LMFDB - Embedded newform 1728.2.r.e.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,2,Mod(289,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1728.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.r (of order $6$, 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:	$13.7981494693$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 $ x^12 - 16x^8 - 24x^7 + 96x^5 + 304x^4 + 384x^3 + 288x^2 + 144*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 576)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.2
Root			$0.583700 + 2.17840i$ of defining polynomial
Character	$\chi$	$=$	1728.289
Dual form			1728.2.r.e.1441.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{5} +(-1.80664 + 3.12920i) q^{7} +O(q^{10})$	$q+(-1.50000 + 0.866025i) q^{5} +(-1.80664 + 3.12920i) q^{7} +(0.635828 + 0.367095i) q^{11} +(-0.527909 + 0.304788i) q^{13} +5.52420 q^{17} +2.00000i q^{19} +(-2.36788 - 4.10129i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(-6.78630 - 3.91807i) q^{29} +(4.70951 + 8.15710i) q^{31} -6.25839i q^{35} +2.34163i q^{37} +(-4.26210 - 7.38217i) q^{41} +(-8.88403 - 5.12920i) q^{43} +(-5.88032 + 10.1850i) q^{47} +(-3.02791 - 5.24449i) q^{49} -13.0323i q^{53} -1.27166 q^{55} +(1.04788 - 0.604996i) q^{59} +(-9.78630 - 5.65012i) q^{61} +(0.527909 - 0.914365i) q^{65} +(-5.46826 + 3.15710i) q^{67} -2.63999 q^{71} -2.05582 q^{73} +(-2.29743 + 1.32642i) q^{77} +(-1.24540 + 2.15710i) q^{79} +(-10.6161 - 6.12920i) q^{83} +(-8.28630 + 4.78410i) q^{85} +1.94418 q^{89} -2.20257i q^{91} +(-1.73205 - 3.00000i) q^{95} +(7.78630 - 13.4863i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{5}+O(q^{10}) $ 12 * q - 18 * q^5	$ 12 q - 18 q^{5} + 6 q^{13} - 12 q^{25} + 18 q^{29} - 18 q^{41} - 24 q^{49} - 18 q^{61} - 6 q^{65} - 90 q^{77} + 48 q^{89} - 6 q^{97}+O(q^{100}) $ 12 * q - 18 * q^5 + 6 * q^13 - 12 * q^25 + 18 * q^29 - 18 * q^41 - 24 * q^49 - 18 * q^61 - 6 * q^65 - 90 * q^77 + 48 * q^89 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$		0			0
$7$	−1.80664	+	3.12920i	−0.682846	+	1.18272i	0.291262	+	0.956643i	$0.405925\pi$
$7$	−1.80664	+	3.12920i	−0.682846	+	1.18272i	−0.974108	+	0.226081i	$0.927408\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.635828	+	0.367095i	0.191709	+	0.110683i	0.592783	−	0.805363i	$-0.298029\pi$
$11$	0.635828	+	0.367095i	0.191709	+	0.110683i	−0.401073	+	0.916046i	$0.631363\pi$
$12$		0			0
$13$	−0.527909	+	0.304788i	−0.146416	+	0.0845331i	−0.571418	−	0.820659i	$-0.693607\pi$
$13$	−0.527909	+	0.304788i	−0.146416	+	0.0845331i	0.425003	+	0.905192i	$0.360273\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.52420			1.33982			0.669908	−	0.742444i	$-0.266334\pi$
$17$	5.52420			1.33982			0.669908	+	0.742444i	$0.266334\pi$
$18$		0			0
$19$			2.00000i			0.458831i	0.973329	+	0.229416i	$0.0736815\pi$
$19$			2.00000i			0.458831i	−0.973329	+	0.229416i	$0.926318\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.36788	−	4.10129i	−0.493737	−	0.855177i	0.506237	−	0.862394i	$-0.331036\pi$
$23$	−2.36788	−	4.10129i	−0.493737	−	0.855177i	−0.999974	+	0.00721700i	$0.997703\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.78630	−	3.91807i	−1.26018	−	0.727568i	−0.287074	−	0.957908i	$-0.592683\pi$
$29$	−6.78630	−	3.91807i	−1.26018	−	0.727568i	−0.973110	+	0.230341i	$0.926016\pi$
$30$		0			0
$31$	4.70951	+	8.15710i	0.845852	+	1.46506i	0.884879	+	0.465821i	$0.154241\pi$
$31$	4.70951	+	8.15710i	0.845852	+	1.46506i	−0.0390267	+	0.999238i	$0.512426\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	6.25839i		−	1.05786i
$36$		0			0
$37$			2.34163i			0.384961i	0.981301	+	0.192481i	$0.0616532\pi$
$37$			2.34163i			0.384961i	−0.981301	+	0.192481i	$0.938347\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.26210	−	7.38217i	−0.665628	−	1.15290i	−0.979115	−	0.203309i	$-0.934830\pi$
$41$	−4.26210	−	7.38217i	−0.665628	−	1.15290i	0.313486	−	0.949593i	$-0.398503\pi$
$42$		0			0
$43$	−8.88403	−	5.12920i	−1.35480	−	0.782195i	−0.365884	−	0.930661i	$-0.619233\pi$
$43$	−8.88403	−	5.12920i	−1.35480	−	0.782195i	−0.988918	+	0.148466i	$0.952567\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.88032	+	10.1850i	−0.857733	+	1.48564i	0.0163535	+	0.999866i	$0.494794\pi$
$47$	−5.88032	+	10.1850i	−0.857733	+	1.48564i	−0.874086	+	0.485771i	$0.838539\pi$
$48$		0			0
$49$	−3.02791	−	5.24449i	−0.432558	−	0.749213i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	13.0323i		−	1.79012i	−0.445942	−	0.895062i	$-0.647131\pi$
$53$		−	13.0323i		−	1.79012i	0.445942	−	0.895062i	$-0.352869\pi$
$54$		0			0
$55$	−1.27166			−0.171470
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.04788	−	0.604996i	0.136423	−	0.0787637i	−0.430235	−	0.902717i	$-0.641569\pi$
$59$	1.04788	−	0.604996i	0.136423	−	0.0787637i	0.566658	+	0.823953i	$0.308236\pi$
$60$		0			0
$61$	−9.78630	−	5.65012i	−1.25301	−	0.723424i	−0.281302	−	0.959619i	$-0.590766\pi$
$61$	−9.78630	−	5.65012i	−1.25301	−	0.723424i	−0.971706	+	0.236195i	$0.924099\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.527909	−	0.914365i	0.0654790	−	0.113413i
$66$		0			0
$67$	−5.46826	+	3.15710i	−0.668055	+	0.385702i	−0.795339	−	0.606165i	$-0.792707\pi$
$67$	−5.46826	+	3.15710i	−0.668055	+	0.385702i	0.127284	+	0.991866i	$0.459374\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.63999			−0.313309			−0.156655	−	0.987653i	$-0.550071\pi$
$71$	−2.63999			−0.313309			−0.156655	+	0.987653i	$0.550071\pi$
$72$		0			0
$73$	−2.05582			−0.240615			−0.120308	−	0.992737i	$-0.538388\pi$
$73$	−2.05582			−0.240615			−0.120308	+	0.992737i	$0.538388\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.29743	+	1.32642i	−0.261816	+	0.151160i
$78$		0			0
$79$	−1.24540	+	2.15710i	−0.140119	+	0.242693i	−0.927541	−	0.373721i	$-0.878082\pi$
$79$	−1.24540	+	2.15710i	−0.140119	+	0.242693i	0.787422	+	0.616414i	$0.211415\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−10.6161	−	6.12920i	−1.16527	−	0.672767i	−0.212706	−	0.977116i	$-0.568228\pi$
$83$	−10.6161	−	6.12920i	−1.16527	−	0.672767i	−0.952560	+	0.304350i	$0.901561\pi$
$84$		0			0
$85$	−8.28630	+	4.78410i	−0.898775	+	0.518908i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.94418			0.206083			0.103041	−	0.994677i	$-0.467143\pi$
$89$	1.94418			0.206083			0.103041	+	0.994677i	$0.467143\pi$
$90$		0			0
$91$		−	2.20257i		−	0.230892i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.73205	−	3.00000i	−0.177705	−	0.307794i
$96$		0			0
$97$	7.78630	−	13.4863i	0.790579	−	1.36932i	−0.135030	−	0.990842i	$-0.543113\pi$
$97$	7.78630	−	13.4863i	0.790579	−	1.36932i	0.925609	−	0.378481i	$-0.123554\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.70257	+	5.60178i	0.965442	+	0.557398i	0.897844	−	0.440314i	$-0.145133\pi$
$101$	9.70257	+	5.60178i	0.965442	+	0.557398i	0.0675984	+	0.997713i	$0.478466\pi$
$102$		0			0
$103$	0.684168	+	1.18501i	0.0674130	+	0.116763i	0.897762	−	0.440481i	$-0.145192\pi$
$103$	0.684168	+	1.18501i	0.0674130	+	0.116763i	−0.830349	+	0.557244i	$0.811859\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			13.4684i			1.30204i	0.759062	+	0.651019i	$0.225658\pi$
$107$			13.4684i			1.30204i	−0.759062	+	0.651019i	$0.774342\pi$
$108$		0			0
$109$		−	1.42084i		−	0.136092i	−0.997682	−	0.0680458i	$-0.978324\pi$
$109$		−	1.42084i		−	0.136092i	0.997682	−	0.0680458i	$-0.0216764\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.75839	+	8.24177i	0.447632	+	0.775321i	0.998231	−	0.0594485i	$-0.0189342\pi$
$113$	4.75839	+	8.24177i	0.447632	+	0.775321i	−0.550600	+	0.834769i	$0.685601\pi$
$114$		0			0
$115$	7.10364	+	4.10129i	0.662418	+	0.382447i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−9.98025	+	17.2863i	−0.914888	+	1.58463i
$120$		0			0
$121$	−5.23048	−	9.05946i	−0.475498	−	0.823587i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$	−2.24495			−0.199207			−0.0996035	−	0.995027i	$-0.531757\pi$
$127$	−2.24495			−0.199207			−0.0996035	+	0.995027i	$0.531757\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.223773	−	0.129195i	0.0195511	−	0.0112878i	−0.490193	−	0.871614i	$-0.663074\pi$
$131$	0.223773	−	0.129195i	0.0195511	−	0.0112878i	0.509744	+	0.860326i	$0.329740\pi$
$132$		0			0
$133$	−6.25839	−	3.61328i	−0.542671	−	0.313311i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.00371	+	1.73848i	−0.0857527	+	0.148528i	−0.905712	−	0.423894i	$-0.860663\pi$
$137$	−1.00371	+	1.73848i	−0.0857527	+	0.148528i	0.819959	+	0.572422i	$0.193996\pi$
$138$		0			0
$139$	1.95582	−	1.12920i	0.165891	−	0.0957771i	−0.414756	−	0.909933i	$-0.636133\pi$
$139$	1.95582	−	1.12920i	0.165891	−	0.0957771i	0.580647	+	0.814156i	$0.302800\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.447546			−0.0374256
$144$		0			0
$145$	13.5726			1.12714
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−12.7863	+	7.38217i	−1.04749	+	0.604771i	−0.921947	−	0.387316i	$-0.873402\pi$
$149$	−12.7863	+	7.38217i	−1.04749	+	0.604771i	−0.125548	+	0.992088i	$0.540069\pi$
$150$		0			0
$151$	−2.82827	+	4.89871i	−0.230162	+	0.398652i	−0.957856	−	0.287250i	$-0.907259\pi$
$151$	−2.82827	+	4.89871i	−0.230162	+	0.398652i	0.727694	+	0.685902i	$0.240592\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−14.1285	−	8.15710i	−1.13483	−	0.655194i
$156$		0			0
$157$	−13.7584	+	7.94341i	−1.09804	+	0.633953i	−0.935705	−	0.352783i	$-0.885235\pi$
$157$	−13.7584	+	7.94341i	−1.09804	+	0.633953i	−0.162334	+	0.986736i	$0.551902\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	17.1116			1.34859
$162$		0			0
$163$			8.51678i			0.667086i	0.942735	+	0.333543i	$0.108244\pi$
$163$			8.51678i			0.667086i	−0.942735	+	0.333543i	$0.891756\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.95582	+	3.38759i	0.151346	+	0.262139i	0.931723	−	0.363171i	$-0.118306\pi$
$167$	1.95582	+	3.38759i	0.151346	+	0.262139i	−0.780376	+	0.625310i	$0.784973\pi$
$168$		0			0
$169$	−6.31421	+	10.9365i	−0.485708	+	0.841271i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.5000	+	6.06218i	0.798300	+	0.460899i	0.842876	−	0.538107i	$-0.180860\pi$
$173$	10.5000	+	6.06218i	0.798300	+	0.460899i	−0.0445762	+	0.999006i	$0.514194\pi$
$174$		0			0
$175$	−3.61328	−	6.25839i	−0.273139	−	0.473090i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	6.00000i		−	0.448461i	−0.974536	−	0.224231i	$-0.928013\pi$
$179$		−	6.00000i		−	0.448461i	0.974536	−	0.224231i	$-0.0719869\pi$
$180$		0			0
$181$		−	2.34163i		−	0.174052i	−0.996206	−	0.0870259i	$-0.972264\pi$
$181$		−	2.34163i		−	0.174052i	0.996206	−	0.0870259i	$-0.0277363\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.02791	−	3.51244i	−0.149095	−	0.258240i
$186$		0			0
$187$	3.51244	+	2.02791i	0.256855	+	0.148295i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.684168	−	1.18501i	0.0495046	−	0.0857445i	−0.840211	−	0.542259i	$-0.817569\pi$
$191$	0.684168	−	1.18501i	0.0495046	−	0.0857445i	0.889716	+	0.456515i	$0.150902\pi$
$192$		0			0
$193$	7.73048	+	13.3896i	0.556452	+	0.963804i	0.997789	+	0.0664620i	$0.0211711\pi$
$193$	7.73048	+	13.3896i	0.556452	+	0.963804i	−0.441337	+	0.897342i	$0.645496\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	12.9356i		−	0.921625i	−0.887498	−	0.460812i	$-0.847558\pi$
$197$		−	12.9356i		−	0.921625i	0.887498	−	0.460812i	$-0.152442\pi$
$198$		0			0
$199$	18.7413			1.32854			0.664269	−	0.747493i	$-0.268743\pi$
$199$	18.7413			1.32854			0.664269	+	0.747493i	$0.268743\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	24.5208	−	14.1571i	1.72102	−	0.993634i
$204$		0			0
$205$	12.7863	+	7.38217i	0.893034	+	0.515593i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.734191	+	1.27166i	−0.0507851	+	0.0879623i
$210$		0			0
$211$	7.20032	−	4.15710i	0.495690	−	0.286187i	−0.231242	−	0.972896i	$-0.574279\pi$
$211$	7.20032	−	4.15710i	0.495690	−	0.286187i	0.726932	+	0.686709i	$0.240946\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	17.7681			1.21177
$216$		0			0
$217$	−34.0336			−2.31035
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.91627	+	1.68371i	−0.196170	+	0.113259i
$222$		0			0
$223$	3.99909	−	6.92662i	0.267799	−	0.463841i	−0.700494	−	0.713658i	$-0.747037\pi$
$223$	3.99909	−	6.92662i	0.267799	−	0.463841i	0.968293	+	0.249817i	$0.0803705\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.56032	+	2.63290i	0.302679	+	0.174752i	0.643646	−	0.765323i	$-0.277421\pi$
$227$	4.56032	+	2.63290i	0.302679	+	0.174752i	−0.340967	+	0.940075i	$0.610754\pi$
$228$		0			0
$229$	14.0168	−	8.09259i	0.926255	−	0.534774i	0.0406298	−	0.999174i	$-0.487064\pi$
$229$	14.0168	−	8.09259i	0.926255	−	0.534774i	0.885625	+	0.464401i	$0.153730\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−28.0968			−1.84068			−0.920341	−	0.391116i	$-0.872089\pi$
$233$	−28.0968			−1.84068			−0.920341	+	0.391116i	$0.872089\pi$
$234$		0			0
$235$		−	20.3700i		−	1.32879i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.29608	−	16.1013i	−0.601314	−	1.04151i	−0.992622	−	0.121246i	$-0.961311\pi$
$239$	−9.29608	−	16.1013i	−0.601314	−	1.04151i	0.391309	−	0.920259i	$-0.372022\pi$
$240$		0			0
$241$	4.55582	−	7.89091i	0.293466	−	0.508298i	−0.681161	−	0.732134i	$-0.738525\pi$
$241$	4.55582	−	7.89091i	0.293466	−	0.508298i	0.974627	+	0.223836i	$0.0718579\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	9.08373	+	5.24449i	0.580338	+	0.335058i
$246$		0			0
$247$	−0.609577	−	1.05582i	−0.0387864	−	0.0671801i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			21.5800i			1.36212i	0.732228	+	0.681059i	$0.238480\pi$
$251$			21.5800i			1.36212i	−0.732228	+	0.681059i	$0.761520\pi$
$252$		0			0
$253$		−	3.47695i		−	0.218594i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.70999	−	4.69384i	−0.169045	−	0.292794i	0.769040	−	0.639201i	$-0.220735\pi$
$257$	−2.70999	−	4.69384i	−0.169045	−	0.292794i	−0.938084	+	0.346407i	$0.887402\pi$
$258$		0			0
$259$	−7.32741	−	4.23048i	−0.455303	−	0.262869i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.00787	−	8.67389i	0.308798	−	0.534855i	−0.669301	−	0.742991i	$-0.733406\pi$
$263$	5.00787	−	8.67389i	0.308798	−	0.534855i	0.978100	+	0.208136i	$0.0667398\pi$
$264$		0			0
$265$	11.2863	+	19.5484i	0.693312	+	1.20085i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			12.1115i			0.738452i	0.929340	+	0.369226i	$0.120377\pi$
$269$			12.1115i			0.738452i	−0.929340	+	0.369226i	$0.879623\pi$
$270$		0			0
$271$	−20.0572			−1.21839			−0.609193	−	0.793022i	$-0.708507\pi$
$271$	−20.0572			−1.21839			−0.609193	+	0.793022i	$0.708507\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.27166	+	0.734191i	−0.0766837	+	0.0442734i
$276$		0			0
$277$	4.75839	+	2.74726i	0.285904	+	0.165067i	0.636093	−	0.771612i	$-0.280549\pi$
$277$	4.75839	+	2.74726i	0.285904	+	0.165067i	−0.350189	+	0.936679i	$0.613883\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.58373	+	7.93925i	−0.273442	+	0.473616i	−0.969741	−	0.244136i	$-0.921496\pi$
$281$	−4.58373	+	7.93925i	−0.273442	+	0.473616i	0.696299	+	0.717752i	$0.254829\pi$
$282$		0			0
$283$	−19.7239	+	11.3876i	−1.17246	+	0.676922i	−0.954259	−	0.298981i	$-0.903353\pi$
$283$	−19.7239	+	11.3876i	−1.17246	+	0.676922i	−0.218204	+	0.975903i	$0.570020\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	30.8003			1.81809
$288$		0			0
$289$	13.5168			0.795105
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−18.7026	+	10.7979i	−1.09262	+	0.630822i	−0.934272	−	0.356562i	$-0.883949\pi$
$293$	−18.7026	+	10.7979i	−1.09262	+	0.630822i	−0.158344	+	0.987384i	$0.550616\pi$
$294$		0			0
$295$	−1.04788	+	1.81499i	−0.0610101	+	0.105673i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.50005	+	1.44340i	0.144582	+	0.0834742i
$300$		0			0
$301$	32.1005	−	18.5332i	1.85024	−	1.06824i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	19.5726			1.12072
$306$		0			0
$307$		−	8.51678i		−	0.486078i	−0.970016	−	0.243039i	$-0.921856\pi$
$307$		−	8.51678i		−	0.486078i	0.970016	−	0.243039i	$-0.0781444\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−12.3965	−	21.4713i	−0.702939	−	1.21753i	−0.967430	−	0.253138i	$-0.918537\pi$
$311$	−12.3965	−	21.4713i	−0.702939	−	1.21753i	0.264491	−	0.964388i	$-0.414796\pi$
$312$		0			0
$313$	−7.55582	+	13.0871i	−0.427080	+	0.739724i	−0.996612	−	0.0822447i	$-0.973791\pi$
$313$	−7.55582	+	13.0871i	−0.427080	+	0.739724i	0.569532	+	0.821969i	$0.307124\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.5837	+	6.11052i	0.594441	+	0.343201i	0.766852	−	0.641824i	$-0.221822\pi$
$317$	10.5837	+	6.11052i	0.594441	+	0.343201i	−0.172410	+	0.985025i	$0.555156\pi$
$318$		0			0
$319$	−2.87661	−	4.98244i	−0.161059	−	0.278963i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			11.0484i			0.614749i
$324$		0			0
$325$		−	1.21915i		−	0.0676264i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−21.2473	−	36.8013i	−1.17140	−	2.02892i
$330$		0			0
$331$	21.4076	+	12.3597i	1.17667	+	0.679349i	0.955241	−	0.295828i	$-0.0955955\pi$
$331$	21.4076	+	12.3597i	1.17667	+	0.679349i	0.221426	+	0.975177i	$0.428929\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.46826	−	9.47131i	0.298763	−	0.517473i
$336$		0			0
$337$	−6.75839	−	11.7059i	−0.368153	−	0.637660i	0.621124	−	0.783712i	$-0.286676\pi$
$337$	−6.75839	−	11.7059i	−0.368153	−	0.637660i	−0.989277	+	0.146053i	$0.953343\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			6.91535i			0.374487i
$342$		0			0
$343$	−3.41160			−0.184209
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.3044	+	7.68130i	−0.714218	+	0.412354i	−0.812621	−	0.582793i	$-0.801960\pi$
$347$	−13.3044	+	7.68130i	−0.714218	+	0.412354i	0.0984028	+	0.995147i	$0.468627\pi$
$348$		0			0
$349$	27.3310	+	15.7796i	1.46299	+	0.844660i	0.999149	−	0.0412558i	$-0.0131359\pi$
$349$	27.3310	+	15.7796i	1.46299	+	0.844660i	0.463846	+	0.885916i	$0.346469\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.9963	+	24.2423i	−0.744947	+	1.29029i	0.205272	+	0.978705i	$0.434192\pi$
$353$	−13.9963	+	24.2423i	−0.744947	+	1.29029i	−0.950219	+	0.311582i	$0.899141\pi$
$354$		0			0
$355$	3.95999	−	2.28630i	0.210174	−	0.121344i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.1290			0.692921			0.346460	−	0.938065i	$-0.387384\pi$
$359$	13.1290			0.692921			0.346460	+	0.938065i	$0.387384\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.08373	−	1.78039i	0.161410	−	0.0931899i
$366$		0			0
$367$	6.73992	−	11.6739i	0.351821	−	0.609372i	−0.634748	−	0.772720i	$-0.718896\pi$
$367$	6.73992	−	11.6739i	0.351821	−	0.609372i	0.986569	+	0.163348i	$0.0522292\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	40.7806	+	23.5447i	2.11722	+	1.22238i
$372$		0			0
$373$	4.84212	−	2.79560i	0.250715	−	0.144751i	−0.369376	−	0.929280i	$-0.620429\pi$
$373$	4.84212	−	2.79560i	0.250715	−	0.144751i	0.620092	+	0.784529i	$0.287095\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.77673			0.246014
$378$		0			0
$379$			33.0894i			1.69969i	0.527035	+	0.849844i	$0.323304\pi$
$379$			33.0894i			1.69969i	−0.527035	+	0.849844i	$0.676696\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−7.61237	−	13.1850i	−0.388974	−	0.673723i	0.603338	−	0.797486i	$-0.293837\pi$
$383$	−7.61237	−	13.1850i	−0.388974	−	0.673723i	−0.992312	+	0.123763i	$0.960504\pi$
$384$		0			0
$385$	2.29743	−	3.97926i	0.117088	−	0.202802i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	5.29743	+	3.05847i	0.268590	+	0.155071i	0.628247	−	0.778014i	$-0.283773\pi$
$389$	5.29743	+	3.05847i	0.268590	+	0.155071i	−0.359657	+	0.933085i	$0.617106\pi$
$390$		0			0
$391$	−13.0806	−	22.6563i	−0.661516	−	1.14578i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	4.31421i		−	0.217071i
$396$		0			0
$397$			22.2054i			1.11446i	0.830358	+	0.557230i	$0.188136\pi$
$397$			22.2054i			1.11446i	−0.830358	+	0.557230i	$0.811864\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	15.0521	+	26.0710i	0.751666	+	1.30192i	0.947015	+	0.321190i	$0.104083\pi$
$401$	15.0521	+	26.0710i	0.751666	+	1.30192i	−0.195348	+	0.980734i	$0.562584\pi$
$402$		0			0
$403$	−4.97238	−	2.87080i	−0.247692	−	0.143005i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.859601	+	1.48887i	−0.0426088	+	0.0738007i
$408$		0			0
$409$	4.55582	+	7.89091i	0.225271	+	0.390180i	0.956401	−	0.292058i	$-0.0943400\pi$
$409$	4.55582	+	7.89091i	0.225271	+	0.390180i	−0.731130	+	0.682238i	$0.761007\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			4.37204i			0.215134i
$414$		0			0
$415$	21.2322			1.04225
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−19.7722	+	11.4155i	−0.965936	+	0.557683i	−0.897995	−	0.440006i	$-0.854976\pi$
$419$	−19.7722	+	11.4155i	−0.965936	+	0.557683i	−0.0679411	+	0.997689i	$0.521643\pi$
$420$		0			0
$421$	21.2473	+	12.2671i	1.03553	+	0.597863i	0.918563	−	0.395274i	$-0.129350\pi$
$421$	21.2473	+	12.2671i	1.03553	+	0.597863i	0.116965	+	0.993136i	$0.462684\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−5.52420	+	9.56819i	−0.267963	+	0.464126i
$426$		0			0
$427$	35.3607	−	20.4155i	1.71122	−	0.987975i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.920789			−0.0443529			−0.0221764	−	0.999754i	$-0.507060\pi$
$431$	−0.920789			−0.0443529			−0.0221764	+	0.999754i	$0.507060\pi$
$432$		0			0
$433$	2.05582			0.0987963			0.0493981	−	0.998779i	$-0.484270\pi$
$433$	2.05582			0.0987963			0.0493981	+	0.998779i	$0.484270\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.20257	−	4.73576i	0.392382	−	0.226542i
$438$		0			0
$439$	11.0281	−	19.1013i	0.526344	−	0.911655i	−0.473185	−	0.880963i	$-0.656896\pi$
$439$	11.0281	−	19.1013i	0.526344	−	0.911655i	0.999529	−	0.0306915i	$-0.00977094\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−23.5517	−	13.5976i	−1.11897	−	0.646040i	−0.177836	−	0.984060i	$-0.556910\pi$
$443$	−23.5517	−	13.5976i	−1.11897	−	0.646040i	−0.941139	+	0.338020i	$0.890243\pi$
$444$		0			0
$445$	−2.91627	+	1.68371i	−0.138245	+	0.0798156i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	9.10422			0.429655			0.214827	−	0.976652i	$-0.431081\pi$
$449$	9.10422			0.429655			0.214827	+	0.976652i	$0.431081\pi$
$450$		0			0
$451$		−	6.25839i		−	0.294696i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.90748	+	3.30386i	0.0894242	+	0.154887i
$456$		0			0
$457$	−14.8421	+	25.7073i	−0.694285	+	1.20254i	0.276136	+	0.961119i	$0.410946\pi$
$457$	−14.8421	+	25.7073i	−0.694285	+	1.20254i	−0.970421	+	0.241418i	$0.922387\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	20.3589	+	11.7542i	0.948208	+	0.547448i	0.892524	−	0.451000i	$-0.148933\pi$
$461$	20.3589	+	11.7542i	0.948208	+	0.547448i	0.0556845	+	0.998448i	$0.482266\pi$
$462$		0			0
$463$	3.95075	+	6.84290i	0.183607	+	0.318016i	0.943106	−	0.332492i	$-0.107889\pi$
$463$	3.95075	+	6.84290i	0.183607	+	0.318016i	−0.759499	+	0.650508i	$0.774556\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	3.06324i		−	0.141750i	−0.997485	−	0.0708748i	$-0.977421\pi$
$467$		−	3.06324i		−	0.141750i	0.997485	−	0.0708748i	$-0.0225791\pi$
$468$		0			0
$469$		−	22.8150i		−	1.05350i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.76581	−	6.52257i	−0.173152	−	0.299908i
$474$		0			0
$475$	−3.46410	−	2.00000i	−0.158944	−	0.0917663i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.10364	+	12.3039i	−0.324573	+	0.562178i	−0.981426	−	0.191841i	$-0.938554\pi$
$479$	−7.10364	+	12.3039i	−0.324573	+	0.562178i	0.656852	+	0.754019i	$0.271887\pi$
$480$		0			0
$481$	−0.713701	−	1.23617i	−0.0325419	−	0.0563643i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			26.9725i			1.22476i
$486$		0			0
$487$	−22.1088			−1.00184			−0.500922	−	0.865492i	$-0.667006\pi$
$487$	−22.1088			−1.00184			−0.500922	+	0.865492i	$0.667006\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	34.2340	−	19.7650i	1.54496	−	0.891983i	0.546446	−	0.837494i	$-0.315980\pi$
$491$	34.2340	−	19.7650i	1.54496	−	0.891983i	0.998514	−	0.0544890i	$-0.0173530\pi$
$492$		0			0
$493$	−37.4889	−	21.6442i	−1.68841	−	0.974806i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.76952	−	8.26105i	0.213942	−	0.370559i
$498$		0			0
$499$	10.2652	−	5.92662i	0.459534	−	0.265312i	−0.252314	−	0.967645i	$-0.581192\pi$
$499$	10.2652	−	5.92662i	0.459534	−	0.265312i	0.711848	+	0.702333i	$0.247858\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	23.4246			1.04445			0.522226	−	0.852807i	$-0.325102\pi$
$503$	23.4246			1.04445			0.522226	+	0.852807i	$0.325102\pi$
$504$		0			0
$505$	−19.4051			−0.863518
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.78630	+	3.91807i	−0.300797	+	0.173665i	−0.642801	−	0.766033i	$-0.722228\pi$
$509$	−6.78630	+	3.91807i	−0.300797	+	0.173665i	0.342004	+	0.939699i	$0.388894\pi$
$510$		0			0
$511$	3.71413	−	6.43305i	0.164303	−	0.284582i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.05250	−	1.18501i	−0.0904441	−	0.0522179i
$516$		0			0
$517$	−7.47774	+	4.31728i	−0.328871	+	0.189874i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−27.4535			−1.20276			−0.601381	−	0.798963i	$-0.705383\pi$
$521$	−27.4535			−1.20276			−0.601381	+	0.798963i	$0.705383\pi$
$522$		0			0
$523$			3.83255i			0.167586i	0.996483	+	0.0837928i	$0.0267034\pi$
$523$			3.83255i			0.167586i	−0.996483	+	0.0837928i	$0.973297\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	26.0163	+	45.0615i	1.13329	+	1.96291i
$528$		0			0
$529$	0.286299	−	0.495885i	0.0124478	−	0.0215602i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.50000	+	2.59808i	0.194917	+	0.112535i
$534$		0			0
$535$	−11.6640	−	20.2026i	−0.504277	−	0.873433i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	4.44613i		−	0.191508i
$540$		0			0
$541$		−	15.9707i		−	0.686632i	−0.939220	−	0.343316i	$-0.888450\pi$
$541$		−	15.9707i		−	0.686632i	0.939220	−	0.343316i	$-0.111550\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.23048	+	2.13126i	0.0527080	+	0.0912930i
$546$		0			0
$547$	9.02905	+	5.21292i	0.386054	+	0.222888i	0.680449	−	0.732795i	$-0.261785\pi$
$547$	9.02905	+	5.21292i	0.386054	+	0.222888i	−0.294395	+	0.955684i	$0.595118\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.83614	−	13.5726i	0.333831	−	0.578212i
$552$		0			0
$553$	−4.50000	−	7.79423i	−0.191359	−	0.331444i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	25.0471i		−	1.06128i	−0.847597	−	0.530640i	$-0.821951\pi$
$557$		−	25.0471i		−	1.06128i	0.847597	−	0.530640i	$-0.178049\pi$
$558$		0			0
$559$	6.25327			0.264485
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.28405	+	1.31870i	−0.0962612	+	0.0555764i	−0.547358	−	0.836899i	$-0.684366\pi$
$563$	−2.28405	+	1.31870i	−0.0962612	+	0.0555764i	0.451097	+	0.892475i	$0.351033\pi$
$564$		0			0
$565$	−14.2752	−	8.24177i	−0.600561	−	0.346734i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.0242	+	17.3624i	−0.420236	+	0.727871i	−0.995962	−	0.0897720i	$-0.971386\pi$
$569$	−10.0242	+	17.3624i	−0.420236	+	0.727871i	0.575726	+	0.817643i	$0.304719\pi$
$570$		0			0
$571$	−2.00416	+	1.15710i	−0.0838716	+	0.0484233i	−0.541349	−	0.840798i	$-0.682086\pi$
$571$	−2.00416	+	1.15710i	−0.0838716	+	0.0484233i	0.457478	+	0.889221i	$0.348753\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	9.47152			0.394989
$576$		0			0
$577$	24.4610			1.01832			0.509162	−	0.860671i	$-0.329956\pi$
$577$	24.4610			1.01832			0.509162	+	0.860671i	$0.329956\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	38.3589	−	22.1465i	1.59140	−	0.918792i
$582$		0			0
$583$	4.78410	−	8.28630i	0.198137	−	0.343183i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−17.0839	−	9.86339i	−0.705127	−	0.407106i	0.104127	−	0.994564i	$-0.466795\pi$
$587$	−17.0839	−	9.86339i	−0.705127	−	0.407106i	−0.809254	+	0.587459i	$0.800129\pi$
$588$		0			0
$589$	−16.3142	+	9.41901i	−0.672215	+	0.388104i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−8.46096			−0.347450			−0.173725	−	0.984794i	$-0.555580\pi$
$593$	−8.46096			−0.347450			−0.173725	+	0.984794i	$0.555580\pi$
$594$		0			0
$595$		−	34.5726i		−	1.41734i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.22748	−	5.59016i	−0.131871	−	0.228408i	0.792527	−	0.609837i	$-0.208765\pi$
$599$	−3.22748	−	5.59016i	−0.131871	−	0.228408i	−0.924398	+	0.381430i	$0.875432\pi$
$600$		0			0
$601$	2.52791	−	4.37847i	0.103116	−	0.178601i	−0.809851	−	0.586635i	$-0.800452\pi$
$601$	2.52791	−	4.37847i	0.103116	−	0.178601i	0.912967	+	0.408034i	$0.133786\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	15.6914	+	9.05946i	0.637948	+	0.368319i
$606$		0			0
$607$	0.0220880	+	0.0382575i	0.000896524	+	0.00155282i	0.866473	−	0.499223i	$-0.166381\pi$
$607$	0.0220880	+	0.0382575i	0.000896524	+	0.00155282i	−0.865577	+	0.500776i	$0.833048\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	7.16901i		−	0.290027i
$612$		0			0
$613$			26.8887i			1.08602i	0.839725	+	0.543012i	$0.182716\pi$
$613$			26.8887i			1.08602i	−0.839725	+	0.543012i	$0.817284\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.20628	+	15.9457i	0.370631	+	0.641952i	0.989663	−	0.143414i	$-0.0458081\pi$
$617$	9.20628	+	15.9457i	0.370631	+	0.641952i	−0.619032	+	0.785366i	$0.712475\pi$
$618$		0			0
$619$	−1.65330	−	0.954531i	−0.0664516	−	0.0383658i	0.466406	−	0.884571i	$-0.345549\pi$
$619$	−1.65330	−	0.954531i	−0.0664516	−	0.0383658i	−0.532858	+	0.846205i	$0.678882\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.51244	+	6.08373i	−0.140723	+	0.243739i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			12.9356i			0.515777i
$630$		0			0
$631$	−1.51752			−0.0604114			−0.0302057	−	0.999544i	$-0.509616\pi$
$631$	−1.51752			−0.0604114			−0.0302057	+	0.999544i	$0.509616\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.36742	−	1.94418i	0.133632	−	0.0771525i
$636$		0			0
$637$	3.19692	+	1.84574i	0.126667	+	0.0731310i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.49258	−	14.7096i	0.335437	−	0.580994i	−0.648132	−	0.761528i	$-0.724449\pi$
$641$	8.49258	−	14.7096i	0.335437	−	0.580994i	0.983569	+	0.180535i	$0.0577828\pi$
$642$		0			0
$643$	−9.02905	+	5.21292i	−0.356071	+	0.205578i	−0.667356	−	0.744739i	$-0.732574\pi$
$643$	−9.02905	+	5.21292i	−0.356071	+	0.205578i	0.311285	+	0.950317i	$0.399241\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−44.2802			−1.74083			−0.870417	−	0.492315i	$-0.836151\pi$
$647$	−44.2802			−1.74083			−0.870417	+	0.492315i	$0.836151\pi$
$648$		0			0
$649$	0.888365			0.0348714
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−28.6452	+	16.5383i	−1.12097	+	0.647194i	−0.941649	−	0.336596i	$-0.890724\pi$
$653$	−28.6452	+	16.5383i	−1.12097	+	0.647194i	−0.179324	+	0.983790i	$0.557391\pi$
$654$		0			0
$655$	−0.223773	+	0.387586i	−0.00874353	+	0.0151442i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	27.8882	+	16.1013i	1.08637	+	0.627217i	0.932608	−	0.360891i	$-0.117527\pi$
$659$	27.8882	+	16.1013i	1.08637	+	0.627217i	0.153764	+	0.988108i	$0.450861\pi$
$660$		0			0
$661$	11.2752	−	6.50972i	0.438553	−	0.253199i	−0.264430	−	0.964405i	$-0.585184\pi$
$661$	11.2752	−	6.50972i	0.438553	−	0.253199i	0.702984	+	0.711206i	$0.251851\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	12.5168			0.485380
$666$		0			0
$667$			37.1101i			1.43691i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.14827	−	7.18501i	−0.160142	−	0.277374i
$672$		0			0
$673$	3.73048	−	6.46138i	0.143800	−	0.249068i	−0.785125	−	0.619337i	$-0.787401\pi$
$673$	3.73048	−	6.46138i	0.143800	−	0.249068i	0.928924	+	0.370269i	$0.120735\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−30.8700	−	17.8228i	−1.18643	−	0.684987i	−0.228938	−	0.973441i	$-0.573525\pi$
$677$	−30.8700	−	17.8228i	−1.18643	−	0.684987i	−0.957494	+	0.288455i	$0.906859\pi$
$678$		0			0
$679$	28.1341	+	48.7297i	1.07969	+	1.87007i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			27.4535i			1.05048i	0.850954	+	0.525240i	$0.176025\pi$
$683$			27.4535i			1.05048i	−0.850954	+	0.525240i	$0.823975\pi$
$684$		0			0
$685$		−	3.47695i		−	0.132847i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.97209	+	6.87986i	0.151325	+	0.262102i
$690$		0			0
$691$	−19.3730	−	11.1850i	−0.736984	−	0.425498i	0.0839877	−	0.996467i	$-0.473234\pi$
$691$	−19.3730	−	11.1850i	−0.736984	−	0.425498i	−0.820972	+	0.570969i	$0.806568\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.95582	+	3.38759i	−0.0741886	+	0.128498i
$696$		0			0
$697$	−23.5447	−	40.7806i	−0.891819	−	1.54468i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	10.4633i		−	0.395193i	−0.980283	−	0.197596i	$-0.936686\pi$
$701$		−	10.4633i		−	0.395193i	0.980283	−	0.197596i	$-0.0633136\pi$
$702$		0			0
$703$	−4.68325			−0.176632
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−35.0581	+	20.2408i	−1.31850	+	0.761235i
$708$		0			0
$709$	−20.3884	−	11.7712i	−0.765701	−	0.442078i	0.0656378	−	0.997844i	$-0.479092\pi$
$709$	−20.3884	−	11.7712i	−0.765701	−	0.442078i	−0.831339	+	0.555766i	$0.812425\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	22.3031	−	38.6301i	0.835257	−	1.44671i
$714$		0			0
$715$	0.671318	−	0.387586i	0.0251059	−	0.0144949i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−45.0076			−1.67850			−0.839251	−	0.543745i	$-0.817006\pi$
$719$	−45.0076			−1.67850			−0.839251	+	0.543745i	$0.817006\pi$
$720$		0			0
$721$	−4.94418			−0.184131
$722$		0			0
$723$		0			0
$724$		0			0
$725$	13.5726	−	7.83614i	0.504074	−	0.291027i
$726$		0			0
$727$	−8.37529	+	14.5064i	−0.310622	+	0.538014i	−0.978497	−	0.206260i	$-0.933871\pi$
$727$	−8.37529	+	14.5064i	−0.310622	+	0.538014i	0.667875	+	0.744274i	$0.267204\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−49.0771	−	28.3347i	−1.81518	−	1.04800i
$732$		0			0
$733$	21.0798	−	12.1704i	0.778601	−	0.449525i	−0.0573335	−	0.998355i	$-0.518260\pi$
$733$	21.0798	−	12.1704i	0.778601	−	0.449525i	0.835934	+	0.548830i	$0.184927\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.63583			−0.170763
$738$		0			0
$739$			32.0558i			1.17919i	0.807698	+	0.589596i	$0.200713\pi$
$739$			32.0558i			1.17919i	−0.807698	+	0.589596i	$0.799287\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	8.98071	+	15.5550i	0.329470	+	0.570659i	0.982407	−	0.186753i	$-0.0597966\pi$
$743$	8.98071	+	15.5550i	0.329470	+	0.570659i	−0.652937	+	0.757413i	$0.726463\pi$
$744$		0			0
$745$	12.7863	−	22.1465i	0.468454	−	0.811386i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−42.1452	−	24.3325i	−1.53995	−	0.889092i
$750$		0			0
$751$	−10.9273	−	18.9266i	−0.398742	−	0.690642i	0.594829	−	0.803853i	$-0.297220\pi$
$751$	−10.9273	−	18.9266i	−0.398742	−	0.690642i	−0.993571	+	0.113210i	$0.963887\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	9.79743i		−	0.356565i
$756$		0			0
$757$			52.1292i			1.89467i	0.320248	+	0.947334i	$0.396234\pi$
$757$			52.1292i			1.89467i	−0.320248	+	0.947334i	$0.603766\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	16.0447	+	27.7902i	0.581620	+	1.00739i	0.995288	+	0.0969668i	$0.0309141\pi$
$761$	16.0447	+	27.7902i	0.581620	+	1.00739i	−0.413668	+	0.910428i	$0.635753\pi$
$762$		0			0
$763$	4.44608	+	2.56695i	0.160959	+	0.0929297i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.368791	+	0.638765i	−0.0133163	+	0.0230645i
$768$		0			0
$769$	−1.61164	−	2.79143i	−0.0581171	−	0.100662i	0.835503	−	0.549486i	$-0.185176\pi$
$769$	−1.61164	−	2.79143i	−0.0581171	−	0.100662i	−0.893620	+	0.448824i	$0.851843\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	19.2331i		−	0.691765i	−0.938278	−	0.345883i	$-0.887580\pi$
$773$		−	19.2331i		−	0.691765i	0.938278	−	0.345883i	$-0.112420\pi$
$774$		0			0
$775$	−18.8380			−0.676682
$776$		0			0
$777$		0			0
$778$		0			0
$779$	14.7643	−	8.52420i	0.528988	−	0.305411i
$780$		0			0
$781$	−1.67858	−	0.969129i	−0.0600643	−	0.0346782i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	13.7584	−	23.8302i	0.491058	−	0.850537i
$786$		0			0
$787$	−31.4974	+	18.1850i	−1.12276	+	0.648226i	−0.942104	−	0.335321i	$-0.891155\pi$
$787$	−31.4974	+	18.1850i	−1.12276	+	0.648226i	−0.180656	+	0.983546i	$0.557822\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−34.3868			−1.22265
$792$		0			0
$793$	6.88836			0.244613
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.9538	+	7.47885i	−0.458845	+	0.264915i	−0.711559	−	0.702627i	$-0.752010\pi$
$797$	−12.9538	+	7.47885i	−0.458845	+	0.264915i	0.252713	+	0.967541i	$0.418677\pi$
$798$		0			0
$799$	−32.4841	+	56.2640i	−1.14920	+	1.99048i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.30715	−	0.754681i	−0.0461282	−	0.0266321i
$804$		0			0
$805$	−25.6675	+	14.8191i	−0.904659	+	0.522305i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.0409808			0.00144081			0.000720404	−	1.00000i	$-0.499771\pi$
$809$	0.0409808			0.00144081			0.000720404		1.00000i	$0.499771\pi$
$810$		0			0
$811$		−	43.2568i		−	1.51895i	−0.650535	−	0.759476i	$-0.725455\pi$
$811$		−	43.2568i		−	1.51895i	0.650535	−	0.759476i	$-0.274545\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−7.37575	−	12.7752i	−0.258361	−	0.447495i
$816$		0			0
$817$	10.2584	−	17.7681i	0.358896	−	0.621626i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−24.7863	−	14.3104i	−0.865048	−	0.499436i	0.000651604	−	1.00000i	$-0.499793\pi$
$821$	−24.7863	−	14.3104i	−0.865048	−	0.499436i	−0.865699	+	0.500564i	$0.833126\pi$
$822$		0			0
$823$	21.2059	+	36.7297i	0.739191	+	1.28032i	0.952860	+	0.303411i	$0.0981254\pi$
$823$	21.2059	+	36.7297i	0.739191	+	1.28032i	−0.213669	+	0.976906i	$0.568541\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			14.1116i			0.490710i	0.969433	+	0.245355i	$0.0789045\pi$
$827$			14.1116i			0.490710i	−0.969433	+	0.245355i	$0.921096\pi$
$828$		0			0
$829$		−	22.6088i		−	0.785237i	−0.919701	−	0.392618i	$-0.871569\pi$
$829$		−	22.6088i		−	0.785237i	0.919701	−	0.392618i	$-0.128431\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−16.7268	−	28.9716i	−0.579548	−	1.00381i
$834$		0			0
$835$	−5.86747	−	3.38759i	−0.203052	−	0.117232i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	7.05530	−	12.2201i	0.243576	−	0.421886i	−0.718154	−	0.695884i	$-0.755013\pi$
$839$	7.05530	−	12.2201i	0.243576	−	0.421886i	0.961730	+	0.273998i	$0.0883462\pi$
$840$		0			0
$841$	16.2026	+	28.0637i	0.558709	+	0.967713i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	21.8731i		−	0.752456i
$846$		0			0
$847$	37.7984			1.29877
$848$		0			0
$849$		0			0
$850$		0			0
$851$	9.60368	−	5.54469i	0.329210	−	0.190070i
$852$		0			0
$853$	36.7863	+	21.2386i	1.25954	+	0.727195i	0.972985	−	0.230869i	$-0.0741569\pi$
$853$	36.7863	+	21.2386i	1.25954	+	0.727195i	0.286554	+	0.958064i	$0.407490\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.8421	−	29.1714i	0.575316	−	0.996476i	−0.420691	−	0.907204i	$-0.638213\pi$
$857$	16.8421	−	29.1714i	0.575316	−	0.996476i	0.996007	−	0.0892724i	$-0.0284542\pi$
$858$		0			0
$859$	−39.8165	+	22.9881i	−1.35852	+	0.784344i	−0.989425	−	0.145047i	$-0.953667\pi$
$859$	−39.8165	+	22.9881i	−1.35852	+	0.784344i	−0.369098	+	0.929390i	$0.620333\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−31.8786			−1.08516			−0.542581	−	0.840004i	$-0.682553\pi$
$863$	−31.8786			−1.08516			−0.542581	+	0.840004i	$0.682553\pi$
$864$		0			0
$865$	−21.0000			−0.714021
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.58373	+	0.914365i	−0.0537242	+	0.0310177i
$870$		0			0
$871$	1.92450	−	3.33333i	0.0652091	−	0.112945i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	37.9395	+	21.9044i	1.28259	+	0.740503i
$876$		0			0
$877$	−45.3925	+	26.2073i	−1.53279	+	0.884959i	−0.533563	+	0.845760i	$0.679147\pi$
$877$	−45.3925	+	26.2073i	−1.53279	+	0.884959i	−0.999231	+	0.0391990i	$0.987519\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−34.0558			−1.14737			−0.573685	−	0.819076i	$-0.694487\pi$
$881$	−34.0558			−1.14737			−0.573685	+	0.819076i	$0.694487\pi$
$882$		0			0
$883$		−	10.0000i		−	0.336527i	−0.985742	−	0.168263i	$-0.946184\pi$
$883$		−	10.0000i		−	0.336527i	0.985742	−	0.168263i	$-0.0538159\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	18.0530	+	31.2687i	0.606161	+	1.04990i	0.991867	+	0.127280i	$0.0406246\pi$
$887$	18.0530	+	31.2687i	0.606161	+	1.04990i	−0.385706	+	0.922622i	$0.626042\pi$
$888$		0			0
$889$	4.05582	−	7.02488i	0.136028	−	0.235607i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−20.3700	−	11.7606i	−0.681657	−	0.393555i
$894$		0			0
$895$	5.19615	+	9.00000i	0.173688	+	0.300837i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	73.8087i		−	2.46166i
$900$		0			0
$901$		−	71.9930i		−	2.39843i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.02791	+	3.51244i	0.0674100	+	0.116757i
$906$		0			0
$907$	−36.6935	−	21.1850i	−1.21839	−	0.703437i	−0.253815	−	0.967253i	$-0.581686\pi$
$907$	−36.6935	−	21.1850i	−1.21839	−	0.703437i	−0.964573	+	0.263816i	$0.915019\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	25.3321	−	43.8765i	0.839289	−	1.45369i	−0.0512002	−	0.998688i	$-0.516305\pi$
$911$	25.3321	−	43.8765i	0.839289	−	1.45369i	0.890490	−	0.455004i	$-0.150362\pi$
$912$		0			0
$913$	−4.50000	−	7.79423i	−0.148928	−	0.257951i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			0.933638i			0.0308315i
$918$		0			0
$919$	25.3372			0.835796			0.417898	−	0.908494i	$-0.362767\pi$
$919$	25.3372			0.835796			0.417898	+	0.908494i	$0.362767\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.39367	−	0.804638i	0.0458734	−	0.0264850i
$924$		0			0
$925$	−4.05582	−	2.34163i	−0.133354	−	0.0769922i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−7.67466	+	13.2929i	−0.251798	+	0.436126i	−0.964021	−	0.265827i	$-0.914355\pi$
$929$	−7.67466	+	13.2929i	−0.251798	+	0.436126i	0.712223	+	0.701953i	$0.247688\pi$
$930$		0			0
$931$	10.4890	−	6.05582i	0.343763	−	0.198471i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.02488			−0.229738
$936$		0			0
$937$	−11.5390			−0.376964			−0.188482	−	0.982077i	$-0.560357\pi$
$937$	−11.5390			−0.376964			−0.188482	+	0.982077i	$0.560357\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	28.6675	−	16.5512i	0.934532	−	0.539552i	0.0462901	−	0.998928i	$-0.485260\pi$
$941$	28.6675	−	16.5512i	0.934532	−	0.539552i	0.888242	+	0.459376i	$0.151927\pi$
$942$		0			0
$943$	−20.1843	+	34.9602i	−0.657290	+	1.13846i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.9526	+	8.63290i	0.485895	+	0.280532i	0.722870	−	0.690984i	$-0.242823\pi$
$947$	14.9526	+	8.63290i	0.485895	+	0.280532i	−0.236975	+	0.971516i	$0.576156\pi$
$948$		0			0
$949$	1.08528	−	0.626589i	0.0352298	−	0.0203399i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	29.2159			0.946394			0.473197	−	0.880957i	$-0.343100\pi$
$953$	29.2159			0.946394			0.473197	+	0.880957i	$0.343100\pi$
$954$		0			0
$955$			2.37003i			0.0766922i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.62669	−	6.28160i	−0.117112	−	0.202844i
$960$		0			0
$961$	−28.8589	+	49.9851i	−0.930932	+	1.61242i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−23.1914	−	13.3896i	−0.746559	−	0.431026i
$966$		0			0
$967$	2.00416	+	3.47131i	0.0644495	+	0.111630i	0.896450	−	0.443146i	$-0.146138\pi$
$967$	2.00416	+	3.47131i	0.0644495	+	0.111630i	−0.832000	+	0.554775i	$0.812804\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	20.2791i		−	0.650787i	−0.945579	−	0.325393i	$-0.894503\pi$
$971$		−	20.2791i		−	0.650787i	0.945579	−	0.325393i	$-0.105497\pi$
$972$		0			0
$973$			8.16021i			0.261604i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.65417	+	2.86511i	0.0529217	+	0.0916631i	0.891273	−	0.453468i	$-0.149813\pi$
$977$	1.65417	+	2.86511i	0.0529217	+	0.0916631i	−0.838351	+	0.545131i	$0.816480\pi$
$978$		0			0
$979$	1.23617	+	0.713701i	0.0395080	+	0.0228100i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−20.5963	+	35.6739i	−0.656921	+	1.13782i	0.324488	+	0.945890i	$0.394808\pi$
$983$	−20.5963	+	35.6739i	−0.656921	+	1.13782i	−0.981409	+	0.191930i	$0.938525\pi$
$984$		0			0
$985$	11.2026	+	19.4034i	0.356944	+	0.618245i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			48.5813i			1.54479i
$990$		0			0
$991$	−44.2802			−1.40661			−0.703303	−	0.710890i	$-0.748292\pi$
$991$	−44.2802			−1.40661			−0.703303	+	0.710890i	$0.748292\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−28.1120	+	16.2305i	−0.891211	+	0.514541i
$996$		0			0
$997$	−30.8478	−	17.8100i	−0.976959	−	0.564047i	−0.0756081	−	0.997138i	$-0.524090\pi$
$997$	−30.8478	−	17.8100i	−0.976959	−	0.564047i	−0.901351	+	0.433090i	$0.857423\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.r.e.289.2		12
3.2	odd	2		576.2.r.f.97.1	yes	12
4.3	odd	2	inner	1728.2.r.e.289.5		12
8.3	odd	2		1728.2.r.f.289.5		12
8.5	even	2		1728.2.r.f.289.2		12
9.2	odd	6		5184.2.d.q.2593.11		12
9.4	even	3		1728.2.r.f.1441.2		12
9.5	odd	6		576.2.r.e.481.6	yes	12
9.7	even	3		5184.2.d.r.2593.5		12
12.11	even	2		576.2.r.f.97.6	yes	12
24.5	odd	2		576.2.r.e.97.6	yes	12
24.11	even	2		576.2.r.e.97.1	✓	12
36.7	odd	6		5184.2.d.r.2593.2		12
36.11	even	6		5184.2.d.q.2593.8		12
36.23	even	6		576.2.r.e.481.1	yes	12
36.31	odd	6		1728.2.r.f.1441.5		12
72.5	odd	6		576.2.r.f.481.1	yes	12
72.11	even	6		5184.2.d.q.2593.2		12
72.13	even	6	inner	1728.2.r.e.1441.2		12
72.29	odd	6		5184.2.d.q.2593.5		12
72.43	odd	6		5184.2.d.r.2593.8		12
72.59	even	6		576.2.r.f.481.6	yes	12
72.61	even	6		5184.2.d.r.2593.11		12
72.67	odd	6	inner	1728.2.r.e.1441.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.r.e.97.1	✓	12	24.11	even	2
576.2.r.e.97.6	yes	12	24.5	odd	2
576.2.r.e.481.1	yes	12	36.23	even	6
576.2.r.e.481.6	yes	12	9.5	odd	6
576.2.r.f.97.1	yes	12	3.2	odd	2
576.2.r.f.97.6	yes	12	12.11	even	2
576.2.r.f.481.1	yes	12	72.5	odd	6
576.2.r.f.481.6	yes	12	72.59	even	6
1728.2.r.e.289.2		12	1.1	even	1	trivial
1728.2.r.e.289.5		12	4.3	odd	2	inner
1728.2.r.e.1441.2		12	72.13	even	6	inner
1728.2.r.e.1441.5		12	72.67	odd	6	inner
1728.2.r.f.289.2		12	8.5	even	2
1728.2.r.f.289.5		12	8.3	odd	2
1728.2.r.f.1441.2		12	9.4	even	3
1728.2.r.f.1441.5		12	36.31	odd	6
5184.2.d.q.2593.2		12	72.11	even	6
5184.2.d.q.2593.5		12	72.29	odd	6
5184.2.d.q.2593.8		12	36.11	even	6
5184.2.d.q.2593.11		12	9.2	odd	6
5184.2.d.r.2593.2		12	36.7	odd	6
5184.2.d.r.2593.5		12	9.7	even	3
5184.2.d.r.2593.8		12	72.43	odd	6
5184.2.d.r.2593.11		12	72.61	even	6

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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{5} +(-1.80664 + 3.12920i) q^{7} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{5} +(-1.80664 + 3.12920i) q^{7} +(0.635828 + 0.367095i) q^{11} +(-0.527909 + 0.304788i) q^{13} +5.52420 q^{17} +2.00000i q^{19} +(-2.36788 - 4.10129i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(-6.78630 - 3.91807i) q^{29} +(4.70951 + 8.15710i) q^{31} -6.25839i q^{35} +2.34163i q^{37} +(-4.26210 - 7.38217i) q^{41} +(-8.88403 - 5.12920i) q^{43} +(-5.88032 + 10.1850i) q^{47} +(-3.02791 - 5.24449i) q^{49} -13.0323i q^{53} -1.27166 q^{55} +(1.04788 - 0.604996i) q^{59} +(-9.78630 - 5.65012i) q^{61} +(0.527909 - 0.914365i) q^{65} +(-5.46826 + 3.15710i) q^{67} -2.63999 q^{71} -2.05582 q^{73} +(-2.29743 + 1.32642i) q^{77} +(-1.24540 + 2.15710i) q^{79} +(-10.6161 - 6.12920i) q^{83} +(-8.28630 + 4.78410i) q^{85} +1.94418 q^{89} -2.20257i q^{91} +(-1.73205 - 3.00000i) q^{95} +(7.78630 - 13.4863i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{5}+O(q^{10}) \) 12 * q - 18 * q^5	\( 12 q - 18 q^{5} + 6 q^{13} - 12 q^{25} + 18 q^{29} - 18 q^{41} - 24 q^{49} - 18 q^{61} - 6 q^{65} - 90 q^{77} + 48 q^{89} - 6 q^{97}+O(q^{100}) \) 12 * q - 18 * q^5 + 6 * q^13 - 12 * q^25 + 18 * q^29 - 18 * q^41 - 24 * q^49 - 18 * q^61 - 6 * q^65 - 90 * q^77 + 48 * q^89 - 6 * q^97

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