LMFDB - Embedded newform 1488.2.q.a.625.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1488,2,Mod(625,1488)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1488, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1488.625"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1488 = 2^{4} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1488.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-1,0,-2,0,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.8817398208$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 744)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1488.625
Dual form			1488.2.q.a.769.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-2.50000 + 4.33013i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +2.00000 q^{15} +(-3.00000 + 5.19615i) q^{17} +(3.00000 - 5.19615i) q^{19} +(-2.50000 - 4.33013i) q^{21} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{27} -3.00000 q^{29} +(-3.50000 - 4.33013i) q^{31} -3.00000 q^{33} +10.0000 q^{35} +(4.00000 - 6.92820i) q^{37} +(-2.00000 - 3.46410i) q^{41} +(-4.00000 + 6.92820i) q^{43} +(-1.00000 + 1.73205i) q^{45} -6.00000 q^{47} +(-9.00000 - 15.5885i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(-0.500000 - 0.866025i) q^{53} +(3.00000 - 5.19615i) q^{55} +(3.00000 + 5.19615i) q^{57} +(-5.50000 + 9.52628i) q^{59} -8.00000 q^{61} +5.00000 q^{63} +(-6.00000 - 10.3923i) q^{67} +(-8.00000 - 13.8564i) q^{71} +(-1.00000 - 1.73205i) q^{73} +(0.500000 + 0.866025i) q^{75} -15.0000 q^{77} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.50000 + 9.52628i) q^{83} +12.0000 q^{85} +(1.50000 - 2.59808i) q^{87} -2.00000 q^{89} +(5.50000 - 0.866025i) q^{93} -12.0000 q^{95} +19.0000 q^{97} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} - 2 q^{5} - 5 q^{7} - q^{9} + 3 q^{11} + 4 q^{15} - 6 q^{17} + 6 q^{19} - 5 q^{21} + q^{25} + 2 q^{27} - 6 q^{29} - 7 q^{31} - 6 q^{33} + 20 q^{35} + 8 q^{37} - 4 q^{41} - 8 q^{43} - 2 q^{45}+ \cdots + 3 q^{99}+O(q^{100}) $ 2 * q - q^3 - 2 * q^5 - 5 * q^7 - q^9 + 3 * q^11 + 4 * q^15 - 6 * q^17 + 6 * q^19 - 5 * q^21 + q^25 + 2 * q^27 - 6 * q^29 - 7 * q^31 - 6 * q^33 + 20 * q^35 + 8 * q^37 - 4 * q^41 - 8 * q^43 - 2 * q^45 - 12 * q^47 - 18 * q^49 - 6 * q^51 - q^53 + 6 * q^55 + 6 * q^57 - 11 * q^59 - 16 * q^61 + 10 * q^63 - 12 * q^67 - 16 * q^71 - 2 * q^73 + q^75 - 30 * q^77 - 8 * q^79 - q^81 + 11 * q^83 + 24 * q^85 + 3 * q^87 - 4 * q^89 + 11 * q^93 - 24 * q^95 + 38 * q^97 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1488\mathbb{Z}\right)^\times$.

$n$	$373$	$497$	$559$	$1057$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		0			0
$7$	−2.50000	+	4.33013i	−0.944911	+	1.63663i	−0.188982	+	0.981981i	$0.560519\pi$
$7$	−2.50000	+	4.33013i	−0.944911	+	1.63663i	−0.755929	+	0.654654i	$0.772814\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$13$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$		0			0
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		0			0
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$		0			0
$21$	−2.50000	−	4.33013i	−0.545545	−	0.944911i
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$		0			0
$31$	−3.50000	−	4.33013i	−0.628619	−	0.777714i
$31$	−3.50000	−	4.33013i	−0.628619	−	0.777714i
$32$		0			0
$33$	−3.00000			−0.522233
$34$		0			0
$35$	10.0000			1.69031
$36$		0			0
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	−0.323640	−	0.946180i	$-0.604907\pi$
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	0.981236	−	0.192809i	$-0.0617599\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.00000	−	3.46410i	−0.312348	−	0.541002i	0.666523	−	0.745485i	$-0.267782\pi$
$41$	−2.00000	−	3.46410i	−0.312348	−	0.541002i	−0.978870	+	0.204483i	$0.934449\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$		0			0
$45$	−1.00000	+	1.73205i	−0.149071	+	0.258199i
$46$		0			0
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		0			0
$49$	−9.00000	−	15.5885i	−1.28571	−	2.22692i
$50$		0			0
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$		0			0
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	0.829640	−	0.558298i	$-0.188546\pi$
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	−0.898321	+	0.439340i	$0.855212\pi$
$54$		0			0
$55$	3.00000	−	5.19615i	0.404520	−	0.700649i
$56$		0			0
$57$	3.00000	+	5.19615i	0.397360	+	0.688247i
$58$		0			0
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	0.246518	+	0.969138i	$0.420713\pi$
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	−0.962557	+	0.271078i	$0.912620\pi$
$60$		0			0
$61$	−8.00000			−1.02430			−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000			−1.02430			−0.512148	+	0.858898i	$0.671150\pi$
$62$		0			0
$63$	5.00000			0.629941
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.00000	−	13.8564i	−0.949425	−	1.64445i	−0.746639	−	0.665230i	$-0.768333\pi$
$71$	−8.00000	−	13.8564i	−0.949425	−	1.64445i	−0.202787	−	0.979223i	$-0.565000\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$	−15.0000			−1.70941
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	5.50000	+	9.52628i	0.603703	+	1.04565i	0.992255	+	0.124218i	$0.0396422\pi$
$83$	5.50000	+	9.52628i	0.603703	+	1.04565i	−0.388552	+	0.921427i	$0.627024\pi$
$84$		0			0
$85$	12.0000			1.30158
$86$		0			0
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$		0			0
$89$	−2.00000			−0.212000			−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000			−0.212000			−0.106000	+	0.994366i	$0.533804\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	5.50000	−	0.866025i	0.570323	−	0.0898027i
$94$		0			0
$95$	−12.0000			−1.23117
$96$		0			0
$97$	19.0000			1.92916			0.964579	−	0.263795i	$-0.0849741\pi$
$97$	19.0000			1.92916			0.964579	+	0.263795i	$0.0849741\pi$
$98$		0			0
$99$	1.50000	−	2.59808i	0.150756	−	0.261116i
$100$		0			0
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$		0			0
$103$	−0.500000	−	0.866025i	−0.0492665	−	0.0853320i	0.840341	−	0.542059i	$-0.182355\pi$
$103$	−0.500000	−	0.866025i	−0.0492665	−	0.0853320i	−0.889607	+	0.456727i	$0.849022\pi$
$104$		0			0
$105$	−5.00000	+	8.66025i	−0.487950	+	0.845154i
$106$		0			0
$107$	5.50000	−	9.52628i	0.531705	−	0.920940i	−0.467610	−	0.883935i	$-0.654885\pi$
$107$	5.50000	−	9.52628i	0.531705	−	0.920940i	0.999315	−	0.0370053i	$-0.0117818\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	4.00000	+	6.92820i	0.379663	+	0.657596i
$112$		0			0
$113$	2.00000	+	3.46410i	0.188144	+	0.325875i	0.944632	−	0.328133i	$-0.106419\pi$
$113$	2.00000	+	3.46410i	0.188144	+	0.325875i	−0.756487	+	0.654008i	$0.773086\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−15.0000	−	25.9808i	−1.37505	−	2.38165i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	4.00000			0.360668
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−1.50000	+	2.59808i	−0.133103	+	0.230542i	−0.924871	−	0.380280i	$-0.875828\pi$
$127$	−1.50000	+	2.59808i	−0.133103	+	0.230542i	0.791768	+	0.610822i	$0.209161\pi$
$128$		0			0
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$		0			0
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$		0			0
$133$	15.0000	+	25.9808i	1.30066	+	2.25282i
$134$		0			0
$135$	−1.00000	−	1.73205i	−0.0860663	−	0.149071i
$136$		0			0
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$		0			0
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$	3.00000	−	5.19615i	0.252646	−	0.437595i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$		0			0
$147$	18.0000			1.48461
$148$		0			0
$149$	2.50000	−	4.33013i	0.204808	−	0.354738i	−0.745264	−	0.666770i	$-0.767676\pi$
$149$	2.50000	−	4.33013i	0.204808	−	0.354738i	0.950072	+	0.312032i	$0.101010\pi$
$150$		0			0
$151$	−11.0000			−0.895167			−0.447584	−	0.894242i	$-0.647715\pi$
$151$	−11.0000			−0.895167			−0.447584	+	0.894242i	$0.647715\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$		0			0
$155$	−4.00000	+	10.3923i	−0.321288	+	0.834730i
$156$		0			0
$157$	16.0000			1.27694			0.638470	−	0.769647i	$-0.279568\pi$
$157$	16.0000			1.27694			0.638470	+	0.769647i	$0.279568\pi$
$158$		0			0
$159$	1.00000			0.0793052
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$		0			0
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$		0			0
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	−0.978259	−	0.207385i	$-0.933505\pi$
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	0.668730	+	0.743505i	$0.266838\pi$
$168$		0			0
$169$	6.50000	−	11.2583i	0.500000	−	0.866025i
$170$		0			0
$171$	−6.00000			−0.458831
$172$		0			0
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$		0			0
$175$	2.50000	+	4.33013i	0.188982	+	0.327327i
$176$		0			0
$177$	−5.50000	−	9.52628i	−0.413405	−	0.716039i
$178$		0			0
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	−0.647397	−	0.762153i	$-0.724142\pi$
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	0.983742	+	0.179585i	$0.0574756\pi$
$180$		0			0
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	0.826465	−	0.562988i	$-0.190348\pi$
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	−0.900794	+	0.434246i	$0.857015\pi$
$182$		0			0
$183$	4.00000	−	6.92820i	0.295689	−	0.512148i
$184$		0			0
$185$	−16.0000			−1.17634
$186$		0			0
$187$	−18.0000			−1.31629
$188$		0			0
$189$	−2.50000	+	4.33013i	−0.181848	+	0.314970i
$190$		0			0
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$		0			0
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	−0.999326	−	0.0366998i	$-0.988315\pi$
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	0.531446	+	0.847092i	$0.321649\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	0.739141	−	0.673550i	$-0.235232\pi$
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	−0.952882	+	0.303340i	$0.901898\pi$
$198$		0			0
$199$	−6.50000	−	11.2583i	−0.460773	−	0.798082i	0.538227	−	0.842800i	$-0.319094\pi$
$199$	−6.50000	−	11.2583i	−0.460773	−	0.798082i	−0.999000	+	0.0447181i	$0.985761\pi$
$200$		0			0
$201$	12.0000			0.846415
$202$		0			0
$203$	7.50000	−	12.9904i	0.526397	−	0.911746i
$204$		0			0
$205$	−4.00000	+	6.92820i	−0.279372	+	0.483887i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	18.0000			1.24509
$210$		0			0
$211$	1.00000	−	1.73205i	0.0688428	−	0.119239i	−0.829549	−	0.558433i	$-0.811403\pi$
$211$	1.00000	−	1.73205i	0.0688428	−	0.119239i	0.898392	+	0.439194i	$0.144736\pi$
$212$		0			0
$213$	16.0000			1.09630
$214$		0			0
$215$	16.0000			1.09119
$216$		0			0
$217$	27.5000	−	4.33013i	1.86682	−	0.293948i
$218$		0			0
$219$	2.00000			0.135147
$220$		0			0
$221$		0			0
$222$		0			0
$223$	7.50000	−	12.9904i	0.502237	−	0.869900i	−0.497760	−	0.867315i	$-0.665844\pi$
$223$	7.50000	−	12.9904i	0.502237	−	0.869900i	0.999997	−	0.00258516i	$-0.000822884\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	−12.5000	−	21.6506i	−0.829654	−	1.43700i	−0.898310	−	0.439363i	$-0.855204\pi$
$227$	−12.5000	−	21.6506i	−0.829654	−	1.43700i	0.0686556	−	0.997640i	$-0.478129\pi$
$228$		0			0
$229$	−8.00000	+	13.8564i	−0.528655	+	0.915657i	0.470787	+	0.882247i	$0.343970\pi$
$229$	−8.00000	+	13.8564i	−0.528655	+	0.915657i	−0.999442	+	0.0334101i	$0.989363\pi$
$230$		0			0
$231$	7.50000	−	12.9904i	0.493464	−	0.854704i
$232$		0			0
$233$	12.0000			0.786146			0.393073	−	0.919507i	$-0.371412\pi$
$233$	12.0000			0.786146			0.393073	+	0.919507i	$0.371412\pi$
$234$		0			0
$235$	6.00000	+	10.3923i	0.391397	+	0.677919i
$236$		0			0
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$		0			0
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	0.934109	+	0.356988i	$0.116196\pi$
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	−0.157893	+	0.987456i	$0.550470\pi$
$240$		0			0
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	−0.999812	−	0.0193858i	$-0.993829\pi$
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	0.516695	+	0.856170i	$0.327162\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−18.0000	+	31.1769i	−1.14998	+	1.99182i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−11.0000			−0.697097
$250$		0			0
$251$	−14.0000	+	24.2487i	−0.883672	+	1.53057i	−0.0364441	+	0.999336i	$0.511603\pi$
$251$	−14.0000	+	24.2487i	−0.883672	+	1.53057i	−0.847228	+	0.531229i	$0.821730\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−6.00000	+	10.3923i	−0.375735	+	0.650791i
$256$		0			0
$257$	8.00000	+	13.8564i	0.499026	+	0.864339i	0.999999	−	0.00112398i	$-0.000357774\pi$
$257$	8.00000	+	13.8564i	0.499026	+	0.864339i	−0.500973	+	0.865463i	$0.667024\pi$
$258$		0			0
$259$	20.0000	+	34.6410i	1.24274	+	2.15249i
$260$		0			0
$261$	1.50000	+	2.59808i	0.0928477	+	0.160817i
$262$		0			0
$263$	−22.0000			−1.35658			−0.678289	−	0.734795i	$-0.737278\pi$
$263$	−22.0000			−1.35658			−0.678289	+	0.734795i	$0.737278\pi$
$264$		0			0
$265$	−1.00000	+	1.73205i	−0.0614295	+	0.106399i
$266$		0			0
$267$	1.00000	−	1.73205i	0.0611990	−	0.106000i
$268$		0			0
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$		0			0
$271$	−31.0000			−1.88312			−0.941558	−	0.336851i	$-0.890638\pi$
$271$	−31.0000			−1.88312			−0.941558	+	0.336851i	$0.890638\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.00000			0.180907
$276$		0			0
$277$	−6.00000			−0.360505			−0.180253	−	0.983620i	$-0.557691\pi$
$277$	−6.00000			−0.360505			−0.180253	+	0.983620i	$0.557691\pi$
$278$		0			0
$279$	−2.00000	+	5.19615i	−0.119737	+	0.311086i
$280$		0			0
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$		0			0
$283$	24.0000			1.42665			0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000			1.42665			0.713326	+	0.700832i	$0.247188\pi$
$284$		0			0
$285$	6.00000	−	10.3923i	0.355409	−	0.615587i
$286$		0			0
$287$	20.0000			1.18056
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$	−9.50000	+	16.4545i	−0.556900	+	0.964579i
$292$		0			0
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	−0.967009	−	0.254741i	$-0.918010\pi$
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	0.704117	+	0.710084i	$0.251343\pi$
$294$		0			0
$295$	22.0000			1.28089
$296$		0			0
$297$	1.50000	+	2.59808i	0.0870388	+	0.150756i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−20.0000	−	34.6410i	−1.15278	−	1.99667i
$302$		0			0
$303$	1.50000	−	2.59808i	0.0861727	−	0.149256i
$304$		0			0
$305$	8.00000	+	13.8564i	0.458079	+	0.793416i
$306$		0			0
$307$	−5.00000	+	8.66025i	−0.285365	+	0.494267i	−0.972698	−	0.232076i	$-0.925448\pi$
$307$	−5.00000	+	8.66025i	−0.285365	+	0.494267i	0.687333	+	0.726343i	$0.258782\pi$
$308$		0			0
$309$	1.00000			0.0568880
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	−4.50000	+	7.79423i	−0.254355	+	0.440556i	−0.964720	−	0.263278i	$-0.915197\pi$
$313$	−4.50000	+	7.79423i	−0.254355	+	0.440556i	0.710365	+	0.703833i	$0.248530\pi$
$314$		0			0
$315$	−5.00000	−	8.66025i	−0.281718	−	0.487950i
$316$		0			0
$317$	−10.5000	+	18.1865i	−0.589739	+	1.02146i	0.404528	+	0.914526i	$0.367436\pi$
$317$	−10.5000	+	18.1865i	−0.589739	+	1.02146i	−0.994266	+	0.106932i	$0.965897\pi$
$318$		0			0
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$		0			0
$321$	5.50000	+	9.52628i	0.306980	+	0.531705i
$322$		0			0
$323$	18.0000	+	31.1769i	1.00155	+	1.73473i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$		0			0
$329$	15.0000	−	25.9808i	0.826977	−	1.43237i
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$		0			0
$333$	−8.00000			−0.438397
$334$		0			0
$335$	−12.0000	+	20.7846i	−0.655630	+	1.13558i
$336$		0			0
$337$	−7.00000			−0.381314			−0.190657	−	0.981657i	$-0.561062\pi$
$337$	−7.00000			−0.381314			−0.190657	+	0.981657i	$0.561062\pi$
$338$		0			0
$339$	−4.00000			−0.217250
$340$		0			0
$341$	6.00000	−	15.5885i	0.324918	−	0.844162i
$342$		0			0
$343$	55.0000			2.96972
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.5000	+	30.3109i	−0.939449	+	1.62717i	−0.172948	+	0.984931i	$0.555329\pi$
$347$	−17.5000	+	30.3109i	−0.939449	+	1.62717i	−0.766501	+	0.642243i	$0.778004\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.0000	+	22.5167i	−0.691920	+	1.19844i	0.279288	+	0.960207i	$0.409902\pi$
$353$	−13.0000	+	22.5167i	−0.691920	+	1.19844i	−0.971208	+	0.238233i	$0.923432\pi$
$354$		0			0
$355$	−16.0000	+	27.7128i	−0.849192	+	1.47084i
$356$		0			0
$357$	30.0000			1.58777
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$		0			0
$363$	1.00000	+	1.73205i	0.0524864	+	0.0909091i
$364$		0			0
$365$	−2.00000	+	3.46410i	−0.104685	+	0.181319i
$366$		0			0
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$		0			0
$369$	−2.00000	+	3.46410i	−0.104116	+	0.180334i
$370$		0			0
$371$	5.00000			0.259587
$372$		0			0
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$		0			0
$375$	6.00000	−	10.3923i	0.309839	−	0.536656i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	9.00000	−	15.5885i	0.462299	−	0.800725i	−0.536776	−	0.843725i	$-0.680358\pi$
$379$	9.00000	−	15.5885i	0.462299	−	0.800725i	0.999075	+	0.0429994i	$0.0136914\pi$
$380$		0			0
$381$	−1.50000	−	2.59808i	−0.0768473	−	0.133103i
$382$		0			0
$383$	−14.0000	−	24.2487i	−0.715367	−	1.23905i	−0.962818	−	0.270151i	$-0.912926\pi$
$383$	−14.0000	−	24.2487i	−0.715367	−	1.23905i	0.247451	−	0.968900i	$-0.420407\pi$
$384$		0			0
$385$	15.0000	+	25.9808i	0.764471	+	1.32410i
$386$		0			0
$387$	8.00000			0.406663
$388$		0			0
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	0.942578	−	0.333987i	$-0.108394\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−6.00000	−	10.3923i	−0.302660	−	0.524222i
$394$		0			0
$395$	16.0000			0.805047
$396$		0			0
$397$	13.0000	−	22.5167i	0.652451	−	1.13008i	−0.330075	−	0.943955i	$-0.607074\pi$
$397$	13.0000	−	22.5167i	0.652451	−	1.13008i	0.982526	−	0.186124i	$-0.0595926\pi$
$398$		0			0
$399$	−30.0000			−1.50188
$400$		0			0
$401$	16.0000			0.799002			0.399501	−	0.916733i	$-0.369183\pi$
$401$	16.0000			0.799002			0.399501	+	0.916733i	$0.369183\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	2.00000			0.0993808
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	0.428063	+	0.903749i	$0.359196\pi$
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	−0.996701	+	0.0811615i	$0.974137\pi$
$410$		0			0
$411$	18.0000			0.887875
$412$		0			0
$413$	−27.5000	−	47.6314i	−1.35319	−	2.34379i
$414$		0			0
$415$	11.0000	−	19.0526i	0.539969	−	0.935253i
$416$		0			0
$417$	−7.00000	+	12.1244i	−0.342791	+	0.593732i
$418$		0			0
$419$	9.00000			0.439679			0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000			0.439679			0.219839	+	0.975536i	$0.429447\pi$
$420$		0			0
$421$	4.00000	+	6.92820i	0.194948	+	0.337660i	0.946883	−	0.321577i	$-0.104213\pi$
$421$	4.00000	+	6.92820i	0.194948	+	0.337660i	−0.751935	+	0.659237i	$0.770879\pi$
$422$		0			0
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$		0			0
$425$	3.00000	+	5.19615i	0.145521	+	0.252050i
$426$		0			0
$427$	20.0000	−	34.6410i	0.967868	−	1.67640i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−19.0000	+	32.9090i	−0.915198	+	1.58517i	−0.108586	+	0.994087i	$0.534632\pi$
$431$	−19.0000	+	32.9090i	−0.915198	+	1.58517i	−0.806611	+	0.591082i	$0.798701\pi$
$432$		0			0
$433$	−30.0000			−1.44171			−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000			−1.44171			−0.720854	+	0.693087i	$0.756250\pi$
$434$		0			0
$435$	−6.00000			−0.287678
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−8.50000	−	14.7224i	−0.405683	−	0.702663i	0.588718	−	0.808339i	$-0.299633\pi$
$439$	−8.50000	−	14.7224i	−0.405683	−	0.702663i	−0.994401	+	0.105675i	$0.966300\pi$
$440$		0			0
$441$	−9.00000	+	15.5885i	−0.428571	+	0.742307i
$442$		0			0
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	0.972626	−	0.232377i	$-0.0746503\pi$
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	−0.687557	+	0.726130i	$0.741317\pi$
$444$		0			0
$445$	2.00000	+	3.46410i	0.0948091	+	0.164214i
$446$		0			0
$447$	2.50000	+	4.33013i	0.118246	+	0.204808i
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	6.00000	−	10.3923i	0.282529	−	0.489355i
$452$		0			0
$453$	5.50000	−	9.52628i	0.258413	−	0.447584i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$		0			0
$459$	−3.00000	+	5.19615i	−0.140028	+	0.242536i
$460$		0			0
$461$	11.0000			0.512321			0.256161	−	0.966634i	$-0.417542\pi$
$461$	11.0000			0.512321			0.256161	+	0.966634i	$0.417542\pi$
$462$		0			0
$463$	−1.00000			−0.0464739			−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000			−0.0464739			−0.0232370	+	0.999730i	$0.507397\pi$
$464$		0			0
$465$	−7.00000	−	8.66025i	−0.324617	−	0.401610i
$466$		0			0
$467$	−3.00000			−0.138823			−0.0694117	−	0.997588i	$-0.522112\pi$
$467$	−3.00000			−0.138823			−0.0694117	+	0.997588i	$0.522112\pi$
$468$		0			0
$469$	60.0000			2.77054
$470$		0			0
$471$	−8.00000	+	13.8564i	−0.368621	+	0.638470i
$472$		0			0
$473$	−24.0000			−1.10352
$474$		0			0
$475$	−3.00000	−	5.19615i	−0.137649	−	0.238416i
$476$		0			0
$477$	−0.500000	+	0.866025i	−0.0228934	+	0.0396526i
$478$		0			0
$479$	5.00000	−	8.66025i	0.228456	−	0.395697i	−0.728895	−	0.684626i	$-0.759966\pi$
$479$	5.00000	−	8.66025i	0.228456	−	0.395697i	0.957351	+	0.288929i	$0.0932990\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−19.0000	−	32.9090i	−0.862746	−	1.49432i
$486$		0			0
$487$	−8.50000	−	14.7224i	−0.385172	−	0.667137i	0.606621	−	0.794991i	$-0.292524\pi$
$487$	−8.50000	−	14.7224i	−0.385172	−	0.667137i	−0.991793	+	0.127854i	$0.959191\pi$
$488$		0			0
$489$	2.00000	−	3.46410i	0.0904431	−	0.156652i
$490$		0			0
$491$	−8.50000	−	14.7224i	−0.383600	−	0.664414i	0.607974	−	0.793957i	$-0.291982\pi$
$491$	−8.50000	−	14.7224i	−0.383600	−	0.664414i	−0.991574	+	0.129543i	$0.958649\pi$
$492$		0			0
$493$	9.00000	−	15.5885i	0.405340	−	0.702069i
$494$		0			0
$495$	−6.00000			−0.269680
$496$		0			0
$497$	80.0000			3.58849
$498$		0			0
$499$	12.0000	−	20.7846i	0.537194	−	0.930447i	−0.461860	−	0.886953i	$-0.652818\pi$
$499$	12.0000	−	20.7846i	0.537194	−	0.930447i	0.999054	−	0.0434940i	$-0.0138489\pi$
$500$		0			0
$501$	−4.00000	−	6.92820i	−0.178707	−	0.309529i
$502$		0			0
$503$	−20.0000	+	34.6410i	−0.891756	+	1.54457i	−0.0539870	+	0.998542i	$0.517193\pi$
$503$	−20.0000	+	34.6410i	−0.891756	+	1.54457i	−0.837769	+	0.546025i	$0.816140\pi$
$504$		0			0
$505$	3.00000	+	5.19615i	0.133498	+	0.231226i
$506$		0			0
$507$	6.50000	+	11.2583i	0.288675	+	0.500000i
$508$		0			0
$509$	3.50000	+	6.06218i	0.155135	+	0.268701i	0.933108	−	0.359596i	$-0.117085\pi$
$509$	3.50000	+	6.06218i	0.155135	+	0.268701i	−0.777973	+	0.628297i	$0.783752\pi$
$510$		0			0
$511$	10.0000			0.442374
$512$		0			0
$513$	3.00000	−	5.19615i	0.132453	−	0.229416i
$514$		0			0
$515$	−1.00000	+	1.73205i	−0.0440653	+	0.0763233i
$516$		0			0
$517$	−9.00000	−	15.5885i	−0.395820	−	0.685580i
$518$		0			0
$519$	−9.00000			−0.395056
$520$		0			0
$521$	−2.00000	+	3.46410i	−0.0876216	+	0.151765i	−0.906505	−	0.422194i	$-0.861260\pi$
$521$	−2.00000	+	3.46410i	−0.0876216	+	0.151765i	0.818884	+	0.573959i	$0.194593\pi$
$522$		0			0
$523$	36.0000			1.57417			0.787085	−	0.616844i	$-0.211589\pi$
$523$	36.0000			1.57417			0.787085	+	0.616844i	$0.211589\pi$
$524$		0			0
$525$	−5.00000			−0.218218
$526$		0			0
$527$	33.0000	−	5.19615i	1.43750	−	0.226348i
$528$		0			0
$529$	−23.0000			−1.00000
$530$		0			0
$531$	11.0000			0.477359
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−22.0000			−0.951143
$536$		0			0
$537$	4.50000	+	7.79423i	0.194189	+	0.336346i
$538$		0			0
$539$	27.0000	−	46.7654i	1.16297	−	2.01433i
$540$		0			0
$541$	6.00000	−	10.3923i	0.257960	−	0.446800i	−0.707735	−	0.706478i	$-0.750283\pi$
$541$	6.00000	−	10.3923i	0.257960	−	0.446800i	0.965695	+	0.259678i	$0.0836163\pi$
$542$		0			0
$543$	2.00000			0.0858282
$544$		0			0
$545$	2.00000	+	3.46410i	0.0856706	+	0.148386i
$546$		0			0
$547$	17.0000	+	29.4449i	0.726868	+	1.25897i	0.958201	+	0.286097i	$0.0923579\pi$
$547$	17.0000	+	29.4449i	0.726868	+	1.25897i	−0.231333	+	0.972875i	$0.574309\pi$
$548$		0			0
$549$	4.00000	+	6.92820i	0.170716	+	0.295689i
$550$		0			0
$551$	−9.00000	+	15.5885i	−0.383413	+	0.664091i
$552$		0			0
$553$	−20.0000	−	34.6410i	−0.850487	−	1.47309i
$554$		0			0
$555$	8.00000	−	13.8564i	0.339581	−	0.588172i
$556$		0			0
$557$	23.0000			0.974541			0.487271	−	0.873251i	$-0.337993\pi$
$557$	23.0000			0.974541			0.487271	+	0.873251i	$0.337993\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$		0			0
$563$	−17.5000	−	30.3109i	−0.737537	−	1.27745i	−0.953601	−	0.301073i	$-0.902655\pi$
$563$	−17.5000	−	30.3109i	−0.737537	−	1.27745i	0.216064	−	0.976379i	$-0.430678\pi$
$564$		0			0
$565$	4.00000	−	6.92820i	0.168281	−	0.291472i
$566$		0			0
$567$	−2.50000	−	4.33013i	−0.104990	−	0.181848i
$568$		0			0
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	0.999994	+	0.00354413i	$0.00112814\pi$
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	−0.496928	+	0.867792i	$0.665539\pi$
$570$		0			0
$571$	−13.0000	−	22.5167i	−0.544033	−	0.942293i	−0.998667	−	0.0516146i	$-0.983563\pi$
$571$	−13.0000	−	22.5167i	−0.544033	−	0.942293i	0.454634	−	0.890678i	$-0.349770\pi$
$572$		0			0
$573$	12.0000			0.501307
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−19.0000	+	32.9090i	−0.790980	+	1.37002i	0.134380	+	0.990930i	$0.457096\pi$
$577$	−19.0000	+	32.9090i	−0.790980	+	1.37002i	−0.925361	+	0.379088i	$0.876238\pi$
$578$		0			0
$579$	−6.50000	−	11.2583i	−0.270131	−	0.467880i
$580$		0			0
$581$	−55.0000			−2.28178
$582$		0			0
$583$	1.50000	−	2.59808i	0.0621237	−	0.107601i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−41.0000			−1.69225			−0.846126	−	0.532984i	$-0.821071\pi$
$587$	−41.0000			−1.69225			−0.846126	+	0.532984i	$0.821071\pi$
$588$		0			0
$589$	−33.0000	+	5.19615i	−1.35974	+	0.214104i
$590$		0			0
$591$	6.00000			0.246807
$592$		0			0
$593$	−42.0000			−1.72473			−0.862367	−	0.506284i	$-0.831019\pi$
$593$	−42.0000			−1.72473			−0.862367	+	0.506284i	$0.831019\pi$
$594$		0			0
$595$	−30.0000	+	51.9615i	−1.22988	+	2.13021i
$596$		0			0
$597$	13.0000			0.532055
$598$		0			0
$599$	−20.0000	−	34.6410i	−0.817178	−	1.41539i	−0.907754	−	0.419504i	$-0.862204\pi$
$599$	−20.0000	−	34.6410i	−0.817178	−	1.41539i	0.0905757	−	0.995890i	$-0.471129\pi$
$600$		0			0
$601$	−11.0000	+	19.0526i	−0.448699	+	0.777170i	−0.998302	−	0.0582563i	$-0.981446\pi$
$601$	−11.0000	+	19.0526i	−0.448699	+	0.777170i	0.549602	+	0.835426i	$0.314779\pi$
$602$		0			0
$603$	−6.00000	+	10.3923i	−0.244339	+	0.423207i
$604$		0			0
$605$	−4.00000			−0.162623
$606$		0			0
$607$	−12.0000	−	20.7846i	−0.487065	−	0.843621i	0.512824	−	0.858494i	$-0.328599\pi$
$607$	−12.0000	−	20.7846i	−0.487065	−	0.843621i	−0.999889	+	0.0148722i	$0.995266\pi$
$608$		0			0
$609$	7.50000	+	12.9904i	0.303915	+	0.526397i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−14.0000	+	24.2487i	−0.565455	+	0.979396i	0.431553	+	0.902088i	$0.357966\pi$
$613$	−14.0000	+	24.2487i	−0.565455	+	0.979396i	−0.997007	+	0.0773084i	$0.975367\pi$
$614$		0			0
$615$	−4.00000	−	6.92820i	−0.161296	−	0.279372i
$616$		0			0
$617$	−6.00000	+	10.3923i	−0.241551	+	0.418378i	−0.961156	−	0.276005i	$-0.910989\pi$
$617$	−6.00000	+	10.3923i	−0.241551	+	0.418378i	0.719605	+	0.694383i	$0.244323\pi$
$618$		0			0
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	5.00000	−	8.66025i	0.200321	−	0.346966i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$		0			0
$627$	−9.00000	+	15.5885i	−0.359425	+	0.622543i
$628$		0			0
$629$	24.0000	+	41.5692i	0.956943	+	1.65747i
$630$		0			0
$631$	−2.50000	−	4.33013i	−0.0995234	−	0.172380i	0.811964	−	0.583707i	$-0.198398\pi$
$631$	−2.50000	−	4.33013i	−0.0995234	−	0.172380i	−0.911487	+	0.411328i	$0.865065\pi$
$632$		0			0
$633$	1.00000	+	1.73205i	0.0397464	+	0.0688428i
$634$		0			0
$635$	6.00000			0.238103
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−8.00000	+	13.8564i	−0.316475	+	0.548151i
$640$		0			0
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	0.722862	−	0.690992i	$-0.242826\pi$
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	−0.959848	+	0.280521i	$0.909493\pi$
$642$		0			0
$643$	16.0000			0.630978			0.315489	−	0.948929i	$-0.397831\pi$
$643$	16.0000			0.630978			0.315489	+	0.948929i	$0.397831\pi$
$644$		0			0
$645$	−8.00000	+	13.8564i	−0.315000	+	0.545595i
$646$		0			0
$647$	6.00000			0.235884			0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000			0.235884			0.117942	+	0.993020i	$0.462370\pi$
$648$		0			0
$649$	−33.0000			−1.29536
$650$		0			0
$651$	−10.0000	+	25.9808i	−0.391931	+	1.01827i
$652$		0			0
$653$	−41.0000			−1.60445			−0.802227	−	0.597019i	$-0.796352\pi$
$653$	−41.0000			−1.60445			−0.802227	+	0.597019i	$0.796352\pi$
$654$		0			0
$655$	24.0000			0.937758
$656$		0			0
$657$	−1.00000	+	1.73205i	−0.0390137	+	0.0675737i
$658$		0			0
$659$	−33.0000			−1.28550			−0.642749	−	0.766077i	$-0.722206\pi$
$659$	−33.0000			−1.28550			−0.642749	+	0.766077i	$0.722206\pi$
$660$		0			0
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	0.933144	+	0.359502i	$0.117053\pi$
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	−0.155235	+	0.987878i	$0.549613\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	30.0000	−	51.9615i	1.16335	−	2.01498i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	7.50000	+	12.9904i	0.289967	+	0.502237i
$670$		0			0
$671$	−12.0000	−	20.7846i	−0.463255	−	0.802381i
$672$		0			0
$673$	−6.50000	−	11.2583i	−0.250557	−	0.433977i	0.713123	−	0.701039i	$-0.247280\pi$
$673$	−6.50000	−	11.2583i	−0.250557	−	0.433977i	−0.963679	+	0.267063i	$0.913947\pi$
$674$		0			0
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$		0			0
$677$	18.5000	+	32.0429i	0.711013	+	1.23151i	0.964477	+	0.264166i	$0.0850965\pi$
$677$	18.5000	+	32.0429i	0.711013	+	1.23151i	−0.253465	+	0.967345i	$0.581570\pi$
$678$		0			0
$679$	−47.5000	+	82.2724i	−1.82288	+	3.15733i
$680$		0			0
$681$	25.0000			0.958002
$682$		0			0
$683$	−5.00000			−0.191320			−0.0956598	−	0.995414i	$-0.530496\pi$
$683$	−5.00000			−0.191320			−0.0956598	+	0.995414i	$0.530496\pi$
$684$		0			0
$685$	−18.0000	+	31.1769i	−0.687745	+	1.19121i
$686$		0			0
$687$	−8.00000	−	13.8564i	−0.305219	−	0.528655i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−11.0000	−	19.0526i	−0.418460	−	0.724793i	0.577325	−	0.816514i	$-0.304097\pi$
$691$	−11.0000	−	19.0526i	−0.418460	−	0.724793i	−0.995785	+	0.0917209i	$0.970763\pi$
$692$		0			0
$693$	7.50000	+	12.9904i	0.284901	+	0.493464i
$694$		0			0
$695$	−14.0000	−	24.2487i	−0.531050	−	0.919806i
$696$		0			0
$697$	24.0000			0.909065
$698$		0			0
$699$	−6.00000	+	10.3923i	−0.226941	+	0.393073i
$700$		0			0
$701$	7.50000	−	12.9904i	0.283271	−	0.490640i	−0.688917	−	0.724840i	$-0.741914\pi$
$701$	7.50000	−	12.9904i	0.283271	−	0.490640i	0.972188	+	0.234200i	$0.0752470\pi$
$702$		0			0
$703$	−24.0000	−	41.5692i	−0.905177	−	1.56781i
$704$		0			0
$705$	−12.0000			−0.451946
$706$		0			0
$707$	7.50000	−	12.9904i	0.282067	−	0.488554i
$708$		0			0
$709$	−4.00000			−0.150223			−0.0751116	−	0.997175i	$-0.523931\pi$
$709$	−4.00000			−0.150223			−0.0751116	+	0.997175i	$0.523931\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−24.0000			−0.896296
$718$		0			0
$719$	−1.00000	+	1.73205i	−0.0372937	+	0.0645946i	−0.884070	−	0.467355i	$-0.845207\pi$
$719$	−1.00000	+	1.73205i	−0.0372937	+	0.0645946i	0.846776	+	0.531949i	$0.178540\pi$
$720$		0			0
$721$	5.00000			0.186210
$722$		0			0
$723$	−7.50000	−	12.9904i	−0.278928	−	0.483117i
$724$		0			0
$725$	−1.50000	+	2.59808i	−0.0557086	+	0.0964901i
$726$		0			0
$727$	−23.5000	+	40.7032i	−0.871567	+	1.50960i	−0.0111912	+	0.999937i	$0.503562\pi$
$727$	−23.5000	+	40.7032i	−0.871567	+	1.50960i	−0.860376	+	0.509661i	$0.829771\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−24.0000	−	41.5692i	−0.887672	−	1.53749i
$732$		0			0
$733$	−17.0000	−	29.4449i	−0.627909	−	1.08757i	−0.987971	−	0.154642i	$-0.950578\pi$
$733$	−17.0000	−	29.4449i	−0.627909	−	1.08757i	0.360061	−	0.932929i	$-0.382756\pi$
$734$		0			0
$735$	−18.0000	−	31.1769i	−0.663940	−	1.14998i
$736$		0			0
$737$	18.0000	−	31.1769i	0.663039	−	1.14842i
$738$		0			0
$739$	7.00000	+	12.1244i	0.257499	+	0.446002i	0.965571	−	0.260138i	$-0.0837682\pi$
$739$	7.00000	+	12.1244i	0.257499	+	0.446002i	−0.708072	+	0.706140i	$0.750435\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	30.0000			1.10059			0.550297	−	0.834969i	$-0.314515\pi$
$743$	30.0000			1.10059			0.550297	+	0.834969i	$0.314515\pi$
$744$		0			0
$745$	−10.0000			−0.366372
$746$		0			0
$747$	5.50000	−	9.52628i	0.201234	−	0.348548i
$748$		0			0
$749$	27.5000	+	47.6314i	1.00483	+	1.74041i
$750$		0			0
$751$	−16.5000	+	28.5788i	−0.602094	+	1.04286i	0.390410	+	0.920641i	$0.372333\pi$
$751$	−16.5000	+	28.5788i	−0.602094	+	1.04286i	−0.992504	+	0.122216i	$0.961000\pi$
$752$		0			0
$753$	−14.0000	−	24.2487i	−0.510188	−	0.883672i
$754$		0			0
$755$	11.0000	+	19.0526i	0.400331	+	0.693394i
$756$		0			0
$757$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$757$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	−0.180957	−	0.983491i	$-0.557920\pi$
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	0.942207	−	0.335032i	$-0.108747\pi$
$762$		0			0
$763$	5.00000	−	8.66025i	0.181012	−	0.313522i
$764$		0			0
$765$	−6.00000	−	10.3923i	−0.216930	−	0.375735i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	27.5000	−	47.6314i	0.991675	−	1.71763i	0.384325	−	0.923198i	$-0.374434\pi$
$769$	27.5000	−	47.6314i	0.991675	−	1.71763i	0.607350	−	0.794434i	$-0.292233\pi$
$770$		0			0
$771$	−16.0000			−0.576226
$772$		0			0
$773$	−26.0000			−0.935155			−0.467578	−	0.883952i	$-0.654873\pi$
$773$	−26.0000			−0.935155			−0.467578	+	0.883952i	$0.654873\pi$
$774$		0			0
$775$	−5.50000	+	0.866025i	−0.197566	+	0.0311086i
$776$		0			0
$777$	−40.0000			−1.43499
$778$		0			0
$779$	−24.0000			−0.859889
$780$		0			0
$781$	24.0000	−	41.5692i	0.858788	−	1.48746i
$782$		0			0
$783$	−3.00000			−0.107211
$784$		0			0
$785$	−16.0000	−	27.7128i	−0.571064	−	0.989113i
$786$		0			0
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$		0			0
$789$	11.0000	−	19.0526i	0.391610	−	0.678289i
$790$		0			0
$791$	−20.0000			−0.711118
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−1.00000	−	1.73205i	−0.0354663	−	0.0614295i
$796$		0			0
$797$	4.50000	+	7.79423i	0.159398	+	0.276086i	0.934652	−	0.355564i	$-0.115711\pi$
$797$	4.50000	+	7.79423i	0.159398	+	0.276086i	−0.775254	+	0.631650i	$0.782378\pi$
$798$		0			0
$799$	18.0000	−	31.1769i	0.636794	−	1.10296i
$800$		0			0
$801$	1.00000	+	1.73205i	0.0353333	+	0.0611990i
$802$		0			0
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−18.0000			−0.633630
$808$		0			0
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$		0			0
$811$	1.00000	+	1.73205i	0.0351147	+	0.0608205i	0.883049	−	0.469281i	$-0.155487\pi$
$811$	1.00000	+	1.73205i	0.0351147	+	0.0608205i	−0.847934	+	0.530102i	$0.822154\pi$
$812$		0			0
$813$	15.5000	−	26.8468i	0.543609	−	0.941558i
$814$		0			0
$815$	4.00000	+	6.92820i	0.140114	+	0.242684i
$816$		0			0
$817$	24.0000	+	41.5692i	0.839654	+	1.45432i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.00000			−0.104701			−0.0523504	−	0.998629i	$-0.516671\pi$
$821$	−3.00000			−0.104701			−0.0523504	+	0.998629i	$0.516671\pi$
$822$		0			0
$823$	24.5000	−	42.4352i	0.854016	−	1.47920i	−0.0235383	−	0.999723i	$-0.507493\pi$
$823$	24.5000	−	42.4352i	0.854016	−	1.47920i	0.877555	−	0.479477i	$-0.159174\pi$
$824$		0			0
$825$	−1.50000	+	2.59808i	−0.0522233	+	0.0904534i
$826$		0			0
$827$	12.0000	+	20.7846i	0.417281	+	0.722752i	0.995665	−	0.0930129i	$-0.0296498\pi$
$827$	12.0000	+	20.7846i	0.417281	+	0.722752i	−0.578384	+	0.815765i	$0.696316\pi$
$828$		0			0
$829$	−6.00000			−0.208389			−0.104194	−	0.994557i	$-0.533226\pi$
$829$	−6.00000			−0.208389			−0.104194	+	0.994557i	$0.533226\pi$
$830$		0			0
$831$	3.00000	−	5.19615i	0.104069	−	0.180253i
$832$		0			0
$833$	108.000			3.74198
$834$		0			0
$835$	16.0000			0.553703
$836$		0			0
$837$	−3.50000	−	4.33013i	−0.120978	−	0.149671i
$838$		0			0
$839$	46.0000			1.58810			0.794048	−	0.607855i	$-0.207970\pi$
$839$	46.0000			1.58810			0.794048	+	0.607855i	$0.207970\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$		0			0
$843$	5.00000	−	8.66025i	0.172209	−	0.298275i
$844$		0			0
$845$	−26.0000			−0.894427
$846$		0			0
$847$	5.00000	+	8.66025i	0.171802	+	0.297570i
$848$		0			0
$849$	−12.0000	+	20.7846i	−0.411839	+	0.713326i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	16.0000			0.547830			0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000			0.547830			0.273915	+	0.961754i	$0.411681\pi$
$854$		0			0
$855$	6.00000	+	10.3923i	0.205196	+	0.355409i
$856$		0			0
$857$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$857$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$858$		0			0
$859$	−24.0000	−	41.5692i	−0.818869	−	1.41832i	−0.906516	−	0.422172i	$-0.861268\pi$
$859$	−24.0000	−	41.5692i	−0.818869	−	1.41832i	0.0876464	−	0.996152i	$-0.472065\pi$
$860$		0			0
$861$	−10.0000	+	17.3205i	−0.340799	+	0.590281i
$862$		0			0
$863$	12.0000	+	20.7846i	0.408485	+	0.707516i	0.994720	−	0.102624i	$-0.0327240\pi$
$863$	12.0000	+	20.7846i	0.408485	+	0.707516i	−0.586235	+	0.810141i	$0.699391\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$		0			0
$867$	19.0000			0.645274
$868$		0			0
$869$	−24.0000			−0.814144
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−9.50000	−	16.4545i	−0.321526	−	0.556900i
$874$		0			0
$875$	30.0000	−	51.9615i	1.01419	−	1.75662i
$876$		0			0
$877$	−12.0000	−	20.7846i	−0.405211	−	0.701846i	0.589135	−	0.808035i	$-0.299469\pi$
$877$	−12.0000	−	20.7846i	−0.405211	−	0.701846i	−0.994346	+	0.106188i	$0.966135\pi$
$878$		0			0
$879$	−4.50000	−	7.79423i	−0.151781	−	0.262893i
$880$		0			0
$881$	8.00000	+	13.8564i	0.269527	+	0.466834i	0.968740	−	0.248079i	$-0.0797994\pi$
$881$	8.00000	+	13.8564i	0.269527	+	0.466834i	−0.699213	+	0.714914i	$0.746466\pi$
$882$		0			0
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$		0			0
$885$	−11.0000	+	19.0526i	−0.369761	+	0.640445i
$886$		0			0
$887$	−13.0000	+	22.5167i	−0.436497	+	0.756035i	−0.997417	−	0.0718351i	$-0.977114\pi$
$887$	−13.0000	+	22.5167i	−0.436497	+	0.756035i	0.560919	+	0.827871i	$0.310448\pi$
$888$		0			0
$889$	−7.50000	−	12.9904i	−0.251542	−	0.435683i
$890$		0			0
$891$	−3.00000			−0.100504
$892$		0			0
$893$	−18.0000	+	31.1769i	−0.602347	+	1.04330i
$894$		0			0
$895$	−18.0000			−0.601674
$896$		0			0
$897$		0			0
$898$		0			0
$899$	10.5000	+	12.9904i	0.350195	+	0.433253i
$900$		0			0
$901$	6.00000			0.199889
$902$		0			0
$903$	40.0000			1.33112
$904$		0			0
$905$	−2.00000	+	3.46410i	−0.0664822	+	0.115151i
$906$		0			0
$907$	16.0000			0.531271			0.265636	−	0.964073i	$-0.414418\pi$
$907$	16.0000			0.531271			0.265636	+	0.964073i	$0.414418\pi$
$908$		0			0
$909$	1.50000	+	2.59808i	0.0497519	+	0.0861727i
$910$		0			0
$911$	15.0000	−	25.9808i	0.496972	−	0.860781i	−0.503022	−	0.864274i	$-0.667778\pi$
$911$	15.0000	−	25.9808i	0.496972	−	0.860781i	0.999994	+	0.00349271i	$0.00111177\pi$
$912$		0			0
$913$	−16.5000	+	28.5788i	−0.546070	+	0.945822i
$914$		0			0
$915$	−16.0000			−0.528944
$916$		0			0
$917$	−30.0000	−	51.9615i	−0.990687	−	1.71592i
$918$		0			0
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	0.760939	−	0.648824i	$-0.224739\pi$
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	−0.942367	+	0.334581i	$0.891405\pi$
$920$		0			0
$921$	−5.00000	−	8.66025i	−0.164756	−	0.285365i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$		0			0
$927$	−0.500000	+	0.866025i	−0.0164222	+	0.0284440i
$928$		0			0
$929$	18.0000			0.590561			0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000			0.590561			0.295280	+	0.955411i	$0.404587\pi$
$930$		0			0
$931$	−108.000			−3.53956
$932$		0			0
$933$		0			0
$934$		0			0
$935$	18.0000	+	31.1769i	0.588663	+	1.01959i
$936$		0			0
$937$	−15.0000	+	25.9808i	−0.490029	+	0.848755i	−0.999934	−	0.0114759i	$-0.996347\pi$
$937$	−15.0000	+	25.9808i	−0.490029	+	0.848755i	0.509906	+	0.860230i	$0.329680\pi$
$938$		0			0
$939$	−4.50000	−	7.79423i	−0.146852	−	0.254355i
$940$		0			0
$941$	10.5000	+	18.1865i	0.342290	+	0.592864i	0.984858	−	0.173365i	$-0.0554641\pi$
$941$	10.5000	+	18.1865i	0.342290	+	0.592864i	−0.642567	+	0.766229i	$0.722131\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	10.0000			0.325300
$946$		0			0
$947$	26.0000	−	45.0333i	0.844886	−	1.46339i	−0.0408333	−	0.999166i	$-0.513001\pi$
$947$	26.0000	−	45.0333i	0.844886	−	1.46339i	0.885720	−	0.464220i	$-0.153665\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−10.5000	−	18.1865i	−0.340486	−	0.589739i
$952$		0			0
$953$	−40.0000			−1.29573			−0.647864	−	0.761756i	$-0.724337\pi$
$953$	−40.0000			−1.29573			−0.647864	+	0.761756i	$0.724337\pi$
$954$		0			0
$955$	−12.0000	+	20.7846i	−0.388311	+	0.672574i
$956$		0			0
$957$	9.00000			0.290929
$958$		0			0
$959$	90.0000			2.90625
$960$		0			0
$961$	−6.50000	+	30.3109i	−0.209677	+	0.977771i
$962$		0			0
$963$	−11.0000			−0.354470
$964$		0			0
$965$	26.0000			0.836970
$966$		0			0
$967$	−12.0000	+	20.7846i	−0.385894	+	0.668388i	−0.991893	−	0.127078i	$-0.959440\pi$
$967$	−12.0000	+	20.7846i	−0.385894	+	0.668388i	0.605999	+	0.795466i	$0.292774\pi$
$968$		0			0
$969$	−36.0000			−1.15649
$970$		0			0
$971$	10.5000	+	18.1865i	0.336961	+	0.583634i	0.983860	−	0.178942i	$-0.0572676\pi$
$971$	10.5000	+	18.1865i	0.336961	+	0.583634i	−0.646899	+	0.762576i	$0.723934\pi$
$972$		0			0
$973$	−35.0000	+	60.6218i	−1.12205	+	1.94344i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	24.0000			0.767828			0.383914	−	0.923369i	$-0.374576\pi$
$977$	24.0000			0.767828			0.383914	+	0.923369i	$0.374576\pi$
$978$		0			0
$979$	−3.00000	−	5.19615i	−0.0958804	−	0.166070i
$980$		0			0
$981$	1.00000	+	1.73205i	0.0319275	+	0.0553001i
$982$		0			0
$983$	17.0000	+	29.4449i	0.542216	+	0.939145i	0.998776	+	0.0494530i	$0.0157478\pi$
$983$	17.0000	+	29.4449i	0.542216	+	0.939145i	−0.456561	+	0.889692i	$0.650919\pi$
$984$		0			0
$985$	−6.00000	+	10.3923i	−0.191176	+	0.331126i
$986$		0			0
$987$	15.0000	+	25.9808i	0.477455	+	0.826977i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	44.0000			1.39771			0.698853	−	0.715265i	$-0.253694\pi$
$991$	44.0000			1.39771			0.698853	+	0.715265i	$0.253694\pi$
$992$		0			0
$993$	−20.0000			−0.634681
$994$		0			0
$995$	−13.0000	+	22.5167i	−0.412128	+	0.713826i
$996$		0			0
$997$	−6.00000	−	10.3923i	−0.190022	−	0.329128i	0.755235	−	0.655454i	$-0.227523\pi$
$997$	−6.00000	−	10.3923i	−0.190022	−	0.329128i	−0.945257	+	0.326326i	$0.894189\pi$
$998$		0			0
$999$	4.00000	−	6.92820i	0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1488.2.q.a.625.1		2
4.3	odd	2		744.2.q.c.625.1	yes	2
12.11	even	2		2232.2.q.e.1369.1		2
31.25	even	3	inner	1488.2.q.a.769.1		2
124.87	odd	6		744.2.q.c.25.1	✓	2
372.335	even	6		2232.2.q.e.1513.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
744.2.q.c.25.1	✓	2	124.87	odd	6
744.2.q.c.625.1	yes	2	4.3	odd	2
1488.2.q.a.625.1		2	1.1	even	1	trivial
1488.2.q.a.769.1		2	31.25	even	3	inner
2232.2.q.e.1369.1		2	12.11	even	2
2232.2.q.e.1513.1		2	372.335	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1488 = 2^{4} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1488.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-2.50000 + 4.33013i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +2.00000 q^{15} +(-3.00000 + 5.19615i) q^{17} +(3.00000 - 5.19615i) q^{19} +(-2.50000 - 4.33013i) q^{21} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{27} -3.00000 q^{29} +(-3.50000 - 4.33013i) q^{31} -3.00000 q^{33} +10.0000 q^{35} +(4.00000 - 6.92820i) q^{37} +(-2.00000 - 3.46410i) q^{41} +(-4.00000 + 6.92820i) q^{43} +(-1.00000 + 1.73205i) q^{45} -6.00000 q^{47} +(-9.00000 - 15.5885i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(-0.500000 - 0.866025i) q^{53} +(3.00000 - 5.19615i) q^{55} +(3.00000 + 5.19615i) q^{57} +(-5.50000 + 9.52628i) q^{59} -8.00000 q^{61} +5.00000 q^{63} +(-6.00000 - 10.3923i) q^{67} +(-8.00000 - 13.8564i) q^{71} +(-1.00000 - 1.73205i) q^{73} +(0.500000 + 0.866025i) q^{75} -15.0000 q^{77} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.50000 + 9.52628i) q^{83} +12.0000 q^{85} +(1.50000 - 2.59808i) q^{87} -2.00000 q^{89} +(5.50000 - 0.866025i) q^{93} -12.0000 q^{95} +19.0000 q^{97} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} - 2 q^{5} - 5 q^{7} - q^{9} + 3 q^{11} + 4 q^{15} - 6 q^{17} + 6 q^{19} - 5 q^{21} + q^{25} + 2 q^{27} - 6 q^{29} - 7 q^{31} - 6 q^{33} + 20 q^{35} + 8 q^{37} - 4 q^{41} - 8 q^{43} - 2 q^{45}+ \cdots + 3 q^{99}+O(q^{100}) \) 2 * q - q^3 - 2 * q^5 - 5 * q^7 - q^9 + 3 * q^11 + 4 * q^15 - 6 * q^17 + 6 * q^19 - 5 * q^21 + q^25 + 2 * q^27 - 6 * q^29 - 7 * q^31 - 6 * q^33 + 20 * q^35 + 8 * q^37 - 4 * q^41 - 8 * q^43 - 2 * q^45 - 12 * q^47 - 18 * q^49 - 6 * q^51 - q^53 + 6 * q^55 + 6 * q^57 - 11 * q^59 - 16 * q^61 + 10 * q^63 - 12 * q^67 - 16 * q^71 - 2 * q^73 + q^75 - 30 * q^77 - 8 * q^79 - q^81 + 11 * q^83 + 24 * q^85 + 3 * q^87 - 4 * q^89 + 11 * q^93 - 24 * q^95 + 38 * q^97 + 3 * q^99

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