LMFDB - Embedded newform 700.2.t.c.199.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(199,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.199"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$700 = 2^{2} \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	700.t (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,2,0,0,0,0,16,0,0,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.9
Character	$\chi$	$=$	700.199
Dual form			700.2.t.c.299.9

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.299797 + 1.38207i) q^{2} +(2.37047 + 1.36859i) q^{3} +(-1.82024 + 0.828682i) q^{4} +(-1.18083 + 3.68646i) q^{6} +(-2.43939 + 1.02440i) q^{7} +(-1.69100 - 2.26727i) q^{8} +(2.24609 + 3.89033i) q^{9} +(-0.0868131 - 0.0501216i) q^{11} +(-5.44896 - 0.526805i) q^{12} -4.11735 q^{13} +(-2.14711 - 3.06430i) q^{14} +(2.62657 - 3.01680i) q^{16} +(-2.69867 + 4.67424i) q^{17} +(-4.70335 + 4.27056i) q^{18} +(3.72967 + 6.45997i) q^{19} +(-7.18448 - 0.910218i) q^{21} +(0.0432453 - 0.135008i) q^{22} +(0.754151 + 1.30623i) q^{23} +(-0.905498 - 7.68879i) q^{24} +(-1.23437 - 5.69048i) q^{26} +4.08434i q^{27} +(3.59138 - 3.88613i) q^{28} +2.37688 q^{29} +(2.72129 - 4.71341i) q^{31} +(4.95688 + 2.72568i) q^{32} +(-0.137192 - 0.237623i) q^{33} +(-7.26919 - 2.32844i) q^{34} +(-7.31227 - 5.22007i) q^{36} +(0.899386 - 0.519260i) q^{37} +(-7.81000 + 7.09135i) q^{38} +(-9.76007 - 5.63498i) q^{39} +7.99125i q^{41} +(-0.895897 - 10.2023i) q^{42} +7.04778 q^{43} +(0.199556 + 0.0192930i) q^{44} +(-1.57921 + 1.43389i) q^{46} +(3.84841 - 2.22188i) q^{47} +(10.3550 - 3.55654i) q^{48} +(4.90122 - 4.99781i) q^{49} +(-12.7943 + 7.38677i) q^{51} +(7.49459 - 3.41198i) q^{52} +(5.31966 + 3.07131i) q^{53} +(-5.64485 + 1.22447i) q^{54} +(6.44759 + 3.79849i) q^{56} +20.4176i q^{57} +(0.712582 + 3.28502i) q^{58} +(4.26148 - 7.38111i) q^{59} +(6.84408 - 3.95143i) q^{61} +(7.33010 + 2.34795i) q^{62} +(-9.46432 - 7.18914i) q^{63} +(-2.28103 + 7.66791i) q^{64} +(0.287283 - 0.260848i) q^{66} +(-0.0549000 + 0.0950895i) q^{67} +(1.03879 - 10.7446i) q^{68} +4.12850i q^{69} -6.73221i q^{71} +(5.02231 - 11.6710i) q^{72} +(-3.07349 + 5.32344i) q^{73} +(0.987288 + 1.08734i) q^{74} +(-12.1422 - 8.66802i) q^{76} +(0.263115 + 0.0333347i) q^{77} +(4.86190 - 15.1785i) q^{78} +(3.70178 - 2.13723i) q^{79} +(1.14846 - 1.98919i) q^{81} +(-11.0445 + 2.39575i) q^{82} -6.50159i q^{83} +(13.8318 - 4.29682i) q^{84} +(2.11290 + 9.74053i) q^{86} +(5.63433 + 3.25298i) q^{87} +(0.0331618 + 0.281584i) q^{88} +(2.76417 - 1.59589i) q^{89} +(10.0438 - 4.21781i) q^{91} +(-2.45519 - 1.75270i) q^{92} +(12.9015 - 7.44866i) q^{93} +(4.22454 + 4.65267i) q^{94} +(8.01978 + 13.2451i) q^{96} -11.0691 q^{97} +(8.37670 + 5.27550i) q^{98} -0.450309i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 2 q^{4} + 16 q^{9} - 14 q^{12} - 8 q^{13} - 2 q^{14} - 14 q^{16} + 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} + 32 q^{28} + 40 q^{29} + 60 q^{32} - 24 q^{33} + 60 q^{36} - 60 q^{37} - 46 q^{38}+ \cdots - 124 q^{98}+O(q^{100})$ 32 * q + 2 * q^4 + 16 * q^9 - 14 * q^12 - 8 * q^13 - 2 * q^14 - 14 * q^16 + 54 * q^18 - 12 * q^21 - 36 * q^24 + 30 * q^26 + 32 * q^28 + 40 * q^29 + 60 * q^32 - 24 * q^33 + 60 * q^36 - 60 * q^37 - 46 * q^38 + 78 * q^42 + 18 * q^44 + 2 * q^46 - 28 * q^48 + 16 * q^49 - 46 * q^52 - 12 * q^53 - 12 * q^54 - 4 * q^56 + 42 * q^58 + 24 * q^61 + 8 * q^62 - 4 * q^64 + 24 * q^66 - 4 * q^68 + 90 * q^72 - 24 * q^73 - 38 * q^74 + 20 * q^77 - 36 * q^81 + 8 * q^82 + 20 * q^84 + 28 * q^86 - 78 * q^88 + 60 * q^89 + 72 * q^93 - 18 * q^94 - 60 * q^96 - 48 * q^97 - 124 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$ .

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.299797	+	1.38207i	0.211988	+	0.977272i
$2$	0.299797	+	1.38207i	0.211988	+	0.977272i
$3$	2.37047	+	1.36859i	1.36859	+	0.790157i	0.990748	−	0.135713i	$-0.0433325\pi$
$3$	2.37047	+	1.36859i	1.36859	+	0.790157i	0.377843	+	0.925870i	$0.376666\pi$
$4$	−1.82024	+	0.828682i	−0.910122	+	0.414341i
$5$		0			0
$5$		0			0
$6$	−1.18083	+	3.68646i	−0.482073	+	1.50499i
$7$	−2.43939	+	1.02440i	−0.922002	+	0.387186i
$7$	−2.43939	+	1.02440i	−0.922002	+	0.387186i
$8$	−1.69100	−	2.26727i	−0.597859	−	0.801601i
$9$	2.24609	+	3.89033i	0.748695	+	1.29678i
$10$		0			0
$11$	−0.0868131	−	0.0501216i	−0.0261751	−	0.0151122i	0.486855	−	0.873483i	$-0.338144\pi$
$11$	−0.0868131	−	0.0501216i	−0.0261751	−	0.0151122i	−0.513030	+	0.858370i	$0.671477\pi$
$12$	−5.44896	−	0.526805i	−1.57298	−	0.152076i
$13$	−4.11735			−1.14195			−0.570974	−	0.820968i	$-0.693434\pi$
$13$	−4.11735			−1.14195			−0.570974	+	0.820968i	$0.693434\pi$
$14$	−2.14711	−	3.06430i	−0.573840	−	0.818967i
$15$		0			0
$16$	2.62657	−	3.01680i	0.656643	−	0.754201i
$17$	−2.69867	+	4.67424i	−0.654525	+	1.13367i	0.327488	+	0.944855i	$0.393798\pi$
$17$	−2.69867	+	4.67424i	−0.654525	+	1.13367i	−0.982013	+	0.188815i	$0.939535\pi$
$18$	−4.70335	+	4.27056i	−1.10859	+	1.00658i
$19$	3.72967	+	6.45997i	0.855645	+	1.48202i	0.876046	+	0.482228i	$0.160172\pi$
$19$	3.72967	+	6.45997i	0.855645	+	1.48202i	−0.0204012	+	0.999792i	$0.506494\pi$
$20$		0			0
$21$	−7.18448	−	0.910218i	−1.56778	−	0.198626i
$22$	0.0432453	−	0.135008i	0.00921993	−	0.0287838i
$23$	0.754151	+	1.30623i	0.157251	+	0.272367i	0.933877	−	0.357596i	$-0.116403\pi$
$23$	0.754151	+	1.30623i	0.157251	+	0.272367i	−0.776625	+	0.629963i	$0.783070\pi$
$24$	−0.905498	−	7.68879i	−0.184834	−	1.56947i
$25$		0			0
$26$	−1.23437	−	5.69048i	−0.242080	−	1.11599i
$27$			4.08434i			0.786032i
$28$	3.59138	−	3.88613i	0.678707	−	0.734409i
$29$	2.37688			0.441376			0.220688	−	0.975344i	$-0.429170\pi$
$29$	2.37688			0.441376			0.220688	+	0.975344i	$0.429170\pi$
$30$		0			0
$31$	2.72129	−	4.71341i	0.488758	−	0.846553i	−0.511159	−	0.859486i	$-0.670783\pi$
$31$	2.72129	−	4.71341i	0.488758	−	0.846553i	0.999916	+	0.0129330i	$0.00411682\pi$
$32$	4.95688	+	2.72568i	0.876261	+	0.481837i
$33$	−0.137192	−	0.237623i	−0.0238820	−	0.0413649i
$34$	−7.26919	−	2.32844i	−1.24666	−	0.399324i
$35$		0			0
$36$	−7.31227	−	5.22007i	−1.21871	−	0.870011i
$37$	0.899386	−	0.519260i	0.147858	−	0.0853659i	−0.424246	−	0.905547i	$-0.639461\pi$
$37$	0.899386	−	0.519260i	0.147858	−	0.0853659i	0.572104	+	0.820181i	$0.306127\pi$
$38$	−7.81000	+	7.09135i	−1.26695	+	1.15037i
$39$	−9.76007	−	5.63498i	−1.56286	−	0.902318i
$40$		0			0
$41$			7.99125i			1.24802i	0.781415	+	0.624012i	$0.214498\pi$
$41$			7.99125i			1.24802i	−0.781415	+	0.624012i	$0.785502\pi$
$42$	−0.895897	−	10.2023i	−0.138240	−	1.57426i
$43$	7.04778			1.07478			0.537388	−	0.843335i	$-0.319411\pi$
$43$	7.04778			1.07478			0.537388	+	0.843335i	$0.319411\pi$
$44$	0.199556	+	0.0192930i	0.0300842	+	0.00290854i
$45$		0			0
$46$	−1.57921	+	1.43389i	−0.232842	+	0.211416i
$47$	3.84841	−	2.22188i	0.561348	−	0.324095i	−0.192338	−	0.981329i	$-0.561607\pi$
$47$	3.84841	−	2.22188i	0.561348	−	0.324095i	0.753686	+	0.657234i	$0.228274\pi$
$48$	10.3550	−	3.55654i	1.49461	−	0.513342i
$49$	4.90122	−	4.99781i	0.700174	−	0.713973i
$50$		0			0
$51$	−12.7943	+	7.38677i	−1.79155	+	1.03435i
$52$	7.49459	−	3.41198i	1.03931	−	0.473156i
$53$	5.31966	+	3.07131i	0.730711	+	0.421876i	0.818682	−	0.574247i	$-0.194705\pi$
$53$	5.31966	+	3.07131i	0.730711	+	0.421876i	−0.0879710	+	0.996123i	$0.528038\pi$
$54$	−5.64485	+	1.22447i	−0.768167	+	0.166630i
$55$		0			0
$56$	6.44759	+	3.79849i	0.861596	+	0.507595i
$57$			20.4176i			2.70437i
$58$	0.712582	+	3.28502i	0.0935666	+	0.431344i
$59$	4.26148	−	7.38111i	0.554798	−	0.960938i	−0.443121	−	0.896462i	$-0.646129\pi$
$59$	4.26148	−	7.38111i	0.554798	−	0.960938i	0.997919	−	0.0644767i	$-0.0205378\pi$
$60$		0			0
$61$	6.84408	−	3.95143i	0.876295	−	0.505929i	0.00685975	−	0.999976i	$-0.497816\pi$
$61$	6.84408	−	3.95143i	0.876295	−	0.505929i	0.869435	+	0.494048i	$0.164483\pi$
$62$	7.33010	+	2.34795i	0.930924	+	0.298190i
$63$	−9.46432	−	7.18914i	−1.19239	−	0.905747i
$64$	−2.28103	+	7.66791i	−0.285129	+	0.958489i
$65$		0			0
$66$	0.287283	−	0.260848i	0.0353621	−	0.0321081i
$67$	−0.0549000	+	0.0950895i	−0.00670710	+	0.0116170i	−0.869359	−	0.494180i	$-0.835468\pi$
$67$	−0.0549000	+	0.0950895i	−0.00670710	+	0.0116170i	0.862652	+	0.505797i	$0.168802\pi$
$68$	1.03879	−	10.7446i	0.125972	−	1.30297i
$69$			4.12850i			0.497013i
$70$		0			0
$71$		−	6.73221i		−	0.798967i	−0.916740	−	0.399483i	$-0.869190\pi$
$71$		−	6.73221i		−	0.798967i	0.916740	−	0.399483i	$-0.130810\pi$
$72$	5.02231	−	11.6710i	0.591885	−	1.37545i
$73$	−3.07349	+	5.32344i	−0.359725	+	0.623062i	−0.987915	−	0.154998i	$-0.950463\pi$
$73$	−3.07349	+	5.32344i	−0.359725	+	0.623062i	0.628190	+	0.778060i	$0.283796\pi$
$74$	0.987288	+	1.08734i	0.114770	+	0.126401i
$75$		0			0
$76$	−12.1422	−	8.66802i	−1.39280	−	0.994290i
$77$	0.263115	+	0.0333347i	0.0299848	+	0.00379884i
$78$	4.86190	−	15.1785i	0.550502	−	1.71862i
$79$	3.70178	−	2.13723i	0.416483	−	0.240457i	−0.277088	−	0.960844i	$-0.589369\pi$
$79$	3.70178	−	2.13723i	0.416483	−	0.240457i	0.693572	+	0.720388i	$0.256036\pi$
$80$		0			0
$81$	1.14846	−	1.98919i	0.127607	−	0.221021i
$82$	−11.0445	+	2.39575i	−1.21966	+	0.264566i
$83$		−	6.50159i		−	0.713642i	−0.934173	−	0.356821i	$-0.883861\pi$
$83$		−	6.50159i		−	0.713642i	0.934173	−	0.356821i	$-0.116139\pi$
$84$	13.8318	−	4.29682i	1.50917	−	0.468822i
$85$		0			0
$86$	2.11290	+	9.74053i	0.227840	+	1.05035i
$87$	5.63433	+	3.25298i	0.604063	+	0.348756i
$88$	0.0331618	+	0.281584i	0.00353506	+	0.0300170i
$89$	2.76417	−	1.59589i	0.293001	−	0.169164i	−0.346293	−	0.938126i	$-0.612560\pi$
$89$	2.76417	−	1.59589i	0.293001	−	0.169164i	0.639294	+	0.768962i	$0.279226\pi$
$90$		0			0
$91$	10.0438	−	4.21781i	1.05288	−	0.442147i
$92$	−2.45519	−	1.75270i	−0.255971	−	0.182732i
$93$	12.9015	−	7.44866i	1.33782	−	0.772391i
$94$	4.22454	+	4.65267i	0.435728	+	0.479886i
$95$		0			0
$96$	8.01978	+	13.2451i	0.818516	+	1.35182i
$97$	−11.0691			−1.12390			−0.561948	−	0.827173i	$-0.689948\pi$
$97$	−11.0691			−1.12390			−0.561948	+	0.827173i	$0.689948\pi$
$98$	8.37670	+	5.27550i	0.846174	+	0.532906i
$99$		−	0.450309i		−	0.0452578i
$100$		0			0
$101$	−6.20412	−	3.58195i	−0.617333	−	0.356418i	0.158497	−	0.987359i	$-0.449335\pi$
$101$	−6.20412	−	3.58195i	−0.617333	−	0.356418i	−0.775830	+	0.630942i	$0.782669\pi$
$102$	−14.0447	−	15.4680i	−1.39063	−	1.53156i
$103$	−4.23147	+	2.44304i	−0.416939	+	0.240720i	−0.693767	−	0.720200i	$-0.744050\pi$
$103$	−4.23147	+	2.44304i	−0.416939	+	0.240720i	0.276828	+	0.960920i	$0.410717\pi$
$104$	6.96245	+	9.33516i	0.682724	+	0.915388i
$105$		0			0
$106$	−2.64995	+	8.27292i	−0.257386	+	0.803537i
$107$	−3.78436	−	6.55470i	−0.365848	−	0.633667i	0.623064	−	0.782171i	$-0.285888\pi$
$107$	−3.78436	−	6.55470i	−0.365848	−	0.633667i	−0.988912	+	0.148504i	$0.952554\pi$
$108$	−3.38462	−	7.43450i	−0.325685	−	0.715385i
$109$	−9.02662	+	15.6346i	−0.864593	+	1.49752i	0.00285729	+	0.999996i	$0.499090\pi$
$109$	−9.02662	+	15.6346i	−0.864593	+	1.49752i	−0.867451	+	0.497523i	$0.834243\pi$
$110$		0			0
$111$	2.84262			0.269810
$112$	−3.31682	+	10.0498i	−0.313410	+	0.949618i
$113$			18.1432i			1.70677i	0.521283	+	0.853384i	$0.325453\pi$
$113$			18.1432i			1.70677i	−0.521283	+	0.853384i	$0.674547\pi$
$114$	−28.2185	+	6.12112i	−2.64291	+	0.573296i
$115$		0			0
$116$	−4.32651	+	1.96968i	−0.401706	+	0.182880i
$117$	−9.24793	−	16.0179i	−0.854971	−	1.48085i
$118$	11.4788	+	3.67684i	1.05671	+	0.338481i
$119$	1.79483	−	14.1668i	0.164531	−	1.29867i
$120$		0			0
$121$	−5.49498	−	9.51758i	−0.499543	−	0.865234i
$122$	7.51299	+	8.27438i	0.680195	+	0.749127i
$123$	−10.9368	+	18.9430i	−0.986134	+	1.70803i
$124$	−1.04749	+	10.8346i	−0.0940676	+	0.972979i
$125$		0			0
$126$	7.09853	−	15.2357i	0.632388	−	1.35730i
$127$	−4.37573			−0.388283			−0.194141	−	0.980974i	$-0.562192\pi$
$127$	−4.37573			−0.388283			−0.194141	+	0.980974i	$0.562192\pi$
$128$	−11.2815	−	0.853736i	−0.997149	−	0.0754603i
$129$	16.7065	+	9.64553i	1.47093	+	0.849241i
$130$		0			0
$131$	1.49073	+	2.58201i	0.130245	+	0.225592i	0.923771	−	0.382945i	$-0.125090\pi$
$131$	1.49073	+	2.58201i	0.130245	+	0.225592i	−0.793526	+	0.608537i	$0.791757\pi$
$132$	0.446637	+	0.318844i	0.0388747	+	0.0277518i
$133$	−15.7157	−	11.9377i	−1.36272	−	1.03513i
$134$	−0.147879	−	0.0473681i	−0.0127748	−	0.00409198i
$135$		0			0
$136$	15.1612	−	1.78552i	1.30007	−	0.153107i
$137$	1.32048	+	0.762377i	0.112816	+	0.0651342i	0.555346	−	0.831619i	$-0.312586\pi$
$137$	1.32048	+	0.762377i	0.112816	+	0.0651342i	−0.442530	+	0.896754i	$0.645919\pi$
$138$	−5.70588	+	1.23771i	−0.485717	+	0.105361i
$139$	7.16082			0.607373			0.303686	−	0.952772i	$-0.401783\pi$
$139$	7.16082			0.607373			0.303686	+	0.952772i	$0.401783\pi$
$140$		0			0
$141$	12.1634			1.02434
$142$	9.30440	−	2.01830i	0.780808	−	0.169372i
$143$	0.357440	+	0.206368i	0.0298907	+	0.0172574i
$144$	17.6359	+	3.44225i	1.46966	+	0.286854i
$145$		0			0
$146$	−8.27880	−	2.65183i	−0.685158	−	0.219467i
$147$	18.4581	−	5.13939i	1.52240	−	0.423890i
$148$	−1.20680	+	1.69048i	−0.0991983	+	0.138957i
$149$	−10.5236	−	18.2275i	−0.862129	−	1.49325i	−0.869870	−	0.493282i	$-0.835797\pi$
$149$	−10.5236	−	18.2275i	−0.862129	−	1.49325i	0.00774027	−	0.999970i	$-0.497536\pi$
$150$		0			0
$151$	3.31081	+	1.91150i	0.269430	+	0.155555i	0.628628	−	0.777706i	$-0.283617\pi$
$151$	3.31081	+	1.91150i	0.269430	+	0.155555i	−0.359199	+	0.933261i	$0.616950\pi$
$152$	8.33964	−	19.3800i	0.676434	−	1.57192i
$153$	−24.2458			−1.96016
$154$	0.0328102	+	0.373638i	0.00264392	+	0.0301086i
$155$		0			0
$156$	22.4353	+	2.16904i	1.79626	+	0.173663i
$157$	0.642065	−	1.11209i	0.0512423	−	0.0887543i	−0.839266	−	0.543720i	$-0.817015\pi$
$157$	0.642065	−	1.11209i	0.0512423	−	0.0887543i	0.890509	+	0.454966i	$0.150349\pi$
$158$	4.06358	+	4.47540i	0.323281	+	0.356044i
$159$	8.40673	+	14.5609i	0.666697	+	1.15475i
$160$		0			0
$161$	−3.17776	−	2.41384i	−0.250443	−	0.190238i
$162$	3.09351	+	0.990900i	0.243049	+	0.0778525i
$163$	−4.30054	−	7.44875i	−0.336844	−	0.583431i	0.646993	−	0.762496i	$-0.276026\pi$
$163$	−4.30054	−	7.44875i	−0.336844	−	0.583431i	−0.983837	+	0.179064i	$0.942693\pi$
$164$	−6.62220	−	14.5460i	−0.517107	−	1.13585i
$165$		0			0
$166$	8.98566	−	1.94916i	0.697422	−	0.151284i
$167$			8.10448i			0.627144i	0.949565	+	0.313572i	$0.101526\pi$
$167$			8.10448i			0.627144i	−0.949565	+	0.313572i	$0.898474\pi$
$168$	10.0852	+	17.8283i	0.778093	+	1.37549i
$169$	3.95261			0.304047
$170$		0			0
$171$	−16.7543	+	29.0193i	−1.28123	+	2.21916i
$172$	−12.8287	+	5.84036i	−0.978177	+	0.445323i
$173$	4.01688	+	6.95744i	0.305398	+	0.528964i	0.977350	−	0.211630i	$-0.0678773\pi$
$173$	4.01688	+	6.95744i	0.305398	+	0.528964i	−0.671952	+	0.740595i	$0.734544\pi$
$174$	−2.80670	+	8.76228i	−0.212775	+	0.664267i
$175$		0			0
$176$	−0.379228	+	0.130250i	−0.0285854	+	0.00981797i
$177$	20.2034	−	11.6645i	1.51858	−	0.876755i
$178$	3.03433	+	3.34183i	0.227432	+	0.250481i
$179$	−7.66309	−	4.42429i	−0.572766	−	0.330687i	0.185487	−	0.982647i	$-0.440614\pi$
$179$	−7.66309	−	4.42429i	−0.572766	−	0.330687i	−0.758253	+	0.651960i	$0.773947\pi$
$180$		0			0
$181$			21.3610i			1.58775i	0.608082	+	0.793874i	$0.291939\pi$
$181$			21.3610i			1.58775i	−0.608082	+	0.793874i	$0.708061\pi$
$182$	8.84042	+	12.6168i	0.655296	+	0.935219i
$183$	21.6316			1.59905
$184$	1.68630	−	3.91870i	0.124316	−	0.288890i
$185$		0			0
$186$	14.1624	+	15.5977i	1.03844	+	1.14368i
$187$	0.468561	−	0.270524i	0.0342645	−	0.0197826i
$188$	−5.16381	+	7.23347i	−0.376610	+	0.527555i
$189$	−4.18399	−	9.96329i	−0.304341	−	0.724723i
$190$		0			0
$191$	21.6710	−	12.5117i	1.56806	−	0.905317i	0.571660	−	0.820491i	$-0.306300\pi$
$191$	21.6710	−	12.5117i	1.56806	−	0.905317i	0.996396	−	0.0848269i	$-0.0270337\pi$
$192$	−15.9014	+	15.0548i	−1.14758	+	1.08648i
$193$	7.06813	+	4.08078i	0.508775	+	0.293741i	0.732330	−	0.680950i	$-0.238433\pi$
$193$	7.06813	+	4.08078i	0.508775	+	0.293741i	−0.223555	+	0.974691i	$0.571766\pi$
$194$	−3.31848	−	15.2983i	−0.238253	−	1.09835i
$195$		0			0
$196$	−4.77982	+	13.1588i	−0.341415	+	0.939913i
$197$		−	12.4517i		−	0.887149i	−0.896238	−	0.443574i	$-0.853710\pi$
$197$		−	12.4517i		−	0.887149i	0.896238	−	0.443574i	$-0.146290\pi$
$198$	0.622359	−	0.135001i	0.0442292	−	0.00959412i
$199$	−11.5867	+	20.0687i	−0.821358	+	1.42263i	0.0833132	+	0.996523i	$0.473450\pi$
$199$	−11.5867	+	20.0687i	−0.821358	+	1.42263i	−0.904671	+	0.426110i	$0.859884\pi$
$200$		0			0
$201$	−0.260277	+	0.150271i	−0.0183586	+	0.0105993i
$202$	3.09054	−	9.64840i	0.217449	−	0.678859i
$203$	−5.79814	+	2.43487i	−0.406949	+	0.170895i
$204$	17.1674	−	24.0481i	1.20196	−	1.68370i
$205$		0			0
$206$	−4.64504	−	5.11578i	−0.323635	−	0.356433i
$207$	−3.38778	+	5.86780i	−0.235467	+	0.407840i
$208$	−10.8145	+	12.4213i	−0.749853	+	0.861259i
$209$		−	0.747747i		−	0.0517228i
$210$		0			0
$211$			10.9759i			0.755613i	0.925885	+	0.377807i	$0.123322\pi$
$211$			10.9759i			0.755613i	−0.925885	+	0.377807i	$0.876678\pi$
$212$	−12.2282	−	1.18222i	−0.839837	−	0.0811954i
$213$	9.21365	−	15.9585i	0.631309	−	1.09346i
$214$	7.92453	−	7.19533i	0.541710	−	0.491863i
$215$		0			0
$216$	9.26031	−	6.90663i	0.630084	−	0.469936i
$217$	−1.80987	+	14.2855i	−0.122862	+	0.969764i
$218$	−24.3142	−	7.78824i	−1.64677	−	0.527486i
$219$	−14.5712	+	8.41270i	−0.984633	+	0.568478i
$220$		0			0
$221$	11.1114	−	19.2455i	0.747434	−	1.29459i
$222$	0.852209	+	3.92871i	0.0571965	+	0.263678i
$223$			14.9798i			1.00312i	0.865123	+	0.501559i	$0.167240\pi$
$223$			14.9798i			1.00312i	−0.865123	+	0.501559i	$0.832760\pi$
$224$	−14.8839	−	1.57118i	−0.994474	−	0.104979i
$225$		0			0
$226$	−25.0752	+	5.43927i	−1.66798	+	0.361815i
$227$	1.30546	+	0.753708i	0.0866465	+	0.0500254i	0.542697	−	0.839928i	$-0.317403\pi$
$227$	1.30546	+	0.753708i	0.0866465	+	0.0500254i	−0.456051	+	0.889954i	$0.650736\pi$
$228$	−16.9197	−	37.1649i	−1.12053	−	2.46131i
$229$	−7.38329	+	4.26274i	−0.487901	+	0.281690i	−0.723703	−	0.690111i	$-0.757562\pi$
$229$	−7.38329	+	4.26274i	−0.487901	+	0.281690i	0.235802	+	0.971801i	$0.424228\pi$
$230$		0			0
$231$	0.578085	+	0.439116i	0.0380352	+	0.0288917i
$232$	−4.01931	−	5.38904i	−0.263881	−	0.353808i
$233$	18.3799	−	10.6117i	1.20411	−	0.695193i	0.242644	−	0.970115i	$-0.421985\pi$
$233$	18.3799	−	10.6117i	1.20411	−	0.695193i	0.961467	+	0.274922i	$0.0886520\pi$
$234$	19.3654	−	17.5834i	1.26595	−	1.14946i
$235$		0			0
$236$	−1.64035	+	16.9668i	−0.106778	+	1.10445i
$237$	11.7000			0.759994
$238$	20.1176	−	1.76659i	1.30403	−	0.114511i
$239$			10.1532i			0.656754i	0.944547	+	0.328377i	$0.106502\pi$
$239$			10.1532i			0.656754i	−0.944547	+	0.328377i	$0.893498\pi$
$240$		0			0
$241$	16.4985	+	9.52539i	1.06276	+	0.613584i	0.926194	−	0.377047i	$-0.123060\pi$
$241$	16.4985	+	9.52539i	1.06276	+	0.613584i	0.136565	+	0.990631i	$0.456394\pi$
$242$	11.5066	−	10.4478i	0.739672	−	0.671609i
$243$	16.0562	−	9.27006i	1.03001	−	0.594674i
$244$	−9.18342	+	12.8641i	−0.587908	+	0.823542i
$245$		0			0
$246$	−29.4594	−	9.43632i	−1.87826	−	0.601638i
$247$	−15.3564	−	26.5980i	−0.977102	−	1.69239i
$248$	−15.2883	+	1.80048i	−0.970807	+	0.114331i
$249$	8.89801	−	15.4118i	0.563889	−	0.976684i
$250$		0			0
$251$	9.46184			0.597226			0.298613	−	0.954374i	$-0.403476\pi$
$251$	9.46184			0.597226			0.298613	+	0.954374i	$0.403476\pi$
$252$	23.1849	+	5.24308i	1.46051	+	0.330283i
$253$		−	0.151197i		−	0.00950567i
$254$	−1.31183	−	6.04757i	−0.0823115	−	0.379458i
$255$		0			0
$256$	−2.20222	−	15.8477i	−0.137639	−	0.990483i
$257$	1.37271	+	2.37760i	0.0856270	+	0.148310i	0.905658	−	0.424008i	$-0.139377\pi$
$257$	1.37271	+	2.37760i	0.0856270	+	0.148310i	−0.820031	+	0.572319i	$0.806044\pi$
$258$	−8.32224	+	25.9813i	−0.518120	+	1.61753i
$259$	−1.66202	+	2.18801i	−0.103273	+	0.135956i
$260$		0			0
$261$	5.33868	+	9.24686i	0.330456	+	0.572367i
$262$	−3.12161	+	2.83437i	−0.192854	+	0.175108i
$263$	12.8384	−	22.2367i	0.791648	−	1.37117i	−0.133298	−	0.991076i	$-0.542557\pi$
$263$	12.8384	−	22.2367i	0.791648	−	1.37117i	0.924946	−	0.380098i	$-0.124110\pi$
$264$	−0.306765	+	0.712872i	−0.0188801	+	0.0438743i
$265$		0			0
$266$	11.7873	−	25.2991i	0.722723	−	1.55119i
$267$	8.73650			0.534665
$268$	0.0211324	−	0.218581i	0.00129087	−	0.0133519i
$269$	−7.10140	−	4.10000i	−0.432980	−	0.249981i	0.267635	−	0.963520i	$-0.413758\pi$
$269$	−7.10140	−	4.10000i	−0.432980	−	0.249981i	−0.700615	+	0.713539i	$0.747091\pi$
$270$		0			0
$271$	−3.20364	−	5.54886i	−0.194607	−	0.337069i	0.752165	−	0.658975i	$-0.229010\pi$
$271$	−3.20364	−	5.54886i	−0.194607	−	0.337069i	−0.946772	+	0.321906i	$0.895676\pi$
$272$	7.01301	+	20.4186i	0.425226	+	1.23806i
$273$	29.5810	+	3.74769i	1.79033	+	0.226821i
$274$	−0.657785	+	2.05355i	−0.0397382	+	0.124059i
$275$		0			0
$276$	−3.42121	−	7.51488i	−0.205933	−	0.452342i
$277$	−13.8297	−	7.98456i	−0.830944	−	0.479746i	0.0232316	−	0.999730i	$-0.492604\pi$
$277$	−13.8297	−	7.98456i	−0.830944	−	0.479746i	−0.854176	+	0.519984i	$0.825938\pi$
$278$	2.14679	+	9.89676i	0.128756	+	0.593568i
$279$	24.4490			1.46372
$280$		0			0
$281$	−9.68409			−0.577704			−0.288852	−	0.957374i	$-0.593274\pi$
$281$	−9.68409			−0.577704			−0.288852	+	0.957374i	$0.593274\pi$
$282$	3.64655	+	16.8107i	0.217149	+	1.00106i
$283$	22.6264	+	13.0633i	1.34500	+	0.776535i	0.987536	−	0.157393i	$-0.0503088\pi$
$283$	22.6264	+	13.0633i	1.34500	+	0.776535i	0.357462	+	0.933928i	$0.383642\pi$
$284$	5.57886	+	12.2543i	0.331044	+	0.727157i
$285$		0			0
$286$	−0.178056	+	0.555877i	−0.0105287	+	0.0328697i
$287$	−8.18622	−	19.4937i	−0.483217	−	1.15068i
$288$	0.529749	+	25.4060i	0.0312158	+	1.49706i
$289$	−6.06569	−	10.5061i	−0.356805	−	0.618005i
$290$		0			0
$291$	−26.2389	−	15.1491i	−1.53815	−	0.888053i
$292$	1.18306	−	12.2369i	0.0692336	−	0.716111i
$293$	−16.2389			−0.948684			−0.474342	−	0.880341i	$-0.657314\pi$
$293$	−16.2389			−0.948684			−0.474342	+	0.880341i	$0.657314\pi$
$294$	12.6367	+	23.9697i	0.736987	+	1.39794i
$295$		0			0
$296$	−2.69817	−	1.16108i	−0.156828	−	0.0674865i
$297$	0.204714	−	0.354574i	0.0118787	−	0.0205745i
$298$	22.0367	−	20.0089i	1.27655	−	1.15909i
$299$	−3.10511	−	5.37821i	−0.179573	−	0.311030i
$300$		0			0
$301$	−17.1923	+	7.21973i	−0.990945	+	0.416138i
$302$	−1.64925	+	5.14883i	−0.0949039	+	0.296282i
$303$	−9.80446	−	16.9818i	−0.563251	−	0.975580i
$304$	29.2847	+	5.71592i	1.67959	+	0.327831i
$305$		0			0
$306$	−7.26882	−	33.5094i	−0.415531	−	1.91561i
$307$			23.5437i			1.34371i	0.740684	+	0.671854i	$0.234502\pi$
$307$			23.5437i			1.34371i	−0.740684	+	0.671854i	$0.765498\pi$
$308$	−0.506557	+	0.157361i	−0.0288638	+	0.00896650i
$309$	−13.3741			−0.760825
$310$		0			0
$311$	2.69773	−	4.67261i	0.152974	−	0.264959i	−0.779345	−	0.626595i	$-0.784448\pi$
$311$	2.69773	−	4.67261i	0.152974	−	0.264959i	0.932320	+	0.361635i	$0.117781\pi$
$312$	3.72826	+	31.6575i	0.211071	+	1.79225i
$313$	−16.2807	−	28.1990i	−0.920240	−	1.59390i	−0.799043	−	0.601274i	$-0.794660\pi$
$313$	−16.2807	−	28.1990i	−0.920240	−	1.59390i	−0.121197	−	0.992629i	$-0.538673\pi$
$314$	1.72948	+	0.553979i	0.0975999	+	0.0312628i
$315$		0			0
$316$	−4.96707	+	6.95787i	−0.279420	+	0.391411i
$317$	11.8747	−	6.85587i	0.666951	−	0.385064i	−0.127970	−	0.991778i	$-0.540846\pi$
$317$	11.8747	−	6.85587i	0.666951	−	0.385064i	0.794920	+	0.606714i	$0.207513\pi$
$318$	−17.6039	+	15.9840i	−0.987176	+	0.896338i
$319$	−0.206344	−	0.119133i	−0.0115531	−	0.00667017i
$320$		0			0
$321$		−	20.7170i		−	1.15631i
$322$	2.38342	−	5.11556i	0.132823	−	0.285079i
$323$	−40.2606			−2.24016
$324$	−0.442071	+	4.57252i	−0.0245595	+	0.254029i
$325$		0			0
$326$	9.00542	−	8.17677i	0.498764	−	0.452869i
$327$	−42.7947	+	24.7075i	−2.36655	+	1.36633i
$328$	18.1183	−	13.5132i	1.00042	−	0.746142i
$329$	−7.11167	+	9.36233i	−0.392079	+	0.516162i
$330$		0			0
$331$	4.92495	−	2.84342i	0.270700	−	0.156289i	−0.358506	−	0.933527i	$-0.616714\pi$
$331$	4.92495	−	2.84342i	0.270700	−	0.156289i	0.629206	+	0.777239i	$0.283380\pi$
$332$	5.38774	+	11.8345i	0.295691	+	0.649501i
$333$	4.04019	+	2.33261i	0.221401	+	0.127826i
$334$	−11.2010	+	2.42970i	−0.612890	+	0.132947i
$335$		0			0
$336$	−21.6165	+	19.2834i	−1.17928	+	1.05200i
$337$		−	14.7219i		−	0.801955i	−0.916088	−	0.400978i	$-0.868670\pi$
$337$		−	14.7219i		−	0.801955i	0.916088	−	0.400978i	$-0.131330\pi$
$338$	1.18498	+	5.46279i	0.0644544	+	0.297137i
$339$	−24.8306	+	43.0079i	−1.34861	+	2.33587i
$340$		0			0
$341$	−0.472487	+	0.272790i	−0.0255866	+	0.0147724i
$342$	−45.1296	−	14.4557i	−2.44033	−	0.781677i
$343$	−6.83621	+	17.2124i	−0.369121	+	0.929381i
$344$	−11.9178	−	15.9792i	−0.642564	−	0.861542i
$345$		0			0
$346$	−8.41143	+	7.63743i	−0.452201	+	0.410591i
$347$	7.73454	−	13.3966i	0.415212	−	0.719168i	−0.580239	−	0.814446i	$-0.697041\pi$
$347$	7.73454	−	13.3966i	0.415212	−	0.719168i	0.995451	+	0.0952784i	$0.0303741\pi$
$348$	−12.9515	−	1.25215i	−0.694275	−	0.0671225i
$349$		−	11.5290i		−	0.617132i	−0.951203	−	0.308566i	$-0.900151\pi$
$349$		−	11.5290i		−	0.617132i	0.951203	−	0.308566i	$-0.0998491\pi$
$350$		0			0
$351$		−	16.8167i		−	0.897608i
$352$	−0.293706	−	0.485072i	−0.0156546	−	0.0258544i
$353$	10.2181	−	17.6983i	0.543855	−	0.941985i	−0.454823	−	0.890582i	$-0.650297\pi$
$353$	10.2181	−	17.6983i	0.543855	−	0.941985i	0.998678	−	0.0514030i	$-0.0163693\pi$
$354$	22.1781	+	24.4256i	1.17875	+	1.29821i
$355$		0			0
$356$	−3.70897	+	5.19553i	−0.196575	+	0.275362i
$357$	23.6431	−	31.1256i	1.25133	−	1.64734i
$358$	3.81731	−	11.9173i	0.201751	−	0.629850i
$359$	18.3761	−	10.6095i	0.969856	−	0.559946i	0.0706634	−	0.997500i	$-0.477488\pi$
$359$	18.3761	−	10.6095i	0.969856	−	0.559946i	0.899192	+	0.437554i	$0.144155\pi$
$360$		0			0
$361$	−18.3208	+	31.7326i	−0.964255	+	1.67014i
$362$	−29.5224	+	6.40395i	−1.55166	+	0.336584i
$363$		−	30.0815i		−	1.57887i
$364$	−14.7870	+	16.0006i	−0.775048	+	0.838658i
$365$		0			0
$366$	6.48508	+	29.8964i	0.338981	+	1.56271i
$367$	−6.62637	−	3.82574i	−0.345894	−	0.199702i	0.316982	−	0.948432i	$-0.397331\pi$
$367$	−6.62637	−	3.82574i	−0.345894	−	0.199702i	−0.662875	+	0.748730i	$0.730664\pi$
$368$	5.92147	+	1.15578i	0.308678	+	0.0602491i
$369$	−31.0886	+	17.9490i	−1.61841	+	0.934389i
$370$		0			0
$371$	−16.1229	−	2.04265i	−0.837062	−	0.106049i
$372$	−17.3112	+	24.2496i	−0.897546	+	1.25728i
$373$	−22.2000	+	12.8172i	−1.14947	+	0.663647i	−0.948758	−	0.316003i	$-0.897659\pi$
$373$	−22.2000	+	12.8172i	−1.14947	+	0.663647i	−0.200713	+	0.979650i	$0.564326\pi$
$374$	0.514356	+	0.566482i	0.0265967	+	0.0292921i
$375$		0			0
$376$	−11.5453	−	4.96819i	−0.595402	−	0.256215i
$377$	−9.78647			−0.504029
$378$	12.5156	−	8.76954i	0.643735	−	0.451057i
$379$		−	29.1039i		−	1.49497i	−0.664279	−	0.747485i	$-0.731261\pi$
$379$		−	29.1039i		−	1.49497i	0.664279	−	0.747485i	$-0.268739\pi$
$380$		0			0
$381$	−10.3725	−	5.98858i	−0.531401	−	0.306804i
$382$	23.7890	+	26.1998i	1.21715	+	1.34050i
$383$	−7.48525	+	4.32161i	−0.382478	+	0.220824i	−0.678896	−	0.734234i	$-0.737541\pi$
$383$	−7.48525	+	4.32161i	−0.382478	+	0.220824i	0.296418	+	0.955058i	$0.404208\pi$
$384$	−25.5739	−	17.4635i	−1.30506	−	0.891178i
$385$		0			0
$386$	−3.52093	+	10.9921i	−0.179211	+	0.559481i
$387$	15.8299	+	27.4182i	0.804679	+	1.39375i
$388$	20.1484	−	9.17274i	1.02288	−	0.465676i
$389$	−7.08846	+	12.2776i	−0.359399	+	0.622498i	−0.987861	−	0.155343i	$-0.950352\pi$
$389$	−7.08846	+	12.2776i	−0.359399	+	0.622498i	0.628461	+	0.777841i	$0.283685\pi$
$390$		0			0
$391$	−8.14084			−0.411700
$392$	−19.6193	−	2.66109i	−0.990926	−	0.134405i
$393$			8.16078i			0.411657i
$394$	17.2092	−	3.73299i	0.866986	−	0.188065i
$395$		0			0
$396$	0.373163	+	0.819672i	0.0187521	+	0.0411901i
$397$	0.0875029	+	0.151559i	0.00439164	+	0.00760655i	0.868213	−	0.496192i	$-0.165269\pi$
$397$	0.0875029	+	0.151559i	0.00439164	+	0.00760655i	−0.863821	+	0.503798i	$0.831935\pi$
$398$	−31.2101	−	9.99708i	−1.56442	−	0.501108i
$399$	−20.9157	−	49.8063i	−1.04710	−	2.49344i
$400$		0			0
$401$	−12.0285	−	20.8339i	−0.600674	−	1.04040i	−0.992719	−	0.120452i	$-0.961566\pi$
$401$	−12.0285	−	20.8339i	−0.600674	−	1.04040i	0.392046	−	0.919946i	$-0.371768\pi$
$402$	−0.285716	−	0.314671i	−0.0142502	−	0.0156944i
$403$	−11.2045	+	19.4068i	−0.558136	+	0.966721i
$404$	14.2613	+	1.37878i	0.709527	+	0.0685970i
$405$		0			0
$406$	−5.10343	−	7.28347i	−0.253279	−	0.361473i
$407$	−0.104105			−0.00516027
$408$	38.3829	+	16.5170i	1.90024	+	0.817714i
$409$	10.3372	+	5.96818i	0.511141	+	0.295108i	0.733303	−	0.679902i	$-0.237978\pi$
$409$	10.3372	+	5.96818i	0.511141	+	0.295108i	−0.222161	+	0.975010i	$0.571311\pi$
$410$		0			0
$411$	2.08676	+	3.61438i	0.102932	+	0.178284i
$412$	5.67780	−	7.95347i	0.279725	−	0.391839i
$413$	−2.83421	+	22.3708i	−0.139463	+	1.10080i
$414$	−9.12536	−	2.92300i	−0.448487	−	0.143658i
$415$		0			0
$416$	−20.4092	−	11.2226i	−1.00064	−	0.550234i
$417$	16.9745	+	9.80023i	0.831245	+	0.479919i
$418$	1.03344	−	0.224172i	0.0505472	−	0.0109646i
$419$	30.1003			1.47050			0.735249	−	0.677798i	$-0.237065\pi$
$419$	30.1003			1.47050			0.735249	+	0.677798i	$0.237065\pi$
$420$		0			0
$421$	6.78256			0.330562			0.165281	−	0.986247i	$-0.447147\pi$
$421$	6.78256			0.330562			0.165281	+	0.986247i	$0.447147\pi$
$422$	−15.1695	+	3.29055i	−0.738440	+	0.160181i
$423$	17.2877	+	9.98107i	0.840557	+	0.485296i
$424$	−2.03206	−	17.2547i	−0.0986857	−	0.837962i
$425$		0			0
$426$	24.8180	+	7.94961i	1.20244	+	0.385160i
$427$	−12.6475	+	16.6501i	−0.612056	+	0.805756i
$428$	12.3202	+	8.79513i	0.595520	+	0.425128i
$429$	0.564868	+	0.978379i	0.0272721	+	0.0472366i
$430$		0			0
$431$	−13.8010	−	7.96802i	−0.664772	−	0.383806i	0.129321	−	0.991603i	$-0.458720\pi$
$431$	−13.8010	−	7.96802i	−0.664772	−	0.383806i	−0.794093	+	0.607797i	$0.792054\pi$
$432$	12.3217	+	10.7278i	0.592826	+	0.516143i
$433$	15.1291			0.727057			0.363529	−	0.931583i	$-0.381572\pi$
$433$	15.1291			0.727057			0.363529	+	0.931583i	$0.381572\pi$
$434$	−20.2862	+	1.78139i	−0.973769	+	0.0855094i
$435$		0			0
$436$	3.47457	−	35.9389i	0.166402	−	1.72116i
$437$	−5.62547	+	9.74360i	−0.269103	+	0.466099i
$438$	−15.9954	−	17.6164i	−0.764288	−	0.841743i
$439$	−2.18337	−	3.78171i	−0.104207	−	0.180491i	0.809207	−	0.587523i	$-0.199897\pi$
$439$	−2.18337	−	3.78171i	−0.104207	−	0.180491i	−0.913414	+	0.407032i	$0.866564\pi$
$440$		0			0
$441$	30.4517	+	7.84186i	1.45008	+	0.373422i
$442$	29.9298	+	9.58701i	1.42362	+	0.456007i
$443$	−7.04909	−	12.2094i	−0.334913	−	0.580086i	0.648555	−	0.761167i	$-0.275373\pi$
$443$	−7.04909	−	12.2094i	−0.334913	−	0.580086i	−0.983468	+	0.181082i	$0.942040\pi$
$444$	−5.17426	+	2.35563i	−0.245560	+	0.111793i
$445$		0			0
$446$	−20.7031	+	4.49088i	−0.980320	+	0.212650i
$447$		−	57.6102i		−	2.72487i
$448$	−2.29067	−	21.0417i	−0.108224	−	0.994127i
$449$	−17.0120			−0.802848			−0.401424	−	0.915892i	$-0.631485\pi$
$449$	−17.0120			−0.802848			−0.401424	+	0.915892i	$0.631485\pi$
$450$		0			0
$451$	0.400534	−	0.693745i	0.0188604	−	0.0326672i
$452$	−15.0349	−	33.0250i	−0.707183	−	1.55337i
$453$	5.23211	+	9.06228i	0.245826	+	0.425783i
$454$	−0.650306	+	2.03020i	−0.0305204	+	0.0952820i
$455$		0			0
$456$	46.2922	−	34.5261i	2.16783	−	1.61683i
$457$	10.1019	−	5.83234i	0.472548	−	0.272825i	−0.244758	−	0.969584i	$-0.578709\pi$
$457$	10.1019	−	5.83234i	0.472548	−	0.272825i	0.717306	+	0.696759i	$0.245375\pi$
$458$	−8.10490	−	8.92627i	−0.378717	−	0.417097i
$459$	−19.0912	−	11.0223i	−0.891101	−	0.514477i
$460$		0			0
$461$		−	26.4488i		−	1.23184i	−0.787808	−	0.615921i	$-0.788784\pi$
$461$		−	26.4488i		−	1.23184i	0.787808	−	0.615921i	$-0.211216\pi$
$462$	−0.433582	+	0.930600i	−0.0201720	+	0.0432954i
$463$	3.13685			0.145782			0.0728909	−	0.997340i	$-0.476778\pi$
$463$	3.13685			0.145782			0.0728909	+	0.997340i	$0.476778\pi$
$464$	6.24306	−	7.17059i	0.289827	−	0.332886i
$465$		0			0
$466$	20.1763	+	22.2211i	0.934651	+	1.02937i
$467$	−7.05043	+	4.07057i	−0.326255	+	0.188363i	−0.654177	−	0.756341i	$-0.726985\pi$
$467$	−7.05043	+	4.07057i	−0.326255	+	0.188363i	0.327922	+	0.944705i	$0.393652\pi$
$468$	30.1072	+	21.4929i	1.39171	+	0.993508i
$469$	0.0365127	−	0.288200i	0.00168600	−	0.0133078i
$470$		0			0
$471$	3.04399	−	1.75745i	0.140260	−	0.0809789i
$472$	−23.9411	+	2.81952i	−1.10198	+	0.129779i
$473$	−0.611839	−	0.353246i	−0.0281324	−	0.0162422i
$474$	3.50761	+	16.1702i	0.161110	+	0.742721i
$475$		0			0
$476$	8.47275	+	27.2744i	0.388348	+	1.25012i
$477$			27.5937i			1.26343i
$478$	−14.0324	+	3.04389i	−0.641827	+	0.139224i
$479$	12.3904	−	21.4608i	0.566131	−	0.980567i	−0.430813	−	0.902441i	$-0.641773\pi$
$479$	12.3904	−	21.4608i	0.566131	−	0.980567i	0.996944	−	0.0781258i	$-0.0248936\pi$
$480$		0			0
$481$	−3.70309	+	2.13798i	−0.168846	+	0.0974835i
$482$	−8.21858	+	25.6577i	−0.374346	+	1.16868i
$483$	−4.22923	−	10.0710i	−0.192437	−	0.458247i
$484$	17.8892	+	12.7707i	0.813147	+	0.580487i
$485$		0			0
$486$	17.6255	+	19.4117i	0.799508	+	0.880532i
$487$	6.34726	−	10.9938i	0.287622	−	0.498175i	−0.685620	−	0.727960i	$-0.740469\pi$
$487$	6.34726	−	10.9938i	0.287622	−	0.498175i	0.973242	+	0.229784i	$0.0738021\pi$
$488$	−20.5323	−	8.83551i	−0.929454	−	0.399965i
$489$		−	23.5427i		−	1.06464i
$490$		0			0
$491$			9.51192i			0.429267i	0.976695	+	0.214633i	$0.0688557\pi$
$491$			9.51192i			0.429267i	−0.976695	+	0.214633i	$0.931144\pi$
$492$	4.20983	−	43.5440i	0.189794	−	1.96311i
$493$	−6.41443	+	11.1101i	−0.288892	+	0.500375i
$494$	32.1566	−	29.1976i	1.44679	−	1.31366i
$495$		0			0
$496$	−7.07177	−	20.5897i	−0.317532	−	0.924506i
$497$	6.89647	+	16.4225i	0.309349	+	0.736649i
$498$	23.9678	+	7.67728i	1.07402	+	0.344027i
$499$	−7.35497	+	4.24639i	−0.329254	+	0.190095i	−0.655510	−	0.755187i	$-0.727546\pi$
$499$	−7.35497	+	4.24639i	−0.329254	+	0.190095i	0.326256	+	0.945281i	$0.394213\pi$
$500$		0			0
$501$	−11.0917	+	19.2114i	−0.495542	+	0.858303i
$502$	2.83663	+	13.0769i	0.126605	+	0.583653i
$503$		−	10.4796i		−	0.467261i	−0.972325	−	0.233630i	$-0.924939\pi$
$503$		−	10.4796i		−	0.467261i	0.972325	−	0.233630i	$-0.0750606\pi$
$504$	−0.295559	+	33.6150i	−0.0131652	+	1.49733i
$505$		0			0
$506$	0.208965	−	0.0453284i	0.00928963	−	0.00201509i
$507$	9.36955	+	5.40951i	0.416116	+	0.240245i
$508$	7.96489	−	3.62608i	0.353385	−	0.160881i
$509$	19.7483	−	11.4017i	0.875329	−	0.505371i	0.00621337	−	0.999981i	$-0.498022\pi$
$509$	19.7483	−	11.4017i	0.875329	−	0.505371i	0.869115	+	0.494609i	$0.164689\pi$
$510$		0			0
$511$	2.04411	−	16.1344i	0.0904259	−	0.713744i
$512$	21.2425	−	7.79472i	0.938793	−	0.344481i
$513$	−26.3847	+	15.2332i	−1.16492	+	0.672564i
$514$	−2.87447	+	2.60997i	−0.126788	+	0.115121i
$515$		0			0
$516$	−38.4031	−	3.71281i	−1.69060	−	0.163447i
$517$	−0.445456			−0.0195912
$518$	−3.52225	−	1.64107i	−0.154759	−	0.0721046i
$519$			21.9899i			0.965248i
$520$		0			0
$521$	−7.88048	−	4.54980i	−0.345250	−	0.199330i	0.317341	−	0.948311i	$-0.397210\pi$
$521$	−7.88048	−	4.54980i	−0.345250	−	0.199330i	−0.662591	+	0.748981i	$0.730543\pi$
$522$	−11.1793	+	10.1506i	−0.489305	+	0.444281i
$523$	−4.12311	+	2.38048i	−0.180291	+	0.104091i	−0.587429	−	0.809275i	$-0.699860\pi$
$523$	−4.12311	+	2.38048i	−0.180291	+	0.104091i	0.407138	+	0.913366i	$0.366527\pi$
$524$	−4.85315	−	3.46456i	−0.212011	−	0.151350i
$525$		0			0
$526$	34.5816	+	11.0771i	1.50783	+	0.482982i
$527$	14.6877	+	25.4399i	0.639808	+	1.10818i
$528$	−1.07721	−	0.210254i	−0.0468794	−	0.00915013i
$529$	10.3625	−	17.9484i	0.450544	−	0.780365i
$530$		0			0
$531$	38.2866			1.66150
$532$	38.4989	+	8.70624i	1.66914	+	0.377463i
$533$		−	32.9028i		−	1.42518i
$534$	2.61918	+	12.0745i	0.113343	+	0.522513i
$535$		0			0
$536$	0.308430	−	0.0363234i	0.0133221	−	0.00156893i
$537$	−12.1101	−	20.9753i	−0.522588	−	0.905150i
$538$	3.53751	−	11.0438i	0.152513	−	0.476133i
$539$	−0.675988	+	0.188219i	−0.0291168	+	0.00810715i
$540$		0			0
$541$	11.2312	+	19.4530i	0.482867	+	0.836350i	0.999806	−	0.0196717i	$-0.00626211\pi$
$541$	11.2312	+	19.4530i	0.482867	+	0.836350i	−0.516939	+	0.856022i	$0.672929\pi$
$542$	6.70848	−	6.09118i	0.288154	−	0.261639i
$543$	−29.2344	+	50.6355i	−1.25457	+	2.17298i
$544$	−26.1175	+	15.8139i	−1.11978	+	0.678016i
$545$		0			0
$546$	3.68872	+	42.0067i	0.157863	+	1.79772i
$547$	24.4644			1.04602			0.523012	−	0.852326i	$-0.324808\pi$
$547$	24.4644			1.04602			0.523012	+	0.852326i	$0.324808\pi$
$548$	−3.03535	−	0.293458i	−0.129664	−	0.0125359i
$549$	30.7448	+	17.7505i	1.31215	+	0.757573i
$550$		0			0
$551$	8.86498	+	15.3546i	0.377661	+	0.654128i
$552$	9.36043	−	6.98130i	0.398406	−	0.297144i
$553$	−6.84071	+	9.00562i	−0.290897	+	0.382958i
$554$	6.88915	−	21.5073i	0.292692	−	0.913759i
$555$		0			0
$556$	−13.0344	+	5.93404i	−0.552783	+	0.251659i
$557$	7.30280	+	4.21627i	0.309430	+	0.178649i	0.646671	−	0.762769i	$-0.276161\pi$
$557$	7.30280	+	4.21627i	0.309430	+	0.178649i	−0.337242	+	0.941418i	$0.609494\pi$
$558$	7.32973	+	33.7902i	0.310292	+	1.43046i
$559$	−29.0182			−1.22734
$560$		0			0
$561$	1.48095			0.0625255
$562$	−2.90326	−	13.3841i	−0.122467	−	0.564574i
$563$	23.5269	+	13.5833i	0.991541	+	0.572467i	0.905735	−	0.423845i	$-0.139320\pi$
$563$	23.5269	+	13.5833i	0.991541	+	0.572467i	0.0858067	+	0.996312i	$0.472653\pi$
$564$	−22.1403	+	10.0796i	−0.932276	+	0.424427i
$565$		0			0
$566$	−11.2712	+	35.1876i	−0.473762	+	1.47905i
$567$	−0.763813	+	6.02888i	−0.0320771	+	0.253189i
$568$	−15.2638	+	11.3842i	−0.640453	+	0.477669i
$569$	7.11643	+	12.3260i	0.298336	+	0.516733i	0.975755	−	0.218864i	$-0.0702350\pi$
$569$	7.11643	+	12.3260i	0.298336	+	0.516733i	−0.677419	+	0.735597i	$0.736902\pi$
$570$		0			0
$571$	14.5870	+	8.42181i	0.610447	+	0.352442i	0.773140	−	0.634235i	$-0.218685\pi$
$571$	14.5870	+	8.42181i	0.610447	+	0.352442i	−0.162693	+	0.986677i	$0.552018\pi$
$572$	−0.821642	−	0.0794363i	−0.0343546	−	0.00332140i
$573$	68.4938			2.86137
$574$	24.4875	−	17.1581i	1.02209	−	0.716166i
$575$		0			0
$576$	−34.9541	+	8.34880i	−1.45642	+	0.347867i
$577$	−1.07668	+	1.86487i	−0.0448230	+	0.0776356i	−0.887566	−	0.460680i	$-0.847606\pi$
$577$	−1.07668	+	1.86487i	−0.0448230	+	0.0776356i	0.842744	+	0.538315i	$0.180939\pi$
$578$	12.7017	−	11.5329i	0.528321	−	0.479706i
$579$	11.1699	+	19.3468i	0.464203	+	0.804024i
$580$		0			0
$581$	6.66021	+	15.8599i	0.276312	+	0.657979i
$582$	13.0707	−	40.8057i	0.541799	−	1.69145i
$583$	−0.307877	−	0.533259i	−0.0127510	−	0.0220853i
$584$	17.2670	−	2.03351i	0.714512	−	0.0841471i
$585$		0			0
$586$	−4.86836	−	22.4433i	−0.201110	−	0.927123i
$587$			11.3061i			0.466652i	0.972399	+	0.233326i	$0.0749609\pi$
$587$			11.3061i			0.466652i	−0.972399	+	0.233326i	$0.925039\pi$
$588$	−29.3394	+	24.6509i	−1.20994	+	1.01658i
$589$	40.5980			1.67281
$590$		0			0
$591$	17.0413	−	29.5164i	0.700986	−	1.21414i
$592$	0.795795	−	4.07715i	0.0327070	−	0.167570i
$593$	−8.51993	−	14.7570i	−0.349872	−	0.605996i	0.636355	−	0.771397i	$-0.280442\pi$
$593$	−8.51993	−	14.7570i	−0.349872	−	0.605996i	−0.986226	+	0.165401i	$0.947108\pi$
$594$	0.551420	+	0.176629i	0.0226250	+	0.00724716i
$595$		0			0
$596$	34.2603	+	24.4577i	1.40336	+	1.00183i
$597$	−54.9318	+	31.7149i	−2.24821	+	1.29800i
$598$	6.50216	−	5.90385i	0.265893	−	0.241426i
$599$	3.39864	+	1.96221i	0.138865	+	0.0801736i	0.567823	−	0.823151i	$-0.307786\pi$
$599$	3.39864	+	1.96221i	0.138865	+	0.0801736i	−0.428958	+	0.903324i	$0.641119\pi$
$600$		0			0
$601$			8.98026i			0.366312i	0.983084	+	0.183156i	$0.0586314\pi$
$601$			8.98026i			0.366312i	−0.983084	+	0.183156i	$0.941369\pi$
$602$	−15.1324	−	21.5965i	−0.616749	−	0.880207i
$603$	−0.493240			−0.0200863
$604$	−7.61050	−	0.735783i	−0.309667	−	0.0299386i
$605$		0			0
$606$	20.5307	−	18.6416i	0.834004	−	0.757262i
$607$	32.5444	−	18.7895i	1.32094	−	0.762644i	0.337059	−	0.941483i	$-0.390568\pi$
$607$	32.5444	−	18.7895i	1.32094	−	0.762644i	0.983878	+	0.178840i	$0.0572344\pi$
$608$	0.879659	+	42.1872i	0.0356749	+	1.71092i
$609$	−17.0767	−	2.16348i	−0.691981	−	0.0876687i
$610$		0			0
$611$	−15.8453	+	9.14827i	−0.641031	+	0.370099i
$612$	44.1333	−	20.0921i	1.78398	−	0.812173i
$613$	−40.0621	−	23.1299i	−1.61809	−	0.934207i	−0.987413	−	0.158165i	$-0.949442\pi$
$613$	−40.0621	−	23.1299i	−1.61809	−	0.934207i	−0.630681	−	0.776042i	$-0.717224\pi$
$614$	−32.5390	+	7.05832i	−1.31317	+	0.284850i
$615$		0			0
$616$	−0.369349	−	0.652922i	−0.0148815	−	0.0263070i
$617$		−	42.8844i		−	1.72646i	−0.504809	−	0.863231i	$-0.668437\pi$
$617$		−	42.8844i		−	1.72646i	0.504809	−	0.863231i	$-0.331563\pi$
$618$	−4.00951	−	18.4840i	−0.161286	−	0.743534i
$619$	−14.7503	+	25.5483i	−0.592865	+	1.02687i	0.400980	+	0.916087i	$0.368670\pi$
$619$	−14.7503	+	25.5483i	−0.592865	+	1.02687i	−0.993844	+	0.110785i	$0.964664\pi$
$620$		0			0
$621$	−5.33508	+	3.08021i	−0.214090	+	0.123605i
$622$	7.26665	+	2.32762i	0.291366	+	0.0933293i
$623$	−5.10804	+	6.72461i	−0.204649	+	0.269416i
$624$	−42.6352	+	14.6435i	−1.70677	+	0.586210i
$625$		0			0
$626$	34.0921	−	30.9551i	1.36260	−	1.23721i
$627$	1.02336	−	1.77251i	0.0408691	−	0.0707873i
$628$	−0.247147	+	2.55634i	−0.00986223	+	0.102009i
$629$			5.60526i			0.223496i
$630$		0			0
$631$			20.5872i			0.819563i	0.912184	+	0.409781i	$0.134395\pi$
$631$			20.5872i			0.819563i	−0.912184	+	0.409781i	$0.865605\pi$
$632$	−11.1054	−	4.77890i	−0.441749	−	0.190094i
$633$	−15.0215	+	26.0181i	−0.597053	+	1.03413i
$634$	13.0353	+	14.3563i	0.517698	+	0.570163i
$635$		0			0
$636$	−27.3686	−	19.5378i	−1.08524	−	0.774726i
$637$	−20.1800	+	20.5777i	−0.799562	+	0.815320i
$638$	0.102789	−	0.320899i	0.00406945	−	0.0127045i
$639$	26.1906	−	15.1211i	1.03608	−	0.598182i
$640$		0			0
$641$	18.4263	−	31.9153i	0.727795	−	1.26058i	−0.230018	−	0.973186i	$-0.573878\pi$
$641$	18.4263	−	31.9153i	0.727795	−	1.26058i	0.957813	−	0.287392i	$-0.0927883\pi$
$642$	28.6323	−	6.21088i	1.13003	−	0.245124i
$643$		−	48.4719i		−	1.91154i	−0.294108	−	0.955772i	$-0.595023\pi$
$643$		−	48.4719i		−	1.91154i	0.294108	−	0.955772i	$-0.404977\pi$
$644$	7.78461	+	1.76043i	0.306757	+	0.0693707i
$645$		0			0
$646$	−12.0700	−	55.6431i	−0.474888	−	2.18925i
$647$	−33.9366	−	19.5933i	−1.33418	−	0.770292i	−0.348247	−	0.937403i	$-0.613223\pi$
$647$	−33.9366	−	19.5933i	−1.33418	−	0.770292i	−0.985938	+	0.167111i	$0.946556\pi$
$648$	−6.45208	+	0.759853i	−0.253462	+	0.0298498i
$649$	−0.739905	+	0.427185i	−0.0290438	+	0.0167685i
$650$		0			0
$651$	−23.8413	+	31.3864i	−0.934413	+	1.23013i
$652$	14.0007	+	9.99477i	0.548309	+	0.391425i
$653$	−5.96105	+	3.44161i	−0.233274	+	0.134681i	−0.612082	−	0.790795i	$-0.709668\pi$
$653$	−5.96105	+	3.44161i	−0.233274	+	0.134681i	0.378808	+	0.925475i	$0.376334\pi$
$654$	−46.9772	−	51.7380i	−1.83696	−	2.02312i
$655$		0			0
$656$	24.1080	+	20.9896i	0.941261	+	0.819506i
$657$	−27.6133			−1.07730
$658$	−15.0715	−	7.02204i	−0.587547	−	0.273748i
$659$			40.9792i			1.59632i	0.602444	+	0.798161i	$0.294194\pi$
$659$			40.9792i			1.59632i	−0.602444	+	0.798161i	$0.705806\pi$
$660$		0			0
$661$	10.4696	+	6.04460i	0.407219	+	0.235108i	0.689594	−	0.724196i	$-0.257789\pi$
$661$	10.4696	+	6.04460i	0.407219	+	0.235108i	−0.282375	+	0.959304i	$0.591122\pi$
$662$	5.40630	+	5.95418i	0.210122	+	0.231416i
$663$	52.6785	−	30.4139i	2.04586	−	1.18118i
$664$	−14.7409	+	10.9942i	−0.572056	+	0.426657i
$665$		0			0
$666$	−2.01259	+	6.28314i	−0.0779863	+	0.243467i
$667$	1.79253	+	3.10475i	0.0694070	+	0.120216i
$668$	−6.71603	−	14.7521i	−0.259851	−	0.570777i
$669$	−20.5012	+	35.5091i	−0.792621	+	1.37286i
$670$		0			0
$671$	−0.792208			−0.0305828
$672$	−33.1316	−	24.0945i	−1.27808	−	0.929464i
$673$		−	29.0006i		−	1.11789i	−0.829205	−	0.558945i	$-0.811206\pi$
$673$		−	29.0006i		−	1.11789i	0.829205	−	0.558945i	$-0.188794\pi$
$674$	20.3468	−	4.41359i	0.783729	−	0.170005i
$675$		0			0
$676$	−7.19472	+	3.27546i	−0.276720	+	0.125979i
$677$	24.1541	+	41.8361i	0.928317	+	1.60789i	0.786138	+	0.618051i	$0.212077\pi$
$677$	24.1541	+	41.8361i	0.928317	+	1.60789i	0.142178	+	0.989841i	$0.454589\pi$
$678$	−66.8841	−	21.4240i	−2.56867	−	0.822786i
$679$	27.0018	−	11.3392i	1.03623	−	0.435157i
$680$		0			0
$681$	2.06304	+	3.57329i	0.0790558	+	0.136929i
$682$	−0.518666	−	0.571229i	−0.0198607	−	0.0218735i
$683$	−6.61231	+	11.4528i	−0.253013	+	0.438231i	−0.964354	−	0.264616i	$-0.914755\pi$
$683$	−6.61231	+	11.4528i	−0.253013	+	0.438231i	0.711341	+	0.702847i	$0.248088\pi$
$684$	6.44915	−	66.7062i	0.246590	−	2.55057i
$685$		0			0
$686$	−25.8382	−	4.28792i	−0.986508	−	0.163713i
$687$	−23.3358			−0.890317
$688$	18.5115	−	21.2618i	0.705745	−	0.810597i
$689$	−21.9029	−	12.6457i	−0.834435	−	0.481761i
$690$		0			0
$691$	19.9447	+	34.5453i	0.758733	+	1.31416i	0.943497	+	0.331382i	$0.107515\pi$
$691$	19.9447	+	34.5453i	0.758733	+	1.31416i	−0.184763	+	0.982783i	$0.559152\pi$
$692$	−13.0772	−	9.33552i	−0.497121	−	0.354883i
$693$	0.461296	+	1.09848i	0.0175232	+	0.0417277i
$694$	20.8339	+	6.67342i	0.790843	+	0.253320i
$695$		0			0
$696$	−2.15226	−	18.2753i	−0.0815813	−	0.692725i
$697$	−37.3530	−	21.5658i	−1.41485	−	0.816862i
$698$	15.9339	−	3.45635i	0.603106	−	0.130825i
$699$	58.0921			2.19725
$700$		0			0
$701$	−5.82647			−0.220063			−0.110031	−	0.993928i	$-0.535095\pi$
$701$	−5.82647			−0.220063			−0.110031	+	0.993928i	$0.535095\pi$
$702$	23.2419	−	5.04159i	0.877208	−	0.190283i
$703$	6.70882	+	3.87334i	0.253028	+	0.146086i
$704$	0.582351	−	0.551346i	0.0219482	−	0.0207796i
$705$		0			0
$706$	27.5237	+	8.81627i	1.03587	+	0.331805i
$707$	18.8036	+	2.38227i	0.707182	+	0.0895946i
$708$	−27.1091	+	37.9744i	−1.01882	+	1.42716i
$709$	−8.29615	−	14.3694i	−0.311569	−	0.539653i	0.667134	−	0.744938i	$-0.267521\pi$
$709$	−8.29615	−	14.3694i	−0.311569	−	0.539653i	−0.978702	+	0.205286i	$0.934188\pi$
$710$		0			0
$711$	16.6290	+	9.60078i	0.623638	+	0.360058i
$712$	−8.29253	−	3.56846i	−0.310776	−	0.133734i
$713$	8.20905			0.307431
$714$	50.1059	+	23.3452i	1.87517	+	0.873671i
$715$		0			0
$716$	17.6150	+	1.70302i	0.658304	+	0.0636448i
$717$	−13.8955	+	24.0678i	−0.518938	+	0.898828i
$718$	20.1722	+	22.2165i	0.752818	+	0.829111i
$719$	1.69923	+	2.94314i	0.0633704	+	0.109761i	0.895970	−	0.444115i	$-0.146482\pi$
$719$	1.69923	+	2.94314i	0.0633704	+	0.109761i	−0.832600	+	0.553875i	$0.813148\pi$
$720$		0			0
$721$	7.81954	−	10.2942i	0.291215	−	0.383377i
$722$	−49.3493	−	15.8074i	−1.83659	−	0.588290i
$723$	26.0727	+	45.1593i	0.969655	+	1.67949i
$724$	−17.7014	−	38.8822i	−0.657869	−	1.44504i
$725$		0			0
$726$	41.5748	−	9.01834i	1.54299	−	0.334702i
$727$			14.3045i			0.530526i	0.964176	+	0.265263i	$0.0854588\pi$
$727$			14.3045i			0.530526i	−0.964176	+	0.265263i	$0.914541\pi$
$728$	−26.5470	−	15.6397i	−0.983898	−	0.579647i
$729$	43.8569			1.62433
$730$		0			0
$731$	−19.0197	+	32.9430i	−0.703468	+	1.21844i
$732$	−39.3747	+	17.9257i	−1.45533	+	0.662553i
$733$	24.7457	+	42.8607i	0.914001	+	1.58310i	0.808357	+	0.588693i	$0.200357\pi$
$733$	24.7457	+	42.8607i	0.914001	+	1.58310i	0.105645	+	0.994404i	$0.466309\pi$
$734$	3.30088	−	10.3051i	0.121838	−	0.380367i
$735$		0			0
$736$	0.177870	+	8.53039i	0.00655637	+	0.314434i
$737$	0.00953207	−	0.00550334i	0.000351118	−	0.000202718i
$738$	−34.1271	−	37.5856i	−1.25624	−	1.38355i
$739$	−23.2184	−	13.4052i	−0.854104	−	0.493117i	0.00792968	−	0.999969i	$-0.497476\pi$
$739$	−23.2184	−	13.4052i	−0.854104	−	0.493117i	−0.862033	+	0.506852i	$0.830809\pi$
$740$		0			0
$741$		−	84.0664i		−	3.08826i
$742$	−2.01051	−	22.8954i	−0.0738083	−	0.840518i
$743$	22.2896			0.817727			0.408863	−	0.912596i	$-0.365925\pi$
$743$	22.2896			0.817727			0.408863	+	0.912596i	$0.365925\pi$
$744$	−38.7045	−	16.6554i	−1.41898	−	0.610617i
$745$		0			0
$746$	−24.3697	−	26.8394i	−0.892238	−	0.982660i
$747$	25.2933	−	14.6031i	0.925435	−	0.534300i
$748$	−0.628717	+	0.880706i	−0.0229882	+	0.0322018i
$749$	15.9461	+	12.1128i	0.582659	+	0.442591i
$750$		0			0
$751$	11.1427	−	6.43324i	0.406603	−	0.234752i	−0.282726	−	0.959201i	$-0.591239\pi$
$751$	11.1427	−	6.43324i	0.406603	−	0.234752i	0.689329	+	0.724448i	$0.257905\pi$
$752$	3.40515	−	17.4458i	0.124173	−	0.636184i
$753$	22.4290	+	12.9494i	0.817359	+	0.471902i
$754$	−2.93395	−	13.5256i	−0.106848	−	0.492573i
$755$		0			0
$756$	15.8723	+	14.6684i	0.577269	+	0.533485i
$757$		−	3.66830i		−	0.133327i	−0.997776	−	0.0666633i	$-0.978765\pi$
$757$		−	3.66830i		−	0.133327i	0.997776	−	0.0666633i	$-0.0212354\pi$
$758$	40.2237	−	8.72527i	1.46099	−	0.316916i
$759$	0.206927	−	0.358408i	0.00751097	−	0.0130094i
$760$		0			0
$761$	−2.56137	+	1.47880i	−0.0928494	+	0.0536066i	−0.545706	−	0.837977i	$-0.683738\pi$
$761$	−2.56137	+	1.47880i	−0.0928494	+	0.0536066i	0.452856	+	0.891583i	$0.350405\pi$
$762$	5.16700	−	16.1309i	0.187181	−	0.584362i
$763$	6.00339	−	47.3856i	0.217337	−	1.71547i
$764$	−29.0782	+	40.7327i	−1.05201	+	1.47366i
$765$		0			0
$766$	−8.21683	−	9.04954i	−0.296886	−	0.326973i
$767$	−17.5460	+	30.3906i	−0.633551	+	1.09734i
$768$	16.4688	−	40.5805i	0.594265	−	1.46432i
$769$			32.6324i			1.17676i	0.808586	+	0.588378i	$0.200233\pi$
$769$			32.6324i			1.17676i	−0.808586	+	0.588378i	$0.799767\pi$
$770$		0			0
$771$			7.51469i			0.270635i
$772$	−16.2474	−	1.57080i	−0.584756	−	0.0565342i
$773$	−2.74844	+	4.76043i	−0.0988544	+	0.171221i	−0.911211	−	0.411941i	$-0.864851\pi$
$773$	−2.74844	+	4.76043i	−0.0988544	+	0.171221i	0.812356	+	0.583161i	$0.198184\pi$
$774$	−33.1482	+	30.0980i	−1.19149	+	1.08185i
$775$		0			0
$776$	18.7178	+	25.0966i	0.671931	+	0.900916i
$777$	−6.93425	+	2.91198i	−0.248765	+	0.104467i
$778$	−19.0936	−	6.11598i	−0.684538	−	0.219269i
$779$	−51.6233	+	29.8047i	−1.84960	+	1.06786i
$780$		0			0
$781$	−0.337429	+	0.584444i	−0.0120742	+	0.0209131i
$782$	−2.44060	−	11.2512i	−0.0872756	−	0.402343i
$783$			9.70800i			0.346936i
$784$	−2.20400	−	27.9131i	−0.0787144	−	0.996897i
$785$		0			0
$786$	−11.2788	+	2.44658i	−0.402301	+	0.0872665i
$787$	27.2677	+	15.7430i	0.971987	+	0.561177i	0.899841	−	0.436217i	$-0.143682\pi$
$787$	27.2677	+	15.7430i	0.971987	+	0.561177i	0.0721455	+	0.997394i	$0.477015\pi$
$788$	10.3185	+	22.6652i	0.367582	+	0.807413i
$789$	60.8659	−	35.1410i	2.16689	−	1.25105i
$790$		0			0
$791$	−18.5858	−	44.2582i	−0.660837	−	1.57364i
$792$	−1.02097	+	0.761473i	−0.0362787	+	0.0270578i
$793$	−28.1795	+	16.2694i	−1.00068	+	0.577745i
$794$	−0.183233	+	0.166372i	−0.00650269	+	0.00590433i
$795$		0			0
$796$	4.46000	−	46.1316i	0.158081	−	1.63509i
$797$	20.2691			0.717968			0.358984	−	0.933344i	$-0.383123\pi$
$797$	20.2691			0.717968			0.358984	+	0.933344i	$0.383123\pi$
$798$	62.5655	−	43.8388i	2.21479	−	1.55188i
$799$			23.9845i			0.848512i
$800$		0			0
$801$	12.4171	+	7.16902i	0.438737	+	0.253305i
$802$	25.1879	−	22.8702i	0.889416	−	0.807574i
$803$	0.533638	−	0.308096i	0.0188317	−	0.0108725i
$804$	0.349241	−	0.489217i	0.0123168	−	0.0172534i
$805$		0			0
$806$	−30.1806	−	9.66734i	−1.06307	−	0.340518i
$807$	−11.2224	−	19.4378i	−0.395049	−	0.684244i
$808$	2.36992	+	20.1235i	0.0833735	+	0.707943i
$809$	−15.6376	+	27.0851i	−0.549789	+	0.952262i	0.448500	+	0.893783i	$0.351958\pi$
$809$	−15.6376	+	27.0851i	−0.549789	+	0.952262i	−0.998289	+	0.0584790i	$0.981375\pi$
$810$		0			0
$811$	−51.4855			−1.80790			−0.903950	−	0.427638i	$-0.859346\pi$
$811$	−51.4855			−1.80790			−0.903950	+	0.427638i	$0.859346\pi$
$812$	8.53628	−	9.23687i	0.299565	−	0.324151i
$813$		−	17.5379i		−	0.615080i
$814$	−0.0312102	−	0.143880i	−0.00109392	−	0.00504299i
$815$		0			0
$816$	−11.3206	+	57.9997i	−0.396301	+	2.03039i
$817$	26.2859	+	45.5285i	0.919626	+	1.59284i
$818$	−5.14940	+	16.0760i	−0.180044	+	0.562084i
$819$	38.9680	+	29.6002i	1.36165	+	1.03432i
$820$		0			0
$821$	24.0601	+	41.6733i	0.839702	+	1.45441i	0.890144	+	0.455680i	$0.150604\pi$
$821$	24.0601	+	41.6733i	0.839702	+	1.45441i	−0.0504413	+	0.998727i	$0.516063\pi$
$822$	−4.36973	+	3.96764i	−0.152412	+	0.138387i
$823$	−12.3490	+	21.3892i	−0.430461	+	0.745580i	−0.996913	−	0.0785148i	$-0.974982\pi$
$823$	−12.3490	+	21.3892i	−0.430461	+	0.745580i	0.566452	+	0.824095i	$0.308316\pi$
$824$	12.6944	+	5.46270i	0.442232	+	0.190302i
$825$		0			0
$826$	−31.7678	+	2.78962i	−1.10534	+	0.0970633i
$827$	19.9120			0.692408			0.346204	−	0.938159i	$-0.387470\pi$
$827$	19.9120			0.692408			0.346204	+	0.938159i	$0.387470\pi$
$828$	1.30404	−	13.4882i	0.0453185	−	0.468748i
$829$	13.8257	+	7.98225i	0.480185	+	0.277235i	0.720494	−	0.693461i	$-0.243915\pi$
$829$	13.8257	+	7.98225i	0.480185	+	0.277235i	−0.240308	+	0.970697i	$0.577249\pi$
$830$		0			0
$831$	−21.8552	−	37.8543i	−0.758149	−	1.31315i
$832$	9.39183	−	31.5715i	0.325603	−	1.09455i
$833$	10.1342	+	36.3969i	0.351128	+	1.26108i
$834$	−8.45572	+	26.3981i	−0.292798	+	0.914090i
$835$		0			0
$836$	0.619644	+	1.36108i	0.0214308	+	0.0470740i
$837$	19.2512	+	11.1147i	0.665418	+	0.384179i
$838$	9.02398	+	41.6008i	0.311728	+	1.43708i
$839$	−14.5375			−0.501889			−0.250944	−	0.968002i	$-0.580741\pi$
$839$	−14.5375			−0.501889			−0.250944	+	0.968002i	$0.580741\pi$
$840$		0			0
$841$	−23.3504			−0.805187
$842$	2.03339	+	9.37398i	0.0700752	+	0.323049i
$843$	−22.9558	−	13.2536i	−0.790641	−	0.456477i
$844$	−9.09554	−	19.9788i	−0.313081	−	0.687700i
$845$		0			0
$846$	−8.61174	+	26.8851i	−0.296078	+	0.924330i
$847$	23.1542	+	17.5880i	0.795586	+	0.604331i
$848$	23.2380	−	7.98136i	0.797996	−	0.274081i
$849$	35.7568	+	61.9325i	1.22717	+	2.12552i
$850$		0			0
$851$	1.35655	+	0.783202i	0.0465018	+	0.0268478i
$852$	−3.54657	+	36.6836i	−0.121503	+	1.25676i
$853$	−36.2299			−1.24049			−0.620245	−	0.784408i	$-0.712967\pi$
$853$	−36.2299			−1.24049			−0.620245	+	0.784408i	$0.712967\pi$
$854$	−26.8034	−	12.4881i	−0.917192	−	0.427335i
$855$		0			0
$856$	−8.46193	+	19.6642i	−0.289223	+	0.672107i
$857$	19.0281	−	32.9576i	0.649986	−	1.12581i	−0.333139	−	0.942878i	$-0.608108\pi$
$857$	19.0281	−	32.9576i	0.649986	−	1.12581i	0.983126	−	0.182932i	$-0.0585588\pi$
$858$	−1.18284	+	1.07400i	−0.0403817	+	0.0366658i
$859$	−13.3104	−	23.0543i	−0.454145	−	0.786602i	0.544494	−	0.838765i	$-0.316722\pi$
$859$	−13.3104	−	23.0543i	−0.454145	−	0.786602i	−0.998639	+	0.0521630i	$0.983388\pi$
$860$		0			0
$861$	7.27378	−	57.4129i	0.247890	−	1.95663i
$862$	6.87487	−	21.4628i	0.234159	−	0.731025i
$863$	−11.6160	−	20.1195i	−0.395413	−	0.684876i	0.597741	−	0.801690i	$-0.296065\pi$
$863$	−11.6160	−	20.1195i	−0.395413	−	0.684876i	−0.993154	+	0.116814i	$0.962732\pi$
$864$	−11.1326	+	20.2456i	−0.378740	+	0.688769i
$865$		0			0
$866$	4.53565	+	20.9095i	0.154128	+	0.710533i
$867$		−	33.2058i		−	1.12773i
$868$	−8.54375	−	27.5029i	−0.289994	−	0.933510i
$869$	−0.428484			−0.0145353
$870$		0			0
$871$	0.226043	−	0.391517i	0.00765916	−	0.0132661i
$872$	50.7118	−	5.97226i	1.71732	−	0.202246i
$873$	−24.8621	−	43.0624i	−0.841455	−	1.45744i
$874$	−15.1528	−	4.85370i	−0.512553	−	0.164179i
$875$		0			0
$876$	19.5517	−	27.3881i	0.660592	−	0.925358i
$877$	−2.22052	+	1.28202i	−0.0749817	+	0.0432907i	−0.537022	−	0.843568i	$-0.680451\pi$
$877$	−2.22052	+	1.28202i	−0.0749817	+	0.0432907i	0.462040	+	0.886859i	$0.347118\pi$
$878$	4.57202	−	4.15132i	0.154298	−	0.140100i
$879$	−38.4937	−	22.2244i	−1.29836	−	0.749609i
$880$		0			0
$881$			11.4074i			0.384324i	0.981363	+	0.192162i	$0.0615498\pi$
$881$			11.4074i			0.384324i	−0.981363	+	0.192162i	$0.938450\pi$
$882$	−1.70869	+	44.4374i	−0.0575347	+	1.49628i
$883$	15.8634			0.533845			0.266922	−	0.963718i	$-0.413993\pi$
$883$	15.8634			0.533845			0.266922	+	0.963718i	$0.413993\pi$
$884$	−4.27706	+	44.2393i	−0.143853	+	1.48793i
$885$		0			0
$886$	14.7610	−	13.4027i	0.495904	−	0.450272i
$887$	23.4277	−	13.5260i	0.786626	−	0.454159i	−0.0521471	−	0.998639i	$-0.516606\pi$
$887$	23.4277	−	13.5260i	0.786626	−	0.454159i	0.838774	+	0.544480i	$0.183273\pi$
$888$	−4.80687	−	6.44499i	−0.161308	−	0.216280i
$889$	10.6741	−	4.48249i	0.357997	−	0.150338i
$890$		0			0
$891$	−0.199403	+	0.115125i	−0.00668024	+	0.00385684i
$892$	−12.4134	−	27.2668i	−0.415633	−	0.912960i
$893$	28.7066	+	16.5738i	0.960629	+	0.554620i
$894$	79.6214	−	17.2714i	2.66294	−	0.577641i
$895$		0			0
$896$	28.3944	−	9.47411i	0.948590	−	0.316508i
$897$		−	16.9985i		−	0.567563i
$898$	−5.10016	−	23.5119i	−0.170194	−	0.784601i
$899$	6.46818	−	11.2032i	0.215726	−	0.373648i
$900$		0			0
$901$	−28.7121	+	16.5769i	−0.956537	+	0.552257i
$902$	1.07888	+	0.345584i	0.0359229	+	0.0115067i
$903$	−50.6346	−	6.41502i	−1.68501	−	0.213478i
$904$	41.1355	−	30.6801i	1.36815	−	1.02041i
$905$		0			0
$906$	−10.9562	+	9.94800i	−0.363994	+	0.330500i
$907$	−5.21256	+	9.02842i	−0.173080	+	0.299784i	−0.939495	−	0.342562i	$-0.888705\pi$
$907$	−5.21256	+	9.02842i	−0.173080	+	0.299784i	0.766415	+	0.642346i	$0.222039\pi$
$908$	−3.00084	−	0.290121i	−0.0995864	−	0.00962801i
$909$		−	32.1815i		−	1.06739i
$910$		0			0
$911$			43.7727i			1.45026i	0.688614	+	0.725128i	$0.258219\pi$
$911$			43.7727i			1.45026i	−0.688614	+	0.725128i	$0.741781\pi$
$912$	61.5958	+	53.6283i	2.03964	+	1.77581i
$913$	−0.325870	+	0.564423i	−0.0107847	+	0.0186797i
$914$	11.0892	+	12.2130i	0.366799	+	0.403972i
$915$		0			0
$916$	9.90692	−	13.8776i	0.327334	−	0.458529i
$917$	−6.28147	−	4.77143i	−0.207432	−	0.157567i
$918$	9.51014	−	29.6899i	0.313881	−	0.979912i
$919$	43.5772	−	25.1593i	1.43748	−	0.829929i	0.439806	−	0.898093i	$-0.355047\pi$
$919$	43.5772	−	25.1593i	1.43748	−	0.829929i	0.997674	+	0.0681637i	$0.0217140\pi$
$920$		0			0
$921$	−32.2216	+	55.8095i	−1.06174	+	1.83899i
$922$	36.5541	−	7.92926i	1.20385	−	0.261136i
$923$			27.7189i			0.912379i
$924$	−1.41614	−	0.320250i	−0.0465877	−	0.0105354i
$925$		0			0
$926$	0.940418	+	4.33535i	0.0309041	+	0.142469i
$927$	−19.0085	−	10.9745i	−0.624320	−	0.360451i
$928$	11.7819	+	6.47863i	0.386760	+	0.212671i
$929$	16.4494	−	9.49704i	0.539686	−	0.311588i	−0.205266	−	0.978706i	$-0.565806\pi$
$929$	16.4494	−	9.49704i	0.539686	−	0.311588i	0.744952	+	0.667118i	$0.232473\pi$
$930$		0			0
$931$	50.5656	+	13.0216i	1.65722	+	0.426765i
$932$	−24.6623	+	34.5469i	−0.807840	+	1.13162i
$933$	12.7898	−	7.38419i	0.418719	−	0.241747i
$934$	−7.73951	−	8.52385i	−0.253244	−	0.278909i
$935$		0			0
$936$	−20.6786	+	48.0538i	−0.675902	+	1.57069i
$937$	44.7192			1.46091			0.730457	−	0.682959i	$-0.239307\pi$
$937$	44.7192			1.46091			0.730457	+	0.682959i	$0.239307\pi$
$938$	0.409259	−	0.0359382i	0.0133628	−	0.00117342i
$939$		−	89.1265i		−	2.90853i
$940$		0			0
$941$	8.88040	+	5.12710i	0.289493	+	0.167139i	0.637713	−	0.770274i	$-0.279881\pi$
$941$	8.88040	+	5.12710i	0.289493	+	0.167139i	−0.348220	+	0.937413i	$0.613214\pi$
$942$	3.34150	+	3.68013i	0.108872	+	0.119905i
$943$	−10.4384	+	6.02661i	−0.339921	+	0.196253i
$944$	−11.0743	−	32.2431i	−0.360436	−	1.04942i
$945$		0			0
$946$	0.304783	−	0.951508i	0.00990936	−	0.0309362i
$947$	−12.4847	−	21.6242i	−0.405699	−	0.702691i	0.588704	−	0.808349i	$-0.299638\pi$
$947$	−12.4847	−	21.6242i	−0.405699	−	0.702691i	−0.994403	+	0.105658i	$0.966305\pi$
$948$	−21.2968	+	9.69554i	−0.691687	+	0.314897i
$949$	12.6546	−	21.9185i	0.410787	−	0.711504i
$950$		0			0
$951$	37.5316			1.21704
$952$	−35.1550	+	19.8867i	−1.13938	+	0.644532i
$953$		−	26.3831i		−	0.854633i	−0.904102	−	0.427317i	$-0.859459\pi$
$953$		−	26.3831i		−	0.854633i	0.904102	−	0.427317i	$-0.140541\pi$
$954$	−38.1364	+	8.27249i	−1.23471	+	0.267832i
$955$		0			0
$956$	−8.41374	−	18.4812i	−0.272120	−	0.597726i
$957$	−0.326089	−	0.564803i	−0.0105410	−	0.0182575i
$958$	33.3749	+	10.6905i	1.07829	+	0.345395i
$959$	−4.00213	−	0.507039i	−0.129235	−	0.0163731i
$960$		0			0
$961$	0.689177	+	1.19369i	0.0222315	+	0.0385061i
$962$	−4.06502	−	4.47697i	−0.131061	−	0.144343i
$963$	17.0000	−	29.4448i	0.547817	−	0.948846i
$964$	−37.9247	−	3.66656i	−1.22147	−	0.118092i
$965$		0			0
$966$	12.6509	−	8.86435i	0.407037	−	0.285206i
$967$	−47.1287			−1.51556			−0.757778	−	0.652512i	$-0.773715\pi$
$967$	−47.1287			−1.51556			−0.757778	+	0.652512i	$0.773715\pi$
$968$	−12.2869	+	28.5528i	−0.394917	+	0.917723i
$969$	−95.4367	−	55.1004i	−3.06587	−	1.77008i
$970$		0			0
$971$	−27.6416	−	47.8767i	−0.887062	−	1.53644i	−0.843332	−	0.537394i	$-0.819409\pi$
$971$	−27.6416	−	47.8767i	−0.887062	−	1.53644i	−0.0437306	−	0.999043i	$-0.513924\pi$
$972$	−21.5443	+	30.1792i	−0.691033	+	0.968000i
$973$	−17.4680	+	7.33553i	−0.559998	+	0.235166i
$974$	17.0971	+	5.47647i	0.547826	+	0.175477i
$975$		0			0
$976$	6.05579	−	31.0260i	0.193841	−	0.993117i
$977$	−7.32085	−	4.22669i	−0.234215	−	0.135224i	0.378300	−	0.925683i	$-0.376509\pi$
$977$	−7.32085	−	4.22669i	−0.234215	−	0.135224i	−0.612515	+	0.790459i	$0.709842\pi$
$978$	32.5377	−	7.05804i	1.04044	−	0.225691i
$979$	−0.319954			−0.0102258
$980$		0			0
$981$	−81.0982			−2.58927
$982$	−13.1461	+	2.85164i	−0.419510	+	0.0909996i
$983$	−28.4854	−	16.4461i	−0.908543	−	0.524548i	−0.0285811	−	0.999591i	$-0.509099\pi$
$983$	−28.4854	−	16.4461i	−0.908543	−	0.524548i	−0.879962	+	0.475044i	$0.842432\pi$
$984$	61.4430	−	7.23606i	1.95873	−	0.230677i
$985$		0			0
$986$	−17.2780	−	5.53442i	−0.550244	−	0.176252i
$987$	−29.6712	+	12.4602i	−0.944445	+	0.396611i
$988$	49.9936	+	35.6893i	1.59051	+	1.13543i
$989$	5.31509	+	9.20601i	0.169010	+	0.292734i
$990$		0			0
$991$	−26.5344	−	15.3196i	−0.842893	−	0.486645i	0.0153535	−	0.999882i	$-0.495113\pi$
$991$	−26.5344	−	15.3196i	−0.842893	−	0.486645i	−0.858247	+	0.513238i	$0.828446\pi$
$992$	26.3364	−	15.9464i	0.836180	−	0.506300i
$993$	15.5659			0.493970
$994$	−20.6295	+	14.4548i	−0.654328	+	0.458479i
$995$		0			0
$996$	−3.42507	+	35.4269i	−0.108527	+	1.12254i
$997$	−21.2349	+	36.7799i	−0.672516	+	1.16483i	0.304673	+	0.952457i	$0.401453\pi$
$997$	−21.2349	+	36.7799i	−0.672516	+	1.16483i	−0.977188	+	0.212374i	$0.931880\pi$
$998$	−8.07382	−	8.89204i	−0.255572	−	0.281473i
$999$	2.12084	+	3.67340i	0.0671003	+	0.116221i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.t.c.199.9		32
4.3	odd	2	inner	700.2.t.c.199.5		32
5.2	odd	4		700.2.p.c.451.1		32
5.3	odd	4		140.2.o.a.31.16	yes	32
5.4	even	2		700.2.t.d.199.8		32
7.5	odd	6		700.2.t.d.299.12		32
20.3	even	4		140.2.o.a.31.4	✓	32
20.7	even	4		700.2.p.c.451.13		32
20.19	odd	2		700.2.t.d.199.12		32
28.19	even	6		700.2.t.d.299.8		32
35.3	even	12		980.2.g.a.391.15		32
35.12	even	12		700.2.p.c.551.13		32
35.13	even	4		980.2.o.f.31.16		32
35.18	odd	12		980.2.g.a.391.16		32
35.19	odd	6	inner	700.2.t.c.299.5		32
35.23	odd	12		980.2.o.f.411.4		32
35.33	even	12		140.2.o.a.131.4	yes	32
140.3	odd	12		980.2.g.a.391.14		32
140.19	even	6	inner	700.2.t.c.299.9		32
140.23	even	12		980.2.o.f.411.16		32
140.47	odd	12		700.2.p.c.551.1		32
140.83	odd	4		980.2.o.f.31.4		32
140.103	odd	12		140.2.o.a.131.16	yes	32
140.123	even	12		980.2.g.a.391.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.4	✓	32	20.3	even	4
140.2.o.a.31.16	yes	32	5.3	odd	4
140.2.o.a.131.4	yes	32	35.33	even	12
140.2.o.a.131.16	yes	32	140.103	odd	12
700.2.p.c.451.1		32	5.2	odd	4
700.2.p.c.451.13		32	20.7	even	4
700.2.p.c.551.1		32	140.47	odd	12
700.2.p.c.551.13		32	35.12	even	12
700.2.t.c.199.5		32	4.3	odd	2	inner
700.2.t.c.199.9		32	1.1	even	1	trivial
700.2.t.c.299.5		32	35.19	odd	6	inner
700.2.t.c.299.9		32	140.19	even	6	inner
700.2.t.d.199.8		32	5.4	even	2
700.2.t.d.199.12		32	20.19	odd	2
700.2.t.d.299.8		32	28.19	even	6
700.2.t.d.299.12		32	7.5	odd	6
980.2.g.a.391.13		32	140.123	even	12
980.2.g.a.391.14		32	140.3	odd	12
980.2.g.a.391.15		32	35.3	even	12
980.2.g.a.391.16		32	35.18	odd	12
980.2.o.f.31.4		32	140.83	odd	4
980.2.o.f.31.16		32	35.13	even	4
980.2.o.f.411.4		32	35.23	odd	12
980.2.o.f.411.16		32	140.23	even	12

Overview	Random
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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	700.2.t.c.199.9

Level	$700$
Weight	$2$
Character	700.199
Analytic conductor	$5.590$
Analytic rank	$0$
Dimension	$32$
Inner twists	$4$