LMFDB - Embedded newform 289.2.d.d.134.1

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			134.1
Root			$-0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.134
Dual form			289.2.d.d.110.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.84776 + 0.765367i) q^{5} +(3.69552 + 1.53073i) q^{7} +(2.12132 - 2.12132i) q^{8} +(2.12132 - 2.12132i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.84776 + 0.765367i) q^{5} +(3.69552 + 1.53073i) q^{7} +(2.12132 - 2.12132i) q^{8} +(2.12132 - 2.12132i) q^{9} +(-1.84776 - 0.765367i) q^{10} +2.00000i q^{13} +(1.53073 + 3.69552i) q^{14} +1.00000 q^{16} +3.00000 q^{18} +(2.82843 + 2.82843i) q^{19} +(0.765367 + 1.84776i) q^{20} +(1.53073 - 3.69552i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(-1.41421 + 1.41421i) q^{26} +(1.53073 - 3.69552i) q^{28} +(-5.54328 + 2.29610i) q^{29} +(-1.53073 - 3.69552i) q^{31} +(-3.53553 - 3.53553i) q^{32} -8.00000 q^{35} +(-2.12132 - 2.12132i) q^{36} +(-0.765367 - 1.84776i) q^{37} +4.00000i q^{38} +(-2.29610 + 5.54328i) q^{40} +(-5.54328 - 2.29610i) q^{41} +(-2.82843 + 2.82843i) q^{43} +(-2.29610 + 5.54328i) q^{45} +(3.69552 - 1.53073i) q^{46} +(6.36396 + 6.36396i) q^{49} -1.00000 q^{50} +2.00000 q^{52} +(-4.24264 - 4.24264i) q^{53} +(11.0866 - 4.59220i) q^{56} +(-5.54328 - 2.29610i) q^{58} +(-8.48528 + 8.48528i) q^{59} +(9.23880 + 3.82683i) q^{61} +(1.53073 - 3.69552i) q^{62} +(11.0866 - 4.59220i) q^{63} -7.00000i q^{64} +(-1.53073 - 3.69552i) q^{65} -4.00000 q^{67} +(-5.65685 - 5.65685i) q^{70} +(-1.53073 - 3.69552i) q^{71} -9.00000i q^{72} +(-5.54328 + 2.29610i) q^{73} +(0.765367 - 1.84776i) q^{74} +(2.82843 - 2.82843i) q^{76} +(-4.59220 + 11.0866i) q^{79} +(-1.84776 + 0.765367i) q^{80} -9.00000i q^{81} +(-2.29610 - 5.54328i) q^{82} +(-2.82843 - 2.82843i) q^{83} -4.00000 q^{86} +10.0000i q^{89} +(-5.54328 + 2.29610i) q^{90} +(-3.06147 + 7.39104i) q^{91} +(-3.69552 - 1.53073i) q^{92} +(-7.39104 - 3.06147i) q^{95} +(-1.84776 + 0.765367i) q^{97} +9.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

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

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	$-0.134973\pi$
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i	−0.411438	+	0.911438i	$0.634973\pi$
$3$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$3$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−1.84776	+	0.765367i	−0.826343	+	0.342282i	−0.755454	−	0.655202i	$-0.772584\pi$
$5$	−1.84776	+	0.765367i	−0.826343	+	0.342282i	−0.0708890	+	0.997484i	$0.522584\pi$
$6$		0			0
$7$	3.69552	+	1.53073i	1.39677	+	0.578563i	0.948912	−	0.315540i	$-0.102186\pi$
$7$	3.69552	+	1.53073i	1.39677	+	0.578563i	0.447862	+	0.894103i	$0.352186\pi$
$8$	2.12132	−	2.12132i	0.750000	−	0.750000i
$9$	2.12132	−	2.12132i	0.707107	−	0.707107i
$10$	−1.84776	−	0.765367i	−0.584313	−	0.242030i
$11$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$11$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$12$		0			0
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	1.53073	+	3.69552i	0.409106	+	0.987669i
$15$		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	$-0.0982682\pi$
$19$	2.82843	+	2.82843i	0.648886	+	0.648886i	−0.303838	+	0.952724i	$0.598268\pi$
$20$	0.765367	+	1.84776i	0.171141	+	0.413171i
$21$		0			0
$22$		0			0
$23$	1.53073	−	3.69552i	0.319180	−	0.770569i	−0.680118	−	0.733103i	$-0.738071\pi$
$23$	1.53073	−	3.69552i	0.319180	−	0.770569i	0.999298	−	0.0374660i	$-0.0119286\pi$
$24$		0			0
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$	−1.41421	+	1.41421i	−0.277350	+	0.277350i
$27$		0			0
$28$	1.53073	−	3.69552i	0.289281	−	0.698387i
$29$	−5.54328	+	2.29610i	−1.02936	+	0.426375i	−0.832482	−	0.554053i	$-0.813081\pi$
$29$	−5.54328	+	2.29610i	−1.02936	+	0.426375i	−0.196879	+	0.980428i	$0.563081\pi$
$30$		0			0
$31$	−1.53073	−	3.69552i	−0.274928	−	0.663735i	0.724753	−	0.689009i	$-0.241954\pi$
$31$	−1.53073	−	3.69552i	−0.274928	−	0.663735i	−0.999681	+	0.0252745i	$0.991954\pi$
$32$	−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
$37$	−0.765367	−	1.84776i	−0.125826	−	0.303770i	0.848396	−	0.529361i	$-0.177568\pi$
$37$	−0.765367	−	1.84776i	−0.125826	−	0.303770i	−0.974222	+	0.225592i	$0.927568\pi$
$38$			4.00000i			0.648886i
$39$		0			0
$40$	−2.29610	+	5.54328i	−0.363045	+	0.876469i
$41$	−5.54328	−	2.29610i	−0.865714	−	0.358591i	−0.0947747	−	0.995499i	$-0.530213\pi$
$41$	−5.54328	−	2.29610i	−0.865714	−	0.358591i	−0.770940	+	0.636908i	$0.780213\pi$
$42$		0			0
$43$	−2.82843	+	2.82843i	−0.431331	+	0.431331i	−0.889081	−	0.457750i	$-0.848656\pi$
$43$	−2.82843	+	2.82843i	−0.431331	+	0.431331i	0.457750	+	0.889081i	$0.348656\pi$
$44$		0			0
$45$	−2.29610	+	5.54328i	−0.342282	+	0.826343i
$46$	3.69552	−	1.53073i	0.544874	−	0.225694i
$47$		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	$-0.385198\pi$
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	−0.935664	+	0.352892i	$0.885198\pi$
$54$		0			0
$55$		0			0
$56$	11.0866	−	4.59220i	1.48150	−	0.613659i
$57$		0			0
$58$	−5.54328	−	2.29610i	−0.727868	−	0.301493i
$59$	−8.48528	+	8.48528i	−1.10469	+	1.10469i	−0.110853	+	0.993837i	$0.535358\pi$
$59$	−8.48528	+	8.48528i	−1.10469	+	1.10469i	−0.993837	+	0.110853i	$0.964642\pi$
$60$		0			0
$61$	9.23880	+	3.82683i	1.18291	+	0.489976i	0.885439	−	0.464756i	$-0.153858\pi$
$61$	9.23880	+	3.82683i	1.18291	+	0.489976i	0.297468	+	0.954732i	$0.403858\pi$
$62$	1.53073	−	3.69552i	0.194403	−	0.469331i
$63$	11.0866	−	4.59220i	1.39677	−	0.578563i
$64$		−	7.00000i		−	0.875000i
$65$	−1.53073	−	3.69552i	−0.189864	−	0.458373i
$66$		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
$71$	−1.53073	−	3.69552i	−0.181665	−	0.438577i	0.806645	−	0.591036i	$-0.201281\pi$
$71$	−1.53073	−	3.69552i	−0.181665	−	0.438577i	−0.988310	+	0.152459i	$0.951281\pi$
$72$		−	9.00000i		−	1.06066i
$73$	−5.54328	+	2.29610i	−0.648792	+	0.268738i	−0.682713	−	0.730686i	$-0.739200\pi$
$73$	−5.54328	+	2.29610i	−0.648792	+	0.268738i	0.0339219	+	0.999424i	$0.489200\pi$
$74$	0.765367	−	1.84776i	0.0889721	−	0.214798i
$75$		0			0
$76$	2.82843	−	2.82843i	0.324443	−	0.324443i
$77$		0			0
$78$		0			0
$79$	−4.59220	+	11.0866i	−0.516663	+	1.24733i	0.423279	+	0.906000i	$0.360879\pi$
$79$	−4.59220	+	11.0866i	−0.516663	+	1.24733i	−0.939942	+	0.341335i	$0.889121\pi$
$80$	−1.84776	+	0.765367i	−0.206586	+	0.0855706i
$81$		−	9.00000i		−	1.00000i
$82$	−2.29610	−	5.54328i	−0.253562	−	0.612153i
$83$	−2.82843	−	2.82843i	−0.310460	−	0.310460i	0.534628	−	0.845088i	$-0.320452\pi$
$83$	−2.82843	−	2.82843i	−0.310460	−	0.310460i	−0.845088	+	0.534628i	$0.820452\pi$
$84$		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	$0.177808\pi$
$89$			10.0000i			1.06000i	−0.847998	+	0.529999i	$0.822192\pi$
$90$	−5.54328	+	2.29610i	−0.584313	+	0.242030i
$91$	−3.06147	+	7.39104i	−0.320929	+	0.774791i
$92$	−3.69552	−	1.53073i	−0.385284	−	0.159590i
$93$		0			0
$94$		0			0
$95$	−7.39104	−	3.06147i	−0.758304	−	0.314100i
$96$		0			0
$97$	−1.84776	+	0.765367i	−0.187612	+	0.0777112i	−0.474511	−	0.880249i	$-0.657375\pi$
$97$	−1.84776	+	0.765367i	−0.187612	+	0.0777112i	0.286900	+	0.957961i	$0.407375\pi$
$98$			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
$107$	7.39104	−	3.06147i	0.714518	−	0.295963i	0.00434556	−	0.999991i	$-0.498617\pi$
$107$	7.39104	−	3.06147i	0.714518	−	0.295963i	0.710173	+	0.704027i	$0.248617\pi$
$108$		0			0
$109$	5.54328	+	2.29610i	0.530950	+	0.219927i	0.632019	−	0.774953i	$-0.282226\pi$
$109$	5.54328	+	2.29610i	0.530950	+	0.219927i	−0.101069	+	0.994879i	$0.532226\pi$
$110$		0			0
$111$		0			0
$112$	3.69552	+	1.53073i	0.349194	+	0.144641i
$113$	5.35757	−	12.9343i	0.503998	−	1.21676i	−0.443291	−	0.896378i	$-0.646189\pi$
$113$	5.35757	−	12.9343i	0.503998	−	1.21676i	0.947289	−	0.320380i	$-0.103811\pi$
$114$		0			0
$115$			8.00000i			0.746004i
$116$	2.29610	+	5.54328i	0.213188	+	0.514680i
$117$	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
$122$	3.82683	+	9.23880i	0.346465	+	0.836441i
$123$		0			0
$124$	−3.69552	+	1.53073i	−0.331867	+	0.137464i
$125$	4.59220	−	11.0866i	0.410739	−	0.991612i
$126$	11.0866	+	4.59220i	0.987669	+	0.409106i
$127$	5.65685	−	5.65685i	0.501965	−	0.501965i	−0.410083	−	0.912048i	$-0.634500\pi$
$127$	5.65685	−	5.65685i	0.501965	−	0.501965i	0.912048	+	0.410083i	$0.134500\pi$
$128$	−2.12132	+	2.12132i	−0.187500	+	0.187500i
$129$		0			0
$130$	1.53073	−	3.69552i	0.134254	−	0.324118i
$131$	−14.7821	+	6.12293i	−1.29152	+	0.534963i	−0.919437	−	0.393238i	$-0.871355\pi$
$131$	−14.7821	+	6.12293i	−1.29152	+	0.534963i	−0.372079	+	0.928201i	$0.621355\pi$
$132$		0			0
$133$	6.12293	+	14.7821i	0.530926	+	1.28177i
$134$	−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
$139$	−3.06147	−	7.39104i	−0.259670	−	0.626900i	0.739246	−	0.673435i	$-0.235182\pi$
$139$	−3.06147	−	7.39104i	−0.259670	−	0.626900i	−0.998917	+	0.0465356i	$0.985182\pi$
$140$			8.00000i			0.676123i
$141$		0			0
$142$	1.53073	−	3.69552i	0.128456	−	0.310121i
$143$		0			0
$144$	2.12132	−	2.12132i	0.176777	−	0.176777i
$145$	8.48528	−	8.48528i	0.704664	−	0.704664i
$146$	−5.54328	−	2.29610i	−0.458765	−	0.190027i
$147$		0			0
$148$	−1.84776	+	0.765367i	−0.151885	+	0.0629128i
$149$			10.0000i			0.819232i	0.912258	+	0.409616i	$0.134337\pi$
$149$			10.0000i			0.819232i	−0.912258	+	0.409616i	$0.865663\pi$
$150$		0			0
$151$	−11.3137	−	11.3137i	−0.920697	−	0.920697i	0.0763821	−	0.997079i	$-0.475663\pi$
$151$	−11.3137	−	11.3137i	−0.920697	−	0.920697i	−0.997079	+	0.0763821i	$0.975663\pi$
$152$	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	$-0.974569\pi$
$157$		−	2.00000i		−	0.159617i	0.996810	−	0.0798087i	$-0.0254309\pi$
$158$	−11.0866	+	4.59220i	−0.881999	+	0.365336i
$159$		0			0
$160$	9.23880	+	3.82683i	0.730391	+	0.302538i
$161$	11.3137	−	11.3137i	0.891645	−	0.891645i
$162$	6.36396	−	6.36396i	0.500000	−	0.500000i
$163$	−22.1731	−	9.18440i	−1.73673	−	0.719378i	−0.999020	−	0.0442623i	$-0.985906\pi$
$163$	−22.1731	−	9.18440i	−1.73673	−	0.719378i	−0.737712	−	0.675116i	$-0.764094\pi$
$164$	−2.29610	+	5.54328i	−0.179295	+	0.432857i
$165$		0			0
$166$		−	4.00000i		−	0.310460i
$167$	1.53073	+	3.69552i	0.118452	+	0.285968i	0.971974	−	0.235089i	$-0.0755381\pi$
$167$	1.53073	+	3.69552i	0.118452	+	0.285968i	−0.853522	+	0.521057i	$0.825538\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$		0			0
$171$	12.0000			0.917663
$172$	2.82843	+	2.82843i	0.215666	+	0.215666i
$173$	8.41904	+	20.3253i	0.640087	+	1.54531i	0.826561	+	0.562848i	$0.190294\pi$
$173$	8.41904	+	20.3253i	0.640087	+	1.54531i	−0.186473	+	0.982460i	$0.559706\pi$
$174$		0			0
$175$	−3.69552	+	1.53073i	−0.279355	+	0.115713i
$176$		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	$-0.898028\pi$
$179$	−8.48528	+	8.48528i	−0.634220	+	0.634220i	0.314904	+	0.949124i	$0.398028\pi$
$180$	5.54328	+	2.29610i	0.413171	+	0.171141i
$181$	0.765367	−	1.84776i	0.0568893	−	0.137343i	−0.892879	−	0.450296i	$-0.851318\pi$
$181$	0.765367	−	1.84776i	0.0568893	−	0.137343i	0.949768	+	0.312953i	$0.101318\pi$
$182$	−7.39104	+	3.06147i	−0.547860	+	0.226931i
$183$		0			0
$184$	−4.59220	−	11.0866i	−0.338542	−	0.817312i
$185$	2.82843	+	2.82843i	0.207950	+	0.207950i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−3.06147	−	7.39104i	−0.222102	−	0.536202i
$191$		−	16.0000i		−	1.15772i	−0.815427	−	0.578860i	$-0.803498\pi$
$191$		−	16.0000i		−	1.15772i	0.815427	−	0.578860i	$-0.196502\pi$
$192$		0			0
$193$	0.765367	−	1.84776i	0.0550923	−	0.133005i	−0.893937	−	0.448193i	$-0.852068\pi$
$193$	0.765367	−	1.84776i	0.0550923	−	0.133005i	0.949029	+	0.315188i	$0.102068\pi$
$194$	−1.84776	−	0.765367i	−0.132661	−	0.0549501i
$195$		0			0
$196$	6.36396	−	6.36396i	0.454569	−	0.454569i
$197$	16.6298	+	6.88830i	1.18483	+	0.490771i	0.886067	−	0.463557i	$-0.153427\pi$
$197$	16.6298	+	6.88830i	1.18483	+	0.490771i	0.298759	+	0.954328i	$0.403427\pi$
$198$		0			0
$199$	18.4776	−	7.65367i	1.30984	−	0.542554i	0.385004	−	0.922915i	$-0.374200\pi$
$199$	18.4776	−	7.65367i	1.30984	−	0.542554i	0.924838	+	0.380361i	$0.124200\pi$
$200$			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
$207$	−4.59220	−	11.0866i	−0.319180	−	0.770569i
$208$			2.00000i			0.138675i
$209$		0			0
$210$		0			0
$211$	7.39104	+	3.06147i	0.508820	+	0.210760i	0.622298	−	0.782780i	$-0.286199\pi$
$211$	7.39104	+	3.06147i	0.508820	+	0.210760i	−0.113478	+	0.993540i	$0.536199\pi$
$212$	−4.24264	+	4.24264i	−0.291386	+	0.291386i
$213$		0			0
$214$	7.39104	+	3.06147i	0.505241	+	0.209278i
$215$	3.06147	−	7.39104i	0.208790	−	0.504064i
$216$		0			0
$217$		−	16.0000i		−	1.08615i
$218$	2.29610	+	5.54328i	0.155512	+	0.375438i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−16.9706	−	16.9706i	−1.13643	−	1.13643i	−0.989085	−	0.147348i	$-0.952926\pi$
$223$	−16.9706	−	16.9706i	−1.13643	−	1.13643i	−0.147348	−	0.989085i	$-0.547074\pi$
$224$	−7.65367	−	18.4776i	−0.511382	−	1.23459i
$225$			3.00000i			0.200000i
$226$	12.9343	−	5.35757i	0.860378	−	0.356380i
$227$	−9.18440	+	22.1731i	−0.609590	+	1.47168i	0.253857	+	0.967242i	$0.418301\pi$
$227$	−9.18440	+	22.1731i	−0.609590	+	1.47168i	−0.863447	+	0.504439i	$0.831699\pi$
$228$		0			0
$229$	4.24264	−	4.24264i	0.280362	−	0.280362i	−0.552892	−	0.833253i	$-0.686476\pi$
$229$	4.24264	−	4.24264i	0.280362	−	0.280362i	0.833253	+	0.552892i	$0.186476\pi$
$230$	−5.65685	+	5.65685i	−0.373002	+	0.373002i
$231$		0			0
$232$	−6.88830	+	16.6298i	−0.452239	+	1.09180i
$233$	5.54328	−	2.29610i	0.363152	−	0.150423i	−0.193644	−	0.981072i	$-0.562031\pi$
$233$	5.54328	−	2.29610i	0.363152	−	0.150423i	0.556796	+	0.830649i	$0.312031\pi$
$234$			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
$241$	6.88830	+	16.6298i	0.443715	+	1.07122i	0.974635	+	0.223800i	$0.0718463\pi$
$241$	6.88830	+	16.6298i	0.443715	+	1.07122i	−0.530921	+	0.847422i	$0.678154\pi$
$242$			11.0000i			0.707107i
$243$		0			0
$244$	3.82683	−	9.23880i	0.244988	−	0.591453i
$245$	−16.6298	−	6.88830i	−1.06244	−	0.440077i
$246$		0			0
$247$	−5.65685	+	5.65685i	−0.359937	+	0.359937i
$248$	−11.0866	−	4.59220i	−0.703997	−	0.291605i
$249$		0			0
$250$	11.0866	−	4.59220i	0.701175	−	0.290436i
$251$		−	12.0000i		−	0.757433i	−0.925513	−	0.378717i	$-0.876365\pi$
$251$		−	12.0000i		−	0.757433i	0.925513	−	0.378717i	$-0.123635\pi$
$252$	−4.59220	−	11.0866i	−0.289281	−	0.698387i
$253$		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	$-0.439739\pi$
$257$	−12.7279	−	12.7279i	−0.793946	−	0.793946i	−0.982133	+	0.188187i	$0.939739\pi$
$258$		0			0
$259$		−	8.00000i		−	0.497096i
$260$	−3.69552	+	1.53073i	−0.229186	+	0.0949321i
$261$	−6.88830	+	16.6298i	−0.426375	+	1.02936i
$262$	−14.7821	−	6.12293i	−0.913239	−	0.378276i
$263$	−11.3137	+	11.3137i	−0.697633	+	0.697633i	−0.963899	−	0.266266i	$-0.914210\pi$
$263$	−11.3137	+	11.3137i	−0.697633	+	0.697633i	0.266266	+	0.963899i	$0.414210\pi$
$264$		0			0
$265$	11.0866	+	4.59220i	0.681042	+	0.282097i
$266$	−6.12293	+	14.7821i	−0.375421	+	0.906347i
$267$		0			0
$268$			4.00000i			0.244339i
$269$	−8.41904	−	20.3253i	−0.513318	−	1.23926i	−0.941942	−	0.335776i	$-0.891002\pi$
$269$	−8.41904	−	20.3253i	−0.513318	−	1.23926i	0.428624	−	0.903483i	$-0.358998\pi$
$270$		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
$277$	12.9343	−	5.35757i	0.777148	−	0.321905i	0.0413838	−	0.999143i	$-0.486823\pi$
$277$	12.9343	−	5.35757i	0.777148	−	0.321905i	0.735764	+	0.677238i	$0.236823\pi$
$278$	3.06147	−	7.39104i	0.183615	−	0.443285i
$279$	−11.0866	−	4.59220i	−0.663735	−	0.274928i
$280$	−16.9706	+	16.9706i	−1.01419	+	1.01419i
$281$	4.24264	−	4.24264i	0.253095	−	0.253095i	−0.569143	−	0.822238i	$-0.692725\pi$
$281$	4.24264	−	4.24264i	0.253095	−	0.253095i	0.822238	+	0.569143i	$0.192725\pi$
$282$		0			0
$283$	6.12293	−	14.7821i	0.363971	−	0.878703i	−0.630741	−	0.775994i	$-0.717249\pi$
$283$	6.12293	−	14.7821i	0.363971	−	0.878703i	0.994711	−	0.102709i	$-0.0327512\pi$
$284$	−3.69552	+	1.53073i	−0.219289	+	0.0908323i
$285$		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
$292$	2.29610	+	5.54328i	0.134369	+	0.324396i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$		0			0
$295$	9.18440	−	22.1731i	0.534737	−	1.29097i
$296$	−5.54328	−	2.29610i	−0.322196	−	0.133458i
$297$		0			0
$298$	−7.07107	+	7.07107i	−0.409616	+	0.409616i
$299$	7.39104	+	3.06147i	0.427435	+	0.177049i
$300$		0			0
$301$	−14.7821	+	6.12293i	−0.852024	+	0.352920i
$302$		−	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
$311$	25.8686	−	10.7151i	1.46688	−	0.607600i	0.500731	−	0.865603i	$-0.333065\pi$
$311$	25.8686	−	10.7151i	1.46688	−	0.607600i	0.966144	+	0.258003i	$0.0830645\pi$
$312$		0			0
$313$	−20.3253	−	8.41904i	−1.14886	−	0.475872i	−0.274707	−	0.961528i	$-0.588581\pi$
$313$	−20.3253	−	8.41904i	−1.14886	−	0.475872i	−0.874150	+	0.485656i	$0.838581\pi$
$314$	1.41421	−	1.41421i	0.0798087	−	0.0798087i
$315$	−16.9706	+	16.9706i	−0.956183	+	0.956183i
$316$	11.0866	+	4.59220i	0.623667	+	0.258331i
$317$	3.82683	−	9.23880i	0.214936	−	0.518902i	−0.779233	−	0.626735i	$-0.784391\pi$
$317$	3.82683	−	9.23880i	0.214936	−	0.518902i	0.994169	+	0.107832i	$0.0343910\pi$
$318$		0			0
$319$		0			0
$320$	5.35757	+	12.9343i	0.299497	+	0.723050i
$321$		0			0
$322$	16.0000			0.891645
$323$		0			0
$324$	−9.00000			−0.500000
$325$	−1.41421	−	1.41421i	−0.0784465	−	0.0784465i
$326$	−9.18440	−	22.1731i	−0.508677	−	1.22805i
$327$		0			0
$328$	−16.6298	+	6.88830i	−0.918229	+	0.380343i
$329$		0			0
$330$		0			0
$331$	2.82843	−	2.82843i	0.155464	−	0.155464i	−0.625089	−	0.780553i	$-0.714937\pi$
$331$	2.82843	−	2.82843i	0.155464	−	0.155464i	0.780553	+	0.625089i	$0.214937\pi$
$332$	−2.82843	+	2.82843i	−0.155230	+	0.155230i
$333$	−5.54328	−	2.29610i	−0.303770	−	0.125826i
$334$	−1.53073	+	3.69552i	−0.0837580	+	0.202210i
$335$	7.39104	−	3.06147i	0.403815	−	0.167266i
$336$		0			0
$337$	5.35757	+	12.9343i	0.291845	+	0.704577i	0.999999	−	0.00148149i	$-0.000471572\pi$
$337$	5.35757	+	12.9343i	0.291845	+	0.704577i	−0.708154	+	0.706058i	$0.750472\pi$
$338$	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
$343$	3.06147	+	7.39104i	0.165304	+	0.399078i
$344$			12.0000i			0.646997i
$345$		0			0
$346$	−8.41904	+	20.3253i	−0.452610	+	1.09270i
$347$	29.5641	+	12.2459i	1.58709	+	0.657393i	0.989516	−	0.144424i	$-0.0461328\pi$
$347$	29.5641	+	12.2459i	1.58709	+	0.657393i	0.597571	+	0.801816i	$0.296133\pi$
$348$		0			0
$349$	12.7279	−	12.7279i	0.681310	−	0.681310i	−0.278985	−	0.960295i	$-0.589998\pi$
$349$	12.7279	−	12.7279i	0.681310	−	0.681310i	0.960295	+	0.278985i	$0.0899981\pi$
$350$	−3.69552	−	1.53073i	−0.197534	−	0.0818212i
$351$		0			0
$352$		0			0
$353$			30.0000i			1.59674i	0.602168	+	0.798369i	$0.294304\pi$
$353$			30.0000i			1.59674i	−0.602168	+	0.798369i	$0.705696\pi$
$354$		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	$-0.250000\pi$
$359$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$360$	6.88830	+	16.6298i	0.363045	+	0.876469i
$361$		−	3.00000i		−	0.157895i
$362$	1.84776	−	0.765367i	0.0971161	−	0.0402268i
$363$		0			0
$364$	7.39104	+	3.06147i	0.387396	+	0.160464i
$365$	8.48528	−	8.48528i	0.444140	−	0.444140i
$366$		0			0
$367$	−25.8686	−	10.7151i	−1.35033	−	0.559326i	−0.413947	−	0.910301i	$-0.635850\pi$
$367$	−25.8686	−	10.7151i	−1.35033	−	0.559326i	−0.936385	+	0.350976i	$0.885850\pi$
$368$	1.53073	−	3.69552i	0.0797950	−	0.192642i
$369$	−16.6298	+	6.88830i	−0.865714	+	0.358591i
$370$			4.00000i			0.207950i
$371$	−9.18440	−	22.1731i	−0.476830	−	1.15117i
$372$		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
$377$	−4.59220	−	11.0866i	−0.236510	−	0.570987i
$378$		0			0
$379$	−7.39104	+	3.06147i	−0.379652	+	0.157257i	−0.564345	−	0.825539i	$-0.690871\pi$
$379$	−7.39104	+	3.06147i	−0.379652	+	0.157257i	0.184693	+	0.982796i	$0.440871\pi$
$380$	−3.06147	+	7.39104i	−0.157050	+	0.379152i
$381$		0			0
$382$	11.3137	−	11.3137i	0.578860	−	0.578860i
$383$	16.9706	−	16.9706i	0.867155	−	0.867155i	−0.125001	−	0.992157i	$-0.539894\pi$
$383$	16.9706	−	16.9706i	0.867155	−	0.867155i	0.992157	+	0.125001i	$0.0398935\pi$
$384$		0			0
$385$		0			0
$386$	1.84776	−	0.765367i	0.0940485	−	0.0389561i
$387$			12.0000i			0.609994i
$388$	0.765367	+	1.84776i	0.0388556	+	0.0938058i
$389$	4.24264	+	4.24264i	0.215110	+	0.215110i	0.806434	−	0.591324i	$-0.201394\pi$
$389$	4.24264	+	4.24264i	0.215110	+	0.215110i	−0.591324	+	0.806434i	$0.701394\pi$
$390$		0			0
$391$		0			0
$392$	27.0000			1.36371
$393$		0			0
$394$	6.88830	+	16.6298i	0.347028	+	0.837799i
$395$		−	24.0000i		−	1.20757i
$396$		0			0
$397$	2.29610	−	5.54328i	0.115238	−	0.278209i	−0.855728	−	0.517425i	$-0.826890\pi$
$397$	2.29610	−	5.54328i	0.115238	−	0.278209i	0.970966	+	0.239216i	$0.0768905\pi$
$398$	18.4776	+	7.65367i	0.926198	+	0.383644i
$399$		0			0
$400$	−0.707107	+	0.707107i	−0.0353553	+	0.0353553i
$401$	12.9343	+	5.35757i	0.645909	+	0.267544i	0.681495	−	0.731822i	$-0.261330\pi$
$401$	12.9343	+	5.35757i	0.645909	+	0.267544i	−0.0355866	+	0.999367i	$0.511330\pi$
$402$		0			0
$403$	7.39104	−	3.06147i	0.368174	−	0.152503i
$404$		−	10.0000i		−	0.497519i
$405$	6.88830	+	16.6298i	0.342282	+	0.826343i
$406$	−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
$413$	−44.3462	+	18.3688i	−2.18213	+	0.903870i
$414$	4.59220	−	11.0866i	0.225694	−	0.544874i
$415$	7.39104	+	3.06147i	0.362812	+	0.150282i
$416$	7.07107	−	7.07107i	0.346688	−	0.346688i
$417$		0			0
$418$		0			0
$419$	−3.06147	+	7.39104i	−0.149562	+	0.361076i	−0.980849	−	0.194768i	$-0.937605\pi$
$419$	−3.06147	+	7.39104i	−0.149562	+	0.361076i	0.831287	+	0.555844i	$0.187605\pi$
$420$		0			0
$421$		−	22.0000i		−	1.07221i	−0.844150	−	0.536107i	$-0.819894\pi$
$421$		−	22.0000i		−	1.07221i	0.844150	−	0.536107i	$-0.180106\pi$
$422$	3.06147	+	7.39104i	0.149030	+	0.359790i
$423$		0			0
$424$	−18.0000			−0.874157
$425$		0			0
$426$		0			0
$427$	28.2843	+	28.2843i	1.36877	+	1.36877i
$428$	−3.06147	−	7.39104i	−0.147982	−	0.357259i
$429$		0			0
$430$	7.39104	−	3.06147i	0.356427	−	0.147637i
$431$	4.59220	−	11.0866i	0.221199	−	0.534021i	−0.773855	−	0.633363i	$-0.781674\pi$
$431$	4.59220	−	11.0866i	0.221199	−	0.534021i	0.995053	+	0.0993426i	$0.0316740\pi$
$432$		0			0
$433$	1.41421	−	1.41421i	0.0679628	−	0.0679628i	−0.672308	−	0.740271i	$-0.734697\pi$
$433$	1.41421	−	1.41421i	0.0679628	−	0.0679628i	0.740271	+	0.672308i	$0.234697\pi$
$434$	11.3137	−	11.3137i	0.543075	−	0.543075i
$435$		0			0
$436$	2.29610	−	5.54328i	0.109963	−	0.265475i
$437$	14.7821	−	6.12293i	0.707122	−	0.292900i
$438$		0			0
$439$	7.65367	+	18.4776i	0.365290	+	0.881887i	0.994508	+	0.104659i	$0.0333751\pi$
$439$	7.65367	+	18.4776i	0.365290	+	0.881887i	−0.629219	+	0.777228i	$0.716625\pi$
$440$		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
$445$	−7.65367	−	18.4776i	−0.362819	−	0.875922i
$446$		−	24.0000i		−	1.13643i
$447$		0			0
$448$	10.7151	−	25.8686i	0.506243	−	1.22218i
$449$	31.4119	+	13.0112i	1.48242	+	0.614038i	0.969652	−	0.244489i	$-0.0786203\pi$
$449$	31.4119	+	13.0112i	1.48242	+	0.614038i	0.512767	+	0.858528i	$0.328620\pi$
$450$	−2.12132	+	2.12132i	−0.100000	+	0.100000i
$451$		0			0
$452$	−12.9343	−	5.35757i	−0.608379	−	0.251999i
$453$		0			0
$454$	−22.1731	+	9.18440i	−1.04064	+	0.431045i
$455$		−	16.0000i		−	0.750092i
$456$		0			0
$457$	−4.24264	−	4.24264i	−0.198462	−	0.198462i	0.600878	−	0.799341i	$-0.294818\pi$
$457$	−4.24264	−	4.24264i	−0.198462	−	0.198462i	−0.799341	+	0.600878i	$0.794818\pi$
$458$	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	$-0.235169\pi$
$461$	1.41421	+	1.41421i	0.0658665	+	0.0658665i	−0.673406	+	0.739273i	$0.735169\pi$
$462$		0			0
$463$			32.0000i			1.48717i	0.668644	+	0.743583i	$0.266875\pi$
$463$			32.0000i			1.48717i	−0.668644	+	0.743583i	$0.733125\pi$
$464$	−5.54328	+	2.29610i	−0.257340	+	0.106594i
$465$		0			0
$466$	5.54328	+	2.29610i	0.256787	+	0.106365i
$467$	8.48528	−	8.48528i	0.392652	−	0.392652i	−0.482980	−	0.875632i	$-0.660445\pi$
$467$	8.48528	−	8.48528i	0.392652	−	0.392652i	0.875632	+	0.482980i	$0.160445\pi$
$468$	4.24264	−	4.24264i	0.196116	−	0.196116i
$469$	−14.7821	−	6.12293i	−0.682573	−	0.282731i
$470$		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
$479$	13.7766	+	33.2597i	0.629469	+	1.51967i	0.840284	+	0.542147i	$0.182388\pi$
$479$	13.7766	+	33.2597i	0.629469	+	1.51967i	−0.210815	+	0.977526i	$0.567612\pi$
$480$		0			0
$481$	3.69552	−	1.53073i	0.168501	−	0.0697955i
$482$	−6.88830	+	16.6298i	−0.313754	+	0.757468i
$483$		0			0
$484$	7.77817	−	7.77817i	0.353553	−	0.353553i
$485$	2.82843	−	2.82843i	0.128432	−	0.128432i
$486$		0			0
$487$	−7.65367	+	18.4776i	−0.346821	+	0.837300i	0.650171	+	0.759788i	$0.274697\pi$
$487$	−7.65367	+	18.4776i	−0.346821	+	0.837300i	−0.996991	+	0.0775113i	$0.975303\pi$
$488$	27.7164	−	11.4805i	1.25466	−	0.519698i
$489$		0			0
$490$	−6.88830	−	16.6298i	−0.311182	−	0.751259i
$491$	14.1421	+	14.1421i	0.638226	+	0.638226i	0.950118	−	0.311892i	$-0.100963\pi$
$491$	14.1421	+	14.1421i	0.638226	+	0.638226i	−0.311892	+	0.950118i	$0.600963\pi$
$492$		0			0
$493$		0			0
$494$	−8.00000			−0.359937
$495$		0			0
$496$	−1.53073	−	3.69552i	−0.0687320	−	0.165934i
$497$		−	16.0000i		−	0.717698i
$498$		0			0
$499$	−15.3073	+	36.9552i	−0.685251	+	1.65434i	0.0688869	+	0.997624i	$0.478055\pi$
$499$	−15.3073	+	36.9552i	−0.685251	+	1.65434i	−0.754137	+	0.656717i	$0.771945\pi$
$500$	−11.0866	−	4.59220i	−0.495806	−	0.205369i
$501$		0			0
$502$	8.48528	−	8.48528i	0.378717	−	0.378717i
$503$	11.0866	+	4.59220i	0.494325	+	0.204756i	0.615897	−	0.787826i	$-0.288794\pi$
$503$	11.0866	+	4.59220i	0.494325	+	0.204756i	−0.121572	+	0.992583i	$0.538794\pi$
$504$	13.7766	−	33.2597i	0.613659	−	1.48150i
$505$	−18.4776	+	7.65367i	−0.822242	+	0.340584i
$506$		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
$515$	−14.7821	+	6.12293i	−0.651376	+	0.269809i
$516$		0			0
$517$		0			0
$518$	5.65685	−	5.65685i	0.248548	−	0.248548i
$519$		0			0
$520$	−11.0866	−	4.59220i	−0.486178	−	0.201381i
$521$	−9.94977	+	24.0209i	−0.435907	+	1.05237i	0.541441	+	0.840738i	$0.317879\pi$
$521$	−9.94977	+	24.0209i	−0.435907	+	1.05237i	−0.977349	+	0.211635i	$0.932121\pi$
$522$	−16.6298	+	6.88830i	−0.727868	+	0.301493i
$523$			36.0000i			1.57417i	0.616844	+	0.787085i	$0.288411\pi$
$523$			36.0000i			1.57417i	−0.616844	+	0.787085i	$0.711589\pi$
$524$	6.12293	+	14.7821i	0.267482	+	0.645758i
$525$		0			0
$526$	−16.0000			−0.697633
$527$		0			0
$528$		0			0
$529$	4.94975	+	4.94975i	0.215206	+	0.215206i
$530$	4.59220	+	11.0866i	0.199472	+	0.481569i
$531$			36.0000i			1.56227i
$532$	14.7821	−	6.12293i	0.640884	−	0.265463i
$533$	4.59220	−	11.0866i	0.198910	−	0.480212i
$534$		0			0
$535$	−11.3137	+	11.3137i	−0.489134	+	0.489134i
$536$	−8.48528	+	8.48528i	−0.366508	+	0.366508i
$537$		0			0
$538$	8.41904	−	20.3253i	0.362970	−	0.876288i
$539$		0			0
$540$		0			0
$541$	−2.29610	−	5.54328i	−0.0987171	−	0.238324i	0.866804	−	0.498649i	$-0.166170\pi$
$541$	−2.29610	−	5.54328i	−0.0987171	−	0.238324i	−0.965521	+	0.260325i	$0.916170\pi$
$542$	11.3137	+	11.3137i	0.485965	+	0.485965i
$543$		0			0
$544$		0			0
$545$	−12.0000			−0.514024
$546$		0			0
$547$	−12.2459	−	29.5641i	−0.523596	−	1.26407i	−0.935655	−	0.352915i	$-0.885191\pi$
$547$	−12.2459	−	29.5641i	−0.523596	−	1.26407i	0.412060	−	0.911157i	$-0.364809\pi$
$548$			6.00000i			0.256307i
$549$	27.7164	−	11.4805i	1.18291	−	0.489976i
$550$		0			0
$551$	−22.1731	−	9.18440i	−0.944606	−	0.391269i
$552$		0			0
$553$	−33.9411	+	33.9411i	−1.44332	+	1.44332i
$554$	12.9343	+	5.35757i	0.549526	+	0.227621i
$555$		0			0
$556$	−7.39104	+	3.06147i	−0.313450	+	0.129835i
$557$		−	30.0000i		−	1.27114i	−0.772043	−	0.635570i	$-0.780765\pi$
$557$		−	30.0000i		−	1.27114i	0.772043	−	0.635570i	$-0.219235\pi$
$558$	−4.59220	−	11.0866i	−0.194403	−	0.469331i
$559$	−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	$-0.223138\pi$
$563$	2.82843	+	2.82843i	0.119204	+	0.119204i	−0.644988	+	0.764192i	$0.723138\pi$
$564$		0			0
$565$			28.0000i			1.17797i
$566$	14.7821	−	6.12293i	0.621337	−	0.257366i
$567$	13.7766	−	33.2597i	0.578563	−	1.39677i
$568$	−11.0866	−	4.59220i	−0.465181	−	0.192684i
$569$	−26.8701	+	26.8701i	−1.12645	+	1.12645i	−0.135702	+	0.990750i	$0.543329\pi$
$569$	−26.8701	+	26.8701i	−1.12645	+	1.12645i	−0.990750	+	0.135702i	$0.956671\pi$
$570$		0			0
$571$	29.5641	+	12.2459i	1.23722	+	0.512474i	0.902845	−	0.429966i	$-0.141474\pi$
$571$	29.5641	+	12.2459i	1.23722	+	0.512474i	0.334376	+	0.942440i	$0.391474\pi$
$572$		0			0
$573$		0			0
$574$		−	24.0000i		−	1.00174i
$575$	1.53073	+	3.69552i	0.0638360	+	0.154114i
$576$	−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
$581$	−6.12293	−	14.7821i	−0.254022	−	0.613264i
$582$		0			0
$583$		0			0
$584$	−6.88830	+	16.6298i	−0.285040	+	0.688147i
$585$	−11.0866	−	4.59220i	−0.458373	−	0.189864i
$586$	−4.24264	+	4.24264i	−0.175262	+	0.175262i
$587$	−2.82843	+	2.82843i	−0.116742	+	0.116742i	−0.763064	−	0.646323i	$-0.776306\pi$
$587$	−2.82843	+	2.82843i	−0.116742	+	0.116742i	0.646323	+	0.763064i	$0.276306\pi$
$588$		0			0
$589$	6.12293	−	14.7821i	0.252291	−	0.609085i
$590$	22.1731	−	9.18440i	0.912852	−	0.378116i
$591$		0			0
$592$	−0.765367	−	1.84776i	−0.0314564	−	0.0759424i
$593$	12.7279	+	12.7279i	0.522673	+	0.522673i	0.918378	−	0.395705i	$-0.129500\pi$
$593$	12.7279	+	12.7279i	0.522673	+	0.522673i	−0.395705	+	0.918378i	$0.629500\pi$
$594$		0			0
$595$		0			0
$596$	10.0000			0.409616
$597$		0			0
$598$	3.06147	+	7.39104i	0.125193	+	0.302242i
$599$		−	24.0000i		−	0.980613i	−0.871550	−	0.490307i	$-0.836885\pi$
$599$		−	24.0000i		−	0.980613i	0.871550	−	0.490307i	$-0.163115\pi$
$600$		0			0
$601$	3.82683	−	9.23880i	0.156100	−	0.376858i	−0.826410	−	0.563069i	$-0.809621\pi$
$601$	3.82683	−	9.23880i	0.156100	−	0.376858i	0.982510	+	0.186210i	$0.0596206\pi$
$602$	−14.7821	−	6.12293i	−0.602472	−	0.249552i
$603$	−8.48528	+	8.48528i	−0.345547	+	0.345547i
$604$	−11.3137	+	11.3137i	−0.460348	+	0.460348i
$605$	−20.3253	−	8.41904i	−0.826343	−	0.342282i
$606$		0			0
$607$	−18.4776	+	7.65367i	−0.749982	+	0.310653i	−0.724734	−	0.689028i	$-0.758038\pi$
$607$	−18.4776	+	7.65367i	−0.749982	+	0.310653i	−0.0252479	+	0.999681i	$0.508038\pi$
$608$		−	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
$617$	−5.54328	+	2.29610i	−0.223164	+	0.0924375i	−0.491464	−	0.870898i	$-0.663538\pi$
$617$	−5.54328	+	2.29610i	−0.223164	+	0.0924375i	0.268300	+	0.963335i	$0.413538\pi$
$618$		0			0
$619$	−44.3462	−	18.3688i	−1.78242	−	0.738305i	−0.992075	−	0.125649i	$-0.959899\pi$
$619$	−44.3462	−	18.3688i	−1.78242	−	0.738305i	−0.790350	−	0.612655i	$-0.790101\pi$
$620$	5.65685	−	5.65685i	0.227185	−	0.227185i
$621$		0			0
$622$	25.8686	+	10.7151i	1.03724	+	0.429638i
$623$	−15.3073	+	36.9552i	−0.613276	+	1.48058i
$624$		0			0
$625$			19.0000i			0.760000i
$626$	−8.41904	−	20.3253i	−0.336492	−	0.812364i
$627$		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	$-0.353171\pi$
$631$	−11.3137	−	11.3137i	−0.450392	−	0.450392i	−0.895484	+	0.445093i	$0.853171\pi$
$632$	13.7766	+	33.2597i	0.548004	+	1.32300i
$633$		0			0
$634$	9.23880	−	3.82683i	0.366919	−	0.151983i
$635$	−6.12293	+	14.7821i	−0.242981	+	0.586609i
$636$		0			0
$637$	−12.7279	+	12.7279i	−0.504299	+	0.504299i
$638$		0			0
$639$	−11.0866	−	4.59220i	−0.438577	−	0.181665i
$640$	2.29610	−	5.54328i	0.0907613	−	0.219117i
$641$	27.7164	−	11.4805i	1.09473	−	0.453453i	0.239077	−	0.971001i	$-0.423155\pi$
$641$	27.7164	−	11.4805i	1.09473	−	0.453453i	0.855654	+	0.517548i	$0.173155\pi$
$642$		0			0
$643$	−12.2459	−	29.5641i	−0.482930	−	1.16590i	−0.958211	−	0.286062i	$-0.907654\pi$
$643$	−12.2459	−	29.5641i	−0.482930	−	1.16590i	0.475281	−	0.879834i	$-0.342346\pi$
$644$	−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
$652$	−9.18440	+	22.1731i	−0.359689	+	0.868366i
$653$	5.54328	+	2.29610i	0.216925	+	0.0898534i	0.488500	−	0.872564i	$-0.337544\pi$
$653$	5.54328	+	2.29610i	0.216925	+	0.0898534i	−0.271575	+	0.962417i	$0.587544\pi$
$654$		0			0
$655$	22.6274	−	22.6274i	0.884126	−	0.884126i
$656$	−5.54328	−	2.29610i	−0.216429	−	0.0896477i
$657$	−6.88830	+	16.6298i	−0.268738	+	0.648792i
$658$		0			0
$659$		−	4.00000i		−	0.155818i	−0.996960	−	0.0779089i	$-0.975176\pi$
$659$		−	4.00000i		−	0.155818i	0.996960	−	0.0779089i	$-0.0248243\pi$
$660$		0			0
$661$	26.8701	+	26.8701i	1.04512	+	1.04512i	0.998933	+	0.0461915i	$0.0147084\pi$
$661$	26.8701	+	26.8701i	1.04512	+	1.04512i	0.0461915	+	0.998933i	$0.485292\pi$
$662$	4.00000			0.155464
$663$		0			0
$664$	−12.0000			−0.465690
$665$	−22.6274	−	22.6274i	−0.877454	−	0.877454i
$666$	−2.29610	−	5.54328i	−0.0889721	−	0.214798i
$667$			24.0000i			0.929284i
$668$	3.69552	−	1.53073i	0.142984	−	0.0592259i
$669$		0			0
$670$	7.39104	+	3.06147i	0.285541	+	0.118275i
$671$		0			0
$672$		0			0
$673$	−1.84776	−	0.765367i	−0.0712259	−	0.0295027i	0.346786	−	0.937944i	$-0.387273\pi$
$673$	−1.84776	−	0.765367i	−0.0712259	−	0.0295027i	−0.418012	+	0.908442i	$0.637273\pi$
$674$	−5.35757	+	12.9343i	−0.206366	+	0.498211i
$675$		0			0
$676$		−	9.00000i		−	0.346154i
$677$	−11.4805	−	27.7164i	−0.441232	−	1.06523i	−0.975517	−	0.219923i	$-0.929419\pi$
$677$	−11.4805	−	27.7164i	−0.441232	−	1.06523i	0.534286	−	0.845304i	$-0.320581\pi$
$678$		0			0
$679$	−8.00000			−0.307012
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15.3073	−	36.9552i	−0.585719	−	1.41405i	−0.887560	−	0.460692i	$-0.847601\pi$
$683$	−15.3073	−	36.9552i	−0.585719	−	1.41405i	0.301841	−	0.953358i	$-0.402399\pi$
$684$		−	12.0000i		−	0.458831i
$685$	11.0866	−	4.59220i	0.423595	−	0.175459i
$686$	−3.06147	+	7.39104i	−0.116887	+	0.282191i
$687$		0			0
$688$	−2.82843	+	2.82843i	−0.107833	+	0.107833i
$689$	8.48528	−	8.48528i	0.323263	−	0.323263i
$690$		0			0
$691$	3.06147	−	7.39104i	0.116464	−	0.281168i	−0.854889	−	0.518811i	$-0.826375\pi$
$691$	3.06147	−	7.39104i	0.116464	−	0.281168i	0.971353	+	0.237643i	$0.0763748\pi$
$692$	20.3253	−	8.41904i	0.772654	−	0.320044i
$693$		0			0
$694$	12.2459	+	29.5641i	0.464847	+	1.12224i
$695$	11.3137	+	11.3137i	0.429153	+	0.429153i
$696$		0			0
$697$		0			0
$698$	18.0000			0.681310
$699$		0			0
$700$	1.53073	+	3.69552i	0.0578563	+	0.139677i
$701$		−	18.0000i		−	0.679851i	−0.940452	−	0.339925i	$-0.889598\pi$
$701$		−	18.0000i		−	0.679851i	0.940452	−	0.339925i	$-0.110402\pi$
$702$		0			0
$703$	3.06147	−	7.39104i	0.115465	−	0.278758i
$704$		0			0
$705$		0			0
$706$	−21.2132	+	21.2132i	−0.798369	+	0.798369i
$707$	36.9552	+	15.3073i	1.38984	+	0.575692i
$708$		0			0
$709$	31.4119	−	13.0112i	1.17970	−	0.488647i	0.295312	−	0.955401i	$-0.404577\pi$
$709$	31.4119	−	13.0112i	1.17970	−	0.488647i	0.884387	+	0.466754i	$0.154577\pi$
$710$			8.00000i			0.300235i
$711$	13.7766	+	33.2597i	0.516663	+	1.24733i
$712$	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
$719$	3.69552	−	1.53073i	0.137820	−	0.0570867i	−0.312708	−	0.949849i	$-0.601236\pi$
$719$	3.69552	−	1.53073i	0.137820	−	0.0570867i	0.450527	+	0.892763i	$0.351236\pi$
$720$	−2.29610	+	5.54328i	−0.0855706	+	0.206586i
$721$	29.5641	+	12.2459i	1.10103	+	0.456060i
$722$	2.12132	−	2.12132i	0.0789474	−	0.0789474i
$723$		0			0
$724$	−1.84776	−	0.765367i	−0.0686714	−	0.0284446i
$725$	2.29610	−	5.54328i	0.0852750	−	0.205872i
$726$		0			0
$727$		−	40.0000i		−	1.48352i	−0.670667	−	0.741759i	$-0.733992\pi$
$727$		−	40.0000i		−	1.48352i	0.670667	−	0.741759i	$-0.266008\pi$
$728$	9.18440	+	22.1731i	0.340397	+	0.821790i
$729$	−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	0.924362	+	0.381518i	$0.124598\pi$
$733$	35.3553	+	35.3553i	1.30588	+	1.30588i	0.381518	+	0.924362i	$0.375402\pi$
$734$	−10.7151	−	25.8686i	−0.395503	−	0.954828i
$735$		0			0
$736$	−18.4776	+	7.65367i	−0.681093	+	0.282118i
$737$		0			0
$738$	−16.6298	−	6.88830i	−0.612153	−	0.253562i
$739$	19.7990	−	19.7990i	0.728318	−	0.728318i	−0.241967	−	0.970285i	$-0.577793\pi$
$739$	19.7990	−	19.7990i	0.728318	−	0.728318i	0.970285	+	0.241967i	$0.0777925\pi$
$740$	2.82843	−	2.82843i	0.103975	−	0.103975i
$741$		0			0
$742$	9.18440	−	22.1731i	0.337170	−	0.814000i
$743$	−11.0866	+	4.59220i	−0.406726	+	0.168472i	−0.576661	−	0.816984i	$-0.695644\pi$
$743$	−11.0866	+	4.59220i	−0.406726	+	0.168472i	0.169934	+	0.985455i	$0.445644\pi$
$744$		0			0
$745$	−7.65367	−	18.4776i	−0.280409	−	0.676967i
$746$	−4.24264	−	4.24264i	−0.155334	−	0.155334i
$747$	−12.0000			−0.439057
$748$		0			0
$749$	32.0000			1.16925
$750$		0			0
$751$	7.65367	+	18.4776i	0.279286	+	0.674257i	0.999816	−	0.0191669i	$-0.00610140\pi$
$751$	7.65367	+	18.4776i	0.279286	+	0.674257i	−0.720530	+	0.693424i	$0.756101\pi$
$752$		0			0
$753$		0			0
$754$	4.59220	−	11.0866i	0.167238	−	0.403748i
$755$	29.5641	+	12.2459i	1.07595	+	0.445673i
$756$		0			0
$757$	−15.5563	+	15.5563i	−0.565405	+	0.565405i	−0.930838	−	0.365433i	$-0.880921\pi$
$757$	−15.5563	+	15.5563i	−0.565405	+	0.565405i	0.365433	+	0.930838i	$0.380921\pi$
$758$	−7.39104	−	3.06147i	−0.268455	−	0.111198i
$759$		0			0
$760$	−22.1731	+	9.18440i	−0.804303	+	0.333153i
$761$			22.0000i			0.797499i	0.917060	+	0.398750i	$0.130556\pi$
$761$			22.0000i			0.797499i	−0.917060	+	0.398750i	$0.869444\pi$
$762$		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	$-0.918771\pi$
$769$		−	14.0000i		−	0.504853i	0.967616	−	0.252426i	$-0.0812286\pi$
$770$		0			0
$771$		0			0
$772$	−1.84776	−	0.765367i	−0.0665023	−	0.0275462i
$773$	−18.3848	+	18.3848i	−0.661254	+	0.661254i	−0.955676	−	0.294421i	$-0.904873\pi$
$773$	−18.3848	+	18.3848i	−0.661254	+	0.661254i	0.294421	+	0.955676i	$0.404873\pi$
$774$	−8.48528	+	8.48528i	−0.304997	+	0.304997i
$775$	3.69552	+	1.53073i	0.132747	+	0.0549856i
$776$	−2.29610	+	5.54328i	−0.0824252	+	0.198992i
$777$		0			0
$778$			6.00000i			0.215110i
$779$	−9.18440	−	22.1731i	−0.329065	−	0.794434i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	6.36396	+	6.36396i	0.227284	+	0.227284i
$785$	1.53073	+	3.69552i	0.0546342	+	0.131899i
$786$		0			0
$787$	−29.5641	+	12.2459i	−1.05385	+	0.436518i	−0.841264	−	0.540625i	$-0.818188\pi$
$787$	−29.5641	+	12.2459i	−1.05385	+	0.436518i	−0.212584	+	0.977143i	$0.568188\pi$
$788$	6.88830	−	16.6298i	0.245386	−	0.592413i
$789$		0			0
$790$	16.9706	−	16.9706i	0.603786	−	0.603786i
$791$	39.5980	−	39.5980i	1.40794	−	1.40794i
$792$		0			0
$793$	−7.65367	+	18.4776i	−0.271790	+	0.656158i
$794$	5.54328	−	2.29610i	0.196724	−	0.0814856i
$795$		0			0
$796$	−7.65367	−	18.4776i	−0.271277	−	0.654921i
$797$	−35.3553	−	35.3553i	−1.25235	−	1.25235i	−0.954664	−	0.297687i	$-0.903785\pi$
$797$	−35.3553	−	35.3553i	−1.25235	−	1.25235i	−0.297687	−	0.954664i	$-0.596215\pi$
$798$		0			0
$799$		0			0
$800$	5.00000			0.176777
$801$	21.2132	+	21.2132i	0.749532	+	0.749532i
$802$	5.35757	+	12.9343i	0.189182	+	0.456726i
$803$		0			0
$804$		0			0
$805$	−12.2459	+	29.5641i	−0.431610	+	1.04200i
$806$	7.39104	+	3.06147i	0.260338	+	0.107836i
$807$		0			0
$808$	21.2132	−	21.2132i	0.746278	−	0.746278i
$809$	−24.0209	−	9.94977i	−0.844529	−	0.349815i	−0.0818911	−	0.996641i	$-0.526096\pi$
$809$	−24.0209	−	9.94977i	−0.844529	−	0.349815i	−0.762638	+	0.646826i	$0.776096\pi$
$810$	−6.88830	+	16.6298i	−0.242030	+	0.584313i
$811$	−36.9552	+	15.3073i	−1.29767	+	0.537513i	−0.921263	−	0.388940i	$-0.872841\pi$
$811$	−36.9552	+	15.3073i	−1.29767	+	0.537513i	−0.376409	+	0.926454i	$0.622841\pi$
$812$			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
$819$	9.18440	+	22.1731i	0.320929	+	0.774791i
$820$		−	12.0000i		−	0.419058i
$821$	−16.6298	+	6.88830i	−0.580385	+	0.240403i	−0.653508	−	0.756920i	$-0.726703\pi$
$821$	−16.6298	+	6.88830i	−0.580385	+	0.240403i	0.0731230	+	0.997323i	$0.476703\pi$
$822$		0			0
$823$	18.4776	+	7.65367i	0.644088	+	0.266790i	0.680726	−	0.732539i	$-0.261665\pi$
$823$	18.4776	+	7.65367i	0.644088	+	0.266790i	−0.0366373	+	0.999329i	$0.511665\pi$
$824$	16.9706	−	16.9706i	0.591198	−	0.591198i
$825$		0			0
$826$	−44.3462	−	18.3688i	−1.54300	−	0.639132i
$827$	18.3688	−	44.3462i	0.638746	−	1.54207i	−0.189606	−	0.981860i	$-0.560721\pi$
$827$	18.3688	−	44.3462i	0.638746	−	1.54207i	0.828351	−	0.560209i	$-0.189279\pi$
$828$	−11.0866	+	4.59220i	−0.385284	+	0.159590i
$829$			34.0000i			1.18087i	0.807086	+	0.590434i	$0.201044\pi$
$829$			34.0000i			1.18087i	−0.807086	+	0.590434i	$0.798956\pi$
$830$	3.06147	+	7.39104i	0.106265	+	0.256547i
$831$		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
$838$	−7.39104	+	3.06147i	−0.255319	+	0.105757i
$839$	7.65367	−	18.4776i	0.264234	−	0.637917i	−0.734958	−	0.678113i	$-0.762798\pi$
$839$	7.65367	−	18.4776i	0.264234	−	0.637917i	0.999192	+	0.0401955i	$0.0127981\pi$
$840$		0			0
$841$	4.94975	−	4.94975i	0.170681	−	0.170681i
$842$	15.5563	−	15.5563i	0.536107	−	0.536107i
$843$		0			0
$844$	3.06147	−	7.39104i	0.105380	−	0.254410i
$845$	−16.6298	+	6.88830i	−0.572084	+	0.236965i
$846$		0			0
$847$	16.8381	+	40.6507i	0.578563	+	1.39677i
$848$	−4.24264	−	4.24264i	−0.145693	−	0.145693i
$849$		0			0
$850$		0			0
$851$	−8.00000			−0.274236
$852$		0			0
$853$	5.35757	+	12.9343i	0.183440	+	0.442862i	0.988671	−	0.150098i	$-0.0479590\pi$
$853$	5.35757	+	12.9343i	0.183440	+	0.442862i	−0.805231	+	0.592961i	$0.797959\pi$
$854$			40.0000i			1.36877i
$855$	−22.1731	+	9.18440i	−0.758304	+	0.314100i
$856$	9.18440	−	22.1731i	0.313916	−	0.757861i
$857$	9.23880	+	3.82683i	0.315591	+	0.130722i	0.534856	−	0.844943i	$-0.320366\pi$
$857$	9.23880	+	3.82683i	0.315591	+	0.130722i	−0.219265	+	0.975665i	$0.570366\pi$
$858$		0			0
$859$	−36.7696	+	36.7696i	−1.25456	+	1.25456i	−0.300908	+	0.953653i	$0.597290\pi$
$859$	−36.7696	+	36.7696i	−1.25456	+	1.25456i	−0.953653	+	0.300908i	$0.902710\pi$
$860$	−7.39104	−	3.06147i	−0.252032	−	0.104395i
$861$		0			0
$862$	11.0866	−	4.59220i	0.377610	−	0.156411i
$863$		−	16.0000i		−	0.544646i	−0.962206	−	0.272323i	$-0.912208\pi$
$863$		−	16.0000i		−	0.544646i	0.962206	−	0.272323i	$-0.0877920\pi$
$864$		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
$872$	16.6298	−	6.88830i	0.563157	−	0.233267i
$873$	−2.29610	+	5.54328i	−0.0777112	+	0.187612i
$874$	14.7821	+	6.12293i	0.500011	+	0.207111i
$875$	33.9411	−	33.9411i	1.14742	−	1.14742i
$876$		0			0
$877$	−5.54328	−	2.29610i	−0.187183	−	0.0775338i	0.287123	−	0.957894i	$-0.407301\pi$
$877$	−5.54328	−	2.29610i	−0.187183	−	0.0775338i	−0.474306	+	0.880360i	$0.657301\pi$
$878$	−7.65367	+	18.4776i	−0.258299	+	0.623588i
$879$		0			0
$880$		0			0
$881$	17.6034	+	42.4985i	0.593075	+	1.43181i	0.880518	+	0.474012i	$0.157195\pi$
$881$	17.6034	+	42.4985i	0.593075	+	1.43181i	−0.287444	+	0.957798i	$0.592805\pi$
$882$	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
$887$	4.59220	+	11.0866i	0.154191	+	0.372250i	0.982032	−	0.188712i	$-0.0604313\pi$
$887$	4.59220	+	11.0866i	0.154191	+	0.372250i	−0.827841	+	0.560962i	$0.810431\pi$
$888$		0			0
$889$	29.5641	−	12.2459i	0.991550	−	0.410713i
$890$	7.65367	−	18.4776i	0.256552	−	0.619370i
$891$		0			0
$892$	−16.9706	+	16.9706i	−0.568216	+	0.568216i
$893$		0			0
$894$		0			0
$895$	9.18440	−	22.1731i	0.307001	−	0.741165i
$896$	−11.0866	+	4.59220i	−0.370376	+	0.153415i
$897$		0			0
$898$	13.0112	+	31.4119i	0.434191	+	1.04823i
$899$	16.9706	+	16.9706i	0.566000	+	0.566000i
$900$	3.00000			0.100000
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−16.0727	−	38.8029i	−0.534570	−	1.29057i
$905$			4.00000i			0.132964i
$906$		0			0
$907$	12.2459	−	29.5641i	0.406617	−	0.981661i	−0.579404	−	0.815041i	$-0.696714\pi$
$907$	12.2459	−	29.5641i	0.406617	−	0.981661i	0.986021	−	0.166621i	$-0.0532855\pi$
$908$	22.1731	+	9.18440i	0.735840	+	0.304795i
$909$	21.2132	−	21.2132i	0.703598	−	0.703598i
$910$	11.3137	−	11.3137i	0.375046	−	0.375046i
$911$	3.69552	+	1.53073i	0.122438	+	0.0507155i	0.443061	−	0.896491i	$-0.353892\pi$
$911$	3.69552	+	1.53073i	0.122438	+	0.0507155i	−0.320623	+	0.947207i	$0.603892\pi$
$912$		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
$923$	7.39104	−	3.06147i	0.243279	−	0.100769i
$924$		0			0
$925$	1.84776	+	0.765367i	0.0607539	+	0.0251651i
$926$	−22.6274	+	22.6274i	−0.743583	+	0.743583i
$927$	16.9706	−	16.9706i	0.557386	−	0.557386i
$928$	27.7164	+	11.4805i	0.909835	+	0.376866i
$929$	11.4805	−	27.7164i	0.376663	−	0.909345i	−0.615924	−	0.787806i	$-0.711217\pi$
$929$	11.4805	−	27.7164i	0.376663	−	0.909345i	0.992587	−	0.121539i	$-0.0387830\pi$
$930$		0			0
$931$			36.0000i			1.17985i
$932$	−2.29610	−	5.54328i	−0.0752113	−	0.181576i
$933$		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	$-0.302228\pi$
$937$	−7.07107	−	7.07107i	−0.231002	−	0.231002i	−0.813111	+	0.582109i	$0.802228\pi$
$938$	−6.12293	−	14.7821i	−0.199921	−	0.482652i
$939$		0			0
$940$		0			0
$941$	2.29610	−	5.54328i	0.0748507	−	0.180706i	−0.882025	−	0.471202i	$-0.843820\pi$
$941$	2.29610	−	5.54328i	0.0748507	−	0.180706i	0.956876	+	0.290496i	$0.0938203\pi$
$942$		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
$947$	−29.5641	+	12.2459i	−0.960706	+	0.397937i	−0.807244	−	0.590217i	$-0.799042\pi$
$947$	−29.5641	+	12.2459i	−0.960706	+	0.397937i	−0.153461	+	0.988155i	$0.549042\pi$
$948$		0			0
$949$	−4.59220	−	11.0866i	−0.149069	−	0.359885i
$950$	−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
$955$	12.2459	+	29.5641i	0.396267	+	0.956673i
$956$			16.0000i			0.517477i
$957$		0			0
$958$	−13.7766	+	33.2597i	−0.445102	+	1.07457i
$959$	−22.1731	−	9.18440i	−0.716007	−	0.296580i
$960$		0			0
$961$	10.6066	−	10.6066i	0.342148	−	0.342148i
$962$	3.69552	+	1.53073i	0.119148	+	0.0493528i
$963$	9.18440	−	22.1731i	0.295963	−	0.714518i
$964$	16.6298	−	6.88830i	0.535611	−	0.221857i
$965$			4.00000i			0.128765i
$966$		0			0
$967$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$967$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$968$	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	$-0.188325\pi$
$971$	8.48528	+	8.48528i	0.272306	+	0.272306i	−0.557722	+	0.830028i	$0.688325\pi$
$972$		0			0
$973$		−	32.0000i		−	1.02587i
$974$	−18.4776	+	7.65367i	−0.592060	+	0.245239i
$975$		0			0
$976$	9.23880	+	3.82683i	0.295727	+	0.122494i
$977$	12.7279	−	12.7279i	0.407202	−	0.407202i	−0.473560	−	0.880762i	$-0.657031\pi$
$977$	12.7279	−	12.7279i	0.407202	−	0.407202i	0.880762	+	0.473560i	$0.157031\pi$
$978$		0			0
$979$		0			0
$980$	−6.88830	+	16.6298i	−0.220039	+	0.531220i
$981$	16.6298	−	6.88830i	0.530950	−	0.219927i
$982$			20.0000i			0.638226i
$983$	−4.59220	−	11.0866i	−0.146468	−	0.353606i	0.833570	−	0.552414i	$-0.186293\pi$
$983$	−4.59220	−	11.0866i	−0.146468	−	0.353606i	−0.980039	+	0.198808i	$0.936293\pi$
$984$		0			0
$985$	−36.0000			−1.14706
$986$		0			0
$987$		0			0
$988$	5.65685	+	5.65685i	0.179969	+	0.179969i
$989$	6.12293	+	14.7821i	0.194698	+	0.470043i
$990$		0			0
$991$	−11.0866	+	4.59220i	−0.352176	+	0.145876i	−0.551756	−	0.834005i	$-0.686042\pi$
$991$	−11.0866	+	4.59220i	−0.352176	+	0.145876i	0.199580	+	0.979881i	$0.436042\pi$
$992$	−7.65367	+	18.4776i	−0.243004	+	0.586664i
$993$		0			0
$994$	11.3137	−	11.3137i	0.358849	−	0.358849i
$995$	−28.2843	+	28.2843i	−0.896672	+	0.896672i
$996$		0			0
$997$	−17.6034	+	42.4985i	−0.557506	+	1.34594i	0.354228	+	0.935159i	$0.384744\pi$
$997$	−17.6034	+	42.4985i	−0.557506	+	1.34594i	−0.911734	+	0.410781i	$0.865256\pi$
$998$	−36.9552	+	15.3073i	−1.16980	+	0.484545i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.d.d.134.1		8
17.2	even	8	inner	289.2.d.d.179.2		8
17.3	odd	16		289.2.b.a.288.1		2
17.4	even	4	inner	289.2.d.d.155.2		8
17.5	odd	16		289.2.a.a.1.1		1
17.6	odd	16		289.2.c.a.251.2		4
17.7	odd	16		289.2.c.a.38.2		4
17.8	even	8	inner	289.2.d.d.110.1		8
17.9	even	8	inner	289.2.d.d.110.2		8
17.10	odd	16		289.2.c.a.38.1		4
17.11	odd	16		289.2.c.a.251.1		4
17.12	odd	16		17.2.a.a.1.1	✓	1
17.13	even	4	inner	289.2.d.d.155.1		8
17.14	odd	16		289.2.b.a.288.2		2
17.15	even	8	inner	289.2.d.d.179.1		8
17.16	even	2	inner	289.2.d.d.134.2		8
51.5	even	16		2601.2.a.g.1.1		1
51.29	even	16		153.2.a.c.1.1		1
68.39	even	16		4624.2.a.d.1.1		1
68.63	even	16		272.2.a.b.1.1		1
85.12	even	16		425.2.b.b.324.1		2
85.29	odd	16		425.2.a.d.1.1		1
85.39	odd	16		7225.2.a.g.1.1		1
85.63	even	16		425.2.b.b.324.2		2
119.12	even	48		833.2.e.a.18.1		2
119.46	odd	48		833.2.e.b.324.1		2
119.80	even	48		833.2.e.a.324.1		2
119.97	even	16		833.2.a.a.1.1		1
119.114	odd	48		833.2.e.b.18.1		2
136.29	odd	16		1088.2.a.i.1.1		1
136.131	even	16		1088.2.a.h.1.1		1
187.131	even	16		2057.2.a.e.1.1		1
204.131	odd	16		2448.2.a.o.1.1		1
221.12	odd	16		2873.2.a.c.1.1		1
255.29	even	16		3825.2.a.d.1.1		1
323.284	even	16		6137.2.a.b.1.1		1
340.199	even	16		6800.2.a.n.1.1		1
357.335	odd	16		7497.2.a.l.1.1		1
391.114	even	16		8993.2.a.a.1.1		1
408.29	even	16		9792.2.a.n.1.1		1
408.131	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	17.12	odd	16
153.2.a.c.1.1		1	51.29	even	16
272.2.a.b.1.1		1	68.63	even	16
289.2.a.a.1.1		1	17.5	odd	16
289.2.b.a.288.1		2	17.3	odd	16
289.2.b.a.288.2		2	17.14	odd	16
289.2.c.a.38.1		4	17.10	odd	16
289.2.c.a.38.2		4	17.7	odd	16
289.2.c.a.251.1		4	17.11	odd	16
289.2.c.a.251.2		4	17.6	odd	16
289.2.d.d.110.1		8	17.8	even	8	inner
289.2.d.d.110.2		8	17.9	even	8	inner
289.2.d.d.134.1		8	1.1	even	1	trivial
289.2.d.d.134.2		8	17.16	even	2	inner
289.2.d.d.155.1		8	17.13	even	4	inner
289.2.d.d.155.2		8	17.4	even	4	inner
289.2.d.d.179.1		8	17.15	even	8	inner
289.2.d.d.179.2		8	17.2	even	8	inner
425.2.a.d.1.1		1	85.29	odd	16
425.2.b.b.324.1		2	85.12	even	16
425.2.b.b.324.2		2	85.63	even	16
833.2.a.a.1.1		1	119.97	even	16
833.2.e.a.18.1		2	119.12	even	48
833.2.e.a.324.1		2	119.80	even	48
833.2.e.b.18.1		2	119.114	odd	48
833.2.e.b.324.1		2	119.46	odd	48
1088.2.a.h.1.1		1	136.131	even	16
1088.2.a.i.1.1		1	136.29	odd	16
2057.2.a.e.1.1		1	187.131	even	16
2448.2.a.o.1.1		1	204.131	odd	16
2601.2.a.g.1.1		1	51.5	even	16
2873.2.a.c.1.1		1	221.12	odd	16
3825.2.a.d.1.1		1	255.29	even	16
4624.2.a.d.1.1		1	68.39	even	16
6137.2.a.b.1.1		1	323.284	even	16
6800.2.a.n.1.1		1	340.199	even	16
7225.2.a.g.1.1		1	85.39	odd	16
7497.2.a.l.1.1		1	357.335	odd	16
8993.2.a.a.1.1		1	391.114	even	16
9792.2.a.i.1.1		1	408.131	odd	16
9792.2.a.n.1.1		1	408.29	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)

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