LMFDB - Embedded newform 702.2.t.a.415.13

Error: no document with id 185959985 found in table mf_hecke_traces.

Error: table True does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(181,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.181"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.13
Character	$\chi$	$=$	702.415
Dual form			702.2.t.a.181.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.40542 + 1.38877i) q^{5} +(-0.759011 + 0.438215i) q^{7} -1.00000i q^{8} +2.77754 q^{10} +(1.92848 - 1.11341i) q^{11} +(0.180130 + 3.60105i) q^{13} +(-0.438215 + 0.759011i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.80878 q^{17} -2.22681i q^{19} +(2.40542 - 1.38877i) q^{20} +(1.11341 - 1.92848i) q^{22} +(-0.259586 + 0.449617i) q^{23} +(1.35738 + 2.35105i) q^{25} +(1.95652 + 3.02853i) q^{26} +0.876431i q^{28} +(3.81355 + 6.60527i) q^{29} +(-4.97617 - 2.87299i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.29850 - 1.90439i) q^{34} -2.43433 q^{35} -11.3538i q^{37} +(-1.11341 - 1.92848i) q^{38} +(1.38877 - 2.40542i) q^{40} +(3.52286 + 2.03392i) q^{41} +(2.81683 + 4.87889i) q^{43} -2.22681i q^{44} +0.519173i q^{46} +(-0.920402 + 0.531395i) q^{47} +(-3.11593 + 5.39696i) q^{49} +(2.35105 + 1.35738i) q^{50} +(3.20866 + 1.64453i) q^{52} -7.29301 q^{53} +6.18508 q^{55} +(0.438215 + 0.759011i) q^{56} +(6.60527 + 3.81355i) q^{58} +(-3.52376 - 2.03444i) q^{59} +(-3.94905 - 6.83995i) q^{61} -5.74599 q^{62} -1.00000 q^{64} +(-4.56775 + 8.91221i) q^{65} +(5.95399 + 3.43754i) q^{67} +(1.90439 - 3.29850i) q^{68} +(-2.10819 + 1.21716i) q^{70} -15.9569i q^{71} -5.24797i q^{73} +(-5.67689 - 9.83267i) q^{74} +(-1.92848 - 1.11341i) q^{76} +(-0.975824 + 1.69018i) q^{77} +(-7.09690 - 12.2922i) q^{79} -2.77754i q^{80} +4.06784 q^{82} +(0.641385 - 0.370304i) q^{83} +(9.16172 + 5.28952i) q^{85} +(4.87889 + 2.81683i) q^{86} +(-1.11341 - 1.92848i) q^{88} +9.89914i q^{89} +(-1.71476 - 2.65430i) q^{91} +(0.259586 + 0.449617i) q^{92} +(-0.531395 + 0.920402i) q^{94} +(3.09254 - 5.35643i) q^{95} +(-13.6212 + 7.86418i) q^{97} +6.23187i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62}+ \cdots - 8 q^{92}+O(q^{100}) $ 28 * q + 14 * q^4 + 2 * q^13 - 8 * q^14 - 14 * q^16 - 16 * q^17 + 8 * q^23 + 14 * q^25 - 8 * q^26 + 16 * q^29 + 68 * q^35 - 4 * q^43 + 10 * q^49 - 2 * q^52 + 120 * q^53 + 8 * q^56 + 28 * q^61 - 68 * q^62 - 28 * q^64 + 8 * q^65 - 8 * q^68 - 16 * q^74 + 24 * q^77 + 28 * q^79 - 48 * q^82 - 8 * q^92

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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			0
$3$		0			0
$4$	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	$0.453362\pi$
$6$		0			0
$7$	−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
$9$		0			0
$10$	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	$0.224359\pi$
$12$		0			0
$13$	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
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.80878			0.923764			0.461882	−	0.886941i	$-0.347174\pi$
$17$	3.80878			0.923764			0.461882	+	0.886941i	$0.347174\pi$
$18$		0			0
$19$		−	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			0
$22$	1.11341	−	1.92848i	0.237379	−	0.411153i
$23$	−0.259586	+	0.449617i	−0.0541275	+	0.0937516i	−0.891820	−	0.452391i	$-0.850571\pi$
$23$	−0.259586	+	0.449617i	−0.0541275	+	0.0937516i	0.837692	+	0.546143i	$0.183904\pi$
$24$		0			0
$25$	1.35738	+	2.35105i	0.271476	+	0.470209i
$26$	1.95652	+	3.02853i	0.383705	+	0.593945i
$27$		0			0
$28$			0.876431i			0.165630i
$29$	3.81355	+	6.60527i	0.708159	+	1.22657i	0.965539	+	0.260257i	$0.0838072\pi$
$29$	3.81355	+	6.60527i	0.708159	+	1.22657i	−0.257381	+	0.966310i	$0.582859\pi$
$30$		0			0
$31$	−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
$33$		0			0
$34$	3.29850	−	1.90439i	0.565688	−	0.326600i
$35$	−2.43433			−0.411476
$36$		0			0
$37$		−	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
$39$		0			0
$40$	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	$0.563775\pi$
$42$		0			0
$43$	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
$45$		0			0
$46$			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	$0.358031\pi$
$48$		0			0
$49$	−3.11593	+	5.39696i	−0.445133	+	0.770994i
$50$	2.35105	+	1.35738i	0.332488	+	0.191962i
$51$		0			0
$52$	3.20866	+	1.64453i	0.444962	+	0.228055i
$53$	−7.29301			−1.00177			−0.500886	−	0.865513i	$-0.666992\pi$
$53$	−7.29301			−1.00177			−0.500886	+	0.865513i	$0.666992\pi$
$54$		0			0
$55$	6.18508			0.833996
$56$	0.438215	+	0.759011i	0.0585590	+	0.101427i
$57$		0			0
$58$	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	$0.751993\pi$
$60$		0			0
$61$	−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
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.56775	+	8.91221i	−0.566560	+	1.10542i
$66$		0			0
$67$	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			0
$70$	−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			0
$73$		−	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
$75$		0			0
$76$	−1.92848	−	1.11341i	−0.221212	−	0.127717i
$77$	−0.975824	+	1.69018i	−0.111206	+	0.192614i
$78$		0			0
$79$	−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
$81$		0			0
$82$	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	$0.320392\pi$
$84$		0			0
$85$	9.16172	+	5.28952i	0.993729	+	0.573729i
$86$	4.87889	+	2.81683i	0.526104	+	0.303746i
$87$		0			0
$88$	−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	$0.824195\pi$
$90$		0			0
$91$	−1.71476	−	2.65430i	−0.179755	−	0.278246i
$92$	0.259586	+	0.449617i	0.0270638	+	0.0468758i
$93$		0			0
$94$	−0.531395	+	0.920402i	−0.0548092	+	0.0949323i
$95$	3.09254	−	5.35643i	0.317288	−	0.549559i
$96$		0			0
$97$	−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
$99$		0			0
$100$	2.71476			0.271476
$101$	9.76705	+	16.9170i	0.971858	+	1.68331i	0.689937	+	0.723870i	$0.257638\pi$
$101$	9.76705	+	16.9170i	0.971858	+	1.68331i	0.281921	+	0.959438i	$0.409028\pi$
$102$		0			0
$103$	−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			0
$106$	−6.31593	+	3.64650i	−0.613457	+	0.354180i
$107$	−13.5605			−1.31094			−0.655470	−	0.755221i	$-0.727529\pi$
$107$	−13.5605			−1.31094			−0.655470	+	0.755221i	$0.727529\pi$
$108$		0			0
$109$		−	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
$111$		0			0
$112$	0.759011	+	0.438215i	0.0717198	+	0.0414075i
$113$	1.65386	−	2.86458i	0.155582	−	0.269477i	−0.777689	−	0.628650i	$-0.783608\pi$
$113$	1.65386	−	2.86458i	0.155582	−	0.269477i	0.933271	+	0.359173i	$0.116941\pi$
$114$		0			0
$115$	−1.24883	+	0.721013i	−0.116454	+	0.0672348i
$116$	7.62710			0.708159
$117$		0			0
$118$	−4.06888			−0.374571
$119$	−2.89090	+	1.66906i	−0.265009	+	0.153003i
$120$		0			0
$121$	−3.02065	+	5.23192i	−0.274604	+	0.475629i
$122$	−6.83995	−	3.94905i	−0.619260	−	0.357530i
$123$		0			0
$124$	−4.97617	+	2.87299i	−0.446873	+	0.258002i
$125$		−	6.34737i		−	0.567726i
$126$		0			0
$127$	−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
$129$		0			0
$130$	0.500318	+	10.0021i	0.0438808	+	0.877240i
$131$	−3.71482	+	6.43426i	−0.324565	+	0.562164i	−0.981424	−	0.191850i	$-0.938551\pi$
$131$	−3.71482	+	6.43426i	−0.324565	+	0.562164i	0.656859	+	0.754013i	$0.271885\pi$
$132$		0			0
$133$	0.975824	+	1.69018i	0.0846147	+	0.146557i
$134$	6.87507			0.593916
$135$		0			0
$136$		−	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			0
$139$	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
$141$		0			0
$142$	−7.97845	−	13.8191i	−0.669537	−	1.15967i
$143$	4.35681	+	6.74399i	0.364335	+	0.563960i
$144$		0			0
$145$			21.1846i			1.75929i
$146$	−2.62398	−	4.54487i	−0.217162	−	0.376136i
$147$		0			0
$148$	−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	$0.867905\pi$
$150$		0			0
$151$	−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
$153$		0			0
$154$			1.95165i			0.157268i
$155$	−7.97987	−	13.8215i	−0.640959	−	1.11017i
$156$		0			0
$157$	−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
$159$		0			0
$160$	−1.38877	−	2.40542i	−0.109792	−	0.190165i
$161$		−	0.455019i		−	0.0358605i
$162$		0			0
$163$			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
$165$		0			0
$166$	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	$0.518127\pi$
$168$		0			0
$169$	−12.9351	+	1.29731i	−0.995008	+	0.0997932i
$170$	10.5790			0.811376
$171$		0			0
$172$	5.63365			0.429562
$173$	−3.62242	−	6.27421i	−0.275407	−	0.477020i	0.694830	−	0.719174i	$-0.255479\pi$
$173$	−3.62242	−	6.27421i	−0.275407	−	0.477020i	−0.970238	+	0.242154i	$0.922146\pi$
$174$		0			0
$175$	−2.06053	−	1.18965i	−0.155761	−	0.0899289i
$176$	−1.92848	−	1.11341i	−0.145364	−	0.0839262i
$177$		0			0
$178$	4.94957	+	8.57290i	0.370986	+	0.642566i
$179$	7.32606			0.547575			0.273788	−	0.961790i	$-0.411723\pi$
$179$	7.32606			0.547575			0.273788	+	0.961790i	$0.411723\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	0.449617	+	0.259586i	0.0331462	+	0.0191370i
$185$	15.7678	−	27.3107i	1.15927	−	2.00792i
$186$		0			0
$187$	7.34514	−	4.24072i	0.537130	−	0.310112i
$188$			1.06279i			0.0775119i
$189$		0			0
$190$		−	6.18508i		−	0.448713i
$191$	−9.39944	−	16.2803i	−0.680120	−	1.17800i	−0.974944	−	0.222451i	$-0.928594\pi$
$191$	−9.39944	−	16.2803i	−0.680120	−	1.17800i	0.294824	−	0.955552i	$-0.404739\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$	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	$0.984654\pi$
$198$		0			0
$199$	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
$201$		0			0
$202$	16.9170	+	9.76705i	1.19028	+	0.687207i
$203$	−5.78906	−	3.34231i	−0.406312	−	0.234584i
$204$		0			0
$205$	5.64931	+	9.78489i	0.394565	+	0.683406i
$206$			8.18508i			0.570281i
$207$		0			0
$208$	3.02853	−	1.95652i	0.209991	−	0.135660i
$209$	−2.47935	−	4.29436i	−0.171500	−	0.297047i
$210$		0			0
$211$	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
$213$		0			0
$214$	−11.7437	+	6.78023i	−0.802784	+	0.463487i
$215$			15.6477i			1.06717i
$216$		0			0
$217$	5.03596			0.341863
$218$	−4.25113	−	7.36317i	−0.287923	−	0.498697i
$219$		0			0
$220$	3.09254	−	5.35643i	0.208499	−	0.361131i
$221$	0.686074	+	13.7156i	0.0461503	+	0.922610i
$222$		0			0
$223$	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
$225$		0			0
$226$		−	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	$0.0652915\pi$
$228$		0			0
$229$	−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
$231$		0			0
$232$	6.60527	−	3.81355i	0.433657	−	0.250372i
$233$	11.1281			0.729027			0.364514	−	0.931198i	$-0.381235\pi$
$233$	11.1281			0.729027			0.364514	+	0.931198i	$0.381235\pi$
$234$		0			0
$235$	−2.95194			−0.192564
$236$	−3.52376	+	2.03444i	−0.229377	+	0.132431i
$237$		0			0
$238$	−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	$0.756913\pi$
$240$		0			0
$241$	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
$243$		0			0
$244$	−7.89810			−0.505624
$245$	−14.9903	+	8.65465i	−0.957694	+	0.552925i
$246$		0			0
$247$	8.01887	−	0.401116i	0.510228	−	0.0255224i
$248$	−2.87299	+	4.97617i	−0.182435	+	0.315987i
$249$		0			0
$250$	−3.17368	−	5.49698i	−0.200721	−	0.347660i
$251$	−22.5341			−1.42234			−0.711170	−	0.703020i	$-0.751834\pi$
$251$	−22.5341			−1.42234			−0.711170	+	0.703020i	$0.751834\pi$
$252$		0			0
$253$			1.15610i			0.0726835i
$254$	−10.9463	+	6.31987i	−0.686834	+	0.396544i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.37154	−	5.83968i	0.210311	−	0.364269i	−0.741501	−	0.670952i	$-0.765886\pi$
$257$	3.37154	−	5.83968i	0.210311	−	0.364269i	0.951812	+	0.306683i	$0.0992190\pi$
$258$		0			0
$259$	4.97540	+	8.61765i	0.309157	+	0.535475i
$260$	5.43433	+	8.41189i	0.337023	+	0.521683i
$261$		0			0
$262$			7.42964i			0.459005i
$263$	4.11486	+	7.12715i	0.253733	+	0.439479i	0.964551	−	0.263898i	$-0.0850081\pi$
$263$	4.11486	+	7.12715i	0.253733	+	0.439479i	−0.710817	+	0.703377i	$0.751675\pi$
$264$		0			0
$265$	−17.5428	−	10.1283i	−1.07764	−	0.622178i
$266$	1.69018	+	0.975824i	0.103631	+	0.0598316i
$267$		0			0
$268$	5.95399	−	3.43754i	0.363698	−	0.209981i
$269$	23.8369			1.45336			0.726680	−	0.686976i	$-0.241062\pi$
$269$	23.8369			1.45336			0.726680	+	0.686976i	$0.241062\pi$
$270$		0			0
$271$		−	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
$273$		0			0
$274$	−8.14752	+	14.1119i	−0.492209	+	0.852532i
$275$	5.23535	+	3.02263i	0.315703	+	0.182271i
$276$		0			0
$277$	−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
$279$		0			0
$280$			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	$0.133160\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	7.14510	+	3.66206i	0.422499	+	0.216542i
$287$	−3.56518			−0.210446
$288$		0			0
$289$	−2.49322			−0.146660
$290$	10.5923	+	18.3464i	0.622002	+	1.07734i
$291$		0			0
$292$	−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	$0.449089\pi$
$294$		0			0
$295$	−5.65075	−	9.78739i	−0.328999	−	0.569844i
$296$	−11.3538			−0.659926
$297$		0			0
$298$	−14.4264			−0.835700
$299$	−1.66585	−	0.853794i	−0.0963387	−	0.0493762i
$300$		0			0
$301$	−4.27601	−	2.46875i	−0.246465	−	0.142297i
$302$	−5.52751	+	9.57392i	−0.318072	+	0.550917i
$303$		0			0
$304$	−1.92848	+	1.11341i	−0.110606	+	0.0638583i
$305$		−	21.9373i		−	1.25613i
$306$		0			0
$307$		−	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
$309$		0			0
$310$	−13.8215	−	7.97987i	−0.785011	−	0.453226i
$311$	−4.85008	+	8.40058i	−0.275023	+	0.476353i	−0.970141	−	0.242542i	$-0.922019\pi$
$311$	−4.85008	+	8.40058i	−0.275023	+	0.476353i	0.695118	+	0.718896i	$0.255352\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$	−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	$0.0412658\pi$
$318$		0			0
$319$	14.7087	+	8.49207i	0.823529	+	0.475465i
$320$	−2.40542	−	1.38877i	−0.134467	−	0.0776347i
$321$		0			0
$322$	−0.227510	−	0.394058i	−0.0126786	−	0.0219600i
$323$		−	8.48144i		−	0.471920i
$324$		0			0
$325$	−8.22173	+	5.31148i	−0.456060	+	0.294628i
$326$	9.75532	+	16.8967i	0.540297	+	0.935823i
$327$		0			0
$328$	2.03392	−	3.52286i	0.112305	−	0.194517i
$329$	0.465731	−	0.806669i	0.0256766	−	0.0444731i
$330$		0			0
$331$	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
$333$		0			0
$334$	11.6279			0.636252
$335$	9.54791	+	16.5375i	0.521658	+	0.903538i
$336$		0			0
$337$	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
$339$		0			0
$340$	9.16172	−	5.28952i	0.496864	−	0.286865i
$341$	−12.7952			−0.692902
$342$		0			0
$343$		−	11.5968i		−	0.626169i
$344$	4.87889	−	2.81683i	0.263052	−	0.151873i
$345$		0			0
$346$	−6.27421	−	3.62242i	−0.337304	−	0.194742i
$347$	−12.7951	+	22.1617i	−0.686876	+	1.18970i	0.285968	+	0.958239i	$0.407685\pi$
$347$	−12.7951	+	22.1617i	−0.686876	+	1.18970i	−0.972843	+	0.231464i	$0.925648\pi$
$348$		0			0
$349$	−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
$351$		0			0
$352$	−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			0
$355$	22.1605	−	38.3831i	1.17616	−	2.03716i
$356$	8.57290	+	4.94957i	0.454363	+	0.262327i
$357$		0			0
$358$	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	$-0.136889\pi$
$360$		0			0
$361$	14.0413			0.739016
$362$	8.70968	−	5.02853i	0.457771	−	0.264294i
$363$		0			0
$364$	−3.15607	+	0.157871i	−0.165423	+	0.00827470i
$365$	7.28823	−	12.6236i	0.381484	−	0.660749i
$366$		0			0
$367$	−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
$369$		0			0
$370$		−	31.5357i		−	1.63946i
$371$	5.53548	−	3.19591i	0.287388	−	0.165923i
$372$		0			0
$373$	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
$375$		0			0
$376$	0.531395	+	0.920402i	0.0274046	+	0.0474661i
$377$	−23.0989	+	14.9226i	−1.18966	+	0.768553i
$378$		0			0
$379$			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
$381$		0			0
$382$	−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	$0.552133\pi$
$384$		0			0
$385$	−4.69454	+	2.71040i	−0.239256	+	0.138135i
$386$	13.2382			0.673809
$387$		0			0
$388$			15.7284i			0.798486i
$389$	9.32704	+	16.1549i	0.472900	+	0.819086i	0.999519	−	0.0310151i	$-0.00987401\pi$
$389$	9.32704	+	16.1549i	0.472900	+	0.819086i	−0.526619	+	0.850101i	$0.676541\pi$
$390$		0			0
$391$	−0.988707	+	1.71249i	−0.0500011	+	0.0866044i
$392$	5.39696	+	3.11593i	0.272587	+	0.157378i
$393$		0			0
$394$	0.676432	+	1.17161i	0.0340781	+	0.0590251i
$395$		−	39.4239i		−	1.98363i
$396$		0			0
$397$		−	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
$399$		0			0
$400$	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	$0.612155\pi$
$402$		0			0
$403$	9.44943	−	18.4369i	0.470710	−	0.918410i
$404$	19.5341			0.971858
$405$		0			0
$406$	−6.68463			−0.331753
$407$	−12.6414	−	21.8955i	−0.626610	−	1.08532i
$408$		0			0
$409$	−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
$411$		0			0
$412$	4.09254	+	7.08848i	0.201625	+	0.349225i
$413$	3.56609			0.175476
$414$		0			0
$415$	2.05707			0.100978
$416$	1.64453	−	3.20866i	0.0806296	−	0.157318i
$417$		0			0
$418$	−4.29436	−	2.47935i	−0.210044	−	0.121269i
$419$	8.68385	−	15.0409i	0.424234	−	0.734794i	−0.572115	−	0.820174i	$-0.693877\pi$
$419$	8.68385	−	15.0409i	0.424234	−	0.734794i	0.996349	+	0.0853793i	$0.0272102\pi$
$420$		0			0
$421$	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
$423$		0			0
$424$			7.29301i			0.354180i
$425$	5.16995	+	8.95461i	0.250779	+	0.434363i
$426$		0			0
$427$	5.99475	+	3.46107i	0.290106	+	0.167493i
$428$	−6.78023	+	11.7437i	−0.327735	+	0.567654i
$429$		0			0
$430$	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	$0.632803\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	−7.36317	−	4.25113i	−0.352632	−	0.203592i
$437$	1.00121	+	0.578051i	0.0478945	+	0.0276519i
$438$		0			0
$439$	−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
$441$		0			0
$442$	7.45195	+	11.5350i	0.354453	+	0.548665i
$443$	1.77937	+	3.08196i	0.0845403	+	0.146428i	0.905195	−	0.424996i	$-0.139724\pi$
$443$	1.77937	+	3.08196i	0.0845403	+	0.146428i	−0.820655	+	0.571424i	$0.806391\pi$
$444$		0			0
$445$	−13.7477	+	23.8116i	−0.651701	+	1.12878i
$446$	14.9028	−	25.8125i	0.705670	−	1.22226i
$447$		0			0
$448$	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	$0.922932\pi$
$450$		0			0
$451$	9.05833			0.426540
$452$	−1.65386	−	2.86458i	−0.0777912	−	0.134738i
$453$		0			0
$454$	11.2401	−	19.4683i	0.527522	−	0.913695i
$455$	−0.438494	−	8.76613i	−0.0205569	−	0.410962i
$456$		0			0
$457$	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
$459$		0			0
$460$			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	$0.500459\pi$
$462$		0			0
$463$	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
$465$		0			0
$466$	9.63723	−	5.56406i	0.446436	−	0.257750i
$467$	21.4529			0.992723			0.496362	−	0.868116i	$-0.334669\pi$
$467$	21.4529			0.992723			0.496362	+	0.868116i	$0.334669\pi$
$468$		0			0
$469$	−6.02552			−0.278233
$470$	−2.55646	+	1.47597i	−0.117921	+	0.0680815i
$471$		0			0
$472$	−2.03444	+	3.52376i	−0.0936427	+	0.162194i
$473$	10.8644	+	6.27255i	0.499544	+	0.288412i
$474$		0			0
$475$	5.23535	−	3.02263i	0.240214	−	0.138688i
$476$			3.33813i			0.153003i
$477$		0			0
$478$	−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	$0.291217\pi$
$480$		0			0
$481$	40.8855	−	2.04515i	1.86422	−	0.0932510i
$482$	1.26499	−	2.19103i	0.0576188	−	0.0997987i
$483$		0			0
$484$	3.02065	+	5.23192i	0.137302	+	0.237814i
$485$	−43.6862			−1.98369
$486$		0			0
$487$		−	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
$489$		0			0
$490$	−8.65465	+	14.9903i	−0.390977	+	0.677192i
$491$	−4.89961	+	8.48638i	−0.221116	+	0.382985i	−0.955147	−	0.296131i	$-0.904303\pi$
$491$	−4.89961	+	8.48638i	−0.221116	+	0.382985i	0.734031	+	0.679116i	$0.237637\pi$
$492$		0			0
$493$	14.5250	+	25.1580i	0.654172	+	1.13306i
$494$	6.74399	−	4.35681i	0.303426	−	0.196022i
$495$		0			0
$496$			5.74599i			0.258002i
$497$	6.99256	+	12.1115i	0.313659	+	0.543274i
$498$		0			0
$499$	−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
$501$		0			0
$502$	−19.5151	+	11.2671i	−0.871002	+	0.502873i
$503$	11.0563			0.492976			0.246488	−	0.969146i	$-0.420723\pi$
$503$	11.0563			0.492976			0.246488	+	0.969146i	$0.420723\pi$
$504$		0			0
$505$			54.2568i			2.41440i
$506$	0.578051	+	1.00121i	0.0256975	+	0.0445094i
$507$		0			0
$508$	−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	$0.658853\pi$
$510$		0			0
$511$	2.29974	+	3.98327i	0.101735	+	0.176209i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	6.74309i		−	0.297425i
$515$	−19.6886	+	11.3672i	−0.867583	+	0.500899i
$516$		0			0
$517$	−1.18332	+	2.04957i	−0.0520422	+	0.0901398i
$518$	8.61765	+	4.97540i	0.378638	+	0.218607i
$519$		0			0
$520$	8.91221	+	4.56775i	0.390826	+	0.200309i
$521$	9.02695			0.395478			0.197739	−	0.980255i	$-0.436640\pi$
$521$	9.02695			0.395478			0.197739	+	0.980255i	$0.436640\pi$
$522$		0			0
$523$	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
$525$		0			0
$526$	7.12715	+	4.11486i	0.310759	+	0.179417i
$527$	−18.9531	−	10.9426i	−0.825611	−	0.476667i
$528$		0			0
$529$	11.3652	+	19.6852i	0.494140	+	0.855876i
$530$	−20.2567			−0.879893
$531$		0			0
$532$	1.95165			0.0846147
$533$	−6.68968	+	13.0523i	−0.289762	+	0.565360i
$534$		0			0
$535$	−32.6187	−	18.8324i	−1.41023	−	0.814196i
$536$	3.43754	−	5.95399i	0.148479	−	0.257173i
$537$		0			0
$538$	20.6433	−	11.9184i	0.889998	−	0.513840i
$539$			13.8772i			0.597734i
$540$		0			0
$541$		−	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
$543$		0			0
$544$	−3.29850	−	1.90439i	−0.141422	−	0.0816500i
$545$	11.8077	−	20.4515i	0.505786	−	0.876047i
$546$		0			0
$547$	−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
$549$		0			0
$550$	6.04526			0.257771
$551$	14.7087	−	8.49207i	0.626612	−	0.361774i
$552$		0			0
$553$	10.7733	+	6.21994i	0.458125	+	0.264499i
$554$	−8.01097	−	4.62513i	−0.340353	−	0.196503i
$555$		0			0
$556$	−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	$-0.0962195\pi$
$558$		0			0
$559$	−17.0617	+	11.0224i	−0.721634	+	0.466196i
$560$	1.21716	+	2.10819i	0.0514345	+	0.0890872i
$561$		0			0
$562$	9.86047	−	17.0788i	0.415939	−	0.720427i
$563$	1.73120	−	2.99852i	0.0729612	−	0.126373i	−0.827237	−	0.561854i	$-0.810088\pi$
$563$	1.73120	−	2.99852i	0.0729612	−	0.126373i	0.900198	+	0.435481i	$0.143422\pi$
$564$		0			0
$565$	7.95649	−	4.59368i	0.334732	−	0.193258i
$566$			7.50235i			0.315347i
$567$		0			0
$568$	−15.9569			−0.669537
$569$	−7.89491	−	13.6744i	−0.330972	−	0.573260i	0.651731	−	0.758450i	$-0.274043\pi$
$569$	−7.89491	−	13.6744i	−0.330972	−	0.573260i	−0.982703	+	0.185190i	$0.940710\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	−3.08754	+	1.78259i	−0.128871	+	0.0744039i
$575$	−1.40943			−0.0587772
$576$		0			0
$577$			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
$579$		0			0
$580$	18.3464	+	10.5923i	0.761794	+	0.439822i
$581$	−0.324546	+	0.562129i	−0.0134644	+	0.0233211i
$582$		0			0
$583$	−14.0644	+	8.12009i	−0.582488	+	0.336300i
$584$	−5.24797			−0.217162
$585$		0			0
$586$	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	$0.419943\pi$
$588$		0			0
$589$	−6.39762	+	11.0810i	−0.263610	+	0.456585i
$590$	−9.78739	−	5.65075i	−0.402940	−	0.232638i
$591$		0			0
$592$	−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	$0.920842\pi$
$594$		0			0
$595$	−9.27180			−0.380107
$596$	−12.4936	+	7.21321i	−0.511760	+	0.295465i
$597$		0			0
$598$	−1.86957	+	0.0935185i	−0.0764523	+	0.00382425i
$599$	−9.75297	+	16.8926i	−0.398495	+	0.690214i	−0.993541	−	0.113478i	$-0.963801\pi$
$599$	−9.75297	+	16.8926i	−0.398495	+	0.690214i	0.595045	+	0.803692i	$0.297134\pi$
$600$		0			0
$601$	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
$603$		0			0
$604$			11.0550i			0.449822i
$605$	−14.5319	+	8.38999i	−0.590805	+	0.341101i
$606$		0			0
$607$	−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
$609$		0			0
$610$	−10.9687	−	18.9983i	−0.444108	−	0.769218i
$611$	−2.07937	−	3.21869i	−0.0841223	−	0.130214i
$612$		0			0
$613$			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
$615$		0			0
$616$	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	$0.612494\pi$
$618$		0			0
$619$	−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
$621$		0			0
$622$			9.70016i			0.388941i
$623$	−4.33795	−	7.51356i	−0.173796	−	0.301024i
$624$		0			0
$625$	15.6019	−	27.0234i	0.624078	−	1.08093i
$626$	27.6364	+	15.9559i	1.10457	+	0.637726i
$627$		0			0
$628$	1.92051	+	3.32643i	0.0766369	+	0.132739i
$629$		−	43.2440i		−	1.72425i
$630$		0			0
$631$			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
$633$		0			0
$634$	14.1389	−	24.4893i	0.561527	−	0.972594i
$635$	−30.4040	−	17.5537i	−1.20654	−	0.696599i
$636$		0			0
$637$	−19.9960	−	10.2485i	−0.792269	−	0.406060i
$638$	16.9841			0.672409
$639$		0			0
$640$	−2.77754			−0.109792
$641$	11.7828	+	20.4085i	0.465394	+	0.806087i	0.999219	−	0.0395083i	$-0.0125792\pi$
$641$	11.7828	+	20.4085i	0.465394	+	0.806087i	−0.533825	+	0.845595i	$0.679246\pi$
$642$		0			0
$643$	−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
$645$		0			0
$646$	−4.24072	−	7.34514i	−0.166849	−	0.288991i
$647$	45.8902			1.80413			0.902065	−	0.431600i	$-0.142051\pi$
$647$	45.8902			1.80413			0.902065	+	0.431600i	$0.142051\pi$
$648$		0			0
$649$	−9.06065			−0.355661
$650$	−4.46449	+	8.71074i	−0.175112	+	0.341663i
$651$		0			0
$652$	16.8967	+	9.75532i	0.661726	+	0.382048i
$653$	−7.28145	+	12.6118i	−0.284945	+	0.493539i	−0.972596	−	0.232502i	$-0.925309\pi$
$653$	−7.28145	+	12.6118i	−0.284945	+	0.493539i	0.687651	+	0.726042i	$0.258642\pi$
$654$		0			0
$655$	−17.8714	+	10.3181i	−0.698295	+	0.403161i
$656$		−	4.06784i		−	0.158823i
$657$		0			0
$658$		−	0.931461i		−	0.0363121i
$659$	−12.3920	−	21.4636i	−0.482724	−	0.836102i	0.517080	−	0.855937i	$-0.327019\pi$
$659$	−12.3920	−	21.4636i	−0.482724	−	0.836102i	−0.999803	+	0.0198353i	$0.993686\pi$
$660$		0			0
$661$	−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
$663$		0			0
$664$	−0.370304	−	0.641385i	−0.0143706	−	0.0248906i
$665$			5.42079i			0.210209i
$666$		0			0
$667$	−3.95979			−0.153324
$668$	10.0701	−	5.81397i	0.389623	−	0.224949i
$669$		0			0
$670$	16.5375	+	9.54791i	0.638898	+	0.368868i
$671$	−15.2313	−	8.79380i	−0.587998	−	0.339481i
$672$		0			0
$673$	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
$675$		0			0
$676$	−5.34405	+	11.8508i	−0.205540	+	0.455799i
$677$	−19.0892	−	33.0634i	−0.733656	−	1.27073i	−0.955311	−	0.295604i	$-0.904479\pi$
$677$	−19.0892	−	33.0634i	−0.733656	−	1.27073i	0.221655	−	0.975125i	$-0.428854\pi$
$678$		0			0
$679$	6.89241	−	11.9380i	0.264506	−	0.458138i
$680$	5.28952	−	9.16172i	0.202844	−	0.351336i
$681$		0			0
$682$	−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	$0.580835\pi$
$684$		0			0
$685$	−45.2602			−1.72930
$686$	−5.79841	−	10.0431i	−0.221384	−	0.383449i
$687$		0			0
$688$	2.81683	−	4.87889i	0.107390	−	0.186006i
$689$	−1.31369	−	26.2625i	−0.0500475	−	1.00052i
$690$		0			0
$691$	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
$693$		0			0
$694$			25.5902i			0.971389i
$695$	25.5664	−	14.7607i	0.969787	−	0.559907i
$696$		0			0
$697$	13.4178	+	7.74675i	0.508234	+	0.293429i
$698$	−1.75430	+	3.03854i	−0.0664013	+	0.115010i
$699$		0			0
$700$	−2.06053	+	1.18965i	−0.0778807	+	0.0449645i
$701$	−17.7794			−0.671519			−0.335759	−	0.941948i	$-0.608993\pi$
$701$	−17.7794			−0.671519			−0.335759	+	0.941948i	$0.608993\pi$
$702$		0			0
$703$	−25.2828			−0.953558
$704$	−1.92848	+	1.11341i	−0.0726822	+	0.0419631i
$705$		0			0
$706$	−3.65314	+	6.32742i	−0.137488	+	0.238135i
$707$	−14.8266	−	8.56014i	−0.557612	−	0.321937i
$708$		0			0
$709$	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
$711$		0			0
$712$	9.89914			0.370986
$713$	2.58349	−	1.49158i	0.0967526	−	0.0558601i
$714$		0			0
$715$	1.11412	+	22.2728i	0.0416656	+	0.832954i
$716$	3.66303	−	6.34455i	0.136894	−	0.237107i
$717$		0			0
$718$	−7.89943	−	13.6822i	−0.294804	−	0.510616i
$719$	39.2187			1.46261			0.731305	−	0.682051i	$-0.238912\pi$
$719$	39.2187			1.46261			0.731305	+	0.682051i	$0.238912\pi$
$720$		0			0
$721$		−	7.17365i		−	0.267161i
$722$	12.1601	−	7.02065i	0.452553	−	0.261281i
$723$		0			0
$724$	5.02853	−	8.70968i	0.186884	−	0.323693i
$725$	−10.3529	+	17.9317i	−0.384496	+	0.665966i
$726$		0			0
$727$	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
$729$		0			0
$730$		−	14.5765i		−	0.539499i
$731$	10.7287	+	18.5826i	0.396814	+	0.687302i
$732$		0			0
$733$	−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
$735$		0			0
$736$	0.449617	−	0.259586i	0.0165731	−	0.00956848i
$737$	15.3095			0.563933
$738$		0			0
$739$			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
$741$		0			0
$742$	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	$0.799650\pi$
$744$		0			0
$745$	−20.0350	−	34.7017i	−0.734026	−	1.27137i
$746$		−	9.73041i		−	0.356256i
$747$		0			0
$748$		−	8.48144i		−	0.310112i
$749$	10.2926	−	5.94241i	0.376082	−	0.217131i
$750$		0			0
$751$	−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
$753$		0			0
$754$	−12.5430	+	24.4728i	−0.456788	+	0.891247i
$755$	−30.7058			−1.11750
$756$		0			0
$757$	−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
$759$		0			0
$760$	−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	$0.534728\pi$
$762$		0			0
$763$	3.72582	+	6.45331i	0.134884	+	0.233625i
$764$	−18.7989			−0.680120
$765$		0			0
$766$	13.7816			0.497949
$767$	6.69139	−	13.0557i	0.241612	−	0.471413i
$768$		0			0
$769$	−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
$771$		0			0
$772$	11.4647	−	6.61912i	0.412622	−	0.238227i
$773$			12.6527i			0.455086i	0.973768	+	0.227543i	$0.0730693\pi$
$773$			12.6527i			0.455086i	−0.973768	+	0.227543i	$0.926931\pi$
$774$		0			0
$775$		−	15.5990i		−	0.560331i
$776$	7.86418	+	13.6212i	0.282308	+	0.488971i
$777$		0			0
$778$	16.1549	+	9.32704i	0.579181	+	0.334390i
$779$	4.52917	−	7.84475i	0.162274	−	0.281067i
$780$		0			0
$781$	−17.7665	−	30.7725i	−0.635736	−	1.10113i
$782$			1.97741i			0.0707122i
$783$		0			0
$784$	6.23187			0.222567
$785$	−9.23931	+	5.33432i	−0.329765	+	0.190390i
$786$		0			0
$787$	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
$789$		0			0
$790$	−19.7120	−	34.1421i	−0.701320	−	1.21472i
$791$			2.89899i			0.103076i
$792$		0			0
$793$	23.9197	−	15.4528i	0.849412	−	0.548745i
$794$	−3.86733	−	6.69841i	−0.137246	−	0.237718i
$795$		0			0
$796$	0.714756	−	1.23799i	0.0253338	−	0.0438795i
$797$	−5.91305	+	10.2417i	−0.209451	+	0.362780i	−0.951542	−	0.307520i	$-0.900501\pi$
$797$	−5.91305	+	10.2417i	−0.209451	+	0.362780i	0.742091	+	0.670300i	$0.233834\pi$
$798$		0			0
$799$	−3.50561	+	2.02396i	−0.124019	+	0.0716027i
$800$		−	2.71476i		−	0.0959811i
$801$		0			0
$802$	6.82526			0.241008
$803$	−5.84313	−	10.1206i	−0.206199	−	0.357148i
$804$		0			0
$805$	0.631918	−	1.09451i	0.0222722	−	0.0385766i
$806$	−1.03502	−	20.6916i	−0.0364571	−	0.728830i
$807$		0			0
$808$	16.9170	−	9.76705i	0.595139	−	0.343604i
$809$	18.4258			0.647815			0.323908	−	0.946089i	$-0.395003\pi$
$809$	18.4258			0.647815			0.323908	+	0.946089i	$0.395003\pi$
$810$		0			0
$811$			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
$813$		0			0
$814$	−21.8955	−	12.6414i	−0.767438	−	0.443080i
$815$	−27.0958	+	46.9314i	−0.949126	+	1.64393i
$816$		0			0
$817$	10.8644	−	6.27255i	0.380096	−	0.219449i
$818$	−31.2562			−1.09285
$819$		0			0
$820$	11.2986			0.394565
$821$	−28.9333	+	16.7047i	−1.00978	+	0.582996i	−0.911127	−	0.412125i	$-0.864787\pi$
$821$	−28.9333	+	16.7047i	−1.00978	+	0.582996i	−0.0986524	+	0.995122i	$0.531453\pi$
$822$		0			0
$823$	−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
$825$		0			0
$826$	3.08833	−	1.78305i	0.107457	−	0.0620401i
$827$			17.9261i			0.623350i	0.950189	+	0.311675i	$0.100890\pi$
$827$			17.9261i			0.623350i	−0.950189	+	0.311675i	$0.899110\pi$
$828$		0			0
$829$	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
$831$		0			0
$832$	−0.180130	−	3.60105i	−0.00624487	−	0.124844i
$833$	−11.8679	+	20.5558i	−0.411198	+	0.712216i
$834$		0			0
$835$	16.1486	+	27.9701i	0.558844	+	0.967946i
$836$	−4.95870			−0.171500
$837$		0			0
$838$		−	17.3677i		−	0.599957i
$839$	−38.0045	+	21.9419i	−1.31206	+	0.757519i	−0.982437	−	0.186594i	$-0.940255\pi$
$839$	−38.0045	+	21.9419i	−1.31206	+	0.757519i	−0.329624	+	0.944112i	$0.606922\pi$
$840$		0			0
$841$	−14.5864	+	25.2643i	−0.502978	+	0.871183i
$842$	3.41788	−	5.91995i	0.117788	−	0.204015i
$843$		0			0
$844$	−6.32982	−	10.9636i	−0.217882	−	0.377382i
$845$	−32.9161	−	14.8433i	−1.13235	−	0.510626i
$846$		0			0
$847$		−	5.29478i		−	0.181931i
$848$	3.64650	+	6.31593i	0.125221	+	0.216890i
$849$		0			0
$850$	8.95461	+	5.16995i	0.307141	+	0.177328i
$851$	5.10486	+	2.94729i	0.174992	+	0.101032i
$852$		0			0
$853$	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
$855$		0			0
$856$			13.5605i			0.463487i
$857$	16.2026	+	28.0637i	0.553470	+	0.958638i	0.998021	+	0.0628846i	$0.0200300\pi$
$857$	16.2026	+	28.0637i	0.553470	+	0.958638i	−0.444551	+	0.895754i	$0.646637\pi$
$858$		0			0
$859$	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			0
$862$	18.9797	+	32.8739i	0.646452	+	1.11969i
$863$			37.5472i			1.27812i	0.769156	+	0.639061i	$0.220677\pi$
$863$			37.5472i			1.27812i	−0.769156	+	0.639061i	$0.779323\pi$
$864$		0			0
$865$		−	20.1229i		−	0.684198i
$866$	5.05305	−	2.91738i	0.171710	−	0.0991366i
$867$		0			0
$868$	2.51798	−	4.36127i	0.0854658	−	0.148031i
$869$	−27.3724	−	15.8035i	−0.928546	−	0.536096i
$870$		0			0
$871$	−11.3062	+	22.0598i	−0.383097	+	0.747468i
$872$	−8.50225			−0.287923
$873$		0			0
$874$	1.15610			0.0391057
$875$	2.78151	+	4.81773i	0.0940324	+	0.162869i
$876$		0			0
$877$	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
$879$		0			0
$880$	−3.09254	−	5.35643i	−0.104249	−	0.180565i
$881$	−1.19345			−0.0402084			−0.0201042	−	0.999798i	$-0.506400\pi$
$881$	−1.19345			−0.0402084			−0.0201042	+	0.999798i	$0.506400\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	3.08196	+	1.77937i	0.103540	+	0.0597790i
$887$	−13.5452	+	23.4610i	−0.454803	+	0.787743i	−0.998677	−	0.0514245i	$-0.983624\pi$
$887$	−13.5452	+	23.4610i	−0.454803	+	0.787743i	0.543873	+	0.839167i	$0.316957\pi$
$888$		0			0
$889$	9.59371	−	5.53893i	0.321763	−	0.185770i
$890$			27.4953i			0.921645i
$891$		0			0
$892$		−	29.8057i		−	0.997968i
$893$	1.18332	+	2.04957i	0.0395982	+	0.0685861i
$894$		0			0
$895$	17.6223	+	10.1742i	0.589048	+	0.340087i
$896$	0.438215	−	0.759011i	0.0146397	−	0.0253568i
$897$		0			0
$898$	5.08037	+	8.79945i	0.169534	+	0.293642i
$899$		−	43.8252i		−	1.46165i
$900$		0			0
$901$	−27.7774			−0.925401
$902$	7.84475	−	4.52917i	0.261202	−	0.150805i
$903$		0			0
$904$	−2.86458	−	1.65386i	−0.0952744	−	0.0550067i
$905$	24.1915	+	13.9670i	0.804153	+	0.464278i
$906$		0			0
$907$	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
$909$		0			0
$910$	−4.76281	−	7.37244i	−0.157886	−	0.244394i
$911$	−21.4808	−	37.2059i	−0.711692	−	1.23269i	−0.964222	−	0.265097i	$-0.914596\pi$
$911$	−21.4808	−	37.2059i	−0.711692	−	1.23269i	0.252530	−	0.967589i	$-0.418737\pi$
$912$		0			0
$913$	0.824598	−	1.42824i	0.0272902	−	0.0472680i
$914$	10.6577	−	18.4597i	0.352525	−	0.610591i
$915$		0			0
$916$	−15.7207	+	9.07634i	−0.519426	+	0.299891i
$917$		−	6.51157i		−	0.215031i
$918$		0			0
$919$	−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
$921$		0			0
$922$	−10.7623	+	18.6408i	−0.354436	+	0.613902i
$923$	57.4616	−	2.87431i	1.89137	−	0.0946092i
$924$		0			0
$925$	26.6933	−	15.4114i	0.877670	−	0.506723i
$926$	35.8128			1.17688
$927$		0			0
$928$		−	7.62710i		−	0.250372i
$929$	−3.51403	+	2.02883i	−0.115292	+	0.0665636i	−0.556537	−	0.830823i	$-0.687870\pi$
$929$	−3.51403	+	2.02883i	−0.115292	+	0.0665636i	0.441245	+	0.897387i	$0.354537\pi$
$930$		0			0
$931$	12.0180	+	6.93861i	0.393875	+	0.227404i
$932$	5.56406	−	9.63723i	0.182257	−	0.315678i
$933$		0			0
$934$	18.5788	−	10.7265i	0.607916	−	0.350981i
$935$	23.5576			0.770415
$936$		0			0
$937$	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
$939$		0			0
$940$	−1.47597	+	2.55646i	−0.0481409	+	0.0833825i
$941$	−38.1340	−	22.0167i	−1.24313	−	0.717723i	−0.273401	−	0.961900i	$-0.588149\pi$
$941$	−38.1340	−	22.0167i	−1.24313	−	0.717723i	−0.969731	+	0.244177i	$0.921482\pi$
$942$		0			0
$943$	−1.82897	+	1.05596i	−0.0595595	+	0.0343867i
$944$			4.06888i			0.132431i
$945$		0			0
$946$	12.5451			0.407876
$947$	15.2058	−	8.77906i	0.494122	−	0.285281i	−0.232161	−	0.972677i	$-0.574580\pi$
$947$	15.2058	−	8.77906i	0.494122	−	0.285281i	0.726283	+	0.687396i	$0.241246\pi$
$948$		0			0
$949$	18.8982	−	0.945315i	0.613461	−	0.0306862i
$950$	3.02263	−	5.23535i	0.0980670	−	0.169857i
$951$		0			0
$952$	1.66906	+	2.89090i	0.0540947	+	0.0936948i
$953$	28.3807			0.919342			0.459671	−	0.888089i	$-0.347967\pi$
$953$	28.3807			0.919342			0.459671	+	0.888089i	$0.347967\pi$
$954$		0			0
$955$		−	52.2148i		−	1.68963i
$956$	−7.49042	+	4.32460i	−0.242258	+	0.139867i
$957$		0			0
$958$	2.88734	−	5.00102i	0.0932857	−	0.161575i
$959$	7.14073	−	12.3681i	0.230586	−	0.399387i
$960$		0			0
$961$	1.00819	+	1.74623i	0.0325221	+	0.0563300i
$962$	34.3853	−	22.2139i	1.10863	−	0.716206i
$963$		0			0
$964$		−	2.52998i		−	0.0814853i
$965$	18.3849	+	31.8436i	0.591831	+	1.02508i
$966$		0			0
$967$	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
$969$		0			0
$970$	−37.8334	+	21.8431i	−1.21476	+	0.701340i
$971$	−32.9658			−1.05792			−0.528962	−	0.848645i	$-0.677419\pi$
$971$	−32.9658			−1.05792			−0.528962	+	0.848645i	$0.677419\pi$
$972$		0			0
$973$			9.31526i			0.298633i
$974$	−16.4562	−	28.5030i	−0.527291	−	0.913294i
$975$		0			0
$976$	−3.94905	+	6.83995i	−0.126406	+	0.218942i
$977$	3.30414	+	1.90765i	0.105709	+	0.0610311i	0.551922	−	0.833895i	$-0.313894\pi$
$977$	3.30414	+	1.90765i	0.105709	+	0.0610311i	−0.446213	+	0.894927i	$0.647228\pi$
$978$		0			0
$979$	11.0218	+	19.0903i	0.352257	+	0.610128i
$980$			17.3093i			0.552925i
$981$		0			0
$982$			9.79923i			0.312706i
$983$	39.1001	−	22.5745i	1.24710	−	0.720013i	0.276570	−	0.960994i	$-0.410802\pi$
$983$	39.1001	−	22.5745i	1.24710	−	0.720013i	0.970530	+	0.240981i	$0.0774690\pi$
$984$		0			0
$985$	−1.87882	+	3.25421i	−0.0598642	+	0.103688i
$986$	25.1580	+	14.5250i	0.801193	+	0.462569i
$987$		0			0
$988$	3.66206	−	7.14510i	0.116506	−	0.227316i
$989$	−2.92484			−0.0930045
$990$		0			0
$991$	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
$993$		0			0
$994$	12.1115	+	6.99256i	0.384153	+	0.221791i
$995$	3.43858	+	1.98527i	0.109010	+	0.0629372i
$996$		0			0
$997$	−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
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.40542 + 1.38877i) q^{5} +(-0.759011 + 0.438215i) q^{7} -1.00000i q^{8} +2.77754 q^{10} +(1.92848 - 1.11341i) q^{11} +(0.180130 + 3.60105i) q^{13} +(-0.438215 + 0.759011i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.80878 q^{17} -2.22681i q^{19} +(2.40542 - 1.38877i) q^{20} +(1.11341 - 1.92848i) q^{22} +(-0.259586 + 0.449617i) q^{23} +(1.35738 + 2.35105i) q^{25} +(1.95652 + 3.02853i) q^{26} +0.876431i q^{28} +(3.81355 + 6.60527i) q^{29} +(-4.97617 - 2.87299i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.29850 - 1.90439i) q^{34} -2.43433 q^{35} -11.3538i q^{37} +(-1.11341 - 1.92848i) q^{38} +(1.38877 - 2.40542i) q^{40} +(3.52286 + 2.03392i) q^{41} +(2.81683 + 4.87889i) q^{43} -2.22681i q^{44} +0.519173i q^{46} +(-0.920402 + 0.531395i) q^{47} +(-3.11593 + 5.39696i) q^{49} +(2.35105 + 1.35738i) q^{50} +(3.20866 + 1.64453i) q^{52} -7.29301 q^{53} +6.18508 q^{55} +(0.438215 + 0.759011i) q^{56} +(6.60527 + 3.81355i) q^{58} +(-3.52376 - 2.03444i) q^{59} +(-3.94905 - 6.83995i) q^{61} -5.74599 q^{62} -1.00000 q^{64} +(-4.56775 + 8.91221i) q^{65} +(5.95399 + 3.43754i) q^{67} +(1.90439 - 3.29850i) q^{68} +(-2.10819 + 1.21716i) q^{70} -15.9569i q^{71} -5.24797i q^{73} +(-5.67689 - 9.83267i) q^{74} +(-1.92848 - 1.11341i) q^{76} +(-0.975824 + 1.69018i) q^{77} +(-7.09690 - 12.2922i) q^{79} -2.77754i q^{80} +4.06784 q^{82} +(0.641385 - 0.370304i) q^{83} +(9.16172 + 5.28952i) q^{85} +(4.87889 + 2.81683i) q^{86} +(-1.11341 - 1.92848i) q^{88} +9.89914i q^{89} +(-1.71476 - 2.65430i) q^{91} +(0.259586 + 0.449617i) q^{92} +(-0.531395 + 0.920402i) q^{94} +(3.09254 - 5.35643i) q^{95} +(-13.6212 + 7.86418i) q^{97} +6.23187i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62}+ \cdots - 8 q^{92}+O(q^{100}) \) 28 * q + 14 * q^4 + 2 * q^13 - 8 * q^14 - 14 * q^16 - 16 * q^17 + 8 * q^23 + 14 * q^25 - 8 * q^26 + 16 * q^29 + 68 * q^35 - 4 * q^43 + 10 * q^49 - 2 * q^52 + 120 * q^53 + 8 * q^56 + 28 * q^61 - 68 * q^62 - 28 * q^64 + 8 * q^65 - 8 * q^68 - 16 * q^74 + 24 * q^77 + 28 * q^79 - 48 * q^82 - 8 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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