LMFDB - Embedded newform 585.2.j.b.451.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(406,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.406"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$4.67124851824$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	585.451
Dual form			585.2.j.b.406.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.73205i) q^{2} +(-1.00000 - 1.73205i) q^{4} +1.00000 q^{5} +(-2.50000 - 4.33013i) q^{7} +(1.00000 - 1.73205i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-2.50000 + 2.59808i) q^{13} -10.0000 q^{14} +(2.00000 - 3.46410i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-1.00000 - 1.73205i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(3.00000 - 5.19615i) q^{23} +1.00000 q^{25} +(2.00000 + 6.92820i) q^{26} +(-5.00000 + 8.66025i) q^{28} +(-2.00000 + 3.46410i) q^{29} -7.00000 q^{31} +(-4.00000 - 6.92820i) q^{32} +4.00000 q^{34} +(-2.50000 - 4.33013i) q^{35} +(1.00000 - 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{41} +(-0.500000 - 0.866025i) q^{43} -4.00000 q^{44} +(-6.00000 - 10.3923i) q^{46} +8.00000 q^{47} +(-9.00000 + 15.5885i) q^{49} +(1.00000 - 1.73205i) q^{50} +(7.00000 + 1.73205i) q^{52} +4.00000 q^{53} +(1.00000 - 1.73205i) q^{55} +(4.00000 + 6.92820i) q^{58} +(6.00000 + 10.3923i) q^{59} +(6.50000 + 11.2583i) q^{61} +(-7.00000 + 12.1244i) q^{62} -8.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +(3.50000 - 6.06218i) q^{67} +(2.00000 - 3.46410i) q^{68} -10.0000 q^{70} +(6.00000 + 10.3923i) q^{71} +15.0000 q^{73} +(-2.00000 - 3.46410i) q^{74} -10.0000 q^{77} +3.00000 q^{79} +(2.00000 - 3.46410i) q^{80} +(-6.00000 - 10.3923i) q^{82} -8.00000 q^{83} +(1.00000 + 1.73205i) q^{85} -2.00000 q^{86} +(7.00000 - 12.1244i) q^{89} +(17.5000 + 4.33013i) q^{91} -12.0000 q^{92} +(8.00000 - 13.8564i) q^{94} +(2.50000 + 4.33013i) q^{97} +(18.0000 + 31.1769i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 5 q^{7} + 2 q^{10} + 2 q^{11} - 5 q^{13} - 20 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{20} - 4 q^{22} + 6 q^{23} + 2 q^{25} + 4 q^{26} - 10 q^{28} - 4 q^{29} - 14 q^{31} - 8 q^{32}+ \cdots + 36 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 5 * q^7 + 2 * q^10 + 2 * q^11 - 5 * q^13 - 20 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^20 - 4 * q^22 + 6 * q^23 + 2 * q^25 + 4 * q^26 - 10 * q^28 - 4 * q^29 - 14 * q^31 - 8 * q^32 + 8 * q^34 - 5 * q^35 + 2 * q^37 + 6 * q^41 - q^43 - 8 * q^44 - 12 * q^46 + 16 * q^47 - 18 * q^49 + 2 * q^50 + 14 * q^52 + 8 * q^53 + 2 * q^55 + 8 * q^58 + 12 * q^59 + 13 * q^61 - 14 * q^62 - 16 * q^64 - 5 * q^65 + 7 * q^67 + 4 * q^68 - 20 * q^70 + 12 * q^71 + 30 * q^73 - 4 * q^74 - 20 * q^77 + 6 * q^79 + 4 * q^80 - 12 * q^82 - 16 * q^83 + 2 * q^85 - 4 * q^86 + 14 * q^89 + 35 * q^91 - 24 * q^92 + 16 * q^94 + 5 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−2.50000	−	4.33013i	−0.944911	−	1.63663i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−2.50000	−	4.33013i	−0.944911	−	1.63663i	−0.188982	−	0.981981i	$-0.560519\pi$
$8$		0			0
$9$		0			0
$10$	1.00000	−	1.73205i	0.316228	−	0.547723i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	−10.0000			−2.67261
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	−1.00000	−	1.73205i	−0.223607	−	0.387298i
$21$		0			0
$22$	−2.00000	−	3.46410i	−0.426401	−	0.738549i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	2.00000	+	6.92820i	0.392232	+	1.35873i
$27$		0			0
$28$	−5.00000	+	8.66025i	−0.944911	+	1.63663i
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	−0.989780	−	0.142605i	$-0.954452\pi$
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	0.618389	+	0.785872i	$0.287786\pi$
$30$		0			0
$31$	−7.00000			−1.25724			−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000			−1.25724			−0.628619	+	0.777714i	$0.716379\pi$
$32$	−4.00000	−	6.92820i	−0.707107	−	1.22474i
$33$		0			0
$34$	4.00000			0.685994
$35$	−2.50000	−	4.33013i	−0.422577	−	0.731925i
$36$		0			0
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$	−4.00000			−0.603023
$45$		0			0
$46$	−6.00000	−	10.3923i	−0.884652	−	1.53226i
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$		0			0
$49$	−9.00000	+	15.5885i	−1.28571	+	2.22692i
$50$	1.00000	−	1.73205i	0.141421	−	0.244949i
$51$		0			0
$52$	7.00000	+	1.73205i	0.970725	+	0.240192i
$53$	4.00000			0.549442			0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000			0.549442			0.274721	+	0.961524i	$0.411414\pi$
$54$		0			0
$55$	1.00000	−	1.73205i	0.134840	−	0.233550i
$56$		0			0
$57$		0			0
$58$	4.00000	+	6.92820i	0.525226	+	0.909718i
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	−7.00000	+	12.1244i	−0.889001	+	1.53979i
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−2.50000	+	2.59808i	−0.310087	+	0.322252i
$66$		0			0
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$		0			0
$70$	−10.0000			−1.19523
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	0.964079	+	0.265615i	$0.0855750\pi$
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	−0.252010	+	0.967725i	$0.581092\pi$
$72$		0			0
$73$	15.0000			1.75562			0.877809	−	0.479012i	$-0.159005\pi$
$73$	15.0000			1.75562			0.877809	+	0.479012i	$0.159005\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$		0			0
$76$		0			0
$77$	−10.0000			−1.13961
$78$		0			0
$79$	3.00000			0.337526			0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000			0.337526			0.168763	+	0.985657i	$0.446023\pi$
$80$	2.00000	−	3.46410i	0.223607	−	0.387298i
$81$		0			0
$82$	−6.00000	−	10.3923i	−0.662589	−	1.14764i
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$		0			0
$85$	1.00000	+	1.73205i	0.108465	+	0.187867i
$86$	−2.00000			−0.215666
$87$		0			0
$88$		0			0
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	−0.209585	−	0.977790i	$-0.567211\pi$
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	0.951584	−	0.307389i	$-0.0994552\pi$
$90$		0			0
$91$	17.5000	+	4.33013i	1.83450	+	0.453921i
$92$	−12.0000			−1.25109
$93$		0			0
$94$	8.00000	−	13.8564i	0.825137	−	1.42918i
$95$		0			0
$96$		0			0
$97$	2.50000	+	4.33013i	0.253837	+	0.439658i	0.964579	−	0.263795i	$-0.0849741\pi$
$97$	2.50000	+	4.33013i	0.253837	+	0.439658i	−0.710742	+	0.703452i	$0.751641\pi$
$98$	18.0000	+	31.1769i	1.81827	+	3.14934i
$99$		0			0
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$		0			0
$103$	−7.00000			−0.689730			−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000			−0.689730			−0.344865	+	0.938652i	$0.612075\pi$
$104$		0			0
$105$		0			0
$106$	4.00000	−	6.92820i	0.388514	−	0.672927i
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	−0.753010	−	0.658009i	$-0.771399\pi$
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	0.946357	+	0.323122i	$0.104732\pi$
$108$		0			0
$109$	−11.0000			−1.05361			−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000			−1.05361			−0.526804	+	0.849987i	$0.676610\pi$
$110$	−2.00000	−	3.46410i	−0.190693	−	0.330289i
$111$		0			0
$112$	−20.0000			−1.88982
$113$	−1.00000	−	1.73205i	−0.0940721	−	0.162938i	0.815149	−	0.579252i	$-0.196655\pi$
$113$	−1.00000	−	1.73205i	−0.0940721	−	0.162938i	−0.909221	+	0.416314i	$0.863322\pi$
$114$		0			0
$115$	3.00000	−	5.19615i	0.279751	−	0.484544i
$116$	8.00000			0.742781
$117$		0			0
$118$	24.0000			2.20938
$119$	5.00000	−	8.66025i	0.458349	−	0.793884i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	26.0000			2.35393
$123$		0			0
$124$	7.00000	+	12.1244i	0.628619	+	1.08880i
$125$	1.00000			0.0894427
$126$		0			0
$127$	5.50000	−	9.52628i	0.488046	−	0.845321i	−0.511859	−	0.859069i	$-0.671043\pi$
$127$	5.50000	−	9.52628i	0.488046	−	0.845321i	0.999905	+	0.0137486i	$0.00437646\pi$
$128$		0			0
$129$		0			0
$130$	2.00000	+	6.92820i	0.175412	+	0.607644i
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$		0			0
$133$		0			0
$134$	−7.00000	−	12.1244i	−0.604708	−	1.04738i
$135$		0			0
$136$		0			0
$137$	−1.00000	−	1.73205i	−0.0854358	−	0.147979i	0.820141	−	0.572161i	$-0.193895\pi$
$137$	−1.00000	−	1.73205i	−0.0854358	−	0.147979i	−0.905577	+	0.424182i	$0.860562\pi$
$138$		0			0
$139$	1.50000	+	2.59808i	0.127228	+	0.220366i	0.922602	−	0.385754i	$-0.126059\pi$
$139$	1.50000	+	2.59808i	0.127228	+	0.220366i	−0.795373	+	0.606120i	$0.792725\pi$
$140$	−5.00000	+	8.66025i	−0.422577	+	0.731925i
$141$		0			0
$142$	24.0000			2.01404
$143$	2.00000	+	6.92820i	0.167248	+	0.579365i
$144$		0			0
$145$	−2.00000	+	3.46410i	−0.166091	+	0.287678i
$146$	15.0000	−	25.9808i	1.24141	−	2.15018i
$147$		0			0
$148$	−4.00000			−0.328798
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	0.508413	−	0.861113i	$-0.330232\pi$
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	−0.999953	+	0.00974235i	$0.996899\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		0			0
$153$		0			0
$154$	−10.0000	+	17.3205i	−0.805823	+	1.39573i
$155$	−7.00000			−0.562254
$156$		0			0
$157$	−15.0000			−1.19713			−0.598565	−	0.801074i	$-0.704262\pi$
$157$	−15.0000			−1.19713			−0.598565	+	0.801074i	$0.704262\pi$
$158$	3.00000	−	5.19615i	0.238667	−	0.413384i
$159$		0			0
$160$	−4.00000	−	6.92820i	−0.316228	−	0.547723i
$161$	−30.0000			−2.36433
$162$		0			0
$163$	7.50000	+	12.9904i	0.587445	+	1.01749i	0.994566	+	0.104111i	$0.0331996\pi$
$163$	7.50000	+	12.9904i	0.587445	+	1.01749i	−0.407120	+	0.913375i	$0.633467\pi$
$164$	−12.0000			−0.937043
$165$		0			0
$166$	−8.00000	+	13.8564i	−0.620920	+	1.07547i
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	4.00000			0.306786
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$		0			0
$175$	−2.50000	−	4.33013i	−0.188982	−	0.327327i
$176$	−4.00000	−	6.92820i	−0.301511	−	0.522233i
$177$		0			0
$178$	−14.0000	−	24.2487i	−1.04934	−	1.81752i
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	−0.956088	−	0.293079i	$-0.905320\pi$
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	0.731858	+	0.681457i	$0.238654\pi$
$180$		0			0
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	25.0000	−	25.9808i	1.85312	−	1.92582i
$183$		0			0
$184$		0			0
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$		0			0
$187$	4.00000			0.292509
$188$	−8.00000	−	13.8564i	−0.583460	−	1.01058i
$189$		0			0
$190$		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
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	−0.597317	−	0.802005i	$-0.703766\pi$
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	0.993215	+	0.116289i	$0.0370998\pi$
$194$	10.0000			0.717958
$195$		0			0
$196$	36.0000			2.57143
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	−0.996649	−	0.0818013i	$-0.973933\pi$
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	0.569166	+	0.822222i	$0.307266\pi$
$198$		0			0
$199$	−8.50000	−	14.7224i	−0.602549	−	1.04365i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$	−8.50000	−	14.7224i	−0.602549	−	1.04365i	0.389885	−	0.920864i	$-0.372515\pi$
$200$		0			0
$201$		0			0
$202$	18.0000	+	31.1769i	1.26648	+	2.19360i
$203$	20.0000			1.40372
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	−7.00000	+	12.1244i	−0.487713	+	0.844744i
$207$		0			0
$208$	4.00000	+	13.8564i	0.277350	+	0.960769i
$209$		0			0
$210$		0			0
$211$	−7.50000	+	12.9904i	−0.516321	+	0.894295i	0.483499	+	0.875345i	$0.339366\pi$
$211$	−7.50000	+	12.9904i	−0.516321	+	0.894295i	−0.999820	+	0.0189499i	$0.993968\pi$
$212$	−4.00000	−	6.92820i	−0.274721	−	0.475831i
$213$		0			0
$214$	−4.00000	−	6.92820i	−0.273434	−	0.473602i
$215$	−0.500000	−	0.866025i	−0.0340997	−	0.0590624i
$216$		0			0
$217$	17.5000	+	30.3109i	1.18798	+	2.05764i
$218$	−11.0000	+	19.0526i	−0.745014	+	1.29040i
$219$		0			0
$220$	−4.00000			−0.269680
$221$	−7.00000	−	1.73205i	−0.470871	−	0.116510i
$222$		0			0
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	−0.700449	−	0.713702i	$-0.747017\pi$
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	0.968309	+	0.249756i	$0.0803503\pi$
$224$	−20.0000	+	34.6410i	−1.33631	+	2.31455i
$225$		0			0
$226$	−4.00000			−0.266076
$227$	5.00000	+	8.66025i	0.331862	+	0.574801i	0.982877	−	0.184263i	$-0.0589899\pi$
$227$	5.00000	+	8.66025i	0.331862	+	0.574801i	−0.651015	+	0.759065i	$0.725657\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	−6.00000	−	10.3923i	−0.395628	−	0.685248i
$231$		0			0
$232$		0			0
$233$	14.0000			0.917170			0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000			0.917170			0.458585	+	0.888650i	$0.348356\pi$
$234$		0			0
$235$	8.00000			0.521862
$236$	12.0000	−	20.7846i	0.781133	−	1.35296i
$237$		0			0
$238$	−10.0000	−	17.3205i	−0.648204	−	1.12272i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	14.0000			0.899954
$243$		0			0
$244$	13.0000	−	22.5167i	0.832240	−	1.44148i
$245$	−9.00000	+	15.5885i	−0.574989	+	0.995910i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	1.00000	−	1.73205i	0.0632456	−	0.109545i
$251$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$		0			0
$253$	−6.00000	−	10.3923i	−0.377217	−	0.653359i
$254$	−11.0000	−	19.0526i	−0.690201	−	1.19546i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	0.286909	+	0.957958i	$0.407372\pi$
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	−0.973070	+	0.230508i	$0.925961\pi$
$258$		0			0
$259$	−10.0000			−0.621370
$260$	7.00000	+	1.73205i	0.434122	+	0.107417i
$261$		0			0
$262$	4.00000	−	6.92820i	0.247121	−	0.428026i
$263$	−5.00000	+	8.66025i	−0.308313	+	0.534014i	−0.977993	−	0.208635i	$-0.933098\pi$
$263$	−5.00000	+	8.66025i	−0.308313	+	0.534014i	0.669680	+	0.742650i	$0.266431\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$		0			0
$267$		0			0
$268$	−14.0000			−0.855186
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$	−14.5000	+	25.1147i	−0.880812	+	1.52561i	−0.0303728	+	0.999539i	$0.509669\pi$
$271$	−14.5000	+	25.1147i	−0.880812	+	1.52561i	−0.850439	+	0.526073i	$0.823664\pi$
$272$	8.00000			0.485071
$273$		0			0
$274$	−4.00000			−0.241649
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$		0			0
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	0.675810	−	0.737075i	$-0.263794\pi$
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	−0.976231	+	0.216731i	$0.930460\pi$
$278$	6.00000			0.359856
$279$		0			0
$280$		0			0
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$		0			0
$283$	−2.50000	+	4.33013i	−0.148610	+	0.257399i	−0.930714	−	0.365748i	$-0.880813\pi$
$283$	−2.50000	+	4.33013i	−0.148610	+	0.257399i	0.782104	+	0.623148i	$0.214146\pi$
$284$	12.0000	−	20.7846i	0.712069	−	1.23334i
$285$		0			0
$286$	14.0000	+	3.46410i	0.827837	+	0.204837i
$287$	−30.0000			−1.77084
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	4.00000	+	6.92820i	0.234888	+	0.406838i
$291$		0			0
$292$	−15.0000	−	25.9808i	−0.877809	−	1.52041i
$293$	8.00000	+	13.8564i	0.467365	+	0.809500i	0.999305	−	0.0372823i	$-0.0118701\pi$
$293$	8.00000	+	13.8564i	0.467365	+	0.809500i	−0.531940	+	0.846782i	$0.678537\pi$
$294$		0			0
$295$	6.00000	+	10.3923i	0.349334	+	0.605063i
$296$		0			0
$297$		0			0
$298$	−24.0000			−1.39028
$299$	6.00000	+	20.7846i	0.346989	+	1.20201i
$300$		0			0
$301$	−2.50000	+	4.33013i	−0.144098	+	0.249584i
$302$	−8.00000	+	13.8564i	−0.460348	+	0.797347i
$303$		0			0
$304$		0			0
$305$	6.50000	+	11.2583i	0.372189	+	0.644650i
$306$		0			0
$307$	−31.0000			−1.76926			−0.884632	−	0.466290i	$-0.845590\pi$
$307$	−31.0000			−1.76926			−0.884632	+	0.466290i	$0.845590\pi$
$308$	10.0000	+	17.3205i	0.569803	+	0.986928i
$309$		0			0
$310$	−7.00000	+	12.1244i	−0.397573	+	0.688617i
$311$	22.0000			1.24751			0.623753	−	0.781622i	$-0.285607\pi$
$311$	22.0000			1.24751			0.623753	+	0.781622i	$0.285607\pi$
$312$		0			0
$313$	−31.0000			−1.75222			−0.876112	−	0.482108i	$-0.839871\pi$
$313$	−31.0000			−1.75222			−0.876112	+	0.482108i	$0.839871\pi$
$314$	−15.0000	+	25.9808i	−0.846499	+	1.46618i
$315$		0			0
$316$	−3.00000	−	5.19615i	−0.168763	−	0.292306i
$317$	−12.0000			−0.673987			−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000			−0.673987			−0.336994	+	0.941507i	$0.609410\pi$
$318$		0			0
$319$	4.00000	+	6.92820i	0.223957	+	0.387905i
$320$	−8.00000			−0.447214
$321$		0			0
$322$	−30.0000	+	51.9615i	−1.67183	+	2.89570i
$323$		0			0
$324$		0			0
$325$	−2.50000	+	2.59808i	−0.138675	+	0.144115i
$326$	30.0000			1.66155
$327$		0			0
$328$		0			0
$329$	−20.0000	−	34.6410i	−1.10264	−	1.90982i
$330$		0			0
$331$	−4.50000	−	7.79423i	−0.247342	−	0.428410i	0.715445	−	0.698669i	$-0.246224\pi$
$331$	−4.50000	−	7.79423i	−0.247342	−	0.428410i	−0.962788	+	0.270259i	$0.912891\pi$
$332$	8.00000	+	13.8564i	0.439057	+	0.760469i
$333$		0			0
$334$	−12.0000	−	20.7846i	−0.656611	−	1.13728i
$335$	3.50000	−	6.06218i	0.191225	−	0.331212i
$336$		0			0
$337$	−1.00000			−0.0544735			−0.0272367	−	0.999629i	$-0.508671\pi$
$337$	−1.00000			−0.0544735			−0.0272367	+	0.999629i	$0.508671\pi$
$338$	−23.0000	−	12.1244i	−1.25104	−	0.659478i
$339$		0			0
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$	−7.00000	+	12.1244i	−0.379071	+	0.656571i
$342$		0			0
$343$	55.0000			2.96972
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	0.567363	−	0.823468i	$-0.307964\pi$
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	−0.996826	+	0.0796169i	$0.974630\pi$
$348$		0			0
$349$	−1.50000	+	2.59808i	−0.0802932	+	0.139072i	−0.903376	−	0.428850i	$-0.858919\pi$
$349$	−1.50000	+	2.59808i	−0.0802932	+	0.139072i	0.823083	+	0.567922i	$0.192252\pi$
$350$	−10.0000			−0.534522
$351$		0			0
$352$	−16.0000			−0.852803
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$		0			0
$355$	6.00000	+	10.3923i	0.318447	+	0.551566i
$356$	−28.0000			−1.48400
$357$		0			0
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	−2.00000			−0.105556			−0.0527780	−	0.998606i	$-0.516808\pi$
$359$	−2.00000			−0.105556			−0.0527780	+	0.998606i	$0.516808\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	−22.0000	+	38.1051i	−1.15629	+	2.00276i
$363$		0			0
$364$	−10.0000	−	34.6410i	−0.524142	−	1.81568i
$365$	15.0000			0.785136
$366$		0			0
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	−0.942799	−	0.333363i	$-0.891817\pi$
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	0.760100	+	0.649806i	$0.225150\pi$
$368$	−12.0000	−	20.7846i	−0.625543	−	1.08347i
$369$		0			0
$370$	−2.00000	−	3.46410i	−0.103975	−	0.180090i
$371$	−10.0000	−	17.3205i	−0.519174	−	0.899236i
$372$		0			0
$373$	−6.50000	−	11.2583i	−0.336557	−	0.582934i	0.647225	−	0.762299i	$-0.275929\pi$
$373$	−6.50000	−	11.2583i	−0.336557	−	0.582934i	−0.983783	+	0.179364i	$0.942596\pi$
$374$	4.00000	−	6.92820i	0.206835	−	0.358249i
$375$		0			0
$376$		0			0
$377$	−4.00000	−	13.8564i	−0.206010	−	0.713641i
$378$		0			0
$379$	2.50000	−	4.33013i	0.128416	−	0.222424i	−0.794647	−	0.607072i	$-0.792344\pi$
$379$	2.50000	−	4.33013i	0.128416	−	0.222424i	0.923063	+	0.384648i	$0.125677\pi$
$380$		0			0
$381$		0			0
$382$	24.0000			1.22795
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$		0			0
$385$	−10.0000			−0.509647
$386$	−11.0000	−	19.0526i	−0.559885	−	0.969750i
$387$		0			0
$388$	5.00000	−	8.66025i	0.253837	−	0.439658i
$389$	−8.00000			−0.405616			−0.202808	−	0.979219i	$-0.565007\pi$
$389$	−8.00000			−0.405616			−0.202808	+	0.979219i	$0.565007\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$		0			0
$393$		0			0
$394$	12.0000	+	20.7846i	0.604551	+	1.04711i
$395$	3.00000			0.150946
$396$		0			0
$397$	7.50000	+	12.9904i	0.376414	+	0.651969i	0.990538	−	0.137241i	$-0.0438236\pi$
$397$	7.50000	+	12.9904i	0.376414	+	0.651969i	−0.614123	+	0.789210i	$0.710490\pi$
$398$	−34.0000			−1.70427
$399$		0			0
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	8.00000	−	13.8564i	0.399501	−	0.691956i	−0.594163	−	0.804344i	$-0.702517\pi$
$401$	8.00000	−	13.8564i	0.399501	−	0.691956i	0.993664	+	0.112388i	$0.0358501\pi$
$402$		0			0
$403$	17.5000	−	18.1865i	0.871737	−	0.905936i
$404$	36.0000			1.79107
$405$		0			0
$406$	20.0000	−	34.6410i	0.992583	−	1.71920i
$407$	−2.00000	−	3.46410i	−0.0991363	−	0.171709i
$408$		0			0
$409$	7.50000	+	12.9904i	0.370851	+	0.642333i	0.989697	−	0.143180i	$-0.0457327\pi$
$409$	7.50000	+	12.9904i	0.370851	+	0.642333i	−0.618846	+	0.785513i	$0.712399\pi$
$410$	−6.00000	−	10.3923i	−0.296319	−	0.513239i
$411$		0			0
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$	30.0000	−	51.9615i	1.47620	−	2.55686i
$414$		0			0
$415$	−8.00000			−0.392705
$416$	28.0000	+	6.92820i	1.37281	+	0.339683i
$417$		0			0
$418$		0			0
$419$	19.0000	−	32.9090i	0.928211	−	1.60771i	0.141896	−	0.989882i	$-0.454680\pi$
$419$	19.0000	−	32.9090i	0.928211	−	1.60771i	0.786314	−	0.617827i	$-0.211987\pi$
$420$		0			0
$421$	−23.0000			−1.12095			−0.560476	−	0.828171i	$-0.689382\pi$
$421$	−23.0000			−1.12095			−0.560476	+	0.828171i	$0.689382\pi$
$422$	15.0000	+	25.9808i	0.730189	+	1.26472i
$423$		0			0
$424$		0			0
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$		0			0
$427$	32.5000	−	56.2917i	1.57279	−	2.72414i
$428$	−8.00000			−0.386695
$429$		0			0
$430$	−2.00000			−0.0964486
$431$	−14.0000	+	24.2487i	−0.674356	+	1.16802i	0.302300	+	0.953213i	$0.402245\pi$
$431$	−14.0000	+	24.2487i	−0.674356	+	1.16802i	−0.976657	+	0.214807i	$0.931088\pi$
$432$		0			0
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	0.853761	−	0.520665i	$-0.174316\pi$
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	−0.877790	+	0.479046i	$0.840983\pi$
$434$	70.0000			3.36011
$435$		0			0
$436$	11.0000	+	19.0526i	0.526804	+	0.912452i
$437$		0			0
$438$		0			0
$439$	−7.50000	+	12.9904i	−0.357955	+	0.619997i	−0.987619	−	0.156871i	$-0.949859\pi$
$439$	−7.50000	+	12.9904i	−0.357955	+	0.619997i	0.629664	+	0.776868i	$0.283193\pi$
$440$		0			0
$441$		0			0
$442$	−10.0000	+	10.3923i	−0.475651	+	0.494312i
$443$	−26.0000			−1.23530			−0.617649	−	0.786454i	$-0.711915\pi$
$443$	−26.0000			−1.23530			−0.617649	+	0.786454i	$0.711915\pi$
$444$		0			0
$445$	7.00000	−	12.1244i	0.331832	−	0.574750i
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$		0			0
$448$	20.0000	+	34.6410i	0.944911	+	1.63663i
$449$	9.00000	+	15.5885i	0.424736	+	0.735665i	0.996396	−	0.0848262i	$-0.0270335\pi$
$449$	9.00000	+	15.5885i	0.424736	+	0.735665i	−0.571660	+	0.820491i	$0.693700\pi$
$450$		0			0
$451$	−6.00000	−	10.3923i	−0.282529	−	0.489355i
$452$	−2.00000	+	3.46410i	−0.0940721	+	0.162938i
$453$		0			0
$454$	20.0000			0.938647
$455$	17.5000	+	4.33013i	0.820413	+	0.202999i
$456$		0			0
$457$	−17.5000	+	30.3109i	−0.818615	+	1.41788i	0.0880870	+	0.996113i	$0.471925\pi$
$457$	−17.5000	+	30.3109i	−0.818615	+	1.41788i	−0.906702	+	0.421771i	$0.861409\pi$
$458$	14.0000	−	24.2487i	0.654177	−	1.13307i
$459$		0			0
$460$	−12.0000			−0.559503
$461$	−1.00000	−	1.73205i	−0.0465746	−	0.0806696i	0.841798	−	0.539792i	$-0.181497\pi$
$461$	−1.00000	−	1.73205i	−0.0465746	−	0.0806696i	−0.888373	+	0.459123i	$0.848164\pi$
$462$		0			0
$463$	3.00000			0.139422			0.0697109	−	0.997567i	$-0.477792\pi$
$463$	3.00000			0.139422			0.0697109	+	0.997567i	$0.477792\pi$
$464$	8.00000	+	13.8564i	0.371391	+	0.643268i
$465$		0			0
$466$	14.0000	−	24.2487i	0.648537	−	1.12330i
$467$	4.00000			0.185098			0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000			0.185098			0.0925490	+	0.995708i	$0.470499\pi$
$468$		0			0
$469$	−35.0000			−1.61615
$470$	8.00000	−	13.8564i	0.369012	−	0.639148i
$471$		0			0
$472$		0			0
$473$	−2.00000			−0.0919601
$474$		0			0
$475$		0			0
$476$	−20.0000			−0.916698
$477$		0			0
$478$	−12.0000	+	20.7846i	−0.548867	+	0.950666i
$479$	21.0000	−	36.3731i	0.959514	−	1.66193i	0.235833	−	0.971794i	$-0.424218\pi$
$479$	21.0000	−	36.3731i	0.959514	−	1.66193i	0.723681	−	0.690134i	$-0.242449\pi$
$480$		0			0
$481$	2.00000	+	6.92820i	0.0911922	+	0.315899i
$482$	−20.0000			−0.910975
$483$		0			0
$484$	7.00000	−	12.1244i	0.318182	−	0.551107i
$485$	2.50000	+	4.33013i	0.113519	+	0.196621i
$486$		0			0
$487$	14.0000	+	24.2487i	0.634401	+	1.09881i	0.986642	+	0.162905i	$0.0520863\pi$
$487$	14.0000	+	24.2487i	0.634401	+	1.09881i	−0.352241	+	0.935909i	$0.614580\pi$
$488$		0			0
$489$		0			0
$490$	18.0000	+	31.1769i	0.813157	+	1.40843i
$491$	−12.0000	+	20.7846i	−0.541552	+	0.937996i	0.457263	+	0.889332i	$0.348830\pi$
$491$	−12.0000	+	20.7846i	−0.541552	+	0.937996i	−0.998815	+	0.0486647i	$0.984503\pi$
$492$		0			0
$493$	−8.00000			−0.360302
$494$		0			0
$495$		0			0
$496$	−14.0000	+	24.2487i	−0.628619	+	1.08880i
$497$	30.0000	−	51.9615i	1.34568	−	2.33079i
$498$		0			0
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$	−1.00000	−	1.73205i	−0.0447214	−	0.0774597i
$501$		0			0
$502$		0			0
$503$	−3.00000	−	5.19615i	−0.133763	−	0.231685i	0.791361	−	0.611349i	$-0.209373\pi$
$503$	−3.00000	−	5.19615i	−0.133763	−	0.231685i	−0.925124	+	0.379664i	$0.876040\pi$
$504$		0			0
$505$	−9.00000	+	15.5885i	−0.400495	+	0.693677i
$506$	−24.0000			−1.06693
$507$		0			0
$508$	−22.0000			−0.976092
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	0.314459	+	0.949271i	$0.398177\pi$
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	−0.979322	+	0.202306i	$0.935156\pi$
$510$		0			0
$511$	−37.5000	−	64.9519i	−1.65890	−	2.87330i
$512$	−32.0000			−1.41421
$513$		0			0
$514$	22.0000	+	38.1051i	0.970378	+	1.68074i
$515$	−7.00000			−0.308457
$516$		0			0
$517$	8.00000	−	13.8564i	0.351840	−	0.609404i
$518$	−10.0000	+	17.3205i	−0.439375	+	0.761019i
$519$		0			0
$520$		0			0
$521$	30.0000			1.31432			0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000			1.31432			0.657162	+	0.753749i	$0.271757\pi$
$522$		0			0
$523$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$523$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$524$	−4.00000	−	6.92820i	−0.174741	−	0.302660i
$525$		0			0
$526$	10.0000	+	17.3205i	0.436021	+	0.755210i
$527$	−7.00000	−	12.1244i	−0.304925	−	0.528145i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	4.00000	−	6.92820i	0.173749	−	0.300942i
$531$		0			0
$532$		0			0
$533$	6.00000	+	20.7846i	0.259889	+	0.900281i
$534$		0			0
$535$	2.00000	−	3.46410i	0.0864675	−	0.149766i
$536$		0			0
$537$		0			0
$538$	−12.0000			−0.517357
$539$	18.0000	+	31.1769i	0.775315	+	1.34288i
$540$		0			0
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$	29.0000	+	50.2295i	1.24566	+	2.15754i
$543$		0			0
$544$	8.00000	−	13.8564i	0.342997	−	0.594089i
$545$	−11.0000			−0.471188
$546$		0			0
$547$	−9.00000			−0.384812			−0.192406	−	0.981315i	$-0.561629\pi$
$547$	−9.00000			−0.384812			−0.192406	+	0.981315i	$0.561629\pi$
$548$	−2.00000	+	3.46410i	−0.0854358	+	0.147979i
$549$		0			0
$550$	−2.00000	−	3.46410i	−0.0852803	−	0.147710i
$551$		0			0
$552$		0			0
$553$	−7.50000	−	12.9904i	−0.318932	−	0.552407i
$554$	−20.0000			−0.849719
$555$		0			0
$556$	3.00000	−	5.19615i	0.127228	−	0.220366i
$557$	−10.0000	+	17.3205i	−0.423714	+	0.733893i	−0.996299	−	0.0859514i	$-0.972607\pi$
$557$	−10.0000	+	17.3205i	−0.423714	+	0.733893i	0.572586	+	0.819845i	$0.305940\pi$
$558$		0			0
$559$	3.50000	+	0.866025i	0.148034	+	0.0366290i
$560$	−20.0000			−0.845154
$561$		0			0
$562$	12.0000	−	20.7846i	0.506189	−	0.876746i
$563$	13.0000	+	22.5167i	0.547885	+	0.948964i	0.998419	+	0.0562051i	$0.0179001\pi$
$563$	13.0000	+	22.5167i	0.547885	+	0.948964i	−0.450535	+	0.892759i	$0.648767\pi$
$564$		0			0
$565$	−1.00000	−	1.73205i	−0.0420703	−	0.0728679i
$566$	5.00000	+	8.66025i	0.210166	+	0.364018i
$567$		0			0
$568$		0			0
$569$	−10.0000	+	17.3205i	−0.419222	+	0.726113i	−0.995861	−	0.0908852i	$-0.971030\pi$
$569$	−10.0000	+	17.3205i	−0.419222	+	0.726113i	0.576640	+	0.816999i	$0.304364\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$	10.0000	−	10.3923i	0.418121	−	0.434524i
$573$		0			0
$574$	−30.0000	+	51.9615i	−1.25218	+	2.16883i
$575$	3.00000	−	5.19615i	0.125109	−	0.216695i
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	−13.0000	−	22.5167i	−0.540729	−	0.936570i
$579$		0			0
$580$	8.00000			0.332182
$581$	20.0000	+	34.6410i	0.829740	+	1.43715i
$582$		0			0
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$		0			0
$585$		0			0
$586$	32.0000			1.32191
$587$	14.0000	−	24.2487i	0.577842	−	1.00085i	−0.417885	−	0.908500i	$-0.637228\pi$
$587$	14.0000	−	24.2487i	0.577842	−	1.00085i	0.995726	−	0.0923513i	$-0.0294383\pi$
$588$		0			0
$589$		0			0
$590$	24.0000			0.988064
$591$		0			0
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	10.0000			0.410651			0.205325	−	0.978694i	$-0.434175\pi$
$593$	10.0000			0.410651			0.205325	+	0.978694i	$0.434175\pi$
$594$		0			0
$595$	5.00000	−	8.66025i	0.204980	−	0.355036i
$596$	−12.0000	+	20.7846i	−0.491539	+	0.851371i
$597$		0			0
$598$	42.0000	+	10.3923i	1.71751	+	0.424973i
$599$	16.0000			0.653742			0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000			0.653742			0.326871	+	0.945069i	$0.394006\pi$
$600$		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	$0.314779\pi$
$602$	5.00000	+	8.66025i	0.203785	+	0.352966i
$603$		0			0
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$		0			0
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	0.656744	−	0.754114i	$-0.271933\pi$
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	−0.981454	+	0.191700i	$0.938600\pi$
$608$		0			0
$609$		0			0
$610$	26.0000			1.05271
$611$	−20.0000	+	20.7846i	−0.809113	+	0.840855i
$612$		0			0
$613$	7.50000	−	12.9904i	0.302922	−	0.524677i	−0.673874	−	0.738846i	$-0.735371\pi$
$613$	7.50000	−	12.9904i	0.302922	−	0.524677i	0.976797	+	0.214169i	$0.0687045\pi$
$614$	−31.0000	+	53.6936i	−1.25106	+	2.16690i
$615$		0			0
$616$		0			0
$617$	3.00000	+	5.19615i	0.120775	+	0.209189i	0.920074	−	0.391745i	$-0.128129\pi$
$617$	3.00000	+	5.19615i	0.120775	+	0.209189i	−0.799298	+	0.600935i	$0.794795\pi$
$618$		0			0
$619$	37.0000			1.48716			0.743578	−	0.668649i	$-0.233127\pi$
$619$	37.0000			1.48716			0.743578	+	0.668649i	$0.233127\pi$
$620$	7.00000	+	12.1244i	0.281127	+	0.486926i
$621$		0			0
$622$	22.0000	−	38.1051i	0.882120	−	1.52788i
$623$	−70.0000			−2.80449
$624$		0			0
$625$	1.00000			0.0400000
$626$	−31.0000	+	53.6936i	−1.23901	+	2.14603i
$627$		0			0
$628$	15.0000	+	25.9808i	0.598565	+	1.03675i
$629$	4.00000			0.159490
$630$		0			0
$631$	−3.50000	−	6.06218i	−0.139333	−	0.241331i	0.787911	−	0.615789i	$-0.211162\pi$
$631$	−3.50000	−	6.06218i	−0.139333	−	0.241331i	−0.927244	+	0.374457i	$0.877829\pi$
$632$		0			0
$633$		0			0
$634$	−12.0000	+	20.7846i	−0.476581	+	0.825462i
$635$	5.50000	−	9.52628i	0.218261	−	0.378039i
$636$		0			0
$637$	−18.0000	−	62.3538i	−0.713186	−	2.47055i
$638$	16.0000			0.633446
$639$		0			0
$640$		0			0
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	0.885098	−	0.465404i	$-0.154091\pi$
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	−0.845601	+	0.533816i	$0.820758\pi$
$642$		0			0
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	0.990274	−	0.139134i	$-0.0444318\pi$
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	−0.615630	+	0.788035i	$0.711098\pi$
$644$	30.0000	+	51.9615i	1.18217	+	2.04757i
$645$		0			0
$646$		0			0
$647$	19.0000	−	32.9090i	0.746967	−	1.29378i	−0.202303	−	0.979323i	$-0.564843\pi$
$647$	19.0000	−	32.9090i	0.746967	−	1.29378i	0.949270	−	0.314462i	$-0.101824\pi$
$648$		0			0
$649$	24.0000			0.942082
$650$	2.00000	+	6.92820i	0.0784465	+	0.271746i
$651$		0			0
$652$	15.0000	−	25.9808i	0.587445	−	1.01749i
$653$	21.0000	−	36.3731i	0.821794	−	1.42339i	−0.0825519	−	0.996587i	$-0.526307\pi$
$653$	21.0000	−	36.3731i	0.821794	−	1.42339i	0.904345	−	0.426801i	$-0.140360\pi$
$654$		0			0
$655$	4.00000			0.156293
$656$	−12.0000	−	20.7846i	−0.468521	−	0.811503i
$657$		0			0
$658$	−80.0000			−3.11872
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	0.531855	−	0.846836i	$-0.321495\pi$
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	−0.999309	+	0.0371821i	$0.988162\pi$
$660$		0			0
$661$	−17.5000	+	30.3109i	−0.680671	+	1.17896i	0.294105	+	0.955773i	$0.404978\pi$
$661$	−17.5000	+	30.3109i	−0.680671	+	1.17896i	−0.974776	+	0.223184i	$0.928355\pi$
$662$	−18.0000			−0.699590
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	12.0000	+	20.7846i	0.464642	+	0.804783i
$668$	−24.0000			−0.928588
$669$		0			0
$670$	−7.00000	−	12.1244i	−0.270434	−	0.468405i
$671$	26.0000			1.00372
$672$		0			0
$673$	−16.5000	+	28.5788i	−0.636028	+	1.10163i	0.350268	+	0.936650i	$0.386091\pi$
$673$	−16.5000	+	28.5788i	−0.636028	+	1.10163i	−0.986296	+	0.164984i	$0.947243\pi$
$674$	−1.00000	+	1.73205i	−0.0385186	+	0.0667161i
$675$		0			0
$676$	−22.0000	+	13.8564i	−0.846154	+	0.532939i
$677$	12.0000			0.461197			0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000			0.461197			0.230599	+	0.973049i	$0.425932\pi$
$678$		0			0
$679$	12.5000	−	21.6506i	0.479706	−	0.830875i
$680$		0			0
$681$		0			0
$682$	14.0000	+	24.2487i	0.536088	+	0.928531i
$683$	−10.0000	−	17.3205i	−0.382639	−	0.662751i	0.608799	−	0.793324i	$-0.291651\pi$
$683$	−10.0000	−	17.3205i	−0.382639	−	0.662751i	−0.991439	+	0.130573i	$0.958318\pi$
$684$		0			0
$685$	−1.00000	−	1.73205i	−0.0382080	−	0.0661783i
$686$	55.0000	−	95.2628i	2.09991	−	3.63715i
$687$		0			0
$688$	−4.00000			−0.152499
$689$	−10.0000	+	10.3923i	−0.380970	+	0.395915i
$690$		0			0
$691$	−18.5000	+	32.0429i	−0.703773	+	1.21897i	0.263359	+	0.964698i	$0.415170\pi$
$691$	−18.5000	+	32.0429i	−0.703773	+	1.21897i	−0.967132	+	0.254273i	$0.918164\pi$
$692$		0			0
$693$		0			0
$694$	−32.0000			−1.21470
$695$	1.50000	+	2.59808i	0.0568982	+	0.0985506i
$696$		0			0
$697$	12.0000			0.454532
$698$	3.00000	+	5.19615i	0.113552	+	0.196677i
$699$		0			0
$700$	−5.00000	+	8.66025i	−0.188982	+	0.327327i
$701$	−40.0000			−1.51078			−0.755390	−	0.655276i	$-0.772552\pi$
$701$	−40.0000			−1.51078			−0.755390	+	0.655276i	$0.772552\pi$
$702$		0			0
$703$		0			0
$704$	−8.00000	+	13.8564i	−0.301511	+	0.522233i
$705$		0			0
$706$	−6.00000	−	10.3923i	−0.225813	−	0.391120i
$707$	90.0000			3.38480
$708$		0			0
$709$	11.5000	+	19.9186i	0.431892	+	0.748058i	0.997036	−	0.0769337i	$-0.0245130\pi$
$709$	11.5000	+	19.9186i	0.431892	+	0.748058i	−0.565145	+	0.824992i	$0.691180\pi$
$710$	24.0000			0.900704
$711$		0			0
$712$		0			0
$713$	−21.0000	+	36.3731i	−0.786456	+	1.36218i
$714$		0			0
$715$	2.00000	+	6.92820i	0.0747958	+	0.259100i
$716$	12.0000			0.448461
$717$		0			0
$718$	−2.00000	+	3.46410i	−0.0746393	+	0.129279i
$719$	20.0000	+	34.6410i	0.745874	+	1.29189i	0.949785	+	0.312903i	$0.101301\pi$
$719$	20.0000	+	34.6410i	0.745874	+	1.29189i	−0.203911	+	0.978989i	$0.565365\pi$
$720$		0			0
$721$	17.5000	+	30.3109i	0.651734	+	1.12884i
$722$	−19.0000	−	32.9090i	−0.707107	−	1.22474i
$723$		0			0
$724$	22.0000	+	38.1051i	0.817624	+	1.41617i
$725$	−2.00000	+	3.46410i	−0.0742781	+	0.128654i
$726$		0			0
$727$	9.00000			0.333792			0.166896	−	0.985975i	$-0.446626\pi$
$727$	9.00000			0.333792			0.166896	+	0.985975i	$0.446626\pi$
$728$		0			0
$729$		0			0
$730$	15.0000	−	25.9808i	0.555175	−	0.961591i
$731$	1.00000	−	1.73205i	0.0369863	−	0.0640622i
$732$		0			0
$733$	7.00000			0.258551			0.129275	−	0.991609i	$-0.458735\pi$
$733$	7.00000			0.258551			0.129275	+	0.991609i	$0.458735\pi$
$734$	7.00000	+	12.1244i	0.258375	+	0.447518i
$735$		0			0
$736$	−48.0000			−1.76930
$737$	−7.00000	−	12.1244i	−0.257848	−	0.446606i
$738$		0			0
$739$	18.0000	−	31.1769i	0.662141	−	1.14686i	−0.317911	−	0.948120i	$-0.602981\pi$
$739$	18.0000	−	31.1769i	0.662141	−	1.14686i	0.980052	−	0.198741i	$-0.0636852\pi$
$740$	−4.00000			−0.147043
$741$		0			0
$742$	−40.0000			−1.46845
$743$	12.0000	−	20.7846i	0.440237	−	0.762513i	−0.557470	−	0.830197i	$-0.688228\pi$
$743$	12.0000	−	20.7846i	0.440237	−	0.762513i	0.997707	+	0.0676840i	$0.0215610\pi$
$744$		0			0
$745$	−6.00000	−	10.3923i	−0.219823	−	0.380745i
$746$	−26.0000			−0.951928
$747$		0			0
$748$	−4.00000	−	6.92820i	−0.146254	−	0.253320i
$749$	−20.0000			−0.730784
$750$		0			0
$751$	14.0000	−	24.2487i	0.510867	−	0.884848i	−0.489053	−	0.872254i	$-0.662658\pi$
$751$	14.0000	−	24.2487i	0.510867	−	0.884848i	0.999921	−	0.0125942i	$-0.00400897\pi$
$752$	16.0000	−	27.7128i	0.583460	−	1.01058i
$753$		0			0
$754$	−28.0000	−	6.92820i	−1.01970	−	0.252310i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	−1.00000	+	1.73205i	−0.0363456	+	0.0629525i	−0.883626	−	0.468193i	$-0.844905\pi$
$757$	−1.00000	+	1.73205i	−0.0363456	+	0.0629525i	0.847280	+	0.531146i	$0.178238\pi$
$758$	−5.00000	−	8.66025i	−0.181608	−	0.314555i
$759$		0			0
$760$		0			0
$761$	−18.0000	−	31.1769i	−0.652499	−	1.13016i	−0.982514	−	0.186187i	$-0.940387\pi$
$761$	−18.0000	−	31.1769i	−0.652499	−	1.13016i	0.330015	−	0.943976i	$-0.392946\pi$
$762$		0			0
$763$	27.5000	+	47.6314i	0.995567	+	1.72437i
$764$	12.0000	−	20.7846i	0.434145	−	0.751961i
$765$		0			0
$766$	−36.0000			−1.30073
$767$	−42.0000	−	10.3923i	−1.51653	−	0.375244i
$768$		0			0
$769$	17.0000	−	29.4449i	0.613036	−	1.06181i	−0.377690	−	0.925932i	$-0.623282\pi$
$769$	17.0000	−	29.4449i	0.613036	−	1.06181i	0.990726	−	0.135877i	$-0.0433852\pi$
$770$	−10.0000	+	17.3205i	−0.360375	+	0.624188i
$771$		0			0
$772$	−22.0000			−0.791797
$773$	23.0000	+	39.8372i	0.827253	+	1.43284i	0.900186	+	0.435507i	$0.143431\pi$
$773$	23.0000	+	39.8372i	0.827253	+	1.43284i	−0.0729331	+	0.997337i	$0.523236\pi$
$774$		0			0
$775$	−7.00000			−0.251447
$776$		0			0
$777$		0			0
$778$	−8.00000	+	13.8564i	−0.286814	+	0.496776i
$779$		0			0
$780$		0			0
$781$	24.0000			0.858788
$782$	12.0000	−	20.7846i	0.429119	−	0.743256i
$783$		0			0
$784$	36.0000	+	62.3538i	1.28571	+	2.22692i
$785$	−15.0000			−0.535373
$786$		0			0
$787$	−8.50000	−	14.7224i	−0.302992	−	0.524798i	0.673820	−	0.738896i	$-0.264652\pi$
$787$	−8.50000	−	14.7224i	−0.302992	−	0.524798i	−0.976812	+	0.214097i	$0.931319\pi$
$788$	24.0000			0.854965
$789$		0			0
$790$	3.00000	−	5.19615i	0.106735	−	0.184871i
$791$	−5.00000	+	8.66025i	−0.177780	+	0.307923i
$792$		0			0
$793$	−45.5000	−	11.2583i	−1.61575	−	0.399795i
$794$	30.0000			1.06466
$795$		0			0
$796$	−17.0000	+	29.4449i	−0.602549	+	1.04365i
$797$	15.0000	+	25.9808i	0.531327	+	0.920286i	0.999331	+	0.0365596i	$0.0116399\pi$
$797$	15.0000	+	25.9808i	0.531327	+	0.920286i	−0.468004	+	0.883726i	$0.655027\pi$
$798$		0			0
$799$	8.00000	+	13.8564i	0.283020	+	0.490204i
$800$	−4.00000	−	6.92820i	−0.141421	−	0.244949i
$801$		0			0
$802$	−16.0000	−	27.7128i	−0.564980	−	0.978573i
$803$	15.0000	−	25.9808i	0.529339	−	0.916841i
$804$		0			0
$805$	−30.0000			−1.05736
$806$	−14.0000	−	48.4974i	−0.493129	−	1.70825i
$807$		0			0
$808$		0			0
$809$	2.00000	−	3.46410i	0.0703163	−	0.121791i	−0.828724	−	0.559658i	$-0.810932\pi$
$809$	2.00000	−	3.46410i	0.0703163	−	0.121791i	0.899040	+	0.437867i	$0.144266\pi$
$810$		0			0
$811$	45.0000			1.58016			0.790082	−	0.613001i	$-0.210038\pi$
$811$	45.0000			1.58016			0.790082	+	0.613001i	$0.210038\pi$
$812$	−20.0000	−	34.6410i	−0.701862	−	1.21566i
$813$		0			0
$814$	−8.00000			−0.280400
$815$	7.50000	+	12.9904i	0.262714	+	0.455033i
$816$		0			0
$817$		0			0
$818$	30.0000			1.04893
$819$		0			0
$820$	−12.0000			−0.419058
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$		0			0
$823$	−10.0000	−	17.3205i	−0.348578	−	0.603755i	0.637419	−	0.770517i	$-0.280002\pi$
$823$	−10.0000	−	17.3205i	−0.348578	−	0.603755i	−0.985997	+	0.166762i	$0.946669\pi$
$824$		0			0
$825$		0			0
$826$	−60.0000	−	103.923i	−2.08767	−	3.61595i
$827$	−46.0000			−1.59958			−0.799788	−	0.600282i	$-0.795055\pi$
$827$	−46.0000			−1.59958			−0.799788	+	0.600282i	$0.795055\pi$
$828$		0			0
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	−0.754567	−	0.656223i	$-0.772153\pi$
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	0.945589	+	0.325362i	$0.105486\pi$
$830$	−8.00000	+	13.8564i	−0.277684	+	0.480963i
$831$		0			0
$832$	20.0000	−	20.7846i	0.693375	−	0.720577i
$833$	−36.0000			−1.24733
$834$		0			0
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$		0			0
$837$		0			0
$838$	−38.0000	−	65.8179i	−1.31269	−	2.27364i
$839$	−17.0000	−	29.4449i	−0.586905	−	1.01655i	−0.994635	−	0.103447i	$-0.967013\pi$
$839$	−17.0000	−	29.4449i	−0.586905	−	1.01655i	0.407730	−	0.913103i	$-0.366321\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	−23.0000	+	39.8372i	−0.792632	+	1.37288i
$843$		0			0
$844$	30.0000			1.03264
$845$	−0.500000	−	12.9904i	−0.0172005	−	0.446883i
$846$		0			0
$847$	17.5000	−	30.3109i	0.601307	−	1.04149i
$848$	8.00000	−	13.8564i	0.274721	−	0.475831i
$849$		0			0
$850$	4.00000			0.137199
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$		0			0
$853$	9.00000			0.308154			0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000			0.308154			0.154077	+	0.988059i	$0.450760\pi$
$854$	−65.0000	−	112.583i	−2.22425	−	3.85252i
$855$		0			0
$856$		0			0
$857$	12.0000			0.409912			0.204956	−	0.978771i	$-0.434295\pi$
$857$	12.0000			0.409912			0.204956	+	0.978771i	$0.434295\pi$
$858$		0			0
$859$	43.0000			1.46714			0.733571	−	0.679613i	$-0.237852\pi$
$859$	43.0000			1.46714			0.733571	+	0.679613i	$0.237852\pi$
$860$	−1.00000	+	1.73205i	−0.0340997	+	0.0590624i
$861$		0			0
$862$	28.0000	+	48.4974i	0.953684	+	1.65183i
$863$	−6.00000			−0.204242			−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000			−0.204242			−0.102121	+	0.994772i	$0.532563\pi$
$864$		0			0
$865$		0			0
$866$	−2.00000			−0.0679628
$867$		0			0
$868$	35.0000	−	60.6218i	1.18798	−	2.05764i
$869$	3.00000	−	5.19615i	0.101768	−	0.176267i
$870$		0			0
$871$	7.00000	+	24.2487i	0.237186	+	0.821636i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.50000	−	4.33013i	−0.0845154	−	0.146385i
$876$		0			0
$877$	−3.00000	−	5.19615i	−0.101303	−	0.175462i	0.810919	−	0.585159i	$-0.198968\pi$
$877$	−3.00000	−	5.19615i	−0.101303	−	0.175462i	−0.912222	+	0.409697i	$0.865634\pi$
$878$	15.0000	+	25.9808i	0.506225	+	0.876808i
$879$		0			0
$880$	−4.00000	−	6.92820i	−0.134840	−	0.233550i
$881$	10.0000	−	17.3205i	0.336909	−	0.583543i	−0.646941	−	0.762540i	$-0.723952\pi$
$881$	10.0000	−	17.3205i	0.336909	−	0.583543i	0.983850	+	0.178997i	$0.0572853\pi$
$882$		0			0
$883$	−25.0000			−0.841317			−0.420658	−	0.907219i	$-0.638201\pi$
$883$	−25.0000			−0.841317			−0.420658	+	0.907219i	$0.638201\pi$
$884$	4.00000	+	13.8564i	0.134535	+	0.466041i
$885$		0			0
$886$	−26.0000	+	45.0333i	−0.873487	+	1.51292i
$887$	−22.0000	+	38.1051i	−0.738688	+	1.27944i	0.214399	+	0.976746i	$0.431221\pi$
$887$	−22.0000	+	38.1051i	−0.738688	+	1.27944i	−0.953086	+	0.302698i	$0.902113\pi$
$888$		0			0
$889$	−55.0000			−1.84464
$890$	−14.0000	−	24.2487i	−0.469281	−	0.812819i
$891$		0			0
$892$	−16.0000			−0.535720
$893$		0			0
$894$		0			0
$895$	−3.00000	+	5.19615i	−0.100279	+	0.173688i
$896$		0			0
$897$		0			0
$898$	36.0000			1.20134
$899$	14.0000	−	24.2487i	0.466926	−	0.808740i
$900$		0			0
$901$	4.00000	+	6.92820i	0.133259	+	0.230812i
$902$	−24.0000			−0.799113
$903$		0			0
$904$		0			0
$905$	−22.0000			−0.731305
$906$		0			0
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	−0.982913	−	0.184073i	$-0.941072\pi$
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	0.650868	+	0.759191i	$0.274405\pi$
$908$	10.0000	−	17.3205i	0.331862	−	0.574801i
$909$		0			0
$910$	25.0000	−	25.9808i	0.828742	−	0.861254i
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	−8.00000	+	13.8564i	−0.264761	+	0.458580i
$914$	35.0000	+	60.6218i	1.15770	+	2.00519i
$915$		0			0
$916$	−14.0000	−	24.2487i	−0.462573	−	0.801200i
$917$	−10.0000	−	17.3205i	−0.330229	−	0.571974i
$918$		0			0
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	0.792480	−	0.609898i	$-0.208790\pi$
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	−0.924427	+	0.381358i	$0.875456\pi$
$920$		0			0
$921$		0			0
$922$	−4.00000			−0.131733
$923$	−42.0000	−	10.3923i	−1.38245	−	0.342067i
$924$		0			0
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$	3.00000	−	5.19615i	0.0985861	−	0.170756i
$927$		0			0
$928$	32.0000			1.05045
$929$	26.0000	+	45.0333i	0.853032	+	1.47750i	0.878459	+	0.477819i	$0.158572\pi$
$929$	26.0000	+	45.0333i	0.853032	+	1.47750i	−0.0254262	+	0.999677i	$0.508094\pi$
$930$		0			0
$931$		0			0
$932$	−14.0000	−	24.2487i	−0.458585	−	0.794293i
$933$		0			0
$934$	4.00000	−	6.92820i	0.130884	−	0.226698i
$935$	4.00000			0.130814
$936$		0			0
$937$	−30.0000			−0.980057			−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000			−0.980057			−0.490029	+	0.871706i	$0.663014\pi$
$938$	−35.0000	+	60.6218i	−1.14279	+	1.97937i
$939$		0			0
$940$	−8.00000	−	13.8564i	−0.260931	−	0.451946i
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$		0			0
$943$	−18.0000	−	31.1769i	−0.586161	−	1.01526i
$944$	48.0000			1.56227
$945$		0			0
$946$	−2.00000	+	3.46410i	−0.0650256	+	0.112628i
$947$	9.00000	−	15.5885i	0.292461	−	0.506557i	−0.681930	−	0.731417i	$-0.738859\pi$
$947$	9.00000	−	15.5885i	0.292461	−	0.506557i	0.974391	+	0.224860i	$0.0721926\pi$
$948$		0			0
$949$	−37.5000	+	38.9711i	−1.21730	+	1.26506i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	0.910516	−	0.413473i	$-0.135685\pi$
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	−0.813337	+	0.581793i	$0.802351\pi$
$954$		0			0
$955$	6.00000	+	10.3923i	0.194155	+	0.336287i
$956$	12.0000	+	20.7846i	0.388108	+	0.672222i
$957$		0			0
$958$	−42.0000	−	72.7461i	−1.35696	−	2.35032i
$959$	−5.00000	+	8.66025i	−0.161458	+	0.279654i
$960$		0			0
$961$	18.0000			0.580645
$962$	14.0000	+	3.46410i	0.451378	+	0.111687i
$963$		0			0
$964$	−10.0000	+	17.3205i	−0.322078	+	0.557856i
$965$	5.50000	−	9.52628i	0.177051	−	0.306662i
$966$		0			0
$967$	−56.0000			−1.80084			−0.900419	−	0.435023i	$-0.856740\pi$
$967$	−56.0000			−1.80084			−0.900419	+	0.435023i	$0.856740\pi$
$968$		0			0
$969$		0			0
$970$	10.0000			0.321081
$971$	10.0000	+	17.3205i	0.320915	+	0.555842i	0.980677	−	0.195633i	$-0.0626762\pi$
$971$	10.0000	+	17.3205i	0.320915	+	0.555842i	−0.659762	+	0.751475i	$0.729343\pi$
$972$		0			0
$973$	7.50000	−	12.9904i	0.240439	−	0.416452i
$974$	56.0000			1.79436
$975$		0			0
$976$	52.0000			1.66448
$977$	30.0000	−	51.9615i	0.959785	−	1.66240i	0.236768	−	0.971566i	$-0.423912\pi$
$977$	30.0000	−	51.9615i	0.959785	−	1.66240i	0.723017	−	0.690830i	$-0.242755\pi$
$978$		0			0
$979$	−14.0000	−	24.2487i	−0.447442	−	0.774992i
$980$	36.0000			1.14998
$981$		0			0
$982$	24.0000	+	41.5692i	0.765871	+	1.32653i
$983$	−38.0000			−1.21201			−0.606006	−	0.795460i	$-0.707229\pi$
$983$	−38.0000			−1.21201			−0.606006	+	0.795460i	$0.707229\pi$
$984$		0			0
$985$	−6.00000	+	10.3923i	−0.191176	+	0.331126i
$986$	−8.00000	+	13.8564i	−0.254772	+	0.441278i
$987$		0			0
$988$		0			0
$989$	−6.00000			−0.190789
$990$		0			0
$991$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$991$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$992$	28.0000	+	48.4974i	0.889001	+	1.53979i
$993$		0			0
$994$	−60.0000	−	103.923i	−1.90308	−	3.29624i
$995$	−8.50000	−	14.7224i	−0.269468	−	0.466732i
$996$		0			0
$997$	−14.5000	−	25.1147i	−0.459220	−	0.795392i	0.539700	−	0.841857i	$-0.318538\pi$
$997$	−14.5000	−	25.1147i	−0.459220	−	0.795392i	−0.998920	+	0.0464655i	$0.985204\pi$
$998$	4.00000	−	6.92820i	0.126618	−	0.219308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.b.451.1		2
3.2	odd	2		195.2.i.a.61.1	yes	2
13.3	even	3	inner	585.2.j.b.406.1		2
13.4	even	6		7605.2.a.s.1.1		1
13.9	even	3		7605.2.a.a.1.1		1
15.2	even	4		975.2.bb.f.724.1		4
15.8	even	4		975.2.bb.f.724.2		4
15.14	odd	2		975.2.i.i.451.1		2
39.17	odd	6		2535.2.a.c.1.1		1
39.29	odd	6		195.2.i.a.16.1	✓	2
39.35	odd	6		2535.2.a.m.1.1		1
195.29	odd	6		975.2.i.i.601.1		2
195.68	even	12		975.2.bb.f.874.1		4
195.107	even	12		975.2.bb.f.874.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.a.16.1	✓	2	39.29	odd	6
195.2.i.a.61.1	yes	2	3.2	odd	2
585.2.j.b.406.1		2	13.3	even	3	inner
585.2.j.b.451.1		2	1.1	even	1	trivial
975.2.i.i.451.1		2	15.14	odd	2
975.2.i.i.601.1		2	195.29	odd	6
975.2.bb.f.724.1		4	15.2	even	4
975.2.bb.f.724.2		4	15.8	even	4
975.2.bb.f.874.1		4	195.68	even	12
975.2.bb.f.874.2		4	195.107	even	12
2535.2.a.c.1.1		1	39.17	odd	6
2535.2.a.m.1.1		1	39.35	odd	6
7605.2.a.a.1.1		1	13.9	even	3
7605.2.a.s.1.1		1	13.4	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.00000 - 1.73205i) q^{4} +1.00000 q^{5} +(-2.50000 - 4.33013i) q^{7} +(1.00000 - 1.73205i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-2.50000 + 2.59808i) q^{13} -10.0000 q^{14} +(2.00000 - 3.46410i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-1.00000 - 1.73205i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(3.00000 - 5.19615i) q^{23} +1.00000 q^{25} +(2.00000 + 6.92820i) q^{26} +(-5.00000 + 8.66025i) q^{28} +(-2.00000 + 3.46410i) q^{29} -7.00000 q^{31} +(-4.00000 - 6.92820i) q^{32} +4.00000 q^{34} +(-2.50000 - 4.33013i) q^{35} +(1.00000 - 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{41} +(-0.500000 - 0.866025i) q^{43} -4.00000 q^{44} +(-6.00000 - 10.3923i) q^{46} +8.00000 q^{47} +(-9.00000 + 15.5885i) q^{49} +(1.00000 - 1.73205i) q^{50} +(7.00000 + 1.73205i) q^{52} +4.00000 q^{53} +(1.00000 - 1.73205i) q^{55} +(4.00000 + 6.92820i) q^{58} +(6.00000 + 10.3923i) q^{59} +(6.50000 + 11.2583i) q^{61} +(-7.00000 + 12.1244i) q^{62} -8.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +(3.50000 - 6.06218i) q^{67} +(2.00000 - 3.46410i) q^{68} -10.0000 q^{70} +(6.00000 + 10.3923i) q^{71} +15.0000 q^{73} +(-2.00000 - 3.46410i) q^{74} -10.0000 q^{77} +3.00000 q^{79} +(2.00000 - 3.46410i) q^{80} +(-6.00000 - 10.3923i) q^{82} -8.00000 q^{83} +(1.00000 + 1.73205i) q^{85} -2.00000 q^{86} +(7.00000 - 12.1244i) q^{89} +(17.5000 + 4.33013i) q^{91} -12.0000 q^{92} +(8.00000 - 13.8564i) q^{94} +(2.50000 + 4.33013i) q^{97} +(18.0000 + 31.1769i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 5 q^{7} + 2 q^{10} + 2 q^{11} - 5 q^{13} - 20 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{20} - 4 q^{22} + 6 q^{23} + 2 q^{25} + 4 q^{26} - 10 q^{28} - 4 q^{29} - 14 q^{31} - 8 q^{32}+ \cdots + 36 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 5 * q^7 + 2 * q^10 + 2 * q^11 - 5 * q^13 - 20 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^20 - 4 * q^22 + 6 * q^23 + 2 * q^25 + 4 * q^26 - 10 * q^28 - 4 * q^29 - 14 * q^31 - 8 * q^32 + 8 * q^34 - 5 * q^35 + 2 * q^37 + 6 * q^41 - q^43 - 8 * q^44 - 12 * q^46 + 16 * q^47 - 18 * q^49 + 2 * q^50 + 14 * q^52 + 8 * q^53 + 2 * q^55 + 8 * q^58 + 12 * q^59 + 13 * q^61 - 14 * q^62 - 16 * q^64 - 5 * q^65 + 7 * q^67 + 4 * q^68 - 20 * q^70 + 12 * q^71 + 30 * q^73 - 4 * q^74 - 20 * q^77 + 6 * q^79 + 4 * q^80 - 12 * q^82 - 16 * q^83 + 2 * q^85 - 4 * q^86 + 14 * q^89 + 35 * q^91 - 24 * q^92 + 16 * q^94 + 5 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more