LMFDB - Embedded newform 702.2.t.a.415.14

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)

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")

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);

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			415.14
Character	$\chi$	$=$	702.415
Dual form			702.2.t.a.181.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.32246 + 1.91822i) q^{5} +(2.91802 - 1.68472i) q^{7} -1.00000i q^{8} +3.83645 q^{10} +(-1.72495 + 0.995899i) q^{11} +(-0.985326 - 3.46830i) q^{13} +(1.68472 - 2.91802i) q^{14} +(-0.500000 - 0.866025i) q^{16} -2.60129 q^{17} +1.99180i q^{19} +(3.32246 - 1.91822i) q^{20} +(-0.995899 + 1.72495i) q^{22} +(-2.13620 + 3.70000i) q^{23} +(4.85917 + 8.41632i) q^{25} +(-2.58747 - 2.51098i) q^{26} -3.36944i q^{28} +(4.37469 + 7.57719i) q^{29} +(-4.57313 - 2.64030i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.25278 + 1.30064i) q^{34} +12.9267 q^{35} -5.08689i q^{37} +(0.995899 + 1.72495i) q^{38} +(1.91822 - 3.32246i) q^{40} +(-7.13885 - 4.12162i) q^{41} +(-5.13184 - 8.88861i) q^{43} +1.99180i q^{44} +4.27239i q^{46} +(4.22784 - 2.44094i) q^{47} +(2.17657 - 3.76993i) q^{49} +(8.41632 + 4.85917i) q^{50} +(-3.49630 - 0.880834i) q^{52} +9.16444 q^{53} -7.64143 q^{55} +(-1.68472 - 2.91802i) q^{56} +(7.57719 + 4.37469i) q^{58} +(-6.33329 - 3.65653i) q^{59} +(5.63669 + 9.76304i) q^{61} -5.28060 q^{62} -1.00000 q^{64} +(3.37927 - 13.4134i) q^{65} +(-4.90591 - 2.83243i) q^{67} +(-1.30064 + 2.25278i) q^{68} +(11.1948 - 6.46335i) q^{70} +1.94505i q^{71} +8.41425i q^{73} +(-2.54345 - 4.40538i) q^{74} +(1.72495 + 0.995899i) q^{76} +(-3.35563 + 5.81211i) q^{77} +(2.97607 + 5.15470i) q^{79} -3.83645i q^{80} -8.24323 q^{82} +(-2.03658 + 1.17582i) q^{83} +(-8.64268 - 4.98985i) q^{85} +(-8.88861 - 5.13184i) q^{86} +(0.995899 + 1.72495i) q^{88} +6.28290i q^{89} +(-8.71833 - 8.46059i) q^{91} +(2.13620 + 3.70000i) q^{92} +(2.44094 - 4.22784i) q^{94} +(-3.82072 + 6.61767i) q^{95} +(8.92313 - 5.15177i) q^{97} -4.35315i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.32246	+	1.91822i	1.48585	+	0.857856i	0.999870	−	0.0161143i	$-0.00512957\pi$
$5$	3.32246	+	1.91822i	1.48585	+	0.857856i	0.485980	+	0.873970i	$0.338463\pi$
$6$		0			0
$7$	2.91802	−	1.68472i	1.10291	−	0.636765i	0.165926	−	0.986138i	$-0.446939\pi$
$7$	2.91802	−	1.68472i	1.10291	−	0.636765i	0.936984	+	0.349373i	$0.113606\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	3.83645			1.21319
$11$	−1.72495	+	0.995899i	−0.520091	+	0.300275i	−0.736972	−	0.675923i	$-0.763745\pi$
$11$	−1.72495	+	0.995899i	−0.520091	+	0.300275i	0.216881	+	0.976198i	$0.430412\pi$
$12$		0			0
$13$	−0.985326	−	3.46830i	−0.273280	−	0.961934i
$13$	−0.985326	−	3.46830i	−0.273280	−	0.961934i
$14$	1.68472	−	2.91802i	0.450261	−	0.779875i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.60129			−0.630905			−0.315452	−	0.948941i	$-0.602156\pi$
$17$	−2.60129			−0.630905			−0.315452	+	0.948941i	$0.602156\pi$
$18$		0			0
$19$			1.99180i			0.456950i	0.973550	+	0.228475i	$0.0733739\pi$
$19$			1.99180i			0.456950i	−0.973550	+	0.228475i	$0.926626\pi$
$20$	3.32246	−	1.91822i	0.742925	−	0.428928i
$21$		0			0
$22$	−0.995899	+	1.72495i	−0.212326	+	0.367760i
$23$	−2.13620	+	3.70000i	−0.445428	+	0.771504i	−0.998082	−	0.0619070i	$-0.980282\pi$
$23$	−2.13620	+	3.70000i	−0.445428	+	0.771504i	0.552654	+	0.833411i	$0.313615\pi$
$24$		0			0
$25$	4.85917	+	8.41632i	0.971833	+	1.68326i
$26$	−2.58747	−	2.51098i	−0.507445	−	0.492443i
$27$		0			0
$28$		−	3.36944i		−	0.636765i
$29$	4.37469	+	7.57719i	0.812360	+	1.40705i	0.911208	+	0.411947i	$0.135151\pi$
$29$	4.37469	+	7.57719i	0.812360	+	1.40705i	−0.0988475	+	0.995103i	$0.531516\pi$
$30$		0			0
$31$	−4.57313	−	2.64030i	−0.821359	−	0.474212i	0.0295262	−	0.999564i	$-0.490600\pi$
$31$	−4.57313	−	2.64030i	−0.821359	−	0.474212i	−0.850885	+	0.525352i	$0.823933\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−2.25278	+	1.30064i	−0.386349	+	0.223059i
$35$	12.9267			2.18501
$36$		0			0
$37$		−	5.08689i		−	0.836280i	−0.908383	−	0.418140i	$-0.862682\pi$
$37$		−	5.08689i		−	0.836280i	0.908383	−	0.418140i	$-0.137318\pi$
$38$	0.995899	+	1.72495i	0.161556	+	0.279824i
$39$		0			0
$40$	1.91822	−	3.32246i	0.303298	−	0.525327i
$41$	−7.13885	−	4.12162i	−1.11490	−	0.643688i	−0.174806	−	0.984603i	$-0.555930\pi$
$41$	−7.13885	−	4.12162i	−1.11490	−	0.643688i	−0.940094	+	0.340915i	$0.889263\pi$
$42$		0			0
$43$	−5.13184	−	8.88861i	−0.782598	−	1.35550i	−0.930423	−	0.366486i	$-0.880561\pi$
$43$	−5.13184	−	8.88861i	−0.782598	−	1.35550i	0.147825	−	0.989014i	$-0.452773\pi$
$44$			1.99180i			0.300275i
$45$		0			0
$46$			4.27239i			0.629930i
$47$	4.22784	−	2.44094i	0.616693	−	0.356048i	−0.158887	−	0.987297i	$-0.550791\pi$
$47$	4.22784	−	2.44094i	0.616693	−	0.356048i	0.775580	+	0.631249i	$0.217457\pi$
$48$		0			0
$49$	2.17657	−	3.76993i	0.310939	−	0.538562i
$50$	8.41632	+	4.85917i	1.19025	+	0.687190i
$51$		0			0
$52$	−3.49630	−	0.880834i	−0.484850	−	0.122150i
$53$	9.16444			1.25883			0.629416	−	0.777068i	$-0.283294\pi$
$53$	9.16444			1.25883			0.629416	+	0.777068i	$0.283294\pi$
$54$		0			0
$55$	−7.64143			−1.03037
$56$	−1.68472	−	2.91802i	−0.225130	−	0.389937i
$57$		0			0
$58$	7.57719	+	4.37469i	0.994934	+	0.574426i
$59$	−6.33329	−	3.65653i	−0.824524	−	0.476039i	0.0274501	−	0.999623i	$-0.491261\pi$
$59$	−6.33329	−	3.65653i	−0.824524	−	0.476039i	−0.851974	+	0.523584i	$0.824595\pi$
$60$		0			0
$61$	5.63669	+	9.76304i	0.721705	+	1.25003i	0.960316	+	0.278914i	$0.0899744\pi$
$61$	5.63669	+	9.76304i	0.721705	+	1.25003i	−0.238612	+	0.971115i	$0.576692\pi$
$62$	−5.28060			−0.670636
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.37927	−	13.4134i	0.419147	−	1.66373i
$66$		0			0
$67$	−4.90591	−	2.83243i	−0.599353	−	0.346037i	0.169434	−	0.985542i	$-0.445806\pi$
$67$	−4.90591	−	2.83243i	−0.599353	−	0.346037i	−0.768787	+	0.639505i	$0.779139\pi$
$68$	−1.30064	+	2.25278i	−0.157726	+	0.273190i
$69$		0			0
$70$	11.1948	−	6.46335i	1.33804	−	0.772518i
$71$			1.94505i			0.230835i	0.993317	+	0.115418i	$0.0368206\pi$
$71$			1.94505i			0.230835i	−0.993317	+	0.115418i	$0.963179\pi$
$72$		0			0
$73$			8.41425i			0.984814i	0.870365	+	0.492407i	$0.163883\pi$
$73$			8.41425i			0.984814i	−0.870365	+	0.492407i	$0.836117\pi$
$74$	−2.54345	−	4.40538i	−0.295669	−	0.512115i
$75$		0			0
$76$	1.72495	+	0.995899i	0.197865	+	0.114237i
$77$	−3.35563	+	5.81211i	−0.382409	+	0.662352i
$78$		0			0
$79$	2.97607	+	5.15470i	0.334834	+	0.579949i	0.983453	−	0.181164i	$-0.0579866\pi$
$79$	2.97607	+	5.15470i	0.334834	+	0.579949i	−0.648619	+	0.761113i	$0.724653\pi$
$80$		−	3.83645i		−	0.428928i
$81$		0			0
$82$	−8.24323			−0.910313
$83$	−2.03658	+	1.17582i	−0.223544	+	0.129063i	−0.607590	−	0.794251i	$-0.707864\pi$
$83$	−2.03658	+	1.17582i	−0.223544	+	0.129063i	0.384046	+	0.923314i	$0.374530\pi$
$84$		0			0
$85$	−8.64268	−	4.98985i	−0.937430	−	0.541225i
$86$	−8.88861	−	5.13184i	−0.958483	−	0.553381i
$87$		0			0
$88$	0.995899	+	1.72495i	0.106163	+	0.183880i
$89$			6.28290i			0.665986i	0.942929	+	0.332993i	$0.108059\pi$
$89$			6.28290i			0.665986i	−0.942929	+	0.332993i	$0.891941\pi$
$90$		0			0
$91$	−8.71833	−	8.46059i	−0.913929	−	0.886911i
$92$	2.13620	+	3.70000i	0.222714	+	0.385752i
$93$		0			0
$94$	2.44094	−	4.22784i	0.251764	−	0.436068i
$95$	−3.82072	+	6.61767i	−0.391997	+	0.678959i
$96$		0			0
$97$	8.92313	−	5.15177i	0.906006	−	0.523083i	0.0268622	−	0.999639i	$-0.491448\pi$
$97$	8.92313	−	5.15177i	0.906006	−	0.523083i	0.879144	+	0.476556i	$0.158115\pi$
$98$		−	4.35315i		−	0.439734i
$99$		0			0
$100$	9.71833			0.971833
$101$	−1.27960	−	2.21634i	−0.127325	−	0.220534i	0.795314	−	0.606197i	$-0.207306\pi$
$101$	−1.27960	−	2.21634i	−0.127325	−	0.220534i	−0.922639	+	0.385664i	$0.873973\pi$
$102$		0			0
$103$	2.82072	−	4.88562i	0.277933	−	0.481395i	−0.692938	−	0.720998i	$-0.743684\pi$
$103$	2.82072	−	4.88562i	0.277933	−	0.481395i	0.970871	+	0.239603i	$0.0770172\pi$
$104$	−3.46830	+	0.985326i	−0.340095	+	0.0966192i
$105$		0			0
$106$	7.93663	−	4.58222i	0.770874	−	0.445064i
$107$	−18.3051			−1.76962			−0.884812	−	0.465948i	$-0.845713\pi$
$107$	−18.3051			−1.76962			−0.884812	+	0.465948i	$0.845713\pi$
$108$		0			0
$109$			6.74904i			0.646441i	0.946324	+	0.323221i	$0.104766\pi$
$109$			6.74904i			0.646441i	−0.946324	+	0.323221i	$0.895234\pi$
$110$	−6.61767	+	3.82072i	−0.630970	+	0.364291i
$111$		0			0
$112$	−2.91802	−	1.68472i	−0.275727	−	0.159191i
$113$	−2.97526	+	5.15330i	−0.279889	+	0.484781i	−0.971357	−	0.237626i	$-0.923631\pi$
$113$	−2.97526	+	5.15330i	−0.279889	+	0.484781i	0.691468	+	0.722407i	$0.256964\pi$
$114$		0			0
$115$	−14.1949	+	8.19541i	−1.32368	+	0.764226i
$116$	8.74939			0.812360
$117$		0			0
$118$	−7.31305			−0.673221
$119$	−7.59062	+	4.38244i	−0.695831	+	0.401738i
$120$		0			0
$121$	−3.51637	+	6.09053i	−0.319670	+	0.553685i
$122$	9.76304	+	5.63669i	0.883904	+	0.510322i
$123$		0			0
$124$	−4.57313	+	2.64030i	−0.410679	+	0.237106i
$125$			18.1016i			1.61906i
$126$		0			0
$127$	−5.93126			−0.526314			−0.263157	−	0.964753i	$-0.584764\pi$
$127$	−5.93126			−0.526314			−0.263157	+	0.964753i	$0.584764\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−3.78015	−	13.3060i	−0.331541	−	1.16701i
$131$	6.88246	−	11.9208i	0.601324	−	1.04152i	−0.391297	−	0.920264i	$-0.627974\pi$
$131$	6.88246	−	11.9208i	0.601324	−	1.04152i	0.992621	−	0.121259i	$-0.0386931\pi$
$132$		0			0
$133$	3.35563	+	5.81211i	0.290970	+	0.503974i
$134$	−5.66486			−0.489370
$135$		0			0
$136$			2.60129i			0.223059i
$137$	−3.30808	+	1.90992i	−0.282628	+	0.163175i	−0.634613	−	0.772830i	$-0.718840\pi$
$137$	−3.30808	+	1.90992i	−0.282628	+	0.163175i	0.351985	+	0.936006i	$0.385507\pi$
$138$		0			0
$139$	−6.80487	+	11.7864i	−0.577182	+	0.999708i	0.418619	+	0.908162i	$0.362514\pi$
$139$	−6.80487	+	11.7864i	−0.577182	+	0.999708i	−0.995801	+	0.0915462i	$0.970819\pi$
$140$	6.46335	−	11.1948i	0.546252	−	0.946137i
$141$		0			0
$142$	0.972526	+	1.68446i	0.0816125	+	0.141357i
$143$	5.15372	+	5.00136i	0.430976	+	0.418235i
$144$		0			0
$145$			33.5666i			2.78755i
$146$	4.20713	+	7.28696i	0.348184	+	0.603073i
$147$		0			0
$148$	−4.40538	−	2.54345i	−0.362120	−	0.209070i
$149$	−6.74717	−	3.89548i	−0.552749	−	0.319130i	0.197481	−	0.980307i	$-0.436724\pi$
$149$	−6.74717	−	3.89548i	−0.552749	−	0.319130i	−0.750230	+	0.661177i	$0.770057\pi$
$150$		0			0
$151$	18.5033	−	10.6829i	1.50578	−	0.869363i	0.505804	−	0.862649i	$-0.331196\pi$
$151$	18.5033	−	10.6829i	1.50578	−	0.869363i	0.999977	−	0.00671434i	$-0.00213726\pi$
$152$	1.99180			0.161556
$153$		0			0
$154$			6.71125i			0.540808i
$155$	−10.1294	−	17.5446i	−0.813610	−	1.40921i
$156$		0			0
$157$	2.12572	−	3.68185i	0.169651	−	0.293844i	−0.768646	−	0.639674i	$-0.779069\pi$
$157$	2.12572	−	3.68185i	0.169651	−	0.293844i	0.938297	+	0.345830i	$0.112403\pi$
$158$	5.15470	+	2.97607i	0.410086	+	0.236763i
$159$		0			0
$160$	−1.91822	−	3.32246i	−0.151649	−	0.262664i
$161$			14.3956i			1.13453i
$162$		0			0
$163$		−	11.0533i		−	0.865764i	−0.901451	−	0.432882i	$-0.857497\pi$
$163$		−	11.0533i		−	0.865764i	0.901451	−	0.432882i	$-0.142503\pi$
$164$	−7.13885	+	4.12162i	−0.557450	+	0.321844i
$165$		0			0
$166$	−1.17582	+	2.03658i	−0.0912614	+	0.158069i
$167$	−8.14388	−	4.70187i	−0.630193	−	0.363842i	0.150634	−	0.988590i	$-0.451869\pi$
$167$	−8.14388	−	4.70187i	−0.630193	−	0.363842i	−0.780827	+	0.624748i	$0.785202\pi$
$168$		0			0
$169$	−11.0583	+	6.83482i	−0.850636	+	0.525756i
$170$	−9.97970			−0.765408
$171$		0			0
$172$	−10.2637			−0.782598
$173$	1.08885	+	1.88594i	0.0827835	+	0.143385i	0.904445	−	0.426591i	$-0.140286\pi$
$173$	1.08885	+	1.88594i	0.0827835	+	0.143385i	−0.821661	+	0.569976i	$0.806952\pi$
$174$		0			0
$175$	28.3583	+	16.3727i	2.14369	+	1.23766i
$176$	1.72495	+	0.995899i	0.130023	+	0.0750687i
$177$		0			0
$178$	3.14145	+	5.44115i	0.235462	+	0.407831i
$179$	−7.91152			−0.591334			−0.295667	−	0.955291i	$-0.595542\pi$
$179$	−7.91152			−0.591334			−0.295667	+	0.955291i	$0.595542\pi$
$180$		0			0
$181$	−1.02195			−0.0759611			−0.0379806	−	0.999278i	$-0.512092\pi$
$181$	−1.02195			−0.0759611			−0.0379806	+	0.999278i	$0.512092\pi$
$182$	−11.7806	−	2.96792i	−0.873236	−	0.219997i
$183$		0			0
$184$	3.70000	+	2.13620i	0.272768	+	0.157483i
$185$	9.75779	−	16.9010i	0.717407	−	1.24259i
$186$		0			0
$187$	4.48708	−	2.59062i	0.328128	−	0.189445i
$188$		−	4.88188i		−	0.356048i
$189$		0			0
$190$			7.64143i			0.554368i
$191$	2.03054	+	3.51700i	0.146925	+	0.254481i	0.930089	−	0.367333i	$-0.119729\pi$
$191$	2.03054	+	3.51700i	0.146925	+	0.254481i	−0.783165	+	0.621814i	$0.786396\pi$
$192$		0			0
$193$	−14.4121	−	8.32085i	−1.03741	−	0.598948i	−0.118310	−	0.992977i	$-0.537748\pi$
$193$	−14.4121	−	8.32085i	−1.03741	−	0.598948i	−0.919098	+	0.394029i	$0.871081\pi$
$194$	5.15177	−	8.92313i	0.369875	−	0.640643i
$195$		0			0
$196$	−2.17657	−	3.76993i	−0.155469	−	0.269281i
$197$		−	20.8461i		−	1.48522i	−0.669723	−	0.742611i	$-0.733587\pi$
$197$		−	20.8461i		−	1.48522i	0.669723	−	0.742611i	$-0.266413\pi$
$198$		0			0
$199$	15.4367			1.09428			0.547138	−	0.837042i	$-0.315717\pi$
$199$	15.4367			1.09428			0.547138	+	0.837042i	$0.315717\pi$
$200$	8.41632	−	4.85917i	0.595124	−	0.343595i
$201$		0			0
$202$	−2.21634	−	1.27960i	−0.155941	−	0.0900325i
$203$	25.5309	+	14.7403i	1.79192	+	1.03457i
$204$		0			0
$205$	−15.8124	−	27.3878i	−1.10438	−	1.91285i
$206$		−	5.64143i		−	0.393057i
$207$		0			0
$208$	−2.51098	+	2.58747i	−0.174105	+	0.179409i
$209$	−1.98363	−	3.43575i	−0.137211	−	0.237656i
$210$		0			0
$211$	1.86662	−	3.23307i	0.128503	−	0.222574i	−0.794594	−	0.607142i	$-0.792316\pi$
$211$	1.86662	−	3.23307i	0.128503	−	0.222574i	0.923097	+	0.384568i	$0.125649\pi$
$212$	4.58222	−	7.93663i	0.314708	−	0.545090i
$213$		0			0
$214$	−15.8527	+	9.15257i	−1.08367	+	0.625657i
$215$		−	39.3761i		−	2.68543i
$216$		0			0
$217$	−17.7927			−1.20785
$218$	3.37452	+	5.84484i	0.228551	+	0.395863i
$219$		0			0
$220$	−3.82072	+	6.61767i	−0.257593	+	0.446163i
$221$	2.56312	+	9.02205i	0.172414	+	0.606889i
$222$		0			0
$223$	2.38417	−	1.37650i	0.159656	−	0.0921775i	−0.418043	−	0.908427i	$-0.637284\pi$
$223$	2.38417	−	1.37650i	0.159656	−	0.0921775i	0.577699	+	0.816250i	$0.303951\pi$
$224$	−3.36944			−0.225130
$225$		0			0
$226$			5.95051i			0.395822i
$227$	−3.30960	+	1.91080i	−0.219666	+	0.126824i	−0.605795	−	0.795620i	$-0.707145\pi$
$227$	−3.30960	+	1.91080i	−0.219666	+	0.126824i	0.386130	+	0.922444i	$0.373812\pi$
$228$		0			0
$229$	9.50393	+	5.48710i	0.628037	+	0.362597i	0.779992	−	0.625790i	$-0.215223\pi$
$229$	9.50393	+	5.48710i	0.628037	+	0.362597i	−0.151954	+	0.988388i	$0.548557\pi$
$230$	−8.19541	+	14.1949i	−0.540389	+	0.935982i
$231$		0			0
$232$	7.57719	−	4.37469i	0.497467	−	0.287213i
$233$	−2.26098			−0.148122			−0.0740610	−	0.997254i	$-0.523596\pi$
$233$	−2.26098			−0.148122			−0.0740610	+	0.997254i	$0.523596\pi$
$234$		0			0
$235$	18.7291			1.22175
$236$	−6.33329	+	3.65653i	−0.412262	+	0.238020i
$237$		0			0
$238$	−4.38244	+	7.59062i	−0.284072	+	0.492027i
$239$	5.46146	+	3.15318i	0.353273	+	0.203962i	0.666126	−	0.745839i	$-0.267951\pi$
$239$	5.46146	+	3.15318i	0.353273	+	0.203962i	−0.312853	+	0.949802i	$0.601285\pi$
$240$		0			0
$241$	−17.1743	+	9.91557i	−1.10629	+	0.638718i	−0.937867	−	0.346996i	$-0.887202\pi$
$241$	−17.1743	+	9.91557i	−1.10629	+	0.638718i	−0.168426	+	0.985714i	$0.553868\pi$
$242$			7.03274i			0.452082i
$243$		0			0
$244$	11.2734			0.721705
$245$	14.4632	−	8.35031i	0.924017	−	0.533482i
$246$		0			0
$247$	6.90816	−	1.96257i	0.439556	−	0.124875i
$248$	−2.64030	+	4.57313i	−0.167659	+	0.290394i
$249$		0			0
$250$	9.05082	+	15.6765i	0.572424	+	0.991467i
$251$	−0.440795			−0.0278227			−0.0139114	−	0.999903i	$-0.504428\pi$
$251$	−0.440795			−0.0278227			−0.0139114	+	0.999903i	$0.504428\pi$
$252$		0			0
$253$		−	8.50975i		−	0.535003i
$254$	−5.13662	+	2.96563i	−0.322300	+	0.186080i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.78781	−	11.7568i	0.423412	−	0.733371i	−0.572859	−	0.819654i	$-0.694166\pi$
$257$	6.78781	−	11.7568i	0.423412	−	0.733371i	0.996271	+	0.0862832i	$0.0274990\pi$
$258$		0			0
$259$	−8.56999	−	14.8437i	−0.532513	−	0.922340i
$260$	−9.92669	−	9.63323i	−0.615627	−	0.597427i
$261$		0			0
$262$		−	13.7649i		−	0.850400i
$263$	11.1892	+	19.3803i	0.689956	+	1.19504i	0.971852	+	0.235594i	$0.0757035\pi$
$263$	11.1892	+	19.3803i	0.689956	+	1.19504i	−0.281896	+	0.959445i	$0.590963\pi$
$264$		0			0
$265$	30.4485	+	17.5794i	1.87044	+	1.07990i
$266$	5.81211	+	3.35563i	0.356364	+	0.205747i
$267$		0			0
$268$	−4.90591	+	2.83243i	−0.299676	+	0.173018i
$269$	30.4520			1.85669			0.928345	−	0.371719i	$-0.121232\pi$
$269$	30.4520			1.85669			0.928345	+	0.371719i	$0.121232\pi$
$270$		0			0
$271$		−	2.03437i		−	0.123579i	−0.998089	−	0.0617897i	$-0.980319\pi$
$271$		−	2.03437i		−	0.123579i	0.998089	−	0.0617897i	$-0.0196808\pi$
$272$	1.30064	+	2.25278i	0.0788631	+	0.136595i
$273$		0			0
$274$	−1.90992	+	3.30808i	−0.115382	+	0.199848i
$275$	−16.7636	−	9.67848i	−1.01088	−	0.583634i
$276$		0			0
$277$	14.4567	+	25.0398i	0.868621	+	1.50450i	0.863406	+	0.504510i	$0.168327\pi$
$277$	14.4567	+	25.0398i	0.868621	+	1.50450i	0.00521502	+	0.999986i	$0.498340\pi$
$278$			13.6097i			0.816258i
$279$		0			0
$280$		−	12.9267i		−	0.772518i
$281$	−17.7630	+	10.2555i	−1.05965	+	0.611791i	−0.925336	−	0.379148i	$-0.876217\pi$
$281$	−17.7630	+	10.2555i	−1.05965	+	0.611791i	−0.134316	+	0.990939i	$0.542884\pi$
$282$		0			0
$283$	0.819991	−	1.42027i	0.0487434	−	0.0844260i	−0.840624	−	0.541619i	$-0.817812\pi$
$283$	0.819991	−	1.42027i	0.0487434	−	0.0844260i	0.889368	+	0.457193i	$0.151145\pi$
$284$	1.68446	+	0.972526i	0.0999545	+	0.0577088i
$285$		0			0
$286$	6.96393	+	1.75444i	0.411786	+	0.103742i
$287$	−27.7751			−1.63951
$288$		0			0
$289$	−10.2333			−0.601959
$290$	16.7833	+	29.0695i	0.985549	+	1.70702i
$291$		0			0
$292$	7.28696	+	4.20713i	0.426437	+	0.246203i
$293$	−10.7578	−	6.21102i	−0.628477	−	0.362852i	0.151685	−	0.988429i	$-0.451530\pi$
$293$	−10.7578	−	6.21102i	−0.628477	−	0.362852i	−0.780162	+	0.625577i	$0.784863\pi$
$294$		0			0
$295$	−14.0281	−	24.2973i	−0.816746	−	1.41465i
$296$	−5.08689			−0.295669
$297$		0			0
$298$	−7.79096			−0.451318
$299$	14.9376	+	3.76327i	0.863863	+	0.217636i
$300$		0			0
$301$	−29.9497	−	17.2914i	−1.72627	−	0.996662i
$302$	10.6829	−	18.5033i	0.614733	−	1.06475i
$303$		0			0
$304$	1.72495	−	0.995899i	0.0989326	−	0.0571187i
$305$			43.2498i			2.47647i
$306$		0			0
$307$		−	25.8780i		−	1.47693i	−0.674289	−	0.738467i	$-0.735550\pi$
$307$		−	25.8780i		−	1.47693i	0.674289	−	0.738467i	$-0.264450\pi$
$308$	3.35563	+	5.81211i	0.191205	+	0.331176i
$309$		0			0
$310$	−17.5446	−	10.1294i	−0.996465	−	0.575309i
$311$	−12.6911	+	21.9816i	−0.719645	+	1.24646i	0.241495	+	0.970402i	$0.422362\pi$
$311$	−12.6911	+	21.9816i	−0.719645	+	1.24646i	−0.961140	+	0.276060i	$0.910971\pi$
$312$		0			0
$313$	5.09998	+	8.83342i	0.288268	+	0.499294i	0.973396	−	0.229128i	$-0.0735874\pi$
$313$	5.09998	+	8.83342i	0.288268	+	0.499294i	−0.685129	+	0.728422i	$0.740254\pi$
$314$		−	4.25143i		−	0.239922i
$315$		0			0
$316$	5.95213			0.334834
$317$	−10.5613	+	6.09759i	−0.593184	+	0.342475i	−0.766356	−	0.642417i	$-0.777932\pi$
$317$	−10.5613	+	6.09759i	−0.593184	+	0.342475i	0.173171	+	0.984892i	$0.444599\pi$
$318$		0			0
$319$	−15.0922	−	8.71351i	−0.845003	−	0.487863i
$320$	−3.32246	−	1.91822i	−0.185731	−	0.107232i
$321$		0			0
$322$	7.19780	+	12.4669i	0.401117	+	0.694756i
$323$		−	5.18124i		−	0.288292i
$324$		0			0
$325$	24.4025	−	25.1459i	1.35361	−	1.39484i
$326$	−5.52667	−	9.57247i	−0.306094	−	0.530170i
$327$		0			0
$328$	−4.12162	+	7.13885i	−0.227578	+	0.394177i
$329$	8.22461	−	14.2454i	0.453438	−	0.785377i
$330$		0			0
$331$	19.4652	−	11.2383i	1.06991	−	0.617711i	0.141750	−	0.989902i	$-0.454727\pi$
$331$	19.4652	−	11.2383i	1.06991	−	0.617711i	0.928156	+	0.372192i	$0.121394\pi$
$332$			2.35164i			0.129063i
$333$		0			0
$334$	−9.40375			−0.514550
$335$	−10.8665	−	18.8213i	−0.593699	−	1.02832i
$336$		0			0
$337$	15.3975	−	26.6692i	0.838755	−	1.45277i	−0.0521819	−	0.998638i	$-0.516618\pi$
$337$	15.3975	−	26.6692i	0.838755	−	1.45277i	0.890936	−	0.454128i	$-0.150049\pi$
$338$	−6.15933	+	11.4483i	−0.335023	+	0.622703i
$339$		0			0
$340$	−8.64268	+	4.98985i	−0.468715	+	0.270613i
$341$	10.5179			0.569575
$342$		0			0
$343$			8.91842i			0.481550i
$344$	−8.88861	+	5.13184i	−0.479242	+	0.276690i
$345$		0			0
$346$	1.88594	+	1.08885i	0.101389	+	0.0585368i
$347$	−14.5235	+	25.1555i	−0.779664	+	1.35042i	0.152472	+	0.988308i	$0.451277\pi$
$347$	−14.5235	+	25.1555i	−0.779664	+	1.35042i	−0.932136	+	0.362109i	$0.882057\pi$
$348$		0			0
$349$	10.7969	−	6.23358i	0.577943	−	0.333676i	−0.182372	−	0.983230i	$-0.558378\pi$
$349$	10.7969	−	6.23358i	0.577943	−	0.333676i	0.760316	+	0.649554i	$0.225044\pi$
$350$	32.7454			1.75031
$351$		0			0
$352$	1.99180			0.106163
$353$	29.8167	−	17.2147i	1.58698	−	0.916244i	0.593180	−	0.805070i	$-0.297872\pi$
$353$	29.8167	−	17.2147i	1.58698	−	0.916244i	0.993801	−	0.111174i	$-0.0354612\pi$
$354$		0			0
$355$	−3.73104	+	6.46236i	−0.198023	+	0.342986i
$356$	5.44115	+	3.14145i	0.288380	+	0.166496i
$357$		0			0
$358$	−6.85157	+	3.95576i	−0.362117	+	0.209068i
$359$		−	34.2496i		−	1.80762i	−0.427931	−	0.903812i	$-0.640757\pi$
$359$		−	34.2496i		−	1.80762i	0.427931	−	0.903812i	$-0.359243\pi$
$360$		0			0
$361$	15.0327			0.791197
$362$	−0.885037	+	0.510976i	−0.0465165	+	0.0268563i
$363$		0			0
$364$	−11.6863	+	3.32000i	−0.612526	+	0.174015i
$365$	−16.1404	+	27.9560i	−0.844828	+	1.46329i
$366$		0			0
$367$	2.51806	+	4.36140i	0.131441	+	0.227663i	0.924232	−	0.381830i	$-0.124706\pi$
$367$	2.51806	+	4.36140i	0.131441	+	0.227663i	−0.792791	+	0.609494i	$0.791373\pi$
$368$	4.27239			0.222714
$369$		0			0
$370$		−	19.5156i		−	1.01457i
$371$	26.7420	−	15.4395i	1.38838	−	0.801580i
$372$		0			0
$373$	−5.60706	+	9.71171i	−0.290322	+	0.502853i	−0.973886	−	0.227038i	$-0.927096\pi$
$373$	−5.60706	+	9.71171i	−0.290322	+	0.502853i	0.683563	+	0.729891i	$0.260429\pi$
$374$	2.59062	−	4.48708i	0.133958	−	0.232022i
$375$		0			0
$376$	−2.44094	−	4.22784i	−0.125882	−	0.218034i
$377$	21.9695	−	22.6388i	1.13149	−	1.16596i
$378$		0			0
$379$		−	5.12623i		−	0.263317i	−0.991295	−	0.131658i	$-0.957970\pi$
$379$		−	5.12623i		−	0.263317i	0.991295	−	0.131658i	$-0.0420302\pi$
$380$	3.82072	+	6.61767i	0.195999	+	0.339479i
$381$		0			0
$382$	3.51700	+	2.03054i	0.179945	+	0.103891i
$383$	16.4042	+	9.47098i	0.838216	+	0.483944i	0.856658	−	0.515885i	$-0.172537\pi$
$383$	16.4042	+	9.47098i	0.838216	+	0.483944i	−0.0184411	+	0.999830i	$0.505870\pi$
$384$		0			0
$385$	−22.2979	+	12.8737i	−1.13640	+	0.656104i
$386$	−16.6417			−0.847041
$387$		0			0
$388$		−	10.3035i		−	0.523083i
$389$	−10.4199	−	18.0477i	−0.528308	−	0.915057i	−0.999455	−	0.0330020i	$-0.989493\pi$
$389$	−10.4199	−	18.0477i	−0.528308	−	0.915057i	0.471147	−	0.882055i	$-0.343840\pi$
$390$		0			0
$391$	5.55686	−	9.62477i	0.281023	−	0.486745i
$392$	−3.76993	−	2.17657i	−0.190410	−	0.109934i
$393$		0			0
$394$	−10.4230	−	18.0532i	−0.525105	−	0.909509i
$395$			22.8350i			1.14896i
$396$		0			0
$397$		−	2.17152i		−	0.108985i	−0.998514	−	0.0544927i	$-0.982646\pi$
$397$		−	2.17152i		−	0.108985i	0.998514	−	0.0544927i	$-0.0173541\pi$
$398$	13.3685	−	7.71833i	0.670104	−	0.386885i
$399$		0			0
$400$	4.85917	−	8.41632i	0.242958	−	0.420816i
$401$	9.35590	+	5.40163i	0.467211	+	0.269745i	0.715072	−	0.699051i	$-0.246394\pi$
$401$	9.35590	+	5.40163i	0.467211	+	0.269745i	−0.247860	+	0.968796i	$0.579727\pi$
$402$		0			0
$403$	−4.65133	+	18.4626i	−0.231699	+	0.919686i
$404$	−2.55921			−0.127325
$405$		0			0
$406$	29.4806			1.46310
$407$	5.06603	+	8.77462i	0.251114	+	0.434942i
$408$		0			0
$409$	−1.34494	−	0.776503i	−0.0665031	−	0.0383956i	0.466380	−	0.884585i	$-0.345558\pi$
$409$	−1.34494	−	0.776503i	−0.0665031	−	0.0383956i	−0.532883	+	0.846189i	$0.678891\pi$
$410$	−27.3878	−	15.8124i	−1.35259	−	0.780917i
$411$		0			0
$412$	−2.82072	−	4.88562i	−0.138967	−	0.240697i
$413$	−24.6409			−1.21250
$414$		0			0
$415$	−9.02195			−0.442870
$416$	−0.880834	+	3.49630i	−0.0431865	+	0.171420i
$417$		0			0
$418$	−3.43575	−	1.98363i	−0.168048	−	0.0970225i
$419$	2.81453	−	4.87490i	0.137499	−	0.238155i	−0.789051	−	0.614328i	$-0.789427\pi$
$419$	2.81453	−	4.87490i	0.137499	−	0.238155i	0.926549	+	0.376174i	$0.122760\pi$
$420$		0			0
$421$	10.3872	−	5.99704i	0.506240	−	0.292278i	−0.225047	−	0.974348i	$-0.572253\pi$
$421$	10.3872	−	5.99704i	0.506240	−	0.292278i	0.731287	+	0.682070i	$0.238920\pi$
$422$		−	3.73323i		−	0.181731i
$423$		0			0
$424$		−	9.16444i		−	0.445064i
$425$	−12.6401	−	21.8933i	−0.613134	−	1.06198i
$426$		0			0
$427$	32.8960	+	18.9925i	1.59195	+	0.919112i
$428$	−9.15257	+	15.8527i	−0.442406	+	0.766270i
$429$		0			0
$430$	−19.6880	−	34.1007i	−0.949441	−	1.64448i
$431$		−	0.0127142i		−	0.000612420i	−1.00000		0.000306210i	$-0.999903\pi$
$431$		−	0.0127142i		−	0.000612420i	1.00000		0.000306210i	$-9.74697e-5\pi$
$432$		0			0
$433$	30.8717			1.48360			0.741800	−	0.670621i	$-0.233972\pi$
$433$	30.8717			1.48360			0.741800	+	0.670621i	$0.233972\pi$
$434$	−15.4089	+	8.89633i	−0.739651	+	0.427038i
$435$		0			0
$436$	5.84484	+	3.37452i	0.279917	+	0.161610i
$437$	−7.36966	−	4.25487i	−0.352539	−	0.203538i
$438$		0			0
$439$	−8.19780	−	14.1990i	−0.391259	−	0.677681i	0.601357	−	0.798981i	$-0.294627\pi$
$439$	−8.19780	−	14.1990i	−0.391259	−	0.677681i	−0.992616	+	0.121300i	$0.961294\pi$
$440$			7.64143i			0.364291i
$441$		0			0
$442$	6.73075	+	6.53177i	0.320149	+	0.310685i
$443$	−2.02258	−	3.50320i	−0.0960955	−	0.166442i	0.813970	−	0.580907i	$-0.197302\pi$
$443$	−2.02258	−	3.50320i	−0.0960955	−	0.166442i	−0.910065	+	0.414465i	$0.863969\pi$
$444$		0			0
$445$	−12.0520	+	20.8747i	−0.571320	+	0.989555i
$446$	1.37650	−	2.38417i	0.0651793	−	0.112894i
$447$		0			0
$448$	−2.91802	+	1.68472i	−0.137864	+	0.0795956i
$449$			15.8943i			0.750099i	0.927005	+	0.375049i	$0.122374\pi$
$449$			15.8943i			0.750099i	−0.927005	+	0.375049i	$0.877626\pi$
$450$		0			0
$451$	16.4189			0.773134
$452$	2.97526	+	5.15330i	0.139944	+	0.242391i
$453$		0			0
$454$	−1.91080	+	3.30960i	−0.0896781	+	0.155327i
$455$	−12.7370	−	44.8337i	−0.597120	−	2.10184i
$456$		0			0
$457$	25.2372	−	14.5707i	1.18055	−	0.681589i	0.224406	−	0.974496i	$-0.427956\pi$
$457$	25.2372	−	14.5707i	1.18055	−	0.681589i	0.956141	+	0.292907i	$0.0946225\pi$
$458$	10.9742			0.512790
$459$		0			0
$460$			16.3908i			0.764226i
$461$	24.3725	−	14.0714i	1.13514	−	0.655373i	0.189917	−	0.981800i	$-0.439178\pi$
$461$	24.3725	−	14.0714i	1.13514	−	0.655373i	0.945222	+	0.326428i	$0.105845\pi$
$462$		0			0
$463$	27.5978	+	15.9336i	1.28258	+	0.740498i	0.977319	−	0.211771i	$-0.0679231\pi$
$463$	27.5978	+	15.9336i	1.28258	+	0.740498i	0.305261	+	0.952269i	$0.401256\pi$
$464$	4.37469	−	7.57719i	0.203090	−	0.351762i
$465$		0			0
$466$	−1.95807	+	1.13049i	−0.0907058	+	0.0523690i
$467$	−1.94189			−0.0898600			−0.0449300	−	0.998990i	$-0.514306\pi$
$467$	−1.94189			−0.0898600			−0.0449300	+	0.998990i	$0.514306\pi$
$468$		0			0
$469$	−19.0874			−0.881376
$470$	16.2199	−	9.36455i	0.748167	−	0.431954i
$471$		0			0
$472$	−3.65653	+	6.33329i	−0.168305	+	0.291513i
$473$	17.7043	+	10.2216i	0.814045	+	0.469989i
$474$		0			0
$475$	−16.7636	+	9.67848i	−0.769167	+	0.444079i
$476$			8.76489i			0.401738i
$477$		0			0
$478$	6.30635			0.288446
$479$	−9.46110	+	5.46237i	−0.432289	+	0.249582i	−0.700321	−	0.713828i	$-0.746960\pi$
$479$	−9.46110	+	5.46237i	−0.432289	+	0.249582i	0.268033	+	0.963410i	$0.413627\pi$
$480$		0			0
$481$	−17.6429	+	5.01225i	−0.804446	+	0.228539i
$482$	−9.91557	+	17.1743i	−0.451642	+	0.782267i
$483$		0			0
$484$	3.51637	+	6.09053i	0.159835	+	0.276842i
$485$	39.5290			1.79492
$486$		0			0
$487$			38.3978i			1.73997i	0.493078	+	0.869985i	$0.335872\pi$
$487$			38.3978i			1.73997i	−0.493078	+	0.869985i	$0.664128\pi$
$488$	9.76304	−	5.63669i	0.441952	−	0.255161i
$489$		0			0
$490$	8.35031	−	14.4632i	0.377228	−	0.653379i
$491$	5.27663	−	9.13938i	0.238131	−	0.412455i	−0.722047	−	0.691844i	$-0.756799\pi$
$491$	5.27663	−	9.13938i	0.238131	−	0.412455i	0.960178	+	0.279389i	$0.0901320\pi$
$492$		0			0
$493$	−11.3798	−	19.7105i	−0.512522	−	0.887714i
$494$	5.00136	−	5.15372i	0.225022	−	0.231877i
$495$		0			0
$496$			5.28060i			0.237106i
$497$	3.27687	+	5.67571i	0.146988	+	0.254590i
$498$		0			0
$499$	0.859848	+	0.496434i	0.0384921	+	0.0222234i	0.519123	−	0.854700i	$-0.326259\pi$
$499$	0.859848	+	0.496434i	0.0384921	+	0.0222234i	−0.480630	+	0.876923i	$0.659592\pi$
$500$	15.6765	+	9.05082i	0.701073	+	0.404765i
$501$		0			0
$502$	−0.381740	+	0.220397i	−0.0170379	+	0.00983682i
$503$	−9.23683			−0.411850			−0.205925	−	0.978568i	$-0.566020\pi$
$503$	−9.23683			−0.411850			−0.205925	+	0.978568i	$0.566020\pi$
$504$		0			0
$505$		−	9.81826i		−	0.436907i
$506$	−4.25487	−	7.36966i	−0.189152	−	0.327621i
$507$		0			0
$508$	−2.96563	+	5.13662i	−0.131578	+	0.227901i
$509$	−8.35176	−	4.82189i	−0.370185	−	0.213727i	0.303354	−	0.952878i	$-0.401893\pi$
$509$	−8.35176	−	4.82189i	−0.370185	−	0.213727i	−0.673539	+	0.739151i	$0.735227\pi$
$510$		0			0
$511$	14.1757	+	24.5530i	0.627095	+	1.08616i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	13.5756i		−	0.598795i
$515$	18.7434	−	10.8215i	0.825934	−	0.476853i
$516$		0			0
$517$	−4.86186	+	8.42100i	−0.213825	+	0.370355i
$518$	−14.8437	−	8.56999i	−0.652193	−	0.376544i
$519$		0			0
$520$	−13.4134	−	3.37927i	−0.588216	−	0.148191i
$521$	18.9584			0.830581			0.415291	−	0.909689i	$-0.363680\pi$
$521$	18.9584			0.830581			0.415291	+	0.909689i	$0.363680\pi$
$522$		0			0
$523$	24.4694			1.06997			0.534986	−	0.844861i	$-0.320317\pi$
$523$	24.4694			1.06997			0.534986	+	0.844861i	$0.320317\pi$
$524$	−6.88246	−	11.9208i	−0.300662	−	0.520762i
$525$		0			0
$526$	19.3803	+	11.1892i	0.845020	+	0.487873i
$527$	11.8960	+	6.86817i	0.518199	+	0.299182i
$528$		0			0
$529$	2.37332	+	4.11071i	0.103188	+	0.178727i
$530$	35.1589			1.52720
$531$		0			0
$532$	6.71125			0.290970
$533$	−7.26092	+	28.8208i	−0.314505	+	1.24837i
$534$		0			0
$535$	−60.8181	−	35.1133i	−2.62940	−	1.51808i
$536$	−2.83243	+	4.90591i	−0.122342	+	0.211903i
$537$		0			0
$538$	26.3722	−	15.2260i	1.13699	−	0.656439i
$539$			8.67059i			0.373469i
$540$		0			0
$541$		−	6.77020i		−	0.291074i	−0.989353	−	0.145537i	$-0.953509\pi$
$541$		−	6.77020i		−	0.291074i	0.989353	−	0.145537i	$-0.0464909\pi$
$542$	−1.01719	−	1.76182i	−0.0436919	−	0.0756766i
$543$		0			0
$544$	2.25278	+	1.30064i	0.0965872	+	0.0557646i
$545$	−12.9462	+	22.4234i	−0.554553	+	0.960514i
$546$		0			0
$547$	−4.23689	−	7.33850i	−0.181156	−	0.313772i	0.761118	−	0.648613i	$-0.224651\pi$
$547$	−4.23689	−	7.33850i	−0.181156	−	0.313772i	−0.942275	+	0.334841i	$0.891317\pi$
$548$			3.81984i			0.163175i
$549$		0			0
$550$	−19.3570			−0.825383
$551$	−15.0922	+	8.71351i	−0.642951	+	0.371208i
$552$		0			0
$553$	17.3685	+	10.0277i	0.738582	+	0.426420i
$554$	25.0398	+	14.4567i	1.06384	+	0.614208i
$555$		0			0
$556$	6.80487	+	11.7864i	0.288591	+	0.499854i
$557$		−	4.77737i		−	0.202424i	−0.994865	−	0.101212i	$-0.967728\pi$
$557$		−	4.77737i		−	0.202424i	0.994865	−	0.101212i	$-0.0322720\pi$
$558$		0			0
$559$	−25.7719	+	26.5570i	−1.09003	+	1.12324i
$560$	−6.46335	−	11.1948i	−0.273126	−	0.473068i
$561$		0			0
$562$	−10.2555	+	17.7630i	−0.432601	+	0.749287i
$563$	4.96417	−	8.59819i	0.209215	−	0.362370i	−0.742253	−	0.670120i	$-0.766243\pi$
$563$	4.96417	−	8.59819i	0.209215	−	0.362370i	0.951467	+	0.307750i	$0.0995759\pi$
$564$		0			0
$565$	−19.7704	+	11.4144i	−0.831745	+	0.480208i
$566$		−	1.63998i		−	0.0689336i
$567$		0			0
$568$	1.94505			0.0816125
$569$	14.9307	+	25.8608i	0.625929	+	1.08414i	0.988361	+	0.152130i	$0.0486132\pi$
$569$	14.9307	+	25.8608i	0.625929	+	1.08414i	−0.362432	+	0.932010i	$0.618053\pi$
$570$		0			0
$571$	−15.0696	+	26.1014i	−0.630645	+	1.09231i	0.356775	+	0.934190i	$0.383876\pi$
$571$	−15.0696	+	26.1014i	−0.630645	+	1.09231i	−0.987420	+	0.158119i	$0.949457\pi$
$572$	6.90816	−	1.96257i	0.288845	−	0.0820592i
$573$		0			0
$574$	−24.0539	+	13.8875i	−1.00399	+	0.579655i
$575$	−41.5205			−1.73153
$576$		0			0
$577$			7.87256i			0.327739i	0.986482	+	0.163869i	$0.0523976\pi$
$577$			7.87256i			0.327739i	−0.986482	+	0.163869i	$0.947602\pi$
$578$	−8.86230	+	5.11665i	−0.368623	+	0.212825i
$579$		0			0
$580$	29.0695	+	16.7833i	1.20705	+	0.696888i
$581$	−3.96186	+	6.86215i	−0.164366	+	0.284690i
$582$		0			0
$583$	−15.8082	+	9.12685i	−0.654708	+	0.377996i
$584$	8.41425			0.348184
$585$		0			0
$586$	−12.4220			−0.513150
$587$	−18.6643	+	10.7758i	−0.770359	+	0.444767i	−0.833003	−	0.553269i	$-0.813380\pi$
$587$	−18.6643	+	10.7758i	−0.770359	+	0.444767i	0.0626437	+	0.998036i	$0.480047\pi$
$588$		0			0
$589$	5.25894	−	9.10875i	0.216691	−	0.375320i
$590$	−24.2973	−	14.0281i	−1.00031	−	0.577527i
$591$		0			0
$592$	−4.40538	+	2.54345i	−0.181060	+	0.104535i
$593$			8.13186i			0.333935i	0.985962	+	0.166968i	$0.0533975\pi$
$593$			8.13186i			0.333935i	−0.985962	+	0.166968i	$0.946602\pi$
$594$		0			0
$595$	−33.6260			−1.37853
$596$	−6.74717	+	3.89548i	−0.276375	+	0.159565i
$597$		0			0
$598$	14.8180	−	4.20970i	0.605952	−	0.172148i
$599$	23.3019	−	40.3601i	0.952090	−	1.64907i	0.211199	−	0.977443i	$-0.432263\pi$
$599$	23.3019	−	40.3601i	0.952090	−	1.64907i	0.740891	−	0.671625i	$-0.234403\pi$
$600$		0			0
$601$	−10.3826	−	17.9832i	−0.423515	−	0.733550i	0.572765	−	0.819719i	$-0.305871\pi$
$601$	−10.3826	−	17.9832i	−0.423515	−	0.733550i	−0.996280	+	0.0861696i	$0.972537\pi$
$602$	−34.5829			−1.40949
$603$		0			0
$604$		−	21.3658i		−	0.869363i
$605$	−23.3660	+	13.4904i	−0.949963	+	0.548461i
$606$		0			0
$607$	16.3176	−	28.2630i	0.662313	−	1.14716i	−0.317694	−	0.948193i	$-0.602908\pi$
$607$	16.3176	−	28.2630i	0.662313	−	1.14716i	0.980006	−	0.198966i	$-0.0637582\pi$
$608$	0.995899	−	1.72495i	0.0403890	−	0.0699559i
$609$		0			0
$610$	21.6249	+	37.4554i	0.875566	+	1.51652i
$611$	−12.6317	−	12.2583i	−0.511025	−	0.495917i
$612$		0			0
$613$		−	12.8107i		−	0.517421i	−0.965955	−	0.258711i	$-0.916702\pi$
$613$		−	12.8107i		−	0.517421i	0.965955	−	0.258711i	$-0.0832976\pi$
$614$	−12.9390	−	22.4110i	−0.522175	−	0.904434i
$615$		0			0
$616$	5.81211	+	3.35563i	0.234177	+	0.135202i
$617$	18.6017	+	10.7397i	0.748874	+	0.432363i	0.825287	−	0.564714i	$-0.191013\pi$
$617$	18.6017	+	10.7397i	0.748874	+	0.432363i	−0.0764127	+	0.997076i	$0.524347\pi$
$618$		0			0
$619$	−39.6343	+	22.8829i	−1.59304	+	0.919741i	−0.600256	+	0.799808i	$0.704935\pi$
$619$	−39.6343	+	22.8829i	−1.59304	+	0.919741i	−0.992782	+	0.119933i	$0.961732\pi$
$620$	−20.2587			−0.813610
$621$		0			0
$622$			25.3822i			1.01773i
$623$	10.5849	+	18.3336i	0.424076	+	0.734522i
$624$		0			0
$625$	−10.4272	+	18.0604i	−0.417086	+	0.722414i
$626$	8.83342	+	5.09998i	0.353054	+	0.203836i
$627$		0			0
$628$	−2.12572	−	3.68185i	−0.0848253	−	0.146922i
$629$			13.2325i			0.527613i
$630$		0			0
$631$		−	10.7134i		−	0.426495i	−0.976998	−	0.213248i	$-0.931596\pi$
$631$		−	10.7134i		−	0.426495i	0.976998	−	0.213248i	$-0.0684041\pi$
$632$	5.15470	−	2.97607i	0.205043	−	0.118382i
$633$		0			0
$634$	−6.09759	+	10.5613i	−0.242166	+	0.419444i
$635$	−19.7064	−	11.3775i	−0.782023	−	0.451501i
$636$		0			0
$637$	−15.2199	−	3.83440i	−0.603035	−	0.151924i
$638$	−17.4270			−0.689942
$639$		0			0
$640$	−3.83645			−0.151649
$641$	−19.0700	−	33.0303i	−0.753221	−	1.30462i	−0.946254	−	0.323425i	$-0.895166\pi$
$641$	−19.0700	−	33.0303i	−0.753221	−	1.30462i	0.193033	−	0.981192i	$-0.438168\pi$
$642$		0			0
$643$	−7.07558	−	4.08509i	−0.279034	−	0.161100i	0.353952	−	0.935264i	$-0.384838\pi$
$643$	−7.07558	−	4.08509i	−0.279034	−	0.161100i	−0.632986	+	0.774163i	$0.718171\pi$
$644$	12.4669	+	7.19780i	0.491267	+	0.283633i
$645$		0			0
$646$	−2.59062	−	4.48708i	−0.101927	−	0.176542i
$647$	0.977276			0.0384207			0.0192103	−	0.999815i	$-0.493885\pi$
$647$	0.977276			0.0384207			0.0192103	+	0.999815i	$0.493885\pi$
$648$		0			0
$649$	14.5661			0.571770
$650$	8.56024	−	33.9782i	0.335760	−	1.33274i
$651$		0			0
$652$	−9.57247	−	5.52667i	−0.374887	−	0.216441i
$653$	6.98319	−	12.0952i	0.273273	−	0.473323i	−0.696425	−	0.717630i	$-0.745227\pi$
$653$	6.98319	−	12.0952i	0.273273	−	0.473323i	0.969698	+	0.244307i	$0.0785603\pi$
$654$		0			0
$655$	45.7334	−	26.4042i	1.78695	−	1.03170i
$656$			8.24323i			0.321844i
$657$		0			0
$658$		−	16.4492i		−	0.641258i
$659$	−9.48438	−	16.4274i	−0.369459	−	0.639922i	0.620022	−	0.784584i	$-0.287124\pi$
$659$	−9.48438	−	16.4274i	−0.369459	−	0.639922i	−0.989481	+	0.144663i	$0.953790\pi$
$660$		0			0
$661$	15.9467	+	9.20684i	0.620255	+	0.358104i	0.776968	−	0.629540i	$-0.216756\pi$
$661$	15.9467	+	9.20684i	0.620255	+	0.358104i	−0.156713	+	0.987644i	$0.550090\pi$
$662$	11.2383	−	19.4652i	0.436787	−	0.756538i
$663$		0			0
$664$	1.17582	+	2.03658i	0.0456307	+	0.0790347i
$665$			25.7474i			0.998440i
$666$		0			0
$667$	−37.3808			−1.44739
$668$	−8.14388	+	4.70187i	−0.315096	+	0.181921i
$669$		0			0
$670$	−18.8213	−	10.8665i	−0.727130	−	0.419809i
$671$	−19.4460	−	11.2272i	−0.750705	−	0.433420i
$672$		0			0
$673$	13.9695	+	24.1959i	0.538486	+	0.932685i	0.998986	+	0.0450254i	$0.0143369\pi$
$673$	13.9695	+	24.1959i	0.538486	+	0.932685i	−0.460500	+	0.887660i	$0.652330\pi$
$674$		−	30.7950i		−	1.18618i
$675$		0			0
$676$	0.389998	+	12.9941i	0.0149999	+	0.499775i
$677$	−1.78613	−	3.09367i	−0.0686465	−	0.118899i	0.829659	−	0.558270i	$-0.188535\pi$
$677$	−1.78613	−	3.09367i	−0.0686465	−	0.118899i	−0.898306	+	0.439371i	$0.855201\pi$
$678$		0			0
$679$	17.3586	−	30.0660i	0.666162	−	1.15383i
$680$	−4.98985	+	8.64268i	−0.191352	+	0.331431i
$681$		0			0
$682$	9.10875	−	5.25894i	0.348792	−	0.201375i
$683$		−	11.0777i		−	0.423875i	−0.977283	−	0.211938i	$-0.932023\pi$
$683$		−	11.0777i		−	0.423875i	0.977283	−	0.211938i	$-0.0679774\pi$
$684$		0			0
$685$	−14.6546			−0.559924
$686$	4.45921	+	7.72358i	0.170254	+	0.294888i
$687$		0			0
$688$	−5.13184	+	8.88861i	−0.195650	+	0.338875i
$689$	−9.02996	−	31.7850i	−0.344014	−	1.21091i
$690$		0			0
$691$	16.9314	−	9.77532i	0.644099	−	0.371871i	−0.142093	−	0.989853i	$-0.545383\pi$
$691$	16.9314	−	9.77532i	0.644099	−	0.371871i	0.786192	+	0.617983i	$0.212050\pi$
$692$	2.17769			0.0827835
$693$		0			0
$694$			29.0471i			1.10261i
$695$	−45.2179	+	26.1065i	−1.71521	+	0.990277i
$696$		0			0
$697$	18.5702	+	10.7215i	0.703396	+	0.406106i
$698$	6.23358	−	10.7969i	0.235944	−	0.408668i
$699$		0			0
$700$	28.3583	−	16.3727i	1.07184	−	0.618829i
$701$	−46.2105			−1.74535			−0.872673	−	0.488306i	$-0.837615\pi$
$701$	−46.2105			−1.74535			−0.872673	+	0.488306i	$0.837615\pi$
$702$		0			0
$703$	10.1321			0.382138
$704$	1.72495	−	0.995899i	0.0650114	−	0.0375344i
$705$		0			0
$706$	17.2147	−	29.8167i	0.647882	−	1.12217i
$707$	−7.46782	−	4.31155i	−0.280856	−	0.162152i
$708$		0			0
$709$	−28.1320	+	16.2420i	−1.05652	+	0.609983i	−0.924468	−	0.381260i	$-0.875490\pi$
$709$	−28.1320	+	16.2420i	−1.05652	+	0.609983i	−0.132053	+	0.991243i	$0.542157\pi$
$710$			7.46209i			0.280047i
$711$		0			0
$712$	6.28290			0.235462
$713$	19.5382	−	11.2804i	0.731712	−	0.422454i
$714$		0			0
$715$	7.52930	+	26.5028i	0.281580	+	0.991149i
$716$	−3.95576	+	6.85157i	−0.147834	+	0.256055i
$717$		0			0
$718$	−17.1248	−	29.6610i	−0.639091	−	1.10694i
$719$	−30.0876			−1.12208			−0.561038	−	0.827790i	$-0.689598\pi$
$719$	−30.0876			−1.12208			−0.561038	+	0.827790i	$0.689598\pi$
$720$		0			0
$721$		−	19.0085i		−	0.707913i
$722$	13.0187	−	7.51637i	0.484507	−	0.279730i
$723$		0			0
$724$	−0.510976	+	0.885037i	−0.0189903	+	0.0328921i
$725$	−42.5147	+	73.6377i	−1.57896	+	2.73483i
$726$		0			0
$727$	−2.30907	−	3.99942i	−0.0856386	−	0.148330i	0.820025	−	0.572328i	$-0.193960\pi$
$727$	−2.30907	−	3.99942i	−0.0856386	−	0.148330i	−0.905663	+	0.423998i	$0.860626\pi$
$728$	−8.46059	+	8.71833i	−0.313570	+	0.323123i
$729$		0			0
$730$			32.2808i			1.19477i
$731$	13.3494	+	23.1218i	0.493745	+	0.855191i
$732$		0			0
$733$	38.6651	+	22.3233i	1.42813	+	0.824531i	0.996973	−	0.0777462i	$-0.0247724\pi$
$733$	38.6651	+	22.3233i	1.42813	+	0.824531i	0.431156	+	0.902277i	$0.358106\pi$
$734$	4.36140	+	2.51806i	0.160982	+	0.0929432i
$735$		0			0
$736$	3.70000	−	2.13620i	0.136384	−	0.0787413i
$737$	11.2833			0.415624
$738$		0			0
$739$		−	3.94466i		−	0.145107i	−0.997365	−	0.0725534i	$-0.976885\pi$
$739$		−	3.94466i		−	0.145107i	0.997365	−	0.0725534i	$-0.0231148\pi$
$740$	−9.75779	−	16.9010i	−0.358704	−	0.621293i
$741$		0			0
$742$	15.4395	−	26.7420i	0.566803	−	0.981731i
$743$	46.8150	+	27.0287i	1.71748	+	0.991585i	0.923466	+	0.383680i	$0.125343\pi$
$743$	46.8150	+	27.0287i	1.71748	+	0.991585i	0.794010	+	0.607905i	$0.207990\pi$
$744$		0			0
$745$	−14.9448	−	25.8852i	−0.547535	−	0.948359i
$746$			11.2141i			0.410578i
$747$		0			0
$748$		−	5.18124i		−	0.189445i
$749$	−53.4148	+	30.8391i	−1.95173	+	1.12683i
$750$		0			0
$751$	−1.96630	+	3.40573i	−0.0717513	+	0.124277i	−0.899669	−	0.436573i	$-0.856192\pi$
$751$	−1.96630	+	3.40573i	−0.0717513	+	0.124277i	0.827918	+	0.560850i	$0.189525\pi$
$752$	−4.22784	−	2.44094i	−0.154173	−	0.0890120i
$753$		0			0
$754$	7.70676	−	30.5905i	0.280664	−	1.11404i
$755$	81.9689			2.98315
$756$		0			0
$757$	−0.241542			−0.00877899			−0.00438949	−	0.999990i	$-0.501397\pi$
$757$	−0.241542			−0.00877899			−0.00438949	+	0.999990i	$0.501397\pi$
$758$	−2.56312	−	4.43945i	−0.0930965	−	0.161248i
$759$		0			0
$760$	6.61767	+	3.82072i	0.240048	+	0.138592i
$761$	−13.6634	−	7.88855i	−0.495297	−	0.285960i	0.231472	−	0.972841i	$-0.425646\pi$
$761$	−13.6634	−	7.88855i	−0.495297	−	0.285960i	−0.726769	+	0.686882i	$0.758979\pi$
$762$		0			0
$763$	11.3703	+	19.6939i	0.411631	+	0.712966i
$764$	4.06108			0.146925
$765$		0			0
$766$	18.9420			0.684401
$767$	−6.44159	+	25.5686i	−0.232592	+	0.923230i
$768$		0			0
$769$	−7.04227	−	4.06586i	−0.253951	−	0.146619i	0.367621	−	0.929976i	$-0.380172\pi$
$769$	−7.04227	−	4.06586i	−0.253951	−	0.146619i	−0.621572	+	0.783357i	$0.713506\pi$
$770$	−12.8737	+	22.2979i	−0.463935	+	0.803559i
$771$		0			0
$772$	−14.4121	+	8.32085i	−0.518704	+	0.299474i
$773$		−	19.4126i		−	0.698221i	−0.937082	−	0.349110i	$-0.886484\pi$
$773$		−	19.4126i		−	0.698221i	0.937082	−	0.349110i	$-0.113516\pi$
$774$		0			0
$775$		−	51.3186i		−	1.84342i
$776$	−5.15177	−	8.92313i	−0.184938	−	0.320322i
$777$		0			0
$778$	−18.0477	−	10.4199i	−0.647043	−	0.373570i
$779$	8.20943	−	14.2191i	0.294133	−	0.509454i
$780$		0			0
$781$	−1.93708	−	3.35511i	−0.0693140	−	0.120055i
$782$		−	11.1137i		−	0.397426i
$783$		0			0
$784$	−4.35315			−0.155469
$785$	14.1252	−	8.15520i	0.504151	−	0.291072i
$786$		0			0
$787$	−35.6740	−	20.5964i	−1.27164	−	0.734183i	−0.296345	−	0.955081i	$-0.595768\pi$
$787$	−35.6740	−	20.5964i	−1.27164	−	0.734183i	−0.975297	+	0.220899i	$0.929101\pi$
$788$	−18.0532	−	10.4230i	−0.643120	−	0.371306i
$789$		0			0
$790$	11.4175	+	19.7757i	0.406217	+	0.703589i
$791$			20.0499i			0.712893i
$792$		0			0
$793$	28.3072	−	29.1695i	1.00522	−	1.03584i
$794$	−1.08576	−	1.88059i	−0.0385321	−	0.0667396i
$795$		0			0
$796$	7.71833	−	13.3685i	0.273569	−	0.473835i
$797$	−1.79638	+	3.11142i	−0.0636309	+	0.110212i	−0.896086	−	0.443881i	$-0.853601\pi$
$797$	−1.79638	+	3.11142i	−0.0636309	+	0.110212i	0.832455	+	0.554093i	$0.186935\pi$
$798$		0			0
$799$	−10.9978	+	6.34959i	−0.389075	+	0.224632i
$800$		−	9.71833i		−	0.343595i
$801$		0			0
$802$	10.8033			0.381476
$803$	−8.37975	−	14.5141i	−0.295715	−	0.512193i
$804$		0			0
$805$	−27.6140	+	47.8288i	−0.973264	+	1.68574i
$806$	5.20311	+	18.3147i	0.183272	+	0.645108i
$807$		0			0
$808$	−2.21634	+	1.27960i	−0.0779705	+	0.0450163i
$809$	−10.0592			−0.353664			−0.176832	−	0.984241i	$-0.556585\pi$
$809$	−10.0592			−0.353664			−0.176832	+	0.984241i	$0.556585\pi$
$810$		0			0
$811$			29.4252i			1.03326i	0.856209	+	0.516630i	$0.172814\pi$
$811$			29.4252i			1.03326i	−0.856209	+	0.516630i	$0.827186\pi$
$812$	25.5309	−	14.7403i	0.895960	−	0.517283i
$813$		0			0
$814$	8.77462	+	5.06603i	0.307550	+	0.177564i
$815$	21.2028	−	36.7243i	0.742700	−	1.28639i
$816$		0			0
$817$	17.7043	−	10.2216i	0.619396	−	0.357608i
$818$	−1.55301			−0.0542996
$819$		0			0
$820$	−31.6247			−1.10438
$821$	9.46944	−	5.46718i	0.330486	−	0.190806i	−0.325571	−	0.945518i	$-0.605557\pi$
$821$	9.46944	−	5.46718i	0.330486	−	0.190806i	0.656057	+	0.754712i	$0.272223\pi$
$822$		0			0
$823$	−7.88841	+	13.6631i	−0.274973	+	0.476266i	−0.970128	−	0.242593i	$-0.922002\pi$
$823$	−7.88841	+	13.6631i	−0.274973	+	0.476266i	0.695156	+	0.718859i	$0.255335\pi$
$824$	−4.88562	−	2.82072i	−0.170199	−	0.0982643i
$825$		0			0
$826$	−21.3397	+	12.3205i	−0.742502	+	0.428683i
$827$			20.9583i			0.728793i	0.931244	+	0.364396i	$0.118725\pi$
$827$			20.9583i			0.728793i	−0.931244	+	0.364396i	$0.881275\pi$
$828$		0			0
$829$	−30.6108			−1.06316			−0.531579	−	0.847009i	$-0.678401\pi$
$829$	−30.6108			−1.06316			−0.531579	+	0.847009i	$0.678401\pi$
$830$	−7.81324	+	4.51098i	−0.271202	+	0.156578i
$831$		0			0
$832$	0.985326	+	3.46830i	0.0341600	+	0.120242i
$833$	−5.66189	+	9.80668i	−0.196173	+	0.339781i
$834$		0			0
$835$	−18.0385	−	31.2436i	−0.624248	−	1.08123i
$836$	−3.96726			−0.137211
$837$		0			0
$838$		−	5.62905i		−	0.194452i
$839$	−19.6661	+	11.3542i	−0.678949	+	0.391991i	−0.799459	−	0.600721i	$-0.794880\pi$
$839$	−19.6661	+	11.3542i	−0.678949	+	0.391991i	0.120510	+	0.992712i	$0.461547\pi$
$840$		0			0
$841$	−23.7759	+	41.1811i	−0.819859	+	1.42004i
$842$	5.99704	−	10.3872i	0.206672	−	0.357966i
$843$		0			0
$844$	−1.86662	−	3.23307i	−0.0642516	−	0.111287i
$845$	−49.8514	+	1.49621i	−1.71494	+	0.0514710i
$846$		0			0
$847$			23.6964i			0.814218i
$848$	−4.58222	−	7.93663i	−0.157354	−	0.272545i
$849$		0			0
$850$	−21.8933	−	12.6401i	−0.750933	−	0.433551i
$851$	18.8215	+	10.8666i	0.645193	+	0.372502i
$852$		0			0
$853$	−12.6546	+	7.30611i	−0.433284	+	0.250157i	−0.700745	−	0.713412i	$-0.747149\pi$
$853$	−12.6546	+	7.30611i	−0.433284	+	0.250157i	0.267461	+	0.963569i	$0.413815\pi$
$854$	37.9850			1.29982
$855$		0			0
$856$			18.3051i			0.625657i
$857$	7.11150	+	12.3175i	0.242924	+	0.420757i	0.961546	−	0.274644i	$-0.0885601\pi$
$857$	7.11150	+	12.3175i	0.242924	+	0.420757i	−0.718622	+	0.695401i	$0.755227\pi$
$858$		0			0
$859$	−20.8166	+	36.0553i	−0.710252	+	1.23019i	0.254511	+	0.967070i	$0.418086\pi$
$859$	−20.8166	+	36.0553i	−0.710252	+	1.23019i	−0.964762	+	0.263122i	$0.915248\pi$
$860$	−34.1007	−	19.6880i	−1.16282	−	0.671356i
$861$		0			0
$862$	−0.00635709	−	0.0110108i	−0.000216523	−	0.000375029i
$863$			13.5656i			0.461780i	0.972980	+	0.230890i	$0.0741638\pi$
$863$			13.5656i			0.461780i	−0.972980	+	0.230890i	$0.925836\pi$
$864$		0			0
$865$			8.35461i			0.284065i
$866$	26.7357	−	15.4359i	0.908516	−	0.524532i
$867$		0			0
$868$	−8.89633	+	15.4089i	−0.301961	+	0.523012i
$869$	−10.2671	−	5.92772i	−0.348288	−	0.201084i
$870$		0			0
$871$	−4.98981	+	19.8061i	−0.169073	+	0.671103i
$872$	6.74904			0.228551
$873$		0			0
$874$	−8.50975			−0.287847
$875$	30.4962	+	52.8210i	1.03096	+	1.78568i
$876$		0			0
$877$	−36.0166	−	20.7942i	−1.21619	−	0.702170i	−0.252092	−	0.967703i	$-0.581119\pi$
$877$	−36.0166	−	20.7942i	−1.21619	−	0.702170i	−0.964102	+	0.265533i	$0.914452\pi$
$878$	−14.1990	−	8.19780i	−0.479193	−	0.276662i
$879$		0			0
$880$	3.82072	+	6.61767i	0.128796	+	0.223082i
$881$	15.0582			0.507323			0.253662	−	0.967293i	$-0.418365\pi$
$881$	15.0582			0.507323			0.253662	+	0.967293i	$0.418365\pi$
$882$		0			0
$883$	21.3359			0.718010			0.359005	−	0.933336i	$-0.383116\pi$
$883$	21.3359			0.718010			0.359005	+	0.933336i	$0.383116\pi$
$884$	9.09489	+	2.29130i	0.305894	+	0.0770649i
$885$		0			0
$886$	−3.50320	−	2.02258i	−0.117692	−	0.0679498i
$887$	−15.4676	+	26.7906i	−0.519350	+	0.899540i	0.480398	+	0.877051i	$0.340492\pi$
$887$	−15.4676	+	26.7906i	−0.519350	+	0.899540i	−0.999747	+	0.0224890i	$0.992841\pi$
$888$		0			0
$889$	−17.3075	+	9.99251i	−0.580476	+	0.335138i
$890$			24.1040i			0.807968i
$891$		0			0
$892$		−	2.75301i		−	0.0921775i
$893$	4.86186	+	8.42100i	0.162696	+	0.281798i
$894$		0			0
$895$	−26.2857	−	15.1761i	−0.878634	−	0.507280i
$896$	−1.68472	+	2.91802i	−0.0562826	+	0.0974843i
$897$		0			0
$898$	7.94715	+	13.7649i	0.265200	+	0.459340i
$899$		−	46.2020i		−	1.54092i
$900$		0			0
$901$	−23.8393			−0.794203
$902$	14.2191	−	8.20943i	0.473446	−	0.273344i
$903$		0			0
$904$	5.15330	+	2.97526i	0.171396	+	0.0989556i
$905$	−3.39540	−	1.96033i	−0.112867	−	0.0651637i
$906$		0			0
$907$	13.2057	+	22.8730i	0.438490	+	0.759486i	0.997573	−	0.0696249i	$-0.0221802\pi$
$907$	13.2057	+	22.8730i	0.438490	+	0.759486i	−0.559084	+	0.829111i	$0.688847\pi$
$908$			3.82159i			0.126824i
$909$		0			0
$910$	−33.4474	−	32.4586i	−1.10877	−	1.07599i
$911$	8.43375	+	14.6077i	0.279423	+	0.483974i	0.971241	−	0.238097i	$-0.0765237\pi$
$911$	8.43375	+	14.6077i	0.279423	+	0.483974i	−0.691819	+	0.722071i	$0.743190\pi$
$912$		0			0
$913$	2.34200	−	4.05646i	0.0775088	−	0.134249i
$914$	14.5707	−	25.2372i	0.481956	−	0.834773i
$915$		0			0
$916$	9.50393	−	5.48710i	0.314019	−	0.181299i
$917$		−	46.3801i		−	1.53161i
$918$		0			0
$919$	28.6707			0.945758			0.472879	−	0.881127i	$-0.343215\pi$
$919$	28.6707			0.945758			0.472879	+	0.881127i	$0.343215\pi$
$920$	8.19541	+	14.1949i	0.270195	+	0.467991i
$921$		0			0
$922$	14.0714	−	24.3725i	0.463418	−	0.802664i
$923$	6.74603	−	1.91651i	0.222048	−	0.0630827i
$924$		0			0
$925$	42.8129	−	24.7180i	1.40768	−	0.812724i
$926$	31.8672			1.04722
$927$		0			0
$928$		−	8.74939i		−	0.287213i
$929$	36.3750	−	21.0011i	1.19343	−	0.689024i	0.234344	−	0.972154i	$-0.424706\pi$
$929$	36.3750	−	21.0011i	1.19343	−	0.689024i	0.959082	+	0.283129i	$0.0913726\pi$
$930$		0			0
$931$	7.50895	+	4.33529i	0.246096	+	0.142084i
$932$	−1.13049	+	1.95807i	−0.0370305	+	0.0641387i
$933$		0			0
$934$	−1.68173	+	0.970945i	−0.0550278	+	0.0317703i
$935$	19.8776			0.650066
$936$		0			0
$937$	44.9192			1.46745			0.733724	−	0.679448i	$-0.237781\pi$
$937$	44.9192			1.46745			0.733724	+	0.679448i	$0.237781\pi$
$938$	−16.5302	+	9.54372i	−0.539730	+	0.311613i
$939$		0			0
$940$	9.36455	−	16.2199i	0.305438	−	0.529034i
$941$	8.28428	+	4.78293i	0.270060	+	0.155919i	0.628915	−	0.777474i	$-0.283499\pi$
$941$	8.28428	+	4.78293i	0.270060	+	0.155919i	−0.358855	+	0.933393i	$0.616833\pi$
$942$		0			0
$943$	30.5000	−	17.6092i	0.993216	−	0.573433i
$944$			7.31305i			0.238020i
$945$		0			0
$946$	20.4432			0.664665
$947$	−25.3100	+	14.6127i	−0.822465	+	0.474850i	−0.851266	−	0.524735i	$-0.824165\pi$
$947$	−25.3100	+	14.6127i	−0.822465	+	0.474850i	0.0288007	+	0.999585i	$0.490831\pi$
$948$		0			0
$949$	29.1832	−	8.29078i	0.947326	−	0.269130i
$950$	−9.67848	+	16.7636i	−0.314011	+	0.543884i
$951$		0			0
$952$	4.38244	+	7.59062i	0.142036	+	0.246013i
$953$	−6.46873			−0.209543			−0.104771	−	0.994496i	$-0.533411\pi$
$953$	−6.46873			−0.209543			−0.104771	+	0.994496i	$0.533411\pi$
$954$		0			0
$955$			15.5801i			0.504161i
$956$	5.46146	−	3.15318i	0.176636	−	0.101981i
$957$		0			0
$958$	−5.46237	+	9.46110i	−0.176481	+	0.305674i
$959$	−6.43536	+	11.1464i	−0.207809	+	0.359935i
$960$		0			0
$961$	−1.55765	−	2.69793i	−0.0502468	−	0.0870300i
$962$	−12.7731	+	13.1622i	−0.411820	+	0.424366i
$963$		0			0
$964$			19.8311i			0.638718i
$965$	−31.9225	−	55.2914i	−1.02762	−	1.77989i
$966$		0			0
$967$	−42.0071	−	24.2528i	−1.35086	−	0.779918i	−0.362488	−	0.931988i	$-0.618073\pi$
$967$	−42.0071	−	24.2528i	−1.35086	−	0.779918i	−0.988370	+	0.152070i	$0.951406\pi$
$968$	6.09053	+	3.51637i	0.195757	+	0.113020i
$969$		0			0
$970$	34.2331	−	19.7645i	1.09916	−	0.634600i
$971$	4.35773			0.139846			0.0699231	−	0.997552i	$-0.477725\pi$
$971$	4.35773			0.139846			0.0699231	+	0.997552i	$0.477725\pi$
$972$		0			0
$973$			45.8573i			1.47012i
$974$	19.1989	+	33.2535i	0.615172	+	1.06551i
$975$		0			0
$976$	5.63669	−	9.76304i	0.180426	−	0.312507i
$977$	18.7895	+	10.8481i	0.601131	+	0.347063i	0.769486	−	0.638663i	$-0.220512\pi$
$977$	18.7895	+	10.8481i	0.601131	+	0.347063i	−0.168356	+	0.985726i	$0.553846\pi$
$978$		0			0
$979$	−6.25713	−	10.8377i	−0.199979	−	0.346373i
$980$		−	16.7006i		−	0.533482i
$981$		0			0
$982$		−	10.5533i		−	0.336768i
$983$	24.3478	−	14.0572i	0.776573	−	0.448355i	−0.0586415	−	0.998279i	$-0.518677\pi$
$983$	24.3478	−	14.0572i	0.776573	−	0.448355i	0.835214	+	0.549925i	$0.185344\pi$
$984$		0			0
$985$	39.9875	−	69.2603i	1.27411	−	2.20682i
$986$	−19.7105	−	11.3798i	−0.627709	−	0.362408i
$987$		0			0
$988$	1.75444	−	6.96393i	0.0558163	−	0.221552i
$989$	43.8505			1.39436
$990$		0			0
$991$	−42.2239			−1.34129			−0.670643	−	0.741780i	$-0.733982\pi$
$991$	−42.2239			−1.34129			−0.670643	+	0.741780i	$0.733982\pi$
$992$	2.64030	+	4.57313i	0.0838296	+	0.145197i
$993$		0			0
$994$	5.67571	+	3.27687i	0.180022	+	0.103936i
$995$	51.2877	+	29.6110i	1.62593	+	0.938731i
$996$		0			0
$997$	−0.308639	−	0.534579i	−0.00977470	−	0.0169303i	0.861097	−	0.508441i	$-0.169778\pi$
$997$	−0.308639	−	0.534579i	−0.00977470	−	0.0169303i	−0.870871	+	0.491511i	$0.836445\pi$
$998$	0.992867			0.0314287
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.t.a.415.14		28
3.2	odd	2		234.2.t.a.103.3	yes	28
9.2	odd	6		234.2.t.a.25.10	yes	28
9.4	even	3		2106.2.b.d.649.8		14
9.5	odd	6		2106.2.b.c.649.7		14
9.7	even	3	inner	702.2.t.a.181.1		28
13.12	even	2	inner	702.2.t.a.415.1		28
39.38	odd	2		234.2.t.a.103.10	yes	28
117.25	even	6	inner	702.2.t.a.181.14		28
117.38	odd	6		234.2.t.a.25.3	✓	28
117.77	odd	6		2106.2.b.c.649.8		14
117.103	even	6		2106.2.b.d.649.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.t.a.25.3	✓	28	117.38	odd	6
234.2.t.a.25.10	yes	28	9.2	odd	6
234.2.t.a.103.3	yes	28	3.2	odd	2
234.2.t.a.103.10	yes	28	39.38	odd	2
702.2.t.a.181.1		28	9.7	even	3	inner
702.2.t.a.181.14		28	117.25	even	6	inner
702.2.t.a.415.1		28	13.12	even	2	inner
702.2.t.a.415.14		28	1.1	even	1	trivial
2106.2.b.c.649.7		14	9.5	odd	6
2106.2.b.c.649.8		14	117.77	odd	6
2106.2.b.d.649.7		14	117.103	even	6
2106.2.b.d.649.8		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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.32246 + 1.91822i) q^{5} +(2.91802 - 1.68472i) q^{7} -1.00000i q^{8} +3.83645 q^{10} +(-1.72495 + 0.995899i) q^{11} +(-0.985326 - 3.46830i) q^{13} +(1.68472 - 2.91802i) q^{14} +(-0.500000 - 0.866025i) q^{16} -2.60129 q^{17} +1.99180i q^{19} +(3.32246 - 1.91822i) q^{20} +(-0.995899 + 1.72495i) q^{22} +(-2.13620 + 3.70000i) q^{23} +(4.85917 + 8.41632i) q^{25} +(-2.58747 - 2.51098i) q^{26} -3.36944i q^{28} +(4.37469 + 7.57719i) q^{29} +(-4.57313 - 2.64030i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.25278 + 1.30064i) q^{34} +12.9267 q^{35} -5.08689i q^{37} +(0.995899 + 1.72495i) q^{38} +(1.91822 - 3.32246i) q^{40} +(-7.13885 - 4.12162i) q^{41} +(-5.13184 - 8.88861i) q^{43} +1.99180i q^{44} +4.27239i q^{46} +(4.22784 - 2.44094i) q^{47} +(2.17657 - 3.76993i) q^{49} +(8.41632 + 4.85917i) q^{50} +(-3.49630 - 0.880834i) q^{52} +9.16444 q^{53} -7.64143 q^{55} +(-1.68472 - 2.91802i) q^{56} +(7.57719 + 4.37469i) q^{58} +(-6.33329 - 3.65653i) q^{59} +(5.63669 + 9.76304i) q^{61} -5.28060 q^{62} -1.00000 q^{64} +(3.37927 - 13.4134i) q^{65} +(-4.90591 - 2.83243i) q^{67} +(-1.30064 + 2.25278i) q^{68} +(11.1948 - 6.46335i) q^{70} +1.94505i q^{71} +8.41425i q^{73} +(-2.54345 - 4.40538i) q^{74} +(1.72495 + 0.995899i) q^{76} +(-3.35563 + 5.81211i) q^{77} +(2.97607 + 5.15470i) q^{79} -3.83645i q^{80} -8.24323 q^{82} +(-2.03658 + 1.17582i) q^{83} +(-8.64268 - 4.98985i) q^{85} +(-8.88861 - 5.13184i) q^{86} +(0.995899 + 1.72495i) q^{88} +6.28290i q^{89} +(-8.71833 - 8.46059i) q^{91} +(2.13620 + 3.70000i) q^{92} +(2.44094 - 4.22784i) q^{94} +(-3.82072 + 6.61767i) q^{95} +(8.92313 - 5.15177i) q^{97} -4.35315i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62}+ \cdots - 8 q^{92}+O(q^{100}) \) 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

Related objects

Downloads

Learn more