LMFDB - Embedded newform 3024.2.cz.e.2719.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1279,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2, 5]))

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

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

chi := DirichletCharacter("3024.1279");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cz (of order $6$, 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:	$24.1467615712$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2719.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	3024.2719
Dual form			3024.2.cz.e.1279.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.621320 + 0.358719i) q^{5} +(-1.00000 + 2.44949i) q^{7} +(-1.50000 + 0.866025i) q^{11} +(-3.62132 + 2.09077i) q^{13} +(2.74264 + 1.58346i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-2.37868 - 1.37333i) q^{23} +(-2.24264 - 3.88437i) q^{25} +(-0.621320 + 1.07616i) q^{29} -4.00000 q^{31} +(-1.50000 + 1.16320i) q^{35} +(1.62132 + 2.80821i) q^{37} +(8.74264 - 5.04757i) q^{41} +(-5.74264 - 3.31552i) q^{43} -8.48528 q^{47} +(-5.00000 - 4.89898i) q^{49} +(0.621320 - 1.07616i) q^{53} -1.24264 q^{55} +6.00000 q^{59} -6.92820i q^{61} -3.00000 q^{65} -13.2621i q^{71} +(-7.50000 - 4.33013i) q^{73} +(-0.621320 - 4.54026i) q^{77} +2.02922i q^{79} +(-5.74264 + 9.94655i) q^{83} +(1.13604 + 1.96768i) q^{85} +(14.2279 - 8.21449i) q^{89} +(-1.50000 - 10.9612i) q^{91} -0.717439i q^{95} +(-5.74264 - 3.31552i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{5} - 4 q^{7} - 6 q^{11} - 6 q^{13} - 6 q^{17} - 2 q^{19} - 18 q^{23} + 8 q^{25} + 6 q^{29} - 16 q^{31} - 6 q^{35} - 2 q^{37} + 18 q^{41} - 6 q^{43} - 20 q^{49} - 6 q^{53} + 12 q^{55} + 24 q^{59}+ \cdots - 6 q^{97}+O(q^{100}) $ 4 * q - 6 * q^5 - 4 * q^7 - 6 * q^11 - 6 * q^13 - 6 * q^17 - 2 * q^19 - 18 * q^23 + 8 * q^25 + 6 * q^29 - 16 * q^31 - 6 * q^35 - 2 * q^37 + 18 * q^41 - 6 * q^43 - 20 * q^49 - 6 * q^53 + 12 * q^55 + 24 * q^59 - 12 * q^65 - 30 * q^73 + 6 * q^77 - 6 * q^83 + 30 * q^85 + 6 * q^89 - 6 * q^91 - 6 * q^97

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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
$5$	0.621320	+	0.358719i	0.277863	+	0.160424i	0.632456	−	0.774597i	$-0.282047\pi$
$5$	0.621320	+	0.358719i	0.277863	+	0.160424i	−0.354593	+	0.935021i	$0.615380\pi$
$6$		0			0
$7$	−1.00000	+	2.44949i	−0.377964	+	0.925820i
$7$	−1.00000	+	2.44949i	−0.377964	+	0.925820i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	−0.708787	−	0.705422i	$-0.750757\pi$
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	0.256520	+	0.966539i	$0.417424\pi$
$12$		0			0
$13$	−3.62132	+	2.09077i	−1.00437	+	0.579875i	−0.909539	−	0.415618i	$-0.863565\pi$
$13$	−3.62132	+	2.09077i	−1.00437	+	0.579875i	−0.0948342	+	0.995493i	$0.530232\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.74264	+	1.58346i	0.665188	+	0.384047i	0.794251	−	0.607590i	$-0.207864\pi$
$17$	2.74264	+	1.58346i	0.665188	+	0.384047i	−0.129063	+	0.991636i	$0.541197\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.37868	−	1.37333i	−0.495989	−	0.286359i	0.231067	−	0.972938i	$-0.425778\pi$
$23$	−2.37868	−	1.37333i	−0.495989	−	0.286359i	−0.727056	+	0.686579i	$0.759112\pi$
$24$		0			0
$25$	−2.24264	−	3.88437i	−0.448528	−	0.776874i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.621320	+	1.07616i	−0.115376	+	0.199838i	−0.917930	−	0.396742i	$-0.870141\pi$
$29$	−0.621320	+	1.07616i	−0.115376	+	0.199838i	0.802554	+	0.596580i	$0.203474\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.50000	+	1.16320i	−0.253546	+	0.196616i
$36$		0			0
$37$	1.62132	+	2.80821i	0.266543	+	0.461667i	0.967967	−	0.251078i	$-0.0807851\pi$
$37$	1.62132	+	2.80821i	0.266543	+	0.461667i	−0.701423	+	0.712745i	$0.747452\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.74264	−	5.04757i	1.36537	−	0.788297i	0.375038	−	0.927009i	$-0.377630\pi$
$41$	8.74264	−	5.04757i	1.36537	−	0.788297i	0.990333	+	0.138712i	$0.0442962\pi$
$42$		0			0
$43$	−5.74264	−	3.31552i	−0.875744	−	0.505611i	−0.00649156	−	0.999979i	$-0.502066\pi$
$43$	−5.74264	−	3.31552i	−0.875744	−	0.505611i	−0.869253	+	0.494368i	$0.835400\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−8.48528			−1.23771			−0.618853	−	0.785507i	$-0.712402\pi$
$47$	−8.48528			−1.23771			−0.618853	+	0.785507i	$0.712402\pi$
$48$		0			0
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.621320	−	1.07616i	0.0853449	−	0.147822i	−0.820193	−	0.572087i	$-0.806134\pi$
$53$	0.621320	−	1.07616i	0.0853449	−	0.147822i	0.905538	+	0.424265i	$0.139467\pi$
$54$		0			0
$55$	−1.24264			−0.167558
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.00000			0.781133			0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000			0.781133			0.390567	+	0.920575i	$0.372279\pi$
$60$		0			0
$61$		−	6.92820i		−	0.887066i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$		−	6.92820i		−	0.887066i	0.896258	−	0.443533i	$-0.146275\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.00000			−0.372104
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	13.2621i		−	1.57392i	−0.617006	−	0.786959i	$-0.711655\pi$
$71$		−	13.2621i		−	1.57392i	0.617006	−	0.786959i	$-0.288345\pi$
$72$		0			0
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.00787336	−	0.999969i	$-0.502506\pi$
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.869935	+	0.493166i	$0.835840\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.621320	−	4.54026i	−0.0708060	−	0.517411i
$78$		0			0
$79$			2.02922i			0.228306i	0.993463	+	0.114153i	$0.0364153\pi$
$79$			2.02922i			0.228306i	−0.993463	+	0.114153i	$0.963585\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.74264	+	9.94655i	−0.630337	+	1.09178i	0.357146	+	0.934049i	$0.383750\pi$
$83$	−5.74264	+	9.94655i	−0.630337	+	1.09178i	−0.987483	+	0.157727i	$0.949584\pi$
$84$		0			0
$85$	1.13604	+	1.96768i	0.123221	+	0.213425i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	14.2279	−	8.21449i	1.50816	−	0.870735i	0.508202	−	0.861238i	$-0.330310\pi$
$89$	14.2279	−	8.21449i	1.50816	−	0.870735i	0.999955	−	0.00949668i	$-0.00302293\pi$
$90$		0			0
$91$	−1.50000	−	10.9612i	−0.157243	−	1.14904i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	0.717439i		−	0.0736077i
$96$		0			0
$97$	−5.74264	−	3.31552i	−0.583077	−	0.336640i	0.179278	−	0.983798i	$-0.442624\pi$
$97$	−5.74264	−	3.31552i	−0.583077	−	0.336640i	−0.762355	+	0.647159i	$0.775957\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.62132	+	2.09077i	−0.360335	+	0.208039i	−0.669228	−	0.743057i	$-0.733375\pi$
$101$	−3.62132	+	2.09077i	−0.360335	+	0.208039i	0.308893	+	0.951097i	$0.400042\pi$
$102$		0			0
$103$	−5.86396	+	10.1567i	−0.577793	+	1.00077i	0.417939	+	0.908475i	$0.362753\pi$
$103$	−5.86396	+	10.1567i	−0.577793	+	1.00077i	−0.995732	+	0.0922920i	$0.970581\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.98528	+	5.76500i	−0.965314	+	0.557324i	−0.897804	−	0.440395i	$-0.854839\pi$
$107$	−9.98528	+	5.76500i	−0.965314	+	0.557324i	−0.0675093	+	0.997719i	$0.521505\pi$
$108$		0			0
$109$	4.37868	−	7.58410i	0.419401	−	0.726425i	−0.576478	−	0.817113i	$-0.695573\pi$
$109$	4.37868	−	7.58410i	0.419401	−	0.726425i	0.995879	+	0.0906881i	$0.0289066\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.74264	−	9.94655i	−0.540222	−	0.935692i	−0.998891	−	0.0470849i	$-0.985007\pi$
$113$	−5.74264	−	9.94655i	−0.540222	−	0.935692i	0.458669	−	0.888607i	$-0.348326\pi$
$114$		0			0
$115$	−0.985281	−	1.70656i	−0.0918780	−	0.159137i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.62132	+	5.13461i	−0.606975	+	0.470689i
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	6.80511i		−	0.608668i
$126$		0			0
$127$			0.594346i			0.0527397i	0.999652	+	0.0263698i	$0.00839475\pi$
$127$			0.594346i			0.0527397i	−0.999652	+	0.0263698i	$0.991605\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.74264	−	15.1427i	0.763848	−	1.32302i	−0.177005	−	0.984210i	$-0.556641\pi$
$131$	8.74264	−	15.1427i	0.763848	−	1.32302i	0.940853	−	0.338814i	$-0.110026\pi$
$132$		0			0
$133$	2.62132	−	0.358719i	0.227297	−	0.0311049i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$		0			0
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	0.998179	+	0.0603135i	$0.0192101\pi$
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	−0.446857	+	0.894606i	$0.647457\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.62132	−	6.27231i	0.302830	−	0.524517i
$144$		0			0
$145$	−0.772078	+	0.445759i	−0.0641176	+	0.0370183i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.62132	+	16.6646i	−0.788209	+	1.36522i	0.138854	+	0.990313i	$0.455658\pi$
$149$	−9.62132	+	16.6646i	−0.788209	+	1.36522i	−0.927063	+	0.374906i	$0.877675\pi$
$150$		0			0
$151$	−20.5919	+	11.8887i	−1.67574	+	0.967491i	−0.711419	+	0.702768i	$0.751947\pi$
$151$	−20.5919	+	11.8887i	−1.67574	+	0.967491i	−0.964324	+	0.264723i	$0.914719\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.48528	−	1.43488i	−0.199623	−	0.115252i
$156$		0			0
$157$		−	2.02922i		−	0.161950i	−0.996716	−	0.0809748i	$-0.974197\pi$
$157$		−	2.02922i		−	0.161950i	0.996716	−	0.0809748i	$-0.0258033\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.74264	−	4.45322i	0.452583	−	0.350963i
$162$		0			0
$163$	0.257359	−	0.148586i	0.0201579	−	0.0116382i	−0.489887	−	0.871786i	$-0.662962\pi$
$163$	0.257359	−	0.148586i	0.0201579	−	0.0116382i	0.510045	+	0.860148i	$0.329629\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.86396	−	13.6208i	−0.608532	−	1.05401i	−0.991483	−	0.130239i	$-0.958426\pi$
$167$	−7.86396	−	13.6208i	−0.608532	−	1.05401i	0.382951	−	0.923769i	$-0.374908\pi$
$168$		0			0
$169$	2.24264	−	3.88437i	0.172511	−	0.298798i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		−	9.79796i		−	0.744925i	−0.928047	−	0.372463i	$-0.878514\pi$
$173$		−	9.79796i		−	0.744925i	0.928047	−	0.372463i	$-0.121486\pi$
$174$		0			0
$175$	11.7574	−	1.60896i	0.888773	−	0.121626i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.985281	−	0.568852i	−0.0736434	−	0.0425180i	0.462726	−	0.886501i	$-0.346871\pi$
$179$	−0.985281	−	0.568852i	−0.0736434	−	0.0425180i	−0.536370	+	0.843983i	$0.680205\pi$
$180$		0			0
$181$			13.2621i			0.985761i	0.870097	+	0.492881i	$0.164056\pi$
$181$			13.2621i			0.985761i	−0.870097	+	0.492881i	$0.835944\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$			2.32640i			0.171040i
$186$		0			0
$187$	−5.48528			−0.401124
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	18.1610i		−	1.31409i	−0.753853	−	0.657043i	$-0.771807\pi$
$191$		−	18.1610i		−	1.31409i	0.753853	−	0.657043i	$-0.228193\pi$
$192$		0			0
$193$	20.9706			1.50949			0.754747	−	0.656016i	$-0.227760\pi$
$193$	20.9706			1.50949			0.754747	+	0.656016i	$0.227760\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.4853			1.03203			0.516017	−	0.856578i	$-0.327414\pi$
$197$	14.4853			1.03203			0.516017	+	0.856578i	$0.327414\pi$
$198$		0			0
$199$	−9.86396	+	17.0849i	−0.699238	+	1.21112i	0.269493	+	0.963002i	$0.413144\pi$
$199$	−9.86396	+	17.0849i	−0.699238	+	1.21112i	−0.968731	+	0.248113i	$0.920190\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.01472	−	2.59808i	−0.141406	−	0.182349i
$204$		0			0
$205$	7.24264			0.505848
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.50000	+	0.866025i	0.103757	+	0.0599042i
$210$		0			0
$211$	−14.7426	+	8.51167i	−1.01493	+	0.585967i	−0.912630	−	0.408787i	$-0.865952\pi$
$211$	−14.7426	+	8.51167i	−1.01493	+	0.585967i	−0.102295	+	0.994754i	$0.532619\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.37868	−	4.11999i	−0.162225	−	0.280981i
$216$		0			0
$217$	4.00000	−	9.79796i	0.271538	−	0.665129i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−13.2426			−0.890796
$222$		0			0
$223$	−2.62132	+	4.54026i	−0.175537	+	0.304038i	−0.940347	−	0.340217i	$-0.889499\pi$
$223$	−2.62132	+	4.54026i	−0.175537	+	0.304038i	0.764810	+	0.644256i	$0.222833\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.74264	−	15.1427i	−0.580269	−	1.00506i	−0.995447	−	0.0953158i	$-0.969614\pi$
$227$	−8.74264	−	15.1427i	−0.580269	−	1.00506i	0.415178	−	0.909740i	$-0.363719\pi$
$228$		0			0
$229$	−17.3787	−	10.0336i	−1.14842	−	0.663038i	−0.199915	−	0.979813i	$-0.564067\pi$
$229$	−17.3787	−	10.0336i	−1.14842	−	0.663038i	−0.948501	+	0.316775i	$0.897400\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.25736	−	10.8381i	−0.409933	−	0.710025i	0.584949	−	0.811070i	$-0.301115\pi$
$233$	−6.25736	−	10.8381i	−0.409933	−	0.710025i	−0.994882	+	0.101045i	$0.967781\pi$
$234$		0			0
$235$	−5.27208	−	3.04384i	−0.343912	−	0.198558i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.106602	−	0.0615465i	0.00689549	−	0.00398111i	−0.496548	−	0.868009i	$-0.665399\pi$
$239$	0.106602	−	0.0615465i	0.00689549	−	0.00398111i	0.503444	+	0.864028i	$0.332066\pi$
$240$		0			0
$241$	−0.257359	+	0.148586i	−0.0165780	+	0.00957130i	−0.508266	−	0.861200i	$-0.669713\pi$
$241$	−0.257359	+	0.148586i	−0.0165780	+	0.00957130i	0.491688	+	0.870771i	$0.336380\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.34924	−	4.83743i	−0.0861999	−	0.309052i
$246$		0			0
$247$	3.62132	+	2.09077i	0.230419	+	0.133033i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−26.4853			−1.67174			−0.835868	−	0.548930i	$-0.815035\pi$
$251$	−26.4853			−1.67174			−0.835868	+	0.548930i	$0.815035\pi$
$252$		0			0
$253$	4.75736			0.299093
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−21.9853	−	12.6932i	−1.37140	−	0.791781i	−0.380299	−	0.924863i	$-0.624179\pi$
$257$	−21.9853	−	12.6932i	−1.37140	−	0.791781i	−0.991105	+	0.133083i	$0.957512\pi$
$258$		0			0
$259$	−8.50000	+	1.16320i	−0.528164	+	0.0722776i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.1066	+	6.98975i	−0.746525	+	0.431006i	−0.824437	−	0.565954i	$-0.808508\pi$
$263$	−12.1066	+	6.98975i	−0.746525	+	0.431006i	0.0779119	+	0.996960i	$0.475175\pi$
$264$		0			0
$265$	0.772078	−	0.445759i	0.0474284	−	0.0273828i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	19.3492	+	11.1713i	1.17974	+	0.681126i	0.955955	−	0.293512i	$-0.0948241\pi$
$269$	19.3492	+	11.1713i	1.17974	+	0.681126i	0.223789	+	0.974638i	$0.428157\pi$
$270$		0			0
$271$	−5.86396	−	10.1567i	−0.356210	−	0.616974i	0.631114	−	0.775690i	$-0.282598\pi$
$271$	−5.86396	−	10.1567i	−0.356210	−	0.616974i	−0.987324	+	0.158716i	$0.949265\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.72792	+	3.88437i	0.405709	+	0.234236i
$276$		0			0
$277$	5.86396	+	10.1567i	0.352331	+	0.610256i	0.986657	−	0.162810i	$-0.0520557\pi$
$277$	5.86396	+	10.1567i	0.352331	+	0.610256i	−0.634326	+	0.773066i	$0.718722\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−15.9853	+	27.6873i	−0.953602	+	1.65169i	−0.216066	+	0.976379i	$0.569323\pi$
$281$	−15.9853	+	27.6873i	−0.953602	+	1.65169i	−0.737536	+	0.675308i	$0.764011\pi$
$282$		0			0
$283$	−5.51472			−0.327816			−0.163908	−	0.986476i	$-0.552410\pi$
$283$	−5.51472			−0.327816			−0.163908	+	0.986476i	$0.552410\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.62132	+	26.4626i	0.213760	+	1.56204i
$288$		0			0
$289$	−3.48528	−	6.03668i	−0.205017	−	0.355099i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−14.5919	+	8.42463i	−0.852467	+	0.492172i	−0.861482	−	0.507787i	$-0.830464\pi$
$293$	−14.5919	+	8.42463i	−0.852467	+	0.492172i	0.00901553	+	0.999959i	$0.497130\pi$
$294$		0			0
$295$	3.72792	+	2.15232i	0.217048	+	0.125313i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	11.4853			0.664211
$300$		0			0
$301$	13.8640	−	10.7510i	0.799105	−	0.619679i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.48528	−	4.30463i	0.142307	−	0.246483i
$306$		0			0
$307$	18.4853			1.05501			0.527505	−	0.849552i	$-0.323127\pi$
$307$	18.4853			1.05501			0.527505	+	0.849552i	$0.323127\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	22.9706			1.30254			0.651271	−	0.758846i	$-0.274236\pi$
$311$	22.9706			1.30254			0.651271	+	0.758846i	$0.274236\pi$
$312$		0			0
$313$			1.43488i			0.0811041i	0.999177	+	0.0405520i	$0.0129117\pi$
$313$			1.43488i			0.0811041i	−0.999177	+	0.0405520i	$0.987088\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$		0			0
$319$		−	2.15232i		−	0.120507i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	3.16693i		−	0.176213i
$324$		0			0
$325$	16.2426	+	9.37769i	0.900980	+	0.520181i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	8.48528	−	20.7846i	0.467809	−	1.14589i
$330$		0			0
$331$		−	10.9867i		−	0.603881i	−0.953327	−	0.301940i	$-0.902366\pi$
$331$		−	10.9867i		−	0.603881i	0.953327	−	0.301940i	$-0.0976344\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−2.50000	−	4.33013i	−0.136184	−	0.235877i	0.789865	−	0.613280i	$-0.210150\pi$
$337$	−2.50000	−	4.33013i	−0.136184	−	0.235877i	−0.926049	+	0.377403i	$0.876817\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.00000	−	3.46410i	0.324918	−	0.187592i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			27.7128i			1.48770i	0.668346	+	0.743851i	$0.267003\pi$
$347$			27.7128i			1.48770i	−0.668346	+	0.743851i	$0.732997\pi$
$348$		0			0
$349$	2.37868	+	1.37333i	0.127328	+	0.0735127i	0.562311	−	0.826926i	$-0.309912\pi$
$349$	2.37868	+	1.37333i	0.127328	+	0.0735127i	−0.434983	+	0.900439i	$0.643246\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.74264	+	3.31552i	−0.305650	+	0.176467i	−0.644978	−	0.764201i	$-0.723134\pi$
$353$	−5.74264	+	3.31552i	−0.305650	+	0.176467i	0.339328	+	0.940668i	$0.389800\pi$
$354$		0			0
$355$	4.75736	−	8.23999i	0.252494	−	0.437333i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.37868	+	3.10538i	−0.283876	+	0.163896i	−0.635177	−	0.772367i	$-0.719073\pi$
$359$	−5.37868	+	3.10538i	−0.283876	+	0.163896i	0.351301	+	0.936263i	$0.385739\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.10660	−	5.38079i	−0.162607	−	0.281644i
$366$		0			0
$367$	−3.13604	−	5.43178i	−0.163700	−	0.283537i	0.772493	−	0.635023i	$-0.219010\pi$
$367$	−3.13604	−	5.43178i	−0.163700	−	0.283537i	−0.936193	+	0.351487i	$0.885676\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.01472	+	2.59808i	0.104599	+	0.134885i
$372$		0			0
$373$	−17.8640	+	30.9413i	−0.924961	+	1.60208i	−0.133337	+	0.991071i	$0.542569\pi$
$373$	−17.8640	+	30.9413i	−0.924961	+	1.60208i	−0.791624	+	0.611008i	$0.790764\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	5.19615i		−	0.267615i
$378$		0			0
$379$			2.02922i			0.104234i	0.998641	+	0.0521171i	$0.0165969\pi$
$379$			2.02922i			0.104234i	−0.998641	+	0.0521171i	$0.983403\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.62132	−	16.6646i	0.491627	−	0.851522i	−0.508327	−	0.861164i	$-0.669736\pi$
$383$	9.62132	−	16.6646i	0.491627	−	0.851522i	0.999954	+	0.00964204i	$0.00306920\pi$
$384$		0			0
$385$	1.24264	−	3.04384i	0.0633308	−	0.155128i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	14.3787	+	24.9046i	0.729028	+	1.26271i	0.957294	+	0.289115i	$0.0933609\pi$
$389$	14.3787	+	24.9046i	0.729028	+	1.26271i	−0.228266	+	0.973599i	$0.573306\pi$
$390$		0			0
$391$	−4.34924	−	7.53311i	−0.219951	−	0.380966i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.727922	+	1.26080i	−0.0366257	+	0.0634376i
$396$		0			0
$397$	−33.1066	+	19.1141i	−1.66157	+	0.959309i	−0.689608	+	0.724183i	$0.742217\pi$
$397$	−33.1066	+	19.1141i	−1.66157	+	0.959309i	−0.971965	+	0.235127i	$0.924450\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	17.2279	−	29.8396i	0.860321	−	1.49012i	−0.0112975	−	0.999936i	$-0.503596\pi$
$401$	17.2279	−	29.8396i	0.860321	−	1.49012i	0.871619	−	0.490184i	$-0.163070\pi$
$402$		0			0
$403$	14.4853	−	8.36308i	0.721563	−	0.416595i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.86396	−	2.80821i	−0.241098	−	0.139198i
$408$		0			0
$409$		−	12.4215i		−	0.614205i	−0.951676	−	0.307103i	$-0.900641\pi$
$409$		−	12.4215i		−	0.614205i	0.951676	−	0.307103i	$-0.0993595\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.00000	+	14.6969i	−0.295241	+	0.723189i
$414$		0			0
$415$	−7.13604	+	4.11999i	−0.350294	+	0.202243i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.98528	+	6.90271i	0.194694	+	0.337219i	0.946800	−	0.321822i	$-0.104295\pi$
$419$	3.98528	+	6.90271i	0.194694	+	0.337219i	−0.752106	+	0.659042i	$0.770962\pi$
$420$		0			0
$421$	−6.86396	+	11.8887i	−0.334529	+	0.579421i	−0.983394	−	0.181482i	$-0.941911\pi$
$421$	−6.86396	+	11.8887i	−0.334529	+	0.579421i	0.648865	+	0.760903i	$0.275244\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		−	14.2046i		−	0.689023i
$426$		0			0
$427$	16.9706	+	6.92820i	0.821263	+	0.335279i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	33.8345	+	19.5344i	1.62975	+	0.940938i	0.984166	+	0.177250i	$0.0567200\pi$
$431$	33.8345	+	19.5344i	1.62975	+	0.940938i	0.645586	+	0.763688i	$0.276613\pi$
$432$		0			0
$433$		−	13.2621i		−	0.637334i	−0.947867	−	0.318667i	$-0.896765\pi$
$433$		−	13.2621i		−	0.637334i	0.947867	−	0.318667i	$-0.103235\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			2.74666i			0.131391i
$438$		0			0
$439$	26.9706			1.28723			0.643617	−	0.765347i	$-0.277433\pi$
$439$	26.9706			1.28723			0.643617	+	0.765347i	$0.277433\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	8.95743i		−	0.425580i	−0.977098	−	0.212790i	$-0.931745\pi$
$443$		−	8.95743i		−	0.425580i	0.977098	−	0.212790i	$-0.0682551\pi$
$444$		0			0
$445$	11.7868			0.558748
$446$		0			0
$447$		0			0
$448$		0			0
$449$	24.0000			1.13263			0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000			1.13263			0.566315	+	0.824189i	$0.308369\pi$
$450$		0			0
$451$	−8.74264	+	15.1427i	−0.411675	+	0.713042i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.00000	−	7.34847i	0.140642	−	0.344502i
$456$		0			0
$457$	−38.9706			−1.82297			−0.911483	−	0.411338i	$-0.865062\pi$
$457$	−38.9706			−1.82297			−0.911483	+	0.411338i	$0.865062\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	22.8640	+	13.2005i	1.06488	+	0.614809i	0.926778	−	0.375609i	$-0.122566\pi$
$461$	22.8640	+	13.2005i	1.06488	+	0.614809i	0.138102	+	0.990418i	$0.455900\pi$
$462$		0			0
$463$	11.3787	−	6.56948i	0.528812	−	0.305310i	−0.211720	−	0.977330i	$-0.567907\pi$
$463$	11.3787	−	6.56948i	0.528812	−	0.305310i	0.740533	+	0.672020i	$0.234573\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11.7426	+	20.3389i	0.543385	+	0.941170i	0.998707	+	0.0508429i	$0.0161908\pi$
$467$	11.7426	+	20.3389i	0.543385	+	0.941170i	−0.455322	+	0.890327i	$0.650476\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	11.4853			0.528094
$474$		0			0
$475$	−2.24264	+	3.88437i	−0.102899	+	0.178227i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.62132	−	6.27231i	−0.165462	−	0.286589i	0.771357	−	0.636403i	$-0.219578\pi$
$479$	−3.62132	−	6.27231i	−0.165462	−	0.286589i	−0.936819	+	0.349813i	$0.886245\pi$
$480$		0			0
$481$	−11.7426	−	6.77962i	−0.535418	−	0.309124i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.37868	−	4.11999i	−0.108010	−	0.187079i
$486$		0			0
$487$	−11.8934	−	6.86666i	−0.538941	−	0.311158i	0.205708	−	0.978613i	$-0.434050\pi$
$487$	−11.8934	−	6.86666i	−0.538941	−	0.311158i	−0.744650	+	0.667455i	$0.767383\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−12.9853	+	7.49706i	−0.586018	+	0.338337i	−0.763521	−	0.645783i	$-0.776531\pi$
$491$	−12.9853	+	7.49706i	−0.586018	+	0.338337i	0.177504	+	0.984120i	$0.443198\pi$
$492$		0			0
$493$	−3.40812	+	1.96768i	−0.153494	+	0.0886197i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	32.4853	+	13.2621i	1.45716	+	0.594885i
$498$		0			0
$499$	−29.2279	−	16.8747i	−1.30842	−	0.755417i	−0.326589	−	0.945167i	$-0.605899\pi$
$499$	−29.2279	−	16.8747i	−1.30842	−	0.755417i	−0.981833	+	0.189749i	$0.939233\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	−3.00000			−0.133498
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.34924	−	4.24309i	−0.325749	−	0.188072i	0.328203	−	0.944607i	$-0.393557\pi$
$509$	−7.34924	−	4.24309i	−0.325749	−	0.188072i	−0.653952	+	0.756536i	$0.726890\pi$
$510$		0			0
$511$	18.1066	−	14.0410i	0.800989	−	0.621139i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.28680	+	4.20703i	−0.321095	+	0.185384i
$516$		0			0
$517$	12.7279	−	7.34847i	0.559773	−	0.323185i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−7.50000	−	4.33013i	−0.328581	−	0.189706i	0.326630	−	0.945152i	$-0.394087\pi$
$521$	−7.50000	−	4.33013i	−0.328581	−	0.189706i	−0.655211	+	0.755446i	$0.727420\pi$
$522$		0			0
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	0.876750	−	0.480946i	$-0.159707\pi$
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	−0.854887	+	0.518815i	$0.826373\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−10.9706	−	6.33386i	−0.477885	−	0.275907i
$528$		0			0
$529$	−7.72792	−	13.3852i	−0.335997	−	0.581963i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−21.1066	+	36.5577i	−0.914228	+	1.58349i
$534$		0			0
$535$	−8.27208			−0.357633
$536$		0			0
$537$		0			0
$538$		0			0
$539$	11.7426	+	3.01834i	0.505791	+	0.130009i
$540$		0			0
$541$	22.1066	+	38.2898i	0.950437	+	1.64621i	0.744481	+	0.667644i	$0.232697\pi$
$541$	22.1066	+	38.2898i	0.950437	+	1.64621i	0.205956	+	0.978561i	$0.433969\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.44113	−	3.14144i	0.233072	−	0.134564i
$546$		0			0
$547$	23.2279	+	13.4106i	0.993154	+	0.573398i	0.906216	−	0.422816i	$-0.138958\pi$
$547$	23.2279	+	13.4106i	0.993154	+	0.573398i	0.0869386	+	0.996214i	$0.472292\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.24264			0.0529383
$552$		0			0
$553$	−4.97056	−	2.02922i	−0.211370	−	0.0862914i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.10660	+	15.7731i	−0.385859	+	0.668328i	−0.991888	−	0.127115i	$-0.959428\pi$
$557$	−9.10660	+	15.7731i	−0.385859	+	0.668328i	0.606029	+	0.795443i	$0.292762\pi$
$558$		0			0
$559$	27.7279			1.17277
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.02944			0.0433856			0.0216928	−	0.999765i	$-0.493094\pi$
$563$	1.02944			0.0433856			0.0216928	+	0.999765i	$0.493094\pi$
$564$		0			0
$565$		−	8.23999i		−	0.346659i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−22.9706			−0.962976			−0.481488	−	0.876453i	$-0.659904\pi$
$569$	−22.9706			−0.962976			−0.481488	+	0.876453i	$0.659904\pi$
$570$		0			0
$571$		−	32.2636i		−	1.35019i	−0.737730	−	0.675096i	$-0.764102\pi$
$571$		−	32.2636i		−	1.35019i	0.737730	−	0.675096i	$-0.235898\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			12.3196i			0.513761i
$576$		0			0
$577$	−11.9558	−	6.90271i	−0.497728	−	0.287364i	0.230047	−	0.973180i	$-0.426112\pi$
$577$	−11.9558	−	6.90271i	−0.497728	−	0.287364i	−0.727775	+	0.685816i	$0.759445\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−18.6213	−	24.0131i	−0.772543	−	0.996231i
$582$		0			0
$583$			2.15232i			0.0891399i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.98528	−	17.2950i	0.412137	−	0.713842i	−0.582986	−	0.812482i	$-0.698116\pi$
$587$	9.98528	−	17.2950i	0.412137	−	0.713842i	0.995123	+	0.0986402i	$0.0314493\pi$
$588$		0			0
$589$	2.00000	+	3.46410i	0.0824086	+	0.142736i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	11.2279	−	6.48244i	0.461075	−	0.266202i	−0.251421	−	0.967878i	$-0.580898\pi$
$593$	11.2279	−	6.48244i	0.461075	−	0.266202i	0.712496	+	0.701676i	$0.247564\pi$
$594$		0			0
$595$	−5.95584	+	0.815039i	−0.244166	+	0.0334133i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	7.52255i		−	0.307363i	−0.988120	−	0.153682i	$-0.950887\pi$
$599$		−	7.52255i		−	0.307363i	0.988120	−	0.153682i	$-0.0491130\pi$
$600$		0			0
$601$	21.9853	+	12.6932i	0.896798	+	0.517767i	0.876160	−	0.482020i	$-0.160097\pi$
$601$	21.9853	+	12.6932i	0.896798	+	0.517767i	0.0206383	+	0.999787i	$0.493430\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.97056	+	2.86976i	−0.202082	+	0.116672i
$606$		0			0
$607$	17.3492	−	30.0498i	0.704184	−	1.21968i	−0.262801	−	0.964850i	$-0.584646\pi$
$607$	17.3492	−	30.0498i	0.704184	−	1.21968i	0.966985	−	0.254833i	$-0.0820203\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	30.7279	−	17.7408i	1.24312	−	0.717715i
$612$		0			0
$613$	−1.62132	+	2.80821i	−0.0654845	+	0.113423i	−0.896909	−	0.442216i	$-0.854193\pi$
$613$	−1.62132	+	2.80821i	−0.0654845	+	0.113423i	0.831424	+	0.555638i	$0.187526\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.74264	+	4.75039i	0.110415	+	0.191244i	0.915937	−	0.401321i	$-0.131449\pi$
$617$	2.74264	+	4.75039i	0.110415	+	0.191244i	−0.805523	+	0.592565i	$0.798115\pi$
$618$		0			0
$619$	1.01472	+	1.75754i	0.0407850	+	0.0706417i	0.885697	−	0.464263i	$-0.153681\pi$
$619$	1.01472	+	1.75754i	0.0407850	+	0.0706417i	−0.844912	+	0.534905i	$0.820347\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	5.89340	+	43.0656i	0.236114	+	1.72539i
$624$		0			0
$625$	−8.77208	+	15.1937i	−0.350883	+	0.607747i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			10.2692i			0.409460i
$630$		0			0
$631$			15.2913i			0.608736i	0.952554	+	0.304368i	$0.0984453\pi$
$631$			15.2913i			0.608736i	−0.952554	+	0.304368i	$0.901555\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.213203	+	0.369279i	−0.00846072	+	0.0146544i
$636$		0			0
$637$	28.3492	+	7.28692i	1.12324	+	0.288718i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	18.4706	+	31.9920i	0.729543	+	1.26361i	0.957076	+	0.289836i	$0.0936007\pi$
$641$	18.4706	+	31.9920i	0.729543	+	1.26361i	−0.227533	+	0.973770i	$0.573066\pi$
$642$		0			0
$643$	12.2279	+	21.1794i	0.482222	+	0.835233i	0.999792	−	0.0204078i	$-0.00649646\pi$
$643$	12.2279	+	21.1794i	0.482222	+	0.835233i	−0.517570	+	0.855641i	$0.673163\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.86396	+	13.6208i	−0.309164	+	0.535488i	−0.978180	−	0.207760i	$-0.933383\pi$
$647$	−7.86396	+	13.6208i	−0.309164	+	0.535488i	0.669016	+	0.743248i	$0.266716\pi$
$648$		0			0
$649$	−9.00000	+	5.19615i	−0.353281	+	0.203967i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.6213	+	37.4492i	−0.846108	+	1.46550i	0.0385482	+	0.999257i	$0.487727\pi$
$653$	−21.6213	+	37.4492i	−0.846108	+	1.46550i	−0.884656	+	0.466245i	$0.845607\pi$
$654$		0			0
$655$	10.8640	−	6.27231i	0.424490	−	0.245079i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	21.4706	+	12.3960i	0.836374	+	0.482881i	0.856030	−	0.516926i	$-0.172924\pi$
$659$	21.4706	+	12.3960i	0.836374	+	0.482881i	−0.0196558	+	0.999807i	$0.506257\pi$
$660$		0			0
$661$			43.2503i			1.68224i	0.540848	+	0.841121i	$0.318104\pi$
$661$			43.2503i			1.68224i	−0.540848	+	0.841121i	$0.681896\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.75736	+	0.717439i	0.0681475	+	0.0278211i
$666$		0			0
$667$	2.95584	−	1.70656i	0.114451	−	0.0660782i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	6.00000	+	10.3923i	0.231627	+	0.401190i
$672$		0			0
$673$	−11.9853	+	20.7591i	−0.461999	+	0.800205i	−0.999060	−	0.0433378i	$-0.986201\pi$
$673$	−11.9853	+	20.7591i	−0.461999	+	0.800205i	0.537062	+	0.843543i	$0.319534\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			7.76874i			0.298577i	0.988794	+	0.149288i	$0.0476983\pi$
$677$			7.76874i			0.298577i	−0.988794	+	0.149288i	$0.952302\pi$
$678$		0			0
$679$	13.8640	−	10.7510i	0.532050	−	0.412586i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	14.0147	+	8.09140i	0.536258	+	0.309609i	0.743561	−	0.668668i	$-0.233135\pi$
$683$	14.0147	+	8.09140i	0.536258	+	0.309609i	−0.207303	+	0.978277i	$0.566469\pi$
$684$		0			0
$685$			6.45695i			0.246707i
$686$		0			0
$687$		0			0
$688$		0			0
$689$			5.19615i			0.197958i
$690$		0			0
$691$	23.9411			0.910763			0.455382	−	0.890296i	$-0.349503\pi$
$691$	23.9411			0.910763			0.455382	+	0.890296i	$0.349503\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			9.32671i			0.353782i
$696$		0			0
$697$	31.9706			1.21097
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−1.02944			−0.0388813			−0.0194407	−	0.999811i	$-0.506189\pi$
$701$	−1.02944			−0.0388813			−0.0194407	+	0.999811i	$0.506189\pi$
$702$		0			0
$703$	1.62132	−	2.80821i	0.0611493	−	0.105914i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.50000	−	10.9612i	−0.0564133	−	0.412237i
$708$		0			0
$709$	28.4853			1.06979			0.534894	−	0.844919i	$-0.320352\pi$
$709$	28.4853			1.06979			0.534894	+	0.844919i	$0.320352\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.51472	+	5.49333i	0.356329	+	0.205727i
$714$		0			0
$715$	4.50000	−	2.59808i	0.168290	−	0.0971625i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	24.6213	+	42.6454i	0.918220	+	1.59040i	0.802117	+	0.597167i	$0.203707\pi$
$719$	24.6213	+	42.6454i	0.918220	+	1.59040i	0.116103	+	0.993237i	$0.462960\pi$
$720$		0			0
$721$	−19.0147	−	24.5204i	−0.708145	−	0.913187i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	5.57359			0.206998
$726$		0			0
$727$	21.3492	−	36.9780i	0.791800	−	1.37144i	−0.133052	−	0.991109i	$-0.542478\pi$
$727$	21.3492	−	36.9780i	0.791800	−	1.37144i	0.924852	−	0.380328i	$-0.124189\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−10.5000	−	18.1865i	−0.388357	−	0.672653i
$732$		0			0
$733$	−38.3787	−	22.1579i	−1.41755	−	0.818422i	−0.421466	−	0.906844i	$-0.638484\pi$
$733$	−38.3787	−	22.1579i	−1.41755	−	0.818422i	−0.996083	+	0.0884221i	$0.971818\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	27.2574	+	15.7370i	1.00268	+	0.578897i	0.909040	−	0.416710i	$-0.136817\pi$
$739$	27.2574	+	15.7370i	1.00268	+	0.578897i	0.0936386	+	0.995606i	$0.470150\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−13.1360	+	7.58410i	−0.481915	+	0.278233i	−0.721214	−	0.692712i	$-0.756416\pi$
$743$	−13.1360	+	7.58410i	−0.481915	+	0.278233i	0.239299	+	0.970946i	$0.423082\pi$
$744$		0			0
$745$	−11.9558	+	6.90271i	−0.438028	+	0.252896i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−4.13604	−	30.2238i	−0.151128	−	1.10436i
$750$		0			0
$751$	−31.3492	−	18.0995i	−1.14395	−	0.660460i	−0.196544	−	0.980495i	$-0.562972\pi$
$751$	−31.3492	−	18.0995i	−1.14395	−	0.660460i	−0.947406	+	0.320035i	$0.896305\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−17.0589			−0.620836
$756$		0			0
$757$	23.9411			0.870155			0.435078	−	0.900393i	$-0.356721\pi$
$757$	23.9411			0.870155			0.435078	+	0.900393i	$0.356721\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−20.7426	−	11.9758i	−0.751920	−	0.434121i	0.0744671	−	0.997223i	$-0.476274\pi$
$761$	−20.7426	−	11.9758i	−0.751920	−	0.434121i	−0.826387	+	0.563102i	$0.809608\pi$
$762$		0			0
$763$	14.1985	+	18.3096i	0.514020	+	0.662853i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−21.7279	+	12.5446i	−0.784550	+	0.452960i
$768$		0			0
$769$	25.1985	−	14.5484i	0.908681	−	0.524627i	0.0286742	−	0.999589i	$-0.490871\pi$
$769$	25.1985	−	14.5484i	0.908681	−	0.524627i	0.880006	+	0.474962i	$0.157538\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.34924	−	0.778985i	−0.0485289	−	0.0280182i	0.475539	−	0.879694i	$-0.342253\pi$
$773$	−1.34924	−	0.778985i	−0.0485289	−	0.0280182i	−0.524068	+	0.851676i	$0.675586\pi$
$774$		0			0
$775$	8.97056	+	15.5375i	0.322232	+	0.558122i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−8.74264	−	5.04757i	−0.313238	−	0.180848i
$780$		0			0
$781$	11.4853	+	19.8931i	0.410976	+	0.711831i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.727922	−	1.26080i	0.0259807	−	0.0449998i
$786$		0			0
$787$	10.4853			0.373760			0.186880	−	0.982383i	$-0.440162\pi$
$787$	10.4853			0.373760			0.186880	+	0.982383i	$0.440162\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	30.1066	−	4.11999i	1.07047	−	0.146490i
$792$		0			0
$793$	14.4853	+	25.0892i	0.514387	+	0.890945i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.10660	+	3.52565i	−0.216307	+	0.124885i	−0.604239	−	0.796803i	$-0.706523\pi$
$797$	−6.10660	+	3.52565i	−0.216307	+	0.124885i	0.387932	+	0.921688i	$0.373189\pi$
$798$		0			0
$799$	−23.2721	−	13.4361i	−0.823307	−	0.475336i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	15.0000			0.529339
$804$		0			0
$805$	5.16548	−	0.706879i	0.182059	−	0.0249142i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−15.9853	+	27.6873i	−0.562013	+	0.973434i	0.435308	+	0.900282i	$0.356639\pi$
$809$	−15.9853	+	27.6873i	−0.562013	+	0.973434i	−0.997321	+	0.0731528i	$0.976694\pi$
$810$		0			0
$811$	−37.9411			−1.33229			−0.666147	−	0.745821i	$-0.732057\pi$
$811$	−37.9411			−1.33229			−0.666147	+	0.745821i	$0.732057\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.213203			0.00746819
$816$		0			0
$817$			6.63103i			0.231990i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−49.4558			−1.72602			−0.863010	−	0.505186i	$-0.831424\pi$
$821$	−49.4558			−1.72602			−0.863010	+	0.505186i	$0.831424\pi$
$822$		0			0
$823$			48.7436i			1.69910i	0.527512	+	0.849548i	$0.323125\pi$
$823$			48.7436i			1.69910i	−0.527512	+	0.849548i	$0.676875\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			21.6251i			0.751980i	0.926624	+	0.375990i	$0.122697\pi$
$827$			21.6251i			0.751980i	−0.926624	+	0.375990i	$0.877303\pi$
$828$		0			0
$829$	−18.8345	−	10.8741i	−0.654150	−	0.377674i	0.135894	−	0.990723i	$-0.456609\pi$
$829$	−18.8345	−	10.8741i	−0.654150	−	0.377674i	−0.790044	+	0.613050i	$0.789943\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−5.95584	−	21.3535i	−0.206358	−	0.739854i
$834$		0			0
$835$		−	11.2838i		−	0.390493i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	9.62132	−	16.6646i	0.332165	−	0.575326i	−0.650771	−	0.759274i	$-0.725554\pi$
$839$	9.62132	−	16.6646i	0.332165	−	0.575326i	0.982936	+	0.183947i	$0.0588876\pi$
$840$		0			0
$841$	13.7279	+	23.7775i	0.473377	+	0.819912i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.78680	−	1.60896i	0.0958687	−	0.0553498i
$846$		0			0
$847$	−12.9706	−	16.7262i	−0.445674	−	0.574718i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	8.90644i		−	0.305309i
$852$		0			0
$853$	7.86396	+	4.54026i	0.269257	+	0.155456i	0.628550	−	0.777769i	$-0.283649\pi$
$853$	7.86396	+	4.54026i	0.269257	+	0.155456i	−0.359293	+	0.933225i	$0.616982\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.98528	+	2.30090i	−0.136135	+	0.0785974i	−0.566521	−	0.824048i	$-0.691711\pi$
$857$	−3.98528	+	2.30090i	−0.136135	+	0.0785974i	0.430386	+	0.902645i	$0.358377\pi$
$858$		0			0
$859$	16.9853	−	29.4194i	0.579530	−	1.00378i	−0.416003	−	0.909363i	$-0.636569\pi$
$859$	16.9853	−	29.4194i	0.579530	−	1.00378i	0.995533	−	0.0944126i	$-0.0300973\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.59188	+	3.22848i	−0.190350	+	0.109899i	−0.592146	−	0.805830i	$-0.701719\pi$
$863$	−5.59188	+	3.22848i	−0.190350	+	0.109899i	0.401796	+	0.915729i	$0.368386\pi$
$864$		0			0
$865$	3.51472	−	6.08767i	0.119504	−	0.206987i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.75736	−	3.04384i	−0.0596143	−	0.103255i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	16.6690	+	6.80511i	0.563517	+	0.230055i
$876$		0			0
$877$	6.34924	−	10.9972i	0.214399	−	0.371349i	−0.738688	−	0.674048i	$-0.764554\pi$
$877$	6.34924	−	10.9972i	0.214399	−	0.371349i	0.953086	+	0.302698i	$0.0978875\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	22.2195i		−	0.748594i	−0.927309	−	0.374297i	$-0.877884\pi$
$881$		−	22.2195i		−	0.748594i	0.927309	−	0.374297i	$-0.122116\pi$
$882$		0			0
$883$		−	4.89898i		−	0.164864i	−0.996597	−	0.0824319i	$-0.973731\pi$
$883$		−	4.89898i		−	0.164864i	0.996597	−	0.0824319i	$-0.0262687\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	21.8345	−	37.8185i	0.733132	−	1.26982i	−0.222407	−	0.974954i	$-0.571391\pi$
$887$	21.8345	−	37.8185i	0.733132	−	1.26982i	0.955538	−	0.294867i	$-0.0952754\pi$
$888$		0			0
$889$	−1.45584	−	0.594346i	−0.0488274	−	0.0199337i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	4.24264	+	7.34847i	0.141975	+	0.245907i
$894$		0			0
$895$	−0.408117	−	0.706879i	−0.0136418	−	0.0236284i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.48528	−	4.30463i	0.0828888	−	0.143568i
$900$		0			0
$901$	3.40812	−	1.96768i	0.113541	−	0.0655528i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.75736	+	8.23999i	−0.158140	+	0.273906i
$906$		0			0
$907$	−0.985281	+	0.568852i	−0.0327157	+	0.0188884i	−0.516269	−	0.856427i	$-0.672679\pi$
$907$	−0.985281	+	0.568852i	−0.0327157	+	0.0188884i	0.483553	+	0.875315i	$0.339346\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−16.1360	−	9.31615i	−0.534611	−	0.308658i	0.208281	−	0.978069i	$-0.433213\pi$
$911$	−16.1360	−	9.31615i	−0.534611	−	0.308658i	−0.742892	+	0.669411i	$0.766546\pi$
$912$		0			0
$913$		−	19.8931i		−	0.658365i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	28.3492	+	36.5577i	0.936174	+	1.20724i
$918$		0			0
$919$	4.13604	−	2.38794i	0.136435	−	0.0787710i	−0.430229	−	0.902720i	$-0.641567\pi$
$919$	4.13604	−	2.38794i	0.136435	−	0.0787710i	0.566664	+	0.823949i	$0.308234\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	27.7279	+	48.0262i	0.912676	+	1.58080i
$924$		0			0
$925$	7.27208	−	12.5956i	0.239104	−	0.414141i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	47.9031i		−	1.57165i	−0.618450	−	0.785824i	$-0.712239\pi$
$929$		−	47.9031i		−	1.57165i	0.618450	−	0.785824i	$-0.287761\pi$
$930$		0			0
$931$	−1.74264	+	6.77962i	−0.0571127	+	0.222193i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.40812	−	1.96768i	−0.111457	−	0.0643499i
$936$		0			0
$937$		−	52.4539i		−	1.71359i	−0.515654	−	0.856797i	$-0.672451\pi$
$937$		−	52.4539i		−	1.71359i	0.515654	−	0.856797i	$-0.327549\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	36.3221i		−	1.18407i	−0.805914	−	0.592033i	$-0.798326\pi$
$941$		−	36.3221i		−	1.18407i	0.805914	−	0.592033i	$-0.201674\pi$
$942$		0			0
$943$	−27.7279			−0.902945
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	57.7010i		−	1.87503i	−0.347943	−	0.937516i	$-0.613120\pi$
$947$		−	57.7010i		−	1.87503i	0.347943	−	0.937516i	$-0.386880\pi$
$948$		0			0
$949$	36.2132			1.17553
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−27.5147			−0.891289			−0.445645	−	0.895210i	$-0.647025\pi$
$953$	−27.5147			−0.891289			−0.445645	+	0.895210i	$0.647025\pi$
$954$		0			0
$955$	6.51472	−	11.2838i	0.210811	−	0.365136i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−23.5919	+	3.22848i	−0.761822	+	0.104253i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$		0			0
$964$		0			0
$965$	13.0294	+	7.52255i	0.419432	+	0.242159i
$966$		0			0
$967$	−32.5919	+	18.8169i	−1.04808	+	0.605112i	−0.922112	−	0.386922i	$-0.873538\pi$
$967$	−32.5919	+	18.8169i	−1.04808	+	0.605112i	−0.125972	+	0.992034i	$0.540205\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	6.25736	+	10.8381i	0.200808	+	0.347810i	0.948789	−	0.315910i	$-0.102310\pi$
$971$	6.25736	+	10.8381i	0.200808	+	0.347810i	−0.747981	+	0.663720i	$0.768977\pi$
$972$		0			0
$973$	−34.0772	+	4.66335i	−1.09246	+	0.149500i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	16.9706			0.542936			0.271468	−	0.962447i	$-0.412491\pi$
$977$	16.9706			0.542936			0.271468	+	0.962447i	$0.412491\pi$
$978$		0			0
$979$	−14.2279	+	24.6435i	−0.454726	+	0.787609i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	12.6213	+	21.8608i	0.402558	+	0.697250i	0.994034	−	0.109072i	$-0.0347880\pi$
$983$	12.6213	+	21.8608i	0.402558	+	0.697250i	−0.591476	+	0.806322i	$0.701455\pi$
$984$		0			0
$985$	9.00000	+	5.19615i	0.286764	+	0.165563i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	9.10660	+	15.7731i	0.289573	+	0.501555i
$990$		0			0
$991$	25.1360	+	14.5123i	0.798473	+	0.460998i	0.842937	−	0.538013i	$-0.180825\pi$
$991$	25.1360	+	14.5123i	0.798473	+	0.460998i	−0.0444642	+	0.999011i	$0.514158\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−12.2574	+	7.07679i	−0.388584	+	0.224349i
$996$		0			0
$997$	−7.86396	+	4.54026i	−0.249054	+	0.143791i	−0.619331	−	0.785130i	$-0.712596\pi$
$997$	−7.86396	+	4.54026i	−0.249054	+	0.143791i	0.370277	+	0.928921i	$0.379263\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cz.e.2719.2		4
3.2	odd	2		1008.2.cz.e.367.1	yes	4
4.3	odd	2		3024.2.cz.f.2719.2		4
7.5	odd	6		3024.2.bf.e.2287.2		4
9.4	even	3		3024.2.bf.f.1711.1		4
9.5	odd	6		1008.2.bf.e.31.2	✓	4
12.11	even	2		1008.2.cz.f.367.1	yes	4
21.5	even	6		1008.2.bf.f.943.1	yes	4
28.19	even	6		3024.2.bf.f.2287.2		4
36.23	even	6		1008.2.bf.f.31.2	yes	4
36.31	odd	6		3024.2.bf.e.1711.1		4
63.5	even	6		1008.2.cz.f.607.1	yes	4
63.40	odd	6		3024.2.cz.f.1279.2		4
84.47	odd	6		1008.2.bf.e.943.1	yes	4
252.103	even	6	inner	3024.2.cz.e.1279.2		4
252.131	odd	6		1008.2.cz.e.607.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.e.31.2	✓	4	9.5	odd	6
1008.2.bf.e.943.1	yes	4	84.47	odd	6
1008.2.bf.f.31.2	yes	4	36.23	even	6
1008.2.bf.f.943.1	yes	4	21.5	even	6
1008.2.cz.e.367.1	yes	4	3.2	odd	2
1008.2.cz.e.607.1	yes	4	252.131	odd	6
1008.2.cz.f.367.1	yes	4	12.11	even	2
1008.2.cz.f.607.1	yes	4	63.5	even	6
3024.2.bf.e.1711.1		4	36.31	odd	6
3024.2.bf.e.2287.2		4	7.5	odd	6
3024.2.bf.f.1711.1		4	9.4	even	3
3024.2.bf.f.2287.2		4	28.19	even	6
3024.2.cz.e.1279.2		4	252.103	even	6	inner
3024.2.cz.e.2719.2		4	1.1	even	1	trivial
3024.2.cz.f.1279.2		4	63.40	odd	6
3024.2.cz.f.2719.2		4	4.3	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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.621320 + 0.358719i) q^{5} +(-1.00000 + 2.44949i) q^{7} +(-1.50000 + 0.866025i) q^{11} +(-3.62132 + 2.09077i) q^{13} +(2.74264 + 1.58346i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-2.37868 - 1.37333i) q^{23} +(-2.24264 - 3.88437i) q^{25} +(-0.621320 + 1.07616i) q^{29} -4.00000 q^{31} +(-1.50000 + 1.16320i) q^{35} +(1.62132 + 2.80821i) q^{37} +(8.74264 - 5.04757i) q^{41} +(-5.74264 - 3.31552i) q^{43} -8.48528 q^{47} +(-5.00000 - 4.89898i) q^{49} +(0.621320 - 1.07616i) q^{53} -1.24264 q^{55} +6.00000 q^{59} -6.92820i q^{61} -3.00000 q^{65} -13.2621i q^{71} +(-7.50000 - 4.33013i) q^{73} +(-0.621320 - 4.54026i) q^{77} +2.02922i q^{79} +(-5.74264 + 9.94655i) q^{83} +(1.13604 + 1.96768i) q^{85} +(14.2279 - 8.21449i) q^{89} +(-1.50000 - 10.9612i) q^{91} -0.717439i q^{95} +(-5.74264 - 3.31552i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{5} - 4 q^{7} - 6 q^{11} - 6 q^{13} - 6 q^{17} - 2 q^{19} - 18 q^{23} + 8 q^{25} + 6 q^{29} - 16 q^{31} - 6 q^{35} - 2 q^{37} + 18 q^{41} - 6 q^{43} - 20 q^{49} - 6 q^{53} + 12 q^{55} + 24 q^{59}+ \cdots - 6 q^{97}+O(q^{100}) \) 4 * q - 6 * q^5 - 4 * q^7 - 6 * q^11 - 6 * q^13 - 6 * q^17 - 2 * q^19 - 18 * q^23 + 8 * q^25 + 6 * q^29 - 16 * q^31 - 6 * q^35 - 2 * q^37 + 18 * q^41 - 6 * q^43 - 20 * q^49 - 6 * q^53 + 12 * q^55 + 24 * q^59 - 12 * q^65 - 30 * q^73 + 6 * q^77 - 6 * q^83 + 30 * q^85 + 6 * q^89 - 6 * q^91 - 6 * q^97

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