LMFDB - Embedded newform 637.2.c.c.246.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(246,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("637.246");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.c (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:	$5.08647060876$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			246.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	637.246
Dual form			637.2.c.c.246.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} +2.00000 q^{3} -2.00000 q^{4} -1.00000i q^{5} +4.00000i q^{6} +1.00000 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} +2.00000 q^{3} -2.00000 q^{4} -1.00000i q^{5} +4.00000i q^{6} +1.00000 q^{9} +2.00000 q^{10} +2.00000i q^{11} -4.00000 q^{12} +(2.00000 + 3.00000i) q^{13} -2.00000i q^{15} -4.00000 q^{16} +6.00000 q^{17} +2.00000i q^{18} +3.00000i q^{19} +2.00000i q^{20} -4.00000 q^{22} -3.00000 q^{23} +4.00000 q^{25} +(-6.00000 + 4.00000i) q^{26} -4.00000 q^{27} +3.00000 q^{29} +4.00000 q^{30} +3.00000i q^{31} -8.00000i q^{32} +4.00000i q^{33} +12.0000i q^{34} -2.00000 q^{36} -6.00000i q^{37} -6.00000 q^{38} +(4.00000 + 6.00000i) q^{39} -10.0000i q^{41} +1.00000 q^{43} -4.00000i q^{44} -1.00000i q^{45} -6.00000i q^{46} +11.0000i q^{47} -8.00000 q^{48} +8.00000i q^{50} +12.0000 q^{51} +(-4.00000 - 6.00000i) q^{52} -9.00000 q^{53} -8.00000i q^{54} +2.00000 q^{55} +6.00000i q^{57} +6.00000i q^{58} -8.00000i q^{59} +4.00000i q^{60} +8.00000 q^{61} -6.00000 q^{62} +8.00000 q^{64} +(3.00000 - 2.00000i) q^{65} -8.00000 q^{66} -12.0000i q^{67} -12.0000 q^{68} -6.00000 q^{69} -14.0000i q^{71} -9.00000i q^{73} +12.0000 q^{74} +8.00000 q^{75} -6.00000i q^{76} +(-12.0000 + 8.00000i) q^{78} -9.00000 q^{79} +4.00000i q^{80} -11.0000 q^{81} +20.0000 q^{82} -11.0000i q^{83} -6.00000i q^{85} +2.00000i q^{86} +6.00000 q^{87} -5.00000i q^{89} +2.00000 q^{90} +6.00000 q^{92} +6.00000i q^{93} -22.0000 q^{94} +3.00000 q^{95} -16.0000i q^{96} +9.00000i q^{97} +2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{3} - 4 q^{4} + 2 q^{9}+O(q^{10}) $ 2 * q + 4 * q^3 - 4 * q^4 + 2 * q^9	$ 2 q + 4 q^{3} - 4 q^{4} + 2 q^{9} + 4 q^{10} - 8 q^{12} + 4 q^{13} - 8 q^{16} + 12 q^{17} - 8 q^{22} - 6 q^{23} + 8 q^{25} - 12 q^{26} - 8 q^{27} + 6 q^{29} + 8 q^{30} - 4 q^{36} - 12 q^{38} + 8 q^{39} + 2 q^{43} - 16 q^{48} + 24 q^{51} - 8 q^{52} - 18 q^{53} + 4 q^{55} + 16 q^{61} - 12 q^{62} + 16 q^{64} + 6 q^{65} - 16 q^{66} - 24 q^{68} - 12 q^{69} + 24 q^{74} + 16 q^{75} - 24 q^{78} - 18 q^{79} - 22 q^{81} + 40 q^{82} + 12 q^{87} + 4 q^{90} + 12 q^{92} - 44 q^{94} + 6 q^{95}+O(q^{100}) $ 2 * q + 4 * q^3 - 4 * q^4 + 2 * q^9 + 4 * q^10 - 8 * q^12 + 4 * q^13 - 8 * q^16 + 12 * q^17 - 8 * q^22 - 6 * q^23 + 8 * q^25 - 12 * q^26 - 8 * q^27 + 6 * q^29 + 8 * q^30 - 4 * q^36 - 12 * q^38 + 8 * q^39 + 2 * q^43 - 16 * q^48 + 24 * q^51 - 8 * q^52 - 18 * q^53 + 4 * q^55 + 16 * q^61 - 12 * q^62 + 16 * q^64 + 6 * q^65 - 16 * q^66 - 24 * q^68 - 12 * q^69 + 24 * q^74 + 16 * q^75 - 24 * q^78 - 18 * q^79 - 22 * q^81 + 40 * q^82 + 12 * q^87 + 4 * q^90 + 12 * q^92 - 44 * q^94 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			2.00000i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$2$			2.00000i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$3$	2.00000			1.15470			0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000			1.15470			0.577350	+	0.816497i	$0.304087\pi$
$4$	−2.00000			−1.00000
$5$		−	1.00000i		−	0.447214i	−0.974679	−	0.223607i	$-0.928217\pi$
$5$		−	1.00000i		−	0.447214i	0.974679	−	0.223607i	$-0.0717831\pi$
$6$			4.00000i			1.63299i
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.00000			0.333333
$10$	2.00000			0.632456
$11$			2.00000i			0.603023i	0.953463	+	0.301511i	$0.0974911\pi$
$11$			2.00000i			0.603023i	−0.953463	+	0.301511i	$0.902509\pi$
$12$	−4.00000			−1.15470
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$14$		0			0
$15$		−	2.00000i		−	0.516398i
$16$	−4.00000			−1.00000
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$			2.00000i			0.471405i
$19$			3.00000i			0.688247i	0.938924	+	0.344124i	$0.111824\pi$
$19$			3.00000i			0.688247i	−0.938924	+	0.344124i	$0.888176\pi$
$20$			2.00000i			0.447214i
$21$		0			0
$22$	−4.00000			−0.852803
$23$	−3.00000			−0.625543			−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000			−0.625543			−0.312772	+	0.949828i	$0.601257\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	−6.00000	+	4.00000i	−1.17670	+	0.784465i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	4.00000			0.730297
$31$			3.00000i			0.538816i	0.963026	+	0.269408i	$0.0868280\pi$
$31$			3.00000i			0.538816i	−0.963026	+	0.269408i	$0.913172\pi$
$32$		−	8.00000i		−	1.41421i
$33$			4.00000i			0.696311i
$34$			12.0000i			2.05798i
$35$		0			0
$36$	−2.00000			−0.333333
$37$		−	6.00000i		−	0.986394i	−0.869918	−	0.493197i	$-0.835828\pi$
$37$		−	6.00000i		−	0.986394i	0.869918	−	0.493197i	$-0.164172\pi$
$38$	−6.00000			−0.973329
$39$	4.00000	+	6.00000i	0.640513	+	0.960769i
$40$		0			0
$41$		−	10.0000i		−	1.56174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$		−	10.0000i		−	1.56174i	0.624695	−	0.780869i	$-0.285223\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$		−	4.00000i		−	0.603023i
$45$		−	1.00000i		−	0.149071i
$46$		−	6.00000i		−	0.884652i
$47$			11.0000i			1.60451i	0.596978	+	0.802257i	$0.296368\pi$
$47$			11.0000i			1.60451i	−0.596978	+	0.802257i	$0.703632\pi$
$48$	−8.00000			−1.15470
$49$		0			0
$50$			8.00000i			1.13137i
$51$	12.0000			1.68034
$52$	−4.00000	−	6.00000i	−0.554700	−	0.832050i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$		−	8.00000i		−	1.08866i
$55$	2.00000			0.269680
$56$		0			0
$57$			6.00000i			0.794719i
$58$			6.00000i			0.787839i
$59$		−	8.00000i		−	1.04151i	−0.853706	−	0.520756i	$-0.825650\pi$
$59$		−	8.00000i		−	1.04151i	0.853706	−	0.520756i	$-0.174350\pi$
$60$			4.00000i			0.516398i
$61$	8.00000			1.02430			0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000			1.02430			0.512148	+	0.858898i	$0.328850\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	8.00000			1.00000
$65$	3.00000	−	2.00000i	0.372104	−	0.248069i
$66$	−8.00000			−0.984732
$67$		−	12.0000i		−	1.46603i	−0.680211	−	0.733017i	$-0.738112\pi$
$67$		−	12.0000i		−	1.46603i	0.680211	−	0.733017i	$-0.261888\pi$
$68$	−12.0000			−1.45521
$69$	−6.00000			−0.722315
$70$		0			0
$71$		−	14.0000i		−	1.66149i	−0.556650	−	0.830747i	$-0.687914\pi$
$71$		−	14.0000i		−	1.66149i	0.556650	−	0.830747i	$-0.312086\pi$
$72$		0			0
$73$		−	9.00000i		−	1.05337i	−0.850060	−	0.526685i	$-0.823435\pi$
$73$		−	9.00000i		−	1.05337i	0.850060	−	0.526685i	$-0.176565\pi$
$74$	12.0000			1.39497
$75$	8.00000			0.923760
$76$		−	6.00000i		−	0.688247i
$77$		0			0
$78$	−12.0000	+	8.00000i	−1.35873	+	0.905822i
$79$	−9.00000			−1.01258			−0.506290	−	0.862364i	$-0.668983\pi$
$79$	−9.00000			−1.01258			−0.506290	+	0.862364i	$0.668983\pi$
$80$			4.00000i			0.447214i
$81$	−11.0000			−1.22222
$82$	20.0000			2.20863
$83$		−	11.0000i		−	1.20741i	−0.797209	−	0.603703i	$-0.793691\pi$
$83$		−	11.0000i		−	1.20741i	0.797209	−	0.603703i	$-0.206309\pi$
$84$		0			0
$85$		−	6.00000i		−	0.650791i
$86$			2.00000i			0.215666i
$87$	6.00000			0.643268
$88$		0			0
$89$		−	5.00000i		−	0.529999i	−0.964249	−	0.264999i	$-0.914628\pi$
$89$		−	5.00000i		−	0.529999i	0.964249	−	0.264999i	$-0.0853718\pi$
$90$	2.00000			0.210819
$91$		0			0
$92$	6.00000			0.625543
$93$			6.00000i			0.622171i
$94$	−22.0000			−2.26913
$95$	3.00000			0.307794
$96$		−	16.0000i		−	1.63299i
$97$			9.00000i			0.913812i	0.889515	+	0.456906i	$0.151042\pi$
$97$			9.00000i			0.913812i	−0.889515	+	0.456906i	$0.848958\pi$
$98$		0			0
$99$			2.00000i			0.201008i
$100$	−8.00000			−0.800000
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$			24.0000i			2.37635i
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		0			0
$105$		0			0
$106$		−	18.0000i		−	1.74831i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	8.00000			0.769800
$109$			18.0000i			1.72409i	0.506834	+	0.862044i	$0.330816\pi$
$109$			18.0000i			1.72409i	−0.506834	+	0.862044i	$0.669184\pi$
$110$			4.00000i			0.381385i
$111$		−	12.0000i		−	1.13899i
$112$		0			0
$113$	−15.0000			−1.41108			−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000			−1.41108			−0.705541	+	0.708669i	$0.749296\pi$
$114$	−12.0000			−1.12390
$115$			3.00000i			0.279751i
$116$	−6.00000			−0.557086
$117$	2.00000	+	3.00000i	0.184900	+	0.277350i
$118$	16.0000			1.47292
$119$		0			0
$120$		0			0
$121$	7.00000			0.636364
$122$			16.0000i			1.44857i
$123$		−	20.0000i		−	1.80334i
$124$		−	6.00000i		−	0.538816i
$125$		−	9.00000i		−	0.804984i
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$	2.00000			0.176090
$130$	4.00000	+	6.00000i	0.350823	+	0.526235i
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		−	8.00000i		−	0.696311i
$133$		0			0
$134$	24.0000			2.07328
$135$			4.00000i			0.344265i
$136$		0			0
$137$		−	2.00000i		−	0.170872i	−0.996344	−	0.0854358i	$-0.972772\pi$
$137$		−	2.00000i		−	0.170872i	0.996344	−	0.0854358i	$-0.0272282\pi$
$138$		−	12.0000i		−	1.02151i
$139$	18.0000			1.52674			0.763370	−	0.645961i	$-0.223543\pi$
$139$	18.0000			1.52674			0.763370	+	0.645961i	$0.223543\pi$
$140$		0			0
$141$			22.0000i			1.85273i
$142$	28.0000			2.34971
$143$	−6.00000	+	4.00000i	−0.501745	+	0.334497i
$144$	−4.00000			−0.333333
$145$		−	3.00000i		−	0.249136i
$146$	18.0000			1.48969
$147$		0			0
$148$			12.0000i			0.986394i
$149$			10.0000i			0.819232i	0.912258	+	0.409616i	$0.134337\pi$
$149$			10.0000i			0.819232i	−0.912258	+	0.409616i	$0.865663\pi$
$150$			16.0000i			1.30639i
$151$		−	6.00000i		−	0.488273i	−0.969741	−	0.244137i	$-0.921495\pi$
$151$		−	6.00000i		−	0.488273i	0.969741	−	0.244137i	$-0.0785045\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$		0			0
$155$	3.00000			0.240966
$156$	−8.00000	−	12.0000i	−0.640513	−	0.960769i
$157$	18.0000			1.43656			0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000			1.43656			0.718278	+	0.695756i	$0.244931\pi$
$158$		−	18.0000i		−	1.43200i
$159$	−18.0000			−1.42749
$160$	−8.00000			−0.632456
$161$		0			0
$162$		−	22.0000i		−	1.72848i
$163$			12.0000i			0.939913i	0.882690	+	0.469956i	$0.155730\pi$
$163$			12.0000i			0.939913i	−0.882690	+	0.469956i	$0.844270\pi$
$164$			20.0000i			1.56174i
$165$	4.00000			0.311400
$166$	22.0000			1.70753
$167$			1.00000i			0.0773823i	0.999251	+	0.0386912i	$0.0123189\pi$
$167$			1.00000i			0.0773823i	−0.999251	+	0.0386912i	$0.987681\pi$
$168$		0			0
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	12.0000			0.920358
$171$			3.00000i			0.229416i
$172$	−2.00000			−0.152499
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$			12.0000i			0.909718i
$175$		0			0
$176$		−	8.00000i		−	0.603023i
$177$		−	16.0000i		−	1.20263i
$178$	10.0000			0.749532
$179$	9.00000			0.672692			0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000			0.672692			0.336346	+	0.941739i	$0.390809\pi$
$180$			2.00000i			0.149071i
$181$	18.0000			1.33793			0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000			1.33793			0.668965	+	0.743294i	$0.266738\pi$
$182$		0			0
$183$	16.0000			1.18275
$184$		0			0
$185$	−6.00000			−0.441129
$186$	−12.0000			−0.879883
$187$			12.0000i			0.877527i
$188$		−	22.0000i		−	1.60451i
$189$		0			0
$190$			6.00000i			0.435286i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	16.0000			1.15470
$193$			12.0000i			0.863779i	0.901927	+	0.431889i	$0.142153\pi$
$193$			12.0000i			0.863779i	−0.901927	+	0.431889i	$0.857847\pi$
$194$	−18.0000			−1.29232
$195$	6.00000	−	4.00000i	0.429669	−	0.286446i
$196$		0			0
$197$		−	4.00000i		−	0.284988i	−0.989796	−	0.142494i	$-0.954488\pi$
$197$		−	4.00000i		−	0.284988i	0.989796	−	0.142494i	$-0.0455122\pi$
$198$	−4.00000			−0.284268
$199$	−2.00000			−0.141776			−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000			−0.141776			−0.0708881	+	0.997484i	$0.522583\pi$
$200$		0			0
$201$		−	24.0000i		−	1.69283i
$202$			12.0000i			0.844317i
$203$		0			0
$204$	−24.0000			−1.68034
$205$	−10.0000			−0.698430
$206$		0			0
$207$	−3.00000			−0.208514
$208$	−8.00000	−	12.0000i	−0.554700	−	0.832050i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	−9.00000			−0.619586			−0.309793	−	0.950804i	$-0.600260\pi$
$211$	−9.00000			−0.619586			−0.309793	+	0.950804i	$0.600260\pi$
$212$	18.0000			1.23625
$213$		−	28.0000i		−	1.91853i
$214$		−	24.0000i		−	1.64061i
$215$		−	1.00000i		−	0.0681994i
$216$		0			0
$217$		0			0
$218$	−36.0000			−2.43823
$219$		−	18.0000i		−	1.21633i
$220$	−4.00000			−0.269680
$221$	12.0000	+	18.0000i	0.807207	+	1.21081i
$222$	24.0000			1.61077
$223$			21.0000i			1.40626i	0.711059	+	0.703132i	$0.248216\pi$
$223$			21.0000i			1.40626i	−0.711059	+	0.703132i	$0.751784\pi$
$224$		0			0
$225$	4.00000			0.266667
$226$		−	30.0000i		−	1.99557i
$227$			20.0000i			1.32745i	0.747978	+	0.663723i	$0.231025\pi$
$227$			20.0000i			1.32745i	−0.747978	+	0.663723i	$0.768975\pi$
$228$		−	12.0000i		−	0.794719i
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$	−6.00000			−0.395628
$231$		0			0
$232$		0			0
$233$	−3.00000			−0.196537			−0.0982683	−	0.995160i	$-0.531330\pi$
$233$	−3.00000			−0.196537			−0.0982683	+	0.995160i	$0.531330\pi$
$234$	−6.00000	+	4.00000i	−0.392232	+	0.261488i
$235$	11.0000			0.717561
$236$			16.0000i			1.04151i
$237$	−18.0000			−1.16923
$238$		0			0
$239$			8.00000i			0.517477i	0.965947	+	0.258738i	$0.0833068\pi$
$239$			8.00000i			0.517477i	−0.965947	+	0.258738i	$0.916693\pi$
$240$			8.00000i			0.516398i
$241$		−	21.0000i		−	1.35273i	−0.736567	−	0.676364i	$-0.763554\pi$
$241$		−	21.0000i		−	1.35273i	0.736567	−	0.676364i	$-0.236446\pi$
$242$			14.0000i			0.899954i
$243$	−10.0000			−0.641500
$244$	−16.0000			−1.02430
$245$		0			0
$246$	40.0000			2.55031
$247$	−9.00000	+	6.00000i	−0.572656	+	0.381771i
$248$		0			0
$249$		−	22.0000i		−	1.39419i
$250$	18.0000			1.13842
$251$	6.00000			0.378717			0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000			0.378717			0.189358	+	0.981908i	$0.439359\pi$
$252$		0			0
$253$		−	6.00000i		−	0.377217i
$254$		0			0
$255$		−	12.0000i		−	0.751469i
$256$	16.0000			1.00000
$257$	−6.00000			−0.374270			−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$			4.00000i			0.249029i
$259$		0			0
$260$	−6.00000	+	4.00000i	−0.372104	+	0.248069i
$261$	3.00000			0.185695
$262$		−	24.0000i		−	1.48272i
$263$	9.00000			0.554964			0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000			0.554964			0.277482	+	0.960731i	$0.410500\pi$
$264$		0			0
$265$			9.00000i			0.552866i
$266$		0			0
$267$		−	10.0000i		−	0.611990i
$268$			24.0000i			1.46603i
$269$	−24.0000			−1.46331			−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000			−1.46331			−0.731653	+	0.681677i	$0.761251\pi$
$270$	−8.00000			−0.486864
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	−24.0000			−1.45521
$273$		0			0
$274$	4.00000			0.241649
$275$			8.00000i			0.482418i
$276$	12.0000			0.722315
$277$	−17.0000			−1.02143			−0.510716	−	0.859750i	$-0.670619\pi$
$277$	−17.0000			−1.02143			−0.510716	+	0.859750i	$0.670619\pi$
$278$			36.0000i			2.15914i
$279$			3.00000i			0.179605i
$280$		0			0
$281$		−	2.00000i		−	0.119310i	−0.998219	−	0.0596550i	$-0.981000\pi$
$281$		−	2.00000i		−	0.119310i	0.998219	−	0.0596550i	$-0.0190001\pi$
$282$	−44.0000			−2.62016
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$			28.0000i			1.66149i
$285$	6.00000			0.355409
$286$	−8.00000	−	12.0000i	−0.473050	−	0.709575i
$287$		0			0
$288$		−	8.00000i		−	0.471405i
$289$	19.0000			1.11765
$290$	6.00000			0.352332
$291$			18.0000i			1.05518i
$292$			18.0000i			1.05337i
$293$			1.00000i			0.0584206i	0.999573	+	0.0292103i	$0.00929925\pi$
$293$			1.00000i			0.0584206i	−0.999573	+	0.0292103i	$0.990701\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$		0			0
$297$		−	8.00000i		−	0.464207i
$298$	−20.0000			−1.15857
$299$	−6.00000	−	9.00000i	−0.346989	−	0.520483i
$300$	−16.0000			−0.923760
$301$		0			0
$302$	12.0000			0.690522
$303$	12.0000			0.689382
$304$		−	12.0000i		−	0.688247i
$305$		−	8.00000i		−	0.458079i
$306$			12.0000i			0.685994i
$307$		−	33.0000i		−	1.88341i	−0.336440	−	0.941705i	$-0.609223\pi$
$307$		−	33.0000i		−	1.88341i	0.336440	−	0.941705i	$-0.390777\pi$
$308$		0			0
$309$		0			0
$310$			6.00000i			0.340777i
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$			36.0000i			2.03160i
$315$		0			0
$316$	18.0000			1.01258
$317$			20.0000i			1.12331i	0.827371	+	0.561656i	$0.189836\pi$
$317$			20.0000i			1.12331i	−0.827371	+	0.561656i	$0.810164\pi$
$318$		−	36.0000i		−	2.01878i
$319$			6.00000i			0.335936i
$320$		−	8.00000i		−	0.447214i
$321$	−24.0000			−1.33955
$322$		0			0
$323$			18.0000i			1.00155i
$324$	22.0000			1.22222
$325$	8.00000	+	12.0000i	0.443760	+	0.665640i
$326$	−24.0000			−1.32924
$327$			36.0000i			1.99080i
$328$		0			0
$329$		0			0
$330$			8.00000i			0.440386i
$331$			12.0000i			0.659580i	0.944054	+	0.329790i	$0.106978\pi$
$331$			12.0000i			0.659580i	−0.944054	+	0.329790i	$0.893022\pi$
$332$			22.0000i			1.20741i
$333$		−	6.00000i		−	0.328798i
$334$	−2.00000			−0.109435
$335$	−12.0000			−0.655630
$336$		0			0
$337$	27.0000			1.47078			0.735392	−	0.677642i	$-0.236998\pi$
$337$	27.0000			1.47078			0.735392	+	0.677642i	$0.236998\pi$
$338$	−24.0000	−	10.0000i	−1.30543	−	0.543928i
$339$	−30.0000			−1.62938
$340$			12.0000i			0.650791i
$341$	−6.00000			−0.324918
$342$	−6.00000			−0.324443
$343$		0			0
$344$		0			0
$345$			6.00000i			0.323029i
$346$			12.0000i			0.645124i
$347$	−24.0000			−1.28839			−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000			−1.28839			−0.644194	+	0.764862i	$0.722807\pi$
$348$	−12.0000			−0.643268
$349$			27.0000i			1.44528i	0.691226	+	0.722638i	$0.257071\pi$
$349$			27.0000i			1.44528i	−0.691226	+	0.722638i	$0.742929\pi$
$350$		0			0
$351$	−8.00000	−	12.0000i	−0.427008	−	0.640513i
$352$	16.0000			0.852803
$353$		−	2.00000i		−	0.106449i	−0.998583	−	0.0532246i	$-0.983050\pi$
$353$		−	2.00000i		−	0.106449i	0.998583	−	0.0532246i	$-0.0169499\pi$
$354$	32.0000			1.70078
$355$	−14.0000			−0.743043
$356$			10.0000i			0.529999i
$357$		0			0
$358$			18.0000i			0.951330i
$359$		−	22.0000i		−	1.16112i	−0.814219	−	0.580558i	$-0.802835\pi$
$359$		−	22.0000i		−	1.16112i	0.814219	−	0.580558i	$-0.197165\pi$
$360$		0			0
$361$	10.0000			0.526316
$362$			36.0000i			1.89212i
$363$	14.0000			0.734809
$364$		0			0
$365$	−9.00000			−0.471082
$366$			32.0000i			1.67267i
$367$	18.0000			0.939592			0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000			0.939592			0.469796	+	0.882775i	$0.344327\pi$
$368$	12.0000			0.625543
$369$		−	10.0000i		−	0.520579i
$370$		−	12.0000i		−	0.623850i
$371$		0			0
$372$		−	12.0000i		−	0.622171i
$373$	−18.0000			−0.932005			−0.466002	−	0.884783i	$-0.654306\pi$
$373$	−18.0000			−0.932005			−0.466002	+	0.884783i	$0.654306\pi$
$374$	−24.0000			−1.24101
$375$		−	18.0000i		−	0.929516i
$376$		0			0
$377$	6.00000	+	9.00000i	0.309016	+	0.463524i
$378$		0			0
$379$		−	18.0000i		−	0.924598i	−0.886724	−	0.462299i	$-0.847025\pi$
$379$		−	18.0000i		−	0.924598i	0.886724	−	0.462299i	$-0.152975\pi$
$380$	−6.00000			−0.307794
$381$		0			0
$382$		0			0
$383$			8.00000i			0.408781i	0.978889	+	0.204390i	$0.0655212\pi$
$383$			8.00000i			0.408781i	−0.978889	+	0.204390i	$0.934479\pi$
$384$		0			0
$385$		0			0
$386$	−24.0000			−1.22157
$387$	1.00000			0.0508329
$388$		−	18.0000i		−	0.913812i
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$	8.00000	+	12.0000i	0.405096	+	0.607644i
$391$	−18.0000			−0.910299
$392$		0			0
$393$	−24.0000			−1.21064
$394$	8.00000			0.403034
$395$			9.00000i			0.452839i
$396$		−	4.00000i		−	0.201008i
$397$		−	21.0000i		−	1.05396i	−0.849878	−	0.526980i	$-0.823324\pi$
$397$		−	21.0000i		−	1.05396i	0.849878	−	0.526980i	$-0.176676\pi$
$398$		−	4.00000i		−	0.200502i
$399$		0			0
$400$	−16.0000			−0.800000
$401$		−	28.0000i		−	1.39825i	−0.714998	−	0.699127i	$-0.753572\pi$
$401$		−	28.0000i		−	1.39825i	0.714998	−	0.699127i	$-0.246428\pi$
$402$	48.0000			2.39402
$403$	−9.00000	+	6.00000i	−0.448322	+	0.298881i
$404$	−12.0000			−0.597022
$405$			11.0000i			0.546594i
$406$		0			0
$407$	12.0000			0.594818
$408$		0			0
$409$			9.00000i			0.445021i	0.974930	+	0.222511i	$0.0714252\pi$
$409$			9.00000i			0.445021i	−0.974930	+	0.222511i	$0.928575\pi$
$410$		−	20.0000i		−	0.987730i
$411$		−	4.00000i		−	0.197305i
$412$		0			0
$413$		0			0
$414$		−	6.00000i		−	0.294884i
$415$	−11.0000			−0.539969
$416$	24.0000	−	16.0000i	1.17670	−	0.784465i
$417$	36.0000			1.76293
$418$		−	12.0000i		−	0.586939i
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$		−	30.0000i		−	1.46211i	−0.682318	−	0.731055i	$-0.739028\pi$
$421$		−	30.0000i		−	1.46211i	0.682318	−	0.731055i	$-0.260972\pi$
$422$		−	18.0000i		−	0.876226i
$423$			11.0000i			0.534838i
$424$		0			0
$425$	24.0000			1.16417
$426$	56.0000			2.71321
$427$		0			0
$428$	24.0000			1.16008
$429$	−12.0000	+	8.00000i	−0.579365	+	0.386244i
$430$	2.00000			0.0964486
$431$			4.00000i			0.192673i	0.995349	+	0.0963366i	$0.0307125\pi$
$431$			4.00000i			0.192673i	−0.995349	+	0.0963366i	$0.969287\pi$
$432$	16.0000			0.769800
$433$	20.0000			0.961139			0.480569	−	0.876957i	$-0.340430\pi$
$433$	20.0000			0.961139			0.480569	+	0.876957i	$0.340430\pi$
$434$		0			0
$435$		−	6.00000i		−	0.287678i
$436$		−	36.0000i		−	1.72409i
$437$		−	9.00000i		−	0.430528i
$438$	36.0000			1.72015
$439$	−36.0000			−1.71819			−0.859093	−	0.511819i	$-0.828972\pi$
$439$	−36.0000			−1.71819			−0.859093	+	0.511819i	$0.828972\pi$
$440$		0			0
$441$		0			0
$442$	−36.0000	+	24.0000i	−1.71235	+	1.14156i
$443$	27.0000			1.28281			0.641404	−	0.767203i	$-0.278352\pi$
$443$	27.0000			1.28281			0.641404	+	0.767203i	$0.278352\pi$
$444$			24.0000i			1.13899i
$445$	−5.00000			−0.237023
$446$	−42.0000			−1.98876
$447$			20.0000i			0.945968i
$448$		0			0
$449$		−	4.00000i		−	0.188772i	−0.995536	−	0.0943858i	$-0.969911\pi$
$449$		−	4.00000i		−	0.188772i	0.995536	−	0.0943858i	$-0.0300887\pi$
$450$			8.00000i			0.377124i
$451$	20.0000			0.941763
$452$	30.0000			1.41108
$453$		−	12.0000i		−	0.563809i
$454$	−40.0000			−1.87729
$455$		0			0
$456$		0			0
$457$		−	42.0000i		−	1.96468i	−0.187112	−	0.982339i	$-0.559913\pi$
$457$		−	42.0000i		−	1.96468i	0.187112	−	0.982339i	$-0.440087\pi$
$458$	12.0000			0.560723
$459$	−24.0000			−1.12022
$460$		−	6.00000i		−	0.279751i
$461$		−	2.00000i		−	0.0931493i	−0.998915	−	0.0465746i	$-0.985169\pi$
$461$		−	2.00000i		−	0.0931493i	0.998915	−	0.0465746i	$-0.0148305\pi$
$462$		0			0
$463$			30.0000i			1.39422i	0.716965	+	0.697109i	$0.245531\pi$
$463$			30.0000i			1.39422i	−0.716965	+	0.697109i	$0.754469\pi$
$464$	−12.0000			−0.557086
$465$	6.00000			0.278243
$466$		−	6.00000i		−	0.277945i
$467$	42.0000			1.94353			0.971764	−	0.235954i	$-0.0758216\pi$
$467$	42.0000			1.94353			0.971764	+	0.235954i	$0.0758216\pi$
$468$	−4.00000	−	6.00000i	−0.184900	−	0.277350i
$469$		0			0
$470$			22.0000i			1.01478i
$471$	36.0000			1.65879
$472$		0			0
$473$			2.00000i			0.0919601i
$474$		−	36.0000i		−	1.65353i
$475$			12.0000i			0.550598i
$476$		0			0
$477$	−9.00000			−0.412082
$478$	−16.0000			−0.731823
$479$			29.0000i			1.32504i	0.749043	+	0.662522i	$0.230514\pi$
$479$			29.0000i			1.32504i	−0.749043	+	0.662522i	$0.769486\pi$
$480$	−16.0000			−0.730297
$481$	18.0000	−	12.0000i	0.820729	−	0.547153i
$482$	42.0000			1.91305
$483$		0			0
$484$	−14.0000			−0.636364
$485$	9.00000			0.408669
$486$		−	20.0000i		−	0.907218i
$487$			12.0000i			0.543772i	0.962329	+	0.271886i	$0.0876473\pi$
$487$			12.0000i			0.543772i	−0.962329	+	0.271886i	$0.912353\pi$
$488$		0			0
$489$			24.0000i			1.08532i
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$			40.0000i			1.80334i
$493$	18.0000			0.810679
$494$	−12.0000	−	18.0000i	−0.539906	−	0.809858i
$495$	2.00000			0.0898933
$496$		−	12.0000i		−	0.538816i
$497$		0			0
$498$	44.0000			1.97169
$499$			6.00000i			0.268597i	0.990941	+	0.134298i	$0.0428781\pi$
$499$			6.00000i			0.268597i	−0.990941	+	0.134298i	$0.957122\pi$
$500$			18.0000i			0.804984i
$501$			2.00000i			0.0893534i
$502$			12.0000i			0.535586i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$		−	6.00000i		−	0.266996i
$506$	12.0000			0.533465
$507$	−10.0000	+	24.0000i	−0.444116	+	1.06588i
$508$		0			0
$509$		−	37.0000i		−	1.64000i	−0.572366	−	0.819998i	$-0.693974\pi$
$509$		−	37.0000i		−	1.64000i	0.572366	−	0.819998i	$-0.306026\pi$
$510$	24.0000			1.06274
$511$		0			0
$512$			32.0000i			1.41421i
$513$		−	12.0000i		−	0.529813i
$514$		−	12.0000i		−	0.529297i
$515$		0			0
$516$	−4.00000			−0.176090
$517$	−22.0000			−0.967559
$518$		0			0
$519$	12.0000			0.526742
$520$		0			0
$521$	24.0000			1.05146			0.525730	−	0.850652i	$-0.323792\pi$
$521$	24.0000			1.05146			0.525730	+	0.850652i	$0.323792\pi$
$522$			6.00000i			0.262613i
$523$		0			0			−	1.00000i	$-0.5\pi$
$523$		0			0				1.00000i	$0.5\pi$
$524$	24.0000			1.04844
$525$		0			0
$526$			18.0000i			0.784837i
$527$			18.0000i			0.784092i
$528$		−	16.0000i		−	0.696311i
$529$	−14.0000			−0.608696
$530$	−18.0000			−0.781870
$531$		−	8.00000i		−	0.347170i
$532$		0			0
$533$	30.0000	−	20.0000i	1.29944	−	0.866296i
$534$	20.0000			0.865485
$535$			12.0000i			0.518805i
$536$		0			0
$537$	18.0000			0.776757
$538$		−	48.0000i		−	2.06943i
$539$		0			0
$540$		−	8.00000i		−	0.344265i
$541$			18.0000i			0.773880i	0.922105	+	0.386940i	$0.126468\pi$
$541$			18.0000i			0.773880i	−0.922105	+	0.386940i	$0.873532\pi$
$542$		0			0
$543$	36.0000			1.54491
$544$		−	48.0000i		−	2.05798i
$545$	18.0000			0.771035
$546$		0			0
$547$	17.0000			0.726868			0.363434	−	0.931620i	$-0.381604\pi$
$547$	17.0000			0.726868			0.363434	+	0.931620i	$0.381604\pi$
$548$			4.00000i			0.170872i
$549$	8.00000			0.341432
$550$	−16.0000			−0.682242
$551$			9.00000i			0.383413i
$552$		0			0
$553$		0			0
$554$		−	34.0000i		−	1.44452i
$555$	−12.0000			−0.509372
$556$	−36.0000			−1.52674
$557$		−	32.0000i		−	1.35588i	−0.735116	−	0.677942i	$-0.762872\pi$
$557$		−	32.0000i		−	1.35588i	0.735116	−	0.677942i	$-0.237128\pi$
$558$	−6.00000			−0.254000
$559$	2.00000	+	3.00000i	0.0845910	+	0.126886i
$560$		0			0
$561$			24.0000i			1.01328i
$562$	4.00000			0.168730
$563$	−36.0000			−1.51722			−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000			−1.51722			−0.758610	+	0.651546i	$0.774121\pi$
$564$		−	44.0000i		−	1.85273i
$565$			15.0000i			0.631055i
$566$		−	8.00000i		−	0.336265i
$567$		0			0
$568$		0			0
$569$	−15.0000			−0.628833			−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000			−0.628833			−0.314416	+	0.949285i	$0.601809\pi$
$570$			12.0000i			0.502625i
$571$	9.00000			0.376638			0.188319	−	0.982108i	$-0.439696\pi$
$571$	9.00000			0.376638			0.188319	+	0.982108i	$0.439696\pi$
$572$	12.0000	−	8.00000i	0.501745	−	0.334497i
$573$		0			0
$574$		0			0
$575$	−12.0000			−0.500435
$576$	8.00000			0.333333
$577$			42.0000i			1.74848i	0.485491	+	0.874241i	$0.338641\pi$
$577$			42.0000i			1.74848i	−0.485491	+	0.874241i	$0.661359\pi$
$578$			38.0000i			1.58059i
$579$			24.0000i			0.997406i
$580$			6.00000i			0.249136i
$581$		0			0
$582$	−36.0000			−1.49225
$583$		−	18.0000i		−	0.745484i
$584$		0			0
$585$	3.00000	−	2.00000i	0.124035	−	0.0826898i
$586$	−2.00000			−0.0826192
$587$		−	43.0000i		−	1.77480i	−0.461000	−	0.887400i	$-0.652509\pi$
$587$		−	43.0000i		−	1.77480i	0.461000	−	0.887400i	$-0.347491\pi$
$588$		0			0
$589$	−9.00000			−0.370839
$590$		−	16.0000i		−	0.658710i
$591$		−	8.00000i		−	0.329076i
$592$			24.0000i			0.986394i
$593$			13.0000i			0.533846i	0.963718	+	0.266923i	$0.0860069\pi$
$593$			13.0000i			0.533846i	−0.963718	+	0.266923i	$0.913993\pi$
$594$	16.0000			0.656488
$595$		0			0
$596$		−	20.0000i		−	0.819232i
$597$	−4.00000			−0.163709
$598$	18.0000	−	12.0000i	0.736075	−	0.490716i
$599$	−21.0000			−0.858037			−0.429018	−	0.903296i	$-0.641140\pi$
$599$	−21.0000			−0.858037			−0.429018	+	0.903296i	$0.641140\pi$
$600$		0			0
$601$	−44.0000			−1.79480			−0.897399	−	0.441221i	$-0.854546\pi$
$601$	−44.0000			−1.79480			−0.897399	+	0.441221i	$0.854546\pi$
$602$		0			0
$603$		−	12.0000i		−	0.488678i
$604$			12.0000i			0.488273i
$605$		−	7.00000i		−	0.284590i
$606$			24.0000i			0.974933i
$607$	−18.0000			−0.730597			−0.365299	−	0.930890i	$-0.619033\pi$
$607$	−18.0000			−0.730597			−0.365299	+	0.930890i	$0.619033\pi$
$608$	24.0000			0.973329
$609$		0			0
$610$	16.0000			0.647821
$611$	−33.0000	+	22.0000i	−1.33504	+	0.890025i
$612$	−12.0000			−0.485071
$613$			24.0000i			0.969351i	0.874694	+	0.484675i	$0.161062\pi$
$613$			24.0000i			0.969351i	−0.874694	+	0.484675i	$0.838938\pi$
$614$	66.0000			2.66354
$615$	−20.0000			−0.806478
$616$		0			0
$617$			8.00000i			0.322068i	0.986949	+	0.161034i	$0.0514829\pi$
$617$			8.00000i			0.322068i	−0.986949	+	0.161034i	$0.948517\pi$
$618$		0			0
$619$			36.0000i			1.44696i	0.690344	+	0.723481i	$0.257459\pi$
$619$			36.0000i			1.44696i	−0.690344	+	0.723481i	$0.742541\pi$
$620$	−6.00000			−0.240966
$621$	12.0000			0.481543
$622$		−	60.0000i		−	2.40578i
$623$		0			0
$624$	−16.0000	−	24.0000i	−0.640513	−	0.960769i
$625$	11.0000			0.440000
$626$		−	20.0000i		−	0.799361i
$627$	−12.0000			−0.479234
$628$	−36.0000			−1.43656
$629$		−	36.0000i		−	1.43541i
$630$		0			0
$631$			12.0000i			0.477712i	0.971055	+	0.238856i	$0.0767725\pi$
$631$			12.0000i			0.477712i	−0.971055	+	0.238856i	$0.923228\pi$
$632$		0			0
$633$	−18.0000			−0.715436
$634$	−40.0000			−1.58860
$635$		0			0
$636$	36.0000			1.42749
$637$		0			0
$638$	−12.0000			−0.475085
$639$		−	14.0000i		−	0.553831i
$640$		0			0
$641$	39.0000			1.54041			0.770204	−	0.637798i	$-0.220155\pi$
$641$	39.0000			1.54041			0.770204	+	0.637798i	$0.220155\pi$
$642$		−	48.0000i		−	1.89441i
$643$			12.0000i			0.473234i	0.971603	+	0.236617i	$0.0760386\pi$
$643$			12.0000i			0.473234i	−0.971603	+	0.236617i	$0.923961\pi$
$644$		0			0
$645$		−	2.00000i		−	0.0787499i
$646$	−36.0000			−1.41640
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$		0			0
$649$	16.0000			0.628055
$650$	−24.0000	+	16.0000i	−0.941357	+	0.627572i
$651$		0			0
$652$		−	24.0000i		−	0.939913i
$653$	−18.0000			−0.704394			−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000			−0.704394			−0.352197	+	0.935926i	$0.614565\pi$
$654$	−72.0000			−2.81542
$655$			12.0000i			0.468879i
$656$			40.0000i			1.56174i
$657$		−	9.00000i		−	0.351123i
$658$		0			0
$659$	−39.0000			−1.51922			−0.759612	−	0.650376i	$-0.774611\pi$
$659$	−39.0000			−1.51922			−0.759612	+	0.650376i	$0.774611\pi$
$660$	−8.00000			−0.311400
$661$			3.00000i			0.116686i	0.998297	+	0.0583432i	$0.0185818\pi$
$661$			3.00000i			0.116686i	−0.998297	+	0.0583432i	$0.981418\pi$
$662$	−24.0000			−0.932786
$663$	24.0000	+	36.0000i	0.932083	+	1.39812i
$664$		0			0
$665$		0			0
$666$	12.0000			0.464991
$667$	−9.00000			−0.348481
$668$		−	2.00000i		−	0.0773823i
$669$			42.0000i			1.62381i
$670$		−	24.0000i		−	0.927201i
$671$			16.0000i			0.617673i
$672$		0			0
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$			54.0000i			2.08000i
$675$	−16.0000			−0.615840
$676$	10.0000	−	24.0000i	0.384615	−	0.923077i
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$		−	60.0000i		−	2.30429i
$679$		0			0
$680$		0			0
$681$			40.0000i			1.53280i
$682$		−	12.0000i		−	0.459504i
$683$			40.0000i			1.53056i	0.643699	+	0.765279i	$0.277399\pi$
$683$			40.0000i			1.53056i	−0.643699	+	0.765279i	$0.722601\pi$
$684$		−	6.00000i		−	0.229416i
$685$	−2.00000			−0.0764161
$686$		0			0
$687$		−	12.0000i		−	0.457829i
$688$	−4.00000			−0.152499
$689$	−18.0000	−	27.0000i	−0.685745	−	1.02862i
$690$	−12.0000			−0.456832
$691$		−	15.0000i		−	0.570627i	−0.958434	−	0.285313i	$-0.907902\pi$
$691$		−	15.0000i		−	0.570627i	0.958434	−	0.285313i	$-0.0920977\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$		−	48.0000i		−	1.82206i
$695$		−	18.0000i		−	0.682779i
$696$		0			0
$697$		−	60.0000i		−	2.27266i
$698$	−54.0000			−2.04393
$699$	−6.00000			−0.226941
$700$		0			0
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$	24.0000	−	16.0000i	0.905822	−	0.603881i
$703$	18.0000			0.678883
$704$			16.0000i			0.603023i
$705$	22.0000			0.828568
$706$	4.00000			0.150542
$707$		0			0
$708$			32.0000i			1.20263i
$709$			30.0000i			1.12667i	0.826227	+	0.563337i	$0.190483\pi$
$709$			30.0000i			1.12667i	−0.826227	+	0.563337i	$0.809517\pi$
$710$		−	28.0000i		−	1.05082i
$711$	−9.00000			−0.337526
$712$		0			0
$713$		−	9.00000i		−	0.337053i
$714$		0			0
$715$	4.00000	+	6.00000i	0.149592	+	0.224387i
$716$	−18.0000			−0.672692
$717$			16.0000i			0.597531i
$718$	44.0000			1.64207
$719$	18.0000			0.671287			0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000			0.671287			0.335643	+	0.941989i	$0.391046\pi$
$720$			4.00000i			0.149071i
$721$		0			0
$722$			20.0000i			0.744323i
$723$		−	42.0000i		−	1.56200i
$724$	−36.0000			−1.33793
$725$	12.0000			0.445669
$726$			28.0000i			1.03918i
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		−	18.0000i		−	0.666210i
$731$	6.00000			0.221918
$732$	−32.0000			−1.18275
$733$		−	15.0000i		−	0.554038i	−0.960864	−	0.277019i	$-0.910654\pi$
$733$		−	15.0000i		−	0.554038i	0.960864	−	0.277019i	$-0.0893464\pi$
$734$			36.0000i			1.32878i
$735$		0			0
$736$			24.0000i			0.884652i
$737$	24.0000			0.884051
$738$	20.0000			0.736210
$739$		−	30.0000i		−	1.10357i	−0.833987	−	0.551784i	$-0.813947\pi$
$739$		−	30.0000i		−	1.10357i	0.833987	−	0.551784i	$-0.186053\pi$
$740$	12.0000			0.441129
$741$	−18.0000	+	12.0000i	−0.661247	+	0.440831i
$742$		0			0
$743$			44.0000i			1.61420i	0.590412	+	0.807102i	$0.298965\pi$
$743$			44.0000i			1.61420i	−0.590412	+	0.807102i	$0.701035\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$		−	36.0000i		−	1.31805i
$747$		−	11.0000i		−	0.402469i
$748$		−	24.0000i		−	0.877527i
$749$		0			0
$750$	36.0000			1.31453
$751$	13.0000			0.474377			0.237188	−	0.971464i	$-0.423774\pi$
$751$	13.0000			0.474377			0.237188	+	0.971464i	$0.423774\pi$
$752$		−	44.0000i		−	1.60451i
$753$	12.0000			0.437304
$754$	−18.0000	+	12.0000i	−0.655521	+	0.437014i
$755$	−6.00000			−0.218362
$756$		0			0
$757$	9.00000			0.327111			0.163555	−	0.986534i	$-0.447704\pi$
$757$	9.00000			0.327111			0.163555	+	0.986534i	$0.447704\pi$
$758$	36.0000			1.30758
$759$		−	12.0000i		−	0.435572i
$760$		0			0
$761$		−	19.0000i		−	0.688749i	−0.938832	−	0.344375i	$-0.888091\pi$
$761$		−	19.0000i		−	0.688749i	0.938832	−	0.344375i	$-0.111909\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		−	6.00000i		−	0.216930i
$766$	−16.0000			−0.578103
$767$	24.0000	−	16.0000i	0.866590	−	0.577727i
$768$	32.0000			1.15470
$769$		−	9.00000i		−	0.324548i	−0.986746	−	0.162274i	$-0.948117\pi$
$769$		−	9.00000i		−	0.324548i	0.986746	−	0.162274i	$-0.0518829\pi$
$770$		0			0
$771$	−12.0000			−0.432169
$772$		−	24.0000i		−	0.863779i
$773$		−	14.0000i		−	0.503545i	−0.967786	−	0.251773i	$-0.918987\pi$
$773$		−	14.0000i		−	0.503545i	0.967786	−	0.251773i	$-0.0810135\pi$
$774$			2.00000i			0.0718885i
$775$			12.0000i			0.431053i
$776$		0			0
$777$		0			0
$778$		−	60.0000i		−	2.15110i
$779$	30.0000			1.07486
$780$	−12.0000	+	8.00000i	−0.429669	+	0.286446i
$781$	28.0000			1.00192
$782$		−	36.0000i		−	1.28736i
$783$	−12.0000			−0.428845
$784$		0			0
$785$		−	18.0000i		−	0.642448i
$786$		−	48.0000i		−	1.71210i
$787$			21.0000i			0.748569i	0.927314	+	0.374285i	$0.122112\pi$
$787$			21.0000i			0.748569i	−0.927314	+	0.374285i	$0.877888\pi$
$788$			8.00000i			0.284988i
$789$	18.0000			0.640817
$790$	−18.0000			−0.640411
$791$		0			0
$792$		0			0
$793$	16.0000	+	24.0000i	0.568177	+	0.852265i
$794$	42.0000			1.49052
$795$			18.0000i			0.638394i
$796$	4.00000			0.141776
$797$	12.0000			0.425062			0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$		0			0
$799$			66.0000i			2.33491i
$800$		−	32.0000i		−	1.13137i
$801$		−	5.00000i		−	0.176666i
$802$	56.0000			1.97743
$803$	18.0000			0.635206
$804$			48.0000i			1.69283i
$805$		0			0
$806$	−12.0000	−	18.0000i	−0.422682	−	0.634023i
$807$	−48.0000			−1.68968
$808$		0			0
$809$	−15.0000			−0.527372			−0.263686	−	0.964609i	$-0.584938\pi$
$809$	−15.0000			−0.527372			−0.263686	+	0.964609i	$0.584938\pi$
$810$	−22.0000			−0.773001
$811$		−	12.0000i		−	0.421377i	−0.977553	−	0.210688i	$-0.932429\pi$
$811$		−	12.0000i		−	0.421377i	0.977553	−	0.210688i	$-0.0675706\pi$
$812$		0			0
$813$		0			0
$814$			24.0000i			0.841200i
$815$	12.0000			0.420342
$816$	−48.0000			−1.68034
$817$			3.00000i			0.104957i
$818$	−18.0000			−0.629355
$819$		0			0
$820$	20.0000			0.698430
$821$			16.0000i			0.558404i	0.960232	+	0.279202i	$0.0900699\pi$
$821$			16.0000i			0.558404i	−0.960232	+	0.279202i	$0.909930\pi$
$822$	8.00000			0.279032
$823$	−40.0000			−1.39431			−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000			−1.39431			−0.697156	+	0.716919i	$0.745552\pi$
$824$		0			0
$825$			16.0000i			0.557048i
$826$		0			0
$827$			4.00000i			0.139094i	0.997579	+	0.0695468i	$0.0221553\pi$
$827$			4.00000i			0.139094i	−0.997579	+	0.0695468i	$0.977845\pi$
$828$	6.00000			0.208514
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$		−	22.0000i		−	0.763631i
$831$	−34.0000			−1.17945
$832$	16.0000	+	24.0000i	0.554700	+	0.832050i
$833$		0			0
$834$			72.0000i			2.49316i
$835$	1.00000			0.0346064
$836$	12.0000			0.415029
$837$		−	12.0000i		−	0.414781i
$838$		−	12.0000i		−	0.414533i
$839$			16.0000i			0.552381i	0.961103	+	0.276191i	$0.0890721\pi$
$839$			16.0000i			0.552381i	−0.961103	+	0.276191i	$0.910928\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	60.0000			2.06774
$843$		−	4.00000i		−	0.137767i
$844$	18.0000			0.619586
$845$	12.0000	+	5.00000i	0.412813	+	0.172005i
$846$	−22.0000			−0.756376
$847$		0			0
$848$	36.0000			1.23625
$849$	−8.00000			−0.274559
$850$			48.0000i			1.64639i
$851$			18.0000i			0.617032i
$852$			56.0000i			1.91853i
$853$			45.0000i			1.54077i	0.637579	+	0.770385i	$0.279936\pi$
$853$			45.0000i			1.54077i	−0.637579	+	0.770385i	$0.720064\pi$
$854$		0			0
$855$	3.00000			0.102598
$856$		0			0
$857$	36.0000			1.22974			0.614868	−	0.788630i	$-0.289209\pi$
$857$	36.0000			1.22974			0.614868	+	0.788630i	$0.289209\pi$
$858$	−16.0000	−	24.0000i	−0.546231	−	0.819346i
$859$	−4.00000			−0.136478			−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000			−0.136478			−0.0682391	+	0.997669i	$0.521738\pi$
$860$			2.00000i			0.0681994i
$861$		0			0
$862$	−8.00000			−0.272481
$863$			32.0000i			1.08929i	0.838666	+	0.544646i	$0.183336\pi$
$863$			32.0000i			1.08929i	−0.838666	+	0.544646i	$0.816664\pi$
$864$			32.0000i			1.08866i
$865$		−	6.00000i		−	0.204006i
$866$			40.0000i			1.35926i
$867$	38.0000			1.29055
$868$		0			0
$869$		−	18.0000i		−	0.610608i
$870$	12.0000			0.406838
$871$	36.0000	−	24.0000i	1.21981	−	0.813209i
$872$		0			0
$873$			9.00000i			0.304604i
$874$	18.0000			0.608859
$875$		0			0
$876$			36.0000i			1.21633i
$877$			18.0000i			0.607817i	0.952701	+	0.303908i	$0.0982917\pi$
$877$			18.0000i			0.607817i	−0.952701	+	0.303908i	$0.901708\pi$
$878$		−	72.0000i		−	2.42988i
$879$			2.00000i			0.0674583i
$880$	−8.00000			−0.269680
$881$	−12.0000			−0.404290			−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000			−0.404290			−0.202145	+	0.979356i	$0.564791\pi$
$882$		0			0
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$	−24.0000	−	36.0000i	−0.807207	−	1.21081i
$885$	−16.0000			−0.537834
$886$			54.0000i			1.81417i
$887$	−36.0000			−1.20876			−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000			−1.20876			−0.604381	+	0.796696i	$0.706579\pi$
$888$		0			0
$889$		0			0
$890$		−	10.0000i		−	0.335201i
$891$		−	22.0000i		−	0.737028i
$892$		−	42.0000i		−	1.40626i
$893$	−33.0000			−1.10430
$894$	−40.0000			−1.33780
$895$		−	9.00000i		−	0.300837i
$896$		0			0
$897$	−12.0000	−	18.0000i	−0.400668	−	0.601003i
$898$	8.00000			0.266963
$899$			9.00000i			0.300167i
$900$	−8.00000			−0.266667
$901$	−54.0000			−1.79900
$902$			40.0000i			1.33185i
$903$		0			0
$904$		0			0
$905$		−	18.0000i		−	0.598340i
$906$	24.0000			0.797347
$907$	9.00000			0.298840			0.149420	−	0.988774i	$-0.452259\pi$
$907$	9.00000			0.298840			0.149420	+	0.988774i	$0.452259\pi$
$908$		−	40.0000i		−	1.32745i
$909$	6.00000			0.199007
$910$		0			0
$911$	−27.0000			−0.894550			−0.447275	−	0.894397i	$-0.647605\pi$
$911$	−27.0000			−0.894550			−0.447275	+	0.894397i	$0.647605\pi$
$912$		−	24.0000i		−	0.794719i
$913$	22.0000			0.728094
$914$	84.0000			2.77847
$915$		−	16.0000i		−	0.528944i
$916$			12.0000i			0.396491i
$917$		0			0
$918$		−	48.0000i		−	1.58424i
$919$	36.0000			1.18753			0.593765	−	0.804638i	$-0.297641\pi$
$919$	36.0000			1.18753			0.593765	+	0.804638i	$0.297641\pi$
$920$		0			0
$921$		−	66.0000i		−	2.17477i
$922$	4.00000			0.131733
$923$	42.0000	−	28.0000i	1.38245	−	0.921631i
$924$		0			0
$925$		−	24.0000i		−	0.789115i
$926$	−60.0000			−1.97172
$927$		0			0
$928$		−	24.0000i		−	0.787839i
$929$			7.00000i			0.229663i	0.993385	+	0.114831i	$0.0366327\pi$
$929$			7.00000i			0.229663i	−0.993385	+	0.114831i	$0.963367\pi$
$930$			12.0000i			0.393496i
$931$		0			0
$932$	6.00000			0.196537
$933$	−60.0000			−1.96431
$934$			84.0000i			2.74856i
$935$	12.0000			0.392442
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$	−20.0000			−0.652675
$940$	−22.0000			−0.717561
$941$			1.00000i			0.0325991i	0.999867	+	0.0162995i	$0.00518853\pi$
$941$			1.00000i			0.0325991i	−0.999867	+	0.0162995i	$0.994811\pi$
$942$			72.0000i			2.34589i
$943$			30.0000i			0.976934i
$944$			32.0000i			1.04151i
$945$		0			0
$946$	−4.00000			−0.130051
$947$			16.0000i			0.519930i	0.965618	+	0.259965i	$0.0837111\pi$
$947$			16.0000i			0.519930i	−0.965618	+	0.259965i	$0.916289\pi$
$948$	36.0000			1.16923
$949$	27.0000	−	18.0000i	0.876457	−	0.584305i
$950$	−24.0000			−0.778663
$951$			40.0000i			1.29709i
$952$		0			0
$953$	3.00000			0.0971795			0.0485898	−	0.998819i	$-0.484527\pi$
$953$	3.00000			0.0971795			0.0485898	+	0.998819i	$0.484527\pi$
$954$		−	18.0000i		−	0.582772i
$955$		0			0
$956$		−	16.0000i		−	0.517477i
$957$			12.0000i			0.387905i
$958$	−58.0000			−1.87389
$959$		0			0
$960$		−	16.0000i		−	0.516398i
$961$	22.0000			0.709677
$962$	24.0000	+	36.0000i	0.773791	+	1.16069i
$963$	−12.0000			−0.386695
$964$			42.0000i			1.35273i
$965$	12.0000			0.386294
$966$		0			0
$967$		−	54.0000i		−	1.73652i	−0.496107	−	0.868261i	$-0.665238\pi$
$967$		−	54.0000i		−	1.73652i	0.496107	−	0.868261i	$-0.334762\pi$
$968$		0			0
$969$			36.0000i			1.15649i
$970$			18.0000i			0.577945i
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$	20.0000			0.641500
$973$		0			0
$974$	−24.0000			−0.769010
$975$	16.0000	+	24.0000i	0.512410	+	0.768615i
$976$	−32.0000			−1.02430
$977$		−	10.0000i		−	0.319928i	−0.987123	−	0.159964i	$-0.948862\pi$
$977$		−	10.0000i		−	0.319928i	0.987123	−	0.159964i	$-0.0511379\pi$
$978$	−48.0000			−1.53487
$979$	10.0000			0.319601
$980$		0			0
$981$			18.0000i			0.574696i
$982$			24.0000i			0.765871i
$983$			29.0000i			0.924956i	0.886631	+	0.462478i	$0.153040\pi$
$983$			29.0000i			0.924956i	−0.886631	+	0.462478i	$0.846960\pi$
$984$		0			0
$985$	−4.00000			−0.127451
$986$			36.0000i			1.14647i
$987$		0			0
$988$	18.0000	−	12.0000i	0.572656	−	0.381771i
$989$	−3.00000			−0.0953945
$990$			4.00000i			0.127128i
$991$	−56.0000			−1.77890			−0.889449	−	0.457034i	$-0.848912\pi$
$991$	−56.0000			−1.77890			−0.889449	+	0.457034i	$0.848912\pi$
$992$	24.0000			0.762001
$993$			24.0000i			0.761617i
$994$		0			0
$995$			2.00000i			0.0634043i
$996$			44.0000i			1.39419i
$997$	−36.0000			−1.14013			−0.570066	−	0.821599i	$-0.693082\pi$
$997$	−36.0000			−1.14013			−0.570066	+	0.821599i	$0.693082\pi$
$998$	−12.0000			−0.379853
$999$			24.0000i			0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.c.c.246.2	yes	2
7.2	even	3		637.2.r.a.116.2		4
7.3	odd	6		637.2.r.c.324.1		4
7.4	even	3		637.2.r.a.324.1		4
7.5	odd	6		637.2.r.c.116.2		4
7.6	odd	2		637.2.c.a.246.2	yes	2
13.5	odd	4		8281.2.a.m.1.1		1
13.8	odd	4		8281.2.a.b.1.1		1
13.12	even	2	inner	637.2.c.c.246.1	yes	2
91.12	odd	6		637.2.r.c.116.1		4
91.25	even	6		637.2.r.a.324.2		4
91.34	even	4		8281.2.a.a.1.1		1
91.38	odd	6		637.2.r.c.324.2		4
91.51	even	6		637.2.r.a.116.1		4
91.83	even	4		8281.2.a.k.1.1		1
91.90	odd	2		637.2.c.a.246.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.a.246.1	✓	2	91.90	odd	2
637.2.c.a.246.2	yes	2	7.6	odd	2
637.2.c.c.246.1	yes	2	13.12	even	2	inner
637.2.c.c.246.2	yes	2	1.1	even	1	trivial
637.2.r.a.116.1		4	91.51	even	6
637.2.r.a.116.2		4	7.2	even	3
637.2.r.a.324.1		4	7.4	even	3
637.2.r.a.324.2		4	91.25	even	6
637.2.r.c.116.1		4	91.12	odd	6
637.2.r.c.116.2		4	7.5	odd	6
637.2.r.c.324.1		4	7.3	odd	6
637.2.r.c.324.2		4	91.38	odd	6
8281.2.a.a.1.1		1	91.34	even	4
8281.2.a.b.1.1		1	13.8	odd	4
8281.2.a.k.1.1		1	91.83	even	4
8281.2.a.m.1.1		1	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +2.00000 q^{3} -2.00000 q^{4} -1.00000i q^{5} +4.00000i q^{6} +1.00000 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} +2.00000 q^{3} -2.00000 q^{4} -1.00000i q^{5} +4.00000i q^{6} +1.00000 q^{9} +2.00000 q^{10} +2.00000i q^{11} -4.00000 q^{12} +(2.00000 + 3.00000i) q^{13} -2.00000i q^{15} -4.00000 q^{16} +6.00000 q^{17} +2.00000i q^{18} +3.00000i q^{19} +2.00000i q^{20} -4.00000 q^{22} -3.00000 q^{23} +4.00000 q^{25} +(-6.00000 + 4.00000i) q^{26} -4.00000 q^{27} +3.00000 q^{29} +4.00000 q^{30} +3.00000i q^{31} -8.00000i q^{32} +4.00000i q^{33} +12.0000i q^{34} -2.00000 q^{36} -6.00000i q^{37} -6.00000 q^{38} +(4.00000 + 6.00000i) q^{39} -10.0000i q^{41} +1.00000 q^{43} -4.00000i q^{44} -1.00000i q^{45} -6.00000i q^{46} +11.0000i q^{47} -8.00000 q^{48} +8.00000i q^{50} +12.0000 q^{51} +(-4.00000 - 6.00000i) q^{52} -9.00000 q^{53} -8.00000i q^{54} +2.00000 q^{55} +6.00000i q^{57} +6.00000i q^{58} -8.00000i q^{59} +4.00000i q^{60} +8.00000 q^{61} -6.00000 q^{62} +8.00000 q^{64} +(3.00000 - 2.00000i) q^{65} -8.00000 q^{66} -12.0000i q^{67} -12.0000 q^{68} -6.00000 q^{69} -14.0000i q^{71} -9.00000i q^{73} +12.0000 q^{74} +8.00000 q^{75} -6.00000i q^{76} +(-12.0000 + 8.00000i) q^{78} -9.00000 q^{79} +4.00000i q^{80} -11.0000 q^{81} +20.0000 q^{82} -11.0000i q^{83} -6.00000i q^{85} +2.00000i q^{86} +6.00000 q^{87} -5.00000i q^{89} +2.00000 q^{90} +6.00000 q^{92} +6.00000i q^{93} -22.0000 q^{94} +3.00000 q^{95} -16.0000i q^{96} +9.00000i q^{97} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{3} - 4 q^{4} + 2 q^{9}+O(q^{10}) \) 2 * q + 4 * q^3 - 4 * q^4 + 2 * q^9	\( 2 q + 4 q^{3} - 4 q^{4} + 2 q^{9} + 4 q^{10} - 8 q^{12} + 4 q^{13} - 8 q^{16} + 12 q^{17} - 8 q^{22} - 6 q^{23} + 8 q^{25} - 12 q^{26} - 8 q^{27} + 6 q^{29} + 8 q^{30} - 4 q^{36} - 12 q^{38} + 8 q^{39} + 2 q^{43} - 16 q^{48} + 24 q^{51} - 8 q^{52} - 18 q^{53} + 4 q^{55} + 16 q^{61} - 12 q^{62} + 16 q^{64} + 6 q^{65} - 16 q^{66} - 24 q^{68} - 12 q^{69} + 24 q^{74} + 16 q^{75} - 24 q^{78} - 18 q^{79} - 22 q^{81} + 40 q^{82} + 12 q^{87} + 4 q^{90} + 12 q^{92} - 44 q^{94} + 6 q^{95}+O(q^{100}) \) 2 * q + 4 * q^3 - 4 * q^4 + 2 * q^9 + 4 * q^10 - 8 * q^12 + 4 * q^13 - 8 * q^16 + 12 * q^17 - 8 * q^22 - 6 * q^23 + 8 * q^25 - 12 * q^26 - 8 * q^27 + 6 * q^29 + 8 * q^30 - 4 * q^36 - 12 * q^38 + 8 * q^39 + 2 * q^43 - 16 * q^48 + 24 * q^51 - 8 * q^52 - 18 * q^53 + 4 * q^55 + 16 * q^61 - 12 * q^62 + 16 * q^64 + 6 * q^65 - 16 * q^66 - 24 * q^68 - 12 * q^69 + 24 * q^74 + 16 * q^75 - 24 * q^78 - 18 * q^79 - 22 * q^81 + 40 * q^82 + 12 * q^87 + 4 * q^90 + 12 * q^92 - 44 * q^94 + 6 * q^95

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