LMFDB - Embedded newform 234.2.t.a.103.11

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			103.11
Character	$\chi$	$=$	234.103
Dual form			234.2.t.a.25.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.215223 - 1.71863i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.40542 + 1.38877i) q^{5} +(-1.04570 - 1.38076i) q^{6} +(0.759011 - 0.438215i) q^{7} -1.00000i q^{8} +(-2.90736 + 0.739776i) q^{9} +O(q^{10})$	\(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} +(-3.20866 + 1.64453i) 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} +(3.51691 + 5.16056i) 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} +(-0.180130 + 3.60105i) 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} +(-10.0021 - 0.500318i) 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} +(5.62601 + 2.71072i) 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}+O(q^{10}) $ 28 * q + 14 * q^4 - 16 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	0.929744	−	0.368207i	$-0.120028\pi$
$5$	2.40542	+	1.38877i	1.07574	+	0.621078i	0.145995	+	0.989285i	$0.453362\pi$
$6$	−1.04570	−	1.38076i	−0.426906	−	0.563694i
$7$	0.759011	−	0.438215i	0.286879	−	0.165630i	−0.349654	−	0.936879i	$-0.613701\pi$
$7$	0.759011	−	0.438215i	0.286879	−	0.165630i	0.636534	+	0.771249i	$0.280368\pi$
$8$		−	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	−0.180255	−	0.983620i	$-0.557692\pi$
$11$	1.92848	−	1.11341i	0.581458	−	0.335705i	0.761713	+	0.647915i	$0.224359\pi$
$12$	−1.59599	−	0.672925i	−0.460722	−	0.194257i
$13$	−3.20866	+	1.64453i	−0.889923	+	0.456110i
$13$	−3.20866	+	1.64453i	−0.889923	+	0.456110i
$14$	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	$0.0822181\pi$
$19$			2.22681i			0.510866i	−0.966827	+	0.255433i	$0.917782\pi$
$20$	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	0.875166	−	0.483822i	$-0.160752\pi$
$31$	4.97617	+	2.87299i	0.893747	+	0.516005i	0.0185805	+	0.999827i	$0.494085\pi$
$32$	−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	$0.383063\pi$
$37$			11.3538i			1.86655i	−0.359161	+	0.933276i	$0.616937\pi$
$38$	1.11341	+	1.92848i	0.180619	+	0.312840i
$39$	3.51691	+	5.16056i	0.563156	+	0.826351i
$40$	1.38877	−	2.40542i	0.219584	−	0.380331i
$41$	3.52286	+	2.03392i	0.550178	+	0.317645i	0.749194	−	0.662351i	$-0.230441\pi$
$41$	3.52286	+	2.03392i	0.550178	+	0.317645i	−0.199016	+	0.979996i	$0.563775\pi$
$42$	−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	−0.565623	−	0.824664i	$-0.691364\pi$
$47$	−0.920402	+	0.531395i	−0.134254	+	0.0775119i	0.431368	+	0.902176i	$0.358031\pi$
$48$	−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
$52$	−0.180130	+	3.60105i	−0.0249795	+	0.499376i
$53$	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	0.252766	−	0.967527i	$-0.418660\pi$
$59$	−3.52376	−	2.03444i	−0.458754	−	0.264862i	−0.711520	+	0.702666i	$0.751993\pi$
$60$	−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
$65$	−10.0021	−	0.500318i	−1.24060	−	0.0620569i
$66$	−3.55397	−	1.49848i	−0.437463	−	0.184450i
$67$	−5.95399	−	3.43754i	−0.727395	−	0.419962i	0.0900733	−	0.995935i	$-0.471290\pi$
$67$	−5.95399	−	3.43754i	−0.727395	−	0.419962i	−0.817468	+	0.575973i	$0.804623\pi$
$68$	−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	$-0.604228\pi$
$71$		−	15.9569i		−	1.89374i	0.321622	−	0.946868i	$-0.395772\pi$
$72$	0.739776	+	2.90736i	0.0871834	+	0.342635i
$73$			5.24797i			0.614228i	0.951673	+	0.307114i	$0.0993633\pi$
$73$			5.24797i			0.614228i	−0.951673	+	0.307114i	$0.900637\pi$
$74$	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
$78$	5.62601	+	2.71072i	0.637020	+	0.306929i
$79$	−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	−0.464386	−	0.885633i	$-0.653725\pi$
$83$	0.641385	−	0.370304i	0.0704011	−	0.0406461i	0.534787	+	0.844987i	$0.320392\pi$
$84$	−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	$0.175805\pi$
$89$			9.89914i			1.04931i	−0.851316	+	0.524653i	$0.824195\pi$
$90$	−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	0.390503	−	0.920602i	$-0.372301\pi$
$97$	13.6212	−	7.86418i	1.38302	−	0.798486i	0.992516	+	0.122116i	$0.0389678\pi$
$98$			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	$0.298786\pi$
$104$	1.64453	+	3.20866i	0.161259	+	0.314635i
$105$	−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	$0.133489\pi$
$109$			8.50225i			0.814368i	−0.913346	+	0.407184i	$0.866511\pi$
$110$	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
$117$	8.11216	−	7.15492i	0.749969	−	0.661473i
$118$	−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
$130$	−8.91221	+	4.56775i	−0.781653	+	0.400618i
$131$	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	−0.961809	−	0.273723i	$-0.911745\pi$
$137$	−14.1119	+	8.14752i	−1.20566	+	0.696089i	−0.243853	+	0.969812i	$0.578412\pi$
$138$	−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	−0.108398	−	0.994108i	$-0.534572\pi$
$149$	−12.4936	−	7.21321i	−1.02352	−	0.590929i	−0.915121	+	0.403179i	$0.867905\pi$
$150$	1.82683	−	4.33271i	0.149160	−	0.353764i
$151$	9.57392	−	5.52751i	0.779115	−	0.449822i	−0.0570018	−	0.998374i	$-0.518154\pi$
$151$	9.57392	−	5.52751i	0.779115	−	0.449822i	0.836116	+	0.548552i	$0.184821\pi$
$152$	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
$156$	6.22763	−	0.465452i	0.498609	−	0.0372660i
$157$	−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	$-0.723185\pi$
$163$		−	19.5106i		−	1.52819i	0.645103	−	0.764096i	$-0.276815\pi$
$164$	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	0.836163	−	0.548481i	$-0.184794\pi$
$167$	10.0701	+	5.81397i	0.779247	+	0.449898i	−0.0569166	+	0.998379i	$0.518127\pi$
$168$	−1.21014	+	0.916486i	−0.0933646	+	0.0707084i
$169$	7.59106	−	10.5535i	0.583928	−	0.811806i
$170$	−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	$0.378066\pi$
$182$	−0.157871	+	3.15607i	−0.0117022	+	0.233943i
$183$	−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	0.0269777	−	0.999636i	$-0.491412\pi$
$193$	−11.4647	−	6.61912i	−0.825244	−	0.476455i	−0.852221	+	0.523181i	$0.824745\pi$
$194$	7.86418	−	13.6212i	0.564615	−	0.977942i
$195$	1.29282	+	17.2975i	0.0925804	+	1.23870i
$196$	3.11593	+	5.39696i	0.222567	+	0.385497i
$197$			1.35286i			0.0963875i	0.998838	+	0.0481938i	$0.0153465\pi$
$197$			1.35286i			0.0963875i	−0.998838	+	0.0481938i	$0.984654\pi$
$198$	−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
$221$	12.2211	−	6.26364i	0.822079	−	0.421338i
$222$	15.6769	−	11.8727i	1.05216	−	0.796842i
$223$	−25.8125	+	14.9028i	−1.72853	+	0.997968i	−0.832408	+	0.554164i	$0.813038\pi$
$223$	−25.8125	+	14.9028i	−1.72853	+	0.997968i	−0.896124	+	0.443804i	$0.853628\pi$
$224$	−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	0.313123	−	0.949713i	$-0.398625\pi$
$227$	19.4683	−	11.2401i	1.29216	−	0.746029i	0.979037	+	0.203684i	$0.0652915\pi$
$228$	1.49848	−	3.55397i	0.0992392	−	0.235367i
$229$	15.7207	+	9.07634i	1.03885	+	0.599781i	0.919508	−	0.393072i	$-0.128588\pi$
$229$	15.7207	+	9.07634i	1.03885	+	0.599781i	0.119344	+	0.992853i	$0.461921\pi$
$230$	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	$0.618765\pi$
$234$	3.44787	−	10.2524i	0.225394	−	0.670222i
$235$	−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	0.237781	−	0.971319i	$-0.423580\pi$
$239$	−7.49042	−	4.32460i	−0.484515	−	0.279735i	−0.722296	+	0.691584i	$0.756913\pi$
$240$	−4.77356	+	0.597791i	−0.308132	+	0.0385873i
$241$	−2.19103	+	1.26499i	−0.141137	+	0.0814853i	−0.568906	−	0.822403i	$-0.692633\pi$
$241$	−2.19103	+	1.26499i	−0.141137	+	0.0814853i	0.427769	+	0.903888i	$0.359300\pi$
$242$			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
$247$	−3.66206	−	7.14510i	−0.233011	−	0.454632i
$248$	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	$0.155272\pi$
$271$			15.4310i			0.937367i	−0.883366	+	0.468684i	$0.844728\pi$
$272$	1.90439	+	3.29850i	0.115471	+	0.200001i
$273$	4.93081	+	2.37576i	0.298426	+	0.143787i
$274$	−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	0.105071	−	0.994465i	$-0.466493\pi$
$281$	17.0788	−	9.86047i	1.01884	−	0.588226i	0.913767	+	0.406239i	$0.133160\pi$
$282$	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
$286$	−0.401116	+	8.01887i	−0.0237185	+	0.474166i
$287$	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	0.934603	−	0.355694i	$-0.115755\pi$
$293$	18.7239	+	10.8103i	1.09386	+	0.631543i	0.159261	+	0.987236i	$0.449089\pi$
$294$	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
$299$	−0.0935185	+	1.86957i	−0.00540831	+	0.108120i
$300$	−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	$0.0715593\pi$
$307$			7.81179i			0.445842i	−0.974836	+	0.222921i	$0.928441\pi$
$308$	−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	$0.0779813\pi$
$312$	5.16056	−	3.51691i	0.292159	−	0.199106i
$313$	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	0.383847	−	0.923397i	$-0.374599\pi$
$317$	24.4893	−	14.1389i	1.37546	−	0.794119i	0.991608	+	0.129277i	$0.0412658\pi$
$318$	−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	−0.731606	−	0.681727i	$-0.761229\pi$
$331$	−9.22435	+	5.32568i	−0.507016	+	0.292726i	0.224590	+	0.974453i	$0.427896\pi$
$332$		−	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	$0.161101\pi$
$338$	1.29731	−	12.9351i	0.0705645	−	0.703577i
$339$	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	−0.416466	−	0.909151i	$-0.636731\pi$
$349$	3.03854	−	1.75430i	0.162649	−	0.0939056i	0.579115	+	0.815246i	$0.303398\pi$
$350$	2.37930			0.127179
$351$	−14.0426	−	12.4019i	−0.749537	−	0.661963i
$352$	−2.22681			−0.118690
$353$	−6.32742	+	3.65314i	−0.336774	+	0.194437i	−0.658845	−	0.752279i	$-0.728955\pi$
$353$	−6.32742	+	3.65314i	−0.336774	+	0.194437i	0.322070	+	0.946716i	$0.395621\pi$
$354$	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	$-0.863111\pi$
$359$		−	15.7989i		−	0.833832i	0.908945	−	0.416916i	$-0.136889\pi$
$360$	−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
$364$	1.44131	+	2.81217i	0.0755454	+	0.147398i
$365$	−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	$-0.680612\pi$
$379$		−	32.8344i		−	1.68659i	0.537450	−	0.843296i	$-0.319388\pi$
$380$	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	0.772911	−	0.634515i	$-0.218800\pi$
$383$	11.9352	+	6.89079i	0.609860	+	0.352103i	−0.163050	+	0.986618i	$0.552133\pi$
$384$	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	$0.990126\pi$
$390$	9.76837	+	14.3337i	0.494641	+	0.725814i
$391$	−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	$0.0621772\pi$
$397$			7.73466i			0.388191i	−0.980983	+	0.194096i	$0.937823\pi$
$398$	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	0.640273	−	0.768148i	$-0.278821\pi$
$401$	5.91085	+	3.41263i	0.295174	+	0.170419i	−0.345099	+	0.938566i	$0.612155\pi$
$402$	1.47967	+	11.8157i	0.0737994	+	0.589313i
$403$	−20.6916	−	1.03502i	−1.03072	−	0.0515582i
$404$	−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	0.986579	−	0.163285i	$-0.0522089\pi$
$409$	27.0687	+	15.6281i	1.33846	+	0.772760i	0.351881	+	0.936045i	$0.385542\pi$
$410$	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
$416$	3.60105	+	0.180130i	0.176556	+	0.00883159i
$417$	−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	−0.637275	−	0.770637i	$-0.719938\pi$
$421$	−5.91995	+	3.41788i	−0.288521	+	0.166577i	0.348754	+	0.937214i	$0.386605\pi$
$422$		−	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
$429$	12.5281	+	6.03627i	0.604861	+	0.291434i
$430$	7.82386	+	13.5513i	0.377300	+	0.653503i
$431$			37.9595i			1.82844i	0.405215	+	0.914221i	$0.367197\pi$
$431$			37.9595i			1.82844i	−0.405215	+	0.914221i	$0.632803\pi$
$432$	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	$0.0770679\pi$
$449$			10.1607i			0.479515i	−0.970833	+	0.239757i	$0.922932\pi$
$450$	−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
$455$	−7.81094	+	4.00332i	−0.366182	+	0.187678i
$456$	−0.479262	−	3.82706i	−0.0224435	−	0.179219i
$457$	−18.4597	+	10.6577i	−0.863506	+	0.498546i	−0.865185	−	0.501453i	$-0.832799\pi$
$457$	−18.4597	+	10.6577i	−0.863506	+	0.498546i	0.00167864	+	0.999999i	$0.499466\pi$
$458$	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	−0.866746	−	0.498750i	$-0.833792\pi$
$461$	−18.6408	+	10.7623i	−0.868188	+	0.501248i	−0.00144222	+	0.999999i	$0.500459\pi$
$462$	−3.35416	+	0.420040i	−0.156049	+	0.0195420i
$463$	−31.0148	−	17.9064i	−1.44138	−	0.832180i	−0.443437	−	0.896306i	$-0.646241\pi$
$463$	−31.0148	−	17.9064i	−1.44138	−	0.832180i	−0.997942	+	0.0641254i	$0.979574\pi$
$464$	−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	$0.665331\pi$
$468$	−2.14027	−	10.6028i	−0.0989339	−	0.490114i
$469$	−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	−0.381379	−	0.924419i	$-0.624551\pi$
$479$	5.00102	−	2.88734i	0.228502	−	0.131926i	0.609881	+	0.792493i	$0.291217\pi$
$480$	−3.83513	+	2.90448i	−0.175049	+	0.132571i
$481$	−18.6716	−	36.4305i	−0.851352	−	1.66109i
$482$	−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	$0.267886\pi$
$487$			32.9124i			1.49140i	−0.666280	+	0.745702i	$0.732114\pi$
$488$	−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	$0.0423228\pi$
$499$	35.7763	+	20.6555i	1.60157	+	0.924666i	0.610395	+	0.792097i	$0.291011\pi$
$500$	−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
$507$	−19.7713	−	10.7748i	−0.878072	−	0.478528i
$508$	−6.31987	+	10.9463i	−0.280399	+	0.485665i
$509$	0.959102	+	0.553738i	0.0425115	+	0.0245440i	0.521105	−	0.853493i	$-0.325520\pi$
$509$	0.959102	+	0.553738i	0.0425115	+	0.0245440i	−0.478594	+	0.878037i	$0.658853\pi$
$510$	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
$520$	−0.500318	+	10.0021i	−0.0219404	+	0.438620i
$521$	−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
$533$	−14.6485	−	0.732740i	−0.634497	−	0.0317385i
$534$	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	$0.215564\pi$
$541$			29.1499i			1.25325i	−0.779320	+	0.626626i	$0.784436\pi$
$542$	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
$546$	5.45809	−	0.407937i	0.233584	−	0.0174581i
$547$	−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	$-0.903780\pi$
$557$		−	14.0519i		−	0.595400i	0.954659	−	0.297700i	$-0.0962195\pi$
$558$	−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	$0.947023\pi$
$572$	3.66206	+	7.14510i	0.153118	+	0.298752i
$573$	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	$-0.978817\pi$
$577$		−	3.19469i		−	0.132997i	0.997787	−	0.0664984i	$-0.0211827\pi$
$578$	−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
$585$	29.4497	−	5.94469i	1.21760	−	0.245783i
$586$	21.6205			0.893136
$587$	−11.2778	+	6.51126i	−0.465486	+	0.268748i	−0.714348	−	0.699790i	$-0.753277\pi$
$587$	−11.2778	+	6.51126i	−0.465486	+	0.268748i	0.248862	+	0.968539i	$0.419943\pi$
$588$	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	$0.0791581\pi$
$593$			11.9872i			0.492254i	−0.969238	+	0.246127i	$0.920842\pi$
$594$	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
$598$	0.853794	+	1.66585i	0.0349142	+	0.0681217i
$599$	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	$-0.814703\pi$
$613$		−	27.2249i		−	1.09961i	0.835295	−	0.549803i	$-0.185297\pi$
$614$	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	0.639453	−	0.768831i	$-0.279161\pi$
$617$	7.28671	+	4.20698i	0.293352	+	0.169367i	−0.346101	+	0.938197i	$0.612494\pi$
$618$	14.0671	−	1.76162i	0.565862	−	0.0708626i
$619$	30.4315	−	17.5696i	1.22314	−	0.706182i	0.257557	−	0.966263i	$-0.417083\pi$
$619$	30.4315	−	17.5696i	1.22314	−	0.706182i	0.965587	+	0.260081i	$0.0837492\pi$
$620$	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
$624$	2.71072	−	5.62601i	0.108516	−	0.225221i
$625$	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	$-0.862717\pi$
$631$		−	21.0022i		−	0.836083i	0.908428	−	0.418042i	$-0.137283\pi$
$632$	−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
$637$	1.12254	−	22.4413i	0.0444768	−	0.889155i
$638$	−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	0.835806	−	0.549025i	$-0.185001\pi$
$643$	19.7342	+	11.3935i	0.778240	+	0.449317i	−0.0575663	+	0.998342i	$0.518334\pi$
$644$	−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
$650$	−9.77597	−	0.489008i	−0.383445	−	0.0191805i
$651$	−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	0.786392	−	0.617728i	$-0.211947\pi$
$661$	16.5731	+	9.56850i	0.644620	+	0.372172i	−0.141772	+	0.989899i	$0.545280\pi$
$662$	−5.32568	+	9.22435i	−0.206989	+	0.358515i
$663$	−13.3951	−	19.6554i	−0.520223	−	0.763353i
$664$	−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	$0.419165\pi$
$683$			50.5922i			1.93586i	−0.251229	+	0.967928i	$0.580835\pi$
$684$	−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
$689$	−23.4008	+	11.9936i	−0.891500	+	0.456918i
$690$	−2.30145	−	0.970375i	−0.0876148	−	0.0369416i
$691$	−11.4208	+	6.59378i	−0.434466	+	0.250839i	−0.701247	−	0.712918i	$-0.747373\pi$
$691$	−11.4208	+	6.59378i	−0.434466	+	0.250839i	0.266781	+	0.963757i	$0.414040\pi$
$692$	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	$0.391007\pi$
$702$	−18.3622	−	3.71905i	−0.693035	−	0.140366i
$703$	−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	−0.555149	−	0.831751i	$-0.687339\pi$
$709$	−2.99306	+	1.72804i	−0.112407	+	0.0648980i	0.442743	+	0.896649i	$0.354006\pi$
$710$		−	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
$715$	−19.8458	+	10.1715i	−0.742192	+	0.380394i
$716$	−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	0.812465	−	0.583010i	$-0.198125\pi$
$733$	19.3253	+	11.1575i	0.713796	+	0.412110i	−0.0986691	+	0.995120i	$0.531459\pi$
$734$	−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	$-0.962108\pi$
$739$		−	6.45694i		−	0.237522i	0.992923	−	0.118761i	$-0.0378923\pi$
$740$	15.7678	+	27.3107i	0.579637	+	1.00396i
$741$	−11.4916	+	7.83150i	−0.422155	+	0.287697i
$742$	3.19591	−	5.53548i	0.117325	−	0.203214i
$743$	−19.1556	−	11.0595i	−0.702750	−	0.405733i	0.105621	−	0.994406i	$-0.466317\pi$
$743$	−19.1556	−	11.0595i	−0.702750	−	0.405733i	−0.808371	+	0.588673i	$0.799650\pi$
$744$	−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
$754$	27.4656	+	1.37387i	1.00024	+	0.0500333i
$755$	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	0.806433	−	0.591325i	$-0.201395\pi$
$761$	19.2427	+	11.1098i	0.697547	+	0.402729i	−0.108886	+	0.994054i	$0.534728\pi$
$762$	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
$767$	14.6522	+	0.732927i	0.529062	+	0.0264645i
$768$	1.59599	+	0.672925i	0.0575902	+	0.0242821i
$769$	30.5190	+	17.6202i	1.10054	+	0.635399i	0.936364	−	0.351031i	$-0.114169\pi$
$769$	30.5190	+	17.6202i	1.10054	+	0.635399i	0.164180	+	0.986430i	$0.447502\pi$
$770$	2.71040	−	4.69454i	0.0976759	−	0.169180i

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.215223 - 1.71863i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.40542 + 1.38877i) q^{5} +(-1.04570 - 1.38076i) q^{6} +(0.759011 - 0.438215i) q^{7} -1.00000i q^{8} +(-2.90736 + 0.739776i) q^{9} +O(q^{10})\)	\(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} +(-3.20866 + 1.64453i) 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} +(3.51691 + 5.16056i) 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} +(-0.180130 + 3.60105i) 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} +(-10.0021 - 0.500318i) 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} +(5.62601 + 2.71072i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} - 16 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 - 16 * q^9	\( 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49} + 58 q^{51} - 2 q^{52} - 120 q^{53} - 8 q^{56} + 28 q^{61} + 68 q^{62} - 28 q^{64} - 8 q^{65} - 24 q^{66} + 8 q^{68} - 92 q^{69} + 16 q^{74} + 32 q^{75} - 24 q^{77} - 22 q^{78} + 28 q^{79} + 8 q^{81} - 48 q^{82} + 68 q^{87} - 50 q^{90} + 8 q^{92}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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