LMFDB - Embedded newform 2736.2.s.v.577.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(577,2736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2736, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("2736.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.s (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:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.1
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	2736.577
Dual form			2736.2.s.v.1873.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.822876 - 1.42526i) q^{5} -3.64575 q^{7} +O(q^{10})$	$q+(-0.822876 - 1.42526i) q^{5} -3.64575 q^{7} -4.64575 q^{11} +(-1.00000 + 1.73205i) q^{13} +(-1.67712 - 4.02334i) q^{19} +(0.822876 - 1.42526i) q^{23} +(1.14575 - 1.98450i) q^{25} +(0.822876 - 1.42526i) q^{29} +5.64575 q^{31} +(3.00000 + 5.19615i) q^{35} +0.354249 q^{37} +(-0.145751 - 0.252449i) q^{41} +(5.64575 + 9.77873i) q^{43} +(-2.17712 + 3.77089i) q^{47} +6.29150 q^{49} +(-6.29150 + 10.8972i) q^{53} +(3.82288 + 6.62141i) q^{55} +(3.96863 + 6.87386i) q^{59} +(-0.468627 + 0.811686i) q^{61} +3.29150 q^{65} +(0.322876 - 0.559237i) q^{67} +(1.35425 + 2.34563i) q^{71} +(-0.854249 - 1.47960i) q^{73} +16.9373 q^{77} +(-2.00000 - 3.46410i) q^{79} +7.93725 q^{83} +(3.64575 - 6.31463i) q^{91} +(-4.35425 + 5.70105i) q^{95} +(1.85425 + 3.21165i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - 4 q^{7}+O(q^{10}) $ 4 * q + 2 * q^5 - 4 * q^7	$ 4 q + 2 q^{5} - 4 q^{7} - 8 q^{11} - 4 q^{13} - 12 q^{19} - 2 q^{23} - 6 q^{25} - 2 q^{29} + 12 q^{31} + 12 q^{35} + 12 q^{37} + 10 q^{41} + 12 q^{43} - 14 q^{47} + 4 q^{49} - 4 q^{53} + 10 q^{55} + 14 q^{61} - 8 q^{65} - 4 q^{67} + 16 q^{71} - 14 q^{73} + 36 q^{77} - 8 q^{79} + 4 q^{91} - 28 q^{95} + 18 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 - 4 * q^7 - 8 * q^11 - 4 * q^13 - 12 * q^19 - 2 * q^23 - 6 * q^25 - 2 * q^29 + 12 * q^31 + 12 * q^35 + 12 * q^37 + 10 * q^41 + 12 * q^43 - 14 * q^47 + 4 * q^49 - 4 * q^53 + 10 * q^55 + 14 * q^61 - 8 * q^65 - 4 * q^67 + 16 * q^71 - 14 * q^73 + 36 * q^77 - 8 * q^79 + 4 * q^91 - 28 * q^95 + 18 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$5$	−0.822876	−	1.42526i	−0.368001	−	0.637397i	0.621252	−	0.783611i	$-0.286624\pi$
$5$	−0.822876	−	1.42526i	−0.368001	−	0.637397i	−0.989253	+	0.146214i	$0.953291\pi$
$6$		0			0
$7$	−3.64575			−1.37796			−0.688982	−	0.724778i	$-0.741942\pi$
$7$	−3.64575			−1.37796			−0.688982	+	0.724778i	$0.741942\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.64575			−1.40075			−0.700373	−	0.713777i	$-0.746983\pi$
$11$	−4.64575			−1.40075			−0.700373	+	0.713777i	$0.746983\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−1.67712	−	4.02334i	−0.384759	−	0.923017i
$19$	−1.67712	−	4.02334i	−0.384759	−	0.923017i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.822876	−	1.42526i	0.171581	−	0.297188i	−0.767391	−	0.641179i	$-0.778446\pi$
$23$	0.822876	−	1.42526i	0.171581	−	0.297188i	0.938973	+	0.343991i	$0.111779\pi$
$24$		0			0
$25$	1.14575	−	1.98450i	0.229150	−	0.396900i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.822876	−	1.42526i	0.152804	−	0.264665i	−0.779453	−	0.626461i	$-0.784503\pi$
$29$	0.822876	−	1.42526i	0.152804	−	0.264665i	0.932257	+	0.361796i	$0.117836\pi$
$30$		0			0
$31$	5.64575			1.01401			0.507003	−	0.861944i	$-0.330753\pi$
$31$	5.64575			1.01401			0.507003	+	0.861944i	$0.330753\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.00000	+	5.19615i	0.507093	+	0.878310i
$36$		0			0
$37$	0.354249			0.0582381			0.0291191	−	0.999576i	$-0.490730\pi$
$37$	0.354249			0.0582381			0.0291191	+	0.999576i	$0.490730\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.145751	−	0.252449i	−0.0227625	−	0.0394259i	0.854420	−	0.519583i	$-0.173913\pi$
$41$	−0.145751	−	0.252449i	−0.0227625	−	0.0394259i	−0.877182	+	0.480158i	$0.840579\pi$
$42$		0			0
$43$	5.64575	+	9.77873i	0.860969	+	1.49124i	0.870995	+	0.491292i	$0.163475\pi$
$43$	5.64575	+	9.77873i	0.860969	+	1.49124i	−0.0100257	+	0.999950i	$0.503191\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.17712	+	3.77089i	−0.317566	+	0.550041i	−0.979980	−	0.199098i	$-0.936199\pi$
$47$	−2.17712	+	3.77089i	−0.317566	+	0.550041i	0.662413	+	0.749138i	$0.269532\pi$
$48$		0			0
$49$	6.29150			0.898786
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.29150	+	10.8972i	−0.864204	+	1.49685i	0.00363070	+	0.999993i	$0.498844\pi$
$53$	−6.29150	+	10.8972i	−0.864204	+	1.49685i	−0.867835	+	0.496852i	$0.834489\pi$
$54$		0			0
$55$	3.82288	+	6.62141i	0.515476	+	0.892831i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.96863	+	6.87386i	0.516671	+	0.894901i	0.999813	+	0.0193585i	$0.00616237\pi$
$59$	3.96863	+	6.87386i	0.516671	+	0.894901i	−0.483141	+	0.875542i	$0.660504\pi$
$60$		0			0
$61$	−0.468627	+	0.811686i	−0.0600015	+	0.103926i	−0.894466	−	0.447136i	$-0.852444\pi$
$61$	−0.468627	+	0.811686i	−0.0600015	+	0.103926i	0.834464	+	0.551062i	$0.185777\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.29150			0.408261
$66$		0			0
$67$	0.322876	−	0.559237i	0.0394455	−	0.0683217i	−0.845629	−	0.533772i	$-0.820774\pi$
$67$	0.322876	−	0.559237i	0.0394455	−	0.0683217i	0.885074	+	0.465450i	$0.154108\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.35425	+	2.34563i	0.160720	+	0.278375i	0.935127	−	0.354313i	$-0.115285\pi$
$71$	1.35425	+	2.34563i	0.160720	+	0.278375i	−0.774407	+	0.632687i	$0.781952\pi$
$72$		0			0
$73$	−0.854249	−	1.47960i	−0.0999822	−	0.173174i	0.811695	−	0.584082i	$-0.198545\pi$
$73$	−0.854249	−	1.47960i	−0.0999822	−	0.173174i	−0.911677	+	0.410907i	$0.865212\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	16.9373			1.93018
$78$		0			0
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.93725			0.871227			0.435613	−	0.900134i	$-0.356531\pi$
$83$	7.93725			0.871227			0.435613	+	0.900134i	$0.356531\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	3.64575	−	6.31463i	0.382179	−	0.661953i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.35425	+	5.70105i	−0.446736	+	0.584915i
$96$		0			0
$97$	1.85425	+	3.21165i	0.188270	+	0.326094i	0.944674	−	0.328012i	$-0.106379\pi$
$97$	1.85425	+	3.21165i	0.188270	+	0.326094i	−0.756403	+	0.654106i	$0.773045\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.82288	+	11.8176i	−0.678902	+	1.17589i	0.296411	+	0.955061i	$0.404210\pi$
$101$	−6.82288	+	11.8176i	−0.678902	+	1.17589i	−0.975312	+	0.220831i	$0.929123\pi$
$102$		0			0
$103$	13.2915			1.30965			0.654825	−	0.755780i	$-0.272742\pi$
$103$	13.2915			1.30965			0.654825	+	0.755780i	$0.272742\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.2915			1.47829			0.739143	−	0.673549i	$-0.235231\pi$
$107$	15.2915			1.47829			0.739143	+	0.673549i	$0.235231\pi$
$108$		0			0
$109$	−7.29150	−	12.6293i	−0.698399	−	1.20966i	−0.969021	−	0.246977i	$-0.920563\pi$
$109$	−7.29150	−	12.6293i	−0.698399	−	1.20966i	0.270622	−	0.962686i	$-0.412771\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	15.5830			1.46593			0.732963	−	0.680269i	$-0.238137\pi$
$113$	15.5830			1.46593			0.732963	+	0.680269i	$0.238137\pi$
$114$		0			0
$115$	−2.70850			−0.252569
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	10.5830			0.962091
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−6.64575	+	11.5108i	−0.589715	+	1.02142i	0.404554	+	0.914514i	$0.367427\pi$
$127$	−6.64575	+	11.5108i	−0.589715	+	1.02142i	−0.994270	+	0.106903i	$0.965907\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.968627	−	1.67771i	−0.0846293	−	0.146582i	0.820604	−	0.571497i	$-0.193637\pi$
$131$	−0.968627	−	1.67771i	−0.0846293	−	0.146582i	−0.905233	+	0.424915i	$0.860304\pi$
$132$		0			0
$133$	6.11438	+	14.6681i	0.530184	+	1.27188i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.79150	−	13.4953i	0.665673	−	1.15298i	−0.313429	−	0.949612i	$-0.601478\pi$
$137$	7.79150	−	13.4953i	0.665673	−	1.15298i	0.979102	−	0.203368i	$-0.0651888\pi$
$138$		0			0
$139$	9.32288	−	16.1477i	0.790756	−	1.36963i	−0.134743	−	0.990881i	$-0.543021\pi$
$139$	9.32288	−	16.1477i	0.790756	−	1.36963i	0.925499	−	0.378749i	$-0.123646\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.64575	−	8.04668i	0.388497	−	0.672897i
$144$		0			0
$145$	−2.70850			−0.224928
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.46863	+	9.47194i	0.448007	+	0.775972i	0.998256	−	0.0590292i	$-0.0188005\pi$
$149$	5.46863	+	9.47194i	0.448007	+	0.775972i	−0.550249	+	0.835001i	$0.685467\pi$
$150$		0			0
$151$	−12.9373			−1.05282			−0.526409	−	0.850231i	$-0.676462\pi$
$151$	−12.9373			−1.05282			−0.526409	+	0.850231i	$0.676462\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.64575	−	8.04668i	−0.373156	−	0.646325i
$156$		0			0
$157$	5.29150	+	9.16515i	0.422308	+	0.731459i	0.996165	−	0.0874969i	$-0.0278868\pi$
$157$	5.29150	+	9.16515i	0.422308	+	0.731459i	−0.573857	+	0.818956i	$0.694553\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.00000	+	5.19615i	−0.236433	+	0.409514i
$162$		0			0
$163$	−3.93725			−0.308390			−0.154195	−	0.988040i	$-0.549278\pi$
$163$	−3.93725			−0.308390			−0.154195	+	0.988040i	$0.549278\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	−4.17712	+	7.23499i	−0.315761	+	0.546914i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.06275			0.303664			0.151832	−	0.988406i	$-0.451483\pi$
$179$	4.06275			0.303664			0.151832	+	0.988406i	$0.451483\pi$
$180$		0			0
$181$	−11.1144	+	19.2507i	−0.826125	+	1.43089i	0.0749311	+	0.997189i	$0.476126\pi$
$181$	−11.1144	+	19.2507i	−0.826125	+	1.43089i	−0.901056	+	0.433702i	$0.857207\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.291503	−	0.504897i	−0.0214317	−	0.0371208i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.58301			0.476330			0.238165	−	0.971225i	$-0.423454\pi$
$191$	6.58301			0.476330			0.238165	+	0.971225i	$0.423454\pi$
$192$		0			0
$193$	−7.29150	−	12.6293i	−0.524854	−	0.909074i	−0.999581	−	0.0289406i	$-0.990787\pi$
$193$	−7.29150	−	12.6293i	−0.524854	−	0.909074i	0.474727	−	0.880133i	$-0.342547\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.64575			0.544737			0.272369	−	0.962193i	$-0.412193\pi$
$197$	7.64575			0.544737			0.272369	+	0.962193i	$0.412193\pi$
$198$		0			0
$199$	−9.93725	+	17.2118i	−0.704433	+	1.22011i	0.262462	+	0.964942i	$0.415465\pi$
$199$	−9.93725	+	17.2118i	−0.704433	+	1.22011i	−0.966896	+	0.255172i	$0.917868\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.00000	+	5.19615i	−0.210559	+	0.364698i
$204$		0			0
$205$	−0.239870	+	0.415468i	−0.0167533	+	0.0290175i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	7.79150	+	18.6914i	0.538950	+	1.29291i
$210$		0			0
$211$	−6.64575	−	11.5108i	−0.457512	−	0.792435i	0.541316	−	0.840819i	$-0.317926\pi$
$211$	−6.64575	−	11.5108i	−0.457512	−	0.792435i	−0.998829	+	0.0483843i	$0.984593\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	9.29150	−	16.0934i	0.633675	−	1.09756i
$216$		0			0
$217$	−20.5830			−1.39727
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−9.40588	−	16.2915i	−0.629864	−	1.09096i	−0.987579	−	0.157126i	$-0.949777\pi$
$223$	−9.40588	−	16.2915i	−0.629864	−	1.09096i	0.357714	−	0.933831i	$-0.383556\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.35425			−0.488119			−0.244059	−	0.969760i	$-0.578479\pi$
$227$	−7.35425			−0.488119			−0.244059	+	0.969760i	$0.578479\pi$
$228$		0			0
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.43725	+	16.3458i	0.618255	+	1.07085i	0.989804	+	0.142436i	$0.0454935\pi$
$233$	9.43725	+	16.3458i	0.618255	+	1.07085i	−0.371549	+	0.928413i	$0.621173\pi$
$234$		0			0
$235$	7.16601			0.467459
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	3.79150	−	6.56708i	0.244232	−	0.423022i	−0.717683	−	0.696370i	$-0.754797\pi$
$241$	3.79150	−	6.56708i	0.244232	−	0.423022i	0.961915	+	0.273347i	$0.0881308\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.17712	−	8.96704i	−0.330754	−	0.572883i
$246$		0			0
$247$	8.64575	+	1.11847i	0.550116	+	0.0711668i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−14.6144	+	25.3128i	−0.922451	+	1.59773i	−0.126842	+	0.991923i	$0.540484\pi$
$251$	−14.6144	+	25.3128i	−0.922451	+	1.59773i	−0.795610	+	0.605810i	$0.792849\pi$
$252$		0			0
$253$	−3.82288	+	6.62141i	−0.240342	+	0.416285i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.14575	−	10.6448i	0.383361	−	0.664001i	−0.608179	−	0.793800i	$-0.708100\pi$
$257$	6.14575	−	10.6448i	0.383361	−	0.664001i	0.991540	+	0.129798i	$0.0414330\pi$
$258$		0			0
$259$	−1.29150			−0.0802501
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.46863	+	9.47194i	0.337210	+	0.584065i	0.983907	−	0.178682i	$-0.0571834\pi$
$263$	5.46863	+	9.47194i	0.337210	+	0.584065i	−0.646697	+	0.762747i	$0.723850\pi$
$264$		0			0
$265$	20.7085			1.27211
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	6.17712	+	10.6991i	0.375234	+	0.649924i	0.990362	−	0.138503i	$-0.0442292\pi$
$271$	6.17712	+	10.6991i	0.375234	+	0.649924i	−0.615128	+	0.788427i	$0.710896\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.32288	+	9.21949i	−0.320981	+	0.555956i
$276$		0			0
$277$	−27.5203			−1.65353			−0.826766	−	0.562546i	$-0.809822\pi$
$277$	−27.5203			−1.65353			−0.826766	+	0.562546i	$0.809822\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	12.7288	−	22.0469i	0.759334	−	1.31520i	−0.183857	−	0.982953i	$-0.558858\pi$
$281$	12.7288	−	22.0469i	0.759334	−	1.31520i	0.943191	−	0.332252i	$-0.107808\pi$
$282$		0			0
$283$	15.3229	+	26.5400i	0.910850	+	1.57764i	0.812866	+	0.582451i	$0.197906\pi$
$283$	15.3229	+	26.5400i	0.910850	+	1.57764i	0.0979848	+	0.995188i	$0.468760\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.531373	+	0.920365i	0.0313660	+	0.0543274i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−28.9373			−1.69053			−0.845266	−	0.534345i	$-0.820558\pi$
$293$	−28.9373			−1.69053			−0.845266	+	0.534345i	$0.820558\pi$
$294$		0			0
$295$	6.53137	−	11.3127i	0.380271	−	0.658649i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.64575	+	2.85052i	0.0951763	+	0.164850i
$300$		0			0
$301$	−20.5830	−	35.6508i	−1.18638	−	2.05488i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.54249			0.0883225
$306$		0			0
$307$	0.322876	+	0.559237i	0.0184275	+	0.0319173i	0.875092	−	0.483956i	$-0.160801\pi$
$307$	0.322876	+	0.559237i	0.0184275	+	0.0319173i	−0.856665	+	0.515874i	$0.827467\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	13.6458			0.773780			0.386890	−	0.922126i	$-0.373549\pi$
$311$	13.6458			0.773780			0.386890	+	0.922126i	$0.373549\pi$
$312$		0			0
$313$	−4.43725	+	7.68555i	−0.250808	+	0.434413i	−0.963749	−	0.266812i	$-0.914030\pi$
$313$	−4.43725	+	7.68555i	−0.250808	+	0.434413i	0.712940	+	0.701225i	$0.247363\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$		0			0
$319$	−3.82288	+	6.62141i	−0.214040	+	0.370728i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	2.29150	+	3.96900i	0.127110	+	0.220160i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	7.93725	−	13.7477i	0.437595	−	0.757937i
$330$		0			0
$331$	−19.8118			−1.08895			−0.544476	−	0.838776i	$-0.683272\pi$
$331$	−19.8118			−1.08895			−0.544476	+	0.838776i	$0.683272\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.06275			−0.0580640
$336$		0			0
$337$	4.85425	+	8.40781i	0.264428	+	0.458002i	0.967414	−	0.253202i	$-0.0814836\pi$
$337$	4.85425	+	8.40781i	0.264428	+	0.458002i	−0.702986	+	0.711204i	$0.748150\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−26.2288			−1.42037
$342$		0			0
$343$	2.58301			0.139469
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.6144	+	20.1167i	0.623492	+	1.07992i	0.988830	+	0.149046i	$0.0476201\pi$
$347$	11.6144	+	20.1167i	0.623492	+	1.07992i	−0.365338	+	0.930875i	$0.619047\pi$
$348$		0			0
$349$	21.1660			1.13299			0.566495	−	0.824065i	$-0.308299\pi$
$349$	21.1660			1.13299			0.566495	+	0.824065i	$0.308299\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.8745			−0.685241			−0.342620	−	0.939474i	$-0.611314\pi$
$353$	−12.8745			−0.685241			−0.342620	+	0.939474i	$0.611314\pi$
$354$		0			0
$355$	2.22876	−	3.86032i	0.118290	−	0.204884i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.46863	+	4.27579i	0.130289	+	0.225667i	0.923788	−	0.382904i	$-0.125076\pi$
$359$	2.46863	+	4.27579i	0.130289	+	0.225667i	−0.793499	+	0.608572i	$0.791743\pi$
$360$		0			0
$361$	−13.3745	+	13.4953i	−0.703921	+	0.710278i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.40588	+	2.43506i	−0.0735872	+	0.127457i
$366$		0			0
$367$	8.11438	−	14.0545i	0.423567	−	0.733640i	−0.572718	−	0.819752i	$-0.694111\pi$
$367$	8.11438	−	14.0545i	0.423567	−	0.733640i	0.996285	+	0.0861125i	$0.0274444\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	22.9373	−	39.7285i	1.19084	−	2.06260i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.64575	+	2.85052i	0.0847605	+	0.146810i
$378$		0			0
$379$	−10.7085			−0.550059			−0.275029	−	0.961436i	$-0.588688\pi$
$379$	−10.7085			−0.550059			−0.275029	+	0.961436i	$0.588688\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.76013	−	4.78068i	−0.141036	−	0.244282i	0.786851	−	0.617143i	$-0.211710\pi$
$383$	−2.76013	−	4.78068i	−0.141036	−	0.244282i	−0.927887	+	0.372861i	$0.878377\pi$
$384$		0			0
$385$	−13.9373	−	24.1400i	−0.710308	−	1.23029i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	−0.672874	−	0.739758i	$-0.734940\pi$
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	0.977086	+	0.212847i	$0.0682735\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.29150	+	5.70105i	−0.165613	+	0.286851i
$396$		0			0
$397$	−10.5314	−	18.2409i	−0.528554	−	0.915483i	−0.999446	−	0.0332919i	$-0.989401\pi$
$397$	−10.5314	−	18.2409i	−0.528554	−	0.915483i	0.470891	−	0.882191i	$-0.343932\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.7915	+	23.8876i	0.688715	+	1.19289i	0.972254	+	0.233928i	$0.0751581\pi$
$401$	13.7915	+	23.8876i	0.688715	+	1.19289i	−0.283539	+	0.958961i	$0.591509\pi$
$402$		0			0
$403$	−5.64575	+	9.77873i	−0.281235	+	0.487113i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.64575			−0.0815769
$408$		0			0
$409$	3.79150	−	6.56708i	0.187478	−	0.324721i	−0.756931	−	0.653495i	$-0.773302\pi$
$409$	3.79150	−	6.56708i	0.187478	−	0.324721i	0.944409	+	0.328774i	$0.106635\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−14.4686	−	25.0604i	−0.711955	−	1.23314i
$414$		0			0
$415$	−6.53137	−	11.3127i	−0.320612	−	0.555317i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−31.7490			−1.55104			−0.775520	−	0.631322i	$-0.782512\pi$
$419$	−31.7490			−1.55104			−0.775520	+	0.631322i	$0.782512\pi$
$420$		0			0
$421$	12.4059	+	21.4876i	0.604626	+	1.04724i	0.992111	+	0.125366i	$0.0400106\pi$
$421$	12.4059	+	21.4876i	0.604626	+	1.04724i	−0.387485	+	0.921876i	$0.626656\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.70850	−	2.95920i	0.0826800	−	0.143206i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.9373	+	24.1400i	−0.671334	+	1.16278i	0.306192	+	0.951970i	$0.400945\pi$
$431$	−13.9373	+	24.1400i	−0.671334	+	1.16278i	−0.977526	+	0.210815i	$0.932388\pi$
$432$		0			0
$433$	−8.93725	+	15.4798i	−0.429497	+	0.743911i	−0.996829	−	0.0795788i	$-0.974642\pi$
$433$	−8.93725	+	15.4798i	−0.429497	+	0.743911i	0.567332	+	0.823489i	$0.307976\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.11438	−	0.920365i	−0.340327	−	0.0440270i
$438$		0			0
$439$	5.40588	+	9.36326i	0.258009	+	0.446884i	0.965708	−	0.259629i	$-0.0836004\pi$
$439$	5.40588	+	9.36326i	0.258009	+	0.446884i	−0.707700	+	0.706513i	$0.750267\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.32288	+	9.21949i	−0.252897	+	0.438031i	−0.964322	−	0.264731i	$-0.914717\pi$
$443$	−5.32288	+	9.21949i	−0.252897	+	0.438031i	0.711425	+	0.702762i	$0.248050\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	24.2915			1.14639			0.573193	−	0.819420i	$-0.305704\pi$
$449$	24.2915			1.14639			0.573193	+	0.819420i	$0.305704\pi$
$450$		0			0
$451$	0.677124	+	1.17281i	0.0318845	+	0.0552256i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−12.0000			−0.562569
$456$		0			0
$457$	32.8745			1.53780			0.768902	−	0.639366i	$-0.220803\pi$
$457$	32.8745			1.53780			0.768902	+	0.639366i	$0.220803\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.58301	+	16.5983i	0.446325	+	0.773058i	0.998143	−	0.0609066i	$-0.0193992\pi$
$461$	9.58301	+	16.5983i	0.446325	+	0.773058i	−0.551818	+	0.833964i	$0.686066\pi$
$462$		0			0
$463$	38.4575			1.78727			0.893636	−	0.448792i	$-0.148146\pi$
$463$	38.4575			1.78727			0.893636	+	0.448792i	$0.148146\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.3542			−0.895608			−0.447804	−	0.894132i	$-0.647794\pi$
$467$	−19.3542			−0.895608			−0.447804	+	0.894132i	$0.647794\pi$
$468$		0			0
$469$	−1.17712	+	2.03884i	−0.0543546	+	0.0941448i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−26.2288	−	45.4295i	−1.20600	−	2.08885i
$474$		0			0
$475$	−9.90588	−	1.28149i	−0.454513	−	0.0587989i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.29150	+	5.70105i	−0.150393	+	0.260488i	−0.931372	−	0.364069i	$-0.881387\pi$
$479$	−3.29150	+	5.70105i	−0.150393	+	0.260488i	0.780979	+	0.624557i	$0.214720\pi$
$480$		0			0
$481$	−0.354249	+	0.613577i	−0.0161523	+	0.0279767i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.05163	−	5.28558i	0.138567	−	0.240006i
$486$		0			0
$487$	−4.22876			−0.191623			−0.0958116	−	0.995399i	$-0.530545\pi$
$487$	−4.22876			−0.191623			−0.0958116	+	0.995399i	$0.530545\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−19.6458	−	34.0274i	−0.886600	−	1.53564i	−0.843868	−	0.536550i	$-0.819727\pi$
$491$	−19.6458	−	34.0274i	−0.886600	−	1.53564i	−0.0427320	−	0.999087i	$-0.513606\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.93725	−	8.55157i	−0.221466	−	0.383591i
$498$		0			0
$499$	−2.38562	−	4.13202i	−0.106795	−	0.184975i	0.807675	−	0.589628i	$-0.200726\pi$
$499$	−2.38562	−	4.13202i	−0.106795	−	0.184975i	−0.914470	+	0.404653i	$0.867392\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	20.4686	−	35.4527i	0.912651	−	1.58076i	0.102346	−	0.994749i	$-0.467365\pi$
$503$	20.4686	−	35.4527i	0.912651	−	1.58076i	0.810305	−	0.586009i	$-0.199302\pi$
$504$		0			0
$505$	22.4575			0.999346
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−15.8745	+	27.4955i	−0.703625	+	1.21871i	0.263560	+	0.964643i	$0.415103\pi$
$509$	−15.8745	+	27.4955i	−0.703625	+	1.21871i	−0.967185	+	0.254072i	$0.918230\pi$
$510$		0			0
$511$	3.11438	+	5.39426i	0.137772	+	0.238628i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−10.9373	−	18.9439i	−0.481953	−	0.834767i
$516$		0			0
$517$	10.1144	−	17.5186i	0.444830	−	0.770468i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11.7085			0.512959			0.256479	−	0.966550i	$-0.417437\pi$
$521$	11.7085			0.512959			0.256479	+	0.966550i	$0.417437\pi$
$522$		0			0
$523$	−0.937254	+	1.62337i	−0.0409833	+	0.0709851i	−0.885789	−	0.464087i	$-0.846382\pi$
$523$	−0.937254	+	1.62337i	−0.0409833	+	0.0709851i	0.844806	+	0.535072i	$0.179716\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	10.1458	+	17.5730i	0.441120	+	0.764042i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.583005			0.0252528
$534$		0			0
$535$	−12.5830	−	21.7944i	−0.544011	−	0.942254i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−29.2288			−1.25897
$540$		0			0
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−12.0000	+	20.7846i	−0.514024	+	0.890315i
$546$		0			0
$547$	5.64575	−	9.77873i	0.241395	−	0.418108i	−0.719717	−	0.694268i	$-0.755728\pi$
$547$	5.64575	−	9.77873i	0.241395	−	0.418108i	0.961112	+	0.276159i	$0.0890618\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.11438	−	0.920365i	−0.303083	−	0.0392089i
$552$		0			0
$553$	7.29150	+	12.6293i	0.310066	+	0.537050i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.70850	+	4.69126i	−0.114763	+	0.198775i	−0.917685	−	0.397309i	$-0.869944\pi$
$557$	−2.70850	+	4.69126i	−0.114763	+	0.198775i	0.802922	+	0.596084i	$0.203277\pi$
$558$		0			0
$559$	−22.5830			−0.955159
$560$		0			0
$561$		0			0
$562$		0			0
$563$	10.0627			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$563$	10.0627			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$564$		0			0
$565$	−12.8229	−	22.2099i	−0.539462	−	0.934376i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.58301			−0.275974			−0.137987	−	0.990434i	$-0.544063\pi$
$569$	−6.58301			−0.275974			−0.137987	+	0.990434i	$0.544063\pi$
$570$		0			0
$571$	−7.81176			−0.326912			−0.163456	−	0.986551i	$-0.552264\pi$
$571$	−7.81176			−0.326912			−0.163456	+	0.986551i	$0.552264\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.88562	−	3.26599i	−0.0786359	−	0.136201i
$576$		0			0
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−28.9373			−1.20052
$582$		0			0
$583$	29.2288	−	50.6257i	1.21053	−	2.09670i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.06275	+	12.2330i	0.291511	+	0.504911i	0.974167	−	0.225828i	$-0.0725088\pi$
$587$	7.06275	+	12.2330i	0.291511	+	0.504911i	−0.682656	+	0.730739i	$0.739175\pi$
$588$		0			0
$589$	−9.46863	−	22.7148i	−0.390148	−	0.935946i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	14.8542	−	25.7283i	0.609991	−	1.05654i	−0.381250	−	0.924472i	$-0.624506\pi$
$593$	14.8542	−	25.7283i	0.609991	−	1.05654i	0.991241	−	0.132063i	$-0.0421602\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.46863	−	14.6681i	0.346019	−	0.599322i	−0.639520	−	0.768775i	$-0.720867\pi$
$599$	8.46863	−	14.6681i	0.346019	−	0.599322i	0.985538	+	0.169453i	$0.0542000\pi$
$600$		0			0
$601$	10.4170			0.424918			0.212459	−	0.977170i	$-0.431853\pi$
$601$	10.4170			0.424918			0.212459	+	0.977170i	$0.431853\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−8.70850	−	15.0836i	−0.354051	−	0.613234i
$606$		0			0
$607$	−6.93725			−0.281574			−0.140787	−	0.990040i	$-0.544963\pi$
$607$	−6.93725			−0.281574			−0.140787	+	0.990040i	$0.544963\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.35425	−	7.54178i	−0.176154	−	0.305108i
$612$		0			0
$613$	−3.70850	−	6.42331i	−0.149785	−	0.259435i	0.781363	−	0.624077i	$-0.214525\pi$
$613$	−3.70850	−	6.42331i	−0.149785	−	0.259435i	−0.931148	+	0.364642i	$0.881191\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.4373	+	26.7381i	−0.621480	+	1.07644i	0.367730	+	0.929933i	$0.380135\pi$
$617$	−15.4373	+	26.7381i	−0.621480	+	1.07644i	−0.989210	+	0.146503i	$0.953198\pi$
$618$		0			0
$619$	8.45751			0.339936			0.169968	−	0.985450i	$-0.445634\pi$
$619$	8.45751			0.339936			0.169968	+	0.985450i	$0.445634\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	4.14575	+	7.18065i	0.165830	+	0.287226i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−12.4059	+	21.4876i	−0.493870	+	0.855408i	−0.999975	−	0.00706354i	$-0.997752\pi$
$631$	−12.4059	+	21.4876i	−0.493870	+	0.855408i	0.506105	+	0.862472i	$0.331085\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	21.8745			0.868063
$636$		0			0
$637$	−6.29150	+	10.8972i	−0.249278	+	0.431763i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.43725	+	11.1497i	0.254256	+	0.440385i	0.964693	−	0.263376i	$-0.0848360\pi$
$641$	6.43725	+	11.1497i	0.254256	+	0.440385i	−0.710437	+	0.703761i	$0.751503\pi$
$642$		0			0
$643$	−3.26013	−	5.64671i	−0.128567	−	0.222685i	0.794555	−	0.607193i	$-0.207704\pi$
$643$	−3.26013	−	5.64671i	−0.128567	−	0.222685i	−0.923122	+	0.384508i	$0.874371\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−22.4575			−0.882896			−0.441448	−	0.897287i	$-0.645535\pi$
$647$	−22.4575			−0.882896			−0.441448	+	0.897287i	$0.645535\pi$
$648$		0			0
$649$	−18.4373	−	31.9343i	−0.723726	−	1.25353i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$		0			0
$655$	−1.59412	+	2.76110i	−0.0622874	+	0.107885i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.29150	−	16.0934i	0.361946	−	0.626908i	−0.626335	−	0.779554i	$-0.715446\pi$
$659$	9.29150	−	16.0934i	0.361946	−	0.626908i	0.988281	+	0.152646i	$0.0487793\pi$
$660$		0			0
$661$	−8.11438	+	14.0545i	−0.315613	+	0.546657i	−0.979568	−	0.201115i	$-0.935543\pi$
$661$	−8.11438	+	14.0545i	−0.315613	+	0.546657i	0.663955	+	0.747773i	$0.268877\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	15.8745	−	20.7846i	0.615587	−	0.805993i
$666$		0			0
$667$	−1.35425	−	2.34563i	−0.0524367	−	0.0908231i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.17712	−	3.77089i	0.0840470	−	0.145574i
$672$		0			0
$673$	−13.8745			−0.534823			−0.267411	−	0.963582i	$-0.586168\pi$
$673$	−13.8745			−0.534823			−0.267411	+	0.963582i	$0.586168\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.4170			0.438791			0.219395	−	0.975636i	$-0.429592\pi$
$677$	11.4170			0.438791			0.219395	+	0.975636i	$0.429592\pi$
$678$		0			0
$679$	−6.76013	−	11.7089i	−0.259430	−	0.449346i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−5.41699			−0.207276			−0.103638	−	0.994615i	$-0.533048\pi$
$683$	−5.41699			−0.207276			−0.103638	+	0.994615i	$0.533048\pi$
$684$		0			0
$685$	−25.6458			−0.979874
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−12.5830	−	21.7944i	−0.479374	−	0.830301i
$690$		0			0
$691$	−2.58301			−0.0982622			−0.0491311	−	0.998792i	$-0.515645\pi$
$691$	−2.58301			−0.0982622			−0.0491311	+	0.998792i	$0.515645\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−30.6863			−1.16400
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	5.17712	+	8.96704i	0.195537	+	0.338681i	0.947077	−	0.321008i	$-0.104022\pi$
$701$	5.17712	+	8.96704i	0.195537	+	0.338681i	−0.751539	+	0.659688i	$0.770688\pi$
$702$		0			0
$703$	−0.594119	−	1.42526i	−0.0224076	−	0.0537548i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	24.8745	−	43.0839i	0.935502	−	1.62034i
$708$		0			0
$709$	−1.82288	+	3.15731i	−0.0684595	+	0.118575i	−0.898223	−	0.439539i	$-0.855142\pi$
$709$	−1.82288	+	3.15731i	−0.0684595	+	0.118575i	0.829764	+	0.558115i	$0.188475\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.64575	−	8.04668i	0.173985	−	0.301350i
$714$		0			0
$715$	−15.2915			−0.571870
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.35425	−	2.34563i	−0.0505050	−	0.0874771i	0.839668	−	0.543100i	$-0.182750\pi$
$719$	−1.35425	−	2.34563i	−0.0505050	−	0.0874771i	−0.890173	+	0.455623i	$0.849416\pi$
$720$		0			0
$721$	−48.4575			−1.80465
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.88562	−	3.26599i	−0.0700302	−	0.121296i
$726$		0			0
$727$	0.708497	+	1.22715i	0.0262767	+	0.0455126i	0.878865	−	0.477071i	$-0.158302\pi$
$727$	0.708497	+	1.22715i	0.0262767	+	0.0455126i	−0.852588	+	0.522584i	$0.824968\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−16.1033			−0.594788			−0.297394	−	0.954755i	$-0.596117\pi$
$733$	−16.1033			−0.594788			−0.297394	+	0.954755i	$0.596117\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.50000	+	2.59808i	−0.0552532	+	0.0957014i
$738$		0			0
$739$	−16.9059	−	29.2818i	−0.621893	−	1.07715i	−0.989133	−	0.147024i	$-0.953031\pi$
$739$	−16.9059	−	29.2818i	−0.621893	−	1.07715i	0.367240	−	0.930126i	$-0.380303\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	23.7601	+	41.1538i	0.871675	+	1.50978i	0.860263	+	0.509850i	$0.170299\pi$
$743$	23.7601	+	41.1538i	0.871675	+	1.50978i	0.0114112	+	0.999935i	$0.496368\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−55.7490			−2.03702
$750$		0			0
$751$	−3.93725	+	6.81952i	−0.143672	+	0.248848i	−0.928877	−	0.370389i	$-0.879225\pi$
$751$	−3.93725	+	6.81952i	−0.143672	+	0.248848i	0.785204	+	0.619237i	$0.212558\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	10.6458	+	18.4390i	0.387439	+	0.671063i
$756$		0			0
$757$	2.29150	+	3.96900i	0.0832861	+	0.144256i	0.904660	−	0.426135i	$-0.140125\pi$
$757$	2.29150	+	3.96900i	0.0832861	+	0.144256i	−0.821374	+	0.570391i	$0.806792\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−42.8745			−1.55420			−0.777100	−	0.629377i	$-0.783310\pi$
$761$	−42.8745			−1.55420			−0.777100	+	0.629377i	$0.783310\pi$
$762$		0			0
$763$	26.5830	+	46.0431i	0.962369	+	1.66687i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−15.8745			−0.573195
$768$		0			0
$769$	−17.6458	+	30.5633i	−0.636322	+	1.10214i	0.349911	+	0.936783i	$0.386212\pi$
$769$	−17.6458	+	30.5633i	−0.636322	+	1.10214i	−0.986233	+	0.165359i	$0.947122\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−2.46863	+	4.27579i	−0.0887903	+	0.153789i	−0.907000	−	0.421130i	$-0.861633\pi$
$773$	−2.46863	+	4.27579i	−0.0887903	+	0.153789i	0.818210	+	0.574920i	$0.194967\pi$
$774$		0			0
$775$	6.46863	−	11.2040i	0.232360	−	0.402459i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.771243	+	1.00979i	−0.0276327	+	0.0361796i
$780$		0			0
$781$	−6.29150	−	10.8972i	−0.225128	−	0.389933i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	8.70850	−	15.0836i	0.310820	−	0.538355i
$786$		0			0
$787$	42.5203			1.51568			0.757842	−	0.652438i	$-0.226254\pi$
$787$	42.5203			1.51568			0.757842	+	0.652438i	$0.226254\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−56.8118			−2.01999
$792$		0			0
$793$	−0.937254	−	1.62337i	−0.0332829	−	0.0576476i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	44.8118			1.58731			0.793657	−	0.608365i	$-0.208174\pi$
$797$	44.8118			1.58731			0.793657	+	0.608365i	$0.208174\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.96863	+	6.87386i	0.140050	+	0.242573i
$804$		0			0
$805$	9.87451			0.348031
$806$		0			0
$807$		0			0
$808$		0			0
$809$	9.00000			0.316423			0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000			0.316423			0.158212	+	0.987405i	$0.449427\pi$
$810$		0			0
$811$	−15.6458	+	27.0992i	−0.549397	+	0.951583i	0.448919	+	0.893572i	$0.351809\pi$
$811$	−15.6458	+	27.0992i	−0.549397	+	0.951583i	−0.998316	+	0.0580106i	$0.981524\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.23987	+	5.61162i	0.113488	+	0.196566i
$816$		0			0
$817$	29.8745	−	39.1149i	1.04518	−	1.36846i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$		0			0
$823$	−15.9373	+	27.6041i	−0.555538	+	0.962220i	0.442324	+	0.896855i	$0.354154\pi$
$823$	−15.9373	+	27.6041i	−0.555538	+	0.962220i	−0.997861	+	0.0653641i	$0.979179\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	26.3229	−	45.5926i	0.915336	−	1.58541i	0.108928	−	0.994050i	$-0.465258\pi$
$827$	26.3229	−	45.5926i	0.915336	−	1.58541i	0.806408	−	0.591359i	$-0.201408\pi$
$828$		0			0
$829$	−17.1660			−0.596200			−0.298100	−	0.954535i	$-0.596353\pi$
$829$	−17.1660			−0.596200			−0.298100	+	0.954535i	$0.596353\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−19.7490			−0.683443
$836$		0			0
$837$		0			0
$838$		0			0
$839$	20.7601	+	35.9576i	0.716719	+	1.24139i	0.962293	+	0.272016i	$0.0876904\pi$
$839$	20.7601	+	35.9576i	0.716719	+	1.24139i	−0.245573	+	0.969378i	$0.578976\pi$
$840$		0			0
$841$	13.1458	+	22.7691i	0.453302	+	0.785142i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	7.40588	−	12.8274i	0.254770	−	0.441275i
$846$		0			0
$847$	−38.5830			−1.32573
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.291503	−	0.504897i	0.00999258	−	0.0173077i
$852$		0			0
$853$	−4.29150	−	7.43310i	−0.146938	−	0.254505i	0.783156	−	0.621825i	$-0.213609\pi$
$853$	−4.29150	−	7.43310i	−0.146938	−	0.254505i	−0.930094	+	0.367321i	$0.880275\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	0.987739	−	0.156112i	$-0.0498959\pi$
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	−0.629066	+	0.777352i	$0.716563\pi$
$858$		0			0
$859$	6.61438	−	11.4564i	0.225680	−	0.390889i	−0.730843	−	0.682545i	$-0.760873\pi$
$859$	6.61438	−	11.4564i	0.225680	−	0.390889i	0.956523	+	0.291656i	$0.0942064\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−31.0627			−1.05739			−0.528694	−	0.848812i	$-0.677318\pi$
$863$	−31.0627			−1.05739			−0.528694	+	0.848812i	$0.677318\pi$
$864$		0			0
$865$	−4.93725	+	8.55157i	−0.167872	+	0.290762i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	9.29150	+	16.0934i	0.315193	+	0.545930i
$870$		0			0
$871$	0.645751	+	1.11847i	0.0218804	+	0.0378980i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	43.7490			1.47899
$876$		0			0
$877$	20.8229	+	36.0663i	0.703139	+	1.21787i	0.967359	+	0.253409i	$0.0815520\pi$
$877$	20.8229	+	36.0663i	0.703139	+	1.21787i	−0.264221	+	0.964462i	$0.585115\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	36.8745			1.24233			0.621167	−	0.783678i	$-0.286659\pi$
$881$	36.8745			1.24233			0.621167	+	0.783678i	$0.286659\pi$
$882$		0			0
$883$	−14.1974	+	24.5906i	−0.477780	+	0.827539i	−0.999676	−	0.0254701i	$-0.991892\pi$
$883$	−14.1974	+	24.5906i	−0.477780	+	0.827539i	0.521896	+	0.853009i	$0.325225\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.70850	−	15.0836i	0.292403	−	0.506456i	−0.681975	−	0.731376i	$-0.738879\pi$
$887$	8.70850	−	15.0836i	0.292403	−	0.506456i	0.974377	+	0.224919i	$0.0722119\pi$
$888$		0			0
$889$	24.2288	−	41.9654i	0.812606	−	1.40748i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	18.8229	+	2.43506i	0.629884	+	0.0814861i
$894$		0			0
$895$	−3.34313	−	5.79048i	−0.111749	−	0.193554i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	4.64575	−	8.04668i	0.154944	−	0.268372i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	36.5830			1.21606
$906$		0			0
$907$	19.9686	+	34.5867i	0.663047	+	1.14843i	0.979811	+	0.199927i	$0.0640706\pi$
$907$	19.9686	+	34.5867i	0.663047	+	1.14843i	−0.316763	+	0.948505i	$0.602596\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	16.9373			0.561156			0.280578	−	0.959831i	$-0.409474\pi$
$911$	16.9373			0.561156			0.280578	+	0.959831i	$0.409474\pi$
$912$		0			0
$913$	−36.8745			−1.22037
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.53137	+	6.11652i	0.116616	+	0.201985i
$918$		0			0
$919$	19.8745			0.655600			0.327800	−	0.944747i	$-0.393693\pi$
$919$	19.8745			0.655600			0.327800	+	0.944747i	$0.393693\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−5.41699			−0.178303
$924$		0			0
$925$	0.405881	−	0.703006i	0.0133453	−	0.0231147i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−4.79150	−	8.29913i	−0.157204	−	0.272285i	0.776655	−	0.629926i	$-0.216915\pi$
$929$	−4.79150	−	8.29913i	−0.157204	−	0.272285i	−0.933859	+	0.357640i	$0.883581\pi$
$930$		0			0
$931$	−10.5516	−	25.3128i	−0.345816	−	0.829595i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−3.56275	+	6.17086i	−0.116390	+	0.201593i	−0.918334	−	0.395805i	$-0.870466\pi$
$937$	−3.56275	+	6.17086i	−0.116390	+	0.201593i	0.801945	+	0.597398i	$0.203799\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	8.41699	−	14.5787i	0.274386	−	0.475251i	−0.695594	−	0.718435i	$-0.744859\pi$
$941$	8.41699	−	14.5787i	0.274386	−	0.475251i	0.969980	+	0.243184i	$0.0781920\pi$
$942$		0			0
$943$	−0.479741			−0.0156225
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.87451	+	6.71084i	0.125905	+	0.218073i	0.922086	−	0.386985i	$-0.126483\pi$
$947$	3.87451	+	6.71084i	0.125905	+	0.218073i	−0.796182	+	0.605058i	$0.793150\pi$
$948$		0			0
$949$	3.41699			0.110920
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.72876	−	11.6545i	−0.217966	−	0.377528i	0.736220	−	0.676742i	$-0.236609\pi$
$953$	−6.72876	−	11.6545i	−0.217966	−	0.377528i	−0.954186	+	0.299214i	$0.903275\pi$
$954$		0			0
$955$	−5.41699	−	9.38251i	−0.175290	−	0.303611i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−28.4059	+	49.2004i	−0.917274	+	1.58876i
$960$		0			0
$961$	0.874508			0.0282099
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.0000	+	20.7846i	−0.386294	+	0.669080i
$966$		0			0
$967$	−6.64575	−	11.5108i	−0.213713	−	0.370162i	0.739161	−	0.673529i	$-0.235222\pi$
$967$	−6.64575	−	11.5108i	−0.213713	−	0.370162i	−0.952874	+	0.303367i	$0.901889\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	27.1974	+	47.1073i	0.872806	+	1.51174i	0.859082	+	0.511838i	$0.171035\pi$
$971$	27.1974	+	47.1073i	0.872806	+	1.51174i	0.0137234	+	0.999906i	$0.495632\pi$
$972$		0			0
$973$	−33.9889	+	58.8705i	−1.08963	+	1.88730i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	7.45751			0.238587			0.119293	−	0.992859i	$-0.461937\pi$
$977$	7.45751			0.238587			0.119293	+	0.992859i	$0.461937\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−15.8745	−	27.4955i	−0.506318	−	0.876969i	−0.999973	−	0.00731102i	$-0.997673\pi$
$983$	−15.8745	−	27.4955i	−0.506318	−	0.876969i	0.493655	−	0.869658i	$-0.335661\pi$
$984$		0			0
$985$	−6.29150	−	10.8972i	−0.200464	−	0.347214i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	18.5830			0.590905
$990$		0			0
$991$	−1.41699	−	2.45431i	−0.0450123	−	0.0779636i	0.842641	−	0.538475i	$-0.180999\pi$
$991$	−1.41699	−	2.45431i	−0.0450123	−	0.0779636i	−0.887654	+	0.460511i	$0.847666\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	32.7085			1.03693
$996$		0			0
$997$	−8.11438	+	14.0545i	−0.256985	+	0.445111i	−0.965433	−	0.260652i	$-0.916062\pi$
$997$	−8.11438	+	14.0545i	−0.256985	+	0.445111i	0.708448	+	0.705763i	$0.249396\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.s.v.577.1		4
3.2	odd	2		304.2.i.e.273.2		4
4.3	odd	2		342.2.g.f.235.1		4
12.11	even	2		38.2.c.b.7.1	✓	4
19.11	even	3	inner	2736.2.s.v.1873.1		4
24.5	odd	2		1216.2.i.k.577.1		4
24.11	even	2		1216.2.i.l.577.2		4
57.11	odd	6		304.2.i.e.49.2		4
57.26	odd	6		5776.2.a.ba.1.1		2
57.50	even	6		5776.2.a.z.1.2		2
60.23	odd	4		950.2.j.g.349.2		8
60.47	odd	4		950.2.j.g.349.3		8
60.59	even	2		950.2.e.k.501.2		4
76.7	odd	6		6498.2.a.ba.1.2		2
76.11	odd	6		342.2.g.f.163.1		4
76.31	even	6		6498.2.a.bg.1.2		2
228.11	even	6		38.2.c.b.11.1	yes	4
228.23	even	18		722.2.e.n.245.2		12
228.35	even	18		722.2.e.n.595.1		12
228.47	even	18		722.2.e.n.415.1		12
228.59	odd	18		722.2.e.o.389.1		12
228.71	odd	18		722.2.e.o.99.1		12
228.83	even	6		722.2.a.j.1.2		2
228.107	odd	6		722.2.a.g.1.1		2
228.119	even	18		722.2.e.n.99.2		12
228.131	even	18		722.2.e.n.389.2		12
228.143	odd	18		722.2.e.o.415.2		12
228.155	odd	18		722.2.e.o.595.2		12
228.167	odd	18		722.2.e.o.245.1		12
228.179	odd	6		722.2.c.j.429.2		4
228.203	odd	18		722.2.e.o.423.1		12
228.215	even	18		722.2.e.n.423.2		12
228.227	odd	2		722.2.c.j.653.2		4
456.11	even	6		1216.2.i.l.961.2		4
456.125	odd	6		1216.2.i.k.961.1		4
1140.239	even	6		950.2.e.k.201.2		4
1140.467	odd	12		950.2.j.g.49.2		8
1140.923	odd	12		950.2.j.g.49.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.1	✓	4	12.11	even	2
38.2.c.b.11.1	yes	4	228.11	even	6
304.2.i.e.49.2		4	57.11	odd	6
304.2.i.e.273.2		4	3.2	odd	2
342.2.g.f.163.1		4	76.11	odd	6
342.2.g.f.235.1		4	4.3	odd	2
722.2.a.g.1.1		2	228.107	odd	6
722.2.a.j.1.2		2	228.83	even	6
722.2.c.j.429.2		4	228.179	odd	6
722.2.c.j.653.2		4	228.227	odd	2
722.2.e.n.99.2		12	228.119	even	18
722.2.e.n.245.2		12	228.23	even	18
722.2.e.n.389.2		12	228.131	even	18
722.2.e.n.415.1		12	228.47	even	18
722.2.e.n.423.2		12	228.215	even	18
722.2.e.n.595.1		12	228.35	even	18
722.2.e.o.99.1		12	228.71	odd	18
722.2.e.o.245.1		12	228.167	odd	18
722.2.e.o.389.1		12	228.59	odd	18
722.2.e.o.415.2		12	228.143	odd	18
722.2.e.o.423.1		12	228.203	odd	18
722.2.e.o.595.2		12	228.155	odd	18
950.2.e.k.201.2		4	1140.239	even	6
950.2.e.k.501.2		4	60.59	even	2
950.2.j.g.49.2		8	1140.467	odd	12
950.2.j.g.49.3		8	1140.923	odd	12
950.2.j.g.349.2		8	60.23	odd	4
950.2.j.g.349.3		8	60.47	odd	4
1216.2.i.k.577.1		4	24.5	odd	2
1216.2.i.k.961.1		4	456.125	odd	6
1216.2.i.l.577.2		4	24.11	even	2
1216.2.i.l.961.2		4	456.11	even	6
2736.2.s.v.577.1		4	1.1	even	1	trivial
2736.2.s.v.1873.1		4	19.11	even	3	inner
5776.2.a.z.1.2		2	57.50	even	6
5776.2.a.ba.1.1		2	57.26	odd	6
6498.2.a.ba.1.2		2	76.7	odd	6
6498.2.a.bg.1.2		2	76.31	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.822876 - 1.42526i) q^{5} -3.64575 q^{7} +O(q^{10})\)	\(q+(-0.822876 - 1.42526i) q^{5} -3.64575 q^{7} -4.64575 q^{11} +(-1.00000 + 1.73205i) q^{13} +(-1.67712 - 4.02334i) q^{19} +(0.822876 - 1.42526i) q^{23} +(1.14575 - 1.98450i) q^{25} +(0.822876 - 1.42526i) q^{29} +5.64575 q^{31} +(3.00000 + 5.19615i) q^{35} +0.354249 q^{37} +(-0.145751 - 0.252449i) q^{41} +(5.64575 + 9.77873i) q^{43} +(-2.17712 + 3.77089i) q^{47} +6.29150 q^{49} +(-6.29150 + 10.8972i) q^{53} +(3.82288 + 6.62141i) q^{55} +(3.96863 + 6.87386i) q^{59} +(-0.468627 + 0.811686i) q^{61} +3.29150 q^{65} +(0.322876 - 0.559237i) q^{67} +(1.35425 + 2.34563i) q^{71} +(-0.854249 - 1.47960i) q^{73} +16.9373 q^{77} +(-2.00000 - 3.46410i) q^{79} +7.93725 q^{83} +(3.64575 - 6.31463i) q^{91} +(-4.35425 + 5.70105i) q^{95} +(1.85425 + 3.21165i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 4 q^{7}+O(q^{10}) \) 4 * q + 2 * q^5 - 4 * q^7	\( 4 q + 2 q^{5} - 4 q^{7} - 8 q^{11} - 4 q^{13} - 12 q^{19} - 2 q^{23} - 6 q^{25} - 2 q^{29} + 12 q^{31} + 12 q^{35} + 12 q^{37} + 10 q^{41} + 12 q^{43} - 14 q^{47} + 4 q^{49} - 4 q^{53} + 10 q^{55} + 14 q^{61} - 8 q^{65} - 4 q^{67} + 16 q^{71} - 14 q^{73} + 36 q^{77} - 8 q^{79} + 4 q^{91} - 28 q^{95} + 18 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 - 4 * q^7 - 8 * q^11 - 4 * q^13 - 12 * q^19 - 2 * q^23 - 6 * q^25 - 2 * q^29 + 12 * q^31 + 12 * q^35 + 12 * q^37 + 10 * q^41 + 12 * q^43 - 14 * q^47 + 4 * q^49 - 4 * q^53 + 10 * q^55 + 14 * q^61 - 8 * q^65 - 4 * q^67 + 16 * q^71 - 14 * q^73 + 36 * q^77 - 8 * q^79 + 4 * q^91 - 28 * q^95 + 18 * q^97

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