LMFDB - Embedded newform 585.2.bs.c.289.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(289,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("585.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.12
Character	$\chi$	$=$	585.289
Dual form			585.2.bs.c.334.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35625 - 0.783029i) q^{2} +(0.226269 - 0.391909i) q^{4} +(1.90777 + 1.16637i) q^{5} +(0.331025 + 0.191118i) q^{7} +2.42342i q^{8} +O(q^{10})$	\(q+(1.35625 - 0.783029i) q^{2} +(0.226269 - 0.391909i) q^{4} +(1.90777 + 1.16637i) q^{5} +(0.331025 + 0.191118i) q^{7} +2.42342i q^{8} +(3.50070 + 0.0880529i) q^{10} +(-2.30794 - 3.99748i) q^{11} +(3.53060 - 0.731332i) q^{13} +0.598602 q^{14} +(2.35014 + 4.07057i) q^{16} +(4.29069 + 2.47723i) q^{17} +(-2.05288 + 3.55569i) q^{19} +(0.888780 - 0.483757i) q^{20} +(-6.26028 - 3.61437i) q^{22} +(5.72546 - 3.30559i) q^{23} +(2.27915 + 4.45034i) q^{25} +(4.21571 - 3.75643i) q^{26} +(0.149801 - 0.0864878i) q^{28} +(2.65290 + 4.59495i) q^{29} -9.80604 q^{31} +(2.17726 + 1.25704i) q^{32} +7.75897 q^{34} +(0.408604 + 0.750707i) q^{35} +(1.44793 - 0.835962i) q^{37} +6.42985i q^{38} +(-2.82661 + 4.62331i) q^{40} +(-6.22435 - 10.7809i) q^{41} +(-7.10356 - 4.10124i) q^{43} -2.08886 q^{44} +(5.17675 - 8.96640i) q^{46} -2.71238i q^{47} +(-3.42695 - 5.93565i) q^{49} +(6.57582 + 4.25111i) q^{50} +(0.512249 - 1.54915i) q^{52} -2.07646i q^{53} +(0.259532 - 10.3182i) q^{55} +(-0.463157 + 0.802212i) q^{56} +(7.19596 + 4.15459i) q^{58} +(4.11483 - 7.12710i) q^{59} +(1.07641 - 1.86440i) q^{61} +(-13.2994 + 7.67841i) q^{62} -5.46337 q^{64} +(7.58857 + 2.72279i) q^{65} +(-10.1684 + 5.87072i) q^{67} +(1.94170 - 1.12104i) q^{68} +(1.14199 + 0.698194i) q^{70} +(-1.56281 + 2.70687i) q^{71} +13.5863i q^{73} +(1.30916 - 2.26754i) q^{74} +(0.929003 + 1.60908i) q^{76} -1.76435i q^{77} -1.45254 q^{79} +(-0.264278 + 10.5068i) q^{80} +(-16.8835 - 9.74770i) q^{82} -2.02064i q^{83} +(5.29626 + 9.73052i) q^{85} -12.8456 q^{86} +(9.68755 - 5.59311i) q^{88} +(2.60725 + 4.51588i) q^{89} +(1.30849 + 0.432671i) q^{91} -2.99181i q^{92} +(-2.12387 - 3.67866i) q^{94} +(-8.06367 + 4.38900i) q^{95} +(-15.7666 - 9.10286i) q^{97} +(-9.29557 - 5.36680i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4}+O(q^{10}) $ 32 * q + 20 * q^4	$ 32 q + 20 q^{4} - 6 q^{10} - 28 q^{16} - 8 q^{19} + 28 q^{25} + 8 q^{31} - 8 q^{34} - 20 q^{40} - 8 q^{46} + 44 q^{49} + 20 q^{55} - 56 q^{61} - 136 q^{64} - 80 q^{70} + 88 q^{76} - 72 q^{79} - 50 q^{85} - 28 q^{91} + 48 q^{94}+O(q^{100}) $ 32 * q + 20 * q^4 - 6 * q^10 - 28 * q^16 - 8 * q^19 + 28 * q^25 + 8 * q^31 - 8 * q^34 - 20 * q^40 - 8 * q^46 + 44 * q^49 + 20 * q^55 - 56 * q^61 - 136 * q^64 - 80 * q^70 + 88 * q^76 - 72 * q^79 - 50 * q^85 - 28 * q^91 + 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.35625	−	0.783029i	0.959011	−	0.553685i	0.0631423	−	0.998005i	$-0.479888\pi$
$2$	1.35625	−	0.783029i	0.959011	−	0.553685i	0.895868	+	0.444319i	$0.146554\pi$
$3$		0			0
$3$		0			0
$4$	0.226269	−	0.391909i	0.113134	−	0.195954i
$5$	1.90777	+	1.16637i	0.853179	+	0.521618i
$5$	1.90777	+	1.16637i	0.853179	+	0.521618i
$6$		0			0
$7$	0.331025	+	0.191118i	0.125116	+	0.0722356i	0.561252	−	0.827645i	$-0.310320\pi$
$7$	0.331025	+	0.191118i	0.125116	+	0.0722356i	−0.436136	+	0.899881i	$0.643653\pi$
$8$			2.42342i			0.856807i
$9$		0			0
$10$	3.50070	+	0.0880529i	1.10702	+	0.0278448i
$11$	−2.30794	−	3.99748i	−0.695871	−	1.20528i	−0.969886	−	0.243559i	$-0.921685\pi$
$11$	−2.30794	−	3.99748i	−0.695871	−	1.20528i	0.274015	−	0.961726i	$-0.411648\pi$
$12$		0			0
$13$	3.53060	−	0.731332i	0.979213	−	0.202835i
$13$	3.53060	−	0.731332i	0.979213	−	0.202835i
$14$	0.598602			0.159983
$15$		0			0
$16$	2.35014	+	4.07057i	0.587536	+	1.01764i
$17$	4.29069	+	2.47723i	1.04064	+	0.600817i	0.920016	−	0.391881i	$-0.128176\pi$
$17$	4.29069	+	2.47723i	1.04064	+	0.600817i	0.120629	+	0.992698i	$0.461509\pi$
$18$		0			0
$19$	−2.05288	+	3.55569i	−0.470962	+	0.815731i	−0.999448	−	0.0332114i	$-0.989427\pi$
$19$	−2.05288	+	3.55569i	−0.470962	+	0.815731i	0.528486	+	0.848942i	$0.322760\pi$
$20$	0.888780	−	0.483757i	0.198737	−	0.108171i
$21$		0			0
$22$	−6.26028	−	3.61437i	−1.33470	−	0.770587i
$23$	5.72546	−	3.30559i	1.19384	−	0.689264i	0.234665	−	0.972076i	$-0.424601\pi$
$23$	5.72546	−	3.30559i	1.19384	−	0.689264i	0.959175	+	0.282812i	$0.0912674\pi$
$24$		0			0
$25$	2.27915	+	4.45034i	0.455829	+	0.890067i
$26$	4.21571	−	3.75643i	0.826769	−	0.736696i
$27$		0			0
$28$	0.149801	−	0.0864878i	0.0283098	−	0.0163447i
$29$	2.65290	+	4.59495i	0.492630	+	0.853261i	0.999964	−	0.00848878i	$-0.00270209\pi$
$29$	2.65290	+	4.59495i	0.492630	+	0.853261i	−0.507333	+	0.861750i	$0.669369\pi$
$30$		0			0
$31$	−9.80604			−1.76122			−0.880608	−	0.473845i	$-0.842866\pi$
$31$	−9.80604			−1.76122			−0.880608	+	0.473845i	$0.842866\pi$
$32$	2.17726	+	1.25704i	0.384889	+	0.222216i
$33$		0			0
$34$	7.75897			1.33065
$35$	0.408604	+	0.750707i	0.0690668	+	0.126893i
$36$		0			0
$37$	1.44793	−	0.835962i	0.238038	−	0.137431i	−0.376237	−	0.926524i	$-0.622782\pi$
$37$	1.44793	−	0.835962i	0.238038	−	0.137431i	0.614275	+	0.789092i	$0.289449\pi$
$38$			6.42985i			1.04306i
$39$		0			0
$40$	−2.82661	+	4.62331i	−0.446926	+	0.731010i
$41$	−6.22435	−	10.7809i	−0.972081	−	1.68369i	−0.689250	−	0.724524i	$-0.742060\pi$
$41$	−6.22435	−	10.7809i	−0.972081	−	1.68369i	−0.282831	−	0.959170i	$-0.591274\pi$
$42$		0			0
$43$	−7.10356	−	4.10124i	−1.08328	−	0.625433i	−0.151502	−	0.988457i	$-0.548411\pi$
$43$	−7.10356	−	4.10124i	−1.08328	−	0.625433i	−0.931780	+	0.363024i	$0.881744\pi$
$44$	−2.08886			−0.314908
$45$		0			0
$46$	5.17675	−	8.96640i	0.763270	−	1.32202i
$47$		−	2.71238i		−	0.395642i	−0.980238	−	0.197821i	$-0.936614\pi$
$47$		−	2.71238i		−	0.395642i	0.980238	−	0.197821i	$-0.0633864\pi$
$48$		0			0
$49$	−3.42695	−	5.93565i	−0.489564	−	0.847950i
$50$	6.57582	+	4.25111i	0.929962	+	0.601198i
$51$		0			0
$52$	0.512249	−	1.54915i	0.0710362	−	0.214829i
$53$		−	2.07646i		−	0.285224i	−0.989779	−	0.142612i	$-0.954450\pi$
$53$		−	2.07646i		−	0.285224i	0.989779	−	0.142612i	$-0.0455501\pi$
$54$		0			0
$55$	0.259532	−	10.3182i	0.0349953	−	1.39130i
$56$	−0.463157	+	0.802212i	−0.0618920	+	0.107200i
$57$		0			0
$58$	7.19596	+	4.15459i	0.944876	+	0.545524i
$59$	4.11483	−	7.12710i	0.535706	−	0.927870i	−0.463423	−	0.886137i	$-0.653379\pi$
$59$	4.11483	−	7.12710i	0.535706	−	0.927870i	0.999129	−	0.0417324i	$-0.0132877\pi$
$60$		0			0
$61$	1.07641	−	1.86440i	0.137820	−	0.238712i	−0.788851	−	0.614585i	$-0.789324\pi$
$61$	1.07641	−	1.86440i	0.137820	−	0.238712i	0.926671	+	0.375873i	$0.122657\pi$
$62$	−13.2994	+	7.67841i	−1.68903	+	0.975159i
$63$		0			0
$64$	−5.46337			−0.682921
$65$	7.58857	+	2.72279i	0.941246	+	0.337721i
$66$		0			0
$67$	−10.1684	+	5.87072i	−1.24227	+	0.717222i	−0.969555	−	0.244874i	$-0.921253\pi$
$67$	−10.1684	+	5.87072i	−1.24227	+	0.717222i	−0.272710	+	0.962096i	$0.587920\pi$
$68$	1.94170	−	1.12104i	0.235465	−	0.135946i
$69$		0			0
$70$	1.14199	+	0.698194i	0.136494	+	0.0834501i
$71$	−1.56281	+	2.70687i	−0.185472	+	0.321247i	−0.943735	−	0.330701i	$-0.892715\pi$
$71$	−1.56281	+	2.70687i	−0.185472	+	0.321247i	0.758263	+	0.651948i	$0.226048\pi$
$72$		0			0
$73$			13.5863i			1.59016i	0.606505	+	0.795080i	$0.292571\pi$
$73$			13.5863i			1.59016i	−0.606505	+	0.795080i	$0.707429\pi$
$74$	1.30916	−	2.26754i	0.152187	−	0.263596i
$75$		0			0
$76$	0.929003	+	1.60908i	0.106564	+	0.184574i
$77$		−	1.76435i		−	0.201067i
$78$		0			0
$79$	−1.45254			−0.163423			−0.0817116	−	0.996656i	$-0.526039\pi$
$79$	−1.45254			−0.163423			−0.0817116	+	0.996656i	$0.526039\pi$
$80$	−0.264278	+	10.5068i	−0.0295471	+	1.17470i
$81$		0			0
$82$	−16.8835	−	9.74770i	−1.86447	−	1.07645i
$83$		−	2.02064i		−	0.221794i	−0.993832	−	0.110897i	$-0.964628\pi$
$83$		−	2.02064i		−	0.221794i	0.993832	−	0.110897i	$-0.0353724\pi$
$84$		0			0
$85$	5.29626	+	9.73052i	0.574460	+	1.05542i
$86$	−12.8456			−1.38517
$87$		0			0
$88$	9.68755	−	5.59311i	1.03270	−	0.596228i
$89$	2.60725	+	4.51588i	0.276367	+	0.478683i	0.970479	−	0.241185i	$-0.0775360\pi$
$89$	2.60725	+	4.51588i	0.276367	+	0.478683i	−0.694112	+	0.719867i	$0.744203\pi$
$90$		0			0
$91$	1.30849	+	0.432671i	0.137167	+	0.0453562i
$92$		−	2.99181i		−	0.311918i
$93$		0			0
$94$	−2.12387	−	3.67866i	−0.219061	−	0.379425i
$95$	−8.06367	+	4.38900i	−0.827315	+	0.450302i
$96$		0			0
$97$	−15.7666	−	9.10286i	−1.60086	−	0.924255i	−0.991316	−	0.131500i	$-0.958021\pi$
$97$	−15.7666	−	9.10286i	−1.60086	−	0.924255i	−0.609540	−	0.792755i	$-0.708646\pi$
$98$	−9.29557	−	5.36680i	−0.938994	−	0.542129i
$99$		0			0
$100$	2.25983	+	0.113754i	0.225983	+	0.0113754i
$101$	−5.26014	−	9.11083i	−0.523404	−	0.906562i	−0.999629	−	0.0272385i	$-0.991329\pi$
$101$	−5.26014	−	9.11083i	−0.523404	−	0.906562i	0.476225	−	0.879323i	$-0.342005\pi$
$102$		0			0
$103$			7.43801i			0.732889i	0.930440	+	0.366444i	$0.119425\pi$
$103$			7.43801i			0.732889i	−0.930440	+	0.366444i	$0.880575\pi$
$104$	1.77232	+	8.55612i	0.173790	+	0.838997i
$105$		0			0
$106$	−1.62593	−	2.81619i	−0.157924	−	0.273533i
$107$	5.88892	−	3.39997i	0.569304	−	0.328688i	−0.187567	−	0.982252i	$-0.560060\pi$
$107$	5.88892	−	3.39997i	0.569304	−	0.328688i	0.756871	+	0.653564i	$0.226727\pi$
$108$		0			0
$109$	7.51043			0.719369			0.359685	−	0.933074i	$-0.382884\pi$
$109$	7.51043			0.719369			0.359685	+	0.933074i	$0.382884\pi$
$110$	−7.72744	−	14.1972i	−0.736783	−	1.35365i
$111$		0			0
$112$			1.79661i			0.169764i
$113$	−0.692274	−	0.399684i	−0.0651236	−	0.0375991i	0.467085	−	0.884213i	$-0.345304\pi$
$113$	−0.692274	−	0.399684i	−0.0651236	−	0.0375991i	−0.532208	+	0.846613i	$0.678638\pi$
$114$		0			0
$115$	14.7784	+	0.371720i	1.37809	+	0.0346630i
$116$	2.40107			0.222934
$117$		0			0
$118$		−	12.8881i		−	1.18645i
$119$	0.946884	+	1.64005i	0.0868007	+	0.150343i
$120$		0			0
$121$	−5.15322	+	8.92563i	−0.468474	+	0.811421i
$122$		−	3.37144i		−	0.305236i
$123$		0			0
$124$	−2.21880	+	3.84307i	−0.199254	+	0.345118i
$125$	−0.842677	+	11.1485i	−0.0753713	+	0.997156i
$126$		0			0
$127$	7.61580	−	4.39699i	0.675793	−	0.390169i	−0.122475	−	0.992472i	$-0.539083\pi$
$127$	7.61580	−	4.39699i	0.675793	−	0.390169i	0.798268	+	0.602302i	$0.205750\pi$
$128$	−11.7642	+	6.79206i	−1.03982	+	0.600339i
$129$		0			0
$130$	12.4240	−	2.24930i	1.08966	−	0.197276i
$131$	−7.74152			−0.676380			−0.338190	−	0.941078i	$-0.609815\pi$
$131$	−7.74152			−0.676380			−0.338190	+	0.941078i	$0.609815\pi$
$132$		0			0
$133$	−1.35911	+	0.784682i	−0.117850	+	0.0680405i
$134$	−9.19388	+	15.9243i	−0.794230	+	1.37565i
$135$		0			0
$136$	−6.00336	+	10.3981i	−0.514784	+	0.891632i
$137$	−8.03065	−	4.63650i	−0.686105	−	0.396123i	0.116046	−	0.993244i	$-0.462978\pi$
$137$	−8.03065	−	4.63650i	−0.686105	−	0.396123i	−0.802151	+	0.597121i	$0.796311\pi$
$138$		0			0
$139$	−5.40843	+	9.36768i	−0.458737	+	0.794556i	−0.998895	−	0.0470077i	$-0.985031\pi$
$139$	−5.40843	+	9.36768i	−0.458737	+	0.794556i	0.540157	+	0.841564i	$0.318365\pi$
$140$	0.386663	+	0.00972570i	0.0326790	+	0.000821972i
$141$		0			0
$142$			4.89492i			0.410772i
$143$	−11.0719	−	12.4256i	−0.925880	−	1.03908i
$144$		0			0
$145$	−0.298323	+	11.8604i	−0.0247744	+	0.984949i
$146$	10.6385	+	18.4264i	0.880448	+	1.52498i
$147$		0			0
$148$		−	0.756608i		−	0.0621928i
$149$	4.21571	−	7.30183i	0.345365	−	0.598189i	−0.640055	−	0.768329i	$-0.721089\pi$
$149$	4.21571	−	7.30183i	0.345365	−	0.598189i	0.985420	+	0.170140i	$0.0544220\pi$
$150$		0			0
$151$	17.5542			1.42854			0.714269	−	0.699871i	$-0.246759\pi$
$151$	17.5542			1.42854			0.714269	+	0.699871i	$0.246759\pi$
$152$	−8.61691	−	4.97498i	−0.698924	−	0.403524i
$153$		0			0
$154$	−1.38154	−	2.39290i	−0.111328	−	0.192825i
$155$	−18.7076	−	11.4375i	−1.50263	−	0.918682i
$156$		0			0
$157$		−	7.92694i		−	0.632639i	−0.948653	−	0.316319i	$-0.897553\pi$
$157$		−	7.92694i		−	0.632639i	0.948653	−	0.316319i	$-0.102447\pi$
$158$	−1.97000	+	1.13738i	−0.156725	+	0.0904850i
$159$		0			0
$160$	2.68753	+	4.93764i	0.212468	+	0.390355i
$161$	2.52703			0.199158
$162$		0			0
$163$	10.6806	+	6.16646i	0.836571	+	0.482995i	0.856097	−	0.516815i	$-0.172882\pi$
$163$	10.6806	+	6.16646i	0.836571	+	0.482995i	−0.0195260	+	0.999809i	$0.506216\pi$
$164$	−5.63351			−0.439903
$165$		0			0
$166$	−1.58222	−	2.74049i	−0.122804	−	0.212703i
$167$	13.6629	−	7.88828i	1.05727	−	0.610413i	0.132592	−	0.991171i	$-0.457670\pi$
$167$	13.6629	−	7.88828i	1.05727	−	0.610413i	0.924675	+	0.380757i	$0.124337\pi$
$168$		0			0
$169$	11.9303	−	5.16408i	0.917716	−	0.397237i
$170$	14.8023	+	9.04986i	1.13528	+	0.694092i
$171$		0			0
$172$	−3.21462	+	1.85596i	−0.245113	+	0.141516i
$173$	12.8419	+	7.41427i	0.976350	+	0.563696i	0.901166	−	0.433474i	$-0.142712\pi$
$173$	12.8419	+	7.41427i	0.976350	+	0.563696i	0.0751841	+	0.997170i	$0.476046\pi$
$174$		0			0
$175$	−0.0960825	+	1.90876i	−0.00726315	+	0.144289i
$176$	10.8480	−	18.7893i	0.817699	−	1.41630i
$177$		0			0
$178$	7.07213	+	4.08310i	0.530079	+	0.306041i
$179$	−1.20829	−	2.09281i	−0.0903116	−	0.156424i	0.817331	−	0.576169i	$-0.195453\pi$
$179$	−1.20829	−	2.09281i	−0.0903116	−	0.156424i	−0.907642	+	0.419745i	$0.862120\pi$
$180$		0			0
$181$	11.7111			0.870480			0.435240	−	0.900314i	$-0.356663\pi$
$181$	11.7111			0.870480			0.435240	+	0.900314i	$0.356663\pi$
$182$	2.11343	−	0.437777i	0.156658	−	0.0324502i
$183$		0			0
$184$	8.01083	+	13.8752i	0.590566	+	1.02289i
$185$	3.73735	+	0.0940053i	0.274776	+	0.00691141i
$186$		0			0
$187$		−	22.8692i		−	1.67236i
$188$	−1.06301	−	0.613727i	−0.0775277	−	0.0447606i
$189$		0			0
$190$	−7.49961	+	12.2666i	−0.544079	+	0.889916i
$191$	−6.62453	+	11.4740i	−0.479334	+	0.830231i	−0.999719	−	0.0237004i	$-0.992455\pi$
$191$	−6.62453	+	11.4740i	−0.479334	+	0.830231i	0.520385	+	0.853932i	$0.325789\pi$
$192$		0			0
$193$	5.50583	−	3.17879i	0.396318	−	0.228814i	−0.288576	−	0.957457i	$-0.593182\pi$
$193$	5.50583	−	3.17879i	0.396318	−	0.228814i	0.684894	+	0.728643i	$0.259848\pi$
$194$	−28.5112			−2.04698
$195$		0			0
$196$	−3.10164			−0.221546
$197$	−13.8063	+	7.97109i	−0.983660	+	0.567916i	−0.903373	−	0.428855i	$-0.858917\pi$
$197$	−13.8063	+	7.97109i	−0.983660	+	0.567916i	−0.0802870	+	0.996772i	$0.525584\pi$
$198$		0			0
$199$	0.125929	−	0.218115i	0.00892686	−	0.0154618i	−0.861527	−	0.507711i	$-0.830492\pi$
$199$	0.125929	−	0.218115i	0.00892686	−	0.0154618i	0.870454	+	0.492249i	$0.163825\pi$
$200$	−10.7850	+	5.52332i	−0.762616	+	0.390558i
$201$		0			0
$202$	−14.2681	−	8.23769i	−1.00390	−	0.579602i
$203$			2.02806i			0.142342i
$204$		0			0
$205$	0.699939	−	27.8274i	0.0488859	−	1.94355i
$206$	5.82418	+	10.0878i	0.405790	+	0.702848i
$207$		0			0
$208$	11.2744	+	12.6528i	0.781736	+	0.877315i
$209$	18.9517			1.31092
$210$		0			0
$211$	−8.43236	−	14.6053i	−0.580508	−	1.00547i	−0.995419	−	0.0956071i	$-0.969521\pi$
$211$	−8.43236	−	14.6053i	−0.580508	−	1.00547i	0.414911	−	0.909862i	$-0.363813\pi$
$212$	−0.813783	−	0.469838i	−0.0558909	−	0.0322686i
$213$		0			0
$214$	5.32455	−	9.22240i	0.363979	−	0.630430i
$215$	−8.76835	−	16.1096i	−0.597996	−	1.09867i
$216$		0			0
$217$	−3.24605	−	1.87411i	−0.220356	−	0.127223i
$218$	10.1860	−	5.88089i	0.689883	−	0.398304i
$219$		0			0
$220$	−3.98506	−	2.43639i	−0.268673	−	0.164262i
$221$	16.9604	+	5.60820i	1.14088	+	0.377248i
$222$		0			0
$223$	−14.9233	+	8.61599i	−0.999340	+	0.576969i	−0.908053	−	0.418855i	$-0.862431\pi$
$223$	−14.9233	+	8.61599i	−0.999340	+	0.576969i	−0.0912873	+	0.995825i	$0.529098\pi$
$224$	0.480486	+	0.832226i	0.0321038	+	0.0556054i
$225$		0			0
$226$	−1.25186			−0.0832723
$227$	10.5869	+	6.11235i	0.702678	+	0.405691i	0.808344	−	0.588710i	$-0.200364\pi$
$227$	10.5869	+	6.11235i	0.702678	+	0.405691i	−0.105666	+	0.994402i	$0.533698\pi$
$228$		0			0
$229$	−11.1528			−0.736999			−0.368500	−	0.929628i	$-0.620128\pi$
$229$	−11.1528			−0.736999			−0.368500	+	0.929628i	$0.620128\pi$
$230$	20.3342	−	11.0678i	1.34080	−	0.729787i
$231$		0			0
$232$	−11.1355	+	6.42907i	−0.731080	+	0.422089i
$233$			18.9993i			1.24469i	0.782744	+	0.622344i	$0.213820\pi$
$233$			18.9993i			1.24469i	−0.782744	+	0.622344i	$0.786180\pi$
$234$		0			0
$235$	3.16365	−	5.17459i	0.206374	−	0.337553i
$236$	−1.86212	−	3.22528i	−0.121213	−	0.209948i
$237$		0			0
$238$	2.56842	+	1.48288i	0.166486	+	0.0961205i
$239$	−1.63537			−0.105783			−0.0528916	−	0.998600i	$-0.516844\pi$
$239$	−1.63537			−0.105783			−0.0528916	+	0.998600i	$0.516844\pi$
$240$		0			0
$241$	−0.760631	+	1.31745i	−0.0489966	+	0.0848645i	−0.889484	−	0.456967i	$-0.848936\pi$
$241$	−0.760631	+	1.31745i	−0.0489966	+	0.0848645i	0.840487	+	0.541832i	$0.182269\pi$
$242$			16.1405i			1.03755i
$243$		0			0
$244$	−0.487116	−	0.843710i	−0.0311844	−	0.0540130i
$245$	0.385366	−	15.3209i	0.0246201	−	0.978818i
$246$		0			0
$247$	−4.64751	+	14.0551i	−0.295714	+	0.894302i
$248$		−	23.7641i		−	1.50902i
$249$		0			0
$250$	7.58675	+	15.7800i	0.479828	+	0.998015i
$251$	−3.59645	+	6.22923i	−0.227006	+	0.393186i	−0.956919	−	0.290354i	$-0.906227\pi$
$251$	−3.59645	+	6.22923i	−0.227006	+	0.393186i	0.729913	+	0.683540i	$0.239560\pi$
$252$		0			0
$253$	−26.4281	−	15.2583i	−1.66152	−	0.959278i
$254$	6.88594	−	11.9268i	0.432062	−	0.748353i
$255$		0			0
$256$	−5.17339	+	8.96058i	−0.323337	+	0.560036i
$257$	−9.17218	+	5.29556i	−0.572145	+	0.330328i	−0.758006	−	0.652248i	$-0.773826\pi$
$257$	−9.17218	+	5.29556i	−0.572145	+	0.330328i	0.185861	+	0.982576i	$0.440493\pi$
$258$		0			0
$259$	0.639068			0.0397097
$260$	2.78414	−	2.35795i	0.172665	−	0.146234i
$261$		0			0
$262$	−10.4994	+	6.06183i	−0.648655	+	0.374501i
$263$	15.6548	−	9.03831i	0.965317	−	0.557326i	0.0675119	−	0.997718i	$-0.478494\pi$
$263$	15.6548	−	9.03831i	0.965317	−	0.557326i	0.897805	+	0.440392i	$0.145161\pi$
$264$		0			0
$265$	2.42193	−	3.96140i	0.148778	−	0.243347i
$266$	−1.22886	+	2.12844i	−0.0753460	+	0.130503i
$267$		0			0
$268$			5.31344i			0.324570i
$269$	2.36317	−	4.09313i	0.144085	−	0.249563i	−0.784946	−	0.619564i	$-0.787309\pi$
$269$	2.36317	−	4.09313i	0.144085	−	0.249563i	0.929031	+	0.370001i	$0.120643\pi$
$270$		0			0
$271$	−2.43236	−	4.21298i	−0.147756	−	0.255920i	0.782642	−	0.622472i	$-0.213872\pi$
$271$	−2.43236	−	4.21298i	−0.147756	−	0.255920i	−0.930398	+	0.366552i	$0.880538\pi$
$272$			23.2874i			1.41200i
$273$		0			0
$274$	−14.5221			−0.877309
$275$	12.5300	−	19.3820i	0.755586	−	1.16878i
$276$		0			0
$277$	3.98134	+	2.29863i	0.239215	+	0.138111i	0.614816	−	0.788671i	$-0.289230\pi$
$277$	3.98134	+	2.29863i	0.239215	+	0.138111i	−0.375601	+	0.926782i	$0.622564\pi$
$278$			16.9398i			1.01598i
$279$		0			0
$280$	−1.81927	+	0.990219i	−0.108722	+	0.0591769i
$281$	−11.7397			−0.700329			−0.350165	−	0.936688i	$-0.613874\pi$
$281$	−11.7397			−0.700329			−0.350165	+	0.936688i	$0.613874\pi$
$282$		0			0
$283$	3.39585	−	1.96059i	0.201862	−	0.116545i	−0.395662	−	0.918396i	$-0.629485\pi$
$283$	3.39585	−	1.96059i	0.201862	−	0.116545i	0.597524	+	0.801851i	$0.296151\pi$
$284$	0.707232	+	1.22496i	0.0419665	+	0.0726881i
$285$		0			0
$286$	−24.7459	−	8.18258i	−1.46325	−	0.483846i
$287$		−	4.75833i		−	0.280876i
$288$		0			0
$289$	3.77334	+	6.53561i	0.221961	+	0.384448i
$290$	8.88241	+	16.3192i	0.521593	+	0.958294i
$291$		0			0
$292$	5.32460	+	3.07416i	0.311599	+	0.179902i
$293$	21.3017	+	12.2985i	1.24446	+	0.718489i	0.969999	−	0.243110i	$-0.0781675\pi$
$293$	21.3017	+	12.2985i	1.24446	+	0.718489i	0.274460	+	0.961598i	$0.411501\pi$
$294$		0			0
$295$	16.1630	−	8.79741i	0.941047	−	0.512205i
$296$	2.02588	+	3.50893i	0.117752	+	0.203953i
$297$		0			0
$298$		−	13.2041i		−	0.764893i
$299$	17.7968	−	15.8579i	1.02922	−	0.917089i
$300$		0			0
$301$	−1.56764	−	2.71523i	−0.0903571	−	0.156503i
$302$	23.8078	−	13.7454i	1.36998	−	0.790961i
$303$		0			0
$304$	−19.2982			−1.10683
$305$	4.22813	−	2.30134i	0.242102	−	0.131774i
$306$		0			0
$307$			16.8276i			0.960403i	0.877158	+	0.480201i	$0.159436\pi$
$307$			16.8276i			0.960403i	−0.877158	+	0.480201i	$0.840564\pi$
$308$	−0.691466	−	0.399218i	−0.0393999	−	0.0227476i
$309$		0			0
$310$	−34.3280	−	0.863451i	−1.94970	−	0.0490407i
$311$	11.6484			0.660517			0.330259	−	0.943890i	$-0.392864\pi$
$311$	11.6484			0.660517			0.330259	+	0.943890i	$0.392864\pi$
$312$		0			0
$313$			20.9802i			1.18587i	0.805250	+	0.592935i	$0.202031\pi$
$313$			20.9802i			1.18587i	−0.805250	+	0.592935i	$0.797969\pi$
$314$	−6.20703	−	10.7509i	−0.350283	−	0.606708i
$315$		0			0
$316$	−0.328664	+	0.569262i	−0.0184888	+	0.0320235i
$317$		−	13.2782i		−	0.745778i	−0.927876	−	0.372889i	$-0.878367\pi$
$317$		−	13.2782i		−	0.745778i	0.927876	−	0.372889i	$-0.121633\pi$
$318$		0			0
$319$	12.2455	−	21.2098i	0.685615	−	1.18752i
$320$	−10.4228	−	6.37233i	−0.582654	−	0.356224i
$321$		0			0
$322$	3.42727	−	1.97874i	0.190994	−	0.110271i
$323$	−17.6165	+	10.1709i	−0.980209	+	0.565924i
$324$		0			0
$325$	11.3014	+	14.0456i	0.626891	+	0.779107i
$326$	19.3141			1.06971
$327$		0			0
$328$	26.1266	−	15.0842i	1.44260	−	0.832886i
$329$	0.518384	−	0.897867i	0.0285794	−	0.0495010i
$330$		0			0
$331$	2.20775	−	3.82394i	0.121349	−	0.210183i	−0.798951	−	0.601396i	$-0.794611\pi$
$331$	2.20775	−	3.82394i	0.121349	−	0.210183i	0.920300	+	0.391214i	$0.127945\pi$
$332$	−0.791907	−	0.457208i	−0.0434615	−	0.0250925i
$333$		0			0
$334$	12.3535	−	21.3969i	0.675954	−	1.17079i
$335$	−26.2463	−	0.660172i	−1.43399	−	0.0360691i
$336$		0			0
$337$		−	16.6846i		−	0.908870i	−0.890780	−	0.454435i	$-0.849841\pi$
$337$		−	16.6846i		−	0.908870i	0.890780	−	0.454435i	$-0.150159\pi$
$338$	12.1368	−	16.3455i	0.660155	−	0.889080i
$339$		0			0
$340$	5.01185	+	0.126063i	0.271806	+	0.00683671i
$341$	22.6318	+	39.1994i	1.22558	+	2.12277i
$342$		0			0
$343$		−	5.29544i		−	0.285927i
$344$	9.93901	−	17.2149i	0.535876	−	0.928164i
$345$		0			0
$346$	23.2223			1.24844
$347$	4.60585	+	2.65919i	0.247255	+	0.142753i	0.618507	−	0.785780i	$-0.287738\pi$
$347$	4.60585	+	2.65919i	0.247255	+	0.142753i	−0.371252	+	0.928532i	$0.621071\pi$
$348$		0			0
$349$	−6.87909	−	11.9149i	−0.368229	−	0.637792i	0.621060	−	0.783763i	$-0.286703\pi$
$349$	−6.87909	−	11.9149i	−0.368229	−	0.637792i	−0.989289	+	0.145972i	$0.953369\pi$
$350$	1.36430	+	2.66398i	0.0729250	+	0.142396i
$351$		0			0
$352$		−	11.6047i		−	0.618535i
$353$	−17.9736	+	10.3771i	−0.956640	+	0.552316i	−0.895137	−	0.445791i	$-0.852923\pi$
$353$	−17.9736	+	10.3771i	−0.956640	+	0.552316i	−0.0615025	+	0.998107i	$0.519589\pi$
$354$		0			0
$355$	−6.13871	+	3.34126i	−0.325809	+	0.177336i
$356$	2.35975			0.125067
$357$		0			0
$358$	−3.27747	−	1.89225i	−0.173220	−	0.100008i
$359$	−34.8124			−1.83733			−0.918665	−	0.395037i	$-0.870732\pi$
$359$	−34.8124			−1.83733			−0.918665	+	0.395037i	$0.870732\pi$
$360$		0			0
$361$	1.07139	+	1.85570i	0.0563890	+	0.0976687i
$362$	15.8831	−	9.17014i	0.834800	−	0.481972i
$363$		0			0
$364$	0.465637	−	0.414908i	0.0244060	−	0.0217471i
$365$	−15.8467	+	25.9195i	−0.829456	+	1.35669i
$366$		0			0
$367$	11.9091	−	6.87572i	0.621650	−	0.358910i	−0.155861	−	0.987779i	$-0.549815\pi$
$367$	11.9091	−	6.87572i	0.621650	−	0.358910i	0.777511	+	0.628869i	$0.216482\pi$
$368$	26.9113	+	15.5372i	1.40285	+	0.809934i
$369$		0			0
$370$	5.14238	−	2.79896i	0.267339	−	0.145511i
$371$	0.396848	−	0.687361i	0.0206033	−	0.0356860i
$372$		0			0
$373$	−10.7416	−	6.20167i	−0.556179	−	0.321110i	0.195431	−	0.980717i	$-0.437389\pi$
$373$	−10.7416	−	6.20167i	−0.556179	−	0.321110i	−0.751611	+	0.659607i	$0.770723\pi$
$374$	−17.9073	−	31.0163i	−0.925963	−	1.60382i
$375$		0			0
$376$	6.57323			0.338988
$377$	12.7268	+	14.2828i	0.655461	+	0.735602i
$378$		0			0
$379$	6.28456	+	10.8852i	0.322816	+	0.559134i	0.981068	−	0.193664i	$-0.0620371\pi$
$379$	6.28456	+	10.8852i	0.322816	+	0.559134i	−0.658252	+	0.752798i	$0.728704\pi$
$380$	−0.104468	+	4.15332i	−0.00535910	+	0.213061i
$381$		0			0
$382$			20.7488i			1.06160i
$383$	−13.8648	−	8.00485i	−0.708459	−	0.409029i	0.102031	−	0.994781i	$-0.467466\pi$
$383$	−13.8648	−	8.00485i	−0.708459	−	0.409029i	−0.810490	+	0.585752i	$0.800799\pi$
$384$		0			0
$385$	2.05790	−	3.36598i	0.104880	−	0.171546i
$386$	4.97817	−	8.62244i	0.253382	−	0.438871i
$387$		0			0
$388$	−7.13498	+	4.11938i	−0.362224	+	0.209130i
$389$	18.0667			0.916019			0.458009	−	0.888947i	$-0.348563\pi$
$389$	18.0667			0.916019			0.458009	+	0.888947i	$0.348563\pi$
$390$		0			0
$391$	32.7549			1.65648
$392$	14.3845	−	8.30492i	0.726529	−	0.419462i
$393$		0			0
$394$	−12.4832	+	21.6215i	−0.628894	+	1.08928i
$395$	−2.77110	−	1.69420i	−0.139429	−	0.0852445i
$396$		0			0
$397$	26.2468	+	15.1536i	1.31729	+	0.760539i	0.983292	−	0.182035i	$-0.0582683\pi$
$397$	26.2468	+	15.1536i	1.31729	+	0.760539i	0.333999	+	0.942573i	$0.391602\pi$
$398$		−	0.394424i		−	0.0197707i
$399$		0			0
$400$	−12.7591	+	19.7363i	−0.637954	+	0.986817i
$401$	2.50637	+	4.34116i	0.125162	+	0.216787i	0.921796	−	0.387675i	$-0.126722\pi$
$401$	2.50637	+	4.34116i	0.125162	+	0.216787i	−0.796634	+	0.604462i	$0.793388\pi$
$402$		0			0
$403$	−34.6212	+	7.17147i	−1.72461	+	0.357236i
$404$	−4.76082			−0.236860
$405$		0			0
$406$	1.58803	+	2.75055i	0.0788126	+	0.136507i
$407$	−6.68348	−	3.85871i	−0.331288	−	0.191269i
$408$		0			0
$409$	−13.9882	+	24.2283i	−0.691672	+	1.19801i	0.279618	+	0.960111i	$0.409792\pi$
$409$	−13.9882	+	24.2283i	−0.691672	+	1.19801i	−0.971290	+	0.237900i	$0.923541\pi$
$410$	−20.8403	−	38.2888i	−1.02923	−	1.89095i
$411$		0			0
$412$	2.91502	+	1.68299i	0.143613	+	0.0829149i
$413$	2.72423	−	1.57283i	0.134050	−	0.0773941i
$414$		0			0
$415$	2.35682	−	3.85491i	0.115692	−	0.189230i
$416$	8.60636	+	2.84582i	0.421962	+	0.139528i
$417$		0			0
$418$	25.7032	−	14.8397i	1.25718	−	0.725835i
$419$	15.0983	+	26.1510i	0.737599	+	1.27756i	0.953574	+	0.301160i	$0.0973738\pi$
$419$	15.0983	+	26.1510i	0.737599	+	1.27756i	−0.215975	+	0.976399i	$0.569293\pi$
$420$		0			0
$421$	−6.80011			−0.331417			−0.165709	−	0.986175i	$-0.552991\pi$
$421$	−6.80011			−0.331417			−0.165709	+	0.986175i	$0.552991\pi$
$422$	−22.8727	−	13.2056i	−1.11343	−	0.642837i
$423$		0			0
$424$	5.03213			0.244382
$425$	−1.24540	+	24.7410i	−0.0604109	+	1.20011i
$426$		0			0
$427$	0.712638	−	0.411442i	0.0344870	−	0.0199111i
$428$		−	3.07723i		−	0.148743i
$429$		0			0
$430$	−24.5063	−	14.9827i	−1.18180	−	0.722531i
$431$	−2.19749	−	3.80617i	−0.105849	−	0.183337i	0.808235	−	0.588859i	$-0.200423\pi$
$431$	−2.19749	−	3.80617i	−0.105849	−	0.183337i	−0.914085	+	0.405523i	$0.867089\pi$
$432$		0			0
$433$	2.97242	+	1.71613i	0.142845	+	0.0824718i	0.569719	−	0.821839i	$-0.307052\pi$
$433$	2.97242	+	1.71613i	0.142845	+	0.0824718i	−0.426874	+	0.904311i	$0.640385\pi$
$434$	−5.86992			−0.281765
$435$		0			0
$436$	1.69938	−	2.94340i	0.0813853	−	0.140964i
$437$			27.1439i			1.29847i
$438$		0			0
$439$	8.76024	+	15.1732i	0.418103	+	0.724176i	0.995749	−	0.0921117i	$-0.0293617\pi$
$439$	8.76024	+	15.1732i	0.418103	+	0.724176i	−0.577645	+	0.816288i	$0.696028\pi$
$440$	25.0052	+	0.628955i	1.19208	+	0.0299842i
$441$		0			0
$442$	27.3938	−	5.67438i	1.30299	−	0.269903i
$443$		−	35.0797i		−	1.66668i	−0.552757	−	0.833342i	$-0.686424\pi$
$443$		−	35.0797i		−	1.66668i	0.552757	−	0.833342i	$-0.313576\pi$
$444$		0			0
$445$	−0.293189	+	11.6563i	−0.0138985	+	0.552560i
$446$	−13.4931	+	23.3708i	−0.638919	+	1.10664i
$447$		0			0
$448$	−1.80851	−	1.04414i	−0.0854442	−	0.0493312i
$449$	10.3675	−	17.9571i	0.489273	−	0.847446i	−0.510651	−	0.859788i	$-0.670595\pi$
$449$	10.3675	−	17.9571i	0.489273	−	0.847446i	0.999924	+	0.0123424i	$0.00392881\pi$
$450$		0			0
$451$	−28.7309	+	49.7634i	−1.35289	+	2.34327i
$452$	−0.313280	+	0.180872i	−0.0147354	+	0.00850751i
$453$		0			0
$454$	19.1446			0.898501
$455$	1.99164	+	2.35162i	0.0933693	+	0.110246i
$456$		0			0
$457$	33.0995	−	19.1100i	1.54833	−	0.893929i	0.550061	−	0.835125i	$-0.314605\pi$
$457$	33.0995	−	19.1100i	1.54833	−	0.893929i	0.998270	−	0.0588044i	$-0.0187288\pi$
$458$	−15.1260	+	8.73298i	−0.706790	+	0.408065i
$459$		0			0
$460$	3.48957	−	5.70767i	0.162702	−	0.266122i
$461$	−0.497725	+	0.862085i	−0.0231814	+	0.0401513i	−0.877383	−	0.479790i	$-0.840713\pi$
$461$	−0.497725	+	0.862085i	−0.0231814	+	0.0401513i	0.854202	+	0.519941i	$0.174046\pi$
$462$		0			0
$463$		−	25.8530i		−	1.20149i	−0.799441	−	0.600745i	$-0.794871\pi$
$463$		−	25.8530i		−	1.20149i	0.799441	−	0.600745i	$-0.205129\pi$
$464$	−12.4694	+	21.5976i	−0.578876	+	1.00264i
$465$		0			0
$466$	14.8770	+	25.7678i	0.689165	+	1.19367i
$467$		−	8.65497i		−	0.400504i	−0.979744	−	0.200252i	$-0.935824\pi$
$467$		−	8.65497i		−	0.400504i	0.979744	−	0.200252i	$-0.0641761\pi$
$468$		0			0
$469$	−4.48799			−0.207236
$470$	0.238833	−	9.49525i	0.0110166	−	0.437983i
$471$		0			0
$472$	17.2719	+	9.97196i	0.795005	+	0.458996i
$473$			37.8617i			1.74088i
$474$		0			0
$475$	−20.5028	−	1.03206i	−0.940733	−	0.0473543i
$476$	0.857001			0.0392806
$477$		0			0
$478$	−2.21796	+	1.28054i	−0.101447	+	0.0585706i
$479$	7.87072	+	13.6325i	0.359622	+	0.622884i	0.987898	−	0.155107i	$-0.0495722\pi$
$479$	7.87072	+	13.6325i	0.359622	+	0.622884i	−0.628275	+	0.777991i	$0.716239\pi$
$480$		0			0
$481$	4.50069	−	4.01036i	0.205214	−	0.182857i
$482$			2.38238i			0.108515i
$483$		0			0
$484$	2.33202	+	4.03918i	0.106001	+	0.183599i
$485$	−19.4617	−	35.7559i	−0.883709	−	1.62359i
$486$		0			0
$487$	−2.19880	−	1.26948i	−0.0996371	−	0.0575255i	0.449353	−	0.893354i	$-0.351654\pi$
$487$	−2.19880	−	1.26948i	−0.0996371	−	0.0575255i	−0.548991	+	0.835829i	$0.684988\pi$
$488$	4.51821	+	2.60859i	0.204530	+	0.118085i
$489$		0			0
$490$	−11.4741	−	21.0807i	−0.518346	−	0.952329i
$491$	−1.14198	−	1.97796i	−0.0515367	−	0.0892643i	0.839106	−	0.543968i	$-0.183079\pi$
$491$	−1.14198	−	1.97796i	−0.0515367	−	0.0892643i	−0.890643	+	0.454703i	$0.849745\pi$
$492$		0			0
$493$			26.2873i			1.18392i
$494$	4.70235	+	22.7012i	0.211569	+	1.02138i
$495$		0			0
$496$	−23.0456	−	39.9161i	−1.03478	−	1.79229i
$497$	−1.03466	+	0.597363i	−0.0464109	+	0.0267954i
$498$		0			0
$499$	31.3860			1.40503			0.702515	−	0.711669i	$-0.252060\pi$
$499$	31.3860			1.40503			0.702515	+	0.711669i	$0.252060\pi$
$500$	4.17854	+	2.85282i	0.186870	+	0.127582i
$501$		0			0
$502$			11.2645i			0.502759i
$503$	−27.9833	−	16.1562i	−1.24772	−	0.720369i	−0.277062	−	0.960852i	$-0.589361\pi$
$503$	−27.9833	−	16.1562i	−1.24772	−	0.720369i	−0.970653	+	0.240483i	$0.922694\pi$
$504$		0			0
$505$	0.591512	−	23.5166i	0.0263219	−	1.04648i
$506$	−47.7906			−2.12455
$507$		0			0
$508$		−	3.97960i		−	0.176566i
$509$	−4.30701	−	7.45996i	−0.190905	−	0.330657i	0.754645	−	0.656133i	$-0.227809\pi$
$509$	−4.30701	−	7.45996i	−0.190905	−	0.330657i	−0.945550	+	0.325476i	$0.894476\pi$
$510$		0			0
$511$	−2.59659	+	4.49742i	−0.114866	+	0.198954i
$512$		−	10.9646i		−	0.484570i
$513$		0			0
$514$	−8.29315	+	14.3642i	−0.365795	+	0.633576i
$515$	−8.67550	+	14.1900i	−0.382288	+	0.625285i
$516$		0			0
$517$	−10.8427	+	6.26003i	−0.476861	+	0.275316i
$518$	0.866733	−	0.500408i	0.0380821	−	0.0219867i
$519$		0			0
$520$	−6.59845	+	18.3903i	−0.289361	+	0.806467i
$521$	23.3159			1.02149			0.510743	−	0.859733i	$-0.329370\pi$
$521$	23.3159			1.02149			0.510743	+	0.859733i	$0.329370\pi$
$522$		0			0
$523$	−7.63855	+	4.41012i	−0.334011	+	0.192841i	−0.657620	−	0.753350i	$-0.728437\pi$
$523$	−7.63855	+	4.41012i	−0.334011	+	0.192841i	0.323610	+	0.946191i	$0.395104\pi$
$524$	−1.75166	+	3.03397i	−0.0765218	+	0.132540i
$525$		0			0
$526$	14.1545	−	24.5163i	0.617166	−	1.06896i
$527$	−42.0747	−	24.2918i	−1.83280	−	1.05817i
$528$		0			0
$529$	10.3539	−	17.9335i	0.450169	−	0.779716i
$530$	0.182838	−	7.26908i	0.00794200	−	0.315748i
$531$		0			0
$532$			0.710195i			0.0307909i
$533$	−29.8601	−	33.5110i	−1.29339	−	1.45152i
$534$		0			0
$535$	15.2003	+	0.382333i	0.657168	+	0.0165297i
$536$	−14.2272	−	24.6422i	−0.614521	−	1.06438i
$537$		0			0
$538$		−	7.40173i		−	0.319111i
$539$	−15.8184	+	27.3983i	−0.681347	+	1.18013i
$540$		0			0
$541$	−32.6472			−1.40361			−0.701806	−	0.712368i	$-0.747623\pi$
$541$	−32.6472			−1.40361			−0.701806	+	0.712368i	$0.747623\pi$
$542$	−6.59776	−	3.80922i	−0.283398	−	0.163620i
$543$		0			0
$544$	6.22797	+	10.7872i	0.267022	+	0.462496i
$545$	14.3282	+	8.75997i	0.613751	+	0.375236i
$546$		0			0
$547$			37.1900i			1.59013i	0.606523	+	0.795066i	$0.292564\pi$
$547$			37.1900i			1.59013i	−0.606523	+	0.795066i	$0.707436\pi$
$548$	−3.63417	+	2.09819i	−0.155244	+	0.0896302i
$549$		0			0
$550$	1.81709	−	36.0980i	0.0774811	−	1.53923i
$551$	−21.7843			−0.928042
$552$		0			0
$553$	−0.480827	−	0.277605i	−0.0204468	−	0.0118050i
$554$	7.19956			0.305880
$555$		0			0
$556$	2.44752	+	4.23923i	0.103798	+	0.179783i
$557$	−14.7206	+	8.49891i	−0.623730	+	0.360111i	−0.778320	−	0.627868i	$-0.783928\pi$
$557$	−14.7206	+	8.49891i	−0.623730	+	0.360111i	0.154590	+	0.987979i	$0.450594\pi$
$558$		0			0
$559$	−28.0792	−	9.28479i	−1.18762	−	0.392705i
$560$	−2.09552	+	3.42752i	−0.0885520	+	0.144839i
$561$		0			0
$562$	−15.9219	+	9.19249i	−0.671623	+	0.387762i
$563$	16.4675	+	9.50753i	0.694024	+	0.400695i	0.805118	−	0.593115i	$-0.202102\pi$
$563$	16.4675	+	9.50753i	0.694024	+	0.400695i	−0.111094	+	0.993810i	$0.535435\pi$
$564$		0			0
$565$	−0.854515	−	1.56995i	−0.0359497	−	0.0660485i
$566$	3.07040	−	5.31809i	0.129059	−	0.223536i
$567$		0			0
$568$	−6.55988	−	3.78735i	−0.275247	−	0.158914i
$569$	12.7307	+	22.0502i	0.533698	+	0.924392i	0.999225	+	0.0393584i	$0.0125314\pi$
$569$	12.7307	+	22.0502i	0.533698	+	0.924392i	−0.465527	+	0.885034i	$0.654135\pi$
$570$		0			0
$571$	−18.6229			−0.779344			−0.389672	−	0.920954i	$-0.627412\pi$
$571$	−18.6229			−0.779344			−0.389672	+	0.920954i	$0.627412\pi$
$572$	−7.37494	+	1.52765i	−0.308362	+	0.0638743i
$573$		0			0
$574$	−3.72591	−	6.45347i	−0.155517	−	0.269363i
$575$	27.7602	+	17.9463i	1.15768	+	0.748411i
$576$		0			0
$577$			10.8481i			0.451614i	0.974172	+	0.225807i	$0.0725018\pi$
$577$			10.8481i			0.451614i	−0.974172	+	0.225807i	$0.927498\pi$
$578$	10.2351	+	5.90926i	0.425726	+	0.245793i
$579$		0			0
$580$	4.58068	+	2.80054i	0.190202	+	0.116286i
$581$	0.386180	−	0.668883i	0.0160214	−	0.0277499i
$582$		0			0
$583$	−8.30060	+	4.79236i	−0.343776	+	0.198479i
$584$	−32.9253			−1.36246
$585$		0			0
$586$	38.5205			1.59127
$587$	−18.2533	+	10.5385i	−0.753392	+	0.434971i	−0.826918	−	0.562322i	$-0.809908\pi$
$587$	−18.2533	+	10.5385i	−0.753392	+	0.434971i	0.0735260	+	0.997293i	$0.476575\pi$
$588$		0			0
$589$	20.1306	−	34.8672i	0.829467	−	1.43668i
$590$	15.0324	−	24.5876i	0.618873	−	1.01225i
$591$		0			0
$592$	6.80567	+	3.92926i	0.279711	+	0.161491i
$593$		−	15.7704i		−	0.647612i	−0.946124	−	0.323806i	$-0.895038\pi$
$593$		−	15.7704i		−	0.647612i	0.946124	−	0.323806i	$-0.104962\pi$
$594$		0			0
$595$	−0.106479	+	4.23326i	−0.00436520	+	0.173547i
$596$	−1.90777	−	3.30435i	−0.0781452	−	0.135351i
$597$		0			0
$598$	11.7196	−	35.4427i	0.479252	−	1.44936i
$599$	−20.9648			−0.856597			−0.428299	−	0.903637i	$-0.640887\pi$
$599$	−20.9648			−0.856597			−0.428299	+	0.903637i	$0.640887\pi$
$600$		0			0
$601$	−14.2330	−	24.6523i	−0.580576	−	1.00559i	−0.995411	−	0.0956901i	$-0.969494\pi$
$601$	−14.2330	−	24.6523i	−0.580576	−	1.00559i	0.414836	−	0.909896i	$-0.363839\pi$
$602$	−4.25220	−	2.45501i	−0.173307	−	0.100059i
$603$		0			0
$604$	3.97196	−	6.87964i	0.161617	−	0.279928i
$605$	−20.2418	+	11.0174i	−0.822944	+	0.447923i
$606$		0			0
$607$	32.2303	+	18.6082i	1.30819	+	0.755282i	0.981793	−	0.189952i	$-0.0608333\pi$
$607$	32.2303	+	18.6082i	1.30819	+	0.755282i	0.326393	+	0.945234i	$0.394167\pi$
$608$	−8.93930	+	5.16111i	−0.362537	+	0.209311i
$609$		0			0
$610$	3.93236	−	6.43193i	0.159217	−	0.260421i
$611$	−1.98365	−	9.57634i	−0.0802500	−	0.387417i
$612$		0			0
$613$	−26.0082	+	15.0159i	−1.05046	+	0.606485i	−0.922779	−	0.385330i	$-0.874088\pi$
$613$	−26.0082	+	15.0159i	−1.05046	+	0.606485i	−0.127684	+	0.991815i	$0.540754\pi$
$614$	13.1765	+	22.8224i	0.531761	+	0.921037i
$615$		0			0
$616$	4.27577			0.172275
$617$	0.234758	+	0.135537i	0.00945099	+	0.00545653i	0.504718	−	0.863284i	$-0.331596\pi$
$617$	0.234758	+	0.135537i	0.00945099	+	0.00545653i	−0.495267	+	0.868741i	$0.664930\pi$
$618$		0			0
$619$	−33.3139			−1.33900			−0.669500	−	0.742812i	$-0.733492\pi$
$619$	−33.3139			−1.33900			−0.669500	+	0.742812i	$0.733492\pi$
$620$	−8.71541	+	4.74374i	−0.350019	+	0.190513i
$621$		0			0
$622$	15.7980	−	9.12100i	0.633443	−	0.365719i
$623$			1.99316i			0.0798543i
$624$		0			0
$625$	−14.6110	+	20.2859i	−0.584440	+	0.811437i
$626$	16.4281	+	28.4543i	0.656599	+	1.13726i
$627$		0			0
$628$	−3.10664	−	1.79362i	−0.123968	−	0.0715732i
$629$	8.28348			0.330284
$630$		0			0
$631$	22.3283	−	38.6738i	0.888876	−	1.53958i	0.0476701	−	0.998863i	$-0.484820\pi$
$631$	22.3283	−	38.6738i	0.888876	−	1.53958i	0.841206	−	0.540715i	$-0.181846\pi$
$632$		−	3.52010i		−	0.140022i
$633$		0			0
$634$	−10.3972	−	18.0085i	−0.412926	−	0.715209i
$635$	19.6577	+	0.494449i	0.780092	+	0.0196216i
$636$		0			0
$637$	−16.4401	−	18.4502i	−0.651381	−	0.731023i
$638$		−	38.3542i		−	1.51846i
$639$		0			0
$640$	−30.3654	−	0.763779i	−1.20030	−	0.0301910i
$641$	−4.36848	+	7.56644i	−0.172545	+	0.298856i	−0.939309	−	0.343073i	$-0.888532\pi$
$641$	−4.36848	+	7.56644i	−0.172545	+	0.298856i	0.766764	+	0.641929i	$0.221866\pi$
$642$		0			0
$643$	12.6826	+	7.32231i	0.500154	+	0.288764i	0.728777	−	0.684751i	$-0.240089\pi$
$643$	12.6826	+	7.32231i	0.500154	+	0.288764i	−0.228623	+	0.973515i	$0.573422\pi$
$644$	0.571787	−	0.990364i	0.0225316	−	0.0390258i
$645$		0			0
$646$	−15.9282	+	27.5885i	−0.626687	+	1.08545i
$647$	−8.55946	+	4.94180i	−0.336507	+	0.194282i	−0.658726	−	0.752383i	$-0.728904\pi$
$647$	−8.55946	+	4.94180i	−0.336507	+	0.194282i	0.322219	+	0.946665i	$0.395571\pi$
$648$		0			0
$649$	−37.9872			−1.49113
$650$	26.3256	+	10.1999i	1.03257	+	0.400072i
$651$		0			0
$652$	4.83338	−	2.79055i	0.189290	−	0.109287i
$653$	12.5278	−	7.23293i	0.490251	−	0.283046i	−0.234428	−	0.972134i	$-0.575322\pi$
$653$	12.5278	−	7.23293i	0.490251	−	0.283046i	0.724678	+	0.689087i	$0.241988\pi$
$654$		0			0
$655$	−14.7690	−	9.02950i	−0.577073	−	0.352812i
$656$	29.2562	−	50.6733i	1.14226	−	1.97846i
$657$		0			0
$658$		−	1.62364i		−	0.0632960i
$659$	18.9517	−	32.8253i	0.738254	−	1.27869i	−0.215027	−	0.976608i	$-0.568984\pi$
$659$	18.9517	−	32.8253i	0.738254	−	1.27869i	0.953281	−	0.302085i	$-0.0976826\pi$
$660$		0			0
$661$	18.7346	+	32.4494i	0.728693	+	1.26213i	0.957436	+	0.288647i	$0.0932053\pi$
$661$	18.7346	+	32.4494i	0.728693	+	1.26213i	−0.228742	+	0.973487i	$0.573461\pi$
$662$		−	6.91494i		−	0.268757i
$663$		0			0
$664$	4.89685			0.190035
$665$	−3.50809	−	0.0882388i	−0.136038	−	0.00342175i
$666$		0			0
$667$	30.3781	+	17.5388i	1.17624	+	0.679105i
$668$		−	7.13948i		−	0.276235i
$669$		0			0
$670$	−36.1134	+	19.6563i	−1.39518	+	0.759389i
$671$	−9.93719			−0.383621
$672$		0			0
$673$	−38.1855	+	22.0464i	−1.47194	+	0.849827i	−0.999503	−	0.0315359i	$-0.989960\pi$
$673$	−38.1855	+	22.0464i	−1.47194	+	0.849827i	−0.472440	+	0.881363i	$0.656627\pi$
$674$	−13.0646	−	22.6285i	−0.503228	−	0.871616i
$675$		0			0
$676$	0.675604	−	5.84406i	0.0259848	−	0.224772i
$677$			28.9736i			1.11355i	0.830664	+	0.556773i	$0.187961\pi$
$677$			28.9736i			1.11355i	−0.830664	+	0.556773i	$0.812039\pi$
$678$		0			0
$679$	−3.47943	−	6.02655i	−0.133528	−	0.231278i
$680$	−23.5811	+	12.8350i	−0.904294	+	0.492201i
$681$		0			0
$682$	61.3886	+	35.4427i	2.35069	+	1.35717i
$683$	40.9467	+	23.6406i	1.56678	+	0.904583i	0.996541	+	0.0831067i	$0.0264842\pi$
$683$	40.9467	+	23.6406i	1.56678	+	0.904583i	0.570243	+	0.821476i	$0.306849\pi$
$684$		0			0
$685$	−9.91272	−	18.2121i	−0.378746	−	0.695848i
$686$	−4.14649	−	7.18192i	−0.158314	−	0.274207i
$687$		0			0
$688$		−	38.5540i		−	1.46986i
$689$	−1.51858	−	7.33116i	−0.0578534	−	0.279295i
$690$		0			0
$691$	−20.8171	−	36.0562i	−0.791919	−	1.37164i	−0.924777	−	0.380509i	$-0.875749\pi$
$691$	−20.8171	−	36.0562i	−0.791919	−	1.37164i	0.132858	−	0.991135i	$-0.457585\pi$
$692$	5.81143	−	3.35523i	0.220917	−	0.127547i
$693$		0			0
$694$	8.32888			0.316160
$695$	−21.2442	+	11.5631i	−0.805840	+	0.438613i
$696$		0			0
$697$		−	61.6766i		−	2.33617i
$698$	−18.6595	−	10.7731i	−0.706272	−	0.407766i
$699$		0			0
$700$	0.726319	+	0.469548i	0.0274523	+	0.0177472i
$701$	−35.7299			−1.34950			−0.674750	−	0.738046i	$-0.735749\pi$
$701$	−35.7299			−1.34950			−0.674750	+	0.738046i	$0.735749\pi$
$702$		0			0
$703$			6.86451i			0.258900i
$704$	12.6091	+	21.8397i	0.475225	+	0.823114i
$705$		0			0
$706$	−16.2511	+	28.1477i	−0.611618	+	1.05935i
$707$		−	4.02122i		−	0.151234i
$708$		0			0
$709$	−19.0310	+	32.9627i	−0.714726	+	1.23794i	0.248339	+	0.968673i	$0.420115\pi$
$709$	−19.0310	+	32.9627i	−0.714726	+	1.23794i	−0.963065	+	0.269268i	$0.913218\pi$
$710$	−5.70930	+	9.33836i	−0.214266	+	0.350462i
$711$		0			0
$712$	−10.9439	+	6.31844i	−0.410139	+	0.236794i
$713$	−56.1440	+	32.4148i	−2.10261	+	1.21394i
$714$		0			0
$715$	−6.62971	−	36.6192i	−0.247937	−	1.36948i
$716$	−1.09359			−0.0408694
$717$		0			0
$718$	−47.2142	+	27.2591i	−1.76202	+	1.01730i
$719$	−16.5212	+	28.6156i	−0.616138	+	1.06718i	0.374046	+	0.927410i	$0.377970\pi$
$719$	−16.5212	+	28.6156i	−0.616138	+	1.06718i	−0.990184	+	0.139772i	$0.955363\pi$
$720$		0			0
$721$	−1.42153	+	2.46217i	−0.0529407	+	0.0916960i
$722$	2.90614	+	1.67786i	0.108155	+	0.0624435i
$723$		0			0
$724$	2.64986	−	4.58969i	0.0984812	−	0.170574i
$725$	−14.4027	+	22.2788i	−0.534904	+	0.827416i
$726$		0			0
$727$			46.5797i			1.72754i	0.503883	+	0.863772i	$0.331904\pi$
$727$			46.5797i			1.72754i	−0.503883	+	0.863772i	$0.668096\pi$
$728$	−1.04854	+	3.17101i	−0.0388615	+	0.117526i
$729$		0			0
$730$	−1.19632	+	47.5617i	−0.0442777	+	1.76034i
$731$	−20.3194	−	35.1943i	−0.751541	−	1.30171i
$732$		0			0
$733$			31.2147i			1.15294i	0.817118	+	0.576471i	$0.195570\pi$
$733$			31.2147i			1.15294i	−0.817118	+	0.576471i	$0.804430\pi$
$734$	10.7678	−	18.6503i	0.397446	−	0.688397i
$735$		0			0
$736$	16.6211			0.612661
$737$	46.9361	+	27.0986i	1.72891	+	0.998189i
$738$		0			0
$739$	−3.57139	−	6.18583i	−0.131376	−	0.227549i	0.792831	−	0.609441i	$-0.208606\pi$
$739$	−3.57139	−	6.18583i	−0.131376	−	0.227549i	−0.924207	+	0.381892i	$0.875273\pi$
$740$	0.882487	−	1.44343i	0.0324409	−	0.0530616i
$741$		0			0
$742$		−	1.24297i		−	0.0456310i
$743$	−32.8742	+	18.9799i	−1.20604	+	0.696305i	−0.961891	−	0.273433i	$-0.911841\pi$
$743$	−32.8742	+	18.9799i	−1.20604	+	0.696305i	−0.244145	+	0.969739i	$0.578507\pi$
$744$		0			0
$745$	16.5592	−	9.01308i	0.606684	−	0.330214i
$746$	−19.4244			−0.711176
$747$		0			0
$748$	−8.96266	−	5.17459i	−0.327707	−	0.189202i
$749$	2.59918			0.0949719
$750$		0			0
$751$	7.73002	+	13.3888i	0.282073	+	0.488564i	0.971895	−	0.235415i	$-0.0756448\pi$
$751$	7.73002	+	13.3888i	0.282073	+	0.488564i	−0.689823	+	0.723979i	$0.742311\pi$
$752$	11.0409	−	6.37448i	0.402621	−	0.232454i
$753$		0			0
$754$	28.4445	+	9.40557i	1.03589	+	0.342531i
$755$	33.4893	+	20.4747i	1.21880	+	0.745152i
$756$		0			0
$757$	19.0477	−	10.9972i	0.692299	−	0.399699i	−0.112174	−	0.993689i	$-0.535781\pi$
$757$	19.0477	−	10.9972i	0.692299	−	0.399699i	0.804473	+	0.593990i	$0.202448\pi$
$758$	17.0468	+	9.84198i	0.619168	+	0.357477i
$759$		0			0
$760$	−10.6364	−	19.5416i	−0.385822	−	0.708849i
$761$	16.2469	−	28.1405i	0.588950	−	1.02009i	−0.405420	−	0.914130i	$-0.632875\pi$
$761$	16.2469	−	28.1405i	0.588950	−	1.02009i	0.994370	−	0.105961i	$-0.0337919\pi$
$762$		0			0
$763$	2.48614	+	1.43538i	0.0900044	+	0.0519641i
$764$	2.99785	+	5.19243i	0.108458	+	0.187855i
$765$		0			0
$766$	−25.0721			−0.905893
$767$	9.31557	−	28.1723i	0.336366	−	1.01724i
$768$		0			0
$769$	6.69448	+	11.5952i	0.241409	+	0.418133i	0.961116	−	0.276145i	$-0.0890572\pi$
$769$	6.69448	+	11.5952i	0.241409	+	0.418133i	−0.719707	+	0.694278i	$0.755724\pi$
$770$	0.155357	−	6.17648i	0.00559866	−	0.222585i
$771$		0			0
$772$		−	2.87704i		−	0.103547i
$773$	25.6656	+	14.8180i	0.923128	+	0.532968i	0.884632	−	0.466291i	$-0.154410\pi$
$773$	25.6656	+	14.8180i	0.923128	+	0.532968i	0.0384962	+	0.999259i	$0.487743\pi$
$774$		0			0
$775$	−22.3494	−	43.6402i	−0.802814	−	1.56760i
$776$	22.0600	−	38.2091i	0.791908	−	1.37163i
$777$		0			0
$778$	24.5029	−	14.1468i	0.878472	−	0.507186i
$779$	51.1113			1.83125
$780$		0			0
$781$	14.4276			0.516259
$782$	44.4236	−	25.6480i	1.58859	−	0.917171i
$783$		0			0
$784$	16.1076	−	27.8992i	0.575273	−	0.996401i
$785$	9.24578	−	15.1228i	0.329996	−	0.539754i
$786$		0			0
$787$	−10.0344	−	5.79337i	−0.357688	−	0.206511i	0.310378	−	0.950613i	$-0.399544\pi$
$787$	−10.0344	−	5.79337i	−0.357688	−	0.206511i	−0.668066	+	0.744102i	$0.732878\pi$
$788$			7.21443i			0.257003i
$789$		0			0
$790$	−5.08490	−	0.127900i	−0.180913	−	0.00455048i
$791$	−0.152773	−	0.264611i	−0.00543200	−	0.00940849i
$792$		0			0
$793$	2.43689	−	7.36966i	0.0865363	−	0.261704i
$794$	47.4629			1.68440
$795$		0			0
$796$	−0.0569875	−	0.0987053i	−0.00201987	−	0.00349852i
$797$	18.3325	+	10.5843i	0.649372	+	0.374915i	0.788216	−	0.615399i	$-0.211005\pi$
$797$	18.3325	+	10.5843i	0.649372	+	0.374915i	−0.138844	+	0.990314i	$0.544339\pi$
$798$		0			0
$799$	6.71919	−	11.6380i	0.237708	−	0.411722i
$800$	−0.631966	+	12.5545i	−0.0223434	+	0.443870i
$801$		0			0
$802$	6.79850	+	3.92512i	0.240064	+	0.138601i
$803$	54.3110	−	31.3565i	1.91660	−	1.10655i
$804$		0			0
$805$	4.82098	+	2.94746i	0.169917	+	0.103884i
$806$	−41.3394	+	36.8357i	−1.45612	+	1.29748i
$807$		0			0
$808$	22.0793	−	12.7475i	0.776749	−	0.448456i
$809$	−8.57020	−	14.8440i	−0.301312	−	0.521888i	0.675121	−	0.737707i	$-0.264091\pi$
$809$	−8.57020	−	14.8440i	−0.301312	−	0.521888i	−0.976433	+	0.215819i	$0.930758\pi$
$810$		0			0
$811$	9.07623			0.318710			0.159355	−	0.987221i	$-0.449059\pi$
$811$	9.07623			0.318710			0.159355	+	0.987221i	$0.449059\pi$
$812$	0.794814	+	0.458886i	0.0278925	+	0.0161038i
$813$		0			0
$814$	−12.0859			−0.423611
$815$	13.1837	+	24.2218i	0.461806	+	0.848452i
$816$		0			0
$817$	29.1655	−	16.8387i	1.02037	−	0.589111i
$818$			43.8127i			1.53187i
$819$		0			0
$820$	−10.7474	−	6.57077i	−0.375316	−	0.229461i
$821$	−5.78628	−	10.0221i	−0.201943	−	0.349775i	0.747212	−	0.664586i	$-0.231392\pi$
$821$	−5.78628	−	10.0221i	−0.201943	−	0.349775i	−0.949154	+	0.314811i	$0.898059\pi$
$822$		0			0
$823$	7.76202	+	4.48141i	0.270567	+	0.156212i	0.629145	−	0.777288i	$-0.283405\pi$
$823$	7.76202	+	4.48141i	0.270567	+	0.156212i	−0.358578	+	0.933500i	$0.616738\pi$
$824$	−18.0254			−0.627944
$825$		0			0
$826$	2.46315	−	4.26630i	0.0857039	−	0.148444i
$827$		−	35.1240i		−	1.22138i	−0.791869	−	0.610691i	$-0.790892\pi$
$827$		−	35.1240i		−	1.22138i	0.791869	−	0.610691i	$-0.209108\pi$
$828$		0			0
$829$	27.7711	+	48.1010i	0.964530	+	1.67062i	0.710872	+	0.703322i	$0.248301\pi$
$829$	27.7711	+	48.1010i	0.964530	+	1.67062i	0.253659	+	0.967294i	$0.418366\pi$
$830$	0.177923	−	7.07367i	0.00617581	−	0.245531i
$831$		0			0
$832$	−19.2890	+	3.99553i	−0.668725	+	0.138520i
$833$		−	33.9574i		−	1.17655i
$834$		0			0
$835$	35.2663	+	0.887050i	1.22044	+	0.0306976i
$836$	4.28818	−	7.42734i	0.148310	−	0.256880i
$837$		0			0
$838$	40.9539	+	23.6448i	1.41473	+	0.816795i
$839$	−8.45641	+	14.6469i	−0.291948	+	0.505668i	−0.974270	−	0.225383i	$-0.927637\pi$
$839$	−8.45641	+	14.6469i	−0.291948	+	0.505668i	0.682322	+	0.731051i	$0.260970\pi$
$840$		0			0
$841$	0.424282	−	0.734878i	0.0146304	−	0.0253406i
$842$	−9.22262	+	5.32468i	−0.317833	+	0.183501i
$843$		0			0
$844$	−7.63192			−0.262701
$845$	28.7835	+	4.06333i	0.990182	+	0.139783i
$846$		0			0
$847$	−3.41169	+	1.96974i	−0.117227	+	0.0676811i
$848$	8.45237	−	4.87998i	0.290256	−	0.167579i
$849$		0			0
$850$	17.6838	+	34.5300i	0.606550	+	1.18437i
$851$	5.52670	−	9.57252i	0.189453	−	0.328142i
$852$		0			0
$853$		−	20.4066i		−	0.698708i	−0.936991	−	0.349354i	$-0.886401\pi$
$853$		−	20.4066i		−	0.698708i	0.936991	−	0.349354i	$-0.113599\pi$
$854$	0.644342	−	1.11603i	0.0220489	−	0.0381899i
$855$		0			0
$856$	8.23955	+	14.2713i	0.281622	+	0.487784i
$857$		−	25.5936i		−	0.874260i	−0.899398	−	0.437130i	$-0.855995\pi$
$857$		−	25.5936i		−	0.874260i	0.899398	−	0.437130i	$-0.144005\pi$
$858$		0			0
$859$	−0.0519681			−0.00177313			−0.000886565	−	1.00000i	$-0.500282\pi$
$859$	−0.0519681			−0.00177313			−0.000886565		1.00000i	$0.500282\pi$
$860$	−8.29750	−	0.208706i	−0.282942	−	0.00711683i
$861$		0			0
$862$	−5.96068	−	3.44140i	−0.203022	−	0.117215i
$863$		−	5.17282i		−	0.176085i	−0.996117	−	0.0880424i	$-0.971939\pi$
$863$		−	5.17282i		−	0.176085i	0.996117	−	0.0880424i	$-0.0280611\pi$
$864$		0			0
$865$	15.8515	+	29.1231i	0.538968	+	0.990216i
$866$	5.37511			0.182654
$867$		0			0
$868$	−1.46896	+	0.848103i	−0.0498597	+	0.0287865i
$869$	3.35238	+	5.80648i	0.113722	+	0.196972i
$870$		0			0
$871$	−31.6071	+	28.1636i	−1.07096	+	0.954288i
$872$			18.2009i			0.616360i
$873$		0			0
$874$	21.2545	+	36.8138i	0.718943	+	1.24525i
$875$	−2.40963	+	3.52940i	−0.0814603	+	0.119315i
$876$		0			0
$877$	13.5519	+	7.82418i	0.457614	+	0.264204i	0.711041	−	0.703151i	$-0.248224\pi$
$877$	13.5519	+	7.82418i	0.457614	+	0.264204i	−0.253426	+	0.967355i	$0.581558\pi$
$878$	23.7621	+	13.7190i	0.801931	+	0.462995i
$879$		0			0
$880$	42.6108	−	23.1927i	1.43641	−	0.781827i
$881$	−18.8811	−	32.7030i	−0.636119	−	1.10179i	−0.986277	−	0.165100i	$-0.947205\pi$
$881$	−18.8811	−	32.7030i	−0.636119	−	1.10179i	0.350158	−	0.936691i	$-0.386128\pi$
$882$		0			0
$883$		−	10.6910i		−	0.359781i	−0.983687	−	0.179890i	$-0.942426\pi$
$883$		−	10.6910i		−	0.359781i	0.983687	−	0.179890i	$-0.0575743\pi$
$884$	6.03551	−	5.37797i	0.202996	−	0.180881i
$885$		0			0
$886$	−27.4684	−	47.5766i	−0.922818	−	1.59837i
$887$	−29.0202	+	16.7548i	−0.974401	+	0.562571i	−0.900575	−	0.434700i	$-0.856854\pi$
$887$	−29.0202	+	16.7548i	−0.974401	+	0.562571i	−0.0738261	+	0.997271i	$0.523521\pi$
$888$		0			0
$889$	3.36136			0.112737
$890$	8.72956	+	16.0383i	0.292616	+	0.537607i
$891$		0			0
$892$			7.79811i			0.261100i
$893$	9.64438	+	5.56819i	0.322737	+	0.186332i
$894$		0			0
$895$	0.135874	−	5.40192i	0.00454177	−	0.180566i
$896$	−5.19233			−0.173463
$897$		0			0
$898$		−	32.4722i		−	1.08361i
$899$	−26.0144	−	45.0583i	−0.867629	−	1.50278i
$900$		0			0
$901$	5.14387	−	8.90945i	0.171367	−	0.296817i
$902$			89.9886i			2.99629i
$903$		0			0
$904$	0.968602	−	1.67767i	0.0322152	−	0.0557984i
$905$	22.3421	+	13.6595i	0.742676	+	0.454058i
$906$		0			0
$907$	23.0200	−	13.2906i	0.764365	−	0.441307i	−0.0664955	−	0.997787i	$-0.521182\pi$
$907$	23.0200	−	13.2906i	0.764365	−	0.441307i	0.830861	+	0.556480i	$0.187848\pi$
$908$	4.79097	−	2.76607i	0.158994	−	0.0917952i
$909$		0			0
$910$	4.54254	+	1.62987i	0.150584	+	0.0540296i
$911$	−30.7452			−1.01863			−0.509316	−	0.860579i	$-0.670102\pi$
$911$	−30.7452			−1.01863			−0.509316	+	0.860579i	$0.670102\pi$
$912$		0			0
$913$	−8.07747	+	4.66353i	−0.267325	+	0.154340i
$914$	29.9274	−	51.8358i	0.989910	−	1.71457i
$915$		0			0
$916$	−2.52353	+	4.37089i	−0.0833799	+	0.144418i
$917$	−2.56264	−	1.47954i	−0.0846258	−	0.0488587i
$918$		0			0
$919$	6.91237	−	11.9726i	0.228018	−	0.394939i	−0.729203	−	0.684298i	$-0.760109\pi$
$919$	6.91237	−	11.9726i	0.228018	−	0.394939i	0.957221	+	0.289359i	$0.0934422\pi$
$920$	−0.900831	+	35.8142i	−0.0296995	+	1.18076i
$921$		0			0
$922$			1.55893i			0.0513407i
$923$	−3.53805	+	10.6998i	−0.116456	+	0.352189i
$924$		0			0
$925$	7.02035	+	4.53849i	0.230828	+	0.149225i
$926$	−20.2436	−	35.0630i	−0.665247	−	1.15224i
$927$		0			0
$928$			13.3392i			0.437881i
$929$	−14.4478	+	25.0243i	−0.474016	+	0.821020i	−0.999557	−	0.0297480i	$-0.990530\pi$
$929$	−14.4478	+	25.0243i	−0.474016	+	0.821020i	0.525541	+	0.850768i	$0.323863\pi$
$930$		0			0
$931$	28.1404			0.922265
$932$	7.44601	+	4.29896i	0.243902	+	0.140817i
$933$		0			0
$934$	−6.77709	−	11.7383i	−0.221753	−	0.384088i
$935$	26.6741	−	43.6292i	0.872335	−	1.42683i
$936$		0			0
$937$			13.7552i			0.449362i	0.974432	+	0.224681i	$0.0721340\pi$
$937$			13.7552i			0.449362i	−0.974432	+	0.224681i	$0.927866\pi$
$938$	−6.08681	+	3.51422i	−0.198741	+	0.114743i
$939$		0			0
$940$	−1.31213	−	2.41071i	−0.0427971	−	0.0786287i
$941$	44.3498			1.44576			0.722881	−	0.690973i	$-0.242818\pi$
$941$	44.3498			1.44576			0.722881	+	0.690973i	$0.242818\pi$
$942$		0			0
$943$	−71.2745	−	41.1504i	−2.32102	−	1.34004i
$944$	38.6818			1.25898
$945$		0			0
$946$	29.6468	+	51.3498i	0.963902	+	1.66953i
$947$	42.2346	−	24.3842i	1.37244	−	0.792379i	0.381205	−	0.924490i	$-0.375509\pi$
$947$	42.2346	−	24.3842i	1.37244	−	0.792379i	0.991235	+	0.132112i	$0.0421757\pi$
$948$		0			0
$949$	9.93612	+	47.9679i	0.322540	+	1.55710i
$950$	−28.6150	+	14.6546i	−0.928393	+	0.475457i
$951$		0			0
$952$	−3.97453	+	2.29469i	−0.128815	+	0.0743715i
$953$	1.62011	+	0.935373i	0.0524806	+	0.0302997i	0.526011	−	0.850478i	$-0.323687\pi$
$953$	1.62011	+	0.935373i	0.0524806	+	0.0302997i	−0.473530	+	0.880778i	$0.657021\pi$
$954$		0			0
$955$	−26.0211	+	14.1631i	−0.842022	+	0.458307i
$956$	−0.370033	+	0.640916i	−0.0119677	+	0.0207287i
$957$		0			0
$958$	21.3493	+	12.3260i	0.689763	+	0.398235i
$959$	−1.77223	−	3.06960i	−0.0572284	−	0.0991224i
$960$		0			0
$961$	65.1584			2.10188
$962$	2.96381	−	8.96321i	0.0955572	−	0.288986i
$963$		0			0
$964$	0.344214	+	0.596196i	0.0110864	+	0.0192022i
$965$	14.2115	+	0.357460i	0.457484	+	0.0115071i
$966$		0			0
$967$			53.0298i			1.70532i	0.522464	+	0.852661i	$0.325013\pi$
$967$			53.0298i			1.70532i	−0.522464	+	0.852661i	$0.674987\pi$
$968$	−21.6305	−	12.4884i	−0.695231	−	0.401392i
$969$		0			0
$970$	−54.3927	−	33.2547i	−1.74644	−	1.06774i
$971$	−6.08882	+	10.5461i	−0.195400	+	0.338442i	−0.947031	−	0.321141i	$-0.895934\pi$
$971$	−6.08882	+	10.5461i	−0.195400	+	0.338442i	0.751632	+	0.659583i	$0.229267\pi$
$972$		0			0
$973$	−3.58066	+	2.06729i	−0.114791	+	0.0662744i
$974$	−3.97615			−0.127404
$975$		0			0
$976$	10.1189			0.323897
$977$	−0.600137	+	0.346489i	−0.0192001	+	0.0110852i	−0.509569	−	0.860430i	$-0.670195\pi$
$977$	−0.600137	+	0.346489i	−0.0192001	+	0.0110852i	0.490369	+	0.871515i	$0.336862\pi$
$978$		0			0
$979$	12.0348	−	20.8448i	0.384633	−	0.666203i
$980$	−5.91721	−	3.61767i	−0.189018	−	0.115562i
$981$		0			0
$982$	−3.09761	−	1.78840i	−0.0988486	−	0.0570703i
$983$			15.3180i			0.488567i	0.969704	+	0.244284i	$0.0785528\pi$
$983$			15.3180i			0.488567i	−0.969704	+	0.244284i	$0.921447\pi$
$984$		0			0
$985$	−35.6365	−	0.896362i	−1.13547	−	0.0285605i
$986$	20.5837	+	35.6521i	0.655520	+	1.13539i
$987$		0			0
$988$	4.45671	+	5.00162i	0.141787	+	0.159123i
$989$	−54.2281			−1.72435
$990$		0			0
$991$	10.4990	+	18.1849i	0.333513	+	0.577661i	0.983198	−	0.182542i	$-0.0584326\pi$
$991$	10.4990	+	18.1849i	0.333513	+	0.577661i	−0.649685	+	0.760203i	$0.725099\pi$
$992$	−21.3503	−	12.3266i	−0.677873	−	0.391370i
$993$		0			0
$994$	−0.935504	+	1.62034i	−0.0296724	+	0.0513941i
$995$	0.494647	−	0.269233i	0.0156814	−	0.00853525i
$996$		0			0
$997$	−25.0029	−	14.4354i	−0.791850	−	0.457175i	0.0487637	−	0.998810i	$-0.484472\pi$
$997$	−25.0029	−	14.4354i	−0.791850	−	0.457175i	−0.840613	+	0.541636i	$0.817805\pi$
$998$	42.5671	−	24.5761i	1.34744	−	0.777944i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bs.c.289.12	yes	32
3.2	odd	2	inner	585.2.bs.c.289.5	✓	32
5.4	even	2	inner	585.2.bs.c.289.6	yes	32
13.9	even	3	inner	585.2.bs.c.334.6	yes	32
15.14	odd	2	inner	585.2.bs.c.289.11	yes	32
39.35	odd	6	inner	585.2.bs.c.334.11	yes	32
65.9	even	6	inner	585.2.bs.c.334.12	yes	32
195.74	odd	6	inner	585.2.bs.c.334.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bs.c.289.5	✓	32	3.2	odd	2	inner
585.2.bs.c.289.6	yes	32	5.4	even	2	inner
585.2.bs.c.289.11	yes	32	15.14	odd	2	inner
585.2.bs.c.289.12	yes	32	1.1	even	1	trivial
585.2.bs.c.334.5	yes	32	195.74	odd	6	inner
585.2.bs.c.334.6	yes	32	13.9	even	3	inner
585.2.bs.c.334.11	yes	32	39.35	odd	6	inner
585.2.bs.c.334.12	yes	32	65.9	even	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35625 - 0.783029i) q^{2} +(0.226269 - 0.391909i) q^{4} +(1.90777 + 1.16637i) q^{5} +(0.331025 + 0.191118i) q^{7} +2.42342i q^{8} +O(q^{10})\)	\(q+(1.35625 - 0.783029i) q^{2} +(0.226269 - 0.391909i) q^{4} +(1.90777 + 1.16637i) q^{5} +(0.331025 + 0.191118i) q^{7} +2.42342i q^{8} +(3.50070 + 0.0880529i) q^{10} +(-2.30794 - 3.99748i) q^{11} +(3.53060 - 0.731332i) q^{13} +0.598602 q^{14} +(2.35014 + 4.07057i) q^{16} +(4.29069 + 2.47723i) q^{17} +(-2.05288 + 3.55569i) q^{19} +(0.888780 - 0.483757i) q^{20} +(-6.26028 - 3.61437i) q^{22} +(5.72546 - 3.30559i) q^{23} +(2.27915 + 4.45034i) q^{25} +(4.21571 - 3.75643i) q^{26} +(0.149801 - 0.0864878i) q^{28} +(2.65290 + 4.59495i) q^{29} -9.80604 q^{31} +(2.17726 + 1.25704i) q^{32} +7.75897 q^{34} +(0.408604 + 0.750707i) q^{35} +(1.44793 - 0.835962i) q^{37} +6.42985i q^{38} +(-2.82661 + 4.62331i) q^{40} +(-6.22435 - 10.7809i) q^{41} +(-7.10356 - 4.10124i) q^{43} -2.08886 q^{44} +(5.17675 - 8.96640i) q^{46} -2.71238i q^{47} +(-3.42695 - 5.93565i) q^{49} +(6.57582 + 4.25111i) q^{50} +(0.512249 - 1.54915i) q^{52} -2.07646i q^{53} +(0.259532 - 10.3182i) q^{55} +(-0.463157 + 0.802212i) q^{56} +(7.19596 + 4.15459i) q^{58} +(4.11483 - 7.12710i) q^{59} +(1.07641 - 1.86440i) q^{61} +(-13.2994 + 7.67841i) q^{62} -5.46337 q^{64} +(7.58857 + 2.72279i) q^{65} +(-10.1684 + 5.87072i) q^{67} +(1.94170 - 1.12104i) q^{68} +(1.14199 + 0.698194i) q^{70} +(-1.56281 + 2.70687i) q^{71} +13.5863i q^{73} +(1.30916 - 2.26754i) q^{74} +(0.929003 + 1.60908i) q^{76} -1.76435i q^{77} -1.45254 q^{79} +(-0.264278 + 10.5068i) q^{80} +(-16.8835 - 9.74770i) q^{82} -2.02064i q^{83} +(5.29626 + 9.73052i) q^{85} -12.8456 q^{86} +(9.68755 - 5.59311i) q^{88} +(2.60725 + 4.51588i) q^{89} +(1.30849 + 0.432671i) q^{91} -2.99181i q^{92} +(-2.12387 - 3.67866i) q^{94} +(-8.06367 + 4.38900i) q^{95} +(-15.7666 - 9.10286i) q^{97} +(-9.29557 - 5.36680i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4}+O(q^{10}) \) 32 * q + 20 * q^4	\( 32 q + 20 q^{4} - 6 q^{10} - 28 q^{16} - 8 q^{19} + 28 q^{25} + 8 q^{31} - 8 q^{34} - 20 q^{40} - 8 q^{46} + 44 q^{49} + 20 q^{55} - 56 q^{61} - 136 q^{64} - 80 q^{70} + 88 q^{76} - 72 q^{79} - 50 q^{85} - 28 q^{91} + 48 q^{94}+O(q^{100}) \) 32 * q + 20 * q^4 - 6 * q^10 - 28 * q^16 - 8 * q^19 + 28 * q^25 + 8 * q^31 - 8 * q^34 - 20 * q^40 - 8 * q^46 + 44 * q^49 + 20 * q^55 - 56 * q^61 - 136 * q^64 - 80 * q^70 + 88 * q^76 - 72 * q^79 - 50 * q^85 - 28 * q^91 + 48 * q^94

Introduction

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