LMFDB - Embedded newform 585.2.bs.c.289.11

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			289.11
Character	$\chi$	$=$	585.289
Dual form			585.2.bs.c.334.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35625 - 0.783029i) q^{2} +(0.226269 - 0.391909i) q^{4} +(-1.90777 + 1.16637i) q^{5} +(-0.331025 - 0.191118i) q^{7} +2.42342i q^{8} +O(q^{10})$	\(q+(1.35625 - 0.783029i) q^{2} +(0.226269 - 0.391909i) q^{4} +(-1.90777 + 1.16637i) q^{5} +(-0.331025 - 0.191118i) q^{7} +2.42342i q^{8} +(-1.67410 + 3.07573i) q^{10} +(2.30794 + 3.99748i) q^{11} +(-3.53060 + 0.731332i) q^{13} -0.598602 q^{14} +(2.35014 + 4.07057i) q^{16} +(4.29069 + 2.47723i) q^{17} +(-2.05288 + 3.55569i) q^{19} +(0.0254443 + 1.01158i) q^{20} +(6.26028 + 3.61437i) q^{22} +(5.72546 - 3.30559i) q^{23} +(2.27915 - 4.45034i) q^{25} +(-4.21571 + 3.75643i) q^{26} +(-0.149801 + 0.0864878i) q^{28} +(-2.65290 - 4.59495i) q^{29} -9.80604 q^{31} +(2.17726 + 1.25704i) q^{32} +7.75897 q^{34} +(0.854433 - 0.0214915i) q^{35} +(-1.44793 + 0.835962i) q^{37} +6.42985i q^{38} +(-2.82661 - 4.62331i) q^{40} +(6.22435 + 10.7809i) q^{41} +(7.10356 + 4.10124i) q^{43} +2.08886 q^{44} +(5.17675 - 8.96640i) q^{46} -2.71238i q^{47} +(-3.42695 - 5.93565i) q^{49} +(-0.393660 - 7.82039i) q^{50} +(-0.512249 + 1.54915i) q^{52} -2.07646i q^{53} +(-9.06557 - 4.93433i) q^{55} +(0.463157 - 0.802212i) q^{56} +(-7.19596 - 4.15459i) q^{58} +(-4.11483 + 7.12710i) q^{59} +(1.07641 - 1.86440i) q^{61} +(-13.2994 + 7.67841i) q^{62} -5.46337 q^{64} +(5.88256 - 5.51321i) q^{65} +(10.1684 - 5.87072i) q^{67} +(1.94170 - 1.12104i) q^{68} +(1.14199 - 0.698194i) q^{70} +(1.56281 - 2.70687i) q^{71} -13.5863i q^{73} +(-1.30916 + 2.26754i) q^{74} +(0.929003 + 1.60908i) q^{76} -1.76435i q^{77} -1.45254 q^{79} +(-9.23132 - 5.02455i) q^{80} +(16.8835 + 9.74770i) q^{82} -2.02064i q^{83} +(-11.0750 + 0.278569i) q^{85} +12.8456 q^{86} +(-9.68755 + 5.59311i) q^{88} +(-2.60725 - 4.51588i) q^{89} +(1.30849 + 0.432671i) q^{91} -2.99181i q^{92} +(-2.12387 - 3.67866i) q^{94} +(-0.230850 - 9.17784i) q^{95} +(15.7666 + 9.10286i) q^{97} +(-9.29557 - 5.36680i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.436136	−	0.899881i	$-0.356347\pi$
$7$	−0.331025	−	0.191118i	−0.125116	−	0.0722356i	−0.561252	+	0.827645i	$0.689680\pi$
$8$			2.42342i			0.856807i
$9$		0			0
$10$	−1.67410	+	3.07573i	−0.529396	+	0.972630i
$11$	2.30794	+	3.99748i	0.695871	+	1.20528i	0.969886	+	0.243559i	$0.0783150\pi$
$11$	2.30794	+	3.99748i	0.695871	+	1.20528i	−0.274015	+	0.961726i	$0.588352\pi$
$12$		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	$0.322760\pi$
$20$	0.0254443	+	1.01158i	0.00568952	+	0.226197i
$21$		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	0.507333	−	0.861750i	$-0.330631\pi$
$29$	−2.65290	−	4.59495i	−0.492630	−	0.853261i	−0.999964	+	0.00848878i	$0.997298\pi$
$30$		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
$35$	0.854433	−	0.0214915i	0.144426	−	0.00363273i
$36$		0			0
$37$	−1.44793	+	0.835962i	−0.238038	+	0.137431i	−0.614275	−	0.789092i	$-0.710551\pi$
$37$	−1.44793	+	0.835962i	−0.238038	+	0.137431i	0.376237	+	0.926524i	$0.377218\pi$
$38$			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	$0.257940\pi$
$41$	6.22435	+	10.7809i	0.972081	+	1.68369i	0.282831	+	0.959170i	$0.408726\pi$
$42$		0			0
$43$	7.10356	+	4.10124i	1.08328	+	0.625433i	0.931780	−	0.363024i	$-0.118256\pi$
$43$	7.10356	+	4.10124i	1.08328	+	0.625433i	0.151502	+	0.988457i	$0.451589\pi$
$44$	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
$50$	−0.393660	−	7.82039i	−0.0556720	−	1.10597i
$51$		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
$55$	−9.06557	−	4.93433i	−1.22240	−	0.665345i
$56$	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	$0.346621\pi$
$59$	−4.11483	+	7.12710i	−0.535706	+	0.927870i	−0.999129	+	0.0417324i	$0.986712\pi$
$60$		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
$65$	5.88256	−	5.51321i	0.729642	−	0.683830i
$66$		0			0
$67$	10.1684	−	5.87072i	1.24227	−	0.717222i	0.272710	−	0.962096i	$-0.412080\pi$
$67$	10.1684	−	5.87072i	1.24227	−	0.717222i	0.969555	+	0.244874i	$0.0787466\pi$
$68$	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	−0.758263	−	0.651948i	$-0.773952\pi$
$71$	1.56281	−	2.70687i	0.185472	−	0.321247i	0.943735	+	0.330701i	$0.107285\pi$
$72$		0			0
$73$		−	13.5863i		−	1.59016i	−0.606505	−	0.795080i	$-0.707429\pi$
$73$		−	13.5863i		−	1.59016i	0.606505	−	0.795080i	$-0.292571\pi$
$74$	−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	$0.526039\pi$
$80$	−9.23132	−	5.02455i	−1.03209	−	0.561761i
$81$		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
$85$	−11.0750	+	0.278569i	−1.20125	+	0.0302150i
$86$	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	0.694112	−	0.719867i	$-0.255797\pi$
$89$	−2.60725	−	4.51588i	−0.276367	−	0.478683i	−0.970479	+	0.241185i	$0.922464\pi$
$90$		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
$95$	−0.230850	−	9.17784i	−0.0236847	−	0.941627i
$96$		0			0
$97$	15.7666	+	9.10286i	1.60086	+	0.924255i	0.991316	+	0.131500i	$0.0419793\pi$
$97$	15.7666	+	9.10286i	1.60086	+	0.924255i	0.609540	+	0.792755i	$0.291354\pi$
$98$	−9.29557	−	5.36680i	−0.938994	−	0.542129i
$99$		0			0
$100$	−1.22843	−	1.90019i	−0.122843	−	0.190019i
$101$	5.26014	+	9.11083i	0.523404	+	0.906562i	0.999629	+	0.0272385i	$0.00867135\pi$
$101$	5.26014	+	9.11083i	0.523404	+	0.906562i	−0.476225	+	0.879323i	$0.657995\pi$
$102$		0			0
$103$		−	7.43801i		−	0.732889i	−0.930440	−	0.366444i	$-0.880575\pi$
$103$		−	7.43801i		−	0.732889i	0.930440	−	0.366444i	$-0.119425\pi$
$104$	−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	$0.382884\pi$
$110$	−16.1589	+	0.406443i	−1.54069	+	0.0387528i
$111$		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
$115$	−7.06728	+	12.9843i	−0.659027	+	1.21079i
$116$	−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	−0.798268	−	0.602302i	$-0.794250\pi$
$127$	−7.61580	+	4.39699i	−0.675793	+	0.390169i	0.122475	+	0.992472i	$0.460917\pi$
$128$	−11.7642	+	6.79206i	−1.03982	+	0.600339i
$129$		0			0
$130$	3.66119	−	12.0835i	0.321108	−	1.05979i
$131$	7.74152			0.676380			0.338190	−	0.941078i	$-0.390185\pi$
$131$	7.74152			0.676380			0.338190	+	0.941078i	$0.390185\pi$
$132$		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	$0.318365\pi$
$140$	0.184909	−	0.339723i	0.0156276	−	0.0287118i
$141$		0			0
$142$		−	4.89492i		−	0.410772i
$143$	−11.0719	−	12.4256i	−0.925880	−	1.03908i
$144$		0			0
$145$	10.4205	+	5.67183i	0.865378	+	0.471020i
$146$	−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	−0.985420	−	0.170140i	$-0.945578\pi$
$149$	−4.21571	+	7.30183i	−0.345365	+	0.598189i	0.640055	+	0.768329i	$0.278911\pi$
$150$		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	$0.102447\pi$
$157$			7.92694i			0.632639i	−0.948653	+	0.316319i	$0.897553\pi$
$158$	−1.97000	+	1.13738i	−0.156725	+	0.0904850i
$159$		0			0
$160$	−5.61989	+	0.141357i	−0.444291	+	0.0111752i
$161$	−2.52703			−0.199158
$162$		0			0
$163$	−10.6806	−	6.16646i	−0.836571	−	0.482995i	0.0195260	−	0.999809i	$-0.493784\pi$
$163$	−10.6806	−	6.16646i	−0.836571	−	0.482995i	−0.856097	+	0.516815i	$0.827118\pi$
$164$	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
$175$	−1.60499	+	1.03759i	−0.121326	+	0.0784344i
$176$	−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	0.907642	−	0.419745i	$-0.137880\pi$
$179$	1.20829	+	2.09281i	0.0903116	+	0.156424i	−0.817331	+	0.576169i	$0.804547\pi$
$180$		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
$185$	1.78726	−	3.28364i	0.131402	−	0.241418i
$186$		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	−0.520385	−	0.853932i	$-0.674211\pi$
$191$	6.62453	−	11.4740i	0.479334	−	0.830231i	0.999719	+	0.0237004i	$0.00754479\pi$
$192$		0			0
$193$	−5.50583	+	3.17879i	−0.396318	+	0.228814i	−0.684894	−	0.728643i	$-0.740152\pi$
$193$	−5.50583	+	3.17879i	−0.396318	+	0.228814i	0.288576	+	0.957457i	$0.406818\pi$
$194$	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
$205$	−24.4492	−	13.3075i	−1.70760	−	0.929437i
$206$	−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
$215$	−18.3355	+	0.461191i	−1.25047	+	0.0314530i
$216$		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	0.0912873	−	0.995825i	$-0.470902\pi$
$223$	14.9233	−	8.61599i	0.999340	−	0.576969i	0.908053	+	0.418855i	$0.137569\pi$
$224$	−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	$0.620128\pi$
$230$	0.582134	+	23.1438i	0.0383848	+	1.52606i
$231$		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	$-0.483156\pi$
$239$	1.63537			0.105783			0.0528916	+	0.998600i	$0.483156\pi$
$240$		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
$245$	13.4610	+	7.32673i	0.859992	+	0.468088i
$246$		0			0
$247$	4.64751	−	14.0551i	0.295714	−	0.894302i
$248$		−	23.7641i		−	1.50902i
$249$		0			0
$250$	9.87250	+	14.4603i	0.624392	+	0.914551i
$251$	3.59645	−	6.22923i	0.227006	−	0.393186i	−0.729913	−	0.683540i	$-0.760440\pi$
$251$	3.59645	−	6.22923i	0.227006	−	0.393186i	0.956919	+	0.290354i	$0.0937730\pi$
$252$		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
$260$	−0.829637	−	3.55289i	−0.0514519	−	0.220341i
$261$		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	−0.929031	−	0.370001i	$-0.879357\pi$
$269$	−2.36317	+	4.09313i	−0.144085	+	0.249563i	0.784946	+	0.619564i	$0.212691\pi$
$270$		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
$275$	23.0503	−	1.16030i	1.38998	−	0.0699685i
$276$		0			0
$277$	−3.98134	−	2.29863i	−0.239215	−	0.138111i	0.375601	−	0.926782i	$-0.377436\pi$
$277$	−3.98134	−	2.29863i	−0.239215	−	0.138111i	−0.614816	+	0.788671i	$0.710770\pi$
$278$			16.9398i			1.01598i
$279$		0			0
$280$	0.0520828	+	2.07065i	0.00311254	+	0.123745i
$281$	11.7397			0.700329			0.350165	−	0.936688i	$-0.386126\pi$
$281$	11.7397			0.700329			0.350165	+	0.936688i	$0.386126\pi$
$282$		0			0
$283$	−3.39585	+	1.96059i	−0.201862	+	0.116545i	−0.597524	−	0.801851i	$-0.703849\pi$
$283$	−3.39585	+	1.96059i	−0.201862	+	0.116545i	0.395662	+	0.918396i	$0.370515\pi$
$284$	−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
$290$	18.5740	−	0.467191i	1.09070	−	0.0274344i
$291$		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
$295$	−0.462720	−	18.3963i	−0.0269406	−	1.07107i
$296$	−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
$305$	0.121044	+	4.81233i	0.00693097	+	0.275553i
$306$		0			0
$307$		−	16.8276i		−	0.960403i	−0.877158	−	0.480201i	$-0.840564\pi$
$307$		−	16.8276i		−	0.960403i	0.877158	−	0.480201i	$-0.159436\pi$
$308$	−0.691466	−	0.399218i	−0.0393999	−	0.0227476i
$309$		0			0
$310$	16.4163	−	30.1607i	0.932380	−	1.71301i
$311$	−11.6484			−0.660517			−0.330259	−	0.943890i	$-0.607136\pi$
$311$	−11.6484			−0.660517			−0.330259	+	0.943890i	$0.607136\pi$
$312$		0			0
$313$		−	20.9802i		−	1.18587i	−0.805250	−	0.592935i	$-0.797969\pi$
$313$		−	20.9802i		−	1.18587i	0.805250	−	0.592935i	$-0.202031\pi$
$314$	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
$325$	−4.79208	+	17.3792i	−0.265817	+	0.964024i
$326$	−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
$335$	−12.5514	+	23.0601i	−0.685759	+	1.25991i
$336$		0			0
$337$			16.6846i			0.908870i	0.890780	+	0.454435i	$0.150159\pi$
$337$			16.6846i			0.908870i	−0.890780	+	0.454435i	$0.849841\pi$
$338$	12.1368	−	16.3455i	0.660155	−	0.889080i
$339$		0			0
$340$	−2.39675	+	4.40342i	−0.129982	+	0.238809i
$341$	−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
$355$	0.175741	+	6.98691i	0.00932737	+	0.370827i
$356$	−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	$-0.129268\pi$
$359$	34.8124			1.83733			0.918665	+	0.395037i	$0.129268\pi$
$360$		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	−0.777511	−	0.628869i	$-0.783518\pi$
$367$	−11.9091	+	6.87572i	−0.621650	+	0.358910i	0.155861	+	0.987779i	$0.450185\pi$
$368$	26.9113	+	15.5372i	1.40285	+	0.809934i
$369$		0			0
$370$	−0.147218	−	5.85291i	−0.00765349	−	0.304278i
$371$	−0.396848	+	0.687361i	−0.0206033	+	0.0356860i
$372$		0			0
$373$	10.7416	+	6.20167i	0.556179	+	0.321110i	0.751611	−	0.659607i	$-0.229277\pi$
$373$	10.7416	+	6.20167i	0.556179	+	0.321110i	−0.195431	+	0.980717i	$0.562611\pi$
$374$	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	$0.728704\pi$
$380$	−3.64911	−	1.98619i	−0.187195	−	0.101889i
$381$		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	$-0.651437\pi$
$389$	−18.0667			−0.916019			−0.458009	+	0.888947i	$0.651437\pi$
$390$		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	−0.333999	−	0.942573i	$-0.608398\pi$
$397$	−26.2468	−	15.1536i	−1.31729	−	0.760539i	−0.983292	+	0.182035i	$0.941732\pi$
$398$		−	0.394424i		−	0.0197707i
$399$		0			0
$400$	23.4717	−	1.18151i	1.17359	−	0.0590756i
$401$	−2.50637	−	4.34116i	−0.125162	−	0.216787i	0.796634	−	0.604462i	$-0.206612\pi$
$401$	−2.50637	−	4.34116i	−0.125162	−	0.216787i	−0.921796	+	0.387675i	$0.873278\pi$
$402$		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	$0.923541\pi$
$410$	−43.5793	+	1.09615i	−2.15223	+	0.0541348i
$411$		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	$-0.902626\pi$
$419$	−15.0983	−	26.1510i	−0.737599	−	1.27756i	0.215975	−	0.976399i	$-0.430707\pi$
$420$		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
$425$	20.8036	−	13.4490i	1.00912	−	0.652374i
$426$		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	0.914085	−	0.405523i	$-0.132911\pi$
$431$	2.19749	+	3.80617i	0.105849	+	0.183337i	−0.808235	+	0.588859i	$0.799577\pi$
$432$		0			0
$433$	−2.97242	−	1.71613i	−0.142845	−	0.0824718i	0.426874	−	0.904311i	$-0.359615\pi$
$433$	−2.97242	−	1.71613i	−0.142845	−	0.0824718i	−0.569719	+	0.821839i	$0.692948\pi$
$434$	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	$0.696028\pi$
$440$	11.9579	−	21.9697i	0.570072	−	1.04736i
$441$		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
$445$	10.2412	+	5.57423i	0.485480	+	0.264244i
$446$	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	−0.999924	−	0.0123424i	$-0.996071\pi$
$449$	−10.3675	+	17.9571i	−0.489273	+	0.847446i	0.510651	+	0.859788i	$0.329405\pi$
$450$		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
$455$	−3.00095	+	0.700752i	−0.140687	+	0.0328518i
$456$		0			0
$457$	−33.0995	+	19.1100i	−1.54833	+	0.893929i	−0.550061	+	0.835125i	$0.685395\pi$
$457$	−33.0995	+	19.1100i	−1.54833	+	0.893929i	−0.998270	+	0.0588044i	$0.981271\pi$
$458$	−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	−0.854202	−	0.519941i	$-0.825954\pi$
$461$	0.497725	−	0.862085i	0.0231814	−	0.0401513i	0.877383	+	0.479790i	$0.159287\pi$
$462$		0			0
$463$			25.8530i			1.20149i	0.799441	+	0.600745i	$0.205129\pi$
$463$			25.8530i			1.20149i	−0.799441	+	0.600745i	$0.794871\pi$
$464$	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
$470$	8.34254	+	4.54079i	0.384813	+	0.209451i
$471$		0			0
$472$	−17.2719	−	9.97196i	−0.795005	−	0.458996i
$473$			37.8617i			1.74088i
$474$		0			0
$475$	11.1452	+	17.2399i	0.511377	+	0.791022i
$476$	−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	0.628275	−	0.777991i	$-0.283761\pi$
$479$	−7.87072	−	13.6325i	−0.359622	−	0.622884i	−0.987898	+	0.155107i	$0.950428\pi$
$480$		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
$485$	−40.6963	+	1.02363i	−1.84793	+	0.0464807i
$486$		0			0
$487$	2.19880	+	1.26948i	0.0996371	+	0.0575255i	0.548991	−	0.835829i	$-0.315012\pi$
$487$	2.19880	+	1.26948i	0.0996371	+	0.0575255i	−0.449353	+	0.893354i	$0.648346\pi$
$488$	4.51821	+	2.60859i	0.204530	+	0.118085i
$489$		0			0
$490$	23.9935	−	0.603506i	1.08391	−	0.0272636i
$491$	1.14198	+	1.97796i	0.0515367	+	0.0892643i	0.890643	−	0.454703i	$-0.150255\pi$
$491$	1.14198	+	1.97796i	0.0515367	+	0.0892643i	−0.839106	+	0.543968i	$0.816921\pi$
$492$		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	$0.252060\pi$
$500$	4.55988	+	2.19231i	0.203924	+	0.0980432i
$501$		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
$505$	−20.6618	−	11.2461i	−0.919436	−	0.500443i
$506$	47.7906			2.12455
$507$		0			0
$508$			3.97960i			0.176566i
$509$	4.30701	+	7.45996i	0.190905	+	0.330657i	0.945550	−	0.325476i	$-0.105524\pi$
$509$	4.30701	+	7.45996i	0.190905	+	0.330657i	−0.754645	+	0.656133i	$0.772191\pi$
$510$		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
$520$	13.3608	+	14.2559i	0.585910	+	0.625162i
$521$	−23.3159			−1.02149			−0.510743	−	0.859733i	$-0.670630\pi$
$521$	−23.3159			−1.02149			−0.510743	+	0.859733i	$0.670630\pi$
$522$		0			0
$523$	7.63855	−	4.41012i	0.334011	−	0.192841i	−0.323610	−	0.946191i	$-0.604896\pi$
$523$	7.63855	−	4.41012i	0.334011	−	0.192841i	0.657620	+	0.753350i	$0.271563\pi$
$524$	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
$530$	6.38662	+	3.47620i	0.277417	+	0.150996i
$531$		0			0
$532$		−	0.710195i		−	0.0307909i
$533$	−29.8601	−	33.5110i	−1.29339	−	1.45152i
$534$		0			0
$535$	−7.26906	+	13.3550i	−0.314269	+	0.577389i
$536$	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	$-0.707436\pi$
$547$		−	37.1900i		−	1.59013i	0.606523	−	0.795066i	$-0.292564\pi$
$548$	−3.63417	+	2.09819i	−0.155244	+	0.0896302i
$549$		0			0
$550$	30.3533	−	19.6227i	1.29427	−	0.836713i
$551$	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
$565$	1.78688	−	0.0449452i	0.0751745	−	0.00189086i
$566$	−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	$-0.987469\pi$
$569$	−12.7307	−	22.0502i	−0.533698	−	0.924392i	0.465527	−	0.885034i	$-0.345865\pi$
$570$		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
$575$	−1.66186	−	33.0141i	−0.0693042	−	1.37678i
$576$		0			0
$577$		−	10.8481i		−	0.451614i	−0.974172	−	0.225807i	$-0.927498\pi$
$577$		−	10.8481i		−	0.451614i	0.974172	−	0.225807i	$-0.0725018\pi$
$578$	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
$595$	3.71935	+	2.02441i	0.152478	+	0.0829929i
$596$	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	$-0.359113\pi$
$599$	20.9648			0.856597			0.428299	+	0.903637i	$0.359113\pi$
$600$		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
$605$	−0.579488	−	23.0386i	−0.0235595	−	0.936652i
$606$		0			0
$607$	−32.2303	−	18.6082i	−1.30819	−	0.755282i	−0.326393	−	0.945234i	$-0.605833\pi$
$607$	−32.2303	−	18.6082i	−1.30819	−	0.755282i	−0.981793	+	0.189952i	$0.939167\pi$
$608$	−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	0.127684	−	0.991815i	$-0.459246\pi$
$613$	26.0082	−	15.0159i	1.05046	−	0.606485i	0.922779	+	0.385330i	$0.125912\pi$
$614$	−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	$0.733492\pi$
$620$	−0.249508	−	9.91963i	−0.0100205	−	0.398382i
$621$		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
$635$	9.40065	−	17.2713i	0.373053	−	0.685391i
$636$		0			0
$637$	16.4401	+	18.4502i	0.651381	+	0.731023i
$638$		−	38.3542i		−	1.51846i
$639$		0			0
$640$	14.5213	−	26.6791i	0.574003	−	1.05458i
$641$	4.36848	−	7.56644i	0.172545	−	0.298856i	−0.766764	−	0.641929i	$-0.778134\pi$
$641$	4.36848	−	7.56644i	0.172545	−	0.298856i	0.939309	+	0.343073i	$0.111468\pi$
$642$		0			0
$643$	−12.6826	−	7.32231i	−0.500154	−	0.288764i	0.228623	−	0.973515i	$-0.426578\pi$
$643$	−12.6826	−	7.32231i	−0.500154	−	0.288764i	−0.728777	+	0.684751i	$0.759911\pi$
$644$	−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
$650$	7.10916	+	27.3228i	0.278844	+	1.07169i
$651$		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	$0.431016\pi$
$659$	−18.9517	+	32.8253i	−0.738254	+	1.27869i	−0.953281	+	0.302085i	$0.902317\pi$
$660$		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
$665$	−1.67763	+	3.08222i	−0.0650557	+	0.119523i
$666$		0			0
$667$	−30.3781	−	17.5388i	−1.17624	−	0.679105i
$668$		−	7.13948i		−	0.276235i
$669$		0			0
$670$	1.03387	+	41.1033i	0.0399418	+	1.58796i
$671$	9.93719			0.383621
$672$		0			0
$673$	38.1855	−	22.0464i	1.47194	−	0.849827i	0.472440	−	0.881363i	$-0.343373\pi$
$673$	38.1855	−	22.0464i	1.47194	−	0.849827i	0.999503	+	0.0315359i	$0.0100399\pi$
$674$	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
$680$	−0.675088	−	26.8393i	−0.0258884	−	1.02924i
$681$		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
$685$	20.7285	−	0.521382i	0.791995	−	0.0199210i
$686$	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
$695$	−0.608188	−	24.1796i	−0.0230699	−	0.917185i
$696$		0			0
$697$			61.6766i			2.33617i
$698$	−18.6595	−	10.7731i	−0.706272	−	0.407766i
$699$		0			0
$700$	0.0434809	+	0.863784i	0.00164342	+	0.0326480i
$701$	35.7299			1.34950			0.674750	−	0.738046i	$-0.264251\pi$
$701$	35.7299			1.34950			0.674750	+	0.738046i	$0.264251\pi$
$702$		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
$715$	35.6156	+	10.7912i	1.33195	+	0.403568i
$716$	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	$-0.622030\pi$
$719$	16.5212	−	28.6156i	0.616138	−	1.06718i	0.990184	−	0.139772i	$-0.0446368\pi$
$720$		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
$725$	−26.4954	+	1.33372i	−0.984015	+	0.0495330i
$726$		0			0
$727$		−	46.5797i		−	1.72754i	−0.503883	−	0.863772i	$-0.668096\pi$
$727$		−	46.5797i		−	1.72754i	0.503883	−	0.863772i	$-0.331904\pi$
$728$	−1.04854	+	3.17101i	−0.0388615	+	0.117526i
$729$		0			0
$730$	41.7878	+	22.7448i	1.54664	+	0.841824i
$731$	20.3194	+	35.1943i	0.751541	+	1.30171i
$732$		0			0
$733$		−	31.2147i		−	1.15294i	−0.817118	−	0.576471i	$-0.804430\pi$
$733$		−	31.2147i		−	1.15294i	0.817118	−	0.576471i	$-0.195570\pi$
$734$	−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
$745$	−0.474064	−	18.8473i	−0.0173684	−	0.690511i
$746$	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	−0.804473	−	0.593990i	$-0.797552\pi$
$757$	−19.0477	+	10.9972i	−0.692299	+	0.399699i	0.112174	+	0.993689i	$0.464219\pi$
$758$	17.0468	+	9.84198i	0.619168	+	0.357477i
$759$		0			0
$760$	22.2417	−	0.559445i	0.806792	−	0.0202932i
$761$	−16.2469	+	28.1405i	−0.588950	+	1.02009i	0.405420	+	0.914130i	$0.367125\pi$
$761$	−16.2469	+	28.1405i	−0.588950	+	1.02009i	−0.994370	+	0.105961i	$0.966208\pi$
$762$		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	$0.755724\pi$
$770$	5.42667	+	2.95370i	0.195564	+	0.106444i
$771$		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	0.668066	−	0.744102i	$-0.267122\pi$
$787$	10.0344	+	5.79337i	0.357688	+	0.206511i	−0.310378	+	0.950613i	$0.600456\pi$
$788$			7.21443i			0.257003i
$789$		0			0
$790$	2.43169	−	4.46761i	0.0865155	−	0.158950i
$791$	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
$800$	10.5566	−	6.82456i	0.373231	−	0.241285i
$801$		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	0.976433	−	0.215819i	$-0.0692421\pi$
$809$	8.57020	+	14.8440i	0.301312	+	0.521888i	−0.675121	+	0.737707i	$0.735909\pi$
$810$		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
$815$	27.5685	−	0.693429i	0.965684	−	0.0242898i
$816$		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	0.949154	−	0.314811i	$-0.101941\pi$
$821$	5.78628	+	10.0221i	0.201943	+	0.349775i	−0.747212	+	0.664586i	$0.768608\pi$
$822$		0			0
$823$	−7.76202	−	4.48141i	−0.270567	−	0.156212i	0.358578	−	0.933500i	$-0.383262\pi$
$823$	−7.76202	−	4.48141i	−0.270567	−	0.156212i	−0.629145	+	0.777288i	$0.716595\pi$
$824$	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	$0.418366\pi$
$830$	6.21494	+	3.38275i	0.215724	+	0.117417i
$831$		0			0
$832$	19.2890	−	3.99553i	0.668725	−	0.138520i
$833$		−	33.9574i		−	1.17655i
$834$		0			0
$835$	−16.8649	+	30.9850i	−0.583635	+	1.07228i
$836$	−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	−0.682322	−	0.731051i	$-0.739030\pi$
$839$	8.45641	−	14.6469i	0.291948	−	0.505668i	0.974270	+	0.225383i	$0.0723633\pi$
$840$		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
$845$	−16.7370	+	23.7671i	−0.575770	+	0.817612i
$846$		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	$0.113599\pi$
$853$			20.4066i			0.698708i	−0.936991	+	0.349354i	$0.886401\pi$
$854$	−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	$0.500282\pi$
$860$	−3.96800	+	7.29020i	−0.135308	+	0.248594i
$861$		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
$865$	−33.1471	+	0.833747i	−1.12704	+	0.0283482i
$866$	−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
$875$	1.85173	−	3.85150i	0.0626000	−	0.130204i
$876$		0			0
$877$	−13.5519	−	7.82418i	−0.457614	−	0.264204i	0.253426	−	0.967355i	$-0.418442\pi$
$877$	−13.5519	−	7.82418i	−0.457614	−	0.264204i	−0.711041	+	0.703151i	$0.751776\pi$
$878$	23.7621	+	13.7190i	0.801931	+	0.462995i
$879$		0			0
$880$	−1.21988	−	48.4984i	−0.0411220	−	1.63488i
$881$	18.8811	+	32.7030i	0.636119	+	1.10179i	0.986277	+	0.165100i	$0.0527947\pi$
$881$	18.8811	+	32.7030i	0.636119	+	1.10179i	−0.350158	+	0.936691i	$0.613872\pi$
$882$		0			0
$883$			10.6910i			0.359781i	0.983687	+	0.179890i	$0.0575743\pi$
$883$			10.6910i			0.359781i	−0.983687	+	0.179890i	$0.942426\pi$
$884$	−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
$890$	18.2544	−	0.459151i	0.611889	−	0.0153908i
$891$		0			0
$892$		−	7.79811i		−	0.261100i
$893$	9.64438	+	5.56819i	0.322737	+	0.186332i
$894$		0			0
$895$	−4.74613	−	2.58329i	−0.158646	−	0.0863498i
$896$	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	−0.830861	−	0.556480i	$-0.812152\pi$
$907$	−23.0200	+	13.2906i	−0.764365	+	0.441307i	0.0664955	+	0.997787i	$0.478818\pi$
$908$	4.79097	−	2.76607i	0.158994	−	0.0917952i
$909$		0			0
$910$	−3.52131	+	3.30022i	−0.116730	+	0.109401i
$911$	30.7452			1.01863			0.509316	−	0.860579i	$-0.329898\pi$
$911$	30.7452			1.01863			0.509316	+	0.860579i	$0.329898\pi$
$912$		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	$0.0934422\pi$
$920$	−31.4664	−	17.1270i	−1.03742	−	0.564659i
$921$		0			0
$922$		−	1.55893i		−	0.0513407i
$923$	−3.53805	+	10.6998i	−0.116456	+	0.352189i
$924$		0			0
$925$	0.420272	+	8.34905i	0.0138184	+	0.274515i
$926$	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	−0.525541	−	0.850768i	$-0.676137\pi$
$929$	14.4478	−	25.0243i	0.474016	−	0.821020i	0.999557	+	0.0297480i	$0.00947048\pi$
$930$		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	$-0.927866\pi$
$937$		−	13.7552i		−	0.449362i	0.974432	−	0.224681i	$-0.0721340\pi$
$938$	−6.08681	+	3.51422i	−0.198741	+	0.114743i
$939$		0			0
$940$	2.74380	−	0.0690147i	0.0894930	−	0.00225101i
$941$	−44.3498			−1.44576			−0.722881	−	0.690973i	$-0.757182\pi$
$941$	−44.3498			−1.44576			−0.722881	+	0.690973i	$0.757182\pi$
$942$		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
$955$	0.744940	+	29.6164i	0.0241057	+	0.958366i
$956$	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
$965$	6.79617	−	12.4862i	0.218777	−	0.401946i
$966$		0			0
$967$		−	53.0298i		−	1.70532i	−0.522464	−	0.852661i	$-0.674987\pi$
$967$		−	53.0298i		−	1.70532i	0.522464	−	0.852661i	$-0.325013\pi$
$968$	−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	−0.751632	−	0.659583i	$-0.770733\pi$
$971$	6.08882	−	10.5461i	0.195400	−	0.338442i	0.947031	+	0.321141i	$0.104066\pi$
$972$		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
$985$	17.0420	−	31.3103i	0.543003	−	0.997629i
$986$	−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
$995$	0.0141609	+	0.562993i	0.000448931	+	0.0178481i
$996$		0			0
$997$	25.0029	+	14.4354i	0.791850	+	0.457175i	0.840613	−	0.541636i	$-0.182195\pi$
$997$	25.0029	+	14.4354i	0.791850	+	0.457175i	−0.0487637	+	0.998810i	$0.515528\pi$
$998$	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.289.11	yes	32
3.2	odd	2	inner	585.2.bs.c.289.6	yes	32
5.4	even	2	inner	585.2.bs.c.289.5	✓	32
13.9	even	3	inner	585.2.bs.c.334.5	yes	32
15.14	odd	2	inner	585.2.bs.c.289.12	yes	32
39.35	odd	6	inner	585.2.bs.c.334.12	yes	32
65.9	even	6	inner	585.2.bs.c.334.11	yes	32
195.74	odd	6	inner	585.2.bs.c.334.6	yes	32

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

\(f(q)\)	\(=\)	\(q+(1.35625 - 0.783029i) q^{2} +(0.226269 - 0.391909i) q^{4} +(-1.90777 + 1.16637i) q^{5} +(-0.331025 - 0.191118i) q^{7} +2.42342i q^{8} +O(q^{10})\)	\(q+(1.35625 - 0.783029i) q^{2} +(0.226269 - 0.391909i) q^{4} +(-1.90777 + 1.16637i) q^{5} +(-0.331025 - 0.191118i) q^{7} +2.42342i q^{8} +(-1.67410 + 3.07573i) q^{10} +(2.30794 + 3.99748i) q^{11} +(-3.53060 + 0.731332i) q^{13} -0.598602 q^{14} +(2.35014 + 4.07057i) q^{16} +(4.29069 + 2.47723i) q^{17} +(-2.05288 + 3.55569i) q^{19} +(0.0254443 + 1.01158i) q^{20} +(6.26028 + 3.61437i) q^{22} +(5.72546 - 3.30559i) q^{23} +(2.27915 - 4.45034i) q^{25} +(-4.21571 + 3.75643i) q^{26} +(-0.149801 + 0.0864878i) q^{28} +(-2.65290 - 4.59495i) q^{29} -9.80604 q^{31} +(2.17726 + 1.25704i) q^{32} +7.75897 q^{34} +(0.854433 - 0.0214915i) q^{35} +(-1.44793 + 0.835962i) q^{37} +6.42985i q^{38} +(-2.82661 - 4.62331i) q^{40} +(6.22435 + 10.7809i) q^{41} +(7.10356 + 4.10124i) q^{43} +2.08886 q^{44} +(5.17675 - 8.96640i) q^{46} -2.71238i q^{47} +(-3.42695 - 5.93565i) q^{49} +(-0.393660 - 7.82039i) q^{50} +(-0.512249 + 1.54915i) q^{52} -2.07646i q^{53} +(-9.06557 - 4.93433i) q^{55} +(0.463157 - 0.802212i) q^{56} +(-7.19596 - 4.15459i) q^{58} +(-4.11483 + 7.12710i) q^{59} +(1.07641 - 1.86440i) q^{61} +(-13.2994 + 7.67841i) q^{62} -5.46337 q^{64} +(5.88256 - 5.51321i) q^{65} +(10.1684 - 5.87072i) q^{67} +(1.94170 - 1.12104i) q^{68} +(1.14199 - 0.698194i) q^{70} +(1.56281 - 2.70687i) q^{71} -13.5863i q^{73} +(-1.30916 + 2.26754i) q^{74} +(0.929003 + 1.60908i) q^{76} -1.76435i q^{77} -1.45254 q^{79} +(-9.23132 - 5.02455i) q^{80} +(16.8835 + 9.74770i) q^{82} -2.02064i q^{83} +(-11.0750 + 0.278569i) q^{85} +12.8456 q^{86} +(-9.68755 + 5.59311i) q^{88} +(-2.60725 - 4.51588i) q^{89} +(1.30849 + 0.432671i) q^{91} -2.99181i q^{92} +(-2.12387 - 3.67866i) q^{94} +(-0.230850 - 9.17784i) q^{95} +(15.7666 + 9.10286i) q^{97} +(-9.29557 - 5.36680i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4}+O(q^{10}) \) 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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