LMFDB - Embedded newform 819.2.s.g.289.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(289,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,0,44,0,0,4,0,0,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.16
Character	$\chi$	$=$	819.289
Dual form			819.2.s.g.802.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.20299 q^{2} +2.85316 q^{4} +(1.98729 - 3.44208i) q^{5} +(1.55404 - 2.14125i) q^{7} +1.87950 q^{8} +(4.37797 - 7.58287i) q^{10} +(-2.61882 + 4.53594i) q^{11} +(0.0218968 + 3.60548i) q^{13} +(3.42354 - 4.71715i) q^{14} -1.56580 q^{16} +2.66417 q^{17} +(-3.23511 - 5.60337i) q^{19} +(5.67005 - 9.82081i) q^{20} +(-5.76924 + 9.99262i) q^{22} +0.120947 q^{23} +(-5.39862 - 9.35068i) q^{25} +(0.0482383 + 7.94284i) q^{26} +(4.43393 - 6.10933i) q^{28} +(0.968879 + 1.67815i) q^{29} +(3.99935 + 6.92708i) q^{31} -7.20844 q^{32} +5.86914 q^{34} +(-4.28204 - 9.60442i) q^{35} +3.65036 q^{37} +(-7.12690 - 12.3442i) q^{38} +(3.73511 - 6.46939i) q^{40} +(4.53942 + 7.86251i) q^{41} +(0.749656 - 1.29844i) q^{43} +(-7.47193 + 12.9418i) q^{44} +0.266446 q^{46} +(-3.08306 + 5.34002i) q^{47} +(-2.16991 - 6.65518i) q^{49} +(-11.8931 - 20.5994i) q^{50} +(0.0624750 + 10.2870i) q^{52} +(0.337881 + 0.585227i) q^{53} +(10.4087 + 18.0284i) q^{55} +(2.92082 - 4.02448i) q^{56} +(2.13443 + 3.69694i) q^{58} +2.22033 q^{59} +(2.53414 + 4.38925i) q^{61} +(8.81053 + 15.2603i) q^{62} -12.7485 q^{64} +(12.4539 + 7.08976i) q^{65} +(6.99863 - 12.1220i) q^{67} +7.60130 q^{68} +(-9.43328 - 21.1584i) q^{70} +(-5.13356 + 8.89159i) q^{71} +(-0.362401 - 0.627696i) q^{73} +8.04170 q^{74} +(-9.23027 - 15.9873i) q^{76} +(5.64282 + 12.6566i) q^{77} +(-2.09215 + 3.62371i) q^{79} +(-3.11169 + 5.38961i) q^{80} +(10.0003 + 17.3210i) q^{82} -13.7071 q^{83} +(5.29447 - 9.17029i) q^{85} +(1.65148 - 2.86045i) q^{86} +(-4.92208 + 8.52530i) q^{88} -0.253553 q^{89} +(7.75428 + 5.55619i) q^{91} +0.345082 q^{92} +(-6.79195 + 11.7640i) q^{94} -25.7163 q^{95} +(6.46607 - 11.1996i) q^{97} +(-4.78029 - 14.6613i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 44 q^{4} + 4 q^{7} + 8 q^{10} + 20 q^{16} + 4 q^{19} - 10 q^{22} - 22 q^{25} + 16 q^{28} - 18 q^{31} + 8 q^{34} - 20 q^{37} + 14 q^{40} + 20 q^{43} + 8 q^{46} - 12 q^{49} + 10 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) $ 36 * q + 44 * q^4 + 4 * q^7 + 8 * q^10 + 20 * q^16 + 4 * q^19 - 10 * q^22 - 22 * q^25 + 16 * q^28 - 18 * q^31 + 8 * q^34 - 20 * q^37 + 14 * q^40 + 20 * q^43 + 8 * q^46 - 12 * q^49 + 10 * q^52 + 42 * q^55 - 12 * q^58 + 14 * q^61 - 12 * q^64 + 12 * q^67 - 24 * q^70 + 6 * q^73 + 14 * q^76 - 24 * q^79 + 38 * q^82 + 28 * q^85 - 12 * q^88 + 92 * q^91 + 28 * q^94 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	2.20299			1.55775			0.778874	−	0.627180i	$-0.215791\pi$
$2$	2.20299			1.55775			0.778874	+	0.627180i	$0.215791\pi$
$3$		0			0
$3$		0			0
$4$	2.85316			1.42658
$5$	1.98729	−	3.44208i	0.888742	−	1.53935i	0.0473774	−	0.998877i	$-0.484914\pi$
$5$	1.98729	−	3.44208i	0.888742	−	1.53935i	0.841364	−	0.540469i	$-0.181753\pi$
$6$		0			0
$7$	1.55404	−	2.14125i	0.587372	−	0.809317i
$7$	1.55404	−	2.14125i	0.587372	−	0.809317i
$8$	1.87950			0.664504
$9$		0			0
$10$	4.37797	−	7.58287i	1.38444	−	2.39791i
$11$	−2.61882	+	4.53594i	−0.789605	+	1.36764i	0.136603	+	0.990626i	$0.456381\pi$
$11$	−2.61882	+	4.53594i	−0.789605	+	1.36764i	−0.926209	+	0.377011i	$0.876952\pi$
$12$		0			0
$13$	0.0218968	+	3.60548i	0.00607307	+	0.999982i
$13$	0.0218968	+	3.60548i	0.00607307	+	0.999982i
$14$	3.42354	−	4.71715i	0.914978	−	1.26071i
$15$		0			0
$16$	−1.56580			−0.391450
$17$	2.66417			0.646156			0.323078	−	0.946372i	$-0.395282\pi$
$17$	2.66417			0.646156			0.323078	+	0.946372i	$0.395282\pi$
$18$		0			0
$19$	−3.23511	−	5.60337i	−0.742184	−	1.28550i	−0.951499	−	0.307652i	$-0.900457\pi$
$19$	−3.23511	−	5.60337i	−0.742184	−	1.28550i	0.209315	−	0.977848i	$-0.432877\pi$
$20$	5.67005	−	9.82081i	1.26786	−	2.19600i
$21$		0			0
$22$	−5.76924	+	9.99262i	−1.23001	+	2.13043i
$23$	0.120947			0.0252193			0.0126096	−	0.999920i	$-0.495986\pi$
$23$	0.120947			0.0252193			0.0126096	+	0.999920i	$0.495986\pi$
$24$		0			0
$25$	−5.39862	−	9.35068i	−1.07972	−	1.87014i
$26$	0.0482383	+	7.94284i	0.00946032	+	1.55772i
$27$		0			0
$28$	4.43393	−	6.10933i	0.837933	−	1.15455i
$29$	0.968879	+	1.67815i	0.179916	+	0.311624i	0.941852	−	0.336029i	$-0.109084\pi$
$29$	0.968879	+	1.67815i	0.179916	+	0.311624i	−0.761935	+	0.647653i	$0.775751\pi$
$30$		0			0
$31$	3.99935	+	6.92708i	0.718305	+	1.24414i	0.961671	+	0.274206i	$0.0884150\pi$
$31$	3.99935	+	6.92708i	0.718305	+	1.24414i	−0.243366	+	0.969934i	$0.578252\pi$
$32$	−7.20844			−1.27428
$33$		0			0
$34$	5.86914			1.00655
$35$	−4.28204	−	9.60442i	−0.723796	−	1.62344i
$36$		0			0
$37$	3.65036			0.600115			0.300058	−	0.953921i	$-0.402994\pi$
$37$	3.65036			0.600115			0.300058	+	0.953921i	$0.402994\pi$
$38$	−7.12690	−	12.3442i	−1.15614	−	2.00249i
$39$		0			0
$40$	3.73511	−	6.46939i	0.590572	−	1.02290i
$41$	4.53942	+	7.86251i	0.708939	+	1.22792i	0.965251	+	0.261324i	$0.0841590\pi$
$41$	4.53942	+	7.86251i	0.708939	+	1.22792i	−0.256313	+	0.966594i	$0.582508\pi$
$42$		0			0
$43$	0.749656	−	1.29844i	0.114321	−	0.198010i	−0.803187	−	0.595727i	$-0.796864\pi$
$43$	0.749656	−	1.29844i	0.114321	−	0.198010i	0.917508	+	0.397717i	$0.130197\pi$
$44$	−7.47193	+	12.9418i	−1.12644	+	1.95104i
$45$		0			0
$46$	0.266446			0.0392853
$47$	−3.08306	+	5.34002i	−0.449711	+	0.778922i	−0.998367	−	0.0571262i	$-0.981806\pi$
$47$	−3.08306	+	5.34002i	−0.449711	+	0.778922i	0.548656	+	0.836048i	$0.315140\pi$
$48$		0			0
$49$	−2.16991	−	6.65518i	−0.309987	−	0.950741i
$50$	−11.8931	−	20.5994i	−1.68194	−	2.91320i
$51$		0			0
$52$	0.0624750	+	10.2870i	0.00866372	+	1.42655i
$53$	0.337881	+	0.585227i	0.0464115	+	0.0803871i	0.888298	−	0.459268i	$-0.151888\pi$
$53$	0.337881	+	0.585227i	0.0464115	+	0.0803871i	−0.841886	+	0.539655i	$0.818555\pi$
$54$		0			0
$55$	10.4087	+	18.0284i	1.40351	+	2.43095i
$56$	2.92082	−	4.02448i	0.390311	−	0.537794i
$57$		0			0
$58$	2.13443	+	3.69694i	0.280264	+	0.485432i
$59$	2.22033			0.289063			0.144531	−	0.989500i	$-0.453833\pi$
$59$	2.22033			0.289063			0.144531	+	0.989500i	$0.453833\pi$
$60$		0			0
$61$	2.53414	+	4.38925i	0.324463	+	0.561986i	0.981404	−	0.191956i	$-0.0614831\pi$
$61$	2.53414	+	4.38925i	0.324463	+	0.561986i	−0.656941	+	0.753942i	$0.728150\pi$
$62$	8.81053	+	15.2603i	1.11894	+	1.93806i
$63$		0			0
$64$	−12.7485			−1.59356
$65$	12.4539	+	7.08976i	1.54471	+	0.879377i
$66$		0			0
$67$	6.99863	−	12.1220i	0.855018	−	1.48094i	−0.0216096	−	0.999766i	$-0.506879\pi$
$67$	6.99863	−	12.1220i	0.855018	−	1.48094i	0.876628	−	0.481169i	$-0.159788\pi$
$68$	7.60130			0.921793
$69$		0			0
$70$	−9.43328	−	21.1584i	−1.12749	−	2.52891i
$71$	−5.13356	+	8.89159i	−0.609242	+	1.05524i	0.382124	+	0.924111i	$0.375193\pi$
$71$	−5.13356	+	8.89159i	−0.609242	+	1.05524i	−0.991366	+	0.131126i	$0.958141\pi$
$72$		0			0
$73$	−0.362401	−	0.627696i	−0.0424158	−	0.0734663i	0.844038	−	0.536283i	$-0.180172\pi$
$73$	−0.362401	−	0.627696i	−0.0424158	−	0.0734663i	−0.886454	+	0.462817i	$0.846839\pi$
$74$	8.04170			0.934829
$75$		0			0
$76$	−9.23027	−	15.9873i	−1.05878	−	1.83387i
$77$	5.64282	+	12.6566i	0.643059	+	1.44235i
$78$		0			0
$79$	−2.09215	+	3.62371i	−0.235385	+	0.407699i	−0.959385	−	0.282101i	$-0.908969\pi$
$79$	−2.09215	+	3.62371i	−0.235385	+	0.407699i	0.723999	+	0.689801i	$0.242302\pi$
$80$	−3.11169	+	5.38961i	−0.347898	+	0.602577i
$81$		0			0
$82$	10.0003	+	17.3210i	1.10435	+	1.91279i
$83$	−13.7071			−1.50455			−0.752275	−	0.658850i	$-0.771043\pi$
$83$	−13.7071			−1.50455			−0.752275	+	0.658850i	$0.771043\pi$
$84$		0			0
$85$	5.29447	−	9.17029i	0.574266	−	0.994658i
$86$	1.65148	−	2.86045i	0.178084	−	0.308450i
$87$		0			0
$88$	−4.92208	+	8.52530i	−0.524696	+	0.908800i
$89$	−0.253553			−0.0268766			−0.0134383	−	0.999910i	$-0.504278\pi$
$89$	−0.253553			−0.0268766			−0.0134383	+	0.999910i	$0.504278\pi$
$90$		0			0
$91$	7.75428	+	5.55619i	0.812869	+	0.582446i
$92$	0.345082			0.0359773
$93$		0			0
$94$	−6.79195	+	11.7640i	−0.700536	+	1.21336i
$95$	−25.7163			−2.63844
$96$		0			0
$97$	6.46607	−	11.1996i	0.656530	−	1.13714i	−0.324978	−	0.945722i	$-0.605357\pi$
$97$	6.46607	−	11.1996i	0.656530	−	1.13714i	0.981508	−	0.191421i	$-0.0613097\pi$
$98$	−4.78029	−	14.6613i	−0.482882	−	1.48101i
$99$		0			0
$100$	−15.4031	−	26.6790i	−1.54031	−	2.66790i
$101$	6.40829	−	11.0995i	0.637649	−	1.10444i	−0.348299	−	0.937384i	$-0.613240\pi$
$101$	6.40829	−	11.0995i	0.637649	−	1.10444i	0.985947	−	0.167056i	$-0.0534262\pi$
$102$		0			0
$103$	0.116274	−	0.201392i	0.0114568	−	0.0198437i	−0.860240	−	0.509889i	$-0.829686\pi$
$103$	0.116274	−	0.201392i	0.0114568	−	0.0198437i	0.871697	+	0.490045i	$0.163020\pi$
$104$	0.0411550	+	6.77651i	0.00403558	+	0.664492i
$105$		0			0
$106$	0.744348	+	1.28925i	0.0722975	+	0.125223i
$107$	−12.2876			−1.18789			−0.593943	−	0.804507i	$-0.702429\pi$
$107$	−12.2876			−1.18789			−0.593943	+	0.804507i	$0.702429\pi$
$108$		0			0
$109$	2.81785	+	4.88066i	0.269901	+	0.467483i	0.968836	−	0.247703i	$-0.0796756\pi$
$109$	2.81785	+	4.88066i	0.269901	+	0.467483i	−0.698935	+	0.715185i	$0.746342\pi$
$110$	22.9303	+	39.7164i	2.18632	+	3.78681i
$111$		0			0
$112$	−2.43332	+	3.35277i	−0.229927	+	0.316807i
$113$	−6.11906	+	10.5985i	−0.575632	+	0.997024i	0.420340	+	0.907367i	$0.361911\pi$
$113$	−6.11906	+	10.5985i	−0.575632	+	0.997024i	−0.995973	+	0.0896579i	$0.971423\pi$
$114$		0			0
$115$	0.240357	−	0.416311i	0.0224134	−	0.0388212i
$116$	2.76437	+	4.78802i	0.256665	+	0.444557i
$117$		0			0
$118$	4.89137			0.450287
$119$	4.14023	−	5.70466i	0.379534	−	0.522945i
$120$		0			0
$121$	−8.21649	−	14.2314i	−0.746954	−	1.29376i
$122$	5.58267	+	9.66947i	0.505431	+	0.875433i
$123$		0			0
$124$	11.4108	+	19.7641i	1.02472	+	1.77487i
$125$	−23.0415			−2.06090
$126$		0			0
$127$	−1.59001	−	2.75397i	−0.141090	−	0.244376i	0.786817	−	0.617186i	$-0.211727\pi$
$127$	−1.59001	−	2.75397i	−0.141090	−	0.244376i	−0.927907	+	0.372811i	$0.878394\pi$
$128$	−13.6680			−1.20809
$129$		0			0
$130$	27.4358	+	15.6187i	2.40628	+	1.36985i
$131$	1.57705	−	2.73152i	0.137787	−	0.238654i	−0.788872	−	0.614558i	$-0.789334\pi$
$131$	1.57705	−	2.73152i	0.137787	−	0.238654i	0.926659	+	0.375904i	$0.122668\pi$
$132$		0			0
$133$	−17.0257	−	1.78069i	−1.47632	−	0.154405i
$134$	15.4179	−	26.7046i	1.33190	−	2.30692i
$135$		0			0
$136$	5.00731			0.429373
$137$	−10.1389			−0.866222			−0.433111	−	0.901341i	$-0.642584\pi$
$137$	−10.1389			−0.866222			−0.433111	+	0.901341i	$0.642584\pi$
$138$		0			0
$139$	2.40158	−	4.15966i	0.203699	−	0.352817i	−0.746018	−	0.665925i	$-0.768037\pi$
$139$	2.40158	−	4.15966i	0.203699	−	0.352817i	0.949718	+	0.313108i	$0.101370\pi$
$140$	−12.2173	−	27.4029i	−1.03255	−	2.31597i
$141$		0			0
$142$	−11.3092	+	19.5881i	−0.949045	+	1.64379i
$143$	−16.4116	−	9.34281i	−1.37241	−	0.781285i
$144$		0			0
$145$	7.70176			0.639597
$146$	−0.798365	−	1.38281i	−0.0660731	−	0.114442i
$147$		0			0
$148$	10.4151			0.856112
$149$	2.70998	+	4.69383i	0.222011	+	0.384534i	0.955418	−	0.295255i	$-0.0954047\pi$
$149$	2.70998	+	4.69383i	0.222011	+	0.384534i	−0.733408	+	0.679789i	$0.762071\pi$
$150$		0			0
$151$	−7.81955	−	13.5439i	−0.636346	−	1.10218i	−0.986228	−	0.165390i	$-0.947112\pi$
$151$	−7.81955	−	13.5439i	−0.636346	−	1.10218i	0.349882	−	0.936794i	$-0.386222\pi$
$152$	−6.08038	−	10.5315i	−0.493184	−	0.854220i
$153$		0			0
$154$	12.4311	+	27.8823i	1.00172	+	2.24682i
$155$	31.7914			2.55355
$156$		0			0
$157$	2.31526	+	4.01015i	0.184778	+	0.320045i	0.943502	−	0.331368i	$-0.107510\pi$
$157$	2.31526	+	4.01015i	0.184778	+	0.320045i	−0.758724	+	0.651413i	$0.774177\pi$
$158$	−4.60898	+	7.98300i	−0.366671	+	0.635093i
$159$		0			0
$160$	−14.3252	+	24.8120i	−1.13251	+	1.96156i
$161$	0.187957	−	0.258979i	0.0148131	−	0.0204104i
$162$		0			0
$163$	−7.89229	−	13.6699i	−0.618172	−	1.07071i	−0.989819	−	0.142331i	$-0.954540\pi$
$163$	−7.89229	−	13.6699i	−0.618172	−	1.07071i	0.371647	−	0.928374i	$-0.378793\pi$
$164$	12.9517	+	22.4330i	1.01136	+	1.75172i
$165$		0			0
$166$	−30.1966			−2.34371
$167$	−3.03381	−	5.25471i	−0.234763	−	0.406621i	0.724441	−	0.689337i	$-0.242098\pi$
$167$	−3.03381	−	5.25471i	−0.234763	−	0.406621i	−0.959204	+	0.282716i	$0.908765\pi$
$168$		0			0
$169$	−12.9990	+	0.157897i	−0.999926	+	0.0121459i
$170$	11.6637	−	20.2021i	0.894562	−	1.54943i
$171$		0			0
$172$	2.13889	−	3.70466i	0.163089	−	0.282478i
$173$	0.714296	+	1.23720i	0.0543069	+	0.0940624i	0.891901	−	0.452231i	$-0.149372\pi$
$173$	0.714296	+	1.23720i	0.0543069	+	0.0940624i	−0.837594	+	0.546293i	$0.816038\pi$
$174$		0			0
$175$	−28.4118	−	2.97154i	−2.14773	−	0.224628i
$176$	4.10056	−	7.10237i	0.309091	−	0.535362i
$177$		0			0
$178$	−0.558574			−0.0418669
$179$	−10.0281	+	17.3692i	−0.749535	+	1.29823i	0.198511	+	0.980099i	$0.436389\pi$
$179$	−10.0281	+	17.3692i	−0.749535	+	1.29823i	−0.948046	+	0.318133i	$0.896944\pi$
$180$		0			0
$181$	13.2079			0.981739			0.490870	−	0.871233i	$-0.336679\pi$
$181$	13.2079			0.981739			0.490870	+	0.871233i	$0.336679\pi$
$182$	17.0826	+	12.2402i	1.26625	+	0.907305i
$183$		0			0
$184$	0.227321			0.0167583
$185$	7.25431	−	12.5648i	0.533347	−	0.923785i
$186$		0			0
$187$	−6.97700	+	12.0845i	−0.510209	+	0.883707i
$188$	−8.79647	+	15.2359i	−0.641548	+	1.11119i
$189$		0			0
$190$	−56.6528			−4.11003
$191$	0.0857988	+	0.148608i	0.00620819	+	0.0107529i	0.869113	−	0.494614i	$-0.164691\pi$
$191$	0.0857988	+	0.148608i	0.00620819	+	0.0107529i	−0.862905	+	0.505367i	$0.831357\pi$
$192$		0			0
$193$	−12.7178	+	22.0279i	−0.915450	+	1.58561i	−0.109208	+	0.994019i	$0.534831\pi$
$193$	−12.7178	+	22.0279i	−0.915450	+	1.58561i	−0.806242	+	0.591586i	$0.798502\pi$
$194$	14.2447	−	24.6725i	1.02271	−	1.77138i
$195$		0			0
$196$	−6.19111	−	18.9883i	−0.442222	−	1.35631i
$197$	−12.6455	−	21.9026i	−0.900953	−	1.56050i	−0.826260	−	0.563289i	$-0.809536\pi$
$197$	−12.6455	−	21.9026i	−0.900953	−	1.56050i	−0.0746927	−	0.997207i	$-0.523798\pi$
$198$		0			0
$199$	−17.1032			−1.21242			−0.606208	−	0.795306i	$-0.707310\pi$
$199$	−17.1032			−1.21242			−0.606208	+	0.795306i	$0.707310\pi$
$200$	−10.1467	−	17.5746i	−0.717480	−	1.24271i
$201$		0			0
$202$	14.1174	−	24.4520i	0.993296	−	1.72044i
$203$	5.09901	+	0.533297i	0.357881	+	0.0374301i
$204$		0			0
$205$	36.0845			2.52025
$206$	0.256149	−	0.443664i	0.0178468	−	0.0309115i
$207$		0			0
$208$	−0.0342860	−	5.64547i	−0.00237730	−	0.391443i
$209$	33.8887			2.34413
$210$		0			0
$211$	8.47490	+	14.6790i	0.583436	+	1.01054i	0.995068	+	0.0991908i	$0.0316254\pi$
$211$	8.47490	+	14.6790i	0.583436	+	1.01054i	−0.411632	+	0.911350i	$0.635041\pi$
$212$	0.964028	+	1.66975i	0.0662097	+	0.114679i
$213$		0			0
$214$	−27.0694			−1.85043
$215$	−2.97956	−	5.16075i	−0.203204	−	0.351960i
$216$		0			0
$217$	21.0478	+	2.20135i	1.42882	+	0.149437i
$218$	6.20770	+	10.7520i	0.420438	+	0.728220i
$219$		0			0
$220$	29.6977	+	51.4379i	2.00222	+	3.46795i
$221$	0.0583367	+	9.60563i	0.00392415	+	0.646144i
$222$		0			0
$223$	2.70463	+	4.68455i	0.181115	+	0.313701i	0.942261	−	0.334881i	$-0.108696\pi$
$223$	2.70463	+	4.68455i	0.181115	+	0.313701i	−0.761145	+	0.648581i	$0.775363\pi$
$224$	−11.2022	+	15.4351i	−0.748479	+	1.03130i
$225$		0			0
$226$	−13.4802	+	23.3484i	−0.896690	+	1.55311i
$227$	15.9364			1.05773			0.528867	−	0.848705i	$-0.322617\pi$
$227$	15.9364			1.05773			0.528867	+	0.848705i	$0.322617\pi$
$228$		0			0
$229$	5.73283	−	9.92955i	0.378836	−	0.656163i	−0.612057	−	0.790814i	$-0.709658\pi$
$229$	5.73283	−	9.92955i	0.378836	−	0.656163i	0.990893	+	0.134650i	$0.0429911\pi$
$230$	0.529504	−	0.917128i	0.0349145	−	0.0604736i
$231$		0			0
$232$	1.82101	+	3.15408i	0.119555	+	0.207076i
$233$	9.83721	−	17.0386i	0.644457	−	1.11623i	−0.339969	−	0.940437i	$-0.610417\pi$
$233$	9.83721	−	17.0386i	0.644457	−	1.11623i	0.984427	−	0.175796i	$-0.0562500\pi$
$234$		0			0
$235$	12.2539	+	21.2243i	0.799353	+	1.38452i
$236$	6.33497			0.412371
$237$		0			0
$238$	9.12088	−	12.5673i	0.591219	−	0.814617i
$239$	−0.192393			−0.0124449			−0.00622245	−	0.999981i	$-0.501981\pi$
$239$	−0.192393			−0.0124449			−0.00622245	+	0.999981i	$0.501981\pi$
$240$		0			0
$241$	12.6467			0.814648			0.407324	−	0.913284i	$-0.366462\pi$
$241$	12.6467			0.814648			0.407324	+	0.913284i	$0.366462\pi$
$242$	−18.1008	−	31.3516i	−1.16357	−	2.01535i
$243$		0			0
$244$	7.23029	+	12.5232i	0.462872	+	0.801718i
$245$	−27.2199	−	5.75674i	−1.73902	−	0.367785i
$246$		0			0
$247$	20.1320	−	11.7868i	1.28097	−	0.749978i
$248$	7.51678	+	13.0194i	0.477316	+	0.826736i
$249$		0			0
$250$	−50.7602			−3.21036
$251$	−1.61782	+	2.80215i	−0.102116	+	0.176870i	−0.912556	−	0.408951i	$-0.865895\pi$
$251$	−1.61782	+	2.80215i	−0.102116	+	0.176870i	0.810440	+	0.585821i	$0.199228\pi$
$252$		0			0
$253$	−0.316740	+	0.548610i	−0.0199133	+	0.0344908i
$254$	−3.50277	−	6.06697i	−0.219783	−	0.380676i
$255$		0			0
$256$	−4.61331			−0.288332
$257$	−2.13109			−0.132934			−0.0664668	−	0.997789i	$-0.521173\pi$
$257$	−2.13109			−0.132934			−0.0664668	+	0.997789i	$0.521173\pi$
$258$		0			0
$259$	5.67281	−	7.81633i	0.352491	−	0.485683i
$260$	35.5329	+	20.2282i	2.20366	+	1.25450i
$261$		0			0
$262$	3.47422	−	6.01752i	0.214638	−	0.371763i
$263$	6.35331	−	11.0043i	0.391762	−	0.678552i	−0.600920	−	0.799309i	$-0.705199\pi$
$263$	6.35331	−	11.0043i	0.391762	−	0.678552i	0.992682	+	0.120757i	$0.0385323\pi$
$264$		0			0
$265$	2.68586			0.164991
$266$	−37.5074	−	3.92284i	−2.29973	−	0.240525i
$267$		0			0
$268$	19.9682	−	34.5859i	1.21975	−	2.11267i
$269$	25.6727			1.56529			0.782646	−	0.622467i	$-0.213869\pi$
$269$	25.6727			1.56529			0.782646	+	0.622467i	$0.213869\pi$
$270$		0			0
$271$	−15.1084			−0.917770			−0.458885	−	0.888496i	$-0.651751\pi$
$271$	−15.1084			−0.917770			−0.458885	+	0.888496i	$0.651751\pi$
$272$	−4.17156			−0.252938
$273$		0			0
$274$	−22.3358			−1.34936
$275$	56.5521			3.41022
$276$		0			0
$277$	13.5695			0.815311			0.407655	−	0.913136i	$-0.366346\pi$
$277$	13.5695			0.815311			0.407655	+	0.913136i	$0.366346\pi$
$278$	5.29065	−	9.16367i	0.317312	−	0.549601i
$279$		0			0
$280$	−8.04809	−	18.0515i	−0.480965	−	1.07878i
$281$	−6.47090			−0.386021			−0.193011	−	0.981197i	$-0.561825\pi$
$281$	−6.47090			−0.386021			−0.193011	+	0.981197i	$0.561825\pi$
$282$		0			0
$283$	8.80760	−	15.2552i	0.523557	−	0.906828i	−0.476067	−	0.879409i	$-0.657938\pi$
$283$	8.80760	−	15.2552i	0.523557	−	0.906828i	0.999624	−	0.0274188i	$-0.00872877\pi$
$284$	−14.6469	+	25.3691i	−0.869132	+	1.50538i
$285$		0			0
$286$	−36.1546	−	20.5821i	−2.13786	−	1.21705i
$287$	23.8901	+	2.49862i	1.41019	+	0.147489i
$288$		0			0
$289$	−9.90219			−0.582482
$290$	16.9669			0.996331
$291$		0			0
$292$	−1.03399	−	1.79092i	−0.0605095	−	0.104806i
$293$	−3.94143	+	6.82676i	−0.230261	+	0.398824i	−0.957885	−	0.287153i	$-0.907291\pi$
$293$	−3.94143	+	6.82676i	−0.230261	+	0.398824i	0.727624	+	0.685976i	$0.240625\pi$
$294$		0			0
$295$	4.41244	−	7.64257i	0.256902	−	0.444968i
$296$	6.86085			0.398779
$297$		0			0
$298$	5.97006	+	10.3405i	0.345837	+	0.599006i
$299$	0.00264836	+	0.436074i	0.000153158	+	0.0252188i
$300$		0			0
$301$	−1.61529	−	3.62303i	−0.0931040	−	0.208828i
$302$	−17.2264	−	29.8370i	−0.991267	−	1.71693i
$303$		0			0
$304$	5.06553	+	8.77376i	0.290528	+	0.503209i
$305$	20.1442			1.15345
$306$		0			0
$307$	−19.0783			−1.08885			−0.544427	−	0.838808i	$-0.683253\pi$
$307$	−19.0783			−1.08885			−0.544427	+	0.838808i	$0.683253\pi$
$308$	16.0999	+	36.1113i	0.917375	+	2.05763i
$309$		0			0
$310$	70.0362			3.97779
$311$	10.6629	+	18.4686i	0.604635	+	1.04726i	0.992109	+	0.125378i	$0.0400143\pi$
$311$	10.6629	+	18.4686i	0.604635	+	1.04726i	−0.387474	+	0.921881i	$0.626652\pi$
$312$		0			0
$313$	6.27658	−	10.8714i	0.354773	−	0.614485i	−0.632306	−	0.774719i	$-0.717891\pi$
$313$	6.27658	−	10.8714i	0.354773	−	0.614485i	0.987079	+	0.160233i	$0.0512247\pi$
$314$	5.10049	+	8.83432i	0.287838	+	0.498549i
$315$		0			0
$316$	−5.96924	+	10.3390i	−0.335796	+	0.581616i
$317$	6.11756	−	10.5959i	0.343596	−	0.595126i	−0.641502	−	0.767122i	$-0.721688\pi$
$317$	6.11756	−	10.5959i	0.343596	−	0.595126i	0.985098	+	0.171996i	$0.0550215\pi$
$318$		0			0
$319$	−10.1493			−0.568252
$320$	−25.3350	+	43.8814i	−1.41627	+	2.45305i
$321$		0			0
$322$	0.414067	−	0.570527i	0.0230751	−	0.0317942i
$323$	−8.61887	−	14.9283i	−0.479567	−	0.830634i
$324$		0			0
$325$	33.5955	−	19.6694i	1.86354	−	1.09106i
$326$	−17.3866	−	30.1145i	−0.962956	−	1.66789i
$327$		0			0
$328$	8.53185	+	14.7776i	0.471092	+	0.815956i
$329$	6.64312	+	14.9002i	0.366247	+	0.821476i
$330$		0			0
$331$	2.19019	+	3.79352i	0.120384	+	0.208510i	0.919919	−	0.392108i	$-0.128254\pi$
$331$	2.19019	+	3.79352i	0.120384	+	0.208510i	−0.799535	+	0.600619i	$0.794921\pi$
$332$	−39.1085			−2.14636
$333$		0			0
$334$	−6.68344	−	11.5761i	−0.365702	−	0.633414i
$335$	−27.8166	−	48.1797i	−1.51978	−	2.63234i
$336$		0			0
$337$	−8.22172			−0.447866			−0.223933	−	0.974605i	$-0.571890\pi$
$337$	−8.22172			−0.447866			−0.223933	+	0.974605i	$0.571890\pi$
$338$	−28.6367	+	0.347845i	−1.55763	+	0.0189203i
$339$		0			0
$340$	15.1060	−	26.1643i	0.819236	−	1.41896i
$341$	−41.8944			−2.26871
$342$		0			0
$343$	−17.6226	−	5.69610i	−0.951528	−	0.307561i
$344$	1.40898	−	2.44042i	0.0759670	−	0.131579i
$345$		0			0
$346$	1.57359	+	2.72553i	0.0845965	+	0.146525i
$347$	0.0705385			0.00378671			0.00189335	−	0.999998i	$-0.499397\pi$
$347$	0.0705385			0.00378671			0.00189335	+	0.999998i	$0.499397\pi$
$348$		0			0
$349$	−16.2677	−	28.1764i	−0.870789	−	1.50825i	−0.861182	−	0.508296i	$-0.830275\pi$
$349$	−16.2677	−	28.1764i	−0.870789	−	1.50825i	−0.00960659	−	0.999954i	$-0.503058\pi$
$350$	−62.5909	−	6.54628i	−3.34563	−	0.349913i
$351$		0			0
$352$	18.8776	−	32.6970i	1.00618	−	1.74276i
$353$	−3.61431	+	6.26018i	−0.192371	+	0.333196i	−0.946035	−	0.324063i	$-0.894951\pi$
$353$	−3.61431	+	6.26018i	−0.192371	+	0.333196i	0.753665	+	0.657259i	$0.228284\pi$
$354$		0			0
$355$	20.4037	+	35.3403i	1.08292	+	1.87567i
$356$	−0.723427			−0.0383415
$357$		0			0
$358$	−22.0918	+	38.2641i	−1.16759	+	2.02232i
$359$	−5.51794	+	9.55735i	−0.291226	+	0.504418i	−0.974100	−	0.226118i	$-0.927396\pi$
$359$	−5.51794	+	9.55735i	−0.291226	+	0.504418i	0.682874	+	0.730536i	$0.260730\pi$
$360$		0			0
$361$	−11.4318	+	19.8005i	−0.601675	+	1.04213i
$362$	29.0970			1.52930
$363$		0			0
$364$	22.1242	+	15.8527i	1.15962	+	0.830906i
$365$	−2.88078			−0.150787
$366$		0			0
$367$	5.95873	−	10.3208i	0.311043	−	0.538742i	−0.667545	−	0.744569i	$-0.732655\pi$
$367$	5.95873	−	10.3208i	0.311043	−	0.538742i	0.978588	+	0.205827i	$0.0659883\pi$
$368$	−0.189379			−0.00987208
$369$		0			0
$370$	15.9812	−	27.6802i	0.830821	−	1.43902i
$371$	1.77820	+	0.185979i	0.0923195	+	0.00965554i
$372$		0			0
$373$	1.32566	+	2.29612i	0.0686402	+	0.118888i	0.898303	−	0.439377i	$-0.144801\pi$
$373$	1.32566	+	2.29612i	0.0686402	+	0.118888i	−0.829663	+	0.558265i	$0.811467\pi$
$374$	−15.3702	+	26.6220i	−0.794776	+	1.37659i
$375$		0			0
$376$	−5.79462	+	10.0366i	−0.298834	+	0.517596i
$377$	−6.02932	+	3.53003i	−0.310526	+	0.181806i
$378$		0			0
$379$	−4.37607	−	7.57957i	−0.224783	−	0.389336i	0.731471	−	0.681873i	$-0.238834\pi$
$379$	−4.37607	−	7.57957i	−0.224783	−	0.389336i	−0.956254	+	0.292536i	$0.905501\pi$
$380$	−73.3728			−3.76395
$381$		0			0
$382$	0.189014	+	0.327382i	0.00967079	+	0.0167503i
$383$	3.46122	+	5.99501i	0.176860	+	0.306331i	0.940803	−	0.338953i	$-0.110073\pi$
$383$	3.46122	+	5.99501i	0.176860	+	0.306331i	−0.763943	+	0.645283i	$0.776739\pi$
$384$		0			0
$385$	54.7789	+	5.72924i	2.79179	+	0.291989i
$386$	−28.0172	+	48.5273i	−1.42604	+	2.46997i
$387$		0			0
$388$	18.4487	−	31.9541i	0.936592	−	1.62223i
$389$	11.3592	+	19.6747i	0.575933	+	0.997545i	0.995940	+	0.0900237i	$0.0286943\pi$
$389$	11.3592	+	19.6747i	0.575933	+	0.997545i	−0.420007	+	0.907521i	$0.637972\pi$
$390$		0			0
$391$	0.322224			0.0162956
$392$	−4.07835	−	12.5084i	−0.205988	−	0.631771i
$393$		0			0
$394$	−27.8578	−	48.2512i	−1.40346	−	2.43086i
$395$	8.31541	+	14.4027i	0.418394	+	0.724679i
$396$		0			0
$397$	−12.3811	−	21.4446i	−0.621388	−	1.07628i	−0.989228	−	0.146386i	$-0.953236\pi$
$397$	−12.3811	−	21.4446i	−0.621388	−	1.07628i	0.367840	−	0.929889i	$-0.380098\pi$
$398$	−37.6782			−1.88864
$399$		0			0
$400$	8.45316	+	14.6413i	0.422658	+	0.732065i
$401$	18.4572			0.921707			0.460854	−	0.887476i	$-0.347543\pi$
$401$	18.4572			0.921707			0.460854	+	0.887476i	$0.347543\pi$
$402$		0			0
$403$	−24.8879	+	14.5713i	−1.23976	+	0.725847i
$404$	18.2839	−	31.6686i	0.909657	−	1.57557i
$405$		0			0
$406$	11.2331	+	1.17485i	0.557488	+	0.0583067i
$407$	−9.55965	+	16.5578i	−0.473854	+	0.820740i
$408$		0			0
$409$	1.82016			0.0900010			0.0450005	−	0.998987i	$-0.485671\pi$
$409$	1.82016			0.0900010			0.0450005	+	0.998987i	$0.485671\pi$
$410$	79.4938			3.92592
$411$		0			0
$412$	0.331747	−	0.574603i	0.0163440	−	0.0283086i
$413$	3.45049	−	4.75429i	0.169788	−	0.233944i
$414$		0			0
$415$	−27.2399	+	47.1809i	−1.33716	+	2.31602i
$416$	−0.157842	−	25.9899i	−0.00773882	−	1.27426i
$417$		0			0
$418$	74.6564			3.65157
$419$	−1.35670	−	2.34988i	−0.0662793	−	0.114799i	0.830981	−	0.556300i	$-0.187779\pi$
$419$	−1.35670	−	2.34988i	−0.0662793	−	0.114799i	−0.897261	+	0.441501i	$0.854446\pi$
$420$		0			0
$421$	−2.33278			−0.113693			−0.0568463	−	0.998383i	$-0.518104\pi$
$421$	−2.33278			−0.113693			−0.0568463	+	0.998383i	$0.518104\pi$
$422$	18.6701	+	32.3376i	0.908846	+	1.57417i
$423$		0			0
$424$	0.635047	+	1.09993i	0.0308406	+	0.0534175i
$425$	−14.3828	−	24.9118i	−0.697670	−	1.20840i
$426$		0			0
$427$	13.3366	+	1.39486i	0.645405	+	0.0675019i
$428$	−35.0584			−1.69461
$429$		0			0
$430$	−6.56394	−	11.3691i	−0.316541	−	0.548266i
$431$	−4.30893	+	7.46329i	−0.207554	+	0.359494i	−0.950943	−	0.309365i	$-0.899884\pi$
$431$	−4.30893	+	7.46329i	−0.207554	+	0.359494i	0.743390	+	0.668859i	$0.233217\pi$
$432$		0			0
$433$	2.53375	−	4.38858i	0.121764	−	0.210902i	−0.798699	−	0.601730i	$-0.794478\pi$
$433$	2.53375	−	4.38858i	0.121764	−	0.210902i	0.920463	+	0.390829i	$0.127811\pi$
$434$	46.3680	+	4.84955i	2.22574	+	0.232786i
$435$		0			0
$436$	8.03978	+	13.9253i	0.385036	+	0.666901i
$437$	−0.391278	−	0.677713i	−0.0187173	−	0.0324194i
$438$		0			0
$439$	−1.45113			−0.0692586			−0.0346293	−	0.999400i	$-0.511025\pi$
$439$	−1.45113			−0.0692586			−0.0346293	+	0.999400i	$0.511025\pi$
$440$	19.5632	+	33.8844i	0.932638	+	1.61538i
$441$		0			0
$442$	0.128515	+	21.1611i	0.00611284	+	1.00653i
$443$	−9.05774	+	15.6885i	−0.430346	+	0.745381i	−0.996903	−	0.0786412i	$-0.974942\pi$
$443$	−9.05774	+	15.6885i	−0.430346	+	0.745381i	0.566557	+	0.824023i	$0.308275\pi$
$444$		0			0
$445$	−0.503882	+	0.872750i	−0.0238863	+	0.0413723i
$446$	5.95826	+	10.3200i	0.282132	+	0.488667i
$447$		0			0
$448$	−19.8117	+	27.2978i	−0.936016	+	1.28970i
$449$	−4.27784	+	7.40943i	−0.201884	+	0.349673i	−0.949135	−	0.314868i	$-0.898040\pi$
$449$	−4.27784	+	7.40943i	−0.201884	+	0.349673i	0.747252	+	0.664541i	$0.231373\pi$
$450$		0			0
$451$	−47.5518			−2.23913
$452$	−17.4586	+	30.2393i	−0.821185	+	1.42233i
$453$		0			0
$454$	35.1076			1.64768
$455$	34.5348	−	15.6491i	1.61902	−	0.733642i
$456$		0			0
$457$	−8.54438			−0.399689			−0.199845	−	0.979828i	$-0.564044\pi$
$457$	−8.54438			−0.399689			−0.199845	+	0.979828i	$0.564044\pi$
$458$	12.6294	−	21.8747i	0.590131	−	1.02214i
$459$		0			0
$460$	0.685777	−	1.18780i	0.0319745	−	0.0553815i
$461$	11.7203	−	20.3001i	0.545867	−	0.945470i	−0.452685	−	0.891671i	$-0.649534\pi$
$461$	11.7203	−	20.3001i	0.545867	−	0.945470i	0.998552	−	0.0537989i	$-0.0171330\pi$
$462$		0			0
$463$	22.9217			1.06526			0.532630	−	0.846348i	$-0.321204\pi$
$463$	22.9217			1.06526			0.532630	+	0.846348i	$0.321204\pi$
$464$	−1.51707	−	2.62764i	−0.0704283	−	0.121985i
$465$		0			0
$466$	21.6713	−	37.5357i	1.00390	−	1.73881i
$467$	−5.81820	+	10.0774i	−0.269234	+	0.466327i	−0.968664	−	0.248374i	$-0.920104\pi$
$467$	−5.81820	+	10.0774i	−0.269234	+	0.466327i	0.699430	+	0.714701i	$0.253437\pi$
$468$		0			0
$469$	−15.0800	−	33.8239i	−0.696332	−	1.56184i
$470$	26.9951	+	46.7569i	1.24519	+	2.15673i
$471$		0			0
$472$	4.17312			0.192083
$473$	3.92643	+	6.80078i	0.180538	+	0.312700i
$474$		0			0
$475$	−34.9302	+	60.5009i	−1.60271	+	2.77597i
$476$	11.8127	−	16.2763i	0.541436	−	0.746023i
$477$		0			0
$478$	−0.423841			−0.0193860
$479$	9.30624	−	16.1189i	0.425213	−	0.736491i	−0.571227	−	0.820792i	$-0.693533\pi$
$479$	9.30624	−	16.1189i	0.425213	−	0.736491i	0.996440	+	0.0843014i	$0.0268658\pi$
$480$		0			0
$481$	0.0799311	+	13.1613i	0.00364454	+	0.600104i
$482$	27.8606			1.26902
$483$		0			0
$484$	−23.4430	−	40.6044i	−1.06559	−	1.84565i
$485$	−25.6999	−	44.5135i	−1.16697	−	2.02125i
$486$		0			0
$487$	−30.0759			−1.36287			−0.681434	−	0.731879i	$-0.738643\pi$
$487$	−30.0759			−1.36287			−0.681434	+	0.731879i	$0.738643\pi$
$488$	4.76291	+	8.24960i	0.215607	+	0.373442i
$489$		0			0
$490$	−59.9652	−	12.6820i	−2.70895	−	0.572916i
$491$	−6.52770	−	11.3063i	−0.294591	−	0.510246i	0.680299	−	0.732935i	$-0.261850\pi$
$491$	−6.52770	−	11.3063i	−0.294591	−	0.510246i	−0.974890	+	0.222689i	$0.928517\pi$
$492$		0			0
$493$	2.58126	+	4.47087i	0.116254	+	0.201358i
$494$	44.3506	−	25.9662i	1.99543	−	1.16828i
$495$		0			0
$496$	−6.26219	−	10.8464i	−0.281180	−	0.487019i
$497$	11.0614	+	24.8101i	0.496170	+	1.11289i
$498$		0			0
$499$	12.1509	−	21.0461i	0.543951	−	0.942151i	−0.454721	−	0.890634i	$-0.650261\pi$
$499$	12.1509	−	21.0461i	0.543951	−	0.942151i	0.998672	−	0.0515169i	$-0.0164056\pi$
$500$	−65.7411			−2.94003
$501$		0			0
$502$	−3.56405	+	6.17311i	−0.159071	+	0.275519i
$503$	0.976641	−	1.69159i	0.0435463	−	0.0754244i	−0.843431	−	0.537238i	$-0.819468\pi$
$503$	0.976641	−	1.69159i	0.0435463	−	0.0754244i	0.886977	+	0.461814i	$0.152801\pi$
$504$		0			0
$505$	−25.4702	−	44.1157i	−1.13341	−	1.96312i
$506$	−0.697775	+	1.20858i	−0.0310199	+	0.0537280i
$507$		0			0
$508$	−4.53654	−	7.85753i	−0.201277	−	0.348621i
$509$	−26.3433			−1.16765			−0.583823	−	0.811881i	$-0.698444\pi$
$509$	−26.3433			−1.16765			−0.583823	+	0.811881i	$0.698444\pi$
$510$		0			0
$511$	−1.90724	−	0.199475i	−0.0843714	−	0.00882426i
$512$	17.1728			0.758939
$513$		0			0
$514$	−4.69476			−0.207077
$515$	−0.462138	−	0.800446i	−0.0203642	−	0.0352719i
$516$		0			0
$517$	−16.1480	−	27.9692i	−0.710188	−	1.23008i
$518$	12.4971	−	17.2193i	0.549092	−	0.756572i
$519$		0			0
$520$	23.4071	+	13.3252i	1.02647	+	0.584349i
$521$	−15.0429	−	26.0551i	−0.659043	−	1.14150i	−0.980864	−	0.194695i	$-0.937628\pi$
$521$	−15.0429	−	26.0551i	−0.659043	−	1.14150i	0.321821	−	0.946801i	$-0.395705\pi$
$522$		0			0
$523$	27.2949			1.19352			0.596762	−	0.802418i	$-0.296454\pi$
$523$	27.2949			1.19352			0.596762	+	0.802418i	$0.296454\pi$
$524$	4.49956	−	7.79347i	0.196564	−	0.340459i
$525$		0			0
$526$	13.9963	−	24.2423i	0.610267	−	1.05701i
$527$	10.6550	+	18.4549i	0.464137	+	0.803909i
$528$		0			0
$529$	−22.9854			−0.999364
$530$	5.91693			0.257015
$531$		0			0
$532$	−48.5771	−	5.08059i	−2.10608	−	0.220272i
$533$	−28.2488	+	16.5390i	−1.22359	+	0.716383i
$534$		0			0
$535$	−24.4190	+	42.2949i	−1.05572	+	1.82857i
$536$	13.1539	−	22.7833i	0.568163	−	0.984087i
$537$		0			0
$538$	56.5567			2.43833
$539$	35.8701	+	7.58618i	1.54504	+	0.326760i
$540$		0			0
$541$	2.22209	−	3.84877i	0.0955350	−	0.165471i	−0.814297	−	0.580449i	$-0.802877\pi$
$541$	2.22209	−	3.84877i	0.0955350	−	0.165471i	0.909832	+	0.414977i	$0.136210\pi$
$542$	−33.2836			−1.42965
$543$		0			0
$544$	−19.2045			−0.823387
$545$	22.3995			0.959490
$546$		0			0
$547$	3.18590			0.136219			0.0681095	−	0.997678i	$-0.478303\pi$
$547$	3.18590			0.136219			0.0681095	+	0.997678i	$0.478303\pi$
$548$	−28.9278			−1.23574
$549$		0			0
$550$	124.584			5.31227
$551$	6.26885	−	10.8580i	0.267062	−	0.462565i
$552$		0			0
$553$	4.50799	+	10.1112i	0.191699	+	0.429973i
$554$	29.8934			1.27005
$555$		0			0
$556$	6.85209	−	11.8682i	0.290593	−	0.503322i
$557$	18.0888	−	31.3307i	0.766448	−	1.32753i	−0.173030	−	0.984917i	$-0.555356\pi$
$557$	18.0888	−	31.3307i	0.766448	−	1.32753i	0.939478	−	0.342610i	$-0.111311\pi$
$558$		0			0
$559$	4.69793	+	2.67444i	0.198701	+	0.113117i
$560$	6.70481	+	15.0386i	0.283330	+	0.635497i
$561$		0			0
$562$	−14.2553			−0.601324
$563$	−1.22095			−0.0514568			−0.0257284	−	0.999669i	$-0.508191\pi$
$563$	−1.22095			−0.0514568			−0.0257284	+	0.999669i	$0.508191\pi$
$564$		0			0
$565$	24.3206	+	42.1246i	1.02318	+	1.77219i
$566$	19.4030	−	33.6071i	0.815571	−	1.41261i
$567$		0			0
$568$	−9.64853	+	16.7117i	−0.404843	+	0.701209i
$569$	40.2208			1.68614			0.843072	−	0.537801i	$-0.180745\pi$
$569$	40.2208			1.68614			0.843072	+	0.537801i	$0.180745\pi$
$570$		0			0
$571$	5.24994	+	9.09316i	0.219703	+	0.380537i	0.954717	−	0.297515i	$-0.0961578\pi$
$571$	5.24994	+	9.09316i	0.219703	+	0.380537i	−0.735014	+	0.678052i	$0.762825\pi$
$572$	−46.8249	−	26.6565i	−1.95785	−	1.11457i
$573$		0			0
$574$	52.6295	+	5.50443i	2.19671	+	0.229751i
$575$	−0.652948	−	1.13094i	−0.0272298	−	0.0471634i
$576$		0			0
$577$	11.4400	+	19.8146i	0.476252	+	0.824893i	0.999630	−	0.0272078i	$-0.00866158\pi$
$577$	11.4400	+	19.8146i	0.476252	+	0.824893i	−0.523378	+	0.852101i	$0.675328\pi$
$578$	−21.8144			−0.907360
$579$		0			0
$580$	21.9744			0.912436
$581$	−21.3014	+	29.3503i	−0.883731	+	1.21766i
$582$		0			0
$583$	−3.53940			−0.146587
$584$	−0.681132	−	1.17976i	−0.0281855	−	0.0488186i
$585$		0			0
$586$	−8.68293	+	15.0393i	−0.358689	+	0.621267i
$587$	−8.19671	−	14.1971i	−0.338314	−	0.585977i	0.645802	−	0.763505i	$-0.276523\pi$
$587$	−8.19671	−	14.1971i	−0.338314	−	0.585977i	−0.984116	+	0.177528i	$0.943190\pi$
$588$		0			0
$589$	25.8767	−	44.8197i	1.06623	−	1.84676i
$590$	9.72056	−	16.8365i	0.400189	−	0.693148i
$591$		0			0
$592$	−5.71573			−0.234915
$593$	10.1736	−	17.6211i	0.417778	−	0.723613i	−0.577938	−	0.816081i	$-0.696142\pi$
$593$	10.1736	−	17.6211i	0.417778	−	0.723613i	0.995716	+	0.0924682i	$0.0294757\pi$
$594$		0			0
$595$	−11.4081	−	25.5878i	−0.467685	−	1.04900i
$596$	7.73202	+	13.3922i	0.316716	+	0.548568i
$597$		0			0
$598$	0.00583430	+	0.960666i	0.000238582	+	0.0392845i
$599$	19.8375	+	34.3596i	0.810540	+	1.40390i	0.912487	+	0.409106i	$0.134159\pi$
$599$	19.8375	+	34.3596i	0.810540	+	1.40390i	−0.101947	+	0.994790i	$0.532507\pi$
$600$		0			0
$601$	−14.3611	−	24.8742i	−0.585803	−	1.01464i	−0.994775	−	0.102093i	$-0.967446\pi$
$601$	−14.3611	−	24.8742i	−0.585803	−	1.01464i	0.408972	−	0.912547i	$-0.365887\pi$
$602$	−3.55847	−	7.98150i	−0.145033	−	0.325302i
$603$		0			0
$604$	−22.3104	−	38.6428i	−0.907799	−	1.57235i
$605$	−65.3141			−2.65539
$606$		0			0
$607$	13.8195	+	23.9361i	0.560917	+	0.971536i	0.997417	+	0.0718318i	$0.0228845\pi$
$607$	13.8195	+	23.9361i	0.560917	+	0.971536i	−0.436500	+	0.899704i	$0.643782\pi$
$608$	23.3201	+	40.3916i	0.945754	+	1.63809i
$609$		0			0
$610$	44.3775			1.79679
$611$	−19.3209	−	10.9990i	−0.781639	−	0.444972i
$612$		0			0
$613$	14.9175	−	25.8380i	0.602514	−	1.04359i	−0.389925	−	0.920847i	$-0.627499\pi$
$613$	14.9175	−	25.8380i	0.602514	−	1.04359i	0.992439	−	0.122738i	$-0.0391676\pi$
$614$	−42.0292			−1.69616
$615$		0			0
$616$	10.6057	+	23.7881i	0.427315	+	0.958449i
$617$	18.3807	−	31.8364i	0.739981	−	1.28168i	−0.212522	−	0.977156i	$-0.568168\pi$
$617$	18.3807	−	31.8364i	0.739981	−	1.28168i	0.952503	−	0.304529i	$-0.0984989\pi$
$618$		0			0
$619$	16.7456	+	29.0042i	0.673061	+	1.16578i	0.977032	+	0.213095i	$0.0683543\pi$
$619$	16.7456	+	29.0042i	0.673061	+	1.16578i	−0.303970	+	0.952682i	$0.598312\pi$
$620$	90.7060			3.64284
$621$		0			0
$622$	23.4901	+	40.6861i	0.941869	+	1.63137i
$623$	−0.394032	+	0.542920i	−0.0157865	+	0.0217516i
$624$		0			0
$625$	−18.7970	+	32.5574i	−0.751881	+	1.30230i
$626$	13.8272	−	23.9495i	0.552648	−	0.957214i
$627$		0			0
$628$	6.60581	+	11.4416i	0.263600	+	0.456569i
$629$	9.72518			0.387768
$630$		0			0
$631$	−2.53344	+	4.38805i	−0.100855	+	0.174685i	−0.912037	−	0.410108i	$-0.865491\pi$
$631$	−2.53344	+	4.38805i	−0.100855	+	0.174685i	0.811182	+	0.584793i	$0.198824\pi$
$632$	−3.93220	+	6.81077i	−0.156414	+	0.270918i
$633$		0			0
$634$	13.4769	−	23.3427i	0.535236	−	0.927056i
$635$	−12.6392			−0.501571
$636$		0			0
$637$	23.9477	−	7.96931i	0.948841	−	0.315756i
$638$	−22.3588			−0.885193
$639$		0			0
$640$	−27.1621	+	47.0462i	−1.07368	+	1.85966i
$641$	−23.1304			−0.913596			−0.456798	−	0.889571i	$-0.651004\pi$
$641$	−23.1304			−0.913596			−0.456798	+	0.889571i	$0.651004\pi$
$642$		0			0
$643$	16.5920	−	28.7382i	0.654325	−	1.13332i	−0.327738	−	0.944769i	$-0.606286\pi$
$643$	16.5920	−	28.7382i	0.654325	−	1.13332i	0.982063	−	0.188555i	$-0.0603804\pi$
$644$	0.536272	−	0.738907i	0.0211321	−	0.0291170i
$645$		0			0
$646$	−18.9873	−	32.8869i	−0.747045	−	1.29392i
$647$	11.9951	−	20.7761i	0.471576	−	0.816793i	−0.527896	−	0.849309i	$-0.677019\pi$
$647$	11.9951	−	20.7761i	0.471576	−	0.816793i	0.999471	+	0.0325163i	$0.0103521\pi$
$648$		0			0
$649$	−5.81467	+	10.0713i	−0.228246	+	0.395333i
$650$	74.0105	−	43.3314i	2.90293	−	1.69960i
$651$		0			0
$652$	−22.5180	−	39.0023i	−0.881872	−	1.52745i
$653$	16.6097			0.649987			0.324994	−	0.945716i	$-0.394638\pi$
$653$	16.6097			0.649987			0.324994	+	0.945716i	$0.394638\pi$
$654$		0			0
$655$	−6.26809	−	10.8566i	−0.244914	−	0.424204i
$656$	−7.10783	−	12.3111i	−0.277514	−	0.480669i
$657$		0			0
$658$	14.6347	+	32.8250i	0.570520	+	1.27965i
$659$	−9.95720	+	17.2464i	−0.387878	+	0.671824i	−0.992164	−	0.124944i	$-0.960125\pi$
$659$	−9.95720	+	17.2464i	−0.387878	+	0.671824i	0.604286	+	0.796767i	$0.293458\pi$
$660$		0			0
$661$	14.2839	−	24.7405i	0.555581	−	0.962294i	−0.442277	−	0.896878i	$-0.645829\pi$
$661$	14.2839	−	24.7405i	0.555581	−	0.962294i	0.997858	−	0.0654159i	$-0.0208374\pi$
$662$	4.82496	+	8.35707i	0.187527	+	0.324807i
$663$		0			0
$664$	−25.7625			−0.999779
$665$	−39.9642	+	55.0651i	−1.54975	+	2.13533i
$666$		0			0
$667$	0.117183	+	0.202968i	0.00453736	+	0.00785894i
$668$	−8.65593	−	14.9925i	−0.334908	−	0.580078i
$669$		0			0
$670$	−61.2796	−	106.139i	−2.36744	−	4.10052i
$671$	−26.5458			−1.02479
$672$		0			0
$673$	23.9929	+	41.5569i	0.924858	+	1.60190i	0.791789	+	0.610795i	$0.209150\pi$
$673$	23.9929	+	41.5569i	0.924858	+	1.60190i	0.133069	+	0.991107i	$0.457517\pi$
$674$	−18.1124			−0.697662
$675$		0			0
$676$	−37.0883	+	0.450505i	−1.42647	+	0.0173271i
$677$	14.8127	−	25.6564i	0.569299	−	0.986055i	−0.427336	−	0.904093i	$-0.640548\pi$
$677$	14.8127	−	25.6564i	0.569299	−	0.986055i	0.996635	−	0.0819626i	$-0.0261188\pi$
$678$		0			0
$679$	−13.9325	−	31.2501i	−0.534682	−	1.19927i
$680$	9.95096	−	17.2356i	0.381602	−	0.660954i
$681$		0			0
$682$	−92.2929			−3.53408
$683$	2.52910			0.0967734			0.0483867	−	0.998829i	$-0.484592\pi$
$683$	2.52910			0.0967734			0.0483867	+	0.998829i	$0.484592\pi$
$684$		0			0
$685$	−20.1488	+	34.8988i	−0.769848	+	1.33342i
$686$	−38.8223	−	12.5485i	−1.48224	−	0.479102i
$687$		0			0
$688$	−1.17381	+	2.03310i	−0.0447511	+	0.0775112i
$689$	−2.10263	+	1.23104i	−0.0801038	+	0.0468989i
$690$		0			0
$691$	31.1565			1.18525			0.592625	−	0.805478i	$-0.298091\pi$
$691$	31.1565			1.18525			0.592625	+	0.805478i	$0.298091\pi$
$692$	2.03800	+	3.52992i	0.0774732	+	0.134187i
$693$		0			0
$694$	0.155396			0.00589874
$695$	−9.54525	−	16.5329i	−0.362072	−	0.627127i
$696$		0			0
$697$	12.0938	+	20.9471i	0.458085	+	0.793427i
$698$	−35.8375	−	62.0724i	−1.35647	−	2.34947i
$699$		0			0
$700$	−81.0635	−	8.47829i	−3.06391	−	0.320449i
$701$	−12.7508			−0.481591			−0.240795	−	0.970576i	$-0.577408\pi$
$701$	−12.7508			−0.481591			−0.240795	+	0.970576i	$0.577408\pi$
$702$		0			0
$703$	−11.8093	−	20.4543i	−0.445396	−	0.771449i
$704$	33.3861	−	57.8265i	1.25829	−	2.17942i
$705$		0			0
$706$	−7.96229	+	13.7911i	−0.299665	+	0.519035i
$707$	−13.8080	−	30.9708i	−0.519305	−	1.16478i
$708$		0			0
$709$	22.5627	+	39.0797i	0.847359	+	1.46767i	0.883557	+	0.468324i	$0.155142\pi$
$709$	22.5627	+	39.0797i	0.847359	+	1.46767i	−0.0361978	+	0.999345i	$0.511525\pi$
$710$	44.9492	+	77.8542i	1.68691	+	2.92182i
$711$		0			0
$712$	−0.476553			−0.0178596
$713$	0.483711	+	0.837812i	0.0181151	+	0.0313763i
$714$		0			0
$715$	−64.7733	+	37.9232i	−2.42238	+	1.41825i
$716$	−28.6117	+	49.5570i	−1.06927	+	1.85203i
$717$		0			0
$718$	−12.1560	+	21.0547i	−0.453656	+	0.785756i
$719$	23.9848	+	41.5430i	0.894483	+	1.54929i	0.834443	+	0.551095i	$0.185790\pi$
$719$	23.9848	+	41.5430i	0.894483	+	1.54929i	0.0600407	+	0.998196i	$0.480877\pi$
$720$		0			0
$721$	−0.250536	−	0.561942i	−0.00933046	−	0.0209278i
$722$	−25.1842	+	43.6203i	−0.937258	+	1.62338i
$723$		0			0
$724$	37.6844			1.40053
$725$	10.4612	−	18.1194i	0.388520	−	0.672936i
$726$		0			0
$727$	−12.5158			−0.464184			−0.232092	−	0.972694i	$-0.574557\pi$
$727$	−12.5158			−0.464184			−0.232092	+	0.972694i	$0.574557\pi$
$728$	14.5742	+	10.4429i	0.540155	+	0.387038i
$729$		0			0
$730$	−6.34632			−0.234888
$731$	1.99721	−	3.45927i	0.0738695	−	0.127946i
$732$		0			0
$733$	−14.7048	+	25.4694i	−0.543133	+	0.940733i	0.455589	+	0.890190i	$0.349429\pi$
$733$	−14.7048	+	25.4694i	−0.543133	+	0.940733i	−0.998722	+	0.0505432i	$0.983905\pi$
$734$	13.1270	−	22.7367i	0.484527	−	0.839225i
$735$		0			0
$736$	−0.871842			−0.0321365
$737$	36.6564	+	63.4907i	1.35025	+	2.33871i
$738$		0			0
$739$	−3.18599	+	5.51829i	−0.117198	+	0.202994i	−0.918656	−	0.395057i	$-0.870725\pi$
$739$	−3.18599	+	5.51829i	−0.117198	+	0.202994i	0.801458	+	0.598051i	$0.204058\pi$
$740$	20.6977	−	35.8495i	0.760863	−	1.31785i
$741$		0			0
$742$	3.91735	+	0.409709i	0.143810	+	0.0150409i
$743$	4.47867	+	7.75728i	0.164306	+	0.284587i	0.936409	−	0.350911i	$-0.114128\pi$
$743$	4.47867	+	7.75728i	0.164306	+	0.284587i	−0.772102	+	0.635498i	$0.780795\pi$
$744$		0			0
$745$	21.5421			0.789240
$746$	2.92042	+	5.05832i	0.106924	+	0.185198i
$747$		0			0
$748$	−19.9065	+	34.4790i	−0.727853	+	1.26068i
$749$	−19.0954	+	26.3108i	−0.697731	+	0.961376i
$750$		0			0
$751$	−47.0191			−1.71575			−0.857875	−	0.513859i	$-0.828216\pi$
$751$	−47.0191			−1.71575			−0.857875	+	0.513859i	$0.828216\pi$
$752$	4.82746	−	8.36140i	0.176039	−	0.304909i
$753$		0			0
$754$	−13.2825	+	7.77661i	−0.483721	+	0.283207i
$755$	−62.1588			−2.26219
$756$		0			0
$757$	22.4776	+	38.9324i	0.816963	+	1.41502i	0.907910	+	0.419166i	$0.137677\pi$
$757$	22.4776	+	38.9324i	0.816963	+	1.41502i	−0.0909467	+	0.995856i	$0.528989\pi$
$758$	−9.64042	−	16.6977i	−0.350156	−	0.606488i
$759$		0			0
$760$	−48.3339			−1.75325
$761$	3.18724	+	5.52046i	0.115537	+	0.200117i	0.917994	−	0.396593i	$-0.129808\pi$
$761$	3.18724	+	5.52046i	0.115537	+	0.200117i	−0.802457	+	0.596710i	$0.796474\pi$
$762$		0			0
$763$	14.8298	+	1.55102i	0.536874	+	0.0561508i
$764$	0.244798	+	0.424002i	0.00885647	+	0.0153399i
$765$		0			0
$766$	7.62503	+	13.2069i	0.275503	+	0.477186i
$767$	0.0486182	+	8.00538i	0.00175550	+	0.289058i
$768$		0			0
$769$	17.8057	+	30.8404i	0.642091	+	1.11213i	0.984965	+	0.172753i	$0.0552663\pi$
$769$	17.8057	+	30.8404i	0.642091	+	1.11213i	−0.342874	+	0.939381i	$0.611400\pi$
$770$	120.677	+	12.6214i	4.34891	+	0.454845i
$771$		0			0
$772$	−36.2860	+	62.8492i	−1.30596	+	2.26199i
$773$	−37.5227			−1.34960			−0.674798	−	0.738002i	$-0.735769\pi$
$773$	−37.5227			−1.34960			−0.674798	+	0.738002i	$0.735769\pi$
$774$		0			0
$775$	43.1819	−	74.7933i	1.55114	−	2.68665i
$776$	12.1530	−	21.0496i	0.436267	−	0.755636i
$777$		0			0
$778$	25.0241	+	43.3430i	0.897158	+	1.55392i
$779$	29.3710	−	50.8721i	1.05233	−	1.82268i
$780$		0			0
$781$	−26.8878	−	46.5710i	−0.962121	−	1.66644i
$782$	0.709857			0.0253844
$783$		0			0
$784$	3.39765	+	10.4207i	0.121345	+	0.372168i
$785$	18.4044			0.656879
$786$		0			0
$787$	10.2884			0.366741			0.183370	−	0.983044i	$-0.441299\pi$
$787$	10.2884			0.366741			0.183370	+	0.983044i	$0.441299\pi$
$788$	−36.0795	−	62.4916i	−1.28528	−	2.22617i
$789$		0			0
$790$	18.3187	+	31.7290i	0.651752	+	1.12887i
$791$	13.1848	+	29.5730i	0.468798	+	1.05149i
$792$		0			0
$793$	−15.7699	+	9.23290i	−0.560005	+	0.327870i
$794$	−27.2754	−	47.2423i	−0.967966	−	1.67657i
$795$		0			0
$796$	−48.7982			−1.72961
$797$	−10.8455	+	18.7849i	−0.384166	+	0.665394i	−0.991653	−	0.128935i	$-0.958844\pi$
$797$	−10.8455	+	18.7849i	−0.384166	+	0.665394i	0.607487	+	0.794329i	$0.292177\pi$
$798$		0			0
$799$	−8.21380	+	14.2267i	−0.290583	+	0.503305i
$800$	38.9156	+	67.4038i	1.37587	+	2.38308i
$801$		0			0
$802$	40.6609			1.43579
$803$	3.79626			0.133967
$804$		0			0
$805$	−0.517901	−	1.16163i	−0.0182536	−	0.0409420i
$806$	−54.8278	+	32.1004i	−1.93123	+	1.13069i
$807$		0			0
$808$	12.0444	−	20.8615i	0.423720	−	0.733905i
$809$	−14.4693	+	25.0615i	−0.508712	+	0.881116i	0.491237	+	0.871026i	$0.336545\pi$
$809$	−14.4693	+	25.0615i	−0.508712	+	0.881116i	−0.999949	+	0.0100895i	$0.996788\pi$
$810$		0			0
$811$	6.27000			0.220169			0.110085	−	0.993922i	$-0.464888\pi$
$811$	6.27000			0.220169			0.110085	+	0.993922i	$0.464888\pi$
$812$	14.5483	+	1.52158i	0.510545	+	0.0533971i
$813$		0			0
$814$	−21.0598	+	36.4766i	−0.738146	+	1.27851i
$815$	−62.7370			−2.19758
$816$		0			0
$817$	−9.70086			−0.339390
$818$	4.00979			0.140199
$819$		0			0
$820$	102.955			3.59534
$821$	−50.2787			−1.75474			−0.877369	−	0.479817i	$-0.840703\pi$
$821$	−50.2787			−1.75474			−0.877369	+	0.479817i	$0.840703\pi$
$822$		0			0
$823$	−44.7780			−1.56086			−0.780432	−	0.625241i	$-0.785001\pi$
$823$	−44.7780			−1.56086			−0.780432	+	0.625241i	$0.785001\pi$
$824$	0.218536	−	0.378516i	0.00761307	−	0.0131862i
$825$		0			0
$826$	7.60139	−	10.4737i	0.264486	−	0.364425i
$827$	57.0079			1.98236			0.991180	−	0.132522i	$-0.0423075\pi$
$827$	57.0079			1.98236			0.991180	+	0.132522i	$0.0423075\pi$
$828$		0			0
$829$	−19.4987	+	33.7727i	−0.677218	+	1.17298i	0.298598	+	0.954379i	$0.403481\pi$
$829$	−19.4987	+	33.7727i	−0.677218	+	1.17298i	−0.975815	+	0.218596i	$0.929852\pi$
$830$	−60.0093	+	103.939i	−2.08295	+	3.60778i
$831$		0			0
$832$	−0.279151	−	45.9646i	−0.00967783	−	1.59353i
$833$	−5.78102	−	17.7305i	−0.200300	−	0.614327i
$834$		0			0
$835$	−24.1162			−0.834574
$836$	96.6899			3.34409
$837$		0			0
$838$	−2.98880	−	5.17675i	−0.103246	−	0.178828i
$839$	22.9552	−	39.7596i	0.792502	−	1.37265i	−0.131911	−	0.991262i	$-0.542111\pi$
$839$	22.9552	−	39.7596i	0.792502	−	1.37265i	0.924413	−	0.381393i	$-0.124555\pi$
$840$		0			0
$841$	12.6225	−	21.8629i	0.435260	−	0.753893i
$842$	−5.13908			−0.177104
$843$		0			0
$844$	24.1802	+	41.8814i	0.832318	+	1.44162i
$845$	−25.2893	+	45.0575i	−0.869979	+	1.55003i
$846$		0			0
$847$	−43.2417	−	4.52258i	−1.48580	−	0.155398i
$848$	−0.529054	−	0.916349i	−0.0181678	−	0.0314675i
$849$		0			0
$850$	−31.6852	−	54.8804i	−1.08679	−	1.88238i
$851$	0.441501			0.0151345
$852$		0			0
$853$	−14.4116			−0.493444			−0.246722	−	0.969086i	$-0.579353\pi$
$853$	−14.4116			−0.493444			−0.246722	+	0.969086i	$0.579353\pi$
$854$	29.3805	+	3.07285i	1.00538	+	0.105151i
$855$		0			0
$856$	−23.0945			−0.789354
$857$	8.00884	+	13.8717i	0.273577	+	0.473849i	0.969775	−	0.244001i	$-0.0784600\pi$
$857$	8.00884	+	13.8717i	0.273577	+	0.473849i	−0.696198	+	0.717849i	$0.745127\pi$
$858$		0			0
$859$	−9.25285	+	16.0264i	−0.315703	+	0.546814i	−0.979587	−	0.201022i	$-0.935574\pi$
$859$	−9.25285	+	16.0264i	−0.315703	+	0.546814i	0.663884	+	0.747836i	$0.268907\pi$
$860$	−8.50116	−	14.7244i	−0.289887	−	0.502099i
$861$		0			0
$862$	−9.49252	+	16.4415i	−0.323317	+	0.560001i
$863$	−16.5559	+	28.6757i	−0.563570	+	0.976132i	0.433611	+	0.901100i	$0.357239\pi$
$863$	−16.5559	+	28.6757i	−0.563570	+	0.976132i	−0.997181	+	0.0750320i	$0.976094\pi$
$864$		0			0
$865$	5.67804			0.193059
$866$	5.58182	−	9.66800i	0.189678	−	0.328532i
$867$		0			0
$868$	60.0527	+	6.28081i	2.03832	+	0.213184i
$869$	−10.9580	−	18.9797i	−0.371723	−	0.643843i
$870$		0			0
$871$	43.8589	+	24.9680i	1.48610	+	0.846009i
$872$	5.29615	+	9.17321i	0.179350	+	0.310644i
$873$		0			0
$874$	−0.861980	−	1.49299i	−0.0291569	−	0.0505012i
$875$	−35.8075	+	49.3377i	−1.21051	+	1.66792i
$876$		0			0
$877$	−21.9743	−	38.0607i	−0.742021	−	1.28522i	−0.951574	−	0.307420i	$-0.900534\pi$
$877$	−21.9743	−	38.0607i	−0.742021	−	1.28522i	0.209553	−	0.977797i	$-0.432799\pi$
$878$	−3.19682			−0.107888
$879$		0			0
$880$	−16.2980	−	28.2289i	−0.549404	−	0.951596i
$881$	−15.2635	−	26.4372i	−0.514241	−	0.890692i	−0.999863	−	0.0165233i	$-0.994740\pi$
$881$	−15.2635	−	26.4372i	−0.514241	−	0.890692i	0.485622	−	0.874169i	$-0.338593\pi$
$882$		0			0
$883$	14.8290			0.499037			0.249518	−	0.968370i	$-0.419728\pi$
$883$	14.8290			0.499037			0.249518	+	0.968370i	$0.419728\pi$
$884$	0.166444	+	27.4064i	0.00559812	+	0.921776i
$885$		0			0
$886$	−19.9541	+	34.5615i	−0.670371	+	1.16112i
$887$	22.9865			0.771811			0.385906	−	0.922538i	$-0.373889\pi$
$887$	22.9865			0.771811			0.385906	+	0.922538i	$0.373889\pi$
$888$		0			0
$889$	−8.36789	−	0.875183i	−0.280650	−	0.0293527i
$890$	−1.11005	+	1.92266i	−0.0372089	+	0.0644476i
$891$		0			0
$892$	7.71673	+	13.3658i	0.258375	+	0.447519i
$893$	39.8961			1.33507
$894$		0			0
$895$	39.8574	+	69.0350i	1.33229	+	2.30759i
$896$	−21.2406	+	29.2665i	−0.709597	+	0.977726i
$897$		0			0
$898$	−9.42403	+	16.3229i	−0.314484	+	0.544702i
$899$	−7.74978	+	13.4230i	−0.258470	+	0.447682i
$900$		0			0
$901$	0.900172	+	1.55914i	0.0299891	+	0.0519426i
$902$	−104.756			−3.48800
$903$		0			0
$904$	−11.5008	+	19.9199i	−0.382510	+	0.662526i
$905$	26.2480	−	45.4628i	0.872512	−	1.51124i
$906$		0			0
$907$	−18.5900	+	32.1989i	−0.617272	+	1.06915i	0.372710	+	0.927948i	$0.378429\pi$
$907$	−18.5900	+	32.1989i	−0.617272	+	1.06915i	−0.989981	+	0.141198i	$0.954905\pi$
$908$	45.4690			1.50894
$909$		0			0
$910$	76.0798	−	34.4748i	2.52202	−	1.14283i
$911$	17.7963			0.589618			0.294809	−	0.955556i	$-0.404744\pi$
$911$	17.7963			0.589618			0.294809	+	0.955556i	$0.404744\pi$
$912$		0			0
$913$	35.8965	−	62.1745i	1.18800	−	2.05768i
$914$	−18.8232			−0.622615
$915$		0			0
$916$	16.3567	−	28.3306i	0.540440	−	0.936069i
$917$	−3.39808	−	7.62175i	−0.112215	−	0.251692i
$918$		0			0
$919$	22.6185	+	39.1763i	0.746114	+	1.29231i	0.949672	+	0.313245i	$0.101416\pi$
$919$	22.6185	+	39.1763i	0.746114	+	1.29231i	−0.203558	+	0.979063i	$0.565251\pi$
$920$	0.451751	−	0.782456i	0.0148938	−	0.0257968i
$921$		0			0
$922$	25.8196	−	44.7209i	0.850324	−	1.47280i
$923$	−32.1709	−	18.3143i	−1.05892	−	0.602822i
$924$		0			0
$925$	−19.7069	−	34.1333i	−0.647958	−	1.12230i
$926$	50.4962			1.65941
$927$		0			0
$928$	−6.98411	−	12.0968i	−0.229265	−	0.397098i
$929$	−4.54161	−	7.86630i	−0.149005	−	0.258085i	0.781855	−	0.623461i	$-0.214274\pi$
$929$	−4.54161	−	7.86630i	−0.149005	−	0.258085i	−0.930860	+	0.365376i	$0.880941\pi$
$930$		0			0
$931$	−30.2716	+	33.6890i	−0.992110	+	1.10411i
$932$	28.0671	−	48.6137i	0.919370	−	1.59239i
$933$		0			0
$934$	−12.8174	+	22.2004i	−0.419399	+	0.726420i
$935$	27.7306	+	48.0308i	0.906887	+	1.57077i
$936$		0			0
$937$	−13.3301			−0.435476			−0.217738	−	0.976007i	$-0.569868\pi$
$937$	−13.3301			−0.435476			−0.217738	+	0.976007i	$0.569868\pi$
$938$	−33.2212	−	74.5136i	−1.08471	−	2.43296i
$939$		0			0
$940$	34.9622	+	60.5563i	1.14034	+	1.97513i
$941$	18.7875	+	32.5410i	0.612456	+	1.06080i	0.990825	+	0.135150i	$0.0431517\pi$
$941$	18.7875	+	32.5410i	0.612456	+	1.06080i	−0.378369	+	0.925655i	$0.623515\pi$
$942$		0			0
$943$	0.549031	+	0.950950i	0.0178789	+	0.0309672i
$944$	−3.47660			−0.113154
$945$		0			0
$946$	8.64989	+	14.9820i	0.281232	+	0.487108i
$947$	−29.1878			−0.948478			−0.474239	−	0.880396i	$-0.657277\pi$
$947$	−29.1878			−0.948478			−0.474239	+	0.880396i	$0.657277\pi$
$948$		0			0
$949$	2.25521	−	1.32037i	0.0732074	−	0.0428612i
$950$	−76.9508	+	133.283i	−2.49661	+	4.32426i
$951$		0			0
$952$	7.78157	−	10.7219i	0.252202	−	0.347499i
$953$	−7.01755	+	12.1547i	−0.227321	+	0.393731i	−0.957013	−	0.290044i	$-0.906330\pi$
$953$	−7.01755	+	12.1547i	−0.227321	+	0.393731i	0.729692	+	0.683775i	$0.239663\pi$
$954$		0			0
$955$	0.682027			0.0220699
$956$	−0.548929			−0.0177536
$957$		0			0
$958$	20.5015	−	35.5097i	0.662375	−	1.14727i
$959$	−15.7562	+	21.7099i	−0.508795	+	0.701048i
$960$		0			0
$961$	−16.4896	+	28.5609i	−0.531923	+	0.921318i
$962$	0.176087	+	28.9942i	0.00567728	+	0.934811i
$963$		0			0
$964$	36.0832			1.16216
$965$	50.5480	+	87.5516i	1.62720	+	2.81839i
$966$		0			0
$967$	−4.76776			−0.153321			−0.0766604	−	0.997057i	$-0.524426\pi$
$967$	−4.76776			−0.153321			−0.0766604	+	0.997057i	$0.524426\pi$
$968$	−15.4429	−	26.7479i	−0.496353	−	0.859709i
$969$		0			0
$970$	−56.6165	−	98.0627i	−1.81785	−	3.14860i
$971$	−16.7020	−	28.9288i	−0.535994	−	0.928368i	−0.999115	−	0.0420731i	$-0.986604\pi$
$971$	−16.7020	−	28.9288i	−0.535994	−	0.928368i	0.463121	−	0.886295i	$-0.346730\pi$
$972$		0			0
$973$	−5.17472	−	11.6067i	−0.165894	−	0.372092i
$974$	−66.2568			−2.12301
$975$		0			0
$976$	−3.96795	−	6.87269i	−0.127011	−	0.219990i
$977$	7.19954	−	12.4700i	0.230334	−	0.398949i	−0.727573	−	0.686031i	$-0.759352\pi$
$977$	7.19954	−	12.4700i	0.230334	−	0.398949i	0.957906	+	0.287081i	$0.0926849\pi$
$978$		0			0
$979$	0.664011	−	1.15010i	0.0212219	−	0.0367574i
$980$	−77.6628	−	16.4249i	−2.48085	−	0.524674i
$981$		0			0
$982$	−14.3804	−	24.9077i	−0.458898	−	0.794835i
$983$	9.45401	+	16.3748i	0.301536	+	0.522276i	0.976484	−	0.215589i	$-0.0691673\pi$
$983$	9.45401	+	16.3748i	0.301536	+	0.522276i	−0.674948	+	0.737865i	$0.735834\pi$
$984$		0			0
$985$	−100.521			−3.20286
$986$	5.68649	+	9.84928i	0.181095	+	0.313665i
$987$		0			0
$988$	57.4399	−	33.6297i	1.82741	−	1.06990i
$989$	0.0906689	−	0.157043i	0.00288310	−	0.00499368i
$990$		0			0
$991$	3.03676	−	5.25982i	0.0964659	−	0.167084i	−0.813754	−	0.581210i	$-0.802579\pi$
$991$	3.03676	−	5.25982i	0.0964659	−	0.167084i	0.910219	+	0.414126i	$0.135913\pi$
$992$	−28.8291	−	49.9334i	−0.915325	−	1.58539i
$993$		0			0
$994$	24.3681	+	54.6565i	0.772908	+	1.73360i
$995$	−33.9890	+	58.8707i	−1.07752	+	1.86633i
$996$		0			0
$997$	−31.6619			−1.00274			−0.501371	−	0.865232i	$-0.667171\pi$
$997$	−31.6619			−1.00274			−0.501371	+	0.865232i	$0.667171\pi$
$998$	26.7684	−	46.3642i	0.847339	−	1.46763i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.g.289.16	yes	36
3.2	odd	2	inner	819.2.s.g.289.3	yes	36
7.4	even	3		819.2.n.g.172.3	yes	36
13.9	even	3		819.2.n.g.100.3	✓	36
21.11	odd	6		819.2.n.g.172.16	yes	36
39.35	odd	6		819.2.n.g.100.16	yes	36
91.74	even	3	inner	819.2.s.g.802.16	yes	36
273.74	odd	6	inner	819.2.s.g.802.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.n.g.100.3	✓	36	13.9	even	3
819.2.n.g.100.16	yes	36	39.35	odd	6
819.2.n.g.172.3	yes	36	7.4	even	3
819.2.n.g.172.16	yes	36	21.11	odd	6
819.2.s.g.289.3	yes	36	3.2	odd	2	inner
819.2.s.g.289.16	yes	36	1.1	even	1	trivial
819.2.s.g.802.3	yes	36	273.74	odd	6	inner
819.2.s.g.802.16	yes	36	91.74	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.20299 q^{2} +2.85316 q^{4} +(1.98729 - 3.44208i) q^{5} +(1.55404 - 2.14125i) q^{7} +1.87950 q^{8} +(4.37797 - 7.58287i) q^{10} +(-2.61882 + 4.53594i) q^{11} +(0.0218968 + 3.60548i) q^{13} +(3.42354 - 4.71715i) q^{14} -1.56580 q^{16} +2.66417 q^{17} +(-3.23511 - 5.60337i) q^{19} +(5.67005 - 9.82081i) q^{20} +(-5.76924 + 9.99262i) q^{22} +0.120947 q^{23} +(-5.39862 - 9.35068i) q^{25} +(0.0482383 + 7.94284i) q^{26} +(4.43393 - 6.10933i) q^{28} +(0.968879 + 1.67815i) q^{29} +(3.99935 + 6.92708i) q^{31} -7.20844 q^{32} +5.86914 q^{34} +(-4.28204 - 9.60442i) q^{35} +3.65036 q^{37} +(-7.12690 - 12.3442i) q^{38} +(3.73511 - 6.46939i) q^{40} +(4.53942 + 7.86251i) q^{41} +(0.749656 - 1.29844i) q^{43} +(-7.47193 + 12.9418i) q^{44} +0.266446 q^{46} +(-3.08306 + 5.34002i) q^{47} +(-2.16991 - 6.65518i) q^{49} +(-11.8931 - 20.5994i) q^{50} +(0.0624750 + 10.2870i) q^{52} +(0.337881 + 0.585227i) q^{53} +(10.4087 + 18.0284i) q^{55} +(2.92082 - 4.02448i) q^{56} +(2.13443 + 3.69694i) q^{58} +2.22033 q^{59} +(2.53414 + 4.38925i) q^{61} +(8.81053 + 15.2603i) q^{62} -12.7485 q^{64} +(12.4539 + 7.08976i) q^{65} +(6.99863 - 12.1220i) q^{67} +7.60130 q^{68} +(-9.43328 - 21.1584i) q^{70} +(-5.13356 + 8.89159i) q^{71} +(-0.362401 - 0.627696i) q^{73} +8.04170 q^{74} +(-9.23027 - 15.9873i) q^{76} +(5.64282 + 12.6566i) q^{77} +(-2.09215 + 3.62371i) q^{79} +(-3.11169 + 5.38961i) q^{80} +(10.0003 + 17.3210i) q^{82} -13.7071 q^{83} +(5.29447 - 9.17029i) q^{85} +(1.65148 - 2.86045i) q^{86} +(-4.92208 + 8.52530i) q^{88} -0.253553 q^{89} +(7.75428 + 5.55619i) q^{91} +0.345082 q^{92} +(-6.79195 + 11.7640i) q^{94} -25.7163 q^{95} +(6.46607 - 11.1996i) q^{97} +(-4.78029 - 14.6613i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 44 q^{4} + 4 q^{7} + 8 q^{10} + 20 q^{16} + 4 q^{19} - 10 q^{22} - 22 q^{25} + 16 q^{28} - 18 q^{31} + 8 q^{34} - 20 q^{37} + 14 q^{40} + 20 q^{43} + 8 q^{46} - 12 q^{49} + 10 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) \) 36 * q + 44 * q^4 + 4 * q^7 + 8 * q^10 + 20 * q^16 + 4 * q^19 - 10 * q^22 - 22 * q^25 + 16 * q^28 - 18 * q^31 + 8 * q^34 - 20 * q^37 + 14 * q^40 + 20 * q^43 + 8 * q^46 - 12 * q^49 + 10 * q^52 + 42 * q^55 - 12 * q^58 + 14 * q^61 - 12 * q^64 + 12 * q^67 - 24 * q^70 + 6 * q^73 + 14 * q^76 - 24 * q^79 + 38 * q^82 + 28 * q^85 - 12 * q^88 + 92 * q^91 + 28 * q^94 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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