LMFDB - Embedded newform 230.2.l.a.67.7

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			67.7
Character	$\chi$	$=$	230.67
Dual form			230.2.l.a.103.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.212565 + 0.977147i) q^{2} +(-2.69897 - 2.02042i) q^{3} +(-0.909632 + 0.415415i) q^{4} +(0.823826 + 2.07878i) q^{5} +(1.40054 - 3.06676i) q^{6} +(-0.114897 - 1.60647i) q^{7} +(-0.599278 - 0.800541i) q^{8} +(2.35713 + 8.02765i) q^{9} +(-1.85615 + 1.24687i) q^{10} +(2.59443 + 4.03702i) q^{11} +(3.29438 + 0.716649i) q^{12} +(3.73682 + 0.267263i) q^{13} +(1.54534 - 0.453752i) q^{14} +(1.97653 - 7.27503i) q^{15} +(0.654861 - 0.755750i) q^{16} +(1.05573 + 2.83053i) q^{17} +(-7.34315 + 4.00966i) q^{18} +(-0.432881 - 0.947878i) q^{19} +(-1.61293 - 1.54869i) q^{20} +(-2.93565 + 4.56796i) q^{21} +(-3.39327 + 3.39327i) q^{22} +(-0.218958 + 4.79083i) q^{23} +3.37143i q^{24} +(-3.64262 + 3.42510i) q^{25} +(0.533163 + 3.70823i) q^{26} +(6.32284 - 16.9522i) q^{27} +(0.771867 + 1.41357i) q^{28} +(-4.46522 - 2.03920i) q^{29} +(7.52892 + 0.384937i) q^{30} +(-0.275290 + 1.91468i) q^{31} +(0.877679 + 0.479249i) q^{32} +(1.15419 - 16.1376i) q^{33} +(-2.54143 + 1.63328i) q^{34} +(3.24484 - 1.56230i) q^{35} +(-5.47893 - 6.32302i) q^{36} +(3.12776 - 5.72807i) q^{37} +(0.834200 - 0.624475i) q^{38} +(-9.54558 - 8.27129i) q^{39} +(1.17045 - 1.90527i) q^{40} +(5.94139 + 1.74455i) q^{41} +(-5.08759 - 1.89757i) q^{42} +(-3.04813 + 4.07183i) q^{43} +(-4.03702 - 2.59443i) q^{44} +(-14.7458 + 11.5133i) q^{45} +(-4.72789 + 0.804410i) q^{46} +(1.23406 + 1.23406i) q^{47} +(-3.29438 + 0.716649i) q^{48} +(4.36120 - 0.627045i) q^{49} +(-4.12112 - 2.83132i) q^{50} +(2.86948 - 9.77254i) q^{51} +(-3.51016 + 1.30922i) q^{52} +(-5.08474 + 0.363668i) q^{53} +(17.9088 + 2.57490i) q^{54} +(-6.25469 + 8.71905i) q^{55} +(-1.21719 + 1.05470i) q^{56} +(-0.746781 + 3.43290i) q^{57} +(1.04344 - 4.79663i) q^{58} +(6.22131 - 5.39080i) q^{59} +(1.22425 + 7.43868i) q^{60} +(-6.21156 - 0.893088i) q^{61} +(-1.92944 + 0.137997i) q^{62} +(12.6254 - 4.70902i) q^{63} +(-0.281733 + 0.959493i) q^{64} +(2.52291 + 7.98819i) q^{65} +(16.0142 - 2.30249i) q^{66} +(-8.37794 + 1.82251i) q^{67} +(-2.13617 - 2.13617i) q^{68} +(10.2705 - 12.4879i) q^{69} +(2.21634 + 2.83860i) q^{70} +(2.20559 + 1.41744i) q^{71} +(5.01389 - 6.69777i) q^{72} +(0.257869 + 0.0961803i) q^{73} +(6.26202 + 1.83869i) q^{74} +(16.7515 - 1.88461i) q^{75} +(0.787525 + 0.682395i) q^{76} +(6.18727 - 4.63173i) q^{77} +(6.05321 - 11.0856i) q^{78} +(6.22707 + 7.18643i) q^{79} +(2.11053 + 0.738702i) q^{80} +(-30.2006 + 19.4088i) q^{81} +(-0.441748 + 6.17644i) q^{82} +(-2.59404 - 1.41645i) q^{83} +(0.772762 - 5.37468i) q^{84} +(-5.01429 + 4.52650i) q^{85} +(-4.62670 - 2.11294i) q^{86} +(7.93145 + 14.5254i) q^{87} +(1.67701 - 4.49625i) q^{88} +(0.560355 + 3.89736i) q^{89} +(-14.3847 - 11.9615i) q^{90} -6.03381i q^{91} +(-1.79101 - 4.44885i) q^{92} +(4.61147 - 4.61147i) q^{93} +(-0.943540 + 1.46818i) q^{94} +(1.61381 - 1.68075i) q^{95} +(-1.40054 - 3.06676i) q^{96} +(-5.75621 + 3.14313i) q^{97} +(1.53975 + 4.12824i) q^{98} +(-26.2923 + 30.3430i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.212565	+	0.977147i	0.150306	+	0.690947i
$2$	0.212565	+	0.977147i	0.150306	+	0.690947i
$3$	−2.69897	−	2.02042i	−1.55825	−	1.16649i	−0.916813	−	0.399318i	$-0.869247\pi$
$3$	−2.69897	−	2.02042i	−1.55825	−	1.16649i	−0.641439	−	0.767174i	$-0.721662\pi$
$4$	−0.909632	+	0.415415i	−0.454816	+	0.207708i
$5$	0.823826	+	2.07878i	0.368426	+	0.929657i
$5$	0.823826	+	2.07878i	0.368426	+	0.929657i
$6$	1.40054	−	3.06676i	0.571769	−	1.25200i
$7$	−0.114897	−	1.60647i	−0.0434271	−	0.607190i	−0.971840	−	0.235640i	$-0.924281\pi$
$7$	−0.114897	−	1.60647i	−0.0434271	−	0.607190i	0.928413	−	0.371549i	$-0.121173\pi$
$8$	−0.599278	−	0.800541i	−0.211877	−	0.283034i
$9$	2.35713	+	8.02765i	0.785710	+	2.67588i
$10$	−1.85615	+	1.24687i	−0.586967	+	0.394296i
$11$	2.59443	+	4.03702i	0.782251	+	1.21721i	0.971909	+	0.235357i	$0.0756258\pi$
$11$	2.59443	+	4.03702i	0.782251	+	1.21721i	−0.189658	+	0.981850i	$0.560738\pi$
$12$	3.29438	+	0.716649i	0.951007	+	0.206879i
$13$	3.73682	+	0.267263i	1.03641	+	0.0741253i	0.579160	−	0.815214i	$-0.303381\pi$
$13$	3.73682	+	0.267263i	1.03641	+	0.0741253i	0.457248	+	0.889339i	$0.348835\pi$
$14$	1.54534	−	0.453752i	0.413009	−	0.121270i
$15$	1.97653	−	7.27503i	0.510337	−	1.87841i
$16$	0.654861	−	0.755750i	0.163715	−	0.188937i
$17$	1.05573	+	2.83053i	0.256053	+	0.686504i	0.999836	+	0.0180837i	$0.00575652\pi$
$17$	1.05573	+	2.83053i	0.256053	+	0.686504i	−0.743784	+	0.668420i	$0.766971\pi$
$18$	−7.34315	+	4.00966i	−1.73080	+	0.945086i
$19$	−0.432881	−	0.947878i	−0.0993098	−	0.217458i	0.853455	−	0.521166i	$-0.174503\pi$
$19$	−0.432881	−	0.947878i	−0.0993098	−	0.217458i	−0.952765	+	0.303708i	$0.901775\pi$
$20$	−1.61293	−	1.54869i	−0.360663	−	0.346298i
$21$	−2.93565	+	4.56796i	−0.640612	+	0.996811i
$22$	−3.39327	+	3.39327i	−0.723448	+	0.723448i
$23$	−0.218958	+	4.79083i	−0.0456558	+	0.998957i
$23$	−0.218958	+	4.79083i	−0.0456558	+	0.998957i
$24$			3.37143i			0.688191i
$25$	−3.64262	+	3.42510i	−0.728524	+	0.685020i
$26$	0.533163	+	3.70823i	0.104562	+	0.727244i
$27$	6.32284	−	16.9522i	1.21683	−	3.26245i
$28$	0.771867	+	1.41357i	0.145869	+	0.267139i
$29$	−4.46522	−	2.03920i	−0.829170	−	0.378669i	−0.0448255	−	0.998995i	$-0.514273\pi$
$29$	−4.46522	−	2.03920i	−0.829170	−	0.378669i	−0.784344	+	0.620326i	$0.787000\pi$
$30$	7.52892	+	0.384937i	1.37459	+	0.0702795i
$31$	−0.275290	+	1.91468i	−0.0494435	+	0.343887i	0.950051	+	0.312095i	$0.101031\pi$
$31$	−0.275290	+	1.91468i	−0.0494435	+	0.343887i	−0.999494	+	0.0317926i	$0.989878\pi$
$32$	0.877679	+	0.479249i	0.155153	+	0.0847201i
$33$	1.15419	−	16.1376i	0.200918	−	2.80920i
$34$	−2.54143	+	1.63328i	−0.435852	+	0.280105i
$35$	3.24484	−	1.56230i	0.548478	−	0.264077i
$36$	−5.47893	−	6.32302i	−0.913154	−	1.05384i
$37$	3.12776	−	5.72807i	0.514201	−	0.941689i	−0.483592	−	0.875293i	$-0.660668\pi$
$37$	3.12776	−	5.72807i	0.514201	−	0.941689i	0.997793	−	0.0663955i	$-0.0211499\pi$
$38$	0.834200	−	0.624475i	0.135325	−	0.101303i
$39$	−9.54558	−	8.27129i	−1.52852	−	1.32447i
$40$	1.17045	−	1.90527i	0.185064	−	0.301250i
$41$	5.94139	+	1.74455i	0.927889	+	0.272453i	0.710553	−	0.703644i	$-0.248445\pi$
$41$	5.94139	+	1.74455i	0.927889	+	0.272453i	0.217336	+	0.976097i	$0.430263\pi$
$42$	−5.08759	−	1.89757i	−0.785032	−	0.292802i
$43$	−3.04813	+	4.07183i	−0.464836	+	0.620948i	−0.970301	−	0.241899i	$-0.922230\pi$
$43$	−3.04813	+	4.07183i	−0.464836	+	0.620948i	0.505466	+	0.862847i	$0.331321\pi$
$44$	−4.03702	−	2.59443i	−0.608603	−	0.391126i
$45$	−14.7458	+	11.5133i	−2.19818	+	1.71631i
$46$	−4.72789	+	0.804410i	−0.697089	+	0.118604i
$47$	1.23406	+	1.23406i	0.180006	+	0.180006i	0.791359	−	0.611352i	$-0.209374\pi$
$47$	1.23406	+	1.23406i	0.180006	+	0.180006i	−0.611352	+	0.791359i	$0.709374\pi$
$48$	−3.29438	+	0.716649i	−0.475503	+	0.103439i
$49$	4.36120	−	0.627045i	0.623028	−	0.0895779i
$50$	−4.12112	−	2.83132i	−0.582815	−	0.400409i
$51$	2.86948	−	9.77254i	0.401807	−	1.36843i
$52$	−3.51016	+	1.30922i	−0.486771	+	0.181556i
$53$	−5.08474	+	0.363668i	−0.698443	+	0.0499536i	−0.416045	−	0.909344i	$-0.636584\pi$
$53$	−5.08474	+	0.363668i	−0.698443	+	0.0499536i	−0.282398	+	0.959297i	$0.591130\pi$
$54$	17.9088	+	2.57490i	2.43708	+	0.350399i
$55$	−6.25469	+	8.71905i	−0.843383	+	1.17568i
$56$	−1.21719	+	1.05470i	−0.162654	+	0.140941i
$57$	−0.746781	+	3.43290i	−0.0989136	+	0.454698i
$58$	1.04344	−	4.79663i	0.137011	−	0.629829i
$59$	6.22131	−	5.39080i	0.809946	−	0.701822i	−0.147932	−	0.988998i	$-0.547262\pi$
$59$	6.22131	−	5.39080i	0.809946	−	0.701822i	0.957878	+	0.287175i	$0.0927162\pi$
$60$	1.22425	+	7.43868i	0.158050	+	0.960330i
$61$	−6.21156	−	0.893088i	−0.795309	−	0.114348i	−0.267329	−	0.963605i	$-0.586141\pi$
$61$	−6.21156	−	0.893088i	−0.795309	−	0.114348i	−0.527980	+	0.849257i	$0.677050\pi$
$62$	−1.92944	+	0.137997i	−0.245040	+	0.0175256i
$63$	12.6254	−	4.70902i	1.59065	−	0.593281i
$64$	−0.281733	+	0.959493i	−0.0352166	+	0.119937i
$65$	2.52291	+	7.98819i	0.312929	+	0.990813i
$66$	16.0142	−	2.30249i	1.97121	−	0.283417i
$67$	−8.37794	+	1.82251i	−1.02353	+	0.222655i	−0.692845	−	0.721087i	$-0.743643\pi$
$67$	−8.37794	+	1.82251i	−1.02353	+	0.222655i	−0.330684	+	0.943742i	$0.607279\pi$
$68$	−2.13617	−	2.13617i	−0.259049	−	0.259049i
$69$	10.2705	−	12.4879i	1.23642	−	1.50337i
$70$	2.21634	+	2.83860i	0.264903	+	0.339277i
$71$	2.20559	+	1.41744i	0.261755	+	0.168220i	0.664936	−	0.746901i	$-0.268459\pi$
$71$	2.20559	+	1.41744i	0.261755	+	0.168220i	−0.403181	+	0.915120i	$0.632095\pi$
$72$	5.01389	−	6.69777i	0.590892	−	0.789340i
$73$	0.257869	+	0.0961803i	0.0301813	+	0.0112571i	0.364510	−	0.931200i	$-0.381237\pi$
$73$	0.257869	+	0.0961803i	0.0301813	+	0.0112571i	−0.334328	+	0.942457i	$0.608509\pi$
$74$	6.26202	+	1.83869i	0.727945	+	0.213744i
$75$	16.7515	−	1.88461i	1.93429	−	0.217616i
$76$	0.787525	+	0.682395i	0.0903354	+	0.0782760i
$77$	6.18727	−	4.63173i	0.705105	−	0.527835i
$78$	6.05321	−	11.0856i	0.685391	−	1.25520i
$79$	6.22707	+	7.18643i	0.700601	+	0.808536i	0.988834	−	0.149024i	$-0.0476132\pi$
$79$	6.22707	+	7.18643i	0.700601	+	0.808536i	−0.288233	+	0.957560i	$0.593068\pi$
$80$	2.11053	+	0.738702i	0.235964	+	0.0825894i
$81$	−30.2006	+	19.4088i	−3.35562	+	2.15653i
$82$	−0.441748	+	6.17644i	−0.0487829	+	0.682074i
$83$	−2.59404	−	1.41645i	−0.284733	−	0.155476i	0.330536	−	0.943794i	$-0.392771\pi$
$83$	−2.59404	−	1.41645i	−0.284733	−	0.155476i	−0.615269	+	0.788317i	$0.710952\pi$
$84$	0.772762	−	5.37468i	0.0843153	−	0.586426i
$85$	−5.01429	+	4.52650i	−0.543877	+	0.490967i
$86$	−4.62670	−	2.11294i	−0.498910	−	0.227844i
$87$	7.93145	+	14.5254i	0.850340	+	1.55728i
$88$	1.67701	−	4.49625i	0.178770	−	0.479302i
$89$	0.560355	+	3.89736i	0.0593976	+	0.413119i	0.997728	+	0.0673780i	$0.0214634\pi$
$89$	0.560355	+	3.89736i	0.0593976	+	0.413119i	−0.938330	+	0.345741i	$0.887628\pi$
$90$	−14.3847	−	11.9615i	−1.51628	−	1.26085i
$91$		−	6.03381i		−	0.632515i
$92$	−1.79101	−	4.44885i	−0.186726	−	0.463825i
$93$	4.61147	−	4.61147i	0.478187	−	0.478187i
$94$	−0.943540	+	1.46818i	−0.0973187	+	0.151431i
$95$	1.61381	−	1.68075i	0.165573	−	0.172441i
$96$	−1.40054	−	3.06676i	−0.142942	−	0.313000i
$97$	−5.75621	+	3.14313i	−0.584455	+	0.319137i	−0.744132	−	0.668033i	$-0.767137\pi$
$97$	−5.75621	+	3.14313i	−0.584455	+	0.319137i	0.159677	+	0.987169i	$0.448955\pi$
$98$	1.53975	+	4.12824i	0.155539	+	0.417015i
$99$	−26.2923	+	30.3430i	−2.64248	+	3.04958i
$100$	1.89061	−	4.62878i	0.189061	−	0.462878i
$101$	12.1610	−	3.57078i	1.21006	−	0.355306i	0.386369	−	0.922344i	$-0.373729\pi$
$101$	12.1610	−	3.57078i	1.21006	−	0.355306i	0.823691	+	0.567038i	$0.191911\pi$
$102$	10.1592	+	0.726597i	1.00591	+	0.0719438i
$103$	−5.42518	−	1.18018i	−0.534559	−	0.116286i	−0.0628207	−	0.998025i	$-0.520010\pi$
$103$	−5.42518	−	1.18018i	−0.534559	−	0.116286i	−0.471738	+	0.881739i	$0.656373\pi$
$104$	−2.02544	−	3.15164i	−0.198611	−	0.309044i
$105$	−11.9142	−	2.33935i	−1.16271	−	0.228298i
$106$	−1.43620	−	4.89124i	−0.139496	−	0.475079i
$107$	−1.39572	−	1.86446i	−0.134929	−	0.180244i	0.727988	−	0.685590i	$-0.240456\pi$
$107$	−1.39572	−	1.86446i	−0.134929	−	0.180244i	−0.862917	+	0.505346i	$0.831365\pi$
$108$	1.29074	+	18.0469i	0.124201	+	1.73656i
$109$	4.89062	−	10.7090i	0.468437	−	1.02573i	−0.517046	−	0.855957i	$-0.672968\pi$
$109$	4.89062	−	10.7090i	0.468437	−	1.02573i	0.985483	−	0.169775i	$-0.0543043\pi$
$110$	−9.84932	−	4.25839i	−0.939096	−	0.406021i
$111$	−20.0149	+	9.14048i	−1.89973	+	0.867576i
$112$	−1.28933	−	0.965182i	−0.121830	−	0.0912012i
$113$	−2.60658	−	11.9822i	−0.245206	−	1.12719i	−0.920835	−	0.389952i	$-0.872491\pi$
$113$	−2.60658	−	11.9822i	−0.245206	−	1.12719i	0.675629	−	0.737242i	$-0.263872\pi$
$114$	−3.51319			−0.329040
$115$	−10.1394	+	3.49165i	−0.945508	+	0.325598i
$116$	4.90882			0.455772
$117$	6.66268	+	30.6278i	0.615965	+	2.83155i
$118$	6.59004	+	4.93324i	0.606662	+	0.454142i
$119$	4.42587	−	2.02123i	0.405718	−	0.185285i
$120$	−7.00845	+	2.77747i	−0.639781	+	0.253548i
$121$	−4.99686	+	10.9416i	−0.454260	+	0.994691i
$122$	−0.447685	−	6.25945i	−0.0405315	−	0.566704i
$123$	−12.5109	−	16.7126i	−1.12807	−	1.50692i
$124$	−0.544976	−	1.85602i	−0.0489403	−	0.166675i
$125$	−10.1209	−	4.75050i	−0.905241	−	0.424898i
$126$	7.28512	+	11.3359i	0.649010	+	1.00988i
$127$	12.2110	+	2.65635i	1.08355	+	0.235713i	0.718678	−	0.695343i	$-0.244747\pi$
$127$	12.2110	+	2.65635i	1.08355	+	0.235713i	0.364877	+	0.931056i	$0.381111\pi$
$128$	−0.997452	−	0.0713392i	−0.0881631	−	0.00630555i
$129$	16.4536	−	4.83122i	1.44866	−	0.425365i
$130$	−7.26935	+	4.16327i	−0.637564	+	0.365143i
$131$	4.51626	−	5.21204i	0.394587	−	0.455378i	−0.523342	−	0.852123i	$-0.675315\pi$
$131$	4.51626	−	5.21204i	0.394587	−	0.455378i	0.917929	+	0.396745i	$0.129860\pi$
$132$	5.65394	+	15.1588i	0.492112	+	1.31940i
$133$	−1.47300	+	0.804321i	−0.127726	+	0.0697434i
$134$	−3.56172	−	7.79908i	−0.307686	−	0.673738i
$135$	40.4487	−	0.821892i	3.48127	−	0.0707372i
$136$	1.63328	−	2.54143i	0.140052	−	0.217926i
$137$	10.9066	−	10.9066i	0.931816	−	0.931816i	−0.0660030	−	0.997819i	$-0.521025\pi$
$137$	10.9066	−	10.9066i	0.931816	−	0.931816i	0.997819	+	0.0660030i	$0.0210247\pi$
$138$	14.3857	+	7.38126i	1.22459	+	0.628334i
$139$		−	15.5890i		−	1.32224i	−0.750279	−	0.661121i	$-0.770081\pi$
$139$		−	15.5890i		−	1.32224i	0.750279	−	0.661121i	$-0.229919\pi$
$140$	−2.30261	+	2.76907i	−0.194606	+	0.234029i
$141$	−0.837367	−	5.82402i	−0.0705191	−	0.490471i
$142$	−0.916220	+	2.45648i	−0.0768875	+	0.206143i
$143$	8.61599	+	15.7790i	0.720505	+	1.31951i
$144$	7.61048	+	3.47559i	0.634207	+	0.289633i
$145$	0.560469	−	10.9621i	0.0465444	−	0.910355i
$146$	−0.0391682	+	0.272421i	−0.00324158	+	0.0225457i
$147$	−13.0376	−	7.11909i	−1.07533	−	0.587173i
$148$	−0.465587	+	6.50976i	−0.0382710	+	0.535099i
$149$	−9.33018	+	5.99614i	−0.764358	+	0.491223i	−0.863809	−	0.503819i	$-0.831928\pi$
$149$	−9.33018	+	5.99614i	−0.764358	+	0.491223i	0.0994508	+	0.995042i	$0.468291\pi$
$150$	5.40232	+	15.9681i	0.441098	+	1.30379i
$151$	−10.8327	−	12.5016i	−0.881552	−	1.01737i	−0.999703	−	0.0243698i	$-0.992242\pi$
$151$	−10.8327	−	12.5016i	−0.881552	−	1.01737i	0.118151	−	0.992996i	$-0.462303\pi$
$152$	−0.499399	+	0.914582i	−0.0405066	+	0.0741824i
$153$	−20.2340	+	15.1470i	−1.63582	+	1.22456i
$154$	5.84108	+	5.06132i	0.470688	+	0.407853i
$155$	−4.20699	+	1.00510i	−0.337914	+	0.0807317i
$156$	12.1190	+	3.55846i	0.970295	+	0.284904i
$157$	1.06050	+	0.395547i	0.0846373	+	0.0315681i	0.391426	−	0.920210i	$-0.371982\pi$
$157$	1.06050	+	0.395547i	0.0846373	+	0.0315681i	−0.306789	+	0.951778i	$0.599255\pi$
$158$	−5.69853	+	7.61235i	−0.453351	+	0.605606i
$159$	14.4583	+	9.29180i	1.14662	+	0.736888i
$160$	−0.273196	+	2.21932i	−0.0215981	+	0.175452i
$161$	7.72150	−	0.198703i	0.608539	−	0.0156600i
$162$	−25.3848	−	25.3848i	−1.99442	−	1.99442i
$163$	−14.3054	+	3.11194i	−1.12048	+	0.243746i	−0.734399	−	0.678718i	$-0.762536\pi$
$163$	−14.3054	+	3.11194i	−1.12048	+	0.243746i	−0.386083	+	0.922464i	$0.626172\pi$
$164$	−6.12919	+	0.881244i	−0.478609	+	0.0688136i
$165$	34.4974	−	10.8953i	2.68562	−	0.848200i
$166$	0.832680	−	2.83585i	0.0646285	−	0.220105i
$167$	8.91277	−	3.32429i	0.689691	−	0.257241i	0.0199116	−	0.999802i	$-0.493662\pi$
$167$	8.91277	−	3.32429i	0.689691	−	0.257241i	0.669779	+	0.742560i	$0.266389\pi$
$168$	5.41611	−	0.387368i	0.417862	−	0.0298861i
$169$	1.02471	+	0.147332i	0.0788241	+	0.0113332i
$170$	−5.48892	−	3.93753i	−0.420981	−	0.301995i
$171$	6.58887	−	5.70929i	0.503864	−	0.436600i
$172$	1.08118	−	4.97010i	0.0824392	−	0.378967i
$173$	4.51808	−	20.7693i	0.343504	−	1.57906i	−0.403972	−	0.914771i	$-0.632371\pi$
$173$	4.51808	−	20.7693i	0.343504	−	1.57906i	0.747476	−	0.664289i	$-0.231266\pi$
$174$	−12.5075	+	10.8378i	−0.948188	+	0.821610i
$175$	5.92086	+	5.45824i	0.447575	+	0.412604i
$176$	4.74997	+	0.682942i	0.358042	+	0.0514787i
$177$	−27.6828	+	1.97992i	−2.08077	+	0.148820i
$178$	−3.68918	+	1.37599i	−0.276516	+	0.103135i
$179$	−1.35032	+	4.59878i	−0.100928	+	0.343729i	−0.994439	−	0.105312i	$-0.966416\pi$
$179$	−1.35032	+	4.59878i	−0.100928	+	0.343729i	0.893511	+	0.449041i	$0.148234\pi$
$180$	8.63045	−	16.5985i	0.643276	−	1.23718i
$181$	23.0409	−	3.31278i	1.71261	−	0.246237i	0.784925	−	0.619591i	$-0.212701\pi$
$181$	23.0409	−	3.31278i	1.71261	−	0.246237i	0.927689	+	0.373354i	$0.121792\pi$
$182$	5.89592	−	1.28258i	0.437034	−	0.0950710i
$183$	14.9604	+	14.9604i	1.10590	+	1.10590i
$184$	3.96647	−	2.69575i	0.292412	−	0.198734i
$185$	14.4841	+	1.78298i	1.06489	+	0.131088i
$186$	5.48633	+	3.52585i	0.402277	+	0.258528i
$187$	−8.68787	+	11.6056i	−0.635320	+	0.848688i
$188$	−1.63519	−	0.609894i	−0.119258	−	0.0444811i
$189$	−27.9597	−	8.20971i	−2.03377	−	0.597169i
$190$	1.98538	+	1.21966i	0.144035	+	0.0884832i
$191$	8.21279	+	7.11642i	0.594256	+	0.514926i	0.899254	−	0.437427i	$-0.144110\pi$
$191$	8.21279	+	7.11642i	0.594256	+	0.514926i	−0.304998	+	0.952353i	$0.598656\pi$
$192$	2.69897	−	2.02042i	0.194781	−	0.145812i
$193$	−7.32092	+	13.4073i	−0.526972	+	0.965077i	0.469642	+	0.882857i	$0.344383\pi$
$193$	−7.32092	+	13.4073i	−0.526972	+	0.965077i	−0.996614	+	0.0822199i	$0.973799\pi$
$194$	−4.29487	−	4.95655i	−0.308354	−	0.355859i
$195$	9.33027	−	26.6572i	0.668154	−	1.90896i
$196$	−3.70660	+	2.38209i	−0.264757	+	0.170149i
$197$	0.340190	−	4.75648i	0.0242375	−	0.338885i	−0.970836	−	0.239745i	$-0.922936\pi$
$197$	0.340190	−	4.75648i	0.0242375	−	0.338885i	0.995073	−	0.0991401i	$-0.0316092\pi$
$198$	−35.2384	−	19.2416i	−2.50428	−	1.36744i
$199$	1.43619	−	9.98893i	0.101809	−	0.708096i	−0.873431	−	0.486948i	$-0.838110\pi$
$199$	1.43619	−	9.98893i	0.101809	−	0.708096i	0.975240	−	0.221149i	$-0.0709807\pi$
$200$	4.92488	+	0.863481i	0.348241	+	0.0610573i
$201$	26.2941	+	12.0081i	1.85464	+	0.846986i
$202$	6.07417	+	11.1240i	0.427377	+	0.782683i
$203$	−2.76287	+	7.40755i	−0.193916	+	0.519908i
$204$	1.44949	+	10.0814i	0.101485	+	0.705842i
$205$	1.26815	+	13.7880i	0.0885711	+	0.962997i
$206$		−	5.55206i		−	0.386831i
$207$	−38.9752	+	9.53489i	−2.70896	+	0.662721i
$208$	2.64908	−	2.64908i	0.183681	−	0.183681i
$209$	2.70352	−	4.20676i	0.187006	−	0.290987i
$210$	−0.246661	−	12.1392i	−0.0170212	−	0.837686i
$211$	−6.45464	−	14.1337i	−0.444355	−	0.973003i	−0.990778	−	0.135493i	$-0.956738\pi$
$211$	−6.45464	−	14.1337i	−0.444355	−	0.973003i	0.546423	−	0.837509i	$-0.315989\pi$
$212$	4.47417	−	2.44308i	0.307287	−	0.167792i
$213$	−3.08897	−	8.28186i	−0.211653	−	0.567464i
$214$	1.52517	−	1.76014i	0.104259	−	0.120321i
$215$	−10.9755	−	2.98190i	−0.748526	−	0.203364i
$216$	−17.3601	+	5.09738i	−1.18120	+	0.346833i
$217$	3.10752	+	0.222254i	0.210952	+	0.0150876i
$218$	11.5038	+	2.50250i	0.779136	+	0.169491i
$219$	−0.501657	−	0.780593i	−0.0338988	−	0.0527476i
$220$	2.06745	−	10.5294i	0.139387	−	0.709893i
$221$	3.18859	+	10.8593i	0.214488	+	0.730478i
$222$	−13.1861	−	17.6145i	−0.884990	−	1.18221i
$223$	0.0770710	+	1.07759i	0.00516105	+	0.0721610i	0.999380	−	0.0352120i	$-0.0112107\pi$
$223$	0.0770710	+	1.07759i	0.00516105	+	0.0721610i	−0.994219	+	0.107373i	$0.965756\pi$
$224$	0.669058	−	1.46503i	0.0447033	−	0.0978866i
$225$	−36.0816	−	21.1683i	−2.40544	−	1.41122i
$226$	11.1543	−	5.09402i	0.741976	−	0.338849i
$227$	1.68143	+	1.25870i	0.111600	+	0.0835430i	0.653620	−	0.756823i	$-0.273249\pi$
$227$	1.68143	+	1.25870i	0.111600	+	0.0835430i	−0.542020	+	0.840366i	$0.682340\pi$
$228$	−0.746781	−	3.43290i	−0.0494568	−	0.227349i
$229$	1.90049			0.125588			0.0627939	−	0.998027i	$-0.479999\pi$
$229$	1.90049			0.125588			0.0627939	+	0.998027i	$0.479999\pi$
$230$	−5.56715	−	9.16553i	−0.367087	−	0.604357i
$231$	−26.0573			−1.71444
$232$	1.04344	+	4.79663i	0.0685055	+	0.314915i
$233$	−1.12023	−	0.838591i	−0.0733885	−	0.0549379i	0.561954	−	0.827169i	$-0.310050\pi$
$233$	−1.12023	−	0.838591i	−0.0733885	−	0.0549379i	−0.635342	+	0.772231i	$0.719141\pi$
$234$	−28.5116	+	13.0208i	−1.86386	+	0.851198i
$235$	−1.54868	+	3.58199i	−0.101025	+	0.233663i
$236$	−3.41969	+	7.48807i	−0.222603	+	0.487432i
$237$	−2.28706	−	31.9773i	−0.148561	−	2.07715i
$238$	2.91582	+	3.89508i	0.189005	+	0.252480i
$239$	−5.80506	−	19.7702i	−0.375498	−	1.27883i	−0.903134	−	0.429358i	$-0.858740\pi$
$239$	−5.80506	−	19.7702i	−0.375498	−	1.27883i	0.527637	−	0.849470i	$-0.323078\pi$
$240$	−4.20375	−	6.25789i	−0.271351	−	0.403945i
$241$	−6.22601	−	9.68786i	−0.401053	−	0.624050i	0.580721	−	0.814102i	$-0.302771\pi$
$241$	−6.22601	−	9.68786i	−0.401053	−	0.624050i	−0.981774	+	0.190052i	$0.939134\pi$
$242$	−11.7537	−	2.55686i	−0.755558	−	0.164361i
$243$	66.5838	+	4.76217i	4.27136	+	0.305493i
$244$	6.02124	−	1.76799i	0.385470	−	0.113184i
$245$	4.89636	+	8.54938i	0.312817	+	0.546200i
$246$	13.6713	−	15.7775i	0.871649	−	1.00594i
$247$	−1.36427	−	3.65774i	−0.0868063	−	0.232737i
$248$	1.69776	−	0.927046i	0.107808	−	0.0588675i
$249$	4.13940	+	9.06403i	0.262324	+	0.574410i
$250$	2.49059	−	10.8994i	0.157519	−	0.689339i
$251$	−3.31309	+	5.15526i	−0.209120	+	0.325397i	−0.929931	−	0.367735i	$-0.880133\pi$
$251$	−3.31309	+	5.15526i	−0.209120	+	0.325397i	0.720811	+	0.693132i	$0.243770\pi$
$252$	−9.52824	+	9.52824i	−0.600223	+	0.600223i
$253$	−19.9087	+	11.5456i	−1.25165	+	0.725863i
$254$			12.4966i			0.784108i
$255$	22.6789	−	2.08588i	1.42021	−	0.130623i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−9.41072	+	25.2311i	−0.587025	+	1.57387i	0.215019	+	0.976610i	$0.431019\pi$
$257$	−9.41072	+	25.2311i	−0.587025	+	1.57387i	−0.802044	+	0.597265i	$0.796254\pi$
$258$	8.21828	+	15.0507i	0.511648	+	0.937013i
$259$	−9.56136	−	4.36653i	−0.594114	−	0.271323i
$260$	−5.61333	−	6.21826i	−0.348124	−	0.385640i
$261$	5.84485	−	40.6518i	0.361787	−	2.51629i
$262$	6.05293	+	3.30515i	0.373951	+	0.204193i
$263$	−0.890943	+	12.4570i	−0.0549379	+	0.768132i	0.893076	+	0.449905i	$0.148542\pi$
$263$	−0.890943	+	12.4570i	−0.0549379	+	0.768132i	−0.948014	+	0.318227i	$0.896912\pi$
$264$	−13.6105	+	8.74696i	−0.837670	+	0.538338i
$265$	−4.94493	−	10.2704i	−0.303765	−	0.630908i
$266$	−1.09905	−	1.26837i	−0.0673870	−	0.0777687i
$267$	6.36193	−	11.6510i	0.389344	−	0.713030i
$268$	6.86375	−	5.13814i	0.419270	−	0.313862i
$269$	−20.3565	−	17.6390i	−1.24116	−	1.07547i	−0.994322	−	0.106409i	$-0.966065\pi$
$269$	−20.3565	−	17.6390i	−1.24116	−	1.07547i	−0.246833	−	0.969058i	$-0.579390\pi$
$270$	9.40111	+	39.3497i	0.572133	+	2.39474i
$271$	−4.27589	−	1.25551i	−0.259742	−	0.0762670i	0.149269	−	0.988797i	$-0.452308\pi$
$271$	−4.27589	−	1.25551i	−0.259742	−	0.0762670i	−0.409011	+	0.912530i	$0.634126\pi$
$272$	2.83053	+	1.05573i	0.171626	+	0.0640132i
$273$	−12.1908	+	16.2851i	−0.737824	+	0.985617i
$274$	12.9758	+	8.33901i	0.783894	+	0.503778i
$275$	−23.2777	−	5.81913i	−1.40370	−	0.350907i
$276$	−4.15468	+	15.6259i	−0.250082	+	0.940570i
$277$	7.15110	+	7.15110i	0.429668	+	0.429668i	0.888515	−	0.458847i	$-0.151738\pi$
$277$	7.15110	+	7.15110i	0.429668	+	0.429668i	−0.458847	+	0.888515i	$0.651738\pi$
$278$	15.2328	−	3.31368i	0.913600	−	0.198741i
$279$	−16.0193	+	2.30323i	−0.959051	+	0.137891i
$280$	−3.19525	−	1.66138i	−0.190953	−	0.0992863i
$281$	−8.37990	+	28.5393i	−0.499903	+	1.70251i	0.192756	+	0.981247i	$0.438257\pi$
$281$	−8.37990	+	28.5393i	−0.499903	+	1.70251i	−0.692659	+	0.721265i	$0.743561\pi$
$282$	5.51293	−	2.05622i	0.328290	−	0.122446i
$283$	30.7436	−	2.19883i	1.82752	−	0.130707i	0.885155	−	0.465296i	$-0.154052\pi$
$283$	30.7436	−	2.19883i	1.82752	−	0.130707i	0.942364	+	0.334589i	$0.108598\pi$
$284$	−2.59510	−	0.373119i	−0.153991	−	0.0221405i
$285$	−7.75144	+	1.27572i	−0.459156	+	0.0755672i
$286$	−13.5869	+	11.7732i	−0.803413	+	0.696161i
$287$	2.11992	−	9.74512i	0.125135	−	0.575236i
$288$	−1.77844	+	8.17535i	−0.104795	+	0.481737i
$289$	5.95042	−	5.15607i	0.350025	−	0.303298i
$290$	10.8307	−	1.78251i	0.636003	−	0.104672i
$291$	21.8863	+	3.14678i	1.28300	+	0.184467i
$292$	−0.274521	+	0.0196341i	−0.0160651	+	0.00114900i
$293$	−0.0616599	+	0.0229980i	−0.00360221	+	0.00134355i	−0.351265	−	0.936276i	$-0.614248\pi$
$293$	−0.0616599	+	0.0229980i	−0.00360221	+	0.00134355i	0.347662	+	0.937620i	$0.386976\pi$
$294$	4.18505	−	14.2530i	0.244077	−	0.831249i
$295$	16.3315	+	8.49164i	0.950859	+	0.494402i
$296$	−6.45995	+	0.928801i	−0.375477	+	0.0539855i
$297$	84.8405	−	18.4559i	4.92295	−	1.07092i
$298$	−7.84239	−	7.84239i	−0.454297	−	0.454297i
$299$	−2.09862	+	17.8440i	−0.121366	+	1.03194i
$300$	−14.4548	+	8.67312i	−0.834547	+	0.500743i
$301$	6.89150	+	4.42890i	0.397219	+	0.255277i
$302$	9.91324	−	13.2425i	0.570443	−	0.762023i
$303$	−40.0366	−	14.9329i	−2.30004	−	0.857871i
$304$	−0.999835	−	0.293578i	−0.0573445	−	0.0168379i
$305$	−3.26072	−	13.6482i	−0.186708	−	0.781493i
$306$	−19.1019	−	16.5519i	−1.09198	−	0.946207i
$307$	−4.99950	+	3.74258i	−0.285337	+	0.213600i	−0.732352	−	0.680926i	$-0.761578\pi$
$307$	−4.99950	+	3.74258i	−0.285337	+	0.213600i	0.447016	+	0.894526i	$0.352487\pi$
$308$	−3.70405	+	6.78345i	−0.211058	+	0.386523i
$309$	12.2579	+	14.1464i	0.697330	+	0.804762i
$310$	−1.87639	−	3.89720i	−0.106572	−	0.221346i
$311$	−15.7976	+	10.1525i	−0.895801	+	0.575696i	−0.905542	−	0.424256i	$-0.860536\pi$
$311$	−15.7976	+	10.1525i	−0.895801	+	0.575696i	0.00974118	+	0.999953i	$0.496899\pi$
$312$	−0.901058	+	12.5984i	−0.0510123	+	0.713246i
$313$	20.2497	+	11.0572i	1.14458	+	0.624988i	0.935645	−	0.352942i	$-0.114819\pi$
$313$	20.2497	+	11.0572i	1.14458	+	0.624988i	0.208934	+	0.977930i	$0.433001\pi$
$314$	−0.161081	+	1.12035i	−0.00909035	+	0.0632248i
$315$	20.1901	+	22.3659i	1.13758	+	1.26018i
$316$	−8.64970	−	3.95018i	−0.486583	−	0.222215i
$317$	11.5162	+	21.0904i	0.646816	+	1.18455i	0.971118	+	0.238601i	$0.0766887\pi$
$317$	11.5162	+	21.0904i	0.646816	+	1.18455i	−0.324302	+	0.945954i	$0.605129\pi$
$318$	−6.00612	+	16.1030i	−0.336806	+	0.903013i
$319$	−3.35244	−	23.3167i	−0.187701	−	1.30549i
$320$	−2.22667	+	0.204797i	−0.124475	+	0.0114485i
$321$			7.85208i			0.438260i
$322$	1.83548	+	7.50280i	0.102288	+	0.418115i
$323$	2.22599	−	2.22599i	0.123857	−	0.123857i
$324$	19.4088	−	30.2006i	1.07826	−	1.67781i
$325$	−14.5272	+	11.8254i	−0.805825	+	0.655958i
$326$	−6.08165	−	13.3169i	−0.336831	−	0.737557i
$327$	−34.8363	+	19.0221i	−1.92645	+	1.05192i
$328$	−2.16396	−	5.80180i	−0.119485	−	0.320351i
$329$	1.84069	−	2.12427i	0.101481	−	0.117115i
$330$	17.9793	+	31.3931i	0.989727	+	1.72813i
$331$	3.45235	−	1.01370i	0.189758	−	0.0557180i	−0.185473	−	0.982649i	$-0.559382\pi$
$331$	3.45235	−	1.01370i	0.189758	−	0.0557180i	0.375231	+	0.926931i	$0.377563\pi$
$332$	2.94804	+	0.210848i	0.161795	+	0.0115718i
$333$	53.3555	+	11.6068i	2.92386	+	0.636047i
$334$	5.14287	+	8.00245i	0.281405	+	0.437875i
$335$	−10.6906	−	15.9144i	−0.584088	−	0.869498i
$336$	1.52979	+	5.21000i	0.0834571	+	0.284229i
$337$	6.49447	+	8.67560i	0.353777	+	0.472590i	0.941761	−	0.336282i	$-0.109169\pi$
$337$	6.49447	+	8.67560i	0.353777	+	0.472590i	−0.587985	+	0.808872i	$0.700079\pi$
$338$	0.0738540	+	1.03261i	0.00401713	+	0.0561668i
$339$	−17.1741	+	37.6061i	−0.932771	+	2.04248i
$340$	2.68079	−	6.20046i	0.145386	−	0.336267i
$341$	−8.44384	+	3.85617i	−0.457259	+	0.208823i
$342$	6.97938	+	5.22470i	0.377402	+	0.282519i
$343$	−3.90489	−	17.9505i	−0.210844	−	0.969235i
$344$	5.08634			0.274237
$345$	34.4207	+	11.0621i	1.85315	+	0.595565i
$346$	21.2550			1.14268
$347$	−7.16945	−	32.9574i	−0.384876	−	1.76925i	−0.607476	−	0.794338i	$-0.707818\pi$
$347$	−7.16945	−	32.9574i	−0.384876	−	1.76925i	0.222599	−	0.974910i	$-0.428546\pi$
$348$	−13.2487	−	9.91789i	−0.710208	−	0.531655i
$349$	−0.657562	+	0.300298i	−0.0351985	+	0.0160746i	−0.432936	−	0.901424i	$-0.642523\pi$
$349$	−0.657562	+	0.300298i	−0.0351985	+	0.0160746i	0.397738	+	0.917499i	$0.369795\pi$
$350$	−4.07493	+	6.94578i	−0.217814	+	0.371268i
$351$	28.1580	−	61.6574i	1.50296	−	3.29103i
$352$	0.342343	+	4.78659i	0.0182470	+	0.255126i
$353$	1.21824	+	1.62738i	0.0648403	+	0.0866165i	0.831789	−	0.555092i	$-0.187317\pi$
$353$	1.21824	+	1.62738i	0.0648403	+	0.0866165i	−0.766949	+	0.641708i	$0.778226\pi$
$354$	−7.81908	−	26.6293i	−0.415579	−	1.41533i
$355$	−1.12953	+	5.75265i	−0.0599492	+	0.305319i
$356$	−2.12874	−	3.31238i	−0.112823	−	0.175556i
$357$	−16.0290	−	3.48690i	−0.848345	−	0.184546i
$358$	−4.78072	−	0.341924i	−0.252669	−	0.0180712i
$359$	6.13505	−	1.80141i	0.323795	−	0.0950749i	−0.115795	−	0.993273i	$-0.536942\pi$
$359$	6.13505	−	1.80141i	0.323795	−	0.0950749i	0.439591	+	0.898198i	$0.355123\pi$
$360$	18.0537	+	4.90495i	0.951515	+	0.258514i
$361$	11.7313	−	13.5386i	0.617435	−	0.712558i
$362$	8.13476	+	21.8101i	0.427553	+	1.14631i
$363$	35.5931	−	19.4353i	1.86815	−	1.02009i
$364$	2.50653	+	5.48854i	0.131378	+	0.287678i
$365$	0.0125023	+	0.615288i	0.000654398	+	0.0322057i
$366$	−11.4384	+	17.7986i	−0.597897	+	0.930346i
$367$	3.75744	−	3.75744i	0.196137	−	0.196137i	−0.602205	−	0.798342i	$-0.705711\pi$
$367$	3.75744	−	3.75744i	0.196137	−	0.196137i	0.798342	+	0.602205i	$0.205711\pi$
$368$	3.47728	+	3.30280i	0.181266	+	0.172171i
$369$			51.8075i			2.69699i
$370$	1.33658	+	14.5321i	0.0694856	+	0.755488i
$371$	1.16845	+	8.12672i	0.0606627	+	0.421918i
$372$	−2.27907	+	6.11042i	−0.118164	+	0.316810i
$373$	−10.2856	−	18.8367i	−0.532568	−	0.975326i	−0.996014	−	0.0892008i	$-0.971569\pi$
$373$	−10.2856	−	18.8367i	−0.532568	−	0.975326i	0.463445	−	0.886126i	$-0.346613\pi$
$374$	−13.1871	−	6.02237i	−0.681891	−	0.311409i
$375$	17.7180	+	33.2700i	0.914953	+	1.71805i
$376$	0.248371	−	1.72746i	0.0128088	−	0.0890870i
$377$	−16.1407	−	8.81349i	−0.831289	−	0.453918i
$378$	2.07883	−	29.0659i	0.106924	−	1.49499i
$379$	−26.1992	+	16.8372i	−1.34576	+	0.864869i	−0.997370	−	0.0724790i	$-0.976909\pi$
$379$	−26.1992	+	16.8372i	−1.34576	+	0.864869i	−0.348393	+	0.937348i	$0.613273\pi$
$380$	−0.769762	+	2.19926i	−0.0394879	+	0.112820i
$381$	−27.5903	−	31.8409i	−1.41349	−	1.63126i
$382$	−5.20803	+	9.53780i	−0.266466	+	0.487996i
$383$	−26.2327	+	19.6375i	−1.34043	+	1.00343i	−0.342471	+	0.939528i	$0.611264\pi$
$383$	−26.2327	+	19.6375i	−1.34043	+	1.00343i	−0.997956	+	0.0639030i	$0.979645\pi$
$384$	2.54796	+	2.20782i	0.130025	+	0.112667i
$385$	14.7256	+	9.04620i	0.750484	+	0.461037i
$386$	−14.6570	−	4.30370i	−0.746024	−	0.219052i
$387$	−39.8720	−	14.8715i	−2.02681	−	0.755961i
$388$	3.93033	−	5.25031i	0.199532	−	0.266544i
$389$	17.1761	+	11.0384i	0.870863	+	0.559669i	0.898016	−	0.439962i	$-0.145008\pi$
$389$	17.1761	+	11.0384i	0.870863	+	0.559669i	−0.0271539	+	0.999631i	$0.508644\pi$
$390$	28.0313	+	3.45064i	1.41942	+	0.174730i
$391$	−13.7917	+	4.43807i	−0.697478	+	0.224443i
$392$	−3.11554	−	3.11554i	−0.157359	−	0.157359i
$393$	−22.7198	+	4.94239i	−1.14606	+	0.249310i
$394$	4.72009	−	0.678646i	0.237795	−	0.0341897i
$395$	−9.80895	+	18.8651i	−0.493542	+	0.949204i
$396$	11.3114	−	38.5232i	0.568421	−	1.93586i
$397$	−12.2065	+	4.55279i	−0.612627	+	0.228498i	−0.636574	−	0.771215i	$-0.719649\pi$
$397$	−12.2065	+	4.55279i	−0.612627	+	0.228498i	0.0239477	+	0.999713i	$0.492376\pi$
$398$	10.0659	−	0.719930i	0.504560	−	0.0360868i
$399$	5.60066	+	0.805253i	0.280384	+	0.0403131i
$400$	0.203110	+	4.99587i	0.0101555	+	0.249794i
$401$	6.40698	−	5.55168i	0.319949	−	0.277238i	−0.480047	−	0.877243i	$-0.659380\pi$
$401$	6.40698	−	5.55168i	0.319949	−	0.277238i	0.799996	+	0.600005i	$0.204835\pi$
$402$	−6.14447	+	28.2457i	−0.306458	+	1.40877i
$403$	−1.54043	+	7.08126i	−0.0767344	+	0.352742i
$404$	−9.57864	+	8.29994i	−0.476555	+	0.412938i
$405$	−65.2265	−	46.7909i	−3.24113	−	2.32506i
$406$	−7.82555	−	1.12514i	−0.388376	−	0.0558400i
$407$	31.2391	−	2.23426i	1.54846	−	0.110748i
$408$	−9.54293	+	3.55933i	−0.472446	+	0.176213i
$409$	4.19886	−	14.3000i	0.207620	−	0.707090i	−0.788172	−	0.615455i	$-0.788972\pi$
$409$	4.19886	−	14.3000i	0.207620	−	0.707090i	0.995793	−	0.0916356i	$-0.0292095\pi$
$410$	−13.2034	+	4.17002i	−0.652067	+	0.205943i
$411$	−51.4727	+	7.40066i	−2.53896	+	0.365047i
$412$	5.42518	−	1.18018i	0.267279	−	0.0581431i
$413$	−9.37498	−	9.37498i	−0.461313	−	0.461313i
$414$	−17.6018	−	36.0577i	−0.865080	−	1.77214i
$415$	0.807451	−	6.55935i	0.0396362	−	0.321986i
$416$	3.15164	+	2.02544i	0.154522	+	0.0993053i
$417$	−31.4964	+	42.0743i	−1.54239	+	2.06039i
$418$	4.68529	+	1.74752i	0.229165	+	0.0854742i
$419$	2.82030	+	0.828115i	0.137781	+	0.0404561i	0.349896	−	0.936789i	$-0.386217\pi$
$419$	2.82030	+	0.828115i	0.137781	+	0.0404561i	−0.212115	+	0.977245i	$0.568035\pi$
$420$	11.8094	−	2.82140i	0.576239	−	0.137670i
$421$	−4.54989	−	3.94250i	−0.221748	−	0.192146i	0.536901	−	0.843645i	$-0.319595\pi$
$421$	−4.54989	−	3.94250i	−0.221748	−	0.192146i	−0.758649	+	0.651499i	$0.774140\pi$
$422$	12.4386	−	9.31146i	0.605504	−	0.453275i
$423$	−6.99776	+	12.8154i	−0.340243	+	0.623108i
$424$	3.33830	+	3.85261i	0.162122	+	0.187099i
$425$	−13.5405	−	6.69455i	−0.656810	−	0.324733i
$426$	7.43598	−	4.77882i	0.360275	−	0.231534i
$427$	−0.721030	+	10.0813i	−0.0348931	+	0.487869i
$428$	2.04412	+	1.11617i	0.0988062	+	0.0539522i
$429$	8.62598	−	59.9950i	0.416466	−	2.89659i
$430$	0.580738	−	11.3586i	0.0280057	−	0.547759i
$431$	23.7645	+	10.8529i	1.14470	+	0.522765i	0.895224	−	0.445617i	$-0.147016\pi$
$431$	23.7645	+	10.8529i	1.14470	+	0.522765i	0.249472	+	0.968382i	$0.419743\pi$
$432$	−8.67103	−	15.8798i	−0.417185	−	0.764018i
$433$	12.2174	−	32.7560i	0.587129	−	1.57415i	−0.214751	−	0.976669i	$-0.568894\pi$
$433$	12.2174	−	32.7560i	0.587129	−	1.57415i	0.801880	−	0.597485i	$-0.203833\pi$
$434$	0.443376	+	3.08375i	0.0212827	+	0.148025i
$435$	−23.6608	+	28.4541i	−1.13445	+	1.36427i
$436$			11.7729i			0.563818i
$437$	4.63591	−	1.86632i	0.221765	−	0.0892780i
$438$	0.656119	−	0.656119i	0.0313506	−	0.0313506i
$439$	4.50680	−	7.01272i	0.215098	−	0.334699i	−0.716891	−	0.697185i	$-0.754436\pi$
$439$	4.50680	−	7.01272i	0.215098	−	0.334699i	0.931989	+	0.362486i	$0.118072\pi$
$440$	10.7283	−	0.217991i	0.511450	−	0.0103923i
$441$	15.3136	+	33.5321i	0.729219	+	1.59677i
$442$	−9.93338	+	5.42404i	−0.472483	+	0.257995i
$443$	12.7002	+	34.0505i	0.603404	+	1.61779i	0.774528	+	0.632540i	$0.217987\pi$
$443$	12.7002	+	34.0505i	0.603404	+	1.61779i	−0.171124	+	0.985250i	$0.554740\pi$
$444$	14.4091	−	16.6290i	0.683824	−	0.789175i
$445$	−7.64010	+	4.37560i	−0.362175	+	0.207423i
$446$	−1.03658	+	0.304369i	−0.0490837	+	0.0144123i
$447$	37.2966	+	2.66751i	1.76407	+	0.126169i
$448$	1.57377	+	0.342353i	0.0743536	+	0.0161746i
$449$	−17.8186	−	27.7263i	−0.840911	−	1.30848i	−0.949299	−	0.314375i	$-0.898205\pi$
$449$	−17.8186	−	27.7263i	−0.840911	−	1.30848i	0.108387	−	0.994109i	$-0.465431\pi$
$450$	13.0148	−	39.7567i	0.613524	−	1.87415i
$451$	8.37176	+	28.5116i	0.394211	+	1.34256i
$452$	7.34863	+	9.81662i	0.345650	+	0.461735i
$453$	3.97860	+	55.6281i	0.186931	+	2.61363i
$454$	−0.872523	+	1.91056i	−0.0409496	+	0.0896670i
$455$	12.5429	−	4.97081i	0.588022	−	0.233035i
$456$	3.19571	−	1.45943i	0.149653	−	0.0683441i
$457$	2.85193	+	2.13493i	0.133408	+	0.0998677i	0.663898	−	0.747824i	$-0.268901\pi$
$457$	2.85193	+	2.13493i	0.133408	+	0.0998677i	−0.530490	+	0.847691i	$0.677992\pi$
$458$	0.403978	+	1.85706i	0.0188767	+	0.0867746i
$459$	54.6589			2.55126
$460$	7.77268	−	7.38819i	0.362403	−	0.344476i
$461$	12.0071			0.559224			0.279612	−	0.960113i	$-0.409794\pi$
$461$	12.0071			0.559224			0.279612	+	0.960113i	$0.409794\pi$
$462$	−5.53888	−	25.4618i	−0.257692	−	1.18459i
$463$	18.5551	+	13.8901i	0.862327	+	0.645530i	0.936096	−	0.351745i	$-0.114412\pi$
$463$	18.5551	+	13.8901i	0.862327	+	0.645530i	−0.0737687	+	0.997275i	$0.523503\pi$
$464$	−4.46522	+	2.03920i	−0.207292	+	0.0946673i
$465$	13.3853	+	5.78717i	0.620727	+	0.268373i
$466$	0.581305	−	1.27288i	0.0269284	−	0.0589651i
$467$	−0.326909	−	4.57078i	−0.0151275	−	0.211511i	−0.999394	−	0.0348182i	$-0.988915\pi$
$467$	−0.326909	−	4.57078i	−0.0151275	−	0.211511i	0.984266	−	0.176692i	$-0.0565398\pi$
$468$	−18.7839	−	25.0923i	−0.868284	−	1.15989i
$469$	3.89041	+	13.2495i	0.179643	+	0.611807i
$470$	−3.82932	−	0.751886i	−0.176634	−	0.0346819i
$471$	−2.06309	−	3.21023i	−0.0950622	−	0.147920i
$472$	−8.04385	−	1.74983i	−0.370248	−	0.0805426i
$473$	−24.3462	−	1.74128i	−1.11944	−	0.0800639i
$474$	30.7604	−	9.03205i	1.41287	−	0.414856i
$475$	4.82340	+	1.97010i	0.221313	+	0.0903943i
$476$	−3.18626	+	3.67714i	−0.146042	+	0.168542i
$477$	−14.9048	−	39.9613i	−0.682444	−	1.82970i
$478$	18.0844	−	9.87485i	0.827163	−	0.451665i
$479$	4.80171	+	10.5143i	0.219396	+	0.480410i	0.987042	−	0.160465i	$-0.0512992\pi$
$479$	4.80171	+	10.5143i	0.219396	+	0.480410i	−0.767646	+	0.640874i	$0.778572\pi$
$480$	5.22131	−	5.43790i	0.238319	−	0.248205i
$481$	13.2188	−	20.5688i	0.602725	−	0.937858i
$482$	8.14303	−	8.14303i	0.370905	−	0.370905i
$483$	−21.2416	−	15.0644i	−0.966524	−	0.685454i
$484$		−	12.0286i		−	0.546755i
$485$	−11.2760	−	9.37649i	−0.512016	−	0.425764i
$486$	9.50007	+	66.0745i	0.430932	+	2.99720i
$487$	14.5432	−	38.9920i	0.659018	−	1.76689i	0.0174257	−	0.999848i	$-0.494453\pi$
$487$	14.5432	−	38.9920i	0.659018	−	1.76689i	0.641592	−	0.767046i	$-0.278274\pi$
$488$	3.00750	+	5.50782i	0.136143	+	0.249327i
$489$	44.8972	+	20.5039i	2.03032	+	0.927216i
$490$	−7.31320	+	6.60176i	−0.330377	+	0.298237i
$491$	−5.74739	+	39.9740i	−0.259376	+	1.80400i	0.277918	+	0.960605i	$0.410356\pi$
$491$	−5.74739	+	39.9740i	−0.259376	+	1.80400i	−0.537294	+	0.843395i	$0.680554\pi$
$492$	18.3230	+	10.0051i	0.826064	+	0.451065i
$493$	1.05793	−	14.7918i	0.0476467	−	0.666188i
$494$	3.28416	−	2.11060i	0.147761	−	0.0949603i
$495$	−84.7366	−	29.6585i	−3.80863	−	1.33305i
$496$	1.26675	+	1.46190i	0.0568785	+	0.0656413i
$497$	2.02367	−	3.70608i	0.0907740	−	0.166240i
$498$	−7.97700	+	5.97151i	−0.357458	+	0.267590i
$499$	−10.7412	−	9.30729i	−0.480842	−	0.416652i	0.380420	−	0.924814i	$-0.375780\pi$
$499$	−10.7412	−	9.30729i	−0.480842	−	0.416652i	−0.861261	+	0.508162i	$0.830325\pi$
$500$	11.1797	+	0.116834i	0.499973	+	0.00522499i
$501$	−30.7718	−	9.03541i	−1.37478	−	0.403672i
$502$	−5.74169	−	2.14154i	−0.256264	−	0.0955817i
$503$	2.96301	−	3.95812i	0.132114	−	0.176484i	−0.729606	−	0.683868i	$-0.760297\pi$
$503$	2.96301	−	3.95812i	0.132114	−	0.176484i	0.861720	+	0.507384i	$0.169387\pi$
$504$	−11.3359	−	7.28512i	−0.504940	−	0.324505i
$505$	17.4414	+	22.3382i	0.776131	+	0.994037i
$506$	−15.5136	−	16.9996i	−0.689664	−	0.755724i
$507$	−2.46800	−	2.46800i	−0.109608	−	0.109608i
$508$	−12.2110	+	2.65635i	−0.541777	+	0.117856i
$509$	19.2081	−	2.76171i	0.851384	−	0.122411i	0.297211	−	0.954812i	$-0.403944\pi$
$509$	19.2081	−	2.76171i	0.851384	−	0.122411i	0.554173	+	0.832401i	$0.313035\pi$
$510$	6.85895	+	21.7172i	0.303719	+	0.961654i
$511$	0.124883	−	0.425311i	0.00552448	−	0.0188146i
$512$	0.936950	−	0.349464i	0.0414077	−	0.0154443i
$513$	−18.8057	+	1.34501i	−0.830290	+	0.0593835i
$514$	−26.6549	−	3.83240i	−1.17570	−	0.169040i
$515$	−2.01609	−	12.2500i	−0.0888393	−	0.539799i
$516$	−12.9598	+	11.2297i	−0.570523	+	0.494361i
$517$	−1.78024	+	8.18362i	−0.0782947	+	0.359915i
$518$	2.23432	−	10.2710i	0.0981706	−	0.451283i
$519$	−54.1570	+	46.9273i	−2.37723	+	2.05988i
$520$	4.88295	−	6.80684i	0.214132	−	0.298500i
$521$	−38.7729	−	5.57471i	−1.69867	−	0.244232i	−0.776253	−	0.630421i	$-0.782882\pi$
$521$	−38.7729	−	5.57471i	−1.69867	−	0.244232i	−0.922420	+	0.386189i	$0.873791\pi$
$522$	40.9652	−	2.92989i	1.79300	−	0.128238i
$523$	−24.7746	+	9.24043i	−1.08332	+	0.404056i	−0.826807	−	0.562486i	$-0.809845\pi$
$523$	−24.7746	+	9.24043i	−1.08332	+	0.404056i	−0.256509	+	0.966542i	$0.582572\pi$
$524$	−1.94297	+	6.61716i	−0.0848792	+	0.289072i
$525$	−4.95227	−	26.6943i	−0.216135	−	1.16503i
$526$	−12.3617	+	1.77735i	−0.538996	+	0.0774960i
$527$	−5.71020	+	1.24218i	−0.248740	+	0.0541101i
$528$	−11.4402	−	11.4402i	−0.497870	−	0.497870i
$529$	−22.9041	−	2.09798i	−0.995831	−	0.0912165i
$530$	8.98461	−	7.01506i	0.390266	−	0.304715i
$531$	57.9399	+	37.2357i	2.51438	+	1.61589i
$532$	1.00576	−	1.34354i	0.0436054	−	0.0582500i
$533$	21.7356	+	8.10698i	0.941475	+	0.351152i
$534$	12.7371	+	3.73994i	0.551187	+	0.161843i
$535$	2.72597	−	4.43738i	0.117854	−	0.191845i
$536$	6.47971	+	5.61470i	0.279881	+	0.242518i
$537$	12.9360	−	9.68374i	0.558228	−	0.417884i
$538$	12.9088	−	23.6407i	0.556537	−	1.01922i
$539$	13.8462	+	15.9794i	0.596399	+	0.688282i
$540$	−36.4520	+	17.5506i	−1.56865	+	0.755259i
$541$	18.5364	−	11.9126i	0.796944	−	0.512165i	−0.0776734	−	0.996979i	$-0.524749\pi$
$541$	18.5364	−	11.9126i	0.796944	−	0.512165i	0.874617	+	0.484814i	$0.161113\pi$
$542$	0.317916	−	4.44505i	0.0136557	−	0.190931i
$543$	−68.8798	−	37.6112i	−2.95592	−	1.61405i
$544$	−0.429934	+	2.99025i	−0.0184333	+	0.128206i
$545$	26.2906	+	1.34418i	1.12616	+	0.0575783i
$546$	−18.5043	−	8.45061i	−0.791909	−	0.361653i
$547$	3.88815	+	7.12062i	0.166245	+	0.304456i	0.947499	−	0.319758i	$-0.103601\pi$
$547$	3.88815	+	7.12062i	0.166245	+	0.304456i	−0.781254	+	0.624213i	$0.785420\pi$
$548$	−5.39024	+	14.4518i	−0.230260	+	0.617350i
$549$	−7.47206	−	51.9694i	−0.318900	−	2.21800i
$550$	0.738102	−	23.9827i	0.0314728	−	1.02263i
$551$			5.11521i			0.217915i
$552$	−16.1520	−	0.738201i	−0.687473	−	0.0314199i
$553$	10.8293	−	10.8293i	0.460510	−	0.460510i
$554$	−5.46760	+	8.50775i	−0.232296	+	0.361460i
$555$	−35.4898	−	34.0763i	−1.50646	−	1.44646i
$556$	6.47591	+	14.1803i	0.274640	+	0.601377i
$557$	−0.00985060	+	0.00537883i	−0.000417383	+	0.000227908i	−0.479458	−	0.877565i	$-0.659167\pi$
$557$	−0.00985060	+	0.00537883i	−0.000417383	+	0.000227908i	0.479040	+	0.877793i	$0.340985\pi$
$558$	−5.65574	−	15.1636i	−0.239427	−	0.641928i
$559$	−12.4786	+	14.4010i	−0.527787	+	0.609099i
$560$	0.944212	−	3.47538i	0.0399002	−	0.146861i
$561$	46.8966	−	13.7701i	1.97998	−	0.581373i
$562$	−29.6684	−	2.12192i	−1.25148	−	0.0895079i
$563$	33.6571	+	7.32165i	1.41848	+	0.308571i	0.855457	−	0.517873i	$-0.173276\pi$
$563$	33.6571	+	7.32165i	1.41848	+	0.308571i	0.563019	+	0.826444i	$0.309640\pi$
$564$	3.18108	+	4.94986i	0.133948	+	0.208427i
$565$	22.7610	−	15.2898i	0.957564	−	0.643246i
$566$	8.68361	+	29.5737i	0.364999	+	1.24307i
$567$	34.6496	+	46.2864i	1.45515	+	1.94385i
$568$	−0.187036	−	2.61511i	−0.00784786	−	0.109727i
$569$	−5.73880	+	12.5662i	−0.240583	+	0.526803i	−0.990952	−	0.134216i	$-0.957148\pi$
$569$	−5.73880	+	12.5662i	−0.240583	+	0.526803i	0.750369	+	0.661019i	$0.229876\pi$
$570$	−2.89425	−	7.30313i	−0.121227	−	0.305894i
$571$	36.7892	−	16.8011i	1.53958	−	0.703103i	0.548473	−	0.836168i	$-0.315209\pi$
$571$	36.7892	−	16.8011i	1.53958	−	0.703103i	0.991107	+	0.133066i	$0.0424821\pi$
$572$	−14.3922	−	10.7739i	−0.601769	−	0.450478i
$573$	−7.78788	−	35.8003i	−0.325343	−	1.49558i
$574$	9.97304			0.416267
$575$	−15.6115	−	18.2011i	−0.651045	−	0.759040i
$576$	−8.36655			−0.348606
$577$	−6.38013	−	29.3290i	−0.265608	−	1.22098i	−0.895770	−	0.444518i	$-0.853375\pi$
$577$	−6.38013	−	29.3290i	−0.265608	−	1.22098i	0.630162	−	0.776464i	$-0.282989\pi$
$578$	6.30309	+	4.71843i	0.262174	+	0.196261i
$579$	46.8473	−	21.3945i	1.94691	−	0.889123i
$580$	4.04401	+	10.2043i	0.167918	+	0.423712i
$581$	−1.97745	+	4.33000i	−0.0820383	+	0.179639i
$582$	1.57741	+	22.0550i	0.0653856	+	0.914210i
$583$	−14.6602	−	19.5837i	−0.607162	−	0.811073i
$584$	−0.0775390	−	0.264074i	−0.00320859	−	0.0109274i
$585$	−58.1795	+	39.0822i	−2.40543	+	1.61585i
$586$	−0.0355791	−	0.0553622i	−0.00146976	−	0.00228699i
$587$	6.10126	+	1.32725i	0.251826	+	0.0547814i	0.336706	−	0.941610i	$-0.390687\pi$
$587$	6.10126	+	1.32725i	0.251826	+	0.0547814i	−0.0848801	+	0.996391i	$0.527051\pi$
$588$	14.8168	+	1.05972i	0.611036	+	0.0437021i
$589$	1.93405	−	0.567890i	0.0796913	−	0.0233995i
$590$	−4.82606	+	17.7633i	−0.198686	+	0.731305i
$591$	−10.5283	+	12.1503i	−0.433075	+	0.499795i
$592$	−2.28074	−	6.11489i	−0.0937377	−	0.251321i
$593$	−2.98410	+	1.62944i	−0.122542	+	0.0669131i	−0.539351	−	0.842081i	$-0.681330\pi$
$593$	−2.98410	+	1.62944i	−0.122542	+	0.0669131i	0.416809	+	0.908994i	$0.363149\pi$
$594$	36.0683	+	78.9786i	1.47990	+	3.24053i
$595$	7.84782	+	7.53525i	0.321729	+	0.308915i
$596$	5.99614	−	9.33018i	0.245612	−	0.382179i
$597$	−24.0581	+	24.0581i	−0.984633	+	0.984633i
$598$	−17.8823	+	1.74235i	−0.731260	+	0.0712499i
$599$			9.69171i			0.395993i	0.980203	+	0.197996i	$0.0634434\pi$
$599$			9.69171i			0.395993i	−0.980203	+	0.197996i	$0.936557\pi$
$600$	−11.5475	−	12.2808i	−0.471424	−	0.501363i
$601$	−4.97998	−	34.6365i	−0.203138	−	1.41285i	−0.794900	−	0.606741i	$-0.792477\pi$
$601$	−4.97998	−	34.6365i	−0.203138	−	1.41285i	0.591762	−	0.806113i	$-0.298432\pi$
$602$	−2.86279	+	7.67544i	−0.116679	+	0.312827i
$603$	−34.3784	−	62.9593i	−1.40000	−	2.56390i
$604$	15.0471	+	6.87179i	0.612258	+	0.279609i
$605$	−26.8617	−	1.37338i	−1.09208	−	0.0558358i
$606$	6.08122	−	42.2958i	0.247033	−	1.71815i
$607$	−6.14476	−	3.35529i	−0.249408	−	0.136187i	0.349683	−	0.936868i	$-0.386289\pi$
$607$	−6.14476	−	3.35529i	−0.249408	−	0.136187i	−0.599091	+	0.800681i	$0.704471\pi$
$608$	0.0743387	−	1.03939i	0.00301483	−	0.0421529i
$609$	22.4233	−	14.4106i	0.908638	−	0.583946i
$610$	12.6432	−	6.08733i	0.511907	−	0.246469i
$611$	4.28164	+	4.94128i	0.173217	+	0.199903i
$612$	12.1132	−	22.1837i	0.489647	−	0.896722i
$613$	−3.07265	+	2.30016i	−0.124103	+	0.0929025i	−0.659526	−	0.751682i	$-0.729243\pi$
$613$	−3.07265	+	2.30016i	−0.124103	+	0.0929025i	0.535423	+	0.844584i	$0.320152\pi$
$614$	−4.71977	−	4.08970i	−0.190474	−	0.165047i
$615$	24.4350	−	39.7756i	0.985313	−	1.60391i
$616$	−7.41578	−	2.17747i	−0.298790	−	0.0877328i
$617$	−6.43481	−	2.40006i	−0.259056	−	0.0966228i	0.216581	−	0.976265i	$-0.430510\pi$
$617$	−6.43481	−	2.40006i	−0.259056	−	0.0966228i	−0.475637	+	0.879642i	$0.657782\pi$
$618$	−11.2175	+	14.9849i	−0.451235	+	0.602779i
$619$	7.21076	+	4.63407i	0.289825	+	0.186259i	0.677472	−	0.735549i	$-0.263076\pi$
$619$	7.21076	+	4.63407i	0.289825	+	0.186259i	−0.387647	+	0.921808i	$0.626712\pi$
$620$	3.40928	−	2.66192i	0.136920	−	0.106905i
$621$	79.8307	+	34.0035i	3.20349	+	1.36451i
$622$	−13.2785	−	13.2785i	−0.532420	−	0.532420i
$623$	6.19662	−	1.34799i	0.248262	−	0.0540061i
$624$	−12.5021	+	1.79752i	−0.500483	+	0.0719585i
$625$	1.53737	−	24.9527i	0.0614946	−	0.998107i
$626$	−6.50009	+	22.1373i	−0.259796	+	0.884783i
$627$	−15.7961	+	5.89166i	−0.630837	+	0.235290i
$628$	−1.12898	+	0.0807464i	−0.0450513	+	0.00322213i
$629$	19.5155	+	2.80591i	0.778136	+	0.111879i
$630$	−17.5631	+	24.4829i	−0.699729	+	0.975423i
$631$	9.20398	−	7.97529i	0.366405	−	0.317491i	−0.452126	−	0.891954i	$-0.649334\pi$
$631$	9.20398	−	7.97529i	0.366405	−	0.317491i	0.818531	+	0.574463i	$0.194789\pi$
$632$	2.02128	−	9.29170i	0.0804024	−	0.369604i
$633$	−11.1352	+	51.1875i	−0.442583	+	2.03452i
$634$	−18.1605	+	15.7361i	−0.721244	+	0.624961i
$635$	4.53782	+	27.5724i	0.180078	+	1.09418i
$636$	−17.0117	−	2.44592i	−0.674558	−	0.0969869i
$637$	16.4646	−	1.17757i	0.652351	−	0.0466571i
$638$	22.0713	−	8.23215i	0.873809	−	0.325914i
$639$	−6.17989	+	21.0468i	−0.244473	+	0.832597i
$640$	−0.673429	−	2.13225i	−0.0266196	−	0.0842846i
$641$	−21.8939	+	3.14786i	−0.864756	+	0.124333i	−0.560397	−	0.828224i	$-0.689351\pi$
$641$	−21.8939	+	3.14786i	−0.864756	+	0.124333i	−0.304359	+	0.952557i	$0.598442\pi$
$642$	−7.67263	+	1.66908i	−0.302815	+	0.0658733i
$643$	−7.78056	−	7.78056i	−0.306835	−	0.306835i	0.536845	−	0.843681i	$-0.319616\pi$
$643$	−7.78056	−	7.78056i	−0.306835	−	0.306835i	−0.843681	+	0.536845i	$0.819616\pi$
$644$	−6.94118	+	3.38837i	−0.273521	+	0.133521i
$645$	23.5980	+	30.2233i	0.929169	+	1.19004i
$646$	2.64829	+	1.70195i	0.104195	+	0.0669623i
$647$	4.02276	−	5.37378i	0.158151	−	0.211265i	−0.714466	−	0.699670i	$-0.753330\pi$
$647$	4.02276	−	5.37378i	0.158151	−	0.211265i	0.872617	+	0.488405i	$0.162421\pi$
$648$	33.6361	+	12.5456i	1.32135	+	0.492838i
$649$	37.9035	+	11.1295i	1.48784	+	0.436871i
$650$	−14.6432	−	11.6815i	−0.574353	−	0.458188i
$651$	−7.93805	−	6.87836i	−0.311117	−	0.269584i
$652$	11.7199	−	8.77338i	0.458985	−	0.343592i
$653$	−1.85067	+	3.38925i	−0.0724223	+	0.132631i	−0.911381	−	0.411563i	$-0.864983\pi$
$653$	−1.85067	+	3.38925i	−0.0724223	+	0.132631i	0.838959	+	0.544195i	$0.183165\pi$
$654$	−25.9923	−	29.9967i	−1.01638	−	1.17297i
$655$	14.5553	+	5.09447i	0.568722	+	0.199058i
$656$	5.20922	−	3.34776i	0.203386	−	0.130708i
$657$	−0.164270	+	2.29679i	−0.00640878	+	0.0896064i
$658$	2.46700	+	1.34708i	0.0961735	+	0.0525147i
$659$	−6.93213	+	48.2140i	−0.270038	+	1.87815i	0.177843	+	0.984059i	$0.443088\pi$
$659$	−6.93213	+	48.2140i	−0.270038	+	1.87815i	−0.447880	+	0.894094i	$0.647821\pi$
$660$	−26.8539	+	24.2415i	−1.04529	+	0.943598i
$661$	13.0297	+	5.95046i	0.506797	+	0.231446i	0.652369	−	0.757901i	$-0.273775\pi$
$661$	13.0297	+	5.95046i	0.506797	+	0.231446i	−0.145573	+	0.989348i	$0.546502\pi$
$662$	1.72438	+	3.15797i	0.0670201	+	0.122738i
$663$	13.3346	−	35.7513i	0.517871	−	1.38847i
$664$	0.420622	+	2.92549i	0.0163233	+	0.113531i
$665$	−2.88550	−	2.39942i	−0.111895	−	0.0930457i
$666$			54.6033i			2.11584i
$667$	10.7471	−	20.9456i	0.416131	−	0.811017i
$668$	−6.72638	+	6.72638i	−0.260251	+	0.260251i
$669$	1.96918	−	3.06411i	0.0761330	−	0.118465i
$670$	13.2783	−	13.8291i	0.512985	−	0.534265i
$671$	−12.5101	−	27.3932i	−0.482946	−	1.05750i
$672$	−4.76575	+	2.60230i	−0.183843	+	0.100386i
$673$	12.0639	+	32.3446i	0.465030	+	1.24679i	0.931980	+	0.362510i	$0.118080\pi$
$673$	12.0639	+	32.3446i	0.465030	+	1.24679i	−0.466950	+	0.884284i	$0.654647\pi$
$674$	−7.09684	+	8.19019i	−0.273360	+	0.315474i
$675$	35.0313	+	83.4068i	1.34835	+	3.21033i
$676$	−0.993316	+	0.291664i	−0.0382045	+	0.0112178i
$677$	27.1810	+	1.94403i	1.04465	+	0.0747150i	0.583102	−	0.812399i	$-0.301839\pi$
$677$	27.1810	+	1.94403i	1.04465	+	0.0747150i	0.461550	+	0.887114i	$0.347293\pi$
$678$	−40.3973	−	8.78790i	−1.55145	−	0.337497i
$679$	5.71073	+	8.88606i	0.219158	+	0.341016i
$680$	6.62860	+	1.30152i	0.254195	+	0.0499111i
$681$	−1.99502	−	6.79440i	−0.0764492	−	0.260362i
$682$	−5.56291	−	7.43118i	−0.213015	−	0.284555i
$683$	−2.46028	−	34.3993i	−0.0941402	−	1.31625i	−0.796591	−	0.604519i	$-0.793365\pi$
$683$	−2.46028	−	34.3993i	−0.0941402	−	1.31625i	0.702451	−	0.711733i	$-0.252089\pi$
$684$	−3.62172	+	7.93047i	−0.138480	+	0.303229i
$685$	31.6576	+	13.6873i	1.20958	+	0.522964i
$686$	16.7102	−	7.63130i	0.637999	−	0.291364i
$687$	−5.12937	−	3.83979i	−0.195697	−	0.146497i
$688$	1.08118	+	4.97010i	0.0412196	+	0.189483i
$689$	−19.0980			−0.727574
$690$	−3.49268	+	35.9855i	−0.132964	+	1.36994i
$691$	−19.5208			−0.742608			−0.371304	−	0.928511i	$-0.621089\pi$
$691$	−19.5208			−0.742608			−0.371304	+	0.928511i	$0.621089\pi$
$692$	4.51808	+	20.7693i	0.171752	+	0.789530i
$693$	51.7661	+	38.7516i	1.96643	+	1.47205i
$694$	30.6803	−	14.0112i	1.16461	−	0.531859i
$695$	32.4061	−	12.8426i	1.22923	−	0.487149i
$696$	6.87501	−	15.0542i	0.260597	−	0.570627i
$697$	1.33452	+	18.6590i	0.0505486	+	0.706762i
$698$	−0.433210	−	0.578701i	−0.0163973	−	0.0219042i
$699$	1.32915	+	4.52666i	0.0502730	+	0.171214i
$700$	−7.65324	−	2.50537i	−0.289265	−	0.0946942i
$701$	−20.9034	−	32.5263i	−0.789511	−	1.22850i	−0.969562	−	0.244846i	$-0.921263\pi$
$701$	−20.9034	−	32.5263i	−0.789511	−	1.22850i	0.180051	−	0.983657i	$-0.442374\pi$
$702$	66.2338	+	14.4083i	2.49983	+	0.543805i
$703$	−6.78346	−	0.485163i	−0.255843	−	0.0182983i
$704$	−4.60443	+	1.35198i	−0.173536	+	0.0509547i
$705$	11.4170	−	6.53868i	0.429989	−	0.246261i
$706$	−1.33123	+	1.53632i	−0.0501015	+	0.0578202i
$707$	−7.13362	−	19.1260i	−0.268287	−	0.719306i
$708$	24.3587	−	13.3009i	0.915456	−	0.499877i
$709$	4.80799	+	10.5280i	0.180568	+	0.395388i	0.978173	−	0.207791i	$-0.0666275\pi$
$709$	4.80799	+	10.5280i	0.180568	+	0.395388i	−0.797605	+	0.603180i	$0.793900\pi$
$710$	−5.86128	+	0.119097i	−0.219970	+	0.00446965i
$711$	−43.0121	+	66.9281i	−1.61308	+	2.51000i
$712$	2.78419	−	2.78419i	0.104342	−	0.104342i
$713$	−9.11265	−	1.73810i	−0.341271	−	0.0650925i
$714$		−	16.4039i		−	0.613900i
$715$	−25.7029	+	30.9099i	−0.961236	+	1.15596i
$716$	−0.682105	−	4.74414i	−0.0254914	−	0.177297i
$717$	−24.2765	+	65.0879i	−0.906623	+	2.43075i
$718$	3.06434	+	5.61192i	0.114360	+	0.209435i
$719$	2.15282	+	0.983161i	0.0802867	+	0.0366657i	0.455154	−	0.890413i	$-0.349584\pi$
$719$	2.15282	+	0.983161i	0.0802867	+	0.0366657i	−0.374867	+	0.927079i	$0.622312\pi$
$720$	−0.955260	+	18.6838i	−0.0356004	+	0.696303i
$721$	−1.27258	+	8.85100i	−0.0473934	+	0.329629i
$722$	15.7229	+	8.58533i	0.585144	+	0.319513i
$723$	−2.76977	+	38.7264i	−0.103009	+	1.44025i
$724$	−19.5825	+	12.5849i	−0.727779	+	0.467715i
$725$	23.2495	−	7.86580i	0.863466	−	0.292129i
$726$	26.5570	+	30.6484i	0.985622	+	1.13747i
$727$	0.190144	−	0.348223i	0.00705206	−	0.0129149i	−0.874129	−	0.485693i	$-0.838567\pi$
$727$	0.190144	−	0.348223i	0.00705206	−	0.0129149i	0.881181	+	0.472779i	$0.156749\pi$
$728$	−4.83031	+	3.61593i	−0.179023	+	0.134015i
$729$	−88.6930	−	76.8530i	−3.28493	−	2.84641i
$730$	−0.598570	+	0.143006i	−0.0221541	+	0.00529287i
$731$	−14.7434	−	4.32906i	−0.545306	−	0.160116i
$732$	−19.8232	−	7.39369i	−0.732688	−	0.273278i
$733$	−16.9363	+	22.6243i	−0.625557	+	0.835647i	−0.995633	−	0.0933549i	$-0.970241\pi$
$733$	−16.9363	+	22.6243i	−0.625557	+	0.835647i	0.370076	+	0.929002i	$0.379332\pi$
$734$	4.47028	+	2.87287i	0.165001	+	0.106040i
$735$	4.05824	−	32.9672i	0.149691	−	1.21601i
$736$	−2.48818	+	4.09988i	−0.0917154	+	0.151123i
$737$	−29.0935	−	29.0935i	−1.07167	−	1.07167i
$738$	−50.6235	+	11.0125i	−1.86348	+	0.405375i
$739$	16.4525	−	2.36551i	0.605214	−	0.0870166i	0.167106	−	0.985939i	$-0.446558\pi$
$739$	16.4525	−	2.36551i	0.605214	−	0.0870166i	0.438108	+	0.898922i	$0.355649\pi$
$740$	−13.9159	+	4.39506i	−0.511558	+	0.161566i
$741$	−3.70807	+	12.6285i	−0.136219	+	0.463921i
$742$	−7.69262	+	2.86920i	−0.282405	+	0.105332i
$743$	46.4452	−	3.32183i	1.70391	−	0.121866i	0.814855	−	0.579665i	$-0.196817\pi$
$743$	46.4452	−	3.32183i	1.70391	−	0.121866i	0.889056	+	0.457799i	$0.151362\pi$
$744$	−6.45523	−	0.928122i	−0.236660	−	0.0340266i
$745$	−20.1511	−	14.4556i	−0.738279	−	0.529611i
$746$	16.2198	−	14.0546i	0.593851	−	0.514574i
$747$	5.25630	−	24.1628i	0.192318	−	0.884071i
$748$	3.08161	−	14.1659i	0.112675	−	0.517958i
$749$	−2.83485	+	2.45641i	−0.103583	+	0.0897552i
$750$	−28.7434	+	24.3851i	−1.04956	+	0.890419i
$751$	−42.0589	−	6.04715i	−1.53475	−	0.220664i	−0.677484	−	0.735538i	$-0.736930\pi$
$751$	−42.0589	−	6.04715i	−1.53475	−	0.220664i	−0.857266	+	0.514874i	$0.827839\pi$
$752$	1.74078	−	0.124503i	0.0634797	−	0.00454016i
$753$	19.3577	−	7.22006i	0.705435	−	0.263114i
$754$	5.18112	−	17.6453i	0.188685	−	0.642603i
$755$	17.0638	−	32.8179i	0.621014	−	1.19437i
$756$	28.8435	−	4.14707i	1.04903	−	0.150827i
$757$	−13.4189	+	2.91909i	−0.487717	+	0.106096i	−0.449698	−	0.893181i	$-0.648468\pi$
$757$	−13.4189	+	2.91909i	−0.487717	+	0.106096i	−0.0380188	+	0.999277i	$0.512105\pi$
$758$	−22.0215	−	22.0215i	−0.799856	−	0.799856i
$759$	77.0600	+	9.06298i	2.79710	+	0.328965i
$760$	−2.31263	−	0.284683i	−0.0838879	−	0.0103265i
$761$	−26.4072	−	16.9709i	−0.957261	−	0.615194i	−0.0340225	−	0.999421i	$-0.510832\pi$
$761$	−26.4072	−	16.9709i	−0.957261	−	0.615194i	−0.923239	+	0.384227i	$0.874468\pi$
$762$	25.2485	−	33.7280i	0.914656	−	1.22184i
$763$	−17.7656	−	6.62622i	−0.643157	−	0.239885i
$764$	−10.4269	−	3.06161i	−0.377231	−	0.110765i
$765$	−48.1565	−	29.5835i	−1.74110	−	1.06959i
$766$	−24.7649	−	21.4589i	−0.894793	−	0.775342i
$767$	24.6887	−	18.4817i	0.891457	−	0.667336i
$768$	−1.61576	+	2.95903i	−0.0583035	+	0.106775i
$769$	−3.69926	−	4.26917i	−0.133399	−	0.153950i	0.685120	−	0.728430i	$-0.259750\pi$
$769$	−3.69926	−	4.26917i	−0.133399	−	0.153950i	−0.818519	+	0.574480i	$0.805204\pi$
$770$	−5.70932	+	16.3119i	−0.205750	+	0.587842i
$771$	76.3768	−	49.0844i	2.75064	−	1.76773i
$772$	1.08977	−	15.2369i	0.0392215	−	0.548388i
$773$	−18.2398	−	9.95969i	−0.656040	−	0.358225i	0.116500	−	0.993191i	$-0.462832\pi$
$773$	−18.2398	−	9.95969i	−0.656040	−	0.358225i	−0.772540	+	0.634966i	$0.781014\pi$
$774$	6.05623	−	42.1220i	0.217687	−	1.51404i
$775$	−5.55521	−	7.91736i	−0.199549	−	0.284400i
$776$	5.96578	+	2.72448i	0.214159	+	0.0978031i
$777$	16.9836	+	31.1031i	0.609283	+	1.11582i
$778$	−7.13510	+	19.1299i	−0.255806	+	0.685842i
$779$	−0.918297	−	6.38689i	−0.0329014	−	0.228834i
$780$	2.58671	+	28.1242i	0.0926190	+	1.00701i
$781$			12.5815i			0.450200i
$782$	−7.26829	−	12.5332i	−0.259914	−	0.448186i
$783$	−62.8017	+	62.8017i	−2.24435	+	2.24435i
$784$	2.38209	−	3.70660i	0.0850745	−	0.132379i
$785$	0.0514162	+	2.53041i	0.00183512	+	0.0903141i
$786$	−9.65887	−	21.1500i	−0.344521	−	0.754395i
$787$	−16.0509	+	8.76446i	−0.572153	+	0.312419i	−0.739153	−	0.673538i	$-0.764774\pi$
$787$	−16.0509	+	8.76446i	−0.572153	+	0.312419i	0.167000	+	0.985957i	$0.446592\pi$
$788$	1.66646	+	4.46796i	0.0593653	+	0.159165i
$789$	27.5731	−	31.8210i	0.981627	−	1.13286i
$790$	−20.5190	−	5.57472i	−0.730032	−	0.198340i
$791$	−18.9497	+	5.56412i	−0.673772	+	0.197837i
$792$	40.0472	+	2.86423i	1.42302	+	0.101776i
$793$	−22.9728	−	4.99743i	−0.815788	−	0.177464i
$794$	−7.04342	−	10.9598i	−0.249962	−	0.388948i
$795$	−7.40443	+	37.7105i	−0.262608	+	1.33745i
$796$	2.84315	+	9.68287i	0.100773	+	0.343200i
$797$	−30.6002	−	40.8770i	−1.08391	−	1.44794i	−0.883621	−	0.468203i	$-0.844902\pi$
$797$	−30.6002	−	40.8770i	−1.08391	−	1.44794i	−0.200293	−	0.979736i	$-0.564189\pi$
$798$	0.403655	+	5.64384i	0.0142892	+	0.199790i
$799$	−2.19021	+	4.79588i	−0.0774839	+	0.169666i
$800$	−4.83853	+	1.26042i	−0.171068	+	0.0445625i
$801$	−29.9658	+	13.6849i	−1.05879	+	0.483533i
$802$	6.78671	+	5.08047i	0.239647	+	0.179398i
$803$	0.280743	+	1.29056i	0.00990722	+	0.0455428i
$804$	−28.9063			−1.01944
$805$	6.77423	+	15.8876i	0.238760	+	0.559963i
$806$	−7.24687			−0.255260
$807$	19.3033	+	88.7357i	0.679507	+	3.12365i
$808$	−10.1463	−	7.59546i	−0.356947	−	0.267207i
$809$	−29.6396	+	13.5360i	−1.04207	+	0.475899i	−0.861551	−	0.507671i	$-0.830506\pi$
$809$	−29.6396	+	13.5360i	−1.04207	+	0.475899i	−0.180524	+	0.983571i	$0.557779\pi$
$810$	31.8567	−	73.6820i	1.11933	−	2.58892i
$811$	−0.725354	+	1.58830i	−0.0254706	+	0.0557729i	−0.921940	−	0.387333i	$-0.873396\pi$
$811$	−0.725354	+	1.58830i	−0.0254706	+	0.0557729i	0.896469	+	0.443106i	$0.146124\pi$
$812$	−0.564009	−	7.88588i	−0.0197928	−	0.276740i
$813$	9.00382	+	12.0277i	0.315778	+	0.421830i
$814$	8.82355	+	30.0503i	0.309265	+	1.05326i
$815$	−18.2542	−	27.1739i	−0.639415	−	0.951862i
$816$	−5.50648	−	8.56826i	−0.192766	−	0.299949i
$817$	5.17907	+	1.12664i	0.181193	+	0.0394161i
$818$	14.8658	+	1.06322i	0.519769	+	0.0371746i
$819$	48.4373	−	14.2225i	1.69254	−	0.496973i
$820$	−6.88130	−	12.0152i	−0.240305	−	0.419590i
$821$	2.83306	−	3.26952i	0.0988743	−	0.114107i	−0.704156	−	0.710046i	$-0.748674\pi$
$821$	2.83306	−	3.26952i	0.0988743	−	0.114107i	0.803030	+	0.595938i	$0.203220\pi$
$822$	−18.1728	−	48.7233i	−0.633850	−	1.69942i
$823$	27.4031	−	14.9632i	0.955213	−	0.521586i	0.0755284	−	0.997144i	$-0.475936\pi$
$823$	27.4031	−	14.9632i	0.955213	−	0.521586i	0.879684	+	0.475558i	$0.157754\pi$
$824$	2.30641	+	5.05033i	0.0803476	+	0.175937i
$825$	51.0688	+	62.7365i	1.77799	+	2.18421i
$826$	7.16794	−	11.1535i	0.249405	−	0.388081i
$827$	10.6741	−	10.6741i	0.371176	−	0.371176i	−0.496730	−	0.867905i	$-0.665466\pi$
$827$	10.6741	−	10.6741i	0.371176	−	0.371176i	0.867905	+	0.496730i	$0.165466\pi$
$828$	31.4922	−	24.8641i	1.09443	−	0.864088i
$829$		−	1.45658i		−	0.0505890i	−0.999680	−	0.0252945i	$-0.991948\pi$
$829$		−	1.45658i		−	0.0505890i	0.999680	−	0.0252945i	$-0.00805235\pi$
$830$	6.58108	−	0.605291i	0.228433	−	0.0210100i
$831$	−4.85235	−	33.7488i	−0.168326	−	1.17073i
$832$	−1.30922	+	3.51016i	−0.0453891	+	0.121693i
$833$	6.37913	+	11.6825i	0.221024	+	0.404775i
$834$	−47.8078	−	21.8331i	−1.65545	−	0.756018i
$835$	14.2530	+	15.7890i	0.493246	+	0.546401i
$836$	−0.711657	+	4.94968i	−0.0246132	+	0.171188i
$837$	30.7175	+	16.7730i	1.06175	+	0.579760i
$838$	−0.209692	+	2.93188i	−0.00724369	+	0.101280i
$839$	45.0080	−	28.9249i	1.55385	−	0.998599i	0.569579	−	0.821937i	$-0.307106\pi$
$839$	45.0080	−	28.9249i	1.55385	−	0.998599i	0.984272	−	0.176662i	$-0.0565300\pi$
$840$	5.26719	+	10.9398i	0.181735	+	0.377458i
$841$	−3.21112	−	3.70583i	−0.110728	−	0.127787i
$842$	2.88526	−	5.28395i	0.0994325	−	0.182097i
$843$	80.2786	−	60.0958i	2.76494	−	2.06981i
$844$	11.7427	+	10.1751i	0.404200	+	0.350241i
$845$	0.537917	+	2.25153i	0.0185049	+	0.0774549i
$846$	−14.0101	−	4.11372i	−0.481676	−	0.141433i
$847$	18.1515	+	6.77017i	0.623694	+	0.232626i
$848$	−3.05496	+	4.08094i	−0.104908	+	0.140140i
$849$	−87.4187	−	56.1806i	−3.00020	−	1.92811i
$850$	3.66332	−	14.6541i	0.125651	−	0.502630i
$851$	26.7574	+	16.2388i	0.917231	+	0.556658i
$852$	6.25024	+	6.25024i	0.214130	+	0.214130i
$853$	20.5003	−	4.45957i	0.701918	−	0.152693i	0.152577	−	0.988292i	$-0.451243\pi$
$853$	20.5003	−	4.45957i	0.701918	−	0.152693i	0.549340	+	0.835599i	$0.314879\pi$
$854$	−10.0042	+	1.43839i	−0.342336	+	0.0492206i
$855$	17.2964	+	8.99333i	0.591525	+	0.307565i
$856$	−0.656156	+	2.23466i	−0.0224270	+	0.0763792i
$857$	−19.9727	+	7.44944i	−0.682255	+	0.254468i	−0.666607	−	0.745409i	$-0.732254\pi$
$857$	−19.9727	+	7.44944i	−0.682255	+	0.254468i	−0.0156485	+	0.999878i	$0.504981\pi$
$858$	60.4575	−	4.32401i	2.06399	−	0.147619i
$859$	−38.4185	−	5.52374i	−1.31082	−	0.188468i	−0.548764	−	0.835977i	$-0.684902\pi$
$859$	−38.4185	−	5.52374i	−1.31082	−	0.188468i	−0.762057	+	0.647509i	$0.775811\pi$
$860$	11.2224	−	1.84697i	0.382682	−	0.0629812i
$861$	−25.4109	+	22.0187i	−0.866000	+	0.750394i
$862$	−5.55335	+	25.5283i	−0.189148	+	0.869499i
$863$	6.09612	−	28.0234i	0.207514	−	0.953929i	−0.749074	−	0.662486i	$-0.769501\pi$
$863$	6.09612	−	28.0234i	0.207514	−	0.953929i	0.956588	−	0.291442i	$-0.0941351\pi$
$864$	13.6737	−	11.8484i	0.465190	−	0.403090i
$865$	46.8968	−	7.71821i	1.59454	−	0.262427i
$866$	34.6044	+	4.97536i	1.17591	+	0.169070i
$867$	−26.4775	+	1.89371i	−0.899222	+	0.0643136i
$868$	−2.91903	+	1.08874i	−0.0990782	+	0.0369543i
$869$	−12.8560	+	43.7835i	−0.436110	+	1.48525i
$870$	−32.8333	−	17.0718i	−1.11315	−	0.578787i
$871$	−31.7939	+	4.57128i	−1.07730	+	0.154892i
$872$	−11.5038	+	2.50250i	−0.389568	+	0.0847454i
$873$	−38.8001	−	38.8001i	−1.31318	−	1.31318i
$874$	2.80910	+	4.13325i	0.0950191	+	0.139809i
$875$	−6.46869	+	16.8048i	−0.218682	+	0.568105i
$876$	0.780593	+	0.501657i	0.0263738	+	0.0169494i
$877$	−22.4917	+	30.0454i	−0.759492	+	1.01456i	0.239554	+	0.970883i	$0.422999\pi$
$877$	−22.4917	+	30.0454i	−0.759492	+	1.01456i	−0.999046	+	0.0436792i	$0.986092\pi$
$878$	7.81044	+	2.91314i	0.263590	+	0.0983139i
$879$	0.212884	+	0.0625083i	0.00718039	+	0.00210835i
$880$	2.49346	+	10.4367i	0.0840547	+	0.351823i
$881$	19.1281	+	16.5746i	0.644444	+	0.558414i	0.914578	−	0.404409i	$-0.132523\pi$
$881$	19.1281	+	16.5746i	0.644444	+	0.558414i	−0.270135	+	0.962823i	$0.587068\pi$
$882$	−29.5107	+	22.0914i	−0.993676	+	0.743856i
$883$	−2.22792	+	4.08014i	−0.0749756	+	0.137308i	−0.912478	−	0.409127i	$-0.865833\pi$
$883$	−2.22792	+	4.08014i	−0.0749756	+	0.137308i	0.837502	+	0.546434i	$0.184015\pi$
$884$	−7.41157	−	8.55341i	−0.249278	−	0.287682i
$885$	−26.9217	−	55.9153i	−0.904961	−	1.87957i
$886$	−30.5727	+	19.6479i	−1.02711	+	0.660084i
$887$	−0.232393	+	3.24929i	−0.00780301	+	0.109100i	−0.999861	−	0.0166823i	$-0.994690\pi$
$887$	−0.232393	+	3.24929i	−0.00780301	+	0.109100i	0.992058	+	0.125783i	$0.0401442\pi$
$888$	19.3118	+	10.5450i	0.648061	+	0.353868i
$889$	2.86434	−	19.9219i	0.0960668	−	0.668160i
$890$	−5.89962	−	6.53540i	−0.197756	−	0.219067i
$891$	−156.707	−	71.5657i	−5.24988	−	2.39754i
$892$	−0.517754	−	0.948197i	−0.0173357	−	0.0317480i
$893$	0.635537	−	1.70394i	0.0212674	−	0.0570202i
$894$	5.32142	+	37.0113i	0.177975	+	1.23784i
$895$	−10.6723	+	0.981575i	−0.356735	+	0.0328105i
$896$			1.61058i			0.0538056i
$897$	41.7164	−	43.9202i	1.39287	−	1.46645i
$898$	23.3050	−	23.3050i	0.777699	−	0.777699i
$899$	5.13365	−	7.98811i	0.171217	−	0.266418i
$900$	41.6146	+	4.26648i	1.38715	+	0.142216i
$901$	−6.39750	−	14.0086i	−0.213132	−	0.466693i
$902$	−26.0805	+	14.2410i	−0.868385	+	0.474174i
$903$	−9.65170	−	25.8772i	−0.321189	−	0.861140i
$904$	−8.03021	+	9.26736i	−0.267081	+	0.308228i
$905$	25.8682	+	45.1676i	0.859888	+	1.50142i
$906$	−53.5111	+	15.7123i	−1.77779	+	0.522005i
$907$	8.03459	+	0.574645i	0.266784	+	0.0190808i	0.204090	−	0.978952i	$-0.434576\pi$
$907$	8.03459	+	0.574645i	0.266784	+	0.0190808i	0.0626937	+	0.998033i	$0.480031\pi$
$908$	−2.05237	−	0.446465i	−0.0681101	−	0.0148165i
$909$	57.3299	+	89.2071i	1.90151	+	2.95881i
$910$	7.52340	+	11.1997i	0.249398	+	0.371265i
$911$	−2.70385	−	9.20846i	−0.0895825	−	0.305090i	0.902498	−	0.430694i	$-0.141731\pi$
$911$	−2.70385	−	9.20846i	−0.0895825	−	0.305090i	−0.992080	+	0.125604i	$0.959913\pi$
$912$	2.10537	+	2.81245i	0.0697159	+	0.0931295i
$913$	−1.01182	−	14.1471i	−0.0334864	−	0.468200i
$914$	−1.47992	+	3.24056i	−0.0489513	+	0.107188i
$915$	−18.7746	+	43.4241i	−0.620668	+	1.43556i
$916$	−1.72875	+	0.789492i	−0.0571194	+	0.0260855i
$917$	−8.89191	−	6.65640i	−0.293637	−	0.219814i
$918$	11.6186	+	53.4098i	0.383470	+	1.76279i
$919$	8.90819			0.293854			0.146927	−	0.989147i	$-0.453062\pi$
$919$	8.90819			0.293854			0.146927	+	0.989147i	$0.453062\pi$
$920$	8.87155	+	6.02458i	0.292486	+	0.198624i
$921$	21.0551			0.693789
$922$	2.55228	+	11.7327i	0.0840550	+	0.386394i
$923$	7.86305	+	5.88621i	0.258815	+	0.193747i
$924$	23.7026	−	10.8246i	0.779757	−	0.356103i
$925$	8.22597	+	31.5781i	0.270468	+	1.03828i
$926$	−9.62855	+	21.0836i	−0.316414	+	0.692850i
$927$	−3.31382	−	46.3333i	−0.108840	−	1.52178i
$928$	−2.94174	−	3.92971i	−0.0965675	−	0.128999i
$929$	3.50617	+	11.9409i	0.115034	+	0.391769i	0.996802	−	0.0799144i	$-0.0254647\pi$
$929$	3.50617	+	11.9409i	0.115034	+	0.391769i	−0.881768	+	0.471683i	$0.843647\pi$
$930$	−2.80967	+	14.3095i	−0.0921326	+	0.469228i
$931$	−2.48224	−	3.86245i	−0.0813522	−	0.126587i
$932$	1.36736	+	0.297450i	0.0447893	+	0.00974331i
$933$	63.1497	+	4.51656i	2.06743	+	0.147865i
$934$	4.39684	−	1.29103i	0.143869	−	0.0422437i
$935$	−31.2828	−	8.49911i	−1.02306	−	0.277950i
$936$	20.5261	−	23.6883i	0.670915	−	0.774277i
$937$	−9.90592	−	26.5588i	−0.323612	−	0.867639i	−0.992273	−	0.124071i	$-0.960405\pi$
$937$	−9.90592	−	26.5588i	−0.323612	−	0.867639i	0.668661	−	0.743568i	$-0.266868\pi$
$938$	−12.1198	+	6.61790i	−0.395725	+	0.216082i
$939$	−32.3131	−	70.7559i	−1.05450	−	2.30903i
$940$	−0.0792787	−	3.90164i	−0.00258579	−	0.127257i
$941$	22.3133	−	34.7201i	0.727392	−	1.13184i	−0.258751	−	0.965944i	$-0.583311\pi$
$941$	22.3133	−	34.7201i	0.727392	−	1.13184i	0.986143	−	0.165900i	$-0.0530528\pi$
$942$	2.69833	−	2.69833i	0.0879162	−	0.0879162i
$943$	−9.65875	+	28.0822i	−0.314532	+	0.914482i
$944$		−	8.23198i		−	0.267928i
$945$	−5.96779	−	64.8854i	−0.194132	−	2.11072i
$946$	−3.47368	−	24.1600i	−0.112939	−	0.785508i
$947$	15.5352	−	41.6516i	0.504827	−	1.35349i	−0.395574	−	0.918434i	$-0.629454\pi$
$947$	15.5352	−	41.6516i	0.504827	−	1.35349i	0.900401	−	0.435060i	$-0.143273\pi$
$948$	15.3642	+	28.1375i	0.499007	+	0.913863i
$949$	0.937906	+	0.428327i	0.0304457	+	0.0139041i
$950$	−0.899787	+	5.13194i	−0.0291929	+	0.166502i
$951$	11.5296	−	80.1900i	0.373872	−	2.60034i
$952$	−4.27040	−	2.33181i	−0.138404	−	0.0755745i
$953$	−1.67467	+	23.4149i	−0.0542478	+	0.758483i	0.895420	+	0.445223i	$0.146876\pi$
$953$	−1.67467	+	23.4149i	−0.0542478	+	0.758483i	−0.949667	+	0.313260i	$0.898579\pi$
$954$	35.8798	−	23.0586i	1.16165	−	0.746548i
$955$	−8.02753	+	22.9352i	−0.259765	+	0.742167i
$956$	13.4933	+	15.5721i	0.436405	+	0.503638i
$957$	−38.0615	+	69.7045i	−1.23035	+	2.25323i
$958$	−9.25332	+	6.92695i	−0.298961	+	0.223800i
$959$	−18.7743	−	16.2681i	−0.606255	−	0.525323i
$960$	6.42349	+	3.94608i	0.207317	+	0.127359i
$961$	26.1541	+	7.67952i	0.843679	+	0.247727i
$962$	22.9086	+	8.54447i	0.738604	+	0.275485i
$963$	11.6774	−	15.5991i	0.376298	−	0.502675i
$964$	9.68786	+	6.22601i	0.312025	+	0.200526i
$965$	−33.9019	−	4.17330i	−1.09134	−	0.134343i
$966$	10.2049	−	23.9583i	0.328338	−	0.770845i
$967$	0.662148	+	0.662148i	0.0212932	+	0.0212932i	0.717673	−	0.696380i	$-0.245207\pi$
$967$	0.662148	+	0.662148i	0.0212932	+	0.0212932i	−0.696380	+	0.717673i	$0.745207\pi$
$968$	11.7537	−	2.55686i	0.377779	−	0.0821807i
$969$	−10.5053	+	1.51044i	−0.337479	+	0.0485222i
$970$	6.76532	−	13.0114i	0.217221	−	0.417771i
$971$	−4.84343	+	16.4952i	−0.155433	+	0.529356i	−0.999981	−	0.00612341i	$-0.998051\pi$
$971$	−4.84343	+	16.4952i	−0.155433	+	0.529356i	0.844548	+	0.535479i	$0.179869\pi$
$972$	−62.5451	+	23.3281i	−2.00613	+	0.748249i
$973$	−25.0433	+	1.79113i	−0.802852	+	0.0574211i
$974$	41.1923	+	5.92255i	1.31989	+	0.189771i
$975$	63.1009	−	2.56540i	2.02085	−	0.0821585i
$976$	−4.74266	+	4.10954i	−0.151809	+	0.131543i
$977$	−9.64629	+	44.3433i	−0.308612	+	1.41867i	0.517752	+	0.855531i	$0.326769\pi$
$977$	−9.64629	+	44.3433i	−0.308612	+	1.41867i	−0.826364	+	0.563137i	$0.809594\pi$
$978$	−10.4917	+	48.2295i	−0.335487	+	1.54221i
$979$	−14.2799	+	12.3736i	−0.456388	+	0.395462i
$980$	−8.00542	−	5.74277i	−0.255724	−	0.183446i
$981$	97.4956	+	14.0178i	3.11280	+	0.447553i
$982$	−40.2821	+	2.88103i	−1.28545	+	0.0919375i
$983$	36.5712	−	13.6404i	1.16644	−	0.435060i	0.309713	−	0.950830i	$-0.399767\pi$
$983$	36.5712	−	13.6404i	1.16644	−	0.435060i	0.856727	+	0.515770i	$0.172494\pi$
$984$	−5.88163	+	20.0310i	−0.187499	+	0.638564i
$985$	10.1679	−	3.21133i	0.323976	−	0.102322i
$986$	14.6786	−	2.11047i	0.467462	−	0.0672109i
$987$	−9.25992	+	2.01437i	−0.294746	+	0.0641181i
$988$	2.76046	+	2.76046i	0.0878220	+	0.0878220i
$989$	−18.8400	−	15.4946i	−0.599078	−	0.492701i
$990$	10.9687	−	89.1045i	0.348608	−	2.83193i
$991$	18.4994	+	11.8888i	0.587651	+	0.377661i	0.800418	−	0.599442i	$-0.204611\pi$
$991$	18.4994	+	11.8888i	0.587651	+	0.377661i	−0.212766	+	0.977103i	$0.568247\pi$
$992$	−1.15923	+	1.54855i	−0.0368055	+	0.0491664i
$993$	−11.3659	−	4.23926i	−0.360686	−	0.134529i
$994$	4.05154	+	1.18964i	0.128507	+	0.0377331i
$995$	21.9479	−	5.24362i	0.695796	−	0.166234i
$996$	−7.53067	−	6.52536i	−0.238618	−	0.206764i
$997$	−34.4660	+	25.8009i	−1.09155	+	0.817122i	−0.984193	−	0.177098i	$-0.943329\pi$
$997$	−34.4660	+	25.8009i	−1.09155	+	0.817122i	−0.107355	+	0.994221i	$0.534238\pi$
$998$	6.81139	−	12.4741i	0.215611	−	0.394861i
$999$	−77.3270	−	89.2401i	−2.44652	−	2.82343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.67.7	yes	240
5.3	odd	4	inner	230.2.l.a.113.12	yes	240
23.11	odd	22	inner	230.2.l.a.57.12	✓	240
115.103	even	44	inner	230.2.l.a.103.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.12	✓	240	23.11	odd	22	inner
230.2.l.a.67.7	yes	240	1.1	even	1	trivial
230.2.l.a.103.7	yes	240	115.103	even	44	inner
230.2.l.a.113.12	yes	240	5.3	odd	4	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+(0.212565 + 0.977147i) q^{2} +(-2.69897 - 2.02042i) q^{3} +(-0.909632 + 0.415415i) q^{4} +(0.823826 + 2.07878i) q^{5} +(1.40054 - 3.06676i) q^{6} +(-0.114897 - 1.60647i) q^{7} +(-0.599278 - 0.800541i) q^{8} +(2.35713 + 8.02765i) q^{9} +(-1.85615 + 1.24687i) q^{10} +(2.59443 + 4.03702i) q^{11} +(3.29438 + 0.716649i) q^{12} +(3.73682 + 0.267263i) q^{13} +(1.54534 - 0.453752i) q^{14} +(1.97653 - 7.27503i) q^{15} +(0.654861 - 0.755750i) q^{16} +(1.05573 + 2.83053i) q^{17} +(-7.34315 + 4.00966i) q^{18} +(-0.432881 - 0.947878i) q^{19} +(-1.61293 - 1.54869i) q^{20} +(-2.93565 + 4.56796i) q^{21} +(-3.39327 + 3.39327i) q^{22} +(-0.218958 + 4.79083i) q^{23} +3.37143i q^{24} +(-3.64262 + 3.42510i) q^{25} +(0.533163 + 3.70823i) q^{26} +(6.32284 - 16.9522i) q^{27} +(0.771867 + 1.41357i) q^{28} +(-4.46522 - 2.03920i) q^{29} +(7.52892 + 0.384937i) q^{30} +(-0.275290 + 1.91468i) q^{31} +(0.877679 + 0.479249i) q^{32} +(1.15419 - 16.1376i) q^{33} +(-2.54143 + 1.63328i) q^{34} +(3.24484 - 1.56230i) q^{35} +(-5.47893 - 6.32302i) q^{36} +(3.12776 - 5.72807i) q^{37} +(0.834200 - 0.624475i) q^{38} +(-9.54558 - 8.27129i) q^{39} +(1.17045 - 1.90527i) q^{40} +(5.94139 + 1.74455i) q^{41} +(-5.08759 - 1.89757i) q^{42} +(-3.04813 + 4.07183i) q^{43} +(-4.03702 - 2.59443i) q^{44} +(-14.7458 + 11.5133i) q^{45} +(-4.72789 + 0.804410i) q^{46} +(1.23406 + 1.23406i) q^{47} +(-3.29438 + 0.716649i) q^{48} +(4.36120 - 0.627045i) q^{49} +(-4.12112 - 2.83132i) q^{50} +(2.86948 - 9.77254i) q^{51} +(-3.51016 + 1.30922i) q^{52} +(-5.08474 + 0.363668i) q^{53} +(17.9088 + 2.57490i) q^{54} +(-6.25469 + 8.71905i) q^{55} +(-1.21719 + 1.05470i) q^{56} +(-0.746781 + 3.43290i) q^{57} +(1.04344 - 4.79663i) q^{58} +(6.22131 - 5.39080i) q^{59} +(1.22425 + 7.43868i) q^{60} +(-6.21156 - 0.893088i) q^{61} +(-1.92944 + 0.137997i) q^{62} +(12.6254 - 4.70902i) q^{63} +(-0.281733 + 0.959493i) q^{64} +(2.52291 + 7.98819i) q^{65} +(16.0142 - 2.30249i) q^{66} +(-8.37794 + 1.82251i) q^{67} +(-2.13617 - 2.13617i) q^{68} +(10.2705 - 12.4879i) q^{69} +(2.21634 + 2.83860i) q^{70} +(2.20559 + 1.41744i) q^{71} +(5.01389 - 6.69777i) q^{72} +(0.257869 + 0.0961803i) q^{73} +(6.26202 + 1.83869i) q^{74} +(16.7515 - 1.88461i) q^{75} +(0.787525 + 0.682395i) q^{76} +(6.18727 - 4.63173i) q^{77} +(6.05321 - 11.0856i) q^{78} +(6.22707 + 7.18643i) q^{79} +(2.11053 + 0.738702i) q^{80} +(-30.2006 + 19.4088i) q^{81} +(-0.441748 + 6.17644i) q^{82} +(-2.59404 - 1.41645i) q^{83} +(0.772762 - 5.37468i) q^{84} +(-5.01429 + 4.52650i) q^{85} +(-4.62670 - 2.11294i) q^{86} +(7.93145 + 14.5254i) q^{87} +(1.67701 - 4.49625i) q^{88} +(0.560355 + 3.89736i) q^{89} +(-14.3847 - 11.9615i) q^{90} -6.03381i q^{91} +(-1.79101 - 4.44885i) q^{92} +(4.61147 - 4.61147i) q^{93} +(-0.943540 + 1.46818i) q^{94} +(1.61381 - 1.68075i) q^{95} +(-1.40054 - 3.06676i) q^{96} +(-5.75621 + 3.14313i) q^{97} +(1.53975 + 4.12824i) q^{98} +(-26.2923 + 30.3430i) 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

Related objects

Downloads

Learn more