LMFDB - Embedded newform 1872.2.t.p.1153.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1872,2,Mod(289,1872)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1872, 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("1872.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1872 = 2^{4} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1872.t (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:	$14.9479952584$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 10x^{2} + 100 $ x^4 + 10*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1153.2
Root			$-1.58114 - 2.73861i$ of defining polynomial
Character	$\chi$	$=$	1872.1153
Dual form			1872.2.t.p.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.16228 q^{5} +(1.58114 + 2.73861i) q^{7} +O(q^{10})$	$q+4.16228 q^{5} +(1.58114 + 2.73861i) q^{7} +(-0.581139 + 1.00656i) q^{11} +(0.0811388 - 3.60464i) q^{13} +(1.50000 + 2.59808i) q^{17} +(-2.58114 - 4.47066i) q^{19} +(3.58114 - 6.20271i) q^{23} +12.3246 q^{25} +(0.918861 - 1.59151i) q^{29} +6.32456 q^{31} +(6.58114 + 11.3989i) q^{35} +(-1.91886 + 3.32357i) q^{37} +(-1.50000 + 2.59808i) q^{41} +(4.58114 + 7.93477i) q^{43} -4.83772 q^{47} +(-1.50000 + 2.59808i) q^{49} -12.4868 q^{53} +(-2.41886 + 4.18959i) q^{55} +(-1.16228 - 2.01312i) q^{59} +(-0.0811388 - 0.140537i) q^{61} +(0.337722 - 15.0035i) q^{65} +(-1.41886 + 2.45754i) q^{67} +(-3.58114 - 6.20271i) q^{71} -1.00000 q^{73} -3.67544 q^{77} +4.00000 q^{79} +3.48683 q^{83} +(6.24342 + 10.8139i) q^{85} +(-6.00000 + 10.3923i) q^{89} +(10.0000 - 5.47723i) q^{91} +(-10.7434 - 18.6081i) q^{95} +(2.00000 + 3.46410i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5}+O(q^{10}) $ 4 * q + 4 * q^5	$ 4 q + 4 q^{5} + 4 q^{11} - 6 q^{13} + 6 q^{17} - 4 q^{19} + 8 q^{23} + 24 q^{25} + 10 q^{29} + 20 q^{35} - 14 q^{37} - 6 q^{41} + 12 q^{43} - 32 q^{47} - 6 q^{49} - 12 q^{53} - 16 q^{55} + 8 q^{59} + 6 q^{61} + 14 q^{65} - 12 q^{67} - 8 q^{71} - 4 q^{73} - 40 q^{77} + 16 q^{79} - 24 q^{83} + 6 q^{85} - 24 q^{89} + 40 q^{91} - 24 q^{95} + 8 q^{97}+O(q^{100}) $ 4 * q + 4 * q^5 + 4 * q^11 - 6 * q^13 + 6 * q^17 - 4 * q^19 + 8 * q^23 + 24 * q^25 + 10 * q^29 + 20 * q^35 - 14 * q^37 - 6 * q^41 + 12 * q^43 - 32 * q^47 - 6 * q^49 - 12 * q^53 - 16 * q^55 + 8 * q^59 + 6 * q^61 + 14 * q^65 - 12 * q^67 - 8 * q^71 - 4 * q^73 - 40 * q^77 + 16 * q^79 - 24 * q^83 + 6 * q^85 - 24 * q^89 + 40 * q^91 - 24 * q^95 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	4.16228			1.86143			0.930714	−	0.365749i	$-0.119187\pi$
$5$	4.16228			1.86143			0.930714	+	0.365749i	$0.119187\pi$
$6$		0			0
$7$	1.58114	+	2.73861i	0.597614	+	1.03510i	0.993172	+	0.116657i	$0.0372179\pi$
$7$	1.58114	+	2.73861i	0.597614	+	1.03510i	−0.395558	+	0.918441i	$0.629449\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.581139	+	1.00656i	−0.175220	+	0.303490i	−0.940237	−	0.340520i	$-0.889397\pi$
$11$	−0.581139	+	1.00656i	−0.175220	+	0.303490i	0.765017	+	0.644010i	$0.222730\pi$
$12$		0			0
$13$	0.0811388	−	3.60464i	0.0225039	−	0.999747i
$13$	0.0811388	−	3.60464i	0.0225039	−	0.999747i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	−2.58114	−	4.47066i	−0.592154	−	1.02564i	−0.993942	−	0.109908i	$-0.964944\pi$
$19$	−2.58114	−	4.47066i	−0.592154	−	1.02564i	0.401788	−	0.915733i	$-0.368389\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.58114	−	6.20271i	0.746719	−	1.29336i	−0.202668	−	0.979247i	$-0.564961\pi$
$23$	3.58114	−	6.20271i	0.746719	−	1.29336i	0.949387	−	0.314108i	$-0.101705\pi$
$24$		0			0
$25$	12.3246			2.46491
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.918861	−	1.59151i	0.170628	−	0.295537i	−0.768011	−	0.640436i	$-0.778754\pi$
$29$	0.918861	−	1.59151i	0.170628	−	0.295537i	0.938640	+	0.344899i	$0.112087\pi$
$30$		0			0
$31$	6.32456			1.13592			0.567962	−	0.823055i	$-0.307732\pi$
$31$	6.32456			1.13592			0.567962	+	0.823055i	$0.307732\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.58114	+	11.3989i	1.11242	+	1.92676i
$36$		0			0
$37$	−1.91886	+	3.32357i	−0.315459	+	0.546391i	−0.979535	−	0.201274i	$-0.935492\pi$
$37$	−1.91886	+	3.32357i	−0.315459	+	0.546391i	0.664076	+	0.747665i	$0.268825\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	4.58114	+	7.93477i	0.698617	+	1.21004i	0.968946	+	0.247272i	$0.0795342\pi$
$43$	4.58114	+	7.93477i	0.698617	+	1.21004i	−0.270329	+	0.962768i	$0.587132\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.83772			−0.705654			−0.352827	−	0.935689i	$-0.614780\pi$
$47$	−4.83772			−0.705654			−0.352827	+	0.935689i	$0.614780\pi$
$48$		0			0
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−12.4868			−1.71520			−0.857599	−	0.514319i	$-0.828045\pi$
$53$	−12.4868			−1.71520			−0.857599	+	0.514319i	$0.828045\pi$
$54$		0			0
$55$	−2.41886	+	4.18959i	−0.326159	+	0.564924i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.16228	−	2.01312i	−0.151316	−	0.262086i	0.780396	−	0.625286i	$-0.215018\pi$
$59$	−1.16228	−	2.01312i	−0.151316	−	0.262086i	−0.931711	+	0.363200i	$0.881684\pi$
$60$		0			0
$61$	−0.0811388	−	0.140537i	−0.0103888	−	0.0179939i	0.860784	−	0.508970i	$-0.169974\pi$
$61$	−0.0811388	−	0.140537i	−0.0103888	−	0.0179939i	−0.871173	+	0.490976i	$0.836640\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.337722	−	15.0035i	0.0418893	−	1.86096i
$66$		0			0
$67$	−1.41886	+	2.45754i	−0.173341	+	0.300236i	−0.939586	−	0.342313i	$-0.888790\pi$
$67$	−1.41886	+	2.45754i	−0.173341	+	0.300236i	0.766245	+	0.642549i	$0.222123\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.58114	−	6.20271i	−0.425003	−	0.736127i	0.571418	−	0.820659i	$-0.306394\pi$
$71$	−3.58114	−	6.20271i	−0.425003	−	0.736127i	−0.996421	+	0.0845326i	$0.973060\pi$
$72$		0			0
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.67544			−0.418856
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.48683			0.382730			0.191365	−	0.981519i	$-0.438709\pi$
$83$	3.48683			0.382730			0.191365	+	0.981519i	$0.438709\pi$
$84$		0			0
$85$	6.24342	+	10.8139i	0.677194	+	1.17293i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.00000	+	10.3923i	−0.635999	+	1.10158i	0.350304	+	0.936636i	$0.386078\pi$
$89$	−6.00000	+	10.3923i	−0.635999	+	1.10158i	−0.986303	+	0.164946i	$0.947255\pi$
$90$		0			0
$91$	10.0000	−	5.47723i	1.04828	−	0.574169i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−10.7434	−	18.6081i	−1.10225	−	1.90916i
$96$		0			0
$97$	2.00000	+	3.46410i	0.203069	+	0.351726i	0.949516	−	0.313719i	$-0.101575\pi$
$97$	2.00000	+	3.46410i	0.203069	+	0.351726i	−0.746447	+	0.665445i	$0.768242\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.91886	+	6.78767i	−0.389941	+	0.675398i	−0.992441	−	0.122721i	$-0.960838\pi$
$101$	−3.91886	+	6.78767i	−0.389941	+	0.675398i	0.602500	+	0.798119i	$0.294171\pi$
$102$		0			0
$103$	15.8114			1.55794			0.778971	−	0.627060i	$-0.215742\pi$
$103$	15.8114			1.55794			0.778971	+	0.627060i	$0.215742\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.90569	+	15.4251i	−0.860946	+	1.49120i	0.0100711	+	0.999949i	$0.496794\pi$
$107$	−8.90569	+	15.4251i	−0.860946	+	1.49120i	−0.871017	+	0.491253i	$0.836539\pi$
$108$		0			0
$109$	6.64911			0.636869			0.318435	−	0.947945i	$-0.396843\pi$
$109$	6.64911			0.636869			0.318435	+	0.947945i	$0.396843\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.33772	−	5.78110i	−0.313987	−	0.543841i	0.665235	−	0.746634i	$-0.268331\pi$
$113$	−3.33772	−	5.78110i	−0.313987	−	0.543841i	−0.979222	+	0.202793i	$0.934998\pi$
$114$		0			0
$115$	14.9057	−	25.8174i	1.38996	−	2.40749i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.74342	+	8.21584i	−0.434828	+	0.753145i
$120$		0			0
$121$	4.82456	+	8.35637i	0.438596	+	0.759670i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	30.4868			2.72683
$126$		0			0
$127$	−9.16228	+	15.8695i	−0.813021	+	1.40819i	0.0977198	+	0.995214i	$0.468845\pi$
$127$	−9.16228	+	15.8695i	−0.813021	+	1.40819i	−0.910740	+	0.412979i	$0.864488\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−16.6491			−1.45464			−0.727320	−	0.686299i	$-0.759234\pi$
$131$	−16.6491			−1.45464			−0.727320	+	0.686299i	$0.759234\pi$
$132$		0			0
$133$	8.16228	−	14.1375i	0.707759	−	1.22587i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	−3.16228	−	5.47723i	−0.268221	−	0.464572i	0.700182	−	0.713965i	$-0.253102\pi$
$139$	−3.16228	−	5.47723i	−0.268221	−	0.464572i	−0.968402	+	0.249393i	$0.919769\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.58114	+	2.17647i	0.299470	+	0.182005i
$144$		0			0
$145$	3.82456	−	6.62432i	0.317612	−	0.550120i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.243416	−	0.421610i	−0.0199415	−	0.0345396i	0.855882	−	0.517170i	$-0.173015\pi$
$149$	−0.243416	−	0.421610i	−0.0199415	−	0.0345396i	−0.875824	+	0.482631i	$0.839681\pi$
$150$		0			0
$151$	−0.837722			−0.0681729			−0.0340864	−	0.999419i	$-0.510852\pi$
$151$	−0.837722			−0.0681729			−0.0340864	+	0.999419i	$0.510852\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	26.3246			2.11444
$156$		0			0
$157$	−10.4868			−0.836940			−0.418470	−	0.908231i	$-0.637434\pi$
$157$	−10.4868			−0.836940			−0.418470	+	0.908231i	$0.637434\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	22.6491			1.78500
$162$		0			0
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	−0.988227	−	0.152992i	$-0.951109\pi$
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	0.361619	−	0.932326i	$-0.382224\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$		0			0
$169$	−12.9868	−	0.584952i	−0.998987	−	0.0449963i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−11.3246	−	19.6147i	−0.860990	−	1.49128i	−0.870974	−	0.491328i	$-0.836512\pi$
$173$	−11.3246	−	19.6147i	−0.860990	−	1.49128i	0.00998448	−	0.999950i	$-0.496822\pi$
$174$		0			0
$175$	19.4868	+	33.7522i	1.47307	+	2.55143i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.74342	−	13.4120i	0.578770	−	1.00246i	−0.416851	−	0.908975i	$-0.636866\pi$
$179$	7.74342	−	13.4120i	0.578770	−	1.00246i	0.995621	−	0.0934843i	$-0.0298005\pi$
$180$		0			0
$181$	3.83772			0.285256			0.142628	−	0.989776i	$-0.454445\pi$
$181$	3.83772			0.285256			0.142628	+	0.989776i	$0.454445\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−7.98683	+	13.8336i	−0.587204	+	1.01707i
$186$		0			0
$187$	−3.48683			−0.254982
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.16228	+	12.4054i	0.518244	+	0.897625i	0.999775	+	0.0211963i	$0.00674751\pi$
$191$	7.16228	+	12.4054i	0.518244	+	0.897625i	−0.481531	+	0.876429i	$0.659919\pi$
$192$		0			0
$193$	9.98683	−	17.2977i	0.718868	−	1.24512i	−0.242581	−	0.970131i	$-0.577994\pi$
$193$	9.98683	−	17.2977i	0.718868	−	1.24512i	0.961449	−	0.274985i	$-0.0886728\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−9.48683	+	16.4317i	−0.675909	+	1.17071i	0.300293	+	0.953847i	$0.402915\pi$
$197$	−9.48683	+	16.4317i	−0.675909	+	1.17071i	−0.976202	+	0.216862i	$0.930418\pi$
$198$		0			0
$199$	−3.25658	−	5.64057i	−0.230853	−	0.399849i	0.727206	−	0.686419i	$-0.240818\pi$
$199$	−3.25658	−	5.64057i	−0.230853	−	0.399849i	−0.958059	+	0.286570i	$0.907485\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.81139			0.407879
$204$		0			0
$205$	−6.24342	+	10.8139i	−0.436059	+	0.755277i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.00000			0.415029
$210$		0			0
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	−0.926620	−	0.375999i	$-0.877300\pi$
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	0.788935	+	0.614477i	$0.210633\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	19.0680	+	33.0267i	1.30042	+	2.25240i
$216$		0			0
$217$	10.0000	+	17.3205i	0.678844	+	1.17579i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	9.48683	−	5.19615i	0.638153	−	0.349531i
$222$		0			0
$223$	−0.837722	+	1.45098i	−0.0560980	+	0.0971647i	−0.892711	−	0.450630i	$-0.851199\pi$
$223$	−0.837722	+	1.45098i	−0.0560980	+	0.0971647i	0.836613	+	0.547795i	$0.184533\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.74342	−	13.4120i	−0.513949	−	0.890185i	−0.999869	−	0.0161821i	$-0.994849\pi$
$227$	−7.74342	−	13.4120i	−0.513949	−	0.890185i	0.485920	−	0.874003i	$-0.338484\pi$
$228$		0			0
$229$	22.3246			1.47525			0.737624	−	0.675212i	$-0.235948\pi$
$229$	22.3246			1.47525			0.737624	+	0.675212i	$0.235948\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−16.6491			−1.09072			−0.545360	−	0.838202i	$-0.683607\pi$
$233$	−16.6491			−1.09072			−0.545360	+	0.838202i	$0.683607\pi$
$234$		0			0
$235$	−20.1359			−1.31352
$236$		0			0
$237$		0			0
$238$		0			0
$239$	21.4868			1.38987			0.694934	−	0.719074i	$-0.255434\pi$
$239$	21.4868			1.38987			0.694934	+	0.719074i	$0.255434\pi$
$240$		0			0
$241$	−6.66228	−	11.5394i	−0.429155	−	0.743318i	0.567643	−	0.823275i	$-0.307855\pi$
$241$	−6.66228	−	11.5394i	−0.429155	−	0.743318i	−0.996798	+	0.0799563i	$0.974522\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.24342	+	10.8139i	−0.398877	+	0.690876i
$246$		0			0
$247$	−16.3246	+	8.94133i	−1.03871	+	0.568923i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	0.612159	−	0.790735i	$-0.290301\pi$
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	−0.990876	+	0.134778i	$0.956968\pi$
$252$		0			0
$253$	4.16228	+	7.20928i	0.261680	+	0.453243i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.9868	−	19.0298i	0.685340	−	1.18704i	−0.287990	−	0.957633i	$-0.592987\pi$
$257$	10.9868	−	19.0298i	0.685340	−	1.18704i	0.973330	−	0.229410i	$-0.0736797\pi$
$258$		0			0
$259$	−12.1359			−0.754091
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.25658	+	2.17647i	−0.0774843	+	0.134207i	−0.902164	−	0.431393i	$-0.858022\pi$
$263$	−1.25658	+	2.17647i	−0.0774843	+	0.134207i	0.824680	+	0.565600i	$0.191355\pi$
$264$		0			0
$265$	−51.9737			−3.19272
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$	−3.16228	+	5.47723i	−0.192095	+	0.332718i	−0.945944	−	0.324329i	$-0.894861\pi$
$271$	−3.16228	+	5.47723i	−0.192095	+	0.332718i	0.753850	+	0.657047i	$0.228195\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.16228	+	12.4054i	−0.431902	+	0.748076i
$276$		0			0
$277$	−5.40569	−	9.36294i	−0.324797	−	0.562564i	0.656675	−	0.754174i	$-0.271963\pi$
$277$	−5.40569	−	9.36294i	−0.324797	−	0.562564i	−0.981471	+	0.191610i	$0.938629\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.675445			−0.0402937			−0.0201468	−	0.999797i	$-0.506413\pi$
$281$	−0.675445			−0.0402937			−0.0201468	+	0.999797i	$0.506413\pi$
$282$		0			0
$283$	−1.41886	+	2.45754i	−0.0843425	+	0.146086i	−0.905111	−	0.425176i	$-0.860212\pi$
$283$	−1.41886	+	2.45754i	−0.0843425	+	0.146086i	0.820768	+	0.571261i	$0.193546\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.48683			−0.559990
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.918861	−	1.59151i	−0.0536804	−	0.0929773i	0.837937	−	0.545768i	$-0.183762\pi$
$293$	−0.918861	−	1.59151i	−0.0536804	−	0.0929773i	−0.891617	+	0.452790i	$0.850429\pi$
$294$		0			0
$295$	−4.83772	−	8.37918i	−0.281663	−	0.487855i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−22.0680	−	13.4120i	−1.27622	−	0.775635i
$300$		0			0
$301$	−14.4868	+	25.0919i	−0.835007	+	1.44627i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.337722	−	0.584952i	−0.0193379	−	0.0334943i
$306$		0			0
$307$	−11.4868			−0.655588			−0.327794	−	0.944749i	$-0.606305\pi$
$307$	−11.4868			−0.655588			−0.327794	+	0.944749i	$0.606305\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−21.4868			−1.21841			−0.609203	−	0.793014i	$-0.708511\pi$
$311$	−21.4868			−1.21841			−0.609203	+	0.793014i	$0.708511\pi$
$312$		0			0
$313$	−4.00000			−0.226093			−0.113047	−	0.993590i	$-0.536061\pi$
$313$	−4.00000			−0.226093			−0.113047	+	0.993590i	$0.536061\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.4868			0.701330			0.350665	−	0.936501i	$-0.385956\pi$
$317$	12.4868			0.701330			0.350665	+	0.936501i	$0.385956\pi$
$318$		0			0
$319$	1.06797	+	1.84978i	0.0597949	+	0.103568i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	7.74342	−	13.4120i	0.430855	−	0.746263i
$324$		0			0
$325$	1.00000	−	44.4256i	0.0554700	−	2.46429i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.64911	−	13.2486i	−0.421709	−	0.730422i
$330$		0			0
$331$	−5.48683	−	9.50347i	−0.301584	−	0.522358i	0.674911	−	0.737899i	$-0.264182\pi$
$331$	−5.48683	−	9.50347i	−0.301584	−	0.522358i	−0.976495	+	0.215541i	$0.930849\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.90569	+	10.2290i	−0.322663	+	0.558868i
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.67544	+	6.36606i	−0.199036	+	0.344741i
$342$		0			0
$343$	12.6491			0.682988
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.74342	−	13.4120i	−0.415688	−	0.719993i	0.579812	−	0.814750i	$-0.303126\pi$
$347$	−7.74342	−	13.4120i	−0.415688	−	0.719993i	−0.995500	+	0.0947569i	$0.969793\pi$
$348$		0			0
$349$	2.67544	−	4.63401i	0.143213	−	0.248053i	−0.785492	−	0.618872i	$-0.787590\pi$
$349$	2.67544	−	4.63401i	0.143213	−	0.248053i	0.928705	+	0.370820i	$0.120923\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.6623	+	25.3958i	−0.780394	+	1.35168i	0.151318	+	0.988485i	$0.451648\pi$
$353$	−14.6623	+	25.3958i	−0.780394	+	1.35168i	−0.931712	+	0.363197i	$0.881685\pi$
$354$		0			0
$355$	−14.9057	−	25.8174i	−0.791112	−	1.37025i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−28.4605			−1.50209			−0.751044	−	0.660252i	$-0.770449\pi$
$359$	−28.4605			−1.50209			−0.751044	+	0.660252i	$0.770449\pi$
$360$		0			0
$361$	−3.82456	+	6.62432i	−0.201292	+	0.348649i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.16228			−0.217864
$366$		0			0
$367$	−12.7434	+	22.0722i	−0.665201	+	1.15216i	0.314030	+	0.949413i	$0.398321\pi$
$367$	−12.7434	+	22.0722i	−0.665201	+	1.15216i	−0.979231	+	0.202749i	$0.935013\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−19.7434	−	34.1966i	−1.02503	−	1.77540i
$372$		0			0
$373$	8.24342	+	14.2780i	0.426828	+	0.739288i	0.996589	−	0.0825226i	$-0.0262977\pi$
$373$	8.24342	+	14.2780i	0.426828	+	0.739288i	−0.569761	+	0.821810i	$0.692964\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.66228	−	3.44130i	−0.291622	−	0.177236i
$378$		0			0
$379$	8.83772	−	15.3074i	0.453963	−	0.786288i	−0.544665	−	0.838654i	$-0.683343\pi$
$379$	8.83772	−	15.3074i	0.453963	−	0.786288i	0.998628	+	0.0523664i	$0.0166764\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	15.4868	+	26.8240i	0.791340	+	1.37064i	0.925137	+	0.379633i	$0.123950\pi$
$383$	15.4868	+	26.8240i	0.791340	+	1.37064i	−0.133797	+	0.991009i	$0.542717\pi$
$384$		0			0
$385$	−15.2982			−0.779670
$386$		0			0
$387$		0			0
$388$		0			0
$389$	12.4868			0.633108			0.316554	−	0.948575i	$-0.397474\pi$
$389$	12.4868			0.633108			0.316554	+	0.948575i	$0.397474\pi$
$390$		0			0
$391$	21.4868			1.08664
$392$		0			0
$393$		0			0
$394$		0			0
$395$	16.6491			0.837708
$396$		0			0
$397$	−13.0000	−	22.5167i	−0.652451	−	1.13008i	−0.982526	−	0.186124i	$-0.940407\pi$
$397$	−13.0000	−	22.5167i	−0.652451	−	1.13008i	0.330075	−	0.943955i	$-0.392926\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$		0			0
$403$	0.513167	−	22.7977i	0.0255627	−	1.13564i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.23025	−	3.86291i	−0.110549	−	0.191477i
$408$		0			0
$409$	−7.33772	−	12.7093i	−0.362827	−	0.628435i	0.625598	−	0.780146i	$-0.284855\pi$
$409$	−7.33772	−	12.7093i	−0.362827	−	0.628435i	−0.988425	+	0.151711i	$0.951522\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	3.67544	−	6.36606i	0.180857	−	0.313253i
$414$		0			0
$415$	14.5132			0.712423
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−15.4868	+	26.8240i	−0.756581	+	1.31044i	0.188003	+	0.982168i	$0.439799\pi$
$419$	−15.4868	+	26.8240i	−0.756581	+	1.31044i	−0.944584	+	0.328269i	$0.893535\pi$
$420$		0			0
$421$	−23.8377			−1.16178			−0.580890	−	0.813982i	$-0.697295\pi$
$421$	−23.8377			−1.16178			−0.580890	+	0.813982i	$0.697295\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	18.4868	+	32.0201i	0.896743	+	1.55320i
$426$		0			0
$427$	0.256584	−	0.444416i	0.0124169	−	0.0215068i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4.74342	+	8.21584i	−0.228482	+	0.395743i	−0.957359	−	0.288903i	$-0.906710\pi$
$431$	−4.74342	+	8.21584i	−0.228482	+	0.395743i	0.728876	+	0.684646i	$0.240043\pi$
$432$		0			0
$433$	4.66228	+	8.07530i	0.224055	+	0.388074i	0.956035	−	0.293251i	$-0.0947372\pi$
$433$	4.66228	+	8.07530i	0.224055	+	0.388074i	−0.731981	+	0.681325i	$0.761404\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−36.9737			−1.76869
$438$		0			0
$439$	−12.7434	+	22.0722i	−0.608210	+	1.05345i	0.383325	+	0.923613i	$0.374779\pi$
$439$	−12.7434	+	22.0722i	−0.608210	+	1.05345i	−0.991535	+	0.129837i	$0.958554\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$	−24.9737	+	43.2557i	−1.18387	+	2.05051i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−3.67544	−	6.36606i	−0.173455	−	0.300433i	0.766171	−	0.642637i	$-0.222160\pi$
$449$	−3.67544	−	6.36606i	−0.173455	−	0.300433i	−0.939625	+	0.342205i	$0.888826\pi$
$450$		0			0
$451$	−1.74342	−	3.01969i	−0.0820943	−	0.142191i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	41.6228	−	22.7977i	1.95131	−	1.06877i
$456$		0			0
$457$	1.66228	−	2.87915i	0.0777581	−	0.134681i	−0.824524	−	0.565827i	$-0.808557\pi$
$457$	1.66228	−	2.87915i	0.0777581	−	0.134681i	0.902282	+	0.431146i	$0.141890\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.24342	−	16.0101i	−0.430509	−	0.745663i	0.566408	−	0.824125i	$-0.308333\pi$
$461$	−9.24342	−	16.0101i	−0.430509	−	0.745663i	−0.996917	+	0.0784616i	$0.974999\pi$
$462$		0			0
$463$	−15.1623			−0.704651			−0.352325	−	0.935878i	$-0.614609\pi$
$463$	−15.1623			−0.704651			−0.352325	+	0.935878i	$0.614609\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.18861			−0.286375			−0.143187	−	0.989696i	$-0.545735\pi$
$467$	−6.18861			−0.286375			−0.143187	+	0.989696i	$0.545735\pi$
$468$		0			0
$469$	−8.97367			−0.414365
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.6491			−0.489647
$474$		0			0
$475$	−31.8114	−	55.0989i	−1.45961	−	2.52811i
$476$		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
$481$	11.8246	+	7.18647i	0.539153	+	0.327675i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.32456	+	14.4186i	0.377999	+	0.654713i
$486$		0			0
$487$	−6.74342	−	11.6799i	−0.305573	−	0.529269i	0.671815	−	0.740719i	$-0.265515\pi$
$487$	−6.74342	−	11.6799i	−0.305573	−	0.529269i	−0.977389	+	0.211450i	$0.932181\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.90569	−	5.03281i	0.131132	−	0.227128i	−0.792981	−	0.609246i	$-0.791472\pi$
$491$	2.90569	−	5.03281i	0.131132	−	0.227128i	0.924113	+	0.382119i	$0.124805\pi$
$492$		0			0
$493$	5.51317			0.248301
$494$		0			0
$495$		0			0
$496$		0			0
$497$	11.3246	−	19.6147i	0.507976	−	0.879840i
$498$		0			0
$499$	−12.6491			−0.566252			−0.283126	−	0.959083i	$-0.591371\pi$
$499$	−12.6491			−0.566252			−0.283126	+	0.959083i	$0.591371\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−0.0943058	−	0.163343i	−0.00420489	−	0.00728308i	0.863915	−	0.503637i	$-0.168005\pi$
$503$	−0.0943058	−	0.163343i	−0.00420489	−	0.00728308i	−0.868120	+	0.496354i	$0.834672\pi$
$504$		0			0
$505$	−16.3114	+	28.2522i	−0.725847	+	1.25720i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	14.0811	−	24.3892i	0.624136	−	1.08103i	−0.364572	−	0.931175i	$-0.618785\pi$
$509$	14.0811	−	24.3892i	0.624136	−	1.08103i	0.988707	−	0.149859i	$-0.0478820\pi$
$510$		0			0
$511$	−1.58114	−	2.73861i	−0.0699455	−	0.121149i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	65.8114			2.90000
$516$		0			0
$517$	2.81139	−	4.86947i	0.123645	−	0.214159i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−27.0000			−1.18289			−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000			−1.18289			−0.591446	+	0.806345i	$0.701443\pi$
$522$		0			0
$523$	−2.58114	+	4.47066i	−0.112865	+	0.195488i	−0.916924	−	0.399061i	$-0.869336\pi$
$523$	−2.58114	+	4.47066i	−0.112865	+	0.195488i	0.804059	+	0.594549i	$0.202670\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.48683	+	16.4317i	0.413253	+	0.715775i
$528$		0			0
$529$	−14.1491	−	24.5070i	−0.615179	−	1.06552i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	9.24342	+	5.61776i	0.400377	+	0.243332i
$534$		0			0
$535$	−37.0680	+	64.2036i	−1.60259	+	2.77576i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.74342	−	3.01969i	−0.0750943	−	0.130067i
$540$		0			0
$541$	−15.5132			−0.666963			−0.333482	−	0.942757i	$-0.608223\pi$
$541$	−15.5132			−0.666963			−0.333482	+	0.942757i	$0.608223\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	27.6754			1.18549
$546$		0			0
$547$	33.8114			1.44567			0.722835	−	0.691020i	$-0.242839\pi$
$547$	33.8114			1.44567			0.722835	+	0.691020i	$0.242839\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.48683			−0.404153
$552$		0			0
$553$	6.32456	+	10.9545i	0.268947	+	0.465831i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.24342	−	16.0101i	0.391656	−	0.678368i	−0.601012	−	0.799240i	$-0.705236\pi$
$557$	9.24342	−	16.0101i	0.391656	−	0.678368i	0.992668	+	0.120872i	$0.0385690\pi$
$558$		0			0
$559$	28.9737	−	15.8695i	1.22546	−	0.671210i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	20.3246	+	35.2032i	0.856578	+	1.48364i	0.875173	+	0.483809i	$0.160747\pi$
$563$	20.3246	+	35.2032i	0.856578	+	1.48364i	−0.0185956	+	0.999827i	$0.505919\pi$
$564$		0			0
$565$	−13.8925	−	24.0626i	−0.584463	−	1.01232i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.6491	+	23.6410i	−0.572200	+	0.991080i	0.424139	+	0.905597i	$0.360577\pi$
$569$	−13.6491	+	23.6410i	−0.572200	+	0.991080i	−0.996340	+	0.0854833i	$0.972757\pi$
$570$		0			0
$571$	36.1359			1.51224			0.756121	−	0.654432i	$-0.227092\pi$
$571$	36.1359			1.51224			0.756121	+	0.654432i	$0.227092\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	44.1359	−	76.4457i	1.84060	−	3.18801i
$576$		0			0
$577$	0.350889			0.0146077			0.00730386	−	0.999973i	$-0.497675\pi$
$577$	0.350889			0.0146077			0.00730386	+	0.999973i	$0.497675\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	5.51317	+	9.54909i	0.228725	+	0.396163i
$582$		0			0
$583$	7.25658	−	12.5688i	0.300537	−	0.520545i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.3246	−	24.8109i	0.591238	−	1.02405i	−0.402828	−	0.915276i	$-0.631973\pi$
$587$	14.3246	−	24.8109i	0.591238	−	1.02405i	0.994066	−	0.108778i	$-0.0346938\pi$
$588$		0			0
$589$	−16.3246	−	28.2750i	−0.672642	−	1.16505i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.675445			0.0277372			0.0138686	−	0.999904i	$-0.495585\pi$
$593$	0.675445			0.0277372			0.0138686	+	0.999904i	$0.495585\pi$
$594$		0			0
$595$	−19.7434	+	34.1966i	−0.809401	+	1.40192i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	23.6228			0.965200			0.482600	−	0.875841i	$-0.339692\pi$
$599$	23.6228			0.965200			0.482600	+	0.875841i	$0.339692\pi$
$600$		0			0
$601$	17.1491	−	29.7031i	0.699527	−	1.21162i	−0.269104	−	0.963111i	$-0.586727\pi$
$601$	17.1491	−	29.7031i	0.699527	−	1.21162i	0.968631	−	0.248505i	$-0.0799392\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	20.0811	+	34.7816i	0.816414	+	1.41407i
$606$		0			0
$607$	8.64911	+	14.9807i	0.351057	+	0.608048i	0.986435	−	0.164153i	$-0.0524891\pi$
$607$	8.64911	+	14.9807i	0.351057	+	0.608048i	−0.635378	+	0.772201i	$0.719156\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.392527	+	17.4382i	−0.0158799	+	0.705476i
$612$		0			0
$613$	−10.2434	+	17.7421i	−0.413728	+	0.716597i	−0.995294	−	0.0969016i	$-0.969107\pi$
$613$	−10.2434	+	17.7421i	−0.413728	+	0.716597i	0.581566	+	0.813499i	$0.302440\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.3114	+	23.0560i	0.535896	+	0.928200i	0.999119	+	0.0419579i	$0.0133595\pi$
$617$	13.3114	+	23.0560i	0.535896	+	0.928200i	−0.463223	+	0.886242i	$0.653307\pi$
$618$		0			0
$619$	−24.6491			−0.990731			−0.495366	−	0.868685i	$-0.664966\pi$
$619$	−24.6491			−0.990731			−0.495366	+	0.868685i	$0.664966\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−37.9473			−1.52033
$624$		0			0
$625$	65.2719			2.61088
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−11.5132			−0.459060
$630$		0			0
$631$	−12.6491	−	21.9089i	−0.503553	−	0.872180i	−0.999992	−	0.00410769i	$-0.998692\pi$
$631$	−12.6491	−	21.9089i	−0.503553	−	0.872180i	0.496438	−	0.868072i	$-0.334641\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−38.1359	+	66.0534i	−1.51338	+	2.62125i
$636$		0			0
$637$	9.24342	+	5.61776i	0.366237	+	0.222584i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−8.17544	−	14.1603i	−0.322911	−	0.559298i	0.658177	−	0.752864i	$-0.271328\pi$
$641$	−8.17544	−	14.1603i	−0.322911	−	0.559298i	−0.981087	+	0.193566i	$0.937995\pi$
$642$		0			0
$643$	10.0000	+	17.3205i	0.394362	+	0.683054i	0.993019	−	0.117951i	$-0.0376325\pi$
$643$	10.0000	+	17.3205i	0.394362	+	0.683054i	−0.598658	+	0.801005i	$0.704299\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−20.3246	+	35.2032i	−0.799041	+	1.38398i	0.121201	+	0.992628i	$0.461326\pi$
$647$	−20.3246	+	35.2032i	−0.799041	+	1.38398i	−0.920241	+	0.391351i	$0.872008\pi$
$648$		0			0
$649$	2.70178			0.106054
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	0.407628	+	0.913148i	$0.366356\pi$
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	−0.994623	+	0.103558i	$0.966977\pi$
$654$		0			0
$655$	−69.2982			−2.70771
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.51317	−	4.35293i	−0.0978991	−	0.169566i	0.812916	−	0.582381i	$-0.197879\pi$
$659$	−2.51317	−	4.35293i	−0.0978991	−	0.169566i	−0.910815	+	0.412815i	$0.864546\pi$
$660$		0			0
$661$	−13.2434	+	22.9383i	−0.515109	+	0.892195i	0.484737	+	0.874660i	$0.338915\pi$
$661$	−13.2434	+	22.9383i	−0.515109	+	0.892195i	−0.999846	+	0.0175354i	$0.994418\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	33.9737	−	58.8441i	1.31744	−	2.28188i
$666$		0			0
$667$	−6.58114	−	11.3989i	−0.254823	−	0.441366i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.188612			0.00728127
$672$		0			0
$673$	−7.33772	+	12.7093i	−0.282848	+	0.489908i	−0.972085	−	0.234628i	$-0.924613\pi$
$673$	−7.33772	+	12.7093i	−0.282848	+	0.489908i	0.689237	+	0.724536i	$0.257946\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$		0			0
$679$	−6.32456	+	10.9545i	−0.242714	+	0.420393i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−17.8114	−	30.8502i	−0.681534	−	1.18045i	−0.974513	−	0.224332i	$-0.927980\pi$
$683$	−17.8114	−	30.8502i	−0.681534	−	1.18045i	0.292979	−	0.956119i	$-0.405353\pi$
$684$		0			0
$685$	6.24342	+	10.8139i	0.238549	+	0.413178i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.01317	+	45.0105i	−0.0385986	+	1.71476i
$690$		0			0
$691$	4.58114	−	7.93477i	0.174275	−	0.301853i	−0.765635	−	0.643275i	$-0.777575\pi$
$691$	4.58114	−	7.93477i	0.174275	−	0.301853i	0.939910	+	0.341422i	$0.110909\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−13.1623	−	22.7977i	−0.499274	−	0.864767i
$696$		0			0
$697$	−9.00000			−0.340899
$698$		0			0
$699$		0			0
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	19.8114			0.747201
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−24.7851			−0.932138
$708$		0			0
$709$	−22.7302	−	39.3699i	−0.853652	−	1.47857i	−0.877890	−	0.478863i	$-0.841049\pi$
$709$	−22.7302	−	39.3699i	−0.853652	−	1.47857i	0.0242371	−	0.999706i	$-0.492284\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	22.6491	−	39.2294i	0.848216	−	1.46915i
$714$		0			0
$715$	14.9057	+	9.05906i	0.557441	+	0.338790i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−19.1623	−	33.1900i	−0.714632	−	1.23778i	−0.963101	−	0.269140i	$-0.913261\pi$
$719$	−19.1623	−	33.1900i	−0.714632	−	1.23778i	0.248469	−	0.968640i	$-0.420073\pi$
$720$		0			0
$721$	25.0000	+	43.3013i	0.931049	+	1.61262i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	11.3246	−	19.6147i	0.420583	−	0.728472i
$726$		0			0
$727$	8.83772			0.327773			0.163886	−	0.986479i	$-0.447597\pi$
$727$	8.83772			0.327773			0.163886	+	0.986479i	$0.447597\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−13.7434	+	23.8043i	−0.508319	+	0.880434i
$732$		0			0
$733$	21.4605			0.792662			0.396331	−	0.918108i	$-0.370283\pi$
$733$	21.4605			0.792662			0.396331	+	0.918108i	$0.370283\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.64911	−	2.85634i	−0.0607458	−	0.105215i
$738$		0			0
$739$	−19.8114	+	34.3143i	−0.728774	+	1.26227i	0.228628	+	0.973514i	$0.426576\pi$
$739$	−19.8114	+	34.3143i	−0.728774	+	1.26227i	−0.957402	+	0.288759i	$0.906757\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.16228	−	2.01312i	0.0426398	−	0.0738544i	−0.843918	−	0.536472i	$-0.819757\pi$
$743$	1.16228	−	2.01312i	0.0426398	−	0.0738544i	0.886558	+	0.462618i	$0.153090\pi$
$744$		0			0
$745$	−1.01317	−	1.75486i	−0.0371196	−	0.0642930i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−56.3246			−2.05805
$750$		0			0
$751$	19.3925	−	33.5888i	0.707643	−	1.22567i	−0.258086	−	0.966122i	$-0.583092\pi$
$751$	19.3925	−	33.5888i	0.707643	−	1.22567i	0.965729	−	0.259552i	$-0.0835750\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3.48683			−0.126899
$756$		0			0
$757$	13.3246	−	23.0788i	0.484289	−	0.838814i	−0.515548	−	0.856861i	$-0.672412\pi$
$757$	13.3246	−	23.0788i	0.484289	−	0.838814i	0.999837	+	0.0180472i	$0.00574493\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	0.954043	−	0.299670i	$-0.0968765\pi$
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	−0.736543	+	0.676391i	$0.763543\pi$
$762$		0			0
$763$	10.5132	+	18.2093i	0.380602	+	0.659222i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.35089	+	4.02625i	−0.265425	+	0.145379i
$768$		0			0
$769$	−1.67544	+	2.90196i	−0.0604181	+	0.104647i	−0.894652	−	0.446763i	$-0.852577\pi$
$769$	−1.67544	+	2.90196i	−0.0604181	+	0.104647i	0.834234	+	0.551410i	$0.185910\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−11.3246	−	19.6147i	−0.407316	−	0.705492i	0.587272	−	0.809390i	$-0.300202\pi$
$773$	−11.3246	−	19.6147i	−0.407316	−	0.705492i	−0.994588	+	0.103898i	$0.966869\pi$
$774$		0			0
$775$	77.9473			2.79995
$776$		0			0
$777$		0			0
$778$		0			0
$779$	15.4868			0.554873
$780$		0			0
$781$	8.32456			0.297876
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−43.6491			−1.55790
$786$		0			0
$787$	−4.51317	−	7.81703i	−0.160877	−	0.278647i	0.774306	−	0.632811i	$-0.218099\pi$
$787$	−4.51317	−	7.81703i	−0.160877	−	0.278647i	−0.935183	+	0.354164i	$0.884766\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	10.5548	−	18.2815i	0.375286	−	0.650014i
$792$		0			0
$793$	−0.513167	+	0.281073i	−0.0182231	+	0.00998120i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.48683	+	16.4317i	0.336041	+	0.582040i	0.983684	−	0.179904i	$-0.0575786\pi$
$797$	9.48683	+	16.4317i	0.336041	+	0.582040i	−0.647643	+	0.761944i	$0.724245\pi$
$798$		0			0
$799$	−7.25658	−	12.5688i	−0.256719	−	0.444651i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.581139	−	1.00656i	0.0205079	−	0.0355208i
$804$		0			0
$805$	94.2719			3.32265
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.50000	+	2.59808i	−0.0527372	+	0.0913435i	−0.891189	−	0.453632i	$-0.850128\pi$
$809$	−1.50000	+	2.59808i	−0.0527372	+	0.0913435i	0.838452	+	0.544976i	$0.183461\pi$
$810$		0			0
$811$	−1.02633			−0.0360395			−0.0180197	−	0.999838i	$-0.505736\pi$
$811$	−1.02633			−0.0360395			−0.0180197	+	0.999838i	$0.505736\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−33.2982	−	57.6742i	−1.16639	−	2.02024i
$816$		0			0
$817$	23.6491	−	40.9615i	0.827378	−	1.43306i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.32456	+	9.22240i	−0.185828	+	0.321864i	−0.943855	−	0.330359i	$-0.892830\pi$
$821$	−5.32456	+	9.22240i	−0.185828	+	0.321864i	0.758027	+	0.652223i	$0.226163\pi$
$822$		0			0
$823$	26.6491	+	46.1576i	0.928930	+	1.60895i	0.785116	+	0.619348i	$0.212603\pi$
$823$	26.6491	+	46.1576i	0.928930	+	1.60895i	0.143813	+	0.989605i	$0.454064\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.97367			0.242498			0.121249	−	0.992622i	$-0.461310\pi$
$827$	6.97367			0.242498			0.121249	+	0.992622i	$0.461310\pi$
$828$		0			0
$829$	−6.08114	+	10.5328i	−0.211207	+	0.365821i	−0.952092	−	0.305810i	$-0.901073\pi$
$829$	−6.08114	+	10.5328i	−0.211207	+	0.365821i	0.740886	+	0.671631i	$0.234406\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−9.00000			−0.311832
$834$		0			0
$835$	24.9737	−	43.2557i	0.864249	−	1.49692i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	2.32456	+	4.02625i	0.0802526	+	0.139002i	0.903358	−	0.428887i	$-0.141094\pi$
$839$	2.32456	+	4.02625i	0.0802526	+	0.139002i	−0.823106	+	0.567888i	$0.807761\pi$
$840$		0			0
$841$	12.8114	+	22.1900i	0.441772	+	0.765172i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−54.0548	−	2.43473i	−1.85954	−	0.0837574i
$846$		0			0
$847$	−15.2566	+	26.4252i	−0.524222	+	0.907980i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	13.7434	+	23.8043i	0.471118	+	0.816001i
$852$		0			0
$853$	55.1359			1.88782			0.943909	−	0.330205i	$-0.107118\pi$
$853$	55.1359			1.88782			0.943909	+	0.330205i	$0.107118\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−25.6491			−0.876157			−0.438078	−	0.898937i	$-0.644341\pi$
$857$	−25.6491			−0.876157			−0.438078	+	0.898937i	$0.644341\pi$
$858$		0			0
$859$	−28.5132			−0.972857			−0.486428	−	0.873720i	$-0.661701\pi$
$859$	−28.5132			−0.972857			−0.486428	+	0.873720i	$0.661701\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−47.8114			−1.62752			−0.813759	−	0.581202i	$-0.802583\pi$
$863$	−47.8114			−1.62752			−0.813759	+	0.581202i	$0.802583\pi$
$864$		0			0
$865$	−47.1359	−	81.6418i	−1.60267	−	2.77591i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.32456	+	4.02625i	−0.0788551	+	0.136581i
$870$		0			0
$871$	8.74342	+	5.31388i	0.296259	+	0.180054i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	48.2039	+	83.4916i	1.62959	+	2.82253i
$876$		0			0
$877$	22.5680	+	39.0889i	0.762066	+	1.31994i	0.941784	+	0.336219i	$0.109148\pi$
$877$	22.5680	+	39.0889i	0.762066	+	1.31994i	−0.179717	+	0.983718i	$0.557518\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−4.98683	+	8.63745i	−0.168011	+	0.291003i	−0.937720	−	0.347391i	$-0.887068\pi$
$881$	−4.98683	+	8.63745i	−0.168011	+	0.291003i	0.769710	+	0.638394i	$0.220401\pi$
$882$		0			0
$883$	11.3509			0.381988			0.190994	−	0.981591i	$-0.438829\pi$
$883$	11.3509			0.381988			0.190994	+	0.981591i	$0.438829\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.1623	−	33.1900i	0.643406	−	1.11441i	−0.341261	−	0.939969i	$-0.610854\pi$
$887$	19.1623	−	33.1900i	0.643406	−	1.11441i	0.984667	−	0.174444i	$-0.0558127\pi$
$888$		0			0
$889$	−57.9473			−1.94349
$890$		0			0
$891$		0			0
$892$		0			0
$893$	12.4868	+	21.6278i	0.417856	+	0.723748i
$894$		0			0
$895$	32.2302	−	55.8244i	1.07734	−	1.86600i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.81139	−	10.0656i	0.193821	−	0.335707i
$900$		0			0
$901$	−18.7302	−	32.4417i	−0.623995	−	1.08079i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	15.9737			0.530983
$906$		0			0
$907$	18.1359	−	31.4124i	0.602194	−	1.04303i	−0.390294	−	0.920690i	$-0.627627\pi$
$907$	18.1359	−	31.4124i	0.602194	−	1.04303i	0.992488	−	0.122341i	$-0.0390400\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	49.9473			1.65483			0.827414	−	0.561592i	$-0.189811\pi$
$911$	49.9473			1.65483			0.827414	+	0.561592i	$0.189811\pi$
$912$		0			0
$913$	−2.02633	+	3.50971i	−0.0670619	+	0.116155i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−26.3246	−	45.5955i	−0.869313	−	1.50569i
$918$		0			0
$919$	1.67544	+	2.90196i	0.0552678	+	0.0957267i	0.892336	−	0.451372i	$-0.149065\pi$
$919$	1.67544	+	2.90196i	0.0552678	+	0.0957267i	−0.837068	+	0.547099i	$0.815732\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−22.6491	+	12.4054i	−0.745505	+	0.408330i
$924$		0			0
$925$	−23.6491	+	40.9615i	−0.777578	+	1.34680i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−14.4737	−	25.0691i	−0.474866	−	0.822491i	0.524720	−	0.851275i	$-0.324170\pi$
$929$	−14.4737	−	25.0691i	−0.474866	−	0.822491i	−0.999586	+	0.0287835i	$0.990837\pi$
$930$		0			0
$931$	15.4868			0.507560
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−14.5132			−0.474631
$936$		0			0
$937$	14.2982			0.467103			0.233551	−	0.972344i	$-0.424965\pi$
$937$	14.2982			0.467103			0.233551	+	0.972344i	$0.424965\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−48.5964			−1.58420			−0.792099	−	0.610392i	$-0.791012\pi$
$941$	−48.5964			−1.58420			−0.792099	+	0.610392i	$0.791012\pi$
$942$		0			0
$943$	10.7434	+	18.6081i	0.349854	+	0.605965i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.48683	−	16.4317i	0.308281	−	0.533958i	−0.669706	−	0.742627i	$-0.733580\pi$
$947$	9.48683	−	16.4317i	0.308281	−	0.533958i	0.977986	+	0.208669i	$0.0669131\pi$
$948$		0			0
$949$	−0.0811388	+	3.60464i	−0.00263388	+	0.117012i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	13.6491	+	23.6410i	0.442138	+	0.765806i	0.997848	−	0.0655707i	$-0.0208868\pi$
$953$	13.6491	+	23.6410i	0.442138	+	0.765806i	−0.555710	+	0.831376i	$0.687553\pi$
$954$		0			0
$955$	29.8114	+	51.6348i	0.964674	+	1.67086i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.74342	+	8.21584i	−0.153173	+	0.265303i
$960$		0			0
$961$	9.00000			0.290323
$962$		0			0
$963$		0			0
$964$		0			0
$965$	41.5680	−	71.9978i	1.33812	−	2.31769i
$966$		0			0
$967$	−34.5132			−1.10987			−0.554934	−	0.831894i	$-0.687257\pi$
$967$	−34.5132			−1.10987			−0.554934	+	0.831894i	$0.687257\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.48683	−	16.4317i	−0.304447	−	0.527318i	0.672691	−	0.739923i	$-0.265138\pi$
$971$	−9.48683	−	16.4317i	−0.304447	−	0.527318i	−0.977138	+	0.212606i	$0.931805\pi$
$972$		0			0
$973$	10.0000	−	17.3205i	0.320585	−	0.555270i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.5000	+	18.1865i	−0.335925	+	0.581839i	−0.983662	−	0.180025i	$-0.942382\pi$
$977$	−10.5000	+	18.1865i	−0.335925	+	0.581839i	0.647737	+	0.761864i	$0.275715\pi$
$978$		0			0
$979$	−6.97367	−	12.0787i	−0.222879	−	0.386038i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−23.6228			−0.753450			−0.376725	−	0.926325i	$-0.622950\pi$
$983$	−23.6228			−0.753450			−0.376725	+	0.926325i	$0.622950\pi$
$984$		0			0
$985$	−39.4868	+	68.3932i	−1.25816	+	2.17919i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	65.6228			2.08668
$990$		0			0
$991$	13.3925	−	23.1965i	0.425428	−	0.736862i	−0.571033	−	0.820927i	$-0.693457\pi$
$991$	13.3925	−	23.1965i	0.425428	−	0.736862i	0.996460	+	0.0840651i	$0.0267904\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−13.5548	−	23.4776i	−0.429716	−	0.744290i
$996$		0			0
$997$	29.7302	+	51.4943i	0.941566	+	1.63084i	0.762484	+	0.647007i	$0.223979\pi$
$997$	29.7302	+	51.4943i	0.941566	+	1.63084i	0.179082	+	0.983834i	$0.442687\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1872.2.t.p.1153.2		4
3.2	odd	2		1872.2.t.n.1153.1		4
4.3	odd	2		234.2.h.d.217.2	yes	4
12.11	even	2		234.2.h.e.217.1	yes	4
13.3	even	3	inner	1872.2.t.p.289.2		4
39.29	odd	6		1872.2.t.n.289.1		4
52.3	odd	6		234.2.h.d.55.2	✓	4
52.7	even	12		3042.2.b.k.1351.4		4
52.19	even	12		3042.2.b.k.1351.1		4
52.35	odd	6		3042.2.a.w.1.2		2
52.43	odd	6		3042.2.a.q.1.1		2
156.35	even	6		3042.2.a.r.1.1		2
156.59	odd	12		3042.2.b.j.1351.1		4
156.71	odd	12		3042.2.b.j.1351.4		4
156.95	even	6		3042.2.a.x.1.2		2
156.107	even	6		234.2.h.e.55.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.h.d.55.2	✓	4	52.3	odd	6
234.2.h.d.217.2	yes	4	4.3	odd	2
234.2.h.e.55.1	yes	4	156.107	even	6
234.2.h.e.217.1	yes	4	12.11	even	2
1872.2.t.n.289.1		4	39.29	odd	6
1872.2.t.n.1153.1		4	3.2	odd	2
1872.2.t.p.289.2		4	13.3	even	3	inner
1872.2.t.p.1153.2		4	1.1	even	1	trivial
3042.2.a.q.1.1		2	52.43	odd	6
3042.2.a.r.1.1		2	156.35	even	6
3042.2.a.w.1.2		2	52.35	odd	6
3042.2.a.x.1.2		2	156.95	even	6
3042.2.b.j.1351.1		4	156.59	odd	12
3042.2.b.j.1351.4		4	156.71	odd	12
3042.2.b.k.1351.1		4	52.19	even	12
3042.2.b.k.1351.4		4	52.7	even	12

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:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+4.16228 q^{5} +(1.58114 + 2.73861i) q^{7} +O(q^{10})\)	\(q+4.16228 q^{5} +(1.58114 + 2.73861i) q^{7} +(-0.581139 + 1.00656i) q^{11} +(0.0811388 - 3.60464i) q^{13} +(1.50000 + 2.59808i) q^{17} +(-2.58114 - 4.47066i) q^{19} +(3.58114 - 6.20271i) q^{23} +12.3246 q^{25} +(0.918861 - 1.59151i) q^{29} +6.32456 q^{31} +(6.58114 + 11.3989i) q^{35} +(-1.91886 + 3.32357i) q^{37} +(-1.50000 + 2.59808i) q^{41} +(4.58114 + 7.93477i) q^{43} -4.83772 q^{47} +(-1.50000 + 2.59808i) q^{49} -12.4868 q^{53} +(-2.41886 + 4.18959i) q^{55} +(-1.16228 - 2.01312i) q^{59} +(-0.0811388 - 0.140537i) q^{61} +(0.337722 - 15.0035i) q^{65} +(-1.41886 + 2.45754i) q^{67} +(-3.58114 - 6.20271i) q^{71} -1.00000 q^{73} -3.67544 q^{77} +4.00000 q^{79} +3.48683 q^{83} +(6.24342 + 10.8139i) q^{85} +(-6.00000 + 10.3923i) q^{89} +(10.0000 - 5.47723i) q^{91} +(-10.7434 - 18.6081i) q^{95} +(2.00000 + 3.46410i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5}+O(q^{10}) \) 4 * q + 4 * q^5	\( 4 q + 4 q^{5} + 4 q^{11} - 6 q^{13} + 6 q^{17} - 4 q^{19} + 8 q^{23} + 24 q^{25} + 10 q^{29} + 20 q^{35} - 14 q^{37} - 6 q^{41} + 12 q^{43} - 32 q^{47} - 6 q^{49} - 12 q^{53} - 16 q^{55} + 8 q^{59} + 6 q^{61} + 14 q^{65} - 12 q^{67} - 8 q^{71} - 4 q^{73} - 40 q^{77} + 16 q^{79} - 24 q^{83} + 6 q^{85} - 24 q^{89} + 40 q^{91} - 24 q^{95} + 8 q^{97}+O(q^{100}) \) 4 * q + 4 * q^5 + 4 * q^11 - 6 * q^13 + 6 * q^17 - 4 * q^19 + 8 * q^23 + 24 * q^25 + 10 * q^29 + 20 * q^35 - 14 * q^37 - 6 * q^41 + 12 * q^43 - 32 * q^47 - 6 * q^49 - 12 * q^53 - 16 * q^55 + 8 * q^59 + 6 * q^61 + 14 * q^65 - 12 * q^67 - 8 * q^71 - 4 * q^73 - 40 * q^77 + 16 * q^79 - 24 * q^83 + 6 * q^85 - 24 * q^89 + 40 * q^91 - 24 * q^95 + 8 * q^97

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