LMFDB - Embedded newform 1008.2.s.o.865.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(289,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1008.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.s (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1008.865
Dual form			1008.2.s.o.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})$	$q+(1.50000 + 2.59808i) q^{5} +(0.500000 + 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{11} +2.00000 q^{13} +(3.00000 - 5.19615i) q^{17} +(1.00000 + 1.73205i) q^{19} +(3.00000 + 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} -9.00000 q^{29} +(-3.50000 + 6.06218i) q^{31} +(-6.00000 + 5.19615i) q^{35} +(5.00000 + 8.66025i) q^{37} +4.00000 q^{43} +(-6.00000 - 10.3923i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-1.50000 + 2.59808i) q^{53} +9.00000 q^{55} +(1.50000 - 2.59808i) q^{59} +(2.00000 + 3.46410i) q^{61} +(3.00000 + 5.19615i) q^{65} +(1.00000 - 1.73205i) q^{67} +(-1.00000 + 1.73205i) q^{73} +(7.50000 + 2.59808i) q^{77} +(2.50000 + 4.33013i) q^{79} +9.00000 q^{83} +18.0000 q^{85} +(-3.00000 - 5.19615i) q^{89} +(1.00000 + 5.19615i) q^{91} +(-3.00000 + 5.19615i) q^{95} -13.0000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{5} + q^{7}+O(q^{10}) $ 2 * q + 3 * q^5 + q^7	$ 2 q + 3 q^{5} + q^{7} + 3 q^{11} + 4 q^{13} + 6 q^{17} + 2 q^{19} + 6 q^{23} - 4 q^{25} - 18 q^{29} - 7 q^{31} - 12 q^{35} + 10 q^{37} + 8 q^{43} - 12 q^{47} - 13 q^{49} - 3 q^{53} + 18 q^{55} + 3 q^{59} + 4 q^{61} + 6 q^{65} + 2 q^{67} - 2 q^{73} + 15 q^{77} + 5 q^{79} + 18 q^{83} + 36 q^{85} - 6 q^{89} + 2 q^{91} - 6 q^{95} - 26 q^{97}+O(q^{100}) $ 2 * q + 3 * q^5 + q^7 + 3 * q^11 + 4 * q^13 + 6 * q^17 + 2 * q^19 + 6 * q^23 - 4 * q^25 - 18 * q^29 - 7 * q^31 - 12 * q^35 + 10 * q^37 + 8 * q^43 - 12 * q^47 - 13 * q^49 - 3 * q^53 + 18 * q^55 + 3 * q^59 + 4 * q^61 + 6 * q^65 + 2 * q^67 - 2 * q^73 + 15 * q^77 + 5 * q^79 + 18 * q^83 + 36 * q^85 - 6 * q^89 + 2 * q^91 - 6 * q^95 - 26 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$		0			0
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$		0			0
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	0.359211	+	0.933257i	$0.383046\pi$
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.00000	+	5.19615i	−1.01419	+	0.878310i
$36$		0			0
$37$	5.00000	+	8.66025i	0.821995	+	1.42374i	0.904194	+	0.427121i	$0.140472\pi$
$37$	5.00000	+	8.66025i	0.821995	+	1.42374i	−0.0821995	+	0.996616i	$0.526194\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.00000	−	10.3923i	−0.875190	−	1.51587i	−0.856560	−	0.516047i	$-0.827403\pi$
$47$	−6.00000	−	10.3923i	−0.875190	−	1.51587i	−0.0186297	−	0.999826i	$-0.505930\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$		0			0
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.50000	+	2.59808i	0.854704	+	0.296078i
$78$		0			0
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	0.971698	−	0.236225i	$-0.0759104\pi$
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	−0.690426	+	0.723403i	$0.742577\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$		0			0
$85$	18.0000			1.95237
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	1.00000	+	5.19615i	0.104828	+	0.544705i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$		0			0
$97$	−13.0000			−1.31995			−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000			−1.31995			−0.659975	+	0.751288i	$0.729433\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	−0.927030	−	0.374987i	$-0.877647\pi$
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	0.138767	−	0.990325i	$-0.455686\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$		0			0
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	−9.00000	+	15.5885i	−0.839254	+	1.45363i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	15.0000	+	5.19615i	1.37505	+	0.476331i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	1.00000			0.0887357			0.0443678	−	0.999015i	$-0.485873\pi$
$127$	1.00000			0.0887357			0.0443678	+	0.999015i	$0.485873\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	0.981824	+	0.189794i	$0.0607819\pi$
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	−0.326546	+	0.945181i	$0.605885\pi$
$132$		0			0
$133$	−4.00000	+	3.46410i	−0.346844	+	0.300376i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		0			0
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$		0			0
$145$	−13.5000	−	23.3827i	−1.12111	−	1.94183i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	2.50000	−	4.33013i	0.203447	−	0.352381i	−0.746190	−	0.665733i	$-0.768119\pi$
$151$	2.50000	−	4.33013i	0.203447	−	0.352381i	0.949637	+	0.313353i	$0.101452\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−21.0000			−1.68676
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−12.0000	+	10.3923i	−0.945732	+	0.819028i
$162$		0			0
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	0.601035	−	0.799223i	$-0.294755\pi$
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	−0.992665	+	0.120900i	$0.961422\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−18.0000			−1.39288			−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000			−1.39288			−0.696441	+	0.717614i	$0.745234\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	−10.0000	−	3.46410i	−0.755929	−	0.261861i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−15.0000	+	25.9808i	−1.10282	+	1.91014i
$186$		0			0
$187$	−9.00000	−	15.5885i	−0.658145	−	1.13994i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$		0			0
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	−0.712123	−	0.702055i	$-0.752266\pi$
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	0.964059	+	0.265689i	$0.0855996\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.50000	−	23.3827i	−0.315838	−	1.64114i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.00000			0.415029
$210$		0			0
$211$	16.0000			1.10149			0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000			1.10149			0.550743	+	0.834675i	$0.314345\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.00000	+	10.3923i	0.409197	+	0.708749i
$216$		0			0
$217$	−17.5000	−	6.06218i	−1.18798	−	0.411527i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	1.00000			0.0669650			0.0334825	−	0.999439i	$-0.489340\pi$
$223$	1.00000			0.0669650			0.0334825	+	0.999439i	$0.489340\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	−0.999997	−	0.00254715i	$-0.999189\pi$
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	0.502204	+	0.864749i	$0.332523\pi$
$228$		0			0
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	−0.980401	−	0.197013i	$-0.936876\pi$
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	0.319582	−	0.947559i	$-0.396457\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$		0			0
$235$	18.0000	−	31.1769i	1.17419	−	2.03376i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$		0			0
$241$	−11.5000	+	19.9186i	−0.740780	+	1.28307i	0.211360	+	0.977408i	$0.432211\pi$
$241$	−11.5000	+	19.9186i	−0.740780	+	1.28307i	−0.952141	+	0.305661i	$0.901123\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−16.5000	−	12.9904i	−1.05415	−	0.829925i
$246$		0			0
$247$	2.00000	+	3.46410i	0.127257	+	0.220416i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.00000			0.568075			0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000			0.568075			0.284037	+	0.958813i	$0.408326\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$		0			0
$259$	−20.0000	+	17.3205i	−1.24274	+	1.07624i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$		0			0
$265$	−9.00000			−0.552866
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	−0.908124	−	0.418701i	$-0.862486\pi$
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	0.816668	+	0.577108i	$0.195819\pi$
$270$		0			0
$271$	−9.50000	−	16.4545i	−0.577084	−	0.999539i	−0.995812	−	0.0914269i	$-0.970857\pi$
$271$	−9.50000	−	16.4545i	−0.577084	−	0.999539i	0.418728	−	0.908112i	$-0.362476\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$		0			0
$277$	2.00000	−	3.46410i	0.120168	−	0.208138i	−0.799666	−	0.600446i	$-0.794990\pi$
$277$	2.00000	−	3.46410i	0.120168	−	0.208138i	0.919834	+	0.392308i	$0.128323\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	−0.399188	−	0.916869i	$-0.630708\pi$
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	0.993626	−	0.112728i	$-0.0359589\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$		0			0
$295$	9.00000			0.524000
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	2.00000	+	10.3923i	0.115278	+	0.599002i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.00000	+	10.3923i	−0.343559	+	0.595062i
$306$		0			0
$307$	−26.0000			−1.48390			−0.741949	−	0.670456i	$-0.766098\pi$
$307$	−26.0000			−1.48390			−0.741949	+	0.670456i	$0.766098\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$		0			0
$313$	−8.50000	−	14.7224i	−0.480448	−	0.832161i	0.519300	−	0.854592i	$-0.326193\pi$
$313$	−8.50000	−	14.7224i	−0.480448	−	0.832161i	−0.999748	+	0.0224310i	$0.992859\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.5000	+	18.1865i	0.589739	+	1.02146i	0.994266	+	0.106932i	$0.0341026\pi$
$317$	10.5000	+	18.1865i	0.589739	+	1.02146i	−0.404528	+	0.914526i	$0.632564\pi$
$318$		0			0
$319$	−13.5000	+	23.3827i	−0.755855	+	1.30918i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	12.0000			0.667698
$324$		0			0
$325$	−4.00000	+	6.92820i	−0.221880	+	0.384308i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	24.0000	−	20.7846i	1.32316	−	1.14589i
$330$		0			0
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.00000			0.327815
$336$		0			0
$337$	5.00000			0.272367			0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000			0.272367			0.136184	+	0.990684i	$0.456516\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	10.5000	+	18.1865i	0.568607	+	0.984856i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.0000	−	25.9808i	−0.791670	−	1.37121i	−0.924932	−	0.380131i	$-0.875879\pi$
$359$	−15.0000	−	25.9808i	−0.791670	−	1.37121i	0.133263	−	0.991081i	$-0.457455\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.00000			−0.314054
$366$		0			0
$367$	−18.5000	+	32.0429i	−0.965692	+	1.67263i	−0.257948	+	0.966159i	$0.583046\pi$
$367$	−18.5000	+	32.0429i	−0.965692	+	1.67263i	−0.707744	+	0.706469i	$0.750287\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.50000	−	2.59808i	−0.389381	−	0.134885i
$372$		0			0
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−18.0000			−0.927047
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−15.0000	−	25.9808i	−0.766464	−	1.32755i	−0.939469	−	0.342634i	$-0.888681\pi$
$383$	−15.0000	−	25.9808i	−0.766464	−	1.32755i	0.173005	−	0.984921i	$-0.444652\pi$
$384$		0			0
$385$	4.50000	+	23.3827i	0.229341	+	1.19169i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$		0			0
$391$	36.0000			1.82060
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.50000	+	12.9904i	−0.377366	+	0.653617i
$396$		0			0
$397$	−4.00000	−	6.92820i	−0.200754	−	0.347717i	0.748017	−	0.663679i	$-0.231006\pi$
$397$	−4.00000	−	6.92820i	−0.200754	−	0.347717i	−0.948772	+	0.315963i	$0.897673\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	−0.992932	−	0.118686i	$-0.962132\pi$
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	0.393680	−	0.919247i	$-0.371202\pi$
$402$		0			0
$403$	−7.00000	+	12.1244i	−0.348695	+	0.603957i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	30.0000			1.48704
$408$		0			0
$409$	−5.50000	+	9.52628i	−0.271957	+	0.471044i	−0.969363	−	0.245633i	$-0.921004\pi$
$409$	−5.50000	+	9.52628i	−0.271957	+	0.471044i	0.697406	+	0.716677i	$0.254338\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.50000	+	2.59808i	0.369051	+	0.127843i
$414$		0			0
$415$	13.5000	+	23.3827i	0.662689	+	1.14781i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−36.0000			−1.75872			−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000			−1.75872			−0.879358	+	0.476162i	$0.842028\pi$
$420$		0			0
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.0000	+	20.7846i	0.582086	+	1.00820i
$426$		0			0
$427$	−8.00000	+	6.92820i	−0.387147	+	0.335279i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$		0			0
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.00000	+	10.3923i	−0.287019	+	0.497131i
$438$		0			0
$439$	−9.50000	−	16.4545i	−0.453410	−	0.785330i	0.545185	−	0.838316i	$-0.316459\pi$
$439$	−9.50000	−	16.4545i	−0.453410	−	0.785330i	−0.998595	+	0.0529862i	$0.983126\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.50000	+	12.9904i	0.356336	+	0.617192i	0.987346	−	0.158583i	$-0.0506926\pi$
$443$	7.50000	+	12.9904i	0.356336	+	0.617192i	−0.631010	+	0.775775i	$0.717359\pi$
$444$		0			0
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−12.0000	+	10.3923i	−0.562569	+	0.487199i
$456$		0			0
$457$	6.50000	+	11.2583i	0.304057	+	0.526642i	0.977051	−	0.213006i	$-0.0683253\pi$
$457$	6.50000	+	11.2583i	0.304057	+	0.526642i	−0.672994	+	0.739648i	$0.734992\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	0.693153	−	0.720791i	$-0.256221\pi$
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	−0.970799	+	0.239892i	$0.922888\pi$
$468$		0			0
$469$	5.00000	+	1.73205i	0.230879	+	0.0799787i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	6.00000	−	10.3923i	0.275880	−	0.477839i
$474$		0			0
$475$	−8.00000			−0.367065
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$		0			0
$481$	10.0000	+	17.3205i	0.455961	+	0.789747i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−19.5000	−	33.7750i	−0.885449	−	1.53364i
$486$		0			0
$487$	5.50000	−	9.52628i	0.249229	−	0.431677i	−0.714083	−	0.700061i	$-0.753156\pi$
$487$	5.50000	−	9.52628i	0.249229	−	0.431677i	0.963312	+	0.268384i	$0.0864896\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.00000			0.406164			0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000			0.406164			0.203082	+	0.979162i	$0.434904\pi$
$492$		0			0
$493$	−27.0000	+	46.7654i	−1.21602	+	2.10621i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	19.0000	+	32.9090i	0.850557	+	1.47321i	0.880707	+	0.473662i	$0.157068\pi$
$499$	19.0000	+	32.9090i	0.850557	+	1.47321i	−0.0301498	+	0.999545i	$0.509598\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.0000			0.802580			0.401290	−	0.915951i	$-0.368562\pi$
$503$	18.0000			0.802580			0.401290	+	0.915951i	$0.368562\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	0.650556	−	0.759458i	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$		0			0
$511$	−5.00000	−	1.73205i	−0.221187	−	0.0766214i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	24.0000	−	41.5692i	1.05757	−	1.83176i
$516$		0			0
$517$	−36.0000			−1.58328
$518$		0			0
$519$		0			0
$520$		0			0
$521$	12.0000	−	20.7846i	0.525730	−	0.910590i	−0.473821	−	0.880621i	$-0.657126\pi$
$521$	12.0000	−	20.7846i	0.525730	−	0.910590i	0.999551	−	0.0299693i	$-0.00954094\pi$
$522$		0			0
$523$	13.0000	+	22.5167i	0.568450	+	0.984585i	0.996719	+	0.0809336i	$0.0257902\pi$
$523$	13.0000	+	22.5167i	0.568450	+	0.984585i	−0.428269	+	0.903651i	$0.640876\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	21.0000	+	36.3731i	0.914774	+	1.58444i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	4.50000	−	7.79423i	0.194552	−	0.336974i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.00000	+	20.7846i	−0.129219	+	0.895257i
$540$		0			0
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	0.985162	−	0.171628i	$-0.0549027\pi$
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	−0.641215	+	0.767361i	$0.721569\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	30.0000			1.28506
$546$		0			0
$547$	−14.0000			−0.598597			−0.299298	−	0.954160i	$-0.596753\pi$
$547$	−14.0000			−0.598597			−0.299298	+	0.954160i	$0.596753\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.00000	−	15.5885i	−0.383413	−	0.664091i
$552$		0			0
$553$	−10.0000	+	8.66025i	−0.425243	+	0.368271i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.50000	−	12.9904i	0.317785	−	0.550420i	−0.662240	−	0.749291i	$-0.730394\pi$
$557$	7.50000	−	12.9904i	0.317785	−	0.550420i	0.980026	+	0.198871i	$0.0637276\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	−0.832684	−	0.553748i	$-0.813197\pi$
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	0.895902	+	0.444252i	$0.146530\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	0.987786	+	0.155815i	$0.0498003\pi$
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	−0.358954	+	0.933355i	$0.616866\pi$
$570$		0			0
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	−0.308443	−	0.951243i	$-0.599808\pi$
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	0.978022	−	0.208502i	$-0.0668588\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−24.0000			−1.00087
$576$		0			0
$577$	0.500000	−	0.866025i	0.0208153	−	0.0360531i	−0.855430	−	0.517918i	$-0.826707\pi$
$577$	0.500000	−	0.866025i	0.0208153	−	0.0360531i	0.876245	+	0.481865i	$0.160040\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.50000	+	23.3827i	0.186691	+	0.970077i
$582$		0			0
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	27.0000			1.11441			0.557205	−	0.830375i	$-0.311874\pi$
$587$	27.0000			1.11441			0.557205	+	0.830375i	$0.311874\pi$
$588$		0			0
$589$	−14.0000			−0.576860
$590$		0			0
$591$		0			0
$592$		0			0
$593$	15.0000	+	25.9808i	0.615976	+	1.06690i	0.990212	+	0.139569i	$0.0445716\pi$
$593$	15.0000	+	25.9808i	0.615976	+	1.06690i	−0.374236	+	0.927333i	$0.622095\pi$
$594$		0			0
$595$	9.00000	+	46.7654i	0.368964	+	1.91719i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	−0.377869	−	0.925859i	$-0.623343\pi$
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	0.990752	−	0.135686i	$-0.0433238\pi$
$600$		0			0
$601$	23.0000			0.938190			0.469095	−	0.883148i	$-0.344580\pi$
$601$	23.0000			0.938190			0.469095	+	0.883148i	$0.344580\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.00000	+	5.19615i	−0.121967	+	0.211254i
$606$		0			0
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	0.703429	−	0.710766i	$-0.251651\pi$
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	−0.967256	+	0.253804i	$0.918318\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−12.0000	−	20.7846i	−0.485468	−	0.840855i
$612$		0			0
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	0.474509	+	0.880251i	$0.342626\pi$
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	−0.999574	+	0.0291886i	$0.990708\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−36.0000			−1.44931			−0.724653	−	0.689114i	$-0.758000\pi$
$617$	−36.0000			−1.44931			−0.724653	+	0.689114i	$0.758000\pi$
$618$		0			0
$619$	−2.00000	+	3.46410i	−0.0803868	+	0.139234i	−0.903416	−	0.428765i	$-0.858949\pi$
$619$	−2.00000	+	3.46410i	−0.0803868	+	0.139234i	0.823029	+	0.567999i	$0.192282\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	12.0000	−	10.3923i	0.480770	−	0.416359i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	60.0000			2.39236
$630$		0			0
$631$	37.0000			1.47295			0.736473	−	0.676467i	$-0.236490\pi$
$631$	37.0000			1.47295			0.736473	+	0.676467i	$0.236490\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.50000	+	2.59808i	0.0595257	+	0.103102i
$636$		0			0
$637$	−13.0000	+	5.19615i	−0.515079	+	0.205879i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−6.00000	+	10.3923i	−0.236986	+	0.410471i	−0.959848	−	0.280521i	$-0.909493\pi$
$641$	−6.00000	+	10.3923i	−0.236986	+	0.410471i	0.722862	+	0.690992i	$0.242826\pi$
$642$		0			0
$643$	−38.0000			−1.49857			−0.749287	−	0.662246i	$-0.769604\pi$
$643$	−38.0000			−1.49857			−0.749287	+	0.662246i	$0.769604\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	−0.723645	−	0.690172i	$-0.757535\pi$
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	0.959529	+	0.281609i	$0.0908680\pi$
$648$		0			0
$649$	−4.50000	−	7.79423i	−0.176640	−	0.305950i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	0.941248	+	0.337715i	$0.109654\pi$
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	−0.178154	+	0.984003i	$0.557013\pi$
$654$		0			0
$655$	−22.5000	+	38.9711i	−0.879148	+	1.52273i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	−0.155235	−	0.987878i	$-0.549613\pi$
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	0.933144	−	0.359502i	$-0.117053\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−15.0000	−	5.19615i	−0.581675	−	0.201498i
$666$		0			0
$667$	−27.0000	−	46.7654i	−1.04544	−	1.81076i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	12.0000			0.463255
$672$		0			0
$673$	17.0000			0.655302			0.327651	−	0.944799i	$-0.393743\pi$
$673$	17.0000			0.655302			0.327651	+	0.944799i	$0.393743\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	−0.986695	−	0.162581i	$-0.948018\pi$
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	0.352549	−	0.935793i	$-0.385315\pi$
$678$		0			0
$679$	−6.50000	−	33.7750i	−0.249447	−	1.29617i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−25.5000	+	44.1673i	−0.975730	+	1.69001i	−0.298227	+	0.954495i	$0.596395\pi$
$683$	−25.5000	+	44.1673i	−0.975730	+	1.69001i	−0.677503	+	0.735520i	$0.736938\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.00000	+	5.19615i	−0.114291	+	0.197958i
$690$		0			0
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	0.991460	+	0.130410i	$0.0416295\pi$
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	−0.382791	+	0.923835i	$0.625037\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.00000	−	5.19615i	−0.113796	−	0.197101i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−9.00000			−0.339925			−0.169963	−	0.985451i	$-0.554365\pi$
$701$	−9.00000			−0.339925			−0.169963	+	0.985451i	$0.554365\pi$
$702$		0			0
$703$	−10.0000	+	17.3205i	−0.377157	+	0.653255i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	15.0000	+	5.19615i	0.564133	+	0.195421i
$708$		0			0
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	0.704118	−	0.710083i	$-0.251342\pi$
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	−0.967009	+	0.254743i	$0.918009\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−42.0000			−1.57291
$714$		0			0
$715$	18.0000			0.673162
$716$		0			0
$717$		0			0
$718$		0			0
$719$	21.0000	+	36.3731i	0.783168	+	1.35649i	0.930087	+	0.367338i	$0.119731\pi$
$719$	21.0000	+	36.3731i	0.783168	+	1.35649i	−0.146920	+	0.989148i	$0.546936\pi$
$720$		0			0
$721$	32.0000	−	27.7128i	1.19174	−	1.03208i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	18.0000	−	31.1769i	0.668503	−	1.15788i
$726$		0			0
$727$	31.0000			1.14973			0.574863	−	0.818250i	$-0.305055\pi$
$727$	31.0000			1.14973			0.574863	+	0.818250i	$0.305055\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$		0			0
$733$	−10.0000	−	17.3205i	−0.369358	−	0.639748i	0.620107	−	0.784517i	$-0.287089\pi$
$733$	−10.0000	−	17.3205i	−0.369358	−	0.639748i	−0.989465	+	0.144770i	$0.953756\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.00000	−	5.19615i	−0.110506	−	0.191403i
$738$		0			0
$739$	13.0000	−	22.5167i	0.478213	−	0.828289i	−0.521475	−	0.853266i	$-0.674618\pi$
$739$	13.0000	−	22.5167i	0.478213	−	0.828289i	0.999688	+	0.0249776i	$0.00795146\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−54.0000			−1.98107			−0.990534	−	0.137268i	$-0.956168\pi$
$743$	−54.0000			−1.98107			−0.990534	+	0.137268i	$0.956168\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.00000	−	5.19615i	0.219235	−	0.189863i
$750$		0			0
$751$	11.5000	+	19.9186i	0.419641	+	0.726839i	0.995903	−	0.0904254i	$-0.0288227\pi$
$751$	11.5000	+	19.9186i	0.419641	+	0.726839i	−0.576262	+	0.817265i	$0.695489\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	15.0000			0.545906
$756$		0			0
$757$	−28.0000			−1.01768			−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000			−1.01768			−0.508839	+	0.860862i	$0.669925\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	−0.942207	−	0.335032i	$-0.891253\pi$
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	0.180957	−	0.983491i	$-0.442080\pi$
$762$		0			0
$763$	25.0000	+	8.66025i	0.905061	+	0.313522i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.00000	−	5.19615i	0.108324	−	0.187622i
$768$		0			0
$769$	5.00000			0.180305			0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000			0.180305			0.0901523	+	0.995928i	$0.471265\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$		0			0
$775$	−14.0000	−	24.2487i	−0.502895	−	0.871039i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	12.0000			0.428298
$786$		0			0
$787$	−8.00000	+	13.8564i	−0.285169	+	0.493928i	−0.972650	−	0.232275i	$-0.925383\pi$
$787$	−8.00000	+	13.8564i	−0.285169	+	0.493928i	0.687481	+	0.726202i	$0.258716\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4.00000	+	6.92820i	0.142044	+	0.246028i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−27.0000			−0.956389			−0.478195	−	0.878254i	$-0.658709\pi$
$797$	−27.0000			−0.956389			−0.478195	+	0.878254i	$0.658709\pi$
$798$		0			0
$799$	−72.0000			−2.54718
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$		0			0
$805$	−45.0000	−	15.5885i	−1.58604	−	0.549421i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6.00000	+	10.3923i	−0.210949	+	0.365374i	−0.952012	−	0.306062i	$-0.900989\pi$
$809$	−6.00000	+	10.3923i	−0.210949	+	0.365374i	0.741063	+	0.671436i	$0.234322\pi$
$810$		0			0
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	15.0000	−	25.9808i	0.525427	−	0.910066i
$816$		0			0
$817$	4.00000	+	6.92820i	0.139942	+	0.242387i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.50000	−	12.9904i	−0.261752	−	0.453367i	0.704956	−	0.709251i	$-0.250967\pi$
$821$	−7.50000	−	12.9904i	−0.261752	−	0.453367i	−0.966708	+	0.255884i	$0.917634\pi$
$822$		0			0
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	−0.971102	−	0.238664i	$-0.923291\pi$
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	0.692240	+	0.721668i	$0.256624\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	9.00000			0.312961			0.156480	−	0.987681i	$-0.449985\pi$
$827$	9.00000			0.312961			0.156480	+	0.987681i	$0.449985\pi$
$828$		0			0
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	−0.882869	−	0.469620i	$-0.844391\pi$
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	0.848137	+	0.529777i	$0.177724\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−6.00000	+	41.5692i	−0.207888	+	1.44029i
$834$		0			0
$835$	−27.0000	−	46.7654i	−0.934374	−	1.61838i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−54.0000			−1.86429			−0.932144	−	0.362089i	$-0.882064\pi$
$839$	−54.0000			−1.86429			−0.932144	+	0.362089i	$0.882064\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−13.5000	−	23.3827i	−0.464414	−	0.804389i
$846$		0			0
$847$	−4.00000	+	3.46410i	−0.137442	+	0.119028i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−30.0000	+	51.9615i	−1.02839	+	1.78122i
$852$		0			0
$853$	−46.0000			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.00000	+	10.3923i	−0.204956	+	0.354994i	−0.950119	−	0.311888i	$-0.899038\pi$
$857$	−6.00000	+	10.3923i	−0.204956	+	0.354994i	0.745163	+	0.666883i	$0.232372\pi$
$858$		0			0
$859$	−8.00000	−	13.8564i	−0.272956	−	0.472774i	0.696661	−	0.717400i	$-0.254668\pi$
$859$	−8.00000	−	13.8564i	−0.272956	−	0.472774i	−0.969618	+	0.244626i	$0.921335\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	0.912558	−	0.408946i	$-0.134104\pi$
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	−0.810437	+	0.585826i	$0.800770\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	15.0000			0.508840
$870$		0			0
$871$	2.00000	−	3.46410i	0.0677674	−	0.117377i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.50000	+	7.79423i	0.0507093	+	0.263493i
$876$		0			0
$877$	−28.0000	−	48.4974i	−0.945493	−	1.63764i	−0.754761	−	0.655999i	$-0.772247\pi$
$877$	−28.0000	−	48.4974i	−0.945493	−	1.63764i	−0.190731	−	0.981642i	$-0.561086\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.00000	+	5.19615i	0.100730	+	0.174470i	0.911986	−	0.410222i	$-0.134549\pi$
$887$	3.00000	+	5.19615i	0.100730	+	0.174470i	−0.811256	+	0.584692i	$0.801215\pi$
$888$		0			0
$889$	0.500000	+	2.59808i	0.0167695	+	0.0871367i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	12.0000	−	20.7846i	0.401565	−	0.695530i
$894$		0			0
$895$	36.0000			1.20335
$896$		0			0
$897$		0			0
$898$		0			0
$899$	31.5000	−	54.5596i	1.05058	−	1.81966i
$900$		0			0
$901$	9.00000	+	15.5885i	0.299833	+	0.519327i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	30.0000	+	51.9615i	0.997234	+	1.72726i
$906$		0			0
$907$	25.0000	−	43.3013i	0.830111	−	1.43780i	−0.0678380	−	0.997696i	$-0.521610\pi$
$907$	25.0000	−	43.3013i	0.830111	−	1.43780i	0.897949	−	0.440099i	$-0.145057\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	13.5000	−	23.3827i	0.446785	−	0.773854i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−30.0000	+	25.9808i	−0.990687	+	0.857960i
$918$		0			0
$919$	−14.0000	−	24.2487i	−0.461817	−	0.799891i	0.537234	−	0.843433i	$-0.319469\pi$
$919$	−14.0000	−	24.2487i	−0.461817	−	0.799891i	−0.999052	+	0.0435419i	$0.986136\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−40.0000			−1.31519
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−12.0000	−	20.7846i	−0.393707	−	0.681921i	0.599228	−	0.800578i	$-0.295474\pi$
$929$	−12.0000	−	20.7846i	−0.393707	−	0.681921i	−0.992935	+	0.118657i	$0.962141\pi$
$930$		0			0
$931$	−11.0000	−	8.66025i	−0.360510	−	0.283828i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	27.0000	−	46.7654i	0.882994	−	1.52939i
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	−0.717496	−	0.696563i	$-0.754712\pi$
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	0.961989	+	0.273088i	$0.0880451\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	0.751918	−	0.659256i	$-0.229129\pi$
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	−0.946892	+	0.321552i	$0.895796\pi$
$948$		0			0
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	36.0000			1.16615			0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000			1.16615			0.583077	+	0.812417i	$0.301849\pi$
$954$		0			0
$955$	18.0000	−	31.1769i	0.582466	−	1.00886i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	15.0000	+	5.19615i	0.484375	+	0.167793i
$960$		0			0
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	21.0000			0.676014
$966$		0			0
$967$	−29.0000			−0.932577			−0.466289	−	0.884633i	$-0.654409\pi$
$967$	−29.0000			−0.932577			−0.466289	+	0.884633i	$0.654409\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−19.5000	−	33.7750i	−0.625785	−	1.08389i	−0.988389	−	0.151948i	$-0.951445\pi$
$971$	−19.5000	−	33.7750i	−0.625785	−	1.08389i	0.362604	−	0.931943i	$-0.381888\pi$
$972$		0			0
$973$	−1.00000	−	5.19615i	−0.0320585	−	0.166581i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	−0.945899	−	0.324462i	$-0.894817\pi$
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	0.753942	+	0.656941i	$0.228150\pi$
$978$		0			0
$979$	−18.0000			−0.575282
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	−0.991453	−	0.130465i	$-0.958353\pi$
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	0.608712	+	0.793391i	$0.291686\pi$
$984$		0			0
$985$	27.0000	+	46.7654i	0.860292	+	1.49007i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.0000	+	20.7846i	0.381578	+	0.660912i
$990$		0			0
$991$	−9.50000	+	16.4545i	−0.301777	+	0.522694i	−0.976539	−	0.215342i	$-0.930913\pi$
$991$	−9.50000	+	16.4545i	−0.301777	+	0.522694i	0.674761	+	0.738036i	$0.264247\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	24.0000			0.760851
$996$		0			0
$997$	11.0000	−	19.0526i	0.348373	−	0.603401i	−0.637587	−	0.770378i	$-0.720067\pi$
$997$	11.0000	−	19.0526i	0.348373	−	0.603401i	0.985961	+	0.166978i	$0.0534008\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.s.o.865.1		2
3.2	odd	2		1008.2.s.b.865.1		2
4.3	odd	2		126.2.g.d.109.1	yes	2
7.2	even	3	inner	1008.2.s.o.289.1		2
7.3	odd	6		7056.2.a.bx.1.1		1
7.4	even	3		7056.2.a.e.1.1		1
12.11	even	2		126.2.g.a.109.1	yes	2
21.2	odd	6		1008.2.s.b.289.1		2
21.11	odd	6		7056.2.a.by.1.1		1
21.17	even	6		7056.2.a.h.1.1		1
28.3	even	6		882.2.a.e.1.1		1
28.11	odd	6		882.2.a.a.1.1		1
28.19	even	6		882.2.g.g.667.1		2
28.23	odd	6		126.2.g.d.37.1	yes	2
28.27	even	2		882.2.g.g.361.1		2
36.7	odd	6		1134.2.h.j.109.1		2
36.11	even	6		1134.2.h.f.109.1		2
36.23	even	6		1134.2.e.k.865.1		2
36.31	odd	6		1134.2.e.g.865.1		2
84.11	even	6		882.2.a.j.1.1		1
84.23	even	6		126.2.g.a.37.1	✓	2
84.47	odd	6		882.2.g.e.667.1		2
84.59	odd	6		882.2.a.h.1.1		1
84.83	odd	2		882.2.g.e.361.1		2
252.23	even	6		1134.2.h.f.541.1		2
252.79	odd	6		1134.2.e.g.919.1		2
252.191	even	6		1134.2.e.k.919.1		2
252.247	odd	6		1134.2.h.j.541.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.g.a.37.1	✓	2	84.23	even	6
126.2.g.a.109.1	yes	2	12.11	even	2
126.2.g.d.37.1	yes	2	28.23	odd	6
126.2.g.d.109.1	yes	2	4.3	odd	2
882.2.a.a.1.1		1	28.11	odd	6
882.2.a.e.1.1		1	28.3	even	6
882.2.a.h.1.1		1	84.59	odd	6
882.2.a.j.1.1		1	84.11	even	6
882.2.g.e.361.1		2	84.83	odd	2
882.2.g.e.667.1		2	84.47	odd	6
882.2.g.g.361.1		2	28.27	even	2
882.2.g.g.667.1		2	28.19	even	6
1008.2.s.b.289.1		2	21.2	odd	6
1008.2.s.b.865.1		2	3.2	odd	2
1008.2.s.o.289.1		2	7.2	even	3	inner
1008.2.s.o.865.1		2	1.1	even	1	trivial
1134.2.e.g.865.1		2	36.31	odd	6
1134.2.e.g.919.1		2	252.79	odd	6
1134.2.e.k.865.1		2	36.23	even	6
1134.2.e.k.919.1		2	252.191	even	6
1134.2.h.f.109.1		2	36.11	even	6
1134.2.h.f.541.1		2	252.23	even	6
1134.2.h.j.109.1		2	36.7	odd	6
1134.2.h.j.541.1		2	252.247	odd	6
7056.2.a.e.1.1		1	7.4	even	3
7056.2.a.h.1.1		1	21.17	even	6
7056.2.a.bx.1.1		1	7.3	odd	6
7056.2.a.by.1.1		1	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{5} +(0.500000 + 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{11} +2.00000 q^{13} +(3.00000 - 5.19615i) q^{17} +(1.00000 + 1.73205i) q^{19} +(3.00000 + 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} -9.00000 q^{29} +(-3.50000 + 6.06218i) q^{31} +(-6.00000 + 5.19615i) q^{35} +(5.00000 + 8.66025i) q^{37} +4.00000 q^{43} +(-6.00000 - 10.3923i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-1.50000 + 2.59808i) q^{53} +9.00000 q^{55} +(1.50000 - 2.59808i) q^{59} +(2.00000 + 3.46410i) q^{61} +(3.00000 + 5.19615i) q^{65} +(1.00000 - 1.73205i) q^{67} +(-1.00000 + 1.73205i) q^{73} +(7.50000 + 2.59808i) q^{77} +(2.50000 + 4.33013i) q^{79} +9.00000 q^{83} +18.0000 q^{85} +(-3.00000 - 5.19615i) q^{89} +(1.00000 + 5.19615i) q^{91} +(-3.00000 + 5.19615i) q^{95} -13.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{5} + q^{7}+O(q^{10}) \) 2 * q + 3 * q^5 + q^7	\( 2 q + 3 q^{5} + q^{7} + 3 q^{11} + 4 q^{13} + 6 q^{17} + 2 q^{19} + 6 q^{23} - 4 q^{25} - 18 q^{29} - 7 q^{31} - 12 q^{35} + 10 q^{37} + 8 q^{43} - 12 q^{47} - 13 q^{49} - 3 q^{53} + 18 q^{55} + 3 q^{59} + 4 q^{61} + 6 q^{65} + 2 q^{67} - 2 q^{73} + 15 q^{77} + 5 q^{79} + 18 q^{83} + 36 q^{85} - 6 q^{89} + 2 q^{91} - 6 q^{95} - 26 q^{97}+O(q^{100}) \) 2 * q + 3 * q^5 + q^7 + 3 * q^11 + 4 * q^13 + 6 * q^17 + 2 * q^19 + 6 * q^23 - 4 * q^25 - 18 * q^29 - 7 * q^31 - 12 * q^35 + 10 * q^37 + 8 * q^43 - 12 * q^47 - 13 * q^49 - 3 * q^53 + 18 * q^55 + 3 * q^59 + 4 * q^61 + 6 * q^65 + 2 * q^67 - 2 * q^73 + 15 * q^77 + 5 * q^79 + 18 * q^83 + 36 * q^85 - 6 * q^89 + 2 * q^91 - 6 * q^95 - 26 * q^97

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