LMFDB - Embedded newform 3564.2.i.a.2377.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3564,2,Mod(1189,3564)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3564, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3564.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3564 = 2^{2} \cdot 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3564.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$28.4586832804$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2377.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3564.2377
Dual form			3564.2.i.a.1189.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{5} +(-1.00000 - 1.73205i) q^{7} +O(q^{10})$	$q+(-1.50000 + 2.59808i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{11} +(2.00000 - 3.46410i) q^{13} -6.00000 q^{17} +8.00000 q^{19} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-2.50000 + 4.33013i) q^{31} +6.00000 q^{35} -1.00000 q^{37} +(5.00000 + 8.66025i) q^{43} +(1.50000 - 2.59808i) q^{49} +6.00000 q^{53} +3.00000 q^{55} +(1.50000 - 2.59808i) q^{59} +(2.00000 + 3.46410i) q^{61} +(6.00000 + 10.3923i) q^{65} +(0.500000 - 0.866025i) q^{67} -15.0000 q^{71} -4.00000 q^{73} +(-1.00000 + 1.73205i) q^{77} +(-1.00000 - 1.73205i) q^{79} +(3.00000 + 5.19615i) q^{83} +(9.00000 - 15.5885i) q^{85} +9.00000 q^{89} -8.00000 q^{91} +(-12.0000 + 20.7846i) q^{95} +(3.50000 + 6.06218i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{5} - 2 q^{7}+O(q^{10}) $ 2 * q - 3 * q^5 - 2 * q^7	$ 2 q - 3 q^{5} - 2 q^{7} - q^{11} + 4 q^{13} - 12 q^{17} + 16 q^{19} - 3 q^{23} - 4 q^{25} - 5 q^{31} + 12 q^{35} - 2 q^{37} + 10 q^{43} + 3 q^{49} + 12 q^{53} + 6 q^{55} + 3 q^{59} + 4 q^{61} + 12 q^{65} + q^{67} - 30 q^{71} - 8 q^{73} - 2 q^{77} - 2 q^{79} + 6 q^{83} + 18 q^{85} + 18 q^{89} - 16 q^{91} - 24 q^{95} + 7 q^{97}+O(q^{100}) $ 2 * q - 3 * q^5 - 2 * q^7 - q^11 + 4 * q^13 - 12 * q^17 + 16 * q^19 - 3 * q^23 - 4 * q^25 - 5 * q^31 + 12 * q^35 - 2 * q^37 + 10 * q^43 + 3 * q^49 + 12 * q^53 + 6 * q^55 + 3 * q^59 + 4 * q^61 + 12 * q^65 + q^67 - 30 * q^71 - 8 * q^73 - 2 * q^77 - 2 * q^79 + 6 * q^83 + 18 * q^85 + 18 * q^89 - 16 * q^91 - 24 * q^95 + 7 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3564\mathbb{Z}\right)^\times$.

$n$	$1541$	$1783$	$2917$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$	8.00000			1.83533			0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000			1.83533			0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.00000			1.01419
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	3.00000			0.404520
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.00000	+	10.3923i	0.744208	+	1.28901i
$66$		0			0
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i	−0.833866	−	0.551967i	$-0.813877\pi$
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i	0.894951	+	0.446165i	$0.147211\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−15.0000			−1.78017			−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000			−1.78017			−0.890086	+	0.455792i	$0.849356\pi$
$72$		0			0
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.00000	+	1.73205i	−0.113961	+	0.197386i
$78$		0			0
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	0.804272	−	0.594261i	$-0.202555\pi$
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	−0.916781	+	0.399390i	$0.869222\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	0.982372	−	0.186938i	$-0.0598564\pi$
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	−0.653079	+	0.757290i	$0.726523\pi$
$84$		0			0
$85$	9.00000	−	15.5885i	0.976187	−	1.69081i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$		0			0
$91$	−8.00000			−0.838628
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−12.0000	+	20.7846i	−1.23117	+	2.13246i
$96$		0			0
$97$	3.50000	+	6.06218i	0.355371	+	0.615521i	0.987181	−	0.159602i	$-0.0510211\pi$
$97$	3.50000	+	6.06218i	0.355371	+	0.615521i	−0.631810	+	0.775123i	$0.717688\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.0623905	+	0.998052i	$0.480128\pi$
$102$		0			0
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.00000			−0.580042			−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000			−0.580042			−0.290021	+	0.957020i	$0.593662\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	0.260955	+	0.965351i	$0.415962\pi$
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	−0.966496	+	0.256681i	$0.917371\pi$
$114$		0			0
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.00000	+	10.3923i	0.550019	+	0.952661i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		0			0
$133$	−8.00000	−	13.8564i	−0.693688	−	1.20150i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$		0			0
$139$	−7.00000	+	12.1244i	−0.593732	+	1.02837i	0.399992	+	0.916519i	$0.369013\pi$
$139$	−7.00000	+	12.1244i	−0.593732	+	1.02837i	−0.993724	+	0.111856i	$0.964321\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.00000			−0.334497
$144$		0			0
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.50000	−	12.9904i	−0.602414	−	1.04341i
$156$		0			0
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	−0.948373	−	0.317156i	$-0.897272\pi$
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	0.748852	+	0.662738i	$0.230606\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.00000			0.472866
$162$		0			0
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$		0			0
$175$	−4.00000	+	6.92820i	−0.302372	+	0.523723i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.00000			0.672692			0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000			0.672692			0.336346	+	0.941739i	$0.390809\pi$
$180$		0			0
$181$	−13.0000			−0.966282			−0.483141	−	0.875542i	$-0.660504\pi$
$181$	−13.0000			−0.966282			−0.483141	+	0.875542i	$0.660504\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.50000	−	2.59808i	0.110282	−	0.191014i
$186$		0			0
$187$	3.00000	+	5.19615i	0.219382	+	0.379980i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.5000	−	18.1865i	−0.759753	−	1.31593i	−0.942976	−	0.332860i	$-0.891986\pi$
$191$	−10.5000	−	18.1865i	−0.759753	−	1.31593i	0.183223	−	0.983071i	$-0.441347\pi$
$192$		0			0
$193$	−10.0000	+	17.3205i	−0.719816	+	1.24676i	0.241257	+	0.970461i	$0.422440\pi$
$193$	−10.0000	+	17.3205i	−0.719816	+	1.24676i	−0.961073	+	0.276296i	$0.910893\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.00000	−	6.92820i	−0.276686	−	0.479234i
$210$		0			0
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	0.283918	+	0.958849i	$0.408366\pi$
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	−0.972346	+	0.233544i	$0.924968\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−30.0000			−2.04598
$216$		0			0
$217$	10.0000			0.678844
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−12.0000	+	20.7846i	−0.807207	+	1.39812i
$222$		0			0
$223$	−8.50000	−	14.7224i	−0.569202	−	0.985887i	−0.996645	−	0.0818447i	$-0.973919\pi$
$223$	−8.50000	−	14.7224i	−0.569202	−	0.985887i	0.427443	−	0.904042i	$-0.359414\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.00000	+	5.19615i	0.199117	+	0.344881i	0.948242	−	0.317547i	$-0.102859\pi$
$227$	3.00000	+	5.19615i	0.199117	+	0.344881i	−0.749125	+	0.662428i	$0.769526\pi$
$228$		0			0
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	−0.752536	−	0.658551i	$-0.771170\pi$
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	0.946590	+	0.322440i	$0.104503\pi$
$240$		0			0
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	0.707953	−	0.706260i	$-0.249619\pi$
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	−0.965615	+	0.259975i	$0.916286\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.50000	+	7.79423i	0.287494	+	0.497955i
$246$		0			0
$247$	16.0000	−	27.7128i	1.01806	−	1.76332i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.00000			0.568075			0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000			0.568075			0.284037	+	0.958813i	$0.408326\pi$
$252$		0			0
$253$	3.00000			0.188608
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$		0			0
$259$	1.00000	+	1.73205i	0.0621370	+	0.107624i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	0.997906	+	0.0646755i	$0.0206012\pi$
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	−0.442943	+	0.896550i	$0.646065\pi$
$264$		0			0
$265$	−9.00000	+	15.5885i	−0.552866	+	0.957591i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.00000			0.365826			0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000			0.365826			0.182913	+	0.983129i	$0.441447\pi$
$270$		0			0
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	−0.999069	−	0.0431402i	$-0.986264\pi$
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	0.462174	−	0.886789i	$-0.347070\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$293$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$294$		0			0
$295$	4.50000	+	7.79423i	0.262000	+	0.453798i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	10.0000	−	17.3205i	0.576390	−	0.998337i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−12.0000			−0.687118
$306$		0			0
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$		0			0
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	0.879810	−	0.475325i	$-0.157669\pi$
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	−0.851549	+	0.524276i	$0.824336\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	16.5000	+	28.5788i	0.926732	+	1.60515i	0.788751	+	0.614713i	$0.210728\pi$
$317$	16.5000	+	28.5788i	0.926732	+	1.60515i	0.137981	+	0.990435i	$0.455939\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−48.0000			−2.67079
$324$		0			0
$325$	−16.0000			−0.887520
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	0.946038	−	0.324057i	$-0.105047\pi$
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	−0.753660	+	0.657264i	$0.771714\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.50000	+	2.59808i	0.0819538	+	0.141948i
$336$		0			0
$337$	−1.00000	+	1.73205i	−0.0544735	+	0.0943508i	−0.891976	−	0.452082i	$-0.850681\pi$
$337$	−1.00000	+	1.73205i	−0.0544735	+	0.0943508i	0.837503	+	0.546433i	$0.184015\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	5.00000			0.270765
$342$		0			0
$343$	−20.0000			−1.07990
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	−0.997592	−	0.0693543i	$-0.977906\pi$
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	0.438733	−	0.898617i	$-0.355427\pi$
$354$		0			0
$355$	22.5000	−	38.9711i	1.19418	−	2.06837i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	36.0000			1.90001			0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000			1.90001			0.950004	+	0.312239i	$0.101079\pi$
$360$		0			0
$361$	45.0000			2.36842
$362$		0			0
$363$		0			0
$364$		0			0
$365$	6.00000	−	10.3923i	0.314054	−	0.543958i
$366$		0			0
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	0.999989	−	0.00473247i	$-0.00150640\pi$
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	−0.504093	+	0.863649i	$0.668173\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.00000	−	10.3923i	−0.311504	−	0.539542i
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	29.0000			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−13.5000	+	23.3827i	−0.689818	+	1.19480i	0.282079	+	0.959391i	$0.408976\pi$
$383$	−13.5000	+	23.3827i	−0.689818	+	1.19480i	−0.971897	+	0.235408i	$0.924357\pi$
$384$		0			0
$385$	−3.00000	−	5.19615i	−0.152894	−	0.264820i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−13.5000	−	23.3827i	−0.684477	−	1.18555i	−0.973601	−	0.228257i	$-0.926697\pi$
$389$	−13.5000	−	23.3827i	−0.684477	−	1.18555i	0.289124	−	0.957292i	$-0.406636\pi$
$390$		0			0
$391$	9.00000	−	15.5885i	0.455150	−	0.788342i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	6.00000			0.301893
$396$		0			0
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	−0.548911	−	0.835881i	$-0.684957\pi$
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	0.998350	+	0.0574304i	$0.0182907\pi$
$402$		0			0
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.500000	+	0.866025i	0.0247841	+	0.0429273i
$408$		0			0
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	−0.889689	−	0.456566i	$-0.849079\pi$
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	0.840243	+	0.542211i	$0.182412\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.00000			−0.295241
$414$		0			0
$415$	−18.0000			−0.883585
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	−0.681426	−	0.731887i	$-0.738640\pi$
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	0.974546	+	0.224189i	$0.0719734\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.0000	+	20.7846i	0.582086	+	1.00820i
$426$		0			0
$427$	4.00000	−	6.92820i	0.193574	−	0.335279i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−18.0000			−0.867029			−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000			−0.867029			−0.433515	+	0.901146i	$0.642727\pi$
$432$		0			0
$433$	29.0000			1.39365			0.696826	−	0.717241i	$-0.254595\pi$
$433$	29.0000			1.39365			0.696826	+	0.717241i	$0.254595\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−12.0000	+	20.7846i	−0.574038	+	0.994263i
$438$		0			0
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.5000	−	18.1865i	−0.498870	−	0.864068i	0.501129	−	0.865373i	$-0.332918\pi$
$443$	−10.5000	−	18.1865i	−0.498870	−	0.864068i	−0.999999	+	0.00130426i	$0.999585\pi$
$444$		0			0
$445$	−13.5000	+	23.3827i	−0.639961	+	1.10845i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−3.00000			−0.141579			−0.0707894	−	0.997491i	$-0.522552\pi$
$449$	−3.00000			−0.141579			−0.0707894	+	0.997491i	$0.522552\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$	12.0000	−	20.7846i	0.562569	−	0.974398i
$456$		0			0
$457$	14.0000	+	24.2487i	0.654892	+	1.13431i	0.981921	+	0.189292i	$0.0606194\pi$
$457$	14.0000	+	24.2487i	0.654892	+	1.13431i	−0.327028	+	0.945015i	$0.606047\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	0.971248	−	0.238071i	$-0.0765153\pi$
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	−0.691800	+	0.722089i	$0.743182\pi$
$462$		0			0
$463$	−11.5000	+	19.9186i	−0.534450	+	0.925695i	0.464739	+	0.885448i	$0.346148\pi$
$463$	−11.5000	+	19.9186i	−0.534450	+	0.925695i	−0.999190	+	0.0402476i	$0.987185\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.00000			−0.138823			−0.0694117	−	0.997588i	$-0.522112\pi$
$467$	−3.00000			−0.138823			−0.0694117	+	0.997588i	$0.522112\pi$
$468$		0			0
$469$	−2.00000			−0.0923514
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.00000	−	8.66025i	0.229900	−	0.398199i
$474$		0			0
$475$	−16.0000	−	27.7128i	−0.734130	−	1.27155i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	0.695773	−	0.718262i	$-0.255062\pi$
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	−0.969920	+	0.243426i	$0.921729\pi$
$480$		0			0
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−21.0000			−0.953561
$486$		0			0
$487$	29.0000			1.31412			0.657058	−	0.753840i	$-0.271801\pi$
$487$	29.0000			1.31412			0.657058	+	0.753840i	$0.271801\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.0000	−	20.7846i	0.541552	−	0.937996i	−0.457263	−	0.889332i	$-0.651170\pi$
$491$	12.0000	−	20.7846i	0.541552	−	0.937996i	0.998815	−	0.0486647i	$-0.0154966\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	15.0000	+	25.9808i	0.672842	+	1.16540i
$498$		0			0
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	30.0000			1.33763			0.668817	−	0.743427i	$-0.266801\pi$
$503$	30.0000			1.33763			0.668817	+	0.743427i	$0.266801\pi$
$504$		0			0
$505$	−54.0000			−2.40297
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−10.5000	+	18.1865i	−0.465404	+	0.806104i	−0.999220	−	0.0394971i	$-0.987424\pi$
$509$	−10.5000	+	18.1865i	−0.465404	+	0.806104i	0.533815	+	0.845601i	$0.320758\pi$
$510$		0			0
$511$	4.00000	+	6.92820i	0.176950	+	0.306486i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−12.0000	−	20.7846i	−0.528783	−	0.915879i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$		0			0
$523$	8.00000			0.349816			0.174908	−	0.984585i	$-0.444037\pi$
$523$	8.00000			0.349816			0.174908	+	0.984585i	$0.444037\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	15.0000	−	25.9808i	0.653410	−	1.13174i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	9.00000	−	15.5885i	0.389104	−	0.673948i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.00000			−0.129219
$540$		0			0
$541$	−16.0000			−0.687894			−0.343947	−	0.938989i	$-0.611764\pi$
$541$	−16.0000			−0.687894			−0.343947	+	0.938989i	$0.611764\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.00000	+	5.19615i	−0.128506	+	0.222579i
$546$		0			0
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	0.767752	−	0.640747i	$-0.221375\pi$
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	−0.938779	+	0.344519i	$0.888042\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−2.00000	+	3.46410i	−0.0850487	+	0.147309i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.0000			0.762684			0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000			0.762684			0.381342	+	0.924434i	$0.375462\pi$
$558$		0			0
$559$	40.0000			1.69182
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$		0			0
$565$	−22.5000	−	38.9711i	−0.946582	−	1.63953i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$569$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$570$		0			0
$571$	−22.0000	+	38.1051i	−0.920671	+	1.59465i	−0.122292	+	0.992494i	$0.539025\pi$
$571$	−22.0000	+	38.1051i	−0.920671	+	1.59465i	−0.798379	+	0.602155i	$0.794309\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	17.0000			0.707719			0.353860	−	0.935299i	$-0.384869\pi$
$577$	17.0000			0.707719			0.353860	+	0.935299i	$0.384869\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$		0			0
$583$	−3.00000	−	5.19615i	−0.124247	−	0.215203i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.00000	−	10.3923i	−0.247647	−	0.428936i	0.715226	−	0.698893i	$-0.246324\pi$
$587$	−6.00000	−	10.3923i	−0.247647	−	0.428936i	−0.962872	+	0.269957i	$0.912990\pi$
$588$		0			0
$589$	−20.0000	+	34.6410i	−0.824086	+	1.42736i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	36.0000			1.47834			0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000			1.47834			0.739171	+	0.673517i	$0.235217\pi$
$594$		0			0
$595$	−36.0000			−1.47586
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.50000	−	2.59808i	−0.0609837	−	0.105627i
$606$		0			0
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	−0.972396	−	0.233338i	$-0.925035\pi$
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	0.688274	+	0.725450i	$0.258368\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	32.0000			1.29247			0.646234	−	0.763139i	$-0.276343\pi$
$613$	32.0000			1.29247			0.646234	+	0.763139i	$0.276343\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	−0.626017	−	0.779809i	$-0.715316\pi$
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	0.988343	+	0.152242i	$0.0486493\pi$
$618$		0			0
$619$	−8.50000	−	14.7224i	−0.341644	−	0.591744i	0.643094	−	0.765787i	$-0.277650\pi$
$619$	−8.50000	−	14.7224i	−0.341644	−	0.591744i	−0.984738	+	0.174042i	$0.944317\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−9.00000	−	15.5885i	−0.360577	−	0.624538i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	6.00000			0.239236
$630$		0			0
$631$	−43.0000			−1.71180			−0.855901	−	0.517139i	$-0.826997\pi$
$631$	−43.0000			−1.71180			−0.855901	+	0.517139i	$0.826997\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	24.0000	−	41.5692i	0.952411	−	1.64962i
$636$		0			0
$637$	−6.00000	−	10.3923i	−0.237729	−	0.411758i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	0.937451	+	0.348117i	$0.113179\pi$
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	−0.167247	+	0.985915i	$0.553488\pi$
$642$		0			0
$643$	6.50000	−	11.2583i	0.256335	−	0.443985i	−0.708922	−	0.705287i	$-0.750818\pi$
$643$	6.50000	−	11.2583i	0.256335	−	0.443985i	0.965257	+	0.261301i	$0.0841516\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.00000			−0.117942			−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000			−0.117942			−0.0589711	+	0.998260i	$0.518782\pi$
$648$		0			0
$649$	−3.00000			−0.117760
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	−0.835182	−	0.549973i	$-0.814638\pi$
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	0.893882	+	0.448303i	$0.147971\pi$
$654$		0			0
$655$	−9.00000	−	15.5885i	−0.351659	−	0.609091i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−21.0000	−	36.3731i	−0.818044	−	1.41689i	−0.907122	−	0.420869i	$-0.861725\pi$
$659$	−21.0000	−	36.3731i	−0.818044	−	1.41689i	0.0890776	−	0.996025i	$-0.471608\pi$
$660$		0			0
$661$	−8.50000	+	14.7224i	−0.330612	+	0.572636i	−0.982632	−	0.185565i	$-0.940588\pi$
$661$	−8.50000	+	14.7224i	−0.330612	+	0.572636i	0.652020	+	0.758202i	$0.273922\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	48.0000			1.86136
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.00000	−	3.46410i	0.0772091	−	0.133730i
$672$		0			0
$673$	17.0000	+	29.4449i	0.655302	+	1.13502i	0.981818	+	0.189824i	$0.0607919\pi$
$673$	17.0000	+	29.4449i	0.655302	+	1.13502i	−0.326516	+	0.945192i	$0.605875\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	−0.914867	−	0.403755i	$-0.867705\pi$
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	0.107772	−	0.994176i	$-0.465628\pi$
$678$		0			0
$679$	7.00000	−	12.1244i	0.268635	−	0.465290i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−48.0000			−1.83667			−0.918334	−	0.395805i	$-0.870466\pi$
$683$	−48.0000			−1.83667			−0.918334	+	0.395805i	$0.870466\pi$
$684$		0			0
$685$	−27.0000			−1.03162
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$	0.500000	+	0.866025i	0.0190209	+	0.0329452i	0.875379	−	0.483437i	$-0.160612\pi$
$691$	0.500000	+	0.866025i	0.0190209	+	0.0329452i	−0.856358	+	0.516382i	$0.827278\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−21.0000	−	36.3731i	−0.796575	−	1.37971i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	−8.00000			−0.301726
$704$		0			0
$705$		0			0
$706$		0			0
$707$	18.0000	−	31.1769i	0.676960	−	1.17253i
$708$		0			0
$709$	18.5000	+	32.0429i	0.694782	+	1.20340i	0.970254	+	0.242089i	$0.0778325\pi$
$709$	18.5000	+	32.0429i	0.694782	+	1.20340i	−0.275472	+	0.961309i	$0.588834\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.50000	−	12.9904i	−0.280877	−	0.486494i
$714$		0			0
$715$	6.00000	−	10.3923i	0.224387	−	0.388650i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−45.0000			−1.67822			−0.839108	−	0.543964i	$-0.816923\pi$
$719$	−45.0000			−1.67822			−0.839108	+	0.543964i	$0.816923\pi$
$720$		0			0
$721$	16.0000			0.595871
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−8.50000	−	14.7224i	−0.315248	−	0.546025i	0.664243	−	0.747517i	$-0.268754\pi$
$727$	−8.50000	−	14.7224i	−0.315248	−	0.546025i	−0.979490	+	0.201492i	$0.935421\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−30.0000	−	51.9615i	−1.10959	−	1.92187i
$732$		0			0
$733$	2.00000	−	3.46410i	0.0738717	−	0.127950i	−0.826723	−	0.562609i	$-0.809798\pi$
$733$	2.00000	−	3.46410i	0.0738717	−	0.127950i	0.900595	+	0.434659i	$0.143131\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.00000			−0.0368355
$738$		0			0
$739$	−34.0000			−1.25071			−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000			−1.25071			−0.625355	+	0.780340i	$0.715046\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	−0.734725	−	0.678365i	$-0.762689\pi$
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	0.954844	+	0.297108i	$0.0960222\pi$
$744$		0			0
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.00000	+	10.3923i	0.219235	+	0.379727i
$750$		0			0
$751$	−17.5000	+	30.3109i	−0.638584	+	1.10606i	0.347160	+	0.937806i	$0.387146\pi$
$751$	−17.5000	+	30.3109i	−0.638584	+	1.10606i	−0.985744	+	0.168254i	$0.946187\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−30.0000			−1.09181
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	18.0000	−	31.1769i	0.652499	−	1.13016i	−0.330015	−	0.943976i	$-0.607054\pi$
$761$	18.0000	−	31.1769i	0.652499	−	1.13016i	0.982514	−	0.186187i	$-0.0596129\pi$
$762$		0			0
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.00000	−	10.3923i	−0.216647	−	0.375244i
$768$		0			0
$769$	−22.0000	+	38.1051i	−0.793340	+	1.37411i	0.130547	+	0.991442i	$0.458327\pi$
$769$	−22.0000	+	38.1051i	−0.793340	+	1.37411i	−0.923888	+	0.382664i	$0.875007\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−42.0000			−1.51064			−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000			−1.51064			−0.755318	+	0.655359i	$0.772517\pi$
$774$		0			0
$775$	20.0000			0.718421
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	7.50000	+	12.9904i	0.268371	+	0.464832i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.50000	−	12.9904i	−0.267686	−	0.463647i
$786$		0			0
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	0.426193	+	0.904632i	$0.359855\pi$
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	−0.996531	+	0.0832226i	$0.973479\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	30.0000			1.06668
$792$		0			0
$793$	16.0000			0.568177
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.50000	−	7.79423i	0.159398	−	0.276086i	−0.775254	−	0.631650i	$-0.782378\pi$
$797$	4.50000	−	7.79423i	0.159398	−	0.276086i	0.934652	+	0.355564i	$0.115711\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.00000	+	3.46410i	0.0705785	+	0.122245i
$804$		0			0
$805$	−9.00000	+	15.5885i	−0.317208	+	0.549421i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	24.0000			0.843795			0.421898	−	0.906644i	$-0.361364\pi$
$809$	24.0000			0.843795			0.421898	+	0.906644i	$0.361364\pi$
$810$		0			0
$811$	38.0000			1.33436			0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000			1.33436			0.667180	+	0.744896i	$0.267501\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.00000	−	10.3923i	0.210171	−	0.364027i
$816$		0			0
$817$	40.0000	+	69.2820i	1.39942	+	2.42387i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	0.999626	+	0.0273557i	$0.00870868\pi$
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	−0.476122	+	0.879379i	$0.657958\pi$
$822$		0			0
$823$	21.5000	−	37.2391i	0.749443	−	1.29807i	−0.198647	−	0.980071i	$-0.563655\pi$
$823$	21.5000	−	37.2391i	0.749443	−	1.29807i	0.948090	−	0.318002i	$-0.103012\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$		0			0
$829$	−19.0000			−0.659897			−0.329949	−	0.943999i	$-0.607031\pi$
$829$	−19.0000			−0.659897			−0.329949	+	0.943999i	$0.607031\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−9.00000	+	15.5885i	−0.311832	+	0.540108i
$834$		0			0
$835$	−18.0000	−	31.1769i	−0.622916	−	1.07892i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−19.5000	−	33.7750i	−0.673215	−	1.16604i	−0.976987	−	0.213298i	$-0.931580\pi$
$839$	−19.5000	−	33.7750i	−0.673215	−	1.16604i	0.303773	−	0.952745i	$-0.401754\pi$
$840$		0			0
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	9.00000			0.309609
$846$		0			0
$847$	2.00000			0.0687208
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.50000	−	2.59808i	0.0514193	−	0.0890609i
$852$		0			0
$853$	−19.0000	−	32.9090i	−0.650548	−	1.12678i	−0.982990	−	0.183658i	$-0.941206\pi$
$853$	−19.0000	−	32.9090i	−0.650548	−	1.12678i	0.332443	−	0.943123i	$-0.392127\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.0000	+	20.7846i	0.409912	+	0.709989i	0.994880	−	0.101068i	$-0.0322260\pi$
$857$	12.0000	+	20.7846i	0.409912	+	0.709989i	−0.584967	+	0.811057i	$0.698893\pi$
$858$		0			0
$859$	12.5000	−	21.6506i	0.426494	−	0.738710i	−0.570064	−	0.821600i	$-0.693082\pi$
$859$	12.5000	−	21.6506i	0.426494	−	0.738710i	0.996559	+	0.0828900i	$0.0264150\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−48.0000			−1.63394			−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000			−1.63394			−0.816970	+	0.576681i	$0.804348\pi$
$864$		0			0
$865$	−54.0000			−1.83606
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.00000	+	1.73205i	−0.0339227	+	0.0587558i
$870$		0			0
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.00000	+	5.19615i	0.101419	+	0.175662i
$876$		0			0
$877$	26.0000	−	45.0333i	0.877958	−	1.52067i	0.0243792	−	0.999703i	$-0.492239\pi$
$877$	26.0000	−	45.0333i	0.877958	−	1.52067i	0.853578	−	0.520964i	$-0.174428\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	27.0000			0.909653			0.454827	−	0.890580i	$-0.349701\pi$
$881$	27.0000			0.909653			0.454827	+	0.890580i	$0.349701\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	15.0000	−	25.9808i	0.503651	−	0.872349i	−0.496340	−	0.868128i	$-0.665323\pi$
$887$	15.0000	−	25.9808i	0.503651	−	0.872349i	0.999991	−	0.00422062i	$-0.00134347\pi$
$888$		0			0
$889$	16.0000	+	27.7128i	0.536623	+	0.929458i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−13.5000	+	23.3827i	−0.451255	+	0.781597i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−36.0000			−1.19933
$902$		0			0
$903$		0			0
$904$		0			0
$905$	19.5000	−	33.7750i	0.648202	−	1.12272i
$906$		0			0
$907$	2.00000	+	3.46410i	0.0664089	+	0.115024i	0.897318	−	0.441384i	$-0.145512\pi$
$907$	2.00000	+	3.46410i	0.0664089	+	0.115024i	−0.830909	+	0.556408i	$0.812179\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.00000	+	10.3923i	0.198789	+	0.344312i	0.948136	−	0.317865i	$-0.102966\pi$
$911$	6.00000	+	10.3923i	0.198789	+	0.344312i	−0.749347	+	0.662177i	$0.769633\pi$
$912$		0			0
$913$	3.00000	−	5.19615i	0.0992855	−	0.171968i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12.0000			0.396275
$918$		0			0
$919$	−34.0000			−1.12156			−0.560778	−	0.827966i	$-0.689498\pi$
$919$	−34.0000			−1.12156			−0.560778	+	0.827966i	$0.689498\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−30.0000	+	51.9615i	−0.987462	+	1.71033i
$924$		0			0
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	9.00000	+	15.5885i	0.295280	+	0.511441i	0.975050	−	0.221985i	$-0.0712536\pi$
$929$	9.00000	+	15.5885i	0.295280	+	0.511441i	−0.679770	+	0.733426i	$0.737920\pi$
$930$		0			0
$931$	12.0000	−	20.7846i	0.393284	−	0.681188i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−18.0000			−0.588663
$936$		0			0
$937$	32.0000			1.04539			0.522697	−	0.852518i	$-0.324926\pi$
$937$	32.0000			1.04539			0.522697	+	0.852518i	$0.324926\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−15.0000	+	25.9808i	−0.488986	+	0.846949i	−0.999920	−	0.0126715i	$-0.995966\pi$
$941$	−15.0000	+	25.9808i	−0.488986	+	0.846949i	0.510934	+	0.859620i	$0.329300\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	0.997589	−	0.0694014i	$-0.0221089\pi$
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	−0.558898	+	0.829237i	$0.688776\pi$
$948$		0			0
$949$	−8.00000	+	13.8564i	−0.259691	+	0.449798i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−42.0000			−1.36051			−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000			−1.36051			−0.680257	+	0.732974i	$0.738132\pi$
$954$		0			0
$955$	63.0000			2.03863
$956$		0			0
$957$		0			0
$958$		0			0
$959$	9.00000	−	15.5885i	0.290625	−	0.503378i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−30.0000	−	51.9615i	−0.965734	−	1.67270i
$966$		0			0
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	−0.708245	−	0.705967i	$-0.750513\pi$
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	0.965508	+	0.260375i	$0.0838461\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	15.0000			0.481373			0.240686	−	0.970603i	$-0.422627\pi$
$971$	15.0000			0.481373			0.240686	+	0.970603i	$0.422627\pi$
$972$		0			0
$973$	28.0000			0.897639
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22.5000	−	38.9711i	0.719839	−	1.24680i	−0.241225	−	0.970469i	$-0.577549\pi$
$977$	22.5000	−	38.9711i	0.719839	−	1.24680i	0.961063	−	0.276328i	$-0.0891176\pi$
$978$		0			0
$979$	−4.50000	−	7.79423i	−0.143821	−	0.249105i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	22.5000	+	38.9711i	0.717639	+	1.24299i	0.961933	+	0.273285i	$0.0881103\pi$
$983$	22.5000	+	38.9711i	0.717639	+	1.24299i	−0.244294	+	0.969701i	$0.578556\pi$
$984$		0			0
$985$	9.00000	−	15.5885i	0.286764	−	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−30.0000			−0.953945
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−12.0000	+	20.7846i	−0.380426	+	0.658916i
$996$		0			0
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	0.934274	−	0.356555i	$-0.116049\pi$
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	−0.775923	+	0.630828i	$0.782715\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3564.2.i.a.2377.1		2
3.2	odd	2		3564.2.i.j.2377.1		2
9.2	odd	6		3564.2.i.j.1189.1		2
9.4	even	3		396.2.a.c.1.1		1
9.5	odd	6		44.2.a.a.1.1	✓	1
9.7	even	3	inner	3564.2.i.a.1189.1		2
36.23	even	6		176.2.a.a.1.1		1
36.31	odd	6		1584.2.a.p.1.1		1
45.4	even	6		9900.2.a.h.1.1		1
45.13	odd	12		9900.2.c.g.5149.1		2
45.14	odd	6		1100.2.a.b.1.1		1
45.22	odd	12		9900.2.c.g.5149.2		2
45.23	even	12		1100.2.b.c.749.2		2
45.32	even	12		1100.2.b.c.749.1		2
63.5	even	6		2156.2.i.c.1145.1		2
63.23	odd	6		2156.2.i.b.1145.1		2
63.32	odd	6		2156.2.i.b.177.1		2
63.41	even	6		2156.2.a.a.1.1		1
63.59	even	6		2156.2.i.c.177.1		2
72.5	odd	6		704.2.a.f.1.1		1
72.13	even	6		6336.2.a.j.1.1		1
72.59	even	6		704.2.a.i.1.1		1
72.67	odd	6		6336.2.a.i.1.1		1
99.5	odd	30		484.2.e.a.245.1		4
99.14	odd	30		484.2.e.a.9.1		4
99.32	even	6		484.2.a.a.1.1		1
99.41	even	30		484.2.e.b.9.1		4
99.50	even	30		484.2.e.b.245.1		4
99.59	odd	30		484.2.e.a.269.1		4
99.68	even	30		484.2.e.b.81.1		4
99.76	odd	6		4356.2.a.j.1.1		1
99.86	odd	30		484.2.e.a.81.1		4
99.95	even	30		484.2.e.b.269.1		4
117.77	odd	6		7436.2.a.d.1.1		1
144.5	odd	12		2816.2.c.e.1409.1		2
144.59	even	12		2816.2.c.k.1409.2		2
144.77	odd	12		2816.2.c.e.1409.2		2
144.131	even	12		2816.2.c.k.1409.1		2
180.23	odd	12		4400.2.b.k.4049.1		2
180.59	even	6		4400.2.a.v.1.1		1
180.167	odd	12		4400.2.b.k.4049.2		2
252.167	odd	6		8624.2.a.w.1.1		1
396.131	odd	6		1936.2.a.c.1.1		1
792.131	odd	6		7744.2.a.bc.1.1		1
792.725	even	6		7744.2.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.a.a.1.1	✓	1	9.5	odd	6
176.2.a.a.1.1		1	36.23	even	6
396.2.a.c.1.1		1	9.4	even	3
484.2.a.a.1.1		1	99.32	even	6
484.2.e.a.9.1		4	99.14	odd	30
484.2.e.a.81.1		4	99.86	odd	30
484.2.e.a.245.1		4	99.5	odd	30
484.2.e.a.269.1		4	99.59	odd	30
484.2.e.b.9.1		4	99.41	even	30
484.2.e.b.81.1		4	99.68	even	30
484.2.e.b.245.1		4	99.50	even	30
484.2.e.b.269.1		4	99.95	even	30
704.2.a.f.1.1		1	72.5	odd	6
704.2.a.i.1.1		1	72.59	even	6
1100.2.a.b.1.1		1	45.14	odd	6
1100.2.b.c.749.1		2	45.32	even	12
1100.2.b.c.749.2		2	45.23	even	12
1584.2.a.p.1.1		1	36.31	odd	6
1936.2.a.c.1.1		1	396.131	odd	6
2156.2.a.a.1.1		1	63.41	even	6
2156.2.i.b.177.1		2	63.32	odd	6
2156.2.i.b.1145.1		2	63.23	odd	6
2156.2.i.c.177.1		2	63.59	even	6
2156.2.i.c.1145.1		2	63.5	even	6
2816.2.c.e.1409.1		2	144.5	odd	12
2816.2.c.e.1409.2		2	144.77	odd	12
2816.2.c.k.1409.1		2	144.131	even	12
2816.2.c.k.1409.2		2	144.59	even	12
3564.2.i.a.1189.1		2	9.7	even	3	inner
3564.2.i.a.2377.1		2	1.1	even	1	trivial
3564.2.i.j.1189.1		2	9.2	odd	6
3564.2.i.j.2377.1		2	3.2	odd	2
4356.2.a.j.1.1		1	99.76	odd	6
4400.2.a.v.1.1		1	180.59	even	6
4400.2.b.k.4049.1		2	180.23	odd	12
4400.2.b.k.4049.2		2	180.167	odd	12
6336.2.a.i.1.1		1	72.67	odd	6
6336.2.a.j.1.1		1	72.13	even	6
7436.2.a.d.1.1		1	117.77	odd	6
7744.2.a.m.1.1		1	792.725	even	6
7744.2.a.bc.1.1		1	792.131	odd	6
8624.2.a.w.1.1		1	252.167	odd	6
9900.2.a.h.1.1		1	45.4	even	6
9900.2.c.g.5149.1		2	45.13	odd	12
9900.2.c.g.5149.2		2	45.22	odd	12

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:	\( N \)	\(=\)	\( 3564 = 2^{2} \cdot 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3564.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{5} +(-1.00000 - 1.73205i) q^{7} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{11} +(2.00000 - 3.46410i) q^{13} -6.00000 q^{17} +8.00000 q^{19} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-2.50000 + 4.33013i) q^{31} +6.00000 q^{35} -1.00000 q^{37} +(5.00000 + 8.66025i) q^{43} +(1.50000 - 2.59808i) q^{49} +6.00000 q^{53} +3.00000 q^{55} +(1.50000 - 2.59808i) q^{59} +(2.00000 + 3.46410i) q^{61} +(6.00000 + 10.3923i) q^{65} +(0.500000 - 0.866025i) q^{67} -15.0000 q^{71} -4.00000 q^{73} +(-1.00000 + 1.73205i) q^{77} +(-1.00000 - 1.73205i) q^{79} +(3.00000 + 5.19615i) q^{83} +(9.00000 - 15.5885i) q^{85} +9.00000 q^{89} -8.00000 q^{91} +(-12.0000 + 20.7846i) q^{95} +(3.50000 + 6.06218i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{5} - 2 q^{7}+O(q^{10}) \) 2 * q - 3 * q^5 - 2 * q^7	\( 2 q - 3 q^{5} - 2 q^{7} - q^{11} + 4 q^{13} - 12 q^{17} + 16 q^{19} - 3 q^{23} - 4 q^{25} - 5 q^{31} + 12 q^{35} - 2 q^{37} + 10 q^{43} + 3 q^{49} + 12 q^{53} + 6 q^{55} + 3 q^{59} + 4 q^{61} + 12 q^{65} + q^{67} - 30 q^{71} - 8 q^{73} - 2 q^{77} - 2 q^{79} + 6 q^{83} + 18 q^{85} + 18 q^{89} - 16 q^{91} - 24 q^{95} + 7 q^{97}+O(q^{100}) \) 2 * q - 3 * q^5 - 2 * q^7 - q^11 + 4 * q^13 - 12 * q^17 + 16 * q^19 - 3 * q^23 - 4 * q^25 - 5 * q^31 + 12 * q^35 - 2 * q^37 + 10 * q^43 + 3 * q^49 + 12 * q^53 + 6 * q^55 + 3 * q^59 + 4 * q^61 + 12 * q^65 + q^67 - 30 * q^71 - 8 * q^73 - 2 * q^77 - 2 * q^79 + 6 * q^83 + 18 * q^85 + 18 * q^89 - 16 * q^91 - 24 * q^95 + 7 * q^97

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