LMFDB - Embedded newform 864.2.p.b.719.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(143,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("864.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.p (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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 7x^14 - 12x^13 + 16x^12 - 12x^11 - 8x^10 + 36x^9 - 68x^8 + 72x^7 - 32x^6 - 96x^5 + 256x^4 - 384x^3 + 448x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.7
Root			$1.12063 - 0.862658i$ of defining polynomial
Character	$\chi$	$=$	864.719
Dual form			864.2.p.b.143.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60936 - 2.78750i) q^{5} +(-1.82223 + 1.05206i) q^{7} +O(q^{10})$	$q+(1.60936 - 2.78750i) q^{5} +(-1.82223 + 1.05206i) q^{7} +(3.47720 - 2.00756i) q^{11} +(-0.341902 - 0.197397i) q^{13} +1.20474i q^{17} +1.62474 q^{19} +(2.74384 - 4.75248i) q^{23} +(-2.68011 - 4.64208i) q^{25} +(-2.95670 - 5.12116i) q^{29} +(-3.34777 - 1.93284i) q^{31} +6.77261i q^{35} -10.8195i q^{37} +(1.23849 + 0.715041i) q^{41} +(1.21569 + 2.10564i) q^{43} +(0.792576 + 1.37278i) q^{47} +(-1.28633 + 2.22799i) q^{49} +7.07284 q^{53} -12.9236i q^{55} +(-2.29587 - 1.32552i) q^{59} +(-8.18631 + 4.72637i) q^{61} +(-1.10049 + 0.635369i) q^{65} +(2.60947 - 4.51973i) q^{67} -2.69468 q^{71} +9.49652 q^{73} +(-4.22417 + 7.31647i) q^{77} +(-1.53599 + 0.886804i) q^{79} +(-1.30809 + 0.755228i) q^{83} +(3.35821 + 1.93887i) q^{85} -11.2323i q^{89} +0.830698 q^{91} +(2.61480 - 4.52897i) q^{95} +(5.84818 + 10.1294i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 12 q^{11} + 4 q^{19} - 14 q^{25} + 36 q^{41} - 8 q^{43} + 10 q^{49} + 12 q^{59} + 6 q^{65} + 16 q^{67} - 4 q^{73} + 54 q^{83} + 36 q^{91} + 8 q^{97}+O(q^{100}) $ 16 * q + 12 * q^11 + 4 * q^19 - 14 * q^25 + 36 * q^41 - 8 * q^43 + 10 * q^49 + 12 * q^59 + 6 * q^65 + 16 * q^67 - 4 * q^73 + 54 * q^83 + 36 * q^91 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.60936	−	2.78750i	0.719730	−	1.24661i	−0.241377	−	0.970431i	$-0.577599\pi$
$5$	1.60936	−	2.78750i	0.719730	−	1.24661i	0.961107	−	0.276177i	$-0.0890676\pi$
$6$		0			0
$7$	−1.82223	+	1.05206i	−0.688736	+	0.397642i	−0.803139	−	0.595792i	$-0.796838\pi$
$7$	−1.82223	+	1.05206i	−0.688736	+	0.397642i	0.114402	+	0.993435i	$0.463505\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.47720	−	2.00756i	1.04842	−	0.605303i	0.126211	−	0.992003i	$-0.459718\pi$
$11$	3.47720	−	2.00756i	1.04842	−	0.605303i	0.922206	+	0.386700i	$0.126385\pi$
$12$		0			0
$13$	−0.341902	−	0.197397i	−0.0948267	−	0.0547482i	0.451837	−	0.892101i	$-0.350769\pi$
$13$	−0.341902	−	0.197397i	−0.0948267	−	0.0547482i	−0.546663	+	0.837352i	$0.684102\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			1.20474i			0.292192i	0.989270	+	0.146096i	$0.0466709\pi$
$17$			1.20474i			0.292192i	−0.989270	+	0.146096i	$0.953329\pi$
$18$		0			0
$19$	1.62474			0.372741			0.186371	−	0.982480i	$-0.440327\pi$
$19$	1.62474			0.372741			0.186371	+	0.982480i	$0.440327\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.74384	−	4.75248i	0.572131	−	0.990960i	−0.424216	−	0.905561i	$-0.639450\pi$
$23$	2.74384	−	4.75248i	0.572131	−	0.990960i	0.996347	−	0.0853986i	$-0.0272164\pi$
$24$		0			0
$25$	−2.68011	−	4.64208i	−0.536021	−	0.928416i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.95670	−	5.12116i	−0.549046	−	0.950976i	−0.998340	−	0.0575919i	$-0.981658\pi$
$29$	−2.95670	−	5.12116i	−0.549046	−	0.950976i	0.449294	−	0.893384i	$-0.351676\pi$
$30$		0			0
$31$	−3.34777	−	1.93284i	−0.601277	−	0.347148i	0.168267	−	0.985742i	$-0.446183\pi$
$31$	−3.34777	−	1.93284i	−0.601277	−	0.347148i	−0.769544	+	0.638594i	$0.779516\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			6.77261i			1.14478i
$36$		0			0
$37$		−	10.8195i		−	1.77871i	−0.457215	−	0.889356i	$-0.651153\pi$
$37$		−	10.8195i		−	1.77871i	0.457215	−	0.889356i	$-0.348847\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.23849	+	0.715041i	0.193419	+	0.111671i	0.593582	−	0.804773i	$-0.297713\pi$
$41$	1.23849	+	0.715041i	0.193419	+	0.111671i	−0.400163	+	0.916444i	$0.631047\pi$
$42$		0			0
$43$	1.21569	+	2.10564i	0.185391	+	0.321107i	0.943708	−	0.330779i	$-0.107311\pi$
$43$	1.21569	+	2.10564i	0.185391	+	0.321107i	−0.758317	+	0.651886i	$0.773978\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.792576	+	1.37278i	0.115609	+	0.200241i	0.918023	−	0.396527i	$-0.129785\pi$
$47$	0.792576	+	1.37278i	0.115609	+	0.200241i	−0.802414	+	0.596768i	$0.796451\pi$
$48$		0			0
$49$	−1.28633	+	2.22799i	−0.183761	+	0.318284i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.07284			0.971529			0.485765	−	0.874090i	$-0.338541\pi$
$53$	7.07284			0.971529			0.485765	+	0.874090i	$0.338541\pi$
$54$		0			0
$55$		−	12.9236i		−	1.74262i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.29587	−	1.32552i	−0.298897	−	0.172568i	0.343050	−	0.939317i	$-0.388540\pi$
$59$	−2.29587	−	1.32552i	−0.298897	−	0.172568i	−0.641947	+	0.766749i	$0.721873\pi$
$60$		0			0
$61$	−8.18631	+	4.72637i	−1.04815	+	0.605149i	−0.922131	−	0.386879i	$-0.873553\pi$
$61$	−8.18631	+	4.72637i	−1.04815	+	0.605149i	−0.126019	+	0.992028i	$0.540220\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.10049	+	0.635369i	−0.136499	+	0.0788078i
$66$		0			0
$67$	2.60947	−	4.51973i	0.318797	−	0.552173i	−0.661440	−	0.749998i	$-0.730054\pi$
$67$	2.60947	−	4.51973i	0.318797	−	0.552173i	0.980237	+	0.197825i	$0.0633878\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.69468			−0.319800			−0.159900	−	0.987133i	$-0.551117\pi$
$71$	−2.69468			−0.319800			−0.159900	+	0.987133i	$0.551117\pi$
$72$		0			0
$73$	9.49652			1.11148			0.555742	−	0.831355i	$-0.312434\pi$
$73$	9.49652			1.11148			0.555742	+	0.831355i	$0.312434\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.22417	+	7.31647i	−0.481388	+	0.833789i
$78$		0			0
$79$	−1.53599	+	0.886804i	−0.172812	+	0.0997732i	−0.583911	−	0.811818i	$-0.698478\pi$
$79$	−1.53599	+	0.886804i	−0.172812	+	0.0997732i	0.411099	+	0.911591i	$0.365145\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.30809	+	0.755228i	−0.143582	+	0.0828971i	−0.570070	−	0.821596i	$-0.693084\pi$
$83$	−1.30809	+	0.755228i	−0.143582	+	0.0828971i	0.426488	+	0.904493i	$0.359751\pi$
$84$		0			0
$85$	3.35821	+	1.93887i	0.364249	+	0.210300i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	11.2323i		−	1.19062i	−0.803494	−	0.595312i	$-0.797028\pi$
$89$		−	11.2323i		−	1.19062i	0.803494	−	0.595312i	$-0.202972\pi$
$90$		0			0
$91$	0.830698			0.0870808
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.61480	−	4.52897i	0.268273	−	0.464662i
$96$		0			0
$97$	5.84818	+	10.1294i	0.593793	+	1.02848i	0.993716	+	0.111931i	$0.0357036\pi$
$97$	5.84818	+	10.1294i	0.593793	+	1.02848i	−0.399923	+	0.916549i	$0.630963\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.03509	+	3.52487i	0.202499	+	0.350738i	0.949333	−	0.314272i	$-0.101760\pi$
$101$	2.03509	+	3.52487i	0.202499	+	0.350738i	−0.746834	+	0.665010i	$0.768427\pi$
$102$		0			0
$103$	15.6784	+	9.05191i	1.54484	+	0.891911i	0.998523	+	0.0543294i	$0.0173021\pi$
$103$	15.6784	+	9.05191i	1.54484	+	0.891911i	0.546312	+	0.837582i	$0.316031\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	12.3971i		−	1.19848i	−0.800571	−	0.599238i	$-0.795470\pi$
$107$		−	12.3971i		−	1.19848i	0.800571	−	0.599238i	$-0.204530\pi$
$108$		0			0
$109$			1.76155i			0.168726i	0.996435	+	0.0843628i	$0.0268855\pi$
$109$			1.76155i			0.168726i	−0.996435	+	0.0843628i	$0.973115\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	15.7938	+	9.11858i	1.48576	+	0.857804i	0.999869	−	0.0162153i	$-0.00516171\pi$
$113$	15.7938	+	9.11858i	1.48576	+	0.857804i	0.485891	+	0.874019i	$0.338495\pi$
$114$		0			0
$115$	−8.83169	−	15.2969i	−0.823559	−	1.42645i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.26746	−	2.19531i	−0.116188	−	0.201244i
$120$		0			0
$121$	2.56063	−	4.43514i	0.232785	−	0.403195i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.15943			−0.103703
$126$		0			0
$127$			2.09206i			0.185641i	0.995683	+	0.0928203i	$0.0295882\pi$
$127$			2.09206i			0.185641i	−0.995683	+	0.0928203i	$0.970412\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.05457	−	0.608856i	−0.0921382	−	0.0531960i	0.453223	−	0.891397i	$-0.350274\pi$
$131$	−1.05457	−	0.608856i	−0.0921382	−	0.0531960i	−0.545361	+	0.838201i	$0.683607\pi$
$132$		0			0
$133$	−2.96065	+	1.70933i	−0.256721	+	0.148218i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.20436	+	3.58209i	−0.530074	+	0.306038i	−0.741047	−	0.671454i	$-0.765670\pi$
$137$	−6.20436	+	3.58209i	−0.530074	+	0.306038i	0.210973	+	0.977492i	$0.432337\pi$
$138$		0			0
$139$	−11.0378	+	19.1181i	−0.936217	+	1.62158i	−0.163767	+	0.986499i	$0.552365\pi$
$139$	−11.0378	+	19.1181i	−0.936217	+	1.62158i	−0.772450	+	0.635076i	$0.780969\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.58515			−0.132557
$144$		0			0
$145$	−19.0337			−1.58066
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.0838199	−	0.145180i	0.00686679	−	0.0118936i	−0.862572	−	0.505935i	$-0.831148\pi$
$149$	0.0838199	−	0.145180i	0.00686679	−	0.0118936i	0.869438	+	0.494041i	$0.164481\pi$
$150$		0			0
$151$	−16.5201	+	9.53789i	−1.34439	+	0.776182i	−0.987448	−	0.157945i	$-0.949513\pi$
$151$	−16.5201	+	9.53789i	−1.34439	+	0.776182i	−0.356939	+	0.934128i	$0.616180\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10.7756	+	6.22127i	−0.865514	+	0.499705i
$156$		0			0
$157$	13.3563	+	7.71126i	1.06595	+	0.615426i	0.927072	−	0.374884i	$-0.122317\pi$
$157$	13.3563	+	7.71126i	1.06595	+	0.615426i	0.138877	+	0.990310i	$0.455651\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			11.5468i			0.910013i
$162$		0			0
$163$	5.04605			0.395237			0.197619	−	0.980279i	$-0.436679\pi$
$163$	5.04605			0.395237			0.197619	+	0.980279i	$0.436679\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.49899	+	16.4527i	−0.735054	+	1.27315i	0.219646	+	0.975580i	$0.429510\pi$
$167$	−9.49899	+	16.4527i	−0.735054	+	1.27315i	−0.954700	+	0.297571i	$0.903823\pi$
$168$		0			0
$169$	−6.42207	−	11.1233i	−0.494005	−	0.855642i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.26352	+	2.18848i	0.0960636	+	0.166387i	0.910052	−	0.414494i	$-0.136041\pi$
$173$	1.26352	+	2.18848i	0.0960636	+	0.166387i	−0.813988	+	0.580881i	$0.802708\pi$
$174$		0			0
$175$	9.76752	+	5.63928i	0.738355	+	0.426289i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			10.9962i			0.821898i	0.911658	+	0.410949i	$0.134803\pi$
$179$			10.9962i			0.821898i	−0.911658	+	0.410949i	$0.865197\pi$
$180$		0			0
$181$			14.3426i			1.06608i	0.846091	+	0.533038i	$0.178950\pi$
$181$			14.3426i			1.06608i	−0.846091	+	0.533038i	$0.821050\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−30.1593	−	17.4125i	−2.21736	−	1.28019i
$186$		0			0
$187$	2.41859	+	4.18913i	0.176865	+	0.306339i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.237073	+	0.410623i	0.0171540	+	0.0297116i	0.874475	−	0.485071i	$-0.161206\pi$
$191$	0.237073	+	0.410623i	0.0171540	+	0.0297116i	−0.857321	+	0.514782i	$0.827873\pi$
$192$		0			0
$193$	−10.6703	+	18.4815i	−0.768067	+	1.33033i	0.170543	+	0.985350i	$0.445448\pi$
$193$	−10.6703	+	18.4815i	−0.768067	+	1.33033i	−0.938610	+	0.344981i	$0.887885\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−21.4346			−1.52715			−0.763575	−	0.645719i	$-0.776558\pi$
$197$	−21.4346			−1.52715			−0.763575	+	0.645719i	$0.776558\pi$
$198$		0			0
$199$			6.09835i			0.432301i	0.976360	+	0.216150i	$0.0693501\pi$
$199$			6.09835i			0.432301i	−0.976360	+	0.216150i	$0.930650\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.7756	+	6.22127i	0.756296	+	0.436648i
$204$		0			0
$205$	3.98635	−	2.30152i	0.278419	−	0.160745i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.64956	−	3.26177i	0.390788	−	0.225622i
$210$		0			0
$211$	−1.36572	+	2.36549i	−0.0940197	+	0.162847i	−0.909199	−	0.416362i	$-0.863305\pi$
$211$	−1.36572	+	2.36549i	−0.0940197	+	0.162847i	0.815179	+	0.579209i	$0.196638\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	7.82596			0.533726
$216$		0			0
$217$	8.13386			0.552162
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.237813	−	0.411904i	0.0159970	−	0.0277076i
$222$		0			0
$223$	13.4015	−	7.73737i	0.897432	−	0.518133i	0.0210661	−	0.999778i	$-0.493294\pi$
$223$	13.4015	−	7.73737i	0.897432	−	0.518133i	0.876366	+	0.481645i	$0.159961\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.9546	−	8.05671i	0.926202	−	0.534743i	0.0405935	−	0.999176i	$-0.487075\pi$
$227$	13.9546	−	8.05671i	0.926202	−	0.534743i	0.885608	+	0.464433i	$0.153742\pi$
$228$		0			0
$229$	9.60052	+	5.54286i	0.634420	+	0.366283i	0.782462	−	0.622698i	$-0.213964\pi$
$229$	9.60052	+	5.54286i	0.634420	+	0.366283i	−0.148042	+	0.988981i	$0.547297\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	8.96547i		−	0.587348i	−0.955906	−	0.293674i	$-0.905122\pi$
$233$		−	8.96547i		−	0.587348i	0.955906	−	0.293674i	$-0.0948780\pi$
$234$		0			0
$235$	5.10218			0.332829
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.6179	+	20.1228i	−0.751499	+	1.30163i	0.195597	+	0.980684i	$0.437336\pi$
$239$	−11.6179	+	20.1228i	−0.751499	+	1.30163i	−0.947096	+	0.320951i	$0.895998\pi$
$240$		0			0
$241$	−4.27609	−	7.40641i	−0.275447	−	0.477089i	0.694801	−	0.719202i	$-0.255493\pi$
$241$	−4.27609	−	7.40641i	−0.275447	−	0.477089i	−0.970248	+	0.242114i	$0.922159\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.14035	+	7.17129i	0.264517	+	0.458157i
$246$		0			0
$247$	−0.555503	−	0.320720i	−0.0353458	−	0.0204069i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	13.6971i		−	0.864551i	−0.901742	−	0.432275i	$-0.857711\pi$
$251$		−	13.6971i		−	0.864551i	0.901742	−	0.432275i	$-0.142289\pi$
$252$		0			0
$253$		−	22.0338i		−	1.38525i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.88533	−	2.24320i	−0.242360	−	0.139927i	0.373901	−	0.927469i	$-0.378020\pi$
$257$	−3.88533	−	2.24320i	−0.242360	−	0.139927i	−0.616261	+	0.787542i	$0.711353\pi$
$258$		0			0
$259$	11.3828	+	19.7155i	0.707291	+	1.22506i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	11.1123	+	19.2471i	0.685214	+	1.18682i	0.973370	+	0.229241i	$0.0736245\pi$
$263$	11.1123	+	19.2471i	0.685214	+	1.18682i	−0.288156	+	0.957583i	$0.593042\pi$
$264$		0			0
$265$	11.3828	−	19.7155i	0.699238	−	1.21112i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	12.9941			0.792266			0.396133	−	0.918193i	$-0.370352\pi$
$269$	12.9941			0.792266			0.396133	+	0.918193i	$0.370352\pi$
$270$		0			0
$271$			11.1500i			0.677314i	0.940910	+	0.338657i	$0.109973\pi$
$271$			11.1500i			0.677314i	−0.940910	+	0.338657i	$0.890027\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−18.6386	−	10.7610i	−1.12395	−	0.648911i
$276$		0			0
$277$	−1.29497	+	0.747654i	−0.0778074	+	0.0449221i	−0.538399	−	0.842690i	$-0.680971\pi$
$277$	−1.29497	+	0.747654i	−0.0778074	+	0.0449221i	0.460592	+	0.887612i	$0.347637\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.39961	−	5.42687i	0.560734	−	0.323740i	−0.192706	−	0.981256i	$-0.561726\pi$
$281$	9.39961	−	5.42687i	0.560734	−	0.323740i	0.753440	+	0.657517i	$0.228393\pi$
$282$		0			0
$283$	12.0627	−	20.8931i	0.717050	−	1.24197i	−0.245113	−	0.969494i	$-0.578825\pi$
$283$	12.0627	−	20.8931i	0.717050	−	1.24197i	0.962163	−	0.272473i	$-0.0878415\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.00907			−0.177620
$288$		0			0
$289$	15.5486			0.914624
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.54036	+	6.13209i	−0.206830	+	0.358240i	−0.950714	−	0.310068i	$-0.899648\pi$
$293$	−3.54036	+	6.13209i	−0.206830	+	0.358240i	0.743884	+	0.668309i	$0.232981\pi$
$294$		0			0
$295$	−7.38979	+	4.26650i	−0.430250	+	0.248405i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.87625	+	1.08326i	−0.108507	+	0.0626463i
$300$		0			0
$301$	−4.43052	−	2.55796i	−0.255371	−	0.147439i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			30.4258i			1.74218i
$306$		0			0
$307$	−12.9052			−0.736541			−0.368270	−	0.929719i	$-0.620050\pi$
$307$	−12.9052			−0.736541			−0.368270	+	0.929719i	$0.620050\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.89357	−	13.6721i	0.447603	−	0.775271i	−0.550626	−	0.834752i	$-0.685611\pi$
$311$	7.89357	−	13.6721i	0.447603	−	0.775271i	0.998229	+	0.0594804i	$0.0189444\pi$
$312$		0			0
$313$	2.06365	+	3.57434i	0.116644	+	0.202034i	0.918436	−	0.395570i	$-0.129453\pi$
$313$	2.06365	+	3.57434i	0.116644	+	0.202034i	−0.801792	+	0.597604i	$0.796120\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.58238	+	13.1331i	0.425869	+	0.737627i	0.996501	−	0.0835791i	$-0.0266351\pi$
$317$	7.58238	+	13.1331i	0.425869	+	0.737627i	−0.570632	+	0.821206i	$0.693302\pi$
$318$		0			0
$319$	−20.5621	−	11.8715i	−1.15126	−	0.664679i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			1.95739i			0.108912i
$324$		0			0
$325$			2.11619i			0.117385i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.88851	−	1.66768i	−0.159248	−	0.0919421i
$330$		0			0
$331$	−7.09621	−	12.2910i	−0.390043	−	0.675575i	0.602412	−	0.798186i	$-0.294207\pi$
$331$	−7.09621	−	12.2910i	−0.390043	−	0.675575i	−0.992455	+	0.122611i	$0.960873\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−8.39917	−	14.5478i	−0.458896	−	0.794830i
$336$		0			0
$337$	−12.9139	+	22.3675i	−0.703464	+	1.21844i	0.263779	+	0.964583i	$0.415031\pi$
$337$	−12.9139	+	22.3675i	−0.703464	+	1.21844i	−0.967243	+	0.253853i	$0.918302\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.5212			−0.840518
$342$		0			0
$343$		−	20.1421i		−	1.08757i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.4312	+	6.59978i	0.613656	+	0.354295i	0.774395	−	0.632702i	$-0.218054\pi$
$347$	11.4312	+	6.59978i	0.613656	+	0.354295i	−0.160739	+	0.986997i	$0.551388\pi$
$348$		0			0
$349$	12.7838	−	7.38075i	0.684303	−	0.395082i	−0.117171	−	0.993112i	$-0.537383\pi$
$349$	12.7838	−	7.38075i	0.684303	−	0.395082i	0.801474	+	0.598029i	$0.204049\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.21582	−	0.701955i	0.0647116	−	0.0373613i	−0.467295	−	0.884101i	$-0.654771\pi$
$353$	1.21582	−	0.701955i	0.0647116	−	0.0373613i	0.532007	+	0.846740i	$0.321438\pi$
$354$		0			0
$355$	−4.33672	+	7.51142i	−0.230169	+	0.398665i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−11.3107			−0.596953			−0.298477	−	0.954417i	$-0.596479\pi$
$359$	−11.3107			−0.596953			−0.298477	+	0.954417i	$0.596479\pi$
$360$		0			0
$361$	−16.3602			−0.861064
$362$		0			0
$363$		0			0
$364$		0			0
$365$	15.2834	−	26.4716i	0.799967	−	1.38558i
$366$		0			0
$367$	9.82457	−	5.67222i	0.512838	−	0.296087i	−0.221161	−	0.975237i	$-0.570985\pi$
$367$	9.82457	−	5.67222i	0.512838	−	0.296087i	0.734000	+	0.679150i	$0.237651\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−12.8883	+	7.44107i	−0.669127	+	0.386321i
$372$		0			0
$373$	−20.9314	−	12.0848i	−1.08379	−	0.625726i	−0.151873	−	0.988400i	$-0.548530\pi$
$373$	−20.9314	−	12.0848i	−1.08379	−	0.625726i	−0.931916	+	0.362674i	$0.881864\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			2.33458i			0.120237i
$378$		0			0
$379$	−20.7029			−1.06344			−0.531719	−	0.846921i	$-0.678454\pi$
$379$	−20.7029			−1.06344			−0.531719	+	0.846921i	$0.678454\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	15.2027	−	26.3319i	0.776824	−	1.34550i	−0.156940	−	0.987608i	$-0.550163\pi$
$383$	15.2027	−	26.3319i	0.776824	−	1.34550i	0.933764	−	0.357890i	$-0.116504\pi$
$384$		0			0
$385$	13.5964	+	23.5497i	0.692939	+	1.20021i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.1376	−	17.5588i	−0.513995	−	0.890266i	−0.999868	−	0.0162366i	$-0.994831\pi$
$389$	−10.1376	−	17.5588i	−0.513995	−	0.890266i	0.485873	−	0.874030i	$-0.338502\pi$
$390$		0			0
$391$	5.72550	+	3.30562i	0.289551	+	0.167172i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			5.70876i			0.287239i
$396$		0			0
$397$			12.2942i			0.617030i	0.951220	+	0.308515i	$0.0998320\pi$
$397$			12.2942i			0.617030i	−0.951220	+	0.308515i	$0.900168\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	25.3617	+	14.6426i	1.26650	+	0.731216i	0.974325	−	0.225147i	$-0.0722863\pi$
$401$	25.3617	+	14.6426i	1.26650	+	0.731216i	0.292179	+	0.956364i	$0.405620\pi$
$402$		0			0
$403$	0.763074	+	1.32168i	0.0380114	+	0.0658377i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−21.7208	−	37.6216i	−1.07666	−	1.86483i
$408$		0			0
$409$	15.3567	−	26.5986i	0.759342	−	1.31522i	−0.183845	−	0.982955i	$-0.558855\pi$
$409$	15.3567	−	26.5986i	0.759342	−	1.31522i	0.943187	−	0.332263i	$-0.107812\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.57813			0.274482
$414$		0			0
$415$			4.86175i			0.238654i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.5932	+	6.69333i	0.566364	+	0.326991i	0.755696	−	0.654923i	$-0.227299\pi$
$419$	11.5932	+	6.69333i	0.566364	+	0.326991i	−0.189332	+	0.981913i	$0.560632\pi$
$420$		0			0
$421$	−23.9825	+	13.8463i	−1.16884	+	0.674828i	−0.953406	−	0.301691i	$-0.902449\pi$
$421$	−23.9825	+	13.8463i	−1.16884	+	0.674828i	−0.215431	+	0.976519i	$0.569116\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.59250	−	3.22883i	0.271276	−	0.156621i
$426$		0			0
$427$	9.94486	−	17.2250i	0.481266	−	0.833577i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	29.2554			1.40918			0.704592	−	0.709613i	$-0.251130\pi$
$431$	29.2554			1.40918			0.704592	+	0.709613i	$0.251130\pi$
$432$		0			0
$433$	2.57756			0.123870			0.0619348	−	0.998080i	$-0.480273\pi$
$433$	2.57756			0.123870			0.0619348	+	0.998080i	$0.480273\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.45804	−	7.72155i	0.213257	−	0.369372i
$438$		0			0
$439$	24.4758	−	14.1311i	1.16817	−	0.674442i	0.214920	−	0.976632i	$-0.431051\pi$
$439$	24.4758	−	14.1311i	1.16817	−	0.674442i	0.953248	+	0.302189i	$0.0977175\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−23.3499	+	13.4811i	−1.10939	+	0.640506i	−0.938671	−	0.344814i	$-0.887942\pi$
$443$	−23.3499	+	13.4811i	−1.10939	+	0.640506i	−0.170718	+	0.985320i	$0.554609\pi$
$444$		0			0
$445$	−31.3101	−	18.0769i	−1.48424	−	0.856928i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	23.4500i		−	1.10668i	−0.832957	−	0.553338i	$-0.813354\pi$
$449$		−	23.4500i		−	1.10668i	0.832957	−	0.553338i	$-0.186646\pi$
$450$		0			0
$451$	5.74196			0.270378
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.33690	−	2.31557i	0.0626746	−	0.108556i
$456$		0			0
$457$	−8.06063	−	13.9614i	−0.377060	−	0.653088i	0.613573	−	0.789638i	$-0.289732\pi$
$457$	−8.06063	−	13.9614i	−0.377060	−	0.653088i	−0.990633	+	0.136550i	$0.956398\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.14578	−	8.91276i	−0.239663	−	0.415109i	0.720955	−	0.692982i	$-0.243704\pi$
$461$	−5.14578	−	8.91276i	−0.239663	−	0.415109i	−0.960618	+	0.277874i	$0.910370\pi$
$462$		0			0
$463$	−22.3273	−	12.8907i	−1.03764	−	0.599080i	−0.118474	−	0.992957i	$-0.537800\pi$
$463$	−22.3273	−	12.8907i	−1.03764	−	0.599080i	−0.919163	+	0.393877i	$0.871134\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	10.8110i		−	0.500271i	−0.968211	−	0.250136i	$-0.919525\pi$
$467$		−	10.8110i		−	0.500271i	0.968211	−	0.250136i	$-0.0804752\pi$
$468$		0			0
$469$			10.9813i			0.507069i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	8.45441	+	4.88115i	0.388734	+	0.224436i
$474$		0			0
$475$	−4.35448	−	7.54218i	−0.199797	−	0.346059i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.16167	+	10.6723i	0.281534	+	0.487631i	0.971763	−	0.235960i	$-0.0758236\pi$
$479$	6.16167	+	10.6723i	0.281534	+	0.487631i	−0.690229	+	0.723591i	$0.742490\pi$
$480$		0			0
$481$	−2.13574	+	3.69921i	−0.0973813	+	0.168669i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	37.6474			1.70948
$486$		0			0
$487$			7.62691i			0.345608i	0.984956	+	0.172804i	$0.0552828\pi$
$487$			7.62691i			0.345608i	−0.984956	+	0.172804i	$0.944717\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	22.1130	+	12.7670i	0.997948	+	0.576165i	0.907640	−	0.419749i	$-0.137882\pi$
$491$	22.1130	+	12.7670i	0.997948	+	0.576165i	0.0903072	+	0.995914i	$0.471215\pi$
$492$		0			0
$493$	6.16967	−	3.56206i	0.277868	−	0.160427i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.91031	−	2.83497i	0.220258	−	0.127166i
$498$		0			0
$499$	5.58850	−	9.67956i	0.250176	−	0.433317i	−0.713398	−	0.700759i	$-0.752845\pi$
$499$	5.58850	−	9.67956i	0.250176	−	0.433317i	0.963574	+	0.267442i	$0.0861783\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	22.3635			0.997137			0.498569	−	0.866850i	$-0.333859\pi$
$503$	22.3635			0.997137			0.498569	+	0.866850i	$0.333859\pi$
$504$		0			0
$505$	13.1008			0.582977
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.12701	+	10.6123i	−0.271575	+	0.470382i	−0.969265	−	0.246018i	$-0.920878\pi$
$509$	−6.12701	+	10.6123i	−0.271575	+	0.470382i	0.697690	+	0.716399i	$0.254211\pi$
$510$		0			0
$511$	−17.3048	+	9.99093i	−0.765519	+	0.441973i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	50.4644	−	29.1356i	2.22373	−	1.28387i
$516$		0			0
$517$	5.51190	+	3.18230i	0.242413	+	0.139957i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	34.9202i		−	1.52988i	−0.644101	−	0.764940i	$-0.722768\pi$
$521$		−	34.9202i		−	1.52988i	0.644101	−	0.764940i	$-0.277232\pi$
$522$		0			0
$523$	36.8697			1.61220			0.806100	−	0.591779i	$-0.201574\pi$
$523$	36.8697			1.61220			0.806100	+	0.591779i	$0.201574\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.32857	−	4.03319i	0.101434	−	0.175689i
$528$		0			0
$529$	−3.55735	−	6.16151i	−0.154667	−	0.267892i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.282294	−	0.488948i	−0.0122275	−	0.0211787i
$534$		0			0
$535$	−34.5570	−	19.9515i	−1.49403	−	0.862579i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			10.3296i			0.444926i
$540$		0			0
$541$			11.9200i			0.512481i	0.966613	+	0.256240i	$0.0824839\pi$
$541$			11.9200i			0.512481i	−0.966613	+	0.256240i	$0.917516\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.91031	+	2.83497i	0.210335	+	0.121437i
$546$		0			0
$547$	10.3339	+	17.8989i	0.441847	+	0.765302i	0.997827	−	0.0658943i	$-0.0209900\pi$
$547$	10.3339	+	17.8989i	0.441847	+	0.765302i	−0.555979	+	0.831196i	$0.687657\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−4.80388	−	8.32057i	−0.204652	−	0.354468i
$552$		0			0
$553$	1.86595	−	3.23191i	0.0793481	−	0.137435i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−21.6506			−0.917367			−0.458684	−	0.888600i	$-0.651679\pi$
$557$	−21.6506			−0.917367			−0.458684	+	0.888600i	$0.651679\pi$
$558$		0			0
$559$		−	0.959897i		−	0.0405993i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−36.7299	−	21.2060i	−1.54798	−	0.893726i	−0.998296	−	0.0583533i	$-0.981415\pi$
$563$	−36.7299	−	21.2060i	−1.54798	−	0.893726i	−0.549683	−	0.835373i	$-0.685252\pi$
$564$		0			0
$565$	50.8361	−	29.3502i	2.13869	−	1.23477i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−19.3062	+	11.1464i	−0.809357	+	0.467282i	−0.846732	−	0.532019i	$-0.821433\pi$
$569$	−19.3062	+	11.1464i	−0.809357	+	0.467282i	0.0373758	+	0.999301i	$0.488100\pi$
$570$		0			0
$571$	−1.30386	+	2.25835i	−0.0545649	+	0.0945091i	−0.892018	−	0.452001i	$-0.850711\pi$
$571$	−1.30386	+	2.25835i	−0.0545649	+	0.0945091i	0.837453	+	0.546510i	$0.184044\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−29.4152			−1.22670
$576$		0			0
$577$	−12.3081			−0.512394			−0.256197	−	0.966625i	$-0.582470\pi$
$577$	−12.3081			−0.512394			−0.256197	+	0.966625i	$0.582470\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.58909	−	2.75239i	0.0659267	−	0.114188i
$582$		0			0
$583$	24.5937	−	14.1992i	1.01857	−	0.588070i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−23.8189	+	13.7518i	−0.983111	+	0.567599i	−0.903208	−	0.429203i	$-0.858794\pi$
$587$	−23.8189	+	13.7518i	−0.983111	+	0.567599i	−0.0799032	+	0.996803i	$0.525461\pi$
$588$		0			0
$589$	−5.43926	−	3.14036i	−0.224121	−	0.129396i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			33.5909i			1.37941i	0.724088	+	0.689707i	$0.242261\pi$
$593$			33.5909i			1.37941i	−0.724088	+	0.689707i	$0.757739\pi$
$594$		0			0
$595$	−8.15923			−0.334496
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.32570	+	7.49232i	−0.176743	+	0.306128i	−0.940763	−	0.339064i	$-0.889890\pi$
$599$	−4.32570	+	7.49232i	−0.176743	+	0.306128i	0.764020	+	0.645193i	$0.223223\pi$
$600$		0			0
$601$	11.3533	+	19.6644i	0.463109	+	0.802128i	0.999114	−	0.0420865i	$-0.0134005\pi$
$601$	11.3533	+	19.6644i	0.463109	+	0.802128i	−0.536005	+	0.844215i	$0.680067\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−8.24197	−	14.2755i	−0.335084	−	0.580382i
$606$		0			0
$607$	18.9691	+	10.9518i	0.769932	+	0.444520i	0.832850	−	0.553498i	$-0.186708\pi$
$607$	18.9691	+	10.9518i	0.769932	+	0.444520i	−0.0629187	+	0.998019i	$0.520041\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	0.625810i		−	0.0253176i
$612$		0			0
$613$		−	35.2553i		−	1.42395i	−0.702206	−	0.711973i	$-0.747802\pi$
$613$		−	35.2553i		−	1.42395i	0.702206	−	0.711973i	$-0.252198\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.96793	−	2.29088i	−0.159743	−	0.0922275i	0.417998	−	0.908448i	$-0.362732\pi$
$617$	−3.96793	−	2.29088i	−0.159743	−	0.0922275i	−0.577740	+	0.816221i	$0.696065\pi$
$618$		0			0
$619$	8.24726	+	14.2847i	0.331486	+	0.574150i	0.982803	−	0.184655i	$-0.0591169\pi$
$619$	8.24726	+	14.2847i	0.331486	+	0.574150i	−0.651318	+	0.758805i	$0.725784\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.8171	+	20.4678i	0.473443	+	0.820027i
$624$		0			0
$625$	11.5346	−	19.9785i	0.461384	−	0.799140i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	13.0347			0.519726
$630$		0			0
$631$			38.0635i			1.51528i	0.652670	+	0.757642i	$0.273649\pi$
$631$			38.0635i			1.51528i	−0.652670	+	0.757642i	$0.726351\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.83163	+	3.36689i	0.231421	+	0.133611i
$636$		0			0
$637$	0.879598	−	0.507836i	0.0348510	−	0.0201212i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−30.2526	+	17.4663i	−1.19490	+	0.689878i	−0.959415	−	0.281998i	$-0.909003\pi$
$641$	−30.2526	+	17.4663i	−1.19490	+	0.689878i	−0.235490	+	0.971877i	$0.575669\pi$
$642$		0			0
$643$	−18.5870	+	32.1936i	−0.733000	+	1.26959i	0.222596	+	0.974911i	$0.428547\pi$
$643$	−18.5870	+	32.1936i	−0.733000	+	1.26959i	−0.955595	+	0.294682i	$0.904786\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.36933			−0.368346			−0.184173	−	0.982894i	$-0.558961\pi$
$647$	−9.36933			−0.368346			−0.184173	+	0.982894i	$0.558961\pi$
$648$		0			0
$649$	−10.6443			−0.417825
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7.65255	+	13.2546i	−0.299468	+	0.518693i	−0.976014	−	0.217707i	$-0.930142\pi$
$653$	−7.65255	+	13.2546i	−0.299468	+	0.518693i	0.676547	+	0.736400i	$0.263476\pi$
$654$		0			0
$655$	−3.39437	+	1.95974i	−0.132629	+	0.0765735i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	17.2932	−	9.98421i	0.673646	−	0.388930i	−0.123811	−	0.992306i	$-0.539512\pi$
$659$	17.2932	−	9.98421i	0.673646	−	0.388930i	0.797457	+	0.603376i	$0.206178\pi$
$660$		0			0
$661$	−30.6907	−	17.7193i	−1.19373	−	0.689201i	−0.234580	−	0.972097i	$-0.575372\pi$
$661$	−30.6907	−	17.7193i	−1.19373	−	0.689201i	−0.959151	+	0.282896i	$0.908705\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			11.0037i			0.426707i
$666$		0			0
$667$	−32.4509			−1.25650
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−18.9770	+	32.8691i	−0.732598	+	1.26890i
$672$		0			0
$673$	1.95563	+	3.38725i	0.0753841	+	0.130569i	0.901253	−	0.433293i	$-0.142648\pi$
$673$	1.95563	+	3.38725i	0.0753841	+	0.130569i	−0.825869	+	0.563862i	$0.809315\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.69713	−	2.93951i	−0.0652259	−	0.112974i	0.831568	−	0.555423i	$-0.187443\pi$
$677$	−1.69713	−	2.93951i	−0.0652259	−	0.112974i	−0.896794	+	0.442448i	$0.854110\pi$
$678$		0			0
$679$	−21.3134	−	12.3053i	−0.817934	−	0.472234i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	9.70867i		−	0.371492i	−0.982598	−	0.185746i	$-0.940530\pi$
$683$		−	9.70867i		−	0.371492i	0.982598	−	0.185746i	$-0.0594702\pi$
$684$		0			0
$685$			23.0595i			0.881060i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.41822	−	1.39616i	−0.0921269	−	0.0531895i
$690$		0			0
$691$	−19.6458	−	34.0276i	−0.747363	−	1.29447i	−0.949083	−	0.315027i	$-0.897986\pi$
$691$	−19.6458	−	34.0276i	−0.747363	−	1.29447i	0.201720	−	0.979443i	$-0.435347\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	35.5278	+	61.5359i	1.34765	+	2.33419i
$696$		0			0
$697$	−0.861438	+	1.49206i	−0.0326293	+	0.0565156i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−12.0640			−0.455651			−0.227826	−	0.973702i	$-0.573162\pi$
$701$	−12.0640			−0.455651			−0.227826	+	0.973702i	$0.573162\pi$
$702$		0			0
$703$		−	17.5789i		−	0.663000i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.41677	−	4.28208i	−0.278936	−	0.161044i
$708$		0			0
$709$	11.5824	−	6.68709i	0.434985	−	0.251139i	−0.266483	−	0.963840i	$-0.585862\pi$
$709$	11.5824	−	6.68709i	0.434985	−	0.251139i	0.701468	+	0.712701i	$0.252528\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−18.3715	+	10.6068i	−0.688018	+	0.397228i
$714$		0			0
$715$	−2.55109	+	4.41861i	−0.0954053	+	0.165247i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−36.4686			−1.36005			−0.680025	−	0.733189i	$-0.738031\pi$
$719$	−36.4686			−1.36005			−0.680025	+	0.733189i	$0.738031\pi$
$720$		0			0
$721$	−38.0927			−1.41865
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−15.8486	+	27.4505i	−0.588601	+	1.01949i
$726$		0			0
$727$	−4.01460	+	2.31783i	−0.148893	+	0.0859637i	−0.572596	−	0.819838i	$-0.694064\pi$
$727$	−4.01460	+	2.31783i	−0.148893	+	0.0859637i	0.423702	+	0.905801i	$0.360730\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.53675	+	1.46459i	−0.0938250	+	0.0541699i
$732$		0			0
$733$	32.3446	+	18.6742i	1.19467	+	0.689746i	0.959363	−	0.282175i	$-0.0910557\pi$
$733$	32.3446	+	18.6742i	1.19467	+	0.689746i	0.235311	+	0.971920i	$0.424389\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	20.9547i		−	0.771876i
$738$		0			0
$739$	21.7009			0.798279			0.399140	−	0.916890i	$-0.369309\pi$
$739$	21.7009			0.798279			0.399140	+	0.916890i	$0.369309\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	21.4136	−	37.0894i	0.785588	−	1.36068i	−0.143060	−	0.989714i	$-0.545694\pi$
$743$	21.4136	−	37.0894i	0.785588	−	1.36068i	0.928647	−	0.370964i	$-0.120973\pi$
$744$		0			0
$745$	−0.269793	−	0.467296i	−0.00988446	−	0.0171204i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	13.0426	+	22.5904i	0.476565	+	0.825434i
$750$		0			0
$751$	27.3860	+	15.8113i	0.999328	+	0.576962i	0.908049	−	0.418863i	$-0.137571\pi$
$751$	27.3860	+	15.8113i	0.999328	+	0.576962i	0.0912787	+	0.995825i	$0.470905\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			61.3997i			2.23457i
$756$		0			0
$757$			32.2957i			1.17381i	0.809657	+	0.586903i	$0.199653\pi$
$757$			32.2957i			1.17381i	−0.809657	+	0.586903i	$0.800347\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−31.6365	−	18.2653i	−1.14682	−	0.662118i	−0.198711	−	0.980058i	$-0.563676\pi$
$761$	−31.6365	−	18.2653i	−1.14682	−	0.662118i	−0.948111	+	0.317940i	$0.897009\pi$
$762$		0			0
$763$	−1.85326	−	3.20994i	−0.0670924	−	0.116207i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.523309	+	0.906399i	0.0188956	+	0.0327282i
$768$		0			0
$769$	−1.92161	+	3.32832i	−0.0692950	+	0.120022i	−0.898591	−	0.438787i	$-0.855408\pi$
$769$	−1.92161	+	3.32832i	−0.0692950	+	0.120022i	0.829296	+	0.558809i	$0.188742\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	25.4969			0.917059			0.458529	−	0.888679i	$-0.348376\pi$
$773$	25.4969			0.917059			0.458529	+	0.888679i	$0.348376\pi$
$774$		0			0
$775$			20.7208i			0.744314i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.01222	+	1.16176i	0.0720953	+	0.0416243i
$780$		0			0
$781$	−9.36995	+	5.40974i	−0.335283	+	0.193576i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	42.9903	−	24.8205i	1.53439	−	0.885881i
$786$		0			0
$787$	13.2295	−	22.9142i	0.471581	−	0.816802i	−0.527891	−	0.849312i	$-0.677017\pi$
$787$	13.2295	−	22.9142i	0.471581	−	0.816802i	0.999471	+	0.0325104i	$0.0103502\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−38.3733			−1.36440
$792$		0			0
$793$	3.73189			0.132523
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.10557	−	7.11105i	0.145427	−	0.251886i	−0.784105	−	0.620628i	$-0.786878\pi$
$797$	4.10557	−	7.11105i	0.145427	−	0.251886i	0.929532	+	0.368741i	$0.120211\pi$
$798$		0			0
$799$	−1.65385	+	0.954848i	−0.0585089	+	0.0337801i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	33.0213	−	19.0649i	1.16530	−	0.672785i
$804$		0			0
$805$	32.1866	+	18.5830i	1.13443	+	0.654964i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	4.36982i		−	0.153635i	−0.997045	−	0.0768174i	$-0.975524\pi$
$809$		−	4.36982i		−	0.153635i	0.997045	−	0.0768174i	$-0.0244759\pi$
$810$		0			0
$811$	0.393286			0.0138101			0.00690507	−	0.999976i	$-0.497802\pi$
$811$	0.393286			0.0138101			0.00690507	+	0.999976i	$0.497802\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	8.12094	−	14.0659i	0.284464	−	0.492706i
$816$		0			0
$817$	1.97518	+	3.42112i	0.0691029	+	0.119690i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.66193	−	15.0029i	−0.302304	−	0.523605i	0.674354	−	0.738408i	$-0.264422\pi$
$821$	−8.66193	−	15.0029i	−0.302304	−	0.523605i	−0.976657	+	0.214803i	$0.931089\pi$
$822$		0			0
$823$	26.9923	+	15.5840i	0.940893	+	0.543225i	0.890240	−	0.455491i	$-0.150536\pi$
$823$	26.9923	+	15.5840i	0.940893	+	0.543225i	0.0506529	+	0.998716i	$0.483870\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	36.3732i		−	1.26482i	−0.774634	−	0.632410i	$-0.782066\pi$
$827$		−	36.3732i		−	1.26482i	0.774634	−	0.632410i	$-0.217934\pi$
$828$		0			0
$829$			47.9890i			1.66673i	0.552726	+	0.833363i	$0.313588\pi$
$829$			47.9890i			1.66673i	−0.552726	+	0.833363i	$0.686412\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.68415	−	1.54969i	−0.0930002	−	0.0536937i
$834$		0			0
$835$	30.5747	+	52.9569i	1.05808	+	1.83265i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.62312	−	8.00747i	−0.159608	−	0.276449i	0.775120	−	0.631815i	$-0.217690\pi$
$839$	−4.62312	−	8.00747i	−0.159608	−	0.276449i	−0.934727	+	0.355366i	$0.884356\pi$
$840$		0			0
$841$	−2.98420	+	5.16878i	−0.102903	+	0.178234i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−41.3418			−1.42220
$846$		0			0
$847$			10.7758i			0.370260i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−51.4193	−	29.6870i	−1.76263	−	1.01766i
$852$		0			0
$853$	13.1396	−	7.58616i	0.449892	−	0.259745i	−0.257893	−	0.966174i	$-0.583028\pi$
$853$	13.1396	−	7.58616i	0.449892	−	0.259745i	0.707785	+	0.706428i	$0.249695\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	24.4191	−	14.0984i	0.834140	−	0.481591i	−0.0211282	−	0.999777i	$-0.506726\pi$
$857$	24.4191	−	14.0984i	0.834140	−	0.481591i	0.855268	+	0.518186i	$0.173392\pi$
$858$		0			0
$859$	3.33845	−	5.78236i	0.113906	−	0.197292i	−0.803436	−	0.595392i	$-0.796997\pi$
$859$	3.33845	−	5.78236i	0.113906	−	0.197292i	0.917342	+	0.398100i	$0.130330\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	54.3136			1.84885			0.924427	−	0.381358i	$-0.124543\pi$
$863$	54.3136			1.84885			0.924427	+	0.381358i	$0.124543\pi$
$864$		0			0
$865$	8.13386			0.276559
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.56063	+	6.16719i	−0.120786	+	0.209208i
$870$		0			0
$871$	−1.78437	+	1.03020i	−0.0604610	+	0.0349071i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.11274	−	1.21979i	0.0714238	−	0.0412365i
$876$		0			0
$877$	−5.70769	−	3.29534i	−0.192735	−	0.111276i	0.400527	−	0.916285i	$-0.368827\pi$
$877$	−5.70769	−	3.29534i	−0.192735	−	0.111276i	−0.593262	+	0.805009i	$0.702160\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	15.5607i		−	0.524252i	−0.965034	−	0.262126i	$-0.915576\pi$
$881$		−	15.5607i		−	0.524252i	0.965034	−	0.262126i	$-0.0844236\pi$
$882$		0			0
$883$	−41.6548			−1.40180			−0.700898	−	0.713262i	$-0.747217\pi$
$883$	−41.6548			−1.40180			−0.700898	+	0.713262i	$0.747217\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−26.8247	+	46.4617i	−0.900684	+	1.56003i	−0.0740769	+	0.997253i	$0.523601\pi$
$887$	−26.8247	+	46.4617i	−0.900684	+	1.56003i	−0.826608	+	0.562779i	$0.809732\pi$
$888$		0			0
$889$	−2.20098	−	3.81221i	−0.0738186	−	0.127858i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.28773	+	2.23042i	0.0430923	+	0.0746381i
$894$		0			0
$895$	30.6520	+	17.6970i	1.02458	+	0.591544i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			22.8593i			0.762400i
$900$		0			0
$901$			8.52093i			0.283873i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	39.9800	+	23.0824i	1.32898	+	0.767286i
$906$		0			0
$907$	2.86449	+	4.96144i	0.0951139	+	0.164742i	0.909656	−	0.415362i	$-0.136345\pi$
$907$	2.86449	+	4.96144i	0.0951139	+	0.164742i	−0.814542	+	0.580104i	$0.803012\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−21.2846	−	36.8661i	−0.705192	−	1.22143i	−0.966622	−	0.256206i	$-0.917528\pi$
$911$	−21.2846	−	36.8661i	−0.705192	−	1.22143i	0.261430	−	0.965222i	$-0.415806\pi$
$912$		0			0
$913$	−3.03234	+	5.25216i	−0.100356	+	0.173821i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.56222			0.0846119
$918$		0			0
$919$			40.3722i			1.33175i	0.746061	+	0.665877i	$0.231943\pi$
$919$			40.3722i			1.33175i	−0.746061	+	0.665877i	$0.768057\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.921317	+	0.531923i	0.0303255	+	0.0175085i
$924$		0			0
$925$	−50.2249	+	28.9974i	−1.65139	+	0.953428i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−7.87141	+	4.54456i	−0.258253	+	0.149102i	−0.623537	−	0.781794i	$-0.714305\pi$
$929$	−7.87141	+	4.54456i	−0.258253	+	0.149102i	0.365285	+	0.930896i	$0.380972\pi$
$930$		0			0
$931$	−2.08995	+	3.61991i	−0.0684955	+	0.118638i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	15.5696			0.509180
$936$		0			0
$937$	5.39574			0.176271			0.0881355	−	0.996108i	$-0.471909\pi$
$937$	5.39574			0.176271			0.0881355	+	0.996108i	$0.471909\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−22.2304	+	38.5041i	−0.724689	+	1.25520i	0.234413	+	0.972137i	$0.424683\pi$
$941$	−22.2304	+	38.5041i	−0.724689	+	1.25520i	−0.959102	+	0.283061i	$0.908650\pi$
$942$		0			0
$943$	6.79643	−	3.92392i	0.221322	−	0.127780i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−53.2162	+	30.7244i	−1.72930	+	0.998409i	−0.836454	+	0.548037i	$0.815375\pi$
$947$	−53.2162	+	30.7244i	−1.72930	+	0.998409i	−0.892841	+	0.450372i	$0.851292\pi$
$948$		0			0
$949$	−3.24688	−	1.87459i	−0.105398	−	0.0608517i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			22.6195i			0.732716i	0.930474	+	0.366358i	$0.119395\pi$
$953$			22.6195i			0.732716i	−0.930474	+	0.366358i	$0.880605\pi$
$954$		0			0
$955$	1.52615			0.0493850
$956$		0			0
$957$		0			0
$958$		0			0
$959$	7.53716	−	13.0547i	0.243388	−	0.421560i
$960$		0			0
$961$	−8.02829	−	13.9054i	−0.258977	−	0.448562i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	34.3449	+	59.4871i	1.10560	+	1.91496i
$966$		0			0
$967$	−23.8616	−	13.7765i	−0.767337	−	0.443022i	0.0645868	−	0.997912i	$-0.479427\pi$
$967$	−23.8616	−	13.7765i	−0.767337	−	0.443022i	−0.831924	+	0.554890i	$0.812760\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	23.4973i		−	0.754064i	−0.926200	−	0.377032i	$-0.876945\pi$
$971$		−	23.4973i		−	0.754064i	0.926200	−	0.377032i	$-0.123055\pi$
$972$		0			0
$973$		−	46.4500i		−	1.48912i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−26.2982	−	15.1832i	−0.841353	−	0.485755i	0.0163711	−	0.999866i	$-0.494789\pi$
$977$	−26.2982	−	15.1832i	−0.841353	−	0.485755i	−0.857724	+	0.514111i	$0.828122\pi$
$978$		0			0
$979$	−22.5496	−	39.0571i	−0.720689	−	1.24827i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−15.6881	−	27.1725i	−0.500372	−	0.866669i	−1.00000		0.000429288i	$-0.999863\pi$
$983$	−15.6881	−	27.1725i	−0.500372	−	0.866669i	0.499628	−	0.866240i	$-0.333470\pi$
$984$		0			0
$985$	−34.4960	+	59.7489i	−1.09914	+	1.90376i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	13.3427			0.424272
$990$		0			0
$991$		−	19.2702i		−	0.612138i	−0.952009	−	0.306069i	$-0.900986\pi$
$991$		−	19.2702i		−	0.612138i	0.952009	−	0.306069i	$-0.0990138\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	16.9992	+	9.81447i	0.538910	+	0.311140i
$996$		0			0
$997$	−44.0083	+	25.4082i	−1.39376	+	0.804687i	−0.993729	−	0.111816i	$-0.964333\pi$
$997$	−44.0083	+	25.4082i	−1.39376	+	0.804687i	−0.400029	+	0.916502i	$0.631000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.p.b.719.7		16
3.2	odd	2		288.2.p.b.239.3		16
4.3	odd	2		216.2.l.b.179.7		16
8.3	odd	2	inner	864.2.p.b.719.2		16
8.5	even	2		216.2.l.b.179.4		16
9.2	odd	6	inner	864.2.p.b.143.2		16
9.4	even	3		2592.2.f.b.1295.3		16
9.5	odd	6		2592.2.f.b.1295.13		16
9.7	even	3		288.2.p.b.47.4		16
12.11	even	2		72.2.l.b.59.2	yes	16
24.5	odd	2		72.2.l.b.59.5	yes	16
24.11	even	2		288.2.p.b.239.4		16
36.7	odd	6		72.2.l.b.11.5	yes	16
36.11	even	6		216.2.l.b.35.4		16
36.23	even	6		648.2.f.b.323.13		16
36.31	odd	6		648.2.f.b.323.4		16
72.5	odd	6		648.2.f.b.323.3		16
72.11	even	6	inner	864.2.p.b.143.7		16
72.13	even	6		648.2.f.b.323.14		16
72.29	odd	6		216.2.l.b.35.7		16
72.43	odd	6		288.2.p.b.47.3		16
72.59	even	6		2592.2.f.b.1295.4		16
72.61	even	6		72.2.l.b.11.2	✓	16
72.67	odd	6		2592.2.f.b.1295.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.2	✓	16	72.61	even	6
72.2.l.b.11.5	yes	16	36.7	odd	6
72.2.l.b.59.2	yes	16	12.11	even	2
72.2.l.b.59.5	yes	16	24.5	odd	2
216.2.l.b.35.4		16	36.11	even	6
216.2.l.b.35.7		16	72.29	odd	6
216.2.l.b.179.4		16	8.5	even	2
216.2.l.b.179.7		16	4.3	odd	2
288.2.p.b.47.3		16	72.43	odd	6
288.2.p.b.47.4		16	9.7	even	3
288.2.p.b.239.3		16	3.2	odd	2
288.2.p.b.239.4		16	24.11	even	2
648.2.f.b.323.3		16	72.5	odd	6
648.2.f.b.323.4		16	36.31	odd	6
648.2.f.b.323.13		16	36.23	even	6
648.2.f.b.323.14		16	72.13	even	6
864.2.p.b.143.2		16	9.2	odd	6	inner
864.2.p.b.143.7		16	72.11	even	6	inner
864.2.p.b.719.2		16	8.3	odd	2	inner
864.2.p.b.719.7		16	1.1	even	1	trivial
2592.2.f.b.1295.3		16	9.4	even	3
2592.2.f.b.1295.4		16	72.59	even	6
2592.2.f.b.1295.13		16	9.5	odd	6
2592.2.f.b.1295.14		16	72.67	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.60936 - 2.78750i) q^{5} +(-1.82223 + 1.05206i) q^{7} +O(q^{10})\)	\(q+(1.60936 - 2.78750i) q^{5} +(-1.82223 + 1.05206i) q^{7} +(3.47720 - 2.00756i) q^{11} +(-0.341902 - 0.197397i) q^{13} +1.20474i q^{17} +1.62474 q^{19} +(2.74384 - 4.75248i) q^{23} +(-2.68011 - 4.64208i) q^{25} +(-2.95670 - 5.12116i) q^{29} +(-3.34777 - 1.93284i) q^{31} +6.77261i q^{35} -10.8195i q^{37} +(1.23849 + 0.715041i) q^{41} +(1.21569 + 2.10564i) q^{43} +(0.792576 + 1.37278i) q^{47} +(-1.28633 + 2.22799i) q^{49} +7.07284 q^{53} -12.9236i q^{55} +(-2.29587 - 1.32552i) q^{59} +(-8.18631 + 4.72637i) q^{61} +(-1.10049 + 0.635369i) q^{65} +(2.60947 - 4.51973i) q^{67} -2.69468 q^{71} +9.49652 q^{73} +(-4.22417 + 7.31647i) q^{77} +(-1.53599 + 0.886804i) q^{79} +(-1.30809 + 0.755228i) q^{83} +(3.35821 + 1.93887i) q^{85} -11.2323i q^{89} +0.830698 q^{91} +(2.61480 - 4.52897i) q^{95} +(5.84818 + 10.1294i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 12 q^{11} + 4 q^{19} - 14 q^{25} + 36 q^{41} - 8 q^{43} + 10 q^{49} + 12 q^{59} + 6 q^{65} + 16 q^{67} - 4 q^{73} + 54 q^{83} + 36 q^{91} + 8 q^{97}+O(q^{100}) \) 16 * q + 12 * q^11 + 4 * q^19 - 14 * q^25 + 36 * q^41 - 8 * q^43 + 10 * q^49 + 12 * q^59 + 6 * q^65 + 16 * q^67 - 4 * q^73 + 54 * q^83 + 36 * q^91 + 8 * q^97

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