LMFDB - Embedded newform 1960.2.q.h.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,2,Mod(361,1960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1960, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1960.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1960.q (of order $3$, degree $2$, 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:	$15.6506787962$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.h.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	$q+(-0.500000 + 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{9} +(-2.00000 - 3.46410i) q^{11} -2.00000 q^{13} +(-1.00000 - 1.73205i) q^{17} +(-2.00000 + 3.46410i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.00000 q^{29} +(4.00000 + 6.92820i) q^{31} +(-3.00000 + 5.19615i) q^{37} -6.00000 q^{41} -8.00000 q^{43} +(1.50000 + 2.59808i) q^{45} +(-2.00000 + 3.46410i) q^{47} +(-3.00000 - 5.19615i) q^{53} +4.00000 q^{55} +(2.00000 + 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} +(1.00000 - 1.73205i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(3.00000 + 5.19615i) q^{73} +(-4.50000 - 7.79423i) q^{81} -16.0000 q^{83} +2.00000 q^{85} +(3.00000 - 5.19615i) q^{89} +(-2.00000 - 3.46410i) q^{95} -14.0000 q^{97} -12.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{5} + 3 q^{9}+O(q^{10}) $ 2 * q - q^5 + 3 * q^9	$ 2 q - q^{5} + 3 q^{9} - 4 q^{11} - 4 q^{13} - 2 q^{17} - 4 q^{19} - 4 q^{23} - q^{25} - 4 q^{29} + 8 q^{31} - 6 q^{37} - 12 q^{41} - 16 q^{43} + 3 q^{45} - 4 q^{47} - 6 q^{53} + 8 q^{55} + 4 q^{59} + 2 q^{61} + 2 q^{65} - 8 q^{67} + 6 q^{73} - 9 q^{81} - 32 q^{83} + 4 q^{85} + 6 q^{89} - 4 q^{95} - 28 q^{97} - 24 q^{99}+O(q^{100}) $ 2 * q - q^5 + 3 * q^9 - 4 * q^11 - 4 * q^13 - 2 * q^17 - 4 * q^19 - 4 * q^23 - q^25 - 4 * q^29 + 8 * q^31 - 6 * q^37 - 12 * q^41 - 16 * q^43 + 3 * q^45 - 4 * q^47 - 6 * q^53 + 8 * q^55 + 4 * q^59 + 2 * q^61 + 2 * q^65 - 8 * q^67 + 6 * q^73 - 9 * q^81 - 32 * q^83 + 4 * q^85 + 6 * q^89 - 4 * q^95 - 28 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$		0			0
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	−0.999969	−	0.00783774i	$-0.997505\pi$
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	0.506772	+	0.862080i	$0.330838\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$	1.50000	+	2.59808i	0.223607	+	0.387298i
$46$		0			0
$47$	−2.00000	+	3.46410i	−0.291730	+	0.505291i	−0.974219	−	0.225605i	$-0.927564\pi$
$47$	−2.00000	+	3.46410i	−0.291730	+	0.505291i	0.682489	+	0.730896i	$0.260898\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$		0			0
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	0.986447	−	0.164083i	$-0.0524664\pi$
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	−0.635323	+	0.772246i	$0.719133\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−16.0000			−1.75623			−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000			−1.75623			−0.878114	+	0.478451i	$0.841198\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.00000	−	3.46410i	−0.205196	−	0.355409i
$96$		0			0
$97$	−14.0000			−1.42148			−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000			−1.42148			−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$	−12.0000			−1.20605
$100$		0			0
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$		0			0
$117$	−3.00000	+	5.19615i	−0.277350	+	0.480384i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	0.569442	−	0.822031i	$-0.307159\pi$
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	−0.996621	+	0.0821359i	$0.973826\pi$
$138$		0			0
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.00000	+	6.92820i	0.334497	+	0.579365i
$144$		0			0
$145$	1.00000	−	1.73205i	0.0830455	−	0.143839i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$		0			0
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$		0			0
$155$	−8.00000			−0.642575
$156$		0			0
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	0.903167	−	0.429289i	$-0.141236\pi$
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	−0.823359	+	0.567521i	$0.807902\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−8.00000	+	13.8564i	−0.626608	+	1.08532i	0.361619	+	0.932326i	$0.382224\pi$
$163$	−8.00000	+	13.8564i	−0.626608	+	1.08532i	−0.988227	+	0.152992i	$0.951109\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	6.00000	+	10.3923i	0.458831	+	0.794719i
$172$		0			0
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	0.467093	+	0.884208i	$0.345301\pi$
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	−0.999293	+	0.0375896i	$0.988032\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	−0.949048	−	0.315130i	$-0.897952\pi$
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	0.201613	−	0.979465i	$-0.435382\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$		0			0
$187$	−4.00000	+	6.92820i	−0.292509	+	0.506640i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$		0			0
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	0.999990	+	0.00447566i	$0.00142465\pi$
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	−0.496119	+	0.868255i	$0.665242\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	22.0000			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$198$		0			0
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$		0			0
$207$	6.00000	+	10.3923i	0.417029	+	0.722315i
$208$		0			0
$209$	16.0000			1.10674
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.00000	−	6.92820i	0.272798	−	0.472500i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.00000	+	3.46410i	0.134535	+	0.233021i
$222$		0			0
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$		0			0
$225$	−3.00000			−0.200000
$226$		0			0
$227$	12.0000	+	20.7846i	0.796468	+	1.37952i	0.921903	+	0.387421i	$0.126634\pi$
$227$	12.0000	+	20.7846i	0.796468	+	1.37952i	−0.125435	+	0.992102i	$0.540033\pi$
$228$		0			0
$229$	13.0000	−	22.5167i	0.859064	−	1.48794i	−0.0137585	−	0.999905i	$-0.504380\pi$
$229$	13.0000	−	22.5167i	0.859064	−	1.48794i	0.872823	−	0.488037i	$-0.162287\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$		0			0
$235$	−2.00000	−	3.46410i	−0.130466	−	0.225973i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	0.832019	−	0.554747i	$-0.187185\pi$
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	−0.896435	+	0.443176i	$0.853852\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	16.0000			1.00591
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.162247	−	0.986750i	$-0.448126\pi$
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.773427	−	0.633885i	$-0.218541\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$		0			0
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	0.569789	−	0.821791i	$-0.307025\pi$
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	−0.996586	+	0.0825561i	$0.973692\pi$
$270$		0			0
$271$	−12.0000	+	20.7846i	−0.728948	+	1.26258i	0.228380	+	0.973572i	$0.426657\pi$
$271$	−12.0000	+	20.7846i	−0.728948	+	1.26258i	−0.957328	+	0.289003i	$0.906676\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$		0			0
$279$	24.0000			1.43684
$280$		0			0
$281$	10.0000			0.596550			0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000			0.596550			0.298275	+	0.954480i	$0.403589\pi$
$282$		0			0
$283$	−4.00000	−	6.92820i	−0.237775	−	0.411839i	0.722300	−	0.691580i	$-0.243085\pi$
$283$	−4.00000	−	6.92820i	−0.237775	−	0.411839i	−0.960076	+	0.279741i	$0.909752\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−26.0000			−1.51894			−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000			−1.51894			−0.759468	+	0.650545i	$0.774541\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.00000	−	6.92820i	0.231326	−	0.400668i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.00000	+	1.73205i	0.0572598	+	0.0991769i
$306$		0			0
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−16.0000	−	27.7128i	−0.907277	−	1.57145i	−0.817832	−	0.575458i	$-0.804824\pi$
$311$	−16.0000	−	27.7128i	−0.907277	−	1.57145i	−0.0894452	−	0.995992i	$-0.528509\pi$
$312$		0			0
$313$	−13.0000	+	22.5167i	−0.734803	+	1.27272i	0.220006	+	0.975499i	$0.429392\pi$
$313$	−13.0000	+	22.5167i	−0.734803	+	1.27272i	−0.954810	+	0.297218i	$0.903941\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$	4.00000	+	6.92820i	0.223957	+	0.387905i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	8.00000			0.445132
$324$		0			0
$325$	1.00000	+	1.73205i	0.0554700	+	0.0960769i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	−0.652680	−	0.757634i	$-0.726355\pi$
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	0.982470	+	0.186421i	$0.0596888\pi$
$332$		0			0
$333$	9.00000	+	15.5885i	0.493197	+	0.854242i
$334$		0			0
$335$	8.00000			0.437087
$336$		0			0
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	16.0000	−	27.7128i	0.866449	−	1.50073i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.00000	+	13.8564i	0.429463	+	0.743851i	0.996826	−	0.0796169i	$-0.0253697\pi$
$347$	8.00000	+	13.8564i	0.429463	+	0.743851i	−0.567363	+	0.823468i	$0.692036\pi$
$348$		0			0
$349$	30.0000			1.60586			0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000			1.60586			0.802932	+	0.596071i	$0.203272\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.00000	−	1.73205i	−0.0532246	−	0.0921878i	0.838186	−	0.545385i	$-0.183617\pi$
$353$	−1.00000	−	1.73205i	−0.0532246	−	0.0921878i	−0.891410	+	0.453197i	$0.850283\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.00000			−0.314054
$366$		0			0
$367$	−10.0000	−	17.3205i	−0.521996	−	0.904123i	−0.999673	−	0.0255875i	$-0.991854\pi$
$367$	−10.0000	−	17.3205i	−0.521996	−	0.904123i	0.477677	−	0.878536i	$-0.341479\pi$
$368$		0			0
$369$	−9.00000	+	15.5885i	−0.468521	+	0.811503i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	0.427051	+	0.904227i	$0.359552\pi$
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	−0.996610	+	0.0822766i	$0.973781\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.00000			0.206010
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	18.0000	−	31.1769i	0.919757	−	1.59307i	0.119974	−	0.992777i	$-0.461719\pi$
$383$	18.0000	−	31.1769i	0.919757	−	1.59307i	0.799783	−	0.600289i	$-0.204948\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−12.0000	+	20.7846i	−0.609994	+	1.05654i
$388$		0			0
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$		0			0
$391$	8.00000			0.404577
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	−0.839840	−	0.542834i	$-0.817351\pi$
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	0.890028	+	0.455905i	$0.150684\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$		0			0
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$		0			0
$405$	9.00000			0.447214
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	8.00000	−	13.8564i	0.392705	−	0.680184i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	36.0000			1.75872			0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000			1.75872			0.879358	+	0.476162i	$0.157972\pi$
$420$		0			0
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$		0			0
$423$	6.00000	+	10.3923i	0.291730	+	0.505291i
$424$		0			0
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	20.0000	+	34.6410i	0.963366	+	1.66860i	0.713942	+	0.700205i	$0.246908\pi$
$431$	20.0000	+	34.6410i	0.963366	+	1.66860i	0.249424	+	0.968394i	$0.419759\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.00000	−	13.8564i	−0.382692	−	0.662842i
$438$		0			0
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	0.426414	+	0.904528i	$0.359777\pi$
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	−0.996551	+	0.0829786i	$0.973557\pi$
$444$		0			0
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	12.0000	+	20.7846i	0.565058	+	0.978709i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	12.0000			0.557687			0.278844	−	0.960337i	$-0.410049\pi$
$463$	12.0000			0.557687			0.278844	+	0.960337i	$0.410049\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.00000	+	6.92820i	−0.185098	+	0.320599i	−0.943610	−	0.331061i	$-0.892594\pi$
$467$	−4.00000	+	6.92820i	−0.185098	+	0.320599i	0.758512	+	0.651660i	$0.225927\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	16.0000	+	27.7128i	0.735681	+	1.27424i
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$	−18.0000			−0.824163
$478$		0			0
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	0.623332	−	0.781958i	$-0.285779\pi$
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	−0.988861	+	0.148842i	$0.952445\pi$
$480$		0			0
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.00000	−	12.1244i	0.317854	−	0.550539i
$486$		0			0
$487$	10.0000	+	17.3205i	0.453143	+	0.784867i	0.998579	−	0.0532853i	$-0.0169693\pi$
$487$	10.0000	+	17.3205i	0.453143	+	0.784867i	−0.545436	+	0.838152i	$0.683636\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	36.0000			1.62466			0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000			1.62466			0.812329	+	0.583200i	$0.198200\pi$
$492$		0			0
$493$	2.00000	+	3.46410i	0.0900755	+	0.156015i
$494$		0			0
$495$	6.00000	−	10.3923i	0.269680	−	0.467099i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	−0.361478	−	0.932381i	$-0.617728\pi$
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	0.988204	−	0.153141i	$-0.0489388\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.00000	−	1.73205i	0.0443242	−	0.0767718i	−0.843012	−	0.537895i	$-0.819220\pi$
$509$	1.00000	−	1.73205i	0.0443242	−	0.0767718i	0.887336	+	0.461123i	$0.152553\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$		0			0
$517$	16.0000			0.703679
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5.00000	−	8.66025i	−0.219054	−	0.379413i	0.735465	−	0.677563i	$-0.236964\pi$
$521$	−5.00000	−	8.66025i	−0.219054	−	0.379413i	−0.954519	+	0.298150i	$0.903630\pi$
$522$		0			0
$523$	4.00000	−	6.92820i	0.174908	−	0.302949i	−0.765222	−	0.643767i	$-0.777371\pi$
$523$	4.00000	−	6.92820i	0.174908	−	0.302949i	0.940129	+	0.340818i	$0.110704\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.00000	−	13.8564i	0.348485	−	0.603595i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	12.0000			0.520756
$532$		0			0
$533$	12.0000			0.519778
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	1.00000	−	1.73205i	0.0429934	−	0.0744667i	−0.843728	−	0.536771i	$-0.819644\pi$
$541$	1.00000	−	1.73205i	0.0429934	−	0.0744667i	0.886721	+	0.462304i	$0.152977\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	14.0000			0.599694
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$		0			0
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$		0			0
$551$	4.00000	−	6.92820i	0.170406	−	0.295151i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.00000	−	12.1244i	−0.296600	−	0.513725i	0.678756	−	0.734364i	$-0.262519\pi$
$557$	−7.00000	−	12.1244i	−0.296600	−	0.513725i	−0.975356	+	0.220638i	$0.929186\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−8.00000	−	13.8564i	−0.337160	−	0.583978i	0.646737	−	0.762713i	$-0.276133\pi$
$563$	−8.00000	−	13.8564i	−0.337160	−	0.583978i	−0.983897	+	0.178735i	$0.942800\pi$
$564$		0			0
$565$	−9.00000	+	15.5885i	−0.378633	+	0.655811i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11.0000	−	19.0526i	0.461144	−	0.798725i	−0.537874	−	0.843025i	$-0.680772\pi$
$569$	11.0000	−	19.0526i	0.461144	−	0.798725i	0.999018	+	0.0443003i	$0.0141058\pi$
$570$		0			0
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.00000			0.166812
$576$		0			0
$577$	−1.00000	−	1.73205i	−0.0416305	−	0.0721062i	0.844459	−	0.535620i	$-0.179922\pi$
$577$	−1.00000	−	1.73205i	−0.0416305	−	0.0721062i	−0.886090	+	0.463513i	$0.846589\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−12.0000	+	20.7846i	−0.496989	+	0.860811i
$584$		0			0
$585$	−3.00000	−	5.19615i	−0.124035	−	0.214834i
$586$		0			0
$587$	−48.0000			−1.98117			−0.990586	−	0.136892i	$-0.956289\pi$
$587$	−48.0000			−1.98117			−0.990586	+	0.136892i	$0.956289\pi$
$588$		0			0
$589$	−32.0000			−1.31854
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−9.00000	+	15.5885i	−0.369586	+	0.640141i	−0.989501	−	0.144528i	$-0.953834\pi$
$593$	−9.00000	+	15.5885i	−0.369586	+	0.640141i	0.619915	+	0.784669i	$0.287167\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	−24.0000			−0.977356
$604$		0			0
$605$	−2.50000	−	4.33013i	−0.101639	−	0.176045i
$606$		0			0
$607$	6.00000	−	10.3923i	0.243532	−	0.421811i	−0.718186	−	0.695852i	$-0.755027\pi$
$607$	6.00000	−	10.3923i	0.243532	−	0.421811i	0.961718	+	0.274041i	$0.0883604\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.00000	−	6.92820i	0.161823	−	0.280285i
$612$		0			0
$613$	21.0000	+	36.3731i	0.848182	+	1.46909i	0.882829	+	0.469695i	$0.155636\pi$
$613$	21.0000	+	36.3731i	0.848182	+	1.46909i	−0.0346469	+	0.999400i	$0.511031\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	0.903416	−	0.428765i	$-0.141051\pi$
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	−0.823029	+	0.567999i	$0.807718\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	12.0000			0.478471
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.00000	−	10.3923i	0.238103	−	0.412406i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	0.631721	−	0.775196i	$-0.282349\pi$
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	−0.987200	+	0.159489i	$0.949015\pi$
$642$		0			0
$643$	−48.0000			−1.89294			−0.946468	−	0.322799i	$-0.895376\pi$
$643$	−48.0000			−1.89294			−0.946468	+	0.322799i	$0.895376\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	0.723645	−	0.690172i	$-0.242465\pi$
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	−0.959529	+	0.281609i	$0.909132\pi$
$648$		0			0
$649$	8.00000	−	13.8564i	0.314027	−	0.543912i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	17.0000	−	29.4449i	0.665261	−	1.15227i	−0.313953	−	0.949439i	$-0.601653\pi$
$653$	17.0000	−	29.4449i	0.665261	−	1.15227i	0.979214	−	0.202828i	$-0.0650132\pi$
$654$		0			0
$655$	−6.00000	−	10.3923i	−0.234439	−	0.406061i
$656$		0			0
$657$	18.0000			0.702247
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$	21.0000	+	36.3731i	0.816805	+	1.41475i	0.908024	+	0.418917i	$0.137590\pi$
$661$	21.0000	+	36.3731i	0.816805	+	1.41475i	−0.0912190	+	0.995831i	$0.529076\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.00000	−	6.92820i	0.154881	−	0.268261i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−8.00000			−0.308837
$672$		0			0
$673$	18.0000			0.693849			0.346925	−	0.937893i	$-0.387226\pi$
$673$	18.0000			0.693849			0.346925	+	0.937893i	$0.387226\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.0000	+	19.0526i	−0.422764	+	0.732249i	−0.996209	−	0.0869952i	$-0.972274\pi$
$677$	−11.0000	+	19.0526i	−0.422764	+	0.732249i	0.573444	+	0.819244i	$0.305607\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	0.539750	−	0.841825i	$-0.318519\pi$
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	−0.998917	+	0.0465244i	$0.985185\pi$
$684$		0			0
$685$	10.0000			0.382080
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.00000	+	10.3923i	−0.227593	+	0.394203i
$696$		0			0
$697$	6.00000	+	10.3923i	0.227266	+	0.393637i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$		0			0
$703$	−12.0000	−	20.7846i	−0.452589	−	0.783906i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−32.0000			−1.19841
$714$		0			0
$715$	−8.00000			−0.299183
$716$		0			0
$717$		0			0
$718$		0			0
$719$	16.0000	−	27.7128i	0.596699	−	1.03351i	−0.396605	−	0.917989i	$-0.629812\pi$
$719$	16.0000	−	27.7128i	0.596699	−	1.03351i	0.993305	−	0.115524i	$-0.0368548\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$		0			0
$727$	44.0000			1.63187			0.815935	−	0.578144i	$-0.196223\pi$
$727$	44.0000			1.63187			0.815935	+	0.578144i	$0.196223\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	8.00000	+	13.8564i	0.295891	+	0.512498i
$732$		0			0
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	0.443940	+	0.896056i	$0.353580\pi$
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	−0.997978	+	0.0635649i	$0.979753\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.0000	+	27.7128i	−0.589368	+	1.02081i
$738$		0			0
$739$	−18.0000	−	31.1769i	−0.662141	−	1.14686i	−0.980052	−	0.198741i	$-0.936315\pi$
$739$	−18.0000	−	31.1769i	−0.662141	−	1.14686i	0.317911	−	0.948120i	$-0.397019\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	36.0000			1.32071			0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000			1.32071			0.660356	+	0.750953i	$0.270405\pi$
$744$		0			0
$745$	5.00000	+	8.66025i	0.183186	+	0.317287i
$746$		0			0
$747$	−24.0000	+	41.5692i	−0.878114	+	1.52094i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	12.0000	−	20.7846i	0.437886	−	0.758441i	−0.559640	−	0.828736i	$-0.689061\pi$
$751$	12.0000	−	20.7846i	0.437886	−	0.758441i	0.997526	+	0.0702946i	$0.0223939\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−16.0000			−0.582300
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.00000	−	5.19615i	0.108465	−	0.187867i
$766$		0			0
$767$	−4.00000	−	6.92820i	−0.144432	−	0.250163i
$768$		0			0
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	21.0000	+	36.3731i	0.755318	+	1.30825i	0.945216	+	0.326445i	$0.105851\pi$
$773$	21.0000	+	36.3731i	0.755318	+	1.30825i	−0.189899	+	0.981804i	$0.560816\pi$
$774$		0			0
$775$	4.00000	−	6.92820i	0.143684	−	0.248868i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.0000	−	20.7846i	0.429945	−	0.744686i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.00000			−0.0713831
$786$		0			0
$787$	−4.00000	−	6.92820i	−0.142585	−	0.246964i	0.785885	−	0.618373i	$-0.212208\pi$
$787$	−4.00000	−	6.92820i	−0.142585	−	0.246964i	−0.928469	+	0.371409i	$0.878875\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2.00000	+	3.46410i	−0.0710221	+	0.123014i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$		0			0
$799$	8.00000			0.283020
$800$		0			0
$801$	−9.00000	−	15.5885i	−0.317999	−	0.550791i
$802$		0			0
$803$	12.0000	−	20.7846i	0.423471	−	0.733473i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	−0.953251	−	0.302180i	$-0.902286\pi$
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	0.214930	−	0.976629i	$-0.431048\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−8.00000	−	13.8564i	−0.280228	−	0.485369i
$816$		0			0
$817$	16.0000	−	27.7128i	0.559769	−	0.969549i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$		0			0
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	0.829060	−	0.559159i	$-0.188876\pi$
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	−0.898776	+	0.438408i	$0.855543\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	48.0000			1.66912			0.834562	−	0.550914i	$-0.185721\pi$
$827$	48.0000			1.66912			0.834562	+	0.550914i	$0.185721\pi$
$828$		0			0
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−6.00000	+	10.3923i	−0.207639	+	0.359641i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−40.0000			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$		0			0
$853$	38.0000			1.30110			0.650548	−	0.759465i	$-0.274539\pi$
$853$	38.0000			1.30110			0.650548	+	0.759465i	$0.274539\pi$
$854$		0			0
$855$	−12.0000			−0.410391
$856$		0			0
$857$	3.00000	+	5.19615i	0.102478	+	0.177497i	0.912705	−	0.408619i	$-0.133990\pi$
$857$	3.00000	+	5.19615i	0.102478	+	0.177497i	−0.810227	+	0.586116i	$0.800656\pi$
$858$		0			0
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−6.00000	+	10.3923i	−0.204242	+	0.353758i	−0.949891	−	0.312581i	$-0.898806\pi$
$863$	−6.00000	+	10.3923i	−0.204242	+	0.353758i	0.745649	+	0.666339i	$0.232140\pi$
$864$		0			0
$865$	−7.00000	−	12.1244i	−0.238007	−	0.412240i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	8.00000	+	13.8564i	0.271070	+	0.469506i
$872$		0			0
$873$	−21.0000	+	36.3731i	−0.710742	+	1.23104i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−23.0000	+	39.8372i	−0.776655	+	1.34521i	0.157205	+	0.987566i	$0.449752\pi$
$877$	−23.0000	+	39.8372i	−0.776655	+	1.34521i	−0.933860	+	0.357640i	$0.883582\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	−16.0000			−0.538443			−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000			−0.538443			−0.269221	+	0.963078i	$0.586766\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.0000	−	17.3205i	0.335767	−	0.581566i	−0.647865	−	0.761755i	$-0.724338\pi$
$887$	10.0000	−	17.3205i	0.335767	−	0.581566i	0.983632	+	0.180190i	$0.0576711\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−18.0000	+	31.1769i	−0.603023	+	1.04447i
$892$		0			0
$893$	−8.00000	−	13.8564i	−0.267710	−	0.463687i
$894$		0			0
$895$	20.0000			0.668526
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−8.00000	−	13.8564i	−0.266815	−	0.462137i
$900$		0			0
$901$	−6.00000	+	10.3923i	−0.199889	+	0.346218i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.00000	−	8.66025i	0.166206	−	0.287877i
$906$		0			0
$907$	−24.0000	−	41.5692i	−0.796907	−	1.38028i	−0.921621	−	0.388091i	$-0.873135\pi$
$907$	−24.0000	−	41.5692i	−0.796907	−	1.38028i	0.124714	−	0.992193i	$-0.460199\pi$
$908$		0			0
$909$	−18.0000			−0.597022
$910$		0			0
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$		0			0
$913$	32.0000	+	55.4256i	1.05905	+	1.83432i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	6.00000			0.197279
$926$		0			0
$927$	6.00000	+	10.3923i	0.197066	+	0.341328i
$928$		0			0
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	−0.728046	−	0.685529i	$-0.759571\pi$
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	0.957708	+	0.287742i	$0.0929044\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−4.00000	−	6.92820i	−0.130814	−	0.226576i
$936$		0			0
$937$	−38.0000			−1.24141			−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000			−1.24141			−0.620703	+	0.784046i	$0.713153\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−23.0000	−	39.8372i	−0.749779	−	1.29865i	−0.947929	−	0.318483i	$-0.896827\pi$
$941$	−23.0000	−	39.8372i	−0.749779	−	1.29865i	0.198150	−	0.980172i	$-0.436507\pi$
$942$		0			0
$943$	12.0000	−	20.7846i	0.390774	−	0.676840i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.00000	−	6.92820i	0.129983	−	0.225136i	−0.793687	−	0.608326i	$-0.791841\pi$
$947$	4.00000	−	6.92820i	0.129983	−	0.225136i	0.923670	+	0.383190i	$0.125175\pi$
$948$		0			0
$949$	−6.00000	−	10.3923i	−0.194768	−	0.337348i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$	−4.00000	−	6.92820i	−0.129437	−	0.224191i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−14.0000			−0.450676
$966$		0			0
$967$	−36.0000			−1.15768			−0.578841	−	0.815440i	$-0.696495\pi$
$967$	−36.0000			−1.15768			−0.578841	+	0.815440i	$0.696495\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−10.0000	+	17.3205i	−0.320915	+	0.555842i	−0.980677	−	0.195633i	$-0.937324\pi$
$971$	−10.0000	+	17.3205i	−0.320915	+	0.555842i	0.659762	+	0.751475i	$0.270657\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.00000	−	1.73205i	−0.0319928	−	0.0554132i	0.849586	−	0.527451i	$-0.176852\pi$
$977$	−1.00000	−	1.73205i	−0.0319928	−	0.0554132i	−0.881579	+	0.472037i	$0.843519\pi$
$978$		0			0
$979$	−24.0000			−0.767043
$980$		0			0
$981$	−42.0000			−1.34096
$982$		0			0
$983$	−18.0000	−	31.1769i	−0.574111	−	0.994389i	−0.996138	−	0.0878058i	$-0.972015\pi$
$983$	−18.0000	−	31.1769i	−0.574111	−	0.994389i	0.422027	−	0.906583i	$-0.361319\pi$
$984$		0			0
$985$	−11.0000	+	19.0526i	−0.350489	+	0.607065i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	16.0000	−	27.7128i	0.508770	−	0.881216i
$990$		0			0
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	0.986447	+	0.164080i	$0.0524655\pi$
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	−0.351126	+	0.936328i	$0.614201\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8.00000			0.253617
$996$		0			0
$997$	21.0000	+	36.3731i	0.665077	+	1.15195i	0.979265	+	0.202586i	$0.0649345\pi$
$997$	21.0000	+	36.3731i	0.665077	+	1.15195i	−0.314188	+	0.949361i	$0.601732\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.h.961.1		2
7.2	even	3		40.2.a.a.1.1	✓	1
7.3	odd	6		1960.2.q.i.361.1		2
7.4	even	3	inner	1960.2.q.h.361.1		2
7.5	odd	6		1960.2.a.g.1.1		1
7.6	odd	2		1960.2.q.i.961.1		2
21.2	odd	6		360.2.a.a.1.1		1
28.19	even	6		3920.2.a.s.1.1		1
28.23	odd	6		80.2.a.a.1.1		1
35.2	odd	12		200.2.c.b.49.1		2
35.9	even	6		200.2.a.c.1.1		1
35.19	odd	6		9800.2.a.x.1.1		1
35.23	odd	12		200.2.c.b.49.2		2
56.37	even	6		320.2.a.c.1.1		1
56.51	odd	6		320.2.a.d.1.1		1
63.2	odd	6		3240.2.q.x.1081.1		2
63.16	even	3		3240.2.q.k.1081.1		2
63.23	odd	6		3240.2.q.x.2161.1		2
63.58	even	3		3240.2.q.k.2161.1		2
77.65	odd	6		4840.2.a.f.1.1		1
84.23	even	6		720.2.a.e.1.1		1
91.51	even	6		6760.2.a.i.1.1		1
105.2	even	12		1800.2.f.a.649.1		2
105.23	even	12		1800.2.f.a.649.2		2
105.44	odd	6		1800.2.a.v.1.1		1
112.37	even	12		1280.2.d.j.641.2		2
112.51	odd	12		1280.2.d.a.641.1		2
112.93	even	12		1280.2.d.j.641.1		2
112.107	odd	12		1280.2.d.a.641.2		2
140.23	even	12		400.2.c.d.49.1		2
140.79	odd	6		400.2.a.e.1.1		1
140.107	even	12		400.2.c.d.49.2		2
168.107	even	6		2880.2.a.bg.1.1		1
168.149	odd	6		2880.2.a.t.1.1		1
280.37	odd	12		1600.2.c.k.449.1		2
280.93	odd	12		1600.2.c.k.449.2		2
280.107	even	12		1600.2.c.m.449.2		2
280.149	even	6		1600.2.a.o.1.1		1
280.163	even	12		1600.2.c.m.449.1		2
280.219	odd	6		1600.2.a.k.1.1		1
308.219	even	6		9680.2.a.q.1.1		1
420.23	odd	12		3600.2.f.t.2449.1		2
420.107	odd	12		3600.2.f.t.2449.2		2
420.359	even	6		3600.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.a.a.1.1	✓	1	7.2	even	3
80.2.a.a.1.1		1	28.23	odd	6
200.2.a.c.1.1		1	35.9	even	6
200.2.c.b.49.1		2	35.2	odd	12
200.2.c.b.49.2		2	35.23	odd	12
320.2.a.c.1.1		1	56.37	even	6
320.2.a.d.1.1		1	56.51	odd	6
360.2.a.a.1.1		1	21.2	odd	6
400.2.a.e.1.1		1	140.79	odd	6
400.2.c.d.49.1		2	140.23	even	12
400.2.c.d.49.2		2	140.107	even	12
720.2.a.e.1.1		1	84.23	even	6
1280.2.d.a.641.1		2	112.51	odd	12
1280.2.d.a.641.2		2	112.107	odd	12
1280.2.d.j.641.1		2	112.93	even	12
1280.2.d.j.641.2		2	112.37	even	12
1600.2.a.k.1.1		1	280.219	odd	6
1600.2.a.o.1.1		1	280.149	even	6
1600.2.c.k.449.1		2	280.37	odd	12
1600.2.c.k.449.2		2	280.93	odd	12
1600.2.c.m.449.1		2	280.163	even	12
1600.2.c.m.449.2		2	280.107	even	12
1800.2.a.v.1.1		1	105.44	odd	6
1800.2.f.a.649.1		2	105.2	even	12
1800.2.f.a.649.2		2	105.23	even	12
1960.2.a.g.1.1		1	7.5	odd	6
1960.2.q.h.361.1		2	7.4	even	3	inner
1960.2.q.h.961.1		2	1.1	even	1	trivial
1960.2.q.i.361.1		2	7.3	odd	6
1960.2.q.i.961.1		2	7.6	odd	2
2880.2.a.t.1.1		1	168.149	odd	6
2880.2.a.bg.1.1		1	168.107	even	6
3240.2.q.k.1081.1		2	63.16	even	3
3240.2.q.k.2161.1		2	63.58	even	3
3240.2.q.x.1081.1		2	63.2	odd	6
3240.2.q.x.2161.1		2	63.23	odd	6
3600.2.a.h.1.1		1	420.359	even	6
3600.2.f.t.2449.1		2	420.23	odd	12
3600.2.f.t.2449.2		2	420.107	odd	12
3920.2.a.s.1.1		1	28.19	even	6
4840.2.a.f.1.1		1	77.65	odd	6
6760.2.a.i.1.1		1	91.51	even	6
9680.2.a.q.1.1		1	308.219	even	6
9800.2.a.x.1.1		1	35.19	odd	6

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:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{9} +(-2.00000 - 3.46410i) q^{11} -2.00000 q^{13} +(-1.00000 - 1.73205i) q^{17} +(-2.00000 + 3.46410i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.00000 q^{29} +(4.00000 + 6.92820i) q^{31} +(-3.00000 + 5.19615i) q^{37} -6.00000 q^{41} -8.00000 q^{43} +(1.50000 + 2.59808i) q^{45} +(-2.00000 + 3.46410i) q^{47} +(-3.00000 - 5.19615i) q^{53} +4.00000 q^{55} +(2.00000 + 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} +(1.00000 - 1.73205i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(3.00000 + 5.19615i) q^{73} +(-4.50000 - 7.79423i) q^{81} -16.0000 q^{83} +2.00000 q^{85} +(3.00000 - 5.19615i) q^{89} +(-2.00000 - 3.46410i) q^{95} -14.0000 q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{5} + 3 q^{9}+O(q^{10}) \) 2 * q - q^5 + 3 * q^9	\( 2 q - q^{5} + 3 q^{9} - 4 q^{11} - 4 q^{13} - 2 q^{17} - 4 q^{19} - 4 q^{23} - q^{25} - 4 q^{29} + 8 q^{31} - 6 q^{37} - 12 q^{41} - 16 q^{43} + 3 q^{45} - 4 q^{47} - 6 q^{53} + 8 q^{55} + 4 q^{59} + 2 q^{61} + 2 q^{65} - 8 q^{67} + 6 q^{73} - 9 q^{81} - 32 q^{83} + 4 q^{85} + 6 q^{89} - 4 q^{95} - 28 q^{97} - 24 q^{99}+O(q^{100}) \) 2 * q - q^5 + 3 * q^9 - 4 * q^11 - 4 * q^13 - 2 * q^17 - 4 * q^19 - 4 * q^23 - q^25 - 4 * q^29 + 8 * q^31 - 6 * q^37 - 12 * q^41 - 16 * q^43 + 3 * q^45 - 4 * q^47 - 6 * q^53 + 8 * q^55 + 4 * q^59 + 2 * q^61 + 2 * q^65 - 8 * q^67 + 6 * q^73 - 9 * q^81 - 32 * q^83 + 4 * q^85 + 6 * q^89 - 4 * q^95 - 28 * q^97 - 24 * q^99

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