LMFDB - Embedded newform 2736.2.s.v.1873.2

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			1873.2
Root			$1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	2736.1873
Dual form			2736.2.s.v.577.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82288 - 3.15731i) q^{5} +1.64575 q^{7} +O(q^{10})$	$q+(1.82288 - 3.15731i) q^{5} +1.64575 q^{7} +0.645751 q^{11} +(-1.00000 - 1.73205i) q^{13} +(-4.32288 - 0.559237i) q^{19} +(-1.82288 - 3.15731i) q^{23} +(-4.14575 - 7.18065i) q^{25} +(-1.82288 - 3.15731i) q^{29} +0.354249 q^{31} +(3.00000 - 5.19615i) q^{35} +5.64575 q^{37} +(5.14575 - 8.91270i) q^{41} +(0.354249 - 0.613577i) q^{43} +(-4.82288 - 8.35347i) q^{47} -4.29150 q^{49} +(4.29150 + 7.43310i) q^{53} +(1.17712 - 2.03884i) q^{55} +(-3.96863 + 6.87386i) q^{59} +(7.46863 + 12.9360i) q^{61} -7.29150 q^{65} +(-2.32288 - 4.02334i) q^{67} +(6.64575 - 11.5108i) q^{71} +(-6.14575 + 10.6448i) q^{73} +1.06275 q^{77} +(-2.00000 + 3.46410i) q^{79} -7.93725 q^{83} +(-1.64575 - 2.85052i) q^{91} +(-9.64575 + 12.6293i) q^{95} +(7.14575 - 12.3768i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$5$	1.82288	−	3.15731i	0.815215	−	1.41199i	−0.0939588	−	0.995576i	$-0.529952\pi$
$5$	1.82288	−	3.15731i	0.815215	−	1.41199i	0.909174	−	0.416417i	$-0.136714\pi$
$6$		0			0
$7$	1.64575			0.622036			0.311018	−	0.950404i	$-0.399330\pi$
$7$	1.64575			0.622036			0.311018	+	0.950404i	$0.399330\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.645751			0.194701			0.0973507	−	0.995250i	$-0.468963\pi$
$11$	0.645751			0.194701			0.0973507	+	0.995250i	$0.468963\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	−4.32288	−	0.559237i	−0.991736	−	0.128298i
$19$	−4.32288	−	0.559237i	−0.991736	−	0.128298i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.82288	−	3.15731i	−0.380096	−	0.658345i	0.610980	−	0.791646i	$-0.290776\pi$
$23$	−1.82288	−	3.15731i	−0.380096	−	0.658345i	−0.991076	+	0.133301i	$0.957442\pi$
$24$		0			0
$25$	−4.14575	−	7.18065i	−0.829150	−	1.43613i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.82288	−	3.15731i	−0.338500	−	0.586298i	0.645651	−	0.763632i	$-0.276586\pi$
$29$	−1.82288	−	3.15731i	−0.338500	−	0.586298i	−0.984151	+	0.177334i	$0.943253\pi$
$30$		0			0
$31$	0.354249			0.0636249			0.0318125	−	0.999494i	$-0.489872\pi$
$31$	0.354249			0.0636249			0.0318125	+	0.999494i	$0.489872\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.00000	−	5.19615i	0.507093	−	0.878310i
$36$		0			0
$37$	5.64575			0.928156			0.464078	−	0.885794i	$-0.346386\pi$
$37$	5.64575			0.928156			0.464078	+	0.885794i	$0.346386\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.14575	−	8.91270i	0.803631	−	1.39193i	−0.113580	−	0.993529i	$-0.536232\pi$
$41$	5.14575	−	8.91270i	0.803631	−	1.39193i	0.917211	−	0.398401i	$-0.130435\pi$
$42$		0			0
$43$	0.354249	−	0.613577i	0.0540224	−	0.0935696i	−0.837750	−	0.546055i	$-0.816129\pi$
$43$	0.354249	−	0.613577i	0.0540224	−	0.0935696i	0.891772	+	0.452485i	$0.149462\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.82288	−	8.35347i	−0.703489	−	1.21848i	−0.967234	−	0.253886i	$-0.918291\pi$
$47$	−4.82288	−	8.35347i	−0.703489	−	1.21848i	0.263745	−	0.964592i	$-0.415042\pi$
$48$		0			0
$49$	−4.29150			−0.613072
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.29150	+	7.43310i	0.589483	+	1.02101i	0.994300	+	0.106617i	$0.0340019\pi$
$53$	4.29150	+	7.43310i	0.589483	+	1.02101i	−0.404817	+	0.914398i	$0.632665\pi$
$54$		0			0
$55$	1.17712	−	2.03884i	0.158723	−	0.274917i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.96863	+	6.87386i	−0.516671	+	0.894901i	0.483141	+	0.875542i	$0.339496\pi$
$59$	−3.96863	+	6.87386i	−0.516671	+	0.894901i	−0.999813	+	0.0193585i	$0.993838\pi$
$60$		0			0
$61$	7.46863	+	12.9360i	0.956260	+	1.65629i	0.731459	+	0.681886i	$0.238840\pi$
$61$	7.46863	+	12.9360i	0.956260	+	1.65629i	0.224801	+	0.974405i	$0.427827\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.29150			−0.904400
$66$		0			0
$67$	−2.32288	−	4.02334i	−0.283784	−	0.491529i	0.688529	−	0.725209i	$-0.258257\pi$
$67$	−2.32288	−	4.02334i	−0.283784	−	0.491529i	−0.972314	+	0.233680i	$0.924923\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.64575	−	11.5108i	0.788706	−	1.36608i	−0.138055	−	0.990425i	$-0.544085\pi$
$71$	6.64575	−	11.5108i	0.788706	−	1.36608i	0.926760	−	0.375654i	$-0.122582\pi$
$72$		0			0
$73$	−6.14575	+	10.6448i	−0.719306	+	1.24587i	0.241969	+	0.970284i	$0.422207\pi$
$73$	−6.14575	+	10.6448i	−0.719306	+	1.24587i	−0.961275	+	0.275590i	$0.911127\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.06275			0.121111
$78$		0			0
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.93725			−0.871227			−0.435613	−	0.900134i	$-0.643469\pi$
$83$	−7.93725			−0.871227			−0.435613	+	0.900134i	$0.643469\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	−1.64575	−	2.85052i	−0.172522	−	0.298816i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−9.64575	+	12.6293i	−0.989633	+	1.29573i
$96$		0			0
$97$	7.14575	−	12.3768i	0.725541	−	1.25667i	−0.233210	−	0.972426i	$-0.574923\pi$
$97$	7.14575	−	12.3768i	0.725541	−	1.25667i	0.958751	−	0.284248i	$-0.0917438\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.17712	−	7.23499i	−0.415639	−	0.719909i	0.579856	−	0.814719i	$-0.303109\pi$
$101$	−4.17712	−	7.23499i	−0.415639	−	0.719909i	−0.995495	+	0.0948105i	$0.969775\pi$
$102$		0			0
$103$	2.70850			0.266876			0.133438	−	0.991057i	$-0.457398\pi$
$103$	2.70850			0.266876			0.133438	+	0.991057i	$0.457398\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.70850			0.455188			0.227594	−	0.973756i	$-0.426914\pi$
$107$	4.70850			0.455188			0.227594	+	0.973756i	$0.426914\pi$
$108$		0			0
$109$	3.29150	−	5.70105i	0.315269	−	0.546062i	−0.664226	−	0.747532i	$-0.731239\pi$
$109$	3.29150	−	5.70105i	0.315269	−	0.546062i	0.979495	+	0.201470i	$0.0645720\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.58301			−0.525205			−0.262602	−	0.964904i	$-0.584581\pi$
$113$	−5.58301			−0.525205			−0.262602	+	0.964904i	$0.584581\pi$
$114$		0			0
$115$	−13.2915			−1.23944
$116$		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
$127$	−1.35425	−	2.34563i	−0.120170	−	0.208141i	0.799665	−	0.600447i	$-0.205011\pi$
$127$	−1.35425	−	2.34563i	−0.120170	−	0.208141i	−0.919835	+	0.392306i	$0.871677\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.96863	−	12.0700i	0.608852	−	1.05456i	−0.382578	−	0.923923i	$-0.624964\pi$
$131$	6.96863	−	12.0700i	0.608852	−	1.05456i	0.991430	−	0.130639i	$-0.0417029\pi$
$132$		0			0
$133$	−7.11438	−	0.920365i	−0.616895	−	0.0798058i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.79150	−	4.83502i	−0.238494	−	0.413084i	0.721788	−	0.692114i	$-0.243320\pi$
$137$	−2.79150	−	4.83502i	−0.238494	−	0.413084i	−0.960282	+	0.279030i	$0.909987\pi$
$138$		0			0
$139$	6.67712	+	11.5651i	0.566346	+	0.980941i	0.996923	+	0.0783866i	$0.0249768\pi$
$139$	6.67712	+	11.5651i	0.566346	+	0.980941i	−0.430577	+	0.902554i	$0.641690\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.645751	−	1.11847i	−0.0540004	−	0.0935315i
$144$		0			0
$145$	−13.2915			−1.10380
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.46863	+	4.27579i	−0.202238	+	0.350286i	−0.949249	−	0.314525i	$-0.898155\pi$
$149$	−2.46863	+	4.27579i	−0.202238	+	0.350286i	0.747011	+	0.664811i	$0.231488\pi$
$150$		0			0
$151$	2.93725			0.239030			0.119515	−	0.992832i	$-0.461866\pi$
$151$	2.93725			0.239030			0.119515	+	0.992832i	$0.461866\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.645751	−	1.11847i	0.0518680	−	0.0898380i
$156$		0			0
$157$	−5.29150	+	9.16515i	−0.422308	+	0.731459i	−0.996165	−	0.0874969i	$-0.972113\pi$
$157$	−5.29150	+	9.16515i	−0.422308	+	0.731459i	0.573857	+	0.818956i	$0.305447\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.00000	−	5.19615i	−0.236433	−	0.409514i
$162$		0			0
$163$	11.9373			0.934998			0.467499	−	0.883994i	$-0.345155\pi$
$163$	11.9373			0.934998			0.467499	+	0.883994i	$0.345155\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$		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	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	−6.82288	−	11.8176i	−0.515761	−	0.893324i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	19.9373			1.49018			0.745090	−	0.666964i	$-0.232406\pi$
$179$	19.9373			1.49018			0.745090	+	0.666964i	$0.232406\pi$
$180$		0			0
$181$	2.11438	+	3.66221i	0.157160	+	0.272210i	0.933844	−	0.357682i	$-0.116433\pi$
$181$	2.11438	+	3.66221i	0.157160	+	0.272210i	−0.776683	+	0.629892i	$0.783099\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.2915	−	17.8254i	0.756646	−	1.31055i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−14.5830			−1.05519			−0.527595	−	0.849496i	$-0.676906\pi$
$191$	−14.5830			−1.05519			−0.527595	+	0.849496i	$0.676906\pi$
$192$		0			0
$193$	3.29150	−	5.70105i	0.236928	−	0.410371i	−0.722904	−	0.690949i	$-0.757193\pi$
$193$	3.29150	−	5.70105i	0.236928	−	0.410371i	0.959831	+	0.280578i	$0.0905263\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.35425			0.167733			0.0838666	−	0.996477i	$-0.473273\pi$
$197$	2.35425			0.167733			0.0838666	+	0.996477i	$0.473273\pi$
$198$		0			0
$199$	5.93725	+	10.2836i	0.420881	+	0.728987i	0.996026	−	0.0890645i	$-0.0283877\pi$
$199$	5.93725	+	10.2836i	0.420881	+	0.728987i	−0.575145	+	0.818051i	$0.695054\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.00000	−	5.19615i	−0.210559	−	0.364698i
$204$		0			0
$205$	−18.7601	−	32.4935i	−1.31026	−	2.26944i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.79150	−	0.361128i	−0.193092	−	0.0249797i
$210$		0			0
$211$	−1.35425	+	2.34563i	−0.0932303	+	0.161480i	−0.908869	−	0.417082i	$-0.863053\pi$
$211$	−1.35425	+	2.34563i	−0.0932303	+	0.161480i	0.815638	+	0.578562i	$0.196386\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.29150	−	2.23695i	−0.0880797	−	0.152559i
$216$		0			0
$217$	0.583005			0.0395770
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	14.4059	−	24.9517i	0.964689	−	1.67089i	0.254241	−	0.967141i	$-0.418174\pi$
$223$	14.4059	−	24.9517i	0.964689	−	1.67089i	0.710448	−	0.703750i	$-0.248492\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.6458			−0.839328			−0.419664	−	0.907680i	$-0.637852\pi$
$227$	−12.6458			−0.839328			−0.419664	+	0.907680i	$0.637852\pi$
$228$		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
$233$	−6.43725	+	11.1497i	−0.421719	+	0.730438i	−0.996108	−	0.0881444i	$-0.971906\pi$
$233$	−6.43725	+	11.1497i	−0.421719	+	0.730438i	0.574389	+	0.818582i	$0.305240\pi$
$234$		0			0
$235$	−35.1660			−2.29398
$236$		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
$241$	−6.79150	−	11.7632i	−0.437479	−	0.757736i	0.560015	−	0.828482i	$-0.310795\pi$
$241$	−6.79150	−	11.7632i	−0.437479	−	0.757736i	−0.997494	+	0.0707462i	$0.977462\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.82288	+	13.5496i	−0.499785	+	0.865653i
$246$		0			0
$247$	3.35425	+	8.04668i	0.213426	+	0.511998i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.38562	−	2.39997i	−0.0874597	−	0.151485i	0.818977	−	0.573826i	$-0.194542\pi$
$251$	−1.38562	−	2.39997i	−0.0874597	−	0.151485i	−0.906437	+	0.422342i	$0.861208\pi$
$252$		0			0
$253$	−1.17712	−	2.03884i	−0.0740052	−	0.128181i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.854249	+	1.47960i	0.0532866	+	0.0922950i	0.891438	−	0.453142i	$-0.149697\pi$
$257$	0.854249	+	1.47960i	0.0532866	+	0.0922950i	−0.838152	+	0.545437i	$0.816364\pi$
$258$		0			0
$259$	9.29150			0.577346
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.46863	+	4.27579i	−0.152222	+	0.263656i	−0.932044	−	0.362345i	$-0.881976\pi$
$263$	−2.46863	+	4.27579i	−0.152222	+	0.263656i	0.779822	+	0.626001i	$0.215310\pi$
$264$		0			0
$265$	31.2915			1.92222
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	8.82288	−	15.2817i	0.535952	−	0.928295i	−0.463165	−	0.886272i	$-0.653286\pi$
$271$	8.82288	−	15.2817i	0.535952	−	0.928295i	0.999117	−	0.0420233i	$-0.0133804\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.67712	−	4.63692i	−0.161437	−	0.279617i
$276$		0			0
$277$	9.52026			0.572017			0.286008	−	0.958227i	$-0.407671\pi$
$277$	9.52026			0.572017			0.286008	+	0.958227i	$0.407671\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.7288	−	23.7789i	−0.818989	−	1.41853i	−0.906428	−	0.422361i	$-0.861202\pi$
$281$	−13.7288	−	23.7789i	−0.818989	−	1.41853i	0.0874389	−	0.996170i	$-0.472132\pi$
$282$		0			0
$283$	12.6771	−	21.9574i	0.753577	−	1.30523i	−0.192502	−	0.981297i	$-0.561660\pi$
$283$	12.6771	−	21.9574i	0.753577	−	1.30523i	0.946079	−	0.323937i	$-0.105007\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.46863	−	14.6681i	0.499887	−	0.865830i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−13.0627			−0.763134			−0.381567	−	0.924341i	$-0.624615\pi$
$293$	−13.0627			−0.763134			−0.381567	+	0.924341i	$0.624615\pi$
$294$		0			0
$295$	14.4686	+	25.0604i	0.842396	+	1.45907i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.64575	+	6.31463i	−0.210839	+	0.365184i
$300$		0			0
$301$	0.583005	−	1.00979i	0.0336039	−	0.0582036i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	54.4575			3.11823
$306$		0			0
$307$	−2.32288	+	4.02334i	−0.132574	+	0.229624i	−0.924668	−	0.380775i	$-0.875657\pi$
$307$	−2.32288	+	4.02334i	−0.132574	+	0.229624i	0.792094	+	0.610399i	$0.208991\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.35425			0.473726			0.236863	−	0.971543i	$-0.423881\pi$
$311$	8.35425			0.473726			0.236863	+	0.971543i	$0.423881\pi$
$312$		0			0
$313$	11.4373	+	19.8099i	0.646472	+	1.11972i	0.983959	+	0.178392i	$0.0570895\pi$
$313$	11.4373	+	19.8099i	0.646472	+	1.11972i	−0.337488	+	0.941330i	$0.609577\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	−1.17712	−	2.03884i	−0.0659063	−	0.114153i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−8.29150	+	14.3613i	−0.459930	+	0.796622i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.93725	−	13.7477i	−0.437595	−	0.757937i
$330$		0			0
$331$	27.8118			1.52867			0.764336	−	0.644818i	$-0.223067\pi$
$331$	27.8118			1.52867			0.764336	+	0.644818i	$0.223067\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−16.9373			−0.925381
$336$		0			0
$337$	10.1458	−	17.5730i	0.552674	−	0.957260i	−0.445406	−	0.895329i	$-0.646941\pi$
$337$	10.1458	−	17.5730i	0.552674	−	0.957260i	0.998080	−	0.0619313i	$-0.0197260\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.228757			0.0123879
$342$		0			0
$343$	−18.5830			−1.00339
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.61438	+	2.79619i	−0.0866644	+	0.150107i	−0.906099	−	0.423065i	$-0.860954\pi$
$347$	−1.61438	+	2.79619i	−0.0866644	+	0.150107i	0.819435	+	0.573172i	$0.194287\pi$
$348$		0			0
$349$	−21.1660			−1.13299			−0.566495	−	0.824065i	$-0.691701\pi$
$349$	−21.1660			−1.13299			−0.566495	+	0.824065i	$0.691701\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	18.8745			1.00459			0.502294	−	0.864697i	$-0.332489\pi$
$353$	18.8745			1.00459			0.502294	+	0.864697i	$0.332489\pi$
$354$		0			0
$355$	−24.2288	−	41.9654i	−1.28593	−	2.22729i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.46863	+	9.47194i	−0.288623	+	0.499910i	−0.973481	−	0.228766i	$-0.926531\pi$
$359$	−5.46863	+	9.47194i	−0.288623	+	0.499910i	0.684858	+	0.728676i	$0.259864\pi$
$360$		0			0
$361$	18.3745	+	4.83502i	0.967079	+	0.254475i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	22.4059	+	38.8081i	1.17278	+	2.03131i
$366$		0			0
$367$	−5.11438	−	8.85836i	−0.266968	−	0.462403i	0.701109	−	0.713054i	$-0.252689\pi$
$367$	−5.11438	−	8.85836i	−0.266968	−	0.462403i	−0.968077	+	0.250651i	$0.919355\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7.06275	+	12.2330i	0.366680	+	0.635108i
$372$		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
$377$	−3.64575	+	6.31463i	−0.187766	+	0.325220i
$378$		0			0
$379$	−21.2915			−1.09367			−0.546836	−	0.837240i	$-0.684168\pi$
$379$	−21.2915			−1.09367			−0.546836	+	0.837240i	$0.684168\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	15.7601	−	27.2973i	0.805305	−	1.39483i	−0.110780	−	0.993845i	$-0.535335\pi$
$383$	15.7601	−	27.2973i	0.805305	−	1.39483i	0.916085	−	0.400984i	$-0.131332\pi$
$384$		0			0
$385$	1.93725	−	3.35542i	0.0987316	−	0.171008i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	0.977086	−	0.212847i	$-0.0682735\pi$
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	−0.672874	+	0.739758i	$0.734940\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7.29150	+	12.6293i	0.366875	+	0.635447i
$396$		0			0
$397$	−18.4686	+	31.9886i	−0.926914	+	1.60546i	−0.138460	+	0.990368i	$0.544215\pi$
$397$	−18.4686	+	31.9886i	−0.926914	+	1.60546i	−0.788454	+	0.615094i	$0.789118\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.20850	−	5.55728i	0.160225	−	0.277517i	−0.774724	−	0.632299i	$-0.782111\pi$
$401$	3.20850	−	5.55728i	0.160225	−	0.277517i	0.934949	+	0.354782i	$0.115445\pi$
$402$		0			0
$403$	−0.354249	−	0.613577i	−0.0176464	−	0.0305644i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.64575			0.180713
$408$		0			0
$409$	−6.79150	−	11.7632i	−0.335818	−	0.581654i	0.647823	−	0.761790i	$-0.275679\pi$
$409$	−6.79150	−	11.7632i	−0.335818	−	0.581654i	−0.983642	+	0.180136i	$0.942346\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.53137	+	11.3127i	−0.321388	+	0.556660i
$414$		0			0
$415$	−14.4686	+	25.0604i	−0.710237	+	1.23017i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	31.7490			1.55104			0.775520	−	0.631322i	$-0.217488\pi$
$419$	31.7490			1.55104			0.775520	+	0.631322i	$0.217488\pi$
$420$		0			0
$421$	−11.4059	+	19.7556i	−0.555889	+	0.962827i	0.441945	+	0.897042i	$0.354289\pi$
$421$	−11.4059	+	19.7556i	−0.555889	+	0.962827i	−0.997834	+	0.0657853i	$0.979045\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	12.2915	+	21.2895i	0.594828	+	1.03027i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.93725	+	3.35542i	0.0933142	+	0.161625i	0.908904	−	0.417006i	$-0.136921\pi$
$431$	1.93725	+	3.35542i	0.0933142	+	0.161625i	−0.815590	+	0.578631i	$0.803587\pi$
$432$		0			0
$433$	6.93725	+	12.0157i	0.333383	+	0.577437i	0.983173	−	0.182677i	$-0.0584764\pi$
$433$	6.93725	+	12.0157i	0.333383	+	0.577437i	−0.649790	+	0.760114i	$0.725143\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.11438	+	14.6681i	0.292490	+	0.701670i
$438$		0			0
$439$	−18.4059	+	31.8799i	−0.878465	+	1.52155i	−0.0254393	+	0.999676i	$0.508098\pi$
$439$	−18.4059	+	31.8799i	−0.878465	+	1.52155i	−0.853025	+	0.521869i	$0.825235\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.67712	−	4.63692i	−0.127194	−	0.220306i	0.795394	−	0.606092i	$-0.207264\pi$
$443$	−2.67712	−	4.63692i	−0.127194	−	0.220306i	−0.922588	+	0.385786i	$0.873930\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	13.7085			0.646944			0.323472	−	0.946238i	$-0.395150\pi$
$449$	13.7085			0.646944			0.323472	+	0.946238i	$0.395150\pi$
$450$		0			0
$451$	3.32288	−	5.75539i	0.156468	−	0.271011i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−12.0000			−0.562569
$456$		0			0
$457$	1.12549			0.0526483			0.0263242	−	0.999653i	$-0.491620\pi$
$457$	1.12549			0.0526483			0.0263242	+	0.999653i	$0.491620\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−11.5830	+	20.0624i	−0.539474	+	0.934397i	0.459458	+	0.888200i	$0.348044\pi$
$461$	−11.5830	+	20.0624i	−0.539474	+	0.934397i	−0.998932	+	0.0461975i	$0.985290\pi$
$462$		0			0
$463$	−14.4575			−0.671898			−0.335949	−	0.941880i	$-0.609057\pi$
$463$	−14.4575			−0.671898			−0.335949	+	0.941880i	$0.609057\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−24.6458			−1.14047			−0.570235	−	0.821482i	$-0.693148\pi$
$467$	−24.6458			−1.14047			−0.570235	+	0.821482i	$0.693148\pi$
$468$		0			0
$469$	−3.82288	−	6.62141i	−0.176524	−	0.305749i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.228757	−	0.396218i	0.0105182	−	0.0182181i
$474$		0			0
$475$	13.9059	+	33.3595i	0.638046	+	1.53064i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.29150	+	12.6293i	0.333157	+	0.577045i	0.983129	−	0.182913i	$-0.0585527\pi$
$479$	7.29150	+	12.6293i	0.333157	+	0.577045i	−0.649972	+	0.759958i	$0.725219\pi$
$480$		0			0
$481$	−5.64575	−	9.77873i	−0.257424	−	0.445872i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−26.0516	−	45.1228i	−1.18294	−	2.04892i
$486$		0			0
$487$	22.2288			1.00728			0.503641	−	0.863913i	$-0.331994\pi$
$487$	22.2288			1.00728			0.503641	+	0.863913i	$0.331994\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−14.3542	+	24.8623i	−0.647798	+	1.12202i	0.335849	+	0.941916i	$0.390977\pi$
$491$	−14.3542	+	24.8623i	−0.647798	+	1.12202i	−0.983648	+	0.180104i	$0.942357\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.9373	−	18.9439i	0.490603	−	0.849749i
$498$		0			0
$499$	−15.6144	+	27.0449i	−0.698996	+	1.21070i	0.269819	+	0.962911i	$0.413036\pi$
$499$	−15.6144	+	27.0449i	−0.698996	+	1.21070i	−0.968815	+	0.247785i	$0.920297\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.5314	+	21.7050i	0.558746	+	0.967777i	0.997601	+	0.0692192i	$0.0220508\pi$
$503$	12.5314	+	21.7050i	0.558746	+	0.967777i	−0.438855	+	0.898558i	$0.644616\pi$
$504$		0			0
$505$	−30.4575			−1.35534
$506$		0			0
$507$		0			0
$508$		0			0
$509$	15.8745	+	27.4955i	0.703625	+	1.21871i	0.967185	+	0.254072i	$0.0817699\pi$
$509$	15.8745	+	27.4955i	0.703625	+	1.21871i	−0.263560	+	0.964643i	$0.584897\pi$
$510$		0			0
$511$	−10.1144	+	17.5186i	−0.447434	+	0.774978i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.93725	−	8.55157i	0.217561	−	0.376827i
$516$		0			0
$517$	−3.11438	−	5.39426i	−0.136970	−	0.237239i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	22.2915			0.976608			0.488304	−	0.872673i	$-0.337616\pi$
$521$	22.2915			0.976608			0.488304	+	0.872673i	$0.337616\pi$
$522$		0			0
$523$	14.9373	+	25.8721i	0.653161	+	1.13131i	0.982352	+	0.187044i	$0.0598906\pi$
$523$	14.9373	+	25.8721i	0.653161	+	1.13131i	−0.329191	+	0.944263i	$0.606776\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	4.85425	−	8.40781i	0.211054	−	0.365557i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−20.5830			−0.891549
$534$		0			0
$535$	8.58301	−	14.8662i	0.371076	−	0.642722i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−2.77124			−0.119366
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−12.0000	−	20.7846i	−0.514024	−	0.890315i
$546$		0			0
$547$	0.354249	+	0.613577i	0.0151466	+	0.0262346i	0.873499	−	0.486825i	$-0.161845\pi$
$547$	0.354249	+	0.613577i	0.0151466	+	0.0262346i	−0.858353	+	0.513060i	$0.828512\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.11438	+	14.6681i	0.260481	+	0.624882i
$552$		0			0
$553$	−3.29150	+	5.70105i	−0.139969	+	0.242433i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13.2915	−	23.0216i	−0.563179	−	0.975455i	−0.997217	−	0.0745599i	$-0.976245\pi$
$557$	−13.2915	−	23.0216i	−0.563179	−	0.975455i	0.434037	−	0.900895i	$-0.357089\pi$
$558$		0			0
$559$	−1.41699			−0.0599325
$560$		0			0
$561$		0			0
$562$		0			0
$563$	25.9373			1.09312			0.546562	−	0.837418i	$-0.315936\pi$
$563$	25.9373			1.09312			0.546562	+	0.837418i	$0.315936\pi$
$564$		0			0
$565$	−10.1771	+	17.6273i	−0.428155	+	0.741586i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	14.5830			0.611351			0.305676	−	0.952136i	$-0.401118\pi$
$569$	14.5830			0.611351			0.305676	+	0.952136i	$0.401118\pi$
$570$		0			0
$571$	39.8118			1.66607			0.833035	−	0.553220i	$-0.186601\pi$
$571$	39.8118			1.66607			0.833035	+	0.553220i	$0.186601\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−15.1144	+	26.1789i	−0.630313	+	1.09173i
$576$		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
$581$	−13.0627			−0.541934
$582$		0			0
$583$	2.77124	+	4.79993i	0.114773	+	0.198793i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	22.9373	−	39.7285i	0.946722	−	1.63977i	0.194455	−	0.980911i	$-0.437706\pi$
$587$	22.9373	−	39.7285i	0.946722	−	1.63977i	0.752267	−	0.658859i	$-0.228961\pi$
$588$		0			0
$589$	−1.53137	−	0.198109i	−0.0630991	−	0.00816294i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	20.1458	+	34.8935i	0.827287	+	1.43290i	0.900159	+	0.435562i	$0.143450\pi$
$593$	20.1458	+	34.8935i	0.827287	+	1.43290i	−0.0728721	+	0.997341i	$0.523216\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.531373	+	0.920365i	0.0217113	+	0.0376051i	0.876677	−	0.481080i	$-0.159755\pi$
$599$	0.531373	+	0.920365i	0.0217113	+	0.0376051i	−0.854966	+	0.518685i	$0.826422\pi$
$600$		0			0
$601$	31.5830			1.28830			0.644149	−	0.764900i	$-0.277212\pi$
$601$	31.5830			1.28830			0.644149	+	0.764900i	$0.277212\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−19.2915	+	33.4139i	−0.784311	+	1.35847i
$606$		0			0
$607$	8.93725			0.362752			0.181376	−	0.983414i	$-0.441945\pi$
$607$	8.93725			0.362752			0.181376	+	0.983414i	$0.441945\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−9.64575	+	16.7069i	−0.390225	+	0.675890i
$612$		0			0
$613$	−14.2915	+	24.7536i	−0.577228	+	0.999789i	0.418567	+	0.908186i	$0.362532\pi$
$613$	−14.2915	+	24.7536i	−0.577228	+	0.999789i	−0.995796	+	0.0916030i	$0.970801\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.437254	+	0.757346i	0.0176032	+	0.0304896i	0.874693	−	0.484678i	$-0.161063\pi$
$617$	0.437254	+	0.757346i	0.0176032	+	0.0304896i	−0.857090	+	0.515167i	$0.827730\pi$
$618$		0			0
$619$	−44.4575			−1.78690			−0.893449	−	0.449164i	$-0.851722\pi$
$619$	−44.4575			−1.78690			−0.893449	+	0.449164i	$0.851722\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−1.14575	+	1.98450i	−0.0458301	+	0.0793800i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	11.4059	+	19.7556i	0.454061	+	0.786457i	0.998634	−	0.0522570i	$-0.0166415\pi$
$631$	11.4059	+	19.7556i	0.454061	+	0.786457i	−0.544573	+	0.838714i	$0.683308\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−9.87451			−0.391858
$636$		0			0
$637$	4.29150	+	7.43310i	0.170036	+	0.294510i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.43725	+	16.3458i	−0.372749	+	0.645620i	−0.989987	−	0.141156i	$-0.954918\pi$
$641$	−9.43725	+	16.3458i	−0.372749	+	0.645620i	0.617238	+	0.786776i	$0.288251\pi$
$642$		0			0
$643$	15.2601	−	26.4313i	0.601801	−	1.04235i	−0.390748	−	0.920498i	$-0.627783\pi$
$643$	15.2601	−	26.4313i	0.601801	−	1.04235i	0.992548	−	0.121852i	$-0.0388832\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	30.4575			1.19741			0.598704	−	0.800970i	$-0.295683\pi$
$647$	30.4575			1.19741			0.598704	+	0.800970i	$0.295683\pi$
$648$		0			0
$649$	−2.56275	+	4.43881i	−0.100597	+	0.174238i
$650$		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
$655$	−25.4059	−	44.0043i	−0.992690	−	1.71939i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.29150	−	2.23695i	−0.0503098	−	0.0871391i	0.839774	−	0.542936i	$-0.182688\pi$
$659$	−1.29150	−	2.23695i	−0.0503098	−	0.0871391i	−0.890084	+	0.455797i	$0.849354\pi$
$660$		0			0
$661$	5.11438	+	8.85836i	0.198926	+	0.344550i	0.948181	−	0.317732i	$-0.102921\pi$
$661$	5.11438	+	8.85836i	0.198926	+	0.344550i	−0.749254	+	0.662282i	$0.769588\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−15.8745	+	20.7846i	−0.615587	+	0.805993i
$666$		0			0
$667$	−6.64575	+	11.5108i	−0.257325	+	0.445699i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.82288	+	8.35347i	0.186185	+	0.322482i
$672$		0			0
$673$	17.8745			0.689012			0.344506	−	0.938784i	$-0.388046\pi$
$673$	17.8745			0.689012			0.344506	+	0.938784i	$0.388046\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	32.5830			1.25227			0.626133	−	0.779716i	$-0.284637\pi$
$677$	32.5830			1.25227			0.626133	+	0.779716i	$0.284637\pi$
$678$		0			0
$679$	11.7601	−	20.3691i	0.451312	−	0.781696i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−26.5830			−1.01717			−0.508585	−	0.861012i	$-0.669831\pi$
$683$	−26.5830			−1.01717			−0.508585	+	0.861012i	$0.669831\pi$
$684$		0			0
$685$	−20.3542			−0.777696
$686$		0			0
$687$		0			0
$688$		0			0
$689$	8.58301	−	14.8662i	0.326986	−	0.566357i
$690$		0			0
$691$	18.5830			0.706931			0.353465	−	0.935448i	$-0.385003\pi$
$691$	18.5830			0.706931			0.353465	+	0.935448i	$0.385003\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	48.6863			1.84678
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	7.82288	−	13.5496i	0.295466	−	0.511762i	−0.679627	−	0.733558i	$-0.737858\pi$
$701$	7.82288	−	13.5496i	0.295466	−	0.511762i	0.975093	+	0.221796i	$0.0711918\pi$
$702$		0			0
$703$	−24.4059	−	3.15731i	−0.920485	−	0.119080i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.87451	−	11.9070i	−0.258542	−	0.447809i
$708$		0			0
$709$	0.822876	+	1.42526i	0.0309037	+	0.0535269i	0.881064	−	0.472998i	$-0.156828\pi$
$709$	0.822876	+	1.42526i	0.0309037	+	0.0535269i	−0.850160	+	0.526525i	$0.823495\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.645751	−	1.11847i	−0.0241836	−	0.0418872i
$714$		0			0
$715$	−4.70850			−0.176088
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.64575	+	11.5108i	−0.247845	+	0.429280i	−0.962928	−	0.269760i	$-0.913056\pi$
$719$	−6.64575	+	11.5108i	−0.247845	+	0.429280i	0.715083	+	0.699040i	$0.246389\pi$
$720$		0			0
$721$	4.45751			0.166006
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−15.1144	+	26.1789i	−0.561334	+	0.972259i
$726$		0			0
$727$	11.2915	−	19.5575i	0.418779	−	0.725346i	−0.577038	−	0.816717i	$-0.695792\pi$
$727$	11.2915	−	19.5575i	0.418779	−	0.725346i	0.995817	+	0.0913712i	$0.0291250\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	42.1033			1.55512			0.777560	−	0.628809i	$-0.216457\pi$
$733$	42.1033			1.55512			0.777560	+	0.628809i	$0.216457\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.50000	−	2.59808i	−0.0552532	−	0.0957014i
$738$		0			0
$739$	6.90588	−	11.9613i	0.254037	−	0.440005i	−0.710597	−	0.703600i	$-0.751575\pi$
$739$	6.90588	−	11.9613i	0.254037	−	0.440005i	0.964633	+	0.263595i	$0.0849082\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.23987	−	9.07572i	0.192232	−	0.332956i	−0.753757	−	0.657153i	$-0.771761\pi$
$743$	5.23987	−	9.07572i	0.192232	−	0.332956i	0.945990	+	0.324197i	$0.105094\pi$
$744$		0			0
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	7.74902			0.283143
$750$		0			0
$751$	11.9373	+	20.6759i	0.435597	+	0.754475i	0.997344	−	0.0728333i	$-0.0232041\pi$
$751$	11.9373	+	20.6759i	0.435597	+	0.754475i	−0.561748	+	0.827309i	$0.689871\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.35425	−	9.27383i	0.194861	−	0.337509i
$756$		0			0
$757$	−8.29150	+	14.3613i	−0.301360	+	0.521970i	−0.976444	−	0.215770i	$-0.930774\pi$
$757$	−8.29150	+	14.3613i	−0.301360	+	0.521970i	0.675084	+	0.737740i	$0.264107\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.1255			−0.403299			−0.201649	−	0.979458i	$-0.564630\pi$
$761$	−11.1255			−0.403299			−0.201649	+	0.979458i	$0.564630\pi$
$762$		0			0
$763$	5.41699	−	9.38251i	0.196108	−	0.339670i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	15.8745			0.573195
$768$		0			0
$769$	−12.3542	−	21.3982i	−0.445506	−	0.771638i	0.552582	−	0.833459i	$-0.313643\pi$
$769$	−12.3542	−	21.3982i	−0.445506	−	0.771638i	−0.998087	+	0.0618204i	$0.980309\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	5.46863	+	9.47194i	0.196693	+	0.340682i	0.947454	−	0.319892i	$-0.103646\pi$
$773$	5.46863	+	9.47194i	0.196693	+	0.340682i	−0.750761	+	0.660574i	$0.770313\pi$
$774$		0			0
$775$	−1.46863	−	2.54374i	−0.0527546	−	0.0913737i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−27.2288	+	35.6508i	−0.975571	+	1.27732i
$780$		0			0
$781$	4.29150	−	7.43310i	0.153562	−	0.265977i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	19.2915	+	33.4139i	0.688543	+	1.19259i
$786$		0			0
$787$	5.47974			0.195332			0.0976658	−	0.995219i	$-0.468862\pi$
$787$	5.47974			0.195332			0.0976658	+	0.995219i	$0.468862\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−9.18824			−0.326696
$792$		0			0
$793$	14.9373	−	25.8721i	0.530437	−	0.918745i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.81176			−0.0995977			−0.0497989	−	0.998759i	$-0.515858\pi$
$797$	−2.81176			−0.0995977			−0.0497989	+	0.998759i	$0.515858\pi$
$798$		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
$805$	−21.8745			−0.770975
$806$		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
$811$	−10.3542	−	17.9341i	−0.363587	−	0.629751i	0.624961	−	0.780656i	$-0.285115\pi$
$811$	−10.3542	−	17.9341i	−0.363587	−	0.629751i	−0.988548	+	0.150905i	$0.951781\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	21.7601	−	37.6897i	0.762224	−	1.32021i
$816$		0			0
$817$	−1.87451	+	2.45431i	−0.0655807	+	0.0858653i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	0.808915	−	0.587925i	$-0.200055\pi$
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	−0.913616	+	0.406578i	$0.866722\pi$
$822$		0			0
$823$	−0.0627461	−	0.108679i	−0.00218719	−	0.00378832i	0.864930	−	0.501893i	$-0.167363\pi$
$823$	−0.0627461	−	0.108679i	−0.00218719	−	0.00378832i	−0.867117	+	0.498105i	$0.834030\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	23.6771	+	41.0100i	0.823334	+	1.42606i	0.903186	+	0.429250i	$0.141222\pi$
$827$	23.6771	+	41.0100i	0.823334	+	1.42606i	−0.0798514	+	0.996807i	$0.525445\pi$
$828$		0			0
$829$	25.1660			0.874052			0.437026	−	0.899449i	$-0.356032\pi$
$829$	25.1660			0.874052			0.437026	+	0.899449i	$0.356032\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	43.7490			1.51400
$836$		0			0
$837$		0			0
$838$		0			0
$839$	2.23987	−	3.87957i	0.0773289	−	0.133938i	−0.824768	−	0.565472i	$-0.808694\pi$
$839$	2.23987	−	3.87957i	0.0773289	−	0.133938i	0.902097	+	0.431534i	$0.142028\pi$
$840$		0			0
$841$	7.85425	−	13.6040i	0.270836	−	0.469102i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−16.4059	−	28.4158i	−0.564379	−	0.977534i
$846$		0			0
$847$	−17.4170			−0.598455
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−10.2915	−	17.8254i	−0.352788	−	0.611047i
$852$		0			0
$853$	6.29150	−	10.8972i	0.215417	−	0.373113i	−0.737985	−	0.674818i	$-0.764222\pi$
$853$	6.29150	−	10.8972i	0.215417	−	0.373113i	0.953401	+	0.301705i	$0.0975556\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.5000	−	18.1865i	0.358673	−	0.621240i	−0.629066	−	0.777352i	$-0.716563\pi$
$857$	10.5000	−	18.1865i	0.358673	−	0.621240i	0.987739	+	0.156112i	$0.0498959\pi$
$858$		0			0
$859$	−6.61438	−	11.4564i	−0.225680	−	0.390889i	0.730843	−	0.682545i	$-0.239127\pi$
$859$	−6.61438	−	11.4564i	−0.225680	−	0.390889i	−0.956523	+	0.291656i	$0.905794\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−46.9373			−1.59776			−0.798881	−	0.601489i	$-0.794575\pi$
$863$	−46.9373			−1.59776			−0.798881	+	0.601489i	$0.794575\pi$
$864$		0			0
$865$	10.9373	+	18.9439i	0.371878	+	0.644111i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.29150	+	2.23695i	−0.0438112	+	0.0758833i
$870$		0			0
$871$	−4.64575	+	8.04668i	−0.157415	+	0.272651i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−19.7490			−0.667639
$876$		0			0
$877$	18.1771	−	31.4837i	0.613798	−	1.06313i	−0.376796	−	0.926296i	$-0.622974\pi$
$877$	18.1771	−	31.4837i	0.613798	−	1.06313i	0.990594	−	0.136833i	$-0.0436924\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	5.12549			0.172682			0.0863411	−	0.996266i	$-0.472483\pi$
$881$	5.12549			0.172682			0.0863411	+	0.996266i	$0.472483\pi$
$882$		0			0
$883$	20.1974	+	34.9829i	0.679696	+	1.17727i	0.975072	+	0.221887i	$0.0712217\pi$
$883$	20.1974	+	34.9829i	0.679696	+	1.17727i	−0.295376	+	0.955381i	$0.595445\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.2915	+	33.4139i	0.647745	+	1.12193i	0.983660	+	0.180035i	$0.0576212\pi$
$887$	19.2915	+	33.4139i	0.647745	+	1.12193i	−0.335915	+	0.941892i	$0.609045\pi$
$888$		0			0
$889$	−2.22876	−	3.86032i	−0.0747501	−	0.129471i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	16.1771	+	38.8081i	0.541347	+	1.29866i
$894$		0			0
$895$	36.3431	−	62.9482i	1.21482	−	2.10412i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.645751	−	1.11847i	−0.0215370	−	0.0373032i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	15.4170			0.512478
$906$		0			0
$907$	12.0314	−	20.8389i	0.399495	−	0.691946i	−0.594168	−	0.804341i	$-0.702519\pi$
$907$	12.0314	−	20.8389i	0.399495	−	0.691946i	0.993664	+	0.112395i	$0.0358521\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.06275			0.0352103			0.0176052	−	0.999845i	$-0.494396\pi$
$911$	1.06275			0.0352103			0.0176052	+	0.999845i	$0.494396\pi$
$912$		0			0
$913$	−5.12549			−0.169629
$914$		0			0
$915$		0			0
$916$		0			0
$917$	11.4686	−	19.8642i	0.378727	−	0.655975i
$918$		0			0
$919$	−11.8745			−0.391704			−0.195852	−	0.980633i	$-0.562747\pi$
$919$	−11.8745			−0.391704			−0.195852	+	0.980633i	$0.562747\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−26.5830			−0.874990
$924$		0			0
$925$	−23.4059	−	40.5402i	−0.769581	−	1.33295i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	5.79150	−	10.0312i	0.190013	−	0.329112i	−0.755241	−	0.655447i	$-0.772480\pi$
$929$	5.79150	−	10.0312i	0.190013	−	0.329112i	0.945254	+	0.326335i	$0.105814\pi$
$930$		0			0
$931$	18.5516	+	2.39997i	0.608005	+	0.0786557i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−19.4373	−	33.6663i	−0.634987	−	1.09983i	−0.986518	−	0.163654i	$-0.947672\pi$
$937$	−19.4373	−	33.6663i	−0.634987	−	1.09983i	0.351530	−	0.936176i	$-0.385661\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	29.5830	+	51.2393i	0.964378	+	1.67035i	0.711276	+	0.702913i	$0.248118\pi$
$941$	29.5830	+	51.2393i	0.964378	+	1.67035i	0.253103	+	0.967439i	$0.418549\pi$
$942$		0			0
$943$	−37.5203			−1.22183
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−27.8745	+	48.2801i	−0.905800	+	1.56889i	−0.0859598	+	0.996299i	$0.527396\pi$
$947$	−27.8745	+	48.2801i	−0.905800	+	1.56889i	−0.819840	+	0.572593i	$0.805938\pi$
$948$		0			0
$949$	24.5830			0.797998
$950$		0			0
$951$		0			0
$952$		0			0
$953$	19.7288	−	34.1712i	0.639077	−	1.10691i	−0.346559	−	0.938028i	$-0.612650\pi$
$953$	19.7288	−	34.1712i	0.639077	−	1.10691i	0.985636	−	0.168886i	$-0.0540169\pi$
$954$		0			0
$955$	−26.5830	+	46.0431i	−0.860206	+	1.48992i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.59412	−	7.95725i	−0.148352	−	0.256953i
$960$		0			0
$961$	−30.8745			−0.995952
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.0000	−	20.7846i	−0.386294	−	0.669080i
$966$		0			0
$967$	−1.35425	+	2.34563i	−0.0435497	+	0.0754303i	−0.886979	−	0.461810i	$-0.847200\pi$
$967$	−1.35425	+	2.34563i	−0.0435497	+	0.0754303i	0.843429	+	0.537241i	$0.180533\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.19738	+	12.4662i	−0.230975	+	0.400060i	−0.958095	−	0.286450i	$-0.907525\pi$
$971$	−7.19738	+	12.4662i	−0.230975	+	0.400060i	0.727120	+	0.686510i	$0.240858\pi$
$972$		0			0
$973$	10.9889	+	19.0333i	0.352288	+	0.610180i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−45.4575			−1.45431			−0.727157	−	0.686471i	$-0.759159\pi$
$977$	−45.4575			−1.45431			−0.727157	+	0.686471i	$0.759159\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$	15.8745	−	27.4955i	0.506318	−	0.876969i	−0.493655	−	0.869658i	$-0.664339\pi$
$983$	15.8745	−	27.4955i	0.506318	−	0.876969i	0.999973	−	0.00731102i	$-0.00232719\pi$
$984$		0			0
$985$	4.29150	−	7.43310i	0.136739	−	0.236838i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.58301			−0.0821348
$990$		0			0
$991$	−22.5830	+	39.1149i	−0.717373	+	1.24253i	0.244664	+	0.969608i	$0.421322\pi$
$991$	−22.5830	+	39.1149i	−0.717373	+	1.24253i	−0.962037	+	0.272918i	$0.912011\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	43.2915			1.37243
$996$		0			0
$997$	5.11438	+	8.85836i	0.161974	+	0.280547i	0.935577	−	0.353124i	$-0.114881\pi$
$997$	5.11438	+	8.85836i	0.161974	+	0.280547i	−0.773603	+	0.633671i	$0.781547\pi$
$998$		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.1873.2		4
3.2	odd	2		304.2.i.e.49.1		4
4.3	odd	2		342.2.g.f.163.2		4
12.11	even	2		38.2.c.b.11.2	yes	4
19.7	even	3	inner	2736.2.s.v.577.2		4
24.5	odd	2		1216.2.i.k.961.2		4
24.11	even	2		1216.2.i.l.961.1		4
57.8	even	6		5776.2.a.z.1.1		2
57.11	odd	6		5776.2.a.ba.1.2		2
57.26	odd	6		304.2.i.e.273.1		4
60.23	odd	4		950.2.j.g.49.4		8
60.47	odd	4		950.2.j.g.49.1		8
60.59	even	2		950.2.e.k.201.1		4
76.7	odd	6		342.2.g.f.235.2		4
76.11	odd	6		6498.2.a.ba.1.1		2
76.27	even	6		6498.2.a.bg.1.1		2
228.11	even	6		722.2.a.j.1.1		2
228.23	even	18		722.2.e.n.423.1		12
228.35	even	18		722.2.e.n.99.1		12
228.47	even	18		722.2.e.n.245.1		12
228.59	odd	18		722.2.e.o.595.1		12
228.71	odd	18		722.2.e.o.389.2		12
228.83	even	6		38.2.c.b.7.2	✓	4
228.107	odd	6		722.2.c.j.653.1		4
228.119	even	18		722.2.e.n.389.1		12
228.131	even	18		722.2.e.n.595.2		12
228.143	odd	18		722.2.e.o.245.2		12
228.155	odd	18		722.2.e.o.99.2		12
228.167	odd	18		722.2.e.o.423.2		12
228.179	odd	6		722.2.a.g.1.2		2
228.203	odd	18		722.2.e.o.415.1		12
228.215	even	18		722.2.e.n.415.2		12
228.227	odd	2		722.2.c.j.429.1		4
456.83	even	6		1216.2.i.l.577.1		4
456.197	odd	6		1216.2.i.k.577.2		4
1140.83	odd	12		950.2.j.g.349.1		8
1140.539	even	6		950.2.e.k.501.1		4
1140.767	odd	12		950.2.j.g.349.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.2	✓	4	228.83	even	6
38.2.c.b.11.2	yes	4	12.11	even	2
304.2.i.e.49.1		4	3.2	odd	2
304.2.i.e.273.1		4	57.26	odd	6
342.2.g.f.163.2		4	4.3	odd	2
342.2.g.f.235.2		4	76.7	odd	6
722.2.a.g.1.2		2	228.179	odd	6
722.2.a.j.1.1		2	228.11	even	6
722.2.c.j.429.1		4	228.227	odd	2
722.2.c.j.653.1		4	228.107	odd	6
722.2.e.n.99.1		12	228.35	even	18
722.2.e.n.245.1		12	228.47	even	18
722.2.e.n.389.1		12	228.119	even	18
722.2.e.n.415.2		12	228.215	even	18
722.2.e.n.423.1		12	228.23	even	18
722.2.e.n.595.2		12	228.131	even	18
722.2.e.o.99.2		12	228.155	odd	18
722.2.e.o.245.2		12	228.143	odd	18
722.2.e.o.389.2		12	228.71	odd	18
722.2.e.o.415.1		12	228.203	odd	18
722.2.e.o.423.2		12	228.167	odd	18
722.2.e.o.595.1		12	228.59	odd	18
950.2.e.k.201.1		4	60.59	even	2
950.2.e.k.501.1		4	1140.539	even	6
950.2.j.g.49.1		8	60.47	odd	4
950.2.j.g.49.4		8	60.23	odd	4
950.2.j.g.349.1		8	1140.83	odd	12
950.2.j.g.349.4		8	1140.767	odd	12
1216.2.i.k.577.2		4	456.197	odd	6
1216.2.i.k.961.2		4	24.5	odd	2
1216.2.i.l.577.1		4	456.83	even	6
1216.2.i.l.961.1		4	24.11	even	2
2736.2.s.v.577.2		4	19.7	even	3	inner
2736.2.s.v.1873.2		4	1.1	even	1	trivial
5776.2.a.z.1.1		2	57.8	even	6
5776.2.a.ba.1.2		2	57.11	odd	6
6498.2.a.ba.1.1		2	76.11	odd	6
6498.2.a.bg.1.1		2	76.27	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)

\(f(q)\)	\(=\)	\(q+(1.82288 - 3.15731i) q^{5} +1.64575 q^{7} +O(q^{10})\)	\(q+(1.82288 - 3.15731i) q^{5} +1.64575 q^{7} +0.645751 q^{11} +(-1.00000 - 1.73205i) q^{13} +(-4.32288 - 0.559237i) q^{19} +(-1.82288 - 3.15731i) q^{23} +(-4.14575 - 7.18065i) q^{25} +(-1.82288 - 3.15731i) q^{29} +0.354249 q^{31} +(3.00000 - 5.19615i) q^{35} +5.64575 q^{37} +(5.14575 - 8.91270i) q^{41} +(0.354249 - 0.613577i) q^{43} +(-4.82288 - 8.35347i) q^{47} -4.29150 q^{49} +(4.29150 + 7.43310i) q^{53} +(1.17712 - 2.03884i) q^{55} +(-3.96863 + 6.87386i) q^{59} +(7.46863 + 12.9360i) q^{61} -7.29150 q^{65} +(-2.32288 - 4.02334i) q^{67} +(6.64575 - 11.5108i) q^{71} +(-6.14575 + 10.6448i) q^{73} +1.06275 q^{77} +(-2.00000 + 3.46410i) q^{79} -7.93725 q^{83} +(-1.64575 - 2.85052i) q^{91} +(-9.64575 + 12.6293i) q^{95} +(7.14575 - 12.3768i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 4 q^{7}+O(q^{10}) \) 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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