LMFDB - Embedded newform 234.2.t.a.103.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(25,234)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			103.4
Character	$\chi$	$=$	234.103
Dual form			234.2.t.a.25.4

$q$-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} +(-0.215223 - 1.71863i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.40542 - 1.38877i) q^{5} +(1.04570 + 1.38076i) q^{6} +(-0.759011 + 0.438215i) q^{7} +1.00000i q^{8} +(-2.90736 + 0.739776i) q^{9} +2.77754 q^{10} +(-1.92848 + 1.11341i) q^{11} +(-1.59599 - 0.672925i) q^{12} +(0.180130 + 3.60105i) q^{13} +(0.438215 - 0.759011i) q^{14} +(-1.86908 + 4.43292i) q^{15} +(-0.500000 - 0.866025i) q^{16} -3.80878 q^{17} +(2.14796 - 2.09434i) q^{18} -2.22681i q^{19} +(-2.40542 + 1.38877i) q^{20} +(0.916486 + 1.21014i) q^{21} +(1.11341 - 1.92848i) q^{22} +(0.259586 - 0.449617i) q^{23} +(1.71863 - 0.215223i) q^{24} +(1.35738 + 2.35105i) q^{25} +(-1.95652 - 3.02853i) q^{26} +(1.89713 + 4.83745i) q^{27} +0.876431i q^{28} +(-3.81355 - 6.60527i) q^{29} +(-0.597791 - 4.77356i) q^{30} +(-4.97617 - 2.87299i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.32858 + 3.07470i) q^{33} +(3.29850 - 1.90439i) q^{34} +2.43433 q^{35} +(-0.813014 + 2.88773i) q^{36} -11.3538i q^{37} +(1.11341 + 1.92848i) q^{38} +(6.15009 - 1.08460i) q^{39} +(1.38877 - 2.40542i) q^{40} +(-3.52286 - 2.03392i) q^{41} +(-1.39877 - 0.589772i) q^{42} +(2.81683 + 4.87889i) q^{43} +2.22681i q^{44} +(8.02081 + 2.25818i) q^{45} +0.519173i q^{46} +(0.920402 - 0.531395i) q^{47} +(-1.38076 + 1.04570i) q^{48} +(-3.11593 + 5.39696i) q^{49} +(-2.35105 - 1.35738i) q^{50} +(0.819736 + 6.54587i) q^{51} +(3.20866 + 1.64453i) q^{52} +7.29301 q^{53} +(-4.06169 - 3.24079i) q^{54} +6.18508 q^{55} +(-0.438215 - 0.759011i) q^{56} +(-3.82706 + 0.479262i) q^{57} +(6.60527 + 3.81355i) q^{58} +(3.52376 + 2.03444i) q^{59} +(2.90448 + 3.83513i) q^{60} +(-3.94905 - 6.83995i) q^{61} +5.74599 q^{62} +(1.88254 - 1.83555i) q^{63} -1.00000 q^{64} +(4.56775 - 8.91221i) q^{65} +(-3.55397 - 1.49848i) q^{66} +(5.95399 + 3.43754i) q^{67} +(-1.90439 + 3.29850i) q^{68} +(-0.828593 - 0.349364i) q^{69} +(-2.10819 + 1.21716i) q^{70} +15.9569i q^{71} +(-0.739776 - 2.90736i) q^{72} -5.24797i q^{73} +(5.67689 + 9.83267i) q^{74} +(3.74843 - 2.83883i) q^{75} +(-1.92848 - 1.11341i) q^{76} +(0.975824 - 1.69018i) q^{77} +(-4.78383 + 4.01434i) q^{78} +(-7.09690 - 12.2922i) q^{79} +2.77754i q^{80} +(7.90546 - 4.30159i) q^{81} +4.06784 q^{82} +(-0.641385 + 0.370304i) q^{83} +(1.50626 - 0.188628i) q^{84} +(9.16172 + 5.28952i) q^{85} +(-4.87889 - 2.81683i) q^{86} +(-10.5312 + 7.97568i) q^{87} +(-1.11341 - 1.92848i) q^{88} -9.89914i q^{89} +(-8.07532 + 2.05476i) q^{90} +(-1.71476 - 2.65430i) q^{91} +(-0.259586 - 0.449617i) q^{92} +(-3.86662 + 9.17052i) q^{93} +(-0.531395 + 0.920402i) q^{94} +(-3.09254 + 5.35643i) q^{95} +(0.672925 - 1.59599i) q^{96} +(-13.6212 + 7.86418i) q^{97} -6.23187i q^{98} +(4.78310 - 4.66372i) 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
$3$	−0.215223	−	1.71863i	−0.124259	−	0.992250i
$3$	−0.215223	−	1.71863i	−0.124259	−	0.992250i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.40542	−	1.38877i	−1.07574	−	0.621078i	−0.145995	−	0.989285i	$-0.546638\pi$
$5$	−2.40542	−	1.38877i	−1.07574	−	0.621078i	−0.929744	+	0.368207i	$0.879972\pi$
$6$	1.04570	+	1.38076i	0.426906	+	0.563694i
$7$	−0.759011	+	0.438215i	−0.286879	+	0.165630i	−0.636534	−	0.771249i	$-0.719632\pi$
$7$	−0.759011	+	0.438215i	−0.286879	+	0.165630i	0.349654	+	0.936879i	$0.386299\pi$
$8$			1.00000i			0.353553i
$9$	−2.90736	+	0.739776i	−0.969119	+	0.246592i
$10$	2.77754			0.878337
$11$	−1.92848	+	1.11341i	−0.581458	+	0.335705i	−0.761713	−	0.647915i	$-0.775641\pi$
$11$	−1.92848	+	1.11341i	−0.581458	+	0.335705i	0.180255	+	0.983620i	$0.442308\pi$
$12$	−1.59599	−	0.672925i	−0.460722	−	0.194257i
$13$	0.180130	+	3.60105i	0.0499590	+	0.998751i
$13$	0.180130	+	3.60105i	0.0499590	+	0.998751i
$14$	0.438215	−	0.759011i	0.117118	−	0.202854i
$15$	−1.86908	+	4.43292i	−0.482594	+	1.14458i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.80878			−0.923764			−0.461882	−	0.886941i	$-0.652826\pi$
$17$	−3.80878			−0.923764			−0.461882	+	0.886941i	$0.652826\pi$
$18$	2.14796	−	2.09434i	0.506279	−	0.493642i
$19$		−	2.22681i		−	0.510866i	−0.966827	−	0.255433i	$-0.917782\pi$
$19$		−	2.22681i		−	0.510866i	0.966827	−	0.255433i	$-0.0822181\pi$
$20$	−2.40542	+	1.38877i	−0.537869	+	0.310539i
$21$	0.916486	+	1.21014i	0.199994	+	0.264075i
$22$	1.11341	−	1.92848i	0.237379	−	0.411153i
$23$	0.259586	−	0.449617i	0.0541275	−	0.0937516i	−0.837692	−	0.546143i	$-0.816096\pi$
$23$	0.259586	−	0.449617i	0.0541275	−	0.0937516i	0.891820	+	0.452391i	$0.149429\pi$
$24$	1.71863	−	0.215223i	0.350813	−	0.0439322i
$25$	1.35738	+	2.35105i	0.271476	+	0.470209i
$26$	−1.95652	−	3.02853i	−0.383705	−	0.593945i
$27$	1.89713	+	4.83745i	0.365103	+	0.930967i
$28$			0.876431i			0.165630i
$29$	−3.81355	−	6.60527i	−0.708159	−	1.22657i	−0.965539	−	0.260257i	$-0.916193\pi$
$29$	−3.81355	−	6.60527i	−0.708159	−	1.22657i	0.257381	−	0.966310i	$-0.417141\pi$
$30$	−0.597791	−	4.77356i	−0.109141	−	0.871530i
$31$	−4.97617	−	2.87299i	−0.893747	−	0.516005i	−0.0185805	−	0.999827i	$-0.505915\pi$
$31$	−4.97617	−	2.87299i	−0.893747	−	0.516005i	−0.875166	+	0.483822i	$0.839248\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	2.32858	+	3.07470i	0.405355	+	0.535237i
$34$	3.29850	−	1.90439i	0.565688	−	0.326600i
$35$	2.43433			0.411476
$36$	−0.813014	+	2.88773i	−0.135502	+	0.481289i
$37$		−	11.3538i		−	1.86655i	−0.359161	−	0.933276i	$-0.616937\pi$
$37$		−	11.3538i		−	1.86655i	0.359161	−	0.933276i	$-0.383063\pi$
$38$	1.11341	+	1.92848i	0.180619	+	0.312840i
$39$	6.15009	−	1.08460i	0.984803	−	0.173676i
$40$	1.38877	−	2.40542i	0.219584	−	0.380331i
$41$	−3.52286	−	2.03392i	−0.550178	−	0.317645i	0.199016	−	0.979996i	$-0.436225\pi$
$41$	−3.52286	−	2.03392i	−0.550178	−	0.317645i	−0.749194	+	0.662351i	$0.769559\pi$
$42$	−1.39877	−	0.589772i	−0.215835	−	0.0910038i
$43$	2.81683	+	4.87889i	0.429562	+	0.744023i	0.996834	−	0.0795072i	$-0.0253347\pi$
$43$	2.81683	+	4.87889i	0.429562	+	0.744023i	−0.567272	+	0.823530i	$0.692001\pi$
$44$			2.22681i			0.335705i
$45$	8.02081	+	2.25818i	1.19567	+	0.336630i
$46$			0.519173i			0.0765479i
$47$	0.920402	−	0.531395i	0.134254	−	0.0775119i	−0.431368	−	0.902176i	$-0.641969\pi$
$47$	0.920402	−	0.531395i	0.134254	−	0.0775119i	0.565623	+	0.824664i	$0.308636\pi$
$48$	−1.38076	+	1.04570i	−0.199296	+	0.150934i
$49$	−3.11593	+	5.39696i	−0.445133	+	0.770994i
$50$	−2.35105	−	1.35738i	−0.332488	−	0.191962i
$51$	0.819736	+	6.54587i	0.114786	+	0.916605i
$52$	3.20866	+	1.64453i	0.444962	+	0.228055i
$53$	7.29301			1.00177			0.500886	−	0.865513i	$-0.333008\pi$
$53$	7.29301			1.00177			0.500886	+	0.865513i	$0.333008\pi$
$54$	−4.06169	−	3.24079i	−0.552725	−	0.441015i
$55$	6.18508			0.833996
$56$	−0.438215	−	0.759011i	−0.0585590	−	0.101427i
$57$	−3.82706	+	0.479262i	−0.506907	+	0.0634797i
$58$	6.60527	+	3.81355i	0.867314	+	0.500744i
$59$	3.52376	+	2.03444i	0.458754	+	0.264862i	0.711520	−	0.702666i	$-0.248007\pi$
$59$	3.52376	+	2.03444i	0.458754	+	0.264862i	−0.252766	+	0.967527i	$0.581340\pi$
$60$	2.90448	+	3.83513i	0.374967	+	0.495113i
$61$	−3.94905	−	6.83995i	−0.505624	−	0.875766i	−0.999979	−	0.00650624i	$-0.997929\pi$
$61$	−3.94905	−	6.83995i	−0.505624	−	0.875766i	0.494355	−	0.869260i	$-0.335404\pi$
$62$	5.74599			0.729741
$63$	1.88254	−	1.83555i	0.237177	−	0.231257i
$64$	−1.00000			−0.125000
$65$	4.56775	−	8.91221i	0.566560	−	1.10542i
$66$	−3.55397	−	1.49848i	−0.437463	−	0.184450i
$67$	5.95399	+	3.43754i	0.727395	+	0.419962i	0.817468	−	0.575973i	$-0.195377\pi$
$67$	5.95399	+	3.43754i	0.727395	+	0.419962i	−0.0900733	+	0.995935i	$0.528710\pi$
$68$	−1.90439	+	3.29850i	−0.230941	+	0.400002i
$69$	−0.828593	−	0.349364i	−0.0997508	−	0.0420585i
$70$	−2.10819	+	1.21716i	−0.251977	+	0.145479i
$71$			15.9569i			1.89374i	0.321622	+	0.946868i	$0.395772\pi$
$71$			15.9569i			1.89374i	−0.321622	+	0.946868i	$0.604228\pi$
$72$	−0.739776	−	2.90736i	−0.0871834	−	0.342635i
$73$		−	5.24797i		−	0.614228i	−0.951673	−	0.307114i	$-0.900637\pi$
$73$		−	5.24797i		−	0.614228i	0.951673	−	0.307114i	$-0.0993633\pi$
$74$	5.67689	+	9.83267i	0.659926	+	1.14302i
$75$	3.74843	−	2.83883i	0.432832	−	0.327799i
$76$	−1.92848	−	1.11341i	−0.221212	−	0.127717i
$77$	0.975824	−	1.69018i	0.111206	−	0.192614i
$78$	−4.78383	+	4.01434i	−0.541663	+	0.454535i
$79$	−7.09690	−	12.2922i	−0.798463	−	1.38298i	−0.920617	−	0.390468i	$-0.872313\pi$
$79$	−7.09690	−	12.2922i	−0.798463	−	1.38298i	0.122153	−	0.992511i	$-0.461020\pi$
$80$			2.77754i			0.310539i
$81$	7.90546	−	4.30159i	0.878385	−	0.477954i
$82$	4.06784			0.449218
$83$	−0.641385	+	0.370304i	−0.0704011	+	0.0406461i	−0.534787	−	0.844987i	$-0.679608\pi$
$83$	−0.641385	+	0.370304i	−0.0704011	+	0.0406461i	0.464386	+	0.885633i	$0.346275\pi$
$84$	1.50626	−	0.188628i	0.164346	−	0.0205810i
$85$	9.16172	+	5.28952i	0.993729	+	0.573729i
$86$	−4.87889	−	2.81683i	−0.526104	−	0.303746i
$87$	−10.5312	+	7.97568i	−1.12907	+	0.855082i
$88$	−1.11341	−	1.92848i	−0.118690	−	0.205576i
$89$		−	9.89914i		−	1.04931i	−0.851316	−	0.524653i	$-0.824195\pi$
$89$		−	9.89914i		−	1.04931i	0.851316	−	0.524653i	$-0.175805\pi$
$90$	−8.07532	+	2.05476i	−0.851213	+	0.216591i
$91$	−1.71476	−	2.65430i	−0.179755	−	0.278246i
$92$	−0.259586	−	0.449617i	−0.0270638	−	0.0468758i
$93$	−3.86662	+	9.17052i	−0.400950	+	0.950938i
$94$	−0.531395	+	0.920402i	−0.0548092	+	0.0949323i
$95$	−3.09254	+	5.35643i	−0.317288	+	0.549559i
$96$	0.672925	−	1.59599i	0.0686801	−	0.162890i
$97$	−13.6212	+	7.86418i	−1.38302	+	0.798486i	−0.992516	−	0.122116i	$-0.961032\pi$
$97$	−13.6212	+	7.86418i	−1.38302	+	0.798486i	−0.390503	+	0.920602i	$0.627699\pi$
$98$		−	6.23187i		−	0.629514i
$99$	4.78310	−	4.66372i	0.480720	−	0.468721i
$100$	2.71476			0.271476
$101$	−9.76705	−	16.9170i	−0.971858	−	1.68331i	−0.689937	−	0.723870i	$-0.742362\pi$
$101$	−9.76705	−	16.9170i	−0.971858	−	1.68331i	−0.281921	−	0.959438i	$-0.590972\pi$
$102$	−3.98285	−	5.25902i	−0.394360	−	0.520720i
$103$	−4.09254	+	7.08848i	−0.403250	+	0.698449i	−0.994116	−	0.108320i	$-0.965453\pi$
$103$	−4.09254	+	7.08848i	−0.403250	+	0.698449i	0.590866	+	0.806770i	$0.298786\pi$
$104$	−3.60105	+	0.180130i	−0.353112	+	0.0176632i
$105$	−0.523923	−	4.18370i	−0.0511296	−	0.408287i
$106$	−6.31593	+	3.64650i	−0.613457	+	0.354180i
$107$	13.5605			1.31094			0.655470	−	0.755221i	$-0.272471\pi$
$107$	13.5605			1.31094			0.655470	+	0.755221i	$0.272471\pi$
$108$	5.13792	+	0.775762i	0.494396	+	0.0746477i
$109$		−	8.50225i		−	0.814368i	−0.913346	−	0.407184i	$-0.866511\pi$
$109$		−	8.50225i		−	0.814368i	0.913346	−	0.407184i	$-0.133489\pi$
$110$	−5.35643	+	3.09254i	−0.510716	+	0.294862i
$111$	−19.5129	+	2.44360i	−1.85209	+	0.231936i
$112$	0.759011	+	0.438215i	0.0717198	+	0.0414075i
$113$	−1.65386	+	2.86458i	−0.155582	+	0.269477i	−0.933271	−	0.359173i	$-0.883059\pi$
$113$	−1.65386	+	2.86458i	−0.155582	+	0.269477i	0.777689	+	0.628650i	$0.216392\pi$
$114$	3.07470	−	2.32858i	0.287972	−	0.218092i
$115$	−1.24883	+	0.721013i	−0.116454	+	0.0672348i
$116$	−7.62710			−0.708159
$117$	−3.18767	−	10.3363i	−0.294700	−	0.955590i
$118$	−4.06888			−0.374571
$119$	2.89090	−	1.66906i	0.265009	−	0.153003i
$120$	−4.43292	−	1.86908i	−0.404669	−	0.170623i
$121$	−3.02065	+	5.23192i	−0.274604	+	0.475629i
$122$	6.83995	+	3.94905i	0.619260	+	0.357530i
$123$	−2.73735	+	6.49222i	−0.246819	+	0.585384i
$124$	−4.97617	+	2.87299i	−0.446873	+	0.258002i
$125$			6.34737i			0.567726i
$126$	−0.712551	+	2.53090i	−0.0634791	+	0.225470i
$127$	−12.6397			−1.12160			−0.560798	−	0.827953i	$-0.689506\pi$
$127$	−12.6397			−1.12160			−0.560798	+	0.827953i	$0.689506\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	7.77874	−	5.89112i	0.684880	−	0.518684i
$130$	0.500318	+	10.0021i	0.0438808	+	0.877240i
$131$	3.71482	−	6.43426i	0.324565	−	0.562164i	−0.656859	−	0.754013i	$-0.728115\pi$
$131$	3.71482	−	6.43426i	0.324565	−	0.562164i	0.981424	+	0.191850i	$0.0614486\pi$
$132$	3.82706	−	0.479262i	0.333103	−	0.0417144i
$133$	0.975824	+	1.69018i	0.0846147	+	0.146557i
$134$	−6.87507			−0.593916
$135$	2.15471	−	14.2708i	0.185448	−	1.22823i
$136$		−	3.80878i		−	0.326600i
$137$	14.1119	−	8.14752i	1.20566	−	0.696089i	0.243853	−	0.969812i	$-0.421588\pi$
$137$	14.1119	−	8.14752i	1.20566	−	0.696089i	0.961809	+	0.273723i	$0.0882551\pi$
$138$	0.892265	−	0.111738i	0.0759546	−	0.00951176i
$139$	5.31431	−	9.20466i	0.450754	−	0.780729i	−0.547679	−	0.836689i	$-0.684488\pi$
$139$	5.31431	−	9.20466i	0.450754	−	0.780729i	0.998433	+	0.0559594i	$0.0178218\pi$
$140$	1.21716	−	2.10819i	0.102869	−	0.178174i
$141$	−1.11136	−	1.46746i	−0.0935935	−	0.123582i
$142$	−7.97845	−	13.8191i	−0.669537	−	1.15967i
$143$	−4.35681	−	6.74399i	−0.364335	−	0.563960i
$144$	2.09434	+	2.14796i	0.174529	+	0.178997i
$145$			21.1846i			1.75929i
$146$	2.62398	+	4.54487i	0.217162	+	0.376136i
$147$	9.94598	+	4.19358i	0.820330	+	0.345881i
$148$	−9.83267	−	5.67689i	−0.808240	−	0.466638i
$149$	12.4936	+	7.21321i	1.02352	+	0.590929i	0.915121	−	0.403179i	$-0.132095\pi$
$149$	12.4936	+	7.21321i	1.02352	+	0.590929i	0.108398	+	0.994108i	$0.465428\pi$
$150$	−1.82683	+	4.33271i	−0.149160	+	0.353764i
$151$	−9.57392	+	5.52751i	−0.779115	+	0.449822i	−0.836116	−	0.548552i	$-0.815179\pi$
$151$	−9.57392	+	5.52751i	−0.779115	+	0.449822i	0.0570018	+	0.998374i	$0.481846\pi$
$152$	2.22681			0.180619
$153$	11.0735	−	2.81764i	0.895238	−	0.227793i
$154$			1.95165i			0.157268i
$155$	7.97987	+	13.8215i	0.640959	+	1.11017i
$156$	2.13575	−	5.86844i	0.170997	−	0.469851i
$157$	−1.92051	+	3.32643i	−0.153274	+	0.265478i	−0.932429	−	0.361353i	$-0.882315\pi$
$157$	−1.92051	+	3.32643i	−0.153274	+	0.265478i	0.779155	+	0.626831i	$0.215648\pi$
$158$	12.2922	+	7.09690i	0.977914	+	0.564599i
$159$	−1.56962	−	12.5340i	−0.124479	−	0.994008i
$160$	−1.38877	−	2.40542i	−0.109792	−	0.190165i
$161$			0.455019i			0.0358605i
$162$	−4.69554	+	7.67802i	−0.368916	+	0.603242i
$163$			19.5106i			1.52819i	0.645103	+	0.764096i	$0.276815\pi$
$163$			19.5106i			1.52819i	−0.645103	+	0.764096i	$0.723185\pi$
$164$	−3.52286	+	2.03392i	−0.275089	+	0.158823i
$165$	−1.33117	−	10.6298i	−0.103631	−	0.827532i
$166$	0.370304	−	0.641385i	0.0287411	−	0.0497811i
$167$	−10.0701	−	5.81397i	−0.779247	−	0.449898i	0.0569166	−	0.998379i	$-0.481873\pi$
$167$	−10.0701	−	5.81397i	−0.779247	−	0.449898i	−0.836163	+	0.548481i	$0.815206\pi$
$168$	−1.21014	+	0.916486i	−0.0933646	+	0.0707084i
$169$	−12.9351	+	1.29731i	−0.995008	+	0.0997932i
$170$	−10.5790			−0.811376
$171$	1.64734	+	6.47415i	0.125976	+	0.495090i
$172$	5.63365			0.429562
$173$	3.62242	+	6.27421i	0.275407	+	0.477020i	0.970238	−	0.242154i	$-0.0778539\pi$
$173$	3.62242	+	6.27421i	0.275407	+	0.477020i	−0.694830	+	0.719174i	$0.744521\pi$
$174$	5.13247	−	12.1728i	0.389091	−	0.922814i
$175$	−2.06053	−	1.18965i	−0.155761	−	0.0899289i
$176$	1.92848	+	1.11341i	0.145364	+	0.0839262i
$177$	2.73805	−	6.49388i	0.205805	−	0.488110i
$178$	4.94957	+	8.57290i	0.370986	+	0.642566i
$179$	−7.32606			−0.547575			−0.273788	−	0.961790i	$-0.588277\pi$
$179$	−7.32606			−0.547575			−0.273788	+	0.961790i	$0.588277\pi$
$180$	5.96605	−	5.81713i	0.444683	−	0.433584i
$181$	10.0571			0.747536			0.373768	−	0.927522i	$-0.378066\pi$
$181$	10.0571			0.747536			0.373768	+	0.927522i	$0.378066\pi$
$182$	2.81217	+	1.44131i	0.208452	+	0.106837i
$183$	−10.9054	+	8.25906i	−0.806151	+	0.610527i
$184$	0.449617	+	0.259586i	0.0331462	+	0.0191370i
$185$	−15.7678	+	27.3107i	−1.15927	+	2.00792i
$186$	−1.23667	−	9.87521i	−0.0906769	−	0.724086i
$187$	7.34514	−	4.24072i	0.537130	−	0.310112i
$188$		−	1.06279i		−	0.0775119i
$189$	−3.55979	−	2.84033i	−0.258936	−	0.206603i
$190$		−	6.18508i		−	0.448713i
$191$	9.39944	+	16.2803i	0.680120	+	1.17800i	0.974944	+	0.222451i	$0.0714056\pi$
$191$	9.39944	+	16.2803i	0.680120	+	1.17800i	−0.294824	+	0.955552i	$0.595261\pi$
$192$	0.215223	+	1.71863i	0.0155324	+	0.124031i
$193$	11.4647	+	6.61912i	0.825244	+	0.476455i	0.852221	−	0.523181i	$-0.175255\pi$
$193$	11.4647	+	6.61912i	0.825244	+	0.476455i	−0.0269777	+	0.999636i	$0.508588\pi$
$194$	7.86418	−	13.6212i	0.564615	−	0.977942i
$195$	−16.2999	−	5.93215i	−1.16726	−	0.424810i
$196$	3.11593	+	5.39696i	0.222567	+	0.385497i
$197$		−	1.35286i		−	0.0963875i	−0.998838	−	0.0481938i	$-0.984654\pi$
$197$		−	1.35286i		−	0.0963875i	0.998838	−	0.0481938i	$-0.0153465\pi$
$198$	−1.81043	+	6.43045i	−0.128662	+	0.456992i
$199$	1.42951			0.101335			0.0506677	−	0.998716i	$-0.483865\pi$
$199$	1.42951			0.101335			0.0506677	+	0.998716i	$0.483865\pi$
$200$	−2.35105	+	1.35738i	−0.166244	+	0.0959811i
$201$	4.62641	−	10.9725i	0.326322	−	0.773942i
$202$	16.9170	+	9.76705i	1.19028	+	0.687207i
$203$	5.78906	+	3.34231i	0.406312	+	0.234584i
$204$	6.07875	+	2.56302i	0.425598	+	0.179447i
$205$	5.64931	+	9.78489i	0.394565	+	0.683406i
$206$		−	8.18508i		−	0.570281i
$207$	−0.422095	+	1.49923i	−0.0293376	+	0.104204i
$208$	3.02853	−	1.95652i	0.209991	−	0.135660i
$209$	2.47935	+	4.29436i	0.171500	+	0.297047i
$210$	2.54558	+	3.36123i	0.175662	+	0.231947i
$211$	6.32982	−	10.9636i	0.435763	−	0.754764i	−0.561595	−	0.827413i	$-0.689812\pi$
$211$	6.32982	−	10.9636i	0.435763	−	0.754764i	0.997358	+	0.0726489i	$0.0231453\pi$
$212$	3.64650	−	6.31593i	0.250443	−	0.433780i
$213$	27.4240	−	3.43429i	1.87906	−	0.235314i
$214$	−11.7437	+	6.78023i	−0.802784	+	0.463487i
$215$		−	15.6477i		−	1.06717i
$216$	−4.83745	+	1.89713i	−0.329147	+	0.129083i
$217$	5.03596			0.341863
$218$	4.25113	+	7.36317i	0.287923	+	0.498697i
$219$	−9.01930	+	1.12948i	−0.609468	+	0.0763234i
$220$	3.09254	−	5.35643i	0.208499	−	0.361131i
$221$	−0.686074	−	13.7156i	−0.0461503	−	0.922610i
$222$	15.6769	−	11.8727i	1.05216	−	0.796842i
$223$	25.8125	−	14.9028i	1.72853	−	0.997968i	0.832408	−	0.554164i	$-0.186962\pi$
$223$	25.8125	−	14.9028i	1.72853	−	0.997968i	0.896124	−	0.443804i	$-0.146372\pi$
$224$	−0.876431			−0.0585590
$225$	−5.68563	−	5.83118i	−0.379042	−	0.388745i
$226$		−	3.30773i		−	0.220027i
$227$	−19.4683	+	11.2401i	−1.29216	+	0.746029i	−0.979037	−	0.203684i	$-0.934708\pi$
$227$	−19.4683	+	11.2401i	−1.29216	+	0.746029i	−0.313123	+	0.949713i	$0.601375\pi$
$228$	−1.49848	+	3.55397i	−0.0992392	+	0.235367i
$229$	−15.7207	−	9.07634i	−1.03885	−	0.599781i	−0.119344	−	0.992853i	$-0.538079\pi$
$229$	−15.7207	−	9.07634i	−1.03885	−	0.599781i	−0.919508	+	0.393072i	$0.871412\pi$
$230$	0.721013	−	1.24883i	0.0475422	−	0.0823455i
$231$	−3.11480	−	1.31331i	−0.204939	−	0.0864097i
$232$	6.60527	−	3.81355i	0.433657	−	0.250372i
$233$	−11.1281			−0.729027			−0.364514	−	0.931198i	$-0.618765\pi$
$233$	−11.1281			−0.729027			−0.364514	+	0.931198i	$0.618765\pi$
$234$	7.92875	+	7.35765i	0.518318	+	0.480985i
$235$	−2.95194			−0.192564
$236$	3.52376	−	2.03444i	0.229377	−	0.132431i
$237$	−19.5983	+	14.8425i	−1.27304	+	0.964123i
$238$	−1.66906	+	2.89090i	−0.108189	+	0.187390i
$239$	7.49042	+	4.32460i	0.484515	+	0.279735i	0.722296	−	0.691584i	$-0.243087\pi$
$239$	7.49042	+	4.32460i	0.484515	+	0.279735i	−0.237781	+	0.971319i	$0.576420\pi$
$240$	4.77356	−	0.597791i	0.308132	−	0.0385873i
$241$	2.19103	−	1.26499i	0.141137	−	0.0814853i	−0.427769	−	0.903888i	$-0.640700\pi$
$241$	2.19103	−	1.26499i	0.141137	−	0.0814853i	0.568906	+	0.822403i	$0.307367\pi$
$242$		−	6.04130i		−	0.388349i
$243$	−9.09426	−	12.6607i	−0.583397	−	0.812187i
$244$	−7.89810			−0.505624
$245$	14.9903	−	8.65465i	0.957694	−	0.552925i
$246$	−0.875493	−	6.99111i	−0.0558194	−	0.445737i
$247$	8.01887	−	0.401116i	0.510228	−	0.0255224i
$248$	2.87299	−	4.97617i	0.182435	−	0.315987i
$249$	0.774455	+	1.02260i	0.0490791	+	0.0648049i
$250$	−3.17368	−	5.49698i	−0.200721	−	0.347660i
$251$	22.5341			1.42234			0.711170	−	0.703020i	$-0.248166\pi$
$251$	22.5341			1.42234			0.711170	+	0.703020i	$0.248166\pi$
$252$	−0.648362	−	2.54810i	−0.0408430	−	0.160515i
$253$			1.15610i			0.0726835i
$254$	10.9463	−	6.31987i	0.686834	−	0.396544i
$255$	7.11891	−	16.8840i	0.445803	−	1.05732i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.37154	+	5.83968i	−0.210311	+	0.364269i	−0.951812	−	0.306683i	$-0.900781\pi$
$257$	−3.37154	+	5.83968i	−0.210311	+	0.364269i	0.741501	+	0.670952i	$0.234114\pi$
$258$	−3.79103	+	8.99123i	−0.236019	+	0.559770i
$259$	4.97540	+	8.61765i	0.309157	+	0.535475i
$260$	−5.43433	−	8.41189i	−0.337023	−	0.521683i
$261$	15.9738	+	16.3827i	0.988752	+	1.01406i
$262$			7.42964i			0.459005i
$263$	−4.11486	−	7.12715i	−0.253733	−	0.439479i	0.710817	−	0.703377i	$-0.248325\pi$
$263$	−4.11486	−	7.12715i	−0.253733	−	0.439479i	−0.964551	+	0.263898i	$0.914992\pi$
$264$	−3.07470	+	2.32858i	−0.189235	+	0.143314i
$265$	−17.5428	−	10.1283i	−1.07764	−	0.622178i
$266$	−1.69018	−	0.975824i	−0.103631	−	0.0598316i
$267$	−17.0129	+	2.13052i	−1.04117	+	0.130386i
$268$	5.95399	−	3.43754i	0.363698	−	0.209981i
$269$	−23.8369			−1.45336			−0.726680	−	0.686976i	$-0.758938\pi$
$269$	−23.8369			−1.45336			−0.726680	+	0.686976i	$0.758938\pi$
$270$	5.26936	+	13.4362i	0.320683	+	0.817703i
$271$		−	15.4310i		−	0.937367i	−0.883366	−	0.468684i	$-0.844728\pi$
$271$		−	15.4310i		−	0.937367i	0.883366	−	0.468684i	$-0.155272\pi$
$272$	1.90439	+	3.29850i	0.115471	+	0.200001i
$273$	−4.19270	+	3.51829i	−0.253754	+	0.212937i
$274$	−8.14752	+	14.1119i	−0.492209	+	0.852532i
$275$	−5.23535	−	3.02263i	−0.315703	−	0.182271i
$276$	−0.716855	+	0.542900i	−0.0431496	+	0.0326788i
$277$	−4.62513	−	8.01097i	−0.277897	−	0.481332i	0.692965	−	0.720972i	$-0.256304\pi$
$277$	−4.62513	−	8.01097i	−0.277897	−	0.481332i	−0.970862	+	0.239639i	$0.922971\pi$
$278$			10.6286i			0.637463i
$279$	16.5929	+	4.67157i	0.993390	+	0.279680i
$280$			2.43433i			0.145479i
$281$	−17.0788	+	9.86047i	−1.01884	+	0.588226i	−0.913767	−	0.406239i	$-0.866840\pi$
$281$	−17.0788	+	9.86047i	−1.01884	+	0.588226i	−0.105071	+	0.994465i	$0.533507\pi$
$282$	1.69620	+	0.715177i	0.101007	+	0.0425882i
$283$	−3.75118	+	6.49723i	−0.222984	+	0.386220i	−0.955713	−	0.294301i	$-0.904913\pi$
$283$	−3.75118	+	6.49723i	−0.222984	+	0.386220i	0.732728	+	0.680521i	$0.238247\pi$
$284$	13.8191	+	7.97845i	0.820012	+	0.473434i
$285$	9.87130	+	4.16209i	0.584725	+	0.246541i
$286$	7.14510	+	3.66206i	0.422499	+	0.216542i
$287$	3.56518			0.210446
$288$	−2.88773	−	0.813014i	−0.170161	−	0.0479073i
$289$	−2.49322			−0.146660
$290$	−10.5923	−	18.3464i	−0.622002	−	1.07734i
$291$	16.4472	+	21.7171i	0.964150	+	1.27308i
$292$	−4.54487	−	2.62398i	−0.265969	−	0.153557i
$293$	−18.7239	−	10.8103i	−1.09386	−	0.631543i	−0.159261	−	0.987236i	$-0.550911\pi$
$293$	−18.7239	−	10.8103i	−1.09386	−	0.631543i	−0.934603	+	0.355694i	$0.884245\pi$
$294$	−10.7103	+	1.34124i	−0.624635	+	0.0782228i
$295$	−5.65075	−	9.78739i	−0.328999	−	0.569844i
$296$	11.3538			0.659926
$297$	−9.04462	−	7.21663i	−0.524822	−	0.418752i
$298$	−14.4264			−0.835700
$299$	1.66585	+	0.853794i	0.0963387	+	0.0493762i
$300$	−0.584278	−	4.66565i	−0.0337333	−	0.269372i
$301$	−4.27601	−	2.46875i	−0.246465	−	0.142297i
$302$	5.52751	−	9.57392i	0.318072	−	0.550917i
$303$	−26.9720	+	20.4269i	−1.54950	+	1.17349i
$304$	−1.92848	+	1.11341i	−0.110606	+	0.0638583i
$305$			21.9373i			1.25613i
$306$	−8.18109	+	7.97689i	−0.467682	+	0.456008i
$307$		−	7.81179i		−	0.445842i	−0.974836	−	0.222921i	$-0.928441\pi$
$307$		−	7.81179i		−	0.445842i	0.974836	−	0.222921i	$-0.0715593\pi$
$308$	−0.975824	−	1.69018i	−0.0556028	−	0.0963068i
$309$	13.0633	+	5.50794i	0.743143	+	0.313336i
$310$	−13.8215	−	7.97987i	−0.785011	−	0.453226i
$311$	4.85008	−	8.40058i	0.275023	−	0.476353i	−0.695118	−	0.718896i	$-0.744648\pi$
$311$	4.85008	−	8.40058i	0.275023	−	0.476353i	0.970141	+	0.242542i	$0.0779813\pi$
$312$	1.08460	+	6.15009i	0.0614036	+	0.348180i
$313$	15.9559	+	27.6364i	0.901880	+	1.56210i	0.825051	+	0.565058i	$0.191146\pi$
$313$	15.9559	+	27.6364i	0.901880	+	1.56210i	0.0768289	+	0.997044i	$0.475520\pi$
$314$		−	3.84103i		−	0.216762i
$315$	−7.07746	+	1.80086i	−0.398770	+	0.101467i
$316$	−14.1938			−0.798463
$317$	−24.4893	+	14.1389i	−1.37546	+	0.794119i	−0.991608	−	0.129277i	$-0.958734\pi$
$317$	−24.4893	+	14.1389i	−1.37546	+	0.794119i	−0.383847	+	0.923397i	$0.625401\pi$
$318$	7.62631	+	10.0699i	0.427662	+	0.564693i
$319$	14.7087	+	8.49207i	0.823529	+	0.475465i
$320$	2.40542	+	1.38877i	0.134467	+	0.0776347i
$321$	−2.91852	−	23.3054i	−0.162896	−	1.30078i
$322$	−0.227510	−	0.394058i	−0.0126786	−	0.0219600i
$323$			8.48144i			0.471920i
$324$	0.227448	−	8.99713i	0.0126360	−	0.499840i
$325$	−8.22173	+	5.31148i	−0.456060	+	0.294628i
$326$	−9.75532	−	16.8967i	−0.540297	−	0.935823i
$327$	−14.6122	+	1.82988i	−0.808057	+	0.101193i
$328$	2.03392	−	3.52286i	0.112305	−	0.194517i
$329$	−0.465731	+	0.806669i	−0.0256766	+	0.0444731i
$330$	6.46775	+	8.54013i	0.356038	+	0.470119i
$331$	9.22435	−	5.32568i	0.507016	−	0.292726i	−0.224590	−	0.974453i	$-0.572104\pi$
$331$	9.22435	−	5.32568i	0.507016	−	0.292726i	0.731606	+	0.681727i	$0.238771\pi$
$332$			0.740607i			0.0406461i
$333$	8.39926	+	33.0095i	0.460277	+	1.80891i
$334$	11.6279			0.636252
$335$	−9.54791	−	16.5375i	−0.521658	−	0.903538i
$336$	0.589772	−	1.39877i	0.0321747	−	0.0763092i
$337$	0.320956	−	0.555913i	0.0174836	−	0.0302825i	−0.857151	−	0.515065i	$-0.827768\pi$
$337$	0.320956	−	0.555913i	0.0174836	−	0.0302825i	0.874635	+	0.484782i	$0.161101\pi$
$338$	10.5535	−	7.59106i	0.574033	−	0.412899i
$339$	5.27909	+	2.22585i	0.286721	+	0.120892i
$340$	9.16172	−	5.28952i	0.496864	−	0.286865i
$341$	12.7952			0.692902
$342$	−4.66372	−	4.78310i	−0.252185	−	0.258641i
$343$		−	11.5968i		−	0.626169i
$344$	−4.87889	+	2.81683i	−0.263052	+	0.151873i
$345$	1.50793	+	1.99110i	0.0811842	+	0.107197i
$346$	−6.27421	−	3.62242i	−0.337304	−	0.194742i
$347$	12.7951	−	22.1617i	0.686876	−	1.18970i	−0.285968	−	0.958239i	$-0.592315\pi$
$347$	12.7951	−	22.1617i	0.686876	−	1.18970i	0.972843	−	0.231464i	$-0.0743517\pi$
$348$	1.64153	+	13.1081i	0.0879951	+	0.702670i
$349$	−3.03854	+	1.75430i	−0.162649	+	0.0939056i	−0.579115	−	0.815246i	$-0.696602\pi$
$349$	−3.03854	+	1.75430i	−0.162649	+	0.0939056i	0.416466	+	0.909151i	$0.363269\pi$
$350$	2.37930			0.127179
$351$	−17.0782	+	7.70302i	−0.911565	+	0.411157i
$352$	−2.22681			−0.118690
$353$	6.32742	−	3.65314i	0.336774	−	0.194437i	−0.322070	−	0.946716i	$-0.604379\pi$
$353$	6.32742	−	3.65314i	0.336774	−	0.194437i	0.658845	+	0.752279i	$0.271045\pi$
$354$	0.875717	+	6.99289i	0.0465438	+	0.371668i
$355$	22.1605	−	38.3831i	1.17616	−	2.03716i
$356$	−8.57290	−	4.94957i	−0.454363	−	0.262327i
$357$	−3.49069	−	4.60917i	−0.184747	−	0.243943i
$358$	6.34455	−	3.66303i	0.335320	−	0.193597i
$359$			15.7989i			0.833832i	0.908945	+	0.416916i	$0.136889\pi$
$359$			15.7989i			0.833832i	−0.908945	+	0.416916i	$0.863111\pi$
$360$	−2.25818	+	8.02081i	−0.119017	+	0.422734i
$361$	14.0413			0.739016
$362$	−8.70968	+	5.02853i	−0.457771	+	0.264294i
$363$	9.64183	+	4.06534i	0.506065	+	0.213375i
$364$	−3.15607	+	0.157871i	−0.165423	+	0.00827470i
$365$	−7.28823	+	12.6236i	−0.381484	+	0.660749i
$366$	5.31483	−	12.6053i	0.277811	−	0.658887i
$367$	−5.26543	−	9.11999i	−0.274853	−	0.476060i	0.695245	−	0.718773i	$-0.255296\pi$
$367$	−5.26543	−	9.11999i	−0.274853	−	0.476060i	−0.970098	+	0.242713i	$0.921963\pi$
$368$	−0.519173			−0.0270638
$369$	11.7469	+	3.30722i	0.611517	+	0.172167i
$370$		−	31.5357i		−	1.63946i
$371$	−5.53548	+	3.19591i	−0.287388	+	0.165923i
$372$	6.00859	+	7.93385i	0.311531	+	0.411351i
$373$	4.86520	−	8.42678i	0.251911	−	0.436322i	−0.712141	−	0.702036i	$-0.752274\pi$
$373$	4.86520	−	8.42678i	0.251911	−	0.436322i	0.964052	+	0.265714i	$0.0856077\pi$
$374$	−4.24072	+	7.34514i	−0.219282	+	0.379808i
$375$	10.9088	−	1.36610i	0.563326	−	0.0705451i
$376$	0.531395	+	0.920402i	0.0274046	+	0.0474661i
$377$	23.0989	−	14.9226i	1.18966	−	0.768553i
$378$	4.50303	+	0.679902i	0.231611	+	0.0349704i
$379$			32.8344i			1.68659i	0.537450	+	0.843296i	$0.319388\pi$
$379$			32.8344i			1.68659i	−0.537450	+	0.843296i	$0.680612\pi$
$380$	3.09254	+	5.35643i	0.158644	+	0.274779i
$381$	2.72036	+	21.7230i	0.139368	+	1.11290i
$382$	−16.2803	−	9.39944i	−0.832973	−	0.480917i
$383$	−11.9352	−	6.89079i	−0.609860	−	0.352103i	0.163050	−	0.986618i	$-0.447867\pi$
$383$	−11.9352	−	6.89079i	−0.609860	−	0.352103i	−0.772911	+	0.634515i	$0.781200\pi$
$384$	−1.04570	−	1.38076i	−0.0533633	−	0.0704618i
$385$	−4.69454	+	2.71040i	−0.239256	+	0.138135i
$386$	−13.2382			−0.673809
$387$	−11.7988	−	12.1008i	−0.599767	−	0.615121i
$388$			15.7284i			0.798486i
$389$	−9.32704	−	16.1549i	−0.472900	−	0.819086i	0.526619	−	0.850101i	$-0.323459\pi$
$389$	−9.32704	−	16.1549i	−0.472900	−	0.819086i	−0.999519	+	0.0310151i	$0.990126\pi$
$390$	17.0822	−	3.01254i	0.864989	−	0.152546i
$391$	−0.988707	+	1.71249i	−0.0500011	+	0.0866044i
$392$	−5.39696	−	3.11593i	−0.272587	−	0.157378i
$393$	−11.8576	−	4.99959i	−0.598137	−	0.252196i
$394$	0.676432	+	1.17161i	0.0340781	+	0.0590251i
$395$			39.4239i			1.98363i
$396$	−1.64734	−	6.47415i	−0.0827821	−	0.325338i
$397$		−	7.73466i		−	0.388191i	−0.980983	−	0.194096i	$-0.937823\pi$
$397$		−	7.73466i		−	0.388191i	0.980983	−	0.194096i	$-0.0621772\pi$
$398$	−1.23799	+	0.714756i	−0.0620550	+	0.0358275i
$399$	2.69477	−	2.04084i	0.134907	−	0.102170i
$400$	1.35738	−	2.35105i	0.0678689	−	0.117552i
$401$	−5.91085	−	3.41263i	−0.295174	−	0.170419i	0.345099	−	0.938566i	$-0.387845\pi$
$401$	−5.91085	−	3.41263i	−0.295174	−	0.170419i	−0.640273	+	0.768148i	$0.721179\pi$
$402$	1.47967	+	11.8157i	0.0737994	+	0.589313i
$403$	9.44943	−	18.4369i	0.470710	−	0.918410i
$404$	−19.5341			−0.971858
$405$	−24.9899	−	0.631746i	−1.24176	−	0.0313917i
$406$	−6.68463			−0.331753
$407$	12.6414	+	21.8955i	0.626610	+	1.08532i
$408$	−6.54587	+	0.819736i	−0.324069	+	0.0405830i
$409$	−27.0687	−	15.6281i	−1.33846	−	0.772760i	−0.351881	−	0.936045i	$-0.614458\pi$
$409$	−27.0687	−	15.6281i	−1.33846	−	0.772760i	−0.986579	+	0.163285i	$0.947791\pi$
$410$	−9.78489	−	5.64931i	−0.483241	−	0.278999i
$411$	−17.0397	−	22.4996i	−0.840509	−	1.10982i
$412$	4.09254	+	7.08848i	0.201625	+	0.349225i
$413$	−3.56609			−0.175476
$414$	−0.384072	−	1.50942i	−0.0188761	−	0.0741840i
$415$	2.05707			0.100978
$416$	−1.64453	+	3.20866i	−0.0806296	+	0.157318i
$417$	−16.9631	−	7.15227i	−0.830689	−	0.350248i
$418$	−4.29436	−	2.47935i	−0.210044	−	0.121269i
$419$	−8.68385	+	15.0409i	−0.424234	+	0.734794i	−0.996349	−	0.0853793i	$-0.972790\pi$
$419$	−8.68385	+	15.0409i	−0.424234	+	0.734794i	0.572115	+	0.820174i	$0.306123\pi$
$420$	−3.88515	−	1.63812i	−0.189576	−	0.0799320i
$421$	5.91995	−	3.41788i	0.288521	−	0.166577i	−0.348754	−	0.937214i	$-0.613395\pi$
$421$	5.91995	−	3.41788i	0.288521	−	0.166577i	0.637275	+	0.770637i	$0.280062\pi$
$422$			12.6596i			0.616262i
$423$	−2.28283	+	2.22585i	−0.110995	+	0.108224i
$424$			7.29301i			0.354180i
$425$	−5.16995	−	8.95461i	−0.250779	−	0.434363i
$426$	−22.0327	+	16.6862i	−1.06749	+	0.808447i
$427$	5.99475	+	3.46107i	0.290106	+	0.167493i
$428$	6.78023	−	11.7437i	0.327735	−	0.567654i
$429$	−10.6527	+	8.93919i	−0.514318	+	0.431588i
$430$	7.82386	+	13.5513i	0.377300	+	0.653503i
$431$		−	37.9595i		−	1.82844i	−0.405215	−	0.914221i	$-0.632803\pi$
$431$		−	37.9595i		−	1.82844i	0.405215	−	0.914221i	$-0.367197\pi$
$432$	3.24079	−	4.06169i	0.155922	−	0.195418i
$433$	5.83476			0.280401			0.140200	−	0.990123i	$-0.455225\pi$
$433$	5.83476			0.280401			0.140200	+	0.990123i	$0.455225\pi$
$434$	−4.36127	+	2.51798i	−0.209348	+	0.120867i
$435$	36.4085	−	4.55942i	1.74565	−	0.218607i
$436$	−7.36317	−	4.25113i	−0.352632	−	0.203592i
$437$	−1.00121	−	0.578051i	−0.0478945	−	0.0276519i
$438$	7.24620	−	5.48781i	0.346237	−	0.262218i
$439$	−0.772490	−	1.33799i	−0.0368690	−	0.0638589i	0.847002	−	0.531590i	$-0.178405\pi$
$439$	−0.772490	−	1.33799i	−0.0368690	−	0.0638589i	−0.883871	+	0.467731i	$0.845072\pi$
$440$			6.18508i			0.294862i
$441$	5.06660	−	17.9960i	0.241267	−	0.856951i
$442$	7.45195	+	11.5350i	0.354453	+	0.548665i
$443$	−1.77937	−	3.08196i	−0.0845403	−	0.146428i	0.820655	−	0.571424i	$-0.193609\pi$
$443$	−1.77937	−	3.08196i	−0.0845403	−	0.146428i	−0.905195	+	0.424996i	$0.860276\pi$
$444$	−7.64025	+	18.1205i	−0.362590	+	0.859960i
$445$	−13.7477	+	23.8116i	−0.651701	+	1.12878i
$446$	−14.9028	+	25.8125i	−0.705670	+	1.22226i
$447$	9.70790	−	23.0244i	0.459168	−	1.08902i
$448$	0.759011	−	0.438215i	0.0358599	−	0.0207037i
$449$		−	10.1607i		−	0.479515i	−0.970833	−	0.239757i	$-0.922932\pi$
$449$		−	10.1607i		−	0.479515i	0.970833	−	0.239757i	$-0.0770679\pi$
$450$	7.83949	+	2.20714i	0.369557	+	0.104045i
$451$	9.05833			0.426540
$452$	1.65386	+	2.86458i	0.0777912	+	0.134738i
$453$	11.5602	+	15.2644i	0.543148	+	0.717182i
$454$	11.2401	−	19.4683i	0.527522	−	0.913695i
$455$	0.438494	+	8.76613i	0.0205569	+	0.410962i
$456$	−0.479262	−	3.82706i	−0.0224435	−	0.179219i
$457$	18.4597	−	10.6577i	0.863506	−	0.498546i	−0.00167864	−	0.999999i	$-0.500534\pi$
$457$	18.4597	−	10.6577i	0.863506	−	0.498546i	0.865185	+	0.501453i	$0.167201\pi$
$458$	18.1527			0.848219
$459$	−7.22574	−	18.4248i	−0.337269	−	0.859994i
$460$			1.44203i			0.0672348i
$461$	18.6408	−	10.7623i	0.868188	−	0.501248i	0.00144222	−	0.999999i	$-0.499541\pi$
$461$	18.6408	−	10.7623i	0.868188	−	0.501248i	0.866746	+	0.498750i	$0.166208\pi$
$462$	3.35416	−	0.420040i	0.156049	−	0.0195420i
$463$	31.0148	+	17.9064i	1.44138	+	0.832180i	0.997942	−	0.0641254i	$-0.0204258\pi$
$463$	31.0148	+	17.9064i	1.44138	+	0.832180i	0.443437	+	0.896306i	$0.353759\pi$
$464$	−3.81355	+	6.60527i	−0.177040	+	0.306642i
$465$	22.0366	−	16.6891i	1.02192	−	0.773940i
$466$	9.63723	−	5.56406i	0.446436	−	0.257750i
$467$	−21.4529			−0.992723			−0.496362	−	0.868116i	$-0.665331\pi$
$467$	−21.4529			−0.992723			−0.496362	+	0.868116i	$0.665331\pi$
$468$	−10.5453	−	2.40754i	−0.487458	−	0.111288i
$469$	−6.02552			−0.278233
$470$	2.55646	−	1.47597i	0.117921	−	0.0680815i
$471$	6.13023	+	2.58472i	0.282466	+	0.119098i
$472$	−2.03444	+	3.52376i	−0.0936427	+	0.162194i
$473$	−10.8644	−	6.27255i	−0.499544	−	0.288412i
$474$	9.55136	−	22.6531i	0.438709	−	1.04049i
$475$	5.23535	−	3.02263i	0.240214	−	0.138688i
$476$		−	3.33813i		−	0.153003i
$477$	−21.2034	+	5.39519i	−0.970836	+	0.247029i
$478$	−8.64919			−0.395605
$479$	−5.00102	+	2.88734i	−0.228502	+	0.131926i	−0.609881	−	0.792493i	$-0.708783\pi$
$479$	−5.00102	+	2.88734i	−0.228502	+	0.131926i	0.381379	+	0.924419i	$0.375449\pi$
$480$	−3.83513	+	2.90448i	−0.175049	+	0.132571i
$481$	40.8855	−	2.04515i	1.86422	−	0.0932510i
$482$	−1.26499	+	2.19103i	−0.0576188	+	0.0997987i
$483$	0.782008	−	0.0979306i	0.0355826	−	0.00445599i
$484$	3.02065	+	5.23192i	0.137302	+	0.237814i
$485$	43.6862			1.98369
$486$	14.2062	+	6.41739i	0.644408	+	0.291099i
$487$		−	32.9124i		−	1.49140i	−0.666280	−	0.745702i	$-0.732114\pi$
$487$		−	32.9124i		−	1.49140i	0.666280	−	0.745702i	$-0.267886\pi$
$488$	6.83995	−	3.94905i	0.309630	−	0.178765i
$489$	33.5315	−	4.19914i	1.51635	−	0.189892i
$490$	−8.65465	+	14.9903i	−0.390977	+	0.677192i
$491$	4.89961	−	8.48638i	0.221116	−	0.382985i	−0.734031	−	0.679116i	$-0.762363\pi$
$491$	4.89961	−	8.48638i	0.221116	−	0.382985i	0.955147	+	0.296131i	$0.0956966\pi$
$492$	4.25375	+	5.61673i	0.191774	+	0.253222i
$493$	14.5250	+	25.1580i	0.654172	+	1.13306i
$494$	−6.74399	+	4.35681i	−0.303426	+	0.196022i
$495$	−17.9822	+	4.57557i	−0.808241	+	0.205657i
$496$			5.74599i			0.258002i
$497$	−6.99256	−	12.1115i	−0.313659	−	0.543274i
$498$	−1.18200	−	0.498373i	−0.0529666	−	0.0223326i
$499$	−35.7763	−	20.6555i	−1.60157	−	0.924666i	−0.991174	−	0.132569i	$-0.957677\pi$
$499$	−35.7763	−	20.6555i	−1.60157	−	0.924666i	−0.610395	−	0.792097i	$-0.708989\pi$
$500$	5.49698	+	3.17368i	0.245833	+	0.141931i
$501$	−7.82473	+	18.5580i	−0.349583	+	0.829111i
$502$	−19.5151	+	11.2671i	−0.871002	+	0.502873i
$503$	−11.0563			−0.492976			−0.246488	−	0.969146i	$-0.579277\pi$
$503$	−11.0563			−0.492976			−0.246488	+	0.969146i	$0.579277\pi$
$504$	1.83555	+	1.88254i	0.0817618	+	0.0838548i
$505$			54.2568i			2.41440i
$506$	−0.578051	−	1.00121i	−0.0256975	−	0.0445094i
$507$	5.01353	+	21.9514i	0.222659	+	0.974896i
$508$	−6.31987	+	10.9463i	−0.280399	+	0.485665i
$509$	−0.959102	−	0.553738i	−0.0425115	−	0.0245440i	0.478594	−	0.878037i	$-0.341147\pi$
$509$	−0.959102	−	0.553738i	−0.0425115	−	0.0245440i	−0.521105	+	0.853493i	$0.674480\pi$
$510$	2.27685	+	18.1814i	0.100821	+	0.805088i
$511$	2.29974	+	3.98327i	0.101735	+	0.176209i
$512$		−	1.00000i		−	0.0441942i
$513$	10.7721	−	4.22455i	0.475600	−	0.186519i
$514$		−	6.74309i		−	0.297425i
$515$	19.6886	−	11.3672i	0.867583	−	0.500899i
$516$	−1.21249	−	9.68215i	−0.0533769	−	0.426233i
$517$	−1.18332	+	2.04957i	−0.0520422	+	0.0901398i
$518$	−8.61765	−	4.97540i	−0.378638	−	0.218607i
$519$	10.0034	−	7.57594i	0.439101	−	0.332547i
$520$	8.91221	+	4.56775i	0.390826	+	0.200309i
$521$	−9.02695			−0.395478			−0.197739	−	0.980255i	$-0.563360\pi$
$521$	−9.02695			−0.395478			−0.197739	+	0.980255i	$0.563360\pi$
$522$	−22.0250	−	6.20094i	−0.964010	−	0.271408i
$523$	9.47081			0.414130			0.207065	−	0.978327i	$-0.433609\pi$
$523$	9.47081			0.414130			0.207065	+	0.978327i	$0.433609\pi$
$524$	−3.71482	−	6.43426i	−0.162283	−	0.281082i
$525$	−1.60109	+	3.79732i	−0.0698772	+	0.165729i
$526$	7.12715	+	4.11486i	0.310759	+	0.179417i
$527$	18.9531	+	10.9426i	0.825611	+	0.476667i
$528$	1.49848	−	3.55397i	0.0652129	−	0.154666i
$529$	11.3652	+	19.6852i	0.494140	+	0.855876i
$530$	20.2567			0.879893
$531$	−11.7499	−	3.30806i	−0.509900	−	0.143558i
$532$	1.95165			0.0846147
$533$	6.68968	−	13.0523i	0.289762	−	0.565360i
$534$	13.6684	−	10.3515i	0.591488	−	0.447955i
$535$	−32.6187	−	18.8324i	−1.41023	−	0.814196i
$536$	−3.43754	+	5.95399i	−0.148479	+	0.257173i
$537$	1.57674	+	12.5908i	0.0680412	+	0.543331i
$538$	20.6433	−	11.9184i	0.889998	−	0.513840i
$539$		−	13.8772i		−	0.597734i
$540$	−11.2815	−	9.00143i	−0.485479	−	0.387360i
$541$		−	29.1499i		−	1.25325i	−0.779320	−	0.626626i	$-0.784436\pi$
$541$		−	29.1499i		−	1.25325i	0.779320	−	0.626626i	$-0.215564\pi$
$542$	7.71551	+	13.3637i	0.331409	+	0.574018i
$543$	−2.16451	−	17.2844i	−0.0928881	−	0.741743i
$544$	−3.29850	−	1.90439i	−0.141422	−	0.0816500i
$545$	−11.8077	+	20.4515i	−0.505786	+	0.876047i
$546$	1.87184	−	5.14328i	0.0801073	−	0.220112i
$547$	−14.6450	−	25.3659i	−0.626175	−	1.08457i	−0.988312	−	0.152442i	$-0.951286\pi$
$547$	−14.6450	−	25.3659i	−0.626175	−	1.08457i	0.362137	−	0.932125i	$-0.382047\pi$
$548$		−	16.2950i		−	0.696089i
$549$	16.5413	+	16.9648i	0.705967	+	0.724039i
$550$	6.04526			0.257771
$551$	−14.7087	+	8.49207i	−0.626612	+	0.361774i
$552$	0.349364	−	0.828593i	0.0148699	−	0.0352673i
$553$	10.7733	+	6.21994i	0.458125	+	0.264499i
$554$	8.01097	+	4.62513i	0.340353	+	0.196503i
$555$	50.3305	+	21.2211i	2.13641	+	0.900787i
$556$	−5.31431	−	9.20466i	−0.225377	−	0.390365i
$557$			14.0519i			0.595400i	0.954659	+	0.297700i	$0.0962195\pi$
$557$			14.0519i			0.595400i	−0.954659	+	0.297700i	$0.903780\pi$
$558$	−16.7056	+	4.25074i	−0.707206	+	0.179948i
$559$	−17.0617	+	11.0224i	−0.721634	+	0.466196i
$560$	−1.21716	−	2.10819i	−0.0514345	−	0.0890872i
$561$	−8.86906	−	11.7109i	−0.374452	−	0.494433i
$562$	9.86047	−	17.0788i	0.415939	−	0.720427i
$563$	−1.73120	+	2.99852i	−0.0729612	+	0.126373i	−0.900198	−	0.435481i	$-0.856578\pi$
$563$	−1.73120	+	2.99852i	−0.0729612	+	0.126373i	0.827237	+	0.561854i	$0.189912\pi$
$564$	−1.82654	+	0.228737i	−0.0769111	+	0.00963155i
$565$	7.95649	−	4.59368i	0.334732	−	0.193258i
$566$		−	7.50235i		−	0.315347i
$567$	−4.11531	+	6.72925i	−0.172827	+	0.282602i
$568$	−15.9569			−0.669537
$569$	7.89491	+	13.6744i	0.330972	+	0.573260i	0.982703	−	0.185190i	$-0.0592901\pi$
$569$	7.89491	+	13.6744i	0.330972	+	0.573260i	−0.651731	+	0.758450i	$0.725957\pi$
$570$	−10.6298	+	1.33117i	−0.445235	+	0.0557566i
$571$	−15.2110	+	26.3463i	−0.636562	+	1.10256i	0.349620	+	0.936892i	$0.386311\pi$
$571$	−15.2110	+	26.3463i	−0.636562	+	1.10256i	−0.986182	+	0.165666i	$0.947023\pi$
$572$	−8.01887	+	0.401116i	−0.335286	+	0.0167715i
$573$	25.9568	−	19.6580i	1.08436	−	0.821226i
$574$	−3.08754	+	1.78259i	−0.128871	+	0.0744039i
$575$	1.40943			0.0587772
$576$	2.90736	−	0.739776i	0.121140	−	0.0308240i
$577$			3.19469i			0.132997i	0.997787	+	0.0664984i	$0.0211827\pi$
$577$			3.19469i			0.132997i	−0.997787	+	0.0664984i	$0.978817\pi$
$578$	2.15919	−	1.24661i	0.0898106	−	0.0518521i
$579$	8.90834	−	21.1280i	0.370218	−	0.878052i
$580$	18.3464	+	10.5923i	0.761794	+	0.439822i
$581$	0.324546	−	0.562129i	0.0134644	−	0.0233211i
$582$	−25.1022	−	10.5840i	−1.04052	−	0.438721i
$583$	−14.0644	+	8.12009i	−0.582488	+	0.336300i
$584$	5.24797			0.217162
$585$	−6.68704	+	29.2901i	−0.276475	+	1.21100i
$586$	21.6205			0.893136
$587$	11.2778	−	6.51126i	0.465486	−	0.268748i	−0.248862	−	0.968539i	$-0.580057\pi$
$587$	11.2778	−	6.51126i	0.465486	−	0.268748i	0.714348	+	0.699790i	$0.246723\pi$
$588$	8.60474	−	6.51668i	0.354853	−	0.268743i
$589$	−6.39762	+	11.0810i	−0.263610	+	0.456585i
$590$	9.78739	+	5.65075i	0.402940	+	0.232638i
$591$	−2.32507	+	0.291167i	−0.0956405	+	0.0119770i
$592$	−9.83267	+	5.67689i	−0.404120	+	0.233319i
$593$		−	11.9872i		−	0.492254i	−0.969238	−	0.246127i	$-0.920842\pi$
$593$		−	11.9872i		−	0.492254i	0.969238	−	0.246127i	$-0.0791581\pi$
$594$	11.4412	+	1.72748i	0.469438	+	0.0708793i
$595$	−9.27180			−0.380107
$596$	12.4936	−	7.21321i	0.511760	−	0.295465i
$597$	−0.307664	−	2.45680i	−0.0125918	−	0.100550i
$598$	−1.86957	+	0.0935185i	−0.0764523	+	0.00382425i
$599$	9.75297	−	16.8926i	0.398495	−	0.690214i	−0.595045	−	0.803692i	$-0.702866\pi$
$599$	9.75297	−	16.8926i	0.398495	−	0.690214i	0.993541	+	0.113478i	$0.0361992\pi$
$600$	2.83883	+	3.74843i	0.115895	+	0.153029i
$601$	8.24140	+	14.2745i	0.336174	+	0.582270i	0.983710	−	0.179765i	$-0.0575337\pi$
$601$	8.24140	+	14.2745i	0.336174	+	0.582270i	−0.647536	+	0.762035i	$0.724200\pi$
$602$	4.93751			0.201238
$603$	−19.8534	−	5.58953i	−0.808492	−	0.227623i
$604$			11.0550i			0.449822i
$605$	14.5319	−	8.38999i	0.590805	−	0.341101i
$606$	13.1450	−	31.1762i	0.533979	−	1.26644i
$607$	−1.49710	+	2.59306i	−0.0607655	+	0.105249i	−0.894808	−	0.446452i	$-0.852688\pi$
$607$	−1.49710	+	2.59306i	−0.0607655	+	0.105249i	0.834042	+	0.551700i	$0.186021\pi$
$608$	1.11341	−	1.92848i	0.0451546	−	0.0782101i
$609$	4.49825	−	10.6686i	0.182278	−	0.432312i
$610$	−10.9687	−	18.9983i	−0.444108	−	0.769218i
$611$	2.07937	+	3.21869i	0.0841223	+	0.130214i
$612$	3.09659	−	10.9987i	0.125172	−	0.444597i
$613$			27.2249i			1.09961i	0.835295	+	0.549803i	$0.185297\pi$
$613$			27.2249i			1.09961i	−0.835295	+	0.549803i	$0.814703\pi$
$614$	3.90590	+	6.76521i	0.157629	+	0.273022i
$615$	15.6007	−	11.8150i	0.629082	−	0.476426i
$616$	1.69018	+	0.975824i	0.0680992	+	0.0393171i
$617$	−7.28671	−	4.20698i	−0.293352	−	0.169367i	0.346101	−	0.938197i	$-0.387506\pi$
$617$	−7.28671	−	4.20698i	−0.293352	−	0.169367i	−0.639453	+	0.768831i	$0.720839\pi$
$618$	−14.0671	+	1.76162i	−0.565862	+	0.0708626i
$619$	−30.4315	+	17.5696i	−1.22314	+	0.706182i	−0.965587	−	0.260081i	$-0.916251\pi$
$619$	−30.4315	+	17.5696i	−1.22314	+	0.706182i	−0.257557	+	0.966263i	$0.582917\pi$
$620$	15.9597			0.640959
$621$	2.66747	+	0.402755i	0.107042	+	0.0161620i
$622$			9.70016i			0.388941i
$623$	4.33795	+	7.51356i	0.173796	+	0.301024i
$624$	−4.01434	−	4.78383i	−0.160702	−	0.191507i
$625$	15.6019	−	27.0234i	0.624078	−	1.08093i
$626$	−27.6364	−	15.9559i	−1.10457	−	0.637726i
$627$	6.84679	−	5.18533i	0.273435	−	0.207082i
$628$	1.92051	+	3.32643i	0.0766369	+	0.132739i
$629$			43.2440i			1.72425i
$630$	5.22883	−	5.09832i	0.208322	−	0.203122i
$631$			21.0022i			0.836083i	0.908428	+	0.418042i	$0.137283\pi$
$631$			21.0022i			0.836083i	−0.908428	+	0.418042i	$0.862717\pi$
$632$	12.2922	−	7.09690i	0.488957	−	0.282299i
$633$	−20.2046	−	8.51899i	−0.803062	−	0.338600i
$634$	14.1389	−	24.4893i	0.561527	−	0.972594i
$635$	30.4040	+	17.5537i	1.20654	+	0.696599i
$636$	−11.6395	−	4.90765i	−0.461538	−	0.194601i
$637$	−19.9960	−	10.2485i	−0.792269	−	0.406060i
$638$	−16.9841			−0.672409
$639$	−11.8045	−	46.3924i	−0.466980	−	1.83526i
$640$	−2.77754			−0.109792
$641$	−11.7828	−	20.4085i	−0.465394	−	0.806087i	0.533825	−	0.845595i	$-0.320754\pi$
$641$	−11.7828	−	20.4085i	−0.465394	−	0.806087i	−0.999219	+	0.0395083i	$0.987421\pi$
$642$	14.1802	+	18.7238i	0.559648	+	0.738969i
$643$	−19.7342	−	11.3935i	−0.778240	−	0.449317i	0.0575663	−	0.998342i	$-0.481666\pi$
$643$	−19.7342	−	11.3935i	−0.778240	−	0.449317i	−0.835806	+	0.549025i	$0.814999\pi$
$644$	0.394058	+	0.227510i	0.0155281	+	0.00896513i
$645$	−26.8926	+	3.36775i	−1.05889	+	0.132605i
$646$	−4.24072	−	7.34514i	−0.166849	−	0.288991i
$647$	−45.8902			−1.80413			−0.902065	−	0.431600i	$-0.857949\pi$
$647$	−45.8902			−1.80413			−0.902065	+	0.431600i	$0.857949\pi$
$648$	4.30159	+	7.90546i	0.168982	+	0.310556i
$649$	−9.06065			−0.355661
$650$	4.46449	−	8.71074i	0.175112	−	0.341663i
$651$	−1.08385	−	8.65494i	−0.0424796	−	0.339214i
$652$	16.8967	+	9.75532i	0.661726	+	0.382048i
$653$	7.28145	−	12.6118i	0.284945	−	0.493539i	−0.687651	−	0.726042i	$-0.741358\pi$
$653$	7.28145	−	12.6118i	0.284945	−	0.493539i	0.972596	+	0.232502i	$0.0746913\pi$
$654$	11.7396	−	8.89082i	0.459055	−	0.347659i
$655$	−17.8714	+	10.3181i	−0.698295	+	0.403161i
$656$			4.06784i			0.158823i
$657$	3.88232	+	15.2577i	0.151464	+	0.595260i
$658$		−	0.931461i		−	0.0363121i
$659$	12.3920	+	21.4636i	0.482724	+	0.836102i	0.999803	−	0.0198353i	$-0.00631420\pi$
$659$	12.3920	+	21.4636i	0.482724	+	0.836102i	−0.517080	+	0.855937i	$0.672981\pi$
$660$	−9.87130	−	4.16209i	−0.384240	−	0.162009i
$661$	−16.5731	−	9.56850i	−0.644620	−	0.372172i	0.141772	−	0.989899i	$-0.454720\pi$
$661$	−16.5731	−	9.56850i	−0.644620	−	0.372172i	−0.786392	+	0.617728i	$0.788053\pi$
$662$	−5.32568	+	9.22435i	−0.206989	+	0.358515i
$663$	−23.4243	+	4.13102i	−0.909726	+	0.160435i
$664$	−0.370304	−	0.641385i	−0.0143706	−	0.0248906i
$665$		−	5.42079i		−	0.210209i
$666$	−23.7787	−	24.3875i	−0.921407	−	0.944995i
$667$	−3.95979			−0.153324
$668$	−10.0701	+	5.81397i	−0.389623	+	0.224949i
$669$	−31.1679	−	41.1546i	−1.20502	−	1.59113i
$670$	16.5375	+	9.54791i	0.638898	+	0.368868i
$671$	15.2313	+	8.79380i	0.587998	+	0.339481i
$672$	0.188628	+	1.50626i	0.00727648	+	0.0581052i
$673$	7.35301	+	12.7358i	0.283438	+	0.490929i	0.972229	−	0.234031i	$-0.0751917\pi$
$673$	7.35301	+	12.7358i	0.283438	+	0.490929i	−0.688791	+	0.724960i	$0.741858\pi$
$674$			0.641913i			0.0247256i
$675$	−8.79795	+	11.0265i	−0.338633	+	0.424410i
$676$	−5.34405	+	11.8508i	−0.205540	+	0.455799i
$677$	19.0892	+	33.0634i	0.733656	+	1.27073i	0.955311	+	0.295604i	$0.0955209\pi$
$677$	19.0892	+	33.0634i	0.733656	+	1.27073i	−0.221655	+	0.975125i	$0.571146\pi$
$678$	−5.68475	+	0.711899i	−0.218321	+	0.0273403i
$679$	6.89241	−	11.9380i	0.264506	−	0.458138i
$680$	−5.28952	+	9.16172i	−0.202844	+	0.351336i
$681$	23.5075	+	31.0397i	0.900809	+	1.18944i
$682$	−11.0810	+	6.39762i	−0.424314	+	0.244978i
$683$		−	50.5922i		−	1.93586i	−0.251229	−	0.967928i	$-0.580835\pi$
$683$		−	50.5922i		−	1.93586i	0.251229	−	0.967928i	$-0.419165\pi$
$684$	6.43045	+	1.81043i	0.245874	+	0.0692236i
$685$	−45.2602			−1.72930
$686$	5.79841	+	10.0431i	0.221384	+	0.383449i
$687$	−12.2154	+	28.9714i	−0.466046	+	1.10533i
$688$	2.81683	−	4.87889i	0.107390	−	0.186006i
$689$	1.31369	+	26.2625i	0.0500475	+	1.00052i
$690$	−2.30145	−	0.970375i	−0.0876148	−	0.0369416i
$691$	11.4208	−	6.59378i	0.434466	−	0.250839i	−0.266781	−	0.963757i	$-0.585960\pi$
$691$	11.4208	−	6.59378i	0.434466	−	0.250839i	0.701247	+	0.712918i	$0.252627\pi$
$692$	7.24484			0.275407
$693$	−1.58672	+	5.63584i	−0.0602745	+	0.214088i
$694$			25.5902i			0.971389i
$695$	−25.5664	+	14.7607i	−0.969787	+	0.559907i
$696$	−7.97568	−	10.5312i	−0.302317	−	0.399185i
$697$	13.4178	+	7.74675i	0.508234	+	0.293429i
$698$	1.75430	−	3.03854i	0.0664013	−	0.115010i
$699$	2.39503	+	19.1251i	0.0905882	+	0.723377i
$700$	−2.06053	+	1.18965i	−0.0778807	+	0.0449645i
$701$	17.7794			0.671519			0.335759	−	0.941948i	$-0.391007\pi$
$701$	17.7794			0.671519			0.335759	+	0.941948i	$0.391007\pi$
$702$	10.9386	−	15.2101i	0.412851	−	0.574068i
$703$	−25.2828			−0.953558
$704$	1.92848	−	1.11341i	0.0726822	−	0.0419631i
$705$	0.635326	+	5.07329i	0.0239278	+	0.191071i
$706$	−3.65314	+	6.32742i	−0.137488	+	0.238135i
$707$	14.8266	+	8.56014i	0.557612	+	0.321937i
$708$	−4.25484	−	5.61816i	−0.159907	−	0.211144i
$709$	2.99306	−	1.72804i	0.112407	−	0.0648980i	−0.442743	−	0.896649i	$-0.645994\pi$
$709$	2.99306	−	1.72804i	0.112407	−	0.0648980i	0.555149	+	0.831751i	$0.312661\pi$
$710$			44.3210i			1.66334i
$711$	29.7267	+	30.4877i	1.11484	+	1.14338i
$712$	9.89914			0.370986
$713$	−2.58349	+	1.49158i	−0.0967526	+	0.0558601i
$714$	5.32761	+	2.24631i	0.199381	+	0.0840661i
$715$	1.11412	+	22.2728i	0.0416656	+	0.832954i
$716$	−3.66303	+	6.34455i	−0.136894	+	0.237107i
$717$	5.82026	−	13.8040i	0.217362	−	0.515520i
$718$	−7.89943	−	13.6822i	−0.294804	−	0.510616i
$719$	−39.2187			−1.46261			−0.731305	−	0.682051i	$-0.761088\pi$
$719$	−39.2187			−1.46261			−0.731305	+	0.682051i	$0.761088\pi$
$720$	−2.05476	−	8.07532i	−0.0765764	−	0.300949i
$721$		−	7.17365i		−	0.267161i
$722$	−12.1601	+	7.02065i	−0.452553	+	0.261281i
$723$	−2.64561	−	3.49331i	−0.0983913	−	0.129918i
$724$	5.02853	−	8.70968i	0.186884	−	0.323693i
$725$	10.3529	−	17.9317i	0.384496	−	0.665966i
$726$	−10.3827	+	1.30023i	−0.385340	+	0.0482559i
$727$	1.64755	+	2.85364i	0.0611042	+	0.105836i	0.894959	−	0.446148i	$-0.147204\pi$
$727$	1.64755	+	2.85364i	0.0611042	+	0.105836i	−0.833855	+	0.551983i	$0.813871\pi$
$728$	2.65430	−	1.71476i	0.0983750	−	0.0635531i
$729$	−19.8018	+	18.3545i	−0.733400	+	0.679797i
$730$		−	14.5765i		−	0.539499i
$731$	−10.7287	−	18.5826i	−0.396814	−	0.687302i
$732$	1.69985	+	13.5739i	0.0628283	+	0.501705i
$733$	−19.3253	−	11.1575i	−0.713796	−	0.412110i	0.0986691	−	0.995120i	$-0.468541\pi$
$733$	−19.3253	−	11.1575i	−0.713796	−	0.412110i	−0.812465	+	0.583010i	$0.801875\pi$
$734$	9.11999	+	5.26543i	0.336625	+	0.194351i
$735$	−18.1004	−	23.9000i	−0.667642	−	0.881566i
$736$	0.449617	−	0.259586i	0.0165731	−	0.00956848i
$737$	−15.3095			−0.563933
$738$	−11.8267	+	3.00929i	−0.435346	+	0.110774i
$739$			6.45694i			0.237522i	0.992923	+	0.118761i	$0.0378923\pi$
$739$			6.45694i			0.237522i	−0.992923	+	0.118761i	$0.962108\pi$
$740$	15.7678	+	27.3107i	0.579637	+	1.00396i
$741$	−2.41521	−	13.6951i	−0.0887250	−	0.503103i
$742$	3.19591	−	5.53548i	0.117325	−	0.203214i
$743$	19.1556	+	11.0595i	0.702750	+	0.405733i	0.808371	−	0.588673i	$-0.200350\pi$
$743$	19.1556	+	11.0595i	0.702750	+	0.405733i	−0.105621	+	0.994406i	$0.533683\pi$
$744$	−9.17052	−	3.86662i	−0.336207	−	0.141757i
$745$	−20.0350	−	34.7017i	−0.734026	−	1.27137i
$746$			9.73041i			0.356256i
$747$	1.59079	−	1.55109i	0.0582041	−	0.0567513i
$748$		−	8.48144i		−	0.310112i
$749$	−10.2926	+	5.94241i	−0.376082	+	0.217131i
$750$	−8.76421	+	6.63746i	−0.320024	+	0.242366i
$751$	−7.90342	+	13.6891i	−0.288400	+	0.499523i	−0.973428	−	0.228993i	$-0.926457\pi$
$751$	−7.90342	+	13.6891i	−0.288400	+	0.499523i	0.685028	+	0.728517i	$0.259790\pi$
$752$	−0.920402	−	0.531395i	−0.0335636	−	0.0193780i
$753$	−4.84986	−	38.7277i	−0.176739	−	1.41132i
$754$	−12.5430	+	24.4728i	−0.456788	+	0.891247i
$755$	30.7058			1.11750
$756$	−4.23969	+	1.66270i	−0.154196	+	0.0604719i
$757$	−44.5733			−1.62004			−0.810021	−	0.586400i	$-0.800545\pi$
$757$	−44.5733			−1.62004			−0.810021	+	0.586400i	$0.800545\pi$
$758$	−16.4172	−	28.4354i	−0.596300	−	1.03282i
$759$	1.98691	−	0.248820i	0.0721202	−	0.00903158i
$760$	−5.35643	−	3.09254i	−0.194298	−	0.112178i
$761$	−19.2427	−	11.1098i	−0.697547	−	0.402729i	0.108886	−	0.994054i	$-0.465272\pi$
$761$	−19.2427	−	11.1098i	−0.697547	−	0.402729i	−0.806433	+	0.591325i	$0.798605\pi$
$762$	−13.2174	−	17.4525i	−0.478816	−	0.632237i
$763$	3.72582	+	6.45331i	0.134884	+	0.233625i
$764$	18.7989			0.680120
$765$	−30.5495	−	8.60092i	−1.10452	−	0.310967i
$766$	13.7816			0.497949
$767$	−6.69139	+	13.0557i	−0.241612	+	0.471413i
$768$	1.59599	+	0.672925i	0.0575902	+	0.0242821i
$769$	−30.5190	−	17.6202i	−1.10054	−	0.635399i	−0.164180	−	0.986430i	$-0.552498\pi$
$769$	−30.5190	−	17.6202i	−1.10054	−	0.635399i	−0.936364	+	0.351031i	$0.885831\pi$
$770$	2.71040	−	4.69454i	0.0976759	−	0.169180i
$771$	10.7619	+	4.53759i	0.387579	+	0.163417i
$772$	11.4647	−	6.61912i	0.412622	−	0.238227i
$773$		−	12.6527i		−	0.455086i	−0.973768	−	0.227543i	$-0.926931\pi$
$773$		−	12.6527i		−	0.455086i	0.973768	−	0.227543i	$-0.0730693\pi$
$774$	16.2685	+	4.58024i	0.584759	+	0.164633i
$775$		−	15.5990i		−	0.560331i
$776$	−7.86418	−	13.6212i	−0.282308	−	0.488971i
$777$	13.7397	−	10.4056i	0.492909	−	0.373298i
$778$	16.1549	+	9.32704i	0.579181	+	0.334390i
$779$	−4.52917	+	7.84475i	−0.162274	+	0.281067i
$780$	−13.2873	+	11.1500i	−0.475762	+	0.399234i
$781$	−17.7665	−	30.7725i	−0.635736	−	1.10113i
$782$		−	1.97741i		−	0.0707122i
$783$	24.7178	−	30.9789i	0.883343	−	1.10710i
$784$	6.23187			0.222567
$785$	9.23931	−	5.33432i	0.329765	−	0.190390i
$786$	12.7688	−	1.59903i	0.455447	−	0.0570355i
$787$	13.1205	+	7.57513i	0.467695	+	0.270024i	0.715274	−	0.698844i	$-0.246302\pi$
$787$	13.1205	+	7.57513i	0.467695	+	0.270024i	−0.247579	+	0.968868i	$0.579635\pi$
$788$	−1.17161	−	0.676432i	−0.0417370	−	0.0240969i
$789$	−11.3633	+	8.60584i	−0.404544	+	0.306376i
$790$	−19.7120	−	34.1421i	−0.701320	−	1.21472i
$791$		−	2.89899i		−	0.103076i
$792$	4.66372	+	4.78310i	0.165718	+	0.169960i
$793$	23.9197	−	15.4528i	0.849412	−	0.548745i
$794$	3.86733	+	6.69841i	0.137246	+	0.237718i
$795$	−13.6312	+	32.3293i	−0.483449	+	1.14660i
$796$	0.714756	−	1.23799i	0.0253338	−	0.0438795i
$797$	5.91305	−	10.2417i	0.209451	−	0.362780i	−0.742091	−	0.670300i	$-0.766166\pi$
$797$	5.91305	−	10.2417i	0.209451	−	0.362780i	0.951542	+	0.307520i	$0.0994990\pi$
$798$	−1.31331	+	3.11480i	−0.0464908	+	0.110263i
$799$	−3.50561	+	2.02396i	−0.124019	+	0.0716027i
$800$			2.71476i			0.0959811i
$801$	7.32314	+	28.7803i	0.258751	+	1.01690i
$802$	6.82526			0.241008
$803$	5.84313	+	10.1206i	0.206199	+	0.357148i
$804$	−7.18928	−	9.49285i	−0.253546	−	0.334787i
$805$	0.631918	−	1.09451i	0.0222722	−	0.0385766i
$806$	1.03502	+	20.6916i	0.0364571	+	0.728830i
$807$	5.13024	+	40.9667i	0.180593	+	1.44210i
$808$	16.9170	−	9.76705i	0.595139	−	0.343604i
$809$	−18.4258			−0.647815			−0.323908	−	0.946089i	$-0.604997\pi$
$809$	−18.4258			−0.647815			−0.323908	+	0.946089i	$0.604997\pi$
$810$	21.9578	−	11.9479i	0.771518	−	0.419805i
$811$			32.9748i			1.15790i	0.815362	+	0.578952i	$0.196538\pi$
$811$			32.9748i			1.15790i	−0.815362	+	0.578952i	$0.803462\pi$
$812$	5.78906	−	3.34231i	0.203156	−	0.117292i
$813$	−26.5202	+	3.32111i	−0.930103	+	0.116476i
$814$	−21.8955	−	12.6414i	−0.767438	−	0.443080i
$815$	27.0958	−	46.9314i	0.949126	−	1.64393i
$816$	5.25902	−	3.98285i	0.184102	−	0.139427i
$817$	10.8644	−	6.27255i	0.380096	−	0.219449i
$818$	31.2562			1.09285
$819$	6.94900	+	6.44847i	0.242818	+	0.225328i
$820$	11.2986			0.394565
$821$	28.9333	−	16.7047i	1.00978	−	0.582996i	0.0986524	−	0.995122i	$-0.468547\pi$
$821$	28.9333	−	16.7047i	1.00978	−	0.582996i	0.911127	+	0.412125i	$0.135213\pi$
$822$	26.0066	+	10.9653i	0.907086	+	0.382460i
$823$	−25.3516	+	43.9103i	−0.883702	+	1.53062i	−0.0365085	+	0.999333i	$0.511624\pi$
$823$	−25.3516	+	43.9103i	−0.883702	+	1.53062i	−0.847194	+	0.531284i	$0.821710\pi$
$824$	−7.08848	−	4.09254i	−0.246939	−	0.142570i
$825$	−4.06800	+	9.64815i	−0.141630	+	0.335905i
$826$	3.08833	−	1.78305i	0.107457	−	0.0620401i
$827$		−	17.9261i		−	0.623350i	−0.950189	−	0.311675i	$-0.899110\pi$
$827$		−	17.9261i		−	0.623350i	0.950189	−	0.311675i	$-0.100890\pi$
$828$	1.08733	+	1.11516i	0.0377872	+	0.0387545i
$829$	18.4342			0.640247			0.320123	−	0.947376i	$-0.396276\pi$
$829$	18.4342			0.640247			0.320123	+	0.947376i	$0.396276\pi$
$830$	−1.78147	+	1.02853i	−0.0618359	+	0.0357010i
$831$	−12.7724	+	9.67302i	−0.443071	+	0.335553i
$832$	−0.180130	−	3.60105i	−0.00624487	−	0.124844i
$833$	11.8679	−	20.5558i	0.411198	−	0.712216i
$834$	18.2666	−	2.28752i	0.632522	−	0.0792105i
$835$	16.1486	+	27.9701i	0.558844	+	0.967946i
$836$	4.95870			0.171500
$837$	4.45752	−	29.5224i	0.154074	−	1.02044i
$838$		−	17.3677i		−	0.599957i
$839$	38.0045	−	21.9419i	1.31206	−	0.757519i	0.329624	−	0.944112i	$-0.393078\pi$
$839$	38.0045	−	21.9419i	1.31206	−	0.757519i	0.982437	+	0.186594i	$0.0597448\pi$
$840$	4.18370	−	0.523923i	0.144351	−	0.0180771i
$841$	−14.5864	+	25.2643i	−0.502978	+	0.871183i
$842$	−3.41788	+	5.91995i	−0.117788	+	0.204015i
$843$	20.6222	+	27.2299i	0.710267	+	0.937849i
$844$	−6.32982	−	10.9636i	−0.217882	−	0.377382i
$845$	32.9161	+	14.8433i	1.13235	+	0.510626i
$846$	0.864063	−	3.06905i	0.0297071	−	0.105516i
$847$		−	5.29478i		−	0.181931i
$848$	−3.64650	−	6.31593i	−0.125221	−	0.216890i
$849$	11.9737	+	5.04852i	0.410935	+	0.173265i
$850$	8.95461	+	5.16995i	0.307141	+	0.177328i
$851$	−5.10486	−	2.94729i	−0.174992	−	0.101032i
$852$	10.7378	−	25.4670i	0.367871	−	0.872485i
$853$	18.1041	−	10.4524i	0.619872	−	0.357884i	−0.156947	−	0.987607i	$-0.550165\pi$
$853$	18.1041	−	10.4524i	0.619872	−	0.357884i	0.776819	+	0.629723i	$0.216832\pi$
$854$	−6.92214			−0.236871
$855$	5.02856	−	17.8609i	0.171973	−	0.610828i
$856$			13.5605i			0.463487i
$857$	−16.2026	−	28.0637i	−0.553470	−	0.958638i	−0.998021	−	0.0628846i	$-0.979970\pi$
$857$	−16.2026	−	28.0637i	−0.553470	−	0.958638i	0.444551	−	0.895754i	$-0.353363\pi$
$858$	4.75592	−	13.0679i	0.162365	−	0.446132i
$859$	12.7736	−	22.1245i	0.435829	−	0.754877i	−0.561534	−	0.827454i	$-0.689789\pi$
$859$	12.7736	−	22.1245i	0.435829	−	0.754877i	0.997363	+	0.0725761i	$0.0231220\pi$
$860$	−13.5513	−	7.82386i	−0.462096	−	0.266791i
$861$	−0.767309	−	6.12722i	−0.0261498	−	0.208815i
$862$	18.9797	+	32.8739i	0.646452	+	1.11969i
$863$		−	37.5472i		−	1.27812i	−0.769156	−	0.639061i	$-0.779323\pi$
$863$		−	37.5472i		−	1.27812i	0.769156	−	0.639061i	$-0.220677\pi$
$864$	−0.775762	+	5.13792i	−0.0263920	+	0.174795i
$865$		−	20.1229i		−	0.684198i
$866$	−5.05305	+	2.91738i	−0.171710	+	0.0991366i
$867$	0.536598	+	4.28492i	0.0182238	+	0.145523i
$868$	2.51798	−	4.36127i	0.0854658	−	0.148031i
$869$	27.3724	+	15.8035i	0.928546	+	0.536096i
$870$	−29.2509	+	22.1528i	−0.991700	+	0.751050i
$871$	−11.3062	+	22.0598i	−0.383097	+	0.747468i
$872$	8.50225			0.287923
$873$	33.7838	−	32.9406i	1.14341	−	1.11487i
$874$	1.15610			0.0391057
$875$	−2.78151	−	4.81773i	−0.0940324	−	0.162869i
$876$	−3.53149	+	8.37568i	−0.119318	+	0.282988i
$877$	13.1982	+	7.61997i	0.445670	+	0.257308i	0.706000	−	0.708212i	$-0.250498\pi$
$877$	13.1982	+	7.61997i	0.445670	+	0.257308i	−0.260329	+	0.965520i	$0.583831\pi$
$878$	1.33799	+	0.772490i	0.0451551	+	0.0260703i
$879$	−14.5490	+	34.5061i	−0.490726	+	1.16386i
$880$	−3.09254	−	5.35643i	−0.104249	−	0.180565i
$881$	1.19345			0.0402084			0.0201042	−	0.999798i	$-0.493600\pi$
$881$	1.19345			0.0402084			0.0201042	+	0.999798i	$0.493600\pi$
$882$	4.61019	+	18.1183i	0.155233	+	0.610074i
$883$	8.26791			0.278237			0.139119	−	0.990276i	$-0.455573\pi$
$883$	8.26791			0.278237			0.139119	+	0.990276i	$0.455573\pi$
$884$	−12.2211	−	6.26364i	−0.411040	−	0.210669i
$885$	−15.6047	+	11.8180i	−0.524546	+	0.397258i
$886$	3.08196	+	1.77937i	0.103540	+	0.0597790i
$887$	13.5452	−	23.4610i	0.454803	−	0.787743i	−0.543873	−	0.839167i	$-0.683043\pi$
$887$	13.5452	−	23.4610i	0.454803	−	0.787743i	0.998677	+	0.0514245i	$0.0163762\pi$
$888$	−2.44360	−	19.5129i	−0.0820017	−	0.654811i
$889$	9.59371	−	5.53893i	0.321763	−	0.185770i
$890$		−	27.4953i		−	0.921645i
$891$	−10.4561	+	17.0975i	−0.350292	+	0.572788i
$892$		−	29.8057i		−	0.997968i
$893$	−1.18332	−	2.04957i	−0.0395982	−	0.0685861i
$894$	3.10490	+	24.7936i	0.103843	+	0.829223i
$895$	17.6223	+	10.1742i	0.589048	+	0.340087i
$896$	−0.438215	+	0.759011i	−0.0146397	+	0.0253568i
$897$	1.10882	−	3.04673i	0.0370226	−	0.101727i
$898$	5.08037	+	8.79945i	0.169534	+	0.293642i
$899$			43.8252i			1.46165i
$900$	−7.89277	+	2.00831i	−0.263092	+	0.0669437i
$901$	−27.7774			−0.925401
$902$	−7.84475	+	4.52917i	−0.261202	+	0.150805i
$903$	−3.32257	+	7.88019i	−0.110568	+	0.262236i
$904$	−2.86458	−	1.65386i	−0.0952744	−	0.0550067i
$905$	−24.1915	−	13.9670i	−0.804153	−	0.464278i
$906$	−17.6436	−	7.43919i	−0.586171	−	0.247151i
$907$	20.9922	+	36.3595i	0.697033	+	1.20730i	0.969490	+	0.245129i	$0.0788303\pi$
$907$	20.9922	+	36.3595i	0.697033	+	1.20730i	−0.272457	+	0.962168i	$0.587836\pi$
$908$			22.4801i			0.746029i
$909$	40.9111	+	41.9584i	1.35694	+	1.39167i
$910$	−4.76281	−	7.37244i	−0.157886	−	0.244394i
$911$	21.4808	+	37.2059i	0.711692	+	1.23269i	0.964222	+	0.265097i	$0.0854040\pi$
$911$	21.4808	+	37.2059i	0.711692	+	1.23269i	−0.252530	+	0.967589i	$0.581263\pi$
$912$	2.32858	+	3.07470i	0.0771071	+	0.101814i
$913$	0.824598	−	1.42824i	0.0272902	−	0.0472680i
$914$	−10.6577	+	18.4597i	−0.352525	+	0.610591i
$915$	37.7021	−	4.72142i	1.24639	−	0.156085i
$916$	−15.7207	+	9.07634i	−0.519426	+	0.299891i
$917$			6.51157i			0.215031i
$918$	15.4701	+	12.3434i	0.510588	+	0.407394i
$919$	−7.24189			−0.238888			−0.119444	−	0.992841i	$-0.538111\pi$
$919$	−7.24189			−0.238888			−0.119444	+	0.992841i	$0.538111\pi$
$920$	−0.721013	−	1.24883i	−0.0237711	−	0.0411727i
$921$	−13.4256	+	1.68128i	−0.442387	+	0.0554000i
$922$	−10.7623	+	18.6408i	−0.354436	+	0.613902i
$923$	−57.4616	+	2.87431i	−1.89137	+	0.0946092i
$924$	−2.69477	+	2.04084i	−0.0886513	+	0.0671388i
$925$	26.6933	−	15.4114i	0.877670	−	0.506723i
$926$	−35.8128			−1.17688
$927$	6.65459	−	23.6363i	0.218565	−	0.776319i
$928$		−	7.62710i		−	0.250372i
$929$	3.51403	−	2.02883i	0.115292	−	0.0665636i	−0.441245	−	0.897387i	$-0.645463\pi$
$929$	3.51403	−	2.02883i	0.115292	−	0.0665636i	0.556537	+	0.830823i	$0.312130\pi$
$930$	−10.7397	+	25.4715i	−0.352169	+	0.835244i
$931$	12.0180	+	6.93861i	0.393875	+	0.227404i
$932$	−5.56406	+	9.63723i	−0.182257	+	0.315678i
$933$	−15.4813	−	6.52748i	−0.506835	−	0.213700i
$934$	18.5788	−	10.7265i	0.607916	−	0.350981i
$935$	−23.5576			−0.770415
$936$	10.3363	−	3.18767i	0.337852	−	0.104192i
$937$	60.3456			1.97140			0.985702	−	0.168497i	$-0.0538915\pi$
$937$	60.3456			1.97140			0.985702	+	0.168497i	$0.0538915\pi$
$938$	5.21826	−	3.01276i	0.170382	−	0.0983702i
$939$	44.0626	−	33.3702i	1.43793	−	1.08900i
$940$	−1.47597	+	2.55646i	−0.0481409	+	0.0833825i
$941$	38.1340	+	22.0167i	1.24313	+	0.717723i	0.969731	−	0.244177i	$-0.0785179\pi$
$941$	38.1340	+	22.0167i	1.24313	+	0.717723i	0.273401	+	0.961900i	$0.411851\pi$
$942$	−6.60130	+	0.826678i	−0.215082	+	0.0269346i
$943$	−1.82897	+	1.05596i	−0.0595595	+	0.0343867i
$944$		−	4.06888i		−	0.132431i
$945$	4.61823	+	11.7759i	0.150231	+	0.383071i
$946$	12.5451			0.407876
$947$	−15.2058	+	8.77906i	−0.494122	+	0.285281i	−0.726283	−	0.687396i	$-0.758754\pi$
$947$	−15.2058	+	8.77906i	−0.494122	+	0.285281i	0.232161	+	0.972677i	$0.425420\pi$
$948$	3.05483	+	24.3938i	0.0992163	+	0.792275i
$949$	18.8982	−	0.945315i	0.613461	−	0.0306862i
$950$	−3.02263	+	5.23535i	−0.0980670	+	0.169857i
$951$	29.5701	+	39.0449i	0.958878	+	1.26612i
$952$	1.66906	+	2.89090i	0.0540947	+	0.0936948i
$953$	−28.3807			−0.919342			−0.459671	−	0.888089i	$-0.652033\pi$
$953$	−28.3807			−0.919342			−0.459671	+	0.888089i	$0.652033\pi$
$954$	15.6651	−	15.2741i	0.507176	−	0.494516i
$955$		−	52.2148i		−	1.68963i
$956$	7.49042	−	4.32460i	0.242258	−	0.139867i
$957$	11.4291	−	27.1065i	0.369449	−	0.876227i
$958$	2.88734	−	5.00102i	0.0932857	−	0.161575i
$959$	−7.14073	+	12.3681i	−0.230586	+	0.399387i
$960$	1.86908	−	4.43292i	0.0603243	−	0.143072i
$961$	1.00819	+	1.74623i	0.0325221	+	0.0563300i
$962$	−34.3853	+	22.2139i	−1.10863	+	0.716206i
$963$	−39.4251	+	10.0317i	−1.27046	+	0.323267i
$964$		−	2.52998i		−	0.0814853i
$965$	−18.3849	−	31.8436i	−0.591831	−	1.02508i
$966$	−0.628274	+	0.475814i	−0.0202144	+	0.0153091i
$967$	6.52590	+	3.76773i	0.209859	+	0.121162i	0.601246	−	0.799064i	$-0.294671\pi$
$967$	6.52590	+	3.76773i	0.209859	+	0.121162i	−0.391387	+	0.920226i	$0.628005\pi$
$968$	−5.23192	−	3.02065i	−0.168160	−	0.0970873i
$969$	14.5764	−	1.82540i	0.468262	−	0.0586403i
$970$	−37.8334	+	21.8431i	−1.21476	+	0.701340i
$971$	32.9658			1.05792			0.528962	−	0.848645i	$-0.322581\pi$
$971$	32.9658			1.05792			0.528962	+	0.848645i	$0.322581\pi$
$972$	−15.5117	+	1.54549i	−0.497537	+	0.0495716i
$973$			9.31526i			0.298633i
$974$	16.4562	+	28.5030i	0.527291	+	0.913294i
$975$	10.8980	+	12.9869i	0.349014	+	0.415915i
$976$	−3.94905	+	6.83995i	−0.126406	+	0.218942i
$977$	−3.30414	−	1.90765i	−0.105709	−	0.0610311i	0.446213	−	0.894927i	$-0.352772\pi$
$977$	−3.30414	−	1.90765i	−0.105709	−	0.0610311i	−0.551922	+	0.833895i	$0.686106\pi$
$978$	−26.9396	+	20.4023i	−0.861433	+	0.652394i
$979$	11.0218	+	19.0903i	0.352257	+	0.610128i
$980$		−	17.3093i		−	0.552925i
$981$	6.28976	+	24.7191i	0.200817	+	0.789220i
$982$			9.79923i			0.312706i
$983$	−39.1001	+	22.5745i	−1.24710	+	0.720013i	−0.970530	−	0.240981i	$-0.922531\pi$
$983$	−39.1001	+	22.5745i	−1.24710	+	0.720013i	−0.276570	+	0.960994i	$0.589198\pi$
$984$	−6.49222	−	2.73735i	−0.206964	−	0.0872637i
$985$	−1.87882	+	3.25421i	−0.0598642	+	0.103688i
$986$	−25.1580	−	14.5250i	−0.801193	−	0.462569i
$987$	1.48660	+	0.626804i	0.0473190	+	0.0199514i
$988$	3.66206	−	7.14510i	0.116506	−	0.227316i
$989$	2.92484			0.0930045
$990$	13.2853	−	12.9537i	0.422234	−	0.411695i
$991$	43.7885			1.39099			0.695493	−	0.718533i	$-0.255186\pi$
$991$	43.7885			1.39099			0.695493	+	0.718533i	$0.255186\pi$
$992$	−2.87299	−	4.97617i	−0.0912176	−	0.157994i
$993$	−11.1382	−	14.7070i	−0.353459	−	0.466713i
$994$	12.1115	+	6.99256i	0.384153	+	0.221791i
$995$	−3.43858	−	1.98527i	−0.109010	−	0.0629372i
$996$	1.27283	−	0.159396i	0.0403311	−	0.00505065i
$997$	−27.1339	−	46.9972i	−0.859338	−	1.48842i	−0.872561	−	0.488504i	$-0.837543\pi$
$997$	−27.1339	−	46.9972i	−0.859338	−	1.48842i	0.0132236	−	0.999913i	$-0.495791\pi$
$998$	41.3110			1.30768
$999$	54.9234	−	21.5396i	1.73770	−	0.681483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.t.a.103.4	yes	28
3.2	odd	2		702.2.t.a.415.13		28
9.2	odd	6		702.2.t.a.181.2		28
9.4	even	3		2106.2.b.c.649.6		14
9.5	odd	6		2106.2.b.d.649.9		14
9.7	even	3	inner	234.2.t.a.25.11	yes	28
13.12	even	2	inner	234.2.t.a.103.11	yes	28
39.38	odd	2		702.2.t.a.415.2		28
117.25	even	6	inner	234.2.t.a.25.4	✓	28
117.38	odd	6		702.2.t.a.181.13		28
117.77	odd	6		2106.2.b.d.649.6		14
117.103	even	6		2106.2.b.c.649.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.t.a.25.4	✓	28	117.25	even	6	inner
234.2.t.a.25.11	yes	28	9.7	even	3	inner
234.2.t.a.103.4	yes	28	1.1	even	1	trivial
234.2.t.a.103.11	yes	28	13.12	even	2	inner
702.2.t.a.181.2		28	9.2	odd	6
702.2.t.a.181.13		28	117.38	odd	6
702.2.t.a.415.2		28	39.38	odd	2
702.2.t.a.415.13		28	3.2	odd	2
2106.2.b.c.649.6		14	9.4	even	3
2106.2.b.c.649.9		14	117.103	even	6
2106.2.b.d.649.6		14	117.77	odd	6
2106.2.b.d.649.9		14	9.5	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 $\F_{q}$

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} +(-0.215223 - 1.71863i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.40542 - 1.38877i) q^{5} +(1.04570 + 1.38076i) q^{6} +(-0.759011 + 0.438215i) q^{7} +1.00000i q^{8} +(-2.90736 + 0.739776i) q^{9} +2.77754 q^{10} +(-1.92848 + 1.11341i) q^{11} +(-1.59599 - 0.672925i) q^{12} +(0.180130 + 3.60105i) q^{13} +(0.438215 - 0.759011i) q^{14} +(-1.86908 + 4.43292i) q^{15} +(-0.500000 - 0.866025i) q^{16} -3.80878 q^{17} +(2.14796 - 2.09434i) q^{18} -2.22681i q^{19} +(-2.40542 + 1.38877i) q^{20} +(0.916486 + 1.21014i) q^{21} +(1.11341 - 1.92848i) q^{22} +(0.259586 - 0.449617i) q^{23} +(1.71863 - 0.215223i) q^{24} +(1.35738 + 2.35105i) q^{25} +(-1.95652 - 3.02853i) q^{26} +(1.89713 + 4.83745i) q^{27} +0.876431i q^{28} +(-3.81355 - 6.60527i) q^{29} +(-0.597791 - 4.77356i) q^{30} +(-4.97617 - 2.87299i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.32858 + 3.07470i) q^{33} +(3.29850 - 1.90439i) q^{34} +2.43433 q^{35} +(-0.813014 + 2.88773i) q^{36} -11.3538i q^{37} +(1.11341 + 1.92848i) q^{38} +(6.15009 - 1.08460i) q^{39} +(1.38877 - 2.40542i) q^{40} +(-3.52286 - 2.03392i) q^{41} +(-1.39877 - 0.589772i) q^{42} +(2.81683 + 4.87889i) q^{43} +2.22681i q^{44} +(8.02081 + 2.25818i) q^{45} +0.519173i q^{46} +(0.920402 - 0.531395i) q^{47} +(-1.38076 + 1.04570i) q^{48} +(-3.11593 + 5.39696i) q^{49} +(-2.35105 - 1.35738i) q^{50} +(0.819736 + 6.54587i) q^{51} +(3.20866 + 1.64453i) q^{52} +7.29301 q^{53} +(-4.06169 - 3.24079i) q^{54} +6.18508 q^{55} +(-0.438215 - 0.759011i) q^{56} +(-3.82706 + 0.479262i) q^{57} +(6.60527 + 3.81355i) q^{58} +(3.52376 + 2.03444i) q^{59} +(2.90448 + 3.83513i) q^{60} +(-3.94905 - 6.83995i) q^{61} +5.74599 q^{62} +(1.88254 - 1.83555i) q^{63} -1.00000 q^{64} +(4.56775 - 8.91221i) q^{65} +(-3.55397 - 1.49848i) q^{66} +(5.95399 + 3.43754i) q^{67} +(-1.90439 + 3.29850i) q^{68} +(-0.828593 - 0.349364i) q^{69} +(-2.10819 + 1.21716i) q^{70} +15.9569i q^{71} +(-0.739776 - 2.90736i) q^{72} -5.24797i q^{73} +(5.67689 + 9.83267i) q^{74} +(3.74843 - 2.83883i) q^{75} +(-1.92848 - 1.11341i) q^{76} +(0.975824 - 1.69018i) q^{77} +(-4.78383 + 4.01434i) q^{78} +(-7.09690 - 12.2922i) q^{79} +2.77754i q^{80} +(7.90546 - 4.30159i) q^{81} +4.06784 q^{82} +(-0.641385 + 0.370304i) q^{83} +(1.50626 - 0.188628i) q^{84} +(9.16172 + 5.28952i) q^{85} +(-4.87889 - 2.81683i) q^{86} +(-10.5312 + 7.97568i) q^{87} +(-1.11341 - 1.92848i) q^{88} -9.89914i q^{89} +(-8.07532 + 2.05476i) q^{90} +(-1.71476 - 2.65430i) q^{91} +(-0.259586 - 0.449617i) q^{92} +(-3.86662 + 9.17052i) q^{93} +(-0.531395 + 0.920402i) q^{94} +(-3.09254 + 5.35643i) q^{95} +(0.672925 - 1.59599i) q^{96} +(-13.6212 + 7.86418i) q^{97} -6.23187i q^{98} +(4.78310 - 4.66372i) 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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