LMFDB - Embedded newform 744.2.q.c.625.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [744,2,Mod(25,744)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(744, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("744.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 744 = 2^{3} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	744.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.94086991038$
Analytic rank:	$0$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	744.625
Dual form			744.2.q.c.25.1

$q$-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 $\left(\mathbb{Z}/744\mathbb{Z}\right)^\times$.

$n$	$313$	$373$	$497$	$559$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	−	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	$-0.439481\pi$
$7$	2.50000	−	4.33013i	0.944911	−	1.63663i	0.755929	−	0.654654i	$-0.227186\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		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	$0.408286\pi$
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	−0.972404	+	0.233301i	$0.925047\pi$
$20$		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	$-0.624505\pi$
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$		0			0
$45$	−1.00000	+	1.73205i	−0.149071	+	0.258199i
$46$		0			0
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$		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	$-0.579287\pi$
$59$	5.50000	−	9.52628i	0.716039	−	1.24022i	0.962557	−	0.271078i	$-0.0873801\pi$
$60$		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	$0.0952216\pi$
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	−0.222571	+	0.974916i	$0.571445\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.00000	+	13.8564i	0.949425	+	1.64445i	0.746639	+	0.665230i	$0.231667\pi$
$71$	8.00000	+	13.8564i	0.949425	+	1.64445i	0.202787	+	0.979223i	$0.435000\pi$
$72$		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	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$		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	$-0.960358\pi$
$83$	−5.50000	−	9.52628i	−0.603703	−	1.04565i	0.388552	−	0.921427i	$-0.372976\pi$
$84$		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	0.889607	−	0.456727i	$-0.150978\pi$
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	−0.840341	+	0.542059i	$0.817645\pi$
$104$		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	$0.345115\pi$
$107$	−5.50000	+	9.52628i	−0.531705	+	0.920940i	−0.999315	+	0.0370053i	$0.988218\pi$
$108$		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	−0.791768	−	0.610822i	$-0.790839\pi$
$127$	1.50000	−	2.59808i	0.133103	−	0.230542i	0.924871	+	0.380280i	$0.124172\pi$
$128$		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	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		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	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$		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	$-0.352285\pi$
$151$	11.0000			0.895167			0.447584	+	0.894242i	$0.352285\pi$
$152$		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	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$		0			0
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$		0			0
$167$	4.00000	−	6.92820i	0.309529	−	0.536120i	−0.668730	−	0.743505i	$-0.733162\pi$
$167$	4.00000	−	6.92820i	0.309529	−	0.536120i	0.978259	+	0.207385i	$0.0664952\pi$
$168$		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	−0.983742	−	0.179585i	$-0.942524\pi$
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	0.647397	+	0.762153i	$0.275858\pi$
$180$		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	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		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	0.999000	−	0.0447181i	$-0.0142390\pi$
$199$	6.50000	+	11.2583i	0.460773	+	0.798082i	−0.538227	+	0.842800i	$0.680906\pi$
$200$		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	−0.898392	−	0.439194i	$-0.855264\pi$
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	0.829549	+	0.558433i	$0.188597\pi$
$212$		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	$0.334156\pi$
$223$	−7.50000	+	12.9904i	−0.502237	+	0.869900i	−0.999997	+	0.00258516i	$0.999177\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	12.5000	+	21.6506i	0.829654	+	1.43700i	0.898310	+	0.439363i	$0.144796\pi$
$227$	12.5000	+	21.6506i	0.829654	+	1.43700i	−0.0686556	+	0.997640i	$0.521871\pi$
$228$		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	$-0.883804\pi$
$239$	−12.0000	−	20.7846i	−0.776215	−	1.34444i	0.157893	−	0.987456i	$-0.449530\pi$
$240$		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	$-0.488397\pi$
$251$	14.0000	−	24.2487i	0.883672	−	1.53057i	0.847228	−	0.531229i	$-0.178270\pi$
$252$		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	$-0.262722\pi$
$263$	22.0000			1.35658			0.678289	+	0.734795i	$0.262722\pi$
$264$		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	$-0.109362\pi$
$271$	31.0000			1.88312			0.941558	+	0.336851i	$0.109362\pi$
$272$		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	$-0.752812\pi$
$283$	−24.0000			−1.42665			−0.713326	+	0.700832i	$0.752812\pi$
$284$		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	−0.687333	−	0.726343i	$-0.741218\pi$
$307$	5.00000	−	8.66025i	0.285365	−	0.494267i	0.972698	+	0.232076i	$0.0745518\pi$
$308$		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	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$		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	$-0.444671\pi$
$347$	17.5000	−	30.3109i	0.939449	−	1.62717i	0.766501	−	0.642243i	$-0.221996\pi$
$348$		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	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$		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	−0.999075	−	0.0429994i	$-0.986309\pi$
$379$	−9.00000	+	15.5885i	−0.462299	+	0.800725i	0.536776	+	0.843725i	$0.319642\pi$
$380$		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	$0.0870736\pi$
$383$	14.0000	+	24.2487i	0.715367	+	1.23905i	−0.247451	+	0.968900i	$0.579593\pi$
$384$		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	$-0.570553\pi$
$419$	−9.00000			−0.439679			−0.219839	+	0.975536i	$0.570553\pi$
$420$		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	$-0.465368\pi$
$431$	19.0000	−	32.9090i	0.915198	−	1.58517i	0.806611	−	0.591082i	$-0.201299\pi$
$432$		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	0.994401	−	0.105675i	$-0.0337004\pi$
$439$	8.50000	+	14.7224i	0.405683	+	0.702663i	−0.588718	+	0.808339i	$0.700367\pi$
$440$		0			0
$441$	−9.00000	+	15.5885i	−0.428571	+	0.742307i
$442$		0			0
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$		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	$-0.492603\pi$
$463$	1.00000			0.0464739			0.0232370	+	0.999730i	$0.492603\pi$
$464$		0			0
$465$	−7.00000	−	8.66025i	−0.324617	−	0.401610i
$466$		0			0
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$		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	−0.957351	−	0.288929i	$-0.906701\pi$
$479$	−5.00000	+	8.66025i	−0.228456	+	0.395697i	0.728895	+	0.684626i	$0.240034\pi$
$480$		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	0.991793	−	0.127854i	$-0.0408089\pi$
$487$	8.50000	+	14.7224i	0.385172	+	0.667137i	−0.606621	+	0.794991i	$0.707476\pi$
$488$		0			0
$489$	2.00000	−	3.46410i	0.0904431	−	0.156652i
$490$		0			0
$491$	8.50000	+	14.7224i	0.383600	+	0.664414i	0.991574	−	0.129543i	$-0.0413509\pi$
$491$	8.50000	+	14.7224i	0.383600	+	0.664414i	−0.607974	+	0.793957i	$0.708018\pi$
$492$		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	$0.347182\pi$
$499$	−12.0000	+	20.7846i	−0.537194	+	0.930447i	−0.999054	+	0.0434940i	$0.986151\pi$
$500$		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	$-0.482807\pi$
$503$	20.0000	−	34.6410i	0.891756	−	1.54457i	0.837769	−	0.546025i	$-0.183860\pi$
$504$		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	$-0.788411\pi$
$523$	−36.0000			−1.57417			−0.787085	+	0.616844i	$0.788411\pi$
$524$		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	$-0.907642\pi$
$547$	−17.0000	−	29.4449i	−0.726868	−	1.25897i	0.231333	−	0.972875i	$-0.425691\pi$
$548$		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	$0.0973446\pi$
$563$	17.5000	+	30.3109i	0.737537	+	1.27745i	−0.216064	+	0.976379i	$0.569322\pi$
$564$		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	$0.0164367\pi$
$571$	13.0000	+	22.5167i	0.544033	+	0.942293i	−0.454634	+	0.890678i	$0.650230\pi$
$572$		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	$-0.178929\pi$
$587$	41.0000			1.69225			0.846126	+	0.532984i	$0.178929\pi$
$588$		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	$0.137796\pi$
$599$	20.0000	+	34.6410i	0.817178	+	1.41539i	−0.0905757	+	0.995890i	$0.528871\pi$
$600$		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	0.999889	−	0.0148722i	$-0.00473415\pi$
$607$	12.0000	+	20.7846i	0.487065	+	0.843621i	−0.512824	+	0.858494i	$0.671401\pi$
$608$		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	$-0.435592\pi$
$619$	10.0000			0.401934			0.200967	+	0.979598i	$0.435592\pi$
$620$		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	0.911487	−	0.411328i	$-0.134935\pi$
$631$	2.50000	+	4.33013i	0.0995234	+	0.172380i	−0.811964	+	0.583707i	$0.801602\pi$
$632$		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	$-0.602169\pi$
$643$	−16.0000			−0.630978			−0.315489	+	0.948929i	$0.602169\pi$
$644$		0			0
$645$	−8.00000	+	13.8564i	−0.315000	+	0.545595i
$646$		0			0
$647$	−6.00000			−0.235884			−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000			−0.235884			−0.117942	+	0.993020i	$0.537630\pi$
$648$		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	$-0.277794\pi$
$659$	33.0000			1.28550			0.642749	+	0.766077i	$0.277794\pi$
$660$		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	$-0.469504\pi$
$683$	5.00000			0.191320			0.0956598	+	0.995414i	$0.469504\pi$
$684$		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	0.995785	−	0.0917209i	$-0.0292368\pi$
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	−0.577325	+	0.816514i	$0.695903\pi$
$692$		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	−0.846776	−	0.531949i	$-0.821460\pi$
$719$	1.00000	−	1.73205i	0.0372937	−	0.0645946i	0.884070	+	0.467355i	$0.154793\pi$
$720$		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	$-0.496438\pi$
$727$	23.5000	−	40.7032i	0.871567	−	1.50960i	0.860376	−	0.509661i	$-0.170229\pi$
$728$		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	0.708072	−	0.706140i	$-0.249565\pi$
$739$	−7.00000	−	12.1244i	−0.257499	−	0.446002i	−0.965571	+	0.260138i	$0.916232\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−30.0000			−1.10059			−0.550297	−	0.834969i	$-0.685485\pi$
$743$	−30.0000			−1.10059			−0.550297	+	0.834969i	$0.685485\pi$
$744$		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	$-0.627667\pi$
$751$	16.5000	−	28.5788i	0.602094	−	1.04286i	0.992504	−	0.122216i	$-0.0389999\pi$
$752$		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	−0.999999	−	0.00110111i	$-0.999650\pi$
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	0.500953	+	0.865474i	$0.332983\pi$
$788$		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	0.847934	−	0.530102i	$-0.177846\pi$
$811$	−1.00000	−	1.73205i	−0.0351147	−	0.0608205i	−0.883049	+	0.469281i	$0.844513\pi$
$812$		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	$0.492507\pi$
$823$	−24.5000	+	42.4352i	−0.854016	+	1.47920i	−0.877555	+	0.479477i	$0.840826\pi$
$824$		0			0
$825$	−1.50000	+	2.59808i	−0.0522233	+	0.0904534i
$826$		0			0
$827$	−12.0000	−	20.7846i	−0.417281	−	0.722752i	0.578384	−	0.815765i	$-0.303684\pi$
$827$	−12.0000	−	20.7846i	−0.417281	−	0.722752i	−0.995665	+	0.0930129i	$0.970350\pi$
$828$		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	$-0.792030\pi$
$839$	−46.0000			−1.58810			−0.794048	+	0.607855i	$0.792030\pi$
$840$		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	$0.138732\pi$
$859$	24.0000	+	41.5692i	0.818869	+	1.41832i	−0.0876464	+	0.996152i	$0.527935\pi$
$860$		0			0
$861$	−10.0000	+	17.3205i	−0.340799	+	0.590281i
$862$		0			0
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	0.586235	−	0.810141i	$-0.300609\pi$
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	−0.994720	+	0.102624i	$0.967276\pi$
$864$		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	$-0.292874\pi$
$883$	36.0000			1.21150			0.605748	+	0.795656i	$0.292874\pi$
$884$		0			0
$885$	−11.0000	+	19.0526i	−0.369761	+	0.640445i
$886$		0			0
$887$	13.0000	−	22.5167i	0.436497	−	0.756035i	−0.560919	−	0.827871i	$-0.689552\pi$
$887$	13.0000	−	22.5167i	0.436497	−	0.756035i	0.997417	+	0.0718351i	$0.0228855\pi$
$888$		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	$-0.585582\pi$
$907$	−16.0000			−0.531271			−0.265636	+	0.964073i	$0.585582\pi$
$908$		0			0
$909$	1.50000	+	2.59808i	0.0497519	+	0.0861727i
$910$		0			0
$911$	−15.0000	+	25.9808i	−0.496972	+	0.860781i	−0.999994	−	0.00349271i	$-0.998888\pi$
$911$	−15.0000	+	25.9808i	−0.496972	+	0.860781i	0.503022	+	0.864274i	$0.332222\pi$
$912$		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	0.942367	−	0.334581i	$-0.108595\pi$
$919$	5.50000	+	9.52628i	0.181428	+	0.314243i	−0.760939	+	0.648824i	$0.775261\pi$
$920$		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	$0.486999\pi$
$947$	−26.0000	+	45.0333i	−0.844886	+	1.46339i	−0.885720	+	0.464220i	$0.846335\pi$
$948$		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	−0.605999	−	0.795466i	$-0.707226\pi$
$967$	12.0000	−	20.7846i	0.385894	−	0.668388i	0.991893	+	0.127078i	$0.0405597\pi$
$968$		0			0
$969$	−36.0000			−1.15649
$970$		0			0
$971$	−10.5000	−	18.1865i	−0.336961	−	0.583634i	0.646899	−	0.762576i	$-0.276066\pi$
$971$	−10.5000	−	18.1865i	−0.336961	−	0.583634i	−0.983860	+	0.178942i	$0.942732\pi$
$972$		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	$-0.984252\pi$
$983$	−17.0000	−	29.4449i	−0.542216	−	0.939145i	0.456561	−	0.889692i	$-0.349081\pi$
$984$		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	$-0.746306\pi$
$991$	−44.0000			−1.39771			−0.698853	+	0.715265i	$0.746306\pi$
$992$		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	744.2.q.c.625.1	yes	2
3.2	odd	2		2232.2.q.e.1369.1		2
4.3	odd	2		1488.2.q.a.625.1		2
31.25	even	3	inner	744.2.q.c.25.1	✓	2
93.56	odd	6		2232.2.q.e.1513.1		2
124.87	odd	6		1488.2.q.a.769.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
744.2.q.c.25.1	✓	2	31.25	even	3	inner
744.2.q.c.625.1	yes	2	1.1	even	1	trivial
1488.2.q.a.625.1		2	4.3	odd	2
1488.2.q.a.769.1		2	124.87	odd	6
2232.2.q.e.1369.1		2	3.2	odd	2
2232.2.q.e.1513.1		2	93.56	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 744 = 2^{3} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	744.q (of order \(3\), degree \(2\), 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more