LMFDB - Embedded newform 3456.2.i.h.2305.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3456,2,Mod(1153,3456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("3456.1153");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3456 = 2^{7} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3456.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$27.5962989386$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.8528759163648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 $ x^10 - 2x^9 + x^8 + 9x^6 - 36x^5 + 27x^4 + 27x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 1152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2305.4
Root			$0.756905 - 1.55791i$ of defining polynomial
Character	$\chi$	$=$	3456.2305
Dual form			3456.2.i.h.1153.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07447 - 1.86104i) q^{5} +(-0.153174 - 0.265305i) q^{7} +O(q^{10})$	$q+(1.07447 - 1.86104i) q^{5} +(-0.153174 - 0.265305i) q^{7} +(-2.50736 - 4.34288i) q^{11} +(-0.470741 + 0.815346i) q^{13} +4.70838 q^{17} +1.61796 q^{19} +(4.08184 - 7.06995i) q^{23} +(0.191022 + 0.330859i) q^{25} +(2.39504 + 4.14834i) q^{29} +(1.29776 - 2.24778i) q^{31} -0.658323 q^{35} -10.2093 q^{37} +(-3.86537 + 6.69502i) q^{41} +(0.138140 + 0.239265i) q^{43} +(1.92007 + 3.32566i) q^{47} +(3.45308 - 5.98090i) q^{49} +2.23508 q^{53} -10.7764 q^{55} +(4.95830 - 8.58802i) q^{59} +(-5.36414 - 9.29097i) q^{61} +(1.01159 + 1.75213i) q^{65} +(2.02117 - 3.50078i) q^{67} -3.59379 q^{71} -5.43811 q^{73} +(-0.768124 + 1.33043i) q^{77} +(-8.30403 - 14.3830i) q^{79} +(-2.91867 - 5.05528i) q^{83} +(5.05902 - 8.76248i) q^{85} +1.94577 q^{89} +0.288420 q^{91} +(1.73845 - 3.01108i) q^{95} +(7.07283 + 12.2505i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{7}+O(q^{10}) $ 10 * q + 4 * q^7	$ 10 q + 4 q^{7} + q^{11} + 6 q^{13} + 6 q^{17} + 18 q^{19} + 4 q^{23} + q^{25} + 4 q^{29} + 8 q^{31} + 24 q^{35} - 20 q^{37} + 5 q^{41} - 13 q^{43} - 6 q^{47} + 3 q^{49} - 12 q^{55} + 13 q^{59} + 10 q^{61} - 17 q^{67} + 8 q^{71} - 34 q^{73} - 8 q^{77} + 6 q^{79} - 12 q^{83} + 18 q^{85} - 44 q^{89} + 36 q^{91} - 6 q^{95} + 27 q^{97}+O(q^{100}) $ 10 * q + 4 * q^7 + q^11 + 6 * q^13 + 6 * q^17 + 18 * q^19 + 4 * q^23 + q^25 + 4 * q^29 + 8 * q^31 + 24 * q^35 - 20 * q^37 + 5 * q^41 - 13 * q^43 - 6 * q^47 + 3 * q^49 - 12 * q^55 + 13 * q^59 + 10 * q^61 - 17 * q^67 + 8 * q^71 - 34 * q^73 - 8 * q^77 + 6 * q^79 - 12 * q^83 + 18 * q^85 - 44 * q^89 + 36 * q^91 - 6 * q^95 + 27 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times$.

$n$	$2053$	$2431$	$2945$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.07447	−	1.86104i	0.480518	−	0.832282i	−0.519232	−	0.854633i	$-0.673782\pi$
$5$	1.07447	−	1.86104i	0.480518	−	0.832282i	0.999750	+	0.0223513i	$0.00711523\pi$
$6$		0			0
$7$	−0.153174	−	0.265305i	−0.0578942	−	0.100276i	0.835626	−	0.549299i	$-0.185105\pi$
$7$	−0.153174	−	0.265305i	−0.0578942	−	0.100276i	−0.893520	+	0.449024i	$0.851772\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.50736	−	4.34288i	−0.755999	−	1.30943i	−0.944876	−	0.327428i	$-0.893818\pi$
$11$	−2.50736	−	4.34288i	−0.755999	−	1.30943i	0.188878	−	0.982001i	$-0.439515\pi$
$12$		0			0
$13$	−0.470741	+	0.815346i	−0.130560	+	0.226136i	−0.923893	−	0.382652i	$-0.875011\pi$
$13$	−0.470741	+	0.815346i	−0.130560	+	0.226136i	0.793333	+	0.608788i	$0.208344\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.70838			1.14195			0.570975	−	0.820967i	$-0.306565\pi$
$17$	4.70838			1.14195			0.570975	+	0.820967i	$0.306565\pi$
$18$		0			0
$19$	1.61796			0.371185			0.185592	−	0.982627i	$-0.440580\pi$
$19$	1.61796			0.371185			0.185592	+	0.982627i	$0.440580\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.08184	−	7.06995i	0.851122	−	1.47419i	−0.0290754	−	0.999577i	$-0.509256\pi$
$23$	4.08184	−	7.06995i	0.851122	−	1.47419i	0.880197	−	0.474609i	$-0.157410\pi$
$24$		0			0
$25$	0.191022	+	0.330859i	0.0382043	+	0.0661718i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.39504	+	4.14834i	0.444749	+	0.770327i	0.998035	−	0.0626641i	$-0.0199597\pi$
$29$	2.39504	+	4.14834i	0.444749	+	0.770327i	−0.553286	+	0.832991i	$0.686626\pi$
$30$		0			0
$31$	1.29776	−	2.24778i	0.233084	−	0.403714i	−0.725630	−	0.688085i	$-0.758452\pi$
$31$	1.29776	−	2.24778i	0.233084	−	0.403714i	0.958714	+	0.284371i	$0.0917848\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.658323			−0.111277
$36$		0			0
$37$	−10.2093			−1.67840			−0.839199	−	0.543824i	$-0.816976\pi$
$37$	−10.2093			−1.67840			−0.839199	+	0.543824i	$0.816976\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.86537	+	6.69502i	−0.603669	+	1.04559i	0.388591	+	0.921410i	$0.372962\pi$
$41$	−3.86537	+	6.69502i	−0.603669	+	1.04559i	−0.992260	+	0.124175i	$0.960371\pi$
$42$		0			0
$43$	0.138140	+	0.239265i	0.0210661	+	0.0364876i	0.876366	−	0.481645i	$-0.159961\pi$
$43$	0.138140	+	0.239265i	0.0210661	+	0.0364876i	−0.855300	+	0.518133i	$0.826627\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.92007	+	3.32566i	0.280072	+	0.485098i	0.971402	−	0.237441i	$-0.0763085\pi$
$47$	1.92007	+	3.32566i	0.280072	+	0.485098i	−0.691331	+	0.722539i	$0.742975\pi$
$48$		0			0
$49$	3.45308	−	5.98090i	0.493297	−	0.854415i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.23508			0.307012			0.153506	−	0.988148i	$-0.450944\pi$
$53$	2.23508			0.307012			0.153506	+	0.988148i	$0.450944\pi$
$54$		0			0
$55$	−10.7764			−1.45308
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.95830	−	8.58802i	0.645515	−	1.11807i	−0.338667	−	0.940906i	$-0.609976\pi$
$59$	4.95830	−	8.58802i	0.645515	−	1.11807i	0.984182	−	0.177159i	$-0.0566907\pi$
$60$		0			0
$61$	−5.36414	−	9.29097i	−0.686808	−	1.18959i	−0.972865	−	0.231374i	$-0.925678\pi$
$61$	−5.36414	−	9.29097i	−0.686808	−	1.18959i	0.286057	−	0.958213i	$-0.407655\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.01159	+	1.75213i	0.125473	+	0.217325i
$66$		0			0
$67$	2.02117	−	3.50078i	0.246926	−	0.427688i	−0.715746	−	0.698361i	$-0.753913\pi$
$67$	2.02117	−	3.50078i	0.246926	−	0.427688i	0.962671	+	0.270673i	$0.0872463\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.59379			−0.426505			−0.213252	−	0.976997i	$-0.568406\pi$
$71$	−3.59379			−0.426505			−0.213252	+	0.976997i	$0.568406\pi$
$72$		0			0
$73$	−5.43811			−0.636483			−0.318242	−	0.948010i	$-0.603092\pi$
$73$	−5.43811			−0.636483			−0.318242	+	0.948010i	$0.603092\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.768124	+	1.33043i	−0.0875359	+	0.151617i
$78$		0			0
$79$	−8.30403	−	14.3830i	−0.934276	−	1.61821i	−0.775920	−	0.630831i	$-0.782714\pi$
$79$	−8.30403	−	14.3830i	−0.934276	−	1.61821i	−0.158356	−	0.987382i	$-0.550619\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.91867	−	5.05528i	−0.320365	−	0.554889i	0.660198	−	0.751092i	$-0.270472\pi$
$83$	−2.91867	−	5.05528i	−0.320365	−	0.554889i	−0.980563	+	0.196203i	$0.937139\pi$
$84$		0			0
$85$	5.05902	−	8.76248i	0.548728	−	0.950425i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.94577			0.206251			0.103125	−	0.994668i	$-0.467116\pi$
$89$	1.94577			0.206251			0.103125	+	0.994668i	$0.467116\pi$
$90$		0			0
$91$	0.288420			0.0302347
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.73845	−	3.01108i	0.178361	−	0.308930i
$96$		0			0
$97$	7.07283	+	12.2505i	0.718137	+	1.24385i	0.961737	+	0.273974i	$0.0883383\pi$
$97$	7.07283	+	12.2505i	0.718137	+	1.24385i	−0.243600	+	0.969876i	$0.578328\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.41272	−	16.3033i	−0.936601	−	1.62224i	−0.771754	−	0.635922i	$-0.780620\pi$
$101$	−9.41272	−	16.3033i	−0.936601	−	1.62224i	−0.164847	−	0.986319i	$-0.552713\pi$
$102$		0			0
$103$	2.95014	−	5.10979i	0.290686	−	0.503483i	−0.683286	−	0.730151i	$-0.739450\pi$
$103$	2.95014	−	5.10979i	0.290686	−	0.503483i	0.973972	+	0.226668i	$0.0727831\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.86061			−0.373219			−0.186609	−	0.982434i	$-0.559750\pi$
$107$	−3.86061			−0.373219			−0.186609	+	0.982434i	$0.559750\pi$
$108$		0			0
$109$	−10.8821			−1.04232			−0.521159	−	0.853459i	$-0.674500\pi$
$109$	−10.8821			−1.04232			−0.521159	+	0.853459i	$0.674500\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.15157	+	5.45869i	−0.296475	+	0.513510i	−0.975327	−	0.220765i	$-0.929145\pi$
$113$	−3.15157	+	5.45869i	−0.296475	+	0.513510i	0.678852	+	0.734275i	$0.262478\pi$
$114$		0			0
$115$	−8.77163	−	15.1929i	−0.817959	−	1.41675i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.721200	−	1.24915i	−0.0661123	−	0.114510i
$120$		0			0
$121$	−7.07375	+	12.2521i	−0.643068	+	1.11383i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.5657			1.03447
$126$		0			0
$127$	−11.7659			−1.04406			−0.522028	−	0.852928i	$-0.674825\pi$
$127$	−11.7659			−1.04406			−0.522028	+	0.852928i	$0.674825\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.64077	+	4.57395i	−0.230725	+	0.399628i	−0.958022	−	0.286696i	$-0.907443\pi$
$131$	−2.64077	+	4.57395i	−0.230725	+	0.399628i	0.727297	+	0.686323i	$0.240777\pi$
$132$		0			0
$133$	−0.247828	−	0.429251i	−0.0214894	−	0.0372208i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.23452	+	12.5306i	0.618087	+	1.07056i	0.989834	+	0.142224i	$0.0454253\pi$
$137$	7.23452	+	12.5306i	0.618087	+	1.07056i	−0.371748	+	0.928334i	$0.621241\pi$
$138$		0			0
$139$	−10.7880	+	18.6854i	−0.915026	+	1.58487i	−0.108164	+	0.994133i	$0.534497\pi$
$139$	−10.7880	+	18.6854i	−0.915026	+	1.58487i	−0.806863	+	0.590739i	$0.798836\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.72127			0.394813
$144$		0			0
$145$	10.2936			0.854839
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.80471	−	13.5181i	0.639386	−	1.10745i	−0.346181	−	0.938168i	$-0.612522\pi$
$149$	7.80471	−	13.5181i	0.639386	−	1.10745i	0.985568	−	0.169282i	$-0.0541449\pi$
$150$		0			0
$151$	8.58275	+	14.8658i	0.698455	+	1.20976i	0.969002	+	0.247052i	$0.0794620\pi$
$151$	8.58275	+	14.8658i	0.698455	+	1.20976i	−0.270547	+	0.962707i	$0.587205\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.78881	−	4.83036i	−0.224003	−	0.387984i
$156$		0			0
$157$	−2.59257	+	4.49046i	−0.206909	+	0.358378i	−0.950739	−	0.309991i	$-0.899674\pi$
$157$	−2.59257	+	4.49046i	−0.206909	+	0.358378i	0.743830	+	0.668369i	$0.233007\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.50092			−0.197100
$162$		0			0
$163$	−17.8955			−1.40168			−0.700842	−	0.713317i	$-0.747192\pi$
$163$	−17.8955			−1.40168			−0.700842	+	0.713317i	$0.747192\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.48714	−	9.50401i	0.424608	−	0.735442i	−0.571776	−	0.820410i	$-0.693745\pi$
$167$	5.48714	−	9.50401i	0.424608	−	0.735442i	0.996384	+	0.0849677i	$0.0270787\pi$
$168$		0			0
$169$	6.05681	+	10.4907i	0.465908	+	0.806977i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.63146	−	14.9501i	−0.656238	−	1.13664i	−0.981582	−	0.191042i	$-0.938813\pi$
$173$	−8.63146	−	14.9501i	−0.656238	−	1.13664i	0.325344	−	0.945596i	$-0.394520\pi$
$174$		0			0
$175$	0.0585190	−	0.101358i	0.00442362	−	0.00766193i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	15.0571			1.12542			0.562709	−	0.826655i	$-0.309759\pi$
$179$	15.0571			1.12542			0.562709	+	0.826655i	$0.309759\pi$
$180$		0			0
$181$	17.6813			1.31424			0.657120	−	0.753786i	$-0.271774\pi$
$181$	17.6813			1.31424			0.657120	+	0.753786i	$0.271774\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−10.9696	+	18.9999i	−0.806501	+	1.39690i
$186$		0			0
$187$	−11.8056	−	20.4479i	−0.863313	−	1.49530i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.3168	−	17.8693i	−0.746501	−	1.29298i	−0.949490	−	0.313796i	$-0.898399\pi$
$191$	−10.3168	−	17.8693i	−0.746501	−	1.29298i	0.202990	−	0.979181i	$-0.434934\pi$
$192$		0			0
$193$	11.6134	−	20.1149i	0.835948	−	1.44791i	−0.0573076	−	0.998357i	$-0.518252\pi$
$193$	11.6134	−	20.1149i	0.835948	−	1.44791i	0.893256	−	0.449548i	$-0.148415\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.78497			0.340915			0.170458	−	0.985365i	$-0.445475\pi$
$197$	4.78497			0.340915			0.170458	+	0.985365i	$0.445475\pi$
$198$		0			0
$199$	−11.5938			−0.821862			−0.410931	−	0.911666i	$-0.634796\pi$
$199$	−11.5938			−0.821862			−0.410931	+	0.911666i	$0.634796\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.733715	−	1.27083i	0.0514967	−	0.0891950i
$204$		0			0
$205$	8.30646	+	14.3872i	0.580148	+	1.00485i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.05681	−	7.02660i	−0.280615	−	0.486040i
$210$		0			0
$211$	0.888671	−	1.53922i	0.0611786	−	0.105964i	−0.833814	−	0.552046i	$-0.813847\pi$
$211$	0.888671	−	1.53922i	0.0611786	−	0.105964i	0.894993	+	0.446081i	$0.147181\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.593709			0.0404906
$216$		0			0
$217$	−0.795130			−0.0539769
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.21643	+	3.83896i	−0.149093	+	0.258237i
$222$		0			0
$223$	5.02422	+	8.70221i	0.336447	+	0.582743i	0.983762	−	0.179480i	$-0.0574415\pi$
$223$	5.02422	+	8.70221i	0.336447	+	0.582743i	−0.647315	+	0.762223i	$0.724108\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.27671	−	9.13953i	−0.350228	−	0.606612i	0.636061	−	0.771638i	$-0.280562\pi$
$227$	−5.27671	−	9.13953i	−0.350228	−	0.606612i	−0.986289	+	0.165026i	$0.947229\pi$
$228$		0			0
$229$	11.3955	−	19.7377i	0.753039	−	1.30430i	−0.193304	−	0.981139i	$-0.561920\pi$
$229$	11.3955	−	19.7377i	0.753039	−	1.30430i	0.946343	−	0.323163i	$-0.104746\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.97108			−0.391179			−0.195589	−	0.980686i	$-0.562662\pi$
$233$	−5.97108			−0.391179			−0.195589	+	0.980686i	$0.562662\pi$
$234$		0			0
$235$	8.25226			0.538318
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.77549	+	10.0034i	−0.373585	+	0.647069i	−0.990114	−	0.140264i	$-0.955205\pi$
$239$	−5.77549	+	10.0034i	−0.373585	+	0.647069i	0.616529	+	0.787332i	$0.288538\pi$
$240$		0			0
$241$	7.75827	+	13.4377i	0.499754	+	0.865600i	1.00000		0.000283894i	$-9.03662e-5\pi$
$241$	7.75827	+	13.4377i	0.499754	+	0.865600i	−0.500246	+	0.865883i	$0.666757\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.42046	−	12.8526i	−0.474076	−	0.821124i
$246$		0			0
$247$	−0.761638	+	1.31920i	−0.0484619	+	0.0839384i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	14.5685			0.919557			0.459778	−	0.888034i	$-0.347929\pi$
$251$	14.5685			0.919557			0.459778	+	0.888034i	$0.347929\pi$
$252$		0			0
$253$	−40.9386			−2.57379
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.78071	−	13.4766i	0.485347	−	0.840646i	−0.514511	−	0.857484i	$-0.672026\pi$
$257$	7.78071	−	13.4766i	0.485347	−	0.840646i	0.999858	+	0.0168376i	$0.00535983\pi$
$258$		0			0
$259$	1.56380	+	2.70857i	0.0971695	+	0.168303i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−11.2231	−	19.4389i	−0.692044	−	1.19866i	−0.971167	−	0.238400i	$-0.923377\pi$
$263$	−11.2231	−	19.4389i	−0.692044	−	1.19866i	0.279123	−	0.960255i	$-0.409956\pi$
$264$		0			0
$265$	2.40153	−	4.15957i	0.147525	−	0.255521i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−26.0256			−1.58681			−0.793403	−	0.608696i	$-0.791693\pi$
$269$	−26.0256			−1.58681			−0.793403	+	0.608696i	$0.791693\pi$
$270$		0			0
$271$	5.59761			0.340031			0.170015	−	0.985441i	$-0.445618\pi$
$271$	5.59761			0.340031			0.170015	+	0.985441i	$0.445618\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.957922	−	1.65917i	0.0577648	−	0.100052i
$276$		0			0
$277$	1.57957	+	2.73589i	0.0949069	+	0.164384i	0.909570	−	0.415551i	$-0.136411\pi$
$277$	1.57957	+	2.73589i	0.0949069	+	0.164384i	−0.814663	+	0.579935i	$0.803078\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	8.02031	+	13.8916i	0.478452	+	0.828703i	0.999695	−	0.0247057i	$-0.00786487\pi$
$281$	8.02031	+	13.8916i	0.478452	+	0.828703i	−0.521243	+	0.853408i	$0.674532\pi$
$282$		0			0
$283$	1.87142	−	3.24140i	0.111245	−	0.192681i	−0.805028	−	0.593237i	$-0.797850\pi$
$283$	1.87142	−	3.24140i	0.111245	−	0.192681i	0.916272	+	0.400556i	$0.131183\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.36829			0.139796
$288$		0			0
$289$	5.16885			0.304050
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.49886	−	9.52431i	0.321247	−	0.556416i	−0.659499	−	0.751706i	$-0.729231\pi$
$293$	5.49886	−	9.52431i	0.321247	−	0.556416i	0.980746	+	0.195290i	$0.0625647\pi$
$294$		0			0
$295$	−10.6551	−	18.4552i	−0.620364	−	1.07450i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.84297	+	6.65622i	0.222245	+	0.384939i
$300$		0			0
$301$	0.0423188	−	0.0732983i	0.00243921	−	0.00422484i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−23.0545			−1.32010
$306$		0			0
$307$	6.08416			0.347241			0.173621	−	0.984813i	$-0.444453\pi$
$307$	6.08416			0.347241			0.173621	+	0.984813i	$0.444453\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.75633	−	6.50616i	0.213002	−	0.368930i	−0.739651	−	0.672991i	$-0.765009\pi$
$311$	3.75633	−	6.50616i	0.213002	−	0.368930i	0.952653	+	0.304061i	$0.0983426\pi$
$312$		0			0
$313$	6.18076	+	10.7054i	0.349357	+	0.605105i	0.986135	−	0.165942i	$-0.0530666\pi$
$313$	6.18076	+	10.7054i	0.349357	+	0.605105i	−0.636778	+	0.771047i	$0.719733\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.3204	+	21.3395i	0.691980	+	1.19854i	0.971188	+	0.238314i	$0.0765947\pi$
$317$	12.3204	+	21.3395i	0.691980	+	1.19854i	−0.279208	+	0.960231i	$0.590072\pi$
$318$		0			0
$319$	12.0105	−	20.8028i	0.672459	−	1.16473i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	7.61796			0.423874
$324$		0			0
$325$	−0.359686			−0.0199518
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.588209	−	1.01881i	0.0324290	−	0.0561687i
$330$		0			0
$331$	−11.0695	−	19.1730i	−0.608436	−	1.05384i	−0.991498	−	0.130119i	$-0.958464\pi$
$331$	−11.0695	−	19.1730i	−0.608436	−	1.05384i	0.383063	−	0.923722i	$-0.374869\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.34339	−	7.52297i	−0.237305	−	0.411024i
$336$		0			0
$337$	−5.63803	+	9.76536i	−0.307123	+	0.531953i	−0.977732	−	0.209858i	$-0.932700\pi$
$337$	−5.63803	+	9.76536i	−0.307123	+	0.531953i	0.670609	+	0.741811i	$0.266033\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−13.0158			−0.704846
$342$		0			0
$343$	−4.26011			−0.230024
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.3903	−	19.7286i	0.611465	−	1.05909i	−0.379529	−	0.925180i	$-0.623914\pi$
$347$	11.3903	−	19.7286i	0.611465	−	1.05909i	0.990994	−	0.133908i	$-0.0427527\pi$
$348$		0			0
$349$	−1.44215	−	2.49788i	−0.0771966	−	0.133708i	0.824843	−	0.565362i	$-0.191264\pi$
$349$	−1.44215	−	2.49788i	−0.0771966	−	0.133708i	−0.902039	+	0.431654i	$0.857930\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−9.41192	−	16.3019i	−0.500946	−	0.867663i	−0.999999	−	0.00109240i	$-0.999652\pi$
$353$	−9.41192	−	16.3019i	−0.500946	−	0.867663i	0.499054	−	0.866571i	$-0.333681\pi$
$354$		0			0
$355$	−3.86143	+	6.68819i	−0.204943	+	0.354972i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−26.6316			−1.40556			−0.702782	−	0.711406i	$-0.748059\pi$
$359$	−26.6316			−1.40556			−0.702782	+	0.711406i	$0.748059\pi$
$360$		0			0
$361$	−16.3822			−0.862222
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.84310	+	10.1205i	−0.305842	+	0.529733i
$366$		0			0
$367$	12.6413	+	21.8953i	0.659869	+	1.14293i	0.980649	+	0.195773i	$0.0627216\pi$
$367$	12.6413	+	21.8953i	0.659869	+	1.14293i	−0.320780	+	0.947154i	$0.603945\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.342356	−	0.592977i	−0.0177742	−	0.0307858i
$372$		0			0
$373$	−0.427926	+	0.741189i	−0.0221571	+	0.0383773i	−0.876891	−	0.480689i	$-0.840387\pi$
$373$	−0.427926	+	0.741189i	−0.0221571	+	0.0383773i	0.854734	+	0.519066i	$0.173720\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.50978			−0.232265
$378$		0			0
$379$	5.34571			0.274591			0.137295	−	0.990530i	$-0.456159\pi$
$379$	5.34571			0.274591			0.137295	+	0.990530i	$0.456159\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.132433	+	0.229381i	−0.00676702	+	0.0117208i	−0.869389	−	0.494128i	$-0.835487\pi$
$383$	−0.132433	+	0.229381i	−0.00676702	+	0.0117208i	0.862622	+	0.505849i	$0.168821\pi$
$384$		0			0
$385$	1.65066	+	2.85902i	0.0841252	+	0.145709i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	10.9697	+	19.0001i	0.556187	+	0.963343i	0.997810	+	0.0661429i	$0.0210693\pi$
$389$	10.9697	+	19.0001i	0.556187	+	0.963343i	−0.441624	+	0.897200i	$0.645597\pi$
$390$		0			0
$391$	19.2188	−	33.2880i	0.971938	−	1.68345i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−35.6898			−1.79575
$396$		0			0
$397$	2.19238			0.110032			0.0550161	−	0.998485i	$-0.482479\pi$
$397$	2.19238			0.110032			0.0550161	+	0.998485i	$0.482479\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	18.8864	−	32.7121i	0.943140	−	1.63357i	0.183707	−	0.982981i	$-0.441190\pi$
$401$	18.8864	−	32.7121i	0.943140	−	1.63357i	0.759433	−	0.650585i	$-0.225476\pi$
$402$		0			0
$403$	1.22182	+	2.11625i	0.0608630	+	0.105418i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	25.5984	+	44.3378i	1.26887	+	2.19774i
$408$		0			0
$409$	15.9676	−	27.6566i	0.789546	−	1.36753i	−0.136700	−	0.990612i	$-0.543650\pi$
$409$	15.9676	−	27.6566i	0.789546	−	1.36753i	0.926246	−	0.376920i	$-0.123017\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.03792			−0.149486
$414$		0			0
$415$	−12.5441			−0.615766
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.83505	+	3.17840i	−0.0896480	+	0.155275i	−0.907362	−	0.420349i	$-0.861908\pi$
$419$	−1.83505	+	3.17840i	−0.0896480	+	0.155275i	0.817714	+	0.575624i	$0.195241\pi$
$420$		0			0
$421$	7.72300	+	13.3766i	0.376396	+	0.651937i	0.990535	−	0.137261i	$-0.0438299\pi$
$421$	7.72300	+	13.3766i	0.376396	+	0.651937i	−0.614139	+	0.789198i	$0.710497\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.899403	+	1.55781i	0.0436274	+	0.0755649i
$426$		0			0
$427$	−1.64329	+	2.84626i	−0.0795244	+	0.137740i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	18.9913			0.914779			0.457390	−	0.889266i	$-0.348784\pi$
$431$	18.9913			0.914779			0.457390	+	0.889266i	$0.348784\pi$
$432$		0			0
$433$	12.7931			0.614796			0.307398	−	0.951581i	$-0.400542\pi$
$433$	12.7931			0.614796			0.307398	+	0.951581i	$0.400542\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.60423	−	11.4389i	0.315923	−	0.547195i
$438$		0			0
$439$	14.5259	+	25.1595i	0.693281	+	1.20080i	0.970757	+	0.240065i	$0.0771689\pi$
$439$	14.5259	+	25.1595i	0.693281	+	1.20080i	−0.277476	+	0.960733i	$0.589498\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	18.4010	+	31.8714i	0.874256	+	1.51426i	0.857554	+	0.514395i	$0.171983\pi$
$443$	18.4010	+	31.8714i	0.874256	+	1.51426i	0.0167020	+	0.999861i	$0.494683\pi$
$444$		0			0
$445$	2.09067	−	3.62115i	0.0991073	−	0.171659i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	18.4952			0.872842			0.436421	−	0.899743i	$-0.356246\pi$
$449$	18.4952			0.872842			0.436421	+	0.899743i	$0.356246\pi$
$450$		0			0
$451$	38.7675			1.82549
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.309899	−	0.536761i	0.0145283	−	0.0251638i
$456$		0			0
$457$	9.79321	+	16.9623i	0.458107	+	0.793465i	0.998861	−	0.0477162i	$-0.0151943\pi$
$457$	9.79321	+	16.9623i	0.458107	+	0.793465i	−0.540754	+	0.841181i	$0.681861\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.17311	+	10.6921i	0.287510	+	0.497983i	0.973215	−	0.229897i	$-0.0738391\pi$
$461$	6.17311	+	10.6921i	0.287510	+	0.497983i	−0.685704	+	0.727880i	$0.740506\pi$
$462$		0			0
$463$	−18.6089	+	32.2316i	−0.864830	+	1.49793i	0.00238525	+	0.999997i	$0.499241\pi$
$463$	−18.6089	+	32.2316i	−0.864830	+	1.49793i	−0.867216	+	0.497933i	$0.834093\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.6412			−0.492415			−0.246208	−	0.969217i	$-0.579185\pi$
$467$	−10.6412			−0.492415			−0.246208	+	0.969217i	$0.579185\pi$
$468$		0			0
$469$	−1.23836			−0.0571823
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.692734	−	1.19985i	0.0318519	−	0.0551692i
$474$		0			0
$475$	0.309065	+	0.535316i	0.0141809	+	0.0245620i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.22894	−	10.7888i	−0.284608	−	0.492955i	0.687906	−	0.725799i	$-0.258530\pi$
$479$	−6.22894	−	10.7888i	−0.284608	−	0.492955i	−0.972514	+	0.232845i	$0.925197\pi$
$480$		0			0
$481$	4.80593	−	8.32412i	0.219132	−	0.379547i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	30.3982			1.38031
$486$		0			0
$487$	12.5254			0.567580			0.283790	−	0.958886i	$-0.408408\pi$
$487$	12.5254			0.567580			0.283790	+	0.958886i	$0.408408\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.581151	−	1.00658i	0.0262270	−	0.0454264i	−0.852614	−	0.522541i	$-0.824984\pi$
$491$	0.581151	−	1.00658i	0.0262270	−	0.0454264i	0.878841	+	0.477115i	$0.158317\pi$
$492$		0			0
$493$	11.2768	+	19.5320i	0.507881	+	0.879675i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.550474	+	0.953449i	0.0246921	+	0.0427680i
$498$		0			0
$499$	−12.8699	+	22.2912i	−0.576134	+	0.997893i	0.419784	+	0.907624i	$0.362106\pi$
$499$	−12.8699	+	22.2912i	−0.576134	+	0.997893i	−0.995917	+	0.0902688i	$0.971227\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	24.1469			1.07666			0.538328	−	0.842736i	$-0.319056\pi$
$503$	24.1469			1.07666			0.538328	+	0.842736i	$0.319056\pi$
$504$		0			0
$505$	−40.4548			−1.80022
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.55763	+	7.89404i	−0.202013	+	0.349897i	−0.949177	−	0.314743i	$-0.898082\pi$
$509$	−4.55763	+	7.89404i	−0.202013	+	0.349897i	0.747164	+	0.664640i	$0.231415\pi$
$510$		0			0
$511$	0.832976	+	1.44276i	0.0368487	+	0.0638238i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.33969	−	10.9807i	−0.279360	−	0.483866i
$516$		0			0
$517$	9.62865	−	16.6773i	0.423467	−	0.733467i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.18121			0.402236			0.201118	−	0.979567i	$-0.435542\pi$
$521$	9.18121			0.402236			0.201118	+	0.979567i	$0.435542\pi$
$522$		0			0
$523$	8.94824			0.391279			0.195640	−	0.980676i	$-0.437322\pi$
$523$	8.94824			0.391279			0.195640	+	0.980676i	$0.437322\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.11034	−	10.5834i	0.266171	−	0.461021i
$528$		0			0
$529$	−21.8228	−	37.7981i	−0.948816	−	1.64340i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.63917	−	6.30323i	−0.157630	−	0.273023i
$534$		0			0
$535$	−4.14811	+	7.18474i	−0.179338	+	0.310623i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−34.6325			−1.49173
$540$		0			0
$541$	−26.6203			−1.14450			−0.572249	−	0.820080i	$-0.693929\pi$
$541$	−26.6203			−1.14450			−0.572249	+	0.820080i	$0.693929\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−11.6925	+	20.2521i	−0.500853	+	0.867503i
$546$		0			0
$547$	−2.18028	−	3.77635i	−0.0932219	−	0.161465i	0.815643	−	0.578555i	$-0.196383\pi$
$547$	−2.18028	−	3.77635i	−0.0932219	−	0.161465i	−0.908865	+	0.417090i	$0.863050\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.87508	+	6.71183i	0.165084	+	0.285934i
$552$		0			0
$553$	−2.54392	+	4.40619i	−0.108178	+	0.187370i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.33947			0.395726			0.197863	−	0.980230i	$-0.436600\pi$
$557$	9.33947			0.395726			0.197863	+	0.980230i	$0.436600\pi$
$558$		0			0
$559$	−0.260112			−0.0110016
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.603050	−	1.04451i	0.0254155	−	0.0440210i	−0.853038	−	0.521849i	$-0.825242\pi$
$563$	0.603050	−	1.04451i	0.0254155	−	0.0440210i	0.878453	+	0.477828i	$0.158576\pi$
$564$		0			0
$565$	6.77255	+	11.7304i	0.284923	+	0.493502i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.83998	+	6.65104i	0.160980	+	0.278826i	0.935221	−	0.354066i	$-0.115201\pi$
$569$	3.83998	+	6.65104i	0.160980	+	0.278826i	−0.774240	+	0.632892i	$0.781868\pi$
$570$		0			0
$571$	4.44038	−	7.69097i	0.185824	−	0.321857i	−0.758030	−	0.652220i	$-0.773838\pi$
$571$	4.44038	−	7.69097i	0.185824	−	0.321857i	0.943854	+	0.330363i	$0.107171\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.11888			0.130066
$576$		0			0
$577$	−33.1358			−1.37946			−0.689732	−	0.724065i	$-0.742271\pi$
$577$	−33.1358			−1.37946			−0.689732	+	0.724065i	$0.742271\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.894126	+	1.54867i	−0.0370946	+	0.0642497i
$582$		0			0
$583$	−5.60416	−	9.70669i	−0.232101	−	0.402010i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.0712	+	31.3002i	0.745877	+	1.29190i	0.949784	+	0.312906i	$0.101302\pi$
$587$	18.0712	+	31.3002i	0.745877	+	1.29190i	−0.203908	+	0.978990i	$0.565364\pi$
$588$		0			0
$589$	2.09972	−	3.63682i	0.0865174	−	0.149852i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	34.4076			1.41295			0.706476	−	0.707737i	$-0.250284\pi$
$593$	34.4076			1.41295			0.706476	+	0.707737i	$0.250284\pi$
$594$		0			0
$595$	−3.09964			−0.127073
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−21.2939	+	36.8822i	−0.870047	+	1.50697i	−0.00809947	+	0.999967i	$0.502578\pi$
$599$	−21.2939	+	36.8822i	−0.870047	+	1.50697i	−0.861947	+	0.506998i	$0.830755\pi$
$600$		0			0
$601$	−11.6910	−	20.2495i	−0.476888	−	0.825994i	0.522762	−	0.852479i	$-0.324902\pi$
$601$	−11.6910	−	20.2495i	−0.476888	−	0.825994i	−0.999649	+	0.0264854i	$0.991568\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	15.2011	+	26.3291i	0.618012	+	1.07043i
$606$		0			0
$607$	12.6852	−	21.9714i	0.514875	−	0.891790i	−0.484976	−	0.874527i	$-0.661172\pi$
$607$	12.6852	−	21.9714i	0.514875	−	0.891790i	0.999851	−	0.0172622i	$-0.00549499\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.61543			−0.146264
$612$		0			0
$613$	12.9459			0.522882			0.261441	−	0.965220i	$-0.415802\pi$
$613$	12.9459			0.522882			0.261441	+	0.965220i	$0.415802\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.01514	+	10.4185i	−0.242161	+	0.419434i	−0.961329	−	0.275401i	$-0.911189\pi$
$617$	−6.01514	+	10.4185i	−0.242161	+	0.419434i	0.719169	+	0.694835i	$0.244523\pi$
$618$		0			0
$619$	21.9475	+	38.0142i	0.882144	+	1.52792i	0.848952	+	0.528469i	$0.177234\pi$
$619$	21.9475	+	38.0142i	0.882144	+	1.52792i	0.0331916	+	0.999449i	$0.489433\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.298040	−	0.516221i	−0.0119407	−	0.0206820i
$624$		0			0
$625$	11.4719	−	19.8699i	0.458877	−	0.794797i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−48.0693			−1.91665
$630$		0			0
$631$	−25.8646			−1.02965			−0.514827	−	0.857294i	$-0.672144\pi$
$631$	−25.8646			−1.02965			−0.514827	+	0.857294i	$0.672144\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−12.6422	+	21.8968i	−0.501688	+	0.868950i
$636$		0			0
$637$	3.25101	+	5.63091i	0.128810	+	0.223105i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.81826	−	6.61342i	−0.150812	−	0.261215i	0.780714	−	0.624888i	$-0.214856\pi$
$641$	−3.81826	−	6.61342i	−0.150812	−	0.261215i	−0.931526	+	0.363674i	$0.881522\pi$
$642$		0			0
$643$	−21.8623	+	37.8667i	−0.862166	+	1.49332i	0.00766794	+	0.999971i	$0.497559\pi$
$643$	−21.8623	+	37.8667i	−0.862166	+	1.49332i	−0.869834	+	0.493345i	$0.835774\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−24.1808			−0.950647			−0.475324	−	0.879811i	$-0.657669\pi$
$647$	−24.1808			−0.950647			−0.475324	+	0.879811i	$0.657669\pi$
$648$		0			0
$649$	−49.7290			−1.95203
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.95033	+	6.84218i	−0.154589	+	0.267755i	−0.932909	−	0.360112i	$-0.882739\pi$
$653$	−3.95033	+	6.84218i	−0.154589	+	0.267755i	0.778321	+	0.627867i	$0.216072\pi$
$654$		0			0
$655$	5.67487	+	9.82916i	0.221735	+	0.384057i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−12.9895	−	22.4985i	−0.506001	−	0.876419i	−0.999976	−	0.00694272i	$-0.997790\pi$
$659$	−12.9895	−	22.4985i	−0.506001	−	0.876419i	0.493975	−	0.869476i	$-0.335543\pi$
$660$		0			0
$661$	−0.254233	+	0.440344i	−0.00988850	+	0.0171274i	−0.870927	−	0.491412i	$-0.836481\pi$
$661$	−0.254233	+	0.440344i	−0.00988850	+	0.0171274i	0.861039	+	0.508539i	$0.169814\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.06514			−0.0413043
$666$		0			0
$667$	39.1047			1.51414
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−26.8997	+	46.5917i	−1.03845	+	1.79865i
$672$		0			0
$673$	11.2425	+	19.4726i	0.433367	+	0.750613i	0.997161	−	0.0753024i	$-0.0239922\pi$
$673$	11.2425	+	19.4726i	0.433367	+	0.750613i	−0.563794	+	0.825915i	$0.690659\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.34992	+	4.07018i	0.0903147	+	0.156430i	0.907644	−	0.419742i	$-0.137879\pi$
$677$	2.34992	+	4.07018i	0.0903147	+	0.156430i	−0.817329	+	0.576171i	$0.804546\pi$
$678$		0			0
$679$	2.16674	−	3.75291i	0.0831520	−	0.144023i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	15.4013			0.589315			0.294657	−	0.955603i	$-0.404794\pi$
$683$	15.4013			0.589315			0.294657	+	0.955603i	$0.404794\pi$
$684$		0			0
$685$	31.0932			1.18801
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.05214	+	1.82237i	−0.0400835	+	0.0694266i
$690$		0			0
$691$	13.9618	+	24.1825i	0.531131	+	0.919945i	0.999340	+	0.0363275i	$0.0115660\pi$
$691$	13.9618	+	24.1825i	0.531131	+	0.919945i	−0.468209	+	0.883618i	$0.655101\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	23.1828	+	40.1538i	0.879374	+	1.52312i
$696$		0			0
$697$	−18.1996	+	31.5227i	−0.689360	+	1.19401i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	7.33870			0.277179			0.138589	−	0.990350i	$-0.455743\pi$
$701$	7.33870			0.277179			0.138589	+	0.990350i	$0.455743\pi$
$702$		0			0
$703$	−16.5182			−0.622996
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.88356	+	4.99448i	−0.108448	+	0.187837i
$708$		0			0
$709$	−7.31665	−	12.6728i	−0.274783	−	0.475938i	0.695298	−	0.718722i	$-0.255273\pi$
$709$	−7.31665	−	12.6728i	−0.274783	−	0.475938i	−0.970080	+	0.242784i	$0.921939\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−10.5945	−	18.3502i	−0.396766	−	0.687219i
$714$		0			0
$715$	5.07287	−	8.78647i	0.189715	−	0.328595i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	28.7125			1.07080			0.535398	−	0.844600i	$-0.320162\pi$
$719$	28.7125			1.07080			0.535398	+	0.844600i	$0.320162\pi$
$720$		0			0
$721$	−1.80754			−0.0673161
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.915011	+	1.58484i	−0.0339826	+	0.0588597i
$726$		0			0
$727$	12.8923	+	22.3301i	0.478149	+	0.828178i	0.999686	−	0.0250502i	$-0.00797457\pi$
$727$	12.8923	+	22.3301i	0.478149	+	0.828178i	−0.521537	+	0.853229i	$0.674641\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.650415	+	1.12655i	0.0240565	+	0.0416670i
$732$		0			0
$733$	5.34424	−	9.25649i	0.197394	−	0.341896i	−0.750289	−	0.661110i	$-0.770086\pi$
$733$	5.34424	−	9.25649i	0.197394	−	0.341896i	0.947683	+	0.319214i	$0.103419\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−20.2713			−0.746702
$738$		0			0
$739$	19.5440			0.718937			0.359469	−	0.933157i	$-0.382958\pi$
$739$	19.5440			0.718937			0.359469	+	0.933157i	$0.382958\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.396827	+	0.687325i	−0.0145582	+	0.0252155i	−0.873213	−	0.487339i	$-0.837968\pi$
$743$	−0.396827	+	0.687325i	−0.0145582	+	0.0252155i	0.858655	+	0.512555i	$0.171301\pi$
$744$		0			0
$745$	−16.7719	−	29.0497i	−0.614474	−	1.06430i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.591343	+	1.02424i	0.0216072	+	0.0374248i
$750$		0			0
$751$	−2.55092	+	4.41832i	−0.0930844	+	0.161227i	−0.908808	−	0.417216i	$-0.863006\pi$
$751$	−2.55092	+	4.41832i	−0.0930844	+	0.161227i	0.815723	+	0.578443i	$0.196339\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	36.8877			1.34248
$756$		0			0
$757$	−19.8422			−0.721177			−0.360589	−	0.932725i	$-0.617424\pi$
$757$	−19.8422			−0.721177			−0.360589	+	0.932725i	$0.617424\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	21.3960	−	37.0590i	0.775605	−	1.34339i	−0.158849	−	0.987303i	$-0.550778\pi$
$761$	21.3960	−	37.0590i	0.775605	−	1.34339i	0.934454	−	0.356084i	$-0.115888\pi$
$762$		0			0
$763$	1.66686	+	2.88708i	0.0603442	+	0.104519i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.66814	+	8.08546i	0.168557	+	0.291949i
$768$		0			0
$769$	17.8574	−	30.9300i	0.643955	−	1.11536i	−0.340587	−	0.940213i	$-0.610626\pi$
$769$	17.8574	−	30.9300i	0.643955	−	1.11536i	0.984542	−	0.175150i	$-0.0560410\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	17.1522			0.616923			0.308461	−	0.951237i	$-0.400186\pi$
$773$	17.1522			0.616923			0.308461	+	0.951237i	$0.400186\pi$
$774$		0			0
$775$	0.991600			0.0356193
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.25400	+	10.8322i	−0.224073	+	0.388105i
$780$		0			0
$781$	9.01094	+	15.6074i	0.322437	+	0.558477i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.57128	+	9.64974i	0.198848	+	0.344414i
$786$		0			0
$787$	10.5790	−	18.3233i	0.377100	−	0.653156i	−0.613539	−	0.789664i	$-0.710255\pi$
$787$	10.5790	−	18.3233i	0.377100	−	0.653156i	0.990639	+	0.136509i	$0.0435881\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.93095			0.0686568
$792$		0			0
$793$	10.1005			0.358679
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.45601	−	9.45009i	0.193262	−	0.334739i	−0.753067	−	0.657943i	$-0.771427\pi$
$797$	5.45601	−	9.45009i	0.193262	−	0.334739i	0.946329	+	0.323204i	$0.104760\pi$
$798$		0			0
$799$	9.04044	+	15.6585i	0.319828	+	0.553958i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	13.6353	+	23.6171i	0.481180	+	0.833429i
$804$		0			0
$805$	−2.68717	+	4.65431i	−0.0947102	+	0.164043i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−14.6688			−0.515729			−0.257865	−	0.966181i	$-0.583019\pi$
$809$	−14.6688			−0.515729			−0.257865	+	0.966181i	$0.583019\pi$
$810$		0			0
$811$	−7.96618			−0.279731			−0.139865	−	0.990171i	$-0.544667\pi$
$811$	−7.96618			−0.279731			−0.139865	+	0.990171i	$0.544667\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−19.2282	+	33.3042i	−0.673535	+	1.16660i
$816$		0			0
$817$	0.223504	+	0.387121i	0.00781943	+	0.0135436i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	15.9260	+	27.5847i	0.555822	+	0.962712i	0.997839	+	0.0657057i	$0.0209298\pi$
$821$	15.9260	+	27.5847i	0.555822	+	0.962712i	−0.442017	+	0.897007i	$0.645737\pi$
$822$		0			0
$823$	−5.06901	+	8.77978i	−0.176694	+	0.306044i	−0.940746	−	0.339111i	$-0.889874\pi$
$823$	−5.06901	+	8.77978i	−0.176694	+	0.306044i	0.764052	+	0.645155i	$0.223207\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−16.2236			−0.564148			−0.282074	−	0.959393i	$-0.591022\pi$
$827$	−16.2236			−0.564148			−0.282074	+	0.959393i	$0.591022\pi$
$828$		0			0
$829$	21.2902			0.739439			0.369720	−	0.929143i	$-0.379454\pi$
$829$	21.2902			0.739439			0.369720	+	0.929143i	$0.379454\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	16.2584	−	28.1604i	0.563320	−	0.975699i
$834$		0			0
$835$	−11.7916	−	20.4236i	−0.408063	−	0.706787i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	0.962971	+	1.66791i	0.0332454	+	0.0575828i	0.882169	−	0.470932i	$-0.156082\pi$
$839$	0.962971	+	1.66791i	0.0332454	+	0.0575828i	−0.848924	+	0.528515i	$0.822749\pi$
$840$		0			0
$841$	3.02752	−	5.24382i	0.104397	−	0.180821i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	26.0315			0.895510
$846$		0			0
$847$	4.33405			0.148920
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−41.6727	+	72.1792i	−1.42852	+	2.47427i
$852$		0			0
$853$	19.7403	+	34.1912i	0.675895	+	1.17069i	0.976206	+	0.216844i	$0.0695763\pi$
$853$	19.7403	+	34.1912i	0.675895	+	1.17069i	−0.300311	+	0.953841i	$0.597090\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−15.0539	−	26.0742i	−0.514233	−	0.890677i	−0.999864	−	0.0165134i	$-0.994743\pi$
$857$	−15.0539	−	26.0742i	−0.514233	−	0.890677i	0.485631	−	0.874164i	$-0.338590\pi$
$858$		0			0
$859$	−20.2994	+	35.1597i	−0.692608	+	1.19963i	0.278373	+	0.960473i	$0.410205\pi$
$859$	−20.2994	+	35.1597i	−0.692608	+	1.19963i	−0.970980	+	0.239159i	$0.923128\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.46113			0.0497374			0.0248687	−	0.999691i	$-0.492083\pi$
$863$	1.46113			0.0497374			0.0248687	+	0.999691i	$0.492083\pi$
$864$		0			0
$865$	−37.0970			−1.26134
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−41.6424	+	72.1268i	−1.41262	+	2.44673i
$870$		0			0
$871$	1.90290	+	3.29591i	0.0644772	+	0.111678i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.77156	−	3.06843i	−0.0598897	−	0.103732i
$876$		0			0
$877$	5.07742	−	8.79435i	0.171452	−	0.296964i	−0.767475	−	0.641078i	$-0.778487\pi$
$877$	5.07742	−	8.79435i	0.171452	−	0.296964i	0.938928	+	0.344114i	$0.111821\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−12.6952			−0.427711			−0.213855	−	0.976865i	$-0.568602\pi$
$881$	−12.6952			−0.427711			−0.213855	+	0.976865i	$0.568602\pi$
$882$		0			0
$883$	35.3754			1.19048			0.595238	−	0.803549i	$-0.297058\pi$
$883$	35.3754			1.19048			0.595238	+	0.803549i	$0.297058\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	27.7610	−	48.0835i	0.932124	−	1.61449i	0.152439	−	0.988313i	$-0.451287\pi$
$887$	27.7610	−	48.0835i	0.932124	−	1.61449i	0.779685	−	0.626172i	$-0.215379\pi$
$888$		0			0
$889$	1.80223	+	3.12155i	0.0604448	+	0.104694i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.10660	+	5.38078i	0.103958	+	0.180061i
$894$		0			0
$895$	16.1784	−	28.0218i	0.540784	−	0.936666i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	12.4328			0.414656
$900$		0			0
$901$	10.5236			0.350592
$902$		0			0
$903$		0			0
$904$		0			0
$905$	18.9981	−	32.9056i	0.631517	−	1.09382i
$906$		0			0
$907$	−17.1123	−	29.6393i	−0.568204	−	0.984158i	−0.996744	−	0.0806350i	$-0.974305\pi$
$907$	−17.1123	−	29.6393i	−0.568204	−	0.984158i	0.428540	−	0.903523i	$-0.359028\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−8.27615	−	14.3347i	−0.274201	−	0.474930i	0.695732	−	0.718301i	$-0.255080\pi$
$911$	−8.27615	−	14.3347i	−0.274201	−	0.474930i	−0.969933	+	0.243371i	$0.921747\pi$
$912$		0			0
$913$	−14.6363	+	25.3509i	−0.484392	+	0.838991i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.61799			0.0534306
$918$		0			0
$919$	45.3120			1.49470			0.747352	−	0.664428i	$-0.231325\pi$
$919$	45.3120			1.49470			0.747352	+	0.664428i	$0.231325\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.69174	−	2.93019i	0.0556844	−	0.0964482i
$924$		0			0
$925$	−1.95020	−	3.37784i	−0.0641221	−	0.111063i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	10.0403	+	17.3903i	0.329412	+	0.570558i	0.982395	−	0.186814i	$-0.0598163\pi$
$929$	10.0403	+	17.3903i	0.329412	+	0.570558i	−0.652984	+	0.757372i	$0.726483\pi$
$930$		0			0
$931$	5.58693	−	9.67684i	0.183104	−	0.317146i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−50.7392			−1.65935
$936$		0			0
$937$	57.3842			1.87466			0.937330	−	0.348443i	$-0.113289\pi$
$937$	57.3842			1.87466			0.937330	+	0.348443i	$0.113289\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−16.7615	+	29.0318i	−0.546409	+	0.946409i	0.452107	+	0.891963i	$0.350672\pi$
$941$	−16.7615	+	29.0318i	−0.546409	+	0.946409i	−0.998517	+	0.0544452i	$0.982661\pi$
$942$		0			0
$943$	31.5556	+	54.6559i	1.02759	+	1.77984i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.66775	+	6.35274i	0.119186	+	0.206436i	0.919445	−	0.393218i	$-0.128638\pi$
$947$	3.66775	+	6.35274i	0.119186	+	0.206436i	−0.800259	+	0.599654i	$0.795305\pi$
$948$		0			0
$949$	2.55994	−	4.43395i	0.0830992	−	0.143932i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	7.30761			0.236717			0.118358	−	0.992971i	$-0.462237\pi$
$953$	7.30761			0.236717			0.118358	+	0.992971i	$0.462237\pi$
$954$		0			0
$955$	−44.3406			−1.43483
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.21628	−	3.83870i	0.0715673	−	0.123958i
$960$		0			0
$961$	12.1316	+	21.0126i	0.391343	+	0.677827i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−24.9565	−	43.2259i	−0.803377	−	1.39149i
$966$		0			0
$967$	13.1258	−	22.7346i	0.422097	−	0.731094i	−0.574047	−	0.818822i	$-0.694627\pi$
$967$	13.1258	−	22.7346i	0.422097	−	0.731094i	0.996144	+	0.0877283i	$0.0279607\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	15.9643			0.512318			0.256159	−	0.966635i	$-0.417543\pi$
$971$	15.9643			0.512318			0.256159	+	0.966635i	$0.417543\pi$
$972$		0			0
$973$	6.60975			0.211899
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.96119	+	6.86099i	−0.126730	+	0.219502i	−0.922408	−	0.386217i	$-0.873781\pi$
$977$	−3.96119	+	6.86099i	−0.126730	+	0.219502i	0.795678	+	0.605720i	$0.207115\pi$
$978$		0			0
$979$	−4.87875	−	8.45024i	−0.155925	−	0.270071i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.86126	+	11.8841i	0.218840	+	0.379042i	0.954454	−	0.298359i	$-0.0964393\pi$
$983$	6.86126	+	11.8841i	0.218840	+	0.379042i	−0.735613	+	0.677402i	$0.763106\pi$
$984$		0			0
$985$	5.14131	−	8.90502i	0.163816	−	0.283737i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.25546			0.0717194
$990$		0			0
$991$	36.0366			1.14474			0.572370	−	0.819996i	$-0.306024\pi$
$991$	36.0366			1.14474			0.572370	+	0.819996i	$0.306024\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−12.4572	+	21.5765i	−0.394920	+	0.684021i
$996$		0			0
$997$	11.9518	+	20.7011i	0.378517	+	0.655610i	0.990847	−	0.134992i	$-0.0431009\pi$
$997$	11.9518	+	20.7011i	0.378517	+	0.655610i	−0.612330	+	0.790602i	$0.709768\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3456.2.i.h.2305.4		10
3.2	odd	2		1152.2.i.h.769.2	yes	10
4.3	odd	2		3456.2.i.e.2305.4		10
8.3	odd	2		3456.2.i.f.2305.2		10
8.5	even	2		3456.2.i.g.2305.2		10
9.2	odd	6		1152.2.i.h.385.2	yes	10
9.7	even	3	inner	3456.2.i.h.1153.4		10
12.11	even	2		1152.2.i.e.769.4	yes	10
24.5	odd	2		1152.2.i.f.769.4	yes	10
24.11	even	2		1152.2.i.g.769.2	yes	10
36.7	odd	6		3456.2.i.e.1153.4		10
36.11	even	6		1152.2.i.e.385.4	✓	10
72.11	even	6		1152.2.i.g.385.2	yes	10
72.29	odd	6		1152.2.i.f.385.4	yes	10
72.43	odd	6		3456.2.i.f.1153.2		10
72.61	even	6		3456.2.i.g.1153.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.e.385.4	✓	10	36.11	even	6
1152.2.i.e.769.4	yes	10	12.11	even	2
1152.2.i.f.385.4	yes	10	72.29	odd	6
1152.2.i.f.769.4	yes	10	24.5	odd	2
1152.2.i.g.385.2	yes	10	72.11	even	6
1152.2.i.g.769.2	yes	10	24.11	even	2
1152.2.i.h.385.2	yes	10	9.2	odd	6
1152.2.i.h.769.2	yes	10	3.2	odd	2
3456.2.i.e.1153.4		10	36.7	odd	6
3456.2.i.e.2305.4		10	4.3	odd	2
3456.2.i.f.1153.2		10	72.43	odd	6
3456.2.i.f.2305.2		10	8.3	odd	2
3456.2.i.g.1153.2		10	72.61	even	6
3456.2.i.g.2305.2		10	8.5	even	2
3456.2.i.h.1153.4		10	9.7	even	3	inner
3456.2.i.h.2305.4		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3456 = 2^{7} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3456.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.07447 - 1.86104i) q^{5} +(-0.153174 - 0.265305i) q^{7} +O(q^{10})\)	\(q+(1.07447 - 1.86104i) q^{5} +(-0.153174 - 0.265305i) q^{7} +(-2.50736 - 4.34288i) q^{11} +(-0.470741 + 0.815346i) q^{13} +4.70838 q^{17} +1.61796 q^{19} +(4.08184 - 7.06995i) q^{23} +(0.191022 + 0.330859i) q^{25} +(2.39504 + 4.14834i) q^{29} +(1.29776 - 2.24778i) q^{31} -0.658323 q^{35} -10.2093 q^{37} +(-3.86537 + 6.69502i) q^{41} +(0.138140 + 0.239265i) q^{43} +(1.92007 + 3.32566i) q^{47} +(3.45308 - 5.98090i) q^{49} +2.23508 q^{53} -10.7764 q^{55} +(4.95830 - 8.58802i) q^{59} +(-5.36414 - 9.29097i) q^{61} +(1.01159 + 1.75213i) q^{65} +(2.02117 - 3.50078i) q^{67} -3.59379 q^{71} -5.43811 q^{73} +(-0.768124 + 1.33043i) q^{77} +(-8.30403 - 14.3830i) q^{79} +(-2.91867 - 5.05528i) q^{83} +(5.05902 - 8.76248i) q^{85} +1.94577 q^{89} +0.288420 q^{91} +(1.73845 - 3.01108i) q^{95} +(7.07283 + 12.2505i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{7}+O(q^{10}) \) 10 * q + 4 * q^7	\( 10 q + 4 q^{7} + q^{11} + 6 q^{13} + 6 q^{17} + 18 q^{19} + 4 q^{23} + q^{25} + 4 q^{29} + 8 q^{31} + 24 q^{35} - 20 q^{37} + 5 q^{41} - 13 q^{43} - 6 q^{47} + 3 q^{49} - 12 q^{55} + 13 q^{59} + 10 q^{61} - 17 q^{67} + 8 q^{71} - 34 q^{73} - 8 q^{77} + 6 q^{79} - 12 q^{83} + 18 q^{85} - 44 q^{89} + 36 q^{91} - 6 q^{95} + 27 q^{97}+O(q^{100}) \) 10 * q + 4 * q^7 + q^11 + 6 * q^13 + 6 * q^17 + 18 * q^19 + 4 * q^23 + q^25 + 4 * q^29 + 8 * q^31 + 24 * q^35 - 20 * q^37 + 5 * q^41 - 13 * q^43 - 6 * q^47 + 3 * q^49 - 12 * q^55 + 13 * q^59 + 10 * q^61 - 17 * q^67 + 8 * q^71 - 34 * q^73 - 8 * q^77 + 6 * q^79 - 12 * q^83 + 18 * q^85 - 44 * q^89 + 36 * q^91 - 6 * q^95 + 27 * q^97

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