LMFDB - Embedded newform 1665.2.g.e.739.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1665,2,Mod(739,1665)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1665, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("1665.739");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1665 = 3^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1665.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.2950919365$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 555)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.2
Character	$\chi$	$=$	1665.739
Dual form			1665.2.g.e.739.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71549 q^{2} +5.37390 q^{4} +(0.734693 + 2.11192i) q^{5} -1.35808i q^{7} -9.16180 q^{8} +O(q^{10})$	\(q-2.71549 q^{2} +5.37390 q^{4} +(0.734693 + 2.11192i) q^{5} -1.35808i q^{7} -9.16180 q^{8} +(-1.99505 - 5.73492i) q^{10} -2.97912 q^{11} -5.29371 q^{13} +3.68784i q^{14} +14.1310 q^{16} +5.19397 q^{17} +8.16246i q^{19} +(3.94816 + 11.3493i) q^{20} +8.08977 q^{22} -2.36681 q^{23} +(-3.92045 + 3.10323i) q^{25} +14.3750 q^{26} -7.29816i q^{28} -8.38167i q^{29} -6.98231i q^{31} -20.0490 q^{32} -14.1042 q^{34} +(2.86815 - 0.997769i) q^{35} +(-5.71477 - 2.08360i) q^{37} -22.1651i q^{38} +(-6.73111 - 19.3490i) q^{40} -0.765086 q^{41} +2.65872 q^{43} -16.0095 q^{44} +6.42707 q^{46} -2.48237i q^{47} +5.15563 q^{49} +(10.6460 - 8.42680i) q^{50} -28.4479 q^{52} +3.57466i q^{53} +(-2.18874 - 6.29167i) q^{55} +12.4424i q^{56} +22.7604i q^{58} -0.162508i q^{59} -11.2982i q^{61} +18.9604i q^{62} +26.1809 q^{64} +(-3.88925 - 11.1799i) q^{65} -2.92828i q^{67} +27.9119 q^{68} +(-7.78845 + 2.70943i) q^{70} +7.77585 q^{71} +1.81844i q^{73} +(15.5184 + 5.65800i) q^{74} +43.8643i q^{76} +4.04587i q^{77} -10.6681i q^{79} +(10.3819 + 29.8436i) q^{80} +2.07758 q^{82} -6.27919i q^{83} +(3.81597 + 10.9693i) q^{85} -7.21972 q^{86} +27.2941 q^{88} +7.15474i q^{89} +7.18926i q^{91} -12.7190 q^{92} +6.74086i q^{94} +(-17.2385 + 5.99690i) q^{95} +9.38896 q^{97} -14.0001 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4}+O(q^{10}) $ 40 * q + 44 * q^4	$ 40 q + 44 q^{4} + 4 q^{10} - 8 q^{11} + 52 q^{16} + 8 q^{25} + 16 q^{26} - 32 q^{34} - 28 q^{40} - 8 q^{41} - 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} + 48 q^{65} - 56 q^{70} - 24 q^{71} + 68 q^{74} - 64 q^{85} - 80 q^{86} - 32 q^{95}+O(q^{100}) $ 40 * q + 44 * q^4 + 4 * q^10 - 8 * q^11 + 52 * q^16 + 8 * q^25 + 16 * q^26 - 32 * q^34 - 28 * q^40 - 8 * q^41 - 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 + 48 * q^65 - 56 * q^70 - 24 * q^71 + 68 * q^74 - 64 * q^85 - 80 * q^86 - 32 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1665\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.71549			−1.92014			−0.960072	−	0.279755i	$-0.909747\pi$
$2$	−2.71549			−1.92014			−0.960072	+	0.279755i	$0.909747\pi$
$3$		0			0
$3$		0			0
$4$	5.37390			2.68695
$5$	0.734693	+	2.11192i	0.328565	+	0.944482i
$5$	0.734693	+	2.11192i	0.328565	+	0.944482i
$6$		0			0
$7$		−	1.35808i		−	0.513304i	−0.966504	−	0.256652i	$-0.917381\pi$
$7$		−	1.35808i		−	0.513304i	0.966504	−	0.256652i	$-0.0826195\pi$
$8$	−9.16180			−3.23918
$9$		0			0
$10$	−1.99505	−	5.73492i	−0.630891	−	1.81354i
$11$	−2.97912			−0.898238			−0.449119	−	0.893472i	$-0.648262\pi$
$11$	−2.97912			−0.898238			−0.449119	+	0.893472i	$0.648262\pi$
$12$		0			0
$13$	−5.29371			−1.46821			−0.734106	−	0.679035i	$-0.762398\pi$
$13$	−5.29371			−1.46821			−0.734106	+	0.679035i	$0.762398\pi$
$14$			3.68784i			0.985618i
$15$		0			0
$16$	14.1310			3.53275
$17$	5.19397			1.25972			0.629861	−	0.776708i	$-0.283112\pi$
$17$	5.19397			1.25972			0.629861	+	0.776708i	$0.283112\pi$
$18$		0			0
$19$			8.16246i			1.87260i	0.351204	+	0.936299i	$0.385772\pi$
$19$			8.16246i			1.87260i	−0.351204	+	0.936299i	$0.614228\pi$
$20$	3.94816	+	11.3493i	0.882836	+	2.53777i
$21$		0			0
$22$	8.08977			1.72475
$23$	−2.36681			−0.493515			−0.246757	−	0.969077i	$-0.579365\pi$
$23$	−2.36681			−0.493515			−0.246757	+	0.969077i	$0.579365\pi$
$24$		0			0
$25$	−3.92045	+	3.10323i	−0.784091	+	0.620646i
$26$	14.3750			2.81918
$27$		0			0
$28$		−	7.29816i		−	1.37922i
$29$		−	8.38167i		−	1.55644i	−0.627993	−	0.778219i	$-0.716123\pi$
$29$		−	8.38167i		−	1.55644i	0.627993	−	0.778219i	$-0.283877\pi$
$30$		0			0
$31$		−	6.98231i		−	1.25406i	−0.778995	−	0.627030i	$-0.784270\pi$
$31$		−	6.98231i		−	1.25406i	0.778995	−	0.627030i	$-0.215730\pi$
$32$	−20.0490			−3.54420
$33$		0			0
$34$	−14.1042			−2.41885
$35$	2.86815	−	0.997769i	0.484807	−	0.168654i
$36$		0			0
$37$	−5.71477	−	2.08360i	−0.939503	−	0.342542i
$37$	−5.71477	−	2.08360i	−0.939503	−	0.342542i
$38$		−	22.1651i		−	3.59566i
$39$		0			0
$40$	−6.73111	−	19.3490i	−1.06428	−	3.05935i
$41$	−0.765086			−0.119486			−0.0597432	−	0.998214i	$-0.519028\pi$
$41$	−0.765086			−0.119486			−0.0597432	+	0.998214i	$0.519028\pi$
$42$		0			0
$43$	2.65872			0.405450			0.202725	−	0.979236i	$-0.435020\pi$
$43$	2.65872			0.405450			0.202725	+	0.979236i	$0.435020\pi$
$44$	−16.0095			−2.41352
$45$		0			0
$46$	6.42707			0.947619
$47$		−	2.48237i		−	0.362091i	−0.983475	−	0.181046i	$-0.942052\pi$
$47$		−	2.48237i		−	0.362091i	0.983475	−	0.181046i	$-0.0579482\pi$
$48$		0			0
$49$	5.15563			0.736519
$50$	10.6460	−	8.42680i	1.50557	−	1.19173i
$51$		0			0
$52$	−28.4479			−3.94501
$53$			3.57466i			0.491017i	0.969394	+	0.245509i	$0.0789549\pi$
$53$			3.57466i			0.491017i	−0.969394	+	0.245509i	$0.921045\pi$
$54$		0			0
$55$	−2.18874	−	6.29167i	−0.295129	−	0.848369i
$56$			12.4424i			1.66269i
$57$		0			0
$58$			22.7604i			2.98858i
$59$		−	0.162508i		−	0.0211568i	−0.999944	−	0.0105784i	$-0.996633\pi$
$59$		−	0.162508i		−	0.0211568i	0.999944	−	0.0105784i	$-0.00336727\pi$
$60$		0			0
$61$		−	11.2982i		−	1.44659i	−0.690540	−	0.723294i	$-0.742627\pi$
$61$		−	11.2982i		−	1.44659i	0.690540	−	0.723294i	$-0.257373\pi$
$62$			18.9604i			2.40797i
$63$		0			0
$64$	26.1809			3.27262
$65$	−3.88925	−	11.1799i	−0.482402	−	1.38670i
$66$		0			0
$67$		−	2.92828i		−	0.357747i	−0.983872	−	0.178873i	$-0.942755\pi$
$67$		−	2.92828i		−	0.357747i	0.983872	−	0.178873i	$-0.0572453\pi$
$68$	27.9119			3.38481
$69$		0			0
$70$	−7.78845	+	2.70943i	−0.930898	+	0.323839i
$71$	7.77585			0.922824			0.461412	−	0.887186i	$-0.347343\pi$
$71$	7.77585			0.922824			0.461412	+	0.887186i	$0.347343\pi$
$72$		0			0
$73$			1.81844i			0.212832i	0.994322	+	0.106416i	$0.0339375\pi$
$73$			1.81844i			0.212832i	−0.994322	+	0.106416i	$0.966063\pi$
$74$	15.5184	+	5.65800i	1.80398	+	0.657729i
$75$		0			0
$76$			43.8643i			5.03158i
$77$			4.04587i			0.461070i
$78$		0			0
$79$		−	10.6681i		−	1.20026i	−0.799904	−	0.600128i	$-0.795116\pi$
$79$		−	10.6681i		−	1.20026i	0.799904	−	0.600128i	$-0.204884\pi$
$80$	10.3819	+	29.8436i	1.16074	+	3.33661i
$81$		0			0
$82$	2.07758			0.229431
$83$		−	6.27919i		−	0.689231i	−0.938744	−	0.344615i	$-0.888009\pi$
$83$		−	6.27919i		−	0.689231i	0.938744	−	0.344615i	$-0.111991\pi$
$84$		0			0
$85$	3.81597	+	10.9693i	0.413900	+	1.18978i
$86$	−7.21972			−0.778523
$87$		0			0
$88$	27.2941			2.90956
$89$			7.15474i			0.758401i	0.925314	+	0.379201i	$0.123801\pi$
$89$			7.15474i			0.758401i	−0.925314	+	0.379201i	$0.876199\pi$
$90$		0			0
$91$			7.18926i			0.753640i
$92$	−12.7190			−1.32605
$93$		0			0
$94$			6.74086i			0.695267i
$95$	−17.2385	+	5.99690i	−1.76863	+	0.615269i
$96$		0			0
$97$	9.38896			0.953304			0.476652	−	0.879092i	$-0.341850\pi$
$97$	9.38896			0.953304			0.476652	+	0.879092i	$0.341850\pi$
$98$	−14.0001			−1.41422
$99$		0			0
$100$	−21.0681	+	16.6765i	−2.10681	+	1.66765i
$101$	−14.5422			−1.44701			−0.723503	−	0.690321i	$-0.757469\pi$
$101$	−14.5422			−1.44701			−0.723503	+	0.690321i	$0.757469\pi$
$102$		0			0
$103$	−4.71423			−0.464507			−0.232253	−	0.972655i	$-0.574610\pi$
$103$	−4.71423			−0.464507			−0.232253	+	0.972655i	$0.574610\pi$
$104$	48.4999			4.75581
$105$		0			0
$106$		−	9.70696i		−	0.942823i
$107$		−	3.63552i		−	0.351459i	−0.984439	−	0.175729i	$-0.943772\pi$
$107$		−	3.63552i		−	0.351459i	0.984439	−	0.175729i	$-0.0562284\pi$
$108$		0			0
$109$		−	8.22404i		−	0.787720i	−0.919170	−	0.393860i	$-0.871140\pi$
$109$		−	8.22404i		−	0.787720i	0.919170	−	0.393860i	$-0.128860\pi$
$110$	5.94350	+	17.0850i	0.566690	+	1.62899i
$111$		0			0
$112$		−	19.1910i		−	1.81337i
$113$	3.27536			0.308120			0.154060	−	0.988061i	$-0.450765\pi$
$113$	3.27536			0.308120			0.154060	+	0.988061i	$0.450765\pi$
$114$		0			0
$115$	−1.73888	−	4.99853i	−0.162152	−	0.466116i
$116$		−	45.0423i		−	4.18207i
$117$		0			0
$118$			0.441290i			0.0406240i
$119$		−	7.05381i		−	0.646621i
$120$		0			0
$121$	−2.12486			−0.193169
$122$			30.6802i			2.77766i
$123$		0			0
$124$		−	37.5222i		−	3.36959i
$125$	−9.43412	−	5.99978i	−0.843813	−	0.536637i
$126$		0			0
$127$		−	7.69097i		−	0.682463i	−0.939979	−	0.341232i	$-0.889156\pi$
$127$		−	7.69097i		−	0.682463i	0.939979	−	0.341232i	$-0.110844\pi$
$128$	−30.9961			−2.73970
$129$		0			0
$130$	10.5612	+	30.3590i	0.926282	+	2.66266i
$131$		−	5.84994i		−	0.511111i	−0.966794	−	0.255556i	$-0.917742\pi$
$131$		−	5.84994i		−	0.511111i	0.966794	−	0.255556i	$-0.0822584\pi$
$132$		0			0
$133$	11.0852			0.961213
$134$			7.95173i			0.686925i
$135$		0			0
$136$	−47.5861			−4.08047
$137$			11.5569i			0.987370i	0.869641	+	0.493685i	$0.164350\pi$
$137$			11.5569i			0.987370i	−0.869641	+	0.493685i	$0.835650\pi$
$138$		0			0
$139$	9.45387			0.801867			0.400933	−	0.916107i	$-0.368686\pi$
$139$	9.45387			0.801867			0.400933	+	0.916107i	$0.368686\pi$
$140$	15.4132	−	5.36191i	1.30265	−	0.453164i
$141$		0			0
$142$	−21.1153			−1.77195
$143$	15.7706			1.31880
$144$		0			0
$145$	17.7015	−	6.15796i	1.47003	−	0.511390i
$146$		−	4.93795i		−	0.408668i
$147$		0			0
$148$	−30.7106	−	11.1970i	−2.52440	−	0.920392i
$149$	6.02914			0.493927			0.246963	−	0.969025i	$-0.420567\pi$
$149$	6.02914			0.493927			0.246963	+	0.969025i	$0.420567\pi$
$150$		0			0
$151$	−16.6226			−1.35273			−0.676363	−	0.736568i	$-0.736445\pi$
$151$	−16.6226			−1.35273			−0.676363	+	0.736568i	$0.736445\pi$
$152$		−	74.7828i		−	6.06569i
$153$		0			0
$154$		−	10.9865i		−	0.885319i
$155$	14.7461	−	5.12985i	1.18444	−	0.412040i
$156$		0			0
$157$			11.5569i			0.922343i	0.887311	+	0.461171i	$0.152571\pi$
$157$			11.5569i			0.922343i	−0.887311	+	0.461171i	$0.847429\pi$
$158$			28.9692i			2.30466i
$159$		0			0
$160$	−14.7299	−	42.3420i	−1.16450	−	3.34743i
$161$			3.21431i			0.253323i
$162$		0			0
$163$	2.82071			0.220935			0.110468	−	0.993880i	$-0.464765\pi$
$163$	2.82071			0.220935			0.110468	+	0.993880i	$0.464765\pi$
$164$	−4.11149			−0.321054
$165$		0			0
$166$			17.0511i			1.32342i
$167$	−14.1477			−1.09478			−0.547390	−	0.836878i	$-0.684379\pi$
$167$	−14.1477			−1.09478			−0.547390	+	0.836878i	$0.684379\pi$
$168$		0			0
$169$	15.0234			1.15565
$170$	−10.3622	−	29.7870i	−0.794748	−	2.28456i
$171$		0			0
$172$	14.2877			1.08942
$173$		−	12.9160i		−	0.981989i	−0.871163	−	0.490994i	$-0.836634\pi$
$173$		−	12.9160i		−	0.981989i	0.871163	−	0.490994i	$-0.163366\pi$
$174$		0			0
$175$	4.21442	+	5.32427i	0.318581	+	0.402477i
$176$	−42.0979			−3.17325
$177$		0			0
$178$		−	19.4286i		−	1.45624i
$179$		−	15.2614i		−	1.14069i	−0.821404	−	0.570346i	$-0.806809\pi$
$179$		−	15.2614i		−	1.14069i	0.821404	−	0.570346i	$-0.193191\pi$
$180$		0			0
$181$	−2.21198			−0.164415			−0.0822077	−	0.996615i	$-0.526197\pi$
$181$	−2.21198			−0.164415			−0.0822077	+	0.996615i	$0.526197\pi$
$182$		−	19.5224i		−	1.44710i
$183$		0			0
$184$	21.6843			1.59859
$185$	0.201802	−	13.6000i	0.0148368	−	0.999890i
$186$		0			0
$187$	−15.4735			−1.13153
$188$		−	13.3400i		−	0.972921i
$189$		0			0
$190$	46.8110	−	16.2845i	3.39603	−	1.18141i
$191$		−	22.7972i		−	1.64955i	−0.565461	−	0.824775i	$-0.691302\pi$
$191$		−	22.7972i		−	1.64955i	0.565461	−	0.824775i	$-0.308698\pi$
$192$		0			0
$193$	20.1256			1.44867			0.724336	−	0.689448i	$-0.242147\pi$
$193$	20.1256			1.44867			0.724336	+	0.689448i	$0.242147\pi$
$194$	−25.4956			−1.83048
$195$		0			0
$196$	27.7058			1.97899
$197$			8.87079i			0.632018i	0.948756	+	0.316009i	$0.102343\pi$
$197$			8.87079i			0.632018i	−0.948756	+	0.316009i	$0.897657\pi$
$198$		0			0
$199$		−	9.34694i		−	0.662587i	−0.943528	−	0.331293i	$-0.892515\pi$
$199$		−	9.34694i		−	0.662587i	0.943528	−	0.331293i	$-0.107485\pi$
$200$	35.9184	−	28.4312i	2.53981	−	2.01039i
$201$		0			0
$202$	39.4893			2.77846
$203$	−11.3829			−0.798926
$204$		0			0
$205$	−0.562103	−	1.61580i	−0.0392590	−	0.112853i
$206$	12.8015			0.891920
$207$		0			0
$208$	−74.8054			−5.18682
$209$		−	24.3169i		−	1.68204i
$210$		0			0
$211$	−8.75665			−0.602832			−0.301416	−	0.953493i	$-0.597459\pi$
$211$	−8.75665			−0.602832			−0.301416	+	0.953493i	$0.597459\pi$
$212$			19.2099i			1.31934i
$213$		0			0
$214$			9.87222i			0.674851i
$215$	1.95334	+	5.61501i	0.133217	+	0.382940i
$216$		0			0
$217$	−9.48250			−0.643714
$218$			22.3323i			1.51253i
$219$		0			0
$220$	−11.7620	−	33.8108i	−0.792997	−	2.27952i
$221$	−27.4954			−1.84954
$222$		0			0
$223$		−	13.8965i		−	0.930582i	−0.885158	−	0.465291i	$-0.845950\pi$
$223$		−	13.8965i		−	0.930582i	0.885158	−	0.465291i	$-0.154050\pi$
$224$			27.2281i			1.81925i
$225$		0			0
$226$	−8.89423			−0.591635
$227$	−19.3784			−1.28619			−0.643095	−	0.765787i	$-0.722350\pi$
$227$	−19.3784			−1.28619			−0.643095	+	0.765787i	$0.722350\pi$
$228$		0			0
$229$	−7.60630			−0.502639			−0.251319	−	0.967904i	$-0.580864\pi$
$229$	−7.60630			−0.502639			−0.251319	+	0.967904i	$0.580864\pi$
$230$	4.72192	+	13.5735i	0.311354	+	0.895009i
$231$		0			0
$232$			76.7912i			5.04159i
$233$		−	26.7665i		−	1.75353i	−0.480920	−	0.876764i	$-0.659697\pi$
$233$		−	26.7665i		−	1.75353i	0.480920	−	0.876764i	$-0.340303\pi$
$234$		0			0
$235$	5.24258	−	1.82378i	0.341988	−	0.118970i
$236$		−	0.873303i		−	0.0568472i
$237$		0			0
$238$			19.1546i			1.24161i
$239$		−	10.2977i		−	0.666104i	−0.942908	−	0.333052i	$-0.891921\pi$
$239$		−	10.2977i		−	0.666104i	0.942908	−	0.333052i	$-0.108079\pi$
$240$		0			0
$241$			19.3983i			1.24956i	0.780802	+	0.624778i	$0.214811\pi$
$241$			19.3983i			1.24956i	−0.780802	+	0.624778i	$0.785189\pi$
$242$	5.77003			0.370911
$243$		0			0
$244$		−	60.7154i		−	3.88691i
$245$	3.78780	+	10.8883i	0.241994	+	0.695628i
$246$		0			0
$247$		−	43.2097i		−	2.74937i
$248$			63.9705i			4.06213i
$249$		0			0
$250$	25.6183	+	16.2924i	1.62024	+	1.03042i
$251$			23.1675i			1.46232i	0.682206	+	0.731160i	$0.261021\pi$
$251$			23.1675i			1.46232i	−0.682206	+	0.731160i	$0.738979\pi$
$252$		0			0
$253$	7.05102			0.443294
$254$			20.8848i			1.31043i
$255$		0			0
$256$	31.8079			1.98799
$257$	26.8211			1.67305			0.836527	−	0.547925i	$-0.184582\pi$
$257$	26.8211			1.67305			0.836527	+	0.547925i	$0.184582\pi$
$258$		0			0
$259$	−2.82969	+	7.76109i	−0.175828	+	0.482251i
$260$	−20.9004	−	60.0798i	−1.29619	−	3.72599i
$261$		0			0
$262$			15.8855i			0.981407i
$263$		−	6.86941i		−	0.423586i	−0.977315	−	0.211793i	$-0.932070\pi$
$263$		−	6.86941i		−	0.423586i	0.977315	−	0.211793i	$-0.0679303\pi$
$264$		0			0
$265$	−7.54941	+	2.62628i	−0.463757	+	0.161331i
$266$	−30.1019			−1.84567
$267$		0			0
$268$		−	15.7363i		−	0.961248i
$269$	−6.29440			−0.383777			−0.191888	−	0.981417i	$-0.561461\pi$
$269$	−6.29440			−0.383777			−0.191888	+	0.981417i	$0.561461\pi$
$270$		0			0
$271$	2.40375			0.146017			0.0730086	−	0.997331i	$-0.476740\pi$
$271$	2.40375			0.146017			0.0730086	+	0.997331i	$0.476740\pi$
$272$	73.3959			4.45028
$273$		0			0
$274$		−	31.3826i		−	1.89589i
$275$	11.6795	−	9.24489i	0.704300	−	0.557488i
$276$		0			0
$277$	−1.97632			−0.118746			−0.0593728	−	0.998236i	$-0.518910\pi$
$277$	−1.97632			−0.118746			−0.0593728	+	0.998236i	$0.518910\pi$
$278$	−25.6719			−1.53970
$279$		0			0
$280$	−26.2774	+	9.14135i	−1.57038	+	0.546300i
$281$		−	6.49523i		−	0.387473i	−0.981054	−	0.193736i	$-0.937939\pi$
$281$		−	6.49523i		−	0.387473i	0.981054	−	0.193736i	$-0.0620606\pi$
$282$		0			0
$283$	−17.7124			−1.05289			−0.526446	−	0.850209i	$-0.676476\pi$
$283$	−17.7124			−1.05289			−0.526446	+	0.850209i	$0.676476\pi$
$284$	41.7866			2.47958
$285$		0			0
$286$	−42.8249			−2.53229
$287$			1.03904i			0.0613329i
$288$		0			0
$289$	9.97733			0.586902
$290$	−48.0682	+	16.7219i	−2.82266	+	0.981943i
$291$		0			0
$292$			9.77209i			0.571868i
$293$		−	10.8660i		−	0.634796i	−0.948292	−	0.317398i	$-0.897191\pi$
$293$		−	10.8660i		−	0.634796i	0.948292	−	0.317398i	$-0.102809\pi$
$294$		0			0
$295$	0.343205	−	0.119394i	0.0199822	−	0.00695137i
$296$	52.3576	+	19.0895i	3.04322	+	1.10955i
$297$		0			0
$298$	−16.3721			−0.948410
$299$	12.5292			0.724584
$300$		0			0
$301$		−	3.61074i		−	0.208120i
$302$	45.1385			2.59743
$303$		0			0
$304$			115.344i			6.61541i
$305$	23.8610	−	8.30071i	1.36628	−	0.475297i
$306$		0			0
$307$		−	27.1188i		−	1.54775i	−0.633336	−	0.773877i	$-0.718315\pi$
$307$		−	27.1188i		−	1.54775i	0.633336	−	0.773877i	$-0.281685\pi$
$308$			21.7421i			1.23887i
$309$		0			0
$310$	−40.0430	+	13.9301i	−2.27429	+	0.791175i
$311$			7.37607i			0.418259i	0.977888	+	0.209129i	$0.0670630\pi$
$311$			7.37607i			0.418259i	−0.977888	+	0.209129i	$0.932937\pi$
$312$		0			0
$313$	20.2055			1.14208			0.571041	−	0.820921i	$-0.306540\pi$
$313$	20.2055			1.14208			0.571041	+	0.820921i	$0.306540\pi$
$314$		−	31.3827i		−	1.77103i
$315$		0			0
$316$		−	57.3293i		−	3.22503i
$317$			8.25242i			0.463502i	0.972775	+	0.231751i	$0.0744455\pi$
$317$			8.25242i			0.463502i	−0.972775	+	0.231751i	$0.925555\pi$
$318$		0			0
$319$			24.9700i			1.39805i
$320$	19.2349	+	55.2922i	1.07527	+	3.09093i
$321$		0			0
$322$		−	8.72844i		−	0.486417i
$323$			42.3956i			2.35895i
$324$		0			0
$325$	20.7538	−	16.4276i	1.15121	−	0.911240i
$326$	−7.65962			−0.424227
$327$		0			0
$328$	7.00956			0.387038
$329$	−3.37125			−0.185863
$330$		0			0
$331$		−	15.0653i		−	0.828065i	−0.910262	−	0.414033i	$-0.864120\pi$
$331$		−	15.0653i		−	0.828065i	0.910262	−	0.414033i	$-0.135880\pi$
$332$		−	33.7437i		−	1.85193i
$333$		0			0
$334$	38.4179			2.10213
$335$	6.18432	−	2.15139i	0.337885	−	0.117543i
$336$		0			0
$337$		−	19.3435i		−	1.05371i	−0.849956	−	0.526854i	$-0.823372\pi$
$337$		−	19.3435i		−	1.05371i	0.849956	−	0.526854i	$-0.176628\pi$
$338$	−40.7959			−2.21901
$339$		0			0
$340$	20.5066	+	58.9478i	1.11213	+	3.19689i
$341$			20.8011i			1.12644i
$342$		0			0
$343$		−	16.5083i		−	0.891363i
$344$	−24.3586			−1.31333
$345$		0			0
$346$			35.0734i			1.88556i
$347$	−13.7394			−0.737571			−0.368785	−	0.929515i	$-0.620226\pi$
$347$	−13.7394			−0.737571			−0.368785	+	0.929515i	$0.620226\pi$
$348$		0			0
$349$	30.3935			1.62693			0.813464	−	0.581615i	$-0.197579\pi$
$349$	30.3935			1.62693			0.813464	+	0.581615i	$0.197579\pi$
$350$	−11.4442	−	14.4580i	−0.611720	−	0.772814i
$351$		0			0
$352$	59.7283			3.18353
$353$	13.6907			0.728684			0.364342	−	0.931265i	$-0.381294\pi$
$353$	13.6907			0.728684			0.364342	+	0.931265i	$0.381294\pi$
$354$		0			0
$355$	5.71286	+	16.4220i	0.303207	+	0.871590i
$356$			38.4489i			2.03779i
$357$		0			0
$358$			41.4423i			2.19029i
$359$	−20.6617			−1.09048			−0.545240	−	0.838280i	$-0.683562\pi$
$359$	−20.6617			−1.09048			−0.545240	+	0.838280i	$0.683562\pi$
$360$		0			0
$361$	−47.6258			−2.50662
$362$	6.00662			0.315701
$363$		0			0
$364$			38.6344i			2.02499i
$365$	−3.84040	+	1.33599i	−0.201016	+	0.0699290i
$366$		0			0
$367$		−	3.21064i		−	0.167594i	−0.996483	−	0.0837971i	$-0.973295\pi$
$367$		−	3.21064i		−	0.167594i	0.996483	−	0.0837971i	$-0.0267048\pi$
$368$	−33.4454			−1.74346
$369$		0			0
$370$	−0.547992	+	36.9306i	−0.0284888	+	1.91993i
$371$	4.85466			0.252041
$372$		0			0
$373$		−	30.9683i		−	1.60348i	−0.597676	−	0.801738i	$-0.703909\pi$
$373$		−	30.9683i		−	1.60348i	0.597676	−	0.801738i	$-0.296091\pi$
$374$	42.0180			2.17270
$375$		0			0
$376$			22.7430i			1.17288i
$377$			44.3702i			2.28518i
$378$		0			0
$379$	−11.0626			−0.568246			−0.284123	−	0.958788i	$-0.591702\pi$
$379$	−11.0626			−0.568246			−0.284123	+	0.958788i	$0.591702\pi$
$380$	−92.6380	+	32.2268i	−4.75223	+	1.65320i
$381$		0			0
$382$			61.9057i			3.16737i
$383$	−19.1650			−0.979286			−0.489643	−	0.871923i	$-0.662873\pi$
$383$	−19.1650			−0.979286			−0.489643	+	0.871923i	$0.662873\pi$
$384$		0			0
$385$	−8.54457	+	2.97247i	−0.435472	+	0.151491i
$386$	−54.6509			−2.78166
$387$		0			0
$388$	50.4553			2.56148
$389$			30.7456i			1.55886i	0.626487	+	0.779432i	$0.284492\pi$
$389$			30.7456i			1.55886i	−0.626487	+	0.779432i	$0.715508\pi$
$390$		0			0
$391$	−12.2932			−0.621692
$392$	−47.2348			−2.38572
$393$		0			0
$394$		−	24.0886i		−	1.21356i
$395$	22.5302	−	7.83778i	1.13362	−	0.394362i
$396$		0			0
$397$			30.1572i			1.51354i	0.653678	+	0.756772i	$0.273225\pi$
$397$			30.1572i			1.51354i	−0.653678	+	0.756772i	$0.726775\pi$
$398$			25.3815i			1.27226i
$399$		0			0
$400$	−55.3999	+	43.8517i	−2.76999	+	2.19259i
$401$			10.1698i			0.507855i	0.967223	+	0.253927i	$0.0817224\pi$
$401$			10.1698i			0.507855i	−0.967223	+	0.253927i	$0.918278\pi$
$402$		0			0
$403$			36.9623i			1.84123i
$404$	−78.1485			−3.88803
$405$		0			0
$406$	30.9103			1.53405
$407$	17.0250	+	6.20729i	0.843897	+	0.307684i
$408$		0			0
$409$			5.79195i			0.286393i	0.989694	+	0.143197i	$0.0457381\pi$
$409$			5.79195i			0.286393i	−0.989694	+	0.143197i	$0.954262\pi$
$410$	1.52639	+	4.38770i	0.0753828	+	0.216693i
$411$		0			0
$412$	−25.3338			−1.24811
$413$	−0.220699			−0.0108599
$414$		0			0
$415$	13.2612	−	4.61328i	0.650966	−	0.226457i
$416$	106.134			5.20363
$417$		0			0
$418$			66.0325i			3.22975i
$419$	15.6425			0.764187			0.382094	−	0.924124i	$-0.375203\pi$
$419$	15.6425			0.764187			0.382094	+	0.924124i	$0.375203\pi$
$420$		0			0
$421$		−	0.256794i		−	0.0125154i	−0.999980	−	0.00625768i	$-0.998008\pi$
$421$		−	0.256794i		−	0.0125154i	0.999980	−	0.00625768i	$-0.00199189\pi$
$422$	23.7786			1.15752
$423$		0			0
$424$		−	32.7503i		−	1.59049i
$425$	−20.3627	+	16.1181i	−0.987737	+	0.781842i
$426$		0			0
$427$	−15.3438			−0.742540
$428$		−	19.5369i		−	0.944352i
$429$		0			0
$430$	−5.30428	−	15.2475i	−0.255795	−	0.735301i
$431$		−	29.8357i		−	1.43713i	−0.695458	−	0.718567i	$-0.744798\pi$
$431$		−	29.8357i		−	1.43713i	0.695458	−	0.718567i	$-0.255202\pi$
$432$		0			0
$433$			19.2262i			0.923953i	0.886892	+	0.461977i	$0.152860\pi$
$433$			19.2262i			0.923953i	−0.886892	+	0.461977i	$0.847140\pi$
$434$	25.7497			1.23602
$435$		0			0
$436$		−	44.1951i		−	2.11656i
$437$		−	19.3190i		−	0.924155i
$438$		0			0
$439$			6.51507i			0.310947i	0.987840	+	0.155474i	$0.0496904\pi$
$439$			6.51507i			0.310947i	−0.987840	+	0.155474i	$0.950310\pi$
$440$	20.0528	+	57.6430i	0.955978	+	2.74802i
$441$		0			0
$442$	74.6635			3.55138
$443$		−	21.7286i		−	1.03236i	−0.856480	−	0.516180i	$-0.827354\pi$
$443$		−	21.7286i		−	1.03236i	0.856480	−	0.516180i	$-0.172646\pi$
$444$		0			0
$445$	−15.1103	+	5.25654i	−0.716296	+	0.249184i
$446$			37.7360i			1.78685i
$447$		0			0
$448$		−	35.5557i		−	1.67985i
$449$		−	10.8252i		−	0.510873i	−0.966826	−	0.255437i	$-0.917781\pi$
$449$		−	10.8252i		−	0.510873i	0.966826	−	0.255437i	$-0.0822192\pi$
$450$		0			0
$451$	2.27928			0.107327
$452$	17.6015			0.827904
$453$		0			0
$454$	52.6219			2.46967
$455$	−15.1832	+	5.28190i	−0.711799	+	0.247619i
$456$		0			0
$457$	9.33380			0.436617			0.218308	−	0.975880i	$-0.429946\pi$
$457$	9.33380			0.436617			0.218308	+	0.975880i	$0.429946\pi$
$458$	20.6549			0.965138
$459$		0			0
$460$	−9.34457	−	26.8616i	−0.435693	−	1.25243i
$461$		−	5.96486i		−	0.277811i	−0.990306	−	0.138906i	$-0.955642\pi$
$461$		−	5.96486i		−	0.277811i	0.990306	−	0.138906i	$-0.0443585\pi$
$462$		0			0
$463$	−35.7571			−1.66177			−0.830887	−	0.556441i	$-0.812166\pi$
$463$	−35.7571			−1.66177			−0.830887	+	0.556441i	$0.812166\pi$
$464$		−	118.441i		−	5.49850i
$465$		0			0
$466$			72.6841i			3.36703i
$467$	0.575842			0.0266468			0.0133234	−	0.999911i	$-0.495759\pi$
$467$	0.575842			0.0266468			0.0133234	+	0.999911i	$0.495759\pi$
$468$		0			0
$469$	−3.97683			−0.183633
$470$	−14.2362	+	4.95246i	−0.656667	+	0.228440i
$471$		0			0
$472$			1.48887i			0.0685307i
$473$	−7.92063			−0.364191
$474$		0			0
$475$	−25.3300	−	32.0006i	−1.16222	−	1.46829i
$476$		−	37.9064i		−	1.73744i
$477$		0			0
$478$			27.9634i			1.27902i
$479$			10.6374i			0.486034i	0.970022	+	0.243017i	$0.0781371\pi$
$479$			10.6374i			0.486034i	−0.970022	+	0.243017i	$0.921863\pi$
$480$		0			0
$481$	30.2524	+	11.0300i	1.37939	+	0.502923i
$482$		−	52.6760i		−	2.39933i
$483$		0			0
$484$	−11.4188			−0.519034
$485$	6.89800	+	19.8288i	0.313222	+	0.900378i
$486$		0			0
$487$	−0.182304			−0.00826099			−0.00413050	−	0.999991i	$-0.501315\pi$
$487$	−0.182304			−0.00826099			−0.00413050	+	0.999991i	$0.501315\pi$
$488$			103.512i			4.68576i
$489$		0			0
$490$	−10.2858	−	29.5671i	−0.464663	−	1.33571i
$491$	−8.92187			−0.402638			−0.201319	−	0.979526i	$-0.564523\pi$
$491$	−8.92187			−0.402638			−0.201319	+	0.979526i	$0.564523\pi$
$492$		0			0
$493$		−	43.5342i		−	1.96068i
$494$			117.336i			5.27918i
$495$		0			0
$496$		−	98.6669i		−	4.43028i
$497$		−	10.5602i		−	0.473689i
$498$		0			0
$499$			28.1796i			1.26149i	0.775990	+	0.630746i	$0.217251\pi$
$499$			28.1796i			1.26149i	−0.775990	+	0.630746i	$0.782749\pi$
$500$	−50.6980	−	32.2422i	−2.26728	−	1.44192i
$501$		0			0
$502$		−	62.9112i		−	2.80786i
$503$	24.4775			1.09140			0.545698	−	0.837982i	$-0.316264\pi$
$503$	24.4775			1.09140			0.545698	+	0.837982i	$0.316264\pi$
$504$		0			0
$505$	−10.6841	−	30.7121i	−0.475435	−	1.36667i
$506$	−19.1470			−0.851188
$507$		0			0
$508$		−	41.3305i		−	1.83374i
$509$	8.39148			0.371946			0.185973	−	0.982555i	$-0.440456\pi$
$509$	8.39148			0.371946			0.185973	+	0.982555i	$0.440456\pi$
$510$		0			0
$511$	2.46957			0.109248
$512$	−24.3817			−1.07753
$513$		0			0
$514$	−72.8325			−3.21250
$515$	−3.46351	−	9.95610i	−0.152621	−	0.438718i
$516$		0			0
$517$			7.39528i			0.325244i
$518$	7.68399	−	21.0752i	0.337615	−	0.925991i
$519$		0			0
$520$	35.6325	+	102.428i	1.56259	+	4.49177i
$521$	18.9435			0.829929			0.414964	−	0.909838i	$-0.363794\pi$
$521$	18.9435			0.829929			0.414964	+	0.909838i	$0.363794\pi$
$522$		0			0
$523$	−34.6966			−1.51718			−0.758589	−	0.651570i	$-0.774111\pi$
$523$	−34.6966			−1.51718			−0.758589	+	0.651570i	$0.774111\pi$
$524$		−	31.4370i		−	1.37333i
$525$		0			0
$526$			18.6538i			0.813346i
$527$		−	36.2659i		−	1.57977i
$528$		0			0
$529$	−17.3982			−0.756443
$530$	20.5004	−	7.13163i	0.890479	−	0.309778i
$531$		0			0
$532$	59.5710			2.58273
$533$	4.05014			0.175431
$534$		0			0
$535$	7.67794	−	2.67099i	0.331946	−	0.115477i
$536$			26.8283i			1.15881i
$537$		0			0
$538$	17.0924			0.736906
$539$	−15.3592			−0.661569
$540$		0			0
$541$			3.84115i			0.165144i	0.996585	+	0.0825720i	$0.0263134\pi$
$541$			3.84115i			0.165144i	−0.996585	+	0.0825720i	$0.973687\pi$
$542$	−6.52736			−0.280374
$543$		0			0
$544$	−104.134			−4.46471
$545$	17.3685	−	6.04214i	0.743987	−	0.258817i
$546$		0			0
$547$	17.3358			0.741227			0.370614	−	0.928787i	$-0.379147\pi$
$547$	17.3358			0.741227			0.370614	+	0.928787i	$0.379147\pi$
$548$			62.1054i			2.65301i
$549$		0			0
$550$	−31.7156	+	25.1044i	−1.35236	+	1.07046i
$551$	68.4151			2.91458
$552$		0			0
$553$	−14.4881			−0.616097
$554$	5.36668			0.228009
$555$		0			0
$556$	50.8041			2.15458
$557$	−36.9913			−1.56737			−0.783687	−	0.621156i	$-0.786663\pi$
$557$	−36.9913			−1.56737			−0.783687	+	0.621156i	$0.786663\pi$
$558$		0			0
$559$	−14.0745			−0.595287
$560$	40.5299	−	14.0995i	1.71270	−	0.595811i
$561$		0			0
$562$			17.6377i			0.744003i
$563$	2.67097			0.112568			0.0562840	−	0.998415i	$-0.482075\pi$
$563$	2.67097			0.112568			0.0562840	+	0.998415i	$0.482075\pi$
$564$		0			0
$565$	2.40639	+	6.91732i	0.101237	+	0.291014i
$566$	48.0978			2.02170
$567$		0			0
$568$	−71.2407			−2.98920
$569$			17.5044i			0.733824i	0.930256	+	0.366912i	$0.119585\pi$
$569$			17.5044i			0.733824i	−0.930256	+	0.366912i	$0.880415\pi$
$570$		0			0
$571$	3.43218			0.143632			0.0718161	−	0.997418i	$-0.477121\pi$
$571$	3.43218			0.143632			0.0718161	+	0.997418i	$0.477121\pi$
$572$	84.7496			3.54356
$573$		0			0
$574$		−	2.82152i		−	0.117768i
$575$	9.27899	−	7.34477i	0.386960	−	0.306298i
$576$		0			0
$577$	−26.5724			−1.10622			−0.553111	−	0.833107i	$-0.686560\pi$
$577$	−26.5724			−1.10622			−0.553111	+	0.833107i	$0.686560\pi$
$578$	−27.0934			−1.12694
$579$		0			0
$580$	95.1259	−	33.0922i	3.94989	−	1.37408i
$581$	−8.52762			−0.353785
$582$		0			0
$583$		−	10.6493i		−	0.441050i
$584$		−	16.6601i		−	0.689401i
$585$		0			0
$586$			29.5064i			1.21890i
$587$	−1.40819			−0.0581221			−0.0290610	−	0.999578i	$-0.509252\pi$
$587$	−1.40819			−0.0581221			−0.0290610	+	0.999578i	$0.509252\pi$
$588$		0			0
$589$	56.9928			2.34835
$590$	−0.931971	+	0.324212i	−0.0383686	+	0.0133476i
$591$		0			0
$592$	−80.7554	−	29.4433i	−3.31903	−	1.21011i
$593$		−	13.8523i		−	0.568847i	−0.958699	−	0.284424i	$-0.908198\pi$
$593$		−	13.8523i		−	0.568847i	0.958699	−	0.284424i	$-0.0918022\pi$
$594$		0			0
$595$	14.8971	−	5.18238i	0.610722	−	0.212457i
$596$	32.4000			1.32716
$597$		0			0
$598$	−34.0230			−1.39131
$599$	22.6069			0.923692			0.461846	−	0.886960i	$-0.347187\pi$
$599$	22.6069			0.923692			0.461846	+	0.886960i	$0.347187\pi$
$600$		0			0
$601$	14.6690			0.598362			0.299181	−	0.954196i	$-0.403287\pi$
$601$	14.6690			0.598362			0.299181	+	0.954196i	$0.403287\pi$
$602$			9.80493i			0.399619i
$603$		0			0
$604$	−89.3281			−3.63471
$605$	−1.56112	−	4.48753i	−0.0634684	−	0.182444i
$606$		0			0
$607$	−22.9716			−0.932390			−0.466195	−	0.884682i	$-0.654375\pi$
$607$	−22.9716			−0.932390			−0.466195	+	0.884682i	$0.654375\pi$
$608$		−	163.649i		−	6.63685i
$609$		0			0
$610$	−64.7943	+	22.5405i	−2.62344	+	0.912639i
$611$			13.1410i			0.531627i
$612$		0			0
$613$			37.2360i			1.50395i	0.659193	+	0.751974i	$0.270898\pi$
$613$			37.2360i			1.50395i	−0.659193	+	0.751974i	$0.729102\pi$
$614$			73.6410i			2.97191i
$615$		0			0
$616$		−	37.0674i		−	1.49349i
$617$		−	23.2097i		−	0.934388i	−0.884155	−	0.467194i	$-0.845265\pi$
$617$		−	23.2097i		−	0.934388i	0.884155	−	0.467194i	$-0.154735\pi$
$618$		0			0
$619$	−12.2705			−0.493191			−0.246596	−	0.969118i	$-0.579312\pi$
$619$	−12.2705			−0.493191			−0.246596	+	0.969118i	$0.579312\pi$
$620$	79.2441	−	27.5673i	3.18252	−	1.10713i
$621$		0			0
$622$		−	20.0297i		−	0.803116i
$623$	9.71668			0.389291
$624$		0			0
$625$	5.73990	−	24.3321i	0.229596	−	0.973286i
$626$	−54.8679			−2.19296
$627$		0			0
$628$			62.1057i			2.47829i
$629$	−29.6824	−	10.8221i	−1.18351	−	0.431507i
$630$		0			0
$631$		−	35.6225i		−	1.41811i	−0.705154	−	0.709055i	$-0.749122\pi$
$631$		−	35.6225i		−	1.41811i	0.705154	−	0.709055i	$-0.250878\pi$
$632$			97.7390i			3.88785i
$633$		0			0
$634$		−	22.4094i		−	0.889990i
$635$	16.2428	−	5.65050i	0.644574	−	0.224233i
$636$		0			0
$637$	−27.2924			−1.08137
$638$		−	67.8058i		−	2.68446i
$639$		0			0
$640$	−22.7726	−	65.4615i	−0.900167	−	2.58759i
$641$	−38.0197			−1.50169			−0.750844	−	0.660480i	$-0.770353\pi$
$641$	−38.0197			−1.50169			−0.750844	+	0.660480i	$0.770353\pi$
$642$		0			0
$643$	47.3400			1.86691			0.933453	−	0.358698i	$-0.116779\pi$
$643$	47.3400			1.86691			0.933453	+	0.358698i	$0.116779\pi$
$644$			17.2734i			0.680667i
$645$		0			0
$646$		−	115.125i		−	4.52953i
$647$	15.4200			0.606223			0.303111	−	0.952955i	$-0.401975\pi$
$647$	15.4200			0.606223			0.303111	+	0.952955i	$0.401975\pi$
$648$		0			0
$649$			0.484131i			0.0190038i
$650$	−56.3567	+	44.6091i	−2.21049	+	1.74971i
$651$		0			0
$652$	15.1582			0.593641
$653$	5.09201			0.199266			0.0996328	−	0.995024i	$-0.468233\pi$
$653$	5.09201			0.199266			0.0996328	+	0.995024i	$0.468233\pi$
$654$		0			0
$655$	12.3546	−	4.29791i	0.482735	−	0.167933i
$656$	−10.8114			−0.422115
$657$		0			0
$658$	9.15460			0.356884
$659$	−14.6572			−0.570964			−0.285482	−	0.958384i	$-0.592154\pi$
$659$	−14.6572			−0.570964			−0.285482	+	0.958384i	$0.592154\pi$
$660$		0			0
$661$			50.7078i			1.97231i	0.165841	+	0.986153i	$0.446966\pi$
$661$			50.7078i			1.97231i	−0.165841	+	0.986153i	$0.553034\pi$
$662$			40.9098i			1.59000i
$663$		0			0
$664$			57.5287i			2.23255i
$665$	8.14425	+	23.4112i	0.315820	+	0.907848i
$666$		0			0
$667$			19.8379i			0.768125i
$668$	−76.0282			−2.94162
$669$		0			0
$670$	−16.7935	+	5.84208i	−0.648788	+	0.225699i
$671$			33.6587i			1.29938i
$672$		0			0
$673$		−	6.95057i		−	0.267925i	−0.990986	−	0.133962i	$-0.957230\pi$
$673$		−	6.95057i		−	0.267925i	0.990986	−	0.133962i	$-0.0427701\pi$
$674$			52.5271i			2.02327i
$675$		0			0
$676$	80.7342			3.10516
$677$			15.0561i			0.578654i	0.957230	+	0.289327i	$0.0934316\pi$
$677$			15.0561i			0.578654i	−0.957230	+	0.289327i	$0.906568\pi$
$678$		0			0
$679$		−	12.7509i		−	0.489335i
$680$	−34.9612	−	100.498i	−1.34070	−	3.85393i
$681$		0			0
$682$		−	56.4853i		−	2.16293i
$683$	−11.1313			−0.425926			−0.212963	−	0.977060i	$-0.568311\pi$
$683$	−11.1313			−0.425926			−0.212963	+	0.977060i	$0.568311\pi$
$684$		0			0
$685$	−24.4072	+	8.49075i	−0.932553	+	0.324415i
$686$			44.8281i			1.71154i
$687$		0			0
$688$	37.5703			1.43235
$689$		−	18.9232i		−	0.720917i
$690$		0			0
$691$	−38.4529			−1.46282			−0.731409	−	0.681939i	$-0.761137\pi$
$691$	−38.4529			−1.46282			−0.731409	+	0.681939i	$0.761137\pi$
$692$		−	69.4095i		−	2.63855i
$693$		0			0
$694$	37.3093			1.41624
$695$	6.94569	+	19.9659i	0.263465	+	0.757348i
$696$		0			0
$697$	−3.97383			−0.150520
$698$	−82.5334			−3.12394
$699$		0			0
$700$	22.6479	+	28.6121i	0.856010	+	1.08144i
$701$			5.43667i			0.205340i	0.994715	+	0.102670i	$0.0327386\pi$
$701$			5.43667i			0.205340i	−0.994715	+	0.102670i	$0.967261\pi$
$702$		0			0
$703$	17.0073	−	46.6466i	0.641442	−	1.75931i
$704$	−77.9961			−2.93959
$705$		0			0
$706$	−37.1771			−1.39918
$707$			19.7495i			0.742755i
$708$		0			0
$709$			6.18233i			0.232182i	0.993239	+	0.116091i	$0.0370365\pi$
$709$			6.18233i			0.232182i	−0.993239	+	0.116091i	$0.962964\pi$
$710$	−15.5132	−	44.5938i	−0.582201	−	1.67358i
$711$		0			0
$712$		−	65.5503i		−	2.45660i
$713$			16.5258i			0.618897i
$714$		0			0
$715$	11.5865	+	33.3063i	0.433312	+	1.24559i
$716$		−	82.0133i		−	3.06498i
$717$		0			0
$718$	56.1066			2.09388
$719$	36.0943			1.34609			0.673044	−	0.739602i	$-0.264986\pi$
$719$	36.0943			1.34609			0.673044	+	0.739602i	$0.264986\pi$
$720$		0			0
$721$			6.40228i			0.238433i
$722$	129.328			4.81307
$723$		0			0
$724$	−11.8870			−0.441776
$725$	26.0103	+	32.8600i	0.965998	+	1.22039i
$726$		0			0
$727$	36.1116			1.33931			0.669653	−	0.742674i	$-0.266443\pi$
$727$	36.1116			1.33931			0.669653	+	0.742674i	$0.266443\pi$
$728$		−	65.8666i		−	2.44118i
$729$		0			0
$730$	10.4286	−	3.62788i	0.385979	−	0.134274i
$731$	13.8093			0.510755
$732$		0			0
$733$			36.5087i			1.34848i	0.738512	+	0.674240i	$0.235529\pi$
$733$			36.5087i			1.34848i	−0.738512	+	0.674240i	$0.764471\pi$
$734$			8.71847i			0.321805i
$735$		0			0
$736$	47.4523			1.74911
$737$			8.72370i			0.321342i
$738$		0			0
$739$	4.00770			0.147425			0.0737127	−	0.997280i	$-0.476515\pi$
$739$	4.00770			0.147425			0.0737127	+	0.997280i	$0.476515\pi$
$740$	1.08446	−	73.0849i	0.0398657	−	2.68665i
$741$		0			0
$742$	−13.1828			−0.483955
$743$		−	0.829522i		−	0.0304322i	−0.999884	−	0.0152161i	$-0.995156\pi$
$743$		−	0.829522i		−	0.0304322i	0.999884	−	0.0152161i	$-0.00484362\pi$
$744$		0			0
$745$	4.42957	+	12.7331i	0.162287	+	0.466505i
$746$			84.0941i			3.07890i
$747$		0			0
$748$	−83.1528			−3.04037
$749$	−4.93731			−0.180405
$750$		0			0
$751$	9.47652			0.345803			0.172902	−	0.984939i	$-0.444686\pi$
$751$	9.47652			0.345803			0.172902	+	0.984939i	$0.444686\pi$
$752$		−	35.0784i		−	1.27918i
$753$		0			0
$754$		−	120.487i		−	4.38787i
$755$	−12.2125	−	35.1056i	−0.444458	−	1.27763i
$756$		0			0
$757$	−17.4897			−0.635675			−0.317838	−	0.948145i	$-0.602957\pi$
$757$	−17.4897			−0.635675			−0.317838	+	0.948145i	$0.602957\pi$
$758$	30.0403			1.09111
$759$		0			0
$760$	157.936	−	54.9424i	5.72893	−	1.99297i
$761$	29.7483			1.07837			0.539187	−	0.842186i	$-0.318732\pi$
$761$	29.7483			1.07837			0.539187	+	0.842186i	$0.318732\pi$
$762$		0			0
$763$	−11.1689			−0.404340
$764$		−	122.510i		−	4.43226i
$765$		0			0
$766$	52.0424			1.88037
$767$			0.860272i			0.0310626i
$768$		0			0
$769$			19.7672i			0.712823i	0.934329	+	0.356412i	$0.116000\pi$
$769$			19.7672i			0.712823i	−0.934329	+	0.356412i	$0.884000\pi$
$770$	23.2027	−	8.07172i	0.836168	−	0.290885i
$771$		0			0
$772$	108.153			3.89251
$773$			32.2770i			1.16092i	0.814288	+	0.580461i	$0.197128\pi$
$773$			32.2770i			1.16092i	−0.814288	+	0.580461i	$0.802872\pi$
$774$		0			0
$775$	21.6677	+	27.3738i	0.778328	+	0.983296i
$776$	−86.0197			−3.08793
$777$		0			0
$778$		−	83.4895i		−	2.99324i
$779$		−	6.24499i		−	0.223750i
$780$		0			0
$781$	−23.1652			−0.828915
$782$	33.3820			1.19374
$783$		0			0
$784$	72.8542			2.60193
$785$	−24.4073	+	8.49078i	−0.871135	+	0.303049i
$786$		0			0
$787$		−	29.3025i		−	1.04452i	−0.852786	−	0.522260i	$-0.825089\pi$
$787$		−	29.3025i		−	1.04452i	0.852786	−	0.522260i	$-0.174911\pi$
$788$			47.6707i			1.69820i
$789$		0			0
$790$	−61.1807	+	21.2834i	−2.17671	+	0.757231i
$791$		−	4.44819i		−	0.158160i
$792$		0			0
$793$			59.8095i			2.12390i
$794$		−	81.8916i		−	2.90622i
$795$		0			0
$796$		−	50.2295i		−	1.78034i
$797$	−3.21200			−0.113775			−0.0568874	−	0.998381i	$-0.518118\pi$
$797$	−3.21200			−0.113775			−0.0568874	+	0.998381i	$0.518118\pi$
$798$		0			0
$799$		−	12.8934i		−	0.456135i
$800$	78.6012	−	62.2167i	2.77897	−	2.19969i
$801$		0			0
$802$		−	27.6160i		−	0.975153i
$803$		−	5.41734i		−	0.191174i
$804$		0			0
$805$	−6.78839	+	2.36153i	−0.239259	+	0.0832331i
$806$		−	100.371i		−	3.53542i
$807$		0			0
$808$	133.233			4.68712
$809$			5.99060i			0.210618i	0.994440	+	0.105309i	$0.0335832\pi$
$809$			5.99060i			0.210618i	−0.994440	+	0.105309i	$0.966417\pi$
$810$		0			0
$811$	−34.8651			−1.22428			−0.612139	−	0.790750i	$-0.709691\pi$
$811$	−34.8651			−1.22428			−0.612139	+	0.790750i	$0.709691\pi$
$812$	−61.1708			−2.14667
$813$		0			0
$814$	−46.2312	−	16.8558i	−1.62040	−	0.590797i
$815$	2.07235	+	5.95713i	0.0725914	+	0.208669i
$816$		0			0
$817$			21.7017i			0.759246i
$818$		−	15.7280i		−	0.549916i
$819$		0			0
$820$	−3.02068	−	8.68316i	−0.105487	−	0.303229i
$821$	−20.6185			−0.719589			−0.359795	−	0.933032i	$-0.617153\pi$
$821$	−20.6185			−0.719589			−0.359795	+	0.933032i	$0.617153\pi$
$822$		0			0
$823$			25.4237i			0.886216i	0.896468	+	0.443108i	$0.146124\pi$
$823$			25.4237i			0.886216i	−0.896468	+	0.443108i	$0.853876\pi$
$824$	43.1908			1.50462
$825$		0			0
$826$	0.599305			0.0208525
$827$	−23.0406			−0.801199			−0.400600	−	0.916253i	$-0.631198\pi$
$827$	−23.0406			−0.801199			−0.400600	+	0.916253i	$0.631198\pi$
$828$		0			0
$829$		−	56.0107i		−	1.94533i	−0.232210	−	0.972666i	$-0.574596\pi$
$829$		−	56.0107i		−	1.94533i	0.232210	−	0.972666i	$-0.425404\pi$
$830$	−36.0106	+	12.5273i	−1.24995	+	0.434829i
$831$		0			0
$832$	−138.594			−4.80489
$833$	26.7782			0.927809
$834$		0			0
$835$	−10.3942	−	29.8788i	−0.359706	−	1.03400i
$836$		−	130.677i		−	4.51955i
$837$		0			0
$838$	−42.4771			−1.46735
$839$	27.4024			0.946037			0.473019	−	0.881052i	$-0.343164\pi$
$839$	27.4024			0.946037			0.473019	+	0.881052i	$0.343164\pi$
$840$		0			0
$841$	−41.2525			−1.42250
$842$			0.697321i			0.0240313i
$843$		0			0
$844$	−47.0573			−1.61978
$845$	11.0376	+	31.7283i	0.379704	+	1.09149i
$846$		0			0
$847$			2.88571i			0.0991543i
$848$			50.5135i			1.73464i
$849$		0			0
$850$	55.2948	−	43.7686i	1.89660	−	1.50125i
$851$	13.5258	+	4.93149i	0.463659	+	0.169049i
$852$		0			0
$853$	17.1168			0.586068			0.293034	−	0.956102i	$-0.405335\pi$
$853$	17.1168			0.586068			0.293034	+	0.956102i	$0.405335\pi$
$854$	41.6660			1.42578
$855$		0			0
$856$			33.3079i			1.13844i
$857$	−53.2478			−1.81891			−0.909455	−	0.415802i	$-0.863501\pi$
$857$	−53.2478			−1.81891			−0.909455	+	0.415802i	$0.863501\pi$
$858$		0			0
$859$			29.2811i			0.999058i	0.866297	+	0.499529i	$0.166494\pi$
$859$			29.2811i			0.999058i	−0.866297	+	0.499529i	$0.833506\pi$
$860$	10.4971	+	30.1745i	0.357946	+	1.02894i
$861$		0			0
$862$			81.0185i			2.75950i
$863$		−	35.9842i		−	1.22492i	−0.790503	−	0.612458i	$-0.790181\pi$
$863$		−	35.9842i		−	1.22492i	0.790503	−	0.612458i	$-0.209819\pi$
$864$		0			0
$865$	27.2777	−	9.48933i	0.927470	−	0.322647i
$866$		−	52.2087i		−	1.77412i
$867$		0			0
$868$	−50.9580			−1.72963
$869$			31.7816i			1.07812i
$870$		0			0
$871$			15.5015i			0.525248i
$872$			75.3469i			2.55157i
$873$		0			0
$874$			52.4607i			1.77451i
$875$	−8.14816	+	12.8123i	−0.275458	+	0.433133i
$876$		0			0
$877$			49.6342i			1.67603i	0.545649	+	0.838014i	$0.316283\pi$
$877$			49.6342i			1.67603i	−0.545649	+	0.838014i	$0.683717\pi$
$878$		−	17.6916i		−	0.597063i
$879$		0			0
$880$	−30.9290	−	88.9076i	−1.04262	−	2.99707i
$881$	−32.4663			−1.09382			−0.546909	−	0.837192i	$-0.684196\pi$
$881$	−32.4663			−1.09382			−0.546909	+	0.837192i	$0.684196\pi$
$882$		0			0
$883$	−27.5070			−0.925684			−0.462842	−	0.886441i	$-0.653170\pi$
$883$	−27.5070			−0.925684			−0.462842	+	0.886441i	$0.653170\pi$
$884$	−147.757			−4.96962
$885$		0			0
$886$			59.0040i			1.98228i
$887$			43.1579i			1.44910i	0.689222	+	0.724550i	$0.257952\pi$
$887$			43.1579i			1.44910i	−0.689222	+	0.724550i	$0.742048\pi$
$888$		0			0
$889$	−10.4449			−0.350312
$890$	41.0318	−	14.2741i	1.37539	−	0.478469i
$891$		0			0
$892$		−	74.6786i		−	2.50043i
$893$	20.2623			0.678051
$894$		0			0
$895$	32.2310	−	11.2125i	1.07736	−	0.374791i
$896$			42.0951i			1.40630i
$897$		0			0
$898$			29.3958i			0.980949i
$899$	−58.5234			−1.95187
$900$		0			0
$901$			18.5667i			0.618545i
$902$	−6.18937			−0.206083
$903$		0			0
$904$	−30.0082			−0.998058
$905$	−1.62513	−	4.67154i	−0.0540211	−	0.155287i
$906$		0			0
$907$	49.2354			1.63484			0.817418	−	0.576046i	$-0.195405\pi$
$907$	49.2354			1.63484			0.817418	+	0.576046i	$0.195405\pi$
$908$	−104.138			−3.45593
$909$		0			0
$910$	41.2298	−	14.3430i	1.36676	−	0.475464i
$911$			52.8697i			1.75165i	0.482627	+	0.875826i	$0.339683\pi$
$911$			52.8697i			1.75165i	−0.482627	+	0.875826i	$0.660317\pi$
$912$		0			0
$913$			18.7065i			0.619093i
$914$	−25.3459			−0.838366
$915$		0			0
$916$	−40.8755			−1.35056
$917$	−7.94466			−0.262356
$918$		0			0
$919$			43.6488i			1.43984i	0.694056	+	0.719921i	$0.255822\pi$
$919$			43.6488i			1.43984i	−0.694056	+	0.719921i	$0.744178\pi$
$920$	15.9313	+	45.7956i	0.525239	+	1.50983i
$921$		0			0
$922$			16.1975i			0.533437i
$923$	−41.1631			−1.35490
$924$		0			0
$925$	28.8704	−	9.56561i	0.949252	−	0.314515i
$926$	97.0982			3.19084
$927$		0			0
$928$			168.044i			5.51632i
$929$	32.2873			1.05931			0.529656	−	0.848213i	$-0.322321\pi$
$929$	32.2873			1.05931			0.529656	+	0.848213i	$0.322321\pi$
$930$		0			0
$931$			42.0826i			1.37920i
$932$		−	143.840i		−	4.71164i
$933$		0			0
$934$	−1.56370			−0.0511657
$935$	−11.3682	−	32.6788i	−0.371781	−	1.06871i
$936$		0			0
$937$		−	20.2761i		−	0.662391i	−0.943562	−	0.331196i	$-0.892548\pi$
$937$		−	20.2761i		−	0.662391i	0.943562	−	0.331196i	$-0.107452\pi$
$938$	10.7991			0.352602
$939$		0			0
$940$	28.1731	−	9.80081i	0.918906	−	0.319667i
$941$	−55.6176			−1.81308			−0.906541	−	0.422117i	$-0.861287\pi$
$941$	−55.6176			−1.81308			−0.906541	+	0.422117i	$0.861287\pi$
$942$		0			0
$943$	1.81082			0.0589683
$944$		−	2.29640i		−	0.0747415i
$945$		0			0
$946$	21.5084			0.699299
$947$	−22.9741			−0.746558			−0.373279	−	0.927719i	$-0.621767\pi$
$947$	−22.9741			−0.746558			−0.373279	+	0.927719i	$0.621767\pi$
$948$		0			0
$949$		−	9.62628i		−	0.312482i
$950$	68.7835	+	86.8973i	2.23163	+	2.81932i
$951$		0			0
$952$			64.6255i			2.09453i
$953$			39.0708i			1.26563i	0.774304	+	0.632813i	$0.218100\pi$
$953$			39.0708i			1.26563i	−0.774304	+	0.632813i	$0.781900\pi$
$954$		0			0
$955$	48.1461	−	16.7490i	1.55797	−	0.541984i
$956$		−	55.3389i		−	1.78979i
$957$		0			0
$958$		−	28.8857i		−	0.933255i
$959$	15.6951			0.506821
$960$		0			0
$961$	−17.7526			−0.572666
$962$	−82.1501	−	29.9518i	−2.64862	−	0.965685i
$963$		0			0
$964$			104.245i			3.35749i
$965$	14.7861	+	42.5037i	0.475982	+	1.36824i
$966$		0			0
$967$	−44.8354			−1.44181			−0.720904	−	0.693035i	$-0.756273\pi$
$967$	−44.8354			−1.44181			−0.720904	+	0.693035i	$0.756273\pi$
$968$	19.4675			0.625709
$969$		0			0
$970$	−18.7315	−	53.8449i	−0.601431	−	1.72886i
$971$	−42.5845			−1.36660			−0.683301	−	0.730137i	$-0.739456\pi$
$971$	−42.5845			−1.36660			−0.683301	+	0.730137i	$0.739456\pi$
$972$		0			0
$973$		−	12.8391i		−	0.411602i
$974$	0.495046			0.0158623
$975$		0			0
$976$		−	159.655i		−	5.11043i
$977$	−40.3923			−1.29226			−0.646132	−	0.763226i	$-0.723615\pi$
$977$	−40.3923			−1.29226			−0.646132	+	0.763226i	$0.723615\pi$
$978$		0			0
$979$		−	21.3148i		−	0.681225i
$980$	20.3553	+	58.5126i	0.650225	+	1.86912i
$981$		0			0
$982$	24.2273			0.773123
$983$		−	21.7910i		−	0.695024i	−0.937676	−	0.347512i	$-0.887027\pi$
$983$		−	21.7910i		−	0.695024i	0.937676	−	0.347512i	$-0.112973\pi$
$984$		0			0
$985$	−18.7344	+	6.51731i	−0.596929	+	0.207659i
$986$			118.217i			3.76479i
$987$		0			0
$988$		−	232.205i		−	7.38742i
$989$	−6.29269			−0.200096
$990$		0			0
$991$			10.7251i			0.340694i	0.985384	+	0.170347i	$0.0544889\pi$
$991$			10.7251i			0.340694i	−0.985384	+	0.170347i	$0.945511\pi$
$992$			139.988i			4.44463i
$993$		0			0
$994$			28.6761i			0.909551i
$995$	19.7400	−	6.86713i	0.625801	−	0.217703i
$996$		0			0
$997$	22.1046			0.700059			0.350029	−	0.936739i	$-0.386172\pi$
$997$	22.1046			0.700059			0.350029	+	0.936739i	$0.386172\pi$
$998$		−	76.5214i		−	2.42224i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1665.2.g.e.739.2		40
3.2	odd	2		555.2.g.a.184.40	yes	40
5.4	even	2	inner	1665.2.g.e.739.39		40
15.14	odd	2		555.2.g.a.184.1	✓	40
37.36	even	2	inner	1665.2.g.e.739.40		40
111.110	odd	2		555.2.g.a.184.2	yes	40
185.184	even	2	inner	1665.2.g.e.739.1		40
555.554	odd	2		555.2.g.a.184.39	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.g.a.184.1	✓	40	15.14	odd	2
555.2.g.a.184.2	yes	40	111.110	odd	2
555.2.g.a.184.39	yes	40	555.554	odd	2
555.2.g.a.184.40	yes	40	3.2	odd	2
1665.2.g.e.739.1		40	185.184	even	2	inner
1665.2.g.e.739.2		40	1.1	even	1	trivial
1665.2.g.e.739.39		40	5.4	even	2	inner
1665.2.g.e.739.40		40	37.36	even	2	inner

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:	\( N \)	\(=\)	\( 1665 = 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1665.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.71549 q^{2} +5.37390 q^{4} +(0.734693 + 2.11192i) q^{5} -1.35808i q^{7} -9.16180 q^{8} +O(q^{10})\)	\(q-2.71549 q^{2} +5.37390 q^{4} +(0.734693 + 2.11192i) q^{5} -1.35808i q^{7} -9.16180 q^{8} +(-1.99505 - 5.73492i) q^{10} -2.97912 q^{11} -5.29371 q^{13} +3.68784i q^{14} +14.1310 q^{16} +5.19397 q^{17} +8.16246i q^{19} +(3.94816 + 11.3493i) q^{20} +8.08977 q^{22} -2.36681 q^{23} +(-3.92045 + 3.10323i) q^{25} +14.3750 q^{26} -7.29816i q^{28} -8.38167i q^{29} -6.98231i q^{31} -20.0490 q^{32} -14.1042 q^{34} +(2.86815 - 0.997769i) q^{35} +(-5.71477 - 2.08360i) q^{37} -22.1651i q^{38} +(-6.73111 - 19.3490i) q^{40} -0.765086 q^{41} +2.65872 q^{43} -16.0095 q^{44} +6.42707 q^{46} -2.48237i q^{47} +5.15563 q^{49} +(10.6460 - 8.42680i) q^{50} -28.4479 q^{52} +3.57466i q^{53} +(-2.18874 - 6.29167i) q^{55} +12.4424i q^{56} +22.7604i q^{58} -0.162508i q^{59} -11.2982i q^{61} +18.9604i q^{62} +26.1809 q^{64} +(-3.88925 - 11.1799i) q^{65} -2.92828i q^{67} +27.9119 q^{68} +(-7.78845 + 2.70943i) q^{70} +7.77585 q^{71} +1.81844i q^{73} +(15.5184 + 5.65800i) q^{74} +43.8643i q^{76} +4.04587i q^{77} -10.6681i q^{79} +(10.3819 + 29.8436i) q^{80} +2.07758 q^{82} -6.27919i q^{83} +(3.81597 + 10.9693i) q^{85} -7.21972 q^{86} +27.2941 q^{88} +7.15474i q^{89} +7.18926i q^{91} -12.7190 q^{92} +6.74086i q^{94} +(-17.2385 + 5.99690i) q^{95} +9.38896 q^{97} -14.0001 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4}+O(q^{10}) \) 40 * q + 44 * q^4	\( 40 q + 44 q^{4} + 4 q^{10} - 8 q^{11} + 52 q^{16} + 8 q^{25} + 16 q^{26} - 32 q^{34} - 28 q^{40} - 8 q^{41} - 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} + 48 q^{65} - 56 q^{70} - 24 q^{71} + 68 q^{74} - 64 q^{85} - 80 q^{86} - 32 q^{95}+O(q^{100}) \) 40 * q + 44 * q^4 + 4 * q^10 - 8 * q^11 + 52 * q^16 + 8 * q^25 + 16 * q^26 - 32 * q^34 - 28 * q^40 - 8 * q^41 - 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 + 48 * q^65 - 56 * q^70 - 24 * q^71 + 68 * q^74 - 64 * q^85 - 80 * q^86 - 32 * q^95

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