LMFDB - Embedded newform 864.2.p.b.719.1

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			719.1
Root			$1.40985 - 0.111062i$ of defining polynomial
Character	$\chi$	$=$	864.719
Dual form			864.2.p.b.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74322 + 3.01934i) q^{5} +(-1.80802 + 1.04386i) q^{7} +O(q^{10})$	$q+(-1.74322 + 3.01934i) q^{5} +(-1.80802 + 1.04386i) q^{7} +(-0.116985 + 0.0675415i) q^{11} +(-2.63890 - 1.52357i) q^{13} -4.19800i q^{17} -0.919111 q^{19} +(0.689877 - 1.19490i) q^{23} +(-3.57762 - 6.19662i) q^{25} +(-4.24111 - 7.34582i) q^{29} +(4.39877 + 2.53963i) q^{31} -7.27870i q^{35} +1.61676i q^{37} +(-1.79408 - 1.03581i) q^{41} +(-5.41106 - 9.37224i) q^{43} +(-0.205809 - 0.356471i) q^{47} +(-1.32071 + 2.28754i) q^{49} +0.968137 q^{53} -0.470958i q^{55} +(3.88770 + 2.24457i) q^{59} +(-7.44553 + 4.29868i) q^{61} +(9.20037 - 5.31183i) q^{65} +(-3.15416 + 5.46316i) q^{67} -11.9687 q^{71} -4.06264 q^{73} +(0.141008 - 0.244232i) q^{77} +(-10.8672 + 6.27416i) q^{79} +(5.23875 - 3.02459i) q^{83} +(12.6752 + 7.31802i) q^{85} +8.35848i q^{89} +6.36158 q^{91} +(1.60221 - 2.77511i) q^{95} +(-0.477065 - 0.826300i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.74322	+	3.01934i	−0.779591	+	1.35029i	0.152587	+	0.988290i	$0.451240\pi$
$5$	−1.74322	+	3.01934i	−0.779591	+	1.35029i	−0.932178	+	0.362001i	$0.882094\pi$
$6$		0			0
$7$	−1.80802	+	1.04386i	−0.683367	+	0.394542i	−0.801122	−	0.598501i	$-0.795763\pi$
$7$	−1.80802	+	1.04386i	−0.683367	+	0.394542i	0.117756	+	0.993043i	$0.462430\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.116985	+	0.0675415i	−0.0352724	+	0.0203645i	−0.517533	−	0.855664i	$-0.673149\pi$
$11$	−0.116985	+	0.0675415i	−0.0352724	+	0.0203645i	0.482260	+	0.876028i	$0.339816\pi$
$12$		0			0
$13$	−2.63890	−	1.52357i	−0.731900	−	0.422563i	0.0872168	−	0.996189i	$-0.472203\pi$
$13$	−2.63890	−	1.52357i	−0.731900	−	0.422563i	−0.819117	+	0.573627i	$0.805536\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	4.19800i		−	1.01816i	−0.860718	−	0.509082i	$-0.829985\pi$
$17$		−	4.19800i		−	1.01816i	0.860718	−	0.509082i	$-0.170015\pi$
$18$		0			0
$19$	−0.919111			−0.210858			−0.105429	−	0.994427i	$-0.533622\pi$
$19$	−0.919111			−0.210858			−0.105429	+	0.994427i	$0.533622\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.689877	−	1.19490i	0.143849	−	0.249154i	−0.785094	−	0.619377i	$-0.787385\pi$
$23$	0.689877	−	1.19490i	0.143849	−	0.249154i	0.928943	+	0.370223i	$0.120719\pi$
$24$		0			0
$25$	−3.57762	−	6.19662i	−0.715524	−	1.23932i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.24111	−	7.34582i	−0.787555	−	1.36409i	−0.927461	−	0.373921i	$-0.878013\pi$
$29$	−4.24111	−	7.34582i	−0.787555	−	1.36409i	0.139906	−	0.990165i	$-0.455320\pi$
$30$		0			0
$31$	4.39877	+	2.53963i	0.790042	+	0.456131i	0.839977	−	0.542621i	$-0.182568\pi$
$31$	4.39877	+	2.53963i	0.790042	+	0.456131i	−0.0499352	+	0.998752i	$0.515901\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	7.27870i		−	1.23033i
$36$		0			0
$37$			1.61676i			0.265794i	0.991130	+	0.132897i	$0.0424280\pi$
$37$			1.61676i			0.265794i	−0.991130	+	0.132897i	$0.957572\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.79408	−	1.03581i	−0.280188	−	0.161767i	0.353320	−	0.935502i	$-0.385053\pi$
$41$	−1.79408	−	1.03581i	−0.280188	−	0.161767i	−0.633509	+	0.773736i	$0.718386\pi$
$42$		0			0
$43$	−5.41106	−	9.37224i	−0.825180	−	1.42925i	−0.901782	−	0.432191i	$-0.857741\pi$
$43$	−5.41106	−	9.37224i	−0.825180	−	1.42925i	0.0766025	−	0.997062i	$-0.475593\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.205809	−	0.356471i	−0.0300203	−	0.0519966i	0.850625	−	0.525773i	$-0.176224\pi$
$47$	−0.205809	−	0.356471i	−0.0300203	−	0.0519966i	−0.880645	+	0.473776i	$0.842891\pi$
$48$		0			0
$49$	−1.32071	+	2.28754i	−0.188673	+	0.326791i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.968137			0.132984			0.0664919	−	0.997787i	$-0.478819\pi$
$53$	0.968137			0.132984			0.0664919	+	0.997787i	$0.478819\pi$
$54$		0			0
$55$		−	0.470958i		−	0.0635040i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.88770	+	2.24457i	0.506136	+	0.292218i	0.731244	−	0.682116i	$-0.238940\pi$
$59$	3.88770	+	2.24457i	0.506136	+	0.292218i	−0.225108	+	0.974334i	$0.572274\pi$
$60$		0			0
$61$	−7.44553	+	4.29868i	−0.953303	+	0.550390i	−0.894105	−	0.447857i	$-0.852188\pi$
$61$	−7.44553	+	4.29868i	−0.953303	+	0.550390i	−0.0591976	+	0.998246i	$0.518854\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.20037	−	5.31183i	1.14117	−	0.658852i
$66$		0			0
$67$	−3.15416	+	5.46316i	−0.385342	+	0.667432i	−0.991817	−	0.127671i	$-0.959250\pi$
$67$	−3.15416	+	5.46316i	−0.385342	+	0.667432i	0.606475	+	0.795103i	$0.292583\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−11.9687			−1.42042			−0.710210	−	0.703990i	$-0.751400\pi$
$71$	−11.9687			−1.42042			−0.710210	+	0.703990i	$0.751400\pi$
$72$		0			0
$73$	−4.06264			−0.475496			−0.237748	−	0.971327i	$-0.576409\pi$
$73$	−4.06264			−0.475496			−0.237748	+	0.971327i	$0.576409\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.141008	−	0.244232i	0.0160693	−	0.0278329i
$78$		0			0
$79$	−10.8672	+	6.27416i	−1.22265	+	0.705899i	−0.965483	−	0.260468i	$-0.916123\pi$
$79$	−10.8672	+	6.27416i	−1.22265	+	0.705899i	−0.257170	+	0.966366i	$0.582790\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.23875	−	3.02459i	0.575027	−	0.331992i	−0.184128	−	0.982902i	$-0.558946\pi$
$83$	5.23875	−	3.02459i	0.575027	−	0.331992i	0.759155	+	0.650910i	$0.225613\pi$
$84$		0			0
$85$	12.6752	+	7.31802i	1.37482	+	0.793751i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			8.35848i			0.885997i	0.896522	+	0.442999i	$0.146085\pi$
$89$			8.35848i			0.885997i	−0.896522	+	0.442999i	$0.853915\pi$
$90$		0			0
$91$	6.36158			0.666875
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.60221	−	2.77511i	0.164383	−	0.284720i
$96$		0			0
$97$	−0.477065	−	0.826300i	−0.0484386	−	0.0838981i	0.840790	−	0.541362i	$-0.182091\pi$
$97$	−0.477065	−	0.826300i	−0.0484386	−	0.0838981i	−0.889228	+	0.457464i	$0.848758\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.35926	+	9.28250i	0.533266	+	0.923644i	0.999245	+	0.0388479i	$0.0123688\pi$
$101$	5.35926	+	9.28250i	0.533266	+	0.923644i	−0.465979	+	0.884796i	$0.654298\pi$
$102$		0			0
$103$	−7.46070	−	4.30743i	−0.735124	−	0.424424i	0.0851696	−	0.996366i	$-0.472857\pi$
$103$	−7.46070	−	4.30743i	−0.735124	−	0.424424i	−0.820294	+	0.571942i	$0.806190\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			4.80774i			0.464781i	0.972623	+	0.232391i	$0.0746548\pi$
$107$			4.80774i			0.464781i	−0.972623	+	0.232391i	$0.925345\pi$
$108$		0			0
$109$		−	7.16698i		−	0.686472i	−0.939249	−	0.343236i	$-0.888477\pi$
$109$		−	7.16698i		−	0.686472i	0.939249	−	0.343236i	$-0.111523\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.213928	+	0.123511i	0.0201246	+	0.0116190i	0.510029	−	0.860157i	$-0.329635\pi$
$113$	0.213928	+	0.123511i	0.0201246	+	0.0116190i	−0.489904	+	0.871776i	$0.662968\pi$
$114$		0			0
$115$	2.40521	+	4.16595i	0.224287	+	0.388477i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.38212	+	7.59006i	0.401708	+	0.695779i
$120$		0			0
$121$	−5.49088	+	9.51048i	−0.499171	+	0.864589i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	7.51409			0.672081
$126$		0			0
$127$		−	17.6276i		−	1.56420i	−0.623156	−	0.782098i	$-0.714150\pi$
$127$		−	17.6276i		−	1.56420i	0.623156	−	0.782098i	$-0.285850\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−12.7802	−	7.37864i	−1.11661	−	0.644675i	−0.176076	−	0.984377i	$-0.556341\pi$
$131$	−12.7802	−	7.37864i	−1.11661	−	0.644675i	−0.940533	+	0.339702i	$0.889674\pi$
$132$		0			0
$133$	1.66177	−	0.959423i	0.144094	−	0.0831925i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−14.8589	+	8.57878i	−1.26948	+	0.732934i	−0.974889	−	0.222689i	$-0.928516\pi$
$137$	−14.8589	+	8.57878i	−1.26948	+	0.732934i	−0.294590	+	0.955624i	$0.595183\pi$
$138$		0			0
$139$	0.607862	−	1.05285i	0.0515581	−	0.0893013i	−0.839095	−	0.543986i	$-0.816915\pi$
$139$	0.607862	−	1.05285i	0.0515581	−	0.0893013i	0.890653	+	0.454684i	$0.150248\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.411617			0.0344211
$144$		0			0
$145$	29.5727			2.45588
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.46357	−	7.73113i	0.365670	−	0.633359i	−0.623214	−	0.782052i	$-0.714173\pi$
$149$	4.46357	−	7.73113i	0.365670	−	0.633359i	0.988883	+	0.148693i	$0.0475066\pi$
$150$		0			0
$151$	18.9453	−	10.9381i	1.54175	−	0.890127i	0.543017	−	0.839722i	$-0.317282\pi$
$151$	18.9453	−	10.9381i	1.54175	−	0.890127i	0.998729	−	0.0504058i	$-0.0160515\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−15.3360	+	8.85426i	−1.23182	+	0.711191i
$156$		0			0
$157$	4.85478	+	2.80291i	0.387454	+	0.223697i	0.681056	−	0.732231i	$-0.261521\pi$
$157$	4.85478	+	2.80291i	0.387454	+	0.223697i	−0.293602	+	0.955928i	$0.594854\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			2.88054i			0.227018i
$162$		0			0
$163$	17.1763			1.34535			0.672676	−	0.739937i	$-0.265145\pi$
$163$	17.1763			1.34535			0.672676	+	0.739937i	$0.265145\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.31249	−	4.00535i	0.178946	−	0.309943i	−0.762574	−	0.646901i	$-0.776065\pi$
$167$	2.31249	−	4.00535i	0.178946	−	0.309943i	0.941520	+	0.336958i	$0.109398\pi$
$168$		0			0
$169$	−1.85746	−	3.21721i	−0.142881	−	0.247478i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.52076	+	2.63404i	0.115621	+	0.200262i	0.918028	−	0.396516i	$-0.129781\pi$
$173$	1.52076	+	2.63404i	0.115621	+	0.200262i	−0.802407	+	0.596778i	$0.796447\pi$
$174$		0			0
$175$	12.9368	+	7.46907i	0.977930	+	0.564608i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			17.9997i			1.34536i	0.739935	+	0.672679i	$0.234856\pi$
$179$			17.9997i			1.34536i	−0.739935	+	0.672679i	$0.765144\pi$
$180$		0			0
$181$		−	15.9507i		−	1.18561i	−0.805347	−	0.592804i	$-0.798021\pi$
$181$		−	15.9507i		−	1.18561i	0.805347	−	0.592804i	$-0.201979\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.88156	−	2.81837i	−0.358899	−	0.207211i
$186$		0			0
$187$	0.283539	+	0.491104i	0.0207344	+	0.0359131i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.21964	+	3.84452i	0.160607	+	0.278180i	0.935087	−	0.354419i	$-0.115321\pi$
$191$	2.21964	+	3.84452i	0.160607	+	0.278180i	−0.774479	+	0.632599i	$0.781988\pi$
$192$		0			0
$193$	0.673862	−	1.16716i	0.0485057	−	0.0840143i	−0.840753	−	0.541419i	$-0.817887\pi$
$193$	0.673862	−	1.16716i	0.0485057	−	0.0840143i	0.889259	+	0.457404i	$0.151221\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−9.16835			−0.653218			−0.326609	−	0.945160i	$-0.605906\pi$
$197$	−9.16835			−0.653218			−0.326609	+	0.945160i	$0.605906\pi$
$198$		0			0
$199$			24.0240i			1.70301i	0.524344	+	0.851507i	$0.324311\pi$
$199$			24.0240i			1.70301i	−0.524344	+	0.851507i	$0.675689\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	15.3360	+	8.85426i	1.07638	+	0.621447i
$204$		0			0
$205$	6.25494	−	3.61129i	0.436864	−	0.252224i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.107522	−	0.0620781i	0.00743748	−	0.00429403i
$210$		0			0
$211$	−10.1275	+	17.5414i	−0.697208	+	1.20760i	0.272223	+	0.962234i	$0.412241\pi$
$211$	−10.1275	+	17.5414i	−0.697208	+	1.20760i	−0.969431	+	0.245365i	$0.921092\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	37.7307			2.57321
$216$		0			0
$217$	−10.6041			−0.719852
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.39595	+	11.0781i	−0.430238	+	0.745194i
$222$		0			0
$223$	−0.521119	+	0.300868i	−0.0348967	+	0.0201476i	−0.517347	−	0.855776i	$-0.673080\pi$
$223$	−0.521119	+	0.300868i	−0.0348967	+	0.0201476i	0.482450	+	0.875923i	$0.339747\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.23720	−	5.33310i	0.613095	−	0.353970i	−0.161081	−	0.986941i	$-0.551498\pi$
$227$	9.23720	−	5.33310i	0.613095	−	0.353970i	0.774176	+	0.632971i	$0.218165\pi$
$228$		0			0
$229$	−22.1574	−	12.7926i	−1.46420	−	0.845356i	−0.464998	−	0.885312i	$-0.653945\pi$
$229$	−22.1574	−	12.7926i	−1.46420	−	0.845356i	−0.999201	+	0.0399555i	$0.987278\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			4.71086i			0.308619i	0.988023	+	0.154309i	$0.0493152\pi$
$233$			4.71086i			0.308619i	−0.988023	+	0.154309i	$0.950685\pi$
$234$		0			0
$235$	1.43508			0.0936141
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.51034	+	13.0083i	−0.485803	+	0.841436i	−0.999867	−	0.0163162i	$-0.994806\pi$
$239$	−7.51034	+	13.0083i	−0.485803	+	0.841436i	0.514064	+	0.857752i	$0.328139\pi$
$240$		0			0
$241$	12.8731	+	22.2969i	0.829230	+	1.43627i	0.898643	+	0.438681i	$0.144554\pi$
$241$	12.8731	+	22.2969i	0.829230	+	1.43627i	−0.0694129	+	0.997588i	$0.522113\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.60458	−	7.97536i	−0.294176	−	0.509527i
$246$		0			0
$247$	2.42544	+	1.40033i	0.154327	+	0.0891009i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	5.30436i		−	0.334808i	−0.985888	−	0.167404i	$-0.946462\pi$
$251$		−	5.30436i		−	0.334808i	0.985888	−	0.167404i	$-0.0535385\pi$
$252$		0			0
$253$			0.186381i			0.0117177i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	21.4984	+	12.4121i	1.34104	+	0.774248i	0.986959	−	0.160969i	$-0.0514619\pi$
$257$	21.4984	+	12.4121i	1.34104	+	0.774248i	0.354077	+	0.935216i	$0.384795\pi$
$258$		0			0
$259$	−1.68767	−	2.92314i	−0.104867	−	0.181635i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.95859	−	17.2488i	−0.614073	−	1.06361i	−0.990546	−	0.137178i	$-0.956197\pi$
$263$	−9.95859	−	17.2488i	−0.614073	−	1.06361i	0.376473	−	0.926427i	$-0.377137\pi$
$264$		0			0
$265$	−1.68767	+	2.92314i	−0.103673	+	0.179567i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.35540			−0.143611			−0.0718057	−	0.997419i	$-0.522876\pi$
$269$	−2.35540			−0.143611			−0.0718057	+	0.997419i	$0.522876\pi$
$270$		0			0
$271$		−	12.0774i		−	0.733648i	−0.930290	−	0.366824i	$-0.880445\pi$
$271$		−	12.0774i		−	0.733648i	0.930290	−	0.366824i	$-0.119555\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.837057	+	0.483275i	0.0504764	+	0.0291426i
$276$		0			0
$277$	−14.5504	+	8.40069i	−0.874250	+	0.504748i	−0.868758	−	0.495237i	$-0.835081\pi$
$277$	−14.5504	+	8.40069i	−0.874250	+	0.504748i	−0.00549164	+	0.999985i	$0.501748\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.9853	+	6.91973i	−0.714984	+	0.412796i	−0.812904	−	0.582398i	$-0.802115\pi$
$281$	−11.9853	+	6.91973i	−0.714984	+	0.412796i	0.0979194	+	0.995194i	$0.468781\pi$
$282$		0			0
$283$	−2.58123	+	4.47082i	−0.153438	+	0.265763i	−0.932489	−	0.361198i	$-0.882368\pi$
$283$	−2.58123	+	4.47082i	−0.153438	+	0.265763i	0.779051	+	0.626960i	$0.215701\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.32497			0.255295
$288$		0			0
$289$	−0.623177			−0.0366574
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.41881	−	9.38566i	0.316571	−	0.548316i	−0.663200	−	0.748443i	$-0.730802\pi$
$293$	5.41881	−	9.38566i	0.316571	−	0.548316i	0.979770	+	0.200126i	$0.0641353\pi$
$294$		0			0
$295$	−13.5542	+	7.82554i	−0.789158	+	0.455620i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.64104	+	2.10215i	−0.210567	+	0.121571i
$300$		0			0
$301$	19.5666	+	11.2968i	1.12780	+	0.651136i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	29.9742i		−	1.71632i
$306$		0			0
$307$	−16.6551			−0.950557			−0.475279	−	0.879835i	$-0.657653\pi$
$307$	−16.6551			−0.950557			−0.475279	+	0.879835i	$0.657653\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.47216	+	11.2101i	−0.367002	+	0.635667i	−0.989095	−	0.147277i	$-0.952949\pi$
$311$	−6.47216	+	11.2101i	−0.367002	+	0.635667i	0.622093	+	0.782943i	$0.286283\pi$
$312$		0			0
$313$	−13.3593	−	23.1390i	−0.755112	−	1.30789i	−0.945318	−	0.326149i	$-0.894249\pi$
$313$	−13.3593	−	23.1390i	−0.755112	−	1.30789i	0.190206	−	0.981744i	$-0.439084\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.5342	+	21.7098i	0.703990	+	1.21935i	0.967055	+	0.254568i	$0.0819332\pi$
$317$	12.5342	+	21.7098i	0.703990	+	1.21935i	−0.263065	+	0.964778i	$0.584733\pi$
$318$		0			0
$319$	0.992296	+	0.572902i	0.0555579	+	0.0320764i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			3.85842i			0.214688i
$324$		0			0
$325$			21.8030i			1.20941i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.744211	+	0.429671i	0.0410297	+	0.0236885i
$330$		0			0
$331$	8.47956	+	14.6870i	0.466079	+	0.807272i	0.999249	−	0.0387357i	$-0.0123330\pi$
$331$	8.47956	+	14.6870i	0.466079	+	0.807272i	−0.533171	+	0.846008i	$0.679000\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−10.9968	−	19.0470i	−0.600818	−	1.04065i
$336$		0			0
$337$	4.47220	−	7.74608i	0.243616	−	0.421956i	−0.718125	−	0.695914i	$-0.755000\pi$
$337$	4.47220	−	7.74608i	0.243616	−	0.421956i	0.961742	+	0.273958i	$0.0883329\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.686122			−0.0371556
$342$		0			0
$343$		−	20.1286i		−	1.08684i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.29330	−	2.47874i	−0.230476	−	0.133066i	0.380315	−	0.924857i	$-0.375815\pi$
$347$	−4.29330	−	2.47874i	−0.230476	−	0.133066i	−0.610792	+	0.791791i	$0.709149\pi$
$348$		0			0
$349$	22.9731	−	13.2635i	1.22972	−	0.709980i	0.262749	−	0.964864i	$-0.415371\pi$
$349$	22.9731	−	13.2635i	1.22972	−	0.709980i	0.966972	+	0.254884i	$0.0820374\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	28.7458	−	16.5964i	1.52998	−	0.883337i	0.530623	−	0.847608i	$-0.321958\pi$
$353$	28.7458	−	16.5964i	1.52998	−	0.883337i	0.999362	−	0.0357291i	$-0.0113753\pi$
$354$		0			0
$355$	20.8640	−	36.1375i	1.10735	−	1.91798i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−20.6138			−1.08795			−0.543977	−	0.839100i	$-0.683082\pi$
$359$	−20.6138			−1.08795			−0.543977	+	0.839100i	$0.683082\pi$
$360$		0			0
$361$	−18.1552			−0.955539
$362$		0			0
$363$		0			0
$364$		0			0
$365$	7.08207	−	12.2665i	0.370693	−	0.642058i
$366$		0			0
$367$	−10.1478	+	5.85881i	−0.529708	+	0.305827i	−0.740898	−	0.671618i	$-0.765600\pi$
$367$	−10.1478	+	5.85881i	−0.529708	+	0.305827i	0.211189	+	0.977445i	$0.432266\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.75041	+	1.01060i	−0.0908767	+	0.0524677i
$372$		0			0
$373$	−3.02771	−	1.74805i	−0.156769	−	0.0905105i	0.419563	−	0.907726i	$-0.362183\pi$
$373$	−3.02771	−	1.74805i	−0.156769	−	0.0905105i	−0.576332	+	0.817216i	$0.695517\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			25.8466i			1.33117i
$378$		0			0
$379$	−20.1604			−1.03557			−0.517785	−	0.855511i	$-0.673243\pi$
$379$	−20.1604			−1.03557			−0.517785	+	0.855511i	$0.673243\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.33120	−	9.23391i	0.272412	−	0.471831i	−0.697067	−	0.717006i	$-0.745512\pi$
$383$	5.33120	−	9.23391i	0.272412	−	0.471831i	0.969479	+	0.245175i	$0.0788454\pi$
$384$		0			0
$385$	0.491614	+	0.851501i	0.0250550	+	0.0433965i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.34122	−	14.4474i	−0.422917	−	0.732513i	0.573307	−	0.819341i	$-0.305660\pi$
$389$	−8.34122	−	14.4474i	−0.422917	−	0.732513i	−0.996223	+	0.0868277i	$0.972327\pi$
$390$		0			0
$391$	−5.01619	−	2.89610i	−0.253680	−	0.146462i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	43.7489i		−	2.20125i
$396$		0			0
$397$			22.9869i			1.15368i	0.816857	+	0.576840i	$0.195715\pi$
$397$			22.9869i			1.15368i	−0.816857	+	0.576840i	$0.804285\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−27.3094	−	15.7671i	−1.36377	−	0.787371i	−0.373644	−	0.927572i	$-0.621892\pi$
$401$	−27.3094	−	15.7671i	−1.36377	−	0.787371i	−0.990123	+	0.140201i	$0.955225\pi$
$402$		0			0
$403$	−7.73862	−	13.4037i	−0.385488	−	0.667685i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.109199	−	0.189137i	−0.00541277	−	0.00937519i
$408$		0			0
$409$	3.59259	−	6.22255i	0.177642	−	0.307686i	−0.763430	−	0.645890i	$-0.776486\pi$
$409$	3.59259	−	6.22255i	0.177642	−	0.307686i	0.941073	+	0.338205i	$0.109820\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−9.37205			−0.461169
$414$		0			0
$415$			21.0901i			1.03527i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−12.5999	−	7.27453i	−0.615543	−	0.355384i	0.159589	−	0.987184i	$-0.448983\pi$
$419$	−12.5999	−	7.27453i	−0.615543	−	0.355384i	−0.775132	+	0.631800i	$0.782317\pi$
$420$		0			0
$421$	9.38587	−	5.41893i	0.457439	−	0.264103i	−0.253528	−	0.967328i	$-0.581591\pi$
$421$	9.38587	−	5.41893i	0.457439	−	0.264103i	0.710967	+	0.703225i	$0.248258\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−26.0134	+	15.0188i	−1.26183	+	0.728520i
$426$		0			0
$427$	8.97444	−	15.5442i	0.434304	−	0.752236i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.8604			−0.523129			−0.261565	−	0.965186i	$-0.584238\pi$
$431$	−10.8604			−0.523129			−0.261565	+	0.965186i	$0.584238\pi$
$432$		0			0
$433$	9.41382			0.452399			0.226200	−	0.974081i	$-0.427370\pi$
$433$	9.41382			0.452399			0.226200	+	0.974081i	$0.427370\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.634073	+	1.09825i	−0.0303318	+	0.0525363i
$438$		0			0
$439$	9.25745	−	5.34479i	0.441834	−	0.255093i	−0.262541	−	0.964921i	$-0.584561\pi$
$439$	9.25745	−	5.34479i	0.441834	−	0.255093i	0.704375	+	0.709828i	$0.251227\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	18.9818	−	10.9592i	0.901854	−	0.520686i	0.0240526	−	0.999711i	$-0.492343\pi$
$443$	18.9818	−	10.9592i	0.901854	−	0.520686i	0.877801	+	0.479025i	$0.159010\pi$
$444$		0			0
$445$	−25.2371	−	14.5707i	−1.19635	−	0.690715i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	18.7436i		−	0.884565i	−0.896876	−	0.442282i	$-0.854169\pi$
$449$		−	18.7436i		−	0.884565i	0.896876	−	0.442282i	$-0.145831\pi$
$450$		0			0
$451$	0.279841			0.0131772
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−11.0896	+	19.2078i	−0.519890	+	0.900475i
$456$		0			0
$457$	−0.00912370	−	0.0158027i	−0.000426789	−	0.000739220i	0.865812	−	0.500370i	$-0.166803\pi$
$457$	−0.00912370	−	0.0158027i	−0.000426789	−	0.000739220i	−0.866239	+	0.499630i	$0.833469\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.25915	+	2.18091i	0.0586444	+	0.101575i	0.893857	−	0.448352i	$-0.147989\pi$
$461$	1.25915	+	2.18091i	0.0586444	+	0.101575i	−0.835213	+	0.549927i	$0.814656\pi$
$462$		0			0
$463$	−23.9003	−	13.7988i	−1.11074	−	0.641286i	−0.171719	−	0.985146i	$-0.554932\pi$
$463$	−23.9003	−	13.7988i	−1.11074	−	0.641286i	−0.939021	+	0.343860i	$0.888265\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			28.4629i			1.31711i	0.752533	+	0.658554i	$0.228832\pi$
$467$			28.4629i			1.31711i	−0.752533	+	0.658554i	$0.771168\pi$
$468$		0			0
$469$		−	13.1700i		−	0.608134i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.26603	+	0.730942i	0.0582121	+	0.0336088i
$474$		0			0
$475$	3.28823	+	5.69538i	0.150874	+	0.261322i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	19.1602	+	33.1865i	0.875454	+	1.51633i	0.856279	+	0.516514i	$0.172771\pi$
$479$	19.1602	+	33.1865i	0.875454	+	1.51633i	0.0191747	+	0.999816i	$0.493896\pi$
$480$		0			0
$481$	2.46325	−	4.26648i	0.112315	−	0.194535i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.32651			0.151049
$486$		0			0
$487$			2.25659i			0.102256i	0.998692	+	0.0511280i	$0.0162817\pi$
$487$			2.25659i			0.102256i	−0.998692	+	0.0511280i	$0.983718\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.7659	−	10.2572i	−0.801765	−	0.462899i	0.0423228	−	0.999104i	$-0.486524\pi$
$491$	−17.7659	−	10.2572i	−0.801765	−	0.462899i	−0.844088	+	0.536205i	$0.819858\pi$
$492$		0			0
$493$	−30.8377	+	17.8042i	−1.38886	+	0.801860i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	21.6396	−	12.4936i	0.970667	−	0.560415i
$498$		0			0
$499$	−1.87815	+	3.25306i	−0.0840777	+	0.145627i	−0.904998	−	0.425416i	$-0.860128\pi$
$499$	−1.87815	+	3.25306i	−0.0840777	+	0.145627i	0.820920	+	0.571043i	$0.193461\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−33.3322			−1.48621			−0.743104	−	0.669175i	$-0.766647\pi$
$503$	−33.3322			−1.48621			−0.743104	+	0.669175i	$0.766647\pi$
$504$		0			0
$505$	−37.3694			−1.66292
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.41788	+	5.91994i	−0.151495	+	0.262397i	−0.931777	−	0.363031i	$-0.881742\pi$
$509$	−3.41788	+	5.91994i	−0.151495	+	0.262397i	0.780282	+	0.625427i	$0.215075\pi$
$510$		0			0
$511$	7.34533	−	4.24083i	0.324938	−	0.187603i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	26.0112	−	15.0176i	1.14619	−	0.661754i
$516$		0			0
$517$	0.0481531	+	0.0278012i	0.00211777	+	0.00122270i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	19.9468i		−	0.873887i	−0.899489	−	0.436943i	$-0.856061\pi$
$521$		−	19.9468i		−	0.873887i	0.899489	−	0.436943i	$-0.143939\pi$
$522$		0			0
$523$	5.50358			0.240655			0.120327	−	0.992734i	$-0.461606\pi$
$523$	5.50358			0.240655			0.120327	+	0.992734i	$0.461606\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	10.6614	−	18.4660i	0.464416	−	0.804392i
$528$		0			0
$529$	10.5481	+	18.2699i	0.458615	+	0.794344i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.15627	+	5.46682i	0.136713	+	0.236794i
$534$		0			0
$535$	−14.5162	−	8.38093i	−0.627590	−	0.362339i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	0.356811i		−	0.0153690i
$540$		0			0
$541$			12.1375i			0.521831i	0.965362	+	0.260915i	$0.0840243\pi$
$541$			12.1375i			0.521831i	−0.965362	+	0.260915i	$0.915976\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	21.6396	+	12.4936i	0.926937	+	0.535167i
$546$		0			0
$547$	−5.02439	−	8.70250i	−0.214827	−	0.372092i	0.738392	−	0.674372i	$-0.235586\pi$
$547$	−5.02439	−	8.70250i	−0.214827	−	0.372092i	−0.953219	+	0.302280i	$0.902252\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.89805	+	6.75163i	0.166063	+	0.287629i
$552$		0			0
$553$	13.0987	−	22.6876i	0.557013	−	0.964775i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.4323			−0.653887			−0.326944	−	0.945044i	$-0.606019\pi$
$557$	−15.4323			−0.653887			−0.326944	+	0.945044i	$0.606019\pi$
$558$		0			0
$559$			32.9766i			1.39476i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	5.08901	+	2.93814i	0.214476	+	0.123828i	0.603390	−	0.797446i	$-0.293816\pi$
$563$	5.08901	+	2.93814i	0.214476	+	0.123828i	−0.388914	+	0.921274i	$0.627150\pi$
$564$		0			0
$565$	−0.745845	+	0.430614i	−0.0313779	+	0.0181161i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	28.3228	−	16.3522i	1.18735	−	0.685519i	0.229650	−	0.973273i	$-0.426242\pi$
$569$	28.3228	−	16.3522i	1.18735	−	0.685519i	0.957704	+	0.287754i	$0.0929087\pi$
$570$		0			0
$571$	−16.4253	+	28.4495i	−0.687377	+	1.19057i	0.285306	+	0.958437i	$0.407905\pi$
$571$	−16.4253	+	28.4495i	−0.687377	+	1.19057i	−0.972683	+	0.232136i	$0.925428\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−9.87246			−0.411710
$576$		0			0
$577$	−16.7158			−0.695887			−0.347943	−	0.937516i	$-0.613120\pi$
$577$	−16.7158			−0.695887			−0.347943	+	0.937516i	$0.613120\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.31450	+	10.9370i	−0.261970	+	0.453745i
$582$		0			0
$583$	−0.113258	+	0.0653894i	−0.00469066	+	0.00270815i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−23.7005	+	13.6835i	−0.978222	+	0.564777i	−0.901733	−	0.432293i	$-0.857704\pi$
$587$	−23.7005	+	13.6835i	−0.978222	+	0.564777i	−0.0764895	+	0.997070i	$0.524371\pi$
$588$		0			0
$589$	−4.04296	−	2.33420i	−0.166587	−	0.0961791i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			25.6865i			1.05482i	0.849612	+	0.527408i	$0.176836\pi$
$593$			25.6865i			1.05482i	−0.849612	+	0.527408i	$0.823164\pi$
$594$		0			0
$595$	−30.5560			−1.25267
$596$		0			0
$597$		0			0
$598$		0			0
$599$	19.9859	−	34.6166i	0.816601	−	1.41439i	−0.0915718	−	0.995798i	$-0.529189\pi$
$599$	19.9859	−	34.6166i	0.816601	−	1.41439i	0.908173	−	0.418596i	$-0.137478\pi$
$600$		0			0
$601$	2.01867	+	3.49645i	0.0823434	+	0.142623i	0.904256	−	0.426991i	$-0.140426\pi$
$601$	2.01867	+	3.49645i	0.0823434	+	0.142623i	−0.821913	+	0.569613i	$0.807093\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−19.1436	−	33.1577i	−0.778298	−	1.34805i
$606$		0			0
$607$	11.2251	+	6.48081i	0.455612	+	0.263048i	0.710198	−	0.704002i	$-0.248606\pi$
$607$	11.2251	+	6.48081i	0.455612	+	0.263048i	−0.254585	+	0.967050i	$0.581939\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			1.25426i			0.0507418i
$612$		0			0
$613$			22.0890i			0.892167i	0.894991	+	0.446084i	$0.147182\pi$
$613$			22.0890i			0.892167i	−0.894991	+	0.446084i	$0.852818\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−20.0171	−	11.5569i	−0.805859	−	0.465263i	0.0396569	−	0.999213i	$-0.487374\pi$
$617$	−20.0171	−	11.5569i	−0.805859	−	0.465263i	−0.845516	+	0.533951i	$0.820707\pi$
$618$		0			0
$619$	2.24675	+	3.89149i	0.0903046	+	0.156412i	0.907639	−	0.419751i	$-0.137883\pi$
$619$	2.24675	+	3.89149i	0.0903046	+	0.156412i	−0.817335	+	0.576163i	$0.804549\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.72509	−	15.1123i	−0.349563	−	0.605461i
$624$		0			0
$625$	4.78939	−	8.29547i	0.191576	−	0.331819i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	6.78716			0.270622
$630$		0			0
$631$			30.8693i			1.22889i	0.788961	+	0.614443i	$0.210619\pi$
$631$			30.8693i			1.22889i	−0.788961	+	0.614443i	$0.789381\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	53.2237	+	30.7287i	2.11212	+	1.21943i
$636$		0			0
$637$	6.97046	−	4.02440i	0.276180	−	0.159452i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−23.7137	+	13.6911i	−0.936633	+	0.540766i	−0.888903	−	0.458095i	$-0.848532\pi$
$641$	−23.7137	+	13.6911i	−0.936633	+	0.540766i	−0.0477300	+	0.998860i	$0.515199\pi$
$642$		0			0
$643$	19.9857	−	34.6162i	0.788158	−	1.36513i	−0.138937	−	0.990301i	$-0.544369\pi$
$643$	19.9857	−	34.6162i	0.788158	−	1.36513i	0.927094	−	0.374828i	$-0.122298\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	30.9768			1.21782			0.608912	−	0.793238i	$-0.291606\pi$
$647$	30.9768			1.21782			0.608912	+	0.793238i	$0.291606\pi$
$648$		0			0
$649$	−0.606405			−0.0238035
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.78891	−	4.83053i	0.109138	−	0.189033i	−0.806283	−	0.591530i	$-0.798524\pi$
$653$	2.78891	−	4.83053i	0.109138	−	0.189033i	0.915421	+	0.402497i	$0.131857\pi$
$654$		0			0
$655$	44.5573	−	25.7252i	1.74100	−	1.00517i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−5.69959	+	3.29066i	−0.222025	+	0.128186i	−0.606887	−	0.794788i	$-0.707582\pi$
$659$	−5.69959	+	3.29066i	−0.222025	+	0.128186i	0.384863	+	0.922974i	$0.374249\pi$
$660$		0			0
$661$	26.9562	+	15.5632i	1.04847	+	0.605337i	0.922222	−	0.386661i	$-0.126372\pi$
$661$	26.9562	+	15.5632i	1.04847	+	0.605337i	0.126253	+	0.991998i	$0.459705\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			6.68993i			0.259425i
$666$		0			0
$667$	−11.7034			−0.453157
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.580679	−	1.00576i	0.0224168	−	0.0388271i
$672$		0			0
$673$	−3.54087	−	6.13297i	−0.136491	−	0.236409i	0.789675	−	0.613525i	$-0.210249\pi$
$673$	−3.54087	−	6.13297i	−0.136491	−	0.236409i	−0.926166	+	0.377116i	$0.876916\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.18253	+	5.51231i	0.122315	+	0.211855i	0.920680	−	0.390318i	$-0.127635\pi$
$677$	3.18253	+	5.51231i	0.122315	+	0.211855i	−0.798365	+	0.602173i	$0.794302\pi$
$678$		0			0
$679$	1.72508	+	0.995978i	0.0662026	+	0.0382221i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	51.9104i		−	1.98630i	−0.116864	−	0.993148i	$-0.537284\pi$
$683$		−	51.9104i		−	1.98630i	0.116864	−	0.993148i	$-0.462716\pi$
$684$		0			0
$685$		−	59.8187i		−	2.28556i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.55482	−	1.47503i	−0.0973309	−	0.0561940i
$690$		0			0
$691$	17.9150	+	31.0297i	0.681519	+	1.18043i	0.974517	+	0.224313i	$0.0720138\pi$
$691$	17.9150	+	31.0297i	0.681519	+	1.18043i	−0.292998	+	0.956113i	$0.594653\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.11927	+	3.67068i	0.0803885	+	0.139237i
$696$		0			0
$697$	−4.34834	+	7.53154i	−0.164705	+	0.285277i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	19.0081			0.717927			0.358964	−	0.933352i	$-0.383130\pi$
$701$	19.0081			0.717927			0.358964	+	0.933352i	$0.383130\pi$
$702$		0			0
$703$		−	1.48598i		−	0.0560449i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−19.3793	−	11.1886i	−0.728832	−	0.420792i
$708$		0			0
$709$	38.5758	−	22.2717i	1.44874	−	0.836433i	0.450337	−	0.892859i	$-0.351304\pi$
$709$	38.5758	−	22.2717i	1.44874	−	0.836433i	0.998407	+	0.0564260i	$0.0179705\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6.06922	−	3.50407i	0.227294	−	0.131228i
$714$		0			0
$715$	−0.717538	+	1.24281i	−0.0268344	+	0.0464786i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	40.5385			1.51183			0.755915	−	0.654670i	$-0.227192\pi$
$719$	40.5385			1.51183			0.755915	+	0.654670i	$0.227192\pi$
$720$		0			0
$721$	17.9854			0.669813
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−30.3462	+	52.5611i	−1.12703	+	1.95207i
$726$		0			0
$727$	−16.5719	+	9.56779i	−0.614618	+	0.354850i	−0.774770	−	0.632243i	$-0.782135\pi$
$727$	−16.5719	+	9.56779i	−0.614618	+	0.354850i	0.160153	+	0.987092i	$0.448801\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−39.3446	+	22.7156i	−1.45521	+	0.840168i
$732$		0			0
$733$	−25.4597	−	14.6992i	−0.940377	−	0.542927i	−0.0502985	−	0.998734i	$-0.516017\pi$
$733$	−25.4597	−	14.6992i	−0.940377	−	0.542927i	−0.890078	+	0.455807i	$0.849351\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	0.852146i		−	0.0313892i
$738$		0			0
$739$	0.807511			0.0297048			0.0148524	−	0.999890i	$-0.495272\pi$
$739$	0.807511			0.0297048			0.0148524	+	0.999890i	$0.495272\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	13.2127	−	22.8850i	0.484725	−	0.839569i	−0.515121	−	0.857118i	$-0.672253\pi$
$743$	13.2127	−	22.8850i	0.484725	−	0.839569i	0.999846	+	0.0175489i	$0.00558629\pi$
$744$		0			0
$745$	15.5620	+	26.9541i	0.570146	+	0.987521i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.01860	−	8.69248i	−0.183376	−	0.317616i
$750$		0			0
$751$	−2.08658	−	1.20469i	−0.0761405	−	0.0439597i	0.461446	−	0.887168i	$-0.347331\pi$
$751$	−2.08658	−	1.20469i	−0.0761405	−	0.0439597i	−0.537587	+	0.843208i	$0.680664\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			76.2698i			2.77574i
$756$		0			0
$757$		−	3.61528i		−	0.131400i	−0.997839	−	0.0656998i	$-0.979072\pi$
$757$		−	3.61528i		−	0.131400i	0.997839	−	0.0656998i	$-0.0209280\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.79878	−	4.50263i	−0.282706	−	0.163220i	0.351942	−	0.936022i	$-0.385521\pi$
$761$	−7.79878	−	4.50263i	−0.282706	−	0.163220i	−0.634648	+	0.772802i	$0.718855\pi$
$762$		0			0
$763$	7.48133	+	12.9580i	0.270842	+	0.469112i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.83951	−	11.8464i	−0.246961	−	0.427748i
$768$		0			0
$769$	7.58489	−	13.1374i	0.273518	−	0.473747i	−0.696242	−	0.717807i	$-0.745146\pi$
$769$	7.58489	−	13.1374i	0.273518	−	0.473747i	0.969760	+	0.244060i	$0.0784794\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	31.6926			1.13990			0.569952	−	0.821678i	$-0.306962\pi$
$773$	31.6926			1.13990			0.569952	+	0.821678i	$0.306962\pi$
$774$		0			0
$775$		−	36.3433i		−	1.30549i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.64896	+	0.952026i	0.0590800	+	0.0341099i
$780$		0			0
$781$	1.40016	−	0.808381i	0.0501016	−	0.0289262i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−16.9259	+	9.77217i	−0.604111	+	0.348784i
$786$		0			0
$787$	−10.3290	+	17.8904i	−0.368189	+	0.637723i	−0.989283	−	0.146014i	$-0.953356\pi$
$787$	−10.3290	+	17.8904i	−0.368189	+	0.637723i	0.621093	+	0.783737i	$0.286689\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.515713			−0.0183367
$792$		0			0
$793$	26.1974			0.930297
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.8453	−	30.9089i	0.632112	−	1.09485i	−0.355007	−	0.934864i	$-0.615521\pi$
$797$	17.8453	−	30.9089i	0.632112	−	1.09485i	0.987119	−	0.159987i	$-0.0511452\pi$
$798$		0			0
$799$	−1.49646	+	0.863984i	−0.0529411	+	0.0305655i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.475269	−	0.274397i	0.0167719	−	0.00968325i
$804$		0			0
$805$	−8.69734	−	5.02141i	−0.306541	−	0.176981i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			18.7528i			0.659314i	0.944101	+	0.329657i	$0.106933\pi$
$809$			18.7528i			0.659314i	−0.944101	+	0.329657i	$0.893067\pi$
$810$		0			0
$811$	33.9206			1.19111			0.595556	−	0.803314i	$-0.296932\pi$
$811$	33.9206			1.19111			0.595556	+	0.803314i	$0.296932\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−29.9421	+	51.8612i	−1.04882	+	1.81662i
$816$		0			0
$817$	4.97337	+	8.61412i	0.173996	+	0.301370i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.34636	+	9.26017i	0.186589	+	0.323182i	0.944111	−	0.329628i	$-0.106923\pi$
$821$	5.34636	+	9.26017i	0.186589	+	0.323182i	−0.757522	+	0.652810i	$0.773590\pi$
$822$		0			0
$823$	33.4172	+	19.2934i	1.16485	+	0.672527i	0.952462	−	0.304658i	$-0.0985421\pi$
$823$	33.4172	+	19.2934i	1.16485	+	0.672527i	0.212390	+	0.977185i	$0.431875\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			0.214418i			0.00745604i	0.999993	+	0.00372802i	$0.00118667\pi$
$827$			0.214418i			0.00745604i	−0.999993	+	0.00372802i	$0.998813\pi$
$828$		0			0
$829$			35.5733i			1.23551i	0.786369	+	0.617757i	$0.211958\pi$
$829$			35.5733i			1.23551i	−0.786369	+	0.617757i	$0.788042\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.60309	+	5.54434i	0.332727	+	0.192100i
$834$		0			0
$835$	8.06235	+	13.9644i	0.279009	+	0.483258i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	20.5867	+	35.6571i	0.710730	+	1.23102i	0.964583	+	0.263778i	$0.0849687\pi$
$839$	20.5867	+	35.6571i	0.710730	+	1.23102i	−0.253853	+	0.967243i	$0.581698\pi$
$840$		0			0
$841$	−21.4741	+	37.1942i	−0.740486	+	1.28256i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	12.9518			0.445556
$846$		0			0
$847$		−	22.9268i		−	0.787775i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.93187	+	1.11537i	0.0662237	+	0.0382343i
$852$		0			0
$853$	−30.9858	+	17.8897i	−1.06093	+	0.612530i	−0.925690	−	0.378282i	$-0.876515\pi$
$853$	−30.9858	+	17.8897i	−1.06093	+	0.612530i	−0.135243	+	0.990812i	$0.543181\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−26.3688	+	15.2241i	−0.900742	+	0.520044i	−0.877441	−	0.479685i	$-0.840751\pi$
$857$	−26.3688	+	15.2241i	−0.900742	+	0.520044i	−0.0233014	+	0.999728i	$0.507418\pi$
$858$		0			0
$859$	11.7147	−	20.2904i	0.399700	−	0.692301i	−0.593989	−	0.804473i	$-0.702448\pi$
$859$	11.7147	−	20.2904i	0.399700	−	0.692301i	0.993689	+	0.112172i	$0.0357809\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−32.2240			−1.09692			−0.548458	−	0.836178i	$-0.684785\pi$
$863$	−32.2240			−1.09692			−0.548458	+	0.836178i	$0.684785\pi$
$864$		0			0
$865$	−10.6041			−0.360549
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.847532	−	1.46797i	0.0287506	−	0.0497974i
$870$		0			0
$871$	16.6470	−	9.61117i	0.564063	−	0.325662i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−13.5856	+	7.84366i	−0.459278	+	0.265164i
$876$		0			0
$877$	−1.74081	−	1.00506i	−0.0587829	−	0.0339384i	0.470320	−	0.882496i	$-0.344138\pi$
$877$	−1.74081	−	1.00506i	−0.0587829	−	0.0339384i	−0.529103	+	0.848557i	$0.677472\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			21.6545i			0.729558i	0.931094	+	0.364779i	$0.118855\pi$
$881$			21.6545i			0.729558i	−0.931094	+	0.364779i	$0.881145\pi$
$882$		0			0
$883$	23.3462			0.785664			0.392832	−	0.919610i	$-0.371495\pi$
$883$	23.3462			0.785664			0.392832	+	0.919610i	$0.371495\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.4901	+	42.4181i	−0.822297	+	1.42426i	0.0816710	+	0.996659i	$0.473974\pi$
$887$	−24.4901	+	42.4181i	−0.822297	+	1.42426i	−0.903968	+	0.427600i	$0.859359\pi$
$888$		0			0
$889$	18.4007	+	31.8710i	0.617141	+	1.06892i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.189161	+	0.327636i	0.00633003	+	0.0109639i
$894$		0			0
$895$	−54.3471	−	31.3773i	−1.81662	−	1.04883i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	43.0834i		−	1.43691i
$900$		0			0
$901$		−	4.06424i		−	0.135399i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	48.1607	+	27.8056i	1.60092	+	0.924289i
$906$		0			0
$907$	9.93443	+	17.2069i	0.329867	+	0.571347i	0.982485	−	0.186340i	$-0.0596627\pi$
$907$	9.93443	+	17.2069i	0.329867	+	0.571347i	−0.652618	+	0.757687i	$0.726329\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	24.0672	+	41.6857i	0.797383	+	1.38111i	0.921315	+	0.388817i	$0.127116\pi$
$911$	24.0672	+	41.6857i	0.797383	+	1.38111i	−0.123932	+	0.992291i	$0.539550\pi$
$912$		0			0
$913$	−0.408571	+	0.707665i	−0.0135217	+	0.0234203i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	30.8091			1.01741
$918$		0			0
$919$		−	34.3644i		−	1.13358i	−0.823864	−	0.566788i	$-0.808186\pi$
$919$		−	34.3644i		−	1.13358i	0.823864	−	0.566788i	$-0.191814\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	31.5841	+	18.2351i	1.03960	+	0.600216i
$924$		0			0
$925$	10.0185	−	5.78416i	0.329405	−	0.190182i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−15.1165	+	8.72750i	−0.495955	+	0.286340i	−0.727042	−	0.686593i	$-0.759105\pi$
$929$	−15.1165	+	8.72750i	−0.495955	+	0.286340i	0.231086	+	0.972933i	$0.425772\pi$
$930$		0			0
$931$	1.21388	−	2.10250i	0.0397833	−	0.0689067i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.97708			−0.0646574
$936$		0			0
$937$	42.3068			1.38210			0.691051	−	0.722806i	$-0.257148\pi$
$937$	42.3068			1.38210			0.691051	+	0.722806i	$0.257148\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−11.6752	+	20.2221i	−0.380602	+	0.659222i	−0.991148	−	0.132758i	$-0.957617\pi$
$941$	−11.6752	+	20.2221i	−0.380602	+	0.659222i	0.610546	+	0.791980i	$0.290950\pi$
$942$		0			0
$943$	−2.47539	+	1.42917i	−0.0806097	+	0.0465400i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	28.1206	−	16.2354i	0.913796	−	0.527580i	0.0321454	−	0.999483i	$-0.489766\pi$
$947$	28.1206	−	16.2354i	0.913796	−	0.527580i	0.881651	+	0.471903i	$0.156433\pi$
$948$		0			0
$949$	10.7209	+	6.18973i	0.348016	+	0.200927i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	11.0705i		−	0.358607i	−0.983794	−	0.179304i	$-0.942616\pi$
$953$		−	11.0705i		−	0.358607i	0.983794	−	0.179304i	$-0.0573844\pi$
$954$		0			0
$955$	−15.4772			−0.500832
$956$		0			0
$957$		0			0
$958$		0			0
$959$	17.9101	−	31.0212i	0.578347	−	1.00173i
$960$		0			0
$961$	−2.60055	−	4.50429i	−0.0838888	−	0.145300i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.34938	+	4.06924i	0.0756291	+	0.130993i
$966$		0			0
$967$	40.9201	+	23.6252i	1.31590	+	0.759736i	0.983066	−	0.183249i	$-0.0586616\pi$
$967$	40.9201	+	23.6252i	1.31590	+	0.759736i	0.332835	+	0.942985i	$0.391995\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			33.9428i			1.08928i	0.838671	+	0.544638i	$0.183333\pi$
$971$			33.9428i			1.08928i	−0.838671	+	0.544638i	$0.816667\pi$
$972$		0			0
$973$			2.53809i			0.0813674i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−26.9476	−	15.5582i	−0.862131	−	0.497752i	0.00259421	−	0.999997i	$-0.499174\pi$
$977$	−26.9476	−	15.5582i	−0.862131	−	0.497752i	−0.864725	+	0.502245i	$0.832508\pi$
$978$		0			0
$979$	−0.564544	−	0.977819i	−0.0180429	−	0.0312512i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−18.2288	−	31.5733i	−0.581410	−	1.00703i	−0.995313	−	0.0967103i	$-0.969168\pi$
$983$	−18.2288	−	31.5733i	−0.581410	−	1.00703i	0.413903	−	0.910321i	$-0.364165\pi$
$984$		0			0
$985$	15.9824	−	27.6824i	0.509243	−	0.882034i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−14.9319			−0.474806
$990$		0			0
$991$			21.5164i			0.683490i	0.939793	+	0.341745i	$0.111018\pi$
$991$			21.5164i			0.683490i	−0.939793	+	0.341745i	$0.888982\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−72.5365	−	41.8790i	−2.29956	−	1.32765i
$996$		0			0
$997$	49.4923	−	28.5744i	1.56744	−	0.904961i	0.570971	−	0.820970i	$-0.306567\pi$
$997$	49.4923	−	28.5744i	1.56744	−	0.904961i	0.996467	−	0.0839906i	$-0.0267666\pi$
$998$		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.719.1		16
3.2	odd	2		288.2.p.b.239.8		16
4.3	odd	2		216.2.l.b.179.8		16
8.3	odd	2	inner	864.2.p.b.719.8		16
8.5	even	2		216.2.l.b.179.5		16
9.2	odd	6	inner	864.2.p.b.143.8		16
9.4	even	3		2592.2.f.b.1295.15		16
9.5	odd	6		2592.2.f.b.1295.1		16
9.7	even	3		288.2.p.b.47.7		16
12.11	even	2		72.2.l.b.59.1	yes	16
24.5	odd	2		72.2.l.b.59.4	yes	16
24.11	even	2		288.2.p.b.239.7		16
36.7	odd	6		72.2.l.b.11.4	yes	16
36.11	even	6		216.2.l.b.35.5		16
36.23	even	6		648.2.f.b.323.9		16
36.31	odd	6		648.2.f.b.323.8		16
72.5	odd	6		648.2.f.b.323.7		16
72.11	even	6	inner	864.2.p.b.143.1		16
72.13	even	6		648.2.f.b.323.10		16
72.29	odd	6		216.2.l.b.35.8		16
72.43	odd	6		288.2.p.b.47.8		16
72.59	even	6		2592.2.f.b.1295.16		16
72.61	even	6		72.2.l.b.11.1	✓	16
72.67	odd	6		2592.2.f.b.1295.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.1	✓	16	72.61	even	6
72.2.l.b.11.4	yes	16	36.7	odd	6
72.2.l.b.59.1	yes	16	12.11	even	2
72.2.l.b.59.4	yes	16	24.5	odd	2
216.2.l.b.35.5		16	36.11	even	6
216.2.l.b.35.8		16	72.29	odd	6
216.2.l.b.179.5		16	8.5	even	2
216.2.l.b.179.8		16	4.3	odd	2
288.2.p.b.47.7		16	9.7	even	3
288.2.p.b.47.8		16	72.43	odd	6
288.2.p.b.239.7		16	24.11	even	2
288.2.p.b.239.8		16	3.2	odd	2
648.2.f.b.323.7		16	72.5	odd	6
648.2.f.b.323.8		16	36.31	odd	6
648.2.f.b.323.9		16	36.23	even	6
648.2.f.b.323.10		16	72.13	even	6
864.2.p.b.143.1		16	72.11	even	6	inner
864.2.p.b.143.8		16	9.2	odd	6	inner
864.2.p.b.719.1		16	1.1	even	1	trivial
864.2.p.b.719.8		16	8.3	odd	2	inner
2592.2.f.b.1295.1		16	9.5	odd	6
2592.2.f.b.1295.2		16	72.67	odd	6
2592.2.f.b.1295.15		16	9.4	even	3
2592.2.f.b.1295.16		16	72.59	even	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)

\(f(q)\)	\(=\)	\(q+(-1.74322 + 3.01934i) q^{5} +(-1.80802 + 1.04386i) q^{7} +O(q^{10})\)	\(q+(-1.74322 + 3.01934i) q^{5} +(-1.80802 + 1.04386i) q^{7} +(-0.116985 + 0.0675415i) q^{11} +(-2.63890 - 1.52357i) q^{13} -4.19800i q^{17} -0.919111 q^{19} +(0.689877 - 1.19490i) q^{23} +(-3.57762 - 6.19662i) q^{25} +(-4.24111 - 7.34582i) q^{29} +(4.39877 + 2.53963i) q^{31} -7.27870i q^{35} +1.61676i q^{37} +(-1.79408 - 1.03581i) q^{41} +(-5.41106 - 9.37224i) q^{43} +(-0.205809 - 0.356471i) q^{47} +(-1.32071 + 2.28754i) q^{49} +0.968137 q^{53} -0.470958i q^{55} +(3.88770 + 2.24457i) q^{59} +(-7.44553 + 4.29868i) q^{61} +(9.20037 - 5.31183i) q^{65} +(-3.15416 + 5.46316i) q^{67} -11.9687 q^{71} -4.06264 q^{73} +(0.141008 - 0.244232i) q^{77} +(-10.8672 + 6.27416i) q^{79} +(5.23875 - 3.02459i) q^{83} +(12.6752 + 7.31802i) q^{85} +8.35848i q^{89} +6.36158 q^{91} +(1.60221 - 2.77511i) q^{95} +(-0.477065 - 0.826300i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 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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