LMFDB - Embedded newform 1600.2.l.h.401.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(401,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("1600.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.l (of order $4$, 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			401.3
Root			$0.841995 - 1.13624i$ of defining polynomial
Character	$\chi$	$=$	1600.401
Dual form			1600.2.l.h.1201.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.734294 - 0.734294i) q^{3} +1.71452i q^{7} -1.92163i q^{9} +O(q^{10})$	$q+(-0.734294 - 0.734294i) q^{3} +1.71452i q^{7} -1.92163i q^{9} +(-2.82684 + 2.82684i) q^{11} +(-2.59462 - 2.59462i) q^{13} +1.89939 q^{17} +(2.89623 + 2.89623i) q^{19} +(1.25896 - 1.25896i) q^{21} -2.00613i q^{23} +(-3.61392 + 3.61392i) q^{27} +(6.72307 + 6.72307i) q^{29} +7.11778 q^{31} +4.15146 q^{33} +(2.25207 - 2.25207i) q^{37} +3.81042i q^{39} +1.59630i q^{41} +(-8.06886 + 8.06886i) q^{43} -4.43823 q^{47} +4.06040 q^{49} +(-1.39471 - 1.39471i) q^{51} +(-0.481758 + 0.481758i) q^{53} -4.25336i q^{57} +(3.08580 - 3.08580i) q^{59} +(3.46410 + 3.46410i) q^{61} +3.29468 q^{63} +(1.80454 + 1.80454i) q^{67} +(-1.47309 + 1.47309i) q^{69} -0.379150i q^{71} +8.37718i q^{73} +(-4.84668 - 4.84668i) q^{77} +11.2566 q^{79} -0.457524 q^{81} +(8.24890 + 8.24890i) q^{83} -9.87341i q^{87} +11.9820i q^{89} +(4.44854 - 4.44854i) q^{91} +(-5.22654 - 5.22654i) q^{93} +6.50543 q^{97} +(5.43213 + 5.43213i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{19} - 16 q^{21} + 16 q^{29} - 16 q^{31} - 16 q^{49} + 16 q^{51} - 24 q^{59} - 32 q^{69} + 16 q^{79} - 16 q^{81} + 16 q^{91} + 88 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^19 - 16 * q^21 + 16 * q^29 - 16 * q^31 - 16 * q^49 + 16 * q^51 - 24 * q^59 - 32 * q^69 + 16 * q^79 - 16 * q^81 + 16 * q^91 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−0.734294	−	0.734294i	−0.423945	−	0.423945i	0.462615	−	0.886559i	$-0.346911\pi$
$3$	−0.734294	−	0.734294i	−0.423945	−	0.423945i	−0.886559	+	0.462615i	$0.846911\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			1.71452i			0.648029i	0.946052	+	0.324015i	$0.105033\pi$
$7$			1.71452i			0.648029i	−0.946052	+	0.324015i	$0.894967\pi$
$8$		0			0
$9$		−	1.92163i		−	0.640542i
$10$		0			0
$11$	−2.82684	+	2.82684i	−0.852324	+	0.852324i	−0.990419	−	0.138095i	$-0.955902\pi$
$11$	−2.82684	+	2.82684i	−0.852324	+	0.852324i	0.138095	+	0.990419i	$0.455902\pi$
$12$		0			0
$13$	−2.59462	−	2.59462i	−0.719618	−	0.719618i	0.248909	−	0.968527i	$-0.419928\pi$
$13$	−2.59462	−	2.59462i	−0.719618	−	0.719618i	−0.968527	+	0.248909i	$0.919928\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.89939			0.460671			0.230335	−	0.973111i	$-0.426018\pi$
$17$	1.89939			0.460671			0.230335	+	0.973111i	$0.426018\pi$
$18$		0			0
$19$	2.89623	+	2.89623i	0.664440	+	0.664440i	0.956423	−	0.291983i	$-0.0943151\pi$
$19$	2.89623	+	2.89623i	0.664440	+	0.664440i	−0.291983	+	0.956423i	$0.594315\pi$
$20$		0			0
$21$	1.25896	−	1.25896i	0.274729	−	0.274729i
$22$		0			0
$23$		−	2.00613i		−	0.418306i	−0.977883	−	0.209153i	$-0.932929\pi$
$23$		−	2.00613i		−	0.418306i	0.977883	−	0.209153i	$-0.0670707\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.61392	+	3.61392i	−0.695499	+	0.695499i
$28$		0			0
$29$	6.72307	+	6.72307i	1.24844	+	1.24844i	0.956408	+	0.292034i	$0.0943321\pi$
$29$	6.72307	+	6.72307i	1.24844	+	1.24844i	0.292034	+	0.956408i	$0.405668\pi$
$30$		0			0
$31$	7.11778			1.27839			0.639195	−	0.769044i	$-0.279268\pi$
$31$	7.11778			1.27839			0.639195	+	0.769044i	$0.279268\pi$
$32$		0			0
$33$	4.15146			0.722676
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.25207	−	2.25207i	0.370237	−	0.370237i	−0.497326	−	0.867564i	$-0.665685\pi$
$37$	2.25207	−	2.25207i	0.370237	−	0.370237i	0.867564	+	0.497326i	$0.165685\pi$
$38$		0			0
$39$			3.81042i			0.610156i
$40$		0			0
$41$			1.59630i			0.249301i	0.992201	+	0.124650i	$0.0397809\pi$
$41$			1.59630i			0.249301i	−0.992201	+	0.124650i	$0.960219\pi$
$42$		0			0
$43$	−8.06886	+	8.06886i	−1.23049	+	1.23049i	−0.266715	+	0.963776i	$0.585938\pi$
$43$	−8.06886	+	8.06886i	−1.23049	+	1.23049i	−0.963776	+	0.266715i	$0.914062\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.43823			−0.647383			−0.323691	−	0.946163i	$-0.604924\pi$
$47$	−4.43823			−0.647383			−0.323691	+	0.946163i	$0.604924\pi$
$48$		0			0
$49$	4.06040			0.580058
$50$		0			0
$51$	−1.39471	−	1.39471i	−0.195299	−	0.195299i
$52$		0			0
$53$	−0.481758	+	0.481758i	−0.0661746	+	0.0661746i	−0.739420	−	0.673245i	$-0.764900\pi$
$53$	−0.481758	+	0.481758i	−0.0661746	+	0.0661746i	0.673245	+	0.739420i	$0.264900\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	4.25336i		−	0.563372i
$58$		0			0
$59$	3.08580	−	3.08580i	0.401737	−	0.401737i	−0.477108	−	0.878845i	$-0.658315\pi$
$59$	3.08580	−	3.08580i	0.401737	−	0.401737i	0.878845	+	0.477108i	$0.158315\pi$
$60$		0			0
$61$	3.46410	+	3.46410i	0.443533	+	0.443533i	0.893197	−	0.449665i	$-0.148457\pi$
$61$	3.46410	+	3.46410i	0.443533	+	0.443533i	−0.449665	+	0.893197i	$0.648457\pi$
$62$		0			0
$63$	3.29468			0.415090
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.80454	+	1.80454i	0.220460	+	0.220460i	0.808692	−	0.588232i	$-0.200176\pi$
$67$	1.80454	+	1.80454i	0.220460	+	0.220460i	−0.588232	+	0.808692i	$0.700176\pi$
$68$		0			0
$69$	−1.47309	+	1.47309i	−0.177339	+	0.177339i
$70$		0			0
$71$		−	0.379150i		−	0.0449969i	−0.999747	−	0.0224984i	$-0.992838\pi$
$71$		−	0.379150i		−	0.0449969i	0.999747	−	0.0224984i	$-0.00716208\pi$
$72$		0			0
$73$			8.37718i			0.980475i	0.871589	+	0.490237i	$0.163090\pi$
$73$			8.37718i			0.980475i	−0.871589	+	0.490237i	$0.836910\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.84668	−	4.84668i	−0.552331	−	0.552331i
$78$		0			0
$79$	11.2566			1.26646			0.633231	−	0.773963i	$-0.281728\pi$
$79$	11.2566			1.26646			0.633231	+	0.773963i	$0.281728\pi$
$80$		0			0
$81$	−0.457524			−0.0508360
$82$		0			0
$83$	8.24890	+	8.24890i	0.905435	+	0.905435i	0.995900	−	0.0904649i	$-0.0288353\pi$
$83$	8.24890	+	8.24890i	0.905435	+	0.905435i	−0.0904649	+	0.995900i	$0.528835\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	9.87341i		−	1.05854i
$88$		0			0
$89$			11.9820i			1.27009i	0.772474	+	0.635046i	$0.219019\pi$
$89$			11.9820i			1.27009i	−0.772474	+	0.635046i	$0.780981\pi$
$90$		0			0
$91$	4.44854	−	4.44854i	0.466334	−	0.466334i
$92$		0			0
$93$	−5.22654	−	5.22654i	−0.541967	−	0.541967i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	6.50543			0.660526			0.330263	−	0.943889i	$-0.392863\pi$
$97$	6.50543			0.660526			0.330263	+	0.943889i	$0.392863\pi$
$98$		0			0
$99$	5.43213	+	5.43213i	0.545949	+	0.545949i
$100$		0			0
$101$	−6.72307	+	6.72307i	−0.668970	+	0.668970i	−0.957478	−	0.288508i	$-0.906841\pi$
$101$	−6.72307	+	6.72307i	−0.668970	+	0.668970i	0.288508	+	0.957478i	$0.406841\pi$
$102$		0			0
$103$		−	15.1733i		−	1.49506i	−0.664225	−	0.747532i	$-0.731238\pi$
$103$		−	15.1733i		−	1.49506i	0.664225	−	0.747532i	$-0.268762\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.69781	−	1.69781i	0.164134	−	0.164134i	−0.620262	−	0.784395i	$-0.712974\pi$
$107$	1.69781	−	1.69781i	0.164134	−	0.164134i	0.784395	+	0.620262i	$0.212974\pi$
$108$		0			0
$109$	−3.11120	−	3.11120i	−0.297999	−	0.297999i	0.542231	−	0.840230i	$-0.317580\pi$
$109$	−3.11120	−	3.11120i	−0.297999	−	0.297999i	−0.840230	+	0.542231i	$0.817580\pi$
$110$		0			0
$111$	−3.30735			−0.313920
$112$		0			0
$113$	15.8259			1.48877			0.744387	−	0.667748i	$-0.232742\pi$
$113$	15.8259			1.48877			0.744387	+	0.667748i	$0.232742\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−4.98589	+	4.98589i	−0.460946	+	0.460946i
$118$		0			0
$119$			3.25656i			0.298528i
$120$		0			0
$121$		−	4.98203i		−	0.452912i
$122$		0			0
$123$	1.17216	−	1.17216i	0.105690	−	0.105690i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	18.3239			1.62598			0.812991	−	0.582276i	$-0.197838\pi$
$127$	18.3239			1.62598			0.812991	+	0.582276i	$0.197838\pi$
$128$		0			0
$129$	11.8498			1.04332
$130$		0			0
$131$	10.2036	+	10.2036i	0.891491	+	0.891491i	0.994663	−	0.103172i	$-0.0328994\pi$
$131$	10.2036	+	10.2036i	0.891491	+	0.891491i	−0.103172	+	0.994663i	$0.532899\pi$
$132$		0			0
$133$	−4.96565	+	4.96565i	−0.430577	+	0.430577i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			14.9845i			1.28021i	0.768286	+	0.640107i	$0.221110\pi$
$137$			14.9845i			1.28021i	−0.768286	+	0.640107i	$0.778890\pi$
$138$		0			0
$139$	−8.29094	+	8.29094i	−0.703228	+	0.703228i	−0.965102	−	0.261874i	$-0.915660\pi$
$139$	−8.29094	+	8.29094i	−0.703228	+	0.703228i	0.261874	+	0.965102i	$0.415660\pi$
$140$		0			0
$141$	3.25896	+	3.25896i	0.274454	+	0.274454i
$142$		0			0
$143$	14.6691			1.22670
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−2.98153	−	2.98153i	−0.245912	−	0.245912i
$148$		0			0
$149$	7.30735	−	7.30735i	0.598642	−	0.598642i	−0.341309	−	0.939951i	$-0.610870\pi$
$149$	7.30735	−	7.30735i	0.598642	−	0.598642i	0.939951	+	0.341309i	$0.110870\pi$
$150$		0			0
$151$			4.56873i			0.371798i	0.982569	+	0.185899i	$0.0595197\pi$
$151$			4.56873i			0.371798i	−0.982569	+	0.185899i	$0.940480\pi$
$152$		0			0
$153$		−	3.64992i		−	0.295079i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.52966	+	1.52966i	0.122080	+	0.122080i	0.765507	−	0.643427i	$-0.222488\pi$
$157$	1.52966	+	1.52966i	0.122080	+	0.122080i	−0.643427	+	0.765507i	$0.722488\pi$
$158$		0			0
$159$	0.707504			0.0561087
$160$		0			0
$161$	3.43955			0.271075
$162$		0			0
$163$	−10.1361	−	10.1361i	−0.793918	−	0.793918i	0.188211	−	0.982129i	$-0.439731\pi$
$163$	−10.1361	−	10.1361i	−0.793918	−	0.793918i	−0.982129	+	0.188211i	$0.939731\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			2.57967i			0.199621i	0.995006	+	0.0998105i	$0.0318237\pi$
$167$			2.57967i			0.199621i	−0.995006	+	0.0998105i	$0.968176\pi$
$168$		0			0
$169$			0.464102i			0.0357001i
$170$		0			0
$171$	5.56547	−	5.56547i	0.425602	−	0.425602i
$172$		0			0
$173$	−14.1773	−	14.1773i	−1.07788	−	1.07788i	−0.996700	−	0.0811779i	$-0.974132\pi$
$173$	−14.1773	−	14.1773i	−1.07788	−	1.07788i	−0.0811779	−	0.996700i	$-0.525868\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.53177			−0.340629
$178$		0			0
$179$	−9.88067	−	9.88067i	−0.738516	−	0.738516i	0.233775	−	0.972291i	$-0.424892\pi$
$179$	−9.88067	−	9.88067i	−0.738516	−	0.738516i	−0.972291	+	0.233775i	$0.924892\pi$
$180$		0			0
$181$	6.20514	−	6.20514i	0.461224	−	0.461224i	−0.437832	−	0.899057i	$-0.644254\pi$
$181$	6.20514	−	6.20514i	0.461224	−	0.461224i	0.899057	+	0.437832i	$0.144254\pi$
$182$		0			0
$183$		−	5.08733i		−	0.376067i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−5.36928	+	5.36928i	−0.392641	+	0.392641i
$188$		0			0
$189$	−6.19615	−	6.19615i	−0.450704	−	0.450704i
$190$		0			0
$191$	−18.9282			−1.36960			−0.684798	−	0.728733i	$-0.740110\pi$
$191$	−18.9282			−1.36960			−0.684798	+	0.728733i	$0.740110\pi$
$192$		0			0
$193$	4.42987			0.318869			0.159434	−	0.987209i	$-0.449033\pi$
$193$	4.42987			0.318869			0.159434	+	0.987209i	$0.449033\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.39341	+	6.39341i	−0.455511	+	0.455511i	−0.897179	−	0.441667i	$-0.854387\pi$
$197$	−6.39341	+	6.39341i	−0.455511	+	0.455511i	0.441667	+	0.897179i	$0.354387\pi$
$198$		0			0
$199$		−	5.85641i		−	0.415150i	−0.978219	−	0.207575i	$-0.933443\pi$
$199$		−	5.85641i		−	0.415150i	0.978219	−	0.207575i	$-0.0665570\pi$
$200$		0			0
$201$		−	2.65013i		−	0.186926i
$202$		0			0
$203$	−11.5269	+	11.5269i	−0.809027	+	0.809027i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.85503			−0.267943
$208$		0			0
$209$	−16.3743			−1.13264
$210$		0			0
$211$	−7.60373	−	7.60373i	−0.523462	−	0.523462i	0.395153	−	0.918615i	$-0.370692\pi$
$211$	−7.60373	−	7.60373i	−0.523462	−	0.523462i	−0.918615	+	0.395153i	$0.870692\pi$
$212$		0			0
$213$	−0.278408	+	0.278408i	−0.0190762	+	0.0190762i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			12.2036i			0.828435i
$218$		0			0
$219$	6.15131	−	6.15131i	0.415667	−	0.415667i
$220$		0			0
$221$	−4.92820	−	4.92820i	−0.331507	−	0.331507i
$222$		0			0
$223$	−9.22430			−0.617705			−0.308853	−	0.951110i	$-0.599945\pi$
$223$	−9.22430			−0.617705			−0.308853	+	0.951110i	$0.599945\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.21725	+	9.21725i	0.611770	+	0.611770i	0.943407	−	0.331637i	$-0.107601\pi$
$227$	9.21725	+	9.21725i	0.611770	+	0.611770i	−0.331637	+	0.943407i	$0.607601\pi$
$228$		0			0
$229$	−1.63811	+	1.63811i	−0.108250	+	0.108250i	−0.759157	−	0.650907i	$-0.774389\pi$
$229$	−1.63811	+	1.63811i	−0.108250	+	0.108250i	0.650907	+	0.759157i	$0.274389\pi$
$230$		0			0
$231$			7.11778i			0.468315i
$232$		0			0
$233$			12.3798i			0.811026i	0.914089	+	0.405513i	$0.132907\pi$
$233$			12.3798i			0.811026i	−0.914089	+	0.405513i	$0.867093\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−8.26562	−	8.26562i	−0.536910	−	0.536910i
$238$		0			0
$239$	−7.77449			−0.502890			−0.251445	−	0.967872i	$-0.580906\pi$
$239$	−7.77449			−0.502890			−0.251445	+	0.967872i	$0.580906\pi$
$240$		0			0
$241$	−3.47068			−0.223566			−0.111783	−	0.993733i	$-0.535656\pi$
$241$	−3.47068			−0.223566			−0.111783	+	0.993733i	$0.535656\pi$
$242$		0			0
$243$	11.1777	+	11.1777i	0.717051	+	0.717051i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		−	15.0292i		−	0.956286i
$248$		0			0
$249$		−	12.1142i		−	0.767708i
$250$		0			0
$251$	−8.94765	+	8.94765i	−0.564771	+	0.564771i	−0.930659	−	0.365888i	$-0.880765\pi$
$251$	−8.94765	+	8.94765i	−0.564771	+	0.564771i	0.365888	+	0.930659i	$0.380765\pi$
$252$		0			0
$253$	5.67100	+	5.67100i	0.356533	+	0.356533i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.62228			−0.225952			−0.112976	−	0.993598i	$-0.536038\pi$
$257$	−3.62228			−0.225952			−0.112976	+	0.993598i	$0.536038\pi$
$258$		0			0
$259$	3.86122	+	3.86122i	0.239925	+	0.239925i
$260$		0			0
$261$	12.9192	−	12.9192i	0.799680	−	0.799680i
$262$		0			0
$263$		−	13.7416i		−	0.847345i	−0.905815	−	0.423673i	$-0.860741\pi$
$263$		−	13.7416i		−	0.847345i	0.905815	−	0.423673i	$-0.139259\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	8.79833	−	8.79833i	0.538449	−	0.538449i
$268$		0			0
$269$	4.22240	+	4.22240i	0.257444	+	0.257444i	0.824014	−	0.566570i	$-0.191730\pi$
$269$	4.22240	+	4.22240i	0.257444	+	0.257444i	−0.566570	+	0.824014i	$0.691730\pi$
$270$		0			0
$271$	5.40015			0.328036			0.164018	−	0.986457i	$-0.447555\pi$
$271$	5.40015			0.328036			0.164018	+	0.986457i	$0.447555\pi$
$272$		0			0
$273$	−6.53307			−0.395399
$274$		0			0
$275$		0			0
$276$		0			0
$277$	5.08733	−	5.08733i	0.305668	−	0.305668i	−0.537558	−	0.843227i	$-0.680653\pi$
$277$	5.08733	−	5.08733i	0.305668	−	0.305668i	0.843227	+	0.537558i	$0.180653\pi$
$278$		0			0
$279$		−	13.6777i		−	0.818863i
$280$		0			0
$281$			21.2780i			1.26934i	0.772784	+	0.634669i	$0.218864\pi$
$281$			21.2780i			1.26934i	−0.772784	+	0.634669i	$0.781136\pi$
$282$		0			0
$283$	−4.08521	+	4.08521i	−0.242840	+	0.242840i	−0.818024	−	0.575184i	$-0.804931\pi$
$283$	−4.08521	+	4.08521i	−0.242840	+	0.242840i	0.575184	+	0.818024i	$0.304931\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.73690			−0.161554
$288$		0			0
$289$	−13.3923			−0.787783
$290$		0			0
$291$	−4.77689	−	4.77689i	−0.280026	−	0.280026i
$292$		0			0
$293$	−7.40400	+	7.40400i	−0.432547	+	0.432547i	−0.889494	−	0.456947i	$-0.848943\pi$
$293$	−7.40400	+	7.40400i	−0.432547	+	0.432547i	0.456947	+	0.889494i	$0.348943\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	20.4319i		−	1.18558i
$298$		0			0
$299$	−5.20514	+	5.20514i	−0.301021	+	0.301021i
$300$		0			0
$301$	−13.8343	−	13.8343i	−0.797394	−	0.797394i
$302$		0			0
$303$	9.87341			0.567212
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−16.6634	−	16.6634i	−0.951030	−	0.951030i	0.0478262	−	0.998856i	$-0.484771\pi$
$307$	−16.6634	−	16.6634i	−0.951030	−	0.951030i	−0.998856	+	0.0478262i	$0.984771\pi$
$308$		0			0
$309$	−11.1416	+	11.1416i	−0.633825	+	0.633825i
$310$		0			0
$311$		−	21.9072i		−	1.24224i	−0.783714	−	0.621122i	$-0.786677\pi$
$311$		−	21.9072i		−	1.24224i	0.783714	−	0.621122i	$-0.213323\pi$
$312$		0			0
$313$			12.4820i			0.705525i	0.935713	+	0.352763i	$0.114758\pi$
$313$			12.4820i			0.705525i	−0.935713	+	0.352763i	$0.885242\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.24325	+	4.24325i	0.238324	+	0.238324i	0.816156	−	0.577832i	$-0.196101\pi$
$317$	4.24325	+	4.24325i	0.238324	+	0.238324i	−0.577832	+	0.816156i	$0.696101\pi$
$318$		0			0
$319$	−38.0100			−2.12815
$320$		0			0
$321$	−2.49338			−0.139167
$322$		0			0
$323$	5.50108	+	5.50108i	0.306088	+	0.306088i
$324$		0			0
$325$		0			0
$326$		0			0
$327$			4.56907i			0.252670i
$328$		0			0
$329$		−	7.60946i		−	0.419523i
$330$		0			0
$331$	−1.10377	+	1.10377i	−0.0606688	+	0.0606688i	−0.736790	−	0.676121i	$-0.763659\pi$
$331$	−1.10377	+	1.10377i	−0.0606688	+	0.0606688i	0.676121	+	0.736790i	$0.263659\pi$
$332$		0			0
$333$	−4.32763	−	4.32763i	−0.237152	−	0.237152i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	7.47635			0.407263			0.203631	−	0.979048i	$-0.434726\pi$
$337$	7.47635			0.407263			0.203631	+	0.979048i	$0.434726\pi$
$338$		0			0
$339$	−11.6208	−	11.6208i	−0.631158	−	0.631158i
$340$		0			0
$341$	−20.1208	+	20.1208i	−1.08960	+	1.08960i
$342$		0			0
$343$			18.9633i			1.02392i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.56074	+	8.56074i	−0.459565	+	0.459565i	−0.898512	−	0.438948i	$-0.855351\pi$
$347$	−8.56074	+	8.56074i	−0.459565	+	0.459565i	0.438948	+	0.898512i	$0.355351\pi$
$348$		0			0
$349$	−7.91567	−	7.91567i	−0.423716	−	0.423716i	0.462765	−	0.886481i	$-0.346857\pi$
$349$	−7.91567	−	7.91567i	−0.423716	−	0.423716i	−0.886481	+	0.462765i	$0.846857\pi$
$350$		0			0
$351$	18.7535			1.00099
$352$		0			0
$353$	−9.67314			−0.514849			−0.257425	−	0.966298i	$-0.582874\pi$
$353$	−9.67314			−0.514849			−0.257425	+	0.966298i	$0.582874\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.39127	−	2.39127i	0.126559	−	0.126559i
$358$		0			0
$359$			17.0867i			0.901799i	0.892575	+	0.450900i	$0.148897\pi$
$359$			17.0867i			0.901799i	−0.892575	+	0.450900i	$0.851103\pi$
$360$		0			0
$361$		−	2.22373i		−	0.117038i
$362$		0			0
$363$	−3.65827	+	3.65827i	−0.192010	+	0.192010i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−13.4500			−0.702086			−0.351043	−	0.936359i	$-0.614173\pi$
$367$	−13.4500			−0.702086			−0.351043	+	0.936359i	$0.614173\pi$
$368$		0			0
$369$	3.06750			0.159688
$370$		0			0
$371$	−0.825987	−	0.825987i	−0.0428831	−	0.0428831i
$372$		0			0
$373$	12.0271	−	12.0271i	0.622740	−	0.622740i	−0.323491	−	0.946231i	$-0.604857\pi$
$373$	12.0271	−	12.0271i	0.622740	−	0.622740i	0.946231	+	0.323491i	$0.104857\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	34.8876i		−	1.79680i
$378$		0			0
$379$	19.1552	−	19.1552i	0.983936	−	0.983936i	−0.0159369	−	0.999873i	$-0.505073\pi$
$379$	19.1552	−	19.1552i	0.983936	−	0.983936i	0.999873	+	0.0159369i	$0.00507308\pi$
$380$		0			0
$381$	−13.4551	−	13.4551i	−0.689327	−	0.689327i
$382$		0			0
$383$	−17.7503			−0.907000			−0.453500	−	0.891256i	$-0.649825\pi$
$383$	−17.7503			−0.907000			−0.453500	+	0.891256i	$0.649825\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	15.5053	+	15.5053i	0.788181	+	0.788181i
$388$		0			0
$389$	1.18654	−	1.18654i	0.0601602	−	0.0601602i	−0.676387	−	0.736547i	$-0.736455\pi$
$389$	1.18654	−	1.18654i	0.0601602	−	0.0601602i	0.736547	+	0.676387i	$0.236455\pi$
$390$		0			0
$391$		−	3.81042i		−	0.192701i
$392$		0			0
$393$		−	14.9848i		−	0.755886i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.74478	+	4.74478i	0.238134	+	0.238134i	0.816077	−	0.577943i	$-0.196145\pi$
$397$	4.74478	+	4.74478i	0.238134	+	0.238134i	−0.577943	+	0.816077i	$0.696145\pi$
$398$		0			0
$399$	7.29250			0.365081
$400$		0			0
$401$	0.632677			0.0315944			0.0157972	−	0.999875i	$-0.494971\pi$
$401$	0.632677			0.0315944			0.0157972	+	0.999875i	$0.494971\pi$
$402$		0			0
$403$	−18.4679	−	18.4679i	−0.919953	−	0.919953i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			12.7324i			0.631124i
$408$		0			0
$409$		−	26.3809i		−	1.30445i	−0.758024	−	0.652226i	$-0.773835\pi$
$409$		−	26.3809i		−	1.30445i	0.758024	−	0.652226i	$-0.226165\pi$
$410$		0			0
$411$	11.0030	−	11.0030i	0.542739	−	0.542739i
$412$		0			0
$413$	5.29069	+	5.29069i	0.260338	+	0.260338i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	12.1760			0.596260
$418$		0			0
$419$	−1.37589	−	1.37589i	−0.0672167	−	0.0672167i	0.672699	−	0.739916i	$-0.265135\pi$
$419$	−1.37589	−	1.37589i	−0.0672167	−	0.0672167i	−0.739916	+	0.672699i	$0.765135\pi$
$420$		0			0
$421$	6.65671	−	6.65671i	0.324428	−	0.324428i	−0.526035	−	0.850463i	$-0.676322\pi$
$421$	6.65671	−	6.65671i	0.324428	−	0.324428i	0.850463	+	0.526035i	$0.176322\pi$
$422$		0			0
$423$			8.52862i			0.414676i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−5.93929	+	5.93929i	−0.287422	+	0.287422i
$428$		0			0
$429$	−10.7715	−	10.7715i	−0.520051	−	0.520051i
$430$		0			0
$431$	−4.08798			−0.196911			−0.0984556	−	0.995141i	$-0.531390\pi$
$431$	−4.08798			−0.196911			−0.0984556	+	0.995141i	$0.531390\pi$
$432$		0			0
$433$	29.2913			1.40765			0.703826	−	0.710373i	$-0.251474\pi$
$433$	29.2913			1.40765			0.703826	+	0.710373i	$0.251474\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.81020	−	5.81020i	0.277940	−	0.277940i
$438$		0			0
$439$		−	26.9790i		−	1.28764i	−0.765178	−	0.643819i	$-0.777349\pi$
$439$		−	26.9790i		−	1.28764i	0.765178	−	0.643819i	$-0.222651\pi$
$440$		0			0
$441$		−	7.80258i		−	0.371551i
$442$		0			0
$443$	14.5286	−	14.5286i	0.690276	−	0.690276i	−0.272017	−	0.962293i	$-0.587691\pi$
$443$	14.5286	−	14.5286i	0.690276	−	0.690276i	0.962293	+	0.272017i	$0.0876906\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−10.7315			−0.507582
$448$		0			0
$449$	−23.1572			−1.09286			−0.546428	−	0.837506i	$-0.684013\pi$
$449$	−23.1572			−1.09286			−0.546428	+	0.837506i	$0.684013\pi$
$450$		0			0
$451$	−4.51249	−	4.51249i	−0.212485	−	0.212485i
$452$		0			0
$453$	3.35479	−	3.35479i	0.157622	−	0.157622i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			37.7026i			1.76365i	0.471572	+	0.881827i	$0.343687\pi$
$457$			37.7026i			1.76365i	−0.471572	+	0.881827i	$0.656313\pi$
$458$		0			0
$459$	−6.86425	+	6.86425i	−0.320396	+	0.320396i
$460$		0			0
$461$	11.3737	+	11.3737i	0.529727	+	0.529727i	0.920491	−	0.390764i	$-0.127789\pi$
$461$	11.3737	+	11.3737i	0.529727	+	0.529727i	−0.390764	+	0.920491i	$0.627789\pi$
$462$		0			0
$463$	7.94895			0.369419			0.184710	−	0.982793i	$-0.440866\pi$
$463$	7.94895			0.369419			0.184710	+	0.982793i	$0.440866\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.34999	+	5.34999i	0.247568	+	0.247568i	0.819972	−	0.572404i	$-0.193989\pi$
$467$	5.34999	+	5.34999i	0.247568	+	0.247568i	−0.572404	+	0.819972i	$0.693989\pi$
$468$		0			0
$469$	−3.09394	+	3.09394i	−0.142865	+	0.142865i
$470$		0			0
$471$		−	2.24643i		−	0.103510i
$472$		0			0
$473$		−	45.6187i		−	2.09755i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.925759	+	0.925759i	0.0423876	+	0.0423876i
$478$		0			0
$479$	−9.58973			−0.438166			−0.219083	−	0.975706i	$-0.570307\pi$
$479$	−9.58973			−0.438166			−0.219083	+	0.975706i	$0.570307\pi$
$480$		0			0
$481$	−11.6865			−0.532859
$482$		0			0
$483$	−2.52564	−	2.52564i	−0.114921	−	0.114921i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			36.6487i			1.66071i	0.557232	+	0.830357i	$0.311863\pi$
$487$			36.6487i			1.66071i	−0.557232	+	0.830357i	$0.688137\pi$
$488$		0			0
$489$			14.8857i			0.673154i
$490$		0			0
$491$	−23.4273	+	23.4273i	−1.05726	+	1.05726i	−0.0590019	+	0.998258i	$0.518792\pi$
$491$	−23.4273	+	23.4273i	−1.05726	+	1.05726i	−0.998258	+	0.0590019i	$0.981208\pi$
$492$		0			0
$493$	12.7697	+	12.7697i	0.575120	+	0.575120i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.650063			0.0291593
$498$		0			0
$499$	−9.50152	−	9.50152i	−0.425346	−	0.425346i	0.461693	−	0.887040i	$-0.347242\pi$
$499$	−9.50152	−	9.50152i	−0.425346	−	0.425346i	−0.887040	+	0.461693i	$0.847242\pi$
$500$		0			0
$501$	1.89424	−	1.89424i	0.0846283	−	0.0846283i
$502$		0			0
$503$			20.6875i			0.922411i	0.887293	+	0.461206i	$0.152583\pi$
$503$			20.6875i			0.922411i	−0.887293	+	0.461206i	$0.847417\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.340787	−	0.340787i	0.0151349	−	0.0151349i
$508$		0			0
$509$	−11.6381	−	11.6381i	−0.515850	−	0.515850i	0.400463	−	0.916313i	$-0.368849\pi$
$509$	−11.6381	−	11.6381i	−0.515850	−	0.515850i	−0.916313	+	0.400463i	$0.868849\pi$
$510$		0			0
$511$	−14.3629			−0.635377
$512$		0			0
$513$	−20.9335			−0.924235
$514$		0			0
$515$		0			0
$516$		0			0
$517$	12.5462	−	12.5462i	0.551780	−	0.551780i
$518$		0			0
$519$			20.8205i			0.913921i
$520$		0			0
$521$		−	5.18654i		−	0.227227i	−0.993525	−	0.113613i	$-0.963758\pi$
$521$		−	5.18654i		−	0.227227i	0.993525	−	0.113613i	$-0.0362425\pi$
$522$		0			0
$523$	26.9589	−	26.9589i	1.17883	−	1.17883i	0.198788	−	0.980043i	$-0.436300\pi$
$523$	26.9589	−	26.9589i	1.17883	−	1.17883i	0.980043	−	0.198788i	$-0.0637004\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.5195			0.588917
$528$		0			0
$529$	18.9755			0.825020
$530$		0			0
$531$	−5.92976	−	5.92976i	−0.257330	−	0.257330i
$532$		0			0
$533$	4.14180	−	4.14180i	0.179401	−	0.179401i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			14.5106i			0.626179i
$538$		0			0
$539$	−11.4781	+	11.4781i	−0.494397	+	0.494397i
$540$		0			0
$541$	27.4945	+	27.4945i	1.18208	+	1.18208i	0.979204	+	0.202878i	$0.0650294\pi$
$541$	27.4945	+	27.4945i	1.18208	+	1.18208i	0.202878	+	0.979204i	$0.434971\pi$
$542$		0			0
$543$	−9.11278			−0.391067
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−22.5197	−	22.5197i	−0.962873	−	0.962873i	0.0364619	−	0.999335i	$-0.488391\pi$
$547$	−22.5197	−	22.5197i	−0.962873	−	0.962873i	−0.999335	+	0.0364619i	$0.988391\pi$
$548$		0			0
$549$	6.65671	−	6.65671i	0.284101	−	0.284101i
$550$		0			0
$551$			38.9431i			1.65903i
$552$		0			0
$553$			19.2996i			0.820704i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.7333	+	13.7333i	0.581897	+	0.581897i	0.935424	−	0.353527i	$-0.115018\pi$
$557$	13.7333	+	13.7333i	0.581897	+	0.581897i	−0.353527	+	0.935424i	$0.615018\pi$
$558$		0			0
$559$	41.8713			1.77097
$560$		0			0
$561$	7.88525			0.332916
$562$		0			0
$563$	−0.229223	−	0.229223i	−0.00966061	−	0.00966061i	0.702260	−	0.711921i	$-0.252174\pi$
$563$	−0.229223	−	0.229223i	−0.00966061	−	0.00966061i	−0.711921	+	0.702260i	$0.752174\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	0.784437i		−	0.0329433i
$568$		0			0
$569$			23.0376i			0.965787i	0.875679	+	0.482894i	$0.160414\pi$
$569$			23.0376i			0.965787i	−0.875679	+	0.482894i	$0.839586\pi$
$570$		0			0
$571$	11.8610	−	11.8610i	0.496367	−	0.496367i	−0.413938	−	0.910305i	$-0.635847\pi$
$571$	11.8610	−	11.8610i	0.496367	−	0.496367i	0.910305	+	0.413938i	$0.135847\pi$
$572$		0			0
$573$	13.8989	+	13.8989i	0.580633	+	0.580633i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−39.7168			−1.65343			−0.826715	−	0.562621i	$-0.809793\pi$
$577$	−39.7168			−1.65343			−0.826715	+	0.562621i	$0.809793\pi$
$578$		0			0
$579$	−3.25282	−	3.25282i	−0.135183	−	0.135183i
$580$		0			0
$581$	−14.1429	+	14.1429i	−0.586748	+	0.586748i
$582$		0			0
$583$		−	2.72371i		−	0.112804i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.63887	−	8.63887i	0.356564	−	0.356564i	−0.505980	−	0.862545i	$-0.668869\pi$
$587$	8.63887	−	8.63887i	0.356564	−	0.356564i	0.862545	+	0.505980i	$0.168869\pi$
$588$		0			0
$589$	20.6147	+	20.6147i	0.849414	+	0.849414i
$590$		0			0
$591$	9.38927			0.386223
$592$		0			0
$593$	−45.8229			−1.88172			−0.940860	−	0.338795i	$-0.889981\pi$
$593$	−45.8229			−1.88172			−0.940860	+	0.338795i	$0.889981\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.30032	+	4.30032i	−0.176000	+	0.176000i
$598$		0			0
$599$		−	17.0609i		−	0.697090i	−0.937292	−	0.348545i	$-0.886676\pi$
$599$		−	17.0609i		−	0.697090i	0.937292	−	0.348545i	$-0.113324\pi$
$600$		0			0
$601$		−	38.0363i		−	1.55153i	−0.631020	−	0.775766i	$-0.717364\pi$
$601$		−	38.0363i		−	1.55153i	0.631020	−	0.775766i	$-0.282636\pi$
$602$		0			0
$603$	3.46766	−	3.46766i	0.141214	−	0.141214i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	8.67169			0.351973			0.175987	−	0.984393i	$-0.443688\pi$
$607$	8.67169			0.351973			0.175987	+	0.984393i	$0.443688\pi$
$608$		0			0
$609$	16.9282			0.685965
$610$		0			0
$611$	11.5155	+	11.5155i	0.465868	+	0.465868i
$612$		0			0
$613$	13.9739	−	13.9739i	0.564401	−	0.564401i	−0.366153	−	0.930554i	$-0.619325\pi$
$613$	13.9739	−	13.9739i	0.564401	−	0.564401i	0.930554	+	0.366153i	$0.119325\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	37.3904i		−	1.50528i	−0.658431	−	0.752641i	$-0.728780\pi$
$617$		−	37.3904i		−	1.50528i	0.658431	−	0.752641i	$-0.271220\pi$
$618$		0			0
$619$	−23.2754	+	23.2754i	−0.935516	+	0.935516i	−0.998043	−	0.0625269i	$-0.980084\pi$
$619$	−23.2754	+	23.2754i	−0.935516	+	0.935516i	0.0625269	+	0.998043i	$0.480084\pi$
$620$		0			0
$621$	7.24998	+	7.24998i	0.290932	+	0.290932i
$622$		0			0
$623$	−20.5435			−0.823058
$624$		0			0
$625$		0			0
$626$		0			0
$627$	12.0236	+	12.0236i	0.480175	+	0.480175i
$628$		0			0
$629$	4.27756	−	4.27756i	0.170557	−	0.170557i
$630$		0			0
$631$		−	19.1834i		−	0.763680i	−0.924228	−	0.381840i	$-0.875290\pi$
$631$		−	19.1834i		−	0.763680i	0.924228	−	0.381840i	$-0.124710\pi$
$632$		0			0
$633$			11.1667i			0.443838i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−10.5352	−	10.5352i	−0.417420	−	0.417420i
$638$		0			0
$639$	−0.728585			−0.0288224
$640$		0			0
$641$	−16.1765			−0.638933			−0.319466	−	0.947598i	$-0.603504\pi$
$641$	−16.1765			−0.638933			−0.319466	+	0.947598i	$0.603504\pi$
$642$		0			0
$643$	15.0289	+	15.0289i	0.592681	+	0.592681i	0.938355	−	0.345674i	$-0.112350\pi$
$643$	15.0289	+	15.0289i	0.592681	+	0.592681i	−0.345674	+	0.938355i	$0.612350\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	49.3812i		−	1.94138i	−0.240345	−	0.970688i	$-0.577261\pi$
$647$		−	49.3812i		−	1.94138i	0.240345	−	0.970688i	$-0.422739\pi$
$648$		0			0
$649$			17.4461i			0.684821i
$650$		0			0
$651$	8.96103	−	8.96103i	0.351210	−	0.351210i
$652$		0			0
$653$	19.8685	+	19.8685i	0.777514	+	0.777514i	0.979408	−	0.201893i	$-0.0647094\pi$
$653$	19.8685	+	19.8685i	0.777514	+	0.777514i	−0.201893	+	0.979408i	$0.564709\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	16.0978			0.628035
$658$		0			0
$659$	4.94765	+	4.94765i	0.192733	+	0.192733i	0.796876	−	0.604143i	$-0.206484\pi$
$659$	4.94765	+	4.94765i	0.192733	+	0.192733i	−0.604143	+	0.796876i	$0.706484\pi$
$660$		0			0
$661$	12.1602	−	12.1602i	0.472977	−	0.472977i	−0.429899	−	0.902877i	$-0.641451\pi$
$661$	12.1602	−	12.1602i	0.472977	−	0.472977i	0.902877	+	0.429899i	$0.141451\pi$
$662$		0			0
$663$			7.23750i			0.281081i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	13.4873	−	13.4873i	0.522231	−	0.522231i
$668$		0			0
$669$	6.77335	+	6.77335i	0.261873	+	0.261873i
$670$		0			0
$671$	−19.5849			−0.756067
$672$		0			0
$673$	−32.9882			−1.27160			−0.635801	−	0.771853i	$-0.719330\pi$
$673$	−32.9882			−1.27160			−0.635801	+	0.771853i	$0.719330\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−18.4610	+	18.4610i	−0.709513	+	0.709513i	−0.966433	−	0.256920i	$-0.917292\pi$
$677$	−18.4610	+	18.4610i	−0.709513	+	0.709513i	0.256920	+	0.966433i	$0.417292\pi$
$678$		0			0
$679$			11.1537i			0.428040i
$680$		0			0
$681$		−	13.5363i		−	0.518713i
$682$		0			0
$683$	12.2374	−	12.2374i	0.468251	−	0.468251i	−0.433097	−	0.901347i	$-0.642579\pi$
$683$	12.2374	−	12.2374i	0.468251	−	0.468251i	0.901347	+	0.433097i	$0.142579\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	2.40571			0.0917837
$688$		0			0
$689$	2.49996			0.0952409
$690$		0			0
$691$	9.46014	+	9.46014i	0.359881	+	0.359881i	0.863769	−	0.503888i	$-0.168098\pi$
$691$	9.46014	+	9.46014i	0.359881	+	0.359881i	−0.503888	+	0.863769i	$0.668098\pi$
$692$		0			0
$693$	−9.31352	+	9.31352i	−0.353791	+	0.353791i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			3.03201i			0.114845i
$698$		0			0
$699$	9.09039	−	9.09039i	0.343830	−	0.343830i
$700$		0			0
$701$	−5.14714	−	5.14714i	−0.194405	−	0.194405i	0.603192	−	0.797596i	$-0.293895\pi$
$701$	−5.14714	−	5.14714i	−0.194405	−	0.194405i	−0.797596	+	0.603192i	$0.793895\pi$
$702$		0			0
$703$	13.0450			0.492001
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−11.5269	−	11.5269i	−0.433512	−	0.433512i
$708$		0			0
$709$	18.0125	−	18.0125i	0.676472	−	0.676472i	−0.282728	−	0.959200i	$-0.591239\pi$
$709$	18.0125	−	18.0125i	0.676472	−	0.676472i	0.959200	+	0.282728i	$0.0912395\pi$
$710$		0			0
$711$		−	21.6309i		−	0.811222i
$712$		0			0
$713$		−	14.2792i		−	0.534759i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.70875	+	5.70875i	0.213197	+	0.213197i
$718$		0			0
$719$	34.5017			1.28669			0.643347	−	0.765574i	$-0.277545\pi$
$719$	34.5017			1.28669			0.643347	+	0.765574i	$0.277545\pi$
$720$		0			0
$721$	26.0149			0.968846
$722$		0			0
$723$	2.54850	+	2.54850i	0.0947796	+	0.0947796i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			12.8421i			0.476288i	0.971230	+	0.238144i	$0.0765391\pi$
$727$			12.8421i			0.476288i	−0.971230	+	0.238144i	$0.923461\pi$
$728$		0			0
$729$		−	15.0429i		−	0.557143i
$730$		0			0
$731$	−15.3259	+	15.3259i	−0.566851	+	0.566851i
$732$		0			0
$733$	24.1490	+	24.1490i	0.891965	+	0.891965i	0.994708	−	0.102743i	$-0.0327618\pi$
$733$	24.1490	+	24.1490i	0.891965	+	0.891965i	−0.102743	+	0.994708i	$0.532762\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.2023			−0.375807
$738$		0			0
$739$	35.9398	+	35.9398i	1.32207	+	1.32207i	0.912101	+	0.409966i	$0.134460\pi$
$739$	35.9398	+	35.9398i	1.32207	+	1.32207i	0.409966	+	0.912101i	$0.365540\pi$
$740$		0			0
$741$	−11.0359	+	11.0359i	−0.405412	+	0.405412i
$742$		0			0
$743$			45.9502i			1.68575i	0.538109	+	0.842875i	$0.319139\pi$
$743$			45.9502i			1.68575i	−0.538109	+	0.842875i	$0.680861\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	15.8513	−	15.8513i	0.579969	−	0.579969i
$748$		0			0
$749$	2.91094	+	2.91094i	0.106363	+	0.106363i
$750$		0			0
$751$	24.4820			0.893361			0.446680	−	0.894694i	$-0.352606\pi$
$751$	24.4820			0.893361			0.446680	+	0.894694i	$0.352606\pi$
$752$		0			0
$753$	13.1404			0.478863
$754$		0			0
$755$		0			0
$756$		0			0
$757$	17.0328	−	17.0328i	0.619067	−	0.619067i	−0.326225	−	0.945292i	$-0.605777\pi$
$757$	17.0328	−	17.0328i	0.619067	−	0.619067i	0.945292	+	0.326225i	$0.105777\pi$
$758$		0			0
$759$		−	8.32835i		−	0.302300i
$760$		0			0
$761$			8.53590i			0.309426i	0.987959	+	0.154713i	$0.0494453\pi$
$761$			8.53590i			0.309426i	−0.987959	+	0.154713i	$0.950555\pi$
$762$		0			0
$763$	5.33423	−	5.33423i	0.193112	−	0.193112i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.0130			−0.578195
$768$		0			0
$769$	1.87438			0.0675917			0.0337959	−	0.999429i	$-0.489240\pi$
$769$	1.87438			0.0675917			0.0337959	+	0.999429i	$0.489240\pi$
$770$		0			0
$771$	2.65982	+	2.65982i	0.0957911	+	0.0957911i
$772$		0			0
$773$	−21.5374	+	21.5374i	−0.774645	+	0.774645i	−0.978915	−	0.204270i	$-0.934518\pi$
$773$	−21.5374	+	21.5374i	−0.774645	+	0.774645i	0.204270	+	0.978915i	$0.434518\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		−	5.67054i		−	0.203429i
$778$		0			0
$779$	−4.62326	+	4.62326i	−0.165645	+	0.165645i
$780$		0			0
$781$	1.07180	+	1.07180i	0.0383519	+	0.0383519i
$782$		0			0
$783$	−48.5932			−1.73658
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−7.03687	−	7.03687i	−0.250837	−	0.250837i	0.570477	−	0.821314i	$-0.306759\pi$
$787$	−7.03687	−	7.03687i	−0.250837	−	0.250837i	−0.821314	+	0.570477i	$0.806759\pi$
$788$		0			0
$789$	−10.0904	+	10.0904i	−0.359227	+	0.359227i
$790$		0			0
$791$			27.1339i			0.964770i
$792$		0			0
$793$		−	17.9761i		−	0.638348i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.07933	+	8.07933i	0.286185	+	0.286185i	0.835569	−	0.549385i	$-0.185138\pi$
$797$	8.07933	+	8.07933i	0.286185	+	0.286185i	−0.549385	+	0.835569i	$0.685138\pi$
$798$		0			0
$799$	−8.42995			−0.298230
$800$		0			0
$801$	23.0250			0.813548
$802$		0			0
$803$	−23.6809	−	23.6809i	−0.835682	−	0.835682i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	6.20097i		−	0.218284i
$808$		0			0
$809$		−	5.40185i		−	0.189919i	−0.995481	−	0.0949595i	$-0.969728\pi$
$809$		−	5.40185i		−	0.189919i	0.995481	−	0.0949595i	$-0.0302722\pi$
$810$		0			0
$811$	10.3478	−	10.3478i	0.363360	−	0.363360i	−0.501688	−	0.865049i	$-0.667288\pi$
$811$	10.3478	−	10.3478i	0.363360	−	0.363360i	0.865049	+	0.501688i	$0.167288\pi$
$812$		0			0
$813$	−3.96530	−	3.96530i	−0.139069	−	0.139069i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−46.7385			−1.63517
$818$		0			0
$819$	−8.54843	−	8.54843i	−0.298706	−	0.298706i
$820$		0			0
$821$	10.7321	−	10.7321i	0.374551	−	0.374551i	−0.494581	−	0.869132i	$-0.664678\pi$
$821$	10.7321	−	10.7321i	0.374551	−	0.374551i	0.869132	+	0.494581i	$0.164678\pi$
$822$		0			0
$823$			3.51588i			0.122556i	0.998121	+	0.0612780i	$0.0195176\pi$
$823$			3.51588i			0.122556i	−0.998121	+	0.0612780i	$0.980482\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	27.7375	−	27.7375i	0.964529	−	0.964529i	−0.0348631	−	0.999392i	$-0.511100\pi$
$827$	27.7375	−	27.7375i	0.964529	−	0.964529i	0.999392	+	0.0348631i	$0.0110995\pi$
$828$		0			0
$829$	19.5849	+	19.5849i	0.680212	+	0.680212i	0.960048	−	0.279836i	$-0.0902800\pi$
$829$	19.5849	+	19.5849i	0.680212	+	0.680212i	−0.279836	+	0.960048i	$0.590280\pi$
$830$		0			0
$831$	−7.47119			−0.259173
$832$		0			0
$833$	7.71231			0.267216
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−25.7231	+	25.7231i	−0.889119	+	0.889119i
$838$		0			0
$839$			40.0520i			1.38275i	0.722496	+	0.691375i	$0.242995\pi$
$839$			40.0520i			1.38275i	−0.722496	+	0.691375i	$0.757005\pi$
$840$		0			0
$841$			61.3992i			2.11722i
$842$		0			0
$843$	15.6243	−	15.6243i	0.538129	−	0.538129i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	8.54182			0.293500
$848$		0			0
$849$	5.99948			0.205902
$850$		0			0
$851$	−4.51793	−	4.51793i	−0.154873	−	0.154873i
$852$		0			0
$853$	13.7328	−	13.7328i	0.470202	−	0.470202i	−0.431778	−	0.901980i	$-0.642114\pi$
$853$	13.7328	−	13.7328i	0.470202	−	0.470202i	0.901980	+	0.431778i	$0.142114\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			39.9485i			1.36462i	0.731065	+	0.682308i	$0.239024\pi$
$857$			39.9485i			1.36462i	−0.731065	+	0.682308i	$0.760976\pi$
$858$		0			0
$859$	33.6366	−	33.6366i	1.14766	−	1.14766i	0.160654	−	0.987011i	$-0.448640\pi$
$859$	33.6366	−	33.6366i	1.14766	−	1.14766i	0.987011	−	0.160654i	$-0.0513602\pi$
$860$		0			0
$861$	2.00969	+	2.00969i	0.0684900	+	0.0684900i
$862$		0			0
$863$	16.5303			0.562697			0.281349	−	0.959606i	$-0.409218\pi$
$863$	16.5303			0.562697			0.281349	+	0.959606i	$0.409218\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	9.83388	+	9.83388i	0.333976	+	0.333976i
$868$		0			0
$869$	−31.8205	+	31.8205i	−1.07944	+	1.07944i
$870$		0			0
$871$		−	9.36421i		−	0.317294i
$872$		0			0
$873$		−	12.5010i		−	0.423095i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−9.66381	−	9.66381i	−0.326324	−	0.326324i	0.524863	−	0.851187i	$-0.324117\pi$
$877$	−9.66381	−	9.66381i	−0.326324	−	0.326324i	−0.851187	+	0.524863i	$0.824117\pi$
$878$		0			0
$879$	10.8734			0.366752
$880$		0			0
$881$	−43.4299			−1.46319			−0.731596	−	0.681739i	$-0.761224\pi$
$881$	−43.4299			−1.46319			−0.731596	+	0.681739i	$0.761224\pi$
$882$		0			0
$883$	−22.3879	−	22.3879i	−0.753413	−	0.753413i	0.221701	−	0.975115i	$-0.428839\pi$
$883$	−22.3879	−	22.3879i	−0.753413	−	0.753413i	−0.975115	+	0.221701i	$0.928839\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			31.6913i			1.06409i	0.846716	+	0.532045i	$0.178576\pi$
$887$			31.6913i			1.06409i	−0.846716	+	0.532045i	$0.821424\pi$
$888$		0			0
$889$			31.4168i			1.05368i
$890$		0			0
$891$	1.29335	−	1.29335i	0.0433288	−	0.0433288i
$892$		0			0
$893$	−12.8541	−	12.8541i	−0.430147	−	0.430147i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	7.64420			0.255232
$898$		0			0
$899$	47.8533	+	47.8533i	1.59600	+	1.59600i
$900$		0			0
$901$	−0.915049	+	0.915049i	−0.0304847	+	0.0304847i
$902$		0			0
$903$			20.3168i			0.676102i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−24.9184	+	24.9184i	−0.827401	+	0.827401i	−0.987157	−	0.159755i	$-0.948929\pi$
$907$	−24.9184	+	24.9184i	−0.827401	+	0.827401i	0.159755	+	0.987157i	$0.448929\pi$
$908$		0			0
$909$	12.9192	+	12.9192i	0.428503	+	0.428503i
$910$		0			0
$911$	47.0459			1.55870			0.779350	−	0.626589i	$-0.215549\pi$
$911$	47.0459			1.55870			0.779350	+	0.626589i	$0.215549\pi$
$912$		0			0
$913$	−46.6366			−1.54345
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−17.4943	+	17.4943i	−0.577712	+	0.577712i
$918$		0			0
$919$			12.5442i			0.413796i	0.978362	+	0.206898i	$0.0663369\pi$
$919$			12.5442i			0.413796i	−0.978362	+	0.206898i	$0.933663\pi$
$920$		0			0
$921$			24.4716i			0.806368i
$922$		0			0
$923$	−0.983751	+	0.983751i	−0.0323806	+	0.0323806i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−29.1573			−0.957652
$928$		0			0
$929$	26.7421			0.877380			0.438690	−	0.898639i	$-0.355443\pi$
$929$	26.7421			0.877380			0.438690	+	0.898639i	$0.355443\pi$
$930$		0			0
$931$	11.7599	+	11.7599i	0.385414	+	0.385414i
$932$		0			0
$933$	−16.0863	+	16.0863i	−0.526642	+	0.526642i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			3.06580i			0.100155i	0.998745	+	0.0500777i	$0.0159469\pi$
$937$			3.06580i			0.100155i	−0.998745	+	0.0500777i	$0.984053\pi$
$938$		0			0
$939$	9.16546	−	9.16546i	0.299104	−	0.299104i
$940$		0			0
$941$	−14.6023	−	14.6023i	−0.476020	−	0.476020i	0.427836	−	0.903856i	$-0.359276\pi$
$941$	−14.6023	−	14.6023i	−0.476020	−	0.476020i	−0.903856	+	0.427836i	$0.859276\pi$
$942$		0			0
$943$	3.20239			0.104284
$944$		0			0
$945$		0			0
$946$		0			0
$947$	29.4872	+	29.4872i	0.958204	+	0.958204i	0.999161	−	0.0409570i	$-0.0130407\pi$
$947$	29.4872	+	29.4872i	0.958204	+	0.958204i	−0.0409570	+	0.999161i	$0.513041\pi$
$948$		0			0
$949$	21.7356	−	21.7356i	0.705567	−	0.705567i
$950$		0			0
$951$		−	6.23158i		−	0.202073i
$952$		0			0
$953$			33.6807i			1.09103i	0.838103	+	0.545513i	$0.183665\pi$
$953$			33.6807i			1.09103i	−0.838103	+	0.545513i	$0.816335\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	27.9105	+	27.9105i	0.902219	+	0.902219i
$958$		0			0
$959$	−25.6913			−0.829616
$960$		0			0
$961$	19.6628			0.634283
$962$		0			0
$963$	−3.26256	−	3.26256i	−0.105134	−	0.105134i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			8.70089i			0.279802i	0.990166	+	0.139901i	$0.0446784\pi$
$967$			8.70089i			0.279802i	−0.990166	+	0.139901i	$0.955322\pi$
$968$		0			0
$969$		−	8.07881i		−	0.259529i
$970$		0			0
$971$	5.87523	−	5.87523i	0.188545	−	0.188545i	−0.606522	−	0.795067i	$-0.707436\pi$
$971$	5.87523	−	5.87523i	0.188545	−	0.188545i	0.795067	+	0.606522i	$0.207436\pi$
$972$		0			0
$973$	−14.2150	−	14.2150i	−0.455713	−	0.455713i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	41.8541			1.33903			0.669516	−	0.742798i	$-0.266502\pi$
$977$	41.8541			1.33903			0.669516	+	0.742798i	$0.266502\pi$
$978$		0			0
$979$	−33.8713	−	33.8713i	−1.08253	−	1.08253i
$980$		0			0
$981$	−5.97856	+	5.97856i	−0.190881	+	0.190881i
$982$		0			0
$983$		−	57.4539i		−	1.83250i	−0.400612	−	0.916248i	$-0.631203\pi$
$983$		−	57.4539i		−	1.83250i	0.400612	−	0.916248i	$-0.368797\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−5.58758	+	5.58758i	−0.177854	+	0.177854i
$988$		0			0
$989$	16.1872	+	16.1872i	0.514722	+	0.514722i
$990$		0			0
$991$	−12.8205			−0.407258			−0.203629	−	0.979048i	$-0.565274\pi$
$991$	−12.8205			−0.407258			−0.203629	+	0.979048i	$0.565274\pi$
$992$		0			0
$993$	1.62099			0.0514404
$994$		0			0
$995$		0			0
$996$		0			0
$997$	15.0860	−	15.0860i	0.477777	−	0.477777i	−0.426643	−	0.904420i	$-0.640304\pi$
$997$	15.0860	−	15.0860i	0.477777	−	0.477777i	0.904420	+	0.426643i	$0.140304\pi$
$998$		0			0
$999$			16.2776i			0.514999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.l.h.401.3		16
4.3	odd	2		400.2.l.i.301.1		16
5.2	odd	4		320.2.q.c.209.3		16
5.3	odd	4		320.2.q.c.209.6		16
5.4	even	2	inner	1600.2.l.h.401.6		16
16.5	even	4	inner	1600.2.l.h.1201.3		16
16.11	odd	4		400.2.l.i.101.1		16
20.3	even	4		80.2.q.c.29.5	yes	16
20.7	even	4		80.2.q.c.29.4	✓	16
20.19	odd	2		400.2.l.i.301.8		16
40.3	even	4		640.2.q.e.289.6		16
40.13	odd	4		640.2.q.f.289.3		16
40.27	even	4		640.2.q.e.289.3		16
40.37	odd	4		640.2.q.f.289.6		16
60.23	odd	4		720.2.bm.f.109.4		16
60.47	odd	4		720.2.bm.f.109.5		16
80.3	even	4		640.2.q.e.609.3		16
80.13	odd	4		640.2.q.f.609.6		16
80.27	even	4		80.2.q.c.69.5	yes	16
80.37	odd	4		320.2.q.c.49.6		16
80.43	even	4		80.2.q.c.69.4	yes	16
80.53	odd	4		320.2.q.c.49.3		16
80.59	odd	4		400.2.l.i.101.8		16
80.67	even	4		640.2.q.e.609.6		16
80.69	even	4	inner	1600.2.l.h.1201.6		16
80.77	odd	4		640.2.q.f.609.3		16
240.107	odd	4		720.2.bm.f.469.4		16
240.203	odd	4		720.2.bm.f.469.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.4	✓	16	20.7	even	4
80.2.q.c.29.5	yes	16	20.3	even	4
80.2.q.c.69.4	yes	16	80.43	even	4
80.2.q.c.69.5	yes	16	80.27	even	4
320.2.q.c.49.3		16	80.53	odd	4
320.2.q.c.49.6		16	80.37	odd	4
320.2.q.c.209.3		16	5.2	odd	4
320.2.q.c.209.6		16	5.3	odd	4
400.2.l.i.101.1		16	16.11	odd	4
400.2.l.i.101.8		16	80.59	odd	4
400.2.l.i.301.1		16	4.3	odd	2
400.2.l.i.301.8		16	20.19	odd	2
640.2.q.e.289.3		16	40.27	even	4
640.2.q.e.289.6		16	40.3	even	4
640.2.q.e.609.3		16	80.3	even	4
640.2.q.e.609.6		16	80.67	even	4
640.2.q.f.289.3		16	40.13	odd	4
640.2.q.f.289.6		16	40.37	odd	4
640.2.q.f.609.3		16	80.77	odd	4
640.2.q.f.609.6		16	80.13	odd	4
720.2.bm.f.109.4		16	60.23	odd	4
720.2.bm.f.109.5		16	60.47	odd	4
720.2.bm.f.469.4		16	240.107	odd	4
720.2.bm.f.469.5		16	240.203	odd	4
1600.2.l.h.401.3		16	1.1	even	1	trivial
1600.2.l.h.401.6		16	5.4	even	2	inner
1600.2.l.h.1201.3		16	16.5	even	4	inner
1600.2.l.h.1201.6		16	80.69	even	4	inner

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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.734294 - 0.734294i) q^{3} +1.71452i q^{7} -1.92163i q^{9} +O(q^{10})\)	\(q+(-0.734294 - 0.734294i) q^{3} +1.71452i q^{7} -1.92163i q^{9} +(-2.82684 + 2.82684i) q^{11} +(-2.59462 - 2.59462i) q^{13} +1.89939 q^{17} +(2.89623 + 2.89623i) q^{19} +(1.25896 - 1.25896i) q^{21} -2.00613i q^{23} +(-3.61392 + 3.61392i) q^{27} +(6.72307 + 6.72307i) q^{29} +7.11778 q^{31} +4.15146 q^{33} +(2.25207 - 2.25207i) q^{37} +3.81042i q^{39} +1.59630i q^{41} +(-8.06886 + 8.06886i) q^{43} -4.43823 q^{47} +4.06040 q^{49} +(-1.39471 - 1.39471i) q^{51} +(-0.481758 + 0.481758i) q^{53} -4.25336i q^{57} +(3.08580 - 3.08580i) q^{59} +(3.46410 + 3.46410i) q^{61} +3.29468 q^{63} +(1.80454 + 1.80454i) q^{67} +(-1.47309 + 1.47309i) q^{69} -0.379150i q^{71} +8.37718i q^{73} +(-4.84668 - 4.84668i) q^{77} +11.2566 q^{79} -0.457524 q^{81} +(8.24890 + 8.24890i) q^{83} -9.87341i q^{87} +11.9820i q^{89} +(4.44854 - 4.44854i) q^{91} +(-5.22654 - 5.22654i) q^{93} +6.50543 q^{97} +(5.43213 + 5.43213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{19} - 16 q^{21} + 16 q^{29} - 16 q^{31} - 16 q^{49} + 16 q^{51} - 24 q^{59} - 32 q^{69} + 16 q^{79} - 16 q^{81} + 16 q^{91} + 88 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^19 - 16 * q^21 + 16 * q^29 - 16 * q^31 - 16 * q^49 + 16 * q^51 - 24 * q^59 - 32 * q^69 + 16 * q^79 - 16 * q^81 + 16 * q^91 + 88 * q^99

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