LMFDB - Embedded newform 224.3.s.a.33.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(33,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("224.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 36x^{14} + 522x^{12} + 3644x^{10} + 12219x^{8} + 15156x^{6} + 15478x^{4} - 10992x^{2} + 11025 $ x^16 + 36x^14 + 522x^12 + 3644x^10 + 12219x^8 + 15156x^6 + 15478x^4 - 10992*x^2 + 11025
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			33.8
Root			$0.707107 + 3.42121i$ of defining polynomial
Character	$\chi$	$=$	224.33
Dual form			224.3.s.a.129.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.19011 - 2.41916i) q^{3} +(-0.0446470 - 0.0257769i) q^{5} +(6.12357 + 3.39144i) q^{7} +(7.20469 - 12.4789i) q^{9} +O(q^{10})$	\(q+(4.19011 - 2.41916i) q^{3} +(-0.0446470 - 0.0257769i) q^{5} +(6.12357 + 3.39144i) q^{7} +(7.20469 - 12.4789i) q^{9} +(0.894964 + 1.55012i) q^{11} +5.87602i q^{13} -0.249434 q^{15} +(23.0248 - 13.2934i) q^{17} +(-22.8134 - 13.1713i) q^{19} +(33.8629 - 0.603422i) q^{21} +(-12.8386 + 22.2371i) q^{23} +(-12.4987 - 21.6483i) q^{25} -26.1723i q^{27} -27.1749 q^{29} +(-25.7249 + 14.8523i) q^{31} +(7.50000 + 4.33013i) q^{33} +(-0.185978 - 0.309264i) q^{35} +(30.8629 - 53.4561i) q^{37} +(14.2150 + 24.6212i) q^{39} +65.7376i q^{41} +9.52546 q^{43} +(-0.643335 + 0.371430i) q^{45} +(61.2978 + 35.3903i) q^{47} +(25.9963 + 41.5354i) q^{49} +(64.3176 - 111.401i) q^{51} +(-4.86555 - 8.42738i) q^{53} -0.0922778i q^{55} -127.454 q^{57} +(-54.3535 + 31.3810i) q^{59} +(-66.1830 - 38.2108i) q^{61} +(86.4398 - 51.9811i) q^{63} +(0.151466 - 0.262346i) q^{65} +(51.5236 + 89.2415i) q^{67} +124.234i q^{69} -90.1681 q^{71} +(-28.8184 + 16.6383i) q^{73} +(-104.742 - 60.4726i) q^{75} +(0.223235 + 12.5275i) q^{77} +(-32.4323 + 56.1743i) q^{79} +(1.52712 + 2.64505i) q^{81} -29.1364i q^{83} -1.37065 q^{85} +(-113.866 + 65.7405i) q^{87} +(18.7689 + 10.8362i) q^{89} +(-19.9281 + 35.9822i) q^{91} +(-71.8602 + 124.466i) q^{93} +(0.679033 + 1.17612i) q^{95} -123.061i q^{97} +25.7918 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^9	$ 16 q + 8 q^{9} + 48 q^{17} + 56 q^{21} + 16 q^{25} + 112 q^{29} + 120 q^{33} + 8 q^{37} - 72 q^{45} - 128 q^{49} - 24 q^{53} - 528 q^{57} - 360 q^{61} - 8 q^{65} + 72 q^{73} + 32 q^{81} + 720 q^{85} + 408 q^{89} - 232 q^{93}+O(q^{100}) $ 16 * q + 8 * q^9 + 48 * q^17 + 56 * q^21 + 16 * q^25 + 112 * q^29 + 120 * q^33 + 8 * q^37 - 72 * q^45 - 128 * q^49 - 24 * q^53 - 528 * q^57 - 360 * q^61 - 8 * q^65 + 72 * q^73 + 32 * q^81 + 720 * q^85 + 408 * q^89 - 232 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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			0
$2$		0			0
$3$	4.19011	−	2.41916i	1.39670	−	0.806387i	0.402658	−	0.915351i	$-0.368086\pi$
$3$	4.19011	−	2.41916i	1.39670	−	0.806387i	0.994046	+	0.108963i	$0.0347531\pi$
$4$		0			0
$5$	−0.0446470	−	0.0257769i	−0.00892939	−	0.00515539i	0.495529	−	0.868592i	$-0.334974\pi$
$5$	−0.0446470	−	0.0257769i	−0.00892939	−	0.00515539i	−0.504458	+	0.863436i	$0.668308\pi$
$6$		0			0
$7$	6.12357	+	3.39144i	0.874796	+	0.484491i
$7$	6.12357	+	3.39144i	0.874796	+	0.484491i
$8$		0			0
$9$	7.20469	−	12.4789i	0.800521	−	1.38654i
$10$		0			0
$11$	0.894964	+	1.55012i	0.0813604	+	0.140920i	0.903835	−	0.427882i	$-0.140740\pi$
$11$	0.894964	+	1.55012i	0.0813604	+	0.140920i	−0.822474	+	0.568803i	$0.807407\pi$
$12$		0			0
$13$			5.87602i			0.452002i	0.974127	+	0.226001i	$0.0725652\pi$
$13$			5.87602i			0.452002i	−0.974127	+	0.226001i	$0.927435\pi$
$14$		0			0
$15$	−0.249434			−0.0166290
$16$		0			0
$17$	23.0248	−	13.2934i	1.35440	−	0.781962i	0.365536	−	0.930797i	$-0.380886\pi$
$17$	23.0248	−	13.2934i	1.35440	−	0.781962i	0.988862	+	0.148835i	$0.0475523\pi$
$18$		0			0
$19$	−22.8134	−	13.1713i	−1.20071	−	0.693227i	−0.239993	−	0.970775i	$-0.577145\pi$
$19$	−22.8134	−	13.1713i	−1.20071	−	0.693227i	−0.960712	+	0.277547i	$0.910478\pi$
$20$		0			0
$21$	33.8629	−	0.603422i	1.61252	−	0.0287344i
$22$		0			0
$23$	−12.8386	+	22.2371i	−0.558199	+	0.966830i	0.439448	+	0.898268i	$0.355174\pi$
$23$	−12.8386	+	22.2371i	−0.558199	+	0.966830i	−0.997647	+	0.0685614i	$0.978159\pi$
$24$		0			0
$25$	−12.4987	−	21.6483i	−0.499947	−	0.865933i
$26$		0			0
$27$		−	26.1723i		−	0.969345i
$28$		0			0
$29$	−27.1749			−0.937066			−0.468533	−	0.883446i	$-0.655217\pi$
$29$	−27.1749			−0.937066			−0.468533	+	0.883446i	$0.655217\pi$
$30$		0			0
$31$	−25.7249	+	14.8523i	−0.829837	+	0.479106i	−0.853797	−	0.520606i	$-0.825706\pi$
$31$	−25.7249	+	14.8523i	−0.829837	+	0.479106i	0.0239601	+	0.999713i	$0.492373\pi$
$32$		0			0
$33$	7.50000	+	4.33013i	0.227273	+	0.131216i
$34$		0			0
$35$	−0.185978	−	0.309264i	−0.00531366	−	0.00883612i
$36$		0			0
$37$	30.8629	−	53.4561i	0.834132	−	1.44476i	−0.0606029	−	0.998162i	$-0.519302\pi$
$37$	30.8629	−	53.4561i	0.834132	−	1.44476i	0.894735	−	0.446597i	$-0.147364\pi$
$38$		0			0
$39$	14.2150	+	24.6212i	0.364488	+	0.631312i
$40$		0			0
$41$			65.7376i			1.60336i	0.597755	+	0.801679i	$0.296059\pi$
$41$			65.7376i			1.60336i	−0.597755	+	0.801679i	$0.703941\pi$
$42$		0			0
$43$	9.52546			0.221522			0.110761	−	0.993847i	$-0.464671\pi$
$43$	9.52546			0.221522			0.110761	+	0.993847i	$0.464671\pi$
$44$		0			0
$45$	−0.643335	+	0.371430i	−0.0142963	+	0.00825399i
$46$		0			0
$47$	61.2978	+	35.3903i	1.30421	+	0.752986i	0.981123	−	0.193384i	$-0.0619463\pi$
$47$	61.2978	+	35.3903i	1.30421	+	0.752986i	0.323086	+	0.946370i	$0.395280\pi$
$48$		0			0
$49$	25.9963	+	41.5354i	0.530537	+	0.847662i
$50$		0			0
$51$	64.3176	−	111.401i	1.26113	−	2.18434i
$52$		0			0
$53$	−4.86555	−	8.42738i	−0.0918028	−	0.159007i	0.816467	−	0.577392i	$-0.195930\pi$
$53$	−4.86555	−	8.42738i	−0.0918028	−	0.159007i	−0.908270	+	0.418385i	$0.862596\pi$
$54$		0			0
$55$		−	0.0922778i		−	0.00167778i
$56$		0			0
$57$	−127.454			−2.23604
$58$		0			0
$59$	−54.3535	+	31.3810i	−0.921246	+	0.531881i	−0.884032	−	0.467426i	$-0.845181\pi$
$59$	−54.3535	+	31.3810i	−0.921246	+	0.531881i	−0.0372134	+	0.999307i	$0.511848\pi$
$60$		0			0
$61$	−66.1830	−	38.2108i	−1.08497	−	0.626406i	−0.152735	−	0.988267i	$-0.548808\pi$
$61$	−66.1830	−	38.2108i	−1.08497	−	0.626406i	−0.932232	+	0.361861i	$0.882141\pi$
$62$		0			0
$63$	86.4398	−	51.9811i	1.37206	−	0.825098i
$64$		0			0
$65$	0.151466	−	0.262346i	0.00233024	−	0.00403610i
$66$		0			0
$67$	51.5236	+	89.2415i	0.769009	+	1.33196i	0.938101	+	0.346363i	$0.112583\pi$
$67$	51.5236	+	89.2415i	0.769009	+	1.33196i	−0.169091	+	0.985600i	$0.554083\pi$
$68$		0			0
$69$			124.234i			1.80050i
$70$		0			0
$71$	−90.1681			−1.26997			−0.634986	−	0.772523i	$-0.718994\pi$
$71$	−90.1681			−1.26997			−0.634986	+	0.772523i	$0.718994\pi$
$72$		0			0
$73$	−28.8184	+	16.6383i	−0.394773	+	0.227922i	−0.684226	−	0.729270i	$-0.739860\pi$
$73$	−28.8184	+	16.6383i	−0.394773	+	0.227922i	0.289453	+	0.957192i	$0.406527\pi$
$74$		0			0
$75$	−104.742	−	60.4726i	−1.39656	−	0.806302i
$76$		0			0
$77$	0.223235	+	12.5275i	0.00289915	+	0.162695i
$78$		0			0
$79$	−32.4323	+	56.1743i	−0.410535	+	0.711068i	−0.994948	−	0.100389i	$-0.967991\pi$
$79$	−32.4323	+	56.1743i	−0.410535	+	0.711068i	0.584413	+	0.811456i	$0.301325\pi$
$80$		0			0
$81$	1.52712	+	2.64505i	0.0188534	+	0.0326550i
$82$		0			0
$83$		−	29.1364i		−	0.351041i	−0.984476	−	0.175520i	$-0.943839\pi$
$83$		−	29.1364i		−	0.351041i	0.984476	−	0.175520i	$-0.0561608\pi$
$84$		0			0
$85$	−1.37065			−0.0161253
$86$		0			0
$87$	−113.866	+	65.7405i	−1.30880	+	0.755638i
$88$		0			0
$89$	18.7689	+	10.8362i	0.210887	+	0.121755i	0.601723	−	0.798705i	$-0.294481\pi$
$89$	18.7689	+	10.8362i	0.210887	+	0.121755i	−0.390837	+	0.920460i	$0.627814\pi$
$90$		0			0
$91$	−19.9281	+	35.9822i	−0.218991	+	0.395409i
$92$		0			0
$93$	−71.8602	+	124.466i	−0.772691	+	1.33834i
$94$		0			0
$95$	0.679033	+	1.17612i	0.00714771	+	0.0123802i
$96$		0			0
$97$		−	123.061i		−	1.26867i	−0.773056	−	0.634337i	$-0.781273\pi$
$97$		−	123.061i		−	1.26867i	0.773056	−	0.634337i	$-0.218727\pi$
$98$		0			0
$99$	25.7918			0.260523
$100$		0			0
$101$	−48.9543	+	28.2638i	−0.484696	+	0.279840i	−0.722372	−	0.691505i	$-0.756948\pi$
$101$	−48.9543	+	28.2638i	−0.484696	+	0.279840i	0.237675	+	0.971345i	$0.423615\pi$
$102$		0			0
$103$	−25.6062	−	14.7838i	−0.248604	−	0.143532i	0.370521	−	0.928824i	$-0.379179\pi$
$103$	−25.6062	−	14.7838i	−0.248604	−	0.143532i	−0.619125	+	0.785293i	$0.712513\pi$
$104$		0			0
$105$	−1.52743	−	0.845941i	−0.0145469	−	0.00805658i
$106$		0			0
$107$	−14.9054	+	25.8169i	−0.139303	+	0.241279i	−0.927233	−	0.374485i	$-0.877819\pi$
$107$	−14.9054	+	25.8169i	−0.139303	+	0.241279i	0.787930	+	0.615765i	$0.211153\pi$
$108$		0			0
$109$	−40.7751	−	70.6246i	−0.374084	−	0.647932i	0.616106	−	0.787663i	$-0.288709\pi$
$109$	−40.7751	−	70.6246i	−0.374084	−	0.647932i	−0.990189	+	0.139731i	$0.955376\pi$
$110$		0			0
$111$		−	298.649i		−	2.69053i
$112$		0			0
$113$	43.3994			0.384065			0.192033	−	0.981389i	$-0.438492\pi$
$113$	43.3994			0.384065			0.192033	+	0.981389i	$0.438492\pi$
$114$		0			0
$115$	1.14641	−	0.661879i	0.00996876	−	0.00575547i
$116$		0			0
$117$	73.3262	+	42.3349i	0.626720	+	0.361837i
$118$		0			0
$119$	186.077	−	3.31582i	1.56368	−	0.0278640i
$120$		0			0
$121$	58.8981	−	102.014i	0.486761	−	0.843095i
$122$		0			0
$123$	159.030	+	275.448i	1.29293	+	2.23942i
$124$		0			0
$125$			2.57756i			0.0206205i
$126$		0			0
$127$	94.0304			0.740397			0.370199	−	0.928953i	$-0.379290\pi$
$127$	94.0304			0.740397			0.370199	+	0.928953i	$0.379290\pi$
$128$		0			0
$129$	39.9127	−	23.0436i	0.309401	−	0.178633i
$130$		0			0
$131$	−108.932	−	62.8918i	−0.831540	−	0.480090i	0.0228396	−	0.999739i	$-0.492729\pi$
$131$	−108.932	−	62.8918i	−0.831540	−	0.480090i	−0.854380	+	0.519649i	$0.826063\pi$
$132$		0			0
$133$	−95.0298	−	158.026i	−0.714510	−	1.18816i
$134$		0			0
$135$	−0.674642	+	1.16851i	−0.00499735	+	0.00865566i
$136$		0			0
$137$	124.928	+	216.382i	0.911884	+	1.57943i	0.811400	+	0.584491i	$0.198706\pi$
$137$	124.928	+	216.382i	0.911884	+	1.57943i	0.100484	+	0.994939i	$0.467961\pi$
$138$		0			0
$139$		−	2.08301i		−	0.0149857i	−0.999972	−	0.00749284i	$-0.997615\pi$
$139$		−	2.08301i		−	0.0149857i	0.999972	−	0.00749284i	$-0.00238507\pi$
$140$		0			0
$141$	342.460			2.42879
$142$		0			0
$143$	−9.10856	+	5.25883i	−0.0636962	+	0.0367750i
$144$		0			0
$145$	1.21328	+	0.700486i	0.00836743	+	0.00483094i
$146$		0			0
$147$	209.408	+	111.149i	1.42455	+	0.756114i
$148$		0			0
$149$	10.8122	−	18.7273i	0.0725652	−	0.125687i	−0.827460	−	0.561525i	$-0.810215\pi$
$149$	10.8122	−	18.7273i	0.0725652	−	0.125687i	0.900025	+	0.435838i	$0.143548\pi$
$150$		0			0
$151$	−44.0090	−	76.2258i	−0.291450	−	0.504807i	0.682703	−	0.730696i	$-0.260804\pi$
$151$	−44.0090	−	76.2258i	−0.291450	−	0.504807i	−0.974153	+	0.225890i	$0.927471\pi$
$152$		0			0
$153$		−	383.098i		−	2.50391i
$154$		0			0
$155$	1.53139			0.00987992
$156$		0			0
$157$	142.568	−	82.3115i	0.908075	−	0.524277i	0.0282634	−	0.999601i	$-0.491002\pi$
$157$	142.568	−	82.3115i	0.908075	−	0.524277i	0.879811	+	0.475323i	$0.157669\pi$
$158$		0			0
$159$	−40.7744	−	23.5411i	−0.256443	−	0.148057i
$160$		0			0
$161$	−154.034	+	92.6292i	−0.956731	+	0.575337i
$162$		0			0
$163$	82.4420	−	142.794i	0.505779	−	0.876035i	−0.494199	−	0.869349i	$-0.664538\pi$
$163$	82.4420	−	142.794i	0.505779	−	0.876035i	0.999978	−	0.00668599i	$-0.00212823\pi$
$164$		0			0
$165$	−0.223235	−	0.386654i	−0.00135294	−	0.00234336i
$166$		0			0
$167$			18.8929i			0.113131i	0.998399	+	0.0565655i	$0.0180150\pi$
$167$			18.8929i			0.113131i	−0.998399	+	0.0565655i	$0.981985\pi$
$168$		0			0
$169$	134.472			0.795695
$170$		0			0
$171$	−328.727	+	189.791i	−1.92238	+	1.10989i
$172$		0			0
$173$	−85.2911	−	49.2428i	−0.493012	−	0.284641i	0.232811	−	0.972522i	$-0.425208\pi$
$173$	−85.2911	−	49.2428i	−0.493012	−	0.284641i	−0.725823	+	0.687881i	$0.758541\pi$
$174$		0			0
$175$	−3.11760	−	174.954i	−0.0178148	−	0.999735i
$176$		0			0
$177$	−151.831	+	262.980i	−0.857805	+	1.48576i
$178$		0			0
$179$	35.1481	+	60.8784i	0.196358	+	0.340103i	0.947345	−	0.320215i	$-0.103755\pi$
$179$	35.1481	+	60.8784i	0.196358	+	0.340103i	−0.750987	+	0.660317i	$0.770422\pi$
$180$		0			0
$181$		−	204.167i		−	1.12800i	−0.825776	−	0.563999i	$-0.809262\pi$
$181$		−	204.167i		−	1.12800i	0.825776	−	0.563999i	$-0.190738\pi$
$182$		0			0
$183$	−369.752			−2.02050
$184$		0			0
$185$	−2.75587	+	1.59110i	−0.0148966	+	0.00860055i
$186$		0			0
$187$	41.2127	+	23.7942i	0.220389	+	0.127242i
$188$		0			0
$189$	88.7617	−	160.268i	0.469639	−	0.847980i
$190$		0			0
$191$	95.3517	−	165.154i	0.499224	−	0.864681i	−0.500776	−	0.865577i	$-0.666952\pi$
$191$	95.3517	−	165.154i	0.499224	−	0.864681i	1.00000		0.000896163i	$0.000285258\pi$
$192$		0			0
$193$	−42.7740	−	74.0868i	−0.221627	−	0.383869i	0.733675	−	0.679500i	$-0.237803\pi$
$193$	−42.7740	−	74.0868i	−0.221627	−	0.383869i	−0.955302	+	0.295631i	$0.904470\pi$
$194$		0			0
$195$		−	1.46568i		−	0.00751631i
$196$		0			0
$197$	275.164			1.39677			0.698386	−	0.715721i	$-0.253902\pi$
$197$	275.164			1.39677			0.698386	+	0.715721i	$0.253902\pi$
$198$		0			0
$199$	−179.161	+	103.439i	−0.900308	+	0.519793i	−0.877300	−	0.479942i	$-0.840658\pi$
$199$	−179.161	+	103.439i	−0.900308	+	0.519793i	−0.0230082	+	0.999735i	$0.507324\pi$
$200$		0			0
$201$	431.779	+	249.288i	2.14816	+	1.24024i
$202$		0			0
$203$	−166.408	−	92.1620i	−0.819742	−	0.454000i
$204$		0			0
$205$	1.69452	−	2.93499i	0.00826593	−	0.0143170i
$206$		0			0
$207$	184.996	+	320.423i	0.893701	+	1.54793i
$208$		0			0
$209$		−	47.1514i		−	0.225605i
$210$		0			0
$211$	−78.7325			−0.373140			−0.186570	−	0.982442i	$-0.559737\pi$
$211$	−78.7325			−0.373140			−0.186570	+	0.982442i	$0.559737\pi$
$212$		0			0
$213$	−377.814	+	218.131i	−1.77378	+	1.02409i
$214$		0			0
$215$	−0.425283	−	0.245537i	−0.00197806	−	0.00114203i
$216$		0			0
$217$	−207.899	+	3.70467i	−0.958061	+	0.0170722i
$218$		0			0
$219$	−80.5017	+	139.433i	−0.367588	+	0.636680i
$220$		0			0
$221$	78.1120	+	135.294i	0.353448	+	0.612190i
$222$		0			0
$223$		−	155.408i		−	0.696896i	−0.937328	−	0.348448i	$-0.886709\pi$
$223$		−	155.408i		−	0.696896i	0.937328	−	0.348448i	$-0.113291\pi$
$224$		0			0
$225$	−360.196			−1.60087
$226$		0			0
$227$	70.8987	−	40.9334i	0.312329	−	0.180323i	−0.335639	−	0.941991i	$-0.608952\pi$
$227$	70.8987	−	40.9334i	0.312329	−	0.180323i	0.647968	+	0.761667i	$0.275619\pi$
$228$		0			0
$229$	−355.669	−	205.346i	−1.55314	−	0.896707i	−0.997883	−	0.0650290i	$-0.979286\pi$
$229$	−355.669	−	205.346i	−1.55314	−	0.896707i	−0.555258	−	0.831678i	$-0.687381\pi$
$230$		0			0
$231$	31.2415	+	51.9516i	0.135244	+	0.224899i
$232$		0			0
$233$	−18.9359	+	32.7979i	−0.0812699	+	0.140764i	−0.903796	−	0.427964i	$-0.859231\pi$
$233$	−18.9359	+	32.7979i	−0.0812699	+	0.140764i	0.822526	+	0.568728i	$0.192564\pi$
$234$		0			0
$235$	−1.82451	−	3.16014i	−0.00776387	−	0.0134474i
$236$		0			0
$237$			313.836i			1.32420i
$238$		0			0
$239$	428.133			1.79135			0.895676	−	0.444707i	$-0.146692\pi$
$239$	428.133			1.79135			0.895676	+	0.444707i	$0.146692\pi$
$240$		0			0
$241$	180.155	−	104.012i	0.747530	−	0.431587i	−0.0772706	−	0.997010i	$-0.524621\pi$
$241$	180.155	−	104.012i	0.747530	−	0.431587i	0.824801	+	0.565423i	$0.191287\pi$
$242$		0			0
$243$	216.791	+	125.164i	0.892143	+	0.515079i
$244$		0			0
$245$	−0.0900009	−	2.52454i	−0.000367350	−	0.0103042i
$246$		0			0
$247$	77.3949	−	134.052i	0.313340	−	0.542721i
$248$		0			0
$249$	−70.4856	−	122.085i	−0.283075	−	0.490300i
$250$		0			0
$251$		−	375.625i		−	1.49652i	−0.663408	−	0.748258i	$-0.730891\pi$
$251$		−	375.625i		−	1.49652i	0.663408	−	0.748258i	$-0.269109\pi$
$252$		0			0
$253$	−45.9603			−0.181661
$254$		0			0
$255$	−5.74317	+	3.31582i	−0.0225222	+	0.0130032i
$256$		0			0
$257$	−62.4373	−	36.0482i	−0.242947	−	0.140265i	0.373584	−	0.927597i	$-0.378129\pi$
$257$	−62.4373	−	36.0482i	−0.242947	−	0.140265i	−0.616530	+	0.787331i	$0.711462\pi$
$258$		0			0
$259$	370.284	−	222.673i	1.42967	−	0.859741i
$260$		0			0
$261$	−195.787	+	339.113i	−0.750141	+	1.29928i
$262$		0			0
$263$	104.550	+	181.086i	0.397529	+	0.688541i	0.993420	−	0.114524i	$-0.0365344\pi$
$263$	104.550	+	181.086i	0.397529	+	0.688541i	−0.595891	+	0.803065i	$0.703201\pi$
$264$		0			0
$265$			0.501676i			0.00189312i
$266$		0			0
$267$	104.858			0.392728
$268$		0			0
$269$	−244.956	+	141.425i	−0.910616	+	0.525744i	−0.880629	−	0.473806i	$-0.842880\pi$
$269$	−244.956	+	141.425i	−0.910616	+	0.525744i	−0.0299865	+	0.999550i	$0.509546\pi$
$270$		0			0
$271$	−171.410	−	98.9636i	−0.632509	−	0.365179i	0.149214	−	0.988805i	$-0.452326\pi$
$271$	−171.410	−	98.9636i	−0.632509	−	0.365179i	−0.781723	+	0.623625i	$0.785659\pi$
$272$		0			0
$273$	3.54572	+	198.979i	0.0129880	+	0.728861i
$274$		0			0
$275$	22.3717	−	38.7490i	0.0813517	−	0.140905i
$276$		0			0
$277$	118.659	+	205.524i	0.428372	+	0.741963i	0.996729	−	0.0808197i	$-0.0257538\pi$
$277$	118.659	+	205.524i	0.428372	+	0.741963i	−0.568356	+	0.822783i	$0.692420\pi$
$278$		0			0
$279$			428.025i			1.53414i
$280$		0			0
$281$	−239.870			−0.853628			−0.426814	−	0.904339i	$-0.640364\pi$
$281$	−239.870			−0.853628			−0.426814	+	0.904339i	$0.640364\pi$
$282$		0			0
$283$	119.663	−	69.0872i	0.422836	−	0.244124i	−0.273454	−	0.961885i	$-0.588166\pi$
$283$	119.663	−	69.0872i	0.422836	−	0.244124i	0.696290	+	0.717761i	$0.254833\pi$
$284$		0			0
$285$	5.69044	+	3.28538i	0.0199665	+	0.0115276i
$286$		0			0
$287$	−222.945	+	402.549i	−0.776812	+	1.40261i
$288$		0			0
$289$	208.927	−	361.872i	0.722930	−	1.25215i
$290$		0			0
$291$	−297.705	−	515.641i	−1.02304	−	1.77196i
$292$		0			0
$293$			385.332i			1.31513i	0.753400	+	0.657563i	$0.228413\pi$
$293$			385.332i			1.31513i	−0.753400	+	0.657563i	$0.771587\pi$
$294$		0			0
$295$	3.23562			0.0109682
$296$		0			0
$297$	40.5703	−	23.4233i	0.136600	−	0.0788663i
$298$		0			0
$299$	−130.666	−	75.4398i	−0.437009	−	0.252307i
$300$		0			0
$301$	58.3299	+	32.3050i	0.193787	+	0.107326i
$302$		0			0
$303$	−136.749	+	236.857i	−0.451318	+	0.781706i
$304$		0			0
$305$	1.96991	+	3.41199i	0.00645873	+	0.0111868i
$306$		0			0
$307$			222.533i			0.724864i	0.932010	+	0.362432i	$0.118054\pi$
$307$			222.533i			0.724864i	−0.932010	+	0.362432i	$0.881946\pi$
$308$		0			0
$309$	−143.057			−0.462968
$310$		0			0
$311$	171.841	−	99.2124i	0.552543	−	0.319011i	−0.197604	−	0.980282i	$-0.563316\pi$
$311$	171.841	−	99.2124i	0.552543	−	0.319011i	0.750147	+	0.661271i	$0.229983\pi$
$312$		0			0
$313$	−328.619	−	189.729i	−1.04990	−	0.606161i	−0.127280	−	0.991867i	$-0.540625\pi$
$313$	−328.619	−	189.729i	−1.04990	−	0.606161i	−0.922622	+	0.385705i	$0.873958\pi$
$314$		0			0
$315$	−5.19919	+	0.0926473i	−0.0165054	+	0.000294118i
$316$		0			0
$317$	129.813	−	224.843i	0.409505	−	0.709284i	−0.585329	−	0.810796i	$-0.699035\pi$
$317$	129.813	−	224.843i	0.409505	−	0.709284i	0.994834	+	0.101512i	$0.0323680\pi$
$318$		0			0
$319$	−24.3206	−	42.1245i	−0.0762400	−	0.132052i
$320$		0			0
$321$			144.234i			0.449327i
$322$		0			0
$323$	−700.364			−2.16831
$324$		0			0
$325$	127.206	−	73.4425i	0.391403	−	0.225977i
$326$		0			0
$327$	−341.705	−	197.283i	−1.04497	−	0.603313i
$328$		0			0
$329$	255.338	+	424.603i	0.776103	+	1.29059i
$330$		0			0
$331$	−273.589	+	473.869i	−0.826552	+	1.43163i	0.0741761	+	0.997245i	$0.476367\pi$
$331$	−273.589	+	473.869i	−0.826552	+	1.43163i	−0.900728	+	0.434384i	$0.856966\pi$
$332$		0			0
$333$	−444.715	−	770.269i	−1.33548	−	2.31312i
$334$		0			0
$335$		−	5.31248i		−	0.0158582i
$336$		0			0
$337$	−408.705			−1.21277			−0.606387	−	0.795170i	$-0.707382\pi$
$337$	−408.705			−1.21277			−0.606387	+	0.795170i	$0.707382\pi$
$338$		0			0
$339$	181.848	−	104.990i	0.536425	−	0.309705i
$340$		0			0
$341$	−46.0458	−	26.5846i	−0.135032	−	0.0779606i
$342$		0			0
$343$	18.3257	+	342.510i	0.0534276	+	0.998572i
$344$		0			0
$345$	3.20238	−	5.54669i	0.00928227	−	0.0160774i
$346$		0			0
$347$	−133.575	−	231.358i	−0.384941	−	0.666738i	0.606820	−	0.794839i	$-0.292445\pi$
$347$	−133.575	−	231.358i	−0.384941	−	0.666738i	−0.991761	+	0.128102i	$0.959112\pi$
$348$		0			0
$349$			466.080i			1.33547i	0.744398	+	0.667736i	$0.232737\pi$
$349$			466.080i			1.33547i	−0.744398	+	0.667736i	$0.767263\pi$
$350$		0			0
$351$	153.789			0.438146
$352$		0			0
$353$	230.205	−	132.909i	0.652139	−	0.376513i	−0.137136	−	0.990552i	$-0.543790\pi$
$353$	230.205	−	132.909i	0.652139	−	0.376513i	0.789275	+	0.614039i	$0.210456\pi$
$354$		0			0
$355$	4.02573	+	2.32426i	0.0113401	+	0.00654720i
$356$		0			0
$357$	771.664	−	464.045i	2.16152	−	1.29985i
$358$		0			0
$359$	144.903	−	250.979i	0.403628	−	0.699105i	−0.590532	−	0.807014i	$-0.701082\pi$
$359$	144.903	−	250.979i	0.403628	−	0.699105i	0.994161	+	0.107909i	$0.0344155\pi$
$360$		0			0
$361$	166.467	+	288.330i	0.461128	+	0.798698i
$362$		0			0
$363$		−	569.936i		−	1.57007i
$364$		0			0
$365$	1.71554			0.00470011
$366$		0			0
$367$	−6.07460	+	3.50717i	−0.0165520	+	0.00955632i	−0.508253	−	0.861208i	$-0.669709\pi$
$367$	−6.07460	+	3.50717i	−0.0165520	+	0.00955632i	0.491701	+	0.870764i	$0.336375\pi$
$368$		0			0
$369$	820.333	+	473.619i	2.22312	+	1.28352i
$370$		0			0
$371$	−1.21363	−	68.1069i	−0.00327125	−	0.183576i
$372$		0			0
$373$	286.998	−	497.096i	0.769433	−	1.33270i	−0.168438	−	0.985712i	$-0.553872\pi$
$373$	286.998	−	497.096i	0.769433	−	1.33270i	0.937871	−	0.346984i	$-0.112794\pi$
$374$		0			0
$375$	6.23553	+	10.8002i	0.0166281	+	0.0288007i
$376$		0			0
$377$		−	159.680i		−	0.423555i
$378$		0			0
$379$	678.807			1.79105			0.895524	−	0.445014i	$-0.146801\pi$
$379$	678.807			1.79105			0.895524	+	0.445014i	$0.146801\pi$
$380$		0			0
$381$	393.998	−	227.475i	1.03412	−	0.597047i
$382$		0			0
$383$	358.444	+	206.948i	0.935886	+	0.540334i	0.888668	−	0.458550i	$-0.151631\pi$
$383$	358.444	+	206.948i	0.935886	+	0.540334i	0.0472179	+	0.998885i	$0.484964\pi$
$384$		0			0
$385$	0.312954	−	0.565070i	0.000812868	−	0.00146771i
$386$		0			0
$387$	68.6280	−	118.867i	0.177333	−	0.307150i
$388$		0			0
$389$	−69.2438	−	119.934i	−0.178005	−	0.308313i	0.763192	−	0.646171i	$-0.223631\pi$
$389$	−69.2438	−	119.934i	−0.178005	−	0.308313i	−0.941197	+	0.337858i	$0.890298\pi$
$390$		0			0
$391$			682.672i			1.74596i
$392$		0			0
$393$	−608.582			−1.54855
$394$		0			0
$395$	2.89600	−	1.67201i	0.00733166	−	0.00423293i
$396$		0			0
$397$	3.62003	+	2.09002i	0.00911846	+	0.00526455i	0.504552	−	0.863381i	$-0.331658\pi$
$397$	3.62003	+	2.09002i	0.00911846	+	0.00526455i	−0.495434	+	0.868646i	$0.664991\pi$
$398$		0			0
$399$	−780.475	−	432.253i	−1.95608	−	1.08334i
$400$		0			0
$401$	301.027	−	521.394i	0.750690	−	1.30023i	−0.196798	−	0.980444i	$-0.563054\pi$
$401$	301.027	−	521.394i	0.750690	−	1.30023i	0.947489	−	0.319790i	$-0.103612\pi$
$402$		0			0
$403$	−87.2724	−	151.160i	−0.216557	−	0.375088i
$404$		0			0
$405$		−	0.157458i		−	0.000388785i
$406$		0			0
$407$	110.485			0.271461
$408$		0			0
$409$	−155.272	+	89.6463i	−0.379638	+	0.219184i	−0.677661	−	0.735375i	$-0.737006\pi$
$409$	−155.272	+	89.6463i	−0.379638	+	0.219184i	0.298023	+	0.954559i	$0.403673\pi$
$410$		0			0
$411$	1046.93	+	604.443i	2.54726	+	1.47066i
$412$		0			0
$413$	−439.264	+	7.82750i	−1.06359	+	0.0189528i
$414$		0			0
$415$	−0.751046	+	1.30085i	−0.00180975	+	0.00313458i
$416$		0			0
$417$	−5.03914	−	8.72804i	−0.0120843	−	0.0209305i
$418$		0			0
$419$			605.541i			1.44521i	0.691263	+	0.722603i	$0.257054\pi$
$419$			605.541i			1.44521i	−0.691263	+	0.722603i	$0.742946\pi$
$420$		0			0
$421$	582.852			1.38445			0.692224	−	0.721683i	$-0.256631\pi$
$421$	582.852			1.38445			0.692224	+	0.721683i	$0.256631\pi$
$422$		0			0
$423$	883.264	−	509.953i	2.08809	−	1.20556i
$424$		0			0
$425$	−575.558	−	332.299i	−1.35425	−	0.781879i
$426$		0			0
$427$	−275.687	−	458.442i	−0.645637	−	1.07363i
$428$		0			0
$429$	−25.4439	+	44.0702i	−0.0593098	+	0.102728i
$430$		0			0
$431$	137.702	+	238.507i	0.319495	+	0.553382i	0.980383	−	0.197103i	$-0.0631534\pi$
$431$	137.702	+	238.507i	0.319495	+	0.553382i	−0.660888	+	0.750485i	$0.729820\pi$
$432$		0			0
$433$		−	27.7972i		−	0.0641967i	−0.999485	−	0.0320984i	$-0.989781\pi$
$433$		−	27.7972i		−	0.0641967i	0.999485	−	0.0320984i	$-0.0102190\pi$
$434$		0			0
$435$	6.77836			0.0155824
$436$		0			0
$437$	585.783	−	338.202i	1.34047	−	0.773918i
$438$		0			0
$439$	−254.750	−	147.080i	−0.580295	−	0.335034i	0.180955	−	0.983491i	$-0.442081\pi$
$439$	−254.750	−	147.080i	−0.580295	−	0.335034i	−0.761251	+	0.648458i	$0.775414\pi$
$440$		0			0
$441$	705.611	−	25.1554i	1.60003	−	0.0570416i
$442$		0			0
$443$	−145.445	+	251.918i	−0.328319	+	0.568665i	−0.982178	−	0.187951i	$-0.939815\pi$
$443$	−145.445	+	251.918i	−0.328319	+	0.568665i	0.653860	+	0.756616i	$0.273149\pi$
$444$		0			0
$445$	−0.558650	−	0.967610i	−0.00125539	−	0.00217440i
$446$		0			0
$447$		−	104.626i		−	0.234063i
$448$		0			0
$449$	433.407			0.965271			0.482635	−	0.875821i	$-0.339680\pi$
$449$	433.407			0.965271			0.482635	+	0.875821i	$0.339680\pi$
$450$		0			0
$451$	−101.901	+	58.8328i	−0.225946	+	0.130450i
$452$		0			0
$453$	−368.805	−	212.930i	−0.814139	−	0.470043i
$454$		0			0
$455$	1.81724	−	1.09281i	0.00399394	−	0.00240178i
$456$		0			0
$457$	28.6828	−	49.6801i	0.0627632	−	0.108709i	−0.832936	−	0.553369i	$-0.813342\pi$
$457$	28.6828	−	49.6801i	0.0627632	−	0.108709i	0.895700	+	0.444660i	$0.146675\pi$
$458$		0			0
$459$	−347.918	−	602.612i	−0.757991	−	1.31288i
$460$		0			0
$461$			567.060i			1.23007i	0.788501	+	0.615033i	$0.210857\pi$
$461$			567.060i			1.23007i	−0.788501	+	0.615033i	$0.789143\pi$
$462$		0			0
$463$	0.548177			0.00118397			0.000591984	−	1.00000i	$-0.499812\pi$
$463$	0.548177			0.00118397			0.000591984		1.00000i	$0.499812\pi$
$464$		0			0
$465$	6.41668	−	3.70467i	0.0137993	−	0.00796704i
$466$		0			0
$467$	88.5154	+	51.1044i	0.189540	+	0.109431i	0.591767	−	0.806109i	$-0.298430\pi$
$467$	88.5154	+	51.1044i	0.189540	+	0.109431i	−0.402227	+	0.915540i	$0.631764\pi$
$468$		0			0
$469$	12.8518	+	721.216i	0.0274025	+	1.53777i
$470$		0			0
$471$	398.250	−	689.789i	0.845541	−	1.46452i
$472$		0			0
$473$	8.52495	+	14.7656i	0.0180231	+	0.0312170i
$474$		0			0
$475$			658.496i			1.38631i
$476$		0			0
$477$	−140.219			−0.293960
$478$		0			0
$479$	−389.828	+	225.067i	−0.813837	+	0.469869i	−0.848287	−	0.529537i	$-0.822365\pi$
$479$	−389.828	+	225.067i	−0.813837	+	0.469869i	0.0344496	+	0.999406i	$0.489032\pi$
$480$		0			0
$481$	314.109	+	181.351i	0.653034	+	0.377029i
$482$		0			0
$483$	−421.333	+	760.759i	−0.872326	+	1.57507i
$484$		0			0
$485$	−3.17215	+	5.49432i	−0.00654051	+	0.0113285i
$486$		0			0
$487$	−470.386	−	814.732i	−0.965885	−	1.67296i	−0.707219	−	0.706995i	$-0.750050\pi$
$487$	−470.386	−	814.732i	−0.965885	−	1.67296i	−0.258666	−	0.965967i	$-0.583283\pi$
$488$		0			0
$489$		−	797.762i		−	1.63142i
$490$		0			0
$491$	−514.670			−1.04821			−0.524103	−	0.851655i	$-0.675599\pi$
$491$	−514.670			−1.04821			−0.524103	+	0.851655i	$0.675599\pi$
$492$		0			0
$493$	−625.696	+	361.246i	−1.26916	+	0.732750i
$494$		0			0
$495$	−1.15152	−	0.664832i	−0.00232631	−	0.00134310i
$496$		0			0
$497$	−552.151	−	305.799i	−1.11097	−	0.615290i
$498$		0			0
$499$	−124.004	+	214.780i	−0.248504	+	0.430422i	−0.963111	−	0.269105i	$-0.913272\pi$
$499$	−124.004	+	214.780i	−0.248504	+	0.430422i	0.714607	+	0.699526i	$0.246606\pi$
$500$		0			0
$501$	45.7049	+	79.1633i	0.0912274	+	0.158011i
$502$		0			0
$503$		−	164.798i		−	0.327630i	−0.986491	−	0.163815i	$-0.947620\pi$
$503$		−	164.798i		−	0.327630i	0.986491	−	0.163815i	$-0.0523800\pi$
$504$		0			0
$505$	2.91422			0.00577073
$506$		0			0
$507$	563.454	−	325.310i	1.11135	−	0.641638i
$508$		0			0
$509$	109.542	+	63.2438i	0.215209	+	0.124251i	0.603730	−	0.797189i	$-0.293680\pi$
$509$	109.542	+	63.2438i	0.215209	+	0.124251i	−0.388521	+	0.921440i	$0.627014\pi$
$510$		0			0
$511$	−232.900	+	4.15017i	−0.455773	+	0.00812167i
$512$		0			0
$513$	−344.724	+	597.079i	−0.671977	+	1.16390i
$514$		0			0
$515$	0.762160	+	1.32010i	0.00147992	+	0.00256330i
$516$		0			0
$517$			126.692i			0.245053i
$518$		0			0
$519$	−476.505			−0.918122
$520$		0			0
$521$	−44.7559	+	25.8398i	−0.0859039	+	0.0495966i	−0.542337	−	0.840161i	$-0.682460\pi$
$521$	−44.7559	+	25.8398i	−0.0859039	+	0.0495966i	0.456433	+	0.889758i	$0.349127\pi$
$522$		0			0
$523$	−297.579	−	171.808i	−0.568986	−	0.328504i	0.187758	−	0.982215i	$-0.439878\pi$
$523$	−297.579	−	171.808i	−0.568986	−	0.328504i	−0.756744	+	0.653711i	$0.773211\pi$
$524$		0			0
$525$	−436.304	−	725.533i	−0.831056	−	1.38197i
$526$		0			0
$527$	−394.874	+	683.942i	−0.749286	+	1.29780i
$528$		0			0
$529$	−65.1585	−	112.858i	−0.123173	−	0.213342i
$530$		0			0
$531$			904.361i			1.70313i
$532$		0			0
$533$	−386.276			−0.724720
$534$		0			0
$535$	1.33096	−	0.768430i	0.00248778	−	0.00143632i
$536$		0			0
$537$	294.549	+	170.058i	0.548509	+	0.316682i
$538$		0			0
$539$	−41.1193	+	77.4702i	−0.0762881	+	0.143730i
$540$		0			0
$541$	−382.006	+	661.654i	−0.706111	+	1.22302i	0.260177	+	0.965561i	$0.416219\pi$
$541$	−382.006	+	661.654i	−0.706111	+	1.22302i	−0.966289	+	0.257460i	$0.917114\pi$
$542$		0			0
$543$	−493.914	−	855.485i	−0.909603	−	1.57548i
$544$		0			0
$545$			4.20423i			0.00771419i
$546$		0			0
$547$	59.3354			0.108474			0.0542371	−	0.998528i	$-0.482727\pi$
$547$	59.3354			0.108474			0.0542371	+	0.998528i	$0.482727\pi$
$548$		0			0
$549$	−953.655	+	550.593i	−1.73708	+	1.00290i
$550$		0			0
$551$	619.952	+	357.929i	1.12514	+	0.649600i
$552$		0			0
$553$	−389.113	+	233.996i	−0.703640	+	0.423139i
$554$		0			0
$555$	−7.69826	+	13.3338i	−0.0138707	+	0.0240248i
$556$		0			0
$557$	365.048	+	632.281i	0.655382	+	1.13515i	0.981798	+	0.189929i	$0.0608257\pi$
$557$	365.048	+	632.281i	0.655382	+	1.13515i	−0.326416	+	0.945226i	$0.605841\pi$
$558$		0			0
$559$			55.9718i			0.100128i
$560$		0			0
$561$	230.248			0.410424
$562$		0			0
$563$	412.415	−	238.108i	0.732531	−	0.422927i	−0.0868167	−	0.996224i	$-0.527669\pi$
$563$	412.415	−	238.108i	0.732531	−	0.422927i	0.819347	+	0.573298i	$0.194336\pi$
$564$		0			0
$565$	−1.93765	−	1.11870i	−0.00342947	−	0.00198000i
$566$		0			0
$567$	0.380917	+	21.3763i	0.000671811	+	0.0377007i
$568$		0			0
$569$	−208.701	+	361.480i	−0.366785	+	0.635291i	−0.989061	−	0.147508i	$-0.952875\pi$
$569$	−208.701	+	361.480i	−0.366785	+	0.635291i	0.622276	+	0.782798i	$0.286208\pi$
$570$		0			0
$571$	492.001	+	852.171i	0.861648	+	1.49242i	0.870337	+	0.492456i	$0.163901\pi$
$571$	492.001	+	852.171i	0.861648	+	1.49242i	−0.00868931	+	0.999962i	$0.502766\pi$
$572$		0			0
$573$		−	922.685i		−	1.61027i
$574$		0			0
$575$	641.861			1.11628
$576$		0			0
$577$	80.3564	−	46.3938i	0.139266	−	0.0804052i	−0.428748	−	0.903424i	$-0.641045\pi$
$577$	80.3564	−	46.3938i	0.139266	−	0.0804052i	0.568014	+	0.823019i	$0.307712\pi$
$578$		0			0
$579$	−358.456	−	206.955i	−0.619095	−	0.357435i
$580$		0			0
$581$	98.8141	−	178.419i	0.170076	−	0.307089i
$582$		0			0
$583$	8.70898	−	15.0844i	0.0149382	−	0.0258738i
$584$		0			0
$585$	−2.18253	−	3.78025i	−0.00373082	−	0.00646196i
$586$		0			0
$587$		−	648.667i		−	1.10506i	−0.833495	−	0.552528i	$-0.813663\pi$
$587$		−	648.667i		−	1.10506i	0.833495	−	0.552528i	$-0.186337\pi$
$588$		0			0
$589$	782.498			1.32852
$590$		0			0
$591$	1152.97	−	665.667i	1.95088	−	1.12634i
$592$		0			0
$593$	−453.392	−	261.766i	−0.764574	−	0.441427i	0.0663617	−	0.997796i	$-0.478861\pi$
$593$	−453.392	−	261.766i	−0.764574	−	0.441427i	−0.830936	+	0.556369i	$0.812194\pi$
$594$		0			0
$595$	−8.39327	−	4.64847i	−0.0141063	−	0.00781255i
$596$		0			0
$597$	−500.471	+	866.841i	−0.838309	+	1.45199i
$598$		0			0
$599$	−445.522	−	771.668i	−0.743777	−	1.28826i	−0.950764	−	0.309916i	$-0.899699\pi$
$599$	−445.522	−	771.668i	−0.743777	−	1.28826i	0.206987	−	0.978344i	$-0.433634\pi$
$600$		0			0
$601$			502.034i			0.835331i	0.908601	+	0.417666i	$0.137152\pi$
$601$			502.034i			0.835331i	−0.908601	+	0.417666i	$0.862848\pi$
$602$		0			0
$603$	1484.85			2.46243
$604$		0			0
$605$	−5.25924	+	3.03642i	−0.00869296	+	0.00501888i
$606$		0			0
$607$	−263.638	−	152.212i	−0.434330	−	0.250760i	0.266860	−	0.963735i	$-0.414014\pi$
$607$	−263.638	−	152.212i	−0.434330	−	0.250760i	−0.701189	+	0.712975i	$0.747347\pi$
$608$		0			0
$609$	−920.221	+	16.3979i	−1.51104	+	0.0269260i
$610$		0			0
$611$	−207.954	+	360.187i	−0.340351	+	0.589505i
$612$		0			0
$613$	249.053	+	431.373i	0.406286	+	0.703708i	0.994470	−	0.105019i	$-0.0334904\pi$
$613$	249.053	+	431.373i	0.406286	+	0.703708i	−0.588184	+	0.808727i	$0.700157\pi$
$614$		0			0
$615$		−	16.3972i		−	0.0266622i
$616$		0			0
$617$	242.250			0.392626			0.196313	−	0.980541i	$-0.437103\pi$
$617$	242.250			0.392626			0.196313	+	0.980541i	$0.437103\pi$
$618$		0			0
$619$	468.171	−	270.298i	0.756334	−	0.436669i	−0.0716442	−	0.997430i	$-0.522825\pi$
$619$	468.171	−	270.298i	0.756334	−	0.436669i	0.827978	+	0.560761i	$0.189491\pi$
$620$		0			0
$621$	581.996	+	336.016i	0.937192	+	0.541088i
$622$		0			0
$623$	78.1824	+	130.010i	0.125493	+	0.208684i
$624$		0			0
$625$	−312.400	+	541.093i	−0.499841	+	0.865749i
$626$		0			0
$627$	−114.067	−	197.570i	−0.181925	−	0.315103i
$628$		0			0
$629$		−	1641.09i		−	2.60904i
$630$		0			0
$631$	808.138			1.28073			0.640363	−	0.768073i	$-0.278784\pi$
$631$	808.138			1.28073			0.640363	+	0.768073i	$0.278784\pi$
$632$		0			0
$633$	−329.898	+	190.467i	−0.521166	+	0.300895i
$634$		0			0
$635$	−4.19817	−	2.42382i	−0.00661130	−	0.00381703i
$636$		0			0
$637$	−244.063	+	152.755i	−0.383144	+	0.239804i
$638$		0			0
$639$	−649.633	+	1125.20i	−1.01664	+	1.76087i
$640$		0			0
$641$	−155.277	−	268.947i	−0.242241	−	0.419574i	0.719111	−	0.694895i	$-0.244549\pi$
$641$	−155.277	−	268.947i	−0.242241	−	0.419574i	−0.961352	+	0.275321i	$0.911216\pi$
$642$		0			0
$643$			342.761i			0.533065i	0.963826	+	0.266533i	$0.0858780\pi$
$643$			342.761i			0.533065i	−0.963826	+	0.266533i	$0.914122\pi$
$644$		0			0
$645$	−2.37598			−0.00368369
$646$		0			0
$647$	447.656	−	258.454i	0.691895	−	0.399466i	−0.112427	−	0.993660i	$-0.535862\pi$
$647$	447.656	−	258.454i	0.691895	−	0.399466i	0.804321	+	0.594195i	$0.202529\pi$
$648$		0			0
$649$	−97.2889	−	56.1698i	−0.149906	−	0.0865482i
$650$		0			0
$651$	−862.159	+	518.465i	−1.32436	+	0.796413i
$652$		0			0
$653$	381.777	−	661.256i	0.584650	−	1.01264i	−0.410269	−	0.911965i	$-0.634565\pi$
$653$	381.777	−	661.256i	0.584650	−	1.01264i	0.994919	−	0.100679i	$-0.0321016\pi$
$654$		0			0
$655$	3.24231	+	5.61585i	0.00495010	+	0.00857382i
$656$		0			0
$657$			479.496i			0.729827i
$658$		0			0
$659$	−593.617			−0.900785			−0.450392	−	0.892831i	$-0.648716\pi$
$659$	−593.617			−0.900785			−0.450392	+	0.892831i	$0.648716\pi$
$660$		0			0
$661$	−275.162	+	158.865i	−0.416282	+	0.240340i	−0.693485	−	0.720471i	$-0.743926\pi$
$661$	−275.162	+	158.865i	−0.416282	+	0.240340i	0.277204	+	0.960811i	$0.410592\pi$
$662$		0			0
$663$	654.596	+	377.931i	0.987325	+	0.570032i
$664$		0			0
$665$	0.169374	+	9.50495i	0.000254698	+	0.0142932i
$666$		0			0
$667$	348.887	−	604.291i	0.523070	−	0.905983i
$668$		0			0
$669$	−375.957	−	651.176i	−0.561968	−	0.973358i
$670$		0			0
$671$		−	136.789i		−	0.203859i
$672$		0			0
$673$	567.441			0.843152			0.421576	−	0.906793i	$-0.361477\pi$
$673$	567.441			0.843152			0.421576	+	0.906793i	$0.361477\pi$
$674$		0			0
$675$	−566.587	+	327.119i	−0.839388	+	0.484621i
$676$		0			0
$677$	−541.094	−	312.401i	−0.799253	−	0.461449i	0.0439568	−	0.999033i	$-0.486004\pi$
$677$	−541.094	−	312.401i	−0.799253	−	0.461449i	−0.843210	+	0.537584i	$0.819337\pi$
$678$		0			0
$679$	417.355	−	753.576i	0.614661	−	1.10983i
$680$		0			0
$681$	198.049	−	343.031i	0.290821	−	0.503717i
$682$		0			0
$683$	−46.4425	−	80.4407i	−0.0679977	−	0.117776i	0.830022	−	0.557731i	$-0.188328\pi$
$683$	−46.4425	−	80.4407i	−0.0679977	−	0.117776i	−0.898020	+	0.439955i	$0.854994\pi$
$684$		0			0
$685$		−	12.8811i		−	0.0188045i
$686$		0			0
$687$	−1987.06			−2.89237
$688$		0			0
$689$	49.5194	−	28.5901i	0.0718715	−	0.0414950i
$690$		0			0
$691$	−422.387	−	243.865i	−0.611269	−	0.352916i	0.162193	−	0.986759i	$-0.448143\pi$
$691$	−422.387	−	243.865i	−0.611269	−	0.352916i	−0.773462	+	0.633843i	$0.781477\pi$
$692$		0			0
$693$	157.938	+	87.4711i	0.227904	+	0.126221i
$694$		0			0
$695$	−0.0536936	+	0.0930000i	−7.72570e−5	+	0.000133813i
$696$		0			0
$697$	873.874	+	1513.59i	1.25376	+	2.17158i
$698$		0			0
$699$			183.236i			0.262140i
$700$		0			0
$701$	548.723			0.782772			0.391386	−	0.920227i	$-0.371996\pi$
$701$	548.723			0.782772			0.391386	+	0.920227i	$0.371996\pi$
$702$		0			0
$703$	−1408.17	+	813.010i	−2.00309	+	1.15649i
$704$		0			0
$705$	−15.2898	−	8.82756i	−0.0216876	−	0.0125214i
$706$		0			0
$707$	−395.630	+	7.04996i	−0.559590	+	0.00997166i
$708$		0			0
$709$	125.886	−	218.041i	0.177555	−	0.307533i	−0.763488	−	0.645822i	$-0.776515\pi$
$709$	125.886	−	218.041i	0.177555	−	0.307533i	0.941042	+	0.338289i	$0.109848\pi$
$710$		0			0
$711$	467.329	+	809.437i	0.657284	+	1.13845i
$712$		0			0
$713$		−	762.730i		−	1.06975i
$714$		0			0
$715$	0.542226			0.000758358
$716$		0			0
$717$	1793.93	−	1035.72i	2.50199	−	1.44452i
$718$		0			0
$719$	348.643	+	201.289i	0.484900	+	0.279957i	0.722456	−	0.691417i	$-0.243013\pi$
$719$	348.643	+	201.289i	0.484900	+	0.279957i	−0.237556	+	0.971374i	$0.576346\pi$
$720$		0			0
$721$	−106.663	−	177.371i	−0.147938	−	0.246007i
$722$		0			0
$723$	503.246	−	871.647i	0.696052	−	1.20560i
$724$		0			0
$725$	339.650	+	588.291i	0.468483	+	0.811437i
$726$		0			0
$727$			419.973i			0.577680i	0.957377	+	0.288840i	$0.0932695\pi$
$727$			419.973i			0.577680i	−0.957377	+	0.288840i	$0.906730\pi$
$728$		0			0
$729$	1183.68			1.62371
$730$		0			0
$731$	219.322	−	126.625i	0.300030	−	0.173222i
$732$		0			0
$733$	382.547	+	220.863i	0.521892	+	0.301314i	0.737708	−	0.675120i	$-0.235908\pi$
$733$	382.547	+	220.863i	0.521892	+	0.301314i	−0.215817	+	0.976434i	$0.569241\pi$
$734$		0			0
$735$	−6.48437	−	10.3604i	−0.00882228	−	0.0140957i
$736$		0			0
$737$	−92.2236	+	159.736i	−0.125134	+	0.216738i
$738$		0			0
$739$	−219.526	−	380.231i	−0.297059	−	0.514521i	0.678403	−	0.734690i	$-0.262672\pi$
$739$	−219.526	−	380.231i	−0.297059	−	0.514521i	−0.975462	+	0.220169i	$0.929339\pi$
$740$		0			0
$741$		−	748.924i		−	1.01069i
$742$		0			0
$743$	−882.165			−1.18730			−0.593651	−	0.804723i	$-0.702314\pi$
$743$	−882.165			−1.18730			−0.593651	+	0.804723i	$0.702314\pi$
$744$		0			0
$745$	−0.965466	+	0.557412i	−0.00129593	+	0.000748204i
$746$		0			0
$747$	−363.589	−	209.918i	−0.486733	−	0.281015i
$748$		0			0
$749$	−178.830	+	107.541i	−0.238759	+	0.143579i
$750$		0			0
$751$	57.8178	−	100.143i	0.0769877	−	0.133347i	−0.824961	−	0.565189i	$-0.808803\pi$
$751$	57.8178	−	100.143i	0.0769877	−	0.133347i	0.901949	+	0.431843i	$0.142136\pi$
$752$		0			0
$753$	−908.699	−	1573.91i	−1.20677	−	2.09019i
$754$		0			0
$755$			4.53767i			0.00601015i
$756$		0			0
$757$	−885.222			−1.16938			−0.584691	−	0.811256i	$-0.698784\pi$
$757$	−885.222			−1.16938			−0.584691	+	0.811256i	$0.698784\pi$
$758$		0			0
$759$	−192.579	+	111.185i	−0.253727	+	0.146489i
$760$		0			0
$761$	479.807	+	277.017i	0.630495	+	0.364017i	0.780944	−	0.624601i	$-0.214738\pi$
$761$	479.807	+	277.017i	0.630495	+	0.364017i	−0.150448	+	0.988618i	$0.548072\pi$
$762$		0			0
$763$	−10.1707	−	570.761i	−0.0133299	−	0.748049i
$764$		0			0
$765$	−9.87509	+	17.1042i	−0.0129086	+	0.0223584i
$766$		0			0
$767$	−184.395	−	319.382i	−0.240411	−	0.416405i
$768$		0			0
$769$			502.045i			0.652854i	0.945222	+	0.326427i	$0.105845\pi$
$769$			502.045i			0.652854i	−0.945222	+	0.326427i	$0.894155\pi$
$770$		0			0
$771$	−348.826			−0.452433
$772$		0			0
$773$	−1029.64	+	594.462i	−1.33200	+	0.769032i	−0.985606	−	0.169057i	$-0.945928\pi$
$773$	−1029.64	+	594.462i	−1.33200	+	0.769032i	−0.346396	+	0.938088i	$0.612595\pi$
$774$		0			0
$775$	643.055	+	371.268i	0.829748	+	0.479055i
$776$		0			0
$777$	1012.85	−	1828.80i	1.30354	−	2.35367i
$778$		0			0
$779$	865.852	−	1499.70i	1.11149	−	1.92516i
$780$		0			0
$781$	−80.6972	−	139.772i	−0.103325	−	0.178965i
$782$		0			0
$783$			711.230i			0.908340i
$784$		0			0
$785$	−8.48695			−0.0108114
$786$		0			0
$787$	245.089	−	141.502i	0.311421	−	0.179799i	−0.336141	−	0.941812i	$-0.609122\pi$
$787$	245.089	−	141.502i	0.311421	−	0.179799i	0.647562	+	0.762013i	$0.275789\pi$
$788$		0			0
$789$	876.154	+	505.848i	1.11046	+	0.641125i
$790$		0			0
$791$	265.759	+	147.186i	0.335979	+	0.186076i
$792$		0			0
$793$	224.527	−	388.893i	0.283136	−	0.490407i
$794$		0			0
$795$	1.21363	+	2.10208i	0.00152658	+	0.00264412i
$796$		0			0
$797$			999.015i			1.25347i	0.779233	+	0.626735i	$0.215609\pi$
$797$			999.015i			1.25347i	−0.779233	+	0.626735i	$0.784391\pi$
$798$		0			0
$799$	1881.83			2.35523
$800$		0			0
$801$	270.448	−	156.143i	0.337638	−	0.194936i
$802$		0			0
$803$	−51.5830	−	29.7814i	−0.0642378	−	0.0370877i
$804$		0			0
$805$	9.26483	−	0.165095i	0.0115091	−	0.000205087i
$806$		0			0
$807$	−684.261	+	1185.17i	−0.847907	+	1.46862i
$808$		0			0
$809$	−353.113	−	611.610i	−0.436481	−	0.756007i	0.560934	−	0.827860i	$-0.310442\pi$
$809$	−353.113	−	611.610i	−0.436481	−	0.756007i	−0.997415	+	0.0718530i	$0.977109\pi$
$810$		0			0
$811$			357.615i			0.440955i	0.975392	+	0.220478i	$0.0707616\pi$
$811$			357.615i			0.440955i	−0.975392	+	0.220478i	$0.929238\pi$
$812$		0			0
$813$	−957.636			−1.17790
$814$		0			0
$815$	−7.36157	+	4.25020i	−0.00903260	+	0.00521497i
$816$		0			0
$817$	−217.308	−	125.463i	−0.265983	−	0.153565i
$818$		0			0
$819$	305.442	+	507.922i	0.372945	+	0.620173i
$820$		0			0
$821$	668.782	−	1158.36i	0.814594	−	1.41092i	−0.0950249	−	0.995475i	$-0.530293\pi$
$821$	668.782	−	1158.36i	0.814594	−	1.41092i	0.909619	−	0.415443i	$-0.136374\pi$
$822$		0			0
$823$	−239.300	−	414.480i	−0.290766	−	0.503621i	0.683225	−	0.730207i	$-0.260577\pi$
$823$	−239.300	−	414.480i	−0.290766	−	0.503621i	−0.973991	+	0.226587i	$0.927243\pi$
$824$		0			0
$825$		−	216.483i		−	0.262404i
$826$		0			0
$827$	572.317			0.692040			0.346020	−	0.938227i	$-0.387533\pi$
$827$	572.317			0.692040			0.346020	+	0.938227i	$0.387533\pi$
$828$		0			0
$829$	1027.50	−	593.229i	1.23945	−	0.715596i	0.270467	−	0.962729i	$-0.412822\pi$
$829$	1027.50	−	593.229i	1.23945	−	0.715596i	0.968981	+	0.247133i	$0.0794886\pi$
$830$		0			0
$831$	994.390	+	574.112i	1.19662	+	0.690868i
$832$		0			0
$833$	1150.70	+	610.765i	1.38140	+	0.733212i
$834$		0			0
$835$	0.487001	−	0.843510i	0.000583234	−	0.00101019i
$836$		0			0
$837$	388.719	+	673.281i	0.464419	+	0.804398i
$838$		0			0
$839$		−	979.116i		−	1.16700i	−0.812112	−	0.583502i	$-0.801682\pi$
$839$		−	979.116i		−	1.16700i	0.812112	−	0.583502i	$-0.198318\pi$
$840$		0			0
$841$	−102.524			−0.121908
$842$		0			0
$843$	−1005.08	+	580.283i	−1.19227	+	0.688355i
$844$		0			0
$845$	−6.00378	−	3.46629i	−0.00710507	−	0.00410211i
$846$		0			0
$847$	706.642	−	424.944i	0.834288	−	0.501705i
$848$		0			0
$849$	334.266	−	578.966i	0.393718	−	0.681939i
$850$		0			0
$851$	792.472	+	1372.60i	0.931224	+	1.61293i
$852$		0			0
$853$			683.331i			0.801091i	0.916277	+	0.400546i	$0.131179\pi$
$853$			683.331i			0.801091i	−0.916277	+	0.400546i	$0.868821\pi$
$854$		0			0
$855$	19.5689			0.0228876
$856$		0			0
$857$	−7.04833	+	4.06936i	−0.00822443	+	0.00474837i	−0.504107	−	0.863641i	$-0.668178\pi$
$857$	−7.04833	+	4.06936i	−0.00822443	+	0.00474837i	0.495882	+	0.868390i	$0.334845\pi$
$858$		0			0
$859$	−911.901	−	526.487i	−1.06158	−	0.612906i	−0.135715	−	0.990748i	$-0.543333\pi$
$859$	−911.901	−	526.487i	−1.06158	−	0.612906i	−0.925870	+	0.377842i	$0.876666\pi$
$860$		0			0
$861$	39.6675	+	2226.07i	0.0460715	+	2.58544i
$862$		0			0
$863$	521.994	−	904.120i	0.604860	−	1.04765i	−0.387214	−	0.921990i	$-0.626562\pi$
$863$	521.994	−	904.120i	0.604860	−	1.04765i	0.992074	−	0.125658i	$-0.0401043\pi$
$864$		0			0
$865$	2.53866	+	4.39708i	0.00293486	+	0.00508333i
$866$		0			0
$867$		−	2021.71i		−	2.33185i
$868$		0			0
$869$	−116.103			−0.133605
$870$		0			0
$871$	−524.385	+	302.754i	−0.602050	+	0.347593i
$872$		0			0
$873$	−1535.67	−	886.619i	−1.75907	−	1.01560i
$874$		0			0
$875$	−8.74162	+	15.7839i	−0.00999042	+	0.0180387i
$876$		0			0
$877$	−403.776	+	699.361i	−0.460406	+	0.797447i	−0.998981	−	0.0451308i	$-0.985630\pi$
$877$	−403.776	+	699.361i	−0.460406	+	0.797447i	0.538575	+	0.842578i	$0.318963\pi$
$878$		0			0
$879$	932.180	+	1614.58i	1.06050	+	1.83684i
$880$		0			0
$881$			681.043i			0.773034i	0.922282	+	0.386517i	$0.126322\pi$
$881$			681.043i			0.773034i	−0.922282	+	0.386517i	$0.873678\pi$
$882$		0			0
$883$	996.177			1.12817			0.564086	−	0.825716i	$-0.309228\pi$
$883$	996.177			1.12817			0.564086	+	0.825716i	$0.309228\pi$
$884$		0			0
$885$	13.5576	−	7.82750i	0.0153194	−	0.00884463i
$886$		0			0
$887$	−236.794	−	136.713i	−0.266961	−	0.154130i	0.360545	−	0.932742i	$-0.382591\pi$
$887$	−236.794	−	136.713i	−0.266961	−	0.154130i	−0.627506	+	0.778612i	$0.715924\pi$
$888$		0			0
$889$	575.802	+	318.898i	0.647697	+	0.358716i
$890$		0			0
$891$	−2.73344	+	4.73446i	−0.00306783	+	0.00531364i
$892$		0			0
$893$	−932.275	−	1614.75i	−1.04398	−	1.80823i
$894$		0			0
$895$		−	3.62405i		−	0.00404921i
$896$		0			0
$897$	−730.004			−0.813829
$898$		0			0
$899$	699.073	−	403.610i	0.777612	−	0.448954i
$900$		0			0
$901$	−224.056	−	129.359i	−0.248675	−	0.143573i
$902$		0			0
$903$	322.560	−	5.74787i	0.357209	−	0.00636531i
$904$		0			0
$905$	−5.26281	+	9.11546i	−0.00581526	+	0.0100723i
$906$		0			0
$907$	−15.9679	−	27.6573i	−0.0176052	−	0.0304932i	0.857089	−	0.515169i	$-0.172271\pi$
$907$	−15.9679	−	27.6573i	−0.0176052	−	0.0304932i	−0.874694	+	0.484676i	$0.838938\pi$
$908$		0			0
$909$			814.527i			0.896070i
$910$		0			0
$911$	−1257.16			−1.37998			−0.689991	−	0.723818i	$-0.742385\pi$
$911$	−1257.16			−1.37998			−0.689991	+	0.723818i	$0.742385\pi$
$912$		0			0
$913$	45.1650	−	26.0760i	0.0494688	−	0.0285608i
$914$		0			0
$915$	16.5083	+	9.53107i	0.0180419	+	0.0104165i
$916$		0			0
$917$	−453.758	−	754.558i	−0.494829	−	0.822855i
$918$		0			0
$919$	−691.491	+	1197.70i	−0.752438	+	1.30326i	0.194200	+	0.980962i	$0.437789\pi$
$919$	−691.491	+	1197.70i	−0.752438	+	1.30326i	−0.946638	+	0.322299i	$0.895544\pi$
$920$		0			0
$921$	538.344	+	932.439i	0.584521	+	1.01242i
$922$		0			0
$923$		−	529.829i		−	0.574030i
$924$		0			0
$925$	−1542.98			−1.66809
$926$		0			0
$927$	−368.970	+	213.025i	−0.398026	+	0.229800i
$928$		0			0
$929$	−424.420	−	245.039i	−0.456857	−	0.263766i	0.253865	−	0.967240i	$-0.418298\pi$
$929$	−424.420	−	245.039i	−0.456857	−	0.263766i	−0.710722	+	0.703473i	$0.751631\pi$
$930$		0			0
$931$	−45.9880	−	1289.97i	−0.0493964	−	1.38557i
$932$		0			0
$933$	480.022	−	831.422i	0.514493	−	0.891128i
$934$		0			0
$935$	−1.22668	−	2.12467i	−0.00131196	−	0.00227238i
$936$		0			0
$937$			1136.61i			1.21303i	0.795072	+	0.606515i	$0.207433\pi$
$937$			1136.61i			1.21303i	−0.795072	+	0.606515i	$0.792567\pi$
$938$		0			0
$939$	−1835.94			−1.95520
$940$		0			0
$941$	458.248	−	264.570i	0.486980	−	0.281158i	−0.236341	−	0.971670i	$-0.575948\pi$
$941$	458.248	−	264.570i	0.486980	−	0.281158i	0.723321	+	0.690512i	$0.242615\pi$
$942$		0			0
$943$	−1461.81	−	843.978i	−1.55017	−	0.894993i
$944$		0			0
$945$	−8.09416	+	4.86748i	−0.00856525	+	0.00515077i
$946$		0			0
$947$	−582.080	+	1008.19i	−0.614657	+	1.06462i	0.375788	+	0.926706i	$0.377372\pi$
$947$	−582.080	+	1008.19i	−0.614657	+	1.06462i	−0.990445	+	0.137911i	$0.955961\pi$
$948$		0			0
$949$	−97.7672	−	169.338i	−0.103021	−	0.178438i
$950$		0			0
$951$		−	1256.16i		−	1.32088i
$952$		0			0
$953$	−616.861			−0.647283			−0.323642	−	0.946180i	$-0.604907\pi$
$953$	−616.861			−0.647283			−0.323642	+	0.946180i	$0.604907\pi$
$954$		0			0
$955$	−8.51433	+	4.91575i	−0.00891553	+	0.00514738i
$956$		0			0
$957$	−203.812	−	117.671i	−0.212970	−	0.122958i
$958$		0			0
$959$	31.1614	+	1748.72i	0.0324936	+	1.82348i
$960$		0			0
$961$	−39.3184	+	68.1015i	−0.0409141	+	0.0708652i
$962$		0			0
$963$	214.777	+	372.005i	0.223029	+	0.386298i
$964$		0			0
$965$			4.41034i			0.00457030i
$966$		0			0
$967$	624.887			0.646212			0.323106	−	0.946363i	$-0.395273\pi$
$967$	624.887			0.646212			0.323106	+	0.946363i	$0.395273\pi$
$968$		0			0
$969$	−2934.60	+	1694.29i	−3.02849	+	1.74850i
$970$		0			0
$971$	−644.984	−	372.382i	−0.664248	−	0.383504i	0.129646	−	0.991560i	$-0.458616\pi$
$971$	−644.984	−	372.382i	−0.664248	−	0.383504i	−0.793894	+	0.608057i	$0.791949\pi$
$972$		0			0
$973$	7.06439	−	12.7555i	0.00726042	−	0.0131094i
$974$		0			0
$975$	355.338	−	615.464i	0.364450	−	0.631245i
$976$		0			0
$977$	342.196	+	592.702i	0.350252	+	0.606655i	0.986294	−	0.165000i	$-0.0527625\pi$
$977$	342.196	+	592.702i	0.350252	+	0.606655i	−0.636041	+	0.771655i	$0.719429\pi$
$978$		0			0
$979$			38.7922i			0.0396243i
$980$		0			0
$981$	−1175.09			−1.19785
$982$		0			0
$983$	−787.512	+	454.670i	−0.801131	+	0.462533i	−0.843867	−	0.536553i	$-0.819726\pi$
$983$	−787.512	+	454.670i	−0.801131	+	0.462533i	0.0427352	+	0.999086i	$0.486393\pi$
$984$		0			0
$985$	−12.2852	−	7.09289i	−0.0124723	−	0.00720091i
$986$		0			0
$987$	2097.08	+	1161.43i	2.12470	+	1.17673i
$988$		0			0
$989$	−122.293	+	211.818i	−0.123654	+	0.214174i
$990$		0			0
$991$	−662.509	−	1147.50i	−0.668526	−	1.15792i	−0.978316	−	0.207116i	$-0.933592\pi$
$991$	−662.509	−	1147.50i	−0.668526	−	1.15792i	0.309791	−	0.950805i	$-0.399741\pi$
$992$		0			0
$993$			2647.42i			2.66608i
$994$		0			0
$995$	10.6653			0.0107189
$996$		0			0
$997$	811.560	−	468.554i	0.814002	−	0.469964i	−0.0343418	−	0.999410i	$-0.510933\pi$
$997$	811.560	−	468.554i	0.814002	−	0.469964i	0.848344	+	0.529446i	$0.177600\pi$
$998$		0			0
$999$	−1399.07	−	807.753i	−1.40047	−	0.808562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.s.a.33.8	yes	16
4.3	odd	2	inner	224.3.s.a.33.1	✓	16
7.2	even	3		1568.3.c.h.97.16		16
7.3	odd	6	inner	224.3.s.a.129.8	yes	16
7.5	odd	6		1568.3.c.h.97.1		16
8.3	odd	2		448.3.s.g.257.8		16
8.5	even	2		448.3.s.g.257.1		16
28.3	even	6	inner	224.3.s.a.129.1	yes	16
28.19	even	6		1568.3.c.h.97.15		16
28.23	odd	6		1568.3.c.h.97.2		16
56.3	even	6		448.3.s.g.129.8		16
56.45	odd	6		448.3.s.g.129.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.s.a.33.1	✓	16	4.3	odd	2	inner
224.3.s.a.33.8	yes	16	1.1	even	1	trivial
224.3.s.a.129.1	yes	16	28.3	even	6	inner
224.3.s.a.129.8	yes	16	7.3	odd	6	inner
448.3.s.g.129.1		16	56.45	odd	6
448.3.s.g.129.8		16	56.3	even	6
448.3.s.g.257.1		16	8.5	even	2
448.3.s.g.257.8		16	8.3	odd	2
1568.3.c.h.97.1		16	7.5	odd	6
1568.3.c.h.97.2		16	28.23	odd	6
1568.3.c.h.97.15		16	28.19	even	6
1568.3.c.h.97.16		16	7.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.19011 - 2.41916i) q^{3} +(-0.0446470 - 0.0257769i) q^{5} +(6.12357 + 3.39144i) q^{7} +(7.20469 - 12.4789i) q^{9} +O(q^{10})\)	\(q+(4.19011 - 2.41916i) q^{3} +(-0.0446470 - 0.0257769i) q^{5} +(6.12357 + 3.39144i) q^{7} +(7.20469 - 12.4789i) q^{9} +(0.894964 + 1.55012i) q^{11} +5.87602i q^{13} -0.249434 q^{15} +(23.0248 - 13.2934i) q^{17} +(-22.8134 - 13.1713i) q^{19} +(33.8629 - 0.603422i) q^{21} +(-12.8386 + 22.2371i) q^{23} +(-12.4987 - 21.6483i) q^{25} -26.1723i q^{27} -27.1749 q^{29} +(-25.7249 + 14.8523i) q^{31} +(7.50000 + 4.33013i) q^{33} +(-0.185978 - 0.309264i) q^{35} +(30.8629 - 53.4561i) q^{37} +(14.2150 + 24.6212i) q^{39} +65.7376i q^{41} +9.52546 q^{43} +(-0.643335 + 0.371430i) q^{45} +(61.2978 + 35.3903i) q^{47} +(25.9963 + 41.5354i) q^{49} +(64.3176 - 111.401i) q^{51} +(-4.86555 - 8.42738i) q^{53} -0.0922778i q^{55} -127.454 q^{57} +(-54.3535 + 31.3810i) q^{59} +(-66.1830 - 38.2108i) q^{61} +(86.4398 - 51.9811i) q^{63} +(0.151466 - 0.262346i) q^{65} +(51.5236 + 89.2415i) q^{67} +124.234i q^{69} -90.1681 q^{71} +(-28.8184 + 16.6383i) q^{73} +(-104.742 - 60.4726i) q^{75} +(0.223235 + 12.5275i) q^{77} +(-32.4323 + 56.1743i) q^{79} +(1.52712 + 2.64505i) q^{81} -29.1364i q^{83} -1.37065 q^{85} +(-113.866 + 65.7405i) q^{87} +(18.7689 + 10.8362i) q^{89} +(-19.9281 + 35.9822i) q^{91} +(-71.8602 + 124.466i) q^{93} +(0.679033 + 1.17612i) q^{95} -123.061i q^{97} +25.7918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^9	\( 16 q + 8 q^{9} + 48 q^{17} + 56 q^{21} + 16 q^{25} + 112 q^{29} + 120 q^{33} + 8 q^{37} - 72 q^{45} - 128 q^{49} - 24 q^{53} - 528 q^{57} - 360 q^{61} - 8 q^{65} + 72 q^{73} + 32 q^{81} + 720 q^{85} + 408 q^{89} - 232 q^{93}+O(q^{100}) \) 16 * q + 8 * q^9 + 48 * q^17 + 56 * q^21 + 16 * q^25 + 112 * q^29 + 120 * q^33 + 8 * q^37 - 72 * q^45 - 128 * q^49 - 24 * q^53 - 528 * q^57 - 360 * q^61 - 8 * q^65 + 72 * q^73 + 32 * q^81 + 720 * q^85 + 408 * q^89 - 232 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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