LMFDB - Embedded newform 2736.2.s.ba.1873.4

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 1368)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1873.4
Root			$-0.758290 + 1.31340i$ of defining polynomial
Character	$\chi$	$=$	2736.1873
Dual form			2736.2.s.ba.577.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16659 - 2.02059i) q^{5} -0.538445 q^{7} +O(q^{10})$	$q+(1.16659 - 2.02059i) q^{5} -0.538445 q^{7} +4.33317 q^{11} +(-1.31659 - 2.28041i) q^{13} +(-1.53844 + 2.66466i) q^{17} +(-0.0218647 + 4.35884i) q^{19} +(4.40502 + 7.62971i) q^{23} +(-0.221850 - 0.384256i) q^{25} +(-0.699986 - 1.21241i) q^{29} +5.57160 q^{31} +(-0.628142 + 1.08797i) q^{35} +12.1432 q^{37} +(-0.838459 + 1.45225i) q^{41} +(4.32425 - 7.48981i) q^{43} +(2.79473 + 4.84061i) q^{47} -6.71008 q^{49} +(-5.96132 - 10.3253i) q^{53} +(5.05502 - 8.75556i) q^{55} +(-0.866573 + 1.50095i) q^{59} +(4.34975 + 7.53399i) q^{61} -6.14369 q^{65} +(-2.36397 - 4.09451i) q^{67} +(3.17163 - 5.49343i) q^{71} +(6.16635 - 10.6804i) q^{73} -2.33317 q^{77} +(-2.41899 + 4.18981i) q^{79} -6.34327 q^{83} +(3.58946 + 6.21713i) q^{85} +(-2.94346 - 5.09823i) q^{89} +(0.708913 + 1.22787i) q^{91} +(8.78192 + 5.12915i) q^{95} +(0.644961 - 1.11711i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} + 4 q^{7}+O(q^{10}) $ 8 * q - 4 * q^5 + 4 * q^7	$ 8 q - 4 q^{5} + 4 q^{7} + 8 q^{11} - 4 q^{17} - 8 q^{19} + 8 q^{23} - 4 q^{25} + 4 q^{31} + 16 q^{37} - 4 q^{41} + 6 q^{43} + 4 q^{47} - 16 q^{49} - 16 q^{53} + 16 q^{55} + 12 q^{59} - 8 q^{61} - 48 q^{65} - 2 q^{67} - 4 q^{71} - 4 q^{73} + 8 q^{77} + 22 q^{79} + 8 q^{83} - 8 q^{85} + 12 q^{89} + 2 q^{91} + 32 q^{95} + 24 q^{97}+O(q^{100}) $ 8 * q - 4 * q^5 + 4 * q^7 + 8 * q^11 - 4 * q^17 - 8 * q^19 + 8 * q^23 - 4 * q^25 + 4 * q^31 + 16 * q^37 - 4 * q^41 + 6 * q^43 + 4 * q^47 - 16 * q^49 - 16 * q^53 + 16 * q^55 + 12 * q^59 - 8 * q^61 - 48 * q^65 - 2 * q^67 - 4 * q^71 - 4 * q^73 + 8 * q^77 + 22 * q^79 + 8 * q^83 - 8 * q^85 + 12 * q^89 + 2 * q^91 + 32 * q^95 + 24 * 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
$5$	1.16659	−	2.02059i	0.521714	−	0.903634i	−0.477967	−	0.878378i	$-0.658626\pi$
$5$	1.16659	−	2.02059i	0.521714	−	0.903634i	0.999681	−	0.0252568i	$-0.00804036\pi$
$6$		0			0
$7$	−0.538445			−0.203513			−0.101756	−	0.994809i	$-0.532446\pi$
$7$	−0.538445			−0.203513			−0.101756	+	0.994809i	$0.532446\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.33317			1.30650			0.653251	−	0.757142i	$-0.273405\pi$
$11$	4.33317			1.30650			0.653251	+	0.757142i	$0.273405\pi$
$12$		0			0
$13$	−1.31659	−	2.28041i	−0.365158	−	0.632471i	0.623644	−	0.781709i	$-0.285652\pi$
$13$	−1.31659	−	2.28041i	−0.365158	−	0.632471i	−0.988801	+	0.149237i	$0.952318\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.53844	+	2.66466i	−0.373128	+	0.646276i	−0.990045	−	0.140752i	$-0.955048\pi$
$17$	−1.53844	+	2.66466i	−0.373128	+	0.646276i	0.616917	+	0.787028i	$0.288381\pi$
$18$		0			0
$19$	−0.0218647	+	4.35884i	−0.00501612	+	0.999987i
$19$	−0.0218647	+	4.35884i	−0.00501612	+	0.999987i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.40502	+	7.62971i	0.918510	+	1.59091i	0.801680	+	0.597753i	$0.203940\pi$
$23$	4.40502	+	7.62971i	0.918510	+	1.59091i	0.116829	+	0.993152i	$0.462727\pi$
$24$		0			0
$25$	−0.221850	−	0.384256i	−0.0443701	−	0.0768512i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.699986	−	1.21241i	−0.129984	−	0.225139i	0.793686	−	0.608328i	$-0.208159\pi$
$29$	−0.699986	−	1.21241i	−0.129984	−	0.225139i	−0.923670	+	0.383189i	$0.874826\pi$
$30$		0			0
$31$	5.57160			1.00069			0.500345	−	0.865826i	$-0.333207\pi$
$31$	5.57160			1.00069			0.500345	+	0.865826i	$0.333207\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.628142	+	1.08797i	−0.106175	+	0.183901i
$36$		0			0
$37$	12.1432			1.99633			0.998166	−	0.0605431i	$-0.0192833\pi$
$37$	12.1432			1.99633			0.998166	+	0.0605431i	$0.0192833\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.838459	+	1.45225i	−0.130945	+	0.226804i	−0.924041	−	0.382293i	$-0.875135\pi$
$41$	−0.838459	+	1.45225i	−0.130945	+	0.226804i	0.793096	+	0.609097i	$0.208468\pi$
$42$		0			0
$43$	4.32425	−	7.48981i	0.659441	−	1.14219i	−0.321319	−	0.946971i	$-0.604126\pi$
$43$	4.32425	−	7.48981i	0.659441	−	1.14219i	0.980760	−	0.195215i	$-0.0625405\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.79473	+	4.84061i	0.407653	+	0.706076i	0.994626	−	0.103530i	$-0.0330139\pi$
$47$	2.79473	+	4.84061i	0.407653	+	0.706076i	−0.586973	+	0.809606i	$0.699681\pi$
$48$		0			0
$49$	−6.71008			−0.958582
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.96132	−	10.3253i	−0.818850	−	1.41829i	−0.906530	−	0.422141i	$-0.861279\pi$
$53$	−5.96132	−	10.3253i	−0.818850	−	1.41829i	0.0876805	−	0.996149i	$-0.472055\pi$
$54$		0			0
$55$	5.05502	−	8.75556i	0.681619	−	1.18060i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.866573	+	1.50095i	−0.112818	+	0.195407i	−0.916905	−	0.399104i	$-0.869321\pi$
$59$	−0.866573	+	1.50095i	−0.112818	+	0.195407i	0.804087	+	0.594511i	$0.202654\pi$
$60$		0			0
$61$	4.34975	+	7.53399i	0.556929	+	0.964629i	0.997751	+	0.0670345i	$0.0213538\pi$
$61$	4.34975	+	7.53399i	0.556929	+	0.964629i	−0.440822	+	0.897595i	$0.645313\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.14369			−0.762031
$66$		0			0
$67$	−2.36397	−	4.09451i	−0.288804	−	0.500224i	0.684720	−	0.728806i	$-0.259924\pi$
$67$	−2.36397	−	4.09451i	−0.288804	−	0.500224i	−0.973525	+	0.228582i	$0.926591\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.17163	−	5.49343i	0.376404	−	0.651950i	−0.614132	−	0.789203i	$-0.710494\pi$
$71$	3.17163	−	5.49343i	0.376404	−	0.651950i	0.990536	+	0.137253i	$0.0438273\pi$
$72$		0			0
$73$	6.16635	−	10.6804i	0.721716	−	1.25005i	−0.238595	−	0.971119i	$-0.576687\pi$
$73$	6.16635	−	10.6804i	0.721716	−	1.25005i	0.960311	−	0.278930i	$-0.0899799\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.33317			−0.265890
$78$		0			0
$79$	−2.41899	+	4.18981i	−0.272158	+	0.471391i	−0.969414	−	0.245431i	$-0.921071\pi$
$79$	−2.41899	+	4.18981i	−0.272158	+	0.471391i	0.697256	+	0.716822i	$0.254404\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6.34327			−0.696264			−0.348132	−	0.937446i	$-0.613184\pi$
$83$	−6.34327			−0.696264			−0.348132	+	0.937446i	$0.613184\pi$
$84$		0			0
$85$	3.58946	+	6.21713i	0.389331	+	0.674342i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.94346	−	5.09823i	−0.312006	−	0.540411i	0.666790	−	0.745245i	$-0.267668\pi$
$89$	−2.94346	−	5.09823i	−0.312006	−	0.540411i	−0.978797	+	0.204835i	$0.934334\pi$
$90$		0			0
$91$	0.708913	+	1.22787i	0.0743143	+	0.128716i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.78192	+	5.12915i	0.901006	+	0.526240i
$96$		0			0
$97$	0.644961	−	1.11711i	0.0654859	−	0.113425i	−0.831424	−	0.555639i	$-0.812474\pi$
$97$	0.644961	−	1.11711i	0.0654859	−	0.113425i	0.896909	+	0.442214i	$0.145807\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.20479	−	10.7470i	−0.617400	−	1.06937i	−0.989958	−	0.141359i	$-0.954853\pi$
$101$	−6.20479	−	10.7470i	−0.617400	−	1.06937i	0.372558	−	0.928009i	$-0.378481\pi$
$102$		0			0
$103$	8.79425			0.866523			0.433262	−	0.901268i	$-0.357363\pi$
$103$	8.79425			0.866523			0.433262	+	0.901268i	$0.357363\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.55375			0.343554			0.171777	−	0.985136i	$-0.445049\pi$
$107$	3.55375			0.343554			0.171777	+	0.985136i	$0.445049\pi$
$108$		0			0
$109$	5.35504	−	9.27520i	0.512920	−	0.888403i	−0.486968	−	0.873420i	$-0.661897\pi$
$109$	5.35504	−	9.27520i	0.512920	−	0.888403i	0.999888	−	0.0149832i	$-0.00476947\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.41006			−0.885224			−0.442612	−	0.896713i	$-0.645948\pi$
$113$	−9.41006			−0.885224			−0.442612	+	0.896713i	$0.645948\pi$
$114$		0			0
$115$	20.5553			1.91680
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.828367	−	1.43477i	0.0759363	−	0.131526i
$120$		0			0
$121$	7.77640			0.706945
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.6306			0.950833
$126$		0			0
$127$	7.69951	+	13.3359i	0.683221	+	1.18337i	0.973992	+	0.226581i	$0.0727547\pi$
$127$	7.69951	+	13.3359i	0.683221	+	1.18337i	−0.290772	+	0.956792i	$0.593912\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.49472	+	9.51713i	−0.480075	+	0.831515i	−0.999739	−	0.0228560i	$-0.992724\pi$
$131$	−5.49472	+	9.51713i	−0.480075	+	0.831515i	0.519663	+	0.854371i	$0.326057\pi$
$132$		0			0
$133$	0.0117730	−	2.34700i	0.00102084	−	0.203510i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.44322	+	14.6241i	0.721353	+	1.24942i	0.960458	+	0.278427i	$0.0898129\pi$
$137$	8.44322	+	14.6241i	0.721353	+	1.24942i	−0.239104	+	0.970994i	$0.576854\pi$
$138$		0			0
$139$	−2.32425	−	4.02571i	−0.197140	−	0.341457i	0.750460	−	0.660916i	$-0.229832\pi$
$139$	−2.32425	−	4.02571i	−0.197140	−	0.341457i	−0.947600	+	0.319459i	$0.896499\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.70503	−	9.88140i	−0.477079	−	0.826325i
$144$		0			0
$145$	−3.26638			−0.271258
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.07184	−	8.78469i	0.415502	−	0.719670i	−0.579979	−	0.814631i	$-0.696939\pi$
$149$	5.07184	−	8.78469i	0.415502	−	0.719670i	0.995481	+	0.0949613i	$0.0302727\pi$
$150$		0			0
$151$	−10.5328			−0.857143			−0.428572	−	0.903508i	$-0.640983\pi$
$151$	−10.5328			−0.857143			−0.428572	+	0.903508i	$0.640983\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.49976	−	11.2579i	0.522073	−	0.904258i
$156$		0			0
$157$	5.11533	−	8.86002i	0.408248	−	0.707106i	−0.586445	−	0.809989i	$-0.699473\pi$
$157$	5.11533	−	8.86002i	0.408248	−	0.707106i	0.994694	+	0.102882i	$0.0328065\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.37186	−	4.10818i	−0.186929	−	0.323770i
$162$		0			0
$163$	0.261498			0.0204821			0.0102411	−	0.999948i	$-0.496740\pi$
$163$	0.261498			0.0204821			0.0102411	+	0.999948i	$0.496740\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.738191	−	1.27858i	−0.0571229	−	0.0989399i	0.836050	−	0.548654i	$-0.184859\pi$
$167$	−0.738191	−	1.27858i	−0.0571229	−	0.0989399i	−0.893173	+	0.449714i	$0.851526\pi$
$168$		0			0
$169$	3.03316	−	5.25359i	0.233320	−	0.404122i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.36633	+	16.2230i	−0.712109	+	1.23341i	0.251955	+	0.967739i	$0.418927\pi$
$173$	−9.36633	+	16.2230i	−0.712109	+	1.23341i	−0.964064	+	0.265670i	$0.914407\pi$
$174$		0			0
$175$	0.119454	+	0.206901i	0.00902988	+	0.0156402i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.44577			0.706010			0.353005	−	0.935621i	$-0.385160\pi$
$179$	9.44577			0.706010			0.353005	+	0.935621i	$0.385160\pi$
$180$		0			0
$181$	9.78817	+	16.9536i	0.727549	+	1.26015i	0.957916	+	0.287048i	$0.0926739\pi$
$181$	9.78817	+	16.9536i	0.727549	+	1.26015i	−0.230367	+	0.973104i	$0.573993\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	14.1661	−	24.5364i	1.04151	−	1.80395i
$186$		0			0
$187$	−6.66635	+	11.5465i	−0.487492	+	0.844360i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−19.4101			−1.40446			−0.702231	−	0.711949i	$-0.747813\pi$
$191$	−19.4101			−1.40446			−0.702231	+	0.711949i	$0.747813\pi$
$192$		0			0
$193$	7.84447	−	13.5870i	0.564657	−	0.978015i	−0.432424	−	0.901670i	$-0.642342\pi$
$193$	7.84447	−	13.5870i	0.564657	−	0.978015i	0.997081	−	0.0763447i	$-0.0243250\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.26685			0.304001			0.152000	−	0.988380i	$-0.451428\pi$
$197$	4.26685			0.304001			0.152000	+	0.988380i	$0.451428\pi$
$198$		0			0
$199$	−5.86269	−	10.1545i	−0.415595	−	0.719832i	0.579896	−	0.814691i	$-0.303093\pi$
$199$	−5.86269	−	10.1545i	−0.415595	−	0.719832i	−0.995491	+	0.0948589i	$0.969760\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.376903	+	0.652816i	0.0264534	+	0.0458187i
$204$		0			0
$205$	1.95627	+	3.38836i	0.136632	+	0.236653i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0947438	+	18.8876i	−0.00655356	+	1.30648i
$210$		0			0
$211$	12.4522	−	21.5678i	0.857241	−	1.48479i	−0.0173086	−	0.999850i	$-0.505510\pi$
$211$	12.4522	−	21.5678i	0.857241	−	1.48479i	0.874550	−	0.484935i	$-0.161157\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.0892	−	17.4750i	−0.688079	−	1.19179i
$216$		0			0
$217$	−3.00000			−0.203653
$218$		0			0
$219$		0			0
$220$		0			0
$221$	8.10203			0.545001
$222$		0			0
$223$	9.51373	−	16.4783i	0.637087	−	1.10347i	−0.348982	−	0.937129i	$-0.613473\pi$
$223$	9.51373	−	16.4783i	0.637087	−	1.10347i	0.986069	−	0.166337i	$-0.0531940\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.8975			−0.856037			−0.428018	−	0.903770i	$-0.640788\pi$
$227$	−12.8975			−0.856037			−0.428018	+	0.903770i	$0.640788\pi$
$228$		0			0
$229$	−4.85329			−0.320714			−0.160357	−	0.987059i	$-0.551265\pi$
$229$	−4.85329			−0.320714			−0.160357	+	0.987059i	$0.551265\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.05101	+	13.9448i	−0.527439	+	0.913552i	0.472049	+	0.881572i	$0.343515\pi$
$233$	−8.05101	+	13.9448i	−0.527439	+	0.913552i	−0.999489	+	0.0319797i	$0.989819\pi$
$234$		0			0
$235$	13.0412			0.850713
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.33317			−0.539028			−0.269514	−	0.962996i	$-0.586863\pi$
$239$	−8.33317			−0.539028			−0.269514	+	0.962996i	$0.586863\pi$
$240$		0			0
$241$	−12.1995	−	21.1302i	−0.785839	−	1.36111i	−0.928496	−	0.371342i	$-0.878898\pi$
$241$	−12.1995	−	21.1302i	−0.785839	−	1.36111i	0.142657	−	0.989772i	$-0.454435\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.82789	+	13.5583i	−0.500105	+	0.866208i
$246$		0			0
$247$	9.96873	−	5.68897i	0.634295	−	0.361980i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	10.3433	+	17.9151i	0.652861	+	1.13079i	0.982425	+	0.186656i	$0.0597648\pi$
$251$	10.3433	+	17.9151i	0.652861	+	1.13079i	−0.329564	+	0.944133i	$0.606902\pi$
$252$		0			0
$253$	19.0877	+	33.0609i	1.20003	+	2.07852i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	12.4382	+	21.5436i	0.775872	+	1.34385i	0.934303	+	0.356480i	$0.116023\pi$
$257$	12.4382	+	21.5436i	0.775872	+	1.34385i	−0.158431	+	0.987370i	$0.550643\pi$
$258$		0			0
$259$	−6.53844			−0.406279
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.58217	+	9.66861i	−0.344212	+	0.596192i	−0.985210	−	0.171350i	$-0.945187\pi$
$263$	−5.58217	+	9.66861i	−0.344212	+	0.596192i	0.640999	+	0.767542i	$0.278520\pi$
$264$		0			0
$265$	−27.8176			−1.70882
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.77183	+	3.06890i	−0.108030	+	0.187114i	−0.914972	−	0.403517i	$-0.867788\pi$
$269$	−1.77183	+	3.06890i	−0.108030	+	0.187114i	0.806942	+	0.590631i	$0.201121\pi$
$270$		0			0
$271$	−1.76678	+	3.06016i	−0.107324	+	0.185891i	−0.914685	−	0.404166i	$-0.867562\pi$
$271$	−1.76678	+	3.06016i	−0.107324	+	0.185891i	0.807361	+	0.590058i	$0.200895\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.961316	−	1.66505i	−0.0579696	−	0.100406i
$276$		0			0
$277$	5.51002			0.331065			0.165533	−	0.986204i	$-0.447066\pi$
$277$	5.51002			0.331065			0.165533	+	0.986204i	$0.447066\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.83341	−	8.37172i	−0.288337	−	0.499415i	0.685076	−	0.728472i	$-0.259769\pi$
$281$	−4.83341	−	8.37172i	−0.288337	−	0.499415i	−0.973413	+	0.229057i	$0.926436\pi$
$282$		0			0
$283$	−15.8533	+	27.4587i	−0.942380	+	1.63225i	−0.181466	+	0.983397i	$0.558084\pi$
$283$	−15.8533	+	27.4587i	−0.942380	+	1.63225i	−0.760914	+	0.648853i	$0.775249\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.451464	−	0.781958i	0.0266491	−	0.0461575i
$288$		0			0
$289$	3.76638	+	6.52356i	0.221552	+	0.383739i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	19.6191			1.14616			0.573080	−	0.819499i	$-0.305748\pi$
$293$	19.6191			1.14616			0.573080	+	0.819499i	$0.305748\pi$
$294$		0			0
$295$	2.02186	+	3.50197i	0.117718	+	0.203893i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	11.5992	−	20.0905i	0.670801	−	1.16186i
$300$		0			0
$301$	−2.32837	+	4.03285i	−0.134205	+	0.232450i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	20.2975			1.16223
$306$		0			0
$307$	−5.35456	+	9.27437i	−0.305601	+	0.529316i	−0.977395	−	0.211422i	$-0.932191\pi$
$307$	−5.35456	+	9.27437i	−0.305601	+	0.529316i	0.671794	+	0.740738i	$0.265524\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.45620			−0.309393			−0.154696	−	0.987962i	$-0.549440\pi$
$311$	−5.45620			−0.309393			−0.154696	+	0.987962i	$0.549440\pi$
$312$		0			0
$313$	−2.60123	−	4.50547i	−0.147030	−	0.254664i	0.783098	−	0.621898i	$-0.213638\pi$
$313$	−2.60123	−	4.50547i	−0.147030	−	0.254664i	−0.930129	+	0.367234i	$0.880305\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.8050	+	22.1789i	0.719200	+	1.24569i	0.961317	+	0.275444i	$0.0888247\pi$
$317$	12.8050	+	22.1789i	0.719200	+	1.24569i	−0.242117	+	0.970247i	$0.577842\pi$
$318$		0			0
$319$	−3.03316	−	5.25359i	−0.169824	−	0.294144i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−11.5812	−	6.76410i	−0.644396	−	0.376365i
$324$		0			0
$325$	−0.584174	+	1.01182i	−0.0324041	+	0.0561256i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.50481	−	2.60640i	−0.0829627	−	0.143696i
$330$		0			0
$331$	−2.27462			−0.125024			−0.0625121	−	0.998044i	$-0.519911\pi$
$331$	−2.27462			−0.125024			−0.0625121	+	0.998044i	$0.519911\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.0311			−0.602693
$336$		0			0
$337$	−3.37563	+	5.84676i	−0.183882	+	0.318493i	−0.943199	−	0.332227i	$-0.892200\pi$
$337$	−3.37563	+	5.84676i	−0.183882	+	0.318493i	0.759317	+	0.650721i	$0.225533\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	24.1427			1.30740
$342$		0			0
$343$	7.38212			0.398597
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.02290	−	10.4320i	0.323326	−	0.560017i	−0.657846	−	0.753153i	$-0.728532\pi$
$347$	6.02290	−	10.4320i	0.323326	−	0.560017i	0.981172	+	0.193135i	$0.0618655\pi$
$348$		0			0
$349$	20.1197			1.07698			0.538490	−	0.842632i	$-0.318995\pi$
$349$	20.1197			1.07698			0.538490	+	0.842632i	$0.318995\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	11.7227			0.623937			0.311969	−	0.950092i	$-0.399012\pi$
$353$	11.7227			0.623937			0.311969	+	0.950092i	$0.399012\pi$
$354$		0			0
$355$	−7.39997	−	12.8171i	−0.392750	−	0.680262i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.14321	−	15.8365i	0.482560	−	0.835819i	−0.517239	−	0.855841i	$-0.673040\pi$
$359$	9.14321	−	15.8365i	0.482560	−	0.835819i	0.999800	+	0.0200221i	$0.00637367\pi$
$360$		0			0
$361$	−18.9990	−	0.190610i	−0.999950	−	0.0100321i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−14.3872	−	24.9193i	−0.753059	−	1.30434i
$366$		0			0
$367$	8.41899	+	14.5821i	0.439468	+	0.761180i	0.997648	−	0.0685390i	$-0.0218338\pi$
$367$	8.41899	+	14.5821i	0.439468	+	0.761180i	−0.558181	+	0.829719i	$0.688500\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.20984	+	5.55960i	0.166647	+	0.288640i
$372$		0			0
$373$	11.7513			0.608457			0.304229	−	0.952599i	$-0.401601\pi$
$373$	11.7513			0.608457			0.304229	+	0.952599i	$0.401601\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.84319	+	3.19251i	−0.0949293	+	0.164422i
$378$		0			0
$379$	5.15064			0.264570			0.132285	−	0.991212i	$-0.457769\pi$
$379$	5.15064			0.264570			0.132285	+	0.991212i	$0.457769\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.37138	+	11.0356i	−0.325562	+	0.563890i	−0.981626	−	0.190815i	$-0.938887\pi$
$383$	−6.37138	+	11.0356i	−0.325562	+	0.563890i	0.656064	+	0.754706i	$0.272220\pi$
$384$		0			0
$385$	−2.72185	+	4.71438i	−0.138718	+	0.240267i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	11.9430	+	20.6859i	0.605533	+	1.04881i	0.991967	+	0.126497i	$0.0403735\pi$
$389$	11.9430	+	20.6859i	0.605533	+	1.04881i	−0.386434	+	0.922317i	$0.626293\pi$
$390$		0			0
$391$	−27.1075			−1.37089
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.64393	+	9.77557i	0.283977	+	0.491862i
$396$		0			0
$397$	−4.74973	+	8.22677i	−0.238382	+	0.412890i	−0.960250	−	0.279141i	$-0.909950\pi$
$397$	−4.74973	+	8.22677i	−0.238382	+	0.412890i	0.721868	+	0.692031i	$0.243284\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.34343	−	14.4513i	0.416651	−	0.721661i	−0.578949	−	0.815364i	$-0.696537\pi$
$401$	8.34343	−	14.4513i	0.416651	−	0.721661i	0.995600	+	0.0937027i	$0.0298703\pi$
$402$		0			0
$403$	−7.33554	−	12.7055i	−0.365409	−	0.632908i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	52.6186			2.60821
$408$		0			0
$409$	−13.3339	−	23.0950i	−0.659319	−	1.14197i	−0.980792	−	0.195055i	$-0.937511\pi$
$409$	−13.3339	−	23.0950i	−0.659319	−	1.14197i	0.321473	−	0.946919i	$-0.395822\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.466601	−	0.808177i	0.0229600	−	0.0397678i
$414$		0			0
$415$	−7.39997	+	12.8171i	−0.363250	+	0.629168i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−34.5890			−1.68978			−0.844891	−	0.534938i	$-0.820335\pi$
$419$	−34.5890			−1.68978			−0.844891	+	0.534938i	$0.820335\pi$
$420$		0			0
$421$	4.83445	−	8.37351i	0.235617	−	0.408100i	−0.723835	−	0.689973i	$-0.757622\pi$
$421$	4.83445	−	8.37351i	0.235617	−	0.408100i	0.959452	+	0.281873i	$0.0909557\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.36522			0.0662228
$426$		0			0
$427$	−2.34210	−	4.05664i	−0.113342	−	0.196314i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.8043	−	23.9098i	−0.664932	−	1.15170i	−0.979304	−	0.202396i	$-0.935127\pi$
$431$	−13.8043	−	23.9098i	−0.664932	−	1.15170i	0.314372	−	0.949300i	$-0.398206\pi$
$432$		0			0
$433$	−9.36506	−	16.2208i	−0.450056	−	0.779520i	0.548333	−	0.836260i	$-0.315263\pi$
$433$	−9.36506	−	16.2208i	−0.450056	−	0.779520i	−0.998389	+	0.0567402i	$0.981929\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−33.3530	+	19.0340i	−1.59549	+	0.910518i
$438$		0			0
$439$	−6.05619	+	10.4896i	−0.289046	+	0.500643i	−0.973582	−	0.228336i	$-0.926671\pi$
$439$	−6.05619	+	10.4896i	−0.289046	+	0.500643i	0.684536	+	0.728979i	$0.260005\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−18.1865	−	31.4999i	−0.864065	−	1.49660i	−0.867973	−	0.496612i	$-0.834577\pi$
$443$	−18.1865	−	31.4999i	−0.864065	−	1.49660i	0.00390802	−	0.999992i	$-0.498756\pi$
$444$		0			0
$445$	−13.7352			−0.651112
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−9.77895			−0.461497			−0.230749	−	0.973013i	$-0.574117\pi$
$449$	−9.77895			−0.461497			−0.230749	+	0.973013i	$0.574117\pi$
$450$		0			0
$451$	−3.63319	+	6.29287i	−0.171080	+	0.296320i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.30803			0.155083
$456$		0			0
$457$	2.53116			0.118403			0.0592013	−	0.998246i	$-0.481145\pi$
$457$	2.53116			0.118403			0.0592013	+	0.998246i	$0.481145\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.1151	+	27.9122i	−0.750555	+	1.30000i	0.196999	+	0.980404i	$0.436880\pi$
$461$	−16.1151	+	27.9122i	−0.750555	+	1.30000i	−0.947554	+	0.319595i	$0.896453\pi$
$462$		0			0
$463$	−38.0395			−1.76784			−0.883922	−	0.467633i	$-0.845107\pi$
$463$	−38.0395			−1.76784			−0.883922	+	0.467633i	$0.845107\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−16.5643			−0.766505			−0.383253	−	0.923644i	$-0.625196\pi$
$467$	−16.5643			−0.766505			−0.383253	+	0.923644i	$0.625196\pi$
$468$		0			0
$469$	1.27286	+	2.20467i	0.0587754	+	0.101802i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	18.7377	−	32.4547i	0.861561	−	1.49227i
$474$		0			0
$475$	1.67976	−	0.958610i	0.0770728	−	0.0439840i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.94097	+	3.36185i	0.0886850	+	0.153607i	0.906956	−	0.421226i	$-0.138400\pi$
$479$	1.94097	+	3.36185i	0.0886850	+	0.153607i	−0.818271	+	0.574833i	$0.805067\pi$
$480$		0			0
$481$	−15.9877	−	27.6915i	−0.728975	−	1.26262i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.50481	−	2.60640i	−0.0683298	−	0.118351i
$486$		0			0
$487$	29.6403			1.34313			0.671564	−	0.740947i	$-0.265623\pi$
$487$	29.6403			1.34313			0.671564	+	0.740947i	$0.265623\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−21.1505	+	36.6337i	−0.954508	+	1.65326i	−0.219019	+	0.975721i	$0.570286\pi$
$491$	−21.1505	+	36.6337i	−0.954508	+	1.65326i	−0.735489	+	0.677536i	$0.763048\pi$
$492$		0			0
$493$	4.30756			0.194003
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.70775	+	2.95791i	−0.0766030	+	0.132680i
$498$		0			0
$499$	−1.50244	+	2.60230i	−0.0672584	+	0.116495i	−0.897694	−	0.440620i	$-0.854759\pi$
$499$	−1.50244	+	2.60230i	−0.0672584	+	0.116495i	0.830435	+	0.557115i	$0.188092\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	14.6327	+	25.3446i	0.652440	+	1.13006i	0.982529	+	0.186110i	$0.0595880\pi$
$503$	14.6327	+	25.3446i	0.652440	+	1.13006i	−0.330089	+	0.943950i	$0.607079\pi$
$504$		0			0
$505$	−28.9537			−1.28842
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−20.6663	−	35.7952i	−0.916020	−	1.58659i	−0.805401	−	0.592730i	$-0.798050\pi$
$509$	−20.6663	−	35.7952i	−0.916020	−	1.58659i	−0.110618	−	0.993863i	$-0.535283\pi$
$510$		0			0
$511$	−3.32024	+	5.75082i	−0.146879	+	0.254401i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	10.2593	−	17.7696i	0.452077	−	0.783020i
$516$		0			0
$517$	12.1100	+	20.9752i	0.532599	+	0.922489i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−27.3437			−1.19795			−0.598976	−	0.800767i	$-0.704425\pi$
$521$	−27.3437			−1.19795			−0.598976	+	0.800767i	$0.704425\pi$
$522$		0			0
$523$	16.4740	+	28.5338i	0.720358	+	1.24770i	0.960856	+	0.277048i	$0.0893560\pi$
$523$	16.4740	+	28.5338i	0.720358	+	1.24770i	−0.240498	+	0.970650i	$0.577311\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.57160	+	14.8465i	−0.373385	+	0.646722i
$528$		0			0
$529$	−27.3084	+	47.2995i	−1.18732	+	2.05650i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.41564			0.191263
$534$		0			0
$535$	4.14576	−	7.18066i	0.179237	−	0.310447i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−29.0759			−1.25239
$540$		0			0
$541$	−1.90485	−	3.29930i	−0.0818959	−	0.141848i	0.822168	−	0.569244i	$-0.192764\pi$
$541$	−1.90485	−	3.29930i	−0.0818959	−	0.141848i	−0.904064	+	0.427397i	$0.859431\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−12.4942	−	21.6407i	−0.535194	−	0.926984i
$546$		0			0
$547$	0.214198	+	0.371002i	0.00915844	+	0.0158629i	0.870568	−	0.492048i	$-0.163751\pi$
$547$	0.214198	+	0.371002i	0.00915844	+	0.0158629i	−0.861410	+	0.507910i	$0.830418\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.30001	−	3.02462i	0.225788	−	0.128853i
$552$		0			0
$553$	1.30249	−	2.25598i	0.0553876	−	0.0959341i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.97693	+	8.62030i	0.210879	+	0.365254i	0.951990	−	0.306129i	$-0.0990339\pi$
$557$	4.97693	+	8.62030i	0.210879	+	0.365254i	−0.741111	+	0.671383i	$0.765701\pi$
$558$		0			0
$559$	−22.7731			−0.963200
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.9327			0.502904			0.251452	−	0.967870i	$-0.419092\pi$
$563$	11.9327			0.502904			0.251452	+	0.967870i	$0.419092\pi$
$564$		0			0
$565$	−10.9777	+	19.0139i	−0.461834	+	0.799919i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−18.4557			−0.773704			−0.386852	−	0.922142i	$-0.626438\pi$
$569$	−18.4557			−0.773704			−0.386852	+	0.922142i	$0.626438\pi$
$570$		0			0
$571$	−18.5479			−0.776206			−0.388103	−	0.921616i	$-0.626870\pi$
$571$	−18.5479			−0.776206			−0.388103	+	0.921616i	$0.626870\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.95451	−	3.38531i	0.0815087	−	0.141177i
$576$		0			0
$577$	−2.62262			−0.109181			−0.0545905	−	0.998509i	$-0.517385\pi$
$577$	−2.62262			−0.109181			−0.0545905	+	0.998509i	$0.517385\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.41550			0.141699
$582$		0			0
$583$	−25.8314	−	44.7413i	−1.06983	−	1.85300i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.50752	−	9.53931i	0.227320	−	0.393730i	−0.729693	−	0.683775i	$-0.760337\pi$
$587$	5.50752	−	9.53931i	0.227320	−	0.393730i	0.957013	+	0.290045i	$0.0936704\pi$
$588$		0			0
$589$	−0.121822	+	24.2858i	−0.00501958	+	1.00068i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.94394	−	6.83110i	−0.161958	−	0.280520i	0.773613	−	0.633659i	$-0.218448\pi$
$593$	−3.94394	−	6.83110i	−0.161958	−	0.280520i	−0.935571	+	0.353139i	$0.885114\pi$
$594$		0			0
$595$	−1.93272	−	3.34758i	−0.0792340	−	0.137237i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.894997	−	1.55018i	−0.0365686	−	0.0633387i	0.847162	−	0.531335i	$-0.178309\pi$
$599$	−0.894997	−	1.55018i	−0.0365686	−	0.0633387i	−0.883730	+	0.467996i	$0.844976\pi$
$600$		0			0
$601$	−16.3511			−0.666977			−0.333489	−	0.942754i	$-0.608226\pi$
$601$	−16.3511			−0.666977			−0.333489	+	0.942754i	$0.608226\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.07184	−	15.7129i	0.368823	−	0.638820i
$606$		0			0
$607$	−17.8274			−0.723592			−0.361796	−	0.932257i	$-0.617836\pi$
$607$	−17.8274			−0.723592			−0.361796	+	0.932257i	$0.617836\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.35905	−	12.7462i	0.297715	−	0.515658i
$612$		0			0
$613$	−13.8982	+	24.0724i	−0.561344	+	0.972276i	0.436036	+	0.899929i	$0.356382\pi$
$613$	−13.8982	+	24.0724i	−0.561344	+	0.972276i	−0.997380	+	0.0723466i	$0.976951\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.7276	−	32.4372i	−0.753946	−	1.30587i	−0.945897	−	0.324468i	$-0.894815\pi$
$617$	−18.7276	−	32.4372i	−0.753946	−	1.30587i	0.191951	−	0.981404i	$-0.438518\pi$
$618$		0			0
$619$	−31.4404			−1.26370			−0.631849	−	0.775092i	$-0.717704\pi$
$619$	−31.4404			−1.26370			−0.631849	+	0.775092i	$0.717704\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.58489	+	2.74511i	0.0634973	+	0.109981i
$624$		0			0
$625$	13.5108	−	23.4014i	0.540433	−	0.936057i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−18.6817	+	32.3576i	−0.744886	+	1.29018i
$630$		0			0
$631$	0.636034	+	1.10164i	0.0253201	+	0.0438557i	0.878408	−	0.477912i	$-0.158606\pi$
$631$	0.636034	+	1.10164i	0.0253201	+	0.0438557i	−0.853088	+	0.521768i	$0.825273\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	35.9286			1.42578
$636$		0			0
$637$	8.83445	+	15.3017i	0.350034	+	0.606276i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	20.9711	−	36.3230i	0.828309	−	1.43467i	−0.0710557	−	0.997472i	$-0.522637\pi$
$641$	20.9711	−	36.3230i	0.828309	−	1.43467i	0.899364	−	0.437200i	$-0.144030\pi$
$642$		0			0
$643$	−0.836091	+	1.44815i	−0.0329722	+	0.0571096i	−0.882041	−	0.471173i	$-0.843831\pi$
$643$	−0.836091	+	1.44815i	−0.0329722	+	0.0571096i	0.849068	+	0.528283i	$0.177164\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.06536			0.317082			0.158541	−	0.987352i	$-0.449321\pi$
$647$	8.06536			0.317082			0.158541	+	0.987352i	$0.449321\pi$
$648$		0			0
$649$	−3.75501	+	6.50387i	−0.147397	+	0.255299i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−25.0961			−0.982087			−0.491043	−	0.871135i	$-0.663384\pi$
$653$	−25.0961			−0.982087			−0.491043	+	0.871135i	$0.663384\pi$
$654$		0			0
$655$	12.8201	+	22.2051i	0.500924	+	0.867625i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.8993	+	22.3422i	0.502484	+	0.870327i	0.999996	+	0.00287020i	$0.000913613\pi$
$659$	12.8993	+	22.3422i	0.502484	+	0.870327i	−0.497512	+	0.867457i	$0.665753\pi$
$660$		0			0
$661$	13.8201	+	23.9372i	0.537541	+	0.931048i	0.999036	+	0.0439049i	$0.0139799\pi$
$661$	13.8201	+	23.9372i	0.537541	+	0.931048i	−0.461495	+	0.887143i	$0.652687\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.72858	−	2.76176i	−0.183366	−	0.107097i
$666$		0			0
$667$	6.16690	−	10.6814i	0.238783	−	0.413585i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	18.8482	+	32.6461i	0.727628	+	1.26029i
$672$		0			0
$673$	−41.8427			−1.61292			−0.806459	−	0.591290i	$-0.798619\pi$
$673$	−41.8427			−1.61292			−0.806459	+	0.591290i	$0.798619\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.50761			0.0579423			0.0289712	−	0.999580i	$-0.490777\pi$
$677$	1.50761			0.0579423			0.0289712	+	0.999580i	$0.490777\pi$
$678$		0			0
$679$	−0.347276	+	0.601499i	−0.0133272	+	0.0230834i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	50.2283			1.92193			0.960966	−	0.276667i	$-0.0892300\pi$
$683$	50.2283			1.92193			0.960966	+	0.276667i	$0.0892300\pi$
$684$		0			0
$685$	39.3990			1.50536
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−15.6973	+	27.1885i	−0.598018	+	1.03580i
$690$		0			0
$691$	−3.84112			−0.146123			−0.0730616	−	0.997327i	$-0.523277\pi$
$691$	−3.84112			−0.146123			−0.0730616	+	0.997327i	$0.523277\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−10.8457			−0.411403
$696$		0			0
$697$	−2.57985	−	4.46842i	−0.0977186	−	0.169254i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	7.88916	−	13.6644i	0.297970	−	0.516098i	−0.677702	−	0.735337i	$-0.737024\pi$
$701$	7.88916	−	13.6644i	0.297970	−	0.516098i	0.975671	+	0.219238i	$0.0703573\pi$
$702$		0			0
$703$	−0.265508	+	52.9304i	−0.0100138	+	1.99631i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.34094	+	5.78667i	0.125649	+	0.217630i
$708$		0			0
$709$	−22.3925	−	38.7850i	−0.840969	−	1.45660i	−0.889076	−	0.457759i	$-0.848652\pi$
$709$	−22.3925	−	38.7850i	−0.840969	−	1.45660i	0.0481074	−	0.998842i	$-0.484681\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	24.5430	+	42.5097i	0.919143	+	1.59200i
$714$		0			0
$715$	−26.6217			−0.995594
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−17.7998	+	30.8301i	−0.663820	+	1.14977i	0.315784	+	0.948831i	$0.397732\pi$
$719$	−17.7998	+	30.8301i	−0.663820	+	1.14977i	−0.979604	+	0.200938i	$0.935601\pi$
$720$		0			0
$721$	−4.73522			−0.176349
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.310584	+	0.537948i	−0.0115348	+	0.0199789i
$726$		0			0
$727$	11.9906	−	20.7683i	0.444707	−	0.770254i	−0.553325	−	0.832965i	$-0.686641\pi$
$727$	11.9906	−	20.7683i	0.444707	−	0.770254i	0.998032	+	0.0627110i	$0.0199746\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	13.3052	+	23.0453i	0.492112	+	0.852362i
$732$		0			0
$733$	−40.5301			−1.49701			−0.748506	−	0.663128i	$-0.769228\pi$
$733$	−40.5301			−1.49701			−0.748506	+	0.663128i	$0.769228\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.2435	−	17.7422i	−0.377323	−	0.653543i
$738$		0			0
$739$	22.8220	−	39.5289i	0.839521	−	1.45409i	−0.0507739	−	0.998710i	$-0.516169\pi$
$739$	22.8220	−	39.5289i	0.839521	−	1.45409i	0.890295	−	0.455384i	$-0.150498\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−2.68437	+	4.64947i	−0.0984800	+	0.170572i	−0.911056	−	0.412283i	$-0.864731\pi$
$743$	−2.68437	+	4.64947i	−0.0984800	+	0.170572i	0.812576	+	0.582856i	$0.198065\pi$
$744$		0			0
$745$	−11.8335	−	20.4962i	−0.433546	−	0.750923i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.91350			−0.0699177
$750$		0			0
$751$	20.2457	+	35.0665i	0.738775	+	1.27960i	0.953047	+	0.302822i	$0.0979288\pi$
$751$	20.2457	+	35.0665i	0.738775	+	1.27960i	−0.214272	+	0.976774i	$0.568738\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−12.2874	+	21.2824i	−0.447183	+	0.774544i
$756$		0			0
$757$	−7.78543	+	13.4848i	−0.282966	+	0.490112i	−0.972114	−	0.234509i	$-0.924652\pi$
$757$	−7.78543	+	13.4848i	−0.282966	+	0.490112i	0.689148	+	0.724621i	$0.257985\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	33.2351			1.20477			0.602387	−	0.798205i	$-0.294217\pi$
$761$	33.2351			1.20477			0.602387	+	0.798205i	$0.294217\pi$
$762$		0			0
$763$	−2.88339	+	4.99418i	−0.104386	+	0.180801i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.56370			0.164786
$768$		0			0
$769$	−19.5226	−	33.8141i	−0.704003	−	1.21937i	−0.967050	−	0.254585i	$-0.918061\pi$
$769$	−19.5226	−	33.8141i	−0.704003	−	1.21937i	0.263048	−	0.964783i	$-0.415272\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.07408	−	5.32447i	−0.110567	−	0.191508i	0.805432	−	0.592688i	$-0.201933\pi$
$773$	−3.07408	−	5.32447i	−0.110567	−	0.191508i	−0.915999	+	0.401180i	$0.868600\pi$
$774$		0			0
$775$	−1.23606	−	2.14092i	−0.0444007	−	0.0769042i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.31181	−	3.68646i	−0.226144	−	0.132081i
$780$		0			0
$781$	13.7432	−	23.8040i	0.491772	−	0.851774i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−11.9350	−	20.6720i	−0.425977	−	0.737814i
$786$		0			0
$787$	−45.0355			−1.60534			−0.802671	−	0.596422i	$-0.796588\pi$
$787$	−45.0355			−1.60534			−0.802671	+	0.596422i	$0.796588\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	5.06680			0.180155
$792$		0			0
$793$	11.4537	−	19.8384i	0.406734	−	0.704483i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	47.0750			1.66748			0.833741	−	0.552156i	$-0.186195\pi$
$797$	47.0750			1.66748			0.833741	+	0.552156i	$0.186195\pi$
$798$		0			0
$799$	−17.1981			−0.608427
$800$		0			0
$801$		0			0
$802$		0			0
$803$	26.7199	−	46.2802i	0.942923	−	1.63319i
$804$		0			0
$805$	−11.0679			−0.390093
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−8.79451			−0.309198			−0.154599	−	0.987977i	$-0.549409\pi$
$809$	−8.79451			−0.309198			−0.154599	+	0.987977i	$0.549409\pi$
$810$		0			0
$811$	12.5869	+	21.8012i	0.441986	+	0.765542i	0.997837	−	0.0657397i	$-0.0209407\pi$
$811$	12.5869	+	21.8012i	0.441986	+	0.765542i	−0.555851	+	0.831282i	$0.687607\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.305060	−	0.528380i	0.0106858	−	0.0185083i
$816$		0			0
$817$	32.5524	+	19.0125i	1.13886	+	0.665162i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−26.4789	−	45.8629i	−0.924121	−	1.60062i	−0.792969	−	0.609262i	$-0.791466\pi$
$821$	−26.4789	−	45.8629i	−0.924121	−	1.60062i	−0.131152	−	0.991362i	$-0.541868\pi$
$822$		0			0
$823$	−9.76678	−	16.9166i	−0.340449	−	0.589674i	0.644067	−	0.764969i	$-0.277246\pi$
$823$	−9.76678	−	16.9166i	−0.340449	−	0.589674i	−0.984516	+	0.175294i	$0.943912\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−7.71056	−	13.3551i	−0.268122	−	0.464401i	0.700255	−	0.713893i	$-0.253070\pi$
$827$	−7.71056	−	13.3551i	−0.268122	−	0.464401i	−0.968377	+	0.249492i	$0.919736\pi$
$828$		0			0
$829$	11.6744			0.405468			0.202734	−	0.979234i	$-0.435017\pi$
$829$	11.6744			0.405468			0.202734	+	0.979234i	$0.435017\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	10.3231	−	17.8801i	0.357674	−	0.619509i
$834$		0			0
$835$	−3.44466			−0.119207
$836$		0			0
$837$		0			0
$838$		0			0
$839$	13.1407	−	22.7604i	0.453668	−	0.785776i	−0.544943	−	0.838473i	$-0.683449\pi$
$839$	13.1407	−	22.7604i	0.453668	−	0.785776i	0.998611	+	0.0526976i	$0.0167820\pi$
$840$		0			0
$841$	13.5200	−	23.4174i	0.466208	−	0.807496i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−7.07689	−	12.2575i	−0.243452	−	0.421672i
$846$		0			0
$847$	−4.18716			−0.143872
$848$		0			0
$849$		0			0
$850$		0			0
$851$	53.4910	+	92.6492i	1.83365	+	3.17597i
$852$		0			0
$853$	−0.671633	+	1.16330i	−0.0229963	+	0.0398307i	−0.877295	−	0.479952i	$-0.840654\pi$
$853$	−0.671633	+	1.16330i	−0.0229963	+	0.0398307i	0.854298	+	0.519783i	$0.173987\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−25.3327	+	43.8775i	−0.865348	+	1.49883i	0.00135241	+	0.999999i	$0.499570\pi$
$857$	−25.3327	+	43.8775i	−0.865348	+	1.49883i	−0.866701	+	0.498828i	$0.833764\pi$
$858$		0			0
$859$	27.4658	+	47.5721i	0.937120	+	1.62314i	0.770809	+	0.637066i	$0.219852\pi$
$859$	27.4658	+	47.5721i	0.937120	+	1.62314i	0.166311	+	0.986073i	$0.446814\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	30.3474			1.03304			0.516519	−	0.856276i	$-0.327228\pi$
$863$	30.3474			1.03304			0.516519	+	0.856276i	$0.327228\pi$
$864$		0			0
$865$	21.8533	+	37.8510i	0.743034	+	1.28697i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−10.4819	+	18.1552i	−0.355574	+	0.615873i
$870$		0			0
$871$	−6.22477	+	10.7816i	−0.210918	+	0.365321i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.72401			−0.193507
$876$		0			0
$877$	−14.0706	+	24.3711i	−0.475132	+	0.822953i	−0.999594	−	0.0284809i	$-0.990933\pi$
$877$	−14.0706	+	24.3711i	−0.475132	+	0.822953i	0.524462	+	0.851434i	$0.324266\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.45087			0.0488811			0.0244406	−	0.999701i	$-0.492220\pi$
$881$	1.45087			0.0488811			0.0244406	+	0.999701i	$0.492220\pi$
$882$		0			0
$883$	−5.71948	−	9.90643i	−0.192476	−	0.333378i	0.753594	−	0.657340i	$-0.228318\pi$
$883$	−5.71948	−	9.90643i	−0.192476	−	0.333378i	−0.946070	+	0.323962i	$0.894985\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−27.1631	−	47.0478i	−0.912047	−	1.57971i	−0.811168	−	0.584813i	$-0.801168\pi$
$887$	−27.1631	−	47.0478i	−0.912047	−	1.57971i	−0.100879	−	0.994899i	$-0.532165\pi$
$888$		0			0
$889$	−4.14576	−	7.18066i	−0.139044	−	0.240832i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−21.1606	+	12.0760i	−0.708112	+	0.404106i
$894$		0			0
$895$	11.0193	−	19.0860i	0.368335	−	0.637975i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.90004	−	6.75507i	−0.130074	−	0.225294i
$900$		0			0
$901$	36.6846			1.22214
$902$		0			0
$903$		0			0
$904$		0			0
$905$	45.6750			1.51829
$906$		0			0
$907$	−0.512570	+	0.887797i	−0.0170196	+	0.0294788i	−0.874410	−	0.485188i	$-0.838751\pi$
$907$	−0.512570	+	0.887797i	−0.0170196	+	0.0294788i	0.857390	+	0.514667i	$0.172084\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−24.2549			−0.803599			−0.401800	−	0.915728i	$-0.631615\pi$
$911$	−24.2549			−0.803599			−0.401800	+	0.915728i	$0.631615\pi$
$912$		0			0
$913$	−27.4865			−0.909670
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.95860	−	5.12444i	0.0977016	−	0.169224i
$918$		0			0
$919$	37.0952			1.22366			0.611829	−	0.790990i	$-0.290434\pi$
$919$	37.0952			1.22366			0.611829	+	0.790990i	$0.290434\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−16.7030			−0.549786
$924$		0			0
$925$	−2.69398	−	4.66610i	−0.0885774	−	0.153421i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−10.1560	+	17.5907i	−0.333208	+	0.577133i	−0.983139	−	0.182860i	$-0.941465\pi$
$929$	−10.1560	+	17.5907i	−0.333208	+	0.577133i	0.649931	+	0.759993i	$0.274798\pi$
$930$		0			0
$931$	0.146714	−	29.2482i	0.00480836	−	0.958570i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	15.5537	+	26.9399i	0.508662	+	0.881028i
$936$		0			0
$937$	22.2776	+	38.5859i	0.727777	+	1.26055i	0.957821	+	0.287367i	$0.0927800\pi$
$937$	22.2776	+	38.5859i	0.727777	+	1.26055i	−0.230043	+	0.973180i	$0.573887\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−9.62007	−	16.6624i	−0.313605	−	0.543180i	0.665535	−	0.746367i	$-0.268204\pi$
$941$	−9.62007	−	16.6624i	−0.313605	−	0.543180i	−0.979140	+	0.203187i	$0.934870\pi$
$942$		0			0
$943$	−14.7737			−0.481098
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.56103	−	6.16789i	0.115718	−	0.200430i	−0.802348	−	0.596856i	$-0.796416\pi$
$947$	3.56103	−	6.16789i	0.115718	−	0.200430i	0.918067	+	0.396426i	$0.129750\pi$
$948$		0			0
$949$	−32.4743			−1.05416
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−25.4426	+	44.0678i	−0.824166	+	1.42750i	0.0783892	+	0.996923i	$0.475022\pi$
$953$	−25.4426	+	44.0678i	−0.824166	+	1.42750i	−0.902555	+	0.430574i	$0.858311\pi$
$954$		0			0
$955$	−22.6435	+	39.2197i	−0.732727	+	1.26912i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.54621	−	7.87426i	−0.146805	−	0.254273i
$960$		0			0
$961$	0.0427734			0.00137979
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−18.3025	−	31.7009i	−0.589179	−	1.02049i
$966$		0			0
$967$	6.82151	−	11.8152i	0.219365	−	0.379951i	−0.735249	−	0.677797i	$-0.762935\pi$
$967$	6.82151	−	11.8152i	0.219365	−	0.379951i	0.954614	+	0.297846i	$0.0962681\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−18.7581	+	32.4899i	−0.601975	+	1.04265i	0.390547	+	0.920583i	$0.372286\pi$
$971$	−18.7581	+	32.4899i	−0.601975	+	1.04265i	−0.992522	+	0.122068i	$0.961047\pi$
$972$		0			0
$973$	1.25148	+	2.16762i	0.0401205	+	0.0694908i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−33.1230			−1.05970			−0.529850	−	0.848092i	$-0.677752\pi$
$977$	−33.1230			−1.05970			−0.529850	+	0.848092i	$0.677752\pi$
$978$		0			0
$979$	−12.7545	−	22.0915i	−0.407637	−	0.706047i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−11.6225	+	20.1307i	−0.370699	+	0.642069i	−0.989673	−	0.143342i	$-0.954215\pi$
$983$	−11.6225	+	20.1307i	−0.370699	+	0.642069i	0.618975	+	0.785411i	$0.287548\pi$
$984$		0			0
$985$	4.97766	−	8.62156i	0.158601	−	0.274706i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	76.1935			2.42281
$990$		0			0
$991$	18.8060	−	32.5729i	0.597392	−	1.03471i	−0.395813	−	0.918331i	$-0.629537\pi$
$991$	18.8060	−	32.5729i	0.597392	−	1.03471i	0.993205	−	0.116382i	$-0.0371296\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−27.3574			−0.867287
$996$		0			0
$997$	−3.00274	−	5.20089i	−0.0950976	−	0.164714i	0.814552	−	0.580091i	$-0.196983\pi$
$997$	−3.00274	−	5.20089i	−0.0950976	−	0.164714i	−0.909649	+	0.415377i	$0.863650\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.s.ba.1873.4		8
3.2	odd	2		2736.2.s.bc.1873.1		8
4.3	odd	2		1368.2.s.l.505.4	✓	8
12.11	even	2		1368.2.s.m.505.1	yes	8
19.7	even	3	inner	2736.2.s.ba.577.4		8
57.26	odd	6		2736.2.s.bc.577.1		8
76.7	odd	6		1368.2.s.l.577.4	yes	8
228.83	even	6		1368.2.s.m.577.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.s.l.505.4	✓	8	4.3	odd	2
1368.2.s.l.577.4	yes	8	76.7	odd	6
1368.2.s.m.505.1	yes	8	12.11	even	2
1368.2.s.m.577.1	yes	8	228.83	even	6
2736.2.s.ba.577.4		8	19.7	even	3	inner
2736.2.s.ba.1873.4		8	1.1	even	1	trivial
2736.2.s.bc.577.1		8	57.26	odd	6
2736.2.s.bc.1873.1		8	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(1.16659 - 2.02059i) q^{5} -0.538445 q^{7} +O(q^{10})\)	\(q+(1.16659 - 2.02059i) q^{5} -0.538445 q^{7} +4.33317 q^{11} +(-1.31659 - 2.28041i) q^{13} +(-1.53844 + 2.66466i) q^{17} +(-0.0218647 + 4.35884i) q^{19} +(4.40502 + 7.62971i) q^{23} +(-0.221850 - 0.384256i) q^{25} +(-0.699986 - 1.21241i) q^{29} +5.57160 q^{31} +(-0.628142 + 1.08797i) q^{35} +12.1432 q^{37} +(-0.838459 + 1.45225i) q^{41} +(4.32425 - 7.48981i) q^{43} +(2.79473 + 4.84061i) q^{47} -6.71008 q^{49} +(-5.96132 - 10.3253i) q^{53} +(5.05502 - 8.75556i) q^{55} +(-0.866573 + 1.50095i) q^{59} +(4.34975 + 7.53399i) q^{61} -6.14369 q^{65} +(-2.36397 - 4.09451i) q^{67} +(3.17163 - 5.49343i) q^{71} +(6.16635 - 10.6804i) q^{73} -2.33317 q^{77} +(-2.41899 + 4.18981i) q^{79} -6.34327 q^{83} +(3.58946 + 6.21713i) q^{85} +(-2.94346 - 5.09823i) q^{89} +(0.708913 + 1.22787i) q^{91} +(8.78192 + 5.12915i) q^{95} +(0.644961 - 1.11711i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} + 4 q^{7}+O(q^{10}) \) 8 * q - 4 * q^5 + 4 * q^7	\( 8 q - 4 q^{5} + 4 q^{7} + 8 q^{11} - 4 q^{17} - 8 q^{19} + 8 q^{23} - 4 q^{25} + 4 q^{31} + 16 q^{37} - 4 q^{41} + 6 q^{43} + 4 q^{47} - 16 q^{49} - 16 q^{53} + 16 q^{55} + 12 q^{59} - 8 q^{61} - 48 q^{65} - 2 q^{67} - 4 q^{71} - 4 q^{73} + 8 q^{77} + 22 q^{79} + 8 q^{83} - 8 q^{85} + 12 q^{89} + 2 q^{91} + 32 q^{95} + 24 q^{97}+O(q^{100}) \) 8 * q - 4 * q^5 + 4 * q^7 + 8 * q^11 - 4 * q^17 - 8 * q^19 + 8 * q^23 - 4 * q^25 + 4 * q^31 + 16 * q^37 - 4 * q^41 + 6 * q^43 + 4 * q^47 - 16 * q^49 - 16 * q^53 + 16 * q^55 + 12 * q^59 - 8 * q^61 - 48 * q^65 - 2 * q^67 - 4 * q^71 - 4 * q^73 + 8 * q^77 + 22 * q^79 + 8 * q^83 - 8 * q^85 + 12 * q^89 + 2 * q^91 + 32 * q^95 + 24 * q^97

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