LMFDB - Embedded newform 2160.2.q.k.721.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2160,2,Mod(721,2160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2160, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("2160.721");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2160 = 2^{4} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2160.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$17.2476868366$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			721.1
Root			$0.403374 - 1.68443i$ of defining polynomial
Character	$\chi$	$=$	2160.721
Dual form			2160.2.q.k.1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{5} +(-0.257068 + 0.445256i) q^{7} +(1.66044 - 2.87597i) q^{11} +(0.660442 + 1.14392i) q^{13} +3.32088 q^{17} +1.32088 q^{19} +(-2.06382 - 3.57463i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.693252 + 1.20075i) q^{29} +(4.36783 + 7.56531i) q^{31} -0.514137 q^{35} +0.292611 q^{37} +(-5.67458 - 9.82866i) q^{41} +(5.17458 - 8.96263i) q^{43} +(2.43165 - 4.21174i) q^{47} +(3.36783 + 5.83326i) q^{49} +5.02827 q^{53} +3.32088 q^{55} +(2.51414 + 4.35461i) q^{59} +(-3.67458 + 6.36456i) q^{61} +(-0.660442 + 1.14392i) q^{65} +(4.72426 + 8.18266i) q^{67} +8.99093 q^{71} +6.05655 q^{73} +(0.853695 + 1.47864i) q^{77} +(-4.02827 + 6.97717i) q^{79} +(-0.771205 + 1.33577i) q^{83} +(1.66044 + 2.87597i) q^{85} +3.00000 q^{89} -0.679116 q^{91} +(0.660442 + 1.14392i) q^{95} +(6.12763 - 10.6134i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 5 q^{7} + 2 q^{11} - 4 q^{13} + 4 q^{17} - 8 q^{19} - 3 q^{23} - 3 q^{25} - 7 q^{29} + 8 q^{31} + 10 q^{35} + 12 q^{37} - 13 q^{41} + 10 q^{43} - 13 q^{47} + 2 q^{49} + 4 q^{53} + 4 q^{55}+ \cdots + 18 q^{97}+O(q^{100}) $ 6 * q + 3 * q^5 + 5 * q^7 + 2 * q^11 - 4 * q^13 + 4 * q^17 - 8 * q^19 - 3 * q^23 - 3 * q^25 - 7 * q^29 + 8 * q^31 + 10 * q^35 + 12 * q^37 - 13 * q^41 + 10 * q^43 - 13 * q^47 + 2 * q^49 + 4 * q^53 + 4 * q^55 + 2 * q^59 - q^61 + 4 * q^65 + 11 * q^67 - 20 * q^71 - 16 * q^73 + 2 * q^79 + 15 * q^83 + 2 * q^85 + 18 * q^89 - 20 * q^91 - 4 * q^95 + 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times$.

$n$	$271$	$1297$	$1621$	$2081$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.257068	+	0.445256i	−0.0971627	+	0.168291i	−0.910509	−	0.413489i	$-0.864310\pi$
$7$	−0.257068	+	0.445256i	−0.0971627	+	0.168291i	0.813346	+	0.581780i	$0.197643\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.66044	−	2.87597i	0.500642	−	0.867138i	−0.499358	−	0.866396i	$-0.666431\pi$
$11$	1.66044	−	2.87597i	0.500642	−	0.867138i	1.00000		0.000741679i	$-0.000236084\pi$
$12$		0			0
$13$	0.660442	+	1.14392i	0.183174	+	0.317266i	0.942960	−	0.332907i	$-0.108030\pi$
$13$	0.660442	+	1.14392i	0.183174	+	0.317266i	−0.759786	+	0.650173i	$0.774696\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.32088			0.805433			0.402716	−	0.915325i	$-0.368066\pi$
$17$	3.32088			0.805433			0.402716	+	0.915325i	$0.368066\pi$
$18$		0			0
$19$	1.32088			0.303032			0.151516	−	0.988455i	$-0.451585\pi$
$19$	1.32088			0.303032			0.151516	+	0.988455i	$0.451585\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.06382	−	3.57463i	−0.430335	−	0.745363i	0.566567	−	0.824016i	$-0.308271\pi$
$23$	−2.06382	−	3.57463i	−0.430335	−	0.745363i	−0.996902	+	0.0786532i	$0.974938\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.693252	+	1.20075i	−0.128734	+	0.222973i	−0.923186	−	0.384353i	$-0.874425\pi$
$29$	−0.693252	+	1.20075i	−0.128734	+	0.222973i	0.794453	+	0.607326i	$0.207758\pi$
$30$		0			0
$31$	4.36783	+	7.56531i	0.784486	+	1.35877i	0.929306	+	0.369311i	$0.120406\pi$
$31$	4.36783	+	7.56531i	0.784486	+	1.35877i	−0.144820	+	0.989458i	$0.546260\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.514137			−0.0869050
$36$		0			0
$37$	0.292611			0.0481049			0.0240524	−	0.999711i	$-0.492343\pi$
$37$	0.292611			0.0481049			0.0240524	+	0.999711i	$0.492343\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.67458	−	9.82866i	−0.886220	−	1.53498i	−0.844308	−	0.535857i	$-0.819988\pi$
$41$	−5.67458	−	9.82866i	−0.886220	−	1.53498i	−0.0419119	−	0.999121i	$-0.513345\pi$
$42$		0			0
$43$	5.17458	−	8.96263i	0.789116	−	1.36679i	−0.137393	−	0.990517i	$-0.543872\pi$
$43$	5.17458	−	8.96263i	0.789116	−	1.36679i	0.926509	−	0.376272i	$-0.122794\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.43165	−	4.21174i	0.354692	−	0.614345i	−0.632373	−	0.774664i	$-0.717919\pi$
$47$	2.43165	−	4.21174i	0.354692	−	0.614345i	0.987065	+	0.160319i	$0.0512523\pi$
$48$		0			0
$49$	3.36783	+	5.83326i	0.481119	+	0.833322i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.02827			0.690687			0.345343	−	0.938476i	$-0.387762\pi$
$53$	5.02827			0.690687			0.345343	+	0.938476i	$0.387762\pi$
$54$		0			0
$55$	3.32088			0.447788
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.51414	+	4.35461i	0.327313	+	0.566922i	0.981978	−	0.188997i	$-0.0605236\pi$
$59$	2.51414	+	4.35461i	0.327313	+	0.566922i	−0.654665	+	0.755919i	$0.727190\pi$
$60$		0			0
$61$	−3.67458	+	6.36456i	−0.470482	+	0.814898i	−0.999430	−	0.0337558i	$-0.989253\pi$
$61$	−3.67458	+	6.36456i	−0.470482	+	0.814898i	0.528948	+	0.848654i	$0.322586\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.660442	+	1.14392i	−0.0819178	+	0.141886i
$66$		0			0
$67$	4.72426	+	8.18266i	0.577160	+	0.999670i	0.995803	+	0.0915197i	$0.0291724\pi$
$67$	4.72426	+	8.18266i	0.577160	+	0.999670i	−0.418643	+	0.908151i	$0.637494\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.99093			1.06703			0.533513	−	0.845792i	$-0.320871\pi$
$71$	8.99093			1.06703			0.533513	+	0.845792i	$0.320871\pi$
$72$		0			0
$73$	6.05655			0.708865			0.354433	−	0.935082i	$-0.384674\pi$
$73$	6.05655			0.708865			0.354433	+	0.935082i	$0.384674\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.853695	+	1.47864i	0.0972875	+	0.168507i
$78$		0			0
$79$	−4.02827	+	6.97717i	−0.453216	+	0.784994i	−0.998584	−	0.0532036i	$-0.983057\pi$
$79$	−4.02827	+	6.97717i	−0.453216	+	0.784994i	0.545367	+	0.838197i	$0.316390\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.771205	+	1.33577i	−0.0846508	+	0.146619i	−0.905242	−	0.424896i	$-0.860311\pi$
$83$	−0.771205	+	1.33577i	−0.0846508	+	0.146619i	0.820592	+	0.571515i	$0.193644\pi$
$84$		0			0
$85$	1.66044	+	2.87597i	0.180100	+	0.311943i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		0			0
$91$	−0.679116			−0.0711906
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.660442	+	1.14392i	0.0677599	+	0.117364i
$96$		0			0
$97$	6.12763	−	10.6134i	0.622167	−	1.07762i	−0.366915	−	0.930255i	$-0.619586\pi$
$97$	6.12763	−	10.6134i	0.622167	−	1.07762i	0.989081	−	0.147370i	$-0.0470808\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.83502	−	10.1066i	0.580606	−	1.00564i	−0.414801	−	0.909912i	$-0.636149\pi$
$101$	5.83502	−	10.1066i	0.580606	−	1.00564i	0.995408	−	0.0957276i	$-0.0305178\pi$
$102$		0			0
$103$	0.146305	+	0.253408i	0.0144159	+	0.0249691i	0.873143	−	0.487464i	$-0.162078\pi$
$103$	0.146305	+	0.253408i	0.0144159	+	0.0249691i	−0.858727	+	0.512433i	$0.828744\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.87237			0.181009			0.0905043	−	0.995896i	$-0.471152\pi$
$107$	1.87237			0.181009			0.0905043	+	0.995896i	$0.471152\pi$
$108$		0			0
$109$	5.54787			0.531390			0.265695	−	0.964057i	$-0.414399\pi$
$109$	5.54787			0.531390			0.265695	+	0.964057i	$0.414399\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.90064	+	6.75611i	0.366942	+	0.635561i	0.989086	−	0.147341i	$-0.0470716\pi$
$113$	3.90064	+	6.75611i	0.366942	+	0.635561i	−0.622144	+	0.782903i	$0.713738\pi$
$114$		0			0
$115$	2.06382	−	3.57463i	0.192452	−	0.333336i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.853695	+	1.47864i	−0.0782581	+	0.135547i
$120$		0			0
$121$	−0.0141369	−	0.0244859i	−0.00128518	−	0.00222599i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−17.8916			−1.58762			−0.793810	−	0.608166i	$-0.791906\pi$
$127$	−17.8916			−1.58762			−0.793810	+	0.608166i	$0.791906\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	0.966803	−	0.255524i	$-0.0822479\pi$
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	−0.704692	+	0.709514i	$0.748915\pi$
$132$		0			0
$133$	−0.339558	+	0.588131i	−0.0294434	+	0.0509974i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.83502	−	4.91040i	0.242212	−	0.419524i	−0.719132	−	0.694874i	$-0.755460\pi$
$137$	2.83502	−	4.91040i	0.242212	−	0.419524i	0.961344	+	0.275350i	$0.0887936\pi$
$138$		0			0
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.38650			0.366818
$144$		0			0
$145$	−1.38650			−0.115143
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.83049	+	15.2948i	0.723422	+	1.25300i	0.959620	+	0.281298i	$0.0907650\pi$
$149$	8.83049	+	15.2948i	0.723422	+	1.25300i	−0.236199	+	0.971705i	$0.575902\pi$
$150$		0			0
$151$	0.632168	−	1.09495i	0.0514451	−	0.0891056i	−0.839156	−	0.543891i	$-0.816951\pi$
$151$	0.632168	−	1.09495i	0.0514451	−	0.0891056i	0.890601	+	0.454785i	$0.150284\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.36783	+	7.56531i	−0.350833	+	0.607660i
$156$		0			0
$157$	7.83502	+	13.5707i	0.625303	+	1.08306i	0.988482	+	0.151337i	$0.0483579\pi$
$157$	7.83502	+	13.5707i	0.625303	+	1.08306i	−0.363179	+	0.931719i	$0.618309\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.12217			0.167250
$162$		0			0
$163$	−15.7074			−1.23030			−0.615149	−	0.788411i	$-0.710904\pi$
$163$	−15.7074			−1.23030			−0.615149	+	0.788411i	$0.710904\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.08249	−	5.33903i	−0.238530	−	0.413146i	0.721763	−	0.692141i	$-0.243332\pi$
$167$	−3.08249	−	5.33903i	−0.238530	−	0.413146i	−0.960293	+	0.278994i	$0.909999\pi$
$168$		0			0
$169$	5.62763	−	9.74734i	0.432895	−	0.749796i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.29261	−	7.43502i	0.326361	−	0.565274i	−0.655426	−	0.755260i	$-0.727511\pi$
$173$	4.29261	−	7.43502i	0.326361	−	0.565274i	0.981787	+	0.189986i	$0.0608441\pi$
$174$		0			0
$175$	−0.257068	−	0.445256i	−0.0194325	−	0.0336582i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.06562			−0.0796482			−0.0398241	−	0.999207i	$-0.512680\pi$
$179$	−1.06562			−0.0796482			−0.0398241	+	0.999207i	$0.512680\pi$
$180$		0			0
$181$	−12.6700			−0.941757			−0.470878	−	0.882198i	$-0.656063\pi$
$181$	−12.6700			−0.941757			−0.470878	+	0.882198i	$0.656063\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.146305	+	0.253408i	0.0107566	+	0.0186309i
$186$		0			0
$187$	5.51414	−	9.55077i	0.403234	−	0.698421i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.46719	−	14.6656i	0.612664	−	1.06117i	−0.378125	−	0.925754i	$-0.623431\pi$
$191$	8.46719	−	14.6656i	0.612664	−	1.06117i	0.990789	−	0.135411i	$-0.0432356\pi$
$192$		0			0
$193$	−13.3588	−	23.1380i	−0.961585	−	1.66551i	−0.718524	−	0.695502i	$-0.755182\pi$
$193$	−13.3588	−	23.1380i	−0.961585	−	1.66551i	−0.243060	−	0.970011i	$-0.578151\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.2553			1.01565			0.507823	−	0.861462i	$-0.330450\pi$
$197$	14.2553			1.01565			0.507823	+	0.861462i	$0.330450\pi$
$198$		0			0
$199$	24.6610			1.74817			0.874085	−	0.485773i	$-0.161462\pi$
$199$	24.6610			1.74817			0.874085	+	0.485773i	$0.161462\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.356427	−	0.617349i	−0.0250162	−	0.0433294i
$204$		0			0
$205$	5.67458	−	9.82866i	0.396330	−	0.686463i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.19325	−	3.79882i	0.151710	−	0.262770i
$210$		0			0
$211$	−2.68872	−	4.65699i	−0.185099	−	0.320601i	0.758511	−	0.651660i	$-0.225927\pi$
$211$	−2.68872	−	4.65699i	−0.185099	−	0.320601i	−0.943610	+	0.331060i	$0.892594\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	10.3492			0.705807
$216$		0			0
$217$	−4.49133			−0.304891
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.19325	+	3.79882i	0.147534	+	0.255537i
$222$		0			0
$223$	4.33229	−	7.50375i	0.290112	−	0.502488i	−0.683724	−	0.729740i	$-0.739641\pi$
$223$	4.33229	−	7.50375i	0.290112	−	0.502488i	0.973836	+	0.227252i	$0.0729743\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.66044	+	2.87597i	−0.110207	+	0.190885i	−0.915854	−	0.401512i	$-0.868485\pi$
$227$	−1.66044	+	2.87597i	−0.110207	+	0.190885i	0.805646	+	0.592397i	$0.201818\pi$
$228$		0			0
$229$	12.6559	+	21.9207i	0.836326	+	1.44856i	0.892946	+	0.450163i	$0.148634\pi$
$229$	12.6559	+	21.9207i	0.836326	+	1.44856i	−0.0566206	+	0.998396i	$0.518033\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−27.6327			−1.81028			−0.905139	−	0.425116i	$-0.860233\pi$
$233$	−27.6327			−1.81028			−0.905139	+	0.425116i	$0.860233\pi$
$234$		0			0
$235$	4.86330			0.317246
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.09936	+	3.63620i	0.135796	+	0.235206i	0.925901	−	0.377765i	$-0.123307\pi$
$239$	2.09936	+	3.63620i	0.135796	+	0.235206i	−0.790105	+	0.612971i	$0.789974\pi$
$240$		0			0
$241$	−1.80221	+	3.12152i	−0.116091	+	0.201075i	−0.918215	−	0.396082i	$-0.870370\pi$
$241$	−1.80221	+	3.12152i	−0.116091	+	0.201075i	0.802125	+	0.597157i	$0.203703\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.36783	+	5.83326i	−0.215163	+	0.372673i
$246$		0			0
$247$	0.872368	+	1.51099i	0.0555074	+	0.0961417i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.87783			−0.434125			−0.217062	−	0.976158i	$-0.569648\pi$
$251$	−6.87783			−0.434125			−0.217062	+	0.976158i	$0.569648\pi$
$252$		0			0
$253$	−13.7074			−0.861776
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$		0			0
$259$	−0.0752210	+	0.130287i	−0.00467400	+	0.00809561i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.11803	+	5.40059i	−0.192266	+	0.333015i	−0.946001	−	0.324164i	$-0.894917\pi$
$263$	−3.11803	+	5.40059i	−0.192266	+	0.333015i	0.753735	+	0.657179i	$0.228250\pi$
$264$		0			0
$265$	2.51414	+	4.35461i	0.154442	+	0.267502i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.92345			−0.605044			−0.302522	−	0.953142i	$-0.597828\pi$
$269$	−9.92345			−0.605044			−0.302522	+	0.953142i	$0.597828\pi$
$270$		0			0
$271$	−6.60442			−0.401190			−0.200595	−	0.979674i	$-0.564288\pi$
$271$	−6.60442			−0.401190			−0.200595	+	0.979674i	$0.564288\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.66044	+	2.87597i	0.100128	+	0.173428i
$276$		0			0
$277$	−11.3305	+	19.6250i	−0.680783	+	1.17915i	0.293959	+	0.955818i	$0.405027\pi$
$277$	−11.3305	+	19.6250i	−0.680783	+	1.17915i	−0.974742	+	0.223333i	$0.928306\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.77394	+	13.4649i	−0.463754	+	0.803246i	−0.999144	−	0.0413590i	$-0.986831\pi$
$281$	−7.77394	+	13.4649i	−0.463754	+	0.803246i	0.535390	+	0.844605i	$0.320165\pi$
$282$		0			0
$283$	0.322689	+	0.558913i	0.0191819	+	0.0332240i	0.875457	−	0.483296i	$-0.160561\pi$
$283$	0.322689	+	0.558913i	0.0191819	+	0.0332240i	−0.856275	+	0.516520i	$0.827227\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.83502			0.344430
$288$		0			0
$289$	−5.97173			−0.351278
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.688716	−	1.19289i	−0.0402352	−	0.0696895i	0.845207	−	0.534440i	$-0.179477\pi$
$293$	−0.688716	−	1.19289i	−0.0402352	−	0.0696895i	−0.885442	+	0.464750i	$0.846144\pi$
$294$		0			0
$295$	−2.51414	+	4.35461i	−0.146379	+	0.253535i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.72606	−	4.72168i	0.157652	−	0.273062i
$300$		0			0
$301$	2.66044	+	4.60802i	0.153345	+	0.265602i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.34916			−0.420812
$306$		0			0
$307$	7.98546			0.455754			0.227877	−	0.973690i	$-0.426822\pi$
$307$	7.98546			0.455754			0.227877	+	0.973690i	$0.426822\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.81635	−	8.34216i	−0.273110	−	0.473040i	0.696547	−	0.717512i	$-0.254719\pi$
$311$	−4.81635	−	8.34216i	−0.273110	−	0.473040i	−0.969657	+	0.244471i	$0.921386\pi$
$312$		0			0
$313$	12.2685	−	21.2496i	0.693455	−	1.20110i	−0.277244	−	0.960800i	$-0.589421\pi$
$313$	12.2685	−	21.2496i	0.693455	−	1.20110i	0.970699	−	0.240300i	$-0.0772458\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.1746	+	17.6229i	−0.571461	+	0.989800i	0.424955	+	0.905215i	$0.360290\pi$
$317$	−10.1746	+	17.6229i	−0.571461	+	0.989800i	−0.996416	+	0.0845855i	$0.973043\pi$
$318$		0			0
$319$	2.30221	+	3.98755i	0.128899	+	0.223260i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.38650			0.244072
$324$		0			0
$325$	−1.32088			−0.0732695
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.25020	+	2.16541i	0.0689257	+	0.119383i
$330$		0			0
$331$	8.22153	−	14.2401i	0.451896	−	0.782707i	−0.546608	−	0.837389i	$-0.684081\pi$
$331$	8.22153	−	14.2401i	0.451896	−	0.782707i	0.998504	+	0.0546819i	$0.0174145\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.72426	+	8.18266i	−0.258114	+	0.447066i
$336$		0			0
$337$	−2.44852	−	4.24096i	−0.133379	−	0.231020i	0.791598	−	0.611042i	$-0.209249\pi$
$337$	−2.44852	−	4.24096i	−0.133379	−	0.231020i	−0.924977	+	0.380023i	$0.875916\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	29.0101			1.57099
$342$		0			0
$343$	−7.06201			−0.381313
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−11.1372	−	19.2903i	−0.597878	−	1.03556i	−0.993134	−	0.116984i	$-0.962677\pi$
$347$	−11.1372	−	19.2903i	−0.597878	−	1.03556i	0.395256	−	0.918571i	$-0.370656\pi$
$348$		0			0
$349$	1.47173	−	2.54910i	0.0787797	−	0.136450i	−0.823944	−	0.566671i	$-0.808231\pi$
$349$	1.47173	−	2.54910i	0.0787797	−	0.136450i	0.902724	+	0.430221i	$0.141564\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.41478	−	16.3069i	0.501098	−	0.867927i	−0.498901	−	0.866659i	$-0.666263\pi$
$353$	9.41478	−	16.3069i	0.501098	−	0.867927i	0.999999	−	0.00126845i	$-0.000403761\pi$
$354$		0			0
$355$	4.49546	+	7.78637i	0.238594	+	0.413258i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−31.8770			−1.68241			−0.841203	−	0.540720i	$-0.818152\pi$
$359$	−31.8770			−1.68241			−0.841203	+	0.540720i	$0.818152\pi$
$360$		0			0
$361$	−17.2553			−0.908172
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.02827	+	5.24512i	0.158507	+	0.274542i
$366$		0			0
$367$	−9.17458	+	15.8908i	−0.478909	+	0.829495i	−0.999708	−	0.0241848i	$-0.992301\pi$
$367$	−9.17458	+	15.8908i	−0.478909	+	0.829495i	0.520798	+	0.853680i	$0.325634\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.29261	+	2.23887i	−0.0671090	+	0.116236i
$372$		0			0
$373$	1.09936	+	1.90414i	0.0569226	+	0.0985929i	0.893083	−	0.449893i	$-0.148538\pi$
$373$	1.09936	+	1.90414i	0.0569226	+	0.0985929i	−0.836160	+	0.548486i	$0.815205\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.83141			−0.0943226
$378$		0			0
$379$	−15.4713			−0.794709			−0.397354	−	0.917665i	$-0.630072\pi$
$379$	−15.4713			−0.794709			−0.397354	+	0.917665i	$0.630072\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.85369	−	6.67479i	−0.196915	−	0.341066i	0.750612	−	0.660743i	$-0.229759\pi$
$383$	−3.85369	−	6.67479i	−0.196915	−	0.341066i	−0.947526	+	0.319677i	$0.896426\pi$
$384$		0			0
$385$	−0.853695	+	1.47864i	−0.0435083	+	0.0753586i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.3163	+	21.3325i	−0.624464	+	1.08160i	0.364181	+	0.931328i	$0.381349\pi$
$389$	−12.3163	+	21.3325i	−0.624464	+	1.08160i	−0.988644	+	0.150274i	$0.951984\pi$
$390$		0			0
$391$	−6.85369	−	11.8709i	−0.346606	−	0.600340i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.05655			−0.405369
$396$		0			0
$397$	−6.77301			−0.339928			−0.169964	−	0.985450i	$-0.554365\pi$
$397$	−6.77301			−0.339928			−0.169964	+	0.985450i	$0.554365\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.24980	−	16.0211i	−0.461913	−	0.800057i	0.537143	−	0.843491i	$-0.319503\pi$
$401$	−9.24980	−	16.0211i	−0.461913	−	0.800057i	−0.999056	+	0.0434343i	$0.986170\pi$
$402$		0			0
$403$	−5.76940	+	9.99290i	−0.287394	+	0.497782i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.485863	−	0.841540i	0.0240833	−	0.0417136i
$408$		0			0
$409$	6.70739	+	11.6175i	0.331659	+	0.574450i	0.982837	−	0.184474i	$-0.0590583\pi$
$409$	6.70739	+	11.6175i	0.331659	+	0.574450i	−0.651178	+	0.758925i	$0.725725\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.58522			−0.127210
$414$		0			0
$415$	−1.54241			−0.0757140
$416$		0			0
$417$		0			0
$418$		0			0
$419$	16.5575	+	28.6784i	0.808886	+	1.40103i	0.913636	+	0.406532i	$0.133262\pi$
$419$	16.5575	+	28.6784i	0.808886	+	1.40103i	−0.104751	+	0.994499i	$0.533404\pi$
$420$		0			0
$421$	7.34916	−	12.7291i	0.358176	−	0.620379i	−0.629480	−	0.777017i	$-0.716732\pi$
$421$	7.34916	−	12.7291i	0.358176	−	0.620379i	0.987656	+	0.156637i	$0.0500654\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.66044	+	2.87597i	−0.0805433	+	0.139505i
$426$		0			0
$427$	−1.88924	−	3.27225i	−0.0914266	−	0.158355i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−32.7549			−1.57775			−0.788873	−	0.614556i	$-0.789335\pi$
$431$	−32.7549			−1.57775			−0.788873	+	0.614556i	$0.789335\pi$
$432$		0			0
$433$	−11.8314			−0.568581			−0.284291	−	0.958738i	$-0.591758\pi$
$433$	−11.8314			−0.568581			−0.284291	+	0.958738i	$0.591758\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.72606	−	4.72168i	−0.130405	−	0.225869i
$438$		0			0
$439$	4.15591	−	7.19824i	0.198351	−	0.343553i	−0.749643	−	0.661842i	$-0.769775\pi$
$439$	4.15591	−	7.19824i	0.198351	−	0.343553i	0.947994	+	0.318289i	$0.103108\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.5876	−	25.2664i	0.693076	−	1.20044i	−0.277750	−	0.960654i	$-0.589589\pi$
$443$	14.5876	−	25.2664i	0.693076	−	1.20044i	0.970825	−	0.239789i	$-0.0770781\pi$
$444$		0			0
$445$	1.50000	+	2.59808i	0.0711068	+	0.123161i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−18.9717			−0.895331			−0.447666	−	0.894201i	$-0.647744\pi$
$449$	−18.9717			−0.895331			−0.447666	+	0.894201i	$0.647744\pi$
$450$		0			0
$451$	−37.6892			−1.77472
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.339558	−	0.588131i	−0.0159187	−	0.0275720i
$456$		0			0
$457$	11.6176	−	20.1223i	0.543450	−	0.941283i	−0.455253	−	0.890362i	$-0.650451\pi$
$457$	11.6176	−	20.1223i	0.543450	−	0.941283i	0.998703	−	0.0509206i	$-0.0162155\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.21285	−	3.83277i	0.103063	−	0.178510i	−0.809882	−	0.586592i	$-0.800469\pi$
$461$	2.21285	−	3.83277i	0.103063	−	0.178510i	0.912945	+	0.408082i	$0.133802\pi$
$462$		0			0
$463$	−9.75434	−	16.8950i	−0.453322	−	0.785178i	0.545268	−	0.838262i	$-0.316428\pi$
$463$	−9.75434	−	16.8950i	−0.453322	−	0.785178i	−0.998590	+	0.0530845i	$0.983095\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−24.5935			−1.13805			−0.569026	−	0.822320i	$-0.692679\pi$
$467$	−24.5935			−1.13805			−0.569026	+	0.822320i	$0.692679\pi$
$468$		0			0
$469$	−4.85783			−0.224314
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−17.1842	−	29.7639i	−0.790129	−	1.36854i
$474$		0			0
$475$	−0.660442	+	1.14392i	−0.0303032	+	0.0524866i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−16.3774	+	28.3665i	−0.748304	+	1.29610i	0.200331	+	0.979728i	$0.435798\pi$
$479$	−16.3774	+	28.3665i	−0.748304	+	1.29610i	−0.948635	+	0.316372i	$0.897535\pi$
$480$		0			0
$481$	0.193252	+	0.334723i	0.00881155	+	0.0152621i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	12.2553			0.556483
$486$		0			0
$487$	6.03735			0.273578			0.136789	−	0.990600i	$-0.456322\pi$
$487$	6.03735			0.273578			0.136789	+	0.990600i	$0.456322\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.22153	−	12.5081i	−0.325903	−	0.564480i	0.655792	−	0.754942i	$-0.272335\pi$
$491$	−7.22153	−	12.5081i	−0.325903	−	0.564480i	−0.981695	+	0.190461i	$0.939002\pi$
$492$		0			0
$493$	−2.30221	+	3.98755i	−0.103686	+	0.179590i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.31128	+	4.00326i	−0.103675	+	0.179571i
$498$		0			0
$499$	10.4859	+	18.1620i	0.469412	+	0.813045i	0.999388	−	0.0349673i	$-0.0111327\pi$
$499$	10.4859	+	18.1620i	0.469412	+	0.813045i	−0.529977	+	0.848012i	$0.677799\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−5.31728			−0.237086			−0.118543	−	0.992949i	$-0.537822\pi$
$503$	−5.31728			−0.237086			−0.118543	+	0.992949i	$0.537822\pi$
$504$		0			0
$505$	11.6700			0.519310
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.11350	+	15.7850i	0.403949	+	0.699659i	0.994198	−	0.107561i	$-0.0343041\pi$
$509$	9.11350	+	15.7850i	0.403949	+	0.699659i	−0.590250	+	0.807221i	$0.700971\pi$
$510$		0			0
$511$	−1.55695	+	2.69671i	−0.0688753	+	0.119296i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.146305	+	0.253408i	−0.00644698	+	0.0111665i
$516$		0			0
$517$	−8.07522	−	13.9867i	−0.355148	−	0.615134i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−40.1232			−1.75783			−0.878915	−	0.476978i	$-0.841732\pi$
$521$	−40.1232			−1.75783			−0.878915	+	0.476978i	$0.841732\pi$
$522$		0			0
$523$	−18.9873			−0.830257			−0.415129	−	0.909763i	$-0.636263\pi$
$523$	−18.9873			−0.830257			−0.415129	+	0.909763i	$0.636263\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.5051	+	25.1235i	0.631851	+	1.09440i
$528$		0			0
$529$	2.98133	−	5.16381i	0.129623	−	0.224513i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7.49546	−	12.9825i	0.324665	−	0.562336i
$534$		0			0
$535$	0.936184	+	1.62152i	0.0404748	+	0.0701043i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	22.3684			0.963473
$540$		0			0
$541$	16.5279			0.710589			0.355294	−	0.934754i	$-0.384381\pi$
$541$	16.5279			0.710589			0.355294	+	0.934754i	$0.384381\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.77394	+	4.80460i	0.118822	+	0.205806i
$546$		0			0
$547$	8.83683	−	15.3058i	0.377835	−	0.654430i	−0.612912	−	0.790151i	$-0.710002\pi$
$547$	8.83683	−	15.3058i	0.377835	−	0.654430i	0.990747	+	0.135721i	$0.0433352\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.915706	+	1.58605i	−0.0390104	+	0.0675680i
$552$		0			0
$553$	−2.07108	−	3.58722i	−0.0880715	−	0.152544i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.3401			−0.734723			−0.367362	−	0.930078i	$-0.619739\pi$
$557$	−17.3401			−0.734723			−0.367362	+	0.930078i	$0.619739\pi$
$558$		0			0
$559$	13.6700			0.578181
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.49727	−	11.2536i	−0.273827	−	0.474283i	0.696011	−	0.718031i	$-0.254956\pi$
$563$	−6.49727	−	11.2536i	−0.273827	−	0.474283i	−0.969839	+	0.243748i	$0.921623\pi$
$564$		0			0
$565$	−3.90064	+	6.75611i	−0.164101	+	0.284232i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.34009	+	14.4455i	−0.349635	+	0.605585i	−0.986184	−	0.165651i	$-0.947028\pi$
$569$	−8.34009	+	14.4455i	−0.349635	+	0.605585i	0.636550	+	0.771236i	$0.280361\pi$
$570$		0			0
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	0.995788	−	0.0916910i	$-0.0292272\pi$
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	−0.577301	+	0.816532i	$0.695894\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.12763			0.172134
$576$		0			0
$577$	−23.5953			−0.982287			−0.491144	−	0.871079i	$-0.663421\pi$
$577$	−23.5953			−0.982287			−0.491144	+	0.871079i	$0.663421\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.396505	−	0.686767i	−0.0164498	−	0.0284919i
$582$		0			0
$583$	8.34916	−	14.4612i	0.345787	−	0.598920i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.0638	+	24.3592i	−0.580476	+	1.00541i	0.414947	+	0.909846i	$0.363800\pi$
$587$	−14.0638	+	24.3592i	−0.580476	+	1.00541i	−0.995423	+	0.0955681i	$0.969533\pi$
$588$		0			0
$589$	5.76940	+	9.99290i	0.237724	+	0.411750i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.17872			0.376925			0.188462	−	0.982080i	$-0.439650\pi$
$593$	9.17872			0.376925			0.188462	+	0.982080i	$0.439650\pi$
$594$		0			0
$595$	−1.70739			−0.0699961
$596$		0			0
$597$		0			0
$598$		0			0
$599$	15.7357	+	27.2550i	0.642942	+	1.11361i	0.984773	+	0.173846i	$0.0556196\pi$
$599$	15.7357	+	27.2550i	0.642942	+	1.11361i	−0.341831	+	0.939761i	$0.611047\pi$
$600$		0			0
$601$	14.6327	−	25.3446i	0.596880	−	1.03383i	−0.396398	−	0.918079i	$-0.629740\pi$
$601$	14.6327	−	25.3446i	0.596880	−	1.03383i	0.993279	−	0.115748i	$-0.0369265\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.0141369	−	0.0244859i	0.000574748	−	0.000995493i
$606$		0			0
$607$	−22.1017	−	38.2813i	−0.897080	−	1.55379i	−0.831209	−	0.555960i	$-0.812351\pi$
$607$	−22.1017	−	38.2813i	−0.897080	−	1.55379i	−0.0658708	−	0.997828i	$-0.520983\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.42385			0.259881
$612$		0			0
$613$	−35.1715			−1.42056			−0.710282	−	0.703918i	$-0.751432\pi$
$613$	−35.1715			−1.42056			−0.710282	+	0.703918i	$0.751432\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.71285	−	6.43085i	−0.149474	−	0.258896i	0.781559	−	0.623831i	$-0.214425\pi$
$617$	−3.71285	−	6.43085i	−0.149474	−	0.258896i	−0.931033	+	0.364935i	$0.881091\pi$
$618$		0			0
$619$	4.27394	−	7.40268i	0.171784	−	0.297539i	−0.767260	−	0.641337i	$-0.778380\pi$
$619$	4.27394	−	7.40268i	0.171784	−	0.297539i	0.939044	+	0.343798i	$0.111714\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.771205	+	1.33577i	−0.0308977	+	0.0535164i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.971726			0.0387453
$630$		0			0
$631$	2.36836			0.0942829			0.0471415	−	0.998888i	$-0.484989\pi$
$631$	2.36836			0.0942829			0.0471415	+	0.998888i	$0.484989\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.94578	−	15.4946i	−0.355003	−	0.614883i
$636$		0			0
$637$	−4.44852	+	7.70506i	−0.176257	+	0.305285i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.0665480	+	0.115265i	−0.00262849	+	0.00455268i	−0.867337	−	0.497722i	$-0.834170\pi$
$641$	−0.0665480	+	0.115265i	−0.00262849	+	0.00455268i	0.864708	+	0.502275i	$0.167503\pi$
$642$		0			0
$643$	−11.3232	−	19.6124i	−0.446544	−	0.773437i	0.551614	−	0.834099i	$-0.314012\pi$
$643$	−11.3232	−	19.6124i	−0.446544	−	0.773437i	−0.998158	+	0.0606623i	$0.980679\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	46.3912			1.82383			0.911913	−	0.410385i	$-0.134606\pi$
$647$	46.3912			1.82383			0.911913	+	0.410385i	$0.134606\pi$
$648$		0			0
$649$	16.6983			0.655466
$650$		0			0
$651$		0			0
$652$		0			0
$653$	18.2029	+	31.5283i	0.712333	+	1.23380i	0.963979	+	0.265977i	$0.0856946\pi$
$653$	18.2029	+	31.5283i	0.712333	+	1.23380i	−0.251647	+	0.967819i	$0.580972\pi$
$654$		0			0
$655$	−3.00000	+	5.19615i	−0.117220	+	0.203030i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−9.57068	+	16.5769i	−0.372821	+	0.645745i	−0.989998	−	0.141079i	$-0.954943\pi$
$659$	−9.57068	+	16.5769i	−0.372821	+	0.645745i	0.617177	+	0.786824i	$0.288276\pi$
$660$		0			0
$661$	−19.9536	−	34.5606i	−0.776104	−	1.34425i	−0.934172	−	0.356824i	$-0.883860\pi$
$661$	−19.9536	−	34.5606i	−0.776104	−	1.34425i	0.158067	−	0.987428i	$-0.449474\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.679116			−0.0263350
$666$		0			0
$667$	5.72298			0.221595
$668$		0			0
$669$		0			0
$670$		0			0
$671$	12.2029	+	21.1360i	0.471086	+	0.815945i
$672$		0			0
$673$	−11.8254	+	20.4822i	−0.455836	+	0.789532i	−0.998736	−	0.0502658i	$-0.983993\pi$
$673$	−11.8254	+	20.4822i	−0.455836	+	0.789532i	0.542899	+	0.839798i	$0.317326\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.40157	+	12.8199i	−0.284465	+	0.492709i	−0.972479	−	0.232989i	$-0.925149\pi$
$677$	−7.40157	+	12.8199i	−0.284465	+	0.492709i	0.688014	+	0.725697i	$0.258483\pi$
$678$		0			0
$679$	3.15044	+	5.45673i	0.120903	+	0.209410i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−4.95252			−0.189503			−0.0947515	−	0.995501i	$-0.530206\pi$
$683$	−4.95252			−0.189503			−0.0947515	+	0.995501i	$0.530206\pi$
$684$		0			0
$685$	5.67004			0.216641
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.32088	+	5.75194i	0.126516	+	0.219131i
$690$		0			0
$691$	−9.60442	+	16.6353i	−0.365369	+	0.632838i	−0.988835	−	0.149012i	$-0.952391\pi$
$691$	−9.60442	+	16.6353i	−0.365369	+	0.632838i	0.623466	+	0.781851i	$0.285724\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.00000	+	6.92820i	−0.151729	+	0.262802i
$696$		0			0
$697$	−18.8446	−	32.6398i	−0.713791	−	1.23632i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	29.3492			1.10850			0.554251	−	0.832349i	$-0.313005\pi$
$701$	29.3492			1.10850			0.554251	+	0.832349i	$0.313005\pi$
$702$		0			0
$703$	0.386505			0.0145773
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.00000	+	5.19615i	0.112827	+	0.195421i
$708$		0			0
$709$	−19.3633	+	33.5382i	−0.727204	+	1.25955i	0.230857	+	0.972988i	$0.425847\pi$
$709$	−19.3633	+	33.5382i	−0.727204	+	1.25955i	−0.958060	+	0.286566i	$0.907486\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	18.0288	−	31.2268i	0.675184	−	1.16945i
$714$		0			0
$715$	2.19325	+	3.79882i	0.0820230	+	0.142068i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−15.0848			−0.562569			−0.281284	−	0.959624i	$-0.590760\pi$
$719$	−15.0848			−0.562569			−0.281284	+	0.959624i	$0.590760\pi$
$720$		0			0
$721$	−0.150442			−0.00560275
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.693252	−	1.20075i	−0.0257467	−	0.0445947i
$726$		0			0
$727$	6.17277	−	10.6916i	0.228936	−	0.396528i	−0.728557	−	0.684985i	$-0.759809\pi$
$727$	6.17277	−	10.6916i	0.228936	−	0.396528i	0.957493	+	0.288457i	$0.0931422\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	17.1842	−	29.7639i	0.635580	−	1.10086i
$732$		0			0
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	31.3774			1.15580
$738$		0			0
$739$	−29.7266			−1.09351			−0.546755	−	0.837293i	$-0.684137\pi$
$739$	−29.7266			−1.09351			−0.546755	+	0.837293i	$0.684137\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−24.1824	−	41.8851i	−0.887165	−	1.53662i	−0.843212	−	0.537582i	$-0.819338\pi$
$743$	−24.1824	−	41.8851i	−0.887165	−	1.53662i	−0.0439537	−	0.999034i	$-0.513995\pi$
$744$		0			0
$745$	−8.83049	+	15.2948i	−0.323524	+	0.560360i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.481327	+	0.833682i	−0.0175873	+	0.0304621i
$750$		0			0
$751$	−15.9102	−	27.5573i	−0.580573	−	1.00558i	−0.995411	−	0.0956869i	$-0.969495\pi$
$751$	−15.9102	−	27.5573i	−0.580573	−	1.00558i	0.414838	−	0.909895i	$-0.363838\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.26434			0.0460139
$756$		0			0
$757$	4.94531			0.179740			0.0898701	−	0.995953i	$-0.471355\pi$
$757$	4.94531			0.179740			0.0898701	+	0.995953i	$0.471355\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	17.7125	+	30.6789i	0.642076	+	1.11211i	0.984969	+	0.172734i	$0.0552600\pi$
$761$	17.7125	+	30.6789i	0.642076	+	1.11211i	−0.342893	+	0.939375i	$0.611407\pi$
$762$		0			0
$763$	−1.42618	+	2.47022i	−0.0516313	+	0.0894281i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.32088	+	5.75194i	−0.119910	+	0.207691i
$768$		0			0
$769$	−24.7125	−	42.8032i	−0.891154	−	1.54352i	−0.838494	−	0.544911i	$-0.816563\pi$
$769$	−24.7125	−	42.8032i	−0.891154	−	1.54352i	−0.0526602	−	0.998612i	$-0.516770\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−12.6599			−0.455345			−0.227673	−	0.973738i	$-0.573112\pi$
$773$	−12.6599			−0.455345			−0.227673	+	0.973738i	$0.573112\pi$
$774$		0			0
$775$	−8.73566			−0.313794
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.49546	−	12.9825i	−0.268553	−	0.465147i
$780$		0			0
$781$	14.9289	−	25.8576i	0.534199	−	0.925259i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.83502	+	13.5707i	−0.279644	+	0.484357i
$786$		0			0
$787$	15.4672	+	26.7900i	0.551346	+	0.954959i	0.998178	+	0.0603410i	$0.0192188\pi$
$787$	15.4672	+	26.7900i	0.551346	+	0.954959i	−0.446832	+	0.894618i	$0.647448\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−4.01093			−0.142612
$792$		0			0
$793$	−9.70739			−0.344720
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.2967	−	26.4947i	−0.541839	−	0.938492i	−0.998799	−	0.0490047i	$-0.984395\pi$
$797$	−15.2967	−	26.4947i	−0.541839	−	0.938492i	0.456960	−	0.889487i	$-0.348938\pi$
$798$		0			0
$799$	8.07522	−	13.9867i	0.285681	−	0.494814i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.0565	−	17.4185i	0.354888	−	0.614684i
$804$		0			0
$805$	1.06108	+	1.83785i	0.0373983	+	0.0647758i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.89703			0.101854			0.0509271	−	0.998702i	$-0.483782\pi$
$809$	2.89703			0.101854			0.0509271	+	0.998702i	$0.483782\pi$
$810$		0			0
$811$	14.8861			0.522722			0.261361	−	0.965241i	$-0.415829\pi$
$811$	14.8861			0.522722			0.261361	+	0.965241i	$0.415829\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−7.85369	−	13.6030i	−0.275103	−	0.476492i
$816$		0			0
$817$	6.83502	−	11.8386i	0.239127	−	0.414180i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.47586	+	7.75242i	−0.156209	+	0.270561i	−0.933498	−	0.358581i	$-0.883261\pi$
$821$	−4.47586	+	7.75242i	−0.156209	+	0.270561i	0.777290	+	0.629143i	$0.216594\pi$
$822$		0			0
$823$	1.49727	+	2.59334i	0.0521915	+	0.0903983i	0.890941	−	0.454119i	$-0.150046\pi$
$823$	1.49727	+	2.59334i	0.0521915	+	0.0903983i	−0.838749	+	0.544518i	$0.816713\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	31.9663			1.11158			0.555788	−	0.831324i	$-0.312417\pi$
$827$	31.9663			1.11158			0.555788	+	0.831324i	$0.312417\pi$
$828$		0			0
$829$	22.7458			0.789994			0.394997	−	0.918682i	$-0.370746\pi$
$829$	22.7458			0.789994			0.394997	+	0.918682i	$0.370746\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	11.1842	+	19.3716i	0.387509	+	0.671185i
$834$		0			0
$835$	3.08249	−	5.33903i	0.106674	−	0.184765i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11.6322	−	20.1475i	0.401587	−	0.695569i	−0.592331	−	0.805695i	$-0.701792\pi$
$839$	11.6322	−	20.1475i	0.401587	−	0.695569i	0.993918	+	0.110126i	$0.0351254\pi$
$840$		0			0
$841$	13.5388	+	23.4499i	0.466855	+	0.808617i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	11.2553			0.387193
$846$		0			0
$847$	0.0145366			0.000499485
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.603895	−	1.04598i	−0.0207012	−	0.0358556i
$852$		0			0
$853$	−5.49546	+	9.51842i	−0.188161	+	0.325905i	−0.944637	−	0.328117i	$-0.893586\pi$
$853$	−5.49546	+	9.51842i	−0.188161	+	0.325905i	0.756476	+	0.654021i	$0.226919\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.07522	+	13.9867i	−0.275844	+	0.477776i	−0.970348	−	0.241713i	$-0.922291\pi$
$857$	−8.07522	+	13.9867i	−0.275844	+	0.477776i	0.694503	+	0.719489i	$0.255624\pi$
$858$		0			0
$859$	14.2594	+	24.6980i	0.486524	+	0.842685i	0.999880	−	0.0154909i	$-0.00493111\pi$
$859$	14.2594	+	24.6980i	0.486524	+	0.842685i	−0.513356	+	0.858176i	$0.671598\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	12.2890			0.418322			0.209161	−	0.977881i	$-0.432927\pi$
$863$	12.2890			0.418322			0.209161	+	0.977881i	$0.432927\pi$
$864$		0			0
$865$	8.58522			0.291906
$866$		0			0
$867$		0			0
$868$		0			0
$869$	13.3774	+	23.1704i	0.453798	+	0.786002i
$870$		0			0
$871$	−6.24020	+	10.8083i	−0.211441	+	0.366227i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.257068	−	0.445256i	0.00869050	−	0.0150524i
$876$		0			0
$877$	19.8501	+	34.3814i	0.670290	+	1.16098i	0.977822	+	0.209438i	$0.0671635\pi$
$877$	19.8501	+	34.3814i	0.670290	+	1.16098i	−0.307532	+	0.951538i	$0.599503\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−32.1040			−1.08161			−0.540806	−	0.841147i	$-0.681881\pi$
$881$	−32.1040			−1.08161			−0.540806	+	0.841147i	$0.681881\pi$
$882$		0			0
$883$	−13.5051			−0.454482			−0.227241	−	0.973839i	$-0.572970\pi$
$883$	−13.5051			−0.454482			−0.227241	+	0.973839i	$0.572970\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−17.5611	−	30.4167i	−0.589643	−	1.02129i	−0.994279	−	0.106814i	$-0.965935\pi$
$887$	−17.5611	−	30.4167i	−0.589643	−	1.02129i	0.404635	−	0.914478i	$-0.367398\pi$
$888$		0			0
$889$	4.59936	−	7.96632i	0.154258	−	0.267182i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.21193	−	5.56322i	0.107483	−	0.186166i
$894$		0			0
$895$	−0.532810	−	0.922854i	−0.0178099	−	0.0308476i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.1120			−0.403959
$900$		0			0
$901$	16.6983			0.556302
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.33502	−	10.9726i	−0.210583	−	0.364741i
$906$		0			0
$907$	7.55928	−	13.0931i	0.251002	−	0.434748i	−0.712800	−	0.701367i	$-0.752573\pi$
$907$	7.55928	−	13.0931i	0.251002	−	0.434748i	0.963802	+	0.266619i	$0.0859067\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−26.2781	+	45.5150i	−0.870631	+	1.50798i	−0.00928675	+	0.999957i	$0.502956\pi$
$911$	−26.2781	+	45.5150i	−0.870631	+	1.50798i	−0.861345	+	0.508021i	$0.830377\pi$
$912$		0			0
$913$	2.56108	+	4.43593i	0.0847595	+	0.146808i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3.08482			−0.101870
$918$		0			0
$919$	54.5489			1.79940			0.899702	−	0.436505i	$-0.143784\pi$
$919$	54.5489			1.79940			0.899702	+	0.436505i	$0.143784\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.93799	+	10.2849i	0.195451	+	0.338532i
$924$		0			0
$925$	−0.146305	+	0.253408i	−0.00481049	+	0.00833201i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	10.1896	−	17.6490i	0.334311	−	0.579044i	−0.649041	−	0.760753i	$-0.724830\pi$
$929$	10.1896	−	17.6490i	0.334311	−	0.579044i	0.983352	+	0.181709i	$0.0581630\pi$
$930$		0			0
$931$	4.44852	+	7.70506i	0.145794	+	0.252523i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	11.0283			0.360663
$936$		0			0
$937$	49.1979			1.60723			0.803613	−	0.595152i	$-0.202908\pi$
$937$	49.1979			1.60723			0.803613	+	0.595152i	$0.202908\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−11.6186	−	20.1239i	−0.378754	−	0.656022i	0.612127	−	0.790759i	$-0.290314\pi$
$941$	−11.6186	−	20.1239i	−0.378754	−	0.656022i	−0.990881	+	0.134738i	$0.956981\pi$
$942$		0			0
$943$	−23.4226	+	40.5691i	−0.762744	+	1.32111i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.5821	+	32.1851i	−0.603837	+	1.04588i	0.388397	+	0.921492i	$0.373029\pi$
$947$	−18.5821	+	32.1851i	−0.603837	+	1.04588i	−0.992234	+	0.124384i	$0.960305\pi$
$948$		0			0
$949$	4.00000	+	6.92820i	0.129845	+	0.224899i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	23.5761			0.763706			0.381853	−	0.924223i	$-0.375286\pi$
$953$	23.5761			0.763706			0.381853	+	0.924223i	$0.375286\pi$
$954$		0			0
$955$	16.9344			0.547984
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.45759	+	2.52462i	0.0470680	+	0.0815242i
$960$		0			0
$961$	−22.6559	+	39.2412i	−0.730836	+	1.26584i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	13.3588	−	23.1380i	0.430034	−	0.744840i
$966$		0			0
$967$	4.19145	+	7.25980i	0.134788	+	0.233459i	0.925516	−	0.378708i	$-0.123631\pi$
$967$	4.19145	+	7.25980i	0.134788	+	0.233459i	−0.790729	+	0.612167i	$0.790298\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.2078			0.423858			0.211929	−	0.977285i	$-0.432025\pi$
$971$	13.2078			0.423858			0.211929	+	0.977285i	$0.432025\pi$
$972$		0			0
$973$	−4.11310			−0.131860
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.16551	−	12.4110i	−0.229245	−	0.397064i	0.728340	−	0.685216i	$-0.240292\pi$
$977$	−7.16551	−	12.4110i	−0.229245	−	0.397064i	−0.957585	+	0.288153i	$0.906959\pi$
$978$		0			0
$979$	4.98133	−	8.62791i	0.159204	−	0.275749i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	16.1541	−	27.9797i	0.515236	−	0.892415i	−0.484608	−	0.874732i	$-0.661038\pi$
$983$	16.1541	−	27.9797i	0.515236	−	0.892415i	0.999844	−	0.0176831i	$-0.00562899\pi$
$984$		0			0
$985$	7.12763	+	12.3454i	0.227105	+	0.393358i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−42.7175			−1.35834
$990$		0			0
$991$	39.6700			1.26016			0.630080	−	0.776530i	$-0.283022\pi$
$991$	39.6700			1.26016			0.630080	+	0.776530i	$0.283022\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	12.3305	+	21.3570i	0.390903	+	0.677063i
$996$		0			0
$997$	−19.3437	+	33.5043i	−0.612621	+	1.06109i	0.378176	+	0.925734i	$0.376551\pi$
$997$	−19.3437	+	33.5043i	−0.612621	+	1.06109i	−0.990797	+	0.135357i	$0.956782\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2160.2.q.k.721.1		6
3.2	odd	2		720.2.q.i.241.1		6
4.3	odd	2		135.2.e.b.46.3		6
9.2	odd	6		6480.2.a.bv.1.3		3
9.4	even	3	inner	2160.2.q.k.1441.1		6
9.5	odd	6		720.2.q.i.481.1		6
9.7	even	3		6480.2.a.bs.1.3		3
12.11	even	2		45.2.e.b.16.1	✓	6
20.3	even	4		675.2.k.b.424.1		12
20.7	even	4		675.2.k.b.424.6		12
20.19	odd	2		675.2.e.b.451.1		6
36.7	odd	6		405.2.a.i.1.1		3
36.11	even	6		405.2.a.j.1.3		3
36.23	even	6		45.2.e.b.31.1	yes	6
36.31	odd	6		135.2.e.b.91.3		6
60.23	odd	4		225.2.k.b.124.6		12
60.47	odd	4		225.2.k.b.124.1		12
60.59	even	2		225.2.e.b.151.3		6
180.7	even	12		2025.2.b.m.649.1		6
180.23	odd	12		225.2.k.b.49.1		12
180.43	even	12		2025.2.b.m.649.6		6
180.47	odd	12		2025.2.b.l.649.6		6
180.59	even	6		225.2.e.b.76.3		6
180.67	even	12		675.2.k.b.199.1		12
180.79	odd	6		2025.2.a.o.1.3		3
180.83	odd	12		2025.2.b.l.649.1		6
180.103	even	12		675.2.k.b.199.6		12
180.119	even	6		2025.2.a.n.1.1		3
180.139	odd	6		675.2.e.b.226.1		6
180.167	odd	12		225.2.k.b.49.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.1	✓	6	12.11	even	2
45.2.e.b.31.1	yes	6	36.23	even	6
135.2.e.b.46.3		6	4.3	odd	2
135.2.e.b.91.3		6	36.31	odd	6
225.2.e.b.76.3		6	180.59	even	6
225.2.e.b.151.3		6	60.59	even	2
225.2.k.b.49.1		12	180.23	odd	12
225.2.k.b.49.6		12	180.167	odd	12
225.2.k.b.124.1		12	60.47	odd	4
225.2.k.b.124.6		12	60.23	odd	4
405.2.a.i.1.1		3	36.7	odd	6
405.2.a.j.1.3		3	36.11	even	6
675.2.e.b.226.1		6	180.139	odd	6
675.2.e.b.451.1		6	20.19	odd	2
675.2.k.b.199.1		12	180.67	even	12
675.2.k.b.199.6		12	180.103	even	12
675.2.k.b.424.1		12	20.3	even	4
675.2.k.b.424.6		12	20.7	even	4
720.2.q.i.241.1		6	3.2	odd	2
720.2.q.i.481.1		6	9.5	odd	6
2025.2.a.n.1.1		3	180.119	even	6
2025.2.a.o.1.3		3	180.79	odd	6
2025.2.b.l.649.1		6	180.83	odd	12
2025.2.b.l.649.6		6	180.47	odd	12
2025.2.b.m.649.1		6	180.7	even	12
2025.2.b.m.649.6		6	180.43	even	12
2160.2.q.k.721.1		6	1.1	even	1	trivial
2160.2.q.k.1441.1		6	9.4	even	3	inner
6480.2.a.bs.1.3		3	9.7	even	3
6480.2.a.bv.1.3		3	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2160.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{5} +(-0.257068 + 0.445256i) q^{7} +(1.66044 - 2.87597i) q^{11} +(0.660442 + 1.14392i) q^{13} +3.32088 q^{17} +1.32088 q^{19} +(-2.06382 - 3.57463i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.693252 + 1.20075i) q^{29} +(4.36783 + 7.56531i) q^{31} -0.514137 q^{35} +0.292611 q^{37} +(-5.67458 - 9.82866i) q^{41} +(5.17458 - 8.96263i) q^{43} +(2.43165 - 4.21174i) q^{47} +(3.36783 + 5.83326i) q^{49} +5.02827 q^{53} +3.32088 q^{55} +(2.51414 + 4.35461i) q^{59} +(-3.67458 + 6.36456i) q^{61} +(-0.660442 + 1.14392i) q^{65} +(4.72426 + 8.18266i) q^{67} +8.99093 q^{71} +6.05655 q^{73} +(0.853695 + 1.47864i) q^{77} +(-4.02827 + 6.97717i) q^{79} +(-0.771205 + 1.33577i) q^{83} +(1.66044 + 2.87597i) q^{85} +3.00000 q^{89} -0.679116 q^{91} +(0.660442 + 1.14392i) q^{95} +(6.12763 - 10.6134i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 5 q^{7} + 2 q^{11} - 4 q^{13} + 4 q^{17} - 8 q^{19} - 3 q^{23} - 3 q^{25} - 7 q^{29} + 8 q^{31} + 10 q^{35} + 12 q^{37} - 13 q^{41} + 10 q^{43} - 13 q^{47} + 2 q^{49} + 4 q^{53} + 4 q^{55}+ \cdots + 18 q^{97}+O(q^{100}) \) 6 * q + 3 * q^5 + 5 * q^7 + 2 * q^11 - 4 * q^13 + 4 * q^17 - 8 * q^19 - 3 * q^23 - 3 * q^25 - 7 * q^29 + 8 * q^31 + 10 * q^35 + 12 * q^37 - 13 * q^41 + 10 * q^43 - 13 * q^47 + 2 * q^49 + 4 * q^53 + 4 * q^55 + 2 * q^59 - q^61 + 4 * q^65 + 11 * q^67 - 20 * q^71 - 16 * q^73 + 2 * q^79 + 15 * q^83 + 2 * q^85 + 18 * q^89 - 20 * q^91 - 4 * q^95 + 18 * q^97

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