LMFDB - Embedded newform 289.2.d.d.110.2

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			110.2
Root			$0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.110
Dual form			289.2.d.d.134.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{8}\right)$

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	−0.411438	−	0.911438i	$-0.634973\pi$
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i	0.911438	+	0.411438i	$0.134973\pi$
$3$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$3$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$4$			1.00000i			0.500000i
$5$	1.84776	+	0.765367i	0.826343	+	0.342282i	0.755454	−	0.655202i	$-0.227416\pi$
$5$	1.84776	+	0.765367i	0.826343	+	0.342282i	0.0708890	+	0.997484i	$0.477416\pi$
$6$		0			0
$7$	−3.69552	+	1.53073i	−1.39677	+	0.578563i	−0.948912	−	0.315540i	$-0.897814\pi$
$7$	−3.69552	+	1.53073i	−1.39677	+	0.578563i	−0.447862	+	0.894103i	$0.647814\pi$
$8$	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	$-0.125000\pi$
$11$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−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	−0.303838	−	0.952724i	$-0.598268\pi$
$19$	2.82843	−	2.82843i	0.648886	−	0.648886i	0.952724	+	0.303838i	$0.0982682\pi$
$20$	−0.765367	+	1.84776i	−0.171141	+	0.413171i
$21$		0			0
$22$		0			0
$23$	−1.53073	−	3.69552i	−0.319180	−	0.770569i	−0.999298	−	0.0374660i	$-0.988071\pi$
$23$	−1.53073	−	3.69552i	−0.319180	−	0.770569i	0.680118	−	0.733103i	$-0.261929\pi$
$24$		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	$-0.186919\pi$
$29$	5.54328	+	2.29610i	1.02936	+	0.426375i	0.196879	+	0.980428i	$0.436919\pi$
$30$		0			0
$31$	1.53073	−	3.69552i	0.274928	−	0.663735i	−0.724753	−	0.689009i	$-0.758046\pi$
$31$	1.53073	−	3.69552i	0.274928	−	0.663735i	0.999681	+	0.0252745i	$0.00804598\pi$
$32$	−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	$-0.822432\pi$
$37$	0.765367	−	1.84776i	0.125826	−	0.303770i	0.974222	+	0.225592i	$0.0724315\pi$
$38$		−	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	$-0.469787\pi$
$41$	5.54328	−	2.29610i	0.865714	−	0.358591i	0.770940	+	0.636908i	$0.219787\pi$
$42$		0			0
$43$	−2.82843	−	2.82843i	−0.431331	−	0.431331i	0.457750	−	0.889081i	$-0.348656\pi$
$43$	−2.82843	−	2.82843i	−0.431331	−	0.431331i	−0.889081	+	0.457750i	$0.848656\pi$
$44$		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	−0.935664	−	0.352892i	$-0.885198\pi$
$53$	−4.24264	+	4.24264i	−0.582772	+	0.582772i	0.352892	+	0.935664i	$0.385198\pi$
$54$		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	−0.993837	−	0.110853i	$-0.964642\pi$
$59$	−8.48528	−	8.48528i	−1.10469	−	1.10469i	−0.110853	−	0.993837i	$-0.535358\pi$
$60$		0			0
$61$	−9.23880	+	3.82683i	−1.18291	+	0.489976i	−0.885439	−	0.464756i	$-0.846142\pi$
$61$	−9.23880	+	3.82683i	−1.18291	+	0.489976i	−0.297468	+	0.954732i	$0.596142\pi$
$62$	−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	$-0.798719\pi$
$71$	1.53073	−	3.69552i	0.181665	−	0.438577i	0.988310	+	0.152459i	$0.0487191\pi$
$72$			9.00000i			1.06066i
$73$	5.54328	+	2.29610i	0.648792	+	0.268738i	0.682713	−	0.730686i	$-0.260800\pi$
$73$	5.54328	+	2.29610i	0.648792	+	0.268738i	−0.0339219	+	0.999424i	$0.510800\pi$
$74$	−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	0.939942	+	0.341335i	$0.110879\pi$
$79$	4.59220	+	11.0866i	0.516663	+	1.24733i	−0.423279	+	0.906000i	$0.639121\pi$
$80$	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	−0.845088	−	0.534628i	$-0.820452\pi$
$83$	−2.82843	+	2.82843i	−0.310460	+	0.310460i	0.534628	+	0.845088i	$0.320452\pi$
$84$		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	$-0.177808\pi$
$90$	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	$-0.342625\pi$
$97$	1.84776	+	0.765367i	0.187612	+	0.0777112i	−0.286900	+	0.957961i	$0.592625\pi$
$98$		−	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	$-0.501383\pi$
$107$	−7.39104	−	3.06147i	−0.714518	−	0.295963i	−0.710173	+	0.704027i	$0.751383\pi$
$108$		0			0
$109$	−5.54328	+	2.29610i	−0.530950	+	0.219927i	−0.632019	−	0.774953i	$-0.717774\pi$
$109$	−5.54328	+	2.29610i	−0.530950	+	0.219927i	0.101069	+	0.994879i	$0.467774\pi$
$110$		0			0
$111$		0			0
$112$	−3.69552	+	1.53073i	−0.349194	+	0.144641i
$113$	−5.35757	−	12.9343i	−0.503998	−	1.21676i	−0.947289	−	0.320380i	$-0.896189\pi$
$113$	−5.35757	−	12.9343i	−0.503998	−	1.21676i	0.443291	−	0.896378i	$-0.353811\pi$
$114$		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	0.912048	−	0.410083i	$-0.134500\pi$
$127$	5.65685	+	5.65685i	0.501965	+	0.501965i	−0.410083	+	0.912048i	$0.634500\pi$
$128$	−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	$-0.128645\pi$
$131$	14.7821	+	6.12293i	1.29152	+	0.534963i	0.372079	+	0.928201i	$0.378645\pi$
$132$		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	$-0.764818\pi$
$139$	3.06147	−	7.39104i	0.259670	−	0.626900i	0.998917	+	0.0465356i	$0.0148181\pi$
$140$		−	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	$-0.865663\pi$
$149$		−	10.0000i		−	0.819232i	0.912258	−	0.409616i	$-0.134337\pi$
$150$		0			0
$151$	−11.3137	+	11.3137i	−0.920697	+	0.920697i	−0.997079	−	0.0763821i	$-0.975663\pi$
$151$	−11.3137	+	11.3137i	−0.920697	+	0.920697i	0.0763821	+	0.997079i	$0.475663\pi$
$152$	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	$0.974569\pi$
$158$	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	0.737712	−	0.675116i	$-0.235906\pi$
$163$	22.1731	−	9.18440i	1.73673	−	0.719378i	0.999020	−	0.0442623i	$-0.0140937\pi$
$164$	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	$-0.924462\pi$
$167$	−1.53073	+	3.69552i	−0.118452	+	0.285968i	0.853522	+	0.521057i	$0.174462\pi$
$168$		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	0.186473	+	0.982460i	$0.440294\pi$
$173$	−8.41904	+	20.3253i	−0.640087	+	1.54531i	−0.826561	+	0.562848i	$0.809706\pi$
$174$		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	0.314904	−	0.949124i	$-0.398028\pi$
$179$	−8.48528	−	8.48528i	−0.634220	−	0.634220i	−0.949124	+	0.314904i	$0.898028\pi$
$180$	−5.54328	+	2.29610i	−0.413171	+	0.171141i
$181$	−0.765367	−	1.84776i	−0.0568893	−	0.137343i	0.892879	−	0.450296i	$-0.148682\pi$
$181$	−0.765367	−	1.84776i	−0.0568893	−	0.137343i	−0.949768	+	0.312953i	$0.898682\pi$
$182$	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	$0.196502\pi$
$191$			16.0000i			1.15772i	−0.815427	+	0.578860i	$0.803498\pi$
$192$		0			0
$193$	−0.765367	−	1.84776i	−0.0550923	−	0.133005i	0.893937	−	0.448193i	$-0.147932\pi$
$193$	−0.765367	−	1.84776i	−0.0550923	−	0.133005i	−0.949029	+	0.315188i	$0.897932\pi$
$194$	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	$-0.846573\pi$
$197$	−16.6298	+	6.88830i	−1.18483	+	0.490771i	−0.298759	+	0.954328i	$0.596573\pi$
$198$		0			0
$199$	−18.4776	−	7.65367i	−1.30984	−	0.542554i	−0.385004	−	0.922915i	$-0.625800\pi$
$199$	−18.4776	−	7.65367i	−1.30984	−	0.542554i	−0.924838	+	0.380361i	$0.875800\pi$
$200$		−	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	$-0.713801\pi$
$211$	−7.39104	+	3.06147i	−0.508820	+	0.210760i	0.113478	+	0.993540i	$0.463801\pi$
$212$	−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	−0.147348	+	0.989085i	$0.547074\pi$
$223$	−16.9706	+	16.9706i	−1.13643	+	1.13643i	−0.989085	+	0.147348i	$0.952926\pi$
$224$	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	0.863447	+	0.504439i	$0.168301\pi$
$227$	9.18440	+	22.1731i	0.609590	+	1.47168i	−0.253857	+	0.967242i	$0.581699\pi$
$228$		0			0
$229$	4.24264	+	4.24264i	0.280362	+	0.280362i	0.833253	−	0.552892i	$-0.186476\pi$
$229$	4.24264	+	4.24264i	0.280362	+	0.280362i	−0.552892	+	0.833253i	$0.686476\pi$
$230$	−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	$-0.437969\pi$
$233$	−5.54328	−	2.29610i	−0.363152	−	0.150423i	−0.556796	+	0.830649i	$0.687969\pi$
$234$		−	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	0.530921	+	0.847422i	$0.321846\pi$
$241$	−6.88830	+	16.6298i	−0.443715	+	1.07122i	−0.974635	+	0.223800i	$0.928154\pi$
$242$		−	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	$0.123635\pi$
$251$			12.0000i			0.757433i	−0.925513	+	0.378717i	$0.876365\pi$
$252$	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	−0.982133	−	0.188187i	$-0.939739\pi$
$257$	−12.7279	+	12.7279i	−0.793946	+	0.793946i	0.188187	+	0.982133i	$0.439739\pi$
$258$		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	0.266266	−	0.963899i	$-0.414210\pi$
$263$	−11.3137	−	11.3137i	−0.697633	−	0.697633i	−0.963899	+	0.266266i	$0.914210\pi$
$264$		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	−0.428624	−	0.903483i	$-0.641002\pi$
$269$	8.41904	−	20.3253i	0.513318	−	1.23926i	0.941942	−	0.335776i	$-0.108998\pi$
$270$		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	$-0.513177\pi$
$277$	−12.9343	−	5.35757i	−0.777148	−	0.321905i	−0.735764	+	0.677238i	$0.763177\pi$
$278$	−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	0.822238	−	0.569143i	$-0.192725\pi$
$281$	4.24264	+	4.24264i	0.253095	+	0.253095i	−0.569143	+	0.822238i	$0.692725\pi$
$282$		0			0
$283$	−6.12293	−	14.7821i	−0.363971	−	0.878703i	−0.994711	−	0.102709i	$-0.967249\pi$
$283$	−6.12293	−	14.7821i	−0.363971	−	0.878703i	0.630741	−	0.775994i	$-0.282751\pi$
$284$	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	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$		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	$-0.666935\pi$
$311$	−25.8686	−	10.7151i	−1.46688	−	0.607600i	−0.966144	+	0.258003i	$0.916935\pi$
$312$		0			0
$313$	20.3253	−	8.41904i	1.14886	−	0.475872i	0.274707	−	0.961528i	$-0.411419\pi$
$313$	20.3253	−	8.41904i	1.14886	−	0.475872i	0.874150	+	0.485656i	$0.161419\pi$
$314$	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	$-0.215609\pi$
$317$	−3.82683	−	9.23880i	−0.214936	−	0.518902i	−0.994169	+	0.107832i	$0.965609\pi$
$318$		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	0.780553	−	0.625089i	$-0.214937\pi$
$331$	2.82843	+	2.82843i	0.155464	+	0.155464i	−0.625089	+	0.780553i	$0.714937\pi$
$332$	−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	$-0.999528\pi$
$337$	−5.35757	+	12.9343i	−0.291845	+	0.704577i	0.708154	+	0.706058i	$0.249528\pi$
$338$	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	$-0.953867\pi$
$347$	−29.5641	+	12.2459i	−1.58709	+	0.657393i	−0.597571	+	0.801816i	$0.703867\pi$
$348$		0			0
$349$	12.7279	+	12.7279i	0.681310	+	0.681310i	0.960295	−	0.278985i	$-0.0899981\pi$
$349$	12.7279	+	12.7279i	0.681310	+	0.681310i	−0.278985	+	0.960295i	$0.589998\pi$
$350$	3.69552	−	1.53073i	0.197534	−	0.0818212i
$351$		0			0
$352$		0			0
$353$		−	30.0000i		−	1.59674i	−0.602168	−	0.798369i	$-0.705696\pi$
$353$		−	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	$0.250000\pi$
$360$	−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	$-0.364150\pi$
$367$	25.8686	−	10.7151i	1.35033	−	0.559326i	0.936385	+	0.350976i	$0.114150\pi$
$368$	−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	$-0.309129\pi$
$379$	7.39104	+	3.06147i	0.379652	+	0.157257i	−0.184693	+	0.982796i	$0.559129\pi$
$380$	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	0.992157	−	0.125001i	$-0.0398935\pi$
$383$	16.9706	+	16.9706i	0.867155	+	0.867155i	−0.125001	+	0.992157i	$0.539894\pi$
$384$		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	−0.591324	−	0.806434i	$-0.701394\pi$
$389$	4.24264	−	4.24264i	0.215110	−	0.215110i	0.806434	+	0.591324i	$0.201394\pi$
$390$		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	$-0.173110\pi$
$397$	−2.29610	−	5.54328i	−0.115238	−	0.278209i	−0.970966	+	0.239216i	$0.923110\pi$
$398$	−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	$-0.738670\pi$
$401$	−12.9343	+	5.35757i	−0.645909	+	0.267544i	0.0355866	+	0.999367i	$0.488670\pi$
$402$		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	$-0.0623953\pi$
$419$	3.06147	+	7.39104i	0.149562	+	0.361076i	−0.831287	+	0.555844i	$0.812395\pi$
$420$		0			0
$421$			22.0000i			1.07221i	0.844150	+	0.536107i	$0.180106\pi$
$421$			22.0000i			1.07221i	−0.844150	+	0.536107i	$0.819894\pi$
$422$	−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	$-0.218326\pi$
$431$	−4.59220	−	11.0866i	−0.221199	−	0.534021i	−0.995053	+	0.0993426i	$0.968326\pi$
$432$		0			0
$433$	1.41421	+	1.41421i	0.0679628	+	0.0679628i	0.740271	−	0.672308i	$-0.234697\pi$
$433$	1.41421	+	1.41421i	0.0679628	+	0.0679628i	−0.672308	+	0.740271i	$0.734697\pi$
$434$	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	0.629219	+	0.777228i	$0.283375\pi$
$439$	−7.65367	+	18.4776i	−0.365290	+	0.881887i	−0.994508	+	0.104659i	$0.966625\pi$
$440$		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	$-0.921380\pi$
$449$	−31.4119	+	13.0112i	−1.48242	+	0.614038i	−0.512767	+	0.858528i	$0.671380\pi$
$450$	−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	−0.799341	−	0.600878i	$-0.794818\pi$
$457$	−4.24264	+	4.24264i	−0.198462	+	0.198462i	0.600878	+	0.799341i	$0.294818\pi$
$458$	6.00000			0.280362
$459$		0			0
$460$	8.00000			0.373002
$461$	1.41421	−	1.41421i	0.0658665	−	0.0658665i	−0.673406	−	0.739273i	$-0.735169\pi$
$461$	1.41421	−	1.41421i	0.0658665	−	0.0658665i	0.739273	+	0.673406i	$0.235169\pi$
$462$		0			0
$463$		−	32.0000i		−	1.48717i	−0.668644	−	0.743583i	$-0.733125\pi$
$463$		−	32.0000i		−	1.48717i	0.668644	−	0.743583i	$-0.266875\pi$
$464$	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	0.875632	−	0.482980i	$-0.160445\pi$
$467$	8.48528	+	8.48528i	0.392652	+	0.392652i	−0.482980	+	0.875632i	$0.660445\pi$
$468$	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	0.210815	+	0.977526i	$0.432388\pi$
$479$	−13.7766	+	33.2597i	−0.629469	+	1.51967i	−0.840284	+	0.542147i	$0.817612\pi$
$480$		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	0.996991	+	0.0775113i	$0.0246974\pi$
$487$	7.65367	+	18.4776i	0.346821	+	0.837300i	−0.650171	+	0.759788i	$0.725303\pi$
$488$	−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	−0.311892	−	0.950118i	$-0.600963\pi$
$491$	14.1421	−	14.1421i	0.638226	−	0.638226i	0.950118	+	0.311892i	$0.100963\pi$
$492$		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	0.754137	+	0.656717i	$0.228055\pi$
$499$	15.3073	+	36.9552i	0.685251	+	1.65434i	−0.0688869	+	0.997624i	$0.521945\pi$
$500$	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	$-0.711206\pi$
$503$	−11.0866	+	4.59220i	−0.494325	+	0.204756i	0.121572	+	0.992583i	$0.461206\pi$
$504$	−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	0.977349	+	0.211635i	$0.0678788\pi$
$521$	9.94977	+	24.0209i	0.435907	+	1.05237i	−0.541441	+	0.840738i	$0.682121\pi$
$522$	16.6298	+	6.88830i	0.727868	+	0.301493i
$523$		−	36.0000i		−	1.57417i	−0.616844	−	0.787085i	$-0.711589\pi$
$523$		−	36.0000i		−	1.57417i	0.616844	−	0.787085i	$-0.288411\pi$
$524$	−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	$-0.833830\pi$
$541$	2.29610	−	5.54328i	0.0987171	−	0.238324i	0.965521	+	0.260325i	$0.0838297\pi$
$542$	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	−0.412060	−	0.911157i	$-0.635191\pi$
$547$	12.2459	−	29.5641i	0.523596	−	1.26407i	0.935655	−	0.352915i	$-0.114809\pi$
$548$		−	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	$0.219235\pi$
$557$			30.0000i			1.27114i	−0.772043	+	0.635570i	$0.780765\pi$
$558$	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	−0.644988	−	0.764192i	$-0.723138\pi$
$563$	2.82843	−	2.82843i	0.119204	−	0.119204i	0.764192	+	0.644988i	$0.223138\pi$
$564$		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	−0.990750	−	0.135702i	$-0.956671\pi$
$569$	−26.8701	−	26.8701i	−1.12645	−	1.12645i	−0.135702	−	0.990750i	$-0.543329\pi$
$570$		0			0
$571$	−29.5641	+	12.2459i	−1.23722	+	0.512474i	−0.902845	−	0.429966i	$-0.858526\pi$
$571$	−29.5641	+	12.2459i	−1.23722	+	0.512474i	−0.334376	+	0.942440i	$0.608526\pi$
$572$		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	0.646323	−	0.763064i	$-0.276306\pi$
$587$	−2.82843	−	2.82843i	−0.116742	−	0.116742i	−0.763064	+	0.646323i	$0.776306\pi$
$588$		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	−0.395705	−	0.918378i	$-0.629500\pi$
$593$	12.7279	−	12.7279i	0.522673	−	0.522673i	0.918378	+	0.395705i	$0.129500\pi$
$594$		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	$0.163115\pi$
$599$			24.0000i			0.980613i	−0.871550	+	0.490307i	$0.836885\pi$
$600$		0			0
$601$	−3.82683	−	9.23880i	−0.156100	−	0.376858i	0.826410	−	0.563069i	$-0.190379\pi$
$601$	−3.82683	−	9.23880i	−0.156100	−	0.376858i	−0.982510	+	0.186210i	$0.940379\pi$
$602$	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	$-0.241962\pi$
$607$	18.4776	+	7.65367i	0.749982	+	0.310653i	0.0252479	+	0.999681i	$0.491962\pi$
$608$			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	$-0.336462\pi$
$617$	5.54328	+	2.29610i	0.223164	+	0.0924375i	−0.268300	+	0.963335i	$0.586462\pi$
$618$		0			0
$619$	44.3462	−	18.3688i	1.78242	−	0.738305i	0.790350	−	0.612655i	$-0.209899\pi$
$619$	44.3462	−	18.3688i	1.78242	−	0.738305i	0.992075	−	0.125649i	$-0.0401014\pi$
$620$	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	−0.895484	−	0.445093i	$-0.853171\pi$
$631$	−11.3137	+	11.3137i	−0.450392	+	0.450392i	0.445093	+	0.895484i	$0.353171\pi$
$632$	−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	$-0.576845\pi$
$641$	−27.7164	−	11.4805i	−1.09473	−	0.453453i	−0.855654	+	0.517548i	$0.826845\pi$
$642$		0			0
$643$	12.2459	−	29.5641i	0.482930	−	1.16590i	−0.475281	−	0.879834i	$-0.657654\pi$
$643$	12.2459	−	29.5641i	0.482930	−	1.16590i	0.958211	−	0.286062i	$-0.0923464\pi$
$644$	−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	$-0.662456\pi$
$653$	−5.54328	+	2.29610i	−0.216925	+	0.0898534i	0.271575	+	0.962417i	$0.412456\pi$
$654$		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	$0.0248243\pi$
$659$			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	$-0.485292\pi$
$661$	26.8701	−	26.8701i	1.04512	−	1.04512i	0.998933	−	0.0461915i	$-0.0147084\pi$
$662$	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	$-0.612727\pi$
$673$	1.84776	−	0.765367i	0.0712259	−	0.0295027i	0.418012	+	0.908442i	$0.362727\pi$
$674$	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	−0.534286	−	0.845304i	$-0.679419\pi$
$677$	11.4805	−	27.7164i	0.441232	−	1.06523i	0.975517	−	0.219923i	$-0.0705807\pi$
$678$		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	−0.301841	−	0.953358i	$-0.597601\pi$
$683$	15.3073	−	36.9552i	0.585719	−	1.41405i	0.887560	−	0.460692i	$-0.152399\pi$
$684$			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	$-0.173625\pi$
$691$	−3.06147	−	7.39104i	−0.116464	−	0.281168i	−0.971353	+	0.237643i	$0.923625\pi$
$692$	−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	$0.110402\pi$
$701$			18.0000i			0.679851i	−0.940452	+	0.339925i	$0.889598\pi$
$702$		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	$-0.595423\pi$
$709$	−31.4119	−	13.0112i	−1.17970	−	0.488647i	−0.884387	+	0.466754i	$0.845423\pi$
$710$		−	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	$-0.398764\pi$
$719$	−3.69552	−	1.53073i	−0.137820	−	0.0570867i	−0.450527	+	0.892763i	$0.648764\pi$
$720$	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	$0.266008\pi$
$727$			40.0000i			1.48352i	−0.670667	+	0.741759i	$0.733992\pi$
$728$	−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	0.381518	−	0.924362i	$-0.375402\pi$
$733$	35.3553	−	35.3553i	1.30588	−	1.30588i	0.924362	−	0.381518i	$-0.124598\pi$
$734$	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	0.970285	−	0.241967i	$-0.0777925\pi$
$739$	19.7990	+	19.7990i	0.728318	+	0.728318i	−0.241967	+	0.970285i	$0.577793\pi$
$740$	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	$-0.304356\pi$
$743$	11.0866	+	4.59220i	0.406726	+	0.168472i	−0.169934	+	0.985455i	$0.554356\pi$
$744$		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	$-0.993899\pi$
$751$	−7.65367	+	18.4776i	−0.279286	+	0.674257i	0.720530	+	0.693424i	$0.243899\pi$
$752$		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	0.365433	−	0.930838i	$-0.380921\pi$
$757$	−15.5563	−	15.5563i	−0.565405	−	0.565405i	−0.930838	+	0.365433i	$0.880921\pi$
$758$	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	$-0.869444\pi$
$761$		−	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
$772$	1.84776	−	0.765367i	0.0665023	−	0.0275462i
$773$	−18.3848	−	18.3848i	−0.661254	−	0.661254i	0.294421	−	0.955676i	$-0.404873\pi$
$773$	−18.3848	−	18.3848i	−0.661254	−	0.661254i	−0.955676	+	0.294421i	$0.904873\pi$
$774$	−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	$-0.181812\pi$
$787$	29.5641	+	12.2459i	1.05385	+	0.436518i	0.212584	+	0.977143i	$0.431812\pi$
$788$	−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	−0.297687	+	0.954664i	$0.596215\pi$
$797$	−35.3553	+	35.3553i	−1.25235	+	1.25235i	−0.954664	+	0.297687i	$0.903785\pi$
$798$		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	$-0.473904\pi$
$809$	24.0209	−	9.94977i	0.844529	−	0.349815i	0.762638	+	0.646826i	$0.223904\pi$
$810$	6.88830	+	16.6298i	0.242030	+	0.584313i
$811$	36.9552	+	15.3073i	1.29767	+	0.537513i	0.921263	−	0.388940i	$-0.127159\pi$
$811$	36.9552	+	15.3073i	1.29767	+	0.537513i	0.376409	+	0.926454i	$0.377159\pi$
$812$		−	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	$-0.273297\pi$
$821$	16.6298	+	6.88830i	0.580385	+	0.240403i	−0.0731230	+	0.997323i	$0.523297\pi$
$822$		0			0
$823$	−18.4776	+	7.65367i	−0.644088	+	0.266790i	−0.680726	−	0.732539i	$-0.738335\pi$
$823$	−18.4776	+	7.65367i	−0.644088	+	0.266790i	0.0366373	+	0.999329i	$0.488335\pi$
$824$	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	−0.828351	−	0.560209i	$-0.810721\pi$
$827$	−18.3688	−	44.3462i	−0.638746	−	1.54207i	0.189606	−	0.981860i	$-0.439279\pi$
$828$	11.0866	+	4.59220i	0.385284	+	0.159590i
$829$		−	34.0000i		−	1.18087i	−0.807086	−	0.590434i	$-0.798956\pi$
$829$		−	34.0000i		−	1.18087i	0.807086	−	0.590434i	$-0.201044\pi$
$830$	−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	$-0.237202\pi$
$839$	−7.65367	−	18.4776i	−0.264234	−	0.637917i	−0.999192	+	0.0401955i	$0.987202\pi$
$840$		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	$-0.952041\pi$
$853$	−5.35757	+	12.9343i	−0.183440	+	0.442862i	0.805231	+	0.592961i	$0.202041\pi$
$854$		−	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	$-0.679634\pi$
$857$	−9.23880	+	3.82683i	−0.315591	+	0.130722i	0.219265	+	0.975665i	$0.429634\pi$
$858$		0			0
$859$	−36.7696	−	36.7696i	−1.25456	−	1.25456i	−0.953653	−	0.300908i	$-0.902710\pi$
$859$	−36.7696	−	36.7696i	−1.25456	−	1.25456i	−0.300908	−	0.953653i	$-0.597290\pi$
$860$	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	$0.0877920\pi$
$863$			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
$872$	−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	$-0.592699\pi$
$877$	5.54328	−	2.29610i	0.187183	−	0.0775338i	0.474306	+	0.880360i	$0.342699\pi$
$878$	7.65367	+	18.4776i	0.258299	+	0.623588i
$879$		0			0
$880$		0			0
$881$	−17.6034	+	42.4985i	−0.593075	+	1.43181i	0.287444	+	0.957798i	$0.407195\pi$
$881$	−17.6034	+	42.4985i	−0.593075	+	1.43181i	−0.880518	+	0.474012i	$0.842805\pi$
$882$	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	$-0.939569\pi$
$887$	−4.59220	+	11.0866i	−0.154191	+	0.372250i	0.827841	+	0.560962i	$0.189569\pi$
$888$		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	−0.986021	−	0.166621i	$-0.946714\pi$
$907$	−12.2459	−	29.5641i	−0.406617	−	0.981661i	0.579404	−	0.815041i	$-0.303286\pi$
$908$	−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	$-0.646108\pi$
$911$	−3.69552	+	1.53073i	−0.122438	+	0.0507155i	0.320623	+	0.947207i	$0.396108\pi$
$912$		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	−0.992587	−	0.121539i	$-0.961217\pi$
$929$	−11.4805	−	27.7164i	−0.376663	−	0.909345i	0.615924	−	0.787806i	$-0.288783\pi$
$930$		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	−0.813111	−	0.582109i	$-0.802228\pi$
$937$	−7.07107	+	7.07107i	−0.231002	+	0.231002i	0.582109	+	0.813111i	$0.302228\pi$
$938$	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	$-0.156180\pi$
$941$	−2.29610	−	5.54328i	−0.0748507	−	0.180706i	−0.956876	+	0.290496i	$0.906180\pi$
$942$		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	$-0.200958\pi$
$947$	29.5641	+	12.2459i	0.960706	+	0.397937i	0.153461	+	0.988155i	$0.450958\pi$
$948$		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	$-0.750000\pi$
$967$		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	−0.557722	−	0.830028i	$-0.688325\pi$
$971$	8.48528	−	8.48528i	0.272306	−	0.272306i	0.830028	+	0.557722i	$0.188325\pi$
$972$		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	0.880762	−	0.473560i	$-0.157031\pi$
$977$	12.7279	+	12.7279i	0.407202	+	0.407202i	−0.473560	+	0.880762i	$0.657031\pi$
$978$		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	$-0.813707\pi$
$983$	4.59220	−	11.0866i	0.146468	−	0.353606i	0.980039	+	0.198808i	$0.0637069\pi$
$984$		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	$-0.313958\pi$
$991$	11.0866	+	4.59220i	0.352176	+	0.145876i	−0.199580	+	0.979881i	$0.563958\pi$
$992$	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	0.911734	+	0.410781i	$0.134744\pi$
$997$	17.6034	+	42.4985i	0.557506	+	1.34594i	−0.354228	+	0.935159i	$0.615256\pi$
$998$	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.110.2		8
17.2	even	8	inner	289.2.d.d.134.1		8
17.3	odd	16		289.2.c.a.38.1		4
17.4	even	4	inner	289.2.d.d.179.2		8
17.5	odd	16		289.2.c.a.251.1		4
17.6	odd	16		289.2.b.a.288.1		2
17.7	odd	16		17.2.a.a.1.1	✓	1
17.8	even	8	inner	289.2.d.d.155.2		8
17.9	even	8	inner	289.2.d.d.155.1		8
17.10	odd	16		289.2.a.a.1.1		1
17.11	odd	16		289.2.b.a.288.2		2
17.12	odd	16		289.2.c.a.251.2		4
17.13	even	4	inner	289.2.d.d.179.1		8
17.14	odd	16		289.2.c.a.38.2		4
17.15	even	8	inner	289.2.d.d.134.2		8
17.16	even	2	inner	289.2.d.d.110.1		8
51.41	even	16		153.2.a.c.1.1		1
51.44	even	16		2601.2.a.g.1.1		1
68.7	even	16		272.2.a.b.1.1		1
68.27	even	16		4624.2.a.d.1.1		1
85.7	even	16		425.2.b.b.324.1		2
85.24	odd	16		425.2.a.d.1.1		1
85.44	odd	16		7225.2.a.g.1.1		1
85.58	even	16		425.2.b.b.324.2		2
119.24	even	48		833.2.e.a.324.1		2
119.41	even	16		833.2.a.a.1.1		1
119.58	odd	48		833.2.e.b.18.1		2
119.75	even	48		833.2.e.a.18.1		2
119.109	odd	48		833.2.e.b.324.1		2
136.75	even	16		1088.2.a.h.1.1		1
136.109	odd	16		1088.2.a.i.1.1		1
187.109	even	16		2057.2.a.e.1.1		1
204.143	odd	16		2448.2.a.o.1.1		1
221.194	odd	16		2873.2.a.c.1.1		1
255.194	even	16		3825.2.a.d.1.1		1
323.75	even	16		6137.2.a.b.1.1		1
340.279	even	16		6800.2.a.n.1.1		1
357.41	odd	16		7497.2.a.l.1.1		1
391.160	even	16		8993.2.a.a.1.1		1
408.245	even	16		9792.2.a.n.1.1		1
408.347	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	17.7	odd	16
153.2.a.c.1.1		1	51.41	even	16
272.2.a.b.1.1		1	68.7	even	16
289.2.a.a.1.1		1	17.10	odd	16
289.2.b.a.288.1		2	17.6	odd	16
289.2.b.a.288.2		2	17.11	odd	16
289.2.c.a.38.1		4	17.3	odd	16
289.2.c.a.38.2		4	17.14	odd	16
289.2.c.a.251.1		4	17.5	odd	16
289.2.c.a.251.2		4	17.12	odd	16
289.2.d.d.110.1		8	17.16	even	2	inner
289.2.d.d.110.2		8	1.1	even	1	trivial
289.2.d.d.134.1		8	17.2	even	8	inner
289.2.d.d.134.2		8	17.15	even	8	inner
289.2.d.d.155.1		8	17.9	even	8	inner
289.2.d.d.155.2		8	17.8	even	8	inner
289.2.d.d.179.1		8	17.13	even	4	inner
289.2.d.d.179.2		8	17.4	even	4	inner
425.2.a.d.1.1		1	85.24	odd	16
425.2.b.b.324.1		2	85.7	even	16
425.2.b.b.324.2		2	85.58	even	16
833.2.a.a.1.1		1	119.41	even	16
833.2.e.a.18.1		2	119.75	even	48
833.2.e.a.324.1		2	119.24	even	48
833.2.e.b.18.1		2	119.58	odd	48
833.2.e.b.324.1		2	119.109	odd	48
1088.2.a.h.1.1		1	136.75	even	16
1088.2.a.i.1.1		1	136.109	odd	16
2057.2.a.e.1.1		1	187.109	even	16
2448.2.a.o.1.1		1	204.143	odd	16
2601.2.a.g.1.1		1	51.44	even	16
2873.2.a.c.1.1		1	221.194	odd	16
3825.2.a.d.1.1		1	255.194	even	16
4624.2.a.d.1.1		1	68.27	even	16
6137.2.a.b.1.1		1	323.75	even	16
6800.2.a.n.1.1		1	340.279	even	16
7225.2.a.g.1.1		1	85.44	odd	16
7497.2.a.l.1.1		1	357.41	odd	16
8993.2.a.a.1.1		1	391.160	even	16
9792.2.a.i.1.1		1	408.347	odd	16
9792.2.a.n.1.1		1	408.245	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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