LMFDB - Embedded newform 1800.2.d.i.1549.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1800,2,Mod(1549,1800)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1800.1549"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1800, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,2,0,0,0,0,0,-4,0,0,0,0,8,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1549.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1800.1549
Dual form			1800.2.d.i.1549.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +2.00000i q^{7} +(-2.00000 - 2.00000i) q^{8} +4.00000 q^{13} +(2.00000 + 2.00000i) q^{14} -4.00000 q^{16} -2.00000i q^{17} -4.00000i q^{19} -4.00000i q^{23} +(4.00000 - 4.00000i) q^{26} +4.00000 q^{28} -6.00000i q^{29} +2.00000 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-2.00000 - 2.00000i) q^{34} +8.00000 q^{37} +(-4.00000 - 4.00000i) q^{38} -2.00000 q^{41} +4.00000 q^{43} +(-4.00000 - 4.00000i) q^{46} -12.0000i q^{47} +3.00000 q^{49} -8.00000i q^{52} +6.00000 q^{53} +(4.00000 - 4.00000i) q^{56} +(-6.00000 - 6.00000i) q^{58} +4.00000i q^{59} +(2.00000 - 2.00000i) q^{62} +8.00000i q^{64} -12.0000 q^{67} -4.00000 q^{68} -12.0000 q^{71} -6.00000i q^{73} +(8.00000 - 8.00000i) q^{74} -8.00000 q^{76} -10.0000 q^{79} +(-2.00000 + 2.00000i) q^{82} +16.0000 q^{83} +(4.00000 - 4.00000i) q^{86} -10.0000 q^{89} +8.00000i q^{91} -8.00000 q^{92} +(-12.0000 - 12.0000i) q^{94} +2.00000i q^{97} +(3.00000 - 3.00000i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{8} + 8 q^{13} + 4 q^{14} - 8 q^{16} + 8 q^{26} + 8 q^{28} + 4 q^{31} - 8 q^{32} - 4 q^{34} + 16 q^{37} - 8 q^{38} - 4 q^{41} + 8 q^{43} - 8 q^{46} + 6 q^{49} + 12 q^{53} + 8 q^{56}+ \cdots + 6 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^8 + 8 * q^13 + 4 * q^14 - 8 * q^16 + 8 * q^26 + 8 * q^28 + 4 * q^31 - 8 * q^32 - 4 * q^34 + 16 * q^37 - 8 * q^38 - 4 * q^41 + 8 * q^43 - 8 * q^46 + 6 * q^49 + 12 * q^53 + 8 * q^56 - 12 * q^58 + 4 * q^62 - 24 * q^67 - 8 * q^68 - 24 * q^71 + 16 * q^74 - 16 * q^76 - 20 * q^79 - 4 * q^82 + 32 * q^83 + 8 * q^86 - 20 * q^89 - 16 * q^92 - 24 * q^94 + 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$-1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.707107	−	0.707107i
$2$	1.00000	−	1.00000i	0.707107	−	0.707107i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	1.00000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$		0			0
$10$		0			0
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		0			0
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$	2.00000	+	2.00000i	0.534522	+	0.534522i
$15$		0			0
$16$	−4.00000			−1.00000
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$		0			0
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$		0			0
$25$		0			0
$26$	4.00000	−	4.00000i	0.784465	−	0.784465i
$27$		0			0
$28$	4.00000			0.755929
$29$		−	6.00000i		−	1.11417i	−0.830455	−	0.557086i	$-0.811919\pi$
$29$		−	6.00000i		−	1.11417i	0.830455	−	0.557086i	$-0.188081\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	−4.00000	+	4.00000i	−0.707107	+	0.707107i
$33$		0			0
$34$	−2.00000	−	2.00000i	−0.342997	−	0.342997i
$35$		0			0
$36$		0			0
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	−4.00000	−	4.00000i	−0.648886	−	0.648886i
$39$		0			0
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$		0			0
$46$	−4.00000	−	4.00000i	−0.589768	−	0.589768i
$47$		−	12.0000i		−	1.75038i	−0.483779	−	0.875190i	$-0.660736\pi$
$47$		−	12.0000i		−	1.75038i	0.483779	−	0.875190i	$-0.339264\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$		0			0
$51$		0			0
$52$		−	8.00000i		−	1.10940i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$		0			0
$56$	4.00000	−	4.00000i	0.534522	−	0.534522i
$57$		0			0
$58$	−6.00000	−	6.00000i	−0.787839	−	0.787839i
$59$			4.00000i			0.520756i	0.965507	+	0.260378i	$0.0838471\pi$
$59$			4.00000i			0.520756i	−0.965507	+	0.260378i	$0.916153\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	2.00000	−	2.00000i	0.254000	−	0.254000i
$63$		0			0
$64$			8.00000i			1.00000i
$65$		0			0
$66$		0			0
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	−4.00000			−0.485071
$69$		0			0
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$	8.00000	−	8.00000i	0.929981	−	0.929981i
$75$		0			0
$76$	−8.00000			−0.917663
$77$		0			0
$78$		0			0
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$		0			0
$81$		0			0
$82$	−2.00000	+	2.00000i	−0.220863	+	0.220863i
$83$	16.0000			1.75623			0.878114	−	0.478451i	$-0.158802\pi$
$83$	16.0000			1.75623			0.878114	+	0.478451i	$0.158802\pi$
$84$		0			0
$85$		0			0
$86$	4.00000	−	4.00000i	0.431331	−	0.431331i
$87$		0			0
$88$		0			0
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$			8.00000i			0.838628i
$92$	−8.00000			−0.834058
$93$		0			0
$94$	−12.0000	−	12.0000i	−1.23771	−	1.23771i
$95$		0			0
$96$		0			0
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$	3.00000	−	3.00000i	0.303046	−	0.303046i
$99$		0			0
$100$		0			0
$101$			10.0000i			0.995037i	0.867453	+	0.497519i	$0.165755\pi$
$101$			10.0000i			0.995037i	−0.867453	+	0.497519i	$0.834245\pi$
$102$		0			0
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$	−8.00000	−	8.00000i	−0.784465	−	0.784465i
$105$		0			0
$106$	6.00000	−	6.00000i	0.582772	−	0.582772i
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$		0			0
$111$		0			0
$112$		−	8.00000i		−	0.755929i
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$		0			0
$115$		0			0
$116$	−12.0000			−1.11417
$117$		0			0
$118$	4.00000	+	4.00000i	0.368230	+	0.368230i
$119$	4.00000			0.366679
$120$		0			0
$121$	11.0000			1.00000
$122$		0			0
$123$		0			0
$124$		−	4.00000i		−	0.359211i
$125$		0			0
$126$		0			0
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$	8.00000	+	8.00000i	0.707107	+	0.707107i
$129$		0			0
$130$		0			0
$131$			20.0000i			1.74741i	0.486458	+	0.873704i	$0.338289\pi$
$131$			20.0000i			1.74741i	−0.486458	+	0.873704i	$0.661711\pi$
$132$		0			0
$133$	8.00000			0.693688
$134$	−12.0000	+	12.0000i	−1.03664	+	1.03664i
$135$		0			0
$136$	−4.00000	+	4.00000i	−0.342997	+	0.342997i
$137$			18.0000i			1.53784i	0.639343	+	0.768922i	$0.279207\pi$
$137$			18.0000i			1.53784i	−0.639343	+	0.768922i	$0.720793\pi$
$138$		0			0
$139$		−	4.00000i		−	0.339276i	−0.985506	−	0.169638i	$-0.945740\pi$
$139$		−	4.00000i		−	0.339276i	0.985506	−	0.169638i	$-0.0542598\pi$
$140$		0			0
$141$		0			0
$142$	−12.0000	+	12.0000i	−1.00702	+	1.00702i
$143$		0			0
$144$		0			0
$145$		0			0
$146$	−6.00000	−	6.00000i	−0.496564	−	0.496564i
$147$		0			0
$148$		−	16.0000i		−	1.31519i
$149$		−	6.00000i		−	0.491539i	−0.969328	−	0.245770i	$-0.920959\pi$
$149$		−	6.00000i		−	0.491539i	0.969328	−	0.245770i	$-0.0790407\pi$
$150$		0			0
$151$	−18.0000			−1.46482			−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000			−1.46482			−0.732410	+	0.680864i	$0.761604\pi$
$152$	−8.00000	+	8.00000i	−0.648886	+	0.648886i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.00000			0.638470			0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000			0.638470			0.319235	+	0.947676i	$0.396574\pi$
$158$	−10.0000	+	10.0000i	−0.795557	+	0.795557i
$159$		0			0
$160$		0			0
$161$	8.00000			0.630488
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$			4.00000i			0.312348i
$165$		0			0
$166$	16.0000	−	16.0000i	1.24184	−	1.24184i
$167$			8.00000i			0.619059i	0.950890	+	0.309529i	$0.100171\pi$
$167$			8.00000i			0.619059i	−0.950890	+	0.309529i	$0.899829\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$		0			0
$172$		−	8.00000i		−	0.609994i
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−10.0000	+	10.0000i	−0.749532	+	0.749532i
$179$			4.00000i			0.298974i	0.988764	+	0.149487i	$0.0477622\pi$
$179$			4.00000i			0.298974i	−0.988764	+	0.149487i	$0.952238\pi$
$180$		0			0
$181$		−	20.0000i		−	1.48659i	−0.668965	−	0.743294i	$-0.733262\pi$
$181$		−	20.0000i		−	1.48659i	0.668965	−	0.743294i	$-0.266738\pi$
$182$	8.00000	+	8.00000i	0.592999	+	0.592999i
$183$		0			0
$184$	−8.00000	+	8.00000i	−0.589768	+	0.589768i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−24.0000			−1.75038
$189$		0			0
$190$		0			0
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$		−	6.00000i		−	0.431889i	−0.976406	−	0.215945i	$-0.930717\pi$
$193$		−	6.00000i		−	0.431889i	0.976406	−	0.215945i	$-0.0692831\pi$
$194$	2.00000	+	2.00000i	0.143592	+	0.143592i
$195$		0			0
$196$		−	6.00000i		−	0.428571i
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$		0			0
$201$		0			0
$202$	10.0000	+	10.0000i	0.703598	+	0.703598i
$203$	12.0000			0.842235
$204$		0			0
$205$		0			0
$206$	−6.00000	−	6.00000i	−0.418040	−	0.418040i
$207$		0			0
$208$	−16.0000			−1.10940
$209$		0			0
$210$		0			0
$211$			20.0000i			1.37686i	0.725304	+	0.688428i	$0.241699\pi$
$211$			20.0000i			1.37686i	−0.725304	+	0.688428i	$0.758301\pi$
$212$		−	12.0000i		−	0.824163i
$213$		0			0
$214$	12.0000	−	12.0000i	0.820303	−	0.820303i
$215$		0			0
$216$		0			0
$217$			4.00000i			0.271538i
$218$	−4.00000	−	4.00000i	−0.270914	−	0.270914i
$219$		0			0
$220$		0			0
$221$		−	8.00000i		−	0.538138i
$222$		0			0
$223$			14.0000i			0.937509i	0.883328	+	0.468755i	$0.155297\pi$
$223$			14.0000i			0.937509i	−0.883328	+	0.468755i	$0.844703\pi$
$224$	−8.00000	−	8.00000i	−0.534522	−	0.534522i
$225$		0			0
$226$	6.00000	+	6.00000i	0.399114	+	0.399114i
$227$	−8.00000			−0.530979			−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000			−0.530979			−0.265489	+	0.964114i	$0.585534\pi$
$228$		0			0
$229$		−	4.00000i		−	0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$		−	4.00000i		−	0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$		0			0
$231$		0			0
$232$	−12.0000	+	12.0000i	−0.787839	+	0.787839i
$233$		−	14.0000i		−	0.917170i	−0.888650	−	0.458585i	$-0.848356\pi$
$233$		−	14.0000i		−	0.917170i	0.888650	−	0.458585i	$-0.151644\pi$
$234$		0			0
$235$		0			0
$236$	8.00000			0.520756
$237$		0			0
$238$	4.00000	−	4.00000i	0.259281	−	0.259281i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	2.00000			0.128831			0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000			0.128831			0.0644157	+	0.997923i	$0.479482\pi$
$242$	11.0000	−	11.0000i	0.707107	−	0.707107i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		−	16.0000i		−	1.01806i
$248$	−4.00000	−	4.00000i	−0.254000	−	0.254000i
$249$		0			0
$250$		0			0
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$	2.00000	+	2.00000i	0.125491	+	0.125491i
$255$		0			0
$256$	16.0000			1.00000
$257$			18.0000i			1.12281i	0.827541	+	0.561405i	$0.189739\pi$
$257$			18.0000i			1.12281i	−0.827541	+	0.561405i	$0.810261\pi$
$258$		0			0
$259$			16.0000i			0.994192i
$260$		0			0
$261$		0			0
$262$	20.0000	+	20.0000i	1.23560	+	1.23560i
$263$			16.0000i			0.986602i	0.869859	+	0.493301i	$0.164210\pi$
$263$			16.0000i			0.986602i	−0.869859	+	0.493301i	$0.835790\pi$
$264$		0			0
$265$		0			0
$266$	8.00000	−	8.00000i	0.490511	−	0.490511i
$267$		0			0
$268$			24.0000i			1.46603i
$269$		−	6.00000i		−	0.365826i	−0.983129	−	0.182913i	$-0.941447\pi$
$269$		−	6.00000i		−	0.365826i	0.983129	−	0.182913i	$-0.0585527\pi$
$270$		0			0
$271$	−18.0000			−1.09342			−0.546711	−	0.837321i	$-0.684120\pi$
$271$	−18.0000			−1.09342			−0.546711	+	0.837321i	$0.684120\pi$
$272$			8.00000i			0.485071i
$273$		0			0
$274$	18.0000	+	18.0000i	1.08742	+	1.08742i
$275$		0			0
$276$		0			0
$277$	28.0000			1.68236			0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000			1.68236			0.841178	+	0.540758i	$0.181862\pi$
$278$	−4.00000	−	4.00000i	−0.239904	−	0.239904i
$279$		0			0
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	4.00000			0.237775			0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000			0.237775			0.118888	+	0.992908i	$0.462067\pi$
$284$			24.0000i			1.42414i
$285$		0			0
$286$		0			0
$287$		−	4.00000i		−	0.236113i
$288$		0			0
$289$	13.0000			0.764706
$290$		0			0
$291$		0			0
$292$	−12.0000			−0.702247
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$		0			0
$295$		0			0
$296$	−16.0000	−	16.0000i	−0.929981	−	0.929981i
$297$		0			0
$298$	−6.00000	−	6.00000i	−0.347571	−	0.347571i
$299$		−	16.0000i		−	0.925304i
$300$		0			0
$301$			8.00000i			0.461112i
$302$	−18.0000	+	18.0000i	−1.03578	+	1.03578i
$303$		0			0
$304$			16.0000i			0.917663i
$305$		0			0
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.00000			0.453638			0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000			0.453638			0.226819	+	0.973937i	$0.427167\pi$
$312$		0			0
$313$			14.0000i			0.791327i	0.918396	+	0.395663i	$0.129485\pi$
$313$			14.0000i			0.791327i	−0.918396	+	0.395663i	$0.870515\pi$
$314$	8.00000	−	8.00000i	0.451466	−	0.451466i
$315$		0			0
$316$			20.0000i			1.12509i
$317$	22.0000			1.23564			0.617822	−	0.786318i	$-0.288015\pi$
$317$	22.0000			1.23564			0.617822	+	0.786318i	$0.288015\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$	8.00000	−	8.00000i	0.445823	−	0.445823i
$323$	−8.00000			−0.445132
$324$		0			0
$325$		0			0
$326$	4.00000	−	4.00000i	0.221540	−	0.221540i
$327$		0			0
$328$	4.00000	+	4.00000i	0.220863	+	0.220863i
$329$	24.0000			1.32316
$330$		0			0
$331$			20.0000i			1.09930i	0.835395	+	0.549650i	$0.185239\pi$
$331$			20.0000i			1.09930i	−0.835395	+	0.549650i	$0.814761\pi$
$332$		−	32.0000i		−	1.75623i
$333$		0			0
$334$	8.00000	+	8.00000i	0.437741	+	0.437741i
$335$		0			0
$336$		0			0
$337$			2.00000i			0.108947i	0.998515	+	0.0544735i	$0.0173480\pi$
$337$			2.00000i			0.108947i	−0.998515	+	0.0544735i	$0.982652\pi$
$338$	3.00000	−	3.00000i	0.163178	−	0.163178i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$			20.0000i			1.07990i
$344$	−8.00000	−	8.00000i	−0.431331	−	0.431331i
$345$		0			0
$346$	6.00000	−	6.00000i	0.322562	−	0.322562i
$347$	−8.00000			−0.429463			−0.214731	−	0.976673i	$-0.568888\pi$
$347$	−8.00000			−0.429463			−0.214731	+	0.976673i	$0.568888\pi$
$348$		0			0
$349$			16.0000i			0.856460i	0.903670	+	0.428230i	$0.140863\pi$
$349$			16.0000i			0.856460i	−0.903670	+	0.428230i	$0.859137\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			6.00000i			0.319348i	0.987170	+	0.159674i	$0.0510443\pi$
$353$			6.00000i			0.319348i	−0.987170	+	0.159674i	$0.948956\pi$
$354$		0			0
$355$		0			0
$356$			20.0000i			1.06000i
$357$		0			0
$358$	4.00000	+	4.00000i	0.211407	+	0.211407i
$359$	−20.0000			−1.05556			−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000			−1.05556			−0.527780	+	0.849381i	$0.676975\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−20.0000	−	20.0000i	−1.05118	−	1.05118i
$363$		0			0
$364$	16.0000			0.838628
$365$		0			0
$366$		0			0
$367$		−	18.0000i		−	0.939592i	−0.882775	−	0.469796i	$-0.844327\pi$
$367$		−	18.0000i		−	0.939592i	0.882775	−	0.469796i	$-0.155673\pi$
$368$			16.0000i			0.834058i
$369$		0			0
$370$		0			0
$371$			12.0000i			0.623009i
$372$		0			0
$373$	−16.0000			−0.828449			−0.414224	−	0.910175i	$-0.635947\pi$
$373$	−16.0000			−0.828449			−0.414224	+	0.910175i	$0.635947\pi$
$374$		0			0
$375$		0			0
$376$	−24.0000	+	24.0000i	−1.23771	+	1.23771i
$377$		−	24.0000i		−	1.23606i
$378$		0			0
$379$		−	4.00000i		−	0.205466i	−0.994709	−	0.102733i	$-0.967241\pi$
$379$		−	4.00000i		−	0.205466i	0.994709	−	0.102733i	$-0.0327588\pi$
$380$		0			0
$381$		0			0
$382$	8.00000	−	8.00000i	0.409316	−	0.409316i
$383$		−	24.0000i		−	1.22634i	−0.789950	−	0.613171i	$-0.789894\pi$
$383$		−	24.0000i		−	1.22634i	0.789950	−	0.613171i	$-0.210106\pi$
$384$		0			0
$385$		0			0
$386$	−6.00000	−	6.00000i	−0.305392	−	0.305392i
$387$		0			0
$388$	4.00000			0.203069
$389$			34.0000i			1.72387i	0.507020	+	0.861934i	$0.330747\pi$
$389$			34.0000i			1.72387i	−0.507020	+	0.861934i	$0.669253\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	−6.00000	−	6.00000i	−0.303046	−	0.303046i
$393$		0			0
$394$	2.00000	−	2.00000i	0.100759	−	0.100759i
$395$		0			0
$396$		0			0
$397$	−32.0000			−1.60603			−0.803017	−	0.595956i	$-0.796773\pi$
$397$	−32.0000			−1.60603			−0.803017	+	0.595956i	$0.796773\pi$
$398$	−10.0000	+	10.0000i	−0.501255	+	0.501255i
$399$		0			0
$400$		0			0
$401$	18.0000			0.898877			0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000			0.898877			0.449439	+	0.893311i	$0.351624\pi$
$402$		0			0
$403$	8.00000			0.398508
$404$	20.0000			0.995037
$405$		0			0
$406$	12.0000	−	12.0000i	0.595550	−	0.595550i
$407$		0			0
$408$		0			0
$409$	−10.0000			−0.494468			−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000			−0.494468			−0.247234	+	0.968956i	$0.579522\pi$
$410$		0			0
$411$		0			0
$412$	−12.0000			−0.591198
$413$	−8.00000			−0.393654
$414$		0			0
$415$		0			0
$416$	−16.0000	+	16.0000i	−0.784465	+	0.784465i
$417$		0			0
$418$		0			0
$419$			24.0000i			1.17248i	0.810139	+	0.586238i	$0.199392\pi$
$419$			24.0000i			1.17248i	−0.810139	+	0.586238i	$0.800608\pi$
$420$		0			0
$421$		−	20.0000i		−	0.974740i	−0.873195	−	0.487370i	$-0.837956\pi$
$421$		−	20.0000i		−	0.974740i	0.873195	−	0.487370i	$-0.162044\pi$
$422$	20.0000	+	20.0000i	0.973585	+	0.973585i
$423$		0			0
$424$	−12.0000	−	12.0000i	−0.582772	−	0.582772i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		−	24.0000i		−	1.16008i
$429$		0			0
$430$		0			0
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$		0			0
$433$			14.0000i			0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$	4.00000	+	4.00000i	0.192006	+	0.192006i
$435$		0			0
$436$	−8.00000			−0.383131
$437$	−16.0000			−0.765384
$438$		0			0
$439$	30.0000			1.43182			0.715911	−	0.698192i	$-0.246012\pi$
$439$	30.0000			1.43182			0.715911	+	0.698192i	$0.246012\pi$
$440$		0			0
$441$		0			0
$442$	−8.00000	−	8.00000i	−0.380521	−	0.380521i
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$		0			0
$445$		0			0
$446$	14.0000	+	14.0000i	0.662919	+	0.662919i
$447$		0			0
$448$	−16.0000			−0.755929
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$		0			0
$452$	12.0000			0.564433
$453$		0			0
$454$	−8.00000	+	8.00000i	−0.375459	+	0.375459i
$455$		0			0
$456$		0			0
$457$			22.0000i			1.02912i	0.857455	+	0.514558i	$0.172044\pi$
$457$			22.0000i			1.02912i	−0.857455	+	0.514558i	$0.827956\pi$
$458$	−4.00000	−	4.00000i	−0.186908	−	0.186908i
$459$		0			0
$460$		0			0
$461$		−	30.0000i		−	1.39724i	−0.715493	−	0.698620i	$-0.753798\pi$
$461$		−	30.0000i		−	1.39724i	0.715493	−	0.698620i	$-0.246202\pi$
$462$		0			0
$463$		−	26.0000i		−	1.20832i	−0.796862	−	0.604161i	$-0.793508\pi$
$463$		−	26.0000i		−	1.20832i	0.796862	−	0.604161i	$-0.206492\pi$
$464$			24.0000i			1.11417i
$465$		0			0
$466$	−14.0000	−	14.0000i	−0.648537	−	0.648537i
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$		0			0
$469$		−	24.0000i		−	1.10822i
$470$		0			0
$471$		0			0
$472$	8.00000	−	8.00000i	0.368230	−	0.368230i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		−	8.00000i		−	0.366679i
$477$		0			0
$478$		0			0
$479$	20.0000			0.913823			0.456912	−	0.889512i	$-0.348956\pi$
$479$	20.0000			0.913823			0.456912	+	0.889512i	$0.348956\pi$
$480$		0			0
$481$	32.0000			1.45907
$482$	2.00000	−	2.00000i	0.0910975	−	0.0910975i
$483$		0			0
$484$		−	22.0000i		−	1.00000i
$485$		0			0
$486$		0			0
$487$		−	38.0000i		−	1.72194i	−0.508652	−	0.860972i	$-0.669856\pi$
$487$		−	38.0000i		−	1.72194i	0.508652	−	0.860972i	$-0.330144\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			20.0000i			0.902587i	0.892375	+	0.451294i	$0.149037\pi$
$491$			20.0000i			0.902587i	−0.892375	+	0.451294i	$0.850963\pi$
$492$		0			0
$493$	−12.0000			−0.540453
$494$	−16.0000	−	16.0000i	−0.719874	−	0.719874i
$495$		0			0
$496$	−8.00000			−0.359211
$497$		−	24.0000i		−	1.07655i
$498$		0			0
$499$			36.0000i			1.61158i	0.592200	+	0.805791i	$0.298259\pi$
$499$			36.0000i			1.61158i	−0.592200	+	0.805791i	$0.701741\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			36.0000i			1.60516i	0.596544	+	0.802580i	$0.296540\pi$
$503$			36.0000i			1.60516i	−0.596544	+	0.802580i	$0.703460\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$	4.00000			0.177471
$509$		−	6.00000i		−	0.265945i	−0.991120	−	0.132973i	$-0.957548\pi$
$509$		−	6.00000i		−	0.265945i	0.991120	−	0.132973i	$-0.0424523\pi$
$510$		0			0
$511$	12.0000			0.530849
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$	18.0000	+	18.0000i	0.793946	+	0.793946i
$515$		0			0
$516$		0			0
$517$		0			0
$518$	16.0000	+	16.0000i	0.703000	+	0.703000i
$519$		0			0
$520$		0			0
$521$	−42.0000			−1.84005			−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000			−1.84005			−0.920027	+	0.391856i	$0.871833\pi$
$522$		0			0
$523$	−36.0000			−1.57417			−0.787085	−	0.616844i	$-0.788411\pi$
$523$	−36.0000			−1.57417			−0.787085	+	0.616844i	$0.788411\pi$
$524$	40.0000			1.74741
$525$		0			0
$526$	16.0000	+	16.0000i	0.697633	+	0.697633i
$527$		−	4.00000i		−	0.174243i
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$		0			0
$532$		−	16.0000i		−	0.693688i
$533$	−8.00000			−0.346518
$534$		0			0
$535$		0			0
$536$	24.0000	+	24.0000i	1.03664	+	1.03664i
$537$		0			0
$538$	−6.00000	−	6.00000i	−0.258678	−	0.258678i
$539$		0			0
$540$		0			0
$541$			20.0000i			0.859867i	0.902861	+	0.429934i	$0.141463\pi$
$541$			20.0000i			0.859867i	−0.902861	+	0.429934i	$0.858537\pi$
$542$	−18.0000	+	18.0000i	−0.773166	+	0.773166i
$543$		0			0
$544$	8.00000	+	8.00000i	0.342997	+	0.342997i
$545$		0			0
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	36.0000			1.53784
$549$		0			0
$550$		0			0
$551$	−24.0000			−1.02243
$552$		0			0
$553$		−	20.0000i		−	0.850487i
$554$	28.0000	−	28.0000i	1.18961	−	1.18961i
$555$		0			0
$556$	−8.00000			−0.339276
$557$	42.0000			1.77960			0.889799	−	0.456354i	$-0.150845\pi$
$557$	42.0000			1.77960			0.889799	+	0.456354i	$0.150845\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$		0			0
$561$		0			0
$562$	18.0000	−	18.0000i	0.759284	−	0.759284i
$563$	−24.0000			−1.01148			−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000			−1.01148			−0.505740	+	0.862686i	$0.668780\pi$
$564$		0			0
$565$		0			0
$566$	4.00000	−	4.00000i	0.168133	−	0.168133i
$567$		0			0
$568$	24.0000	+	24.0000i	1.00702	+	1.00702i
$569$	−30.0000			−1.25767			−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000			−1.25767			−0.628833	+	0.777541i	$0.716467\pi$
$570$		0			0
$571$		−	20.0000i		−	0.836974i	−0.908223	−	0.418487i	$-0.862561\pi$
$571$		−	20.0000i		−	0.836974i	0.908223	−	0.418487i	$-0.137439\pi$
$572$		0			0
$573$		0			0
$574$	−4.00000	−	4.00000i	−0.166957	−	0.166957i
$575$		0			0
$576$		0			0
$577$			42.0000i			1.74848i	0.485491	+	0.874241i	$0.338641\pi$
$577$			42.0000i			1.74848i	−0.485491	+	0.874241i	$0.661359\pi$
$578$	13.0000	−	13.0000i	0.540729	−	0.540729i
$579$		0			0
$580$		0			0
$581$			32.0000i			1.32758i
$582$		0			0
$583$		0			0
$584$	−12.0000	+	12.0000i	−0.496564	+	0.496564i
$585$		0			0
$586$	6.00000	−	6.00000i	0.247858	−	0.247858i
$587$	−28.0000			−1.15568			−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000			−1.15568			−0.577842	+	0.816149i	$0.696105\pi$
$588$		0			0
$589$		−	8.00000i		−	0.329634i
$590$		0			0
$591$		0			0
$592$	−32.0000			−1.31519
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$		0			0
$595$		0			0
$596$	−12.0000			−0.491539
$597$		0			0
$598$	−16.0000	−	16.0000i	−0.654289	−	0.654289i
$599$	−20.0000			−0.817178			−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000			−0.817178			−0.408589	+	0.912719i	$0.633979\pi$
$600$		0			0
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$	8.00000	+	8.00000i	0.326056	+	0.326056i
$603$		0			0
$604$			36.0000i			1.46482i
$605$		0			0
$606$		0			0
$607$			2.00000i			0.0811775i	0.999176	+	0.0405887i	$0.0129233\pi$
$607$			2.00000i			0.0811775i	−0.999176	+	0.0405887i	$0.987077\pi$
$608$	16.0000	+	16.0000i	0.648886	+	0.648886i
$609$		0			0
$610$		0			0
$611$		−	48.0000i		−	1.94187i
$612$		0			0
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$	−12.0000	+	12.0000i	−0.484281	+	0.484281i
$615$		0			0
$616$		0			0
$617$		−	2.00000i		−	0.0805170i	−0.999189	−	0.0402585i	$-0.987182\pi$
$617$		−	2.00000i		−	0.0805170i	0.999189	−	0.0402585i	$-0.0128181\pi$
$618$		0			0
$619$			36.0000i			1.44696i	0.690344	+	0.723481i	$0.257459\pi$
$619$			36.0000i			1.44696i	−0.690344	+	0.723481i	$0.742541\pi$
$620$		0			0
$621$		0			0
$622$	8.00000	−	8.00000i	0.320771	−	0.320771i
$623$		−	20.0000i		−	0.801283i
$624$		0			0
$625$		0			0
$626$	14.0000	+	14.0000i	0.559553	+	0.559553i
$627$		0			0
$628$		−	16.0000i		−	0.638470i
$629$		−	16.0000i		−	0.637962i
$630$		0			0
$631$	22.0000			0.875806			0.437903	−	0.899022i	$-0.355721\pi$
$631$	22.0000			0.875806			0.437903	+	0.899022i	$0.355721\pi$
$632$	20.0000	+	20.0000i	0.795557	+	0.795557i
$633$		0			0
$634$	22.0000	−	22.0000i	0.873732	−	0.873732i
$635$		0			0
$636$		0			0
$637$	12.0000			0.475457
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−22.0000			−0.868948			−0.434474	−	0.900684i	$-0.643066\pi$
$641$	−22.0000			−0.868948			−0.434474	+	0.900684i	$0.643066\pi$
$642$		0			0
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$		−	16.0000i		−	0.630488i
$645$		0			0
$646$	−8.00000	+	8.00000i	−0.314756	+	0.314756i
$647$		−	12.0000i		−	0.471769i	−0.971781	−	0.235884i	$-0.924201\pi$
$647$		−	12.0000i		−	0.471769i	0.971781	−	0.235884i	$-0.0757987\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		−	8.00000i		−	0.313304i
$653$	6.00000			0.234798			0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000			0.234798			0.117399	+	0.993085i	$0.462544\pi$
$654$		0			0
$655$		0			0
$656$	8.00000			0.312348
$657$		0			0
$658$	24.0000	−	24.0000i	0.935617	−	0.935617i
$659$		−	36.0000i		−	1.40236i	−0.712984	−	0.701180i	$-0.752657\pi$
$659$		−	36.0000i		−	1.40236i	0.712984	−	0.701180i	$-0.247343\pi$
$660$		0			0
$661$		−	40.0000i		−	1.55582i	−0.628376	−	0.777910i	$-0.716280\pi$
$661$		−	40.0000i		−	1.55582i	0.628376	−	0.777910i	$-0.283720\pi$
$662$	20.0000	+	20.0000i	0.777322	+	0.777322i
$663$		0			0
$664$	−32.0000	−	32.0000i	−1.24184	−	1.24184i
$665$		0			0
$666$		0			0
$667$	−24.0000			−0.929284
$668$	16.0000			0.619059
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$			14.0000i			0.539660i	0.962908	+	0.269830i	$0.0869676\pi$
$673$			14.0000i			0.539660i	−0.962908	+	0.269830i	$0.913032\pi$
$674$	2.00000	+	2.00000i	0.0770371	+	0.0770371i
$675$		0			0
$676$		−	6.00000i		−	0.230769i
$677$	−18.0000			−0.691796			−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000			−0.691796			−0.345898	+	0.938272i	$0.612426\pi$
$678$		0			0
$679$	−4.00000			−0.153506
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.0000			0.612223			0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000			0.612223			0.306111	+	0.951996i	$0.400972\pi$
$684$		0			0
$685$		0			0
$686$	20.0000	+	20.0000i	0.763604	+	0.763604i
$687$		0			0
$688$	−16.0000			−0.609994
$689$	24.0000			0.914327
$690$		0			0
$691$		−	20.0000i		−	0.760836i	−0.924815	−	0.380418i	$-0.875780\pi$
$691$		−	20.0000i		−	0.760836i	0.924815	−	0.380418i	$-0.124220\pi$
$692$		−	12.0000i		−	0.456172i
$693$		0			0
$694$	−8.00000	+	8.00000i	−0.303676	+	0.303676i
$695$		0			0
$696$		0			0
$697$			4.00000i			0.151511i
$698$	16.0000	+	16.0000i	0.605609	+	0.605609i
$699$		0			0
$700$		0			0
$701$		−	50.0000i		−	1.88847i	−0.329267	−	0.944237i	$-0.606802\pi$
$701$		−	50.0000i		−	1.88847i	0.329267	−	0.944237i	$-0.393198\pi$
$702$		0			0
$703$		−	32.0000i		−	1.20690i
$704$		0			0
$705$		0			0
$706$	6.00000	+	6.00000i	0.225813	+	0.225813i
$707$	−20.0000			−0.752177
$708$		0			0
$709$		−	4.00000i		−	0.150223i	−0.997175	−	0.0751116i	$-0.976069\pi$
$709$		−	4.00000i		−	0.150223i	0.997175	−	0.0751116i	$-0.0239313\pi$
$710$		0			0
$711$		0			0
$712$	20.0000	+	20.0000i	0.749532	+	0.749532i
$713$		−	8.00000i		−	0.299602i
$714$		0			0
$715$		0			0
$716$	8.00000			0.298974
$717$		0			0
$718$	−20.0000	+	20.0000i	−0.746393	+	0.746393i
$719$	−20.0000			−0.745874			−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000			−0.745874			−0.372937	+	0.927857i	$0.621649\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$	3.00000	−	3.00000i	0.111648	−	0.111648i
$723$		0			0
$724$	−40.0000			−1.48659
$725$		0			0
$726$		0			0
$727$			42.0000i			1.55769i	0.627214	+	0.778847i	$0.284195\pi$
$727$			42.0000i			1.55769i	−0.627214	+	0.778847i	$0.715805\pi$
$728$	16.0000	−	16.0000i	0.592999	−	0.592999i
$729$		0			0
$730$		0			0
$731$		−	8.00000i		−	0.295891i
$732$		0			0
$733$	4.00000			0.147743			0.0738717	−	0.997268i	$-0.476464\pi$
$733$	4.00000			0.147743			0.0738717	+	0.997268i	$0.476464\pi$
$734$	−18.0000	−	18.0000i	−0.664392	−	0.664392i
$735$		0			0
$736$	16.0000	+	16.0000i	0.589768	+	0.589768i
$737$		0			0
$738$		0			0
$739$		−	44.0000i		−	1.61857i	−0.587419	−	0.809283i	$-0.699856\pi$
$739$		−	44.0000i		−	1.61857i	0.587419	−	0.809283i	$-0.300144\pi$
$740$		0			0
$741$		0			0
$742$	12.0000	+	12.0000i	0.440534	+	0.440534i
$743$			16.0000i			0.586983i	0.955962	+	0.293492i	$0.0948173\pi$
$743$			16.0000i			0.586983i	−0.955962	+	0.293492i	$0.905183\pi$
$744$		0			0
$745$		0			0
$746$	−16.0000	+	16.0000i	−0.585802	+	0.585802i
$747$		0			0
$748$		0			0
$749$			24.0000i			0.876941i
$750$		0			0
$751$	2.00000			0.0729810			0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000			0.0729810			0.0364905	+	0.999334i	$0.488382\pi$
$752$			48.0000i			1.75038i
$753$		0			0
$754$	−24.0000	−	24.0000i	−0.874028	−	0.874028i
$755$		0			0
$756$		0			0
$757$	−12.0000			−0.436147			−0.218074	−	0.975932i	$-0.569977\pi$
$757$	−12.0000			−0.436147			−0.218074	+	0.975932i	$0.569977\pi$
$758$	−4.00000	−	4.00000i	−0.145287	−	0.145287i
$759$		0			0
$760$		0			0
$761$	38.0000			1.37750			0.688749	−	0.724999i	$-0.258160\pi$
$761$	38.0000			1.37750			0.688749	+	0.724999i	$0.258160\pi$
$762$		0			0
$763$	8.00000			0.289619
$764$		−	16.0000i		−	0.578860i
$765$		0			0
$766$	−24.0000	−	24.0000i	−0.867155	−	0.867155i
$767$			16.0000i			0.577727i
$768$		0			0
$769$	−10.0000			−0.360609			−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000			−0.360609			−0.180305	+	0.983611i	$0.557708\pi$
$770$		0			0
$771$		0			0
$772$	−12.0000			−0.431889
$773$	−34.0000			−1.22290			−0.611448	−	0.791285i	$-0.709412\pi$
$773$	−34.0000			−1.22290			−0.611448	+	0.791285i	$0.709412\pi$
$774$		0			0
$775$		0			0
$776$	4.00000	−	4.00000i	0.143592	−	0.143592i
$777$		0			0
$778$	34.0000	+	34.0000i	1.21896	+	1.21896i
$779$			8.00000i			0.286630i
$780$		0			0
$781$		0			0
$782$	−8.00000	+	8.00000i	−0.286079	+	0.286079i
$783$		0			0
$784$	−12.0000			−0.428571
$785$		0			0
$786$		0			0
$787$	−12.0000			−0.427754			−0.213877	−	0.976861i	$-0.568609\pi$
$787$	−12.0000			−0.427754			−0.213877	+	0.976861i	$0.568609\pi$
$788$		−	4.00000i		−	0.142494i
$789$		0			0
$790$		0			0
$791$	−12.0000			−0.426671
$792$		0			0
$793$		0			0
$794$	−32.0000	+	32.0000i	−1.13564	+	1.13564i
$795$		0			0
$796$			20.0000i			0.708881i
$797$	2.00000			0.0708436			0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000			0.0708436			0.0354218	+	0.999372i	$0.488723\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$		0			0
$801$		0			0
$802$	18.0000	−	18.0000i	0.635602	−	0.635602i
$803$		0			0
$804$		0			0
$805$		0			0
$806$	8.00000	−	8.00000i	0.281788	−	0.281788i
$807$		0			0
$808$	20.0000	−	20.0000i	0.703598	−	0.703598i
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$		0			0
$811$			20.0000i			0.702295i	0.936320	+	0.351147i	$0.114208\pi$
$811$			20.0000i			0.702295i	−0.936320	+	0.351147i	$0.885792\pi$
$812$		−	24.0000i		−	0.842235i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		−	16.0000i		−	0.559769i
$818$	−10.0000	+	10.0000i	−0.349642	+	0.349642i
$819$		0			0
$820$		0			0
$821$			10.0000i			0.349002i	0.984657	+	0.174501i	$0.0558313\pi$
$821$			10.0000i			0.349002i	−0.984657	+	0.174501i	$0.944169\pi$
$822$		0			0
$823$			14.0000i			0.488009i	0.969774	+	0.244005i	$0.0784612\pi$
$823$			14.0000i			0.488009i	−0.969774	+	0.244005i	$0.921539\pi$
$824$	−12.0000	+	12.0000i	−0.418040	+	0.418040i
$825$		0			0
$826$	−8.00000	+	8.00000i	−0.278356	+	0.278356i
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$		−	4.00000i		−	0.138926i	−0.997585	−	0.0694629i	$-0.977871\pi$
$829$		−	4.00000i		−	0.138926i	0.997585	−	0.0694629i	$-0.0221285\pi$
$830$		0			0
$831$		0			0
$832$			32.0000i			1.10940i
$833$		−	6.00000i		−	0.207888i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	24.0000	+	24.0000i	0.829066	+	0.829066i
$839$	20.0000			0.690477			0.345238	−	0.938515i	$-0.387798\pi$
$839$	20.0000			0.690477			0.345238	+	0.938515i	$0.387798\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$	−20.0000	−	20.0000i	−0.689246	−	0.689246i
$843$		0			0
$844$	40.0000			1.37686
$845$		0			0
$846$		0			0
$847$			22.0000i			0.755929i
$848$	−24.0000			−0.824163
$849$		0			0
$850$		0			0
$851$		−	32.0000i		−	1.09695i
$852$		0			0
$853$	24.0000			0.821744			0.410872	−	0.911693i	$-0.365224\pi$
$853$	24.0000			0.821744			0.410872	+	0.911693i	$0.365224\pi$
$854$		0			0
$855$		0			0
$856$	−24.0000	−	24.0000i	−0.820303	−	0.820303i
$857$			18.0000i			0.614868i	0.951569	+	0.307434i	$0.0994704\pi$
$857$			18.0000i			0.614868i	−0.951569	+	0.307434i	$0.900530\pi$
$858$		0			0
$859$		−	44.0000i		−	1.50126i	−0.660722	−	0.750630i	$-0.729750\pi$
$859$		−	44.0000i		−	1.50126i	0.660722	−	0.750630i	$-0.270250\pi$
$860$		0			0
$861$		0			0
$862$	−12.0000	+	12.0000i	−0.408722	+	0.408722i
$863$		−	24.0000i		−	0.816970i	−0.912765	−	0.408485i	$-0.866057\pi$
$863$		−	24.0000i		−	0.816970i	0.912765	−	0.408485i	$-0.133943\pi$
$864$		0			0
$865$		0			0
$866$	14.0000	+	14.0000i	0.475739	+	0.475739i
$867$		0			0
$868$	8.00000			0.271538
$869$		0			0
$870$		0			0
$871$	−48.0000			−1.62642
$872$	−8.00000	+	8.00000i	−0.270914	+	0.270914i
$873$		0			0
$874$	−16.0000	+	16.0000i	−0.541208	+	0.541208i
$875$		0			0
$876$		0			0
$877$	−32.0000			−1.08056			−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000			−1.08056			−0.540282	+	0.841484i	$0.681682\pi$
$878$	30.0000	−	30.0000i	1.01245	−	1.01245i
$879$		0			0
$880$		0			0
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	−16.0000			−0.538138
$885$		0			0
$886$	−24.0000	+	24.0000i	−0.806296	+	0.806296i
$887$			48.0000i			1.61168i	0.592132	+	0.805841i	$0.298286\pi$
$887$			48.0000i			1.61168i	−0.592132	+	0.805841i	$0.701714\pi$
$888$		0			0
$889$	−4.00000			−0.134156
$890$		0			0
$891$		0			0
$892$	28.0000			0.937509
$893$	−48.0000			−1.60626
$894$		0			0
$895$		0			0
$896$	−16.0000	+	16.0000i	−0.534522	+	0.534522i
$897$		0			0
$898$	30.0000	−	30.0000i	1.00111	−	1.00111i
$899$		−	12.0000i		−	0.400222i
$900$		0			0
$901$		−	12.0000i		−	0.399778i
$902$		0			0
$903$		0			0
$904$	12.0000	−	12.0000i	0.399114	−	0.399114i
$905$		0			0
$906$		0			0
$907$	28.0000			0.929725			0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000			0.929725			0.464862	+	0.885383i	$0.346104\pi$
$908$			16.0000i			0.530979i
$909$		0			0
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$		0			0
$914$	22.0000	+	22.0000i	0.727695	+	0.727695i
$915$		0			0
$916$	−8.00000			−0.264327
$917$	−40.0000			−1.32092
$918$		0			0
$919$	−30.0000			−0.989609			−0.494804	−	0.869004i	$-0.664760\pi$
$919$	−30.0000			−0.989609			−0.494804	+	0.869004i	$0.664760\pi$
$920$		0			0
$921$		0			0
$922$	−30.0000	−	30.0000i	−0.987997	−	0.987997i
$923$	−48.0000			−1.57994
$924$		0			0
$925$		0			0
$926$	−26.0000	−	26.0000i	−0.854413	−	0.854413i
$927$		0			0
$928$	24.0000	+	24.0000i	0.787839	+	0.787839i
$929$	−50.0000			−1.64045			−0.820223	−	0.572043i	$-0.806151\pi$
$929$	−50.0000			−1.64045			−0.820223	+	0.572043i	$0.806151\pi$
$930$		0			0
$931$		−	12.0000i		−	0.393284i
$932$	−28.0000			−0.917170
$933$		0			0
$934$	−8.00000	+	8.00000i	−0.261768	+	0.261768i
$935$		0			0
$936$		0			0
$937$		−	38.0000i		−	1.24141i	−0.784046	−	0.620703i	$-0.786847\pi$
$937$		−	38.0000i		−	1.24141i	0.784046	−	0.620703i	$-0.213153\pi$
$938$	−24.0000	−	24.0000i	−0.783628	−	0.783628i
$939$		0			0
$940$		0			0
$941$		−	30.0000i		−	0.977972i	−0.872292	−	0.488986i	$-0.837367\pi$
$941$		−	30.0000i		−	0.977972i	0.872292	−	0.488986i	$-0.162633\pi$
$942$		0			0
$943$			8.00000i			0.260516i
$944$		−	16.0000i		−	0.520756i
$945$		0			0
$946$		0			0
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		0			0
$949$		−	24.0000i		−	0.779073i
$950$		0			0
$951$		0			0
$952$	−8.00000	−	8.00000i	−0.259281	−	0.259281i
$953$			6.00000i			0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$			6.00000i			0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$	20.0000	−	20.0000i	0.646171	−	0.646171i
$959$	−36.0000			−1.16250
$960$		0			0
$961$	−27.0000			−0.870968
$962$	32.0000	−	32.0000i	1.03172	−	1.03172i
$963$		0			0
$964$		−	4.00000i		−	0.128831i
$965$		0			0
$966$		0			0
$967$			22.0000i			0.707472i	0.935345	+	0.353736i	$0.115089\pi$
$967$			22.0000i			0.707472i	−0.935345	+	0.353736i	$0.884911\pi$
$968$	−22.0000	−	22.0000i	−0.707107	−	0.707107i
$969$		0			0
$970$		0			0
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$		0			0
$973$	8.00000			0.256468
$974$	−38.0000	−	38.0000i	−1.21760	−	1.21760i
$975$		0			0
$976$		0			0
$977$		−	2.00000i		−	0.0639857i	−0.999488	−	0.0319928i	$-0.989815\pi$
$977$		−	2.00000i		−	0.0639857i	0.999488	−	0.0319928i	$-0.0101854\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	20.0000	+	20.0000i	0.638226	+	0.638226i
$983$			16.0000i			0.510321i	0.966899	+	0.255160i	$0.0821283\pi$
$983$			16.0000i			0.510321i	−0.966899	+	0.255160i	$0.917872\pi$
$984$		0			0
$985$		0			0
$986$	−12.0000	+	12.0000i	−0.382158	+	0.382158i
$987$		0			0
$988$	−32.0000			−1.01806
$989$		−	16.0000i		−	0.508770i
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	−8.00000	+	8.00000i	−0.254000	+	0.254000i
$993$		0			0
$994$	−24.0000	−	24.0000i	−0.761234	−	0.761234i
$995$		0			0
$996$		0			0
$997$	48.0000			1.52018			0.760088	−	0.649821i	$-0.225156\pi$
$997$	48.0000			1.52018			0.760088	+	0.649821i	$0.225156\pi$
$998$	36.0000	+	36.0000i	1.13956	+	1.13956i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.d.i.1549.1		2
3.2	odd	2		600.2.d.b.349.2		2
4.3	odd	2		7200.2.d.g.2449.1		2
5.2	odd	4		72.2.d.b.37.2		2
5.3	odd	4		1800.2.k.a.901.1		2
5.4	even	2		1800.2.d.b.1549.2		2
8.3	odd	2		7200.2.d.d.2449.1		2
8.5	even	2		1800.2.d.b.1549.1		2
12.11	even	2		2400.2.d.b.49.1		2
15.2	even	4		24.2.d.a.13.1	✓	2
15.8	even	4		600.2.k.b.301.2		2
15.14	odd	2		600.2.d.c.349.1		2
20.3	even	4		7200.2.k.d.3601.2		2
20.7	even	4		288.2.d.b.145.1		2
20.19	odd	2		7200.2.d.d.2449.2		2
24.5	odd	2		600.2.d.c.349.2		2
24.11	even	2		2400.2.d.c.49.1		2
40.3	even	4		7200.2.k.d.3601.1		2
40.13	odd	4		1800.2.k.a.901.2		2
40.19	odd	2		7200.2.d.g.2449.2		2
40.27	even	4		288.2.d.b.145.2		2
40.29	even	2	inner	1800.2.d.i.1549.2		2
40.37	odd	4		72.2.d.b.37.1		2
45.2	even	12		648.2.n.k.109.1		4
45.7	odd	12		648.2.n.c.109.2		4
45.22	odd	12		648.2.n.c.541.1		4
45.32	even	12		648.2.n.k.541.2		4
60.23	odd	4		2400.2.k.a.1201.1		2
60.47	odd	4		96.2.d.a.49.2		2
60.59	even	2		2400.2.d.c.49.2		2
80.27	even	4		2304.2.a.l.1.1		1
80.37	odd	4		2304.2.a.o.1.1		1
80.67	even	4		2304.2.a.b.1.1		1
80.77	odd	4		2304.2.a.e.1.1		1
105.62	odd	4		1176.2.c.a.589.1		2
120.29	odd	2		600.2.d.b.349.1		2
120.53	even	4		600.2.k.b.301.1		2
120.59	even	2		2400.2.d.b.49.2		2
120.77	even	4		24.2.d.a.13.2	yes	2
120.83	odd	4		2400.2.k.a.1201.2		2
120.107	odd	4		96.2.d.a.49.1		2
180.7	even	12		2592.2.r.g.433.2		4
180.47	odd	12		2592.2.r.f.433.1		4
180.67	even	12		2592.2.r.g.2161.1		4
180.167	odd	12		2592.2.r.f.2161.2		4
240.77	even	4		768.2.a.h.1.1		1
240.107	odd	4		768.2.a.e.1.1		1
240.197	even	4		768.2.a.a.1.1		1
240.227	odd	4		768.2.a.d.1.1		1
360.67	even	12		2592.2.r.g.2161.2		4
360.77	even	12		648.2.n.k.541.1		4
360.157	odd	12		648.2.n.c.541.2		4
360.187	even	12		2592.2.r.g.433.1		4
360.227	odd	12		2592.2.r.f.433.2		4
360.277	odd	12		648.2.n.c.109.1		4
360.317	even	12		648.2.n.k.109.2		4
360.347	odd	12		2592.2.r.f.2161.1		4
420.167	even	4		4704.2.c.a.2353.1		2
840.587	even	4		4704.2.c.a.2353.2		2
840.797	odd	4		1176.2.c.a.589.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.2.d.a.13.1	✓	2	15.2	even	4
24.2.d.a.13.2	yes	2	120.77	even	4
72.2.d.b.37.1		2	40.37	odd	4
72.2.d.b.37.2		2	5.2	odd	4
96.2.d.a.49.1		2	120.107	odd	4
96.2.d.a.49.2		2	60.47	odd	4
288.2.d.b.145.1		2	20.7	even	4
288.2.d.b.145.2		2	40.27	even	4
600.2.d.b.349.1		2	120.29	odd	2
600.2.d.b.349.2		2	3.2	odd	2
600.2.d.c.349.1		2	15.14	odd	2
600.2.d.c.349.2		2	24.5	odd	2
600.2.k.b.301.1		2	120.53	even	4
600.2.k.b.301.2		2	15.8	even	4
648.2.n.c.109.1		4	360.277	odd	12
648.2.n.c.109.2		4	45.7	odd	12
648.2.n.c.541.1		4	45.22	odd	12
648.2.n.c.541.2		4	360.157	odd	12
648.2.n.k.109.1		4	45.2	even	12
648.2.n.k.109.2		4	360.317	even	12
648.2.n.k.541.1		4	360.77	even	12
648.2.n.k.541.2		4	45.32	even	12
768.2.a.a.1.1		1	240.197	even	4
768.2.a.d.1.1		1	240.227	odd	4
768.2.a.e.1.1		1	240.107	odd	4
768.2.a.h.1.1		1	240.77	even	4
1176.2.c.a.589.1		2	105.62	odd	4
1176.2.c.a.589.2		2	840.797	odd	4
1800.2.d.b.1549.1		2	8.5	even	2
1800.2.d.b.1549.2		2	5.4	even	2
1800.2.d.i.1549.1		2	1.1	even	1	trivial
1800.2.d.i.1549.2		2	40.29	even	2	inner
1800.2.k.a.901.1		2	5.3	odd	4
1800.2.k.a.901.2		2	40.13	odd	4
2304.2.a.b.1.1		1	80.67	even	4
2304.2.a.e.1.1		1	80.77	odd	4
2304.2.a.l.1.1		1	80.27	even	4
2304.2.a.o.1.1		1	80.37	odd	4
2400.2.d.b.49.1		2	12.11	even	2
2400.2.d.b.49.2		2	120.59	even	2
2400.2.d.c.49.1		2	24.11	even	2
2400.2.d.c.49.2		2	60.59	even	2
2400.2.k.a.1201.1		2	60.23	odd	4
2400.2.k.a.1201.2		2	120.83	odd	4
2592.2.r.f.433.1		4	180.47	odd	12
2592.2.r.f.433.2		4	360.227	odd	12
2592.2.r.f.2161.1		4	360.347	odd	12
2592.2.r.f.2161.2		4	180.167	odd	12
2592.2.r.g.433.1		4	360.187	even	12
2592.2.r.g.433.2		4	180.7	even	12
2592.2.r.g.2161.1		4	180.67	even	12
2592.2.r.g.2161.2		4	360.67	even	12
4704.2.c.a.2353.1		2	420.167	even	4
4704.2.c.a.2353.2		2	840.587	even	4
7200.2.d.d.2449.1		2	8.3	odd	2
7200.2.d.d.2449.2		2	20.19	odd	2
7200.2.d.g.2449.1		2	4.3	odd	2
7200.2.d.g.2449.2		2	40.19	odd	2
7200.2.k.d.3601.1		2	40.3	even	4
7200.2.k.d.3601.2		2	20.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +2.00000i q^{7} +(-2.00000 - 2.00000i) q^{8} +4.00000 q^{13} +(2.00000 + 2.00000i) q^{14} -4.00000 q^{16} -2.00000i q^{17} -4.00000i q^{19} -4.00000i q^{23} +(4.00000 - 4.00000i) q^{26} +4.00000 q^{28} -6.00000i q^{29} +2.00000 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-2.00000 - 2.00000i) q^{34} +8.00000 q^{37} +(-4.00000 - 4.00000i) q^{38} -2.00000 q^{41} +4.00000 q^{43} +(-4.00000 - 4.00000i) q^{46} -12.0000i q^{47} +3.00000 q^{49} -8.00000i q^{52} +6.00000 q^{53} +(4.00000 - 4.00000i) q^{56} +(-6.00000 - 6.00000i) q^{58} +4.00000i q^{59} +(2.00000 - 2.00000i) q^{62} +8.00000i q^{64} -12.0000 q^{67} -4.00000 q^{68} -12.0000 q^{71} -6.00000i q^{73} +(8.00000 - 8.00000i) q^{74} -8.00000 q^{76} -10.0000 q^{79} +(-2.00000 + 2.00000i) q^{82} +16.0000 q^{83} +(4.00000 - 4.00000i) q^{86} -10.0000 q^{89} +8.00000i q^{91} -8.00000 q^{92} +(-12.0000 - 12.0000i) q^{94} +2.00000i q^{97} +(3.00000 - 3.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{8} + 8 q^{13} + 4 q^{14} - 8 q^{16} + 8 q^{26} + 8 q^{28} + 4 q^{31} - 8 q^{32} - 4 q^{34} + 16 q^{37} - 8 q^{38} - 4 q^{41} + 8 q^{43} - 8 q^{46} + 6 q^{49} + 12 q^{53} + 8 q^{56}+ \cdots + 6 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^8 + 8 * q^13 + 4 * q^14 - 8 * q^16 + 8 * q^26 + 8 * q^28 + 4 * q^31 - 8 * q^32 - 4 * q^34 + 16 * q^37 - 8 * q^38 - 4 * q^41 + 8 * q^43 - 8 * q^46 + 6 * q^49 + 12 * q^53 + 8 * q^56 - 12 * q^58 + 4 * q^62 - 24 * q^67 - 8 * q^68 - 24 * q^71 + 16 * q^74 - 16 * q^76 - 20 * q^79 - 4 * q^82 + 32 * q^83 + 8 * q^86 - 20 * q^89 - 16 * q^92 - 24 * q^94 + 6 * q^98

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