LMFDB - Embedded newform 650.2.c.a.649.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(649,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("650.649");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.c (of order $2$, degree $1$, not 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:	$5.19027613138$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			649.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	650.649
Dual form			650.2.c.a.649.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} -3.00000 q^{7} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} -3.00000 q^{7} -1.00000 q^{8} +2.00000 q^{9} -1.00000i q^{12} +(3.00000 + 2.00000i) q^{13} +3.00000 q^{14} +1.00000 q^{16} -3.00000i q^{17} -2.00000 q^{18} -6.00000i q^{19} +3.00000i q^{21} -6.00000i q^{23} +1.00000i q^{24} +(-3.00000 - 2.00000i) q^{26} -5.00000i q^{27} -3.00000 q^{28} -1.00000 q^{32} +3.00000i q^{34} +2.00000 q^{36} -3.00000 q^{37} +6.00000i q^{38} +(2.00000 - 3.00000i) q^{39} -3.00000i q^{42} -1.00000i q^{43} +6.00000i q^{46} -3.00000 q^{47} -1.00000i q^{48} +2.00000 q^{49} -3.00000 q^{51} +(3.00000 + 2.00000i) q^{52} -6.00000i q^{53} +5.00000i q^{54} +3.00000 q^{56} -6.00000 q^{57} -6.00000i q^{59} -8.00000 q^{61} -6.00000 q^{63} +1.00000 q^{64} +12.0000 q^{67} -3.00000i q^{68} -6.00000 q^{69} -15.0000i q^{71} -2.00000 q^{72} +6.00000 q^{73} +3.00000 q^{74} -6.00000i q^{76} +(-2.00000 + 3.00000i) q^{78} -10.0000 q^{79} +1.00000 q^{81} +6.00000 q^{83} +3.00000i q^{84} +1.00000i q^{86} -6.00000i q^{89} +(-9.00000 - 6.00000i) q^{91} -6.00000i q^{92} +3.00000 q^{94} +1.00000i q^{96} +12.0000 q^{97} -2.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 6 q^{7} - 2 q^{8} + 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 6 * q^7 - 2 * q^8 + 4 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 6 q^{7} - 2 q^{8} + 4 q^{9} + 6 q^{13} + 6 q^{14} + 2 q^{16} - 4 q^{18} - 6 q^{26} - 6 q^{28} - 2 q^{32} + 4 q^{36} - 6 q^{37} + 4 q^{39} - 6 q^{47} + 4 q^{49} - 6 q^{51} + 6 q^{52} + 6 q^{56} - 12 q^{57} - 16 q^{61} - 12 q^{63} + 2 q^{64} + 24 q^{67} - 12 q^{69} - 4 q^{72} + 12 q^{73} + 6 q^{74} - 4 q^{78} - 20 q^{79} + 2 q^{81} + 12 q^{83} - 18 q^{91} + 6 q^{94} + 24 q^{97} - 4 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 6 * q^7 - 2 * q^8 + 4 * q^9 + 6 * q^13 + 6 * q^14 + 2 * q^16 - 4 * q^18 - 6 * q^26 - 6 * q^28 - 2 * q^32 + 4 * q^36 - 6 * q^37 + 4 * q^39 - 6 * q^47 + 4 * q^49 - 6 * q^51 + 6 * q^52 + 6 * q^56 - 12 * q^57 - 16 * q^61 - 12 * q^63 + 2 * q^64 + 24 * q^67 - 12 * q^69 - 4 * q^72 + 12 * q^73 + 6 * q^74 - 4 * q^78 - 20 * q^79 + 2 * q^81 + 12 * q^83 - 18 * q^91 + 6 * q^94 + 24 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	1.00000i		−	0.577350i	−0.957427	−	0.288675i	$-0.906785\pi$
$3$		−	1.00000i		−	0.577350i	0.957427	−	0.288675i	$-0.0932147\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$	−1.00000			−0.353553
$9$	2.00000			0.666667
$10$		0			0
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		−	1.00000i		−	0.288675i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$14$	3.00000			0.801784
$15$		0			0
$16$	1.00000			0.250000
$17$		−	3.00000i		−	0.727607i	−0.931476	−	0.363803i	$-0.881478\pi$
$17$		−	3.00000i		−	0.727607i	0.931476	−	0.363803i	$-0.118522\pi$
$18$	−2.00000			−0.471405
$19$		−	6.00000i		−	1.37649i	−0.725476	−	0.688247i	$-0.758380\pi$
$19$		−	6.00000i		−	1.37649i	0.725476	−	0.688247i	$-0.241620\pi$
$20$		0			0
$21$			3.00000i			0.654654i
$22$		0			0
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$			1.00000i			0.204124i
$25$		0			0
$26$	−3.00000	−	2.00000i	−0.588348	−	0.392232i
$27$		−	5.00000i		−	0.962250i
$28$	−3.00000			−0.566947
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$			3.00000i			0.514496i
$35$		0			0
$36$	2.00000			0.333333
$37$	−3.00000			−0.493197			−0.246598	−	0.969118i	$-0.579313\pi$
$37$	−3.00000			−0.493197			−0.246598	+	0.969118i	$0.579313\pi$
$38$			6.00000i			0.973329i
$39$	2.00000	−	3.00000i	0.320256	−	0.480384i
$40$		0			0
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		−	3.00000i		−	0.462910i
$43$		−	1.00000i		−	0.152499i	−0.997089	−	0.0762493i	$-0.975706\pi$
$43$		−	1.00000i		−	0.152499i	0.997089	−	0.0762493i	$-0.0242945\pi$
$44$		0			0
$45$		0			0
$46$			6.00000i			0.884652i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$		−	1.00000i		−	0.144338i
$49$	2.00000			0.285714
$50$		0			0
$51$	−3.00000			−0.420084
$52$	3.00000	+	2.00000i	0.416025	+	0.277350i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$			5.00000i			0.680414i
$55$		0			0
$56$	3.00000			0.400892
$57$	−6.00000			−0.794719
$58$		0			0
$59$		−	6.00000i		−	0.781133i	−0.920575	−	0.390567i	$-0.872279\pi$
$59$		−	6.00000i		−	0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$		0			0
$61$	−8.00000			−1.02430			−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000			−1.02430			−0.512148	+	0.858898i	$0.671150\pi$
$62$		0			0
$63$	−6.00000			−0.755929
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$		−	3.00000i		−	0.363803i
$69$	−6.00000			−0.722315
$70$		0			0
$71$		−	15.0000i		−	1.78017i	−0.455792	−	0.890086i	$-0.650644\pi$
$71$		−	15.0000i		−	1.78017i	0.455792	−	0.890086i	$-0.349356\pi$
$72$	−2.00000			−0.235702
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	3.00000			0.348743
$75$		0			0
$76$		−	6.00000i		−	0.688247i
$77$		0			0
$78$	−2.00000	+	3.00000i	−0.226455	+	0.339683i
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$			3.00000i			0.327327i
$85$		0			0
$86$			1.00000i			0.107833i
$87$		0			0
$88$		0			0
$89$		−	6.00000i		−	0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$		−	6.00000i		−	0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$		0			0
$91$	−9.00000	−	6.00000i	−0.943456	−	0.628971i
$92$		−	6.00000i		−	0.625543i
$93$		0			0
$94$	3.00000			0.309426
$95$		0			0
$96$			1.00000i			0.102062i
$97$	12.0000			1.21842			0.609208	−	0.793011i	$-0.291488\pi$
$97$	12.0000			1.21842			0.609208	+	0.793011i	$0.291488\pi$
$98$	−2.00000			−0.202031
$99$		0			0
$100$		0			0
$101$	12.0000			1.19404			0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000			1.19404			0.597022	+	0.802225i	$0.296350\pi$
$102$	3.00000			0.297044
$103$			14.0000i			1.37946i	0.724066	+	0.689730i	$0.242271\pi$
$103$			14.0000i			1.37946i	−0.724066	+	0.689730i	$0.757729\pi$
$104$	−3.00000	−	2.00000i	−0.294174	−	0.196116i
$105$		0			0
$106$			6.00000i			0.582772i
$107$			12.0000i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$			12.0000i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$		−	5.00000i		−	0.481125i
$109$			9.00000i			0.862044i	0.902342	+	0.431022i	$0.141847\pi$
$109$			9.00000i			0.862044i	−0.902342	+	0.431022i	$0.858153\pi$
$110$		0			0
$111$			3.00000i			0.284747i
$112$	−3.00000			−0.283473
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	6.00000			0.561951
$115$		0			0
$116$		0			0
$117$	6.00000	+	4.00000i	0.554700	+	0.369800i
$118$			6.00000i			0.552345i
$119$			9.00000i			0.825029i
$120$		0			0
$121$	11.0000			1.00000
$122$	8.00000			0.724286
$123$		0			0
$124$		0			0
$125$		0			0
$126$	6.00000			0.534522
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$	−1.00000			−0.0883883
$129$	−1.00000			−0.0880451
$130$		0			0
$131$	−3.00000			−0.262111			−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000			−0.262111			−0.131056	+	0.991375i	$0.541837\pi$
$132$		0			0
$133$			18.0000i			1.56080i
$134$	−12.0000			−1.03664
$135$		0			0
$136$			3.00000i			0.257248i
$137$	−18.0000			−1.53784			−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000			−1.53784			−0.768922	+	0.639343i	$0.779207\pi$
$138$	6.00000			0.510754
$139$	−5.00000			−0.424094			−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000			−0.424094			−0.212047	+	0.977259i	$0.568013\pi$
$140$		0			0
$141$			3.00000i			0.252646i
$142$			15.0000i			1.25877i
$143$		0			0
$144$	2.00000			0.166667
$145$		0			0
$146$	−6.00000			−0.496564
$147$		−	2.00000i		−	0.164957i
$148$	−3.00000			−0.246598
$149$		−	6.00000i		−	0.491539i	−0.969328	−	0.245770i	$-0.920959\pi$
$149$		−	6.00000i		−	0.491539i	0.969328	−	0.245770i	$-0.0790407\pi$
$150$		0			0
$151$			15.0000i			1.22068i	0.792139	+	0.610341i	$0.208968\pi$
$151$			15.0000i			1.22068i	−0.792139	+	0.610341i	$0.791032\pi$
$152$			6.00000i			0.486664i
$153$		−	6.00000i		−	0.485071i
$154$		0			0
$155$		0			0
$156$	2.00000	−	3.00000i	0.160128	−	0.240192i
$157$			22.0000i			1.75579i	0.478852	+	0.877896i	$0.341053\pi$
$157$			22.0000i			1.75579i	−0.478852	+	0.877896i	$0.658947\pi$
$158$	10.0000			0.795557
$159$	−6.00000			−0.475831
$160$		0			0
$161$			18.0000i			1.41860i
$162$	−1.00000			−0.0785674
$163$	6.00000			0.469956			0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000			0.469956			0.234978	+	0.972001i	$0.424498\pi$
$164$		0			0
$165$		0			0
$166$	−6.00000			−0.465690
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		−	3.00000i		−	0.231455i
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$		0			0
$171$		−	12.0000i		−	0.917663i
$172$		−	1.00000i		−	0.0762493i
$173$		−	6.00000i		−	0.456172i	−0.973641	−	0.228086i	$-0.926753\pi$
$173$		−	6.00000i		−	0.456172i	0.973641	−	0.228086i	$-0.0732467\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.00000			−0.450988
$178$			6.00000i			0.449719i
$179$	−15.0000			−1.12115			−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000			−1.12115			−0.560576	+	0.828103i	$0.689420\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	9.00000	+	6.00000i	0.667124	+	0.444750i
$183$			8.00000i			0.591377i
$184$			6.00000i			0.442326i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−3.00000			−0.218797
$189$			15.0000i			1.09109i
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	6.00000			0.431889			0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000			0.431889			0.215945	+	0.976406i	$0.430717\pi$
$194$	−12.0000			−0.861550
$195$		0			0
$196$	2.00000			0.142857
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$		0			0
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$		0			0
$201$		−	12.0000i		−	0.846415i
$202$	−12.0000			−0.844317
$203$		0			0
$204$	−3.00000			−0.210042
$205$		0			0
$206$		−	14.0000i		−	0.975426i
$207$		−	12.0000i		−	0.834058i
$208$	3.00000	+	2.00000i	0.208013	+	0.138675i
$209$		0			0
$210$		0			0
$211$	−23.0000			−1.58339			−0.791693	−	0.610920i	$-0.790800\pi$
$211$	−23.0000			−1.58339			−0.791693	+	0.610920i	$0.790800\pi$
$212$		−	6.00000i		−	0.412082i
$213$	−15.0000			−1.02778
$214$		−	12.0000i		−	0.820303i
$215$		0			0
$216$			5.00000i			0.340207i
$217$		0			0
$218$		−	9.00000i		−	0.609557i
$219$		−	6.00000i		−	0.405442i
$220$		0			0
$221$	6.00000	−	9.00000i	0.403604	−	0.605406i
$222$		−	3.00000i		−	0.201347i
$223$	−9.00000			−0.602685			−0.301342	−	0.953516i	$-0.597435\pi$
$223$	−9.00000			−0.602685			−0.301342	+	0.953516i	$0.597435\pi$
$224$	3.00000			0.200446
$225$		0			0
$226$			6.00000i			0.399114i
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$	−6.00000			−0.397360
$229$			9.00000i			0.594737i	0.954763	+	0.297368i	$0.0961089\pi$
$229$			9.00000i			0.594737i	−0.954763	+	0.297368i	$0.903891\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	21.0000i		−	1.37576i	−0.725826	−	0.687878i	$-0.758542\pi$
$233$		−	21.0000i		−	1.37576i	0.725826	−	0.687878i	$-0.241458\pi$
$234$	−6.00000	−	4.00000i	−0.392232	−	0.261488i
$235$		0			0
$236$		−	6.00000i		−	0.390567i
$237$			10.0000i			0.649570i
$238$		−	9.00000i		−	0.583383i
$239$			9.00000i			0.582162i	0.956698	+	0.291081i	$0.0940149\pi$
$239$			9.00000i			0.582162i	−0.956698	+	0.291081i	$0.905985\pi$
$240$		0			0
$241$			30.0000i			1.93247i	0.257663	+	0.966235i	$0.417048\pi$
$241$			30.0000i			1.93247i	−0.257663	+	0.966235i	$0.582952\pi$
$242$	−11.0000			−0.707107
$243$		−	16.0000i		−	1.02640i
$244$	−8.00000			−0.512148
$245$		0			0
$246$		0			0
$247$	12.0000	−	18.0000i	0.763542	−	1.14531i
$248$		0			0
$249$		−	6.00000i		−	0.380235i
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	−6.00000			−0.377964
$253$		0			0
$254$		−	2.00000i		−	0.125491i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	3.00000i		−	0.187135i	−0.995613	−	0.0935674i	$-0.970173\pi$
$257$		−	3.00000i		−	0.187135i	0.995613	−	0.0935674i	$-0.0298271\pi$
$258$	1.00000			0.0622573
$259$	9.00000			0.559233
$260$		0			0
$261$		0			0
$262$	3.00000			0.185341
$263$			24.0000i			1.47990i	0.672660	+	0.739952i	$0.265152\pi$
$263$			24.0000i			1.47990i	−0.672660	+	0.739952i	$0.734848\pi$
$264$		0			0
$265$		0			0
$266$		−	18.0000i		−	1.10365i
$267$	−6.00000			−0.367194
$268$	12.0000			0.733017
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$		−	15.0000i		−	0.911185i	−0.890188	−	0.455593i	$-0.849427\pi$
$271$		−	15.0000i		−	0.911185i	0.890188	−	0.455593i	$-0.150573\pi$
$272$		−	3.00000i		−	0.181902i
$273$	−6.00000	+	9.00000i	−0.363137	+	0.544705i
$274$	18.0000			1.08742
$275$		0			0
$276$	−6.00000			−0.361158
$277$		−	8.00000i		−	0.480673i	−0.970690	−	0.240337i	$-0.922742\pi$
$277$		−	8.00000i		−	0.480673i	0.970690	−	0.240337i	$-0.0772579\pi$
$278$	5.00000			0.299880
$279$		0			0
$280$		0			0
$281$			30.0000i			1.78965i	0.446417	+	0.894825i	$0.352700\pi$
$281$			30.0000i			1.78965i	−0.446417	+	0.894825i	$0.647300\pi$
$282$		−	3.00000i		−	0.178647i
$283$			4.00000i			0.237775i	0.992908	+	0.118888i	$0.0379328\pi$
$283$			4.00000i			0.237775i	−0.992908	+	0.118888i	$0.962067\pi$
$284$		−	15.0000i		−	0.890086i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.00000			−0.117851
$289$	8.00000			0.470588
$290$		0			0
$291$		−	12.0000i		−	0.703452i
$292$	6.00000			0.351123
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$			2.00000i			0.116642i
$295$		0			0
$296$	3.00000			0.174371
$297$		0			0
$298$			6.00000i			0.347571i
$299$	12.0000	−	18.0000i	0.693978	−	1.04097i
$300$		0			0
$301$			3.00000i			0.172917i
$302$		−	15.0000i		−	0.863153i
$303$		−	12.0000i		−	0.689382i
$304$		−	6.00000i		−	0.344124i
$305$		0			0
$306$			6.00000i			0.342997i
$307$	−18.0000			−1.02731			−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$		0			0
$309$	14.0000			0.796432
$310$		0			0
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$	−2.00000	+	3.00000i	−0.113228	+	0.169842i
$313$			19.0000i			1.07394i	0.843600	+	0.536972i	$0.180432\pi$
$313$			19.0000i			1.07394i	−0.843600	+	0.536972i	$0.819568\pi$
$314$		−	22.0000i		−	1.24153i
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$	6.00000			0.336463
$319$		0			0
$320$		0			0
$321$	12.0000			0.669775
$322$		−	18.0000i		−	1.00310i
$323$	−18.0000			−1.00155
$324$	1.00000			0.0555556
$325$		0			0
$326$	−6.00000			−0.332309
$327$	9.00000			0.497701
$328$		0			0
$329$	9.00000			0.496186
$330$		0			0
$331$		−	30.0000i		−	1.64895i	−0.565899	−	0.824475i	$-0.691471\pi$
$331$		−	30.0000i		−	1.64895i	0.565899	−	0.824475i	$-0.308529\pi$
$332$	6.00000			0.329293
$333$	−6.00000			−0.328798
$334$	−12.0000			−0.656611
$335$		0			0
$336$			3.00000i			0.163663i
$337$		−	13.0000i		−	0.708155i	−0.935216	−	0.354078i	$-0.884795\pi$
$337$		−	13.0000i		−	0.708155i	0.935216	−	0.354078i	$-0.115205\pi$
$338$	−5.00000	−	12.0000i	−0.271964	−	0.652714i
$339$	−6.00000			−0.325875
$340$		0			0
$341$		0			0
$342$			12.0000i			0.648886i
$343$	15.0000			0.809924
$344$			1.00000i			0.0539164i
$345$		0			0
$346$			6.00000i			0.322562i
$347$		−	33.0000i		−	1.77153i	−0.464131	−	0.885766i	$-0.653633\pi$
$347$		−	33.0000i		−	1.77153i	0.464131	−	0.885766i	$-0.346367\pi$
$348$		0			0
$349$		−	21.0000i		−	1.12410i	−0.827102	−	0.562052i	$-0.810012\pi$
$349$		−	21.0000i		−	1.12410i	0.827102	−	0.562052i	$-0.189988\pi$
$350$		0			0
$351$	10.0000	−	15.0000i	0.533761	−	0.800641i
$352$		0			0
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$	6.00000			0.318896
$355$		0			0
$356$		−	6.00000i		−	0.317999i
$357$	9.00000			0.476331
$358$	15.0000			0.792775
$359$			24.0000i			1.26667i	0.773877	+	0.633336i	$0.218315\pi$
$359$			24.0000i			1.26667i	−0.773877	+	0.633336i	$0.781685\pi$
$360$		0			0
$361$	−17.0000			−0.894737
$362$	−2.00000			−0.105118
$363$		−	11.0000i		−	0.577350i
$364$	−9.00000	−	6.00000i	−0.471728	−	0.314485i
$365$		0			0
$366$		−	8.00000i		−	0.418167i
$367$		−	8.00000i		−	0.417597i	−0.977959	−	0.208798i	$-0.933045\pi$
$367$		−	8.00000i		−	0.417597i	0.977959	−	0.208798i	$-0.0669552\pi$
$368$		−	6.00000i		−	0.312772i
$369$		0			0
$370$		0			0
$371$			18.0000i			0.934513i
$372$		0			0
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$		0			0
$375$		0			0
$376$	3.00000			0.154713
$377$		0			0
$378$		−	15.0000i		−	0.771517i
$379$		−	6.00000i		−	0.308199i	−0.988055	−	0.154100i	$-0.950752\pi$
$379$		−	6.00000i		−	0.308199i	0.988055	−	0.154100i	$-0.0492477\pi$
$380$		0			0
$381$	2.00000			0.102463
$382$	−12.0000			−0.613973
$383$	−9.00000			−0.459879			−0.229939	−	0.973205i	$-0.573853\pi$
$383$	−9.00000			−0.459879			−0.229939	+	0.973205i	$0.573853\pi$
$384$			1.00000i			0.0510310i
$385$		0			0
$386$	−6.00000			−0.305392
$387$		−	2.00000i		−	0.101666i
$388$	12.0000			0.609208
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$	−2.00000			−0.101015
$393$			3.00000i			0.151330i
$394$	3.00000			0.151138
$395$		0			0
$396$		0			0
$397$	−18.0000			−0.903394			−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000			−0.903394			−0.451697	+	0.892171i	$0.649181\pi$
$398$	−20.0000			−1.00251
$399$	18.0000			0.901127
$400$		0			0
$401$		−	30.0000i		−	1.49813i	−0.662497	−	0.749064i	$-0.730503\pi$
$401$		−	30.0000i		−	1.49813i	0.662497	−	0.749064i	$-0.269497\pi$
$402$			12.0000i			0.598506i
$403$		0			0
$404$	12.0000			0.597022
$405$		0			0
$406$		0			0
$407$		0			0
$408$	3.00000			0.148522
$409$		−	6.00000i		−	0.296681i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$		−	6.00000i		−	0.296681i	0.988936	−	0.148340i	$-0.0473931\pi$
$410$		0			0
$411$			18.0000i			0.887875i
$412$			14.0000i			0.689730i
$413$			18.0000i			0.885722i
$414$			12.0000i			0.589768i
$415$		0			0
$416$	−3.00000	−	2.00000i	−0.147087	−	0.0980581i
$417$			5.00000i			0.244851i
$418$		0			0
$419$	−15.0000			−0.732798			−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000			−0.732798			−0.366399	+	0.930458i	$0.619409\pi$
$420$		0			0
$421$			15.0000i			0.731055i	0.930800	+	0.365528i	$0.119111\pi$
$421$			15.0000i			0.731055i	−0.930800	+	0.365528i	$0.880889\pi$
$422$	23.0000			1.11962
$423$	−6.00000			−0.291730
$424$			6.00000i			0.291386i
$425$		0			0
$426$	15.0000			0.726752
$427$	24.0000			1.16144
$428$			12.0000i			0.580042i
$429$		0			0
$430$		0			0
$431$			15.0000i			0.722525i	0.932464	+	0.361262i	$0.117654\pi$
$431$			15.0000i			0.722525i	−0.932464	+	0.361262i	$0.882346\pi$
$432$		−	5.00000i		−	0.240563i
$433$		−	11.0000i		−	0.528626i	−0.964437	−	0.264313i	$-0.914855\pi$
$433$		−	11.0000i		−	0.528626i	0.964437	−	0.264313i	$-0.0851452\pi$
$434$		0			0
$435$		0			0
$436$			9.00000i			0.431022i
$437$	−36.0000			−1.72211
$438$			6.00000i			0.286691i
$439$	10.0000			0.477274			0.238637	−	0.971109i	$-0.423299\pi$
$439$	10.0000			0.477274			0.238637	+	0.971109i	$0.423299\pi$
$440$		0			0
$441$	4.00000			0.190476
$442$	−6.00000	+	9.00000i	−0.285391	+	0.428086i
$443$		−	21.0000i		−	0.997740i	−0.866677	−	0.498870i	$-0.833748\pi$
$443$		−	21.0000i		−	0.997740i	0.866677	−	0.498870i	$-0.166252\pi$
$444$			3.00000i			0.142374i
$445$		0			0
$446$	9.00000			0.426162
$447$	−6.00000			−0.283790
$448$	−3.00000			−0.141737
$449$			24.0000i			1.13263i	0.824189	+	0.566315i	$0.191631\pi$
$449$			24.0000i			1.13263i	−0.824189	+	0.566315i	$0.808369\pi$
$450$		0			0
$451$		0			0
$452$		−	6.00000i		−	0.282216i
$453$	15.0000			0.704761
$454$	−12.0000			−0.563188
$455$		0			0
$456$	6.00000			0.280976
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$		−	9.00000i		−	0.420542i
$459$	−15.0000			−0.700140
$460$		0			0
$461$			15.0000i			0.698620i	0.937007	+	0.349310i	$0.113584\pi$
$461$			15.0000i			0.698620i	−0.937007	+	0.349310i	$0.886416\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$		0			0
$465$		0			0
$466$			21.0000i			0.972806i
$467$			12.0000i			0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$			12.0000i			0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$	6.00000	+	4.00000i	0.277350	+	0.184900i
$469$	−36.0000			−1.66233
$470$		0			0
$471$	22.0000			1.01371
$472$			6.00000i			0.276172i
$473$		0			0
$474$		−	10.0000i		−	0.459315i
$475$		0			0
$476$			9.00000i			0.412514i
$477$		−	12.0000i		−	0.549442i
$478$		−	9.00000i		−	0.411650i
$479$			39.0000i			1.78196i	0.454047	+	0.890978i	$0.349980\pi$
$479$			39.0000i			1.78196i	−0.454047	+	0.890978i	$0.650020\pi$
$480$		0			0
$481$	−9.00000	−	6.00000i	−0.410365	−	0.273576i
$482$		−	30.0000i		−	1.36646i
$483$	18.0000			0.819028
$484$	11.0000			0.500000
$485$		0			0
$486$			16.0000i			0.725775i
$487$	12.0000			0.543772			0.271886	−	0.962329i	$-0.412353\pi$
$487$	12.0000			0.543772			0.271886	+	0.962329i	$0.412353\pi$
$488$	8.00000			0.362143
$489$		−	6.00000i		−	0.271329i
$490$		0			0
$491$	27.0000			1.21849			0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000			1.21849			0.609246	+	0.792981i	$0.291472\pi$
$492$		0			0
$493$		0			0
$494$	−12.0000	+	18.0000i	−0.539906	+	0.809858i
$495$		0			0
$496$		0			0
$497$			45.0000i			2.01853i
$498$			6.00000i			0.268866i
$499$		−	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
$501$		−	12.0000i		−	0.536120i
$502$	−12.0000			−0.535586
$503$		−	6.00000i		−	0.267527i	−0.991013	−	0.133763i	$-0.957294\pi$
$503$		−	6.00000i		−	0.267527i	0.991013	−	0.133763i	$-0.0427062\pi$
$504$	6.00000			0.267261
$505$		0			0
$506$		0			0
$507$	12.0000	−	5.00000i	0.532939	−	0.222058i
$508$			2.00000i			0.0887357i
$509$		−	6.00000i		−	0.265945i	−0.991120	−	0.132973i	$-0.957548\pi$
$509$		−	6.00000i		−	0.265945i	0.991120	−	0.132973i	$-0.0424523\pi$
$510$		0			0
$511$	−18.0000			−0.796273
$512$	−1.00000			−0.0441942
$513$	−30.0000			−1.32453
$514$			3.00000i			0.132324i
$515$		0			0
$516$	−1.00000			−0.0440225
$517$		0			0
$518$	−9.00000			−0.395437
$519$	−6.00000			−0.263371
$520$		0			0
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$		0			0
$523$		−	16.0000i		−	0.699631i	−0.936819	−	0.349816i	$-0.886244\pi$
$523$		−	16.0000i		−	0.699631i	0.936819	−	0.349816i	$-0.113756\pi$
$524$	−3.00000			−0.131056
$525$		0			0
$526$		−	24.0000i		−	1.04645i
$527$		0			0
$528$		0			0
$529$	−13.0000			−0.565217
$530$		0			0
$531$		−	12.0000i		−	0.520756i
$532$			18.0000i			0.780399i
$533$		0			0
$534$	6.00000			0.259645
$535$		0			0
$536$	−12.0000			−0.518321
$537$			15.0000i			0.647298i
$538$		0			0
$539$		0			0
$540$		0			0
$541$			15.0000i			0.644900i	0.946586	+	0.322450i	$0.104506\pi$
$541$			15.0000i			0.644900i	−0.946586	+	0.322450i	$0.895494\pi$
$542$			15.0000i			0.644305i
$543$		−	2.00000i		−	0.0858282i
$544$			3.00000i			0.128624i
$545$		0			0
$546$	6.00000	−	9.00000i	0.256776	−	0.385164i
$547$			37.0000i			1.58201i	0.611812	+	0.791003i	$0.290441\pi$
$547$			37.0000i			1.58201i	−0.611812	+	0.791003i	$0.709559\pi$
$548$	−18.0000			−0.768922
$549$	−16.0000			−0.682863
$550$		0			0
$551$		0			0
$552$	6.00000			0.255377
$553$	30.0000			1.27573
$554$			8.00000i			0.339887i
$555$		0			0
$556$	−5.00000			−0.212047
$557$	27.0000			1.14403			0.572013	−	0.820244i	$-0.306163\pi$
$557$	27.0000			1.14403			0.572013	+	0.820244i	$0.306163\pi$
$558$		0			0
$559$	2.00000	−	3.00000i	0.0845910	−	0.126886i
$560$		0			0
$561$		0			0
$562$		−	30.0000i		−	1.26547i
$563$			39.0000i			1.64365i	0.569737	+	0.821827i	$0.307045\pi$
$563$			39.0000i			1.64365i	−0.569737	+	0.821827i	$0.692955\pi$
$564$			3.00000i			0.126323i
$565$		0			0
$566$		−	4.00000i		−	0.168133i
$567$	−3.00000			−0.125988
$568$			15.0000i			0.629386i
$569$	−45.0000			−1.88650			−0.943249	−	0.332086i	$-0.892248\pi$
$569$	−45.0000			−1.88650			−0.943249	+	0.332086i	$0.892248\pi$
$570$		0			0
$571$	−23.0000			−0.962520			−0.481260	−	0.876578i	$-0.659821\pi$
$571$	−23.0000			−0.962520			−0.481260	+	0.876578i	$0.659821\pi$
$572$		0			0
$573$		−	12.0000i		−	0.501307i
$574$		0			0
$575$		0			0
$576$	2.00000			0.0833333
$577$	42.0000			1.74848			0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000			1.74848			0.874241	+	0.485491i	$0.161359\pi$
$578$	−8.00000			−0.332756
$579$		−	6.00000i		−	0.249351i
$580$		0			0
$581$	−18.0000			−0.746766
$582$			12.0000i			0.497416i
$583$		0			0
$584$	−6.00000			−0.248282
$585$		0			0
$586$	9.00000			0.371787
$587$	−18.0000			−0.742940			−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000			−0.742940			−0.371470	+	0.928445i	$0.621146\pi$
$588$		−	2.00000i		−	0.0824786i
$589$		0			0
$590$		0			0
$591$			3.00000i			0.123404i
$592$	−3.00000			−0.123299
$593$	36.0000			1.47834			0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000			1.47834			0.739171	+	0.673517i	$0.235217\pi$
$594$		0			0
$595$		0			0
$596$		−	6.00000i		−	0.245770i
$597$		−	20.0000i		−	0.818546i
$598$	−12.0000	+	18.0000i	−0.490716	+	0.736075i
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		0			0
$601$	37.0000			1.50926			0.754631	−	0.656150i	$-0.227816\pi$
$601$	37.0000			1.50926			0.754631	+	0.656150i	$0.227816\pi$
$602$		−	3.00000i		−	0.122271i
$603$	24.0000			0.977356
$604$			15.0000i			0.610341i
$605$		0			0
$606$			12.0000i			0.487467i
$607$			22.0000i			0.892952i	0.894795	+	0.446476i	$0.147321\pi$
$607$			22.0000i			0.892952i	−0.894795	+	0.446476i	$0.852679\pi$
$608$			6.00000i			0.243332i
$609$		0			0
$610$		0			0
$611$	−9.00000	−	6.00000i	−0.364101	−	0.242734i
$612$		−	6.00000i		−	0.242536i
$613$	6.00000			0.242338			0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000			0.242338			0.121169	+	0.992632i	$0.461336\pi$
$614$	18.0000			0.726421
$615$		0			0
$616$		0			0
$617$	12.0000			0.483102			0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000			0.483102			0.241551	+	0.970388i	$0.422344\pi$
$618$	−14.0000			−0.563163
$619$			24.0000i			0.964641i	0.875995	+	0.482321i	$0.160206\pi$
$619$			24.0000i			0.964641i	−0.875995	+	0.482321i	$0.839794\pi$
$620$		0			0
$621$	−30.0000			−1.20386
$622$	18.0000			0.721734
$623$			18.0000i			0.721155i
$624$	2.00000	−	3.00000i	0.0800641	−	0.120096i
$625$		0			0
$626$		−	19.0000i		−	0.759393i
$627$		0			0
$628$			22.0000i			0.877896i
$629$			9.00000i			0.358854i
$630$		0			0
$631$			15.0000i			0.597141i	0.954388	+	0.298570i	$0.0965097\pi$
$631$			15.0000i			0.597141i	−0.954388	+	0.298570i	$0.903490\pi$
$632$	10.0000			0.397779
$633$			23.0000i			0.914168i
$634$	18.0000			0.714871
$635$		0			0
$636$	−6.00000			−0.237915
$637$	6.00000	+	4.00000i	0.237729	+	0.158486i
$638$		0			0
$639$		−	30.0000i		−	1.18678i
$640$		0			0
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$	−12.0000			−0.473602
$643$	36.0000			1.41970			0.709851	−	0.704352i	$-0.248762\pi$
$643$	36.0000			1.41970			0.709851	+	0.704352i	$0.248762\pi$
$644$			18.0000i			0.709299i
$645$		0			0
$646$	18.0000			0.708201
$647$			42.0000i			1.65119i	0.564263	+	0.825595i	$0.309160\pi$
$647$			42.0000i			1.65119i	−0.564263	+	0.825595i	$0.690840\pi$
$648$	−1.00000			−0.0392837
$649$		0			0
$650$		0			0
$651$		0			0
$652$	6.00000			0.234978
$653$		−	36.0000i		−	1.40879i	−0.709809	−	0.704394i	$-0.751219\pi$
$653$		−	36.0000i		−	1.40879i	0.709809	−	0.704394i	$-0.248781\pi$
$654$	−9.00000			−0.351928
$655$		0			0
$656$		0			0
$657$	12.0000			0.468165
$658$	−9.00000			−0.350857
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$		−	30.0000i		−	1.16686i	−0.812162	−	0.583432i	$-0.801709\pi$
$661$		−	30.0000i		−	1.16686i	0.812162	−	0.583432i	$-0.198291\pi$
$662$			30.0000i			1.16598i
$663$	−9.00000	−	6.00000i	−0.349531	−	0.233021i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	6.00000			0.232495
$667$		0			0
$668$	12.0000			0.464294
$669$			9.00000i			0.347960i
$670$		0			0
$671$		0			0
$672$		−	3.00000i		−	0.115728i
$673$		−	1.00000i		−	0.0385472i	−0.999814	−	0.0192736i	$-0.993865\pi$
$673$		−	1.00000i		−	0.0385472i	0.999814	−	0.0192736i	$-0.00613535\pi$
$674$			13.0000i			0.500741i
$675$		0			0
$676$	5.00000	+	12.0000i	0.192308	+	0.461538i
$677$		−	18.0000i		−	0.691796i	−0.938272	−	0.345898i	$-0.887574\pi$
$677$		−	18.0000i		−	0.691796i	0.938272	−	0.345898i	$-0.112426\pi$
$678$	6.00000			0.230429
$679$	−36.0000			−1.38155
$680$		0			0
$681$		−	12.0000i		−	0.459841i
$682$		0			0
$683$	6.00000			0.229584			0.114792	−	0.993390i	$-0.463380\pi$
$683$	6.00000			0.229584			0.114792	+	0.993390i	$0.463380\pi$
$684$		−	12.0000i		−	0.458831i
$685$		0			0
$686$	−15.0000			−0.572703
$687$	9.00000			0.343371
$688$		−	1.00000i		−	0.0381246i
$689$	12.0000	−	18.0000i	0.457164	−	0.685745i
$690$		0			0
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		−	6.00000i		−	0.228086i
$693$		0			0
$694$			33.0000i			1.25266i
$695$		0			0
$696$		0			0
$697$		0			0
$698$			21.0000i			0.794862i
$699$	−21.0000			−0.794293
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$	−10.0000	+	15.0000i	−0.377426	+	0.566139i
$703$			18.0000i			0.678883i
$704$		0			0
$705$		0			0
$706$	−6.00000			−0.225813
$707$	−36.0000			−1.35392
$708$	−6.00000			−0.225494
$709$		−	6.00000i		−	0.225335i	−0.993633	−	0.112667i	$-0.964061\pi$
$709$		−	6.00000i		−	0.225335i	0.993633	−	0.112667i	$-0.0359394\pi$
$710$		0			0
$711$	−20.0000			−0.750059
$712$			6.00000i			0.224860i
$713$		0			0
$714$	−9.00000			−0.336817
$715$		0			0
$716$	−15.0000			−0.560576
$717$	9.00000			0.336111
$718$		−	24.0000i		−	0.895672i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$		−	42.0000i		−	1.56416i
$722$	17.0000			0.632674
$723$	30.0000			1.11571
$724$	2.00000			0.0743294
$725$		0			0
$726$			11.0000i			0.408248i
$727$		−	28.0000i		−	1.03846i	−0.854634	−	0.519231i	$-0.826218\pi$
$727$		−	28.0000i		−	1.03846i	0.854634	−	0.519231i	$-0.173782\pi$
$728$	9.00000	+	6.00000i	0.333562	+	0.222375i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−3.00000			−0.110959
$732$			8.00000i			0.295689i
$733$	−9.00000			−0.332423			−0.166211	−	0.986090i	$-0.553153\pi$
$733$	−9.00000			−0.332423			−0.166211	+	0.986090i	$0.553153\pi$
$734$			8.00000i			0.295285i
$735$		0			0
$736$			6.00000i			0.221163i
$737$		0			0
$738$		0			0
$739$		−	36.0000i		−	1.32428i	−0.749380	−	0.662141i	$-0.769648\pi$
$739$		−	36.0000i		−	1.32428i	0.749380	−	0.662141i	$-0.230352\pi$
$740$		0			0
$741$	−18.0000	−	12.0000i	−0.661247	−	0.440831i
$742$		−	18.0000i		−	0.660801i
$743$	−39.0000			−1.43077			−0.715386	−	0.698730i	$-0.753749\pi$
$743$	−39.0000			−1.43077			−0.715386	+	0.698730i	$0.753749\pi$
$744$		0			0
$745$		0			0
$746$		−	4.00000i		−	0.146450i
$747$	12.0000			0.439057
$748$		0			0
$749$		−	36.0000i		−	1.31541i
$750$		0			0
$751$	32.0000			1.16770			0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000			1.16770			0.583848	+	0.811863i	$0.301546\pi$
$752$	−3.00000			−0.109399
$753$		−	12.0000i		−	0.437304i
$754$		0			0
$755$		0			0
$756$			15.0000i			0.545545i
$757$			2.00000i			0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$			6.00000i			0.217930i
$759$		0			0
$760$		0			0
$761$			30.0000i			1.08750i	0.839248	+	0.543750i	$0.182996\pi$
$761$			30.0000i			1.08750i	−0.839248	+	0.543750i	$0.817004\pi$
$762$	−2.00000			−0.0724524
$763$		−	27.0000i		−	0.977466i
$764$	12.0000			0.434145
$765$		0			0
$766$	9.00000			0.325183
$767$	12.0000	−	18.0000i	0.433295	−	0.649942i
$768$		−	1.00000i		−	0.0360844i
$769$			24.0000i			0.865462i	0.901523	+	0.432731i	$0.142450\pi$
$769$			24.0000i			0.865462i	−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$	−3.00000			−0.108042
$772$	6.00000			0.215945
$773$	21.0000			0.755318			0.377659	−	0.925945i	$-0.376729\pi$
$773$	21.0000			0.755318			0.377659	+	0.925945i	$0.376729\pi$
$774$			2.00000i			0.0718885i
$775$		0			0
$776$	−12.0000			−0.430775
$777$		−	9.00000i		−	0.322873i
$778$	−30.0000			−1.07555
$779$		0			0
$780$		0			0
$781$		0			0
$782$	18.0000			0.643679
$783$		0			0
$784$	2.00000			0.0714286
$785$		0			0
$786$		−	3.00000i		−	0.107006i
$787$	12.0000			0.427754			0.213877	−	0.976861i	$-0.431391\pi$
$787$	12.0000			0.427754			0.213877	+	0.976861i	$0.431391\pi$
$788$	−3.00000			−0.106871
$789$	24.0000			0.854423
$790$		0			0
$791$			18.0000i			0.640006i
$792$		0			0
$793$	−24.0000	−	16.0000i	−0.852265	−	0.568177i
$794$	18.0000			0.638796
$795$		0			0
$796$	20.0000			0.708881
$797$		−	18.0000i		−	0.637593i	−0.947823	−	0.318796i	$-0.896721\pi$
$797$		−	18.0000i		−	0.637593i	0.947823	−	0.318796i	$-0.103279\pi$
$798$	−18.0000			−0.637193
$799$			9.00000i			0.318397i
$800$		0			0
$801$		−	12.0000i		−	0.423999i
$802$			30.0000i			1.05934i
$803$		0			0
$804$		−	12.0000i		−	0.423207i
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−12.0000			−0.422159
$809$	−15.0000			−0.527372			−0.263686	−	0.964609i	$-0.584938\pi$
$809$	−15.0000			−0.527372			−0.263686	+	0.964609i	$0.584938\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	−15.0000			−0.526073
$814$		0			0
$815$		0			0
$816$	−3.00000			−0.105021
$817$	−6.00000			−0.209913
$818$			6.00000i			0.209785i
$819$	−18.0000	−	12.0000i	−0.628971	−	0.419314i
$820$		0			0
$821$		−	45.0000i		−	1.57051i	−0.619172	−	0.785255i	$-0.712532\pi$
$821$		−	45.0000i		−	1.57051i	0.619172	−	0.785255i	$-0.287468\pi$
$822$		−	18.0000i		−	0.627822i
$823$			14.0000i			0.488009i	0.969774	+	0.244005i	$0.0784612\pi$
$823$			14.0000i			0.488009i	−0.969774	+	0.244005i	$0.921539\pi$
$824$		−	14.0000i		−	0.487713i
$825$		0			0
$826$		−	18.0000i		−	0.626300i
$827$	−18.0000			−0.625921			−0.312961	−	0.949766i	$-0.601321\pi$
$827$	−18.0000			−0.625921			−0.312961	+	0.949766i	$0.601321\pi$
$828$		−	12.0000i		−	0.417029i
$829$	20.0000			0.694629			0.347314	−	0.937749i	$-0.387094\pi$
$829$	20.0000			0.694629			0.347314	+	0.937749i	$0.387094\pi$
$830$		0			0
$831$	−8.00000			−0.277517
$832$	3.00000	+	2.00000i	0.104006	+	0.0693375i
$833$		−	6.00000i		−	0.207888i
$834$		−	5.00000i		−	0.173136i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	15.0000			0.518166
$839$			24.0000i			0.828572i	0.910147	+	0.414286i	$0.135969\pi$
$839$			24.0000i			0.828572i	−0.910147	+	0.414286i	$0.864031\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$		−	15.0000i		−	0.516934i
$843$	30.0000			1.03325
$844$	−23.0000			−0.791693
$845$		0			0
$846$	6.00000			0.206284
$847$	−33.0000			−1.13389
$848$		−	6.00000i		−	0.206041i
$849$	4.00000			0.137280
$850$		0			0
$851$			18.0000i			0.617032i
$852$	−15.0000			−0.513892
$853$	−39.0000			−1.33533			−0.667667	−	0.744460i	$-0.732707\pi$
$853$	−39.0000			−1.33533			−0.667667	+	0.744460i	$0.732707\pi$
$854$	−24.0000			−0.821263
$855$		0			0
$856$		−	12.0000i		−	0.410152i
$857$		−	18.0000i		−	0.614868i	−0.951569	−	0.307434i	$-0.900530\pi$
$857$		−	18.0000i		−	0.614868i	0.951569	−	0.307434i	$-0.0994704\pi$
$858$		0			0
$859$	−40.0000			−1.36478			−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000			−1.36478			−0.682391	+	0.730987i	$0.739060\pi$
$860$		0			0
$861$		0			0
$862$		−	15.0000i		−	0.510902i
$863$	−39.0000			−1.32758			−0.663788	−	0.747921i	$-0.731052\pi$
$863$	−39.0000			−1.32758			−0.663788	+	0.747921i	$0.731052\pi$
$864$			5.00000i			0.170103i
$865$		0			0
$866$			11.0000i			0.373795i
$867$		−	8.00000i		−	0.271694i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	36.0000	+	24.0000i	1.21981	+	0.813209i
$872$		−	9.00000i		−	0.304778i
$873$	24.0000			0.812277
$874$	36.0000			1.21772
$875$		0			0
$876$		−	6.00000i		−	0.202721i
$877$	−3.00000			−0.101303			−0.0506514	−	0.998716i	$-0.516130\pi$
$877$	−3.00000			−0.101303			−0.0506514	+	0.998716i	$0.516130\pi$
$878$	−10.0000			−0.337484
$879$			9.00000i			0.303562i
$880$		0			0
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$	−4.00000			−0.134687
$883$		−	11.0000i		−	0.370179i	−0.982722	−	0.185090i	$-0.940742\pi$
$883$		−	11.0000i		−	0.370179i	0.982722	−	0.185090i	$-0.0592576\pi$
$884$	6.00000	−	9.00000i	0.201802	−	0.302703i
$885$		0			0
$886$			21.0000i			0.705509i
$887$			12.0000i			0.402921i	0.979497	+	0.201460i	$0.0645687\pi$
$887$			12.0000i			0.402921i	−0.979497	+	0.201460i	$0.935431\pi$
$888$		−	3.00000i		−	0.100673i
$889$		−	6.00000i		−	0.201234i
$890$		0			0
$891$		0			0
$892$	−9.00000			−0.301342
$893$			18.0000i			0.602347i
$894$	6.00000			0.200670
$895$		0			0
$896$	3.00000			0.100223
$897$	−18.0000	−	12.0000i	−0.601003	−	0.400668i
$898$		−	24.0000i		−	0.800890i
$899$		0			0
$900$		0			0
$901$	−18.0000			−0.599667
$902$		0			0
$903$	3.00000			0.0998337
$904$			6.00000i			0.199557i
$905$		0			0
$906$	−15.0000			−0.498342
$907$			17.0000i			0.564476i	0.959344	+	0.282238i	$0.0910767\pi$
$907$			17.0000i			0.564476i	−0.959344	+	0.282238i	$0.908923\pi$
$908$	12.0000			0.398234
$909$	24.0000			0.796030
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−6.00000			−0.198680
$913$		0			0
$914$	18.0000			0.595387
$915$		0			0
$916$			9.00000i			0.297368i
$917$	9.00000			0.297206
$918$	15.0000			0.495074
$919$	20.0000			0.659739			0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000			0.659739			0.329870	+	0.944027i	$0.392995\pi$
$920$		0			0
$921$			18.0000i			0.593120i
$922$		−	15.0000i		−	0.493999i
$923$	30.0000	−	45.0000i	0.987462	−	1.48119i
$924$		0			0
$925$		0			0
$926$	24.0000			0.788689
$927$			28.0000i			0.919641i
$928$		0			0
$929$		−	36.0000i		−	1.18112i	−0.806993	−	0.590561i	$-0.798907\pi$
$929$		−	36.0000i		−	1.18112i	0.806993	−	0.590561i	$-0.201093\pi$
$930$		0			0
$931$		−	12.0000i		−	0.393284i
$932$		−	21.0000i		−	0.687878i
$933$			18.0000i			0.589294i
$934$		−	12.0000i		−	0.392652i
$935$		0			0
$936$	−6.00000	−	4.00000i	−0.196116	−	0.130744i
$937$			2.00000i			0.0653372i	0.999466	+	0.0326686i	$0.0104006\pi$
$937$			2.00000i			0.0653372i	−0.999466	+	0.0326686i	$0.989599\pi$
$938$	36.0000			1.17544
$939$	19.0000			0.620042
$940$		0			0
$941$			45.0000i			1.46696i	0.679712	+	0.733479i	$0.262105\pi$
$941$			45.0000i			1.46696i	−0.679712	+	0.733479i	$0.737895\pi$
$942$	−22.0000			−0.716799
$943$		0			0
$944$		−	6.00000i		−	0.195283i
$945$		0			0
$946$		0			0
$947$	−48.0000			−1.55979			−0.779895	−	0.625910i	$-0.784728\pi$
$947$	−48.0000			−1.55979			−0.779895	+	0.625910i	$0.784728\pi$
$948$			10.0000i			0.324785i
$949$	18.0000	+	12.0000i	0.584305	+	0.389536i
$950$		0			0
$951$			18.0000i			0.583690i
$952$		−	9.00000i		−	0.291692i
$953$			9.00000i			0.291539i	0.989319	+	0.145769i	$0.0465657\pi$
$953$			9.00000i			0.291539i	−0.989319	+	0.145769i	$0.953434\pi$
$954$			12.0000i			0.388514i
$955$		0			0
$956$			9.00000i			0.291081i
$957$		0			0
$958$		−	39.0000i		−	1.26003i
$959$	54.0000			1.74375
$960$		0			0
$961$	31.0000			1.00000
$962$	9.00000	+	6.00000i	0.290172	+	0.193448i
$963$			24.0000i			0.773389i
$964$			30.0000i			0.966235i
$965$		0			0
$966$	−18.0000			−0.579141
$967$	−3.00000			−0.0964735			−0.0482367	−	0.998836i	$-0.515360\pi$
$967$	−3.00000			−0.0964735			−0.0482367	+	0.998836i	$0.515360\pi$
$968$	−11.0000			−0.353553
$969$			18.0000i			0.578243i
$970$		0			0
$971$	27.0000			0.866471			0.433236	−	0.901281i	$-0.357372\pi$
$971$	27.0000			0.866471			0.433236	+	0.901281i	$0.357372\pi$
$972$		−	16.0000i		−	0.513200i
$973$	15.0000			0.480878
$974$	−12.0000			−0.384505
$975$		0			0
$976$	−8.00000			−0.256074
$977$	12.0000			0.383914			0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000			0.383914			0.191957	+	0.981403i	$0.438517\pi$
$978$			6.00000i			0.191859i
$979$		0			0
$980$		0			0
$981$			18.0000i			0.574696i
$982$	−27.0000			−0.861605
$983$	−9.00000			−0.287055			−0.143528	−	0.989646i	$-0.545845\pi$
$983$	−9.00000			−0.287055			−0.143528	+	0.989646i	$0.545845\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	9.00000i		−	0.286473i
$988$	12.0000	−	18.0000i	0.381771	−	0.572656i
$989$	−6.00000			−0.190789
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$		0			0
$993$	−30.0000			−0.952021
$994$		−	45.0000i		−	1.42731i
$995$		0			0
$996$		−	6.00000i		−	0.190117i
$997$		−	8.00000i		−	0.253363i	−0.991943	−	0.126681i	$-0.959567\pi$
$997$		−	8.00000i		−	0.253363i	0.991943	−	0.126681i	$-0.0404325\pi$
$998$			36.0000i			1.13956i
$999$			15.0000i			0.474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.c.a.649.1		2
5.2	odd	4		26.2.b.a.25.1	✓	2
5.3	odd	4		650.2.d.b.51.2		2
5.4	even	2		650.2.c.d.649.2		2
13.12	even	2		650.2.c.d.649.1		2
15.2	even	4		234.2.b.b.181.2		2
20.7	even	4		208.2.f.a.129.2		2
35.2	odd	12		1274.2.n.d.753.1		4
35.12	even	12		1274.2.n.c.753.1		4
35.17	even	12		1274.2.n.c.961.2		4
35.27	even	4		1274.2.d.c.883.1		2
35.32	odd	12		1274.2.n.d.961.2		4
40.27	even	4		832.2.f.b.129.1		2
40.37	odd	4		832.2.f.d.129.1		2
60.47	odd	4		1872.2.c.f.1585.1		2
65.2	even	12		338.2.c.f.191.1		2
65.7	even	12		338.2.c.b.315.1		2
65.8	even	4		8450.2.a.h.1.1		1
65.12	odd	4		26.2.b.a.25.2	yes	2
65.17	odd	12		338.2.e.c.23.2		4
65.18	even	4		8450.2.a.u.1.1		1
65.22	odd	12		338.2.e.c.23.1		4
65.32	even	12		338.2.c.f.315.1		2
65.37	even	12		338.2.c.b.191.1		2
65.38	odd	4		650.2.d.b.51.1		2
65.42	odd	12		338.2.e.c.147.2		4
65.47	even	4		338.2.a.d.1.1		1
65.57	even	4		338.2.a.b.1.1		1
65.62	odd	12		338.2.e.c.147.1		4
65.64	even	2	inner	650.2.c.a.649.2		2
195.47	odd	4		3042.2.a.g.1.1		1
195.77	even	4		234.2.b.b.181.1		2
195.122	odd	4		3042.2.a.j.1.1		1
260.47	odd	4		2704.2.a.j.1.1		1
260.187	odd	4		2704.2.a.k.1.1		1
260.207	even	4		208.2.f.a.129.1		2
455.12	even	12		1274.2.n.c.753.2		4
455.142	odd	12		1274.2.n.d.753.2		4
455.207	odd	12		1274.2.n.d.961.1		4
455.272	even	4		1274.2.d.c.883.2		2
455.402	even	12		1274.2.n.c.961.1		4
520.77	odd	4		832.2.f.d.129.2		2
520.467	even	4		832.2.f.b.129.2		2
780.467	odd	4		1872.2.c.f.1585.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.2.b.a.25.1	✓	2	5.2	odd	4
26.2.b.a.25.2	yes	2	65.12	odd	4
208.2.f.a.129.1		2	260.207	even	4
208.2.f.a.129.2		2	20.7	even	4
234.2.b.b.181.1		2	195.77	even	4
234.2.b.b.181.2		2	15.2	even	4
338.2.a.b.1.1		1	65.57	even	4
338.2.a.d.1.1		1	65.47	even	4
338.2.c.b.191.1		2	65.37	even	12
338.2.c.b.315.1		2	65.7	even	12
338.2.c.f.191.1		2	65.2	even	12
338.2.c.f.315.1		2	65.32	even	12
338.2.e.c.23.1		4	65.22	odd	12
338.2.e.c.23.2		4	65.17	odd	12
338.2.e.c.147.1		4	65.62	odd	12
338.2.e.c.147.2		4	65.42	odd	12
650.2.c.a.649.1		2	1.1	even	1	trivial
650.2.c.a.649.2		2	65.64	even	2	inner
650.2.c.d.649.1		2	13.12	even	2
650.2.c.d.649.2		2	5.4	even	2
650.2.d.b.51.1		2	65.38	odd	4
650.2.d.b.51.2		2	5.3	odd	4
832.2.f.b.129.1		2	40.27	even	4
832.2.f.b.129.2		2	520.467	even	4
832.2.f.d.129.1		2	40.37	odd	4
832.2.f.d.129.2		2	520.77	odd	4
1274.2.d.c.883.1		2	35.27	even	4
1274.2.d.c.883.2		2	455.272	even	4
1274.2.n.c.753.1		4	35.12	even	12
1274.2.n.c.753.2		4	455.12	even	12
1274.2.n.c.961.1		4	455.402	even	12
1274.2.n.c.961.2		4	35.17	even	12
1274.2.n.d.753.1		4	35.2	odd	12
1274.2.n.d.753.2		4	455.142	odd	12
1274.2.n.d.961.1		4	455.207	odd	12
1274.2.n.d.961.2		4	35.32	odd	12
1872.2.c.f.1585.1		2	60.47	odd	4
1872.2.c.f.1585.2		2	780.467	odd	4
2704.2.a.j.1.1		1	260.47	odd	4
2704.2.a.k.1.1		1	260.187	odd	4
3042.2.a.g.1.1		1	195.47	odd	4
3042.2.a.j.1.1		1	195.122	odd	4
8450.2.a.h.1.1		1	65.8	even	4
8450.2.a.u.1.1		1	65.18	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} -3.00000 q^{7} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} -3.00000 q^{7} -1.00000 q^{8} +2.00000 q^{9} -1.00000i q^{12} +(3.00000 + 2.00000i) q^{13} +3.00000 q^{14} +1.00000 q^{16} -3.00000i q^{17} -2.00000 q^{18} -6.00000i q^{19} +3.00000i q^{21} -6.00000i q^{23} +1.00000i q^{24} +(-3.00000 - 2.00000i) q^{26} -5.00000i q^{27} -3.00000 q^{28} -1.00000 q^{32} +3.00000i q^{34} +2.00000 q^{36} -3.00000 q^{37} +6.00000i q^{38} +(2.00000 - 3.00000i) q^{39} -3.00000i q^{42} -1.00000i q^{43} +6.00000i q^{46} -3.00000 q^{47} -1.00000i q^{48} +2.00000 q^{49} -3.00000 q^{51} +(3.00000 + 2.00000i) q^{52} -6.00000i q^{53} +5.00000i q^{54} +3.00000 q^{56} -6.00000 q^{57} -6.00000i q^{59} -8.00000 q^{61} -6.00000 q^{63} +1.00000 q^{64} +12.0000 q^{67} -3.00000i q^{68} -6.00000 q^{69} -15.0000i q^{71} -2.00000 q^{72} +6.00000 q^{73} +3.00000 q^{74} -6.00000i q^{76} +(-2.00000 + 3.00000i) q^{78} -10.0000 q^{79} +1.00000 q^{81} +6.00000 q^{83} +3.00000i q^{84} +1.00000i q^{86} -6.00000i q^{89} +(-9.00000 - 6.00000i) q^{91} -6.00000i q^{92} +3.00000 q^{94} +1.00000i q^{96} +12.0000 q^{97} -2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 6 q^{7} - 2 q^{8} + 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 6 * q^7 - 2 * q^8 + 4 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 6 q^{7} - 2 q^{8} + 4 q^{9} + 6 q^{13} + 6 q^{14} + 2 q^{16} - 4 q^{18} - 6 q^{26} - 6 q^{28} - 2 q^{32} + 4 q^{36} - 6 q^{37} + 4 q^{39} - 6 q^{47} + 4 q^{49} - 6 q^{51} + 6 q^{52} + 6 q^{56} - 12 q^{57} - 16 q^{61} - 12 q^{63} + 2 q^{64} + 24 q^{67} - 12 q^{69} - 4 q^{72} + 12 q^{73} + 6 q^{74} - 4 q^{78} - 20 q^{79} + 2 q^{81} + 12 q^{83} - 18 q^{91} + 6 q^{94} + 24 q^{97} - 4 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 6 * q^7 - 2 * q^8 + 4 * q^9 + 6 * q^13 + 6 * q^14 + 2 * q^16 - 4 * q^18 - 6 * q^26 - 6 * q^28 - 2 * q^32 + 4 * q^36 - 6 * q^37 + 4 * q^39 - 6 * q^47 + 4 * q^49 - 6 * q^51 + 6 * q^52 + 6 * q^56 - 12 * q^57 - 16 * q^61 - 12 * q^63 + 2 * q^64 + 24 * q^67 - 12 * q^69 - 4 * q^72 + 12 * q^73 + 6 * q^74 - 4 * q^78 - 20 * q^79 + 2 * q^81 + 12 * q^83 - 18 * q^91 + 6 * q^94 + 24 * q^97 - 4 * q^98

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