LMFDB - Embedded newform 224.3.s.a.33.1

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			33.1
Root			$-0.707107 + 3.42121i$ of defining polynomial
Character	$\chi$	$=$	224.33
Dual form			224.3.s.a.129.1

$q$-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	−0.994046	−	0.108963i	$-0.965247\pi$
$3$	−4.19011	+	2.41916i	−1.39670	+	0.806387i	−0.402658	+	0.915351i	$0.631914\pi$
$4$		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	0.822474	−	0.568803i	$-0.192593\pi$
$11$	−0.894964	−	1.55012i	−0.0813604	−	0.140920i	−0.903835	+	0.427882i	$0.859260\pi$
$12$		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	0.960712	−	0.277547i	$-0.0895215\pi$
$19$	22.8134	+	13.1713i	1.20071	+	0.693227i	0.239993	+	0.970775i	$0.422855\pi$
$20$		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	$-0.644826\pi$
$23$	12.8386	−	22.2371i	0.558199	−	0.966830i	0.997647	−	0.0685614i	$-0.0218409\pi$
$24$		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	−0.0239601	−	0.999713i	$-0.507627\pi$
$31$	25.7249	−	14.8523i	0.829837	−	0.479106i	0.853797	+	0.520606i	$0.174294\pi$
$32$		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	$-0.535329\pi$
$43$	−9.52546			−0.221522			−0.110761	+	0.993847i	$0.535329\pi$
$44$		0			0
$45$	−0.643335	+	0.371430i	−0.0142963	+	0.00825399i
$46$		0			0
$47$	−61.2978	−	35.3903i	−1.30421	−	0.752986i	−0.323086	−	0.946370i	$-0.604720\pi$
$47$	−61.2978	−	35.3903i	−1.30421	−	0.752986i	−0.981123	+	0.193384i	$0.938054\pi$
$48$		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	0.0372134	−	0.999307i	$-0.488152\pi$
$59$	54.3535	−	31.3810i	0.921246	−	0.531881i	0.884032	+	0.467426i	$0.154819\pi$
$60$		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	$-0.887417\pi$
$67$	−51.5236	−	89.2415i	−0.769009	−	1.33196i	0.169091	−	0.985600i	$-0.445917\pi$
$68$		0			0
$69$			124.234i			1.80050i
$70$		0			0
$71$	90.1681			1.26997			0.634986	−	0.772523i	$-0.281006\pi$
$71$	90.1681			1.26997			0.634986	+	0.772523i	$0.281006\pi$
$72$		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	−0.584413	−	0.811456i	$-0.698675\pi$
$79$	32.4323	−	56.1743i	0.410535	−	0.711068i	0.994948	+	0.100389i	$0.0320086\pi$
$80$		0			0
$81$	1.52712	+	2.64505i	0.0188534	+	0.0326550i
$82$		0			0
$83$			29.1364i			0.351041i	0.984476	+	0.175520i	$0.0561608\pi$
$83$			29.1364i			0.351041i	−0.984476	+	0.175520i	$0.943839\pi$
$84$		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	0.619125	−	0.785293i	$-0.287487\pi$
$103$	25.6062	+	14.7838i	0.248604	+	0.143532i	−0.370521	+	0.928824i	$0.620821\pi$
$104$		0			0
$105$	−1.52743	−	0.845941i	−0.0145469	−	0.00805658i
$106$		0			0
$107$	14.9054	−	25.8169i	0.139303	−	0.241279i	−0.787930	−	0.615765i	$-0.788847\pi$
$107$	14.9054	−	25.8169i	0.139303	−	0.241279i	0.927233	+	0.374485i	$0.122181\pi$
$108$		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	$-0.620710\pi$
$127$	−94.0304			−0.740397			−0.370199	+	0.928953i	$0.620710\pi$
$128$		0			0
$129$	39.9127	−	23.0436i	0.309401	−	0.178633i
$130$		0			0
$131$	108.932	+	62.8918i	0.831540	+	0.480090i	0.854380	−	0.519649i	$-0.173937\pi$
$131$	108.932	+	62.8918i	0.831540	+	0.480090i	−0.0228396	+	0.999739i	$0.507271\pi$
$132$		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	$0.00238507\pi$
$139$			2.08301i			0.0149857i	−0.999972	+	0.00749284i	$0.997615\pi$
$140$		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	0.974153	−	0.225890i	$-0.0725289\pi$
$151$	44.0090	+	76.2258i	0.291450	+	0.504807i	−0.682703	+	0.730696i	$0.739196\pi$
$152$		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	$0.335462\pi$
$163$	−82.4420	+	142.794i	−0.505779	+	0.876035i	−0.999978	+	0.00668599i	$0.997872\pi$
$164$		0			0
$165$	−0.223235	−	0.386654i	−0.00135294	−	0.00234336i
$166$		0			0
$167$		−	18.8929i		−	0.113131i	−0.998399	−	0.0565655i	$-0.981985\pi$
$167$		−	18.8929i		−	0.113131i	0.998399	−	0.0565655i	$-0.0180150\pi$
$168$		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	0.750987	−	0.660317i	$-0.229578\pi$
$179$	−35.1481	−	60.8784i	−0.196358	−	0.340103i	−0.947345	+	0.320215i	$0.896245\pi$
$180$		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	−1.00000		0.000896163i	$-0.999715\pi$
$191$	−95.3517	+	165.154i	−0.499224	+	0.864681i	0.500776	+	0.865577i	$0.333048\pi$
$192$		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	0.0230082	−	0.999735i	$-0.492676\pi$
$199$	179.161	−	103.439i	0.900308	−	0.519793i	0.877300	+	0.479942i	$0.159342\pi$
$200$		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	$-0.440263\pi$
$211$	78.7325			0.373140			0.186570	+	0.982442i	$0.440263\pi$
$212$		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	$0.113291\pi$
$223$			155.408i			0.696896i	−0.937328	+	0.348448i	$0.886709\pi$
$224$		0			0
$225$	−360.196			−1.60087
$226$		0			0
$227$	−70.8987	+	40.9334i	−0.312329	+	0.180323i	−0.647968	−	0.761667i	$-0.724381\pi$
$227$	−70.8987	+	40.9334i	−0.312329	+	0.180323i	0.335639	+	0.941991i	$0.391048\pi$
$228$		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	$-0.853308\pi$
$239$	−428.133			−1.79135			−0.895676	+	0.444707i	$0.853308\pi$
$240$		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	$0.269109\pi$
$251$			375.625i			1.49652i	−0.663408	+	0.748258i	$0.730891\pi$
$252$		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	0.595891	−	0.803065i	$-0.296799\pi$
$263$	−104.550	−	181.086i	−0.397529	−	0.688541i	−0.993420	+	0.114524i	$0.963466\pi$
$264$		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	0.781723	−	0.623625i	$-0.214341\pi$
$271$	171.410	+	98.9636i	0.632509	+	0.365179i	−0.149214	+	0.988805i	$0.547674\pi$
$272$		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	−0.696290	−	0.717761i	$-0.745167\pi$
$283$	−119.663	+	69.0872i	−0.422836	+	0.244124i	0.273454	+	0.961885i	$0.411834\pi$
$284$		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	$-0.881946\pi$
$307$		−	222.533i		−	0.724864i	0.932010	−	0.362432i	$-0.118054\pi$
$308$		0			0
$309$	−143.057			−0.462968
$310$		0			0
$311$	−171.841	+	99.2124i	−0.552543	+	0.319011i	−0.750147	−	0.661271i	$-0.770017\pi$
$311$	−171.841	+	99.2124i	−0.552543	+	0.319011i	0.197604	+	0.980282i	$0.436684\pi$
$312$		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	$-0.523633\pi$
$331$	273.589	−	473.869i	0.826552	−	1.43163i	0.900728	−	0.434384i	$-0.143034\pi$
$332$		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	0.991761	−	0.128102i	$-0.0408884\pi$
$347$	133.575	+	231.358i	0.384941	+	0.666738i	−0.606820	+	0.794839i	$0.707555\pi$
$348$		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	−0.994161	−	0.107909i	$-0.965584\pi$
$359$	−144.903	+	250.979i	−0.403628	+	0.699105i	0.590532	+	0.807014i	$0.298918\pi$
$360$		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	−0.491701	−	0.870764i	$-0.663625\pi$
$367$	6.07460	−	3.50717i	0.0165520	−	0.00955632i	0.508253	+	0.861208i	$0.330291\pi$
$368$		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	$-0.853199\pi$
$379$	−678.807			−1.79105			−0.895524	+	0.445014i	$0.853199\pi$
$380$		0			0
$381$	393.998	−	227.475i	1.03412	−	0.597047i
$382$		0			0
$383$	−358.444	−	206.948i	−0.935886	−	0.540334i	−0.0472179	−	0.998885i	$-0.515036\pi$
$383$	−358.444	−	206.948i	−0.935886	−	0.540334i	−0.888668	+	0.458550i	$0.848369\pi$
$384$		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	$-0.742946\pi$
$419$		−	605.541i		−	1.44521i	0.691263	−	0.722603i	$-0.257054\pi$
$420$		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	0.660888	−	0.750485i	$-0.270180\pi$
$431$	−137.702	−	238.507i	−0.319495	−	0.553382i	−0.980383	+	0.197103i	$0.936847\pi$
$432$		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	0.761251	−	0.648458i	$-0.224586\pi$
$439$	254.750	+	147.080i	0.580295	+	0.335034i	−0.180955	+	0.983491i	$0.557919\pi$
$440$		0			0
$441$	705.611	−	25.1554i	1.60003	−	0.0570416i
$442$		0			0
$443$	145.445	−	251.918i	0.328319	−	0.568665i	−0.653860	−	0.756616i	$-0.726851\pi$
$443$	145.445	−	251.918i	0.328319	−	0.568665i	0.982178	+	0.187951i	$0.0601847\pi$
$444$		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	$-0.500188\pi$
$463$	−0.548177			−0.00118397			−0.000591984		1.00000i	$0.500188\pi$
$464$		0			0
$465$	6.41668	−	3.70467i	0.0137993	−	0.00796704i
$466$		0			0
$467$	−88.5154	−	51.1044i	−0.189540	−	0.109431i	0.402227	−	0.915540i	$-0.368236\pi$
$467$	−88.5154	−	51.1044i	−0.189540	−	0.109431i	−0.591767	+	0.806109i	$0.701570\pi$
$468$		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	−0.0344496	−	0.999406i	$-0.510968\pi$
$479$	389.828	−	225.067i	0.813837	−	0.469869i	0.848287	+	0.529537i	$0.177635\pi$
$480$		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	$0.249950\pi$
$487$	470.386	+	814.732i	0.965885	+	1.67296i	0.258666	+	0.965967i	$0.416717\pi$
$488$		0			0
$489$		−	797.762i		−	1.63142i
$490$		0			0
$491$	514.670			1.04821			0.524103	−	0.851655i	$-0.324401\pi$
$491$	514.670			1.04821			0.524103	+	0.851655i	$0.324401\pi$
$492$		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	−0.714607	−	0.699526i	$-0.753394\pi$
$499$	124.004	−	214.780i	0.248504	−	0.430422i	0.963111	+	0.269105i	$0.0867277\pi$
$500$		0			0
$501$	45.7049	+	79.1633i	0.0912274	+	0.158011i
$502$		0			0
$503$			164.798i			0.327630i	0.986491	+	0.163815i	$0.0523800\pi$
$503$			164.798i			0.327630i	−0.986491	+	0.163815i	$0.947620\pi$
$504$		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	0.756744	−	0.653711i	$-0.226789\pi$
$523$	297.579	+	171.808i	0.568986	+	0.328504i	−0.187758	+	0.982215i	$0.560122\pi$
$524$		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	$-0.517273\pi$
$547$	−59.3354			−0.108474			−0.0542371	+	0.998528i	$0.517273\pi$
$548$		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	−0.819347	−	0.573298i	$-0.805664\pi$
$563$	−412.415	+	238.108i	−0.732531	+	0.422927i	0.0868167	+	0.996224i	$0.472331\pi$
$564$		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	$-0.836099\pi$
$571$	−492.001	−	852.171i	−0.861648	−	1.49242i	0.00868931	−	0.999962i	$-0.497234\pi$
$572$		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	$0.186337\pi$
$587$			648.667i			1.10506i	−0.833495	+	0.552528i	$0.813663\pi$
$588$		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	$0.100301\pi$
$599$	445.522	+	771.668i	0.743777	+	1.28826i	−0.206987	+	0.978344i	$0.566366\pi$
$600$		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	0.701189	−	0.712975i	$-0.252653\pi$
$607$	263.638	+	152.212i	0.434330	+	0.250760i	−0.266860	+	0.963735i	$0.585986\pi$
$608$		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	−0.827978	−	0.560761i	$-0.810509\pi$
$619$	−468.171	+	270.298i	−0.756334	+	0.436669i	0.0716442	+	0.997430i	$0.477175\pi$
$620$		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	$-0.721216\pi$
$631$	−808.138			−1.28073			−0.640363	+	0.768073i	$0.721216\pi$
$632$		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	$-0.914122\pi$
$643$		−	342.761i		−	0.533065i	0.963826	−	0.266533i	$-0.0858780\pi$
$644$		0			0
$645$	−2.37598			−0.00368369
$646$		0			0
$647$	−447.656	+	258.454i	−0.691895	+	0.399466i	−0.804321	−	0.594195i	$-0.797471\pi$
$647$	−447.656	+	258.454i	−0.691895	+	0.399466i	0.112427	+	0.993660i	$0.464138\pi$
$648$		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	$-0.351284\pi$
$659$	593.617			0.900785			0.450392	+	0.892831i	$0.351284\pi$
$660$		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	0.898020	−	0.439955i	$-0.145006\pi$
$683$	46.4425	+	80.4407i	0.0679977	+	0.117776i	−0.830022	+	0.557731i	$0.811672\pi$
$684$		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	0.773462	−	0.633843i	$-0.218523\pi$
$691$	422.387	+	243.865i	0.611269	+	0.352916i	−0.162193	+	0.986759i	$0.551857\pi$
$692$		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	0.237556	−	0.971374i	$-0.423654\pi$
$719$	−348.643	−	201.289i	−0.484900	−	0.279957i	−0.722456	+	0.691417i	$0.756987\pi$
$720$		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	$-0.906730\pi$
$727$		−	419.973i		−	0.577680i	0.957377	−	0.288840i	$-0.0932695\pi$
$728$		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	0.975462	−	0.220169i	$-0.0706610\pi$
$739$	219.526	+	380.231i	0.297059	+	0.514521i	−0.678403	+	0.734690i	$0.737328\pi$
$740$		0			0
$741$		−	748.924i		−	1.01069i
$742$		0			0
$743$	882.165			1.18730			0.593651	−	0.804723i	$-0.297686\pi$
$743$	882.165			1.18730			0.593651	+	0.804723i	$0.297686\pi$
$744$		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	−0.901949	−	0.431843i	$-0.857864\pi$
$751$	−57.8178	+	100.143i	−0.0769877	+	0.133347i	0.824961	+	0.565189i	$0.191197\pi$
$752$		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	−0.647562	−	0.762013i	$-0.724211\pi$
$787$	−245.089	+	141.502i	−0.311421	+	0.179799i	0.336141	+	0.941812i	$0.390878\pi$
$788$		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	$-0.929238\pi$
$811$		−	357.615i		−	0.440955i	0.975392	−	0.220478i	$-0.0707616\pi$
$812$		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	0.973991	−	0.226587i	$-0.0727567\pi$
$823$	239.300	+	414.480i	0.290766	+	0.503621i	−0.683225	+	0.730207i	$0.739423\pi$
$824$		0			0
$825$		−	216.483i		−	0.262404i
$826$		0			0
$827$	−572.317			−0.692040			−0.346020	−	0.938227i	$-0.612467\pi$
$827$	−572.317			−0.692040			−0.346020	+	0.938227i	$0.612467\pi$
$828$		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	$0.198318\pi$
$839$			979.116i			1.16700i	−0.812112	+	0.583502i	$0.801682\pi$
$840$		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	0.925870	−	0.377842i	$-0.123334\pi$
$859$	911.901	+	526.487i	1.06158	+	0.612906i	0.135715	+	0.990748i	$0.456667\pi$
$860$		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	$0.373438\pi$
$863$	−521.994	+	904.120i	−0.604860	+	1.04765i	−0.992074	+	0.125658i	$0.959896\pi$
$864$		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	$-0.690772\pi$
$883$	−996.177			−1.12817			−0.564086	+	0.825716i	$0.690772\pi$
$884$		0			0
$885$	13.5576	−	7.82750i	0.0153194	−	0.00884463i
$886$		0			0
$887$	236.794	+	136.713i	0.266961	+	0.154130i	0.627506	−	0.778612i	$-0.284076\pi$
$887$	236.794	+	136.713i	0.266961	+	0.154130i	−0.360545	+	0.932742i	$0.617409\pi$
$888$		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	0.874694	−	0.484676i	$-0.161062\pi$
$907$	15.9679	+	27.6573i	0.0176052	+	0.0304932i	−0.857089	+	0.515169i	$0.827729\pi$
$908$		0			0
$909$			814.527i			0.896070i
$910$		0			0
$911$	1257.16			1.37998			0.689991	−	0.723818i	$-0.257615\pi$
$911$	1257.16			1.37998			0.689991	+	0.723818i	$0.257615\pi$
$912$		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	$-0.562211\pi$
$919$	691.491	−	1197.70i	0.752438	−	1.30326i	0.946638	−	0.322299i	$-0.104456\pi$
$920$		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	$-0.622628\pi$
$947$	582.080	−	1008.19i	0.614657	−	1.06462i	0.990445	−	0.137911i	$-0.0440388\pi$
$948$		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	$-0.604727\pi$
$967$	−624.887			−0.646212			−0.323106	+	0.946363i	$0.604727\pi$
$968$		0			0
$969$	−2934.60	+	1694.29i	−3.02849	+	1.74850i
$970$		0			0
$971$	644.984	+	372.382i	0.664248	+	0.383504i	0.793894	−	0.608057i	$-0.208051\pi$
$971$	644.984	+	372.382i	0.664248	+	0.383504i	−0.129646	+	0.991560i	$0.541384\pi$
$972$		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	−0.0427352	−	0.999086i	$-0.513607\pi$
$983$	787.512	−	454.670i	0.801131	−	0.462533i	0.843867	+	0.536553i	$0.180274\pi$
$984$		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	$0.0664077\pi$
$991$	662.509	+	1147.50i	0.668526	+	1.15792i	−0.309791	+	0.950805i	$0.600259\pi$
$992$		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.33.1	✓	16
4.3	odd	2	inner	224.3.s.a.33.8	yes	16
7.2	even	3		1568.3.c.h.97.2		16
7.3	odd	6	inner	224.3.s.a.129.1	yes	16
7.5	odd	6		1568.3.c.h.97.15		16
8.3	odd	2		448.3.s.g.257.1		16
8.5	even	2		448.3.s.g.257.8		16
28.3	even	6	inner	224.3.s.a.129.8	yes	16
28.19	even	6		1568.3.c.h.97.1		16
28.23	odd	6		1568.3.c.h.97.16		16
56.3	even	6		448.3.s.g.129.1		16
56.45	odd	6		448.3.s.g.129.8		16

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

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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