858054	+	0.513559i	$0.828327\pi$
$14$	−0.280911	−	0.615108i	−0.0750765	−	0.164395i
$15$	1.77725	+	2.52736i	0.458884	+	0.652561i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−4.63719	−	3.47136i	−1.12468	−	0.841928i	−0.135817	−	0.990734i	$-0.543366\pi$
$17$	−4.63719	−	3.47136i	−1.12468	−	0.841928i	−0.988866	+	0.148806i	$0.952457\pi$
$18$	0.381184	+	1.02199i	0.0898458	+	0.240886i
$19$	0.740929	−	5.15327i	0.169981	−	1.18224i	−0.708938	−	0.705270i	$-0.750826\pi$
$19$	0.740929	−	5.15327i	0.169981	−	1.18224i	0.878919	−	0.476971i	$-0.158265\pi$
$20$	0.565930	+	2.16327i	0.126546	+	0.483721i
$21$	−0.706144	+	0.611878i	−0.154093	+	0.133523i
$22$	−2.76288	+	2.76288i	−0.589048	+	0.589048i
$23$	−4.71268	+	0.889192i	−0.982661	+	0.185409i
$23$	−4.71268	+	0.889192i	−0.982661	+	0.185409i
$24$		−	1.38175i		−	0.282049i
$25$	−3.49303	+	3.57753i	−0.698606	+	0.715506i
$26$	5.22897	+	3.36046i	1.02549	+	0.659040i
$27$	4.52499	−	3.38737i	0.870835	−	0.651899i
$28$	−0.633581	+	0.236314i	−0.119736	+	0.0446591i
$29$	7.94969	−	1.14299i	1.47622	−	0.212248i	0.643288	−	0.765624i	$-0.277570\pi$
$29$	7.94969	−	1.14299i	1.47622	−	0.212248i	0.832932	+	0.553376i	$0.186661\pi$
$30$	2.64771	−	1.59242i	0.483403	−	0.290735i
$31$	7.58954	−	4.87750i	1.36312	−	0.876025i	0.364643	−	0.931148i	$-0.381191\pi$
$31$	7.58954	−	4.87750i	1.36312	−	0.876025i	0.998480	+	0.0551221i	$0.0175548\pi$
$32$	0.349464	−	0.936950i	0.0617771	−	0.165631i
$33$	4.73852	+	2.58743i	0.824870	+	0.450413i
$34$	−3.79333	+	4.37773i	−0.650550	+	0.750775i
$35$	−1.18301	−	0.941723i	−0.199964	−	0.159180i
$36$	1.04658	−	0.307304i	0.174430	−	0.0512174i
$37$	0.809417	+	0.301897i	0.133067	+	0.0496315i	0.415116	−	0.909769i	$-0.363741\pi$
$37$	0.809417	+	0.301897i	0.133067	+	0.0496315i	−0.282048	+	0.959400i	$0.591014\pi$
$38$	−5.08728	−	1.10667i	−0.825266	−	0.179526i
$39$	2.41967	−	8.24064i	0.387457	−	1.31956i
$40$	2.19813	−	0.410162i	0.347555	−	0.0648524i
$41$	−0.603651	+	1.32181i	−0.0942744	+	0.206432i	−0.950894	−	0.309516i	$-0.899833\pi$
$41$	−0.603651	+	1.32181i	−0.0942744	+	0.206432i	0.856620	+	0.515948i	$0.172560\pi$
$42$	0.559943	+	0.747996i	0.0864010	+	0.115418i
$43$	−0.776180	−	3.56804i	−0.118366	−	0.544121i	−0.997692	−	0.0679005i	$-0.978370\pi$
$43$	−0.776180	−	3.56804i	−0.118366	−	0.544121i	0.879326	−	0.476221i	$-0.157994\pi$
$44$	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	$0.595073\pi$
$48$	−1.37823	−	0.0985729i	−0.198930	−	0.0142278i
$49$	−3.53727	+	5.50410i	−0.505324	+	0.786299i
$50$	3.31923	+	3.73935i	0.469409	+	0.528824i
$51$	7.28059	+	3.32493i	1.01949	+	0.465584i
$52$	3.72493	−	4.97592i	0.516554	−	0.690036i
$53$	−4.83850	−	8.86106i	−0.664620	−	1.21716i	−0.964726	−	0.263254i	$-0.915204\pi$
$53$	−4.83850	−	8.86106i	−0.664620	−	1.21716i	0.300107	−	0.953906i	$-0.402978\pi$
$54$	−3.05593	−	4.75512i	−0.415859	−	0.647089i
$55$	−2.70956	+	8.30622i	−0.365357	+	1.12001i
$56$	0.190512	+	0.648825i	0.0254583	+	0.0867029i
$57$	0.513197	+	7.17543i	0.0679746	+	0.950409i
$58$	−0.572956	−	8.01097i	−0.0752328	−	1.05189i
$59$	−2.82083	−	9.60688i	−0.367241	−	1.25071i	−0.911328	−	0.411681i	$-0.864942\pi$
$59$	−2.82083	−	9.60688i	−0.367241	−	1.25071i	0.544087	−	0.839029i	$-0.316876\pi$
$60$	−1.39948	−	2.75456i	−0.180672	−	0.355613i
$61$	−4.29089	−	6.67676i	−0.549393	−	0.854871i	0.449877	−	0.893091i	$-0.351468\pi$
$61$	−4.29089	−	6.67676i	−0.549393	−	0.854871i	−0.999269	+	0.0382192i	$0.987832\pi$
$62$	−4.32364	−	7.91816i	−0.549103	−	1.00561i
$63$	−0.442024	+	0.590475i	−0.0556898	+	0.0743928i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	13.8277	+	1.40311i	1.71512	+	0.174034i
$66$	2.91887	−	4.54186i	0.359289	−	0.559064i
$67$	−5.82046	−	0.416288i	−0.711083	−	0.0508576i	−0.288888	−	0.957363i	$-0.593286\pi$
$67$	−5.82046	−	0.416288i	−0.711083	−	0.0508576i	−0.422195	+	0.906505i	$0.638740\pi$
$68$	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	0.465685	−	0.884951i	$-0.345808\pi$
$71$	−4.01533	−	4.63394i	−0.476532	−	0.549948i	−0.942217	+	0.335003i	$0.891263\pi$
$72$	−0.231859	−	1.06584i	−0.0273248	−	0.125610i
$73$	7.42224	+	9.91495i	0.868707	+	1.16046i	0.985898	+	0.167347i	$0.0535201\pi$
$73$	7.42224	+	9.91495i	0.868707	+	1.16046i	−0.117191	+	0.993109i	$0.537389\pi$
$74$	0.358871	−	0.785817i	0.0417179	−	0.0913494i
$75$	3.66543	−	5.85623i	0.423248	−	0.676219i
$76$	−1.46677	+	4.99537i	−0.168251	+	0.573009i
$77$	−2.58180	−	0.561636i	−0.294224	−	0.0640044i
$78$	−8.04703	−	3.00139i	−0.911146	−	0.339840i
$79$	−5.43844	+	1.59687i	−0.611872	+	0.179662i	−0.572964	−	0.819581i	$-0.694206\pi$
$79$	−5.43844	+	1.59687i	−0.611872	+	0.179662i	−0.0389088	+	0.999243i	$0.512388\pi$
$80$	−0.252305	−	2.22179i	−0.0282085	−	0.248403i
$81$	−2.97171	+	3.42954i	−0.330190	+	0.381060i
$82$	1.27538	+	0.696409i	0.140842	+	0.0769055i
$83$	2.45502	−	6.58215i	0.269473	−	0.722485i	−0.729774	−	0.683688i	$-0.760375\pi$
$83$	2.45502	−	6.58215i	0.269473	−	0.722485i	0.999247	−	0.0387968i	$-0.0123525\pi$
$84$	0.786036	−	0.505155i	0.0857636	−	0.0551169i
$85$	−3.12821	+	12.5692i	−0.339302	+	1.36332i
$86$	−3.61432	+	0.519661i	−0.389742	+	0.0560365i
$87$	−10.3977	+	3.87816i	−1.11475	+	0.415782i
$88$	3.12796	−	2.34156i	0.333441	−	0.249611i
$89$	6.82908	+	4.38878i	0.723881	+	0.465210i	0.849985	−	0.526807i	$-0.176611\pi$
$89$	6.82908	+	4.38878i	0.723881	+	0.465210i	−0.126104	+	0.992017i	$0.540247\pi$
$90$	1.77515	−	1.67263i	0.187117	−	0.176311i
$91$			4.20316i			0.440610i
$92$	4.79126	−	0.209457i	0.499523	−	0.0218374i
$93$	−8.81462	+	8.81462i	−0.914033	+	0.914033i
$94$	4.84674	−	4.19973i	0.499903	−	0.433169i
$95$	−11.2625	+	2.94638i	−1.15551	+	0.302292i
$96$	−0.196644	+	1.36769i	−0.0200699	+	0.139589i
$97$	−1.15625	−	3.10002i	−0.117399	−	0.314760i	0.864938	−	0.501879i	$-0.167358\pi$
$97$	−1.15625	−	3.10002i	−0.117399	−	0.314760i	−0.982337	+	0.187119i	$0.940085\pi$
$98$	5.23773	+	3.92091i	0.529090	+	0.396072i
$99$	4.08931	+	1.20073i	0.410991	+	0.120678i
$100$	3.96661	−	3.04401i	0.396661	−	0.304401i
$101$	−2.55404	−	5.59257i	−0.254137	−	0.556482i	0.738964	−	0.673745i	$-0.235315\pi$
$101$	−2.55404	−	5.59257i	−0.254137	−	0.556482i	−0.993101	+	0.117263i	$0.962588\pi$
$102$	3.83585	−	7.02484i	0.379806	−	0.695563i
$103$	−2.65182	+	0.189662i	−0.261291	+	0.0186879i	−0.201370	−	0.979515i	$-0.564539\pi$
$103$	−2.65182	+	0.189662i	−0.261291	+	0.0186879i	−0.0599211	+	0.998203i	$0.519085\pi$
$104$	−4.69751	−	4.07041i	−0.460629	−	0.399137i
$105$	1.87386	+	0.924026i	0.182870	+	0.0901757i
$106$	−9.18365	+	4.19403i	−0.891995	+	0.407361i
$107$	−0.795033	+	3.65471i	−0.0768587	+	0.353314i	−0.999475	−	0.0324057i	$-0.989683\pi$
$107$	−0.795033	+	3.65471i	−0.0768587	+	0.353314i	0.922616	+	0.385720i	$0.126047\pi$
$108$	−4.96101	+	2.70892i	−0.477373	+	0.260665i
$109$	0.217674	+	1.51396i	0.0208494	+	0.145011i	0.997587	−	0.0694272i	$-0.0221172\pi$
$109$	0.217674	+	1.51396i	0.0208494	+	0.145011i	−0.976738	+	0.214438i	$0.931208\pi$
$110$	8.09176	+	3.29521i	0.771519	+	0.314186i
$111$	−1.18152	−	0.169877i	−0.112145	−	0.0161241i
$112$	0.660763	−	0.143740i	0.0624362	−	0.0135822i
$113$	−0.902862	+	12.6237i	−0.0849341	+	1.18753i	0.759001	+	0.651089i	$0.225688\pi$
$113$	−0.902862	+	12.6237i	−0.0849341	+	1.18753i	−0.843936	+	0.536445i	$0.819767\pi$
$114$	7.19376			0.673757
$115$	5.92313	+	8.93960i	0.552335	+	0.833622i
$116$	−8.03143			−0.745700
$117$	0.483670	−	6.76259i	0.0447153	−	0.625202i
$118$	−9.78364	+	2.12830i	−0.900657	+	0.195926i
$119$	−3.87716	−	0.557452i	−0.355419	−	0.0511015i
$120$	−2.84738	+	1.19941i	−0.259929	+	0.109490i
$121$	0.607259	+	4.22358i	0.0552053	+	0.383962i
$122$	−6.96586	+	3.80365i	−0.630659	+	0.344366i
$123$	0.426801	−	1.96197i	0.0384833	−	0.176905i
$124$	−8.20643	+	3.74775i	−0.736960	+	0.336558i
$125$	10.4043	+	4.09270i	0.930590	+	0.366062i
$126$	0.557436	+	0.483021i	0.0496604	+	0.0430310i
$127$	2.36044	−	0.168822i	0.209455	−	0.0149805i	0.0337828	−	0.999429i	$-0.489245\pi$
$127$	2.36044	−	0.168822i	0.209455	−	0.0149805i	0.175673	+	0.984449i	$0.443790\pi$
$128$	−0.479249	+	0.877679i	−0.0423600	+	0.0775766i
$129$	2.09595	+	4.58950i	0.184539	+	0.404083i
$130$	2.38599	−	13.6924i	0.209265	−	1.20090i
$131$	5.51871	+	1.62044i	0.482172	+	0.141579i	0.513780	−	0.857922i	$-0.328245\pi$
$131$	5.51871	+	1.62044i	0.482172	+	0.141579i	−0.0316081	+	0.999500i	$0.510063\pi$
$132$	−4.32206	−	3.23545i	−0.376187	−	0.281610i
$133$	−1.23031	−	3.29859i	−0.106681	−	0.286024i
$134$	−0.830454	+	5.77594i	−0.0717403	+	0.498965i
$135$	−10.9082	−	6.38434i	−0.938830	−	0.549476i
$136$	4.37773	−	3.79333i	0.375387	−	0.325275i
$137$	−2.78731	+	2.78731i	−0.238136	+	0.238136i	−0.816078	−	0.577942i	$-0.803856\pi$
$137$	−2.78731	+	2.78731i	−0.238136	+	0.238136i	0.577942	+	0.816078i	$0.303856\pi$
$138$	−2.14285	−	6.27061i	−0.182412	−	0.533790i
$139$			10.7390i			0.910868i	0.890269	+	0.455434i	$0.150516\pi$
$139$			10.7390i			0.910868i	−0.890269	+	0.455434i	$0.849484\pi$
$140$	1.03694	+	1.10050i	0.0876377	+	0.0930090i
$141$	−7.45467	−	4.79083i	−0.627797	−	0.403460i
$142$	−4.90858	+	3.67452i	−0.411919	+	0.308359i
$143$	22.7553	−	8.48729i	1.90289	−	0.709743i
$144$	−1.07966	+	0.155232i	−0.0899719	+	0.0129360i
$145$	−9.25597	−	15.3898i	−0.768667	−	1.27806i
$146$	10.4192	−	6.69600i	0.862298	−	0.554165i
$147$	3.15930	−	8.47042i	0.260575	−	0.698628i
$148$	−0.758214	−	0.414016i	−0.0623248	−	0.0340319i
$149$	−8.19158	+	9.45359i	−0.671081	+	0.774468i	−0.984545	−	0.175132i	$-0.943965\pi$
$149$	−8.19158	+	9.45359i	−0.671081	+	0.774468i	0.313464	+	0.949600i	$0.398510\pi$
$150$	−5.57982	−	4.07387i	−0.455591	−	0.332630i
$151$	−12.2539	+	3.59807i	−0.997209	+	0.292807i	−0.739310	−	0.673365i	$-0.764848\pi$
$151$	−12.2539	+	3.59807i	−0.997209	+	0.292807i	−0.257899	+	0.966172i	$0.583030\pi$
$152$	4.87801	+	1.81940i	0.395659	+	0.147573i
$153$	6.17394	+	1.34306i	0.499134	+	0.108580i
$154$	−0.744389	+	2.53516i	−0.0599846	+	0.204289i
$155$	−16.6391	−	11.4060i	−1.33648	−	0.916151i
$156$	−3.56781	+	7.81241i	−0.285653	+	0.625493i
$157$	−7.77616	−	10.3877i	−0.620605	−	0.829031i	0.374565	−	0.927201i	$-0.377792\pi$
$157$	−7.77616	−	10.3877i	−0.620605	−	0.829031i	−0.995170	+	0.0981696i	$0.968701\pi$
$158$	1.20483	+	5.53850i	0.0958509	+	0.440620i
$159$	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
$163$	−5.55948	−	0.397622i	−0.435452	−	0.0311442i	−0.148107	−	0.988971i	$-0.547318\pi$
$163$	−5.55948	−	0.397622i	−0.435452	−	0.0311442i	−0.287345	+	0.957827i	$0.592773\pi$
$164$	0.785619	−	1.22245i	0.0613466	−	0.0954571i
$165$	1.21873	−	12.0107i	0.0948782	−	0.935029i
$166$	−6.39024	−	2.91833i	−0.495979	−	0.226506i
$167$	5.26725	−	7.03622i	0.407592	−	0.544479i	−0.549033	−	0.835800i	$-0.685004\pi$
$167$	5.26725	−	7.03622i	0.407592	−	0.544479i	0.956625	+	0.291321i	$0.0940949\pi$
$168$	−0.447792	−	0.820071i	−0.0345479	−	0.0632698i
$169$	−13.8592	−	21.5654i	−1.06610	−	1.65888i
$170$	12.3140	+	4.01691i	0.944438	+	0.308083i
$171$	1.59991	+	5.44878i	0.122348	+	0.416679i
$172$	0.260494	+	3.64219i	0.0198625	+	0.277714i
$173$	−1.48145	−	20.7134i	−0.112633	−	1.57481i	−0.668608	−	0.743615i	$-0.733110\pi$
$173$	−1.48145	−	20.7134i	−0.112633	−	1.57481i	0.555975	−	0.831199i	$-0.312345\pi$
$174$	3.12651	+	10.6479i	0.237020	+	0.807216i
$175$	−0.913726	+	3.25528i	−0.0690712	+	0.246076i
$176$	−2.11245	−	3.28703i	−0.159232	−	0.247769i
$177$	6.63027	+	12.1424i	0.498362	+	0.912682i
$178$	4.86478	−	6.49859i	0.364631	−	0.487090i
$179$	19.6913	+	8.99270i	1.47179	+	0.672146i	0.980079	−	0.198609i	$-0.0636425\pi$
$179$	19.6913	+	8.99270i	1.47179	+	0.672146i	0.491716	+	0.870756i	$0.336370\pi$
$180$	−1.54173	−	1.88995i	−0.114914	−	0.140868i
$181$	−6.16120	+	9.58702i	−0.457958	+	0.712597i	−0.991055	−	0.133457i	$-0.957392\pi$
$181$	−6.16120	+	9.58702i	−0.457958	+	0.712597i	0.533096	+	0.846055i	$0.321028\pi$
$182$	4.19245	+	0.299850i	0.310765	+	0.0222263i
$183$	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
$187$	4.81106	+	22.1161i	0.351819	+	1.61729i
$188$	−3.84326	−	5.13400i	−0.280299	−	0.374435i
$189$	1.58782	−	3.47685i	0.115497	−	0.252904i
$190$	2.13541	+	11.4440i	0.154919	+	0.830238i
$191$	3.98172	−	13.5605i	0.288107	−	0.981202i	−0.680530	−	0.732720i	$-0.738250\pi$
$191$	3.98172	−	13.5605i	0.288107	−	0.981202i	0.968637	−	0.248482i	$-0.0799315\pi$
$192$	1.35017	+	0.293712i	0.0974403	+	0.0211969i
$193$	12.2042	+	4.55192i	0.878476	+	0.327655i	0.747922	−	0.663787i	$-0.231052\pi$
$193$	12.2042	+	4.55192i	0.878476	+	0.327655i	0.130554	+	0.991441i	$0.458324\pi$
$194$	−3.17461	+	0.932150i	−0.227924	+	0.0669245i
$195$	−19.0819	+	2.16693i	−1.36648	+	0.155177i
$196$	4.28458	−	4.94467i	0.306041	−	0.353190i
$197$	−7.77465	−	4.24528i	−0.553921	−	0.302464i	0.177802	−	0.984066i	$-0.443102\pi$
$197$	−7.77465	−	4.24528i	−0.553921	−	0.302464i	−0.731723	+	0.681603i	$0.761283\pi$
$198$	1.48940	−	3.99323i	0.105847	−	0.283787i
$199$	8.54887	−	5.49403i	0.606013	−	0.389461i	−0.201347	−	0.979520i	$-0.564532\pi$
$199$	8.54887	−	5.49403i	0.606013	−	0.389461i	0.807360	+	0.590059i	$0.200895\pi$
$200$	−2.75328	−	4.17366i	−0.194686	−	0.295123i
$201$	7.98090	−	1.14748i	0.562929	−	0.0809370i
$202$	−5.76053	+	2.14856i	−0.405309	+	0.151172i
$203$	4.34773	−	3.25467i	0.305151	−	0.228433i
$204$	−6.73330	−	4.32723i	−0.471425	−	0.302966i
$205$	3.24785	+	0.0965703i	0.226840	+	0.00674476i
$206$			2.65859i			0.185233i
$207$	4.27299	−	3.01766i	0.296993	−	0.209742i
$208$	−4.39516	+	4.39516i	−0.304749	+	0.304749i
$209$	−15.3738	+	13.3215i	−1.06343	+	0.921465i
$210$	1.05535	−	1.80316i	0.0728262	−	0.124430i
$211$	2.29354	−	15.9519i	0.157893	−	1.09817i	−0.744613	−	0.667497i	$-0.767366\pi$
$211$	2.29354	−	15.9519i	0.157893	−	1.09817i	0.902506	−	0.430677i	$-0.141725\pi$
$212$	3.52819	+	9.45945i	0.242317	+	0.649678i
$213$	6.78244	+	5.07727i	0.464725	+	0.347889i
$214$	3.58868	+	1.05373i	0.245317	+	0.0720316i
$215$	−6.67894	+	4.69666i	−0.455500	+	0.320310i
$216$	2.34810	+	5.14162i	0.159768	+	0.349843i
$217$	2.92372	−	5.35439i	0.198475	−	0.363480i
$218$	1.52563	−	0.109115i	0.103328	−	0.00739020i
$219$	−12.9334	−	11.2069i	−0.873961	−	0.757292i
$220$	3.86408	−	7.83607i	0.260516	−	0.528308i
$221$	32.7511	−	14.9569i	2.20308	−	1.00611i
$222$	−0.253734	+	1.16639i	−0.0170295	+	0.0782833i
$223$	14.2750	−	7.79475i	0.955926	−	0.521975i	0.0760114	−	0.997107i	$-0.475781\pi$
$223$	14.2750	−	7.79475i	0.955926	−	0.521975i	0.879915	+	0.475132i	$0.157600\pi$
$224$	−0.0962357	−	0.669334i	−0.00643002	−	0.0447218i
$225$	1.84472	−	5.13237i	0.122981	−	0.342158i
$226$	12.5271	+	1.80112i	0.833289	+	0.119809i
$227$	−4.76243	+	1.03600i	−0.316094	+	0.0687620i	−0.367813	−	0.929900i	$-0.619893\pi$
$227$	−4.76243	+	1.03600i	−0.316094	+	0.0687620i	0.0517195	+	0.998662i	$0.483530\pi$
$228$	0.513197	−	7.17543i	0.0339873	−	0.475204i
$229$	14.2072			0.938839			0.469420	−	0.882975i	$-0.344463\pi$
$229$	14.2072			0.938839			0.469420	+	0.882975i	$0.344463\pi$
$230$	9.33938	−	5.27030i	0.615820	−	0.347513i
$231$	3.65084			0.240207
$232$	−0.572956	+	8.01097i	−0.0376164	+	0.525946i
$233$	−15.4579	+	3.36267i	−1.01268	+	0.220296i	−0.688142	−	0.725576i	$-0.741573\pi$
$233$	−15.4579	+	3.36267i	−1.01268	+	0.220296i	−0.324541	+	0.945872i	$0.605210\pi$
$234$	−6.71086	−	0.964875i	−0.438702	−	0.0630759i
$235$	5.40852	−	13.2812i	0.352813	−	0.866372i
$236$	1.42492	+	9.91054i	0.0927545	+	0.645121i
$237$	6.87382	−	3.75339i	0.446502	−	0.243809i
$238$	−0.832625	+	3.82752i	−0.0539711	+	0.248101i
$239$	−9.90756	+	4.52463i	−0.640867	+	0.292674i	−0.709220	−	0.704987i	$-0.750953\pi$
$239$	−9.90756	+	4.52463i	−0.640867	+	0.292674i	0.0683534	+	0.997661i	$0.478225\pi$
$240$	0.993221	+	2.92569i	0.0641121	+	0.188853i
$241$	−9.27791	−	8.03936i	−0.597643	−	0.517860i	0.302675	−	0.953094i	$-0.402120\pi$
$241$	−9.27791	−	8.03936i	−0.597643	−	0.517860i	−0.900318	+	0.435233i	$0.856666\pi$
$242$	4.25614	−	0.304405i	0.273595	−	0.0195679i
$243$	−5.12172	+	9.37972i	−0.328558	+	0.601709i
$244$	3.29702	+	7.21946i	0.211070	+	0.462178i
$245$	14.4128	+	2.51153i	0.920800	+	0.160456i
$246$	−1.92653	−	0.565679i	−0.122831	−	0.0360664i
$247$	25.9059	+	19.3929i	1.64836	+	1.23394i
$248$	3.15276	+	8.45289i	0.200201	+	0.536759i
$249$	−1.38144	+	9.60811i	−0.0875451	+	0.608890i
$250$	4.82451	−	10.0858i	0.305129	−	0.637884i
$251$	−3.57725	+	3.09970i	−0.225794	+	0.195651i	−0.760410	−	0.649444i	$-0.775002\pi$
$251$	−3.57725	+	3.09970i	−0.225794	+	0.195651i	0.534616	+	0.845095i	$0.320456\pi$
$252$	0.521558	−	0.521558i	0.0328551	−	0.0328551i
$253$	16.1915	+	9.43278i	1.01795	+	0.593034i
$254$		−	2.36647i		−	0.148486i
$255$	0.531914	−	17.8893i	0.0333097	−	1.12027i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−6.12371	+	4.58415i	−0.381986	+	0.285951i	−0.772965	−	0.634448i	$-0.781227\pi$
$257$	−6.12371	+	4.58415i	−0.381986	+	0.285951i	0.390979	+	0.920400i	$0.372136\pi$
$258$	4.72733	−	1.76320i	0.294311	−	0.109772i
$259$	0.578227	−	0.0831366i	0.0359293	−	0.00516585i
$260$	−13.4873	−	3.35671i	−0.836445	−	0.208175i
$261$	−7.36973	+	4.73624i	−0.456175	+	0.293166i
$262$	2.01001	−	5.38905i	0.124179	−	0.332937i
$263$	−17.0357	−	9.30221i	−1.05047	−	0.573599i	−0.141274	−	0.989971i	$-0.545120\pi$
$263$	−17.0357	−	9.30221i	−1.05047	−	0.573599i	−0.909194	+	0.416372i	$0.863302\pi$
$264$	−3.53554	+	4.08023i	−0.217597	+	0.251121i
$265$	−14.0601	+	17.6624i	−0.863703	+	1.08500i
$266$	−3.37796	+	0.991857i	−0.207116	+	0.0608147i
$267$	−10.5095	−	3.91983i	−0.643170	−	0.239890i
$268$	5.70198	+	1.24039i	0.348304	+	0.0757688i
$269$	−1.91055	+	6.50675i	−0.116488	+	0.396723i	−0.997009	−	0.0772846i	$-0.975375\pi$
$269$	−1.91055	+	6.50675i	−0.116488	+	0.396723i	0.880521	+	0.474008i	$0.157193\pi$
$270$	−7.14625	+	10.4250i	−0.434907	+	0.634444i
$271$	−3.83102	+	8.38876i	−0.232718	+	0.509581i	−0.989578	−	0.143996i	$-0.954005\pi$
$271$	−3.83102	+	8.38876i	−0.232718	+	0.509581i	0.756861	+	0.653576i	$0.226732\pi$
$272$	−3.47136	−	4.63719i	−0.210482	−	0.281171i
$273$	−1.23452	−	5.67499i	−0.0747164	−	0.343466i
$274$	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	$0.813898\pi$
$278$	10.7116	+	0.766110i	0.642440	+	0.0459482i
$279$	−5.32021	+	8.27841i	−0.318513	+	0.495616i
$280$	1.17167	−	0.955793i	0.0700206	−	0.0571195i
$281$	−3.90494	−	1.78333i	−0.232949	−	0.106384i	0.295521	−	0.955336i	$-0.404507\pi$
$281$	−3.90494	−	1.78333i	−0.232949	−	0.106384i	−0.528470	+	0.848952i	$0.677234\pi$
$282$	−5.31043	+	7.09390i	−0.316232	+	0.422436i
$283$	−1.29752	−	2.37622i	−0.0771293	−	0.141252i	0.836268	−	0.548321i	$-0.184733\pi$
$283$	−1.29752	−	2.37622i	−0.0771293	−	0.141252i	−0.913397	+	0.407069i	$0.866551\pi$
$284$	3.31498	+	5.15822i	0.196708	+	0.306084i
$285$	14.3410	−	7.28607i	0.849487	−	0.431589i
$286$	−6.84232	−	23.3028i	−0.404595	−	1.37792i
$287$	0.0700999	+	0.980125i	0.00413787	+	0.0578549i
$288$	0.0778143	+	1.08799i	0.00458525	+	0.0641102i
$289$	4.66376	+	15.8833i	0.274339	+	0.934312i
$290$	−16.0109	+	8.13449i	−0.940194	+	0.477674i
$291$	2.47165	+	3.84596i	0.144891	+	0.225454i
$292$	−5.93564	−	10.8703i	−0.347357	−	0.636137i
$293$	11.4828	−	15.3392i	0.670833	−	0.896128i	−0.327988	−	0.944682i	$-0.606370\pi$
$293$	11.4828	−	15.3392i	0.670833	−	0.896128i	0.998821	+	0.0485542i	$0.0154614\pi$
$294$	−8.22346	−	3.75553i	−0.479602	−	0.219027i
$295$	−17.3484	+	14.1520i	−1.01006	+	0.823963i
$296$	−0.467051	+	0.726746i	−0.0271468	+	0.0422413i
$297$	−22.0294	−	1.57558i	−1.27828	−	0.0914242i
$298$	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
$302$	2.71472	+	12.4794i	0.156215	+	0.718107i
$303$	5.09100	+	6.80079i	0.292471	+	0.390695i
$304$	2.16276	−	4.73578i	0.124043	−	0.271616i
$305$	−10.0342	+	14.6379i	−0.574557	+	0.838166i
$306$	1.78008	−	6.06240i	0.101760	−	0.346564i
$307$	19.8687	+	4.32217i	1.13397	+	0.246680i	0.740106	−	0.672490i	$-0.234775\pi$
$307$	19.8687	+	4.32217i	1.13397	+	0.246680i	0.393862	+	0.919170i	$0.371139\pi$
$308$	2.47559	+	0.923348i	0.141060	+	0.0526127i
$309$	3.52471	−	1.03495i	0.200514	−	0.0588761i
$310$	−12.5639	+	15.7830i	−0.713584	+	0.896414i
$311$	−0.577829	+	0.666850i	−0.0327657	+	0.0378136i	−0.771896	−	0.635749i	$-0.780691\pi$
$311$	−0.577829	+	0.666850i	−0.0327657	+	0.0378136i	0.739130	+	0.673563i	$0.235237\pi$
$312$	7.53798	+	4.11605i	0.426754	+	0.233025i
$313$	6.92340	−	18.5624i	0.391334	−	1.04921i	−0.580649	−	0.814154i	$-0.697201\pi$
$313$	6.92340	−	18.5624i	0.391334	−	1.04921i	0.971983	−	0.235052i	$-0.0755261\pi$
$314$	−10.9160	+	7.01529i	−0.616026	+	0.395896i
$315$	1.60049	+	0.398329i	0.0901772	+	0.0224433i
$316$	5.61034	−	0.806646i	0.315606	−	0.0453774i
$317$	−0.559756	+	0.208778i	−0.0314390	+	0.0117261i	−0.365134	−	0.930955i	$-0.618977\pi$
$317$	−0.559756	+	0.208778i	−0.0314390	+	0.0117261i	0.333695	+	0.942681i	$0.391704\pi$
$318$	11.1677	−	8.36002i	0.626253	−	0.468807i
$319$	−26.3996	−	16.9660i	−1.47809	−	0.949912i
$320$	−0.0664569	+	2.23508i	−0.00371506	+	0.124945i
$321$		−	5.16800i		−	0.288449i
$322$	1.87079	+	2.64902i	0.104255	+	0.147624i
$323$	−21.3247	+	21.3247i	−1.18654	+	1.18654i
$324$	3.42954	−	2.97171i	0.190530	−	0.165095i
$325$	−9.11153	−	29.7128i	−0.505417	−	1.64817i
$326$	−0.793218	+	5.51695i	−0.0439323	+	0.305556i
$327$	−0.738564	−	1.98017i	−0.0408427	−	0.109504i
$328$	−1.16329	−	0.870826i	−0.0642318	−	0.0480833i
$329$	4.16102	+	1.22179i	0.229404	+	0.0673592i
$330$	−11.8931	−	2.07246i	−0.654695	−	0.114085i
$331$	−11.0245	−	24.1402i	−0.605959	−	1.32687i	−0.925304	−	0.379227i	$-0.876190\pi$
$331$	−11.0245	−	24.1402i	−0.605959	−	1.32687i	0.319344	−	0.947639i	$-0.396537\pi$
$332$	−3.36677	+	6.16577i	−0.184775	+	0.338391i
$333$	−0.939895	+	0.0672226i	−0.0515059	+	0.00368378i
$334$	−6.64253	−	5.75579i	−0.363463	−	0.314943i
$335$	4.19452	+	12.3556i	0.229171	+	0.675060i
$336$	−0.849926	+	0.388148i	−0.0463673	+	0.0211752i
$337$	−0.0276093	+	0.126918i	−0.00150397	+	0.00691365i	−0.977893	−	0.209107i	$-0.932944\pi$
$337$	−0.0276093	+	0.126918i	−0.00150397	+	0.00691365i	0.976389	+	0.216021i	$0.0693079\pi$
$338$	−22.4992	+	12.2855i	−1.22379	+	0.668242i
$339$	−2.48870	−	17.3093i	−0.135168	−	0.940112i
$340$	4.88515	−	11.9960i	0.264934	−	0.650576i
$341$	−34.8917	−	5.01667i	−1.88949	−	0.271668i
$342$	5.54904	−	1.20712i	0.300057	−	0.0652735i
$343$	−0.653312	+	9.13449i	−0.0352755	+	0.493216i
$344$	3.65149			0.196875
$345$	−10.6229	−	10.3303i	−0.571919	−	0.556166i
$346$	−20.7664			−1.11641
$347$	−0.729882	+	10.2051i	−0.0391821	+	0.547837i	0.939512	+	0.342515i	$0.111279\pi$
$347$	−0.729882	+	10.2051i	−0.0391821	+	0.547837i	−0.978694	+	0.205322i	$0.934176\pi$
$348$	10.8438	−	2.35893i	0.581290	−	0.126452i
$349$	−13.2652	−	1.90725i	−0.710072	−	0.102093i	−0.222191	−	0.975003i	$-0.571321\pi$
$349$	−13.2652	−	1.90725i	−0.710072	−	0.102093i	−0.487881	+	0.872910i	$0.662230\pi$
$350$	3.18180	+	1.14363i	0.170074	+	0.0611294i
$351$	5.00005	+	34.7761i	0.266883	+	1.85621i
$352$	−3.42936	+	1.87257i	−0.182785	+	0.0998083i
$353$	3.69053	−	16.9651i	0.196427	−	0.902961i	−0.768378	−	0.639996i	$-0.778936\pi$
$353$	3.69053	−	16.9651i	0.196427	−	0.902961i	0.964805	−	0.262965i	$-0.0847003\pi$
$354$	12.5845	−	5.74715i	0.668859	−	0.305457i
$355$	−6.06375	+	12.2968i	−0.321830	+	0.652649i
$356$	−6.13498	−	5.31599i	−0.325153	−	0.281747i
$357$	5.39857	−	0.386113i	0.285723	−	0.0204353i
$358$	10.3745	−	18.9996i	0.548312	−	1.00416i
$359$	−0.355602	−	0.778660i	−0.0187680	−	0.0410961i	0.900016	−	0.435857i	$-0.143555\pi$
$359$	−0.355602	−	0.778660i	−0.0187680	−	0.0410961i	−0.918784	+	0.394761i	$0.870827\pi$
$360$	−1.99512	+	1.40298i	−0.105152	+	0.0739434i
$361$	−7.77687	−	2.28349i	−0.409309	−	0.120184i
$362$	9.12305	+	6.82943i	0.479497	+	0.358947i
$363$	−2.06042	−	5.52420i	−0.108144	−	0.289945i
$364$	0.598171	−	4.16037i	0.0313527	−	0.218063i
$365$	13.9891	−	23.9016i	0.732220	−	1.25107i
$366$	8.28793	−	7.18154i	0.433217	−	0.375385i
$367$	18.4177	−	18.4177i	0.961398	−	0.961398i	−0.0378842	−	0.999282i	$-0.512062\pi$
$367$	18.4177	−	18.4177i	0.961398	−	0.961398i	0.999282	+	0.0378842i	$0.0120618\pi$
$368$	−4.77230	−	0.474542i	−0.248773	−	0.0247372i
$369$		−	1.58502i		−	0.0825129i
$370$	−1.93085	−	0.0574111i	−0.100380	−	0.00298466i
$371$	−5.74332	−	3.69100i	−0.298178	−	0.191627i
$372$	9.97935	−	7.47044i	0.517405	−	0.387325i
$373$	0.0312684	−	0.0116625i	0.00161902	−	0.000603862i	−0.348655	−	0.937251i	$-0.613361\pi$
$373$	0.0312684	−	0.0116625i	0.00161902	−	0.000603862i	0.350274	+	0.936647i	$0.386089\pi$
$374$	22.4029	−	3.22106i	1.15843	−	0.166557i
$375$	−15.2497	−	2.46998i	−0.787491	−	0.127549i
$376$	−5.39509	+	3.46722i	−0.278231	+	0.178808i
$377$	−17.4456	+	46.7734i	−0.898493	+	2.40895i
$378$	−3.35472	−	1.83181i	−0.172548	−	0.0942183i
$379$	1.00552	−	1.16043i	0.0516500	−	0.0596073i	−0.729337	−	0.684155i	$-0.760171\pi$
$379$	1.00552	−	1.16043i	0.0516500	−	0.0596073i	0.780987	+	0.624548i	$0.214717\pi$
$380$	11.5672	−	1.31356i	0.593386	−	0.0673844i
$381$	−3.13742	+	0.921229i	−0.160735	+	0.0471960i
$382$	−13.2419	−	4.93897i	−0.677513	−	0.252699i
$383$	−13.0090	−	2.82993i	−0.664727	−	0.144603i	−0.132472	−	0.991187i	$-0.542292\pi$
$383$	−13.0090	−	2.82993i	−0.664727	−	0.144603i	−0.532255	+	0.846584i	$0.678655\pi$
$384$	0.389284	−	1.32578i	0.0198656	−	0.0676559i
$385$	1.08372	+	5.80786i	0.0552317	+	0.295996i
$386$	5.41096	−	11.8484i	0.275411	−	0.603065i
$387$	2.38688	+	3.18849i	0.121332	+	0.162080i
$388$	0.703301	+	3.23302i	0.0357047	+	0.164132i
$389$	7.09896	+	8.19264i	0.359932	+	0.415383i	0.906617	−	0.421955i	$-0.138656\pi$
$389$	7.09896	+	8.19264i	0.359932	+	0.415383i	−0.546685	+	0.837338i	$0.684111\pi$
$390$	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
$393$	−7.92716	−	0.566962i	−0.399872	−	0.0285994i
$394$	−4.78910	+	7.45199i	−0.241271	+	0.375426i
$395$	8.01144	+	9.82090i	0.403099	+	0.494143i
$396$	−3.87681	−	1.77048i	−0.194817	−	0.0889699i
$397$	20.2026	−	26.9875i	1.01394	−	1.35446i	0.0800914	−	0.996788i	$-0.474479\pi$
$397$	20.2026	−	26.9875i	1.01394	−	1.35446i	0.933846	−	0.357675i	$-0.116430\pi$
$398$	−4.87016	−	8.91903i	−0.244119	−	0.447070i
$399$	2.62997	+	4.09231i	0.131663	+	0.204872i
$400$	−4.35945	+	2.44851i	−0.217972	+	0.122426i
$401$	7.99637	+	27.2331i	0.399320	+	1.35996i	0.876606	+	0.481210i	$0.159802\pi$
$401$	7.99637	+	27.2331i	0.399320	+	1.35996i	−0.477286	+	0.878748i	$0.658379\pi$
$402$	−0.575206	−	8.04243i	−0.0286887	−	0.401120i
$403$	4.00043	+	55.9333i	0.199276	+	2.78624i
$404$	1.73214	+	5.89912i	0.0861772	+	0.293492i
$405$	9.64683	+	3.14687i	0.479355	+	0.156369i
$406$	−2.93622	−	4.56884i	−0.145722	−	0.226748i
$407$	−1.61769	−	2.96257i	−0.0801857	−	0.146849i
$408$	−4.79655	+	6.40744i	−0.237465	+	0.317216i
$409$	15.9120	+	7.26675i	0.786796	+	0.359318i	0.767954	−	0.640505i	$-0.221275\pi$
$409$	15.9120	+	7.26675i	0.786796	+	0.359318i	0.0188417	+	0.999822i	$0.494002\pi$
$410$	0.328024	−	3.23269i	0.0161999	−	0.159651i
$411$	2.94469	−	4.58202i	0.145251	−	0.226014i
$412$	2.65182	+	0.189662i	0.130646	+	0.00934396i
$413$	−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
$417$	−3.15417	−	14.4995i	−0.154460	−	0.710043i
$418$	12.1908	+	16.2850i	0.596270	+	0.796524i
$419$	−13.7438	+	30.0947i	−0.671429	+	1.47022i	0.200048	+	0.979786i	$0.435890\pi$
$419$	−13.7438	+	30.0947i	−0.671429	+	1.47022i	−0.871476	+	0.490437i	$0.836837\pi$
$420$	−1.72328	−	1.18130i	−0.0840876	−	0.0576415i
$421$	−10.0658	+	34.2810i	−0.490577	+	1.67075i	0.226699	+	0.973965i	$0.427207\pi$
$421$	−10.0658	+	34.2810i	−0.490577	+	1.67075i	−0.717277	+	0.696789i	$0.754612\pi$
$422$	−15.7476	−	3.42569i	−0.766582	−	0.166760i
$423$	−6.55420	−	2.44459i	−0.318676	−	0.118860i
$424$	9.68705	−	2.84438i	0.470445	−	0.138135i
$425$	28.6167	−	4.46413i	1.38812	−	0.216542i
$426$	5.54819	−	6.40295i	0.268811	−	0.310224i
$427$	−4.71043	−	2.57209i	−0.227954	−	0.124472i
$428$	1.30706	−	3.50436i	0.0631791	−	0.169390i
$429$	−28.2308	+	18.1428i	−1.36300	+	0.875944i
$430$	4.20823	+	6.99698i	0.202939	+	0.337424i
$431$	−6.94987	+	0.999241i	−0.334763	+	0.0481317i	−0.307647	−	0.951501i	$-0.599542\pi$
$431$	−6.94987	+	0.999241i	−0.334763	+	0.0481317i	−0.0271165	+	0.999632i	$0.508632\pi$
$432$	5.29603	−	1.97532i	0.254805	−	0.0950375i
$433$	28.1925	−	21.1046i	1.35484	−	1.01422i	0.358091	−	0.933687i	$-0.383428\pi$
$433$	28.1925	−	21.1046i	1.35484	−	1.01422i	0.996752	−	0.0805360i	$-0.0256632\pi$
$434$	−5.13218	−	3.29825i	−0.246352	−	0.158321i
$435$	17.0173	+	18.0603i	0.815919	+	0.865927i
$436$		−	1.52952i		−	0.0732509i
$437$	1.09049	+	24.9445i	0.0521651	+	1.19326i
$438$	−12.1010	+	12.1010i	−0.578208	+	0.578208i
$439$	28.3482	−	24.5638i	1.35298	−	1.17237i	0.384547	−	0.923105i	$-0.374357\pi$
$439$	28.3482	−	24.5638i	1.35298	−	1.17237i	0.968436	−	0.249262i	$-0.0801880\pi$
$440$	−7.54044	−	4.41325i	−0.359476	−	0.210393i
$441$	1.01564	−	7.06395i	0.0483639	−	0.336378i
$442$	−12.5824	−	33.7347i	−0.598484	−	1.60460i
$443$	−17.4103	−	13.0332i	−0.827188	−	0.619226i	0.0995077	−	0.995037i	$-0.468273\pi$
$443$	−17.4103	−	13.0332i	−0.827188	−	0.619226i	−0.926696	+	0.375811i	$0.877364\pi$
$444$	1.14532	+	0.336297i	0.0543545	+	0.0159599i
$445$	3.11612	−	17.8824i	0.147718	−	0.847705i
$446$	−6.75652	−	14.7947i	−0.319931	−	0.700550i
$447$	8.28342	−	15.1700i	0.391792	−	0.717514i
$448$	−0.674494	+	0.0482408i	−0.0318668	+	0.00227916i
$449$	−13.3091	−	11.5324i	−0.628094	−	0.544246i	0.281597	−	0.959533i	$-0.409136\pi$
$449$	−13.3091	−	11.5324i	−0.628094	−	0.544246i	−0.909691	+	0.415286i	$0.863681\pi$
$450$	−4.98770	−	2.20616i	−0.235122	−	0.103999i
$451$	5.16471	−	2.35864i	0.243197	−	0.111064i
$452$	2.69021	−	12.3667i	0.126537	−	0.581679i
$453$	15.4881	−	8.45714i	0.727694	−	0.397351i
$454$	0.693616	+	4.82421i	0.0325530	+	0.226411i
$455$	8.66148	−	3.64848i	0.406056	−	0.171044i
$456$	−7.12053	−	1.02378i	−0.333450	−	0.0479428i
$457$	26.8391	−	5.83849i	1.25548	−	0.273113i	0.464841	−	0.885394i	$-0.346112\pi$
$457$	26.8391	−	5.83849i	1.25548	−	0.273113i	0.790640	+	0.612281i	$0.209748\pi$
$458$	1.01353	−	14.1710i	0.0473592	−	0.662168i
$459$	−32.7420			−1.52827
$460$	−4.59060	−	9.69156i	−0.214038	−	0.451871i
$461$	23.0791			1.07490			0.537451	−	0.843295i	$-0.319387\pi$
$461$	23.0791			1.07490			0.537451	+	0.843295i	$0.319387\pi$
$462$	0.260448	−	3.64154i	0.0121171	−	0.169420i
$463$	−2.04315	+	0.444460i	−0.0949531	+	0.0206558i	−0.259791	−	0.965665i	$-0.583654\pi$
$463$	−2.04315	+	0.444460i	−0.0949531	+	0.0206558i	0.164838	+	0.986321i	$0.447290\pi$
$464$	7.94969	+	1.14299i	0.369055	+	0.0530621i
$465$	25.8157	+	10.5130i	1.19718	+	0.487527i
$466$	2.25134	+	15.6584i	0.104291	+	0.725363i
$467$	−22.2920	+	12.1723i	−1.03155	+	0.563269i	−0.903540	−	0.428504i	$-0.859041\pi$
$467$	−22.2920	+	12.1723i	−1.03155	+	0.563269i	−0.128010	+	0.991773i	$0.540859\pi$
$468$	−1.44116	+	6.62492i	−0.0666178	+	0.306237i
$469$	−3.58936	+	1.63921i	−0.165741	+	0.0756915i
$470$	−12.8615	−	6.34221i	−0.593259	−	0.292544i
$471$	13.5502	+	11.7413i	0.624359	+	0.541010i
$472$	9.98695	−	0.714280i	0.459686	−	0.0328774i
$473$	−6.83767	+	12.5223i	−0.314396	+	0.575774i
$474$	−3.25345	−	7.12407i	−0.149436	−	0.327219i
$475$	15.8479	+	20.6512i	0.727152	+	0.947544i
$476$	3.75837	+	1.10356i	0.172264	+	0.0505814i
$477$	8.81587	+	6.59948i	0.403651	+	0.302169i
$478$	3.80630	+	10.2051i	0.174096	+	0.466770i
$479$	1.57973	−	10.9873i	0.0721798	−	0.502021i	−0.921376	−	0.388673i	$-0.872933\pi$
$479$	1.57973	−	10.9873i	0.0721798	−	0.502021i	0.993555	−	0.113348i	$-0.0361575\pi$
$480$	2.98909	−	0.781974i	0.136433	−	0.0356921i
$481$	−4.05811	+	3.51637i	−0.185034	+	0.160333i
$482$	−8.68075	+	8.68075i	−0.395397	+	0.395397i
$483$	2.78375	−	3.51148i	0.126665	−	0.159778i
$484$		−	4.26701i		−	0.193955i
$485$	−5.38458	+	5.07362i	−0.244501	+	0.230381i
$486$	8.99044	+	5.77781i	0.407815	+	0.262087i
$487$	−5.10844	+	3.82413i	−0.231486	+	0.173288i	−0.708724	−	0.705486i	$-0.750729\pi$
$487$	−5.10844	+	3.82413i	−0.231486	+	0.173288i	0.477238	+	0.878774i	$0.341638\pi$
$488$	7.43627	−	2.77359i	0.336624	−	0.125554i
$489$	7.62305	−	1.09603i	0.344726	−	0.0495641i
$490$	3.53333	−	14.1969i	0.159619	−	0.641351i
$491$	9.22863	−	5.93088i	0.416482	−	0.267657i	−0.315574	−	0.948901i	$-0.602197\pi$
$491$	9.22863	−	5.93088i	0.416482	−	0.267657i	0.732056	+	0.681244i	$0.238561\pi$
$492$	−0.701674	+	1.88126i	−0.0316339	+	0.0848138i
$493$	−40.8319	−	22.2959i	−1.83898	−	1.00416i
$494$	21.1916	−	24.4565i	0.953457	−	1.10035i
$495$	−1.07531	−	9.46915i	−0.0483316	−	0.425607i
$496$	8.65627	−	2.54171i	0.388678	−	0.114126i
$497$	−3.88486	−	1.44898i	−0.174260	−	0.0649955i
$498$	9.48508	+	2.06335i	0.425037	+	0.0924611i
$499$	−3.05762	+	10.4133i	−0.136878	+	0.466163i	−0.999191	−	0.0402119i	$-0.987197\pi$
$499$	−3.05762	+	10.4133i	−0.136878	+	0.466163i	0.862313	+	0.506375i	$0.169015\pi$
$500$	−9.71596	−	5.53173i	−0.434511	−	0.247386i
$501$	−5.04507	+	11.0472i	−0.225397	+	0.493551i
$502$	2.83661	+	3.78926i	0.126604	+	0.169123i
$503$	5.71457	+	26.2694i	0.254800	+	1.17130i	0.909597	+	0.415492i	$0.136390\pi$
$503$	5.71457	+	26.2694i	0.254800	+	1.17130i	−0.654797	+	0.755805i	$0.727246\pi$
$504$	−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
$508$	−2.36044	−	0.168822i	−0.104728	−	0.00749027i
$509$	7.74865	−	12.0571i	0.343453	−	0.534423i	−0.625961	−	0.779854i	$-0.715293\pi$
$509$	7.74865	−	12.0571i	0.343453	−	0.534423i	0.969414	+	0.245431i	$0.0789295\pi$
$510$	−17.8058	−	1.80677i	−0.788454	−	0.0800050i
$511$	7.61831	+	3.47916i	0.337014	+	0.153909i
$512$	0.599278	−	0.800541i	0.0264846	−	0.0353793i
$513$	−14.1033	−	25.8283i	−0.622677	−	1.14035i
$514$	4.13561	+	6.43513i	0.182414	+	0.283842i
$515$	2.69271	+	5.29999i	0.118655	+	0.233545i
$516$	−1.42147	−	4.84107i	−0.0625766	−	0.213116i
$517$	−1.78763	−	24.9943i	−0.0786198	−	1.09925i
$518$	−0.0416745	−	0.582685i	−0.00183107	−	0.0256017i
$519$	8.08401	+	27.5316i	0.354849	+	1.20850i
$520$	−4.31033	+	13.2134i	−0.189021	+	0.579448i
$521$	8.84745	+	13.7669i	0.387614	+	0.603139i	0.979150	−	0.203140i	$-0.0651146\pi$
$521$	8.84745	+	13.7669i	0.387614	+	0.603139i	−0.591536	+	0.806279i	$0.701478\pi$
$522$	4.19842	+	7.68883i	0.183760	+	0.336531i
$523$	9.30135	−	12.4251i	0.406720	−	0.543314i	−0.549680	−	0.835375i	$-0.685250\pi$
$523$	9.30135	−	12.4251i	0.406720	−	0.543314i	0.956399	+	0.292062i	$0.0943412\pi$
$524$	−5.23193	−	2.38934i	−0.228558	−	0.104379i
$525$	0.277574	−	4.66356i	0.0121143	−	0.203534i
$526$	−10.4938	+	16.3287i	−0.457553	+	0.711966i
$527$	−52.1257	−	3.72810i	−2.27063	−	0.162399i
$528$	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
$532$	0.748349	+	3.44011i	0.0324451	+	0.149148i
$533$	−5.41279	−	7.23064i	−0.234454	−	0.313194i
$534$	−4.65958	+	10.2031i	−0.201640	+	0.441530i
$535$	8.22140	−	1.53408i	0.355442	−	0.0663241i
$536$	1.64400	−	5.59896i	0.0710101	−	0.241838i
$537$	−29.2279	−	6.35814i	−1.26128	−	0.274374i
$538$	6.35387	+	2.36987i	0.273935	+	0.102172i
$539$	24.5289	−	7.20233i	1.05653	−	0.310226i
$540$	9.88861	+	7.87176i	0.425538	+	0.338746i
$541$	4.92446	−	5.68313i	0.211719	−	0.244337i	−0.639950	−	0.768416i	$-0.721045\pi$
$541$	4.92446	−	5.68313i	0.211719	−	0.244337i	0.851669	+	0.524080i	$0.175591\pi$
$542$	8.09408	+	4.41970i	0.347671	+	0.189843i
$543$	5.50286	−	14.7538i	0.236151	−	0.633144i
$544$	−4.87302	+	3.13170i	−0.208929	+	0.134270i
$545$	2.93087	−	1.76273i	0.125545	−	0.0755069i
$546$	−5.74860	+	0.826524i	−0.246017	+	0.0353719i
$547$	0.435103	−	0.162285i	0.0186037	−	0.00693881i	−0.340145	−	0.940373i	$-0.610476\pi$
$547$	0.435103	−	0.162285i	0.0186037	−	0.00693881i	0.358749	+	0.933434i	$0.383203\pi$
$548$	3.15562	−	2.36227i	0.134801	−	0.100911i
$549$	7.28278	+	4.68036i	0.310822	+	0.199753i
$550$	−0.233459	−	19.5351i	−0.00995474	−	0.832980i
$551$		−	41.8138i		−	1.78133i
$552$	1.22864	+	6.51175i	0.0522944	+	0.277158i
$553$	−2.71021	+	2.71021i	−0.115250	+	0.115250i
$554$	−5.01610	+	4.34647i	−0.213114	+	0.184664i
$555$	0.675535	+	2.58223i	0.0286749	+	0.109610i
$556$	1.52832	−	10.6297i	0.0648150	−	0.450798i
$557$	−7.31535	−	19.6132i	−0.309961	−	0.831038i	−0.994754	−	0.102300i	$-0.967380\pi$
$557$	−7.31535	−	19.6132i	−0.309961	−	0.831038i	0.684792	−	0.728738i	$-0.259893\pi$
$558$	7.87778	+	5.89723i	0.333493	+	0.249650i
$559$	21.7772	+	6.39435i	0.921076	+	0.270452i
$560$	−0.869772	−	1.23687i	−0.0367546	−	0.0522672i
$561$	−12.9915	−	28.4475i	−0.548502	−	1.20105i
$562$	−2.05736	+	3.76777i	−0.0867844	+	0.158934i
$563$	−32.9993	+	2.36016i	−1.39075	+	0.0994687i	−0.746522	−	0.665361i	$-0.768278\pi$
$563$	−32.9993	+	2.36016i	−1.39075	+	0.0994687i	−0.644232	+	0.764830i	$0.722823\pi$
$564$	6.69699	+	5.80297i	0.281994	+	0.244349i
$565$	26.7974	−	9.09723i	1.12737	−	0.382724i
$566$	−2.46273	+	1.12469i	−0.103516	+	0.0472744i
$567$	−0.652283	+	2.99850i	−0.0273933	+	0.125925i
$568$	5.38156	−	2.93855i	0.225805	−	0.123299i
$569$	4.10345	+	28.5401i	0.172026	+	1.19646i	0.874597	+	0.484851i	$0.161126\pi$
$569$	4.10345	+	28.5401i	0.172026	+	1.19646i	−0.702571	+	0.711613i	$0.747965\pi$
$570$	−6.24443	−	14.8242i	−0.261550	−	0.620919i
$571$	37.5317	+	5.39624i	1.57065	+	0.225826i	0.871953	−	0.489589i	$-0.162853\pi$
$571$	37.5317	+	5.39624i	1.57065	+	0.225826i	0.698700	+	0.715415i	$0.253762\pi$
$572$	−23.7316	+	5.16249i	−0.992267	+	0.215854i
$573$	−1.39313	+	19.4785i	−0.0581988	+	0.813725i
$574$	0.982628			0.0410141
$575$	13.2804	−	19.9657i	0.553832	−	0.832628i
$576$	1.09077			0.0454486
$577$	−0.705051	+	9.85791i	−0.0293517	+	0.410390i	0.961442	+	0.275008i	$0.0886806\pi$
$577$	−0.705051	+	9.85791i	−0.0293517	+	0.410390i	−0.990794	+	0.135382i	$0.956774\pi$
$578$	16.1755	−	3.51878i	0.672814	−	0.146362i
$579$	−17.8147	−	2.56137i	−0.740354	−	0.106447i
$580$	6.97156	+	16.5504i	0.289478	+	0.687219i
$581$	−0.676064	−	4.70213i	−0.0280479	−	0.195077i
$582$	4.01249	−	2.19099i	0.166323	−	0.0908193i
$583$	−8.38531	+	38.5467i	−0.347284	+	1.59644i
$584$	−11.2661	+	5.14504i	−0.466193	+	0.212903i
$585$	−14.3556	+	4.87346i	−0.593530	+	0.201493i
$586$	−14.4810	−	12.5478i	−0.598204	−	0.518347i
$587$	42.5472	−	3.04303i	1.75611	−	0.125599i	0.844210	−	0.536013i	$-0.180070\pi$
$587$	42.5472	−	3.04303i	1.75611	−	0.125599i	0.911899	+	0.410414i	$0.134616\pi$
$588$	−4.33261	+	7.93459i	−0.178674	+	0.327217i
$589$	−19.5118	−	42.7249i	−0.803969	−	1.76045i
$590$	12.8783	+	18.3138i	0.530193	+	0.753967i
$591$	11.7440	+	3.44835i	0.483084	+	0.141846i
$592$	0.691576	+	0.517707i	0.0284236	+	0.0212776i
$593$	−2.94683	−	7.90076i	−0.121012	−	0.324445i	0.862293	−	0.506409i	$-0.169027\pi$
$593$	−2.94683	−	7.90076i	−0.121012	−	0.324445i	−0.983305	+	0.181964i	$0.941755\pi$
$594$	−3.14312	+	21.8609i	−0.128964	+	0.896964i
$595$	2.21677	+	8.47359i	0.0908785	+	0.347383i
$596$	9.45359	−	8.19158i	0.387234	−	0.335540i
$597$	−9.92879	+	9.92879i	−0.406358	+	0.406358i
$598$	−27.6306	−	11.1872i	−1.12990	−	0.457478i
$599$		−	38.4922i		−	1.57275i	−0.617750	−	0.786374i	$-0.711956\pi$
$599$		−	38.4922i		−	1.57275i	0.617750	−	0.786374i	$-0.288044\pi$
$600$	4.94325	+	4.82650i	0.201808	+	0.197041i
$601$	17.0101	+	10.9318i	0.693858	+	0.445915i	0.839456	−	0.543428i	$-0.182874\pi$
$601$	17.0101	+	10.9318i	0.693858	+	0.445915i	−0.145597	+	0.989344i	$0.546510\pi$
$602$	−1.97670	+	1.47974i	−0.0805641	+	0.0603095i
$603$	5.96367	−	2.22433i	0.242859	−	0.0905818i
$604$	12.6412	−	1.81754i	0.514365	−	0.0739545i
$605$	8.17644	−	4.91759i	0.332419	−	0.199929i
$606$	7.14665	−	4.59287i	0.290313	−	0.186573i
$607$	4.83416	−	12.9609i	0.196213	−	0.526066i	−0.801165	−	0.598444i	$-0.795786\pi$
$607$	4.83416	−	12.9609i	0.196213	−	0.526066i	0.997377	+	0.0723776i	$0.0230587\pi$
$608$	−4.56943	−	2.49510i	−0.185315	−	0.101190i
$609$	−4.91425	+	5.67135i	−0.199136	+	0.229815i
$610$	13.8848	+	11.0529i	0.562179	+	0.447519i
$611$	−38.2475	+	11.2305i	−1.54733	+	0.454337i
$612$	−5.91996	−	2.20803i	−0.239300	−	0.0892544i
$613$	−18.8291	−	4.09602i	−0.760500	−	0.165437i	−0.184440	−	0.982844i	$-0.559047\pi$
$613$	−18.8291	−	4.09602i	−0.760500	−	0.165437i	−0.576060	+	0.817407i	$0.695411\pi$
$614$	5.72858	−	19.5098i	0.231187	−	0.787350i
$615$	−4.41353	+	0.823548i	−0.177971	+	0.0332086i
$616$	1.09760	−	2.40341i	0.0442237	−	0.0968363i
$617$	−20.7407	−	27.7063i	−0.834988	−	1.11541i	−0.991802	−	0.127785i	$-0.959213\pi$
$617$	−20.7407	−	27.7063i	−0.834988	−	1.11541i	0.156814	−	0.987628i	$-0.449878\pi$
$618$	−0.780861	−	3.58956i	−0.0314108	−	0.144393i
$619$	−10.8820	−	12.5585i	−0.437383	−	0.504767i	0.493671	−	0.869649i	$-0.335655\pi$
$619$	−10.8820	−	12.5585i	−0.437383	−	0.504767i	−0.931054	+	0.364882i	$0.881109\pi$
$620$	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
$623$	5.47537	+	0.391606i	0.219366	+	0.0156894i
$624$	4.64331	−	7.22514i	0.185881	−	0.289237i
$625$	−0.597453	−	24.9929i	−0.0238981	−	0.999714i
$626$	−18.0211	−	8.22998i	−0.720270	−	0.328936i
$627$	16.8446	−	22.5018i	0.672709	−	0.898634i
$628$	6.21868	+	11.3887i	0.248152	+	0.454457i
$629$	−2.70543	−	4.20973i	−0.107872	−	0.167853i
$630$	0.511492	−	1.56799i	0.0203783	−	0.0624703i
$631$	11.5001	+	39.1659i	0.457813	+	1.55917i	0.788259	+	0.615343i	$0.210983\pi$
$631$	11.5001	+	39.1659i	0.457813	+	1.55917i	−0.330446	+	0.943825i	$0.607199\pi$
$632$	−0.404353	−	5.65359i	−0.0160843	−	0.224888i
$633$	1.58859	+	22.2114i	0.0631409	+	0.882826i
$634$	0.168314	+	0.573223i	0.00668459	+	0.0227656i
$635$	−2.39684	−	4.71764i	−0.0951156	−	0.187214i
$636$	−7.54203	−	11.7356i	−0.299061	−	0.465348i
$637$	−19.4899	−	35.6931i	−0.772218	−	1.41421i
$638$	−18.8061	+	25.1220i	−0.744540	+	0.994589i
$639$	6.08373	+	2.77835i	0.240669	+	0.109910i
$640$	2.22464	+	0.225736i	0.0879368	+	0.00892301i
$641$	16.1214	−	25.0853i	0.636755	−	0.990811i	−0.361535	−	0.932359i	$-0.617747\pi$
$641$	16.1214	−	25.0853i	0.636755	−	0.990811i	0.998290	−	0.0584521i	$-0.0186165\pi$
$642$	−5.15483	−	0.368681i	−0.203445	−	0.0145507i
$643$	−15.0124	−	15.0124i	−0.592031	−	0.592031i	0.346149	−	0.938180i	$-0.387489\pi$
$643$	−15.0124	−	15.0124i	−0.592031	−	0.592031i	−0.938180	+	0.346149i	$0.887489\pi$
$644$	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
$647$	−8.82492	−	40.5675i	−0.346943	−	1.59487i	−0.738194	−	0.674589i	$-0.764321\pi$
$647$	−8.82492	−	40.5675i	−0.346943	−	1.59487i	0.391250	−	0.920284i	$-0.372043\pi$
$648$	−2.71948	−	3.63280i	−0.106831	−	0.142710i
$649$	−16.2517	+	35.5863i	−0.637937	+	1.39689i
$650$	−30.2871	+	6.96863i	−1.18796	+	0.273332i
$651$	−2.37488	+	8.08809i	−0.0930788	+	0.316997i
$652$	5.44631	+	1.18477i	0.213294	+	0.0463992i
$653$	−3.44241	−	1.28395i	−0.134712	−	0.0502450i	0.281204	−	0.959648i	$-0.409266\pi$
$653$	−3.44241	−	1.28395i	−0.134712	−	0.0502450i	−0.415916	+	0.909403i	$0.636539\pi$
$654$	−2.02781	+	0.595419i	−0.0792937	+	0.0232827i
$655$	−1.45118	−	12.7791i	−0.0567023	−	0.499319i
$656$	−0.951595	+	1.09820i	−0.0371536	+	0.0428775i
$657$	−11.8570	−	6.47440i	−0.462585	−	0.252590i
$658$	1.51552	−	4.06326i	0.0590810	−	0.158402i
$659$	−1.74793	+	1.12333i	−0.0680897	+	0.0437586i	−0.574243	−	0.818685i	$-0.694703\pi$
$659$	−1.74793	+	1.12333i	−0.0680897	+	0.0437586i	0.506153	+	0.862444i	$0.331067\pi$
$660$	−2.91562	+	11.7150i	−0.113490	+	0.456005i
$661$	19.0113	−	2.73341i	0.739453	−	0.106317i	0.237713	−	0.971336i	$-0.423602\pi$
$661$	19.0113	−	2.73341i	0.739453	−	0.106317i	0.501740	+	0.865018i	$0.332693\pi$
$662$	−24.8652	+	9.27423i	−0.966412	+	0.360453i
$663$	−39.8267	+	29.8139i	−1.54674	+	1.15788i
$664$	5.90988	+	3.79805i	0.229348	+	0.147393i
$665$	−5.72948	+	5.39860i	−0.222180	+	0.209349i
$666$			0.942296i			0.0365132i
$667$	−36.4480	+	12.4553i	−1.41127	+	0.482273i
$668$	−6.21499	+	6.21499i	−0.240465	+	0.240465i
$669$	−16.9843	+	14.7170i	−0.656652	+	0.568992i
$670$	12.6234	−	3.30239i	0.487684	−	0.127582i
$671$	−4.41333	+	30.6954i	−0.170375	+	1.18498i
$672$	0.326526	+	0.875451i	0.0125960	+	0.0337713i
$673$	−10.5304	−	7.88296i	−0.405917	−	0.303866i	0.376740	−	0.926319i	$-0.377045\pi$
$673$	−10.5304	−	7.88296i	−0.405917	−	0.303866i	−0.782657	+	0.622453i	$0.786136\pi$
$674$	0.124625	+	0.0365931i	0.00480036	+	0.00140951i
$675$	−3.68754	+	28.0205i	−0.141933	+	1.07851i
$676$	10.6491	+	23.3183i	0.409581	+	0.896857i
$677$	10.5269	−	19.2786i	0.404583	−	0.740938i	−0.593367	−	0.804932i	$-0.702202\pi$
$677$	10.5269	−	19.2786i	0.404583	−	0.740938i	0.997950	+	0.0639936i	$0.0203837\pi$
$678$	−17.4427	+	1.24753i	−0.669884	+	0.0479111i
$679$	−1.69088	−	1.46516i	−0.0648900	−	0.0562275i
$680$	−11.6170	−	5.72849i	−0.445490	−	0.219677i
$681$	6.12582	−	2.79757i	0.234742	−	0.107203i
$682$	−7.49304	+	34.4450i	−0.286923	+	1.31897i
$683$	6.28711	−	3.43302i	0.240570	−	0.131361i	−0.354442	−	0.935078i	$-0.615329\pi$
$683$	6.28711	−	3.43302i	0.240570	−	0.131361i	0.595012	+	0.803717i	$0.297147\pi$
$684$	−0.808180	−	5.62101i	−0.0309015	−	0.214925i
$685$	8.16332	+	3.32435i	0.311904	+	0.127017i
$686$	9.06461	+	1.30329i	0.346088	+	0.0497600i
$687$	−19.1822	+	4.17283i	−0.731846	+	0.159203i
$688$	0.260494	−	3.64219i	0.00993125	−	0.138857i
$689$	62.7537			2.39073
$690$	−11.0618	+	9.85890i	−0.421117	+	0.375322i
$691$	−29.2883			−1.11418			−0.557090	−	0.830452i	$-0.688082\pi$
$691$	−29.2883			−1.11418			−0.557090	+	0.830452i	$0.688082\pi$
$692$	−1.48145	+	20.7134i	−0.0563165	+	0.787407i
$693$	2.81614	−	0.612614i	0.106976	−	0.0232713i
$694$	10.1270	+	1.45604i	0.384416	+	0.0552707i
$695$	22.1299	−	9.32180i	0.839435	−	0.353596i
$696$	−1.57933	−	10.9845i	−0.0598643	−	0.416366i
$697$	7.38772	−	4.03400i	0.279830	−	0.152799i
$698$	−2.84873	+	13.0954i	−0.107826	+	0.495668i
$699$	19.8832	−	9.08037i	0.752053	−	0.343451i
$700$	1.36770	−	3.09211i	0.0516942	−	0.116871i
$701$	10.3014	+	8.92624i	0.389080	+	0.337140i	0.827333	−	0.561712i	$-0.189857\pi$
$701$	10.3014	+	8.92624i	0.389080	+	0.337140i	−0.438253	+	0.898852i	$0.644403\pi$
$702$	35.0442	−	2.50641i	1.32266	−	0.0945983i
$703$	2.15548	−	3.94746i	0.0812953	−	0.148881i
$704$	1.62315	+	3.55421i	0.0611748	+	0.133954i
$705$	−3.40158	+	19.5205i	−0.128111	+	0.735185i
$706$	−16.6586	−	4.89140i	−0.626954	−	0.184090i
$707$	−3.32825	−	2.49149i	−0.125172	−	0.0937023i
$708$	−4.83474	−	12.9624i	−0.181701	−	0.487158i
$709$	−3.42866	+	23.8468i	−0.128766	+	0.895587i	0.818356	+	0.574712i	$0.194886\pi$
$709$	−3.42866	+	23.8468i	−0.128766	+	0.895587i	−0.947122	+	0.320875i	$0.896023\pi$
$710$	11.8329	+	6.92555i	0.444082	+	0.259911i
$711$	4.67242	−	4.04868i	0.175229	−	0.151837i
$712$	−5.74011	+	5.74011i	−0.215120	+	0.215120i
$713$	−31.4300	+	29.7347i	−1.17706	+	1.11357i
$714$		−	5.41236i		−	0.202553i
$715$	−37.2422	−	39.5248i	−1.39278	−	1.47814i
$716$	−18.2110	−	11.7035i	−0.680579	−	0.437381i
$717$	12.0480	−	9.01900i	0.449940	−	0.336821i
$718$	−0.802045	+	0.299147i	−0.0299321	+	0.0111641i
$719$	−37.3531	+	5.37056i	−1.39303	+	0.200288i	−0.797634	−	0.603141i	$-0.793916\pi$
$719$	−37.3531	+	5.37056i	−1.39303	+	0.200288i	−0.595400	+	0.803429i	$0.703006\pi$
$720$	1.25707	+	2.09012i	0.0468484	+	0.0778943i
$721$	−1.51239	+	0.971956i	−0.0563244	+	0.0361975i
$722$	−2.83247	+	7.59415i	−0.105414	+	0.282625i
$723$	14.8880	+	8.12949i	0.553692	+	0.302339i
$724$	7.46286	−	8.61260i	0.277355	−	0.320085i
$725$	−23.6794	+	32.4328i	−0.879431	+	1.20452i
$726$	−5.65711	+	1.66108i	−0.209955	+	0.0616484i
$727$	−14.6060	−	5.44774i	−0.541705	−	0.202046i	0.0636913	−	0.997970i	$-0.479713\pi$
$727$	−14.6060	−	5.44774i	−0.541705	−	0.202046i	−0.605397	+	0.795924i	$0.706985\pi$
$728$	−4.10710	−	0.893445i	−0.152219	−	0.0331133i
$729$	7.99571	−	27.2309i	0.296138	−	1.00855i
$730$	−22.8427	−	15.6585i	−0.845447	−	0.579548i
$731$	−8.78665	+	19.2401i	−0.324986	+	0.711620i
$732$	−6.57198	−	8.77914i	−0.242908	−	0.324486i
$733$	4.77692	+	21.9592i	0.176440	+	0.811080i	0.977238	+	0.212146i	$0.0680452\pi$
$733$	4.77692	+	21.9592i	0.176440	+	0.811080i	−0.800798	+	0.598934i	$0.795591\pi$
$734$	−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
$738$	−1.58098	−	0.113074i	−0.0581968	−	0.00416231i
$739$	2.00965	−	3.12708i	0.0739262	−	0.115031i	−0.802322	−	0.596891i	$-0.796402\pi$
$739$	2.00965	−	3.12708i	0.0739262	−	0.115031i	0.876248	+	0.481860i	$0.160039\pi$
$740$	−0.195010	+	1.92184i	−0.00716872	+	0.0706481i
$741$	−40.6735	−	18.5749i	−1.49418	−	0.682368i
$742$	−4.09132	+	5.46537i	−0.150197	+	0.200640i
$743$	0.0155199	+	0.0284225i	0.000569369	+	0.00104272i	0.877964	−	0.478728i	$-0.158902\pi$
$743$	0.0155199	+	0.0284225i	0.000569369	+	0.00104272i	−0.877394	+	0.479770i	$0.840720\pi$
$744$	−6.73949	−	10.4869i	−0.247082	−	0.384467i
$745$	26.5917	+	8.67441i	0.974243	+	0.317806i
$746$	−0.00940214	−	0.0320208i	−0.000344237	−	0.00117236i
$747$	0.546653	+	7.64320i	0.0200010	+	0.279650i
$748$	−1.61464	−	22.5756i	−0.0590372	−	0.825448i
$749$	0.712551	+	2.42672i	0.0260360	+	0.0886706i
$750$	−3.55158	+	15.0346i	−0.129686	+	0.548988i
$751$	−27.3719	−	42.5916i	−0.998816	−	1.55419i	−0.821638	−	0.570009i	$-0.806940\pi$
$751$	−27.3719	−	42.5916i	−0.998816	−	1.55419i	−0.177178	−	0.984179i	$-0.556697\pi$
$752$	3.07350	+	5.62870i	0.112079	+	0.205257i
$753$	3.91948	−	5.23581i	0.142834	−	0.190804i
$754$	45.4097	+	20.7379i	1.65372	+	0.755230i
$755$	18.0514	+	22.1285i	0.656957	+	0.805337i
$756$	−2.06647	+	3.21549i	−0.0751568	+	0.116946i
$757$	44.1485	+	3.15757i	1.60461	+	0.114764i	0.844689	−	0.535257i	$-0.179785\pi$
$757$	44.1485	+	3.15757i	1.60461	+	0.114764i	0.759917	+	0.650021i	$0.225240\pi$
$758$	−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	0.411583	−	0.911372i	$-0.364976\pi$
$761$	−15.1473	−	17.4809i	−0.549088	−	0.633681i	−0.960670	+	0.277692i	$0.910431\pi$
$762$	0.695061	+	3.19515i	0.0251794	+	0.115748i
$763$	0.619827	+	0.827991i	0.0224392	+	0.0299753i
$764$	−5.87105	+	12.8558i	−0.212407	+	0.465106i
$765$	−2.59154	−	13.8885i	−0.0936974	−	0.502140i
$766$	−3.75077	+	12.7739i	−0.135521	+	0.461541i
$767$	60.8121	+	13.2289i	2.19580	+	0.477667i
$768$	−1.29463	−	0.482872i	−0.0467160	−	0.0174242i
$769$	−6.70935	+	1.97004i	−0.241945	+	0.0710416i	−0.400457	−	0.916316i	$-0.631149\pi$
$769$	−6.70935	+	1.97004i	−0.241945	+	0.0710416i	0.158512	+	0.987357i	$0.449330\pi$
$770$	5.87037	−	0.666635i	0.211554	−	0.0240239i
$771$	6.92164	−	7.98800i	0.249277	−	0.287681i
$772$	−11.4322	−	6.24243i	−0.411452	−	0.224670i
$773$	−11.2722	+	30.2219i	−0.405433	+	1.08701i	0.560487	+	0.828163i	$0.310614\pi$
$773$	−11.2722	+	30.2219i	−0.405433	+	1.08701i	−0.965919	+	0.258843i	$0.916659\pi$
$774$	3.35065	−	2.15333i	0.120436	−	0.0773998i
$775$	−9.06110	+	44.1891i	−0.325484	+	1.58732i
$776$	3.27496	−	0.470868i	0.117564	−	0.0169032i
$777$	−0.756289	+	0.282081i	−0.0271317	+	0.0101196i
$778$	8.67820	−	6.49642i	0.311128	−	0.232908i
$779$	6.36439	+	4.09014i	0.228028	+	0.146545i
$780$	19.1961	+	0.570768i	0.687329	+	0.0204368i
$781$			23.9579i			0.857283i
$782$	13.9841	−	24.0038i	0.500070	−	0.858375i
$783$	32.1005	−	32.1005i	1.14718	−	1.14718i
$784$	−4.94467	+	4.28458i	−0.176595	+	0.153021i
$785$	−14.6561	+	25.0413i	−0.523099	+	0.893762i
$786$	−1.13103	+	7.86652i	−0.0403427	+	0.280589i
$787$	7.88623	+	21.1438i	0.281114	+	0.753695i	0.998380	+	0.0568960i	$0.0181203\pi$
$787$	7.88623	+	21.1438i	0.281114	+	0.753695i	−0.717266	+	0.696799i	$0.754607\pi$
$788$	7.09135	+	5.30852i	0.252619	+	0.189108i
$789$	25.7334	+	7.55599i	0.916132	+	0.269001i
$790$	10.3674	−	7.29041i	0.368856	−	0.259381i
$791$	3.55518	+	7.78475i	0.126408	+	0.276794i
$792$	−2.04254	+	3.74063i	−0.0725784	+	0.132917i
$793$	49.2063	−	3.51930i	1.74737	−	0.124974i
$794$	−25.4775	−	22.0764i	−0.904162	−	0.783461i
$795$	13.7958	−	27.9770i	0.489288	−	0.992241i
$796$	−9.24374	+	4.22147i	−0.327636	+	0.149626i
$797$	0.384867	−	1.76920i	0.0136327	−	0.0626684i	−0.969828	−	0.243790i	$-0.921609\pi$
$797$	0.384867	−	1.76920i	0.0136327	−	0.0626684i	0.983461	+	0.181122i	$0.0579728\pi$
$798$	4.26950	−	2.33133i	0.151139	−	0.0825280i
$799$	−5.28681	−	36.7705i	−0.187034	−	1.30085i
$800$	2.13128	+	4.52301i	0.0753520	+	0.159913i
$801$	−8.76443	−	1.26013i	−0.309676	−	0.0445247i
$802$	27.7342	−	6.03321i	0.979329	−	0.213040i
$803$	3.45233	−	48.2698i	0.121830	−	1.70341i
$804$	−8.06297			−0.284359
$805$	6.41250	+	3.38612i	0.226011	+	0.119345i
$806$	56.0762			1.97520
$807$	0.668467	−	9.34639i	0.0235311	−	0.329008i
$808$	6.00766	−	1.30689i	0.211349	−	0.0459761i
$809$	−17.5210	−	2.51914i	−0.616005	−	0.0885681i	−0.172753	−	0.984965i	$-0.555266\pi$
$809$	−17.5210	−	2.51914i	−0.616005	−	0.0885681i	−0.443252	+	0.896397i	$0.646175\pi$
$810$	3.82705	−	9.39776i	0.134469	−	0.330203i
$811$	−7.05851	−	49.0930i	−0.247858	−	1.72389i	−0.610547	−	0.791980i	$-0.709050\pi$
$811$	−7.05851	−	49.0930i	−0.247858	−	1.72389i	0.362689	−	0.931910i	$-0.381859\pi$
$812$	−4.76667	+	2.60280i	−0.167277	+	0.0913403i
$813$	2.70866	−	12.4515i	0.0949967	−	0.436693i
$814$	−3.07043	+	1.40222i	−0.107618	+	0.0491477i
$815$	4.00644	+	11.8016i	0.140339	+	0.413393i
$816$	6.04893	+	5.24143i	0.211755	+	0.183487i
$817$	−18.9622	+	1.35620i	−0.663403	+	0.0474475i
$818$	8.38338	−	15.3530i	0.293118	−	0.536806i
$819$	−1.90454	−	4.17035i	−0.0665499	−	0.145724i
$820$	−3.20105	−	0.557805i	−0.111786	−	0.0194794i
$821$	16.9342	+	4.97234i	0.591009	+	0.173536i	0.563543	−	0.826087i	$-0.309438\pi$
$821$	16.9342	+	4.97234i	0.591009	+	0.173536i	0.0274659	+	0.999623i	$0.491256\pi$
$822$	−4.36028	−	3.26406i	−0.152082	−	0.113847i
$823$	−9.41863	−	25.2523i	−0.328313	−	0.880241i	−0.991301	−	0.131611i	$-0.957985\pi$
$823$	−9.41863	−	25.2523i	−0.328313	−	0.880241i	0.662988	−	0.748630i	$-0.269288\pi$
$824$	0.378357	−	2.63153i	0.0131807	−	0.0916737i
$825$	−25.8084	+	7.91423i	−0.898532	+	0.275538i
$826$	−5.11687	+	4.43379i	−0.178039	+	0.154271i
$827$	−7.60159	+	7.60159i	−0.264333	+	0.264333i	−0.826812	−	0.562479i	$-0.809848\pi$
$827$	−7.60159	+	7.60159i	−0.264333	+	0.264333i	0.562479	+	0.826812i	$0.309848\pi$
$828$	−4.65895	+	2.37884i	−0.161910	+	0.0826703i
$829$		−	26.4541i		−	0.918790i	−0.888232	−	0.459395i	$-0.848066\pi$
$829$		−	26.4541i		−	0.918790i	0.888232	−	0.459395i	$-0.151934\pi$
$830$	−0.466866	+	15.7016i	−0.0162051	+	0.545012i
$831$	7.71516	+	4.95823i	0.267636	+	0.171999i
$832$	4.97592	−	3.72493i	0.172509	−	0.129139i
$833$	35.5097	−	13.2444i	1.23034	−	0.458892i
$834$	−14.6876	+	2.11175i	−0.508588	+	0.0731240i
$835$	−19.0717	−	4.74658i	−0.660005	−	0.164262i
$836$	17.1132	−	10.9980i	0.591871	−	0.380372i
$837$	17.8207	−	47.7792i	0.615975	−	1.65149i
$838$	29.0376	+	15.8557i	1.00309	+	0.547727i
$839$	2.43822	−	2.81386i	0.0841768	−	0.0971452i	−0.712099	−	0.702079i	$-0.752255\pi$
$839$	2.43822	−	2.81386i	0.0841768	−	0.0971452i	0.796275	+	0.604934i	$0.206801\pi$
$840$	−1.30123	+	1.63462i	−0.0448966	+	0.0563997i
$841$	34.0658	−	10.0026i	1.17468	−	0.344918i
$842$	33.4756	+	12.4857i	1.15364	+	0.430287i
$843$	5.79613	+	1.26087i	0.199629	+	0.0434267i
$844$	−4.54038	+	15.4631i	−0.156286	+	0.532262i
$845$	−32.4097	+	47.2794i	−1.11493	+	1.62646i
$846$	−2.90593	+	6.36311i	−0.0999081	+	0.218768i
$847$	1.72917	+	2.30990i	0.0594150	+	0.0793691i
$848$	−2.14606	−	9.86529i	−0.0736961	−	0.338775i
$849$	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
$853$	−34.9034	−	2.49634i	−1.19507	−	0.0854732i	−0.540414	−	0.841399i	$-0.681732\pi$
$853$	−34.9034	−	2.49634i	−1.19507	−	0.0854732i	−0.654657	+	0.755926i	$0.727187\pi$
$854$	−2.90157	+	4.51494i	−0.0992898	+	0.154498i
$855$	9.83957	−	8.02667i	0.336506	−	0.274506i
$856$	−3.40219	−	1.55373i	−0.116284	−	0.0531053i
$857$	−14.4336	+	19.2810i	−0.493041	+	0.658625i	−0.976191	−	0.216912i	$-0.930402\pi$
$857$	−14.4336	+	19.2810i	−0.493041	+	0.658625i	0.483150	+	0.875537i	$0.339492\pi$
$858$	16.0826	+	29.4532i	0.549052	+	1.00551i
$859$	−10.2753	−	15.9887i	−0.350588	−	0.545526i	0.620512	−	0.784197i	$-0.286925\pi$
$859$	−10.2753	−	15.9887i	−0.350588	−	0.545526i	−0.971101	+	0.238671i	$0.923288\pi$
$860$	7.27936	−	3.69835i	0.248224	−	0.126113i
$861$	−0.382522	−	1.30275i	−0.0130363	−	0.0443976i
$862$	0.500897	+	7.00345i	0.0170606	+	0.238538i
$863$	0.360617	+	5.04209i	0.0122755	+	0.171635i	0.999891	+	0.0147427i	$0.00469290\pi$
$863$	0.360617	+	5.04209i	0.0122755	+	0.171635i	−0.987616	+	0.156892i	$0.949853\pi$
$864$	−1.59247	−	5.42345i	−0.0541769	−	0.184510i
$865$	−41.3984	+	21.0328i	−1.40759	+	0.715138i
$866$	−19.0396	−	29.6262i	−0.646992	−	1.00674i
$867$	−10.9620	−	20.0754i	−0.372289	−	0.681797i
$868$	−3.65597	+	4.88381i	−0.124092	+	0.165767i
$869$	20.1454	+	9.20008i	0.683385	+	0.312091i
$870$	19.2283	−	15.6856i	0.651901	−	0.531791i
$871$	19.6094	−	30.5128i	0.664439	−	1.03389i
$872$	−1.52563	−	0.109115i	−0.0516642	−	0.00369510i
$873$	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
$877$	7.41117	+	34.0686i	0.250257	+	1.15041i	0.915035	+	0.403374i	$0.132162\pi$
$877$	7.41117	+	34.0686i	0.250257	+	1.15041i	−0.664778	+	0.747041i	$0.731474\pi$
$878$	−22.4789	−	30.0283i	−0.758626	−	1.01341i
$879$	−10.9985	+	24.0833i	−0.370969	+	0.812308i
$880$	−4.93993	+	7.20639i	−0.166525	+	0.242927i
$881$	−10.7539	+	36.6243i	−0.362307	+	1.23391i	0.553690	+	0.832723i	$0.313219\pi$
$881$	−10.7539	+	36.6243i	−0.362307	+	1.23391i	−0.915998	+	0.401183i	$0.868599\pi$
$882$	−6.97349	−	1.51699i	−0.234810	−	0.0510797i
$883$	3.99832	+	1.49129i	0.134554	+	0.0501861i	0.415839	−	0.909438i	$-0.363488\pi$
$883$	3.99832	+	1.49129i	0.134554	+	0.0501861i	−0.281285	+	0.959624i	$0.590761\pi$
$884$	−34.5464	+	10.1437i	−1.16192	+	0.341171i
$885$	19.2667	−	24.2031i	0.647643	−	0.813579i
$886$	−14.2420	+	16.4362i	−0.478470	+	0.552184i
$887$	17.8373	+	9.73989i	0.598917	+	0.327034i	0.749949	−	0.661495i	$-0.230078\pi$
$887$	17.8373	+	9.73989i	0.598917	+	0.327034i	−0.151032	+	0.988529i	$0.548260\pi$
$888$	0.417146	−	1.11841i	0.0139985	−	0.0375314i
$889$	1.34621	−	0.865159i	0.0451506	−	0.0290165i
$890$	−17.6145	−	4.38389i	−0.590439	−	0.146948i
$891$	17.5506	−	2.52339i	0.587967	−	0.0845369i
$892$	−15.2390	+	5.68386i	−0.510240	+	0.190310i
$893$	26.7290	−	20.0090i	0.894450	−	0.669577i
$894$	−14.5404	−	9.34453i	−0.486303	−	0.312528i
$895$	1.43863	−	48.3839i	0.0480880	−	1.61730i
$896$			0.676217i			0.0225908i
$897$	−4.07562	+	40.9870i	−0.136081	+	1.36852i
$898$	−12.4524	+	12.4524i	−0.415544	+	0.415544i
$899$	54.7595	−	47.4494i	1.82633	−	1.58253i
$900$	−2.55635	+	4.81760i	−0.0852118	+	0.160587i
$901$	−8.32283	+	57.8866i	−0.277274	+	1.92848i
$902$	−1.98419	−	5.31982i	−0.0660663	−	0.177131i
$903$	2.73130	+	2.04463i	0.0908920	+	0.0680409i
$904$	−12.1432	−	3.56558i	−0.403878	−	0.118589i
$905$	25.1042	+	4.37457i	0.834491	+	0.145416i
$906$	−7.33068	−	16.0520i	−0.243546	−	0.533291i
$907$	−19.7378	+	36.1471i	−0.655383	+	1.20024i	0.312756	+	0.949833i	$0.398748\pi$
$907$	−19.7378	+	36.1471i	−0.655383	+	1.20024i	−0.968139	+	0.250412i	$0.919434\pi$
$908$	4.86140	−	0.347694i	0.161331	−	0.0115386i
$909$	5.06822	+	4.39164i	0.168102	+	0.145661i
$910$	−3.02129	−	8.89969i	−0.100155	−	0.295022i
$911$	46.4880	−	21.2304i	1.54022	−	0.703393i	0.549022	−	0.835808i	$-0.315000\pi$
$911$	46.4880	−	21.2304i	1.54022	−	0.703393i	0.991194	+	0.132415i	$0.0422731\pi$
$912$	−1.52914	+	7.02936i	−0.0506350	+	0.232765i
$913$	−24.0915	+	13.1550i	−0.797313	+	0.435366i
$914$	−3.90894	−	27.1872i	−0.129296	−	0.899274i
$915$	9.24858	−	22.7109i	0.305748	−	0.750800i
$916$	−14.0626	−	2.02190i	−0.464641	−	0.0668054i
$917$	3.80051	−	0.826750i	0.125504	−	0.0273017i
$918$	−2.33579	+	32.6586i	−0.0770925	+	1.07789i
$919$	−55.9704			−1.84629			−0.923146	−	0.384448i	$-0.874392\pi$
$919$	−55.9704			−1.84629			−0.923146	+	0.384448i	$0.874392\pi$
$920$	−9.99436	+	3.88752i	−0.329504	+	0.128168i
$921$	−28.0957			−0.925784
$922$	1.64645	−	23.0203i	0.0542228	−	0.758134i
$923$	37.2411	−	8.10130i	1.22580	−	0.266657i
$924$	−3.61368	−	0.519568i	−0.118881	−	0.0170925i
$925$	−3.90736	+	1.84118i	−0.128473	+	0.0605376i
$926$	0.297571	+	2.06965i	0.00977878	+	0.0680129i
$927$	2.54518	−	1.38977i	0.0835947	−	0.0456462i
$928$	1.70720	−	7.84789i	0.0560417	−	0.257620i
$929$	−16.7331	+	7.64176i	−0.548996	+	0.250718i	−0.670547	−	0.741867i	$-0.733941\pi$
$929$	−16.7331	+	7.64176i	−0.548996	+	0.250718i	0.121551	+	0.992585i	$0.461213\pi$
$930$	12.3278	−	25.0000i	0.404246	−	0.819781i
$931$	25.7432	+	22.3066i	0.843700	+	0.731071i
$932$	15.7792	−	1.12855i	0.516863	−	0.0369668i
$933$	0.584307	−	1.07008i	0.0191294	−	0.0350328i
$934$	10.5510	+	23.1035i	0.345240	+	0.755971i
$935$	41.3986	−	29.1117i	1.35388	−	0.952054i
$936$	6.50523	+	1.91011i	0.212630	+	0.0624339i
$937$	21.8117	+	16.3280i	0.712556	+	0.533413i	0.892936	−	0.450184i	$-0.148642\pi$
$937$	21.8117	+	16.3280i	0.712556	+	0.533413i	−0.180379	+	0.983597i	$0.557733\pi$
$938$	1.37897	+	3.69716i	0.0450249	+	0.120716i
$939$	−3.89580	+	27.0959i	−0.127135	+	0.884240i
$940$	−7.24358	+	12.3763i	−0.236260	+	0.403671i
$941$	−22.9066	+	19.8487i	−0.746733	+	0.647048i	−0.942730	−	0.333556i	$-0.891751\pi$
$941$	−22.9066	+	19.8487i	−0.746733	+	0.647048i	0.195997	+	0.980605i	$0.437206\pi$
$942$	12.6780	−	12.6780i	0.413072	−	0.413072i
$943$	1.66947	−	6.76603i	0.0543654	−	0.220332i
$944$		−	10.0125i		−	0.325878i
$945$	−8.54306	−	0.254016i	−0.277906	−	0.00826313i
$946$	12.0026	+	7.71358i	0.390237	+	0.250790i
$947$	−23.0687	+	17.2690i	−0.749633	+	0.561168i	−0.904350	−	0.426791i	$-0.859644\pi$
$947$	−23.0687	+	17.2690i	−0.749633	+	0.561168i	0.154718	+	0.987959i	$0.450553\pi$
$948$	−7.33801	+	2.73694i	−0.238328	+	0.0888916i
$949$	−76.1997	+	10.9559i	−2.47355	+	0.355642i
$950$	21.7292	−	14.3343i	0.704988	−	0.465065i
$951$	0.694446	−	0.446294i	0.0225190	−	0.0144721i
$952$	1.36886	−	3.67006i	0.0443651	−	0.118947i
$953$	31.3191	+	17.1015i	1.01453	+	0.553973i	0.898361	−	0.439257i	$-0.144758\pi$
$953$	31.3191	+	17.1015i	1.01453	+	0.553973i	0.116164	+	0.993230i	$0.462940\pi$
$954$	7.21158	−	8.32260i	0.233483	−	0.269454i
$955$	−31.4005	+	3.56581i	−1.01609	+	0.115387i
$956$	10.4506	−	3.06858i	0.337998	−	0.0992451i
$957$	40.6271	+	15.1531i	1.31329	+	0.489831i
$958$	−10.8466	−	2.35953i	−0.350437	−	0.0762329i
$959$	−0.750972	+	2.55758i	−0.0242501	+	0.0825884i
$960$	−0.566742	−	3.03726i	−0.0182915	−	0.0980273i
$961$	20.9333	−	45.8375i	0.675267	−	1.47863i
$962$	3.21791	+	4.29862i	0.103750	+	0.138593i
$963$	−0.867195	−	3.98643i	−0.0279450	−	0.128461i
$964$	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	$0.607413\pi$
$968$	−4.25614	−	0.304405i	−0.136797	−	0.00978395i
$969$	22.5287	−	35.0553i	0.723726	−	1.12614i
$970$	4.67656	+	5.73281i	0.150155	+	0.184069i
$971$	−12.7822	−	5.83743i	−0.410200	−	0.187332i	0.199618	−	0.979874i	$-0.436030\pi$
$971$	−12.7822	−	5.83743i	−0.410200	−	0.187332i	−0.609817	+	0.792542i	$0.708757\pi$
$972$	6.40446	−	8.55535i	0.205423	−	0.274413i
$973$	3.48025	+	6.37360i	0.111572	+	0.204328i
$974$	3.44996	+	5.36824i	0.110544	+	0.172009i
$975$	21.0292	+	37.4413i	0.673472	+	1.19908i
$976$	−2.23602	−	7.61519i	−0.0715733	−	0.243756i
$977$	−0.379106	−	5.30060i	−0.0121287	−	0.169581i	−0.999906	−	0.0137096i	$-0.995636\pi$
$977$	−0.379106	−	5.30060i	−0.0121287	−	0.169581i	0.987777	−	0.155872i	$-0.0498186\pi$
$978$	−0.549414	−	7.68182i	−0.0175683	−	0.245637i
$979$	−8.93613	−	30.4337i	−0.285600	−	0.972664i
$980$	−13.9087	−	4.53712i	−0.444296	−	0.144933i
$981$	−0.901979	−	1.40351i	−0.0287980	−	0.0448105i
$982$	−5.25741	−	9.62822i	−0.167771	−	0.307249i
$983$	−23.7159	+	31.6807i	−0.756419	+	1.01046i	0.242766	+	0.970085i	$0.421945\pi$
$983$	−23.7159	+	31.6807i	−0.756419	+	1.01046i	−0.999185	+	0.0403725i	$0.987146\pi$
$984$	1.82641	+	0.834094i	0.0582239	+	0.0265900i
$985$	−1.99962	+	19.7063i	−0.0637131	+	0.627896i
$986$	−25.1520	+	39.1373i	−0.801004	+	1.24639i
$987$	−5.97695	−	0.427480i	−0.190248	−	0.0136068i
$988$	−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	0.562703	−	0.826659i	$-0.309762\pi$
$991$	−10.5655	−	12.1932i	−0.335623	−	0.387330i	−0.898326	+	0.439329i	$0.855216\pi$
$992$	−1.91770	−	8.81553i	−0.0608871	−	0.279893i
$993$	21.9752	+	29.3554i	0.697362	+	0.931567i
$994$	−1.72243	+	3.77159i	−0.0546321	+	0.119628i
$995$	−18.7423	−	12.8477i	−0.594171	−	0.407300i
$996$	2.73475	−	9.31372i	0.0866540	−	0.295116i
$997$	−14.4027	−	3.13312i	−0.456139	−	0.0992269i	−0.0213751	−	0.999772i	$-0.506804\pi$
$997$	−14.4027	−	3.13312i	−0.456139	−	0.0992269i	−0.434764	+	0.900545i	$0.643168\pi$
$998$	10.1686	+	3.79271i	0.321883	+	0.120056i
$999$	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.217.9	yes	240
5.3	odd	4	inner	230.2.l.a.33.3	yes	240
23.7	odd	22	inner	230.2.l.a.7.3	✓	240
115.53	even	44	inner	230.2.l.a.53.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.3	✓	240	23.7	odd	22	inner
230.2.l.a.33.3	yes	240	5.3	odd	4	inner
230.2.l.a.53.9	yes	240	115.53	even	44	inner
230.2.l.a.217.9	yes	240	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.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0713392 - 0.997452i) q^{2} +(-1.35017 + 0.293712i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.868035 - 2.06071i) q^{5} +(0.196644 + 1.36769i) q^{6} +(0.593501 - 0.324076i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(-0.992195 + 0.453120i) q^{9} +(-2.11738 + 0.718814i) q^{10} +(-2.95294 - 2.55874i) q^{11} +(1.37823 - 0.0985729i) q^{12} +(-2.97886 + 5.45538i) q^{13} +(-0.280911 - 0.615108i) q^{14} +(1.77725 + 2.52736i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-4.63719 - 3.47136i) q^{17} +(0.381184 + 1.02199i) q^{18} +(0.740929 - 5.15327i) q^{19} +(0.565930 + 2.16327i) q^{20} +(-0.706144 + 0.611878i) q^{21} +(-2.76288 + 2.76288i) q^{22} +(-4.71268 + 0.889192i) q^{23} -1.38175i q^{24} +(-3.49303 + 3.57753i) q^{25} +(5.22897 + 3.36046i) q^{26} +(4.52499 - 3.38737i) q^{27} +(-0.633581 + 0.236314i) q^{28} +(7.94969 - 1.14299i) q^{29} +(2.64771 - 1.59242i) q^{30} +(7.58954 - 4.87750i) q^{31} +(0.349464 - 0.936950i) q^{32} +(4.73852 + 2.58743i) q^{33} +(-3.79333 + 4.37773i) q^{34} +(-1.18301 - 0.941723i) q^{35} +(1.04658 - 0.307304i) q^{36} +(0.809417 + 0.301897i) q^{37} +(-5.08728 - 1.10667i) q^{38} +(2.41967 - 8.24064i) q^{39} +(2.19813 - 0.410162i) q^{40} +(-0.603651 + 1.32181i) q^{41} +(0.559943 + 0.747996i) q^{42} +(-0.776180 - 3.56804i) 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} +(-1.37823 - 0.0985729i) q^{48} +(-3.53727 + 5.50410i) q^{49} +(3.31923 + 3.73935i) q^{50} +(7.28059 + 3.32493i) q^{51} +(3.72493 - 4.97592i) q^{52} +(-4.83850 - 8.86106i) q^{53} +(-3.05593 - 4.75512i) q^{54} +(-2.70956 + 8.30622i) q^{55} +(0.190512 + 0.648825i) q^{56} +(0.513197 + 7.17543i) q^{57} +(-0.572956 - 8.01097i) q^{58} +(-2.82083 - 9.60688i) q^{59} +(-1.39948 - 2.75456i) q^{60} +(-4.29089 - 6.67676i) q^{61} +(-4.32364 - 7.91816i) q^{62} +(-0.442024 + 0.590475i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(13.8277 + 1.40311i) q^{65} +(2.91887 - 4.54186i) q^{66} +(-5.82046 - 0.416288i) 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} +(-0.231859 - 1.06584i) q^{72} +(7.42224 + 9.91495i) q^{73} +(0.358871 - 0.785817i) q^{74} +(3.66543 - 5.85623i) q^{75} +(-1.46677 + 4.99537i) q^{76} +(-2.58180 - 0.561636i) q^{77} +(-8.04703 - 3.00139i) q^{78} +(-5.43844 + 1.59687i) q^{79} +(-0.252305 - 2.22179i) q^{80} +(-2.97171 + 3.42954i) q^{81} +(1.27538 + 0.696409i) q^{82} +(2.45502 - 6.58215i) q^{83} +(0.786036 - 0.505155i) q^{84} +(-3.12821 + 12.5692i) q^{85} +(-3.61432 + 0.519661i) q^{86} +(-10.3977 + 3.87816i) q^{87} +(3.12796 - 2.34156i) q^{88} +(6.82908 + 4.38878i) q^{89} +(1.77515 - 1.67263i) q^{90} +4.20316i q^{91} +(4.79126 - 0.209457i) q^{92} +(-8.81462 + 8.81462i) q^{93} +(4.84674 - 4.19973i) q^{94} +(-11.2625 + 2.94638i) q^{95} +(-0.196644 + 1.36769i) q^{96} +(-1.15625 - 3.10002i) q^{97} +(5.23773 + 3.92091i) 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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