LMFDB - Embedded newform 2916.2.e.d.973.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2916,2,Mod(973,2916)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2916, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("2916.973");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2916 = 2^{2} \cdot 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2916.e (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:	$23.2843772294$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 $ x^18 - 6x^17 + 24x^16 - 66x^15 + 153x^14 - 315x^13 + 651x^12 - 1350x^11 + 2700x^10 - 4941x^9 + 8100x^8 - 12150x^7 + 17577x^6 - 25515x^5 + 37179x^4 - 48114x^3 + 52488x^2 - 39366*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			973.5
Root			$-0.219955 + 1.71803i$ of defining polynomial
Character	$\chi$	$=$	2916.973
Dual form			2916.2.e.d.1945.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0506977 + 0.0878110i) q^{5} +(-0.475194 - 0.823060i) q^{7} +O(q^{10})$	$q+(-0.0506977 + 0.0878110i) q^{5} +(-0.475194 - 0.823060i) q^{7} +(2.02286 + 3.50370i) q^{11} +(-2.48091 + 4.29707i) q^{13} -6.22979 q^{17} +1.02915 q^{19} +(1.73554 - 3.00604i) q^{23} +(2.49486 + 4.32122i) q^{25} +(-1.99043 - 3.44753i) q^{29} +(2.13250 - 3.69360i) q^{31} +0.0963650 q^{35} -8.39203 q^{37} +(1.40338 - 2.43072i) q^{41} +(-3.36560 - 5.82939i) q^{43} +(-3.91081 - 6.77373i) q^{47} +(3.04838 - 5.27995i) q^{49} -12.9766 q^{53} -0.410217 q^{55} +(-7.12606 + 12.3427i) q^{59} +(1.35274 + 2.34301i) q^{61} +(-0.251553 - 0.435703i) q^{65} +(1.65540 - 2.86724i) q^{67} -14.5247 q^{71} +11.6434 q^{73} +(1.92250 - 3.32987i) q^{77} +(0.640827 + 1.10995i) q^{79} +(2.62820 + 4.55217i) q^{83} +(0.315836 - 0.547044i) q^{85} -9.61118 q^{89} +4.71566 q^{91} +(-0.0521756 + 0.0903707i) q^{95} +(-1.97314 - 3.41758i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{5}+O(q^{10}) $ 18 * q + 6 * q^5	$ 18 q + 6 q^{5} + 6 q^{11} - 24 q^{17} + 3 q^{23} - 9 q^{25} + 24 q^{29} - 42 q^{35} + 33 q^{41} + 9 q^{47} - 9 q^{49} - 66 q^{53} + 30 q^{59} + 9 q^{61} + 39 q^{65} + 9 q^{67} - 24 q^{71} - 18 q^{73} + 39 q^{77} + 36 q^{83} - 96 q^{89} - 18 q^{91} + 12 q^{95}+O(q^{100}) $ 18 * q + 6 * q^5 + 6 * q^11 - 24 * q^17 + 3 * q^23 - 9 * q^25 + 24 * q^29 - 42 * q^35 + 33 * q^41 + 9 * q^47 - 9 * q^49 - 66 * q^53 + 30 * q^59 + 9 * q^61 + 39 * q^65 + 9 * q^67 - 24 * q^71 - 18 * q^73 + 39 * q^77 + 36 * q^83 - 96 * q^89 - 18 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2916\mathbb{Z}\right)^\times$.

$n$	$1459$	$2189$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−0.0506977	+	0.0878110i	−0.0226727	+	0.0392703i	−0.877139	−	0.480236i	$-0.840551\pi$
$5$	−0.0506977	+	0.0878110i	−0.0226727	+	0.0392703i	0.854466	+	0.519507i	$0.173884\pi$
$6$		0			0
$7$	−0.475194	−	0.823060i	−0.179606	−	0.311088i	0.762139	−	0.647413i	$-0.224149\pi$
$7$	−0.475194	−	0.823060i	−0.179606	−	0.311088i	−0.941746	+	0.336326i	$0.890816\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.02286	+	3.50370i	0.609915	+	1.05640i	0.991254	+	0.131969i	$0.0421298\pi$
$11$	2.02286	+	3.50370i	0.609915	+	1.05640i	−0.381339	+	0.924435i	$0.624537\pi$
$12$		0			0
$13$	−2.48091	+	4.29707i	−0.688082	+	1.19179i	0.284376	+	0.958713i	$0.408214\pi$
$13$	−2.48091	+	4.29707i	−0.688082	+	1.19179i	−0.972458	+	0.233079i	$0.925120\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.22979			−1.51095			−0.755473	−	0.655180i	$-0.772593\pi$
$17$	−6.22979			−1.51095			−0.755473	+	0.655180i	$0.772593\pi$
$18$		0			0
$19$	1.02915			0.236103			0.118052	−	0.993007i	$-0.462335\pi$
$19$	1.02915			0.236103			0.118052	+	0.993007i	$0.462335\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.73554	−	3.00604i	0.361885	−	0.626804i	−0.626386	−	0.779513i	$-0.715467\pi$
$23$	1.73554	−	3.00604i	0.361885	−	0.626804i	0.988271	+	0.152710i	$0.0487999\pi$
$24$		0			0
$25$	2.49486	+	4.32122i	0.498972	+	0.864245i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.99043	−	3.44753i	−0.369614	−	0.640191i	0.619891	−	0.784688i	$-0.287177\pi$
$29$	−1.99043	−	3.44753i	−0.369614	−	0.640191i	−0.989505	+	0.144497i	$0.953844\pi$
$30$		0			0
$31$	2.13250	−	3.69360i	0.383008	−	0.663390i	−0.608482	−	0.793567i	$-0.708221\pi$
$31$	2.13250	−	3.69360i	0.383008	−	0.663390i	0.991491	+	0.130178i	$0.0415547\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.0963650			0.0162887
$36$		0			0
$37$	−8.39203			−1.37964			−0.689820	−	0.723981i	$-0.742310\pi$
$37$	−8.39203			−1.37964			−0.689820	+	0.723981i	$0.742310\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.40338	−	2.43072i	0.219171	−	0.379615i	−0.735384	−	0.677651i	$-0.762998\pi$
$41$	1.40338	−	2.43072i	0.219171	−	0.379615i	0.954555	+	0.298036i	$0.0963314\pi$
$42$		0			0
$43$	−3.36560	−	5.82939i	−0.513249	−	0.888974i	−0.999882	−	0.0153673i	$-0.995108\pi$
$43$	−3.36560	−	5.82939i	−0.513249	−	0.888974i	0.486633	−	0.873607i	$-0.338225\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.91081	−	6.77373i	−0.570451	−	0.988050i	−0.996520	−	0.0833588i	$-0.973435\pi$
$47$	−3.91081	−	6.77373i	−0.570451	−	0.988050i	0.426069	−	0.904691i	$-0.359898\pi$
$48$		0			0
$49$	3.04838	−	5.27995i	0.435483	−	0.754279i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−12.9766			−1.78248			−0.891238	−	0.453536i	$-0.850162\pi$
$53$	−12.9766			−1.78248			−0.891238	+	0.453536i	$0.850162\pi$
$54$		0			0
$55$	−0.410217			−0.0553137
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.12606	+	12.3427i	−0.927734	+	1.60688i	−0.140631	+	0.990062i	$0.544913\pi$
$59$	−7.12606	+	12.3427i	−0.927734	+	1.60688i	−0.787103	+	0.616821i	$0.788420\pi$
$60$		0			0
$61$	1.35274	+	2.34301i	0.173201	+	0.299992i	0.939537	−	0.342447i	$-0.111256\pi$
$61$	1.35274	+	2.34301i	0.173201	+	0.299992i	−0.766336	+	0.642439i	$0.777922\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.251553	−	0.435703i	−0.0312013	−	0.0540423i
$66$		0			0
$67$	1.65540	−	2.86724i	0.202240	−	0.350289i	−0.747010	−	0.664813i	$-0.768511\pi$
$67$	1.65540	−	2.86724i	0.202240	−	0.350289i	0.949250	+	0.314523i	$0.101845\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−14.5247			−1.72376			−0.861880	−	0.507113i	$-0.830713\pi$
$71$	−14.5247			−1.72376			−0.861880	+	0.507113i	$0.830713\pi$
$72$		0			0
$73$	11.6434			1.36276			0.681379	−	0.731930i	$-0.261380\pi$
$73$	11.6434			1.36276			0.681379	+	0.731930i	$0.261380\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.92250	−	3.32987i	0.219089	−	0.379474i
$78$		0			0
$79$	0.640827	+	1.10995i	0.0720987	+	0.124879i	0.899821	−	0.436259i	$-0.143697\pi$
$79$	0.640827	+	1.10995i	0.0720987	+	0.124879i	−0.827722	+	0.561138i	$0.810364\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.62820	+	4.55217i	0.288482	+	0.499665i	0.973448	−	0.228910i	$-0.0735161\pi$
$83$	2.62820	+	4.55217i	0.288482	+	0.499665i	−0.684966	+	0.728575i	$0.740183\pi$
$84$		0			0
$85$	0.315836	−	0.547044i	0.0342572	−	0.0593352i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.61118			−1.01878			−0.509392	−	0.860535i	$-0.670130\pi$
$89$	−9.61118			−1.01878			−0.509392	+	0.860535i	$0.670130\pi$
$90$		0			0
$91$	4.71566			0.494336
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0521756	+	0.0903707i	−0.00535310	+	0.00927184i
$96$		0			0
$97$	−1.97314	−	3.41758i	−0.200342	−	0.347003i	0.748296	−	0.663364i	$-0.230872\pi$
$97$	−1.97314	−	3.41758i	−0.200342	−	0.347003i	−0.948639	+	0.316362i	$0.897539\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.64958	+	8.05331i	0.462650	+	0.801334i	0.999092	−	0.0426035i	$-0.0135652\pi$
$101$	4.64958	+	8.05331i	0.462650	+	0.801334i	−0.536442	+	0.843937i	$0.680232\pi$
$102$		0			0
$103$	−4.37632	+	7.58000i	−0.431211	+	0.746880i	−0.996978	−	0.0776857i	$-0.975247\pi$
$103$	−4.37632	+	7.58000i	−0.431211	+	0.746880i	0.565767	+	0.824565i	$0.308580\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.0129			−0.967983			−0.483992	−	0.875073i	$-0.660813\pi$
$107$	−10.0129			−0.967983			−0.483992	+	0.875073i	$0.660813\pi$
$108$		0			0
$109$	1.78337			0.170816			0.0854081	−	0.996346i	$-0.472781\pi$
$109$	1.78337			0.170816			0.0854081	+	0.996346i	$0.472781\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.43614	−	11.1477i	0.605461	−	1.04869i	−0.386518	−	0.922282i	$-0.626322\pi$
$113$	6.43614	−	11.1477i	0.605461	−	1.04869i	0.991978	−	0.126407i	$-0.0403444\pi$
$114$		0			0
$115$	0.175976	+	0.304799i	0.0164098	+	0.0284227i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.96036	+	5.12749i	0.271375	+	0.470036i
$120$		0			0
$121$	−2.68392	+	4.64869i	−0.243993	+	0.422608i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.01291			−0.0905976
$126$		0			0
$127$	−13.5811			−1.20512			−0.602562	−	0.798072i	$-0.705854\pi$
$127$	−13.5811			−1.20512			−0.602562	+	0.798072i	$0.705854\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.72732	+	9.92001i	−0.500399	+	0.866716i	0.499601	+	0.866255i	$0.333480\pi$
$131$	−5.72732	+	9.92001i	−0.500399	+	0.866716i	−1.00000		0.000460260i	$0.999853\pi$
$132$		0			0
$133$	−0.489046	−	0.847053i	−0.0424057	−	0.0734488i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.0827316	+	0.143295i	0.00706823	+	0.0122425i	0.869538	−	0.493866i	$-0.164417\pi$
$137$	0.0827316	+	0.143295i	0.00706823	+	0.0122425i	−0.862470	+	0.506109i	$0.831083\pi$
$138$		0			0
$139$	−5.78136	+	10.0136i	−0.490369	+	0.849343i	−0.999939	−	0.0110859i	$-0.996471\pi$
$139$	−5.78136	+	10.0136i	−0.490369	+	0.849343i	0.509570	+	0.860429i	$0.329804\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−20.0742			−1.67869
$144$		0			0
$145$	0.403642			0.0335206
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.51936	+	6.09572i	−0.288318	+	0.499381i	−0.973408	−	0.229077i	$-0.926429\pi$
$149$	−3.51936	+	6.09572i	−0.288318	+	0.499381i	0.685091	+	0.728458i	$0.259763\pi$
$150$		0			0
$151$	10.7835	+	18.6776i	0.877550	+	1.51996i	0.854021	+	0.520238i	$0.174157\pi$
$151$	10.7835	+	18.6776i	0.877550	+	1.51996i	0.0235291	+	0.999723i	$0.492510\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.216226	+	0.374514i	0.0173677	+	0.0300817i
$156$		0			0
$157$	1.46162	−	2.53160i	0.116650	−	0.202044i	−0.801788	−	0.597608i	$-0.796118\pi$
$157$	1.46162	−	2.53160i	0.116650	−	0.202044i	0.918438	+	0.395565i	$0.129451\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.29887			−0.259988
$162$		0			0
$163$	−3.59864			−0.281867			−0.140933	−	0.990019i	$-0.545010\pi$
$163$	−3.59864			−0.281867			−0.140933	+	0.990019i	$0.545010\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.29844	−	3.98101i	0.177859	−	0.308060i	−0.763288	−	0.646058i	$-0.776416\pi$
$167$	2.29844	−	3.98101i	0.177859	−	0.308060i	0.941147	+	0.337998i	$0.109750\pi$
$168$		0			0
$169$	−5.80986	−	10.0630i	−0.446912	−	0.774075i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.97017	−	13.8047i	−0.605960	−	1.04955i	−0.991899	−	0.127030i	$-0.959456\pi$
$173$	−7.97017	−	13.8047i	−0.605960	−	1.04955i	0.385938	−	0.922525i	$-0.373878\pi$
$174$		0			0
$175$	2.37108	−	4.10684i	0.179237	−	0.310448i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−14.3095			−1.06954			−0.534770	−	0.844998i	$-0.679602\pi$
$179$	−14.3095			−1.06954			−0.534770	+	0.844998i	$0.679602\pi$
$180$		0			0
$181$	−16.0508			−1.19305			−0.596523	−	0.802596i	$-0.703451\pi$
$181$	−16.0508			−1.19305			−0.596523	+	0.802596i	$0.703451\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.425456	−	0.736912i	0.0312802	−	0.0541789i
$186$		0			0
$187$	−12.6020	−	21.8273i	−0.921548	−	1.59617i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.44137	−	4.22858i	−0.176652	−	0.305970i	0.764080	−	0.645122i	$-0.223193\pi$
$191$	−2.44137	−	4.22858i	−0.176652	−	0.305970i	−0.940732	+	0.339152i	$0.889860\pi$
$192$		0			0
$193$	3.04147	−	5.26797i	0.218929	−	0.379197i	−0.735551	−	0.677469i	$-0.763077\pi$
$193$	3.04147	−	5.26797i	0.218929	−	0.379197i	0.954481	+	0.298272i	$0.0964102\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−19.9743			−1.42311			−0.711555	−	0.702631i	$-0.752009\pi$
$197$	−19.9743			−1.42311			−0.711555	+	0.702631i	$0.752009\pi$
$198$		0			0
$199$	17.4164			1.23462			0.617310	−	0.786720i	$-0.288223\pi$
$199$	17.4164			1.23462			0.617310	+	0.786720i	$0.288223\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.89169	+	3.27649i	−0.132770	+	0.229965i
$204$		0			0
$205$	0.142296	+	0.246464i	0.00993840	+	0.0172138i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.08183	+	3.60583i	0.144003	+	0.249421i
$210$		0			0
$211$	−3.70559	+	6.41828i	−0.255104	+	0.441852i	−0.964924	−	0.262531i	$-0.915443\pi$
$211$	−3.70559	+	6.41828i	−0.255104	+	0.441852i	0.709820	+	0.704383i	$0.248776\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.682513			0.0465470
$216$		0			0
$217$	−4.05341			−0.275163
$218$		0			0
$219$		0			0
$220$		0			0
$221$	15.4556	−	26.7698i	1.03965	−	1.80073i
$222$		0			0
$223$	6.44315	+	11.1599i	0.431465	+	0.747320i	0.997000	−	0.0774050i	$-0.0246634\pi$
$223$	6.44315	+	11.1599i	0.431465	+	0.747320i	−0.565535	+	0.824725i	$0.691330\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.31528	−	9.20633i	−0.352787	−	0.611046i	0.633949	−	0.773375i	$-0.281433\pi$
$227$	−5.31528	−	9.20633i	−0.352787	−	0.611046i	−0.986737	+	0.162329i	$0.948099\pi$
$228$		0			0
$229$	8.39960	−	14.5485i	0.555061	−	0.961394i	−0.442837	−	0.896602i	$-0.646028\pi$
$229$	8.39960	−	14.5485i	0.555061	−	0.961394i	0.997899	−	0.0647925i	$-0.0206385\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	18.1358			1.18812			0.594059	−	0.804421i	$-0.297524\pi$
$233$	18.1358			1.18812			0.594059	+	0.804421i	$0.297524\pi$
$234$		0			0
$235$	0.793077			0.0517346
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.96572	+	13.7970i	−0.515259	+	0.892456i	0.484584	+	0.874745i	$0.338971\pi$
$239$	−7.96572	+	13.7970i	−0.515259	+	0.892456i	−0.999843	+	0.0177107i	$0.994362\pi$
$240$		0			0
$241$	4.95211	+	8.57731i	0.318994	+	0.552513i	0.980278	−	0.197622i	$-0.0633218\pi$
$241$	4.95211	+	8.57731i	0.318994	+	0.552513i	−0.661285	+	0.750135i	$0.729988\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.309092	+	0.535363i	0.0197472	+	0.0342031i
$246$		0			0
$247$	−2.55323	+	4.42233i	−0.162458	+	0.281386i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.28251			−0.144070			−0.0720352	−	0.997402i	$-0.522949\pi$
$251$	−2.28251			−0.144070			−0.0720352	+	0.997402i	$0.522949\pi$
$252$		0			0
$253$	14.0430			0.882877
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.83228	−	10.1018i	0.363807	−	0.630133i	−0.624777	−	0.780804i	$-0.714810\pi$
$257$	5.83228	−	10.1018i	0.363807	−	0.630133i	0.988584	+	0.150671i	$0.0481433\pi$
$258$		0			0
$259$	3.98784	+	6.90714i	0.247792	+	0.429189i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.880916	−	1.52579i	−0.0543196	−	0.0940843i	0.837587	−	0.546304i	$-0.183966\pi$
$263$	−0.880916	−	1.52579i	−0.0543196	−	0.0940843i	−0.891907	+	0.452220i	$0.850632\pi$
$264$		0			0
$265$	0.657885	−	1.13949i	0.0404135	−	0.0699983i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−13.3454			−0.813683			−0.406842	−	0.913499i	$-0.633370\pi$
$269$	−13.3454			−0.813683			−0.406842	+	0.913499i	$0.633370\pi$
$270$		0			0
$271$	12.4524			0.756430			0.378215	−	0.925718i	$-0.376538\pi$
$271$	12.4524			0.756430			0.378215	+	0.925718i	$0.376538\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−10.0935	+	17.4825i	−0.608661	+	1.05423i
$276$		0			0
$277$	−2.57798	−	4.46518i	−0.154896	−	0.268287i	0.778125	−	0.628109i	$-0.216171\pi$
$277$	−2.57798	−	4.46518i	−0.154896	−	0.268287i	−0.933021	+	0.359822i	$0.882837\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.93929	−	6.82305i	−0.234998	−	0.407029i	0.724274	−	0.689512i	$-0.242175\pi$
$281$	−3.93929	−	6.82305i	−0.234998	−	0.407029i	−0.959272	+	0.282483i	$0.908842\pi$
$282$		0			0
$283$	15.1757	−	26.2851i	0.902101	−	1.56248i	0.0773388	−	0.997005i	$-0.475358\pi$
$283$	15.1757	−	26.2851i	0.902101	−	1.56248i	0.824762	−	0.565480i	$-0.191309\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.66751			−0.157458
$288$		0			0
$289$	21.8102			1.28295
$290$		0			0
$291$		0			0
$292$		0			0
$293$	10.3086	−	17.8551i	0.602237	−	1.04311i	−0.390244	−	0.920711i	$-0.627609\pi$
$293$	10.3086	−	17.8551i	0.602237	−	1.04311i	0.992482	−	0.122394i	$-0.0390572\pi$
$294$		0			0
$295$	−0.722550	−	1.25149i	−0.0420685	−	0.0728648i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	8.61145	+	14.9155i	0.498013	+	0.862584i
$300$		0			0
$301$	−3.19863	+	5.54019i	−0.184366	+	0.319331i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.274323			−0.0157077
$306$		0			0
$307$	−12.7724			−0.728961			−0.364480	−	0.931211i	$-0.618753\pi$
$307$	−12.7724			−0.728961			−0.364480	+	0.931211i	$0.618753\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.05992	+	3.56789i	−0.116808	+	0.202317i	−0.918501	−	0.395419i	$-0.870599\pi$
$311$	−2.05992	+	3.56789i	−0.116808	+	0.202317i	0.801693	+	0.597736i	$0.203933\pi$
$312$		0			0
$313$	−4.85604	−	8.41091i	−0.274480	−	0.475412i	0.695524	−	0.718503i	$-0.255172\pi$
$313$	−4.85604	−	8.41091i	−0.274480	−	0.475412i	−0.970004	+	0.243090i	$0.921839\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.66199	+	8.07481i	0.261844	+	0.453527i	0.966732	−	0.255792i	$-0.0823362\pi$
$317$	4.66199	+	8.07481i	0.261844	+	0.453527i	−0.704888	+	0.709318i	$0.749003\pi$
$318$		0			0
$319$	8.05274	−	13.9478i	0.450867	−	0.780924i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−6.41139			−0.356739
$324$		0			0
$325$	−24.7581			−1.37333
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.71679	+	6.43767i	−0.204913	+	0.354920i
$330$		0			0
$331$	8.44393	+	14.6253i	0.464120	+	0.803880i	0.999161	−	0.0409461i	$-0.0130372\pi$
$331$	8.44393	+	14.6253i	0.464120	+	0.803880i	−0.535041	+	0.844826i	$0.679704\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.167850	+	0.290725i	0.00917064	+	0.0158840i
$336$		0			0
$337$	−14.0043	+	24.2562i	−0.762865	+	1.32132i	0.178503	+	0.983939i	$0.442874\pi$
$337$	−14.0043	+	24.2562i	−0.762865	+	1.32132i	−0.941368	+	0.337381i	$0.890459\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	17.2550			0.934410
$342$		0			0
$343$	−12.4470			−0.672075
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.58247	+	13.1332i	−0.407048	+	0.705028i	−0.994557	−	0.104189i	$-0.966775\pi$
$347$	−7.58247	+	13.1332i	−0.407048	+	0.705028i	0.587509	+	0.809217i	$0.300109\pi$
$348$		0			0
$349$	−6.02847	−	10.4416i	−0.322696	−	0.558927i	0.658347	−	0.752715i	$-0.271256\pi$
$349$	−6.02847	−	10.4416i	−0.322696	−	0.558927i	−0.981043	+	0.193788i	$0.937923\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	11.0999	+	19.2256i	0.590789	+	1.02328i	0.994126	+	0.108226i	$0.0345170\pi$
$353$	11.0999	+	19.2256i	0.590789	+	1.02328i	−0.403337	+	0.915052i	$0.632150\pi$
$354$		0			0
$355$	0.736367	−	1.27542i	0.0390823	−	0.0676925i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	24.6544			1.30121			0.650604	−	0.759417i	$-0.274516\pi$
$359$	24.6544			1.30121			0.650604	+	0.759417i	$0.274516\pi$
$360$		0			0
$361$	−17.9408			−0.944255
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.590295	+	1.02242i	−0.0308974	+	0.0535159i
$366$		0			0
$367$	−4.73072	−	8.19386i	−0.246942	−	0.427716i	0.715734	−	0.698373i	$-0.246092\pi$
$367$	−4.73072	−	8.19386i	−0.246942	−	0.427716i	−0.962676	+	0.270657i	$0.912759\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.16641	+	10.6805i	0.320144	+	0.554506i
$372$		0			0
$373$	−16.8580	+	29.1989i	−0.872873	+	1.51186i	−0.0138608	+	0.999904i	$0.504412\pi$
$373$	−16.8580	+	29.1989i	−0.872873	+	1.51186i	−0.859012	+	0.511956i	$0.828921\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	19.7524			1.01730
$378$		0			0
$379$	0.919811			0.0472475			0.0236238	−	0.999721i	$-0.492480\pi$
$379$	0.919811			0.0472475			0.0236238	+	0.999721i	$0.492480\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−7.09243	+	12.2844i	−0.362406	+	0.627706i	−0.988356	−	0.152157i	$-0.951378\pi$
$383$	−7.09243	+	12.2844i	−0.362406	+	0.627706i	0.625950	+	0.779863i	$0.284711\pi$
$384$		0			0
$385$	0.194933	+	0.337634i	0.00993470	+	0.0172074i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	14.0003	+	24.2493i	0.709844	+	1.22949i	0.964915	+	0.262564i	$0.0845681\pi$
$389$	14.0003	+	24.2493i	0.709844	+	1.22949i	−0.255070	+	0.966923i	$0.582099\pi$
$390$		0			0
$391$	−10.8120	+	18.7270i	−0.546789	+	0.947066i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.129954			−0.00653869
$396$		0			0
$397$	−1.23234			−0.0618493			−0.0309246	−	0.999522i	$-0.509845\pi$
$397$	−1.23234			−0.0618493			−0.0309246	+	0.999522i	$0.509845\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.54993	−	9.61276i	0.277150	−	0.480039i	−0.693525	−	0.720433i	$-0.743943\pi$
$401$	5.54993	−	9.61276i	0.277150	−	0.480039i	0.970675	+	0.240394i	$0.0772766\pi$
$402$		0			0
$403$	10.5811	+	18.3270i	0.527082	+	0.912933i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−16.9759	−	29.4031i	−0.841464	−	1.45746i
$408$		0			0
$409$	−2.74410	+	4.75292i	−0.135687	+	0.235017i	−0.925860	−	0.377868i	$-0.876657\pi$
$409$	−2.74410	+	4.75292i	−0.135687	+	0.235017i	0.790173	+	0.612884i	$0.209991\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	13.5451			0.666508
$414$		0			0
$415$	−0.532974			−0.0261627
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.52875	+	7.84403i	−0.221244	+	0.383206i	−0.955186	−	0.296006i	$-0.904345\pi$
$419$	−4.52875	+	7.84403i	−0.221244	+	0.383206i	0.733942	+	0.679212i	$0.237678\pi$
$420$		0			0
$421$	−4.47086	−	7.74376i	−0.217897	−	0.377408i	0.736268	−	0.676690i	$-0.236586\pi$
$421$	−4.47086	−	7.74376i	−0.217897	−	0.377408i	−0.954165	+	0.299282i	$0.903253\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−15.5424	−	26.9203i	−0.753919	−	1.30583i
$426$		0			0
$427$	1.28563	−	2.22677i	0.0622159	−	0.107761i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	29.7499			1.43300			0.716502	−	0.697585i	$-0.245742\pi$
$431$	29.7499			1.43300			0.716502	+	0.697585i	$0.245742\pi$
$432$		0			0
$433$	25.3444			1.21798			0.608988	−	0.793179i	$-0.291576\pi$
$433$	25.3444			1.21798			0.608988	+	0.793179i	$0.291576\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.78613	−	3.09367i	0.0854423	−	0.147990i
$438$		0			0
$439$	−20.4802	−	35.4727i	−0.977464	−	1.69302i	−0.671551	−	0.740959i	$-0.734371\pi$
$439$	−20.4802	−	35.4727i	−0.977464	−	1.69302i	−0.305914	−	0.952059i	$-0.598962\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.61124	+	7.98689i	0.219086	+	0.379469i	0.954529	−	0.298118i	$-0.0963590\pi$
$443$	4.61124	+	7.98689i	0.219086	+	0.379469i	−0.735442	+	0.677587i	$0.763026\pi$
$444$		0			0
$445$	0.487265	−	0.843968i	0.0230986	−	0.0400079i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−31.4662			−1.48498			−0.742491	−	0.669856i	$-0.766356\pi$
$449$	−31.4662			−1.48498			−0.742491	+	0.669856i	$0.766356\pi$
$450$		0			0
$451$	11.3554			0.534703
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.239073	+	0.414087i	−0.0112079	+	0.0194127i
$456$		0			0
$457$	14.5449	+	25.1925i	0.680382	+	1.17846i	0.974864	+	0.222799i	$0.0715195\pi$
$457$	14.5449	+	25.1925i	0.680382	+	1.17846i	−0.294482	+	0.955657i	$0.595147\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.1514	−	27.9750i	−0.752244	−	1.30293i	−0.946733	−	0.322020i	$-0.895638\pi$
$461$	−16.1514	−	27.9750i	−0.752244	−	1.30293i	0.194488	−	0.980905i	$-0.437695\pi$
$462$		0			0
$463$	7.55692	−	13.0890i	0.351200	−	0.608296i	−0.635260	−	0.772298i	$-0.719107\pi$
$463$	7.55692	−	13.0890i	0.351200	−	0.608296i	0.986460	+	0.164002i	$0.0524405\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	28.4618			1.31705			0.658527	−	0.752558i	$-0.271180\pi$
$467$	28.4618			1.31705			0.658527	+	0.752558i	$0.271180\pi$
$468$		0			0
$469$	−3.14655			−0.145294
$470$		0			0
$471$		0			0
$472$		0			0
$473$	13.6163	−	23.5841i	0.626077	−	1.08440i
$474$		0			0
$475$	2.56759	+	4.44719i	0.117809	+	0.204051i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−14.1494	−	24.5074i	−0.646502	−	1.11977i	−0.983952	−	0.178431i	$-0.942898\pi$
$479$	−14.1494	−	24.5074i	−0.646502	−	1.11977i	0.337451	−	0.941343i	$-0.390435\pi$
$480$		0			0
$481$	20.8199	−	36.0611i	0.949305	−	1.64424i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.400135			0.0181692
$486$		0			0
$487$	−9.59334			−0.434716			−0.217358	−	0.976092i	$-0.569744\pi$
$487$	−9.59334			−0.434716			−0.217358	+	0.976092i	$0.569744\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.62705	+	6.28223i	−0.163686	+	0.283513i	−0.936188	−	0.351500i	$-0.885672\pi$
$491$	−3.62705	+	6.28223i	−0.163686	+	0.283513i	0.772502	+	0.635013i	$0.219005\pi$
$492$		0			0
$493$	12.4000	+	21.4774i	0.558467	+	0.967293i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.90203	+	11.9547i	0.309598	+	0.536240i
$498$		0			0
$499$	−21.8193	+	37.7921i	−0.976766	+	1.69181i	−0.302786	+	0.953059i	$0.597917\pi$
$499$	−21.8193	+	37.7921i	−0.976766	+	1.69181i	−0.673980	+	0.738750i	$0.735417\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	29.5124			1.31589			0.657946	−	0.753065i	$-0.271426\pi$
$503$	29.5124			1.31589			0.657946	+	0.753065i	$0.271426\pi$
$504$		0			0
$505$	−0.942892			−0.0419581
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.0312	−	17.3746i	0.444627	−	0.770117i	−0.553399	−	0.832916i	$-0.686669\pi$
$509$	10.0312	−	17.3746i	0.444627	−	0.770117i	0.998026	+	0.0627993i	$0.0200028\pi$
$510$		0			0
$511$	−5.53288	−	9.58323i	−0.244760	−	0.423937i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.443738	−	0.768577i	−0.0195534	−	0.0338676i
$516$		0			0
$517$	15.8221	−	27.4046i	0.695853	−	1.20525i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	20.9555			0.918079			0.459039	−	0.888416i	$-0.348194\pi$
$521$	20.9555			0.918079			0.459039	+	0.888416i	$0.348194\pi$
$522$		0			0
$523$	−14.7851			−0.646509			−0.323254	−	0.946312i	$-0.604777\pi$
$523$	−14.7851			−0.646509			−0.323254	+	0.946312i	$0.604777\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.2850	+	23.0103i	−0.578705	+	1.00235i
$528$		0			0
$529$	5.47580	+	9.48436i	0.238078	+	0.412364i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.96332	+	12.0608i	0.301615	+	0.522413i
$534$		0			0
$535$	0.507631	−	0.879242i	0.0219468	−	0.0380130i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	24.6658			1.06243
$540$		0			0
$541$	39.7536			1.70914			0.854571	−	0.519335i	$-0.173820\pi$
$541$	39.7536			1.70914			0.854571	+	0.519335i	$0.173820\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.0904129	+	0.156600i	−0.00387286	+	0.00670800i
$546$		0			0
$547$	0.879436	+	1.52323i	0.0376020	+	0.0651285i	0.884214	−	0.467082i	$-0.154695\pi$
$547$	0.879436	+	1.52323i	0.0376020	+	0.0651285i	−0.846612	+	0.532211i	$0.821361\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.04846	−	3.54803i	−0.0872672	−	0.151151i
$552$		0			0
$553$	0.609035	−	1.05488i	0.0258988	−	0.0448580i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−3.02141			−0.128021			−0.0640107	−	0.997949i	$-0.520389\pi$
$557$	−3.02141			−0.128021			−0.0640107	+	0.997949i	$0.520389\pi$
$558$		0			0
$559$	33.3991			1.41263
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.85903	−	4.95199i	0.120494	−	0.208702i	−0.799469	−	0.600708i	$-0.794886\pi$
$563$	2.85903	−	4.95199i	0.120494	−	0.208702i	0.919963	+	0.392006i	$0.128219\pi$
$564$		0			0
$565$	0.652595	+	1.13033i	0.0274549	+	0.0475532i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.32058	+	9.21551i	0.223050	+	0.386334i	0.955733	−	0.294236i	$-0.0950653\pi$
$569$	5.32058	+	9.21551i	0.223050	+	0.386334i	−0.732683	+	0.680571i	$0.761732\pi$
$570$		0			0
$571$	8.17134	−	14.1532i	0.341960	−	0.592292i	−0.642837	−	0.766003i	$-0.722243\pi$
$571$	8.17134	−	14.1532i	0.341960	−	0.592292i	0.984797	+	0.173711i	$0.0555760\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	17.3197			0.722282
$576$		0			0
$577$	6.14126			0.255664			0.127832	−	0.991796i	$-0.459198\pi$
$577$	6.14126			0.255664			0.127832	+	0.991796i	$0.459198\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.49781	−	4.32633i	0.103626	−	0.179486i
$582$		0			0
$583$	−26.2499	−	45.4661i	−1.08716	−	1.88302i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.01460	+	5.22144i	0.124426	+	0.215512i	0.921508	−	0.388359i	$-0.126958\pi$
$587$	3.01460	+	5.22144i	0.124426	+	0.215512i	−0.797083	+	0.603870i	$0.793624\pi$
$588$		0			0
$589$	2.19466	−	3.80127i	0.0904295	−	0.156629i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	31.3099			1.28574			0.642871	−	0.765974i	$-0.277743\pi$
$593$	31.3099			1.28574			0.642871	+	0.765974i	$0.277743\pi$
$594$		0			0
$595$	−0.600333			−0.0246113
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−13.1227	+	22.7292i	−0.536179	+	0.928689i	0.462927	+	0.886397i	$0.346799\pi$
$599$	−13.1227	+	22.7292i	−0.536179	+	0.928689i	−0.999105	+	0.0422920i	$0.986534\pi$
$600$		0			0
$601$	−9.76324	−	16.9104i	−0.398251	−	0.689791i	0.595259	−	0.803534i	$-0.297049\pi$
$601$	−9.76324	−	16.9104i	−0.398251	−	0.689791i	−0.993510	+	0.113743i	$0.963716\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.272138	−	0.471356i	−0.0110640	−	0.0191634i
$606$		0			0
$607$	9.14567	−	15.8408i	0.371211	−	0.642957i	−0.618541	−	0.785753i	$-0.712276\pi$
$607$	9.14567	−	15.8408i	0.371211	−	0.642957i	0.989752	+	0.142796i	$0.0456092\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	38.8095			1.57007
$612$		0			0
$613$	−15.7303			−0.635339			−0.317669	−	0.948202i	$-0.602900\pi$
$613$	−15.7303			−0.635339			−0.317669	+	0.948202i	$0.602900\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.939286	−	1.62689i	0.0378142	−	0.0654961i	−0.846499	−	0.532390i	$-0.821294\pi$
$617$	0.939286	−	1.62689i	0.0378142	−	0.0654961i	0.884313	+	0.466894i	$0.154627\pi$
$618$		0			0
$619$	13.1692	+	22.8097i	0.529314	+	0.916799i	0.999415	+	0.0341864i	$0.0108840\pi$
$619$	13.1692	+	22.8097i	0.529314	+	0.916799i	−0.470101	+	0.882612i	$0.655783\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.56718	+	7.91058i	0.182980	+	0.316931i
$624$		0			0
$625$	−12.4229	+	21.5172i	−0.496918	+	0.860687i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	52.2805			2.08456
$630$		0			0
$631$	−32.5784			−1.29693			−0.648463	−	0.761246i	$-0.724588\pi$
$631$	−32.5784			−1.29693			−0.648463	+	0.761246i	$0.724588\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.688529	−	1.19257i	0.0273234	−	0.0473256i
$636$		0			0
$637$	15.1255	+	26.1982i	0.599296	+	1.03801i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.18635	−	2.05481i	−0.0468579	−	0.0811602i	0.841645	−	0.540031i	$-0.181587\pi$
$641$	−1.18635	−	2.05481i	−0.0468579	−	0.0811602i	−0.888503	+	0.458871i	$0.848254\pi$
$642$		0			0
$643$	0.902835	−	1.56376i	0.0356043	−	0.0616685i	−0.847674	−	0.530517i	$-0.821998\pi$
$643$	0.902835	−	1.56376i	0.0356043	−	0.0616685i	0.883278	+	0.468849i	$0.155331\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.00144			−0.314569			−0.157284	−	0.987553i	$-0.550274\pi$
$647$	−8.00144			−0.314569			−0.157284	+	0.987553i	$0.550274\pi$
$648$		0			0
$649$	−57.6601			−2.26336
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.90400	−	6.76193i	0.152775	−	0.264615i	−0.779471	−	0.626438i	$-0.784512\pi$
$653$	3.90400	−	6.76193i	0.152775	−	0.264615i	0.932247	+	0.361823i	$0.117846\pi$
$654$		0			0
$655$	−0.580724	−	1.00584i	−0.0226908	−	0.0393016i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	21.3737	+	37.0204i	0.832602	+	1.44211i	0.895968	+	0.444119i	$0.146483\pi$
$659$	21.3737	+	37.0204i	0.832602	+	1.44211i	−0.0633655	+	0.997990i	$0.520183\pi$
$660$		0			0
$661$	11.0501	−	19.1394i	0.429801	−	0.744437i	−0.567054	−	0.823680i	$-0.691917\pi$
$661$	11.0501	−	19.1394i	0.429801	−	0.744437i	0.996855	+	0.0792434i	$0.0252504\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.0991741			0.00384581
$666$		0			0
$667$	−13.8179			−0.535032
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−5.47281	+	9.47918i	−0.211275	+	0.365940i
$672$		0			0
$673$	−11.8145	−	20.4634i	−0.455416	−	0.788804i	0.543296	−	0.839541i	$-0.317176\pi$
$673$	−11.8145	−	20.4634i	−0.455416	−	0.788804i	−0.998712	+	0.0507371i	$0.983843\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.68742	−	2.92270i	−0.0648529	−	0.112329i	0.831776	−	0.555112i	$-0.187324\pi$
$677$	−1.68742	−	2.92270i	−0.0648529	−	0.112329i	−0.896629	+	0.442783i	$0.853991\pi$
$678$		0			0
$679$	−1.87525	+	3.24803i	−0.0719655	+	0.124648i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−19.5787			−0.749158			−0.374579	−	0.927195i	$-0.622213\pi$
$683$	−19.5787			−0.749158			−0.374579	+	0.927195i	$0.622213\pi$
$684$		0			0
$685$	−0.0167772			−0.000641024
$686$		0			0
$687$		0			0
$688$		0			0
$689$	32.1939	−	55.7614i	1.22649	−	2.12434i
$690$		0			0
$691$	−13.4414	−	23.2813i	−0.511337	−	0.885661i	−0.999914	−	0.0131402i	$-0.995817\pi$
$691$	−13.4414	−	23.2813i	−0.511337	−	0.885661i	0.488577	−	0.872521i	$-0.337516\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.586203	−	1.01533i	−0.0222360	−	0.0385138i
$696$		0			0
$697$	−8.74275	+	15.1429i	−0.331155	+	0.573578i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−1.75124			−0.0661433			−0.0330717	−	0.999453i	$-0.510529\pi$
$701$	−1.75124			−0.0661433			−0.0330717	+	0.999453i	$0.510529\pi$
$702$		0			0
$703$	−8.63666			−0.325738
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.41890	−	7.65376i	0.166190	−	0.287849i
$708$		0			0
$709$	20.2869	+	35.1379i	0.761891	+	1.31963i	0.941875	+	0.335964i	$0.109062\pi$
$709$	20.2869	+	35.1379i	0.761891	+	1.31963i	−0.179984	+	0.983669i	$0.557605\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.40208	−	12.8208i	−0.277210	−	0.480142i
$714$		0			0
$715$	1.01771	−	1.76273i	0.0380603	−	0.0659224i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.4156			0.574906			0.287453	−	0.957795i	$-0.407191\pi$
$719$	15.4156			0.574906			0.287453	+	0.957795i	$0.407191\pi$
$720$		0			0
$721$	8.31840			0.309793
$722$		0			0
$723$		0			0
$724$		0			0
$725$	9.93171	−	17.2022i	0.368854	−	0.638875i
$726$		0			0
$727$	10.4601	+	18.1175i	0.387945	+	0.671940i	0.992173	−	0.124871i	$-0.0398518\pi$
$727$	10.4601	+	18.1175i	0.387945	+	0.671940i	−0.604228	+	0.796811i	$0.706518\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	20.9670	+	36.3159i	0.775492	+	1.34319i
$732$		0			0
$733$	−4.01569	+	6.95538i	−0.148323	+	0.256903i	−0.930608	−	0.366018i	$-0.880721\pi$
$733$	−4.01569	+	6.95538i	−0.148323	+	0.256903i	0.782285	+	0.622921i	$0.214054\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.3946			0.493396
$738$		0			0
$739$	42.3366			1.55738			0.778688	−	0.627412i	$-0.215886\pi$
$739$	42.3366			1.55738			0.778688	+	0.627412i	$0.215886\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−23.5369	+	40.7671i	−0.863484	+	1.49560i	0.00505969	+	0.999987i	$0.498389\pi$
$743$	−23.5369	+	40.7671i	−0.863484	+	1.49560i	−0.868544	+	0.495612i	$0.834944\pi$
$744$		0			0
$745$	−0.356847	−	0.618078i	−0.0130739	−	0.0226446i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.75807	+	8.24121i	0.173856	+	0.301127i
$750$		0			0
$751$	−13.4439	+	23.2856i	−0.490576	+	0.849703i	−0.999941	−	0.0108475i	$-0.996547\pi$
$751$	−13.4439	+	23.2856i	−0.490576	+	0.849703i	0.509365	+	0.860551i	$0.329880\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.18680			−0.0795857
$756$		0			0
$757$	26.9419			0.979220			0.489610	−	0.871942i	$-0.337139\pi$
$757$	26.9419			0.979220			0.489610	+	0.871942i	$0.337139\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.33208	−	4.03928i	0.0845377	−	0.146424i	−0.820656	−	0.571422i	$-0.806392\pi$
$761$	2.33208	−	4.03928i	0.0845377	−	0.146424i	0.905194	+	0.424998i	$0.139725\pi$
$762$		0			0
$763$	−0.847448	−	1.46782i	−0.0306797	−	0.0531388i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−35.3583	−	61.2424i	−1.27671	−	2.21133i
$768$		0			0
$769$	3.90057	−	6.75598i	0.140658	−	0.243627i	−0.787087	−	0.616843i	$-0.788412\pi$
$769$	3.90057	−	6.75598i	0.140658	−	0.243627i	0.927745	+	0.373216i	$0.121745\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	46.6151			1.67663			0.838315	−	0.545186i	$-0.183541\pi$
$773$	46.6151			1.67663			0.838315	+	0.545186i	$0.183541\pi$
$774$		0			0
$775$	21.2812			0.764442
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.44429	−	2.50158i	0.0517470	−	0.0896285i
$780$		0			0
$781$	−29.3813	−	50.8900i	−1.05135	−	1.82099i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.148201	+	0.256692i	0.00528954	+	0.00916175i
$786$		0			0
$787$	−20.6639	+	35.7909i	−0.736588	+	1.27581i	0.217435	+	0.976075i	$0.430231\pi$
$787$	−20.6639	+	35.7909i	−0.736588	+	1.27581i	−0.954023	+	0.299733i	$0.903102\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12.2337			−0.434979
$792$		0			0
$793$	−13.4241			−0.476705
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.799020	+	1.38394i	−0.0283027	+	0.0490218i	−0.879830	−	0.475289i	$-0.842344\pi$
$797$	−0.799020	+	1.38394i	−0.0283027	+	0.0490218i	0.851527	+	0.524311i	$0.175677\pi$
$798$		0			0
$799$	24.3635	+	42.1989i	0.861920	+	1.49289i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	23.5530	+	40.7950i	0.831167	+	1.43962i
$804$		0			0
$805$	0.167245	−	0.289677i	0.00589462	−	0.0102098i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	51.3152			1.80415			0.902074	−	0.431582i	$-0.142044\pi$
$809$	51.3152			1.80415			0.902074	+	0.431582i	$0.142044\pi$
$810$		0			0
$811$	2.89450			0.101640			0.0508198	−	0.998708i	$-0.483817\pi$
$811$	2.89450			0.101640			0.0508198	+	0.998708i	$0.483817\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.182443	−	0.316000i	0.00639069	−	0.0110690i
$816$		0			0
$817$	−3.46371	−	5.99932i	−0.121180	−	0.209890i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.90648	−	17.1585i	−0.345738	−	0.598837i	0.639749	−	0.768584i	$-0.279038\pi$
$821$	−9.90648	−	17.1585i	−0.345738	−	0.598837i	−0.985488	+	0.169747i	$0.945705\pi$
$822$		0			0
$823$	−11.8416	+	20.5102i	−0.412772	+	0.714941i	−0.995192	−	0.0979466i	$-0.968773\pi$
$823$	−11.8416	+	20.5102i	−0.412772	+	0.714941i	0.582420	+	0.812888i	$0.302106\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	24.3876			0.848040			0.424020	−	0.905653i	$-0.360619\pi$
$827$	24.3876			0.848040			0.424020	+	0.905653i	$0.360619\pi$
$828$		0			0
$829$	−32.4277			−1.12626			−0.563130	−	0.826369i	$-0.690403\pi$
$829$	−32.4277			−1.12626			−0.563130	+	0.826369i	$0.690403\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−18.9908	+	32.8930i	−0.657991	+	1.13967i
$834$		0			0
$835$	0.233051	+	0.403657i	0.00806507	+	0.0139691i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−9.20338	−	15.9407i	−0.317736	−	0.550335i	0.662279	−	0.749257i	$-0.269589\pi$
$839$	−9.20338	−	15.9407i	−0.317736	−	0.550335i	−0.980015	+	0.198922i	$0.936256\pi$
$840$		0			0
$841$	6.57634	−	11.3906i	0.226770	−	0.392778i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.17819			0.0405308
$846$		0			0
$847$	5.10154			0.175291
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−14.5647	+	25.2268i	−0.499271	+	0.864764i
$852$		0			0
$853$	1.36747	+	2.36853i	0.0468214	+	0.0810970i	0.888486	−	0.458903i	$-0.151758\pi$
$853$	1.36747	+	2.36853i	0.0468214	+	0.0810970i	−0.841665	+	0.540000i	$0.818424\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−27.7693	−	48.0978i	−0.948581	−	1.64299i	−0.748417	−	0.663228i	$-0.769186\pi$
$857$	−27.7693	−	48.0978i	−0.948581	−	1.64299i	−0.200164	−	0.979762i	$-0.564147\pi$
$858$		0			0
$859$	2.79797	−	4.84623i	0.0954655	−	0.165351i	−0.814337	−	0.580392i	$-0.802899\pi$
$859$	2.79797	−	4.84623i	0.0954655	−	0.165351i	0.909803	+	0.415041i	$0.136233\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−27.4069			−0.932941			−0.466470	−	0.884537i	$-0.654475\pi$
$863$	−27.4069			−0.932941			−0.466470	+	0.884537i	$0.654475\pi$
$864$		0			0
$865$	1.61628			0.0549550
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.59261	+	4.49053i	−0.0879482	+	0.152331i
$870$		0			0
$871$	8.21382	+	14.2268i	0.278315	+	0.482055i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.481330	+	0.833687i	0.0162719	+	0.0281838i
$876$		0			0
$877$	16.9823	−	29.4142i	0.573451	−	0.993246i	−0.422757	−	0.906243i	$-0.638938\pi$
$877$	16.9823	−	29.4142i	0.573451	−	0.993246i	0.996208	−	0.0870032i	$-0.0277290\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−2.51718			−0.0848060			−0.0424030	−	0.999101i	$-0.513501\pi$
$881$	−2.51718			−0.0848060			−0.0424030	+	0.999101i	$0.513501\pi$
$882$		0			0
$883$	4.77456			0.160677			0.0803384	−	0.996768i	$-0.474400\pi$
$883$	4.77456			0.160677			0.0803384	+	0.996768i	$0.474400\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.8557	+	29.1949i	−0.565958	+	0.980268i	0.431002	+	0.902351i	$0.358160\pi$
$887$	−16.8557	+	29.1949i	−0.565958	+	0.980268i	−0.996960	+	0.0779170i	$0.975173\pi$
$888$		0			0
$889$	6.45364	+	11.1780i	0.216448	+	0.374899i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.02482	−	6.97118i	−0.134685	−	0.233282i
$894$		0			0
$895$	0.725457	−	1.25653i	0.0242493	−	0.0420011i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−16.9784			−0.566262
$900$		0			0
$901$	80.8416			2.69322
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.813738	−	1.40944i	0.0270496	−	0.0468512i
$906$		0			0
$907$	10.6815	+	18.5009i	0.354672	+	0.614311i	0.987062	−	0.160340i	$-0.0512591\pi$
$907$	10.6815	+	18.5009i	0.354672	+	0.614311i	−0.632389	+	0.774651i	$0.717926\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.73162	+	11.6595i	0.223029	+	0.386297i	0.955726	−	0.294257i	$-0.0950723\pi$
$911$	6.73162	+	11.6595i	0.223029	+	0.386297i	−0.732698	+	0.680554i	$0.761739\pi$
$912$		0			0
$913$	−10.6329	+	18.4168i	−0.351899	+	0.609507i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	10.8864			0.359499
$918$		0			0
$919$	−6.18401			−0.203992			−0.101996	−	0.994785i	$-0.532523\pi$
$919$	−6.18401			−0.203992			−0.101996	+	0.994785i	$0.532523\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	36.0344	−	62.4134i	1.18609	−	2.05436i
$924$		0			0
$925$	−20.9369	−	36.2638i	−0.688402	−	1.19235i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	19.2736	+	33.3829i	0.632347	+	1.09526i	0.987071	+	0.160285i	$0.0512414\pi$
$929$	19.2736	+	33.3829i	0.632347	+	1.09526i	−0.354724	+	0.934971i	$0.615425\pi$
$930$		0			0
$931$	3.13724	−	5.43386i	0.102819	−	0.178088i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.55557			0.0835760
$936$		0			0
$937$	−24.5536			−0.802132			−0.401066	−	0.916049i	$-0.631360\pi$
$937$	−24.5536			−0.802132			−0.401066	+	0.916049i	$0.631360\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−8.95079	+	15.5032i	−0.291787	+	0.505391i	−0.974232	−	0.225546i	$-0.927583\pi$
$941$	−8.95079	+	15.5032i	−0.291787	+	0.505391i	0.682445	+	0.730937i	$0.260917\pi$
$942$		0			0
$943$	−4.87124	−	8.43724i	−0.158630	−	0.274754i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.1880	−	28.0384i	−0.526039	−	0.911127i	−0.999540	−	0.0303331i	$-0.990343\pi$
$947$	−16.1880	−	28.0384i	−0.526039	−	0.911127i	0.473501	−	0.880793i	$-0.342990\pi$
$948$		0			0
$949$	−28.8863	+	50.0326i	−0.937689	+	1.62413i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−29.9596			−0.970487			−0.485243	−	0.874379i	$-0.661269\pi$
$953$	−29.9596			−0.970487			−0.485243	+	0.874379i	$0.661269\pi$
$954$		0			0
$955$	0.495088			0.0160207
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.0786271	−	0.136186i	0.00253900	−	0.00439768i
$960$		0			0
$961$	6.40489	+	11.0936i	0.206609	+	0.357858i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.308391	+	0.534148i	0.00992745	+	0.0171948i
$966$		0			0
$967$	18.3033	−	31.7023i	0.588596	−	1.01948i	−0.405821	−	0.913953i	$-0.633014\pi$
$967$	18.3033	−	31.7023i	0.588596	−	1.01948i	0.994417	−	0.105525i	$-0.0336523\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	25.0872			0.805086			0.402543	−	0.915401i	$-0.368126\pi$
$971$	25.0872			0.805086			0.402543	+	0.915401i	$0.368126\pi$
$972$		0			0
$973$	10.9891			0.352293
$974$		0			0
$975$		0			0
$976$		0			0
$977$	9.64557	−	16.7066i	0.308589	−	0.534492i	−0.669465	−	0.742844i	$-0.733477\pi$
$977$	9.64557	−	16.7066i	0.308589	−	0.534492i	0.978054	+	0.208352i	$0.0668099\pi$
$978$		0			0
$979$	−19.4421	−	33.6747i	−0.621371	−	1.07625i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22.9685	−	39.7827i	−0.732583	−	1.26887i	−0.955776	−	0.294096i	$-0.904981\pi$
$983$	−22.9685	−	39.7827i	−0.732583	−	1.26887i	0.223193	−	0.974774i	$-0.428352\pi$
$984$		0			0
$985$	1.01265	−	1.75396i	0.0322657	−	0.0558859i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−23.3646			−0.742949
$990$		0			0
$991$	−51.1298			−1.62419			−0.812096	−	0.583524i	$-0.801674\pi$
$991$	−51.1298			−1.62419			−0.812096	+	0.583524i	$0.801674\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.882974	+	1.52936i	−0.0279922	+	0.0484838i
$996$		0			0
$997$	−20.8777	−	36.1613i	−0.661205	−	1.14524i	−0.980299	−	0.197517i	$-0.936712\pi$
$997$	−20.8777	−	36.1613i	−0.661205	−	1.14524i	0.319095	−	0.947723i	$-0.396621\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2916.2.e.d.973.5		18
3.2	odd	2		2916.2.e.c.973.5		18
9.2	odd	6		2916.2.e.c.1945.5		18
9.4	even	3		2916.2.a.c.1.5		9
9.5	odd	6		2916.2.a.d.1.5		9
9.7	even	3	inner	2916.2.e.d.1945.5		18
27.2	odd	18		972.2.i.c.757.2		18
27.4	even	9		972.2.i.b.217.2		18
27.5	odd	18		972.2.i.a.541.2		18
27.7	even	9		972.2.i.d.433.2		18
27.11	odd	18		108.2.i.a.49.3	✓	18
27.13	even	9		324.2.i.a.289.2		18
27.14	odd	18		108.2.i.a.97.3	yes	18
27.16	even	9		324.2.i.a.37.2		18
27.20	odd	18		972.2.i.a.433.2		18
27.22	even	9		972.2.i.d.541.2		18
27.23	odd	18		972.2.i.c.217.2		18
27.25	even	9		972.2.i.b.757.2		18
108.11	even	18		432.2.u.d.49.1		18
108.95	even	18		432.2.u.d.97.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.49.3	✓	18	27.11	odd	18
108.2.i.a.97.3	yes	18	27.14	odd	18
324.2.i.a.37.2		18	27.16	even	9
324.2.i.a.289.2		18	27.13	even	9
432.2.u.d.49.1		18	108.11	even	18
432.2.u.d.97.1		18	108.95	even	18
972.2.i.a.433.2		18	27.20	odd	18
972.2.i.a.541.2		18	27.5	odd	18
972.2.i.b.217.2		18	27.4	even	9
972.2.i.b.757.2		18	27.25	even	9
972.2.i.c.217.2		18	27.23	odd	18
972.2.i.c.757.2		18	27.2	odd	18
972.2.i.d.433.2		18	27.7	even	9
972.2.i.d.541.2		18	27.22	even	9
2916.2.a.c.1.5		9	9.4	even	3
2916.2.a.d.1.5		9	9.5	odd	6
2916.2.e.c.973.5		18	3.2	odd	2
2916.2.e.c.1945.5		18	9.2	odd	6
2916.2.e.d.973.5		18	1.1	even	1	trivial
2916.2.e.d.1945.5		18	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2916 = 2^{2} \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2916.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0506977 + 0.0878110i) q^{5} +(-0.475194 - 0.823060i) q^{7} +O(q^{10})\)	\(q+(-0.0506977 + 0.0878110i) q^{5} +(-0.475194 - 0.823060i) q^{7} +(2.02286 + 3.50370i) q^{11} +(-2.48091 + 4.29707i) q^{13} -6.22979 q^{17} +1.02915 q^{19} +(1.73554 - 3.00604i) q^{23} +(2.49486 + 4.32122i) q^{25} +(-1.99043 - 3.44753i) q^{29} +(2.13250 - 3.69360i) q^{31} +0.0963650 q^{35} -8.39203 q^{37} +(1.40338 - 2.43072i) q^{41} +(-3.36560 - 5.82939i) q^{43} +(-3.91081 - 6.77373i) q^{47} +(3.04838 - 5.27995i) q^{49} -12.9766 q^{53} -0.410217 q^{55} +(-7.12606 + 12.3427i) q^{59} +(1.35274 + 2.34301i) q^{61} +(-0.251553 - 0.435703i) q^{65} +(1.65540 - 2.86724i) q^{67} -14.5247 q^{71} +11.6434 q^{73} +(1.92250 - 3.32987i) q^{77} +(0.640827 + 1.10995i) q^{79} +(2.62820 + 4.55217i) q^{83} +(0.315836 - 0.547044i) q^{85} -9.61118 q^{89} +4.71566 q^{91} +(-0.0521756 + 0.0903707i) q^{95} +(-1.97314 - 3.41758i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{5}+O(q^{10}) \) 18 * q + 6 * q^5	\( 18 q + 6 q^{5} + 6 q^{11} - 24 q^{17} + 3 q^{23} - 9 q^{25} + 24 q^{29} - 42 q^{35} + 33 q^{41} + 9 q^{47} - 9 q^{49} - 66 q^{53} + 30 q^{59} + 9 q^{61} + 39 q^{65} + 9 q^{67} - 24 q^{71} - 18 q^{73} + 39 q^{77} + 36 q^{83} - 96 q^{89} - 18 q^{91} + 12 q^{95}+O(q^{100}) \) 18 * q + 6 * q^5 + 6 * q^11 - 24 * q^17 + 3 * q^23 - 9 * q^25 + 24 * q^29 - 42 * q^35 + 33 * q^41 + 9 * q^47 - 9 * q^49 - 66 * q^53 + 30 * q^59 + 9 * q^61 + 39 * q^65 + 9 * q^67 - 24 * q^71 - 18 * q^73 + 39 * q^77 + 36 * q^83 - 96 * q^89 - 18 * q^91 + 12 * q^95

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