LMFDB - Embedded newform 234.2.t.a.103.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(25,234)] 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("234.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.t (of order $6$, degree $2$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.8
Character	$\chi$	$=$	234.103
Dual form			234.2.t.a.25.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.62009 + 0.612619i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.548308 - 0.316566i) q^{5} +(-1.09673 + 1.34059i) q^{6} +(2.15366 - 1.24342i) q^{7} -1.00000i q^{8} +(2.24940 - 1.98500i) q^{9} -0.633132 q^{10} +(4.20891 - 2.43002i) q^{11} +(-0.279503 + 1.70935i) q^{12} +(3.35794 - 1.31310i) q^{13} +(1.24342 - 2.15366i) q^{14} +(1.08224 + 0.176962i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.27837 q^{17} +(0.955536 - 2.84376i) q^{18} +4.86004i q^{19} +(-0.548308 + 0.316566i) q^{20} +(-2.72739 + 3.33382i) q^{21} +(2.43002 - 4.20891i) q^{22} +(-1.77384 + 3.07238i) q^{23} +(0.612619 + 1.62009i) q^{24} +(-2.29957 - 3.98298i) q^{25} +(2.25152 - 2.81615i) q^{26} +(-2.42818 + 4.59390i) q^{27} -2.48683i q^{28} +(0.415447 + 0.719576i) q^{29} +(1.02573 - 0.387868i) q^{30} +(3.73461 + 2.15618i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.33015 + 6.51531i) q^{33} +(-5.43723 + 3.13918i) q^{34} -1.57449 q^{35} +(-0.594360 - 2.94053i) q^{36} -7.81310i q^{37} +(2.43002 + 4.20891i) q^{38} +(-4.63575 + 4.18448i) q^{39} +(-0.316566 + 0.548308i) q^{40} +(-0.0678657 - 0.0391823i) q^{41} +(-0.695076 + 4.25087i) q^{42} +(4.84370 + 8.38954i) q^{43} -4.86004i q^{44} +(-1.86175 + 0.376308i) q^{45} +3.54768i q^{46} +(-4.30069 + 2.48301i) q^{47} +(1.34059 + 1.09673i) q^{48} +(-0.407830 + 0.706382i) q^{49} +(-3.98298 - 2.29957i) q^{50} +(10.1715 - 3.84625i) q^{51} +(0.541797 - 3.56461i) q^{52} -6.36026 q^{53} +(0.194083 + 5.19253i) q^{54} -3.07704 q^{55} +(-1.24342 - 2.15366i) q^{56} +(-2.97735 - 7.87371i) q^{57} +(0.719576 + 0.415447i) q^{58} +(-7.86994 - 4.54371i) q^{59} +(0.694376 - 0.848770i) q^{60} +(5.28535 + 9.15449i) q^{61} +4.31236 q^{62} +(2.37626 - 7.07195i) q^{63} -1.00000 q^{64} +(-2.25687 - 0.343029i) q^{65} +(-1.35839 + 8.30750i) q^{66} +(6.82824 + 3.94228i) q^{67} +(-3.13918 + 5.43723i) q^{68} +(0.991586 - 6.06423i) q^{69} +(-1.36355 + 0.787247i) q^{70} +12.3085i q^{71} +(-1.98500 - 2.24940i) q^{72} -1.05367i q^{73} +(-3.90655 - 6.76635i) q^{74} +(6.16556 + 5.04403i) q^{75} +(4.20891 + 2.43002i) q^{76} +(6.04305 - 10.4669i) q^{77} +(-1.92244 + 5.94174i) q^{78} +(-1.68838 - 2.92436i) q^{79} +0.633132i q^{80} +(1.11957 - 8.93009i) q^{81} -0.0783645 q^{82} +(13.1755 - 7.60686i) q^{83} +(1.52348 + 4.02890i) q^{84} +(3.44248 + 1.98752i) q^{85} +(8.38954 + 4.84370i) q^{86} +(-1.11389 - 0.911268i) q^{87} +(-2.43002 - 4.20891i) q^{88} +0.595093i q^{89} +(-1.42416 + 1.25677i) q^{90} +(5.59914 - 7.00329i) q^{91} +(1.77384 + 3.07238i) q^{92} +(-7.37133 - 1.20531i) q^{93} +(-2.48301 + 4.30069i) q^{94} +(1.53852 - 2.66480i) q^{95} +(1.70935 + 0.279503i) q^{96} +(-14.7770 + 8.53151i) q^{97} +0.815659i q^{98} +(4.64394 - 13.8208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49}+ \cdots + 8 q^{92}+O(q^{100}) $ 28 * q + 14 * q^4 - 16 * q^9 + 2 * q^13 + 8 * q^14 - 14 * q^16 + 16 * q^17 - 8 * q^23 + 14 * q^25 + 8 * q^26 + 18 * q^27 - 16 * q^29 - 8 * q^30 - 68 * q^35 - 8 * q^36 - 8 * q^39 - 10 * q^42 - 4 * q^43 + 10 * q^49 + 58 * q^51 - 2 * q^52 - 120 * q^53 - 8 * q^56 + 28 * q^61 + 68 * q^62 - 28 * q^64 - 8 * q^65 - 24 * q^66 + 8 * q^68 - 92 * q^69 + 16 * q^74 + 32 * q^75 - 24 * q^77 - 22 * q^78 + 28 * q^79 + 8 * q^81 - 48 * q^82 + 68 * q^87 - 50 * q^90 + 8 * q^92

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.62009	+	0.612619i	−0.935361	+	0.353696i
$3$	−1.62009	+	0.612619i	−0.935361	+	0.353696i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.548308	−	0.316566i	−0.245211	−	0.141573i	0.372358	−	0.928089i	$-0.378549\pi$
$5$	−0.548308	−	0.316566i	−0.245211	−	0.141573i	−0.617569	+	0.786516i	$0.711883\pi$
$6$	−1.09673	+	1.34059i	−0.447739	+	0.547293i
$7$	2.15366	−	1.24342i	0.814007	−	0.469967i	−0.0343382	−	0.999410i	$-0.510932\pi$
$7$	2.15366	−	1.24342i	0.814007	−	0.469967i	0.848346	+	0.529443i	$0.177599\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.24940	−	1.98500i	0.749799	−	0.661666i
$10$	−0.633132			−0.200214
$11$	4.20891	−	2.43002i	1.26904	−	0.732678i	0.294230	−	0.955735i	$-0.404937\pi$
$11$	4.20891	−	2.43002i	1.26904	−	0.732678i	0.974805	+	0.223057i	$0.0716035\pi$
$12$	−0.279503	+	1.70935i	−0.0806855	+	0.493447i
$13$	3.35794	−	1.31310i	0.931326	−	0.364187i
$13$	3.35794	−	1.31310i	0.931326	−	0.364187i
$14$	1.24342	−	2.15366i	0.332317	−	0.575590i
$15$	1.08224	+	0.176962i	0.279434	+	0.0456914i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.27837			−1.52273			−0.761364	−	0.648325i	$-0.775470\pi$
$17$	−6.27837			−1.52273			−0.761364	+	0.648325i	$0.775470\pi$
$18$	0.955536	−	2.84376i	0.225222	−	0.670280i
$19$			4.86004i			1.11497i	0.830187	+	0.557484i	$0.188233\pi$
$19$			4.86004i			1.11497i	−0.830187	+	0.557484i	$0.811767\pi$
$20$	−0.548308	+	0.316566i	−0.122605	+	0.0707863i
$21$	−2.72739	+	3.33382i	−0.595165	+	0.727500i
$22$	2.43002	−	4.20891i	0.518082	−	0.897344i
$23$	−1.77384	+	3.07238i	−0.369871	+	0.640636i	−0.989545	−	0.144224i	$-0.953932\pi$
$23$	−1.77384	+	3.07238i	−0.369871	+	0.640636i	0.619674	+	0.784859i	$0.287265\pi$
$24$	0.612619	+	1.62009i	0.125050	+	0.330700i
$25$	−2.29957	−	3.98298i	−0.459914	−	0.796595i
$26$	2.25152	−	2.81615i	0.441559	−	0.552292i
$27$	−2.42818	+	4.59390i	−0.467304	+	0.884097i
$28$		−	2.48683i		−	0.469967i
$29$	0.415447	+	0.719576i	0.0771466	+	0.133622i	0.902018	−	0.431699i	$-0.142086\pi$
$29$	0.415447	+	0.719576i	0.0771466	+	0.133622i	−0.824871	+	0.565321i	$0.808752\pi$
$30$	1.02573	−	0.387868i	0.187272	−	0.0708148i
$31$	3.73461	+	2.15618i	0.670756	+	0.387261i	0.796363	−	0.604819i	$-0.206755\pi$
$31$	3.73461	+	2.15618i	0.670756	+	0.387261i	−0.125607	+	0.992080i	$0.540088\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−5.33015	+	6.51531i	−0.927861	+	1.13417i
$34$	−5.43723	+	3.13918i	−0.932477	+	0.538366i
$35$	−1.57449			−0.266138
$36$	−0.594360	−	2.94053i	−0.0990600	−	0.490089i
$37$		−	7.81310i		−	1.28447i	−0.766509	−	0.642233i	$-0.778008\pi$
$37$		−	7.81310i		−	1.28447i	0.766509	−	0.642233i	$-0.221992\pi$
$38$	2.43002	+	4.20891i	0.394201	+	0.682776i
$39$	−4.63575	+	4.18448i	−0.742314	+	0.670052i
$40$	−0.316566	+	0.548308i	−0.0500535	+	0.0866952i
$41$	−0.0678657	−	0.0391823i	−0.0105988	−	0.00611924i	0.494691	−	0.869069i	$-0.335281\pi$
$41$	−0.0678657	−	0.0391823i	−0.0105988	−	0.00611924i	−0.505290	+	0.862950i	$0.668614\pi$
$42$	−0.695076	+	4.25087i	−0.107253	+	0.655923i
$43$	4.84370	+	8.38954i	0.738658	+	1.27939i	0.953100	+	0.302656i	$0.0978733\pi$
$43$	4.84370	+	8.38954i	0.738658	+	1.27939i	−0.214442	+	0.976737i	$0.568793\pi$
$44$		−	4.86004i		−	0.732678i
$45$	−1.86175	+	0.376308i	−0.277533	+	0.0560967i
$46$			3.54768i			0.523077i
$47$	−4.30069	+	2.48301i	−0.627320	+	0.362184i	−0.779714	−	0.626136i	$-0.784635\pi$
$47$	−4.30069	+	2.48301i	−0.627320	+	0.362184i	0.152393	+	0.988320i	$0.451302\pi$
$48$	1.34059	+	1.09673i	0.193497	+	0.158300i
$49$	−0.407830	+	0.706382i	−0.0582614	+	0.100912i
$50$	−3.98298	−	2.29957i	−0.563278	−	0.325209i
$51$	10.1715	−	3.84625i	1.42430	−	0.538582i
$52$	0.541797	−	3.56461i	0.0751337	−	0.494323i
$53$	−6.36026			−0.873649			−0.436824	−	0.899547i	$-0.643897\pi$
$53$	−6.36026			−0.873649			−0.436824	+	0.899547i	$0.643897\pi$
$54$	0.194083	+	5.19253i	0.0264113	+	0.706613i
$55$	−3.07704			−0.414909
$56$	−1.24342	−	2.15366i	−0.166159	−	0.287795i
$57$	−2.97735	−	7.87371i	−0.394360	−	1.04290i
$58$	0.719576	+	0.415447i	0.0944849	+	0.0545509i
$59$	−7.86994	−	4.54371i	−1.02458	−	0.591541i	−0.109152	−	0.994025i	$-0.534813\pi$
$59$	−7.86994	−	4.54371i	−1.02458	−	0.591541i	−0.915427	+	0.402484i	$0.868147\pi$
$60$	0.694376	−	0.848770i	0.0896435	−	0.109576i
$61$	5.28535	+	9.15449i	0.676719	+	1.17211i	0.975963	+	0.217935i	$0.0699322\pi$
$61$	5.28535	+	9.15449i	0.676719	+	1.17211i	−0.299244	+	0.954177i	$0.596734\pi$
$62$	4.31236			0.547670
$63$	2.37626	−	7.07195i	0.299380	−	0.890982i
$64$	−1.00000			−0.125000
$65$	−2.25687	−	0.343029i	−0.279930	−	0.0425475i
$66$	−1.35839	+	8.30750i	−0.167207	+	1.02258i
$67$	6.82824	+	3.94228i	0.834202	+	0.481627i	0.855289	−	0.518151i	$-0.173380\pi$
$67$	6.82824	+	3.94228i	0.834202	+	0.481627i	−0.0210874	+	0.999778i	$0.506713\pi$
$68$	−3.13918	+	5.43723i	−0.380682	+	0.659361i
$69$	0.991586	−	6.06423i	0.119373	−	0.730047i
$70$	−1.36355	+	0.787247i	−0.162976	+	0.0940940i
$71$			12.3085i			1.46075i	0.683048	+	0.730374i	$0.260654\pi$
$71$			12.3085i			1.46075i	−0.683048	+	0.730374i	$0.739346\pi$
$72$	−1.98500	−	2.24940i	−0.233934	−	0.265094i
$73$		−	1.05367i		−	0.123323i	−0.998097	−	0.0616615i	$-0.980360\pi$
$73$		−	1.05367i		−	0.123323i	0.998097	−	0.0616615i	$-0.0196399\pi$
$74$	−3.90655	−	6.76635i	−0.454127	−	0.786572i
$75$	6.16556	+	5.04403i	0.711938	+	0.582434i
$76$	4.20891	+	2.43002i	0.482796	+	0.278742i
$77$	6.04305	−	10.4669i	0.688669	−	1.19281i
$78$	−1.92244	+	5.94174i	−0.217673	+	0.672769i
$79$	−1.68838	−	2.92436i	−0.189958	−	0.329017i	0.755278	−	0.655404i	$-0.227502\pi$
$79$	−1.68838	−	2.92436i	−0.189958	−	0.329017i	−0.945236	+	0.326388i	$0.894168\pi$
$80$			0.633132i			0.0707863i
$81$	1.11957	−	8.93009i	0.124397	−	0.992233i
$82$	−0.0783645			−0.00865391
$83$	13.1755	−	7.60686i	1.44620	−	0.834961i	0.447943	−	0.894062i	$-0.352157\pi$
$83$	13.1755	−	7.60686i	1.44620	−	0.834961i	0.998252	+	0.0591005i	$0.0188232\pi$
$84$	1.52348	+	4.02890i	0.166225	+	0.439589i
$85$	3.44248	+	1.98752i	0.373390	+	0.215577i
$86$	8.38954	+	4.84370i	0.904667	+	0.522310i
$87$	−1.11389	−	0.911268i	−0.119421	−	0.0976982i
$88$	−2.43002	−	4.20891i	−0.259041	−	0.448672i
$89$			0.595093i			0.0630797i	0.999502	+	0.0315398i	$0.0100411\pi$
$89$			0.595093i			0.0630797i	−0.999502	+	0.0315398i	$0.989959\pi$
$90$	−1.42416	+	1.25677i	−0.150120	+	0.132475i
$91$	5.59914	−	7.00329i	0.586950	−	0.734144i
$92$	1.77384	+	3.07238i	0.184936	+	0.320318i
$93$	−7.37133	−	1.20531i	−0.764371	−	0.124985i
$94$	−2.48301	+	4.30069i	−0.256103	+	0.443583i
$95$	1.53852	−	2.66480i	0.157849	−	0.273403i
$96$	1.70935	+	0.279503i	0.174460	+	0.0285266i
$97$	−14.7770	+	8.53151i	−1.50038	+	0.866244i	−0.500378	+	0.865807i	$0.666806\pi$
$97$	−14.7770	+	8.53151i	−1.50038	+	0.866244i	−1.00000		0.000436560i	$0.999861\pi$
$98$			0.815659i			0.0823940i
$99$	4.64394	−	13.8208i	0.466733	−	1.38904i
$100$	−4.59914			−0.459914
$101$	2.53762	+	4.39529i	0.252503	+	0.437348i	0.964214	−	0.265124i	$-0.0854130\pi$
$101$	2.53762	+	4.39529i	0.252503	+	0.437348i	−0.711712	+	0.702472i	$0.752080\pi$
$102$	6.88568	−	8.41671i	0.681784	−	0.833379i
$103$	0.538522	−	0.932747i	0.0530621	−	0.0919063i	−0.838274	−	0.545249i	$-0.816435\pi$
$103$	0.538522	−	0.932747i	0.0530621	−	0.0919063i	0.891336	+	0.453342i	$0.149769\pi$
$104$	−1.31310	−	3.35794i	−0.128760	−	0.329273i
$105$	2.55082	−	0.964564i	0.248935	−	0.0941318i
$106$	−5.50815	+	3.18013i	−0.534998	+	0.308881i
$107$	−9.16763			−0.886268			−0.443134	−	0.896455i	$-0.646133\pi$
$107$	−9.16763			−0.886268			−0.443134	+	0.896455i	$0.646133\pi$
$108$	2.76434	+	4.39982i	0.265999	+	0.423373i
$109$		−	9.90028i		−	0.948275i	−0.880451	−	0.474138i	$-0.842760\pi$
$109$		−	9.90028i		−	0.948275i	0.880451	−	0.474138i	$-0.157240\pi$
$110$	−2.66480	+	1.53852i	−0.254079	+	0.146692i
$111$	4.78645	+	12.6579i	0.454310	+	1.20144i
$112$	−2.15366	−	1.24342i	−0.203502	−	0.117492i
$113$	−3.31088	+	5.73460i	−0.311461	+	0.539466i	−0.978679	−	0.205396i	$-0.934152\pi$
$113$	−3.31088	+	5.73460i	−0.311461	+	0.539466i	0.667218	+	0.744863i	$0.267485\pi$
$114$	−6.51531	−	5.33015i	−0.610215	−	0.499215i
$115$	1.94522	−	1.12307i	0.181393	−	0.104727i
$116$	0.830894			0.0771466
$117$	4.94685	−	9.61918i	0.457337	−	0.889294i
$118$	−9.08742			−0.836565
$119$	−13.5215	+	7.80663i	−1.23951	+	0.715632i
$120$	0.176962	−	1.08224i	0.0161543	−	0.0987949i
$121$	6.30997	−	10.9292i	0.573634	−	0.993563i
$122$	9.15449	+	5.28535i	0.828808	+	0.478513i
$123$	0.133952	+	0.0219031i	0.0120781	+	0.00197493i
$124$	3.73461	−	2.15618i	0.335378	−	0.193630i
$125$			6.07752i			0.543590i
$126$	−1.47807	−	7.31262i	−0.131677	−	0.651460i
$127$	−17.8088			−1.58028			−0.790138	−	0.612929i	$-0.789991\pi$
$127$	−17.8088			−1.58028			−0.790138	+	0.612929i	$0.789991\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−12.9868	−	10.6245i	−1.14343	−	0.935433i
$130$	−2.12602	+	0.831363i	−0.186464	+	0.0729154i
$131$	6.02780	−	10.4404i	0.526651	−	0.912186i	−0.472867	−	0.881134i	$-0.656781\pi$
$131$	6.02780	−	10.4404i	0.526651	−	0.912186i	0.999518	−	0.0310522i	$-0.00988582\pi$
$132$	2.97735	+	7.87371i	0.259145	+	0.685318i
$133$	6.04305	+	10.4669i	0.523999	+	0.907593i
$134$	7.88457			0.681123
$135$	2.78567	−	1.75019i	0.239752	−	0.150633i
$136$			6.27837i			0.538366i
$137$	−0.263943	+	0.152388i	−0.0225502	+	0.0130194i	−0.511233	−	0.859442i	$-0.670811\pi$
$137$	−0.263943	+	0.152388i	−0.0225502	+	0.0130194i	0.488683	+	0.872462i	$0.337478\pi$
$138$	−2.17338	−	5.74757i	−0.185010	−	0.489265i
$139$	−4.09109	+	7.08598i	−0.347002	+	0.601025i	−0.985715	−	0.168420i	$-0.946134\pi$
$139$	−4.09109	+	7.08598i	−0.347002	+	0.601025i	0.638714	+	0.769445i	$0.279467\pi$
$140$	−0.787247	+	1.36355i	−0.0665345	+	0.115241i
$141$	5.44638	−	6.65738i	0.458668	−	0.560653i
$142$	6.15424	+	10.6595i	0.516452	+	0.894522i
$143$	10.9424	−	13.6866i	0.915053	−	1.14453i
$144$	−2.84376	−	0.955536i	−0.236980	−	0.0796280i
$145$		−	0.526066i		−	0.0436874i
$146$	−0.526836	−	0.912507i	−0.0436013	−	0.0755196i
$147$	0.227979	−	1.39425i	0.0188034	−	0.114996i
$148$	−6.76635	−	3.90655i	−0.556190	−	0.321117i
$149$	15.9905	+	9.23210i	1.30999	+	0.756323i	0.982094	−	0.188391i	$-0.0603273\pi$
$149$	15.9905	+	9.23210i	1.30999	+	0.756323i	0.327895	+	0.944714i	$0.393661\pi$
$150$	7.86155	+	1.28547i	0.641893	+	0.104958i
$151$	4.61608	−	2.66510i	0.375651	−	0.216882i	−0.300273	−	0.953853i	$-0.597078\pi$
$151$	4.61608	−	2.66510i	0.375651	−	0.216882i	0.675925	+	0.736971i	$0.263745\pi$
$152$	4.86004			0.394201
$153$	−14.1225	+	12.4625i	−1.14174	+	1.00754i
$154$		−	12.0861i		−	0.973926i
$155$	−1.36515	−	2.36450i	−0.109651	−	0.189921i
$156$	1.30599	+	6.10691i	0.104563	+	0.488944i
$157$	1.46920	−	2.54473i	0.117255	−	0.203092i	−0.801424	−	0.598097i	$-0.795924\pi$
$157$	1.46920	−	2.54473i	0.117255	−	0.203092i	0.918679	+	0.395005i	$0.129257\pi$
$158$	−2.92436	−	1.68838i	−0.232650	−	0.134320i
$159$	10.3042	−	3.89641i	0.817177	−	0.309006i
$160$	0.316566	+	0.548308i	0.0250267	+	0.0433476i
$161$			8.82249i			0.695310i
$162$	−3.49547	−	8.29347i	−0.274630	−	0.651597i
$163$		−	7.41051i		−	0.580436i	−0.956961	−	0.290218i	$-0.906272\pi$
$163$		−	7.41051i		−	0.580436i	0.956961	−	0.290218i	$-0.0937278\pi$
$164$	−0.0678657	+	0.0391823i	−0.00529942	+	0.00305962i
$165$	4.98509	−	1.88505i	0.388089	−	0.146751i
$166$	7.60686	−	13.1755i	0.590407	−	1.02261i
$167$	0.0771631	+	0.0445501i	0.00597106	+	0.00344739i	0.502983	−	0.864297i	$-0.332236\pi$
$167$	0.0771631	+	0.0445501i	0.00597106	+	0.00344739i	−0.497011	+	0.867744i	$0.665569\pi$
$168$	3.33382	+	2.72739i	0.257210	+	0.210423i
$169$	9.55156	−	8.81860i	0.734735	−	0.678354i
$170$	3.97504			0.304871
$171$	9.64716	+	10.9321i	0.737737	+	0.836002i
$172$	9.68740			0.738658
$173$	3.79919	+	6.58039i	0.288847	+	0.500298i	0.973535	−	0.228539i	$-0.0733948\pi$
$173$	3.79919	+	6.58039i	0.288847	+	0.500298i	−0.684688	+	0.728836i	$0.740061\pi$
$174$	−1.42029	−	0.232237i	−0.107672	−	0.0176059i
$175$	−9.90500	−	5.71865i	−0.748747	−	0.432290i
$176$	−4.20891	−	2.43002i	−0.317259	−	0.183169i
$177$	15.5336	+	2.53996i	1.16758	+	0.190915i
$178$	0.297546	+	0.515365i	0.0223020	+	0.0386283i
$179$	23.7909			1.77822			0.889109	−	0.457695i	$-0.151325\pi$
$179$	23.7909			1.77822			0.889109	+	0.457695i	$0.151325\pi$
$180$	−0.604980	+	1.80047i	−0.0450926	+	0.134199i
$181$	−1.63229			−0.121327			−0.0606637	−	0.998158i	$-0.519322\pi$
$181$	−1.63229			−0.121327			−0.0606637	+	0.998158i	$0.519322\pi$
$182$	1.34736	−	8.86460i	0.0998728	−	0.657088i
$183$	−14.1710	−	11.5932i	−1.04755	−	0.856995i
$184$	3.07238	+	1.77384i	0.226499	+	0.130769i
$185$	−2.47336	+	4.28399i	−0.181845	+	0.314965i
$186$	−6.98641	+	2.64183i	−0.512269	+	0.193708i
$187$	−26.4251	+	15.2565i	−1.93240	+	1.11567i
$188$			4.96601i			0.362184i
$189$	0.482651	+	12.9129i	0.0351077	+	0.939279i
$190$		−	3.07704i		−	0.223232i
$191$	1.58316	+	2.74212i	0.114554	+	0.198413i	0.917601	−	0.397502i	$-0.130123\pi$
$191$	1.58316	+	2.74212i	0.114554	+	0.198413i	−0.803048	+	0.595915i	$0.796790\pi$
$192$	1.62009	−	0.612619i	0.116920	−	0.0442120i
$193$	−14.2560	−	8.23071i	−1.02617	−	0.592459i	−0.110285	−	0.993900i	$-0.535176\pi$
$193$	−14.2560	−	8.23071i	−1.02617	−	0.592459i	−0.915885	+	0.401441i	$0.868510\pi$
$194$	−8.53151	+	14.7770i	−0.612527	+	1.06093i
$195$	3.86648	−	0.826862i	0.276885	−	0.0592129i
$196$	0.407830	+	0.706382i	0.0291307	+	0.0504558i
$197$			11.4351i			0.814719i	0.913268	+	0.407360i	$0.133550\pi$
$197$			11.4351i			0.814719i	−0.913268	+	0.407360i	$0.866450\pi$
$198$	−2.88861	−	14.2911i	−0.205285	−	1.01562i
$199$	−13.1983			−0.935602			−0.467801	−	0.883834i	$-0.654954\pi$
$199$	−13.1983			−0.935602			−0.467801	+	0.883834i	$0.654954\pi$
$200$	−3.98298	+	2.29957i	−0.281639	+	0.162604i
$201$	−13.4775	−	2.20376i	−0.950629	−	0.155441i
$202$	4.39529	+	2.53762i	0.309251	+	0.178546i
$203$	1.78946	+	1.03315i	0.125596	+	0.0725128i
$204$	1.75482	−	10.7319i	0.122862	−	0.751385i
$205$	0.0248075	+	0.0429679i	0.00173263	+	0.00300101i
$206$		−	1.07704i		−	0.0750412i
$207$	2.10860	+	10.4321i	0.146558	+	0.725079i
$208$	−2.81615	−	2.25152i	−0.195265	−	0.156115i
$209$	11.8100	+	20.4555i	0.816913	+	1.41493i
$210$	1.72680	−	2.11075i	0.119160	−	0.145656i
$211$	−4.63857	+	8.03423i	−0.319332	+	0.553099i	−0.980349	−	0.197272i	$-0.936792\pi$
$211$	−4.63857	+	8.03423i	−0.319332	+	0.553099i	0.661017	+	0.750371i	$0.270125\pi$
$212$	−3.18013	+	5.50815i	−0.218412	+	0.378301i
$213$	−7.54041	−	19.9409i	−0.516660	−	1.36633i
$214$	−7.93940	+	4.58381i	−0.542726	+	0.313343i
$215$		−	6.13341i		−	0.418295i
$216$	4.59390	+	2.42818i	0.312575	+	0.165217i
$217$	10.7241			0.728000
$218$	−4.95014	−	8.57390i	−0.335266	−	0.580698i
$219$	0.645499	+	1.70705i	0.0436188	+	0.115351i
$220$	−1.53852	+	2.66480i	−0.103727	+	0.179661i
$221$	−21.0824	+	8.24410i	−1.41816	+	0.554558i
$222$	10.4742	+	8.56888i	0.702980	+	0.575105i
$223$	−12.1351	+	7.00623i	−0.812630	+	0.469172i	−0.847868	−	0.530207i	$-0.822114\pi$
$223$	−12.1351	+	7.00623i	−0.812630	+	0.469172i	0.0352386	+	0.999379i	$0.488781\pi$
$224$	−2.48683			−0.166159
$225$	−13.0788	−	4.39465i	−0.871923	−	0.292976i
$226$			6.62175i			0.440472i
$227$	−2.40085	+	1.38613i	−0.159350	+	0.0920010i	−0.577555	−	0.816352i	$-0.695993\pi$
$227$	−2.40085	+	1.38613i	−0.159350	+	0.0920010i	0.418204	+	0.908353i	$0.362660\pi$
$228$	−8.30750	−	1.35839i	−0.550178	−	0.0899618i
$229$	−14.4165	−	8.32339i	−0.952671	−	0.550025i	−0.0587614	−	0.998272i	$-0.518715\pi$
$229$	−14.4165	−	8.32339i	−0.952671	−	0.550025i	−0.893910	+	0.448247i	$0.852048\pi$
$230$	1.12307	−	1.94522i	0.0740534	−	0.128264i
$231$	−3.37810	+	20.6594i	−0.222262	+	1.35929i
$232$	0.719576	−	0.415447i	0.0472425	−	0.0272754i
$233$	−5.45324			−0.357254			−0.178627	−	0.983917i	$-0.557165\pi$
$233$	−5.45324			−0.357254			−0.178627	+	0.983917i	$0.557165\pi$
$234$	−0.525492	−	10.8039i	−0.0343525	−	0.706272i
$235$	3.14414			0.205101
$236$	−7.86994	+	4.54371i	−0.512289	+	0.295770i
$237$	4.52685	+	3.70340i	0.294051	+	0.240562i
$238$	−7.80663	+	13.5215i	−0.506029	+	0.876467i
$239$	11.8000	+	6.81272i	0.763277	+	0.440678i	0.830471	−	0.557062i	$-0.188071\pi$
$239$	11.8000	+	6.81272i	0.763277	+	0.440678i	−0.0671938	+	0.997740i	$0.521405\pi$
$240$	−0.387868	−	1.02573i	−0.0250368	−	0.0662107i
$241$	16.3780	−	9.45585i	1.05500	−	0.609105i	0.130956	−	0.991388i	$-0.458195\pi$
$241$	16.3780	−	9.45585i	1.05500	−	0.609105i	0.924045	+	0.382283i	$0.124862\pi$
$242$		−	12.6199i		−	0.811241i
$243$	3.65694	+	15.1534i	0.234593	+	0.972094i
$244$	10.5707			0.676719
$245$	0.447233	−	0.258210i	0.0285727	−	0.0164964i
$246$	0.126958	−	0.0480076i	0.00809453	−	0.00306085i
$247$	6.38169	+	16.3197i	0.406058	+	1.03840i
$248$	2.15618	−	3.73461i	0.136917	−	0.237148i
$249$	−16.6854	+	20.3954i	−1.05739	+	1.29250i
$250$	3.03876	+	5.26329i	0.192188	+	0.332880i
$251$	−2.07524			−0.130988			−0.0654940	−	0.997853i	$-0.520862\pi$
$251$	−2.07524			−0.130988			−0.0654940	+	0.997853i	$0.520862\pi$
$252$	−4.93636	−	5.59387i	−0.310961	−	0.352381i
$253$			17.2419i			1.08399i
$254$	−15.4229	+	8.90441i	−0.967718	+	0.558712i
$255$	−6.79473	−	1.11103i	−0.425502	−	0.0695756i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.5009	−	21.6522i	0.779785	−	1.35063i	−0.152280	−	0.988337i	$-0.548662\pi$
$257$	12.5009	−	21.6522i	0.779785	−	1.35063i	0.932065	−	0.362290i	$-0.118005\pi$
$258$	−16.5592	−	2.70765i	−1.03093	−	0.168571i
$259$	−9.71494	−	16.8268i	−0.603657	−	1.04557i
$260$	−1.42551	+	1.78299i	−0.0884061	+	0.110576i
$261$	2.36286	+	0.793949i	0.146257	+	0.0491442i
$262$		−	12.0556i		−	0.744797i
$263$	−12.6267	−	21.8701i	−0.778596	−	1.34857i	−0.932751	−	0.360521i	$-0.882599\pi$
$263$	−12.6267	−	21.8701i	−0.778596	−	1.34857i	0.154155	−	0.988047i	$-0.450734\pi$
$264$	6.51531	+	5.33015i	0.400990	+	0.328048i
$265$	3.48738	+	2.01344i	0.214228	+	0.123685i
$266$	10.4669	+	6.04305i	0.641765	+	0.370523i
$267$	−0.364565	−	0.964105i	−0.0223110	−	0.0590023i
$268$	6.82824	−	3.94228i	0.417101	−	0.240813i
$269$	−23.7793			−1.44985			−0.724925	−	0.688828i	$-0.758126\pi$
$269$	−23.7793			−1.44985			−0.724925	+	0.688828i	$0.758126\pi$
$270$	1.53736	−	2.90855i	0.0935608	−	0.177008i
$271$			14.2050i			0.862894i	0.902138	+	0.431447i	$0.141997\pi$
$271$			14.2050i			0.862894i	−0.902138	+	0.431447i	$0.858003\pi$
$272$	3.13918	+	5.43723i	0.190341	+	0.329680i
$273$	−4.78078	+	14.7761i	−0.289346	+	0.894291i
$274$	−0.152388	+	0.263943i	−0.00920609	+	0.0159454i
$275$	−19.3574	−	11.1760i	−1.16730	−	0.673938i
$276$	−4.75598	−	3.89085i	−0.286276	−	0.234202i
$277$	−4.06786	−	7.04574i	−0.244414	−	0.423337i	0.717553	−	0.696504i	$-0.245262\pi$
$277$	−4.06786	−	7.04574i	−0.244414	−	0.423337i	−0.961967	+	0.273167i	$0.911929\pi$
$278$			8.18218i			0.490735i
$279$	12.6806	−	2.56309i	0.759169	−	0.153448i
$280$			1.57449i			0.0940940i
$281$	28.6610	−	16.5474i	1.70977	−	0.987138i	0.774949	−	0.632023i	$-0.217775\pi$
$281$	28.6610	−	16.5474i	1.70977	−	0.987138i	0.934823	−	0.355114i	$-0.115558\pi$
$282$	1.38801	−	8.48865i	0.0826550	−	0.505492i
$283$	5.92146	−	10.2563i	0.351994	−	0.609672i	−0.634604	−	0.772837i	$-0.718837\pi$
$283$	5.92146	−	10.2563i	0.351994	−	0.609672i	0.986599	+	0.163165i	$0.0521703\pi$
$284$	10.6595	+	6.15424i	0.632522	+	0.365187i
$285$	−0.860042	+	5.25975i	−0.0509445	+	0.311560i
$286$	2.63315	−	17.3241i	0.155701	−	1.02440i
$287$	−0.194879			−0.0115034
$288$	−2.94053	+	0.594360i	−0.173273	+	0.0350230i
$289$	22.4179			1.31870
$290$	−0.263033	−	0.455586i	−0.0154458	−	0.0267530i
$291$	18.7136	−	22.8745i	1.09701	−	1.34093i
$292$	−0.912507	−	0.526836i	−0.0534004	−	0.0308308i
$293$	−12.8880	−	7.44091i	−0.752927	−	0.434702i	0.0738237	−	0.997271i	$-0.476480\pi$
$293$	−12.8880	−	7.44091i	−0.752927	−	0.434702i	−0.826750	+	0.562569i	$0.809813\pi$
$294$	−0.499688	−	1.32144i	−0.0291424	−	0.0770681i
$295$	2.87677	+	4.98271i	0.167492	+	0.290104i
$296$	−7.81310			−0.454127
$297$	0.943249	+	25.2359i	0.0547329	+	1.46433i
$298$	18.4642			1.06960
$299$	−1.92212	+	12.6461i	−0.111159	+	0.731343i
$300$	7.45104	−	2.81752i	0.430186	−	0.162670i
$301$	20.8634	+	12.0455i	1.20255	+	0.694290i
$302$	2.66510	−	4.61608i	0.153359	−	0.265626i
$303$	−6.80382	−	5.56618i	−0.390869	−	0.319769i
$304$	4.20891	−	2.43002i	0.241398	−	0.139371i
$305$		−	6.69264i		−	0.383220i
$306$	−5.99921	+	17.8541i	−0.342952	+	1.02065i
$307$			23.7291i			1.35429i	0.735849	+	0.677145i	$0.236783\pi$
$307$			23.7291i			1.35429i	−0.735849	+	0.677145i	$0.763217\pi$
$308$	−6.04305	−	10.4669i	−0.344335	−	0.596405i
$309$	−0.301037	+	1.84105i	−0.0171254	+	0.104733i
$310$	−2.36450	−	1.36515i	−0.134295	−	0.0775350i
$311$	4.38513	−	7.59527i	0.248658	−	0.430688i	−0.714496	−	0.699640i	$-0.753344\pi$
$311$	4.38513	−	7.59527i	0.248658	−	0.430688i	0.963154	+	0.268952i	$0.0866772\pi$
$312$	4.18448	+	4.63575i	0.236899	+	0.262448i
$313$	−5.14061	−	8.90380i	−0.290565	−	0.503273i	0.683379	−	0.730064i	$-0.260510\pi$
$313$	−5.14061	−	8.90380i	−0.290565	−	0.503273i	−0.973943	+	0.226791i	$0.927176\pi$
$314$		−	2.93840i		−	0.165824i
$315$	−3.54166	+	3.12537i	−0.199550	+	0.176094i
$316$	−3.37676			−0.189958
$317$	5.03088	−	2.90458i	0.282562	−	0.163137i	−0.352020	−	0.935992i	$-0.614505\pi$
$317$	5.03088	−	2.90458i	0.282562	−	0.163137i	0.634583	+	0.772855i	$0.281172\pi$
$318$	6.97550	−	8.52650i	0.391166	−	0.478142i
$319$	3.49716	+	2.01909i	0.195804	+	0.113047i
$320$	0.548308	+	0.316566i	0.0306514	+	0.0176966i
$321$	14.8524	−	5.61626i	0.828980	−	0.313469i
$322$	4.41124	+	7.64050i	0.245829	+	0.425788i
$323$		−	30.5131i		−	1.69779i
$324$	−7.17390	−	5.43462i	−0.398550	−	0.301923i
$325$	−12.9519	−	10.3550i	−0.718440	−	0.574394i
$326$	−3.70526	−	6.41769i	−0.205215	−	0.355443i
$327$	6.06510	+	16.0394i	0.335401	+	0.886979i
$328$	−0.0391823	+	0.0678657i	−0.00216348	+	0.00374725i
$329$	−6.17482	+	10.6951i	−0.340429	+	0.589640i
$330$	3.37469	−	4.12505i	0.185771	−	0.227077i
$331$	9.26705	−	5.35033i	0.509363	−	0.294081i	−0.223209	−	0.974771i	$-0.571653\pi$
$331$	9.26705	−	5.35033i	0.509363	−	0.294081i	0.732572	+	0.680690i	$0.238320\pi$
$332$		−	15.2137i		−	0.834961i
$333$	−15.5090	−	17.5748i	−0.849888	−	0.963091i
$334$	0.0891003			0.00487535
$335$	−2.49599	−	4.32317i	−0.136370	−	0.236200i
$336$	4.25087	+	0.695076i	0.231904	+	0.0379195i
$337$	−0.977254	+	1.69265i	−0.0532344	+	0.0922047i	−0.891415	−	0.453189i	$-0.850286\pi$
$337$	−0.977254	+	1.69265i	−0.0532344	+	0.0922047i	0.838180	+	0.545393i	$0.183620\pi$
$338$	3.86259	−	12.4129i	0.210097	−	0.675173i
$339$	1.85080	−	11.3189i	0.100521	−	0.614758i
$340$	3.44248	−	1.98752i	0.186695	−	0.107788i
$341$	20.9582			1.13495
$342$	13.8208	+	4.64394i	0.747341	+	0.251115i
$343$			19.4362i			1.04946i
$344$	8.38954	−	4.84370i	0.452334	−	0.261155i
$345$	−2.46342	+	3.01116i	−0.132626	+	0.162116i
$346$	6.58039	+	3.79919i	0.353764	+	0.204246i
$347$	−2.17035	+	3.75915i	−0.116510	+	0.201802i	−0.918383	−	0.395694i	$-0.870504\pi$
$347$	−2.17035	+	3.75915i	−0.116510	+	0.201802i	0.801872	+	0.597496i	$0.203838\pi$
$348$	−1.34613	+	0.509022i	−0.0721599	+	0.0272864i
$349$	24.2212	−	13.9841i	1.29653	−	0.748552i	0.316727	−	0.948517i	$-0.397416\pi$
$349$	24.2212	−	13.9841i	1.29653	−	0.748552i	0.979803	+	0.199964i	$0.0640827\pi$
$350$	−11.4373			−0.611350
$351$	−2.12146	+	18.6145i	−0.113235	+	0.993568i
$352$	−4.86004			−0.259041
$353$	14.5560	−	8.40389i	0.774736	−	0.447294i	−0.0598256	−	0.998209i	$-0.519054\pi$
$353$	14.5560	−	8.40389i	0.774736	−	0.447294i	0.834561	+	0.550915i	$0.185721\pi$
$354$	14.7225	−	5.56712i	0.782490	−	0.295889i
$355$	3.89645	−	6.74884i	0.206802	−	0.358191i
$356$	0.515365	+	0.297546i	0.0273143	+	0.0157699i
$357$	17.1235	−	20.9310i	0.906274	−	1.10778i
$358$	20.6036	−	11.8955i	1.08893	−	0.628695i
$359$			20.0302i			1.05715i	0.848886	+	0.528576i	$0.177274\pi$
$359$			20.0302i			1.05715i	−0.848886	+	0.528576i	$0.822726\pi$
$360$	0.376308	+	1.86175i	0.0198332	+	0.0981226i
$361$	−4.61995			−0.243155
$362$	−1.41361	+	0.816146i	−0.0742975	+	0.0428957i
$363$	−3.52731	+	21.5719i	−0.185136	+	1.13223i
$364$	−3.26545	−	8.35064i	−0.171156	−	0.437693i
$365$	−0.333557	+	0.577737i	−0.0174592	+	0.0302402i
$366$	−18.0690	−	2.95454i	−0.944483	−	0.154436i
$367$	−16.8691	−	29.2181i	−0.880560	−	1.52517i	−0.850720	−	0.525620i	$-0.823834\pi$
$367$	−16.8691	−	29.2181i	−0.880560	−	1.52517i	−0.0298400	−	0.999555i	$-0.509500\pi$
$368$	3.54768			0.184936
$369$	−0.230433	+	0.0465767i	−0.0119959	+	0.00242469i
$370$			4.94673i			0.257168i
$371$	−13.6978	+	7.90845i	−0.711156	+	0.410586i
$372$	−4.72950	+	5.78110i	−0.245213	+	0.299736i
$373$	−6.98145	+	12.0922i	−0.361486	+	0.626112i	−0.988206	−	0.153133i	$-0.951064\pi$
$373$	−6.98145	+	12.0922i	−0.361486	+	0.626112i	0.626720	+	0.779245i	$0.284397\pi$
$374$	−15.2565	+	26.4251i	−0.788897	+	1.36641i
$375$	−3.72321	−	9.84615i	−0.192266	−	0.508453i
$376$	2.48301	+	4.30069i	0.128051	+	0.221791i
$377$	2.33992	+	1.87077i	0.120512	+	0.0963496i
$378$	6.87446	+	10.9416i	0.353584	+	0.562776i
$379$		−	29.7828i		−	1.52984i	−0.644124	−	0.764921i	$-0.722778\pi$
$379$		−	29.7828i		−	1.52984i	0.644124	−	0.764921i	$-0.277222\pi$
$380$	−1.53852	−	2.66480i	−0.0789245	−	0.136701i
$381$	28.8519	−	10.9100i	1.47813	−	0.558937i
$382$	2.74212	+	1.58316i	0.140299	+	0.0810018i
$383$	2.06820	+	1.19408i	0.105680	+	0.0610146i	0.551909	−	0.833905i	$-0.313900\pi$
$383$	2.06820	+	1.19408i	0.105680	+	0.0610146i	−0.446228	+	0.894919i	$0.647233\pi$
$384$	1.09673	−	1.34059i	0.0559673	−	0.0684117i
$385$	−6.62691	+	3.82605i	−0.337739	+	0.194993i
$386$	−16.4614			−0.837864
$387$	27.5486	+	9.25666i	1.40038	+	0.470543i
$388$			17.0630i			0.866244i
$389$	−12.3362	−	21.3670i	−0.625473	−	1.08335i	−0.988449	−	0.151552i	$-0.951573\pi$
$389$	−12.3362	−	21.3670i	−0.625473	−	1.08335i	0.362977	−	0.931798i	$-0.381760\pi$
$390$	2.93504	−	2.64932i	0.148622	−	0.134154i
$391$	11.1368	−	19.2895i	0.563213	−	0.975514i
$392$	0.706382	+	0.407830i	0.0356777	+	0.0205985i
$393$	−3.36957	+	20.6072i	−0.169972	+	1.03950i
$394$	5.71756	+	9.90311i	0.288047	+	0.498911i
$395$			2.13794i			0.107571i
$396$	−9.64716	−	10.9321i	−0.484788	−	0.549361i
$397$			9.36279i			0.469905i	0.972007	+	0.234952i	$0.0754934\pi$
$397$			9.36279i			0.469905i	−0.972007	+	0.234952i	$0.924507\pi$
$398$	−11.4301	+	6.59914i	−0.572937	+	0.330785i
$399$	−16.2025	−	13.2552i	−0.811139	−	0.663590i
$400$	−2.29957	+	3.98298i	−0.114979	+	0.199149i
$401$	−5.99814	−	3.46303i	−0.299533	−	0.172935i	0.342700	−	0.939445i	$-0.388659\pi$
$401$	−5.99814	−	3.46303i	−0.299533	−	0.172935i	−0.642233	+	0.766509i	$0.721992\pi$
$402$	−12.7737	+	4.83023i	−0.637095	+	0.240910i
$403$	15.3719	+	2.33642i	0.765728	+	0.116385i
$404$	5.07524			0.252503
$405$	−3.44083	+	4.54203i	−0.170976	+	0.225695i
$406$	2.06630			0.102549
$407$	−18.9860	−	32.8847i	−0.941100	−	1.63003i
$408$	−3.84625	−	10.1715i	−0.190418	−	0.503566i
$409$	−16.1011	−	9.29599i	−0.796149	−	0.459657i	0.0459735	−	0.998943i	$-0.485361\pi$
$409$	−16.1011	−	9.29599i	−0.796149	−	0.459657i	−0.842123	+	0.539286i	$0.818694\pi$
$410$	0.0429679	+	0.0248075i	0.00212203	+	0.00122516i
$411$	0.334257	−	0.408579i	0.0164877	−	0.0201537i
$412$	−0.538522	−	0.932747i	−0.0265311	−	0.0459532i
$413$	−22.5989			−1.11202
$414$	7.04214	+	7.98014i	0.346102	+	0.392202i
$415$	−9.63229			−0.472831
$416$	−3.56461	−	0.541797i	−0.174769	−	0.0265638i
$417$	2.28694	−	13.9862i	0.111992	−	0.684908i
$418$	20.4555	+	11.8100i	1.00051	+	0.577645i
$419$	0.455614	−	0.789146i	0.0222582	−	0.0385523i	−0.854682	−	0.519152i	$-0.826248\pi$
$419$	0.455614	−	0.789146i	0.0222582	−	0.0385523i	0.876940	+	0.480600i	$0.159581\pi$
$420$	0.440075	−	2.69136i	0.0214735	−	0.131325i
$421$	−34.0472	+	19.6572i	−1.65936	+	0.958033i	−0.686351	+	0.727270i	$0.740789\pi$
$421$	−34.0472	+	19.6572i	−1.65936	+	0.958033i	−0.973010	+	0.230763i	$0.925878\pi$
$422$			9.27713i			0.451604i
$423$	−4.74520	+	14.1221i	−0.230720	+	0.686641i
$424$			6.36026i			0.308881i
$425$	14.4376	+	25.0066i	0.700324	+	1.21300i
$426$	−16.5006	−	13.4991i	−0.799458	−	0.654033i
$427$	22.7657	+	13.1438i	1.10171	+	0.636072i
$428$	−4.58381	+	7.93940i	−0.221567	+	0.383765i
$429$	−9.34312	+	28.8771i	−0.451090	+	1.39420i
$430$	−3.06670	−	5.31168i	−0.147890	−	0.256152i
$431$		−	38.0100i		−	1.83088i	−0.402457	−	0.915439i	$-0.631844\pi$
$431$		−	38.0100i		−	1.83088i	0.402457	−	0.915439i	$-0.368156\pi$
$432$	5.19253	−	0.194083i	0.249826	−	0.00933781i
$433$	37.5218			1.80318			0.901592	−	0.432587i	$-0.142399\pi$
$433$	37.5218			1.80318			0.901592	+	0.432587i	$0.142399\pi$
$434$	9.28735	−	5.36206i	0.445807	−	0.257387i
$435$	0.322278	+	0.852275i	0.0154520	+	0.0408635i
$436$	−8.57390	−	4.95014i	−0.410615	−	0.237069i
$437$	−14.9319	−	8.62093i	−0.714289	−	0.412395i
$438$	1.41254	+	1.15560i	0.0674939	+	0.0552165i
$439$	−5.41124	−	9.37255i	−0.258265	−	0.447327i	0.707513	−	0.706701i	$-0.249817\pi$
$439$	−5.41124	−	9.37255i	−0.258265	−	0.447327i	−0.965777	+	0.259373i	$0.916484\pi$
$440$			3.07704i			0.146692i
$441$	0.484795	+	2.39847i	0.0230855	+	0.114213i
$442$	−14.1358	+	17.6808i	−0.672373	+	0.840990i
$443$	10.5311	+	18.2403i	0.500346	+	0.866625i	1.00000		0.000399639i	$0.000127209\pi$
$443$	10.5311	+	18.2403i	0.500346	+	0.866625i	−0.499654	+	0.866225i	$0.666539\pi$
$444$	13.3553	+	2.18378i	0.633816	+	0.103638i
$445$	0.188386	−	0.326294i	0.00893036	−	0.0154678i
$446$	−7.00623	+	12.1351i	−0.331755	+	0.574616i
$447$	−31.5618	−	5.16079i	−1.49282	−	0.244097i
$448$	−2.15366	+	1.24342i	−0.101751	+	0.0587459i
$449$		−	12.0811i		−	0.570140i	−0.958507	−	0.285070i	$-0.907983\pi$
$449$		−	12.0811i		−	0.570140i	0.958507	−	0.285070i	$-0.0920169\pi$
$450$	−13.5239	+	2.73355i	−0.637524	+	0.128861i
$451$	−0.380854			−0.0179337
$452$	3.31088	+	5.73460i	0.155730	+	0.269733i
$453$	−5.84579	+	7.14560i	−0.274659	+	0.335729i
$454$	−1.38613	+	2.40085i	−0.0650545	+	0.112678i
$455$	−5.28706	+	2.06746i	−0.247861	+	0.0969241i
$456$	−7.87371	+	2.97735i	−0.368720	+	0.139427i
$457$	24.6389	−	14.2252i	1.15256	−	0.665429i	0.203048	−	0.979169i	$-0.434915\pi$
$457$	24.6389	−	14.2252i	1.15256	−	0.665429i	0.949509	+	0.313740i	$0.101582\pi$
$458$	−16.6468			−0.777853
$459$	15.2450	−	28.8422i	0.711577	−	1.34624i
$460$		−	2.24615i		−	0.104727i
$461$	14.9740	−	8.64522i	0.697407	−	0.402648i	−0.108974	−	0.994045i	$-0.534756\pi$
$461$	14.9740	−	8.64522i	0.697407	−	0.402648i	0.806381	+	0.591396i	$0.201423\pi$
$462$	7.40417	+	19.5806i	0.344473	+	0.910972i
$463$	−20.5804	−	11.8821i	−0.956452	−	0.552208i	−0.0613728	−	0.998115i	$-0.519548\pi$
$463$	−20.5804	−	11.8821i	−0.956452	−	0.552208i	−0.895079	+	0.445907i	$0.852881\pi$
$464$	0.415447	−	0.719576i	0.0192867	−	0.0334055i
$465$	3.66020	+	2.99440i	0.169738	+	0.138862i
$466$	−4.72264	+	2.72662i	−0.218772	+	0.126308i
$467$	30.5214			1.41236			0.706182	−	0.708030i	$-0.250416\pi$
$467$	30.5214			1.41236			0.706182	+	0.708030i	$0.250416\pi$
$468$	−5.85703	−	9.09369i	−0.270741	−	0.420356i
$469$	19.6076			0.905395
$470$	2.72291	−	1.57207i	0.125598	−	0.0725142i
$471$	−0.821291	+	5.02276i	−0.0378431	+	0.231436i
$472$	−4.54371	+	7.86994i	−0.209141	+	0.362243i
$473$	40.7735	+	23.5406i	1.87477	+	1.08240i
$474$	5.77207	+	0.943814i	0.265120	+	0.0433508i
$475$	19.3574	−	11.1760i	0.888179	−	0.512790i
$476$			15.6133i			0.715632i
$477$	−14.3067	+	12.6251i	−0.655061	+	0.578063i
$478$	13.6254			0.623213
$479$	−19.7570	+	11.4067i	−0.902719	+	0.521185i	−0.878081	−	0.478511i	$-0.841177\pi$
$479$	−19.7570	+	11.4067i	−0.902719	+	0.521185i	−0.0246377	+	0.999696i	$0.507843\pi$
$480$	−0.848770	−	0.694376i	−0.0387409	−	0.0316938i
$481$	−10.2594	−	26.2360i	−0.467786	−	1.19626i
$482$	9.45585	−	16.3780i	0.430702	−	0.745998i
$483$	−5.40482	−	14.2932i	−0.245928	−	0.650365i
$484$	−6.30997	−	10.9292i	−0.286817	−	0.496782i
$485$	10.8031			0.490545
$486$	10.7437	+	11.2948i	0.487345	+	0.512342i
$487$			21.9090i			0.992792i	0.868096	+	0.496396i	$0.165344\pi$
$487$			21.9090i			0.992792i	−0.868096	+	0.496396i	$0.834656\pi$
$488$	9.15449	−	5.28535i	0.414404	−	0.239256i
$489$	4.53982	+	12.0057i	0.205298	+	0.542917i
$490$	0.258210	−	0.447233i	0.0116647	−	0.0202039i
$491$	12.8330	−	22.2274i	0.579145	−	1.00311i	−0.416433	−	0.909167i	$-0.636720\pi$
$491$	12.8330	−	22.2274i	0.579145	−	1.00311i	0.995578	−	0.0939422i	$-0.0299469\pi$
$492$	0.0859448	−	0.105055i	0.00387469	−	0.00473623i
$493$	−2.60833	−	4.51776i	−0.117473	−	0.203470i
$494$	13.6866	+	10.9424i	0.615788	+	0.492324i
$495$	−6.92149	+	6.10792i	−0.311098	+	0.274531i
$496$		−	4.31236i		−	0.193630i
$497$	15.3046	+	26.5083i	0.686504	+	1.18906i
$498$	−4.25227	+	26.0056i	−0.190549	+	1.16534i
$499$	−30.0035	−	17.3226i	−1.34314	−	0.775464i	−0.355876	−	0.934533i	$-0.615817\pi$
$499$	−30.0035	−	17.3226i	−1.34314	−	0.775464i	−0.987267	+	0.159069i	$0.949151\pi$
$500$	5.26329	+	3.03876i	0.235382	+	0.135898i
$501$	−0.152304	−	0.0249038i	−0.00680442	−	0.00111262i
$502$	−1.79721	+	1.03762i	−0.0802135	+	0.0463113i
$503$	−16.8864			−0.752928			−0.376464	−	0.926431i	$-0.622860\pi$
$503$	−16.8864			−0.752928			−0.376464	+	0.926431i	$0.622860\pi$
$504$	−7.07195	−	2.37626i	−0.315010	−	0.105847i
$505$		−	3.21330i		−	0.142990i
$506$	8.62093	+	14.9319i	0.383247	+	0.663803i
$507$	−10.0720	+	20.1384i	−0.447311	+	0.894378i
$508$	−8.90441	+	15.4229i	−0.395069	+	0.684280i
$509$	−10.0617	−	5.80914i	−0.445978	−	0.257485i	0.260152	−	0.965568i	$-0.416227\pi$
$509$	−10.0617	−	5.80914i	−0.445978	−	0.257485i	−0.706130	+	0.708082i	$0.749561\pi$
$510$	−6.43992	+	2.43518i	−0.285165	+	0.107832i
$511$	−1.31015	−	2.26925i	−0.0579578	−	0.100386i
$512$			1.00000i			0.0441942i
$513$	−22.3265	−	11.8011i	−0.985740	−	0.521029i
$514$		−	25.0018i		−	1.10278i
$515$	−0.590552	+	0.340955i	−0.0260228	+	0.0150243i
$516$	−15.6945	+	5.93469i	−0.690911	+	0.261260i
$517$	−12.0675	+	20.9015i	−0.530728	+	0.919248i
$518$	−16.8268	−	9.71494i	−0.739326	−	0.426850i
$519$	−10.1863	−	8.33338i	−0.447129	−	0.365795i
$520$	−0.343029	+	2.25687i	−0.0150428	+	0.0989703i
$521$	−32.5005			−1.42387			−0.711937	−	0.702243i	$-0.752182\pi$
$521$	−32.5005			−1.42387			−0.711937	+	0.702243i	$0.752182\pi$
$522$	2.44327	−	0.493850i	0.106939	−	0.0216152i
$523$	−23.8182			−1.04150			−0.520749	−	0.853710i	$-0.674347\pi$
$523$	−23.8182			−1.04150			−0.520749	+	0.853710i	$0.674347\pi$
$524$	−6.02780	−	10.4404i	−0.263325	−	0.456093i
$525$	19.5504	+	3.19676i	0.853248	+	0.139518i
$526$	−21.8701	−	12.6267i	−0.953581	−	0.550550i
$527$	−23.4473	−	13.5373i	−1.02138	−	0.589693i
$528$	8.30750	+	1.35839i	0.361538	+	0.0591165i
$529$	5.20698	+	9.01876i	0.226391	+	0.392120i
$530$	4.02688			0.174917
$531$	−26.7219	+	5.40120i	−1.15963	+	0.234392i
$532$	12.0861			0.523999
$533$	−0.279339	−	0.0424576i	−0.0120995	−	0.00183904i
$534$	−0.797775	−	0.652657i	−0.0345231	−	0.0282432i
$535$	5.02669	+	2.90216i	0.217323	+	0.125471i
$536$	3.94228	−	6.82824i	0.170281	−	0.294935i
$537$	−38.5435	+	14.5748i	−1.66328	+	0.628948i
$538$	−20.5935	+	11.8897i	−0.887848	+	0.512600i
$539$			3.96413i			0.170747i
$540$	−0.122880	−	3.28755i	−0.00528791	−	0.141474i
$541$			32.5049i			1.39750i	0.715368	+	0.698748i	$0.246259\pi$
$541$			32.5049i			1.39750i	−0.715368	+	0.698748i	$0.753741\pi$
$542$	7.10251	+	12.3019i	0.305079	+	0.528412i
$543$	2.64446	−	0.999973i	0.113485	−	0.0429129i
$544$	5.43723	+	3.13918i	0.233119	+	0.134591i
$545$	−3.13409	+	5.42841i	−0.134250	+	0.232527i
$546$	3.24777	+	15.1869i	0.138992	+	0.649938i
$547$	4.78240	+	8.28337i	0.204481	+	0.354171i	0.949967	−	0.312350i	$-0.101116\pi$
$547$	4.78240	+	8.28337i	0.204481	+	0.354171i	−0.745486	+	0.666521i	$0.767783\pi$
$548$			0.304776i			0.0130194i
$549$	30.0605	+	10.1007i	1.28295	+	0.431086i
$550$	−22.3520			−0.953093
$551$	−3.49716	+	2.01909i	−0.148984	+	0.0860161i
$552$	−6.06423	−	0.991586i	−0.258111	−	0.0422047i
$553$	−7.27240	−	4.19872i	−0.309254	−	0.178548i
$554$	−7.04574	−	4.06786i	−0.299345	−	0.172827i
$555$	1.38262	−	8.45569i	0.0586891	−	0.358924i
$556$	4.09109	+	7.08598i	0.173501	+	0.300512i
$557$			34.6218i			1.46697i	0.679703	+	0.733487i	$0.262109\pi$
$557$			34.6218i			1.46697i	−0.679703	+	0.733487i	$0.737891\pi$
$558$	9.70020	−	8.56002i	0.410642	−	0.362374i
$559$	27.2811	+	21.8113i	1.15387	+	0.922521i
$560$	0.787247	+	1.36355i	0.0332673	+	0.0576206i
$561$	33.4647	−	40.9055i	1.41288	−	1.72703i
$562$	16.5474	−	28.6610i	0.698012	−	1.20899i
$563$	−3.42757	+	5.93673i	−0.144455	+	0.250203i	−0.929169	−	0.369654i	$-0.879476\pi$
$563$	−3.42757	+	5.93673i	−0.144455	+	0.250203i	0.784715	+	0.619857i	$0.212810\pi$
$564$	−3.04227	−	8.04540i	−0.128103	−	0.338772i
$565$	3.63076	−	2.09622i	0.152747	−	0.0881887i
$566$		−	11.8429i		−	0.497795i
$567$	−8.69265	−	20.6245i	−0.365057	−	0.866147i
$568$	12.3085			0.516452
$569$	10.6617	+	18.4665i	0.446960	+	0.774158i	0.998186	−	0.0601979i	$-0.0191732\pi$
$569$	10.6617	+	18.4665i	0.446960	+	0.774158i	−0.551226	+	0.834356i	$0.685840\pi$
$570$	1.88505	+	4.98509i	0.0789563	+	0.208803i
$571$	−4.72379	+	8.18185i	−0.197685	+	0.342400i	−0.947777	−	0.318933i	$-0.896675\pi$
$571$	−4.72379	+	8.18185i	−0.197685	+	0.342400i	0.750093	+	0.661333i	$0.230009\pi$
$572$	−6.38169	−	16.3197i	−0.266832	−	0.682362i
$573$	−4.24475	−	3.47261i	−0.177327	−	0.145071i
$574$	−0.168771	+	0.0974397i	−0.00704435	+	0.00406706i
$575$	16.3163			0.680436
$576$	−2.24940	+	1.98500i	−0.0937249	+	0.0827082i
$577$		−	25.5692i		−	1.06446i	−0.846599	−	0.532231i	$-0.821354\pi$
$577$		−	25.5692i		−	1.06446i	0.846599	−	0.532231i	$-0.178646\pi$
$578$	19.4145	−	11.2090i	0.807536	−	0.466231i
$579$	28.1383	+	4.60101i	1.16939	+	0.191211i
$580$	−0.455586	−	0.263033i	−0.0189172	−	0.0109218i
$581$	18.9170	−	32.7652i	0.784809	−	1.35933i
$582$	4.76916	−	29.1667i	0.197688	−	1.20900i
$583$	−26.7698	+	15.4555i	−1.10869	+	0.640103i
$584$	−1.05367			−0.0436013
$585$	−5.75751	+	3.70827i	−0.238044	+	0.153318i
$586$	−14.8818			−0.614762
$587$	6.72060	−	3.88014i	0.277389	−	0.160151i	−0.354852	−	0.934923i	$-0.615469\pi$
$587$	6.72060	−	3.88014i	0.277389	−	0.160151i	0.632241	+	0.774772i	$0.282135\pi$
$588$	−1.09346	−	0.894559i	−0.0450937	−	0.0368910i
$589$	−10.4791	+	18.1503i	−0.431784	+	0.747872i
$590$	4.98271	+	2.87677i	0.205135	+	0.118435i
$591$	−7.00537	−	18.5260i	−0.288163	−	0.762056i
$592$	−6.76635	+	3.90655i	−0.278095	+	0.160558i
$593$		−	4.65405i		−	0.191119i	−0.995424	−	0.0955594i	$-0.969536\pi$
$593$		−	4.65405i		−	0.191119i	0.995424	−	0.0955594i	$-0.0304640\pi$
$594$	13.4348	+	21.3833i	0.551237	+	0.877366i
$595$	9.88525			0.405256
$596$	15.9905	−	9.23210i	0.654995	−	0.378161i
$597$	21.3824	−	8.08552i	0.875125	−	0.330918i
$598$	4.65845	+	11.9129i	0.190498	+	0.487155i
$599$	−13.2758	+	22.9943i	−0.542433	+	0.939521i	0.456331	+	0.889810i	$0.349163\pi$
$599$	−13.2758	+	22.9943i	−0.542433	+	0.939521i	−0.998764	+	0.0497107i	$0.984170\pi$
$600$	5.04403	−	6.16556i	0.205922	−	0.251708i
$601$	16.7970	+	29.0933i	0.685165	+	1.18674i	0.973385	+	0.229176i	$0.0736033\pi$
$601$	16.7970	+	29.0933i	0.685165	+	1.18674i	−0.288220	+	0.957564i	$0.593063\pi$
$602$	24.0910			0.981874
$603$	23.1848	−	4.68627i	0.944159	−	0.190840i
$604$		−	5.33019i		−	0.216882i
$605$	−6.91962	+	3.99505i	−0.281323	+	0.162422i
$606$	−8.67537	−	1.41854i	−0.352413	−	0.0576244i
$607$	7.17582	−	12.4289i	0.291258	−	0.504473i	−0.682850	−	0.730559i	$-0.739260\pi$
$607$	7.17582	−	12.4289i	0.291258	−	0.504473i	0.974107	+	0.226086i	$0.0725929\pi$
$608$	2.43002	−	4.20891i	0.0985502	−	0.170694i
$609$	−3.53202	−	0.577535i	−0.143125	−	0.0234029i
$610$	−3.34632	−	5.79600i	−0.135489	−	0.234673i
$611$	−11.1811	+	13.9850i	−0.452337	+	0.565773i
$612$	3.73161	+	18.4617i	0.150841	+	0.746272i
$613$		−	32.5357i		−	1.31410i	−0.753845	−	0.657052i	$-0.771803\pi$
$613$		−	32.5357i		−	1.31410i	0.753845	−	0.657052i	$-0.228197\pi$
$614$	11.8645	+	20.5500i	0.478814	+	0.829330i
$615$	−0.0665134	−	0.0544144i	−0.00268208	−	0.00219420i
$616$	−10.4669	−	6.04305i	−0.421722	−	0.243481i
$617$	17.4197	+	10.0573i	0.701292	+	0.404891i	0.807828	−	0.589418i	$-0.200643\pi$
$617$	17.4197	+	10.0573i	0.701292	+	0.404891i	−0.106537	+	0.994309i	$0.533976\pi$
$618$	0.659817	+	1.74491i	0.0265417	+	0.0701906i
$619$	12.2002	−	7.04379i	0.490367	−	0.283114i	−0.234359	−	0.972150i	$-0.575299\pi$
$619$	12.2002	−	7.04379i	0.490367	−	0.283114i	0.724727	+	0.689036i	$0.241966\pi$
$620$	−2.73029			−0.109651
$621$	−9.80701	−	15.6091i	−0.393542	−	0.626374i
$622$		−	8.77026i		−	0.351655i
$623$	0.739948	+	1.28163i	0.0296454	+	0.0513473i
$624$	5.94174	+	1.92244i	0.237860	+	0.0769591i
$625$	−9.57392	+	16.5825i	−0.382957	+	0.663301i
$626$	−8.90380	−	5.14061i	−0.355867	−	0.205460i
$627$	−31.6647	−	25.9047i	−1.26456	−	1.03454i
$628$	−1.46920	−	2.54473i	−0.0586275	−	0.101546i
$629$			49.0535i			1.95589i
$630$	−1.50449	+	4.47748i	−0.0599401	+	0.178387i
$631$		−	15.6969i		−	0.624885i	−0.949937	−	0.312443i	$-0.898853\pi$
$631$		−	15.6969i		−	0.624885i	0.949937	−	0.312443i	$-0.101147\pi$
$632$	−2.92436	+	1.68838i	−0.116325	+	0.0671602i
$633$	2.59298	−	15.8579i	0.103062	−	0.630294i
$634$	2.90458	−	5.03088i	0.115356	−	0.199802i
$635$	9.76472	+	5.63766i	0.387501	+	0.223724i
$636$	1.77771	−	10.8719i	0.0704907	−	0.431099i
$637$	−0.441921	+	2.90751i	−0.0175096	+	0.115200i
$638$	4.03818			0.159873
$639$	24.4323	+	27.6867i	0.966527	+	1.09527i
$640$	0.633132			0.0250267
$641$	6.43804	+	11.1510i	0.254287	+	0.440439i	0.964702	−	0.263345i	$-0.0848258\pi$
$641$	6.43804	+	11.1510i	0.254287	+	0.440439i	−0.710414	+	0.703784i	$0.751492\pi$
$642$	10.0544	−	12.2900i	0.396817	−	0.485049i
$643$	−29.3762	−	16.9604i	−1.15849	−	0.668852i	−0.207545	−	0.978225i	$-0.566547\pi$
$643$	−29.3762	−	16.9604i	−1.15849	−	0.668852i	−0.950941	+	0.309373i	$0.899881\pi$
$644$	7.64050	+	4.41124i	0.301078	+	0.173827i
$645$	3.75744	+	9.93668i	0.147949	+	0.391256i
$646$	−15.2565	−	26.4251i	−0.600261	−	1.03968i
$647$	−4.53172			−0.178160			−0.0890802	−	0.996024i	$-0.528393\pi$
$647$	−4.53172			−0.178160			−0.0890802	+	0.996024i	$0.528393\pi$
$648$	−8.93009	−	1.11957i	−0.350807	−	0.0439808i
$649$	−44.1652			−1.73364
$650$	−16.3942	−	2.49180i	−0.643032	−	0.0977365i
$651$	−17.3740	+	6.56979i	−0.680943	+	0.257490i
$652$	−6.41769	−	3.70526i	−0.251336	−	0.145109i
$653$	−2.39149	+	4.14217i	−0.0935861	+	0.162096i	−0.909018	−	0.416758i	$-0.863166\pi$
$653$	−2.39149	+	4.14217i	−0.0935861	+	0.162096i	0.815432	+	0.578854i	$0.196500\pi$
$654$	13.2722	+	10.8580i	0.518985	+	0.424580i
$655$	−6.61018	+	3.81639i	−0.258281	+	0.149119i
$656$			0.0783645i			0.00305962i
$657$	−2.09154	−	2.37013i	−0.0815986	−	0.0924674i
$658$			12.3496i			0.481439i
$659$	9.88260	+	17.1172i	0.384972	+	0.666790i	0.991765	−	0.128069i	$-0.0408779\pi$
$659$	9.88260	+	17.1172i	0.384972	+	0.666790i	−0.606794	+	0.794859i	$0.707545\pi$
$660$	0.860042	−	5.25975i	0.0334771	−	0.204735i
$661$	23.8446	+	13.7667i	0.927449	+	0.535463i	0.886004	−	0.463678i	$-0.153471\pi$
$661$	23.8446	+	13.7667i	0.927449	+	0.535463i	0.0414449	+	0.999141i	$0.486804\pi$
$662$	5.35033	−	9.26705i	0.207947	−	0.360174i
$663$	29.1049	−	26.2717i	1.13034	−	1.02031i
$664$	−7.60686	−	13.1755i	−0.295203	−	0.511307i
$665$		−	7.65210i		−	0.296736i
$666$	−22.2186	−	7.46570i	−0.860952	−	0.289290i
$667$	−2.94775			−0.114137
$668$	0.0771631	−	0.0445501i	0.00298553	−	0.00172370i
$669$	15.3679	−	18.7850i	0.594158	−	0.726269i
$670$	−4.32317	−	2.49599i	−0.167019	−	0.0964283i
$671$	44.4911	+	25.6870i	1.71756	+	0.991635i
$672$	4.02890	−	1.52348i	0.155418	−	0.0587695i
$673$	−21.7825	−	37.7284i	−0.839653	−	1.45432i	−0.890185	−	0.455600i	$-0.849425\pi$
$673$	−21.7825	−	37.7284i	−0.839653	−	1.45432i	0.0505315	−	0.998722i	$-0.483908\pi$
$674$			1.95451i			0.0752848i
$675$	23.8812	−	0.892614i	0.919187	−	0.0343567i
$676$	−2.86136	−	12.6812i	−0.110052	−	0.487738i
$677$	−24.1766	−	41.8751i	−0.929181	−	1.60939i	−0.784694	−	0.619883i	$-0.787180\pi$
$677$	−24.1766	−	41.8751i	−0.929181	−	1.60939i	−0.144487	−	0.989507i	$-0.546153\pi$
$678$	−4.05661	−	10.7278i	−0.155793	−	0.412000i
$679$	−21.2164	+	36.7480i	−0.814212	+	1.41026i
$680$	1.98752	−	3.44248i	0.0762178	−	0.132013i
$681$	3.04043	−	3.71647i	0.116510	−	0.142416i
$682$	18.1503	−	10.4791i	0.695012	−	0.401266i
$683$			25.6842i			0.982779i	0.870940	+	0.491390i	$0.163511\pi$
$683$			25.6842i			0.982779i	−0.870940	+	0.491390i	$0.836489\pi$
$684$	14.2911	−	2.88861i	0.546434	−	0.110449i
$685$	0.192963			0.00737275
$686$	9.71812	+	16.8323i	0.371040	+	0.642659i
$687$	28.4552	+	4.65282i	1.08563	+	0.177516i
$688$	4.84370	−	8.38954i	0.184664	−	0.319848i
$689$	−21.3574	+	8.35163i	−0.813651	+	0.318172i
$690$	−0.627805	+	3.83946i	−0.0239001	+	0.146166i
$691$	−3.65761	+	2.11172i	−0.139142	+	0.0803338i	−0.567955	−	0.823060i	$-0.692265\pi$
$691$	−3.65761	+	2.11172i	−0.139142	+	0.0803338i	0.428813	+	0.903393i	$0.358932\pi$
$692$	7.59838			0.288847
$693$	−7.18349	−	35.5396i	−0.272878	−	1.35004i
$694$			4.34070i			0.164771i
$695$	4.48636	−	2.59020i	0.170177	−	0.0982519i
$696$	−0.911268	+	1.11389i	−0.0345415	+	0.0422218i
$697$	0.426086	+	0.246001i	0.0161391	+	0.00931794i
$698$	13.9841	−	24.2212i	0.529306	−	0.916785i
$699$	8.83475	−	3.34076i	0.334161	−	0.126359i
$700$	−9.90500	+	5.71865i	−0.374374	+	0.216145i
$701$	−7.76144			−0.293145			−0.146573	−	0.989200i	$-0.546824\pi$
$701$	−7.76144			−0.293145			−0.146573	+	0.989200i	$0.546824\pi$
$702$	7.47001	+	17.1814i	0.281937	+	0.648469i
$703$	37.9720			1.43214
$704$	−4.20891	+	2.43002i	−0.158629	+	0.0915847i
$705$	−5.09380	+	1.92616i	−0.191844	+	0.0725434i
$706$	8.40389	−	14.5560i	0.316285	−	0.547821i
$707$	10.9303	+	6.31064i	0.411078	+	0.237336i
$708$	9.96646	−	12.1825i	0.374563	−	0.457846i
$709$	37.1354	−	21.4401i	1.39465	−	0.805200i	0.400822	−	0.916156i	$-0.368725\pi$
$709$	37.1354	−	21.4401i	1.39465	−	0.805200i	0.993825	+	0.110956i	$0.0353912\pi$
$710$		−	7.79289i		−	0.292462i
$711$	−9.60269	−	3.22662i	−0.360129	−	0.121008i
$712$	0.595093			0.0223020
$713$	−13.2492	+	7.64943i	−0.496186	+	0.286473i
$714$	4.36395	−	26.6885i	0.163317	−	0.998793i
$715$	−10.3325	+	4.04045i	−0.386415	+	0.151104i
$716$	11.8955	−	20.6036i	0.444555	−	0.769991i
$717$	−23.2907	−	3.80835i	−0.869806	−	0.142225i
$718$	10.0151	+	17.3467i	0.373760	+	0.647371i
$719$	−0.181195			−0.00675742			−0.00337871	−	0.999994i	$-0.501075\pi$
$719$	−0.181195			−0.00675742			−0.00337871	+	0.999994i	$0.501075\pi$
$720$	1.25677	+	1.42416i	0.0468369	+	0.0530755i
$721$		−	2.67843i		−	0.0997499i
$722$	−4.00099	+	2.30997i	−0.148902	+	0.0859683i
$723$	−20.7411	+	25.3528i	−0.771369	+	0.942882i
$724$	−0.816146	+	1.41361i	−0.0303318	+	0.0525363i
$725$	1.91070	−	3.30943i	0.0709617	−	0.122909i
$726$	7.73122	+	20.4455i	0.286932	+	0.758803i
$727$	16.1693	+	28.0061i	0.599688	+	1.03869i	0.992867	+	0.119228i	$0.0380420\pi$
$727$	16.1693	+	28.0061i	0.599688	+	1.03869i	−0.393179	+	0.919462i	$0.628625\pi$
$728$	−7.00329	−	5.59914i	−0.259559	−	0.207518i
$729$	−15.2079	−	22.3097i	−0.563254	−	0.826284i
$730$			0.667114i			0.0246910i
$731$	−30.4105	−	52.6726i	−1.12477	−	1.94817i
$732$	−17.1255	+	6.47580i	−0.632976	+	0.239353i
$733$	40.0538	+	23.1251i	1.47942	+	0.854143i	0.999729	−	0.0232941i	$-0.00741540\pi$
$733$	40.0538	+	23.1251i	1.47942	+	0.854143i	0.479691	+	0.877437i	$0.340749\pi$
$734$	−29.2181	−	16.8691i	−1.07846	−	0.622650i
$735$	−0.566374	+	0.692307i	−0.0208910	+	0.0255361i
$736$	3.07238	−	1.77384i	0.113249	−	0.0653846i
$737$	38.3193			1.41151
$738$	−0.176273	+	0.155553i	−0.00648869	+	0.00572600i
$739$		−	8.94056i		−	0.328884i	−0.986387	−	0.164442i	$-0.947418\pi$
$739$		−	8.94056i		−	0.328884i	0.986387	−	0.164442i	$-0.0525823\pi$
$740$	2.47336	+	4.28399i	0.0909226	+	0.157483i
$741$	−20.3367	−	22.5299i	−0.747087	−	0.827657i
$742$	−7.90845	+	13.6978i	−0.290328	+	0.502864i
$743$	13.6805	+	7.89847i	0.501891	+	0.289767i	0.729494	−	0.683987i	$-0.239756\pi$
$743$	13.6805	+	7.89847i	0.501891	+	0.289767i	−0.227603	+	0.973754i	$0.573089\pi$
$744$	−1.20531	+	7.37133i	−0.0441890	+	0.270246i
$745$	−5.84513	−	10.1241i	−0.214149	−	0.370917i
$746$			13.9629i			0.511218i
$747$	14.5373	−	43.2641i	0.531890	−	1.58295i
$748$			30.5131i			1.11567i
$749$	−19.7440	+	11.3992i	−0.721429	+	0.416517i
$750$	−8.14747	−	6.66541i	−0.297503	−	0.243386i
$751$	−23.7961	+	41.2161i	−0.868333	+	1.50400i	−0.00463416	+	0.999989i	$0.501475\pi$
$751$	−23.7961	+	41.2161i	−0.868333	+	1.50400i	−0.863699	+	0.504008i	$0.831858\pi$
$752$	4.30069	+	2.48301i	0.156830	+	0.0905459i
$753$	3.36208	−	1.27133i	0.122521	−	0.0463299i
$754$	2.96182	+	0.450176i	0.107863	+	0.0163944i
$755$	−3.37471			−0.122818
$756$	11.4243	+	6.03849i	0.415497	+	0.219618i
$757$	−36.6710			−1.33283			−0.666414	−	0.745582i	$-0.732172\pi$
$757$	−36.6710			−1.33283			−0.666414	+	0.745582i	$0.732172\pi$
$758$	−14.8914	−	25.7927i	−0.540881	−	0.936833i
$759$	−10.5627	−	27.9334i	−0.383401	−	1.01392i
$760$	−2.66480	−	1.53852i	−0.0966624	−	0.0558081i
$761$	−19.9038	−	11.4915i	−0.721514	−	0.416566i	0.0937959	−	0.995591i	$-0.470100\pi$
$761$	−19.9038	−	11.4915i	−0.721514	−	0.416566i	−0.815310	+	0.579025i	$0.803433\pi$
$762$	19.5315	−	23.8743i	0.707551	−	0.864875i
$763$	−12.3102	−	21.3219i	−0.445658	−	0.771903i
$764$	3.16633			0.114554
$765$	11.6887	−	2.36260i	0.422607	−	0.0854201i
$766$	2.38816			0.0862876
$767$	−32.3931	−	4.92353i	−1.16965	−	0.177778i
$768$	0.279503	−	1.70935i	0.0100857	−	0.0616809i
$769$	−1.49286	−	0.861901i	−0.0538338	−	0.0310810i	0.472842	−	0.881147i	$-0.343228\pi$
$769$	−1.49286	−	0.861901i	−0.0538338	−	0.0310810i	−0.526675	+	0.850067i	$0.676562\pi$
$770$	−3.82605	+	6.62691i	−0.137881	+	0.238817i
$771$	−6.98807	+	42.7369i	−0.251669	+	1.53913i
$772$	−14.2560	+	8.23071i	−0.513085	+	0.296230i
$773$		−	7.86189i		−	0.282772i	−0.989955	−	0.141386i	$-0.954844\pi$
$773$		−	7.86189i		−	0.282772i	0.989955	−	0.141386i	$-0.0451559\pi$
$774$	28.4861	−	5.75781i	1.02391	−	0.206960i
$775$		−	19.8331i		−	0.712428i
$776$	8.53151	+	14.7770i	0.306263	+	0.530464i
$777$	26.0475	+	21.3094i	0.934449	+	0.764469i
$778$	−21.3670	−	12.3362i	−0.766044	−	0.442276i
$779$	0.190427	−	0.329830i	0.00682276	−	0.0118174i
$780$	1.21716	−	3.76190i	0.0435812	−	0.134698i
$781$	29.9098	+	51.8053i	1.07026	+	1.85374i
$782$		−	22.2736i		−	0.796504i
$783$	−4.31444	+	0.161262i	−0.154186	+	0.00576304i
$784$	0.815659			0.0291307
$785$	−1.61115	+	0.930198i	−0.0575044	+	0.0332002i
$786$	7.38548	+	19.5312i	0.263431	+	0.696654i
$787$	22.7512	+	13.1354i	0.810991	+	0.468226i	0.847300	−	0.531115i	$-0.178227\pi$
$787$	22.7512	+	13.1354i	0.810991	+	0.468226i	−0.0363089	+	0.999341i	$0.511560\pi$
$788$	9.90311	+	5.71756i	0.352784	+	0.203680i
$789$	33.8544	+	27.6962i	1.20525	+	0.986011i
$790$	1.06897	+	1.85151i	0.0380322	+	0.0658737i
$791$			16.4672i			0.585506i
$792$	−13.8208	−	4.64394i	−0.491099	−	0.165015i
$793$	29.7686	+	23.8001i	1.05711	+	0.845166i
$794$	4.68139	+	8.10841i	0.166136	+	0.287757i
$795$	−6.88335	−	1.12552i	−0.244127	−	0.0399182i
$796$	−6.59914	+	11.4301i	−0.233900	+	0.405127i
$797$	−5.38194	+	9.32179i	−0.190638	+	0.330195i	−0.945462	−	0.325733i	$-0.894389\pi$
$797$	−5.38194	+	9.32179i	−0.190638	+	0.330195i	0.754824	+	0.655928i	$0.227722\pi$
$798$	−20.6594	−	3.37810i	−0.731334	−	0.119583i
$799$	27.0013	−	15.5892i	0.955238	−	0.551507i
$800$			4.59914i			0.162604i
$801$	1.18126	+	1.33860i	0.0417377	+	0.0472971i
$802$	−6.92606			−0.244568
$803$	−2.56044	−	4.43482i	−0.0903560	−	0.156501i
$804$	−8.64725	+	10.5700i	−0.304965	+	0.372774i
$805$	2.79290	−	4.83744i	0.0984368	−	0.170498i
$806$	14.4806	−	5.66254i	0.510059	−	0.199454i
$807$	38.5247	−	14.5677i	1.35613	−	0.512806i
$808$	4.39529	−	2.53762i	0.154626	−	0.0892732i
$809$	2.05900			0.0723905			0.0361952	−	0.999345i	$-0.488476\pi$
$809$	2.05900			0.0723905			0.0361952	+	0.999345i	$0.488476\pi$
$810$	−0.708835	+	5.65393i	−0.0249059	+	0.198659i
$811$			12.5483i			0.440630i	0.975429	+	0.220315i	$0.0707086\pi$
$811$			12.5483i			0.440630i	−0.975429	+	0.220315i	$0.929291\pi$
$812$	1.78946	−	1.03315i	0.0627979	−	0.0362564i
$813$	−8.70226	−	23.0134i	−0.305202	−	0.807117i
$814$	−32.8847	−	18.9860i	−1.15261	−	0.665458i
$815$	−2.34592	+	4.06325i	−0.0821739	+	0.142329i
$816$	−8.41671	−	6.88568i	−0.294644	−	0.241047i
$817$	−40.7735	+	23.5406i	−1.42648	+	0.823580i
$818$	−18.5920			−0.650053
$819$	−1.30681	−	26.8675i	−0.0456637	−	0.938825i
$820$	0.0496151			0.00173263
$821$	−23.7509	+	13.7126i	−0.828911	+	0.478572i	−0.853480	−	0.521126i	$-0.825512\pi$
$821$	−23.7509	+	13.7126i	−0.828911	+	0.478572i	0.0245686	+	0.999698i	$0.492179\pi$
$822$	0.0851856	−	0.520968i	0.00297119	−	0.0181709i
$823$	1.97058	−	3.41315i	0.0686902	−	0.118975i	−0.829635	−	0.558306i	$-0.811451\pi$
$823$	1.97058	−	3.41315i	0.0686902	−	0.118975i	0.898325	+	0.439332i	$0.144785\pi$
$824$	−0.932747	−	0.538522i	−0.0324938	−	0.0187603i
$825$	38.2074	+	6.24744i	1.33021	+	0.217508i
$826$	−19.5712	+	11.2995i	−0.680970	+	0.393158i
$827$		−	31.5551i		−	1.09728i	−0.836060	−	0.548639i	$-0.815146\pi$
$827$		−	31.5551i		−	1.09728i	0.836060	−	0.548639i	$-0.184854\pi$
$828$	10.0887	+	3.38994i	0.350608	+	0.117808i
$829$	−48.2865			−1.67706			−0.838529	−	0.544857i	$-0.816584\pi$
$829$	−48.2865			−1.67706			−0.838529	+	0.544857i	$0.816584\pi$
$830$	−8.34181	+	4.81615i	−0.289548	+	0.167171i
$831$	10.9067	+	8.92269i	0.378348	+	0.309525i
$832$	−3.35794	+	1.31310i	−0.116416	+	0.0455234i
$833$	2.56050	−	4.43492i	0.0887162	−	0.153661i
$834$	−5.01256	−	13.2559i	−0.173571	−	0.459014i
$835$	−0.0282061	−	0.0488544i	−0.000976113	−	0.00169068i
$836$	23.6199			0.816913
$837$	−18.9736	+	11.9208i	−0.655823	+	0.412044i
$838$		−	0.911227i		−	0.0314778i
$839$	18.8067	−	10.8581i	0.649279	−	0.374862i	−0.138901	−	0.990306i	$-0.544357\pi$
$839$	18.8067	−	10.8581i	0.649279	−	0.374862i	0.788180	+	0.615445i	$0.211024\pi$
$840$	−0.964564	−	2.55082i	−0.0332806	−	0.0880118i
$841$	14.1548	−	24.5168i	0.488097	−	0.845408i
$842$	−19.6572	+	34.0472i	−0.677431	+	1.17335i
$843$	−36.2962	+	44.3666i	−1.25011	+	1.52807i
$844$	4.63857	+	8.03423i	0.159666	+	0.276550i
$845$	−8.02887	+	1.81162i	−0.276201	+	0.0623215i
$846$	2.95160	+	14.6027i	0.101478	+	0.502052i
$847$		−	31.3837i		−	1.07836i
$848$	3.18013	+	5.50815i	0.109206	+	0.189150i
$849$	−3.31013	+	20.2437i	−0.113603	+	0.694762i
$850$	25.0066	+	14.4376i	0.857719	+	0.495204i
$851$	24.0048	+	13.8592i	0.822875	+	0.475087i
$852$	−21.0395	−	3.44025i	−0.720801	−	0.117861i
$853$	12.8491	−	7.41846i	0.439946	−	0.254003i	−0.263629	−	0.964624i	$-0.584919\pi$
$853$	12.8491	−	7.41846i	0.439946	−	0.254003i	0.703575	+	0.710621i	$0.251586\pi$
$854$	26.2876			0.899541
$855$	−1.82887	−	9.04815i	−0.0625461	−	0.309440i
$856$			9.16763i			0.313343i
$857$	−4.26503	−	7.38725i	−0.145691	−	0.252344i	0.783940	−	0.620837i	$-0.213207\pi$
$857$	−4.26503	−	7.38725i	−0.145691	−	0.252344i	−0.929630	+	0.368493i	$0.879874\pi$
$858$	6.34715	+	29.6798i	0.216688	+	1.01325i
$859$	10.1420	−	17.5665i	0.346042	−	0.599362i	−0.639500	−	0.768791i	$-0.720859\pi$
$859$	10.1420	−	17.5665i	0.346042	−	0.599362i	0.985543	+	0.169428i	$0.0541921\pi$
$860$	−5.31168	−	3.06670i	−0.181127	−	0.104574i
$861$	0.315723	−	0.119387i	0.0107598	−	0.00406869i
$862$	−19.0050	−	32.9176i	−0.647313	−	1.12118i
$863$		−	17.3161i		−	0.589447i	−0.955583	−	0.294723i	$-0.904772\pi$
$863$		−	17.3161i		−	0.589447i	0.955583	−	0.294723i	$-0.0952275\pi$
$864$	4.39982	−	2.76434i	0.149685	−	0.0940449i
$865$		−	4.81078i		−	0.163571i
$866$	32.4949	−	18.7609i	1.10422	−	0.637522i
$867$	−36.3191	+	13.7336i	−1.23346	+	0.466418i
$868$	5.36206	−	9.28735i	0.182000	−	0.315233i
$869$	−14.2125	−	8.20560i	−0.482126	−	0.278356i
$870$	0.705238	+	0.576953i	0.0239098	+	0.0195605i
$871$	28.1054	+	4.27183i	0.952316	+	0.144745i
$872$	−9.90028			−0.335266
$873$	−16.3043	+	48.5231i	−0.551818	+	1.64226i
$874$	−17.2419			−0.583214
$875$	7.55690	+	13.0889i	0.255470	+	0.442487i
$876$	1.80109	+	0.294504i	0.0608534	+	0.00995037i
$877$	−7.51181	−	4.33695i	−0.253656	−	0.146448i	0.367781	−	0.929912i	$-0.380118\pi$
$877$	−7.51181	−	4.33695i	−0.253656	−	0.146448i	−0.621437	+	0.783464i	$0.713451\pi$
$878$	−9.37255	−	5.41124i	−0.316308	−	0.182621i
$879$	25.4382	+	4.15951i	0.858010	+	0.140297i
$880$	1.53852	+	2.66480i	0.0518636	+	0.0898303i
$881$	2.08434			0.0702232			0.0351116	−	0.999383i	$-0.488821\pi$
$881$	2.08434			0.0702232			0.0351116	+	0.999383i	$0.488821\pi$
$882$	1.61908	+	1.83474i	0.0545173	+	0.0617789i
$883$	22.5903			0.760224			0.380112	−	0.924941i	$-0.375885\pi$
$883$	22.5903			0.760224			0.380112	+	0.924941i	$0.375885\pi$
$884$	−3.40160	+	22.3799i	−0.114408	+	0.752719i
$885$	−7.71313	−	6.31008i	−0.259274	−	0.212111i
$886$	18.2403	+	10.5311i	0.612796	+	0.353798i
$887$	−26.4409	+	45.7970i	−0.887799	+	1.53771i	−0.0453268	+	0.998972i	$0.514433\pi$
$887$	−26.4409	+	45.7970i	−0.887799	+	1.53771i	−0.842472	+	0.538740i	$0.818900\pi$
$888$	12.6579	−	4.78645i	0.424773	−	0.160623i
$889$	−38.3541	+	22.1438i	−1.28636	+	0.742678i
$890$		−	0.376772i		−	0.0126294i
$891$	−16.9881	−	40.3066i	−0.569123	−	1.35032i
$892$			14.0125i			0.469172i
$893$	−12.0675	−	20.9015i	−0.403823	−	0.699443i
$894$	−29.9137	+	11.3115i	−1.00046	+	0.378314i
$895$	−13.0448	−	7.53140i	−0.436039	−	0.251747i
$896$	−1.24342	+	2.15366i	−0.0415396	+	0.0719488i
$897$	−4.63323	−	21.6654i	−0.154699	−	0.723386i
$898$	−6.04053	−	10.4625i	−0.201575	−	0.349138i
$899$			3.58311i			0.119503i
$900$	−10.3453	+	9.12929i	−0.344843	+	0.304310i
$901$	39.9320			1.33033
$902$	−0.329830	+	0.190427i	−0.0109821	+	0.00634053i
$903$	−41.1799	−	6.73349i	−1.37038	−	0.224076i
$904$	5.73460	+	3.31088i	0.190730	+	0.110118i
$905$	0.894999	+	0.516728i	0.0297508	+	0.0171766i
$906$	−1.48980	+	9.11116i	−0.0494954	+	0.302698i
$907$	27.8451	+	48.2290i	0.924580	+	1.60142i	0.792236	+	0.610215i	$0.208917\pi$
$907$	27.8451	+	48.2290i	0.924580	+	1.60142i	0.132344	+	0.991204i	$0.457750\pi$
$908$			2.77227i			0.0920010i
$909$	14.4328	+	4.84957i	0.478704	+	0.160850i
$910$	−3.54500	+	4.43400i	−0.117516	+	0.146986i
$911$	19.2465	+	33.3359i	0.637665	+	1.10447i	0.985944	+	0.167078i	$0.0534330\pi$
$911$	19.2465	+	33.3359i	0.637665	+	1.10447i	−0.348278	+	0.937391i	$0.613234\pi$
$912$	−5.33015	+	6.51531i	−0.176499	+	0.215744i
$913$	36.9696	−	64.0332i	1.22352	−	2.11919i
$914$	14.2252	−	24.6389i	0.470529	−	0.814981i
$915$	4.10004	+	10.8427i	0.135543	+	0.358449i
$916$	−14.4165	+	8.32339i	−0.476336	+	0.275012i
$917$		−	29.9802i		−	0.990035i
$918$	−1.21852	−	32.6006i	−0.0402172	−	1.07598i
$919$	−26.0262			−0.858525			−0.429263	−	0.903180i	$-0.641227\pi$
$919$	−26.0262			−0.858525			−0.429263	+	0.903180i	$0.641227\pi$
$920$	−1.12307	−	1.94522i	−0.0370267	−	0.0641321i
$921$	−14.5369	−	38.4433i	−0.479007	−	1.26675i
$922$	8.64522	−	14.9740i	0.284715	−	0.493141i
$923$	16.1622	+	41.3312i	0.531986	+	1.36043i
$924$	16.2025	+	13.2552i	0.533023	+	0.436064i
$925$	−31.1194	+	17.9668i	−1.02320	+	0.590745i
$926$	−23.7642			−0.780940
$927$	−0.640152	−	3.16708i	−0.0210253	−	0.104021i
$928$		−	0.830894i		−	0.0272754i
$929$	−1.69730	+	0.979934i	−0.0556865	+	0.0321506i	−0.527585	−	0.849502i	$-0.676902\pi$
$929$	−1.69730	+	0.979934i	−0.0556865	+	0.0321506i	0.471898	+	0.881653i	$0.343569\pi$
$930$	4.66702	+	0.763123i	0.153038	+	0.0250238i
$931$	−3.43304	−	1.98207i	−0.112513	−	0.0649596i
$932$	−2.72662	+	4.72264i	−0.0893134	+	0.154695i
$933$	−2.45131	+	14.9914i	−0.0802523	+	0.490798i
$934$	26.4323	−	15.2607i	0.864893	−	0.499346i
$935$	19.3188			0.631793
$936$	−9.61918	−	4.94685i	−0.314413	−	0.161693i
$937$	−42.2865			−1.38144			−0.690720	−	0.723122i	$-0.742706\pi$
$937$	−42.2865			−1.38144			−0.690720	+	0.723122i	$0.742706\pi$
$938$	16.9807	−	9.80380i	0.554439	−	0.320105i
$939$	13.7829	+	11.2757i	0.449788	+	0.367970i
$940$	1.57207	−	2.72291i	0.0512753	−	0.0888114i
$941$	−50.0947	−	28.9222i	−1.63304	−	0.942836i	−0.983148	−	0.182810i	$-0.941481\pi$
$941$	−50.0947	−	28.9222i	−1.63304	−	0.942836i	−0.649892	−	0.760027i	$-0.725186\pi$
$942$	1.80012	+	4.76048i	0.0586511	+	0.155105i
$943$	0.240766	−	0.139006i	0.00784041	−	0.00452666i
$944$			9.08742i			0.295770i
$945$	3.82316	−	7.23307i	0.124367	−	0.235292i
$946$	47.0811			1.53074
$947$	14.8043	−	8.54727i	0.481075	−	0.277749i	−0.239789	−	0.970825i	$-0.577078\pi$
$947$	14.8043	−	8.54727i	0.481075	−	0.277749i	0.720864	+	0.693076i	$0.243745\pi$
$948$	5.47067	−	2.06867i	0.177679	−	0.0671872i
$949$	−1.38357	−	3.53817i	−0.0449127	−	0.114854i
$950$	11.1760	−	19.3574i	0.362597	−	0.628037i
$951$	−6.37109	+	7.78770i	−0.206597	+	0.252533i
$952$	7.80663	+	13.5215i	0.253014	+	0.438234i
$953$	19.8333			0.642465			0.321233	−	0.947000i	$-0.395903\pi$
$953$	19.8333			0.642465			0.321233	+	0.947000i	$0.395903\pi$
$954$	−6.07745	+	18.0870i	−0.196765	+	0.585589i
$955$		−	2.00470i		−	0.0648707i
$956$	11.8000	−	6.81272i	0.381639	−	0.220339i
$957$	−6.90266	−	1.12868i	−0.223131	−	0.0364851i
$958$	−11.4067	+	19.7570i	−0.368533	+	0.638319i
$959$	−0.378963	+	0.656383i	−0.0122374	+	0.0211957i
$960$	−1.08224	−	0.176962i	−0.0349293	−	0.00571143i
$961$	−6.20179	−	10.7418i	−0.200058	−	0.346510i
$962$	−22.0028	−	17.5913i	−0.709400	−	0.567167i
$963$	−20.6216	+	18.1977i	−0.664523	+	0.586413i
$964$		−	18.9117i		−	0.609105i
$965$	5.21113	+	9.02593i	0.167752	+	0.290555i
$966$	−11.8273	−	9.67590i	−0.380538	−	0.311317i
$967$	19.0476	+	10.9971i	0.612530	+	0.353644i	0.773955	−	0.633241i	$-0.218276\pi$
$967$	19.0476	+	10.9971i	0.612530	+	0.353644i	−0.161425	+	0.986885i	$0.551609\pi$
$968$	−10.9292	−	6.30997i	−0.351278	−	0.202810i
$969$	18.6929	+	49.4340i	0.600502	+	1.58805i
$970$	9.35580	−	5.40157i	0.300397	−	0.173434i
$971$	−16.0662			−0.515589			−0.257794	−	0.966200i	$-0.582996\pi$
$971$	−16.0662			−0.515589			−0.257794	+	0.966200i	$0.582996\pi$
$972$	14.9517	+	4.40972i	0.479577	+	0.141442i
$973$			20.3477i			0.652318i
$974$	10.9545	+	18.9738i	0.351005	+	0.607958i
$975$	27.3269	+	8.84157i	0.875161	+	0.283157i
$976$	5.28535	−	9.15449i	0.169180	−	0.293028i
$977$	−1.21231	−	0.699926i	−0.0387851	−	0.0223926i	0.480482	−	0.877005i	$-0.340462\pi$
$977$	−1.21231	−	0.699926i	−0.0387851	−	0.0223926i	−0.519267	+	0.854612i	$0.673795\pi$
$978$	9.93445	+	8.12734i	0.317669	+	0.259884i
$979$	1.44609	+	2.50469i	0.0462171	+	0.0800504i
$980$		−	0.516420i		−	0.0164964i
$981$	−19.6520	−	22.2697i	−0.627441	−	0.711016i
$982$		−	25.6660i		−	0.819035i
$983$	−11.4778	+	6.62671i	−0.366085	+	0.211359i	−0.671747	−	0.740781i	$-0.734456\pi$
$983$	−11.4778	+	6.62671i	−0.366085	+	0.211359i	0.305662	+	0.952140i	$0.401122\pi$
$984$	0.0219031	−	0.133952i	0.000698245	−	0.00427025i
$985$	3.61997	−	6.26998i	0.115342	−	0.199778i
$986$	−4.51776	−	2.60833i	−0.143875	−	0.0830662i
$987$	3.45176	−	21.1099i	0.109871	−	0.671935i
$988$	17.3241	+	2.63315i	0.551154	+	0.0837717i
$989$	−34.3678			−1.09283
$990$	−2.94023	+	8.75036i	−0.0934465	+	0.278105i
$991$	5.66549			0.179970			0.0899851	−	0.995943i	$-0.471318\pi$
$991$	5.66549			0.179970			0.0899851	+	0.995943i	$0.471318\pi$
$992$	−2.15618	−	3.73461i	−0.0684587	−	0.118574i
$993$	−11.7358	+	14.3452i	−0.372423	+	0.455231i
$994$	26.5083	+	15.3046i	0.840792	+	0.485431i
$995$	7.23673	+	4.17813i	0.229420	+	0.132456i
$996$	9.32021	+	24.6476i	0.295322	+	0.780990i
$997$	−2.82880	−	4.89963i	−0.0895891	−	0.155173i	0.817748	−	0.575576i	$-0.195222\pi$
$997$	−2.82880	−	4.89963i	−0.0895891	−	0.155173i	−0.907338	+	0.420403i	$0.861889\pi$
$998$	−34.6451			−1.09667
$999$	35.8926	+	18.9716i	1.13559	+	0.600236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.t.a.103.8	yes	28
3.2	odd	2		702.2.t.a.415.5		28
9.2	odd	6		702.2.t.a.181.10		28
9.4	even	3		2106.2.b.c.649.12		14
9.5	odd	6		2106.2.b.d.649.3		14
9.7	even	3	inner	234.2.t.a.25.1	✓	28
13.12	even	2	inner	234.2.t.a.103.1	yes	28
39.38	odd	2		702.2.t.a.415.10		28
117.25	even	6	inner	234.2.t.a.25.8	yes	28
117.38	odd	6		702.2.t.a.181.5		28
117.77	odd	6		2106.2.b.d.649.12		14
117.103	even	6		2106.2.b.c.649.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.t.a.25.1	✓	28	9.7	even	3	inner
234.2.t.a.25.8	yes	28	117.25	even	6	inner
234.2.t.a.103.1	yes	28	13.12	even	2	inner
234.2.t.a.103.8	yes	28	1.1	even	1	trivial
702.2.t.a.181.5		28	117.38	odd	6
702.2.t.a.181.10		28	9.2	odd	6
702.2.t.a.415.5		28	3.2	odd	2
702.2.t.a.415.10		28	39.38	odd	2
2106.2.b.c.649.3		14	117.103	even	6
2106.2.b.c.649.12		14	9.4	even	3
2106.2.b.d.649.3		14	9.5	odd	6
2106.2.b.d.649.12		14	117.77	odd	6

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.62009 + 0.612619i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.548308 - 0.316566i) q^{5} +(-1.09673 + 1.34059i) q^{6} +(2.15366 - 1.24342i) q^{7} -1.00000i q^{8} +(2.24940 - 1.98500i) q^{9} -0.633132 q^{10} +(4.20891 - 2.43002i) q^{11} +(-0.279503 + 1.70935i) q^{12} +(3.35794 - 1.31310i) q^{13} +(1.24342 - 2.15366i) q^{14} +(1.08224 + 0.176962i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.27837 q^{17} +(0.955536 - 2.84376i) q^{18} +4.86004i q^{19} +(-0.548308 + 0.316566i) q^{20} +(-2.72739 + 3.33382i) q^{21} +(2.43002 - 4.20891i) q^{22} +(-1.77384 + 3.07238i) q^{23} +(0.612619 + 1.62009i) q^{24} +(-2.29957 - 3.98298i) q^{25} +(2.25152 - 2.81615i) q^{26} +(-2.42818 + 4.59390i) q^{27} -2.48683i q^{28} +(0.415447 + 0.719576i) q^{29} +(1.02573 - 0.387868i) q^{30} +(3.73461 + 2.15618i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.33015 + 6.51531i) q^{33} +(-5.43723 + 3.13918i) q^{34} -1.57449 q^{35} +(-0.594360 - 2.94053i) q^{36} -7.81310i q^{37} +(2.43002 + 4.20891i) q^{38} +(-4.63575 + 4.18448i) q^{39} +(-0.316566 + 0.548308i) q^{40} +(-0.0678657 - 0.0391823i) q^{41} +(-0.695076 + 4.25087i) q^{42} +(4.84370 + 8.38954i) q^{43} -4.86004i q^{44} +(-1.86175 + 0.376308i) q^{45} +3.54768i q^{46} +(-4.30069 + 2.48301i) q^{47} +(1.34059 + 1.09673i) q^{48} +(-0.407830 + 0.706382i) q^{49} +(-3.98298 - 2.29957i) q^{50} +(10.1715 - 3.84625i) q^{51} +(0.541797 - 3.56461i) q^{52} -6.36026 q^{53} +(0.194083 + 5.19253i) q^{54} -3.07704 q^{55} +(-1.24342 - 2.15366i) q^{56} +(-2.97735 - 7.87371i) q^{57} +(0.719576 + 0.415447i) q^{58} +(-7.86994 - 4.54371i) q^{59} +(0.694376 - 0.848770i) q^{60} +(5.28535 + 9.15449i) q^{61} +4.31236 q^{62} +(2.37626 - 7.07195i) q^{63} -1.00000 q^{64} +(-2.25687 - 0.343029i) q^{65} +(-1.35839 + 8.30750i) q^{66} +(6.82824 + 3.94228i) q^{67} +(-3.13918 + 5.43723i) q^{68} +(0.991586 - 6.06423i) q^{69} +(-1.36355 + 0.787247i) q^{70} +12.3085i q^{71} +(-1.98500 - 2.24940i) q^{72} -1.05367i q^{73} +(-3.90655 - 6.76635i) q^{74} +(6.16556 + 5.04403i) q^{75} +(4.20891 + 2.43002i) q^{76} +(6.04305 - 10.4669i) q^{77} +(-1.92244 + 5.94174i) q^{78} +(-1.68838 - 2.92436i) q^{79} +0.633132i q^{80} +(1.11957 - 8.93009i) q^{81} -0.0783645 q^{82} +(13.1755 - 7.60686i) q^{83} +(1.52348 + 4.02890i) q^{84} +(3.44248 + 1.98752i) q^{85} +(8.38954 + 4.84370i) q^{86} +(-1.11389 - 0.911268i) q^{87} +(-2.43002 - 4.20891i) q^{88} +0.595093i q^{89} +(-1.42416 + 1.25677i) q^{90} +(5.59914 - 7.00329i) q^{91} +(1.77384 + 3.07238i) q^{92} +(-7.37133 - 1.20531i) q^{93} +(-2.48301 + 4.30069i) q^{94} +(1.53852 - 2.66480i) q^{95} +(1.70935 + 0.279503i) q^{96} +(-14.7770 + 8.53151i) q^{97} +0.815659i q^{98} +(4.64394 - 13.8208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49}+ \cdots + 8 q^{92}+O(q^{100}) \) 28 * q + 14 * q^4 - 16 * q^9 + 2 * q^13 + 8 * q^14 - 14 * q^16 + 16 * q^17 - 8 * q^23 + 14 * q^25 + 8 * q^26 + 18 * q^27 - 16 * q^29 - 8 * q^30 - 68 * q^35 - 8 * q^36 - 8 * q^39 - 10 * q^42 - 4 * q^43 + 10 * q^49 + 58 * q^51 - 2 * q^52 - 120 * q^53 - 8 * q^56 + 28 * q^61 + 68 * q^62 - 28 * q^64 - 8 * q^65 - 24 * q^66 + 8 * q^68 - 92 * q^69 + 16 * q^74 + 32 * q^75 - 24 * q^77 - 22 * q^78 + 28 * q^79 + 8 * q^81 - 48 * q^82 + 68 * q^87 - 50 * q^90 + 8 * q^92

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