LMFDB - Embedded newform 1800.2.k.a.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(901,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1800.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.k (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:	$14.3730723638$
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			901.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1800.901
Dual form			1800.2.k.a.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +2.00000 q^{7} +(2.00000 - 2.00000i) q^{8} +4.00000i q^{13} +(-2.00000 - 2.00000i) q^{14} -4.00000 q^{16} -2.00000 q^{17} +4.00000i q^{19} +4.00000 q^{23} +(4.00000 - 4.00000i) q^{26} +4.00000i q^{28} +6.00000i q^{29} +2.00000 q^{31} +(4.00000 + 4.00000i) q^{32} +(2.00000 + 2.00000i) q^{34} -8.00000i q^{37} +(4.00000 - 4.00000i) q^{38} -2.00000 q^{41} +4.00000i q^{43} +(-4.00000 - 4.00000i) q^{46} -12.0000 q^{47} -3.00000 q^{49} -8.00000 q^{52} +6.00000i q^{53} +(4.00000 - 4.00000i) q^{56} +(6.00000 - 6.00000i) q^{58} -4.00000i q^{59} +(-2.00000 - 2.00000i) q^{62} -8.00000i q^{64} +12.0000i q^{67} -4.00000i q^{68} -12.0000 q^{71} +6.00000 q^{73} +(-8.00000 + 8.00000i) q^{74} -8.00000 q^{76} +10.0000 q^{79} +(2.00000 + 2.00000i) q^{82} +16.0000i q^{83} +(4.00000 - 4.00000i) q^{86} +10.0000 q^{89} +8.00000i q^{91} +8.00000i q^{92} +(12.0000 + 12.0000i) q^{94} +2.00000 q^{97} +(3.00000 + 3.00000i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 4 q^{7} + 4 q^{8} - 4 q^{14} - 8 q^{16} - 4 q^{17} + 8 q^{23} + 8 q^{26} + 4 q^{31} + 8 q^{32} + 4 q^{34} + 8 q^{38} - 4 q^{41} - 8 q^{46} - 24 q^{47} - 6 q^{49} - 16 q^{52} + 8 q^{56} + 12 q^{58}+ \cdots + 6 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 4 * q^7 + 4 * q^8 - 4 * q^14 - 8 * q^16 - 4 * q^17 + 8 * q^23 + 8 * q^26 + 4 * q^31 + 8 * q^32 + 4 * q^34 + 8 * q^38 - 4 * q^41 - 8 * q^46 - 24 * q^47 - 6 * q^49 - 16 * q^52 + 8 * q^56 + 12 * q^58 - 4 * q^62 - 24 * q^71 + 12 * q^73 - 16 * q^74 - 16 * q^76 + 20 * q^79 + 4 * q^82 + 8 * q^86 + 20 * q^89 + 24 * q^94 + 4 * q^97 + 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
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$	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
$13$			4.00000i			1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$			4.00000i			1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$	−2.00000	−	2.00000i	−0.534522	−	0.534522i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$		0			0
$25$		0			0
$26$	4.00000	−	4.00000i	0.784465	−	0.784465i
$27$		0			0
$28$			4.00000i			0.755929i
$29$			6.00000i			1.11417i	0.830455	+	0.557086i	$0.188081\pi$
$29$			6.00000i			1.11417i	−0.830455	+	0.557086i	$0.811919\pi$
$30$		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
$37$		−	8.00000i		−	1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$		−	8.00000i		−	1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$	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
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$		0			0
$45$		0			0
$46$	−4.00000	−	4.00000i	−0.589768	−	0.589768i
$47$	−12.0000			−1.75038			−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000			−1.75038			−0.875190	+	0.483779i	$0.839264\pi$
$48$		0			0
$49$	−3.00000			−0.428571
$50$		0			0
$51$		0			0
$52$	−8.00000			−1.10940
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		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	$-0.916153\pi$
$59$		−	4.00000i		−	0.520756i	0.965507	−	0.260378i	$-0.0838471\pi$
$60$		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
$67$			12.0000i			1.46603i	0.680211	+	0.733017i	$0.261888\pi$
$67$			12.0000i			1.46603i	−0.680211	+	0.733017i	$0.738112\pi$
$68$		−	4.00000i		−	0.485071i
$69$		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
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	−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	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$		0			0
$81$		0			0
$82$	2.00000	+	2.00000i	0.220863	+	0.220863i
$83$			16.0000i			1.75623i	0.478451	+	0.878114i	$0.341198\pi$
$83$			16.0000i			1.75623i	−0.478451	+	0.878114i	$0.658802\pi$
$84$		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	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$		0			0
$91$			8.00000i			0.838628i
$92$			8.00000i			0.834058i
$93$		0			0
$94$	12.0000	+	12.0000i	1.23771	+	1.23771i
$95$		0			0
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	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
$103$	6.00000			0.591198			0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000			0.591198			0.295599	+	0.955312i	$0.404481\pi$
$104$	8.00000	+	8.00000i	0.784465	+	0.784465i
$105$		0			0
$106$	6.00000	−	6.00000i	0.582772	−	0.582772i
$107$		−	12.0000i		−	1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$		−	12.0000i		−	1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$		0			0
$109$			4.00000i			0.383131i	0.981480	+	0.191565i	$0.0613564\pi$
$109$			4.00000i			0.383131i	−0.981480	+	0.191565i	$0.938644\pi$
$110$		0			0
$111$		0			0
$112$	−8.00000			−0.755929
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		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
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	−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
$133$			8.00000i			0.693688i
$134$	12.0000	−	12.0000i	1.03664	−	1.03664i
$135$		0			0
$136$	−4.00000	+	4.00000i	−0.342997	+	0.342997i
$137$	18.0000			1.53784			0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000			1.53784			0.768922	+	0.639343i	$0.220793\pi$
$138$		0			0
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$		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
$148$	16.0000			1.31519
$149$			6.00000i			0.491539i	0.969328	+	0.245770i	$0.0790407\pi$
$149$			6.00000i			0.491539i	−0.969328	+	0.245770i	$0.920959\pi$
$150$		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
$157$		−	8.00000i		−	0.638470i	−0.947676	−	0.319235i	$-0.896574\pi$
$157$		−	8.00000i		−	0.638470i	0.947676	−	0.319235i	$-0.103426\pi$
$158$	−10.0000	−	10.0000i	−0.795557	−	0.795557i
$159$		0			0
$160$		0			0
$161$	8.00000			0.630488
$162$		0			0
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$		−	4.00000i		−	0.312348i
$165$		0			0
$166$	16.0000	−	16.0000i	1.24184	−	1.24184i
$167$	8.00000			0.619059			0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000			0.619059			0.309529	+	0.950890i	$0.399829\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$		0			0
$171$		0			0
$172$	−8.00000			−0.609994
$173$			6.00000i			0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$			6.00000i			0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$		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	$-0.952238\pi$
$179$		−	4.00000i		−	0.298974i	0.988764	−	0.149487i	$-0.0477622\pi$
$180$		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
$188$		−	24.0000i		−	1.75038i
$189$		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
$193$	6.00000			0.431889			0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000			0.431889			0.215945	+	0.976406i	$0.430717\pi$
$194$	−2.00000	−	2.00000i	−0.143592	−	0.143592i
$195$		0			0
$196$		−	6.00000i		−	0.428571i
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$		0			0
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$		0			0
$201$		0			0
$202$	10.0000	−	10.0000i	0.703598	−	0.703598i
$203$			12.0000i			0.842235i
$204$		0			0
$205$		0			0
$206$	−6.00000	−	6.00000i	−0.418040	−	0.418040i
$207$		0			0
$208$		−	16.0000i		−	1.10940i
$209$		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	$0.758301\pi$
$212$	−12.0000			−0.824163
$213$		0			0
$214$	−12.0000	+	12.0000i	−0.820303	+	0.820303i
$215$		0			0
$216$		0			0
$217$	4.00000			0.271538
$218$	4.00000	−	4.00000i	0.270914	−	0.270914i
$219$		0			0
$220$		0			0
$221$		−	8.00000i		−	0.538138i
$222$		0			0
$223$	−14.0000			−0.937509			−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000			−0.937509			−0.468755	+	0.883328i	$0.655297\pi$
$224$	8.00000	+	8.00000i	0.534522	+	0.534522i
$225$		0			0
$226$	6.00000	+	6.00000i	0.399114	+	0.399114i
$227$			8.00000i			0.530979i	0.964114	+	0.265489i	$0.0855335\pi$
$227$			8.00000i			0.530979i	−0.964114	+	0.265489i	$0.914466\pi$
$228$		0			0
$229$			4.00000i			0.264327i	0.991228	+	0.132164i	$0.0421925\pi$
$229$			4.00000i			0.264327i	−0.991228	+	0.132164i	$0.957808\pi$
$230$		0			0
$231$		0			0
$232$	12.0000	+	12.0000i	0.787839	+	0.787839i
$233$	14.0000			0.917170			0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000			0.917170			0.458585	+	0.888650i	$0.348356\pi$
$234$		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
$247$	−16.0000			−1.01806
$248$	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
$257$	18.0000			1.12281			0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000			1.12281			0.561405	+	0.827541i	$0.310261\pi$
$258$		0			0
$259$		−	16.0000i		−	0.994192i
$260$		0			0
$261$		0			0
$262$	20.0000	−	20.0000i	1.23560	−	1.23560i
$263$	−16.0000			−0.986602			−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000			−0.986602			−0.493301	+	0.869859i	$0.664210\pi$
$264$		0			0
$265$		0			0
$266$	8.00000	−	8.00000i	0.490511	−	0.490511i
$267$		0			0
$268$	−24.0000			−1.46603
$269$			6.00000i			0.365826i	0.983129	+	0.182913i	$0.0585527\pi$
$269$			6.00000i			0.365826i	−0.983129	+	0.182913i	$0.941447\pi$
$270$		0			0
$271$	−18.0000			−1.09342			−0.546711	−	0.837321i	$-0.684120\pi$
$271$	−18.0000			−1.09342			−0.546711	+	0.837321i	$0.684120\pi$
$272$	8.00000			0.485071
$273$		0			0
$274$	−18.0000	−	18.0000i	−1.08742	−	1.08742i
$275$		0			0
$276$		0			0
$277$		−	28.0000i		−	1.68236i	−0.540758	−	0.841178i	$-0.681862\pi$
$277$		−	28.0000i		−	1.68236i	0.540758	−	0.841178i	$-0.318138\pi$
$278$	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
$283$			4.00000i			0.237775i	0.992908	+	0.118888i	$0.0379328\pi$
$283$			4.00000i			0.237775i	−0.992908	+	0.118888i	$0.962067\pi$
$284$		−	24.0000i		−	1.42414i
$285$		0			0
$286$		0			0
$287$	−4.00000			−0.236113
$288$		0			0
$289$	−13.0000			−0.764706
$290$		0			0
$291$		0			0
$292$			12.0000i			0.702247i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$		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
$307$			12.0000i			0.684876i	0.939540	+	0.342438i	$0.111253\pi$
$307$			12.0000i			0.684876i	−0.939540	+	0.342438i	$0.888747\pi$
$308$		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
$313$	−14.0000			−0.791327			−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000			−0.791327			−0.395663	+	0.918396i	$0.629485\pi$
$314$	−8.00000	+	8.00000i	−0.451466	+	0.451466i
$315$		0			0
$316$			20.0000i			1.12509i
$317$		−	22.0000i		−	1.23564i	−0.786318	−	0.617822i	$-0.788015\pi$
$317$		−	22.0000i		−	1.23564i	0.786318	−	0.617822i	$-0.211985\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$	−8.00000	−	8.00000i	−0.445823	−	0.445823i
$323$		−	8.00000i		−	0.445132i
$324$		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	$0.814761\pi$
$332$	−32.0000			−1.75623
$333$		0			0
$334$	−8.00000	−	8.00000i	−0.437741	−	0.437741i
$335$		0			0
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	3.00000	+	3.00000i	0.163178	+	0.163178i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−20.0000			−1.07990
$344$	8.00000	+	8.00000i	0.431331	+	0.431331i
$345$		0			0
$346$	6.00000	−	6.00000i	0.322562	−	0.322562i
$347$			8.00000i			0.429463i	0.976673	+	0.214731i	$0.0688876\pi$
$347$			8.00000i			0.429463i	−0.976673	+	0.214731i	$0.931112\pi$
$348$		0			0
$349$		−	16.0000i		−	0.856460i	−0.903670	−	0.428230i	$-0.859137\pi$
$349$		−	16.0000i		−	0.856460i	0.903670	−	0.428230i	$-0.140863\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		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	$-0.323025\pi$
$359$	20.0000			1.05556			0.527780	+	0.849381i	$0.323025\pi$
$360$		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
$367$	−18.0000			−0.939592			−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000			−0.939592			−0.469796	+	0.882775i	$0.655673\pi$
$368$	−16.0000			−0.834058
$369$		0			0
$370$		0			0
$371$			12.0000i			0.623009i
$372$		0			0
$373$		−	16.0000i		−	0.828449i	−0.910175	−	0.414224i	$-0.864053\pi$
$373$		−	16.0000i		−	0.828449i	0.910175	−	0.414224i	$-0.135947\pi$
$374$		0			0
$375$		0			0
$376$	−24.0000	+	24.0000i	−1.23771	+	1.23771i
$377$	−24.0000			−1.23606
$378$		0			0
$379$			4.00000i			0.205466i	0.994709	+	0.102733i	$0.0327588\pi$
$379$			4.00000i			0.205466i	−0.994709	+	0.102733i	$0.967241\pi$
$380$		0			0
$381$		0			0
$382$	−8.00000	−	8.00000i	−0.409316	−	0.409316i
$383$	24.0000			1.22634			0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000			1.22634			0.613171	+	0.789950i	$0.289894\pi$
$384$		0			0
$385$		0			0
$386$	−6.00000	−	6.00000i	−0.305392	−	0.305392i
$387$		0			0
$388$			4.00000i			0.203069i
$389$		−	34.0000i		−	1.72387i	−0.507020	−	0.861934i	$-0.669253\pi$
$389$		−	34.0000i		−	1.72387i	0.507020	−	0.861934i	$-0.330747\pi$
$390$		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
$397$			32.0000i			1.60603i	0.595956	+	0.803017i	$0.296773\pi$
$397$			32.0000i			1.60603i	−0.595956	+	0.803017i	$0.703227\pi$
$398$	−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
$403$			8.00000i			0.398508i
$404$	−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	$-0.420478\pi$
$409$	10.0000			0.494468			0.247234	+	0.968956i	$0.420478\pi$
$410$		0			0
$411$		0			0
$412$			12.0000i			0.591198i
$413$		−	8.00000i		−	0.393654i
$414$		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	$-0.800608\pi$
$419$		−	24.0000i		−	1.17248i	0.810139	−	0.586238i	$-0.199392\pi$
$420$		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
$428$	24.0000			1.16008
$429$		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
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	−4.00000	−	4.00000i	−0.192006	−	0.192006i
$435$		0			0
$436$	−8.00000			−0.383131
$437$			16.0000i			0.765384i
$438$		0			0
$439$	−30.0000			−1.43182			−0.715911	−	0.698192i	$-0.753988\pi$
$439$	−30.0000			−1.43182			−0.715911	+	0.698192i	$0.753988\pi$
$440$		0			0
$441$		0			0
$442$	−8.00000	+	8.00000i	−0.380521	+	0.380521i
$443$		−	24.0000i		−	1.14027i	−0.821549	−	0.570137i	$-0.806890\pi$
$443$		−	24.0000i		−	1.14027i	0.821549	−	0.570137i	$-0.193110\pi$
$444$		0			0
$445$		0			0
$446$	14.0000	+	14.0000i	0.662919	+	0.662919i
$447$		0			0
$448$		−	16.0000i		−	0.755929i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$		0			0
$452$		−	12.0000i		−	0.564433i
$453$		0			0
$454$	8.00000	−	8.00000i	0.375459	−	0.375459i
$455$		0			0
$456$		0			0
$457$	22.0000			1.02912			0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000			1.02912			0.514558	+	0.857455i	$0.327956\pi$
$458$	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
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$		−	24.0000i		−	1.11417i
$465$		0			0
$466$	−14.0000	−	14.0000i	−0.648537	−	0.648537i
$467$			8.00000i			0.370196i	0.982720	+	0.185098i	$0.0592602\pi$
$467$			8.00000i			0.370196i	−0.982720	+	0.185098i	$0.940740\pi$
$468$		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	$-0.651044\pi$
$479$	−20.0000			−0.913823			−0.456912	+	0.889512i	$0.651044\pi$
$480$		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
$487$	−38.0000			−1.72194			−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000			−1.72194			−0.860972	+	0.508652i	$0.830144\pi$
$488$		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
$493$		−	12.0000i		−	0.540453i
$494$	16.0000	+	16.0000i	0.719874	+	0.719874i
$495$		0			0
$496$	−8.00000			−0.359211
$497$	−24.0000			−1.07655
$498$		0			0
$499$		−	36.0000i		−	1.61158i	−0.592200	−	0.805791i	$-0.701741\pi$
$499$		−	36.0000i		−	1.61158i	0.592200	−	0.805791i	$-0.298259\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−36.0000			−1.60516			−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000			−1.60516			−0.802580	+	0.596544i	$0.796540\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$			4.00000i			0.177471i
$509$			6.00000i			0.265945i	0.991120	+	0.132973i	$0.0424523\pi$
$509$			6.00000i			0.265945i	−0.991120	+	0.132973i	$0.957548\pi$
$510$		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
$523$		−	36.0000i		−	1.57417i	−0.616844	−	0.787085i	$-0.711589\pi$
$523$		−	36.0000i		−	1.57417i	0.616844	−	0.787085i	$-0.288411\pi$
$524$	−40.0000			−1.74741
$525$		0			0
$526$	16.0000	+	16.0000i	0.697633	+	0.697633i
$527$	−4.00000			−0.174243
$528$		0			0
$529$	−7.00000			−0.304348
$530$		0			0
$531$		0			0
$532$	−16.0000			−0.693688
$533$		−	8.00000i		−	0.346518i
$534$		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
$547$		−	28.0000i		−	1.19719i	−0.801050	−	0.598597i	$-0.795725\pi$
$547$		−	28.0000i		−	1.19719i	0.801050	−	0.598597i	$-0.204275\pi$
$548$			36.0000i			1.53784i
$549$		0			0
$550$		0			0
$551$	−24.0000			−1.02243
$552$		0			0
$553$	20.0000			0.850487
$554$	−28.0000	+	28.0000i	−1.18961	+	1.18961i
$555$		0			0
$556$	−8.00000			−0.339276
$557$		−	42.0000i		−	1.77960i	−0.456354	−	0.889799i	$-0.650845\pi$
$557$		−	42.0000i		−	1.77960i	0.456354	−	0.889799i	$-0.349155\pi$
$558$		0			0
$559$	−16.0000			−0.676728
$560$		0			0
$561$		0			0
$562$	−18.0000	−	18.0000i	−0.759284	−	0.759284i
$563$		−	24.0000i		−	1.01148i	−0.862686	−	0.505740i	$-0.831220\pi$
$563$		−	24.0000i		−	1.01148i	0.862686	−	0.505740i	$-0.168780\pi$
$564$		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	$-0.283533\pi$
$569$	30.0000			1.25767			0.628833	+	0.777541i	$0.283533\pi$
$570$		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
$577$	42.0000			1.74848			0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000			1.74848			0.874241	+	0.485491i	$0.161359\pi$
$578$	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
$587$			28.0000i			1.15568i	0.816149	+	0.577842i	$0.196105\pi$
$587$			28.0000i			1.15568i	−0.816149	+	0.577842i	$0.803895\pi$
$588$		0			0
$589$			8.00000i			0.329634i
$590$		0			0
$591$		0			0
$592$			32.0000i			1.31519i
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$		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	$-0.366021\pi$
$599$	20.0000			0.817178			0.408589	+	0.912719i	$0.366021\pi$
$600$		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
$607$	2.00000			0.0811775			0.0405887	−	0.999176i	$-0.487077\pi$
$607$	2.00000			0.0811775			0.0405887	+	0.999176i	$0.487077\pi$
$608$	−16.0000	+	16.0000i	−0.648886	+	0.648886i
$609$		0			0
$610$		0			0
$611$		−	48.0000i		−	1.94187i
$612$		0			0
$613$		−	16.0000i		−	0.646234i	−0.946359	−	0.323117i	$-0.895269\pi$
$613$		−	16.0000i		−	0.646234i	0.946359	−	0.323117i	$-0.104731\pi$
$614$	12.0000	−	12.0000i	0.484281	−	0.484281i
$615$		0			0
$616$		0			0
$617$	−2.00000			−0.0805170			−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000			−0.0805170			−0.0402585	+	0.999189i	$0.512818\pi$
$618$		0			0
$619$		−	36.0000i		−	1.44696i	−0.690344	−	0.723481i	$-0.742541\pi$
$619$		−	36.0000i		−	1.44696i	0.690344	−	0.723481i	$-0.257459\pi$
$620$		0			0
$621$		0			0
$622$	−8.00000	−	8.00000i	−0.320771	−	0.320771i
$623$	20.0000			0.801283
$624$		0			0
$625$		0			0
$626$	14.0000	+	14.0000i	0.559553	+	0.559553i
$627$		0			0
$628$	16.0000			0.638470
$629$			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
$637$		−	12.0000i		−	0.475457i
$638$		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
$643$			4.00000i			0.157745i	0.996885	+	0.0788723i	$0.0251319\pi$
$643$			4.00000i			0.157745i	−0.996885	+	0.0788723i	$0.974868\pi$
$644$			16.0000i			0.630488i
$645$		0			0
$646$	−8.00000	+	8.00000i	−0.314756	+	0.314756i
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−8.00000			−0.313304
$653$			6.00000i			0.234798i	0.993085	+	0.117399i	$0.0374557\pi$
$653$			6.00000i			0.234798i	−0.993085	+	0.117399i	$0.962544\pi$
$654$		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	$0.247343\pi$
$659$			36.0000i			1.40236i	−0.712984	+	0.701180i	$0.752657\pi$
$660$		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
$667$			24.0000i			0.929284i
$668$			16.0000i			0.619059i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$	−2.00000	−	2.00000i	−0.0770371	−	0.0770371i
$675$		0			0
$676$		−	6.00000i		−	0.230769i
$677$			18.0000i			0.691796i	0.938272	+	0.345898i	$0.112426\pi$
$677$			18.0000i			0.691796i	−0.938272	+	0.345898i	$0.887574\pi$
$678$		0			0
$679$	4.00000			0.153506
$680$		0			0
$681$		0			0
$682$		0			0
$683$			16.0000i			0.612223i	0.951996	+	0.306111i	$0.0990280\pi$
$683$			16.0000i			0.612223i	−0.951996	+	0.306111i	$0.900972\pi$
$684$		0			0
$685$		0			0
$686$	20.0000	+	20.0000i	0.763604	+	0.763604i
$687$		0			0
$688$		−	16.0000i		−	0.609994i
$689$	−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	$-0.124220\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	8.00000	−	8.00000i	0.303676	−	0.303676i
$695$		0			0
$696$		0			0
$697$	4.00000			0.151511
$698$	−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
$703$	32.0000			1.20690
$704$		0			0
$705$		0			0
$706$	6.00000	+	6.00000i	0.225813	+	0.225813i
$707$			20.0000i			0.752177i
$708$		0			0
$709$			4.00000i			0.150223i	0.997175	+	0.0751116i	$0.0239313\pi$
$709$			4.00000i			0.150223i	−0.997175	+	0.0751116i	$0.976069\pi$
$710$		0			0
$711$		0			0
$712$	20.0000	−	20.0000i	0.749532	−	0.749532i
$713$	8.00000			0.299602
$714$		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	$-0.378351\pi$
$719$	20.0000			0.745874			0.372937	+	0.927857i	$0.378351\pi$
$720$		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
$727$	42.0000			1.55769			0.778847	−	0.627214i	$-0.215805\pi$
$727$	42.0000			1.55769			0.778847	+	0.627214i	$0.215805\pi$
$728$	16.0000	+	16.0000i	0.592999	+	0.592999i
$729$		0			0
$730$		0			0
$731$		−	8.00000i		−	0.295891i
$732$		0			0
$733$			4.00000i			0.147743i	0.997268	+	0.0738717i	$0.0235355\pi$
$733$			4.00000i			0.147743i	−0.997268	+	0.0738717i	$0.976464\pi$
$734$	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	$0.300144\pi$
$739$			44.0000i			1.61857i	−0.587419	+	0.809283i	$0.699856\pi$
$740$		0			0
$741$		0			0
$742$	12.0000	−	12.0000i	0.440534	−	0.440534i
$743$	−16.0000			−0.586983			−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000			−0.586983			−0.293492	+	0.955962i	$0.594817\pi$
$744$		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	$0.488382\pi$
$752$	48.0000			1.75038
$753$		0			0
$754$	24.0000	+	24.0000i	0.874028	+	0.874028i
$755$		0			0
$756$		0			0
$757$			12.0000i			0.436147i	0.975932	+	0.218074i	$0.0699773\pi$
$757$			12.0000i			0.436147i	−0.975932	+	0.218074i	$0.930023\pi$
$758$	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
$763$			8.00000i			0.289619i
$764$			16.0000i			0.578860i
$765$		0			0
$766$	−24.0000	−	24.0000i	−0.867155	−	0.867155i
$767$	16.0000			0.577727
$768$		0			0
$769$	10.0000			0.360609			0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000			0.360609			0.180305	+	0.983611i	$0.442292\pi$
$770$		0			0
$771$		0			0
$772$			12.0000i			0.431889i
$773$		−	34.0000i		−	1.22290i	−0.791285	−	0.611448i	$-0.790588\pi$
$773$		−	34.0000i		−	1.22290i	0.791285	−	0.611448i	$-0.209412\pi$
$774$		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
$787$			12.0000i			0.427754i	0.976861	+	0.213877i	$0.0686091\pi$
$787$			12.0000i			0.427754i	−0.976861	+	0.213877i	$0.931391\pi$
$788$	4.00000			0.142494
$789$		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
$797$		−	2.00000i		−	0.0708436i	−0.999372	−	0.0354218i	$-0.988723\pi$
$797$		−	2.00000i		−	0.0708436i	0.999372	−	0.0354218i	$-0.0112775\pi$
$798$		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	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$		0			0
$811$			20.0000i			0.702295i	0.936320	+	0.351147i	$0.114208\pi$
$811$			20.0000i			0.702295i	−0.936320	+	0.351147i	$0.885792\pi$
$812$	−24.0000			−0.842235
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−16.0000			−0.559769
$818$	−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
$823$	−14.0000			−0.488009			−0.244005	−	0.969774i	$-0.578461\pi$
$823$	−14.0000			−0.488009			−0.244005	+	0.969774i	$0.578461\pi$
$824$	12.0000	−	12.0000i	0.418040	−	0.418040i
$825$		0			0
$826$	−8.00000	+	8.00000i	−0.278356	+	0.278356i
$827$		−	12.0000i		−	0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$		−	12.0000i		−	0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$		0			0
$829$			4.00000i			0.138926i	0.997585	+	0.0694629i	$0.0221285\pi$
$829$			4.00000i			0.138926i	−0.997585	+	0.0694629i	$0.977871\pi$
$830$		0			0
$831$		0			0
$832$	32.0000			1.10940
$833$	6.00000			0.207888
$834$		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	$-0.612202\pi$
$839$	−20.0000			−0.690477			−0.345238	+	0.938515i	$0.612202\pi$
$840$		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
$847$	22.0000			0.755929
$848$		−	24.0000i		−	0.824163i
$849$		0			0
$850$		0			0
$851$		−	32.0000i		−	1.09695i
$852$		0			0
$853$			24.0000i			0.821744i	0.911693	+	0.410872i	$0.134776\pi$
$853$			24.0000i			0.821744i	−0.911693	+	0.410872i	$0.865224\pi$
$854$		0			0
$855$		0			0
$856$	−24.0000	−	24.0000i	−0.820303	−	0.820303i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$			44.0000i			1.50126i	0.660722	+	0.750630i	$0.270250\pi$
$859$			44.0000i			1.50126i	−0.660722	+	0.750630i	$0.729750\pi$
$860$		0			0
$861$		0			0
$862$	12.0000	+	12.0000i	0.408722	+	0.408722i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$		0			0
$866$	14.0000	+	14.0000i	0.475739	+	0.475739i
$867$		0			0
$868$			8.00000i			0.271538i
$869$		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
$877$			32.0000i			1.08056i	0.841484	+	0.540282i	$0.181682\pi$
$877$			32.0000i			1.08056i	−0.841484	+	0.540282i	$0.818318\pi$
$878$	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
$883$			4.00000i			0.134611i	0.997732	+	0.0673054i	$0.0214402\pi$
$883$			4.00000i			0.134611i	−0.997732	+	0.0673054i	$0.978560\pi$
$884$	16.0000			0.538138
$885$		0			0
$886$	−24.0000	+	24.0000i	−0.806296	+	0.806296i
$887$	48.0000			1.61168			0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000			1.61168			0.805841	+	0.592132i	$0.201714\pi$
$888$		0			0
$889$	4.00000			0.134156
$890$		0			0
$891$		0			0
$892$		−	28.0000i		−	0.937509i
$893$		−	48.0000i		−	1.60626i
$894$		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
$907$		−	28.0000i		−	0.929725i	−0.885383	−	0.464862i	$-0.846104\pi$
$907$		−	28.0000i		−	0.929725i	0.885383	−	0.464862i	$-0.153896\pi$
$908$	−16.0000			−0.530979
$909$		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
$917$			40.0000i			1.32092i
$918$		0			0
$919$	30.0000			0.989609			0.494804	−	0.869004i	$-0.335240\pi$
$919$	30.0000			0.989609			0.494804	+	0.869004i	$0.335240\pi$
$920$		0			0
$921$		0			0
$922$	−30.0000	+	30.0000i	−0.987997	+	0.987997i
$923$		−	48.0000i		−	1.57994i
$924$		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	$-0.193849\pi$
$929$	50.0000			1.64045			0.820223	+	0.572043i	$0.193849\pi$
$930$		0			0
$931$		−	12.0000i		−	0.393284i
$932$			28.0000i			0.917170i
$933$		0			0
$934$	8.00000	−	8.00000i	0.261768	−	0.261768i
$935$		0			0
$936$		0			0
$937$	−38.0000			−1.24141			−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000			−1.24141			−0.620703	+	0.784046i	$0.713153\pi$
$938$	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
$943$	−8.00000			−0.260516
$944$			16.0000i			0.520756i
$945$		0			0
$946$		0			0
$947$		−	12.0000i		−	0.389948i	−0.980808	−	0.194974i	$-0.937538\pi$
$947$		−	12.0000i		−	0.389948i	0.980808	−	0.194974i	$-0.0624622\pi$
$948$		0			0
$949$			24.0000i			0.779073i
$950$		0			0
$951$		0			0
$952$	−8.00000	+	8.00000i	−0.259281	+	0.259281i
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		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
$967$	22.0000			0.707472			0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000			0.707472			0.353736	+	0.935345i	$0.384911\pi$
$968$	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
$973$			8.00000i			0.256468i
$974$	38.0000	+	38.0000i	1.21760	+	1.21760i
$975$		0			0
$976$		0			0
$977$	−2.00000			−0.0639857			−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000			−0.0639857			−0.0319928	+	0.999488i	$0.510185\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	20.0000	−	20.0000i	0.638226	−	0.638226i
$983$	−16.0000			−0.510321			−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000			−0.510321			−0.255160	+	0.966899i	$0.582128\pi$
$984$		0			0
$985$		0			0
$986$	−12.0000	+	12.0000i	−0.382158	+	0.382158i
$987$		0			0
$988$		−	32.0000i		−	1.01806i
$989$			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
$997$		−	48.0000i		−	1.52018i	−0.649821	−	0.760088i	$-0.725156\pi$
$997$		−	48.0000i		−	1.52018i	0.649821	−	0.760088i	$-0.274844\pi$
$998$	−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.k.a.901.1		2
3.2	odd	2		600.2.k.b.301.2		2
4.3	odd	2		7200.2.k.d.3601.2		2
5.2	odd	4		1800.2.d.i.1549.1		2
5.3	odd	4		1800.2.d.b.1549.2		2
5.4	even	2		72.2.d.b.37.2		2
8.3	odd	2		7200.2.k.d.3601.1		2
8.5	even	2	inner	1800.2.k.a.901.2		2
12.11	even	2		2400.2.k.a.1201.1		2
15.2	even	4		600.2.d.b.349.2		2
15.8	even	4		600.2.d.c.349.1		2
15.14	odd	2		24.2.d.a.13.1	✓	2
20.3	even	4		7200.2.d.d.2449.2		2
20.7	even	4		7200.2.d.g.2449.1		2
20.19	odd	2		288.2.d.b.145.1		2
24.5	odd	2		600.2.k.b.301.1		2
24.11	even	2		2400.2.k.a.1201.2		2
40.3	even	4		7200.2.d.g.2449.2		2
40.13	odd	4		1800.2.d.i.1549.2		2
40.19	odd	2		288.2.d.b.145.2		2
40.27	even	4		7200.2.d.d.2449.1		2
40.29	even	2		72.2.d.b.37.1		2
40.37	odd	4		1800.2.d.b.1549.1		2
45.4	even	6		648.2.n.c.541.1		4
45.14	odd	6		648.2.n.k.541.2		4
45.29	odd	6		648.2.n.k.109.1		4
45.34	even	6		648.2.n.c.109.2		4
60.23	odd	4		2400.2.d.c.49.2		2
60.47	odd	4		2400.2.d.b.49.1		2
60.59	even	2		96.2.d.a.49.2		2
80.19	odd	4		2304.2.a.b.1.1		1
80.29	even	4		2304.2.a.e.1.1		1
80.59	odd	4		2304.2.a.l.1.1		1
80.69	even	4		2304.2.a.o.1.1		1
105.104	even	2		1176.2.c.a.589.1		2
120.29	odd	2		24.2.d.a.13.2	yes	2
120.53	even	4		600.2.d.b.349.1		2
120.59	even	2		96.2.d.a.49.1		2
120.77	even	4		600.2.d.c.349.2		2
120.83	odd	4		2400.2.d.b.49.2		2
120.107	odd	4		2400.2.d.c.49.1		2
180.59	even	6		2592.2.r.f.2161.2		4
180.79	odd	6		2592.2.r.g.433.2		4
180.119	even	6		2592.2.r.f.433.1		4
180.139	odd	6		2592.2.r.g.2161.1		4
240.29	odd	4		768.2.a.h.1.1		1
240.59	even	4		768.2.a.e.1.1		1
240.149	odd	4		768.2.a.a.1.1		1
240.179	even	4		768.2.a.d.1.1		1
360.29	odd	6		648.2.n.k.109.2		4
360.59	even	6		2592.2.r.f.2161.1		4
360.139	odd	6		2592.2.r.g.2161.2		4
360.149	odd	6		648.2.n.k.541.1		4
360.229	even	6		648.2.n.c.541.2		4
360.259	odd	6		2592.2.r.g.433.1		4
360.299	even	6		2592.2.r.f.433.2		4
360.349	even	6		648.2.n.c.109.1		4
420.419	odd	2		4704.2.c.a.2353.1		2
840.419	odd	2		4704.2.c.a.2353.2		2
840.629	even	2		1176.2.c.a.589.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.2.d.a.13.1	✓	2	15.14	odd	2
24.2.d.a.13.2	yes	2	120.29	odd	2
72.2.d.b.37.1		2	40.29	even	2
72.2.d.b.37.2		2	5.4	even	2
96.2.d.a.49.1		2	120.59	even	2
96.2.d.a.49.2		2	60.59	even	2
288.2.d.b.145.1		2	20.19	odd	2
288.2.d.b.145.2		2	40.19	odd	2
600.2.d.b.349.1		2	120.53	even	4
600.2.d.b.349.2		2	15.2	even	4
600.2.d.c.349.1		2	15.8	even	4
600.2.d.c.349.2		2	120.77	even	4
600.2.k.b.301.1		2	24.5	odd	2
600.2.k.b.301.2		2	3.2	odd	2
648.2.n.c.109.1		4	360.349	even	6
648.2.n.c.109.2		4	45.34	even	6
648.2.n.c.541.1		4	45.4	even	6
648.2.n.c.541.2		4	360.229	even	6
648.2.n.k.109.1		4	45.29	odd	6
648.2.n.k.109.2		4	360.29	odd	6
648.2.n.k.541.1		4	360.149	odd	6
648.2.n.k.541.2		4	45.14	odd	6
768.2.a.a.1.1		1	240.149	odd	4
768.2.a.d.1.1		1	240.179	even	4
768.2.a.e.1.1		1	240.59	even	4
768.2.a.h.1.1		1	240.29	odd	4
1176.2.c.a.589.1		2	105.104	even	2
1176.2.c.a.589.2		2	840.629	even	2
1800.2.d.b.1549.1		2	40.37	odd	4
1800.2.d.b.1549.2		2	5.3	odd	4
1800.2.d.i.1549.1		2	5.2	odd	4
1800.2.d.i.1549.2		2	40.13	odd	4
1800.2.k.a.901.1		2	1.1	even	1	trivial
1800.2.k.a.901.2		2	8.5	even	2	inner
2304.2.a.b.1.1		1	80.19	odd	4
2304.2.a.e.1.1		1	80.29	even	4
2304.2.a.l.1.1		1	80.59	odd	4
2304.2.a.o.1.1		1	80.69	even	4
2400.2.d.b.49.1		2	60.47	odd	4
2400.2.d.b.49.2		2	120.83	odd	4
2400.2.d.c.49.1		2	120.107	odd	4
2400.2.d.c.49.2		2	60.23	odd	4
2400.2.k.a.1201.1		2	12.11	even	2
2400.2.k.a.1201.2		2	24.11	even	2
2592.2.r.f.433.1		4	180.119	even	6
2592.2.r.f.433.2		4	360.299	even	6
2592.2.r.f.2161.1		4	360.59	even	6
2592.2.r.f.2161.2		4	180.59	even	6
2592.2.r.g.433.1		4	360.259	odd	6
2592.2.r.g.433.2		4	180.79	odd	6
2592.2.r.g.2161.1		4	180.139	odd	6
2592.2.r.g.2161.2		4	360.139	odd	6
4704.2.c.a.2353.1		2	420.419	odd	2
4704.2.c.a.2353.2		2	840.419	odd	2
7200.2.d.d.2449.1		2	40.27	even	4
7200.2.d.d.2449.2		2	20.3	even	4
7200.2.d.g.2449.1		2	20.7	even	4
7200.2.d.g.2449.2		2	40.3	even	4
7200.2.k.d.3601.1		2	8.3	odd	2
7200.2.k.d.3601.2		2	4.3	odd	2

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:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.k (of order \(2\), degree \(1\), minimal)

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

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