LMFDB - Embedded newform 1850.2.d.i.1701.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(1701,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1850.1701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.d (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:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 48 x^{18} + 878 x^{16} + 8102 x^{14} + 41081 x^{12} + 115688 x^{10} + 175041 x^{8} + 134990 x^{6} + \cdots + 1 $ x^20 + 48x^18 + 878x^16 + 8102x^14 + 41081x^12 + 115688x^10 + 175041x^8 + 134990x^6 + 49782x^4 + 6932*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1701.2
Root			$-0.786469i$ of defining polynomial
Character	$\chi$	$=$	1850.1701
Dual form			1850.2.d.i.1701.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.78647 q^{3} -1.00000 q^{4} +1.78647i q^{6} +3.14934 q^{7} +1.00000i q^{8} +0.191472 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.78647 q^{3} -1.00000 q^{4} +1.78647i q^{6} +3.14934 q^{7} +1.00000i q^{8} +0.191472 q^{9} -0.908956 q^{11} +1.78647 q^{12} -2.22269i q^{13} -3.14934i q^{14} +1.00000 q^{16} +2.10043i q^{17} -0.191472i q^{18} -4.16694i q^{19} -5.62620 q^{21} +0.908956i q^{22} +7.66680i q^{23} -1.78647i q^{24} -2.22269 q^{26} +5.01735 q^{27} -3.14934 q^{28} +2.69676i q^{29} -5.96563i q^{31} -1.00000i q^{32} +1.62382 q^{33} +2.10043 q^{34} -0.191472 q^{36} +(5.98240 - 1.10043i) q^{37} -4.16694 q^{38} +3.97076i q^{39} +2.32312 q^{41} +5.62620i q^{42} +5.72663i q^{43} +0.908956 q^{44} +7.66680 q^{46} -8.89435 q^{47} -1.78647 q^{48} +2.91834 q^{49} -3.75235i q^{51} +2.22269i q^{52} +9.37592 q^{53} -5.01735i q^{54} +3.14934i q^{56} +7.44411i q^{57} +2.69676 q^{58} -5.55880i q^{59} -3.16611i q^{61} -5.96563 q^{62} +0.603011 q^{63} -1.00000 q^{64} -1.62382i q^{66} +7.64933 q^{67} -2.10043i q^{68} -13.6965i q^{69} +13.5157 q^{71} +0.191472i q^{72} +2.14851 q^{73} +(-1.10043 - 5.98240i) q^{74} +4.16694i q^{76} -2.86261 q^{77} +3.97076 q^{78} -3.35774i q^{79} -9.53776 q^{81} -2.32312i q^{82} +16.2776 q^{83} +5.62620 q^{84} +5.72663 q^{86} -4.81767i q^{87} -0.908956i q^{88} -8.35832i q^{89} -7.00000i q^{91} -7.66680i q^{92} +10.6574i q^{93} +8.89435i q^{94} +1.78647i q^{96} -5.14283i q^{97} -2.91834i q^{98} -0.174040 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{4} + 16 q^{9}+O(q^{10}) $ 20 * q - 20 * q^4 + 16 * q^9	$ 20 q - 20 q^{4} + 16 q^{9} + 20 q^{16} - 24 q^{21} + 4 q^{26} + 36 q^{34} - 16 q^{36} - 8 q^{41} - 20 q^{46} + 16 q^{49} - 20 q^{64} - 40 q^{71} - 16 q^{74} + 116 q^{81} + 24 q^{84} + 20 q^{86} + 164 q^{99}+O(q^{100}) $ 20 * q - 20 * q^4 + 16 * q^9 + 20 * q^16 - 24 * q^21 + 4 * q^26 + 36 * q^34 - 16 * q^36 - 8 * q^41 - 20 * q^46 + 16 * q^49 - 20 * q^64 - 40 * q^71 - 16 * q^74 + 116 * q^81 + 24 * q^84 + 20 * q^86 + 164 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times$.

$n$	$1001$	$1777$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.78647			−1.03142			−0.515709	−	0.856764i	$-0.672472\pi$
$3$	−1.78647			−1.03142			−0.515709	+	0.856764i	$0.672472\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$			1.78647i			0.729323i
$7$	3.14934			1.19034			0.595169	−	0.803600i	$-0.297085\pi$
$7$	3.14934			1.19034			0.595169	+	0.803600i	$0.297085\pi$
$8$			1.00000i			0.353553i
$9$	0.191472			0.0638241
$10$		0			0
$11$	−0.908956			−0.274061			−0.137030	−	0.990567i	$-0.543756\pi$
$11$	−0.908956			−0.274061			−0.137030	+	0.990567i	$0.543756\pi$
$12$	1.78647			0.515709
$13$		−	2.22269i		−	0.616462i	−0.951311	−	0.308231i	$-0.900263\pi$
$13$		−	2.22269i		−	0.616462i	0.951311	−	0.308231i	$-0.0997370\pi$
$14$		−	3.14934i		−	0.841696i
$15$		0			0
$16$	1.00000			0.250000
$17$			2.10043i			0.509429i	0.967016	+	0.254714i	$0.0819815\pi$
$17$			2.10043i			0.509429i	−0.967016	+	0.254714i	$0.918019\pi$
$18$		−	0.191472i		−	0.0451305i
$19$		−	4.16694i		−	0.955962i	−0.878370	−	0.477981i	$-0.841369\pi$
$19$		−	4.16694i		−	0.955962i	0.878370	−	0.477981i	$-0.158631\pi$
$20$		0			0
$21$	−5.62620			−1.22774
$22$			0.908956i			0.193790i
$23$			7.66680i			1.59864i	0.600907	+	0.799319i	$0.294806\pi$
$23$			7.66680i			1.59864i	−0.600907	+	0.799319i	$0.705194\pi$
$24$		−	1.78647i		−	0.364662i
$25$		0			0
$26$	−2.22269			−0.435905
$27$	5.01735			0.965589
$28$	−3.14934			−0.595169
$29$			2.69676i			0.500775i	0.968146	+	0.250387i	$0.0805580\pi$
$29$			2.69676i			0.500775i	−0.968146	+	0.250387i	$0.919442\pi$
$30$		0			0
$31$		−	5.96563i		−	1.07146i	−0.844390	−	0.535729i	$-0.820037\pi$
$31$		−	5.96563i		−	1.07146i	0.844390	−	0.535729i	$-0.179963\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.62382			0.282671
$34$	2.10043			0.360221
$35$		0			0
$36$	−0.191472			−0.0319121
$37$	5.98240	−	1.10043i	0.983500	−	0.180909i
$37$	5.98240	−	1.10043i	0.983500	−	0.180909i
$38$	−4.16694			−0.675967
$39$			3.97076i			0.635831i
$40$		0			0
$41$	2.32312			0.362810			0.181405	−	0.983409i	$-0.441936\pi$
$41$	2.32312			0.362810			0.181405	+	0.983409i	$0.441936\pi$
$42$			5.62620i			0.868141i
$43$			5.72663i			0.873302i	0.899631	+	0.436651i	$0.143836\pi$
$43$			5.72663i			0.873302i	−0.899631	+	0.436651i	$0.856164\pi$
$44$	0.908956			0.137030
$45$		0			0
$46$	7.66680			1.13041
$47$	−8.89435			−1.29737			−0.648687	−	0.761055i	$-0.724682\pi$
$47$	−8.89435			−1.29737			−0.648687	+	0.761055i	$0.724682\pi$
$48$	−1.78647			−0.257855
$49$	2.91834			0.416906
$50$		0			0
$51$		−	3.75235i		−	0.525434i
$52$			2.22269i			0.308231i
$53$	9.37592			1.28788			0.643941	−	0.765075i	$-0.277298\pi$
$53$	9.37592			1.28788			0.643941	+	0.765075i	$0.277298\pi$
$54$		−	5.01735i		−	0.682775i
$55$		0			0
$56$			3.14934i			0.420848i
$57$			7.44411i			0.985997i
$58$	2.69676			0.354101
$59$		−	5.55880i		−	0.723694i	−0.932238	−	0.361847i	$-0.882146\pi$
$59$		−	5.55880i		−	0.723694i	0.932238	−	0.361847i	$-0.117854\pi$
$60$		0			0
$61$		−	3.16611i		−	0.405378i	−0.979243	−	0.202689i	$-0.935032\pi$
$61$		−	3.16611i		−	0.405378i	0.979243	−	0.202689i	$-0.0649681\pi$
$62$	−5.96563			−0.757636
$63$	0.603011			0.0759723
$64$	−1.00000			−0.125000
$65$		0			0
$66$		−	1.62382i		−	0.199879i
$67$	7.64933			0.934515			0.467257	−	0.884121i	$-0.345242\pi$
$67$	7.64933			0.934515			0.467257	+	0.884121i	$0.345242\pi$
$68$		−	2.10043i		−	0.254714i
$69$		−	13.6965i		−	1.64886i
$70$		0			0
$71$	13.5157			1.60402			0.802008	−	0.597313i	$-0.203765\pi$
$71$	13.5157			1.60402			0.802008	+	0.597313i	$0.203765\pi$
$72$			0.191472i			0.0225652i
$73$	2.14851			0.251464			0.125732	−	0.992064i	$-0.459872\pi$
$73$	2.14851			0.251464			0.125732	+	0.992064i	$0.459872\pi$
$74$	−1.10043	−	5.98240i	−0.127922	−	0.695439i
$75$		0			0
$76$			4.16694i			0.477981i
$77$	−2.86261			−0.326225
$78$	3.97076			0.449600
$79$		−	3.35774i		−	0.377775i	−0.981999	−	0.188888i	$-0.939512\pi$
$79$		−	3.35774i		−	0.377775i	0.981999	−	0.188888i	$-0.0604882\pi$
$80$		0			0
$81$	−9.53776			−1.05975
$82$		−	2.32312i		−	0.256545i
$83$	16.2776			1.78670			0.893350	−	0.449361i	$-0.148348\pi$
$83$	16.2776			1.78670			0.893350	+	0.449361i	$0.148348\pi$
$84$	5.62620			0.613869
$85$		0			0
$86$	5.72663			0.617518
$87$		−	4.81767i		−	0.516509i
$88$		−	0.908956i		−	0.0968951i
$89$		−	8.35832i		−	0.885980i	−0.896527	−	0.442990i	$-0.853918\pi$
$89$		−	8.35832i		−	0.885980i	0.896527	−	0.442990i	$-0.146082\pi$
$90$		0			0
$91$		−	7.00000i		−	0.733799i
$92$		−	7.66680i		−	0.799319i
$93$			10.6574i			1.10512i
$94$			8.89435i			0.917382i
$95$		0			0
$96$			1.78647i			0.182331i
$97$		−	5.14283i		−	0.522175i	−0.965315	−	0.261087i	$-0.915919\pi$
$97$		−	5.14283i		−	0.522175i	0.965315	−	0.261087i	$-0.0840811\pi$
$98$		−	2.91834i		−	0.294797i
$99$	−0.174040			−0.0174917
$100$		0			0
$101$	−3.20212			−0.318623			−0.159311	−	0.987228i	$-0.550927\pi$
$101$	−3.20212			−0.318623			−0.159311	+	0.987228i	$0.550927\pi$
$102$	−3.75235			−0.371538
$103$		−	17.6871i		−	1.74276i	−0.490605	−	0.871382i	$-0.663224\pi$
$103$		−	17.6871i		−	1.74276i	0.490605	−	0.871382i	$-0.336776\pi$
$104$	2.22269			0.217952
$105$		0			0
$106$		−	9.37592i		−	0.910670i
$107$	−6.75126			−0.652669			−0.326335	−	0.945254i	$-0.605814\pi$
$107$	−6.75126			−0.652669			−0.326335	+	0.945254i	$0.605814\pi$
$108$	−5.01735			−0.482795
$109$		−	10.5304i		−	1.00863i	−0.863520	−	0.504314i	$-0.831745\pi$
$109$		−	10.5304i		−	1.00863i	0.863520	−	0.504314i	$-0.168255\pi$
$110$		0			0
$111$	−10.6874	+	1.96588i	−1.01440	+	0.186593i
$112$	3.14934			0.297585
$113$		−	6.32365i		−	0.594879i	−0.954741	−	0.297439i	$-0.903867\pi$
$113$		−	6.32365i		−	0.594879i	0.954741	−	0.297439i	$-0.0961327\pi$
$114$	7.44411			0.697205
$115$		0			0
$116$		−	2.69676i		−	0.250387i
$117$		−	0.425583i		−	0.0393452i
$118$	−5.55880			−0.511729
$119$			6.61496i			0.606393i
$120$		0			0
$121$	−10.1738			−0.924891
$122$	−3.16611			−0.286646
$123$	−4.15017			−0.374209
$124$			5.96563i			0.535729i
$125$		0			0
$126$		−	0.603011i		−	0.0537205i
$127$	−15.0472			−1.33522			−0.667609	−	0.744512i	$-0.732682\pi$
$127$	−15.0472			−1.33522			−0.667609	+	0.744512i	$0.732682\pi$
$128$			1.00000i			0.0883883i
$129$		−	10.2304i		−	0.900740i
$130$		0			0
$131$		−	3.31974i		−	0.290047i	−0.989428	−	0.145024i	$-0.953674\pi$
$131$		−	3.31974i		−	0.290047i	0.989428	−	0.145024i	$-0.0463258\pi$
$132$	−1.62382			−0.141336
$133$		−	13.1231i		−	1.13792i
$134$		−	7.64933i		−	0.660802i
$135$		0			0
$136$	−2.10043			−0.180110
$137$	17.9355			1.53234			0.766168	−	0.642640i	$-0.222161\pi$
$137$	17.9355			1.53234			0.766168	+	0.642640i	$0.222161\pi$
$138$	−13.6965			−1.16592
$139$	−12.7472			−1.08120			−0.540601	−	0.841279i	$-0.681803\pi$
$139$	−12.7472			−1.08120			−0.540601	+	0.841279i	$0.681803\pi$
$140$		0			0
$141$	15.8895			1.33814
$142$		−	13.5157i		−	1.13421i
$143$			2.02033i			0.168948i
$144$	0.191472			0.0159560
$145$		0			0
$146$		−	2.14851i		−	0.177812i
$147$	−5.21353			−0.430004
$148$	−5.98240	+	1.10043i	−0.491750	+	0.0904547i
$149$	6.83795			0.560186			0.280093	−	0.959973i	$-0.409635\pi$
$149$	6.83795			0.560186			0.280093	+	0.959973i	$0.409635\pi$
$150$		0			0
$151$	−2.80702			−0.228432			−0.114216	−	0.993456i	$-0.536436\pi$
$151$	−2.80702			−0.228432			−0.114216	+	0.993456i	$0.536436\pi$
$152$	4.16694			0.337984
$153$			0.402174i			0.0325138i
$154$			2.86261i			0.230676i
$155$		0			0
$156$		−	3.97076i		−	0.317915i
$157$	7.28275			0.581227			0.290613	−	0.956841i	$-0.406141\pi$
$157$	7.28275			0.581227			0.290613	+	0.956841i	$0.406141\pi$
$158$	−3.35774			−0.267127
$159$	−16.7498			−1.32835
$160$		0			0
$161$			24.1454i			1.90292i
$162$			9.53776i			0.749357i
$163$		−	22.2319i		−	1.74134i	−0.491870	−	0.870669i	$-0.663686\pi$
$163$		−	22.2319i		−	1.74134i	0.491870	−	0.870669i	$-0.336314\pi$
$164$	−2.32312			−0.181405
$165$		0			0
$166$		−	16.2776i		−	1.26339i
$167$		−	11.5050i		−	0.890286i	−0.895459	−	0.445143i	$-0.853153\pi$
$167$		−	11.5050i		−	0.890286i	0.895459	−	0.445143i	$-0.146847\pi$
$168$		−	5.62620i		−	0.434071i
$169$	8.05966			0.619974
$170$		0			0
$171$		−	0.797854i		−	0.0610134i
$172$		−	5.72663i		−	0.436651i
$173$	15.7081			1.19427			0.597134	−	0.802142i	$-0.296306\pi$
$173$	15.7081			1.19427			0.597134	+	0.802142i	$0.296306\pi$
$174$	−4.81767			−0.365227
$175$		0			0
$176$	−0.908956			−0.0685152
$177$			9.93062i			0.746431i
$178$	−8.35832			−0.626483
$179$		−	11.3128i		−	0.845560i	−0.906232	−	0.422780i	$-0.861054\pi$
$179$		−	11.3128i		−	0.845560i	0.906232	−	0.422780i	$-0.138946\pi$
$180$		0			0
$181$	18.3136			1.36124			0.680618	−	0.732638i	$-0.261711\pi$
$181$	18.3136			1.36124			0.680618	+	0.732638i	$0.261711\pi$
$182$	−7.00000			−0.518874
$183$			5.65615i			0.418115i
$184$	−7.66680			−0.565204
$185$		0			0
$186$	10.6574			0.781439
$187$		−	1.90920i		−	0.139614i
$188$	8.89435			0.648687
$189$	15.8013			1.14938
$190$		0			0
$191$		−	7.66002i		−	0.554260i	−0.960832	−	0.277130i	$-0.910617\pi$
$191$		−	7.66002i		−	0.554260i	0.960832	−	0.277130i	$-0.0893832\pi$
$192$	1.78647			0.128927
$193$			19.3148i			1.39031i	0.718859	+	0.695156i	$0.244665\pi$
$193$			19.3148i			1.39031i	−0.718859	+	0.695156i	$0.755335\pi$
$194$	−5.14283			−0.369233
$195$		0			0
$196$	−2.91834			−0.208453
$197$	13.1193			0.934709			0.467354	−	0.884070i	$-0.345207\pi$
$197$	13.1193			0.934709			0.467354	+	0.884070i	$0.345207\pi$
$198$			0.174040i			0.0123685i
$199$			6.04548i			0.428553i	0.976773	+	0.214277i	$0.0687394\pi$
$199$			6.04548i			0.428553i	−0.976773	+	0.214277i	$0.931261\pi$
$200$		0			0
$201$	−13.6653			−0.963876
$202$			3.20212i			0.225300i
$203$			8.49300i			0.596092i
$204$			3.75235i			0.262717i
$205$		0			0
$206$	−17.6871			−1.23232
$207$			1.46798i			0.102032i
$208$		−	2.22269i		−	0.154116i
$209$			3.78757i			0.261992i
$210$		0			0
$211$	3.06975			0.211330			0.105665	−	0.994402i	$-0.466303\pi$
$211$	3.06975			0.211330			0.105665	+	0.994402i	$0.466303\pi$
$212$	−9.37592			−0.643941
$213$	−24.1454			−1.65441
$214$			6.75126i			0.461507i
$215$		0			0
$216$			5.01735i			0.341387i
$217$		−	18.7878i		−	1.27540i
$218$	−10.5304			−0.713208
$219$	−3.83824			−0.259364
$220$		0			0
$221$	4.66860			0.314044
$222$	1.96588	+	10.6874i	0.131941	+	0.717289i
$223$	−13.9960			−0.937243			−0.468621	−	0.883399i	$-0.655249\pi$
$223$	−13.9960			−0.937243			−0.468621	+	0.883399i	$0.655249\pi$
$224$		−	3.14934i		−	0.210424i
$225$		0			0
$226$	−6.32365			−0.420643
$227$			11.9087i			0.790409i	0.918593	+	0.395205i	$0.129326\pi$
$227$			11.9087i			0.790409i	−0.918593	+	0.395205i	$0.870674\pi$
$228$		−	7.44411i		−	0.492998i
$229$	7.43448			0.491285			0.245642	−	0.969361i	$-0.421001\pi$
$229$	7.43448			0.491285			0.245642	+	0.969361i	$0.421001\pi$
$230$		0			0
$231$	5.11397			0.336474
$232$	−2.69676			−0.177051
$233$	15.2152			0.996782			0.498391	−	0.866952i	$-0.333924\pi$
$233$	15.2152			0.996782			0.498391	+	0.866952i	$0.333924\pi$
$234$	−0.425583			−0.0278212
$235$		0			0
$236$			5.55880i			0.361847i
$237$			5.99850i			0.389644i
$238$	6.61496			0.428784
$239$			29.1359i			1.88465i	0.334705	+	0.942323i	$0.391363\pi$
$239$			29.1359i			1.88465i	−0.334705	+	0.942323i	$0.608637\pi$
$240$		0			0
$241$			7.08791i			0.456572i	0.973594	+	0.228286i	$0.0733121\pi$
$241$			7.08791i			0.456572i	−0.973594	+	0.228286i	$0.926688\pi$
$242$			10.1738i			0.653997i
$243$	1.98686			0.127457
$244$			3.16611i			0.202689i
$245$		0			0
$246$			4.15017i			0.264605i
$247$	−9.26180			−0.589315
$248$	5.96563			0.378818
$249$	−29.0795			−1.84284
$250$		0			0
$251$			17.3622i			1.09589i	0.836514	+	0.547946i	$0.184590\pi$
$251$			17.3622i			1.09589i	−0.836514	+	0.547946i	$0.815410\pi$
$252$	−0.603011			−0.0379861
$253$		−	6.96879i		−	0.438124i
$254$			15.0472i			0.944142i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	13.9118i		−	0.867797i	−0.900962	−	0.433899i	$-0.857138\pi$
$257$		−	13.9118i		−	0.867797i	0.900962	−	0.433899i	$-0.142862\pi$
$258$	−10.2304			−0.636920
$259$	18.8406	−	3.46562i	1.17070	−	0.215343i
$260$		0			0
$261$			0.516354i			0.0319615i
$262$	−3.31974			−0.205094
$263$	−0.302157			−0.0186318			−0.00931590	−	0.999957i	$-0.502965\pi$
$263$	−0.302157			−0.0186318			−0.00931590	+	0.999957i	$0.502965\pi$
$264$			1.62382i			0.0999394i
$265$		0			0
$266$	−13.1231			−0.804630
$267$			14.9319i			0.913816i
$268$	−7.64933			−0.467257
$269$	28.8001			1.75597			0.877986	−	0.478687i	$-0.158887\pi$
$269$	28.8001			1.75597			0.877986	+	0.478687i	$0.158887\pi$
$270$		0			0
$271$	1.57340			0.0955770			0.0477885	−	0.998857i	$-0.484783\pi$
$271$	1.57340			0.0955770			0.0477885	+	0.998857i	$0.484783\pi$
$272$			2.10043i			0.127357i
$273$			12.5053i			0.756854i
$274$		−	17.9355i		−	1.08353i
$275$		0			0
$276$			13.6965i			0.824432i
$277$			26.3430i			1.58280i	0.611301	+	0.791398i	$0.290646\pi$
$277$			26.3430i			1.58280i	−0.611301	+	0.791398i	$0.709354\pi$
$278$			12.7472i			0.764526i
$279$		−	1.14225i		−	0.0683849i
$280$		0			0
$281$		−	9.45482i		−	0.564027i	−0.959410	−	0.282014i	$-0.908998\pi$
$281$		−	9.45482i		−	0.564027i	0.959410	−	0.282014i	$-0.0910024\pi$
$282$		−	15.8895i		−	0.946205i
$283$			21.7389i			1.29224i	0.763234	+	0.646122i	$0.223610\pi$
$283$			21.7389i			1.29224i	−0.763234	+	0.646122i	$0.776390\pi$
$284$	−13.5157			−0.802008
$285$		0			0
$286$	2.02033			0.119464
$287$	7.31628			0.431866
$288$		−	0.191472i		−	0.0112826i
$289$	12.5882			0.740482
$290$		0			0
$291$			9.18750i			0.538581i
$292$	−2.14851			−0.125732
$293$	11.1283			0.650121			0.325061	−	0.945693i	$-0.394615\pi$
$293$	11.1283			0.650121			0.325061	+	0.945693i	$0.394615\pi$
$294$			5.21353i			0.304059i
$295$		0			0
$296$	1.10043	+	5.98240i	0.0639611	+	0.347720i
$297$	−4.56055			−0.264630
$298$		−	6.83795i		−	0.396112i
$299$	17.0409			0.985500
$300$		0			0
$301$			18.0351i			1.03953i
$302$			2.80702i			0.161526i
$303$	5.72049			0.328633
$304$		−	4.16694i		−	0.238990i
$305$		0			0
$306$	0.402174			0.0229908
$307$	−15.9903			−0.912615			−0.456308	−	0.889822i	$-0.650828\pi$
$307$	−15.9903			−0.912615			−0.456308	+	0.889822i	$0.650828\pi$
$308$	2.86261			0.163112
$309$			31.5975i			1.79752i
$310$		0			0
$311$		−	29.6416i		−	1.68082i	−0.541949	−	0.840411i	$-0.682313\pi$
$311$		−	29.6416i		−	1.68082i	0.541949	−	0.840411i	$-0.317687\pi$
$312$	−3.97076			−0.224800
$313$			10.0000i			0.565233i	0.959233	+	0.282617i	$0.0912024\pi$
$313$			10.0000i			0.565233i	−0.959233	+	0.282617i	$0.908798\pi$
$314$		−	7.28275i		−	0.410989i
$315$		0			0
$316$			3.35774i			0.188888i
$317$	−21.1397			−1.18732			−0.593662	−	0.804715i	$-0.702318\pi$
$317$	−21.1397			−1.18732			−0.593662	+	0.804715i	$0.702318\pi$
$318$			16.7498i			0.939282i
$319$		−	2.45123i		−	0.137243i
$320$		0			0
$321$	12.0609			0.673175
$322$	24.1454			1.34557
$323$	8.75236			0.486994
$324$	9.53776			0.529875
$325$		0			0
$326$	−22.2319			−1.23131
$327$			18.8122i			1.04032i
$328$			2.32312i			0.128273i
$329$	−28.0113			−1.54431
$330$		0			0
$331$			18.7324i			1.02963i	0.857302	+	0.514814i	$0.172139\pi$
$331$			18.7324i			1.02963i	−0.857302	+	0.514814i	$0.827861\pi$
$332$	−16.2776			−0.893350
$333$	1.14546	−	0.210702i	0.0627710	−	0.0115464i
$334$	−11.5050			−0.629528
$335$		0			0
$336$	−5.62620			−0.306934
$337$	−13.9123			−0.757850			−0.378925	−	0.925427i	$-0.623706\pi$
$337$	−13.9123			−0.757850			−0.378925	+	0.925427i	$0.623706\pi$
$338$		−	8.05966i		−	0.438388i
$339$			11.2970i			0.613569i
$340$		0			0
$341$			5.42250i			0.293645i
$342$	−0.797854			−0.0431430
$343$	−12.8545			−0.694079
$344$	−5.72663			−0.308759
$345$		0			0
$346$		−	15.7081i		−	0.844474i
$347$		−	24.5885i		−	1.31998i	−0.751274	−	0.659990i	$-0.770560\pi$
$347$		−	24.5885i		−	1.31998i	0.751274	−	0.659990i	$-0.229440\pi$
$348$			4.81767i			0.258254i
$349$	10.2324			0.547726			0.273863	−	0.961769i	$-0.411699\pi$
$349$	10.2324			0.547726			0.273863	+	0.961769i	$0.411699\pi$
$350$		0			0
$351$		−	11.1520i		−	0.595249i
$352$			0.908956i			0.0484475i
$353$			1.74540i			0.0928981i	0.998921	+	0.0464491i	$0.0147905\pi$
$353$			1.74540i			0.0928981i	−0.998921	+	0.0464491i	$0.985209\pi$
$354$	9.93062			0.527806
$355$		0			0
$356$			8.35832i			0.442990i
$357$		−	11.8174i		−	0.625445i
$358$	−11.3128			−0.597901
$359$	−21.1922			−1.11848			−0.559240	−	0.829006i	$-0.688907\pi$
$359$	−21.1922			−1.11848			−0.559240	+	0.829006i	$0.688907\pi$
$360$		0			0
$361$	1.63660			0.0861371
$362$		−	18.3136i		−	0.962540i
$363$	18.1752			0.953949
$364$			7.00000i			0.366900i
$365$		0			0
$366$	5.65615			0.295652
$367$	9.69901			0.506284			0.253142	−	0.967429i	$-0.418536\pi$
$367$	9.69901			0.506284			0.253142	+	0.967429i	$0.418536\pi$
$368$			7.66680i			0.399659i
$369$	0.444812			0.0231560
$370$		0			0
$371$	29.5280			1.53302
$372$		−	10.6574i		−	0.552561i
$373$	36.8658			1.90884			0.954420	−	0.298466i	$-0.0964748\pi$
$373$	36.8658			1.90884			0.954420	+	0.298466i	$0.0964748\pi$
$374$	−1.90920			−0.0987223
$375$		0			0
$376$		−	8.89435i		−	0.458691i
$377$	5.99404			0.308709
$378$		−	15.8013i		−	0.812733i
$379$	−31.7074			−1.62870			−0.814351	−	0.580372i	$-0.802907\pi$
$379$	−31.7074			−1.62870			−0.814351	+	0.580372i	$0.802907\pi$
$380$		0			0
$381$	26.8813			1.37717
$382$	−7.66002			−0.391921
$383$			3.45325i			0.176453i	0.996100	+	0.0882265i	$0.0281199\pi$
$383$			3.45325i			0.176453i	−0.996100	+	0.0882265i	$0.971880\pi$
$384$		−	1.78647i		−	0.0911654i
$385$		0			0
$386$	19.3148			0.983099
$387$			1.09649i			0.0557378i
$388$			5.14283i			0.261087i
$389$			39.2237i			1.98872i	0.106056	+	0.994360i	$0.466178\pi$
$389$			39.2237i			1.98872i	−0.106056	+	0.994360i	$0.533822\pi$
$390$		0			0
$391$	−16.1036			−0.814392
$392$			2.91834i			0.147399i
$393$			5.93062i			0.299160i
$394$		−	13.1193i		−	0.660939i
$395$		0			0
$396$	0.174040			0.00874584
$397$	5.75234			0.288702			0.144351	−	0.989527i	$-0.453891\pi$
$397$	5.75234			0.288702			0.144351	+	0.989527i	$0.453891\pi$
$398$	6.04548			0.303033
$399$			23.4440i			1.17367i
$400$		0			0
$401$		−	24.6273i		−	1.22983i	−0.788594	−	0.614914i	$-0.789191\pi$
$401$		−	24.6273i		−	1.22983i	0.788594	−	0.614914i	$-0.210809\pi$
$402$			13.6653i			0.681563i
$403$	−13.2597			−0.660514
$404$	3.20212			0.159311
$405$		0			0
$406$	8.49300			0.421501
$407$	−5.43774	+	1.00024i	−0.269539	+	0.0495801i
$408$	3.75235			0.185769
$409$			25.1947i			1.24580i	0.782302	+	0.622899i	$0.214045\pi$
$409$			25.1947i			1.24580i	−0.782302	+	0.622899i	$0.785955\pi$
$410$		0			0
$411$	−32.0413			−1.58048
$412$			17.6871i			0.871382i
$413$		−	17.5065i		−	0.861441i
$414$	1.46798			0.0721473
$415$		0			0
$416$	−2.22269			−0.108976
$417$	22.7725			1.11517
$418$	3.78757			0.185256
$419$	−7.19906			−0.351697			−0.175849	−	0.984417i	$-0.556267\pi$
$419$	−7.19906			−0.351697			−0.175849	+	0.984417i	$0.556267\pi$
$420$		0			0
$421$		−	34.0902i		−	1.66145i	−0.556680	−	0.830727i	$-0.687925\pi$
$421$		−	34.0902i		−	1.66145i	0.556680	−	0.830727i	$-0.312075\pi$
$422$		−	3.06975i		−	0.149433i
$423$	−1.70302			−0.0828038
$424$			9.37592i			0.455335i
$425$		0			0
$426$			24.1454i			1.16985i
$427$		−	9.97114i		−	0.482537i
$428$	6.75126			0.326335
$429$		−	3.60925i		−	0.174256i
$430$		0			0
$431$			25.2123i			1.21443i	0.794536	+	0.607217i	$0.207714\pi$
$431$			25.2123i			1.21443i	−0.794536	+	0.607217i	$0.792286\pi$
$432$	5.01735			0.241397
$433$	−21.8683			−1.05092			−0.525462	−	0.850817i	$-0.676107\pi$
$433$	−21.8683			−1.05092			−0.525462	+	0.850817i	$0.676107\pi$
$434$	−18.7878			−0.901843
$435$		0			0
$436$			10.5304i			0.504314i
$437$	31.9471			1.52824
$438$			3.83824i			0.183398i
$439$		−	9.00956i		−	0.430003i	−0.976614	−	0.215001i	$-0.931024\pi$
$439$		−	9.00956i		−	0.430003i	0.976614	−	0.215001i	$-0.0689756\pi$
$440$		0			0
$441$	0.558782			0.0266086
$442$		−	4.66860i		−	0.222062i
$443$	−2.89007			−0.137311			−0.0686557	−	0.997640i	$-0.521871\pi$
$443$	−2.89007			−0.137311			−0.0686557	+	0.997640i	$0.521871\pi$
$444$	10.6874	−	1.96588i	0.507200	−	0.0932966i
$445$		0			0
$446$			13.9960i			0.662731i
$447$	−12.2158			−0.577787
$448$	−3.14934			−0.148792
$449$		−	18.1539i		−	0.856738i	−0.903604	−	0.428369i	$-0.859088\pi$
$449$		−	18.1539i		−	0.856738i	0.903604	−	0.428369i	$-0.140912\pi$
$450$		0			0
$451$	−2.11161			−0.0994319
$452$			6.32365i			0.297439i
$453$	5.01466			0.235609
$454$	11.9087			0.558904
$455$		0			0
$456$	−7.44411			−0.348602
$457$		−	10.4140i		−	0.487146i	−0.969883	−	0.243573i	$-0.921680\pi$
$457$		−	10.4140i		−	0.487146i	0.969883	−	0.243573i	$-0.0783196\pi$
$458$		−	7.43448i		−	0.347391i
$459$			10.5386i			0.491899i
$460$		0			0
$461$			17.7433i			0.826390i	0.910643	+	0.413195i	$0.135587\pi$
$461$			17.7433i			0.826390i	−0.910643	+	0.413195i	$0.864413\pi$
$462$		−	5.11397i		−	0.237923i
$463$			11.6293i			0.540457i	0.962796	+	0.270229i	$0.0870993\pi$
$463$			11.6293i			0.540457i	−0.962796	+	0.270229i	$0.912901\pi$
$464$			2.69676i			0.125194i
$465$		0			0
$466$		−	15.2152i		−	0.704831i
$467$		−	6.25208i		−	0.289312i	−0.989482	−	0.144656i	$-0.953793\pi$
$467$		−	6.25208i		−	0.289312i	0.989482	−	0.144656i	$-0.0462075\pi$
$468$			0.425583i			0.0196726i
$469$	24.0903			1.11239
$470$		0			0
$471$	−13.0104			−0.599488
$472$	5.55880			0.255864
$473$		−	5.20525i		−	0.239338i
$474$	5.99850			0.275520
$475$		0			0
$476$		−	6.61496i		−	0.303196i
$477$	1.79523			0.0821979
$478$	29.1359			1.33265
$479$			16.4452i			0.751398i	0.926742	+	0.375699i	$0.122597\pi$
$479$			16.4452i			0.751398i	−0.926742	+	0.375699i	$0.877403\pi$
$480$		0			0
$481$	−2.44591	−	13.2970i	−0.111524	−	0.606291i
$482$	7.08791			0.322845
$483$		−	43.1349i		−	1.96271i
$484$	10.1738			0.462445
$485$		0			0
$486$		−	1.98686i		−	0.0901259i
$487$		−	13.7966i		−	0.625184i	−0.949887	−	0.312592i	$-0.898803\pi$
$487$		−	13.7966i		−	0.625184i	0.949887	−	0.312592i	$-0.101197\pi$
$488$	3.16611			0.143323
$489$			39.7166i			1.79605i
$490$		0			0
$491$	−39.0410			−1.76190			−0.880949	−	0.473211i	$-0.843095\pi$
$491$	−39.0410			−1.76190			−0.880949	+	0.473211i	$0.843095\pi$
$492$	4.15017			0.187104
$493$	−5.66434			−0.255109
$494$			9.26180i			0.416708i
$495$		0			0
$496$		−	5.96563i		−	0.267865i
$497$	42.5655			1.90932
$498$			29.0795i			1.30308i
$499$		−	40.0886i		−	1.79461i	−0.441410	−	0.897306i	$-0.645521\pi$
$499$		−	40.0886i		−	1.79461i	0.441410	−	0.897306i	$-0.354479\pi$
$500$		0			0
$501$			20.5534i			0.918258i
$502$	17.3622			0.774913
$503$			12.0731i			0.538312i	0.963097	+	0.269156i	$0.0867447\pi$
$503$			12.0731i			0.538312i	−0.963097	+	0.269156i	$0.913255\pi$
$504$			0.603011i			0.0268603i
$505$		0			0
$506$	−6.96879			−0.309800
$507$	−14.3983			−0.639453
$508$	15.0472			0.667609
$509$	−4.36466			−0.193460			−0.0967300	−	0.995311i	$-0.530838\pi$
$509$	−4.36466			−0.193460			−0.0967300	+	0.995311i	$0.530838\pi$
$510$		0			0
$511$	6.76637			0.299327
$512$		−	1.00000i		−	0.0441942i
$513$		−	20.9070i		−	0.923066i
$514$	−13.9118			−0.613625
$515$		0			0
$516$			10.2304i			0.450370i
$517$	8.08458			0.355559
$518$	−3.46562	−	18.8406i	−0.152271	−	0.827808i
$519$	−28.0621			−1.23179
$520$		0			0
$521$	−16.7088			−0.732025			−0.366013	−	0.930610i	$-0.619277\pi$
$521$	−16.7088			−0.732025			−0.366013	+	0.930610i	$0.619277\pi$
$522$	0.516354			0.0226002
$523$			32.5266i			1.42229i	0.703047	+	0.711144i	$0.251823\pi$
$523$			32.5266i			1.42229i	−0.703047	+	0.711144i	$0.748177\pi$
$524$			3.31974i			0.145024i
$525$		0			0
$526$			0.302157i			0.0131747i
$527$	12.5304			0.545832
$528$	1.62382			0.0706678
$529$	−35.7798			−1.55564
$530$		0			0
$531$		−	1.06436i		−	0.0461891i
$532$			13.1231i			0.568959i
$533$		−	5.16356i		−	0.223659i
$534$	14.9319			0.646166
$535$		0			0
$536$			7.64933i			0.330401i
$537$			20.2100i			0.872126i
$538$		−	28.8001i		−	1.24166i
$539$	−2.65265			−0.114258
$540$		0			0
$541$		−	19.2331i		−	0.826894i	−0.910528	−	0.413447i	$-0.864325\pi$
$541$		−	19.2331i		−	0.826894i	0.910528	−	0.413447i	$-0.135675\pi$
$542$		−	1.57340i		−	0.0675832i
$543$	−32.7166			−1.40400
$544$	2.10043			0.0900551
$545$		0			0
$546$	12.5053			0.535177
$547$			8.88173i			0.379755i	0.981808	+	0.189878i	$0.0608091\pi$
$547$			8.88173i			0.379755i	−0.981808	+	0.189878i	$0.939191\pi$
$548$	−17.9355			−0.766168
$549$		−	0.606222i		−	0.0258729i
$550$		0			0
$551$	11.2372			0.478722
$552$	13.6965			0.582962
$553$		−	10.5747i		−	0.449680i
$554$	26.3430			1.11921
$555$		0			0
$556$	12.7472			0.540601
$557$			44.3010i			1.87709i	0.345150	+	0.938547i	$0.387828\pi$
$557$			44.3010i			1.87709i	−0.345150	+	0.938547i	$0.612172\pi$
$558$	−1.14225			−0.0483554
$559$	12.7285			0.538358
$560$		0			0
$561$			3.41072i			0.144001i
$562$	−9.45482			−0.398828
$563$		−	19.8885i		−	0.838202i	−0.907940	−	0.419101i	$-0.862345\pi$
$563$		−	19.8885i		−	0.838202i	0.907940	−	0.419101i	$-0.137655\pi$
$564$	−15.8895			−0.669068
$565$		0			0
$566$	21.7389			0.913754
$567$	−30.0376			−1.26146
$568$			13.5157i			0.567106i
$569$		−	3.13170i		−	0.131288i	−0.997843	−	0.0656439i	$-0.979090\pi$
$569$		−	3.13170i		−	0.131288i	0.997843	−	0.0656439i	$-0.0209101\pi$
$570$		0			0
$571$	−19.2774			−0.806732			−0.403366	−	0.915039i	$-0.632160\pi$
$571$	−19.2774			−0.806732			−0.403366	+	0.915039i	$0.632160\pi$
$572$		−	2.02033i		−	0.0844741i
$573$			13.6844i			0.571674i
$574$		−	7.31628i		−	0.305376i
$575$		0			0
$576$	−0.191472			−0.00797801
$577$			24.8001i			1.03244i	0.856456	+	0.516220i	$0.172661\pi$
$577$			24.8001i			1.03244i	−0.856456	+	0.516220i	$0.827339\pi$
$578$		−	12.5882i		−	0.523600i
$579$		−	34.5053i		−	1.43399i
$580$		0			0
$581$	51.2637			2.12678
$582$	9.18750			0.380834
$583$	−8.52230			−0.352958
$584$			2.14851i			0.0889058i
$585$		0			0
$586$		−	11.1283i		−	0.459705i
$587$		−	16.1319i		−	0.665836i	−0.942956	−	0.332918i	$-0.891967\pi$
$587$		−	16.1319i		−	0.665836i	0.942956	−	0.332918i	$-0.108033\pi$
$588$	5.21353			0.215002
$589$	−24.8584			−1.02427
$590$		0			0
$591$	−23.4372			−0.964076
$592$	5.98240	−	1.10043i	0.245875	−	0.0452273i
$593$	−28.2040			−1.15820			−0.579100	−	0.815256i	$-0.696596\pi$
$593$	−28.2040			−1.15820			−0.579100	+	0.815256i	$0.696596\pi$
$594$			4.56055i			0.187122i
$595$		0			0
$596$	−6.83795			−0.280093
$597$		−	10.8001i		−	0.442018i
$598$		−	17.0409i		−	0.696854i
$599$	24.8280			1.01444			0.507222	−	0.861815i	$-0.330672\pi$
$599$	24.8280			1.01444			0.507222	+	0.861815i	$0.330672\pi$
$600$		0			0
$601$	−2.87745			−0.117374			−0.0586868	−	0.998276i	$-0.518691\pi$
$601$	−2.87745			−0.117374			−0.0586868	+	0.998276i	$0.518691\pi$
$602$	18.0351			0.735056
$603$	1.46464			0.0596446
$604$	2.80702			0.114216
$605$		0			0
$606$		−	5.72049i		−	0.232379i
$607$		−	25.7881i		−	1.04671i	−0.852116	−	0.523353i	$-0.824681\pi$
$607$		−	25.7881i		−	1.04671i	0.852116	−	0.523353i	$-0.175319\pi$
$608$	−4.16694			−0.168992
$609$		−	15.1725i		−	0.614820i
$610$		0			0
$611$			19.7694i			0.799783i
$612$		−	0.402174i		−	0.0162569i
$613$	−32.4248			−1.30962			−0.654812	−	0.755792i	$-0.727252\pi$
$613$	−32.4248			−1.30962			−0.654812	+	0.755792i	$0.727252\pi$
$614$			15.9903i			0.645317i
$615$		0			0
$616$		−	2.86261i		−	0.115338i
$617$	5.69333			0.229205			0.114602	−	0.993411i	$-0.463441\pi$
$617$	5.69333			0.229205			0.114602	+	0.993411i	$0.463441\pi$
$618$	31.5975			1.27104
$619$	4.76393			0.191478			0.0957392	−	0.995406i	$-0.469479\pi$
$619$	4.76393			0.191478			0.0957392	+	0.995406i	$0.469479\pi$
$620$		0			0
$621$			38.4670i			1.54363i
$622$	−29.6416			−1.18852
$623$		−	26.3232i		−	1.05462i
$624$			3.97076i			0.158958i
$625$		0			0
$626$	10.0000			0.399680
$627$		−	6.76637i		−	0.270223i
$628$	−7.28275			−0.290613
$629$	2.31137	+	12.5656i	0.0921604	+	0.501023i
$630$		0			0
$631$			8.72673i			0.347405i	0.984798	+	0.173703i	$0.0555732\pi$
$631$			8.72673i			0.347405i	−0.984798	+	0.173703i	$0.944427\pi$
$632$	3.35774			0.133564
$633$	−5.48401			−0.217970
$634$			21.1397i			0.839564i
$635$		0			0
$636$	16.7498			0.664173
$637$		−	6.48656i		−	0.257007i
$638$	−2.45123			−0.0970453
$639$	2.58788			0.102375
$640$		0			0
$641$	−41.1790			−1.62647			−0.813237	−	0.581933i	$-0.802297\pi$
$641$	−41.1790			−1.62647			−0.813237	+	0.581933i	$0.802297\pi$
$642$		−	12.0609i		−	0.476007i
$643$		−	6.12834i		−	0.241678i	−0.992672	−	0.120839i	$-0.961441\pi$
$643$		−	6.12834i		−	0.241678i	0.992672	−	0.120839i	$-0.0385585\pi$
$644$		−	24.1454i		−	0.951460i
$645$		0			0
$646$		−	8.75236i		−	0.344357i
$647$			31.3270i			1.23159i	0.787905	+	0.615796i	$0.211166\pi$
$647$			31.3270i			1.23159i	−0.787905	+	0.615796i	$0.788834\pi$
$648$		−	9.53776i		−	0.374678i
$649$			5.05270i			0.198336i
$650$		0			0
$651$			33.5638i			1.31547i
$652$			22.2319i			0.870669i
$653$			0.716146i			0.0280250i	0.999902	+	0.0140125i	$0.00446046\pi$
$653$			0.716146i			0.0280250i	−0.999902	+	0.0140125i	$0.995540\pi$
$654$	18.8122			0.735616
$655$		0			0
$656$	2.32312			0.0907024
$657$	0.411379			0.0160494
$658$			28.0113i			1.09200i
$659$	10.8796			0.423810			0.211905	−	0.977290i	$-0.432033\pi$
$659$	10.8796			0.423810			0.211905	+	0.977290i	$0.432033\pi$
$660$		0			0
$661$		−	37.4927i		−	1.45830i	−0.684355	−	0.729149i	$-0.739916\pi$
$661$		−	37.4927i		−	1.45830i	0.684355	−	0.729149i	$-0.260084\pi$
$662$	18.7324			0.728057
$663$	−8.34030			−0.323910
$664$			16.2776i			0.631694i
$665$		0			0
$666$	−0.210702	−	1.14546i	−0.00816452	−	0.0443858i
$667$	−20.6755			−0.800558
$668$			11.5050i			0.445143i
$669$	25.0035			0.966689
$670$		0			0
$671$			2.87785i			0.111098i
$672$			5.62620i			0.217035i
$673$	38.2532			1.47455			0.737277	−	0.675591i	$-0.236111\pi$
$673$	38.2532			1.47455			0.737277	+	0.675591i	$0.236111\pi$
$674$			13.9123i			0.535881i
$675$		0			0
$676$	−8.05966			−0.309987
$677$	45.0250			1.73045			0.865227	−	0.501381i	$-0.167175\pi$
$677$	45.0250			1.73045			0.865227	+	0.501381i	$0.167175\pi$
$678$	11.2970			0.433859
$679$		−	16.1965i		−	0.621565i
$680$		0			0
$681$		−	21.2746i		−	0.815243i
$682$	5.42250			0.207638
$683$			34.7787i			1.33077i	0.746501	+	0.665384i	$0.231732\pi$
$683$			34.7787i			1.33077i	−0.746501	+	0.665384i	$0.768268\pi$
$684$			0.797854i			0.0305067i
$685$		0			0
$686$			12.8545i			0.490788i
$687$	−13.2815			−0.506720
$688$			5.72663i			0.218326i
$689$		−	20.8397i		−	0.793931i
$690$		0			0
$691$	38.8781			1.47899			0.739497	−	0.673160i	$-0.235063\pi$
$691$	38.8781			1.47899			0.739497	+	0.673160i	$0.235063\pi$
$692$	−15.7081			−0.597134
$693$	−0.548111			−0.0208210
$694$	−24.5885			−0.933367
$695$		0			0
$696$	4.81767			0.182613
$697$			4.87954i			0.184826i
$698$		−	10.2324i		−	0.387301i
$699$	−27.1815			−1.02810
$700$		0			0
$701$			41.6474i			1.57300i	0.617589	+	0.786501i	$0.288110\pi$
$701$			41.6474i			1.57300i	−0.617589	+	0.786501i	$0.711890\pi$
$702$	−11.1520			−0.420905
$703$	−4.58542	−	24.9283i	−0.172942	−	0.940188i
$704$	0.908956			0.0342576
$705$		0			0
$706$	1.74540			0.0656889
$707$	−10.0846			−0.379269
$708$		−	9.93062i		−	0.373216i
$709$		−	3.86911i		−	0.145307i	−0.997357	−	0.0726537i	$-0.976853\pi$
$709$		−	3.86911i		−	0.145307i	0.997357	−	0.0726537i	$-0.0231468\pi$
$710$		0			0
$711$		−	0.642914i		−	0.0241112i
$712$	8.35832			0.313241
$713$	45.7373			1.71287
$714$	−11.8174			−0.442256
$715$		0			0
$716$			11.3128i			0.422780i
$717$		−	52.0504i		−	1.94386i
$718$			21.1922i			0.790884i
$719$	26.4440			0.986194			0.493097	−	0.869974i	$-0.335865\pi$
$719$	26.4440			0.986194			0.493097	+	0.869974i	$0.335865\pi$
$720$		0			0
$721$		−	55.7028i		−	2.07448i
$722$		−	1.63660i		−	0.0609081i
$723$		−	12.6623i		−	0.470917i
$724$	−18.3136			−0.680618
$725$		0			0
$726$		−	18.1752i		−	0.674544i
$727$		−	28.3958i		−	1.05314i	−0.850131	−	0.526571i	$-0.823478\pi$
$727$		−	28.3958i		−	1.05314i	0.850131	−	0.526571i	$-0.176522\pi$
$728$	7.00000			0.259437
$729$	25.0638			0.928289
$730$		0			0
$731$	−12.0284			−0.444885
$732$		−	5.65615i		−	0.209057i
$733$	19.8801			0.734289			0.367144	−	0.930164i	$-0.380336\pi$
$733$	19.8801			0.734289			0.367144	+	0.930164i	$0.380336\pi$
$734$		−	9.69901i		−	0.357997i
$735$		0			0
$736$	7.66680			0.282602
$737$	−6.95291			−0.256114
$738$		−	0.444812i		−	0.0163738i
$739$	42.1224			1.54950			0.774749	−	0.632269i	$-0.217876\pi$
$739$	42.1224			1.54950			0.774749	+	0.632269i	$0.217876\pi$
$740$		0			0
$741$	16.5459			0.607830
$742$		−	29.5280i		−	1.08401i
$743$	−23.5575			−0.864242			−0.432121	−	0.901816i	$-0.642235\pi$
$743$	−23.5575			−0.864242			−0.432121	+	0.901816i	$0.642235\pi$
$744$	−10.6574			−0.390720
$745$		0			0
$746$		−	36.8658i		−	1.34975i
$747$	3.11671			0.114035
$748$			1.90920i			0.0698072i
$749$	−21.2620			−0.776897
$750$		0			0
$751$	32.6454			1.19125			0.595624	−	0.803263i	$-0.296905\pi$
$751$	32.6454			1.19125			0.595624	+	0.803263i	$0.296905\pi$
$752$	−8.89435			−0.324344
$753$		−	31.0170i		−	1.13032i
$754$		−	5.99404i		−	0.218290i
$755$		0			0
$756$	−15.8013			−0.574689
$757$			30.3562i			1.10331i	0.834071	+	0.551657i	$0.186004\pi$
$757$			30.3562i			1.10331i	−0.834071	+	0.551657i	$0.813996\pi$
$758$			31.7074i			1.15167i
$759$			12.4495i			0.451889i
$760$		0			0
$761$	−38.6682			−1.40172			−0.700860	−	0.713299i	$-0.747200\pi$
$761$	−38.6682			−1.40172			−0.700860	+	0.713299i	$0.747200\pi$
$762$		−	26.8813i		−	0.973806i
$763$		−	33.1638i		−	1.20061i
$764$			7.66002i			0.277130i
$765$		0			0
$766$	3.45325			0.124771
$767$	−12.3555			−0.446130
$768$	−1.78647			−0.0644637
$769$			23.8517i			0.860114i	0.902802	+	0.430057i	$0.141506\pi$
$769$			23.8517i			0.860114i	−0.902802	+	0.430057i	$0.858494\pi$
$770$		0			0
$771$			24.8531i			0.895062i
$772$		−	19.3148i		−	0.695156i
$773$	−38.4580			−1.38324			−0.691620	−	0.722262i	$-0.743103\pi$
$773$	−38.4580			−1.38324			−0.691620	+	0.722262i	$0.743103\pi$
$774$	1.09649			0.0394125
$775$		0			0
$776$	5.14283			0.184617
$777$	−33.6581	+	6.19123i	−1.20748	+	0.222109i
$778$	39.2237			1.40624
$779$		−	9.68029i		−	0.346832i
$780$		0			0
$781$	−12.2852			−0.439598
$782$			16.1036i			0.575862i
$783$			13.5306i			0.483543i
$784$	2.91834			0.104226
$785$		0			0
$786$	5.93062			0.211538
$787$	−39.3808			−1.40378			−0.701888	−	0.712288i	$-0.747659\pi$
$787$	−39.3808			−1.40378			−0.701888	+	0.712288i	$0.747659\pi$
$788$	−13.1193			−0.467354
$789$	0.539794			0.0192172
$790$		0			0
$791$		−	19.9153i		−	0.708107i
$792$		−	0.174040i		−	0.00618424i
$793$	−7.03726			−0.249901
$794$		−	5.75234i		−	0.204143i
$795$		0			0
$796$		−	6.04548i		−	0.214277i
$797$		−	28.0428i		−	0.993327i	−0.867943	−	0.496663i	$-0.834558\pi$
$797$		−	28.0428i		−	0.993327i	0.867943	−	0.496663i	$-0.165442\pi$
$798$	23.4440			0.829910
$799$		−	18.6820i		−	0.660920i
$800$		0			0
$801$		−	1.60039i		−	0.0565469i
$802$	−24.6273			−0.869620
$803$	−1.95290			−0.0689163
$804$	13.6653			0.481938
$805$		0			0
$806$			13.2597i			0.467054i
$807$	−51.4504			−1.81114
$808$		−	3.20212i		−	0.112650i
$809$		−	6.86304i		−	0.241292i	−0.992696	−	0.120646i	$-0.961503\pi$
$809$		−	6.86304i		−	0.241292i	0.992696	−	0.120646i	$-0.0384965\pi$
$810$		0			0
$811$	−13.4852			−0.473529			−0.236765	−	0.971567i	$-0.576087\pi$
$811$	−13.4852			−0.473529			−0.236765	+	0.971567i	$0.576087\pi$
$812$		−	8.49300i		−	0.298046i
$813$	−2.81082			−0.0985799
$814$	1.00024	+	5.43774i	0.0350585	+	0.190593i
$815$		0			0
$816$		−	3.75235i		−	0.131359i
$817$	23.8625			0.834844
$818$	25.1947			0.880913
$819$		−	1.34031i		−	0.0468341i
$820$		0			0
$821$	−20.0198			−0.698697			−0.349349	−	0.936993i	$-0.613597\pi$
$821$	−20.0198			−0.698697			−0.349349	+	0.936993i	$0.613597\pi$
$822$			32.0413i			1.11757i
$823$	6.23551			0.217356			0.108678	−	0.994077i	$-0.465338\pi$
$823$	6.23551			0.217356			0.108678	+	0.994077i	$0.465338\pi$
$824$	17.6871			0.616160
$825$		0			0
$826$	−17.5065			−0.609130
$827$			33.7887i			1.17495i	0.809243	+	0.587475i	$0.199878\pi$
$827$			33.7887i			1.17495i	−0.809243	+	0.587475i	$0.800122\pi$
$828$		−	1.46798i		−	0.0510158i
$829$		−	31.8041i		−	1.10460i	−0.833645	−	0.552301i	$-0.813750\pi$
$829$		−	31.8041i		−	1.10460i	0.833645	−	0.552301i	$-0.186250\pi$
$830$		0			0
$831$		−	47.0609i		−	1.63253i
$832$			2.22269i			0.0770578i
$833$			6.12977i			0.212384i
$834$		−	22.7725i		−	0.788546i
$835$		0			0
$836$		−	3.78757i		−	0.130996i
$837$		−	29.9316i		−	1.03459i
$838$			7.19906i			0.248687i
$839$	−1.55322			−0.0536233			−0.0268116	−	0.999641i	$-0.508535\pi$
$839$	−1.55322			−0.0536233			−0.0268116	+	0.999641i	$0.508535\pi$
$840$		0			0
$841$	21.7275			0.749224
$842$	−34.0902			−1.17483
$843$			16.8907i			0.581748i
$844$	−3.06975			−0.105665
$845$		0			0
$846$			1.70302i			0.0585511i
$847$	−32.0407			−1.10093
$848$	9.37592			0.321970
$849$		−	38.8359i		−	1.33284i
$850$		0			0
$851$	8.43677	+	45.8658i	0.289209	+	1.57226i
$852$	24.1454			0.827206
$853$			37.4272i			1.28148i	0.767757	+	0.640741i	$0.221373\pi$
$853$			37.4272i			1.28148i	−0.767757	+	0.640741i	$0.778627\pi$
$854$	−9.97114			−0.341206
$855$		0			0
$856$		−	6.75126i		−	0.230753i
$857$		−	21.2048i		−	0.724341i	−0.932112	−	0.362171i	$-0.882036\pi$
$857$		−	21.2048i		−	0.724341i	0.932112	−	0.362171i	$-0.117964\pi$
$858$	−3.60925			−0.123218
$859$		−	41.1942i		−	1.40553i	−0.711424	−	0.702764i	$-0.751949\pi$
$859$		−	41.1942i		−	1.40553i	0.711424	−	0.702764i	$-0.248051\pi$
$860$		0			0
$861$	−13.0703			−0.445435
$862$	25.2123			0.858734
$863$	−42.7716			−1.45596			−0.727982	−	0.685597i	$-0.759541\pi$
$863$	−42.7716			−1.45596			−0.727982	+	0.685597i	$0.759541\pi$
$864$		−	5.01735i		−	0.170694i
$865$		0			0
$866$			21.8683i			0.743115i
$867$	−22.4884			−0.763747
$868$			18.7878i			0.637699i
$869$			3.05204i			0.103533i
$870$		0			0
$871$		−	17.0021i		−	0.576093i
$872$	10.5304			0.356604
$873$		−	0.984709i		−	0.0333273i
$874$		−	31.9471i		−	1.08063i
$875$		0			0
$876$	3.83824			0.129682
$877$	−50.8976			−1.71869			−0.859345	−	0.511397i	$-0.829128\pi$
$877$	−50.8976			−1.71869			−0.859345	+	0.511397i	$0.829128\pi$
$878$	−9.00956			−0.304058
$879$	−19.8803			−0.670547
$880$		0			0
$881$	−44.1155			−1.48629			−0.743144	−	0.669132i	$-0.766666\pi$
$881$	−44.1155			−1.48629			−0.743144	+	0.669132i	$0.766666\pi$
$882$		−	0.558782i		−	0.0188152i
$883$			46.0708i			1.55041i	0.631713	+	0.775203i	$0.282352\pi$
$883$			46.0708i			1.55041i	−0.631713	+	0.775203i	$0.717648\pi$
$884$	−4.66860			−0.157022
$885$		0			0
$886$			2.89007i			0.0970939i
$887$	41.8693			1.40583			0.702916	−	0.711272i	$-0.251881\pi$
$887$	41.8693			1.40583			0.702916	+	0.711272i	$0.251881\pi$
$888$	−1.96588	−	10.6874i	−0.0659707	−	0.358645i
$889$	−47.3886			−1.58936
$890$		0			0
$891$	8.66940			0.290436
$892$	13.9960			0.468621
$893$			37.0622i			1.24024i
$894$			12.2158i			0.408557i
$895$		0			0
$896$			3.14934i			0.105212i
$897$	−30.4430			−1.01646
$898$	−18.1539			−0.605805
$899$	16.0878			0.536560
$900$		0			0
$901$			19.6935i			0.656084i
$902$			2.11161i			0.0703089i
$903$		−	32.2191i		−	1.07219i
$904$	6.32365			0.210321
$905$		0			0
$906$		−	5.01466i		−	0.166601i
$907$			30.2279i			1.00370i	0.864954	+	0.501851i	$0.167347\pi$
$907$			30.2279i			1.00370i	−0.864954	+	0.501851i	$0.832653\pi$
$908$		−	11.9087i		−	0.395205i
$909$	−0.613117			−0.0203358
$910$		0			0
$911$			8.01080i			0.265409i	0.991156	+	0.132705i	$0.0423662\pi$
$911$			8.01080i			0.265409i	−0.991156	+	0.132705i	$0.957634\pi$
$912$			7.44411i			0.246499i
$913$	−14.7956			−0.489664
$914$	−10.4140			−0.344464
$915$		0			0
$916$	−7.43448			−0.245642
$917$		−	10.4550i		−	0.345255i
$918$	10.5386			0.347825
$919$		−	27.1395i		−	0.895249i	−0.894222	−	0.447624i	$-0.852270\pi$
$919$		−	27.1395i		−	0.895249i	0.894222	−	0.447624i	$-0.147730\pi$
$920$		0			0
$921$	28.5662			0.941288
$922$	17.7433			0.584346
$923$		−	30.0411i		−	0.988816i
$924$	−5.11397			−0.168237
$925$		0			0
$926$	11.6293			0.382161
$927$		−	3.38659i		−	0.111230i
$928$	2.69676			0.0885253
$929$	−47.1557			−1.54713			−0.773564	−	0.633719i	$-0.781528\pi$
$929$	−47.1557			−1.54713			−0.773564	+	0.633719i	$0.781528\pi$
$930$		0			0
$931$		−	12.1606i		−	0.398546i
$932$	−15.2152			−0.498391
$933$			52.9539i			1.73363i
$934$	−6.25208			−0.204574
$935$		0			0
$936$	0.425583			0.0139106
$937$	22.2885			0.728133			0.364066	−	0.931373i	$-0.381388\pi$
$937$	22.2885			0.728133			0.364066	+	0.931373i	$0.381388\pi$
$938$		−	24.0903i		−	0.786578i
$939$		−	17.8647i		−	0.582992i
$940$		0			0
$941$	43.0380			1.40300			0.701499	−	0.712670i	$-0.252514\pi$
$941$	43.0380			1.40300			0.701499	+	0.712670i	$0.252514\pi$
$942$			13.0104i			0.423902i
$943$			17.8109i			0.580001i
$944$		−	5.55880i		−	0.180923i
$945$		0			0
$946$	−5.20525			−0.169237
$947$			16.4353i			0.534075i	0.963686	+	0.267038i	$0.0860448\pi$
$947$			16.4353i			0.534075i	−0.963686	+	0.267038i	$0.913955\pi$
$948$		−	5.99850i		−	0.194822i
$949$		−	4.77545i		−	0.155018i
$950$		0			0
$951$	37.7654			1.22463
$952$	−6.61496			−0.214392
$953$	48.5182			1.57166			0.785830	−	0.618443i	$-0.212236\pi$
$953$	48.5182			1.57166			0.785830	+	0.618443i	$0.212236\pi$
$954$		−	1.79523i		−	0.0581227i
$955$		0			0
$956$		−	29.1359i		−	0.942323i
$957$			4.37905i			0.141555i
$958$	16.4452			0.531319
$959$	56.4851			1.82400
$960$		0			0
$961$	−4.58873			−0.148024
$962$	−13.2970	+	2.44591i	−0.428712	+	0.0788593i
$963$	−1.29268			−0.0416560
$964$		−	7.08791i		−	0.228286i
$965$		0			0
$966$	−43.1349			−1.38784
$967$			21.0002i			0.675322i	0.941268	+	0.337661i	$0.109636\pi$
$967$			21.0002i			0.675322i	−0.941268	+	0.337661i	$0.890364\pi$
$968$		−	10.1738i		−	0.326998i
$969$	−15.6358			−0.502295
$970$		0			0
$971$	11.8732			0.381028			0.190514	−	0.981684i	$-0.438984\pi$
$971$	11.8732			0.381028			0.190514	+	0.981684i	$0.438984\pi$
$972$	−1.98686			−0.0637286
$973$	−40.1452			−1.28700
$974$	−13.7966			−0.442072
$975$		0			0
$976$		−	3.16611i		−	0.101345i
$977$			31.2226i			0.998900i	0.866343	+	0.499450i	$0.166465\pi$
$977$			31.2226i			0.998900i	−0.866343	+	0.499450i	$0.833535\pi$
$978$	39.7166			1.27000
$979$			7.59735i			0.242812i
$980$		0			0
$981$		−	2.01628i		−	0.0643748i
$982$			39.0410i			1.24585i
$983$	−57.5637			−1.83600			−0.917999	−	0.396583i	$-0.870196\pi$
$983$	−57.5637			−1.83600			−0.917999	+	0.396583i	$0.870196\pi$
$984$		−	4.15017i		−	0.132303i
$985$		0			0
$986$			5.66434i			0.180389i
$987$	50.0414			1.59283
$988$	9.26180			0.294657
$989$	−43.9049			−1.39609
$990$		0			0
$991$		−	14.9985i		−	0.476442i	−0.971211	−	0.238221i	$-0.923436\pi$
$991$		−	14.9985i		−	0.476442i	0.971211	−	0.238221i	$-0.0765642\pi$
$992$	−5.96563			−0.189409
$993$		−	33.4649i		−	1.06198i
$994$		−	42.5655i		−	1.35010i
$995$		0			0
$996$	29.0795			0.921418
$997$			1.43497i			0.0454459i	0.999742	+	0.0227229i	$0.00723356\pi$
$997$			1.43497i			0.0454459i	−0.999742	+	0.0227229i	$0.992766\pi$
$998$	−40.0886			−1.26898
$999$	30.0158	−	5.52123i	0.949657	−	0.174684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.d.i.1701.2		20
5.2	odd	4		370.2.c.b.369.9	yes	10
5.3	odd	4		370.2.c.a.369.2	✓	10
5.4	even	2	inner	1850.2.d.i.1701.19		20
15.2	even	4		3330.2.e.c.739.9		10
15.8	even	4		3330.2.e.d.739.1		10
37.36	even	2	inner	1850.2.d.i.1701.12		20
185.73	odd	4		370.2.c.b.369.2	yes	10
185.147	odd	4		370.2.c.a.369.9	yes	10
185.184	even	2	inner	1850.2.d.i.1701.9		20
555.332	even	4		3330.2.e.d.739.2		10
555.443	even	4		3330.2.e.c.739.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.c.a.369.2	✓	10	5.3	odd	4
370.2.c.a.369.9	yes	10	185.147	odd	4
370.2.c.b.369.2	yes	10	185.73	odd	4
370.2.c.b.369.9	yes	10	5.2	odd	4
1850.2.d.i.1701.2		20	1.1	even	1	trivial
1850.2.d.i.1701.9		20	185.184	even	2	inner
1850.2.d.i.1701.12		20	37.36	even	2	inner
1850.2.d.i.1701.19		20	5.4	even	2	inner
3330.2.e.c.739.9		10	15.2	even	4
3330.2.e.c.739.10		10	555.443	even	4
3330.2.e.d.739.1		10	15.8	even	4
3330.2.e.d.739.2		10	555.332	even	4

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:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.78647 q^{3} -1.00000 q^{4} +1.78647i q^{6} +3.14934 q^{7} +1.00000i q^{8} +0.191472 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.78647 q^{3} -1.00000 q^{4} +1.78647i q^{6} +3.14934 q^{7} +1.00000i q^{8} +0.191472 q^{9} -0.908956 q^{11} +1.78647 q^{12} -2.22269i q^{13} -3.14934i q^{14} +1.00000 q^{16} +2.10043i q^{17} -0.191472i q^{18} -4.16694i q^{19} -5.62620 q^{21} +0.908956i q^{22} +7.66680i q^{23} -1.78647i q^{24} -2.22269 q^{26} +5.01735 q^{27} -3.14934 q^{28} +2.69676i q^{29} -5.96563i q^{31} -1.00000i q^{32} +1.62382 q^{33} +2.10043 q^{34} -0.191472 q^{36} +(5.98240 - 1.10043i) q^{37} -4.16694 q^{38} +3.97076i q^{39} +2.32312 q^{41} +5.62620i q^{42} +5.72663i q^{43} +0.908956 q^{44} +7.66680 q^{46} -8.89435 q^{47} -1.78647 q^{48} +2.91834 q^{49} -3.75235i q^{51} +2.22269i q^{52} +9.37592 q^{53} -5.01735i q^{54} +3.14934i q^{56} +7.44411i q^{57} +2.69676 q^{58} -5.55880i q^{59} -3.16611i q^{61} -5.96563 q^{62} +0.603011 q^{63} -1.00000 q^{64} -1.62382i q^{66} +7.64933 q^{67} -2.10043i q^{68} -13.6965i q^{69} +13.5157 q^{71} +0.191472i q^{72} +2.14851 q^{73} +(-1.10043 - 5.98240i) q^{74} +4.16694i q^{76} -2.86261 q^{77} +3.97076 q^{78} -3.35774i q^{79} -9.53776 q^{81} -2.32312i q^{82} +16.2776 q^{83} +5.62620 q^{84} +5.72663 q^{86} -4.81767i q^{87} -0.908956i q^{88} -8.35832i q^{89} -7.00000i q^{91} -7.66680i q^{92} +10.6574i q^{93} +8.89435i q^{94} +1.78647i q^{96} -5.14283i q^{97} -2.91834i q^{98} -0.174040 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) 20 * q - 20 * q^4 + 16 * q^9	\( 20 q - 20 q^{4} + 16 q^{9} + 20 q^{16} - 24 q^{21} + 4 q^{26} + 36 q^{34} - 16 q^{36} - 8 q^{41} - 20 q^{46} + 16 q^{49} - 20 q^{64} - 40 q^{71} - 16 q^{74} + 116 q^{81} + 24 q^{84} + 20 q^{86} + 164 q^{99}+O(q^{100}) \) 20 * q - 20 * q^4 + 16 * q^9 + 20 * q^16 - 24 * q^21 + 4 * q^26 + 36 * q^34 - 16 * q^36 - 8 * q^41 - 20 * q^46 + 16 * q^49 - 20 * q^64 - 40 * q^71 - 16 * q^74 + 116 * q^81 + 24 * q^84 + 20 * q^86 + 164 * q^99

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