LMFDB - Embedded newform 1600.2.l.h.401.6

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			401.6
Root			$-0.841995 + 1.13624i$ of defining polynomial
Character	$\chi$	$=$	1600.401
Dual form			1600.2.l.h.1201.6

$q$-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	0.886559	−	0.462615i	$-0.153089\pi$
$3$	0.734294	+	0.734294i	0.423945	+	0.423945i	−0.462615	+	0.886559i	$0.653089\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	1.71452i		−	0.648029i	−0.946052	−	0.324015i	$-0.894967\pi$
$7$		−	1.71452i		−	0.648029i	0.946052	−	0.324015i	$-0.105033\pi$
$8$		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	0.968527	−	0.248909i	$-0.0800720\pi$
$13$	2.59462	+	2.59462i	0.719618	+	0.719618i	−0.248909	+	0.968527i	$0.580072\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.89939			−0.460671			−0.230335	−	0.973111i	$-0.573982\pi$
$17$	−1.89939			−0.460671			−0.230335	+	0.973111i	$0.573982\pi$
$18$		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	$0.0670707\pi$
$23$			2.00613i			0.418306i	−0.977883	+	0.209153i	$0.932929\pi$
$24$		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	−0.867564	−	0.497326i	$-0.834315\pi$
$37$	−2.25207	+	2.25207i	−0.370237	+	0.370237i	0.497326	+	0.867564i	$0.334315\pi$
$38$		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	$-0.414062\pi$
$43$	8.06886	−	8.06886i	1.23049	−	1.23049i	0.963776	−	0.266715i	$-0.0859381\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.43823			0.647383			0.323691	−	0.946163i	$-0.395076\pi$
$47$	4.43823			0.647383			0.323691	+	0.946163i	$0.395076\pi$
$48$		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	−0.673245	−	0.739420i	$-0.735100\pi$
$53$	0.481758	−	0.481758i	0.0661746	−	0.0661746i	0.739420	+	0.673245i	$0.235100\pi$
$54$		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	0.588232	−	0.808692i	$-0.299824\pi$
$67$	−1.80454	−	1.80454i	−0.220460	−	0.220460i	−0.808692	+	0.588232i	$0.799824\pi$
$68$		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	$-0.836910\pi$
$73$		−	8.37718i		−	0.980475i	0.871589	−	0.490237i	$-0.163090\pi$
$74$		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	0.0904649	−	0.995900i	$-0.471165\pi$
$83$	−8.24890	−	8.24890i	−0.905435	−	0.905435i	−0.995900	+	0.0904649i	$0.971165\pi$
$84$		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	$-0.607137\pi$
$97$	−6.50543			−0.660526			−0.330263	+	0.943889i	$0.607137\pi$
$98$		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	$0.268762\pi$
$103$			15.1733i			1.49506i	−0.664225	+	0.747532i	$0.731238\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.69781	+	1.69781i	−0.164134	+	0.164134i	−0.784395	−	0.620262i	$-0.787026\pi$
$107$	−1.69781	+	1.69781i	−0.164134	+	0.164134i	0.620262	+	0.784395i	$0.287026\pi$
$108$		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	$-0.767258\pi$
$113$	−15.8259			−1.48877			−0.744387	+	0.667748i	$0.767258\pi$
$114$		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	$-0.802162\pi$
$127$	−18.3239			−1.62598			−0.812991	+	0.582276i	$0.802162\pi$
$128$		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	$-0.778890\pi$
$137$		−	14.9845i		−	1.28021i	0.768286	−	0.640107i	$-0.221110\pi$
$138$		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	0.643427	−	0.765507i	$-0.277512\pi$
$157$	−1.52966	−	1.52966i	−0.122080	−	0.122080i	−0.765507	+	0.643427i	$0.777512\pi$
$158$		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	0.982129	−	0.188211i	$-0.0602689\pi$
$163$	10.1361	+	10.1361i	0.793918	+	0.793918i	−0.188211	+	0.982129i	$0.560269\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	2.57967i		−	0.199621i	−0.995006	−	0.0998105i	$-0.968176\pi$
$167$		−	2.57967i		−	0.199621i	0.995006	−	0.0998105i	$-0.0318237\pi$
$168$		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	$0.0258682\pi$
$173$	14.1773	+	14.1773i	1.07788	+	1.07788i	0.0811779	+	0.996700i	$0.474132\pi$
$174$		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	$-0.550967\pi$
$193$	−4.42987			−0.318869			−0.159434	+	0.987209i	$0.550967\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.39341	−	6.39341i	0.455511	−	0.455511i	−0.441667	−	0.897179i	$-0.645613\pi$
$197$	6.39341	−	6.39341i	0.455511	−	0.455511i	0.897179	+	0.441667i	$0.145613\pi$
$198$		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	$-0.400055\pi$
$223$	9.22430			0.617705			0.308853	+	0.951110i	$0.400055\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.21725	−	9.21725i	−0.611770	−	0.611770i	0.331637	−	0.943407i	$-0.392399\pi$
$227$	−9.21725	−	9.21725i	−0.611770	−	0.611770i	−0.943407	+	0.331637i	$0.892399\pi$
$228$		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	$-0.867093\pi$
$233$		−	12.3798i		−	0.811026i	0.914089	−	0.405513i	$-0.132907\pi$
$234$		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	$-0.463962\pi$
$257$	3.62228			0.225952			0.112976	+	0.993598i	$0.463962\pi$
$258$		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	$0.139259\pi$
$263$			13.7416i			0.847345i	−0.905815	+	0.423673i	$0.860741\pi$
$264$		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	−0.843227	−	0.537558i	$-0.819347\pi$
$277$	−5.08733	+	5.08733i	−0.305668	+	0.305668i	0.537558	+	0.843227i	$0.319347\pi$
$278$		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	−0.575184	−	0.818024i	$-0.695069\pi$
$283$	4.08521	−	4.08521i	0.242840	−	0.242840i	0.818024	+	0.575184i	$0.195069\pi$
$284$		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	−0.456947	−	0.889494i	$-0.651057\pi$
$293$	7.40400	−	7.40400i	0.432547	−	0.432547i	0.889494	+	0.456947i	$0.151057\pi$
$294$		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	0.998856	−	0.0478262i	$-0.0152294\pi$
$307$	16.6634	+	16.6634i	0.951030	+	0.951030i	−0.0478262	+	0.998856i	$0.515229\pi$
$308$		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	$-0.885242\pi$
$313$		−	12.4820i		−	0.705525i	0.935713	−	0.352763i	$-0.114758\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.24325	−	4.24325i	−0.238324	−	0.238324i	0.577832	−	0.816156i	$-0.303899\pi$
$317$	−4.24325	−	4.24325i	−0.238324	−	0.238324i	−0.816156	+	0.577832i	$0.803899\pi$
$318$		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	$-0.565274\pi$
$337$	−7.47635			−0.407263			−0.203631	+	0.979048i	$0.565274\pi$
$338$		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	−0.438948	−	0.898512i	$-0.644649\pi$
$347$	8.56074	−	8.56074i	0.459565	−	0.459565i	0.898512	+	0.438948i	$0.144649\pi$
$348$		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	$-0.417126\pi$
$353$	9.67314			0.514849			0.257425	+	0.966298i	$0.417126\pi$
$354$		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	$-0.385827\pi$
$367$	13.4500			0.702086			0.351043	+	0.936359i	$0.385827\pi$
$368$		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	−0.946231	−	0.323491i	$-0.895143\pi$
$373$	−12.0271	+	12.0271i	−0.622740	+	0.622740i	0.323491	+	0.946231i	$0.395143\pi$
$374$		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	$-0.350175\pi$
$383$	17.7503			0.907000			0.453500	+	0.891256i	$0.350175\pi$
$384$		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	0.577943	−	0.816077i	$-0.303855\pi$
$397$	−4.74478	−	4.74478i	−0.238134	−	0.238134i	−0.816077	+	0.577943i	$0.803855\pi$
$398$		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	$-0.748526\pi$
$433$	−29.2913			−1.40765			−0.703826	+	0.710373i	$0.748526\pi$
$434$		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	−0.962293	−	0.272017i	$-0.912309\pi$
$443$	−14.5286	+	14.5286i	−0.690276	+	0.690276i	0.272017	+	0.962293i	$0.412309\pi$
$444$		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	$-0.656313\pi$
$457$		−	37.7026i		−	1.76365i	0.471572	−	0.881827i	$-0.343687\pi$
$458$		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	$-0.559134\pi$
$463$	−7.94895			−0.369419			−0.184710	+	0.982793i	$0.559134\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.34999	−	5.34999i	−0.247568	−	0.247568i	0.572404	−	0.819972i	$-0.306011\pi$
$467$	−5.34999	−	5.34999i	−0.247568	−	0.247568i	−0.819972	+	0.572404i	$0.806011\pi$
$468$		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	$-0.688137\pi$
$487$		−	36.6487i		−	1.66071i	0.557232	−	0.830357i	$-0.311863\pi$
$488$		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	$-0.847417\pi$
$503$		−	20.6875i		−	0.922411i	0.887293	−	0.461206i	$-0.152583\pi$
$504$		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	$0.563700\pi$
$523$	−26.9589	+	26.9589i	−1.17883	+	1.17883i	−0.980043	+	0.198788i	$0.936300\pi$
$524$		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	0.999335	−	0.0364619i	$-0.0116088\pi$
$547$	22.5197	+	22.5197i	0.962873	+	0.962873i	−0.0364619	+	0.999335i	$0.511609\pi$
$548$		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	0.353527	−	0.935424i	$-0.384982\pi$
$557$	−13.7333	−	13.7333i	−0.581897	−	0.581897i	−0.935424	+	0.353527i	$0.884982\pi$
$558$		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	0.711921	−	0.702260i	$-0.247826\pi$
$563$	0.229223	+	0.229223i	0.00966061	+	0.00966061i	−0.702260	+	0.711921i	$0.747826\pi$
$564$		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	$-0.190207\pi$
$577$	39.7168			1.65343			0.826715	+	0.562621i	$0.190207\pi$
$578$		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	−0.862545	−	0.505980i	$-0.831131\pi$
$587$	−8.63887	+	8.63887i	−0.356564	+	0.356564i	0.505980	+	0.862545i	$0.331131\pi$
$588$		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	$-0.110019\pi$
$593$	45.8229			1.88172			0.940860	+	0.338795i	$0.110019\pi$
$594$		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	$-0.556312\pi$
$607$	−8.67169			−0.351973			−0.175987	+	0.984393i	$0.556312\pi$
$608$		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	−0.930554	−	0.366153i	$-0.880675\pi$
$613$	−13.9739	+	13.9739i	−0.564401	+	0.564401i	0.366153	+	0.930554i	$0.380675\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			37.3904i			1.50528i	0.658431	+	0.752641i	$0.271220\pi$
$617$			37.3904i			1.50528i	−0.658431	+	0.752641i	$0.728780\pi$
$618$		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	0.345674	−	0.938355i	$-0.387650\pi$
$643$	−15.0289	−	15.0289i	−0.592681	−	0.592681i	−0.938355	+	0.345674i	$0.887650\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			49.3812i			1.94138i	0.240345	+	0.970688i	$0.422739\pi$
$647$			49.3812i			1.94138i	−0.240345	+	0.970688i	$0.577261\pi$
$648$		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	0.201893	−	0.979408i	$-0.435291\pi$
$653$	−19.8685	−	19.8685i	−0.777514	−	0.777514i	−0.979408	+	0.201893i	$0.935291\pi$
$654$		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	$-0.280670\pi$
$673$	32.9882			1.27160			0.635801	+	0.771853i	$0.280670\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.4610	−	18.4610i	0.709513	−	0.709513i	−0.256920	−	0.966433i	$-0.582708\pi$
$677$	18.4610	−	18.4610i	0.709513	−	0.709513i	0.966433	+	0.256920i	$0.0827076\pi$
$678$		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	−0.901347	−	0.433097i	$-0.857421\pi$
$683$	−12.2374	+	12.2374i	−0.468251	+	0.468251i	0.433097	+	0.901347i	$0.357421\pi$
$684$		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	$-0.923461\pi$
$727$		−	12.8421i		−	0.476288i	0.971230	−	0.238144i	$-0.0765391\pi$
$728$		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	0.102743	−	0.994708i	$-0.467238\pi$
$733$	−24.1490	−	24.1490i	−0.891965	−	0.891965i	−0.994708	+	0.102743i	$0.967238\pi$
$734$		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	$-0.680861\pi$
$743$		−	45.9502i		−	1.68575i	0.538109	−	0.842875i	$-0.319139\pi$
$744$		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	−0.945292	−	0.326225i	$-0.894223\pi$
$757$	−17.0328	+	17.0328i	−0.619067	+	0.619067i	0.326225	+	0.945292i	$0.394223\pi$
$758$		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	−0.204270	−	0.978915i	$-0.565482\pi$
$773$	21.5374	−	21.5374i	0.774645	−	0.774645i	0.978915	+	0.204270i	$0.0654820\pi$
$774$		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	0.821314	−	0.570477i	$-0.193241\pi$
$787$	7.03687	+	7.03687i	0.250837	+	0.250837i	−0.570477	+	0.821314i	$0.693241\pi$
$788$		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	0.549385	−	0.835569i	$-0.314862\pi$
$797$	−8.07933	−	8.07933i	−0.286185	−	0.286185i	−0.835569	+	0.549385i	$0.814862\pi$
$798$		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	$-0.980482\pi$
$823$		−	3.51588i		−	0.122556i	0.998121	−	0.0612780i	$-0.0195176\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−27.7375	+	27.7375i	−0.964529	+	0.964529i	−0.999392	−	0.0348631i	$-0.988900\pi$
$827$	−27.7375	+	27.7375i	−0.964529	+	0.964529i	0.0348631	+	0.999392i	$0.488900\pi$
$828$		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	−0.901980	−	0.431778i	$-0.857886\pi$
$853$	−13.7328	+	13.7328i	−0.470202	+	0.470202i	0.431778	+	0.901980i	$0.357886\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	39.9485i		−	1.36462i	−0.731065	−	0.682308i	$-0.760976\pi$
$857$		−	39.9485i		−	1.36462i	0.731065	−	0.682308i	$-0.239024\pi$
$858$		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	$-0.590782\pi$
$863$	−16.5303			−0.562697			−0.281349	+	0.959606i	$0.590782\pi$
$864$		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	0.851187	−	0.524863i	$-0.175883\pi$
$877$	9.66381	+	9.66381i	0.326324	+	0.326324i	−0.524863	+	0.851187i	$0.675883\pi$
$878$		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	0.975115	−	0.221701i	$-0.0711610\pi$
$883$	22.3879	+	22.3879i	0.753413	+	0.753413i	−0.221701	+	0.975115i	$0.571161\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	31.6913i		−	1.06409i	−0.846716	−	0.532045i	$-0.821424\pi$
$887$		−	31.6913i		−	1.06409i	0.846716	−	0.532045i	$-0.178576\pi$
$888$		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	−0.159755	−	0.987157i	$-0.551071\pi$
$907$	24.9184	−	24.9184i	0.827401	−	0.827401i	0.987157	+	0.159755i	$0.0510705\pi$
$908$		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	$-0.984053\pi$
$937$		−	3.06580i		−	0.100155i	0.998745	−	0.0500777i	$-0.0159469\pi$
$938$		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	0.0409570	−	0.999161i	$-0.486959\pi$
$947$	−29.4872	−	29.4872i	−0.958204	−	0.958204i	−0.999161	+	0.0409570i	$0.986959\pi$
$948$		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	$-0.816335\pi$
$953$		−	33.6807i		−	1.09103i	0.838103	−	0.545513i	$-0.183665\pi$
$954$		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	$-0.955322\pi$
$967$		−	8.70089i		−	0.279802i	0.990166	−	0.139901i	$-0.0446784\pi$
$968$		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	$-0.733498\pi$
$977$	−41.8541			−1.33903			−0.669516	+	0.742798i	$0.733498\pi$
$978$		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	$0.368797\pi$
$983$			57.4539i			1.83250i	−0.400612	+	0.916248i	$0.631203\pi$
$984$		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	−0.904420	−	0.426643i	$-0.859696\pi$
$997$	−15.0860	+	15.0860i	−0.477777	+	0.477777i	0.426643	+	0.904420i	$0.359696\pi$
$998$		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.401.6		16
4.3	odd	2		400.2.l.i.301.8		16
5.2	odd	4		320.2.q.c.209.6		16
5.3	odd	4		320.2.q.c.209.3		16
5.4	even	2	inner	1600.2.l.h.401.3		16
16.5	even	4	inner	1600.2.l.h.1201.6		16
16.11	odd	4		400.2.l.i.101.8		16
20.3	even	4		80.2.q.c.29.4	✓	16
20.7	even	4		80.2.q.c.29.5	yes	16
20.19	odd	2		400.2.l.i.301.1		16
40.3	even	4		640.2.q.e.289.3		16
40.13	odd	4		640.2.q.f.289.6		16
40.27	even	4		640.2.q.e.289.6		16
40.37	odd	4		640.2.q.f.289.3		16
60.23	odd	4		720.2.bm.f.109.5		16
60.47	odd	4		720.2.bm.f.109.4		16
80.3	even	4		640.2.q.e.609.6		16
80.13	odd	4		640.2.q.f.609.3		16
80.27	even	4		80.2.q.c.69.4	yes	16
80.37	odd	4		320.2.q.c.49.3		16
80.43	even	4		80.2.q.c.69.5	yes	16
80.53	odd	4		320.2.q.c.49.6		16
80.59	odd	4		400.2.l.i.101.1		16
80.67	even	4		640.2.q.e.609.3		16
80.69	even	4	inner	1600.2.l.h.1201.3		16
80.77	odd	4		640.2.q.f.609.6		16
240.107	odd	4		720.2.bm.f.469.5		16
240.203	odd	4		720.2.bm.f.469.4		16

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