LMFDB - Embedded newform 648.2.t.a.253.30

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] 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("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.30
Character	$\chi$	$=$	648.253
Dual form			648.2.t.a.397.30

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.32716 + 0.488522i) q^{2} +(1.52269 + 1.29669i) q^{4} +(0.114718 - 0.136716i) q^{5} +(2.42085 + 0.881117i) q^{7} +(1.38739 + 2.46478i) q^{8} +(0.219037 - 0.125401i) q^{10} +(-0.599296 - 0.714213i) q^{11} +(0.368417 + 0.0649618i) q^{13} +(2.78240 + 2.35202i) q^{14} +(0.637188 + 3.94892i) q^{16} +(2.26254 - 3.91883i) q^{17} +(-1.97566 + 1.14065i) q^{19} +(0.351958 - 0.0594221i) q^{20} +(-0.446451 - 1.24064i) q^{22} +(-4.40423 + 1.60301i) q^{23} +(0.862710 + 4.89267i) q^{25} +(0.457212 + 0.266194i) q^{26} +(2.54367 + 4.48076i) q^{28} +(-1.58682 + 0.279799i) q^{29} +(8.17965 - 2.97715i) q^{31} +(-1.08349 + 5.55212i) q^{32} +(4.91718 - 4.09561i) q^{34} +(0.398177 - 0.229888i) q^{35} +(-3.82721 - 2.20964i) q^{37} +(-3.17924 + 0.548665i) q^{38} +(0.496133 + 0.0930767i) q^{40} +(-0.238139 + 1.35055i) q^{41} +(-3.28437 - 3.91416i) q^{43} +(0.0135696 - 1.86463i) q^{44} +(-6.62821 - 0.0241177i) q^{46} +(7.70413 + 2.80407i) q^{47} +(-0.278168 - 0.233411i) q^{49} +(-1.24522 + 6.91480i) q^{50} +(0.476750 + 0.576640i) q^{52} -9.07829i q^{53} -0.166394 q^{55} +(1.18691 + 7.18932i) q^{56} +(-2.24265 - 0.403859i) q^{58} +(-9.44865 + 11.2605i) q^{59} +(5.07860 - 13.9533i) q^{61} +(12.3101 + 0.0447920i) q^{62} +(-4.15029 + 6.83923i) q^{64} +(0.0511453 - 0.0429160i) q^{65} +(1.72274 + 0.303765i) q^{67} +(8.52666 - 3.03337i) q^{68} +(0.640749 - 0.110579i) q^{70} +(-2.77372 + 4.80422i) q^{71} +(-4.77001 - 8.26190i) q^{73} +(-3.99985 - 4.80222i) q^{74} +(-4.48738 - 0.824961i) q^{76} +(-0.821500 - 2.25705i) q^{77} +(-0.704340 - 3.99451i) q^{79} +(0.612976 + 0.365899i) q^{80} +(-0.975822 + 1.67606i) q^{82} +(-15.0319 + 2.65052i) q^{83} +(-0.276212 - 0.758885i) q^{85} +(-2.44672 - 6.79919i) q^{86} +(0.928921 - 2.46803i) q^{88} +(-8.16359 - 14.1397i) q^{89} +(0.834643 + 0.481881i) q^{91} +(-8.78489 - 3.27003i) q^{92} +(8.85474 + 7.48508i) q^{94} +(-0.0706993 + 0.400955i) q^{95} +(-8.94677 + 7.50723i) q^{97} +(-0.255147 - 0.445664i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.32716	+	0.488522i	0.938442	+	0.345437i
$2$	1.32716	+	0.488522i	0.938442	+	0.345437i
$3$		0			0
$3$		0			0
$4$	1.52269	+	1.29669i	0.761346	+	0.648345i
$5$	0.114718	−	0.136716i	0.0513035	−	0.0611411i	−0.739782	−	0.672846i	$-0.765072\pi$
$5$	0.114718	−	0.136716i	0.0513035	−	0.0611411i	0.791086	+	0.611705i	$0.209516\pi$
$6$		0			0
$7$	2.42085	+	0.881117i	0.914995	+	0.333031i	0.756245	−	0.654288i	$-0.227032\pi$
$7$	2.42085	+	0.881117i	0.914995	+	0.333031i	0.158749	+	0.987319i	$0.449254\pi$
$8$	1.38739	+	2.46478i	0.490517	+	0.871432i
$9$		0			0
$10$	0.219037	−	0.125401i	0.0692657	−	0.0396552i
$11$	−0.599296	−	0.714213i	−0.180695	−	0.215343i	0.668093	−	0.744078i	$-0.267111\pi$
$11$	−0.599296	−	0.714213i	−0.180695	−	0.215343i	−0.848787	+	0.528735i	$0.822667\pi$
$12$		0			0
$13$	0.368417	+	0.0649618i	0.102180	+	0.0180172i	0.224505	−	0.974473i	$-0.427924\pi$
$13$	0.368417	+	0.0649618i	0.102180	+	0.0180172i	−0.122324	+	0.992490i	$0.539035\pi$
$14$	2.78240	+	2.35202i	0.743628	+	0.628603i
$15$		0			0
$16$	0.637188	+	3.94892i	0.159297	+	0.987231i
$17$	2.26254	−	3.91883i	0.548746	−	0.950456i	−0.449615	−	0.893223i	$-0.648439\pi$
$17$	2.26254	−	3.91883i	0.548746	−	0.950456i	0.998361	−	0.0572337i	$-0.0182280\pi$
$18$		0			0
$19$	−1.97566	+	1.14065i	−0.453246	+	0.261682i	−0.709200	−	0.705007i	$-0.750944\pi$
$19$	−1.97566	+	1.14065i	−0.453246	+	0.261682i	0.255954	+	0.966689i	$0.417610\pi$
$20$	0.351958	−	0.0594221i	0.0787002	−	0.0132872i
$21$		0			0
$22$	−0.446451	−	1.24064i	−0.0951837	−	0.264506i
$23$	−4.40423	+	1.60301i	−0.918345	+	0.334250i	−0.757580	−	0.652742i	$-0.773618\pi$
$23$	−4.40423	+	1.60301i	−0.918345	+	0.334250i	−0.160765	+	0.986993i	$0.551396\pi$
$24$		0			0
$25$	0.862710	+	4.89267i	0.172542	+	0.978534i
$26$	0.457212	+	0.266194i	0.0896666	+	0.0522050i
$27$		0			0
$28$	2.54367	+	4.48076i	0.480709	+	0.846785i
$29$	−1.58682	+	0.279799i	−0.294665	+	0.0519574i	−0.319026	−	0.947746i	$-0.603356\pi$
$29$	−1.58682	+	0.279799i	−0.294665	+	0.0519574i	0.0243613	+	0.999703i	$0.492245\pi$
$30$		0			0
$31$	8.17965	−	2.97715i	1.46911	−	0.534712i	0.521250	−	0.853404i	$-0.325466\pi$
$31$	8.17965	−	2.97715i	1.46911	−	0.534712i	0.947858	+	0.318692i	$0.103244\pi$
$32$	−1.08349	+	5.55212i	−0.191535	+	0.981486i
$33$		0			0
$34$	4.91718	−	4.09561i	0.843289	−	0.702391i
$35$	0.398177	−	0.229888i	0.0673043	−	0.0388581i
$36$		0			0
$37$	−3.82721	−	2.20964i	−0.629190	−	0.363263i	0.151248	−	0.988496i	$-0.451671\pi$
$37$	−3.82721	−	2.20964i	−0.629190	−	0.363263i	−0.780438	+	0.625233i	$0.785004\pi$
$38$	−3.17924	+	0.548665i	−0.515740	+	0.0890052i
$39$		0			0
$40$	0.496133	+	0.0930767i	0.0784455	+	0.0147167i
$41$	−0.238139	+	1.35055i	−0.0371910	+	0.210921i	−0.997740	−	0.0671892i	$-0.978597\pi$
$41$	−0.238139	+	1.35055i	−0.0371910	+	0.210921i	0.960549	+	0.278110i	$0.0897080\pi$
$42$		0			0
$43$	−3.28437	−	3.91416i	−0.500862	−	0.596904i	0.455083	−	0.890449i	$-0.349609\pi$
$43$	−3.28437	−	3.91416i	−0.500862	−	0.596904i	−0.955945	+	0.293545i	$0.905165\pi$
$44$	0.0135696	−	1.86463i	0.00204570	−	0.281103i
$45$		0			0
$46$	−6.62821	−	0.0241177i	−0.977276	−	0.00355596i
$47$	7.70413	+	2.80407i	1.12376	+	0.409016i	0.836024	−	0.548693i	$-0.184874\pi$
$47$	7.70413	+	2.80407i	1.12376	+	0.409016i	0.287738	+	0.957709i	$0.407097\pi$
$48$		0			0
$49$	−0.278168	−	0.233411i	−0.0397383	−	0.0333444i
$50$	−1.24522	+	6.91480i	−0.176101	+	0.977900i
$51$		0			0
$52$	0.476750	+	0.576640i	0.0661134	+	0.0799655i
$53$		−	9.07829i		−	1.24700i	−0.781824	−	0.623500i	$-0.785710\pi$
$53$		−	9.07829i		−	1.24700i	0.781824	−	0.623500i	$-0.214290\pi$
$54$		0			0
$55$	−0.166394			−0.0224366
$56$	1.18691	+	7.18932i	0.158607	+	0.960713i
$57$		0			0
$58$	−2.24265	−	0.403859i	−0.294474	−	0.0530292i
$59$	−9.44865	+	11.2605i	−1.23011	+	1.46599i	−0.392469	+	0.919765i	$0.628379\pi$
$59$	−9.44865	+	11.2605i	−1.23011	+	1.46599i	−0.837641	+	0.546222i	$0.816066\pi$
$60$		0			0
$61$	5.07860	−	13.9533i	0.650247	−	1.78654i	0.0334206	−	0.999441i	$-0.489360\pi$
$61$	5.07860	−	13.9533i	0.650247	−	1.78654i	0.616827	−	0.787099i	$-0.288418\pi$
$62$	12.3101	+	0.0447920i	1.56338	+	0.00568859i
$63$		0			0
$64$	−4.15029	+	6.83923i	−0.518786	+	0.854904i
$65$	0.0511453	−	0.0429160i	0.00634380	−	0.00532308i
$66$		0			0
$67$	1.72274	+	0.303765i	0.210466	+	0.0371108i	0.277887	−	0.960614i	$-0.410366\pi$
$67$	1.72274	+	0.303765i	0.210466	+	0.0371108i	−0.0674209	+	0.997725i	$0.521477\pi$
$68$	8.52666	−	3.03337i	1.03401	−	0.367850i
$69$		0			0
$70$	0.640749	−	0.110579i	0.0765842	−	0.0132167i
$71$	−2.77372	+	4.80422i	−0.329180	+	0.570156i	−0.982349	−	0.187055i	$-0.940106\pi$
$71$	−2.77372	+	4.80422i	−0.329180	+	0.570156i	0.653169	+	0.757212i	$0.273439\pi$
$72$		0			0
$73$	−4.77001	−	8.26190i	−0.558287	−	0.966982i	−0.997640	−	0.0686670i	$-0.978125\pi$
$73$	−4.77001	−	8.26190i	−0.558287	−	0.966982i	0.439352	−	0.898315i	$-0.355208\pi$
$74$	−3.99985	−	4.80222i	−0.464974	−	0.558247i
$75$		0			0
$76$	−4.48738	−	0.824961i	−0.514738	−	0.0946295i
$77$	−0.821500	−	2.25705i	−0.0936186	−	0.257215i
$78$		0			0
$79$	−0.704340	−	3.99451i	−0.0792444	−	0.449417i	−0.998451	−	0.0556413i	$-0.982280\pi$
$79$	−0.704340	−	3.99451i	−0.0792444	−	0.449417i	0.919206	−	0.393776i	$-0.128831\pi$
$80$	0.612976	+	0.365899i	0.0685328	+	0.0409088i
$81$		0			0
$82$	−0.975822	+	1.67606i	−0.107761	+	0.185090i
$83$	−15.0319	+	2.65052i	−1.64996	+	0.290933i	−0.919813	−	0.392357i	$-0.871660\pi$
$83$	−15.0319	+	2.65052i	−1.64996	+	0.290933i	−0.730148	+	0.683289i	$0.760549\pi$
$84$		0			0
$85$	−0.276212	−	0.758885i	−0.0299594	−	0.0823126i
$86$	−2.44672	−	6.79919i	−0.263837	−	0.733176i
$87$		0			0
$88$	0.928921	−	2.46803i	0.0990233	−	0.263092i
$89$	−8.16359	−	14.1397i	−0.865339	−	1.49881i	−0.866711	−	0.498811i	$-0.833770\pi$
$89$	−8.16359	−	14.1397i	−0.865339	−	1.49881i	0.00137211	−	0.999999i	$-0.499563\pi$
$90$		0			0
$91$	0.834643	+	0.481881i	0.0874943	+	0.0505149i
$92$	−8.78489	−	3.27003i	−0.915888	−	0.340924i
$93$		0			0
$94$	8.85474	+	7.48508i	0.913296	+	0.772027i
$95$	−0.0706993	+	0.400955i	−0.00725359	+	0.0411372i
$96$		0			0
$97$	−8.94677	+	7.50723i	−0.908407	+	0.762244i	−0.971815	−	0.235744i	$-0.924247\pi$
$97$	−8.94677	+	7.50723i	−0.908407	+	0.762244i	0.0634084	+	0.997988i	$0.479803\pi$
$98$	−0.255147	−	0.445664i	−0.0257737	−	0.0450189i
$99$		0			0
$100$	−5.03064	+	8.56870i	−0.503064	+	0.856870i
$101$	0.733566	−	2.01546i	0.0729926	−	0.200545i	−0.897831	−	0.440340i	$-0.854858\pi$
$101$	0.733566	−	2.01546i	0.0729926	−	0.200545i	0.970824	+	0.239795i	$0.0770801\pi$
$102$		0			0
$103$	8.97851	+	7.53386i	0.884679	+	0.742334i	0.967136	−	0.254261i	$-0.0818322\pi$
$103$	8.97851	+	7.53386i	0.884679	+	0.742334i	−0.0824568	+	0.996595i	$0.526277\pi$
$104$	0.351022	+	0.998194i	0.0344205	+	0.0978810i
$105$		0			0
$106$	4.43494	−	12.0483i	0.430760	−	1.17024i
$107$		−	7.40373i		−	0.715745i	−0.933770	−	0.357873i	$-0.883502\pi$
$107$		−	7.40373i		−	0.715745i	0.933770	−	0.357873i	$-0.116498\pi$
$108$		0			0
$109$		−	13.2321i		−	1.26741i	−0.773575	−	0.633704i	$-0.781534\pi$
$109$		−	13.2321i		−	1.26741i	0.773575	−	0.633704i	$-0.218466\pi$
$110$	−0.220831	−	0.0812872i	−0.0210554	−	0.00775043i
$111$		0			0
$112$	−1.93693	+	10.1212i	−0.183023	+	0.956362i
$113$	7.02588	+	5.89541i	0.660939	+	0.554594i	0.910368	−	0.413799i	$-0.135799\pi$
$113$	7.02588	+	5.89541i	0.660939	+	0.554594i	−0.249429	+	0.968393i	$0.580243\pi$
$114$		0			0
$115$	−0.286088	+	0.786020i	−0.0266778	+	0.0732968i
$116$	−2.77905	−	1.63157i	−0.258029	−	0.151487i
$117$		0			0
$118$	−18.0408	+	10.3285i	−1.66079	+	0.950818i
$119$	8.93021	−	7.49334i	0.818631	−	0.686913i
$120$		0			0
$121$	1.75919	−	9.97684i	0.159926	−	0.906985i
$122$	13.5566	−	16.0373i	1.22736	−	1.45194i
$123$		0			0
$124$	16.3155	+	6.07319i	1.46518	+	0.545389i
$125$	1.54067	+	0.889506i	0.137802	+	0.0795598i
$126$		0			0
$127$	−9.58464	−	16.6011i	−0.850500	−	1.47311i	−0.880758	−	0.473567i	$-0.842966\pi$
$127$	−9.58464	−	16.6011i	−0.850500	−	1.47311i	0.0302583	−	0.999542i	$-0.490367\pi$
$128$	−8.84920	+	7.04923i	−0.782166	+	0.623070i
$129$		0			0
$130$	0.0888433	−	0.0319707i	0.00779208	−	0.00280402i
$131$	−0.312406	−	0.858328i	−0.0272950	−	0.0749924i	0.925297	−	0.379244i	$-0.123816\pi$
$131$	−0.312406	−	0.858328i	−0.0272950	−	0.0749924i	−0.952592	+	0.304252i	$0.901594\pi$
$132$		0			0
$133$	−5.78780	+	1.02055i	−0.501866	+	0.0884926i
$134$	2.13795	+	1.24474i	0.184691	+	0.107529i
$135$		0			0
$136$	12.7981	+	0.139708i	1.09743	+	0.0119799i
$137$	−0.995947	−	5.64830i	−0.0850895	−	0.482566i	−0.997337	−	0.0729275i	$-0.976766\pi$
$137$	−0.995947	−	5.64830i	−0.0850895	−	0.482566i	0.912248	−	0.409639i	$-0.134345\pi$
$138$		0			0
$139$	7.23743	+	19.8847i	0.613871	+	1.68660i	0.721509	+	0.692406i	$0.243449\pi$
$139$	7.23743	+	19.8847i	0.613871	+	1.68660i	−0.107638	+	0.994190i	$0.534329\pi$
$140$	0.904395	+	0.166264i	0.0764354	+	0.0140519i
$141$		0			0
$142$	−6.02813	+	5.02094i	−0.505869	+	0.421348i
$143$	−0.174394	−	0.302060i	−0.0145836	−	0.0252595i
$144$		0			0
$145$	−0.143784	+	0.249041i	−0.0119406	+	0.0206817i
$146$	−2.29443	−	13.2951i	−0.189889	−	1.10031i
$147$		0			0
$148$	−2.96245	−	8.32732i	−0.243512	−	0.684501i
$149$	7.83652	+	1.38179i	0.641992	+	0.113201i	0.485161	−	0.874425i	$-0.338761\pi$
$149$	7.83652	+	1.38179i	0.641992	+	0.113201i	0.156831	+	0.987625i	$0.449872\pi$
$150$		0			0
$151$	−2.04551	+	1.71638i	−0.166461	+	0.139677i	−0.722213	−	0.691671i	$-0.756875\pi$
$151$	−2.04551	+	1.71638i	−0.166461	+	0.139677i	0.555752	+	0.831348i	$0.312430\pi$
$152$	−5.55245	−	3.28704i	−0.450363	−	0.266614i
$153$		0			0
$154$	0.0123597	−	3.39678i	0.000995972	−	0.273721i
$155$	0.531330	−	1.45982i	0.0426775	−	0.117255i
$156$		0			0
$157$	−7.93100	+	9.45180i	−0.632963	+	0.754336i	−0.983241	−	0.182310i	$-0.941643\pi$
$157$	−7.93100	+	9.45180i	−0.632963	+	0.754336i	0.350278	+	0.936646i	$0.386087\pi$
$158$	1.01663	−	5.64543i	0.0808791	−	0.449126i
$159$		0			0
$160$	0.634766	+	0.785058i	0.0501827	+	0.0620643i
$161$	−12.0744			−0.951597
$162$		0			0
$163$			13.6508i			1.06922i	0.845100	+	0.534608i	$0.179541\pi$
$163$			13.6508i			1.06922i	−0.845100	+	0.534608i	$0.820459\pi$
$164$	−2.11386	+	1.74768i	−0.165065	+	0.136471i
$165$		0			0
$166$	−21.2445	−	3.82573i	−1.64889	−	0.296934i
$167$	3.21110	+	2.69443i	0.248482	+	0.208502i	0.758519	−	0.651651i	$-0.225924\pi$
$167$	3.21110	+	2.69443i	0.248482	+	0.208502i	−0.510036	+	0.860153i	$0.670368\pi$
$168$		0			0
$169$	−12.0845	−	4.39840i	−0.929576	−	0.338338i
$170$	0.00415568	−	1.14210i	0.000318726	−	0.0875947i
$171$		0			0
$172$	0.0743667	−	10.2189i	0.00567041	−	0.779182i
$173$	12.8781	+	15.3475i	0.979103	+	1.16685i	0.985978	+	0.166873i	$0.0533671\pi$
$173$	12.8781	+	15.3475i	0.979103	+	1.16685i	−0.00687524	+	0.999976i	$0.502188\pi$
$174$		0			0
$175$	−2.22253	+	12.6046i	−0.168007	+	0.952816i
$176$	2.43851	−	2.82166i	0.183809	−	0.212691i
$177$		0			0
$178$	−3.92679	−	22.7538i	−0.294325	−	1.70547i
$179$	6.96829	+	4.02315i	0.520835	+	0.300704i	0.737276	−	0.675592i	$-0.236112\pi$
$179$	6.96829	+	4.02315i	0.520835	+	0.300704i	−0.216441	+	0.976296i	$0.569445\pi$
$180$		0			0
$181$	6.99841	−	4.04053i	0.520188	−	0.300331i	−0.216824	−	0.976211i	$-0.569570\pi$
$181$	6.99841	−	4.04053i	0.520188	−	0.300331i	0.737011	+	0.675880i	$0.236236\pi$
$182$	0.872293	+	1.04727i	0.0646586	+	0.0776291i
$183$		0			0
$184$	−10.0615	−	8.63146i	−0.741740	−	0.636319i
$185$	−0.741143	+	0.269754i	−0.0544899	+	0.0198327i
$186$		0			0
$187$	−4.15481	+	0.732605i	−0.303830	+	0.0535734i
$188$	8.09501	+	14.2596i	0.590389	+	1.03999i
$189$		0			0
$190$	−0.289705	+	0.497593i	−0.0210174	+	0.0360992i
$191$	−2.88972	−	16.3884i	−0.209093	−	1.18582i	−0.890868	−	0.454262i	$-0.849903\pi$
$191$	−2.88972	−	16.3884i	−0.209093	−	1.18582i	0.681776	−	0.731561i	$-0.261208\pi$
$192$		0			0
$193$	−0.775835	+	0.282381i	−0.0558458	+	0.0203262i	−0.369792	−	0.929115i	$-0.620571\pi$
$193$	−0.775835	+	0.282381i	−0.0558458	+	0.0203262i	0.313946	+	0.949441i	$0.398349\pi$
$194$	−15.5412	+	5.59258i	−1.11579	+	0.401524i
$195$		0			0
$196$	−0.120903	−	0.716111i	−0.00863594	−	0.0511508i
$197$	13.0620	−	7.54137i	0.930632	−	0.537301i	0.0436205	−	0.999048i	$-0.486111\pi$
$197$	13.0620	−	7.54137i	0.930632	−	0.537301i	0.887011	+	0.461748i	$0.152777\pi$
$198$		0			0
$199$	−7.77810	+	13.4721i	−0.551375	+	0.955009i	0.446801	+	0.894633i	$0.352563\pi$
$199$	−7.77810	+	13.4721i	−0.551375	+	0.955009i	−0.998176	+	0.0603759i	$0.980770\pi$
$200$	−10.8624	+	8.91444i	−0.768091	+	0.630346i
$201$		0			0
$202$	1.95815	−	2.31647i	0.137775	−	0.162986i
$203$	−4.08799	−	0.720823i	−0.286921	−	0.0505918i
$204$		0			0
$205$	0.157323	+	0.187490i	0.0109879	+	0.0130949i
$206$	8.23544	+	14.3848i	0.573790	+	1.00224i
$207$		0			0
$208$	−0.0217786	+	1.49624i	−0.00151008	+	0.103746i
$209$	1.99867	+	0.727455i	0.138251	+	0.0503191i
$210$		0			0
$211$	3.55232	−	4.23349i	0.244552	−	0.291445i	−0.629781	−	0.776773i	$-0.716855\pi$
$211$	3.55232	−	4.23349i	0.244552	−	0.291445i	0.874332	+	0.485328i	$0.161300\pi$
$212$	11.7717	−	13.8235i	0.808486	−	0.949399i
$213$		0			0
$214$	3.61688	−	9.82591i	0.247245	−	0.671685i
$215$	−0.911903			−0.0621913
$216$		0			0
$217$	22.4249			1.52230
$218$	6.46419	−	17.5611i	0.437810	−	1.18939i
$219$		0			0
$220$	−0.253367	−	0.215762i	−0.0170820	−	0.0145466i
$221$	1.08813	−	1.29679i	0.0731957	−	0.0872312i
$222$		0			0
$223$	4.91216	+	1.78788i	0.328942	+	0.119725i	0.501212	−	0.865325i	$-0.332888\pi$
$223$	4.91216	+	1.78788i	0.328942	+	0.119725i	−0.172269	+	0.985050i	$0.555110\pi$
$224$	−7.51503	+	12.4862i	−0.502119	+	0.834267i
$225$		0			0
$226$	6.44441	+	11.2564i	0.428676	+	0.748767i
$227$	5.65872	+	6.74381i	0.375583	+	0.447602i	0.920415	−	0.390943i	$-0.127851\pi$
$227$	5.65872	+	6.74381i	0.375583	+	0.447602i	−0.544832	+	0.838545i	$0.683407\pi$
$228$		0			0
$229$	8.50987	+	1.50052i	0.562348	+	0.0991572i	0.447594	−	0.894237i	$-0.352281\pi$
$229$	8.50987	+	1.50052i	0.562348	+	0.0991572i	0.114754	+	0.993394i	$0.463392\pi$
$230$	−0.763672	+	0.903413i	−0.0503550	+	0.0595693i
$231$		0			0
$232$	−2.89118	−	3.52297i	−0.189816	−	0.231295i
$233$	0.420645	−	0.728579i	0.0275574	−	0.0477308i	−0.851918	−	0.523676i	$-0.824560\pi$
$233$	0.420645	−	0.728579i	0.0275574	−	0.0477308i	0.879475	+	0.475945i	$0.157894\pi$
$234$		0			0
$235$	1.26716	−	0.731597i	0.0826606	−	0.0477241i
$236$	−28.9887	+	4.89425i	−1.88701	+	0.318589i
$237$		0			0
$238$	15.5125	−	5.58224i	1.00552	−	0.361843i
$239$	−12.9749	+	4.72248i	−0.839276	+	0.305472i	−0.725660	−	0.688053i	$-0.758466\pi$
$239$	−12.9749	+	4.72248i	−0.839276	+	0.305472i	−0.113616	+	0.993525i	$0.536243\pi$
$240$		0			0
$241$	2.61837	+	14.8495i	0.168664	+	0.956542i	0.945206	+	0.326476i	$0.105861\pi$
$241$	2.61837	+	14.8495i	0.168664	+	0.956542i	−0.776541	+	0.630066i	$0.783028\pi$
$242$	7.20862	−	12.3814i	0.463387	−	0.795908i
$243$		0			0
$244$	25.8263	−	14.6613i	1.65336	−	0.938591i
$245$	−0.0638218	+	0.0112535i	−0.00407743	+	0.000718960i
$246$		0			0
$247$	−0.801963	+	0.291891i	−0.0510277	+	0.0185726i
$248$	18.6864	+	16.0306i	1.18659	+	1.01794i
$249$		0			0
$250$	1.61017	+	1.93316i	0.101836	+	0.122264i
$251$	9.73582	−	5.62098i	0.614520	−	0.354793i	−0.160213	−	0.987083i	$-0.551218\pi$
$251$	9.73582	−	5.62098i	0.614520	−	0.354793i	0.774732	+	0.632289i	$0.217885\pi$
$252$		0			0
$253$	3.78432	+	2.18488i	0.237918	+	0.137362i
$254$	−4.61034	−	26.7146i	−0.289278	−	1.67622i
$255$		0			0
$256$	−15.1880	+	5.03241i	−0.949249	+	0.314526i
$257$	−1.23538	+	7.00619i	−0.0770609	+	0.437034i	0.921728	+	0.387837i	$0.126778\pi$
$257$	−1.23538	+	7.00619i	−0.0770609	+	0.437034i	−0.998789	+	0.0491976i	$0.984334\pi$
$258$		0			0
$259$	−7.31815	−	8.72143i	−0.454728	−	0.541923i
$260$	0.133527		0.000971731i	0.00828102		6.02642e-5i
$261$		0			0
$262$	0.00470023	−	1.29175i	0.000290381	−	0.0798048i
$263$	18.0450	+	6.56783i	1.11270	+	0.404990i	0.831983	−	0.554801i	$-0.187205\pi$
$263$	18.0450	+	6.56783i	1.11270	+	0.404990i	0.280717	+	0.959790i	$0.409428\pi$
$264$		0			0
$265$	−1.24114	−	1.04144i	−0.0762429	−	0.0639754i
$266$	−8.17989	−	1.47304i	−0.501541	−	0.0903181i
$267$		0			0
$268$	2.22931	+	2.69640i	0.136177	+	0.164709i
$269$			16.5198i			1.00723i	0.863928	+	0.503616i	$0.167997\pi$
$269$			16.5198i			1.00723i	−0.863928	+	0.503616i	$0.832003\pi$
$270$		0			0
$271$	−1.17854			−0.0715913			−0.0357956	−	0.999359i	$-0.511397\pi$
$271$	−1.17854			−0.0715913			−0.0357956	+	0.999359i	$0.511397\pi$
$272$	16.9168	+	6.43756i	1.02573	+	0.390334i
$273$		0			0
$274$	1.43754	−	7.98272i	0.0868448	−	0.482254i
$275$	2.97739	−	3.54832i	0.179543	−	0.213972i
$276$		0			0
$277$	−7.87030	+	21.6235i	−0.472880	+	1.29923i	0.442547	+	0.896745i	$0.354075\pi$
$277$	−7.87030	+	21.6235i	−0.472880	+	1.29923i	−0.915428	+	0.402483i	$0.868147\pi$
$278$	−0.108889	+	29.9257i	−0.00653073	+	1.79483i
$279$		0			0
$280$	1.11905	+	0.662476i	0.0668761	+	0.0395905i
$281$	−16.4336	+	13.7895i	−0.980348	+	0.822610i	−0.984142	−	0.177383i	$-0.943237\pi$
$281$	−16.4336	+	13.7895i	−0.980348	+	0.822610i	0.00379366	+	0.999993i	$0.498792\pi$
$282$		0			0
$283$	−0.339199	−	0.0598100i	−0.0201633	−	0.00355534i	0.163557	−	0.986534i	$-0.447703\pi$
$283$	−0.339199	−	0.0598100i	−0.0201633	−	0.00355534i	−0.183721	+	0.982978i	$0.558814\pi$
$284$	−10.4531	+	3.71870i	−0.620278	+	0.220664i
$285$		0			0
$286$	−0.0838858	−	0.486076i	−0.00496027	−	0.0287423i
$287$	−1.76649	+	3.05966i	−0.104273	+	0.180606i
$288$		0			0
$289$	−1.73816	−	3.01059i	−0.102245	−	0.177093i
$290$	−0.312486	+	0.260275i	−0.0183498	+	0.0152839i
$291$		0			0
$292$	3.44986	−	18.7656i	0.201888	−	1.09817i
$293$	−9.01139	−	24.7586i	−0.526451	−	1.44641i	−0.863221	−	0.504826i	$-0.831557\pi$
$293$	−9.01139	−	24.7586i	−0.526451	−	1.44641i	0.336770	−	0.941587i	$-0.390665\pi$
$294$		0			0
$295$	0.455551	+	2.58356i	0.0265232	+	0.150420i
$296$	0.136442	−	12.4989i	0.00793051	−	0.726482i
$297$		0			0
$298$	9.72525	+	5.66216i	0.563369	+	0.328000i
$299$	−1.72673	+	0.304468i	−0.0998591	+	0.0176079i
$300$		0			0
$301$	−4.50213	−	12.3695i	−0.259499	−	0.712967i
$302$	−3.55320	+	1.27864i	−0.204464	+	0.0735773i
$303$		0			0
$304$	−5.76318	−	7.07491i	−0.330541	−	0.405774i
$305$	−1.32503	−	2.29502i	−0.0758711	−	0.131413i
$306$		0			0
$307$	14.2917	+	8.25134i	0.815673	+	0.470929i	0.848922	−	0.528518i	$-0.177252\pi$
$307$	14.2917	+	8.25134i	0.815673	+	0.470929i	−0.0332493	+	0.999447i	$0.510586\pi$
$308$	1.67581	−	4.50203i	0.0954879	−	0.256527i
$309$		0			0
$310$	1.41831	−	1.67784i	0.0805547	−	0.0952950i
$311$	−3.58763	+	20.3464i	−0.203436	+	1.15374i	0.696447	+	0.717609i	$0.254763\pi$
$311$	−3.58763	+	20.3464i	−0.203436	+	1.15374i	−0.899882	+	0.436133i	$0.856348\pi$
$312$		0			0
$313$	−9.65918	+	8.10501i	−0.545969	+	0.458122i	−0.873573	−	0.486693i	$-0.838203\pi$
$313$	−9.65918	+	8.10501i	−0.545969	+	0.458122i	0.327604	+	0.944815i	$0.393759\pi$
$314$	−15.1431	+	8.66956i	−0.854574	+	0.489251i
$315$		0			0
$316$	4.10715	−	6.99572i	0.231045	−	0.393540i
$317$	4.18467	−	11.4973i	0.235034	−	0.645752i	−0.764964	−	0.644073i	$-0.777243\pi$
$317$	4.18467	−	11.4973i	0.235034	−	0.645752i	0.999999	−	0.00167879i	$-0.000534375\pi$
$318$		0			0
$319$	1.15081	+	0.965645i	0.0644331	+	0.0540658i
$320$	0.458917	+	1.35199i	0.0256542	+	0.0755787i
$321$		0			0
$322$	−16.0246	−	5.89861i	−0.893018	−	0.328717i
$323$			10.3230i			0.574388i
$324$		0			0
$325$			1.85859i			0.103096i
$326$	−6.66873	+	18.1168i	−0.369347	+	1.00340i
$327$		0			0
$328$	−3.65921	+	1.28678i	−0.202046	+	0.0710508i
$329$	16.1798	+	13.5765i	0.892022	+	0.748495i
$330$		0			0
$331$	−6.93586	+	19.0561i	−0.381230	+	1.04742i	0.589610	+	0.807688i	$0.299282\pi$
$331$	−6.93586	+	19.0561i	−0.381230	+	1.04742i	−0.970839	+	0.239731i	$0.922941\pi$
$332$	−26.3258	−	15.4557i	−1.44482	−	0.848244i
$333$		0			0
$334$	2.94535	+	5.14463i	0.161162	+	0.281502i
$335$	0.239159	−	0.200678i	0.0130666	−	0.0109642i
$336$		0			0
$337$	2.99094	−	16.9625i	0.162927	−	0.924006i	−0.788249	−	0.615357i	$-0.789012\pi$
$337$	2.99094	−	16.9625i	0.162927	−	0.924006i	0.951176	−	0.308649i	$-0.0998769\pi$
$338$	−13.8893	−	11.7409i	−0.755479	−	0.638621i
$339$		0			0
$340$	0.563454	−	1.51371i	0.0305576	−	0.0820924i
$341$	−7.02835	−	4.05782i	−0.380606	−	0.219743i
$342$		0			0
$343$	−9.48449	−	16.4276i	−0.512114	−	0.887008i
$344$	5.09084	−	13.5257i	0.274480	−	0.729258i
$345$		0			0
$346$	9.59366	+	26.6598i	0.515758	+	1.43324i
$347$	2.18170	+	5.99416i	0.117120	+	0.321783i	0.984376	−	0.176078i	$-0.0563411\pi$
$347$	2.18170	+	5.99416i	0.117120	+	0.321783i	−0.867257	+	0.497861i	$0.834119\pi$
$348$		0			0
$349$	13.1972	−	2.32702i	0.706430	−	0.124563i	0.191120	−	0.981567i	$-0.438788\pi$
$349$	13.1972	−	2.32702i	0.706430	−	0.124563i	0.515310	+	0.857004i	$0.327677\pi$
$350$	−9.10725	+	15.6425i	−0.486803	+	0.836126i
$351$		0			0
$352$	4.61473	−	2.55352i	0.245966	−	0.136103i
$353$	1.95983	+	11.1147i	0.104311	+	0.591577i	0.991493	+	0.130158i	$0.0415484\pi$
$353$	1.95983	+	11.1147i	0.104311	+	0.591577i	−0.887182	+	0.461419i	$0.847340\pi$
$354$		0			0
$355$	0.338617	+	0.930342i	0.0179719	+	0.0493774i
$356$	5.90424	−	32.1161i	0.312924	−	1.70215i
$357$		0			0
$358$	7.28263	+	8.74351i	0.384899	+	0.462109i
$359$	13.5862	+	23.5320i	0.717053	+	1.24197i	0.962162	+	0.272477i	$0.0878428\pi$
$359$	13.5862	+	23.5320i	0.717053	+	1.24197i	−0.245109	+	0.969495i	$0.578824\pi$
$360$		0			0
$361$	−6.89786	+	11.9474i	−0.363045	+	0.628813i
$362$	11.2619	−	1.94355i	0.591911	−	0.102151i
$363$		0			0
$364$	0.646054	+	1.81603i	0.0338624	+	0.0951858i
$365$	−1.67674	−	0.295654i	−0.0877644	−	0.0154752i
$366$		0			0
$367$	17.5436	−	14.7209i	0.915771	−	0.768423i	−0.0574375	−	0.998349i	$-0.518293\pi$
$367$	17.5436	−	14.7209i	0.915771	−	0.768423i	0.973208	+	0.229926i	$0.0738485\pi$
$368$	−9.13647	−	16.3705i	−0.476272	−	0.853373i
$369$		0			0
$370$	−1.11539	−	0.00405852i	−0.0579865	−	0.000210992i
$371$	7.99904	−	21.9772i	0.415289	−	1.14100i
$372$		0			0
$373$	−18.2082	+	21.6997i	−0.942786	+	1.12357i	0.0493967	+	0.998779i	$0.484270\pi$
$373$	−18.2082	+	21.6997i	−0.942786	+	1.12357i	−0.992183	+	0.124790i	$0.960174\pi$
$374$	−5.87198	−	1.05743i	−0.303633	−	0.0546786i
$375$		0			0
$376$	3.77722	+	22.8793i	0.194795	+	1.17991i
$377$	−0.602788			−0.0310451
$378$		0			0
$379$		−	9.20463i		−	0.472810i	−0.971655	−	0.236405i	$-0.924031\pi$
$379$		−	9.20463i		−	0.472810i	0.971655	−	0.236405i	$-0.0759692\pi$
$380$	−0.627568	+	0.518857i	−0.0321936	+	0.0266168i
$381$		0			0
$382$	4.17098	−	23.1617i	0.213406	−	1.18505i
$383$	−18.0654	−	15.1587i	−0.923100	−	0.774573i	0.0514658	−	0.998675i	$-0.483611\pi$
$383$	−18.0654	−	15.1587i	−0.923100	−	0.774573i	−0.974566	+	0.224102i	$0.928055\pi$
$384$		0			0
$385$	−0.402815	−	0.146613i	−0.0205294	−	0.00747207i
$386$	−1.16760	−	0.00424850i	−0.0594295	−	0.000216243i
$387$		0			0
$388$	−23.3577	−	0.169983i	−1.18581	−	0.00862959i
$389$	19.3453	+	23.0548i	0.980844	+	1.16892i	0.985627	+	0.168936i	$0.0540332\pi$
$389$	19.3453	+	23.0548i	0.980844	+	1.16892i	−0.00478250	+	0.999989i	$0.501522\pi$
$390$		0			0
$391$	−3.68282	+	20.8863i	−0.186248	+	1.05627i
$392$	0.189378	−	1.00946i	0.00956505	−	0.0509852i
$393$		0			0
$394$	21.0195	−	3.62750i	1.05895	−	0.182751i
$395$	−0.626912	−	0.361948i	−0.0315434	−	0.0182116i
$396$		0			0
$397$	15.4854	−	8.94051i	0.777191	−	0.448711i	−0.0582431	−	0.998302i	$-0.518550\pi$
$397$	15.4854	−	8.94051i	0.777191	−	0.448711i	0.835434	+	0.549591i	$0.185217\pi$
$398$	−16.9042	+	14.0798i	−0.847329	+	0.705756i
$399$		0			0
$400$	−18.7711	+	6.52432i	−0.938554	+	0.326216i
$401$	9.33220	−	3.39664i	0.466028	−	0.169620i	−0.0983243	−	0.995154i	$-0.531348\pi$
$401$	9.33220	−	3.39664i	0.466028	−	0.169620i	0.564352	+	0.825534i	$0.309126\pi$
$402$		0			0
$403$	3.20692	−	0.565467i	0.159748	−	0.0281679i
$404$	3.73042	−	2.11771i	0.185595	−	0.105360i
$405$		0			0
$406$	−5.07327	−	2.95372i	−0.251782	−	0.146590i
$407$	0.715477	+	4.05767i	0.0354649	+	0.201131i
$408$		0			0
$409$	−5.20287	+	1.89369i	−0.257265	+	0.0936369i	−0.467433	−	0.884028i	$-0.654821\pi$
$409$	−5.20287	+	1.89369i	−0.257265	+	0.0936369i	0.210168	+	0.977665i	$0.432599\pi$
$410$	0.117199	+	0.325684i	0.00578805	+	0.0160844i
$411$		0			0
$412$	3.90242	+	23.1141i	0.192259	+	1.13875i
$413$	−32.7955	+	18.9345i	−1.61376	+	0.931706i
$414$		0			0
$415$	−1.36206	+	2.35915i	−0.0668608	+	0.115806i
$416$	−0.759851	+	1.97511i	−0.0372547	+	0.0968377i
$417$		0			0
$418$	2.29717	+	1.94184i	0.112358	+	0.0949784i
$419$	−4.02902	−	0.710424i	−0.196830	−	0.0347065i	0.0743638	−	0.997231i	$-0.476307\pi$
$419$	−4.02902	−	0.710424i	−0.196830	−	0.0347065i	−0.271194	+	0.962525i	$0.587419\pi$
$420$		0			0
$421$	15.7920	+	18.8201i	0.769653	+	0.917237i	0.998417	−	0.0562453i	$-0.0179129\pi$
$421$	15.7920	+	18.8201i	0.769653	+	0.917237i	−0.228764	+	0.973482i	$0.573468\pi$
$422$	6.78263	−	3.88312i	0.330173	−	0.189027i
$423$		0			0
$424$	22.3760	−	12.5951i	1.08667	−	0.611674i
$425$	21.1255	+	7.68904i	1.02474	+	0.372973i
$426$		0			0
$427$	24.5890	−	29.3041i	1.18995	−	1.41812i
$428$	9.60034	−	11.2736i	0.464050	−	0.544930i
$429$		0			0
$430$	−1.21024	−	0.445485i	−0.0583629	−	0.0214832i
$431$	−14.0058			−0.674635			−0.337318	−	0.941391i	$-0.609520\pi$
$431$	−14.0058			−0.674635			−0.337318	+	0.941391i	$0.609520\pi$
$432$		0			0
$433$	12.4899			0.600227			0.300113	−	0.953904i	$-0.402976\pi$
$433$	12.4899			0.600227			0.300113	+	0.953904i	$0.402976\pi$
$434$	29.7614	+	10.9551i	1.42859	+	0.525860i
$435$		0			0
$436$	17.1580	−	20.1485i	0.821718	−	0.964937i
$437$	6.87277	−	8.19065i	0.328769	−	0.391812i
$438$		0			0
$439$	−10.1446	−	3.69232i	−0.484174	−	0.176225i	0.0883886	−	0.996086i	$-0.471828\pi$
$439$	−10.1446	−	3.69232i	−0.484174	−	0.176225i	−0.572562	+	0.819861i	$0.694050\pi$
$440$	−0.230854	−	0.410125i	−0.0110055	−	0.0195519i
$441$		0			0
$442$	2.07763	−	1.18946i	0.0988228	−	0.0565769i
$443$	18.6993	+	22.2849i	0.888430	+	1.05879i	0.997898	+	0.0647991i	$0.0206406\pi$
$443$	18.6993	+	22.2849i	0.888430	+	1.05879i	−0.109469	+	0.993990i	$0.534915\pi$
$444$		0			0
$445$	−2.86963	−	0.505994i	−0.136034	−	0.0239864i
$446$	5.64579	+	4.77249i	0.267336	+	0.225984i
$447$		0			0
$448$	−16.0734	+	12.8999i	−0.759396	+	0.609461i
$449$	15.0485	−	26.0648i	0.710184	−	1.23007i	−0.254604	−	0.967045i	$-0.581945\pi$
$449$	15.0485	−	26.0648i	0.710184	−	1.23007i	0.964788	−	0.263029i	$-0.0847216\pi$
$450$		0			0
$451$	1.10730	−	0.639299i	0.0521406	−	0.0301034i
$452$	3.05373	+	18.0873i	0.143635	+	0.850755i
$453$		0			0
$454$	4.21552	+	11.7145i	0.197844	+	0.549789i
$455$	0.161629	−	0.0588282i	0.00757729	−	0.00275791i
$456$		0			0
$457$	2.71160	+	15.3782i	0.126843	+	0.719363i	0.980196	+	0.198029i	$0.0634542\pi$
$457$	2.71160	+	15.3782i	0.126843	+	0.719363i	−0.853353	+	0.521334i	$0.825435\pi$
$458$	10.5609	+	6.14868i	0.493479	+	0.287309i
$459$		0			0
$460$	−1.45485	+	0.825900i	−0.0678327	+	0.0385078i
$461$	−12.7088	+	2.24090i	−0.591908	+	0.104369i	−0.461575	−	0.887101i	$-0.652716\pi$
$461$	−12.7088	+	2.24090i	−0.591908	+	0.104369i	−0.130332	+	0.991470i	$0.541604\pi$
$462$		0			0
$463$	32.6243	−	11.8743i	1.51618	−	0.551845i	0.555990	−	0.831189i	$-0.312339\pi$
$463$	32.6243	−	11.8743i	1.51618	−	0.551845i	0.960191	+	0.279345i	$0.0901172\pi$
$464$	−2.11601	−	6.08795i	−0.0982332	−	0.282626i
$465$		0			0
$466$	0.914189	−	0.761445i	0.0423490	−	0.0352732i
$467$	12.4213	−	7.17141i	0.574787	−	0.331853i	−0.184272	−	0.982875i	$-0.558993\pi$
$467$	12.4213	−	7.17141i	0.574787	−	0.331853i	0.759059	+	0.651022i	$0.225659\pi$
$468$		0			0
$469$	3.90284	+	2.25330i	0.180216	+	0.104048i
$470$	2.03913	−	0.351907i	0.0940578	−	0.0162323i
$471$		0			0
$472$	−40.8635	−	7.66618i	−1.88090	−	0.352865i
$473$	−0.827235	+	4.69148i	−0.0380363	+	0.215715i
$474$		0			0
$475$	−7.28522	−	8.68219i	−0.334269	−	0.398366i
$476$	23.3145	+	0.169669i	1.06862	+	0.00777675i
$477$		0			0
$478$	−19.5268	−	0.0710509i	−0.893133	−	0.00324979i
$479$	−0.567163	−	0.206430i	−0.0259143	−	0.00943204i	0.329030	−	0.944319i	$-0.393278\pi$
$479$	−0.567163	−	0.206430i	−0.0259143	−	0.00943204i	−0.354945	+	0.934887i	$0.615500\pi$
$480$		0			0
$481$	−1.26647	−	1.06269i	−0.0577459	−	0.0484546i
$482$	−3.77932	+	20.9868i	−0.172144	+	0.955922i
$483$		0			0
$484$	15.6156	−	12.9105i	0.709798	−	0.586843i
$485$			2.08438i			0.0946467i
$486$		0			0
$487$	−22.8735			−1.03650			−0.518249	−	0.855230i	$-0.673416\pi$
$487$	−22.8735			−1.03650			−0.518249	+	0.855230i	$0.673416\pi$
$488$	41.4379	−	6.84110i	1.87581	−	0.309682i
$489$		0			0
$490$	−0.0901992	−	0.0162432i	−0.00407478	−	0.000733792i
$491$	5.76980	−	6.87618i	0.260387	−	0.310318i	−0.619973	−	0.784623i	$-0.712856\pi$
$491$	5.76980	−	6.87618i	0.260387	−	0.310318i	0.880360	+	0.474306i	$0.157301\pi$
$492$		0			0
$493$	−2.49376	+	6.85154i	−0.112313	+	0.308578i
$494$	−1.20693	−	0.00439157i	−0.0543022	−	0.000197586i
$495$		0			0
$496$	16.9685	+	30.4038i	0.761908	+	1.36517i
$497$	−10.9478	+	9.18633i	−0.491078	+	0.412063i
$498$		0			0
$499$	−43.2976	−	7.63454i	−1.93827	−	0.341769i	−0.938276	−	0.345886i	$-0.887578\pi$
$499$	−43.2976	−	7.63454i	−1.93827	−	0.341769i	−0.999992	+	0.00411738i	$0.998689\pi$
$500$	1.19255	+	3.35221i	0.0533325	+	0.149916i
$501$		0			0
$502$	15.6669	−	2.70376i	0.699250	−	0.120675i
$503$	−8.29388	+	14.3654i	−0.369806	+	0.640523i	−0.989535	−	0.144293i	$-0.953909\pi$
$503$	−8.29388	+	14.3654i	−0.369806	+	0.640523i	0.619729	+	0.784816i	$0.287242\pi$
$504$		0			0
$505$	−0.191391	−	0.331499i	−0.00851679	−	0.0147515i
$506$	3.95503	+	4.74841i	0.175823	+	0.211092i
$507$		0			0
$508$	6.93201	−	37.7067i	0.307558	−	1.67296i
$509$	9.18363	+	25.2318i	0.407057	+	1.11838i	0.958730	+	0.284320i	$0.0917677\pi$
$509$	9.18363	+	25.2318i	0.407057	+	1.11838i	−0.551672	+	0.834061i	$0.686010\pi$
$510$		0			0
$511$	−4.26777	−	24.2037i	−0.188795	−	1.07071i
$512$	−22.6153	−	0.740862i	−0.999464	−	0.0327418i
$513$		0			0
$514$	−5.06222	+	8.69481i	−0.223285	+	0.383512i
$515$	2.05999	−	0.363232i	0.0907742	−	0.0160059i
$516$		0			0
$517$	−2.61435	−	7.18286i	−0.114979	−	0.315902i
$518$	−5.45173	−	15.1498i	−0.239535	−	0.665643i
$519$		0			0
$520$	0.176737	+	0.0665207i	0.00775044	+	0.00291713i
$521$	−1.11230	−	1.92655i	−0.0487306	−	0.0844039i	0.840631	−	0.541608i	$-0.182184\pi$
$521$	−1.11230	−	1.92655i	−0.0487306	−	0.0844039i	−0.889362	+	0.457204i	$0.848851\pi$
$522$		0			0
$523$	−3.08920	−	1.78355i	−0.135081	−	0.0779892i	0.430937	−	0.902382i	$-0.358183\pi$
$523$	−3.08920	−	1.78355i	−0.135081	−	0.0779892i	−0.566018	+	0.824393i	$0.691517\pi$
$524$	0.637287	−	1.71206i	0.0278400	−	0.0747918i
$525$		0			0
$526$	20.7400	+	17.5319i	0.904306	+	0.764428i
$527$	6.83983	−	38.7906i	0.297948	−	1.68974i
$528$		0			0
$529$	−0.791437	+	0.664094i	−0.0344103	+	0.0288737i
$530$	−1.13843	−	1.98849i	−0.0494501	−	0.0863743i
$531$		0			0
$532$	−10.1364	−	5.95101i	−0.439468	−	0.258009i
$533$	−0.175469	+	0.482096i	−0.00760039	+	0.0208819i
$534$		0			0
$535$	−1.01220	−	0.849341i	−0.0437614	−	0.0367202i
$536$	1.64140	+	4.66762i	0.0708976	+	0.201610i
$537$		0			0
$538$	−8.07030	+	21.9244i	−0.347935	+	0.945229i
$539$			0.338554i			0.0145825i
$540$		0			0
$541$			16.0298i			0.689174i	0.938754	+	0.344587i	$0.111981\pi$
$541$			16.0298i			0.689174i	−0.938754	+	0.344587i	$0.888019\pi$
$542$	−1.56411	−	0.575743i	−0.0671842	−	0.0247303i
$543$		0			0
$544$	19.3064	+	16.8079i	0.827755	+	0.720633i
$545$	−1.80904	−	1.51796i	−0.0774907	−	0.0650224i
$546$		0			0
$547$	11.0856	−	30.4574i	0.473985	−	1.30226i	−0.440539	−	0.897733i	$-0.645213\pi$
$547$	11.0856	−	30.4574i	0.473985	−	1.30226i	0.914525	−	0.404530i	$-0.132565\pi$
$548$	5.80757	−	9.89205i	0.248087	−	0.422568i
$549$		0			0
$550$	5.68490	−	3.25465i	0.242405	−	0.138779i
$551$	2.81586	−	2.36279i	0.119960	−	0.100658i
$552$		0			0
$553$	1.81453	−	10.2907i	0.0771616	−	0.437605i
$554$	−21.0087	+	24.8529i	−0.892572	+	1.05590i
$555$		0			0
$556$	−14.7639	+	39.6630i	−0.626128	+	1.68208i
$557$	−29.5913	−	17.0845i	−1.25382	−	0.723895i	−0.281956	−	0.959427i	$-0.590983\pi$
$557$	−29.5913	−	17.0845i	−1.25382	−	0.723895i	−0.971867	+	0.235532i	$0.924317\pi$
$558$		0			0
$559$	−0.955747	−	1.65540i	−0.0404238	−	0.0700160i
$560$	1.16152	+	1.42589i	0.0490833	+	0.0602549i
$561$		0			0
$562$	−28.5465	+	10.2726i	−1.20416	+	0.433323i
$563$	2.63340	+	7.23520i	0.110984	+	0.304927i	0.982734	−	0.185025i	$-0.0592365\pi$
$563$	2.63340	+	7.23520i	0.110984	+	0.304927i	−0.871749	+	0.489952i	$0.837014\pi$
$564$		0			0
$565$	1.61199	−	0.284237i	0.0678169	−	0.0119580i
$566$	−0.420952	−	0.245084i	−0.0176939	−	0.0103016i
$567$		0			0
$568$	−15.6896	−	0.171273i	−0.658321	−	0.00718644i
$569$	−2.70678	−	15.3509i	−0.113474	−	0.643544i	−0.987494	−	0.157654i	$-0.949607\pi$
$569$	−2.70678	−	15.3509i	−0.113474	−	0.643544i	0.874020	−	0.485890i	$-0.161504\pi$
$570$		0			0
$571$	−7.83178	−	21.5176i	−0.327750	−	0.900485i	−0.988680	−	0.150038i	$-0.952060\pi$
$571$	−7.83178	−	21.5176i	−0.327750	−	0.900485i	0.660930	−	0.750447i	$-0.270162\pi$
$572$	0.126129	−	0.686079i	0.00527372	−	0.0286864i
$573$		0			0
$574$	−3.83912	+	3.19767i	−0.160242	+	0.133468i
$575$	−11.6426	−	20.1655i	−0.485528	−	0.840960i
$576$		0			0
$577$	13.3039	−	23.0431i	0.553850	−	0.959297i	−0.444141	−	0.895957i	$-0.646491\pi$
$577$	13.3039	−	23.0431i	0.553850	−	0.959297i	0.997992	−	0.0633405i	$-0.0201754\pi$
$578$	−0.836079	−	4.84466i	−0.0347763	−	0.201511i
$579$		0			0
$580$	−0.541868	+	0.192770i	−0.0224998	+	0.00800433i
$581$	−38.7253	−	6.82831i	−1.60660	−	0.283286i
$582$		0			0
$583$	−6.48384	+	5.44058i	−0.268533	+	0.225326i
$584$	13.7459	−	23.2195i	0.568809	−	0.960830i
$585$		0			0
$586$	0.135579	−	37.2608i	0.00560071	−	1.53923i
$587$	14.1595	−	38.9028i	0.584424	−	1.60569i	−0.196113	−	0.980581i	$-0.562832\pi$
$587$	14.1595	−	38.9028i	0.584424	−	1.60569i	0.780537	−	0.625110i	$-0.214946\pi$
$588$		0			0
$589$	−12.7643	+	15.2119i	−0.525944	+	0.626795i
$590$	−0.657536	+	3.65133i	−0.0270703	+	0.150323i
$591$		0			0
$592$	6.28705	−	16.5213i	0.258396	−	0.679022i
$593$	12.1474			0.498833			0.249417	−	0.968396i	$-0.419761\pi$
$593$	12.1474			0.498833			0.249417	+	0.968396i	$0.419761\pi$
$594$		0			0
$595$		−	2.08052i		−	0.0852930i
$596$	10.1409	+	12.2656i	0.415386	+	0.502418i
$597$		0			0
$598$	−2.44038	−	0.439466i	−0.0997944	−	0.0179711i
$599$	−25.1300	−	21.0866i	−1.02679	−	0.861575i	−0.0363204	−	0.999340i	$-0.511564\pi$
$599$	−25.1300	−	21.0866i	−1.02679	−	0.861575i	−0.990465	+	0.137765i	$0.956008\pi$
$600$		0			0
$601$	26.6419	+	9.69685i	1.08674	+	0.395543i	0.822414	−	0.568889i	$-0.192627\pi$
$601$	26.6419	+	9.69685i	1.08674	+	0.395543i	0.264331	+	0.964432i	$0.414849\pi$
$602$	0.0677358	−	18.6157i	0.00276071	−	0.758718i
$603$		0			0
$604$	−5.34030	−	0.0388634i	−0.217294	−	0.00158133i
$605$	−1.16218	−	1.38503i	−0.0472493	−	0.0563095i
$606$		0			0
$607$	−0.218532	+	1.23936i	−0.00886995	+	0.0503040i	−0.988921	−	0.148440i	$-0.952575\pi$
$607$	−0.218532	+	1.23936i	−0.00886995	+	0.0503040i	0.980052	+	0.198744i	$0.0636861\pi$
$608$	−4.19240	−	12.2050i	−0.170024	−	0.494976i
$609$		0			0
$610$	−0.637357	−	3.69316i	−0.0258058	−	0.149532i
$611$	2.65617	+	1.53354i	0.107457	+	0.0620405i
$612$		0			0
$613$	−27.4944	+	15.8739i	−1.11049	+	0.641141i	−0.938956	−	0.344038i	$-0.888205\pi$
$613$	−27.4944	+	15.8739i	−1.11049	+	0.641141i	−0.171532	+	0.985179i	$0.554872\pi$
$614$	14.9364	+	17.9327i	0.602785	+	0.723703i
$615$		0			0
$616$	4.42340	−	5.15623i	0.178224	−	0.207750i
$617$	29.6509	−	10.7920i	1.19370	−	0.434471i	0.332679	−	0.943040i	$-0.392047\pi$
$617$	29.6509	−	10.7920i	1.19370	−	0.434471i	0.861021	+	0.508569i	$0.169825\pi$
$618$		0			0
$619$	−29.3688	+	5.17850i	−1.18043	+	0.208142i	−0.729222	−	0.684277i	$-0.760118\pi$
$619$	−29.3688	+	5.17850i	−1.18043	+	0.208142i	−0.451208	+	0.892419i	$0.649007\pi$
$620$	2.70199	−	1.53388i	0.108514	−	0.0616023i
$621$		0			0
$622$	−14.7010	+	25.2503i	−0.589458	+	1.01244i
$623$	−7.30404	−	41.4233i	−0.292630	−	1.65959i
$624$		0			0
$625$	−23.0443	+	8.38744i	−0.921772	+	0.335498i
$626$	−16.7787	+	6.03791i	−0.670612	+	0.241323i
$627$		0			0
$628$	−24.3325	+	4.10813i	−0.970974	+	0.163932i
$629$	−17.3184	+	9.99880i	−0.690531	+	0.398678i
$630$		0			0
$631$	−15.5109	+	26.8656i	−0.617478	+	1.06950i	0.372466	+	0.928046i	$0.378512\pi$
$631$	−15.5109	+	26.8656i	−0.617478	+	1.06950i	−0.989944	+	0.141458i	$0.954821\pi$
$632$	8.86839	−	7.27799i	0.352766	−	0.289503i
$633$		0			0
$634$	11.1704	−	13.2144i	0.443633	−	0.524811i
$635$	−3.36916	−	0.594074i	−0.133701	−	0.0235751i
$636$		0			0
$637$	−0.0873191	−	0.104063i	−0.00345971	−	0.00412312i
$638$	1.05557	+	1.84376i	0.0417904	+	0.0729951i
$639$		0			0
$640$	−0.0514231	+	2.01850i	−0.00203267	+	0.0797881i
$641$	−34.7901	−	12.6626i	−1.37413	−	0.500142i	−0.453735	−	0.891137i	$-0.649909\pi$
$641$	−34.7901	−	12.6626i	−1.37413	−	0.500142i	−0.920393	+	0.390995i	$0.872131\pi$
$642$		0			0
$643$	21.1010	−	25.1472i	0.832143	−	0.991710i	−0.167839	−	0.985814i	$-0.553679\pi$
$643$	21.1010	−	25.1472i	0.832143	−	0.991710i	0.999983	−	0.00589543i	$-0.00187658\pi$
$644$	−18.3856	−	15.6568i	−0.724495	−	0.616963i
$645$		0			0
$646$	−5.04302	+	13.7003i	−0.198415	+	0.539030i
$647$	32.3509			1.27185			0.635923	−	0.771752i	$-0.280620\pi$
$647$	32.3509			1.27185			0.635923	+	0.771752i	$0.280620\pi$
$648$		0			0
$649$	13.7049			0.537965
$650$	−0.907960	+	2.46664i	−0.0356131	+	0.0967494i
$651$		0			0
$652$	−17.7009	+	20.7860i	−0.693221	+	0.814044i
$653$	7.14706	−	8.51753i	0.279686	−	0.333317i	−0.607853	−	0.794050i	$-0.707969\pi$
$653$	7.14706	−	8.51753i	0.279686	−	0.333317i	0.887539	+	0.460733i	$0.152413\pi$
$654$		0			0
$655$	−0.153185	−	0.0557549i	−0.00598545	−	0.00217852i
$656$	−5.48497	−	0.0798366i	−0.214152	−	0.00311710i
$657$		0			0
$658$	14.8408	+	25.9223i	0.578553	+	1.01056i
$659$	−21.7371	−	25.9052i	−0.846757	−	1.00913i	−0.999782	−	0.0209028i	$-0.993346\pi$
$659$	−21.7371	−	25.9052i	−0.846757	−	1.00913i	0.153025	−	0.988222i	$-0.451099\pi$
$660$		0			0
$661$	26.9698	+	4.75551i	1.04901	+	0.184968i	0.671473	−	0.741029i	$-0.265662\pi$
$661$	26.9698	+	4.75551i	1.04901	+	0.184968i	0.377532	+	0.925997i	$0.376773\pi$
$662$	−18.5143	+	21.9022i	−0.719579	+	0.851252i
$663$		0			0
$664$	−27.3880	−	33.3729i	−1.06286	−	1.29512i
$665$	−0.524441	+	0.908358i	−0.0203369	+	0.0352246i
$666$		0			0
$667$	6.54020	−	3.77598i	0.253237	−	0.146207i
$668$	1.39567	+	8.26660i	0.0540003	+	0.319844i
$669$		0			0
$670$	0.415437	−	0.149497i	0.0160497	−	0.00577557i
$671$	−13.0092	+	4.73497i	−0.502216	+	0.182792i
$672$		0			0
$673$	−3.55472	−	20.1598i	−0.137024	−	0.777103i	−0.973429	−	0.228990i	$-0.926458\pi$
$673$	−3.55472	−	20.1598i	−0.137024	−	0.777103i	0.836404	−	0.548113i	$-0.184654\pi$
$674$	12.2560	−	21.0508i	0.472083	−	0.810845i
$675$		0			0
$676$	−12.6976	−	22.3673i	−0.488370	−	0.860279i
$677$	−32.7893	+	5.78165i	−1.26020	+	0.222207i	−0.763552	−	0.645747i	$-0.776546\pi$
$677$	−32.7893	+	5.78165i	−1.26020	+	0.222207i	−0.496645	+	0.867954i	$0.665435\pi$
$678$		0			0
$679$	−28.2735	+	10.2907i	−1.08504	+	0.394922i
$680$	1.48727	−	1.73367i	0.0570343	−	0.0664833i
$681$		0			0
$682$	−7.34539	−	8.81887i	−0.281270	−	0.337692i
$683$	−11.8895	+	6.86440i	−0.454939	+	0.262659i	−0.709914	−	0.704289i	$-0.751266\pi$
$683$	−11.8895	+	6.86440i	−0.454939	+	0.262659i	0.254975	+	0.966948i	$0.417933\pi$
$684$		0			0
$685$	−0.886463	−	0.511800i	−0.0338700	−	0.0195549i
$686$	−4.56216	−	26.4354i	−0.174184	−	1.00931i
$687$		0			0
$688$	13.3640	−	15.4638i	0.509496	−	0.589551i
$689$	0.589743	−	3.34460i	0.0224674	−	0.127419i
$690$		0			0
$691$	16.4903	+	19.6524i	0.627321	+	0.747612i	0.982311	−	0.187258i	$-0.0599600\pi$
$691$	16.4903	+	19.6524i	0.627321	+	0.747612i	−0.354990	+	0.934870i	$0.615516\pi$
$692$	−0.291593	+	40.0684i	−0.0110847	+	1.52317i
$693$		0			0
$694$	−0.0328242	+	9.02100i	−0.00124599	+	0.342432i
$695$	3.54881	+	1.29166i	0.134614	+	0.0489955i
$696$		0			0
$697$	4.75379	+	3.98890i	0.180063	+	0.151090i
$698$	18.6516	+	3.35880i	0.705972	+	0.127132i
$699$		0			0
$700$	−19.7284	+	16.3110i	−0.745665	+	0.616496i
$701$			0.366433i			0.0138400i	0.999976	+	0.00692000i	$0.00220272\pi$
$701$			0.366433i			0.0138400i	−0.999976	+	0.00692000i	$0.997797\pi$
$702$		0			0
$703$	10.0817			0.380237
$704$	7.37192	−	1.13453i	0.277840	−	0.0427593i
$705$		0			0
$706$	−2.82879	+	15.7084i	−0.106463	+	0.591193i
$707$	3.55171	−	4.23276i	0.133576	−	0.159189i
$708$		0			0
$709$	−2.32486	+	6.38749i	−0.0873118	+	0.239887i	−0.975662	−	0.219279i	$-0.929630\pi$
$709$	−2.32486	+	6.38749i	−0.0873118	+	0.239887i	0.888350	+	0.459166i	$0.151852\pi$
$710$	−0.00509458	+	1.40013i	−0.000191196	+	0.0525460i
$711$		0			0
$712$	23.5253	−	39.7388i	0.881647	−	1.48928i
$713$	−31.2526	+	26.2241i	−1.17042	+	0.982100i
$714$		0			0
$715$	−0.0613024	−	0.0108093i	−0.00229258	−	0.000404244i
$716$	5.39380	+	15.1617i	0.201576	+	0.566621i
$717$		0			0
$718$	6.53514	+	37.8679i	0.243889	+	1.41322i
$719$	6.07495	−	10.5221i	0.226558	−	0.392409i	−0.730228	−	0.683203i	$-0.760586\pi$
$719$	6.07495	−	10.5221i	0.226558	−	0.392409i	0.956786	+	0.290794i	$0.0939195\pi$
$720$		0			0
$721$	15.0974	+	26.1495i	0.562257	+	0.973857i
$722$	−14.9911	+	12.4864i	−0.557912	+	0.464695i
$723$		0			0
$724$	15.8958	+	2.92228i	0.590761	+	0.108606i
$725$	−2.73793	−	7.52240i	−0.101684	−	0.279375i
$726$		0			0
$727$	0.337498	+	1.91405i	0.0125171	+	0.0709881i	0.990426	−	0.138041i	$-0.0440807\pi$
$727$	0.337498	+	1.91405i	0.0125171	+	0.0709881i	−0.977909	+	0.209029i	$0.932970\pi$
$728$	−0.0297554	+	2.72577i	−0.00110281	+	0.101024i
$729$		0			0
$730$	−2.08086	−	1.21150i	−0.0770160	−	0.0448397i
$731$	−22.7700	+	4.01496i	−0.842177	+	0.148499i
$732$		0			0
$733$	−14.2681	−	39.2014i	−0.527006	−	1.44794i	−0.862579	−	0.505923i	$-0.831152\pi$
$733$	−14.2681	−	39.2014i	−0.527006	−	1.44794i	0.335572	−	0.942014i	$-0.391070\pi$
$734$	30.4746	−	10.9664i	1.12484	−	0.404779i
$735$		0			0
$736$	−4.12817	−	26.1896i	−0.152166	−	0.965363i
$737$	−0.815477	−	1.41245i	−0.0300385	−	0.0520282i
$738$		0			0
$739$	−22.3170	−	12.8847i	−0.820943	−	0.473971i	0.0297988	−	0.999556i	$-0.490513\pi$
$739$	−22.3170	−	12.8847i	−0.820943	−	0.473971i	−0.850741	+	0.525584i	$0.823847\pi$
$740$	−1.47832	−	0.550280i	−0.0543441	−	0.0202287i
$741$		0			0
$742$	21.3523	−	25.2595i	0.783868	−	0.927304i
$743$	0.466716	−	2.64688i	0.0171222	−	0.0971046i	−0.975049	−	0.221989i	$-0.928745\pi$
$743$	0.466716	−	2.64688i	0.0171222	−	0.0971046i	0.992171	+	0.124885i	$0.0398561\pi$
$744$		0			0
$745$	1.08790	−	0.912858i	0.0398576	−	0.0334445i
$746$	−34.7660	+	19.9038i	−1.27287	+	0.728731i
$747$		0			0
$748$	−7.27646	−	4.27197i	−0.266054	−	0.156199i
$749$	6.52355	−	17.9233i	0.238365	−	0.654903i
$750$		0			0
$751$	−35.3934	−	29.6986i	−1.29153	−	1.08372i	−0.991544	−	0.129773i	$-0.958575\pi$
$751$	−35.3934	−	29.6986i	−1.29153	−	1.08372i	−0.299982	−	0.953945i	$-0.596981\pi$
$752$	−6.16409	+	32.2097i	−0.224781	+	1.17457i
$753$		0			0
$754$	−0.799994	−	0.294475i	−0.0291341	−	0.0107241i
$755$			0.476553i			0.0173435i
$756$		0			0
$757$		−	41.2974i		−	1.50098i	−0.660883	−	0.750489i	$-0.729818\pi$
$757$		−	41.2974i		−	1.50098i	0.660883	−	0.750489i	$-0.270182\pi$
$758$	4.49666	−	12.2160i	0.163326	−	0.443705i
$759$		0			0
$760$	−1.08635	+	0.382024i	−0.0394062	+	0.0138575i
$761$	−16.6555	−	13.9756i	−0.603762	−	0.506616i	0.288891	−	0.957362i	$-0.406714\pi$
$761$	−16.6555	−	13.9756i	−0.603762	−	0.506616i	−0.892652	+	0.450746i	$0.851158\pi$
$762$		0			0
$763$	11.6591	−	32.0330i	0.422086	−	1.15967i
$764$	16.8505	−	28.7016i	0.609631	−	1.03839i
$765$		0			0
$766$	−16.5703	−	28.9433i	−0.598710	−	1.04576i
$767$	−4.21254	+	3.53474i	−0.152106	+	0.127632i
$768$		0			0
$769$	4.86149	−	27.5709i	0.175310	−	0.994232i	−0.762476	−	0.647017i	$-0.776016\pi$
$769$	4.86149	−	27.5709i	0.175310	−	0.994232i	0.937786	−	0.347215i	$-0.112873\pi$
$770$	−0.462975	−	0.391362i	−0.0166845	−	0.0141037i
$771$		0			0
$772$	−1.54752	−	0.576039i	−0.0556964	−	0.0207321i
$773$	23.6486	+	13.6535i	0.850580	+	0.491083i	0.860847	−	0.508864i	$-0.169935\pi$
$773$	23.6486	+	13.6535i	0.850580	+	0.491083i	−0.0102662	+	0.999947i	$0.503268\pi$
$774$		0			0
$775$	21.6229	+	37.4519i	0.776717	+	1.34531i
$776$	−30.9164	−	11.6364i	−1.10983	−	0.417721i
$777$		0			0
$778$	14.4115	+	40.0479i	0.516676	+	1.43579i
$779$	−1.07002	−	2.93986i	−0.0383375	−	0.105331i
$780$		0			0
$781$	5.09352	−	0.898125i	0.182260	−	0.0321374i
$782$	−15.0911	+	25.9203i	−0.539656	+	0.926907i
$783$		0			0
$784$	0.744476	−	1.24719i	0.0265884	−	0.0445426i
$785$	0.382380	+	2.16858i	0.0136477	+	0.0774001i
$786$		0			0
$787$	7.72182	+	21.2155i	0.275253	+	0.756252i	0.997884	+	0.0650180i	$0.0207105\pi$
$787$	7.72182	+	21.2155i	0.275253	+	0.756252i	−0.722631	+	0.691234i	$0.757067\pi$
$788$	29.6683	+	5.45423i	1.05689	+	0.194299i
$789$		0			0
$790$	−0.655192	−	0.786622i	−0.0233107	−	0.0279868i
$791$	11.8140	+	20.4625i	0.420059	+	0.727564i
$792$		0			0
$793$	2.77747	−	4.81073i	0.0986310	−	0.170834i
$794$	24.9192	−	4.30050i	0.884350	−	0.152619i
$795$		0			0
$796$	−29.3128	+	10.4280i	−1.03896	+	0.369612i
$797$	19.2857	+	3.40058i	0.683133	+	0.120455i	0.504436	−	0.863449i	$-0.331701\pi$
$797$	19.2857	+	3.40058i	0.683133	+	0.120455i	0.178697	+	0.983904i	$0.442812\pi$
$798$		0			0
$799$	28.4196	−	23.8469i	1.00541	−	0.843641i
$800$	−28.0994	−	0.511274i	−0.993465	−	0.0180762i
$801$		0			0
$802$	14.0446	+	0.0511034i	0.495933	+	0.00180452i
$803$	−3.04211	+	8.35812i	−0.107354	+	0.294952i
$804$		0			0
$805$	−1.38515	+	1.65076i	−0.0488202	+	0.0581816i
$806$	4.53233	+	0.816188i	0.159645	+	0.0287490i
$807$		0			0
$808$	5.98540	−	0.988147i	0.210566	−	0.0347629i
$809$	27.8483			0.979094			0.489547	−	0.871977i	$-0.337162\pi$
$809$	27.8483			0.979094			0.489547	+	0.871977i	$0.337162\pi$
$810$		0			0
$811$			7.82601i			0.274808i	0.990515	+	0.137404i	$0.0438759\pi$
$811$			7.82601i			0.274808i	−0.990515	+	0.137404i	$0.956124\pi$
$812$	−5.29007	−	6.39845i	−0.185645	−	0.224541i
$813$		0			0
$814$	−1.03271	+	5.73470i	−0.0361965	+	0.201001i
$815$	1.86628	+	1.56600i	0.0653730	+	0.0548545i
$816$		0			0
$817$	10.9535	+	3.98673i	0.383213	+	0.139478i
$818$	−7.83013	−	0.0284911i	−0.273774	−	0.000996167i
$819$		0			0
$820$	−0.00356220	+	0.489489i	−0.000124397	+	0.0170937i
$821$	9.82911	+	11.7139i	0.343038	+	0.408817i	0.909788	−	0.415073i	$-0.136244\pi$
$821$	9.82911	+	11.7139i	0.343038	+	0.408817i	−0.566750	+	0.823890i	$0.691799\pi$
$822$		0			0
$823$	−4.11133	+	23.3165i	−0.143312	+	0.812763i	0.825395	+	0.564556i	$0.190953\pi$
$823$	−4.11133	+	23.3165i	−0.143312	+	0.812763i	−0.968707	+	0.248207i	$0.920159\pi$
$824$	−6.11262	+	32.5825i	−0.212943	+	1.13506i
$825$		0			0
$826$	−52.7748	+	9.10774i	−1.83627	+	0.316899i
$827$	0.0403168	+	0.0232769i	0.00140195	+	0.000809419i	0.500701	−	0.865620i	$-0.333076\pi$
$827$	0.0403168	+	0.0232769i	0.00140195	+	0.000809419i	−0.499299	+	0.866430i	$0.666409\pi$
$828$		0			0
$829$	−6.44307	+	3.71991i	−0.223777	+	0.129198i	−0.607698	−	0.794168i	$-0.707907\pi$
$829$	−6.44307	+	3.71991i	−0.223777	+	0.129198i	0.383921	+	0.923366i	$0.374574\pi$
$830$	−2.96016	+	2.46557i	−0.102749	+	0.0855812i
$831$		0			0
$832$	−1.97333	+	2.25008i	−0.0684128	+	0.0780074i
$833$	−1.54406	+	0.561994i	−0.0534987	+	0.0194719i
$834$		0			0
$835$	0.736742	−	0.129908i	0.0254960	−	0.00449564i
$836$	2.10007	+	3.69934i	0.0726325	+	0.127944i
$837$		0			0
$838$	−5.00008	−	2.91111i	−0.172725	−	0.100562i
$839$	3.69536	+	20.9574i	0.127578	+	0.723531i	0.979743	+	0.200258i	$0.0641780\pi$
$839$	3.69536	+	20.9574i	0.127578	+	0.723531i	−0.852165	+	0.523273i	$0.824711\pi$
$840$		0			0
$841$	−24.8114	+	9.03060i	−0.855565	+	0.311400i
$842$	11.7644	+	32.6920i	0.405427	+	1.12664i
$843$		0			0
$844$	10.8986	−	1.84004i	0.375146	−	0.0633369i
$845$	−1.98764	+	1.14756i	−0.0683768	+	0.0394774i
$846$		0			0
$847$	13.0495	−	22.6024i	0.448385	−	0.776626i
$848$	35.8495	−	5.78458i	1.23108	−	0.198643i
$849$		0			0
$850$	24.2806	+	20.5248i	0.832816	+	0.703996i
$851$	20.3980	+	3.59671i	0.699234	+	0.123294i
$852$		0			0
$853$	−11.8527	−	14.1255i	−0.405829	−	0.483648i	0.523959	−	0.851744i	$-0.324455\pi$
$853$	−11.8527	−	14.1255i	−0.405829	−	0.483648i	−0.929788	+	0.368095i	$0.880010\pi$
$854$	46.9492	−	26.8788i	1.60657	−	0.919774i
$855$		0			0
$856$	18.2486	−	10.2719i	0.623723	−	0.351085i
$857$	18.6167	+	6.77591i	0.635933	+	0.231461i	0.639812	−	0.768532i	$-0.279012\pi$
$857$	18.6167	+	6.77591i	0.635933	+	0.231461i	−0.00387866	+	0.999992i	$0.501235\pi$
$858$		0			0
$859$	5.06270	−	6.03349i	0.172737	−	0.205860i	−0.672729	−	0.739889i	$-0.734878\pi$
$859$	5.06270	−	6.03349i	0.172737	−	0.205860i	0.845466	+	0.534029i	$0.179323\pi$
$860$	−1.38855	−	1.18246i	−0.0473491	−	0.0403214i
$861$		0			0
$862$	−18.5879	−	6.84214i	−0.633106	−	0.233044i
$863$	3.41425			0.116222			0.0581111	−	0.998310i	$-0.481492\pi$
$863$	3.41425			0.116222			0.0581111	+	0.998310i	$0.481492\pi$
$864$		0			0
$865$	3.57559			0.121574
$866$	16.5761	+	6.10159i	0.563278	+	0.207340i
$867$		0			0
$868$	34.1463	+	29.0782i	1.15900	+	0.986977i
$869$	−2.43082	+	2.89694i	−0.0824600	+	0.0982720i
$870$		0			0
$871$	0.614953	+	0.223825i	0.0208369	+	0.00758401i
$872$	32.6143	−	18.3581i	1.10446	−	0.621685i
$873$		0			0
$874$	13.1226	−	7.51278i	0.443877	−	0.254124i
$875$	2.94597	+	3.51087i	0.0995919	+	0.118689i
$876$		0			0
$877$	13.1746	+	2.32305i	0.444876	+	0.0784437i	0.391599	−	0.920136i	$-0.371922\pi$
$877$	13.1746	+	2.32305i	0.444876	+	0.0784437i	0.0532774	+	0.998580i	$0.483033\pi$
$878$	−11.6597	−	9.85613i	−0.393494	−	0.332628i
$879$		0			0
$880$	−0.106024	−	0.657078i	−0.00357408	−	0.0221501i
$881$	−28.5441	+	49.4399i	−0.961676	+	1.66567i	−0.243384	+	0.969930i	$0.578257\pi$
$881$	−28.5441	+	49.4399i	−0.961676	+	1.66567i	−0.718292	+	0.695742i	$0.755076\pi$
$882$		0			0
$883$	−17.0975	+	9.87122i	−0.575375	+	0.332193i	−0.759293	−	0.650749i	$-0.774455\pi$
$883$	−17.0975	+	9.87122i	−0.575375	+	0.332193i	0.183918	+	0.982942i	$0.441122\pi$
$884$	3.33842	−	0.563635i	0.112283	−	0.0189571i
$885$		0			0
$886$	13.9302	+	38.7106i	0.467995	+	1.30051i
$887$	53.6182	−	19.5154i	1.80032	−	0.655264i	0.802004	−	0.597319i	$-0.203767\pi$
$887$	53.6182	−	19.5154i	1.80032	−	0.655264i	0.998320	−	0.0579452i	$-0.0184549\pi$
$888$		0			0
$889$	−8.57547	−	48.6339i	−0.287612	−	1.63113i
$890$	−3.56127	−	2.07341i	−0.119374	−	0.0695010i
$891$		0			0
$892$	5.16138	+	9.09194i	0.172816	+	0.304421i
$893$	−18.4192	+	3.24779i	−0.616373	+	0.108683i
$894$		0			0
$895$	1.34942	−	0.491147i	0.0451060	−	0.0164172i
$896$	−27.6338	+	9.26794i	−0.923180	+	0.309620i
$897$		0			0
$898$	32.7050	−	27.2406i	1.09138	−	0.909030i
$899$	−12.1466	+	7.01286i	−0.405113	+	0.233892i
$900$		0			0
$901$	−35.5763	−	20.5400i	−1.18522	−	0.684286i
$902$	1.78187	−	0.307511i	0.0593298	−	0.0102390i
$903$		0			0
$904$	−4.78325	+	25.4965i	−0.159089	+	0.848001i
$905$	0.250440	−	1.42031i	0.00832490	−	0.0472128i
$906$		0			0
$907$	15.5646	+	18.5491i	0.516813	+	0.615914i	0.959824	−	0.280602i	$-0.0905342\pi$
$907$	15.5646	+	18.5491i	0.516813	+	0.615914i	−0.443011	+	0.896516i	$0.646090\pi$
$908$	−0.128128	+	17.6064i	−0.00425209	+	0.584288i
$909$		0			0
$910$	0.243246		0.000885087i	0.00806354		2.93403e-5i
$911$	−21.3962	−	7.78758i	−0.708888	−	0.258014i	−0.0376870	−	0.999290i	$-0.511999\pi$
$911$	−21.3962	−	7.78758i	−0.708888	−	0.258014i	−0.671201	+	0.741275i	$0.734221\pi$
$912$		0			0
$913$	10.9016	+	9.14750i	0.360789	+	0.302738i
$914$	−3.91388	+	21.7340i	−0.129460	+	0.718897i
$915$		0			0
$916$	11.0122	+	13.3195i	0.363854	+	0.440089i
$917$		−	2.35315i		−	0.0777078i
$918$		0			0
$919$	3.40847			0.112435			0.0562174	−	0.998419i	$-0.482096\pi$
$919$	3.40847			0.112435			0.0562174	+	0.998419i	$0.482096\pi$
$920$	−2.33428	+	0.385374i	−0.0769591	+	0.0127054i
$921$		0			0
$922$	−17.9613	−	3.23449i	−0.591524	−	0.106522i
$923$	−1.33398	+	1.58977i	−0.0439084	+	0.0523279i
$924$		0			0
$925$	7.50928	−	20.6316i	0.246904	−	0.678362i
$926$	49.0984	+	0.178652i	1.61348	+	0.00587086i
$927$		0			0
$928$	0.165819	−	9.11338i	0.00544328	−	0.299161i
$929$	16.2267	−	13.6158i	0.532381	−	0.446721i	−0.336541	−	0.941669i	$-0.609257\pi$
$929$	16.2267	−	13.6158i	0.532381	−	0.446721i	0.868923	+	0.494948i	$0.164813\pi$
$930$		0			0
$931$	0.815804	+	0.143848i	0.0267369	+	0.00471443i
$932$	1.58526	−	0.563955i	0.0519268	−	0.0184730i
$933$		0			0
$934$	19.9883	−	3.44954i	0.654039	−	0.112872i
$935$	−0.376473	+	0.652071i	−0.0123120	+	0.0213250i
$936$		0			0
$937$	20.8301	+	36.0788i	0.680489	+	1.17864i	0.974832	+	0.222942i	$0.0715661\pi$
$937$	20.8301	+	36.0788i	0.680489	+	1.17864i	−0.294342	+	0.955700i	$0.595101\pi$
$938$	4.07889	+	4.89711i	0.133181	+	0.159896i
$939$		0			0
$940$	2.87815	+	0.529121i	0.0938750	+	0.0172580i
$941$	17.2670	+	47.4407i	0.562888	+	1.54652i	0.815382	+	0.578924i	$0.196527\pi$
$941$	17.2670	+	47.4407i	0.562888	+	1.54652i	−0.252493	+	0.967599i	$0.581251\pi$
$942$		0			0
$943$	−1.11613	−	6.32988i	−0.0363461	−	0.206129i
$944$	−50.4873	−	30.1370i	−1.64322	−	0.980874i
$945$		0			0
$946$	−3.38976	+	5.82221i	−0.110211	+	0.189296i
$947$	−38.1758	+	6.73142i	−1.24055	+	0.218742i	−0.755149	−	0.655553i	$-0.772436\pi$
$947$	−38.1758	+	6.73142i	−1.24055	+	0.218742i	−0.485396	+	0.874294i	$0.661325\pi$
$948$		0			0
$949$	−1.22064	−	3.35369i	−0.0396238	−	0.108865i
$950$	−5.42719	−	15.0816i	−0.176081	−	0.489312i
$951$		0			0
$952$	30.8591	+	11.6148i	1.00015	+	0.376439i
$953$	17.7159	+	30.6848i	0.573873	+	0.993977i	0.996163	+	0.0875165i	$0.0278931\pi$
$953$	17.7159	+	30.6848i	0.573873	+	0.993977i	−0.422290	+	0.906461i	$0.638774\pi$
$954$		0			0
$955$	−2.57205	−	1.48498i	−0.0832297	−	0.0480527i
$956$	−25.8804	−	9.63354i	−0.837031	−	0.311571i
$957$		0			0
$958$	−0.651868	−	0.551037i	−0.0210609	−	0.0178032i
$959$	2.56577	−	14.5512i	0.0828531	−	0.469883i
$960$		0			0
$961$	34.2959	−	28.7776i	1.10632	−	0.928311i
$962$	−1.16165	−	2.02906i	−0.0374532	−	0.0654194i
$963$		0			0
$964$	−15.2683	+	26.0065i	−0.491757	+	0.837612i
$965$	−0.0503964	+	0.138463i	−0.00162232	+	0.00445728i
$966$		0			0
$967$	−1.48262	−	1.24406i	−0.0476777	−	0.0400064i	0.618637	−	0.785677i	$-0.287685\pi$
$967$	−1.48262	−	1.24406i	−0.0476777	−	0.0400064i	−0.666315	+	0.745670i	$0.732129\pi$
$968$	27.0314	−	9.50577i	0.868822	−	0.305527i
$969$		0			0
$970$	−1.01826	+	2.76630i	−0.0326945	+	0.0888204i
$971$		−	30.4220i		−	0.976288i	−0.872763	−	0.488144i	$-0.837674\pi$
$971$		−	30.4220i		−	0.976288i	0.872763	−	0.488144i	$-0.162326\pi$
$972$		0			0
$973$			54.5148i			1.74766i
$974$	−30.3568	−	11.1742i	−0.972693	−	0.358045i
$975$		0			0
$976$	58.3366	+	11.1641i	1.86731	+	0.357354i
$977$	−2.40690	−	2.01963i	−0.0770035	−	0.0646136i	0.603473	−	0.797383i	$-0.293783\pi$
$977$	−2.40690	−	2.01963i	−0.0770035	−	0.0646136i	−0.680477	+	0.732769i	$0.738227\pi$
$978$		0			0
$979$	−5.20639	+	14.3044i	−0.166397	+	0.457172i
$980$	−0.111773	−	0.0656215i	−0.00357047	−	0.00209620i
$981$		0			0
$982$	11.0166	−	6.30710i	0.351554	−	0.201268i
$983$	−44.9828	+	37.7451i	−1.43473	+	1.20388i	−0.491880	+	0.870663i	$0.663690\pi$
$983$	−44.9828	+	37.7451i	−1.43473	+	1.20388i	−0.942850	+	0.333218i	$0.891865\pi$
$984$		0			0
$985$	0.467428	−	2.65092i	0.0148935	−	0.0844652i
$986$	−6.65673	+	7.87482i	−0.211994	+	0.250785i
$987$		0			0
$988$	−1.59964	−	0.595438i	−0.0508912	−	0.0189434i
$989$	20.7395	+	11.9740i	0.659479	+	0.380750i
$990$		0			0
$991$	10.3807	+	17.9799i	0.329754	+	0.571150i	0.982463	−	0.186458i	$-0.0597009\pi$
$991$	10.3807	+	17.9799i	0.329754	+	0.571150i	−0.652709	+	0.757609i	$0.726368\pi$
$992$	7.66695	+	48.6401i	0.243426	+	1.54433i
$993$		0			0
$994$	−19.0172	+	6.84344i	−0.603190	+	0.217061i
$995$	0.949553	+	2.60888i	0.0301029	+	0.0827069i
$996$		0			0
$997$	32.5454	−	5.73863i	1.03072	−	0.181744i	0.367389	−	0.930067i	$-0.380252\pi$
$997$	32.5454	−	5.73863i	1.03072	−	0.181744i	0.663335	+	0.748323i	$0.269141\pi$
$998$	−53.7331	−	31.2841i	−1.70089	−	0.990280i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.253.30		204
3.2	odd	2		216.2.t.a.13.5	✓	204
8.5	even	2	inner	648.2.t.a.253.7		204
12.11	even	2		864.2.bf.a.337.13		204
24.5	odd	2		216.2.t.a.13.28	yes	204
24.11	even	2		864.2.bf.a.337.22		204
27.2	odd	18		216.2.t.a.133.28	yes	204
27.25	even	9	inner	648.2.t.a.397.7		204
108.83	even	18		864.2.bf.a.241.22		204
216.29	odd	18		216.2.t.a.133.5	yes	204
216.83	even	18		864.2.bf.a.241.13		204
216.133	even	18	inner	648.2.t.a.397.30		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.5	✓	204	3.2	odd	2
216.2.t.a.13.28	yes	204	24.5	odd	2
216.2.t.a.133.5	yes	204	216.29	odd	18
216.2.t.a.133.28	yes	204	27.2	odd	18
648.2.t.a.253.7		204	8.5	even	2	inner
648.2.t.a.253.30		204	1.1	even	1	trivial
648.2.t.a.397.7		204	27.25	even	9	inner
648.2.t.a.397.30		204	216.133	even	18	inner
864.2.bf.a.241.13		204	216.83	even	18
864.2.bf.a.241.22		204	108.83	even	18
864.2.bf.a.337.13		204	12.11	even	2
864.2.bf.a.337.22		204	24.11	even	2

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32716 + 0.488522i) q^{2} +(1.52269 + 1.29669i) q^{4} +(0.114718 - 0.136716i) q^{5} +(2.42085 + 0.881117i) q^{7} +(1.38739 + 2.46478i) q^{8} +(0.219037 - 0.125401i) q^{10} +(-0.599296 - 0.714213i) q^{11} +(0.368417 + 0.0649618i) q^{13} +(2.78240 + 2.35202i) q^{14} +(0.637188 + 3.94892i) q^{16} +(2.26254 - 3.91883i) q^{17} +(-1.97566 + 1.14065i) q^{19} +(0.351958 - 0.0594221i) q^{20} +(-0.446451 - 1.24064i) q^{22} +(-4.40423 + 1.60301i) q^{23} +(0.862710 + 4.89267i) q^{25} +(0.457212 + 0.266194i) q^{26} +(2.54367 + 4.48076i) q^{28} +(-1.58682 + 0.279799i) q^{29} +(8.17965 - 2.97715i) q^{31} +(-1.08349 + 5.55212i) q^{32} +(4.91718 - 4.09561i) q^{34} +(0.398177 - 0.229888i) q^{35} +(-3.82721 - 2.20964i) q^{37} +(-3.17924 + 0.548665i) q^{38} +(0.496133 + 0.0930767i) q^{40} +(-0.238139 + 1.35055i) q^{41} +(-3.28437 - 3.91416i) q^{43} +(0.0135696 - 1.86463i) q^{44} +(-6.62821 - 0.0241177i) q^{46} +(7.70413 + 2.80407i) q^{47} +(-0.278168 - 0.233411i) q^{49} +(-1.24522 + 6.91480i) q^{50} +(0.476750 + 0.576640i) q^{52} -9.07829i q^{53} -0.166394 q^{55} +(1.18691 + 7.18932i) q^{56} +(-2.24265 - 0.403859i) q^{58} +(-9.44865 + 11.2605i) q^{59} +(5.07860 - 13.9533i) q^{61} +(12.3101 + 0.0447920i) q^{62} +(-4.15029 + 6.83923i) q^{64} +(0.0511453 - 0.0429160i) q^{65} +(1.72274 + 0.303765i) q^{67} +(8.52666 - 3.03337i) q^{68} +(0.640749 - 0.110579i) q^{70} +(-2.77372 + 4.80422i) q^{71} +(-4.77001 - 8.26190i) q^{73} +(-3.99985 - 4.80222i) q^{74} +(-4.48738 - 0.824961i) q^{76} +(-0.821500 - 2.25705i) q^{77} +(-0.704340 - 3.99451i) q^{79} +(0.612976 + 0.365899i) q^{80} +(-0.975822 + 1.67606i) q^{82} +(-15.0319 + 2.65052i) q^{83} +(-0.276212 - 0.758885i) q^{85} +(-2.44672 - 6.79919i) q^{86} +(0.928921 - 2.46803i) q^{88} +(-8.16359 - 14.1397i) q^{89} +(0.834643 + 0.481881i) q^{91} +(-8.78489 - 3.27003i) q^{92} +(8.85474 + 7.48508i) q^{94} +(-0.0706993 + 0.400955i) q^{95} +(-8.94677 + 7.50723i) q^{97} +(-0.255147 - 0.445664i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

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Database

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