LMFDB - Embedded newform 3024.2.df.e.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(17,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	3024.17
Dual form			3024.2.df.e.1601.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-4.11484 q^{5} +(2.54819 - 0.711830i) q^{7} +5.82138i q^{11} +(-2.52259 - 1.45642i) q^{13} +(-1.58162 + 2.73945i) q^{17} +(-0.722488 + 0.417129i) q^{19} -7.09758i q^{23} +11.9319 q^{25} +(1.91234 - 1.10409i) q^{29} +(-3.66696 + 2.11712i) q^{31} +(-10.4854 + 2.92907i) q^{35} +(1.82507 + 3.16112i) q^{37} +(-2.04811 + 3.54743i) q^{41} +(-0.155460 - 0.269265i) q^{43} +(0.502335 - 0.870070i) q^{47} +(5.98660 - 3.62776i) q^{49} +(1.94801 + 1.12469i) q^{53} -23.9541i q^{55} +(2.51748 + 4.36040i) q^{59} +(-3.98673 - 2.30174i) q^{61} +(10.3801 + 5.99293i) q^{65} +(-4.99726 - 8.65551i) q^{67} -11.4186i q^{71} +(-3.04990 - 1.76086i) q^{73} +(4.14384 + 14.8340i) q^{77} +(-0.579351 + 1.00346i) q^{79} +(-7.57669 - 13.1232i) q^{83} +(6.50813 - 11.2724i) q^{85} +(-4.82266 - 8.35309i) q^{89} +(-7.46478 - 1.91558i) q^{91} +(2.97292 - 1.71642i) q^{95} +(5.06969 - 2.92699i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−4.11484			−1.84021			−0.920106	−	0.391669i	$-0.871898\pi$
$5$	−4.11484			−1.84021			−0.920106	+	0.391669i	$0.871898\pi$
$6$		0			0
$7$	2.54819	−	0.711830i	0.963127	−	0.269047i
$7$	2.54819	−	0.711830i	0.963127	−	0.269047i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			5.82138i			1.75521i	0.479381	+	0.877607i	$0.340861\pi$
$11$			5.82138i			1.75521i	−0.479381	+	0.877607i	$0.659139\pi$
$12$		0			0
$13$	−2.52259	−	1.45642i	−0.699641	−	0.403938i	0.107573	−	0.994197i	$-0.465692\pi$
$13$	−2.52259	−	1.45642i	−0.699641	−	0.403938i	−0.807214	+	0.590259i	$0.799025\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.58162	+	2.73945i	−0.383600	+	0.664415i	−0.991574	−	0.129542i	$-0.958649\pi$
$17$	−1.58162	+	2.73945i	−0.383600	+	0.664415i	0.607974	+	0.793957i	$0.291983\pi$
$18$		0			0
$19$	−0.722488	+	0.417129i	−0.165750	+	0.0956959i	−0.580580	−	0.814203i	$-0.697174\pi$
$19$	−0.722488	+	0.417129i	−0.165750	+	0.0956959i	0.414830	+	0.909899i	$0.363841\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	7.09758i		−	1.47995i	−0.672636	−	0.739973i	$-0.734838\pi$
$23$		−	7.09758i		−	1.47995i	0.672636	−	0.739973i	$-0.265162\pi$
$24$		0			0
$25$	11.9319			2.38638
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.91234	−	1.10409i	0.355113	−	0.205025i	−0.311822	−	0.950141i	$-0.600939\pi$
$29$	1.91234	−	1.10409i	0.355113	−	0.205025i	0.666935	+	0.745116i	$0.267606\pi$
$30$		0			0
$31$	−3.66696	+	2.11712i	−0.658606	+	0.380246i	−0.791746	−	0.610851i	$-0.790827\pi$
$31$	−3.66696	+	2.11712i	−0.658606	+	0.380246i	0.133140	+	0.991097i	$0.457494\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−10.4854	+	2.92907i	−1.77236	+	0.495103i
$36$		0			0
$37$	1.82507	+	3.16112i	0.300040	+	0.519684i	0.976145	−	0.217121i	$-0.0696667\pi$
$37$	1.82507	+	3.16112i	0.300040	+	0.519684i	−0.676105	+	0.736806i	$0.736333\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.04811	+	3.54743i	−0.319861	+	0.554016i	−0.980459	−	0.196724i	$-0.936970\pi$
$41$	−2.04811	+	3.54743i	−0.319861	+	0.554016i	0.660598	+	0.750740i	$0.270303\pi$
$42$		0			0
$43$	−0.155460	−	0.269265i	−0.0237074	−	0.0410625i	0.853928	−	0.520391i	$-0.174214\pi$
$43$	−0.155460	−	0.269265i	−0.0237074	−	0.0410625i	−0.877636	+	0.479328i	$0.840880\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.502335	−	0.870070i	0.0732731	−	0.126913i	−0.827061	−	0.562112i	$-0.809989\pi$
$47$	0.502335	−	0.870070i	0.0732731	−	0.126913i	0.900334	+	0.435200i	$0.143322\pi$
$48$		0			0
$49$	5.98660	−	3.62776i	0.855228	−	0.518252i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.94801	+	1.12469i	0.267580	+	0.154487i	0.627787	−	0.778385i	$-0.283961\pi$
$53$	1.94801	+	1.12469i	0.267580	+	0.154487i	−0.360207	+	0.932872i	$0.617294\pi$
$54$		0			0
$55$		−	23.9541i		−	3.22997i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.51748	+	4.36040i	0.327748	+	0.567676i	0.982065	−	0.188545i	$-0.0603770\pi$
$59$	2.51748	+	4.36040i	0.327748	+	0.567676i	−0.654317	+	0.756221i	$0.727044\pi$
$60$		0			0
$61$	−3.98673	−	2.30174i	−0.510449	−	0.294708i	0.222569	−	0.974917i	$-0.428556\pi$
$61$	−3.98673	−	2.30174i	−0.510449	−	0.294708i	−0.733018	+	0.680209i	$0.761889\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	10.3801	+	5.99293i	1.28749	+	0.743331i
$66$		0			0
$67$	−4.99726	−	8.65551i	−0.610513	−	1.05744i	−0.991154	−	0.132717i	$-0.957630\pi$
$67$	−4.99726	−	8.65551i	−0.610513	−	1.05744i	0.380641	−	0.924723i	$-0.375703\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	11.4186i		−	1.35514i	−0.735458	−	0.677571i	$-0.763033\pi$
$71$		−	11.4186i		−	1.35514i	0.735458	−	0.677571i	$-0.236967\pi$
$72$		0			0
$73$	−3.04990	−	1.76086i	−0.356964	−	0.206093i	0.310784	−	0.950480i	$-0.399408\pi$
$73$	−3.04990	−	1.76086i	−0.356964	−	0.206093i	−0.667748	+	0.744387i	$0.732742\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.14384	+	14.8340i	0.472234	+	1.69049i
$78$		0			0
$79$	−0.579351	+	1.00346i	−0.0651820	+	0.112899i	−0.896775	−	0.442487i	$-0.854096\pi$
$79$	−0.579351	+	1.00346i	−0.0651820	+	0.112899i	0.831593	+	0.555386i	$0.187429\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.57669	−	13.1232i	−0.831650	−	1.44046i	−0.896729	−	0.442579i	$-0.854063\pi$
$83$	−7.57669	−	13.1232i	−0.831650	−	1.44046i	0.0650797	−	0.997880i	$-0.479270\pi$
$84$		0			0
$85$	6.50813	−	11.2724i	0.705905	−	1.22266i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.82266	−	8.35309i	−0.511201	−	0.885426i	−0.999916	−	0.0129824i	$-0.995867\pi$
$89$	−4.82266	−	8.35309i	−0.511201	−	0.885426i	0.488715	−	0.872444i	$-0.337466\pi$
$90$		0			0
$91$	−7.46478	−	1.91558i	−0.782521	−	0.200808i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.97292	−	1.71642i	0.305015	−	0.176101i
$96$		0			0
$97$	5.06969	−	2.92699i	0.514749	−	0.297190i	−0.220035	−	0.975492i	$-0.570617\pi$
$97$	5.06969	−	2.92699i	0.514749	−	0.297190i	0.734784	+	0.678302i	$0.237284\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.85264			−0.582359			−0.291180	−	0.956668i	$-0.594048\pi$
$101$	−5.85264			−0.582359			−0.291180	+	0.956668i	$0.594048\pi$
$102$		0			0
$103$		−	0.780268i		−	0.0768821i	−0.999261	−	0.0384410i	$-0.987761\pi$
$103$		−	0.780268i		−	0.0768821i	0.999261	−	0.0384410i	$-0.0122392\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.15538	+	4.13116i	−0.691737	+	0.399374i	−0.804262	−	0.594274i	$-0.797439\pi$
$107$	−7.15538	+	4.13116i	−0.691737	+	0.399374i	0.112526	+	0.993649i	$0.464106\pi$
$108$		0			0
$109$	3.63584	−	6.29745i	0.348250	−	0.603187i	−0.637689	−	0.770294i	$-0.720109\pi$
$109$	3.63584	−	6.29745i	0.348250	−	0.603187i	0.985939	+	0.167107i	$0.0534427\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	16.0816	+	9.28474i	1.51283	+	0.873435i	0.999887	+	0.0150145i	$0.00477945\pi$
$113$	16.0816	+	9.28474i	1.51283	+	0.873435i	0.512947	+	0.858421i	$0.328554\pi$
$114$		0			0
$115$			29.2054i			2.72342i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.08026	+	8.10650i	−0.190697	+	0.743122i
$120$		0			0
$121$	−22.8885			−2.08077
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−28.5237			−2.55124
$126$		0			0
$127$	−4.38363			−0.388984			−0.194492	−	0.980904i	$-0.562306\pi$
$127$	−4.38363			−0.388984			−0.194492	+	0.980904i	$0.562306\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−15.7084			−1.37245			−0.686224	−	0.727391i	$-0.740733\pi$
$131$	−15.7084			−1.37245			−0.686224	+	0.727391i	$0.740733\pi$
$132$		0			0
$133$	−1.54412	+	1.57721i	−0.133892	+	0.136762i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	18.4638i		−	1.57747i	−0.614734	−	0.788734i	$-0.710737\pi$
$137$		−	18.4638i		−	1.57747i	0.614734	−	0.788734i	$-0.289263\pi$
$138$		0			0
$139$	−3.80522	−	2.19695i	−0.322755	−	0.186343i	0.329865	−	0.944028i	$-0.392997\pi$
$139$	−3.80522	−	2.19695i	−0.322755	−	0.186343i	−0.652620	+	0.757685i	$0.726330\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.47837	−	14.6850i	0.708997	−	1.22802i
$144$		0			0
$145$	−7.86898	+	4.54316i	−0.653483	+	0.377289i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	20.5051i		−	1.67984i	−0.542706	−	0.839922i	$-0.682600\pi$
$149$		−	20.5051i		−	1.67984i	0.542706	−	0.839922i	$-0.317400\pi$
$150$		0			0
$151$	−5.41552			−0.440709			−0.220354	−	0.975420i	$-0.570721\pi$
$151$	−5.41552			−0.440709			−0.220354	+	0.975420i	$0.570721\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	15.0890	−	8.71162i	1.21197	−	0.699734i
$156$		0			0
$157$	9.74596	−	5.62683i	0.777812	−	0.449070i	−0.0578423	−	0.998326i	$-0.518422\pi$
$157$	9.74596	−	5.62683i	0.777812	−	0.449070i	0.835654	+	0.549256i	$0.185089\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.05227	−	18.0860i	−0.398175	−	1.42538i
$162$		0			0
$163$	1.25819	+	2.17924i	0.0985487	+	0.170691i	0.911084	−	0.412220i	$-0.135247\pi$
$163$	1.25819	+	2.17924i	0.0985487	+	0.170691i	−0.812535	+	0.582912i	$0.801913\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.38259	−	16.2511i	0.726047	−	1.25755i	−0.232495	−	0.972598i	$-0.574689\pi$
$167$	9.38259	−	16.2511i	0.726047	−	1.25755i	0.958542	−	0.284952i	$-0.0919777\pi$
$168$		0			0
$169$	−2.25769	−	3.91043i	−0.173668	−	0.300803i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.85857	+	8.41530i	−0.369391	+	0.639803i	−0.989470	−	0.144735i	$-0.953767\pi$
$173$	−4.85857	+	8.41530i	−0.369391	+	0.639803i	0.620080	+	0.784539i	$0.287100\pi$
$174$		0			0
$175$	30.4048	−	8.49349i	2.29839	−	0.642048i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.24569	−	5.33800i	−0.691055	−	0.398981i	0.112952	−	0.993600i	$-0.463969\pi$
$179$	−9.24569	−	5.33800i	−0.691055	−	0.398981i	−0.804007	+	0.594619i	$0.797303\pi$
$180$		0			0
$181$			4.34901i			0.323259i	0.986851	+	0.161630i	$0.0516750\pi$
$181$			4.34901i			0.323259i	−0.986851	+	0.161630i	$0.948325\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−7.50988	−	13.0075i	−0.552137	−	0.956330i
$186$		0			0
$187$	−15.9474	−	9.20724i	−1.16619	−	0.673300i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−21.4704	−	12.3959i	−1.55354	−	0.896937i	−0.997849	−	0.0655476i	$-0.979121\pi$
$191$	−21.4704	−	12.3959i	−1.55354	−	0.896937i	−0.555691	−	0.831389i	$-0.687546\pi$
$192$		0			0
$193$	−13.3256	−	23.0806i	−0.959198	−	1.66138i	−0.724455	−	0.689322i	$-0.757909\pi$
$193$	−13.3256	−	23.0806i	−0.959198	−	1.66138i	−0.234743	−	0.972058i	$-0.575425\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			6.11068i			0.435368i	0.976019	+	0.217684i	$0.0698502\pi$
$197$			6.11068i			0.435368i	−0.976019	+	0.217684i	$0.930150\pi$
$198$		0			0
$199$	0.385220	+	0.222407i	0.0273075	+	0.0157660i	0.513592	−	0.858035i	$-0.328315\pi$
$199$	0.385220	+	0.222407i	0.0273075	+	0.0157660i	−0.486284	+	0.873801i	$0.661648\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.08710	−	4.17470i	0.286858	−	0.293007i
$204$		0			0
$205$	8.42765	−	14.5971i	0.588613	−	1.01951i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.42827	−	4.20588i	−0.167967	−	0.290927i
$210$		0			0
$211$	4.23912	−	7.34236i	0.291833	−	0.505469i	−0.682410	−	0.730969i	$-0.739068\pi$
$211$	4.23912	−	7.34236i	0.291833	−	0.505469i	0.974243	+	0.225500i	$0.0724016\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.639693	+	1.10798i	0.0436267	+	0.0755636i
$216$		0			0
$217$	−7.83710	+	8.00509i	−0.532017	+	0.543421i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.97958	−	4.60701i	0.536764	−	0.309901i
$222$		0			0
$223$	7.25738	−	4.19005i	0.485990	−	0.280587i	−0.236919	−	0.971529i	$-0.576138\pi$
$223$	7.25738	−	4.19005i	0.485990	−	0.280587i	0.722909	+	0.690943i	$0.242804\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.22151			−0.147447			−0.0737233	−	0.997279i	$-0.523488\pi$
$227$	−2.22151			−0.147447			−0.0737233	+	0.997279i	$0.523488\pi$
$228$		0			0
$229$			23.6040i			1.55980i	0.625907	+	0.779898i	$0.284729\pi$
$229$			23.6040i			1.55980i	−0.625907	+	0.779898i	$0.715271\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.69275	−	3.86406i	0.438457	−	0.253143i	−0.264486	−	0.964390i	$-0.585202\pi$
$233$	6.69275	−	3.86406i	0.438457	−	0.253143i	0.702943	+	0.711246i	$0.251869\pi$
$234$		0			0
$235$	−2.06703	+	3.58020i	−0.134838	+	0.233546i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	16.2873	+	9.40346i	1.05354	+	0.608259i	0.923637	−	0.383268i	$-0.125201\pi$
$239$	16.2873	+	9.40346i	1.05354	+	0.608259i	0.129899	+	0.991527i	$0.458535\pi$
$240$		0			0
$241$			24.9125i			1.60476i	0.596815	+	0.802379i	$0.296433\pi$
$241$			24.9125i			1.60476i	−0.596815	+	0.802379i	$0.703567\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−24.6339	+	14.9277i	−1.57380	+	0.953694i
$246$		0			0
$247$	2.43006			0.154621
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−3.39294			−0.214161			−0.107080	−	0.994250i	$-0.534150\pi$
$251$	−3.39294			−0.214161			−0.107080	+	0.994250i	$0.534150\pi$
$252$		0			0
$253$	41.3177			2.59762
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.95421			−0.309035			−0.154518	−	0.987990i	$-0.549382\pi$
$257$	−4.95421			−0.309035			−0.154518	+	0.987990i	$0.549382\pi$
$258$		0			0
$259$	6.90082	+	6.75600i	0.428796	+	0.419797i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	2.91442i		−	0.179711i	−0.995955	−	0.0898553i	$-0.971360\pi$
$263$		−	2.91442i		−	0.179711i	0.995955	−	0.0898553i	$-0.0286405\pi$
$264$		0			0
$265$	−8.01576	−	4.62790i	−0.492404	−	0.284290i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	9.41429	−	16.3060i	0.573999	−	0.994196i	−0.422150	−	0.906526i	$-0.638724\pi$
$269$	9.41429	−	16.3060i	0.573999	−	0.994196i	0.996150	−	0.0876702i	$-0.0279422\pi$
$270$		0			0
$271$	13.6959	−	7.90734i	0.831967	−	0.480336i	−0.0225585	−	0.999746i	$-0.507181\pi$
$271$	13.6959	−	7.90734i	0.831967	−	0.480336i	0.854526	+	0.519409i	$0.173848\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			69.4602i			4.18861i
$276$		0			0
$277$	−4.90462			−0.294690			−0.147345	−	0.989085i	$-0.547073\pi$
$277$	−4.90462			−0.294690			−0.147345	+	0.989085i	$0.547073\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−2.77186	+	1.60034i	−0.165355	+	0.0954680i	−0.580394	−	0.814336i	$-0.697101\pi$
$281$	−2.77186	+	1.60034i	−0.165355	+	0.0954680i	0.415039	+	0.909804i	$0.363768\pi$
$282$		0			0
$283$	−4.38850	+	2.53370i	−0.260869	+	0.150613i	−0.624731	−	0.780840i	$-0.714791\pi$
$283$	−4.38850	+	2.53370i	−0.260869	+	0.150613i	0.363862	+	0.931453i	$0.381458\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.69382	+	10.4975i	−0.159011	+	0.619646i
$288$		0			0
$289$	3.49694	+	6.05687i	0.205702	+	0.356287i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.3751	−	21.4343i	0.722961	−	1.25221i	−0.236847	−	0.971547i	$-0.576114\pi$
$293$	12.3751	−	21.4343i	0.722961	−	1.25221i	0.959808	−	0.280658i	$-0.0905527\pi$
$294$		0			0
$295$	−10.3590	−	17.9424i	−0.603126	−	1.04464i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−10.3370	+	17.9043i	−0.597807	+	1.03543i
$300$		0			0
$301$	−0.587813	−	0.575477i	−0.0338810	−	0.0331700i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	16.4048	+	9.47130i	0.939335	+	0.542325i
$306$		0			0
$307$		−	19.8011i		−	1.13011i	−0.825054	−	0.565055i	$-0.808855\pi$
$307$		−	19.8011i		−	1.13011i	0.825054	−	0.565055i	$-0.191145\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.02449	−	10.4347i	−0.341617	−	0.591699i	0.643116	−	0.765769i	$-0.277641\pi$
$311$	−6.02449	−	10.4347i	−0.341617	−	0.591699i	−0.984733	+	0.174070i	$0.944308\pi$
$312$		0			0
$313$	26.0564	+	15.0437i	1.47279	+	0.850318i	0.999532	−	0.0306036i	$-0.00974294\pi$
$313$	26.0564	+	15.0437i	1.47279	+	0.850318i	0.473262	+	0.880922i	$0.343076\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.9888	+	6.34436i	0.617190	+	0.356335i	0.775774	−	0.631011i	$-0.217360\pi$
$317$	10.9888	+	6.34436i	0.617190	+	0.356335i	−0.158584	+	0.987345i	$0.550693\pi$
$318$		0			0
$319$	6.42734	+	11.1325i	0.359862	+	0.623299i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	2.63896i		−	0.146836i
$324$		0			0
$325$	−30.0993	−	17.3778i	−1.66961	−	0.963950i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.660706	−	2.57469i	0.0364259	−	0.141947i
$330$		0			0
$331$	−2.95408	+	5.11662i	−0.162371	+	0.281235i	−0.935719	−	0.352748i	$-0.885247\pi$
$331$	−2.95408	+	5.11662i	−0.162371	+	0.281235i	0.773348	+	0.633982i	$0.218581\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	20.5629	+	35.6161i	1.12347	+	1.94591i
$336$		0			0
$337$	−10.5675	+	18.3034i	−0.575647	+	0.997051i	0.420323	+	0.907374i	$0.361917\pi$
$337$	−10.5675	+	18.3034i	−0.575647	+	0.997051i	−0.995971	+	0.0896763i	$0.971417\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−12.3246	−	21.3468i	−0.667414	−	1.15599i
$342$		0			0
$343$	12.6727	−	13.5057i	0.684259	−	0.729239i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	25.6322	−	14.7988i	1.37601	−	0.794439i	0.384333	−	0.923195i	$-0.374432\pi$
$347$	25.6322	−	14.7988i	1.37601	−	0.794439i	0.991676	+	0.128756i	$0.0410982\pi$
$348$		0			0
$349$	−6.60232	+	3.81185i	−0.353414	+	0.204044i	−0.666188	−	0.745784i	$-0.732075\pi$
$349$	−6.60232	+	3.81185i	−0.353414	+	0.204044i	0.312774	+	0.949828i	$0.398742\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.4945			−0.558568			−0.279284	−	0.960208i	$-0.590097\pi$
$353$	−10.4945			−0.558568			−0.279284	+	0.960208i	$0.590097\pi$
$354$		0			0
$355$			46.9858i			2.49375i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.65028	−	2.68484i	0.245432	−	0.141700i	−0.372239	−	0.928137i	$-0.621410\pi$
$359$	4.65028	−	2.68484i	0.245432	−	0.141700i	0.617671	+	0.786437i	$0.288076\pi$
$360$		0			0
$361$	−9.15201	+	15.8517i	−0.481685	+	0.834302i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	12.5498	+	7.24566i	0.656889	+	0.379255i
$366$		0			0
$367$		−	11.1054i		−	0.579698i	−0.957072	−	0.289849i	$-0.906395\pi$
$367$		−	11.1054i		−	0.579698i	0.957072	−	0.289849i	$-0.0936051\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	5.76450	+	1.47926i	0.299278	+	0.0767995i
$372$		0			0
$373$	−35.4042			−1.83316			−0.916580	−	0.399850i	$-0.869062\pi$
$373$	−35.4042			−1.83316			−0.916580	+	0.399850i	$0.869062\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.43208			−0.331269
$378$		0			0
$379$	26.5906			1.36587			0.682933	−	0.730481i	$-0.260704\pi$
$379$	26.5906			1.36587			0.682933	+	0.730481i	$0.260704\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−24.5913			−1.25655			−0.628277	−	0.777989i	$-0.716240\pi$
$383$	−24.5913			−1.25655			−0.628277	+	0.777989i	$0.716240\pi$
$384$		0			0
$385$	−17.0512	−	61.0396i	−0.869011	−	3.11087i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			19.0987i			0.968344i	0.874973	+	0.484172i	$0.160879\pi$
$389$			19.0987i			0.968344i	−0.874973	+	0.484172i	$0.839121\pi$
$390$		0			0
$391$	19.4435	+	11.2257i	0.983298	+	0.567708i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.38394	−	4.12910i	0.119949	−	0.207757i
$396$		0			0
$397$	17.8857	−	10.3263i	0.897655	−	0.518261i	0.0212165	−	0.999775i	$-0.493246\pi$
$397$	17.8857	−	10.3263i	0.897655	−	0.518261i	0.876439	+	0.481513i	$0.159913\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			15.4357i			0.770823i	0.922745	+	0.385412i	$0.125941\pi$
$401$			15.4357i			0.770823i	−0.922745	+	0.385412i	$0.874059\pi$
$402$		0			0
$403$	12.3337			0.614384
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−18.4021	+	10.6244i	−0.912157	+	0.526634i
$408$		0			0
$409$	−16.1611	+	9.33064i	−0.799117	+	0.461370i	−0.843162	−	0.537659i	$-0.819309\pi$
$409$	−16.1611	+	9.33064i	−0.799117	+	0.461370i	0.0440453	+	0.999030i	$0.485975\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	9.51889	+	9.31914i	0.468394	+	0.458565i
$414$		0			0
$415$	31.1769	+	53.9999i	1.53041	+	2.65075i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	14.3576	−	24.8681i	0.701414	−	1.21488i	−0.266557	−	0.963819i	$-0.585886\pi$
$419$	14.3576	−	24.8681i	0.701414	−	1.21488i	0.967970	−	0.251065i	$-0.0807807\pi$
$420$		0			0
$421$	12.8338	+	22.2287i	0.625479	+	1.08336i	0.988448	+	0.151560i	$0.0484296\pi$
$421$	12.8338	+	22.2287i	0.625479	+	1.08336i	−0.362969	+	0.931801i	$0.618237\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−18.8718	+	32.6869i	−0.915416	+	1.58555i
$426$		0			0
$427$	−11.7974	−	3.02741i	−0.570918	−	0.146507i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−17.0243	−	9.82896i	−0.820030	−	0.473444i	0.0303970	−	0.999538i	$-0.490323\pi$
$431$	−17.0243	−	9.82896i	−0.820030	−	0.473444i	−0.850427	+	0.526094i	$0.823656\pi$
$432$		0			0
$433$			7.07732i			0.340114i	0.985434	+	0.170057i	$0.0543952\pi$
$433$			7.07732i			0.340114i	−0.985434	+	0.170057i	$0.945605\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.96060	+	5.12791i	0.141625	+	0.245301i
$438$		0			0
$439$	−16.8368	−	9.72072i	−0.803575	−	0.463945i	0.0411444	−	0.999153i	$-0.486900\pi$
$439$	−16.8368	−	9.72072i	−0.803575	−	0.463945i	−0.844720	+	0.535209i	$0.820233\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	29.8951	+	17.2600i	1.42036	+	0.820045i	0.996329	−	0.0856030i	$-0.0272817\pi$
$443$	29.8951	+	17.2600i	1.42036	+	0.820045i	0.424030	+	0.905648i	$0.360615\pi$
$444$		0			0
$445$	19.8445	+	34.3716i	0.940718	+	1.62937i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			10.9491i			0.516720i	0.966049	+	0.258360i	$0.0831821\pi$
$449$			10.9491i			0.516720i	−0.966049	+	0.258360i	$0.916818\pi$
$450$		0			0
$451$	−20.6510	−	11.9228i	−0.972417	−	0.561425i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	30.7164	+	7.88231i	1.44001	+	0.369529i
$456$		0			0
$457$	9.59613	−	16.6210i	0.448888	−	0.777497i	−0.549426	−	0.835542i	$-0.685154\pi$
$457$	9.59613	−	16.6210i	0.448888	−	0.777497i	0.998314	+	0.0580457i	$0.0184869\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.2492	−	28.1444i	−0.756799	−	1.31081i	−0.944475	−	0.328584i	$-0.893429\pi$
$461$	−16.2492	−	28.1444i	−0.756799	−	1.31081i	0.187676	−	0.982231i	$-0.439905\pi$
$462$		0			0
$463$	−13.9136	+	24.0991i	−0.646621	+	1.11998i	0.337303	+	0.941396i	$0.390485\pi$
$463$	−13.9136	+	24.0991i	−0.646621	+	1.11998i	−0.983924	+	0.178585i	$0.942848\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.0869153	−	0.150542i	−0.00402196	−	0.00696624i	0.864007	−	0.503479i	$-0.167947\pi$
$467$	−0.0869153	−	0.150542i	−0.00402196	−	0.00696624i	−0.868029	+	0.496513i	$0.834614\pi$
$468$		0			0
$469$	−18.8953	−	18.4987i	−0.872502	−	0.854192i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.56749	−	0.904992i	0.0720734	−	0.0416116i
$474$		0			0
$475$	−8.62066	+	4.97714i	−0.395543	+	0.228367i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.93195			−0.133964			−0.0669822	−	0.997754i	$-0.521337\pi$
$479$	−2.93195			−0.133964			−0.0669822	+	0.997754i	$0.521337\pi$
$480$		0			0
$481$		−	10.6323i		−	0.484790i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−20.8610	+	12.0441i	−0.947247	+	0.546893i
$486$		0			0
$487$	−18.7014	+	32.3917i	−0.847440	+	1.46781i	0.0360460	+	0.999350i	$0.488524\pi$
$487$	−18.7014	+	32.3917i	−0.847440	+	1.46781i	−0.883486	+	0.468458i	$0.844810\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.27844	−	4.20221i	−0.328472	−	0.189643i	0.326691	−	0.945131i	$-0.394066\pi$
$491$	−7.27844	−	4.20221i	−0.328472	−	0.189643i	−0.655162	+	0.755488i	$0.727400\pi$
$492$		0			0
$493$			6.98503i			0.314590i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.12812	−	29.0969i	−0.364596	−	1.30517i
$498$		0			0
$499$	0.0352479			0.00157791			0.000788956	−	1.00000i	$-0.499749\pi$
$499$	0.0352479			0.00157791			0.000788956		1.00000i	$0.499749\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−14.9085			−0.664736			−0.332368	−	0.943150i	$-0.607848\pi$
$503$	−14.9085			−0.664736			−0.332368	+	0.943150i	$0.607848\pi$
$504$		0			0
$505$	24.0827			1.07166
$506$		0			0
$507$		0			0
$508$		0			0
$509$	14.4128			0.638836			0.319418	−	0.947614i	$-0.396513\pi$
$509$	14.4128			0.638836			0.319418	+	0.947614i	$0.396513\pi$
$510$		0			0
$511$	−9.02517	−	2.31600i	−0.399250	−	0.102454i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			3.21068i			0.141479i
$516$		0			0
$517$	5.06501	+	2.92429i	0.222759	+	0.128610i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	10.4159	−	18.0409i	0.456330	−	0.790386i	−0.542434	−	0.840098i	$-0.682497\pi$
$521$	10.4159	−	18.0409i	0.456330	−	0.790386i	0.998764	+	0.0497124i	$0.0158305\pi$
$522$		0			0
$523$	−12.6684	+	7.31408i	−0.553949	+	0.319822i	−0.750713	−	0.660628i	$-0.770290\pi$
$523$	−12.6684	+	7.31408i	−0.553949	+	0.319822i	0.196764	+	0.980451i	$0.436957\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	13.3940i		−	0.583450i
$528$		0			0
$529$	−27.3756			−1.19024
$530$		0			0
$531$		0			0
$532$		0			0
$533$	10.3331	−	5.96582i	0.447576	−	0.258408i
$534$		0			0
$535$	29.4432	−	16.9991i	1.27294	−	0.734934i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	21.1186	+	34.8503i	0.909643	+	1.50111i
$540$		0			0
$541$	3.60713	+	6.24773i	0.155083	+	0.268611i	0.933089	−	0.359645i	$-0.117102\pi$
$541$	3.60713	+	6.24773i	0.155083	+	0.268611i	−0.778006	+	0.628256i	$0.783769\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−14.9609	+	25.9130i	−0.640854	+	1.10999i
$546$		0			0
$547$	−3.81987	−	6.61620i	−0.163326	−	0.282888i	0.772734	−	0.634730i	$-0.218889\pi$
$547$	−3.81987	−	6.61620i	−0.163326	−	0.282888i	−0.936059	+	0.351842i	$0.885555\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.921096	+	1.59539i	−0.0392400	+	0.0679657i
$552$		0			0
$553$	−0.762002	+	2.96942i	−0.0324036	+	0.126273i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.13965	+	4.69943i	0.344888	+	0.199121i	0.662432	−	0.749122i	$-0.269525\pi$
$557$	8.13965	+	4.69943i	0.344888	+	0.199121i	−0.317543	+	0.948244i	$0.602858\pi$
$558$		0			0
$559$			0.905659i			0.0383053i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.06352	+	3.57413i	0.0869671	+	0.150631i	0.906228	−	0.422790i	$-0.138949\pi$
$563$	2.06352	+	3.57413i	0.0869671	+	0.150631i	−0.819261	+	0.573421i	$0.805616\pi$
$564$		0			0
$565$	−66.1734	−	38.2052i	−2.78394	−	1.60731i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.7740	+	9.10715i	0.661282	+	0.381792i	0.792765	−	0.609527i	$-0.208641\pi$
$569$	15.7740	+	9.10715i	0.661282	+	0.381792i	−0.131483	+	0.991318i	$0.541974\pi$
$570$		0			0
$571$	−22.5913	−	39.1293i	−0.945417	−	1.63751i	−0.754915	−	0.655823i	$-0.772322\pi$
$571$	−22.5913	−	39.1293i	−0.945417	−	1.63751i	−0.190502	−	0.981687i	$-0.561012\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	84.6876i		−	3.53172i
$576$		0			0
$577$	7.04322	+	4.06641i	0.293213	+	0.169287i	0.639390	−	0.768883i	$-0.279187\pi$
$577$	7.04322	+	4.06641i	0.293213	+	0.169287i	−0.346177	+	0.938169i	$0.612520\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−28.6484	−	28.0472i	−1.18853	−	1.16359i
$582$		0			0
$583$	−6.54723	+	11.3401i	−0.271158	+	0.469660i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.4379	+	21.5430i	0.513366	+	0.889175i	0.999880	+	0.0155026i	$0.00493481\pi$
$587$	12.4379	+	21.5430i	0.513366	+	0.889175i	−0.486514	+	0.873673i	$0.661732\pi$
$588$		0			0
$589$	1.76622	−	3.05919i	0.0727760	−	0.126052i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	15.6229	+	27.0596i	0.641554	+	1.11120i	0.985086	+	0.172063i	$0.0550432\pi$
$593$	15.6229	+	27.0596i	0.641554	+	1.11120i	−0.343532	+	0.939141i	$0.611623\pi$
$594$		0			0
$595$	8.55993	−	33.3570i	0.350923	−	1.36750i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−5.54125	+	3.19925i	−0.226410	+	0.130718i	−0.608915	−	0.793236i	$-0.708395\pi$
$599$	−5.54125	+	3.19925i	−0.226410	+	0.130718i	0.382505	+	0.923953i	$0.375061\pi$
$600$		0			0
$601$	36.0541	−	20.8158i	1.47068	−	0.849095i	0.471218	−	0.882017i	$-0.343814\pi$
$601$	36.0541	−	20.8158i	1.47068	−	0.849095i	0.999458	+	0.0329215i	$0.0104811\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	94.1826			3.82907
$606$		0			0
$607$		−	25.0762i		−	1.01781i	−0.860822	−	0.508907i	$-0.830050\pi$
$607$		−	25.0762i		−	1.01781i	0.860822	−	0.508907i	$-0.169950\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.53437	+	1.46322i	−0.102530	+	0.0591956i
$612$		0			0
$613$	15.3779	−	26.6352i	0.621106	−	1.07579i	−0.368174	−	0.929757i	$-0.620017\pi$
$613$	15.3779	−	26.6352i	0.621106	−	1.07579i	0.989280	−	0.146030i	$-0.0466497\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	10.1910	+	5.88375i	0.410272	+	0.236871i	0.690907	−	0.722944i	$-0.257212\pi$
$617$	10.1910	+	5.88375i	0.410272	+	0.236871i	−0.280634	+	0.959815i	$0.590545\pi$
$618$		0			0
$619$		−	7.09698i		−	0.285252i	−0.989777	−	0.142626i	$-0.954445\pi$
$619$		−	7.09698i		−	0.285252i	0.989777	−	0.142626i	$-0.0455546\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−18.2351	−	17.8524i	−0.730572	−	0.715241i
$624$		0			0
$625$	57.7108			2.30843
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−11.5463			−0.460381
$630$		0			0
$631$	−13.0686			−0.520252			−0.260126	−	0.965575i	$-0.583764\pi$
$631$	−13.0686			−0.520252			−0.260126	+	0.965575i	$0.583764\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	18.0379			0.715814
$636$		0			0
$637$	−20.3853	+	0.432378i	−0.807694	+	0.0171314i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			12.6115i			0.498123i	0.968488	+	0.249062i	$0.0801221\pi$
$641$			12.6115i			0.498123i	−0.968488	+	0.249062i	$0.919878\pi$
$642$		0			0
$643$	−12.3449	−	7.12736i	−0.486837	−	0.281076i	0.236424	−	0.971650i	$-0.424025\pi$
$643$	−12.3449	−	7.12736i	−0.486837	−	0.281076i	−0.723261	+	0.690574i	$0.757358\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−20.0060	+	34.6515i	−0.786519	+	1.36229i	0.141569	+	0.989928i	$0.454785\pi$
$647$	−20.0060	+	34.6515i	−0.786519	+	1.36229i	−0.928088	+	0.372362i	$0.878548\pi$
$648$		0			0
$649$	−25.3836	+	14.6552i	−0.996392	+	0.575267i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			14.6331i			0.572638i	0.958134	+	0.286319i	$0.0924317\pi$
$653$			14.6331i			0.572638i	−0.958134	+	0.286319i	$0.907568\pi$
$654$		0			0
$655$	64.6375			2.52559
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−23.7553	+	13.7151i	−0.925374	+	0.534265i	−0.885346	−	0.464934i	$-0.846078\pi$
$659$	−23.7553	+	13.7151i	−0.925374	+	0.534265i	−0.0400285	+	0.999199i	$0.512745\pi$
$660$		0			0
$661$	30.8389	−	17.8048i	1.19949	−	0.692528i	0.239051	−	0.971007i	$-0.423164\pi$
$661$	30.8389	−	17.8048i	1.19949	−	0.692528i	0.960442	+	0.278479i	$0.0898304\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6.35379	−	6.48998i	0.246389	−	0.251671i
$666$		0			0
$667$	−7.83637	−	13.5730i	−0.303426	−	0.525548i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	13.3993	−	23.2083i	0.517275	−	0.895947i
$672$		0			0
$673$	6.35937	+	11.0147i	0.245136	+	0.424587i	0.962170	−	0.272451i	$-0.0878342\pi$
$673$	6.35937	+	11.0147i	0.245136	+	0.424587i	−0.717034	+	0.697038i	$0.754501\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.0278	+	24.2968i	−0.539131	+	0.933803i	0.459820	+	0.888012i	$0.347914\pi$
$677$	−14.0278	+	24.2968i	−0.539131	+	0.933803i	−0.998951	+	0.0457904i	$0.985419\pi$
$678$		0			0
$679$	10.8350	−	11.0673i	0.415810	−	0.424723i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−14.4564	−	8.34638i	−0.553157	−	0.319365i	0.197237	−	0.980356i	$-0.436803\pi$
$683$	−14.4564	−	8.34638i	−0.553157	−	0.319365i	−0.750394	+	0.660990i	$0.770136\pi$
$684$		0			0
$685$			75.9756i			2.90288i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.27603	−	5.67424i	−0.124807	−	0.216171i
$690$		0			0
$691$	−26.3650	−	15.2218i	−1.00297	−	0.579066i	−0.0938458	−	0.995587i	$-0.529916\pi$
$691$	−26.3650	−	15.2218i	−1.00297	−	0.579066i	−0.909126	+	0.416521i	$0.863249\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	15.6579	+	9.04009i	0.593938	+	0.342910i
$696$		0			0
$697$	−6.47868	−	11.2214i	−0.245398	−	0.425041i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	6.16940i		−	0.233015i	−0.993190	−	0.116507i	$-0.962830\pi$
$701$		−	6.16940i		−	0.233015i	0.993190	−	0.116507i	$-0.0371699\pi$
$702$		0			0
$703$	−2.63719	−	1.52258i	−0.0994633	−	0.0574252i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−14.9137	+	4.16608i	−0.560886	+	0.156682i
$708$		0			0
$709$	−12.7487	+	22.0813i	−0.478786	+	0.829282i	−0.999704	−	0.0243250i	$-0.992256\pi$
$709$	−12.7487	+	22.0813i	−0.478786	+	0.829282i	0.520918	+	0.853607i	$0.325590\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	15.0264	+	26.0265i	0.562744	+	0.974702i
$714$		0			0
$715$	−34.8871	+	60.4263i	−1.30471	+	2.25982i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	12.1263	+	21.0034i	0.452236	+	0.783296i	0.998525	−	0.0543012i	$-0.0172931\pi$
$719$	12.1263	+	21.0034i	0.452236	+	0.783296i	−0.546289	+	0.837597i	$0.683960\pi$
$720$		0			0
$721$	−0.555418	−	1.98827i	−0.0206849	−	0.0740472i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	22.8179	−	13.1739i	0.847435	−	0.489267i
$726$		0			0
$727$	13.5251	−	7.80870i	0.501617	−	0.289609i	−0.227764	−	0.973716i	$-0.573141\pi$
$727$	13.5251	−	7.80870i	0.501617	−	0.289609i	0.729381	+	0.684108i	$0.239808\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.983516			0.0363767
$732$		0			0
$733$		−	35.7036i		−	1.31874i	−0.751818	−	0.659371i	$-0.770823\pi$
$733$		−	35.7036i		−	1.31874i	0.751818	−	0.659371i	$-0.229177\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	50.3871	−	29.0910i	1.85603	−	1.07158i
$738$		0			0
$739$	−7.27883	+	12.6073i	−0.267756	+	0.463767i	−0.968282	−	0.249860i	$-0.919615\pi$
$739$	−7.27883	+	12.6073i	−0.267756	+	0.463767i	0.700526	+	0.713627i	$0.252949\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.0287226	+	0.0165830i	0.00105373	+	0.000608372i	0.500527	−	0.865721i	$-0.333140\pi$
$743$	0.0287226	+	0.0165830i	0.00105373	+	0.000608372i	−0.499473	+	0.866329i	$0.666473\pi$
$744$		0			0
$745$			84.3753i			3.09127i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−15.2926	+	15.6204i	−0.558780	+	0.570758i
$750$		0			0
$751$	−23.7899			−0.868106			−0.434053	−	0.900887i	$-0.642917\pi$
$751$	−23.7899			−0.868106			−0.434053	+	0.900887i	$0.642917\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	22.2840			0.810998
$756$		0			0
$757$	−33.2060			−1.20689			−0.603446	−	0.797404i	$-0.706206\pi$
$757$	−33.2060			−1.20689			−0.603446	+	0.797404i	$0.706206\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	42.5675			1.54307			0.771535	−	0.636187i	$-0.219489\pi$
$761$	42.5675			1.54307			0.771535	+	0.636187i	$0.219489\pi$
$762$		0			0
$763$	4.78210	−	18.6352i	0.173124	−	0.674641i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	14.6660i		−	0.529559i
$768$		0			0
$769$	27.1091	+	15.6514i	0.977578	+	0.564405i	0.901538	−	0.432700i	$-0.142439\pi$
$769$	27.1091	+	15.6514i	0.977578	+	0.564405i	0.0760402	+	0.997105i	$0.475772\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−0.165130	+	0.286014i	−0.00593932	+	0.0102872i	−0.868980	−	0.494848i	$-0.835224\pi$
$773$	−0.165130	+	0.286014i	−0.00593932	+	0.0102872i	0.863040	+	0.505135i	$0.168557\pi$
$774$		0			0
$775$	−43.7539	+	25.2613i	−1.57168	+	0.907413i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	3.41730i		−	0.122438i
$780$		0			0
$781$	66.4722			2.37856
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−40.1031	+	23.1535i	−1.43134	+	0.826384i
$786$		0			0
$787$	6.50328	−	3.75467i	0.231817	−	0.133840i	−0.379593	−	0.925154i	$-0.623936\pi$
$787$	6.50328	−	3.75467i	0.231817	−	0.133840i	0.611410	+	0.791314i	$0.290603\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	47.5883	+	12.2119i	1.69205	+	0.434206i
$792$		0			0
$793$	6.70460	+	11.6127i	0.238087	+	0.412379i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.58136	+	6.20310i	−0.126858	+	0.219725i	−0.922458	−	0.386098i	$-0.873823\pi$
$797$	−3.58136	+	6.20310i	−0.126858	+	0.219725i	0.795600	+	0.605823i	$0.207156\pi$
$798$		0			0
$799$	1.58901	+	2.75225i	0.0562151	+	0.0973675i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.2506	−	17.7546i	0.361737	−	0.626547i
$804$		0			0
$805$	20.7893	+	74.4210i	0.732726	+	2.62300i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−39.9767	−	23.0806i	−1.40551	−	0.811469i	−0.410556	−	0.911836i	$-0.634665\pi$
$809$	−39.9767	−	23.0806i	−1.40551	−	0.811469i	−0.994951	+	0.100366i	$0.967999\pi$
$810$		0			0
$811$			22.8560i			0.802581i	0.915951	+	0.401290i	$0.131438\pi$
$811$			22.8560i			0.802581i	−0.915951	+	0.401290i	$0.868562\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.17723	−	8.96723i	−0.181351	−	0.314108i
$816$		0			0
$817$	0.224636	+	0.129694i	0.00785902	+	0.00453741i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.65766	+	0.957051i	0.0578527	+	0.0334013i	0.528647	−	0.848842i	$-0.322699\pi$
$821$	1.65766	+	0.957051i	0.0578527	+	0.0334013i	−0.470795	+	0.882243i	$0.656033\pi$
$822$		0			0
$823$	−7.54735	−	13.0724i	−0.263084	−	0.455675i	0.703976	−	0.710224i	$-0.251406\pi$
$823$	−7.54735	−	13.0724i	−0.263084	−	0.455675i	−0.967060	+	0.254549i	$0.918073\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			14.4077i			0.501004i	0.968116	+	0.250502i	$0.0805956\pi$
$827$			14.4077i			0.501004i	−0.968116	+	0.250502i	$0.919404\pi$
$828$		0			0
$829$	−37.1450	−	21.4457i	−1.29010	−	0.744840i	−0.311429	−	0.950270i	$-0.600807\pi$
$829$	−37.1450	−	21.4457i	−1.29010	−	0.744840i	−0.978672	+	0.205430i	$0.934141\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.469548	+	22.1377i	0.0162689	+	0.767027i
$834$		0			0
$835$	−38.6079	+	66.8708i	−1.33608	+	2.31416i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−12.5327	−	21.7073i	−0.432678	−	0.749421i	0.564425	−	0.825485i	$-0.309098\pi$
$839$	−12.5327	−	21.7073i	−0.432678	−	0.749421i	−0.997103	+	0.0760639i	$0.975765\pi$
$840$		0			0
$841$	−12.0620	+	20.8919i	−0.415930	+	0.720412i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	9.29003	+	16.0908i	0.319587	+	0.553541i
$846$		0			0
$847$	−58.3244	+	16.2927i	−2.00405	+	0.559825i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	22.4363	−	12.9536i	0.769105	−	0.444043i
$852$		0			0
$853$	−14.9013	+	8.60328i	−0.510211	+	0.294571i	−0.732920	−	0.680314i	$-0.761843\pi$
$853$	−14.9013	+	8.60328i	−0.510211	+	0.294571i	0.222709	+	0.974885i	$0.428510\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−48.6968			−1.66345			−0.831726	−	0.555187i	$-0.812647\pi$
$857$	−48.6968			−1.66345			−0.831726	+	0.555187i	$0.812647\pi$
$858$		0			0
$859$		−	3.09785i		−	0.105697i	−0.998603	−	0.0528487i	$-0.983170\pi$
$859$		−	3.09785i		−	0.105697i	0.998603	−	0.0528487i	$-0.0168301\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	22.2443	−	12.8427i	0.757203	−	0.437172i	−0.0710874	−	0.997470i	$-0.522647\pi$
$863$	22.2443	−	12.8427i	0.757203	−	0.437172i	0.828291	+	0.560299i	$0.189314\pi$
$864$		0			0
$865$	19.9923	−	34.6276i	0.679757	−	1.17737i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−5.84156	−	3.37262i	−0.198161	−	0.114408i
$870$		0			0
$871$			29.1124i			0.986437i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−72.6839	+	20.3040i	−2.45716	+	0.686401i
$876$		0			0
$877$	1.25325			0.0423193			0.0211597	−	0.999776i	$-0.493264\pi$
$877$	1.25325			0.0423193			0.0211597	+	0.999776i	$0.493264\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−18.7429			−0.631464			−0.315732	−	0.948848i	$-0.602250\pi$
$881$	−18.7429			−0.631464			−0.315732	+	0.948848i	$0.602250\pi$
$882$		0			0
$883$	−39.3701			−1.32491			−0.662454	−	0.749103i	$-0.730485\pi$
$883$	−39.3701			−1.32491			−0.662454	+	0.749103i	$0.730485\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−37.1909			−1.24875			−0.624374	−	0.781126i	$-0.714646\pi$
$887$	−37.1909			−1.24875			−0.624374	+	0.781126i	$0.714646\pi$
$888$		0			0
$889$	−11.1703	+	3.12040i	−0.374641	+	0.104655i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			0.838154i			0.0280478i
$894$		0			0
$895$	38.0445	+	21.9650i	1.27169	+	0.734210i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.67499	+	8.09732i	−0.155920	+	0.270061i
$900$		0			0
$901$	−6.16204	+	3.55766i	−0.205287	+	0.118523i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	17.8955i		−	0.594866i
$906$		0			0
$907$	30.8590			1.02466			0.512328	−	0.858790i	$-0.328783\pi$
$907$	30.8590			1.02466			0.512328	+	0.858790i	$0.328783\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−14.7486	+	8.51511i	−0.488643	+	0.282118i	−0.724011	−	0.689788i	$-0.757704\pi$
$911$	−14.7486	+	8.51511i	−0.488643	+	0.282118i	0.235368	+	0.971906i	$0.424370\pi$
$912$		0			0
$913$	76.3953	−	44.1068i	2.52831	−	1.45972i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−40.0280	+	11.1817i	−1.32184	+	0.369252i
$918$		0			0
$919$	8.44635	+	14.6295i	0.278619	+	0.482583i	0.971042	−	0.238909i	$-0.0767898\pi$
$919$	8.44635	+	14.6295i	0.278619	+	0.482583i	−0.692422	+	0.721492i	$0.743457\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−16.6303	+	28.8045i	−0.547393	+	0.948112i
$924$		0			0
$925$	21.7766	+	37.7182i	0.716010	+	1.24017i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.39678	−	5.88339i	0.111445	−	0.193028i	−0.804908	−	0.593399i	$-0.797786\pi$
$929$	3.39678	−	5.88339i	0.111445	−	0.193028i	0.916353	+	0.400371i	$0.131119\pi$
$930$		0			0
$931$	−2.81200	+	5.11820i	−0.0921596	+	0.167742i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	65.6210	+	37.8863i	2.14604	+	1.23901i
$936$		0			0
$937$		−	5.14535i		−	0.168091i	−0.996462	−	0.0840456i	$-0.973216\pi$
$937$		−	5.14535i		−	0.168091i	0.996462	−	0.0840456i	$-0.0267841\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.460454	−	0.797529i	−0.0150104	−	0.0259987i	0.858423	−	0.512943i	$-0.171445\pi$
$941$	−0.460454	−	0.797529i	−0.0150104	−	0.0259987i	−0.873433	+	0.486944i	$0.838111\pi$
$942$		0			0
$943$	25.1782	+	14.5366i	0.819914	+	0.473378i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	21.2033	+	12.2417i	0.689015	+	0.397803i	0.803243	−	0.595652i	$-0.203106\pi$
$947$	21.2033	+	12.2417i	0.689015	+	0.397803i	−0.114228	+	0.993455i	$0.536439\pi$
$948$		0			0
$949$	5.12910	+	8.88386i	0.166498	+	0.288382i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			9.80916i			0.317750i	0.987299	+	0.158875i	$0.0507866\pi$
$953$			9.80916i			0.317750i	−0.987299	+	0.158875i	$0.949213\pi$
$954$		0			0
$955$	88.3471	+	51.0072i	2.85884	+	1.65055i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−13.1431	−	47.0494i	−0.424412	−	1.51930i
$960$		0			0
$961$	−6.53559	+	11.3200i	−0.210825	+	0.365160i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	54.8327	+	94.9731i	1.76513	+	3.05729i
$966$		0			0
$967$	18.1376	−	31.4152i	0.583264	−	1.01024i	−0.411825	−	0.911263i	$-0.635108\pi$
$967$	18.1376	−	31.4152i	0.583264	−	1.01024i	0.995089	−	0.0989807i	$-0.0315582\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.09772	−	1.90130i	−0.0352274	−	0.0610157i	0.847874	−	0.530198i	$-0.177882\pi$
$971$	−1.09772	−	1.90130i	−0.0352274	−	0.0610157i	−0.883102	+	0.469182i	$0.844549\pi$
$972$		0			0
$973$	−11.2603	−	2.88958i	−0.360989	−	0.0926356i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	36.9950	−	21.3591i	1.18357	−	0.683337i	0.226736	−	0.973956i	$-0.427195\pi$
$977$	36.9950	−	21.3591i	1.18357	−	0.683337i	0.956839	+	0.290619i	$0.0938612\pi$
$978$		0			0
$979$	48.6266	−	28.0746i	1.55411	−	0.897267i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	45.7562			1.45940			0.729698	−	0.683770i	$-0.239661\pi$
$983$	45.7562			1.45940			0.729698	+	0.683770i	$0.239661\pi$
$984$		0			0
$985$		−	25.1444i		−	0.801169i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.91113	+	1.10339i	−0.0607703	+	0.0350857i
$990$		0			0
$991$	8.30690	−	14.3880i	0.263877	−	0.457049i	−0.703392	−	0.710803i	$-0.748332\pi$
$991$	8.30690	−	14.3880i	0.263877	−	0.457049i	0.967269	+	0.253754i	$0.0816653\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.58512	−	0.915169i	−0.0502517	−	0.0290128i
$996$		0			0
$997$		−	21.4826i		−	0.680361i	−0.940360	−	0.340181i	$-0.889512\pi$
$997$		−	21.4826i		−	0.680361i	0.940360	−	0.340181i	$-0.110488\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.df.e.17.1		48
3.2	odd	2		1008.2.df.e.689.8		48
4.3	odd	2		1512.2.cx.a.17.1		48
7.5	odd	6		3024.2.ca.e.2609.1		48
9.2	odd	6		3024.2.ca.e.2033.1		48
9.7	even	3		1008.2.ca.e.353.2		48
12.11	even	2		504.2.cx.a.185.17	yes	48
21.5	even	6		1008.2.ca.e.257.2		48
28.19	even	6		1512.2.bs.a.1097.1		48
36.7	odd	6		504.2.bs.a.353.23	yes	48
36.11	even	6		1512.2.bs.a.521.1		48
63.47	even	6	inner	3024.2.df.e.1601.1		48
63.61	odd	6		1008.2.df.e.929.8		48
84.47	odd	6		504.2.bs.a.257.23	✓	48
252.47	odd	6		1512.2.cx.a.89.1		48
252.187	even	6		504.2.cx.a.425.17	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.23	✓	48	84.47	odd	6
504.2.bs.a.353.23	yes	48	36.7	odd	6
504.2.cx.a.185.17	yes	48	12.11	even	2
504.2.cx.a.425.17	yes	48	252.187	even	6
1008.2.ca.e.257.2		48	21.5	even	6
1008.2.ca.e.353.2		48	9.7	even	3
1008.2.df.e.689.8		48	3.2	odd	2
1008.2.df.e.929.8		48	63.61	odd	6
1512.2.bs.a.521.1		48	36.11	even	6
1512.2.bs.a.1097.1		48	28.19	even	6
1512.2.cx.a.17.1		48	4.3	odd	2
1512.2.cx.a.89.1		48	252.47	odd	6
3024.2.ca.e.2033.1		48	9.2	odd	6
3024.2.ca.e.2609.1		48	7.5	odd	6
3024.2.df.e.17.1		48	1.1	even	1	trivial
3024.2.df.e.1601.1		48	63.47	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-4.11484 q^{5} +(2.54819 - 0.711830i) q^{7} +5.82138i q^{11} +(-2.52259 - 1.45642i) q^{13} +(-1.58162 + 2.73945i) q^{17} +(-0.722488 + 0.417129i) q^{19} -7.09758i q^{23} +11.9319 q^{25} +(1.91234 - 1.10409i) q^{29} +(-3.66696 + 2.11712i) q^{31} +(-10.4854 + 2.92907i) q^{35} +(1.82507 + 3.16112i) q^{37} +(-2.04811 + 3.54743i) q^{41} +(-0.155460 - 0.269265i) q^{43} +(0.502335 - 0.870070i) q^{47} +(5.98660 - 3.62776i) q^{49} +(1.94801 + 1.12469i) q^{53} -23.9541i q^{55} +(2.51748 + 4.36040i) q^{59} +(-3.98673 - 2.30174i) q^{61} +(10.3801 + 5.99293i) q^{65} +(-4.99726 - 8.65551i) q^{67} -11.4186i q^{71} +(-3.04990 - 1.76086i) q^{73} +(4.14384 + 14.8340i) q^{77} +(-0.579351 + 1.00346i) q^{79} +(-7.57669 - 13.1232i) q^{83} +(6.50813 - 11.2724i) q^{85} +(-4.82266 - 8.35309i) q^{89} +(-7.46478 - 1.91558i) q^{91} +(2.97292 - 1.71642i) q^{95} +(5.06969 - 2.92699i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) \) 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

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