LMFDB - Embedded newform 289.2.d.d.179.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(110,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("289.110");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.d (of order $8$, degree $4$, not 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:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			179.2
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	289.179
Dual form			289.2.d.d.155.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.765367 - 1.84776i) q^{5} +(-1.53073 - 3.69552i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(-2.12132 - 2.12132i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.765367 - 1.84776i) q^{5} +(-1.53073 - 3.69552i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(-2.12132 - 2.12132i) q^{9} +(0.765367 + 1.84776i) q^{10} -2.00000i q^{13} +(3.69552 + 1.53073i) q^{14} +1.00000 q^{16} +3.00000 q^{18} +(-2.82843 + 2.82843i) q^{19} +(1.84776 + 0.765367i) q^{20} +(3.69552 - 1.53073i) q^{23} +(0.707107 + 0.707107i) q^{25} +(1.41421 + 1.41421i) q^{26} +(3.69552 - 1.53073i) q^{28} +(2.29610 - 5.54328i) q^{29} +(-3.69552 - 1.53073i) q^{31} +(3.53553 - 3.53553i) q^{32} -8.00000 q^{35} +(2.12132 - 2.12132i) q^{36} +(-1.84776 - 0.765367i) q^{37} -4.00000i q^{38} +(-5.54328 + 2.29610i) q^{40} +(2.29610 + 5.54328i) q^{41} +(2.82843 + 2.82843i) q^{43} +(-5.54328 + 2.29610i) q^{45} +(-1.53073 + 3.69552i) q^{46} +(-6.36396 + 6.36396i) q^{49} -1.00000 q^{50} +2.00000 q^{52} +(4.24264 - 4.24264i) q^{53} +(-4.59220 + 11.0866i) q^{56} +(2.29610 + 5.54328i) q^{58} +(8.48528 + 8.48528i) q^{59} +(-3.82683 - 9.23880i) q^{61} +(3.69552 - 1.53073i) q^{62} +(-4.59220 + 11.0866i) q^{63} +7.00000i q^{64} +(-3.69552 - 1.53073i) q^{65} -4.00000 q^{67} +(5.65685 - 5.65685i) q^{70} +(-3.69552 - 1.53073i) q^{71} +9.00000i q^{72} +(2.29610 - 5.54328i) q^{73} +(1.84776 - 0.765367i) q^{74} +(-2.82843 - 2.82843i) q^{76} +(-11.0866 + 4.59220i) q^{79} +(0.765367 - 1.84776i) q^{80} +9.00000i q^{81} +(-5.54328 - 2.29610i) q^{82} +(2.82843 - 2.82843i) q^{83} -4.00000 q^{86} -10.0000i q^{89} +(2.29610 - 5.54328i) q^{90} +(-7.39104 + 3.06147i) q^{91} +(1.53073 + 3.69552i) q^{92} +(3.06147 + 7.39104i) q^{95} +(0.765367 - 1.84776i) q^{97} -9.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 8 q^{16} + 24 q^{18} - 64 q^{35} - 8 q^{50} + 16 q^{52} - 32 q^{67} - 32 q^{86}+O(q^{100}) $ 8 * q + 8 * q^16 + 24 * q^18 - 64 * q^35 - 8 * q^50 + 16 * q^52 - 32 * q^67 - 32 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i	−0.911438	−	0.411438i	$-0.865027\pi$
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i	0.411438	+	0.911438i	$0.365027\pi$
$3$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$3$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$4$			1.00000i			0.500000i
$5$	0.765367	−	1.84776i	0.342282	−	0.826343i	−0.655202	−	0.755454i	$-0.727416\pi$
$5$	0.765367	−	1.84776i	0.342282	−	0.826343i	0.997484	−	0.0708890i	$-0.0225836\pi$
$6$		0			0
$7$	−1.53073	−	3.69552i	−0.578563	−	1.39677i	−0.894103	−	0.447862i	$-0.852186\pi$
$7$	−1.53073	−	3.69552i	−0.578563	−	1.39677i	0.315540	−	0.948912i	$-0.397814\pi$
$8$	−2.12132	−	2.12132i	−0.750000	−	0.750000i
$9$	−2.12132	−	2.12132i	−0.707107	−	0.707107i
$10$	0.765367	+	1.84776i	0.242030	+	0.584313i
$11$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$11$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	3.69552	+	1.53073i	0.987669	+	0.409106i
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0
$17$		0			0
$18$	3.00000			0.707107
$19$	−2.82843	+	2.82843i	−0.648886	+	0.648886i	−0.952724	−	0.303838i	$-0.901732\pi$
$19$	−2.82843	+	2.82843i	−0.648886	+	0.648886i	0.303838	+	0.952724i	$0.401732\pi$
$20$	1.84776	+	0.765367i	0.413171	+	0.171141i
$21$		0			0
$22$		0			0
$23$	3.69552	−	1.53073i	0.770569	−	0.319180i	0.0374660	−	0.999298i	$-0.488071\pi$
$23$	3.69552	−	1.53073i	0.770569	−	0.319180i	0.733103	+	0.680118i	$0.238071\pi$
$24$		0			0
$25$	0.707107	+	0.707107i	0.141421	+	0.141421i
$26$	1.41421	+	1.41421i	0.277350	+	0.277350i
$27$		0			0
$28$	3.69552	−	1.53073i	0.698387	−	0.289281i
$29$	2.29610	−	5.54328i	0.426375	−	1.02936i	−0.554053	−	0.832482i	$-0.686919\pi$
$29$	2.29610	−	5.54328i	0.426375	−	1.02936i	0.980428	−	0.196879i	$-0.0630806\pi$
$30$		0			0
$31$	−3.69552	−	1.53073i	−0.663735	−	0.274928i	0.0252745	−	0.999681i	$-0.491954\pi$
$31$	−3.69552	−	1.53073i	−0.663735	−	0.274928i	−0.689009	+	0.724753i	$0.741954\pi$
$32$	3.53553	−	3.53553i	0.625000	−	0.625000i
$33$		0			0
$34$		0			0
$35$	−8.00000			−1.35225
$36$	2.12132	−	2.12132i	0.353553	−	0.353553i
$37$	−1.84776	−	0.765367i	−0.303770	−	0.125826i	0.225592	−	0.974222i	$-0.427568\pi$
$37$	−1.84776	−	0.765367i	−0.303770	−	0.125826i	−0.529361	+	0.848396i	$0.677568\pi$
$38$		−	4.00000i		−	0.648886i
$39$		0			0
$40$	−5.54328	+	2.29610i	−0.876469	+	0.363045i
$41$	2.29610	+	5.54328i	0.358591	+	0.865714i	0.995499	+	0.0947747i	$0.0302131\pi$
$41$	2.29610	+	5.54328i	0.358591	+	0.865714i	−0.636908	+	0.770940i	$0.719787\pi$
$42$		0			0
$43$	2.82843	+	2.82843i	0.431331	+	0.431331i	0.889081	−	0.457750i	$-0.151344\pi$
$43$	2.82843	+	2.82843i	0.431331	+	0.431331i	−0.457750	+	0.889081i	$0.651344\pi$
$44$		0			0
$45$	−5.54328	+	2.29610i	−0.826343	+	0.342282i
$46$	−1.53073	+	3.69552i	−0.225694	+	0.544874i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$		0			0
$49$	−6.36396	+	6.36396i	−0.909137	+	0.909137i
$50$	−1.00000			−0.141421
$51$		0			0
$52$	2.00000			0.277350
$53$	4.24264	−	4.24264i	0.582772	−	0.582772i	−0.352892	−	0.935664i	$-0.614802\pi$
$53$	4.24264	−	4.24264i	0.582772	−	0.582772i	0.935664	+	0.352892i	$0.114802\pi$
$54$		0			0
$55$		0			0
$56$	−4.59220	+	11.0866i	−0.613659	+	1.48150i
$57$		0			0
$58$	2.29610	+	5.54328i	0.301493	+	0.727868i
$59$	8.48528	+	8.48528i	1.10469	+	1.10469i	0.993837	+	0.110853i	$0.0353582\pi$
$59$	8.48528	+	8.48528i	1.10469	+	1.10469i	0.110853	+	0.993837i	$0.464642\pi$
$60$		0			0
$61$	−3.82683	−	9.23880i	−0.489976	−	1.18291i	−0.954732	−	0.297468i	$-0.903858\pi$
$61$	−3.82683	−	9.23880i	−0.489976	−	1.18291i	0.464756	−	0.885439i	$-0.346142\pi$
$62$	3.69552	−	1.53073i	0.469331	−	0.194403i
$63$	−4.59220	+	11.0866i	−0.578563	+	1.39677i
$64$			7.00000i			0.875000i
$65$	−3.69552	−	1.53073i	−0.458373	−	0.189864i
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$		0			0
$70$	5.65685	−	5.65685i	0.676123	−	0.676123i
$71$	−3.69552	−	1.53073i	−0.438577	−	0.181665i	0.152459	−	0.988310i	$-0.451281\pi$
$71$	−3.69552	−	1.53073i	−0.438577	−	0.181665i	−0.591036	+	0.806645i	$0.701281\pi$
$72$			9.00000i			1.06066i
$73$	2.29610	−	5.54328i	0.268738	−	0.648792i	−0.730686	−	0.682713i	$-0.760800\pi$
$73$	2.29610	−	5.54328i	0.268738	−	0.648792i	0.999424	+	0.0339219i	$0.0107997\pi$
$74$	1.84776	−	0.765367i	0.214798	−	0.0889721i
$75$		0			0
$76$	−2.82843	−	2.82843i	−0.324443	−	0.324443i
$77$		0			0
$78$		0			0
$79$	−11.0866	+	4.59220i	−1.24733	+	0.516663i	−0.906000	−	0.423279i	$-0.860879\pi$
$79$	−11.0866	+	4.59220i	−1.24733	+	0.516663i	−0.341335	+	0.939942i	$0.610879\pi$
$80$	0.765367	−	1.84776i	0.0855706	−	0.206586i
$81$			9.00000i			1.00000i
$82$	−5.54328	−	2.29610i	−0.612153	−	0.253562i
$83$	2.82843	−	2.82843i	0.310460	−	0.310460i	−0.534628	−	0.845088i	$-0.679548\pi$
$83$	2.82843	−	2.82843i	0.310460	−	0.310460i	0.845088	+	0.534628i	$0.179548\pi$
$84$		0			0
$85$		0			0
$86$	−4.00000			−0.431331
$87$		0			0
$88$		0			0
$89$		−	10.0000i		−	1.06000i	−0.847998	−	0.529999i	$-0.822192\pi$
$89$		−	10.0000i		−	1.06000i	0.847998	−	0.529999i	$-0.177808\pi$
$90$	2.29610	−	5.54328i	0.242030	−	0.584313i
$91$	−7.39104	+	3.06147i	−0.774791	+	0.320929i
$92$	1.53073	+	3.69552i	0.159590	+	0.385284i
$93$		0			0
$94$		0			0
$95$	3.06147	+	7.39104i	0.314100	+	0.758304i
$96$		0			0
$97$	0.765367	−	1.84776i	0.0777112	−	0.187612i	−0.880249	−	0.474511i	$-0.842625\pi$
$97$	0.765367	−	1.84776i	0.0777112	−	0.187612i	0.957961	+	0.286900i	$0.0926247\pi$
$98$		−	9.00000i		−	0.909137i
$99$		0			0
$100$	−0.707107	+	0.707107i	−0.0707107	+	0.0707107i
$101$	10.0000			0.995037			0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000			0.995037			0.497519	+	0.867453i	$0.334245\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$	−4.24264	+	4.24264i	−0.416025	+	0.416025i
$105$		0			0
$106$			6.00000i			0.582772i
$107$	−3.06147	+	7.39104i	−0.295963	+	0.714518i	0.704027	+	0.710173i	$0.251383\pi$
$107$	−3.06147	+	7.39104i	−0.295963	+	0.714518i	−0.999991	+	0.00434556i	$0.998617\pi$
$108$		0			0
$109$	−2.29610	−	5.54328i	−0.219927	−	0.530950i	0.774953	−	0.632019i	$-0.217774\pi$
$109$	−2.29610	−	5.54328i	−0.219927	−	0.530950i	−0.994879	+	0.101069i	$0.967774\pi$
$110$		0			0
$111$		0			0
$112$	−1.53073	−	3.69552i	−0.144641	−	0.349194i
$113$	12.9343	−	5.35757i	1.21676	−	0.503998i	0.320380	−	0.947289i	$-0.396189\pi$
$113$	12.9343	−	5.35757i	1.21676	−	0.503998i	0.896378	+	0.443291i	$0.146189\pi$
$114$		0			0
$115$		−	8.00000i		−	0.746004i
$116$	5.54328	+	2.29610i	0.514680	+	0.213188i
$117$	−4.24264	+	4.24264i	−0.392232	+	0.392232i
$118$	−12.0000			−1.10469
$119$		0			0
$120$		0			0
$121$	−7.77817	+	7.77817i	−0.707107	+	0.707107i
$122$	9.23880	+	3.82683i	0.836441	+	0.346465i
$123$		0			0
$124$	1.53073	−	3.69552i	0.137464	−	0.331867i
$125$	11.0866	−	4.59220i	0.991612	−	0.410739i
$126$	−4.59220	−	11.0866i	−0.409106	−	0.987669i
$127$	−5.65685	−	5.65685i	−0.501965	−	0.501965i	0.410083	−	0.912048i	$-0.365500\pi$
$127$	−5.65685	−	5.65685i	−0.501965	−	0.501965i	−0.912048	+	0.410083i	$0.865500\pi$
$128$	2.12132	+	2.12132i	0.187500	+	0.187500i
$129$		0			0
$130$	3.69552	−	1.53073i	0.324118	−	0.134254i
$131$	6.12293	−	14.7821i	0.534963	−	1.29152i	−0.393238	−	0.919437i	$-0.628645\pi$
$131$	6.12293	−	14.7821i	0.534963	−	1.29152i	0.928201	−	0.372079i	$-0.121355\pi$
$132$		0			0
$133$	14.7821	+	6.12293i	1.28177	+	0.530926i
$134$	2.82843	−	2.82843i	0.244339	−	0.244339i
$135$		0			0
$136$		0			0
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$		0			0
$139$	−7.39104	−	3.06147i	−0.626900	−	0.259670i	0.0465356	−	0.998917i	$-0.485182\pi$
$139$	−7.39104	−	3.06147i	−0.626900	−	0.259670i	−0.673435	+	0.739246i	$0.735182\pi$
$140$		−	8.00000i		−	0.676123i
$141$		0			0
$142$	3.69552	−	1.53073i	0.310121	−	0.128456i
$143$		0			0
$144$	−2.12132	−	2.12132i	−0.176777	−	0.176777i
$145$	−8.48528	−	8.48528i	−0.704664	−	0.704664i
$146$	2.29610	+	5.54328i	0.190027	+	0.458765i
$147$		0			0
$148$	0.765367	−	1.84776i	0.0629128	−	0.151885i
$149$		−	10.0000i		−	0.819232i	−0.912258	−	0.409616i	$-0.865663\pi$
$149$		−	10.0000i		−	0.819232i	0.912258	−	0.409616i	$-0.134337\pi$
$150$		0			0
$151$	11.3137	−	11.3137i	0.920697	−	0.920697i	−0.0763821	−	0.997079i	$-0.524337\pi$
$151$	11.3137	−	11.3137i	0.920697	−	0.920697i	0.997079	+	0.0763821i	$0.0243369\pi$
$152$	12.0000			0.973329
$153$		0			0
$154$		0			0
$155$	−5.65685	+	5.65685i	−0.454369	+	0.454369i
$156$		0			0
$157$			2.00000i			0.159617i	0.996810	+	0.0798087i	$0.0254309\pi$
$157$			2.00000i			0.159617i	−0.996810	+	0.0798087i	$0.974569\pi$
$158$	4.59220	−	11.0866i	0.365336	−	0.881999i
$159$		0			0
$160$	−3.82683	−	9.23880i	−0.302538	−	0.730391i
$161$	−11.3137	−	11.3137i	−0.891645	−	0.891645i
$162$	−6.36396	−	6.36396i	−0.500000	−	0.500000i
$163$	9.18440	+	22.1731i	0.719378	+	1.73673i	0.675116	+	0.737712i	$0.264094\pi$
$163$	9.18440	+	22.1731i	0.719378	+	1.73673i	0.0442623	+	0.999020i	$0.485906\pi$
$164$	−5.54328	+	2.29610i	−0.432857	+	0.179295i
$165$		0			0
$166$			4.00000i			0.310460i
$167$	3.69552	+	1.53073i	0.285968	+	0.118452i	0.521057	−	0.853522i	$-0.325538\pi$
$167$	3.69552	+	1.53073i	0.285968	+	0.118452i	−0.235089	+	0.971974i	$0.575538\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$		0			0
$171$	12.0000			0.917663
$172$	−2.82843	+	2.82843i	−0.215666	+	0.215666i
$173$	20.3253	+	8.41904i	1.54531	+	0.640087i	0.982460	−	0.186473i	$-0.0597058\pi$
$173$	20.3253	+	8.41904i	1.54531	+	0.640087i	0.562848	+	0.826561i	$0.309706\pi$
$174$		0			0
$175$	1.53073	−	3.69552i	0.115713	−	0.279355i
$176$		0			0
$177$		0			0
$178$	7.07107	+	7.07107i	0.529999	+	0.529999i
$179$	8.48528	+	8.48528i	0.634220	+	0.634220i	0.949124	−	0.314904i	$-0.101972\pi$
$179$	8.48528	+	8.48528i	0.634220	+	0.634220i	−0.314904	+	0.949124i	$0.601972\pi$
$180$	−2.29610	−	5.54328i	−0.171141	−	0.413171i
$181$	1.84776	−	0.765367i	0.137343	−	0.0568893i	−0.312953	−	0.949768i	$-0.601318\pi$
$181$	1.84776	−	0.765367i	0.137343	−	0.0568893i	0.450296	+	0.892879i	$0.351318\pi$
$182$	3.06147	−	7.39104i	0.226931	−	0.547860i
$183$		0			0
$184$	−11.0866	−	4.59220i	−0.817312	−	0.338542i
$185$	−2.82843	+	2.82843i	−0.207950	+	0.207950i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−7.39104	−	3.06147i	−0.536202	−	0.222102i
$191$			16.0000i			1.15772i	0.815427	+	0.578860i	$0.196502\pi$
$191$			16.0000i			1.15772i	−0.815427	+	0.578860i	$0.803498\pi$
$192$		0			0
$193$	1.84776	−	0.765367i	0.133005	−	0.0550923i	−0.315188	−	0.949029i	$-0.602068\pi$
$193$	1.84776	−	0.765367i	0.133005	−	0.0550923i	0.448193	+	0.893937i	$0.352068\pi$
$194$	0.765367	+	1.84776i	0.0549501	+	0.132661i
$195$		0			0
$196$	−6.36396	−	6.36396i	−0.454569	−	0.454569i
$197$	−6.88830	−	16.6298i	−0.490771	−	1.18483i	−0.954328	−	0.298759i	$-0.903427\pi$
$197$	−6.88830	−	16.6298i	−0.490771	−	1.18483i	0.463557	−	0.886067i	$-0.346573\pi$
$198$		0			0
$199$	−7.65367	+	18.4776i	−0.542554	+	1.30984i	0.380361	+	0.924838i	$0.375800\pi$
$199$	−7.65367	+	18.4776i	−0.542554	+	1.30984i	−0.922915	+	0.385004i	$0.874200\pi$
$200$		−	3.00000i		−	0.212132i
$201$		0			0
$202$	−7.07107	+	7.07107i	−0.497519	+	0.497519i
$203$	−24.0000			−1.68447
$204$		0			0
$205$	12.0000			0.838116
$206$	−5.65685	+	5.65685i	−0.394132	+	0.394132i
$207$	−11.0866	−	4.59220i	−0.770569	−	0.319180i
$208$		−	2.00000i		−	0.138675i
$209$		0			0
$210$		0			0
$211$	−3.06147	−	7.39104i	−0.210760	−	0.508820i	0.782780	−	0.622298i	$-0.213801\pi$
$211$	−3.06147	−	7.39104i	−0.210760	−	0.508820i	−0.993540	+	0.113478i	$0.963801\pi$
$212$	4.24264	+	4.24264i	0.291386	+	0.291386i
$213$		0			0
$214$	−3.06147	−	7.39104i	−0.209278	−	0.505241i
$215$	7.39104	−	3.06147i	0.504064	−	0.208790i
$216$		0			0
$217$			16.0000i			1.08615i
$218$	5.54328	+	2.29610i	0.375438	+	0.155512i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	16.9706	−	16.9706i	1.13643	−	1.13643i	0.147348	−	0.989085i	$-0.452926\pi$
$223$	16.9706	−	16.9706i	1.13643	−	1.13643i	0.989085	−	0.147348i	$-0.0470738\pi$
$224$	−18.4776	−	7.65367i	−1.23459	−	0.511382i
$225$		−	3.00000i		−	0.200000i
$226$	−5.35757	+	12.9343i	−0.356380	+	0.860378i
$227$	−22.1731	+	9.18440i	−1.47168	+	0.609590i	−0.967242	−	0.253857i	$-0.918301\pi$
$227$	−22.1731	+	9.18440i	−1.47168	+	0.609590i	−0.504439	+	0.863447i	$0.668301\pi$
$228$		0			0
$229$	−4.24264	−	4.24264i	−0.280362	−	0.280362i	0.552892	−	0.833253i	$-0.313524\pi$
$229$	−4.24264	−	4.24264i	−0.280362	−	0.280362i	−0.833253	+	0.552892i	$0.813524\pi$
$230$	5.65685	+	5.65685i	0.373002	+	0.373002i
$231$		0			0
$232$	−16.6298	+	6.88830i	−1.09180	+	0.452239i
$233$	−2.29610	+	5.54328i	−0.150423	+	0.363152i	−0.981072	−	0.193644i	$-0.937969\pi$
$233$	−2.29610	+	5.54328i	−0.150423	+	0.363152i	0.830649	+	0.556796i	$0.187969\pi$
$234$		−	6.00000i		−	0.392232i
$235$		0			0
$236$	−8.48528	+	8.48528i	−0.552345	+	0.552345i
$237$		0			0
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	16.6298	+	6.88830i	1.07122	+	0.443715i	0.847422	−	0.530921i	$-0.178154\pi$
$241$	16.6298	+	6.88830i	1.07122	+	0.443715i	0.223800	+	0.974635i	$0.428154\pi$
$242$		−	11.0000i		−	0.707107i
$243$		0			0
$244$	9.23880	−	3.82683i	0.591453	−	0.244988i
$245$	6.88830	+	16.6298i	0.440077	+	1.06244i
$246$		0			0
$247$	5.65685	+	5.65685i	0.359937	+	0.359937i
$248$	4.59220	+	11.0866i	0.291605	+	0.703997i
$249$		0			0
$250$	−4.59220	+	11.0866i	−0.290436	+	0.701175i
$251$			12.0000i			0.757433i	0.925513	+	0.378717i	$0.123635\pi$
$251$			12.0000i			0.757433i	−0.925513	+	0.378717i	$0.876365\pi$
$252$	−11.0866	−	4.59220i	−0.698387	−	0.289281i
$253$		0			0
$254$	8.00000			0.501965
$255$		0			0
$256$	−17.0000			−1.06250
$257$	12.7279	−	12.7279i	0.793946	−	0.793946i	−0.188187	−	0.982133i	$-0.560261\pi$
$257$	12.7279	−	12.7279i	0.793946	−	0.793946i	0.982133	+	0.188187i	$0.0602612\pi$
$258$		0			0
$259$			8.00000i			0.497096i
$260$	1.53073	−	3.69552i	0.0949321	−	0.229186i
$261$	−16.6298	+	6.88830i	−1.02936	+	0.426375i
$262$	6.12293	+	14.7821i	0.378276	+	0.913239i
$263$	11.3137	+	11.3137i	0.697633	+	0.697633i	0.963899	−	0.266266i	$-0.0857901\pi$
$263$	11.3137	+	11.3137i	0.697633	+	0.697633i	−0.266266	+	0.963899i	$0.585790\pi$
$264$		0			0
$265$	−4.59220	−	11.0866i	−0.282097	−	0.681042i
$266$	−14.7821	+	6.12293i	−0.906347	+	0.375421i
$267$		0			0
$268$		−	4.00000i		−	0.244339i
$269$	−20.3253	−	8.41904i	−1.23926	−	0.513318i	−0.335776	−	0.941942i	$-0.608998\pi$
$269$	−20.3253	−	8.41904i	−1.23926	−	0.513318i	−0.903483	+	0.428624i	$0.858998\pi$
$270$		0			0
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$		0			0
$273$		0			0
$274$	4.24264	−	4.24264i	0.256307	−	0.256307i
$275$		0			0
$276$		0			0
$277$	−5.35757	+	12.9343i	−0.321905	+	0.777148i	0.677238	+	0.735764i	$0.263177\pi$
$277$	−5.35757	+	12.9343i	−0.321905	+	0.777148i	−0.999143	+	0.0413838i	$0.986823\pi$
$278$	7.39104	−	3.06147i	0.443285	−	0.183615i
$279$	4.59220	+	11.0866i	0.274928	+	0.663735i
$280$	16.9706	+	16.9706i	1.01419	+	1.01419i
$281$	−4.24264	−	4.24264i	−0.253095	−	0.253095i	0.569143	−	0.822238i	$-0.307275\pi$
$281$	−4.24264	−	4.24264i	−0.253095	−	0.253095i	−0.822238	+	0.569143i	$0.807275\pi$
$282$		0			0
$283$	14.7821	−	6.12293i	0.878703	−	0.363971i	0.102709	−	0.994711i	$-0.467249\pi$
$283$	14.7821	−	6.12293i	0.878703	−	0.363971i	0.775994	+	0.630741i	$0.217249\pi$
$284$	1.53073	−	3.69552i	0.0908323	−	0.219289i
$285$		0			0
$286$		0			0
$287$	16.9706	−	16.9706i	1.00174	−	1.00174i
$288$	−15.0000			−0.883883
$289$		0			0
$290$	12.0000			0.704664
$291$		0			0
$292$	5.54328	+	2.29610i	0.324396	+	0.134369i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$		0			0
$295$	22.1731	−	9.18440i	1.29097	−	0.534737i
$296$	2.29610	+	5.54328i	0.133458	+	0.322196i
$297$		0			0
$298$	7.07107	+	7.07107i	0.409616	+	0.409616i
$299$	−3.06147	−	7.39104i	−0.177049	−	0.427435i
$300$		0			0
$301$	6.12293	−	14.7821i	0.352920	−	0.852024i
$302$			16.0000i			0.920697i
$303$		0			0
$304$	−2.82843	+	2.82843i	−0.162221	+	0.162221i
$305$	−20.0000			−1.14520
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$		0			0
$310$		−	8.00000i		−	0.454369i
$311$	−10.7151	+	25.8686i	−0.607600	+	1.46688i	0.258003	+	0.966144i	$0.416935\pi$
$311$	−10.7151	+	25.8686i	−0.607600	+	1.46688i	−0.865603	+	0.500731i	$0.833065\pi$
$312$		0			0
$313$	8.41904	+	20.3253i	0.475872	+	1.14886i	0.961528	+	0.274707i	$0.0885808\pi$
$313$	8.41904	+	20.3253i	0.475872	+	1.14886i	−0.485656	+	0.874150i	$0.661419\pi$
$314$	−1.41421	−	1.41421i	−0.0798087	−	0.0798087i
$315$	16.9706	+	16.9706i	0.956183	+	0.956183i
$316$	−4.59220	−	11.0866i	−0.258331	−	0.623667i
$317$	9.23880	−	3.82683i	0.518902	−	0.214936i	−0.107832	−	0.994169i	$-0.534391\pi$
$317$	9.23880	−	3.82683i	0.518902	−	0.214936i	0.626735	+	0.779233i	$0.284391\pi$
$318$		0			0
$319$		0			0
$320$	12.9343	+	5.35757i	0.723050	+	0.299497i
$321$		0			0
$322$	16.0000			0.891645
$323$		0			0
$324$	−9.00000			−0.500000
$325$	1.41421	−	1.41421i	0.0784465	−	0.0784465i
$326$	−22.1731	−	9.18440i	−1.22805	−	0.508677i
$327$		0			0
$328$	6.88830	−	16.6298i	0.380343	−	0.918229i
$329$		0			0
$330$		0			0
$331$	−2.82843	−	2.82843i	−0.155464	−	0.155464i	0.625089	−	0.780553i	$-0.285063\pi$
$331$	−2.82843	−	2.82843i	−0.155464	−	0.155464i	−0.780553	+	0.625089i	$0.785063\pi$
$332$	2.82843	+	2.82843i	0.155230	+	0.155230i
$333$	2.29610	+	5.54328i	0.125826	+	0.303770i
$334$	−3.69552	+	1.53073i	−0.202210	+	0.0837580i
$335$	−3.06147	+	7.39104i	−0.167266	+	0.403815i
$336$		0			0
$337$	12.9343	+	5.35757i	0.704577	+	0.291845i	0.706058	−	0.708154i	$-0.250472\pi$
$337$	12.9343	+	5.35757i	0.704577	+	0.291845i	−0.00148149	+	0.999999i	$0.500472\pi$
$338$	−6.36396	+	6.36396i	−0.346154	+	0.346154i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−8.48528	+	8.48528i	−0.458831	+	0.458831i
$343$	7.39104	+	3.06147i	0.399078	+	0.165304i
$344$		−	12.0000i		−	0.646997i
$345$		0			0
$346$	−20.3253	+	8.41904i	−1.09270	+	0.452610i
$347$	−12.2459	−	29.5641i	−0.657393	−	1.58709i	−0.801816	−	0.597571i	$-0.796133\pi$
$347$	−12.2459	−	29.5641i	−0.657393	−	1.58709i	0.144424	−	0.989516i	$-0.453867\pi$
$348$		0			0
$349$	−12.7279	−	12.7279i	−0.681310	−	0.681310i	0.278985	−	0.960295i	$-0.410002\pi$
$349$	−12.7279	−	12.7279i	−0.681310	−	0.681310i	−0.960295	+	0.278985i	$0.910002\pi$
$350$	1.53073	+	3.69552i	0.0818212	+	0.197534i
$351$		0			0
$352$		0			0
$353$		−	30.0000i		−	1.59674i	−0.602168	−	0.798369i	$-0.705696\pi$
$353$		−	30.0000i		−	1.59674i	0.602168	−	0.798369i	$-0.294304\pi$
$354$		0			0
$355$	−5.65685	+	5.65685i	−0.300235	+	0.300235i
$356$	10.0000			0.529999
$357$		0			0
$358$	−12.0000			−0.634220
$359$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$359$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$360$	16.6298	+	6.88830i	0.876469	+	0.363045i
$361$			3.00000i			0.157895i
$362$	−0.765367	+	1.84776i	−0.0402268	+	0.0971161i
$363$		0			0
$364$	−3.06147	−	7.39104i	−0.160464	−	0.387396i
$365$	−8.48528	−	8.48528i	−0.444140	−	0.444140i
$366$		0			0
$367$	10.7151	+	25.8686i	0.559326	+	1.35033i	0.910301	+	0.413947i	$0.135850\pi$
$367$	10.7151	+	25.8686i	0.559326	+	1.35033i	−0.350976	+	0.936385i	$0.614150\pi$
$368$	3.69552	−	1.53073i	0.192642	−	0.0797950i
$369$	6.88830	−	16.6298i	0.358591	−	0.865714i
$370$		−	4.00000i		−	0.207950i
$371$	−22.1731	−	9.18440i	−1.15117	−	0.476830i
$372$		0			0
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−11.0866	−	4.59220i	−0.570987	−	0.236510i
$378$		0			0
$379$	3.06147	−	7.39104i	0.157257	−	0.379652i	−0.825539	−	0.564345i	$-0.809129\pi$
$379$	3.06147	−	7.39104i	0.157257	−	0.379652i	0.982796	+	0.184693i	$0.0591289\pi$
$380$	−7.39104	+	3.06147i	−0.379152	+	0.157050i
$381$		0			0
$382$	−11.3137	−	11.3137i	−0.578860	−	0.578860i
$383$	−16.9706	−	16.9706i	−0.867155	−	0.867155i	0.125001	−	0.992157i	$-0.460106\pi$
$383$	−16.9706	−	16.9706i	−0.867155	−	0.867155i	−0.992157	+	0.125001i	$0.960106\pi$
$384$		0			0
$385$		0			0
$386$	−0.765367	+	1.84776i	−0.0389561	+	0.0940485i
$387$		−	12.0000i		−	0.609994i
$388$	1.84776	+	0.765367i	0.0938058	+	0.0388556i
$389$	−4.24264	+	4.24264i	−0.215110	+	0.215110i	−0.806434	−	0.591324i	$-0.798606\pi$
$389$	−4.24264	+	4.24264i	−0.215110	+	0.215110i	0.591324	+	0.806434i	$0.298606\pi$
$390$		0			0
$391$		0			0
$392$	27.0000			1.36371
$393$		0			0
$394$	16.6298	+	6.88830i	0.837799	+	0.347028i
$395$			24.0000i			1.20757i
$396$		0			0
$397$	5.54328	−	2.29610i	0.278209	−	0.115238i	−0.239216	−	0.970966i	$-0.576890\pi$
$397$	5.54328	−	2.29610i	0.278209	−	0.115238i	0.517425	+	0.855728i	$0.326890\pi$
$398$	−7.65367	−	18.4776i	−0.383644	−	0.926198i
$399$		0			0
$400$	0.707107	+	0.707107i	0.0353553	+	0.0353553i
$401$	−5.35757	−	12.9343i	−0.267544	−	0.645909i	0.731822	−	0.681495i	$-0.238670\pi$
$401$	−5.35757	−	12.9343i	−0.267544	−	0.645909i	−0.999367	+	0.0355866i	$0.988670\pi$
$402$		0			0
$403$	−3.06147	+	7.39104i	−0.152503	+	0.368174i
$404$			10.0000i			0.497519i
$405$	16.6298	+	6.88830i	0.826343	+	0.342282i
$406$	16.9706	−	16.9706i	0.842235	−	0.842235i
$407$		0			0
$408$		0			0
$409$	26.0000			1.28562			0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000			1.28562			0.642809	+	0.766027i	$0.277769\pi$
$410$	−8.48528	+	8.48528i	−0.419058	+	0.419058i
$411$		0			0
$412$			8.00000i			0.394132i
$413$	18.3688	−	44.3462i	0.903870	−	2.18213i
$414$	11.0866	−	4.59220i	0.544874	−	0.225694i
$415$	−3.06147	−	7.39104i	−0.150282	−	0.362812i
$416$	−7.07107	−	7.07107i	−0.346688	−	0.346688i
$417$		0			0
$418$		0			0
$419$	−7.39104	+	3.06147i	−0.361076	+	0.149562i	−0.555844	−	0.831287i	$-0.687605\pi$
$419$	−7.39104	+	3.06147i	−0.361076	+	0.149562i	0.194768	+	0.980849i	$0.437605\pi$
$420$		0			0
$421$			22.0000i			1.07221i	0.844150	+	0.536107i	$0.180106\pi$
$421$			22.0000i			1.07221i	−0.844150	+	0.536107i	$0.819894\pi$
$422$	7.39104	+	3.06147i	0.359790	+	0.149030i
$423$		0			0
$424$	−18.0000			−0.874157
$425$		0			0
$426$		0			0
$427$	−28.2843	+	28.2843i	−1.36877	+	1.36877i
$428$	−7.39104	−	3.06147i	−0.357259	−	0.147982i
$429$		0			0
$430$	−3.06147	+	7.39104i	−0.147637	+	0.356427i
$431$	11.0866	−	4.59220i	0.534021	−	0.221199i	−0.0993426	−	0.995053i	$-0.531674\pi$
$431$	11.0866	−	4.59220i	0.534021	−	0.221199i	0.633363	+	0.773855i	$0.281674\pi$
$432$		0			0
$433$	−1.41421	−	1.41421i	−0.0679628	−	0.0679628i	0.672308	−	0.740271i	$-0.265303\pi$
$433$	−1.41421	−	1.41421i	−0.0679628	−	0.0679628i	−0.740271	+	0.672308i	$0.765303\pi$
$434$	−11.3137	−	11.3137i	−0.543075	−	0.543075i
$435$		0			0
$436$	5.54328	−	2.29610i	0.265475	−	0.109963i
$437$	−6.12293	+	14.7821i	−0.292900	+	0.707122i
$438$		0			0
$439$	18.4776	+	7.65367i	0.881887	+	0.365290i	0.777228	−	0.629219i	$-0.216625\pi$
$439$	18.4776	+	7.65367i	0.881887	+	0.365290i	0.104659	+	0.994508i	$0.466625\pi$
$440$		0			0
$441$	27.0000			1.28571
$442$		0			0
$443$	28.0000			1.33032			0.665160	−	0.746701i	$-0.268363\pi$
$443$	28.0000			1.33032			0.665160	+	0.746701i	$0.268363\pi$
$444$		0			0
$445$	−18.4776	−	7.65367i	−0.875922	−	0.362819i
$446$			24.0000i			1.13643i
$447$		0			0
$448$	25.8686	−	10.7151i	1.22218	−	0.506243i
$449$	−13.0112	−	31.4119i	−0.614038	−	1.48242i	−0.858528	−	0.512767i	$-0.828620\pi$
$449$	−13.0112	−	31.4119i	−0.614038	−	1.48242i	0.244489	−	0.969652i	$-0.421380\pi$
$450$	2.12132	+	2.12132i	0.100000	+	0.100000i
$451$		0			0
$452$	5.35757	+	12.9343i	0.251999	+	0.608379i
$453$		0			0
$454$	9.18440	−	22.1731i	0.431045	−	1.04064i
$455$			16.0000i			0.750092i
$456$		0			0
$457$	4.24264	−	4.24264i	0.198462	−	0.198462i	−0.600878	−	0.799341i	$-0.705182\pi$
$457$	4.24264	−	4.24264i	0.198462	−	0.198462i	0.799341	+	0.600878i	$0.205182\pi$
$458$	6.00000			0.280362
$459$		0			0
$460$	8.00000			0.373002
$461$	−1.41421	+	1.41421i	−0.0658665	+	0.0658665i	−0.739273	−	0.673406i	$-0.764831\pi$
$461$	−1.41421	+	1.41421i	−0.0658665	+	0.0658665i	0.673406	+	0.739273i	$0.264831\pi$
$462$		0			0
$463$		−	32.0000i		−	1.48717i	−0.668644	−	0.743583i	$-0.733125\pi$
$463$		−	32.0000i		−	1.48717i	0.668644	−	0.743583i	$-0.266875\pi$
$464$	2.29610	−	5.54328i	0.106594	−	0.257340i
$465$		0			0
$466$	−2.29610	−	5.54328i	−0.106365	−	0.256787i
$467$	−8.48528	−	8.48528i	−0.392652	−	0.392652i	0.482980	−	0.875632i	$-0.339555\pi$
$467$	−8.48528	−	8.48528i	−0.392652	−	0.392652i	−0.875632	+	0.482980i	$0.839555\pi$
$468$	−4.24264	−	4.24264i	−0.196116	−	0.196116i
$469$	6.12293	+	14.7821i	0.282731	+	0.682573i
$470$		0			0
$471$		0			0
$472$		−	36.0000i		−	1.65703i
$473$		0			0
$474$		0			0
$475$	−4.00000			−0.183533
$476$		0			0
$477$	−18.0000			−0.824163
$478$	11.3137	−	11.3137i	0.517477	−	0.517477i
$479$	33.2597	+	13.7766i	1.51967	+	0.629469i	0.977526	−	0.210815i	$-0.0676117\pi$
$479$	33.2597	+	13.7766i	1.51967	+	0.629469i	0.542147	+	0.840284i	$0.317612\pi$
$480$		0			0
$481$	−1.53073	+	3.69552i	−0.0697955	+	0.168501i
$482$	−16.6298	+	6.88830i	−0.757468	+	0.313754i
$483$		0			0
$484$	−7.77817	−	7.77817i	−0.353553	−	0.353553i
$485$	−2.82843	−	2.82843i	−0.128432	−	0.128432i
$486$		0			0
$487$	−18.4776	+	7.65367i	−0.837300	+	0.346821i	−0.759788	−	0.650171i	$-0.774697\pi$
$487$	−18.4776	+	7.65367i	−0.837300	+	0.346821i	−0.0775113	+	0.996991i	$0.524697\pi$
$488$	−11.4805	+	27.7164i	−0.519698	+	1.25466i
$489$		0			0
$490$	−16.6298	−	6.88830i	−0.751259	−	0.311182i
$491$	−14.1421	+	14.1421i	−0.638226	+	0.638226i	−0.950118	−	0.311892i	$-0.899037\pi$
$491$	−14.1421	+	14.1421i	−0.638226	+	0.638226i	0.311892	+	0.950118i	$0.399037\pi$
$492$		0			0
$493$		0			0
$494$	−8.00000			−0.359937
$495$		0			0
$496$	−3.69552	−	1.53073i	−0.165934	−	0.0687320i
$497$			16.0000i			0.717698i
$498$		0			0
$499$	−36.9552	+	15.3073i	−1.65434	+	0.685251i	−0.997624	−	0.0688869i	$-0.978055\pi$
$499$	−36.9552	+	15.3073i	−1.65434	+	0.685251i	−0.656717	+	0.754137i	$0.728055\pi$
$500$	4.59220	+	11.0866i	0.205369	+	0.495806i
$501$		0			0
$502$	−8.48528	−	8.48528i	−0.378717	−	0.378717i
$503$	−4.59220	−	11.0866i	−0.204756	−	0.494325i	0.787826	−	0.615897i	$-0.211206\pi$
$503$	−4.59220	−	11.0866i	−0.204756	−	0.494325i	−0.992583	+	0.121572i	$0.961206\pi$
$504$	33.2597	−	13.7766i	1.48150	−	0.613659i
$505$	7.65367	−	18.4776i	0.340584	−	0.822242i
$506$		0			0
$507$		0			0
$508$	5.65685	−	5.65685i	0.250982	−	0.250982i
$509$	2.00000			0.0886484			0.0443242	−	0.999017i	$-0.485887\pi$
$509$	2.00000			0.0886484			0.0443242	+	0.999017i	$0.485887\pi$
$510$		0			0
$511$	−24.0000			−1.06170
$512$	7.77817	−	7.77817i	0.343750	−	0.343750i
$513$		0			0
$514$			18.0000i			0.793946i
$515$	6.12293	−	14.7821i	0.269809	−	0.651376i
$516$		0			0
$517$		0			0
$518$	−5.65685	−	5.65685i	−0.248548	−	0.248548i
$519$		0			0
$520$	4.59220	+	11.0866i	0.201381	+	0.486178i
$521$	−24.0209	+	9.94977i	−1.05237	+	0.435907i	−0.840738	−	0.541441i	$-0.817879\pi$
$521$	−24.0209	+	9.94977i	−1.05237	+	0.435907i	−0.211635	+	0.977349i	$0.567879\pi$
$522$	6.88830	−	16.6298i	0.301493	−	0.727868i
$523$		−	36.0000i		−	1.57417i	−0.616844	−	0.787085i	$-0.711589\pi$
$523$		−	36.0000i		−	1.57417i	0.616844	−	0.787085i	$-0.288411\pi$
$524$	14.7821	+	6.12293i	0.645758	+	0.267482i
$525$		0			0
$526$	−16.0000			−0.697633
$527$		0			0
$528$		0			0
$529$	−4.94975	+	4.94975i	−0.215206	+	0.215206i
$530$	11.0866	+	4.59220i	0.481569	+	0.199472i
$531$		−	36.0000i		−	1.56227i
$532$	−6.12293	+	14.7821i	−0.265463	+	0.640884i
$533$	11.0866	−	4.59220i	0.480212	−	0.198910i
$534$		0			0
$535$	11.3137	+	11.3137i	0.489134	+	0.489134i
$536$	8.48528	+	8.48528i	0.366508	+	0.366508i
$537$		0			0
$538$	20.3253	−	8.41904i	0.876288	−	0.362970i
$539$		0			0
$540$		0			0
$541$	−5.54328	−	2.29610i	−0.238324	−	0.0987171i	0.260325	−	0.965521i	$-0.416170\pi$
$541$	−5.54328	−	2.29610i	−0.238324	−	0.0987171i	−0.498649	+	0.866804i	$0.666170\pi$
$542$	−11.3137	+	11.3137i	−0.485965	+	0.485965i
$543$		0			0
$544$		0			0
$545$	−12.0000			−0.514024
$546$		0			0
$547$	−29.5641	−	12.2459i	−1.26407	−	0.523596i	−0.352915	−	0.935655i	$-0.614809\pi$
$547$	−29.5641	−	12.2459i	−1.26407	−	0.523596i	−0.911157	+	0.412060i	$0.864809\pi$
$548$		−	6.00000i		−	0.256307i
$549$	−11.4805	+	27.7164i	−0.489976	+	1.18291i
$550$		0			0
$551$	9.18440	+	22.1731i	0.391269	+	0.944606i
$552$		0			0
$553$	33.9411	+	33.9411i	1.44332	+	1.44332i
$554$	−5.35757	−	12.9343i	−0.227621	−	0.549526i
$555$		0			0
$556$	3.06147	−	7.39104i	0.129835	−	0.313450i
$557$			30.0000i			1.27114i	0.772043	+	0.635570i	$0.219235\pi$
$557$			30.0000i			1.27114i	−0.772043	+	0.635570i	$0.780765\pi$
$558$	−11.0866	−	4.59220i	−0.469331	−	0.194403i
$559$	5.65685	−	5.65685i	0.239259	−	0.239259i
$560$	−8.00000			−0.338062
$561$		0			0
$562$	6.00000			0.253095
$563$	−2.82843	+	2.82843i	−0.119204	+	0.119204i	−0.764192	−	0.644988i	$-0.776862\pi$
$563$	−2.82843	+	2.82843i	−0.119204	+	0.119204i	0.644988	+	0.764192i	$0.276862\pi$
$564$		0			0
$565$		−	28.0000i		−	1.17797i
$566$	−6.12293	+	14.7821i	−0.257366	+	0.621337i
$567$	33.2597	−	13.7766i	1.39677	−	0.578563i
$568$	4.59220	+	11.0866i	0.192684	+	0.465181i
$569$	26.8701	+	26.8701i	1.12645	+	1.12645i	0.990750	+	0.135702i	$0.0433289\pi$
$569$	26.8701	+	26.8701i	1.12645	+	1.12645i	0.135702	+	0.990750i	$0.456671\pi$
$570$		0			0
$571$	−12.2459	−	29.5641i	−0.512474	−	1.23722i	−0.942440	−	0.334376i	$-0.891474\pi$
$571$	−12.2459	−	29.5641i	−0.512474	−	1.23722i	0.429966	−	0.902845i	$-0.358526\pi$
$572$		0			0
$573$		0			0
$574$			24.0000i			1.00174i
$575$	3.69552	+	1.53073i	0.154114	+	0.0638360i
$576$	14.8492	−	14.8492i	0.618718	−	0.618718i
$577$	14.0000			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$578$		0			0
$579$		0			0
$580$	8.48528	−	8.48528i	0.352332	−	0.352332i
$581$	−14.7821	−	6.12293i	−0.613264	−	0.254022i
$582$		0			0
$583$		0			0
$584$	−16.6298	+	6.88830i	−0.688147	+	0.285040i
$585$	4.59220	+	11.0866i	0.189864	+	0.458373i
$586$	4.24264	+	4.24264i	0.175262	+	0.175262i
$587$	2.82843	+	2.82843i	0.116742	+	0.116742i	0.763064	−	0.646323i	$-0.223694\pi$
$587$	2.82843	+	2.82843i	0.116742	+	0.116742i	−0.646323	+	0.763064i	$0.723694\pi$
$588$		0			0
$589$	14.7821	−	6.12293i	0.609085	−	0.252291i
$590$	−9.18440	+	22.1731i	−0.378116	+	0.912852i
$591$		0			0
$592$	−1.84776	−	0.765367i	−0.0759424	−	0.0314564i
$593$	−12.7279	+	12.7279i	−0.522673	+	0.522673i	−0.918378	−	0.395705i	$-0.870500\pi$
$593$	−12.7279	+	12.7279i	−0.522673	+	0.522673i	0.395705	+	0.918378i	$0.370500\pi$
$594$		0			0
$595$		0			0
$596$	10.0000			0.409616
$597$		0			0
$598$	7.39104	+	3.06147i	0.302242	+	0.125193i
$599$			24.0000i			0.980613i	0.871550	+	0.490307i	$0.163115\pi$
$599$			24.0000i			0.980613i	−0.871550	+	0.490307i	$0.836885\pi$
$600$		0			0
$601$	9.23880	−	3.82683i	0.376858	−	0.156100i	−0.186210	−	0.982510i	$-0.559621\pi$
$601$	9.23880	−	3.82683i	0.376858	−	0.156100i	0.563069	+	0.826410i	$0.309621\pi$
$602$	6.12293	+	14.7821i	0.249552	+	0.602472i
$603$	8.48528	+	8.48528i	0.345547	+	0.345547i
$604$	11.3137	+	11.3137i	0.460348	+	0.460348i
$605$	8.41904	+	20.3253i	0.342282	+	0.826343i
$606$		0			0
$607$	7.65367	−	18.4776i	0.310653	−	0.749982i	−0.689028	−	0.724734i	$-0.741962\pi$
$607$	7.65367	−	18.4776i	0.310653	−	0.749982i	0.999681	−	0.0252479i	$-0.00803752\pi$
$608$			20.0000i			0.811107i
$609$		0			0
$610$	14.1421	−	14.1421i	0.572598	−	0.572598i
$611$		0			0
$612$		0			0
$613$	−26.0000			−1.05013			−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000			−1.05013			−0.525065	+	0.851062i	$0.675959\pi$
$614$	8.48528	−	8.48528i	0.342438	−	0.342438i
$615$		0			0
$616$		0			0
$617$	2.29610	−	5.54328i	0.0924375	−	0.223164i	−0.870898	−	0.491464i	$-0.836462\pi$
$617$	2.29610	−	5.54328i	0.0924375	−	0.223164i	0.963335	+	0.268300i	$0.0864619\pi$
$618$		0			0
$619$	18.3688	+	44.3462i	0.738305	+	1.78242i	0.612655	+	0.790350i	$0.290101\pi$
$619$	18.3688	+	44.3462i	0.738305	+	1.78242i	0.125649	+	0.992075i	$0.459899\pi$
$620$	−5.65685	−	5.65685i	−0.227185	−	0.227185i
$621$		0			0
$622$	−10.7151	−	25.8686i	−0.429638	−	1.03724i
$623$	−36.9552	+	15.3073i	−1.48058	+	0.613276i
$624$		0			0
$625$		−	19.0000i		−	0.760000i
$626$	−20.3253	−	8.41904i	−0.812364	−	0.336492i
$627$		0			0
$628$	−2.00000			−0.0798087
$629$		0			0
$630$	−24.0000			−0.956183
$631$	11.3137	−	11.3137i	0.450392	−	0.450392i	−0.445093	−	0.895484i	$-0.646829\pi$
$631$	11.3137	−	11.3137i	0.450392	−	0.450392i	0.895484	+	0.445093i	$0.146829\pi$
$632$	33.2597	+	13.7766i	1.32300	+	0.548004i
$633$		0			0
$634$	−3.82683	+	9.23880i	−0.151983	+	0.366919i
$635$	−14.7821	+	6.12293i	−0.586609	+	0.242981i
$636$		0			0
$637$	12.7279	+	12.7279i	0.504299	+	0.504299i
$638$		0			0
$639$	4.59220	+	11.0866i	0.181665	+	0.438577i
$640$	5.54328	−	2.29610i	0.219117	−	0.0907613i
$641$	−11.4805	+	27.7164i	−0.453453	+	1.09473i	0.517548	+	0.855654i	$0.326845\pi$
$641$	−11.4805	+	27.7164i	−0.453453	+	1.09473i	−0.971001	+	0.239077i	$0.923155\pi$
$642$		0			0
$643$	−29.5641	−	12.2459i	−1.16590	−	0.482930i	−0.286062	−	0.958211i	$-0.592346\pi$
$643$	−29.5641	−	12.2459i	−1.16590	−	0.482930i	−0.879834	+	0.475281i	$0.842346\pi$
$644$	11.3137	−	11.3137i	0.445823	−	0.445823i
$645$		0			0
$646$		0			0
$647$	8.00000			0.314512			0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000			0.314512			0.157256	+	0.987558i	$0.449735\pi$
$648$	19.0919	−	19.0919i	0.750000	−	0.750000i
$649$		0			0
$650$			2.00000i			0.0784465i
$651$		0			0
$652$	−22.1731	+	9.18440i	−0.868366	+	0.359689i
$653$	−2.29610	−	5.54328i	−0.0898534	−	0.216925i	0.872564	−	0.488500i	$-0.162456\pi$
$653$	−2.29610	−	5.54328i	−0.0898534	−	0.216925i	−0.962417	+	0.271575i	$0.912456\pi$
$654$		0			0
$655$	−22.6274	−	22.6274i	−0.884126	−	0.884126i
$656$	2.29610	+	5.54328i	0.0896477	+	0.216429i
$657$	−16.6298	+	6.88830i	−0.648792	+	0.268738i
$658$		0			0
$659$			4.00000i			0.155818i	0.996960	+	0.0779089i	$0.0248243\pi$
$659$			4.00000i			0.155818i	−0.996960	+	0.0779089i	$0.975176\pi$
$660$		0			0
$661$	−26.8701	+	26.8701i	−1.04512	+	1.04512i	−0.0461915	+	0.998933i	$0.514708\pi$
$661$	−26.8701	+	26.8701i	−1.04512	+	1.04512i	−0.998933	+	0.0461915i	$0.985292\pi$
$662$	4.00000			0.155464
$663$		0			0
$664$	−12.0000			−0.465690
$665$	22.6274	−	22.6274i	0.877454	−	0.877454i
$666$	−5.54328	−	2.29610i	−0.214798	−	0.0889721i
$667$		−	24.0000i		−	0.929284i
$668$	−1.53073	+	3.69552i	−0.0592259	+	0.142984i
$669$		0			0
$670$	−3.06147	−	7.39104i	−0.118275	−	0.285541i
$671$		0			0
$672$		0			0
$673$	0.765367	+	1.84776i	0.0295027	+	0.0712259i	0.937944	−	0.346786i	$-0.112727\pi$
$673$	0.765367	+	1.84776i	0.0295027	+	0.0712259i	−0.908442	+	0.418012i	$0.862727\pi$
$674$	−12.9343	+	5.35757i	−0.498211	+	0.206366i
$675$		0			0
$676$			9.00000i			0.346154i
$677$	−27.7164	−	11.4805i	−1.06523	−	0.441232i	−0.219923	−	0.975517i	$-0.570581\pi$
$677$	−27.7164	−	11.4805i	−1.06523	−	0.441232i	−0.845304	+	0.534286i	$0.820581\pi$
$678$		0			0
$679$	−8.00000			−0.307012
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−36.9552	−	15.3073i	−1.41405	−	0.585719i	−0.460692	−	0.887560i	$-0.652399\pi$
$683$	−36.9552	−	15.3073i	−1.41405	−	0.585719i	−0.953358	+	0.301841i	$0.902399\pi$
$684$			12.0000i			0.458831i
$685$	−4.59220	+	11.0866i	−0.175459	+	0.423595i
$686$	−7.39104	+	3.06147i	−0.282191	+	0.116887i
$687$		0			0
$688$	2.82843	+	2.82843i	0.107833	+	0.107833i
$689$	−8.48528	−	8.48528i	−0.323263	−	0.323263i
$690$		0			0
$691$	7.39104	−	3.06147i	0.281168	−	0.116464i	−0.237643	−	0.971353i	$-0.576375\pi$
$691$	7.39104	−	3.06147i	0.281168	−	0.116464i	0.518811	+	0.854889i	$0.326375\pi$
$692$	−8.41904	+	20.3253i	−0.320044	+	0.772654i
$693$		0			0
$694$	29.5641	+	12.2459i	1.12224	+	0.464847i
$695$	−11.3137	+	11.3137i	−0.429153	+	0.429153i
$696$		0			0
$697$		0			0
$698$	18.0000			0.681310
$699$		0			0
$700$	3.69552	+	1.53073i	0.139677	+	0.0578563i
$701$			18.0000i			0.679851i	0.940452	+	0.339925i	$0.110402\pi$
$701$			18.0000i			0.679851i	−0.940452	+	0.339925i	$0.889598\pi$
$702$		0			0
$703$	7.39104	−	3.06147i	0.278758	−	0.115465i
$704$		0			0
$705$		0			0
$706$	21.2132	+	21.2132i	0.798369	+	0.798369i
$707$	−15.3073	−	36.9552i	−0.575692	−	1.38984i
$708$		0			0
$709$	−13.0112	+	31.4119i	−0.488647	+	1.17970i	0.466754	+	0.884387i	$0.345423\pi$
$709$	−13.0112	+	31.4119i	−0.488647	+	1.17970i	−0.955401	+	0.295312i	$0.904577\pi$
$710$		−	8.00000i		−	0.300235i
$711$	33.2597	+	13.7766i	1.24733	+	0.516663i
$712$	−21.2132	+	21.2132i	−0.794998	+	0.794998i
$713$	−16.0000			−0.599205
$714$		0			0
$715$		0			0
$716$	−8.48528	+	8.48528i	−0.317110	+	0.317110i
$717$		0			0
$718$		0			0
$719$	−1.53073	+	3.69552i	−0.0570867	+	0.137820i	−0.949849	−	0.312708i	$-0.898764\pi$
$719$	−1.53073	+	3.69552i	−0.0570867	+	0.137820i	0.892763	+	0.450527i	$0.148764\pi$
$720$	−5.54328	+	2.29610i	−0.206586	+	0.0855706i
$721$	−12.2459	−	29.5641i	−0.456060	−	1.10103i
$722$	−2.12132	−	2.12132i	−0.0789474	−	0.0789474i
$723$		0			0
$724$	0.765367	+	1.84776i	0.0284446	+	0.0686714i
$725$	5.54328	−	2.29610i	0.205872	−	0.0852750i
$726$		0			0
$727$			40.0000i			1.48352i	0.670667	+	0.741759i	$0.266008\pi$
$727$			40.0000i			1.48352i	−0.670667	+	0.741759i	$0.733992\pi$
$728$	22.1731	+	9.18440i	0.821790	+	0.340397i
$729$	19.0919	−	19.0919i	0.707107	−	0.707107i
$730$	12.0000			0.444140
$731$		0			0
$732$		0			0
$733$	−35.3553	+	35.3553i	−1.30588	+	1.30588i	−0.381518	+	0.924362i	$0.624598\pi$
$733$	−35.3553	+	35.3553i	−1.30588	+	1.30588i	−0.924362	+	0.381518i	$0.875402\pi$
$734$	−25.8686	−	10.7151i	−0.954828	−	0.395503i
$735$		0			0
$736$	7.65367	−	18.4776i	0.282118	−	0.681093i
$737$		0			0
$738$	6.88830	+	16.6298i	0.253562	+	0.612153i
$739$	−19.7990	−	19.7990i	−0.728318	−	0.728318i	0.241967	−	0.970285i	$-0.422207\pi$
$739$	−19.7990	−	19.7990i	−0.728318	−	0.728318i	−0.970285	+	0.241967i	$0.922207\pi$
$740$	−2.82843	−	2.82843i	−0.103975	−	0.103975i
$741$		0			0
$742$	22.1731	−	9.18440i	0.814000	−	0.337170i
$743$	4.59220	−	11.0866i	0.168472	−	0.406726i	−0.816984	−	0.576661i	$-0.804356\pi$
$743$	4.59220	−	11.0866i	0.168472	−	0.406726i	0.985455	+	0.169934i	$0.0543555\pi$
$744$		0			0
$745$	−18.4776	−	7.65367i	−0.676967	−	0.280409i
$746$	4.24264	−	4.24264i	0.155334	−	0.155334i
$747$	−12.0000			−0.439057
$748$		0			0
$749$	32.0000			1.16925
$750$		0			0
$751$	18.4776	+	7.65367i	0.674257	+	0.279286i	0.693424	−	0.720530i	$-0.256101\pi$
$751$	18.4776	+	7.65367i	0.674257	+	0.279286i	−0.0191669	+	0.999816i	$0.506101\pi$
$752$		0			0
$753$		0			0
$754$	11.0866	−	4.59220i	0.403748	−	0.167238i
$755$	−12.2459	−	29.5641i	−0.445673	−	1.07595i
$756$		0			0
$757$	15.5563	+	15.5563i	0.565405	+	0.565405i	0.930838	−	0.365433i	$-0.119079\pi$
$757$	15.5563	+	15.5563i	0.565405	+	0.565405i	−0.365433	+	0.930838i	$0.619079\pi$
$758$	3.06147	+	7.39104i	0.111198	+	0.268455i
$759$		0			0
$760$	9.18440	−	22.1731i	0.333153	−	0.804303i
$761$		−	22.0000i		−	0.797499i	−0.917060	−	0.398750i	$-0.869444\pi$
$761$		−	22.0000i		−	0.797499i	0.917060	−	0.398750i	$-0.130556\pi$
$762$		0			0
$763$	−16.9706	+	16.9706i	−0.614376	+	0.614376i
$764$	−16.0000			−0.578860
$765$		0			0
$766$	24.0000			0.867155
$767$	16.9706	−	16.9706i	0.612772	−	0.612772i
$768$		0			0
$769$			14.0000i			0.504853i	0.967616	+	0.252426i	$0.0812286\pi$
$769$			14.0000i			0.504853i	−0.967616	+	0.252426i	$0.918771\pi$
$770$		0			0
$771$		0			0
$772$	0.765367	+	1.84776i	0.0275462	+	0.0665023i
$773$	18.3848	+	18.3848i	0.661254	+	0.661254i	0.955676	−	0.294421i	$-0.0951269\pi$
$773$	18.3848	+	18.3848i	0.661254	+	0.661254i	−0.294421	+	0.955676i	$0.595127\pi$
$774$	8.48528	+	8.48528i	0.304997	+	0.304997i
$775$	−1.53073	−	3.69552i	−0.0549856	−	0.132747i
$776$	−5.54328	+	2.29610i	−0.198992	+	0.0824252i
$777$		0			0
$778$		−	6.00000i		−	0.215110i
$779$	−22.1731	−	9.18440i	−0.794434	−	0.329065i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−6.36396	+	6.36396i	−0.227284	+	0.227284i
$785$	3.69552	+	1.53073i	0.131899	+	0.0546342i
$786$		0			0
$787$	12.2459	−	29.5641i	0.436518	−	1.05385i	−0.540625	−	0.841264i	$-0.681812\pi$
$787$	12.2459	−	29.5641i	0.436518	−	1.05385i	0.977143	−	0.212584i	$-0.0681879\pi$
$788$	16.6298	−	6.88830i	0.592413	−	0.245386i
$789$		0			0
$790$	−16.9706	−	16.9706i	−0.603786	−	0.603786i
$791$	−39.5980	−	39.5980i	−1.40794	−	1.40794i
$792$		0			0
$793$	−18.4776	+	7.65367i	−0.656158	+	0.271790i
$794$	−2.29610	+	5.54328i	−0.0814856	+	0.196724i
$795$		0			0
$796$	−18.4776	−	7.65367i	−0.654921	−	0.271277i
$797$	35.3553	−	35.3553i	1.25235	−	1.25235i	0.297687	−	0.954664i	$-0.403785\pi$
$797$	35.3553	−	35.3553i	1.25235	−	1.25235i	0.954664	−	0.297687i	$-0.0962151\pi$
$798$		0			0
$799$		0			0
$800$	5.00000			0.176777
$801$	−21.2132	+	21.2132i	−0.749532	+	0.749532i
$802$	12.9343	+	5.35757i	0.456726	+	0.189182i
$803$		0			0
$804$		0			0
$805$	−29.5641	+	12.2459i	−1.04200	+	0.431610i
$806$	−3.06147	−	7.39104i	−0.107836	−	0.260338i
$807$		0			0
$808$	−21.2132	−	21.2132i	−0.746278	−	0.746278i
$809$	9.94977	+	24.0209i	0.349815	+	0.844529i	0.996641	+	0.0818911i	$0.0260960\pi$
$809$	9.94977	+	24.0209i	0.349815	+	0.844529i	−0.646826	+	0.762638i	$0.723904\pi$
$810$	−16.6298	+	6.88830i	−0.584313	+	0.242030i
$811$	15.3073	−	36.9552i	0.537513	−	1.29767i	−0.388940	−	0.921263i	$-0.627159\pi$
$811$	15.3073	−	36.9552i	0.537513	−	1.29767i	0.926454	−	0.376409i	$-0.122841\pi$
$812$		−	24.0000i		−	0.842235i
$813$		0			0
$814$		0			0
$815$	48.0000			1.68137
$816$		0			0
$817$	−16.0000			−0.559769
$818$	−18.3848	+	18.3848i	−0.642809	+	0.642809i
$819$	22.1731	+	9.18440i	0.774791	+	0.320929i
$820$			12.0000i			0.419058i
$821$	6.88830	−	16.6298i	0.240403	−	0.580385i	−0.756920	−	0.653508i	$-0.773297\pi$
$821$	6.88830	−	16.6298i	0.240403	−	0.580385i	0.997323	+	0.0731230i	$0.0232966\pi$
$822$		0			0
$823$	−7.65367	−	18.4776i	−0.266790	−	0.644088i	0.732539	−	0.680726i	$-0.238335\pi$
$823$	−7.65367	−	18.4776i	−0.266790	−	0.644088i	−0.999329	+	0.0366373i	$0.988335\pi$
$824$	−16.9706	−	16.9706i	−0.591198	−	0.591198i
$825$		0			0
$826$	18.3688	+	44.3462i	0.639132	+	1.54300i
$827$	44.3462	−	18.3688i	1.54207	−	0.638746i	0.560209	−	0.828351i	$-0.310721\pi$
$827$	44.3462	−	18.3688i	1.54207	−	0.638746i	0.981860	+	0.189606i	$0.0607209\pi$
$828$	4.59220	−	11.0866i	0.159590	−	0.385284i
$829$		−	34.0000i		−	1.18087i	−0.807086	−	0.590434i	$-0.798956\pi$
$829$		−	34.0000i		−	1.18087i	0.807086	−	0.590434i	$-0.201044\pi$
$830$	7.39104	+	3.06147i	0.256547	+	0.106265i
$831$		0			0
$832$	14.0000			0.485363
$833$		0			0
$834$		0			0
$835$	5.65685	−	5.65685i	0.195764	−	0.195764i
$836$		0			0
$837$		0			0
$838$	3.06147	−	7.39104i	0.105757	−	0.255319i
$839$	18.4776	−	7.65367i	0.637917	−	0.264234i	−0.0401955	−	0.999192i	$-0.512798\pi$
$839$	18.4776	−	7.65367i	0.637917	−	0.264234i	0.678113	+	0.734958i	$0.262798\pi$
$840$		0			0
$841$	−4.94975	−	4.94975i	−0.170681	−	0.170681i
$842$	−15.5563	−	15.5563i	−0.536107	−	0.536107i
$843$		0			0
$844$	7.39104	−	3.06147i	0.254410	−	0.105380i
$845$	6.88830	−	16.6298i	0.236965	−	0.572084i
$846$		0			0
$847$	40.6507	+	16.8381i	1.39677	+	0.578563i
$848$	4.24264	−	4.24264i	0.145693	−	0.145693i
$849$		0			0
$850$		0			0
$851$	−8.00000			−0.274236
$852$		0			0
$853$	12.9343	+	5.35757i	0.442862	+	0.183440i	0.592961	−	0.805231i	$-0.297959\pi$
$853$	12.9343	+	5.35757i	0.442862	+	0.183440i	−0.150098	+	0.988671i	$0.547959\pi$
$854$		−	40.0000i		−	1.36877i
$855$	9.18440	−	22.1731i	0.314100	−	0.758304i
$856$	22.1731	−	9.18440i	0.757861	−	0.313916i
$857$	−3.82683	−	9.23880i	−0.130722	−	0.315591i	0.844943	−	0.534856i	$-0.179634\pi$
$857$	−3.82683	−	9.23880i	−0.130722	−	0.315591i	−0.975665	+	0.219265i	$0.929634\pi$
$858$		0			0
$859$	36.7696	+	36.7696i	1.25456	+	1.25456i	0.953653	+	0.300908i	$0.0972896\pi$
$859$	36.7696	+	36.7696i	1.25456	+	1.25456i	0.300908	+	0.953653i	$0.402710\pi$
$860$	3.06147	+	7.39104i	0.104395	+	0.252032i
$861$		0			0
$862$	−4.59220	+	11.0866i	−0.156411	+	0.377610i
$863$			16.0000i			0.544646i	0.962206	+	0.272323i	$0.0877920\pi$
$863$			16.0000i			0.544646i	−0.962206	+	0.272323i	$0.912208\pi$
$864$		0			0
$865$	31.1127	−	31.1127i	1.05786	−	1.05786i
$866$	2.00000			0.0679628
$867$		0			0
$868$	−16.0000			−0.543075
$869$		0			0
$870$		0			0
$871$			8.00000i			0.271070i
$872$	−6.88830	+	16.6298i	−0.233267	+	0.563157i
$873$	−5.54328	+	2.29610i	−0.187612	+	0.0777112i
$874$	−6.12293	−	14.7821i	−0.207111	−	0.500011i
$875$	−33.9411	−	33.9411i	−1.14742	−	1.14742i
$876$		0			0
$877$	2.29610	+	5.54328i	0.0775338	+	0.187183i	0.957894	−	0.287123i	$-0.0926989\pi$
$877$	2.29610	+	5.54328i	0.0775338	+	0.187183i	−0.880360	+	0.474306i	$0.842699\pi$
$878$	−18.4776	+	7.65367i	−0.623588	+	0.258299i
$879$		0			0
$880$		0			0
$881$	42.4985	+	17.6034i	1.43181	+	0.593075i	0.957798	−	0.287444i	$-0.0928054\pi$
$881$	42.4985	+	17.6034i	1.43181	+	0.593075i	0.474012	+	0.880518i	$0.342805\pi$
$882$	−19.0919	+	19.0919i	−0.642857	+	0.642857i
$883$	12.0000			0.403832			0.201916	−	0.979403i	$-0.435283\pi$
$883$	12.0000			0.403832			0.201916	+	0.979403i	$0.435283\pi$
$884$		0			0
$885$		0			0
$886$	−19.7990	+	19.7990i	−0.665160	+	0.665160i
$887$	11.0866	+	4.59220i	0.372250	+	0.154191i	0.560962	−	0.827841i	$-0.310431\pi$
$887$	11.0866	+	4.59220i	0.372250	+	0.154191i	−0.188712	+	0.982032i	$0.560431\pi$
$888$		0			0
$889$	−12.2459	+	29.5641i	−0.410713	+	0.991550i
$890$	18.4776	−	7.65367i	0.619370	−	0.256552i
$891$		0			0
$892$	16.9706	+	16.9706i	0.568216	+	0.568216i
$893$		0			0
$894$		0			0
$895$	22.1731	−	9.18440i	0.741165	−	0.307001i
$896$	4.59220	−	11.0866i	0.153415	−	0.370376i
$897$		0			0
$898$	31.4119	+	13.0112i	1.04823	+	0.434191i
$899$	−16.9706	+	16.9706i	−0.566000	+	0.566000i
$900$	3.00000			0.100000
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−38.8029	−	16.0727i	−1.29057	−	0.534570i
$905$		−	4.00000i		−	0.132964i
$906$		0			0
$907$	29.5641	−	12.2459i	0.981661	−	0.406617i	0.166621	−	0.986021i	$-0.446714\pi$
$907$	29.5641	−	12.2459i	0.981661	−	0.406617i	0.815041	+	0.579404i	$0.196714\pi$
$908$	−9.18440	−	22.1731i	−0.304795	−	0.735840i
$909$	−21.2132	−	21.2132i	−0.703598	−	0.703598i
$910$	−11.3137	−	11.3137i	−0.375046	−	0.375046i
$911$	−1.53073	−	3.69552i	−0.0507155	−	0.122438i	0.896491	−	0.443061i	$-0.146108\pi$
$911$	−1.53073	−	3.69552i	−0.0507155	−	0.122438i	−0.947207	+	0.320623i	$0.896108\pi$
$912$		0			0
$913$		0			0
$914$			6.00000i			0.198462i
$915$		0			0
$916$	4.24264	−	4.24264i	0.140181	−	0.140181i
$917$	−64.0000			−2.11347
$918$		0			0
$919$	24.0000			0.791687			0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000			0.791687			0.395843	+	0.918318i	$0.370452\pi$
$920$	−16.9706	+	16.9706i	−0.559503	+	0.559503i
$921$		0			0
$922$		−	2.00000i		−	0.0658665i
$923$	−3.06147	+	7.39104i	−0.100769	+	0.243279i
$924$		0			0
$925$	−0.765367	−	1.84776i	−0.0251651	−	0.0607539i
$926$	22.6274	+	22.6274i	0.743583	+	0.743583i
$927$	−16.9706	−	16.9706i	−0.557386	−	0.557386i
$928$	−11.4805	−	27.7164i	−0.376866	−	0.909835i
$929$	27.7164	−	11.4805i	0.909345	−	0.376663i	0.121539	−	0.992587i	$-0.461217\pi$
$929$	27.7164	−	11.4805i	0.909345	−	0.376663i	0.787806	+	0.615924i	$0.211217\pi$
$930$		0			0
$931$		−	36.0000i		−	1.17985i
$932$	−5.54328	−	2.29610i	−0.181576	−	0.0752113i
$933$		0			0
$934$	12.0000			0.392652
$935$		0			0
$936$	18.0000			0.588348
$937$	7.07107	−	7.07107i	0.231002	−	0.231002i	−0.582109	−	0.813111i	$-0.697772\pi$
$937$	7.07107	−	7.07107i	0.231002	−	0.231002i	0.813111	+	0.582109i	$0.197772\pi$
$938$	−14.7821	−	6.12293i	−0.482652	−	0.199921i
$939$		0			0
$940$		0			0
$941$	5.54328	−	2.29610i	0.180706	−	0.0748507i	−0.290496	−	0.956876i	$-0.593820\pi$
$941$	5.54328	−	2.29610i	0.180706	−	0.0748507i	0.471202	+	0.882025i	$0.343820\pi$
$942$		0			0
$943$	16.9706	+	16.9706i	0.552638	+	0.552638i
$944$	8.48528	+	8.48528i	0.276172	+	0.276172i
$945$		0			0
$946$		0			0
$947$	12.2459	−	29.5641i	0.397937	−	0.960706i	−0.590217	−	0.807244i	$-0.700958\pi$
$947$	12.2459	−	29.5641i	0.397937	−	0.960706i	0.988155	−	0.153461i	$-0.0490420\pi$
$948$		0			0
$949$	−11.0866	−	4.59220i	−0.359885	−	0.149069i
$950$	2.82843	−	2.82843i	0.0917663	−	0.0917663i
$951$		0			0
$952$		0			0
$953$	−22.0000			−0.712650			−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000			−0.712650			−0.356325	+	0.934362i	$0.615970\pi$
$954$	12.7279	−	12.7279i	0.412082	−	0.412082i
$955$	29.5641	+	12.2459i	0.956673	+	0.396267i
$956$		−	16.0000i		−	0.517477i
$957$		0			0
$958$	−33.2597	+	13.7766i	−1.07457	+	0.445102i
$959$	9.18440	+	22.1731i	0.296580	+	0.716007i
$960$		0			0
$961$	−10.6066	−	10.6066i	−0.342148	−	0.342148i
$962$	−1.53073	−	3.69552i	−0.0493528	−	0.119148i
$963$	22.1731	−	9.18440i	0.714518	−	0.295963i
$964$	−6.88830	+	16.6298i	−0.221857	+	0.535611i
$965$		−	4.00000i		−	0.128765i
$966$		0			0
$967$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$967$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$968$	33.0000			1.06066
$969$		0			0
$970$	4.00000			0.128432
$971$	−8.48528	+	8.48528i	−0.272306	+	0.272306i	−0.830028	−	0.557722i	$-0.811675\pi$
$971$	−8.48528	+	8.48528i	−0.272306	+	0.272306i	0.557722	+	0.830028i	$0.311675\pi$
$972$		0			0
$973$			32.0000i			1.02587i
$974$	7.65367	−	18.4776i	0.245239	−	0.592060i
$975$		0			0
$976$	−3.82683	−	9.23880i	−0.122494	−	0.295727i
$977$	−12.7279	−	12.7279i	−0.407202	−	0.407202i	0.473560	−	0.880762i	$-0.342969\pi$
$977$	−12.7279	−	12.7279i	−0.407202	−	0.407202i	−0.880762	+	0.473560i	$0.842969\pi$
$978$		0			0
$979$		0			0
$980$	−16.6298	+	6.88830i	−0.531220	+	0.220039i
$981$	−6.88830	+	16.6298i	−0.219927	+	0.530950i
$982$		−	20.0000i		−	0.638226i
$983$	−11.0866	−	4.59220i	−0.353606	−	0.146468i	0.198808	−	0.980039i	$-0.436293\pi$
$983$	−11.0866	−	4.59220i	−0.353606	−	0.146468i	−0.552414	+	0.833570i	$0.686293\pi$
$984$		0			0
$985$	−36.0000			−1.14706
$986$		0			0
$987$		0			0
$988$	−5.65685	+	5.65685i	−0.179969	+	0.179969i
$989$	14.7821	+	6.12293i	0.470043	+	0.194698i
$990$		0			0
$991$	4.59220	−	11.0866i	0.145876	−	0.352176i	−0.834005	−	0.551756i	$-0.813958\pi$
$991$	4.59220	−	11.0866i	0.145876	−	0.352176i	0.979881	+	0.199580i	$0.0639579\pi$
$992$	−18.4776	+	7.65367i	−0.586664	+	0.243004i
$993$		0			0
$994$	−11.3137	−	11.3137i	−0.358849	−	0.358849i
$995$	28.2843	+	28.2843i	0.896672	+	0.896672i
$996$		0			0
$997$	−42.4985	+	17.6034i	−1.34594	+	0.557506i	−0.935159	−	0.354228i	$-0.884744\pi$
$997$	−42.4985	+	17.6034i	−1.34594	+	0.557506i	−0.410781	+	0.911734i	$0.634744\pi$
$998$	15.3073	−	36.9552i	0.484545	−	1.16980i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.d.d.179.2		8
17.2	even	8	inner	289.2.d.d.155.2		8
17.3	odd	16		289.2.c.a.251.2		4
17.4	even	4	inner	289.2.d.d.110.1		8
17.5	odd	16		289.2.c.a.38.1		4
17.6	odd	16		17.2.a.a.1.1	✓	1
17.7	odd	16		289.2.b.a.288.2		2
17.8	even	8	inner	289.2.d.d.134.2		8
17.9	even	8	inner	289.2.d.d.134.1		8
17.10	odd	16		289.2.b.a.288.1		2
17.11	odd	16		289.2.a.a.1.1		1
17.12	odd	16		289.2.c.a.38.2		4
17.13	even	4	inner	289.2.d.d.110.2		8
17.14	odd	16		289.2.c.a.251.1		4
17.15	even	8	inner	289.2.d.d.155.1		8
17.16	even	2	inner	289.2.d.d.179.1		8
51.11	even	16		2601.2.a.g.1.1		1
51.23	even	16		153.2.a.c.1.1		1
68.11	even	16		4624.2.a.d.1.1		1
68.23	even	16		272.2.a.b.1.1		1
85.23	even	16		425.2.b.b.324.2		2
85.57	even	16		425.2.b.b.324.1		2
85.74	odd	16		425.2.a.d.1.1		1
85.79	odd	16		7225.2.a.g.1.1		1
119.6	even	16		833.2.a.a.1.1		1
119.23	odd	48		833.2.e.b.18.1		2
119.40	even	48		833.2.e.a.18.1		2
119.74	odd	48		833.2.e.b.324.1		2
119.108	even	48		833.2.e.a.324.1		2
136.91	even	16		1088.2.a.h.1.1		1
136.125	odd	16		1088.2.a.i.1.1		1
187.142	even	16		2057.2.a.e.1.1		1
204.23	odd	16		2448.2.a.o.1.1		1
221.142	odd	16		2873.2.a.c.1.1		1
255.74	even	16		3825.2.a.d.1.1		1
323.227	even	16		6137.2.a.b.1.1		1
340.159	even	16		6800.2.a.n.1.1		1
357.125	odd	16		7497.2.a.l.1.1		1
391.91	even	16		8993.2.a.a.1.1		1
408.125	even	16		9792.2.a.n.1.1		1
408.227	odd	16		9792.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.a.a.1.1	✓	1	17.6	odd	16
153.2.a.c.1.1		1	51.23	even	16
272.2.a.b.1.1		1	68.23	even	16
289.2.a.a.1.1		1	17.11	odd	16
289.2.b.a.288.1		2	17.10	odd	16
289.2.b.a.288.2		2	17.7	odd	16
289.2.c.a.38.1		4	17.5	odd	16
289.2.c.a.38.2		4	17.12	odd	16
289.2.c.a.251.1		4	17.14	odd	16
289.2.c.a.251.2		4	17.3	odd	16
289.2.d.d.110.1		8	17.4	even	4	inner
289.2.d.d.110.2		8	17.13	even	4	inner
289.2.d.d.134.1		8	17.9	even	8	inner
289.2.d.d.134.2		8	17.8	even	8	inner
289.2.d.d.155.1		8	17.15	even	8	inner
289.2.d.d.155.2		8	17.2	even	8	inner
289.2.d.d.179.1		8	17.16	even	2	inner
289.2.d.d.179.2		8	1.1	even	1	trivial
425.2.a.d.1.1		1	85.74	odd	16
425.2.b.b.324.1		2	85.57	even	16
425.2.b.b.324.2		2	85.23	even	16
833.2.a.a.1.1		1	119.6	even	16
833.2.e.a.18.1		2	119.40	even	48
833.2.e.a.324.1		2	119.108	even	48
833.2.e.b.18.1		2	119.23	odd	48
833.2.e.b.324.1		2	119.74	odd	48
1088.2.a.h.1.1		1	136.91	even	16
1088.2.a.i.1.1		1	136.125	odd	16
2057.2.a.e.1.1		1	187.142	even	16
2448.2.a.o.1.1		1	204.23	odd	16
2601.2.a.g.1.1		1	51.11	even	16
2873.2.a.c.1.1		1	221.142	odd	16
3825.2.a.d.1.1		1	255.74	even	16
4624.2.a.d.1.1		1	68.11	even	16
6137.2.a.b.1.1		1	323.227	even	16
6800.2.a.n.1.1		1	340.159	even	16
7225.2.a.g.1.1		1	85.79	odd	16
7497.2.a.l.1.1		1	357.125	odd	16
8993.2.a.a.1.1		1	391.91	even	16
9792.2.a.i.1.1		1	408.227	odd	16
9792.2.a.n.1.1		1	408.125	even	16

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.d (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.765367 - 1.84776i) q^{5} +(-1.53073 - 3.69552i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(-2.12132 - 2.12132i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.765367 - 1.84776i) q^{5} +(-1.53073 - 3.69552i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(-2.12132 - 2.12132i) q^{9} +(0.765367 + 1.84776i) q^{10} -2.00000i q^{13} +(3.69552 + 1.53073i) q^{14} +1.00000 q^{16} +3.00000 q^{18} +(-2.82843 + 2.82843i) q^{19} +(1.84776 + 0.765367i) q^{20} +(3.69552 - 1.53073i) q^{23} +(0.707107 + 0.707107i) q^{25} +(1.41421 + 1.41421i) q^{26} +(3.69552 - 1.53073i) q^{28} +(2.29610 - 5.54328i) q^{29} +(-3.69552 - 1.53073i) q^{31} +(3.53553 - 3.53553i) q^{32} -8.00000 q^{35} +(2.12132 - 2.12132i) q^{36} +(-1.84776 - 0.765367i) q^{37} -4.00000i q^{38} +(-5.54328 + 2.29610i) q^{40} +(2.29610 + 5.54328i) q^{41} +(2.82843 + 2.82843i) q^{43} +(-5.54328 + 2.29610i) q^{45} +(-1.53073 + 3.69552i) q^{46} +(-6.36396 + 6.36396i) q^{49} -1.00000 q^{50} +2.00000 q^{52} +(4.24264 - 4.24264i) q^{53} +(-4.59220 + 11.0866i) q^{56} +(2.29610 + 5.54328i) q^{58} +(8.48528 + 8.48528i) q^{59} +(-3.82683 - 9.23880i) q^{61} +(3.69552 - 1.53073i) q^{62} +(-4.59220 + 11.0866i) q^{63} +7.00000i q^{64} +(-3.69552 - 1.53073i) q^{65} -4.00000 q^{67} +(5.65685 - 5.65685i) q^{70} +(-3.69552 - 1.53073i) q^{71} +9.00000i q^{72} +(2.29610 - 5.54328i) q^{73} +(1.84776 - 0.765367i) q^{74} +(-2.82843 - 2.82843i) q^{76} +(-11.0866 + 4.59220i) q^{79} +(0.765367 - 1.84776i) q^{80} +9.00000i q^{81} +(-5.54328 - 2.29610i) q^{82} +(2.82843 - 2.82843i) q^{83} -4.00000 q^{86} -10.0000i q^{89} +(2.29610 - 5.54328i) q^{90} +(-7.39104 + 3.06147i) q^{91} +(1.53073 + 3.69552i) q^{92} +(3.06147 + 7.39104i) q^{95} +(0.765367 - 1.84776i) q^{97} -9.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 8 q^{16} + 24 q^{18} - 64 q^{35} - 8 q^{50} + 16 q^{52} - 32 q^{67} - 32 q^{86}+O(q^{100}) \) 8 * q + 8 * q^16 + 24 * q^18 - 64 * q^35 - 8 * q^50 + 16 * q^52 - 32 * q^67 - 32 * q^86

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