LMFDB - Embedded newform 2790.2.e.a.2789.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2790,2,Mod(2789,2790)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2790, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2790.2789");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2790.e (of order $2$, degree $1$, 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:	$22.2782621639$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2789.18
Character	$\chi$	$=$	2790.2789
Dual form			2790.2.e.a.2789.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(0.432401 - 2.19386i) q^{5} +2.88146i q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.432401 - 2.19386i) q^{5} +2.88146i q^{7} -1.00000 q^{8} +(-0.432401 + 2.19386i) q^{10} -3.34674 q^{11} +5.40542 q^{13} -2.88146i q^{14} +1.00000 q^{16} +1.97280i q^{17} +2.61810 q^{19} +(0.432401 - 2.19386i) q^{20} +3.34674 q^{22} -6.98612i q^{23} +(-4.62606 - 1.89726i) q^{25} -5.40542 q^{26} +2.88146i q^{28} -0.0943650 q^{29} +(-3.14119 - 4.59706i) q^{31} -1.00000 q^{32} -1.97280i q^{34} +(6.32153 + 1.24595i) q^{35} +0.981805 q^{37} -2.61810 q^{38} +(-0.432401 + 2.19386i) q^{40} +4.51651i q^{41} -0.0378825 q^{43} -3.34674 q^{44} +6.98612i q^{46} +6.80601 q^{47} -1.30281 q^{49} +(4.62606 + 1.89726i) q^{50} +5.40542 q^{52} -1.21099i q^{53} +(-1.44714 + 7.34229i) q^{55} -2.88146i q^{56} +0.0943650 q^{58} -1.88085i q^{59} +4.88421i q^{61} +(3.14119 + 4.59706i) q^{62} +1.00000 q^{64} +(2.33731 - 11.8587i) q^{65} +8.30555i q^{67} +1.97280i q^{68} +(-6.32153 - 1.24595i) q^{70} +9.70091i q^{71} +15.9185 q^{73} -0.981805 q^{74} +2.61810 q^{76} -9.64351i q^{77} -9.90754i q^{79} +(0.432401 - 2.19386i) q^{80} -4.51651i q^{82} -8.53533i q^{83} +(4.32805 + 0.853042i) q^{85} +0.0378825 q^{86} +3.34674 q^{88} +13.6895 q^{89} +15.5755i q^{91} -6.98612i q^{92} -6.80601 q^{94} +(1.13207 - 5.74375i) q^{95} +3.17707i q^{97} +1.30281 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} + 32 q^{4} - 4 q^{5} - 32 q^{8}+O(q^{10}) $ 32 * q - 32 * q^2 + 32 * q^4 - 4 * q^5 - 32 * q^8	$ 32 q - 32 q^{2} + 32 q^{4} - 4 q^{5} - 32 q^{8} + 4 q^{10} + 32 q^{16} - 16 q^{19} - 4 q^{20} + 4 q^{25} - 32 q^{32} - 8 q^{35} + 16 q^{38} + 4 q^{40} + 8 q^{47} - 24 q^{49} - 4 q^{50} + 32 q^{64} + 8 q^{70} - 16 q^{76} - 4 q^{80} - 8 q^{94} + 4 q^{95} + 24 q^{98}+O(q^{100}) $ 32 * q - 32 * q^2 + 32 * q^4 - 4 * q^5 - 32 * q^8 + 4 * q^10 + 32 * q^16 - 16 * q^19 - 4 * q^20 + 4 * q^25 - 32 * q^32 - 8 * q^35 + 16 * q^38 + 4 * q^40 + 8 * q^47 - 24 * q^49 - 4 * q^50 + 32 * q^64 + 8 * q^70 - 16 * q^76 - 4 * q^80 - 8 * q^94 + 4 * q^95 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2790\mathbb{Z}\right)^\times$.

$n$	$1117$	$1801$	$2171$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	0.432401	−	2.19386i	0.193376	−	0.981125i
$5$	0.432401	−	2.19386i	0.193376	−	0.981125i
$6$		0			0
$7$			2.88146i			1.08909i	0.838732	+	0.544545i	$0.183298\pi$
$7$			2.88146i			1.08909i	−0.838732	+	0.544545i	$0.816702\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.432401	+	2.19386i	−0.136737	+	0.693760i
$11$	−3.34674			−1.00908			−0.504541	−	0.863388i	$-0.668338\pi$
$11$	−3.34674			−1.00908			−0.504541	+	0.863388i	$0.668338\pi$
$12$		0			0
$13$	5.40542			1.49919			0.749597	−	0.661895i	$-0.230247\pi$
$13$	5.40542			1.49919			0.749597	+	0.661895i	$0.230247\pi$
$14$		−	2.88146i		−	0.770103i
$15$		0			0
$16$	1.00000			0.250000
$17$			1.97280i			0.478475i	0.970961	+	0.239237i	$0.0768974\pi$
$17$			1.97280i			0.478475i	−0.970961	+	0.239237i	$0.923103\pi$
$18$		0			0
$19$	2.61810			0.600633			0.300317	−	0.953840i	$-0.402908\pi$
$19$	2.61810			0.600633			0.300317	+	0.953840i	$0.402908\pi$
$20$	0.432401	−	2.19386i	0.0966879	−	0.490562i
$21$		0			0
$22$	3.34674			0.713528
$23$		−	6.98612i		−	1.45671i	−0.685202	−	0.728353i	$-0.740286\pi$
$23$		−	6.98612i		−	1.45671i	0.685202	−	0.728353i	$-0.259714\pi$
$24$		0			0
$25$	−4.62606	−	1.89726i	−0.925212	−	0.379452i
$26$	−5.40542			−1.06009
$27$		0			0
$28$			2.88146i			0.544545i
$29$	−0.0943650			−0.0175231			−0.00876157	−	0.999962i	$-0.502789\pi$
$29$	−0.0943650			−0.0175231			−0.00876157	+	0.999962i	$0.502789\pi$
$30$		0			0
$31$	−3.14119	−	4.59706i	−0.564174	−	0.825656i
$31$	−3.14119	−	4.59706i	−0.564174	−	0.825656i
$32$	−1.00000			−0.176777
$33$		0			0
$34$		−	1.97280i		−	0.338333i
$35$	6.32153	+	1.24595i	1.06853	+	0.210604i
$36$		0			0
$37$	0.981805			0.161408			0.0807039	−	0.996738i	$-0.474283\pi$
$37$	0.981805			0.161408			0.0807039	+	0.996738i	$0.474283\pi$
$38$	−2.61810			−0.424712
$39$		0			0
$40$	−0.432401	+	2.19386i	−0.0683687	+	0.346880i
$41$			4.51651i			0.705361i	0.935744	+	0.352680i	$0.114730\pi$
$41$			4.51651i			0.705361i	−0.935744	+	0.352680i	$0.885270\pi$
$42$		0			0
$43$	−0.0378825			−0.00577702			−0.00288851	−	0.999996i	$-0.500919\pi$
$43$	−0.0378825			−0.00577702			−0.00288851	+	0.999996i	$0.500919\pi$
$44$	−3.34674			−0.504541
$45$		0			0
$46$			6.98612i			1.03005i
$47$	6.80601			0.992759			0.496380	−	0.868106i	$-0.334662\pi$
$47$	6.80601			0.992759			0.496380	+	0.868106i	$0.334662\pi$
$48$		0			0
$49$	−1.30281			−0.186116
$50$	4.62606	+	1.89726i	0.654223	+	0.268313i
$51$		0			0
$52$	5.40542			0.749597
$53$		−	1.21099i		−	0.166343i	−0.996535	−	0.0831713i	$-0.973495\pi$
$53$		−	1.21099i		−	0.166343i	0.996535	−	0.0831713i	$-0.0265049\pi$
$54$		0			0
$55$	−1.44714	+	7.34229i	−0.195132	+	0.990035i
$56$		−	2.88146i		−	0.385051i
$57$		0			0
$58$	0.0943650			0.0123907
$59$		−	1.88085i		−	0.244866i	−0.992477	−	0.122433i	$-0.960930\pi$
$59$		−	1.88085i		−	0.244866i	0.992477	−	0.122433i	$-0.0390696\pi$
$60$		0			0
$61$			4.88421i			0.625359i	0.949859	+	0.312679i	$0.101227\pi$
$61$			4.88421i			0.625359i	−0.949859	+	0.312679i	$0.898773\pi$
$62$	3.14119	+	4.59706i	0.398931	+	0.583827i
$63$		0			0
$64$	1.00000			0.125000
$65$	2.33731	−	11.8587i	0.289908	−	1.47090i
$66$		0			0
$67$			8.30555i			1.01468i	0.861745	+	0.507342i	$0.169372\pi$
$67$			8.30555i			1.01468i	−0.861745	+	0.507342i	$0.830628\pi$
$68$			1.97280i			0.239237i
$69$		0			0
$70$	−6.32153	−	1.24595i	−0.755567	−	0.148919i
$71$			9.70091i			1.15129i	0.817701	+	0.575643i	$0.195248\pi$
$71$			9.70091i			1.15129i	−0.817701	+	0.575643i	$0.804752\pi$
$72$		0			0
$73$	15.9185			1.86312			0.931560	−	0.363587i	$-0.118448\pi$
$73$	15.9185			1.86312			0.931560	+	0.363587i	$0.118448\pi$
$74$	−0.981805			−0.114132
$75$		0			0
$76$	2.61810			0.300317
$77$		−	9.64351i		−	1.09898i
$78$		0			0
$79$		−	9.90754i		−	1.11469i	−0.830283	−	0.557343i	$-0.811821\pi$
$79$		−	9.90754i		−	1.11469i	0.830283	−	0.557343i	$-0.188179\pi$
$80$	0.432401	−	2.19386i	0.0483439	−	0.245281i
$81$		0			0
$82$		−	4.51651i		−	0.498765i
$83$		−	8.53533i		−	0.936875i	−0.883497	−	0.468437i	$-0.844817\pi$
$83$		−	8.53533i		−	0.936875i	0.883497	−	0.468437i	$-0.155183\pi$
$84$		0			0
$85$	4.32805	+	0.853042i	0.469443	+	0.0925254i
$86$	0.0378825			0.00408497
$87$		0			0
$88$	3.34674			0.356764
$89$	13.6895			1.45109			0.725543	−	0.688177i	$-0.241589\pi$
$89$	13.6895			1.45109			0.725543	+	0.688177i	$0.241589\pi$
$90$		0			0
$91$			15.5755i			1.63276i
$92$		−	6.98612i		−	0.728353i
$93$		0			0
$94$	−6.80601			−0.701987
$95$	1.13207	−	5.74375i	0.116148	−	0.589296i
$96$		0			0
$97$			3.17707i			0.322582i	0.986907	+	0.161291i	$0.0515658\pi$
$97$			3.17707i			0.322582i	−0.986907	+	0.161291i	$0.948434\pi$
$98$	1.30281			0.131604
$99$		0			0
$100$	−4.62606	−	1.89726i	−0.462606	−	0.189726i
$101$		−	12.6771i		−	1.26141i	−0.776021	−	0.630707i	$-0.782765\pi$
$101$		−	12.6771i		−	1.26141i	0.776021	−	0.630707i	$-0.217235\pi$
$102$		0			0
$103$			3.53211i			0.348029i	0.984743	+	0.174014i	$0.0556739\pi$
$103$			3.53211i			0.348029i	−0.984743	+	0.174014i	$0.944326\pi$
$104$	−5.40542			−0.530045
$105$		0			0
$106$			1.21099i			0.117622i
$107$	2.74116			0.264998			0.132499	−	0.991183i	$-0.457700\pi$
$107$	2.74116			0.264998			0.132499	+	0.991183i	$0.457700\pi$
$108$		0			0
$109$	8.96348			0.858546			0.429273	−	0.903175i	$-0.358770\pi$
$109$	8.96348			0.858546			0.429273	+	0.903175i	$0.358770\pi$
$110$	1.44714	−	7.34229i	0.137979	−	0.700060i
$111$		0			0
$112$			2.88146i			0.272272i
$113$	19.0697			1.79393			0.896963	−	0.442106i	$-0.145769\pi$
$113$	19.0697			1.79393			0.896963	+	0.442106i	$0.145769\pi$
$114$		0			0
$115$	−15.3266	−	3.02081i	−1.42921	−	0.281692i
$116$	−0.0943650			−0.00876157
$117$		0			0
$118$			1.88085i			0.173146i
$119$	−5.68455			−0.521102
$120$		0			0
$121$	0.200699			0.0182453
$122$		−	4.88421i		−	0.442196i
$123$		0			0
$124$	−3.14119	−	4.59706i	−0.282087	−	0.412828i
$125$	−6.16264	+	9.32855i	−0.551203	+	0.834371i
$126$		0			0
$127$	−3.67740			−0.326317			−0.163158	−	0.986600i	$-0.552168\pi$
$127$	−3.67740			−0.326317			−0.163158	+	0.986600i	$0.552168\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−2.33731	+	11.8587i	−0.204996	+	1.04008i
$131$		−	17.5922i		−	1.53704i	−0.639828	−	0.768518i	$-0.720995\pi$
$131$		−	17.5922i		−	1.53704i	0.639828	−	0.768518i	$-0.279005\pi$
$132$		0			0
$133$			7.54395i			0.654143i
$134$		−	8.30555i		−	0.717490i
$135$		0			0
$136$		−	1.97280i		−	0.169166i
$137$			3.81234i			0.325710i	0.986650	+	0.162855i	$0.0520703\pi$
$137$			3.81234i			0.325710i	−0.986650	+	0.162855i	$0.947930\pi$
$138$		0			0
$139$		−	8.72630i		−	0.740156i	−0.929001	−	0.370078i	$-0.879331\pi$
$139$		−	8.72630i		−	0.740156i	0.929001	−	0.370078i	$-0.120669\pi$
$140$	6.32153	+	1.24595i	0.534266	+	0.105302i
$141$		0			0
$142$		−	9.70091i		−	0.814083i
$143$	−18.0906			−1.51281
$144$		0			0
$145$	−0.0408036	+	0.207024i	−0.00338855	+	0.0171924i
$146$	−15.9185			−1.31742
$147$		0			0
$148$	0.981805			0.0807039
$149$			6.83126i			0.559638i	0.960053	+	0.279819i	$0.0902745\pi$
$149$			6.83126i			0.559638i	−0.960053	+	0.279819i	$0.909726\pi$
$150$		0			0
$151$		−	6.33168i		−	0.515265i	−0.966243	−	0.257633i	$-0.917058\pi$
$151$		−	6.33168i		−	0.515265i	0.966243	−	0.257633i	$-0.0829424\pi$
$152$	−2.61810			−0.212356
$153$		0			0
$154$			9.64351i			0.777096i
$155$	−11.4436	+	4.90356i	−0.919169	+	0.393863i
$156$		0			0
$157$			4.06609i			0.324509i	0.986749	+	0.162254i	$0.0518765\pi$
$157$			4.06609i			0.324509i	−0.986749	+	0.162254i	$0.948123\pi$
$158$			9.90754i			0.788202i
$159$		0			0
$160$	−0.432401	+	2.19386i	−0.0341843	+	0.173440i
$161$	20.1302			1.58648
$162$		0			0
$163$			3.00570i			0.235425i	0.993048	+	0.117712i	$0.0375561\pi$
$163$			3.00570i			0.235425i	−0.993048	+	0.117712i	$0.962444\pi$
$164$			4.51651i			0.352680i
$165$		0			0
$166$			8.53533i			0.662470i
$167$		−	12.5343i		−	0.969933i	−0.874533	−	0.484967i	$-0.838832\pi$
$167$		−	12.5343i		−	0.969933i	0.874533	−	0.484967i	$-0.161168\pi$
$168$		0			0
$169$	16.2186			1.24758
$170$	−4.32805	−	0.853042i	−0.331947	−	0.0654254i
$171$		0			0
$172$	−0.0378825			−0.00288851
$173$	8.28094			0.629588			0.314794	−	0.949160i	$-0.398065\pi$
$173$	8.28094			0.629588			0.314794	+	0.949160i	$0.398065\pi$
$174$		0			0
$175$	5.46687	−	13.3298i	0.413257	−	1.00764i
$176$	−3.34674			−0.252270
$177$		0			0
$178$	−13.6895			−1.02607
$179$	−19.1770			−1.43336			−0.716679	−	0.697403i	$-0.754339\pi$
$179$	−19.1770			−1.43336			−0.716679	+	0.697403i	$0.754339\pi$
$180$		0			0
$181$		−	15.6510i		−	1.16333i	−0.813428	−	0.581666i	$-0.802401\pi$
$181$		−	15.6510i		−	1.16333i	0.813428	−	0.581666i	$-0.197599\pi$
$182$		−	15.5755i		−	1.15453i
$183$		0			0
$184$			6.98612i			0.515023i
$185$	0.424534	−	2.15394i	0.0312123	−	0.158361i
$186$		0			0
$187$		−	6.60246i		−	0.482820i
$188$	6.80601			0.496380
$189$		0			0
$190$	−1.13207	+	5.74375i	−0.0821290	+	0.416695i
$191$			0.915357i			0.0662329i	0.999452	+	0.0331164i	$0.0105432\pi$
$191$			0.915357i			0.0662329i	−0.999452	+	0.0331164i	$0.989457\pi$
$192$		0			0
$193$		−	2.31500i		−	0.166637i	−0.996523	−	0.0833185i	$-0.973448\pi$
$193$		−	2.31500i		−	0.166637i	0.996523	−	0.0833185i	$-0.0265519\pi$
$194$		−	3.17707i		−	0.228100i
$195$		0			0
$196$	−1.30281			−0.0930581
$197$			8.16561i			0.581776i	0.956757	+	0.290888i	$0.0939507\pi$
$197$			8.16561i			0.581776i	−0.956757	+	0.290888i	$0.906049\pi$
$198$		0			0
$199$		−	16.6301i		−	1.17888i	−0.807813	−	0.589439i	$-0.799349\pi$
$199$		−	16.6301i		−	1.17888i	0.807813	−	0.589439i	$-0.200651\pi$
$200$	4.62606	+	1.89726i	0.327112	+	0.134156i
$201$		0			0
$202$			12.6771i			0.891955i
$203$		−	0.271909i		−	0.0190843i
$204$		0			0
$205$	9.90860	+	1.95295i	0.692047	+	0.136400i
$206$		−	3.53211i		−	0.246094i
$207$		0			0
$208$	5.40542			0.374798
$209$	−8.76211			−0.606088
$210$		0			0
$211$	−4.51019			−0.310494			−0.155247	−	0.987876i	$-0.549617\pi$
$211$	−4.51019			−0.310494			−0.155247	+	0.987876i	$0.549617\pi$
$212$		−	1.21099i		−	0.0831713i
$213$		0			0
$214$	−2.74116			−0.187382
$215$	−0.0163804	+	0.0831089i	−0.00111714	+	0.00566798i
$216$		0			0
$217$	13.2462	−	9.05121i	0.899213	−	0.614436i
$218$	−8.96348			−0.607084
$219$		0			0
$220$	−1.44714	+	7.34229i	−0.0975660	+	0.495017i
$221$			10.6638i			0.717326i
$222$		0			0
$223$	26.4808			1.77328			0.886641	−	0.462458i	$-0.153032\pi$
$223$	26.4808			1.77328			0.886641	+	0.462458i	$0.153032\pi$
$224$		−	2.88146i		−	0.192526i
$225$		0			0
$226$	−19.0697			−1.26850
$227$	15.9176			1.05649			0.528243	−	0.849093i	$-0.322851\pi$
$227$	15.9176			1.05649			0.528243	+	0.849093i	$0.322851\pi$
$228$		0			0
$229$		−	27.6926i		−	1.82998i	−0.403481	−	0.914988i	$-0.632200\pi$
$229$		−	27.6926i		−	1.82998i	0.403481	−	0.914988i	$-0.367800\pi$
$230$	15.3266	+	3.02081i	1.01060	+	0.199186i
$231$		0			0
$232$	0.0943650			0.00619537
$233$	8.50256			0.557021			0.278511	−	0.960433i	$-0.410159\pi$
$233$	8.50256			0.557021			0.278511	+	0.960433i	$0.410159\pi$
$234$		0			0
$235$	2.94293	−	14.9315i	0.191976	−	0.974021i
$236$		−	1.88085i		−	0.122433i
$237$		0			0
$238$	5.68455			0.368475
$239$	−25.6723			−1.66060			−0.830300	−	0.557316i	$-0.811831\pi$
$239$	−25.6723			−1.66060			−0.830300	+	0.557316i	$0.811831\pi$
$240$		0			0
$241$		−	24.1458i		−	1.55537i	−0.628656	−	0.777683i	$-0.716395\pi$
$241$		−	24.1458i		−	1.55537i	0.628656	−	0.777683i	$-0.283605\pi$
$242$	−0.200699			−0.0129014
$243$		0			0
$244$			4.88421i			0.312679i
$245$	−0.563339	+	2.85819i	−0.0359904	+	0.182603i
$246$		0			0
$247$	14.1519			0.900466
$248$	3.14119	+	4.59706i	0.199466	+	0.291913i
$249$		0			0
$250$	6.16264	−	9.32855i	0.389759	−	0.589990i
$251$	28.2723			1.78453			0.892266	−	0.451510i	$-0.149114\pi$
$251$	28.2723			1.78453			0.892266	+	0.451510i	$0.149114\pi$
$252$		0			0
$253$			23.3808i			1.46994i
$254$	3.67740			0.230741
$255$		0			0
$256$	1.00000			0.0625000
$257$	19.3202			1.20516			0.602582	−	0.798057i	$-0.294139\pi$
$257$	19.3202			1.20516			0.602582	+	0.798057i	$0.294139\pi$
$258$		0			0
$259$			2.82903i			0.175787i
$260$	2.33731	−	11.8587i	0.144954	−	0.735448i
$261$		0			0
$262$			17.5922i			1.08685i
$263$			2.28941i			0.141171i	0.997506	+	0.0705856i	$0.0224868\pi$
$263$			2.28941i			0.141171i	−0.997506	+	0.0705856i	$0.977513\pi$
$264$		0			0
$265$	−2.65675	−	0.523635i	−0.163203	−	0.0321666i
$266$		−	7.54395i		−	0.462549i
$267$		0			0
$268$			8.30555i			0.507342i
$269$	17.8436			1.08794			0.543970	−	0.839104i	$-0.316920\pi$
$269$	17.8436			1.08794			0.543970	+	0.839104i	$0.316920\pi$
$270$		0			0
$271$		−	11.5841i		−	0.703685i	−0.936059	−	0.351843i	$-0.885555\pi$
$271$		−	11.5841i		−	0.703685i	0.936059	−	0.351843i	$-0.114445\pi$
$272$			1.97280i			0.119619i
$273$		0			0
$274$		−	3.81234i		−	0.230312i
$275$	15.4822	+	6.34964i	0.933614	+	0.382898i
$276$		0			0
$277$	−12.8867			−0.774286			−0.387143	−	0.922020i	$-0.626538\pi$
$277$	−12.8867			−0.774286			−0.387143	+	0.922020i	$0.626538\pi$
$278$			8.72630i			0.523369i
$279$		0			0
$280$	−6.32153	−	1.24595i	−0.377783	−	0.0744596i
$281$			12.5147i			0.746562i	0.927718	+	0.373281i	$0.121767\pi$
$281$			12.5147i			0.746562i	−0.927718	+	0.373281i	$0.878233\pi$
$282$		0			0
$283$			8.08213i			0.480433i	0.970719	+	0.240216i	$0.0772184\pi$
$283$			8.08213i			0.480433i	−0.970719	+	0.240216i	$0.922782\pi$
$284$			9.70091i			0.575643i
$285$		0			0
$286$	18.0906			1.06972
$287$	−13.0142			−0.768201
$288$		0			0
$289$	13.1081			0.771062
$290$	0.0408036	−	0.207024i	0.00239607	−	0.0121569i
$291$		0			0
$292$	15.9185			0.931560
$293$	−23.4199			−1.36820			−0.684102	−	0.729386i	$-0.739806\pi$
$293$	−23.4199			−1.36820			−0.684102	+	0.729386i	$0.739806\pi$
$294$		0			0
$295$	−4.12632	−	0.813281i	−0.240244	−	0.0473511i
$296$	−0.981805			−0.0570662
$297$		0			0
$298$		−	6.83126i		−	0.395724i
$299$		−	37.7629i		−	2.18389i
$300$		0			0
$301$		−	0.109157i		−	0.00629170i
$302$			6.33168i			0.364348i
$303$		0			0
$304$	2.61810			0.150158
$305$	10.7153	+	2.11194i	0.613555	+	0.120929i
$306$		0			0
$307$		−	5.45436i		−	0.311297i	−0.987813	−	0.155648i	$-0.950253\pi$
$307$		−	5.45436i		−	0.311297i	0.987813	−	0.155648i	$-0.0497467\pi$
$308$		−	9.64351i		−	0.549490i
$309$		0			0
$310$	11.4436	−	4.90356i	0.649951	−	0.278503i
$311$			24.5872i			1.39421i	0.716969	+	0.697105i	$0.245529\pi$
$311$			24.5872i			1.39421i	−0.716969	+	0.697105i	$0.754471\pi$
$312$		0			0
$313$	10.2645			0.580184			0.290092	−	0.956999i	$-0.406314\pi$
$313$	10.2645			0.580184			0.290092	+	0.956999i	$0.406314\pi$
$314$		−	4.06609i		−	0.229462i
$315$		0			0
$316$		−	9.90754i		−	0.557343i
$317$	−21.6688			−1.21704			−0.608521	−	0.793538i	$-0.708237\pi$
$317$	−21.6688			−1.21704			−0.608521	+	0.793538i	$0.708237\pi$
$318$		0			0
$319$	0.315816			0.0176823
$320$	0.432401	−	2.19386i	0.0241720	−	0.122641i
$321$		0			0
$322$	−20.1302			−1.12181
$323$			5.16499i			0.287388i
$324$		0			0
$325$	−25.0058	−	10.2555i	−1.38707	−	0.568871i
$326$		−	3.00570i		−	0.166471i
$327$		0			0
$328$		−	4.51651i		−	0.249383i
$329$			19.6113i			1.08120i
$330$		0			0
$331$			22.4609i			1.23456i	0.786742	+	0.617282i	$0.211766\pi$
$331$			22.4609i			1.23456i	−0.786742	+	0.617282i	$0.788234\pi$
$332$		−	8.53533i		−	0.468437i
$333$		0			0
$334$			12.5343i			0.685846i
$335$	18.2212	+	3.59133i	0.995532	+	0.196215i
$336$		0			0
$337$	0.0802010			0.00436883			0.00218441	−	0.999998i	$-0.499305\pi$
$337$	0.0802010			0.00436883			0.00218441	+	0.999998i	$0.499305\pi$
$338$	−16.2186			−0.882174
$339$		0			0
$340$	4.32805	+	0.853042i	0.234722	+	0.0462627i
$341$	10.5128	+	15.3852i	0.569298	+	0.833154i
$342$		0			0
$343$			16.4162i			0.886392i
$344$	0.0378825			0.00204249
$345$		0			0
$346$	−8.28094			−0.445186
$347$		−	9.43107i		−	0.506287i	−0.967429	−	0.253143i	$-0.918536\pi$
$347$		−	9.43107i		−	0.506287i	0.967429	−	0.253143i	$-0.0814644\pi$
$348$		0			0
$349$	35.8974			1.92154			0.960771	−	0.277343i	$-0.0894540\pi$
$349$	35.8974			1.92154			0.960771	+	0.277343i	$0.0894540\pi$
$350$	−5.46687	+	13.3298i	−0.292217	+	0.712508i
$351$		0			0
$352$	3.34674			0.178382
$353$			20.1730i			1.07370i	0.843677	+	0.536851i	$0.180386\pi$
$353$			20.1730i			1.07370i	−0.843677	+	0.536851i	$0.819614\pi$
$354$		0			0
$355$	21.2825	+	4.19469i	1.12956	+	0.222631i
$356$	13.6895			0.725543
$357$		0			0
$358$	19.1770			1.01354
$359$		−	14.8697i		−	0.784790i	−0.919797	−	0.392395i	$-0.871647\pi$
$359$		−	14.8697i		−	0.784790i	0.919797	−	0.392395i	$-0.128353\pi$
$360$		0			0
$361$	−12.1456			−0.639240
$362$			15.6510i			0.822600i
$363$		0			0
$364$			15.5755i			0.816378i
$365$	6.88318	−	34.9230i	0.360282	−	1.82795i
$366$		0			0
$367$	6.77363			0.353581			0.176790	−	0.984249i	$-0.443429\pi$
$367$	6.77363			0.353581			0.176790	+	0.984249i	$0.443429\pi$
$368$		−	6.98612i		−	0.364177i
$369$		0			0
$370$	−0.424534	+	2.15394i	−0.0220705	+	0.111978i
$371$	3.48943			0.181162
$372$		0			0
$373$			23.4002i			1.21162i	0.795611	+	0.605808i	$0.207150\pi$
$373$			23.4002i			1.21162i	−0.795611	+	0.605808i	$0.792850\pi$
$374$			6.60246i			0.341405i
$375$		0			0
$376$	−6.80601			−0.350993
$377$	−0.510083			−0.0262706
$378$		0			0
$379$	3.91269			0.200981			0.100491	−	0.994938i	$-0.467959\pi$
$379$	3.91269			0.200981			0.100491	+	0.994938i	$0.467959\pi$
$380$	1.13207	−	5.74375i	0.0580740	−	0.294648i
$381$		0			0
$382$		−	0.915357i		−	0.0468337i
$383$			24.9508i			1.27492i	0.770482	+	0.637462i	$0.220016\pi$
$383$			24.9508i			1.27492i	−0.770482	+	0.637462i	$0.779984\pi$
$384$		0			0
$385$	−21.1565	−	4.16987i	−1.07824	−	0.212516i
$386$			2.31500i			0.117830i
$387$		0			0
$388$			3.17707i			0.161291i
$389$	1.10330			0.0559397			0.0279699	−	0.999609i	$-0.491096\pi$
$389$	1.10330			0.0559397			0.0279699	+	0.999609i	$0.491096\pi$
$390$		0			0
$391$	13.7822			0.696997
$392$	1.30281			0.0658020
$393$		0			0
$394$		−	8.16561i		−	0.411378i
$395$	−21.7358	−	4.28403i	−1.09365	−	0.215553i
$396$		0			0
$397$		−	25.8187i		−	1.29580i	−0.761724	−	0.647901i	$-0.775647\pi$
$397$		−	25.8187i		−	1.29580i	0.761724	−	0.647901i	$-0.224353\pi$
$398$			16.6301i			0.833592i
$399$		0			0
$400$	−4.62606	−	1.89726i	−0.231303	−	0.0948629i
$401$	39.9101			1.99301			0.996506	−	0.0835156i	$-0.0266148\pi$
$401$	39.9101			1.99301			0.996506	+	0.0835156i	$0.0266148\pi$
$402$		0			0
$403$	−16.9794	−	24.8490i	−0.845806	−	1.23782i
$404$		−	12.6771i		−	0.630707i
$405$		0			0
$406$			0.271909i			0.0134946i
$407$	−3.28585			−0.162874
$408$		0			0
$409$			7.15668i			0.353875i	0.984222	+	0.176938i	$0.0566191\pi$
$409$			7.15668i			0.353875i	−0.984222	+	0.176938i	$0.943381\pi$
$410$	−9.90860	−	1.95295i	−0.489351	−	0.0964491i
$411$		0			0
$412$			3.53211i			0.174014i
$413$	5.41959			0.266681
$414$		0			0
$415$	−18.7253	−	3.69069i	−0.919191	−	0.181169i
$416$	−5.40542			−0.265023
$417$		0			0
$418$	8.76211			0.428569
$419$			13.3892i			0.654106i	0.945006	+	0.327053i	$0.106056\pi$
$419$			13.3892i			0.654106i	−0.945006	+	0.327053i	$0.893944\pi$
$420$		0			0
$421$	−8.27125			−0.403116			−0.201558	−	0.979477i	$-0.564600\pi$
$421$	−8.27125			−0.403116			−0.201558	+	0.979477i	$0.564600\pi$
$422$	4.51019			0.219553
$423$		0			0
$424$			1.21099i			0.0588110i
$425$	3.74291	−	9.12630i	0.181558	−	0.442690i
$426$		0			0
$427$	−14.0737			−0.681072
$428$	2.74116			0.132499
$429$		0			0
$430$	0.0163804	−	0.0831089i	0.000789935	−	0.00400787i
$431$			11.3898i			0.548625i	0.961641	+	0.274313i	$0.0884503\pi$
$431$			11.3898i			0.548625i	−0.961641	+	0.274313i	$0.911550\pi$
$432$		0			0
$433$	−8.60214			−0.413392			−0.206696	−	0.978405i	$-0.566271\pi$
$433$	−8.60214			−0.413392			−0.206696	+	0.978405i	$0.566271\pi$
$434$	−13.2462	+	9.05121i	−0.635840	+	0.434472i
$435$		0			0
$436$	8.96348			0.429273
$437$		−	18.2904i		−	0.874946i
$438$		0			0
$439$	−16.7228			−0.798134			−0.399067	−	0.916922i	$-0.630666\pi$
$439$	−16.7228			−0.798134			−0.399067	+	0.916922i	$0.630666\pi$
$440$	1.44714	−	7.34229i	0.0689896	−	0.350030i
$441$		0			0
$442$		−	10.6638i		−	0.507226i
$443$	7.92821			0.376681			0.188340	−	0.982104i	$-0.439689\pi$
$443$	7.92821			0.376681			0.188340	+	0.982104i	$0.439689\pi$
$444$		0			0
$445$	5.91936	−	30.0329i	0.280605	−	1.42370i
$446$	−26.4808			−1.25390
$447$		0			0
$448$			2.88146i			0.136136i
$449$	−10.7160			−0.505717			−0.252858	−	0.967503i	$-0.581371\pi$
$449$	−10.7160			−0.505717			−0.252858	+	0.967503i	$0.581371\pi$
$450$		0			0
$451$		−	15.1156i		−	0.711766i
$452$	19.0697			0.896963
$453$		0			0
$454$	−15.9176			−0.747049
$455$	34.1705	+	6.73487i	1.60194	+	0.315736i
$456$		0			0
$457$	−25.1676			−1.17729			−0.588645	−	0.808392i	$-0.700338\pi$
$457$	−25.1676			−1.17729			−0.588645	+	0.808392i	$0.700338\pi$
$458$			27.6926i			1.29399i
$459$		0			0
$460$	−15.3266	−	3.02081i	−0.714605	−	0.140846i
$461$	−19.8117			−0.922725			−0.461362	−	0.887212i	$-0.652639\pi$
$461$	−19.8117			−0.922725			−0.461362	+	0.887212i	$0.652639\pi$
$462$		0			0
$463$	30.9582			1.43875			0.719375	−	0.694622i	$-0.244428\pi$
$463$	30.9582			1.43875			0.719375	+	0.694622i	$0.244428\pi$
$464$	−0.0943650			−0.00438079
$465$		0			0
$466$	−8.50256			−0.393874
$467$	−3.06930			−0.142030			−0.0710151	−	0.997475i	$-0.522624\pi$
$467$	−3.06930			−0.142030			−0.0710151	+	0.997475i	$0.522624\pi$
$468$		0			0
$469$	−23.9321			−1.10508
$470$	−2.94293	+	14.9315i	−0.135747	+	0.688737i
$471$		0			0
$472$			1.88085i			0.0865730i
$473$	0.126783			0.00582949
$474$		0			0
$475$	−12.1115	−	4.96721i	−0.555713	−	0.227911i
$476$	−5.68455			−0.260551
$477$		0			0
$478$	25.6723			1.17422
$479$		−	29.6884i		−	1.35650i	−0.734831	−	0.678250i	$-0.762739\pi$
$479$		−	29.6884i		−	1.35650i	0.734831	−	0.678250i	$-0.237261\pi$
$480$		0			0
$481$	5.30707			0.241981
$482$			24.1458i			1.09981i
$483$		0			0
$484$	0.200699			0.00912267
$485$	6.97004	+	1.37377i	0.316493	+	0.0623796i
$486$		0			0
$487$	−32.8763			−1.48977			−0.744884	−	0.667194i	$-0.767495\pi$
$487$	−32.8763			−1.48977			−0.744884	+	0.667194i	$0.767495\pi$
$488$		−	4.88421i		−	0.221098i
$489$		0			0
$490$	0.563339	−	2.85819i	0.0254490	−	0.129120i
$491$	−18.4934			−0.834598			−0.417299	−	0.908769i	$-0.637023\pi$
$491$	−18.4934			−0.834598			−0.417299	+	0.908769i	$0.637023\pi$
$492$		0			0
$493$		−	0.186164i		−	0.00838438i
$494$	−14.1519			−0.636725
$495$		0			0
$496$	−3.14119	−	4.59706i	−0.141044	−	0.206414i
$497$	−27.9528			−1.25385
$498$		0			0
$499$			11.3300i			0.507202i	0.967309	+	0.253601i	$0.0816151\pi$
$499$			11.3300i			0.507202i	−0.967309	+	0.253601i	$0.918385\pi$
$500$	−6.16264	+	9.32855i	−0.275601	+	0.417186i
$501$		0			0
$502$	−28.2723			−1.26185
$503$	−28.8319			−1.28555			−0.642776	−	0.766054i	$-0.722217\pi$
$503$	−28.8319			−1.28555			−0.642776	+	0.766054i	$0.722217\pi$
$504$		0			0
$505$	−27.8117	−	5.48158i	−1.23761	−	0.243927i
$506$		−	23.3808i		−	1.03940i
$507$		0			0
$508$	−3.67740			−0.163158
$509$	−17.3738			−0.770079			−0.385039	−	0.922900i	$-0.625812\pi$
$509$	−17.3738			−0.770079			−0.385039	+	0.922900i	$0.625812\pi$
$510$		0			0
$511$			45.8685i			2.02910i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−19.3202			−0.852179
$515$	7.74896	+	1.52729i	0.341460	+	0.0673004i
$516$		0			0
$517$	−22.7780			−1.00177
$518$		−	2.82903i		−	0.124301i
$519$		0			0
$520$	−2.33731	+	11.8587i	−0.102498	+	0.520040i
$521$			31.4214i			1.37659i	0.725429	+	0.688297i	$0.241642\pi$
$521$			31.4214i			1.37659i	−0.725429	+	0.688297i	$0.758358\pi$
$522$		0			0
$523$	−4.40776			−0.192738			−0.0963690	−	0.995346i	$-0.530723\pi$
$523$	−4.40776			−0.192738			−0.0963690	+	0.995346i	$0.530723\pi$
$524$		−	17.5922i		−	0.768518i
$525$		0			0
$526$		−	2.28941i		−	0.0998232i
$527$	9.06908	−	6.19694i	0.395055	−	0.269943i
$528$		0			0
$529$	−25.8058			−1.12199
$530$	2.65675	+	0.523635i	0.115402	+	0.0227452i
$531$		0			0
$532$			7.54395i			0.327072i
$533$			24.4136i			1.05747i
$534$		0			0
$535$	1.18528	−	6.01374i	0.0512443	−	0.259996i
$536$		−	8.30555i		−	0.358745i
$537$		0			0
$538$	−17.8436			−0.769290
$539$	4.36019			0.187806
$540$		0			0
$541$	37.8499			1.62729			0.813647	−	0.581359i	$-0.197479\pi$
$541$	37.8499			1.62729			0.813647	+	0.581359i	$0.197479\pi$
$542$			11.5841i			0.497581i
$543$		0			0
$544$		−	1.97280i		−	0.0845832i
$545$	3.87582	−	19.6646i	0.166022	−	0.842341i
$546$		0			0
$547$		−	42.3963i		−	1.81273i	−0.422491	−	0.906367i	$-0.638844\pi$
$547$		−	42.3963i		−	1.81273i	0.422491	−	0.906367i	$-0.361156\pi$
$548$			3.81234i			0.162855i
$549$		0			0
$550$	−15.4822	−	6.34964i	−0.660165	−	0.270749i
$551$	−0.247057			−0.0105250
$552$		0			0
$553$	28.5482			1.21399
$554$	12.8867			0.547503
$555$		0			0
$556$		−	8.72630i		−	0.370078i
$557$			6.97784i			0.295661i	0.989013	+	0.147830i	$0.0472290\pi$
$557$			6.97784i			0.295661i	−0.989013	+	0.147830i	$0.952771\pi$
$558$		0			0
$559$	−0.204771			−0.00866088
$560$	6.32153	+	1.24595i	0.267133	+	0.0526509i
$561$		0			0
$562$		−	12.5147i		−	0.527899i
$563$	−25.3393			−1.06792			−0.533962	−	0.845509i	$-0.679297\pi$
$563$	−25.3393			−1.06792			−0.533962	+	0.845509i	$0.679297\pi$
$564$		0			0
$565$	8.24576	−	41.8363i	0.346902	−	1.76006i
$566$		−	8.08213i		−	0.339717i
$567$		0			0
$568$		−	9.70091i		−	0.407041i
$569$	−7.25954			−0.304336			−0.152168	−	0.988355i	$-0.548625\pi$
$569$	−7.25954			−0.304336			−0.152168	+	0.988355i	$0.548625\pi$
$570$		0			0
$571$			27.7330i			1.16059i	0.814407	+	0.580294i	$0.197062\pi$
$571$			27.7330i			1.16059i	−0.814407	+	0.580294i	$0.802938\pi$
$572$	−18.0906			−0.756404
$573$		0			0
$574$	13.0142			0.543200
$575$	−13.2545	+	32.3182i	−0.552749	+	1.34776i
$576$		0			0
$577$		−	37.1701i		−	1.54741i	−0.633545	−	0.773706i	$-0.718401\pi$
$577$		−	37.1701i		−	1.54741i	0.633545	−	0.773706i	$-0.281599\pi$
$578$	−13.1081			−0.545223
$579$		0			0
$580$	−0.0408036	+	0.207024i	−0.00169428	+	0.00859620i
$581$	24.5942			1.02034
$582$		0			0
$583$			4.05288i			0.167853i
$584$	−15.9185			−0.658712
$585$		0			0
$586$	23.4199			0.967466
$587$			10.3372i			0.426661i	0.976980	+	0.213330i	$0.0684311\pi$
$587$			10.3372i			0.426661i	−0.976980	+	0.213330i	$0.931569\pi$
$588$		0			0
$589$	−8.22395	−	12.0356i	−0.338862	−	0.495916i
$590$	4.12632	+	0.813281i	0.169878	+	0.0334823i
$591$		0			0
$592$	0.981805			0.0403519
$593$	17.0299			0.699333			0.349666	−	0.936874i	$-0.386295\pi$
$593$	17.0299			0.699333			0.349666	+	0.936874i	$0.386295\pi$
$594$		0			0
$595$	−2.45801	+	12.4711i	−0.100768	+	0.511266i
$596$			6.83126i			0.279819i
$597$		0			0
$598$			37.7629i			1.54424i
$599$		−	5.04258i		−	0.206034i	−0.994680	−	0.103017i	$-0.967150\pi$
$599$		−	5.04258i		−	0.206034i	0.994680	−	0.103017i	$-0.0328497\pi$
$600$		0			0
$601$			47.2750i			1.92839i	0.265197	+	0.964194i	$0.414563\pi$
$601$			47.2750i			1.92839i	−0.265197	+	0.964194i	$0.585437\pi$
$602$			0.109157i			0.00444890i
$603$		0			0
$604$		−	6.33168i		−	0.257633i
$605$	0.0867824	−	0.440305i	0.00352821	−	0.0179010i
$606$		0			0
$607$			23.4385i			0.951340i	0.879624	+	0.475670i	$0.157794\pi$
$607$			23.4385i			0.951340i	−0.879624	+	0.475670i	$0.842206\pi$
$608$	−2.61810			−0.106178
$609$		0			0
$610$	−10.7153	−	2.11194i	−0.433849	−	0.0855099i
$611$	36.7894			1.48834
$612$		0			0
$613$	−26.6617			−1.07686			−0.538429	−	0.842671i	$-0.680982\pi$
$613$	−26.6617			−1.07686			−0.538429	+	0.842671i	$0.680982\pi$
$614$			5.45436i			0.220120i
$615$		0			0
$616$			9.64351i			0.388548i
$617$	−17.7486			−0.714531			−0.357265	−	0.934003i	$-0.616291\pi$
$617$	−17.7486			−0.714531			−0.357265	+	0.934003i	$0.616291\pi$
$618$		0			0
$619$		−	7.15959i		−	0.287768i	−0.989595	−	0.143884i	$-0.954041\pi$
$619$		−	7.15959i		−	0.287768i	0.989595	−	0.143884i	$-0.0459593\pi$
$620$	−11.4436	+	4.90356i	−0.459584	+	0.196932i
$621$		0			0
$622$		−	24.5872i		−	0.985855i
$623$			39.4458i			1.58036i
$624$		0			0
$625$	17.8008	+	17.5536i	0.712033	+	0.702146i
$626$	−10.2645			−0.410252
$627$		0			0
$628$			4.06609i			0.162254i
$629$			1.93691i			0.0772295i
$630$		0			0
$631$			9.91745i			0.394808i	0.980322	+	0.197404i	$0.0632510\pi$
$631$			9.91745i			0.394808i	−0.980322	+	0.197404i	$0.936749\pi$
$632$			9.90754i			0.394101i
$633$		0			0
$634$	21.6688			0.860579
$635$	−1.59011	+	8.06771i	−0.0631018	+	0.320157i
$636$		0			0
$637$	−7.04226			−0.279024
$638$	−0.315816			−0.0125033
$639$		0			0
$640$	−0.432401	+	2.19386i	−0.0170922	+	0.0867200i
$641$	−22.3745			−0.883740			−0.441870	−	0.897079i	$-0.645685\pi$
$641$	−22.3745			−0.883740			−0.441870	+	0.897079i	$0.645685\pi$
$642$		0			0
$643$	29.0073			1.14394			0.571968	−	0.820276i	$-0.306180\pi$
$643$	29.0073			1.14394			0.571968	+	0.820276i	$0.306180\pi$
$644$	20.1302			0.793242
$645$		0			0
$646$		−	5.16499i		−	0.203214i
$647$			26.8190i			1.05436i	0.849752	+	0.527182i	$0.176751\pi$
$647$			26.8190i			1.05436i	−0.849752	+	0.527182i	$0.823249\pi$
$648$		0			0
$649$			6.29472i			0.247089i
$650$	25.0058	+	10.2555i	0.980808	+	0.402253i
$651$		0			0
$652$			3.00570i			0.117712i
$653$	−22.8568			−0.894456			−0.447228	−	0.894420i	$-0.647589\pi$
$653$	−22.8568			−0.894456			−0.447228	+	0.894420i	$0.647589\pi$
$654$		0			0
$655$	−38.5948	−	7.60688i	−1.50802	−	0.297226i
$656$			4.51651i			0.176340i
$657$		0			0
$658$		−	19.6113i		−	0.764527i
$659$		−	29.9783i		−	1.16779i	−0.811830	−	0.583893i	$-0.801529\pi$
$659$		−	29.9783i		−	1.16779i	0.811830	−	0.583893i	$-0.198471\pi$
$660$		0			0
$661$	29.3911			1.14318			0.571590	−	0.820540i	$-0.306327\pi$
$661$	29.3911			1.14318			0.571590	+	0.820540i	$0.306327\pi$
$662$		−	22.4609i		−	0.872968i
$663$		0			0
$664$			8.53533i			0.331235i
$665$	16.5504	+	3.26201i	0.641796	+	0.126496i
$666$		0			0
$667$			0.659245i			0.0255261i
$668$		−	12.5343i		−	0.484967i
$669$		0			0
$670$	−18.2212	−	3.59133i	−0.703947	−	0.138745i
$671$		−	16.3462i		−	0.631038i
$672$		0			0
$673$	6.45956			0.248998			0.124499	−	0.992220i	$-0.460268\pi$
$673$	6.45956			0.248998			0.124499	+	0.992220i	$0.460268\pi$
$674$	−0.0802010			−0.00308923
$675$		0			0
$676$	16.2186			0.623791
$677$			25.3464i			0.974141i	0.873363	+	0.487071i	$0.161935\pi$
$677$			25.3464i			0.974141i	−0.873363	+	0.487071i	$0.838065\pi$
$678$		0			0
$679$	−9.15459			−0.351321
$680$	−4.32805	−	0.853042i	−0.165973	−	0.0327127i
$681$		0			0
$682$	−10.5128	−	15.3852i	−0.402554	−	0.589129i
$683$	−37.4814			−1.43418			−0.717092	−	0.696978i	$-0.754527\pi$
$683$	−37.4814			−1.43418			−0.717092	+	0.696978i	$0.754527\pi$
$684$		0			0
$685$	8.36374	+	1.64846i	0.319562	+	0.0629844i
$686$		−	16.4162i		−	0.626774i
$687$		0			0
$688$	−0.0378825			−0.00144426
$689$		−	6.54592i		−	0.249380i
$690$		0			0
$691$	−23.6594			−0.900045			−0.450023	−	0.893017i	$-0.648584\pi$
$691$	−23.6594			−0.900045			−0.450023	+	0.893017i	$0.648584\pi$
$692$	8.28094			0.314794
$693$		0			0
$694$			9.43107i			0.357999i
$695$	−19.1443	−	3.77327i	−0.726185	−	0.143128i
$696$		0			0
$697$	−8.91018			−0.337497
$698$	−35.8974			−1.35874
$699$		0			0
$700$	5.46687	−	13.3298i	0.206628	−	0.503819i
$701$		−	7.55569i		−	0.285374i	−0.989768	−	0.142687i	$-0.954426\pi$
$701$		−	7.55569i		−	0.285374i	0.989768	−	0.142687i	$-0.0455743\pi$
$702$		0			0
$703$	2.57046			0.0969468
$704$	−3.34674			−0.126135
$705$		0			0
$706$		−	20.1730i		−	0.759223i
$707$	36.5285			1.37379
$708$		0			0
$709$			12.6916i			0.476643i	0.971186	+	0.238322i	$0.0765973\pi$
$709$			12.6916i			0.476643i	−0.971186	+	0.238322i	$0.923403\pi$
$710$	−21.2825	−	4.19469i	−0.798717	−	0.157424i
$711$		0			0
$712$	−13.6895			−0.513036
$713$	−32.1156	+	21.9447i	−1.20274	+	0.821836i
$714$		0			0
$715$	−7.82238	+	39.6882i	−0.292541	+	1.48425i
$716$	−19.1770			−0.716679
$717$		0			0
$718$			14.8697i			0.554931i
$719$	7.62764			0.284463			0.142232	−	0.989833i	$-0.454572\pi$
$719$	7.62764			0.284463			0.142232	+	0.989833i	$0.454572\pi$
$720$		0			0
$721$	−10.1776			−0.379035
$722$	12.1456			0.452011
$723$		0			0
$724$		−	15.6510i		−	0.581666i
$725$	0.436538	+	0.179035i	0.0162126	+	0.00664919i
$726$		0			0
$727$			34.3993i			1.27580i	0.770119	+	0.637900i	$0.220197\pi$
$727$			34.3993i			1.27580i	−0.770119	+	0.637900i	$0.779803\pi$
$728$		−	15.5755i		−	0.577267i
$729$		0			0
$730$	−6.88318	+	34.9230i	−0.254758	+	1.29256i
$731$		−	0.0747346i		−	0.00276416i
$732$		0			0
$733$		−	46.2358i		−	1.70776i	−0.520470	−	0.853880i	$-0.674243\pi$
$733$		−	46.2358i		−	1.70776i	0.520470	−	0.853880i	$-0.325757\pi$
$734$	−6.77363			−0.250019
$735$		0			0
$736$			6.98612i			0.257512i
$737$		−	27.7965i		−	1.02390i
$738$		0			0
$739$			5.39139i			0.198326i	0.995071	+	0.0991628i	$0.0316165\pi$
$739$			5.39139i			0.198326i	−0.995071	+	0.0991628i	$0.968384\pi$
$740$	0.424534	−	2.15394i	0.0156062	−	0.0791805i
$741$		0			0
$742$	−3.48943			−0.128101
$743$			44.7420i			1.64143i	0.571341	+	0.820713i	$0.306423\pi$
$743$			44.7420i			1.64143i	−0.571341	+	0.820713i	$0.693577\pi$
$744$		0			0
$745$	14.9868	+	2.95384i	0.549075	+	0.108220i
$746$		−	23.4002i		−	0.856743i
$747$		0			0
$748$		−	6.60246i		−	0.241410i
$749$			7.89856i			0.288607i
$750$		0			0
$751$	−49.2219			−1.79613			−0.898066	−	0.439860i	$-0.855028\pi$
$751$	−49.2219			−1.79613			−0.898066	+	0.439860i	$0.855028\pi$
$752$	6.80601			0.248190
$753$		0			0
$754$	0.510083			0.0185761
$755$	−13.8908	−	2.73783i	−0.505539	−	0.0996398i
$756$		0			0
$757$	−44.0071			−1.59947			−0.799733	−	0.600356i	$-0.795026\pi$
$757$	−44.0071			−1.59947			−0.799733	+	0.600356i	$0.795026\pi$
$758$	−3.91269			−0.142115
$759$		0			0
$760$	−1.13207	+	5.74375i	−0.0410645	+	0.208348i
$761$	−9.49541			−0.344208			−0.172104	−	0.985079i	$-0.555057\pi$
$761$	−9.49541			−0.344208			−0.172104	+	0.985079i	$0.555057\pi$
$762$		0			0
$763$			25.8279i			0.935034i
$764$			0.915357i			0.0331164i
$765$		0			0
$766$		−	24.9508i		−	0.901508i
$767$		−	10.1668i		−	0.367101i
$768$		0			0
$769$	−15.2139			−0.548627			−0.274314	−	0.961640i	$-0.588451\pi$
$769$	−15.2139			−0.548627			−0.274314	+	0.961640i	$0.588451\pi$
$770$	21.1565	+	4.16987i	0.762428	+	0.150272i
$771$		0			0
$772$		−	2.31500i		−	0.0833185i
$773$			16.5491i			0.595229i	0.954686	+	0.297615i	$0.0961911\pi$
$773$			16.5491i			0.595229i	−0.954686	+	0.297615i	$0.903809\pi$
$774$		0			0
$775$	5.80952	+	27.2259i	0.208684	+	0.977983i
$776$		−	3.17707i		−	0.114050i
$777$		0			0
$778$	−1.10330			−0.0395553
$779$			11.8247i			0.423663i
$780$		0			0
$781$		−	32.4665i		−	1.16174i
$782$	−13.7822			−0.492851
$783$		0			0
$784$	−1.30281			−0.0465291
$785$	8.92043	+	1.75818i	0.318384	+	0.0627522i
$786$		0			0
$787$	24.0470			0.857182			0.428591	−	0.903499i	$-0.359010\pi$
$787$	24.0470			0.857182			0.428591	+	0.903499i	$0.359010\pi$
$788$			8.16561i			0.290888i
$789$		0			0
$790$	21.7358	+	4.28403i	0.773324	+	0.152419i
$791$			54.9486i			1.95375i
$792$		0			0
$793$			26.4012i			0.937534i
$794$			25.8187i			0.916271i
$795$		0			0
$796$		−	16.6301i		−	0.589439i
$797$			40.0945i			1.42022i	0.704091	+	0.710110i	$0.251355\pi$
$797$			40.0945i			1.42022i	−0.704091	+	0.710110i	$0.748645\pi$
$798$		0			0
$799$			13.4269i			0.475010i
$800$	4.62606	+	1.89726i	0.163556	+	0.0670782i
$801$		0			0
$802$	−39.9101			−1.40927
$803$	−53.2752			−1.88004
$804$		0			0
$805$	8.70434	−	44.1629i	0.306788	−	1.55654i
$806$	16.9794	+	24.8490i	0.598076	+	0.875270i
$807$		0			0
$808$			12.6771i			0.445978i
$809$	−7.28880			−0.256261			−0.128130	−	0.991757i	$-0.540898\pi$
$809$	−7.28880			−0.256261			−0.128130	+	0.991757i	$0.540898\pi$
$810$		0			0
$811$	−3.11060			−0.109228			−0.0546140	−	0.998508i	$-0.517393\pi$
$811$	−3.11060			−0.109228			−0.0546140	+	0.998508i	$0.517393\pi$
$812$		−	0.271909i		−	0.00954214i
$813$		0			0
$814$	3.28585			0.115169
$815$	6.59410	+	1.29967i	0.230981	+	0.0455255i
$816$		0			0
$817$	−0.0991801			−0.00346987
$818$		−	7.15668i		−	0.250227i
$819$		0			0
$820$	9.90860	+	1.95295i	0.346023	+	0.0681998i
$821$	−2.69857			−0.0941807			−0.0470904	−	0.998891i	$-0.514995\pi$
$821$	−2.69857			−0.0941807			−0.0470904	+	0.998891i	$0.514995\pi$
$822$		0			0
$823$	34.5266			1.20352			0.601761	−	0.798676i	$-0.294466\pi$
$823$	34.5266			1.20352			0.601761	+	0.798676i	$0.294466\pi$
$824$		−	3.53211i		−	0.123047i
$825$		0			0
$826$	−5.41959			−0.188572
$827$		−	50.5611i		−	1.75818i	−0.476654	−	0.879091i	$-0.658151\pi$
$827$		−	50.5611i		−	1.75818i	0.476654	−	0.879091i	$-0.341849\pi$
$828$		0			0
$829$		−	18.6160i		−	0.646561i	−0.946303	−	0.323281i	$-0.895214\pi$
$829$		−	18.6160i		−	0.646561i	0.946303	−	0.323281i	$-0.104786\pi$
$830$	18.7253	+	3.69069i	0.649966	+	0.128106i
$831$		0			0
$832$	5.40542			0.187399
$833$		−	2.57019i		−	0.0890519i
$834$		0			0
$835$	−27.4985	−	5.41985i	−0.951625	−	0.187562i
$836$	−8.76211			−0.303044
$837$		0			0
$838$		−	13.3892i		−	0.462523i
$839$			37.5286i			1.29563i	0.761797	+	0.647815i	$0.224317\pi$
$839$			37.5286i			1.29563i	−0.761797	+	0.647815i	$0.775683\pi$
$840$		0			0
$841$	−28.9911			−0.999693
$842$	8.27125			0.285046
$843$		0			0
$844$	−4.51019			−0.155247
$845$	7.01293	−	35.5813i	0.241252	−	1.22403i
$846$		0			0
$847$			0.578306i			0.0198708i
$848$		−	1.21099i		−	0.0415857i
$849$		0			0
$850$	−3.74291	+	9.12630i	−0.128381	+	0.313029i
$851$		−	6.85900i		−	0.235124i
$852$		0			0
$853$		−	10.6746i		−	0.365490i	−0.983160	−	0.182745i	$-0.941502\pi$
$853$		−	10.6746i		−	0.365490i	0.983160	−	0.182745i	$-0.0584982\pi$
$854$	14.0737			0.481591
$855$		0			0
$856$	−2.74116			−0.0936911
$857$	−24.4885			−0.836511			−0.418256	−	0.908329i	$-0.637358\pi$
$857$	−24.4885			−0.836511			−0.418256	+	0.908329i	$0.637358\pi$
$858$		0			0
$859$			20.8489i			0.711357i	0.934608	+	0.355678i	$0.115750\pi$
$859$			20.8489i			0.711357i	−0.934608	+	0.355678i	$0.884250\pi$
$860$	−0.0163804	+	0.0831089i	−0.000558568	+	0.00283399i
$861$		0			0
$862$		−	11.3898i		−	0.387937i
$863$		−	3.16859i		−	0.107860i	−0.998545	−	0.0539300i	$-0.982825\pi$
$863$		−	3.16859i		−	0.107860i	0.998545	−	0.0539300i	$-0.0171748\pi$
$864$		0			0
$865$	3.58069	−	18.1672i	0.121747	−	0.617704i
$866$	8.60214			0.292312
$867$		0			0
$868$	13.2462	−	9.05121i	0.449607	−	0.307218i
$869$			33.1580i			1.12481i
$870$		0			0
$871$			44.8950i			1.52121i
$872$	−8.96348			−0.303542
$873$		0			0
$874$			18.2904i			0.618680i
$875$	−26.8799	−	17.7574i	−0.908705	−	0.600309i
$876$		0			0
$877$		−	3.66461i		−	0.123745i	−0.998084	−	0.0618726i	$-0.980293\pi$
$877$		−	3.66461i		−	0.123745i	0.998084	−	0.0618726i	$-0.0197072\pi$
$878$	16.7228			0.564366
$879$		0			0
$880$	−1.44714	+	7.34229i	−0.0487830	+	0.247509i
$881$	32.7614			1.10376			0.551880	−	0.833923i	$-0.313911\pi$
$881$	32.7614			1.10376			0.551880	+	0.833923i	$0.313911\pi$
$882$		0			0
$883$	11.3759			0.382831			0.191416	−	0.981509i	$-0.438692\pi$
$883$	11.3759			0.382831			0.191416	+	0.981509i	$0.438692\pi$
$884$			10.6638i			0.358663i
$885$		0			0
$886$	−7.92821			−0.266353
$887$	−21.2056			−0.712015			−0.356007	−	0.934483i	$-0.615862\pi$
$887$	−21.2056			−0.712015			−0.356007	+	0.934483i	$0.615862\pi$
$888$		0			0
$889$		−	10.5963i		−	0.355388i
$890$	−5.91936	+	30.0329i	−0.198418	+	1.00671i
$891$		0			0
$892$	26.4808			0.886641
$893$	17.8188			0.596284
$894$		0			0
$895$	−8.29218	+	42.0718i	−0.277177	+	1.40630i
$896$		−	2.88146i		−	0.0962628i
$897$		0			0
$898$	10.7160			0.357596
$899$	0.296418	+	0.433801i	0.00988611	+	0.0144681i
$900$		0			0
$901$	2.38905			0.0795908
$902$			15.1156i			0.503295i
$903$		0			0
$904$	−19.0697			−0.634248
$905$	−34.3362	−	6.76753i	−1.14137	−	0.224960i
$906$		0			0
$907$			52.1622i			1.73202i	0.500030	+	0.866008i	$0.333322\pi$
$907$			52.1622i			1.73202i	−0.500030	+	0.866008i	$0.666678\pi$
$908$	15.9176			0.528243
$909$		0			0
$910$	−34.1705	−	6.73487i	−1.13274	−	0.223259i
$911$	−53.4403			−1.77056			−0.885278	−	0.465061i	$-0.846032\pi$
$911$	−53.4403			−1.77056			−0.885278	+	0.465061i	$0.846032\pi$
$912$		0			0
$913$			28.5656i			0.945383i
$914$	25.1676			0.832470
$915$		0			0
$916$		−	27.6926i		−	0.914988i
$917$	50.6912			1.67397
$918$		0			0
$919$	0.867910			0.0286297			0.0143149	−	0.999898i	$-0.495443\pi$
$919$	0.867910			0.0286297			0.0143149	+	0.999898i	$0.495443\pi$
$920$	15.3266	+	3.02081i	0.505302	+	0.0995931i
$921$		0			0
$922$	19.8117			0.652465
$923$			52.4375i			1.72600i
$924$		0			0
$925$	−4.54189	−	1.86274i	−0.149336	−	0.0612464i
$926$	−30.9582			−1.01735
$927$		0			0
$928$	0.0943650			0.00309768
$929$	7.29912			0.239476			0.119738	−	0.992805i	$-0.461794\pi$
$929$	7.29912			0.239476			0.119738	+	0.992805i	$0.461794\pi$
$930$		0			0
$931$	−3.41090			−0.111788
$932$	8.50256			0.278511
$933$		0			0
$934$	3.06930			0.100430
$935$	−14.4849	−	2.85491i	−0.473707	−	0.0933657i
$936$		0			0
$937$		−	46.9600i		−	1.53412i	−0.641577	−	0.767058i	$-0.721720\pi$
$937$		−	46.9600i		−	1.53412i	0.641577	−	0.767058i	$-0.278280\pi$
$938$	23.9321			0.781411
$939$		0			0
$940$	2.94293	−	14.9315i	0.0959878	−	0.487010i
$941$	37.0890			1.20907			0.604534	−	0.796579i	$-0.293359\pi$
$941$	37.0890			1.20907			0.604534	+	0.796579i	$0.293359\pi$
$942$		0			0
$943$	31.5529			1.02750
$944$		−	1.88085i		−	0.0612164i
$945$		0			0
$946$	−0.126783			−0.00412207
$947$		−	18.6155i		−	0.604924i	−0.953161	−	0.302462i	$-0.902191\pi$
$947$		−	18.6155i		−	0.604924i	0.953161	−	0.302462i	$-0.0978085\pi$
$948$		0			0
$949$	86.0462			2.79318
$950$	12.1115	+	4.96721i	0.392948	+	0.161158i
$951$		0			0
$952$	5.68455			0.184237
$953$			38.8772i			1.25936i	0.776856	+	0.629678i	$0.216813\pi$
$953$			38.8772i			1.25936i	−0.776856	+	0.629678i	$0.783187\pi$
$954$		0			0
$955$	2.00817	+	0.395802i	0.0649827	+	0.0128078i
$956$	−25.6723			−0.830300
$957$		0			0
$958$			29.6884i			0.959190i
$959$	−10.9851			−0.354727
$960$		0			0
$961$	−11.2659	+	28.8804i	−0.363415	+	0.931627i
$962$	−5.30707			−0.171107
$963$		0			0
$964$		−	24.1458i		−	0.777683i
$965$	−5.07878	−	1.00101i	−0.163492	−	0.0322236i
$966$		0			0
$967$	19.2154			0.617926			0.308963	−	0.951074i	$-0.400018\pi$
$967$	19.2154			0.617926			0.308963	+	0.951074i	$0.400018\pi$
$968$	−0.200699			−0.00645070
$969$		0			0
$970$	−6.97004	−	1.37377i	−0.223795	−	0.0441090i
$971$			2.00820i			0.0644461i	0.999481	+	0.0322231i	$0.0102587\pi$
$971$			2.00820i			0.0644461i	−0.999481	+	0.0322231i	$0.989741\pi$
$972$		0			0
$973$	25.1445			0.806096
$974$	32.8763			1.05343
$975$		0			0
$976$			4.88421i			0.156340i
$977$	22.1519			0.708704			0.354352	−	0.935112i	$-0.384702\pi$
$977$	22.1519			0.708704			0.354352	+	0.935112i	$0.384702\pi$
$978$		0			0
$979$	−45.8153			−1.46426
$980$	−0.563339	+	2.85819i	−0.0179952	+	0.0913017i
$981$		0			0
$982$	18.4934			0.590150
$983$		−	51.4116i		−	1.63977i	−0.572525	−	0.819887i	$-0.694036\pi$
$983$		−	51.4116i		−	1.63977i	0.572525	−	0.819887i	$-0.305964\pi$
$984$		0			0
$985$	17.9142	+	3.53082i	0.570795	+	0.112501i
$986$			0.186164i			0.00592865i
$987$		0			0
$988$	14.1519			0.450233
$989$			0.264651i			0.00841543i
$990$		0			0
$991$			21.2807i			0.676004i	0.941145	+	0.338002i	$0.109751\pi$
$991$			21.2807i			0.676004i	−0.941145	+	0.338002i	$0.890249\pi$
$992$	3.14119	+	4.59706i	0.0997328	+	0.145957i
$993$		0			0
$994$	27.9528			0.886609
$995$	−36.4842	−	7.19088i	−1.15663	−	0.227966i
$996$		0			0
$997$			2.04688i			0.0648254i	0.999475	+	0.0324127i	$0.0103191\pi$
$997$			2.04688i			0.0648254i	−0.999475	+	0.0324127i	$0.989681\pi$
$998$		−	11.3300i		−	0.358646i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2790.2.e.a.2789.18	yes	32
3.2	odd	2		2790.2.e.b.2789.16	yes	32
5.4	even	2		2790.2.e.b.2789.13	yes	32
15.14	odd	2	inner	2790.2.e.a.2789.19	yes	32
31.30	odd	2	inner	2790.2.e.a.2789.17	✓	32
93.92	even	2		2790.2.e.b.2789.15	yes	32
155.154	odd	2		2790.2.e.b.2789.14	yes	32
465.464	even	2	inner	2790.2.e.a.2789.20	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2790.2.e.a.2789.17	✓	32	31.30	odd	2	inner
2790.2.e.a.2789.18	yes	32	1.1	even	1	trivial
2790.2.e.a.2789.19	yes	32	15.14	odd	2	inner
2790.2.e.a.2789.20	yes	32	465.464	even	2	inner
2790.2.e.b.2789.13	yes	32	5.4	even	2
2790.2.e.b.2789.14	yes	32	155.154	odd	2
2790.2.e.b.2789.15	yes	32	93.92	even	2
2790.2.e.b.2789.16	yes	32	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2790.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.432401 - 2.19386i) q^{5} +2.88146i q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.432401 - 2.19386i) q^{5} +2.88146i q^{7} -1.00000 q^{8} +(-0.432401 + 2.19386i) q^{10} -3.34674 q^{11} +5.40542 q^{13} -2.88146i q^{14} +1.00000 q^{16} +1.97280i q^{17} +2.61810 q^{19} +(0.432401 - 2.19386i) q^{20} +3.34674 q^{22} -6.98612i q^{23} +(-4.62606 - 1.89726i) q^{25} -5.40542 q^{26} +2.88146i q^{28} -0.0943650 q^{29} +(-3.14119 - 4.59706i) q^{31} -1.00000 q^{32} -1.97280i q^{34} +(6.32153 + 1.24595i) q^{35} +0.981805 q^{37} -2.61810 q^{38} +(-0.432401 + 2.19386i) q^{40} +4.51651i q^{41} -0.0378825 q^{43} -3.34674 q^{44} +6.98612i q^{46} +6.80601 q^{47} -1.30281 q^{49} +(4.62606 + 1.89726i) q^{50} +5.40542 q^{52} -1.21099i q^{53} +(-1.44714 + 7.34229i) q^{55} -2.88146i q^{56} +0.0943650 q^{58} -1.88085i q^{59} +4.88421i q^{61} +(3.14119 + 4.59706i) q^{62} +1.00000 q^{64} +(2.33731 - 11.8587i) q^{65} +8.30555i q^{67} +1.97280i q^{68} +(-6.32153 - 1.24595i) q^{70} +9.70091i q^{71} +15.9185 q^{73} -0.981805 q^{74} +2.61810 q^{76} -9.64351i q^{77} -9.90754i q^{79} +(0.432401 - 2.19386i) q^{80} -4.51651i q^{82} -8.53533i q^{83} +(4.32805 + 0.853042i) q^{85} +0.0378825 q^{86} +3.34674 q^{88} +13.6895 q^{89} +15.5755i q^{91} -6.98612i q^{92} -6.80601 q^{94} +(1.13207 - 5.74375i) q^{95} +3.17707i q^{97} +1.30281 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} + 32 q^{4} - 4 q^{5} - 32 q^{8}+O(q^{10}) \) 32 * q - 32 * q^2 + 32 * q^4 - 4 * q^5 - 32 * q^8	\( 32 q - 32 q^{2} + 32 q^{4} - 4 q^{5} - 32 q^{8} + 4 q^{10} + 32 q^{16} - 16 q^{19} - 4 q^{20} + 4 q^{25} - 32 q^{32} - 8 q^{35} + 16 q^{38} + 4 q^{40} + 8 q^{47} - 24 q^{49} - 4 q^{50} + 32 q^{64} + 8 q^{70} - 16 q^{76} - 4 q^{80} - 8 q^{94} + 4 q^{95} + 24 q^{98}+O(q^{100}) \) 32 * q - 32 * q^2 + 32 * q^4 - 4 * q^5 - 32 * q^8 + 4 * q^10 + 32 * q^16 - 16 * q^19 - 4 * q^20 + 4 * q^25 - 32 * q^32 - 8 * q^35 + 16 * q^38 + 4 * q^40 + 8 * q^47 - 24 * q^49 - 4 * q^50 + 32 * q^64 + 8 * q^70 - 16 * q^76 - 4 * q^80 - 8 * q^94 + 4 * q^95 + 24 * q^98

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