LMFDB - Embedded newform 891.2.u.e.701.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(107,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("891.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.u (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,0,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			701.3
Character	$\chi$	$=$	891.701
Dual form			891.2.u.e.755.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.931391 - 0.414682i) q^{2} +(-0.642733 - 0.713827i) q^{4} +(-1.26271 - 2.83609i) q^{5} +(0.870416 + 4.09498i) q^{7} +(0.932731 + 2.87065i) q^{8} +3.16513i q^{10} +(2.08952 - 2.57564i) q^{11} +(0.355243 - 0.0373375i) q^{13} +(0.887419 - 4.17498i) q^{14} +(0.120861 - 1.14991i) q^{16} +(2.52248 + 1.83269i) q^{17} +(-0.384024 + 0.124777i) q^{19} +(-1.21289 + 2.72420i) q^{20} +(-3.01423 + 1.53244i) q^{22} +(2.44458 + 1.41138i) q^{23} +(-3.10332 + 3.44658i) q^{25} +(-0.346353 - 0.112537i) q^{26} +(2.36367 - 3.25331i) q^{28} +(6.07102 - 1.29044i) q^{29} +(0.845730 + 8.04658i) q^{31} +(2.42897 - 4.20709i) q^{32} +(-1.58943 - 2.75298i) q^{34} +(10.5147 - 7.63935i) q^{35} +(1.01570 - 3.12601i) q^{37} +(0.409419 + 0.0430317i) q^{38} +(6.96366 - 6.27011i) q^{40} +(-7.43969 - 1.58136i) q^{41} +(8.02668 - 4.63421i) q^{43} +(-3.18156 + 0.163887i) q^{44} +(-1.69159 - 2.32827i) q^{46} +(-9.41156 - 8.47421i) q^{47} +(-9.61646 + 4.28152i) q^{49} +(4.31964 - 1.92323i) q^{50} +(-0.254979 - 0.229584i) q^{52} +(-2.07104 - 2.85055i) q^{53} +(-9.94319 - 2.67380i) q^{55} +(-10.9434 + 6.31818i) q^{56} +(-6.18962 - 1.31564i) q^{58} +(8.65424 - 7.79231i) q^{59} +(1.18232 + 0.124266i) q^{61} +(2.54907 - 7.84522i) q^{62} +(-5.87777 + 4.27045i) q^{64} +(-0.554460 - 0.960353i) q^{65} +(7.66446 - 13.2752i) q^{67} +(-0.313058 - 2.97855i) q^{68} +(-12.9612 + 2.75498i) q^{70} +(0.357651 - 0.492264i) q^{71} +(10.8303 + 3.51899i) q^{73} +(-2.24232 + 2.49035i) q^{74} +(0.335894 + 0.193928i) q^{76} +(12.3659 + 6.31469i) q^{77} +(1.96875 - 4.42189i) q^{79} +(-3.41387 + 1.10923i) q^{80} +(6.27351 + 4.55797i) q^{82} +(0.692635 - 6.58998i) q^{83} +(2.01251 - 9.46814i) q^{85} +(-9.39771 + 0.987739i) q^{86} +(9.34272 + 3.59592i) q^{88} +7.29922i q^{89} +(0.462105 + 1.42221i) q^{91} +(-0.563732 - 2.65215i) q^{92} +(5.25174 + 11.7956i) q^{94} +(0.838788 + 0.931569i) q^{95} +(-4.74976 - 2.11473i) q^{97} +10.7322 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{4} + 4 q^{16} - 36 q^{22} - 8 q^{25} - 200 q^{28} - 8 q^{31} + 64 q^{34} - 24 q^{37} + 60 q^{40} - 40 q^{46} - 100 q^{52} + 16 q^{55} - 24 q^{58} - 60 q^{61} + 72 q^{64} + 24 q^{67} - 8 q^{70}+ \cdots + 24 q^{97}+O(q^{100}) $ 64 * q + 8 * q^4 + 4 * q^16 - 36 * q^22 - 8 * q^25 - 200 * q^28 - 8 * q^31 + 64 * q^34 - 24 * q^37 + 60 * q^40 - 40 * q^46 - 100 * q^52 + 16 * q^55 - 24 * q^58 - 60 * q^61 + 72 * q^64 + 24 * q^67 - 8 * q^70 + 160 * q^73 + 60 * q^79 + 144 * q^82 + 20 * q^85 + 24 * q^88 + 48 * q^91 - 20 * q^94 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.931391	−	0.414682i	−0.658593	−	0.293225i	0.0500971	−	0.998744i	$-0.484047\pi$
$2$	−0.931391	−	0.414682i	−0.658593	−	0.293225i	−0.708690	+	0.705520i	$0.750714\pi$
$3$		0			0
$3$		0			0
$4$	−0.642733	−	0.713827i	−0.321366	−	0.356913i
$5$	−1.26271	−	2.83609i	−0.564700	−	1.26834i	−0.939918	−	0.341401i	$-0.889099\pi$
$5$	−1.26271	−	2.83609i	−0.564700	−	1.26834i	0.375218	−	0.926937i	$-0.377568\pi$
$6$		0			0
$7$	0.870416	+	4.09498i	0.328986	+	1.54776i	0.762727	+	0.646721i	$0.223860\pi$
$7$	0.870416	+	4.09498i	0.328986	+	1.54776i	−0.433740	+	0.901038i	$0.642807\pi$
$8$	0.932731	+	2.87065i	0.329770	+	1.01493i
$9$		0			0
$10$			3.16513i			1.00090i
$11$	2.08952	−	2.57564i	0.630015	−	0.776583i
$11$	2.08952	−	2.57564i	0.630015	−	0.776583i
$12$		0			0
$13$	0.355243	−	0.0373375i	0.0985266	−	0.0103556i	−0.0551369	−	0.998479i	$-0.517560\pi$
$13$	0.355243	−	0.0373375i	0.0985266	−	0.0103556i	0.153663	+	0.988123i	$0.450893\pi$
$14$	0.887419	−	4.17498i	0.237173	−	1.11581i
$15$		0			0
$16$	0.120861	−	1.14991i	0.0302152	−	0.287478i
$17$	2.52248	+	1.83269i	0.611792	+	0.444493i	0.850045	−	0.526710i	$-0.176575\pi$
$17$	2.52248	+	1.83269i	0.611792	+	0.444493i	−0.238253	+	0.971203i	$0.576575\pi$
$18$		0			0
$19$	−0.384024	+	0.124777i	−0.0881011	+	0.0286258i	−0.352736	−	0.935723i	$-0.614749\pi$
$19$	−0.384024	+	0.124777i	−0.0881011	+	0.0286258i	0.264635	+	0.964349i	$0.414749\pi$
$20$	−1.21289	+	2.72420i	−0.271211	+	0.609150i
$21$		0			0
$22$	−3.01423	+	1.53244i	−0.642637	+	0.326717i
$23$	2.44458	+	1.41138i	0.509731	+	0.294293i	0.732723	−	0.680527i	$-0.238249\pi$
$23$	2.44458	+	1.41138i	0.509731	+	0.294293i	−0.222992	+	0.974820i	$0.571582\pi$
$24$		0			0
$25$	−3.10332	+	3.44658i	−0.620663	+	0.689316i
$26$	−0.346353	−	0.112537i	−0.0679254	−	0.0220703i
$27$		0			0
$28$	2.36367	−	3.25331i	0.446691	−	0.614817i
$29$	6.07102	−	1.29044i	1.12736	−	0.239628i	0.393763	−	0.919212i	$-0.371173\pi$
$29$	6.07102	−	1.29044i	1.12736	−	0.239628i	0.733598	+	0.679584i	$0.237840\pi$
$30$		0			0
$31$	0.845730	+	8.04658i	0.151898	+	1.44521i	0.759262	+	0.650785i	$0.225560\pi$
$31$	0.845730	+	8.04658i	0.151898	+	1.44521i	−0.607364	+	0.794423i	$0.707773\pi$
$32$	2.42897	−	4.20709i	0.429384	−	0.743716i
$33$		0			0
$34$	−1.58943	−	2.75298i	−0.272586	−	0.472132i
$35$	10.5147	−	7.63935i	1.77730	−	1.29129i
$36$		0			0
$37$	1.01570	−	3.12601i	0.166981	−	0.513914i	−0.832196	−	0.554481i	$-0.812917\pi$
$37$	1.01570	−	3.12601i	0.166981	−	0.513914i	0.999177	+	0.0405678i	$0.0129167\pi$
$38$	0.409419	+	0.0430317i	0.0664165	+	0.00698066i
$39$		0			0
$40$	6.96366	−	6.27011i	1.10105	−	0.991391i
$41$	−7.43969	−	1.58136i	−1.16188	−	0.246966i	−0.413673	−	0.910426i	$-0.635754\pi$
$41$	−7.43969	−	1.58136i	−1.16188	−	0.246966i	−0.748212	+	0.663459i	$0.769088\pi$
$42$		0			0
$43$	8.02668	−	4.63421i	1.22406	−	0.706710i	0.258277	−	0.966071i	$-0.416845\pi$
$43$	8.02668	−	4.63421i	1.22406	−	0.706710i	0.965781	+	0.259361i	$0.0835118\pi$
$44$	−3.18156	+	0.163887i	−0.479639	+	0.0247069i
$45$		0			0
$46$	−1.69159	−	2.32827i	−0.249411	−	0.343285i
$47$	−9.41156	−	8.47421i	−1.37282	−	1.23609i	−0.942838	−	0.333252i	$-0.891854\pi$
$47$	−9.41156	−	8.47421i	−1.37282	−	1.23609i	−0.429980	−	0.902839i	$-0.641479\pi$
$48$		0			0
$49$	−9.61646	+	4.28152i	−1.37378	+	0.611646i
$50$	4.31964	−	1.92323i	0.610889	−	0.271985i
$51$		0			0
$52$	−0.254979	−	0.229584i	−0.0353592	−	0.0318375i
$53$	−2.07104	−	2.85055i	−0.284480	−	0.391553i	0.642731	−	0.766092i	$-0.277801\pi$
$53$	−2.07104	−	2.85055i	−0.284480	−	0.391553i	−0.927211	+	0.374539i	$0.877801\pi$
$54$		0			0
$55$	−9.94319	−	2.67380i	−1.34074	−	0.360535i
$56$	−10.9434	+	6.31818i	−1.46238	+	0.844303i
$57$		0			0
$58$	−6.18962	−	1.31564i	−0.812737	−	0.172753i
$59$	8.65424	−	7.79231i	1.12669	−	1.01447i	0.126940	−	0.991910i	$-0.459484\pi$
$59$	8.65424	−	7.79231i	1.12669	−	1.01447i	0.999745	−	0.0225622i	$-0.00718238\pi$
$60$		0			0
$61$	1.18232	+	0.124266i	0.151380	+	0.0159107i	0.179915	−	0.983682i	$-0.442418\pi$
$61$	1.18232	+	0.124266i	0.151380	+	0.0159107i	−0.0285353	+	0.999593i	$0.509084\pi$
$62$	2.54907	−	7.84522i	0.323732	−	0.996345i
$63$		0			0
$64$	−5.87777	+	4.27045i	−0.734721	+	0.533806i
$65$	−0.554460	−	0.960353i	−0.0687723	−	0.119117i
$66$		0			0
$67$	7.66446	−	13.2752i	0.936362	−	1.62183i	0.164176	−	0.986431i	$-0.447504\pi$
$67$	7.66446	−	13.2752i	0.936362	−	1.62183i	0.772187	−	0.635396i	$-0.219163\pi$
$68$	−0.313058	−	2.97855i	−0.0379638	−	0.361202i
$69$		0			0
$70$	−12.9612	+	2.75498i	−1.54916	+	0.329283i
$71$	0.357651	−	0.492264i	0.0424453	−	0.0584210i	−0.787267	−	0.616612i	$-0.788505\pi$
$71$	0.357651	−	0.492264i	0.0424453	−	0.0584210i	0.829712	+	0.558192i	$0.188505\pi$
$72$		0			0
$73$	10.8303	+	3.51899i	1.26760	+	0.411867i	0.864195	−	0.503157i	$-0.167828\pi$
$73$	10.8303	+	3.51899i	1.26760	+	0.411867i	0.403401	+	0.915023i	$0.367828\pi$
$74$	−2.24232	+	2.49035i	−0.260664	+	0.289497i
$75$		0			0
$76$	0.335894	+	0.193928i	0.0385296	+	0.0222451i
$77$	12.3659	+	6.31469i	1.40923	+	0.719626i
$78$		0			0
$79$	1.96875	−	4.42189i	0.221502	−	0.497501i	−0.768276	−	0.640119i	$-0.778885\pi$
$79$	1.96875	−	4.42189i	0.221502	−	0.497501i	0.989778	+	0.142617i	$0.0455519\pi$
$80$	−3.41387	+	1.10923i	−0.381682	+	0.124016i
$81$		0			0
$82$	6.27351	+	4.55797i	0.692793	+	0.503343i
$83$	0.692635	−	6.58998i	0.0760265	−	0.723344i	−0.888414	−	0.459044i	$-0.848192\pi$
$83$	0.692635	−	6.58998i	0.0760265	−	0.723344i	0.964440	−	0.264301i	$-0.0851411\pi$
$84$		0			0
$85$	2.01251	−	9.46814i	0.218288	−	1.02696i
$86$	−9.39771	+	0.987739i	−1.01338	+	0.106511i
$87$		0			0
$88$	9.34272	+	3.59592i	0.995937	+	0.383326i
$89$			7.29922i			0.773716i	0.922139	+	0.386858i	$0.126440\pi$
$89$			7.29922i			0.773716i	−0.922139	+	0.386858i	$0.873560\pi$
$90$		0			0
$91$	0.462105	+	1.42221i	0.0484418	+	0.149088i
$92$	−0.563732	−	2.65215i	−0.0587731	−	0.276506i
$93$		0			0
$94$	5.25174	+	11.7956i	0.541676	+	1.21662i
$95$	0.838788	+	0.931569i	0.0860578	+	0.0955769i
$96$		0			0
$97$	−4.74976	−	2.11473i	−0.482266	−	0.214718i	0.151179	−	0.988506i	$-0.451693\pi$
$97$	−4.74976	−	2.11473i	−0.482266	−	0.214718i	−0.633445	+	0.773788i	$0.718360\pi$
$98$	10.7322			1.08411
$99$		0			0
$100$	4.45487			0.445487
$101$	7.43379	+	3.30973i	0.739689	+	0.329331i	0.741759	−	0.670667i	$-0.233992\pi$
$101$	7.43379	+	3.30973i	0.739689	+	0.329331i	−0.00206925	+	0.999998i	$0.500659\pi$
$102$		0			0
$103$	9.23553	+	10.2571i	0.910004	+	1.01066i	0.999892	+	0.0147102i	$0.00468256\pi$
$103$	9.23553	+	10.2571i	0.910004	+	1.01066i	−0.0898876	+	0.995952i	$0.528651\pi$
$104$	0.438529	+	0.984952i	0.0430013	+	0.0965825i
$105$		0			0
$106$	0.746882	+	3.51380i	0.0725435	+	0.341291i
$107$	1.25282	+	3.85579i	0.121115	+	0.372753i	0.993173	−	0.116649i	$-0.0372151\pi$
$107$	1.25282	+	3.85579i	0.121115	+	0.372753i	−0.872058	+	0.489402i	$0.837215\pi$
$108$		0			0
$109$			5.57814i			0.534289i	0.963656	+	0.267145i	$0.0860801\pi$
$109$			5.57814i			0.534289i	−0.963656	+	0.267145i	$0.913920\pi$
$110$	8.15222	+	6.61361i	0.777284	+	0.630583i
$111$		0			0
$112$	4.81408	−	0.505980i	0.454888	−	0.0478106i
$113$	−1.51473	+	7.12624i	−0.142494	+	0.670381i	0.847676	+	0.530514i	$0.178001\pi$
$113$	−1.51473	+	7.12624i	−0.142494	+	0.670381i	−0.990170	+	0.139867i	$0.955332\pi$
$114$		0			0
$115$	0.916007	−	8.71522i	0.0854181	−	0.812699i
$116$	−4.82319	−	3.50426i	−0.447822	−	0.325362i
$117$		0			0
$118$	−11.2918	+	3.66893i	−1.03950	+	0.337753i
$119$	−5.30923	+	11.9247i	−0.486696	+	1.09314i
$120$		0			0
$121$	−2.26779	−	10.7637i	−0.206163	−	0.978518i
$122$	−1.04967	−	0.606026i	−0.0950324	−	0.0548670i
$123$		0			0
$124$	5.20029	−	5.77551i	0.467000	−	0.518656i
$125$	−1.06931	−	0.347441i	−0.0956422	−	0.0310760i
$126$		0			0
$127$	8.05590	−	11.0880i	0.714846	−	0.983901i	−0.284834	−	0.958577i	$-0.591938\pi$
$127$	8.05590	−	11.0880i	0.714846	−	0.983901i	0.999679	−	0.0253237i	$-0.00806165\pi$
$128$	−2.25816	+	0.479987i	−0.199595	+	0.0424253i
$129$		0			0
$130$	0.118178	+	1.12439i	0.0103649	+	0.0986155i
$131$	−9.26411	+	16.0459i	−0.809409	+	1.40194i	0.103865	+	0.994591i	$0.466879\pi$
$131$	−9.26411	+	16.0459i	−0.809409	+	1.40194i	−0.913274	+	0.407346i	$0.866454\pi$
$132$		0			0
$133$	−0.845220	−	1.46396i	−0.0732898	−	0.126942i
$134$	−12.6436	+	9.18612i	−1.09224	+	0.793560i
$135$		0			0
$136$	−2.90822	+	8.95058i	−0.249378	+	0.767506i
$137$	19.3247	+	2.03111i	1.65102	+	0.173530i	0.883805	−	0.467856i	$-0.154973\pi$
$137$	19.3247	+	2.03111i	1.65102	+	0.173530i	0.767219	+	0.641386i	$0.221640\pi$
$138$		0			0
$139$	−2.61445	+	2.35406i	−0.221755	+	0.199669i	−0.772518	−	0.634992i	$-0.781003\pi$
$139$	−2.61445	+	2.35406i	−0.221755	+	0.199669i	0.550764	+	0.834661i	$0.314337\pi$
$140$	−12.2113	−	2.59559i	−1.03204	−	0.219367i
$141$		0			0
$142$	−0.537246	+	0.310179i	−0.0450847	+	0.0260296i
$143$	0.646120	−	0.992993i	0.0540312	−	0.0830382i
$144$		0			0
$145$	−11.3257	−	15.5885i	−0.940550	−	1.29456i
$146$	−8.62803	−	7.76871i	−0.714061	−	0.642943i
$147$		0			0
$148$	−2.88426	+	1.28415i	−0.237085	+	0.105557i
$149$	−0.00872871	+	0.00388627i	−0.000715084	+	0.000318376i	−0.407094	−	0.913386i	$-0.633458\pi$
$149$	−0.00872871	+	0.00388627i	−0.000715084	+	0.000318376i	0.406379	+	0.913705i	$0.366791\pi$
$150$		0			0
$151$	0.286689	+	0.258136i	0.0233304	+	0.0210068i	0.680713	−	0.732550i	$-0.261670\pi$
$151$	0.286689	+	0.258136i	0.0233304	+	0.0210068i	−0.657383	+	0.753557i	$0.728337\pi$
$152$	−0.716382	−	0.986015i	−0.0581062	−	0.0799764i
$153$		0			0
$154$	−8.89894	−	11.0094i	−0.717097	−	0.887161i
$155$	21.7529	−	12.5590i	1.74724	−	1.00877i
$156$		0			0
$157$	−2.86512	−	0.608999i	−0.228661	−	0.0486034i	0.0921560	−	0.995745i	$-0.470624\pi$
$157$	−2.86512	−	0.608999i	−0.228661	−	0.0486034i	−0.320817	+	0.947141i	$0.603957\pi$
$158$	−3.66736	+	3.30210i	−0.291759	+	0.262701i
$159$		0			0
$160$	−14.9988	−	1.57643i	−1.18576	−	0.124628i
$161$	−3.65178	+	11.2390i	−0.287801	+	0.885759i
$162$		0			0
$163$	10.8005	−	7.84704i	0.845962	−	0.614627i	−0.0780678	−	0.996948i	$-0.524875\pi$
$163$	10.8005	−	7.84704i	0.845962	−	0.614627i	0.924030	+	0.382321i	$0.124875\pi$
$164$	3.65292	+	6.32704i	0.285245	+	0.494059i
$165$		0			0
$166$	−3.37786	+	5.85063i	−0.262173	+	0.454097i
$167$	−0.802773	−	7.63787i	−0.0621204	−	0.591036i	−0.980662	−	0.195711i	$-0.937299\pi$
$167$	−0.802773	−	7.63787i	−0.0621204	−	0.591036i	0.918541	−	0.395325i	$-0.129368\pi$
$168$		0			0
$169$	−12.5911	+	2.67632i	−0.968547	+	0.205871i
$170$	−5.80071	+	7.98399i	−0.444894	+	0.612344i
$171$		0			0
$172$	−8.46704	−	2.75111i	−0.645605	−	0.209770i
$173$	−8.30908	+	9.22817i	−0.631728	+	0.701605i	−0.970999	−	0.239084i	$-0.923153\pi$
$173$	−8.30908	+	9.22817i	−0.631728	+	0.701605i	0.339271	+	0.940689i	$0.389820\pi$
$174$		0			0
$175$	−16.8149	−	9.70807i	−1.27109	−	0.733861i
$176$	−2.70922	−	2.71406i	−0.204215	−	0.204580i
$177$		0			0
$178$	3.02686	−	6.79843i	0.226872	−	0.509564i
$179$	−5.04243	+	1.63838i	−0.376889	+	0.122459i	−0.491335	−	0.870971i	$-0.663491\pi$
$179$	−5.04243	+	1.63838i	−0.376889	+	0.122459i	0.114446	+	0.993429i	$0.463491\pi$
$180$		0			0
$181$	13.8366	+	10.0529i	1.02846	+	0.747224i	0.968001	−	0.250947i	$-0.0807419\pi$
$181$	13.8366	+	10.0529i	1.02846	+	0.747224i	0.0604641	+	0.998170i	$0.480742\pi$
$182$	0.159366	−	1.51626i	0.0118130	−	0.112393i
$183$		0			0
$184$	−1.77144	+	8.33399i	−0.130593	+	0.614390i
$185$	−10.1482	+	1.06662i	−0.746110	+	0.0784193i
$186$		0			0
$187$	9.99113	−	2.66755i	0.730623	−	0.195070i
$188$			12.1649i			0.887215i
$189$		0			0
$190$	−0.394935	−	1.21549i	−0.0286516	−	0.0881806i
$191$	−1.84566	−	8.68317i	−0.133548	−	0.628292i	−0.993103	−	0.117249i	$-0.962593\pi$
$191$	−1.84566	−	8.68317i	−0.133548	−	0.628292i	0.859555	−	0.511043i	$-0.170741\pi$
$192$		0			0
$193$	0.587010	+	1.31845i	0.0422539	+	0.0949038i	0.933439	−	0.358736i	$-0.116792\pi$
$193$	0.587010	+	1.31845i	0.0422539	+	0.0949038i	−0.891185	+	0.453639i	$0.850125\pi$
$194$	3.54695	+	3.93929i	0.254656	+	0.282824i
$195$		0			0
$196$	9.23708	+	4.11261i	0.659791	+	0.293758i
$197$	−18.4552			−1.31488			−0.657441	−	0.753506i	$-0.728361\pi$
$197$	−18.4552			−1.31488			−0.657441	+	0.753506i	$0.728361\pi$
$198$		0			0
$199$	18.3392			1.30003			0.650016	−	0.759921i	$-0.274762\pi$
$199$	18.3392			1.30003			0.650016	+	0.759921i	$0.274762\pi$
$200$	−12.7885	−	5.69381i	−0.904283	−	0.402613i
$201$		0			0
$202$	−5.55128	−	6.16532i	−0.390586	−	0.433790i
$203$	10.5686	+	23.7375i	0.741772	+	1.66605i
$204$		0			0
$205$	4.90930	+	23.0964i	0.342880	+	1.61312i
$206$	−4.34846	−	13.3832i	−0.302972	−	0.932451i
$207$		0			0
$208$		−	0.413011i		−	0.0286372i
$209$	−0.481046	+	1.24983i	−0.0332747	+	0.0864525i
$210$		0			0
$211$	4.55309	−	0.478549i	0.313448	−	0.0329447i	0.0535016	−	0.998568i	$-0.482962\pi$
$211$	4.55309	−	0.478549i	0.313448	−	0.0329447i	0.259946	+	0.965623i	$0.416295\pi$
$212$	−0.703670	+	3.31051i	−0.0483283	+	0.227367i
$213$		0			0
$214$	0.432060	−	4.11077i	0.0295350	−	0.281007i
$215$	−23.2784	−	16.9127i	−1.58757	−	1.15344i
$216$		0			0
$217$	−32.2145	+	10.4671i	−2.18686	+	0.710555i
$218$	2.31316	−	5.19543i	0.156667	−	0.351879i
$219$		0			0
$220$	4.48218	+	8.81625i	0.302189	+	0.594392i
$221$	0.964521	+	0.556866i	0.0648807	+	0.0374589i
$222$		0			0
$223$	−7.30352	+	8.11139i	−0.489080	+	0.543179i	−0.936280	−	0.351256i	$-0.885755\pi$
$223$	−7.30352	+	8.11139i	−0.489080	+	0.543179i	0.447199	+	0.894434i	$0.352421\pi$
$224$	19.3422	+	6.28466i	1.29235	+	0.419911i
$225$		0			0
$226$	4.36593	−	6.00919i	0.290418	−	0.399725i
$227$	2.75877	−	0.586395i	0.183106	−	0.0389204i	−0.115446	−	0.993314i	$-0.536830\pi$
$227$	2.75877	−	0.586395i	0.183106	−	0.0389204i	0.298552	+	0.954393i	$0.403496\pi$
$228$		0			0
$229$	−0.208137	−	1.98029i	−0.0137540	−	0.130861i	0.985490	−	0.169733i	$-0.0542904\pi$
$229$	−0.208137	−	1.98029i	−0.0137540	−	0.130861i	−0.999244	+	0.0388715i	$0.987624\pi$
$230$	−4.46721	+	7.73743i	−0.294559	+	0.510191i
$231$		0			0
$232$	9.36703	+	16.2242i	0.614976	+	1.06517i
$233$	19.6843	−	14.3015i	1.28956	−	0.936923i	0.289768	−	0.957097i	$-0.406422\pi$
$233$	19.6843	−	14.3015i	1.28956	−	0.936923i	0.999796	+	0.0201739i	$0.00642200\pi$
$234$		0			0
$235$	−12.1496	+	37.3925i	−0.792550	+	2.43922i
$236$	−11.1247	−	1.16926i	−0.724158	−	0.0761121i
$237$		0			0
$238$	9.88994	−	8.90495i	0.641070	−	0.577222i
$239$	9.81100	+	2.08539i	0.634621	+	0.134893i	0.513978	−	0.857803i	$-0.328171\pi$
$239$	9.81100	+	2.08539i	0.634621	+	0.134893i	0.120643	+	0.992696i	$0.461505\pi$
$240$		0			0
$241$	14.9974	−	8.65877i	0.966069	−	0.557760i	0.0680336	−	0.997683i	$-0.478327\pi$
$241$	14.9974	−	8.65877i	0.966069	−	0.557760i	0.898036	+	0.439923i	$0.144994\pi$
$242$	−2.35131	+	10.9656i	−0.151148	+	0.704897i
$243$		0			0
$244$	−0.671208	−	0.923839i	−0.0429697	−	0.0591427i
$245$	24.2856	+	21.8668i	1.55155	+	1.39702i
$246$		0			0
$247$	−0.131763	+	0.0586645i	−0.00838386	+	0.00373273i
$248$	−22.3101	+	9.93310i	−1.41669	+	0.630752i
$249$		0			0
$250$	0.851871	+	0.767028i	0.0538770	+	0.0485111i
$251$	−9.57729	−	13.1820i	−0.604513	−	0.832041i	0.391599	−	0.920136i	$-0.371922\pi$
$251$	−9.57729	−	13.1820i	−0.604513	−	0.832041i	−0.996112	+	0.0880949i	$0.971922\pi$
$252$		0			0
$253$	8.74322	−	3.34724i	0.549681	−	0.210439i
$254$	−12.1012	+	6.98663i	−0.759296	+	0.438380i
$255$		0			0
$256$	16.5154	+	3.51046i	1.03221	+	0.219403i
$257$	5.52161	−	4.97168i	0.344429	−	0.310125i	−0.478701	−	0.877978i	$-0.658892\pi$
$257$	5.52161	−	4.97168i	0.344429	−	0.310125i	0.823130	+	0.567853i	$0.192226\pi$
$258$		0			0
$259$	13.6851	+	1.43836i	0.850348	+	0.0893752i
$260$	−0.329156	+	1.01304i	−0.0204134	+	0.0628260i
$261$		0			0
$262$	15.2825	−	11.1034i	0.944153	−	0.685968i
$263$	0.812112	+	1.40662i	0.0500769	+	0.0867358i	0.889977	−	0.456005i	$-0.150720\pi$
$263$	0.812112	+	1.40662i	0.0500769	+	0.0867358i	−0.839900	+	0.542741i	$0.817387\pi$
$264$		0			0
$265$	−5.46928	+	9.47308i	−0.335975	+	0.581927i
$266$	0.180151	+	1.71402i	0.0110458	+	0.105093i
$267$		0			0
$268$	−14.4024	+	3.06133i	−0.879767	+	0.187000i
$269$	−7.63802	+	10.5128i	−0.465699	+	0.640979i	−0.975678	−	0.219207i	$-0.929653\pi$
$269$	−7.63802	+	10.5128i	−0.465699	+	0.640979i	0.509980	+	0.860186i	$0.329653\pi$
$270$		0			0
$271$	7.28021	+	2.36548i	0.442241	+	0.143693i	0.521669	−	0.853148i	$-0.325309\pi$
$271$	7.28021	+	2.36548i	0.442241	+	0.143693i	−0.0794282	+	0.996841i	$0.525309\pi$
$272$	2.41231	−	2.67914i	0.146268	−	0.162447i
$273$		0			0
$274$	−17.1566	−	9.90538i	−1.03647	−	0.598406i
$275$	2.39269	+	15.1947i	0.144285	+	0.916276i
$276$		0			0
$277$	−6.86918	+	15.4284i	−0.412729	+	0.927004i	0.580866	+	0.813999i	$0.302714\pi$
$277$	−6.86918	+	15.4284i	−0.412729	+	0.927004i	−0.993594	+	0.113005i	$0.963953\pi$
$278$	3.41126	−	1.10839i	0.204594	−	0.0664766i
$279$		0			0
$280$	31.7373	+	23.0585i	1.89666	+	1.37801i
$281$	−1.13432	+	10.7924i	−0.0676680	+	0.643818i	0.907149	+	0.420810i	$0.138254\pi$
$281$	−1.13432	+	10.7924i	−0.0676680	+	0.643818i	−0.974817	+	0.223008i	$0.928412\pi$
$282$		0			0
$283$	−3.64075	+	17.1284i	−0.216420	+	1.01818i	0.727015	+	0.686621i	$0.240907\pi$
$283$	−3.64075	+	17.1284i	−0.216420	+	1.01818i	−0.943435	+	0.331556i	$0.892426\pi$
$284$	−0.581265	+	0.0610934i	−0.0344917	+	0.00362523i
$285$		0			0
$286$	−1.01357	+	0.656931i	−0.0599334	+	0.0388451i
$287$		−	31.8419i		−	1.87957i
$288$		0			0
$289$	−2.24913	−	6.92210i	−0.132302	−	0.407182i
$290$	4.08440	+	19.2156i	0.239844	+	1.12838i
$291$		0			0
$292$	−4.44907	−	9.99276i	−0.260362	−	0.584782i
$293$	8.73117	+	9.69695i	0.510081	+	0.566502i	0.942087	−	0.335369i	$-0.108861\pi$
$293$	8.73117	+	9.69695i	0.510081	+	0.566502i	−0.432006	+	0.901871i	$0.642194\pi$
$294$		0			0
$295$	−33.0275	−	14.7048i	−1.92293	−	0.856145i
$296$	9.92108			0.576651
$297$		0			0
$298$	0.00974141			0.000564305
$299$	0.921118	+	0.410108i	0.0532696	+	0.0237172i
$300$		0			0
$301$	25.9636	+	28.8355i	1.49652	+	1.66205i
$302$	−0.159975	−	0.359311i	−0.00920555	−	0.0206760i
$303$		0			0
$304$	0.0970692	+	0.456675i	0.00556730	+	0.0261921i
$305$	−1.14049	−	3.51007i	−0.0653042	−	0.200986i
$306$		0			0
$307$		−	27.5790i		−	1.57402i	−0.616941	−	0.787009i	$-0.711628\pi$
$307$		−	27.5790i		−	1.57402i	0.616941	−	0.787009i	$-0.288372\pi$
$308$	−3.44040	−	12.8858i	−0.196035	−	0.734237i
$309$		0			0
$310$	−25.4685	+	2.67685i	−1.44651	+	0.152035i
$311$	−1.58412	+	7.45270i	−0.0898273	+	0.422604i	0.910138	+	0.414305i	$0.135975\pi$
$311$	−1.58412	+	7.45270i	−0.0898273	+	0.422604i	−0.999966	+	0.00829946i	$0.997358\pi$
$312$		0			0
$313$	−1.39540	+	13.2763i	−0.0788725	+	0.750422i	0.881591	+	0.472015i	$0.156473\pi$
$313$	−1.39540	+	13.2763i	−0.0788725	+	0.750422i	−0.960463	+	0.278407i	$0.910194\pi$
$314$	2.41600	+	1.75533i	0.136343	+	0.0990589i
$315$		0			0
$316$	−4.42184	+	1.43674i	−0.248748	+	0.0808232i
$317$	3.11841	−	7.00405i	0.175147	−	0.393387i	−0.804546	−	0.593891i	$-0.797591\pi$
$317$	3.11841	−	7.00405i	0.175147	−	0.393387i	0.979693	+	0.200504i	$0.0642579\pi$
$318$		0			0
$319$	9.36185	−	18.3331i	0.524163	−	1.02646i
$320$	19.5333	+	11.2775i	1.09194	+	0.630434i
$321$		0			0
$322$	8.06186	−	8.95360i	0.449270	−	0.498965i
$323$	−1.19737	−	0.389049i	−0.0666235	−	0.0216473i
$324$		0			0
$325$	−0.973743	+	1.34024i	−0.0540136	+	0.0743433i
$326$	−13.3135	+	2.82988i	−0.737369	+	0.156733i
$327$		0			0
$328$	−2.39971	−	22.8318i	−0.132502	−	1.26067i
$329$	26.5098	−	45.9163i	1.46153	−	2.53145i
$330$		0			0
$331$	3.66294	+	6.34439i	0.201333	+	0.348719i	0.948958	−	0.315402i	$-0.102139\pi$
$331$	3.66294	+	6.34439i	0.201333	+	0.348719i	−0.747625	+	0.664121i	$0.768806\pi$
$332$	−5.14928	+	3.74117i	−0.282604	+	0.205324i
$333$		0			0
$334$	−2.41959	+	7.44675i	−0.132394	+	0.407468i
$335$	−47.3277	−	4.97434i	−2.58579	−	0.271777i
$336$		0			0
$337$	−5.37478	+	4.83947i	−0.292783	+	0.263623i	−0.802411	−	0.596772i	$-0.796450\pi$
$337$	−5.37478	+	4.83947i	−0.292783	+	0.263623i	0.509628	+	0.860395i	$0.329783\pi$
$338$	12.8371	+	2.72861i	0.698245	+	0.148417i
$339$		0			0
$340$	−8.05212	+	4.64889i	−0.436688	+	0.252122i
$341$	22.4922	+	14.6352i	1.21802	+	0.792542i
$342$		0			0
$343$	−8.67788	−	11.9441i	−0.468561	−	0.644919i
$344$	20.7899	+	18.7193i	1.12092	+	1.00928i
$345$		0			0
$346$	11.5658	−	5.14941i	0.621779	−	0.276834i
$347$	−22.5610	+	10.0448i	−1.21114	+	0.539233i	−0.910104	−	0.414381i	$-0.863998\pi$
$347$	−22.5610	+	10.0448i	−1.21114	+	0.539233i	−0.301033	+	0.953614i	$0.597332\pi$
$348$		0			0
$349$	−10.4965	−	9.45108i	−0.561864	−	0.505905i	0.338544	−	0.940950i	$-0.390065\pi$
$349$	−10.4965	−	9.45108i	−0.561864	−	0.505905i	−0.900408	+	0.435046i	$0.856732\pi$
$350$	11.6355	+	16.0148i	0.621942	+	0.856029i
$351$		0			0
$352$	−5.76055	−	15.0469i	−0.307039	−	0.802005i
$353$	13.0466	−	7.53244i	0.694399	−	0.400911i	−0.110859	−	0.993836i	$-0.535360\pi$
$353$	13.0466	−	7.53244i	0.694399	−	0.400911i	0.805258	+	0.592925i	$0.202027\pi$
$354$		0			0
$355$	−1.84771	−	0.392743i	−0.0980664	−	0.0208447i
$356$	5.21038	−	4.69145i	0.276150	−	0.248646i
$357$		0			0
$358$	5.37588	+	0.565028i	0.284124	+	0.0298627i
$359$	−2.21156	+	6.80649i	−0.116722	+	0.359233i	−0.992302	−	0.123840i	$-0.960479\pi$
$359$	−2.21156	+	6.80649i	−0.116722	+	0.359233i	0.875580	+	0.483072i	$0.160479\pi$
$360$		0			0
$361$	−15.2394	+	11.0721i	−0.802075	+	0.582741i
$362$	−8.71853	−	15.1009i	−0.458236	−	0.793687i
$363$		0			0
$364$	0.718204	−	1.24397i	0.0376441	−	0.0652016i
$365$	−3.69539	−	35.1593i	−0.193426	−	1.84032i
$366$		0			0
$367$	−4.15227	+	0.882592i	−0.216747	+	0.0460709i	−0.315005	−	0.949090i	$-0.602006\pi$
$367$	−4.15227	+	0.882592i	−0.216747	+	0.0460709i	0.0982583	+	0.995161i	$0.468673\pi$
$368$	1.91842	−	2.64048i	0.100005	−	0.137645i
$369$		0			0
$370$	9.89424	+	3.21483i	0.514377	+	0.167131i
$371$	9.87028	−	10.9621i	0.512440	−	0.569122i
$372$		0			0
$373$	−17.6199	−	10.1729i	−0.912324	−	0.526730i	−0.0311456	−	0.999515i	$-0.509916\pi$
$373$	−17.6199	−	10.1729i	−0.912324	−	0.526730i	−0.881178	+	0.472785i	$0.843249\pi$
$374$	−10.4118	−	1.65861i	−0.538383	−	0.0857648i
$375$		0			0
$376$	15.5480	−	34.9215i	0.801829	−	1.80094i
$377$	2.10850	−	0.685095i	0.108593	−	0.0352842i
$378$		0			0
$379$	−23.6596	−	17.1897i	−1.21531	−	0.882977i	−0.219611	−	0.975587i	$-0.570479\pi$
$379$	−23.6596	−	17.1897i	−1.21531	−	0.882977i	−0.995702	+	0.0926103i	$0.970479\pi$
$380$	0.125862	−	1.19750i	0.00645660	−	0.0614304i
$381$		0			0
$382$	−1.88172	+	8.85279i	−0.0962771	+	0.452948i
$383$	4.88385	−	0.513314i	0.249553	−	0.0262291i	0.0210741	−	0.999778i	$-0.493291\pi$
$383$	4.88385	−	0.513314i	0.249553	−	0.0262291i	0.228479	+	0.973549i	$0.426625\pi$
$384$		0			0
$385$	2.29445	−	43.0445i	0.116936	−	2.19375i
$386$		−	1.47141i		−	0.0748929i
$387$		0			0
$388$	1.54328	+	4.74972i	0.0783480	+	0.241130i
$389$	−3.56415	−	16.7680i	−0.180710	−	0.850171i	−0.971306	−	0.237834i	$-0.923563\pi$
$389$	−3.56415	−	16.7680i	−0.180710	−	0.850171i	0.790596	−	0.612338i	$-0.209771\pi$
$390$		0			0
$391$	3.57980	+	8.04035i	0.181038	+	0.406618i
$392$	−21.2603	−	23.6120i	−1.07381	−	1.19259i
$393$		0			0
$394$	17.1890	+	7.65306i	0.865972	+	0.385555i
$395$	−15.0268			−0.756082
$396$		0			0
$397$	−7.94416			−0.398706			−0.199353	−	0.979928i	$-0.563884\pi$
$397$	−7.94416			−0.398706			−0.199353	+	0.979928i	$0.563884\pi$
$398$	−17.0810	−	7.60494i	−0.856192	−	0.381201i
$399$		0			0
$400$	3.58820	+	3.98510i	0.179410	+	0.199255i
$401$	−2.62085	−	5.88653i	−0.130879	−	0.293959i	0.836205	−	0.548417i	$-0.184770\pi$
$401$	−2.62085	−	5.88653i	−0.130879	−	0.293959i	−0.967084	+	0.254458i	$0.918103\pi$
$402$		0			0
$403$	0.600878	+	2.82691i	0.0299319	+	0.140818i
$404$	−2.41536	−	7.43371i	−0.120169	−	0.369841i
$405$		0			0
$406$		−	26.4916i		−	1.31475i
$407$	−5.92914	−	9.14796i	−0.293896	−	0.453447i
$408$		0			0
$409$	15.8787	−	1.66892i	0.785152	−	0.0825228i	0.296536	−	0.955022i	$-0.404169\pi$
$409$	15.8787	−	1.66892i	0.785152	−	0.0825228i	0.488616	+	0.872499i	$0.337502\pi$
$410$	5.00520	−	23.5476i	0.247189	−	1.16293i
$411$		0			0
$412$	1.38581	−	13.1851i	0.0682742	−	0.649586i
$413$	39.4422	+	28.6564i	1.94082	+	1.41009i
$414$		0			0
$415$	−19.5644	+	6.35685i	−0.960377	+	0.312045i
$416$	0.705789	−	1.58523i	0.0346042	−	0.0777223i
$417$		0			0
$418$	0.966324	−	0.964598i	0.0472645	−	0.0471800i
$419$	−3.15494	−	1.82151i	−0.154129	−	0.0889865i	0.420952	−	0.907083i	$-0.361696\pi$
$419$	−3.15494	−	1.82151i	−0.154129	−	0.0889865i	−0.575081	+	0.818096i	$0.695029\pi$
$420$		0			0
$421$	8.83523	−	9.81252i	0.430603	−	0.478233i	−0.488323	−	0.872663i	$-0.662391\pi$
$421$	8.83523	−	9.81252i	0.430603	−	0.478233i	0.918926	+	0.394430i	$0.129058\pi$
$422$	−4.43916	−	1.44237i	−0.216095	−	0.0702135i
$423$		0			0
$424$	6.25120	−	8.60405i	0.303585	−	0.417849i
$425$	−14.1446	+	3.00652i	−0.686113	+	0.145838i
$426$		0			0
$427$	0.520237	+	4.94973i	0.0251761	+	0.239534i
$428$	1.94714	−	3.37254i	0.0941184	−	0.163018i
$429$		0			0
$430$	14.6679	+	25.4055i	0.707348	+	1.22516i
$431$	−12.5748	+	9.13610i	−0.605705	+	0.440071i	−0.847899	−	0.530157i	$-0.822133\pi$
$431$	−12.5748	+	9.13610i	−0.605705	+	0.440071i	0.242194	+	0.970228i	$0.422133\pi$
$432$		0			0
$433$	−3.84495	+	11.8336i	−0.184777	+	0.568684i	−0.999944	−	0.0105407i	$-0.996645\pi$
$433$	−3.84495	+	11.8336i	−0.184777	+	0.568684i	0.815168	+	0.579225i	$0.196645\pi$
$434$	34.3448	+	3.60979i	1.64860	+	0.173275i
$435$		0			0
$436$	3.98183	−	3.58525i	0.190695	−	0.171703i
$437$	−1.11489	−	0.236976i	−0.0533322	−	0.0113361i
$438$		0			0
$439$	9.93333	−	5.73501i	0.474092	−	0.273717i	−0.243859	−	0.969811i	$-0.578413\pi$
$439$	9.93333	−	5.73501i	0.474092	−	0.273717i	0.717951	+	0.696094i	$0.245080\pi$
$440$	−1.59878	−	31.0374i	−0.0762190	−	1.47965i
$441$		0			0
$442$	−0.667424	−	0.918630i	−0.0317461	−	0.0436948i
$443$	5.46329	+	4.91916i	0.259569	+	0.233717i	0.788632	−	0.614866i	$-0.210790\pi$
$443$	5.46329	+	4.91916i	0.259569	+	0.233717i	−0.529063	+	0.848582i	$0.677457\pi$
$444$		0			0
$445$	20.7012	−	9.21678i	0.981333	−	0.436917i
$446$	10.1661	−	4.52623i	0.481378	−	0.214323i
$447$		0			0
$448$	−22.6035	−	20.3523i	−1.06792	−	0.961556i
$449$	2.58876	+	3.56312i	0.122171	+	0.168154i	0.865722	−	0.500525i	$-0.166860\pi$
$449$	2.58876	+	3.56312i	0.122171	+	0.168154i	−0.743551	+	0.668680i	$0.766860\pi$
$450$		0			0
$451$	−19.6184	+	15.8577i	−0.923794	+	0.746708i
$452$	6.06047	−	3.49902i	0.285061	−	0.164580i
$453$		0			0
$454$	−2.81266	−	0.597850i	−0.132005	−	0.0280585i
$455$	3.45002	−	3.10641i	0.161739	−	0.145631i
$456$		0			0
$457$	−6.26663	−	0.658649i	−0.293141	−	0.0308103i	−0.0431832	−	0.999067i	$-0.513750\pi$
$457$	−6.26663	−	0.658649i	−0.293141	−	0.0308103i	−0.249957	+	0.968257i	$0.580417\pi$
$458$	−0.627333	+	1.93073i	−0.0293133	+	0.0902172i
$459$		0			0
$460$	−6.80991	+	4.94769i	−0.317514	+	0.230687i
$461$	5.15950	+	8.93652i	0.240302	+	0.416215i	0.960800	−	0.277241i	$-0.0894202\pi$
$461$	5.15950	+	8.93652i	0.240302	+	0.416215i	−0.720498	+	0.693457i	$0.756087\pi$
$462$		0			0
$463$	−0.846612	+	1.46637i	−0.0393454	+	0.0681482i	−0.885028	−	0.465539i	$-0.845861\pi$
$463$	−0.846612	+	1.46637i	−0.0393454	+	0.0681482i	0.845682	+	0.533687i	$0.179194\pi$
$464$	−0.750141	−	7.13712i	−0.0348244	−	0.331332i
$465$		0			0
$466$	−24.2644	+	5.15756i	−1.12403	+	0.238919i
$467$	14.1753	−	19.5106i	0.655953	−	0.902842i	−0.343386	−	0.939194i	$-0.611574\pi$
$467$	14.1753	−	19.5106i	0.655953	−	0.902842i	0.999339	+	0.0363528i	$0.0115740\pi$
$468$		0			0
$469$	61.0331	+	19.8309i	2.81825	+	0.915704i
$470$	26.8220	−	29.7888i	1.23721	−	1.37406i
$471$		0			0
$472$	30.4411	+	17.5752i	1.40117	+	0.808963i
$473$	4.83591	−	30.3571i	0.222355	−	1.39582i
$474$		0			0
$475$	0.761693	−	1.71079i	0.0349489	−	0.0784965i
$476$	11.9246	−	3.87454i	0.546564	−	0.177589i
$477$		0			0
$478$	−8.27311	−	6.01076i	−0.378403	−	0.274926i
$479$	−3.89790	+	37.0860i	−0.178100	+	1.69450i	0.431755	+	0.901991i	$0.357895\pi$
$479$	−3.89790	+	37.0860i	−0.178100	+	1.69450i	−0.609854	+	0.792514i	$0.708772\pi$
$480$		0			0
$481$	0.244104	−	1.14842i	0.0111302	−	0.0523633i
$482$	−17.5591	+	1.84554i	−0.799796	+	0.0840619i
$483$		0			0
$484$	−6.22583	+	8.53699i	−0.282992	+	0.388045i
$485$			16.1410i			0.732927i
$486$		0			0
$487$	11.7540	+	36.1751i	0.532624	+	1.63925i	0.748727	+	0.662879i	$0.230665\pi$
$487$	11.7540	+	36.1751i	0.532624	+	1.63925i	−0.216102	+	0.976371i	$0.569335\pi$
$488$	0.746058	+	3.50992i	0.0337724	+	0.158887i
$489$		0			0
$490$	−13.5516	−	30.4374i	−0.612198	−	1.37502i
$491$	−19.1619	−	21.2814i	−0.864764	−	0.960418i	0.134772	−	0.990877i	$-0.456970\pi$
$491$	−19.1619	−	21.2814i	−0.864764	−	0.960418i	−0.999536	+	0.0304586i	$0.990303\pi$
$492$		0			0
$493$	17.6790	+	7.87121i	0.796223	+	0.354501i
$494$	0.147050			0.00661608
$495$		0			0
$496$	9.35509			0.420056
$497$	2.32712	+	1.03610i	0.104386	+	0.0464754i
$498$		0			0
$499$	−10.2989	−	11.4380i	−0.461041	−	0.512037i	0.467132	−	0.884188i	$-0.345287\pi$
$499$	−10.2989	−	11.4380i	−0.461041	−	0.512037i	−0.928173	+	0.372150i	$0.878621\pi$
$500$	0.439269	+	0.986615i	0.0196447	+	0.0441228i
$501$		0			0
$502$	3.45386	+	16.2491i	0.154153	+	0.725235i
$503$	1.24129	+	3.82031i	0.0553466	+	0.170339i	0.974909	−	0.222606i	$-0.0714563\pi$
$503$	1.24129	+	3.82031i	0.0553466	+	0.170339i	−0.919562	+	0.392945i	$0.871456\pi$
$504$		0			0
$505$		−	25.2621i		−	1.12415i
$506$	−9.53140	−	0.508062i	−0.423722	−	0.0225861i
$507$		0			0
$508$	−13.0927	+	1.37610i	−0.580895	+	0.0610545i
$509$	−4.35214	+	20.4752i	−0.192905	+	0.907548i	0.770070	+	0.637959i	$0.220221\pi$
$509$	−4.35214	+	20.4752i	−0.192905	+	0.907548i	−0.962975	+	0.269589i	$0.913112\pi$
$510$		0			0
$511$	−4.98332	+	47.4131i	−0.220449	+	2.09743i
$512$	−10.1912	−	7.40431i	−0.450390	−	0.327227i
$513$		0			0
$514$	−7.20445	+	2.34087i	−0.317775	+	0.103251i
$515$	17.4283	−	39.1445i	0.767981	−	1.72491i
$516$		0			0
$517$	−41.4921	+	6.53370i	−1.82482	+	0.287352i
$518$	−12.1497	−	7.01463i	−0.533827	−	0.308205i
$519$		0			0
$520$	2.23968	−	2.48741i	0.0982164	−	0.109080i
$521$	34.9601	+	11.3592i	1.53163	+	0.497656i	0.949052	−	0.315120i	$-0.102045\pi$
$521$	34.9601	+	11.3592i	1.53163	+	0.497656i	0.582576	+	0.812776i	$0.302045\pi$
$522$		0			0
$523$	−3.90101	+	5.36927i	−0.170579	+	0.234782i	−0.885744	−	0.464173i	$-0.846351\pi$
$523$	−3.90101	+	5.36927i	−0.170579	+	0.234782i	0.715165	+	0.698955i	$0.246351\pi$
$524$	17.4083	−	3.70026i	0.760487	−	0.161646i
$525$		0			0
$526$	−0.173094	−	1.64688i	−0.00754726	−	0.0718074i
$527$	−12.6136	+	21.8473i	−0.549455	+	0.951684i
$528$		0			0
$529$	−7.51600	−	13.0181i	−0.326783	−	0.566004i
$530$	9.02236	−	6.55513i	0.391906	−	0.284737i
$531$		0			0
$532$	−0.501766	+	1.54428i	−0.0217543	+	0.0669529i
$533$	−2.70194	−	0.283985i	−0.117034	−	0.0123008i
$534$		0			0
$535$	9.35341	−	8.42185i	0.404383	−	0.364108i
$536$	45.2574	+	9.61977i	1.95482	+	0.415511i
$537$		0			0
$538$	11.4735	−	6.62421i	0.494657	−	0.285590i
$539$	−9.06616	+	33.7148i	−0.390507	+	1.45220i
$540$		0			0
$541$	−0.307811	−	0.423665i	−0.0132338	−	0.0182148i	0.802349	−	0.596855i	$-0.203583\pi$
$541$	−0.307811	−	0.423665i	−0.0132338	−	0.0182148i	−0.815583	+	0.578641i	$0.803583\pi$
$542$	−5.79980	−	5.22216i	−0.249123	−	0.224311i
$543$		0			0
$544$	13.8373	−	6.16077i	0.593270	−	0.264141i
$545$	15.8201	−	7.04357i	0.677659	−	0.301713i
$546$		0			0
$547$	−25.2517	−	22.7367i	−1.07969	−	0.972153i	−0.0799890	−	0.996796i	$-0.525489\pi$
$547$	−25.2517	−	22.7367i	−1.07969	−	0.972153i	−0.999696	+	0.0246428i	$0.992155\pi$
$548$	−10.9708	−	15.1000i	−0.468648	−	0.645039i
$549$		0			0
$550$	4.07245	−	15.1444i	0.173650	−	0.645761i
$551$	−2.17040	+	1.25308i	−0.0924622	+	0.0533831i
$552$		0			0
$553$	19.8212	+	4.21312i	0.842883	+	0.179160i
$554$	12.7958	−	11.5214i	0.543641	−	0.489496i
$555$		0			0
$556$	3.36079	+	0.353233i	0.142529	+	0.0149804i
$557$	9.71173	−	29.8896i	0.411499	−	1.26646i	−0.503846	−	0.863794i	$-0.668082\pi$
$557$	9.71173	−	29.8896i	0.411499	−	1.26646i	0.915345	−	0.402671i	$-0.131918\pi$
$558$		0			0
$559$	2.67839	−	1.94596i	0.113284	−	0.0823055i
$560$	−7.51378	−	13.0143i	−0.317515	−	0.549952i
$561$		0			0
$562$	5.53190	−	9.58153i	0.233349	−	0.404172i
$563$	0.313408	+	2.98188i	0.0132086	+	0.125671i	0.999139	−	0.0414840i	$-0.0132086\pi$
$563$	0.313408	+	2.98188i	0.0132086	+	0.125671i	−0.985931	+	0.167155i	$0.946542\pi$
$564$		0			0
$565$	22.1233	−	4.70246i	0.930735	−	0.197834i
$566$	10.4938	−	14.4435i	0.441088	−	0.607105i
$567$		0			0
$568$	1.74671	+	0.567541i	0.0732903	+	0.0238135i
$569$	−27.5009	+	30.5428i	−1.15290	+	1.28042i	−0.199096	+	0.979980i	$0.563801\pi$
$569$	−27.5009	+	30.5428i	−1.15290	+	1.28042i	−0.953800	+	0.300442i	$0.902866\pi$
$570$		0			0
$571$	11.6392	+	6.71989i	0.487085	+	0.281219i	0.723364	−	0.690466i	$-0.242595\pi$
$571$	11.6392	+	6.71989i	0.487085	+	0.281219i	−0.236279	+	0.971685i	$0.575928\pi$
$572$	−1.12411	+	0.177011i	−0.0470013	+	0.00740121i
$573$		0			0
$574$	−13.2043	+	29.6572i	−0.551135	+	1.23787i
$575$	−12.4508	+	4.04550i	−0.519233	+	0.168709i
$576$		0			0
$577$	−6.44828	−	4.68495i	−0.268445	−	0.195037i	0.445417	−	0.895323i	$-0.353056\pi$
$577$	−6.44828	−	4.68495i	−0.268445	−	0.195037i	−0.713862	+	0.700287i	$0.753056\pi$
$578$	−0.775654	+	7.37986i	−0.0322630	+	0.306962i
$579$		0			0
$580$	−3.84809	+	18.1039i	−0.159783	+	0.751722i
$581$	27.5887	−	2.89969i	1.14457	−	0.120300i
$582$		0			0
$583$	−11.6695	−	0.622030i	−0.483300	−	0.0257618i
$584$			34.3724i			1.42234i
$585$		0			0
$586$	−4.11099	−	12.6523i	−0.169823	−	0.522662i
$587$	−4.93390	−	23.2122i	−0.203644	−	0.958069i	−0.954640	−	0.297763i	$-0.903760\pi$
$587$	−4.93390	−	23.2122i	−0.203644	−	0.958069i	0.750996	−	0.660307i	$-0.229574\pi$
$588$		0			0
$589$	−1.32881	−	2.98455i	−0.0547525	−	0.122976i
$590$	24.6637	+	27.3918i	1.01539	+	1.12770i
$591$		0			0
$592$	−3.47189	−	1.54578i	−0.142694	−	0.0635313i
$593$	29.4804			1.21062			0.605308	−	0.795991i	$-0.293050\pi$
$593$	29.4804			1.21062			0.605308	+	0.795991i	$0.293050\pi$
$594$		0			0
$595$	40.5236			1.66131
$596$	0.00838435	+	0.00373295i	0.000343436	+	0.000152908i
$597$		0			0
$598$	−0.687857	−	0.763942i	−0.0281286	−	0.0312399i
$599$	−12.1546	−	27.2996i	−0.496622	−	1.11543i	−0.971857	−	0.235573i	$-0.924303\pi$
$599$	−12.1546	−	27.2996i	−0.496622	−	1.11543i	0.475235	−	0.879859i	$-0.342363\pi$
$600$		0			0
$601$	−1.38398	−	6.51111i	−0.0564537	−	0.265594i	0.940864	−	0.338784i	$-0.110015\pi$
$601$	−1.38398	−	6.51111i	−0.0564537	−	0.265594i	−0.997318	+	0.0731898i	$0.976682\pi$
$602$	−12.2247	−	37.6237i	−0.498241	−	1.53343i
$603$		0			0
$604$		−	0.370559i		−	0.0150778i
$605$	−27.6632	+	20.0231i	−1.12467	+	0.814053i
$606$		0			0
$607$	−31.9190	+	3.35482i	−1.29555	+	0.136168i	−0.727091	−	0.686541i	$-0.759128\pi$
$607$	−31.9190	+	3.35482i	−1.29555	+	0.136168i	−0.568462	+	0.822709i	$0.692462\pi$
$608$	−0.407832	+	1.91870i	−0.0165398	+	0.0778136i
$609$		0			0
$610$	−0.393319	+	3.74218i	−0.0159250	+	0.151517i
$611$	−3.65979	−	2.65900i	−0.148059	−	0.107571i
$612$		0			0
$613$	10.3905	−	3.37608i	0.419668	−	0.136358i	−0.0915678	−	0.995799i	$-0.529188\pi$
$613$	10.3905	−	3.37608i	0.419668	−	0.136358i	0.511236	+	0.859440i	$0.329188\pi$
$614$	−11.4365	+	25.6869i	−0.461541	+	1.03664i
$615$		0			0
$616$	−6.59318	+	41.3882i	−0.265647	+	1.66758i
$617$	6.10692	+	3.52583i	0.245855	+	0.141945i	0.617865	−	0.786284i	$-0.287998\pi$
$617$	6.10692	+	3.52583i	0.245855	+	0.141945i	−0.372010	+	0.928229i	$0.621331\pi$
$618$		0			0
$619$	−25.9808	+	28.8546i	−1.04426	+	1.15976i	−0.0573687	+	0.998353i	$0.518271\pi$
$619$	−25.9808	+	28.8546i	−1.04426	+	1.15976i	−0.986887	+	0.161411i	$0.948396\pi$
$620$	−22.9463	−	7.45570i	−0.921545	−	0.299428i
$621$		0			0
$622$	4.56594	−	6.28448i	0.183077	−	0.251985i
$623$	−29.8902	+	6.35336i	−1.19753	+	0.254542i
$624$		0			0
$625$	2.78878	+	26.5335i	0.111551	+	1.06134i
$626$	6.80511	−	11.7868i	0.271987	−	0.471095i
$627$		0			0
$628$	1.40678	+	2.43662i	0.0561368	+	0.0972317i
$629$	8.29111	−	6.02384i	0.330588	−	0.240186i
$630$		0			0
$631$	−9.93575	+	30.5791i	−0.395536	+	1.21733i	0.533007	+	0.846111i	$0.321062\pi$
$631$	−9.93575	+	30.5791i	−0.395536	+	1.21733i	−0.928543	+	0.371224i	$0.878938\pi$
$632$	14.5300	+	1.52717i	0.577973	+	0.0607474i
$633$		0			0
$634$	−5.80891	+	5.23037i	−0.230701	+	0.207724i
$635$	−41.6188	−	8.84635i	−1.65159	−	0.351057i
$636$		0			0
$637$	−3.25631	+	1.88003i	−0.129020	+	0.0744896i
$638$	−16.3220	+	13.1931i	−0.646193	+	0.522321i
$639$		0			0
$640$	4.21268	+	5.79826i	0.166521	+	0.229196i
$641$	−23.2829	−	20.9640i	−0.919618	−	0.828028i	0.0658602	−	0.997829i	$-0.479021\pi$
$641$	−23.2829	−	20.9640i	−0.919618	−	0.828028i	−0.985478	+	0.169801i	$0.945688\pi$
$642$		0			0
$643$	−9.76506	+	4.34768i	−0.385096	+	0.171456i	−0.590148	−	0.807295i	$-0.700930\pi$
$643$	−9.76506	+	4.34768i	−0.385096	+	0.171456i	0.205051	+	0.978751i	$0.434264\pi$
$644$	10.3698	−	4.61695i	0.408629	−	0.181933i
$645$		0			0
$646$	0.953888	+	0.858885i	0.0375302	+	0.0337924i
$647$	−14.2861	−	19.6631i	−0.561644	−	0.773037i	0.429890	−	0.902881i	$-0.358552\pi$
$647$	−14.2861	−	19.6631i	−0.561644	−	0.773037i	−0.991534	+	0.129844i	$0.958552\pi$
$648$		0			0
$649$	−1.98692	−	38.5724i	−0.0779936	−	1.51410i
$650$	1.46271	−	0.844496i	0.0573722	−	0.0331239i
$651$		0			0
$652$	−12.5433	−	2.66615i	−0.491232	−	0.104415i
$653$	−35.3729	+	31.8499i	−1.38425	+	1.24638i	−0.448470	+	0.893798i	$0.648031\pi$
$653$	−35.3729	+	31.8499i	−1.38425	+	1.24638i	−0.935780	+	0.352585i	$0.885303\pi$
$654$		0			0
$655$	57.2055	+	6.01254i	2.23520	+	0.234929i
$656$	−2.71759	+	8.36388i	−0.106104	+	0.326555i
$657$		0			0
$658$	−43.7316	+	31.7729i	−1.70484	+	1.23864i
$659$	−11.5685	−	20.0373i	−0.450646	−	0.780542i	0.547780	−	0.836622i	$-0.315473\pi$
$659$	−11.5685	−	20.0373i	−0.450646	−	0.780542i	−0.998426	+	0.0560804i	$0.982140\pi$
$660$		0			0
$661$	9.44397	−	16.3574i	0.367328	−	0.636231i	−0.621819	−	0.783161i	$-0.713606\pi$
$661$	9.44397	−	16.3574i	0.367328	−	0.636231i	0.989147	+	0.146930i	$0.0469393\pi$
$662$	−0.780721	−	7.42807i	−0.0303436	−	0.288700i
$663$		0			0
$664$	19.5636	−	4.15837i	0.759214	−	0.161376i
$665$	−3.08466	+	4.24568i	−0.119618	+	0.164640i
$666$		0			0
$667$	16.6624	+	5.41395i	0.645172	+	0.209629i
$668$	−4.93615	+	5.48215i	−0.190985	+	0.212111i
$669$		0			0
$670$	42.0178	+	24.2590i	1.62329	+	0.937207i
$671$	2.79054	−	2.78556i	0.107728	−	0.107535i
$672$		0			0
$673$	11.8676	−	26.6552i	0.457464	−	1.02748i	−0.526672	−	0.850068i	$-0.676560\pi$
$673$	11.8676	−	26.6552i	0.457464	−	1.02748i	0.984136	−	0.177413i	$-0.0567728\pi$
$674$	7.01286	−	2.27862i	0.270125	−	0.0877691i
$675$		0			0
$676$	10.0032	+	7.26772i	0.384737	+	0.279528i
$677$	1.66846	−	15.8743i	0.0641239	−	0.610099i	−0.914521	−	0.404539i	$-0.867432\pi$
$677$	1.66846	−	15.8743i	0.0641239	−	0.610099i	0.978645	−	0.205559i	$-0.0659014\pi$
$678$		0			0
$679$	4.52552	−	21.2909i	0.173674	−	0.817070i
$680$	29.0569	−	3.05400i	1.11428	−	0.117116i
$681$		0			0
$682$	−14.8801	−	22.9582i	−0.569788	−	0.879117i
$683$		−	4.33022i		−	0.165691i	−0.996562	−	0.0828457i	$-0.973599\pi$
$683$		−	4.33022i		−	0.165691i	0.996562	−	0.0828457i	$-0.0264009\pi$
$684$		0			0
$685$	−18.6411	−	57.3714i	−0.712239	−	2.19205i
$686$	3.12950	+	14.7232i	0.119485	+	0.562133i
$687$		0			0
$688$	−4.35883	−	9.79009i	−0.166179	−	0.373244i
$689$	−0.842155	−	0.935308i	−0.0320836	−	0.0356324i
$690$		0			0
$691$	−20.8396	−	9.27838i	−0.792775	−	0.352966i	−0.0299338	−	0.999552i	$-0.509530\pi$
$691$	−20.8396	−	9.27838i	−0.792775	−	0.352966i	−0.762841	+	0.646586i	$0.776196\pi$
$692$	11.9278			0.453428
$693$		0			0
$694$	25.1785			0.955763
$695$	9.97762	+	4.44232i	0.378473	+	0.168507i
$696$		0			0
$697$	−15.8684	−	17.6236i	−0.601057	−	0.667541i
$698$	5.85714	+	13.1554i	0.221696	+	0.497938i
$699$		0			0
$700$	3.87759	+	18.2426i	0.146559	+	0.689506i
$701$	11.9110	+	36.6583i	0.449872	+	1.38456i	0.877052	+	0.480396i	$0.159507\pi$
$701$	11.9110	+	36.6583i	0.449872	+	1.38456i	−0.427180	+	0.904167i	$0.640493\pi$
$702$		0			0
$703$			1.32720i			0.0500563i
$704$	−1.28261	+	24.0622i	−0.0483403	+	0.906878i
$705$		0			0
$706$	−15.2750	+	1.60547i	−0.574883	+	0.0604227i
$707$	−7.08283	+	33.3221i	−0.266377	+	1.25321i
$708$		0			0
$709$	−2.69969	+	25.6859i	−0.101389	+	0.964653i	0.819038	+	0.573739i	$0.194508\pi$
$709$	−2.69969	+	25.6859i	−0.101389	+	0.964653i	−0.920427	+	0.390914i	$0.872159\pi$
$710$	1.55808	+	1.13201i	0.0584737	+	0.0424836i
$711$		0			0
$712$	−20.9535	+	6.80821i	−0.785266	+	0.255148i
$713$	−9.28934	+	20.8642i	−0.347888	+	0.781370i
$714$		0			0
$715$	−3.63208	−	0.578593i	−0.135832	−	0.0216381i
$716$	4.41046	+	2.54638i	0.164826	+	0.0951626i
$717$		0			0
$718$	4.88236	−	5.42241i	0.182208	−	0.202363i
$719$	−28.7908	−	9.35469i	−1.07371	−	0.348871i	−0.281781	−	0.959479i	$-0.590925\pi$
$719$	−28.7908	−	9.35469i	−1.07371	−	0.348871i	−0.791933	+	0.610608i	$0.790925\pi$
$720$		0			0
$721$	−33.9639	+	46.7473i	−1.26488	+	1.74096i
$722$	18.7853	−	3.99293i	0.699115	−	0.148601i
$723$		0			0
$724$	−1.71722	−	16.3382i	−0.0638199	−	0.607206i
$725$	−14.3927	+	24.9289i	−0.534532	+	0.925837i
$726$		0			0
$727$	20.5282	+	35.5559i	0.761349	+	1.31870i	0.942155	+	0.335177i	$0.108796\pi$
$727$	20.5282	+	35.5559i	0.761349	+	1.31870i	−0.180806	+	0.983519i	$0.557871\pi$
$728$	−3.65166	+	2.65309i	−0.135340	+	0.0983299i
$729$		0			0
$730$	−11.1381	+	34.2795i	−0.412239	+	1.26874i
$731$	28.7402	+	3.02072i	1.06300	+	0.111725i
$732$		0			0
$733$	7.38362	−	6.64824i	0.272720	−	0.245558i	−0.521410	−	0.853306i	$-0.674594\pi$
$733$	7.38362	−	6.64824i	0.272720	−	0.245558i	0.794130	+	0.607748i	$0.207927\pi$
$734$	4.23338	+	0.899833i	0.156257	+	0.0332134i
$735$		0			0
$736$	11.8756	−	6.85639i	0.437741	−	0.252730i
$737$	−18.1771	−	47.4797i	−0.669562	−	1.74894i
$738$		0			0
$739$	−16.1574	−	22.2387i	−0.594359	−	0.818065i	0.400818	−	0.916158i	$-0.368726\pi$
$739$	−16.1574	−	22.2387i	−0.594359	−	0.818065i	−0.995177	+	0.0980925i	$0.968726\pi$
$740$	7.28395	+	6.55850i	0.267764	+	0.241095i
$741$		0			0
$742$	−13.7389	+	6.11694i	−0.504370	+	0.224560i
$743$	26.2330	−	11.6797i	0.962396	−	0.428486i	0.135460	−	0.990783i	$-0.456749\pi$
$743$	26.2330	−	11.6797i	0.962396	−	0.428486i	0.826936	+	0.562297i	$0.190082\pi$
$744$		0			0
$745$	0.0220436	+	0.0198482i	0.000807616	+	0.000727181i
$746$	12.1925	+	16.7816i	0.446400	+	0.614417i
$747$		0			0
$748$	−8.32579	−	5.41742i	−0.304421	−	0.198080i
$749$	−14.6989	+	8.48643i	−0.537087	+	0.310087i
$750$		0			0
$751$	−28.0532	−	5.96289i	−1.02367	−	0.217589i	−0.334662	−	0.942338i	$-0.608622\pi$
$751$	−28.0532	−	5.96289i	−1.02367	−	0.217589i	−0.689013	+	0.724749i	$0.741956\pi$
$752$	−10.8821	+	9.79829i	−0.396829	+	0.357307i
$753$		0			0
$754$	−2.24794	−	0.236268i	−0.0818651	−	0.00860437i
$755$	0.370092	−	1.13903i	0.0134690	−	0.0414534i
$756$		0			0
$757$	23.4351	−	17.0266i	0.851763	−	0.618842i	−0.0738684	−	0.997268i	$-0.523534\pi$
$757$	23.4351	−	17.0266i	0.851763	−	0.618842i	0.925632	+	0.378426i	$0.123534\pi$
$758$	14.9081	+	25.8216i	0.541487	+	0.937883i
$759$		0			0
$760$	−1.89185	+	3.27677i	−0.0686244	+	0.118861i
$761$	4.69898	+	44.7078i	0.170338	+	1.62066i	0.661746	+	0.749728i	$0.269816\pi$
$761$	4.69898	+	44.7078i	0.170338	+	1.62066i	−0.491408	+	0.870930i	$0.663518\pi$
$762$		0			0
$763$	−22.8424	+	4.85530i	−0.826951	+	0.175774i
$764$	−5.01201	+	6.89844i	−0.181328	+	0.249577i
$765$		0			0
$766$	−4.76164	−	1.54715i	−0.172045	−	0.0559008i
$767$	2.78341	−	3.09129i	0.100503	−	0.111620i
$768$		0			0
$769$	−0.942343	−	0.544062i	−0.0339818	−	0.0196194i	0.482913	−	0.875668i	$-0.339579\pi$
$769$	−0.942343	−	0.544062i	−0.0339818	−	0.0196194i	−0.516895	+	0.856049i	$0.672912\pi$
$770$	−19.9868	+	39.1398i	−0.720275	+	1.41050i
$771$		0			0
$772$	0.563852	−	1.26643i	0.0202935	−	0.0455799i
$773$	5.28257	−	1.71641i	0.190001	−	0.0617350i	−0.212471	−	0.977167i	$-0.568151\pi$
$773$	5.28257	−	1.71641i	0.190001	−	0.0617350i	0.402472	+	0.915432i	$0.368151\pi$
$774$		0			0
$775$	−30.3578	−	22.0562i	−1.09048	−	0.792282i
$776$	1.64040	−	15.6074i	0.0588871	−	0.560273i
$777$		0			0
$778$	−3.63377	+	17.0956i	−0.130277	+	0.612905i
$779$	3.05433	−	0.321024i	0.109433	−	0.0115019i
$780$		0			0
$781$	−0.520573	−	1.94977i	−0.0186276	−	0.0697684i
$782$		−	8.97319i		−	0.320881i
$783$		0			0
$784$	3.76113	+	11.5756i	0.134326	+	0.413413i
$785$	1.89063	+	8.89471i	0.0674794	+	0.317466i
$786$		0			0
$787$	−9.85328	−	22.1308i	−0.351231	−	0.788879i	−0.999620	−	0.0275689i	$-0.991223\pi$
$787$	−9.85328	−	22.1308i	−0.351231	−	0.788879i	0.648389	−	0.761310i	$-0.275443\pi$
$788$	11.8618	+	13.1738i	0.422559	+	0.469299i
$789$		0			0
$790$	13.9959	+	6.23136i	0.497950	+	0.221702i
$791$	−30.5003			−1.08447
$792$		0			0
$793$	0.424649			0.0150797
$794$	7.39912	+	3.29430i	0.262585	+	0.116910i
$795$		0			0
$796$	−11.7872	−	13.0910i	−0.417787	−	0.463999i
$797$	4.37302	+	9.82197i	0.154900	+	0.347912i	0.974281	−	0.225339i	$-0.0723488\pi$
$797$	4.37302	+	9.82197i	0.154900	+	0.347912i	−0.819380	+	0.573251i	$0.805682\pi$
$798$		0			0
$799$	−8.20990	−	38.6245i	−0.290445	−	1.36644i
$800$	6.96224	+	21.4276i	0.246152	+	0.757579i
$801$		0			0
$802$			6.56948i			0.231976i
$803$	31.6939	−	20.5420i	1.11845	−	0.724912i
$804$		0			0
$805$	36.4860	−	3.83483i	1.28596	−	0.135160i
$806$	0.612616	−	2.88213i	0.0215785	−	0.101519i
$807$		0			0
$808$	−2.56737	+	24.4269i	−0.0903198	+	0.859336i
$809$	12.6347	+	9.17967i	0.444213	+	0.322740i	0.787307	−	0.616561i	$-0.211475\pi$
$809$	12.6347	+	9.17967i	0.444213	+	0.322740i	−0.343093	+	0.939301i	$0.611475\pi$
$810$		0			0
$811$	51.9356	−	16.8749i	1.82370	−	0.592557i	0.824043	−	0.566528i	$-0.191714\pi$
$811$	51.9356	−	16.8749i	1.82370	−	0.592557i	0.999661	−	0.0260296i	$-0.00828640\pi$
$812$	10.1517	−	22.8011i	0.356254	−	0.800160i
$813$		0			0
$814$	1.72885	+	10.9790i	0.0605962	+	0.384815i
$815$	−35.8928	−	20.7227i	−1.25727	−	0.725885i
$816$		0			0
$817$	−2.50419	+	2.78119i	−0.0876107	+	0.0973015i
$818$	−15.4814	−	5.03020i	−0.541294	−	0.175877i
$819$		0			0
$820$	13.3315	−	18.3492i	0.465556	−	0.640782i
$821$	19.6650	−	4.17993i	0.686315	−	0.145881i	0.148460	−	0.988918i	$-0.452568\pi$
$821$	19.6650	−	4.17993i	0.686315	−	0.145881i	0.537854	+	0.843038i	$0.319235\pi$
$822$		0			0
$823$	4.18321	+	39.8005i	0.145817	+	1.38736i	0.785567	+	0.618777i	$0.212371\pi$
$823$	4.18321	+	39.8005i	0.145817	+	1.38736i	−0.639750	+	0.768583i	$0.720962\pi$
$824$	−20.8303	+	36.0791i	−0.725658	+	1.25688i
$825$		0			0
$826$	−24.8528	−	43.0463i	−0.864740	−	1.49777i
$827$	−36.6966	+	26.6617i	−1.27607	+	0.927117i	−0.999427	−	0.0338566i	$-0.989221\pi$
$827$	−36.6966	+	26.6617i	−1.27607	+	0.927117i	−0.276640	+	0.960974i	$0.589221\pi$
$828$		0			0
$829$	−11.8926	+	36.6018i	−0.413049	+	1.27123i	0.500936	+	0.865484i	$0.332989\pi$
$829$	−11.8926	+	36.6018i	−0.413049	+	1.27123i	−0.913985	+	0.405749i	$0.867011\pi$
$830$	20.8582	+	2.19228i	0.723997	+	0.0760951i
$831$		0			0
$832$	−1.92859	+	1.73651i	−0.0668617	+	0.0602025i
$833$	−32.1041	−	6.82393i	−1.11234	−	0.236435i
$834$		0			0
$835$	−20.6480	+	11.9211i	−0.714554	+	0.412548i
$836$	1.20135	−	0.459922i	0.0415494	−	0.0159067i
$837$		0			0
$838$	2.18314	+	3.00484i	0.0754154	+	0.103800i
$839$	−4.40930	−	3.97015i	−0.152226	−	0.137065i	0.589499	−	0.807769i	$-0.299325\pi$
$839$	−4.40930	−	3.97015i	−0.152226	−	0.137065i	−0.741725	+	0.670704i	$0.765992\pi$
$840$		0			0
$841$	8.69929	−	3.87317i	0.299975	−	0.133558i
$842$	−12.2981	+	5.47548i	−0.423822	+	0.188698i
$843$		0			0
$844$	−3.26802	−	2.94254i	−0.112490	−	0.101286i
$845$	23.4892	+	32.3301i	0.808053	+	1.11219i
$846$		0			0
$847$	42.1032	−	18.6555i	1.44668	−	0.641009i
$848$	−3.52819	+	2.03700i	−0.121159	+	0.0699510i
$849$		0			0
$850$	14.4209	+	3.06525i	0.494632	+	0.105137i
$851$	6.89497	−	6.20826i	0.236357	−	0.212816i
$852$		0			0
$853$	−3.11737	−	0.327649i	−0.106737	−	0.0112185i	0.0510094	−	0.998698i	$-0.483756\pi$
$853$	−3.11737	−	0.327649i	−0.106737	−	0.0112185i	−0.157746	+	0.987480i	$0.550423\pi$
$854$	1.56802	−	4.82587i	0.0536565	−	0.165138i
$855$		0			0
$856$	−9.90009	+	7.19283i	−0.338378	+	0.245846i
$857$	21.2277	+	36.7674i	0.725124	+	1.25595i	0.958923	+	0.283666i	$0.0915507\pi$
$857$	21.2277	+	36.7674i	0.725124	+	1.25595i	−0.233800	+	0.972285i	$0.575116\pi$
$858$		0			0
$859$	−0.508100	+	0.880055i	−0.0173361	+	0.0300271i	−0.874563	−	0.484911i	$-0.838852\pi$
$859$	−0.508100	+	0.880055i	−0.0173361	+	0.0300271i	0.857227	+	0.514938i	$0.172185\pi$
$860$	2.88901	+	27.4871i	0.0985145	+	0.937303i
$861$		0			0
$862$	15.5006	−	3.29476i	0.527953	−	0.112220i
$863$	−6.08271	+	8.37213i	−0.207058	+	0.284991i	−0.899898	−	0.436101i	$-0.856359\pi$
$863$	−6.08271	+	8.37213i	−0.207058	+	0.284991i	0.692840	+	0.721091i	$0.256359\pi$
$864$		0			0
$865$	36.6638	+	11.9128i	1.24661	+	0.405048i
$866$	8.48832	−	9.42723i	0.288445	−	0.320350i
$867$		0			0
$868$	28.1770	+	16.2680i	0.956390	+	0.552172i
$869$	−7.27542	−	14.3104i	−0.246802	−	0.485448i
$870$		0			0
$871$	2.22708	−	5.00210i	0.0754616	−	0.169490i
$872$	−16.0129	+	5.20291i	−0.542265	+	0.176193i
$873$		0			0
$874$	0.940125	+	0.683041i	0.0318002	+	0.0231042i
$875$	0.492018	−	4.68123i	0.0166332	−	0.158255i
$876$		0			0
$877$	6.10304	−	28.7126i	0.206085	−	0.969554i	−0.746524	−	0.665358i	$-0.768279\pi$
$877$	6.10304	−	28.7126i	0.206085	−	0.969554i	0.952609	−	0.304196i	$-0.0983878\pi$
$878$	−11.6300	+	1.22236i	−0.392494	+	0.0412528i
$879$		0			0
$880$	−4.27638	+	11.1107i	−0.144157	+	0.374540i
$881$		−	28.0964i		−	0.946592i	−0.880903	−	0.473296i	$-0.843064\pi$
$881$		−	28.0964i		−	0.946592i	0.880903	−	0.473296i	$-0.156936\pi$
$882$		0			0
$883$	−3.44111	−	10.5906i	−0.115802	−	0.356403i	0.876311	−	0.481746i	$-0.159997\pi$
$883$	−3.44111	−	10.5906i	−0.115802	−	0.356403i	−0.992114	+	0.125342i	$0.959997\pi$
$884$	−0.222423	−	1.04642i	−0.00748089	−	0.0351948i
$885$		0			0
$886$	−3.04857	−	6.84719i	−0.102419	−	0.230036i
$887$	−15.9245	−	17.6859i	−0.534691	−	0.593835i	0.413907	−	0.910319i	$-0.364164\pi$
$887$	−15.9245	−	17.6859i	−0.534691	−	0.593835i	−0.948598	+	0.316485i	$0.897497\pi$
$888$		0			0
$889$	52.4172	+	23.3376i	1.75802	+	0.782719i
$890$	−23.1030			−0.774414
$891$		0			0
$892$	10.4843			0.351042
$893$	4.67165	+	2.07995i	0.156331	+	0.0696029i
$894$		0			0
$895$	11.0137	+	12.2320i	0.368148	+	0.408870i
$896$	−3.93108	−	8.82935i	−0.131328	−	0.294968i
$897$		0			0
$898$	−0.933586	−	4.39217i	−0.0311542	−	0.146569i
$899$	15.5180	+	47.7596i	0.517556	+	1.59287i
$900$		0			0
$901$		−	10.9860i		−	0.365998i
$902$	24.8483	−	6.63428i	0.827358	−	0.220897i
$903$		0			0
$904$	−21.8698	+	2.29861i	−0.727379	+	0.0764506i
$905$	11.0393	−	51.9356i	0.366957	−	1.72640i
$906$		0			0
$907$	0.122217	−	1.16282i	0.00405815	−	0.0386107i	−0.992305	−	0.123814i	$-0.960487\pi$
$907$	0.122217	−	1.16282i	0.00405815	−	0.0386107i	0.996364	+	0.0852034i	$0.0271540\pi$
$908$	−2.19174	−	1.59239i	−0.0727353	−	0.0528453i
$909$		0			0
$910$	−4.50149	+	1.46262i	−0.149223	+	0.0484855i
$911$	0.581857	−	1.30687i	0.0192778	−	0.0432986i	−0.903650	−	0.428272i	$-0.859123\pi$
$911$	0.581857	−	1.30687i	0.0192778	−	0.0432986i	0.922928	+	0.384973i	$0.125789\pi$
$912$		0			0
$913$	−15.5261	−	15.5539i	−0.513839	−	0.514758i
$914$	5.56355	+	3.21212i	0.184026	+	0.106247i
$915$		0			0
$916$	−1.27981	+	1.42137i	−0.0422860	+	0.0469633i
$917$	−73.7713	−	23.9698i	−2.43614	−	0.791551i
$918$		0			0
$919$	−7.86498	+	10.8252i	−0.259442	+	0.357091i	−0.918790	−	0.394747i	$-0.870832\pi$
$919$	−7.86498	+	10.8252i	−0.259442	+	0.357091i	0.659348	+	0.751838i	$0.270832\pi$
$920$	25.8728	−	5.49943i	0.853000	−	0.181311i
$921$		0			0
$922$	−1.09970	−	10.4630i	−0.0362167	−	0.344579i
$923$	0.108673	−	0.188227i	0.00357701	−	0.00619556i
$924$		0			0
$925$	7.62201	+	13.2017i	0.250610	+	0.434070i
$926$	1.39661	−	1.01469i	0.0458953	−	0.0333449i
$927$		0			0
$928$	9.31732	−	28.6758i	0.305856	−	0.941328i
$929$	−54.8428	−	5.76422i	−1.79934	−	0.189118i	−0.855116	−	0.518436i	$-0.826514\pi$
$929$	−54.8428	−	5.76422i	−1.79934	−	0.189118i	−0.944219	+	0.329318i	$0.893181\pi$
$930$		0			0
$931$	3.15871	−	2.84412i	0.103523	−	0.0932122i
$932$	−22.8606	−	4.85916i	−0.748823	−	0.159167i
$933$		0			0
$934$	−21.2934	+	12.2937i	−0.696741	+	0.402264i
$935$	−20.1813	−	24.9674i	−0.659998	−	0.816521i
$936$		0			0
$937$	14.4585	+	19.9004i	0.472339	+	0.650118i	0.977010	−	0.213193i	$-0.0683863\pi$
$937$	14.4585	+	19.9004i	0.472339	+	0.650118i	−0.504671	+	0.863312i	$0.668386\pi$
$938$	−48.6222	−	43.7796i	−1.58757	−	1.42946i
$939$		0			0
$940$	34.5007	−	15.3607i	1.12529	−	0.501011i
$941$	−19.9171	+	8.86765i	−0.649278	+	0.289077i	−0.704827	−	0.709379i	$-0.748976\pi$
$941$	−19.9171	+	8.86765i	−0.649278	+	0.289077i	0.0555497	+	0.998456i	$0.482309\pi$
$942$		0			0
$943$	−15.9551	−	14.3660i	−0.519568	−	0.467821i
$944$	−7.91453	−	10.8934i	−0.257596	−	0.354550i
$945$		0			0
$946$	−17.0927	+	26.2690i	−0.555731	+	0.854078i
$947$	−41.1841	+	23.7776i	−1.33830	+	0.772669i	−0.986556	−	0.163426i	$-0.947745\pi$
$947$	−41.1841	+	23.7776i	−1.33830	+	0.772669i	−0.351747	+	0.936095i	$0.614412\pi$
$948$		0			0
$949$	3.97879	+	0.845718i	0.129157	+	0.0274532i
$950$	−1.41887	+	1.27756i	−0.0460342	+	0.0414494i
$951$		0			0
$952$	−39.1838	−	4.11839i	−1.26996	−	0.133478i
$953$	−13.1907	+	40.5969i	−0.427290	+	1.31506i	0.473495	+	0.880797i	$0.342992\pi$
$953$	−13.1907	+	40.5969i	−0.427290	+	1.31506i	−0.900785	+	0.434266i	$0.857008\pi$
$954$		0			0
$955$	−22.2957	+	16.1988i	−0.721472	+	0.524180i
$956$	−4.81724	−	8.34371i	−0.155801	−	0.269855i
$957$		0			0
$958$	19.0094	−	32.9252i	0.614166	−	1.06377i
$959$	8.50318	+	80.9024i	0.274582	+	2.61247i
$960$		0			0
$961$	−33.7096	+	7.16520i	−1.08741	+	0.231136i
$962$	−0.703584	+	0.968400i	−0.0226845	+	0.0312225i
$963$		0			0
$964$	−15.8202	−	5.14029i	−0.509534	−	0.165558i
$965$	2.99801	−	3.32962i	0.0965093	−	0.107184i
$966$		0			0
$967$	1.29188	+	0.745867i	0.0415440	+	0.0239855i	0.520628	−	0.853784i	$-0.325698\pi$
$967$	1.29188	+	0.745867i	0.0415440	+	0.0239855i	−0.479084	+	0.877769i	$0.659031\pi$
$968$	28.7836	−	16.5497i	0.925139	−	0.531927i
$969$		0			0
$970$	6.69340	−	15.0336i	0.214912	−	0.482701i
$971$	2.12249	−	0.689639i	0.0681140	−	0.0221316i	−0.274762	−	0.961512i	$-0.588599\pi$
$971$	2.12249	−	0.689639i	0.0681140	−	0.0221316i	0.342876	+	0.939381i	$0.388599\pi$
$972$		0			0
$973$	−11.9155	−	8.65712i	−0.381994	−	0.277535i
$974$	4.05359	−	38.5673i	0.129885	−	1.23578i
$975$		0			0
$976$	0.285791	−	1.34454i	0.00914796	−	0.0430377i
$977$	−43.9821	+	4.62270i	−1.40711	+	0.147893i	−0.777434	−	0.628964i	$-0.783479\pi$
$977$	−43.9821	+	4.62270i	−1.40711	+	0.147893i	−0.629677	+	0.776857i	$0.716813\pi$
$978$		0			0
$979$	18.8001	+	15.2519i	0.600855	+	0.487452i
$980$		−	31.3902i		−	1.00272i
$981$		0			0
$982$	9.02219	+	27.7674i	0.287910	+	0.886095i
$983$	8.86392	+	41.7015i	0.282715	+	1.33007i	0.858645	+	0.512571i	$0.171307\pi$
$983$	8.86392	+	41.7015i	0.282715	+	1.33007i	−0.575930	+	0.817499i	$0.695360\pi$
$984$		0			0
$985$	23.3036	+	52.3407i	0.742514	+	1.66771i
$986$	−13.2020	−	14.6623i	−0.420438	−	0.466944i
$987$		0			0
$988$	0.126565	+	0.0563501i	0.00402655	+	0.00179274i
$989$	26.1625			0.831920
$990$		0			0
$991$	−1.45490			−0.0462164			−0.0231082	−	0.999733i	$-0.507356\pi$
$991$	−1.45490			−0.0462164			−0.0231082	+	0.999733i	$0.507356\pi$
$992$	35.9069	+	15.9868i	1.14005	+	0.507581i
$993$		0			0
$994$	−1.73781	−	1.93003i	−0.0551198	−	0.0612168i
$995$	−23.1571	−	52.0116i	−0.734128	−	1.64888i
$996$		0			0
$997$	−10.9123	−	51.3381i	−0.345595	−	1.62590i	−0.716754	−	0.697326i	$-0.754373\pi$
$997$	−10.9123	−	51.3381i	−0.345595	−	1.62590i	0.371159	−	0.928569i	$-0.378960\pi$
$998$	4.84912	+	14.9241i	0.153496	+	0.472413i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.e.701.3		64
3.2	odd	2	inner	891.2.u.e.701.6		64
9.2	odd	6	inner	891.2.u.e.107.3		64
9.4	even	3		297.2.k.a.107.6	yes	32
9.5	odd	6		297.2.k.a.107.3	✓	32
9.7	even	3	inner	891.2.u.e.107.6		64
11.7	odd	10	inner	891.2.u.e.458.3		64
33.29	even	10	inner	891.2.u.e.458.6		64
99.7	odd	30	inner	891.2.u.e.755.6		64
99.29	even	30	inner	891.2.u.e.755.3		64
99.40	odd	30		297.2.k.a.161.3	yes	32
99.95	even	30		297.2.k.a.161.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.k.a.107.3	✓	32	9.5	odd	6
297.2.k.a.107.6	yes	32	9.4	even	3
297.2.k.a.161.3	yes	32	99.40	odd	30
297.2.k.a.161.6	yes	32	99.95	even	30
891.2.u.e.107.3		64	9.2	odd	6	inner
891.2.u.e.107.6		64	9.7	even	3	inner
891.2.u.e.458.3		64	11.7	odd	10	inner
891.2.u.e.458.6		64	33.29	even	10	inner
891.2.u.e.701.3		64	1.1	even	1	trivial
891.2.u.e.701.6		64	3.2	odd	2	inner
891.2.u.e.755.3		64	99.29	even	30	inner
891.2.u.e.755.6		64	99.7	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.931391 - 0.414682i) q^{2} +(-0.642733 - 0.713827i) q^{4} +(-1.26271 - 2.83609i) q^{5} +(0.870416 + 4.09498i) q^{7} +(0.932731 + 2.87065i) q^{8} +3.16513i q^{10} +(2.08952 - 2.57564i) q^{11} +(0.355243 - 0.0373375i) q^{13} +(0.887419 - 4.17498i) q^{14} +(0.120861 - 1.14991i) q^{16} +(2.52248 + 1.83269i) q^{17} +(-0.384024 + 0.124777i) q^{19} +(-1.21289 + 2.72420i) q^{20} +(-3.01423 + 1.53244i) q^{22} +(2.44458 + 1.41138i) q^{23} +(-3.10332 + 3.44658i) q^{25} +(-0.346353 - 0.112537i) q^{26} +(2.36367 - 3.25331i) q^{28} +(6.07102 - 1.29044i) q^{29} +(0.845730 + 8.04658i) q^{31} +(2.42897 - 4.20709i) q^{32} +(-1.58943 - 2.75298i) q^{34} +(10.5147 - 7.63935i) q^{35} +(1.01570 - 3.12601i) q^{37} +(0.409419 + 0.0430317i) q^{38} +(6.96366 - 6.27011i) q^{40} +(-7.43969 - 1.58136i) q^{41} +(8.02668 - 4.63421i) q^{43} +(-3.18156 + 0.163887i) q^{44} +(-1.69159 - 2.32827i) q^{46} +(-9.41156 - 8.47421i) q^{47} +(-9.61646 + 4.28152i) q^{49} +(4.31964 - 1.92323i) q^{50} +(-0.254979 - 0.229584i) q^{52} +(-2.07104 - 2.85055i) q^{53} +(-9.94319 - 2.67380i) q^{55} +(-10.9434 + 6.31818i) q^{56} +(-6.18962 - 1.31564i) q^{58} +(8.65424 - 7.79231i) q^{59} +(1.18232 + 0.124266i) q^{61} +(2.54907 - 7.84522i) q^{62} +(-5.87777 + 4.27045i) q^{64} +(-0.554460 - 0.960353i) q^{65} +(7.66446 - 13.2752i) q^{67} +(-0.313058 - 2.97855i) q^{68} +(-12.9612 + 2.75498i) q^{70} +(0.357651 - 0.492264i) q^{71} +(10.8303 + 3.51899i) q^{73} +(-2.24232 + 2.49035i) q^{74} +(0.335894 + 0.193928i) q^{76} +(12.3659 + 6.31469i) q^{77} +(1.96875 - 4.42189i) q^{79} +(-3.41387 + 1.10923i) q^{80} +(6.27351 + 4.55797i) q^{82} +(0.692635 - 6.58998i) q^{83} +(2.01251 - 9.46814i) q^{85} +(-9.39771 + 0.987739i) q^{86} +(9.34272 + 3.59592i) q^{88} +7.29922i q^{89} +(0.462105 + 1.42221i) q^{91} +(-0.563732 - 2.65215i) q^{92} +(5.25174 + 11.7956i) q^{94} +(0.838788 + 0.931569i) q^{95} +(-4.74976 - 2.11473i) q^{97} +10.7322 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{4} + 4 q^{16} - 36 q^{22} - 8 q^{25} - 200 q^{28} - 8 q^{31} + 64 q^{34} - 24 q^{37} + 60 q^{40} - 40 q^{46} - 100 q^{52} + 16 q^{55} - 24 q^{58} - 60 q^{61} + 72 q^{64} + 24 q^{67} - 8 q^{70}+ \cdots + 24 q^{97}+O(q^{100}) \) 64 * q + 8 * q^4 + 4 * q^16 - 36 * q^22 - 8 * q^25 - 200 * q^28 - 8 * q^31 + 64 * q^34 - 24 * q^37 + 60 * q^40 - 40 * q^46 - 100 * q^52 + 16 * q^55 - 24 * q^58 - 60 * q^61 + 72 * q^64 + 24 * q^67 - 8 * q^70 + 160 * q^73 + 60 * q^79 + 144 * q^82 + 20 * q^85 + 24 * q^88 + 48 * q^91 - 20 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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