LMFDB - Embedded newform 931.2.f.b.324.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [931,2,Mod(324,931)] 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("931.324"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(931, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.43407242818$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			324.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	931.324
Dual form			931.2.f.b.704.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(2.00000 - 3.46410i) q^{12} +4.00000 q^{13} -6.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{19} +6.00000 q^{20} +(-2.00000 - 3.46410i) q^{25} -4.00000 q^{27} +6.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-3.00000 + 5.19615i) q^{33} -2.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(-4.00000 - 6.92820i) q^{39} +6.00000 q^{41} -1.00000 q^{43} +(3.00000 - 5.19615i) q^{44} +(1.50000 + 2.59808i) q^{45} +(-1.50000 + 2.59808i) q^{47} +8.00000 q^{48} +(-3.00000 + 5.19615i) q^{51} +(4.00000 + 6.92820i) q^{52} +(-6.00000 - 10.3923i) q^{53} -9.00000 q^{55} -2.00000 q^{57} +(-3.00000 - 5.19615i) q^{59} +(-6.00000 - 10.3923i) q^{60} +(-0.500000 + 0.866025i) q^{61} -8.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{68} +6.00000 q^{71} +(-3.50000 - 6.06218i) q^{73} +(-4.00000 + 6.92820i) q^{75} +2.00000 q^{76} +(-4.00000 + 6.92820i) q^{79} +(6.00000 + 10.3923i) q^{80} +(5.50000 + 9.52628i) q^{81} -12.0000 q^{83} -9.00000 q^{85} +(-6.00000 - 10.3923i) q^{87} +(6.00000 - 10.3923i) q^{89} +(-4.00000 + 6.92820i) q^{93} +(-1.50000 - 2.59808i) q^{95} -8.00000 q^{97} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{4} + 3 q^{5} - q^{9} - 3 q^{11} + 4 q^{12} + 8 q^{13} - 12 q^{15} - 4 q^{16} - 3 q^{17} + q^{19} + 12 q^{20} - 4 q^{25} - 8 q^{27} + 12 q^{29} - 4 q^{31} - 6 q^{33} - 4 q^{36} - 2 q^{37}+ \cdots + 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^4 + 3 * q^5 - q^9 - 3 * q^11 + 4 * q^12 + 8 * q^13 - 12 * q^15 - 4 * q^16 - 3 * q^17 + q^19 + 12 * q^20 - 4 * q^25 - 8 * q^27 + 12 * q^29 - 4 * q^31 - 6 * q^33 - 4 * q^36 - 2 * q^37 - 8 * q^39 + 12 * q^41 - 2 * q^43 + 6 * q^44 + 3 * q^45 - 3 * q^47 + 16 * q^48 - 6 * q^51 + 8 * q^52 - 12 * q^53 - 18 * q^55 - 4 * q^57 - 6 * q^59 - 12 * q^60 - q^61 - 16 * q^64 + 12 * q^65 + 4 * q^67 + 6 * q^68 + 12 * q^71 - 7 * q^73 - 8 * q^75 + 4 * q^76 - 8 * q^79 + 12 * q^80 + 11 * q^81 - 24 * q^83 - 18 * q^85 - 12 * q^87 + 12 * q^89 - 8 * q^93 - 3 * q^95 - 16 * q^97 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		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	$0.982718\pi$
$12$	2.00000	−	3.46410i	0.577350	−	1.00000i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	−6.00000			−1.54919
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$	6.00000			1.34164
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$		0			0
$35$		0			0
$36$	−2.00000			−0.333333
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$		0			0
$39$	−4.00000	−	6.92820i	−0.640513	−	1.10940i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	3.00000	−	5.19615i	0.452267	−	0.783349i
$45$	1.50000	+	2.59808i	0.223607	+	0.387298i
$46$		0			0
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	−0.954441	−	0.298401i	$-0.903547\pi$
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	0.735643	+	0.677369i	$0.236880\pi$
$48$	8.00000			1.15470
$49$		0			0
$50$		0			0
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	4.00000	+	6.92820i	0.554700	+	0.960769i
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	−0.902557	−	0.430570i	$-0.858312\pi$
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	0.0783936	−	0.996922i	$-0.475021\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$		0			0
$57$	−2.00000			−0.264906
$58$		0			0
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	−6.00000	−	10.3923i	−0.774597	−	1.34164i
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	0.832240	+	0.554416i	$0.187058\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	6.00000	−	10.3923i	0.744208	−	1.28901i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$		0			0
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	0.585206	−	0.810885i	$-0.301014\pi$
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	−0.994850	+	0.101361i	$0.967680\pi$
$74$		0			0
$75$	−4.00000	+	6.92820i	−0.461880	+	0.800000i
$76$	2.00000			0.229416
$77$		0			0
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	6.00000	+	10.3923i	0.670820	+	1.16190i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	−9.00000			−0.976187
$86$		0			0
$87$	−6.00000	−	10.3923i	−0.643268	−	1.11417i
$88$		0			0
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	−0.350304	−	0.936636i	$-0.613922\pi$
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	0.986303	−	0.164946i	$-0.0527450\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$		0			0
$95$	−1.50000	−	2.59808i	−0.153897	−	0.266557i
$96$		0			0
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$		0			0
$99$	3.00000			0.301511
$100$	4.00000	−	6.92820i	0.400000	−	0.692820i
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	−0.282194	−	0.959357i	$-0.591062\pi$
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	0.971925	−	0.235291i	$-0.0756043\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.00813215	−	0.999967i	$-0.497411\pi$
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.861931	−	0.507026i	$-0.169255\pi$
$108$	−4.00000	−	6.92820i	−0.384900	−	0.666667i
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	0.939577	+	0.342337i	$0.111218\pi$
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	−0.173316	+	0.984866i	$0.555448\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$		0			0
$116$	6.00000	+	10.3923i	0.557086	+	0.964901i
$117$	−2.00000	+	3.46410i	−0.184900	+	0.320256i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$	3.00000			0.268328
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$		0			0
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$		0			0
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	0.326546	+	0.945181i	$0.394115\pi$
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	−0.981824	+	0.189794i	$0.939218\pi$
$132$	−12.0000			−1.04447
$133$		0			0
$134$		0			0
$135$	−6.00000	+	10.3923i	−0.516398	+	0.894427i
$136$		0			0
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	13.0000			1.10265			0.551323	−	0.834292i	$-0.314123\pi$
$139$	13.0000			1.10265			0.551323	+	0.834292i	$0.314123\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$		0			0
$143$	−6.00000	−	10.3923i	−0.501745	−	0.869048i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	9.00000	−	15.5885i	0.747409	−	1.29455i
$146$		0			0
$147$		0			0
$148$	−4.00000			−0.328798
$149$	−10.5000	+	18.1865i	−0.860194	+	1.48990i	0.0115483	+	0.999933i	$0.496324\pi$
$149$	−10.5000	+	18.1865i	−0.860194	+	1.48990i	−0.871742	+	0.489966i	$0.837009\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$	3.00000			0.242536
$154$		0			0
$155$	−12.0000			−0.963863
$156$	8.00000	−	13.8564i	0.640513	−	1.10940i
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$		0			0
$159$	−12.0000	+	20.7846i	−0.951662	+	1.64833i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	6.00000	+	10.3923i	0.468521	+	0.811503i
$165$	9.00000	+	15.5885i	0.700649	+	1.21356i
$166$		0			0
$167$	18.0000			1.39288			0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000			1.39288			0.696441	+	0.717614i	$0.254766\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$		0			0
$175$		0			0
$176$	12.0000			0.904534
$177$	−6.00000	+	10.3923i	−0.450988	+	0.781133i
$178$		0			0
$179$	9.00000	+	15.5885i	0.672692	+	1.16514i	0.977138	+	0.212607i	$0.0681952\pi$
$179$	9.00000	+	15.5885i	0.672692	+	1.16514i	−0.304446	+	0.952529i	$0.598471\pi$
$180$	−3.00000	+	5.19615i	−0.223607	+	0.387298i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$	−4.50000	+	7.79423i	−0.329073	+	0.569970i
$188$	−6.00000			−0.437595
$189$		0			0
$190$		0			0
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	−0.915177	−	0.403051i	$-0.867950\pi$
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	0.806641	+	0.591041i	$0.201283\pi$
$192$	8.00000	+	13.8564i	0.577350	+	1.00000i
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	0.928986	−	0.370116i	$-0.120682\pi$
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	−0.785022	+	0.619467i	$0.787349\pi$
$194$		0			0
$195$	−24.0000			−1.71868
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	5.50000	+	9.52628i	0.389885	+	0.675300i	0.992434	−	0.122782i	$-0.0391815\pi$
$199$	5.50000	+	9.52628i	0.389885	+	0.675300i	−0.602549	+	0.798082i	$0.705848\pi$
$200$		0			0
$201$	4.00000	−	6.92820i	0.282138	−	0.488678i
$202$		0			0
$203$		0			0
$204$	−12.0000			−0.840168
$205$	9.00000	−	15.5885i	0.628587	−	1.08875i
$206$		0			0
$207$		0			0
$208$	−8.00000	+	13.8564i	−0.554700	+	0.960769i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	12.0000	−	20.7846i	0.824163	−	1.42749i
$213$	−6.00000	−	10.3923i	−0.411113	−	0.712069i
$214$		0			0
$215$	−1.50000	+	2.59808i	−0.102299	+	0.177187i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$	−9.00000	−	15.5885i	−0.606780	−	1.05097i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$		0			0
$223$	10.0000			0.669650			0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000			0.669650			0.334825	+	0.942280i	$0.391323\pi$
$224$		0			0
$225$	4.00000			0.266667
$226$		0			0
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$	−2.00000	−	3.46410i	−0.132453	−	0.229416i
$229$	2.50000	−	4.33013i	0.165205	−	0.286143i	−0.771523	−	0.636201i	$-0.780505\pi$
$229$	2.50000	−	4.33013i	0.165205	−	0.286143i	0.936728	+	0.350058i	$0.113838\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.5000	−	18.1865i	0.687878	−	1.19144i	−0.284645	−	0.958633i	$-0.591876\pi$
$233$	10.5000	−	18.1865i	0.687878	−	1.19144i	0.972523	−	0.232806i	$-0.0747909\pi$
$234$		0			0
$235$	4.50000	+	7.79423i	0.293548	+	0.508439i
$236$	6.00000	−	10.3923i	0.390567	−	0.676481i
$237$	16.0000			1.03931
$238$		0			0
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$	12.0000	−	20.7846i	0.774597	−	1.34164i
$241$	−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	$0.937715\pi$
$242$		0			0
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$	−2.00000			−0.128037
$245$		0			0
$246$		0			0
$247$	2.00000	−	3.46410i	0.127257	−	0.220416i
$248$		0			0
$249$	12.0000	+	20.7846i	0.760469	+	1.31717i
$250$		0			0
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	9.00000	+	15.5885i	0.563602	+	0.976187i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$		0			0
$259$		0			0
$260$	24.0000			1.48842
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$		0			0
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$		0			0
$265$	−36.0000			−2.21146
$266$		0			0
$267$	−24.0000			−1.46878
$268$	−4.00000	+	6.92820i	−0.244339	+	0.423207i
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	0.956176	+	0.292791i	$0.0945841\pi$
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	−0.224523	+	0.974469i	$0.572083\pi$
$270$		0			0
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	−0.999870	−	0.0161307i	$-0.994865\pi$
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	0.513905	+	0.857847i	$0.328199\pi$
$272$	12.0000			0.727607
$273$		0			0
$274$		0			0
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$		0			0
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	0.996484	+	0.0837823i	$0.0267000\pi$
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	−0.425684	+	0.904872i	$0.639967\pi$
$278$		0			0
$279$	4.00000			0.239474
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	−6.50000	−	11.2583i	−0.386385	−	0.669238i	0.605575	−	0.795788i	$-0.292943\pi$
$283$	−6.50000	−	11.2583i	−0.386385	−	0.669238i	−0.991960	+	0.126550i	$0.959610\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$	−3.00000	+	5.19615i	−0.177705	+	0.307794i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	8.00000	+	13.8564i	0.468968	+	0.812277i
$292$	7.00000	−	12.1244i	0.409644	−	0.709524i
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$		0			0
$295$	−18.0000			−1.04800
$296$		0			0
$297$	6.00000	+	10.3923i	0.348155	+	0.603023i
$298$		0			0
$299$		0			0
$300$	−16.0000			−0.923760
$301$		0			0
$302$		0			0
$303$	6.00000	−	10.3923i	0.344691	−	0.597022i
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$	1.50000	+	2.59808i	0.0858898	+	0.148765i
$306$		0			0
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$	−28.0000			−1.59286
$310$		0			0
$311$	−1.50000	−	2.59808i	−0.0850572	−	0.147323i	0.820358	−	0.571850i	$-0.193774\pi$
$311$	−1.50000	−	2.59808i	−0.0850572	−	0.147323i	−0.905416	+	0.424526i	$0.860441\pi$
$312$		0			0
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	−0.972028	−	0.234863i	$-0.924536\pi$
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	0.689412	+	0.724370i	$0.257869\pi$
$314$		0			0
$315$		0			0
$316$	−16.0000			−0.900070
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$		0			0
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$	−12.0000	+	20.7846i	−0.670820	+	1.16190i
$321$	−36.0000			−2.00932
$322$		0			0
$323$	−3.00000			−0.166924
$324$	−11.0000	+	19.0526i	−0.611111	+	1.05848i
$325$	−8.00000	−	13.8564i	−0.443760	−	0.768615i
$326$		0			0
$327$	16.0000	−	27.7128i	0.884802	−	1.53252i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	−12.0000	−	20.7846i	−0.658586	−	1.14070i
$333$	−1.00000	−	1.73205i	−0.0547997	−	0.0949158i
$334$		0			0
$335$	12.0000			0.655630
$336$		0			0
$337$	32.0000			1.74315			0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000			1.74315			0.871576	+	0.490261i	$0.163099\pi$
$338$		0			0
$339$	−6.00000	−	10.3923i	−0.325875	−	0.564433i
$340$	−9.00000	−	15.5885i	−0.488094	−	0.845403i
$341$	−6.00000	+	10.3923i	−0.324918	+	0.562775i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.5000	−	18.1865i	−0.563670	−	0.976304i	−0.997172	−	0.0751519i	$-0.976056\pi$
$347$	−10.5000	−	18.1865i	−0.563670	−	0.976304i	0.433503	−	0.901152i	$-0.357278\pi$
$348$	12.0000	−	20.7846i	0.643268	−	1.11417i
$349$	−17.0000			−0.909989			−0.454995	−	0.890494i	$-0.650359\pi$
$349$	−17.0000			−0.909989			−0.454995	+	0.890494i	$0.650359\pi$
$350$		0			0
$351$	−16.0000			−0.854017
$352$		0			0
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$		0			0
$355$	9.00000	−	15.5885i	0.477670	−	0.827349i
$356$	24.0000			1.27200
$357$		0			0
$358$		0			0
$359$	−7.50000	+	12.9904i	−0.395835	+	0.685606i	−0.993207	−	0.116358i	$-0.962878\pi$
$359$	−7.50000	+	12.9904i	−0.395835	+	0.685606i	0.597372	+	0.801964i	$0.296211\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$		0			0
$363$	−4.00000			−0.209946
$364$		0			0
$365$	−21.0000			−1.09919
$366$		0			0
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$		0			0
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$		0			0
$371$		0			0
$372$	−16.0000			−0.829561
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$		0			0
$375$	−3.00000	−	5.19615i	−0.154919	−	0.268328i
$376$		0			0
$377$	24.0000			1.23606
$378$		0			0
$379$	−34.0000			−1.74646			−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000			−1.74646			−0.873231	+	0.487306i	$0.837980\pi$
$380$	3.00000	−	5.19615i	0.153897	−	0.266557i
$381$	−2.00000	−	3.46410i	−0.102463	−	0.177471i
$382$		0			0
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	−0.671027	−	0.741433i	$-0.734147\pi$
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	0.977613	+	0.210411i	$0.0674801\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.500000	−	0.866025i	0.0254164	−	0.0440225i
$388$	−8.00000	−	13.8564i	−0.406138	−	0.703452i
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	0.610835	−	0.791758i	$-0.290834\pi$
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	−0.991100	+	0.133120i	$0.957501\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	30.0000			1.51330
$394$		0			0
$395$	12.0000	+	20.7846i	0.603786	+	1.04579i
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	−3.50000	+	6.06218i	−0.175660	+	0.304252i	−0.940389	−	0.340099i	$-0.889539\pi$
$397$	−3.50000	+	6.06218i	−0.175660	+	0.304252i	0.764730	+	0.644351i	$0.222873\pi$
$398$		0			0
$399$		0			0
$400$	16.0000			0.800000
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	−0.976050	−	0.217545i	$-0.930195\pi$
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	0.676425	+	0.736512i	$0.263528\pi$
$402$		0			0
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$	−6.00000	+	10.3923i	−0.298511	+	0.517036i
$405$	33.0000			1.63978
$406$		0			0
$407$	6.00000			0.297409
$408$		0			0
$409$	−2.00000	−	3.46410i	−0.0988936	−	0.171289i	0.812333	−	0.583193i	$-0.198197\pi$
$409$	−2.00000	−	3.46410i	−0.0988936	−	0.171289i	−0.911227	+	0.411905i	$0.864864\pi$
$410$		0			0
$411$	3.00000	−	5.19615i	0.147979	−	0.256307i
$412$	28.0000			1.37946
$413$		0			0
$414$		0			0
$415$	−18.0000	+	31.1769i	−0.883585	+	1.53041i
$416$		0			0
$417$	−13.0000	−	22.5167i	−0.636613	−	1.10265i
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$		0			0
$423$	−1.50000	−	2.59808i	−0.0729325	−	0.126323i
$424$		0			0
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$		0			0
$427$		0			0
$428$	36.0000			1.74013
$429$	−12.0000	+	20.7846i	−0.579365	+	1.00349i
$430$		0			0
$431$	12.0000	+	20.7846i	0.578020	+	1.00116i	0.995706	+	0.0925683i	$0.0295076\pi$
$431$	12.0000	+	20.7846i	0.578020	+	1.00116i	−0.417687	+	0.908591i	$0.637159\pi$
$432$	8.00000	−	13.8564i	0.384900	−	0.666667i
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	−36.0000			−1.72607
$436$	−16.0000	+	27.7128i	−0.766261	+	1.32720i
$437$		0			0
$438$		0			0
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.50000	−	2.59808i	0.0712672	−	0.123438i	−0.828190	−	0.560448i	$-0.810629\pi$
$443$	1.50000	−	2.59808i	0.0712672	−	0.123438i	0.899457	+	0.437009i	$0.143962\pi$
$444$	4.00000	+	6.92820i	0.189832	+	0.328798i
$445$	−18.0000	−	31.1769i	−0.853282	−	1.47793i
$446$		0			0
$447$	42.0000			1.98653
$448$		0			0
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	−9.00000	−	15.5885i	−0.423793	−	0.734032i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$	10.0000	−	17.3205i	0.469841	−	0.813788i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	18.5000	−	32.0429i	0.865393	−	1.49891i	−0.00126243	−	0.999999i	$-0.500402\pi$
$457$	18.5000	−	32.0429i	0.865393	−	1.49891i	0.866656	−	0.498906i	$-0.166265\pi$
$458$		0			0
$459$	6.00000	+	10.3923i	0.280056	+	0.485071i
$460$		0			0
$461$	−9.00000			−0.419172			−0.209586	−	0.977790i	$-0.567212\pi$
$461$	−9.00000			−0.419172			−0.209586	+	0.977790i	$0.567212\pi$
$462$		0			0
$463$	−31.0000			−1.44069			−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000			−1.44069			−0.720346	+	0.693615i	$0.756017\pi$
$464$	−12.0000	+	20.7846i	−0.557086	+	0.964901i
$465$	12.0000	+	20.7846i	0.556487	+	0.963863i
$466$		0			0
$467$	−13.5000	+	23.3827i	−0.624705	+	1.08202i	0.363892	+	0.931441i	$0.381448\pi$
$467$	−13.5000	+	23.3827i	−0.624705	+	1.08202i	−0.988598	+	0.150581i	$0.951886\pi$
$468$	−8.00000			−0.369800
$469$		0			0
$470$		0			0
$471$	14.0000	−	24.2487i	0.645086	−	1.11732i
$472$		0			0
$473$	1.50000	+	2.59808i	0.0689701	+	0.119460i
$474$		0			0
$475$	−4.00000			−0.183533
$476$		0			0
$477$	12.0000			0.549442
$478$		0			0
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	0.695773	−	0.718262i	$-0.255062\pi$
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	−0.969920	+	0.243426i	$0.921729\pi$
$480$		0			0
$481$	−4.00000	+	6.92820i	−0.182384	+	0.315899i
$482$		0			0
$483$		0			0
$484$	4.00000			0.181818
$485$	−12.0000	+	20.7846i	−0.544892	+	0.943781i
$486$		0			0
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	0.842479	−	0.538730i	$-0.181096\pi$
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	−0.887793	+	0.460243i	$0.847762\pi$
$488$		0			0
$489$	40.0000			1.80886
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$	12.0000	−	20.7846i	0.541002	−	0.937043i
$493$	−9.00000	−	15.5885i	−0.405340	−	0.702069i
$494$		0			0
$495$	4.50000	−	7.79423i	0.202260	−	0.350325i
$496$	16.0000			0.718421
$497$		0			0
$498$		0			0
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	−0.916542	−	0.399937i	$-0.869032\pi$
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	0.804627	+	0.593780i	$0.202365\pi$
$500$	3.00000	+	5.19615i	0.134164	+	0.232379i
$501$	−18.0000	−	31.1769i	−0.804181	−	1.39288i
$502$		0			0
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$	−3.00000	−	5.19615i	−0.133235	−	0.230769i
$508$	2.00000	+	3.46410i	0.0887357	+	0.153695i
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.00000	+	3.46410i	−0.0883022	+	0.152944i
$514$		0			0
$515$	−21.0000	−	36.3731i	−0.925371	−	1.60279i
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$	9.00000			0.395820
$518$		0			0
$519$	36.0000			1.58022
$520$		0			0
$521$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$521$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$522$		0			0
$523$	19.0000	−	32.9090i	0.830812	−	1.43901i	−0.0665832	−	0.997781i	$-0.521210\pi$
$523$	19.0000	−	32.9090i	0.830812	−	1.43901i	0.897395	−	0.441228i	$-0.145457\pi$
$524$	−30.0000			−1.31056
$525$		0			0
$526$		0			0
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	−12.0000	−	20.7846i	−0.522233	−	0.904534i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	6.00000			0.260378
$532$		0			0
$533$	24.0000			1.03956
$534$		0			0
$535$	−27.0000	−	46.7654i	−1.16731	−	2.02184i
$536$		0			0
$537$	18.0000	−	31.1769i	0.776757	−	1.34538i
$538$		0			0
$539$		0			0
$540$	−24.0000			−1.03280
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	−0.461625	−	0.887075i	$-0.652733\pi$
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	0.999042	−	0.0437584i	$-0.0139332\pi$
$542$		0			0
$543$	2.00000	+	3.46410i	0.0858282	+	0.148659i
$544$		0			0
$545$	48.0000			2.05609
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	−3.00000	+	5.19615i	−0.128154	+	0.221969i
$549$	−0.500000	−	0.866025i	−0.0213395	−	0.0369611i
$550$		0			0
$551$	3.00000	−	5.19615i	0.127804	−	0.221364i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	6.00000	−	10.3923i	0.254686	−	0.441129i
$556$	13.0000	+	22.5167i	0.551323	+	0.954919i
$557$	−10.5000	−	18.1865i	−0.444899	−	0.770588i	0.553146	−	0.833084i	$-0.313427\pi$
$557$	−10.5000	−	18.1865i	−0.444899	−	0.770588i	−0.998045	+	0.0624962i	$0.980094\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$		0			0
$561$	18.0000			0.759961
$562$		0			0
$563$	3.00000	+	5.19615i	0.126435	+	0.218992i	0.922293	−	0.386492i	$-0.126313\pi$
$563$	3.00000	+	5.19615i	0.126435	+	0.218992i	−0.795858	+	0.605483i	$0.792980\pi$
$564$	6.00000	+	10.3923i	0.252646	+	0.437595i
$565$	9.00000	−	15.5885i	0.378633	−	0.655811i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	−0.496928	−	0.867792i	$-0.665539\pi$
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	0.999994	−	0.00354413i	$-0.00112814\pi$
$570$		0			0
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$	12.0000	−	20.7846i	0.501745	−	0.869048i
$573$	6.00000			0.250654
$574$		0			0
$575$		0			0
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	5.50000	+	9.52628i	0.228968	+	0.396584i	0.957503	−	0.288425i	$-0.0931316\pi$
$577$	5.50000	+	9.52628i	0.228968	+	0.396584i	−0.728535	+	0.685009i	$0.759798\pi$
$578$		0			0
$579$	4.00000	−	6.92820i	0.166234	−	0.287926i
$580$	36.0000			1.49482
$581$		0			0
$582$		0			0
$583$	−18.0000	+	31.1769i	−0.745484	+	1.29122i
$584$		0			0
$585$	6.00000	+	10.3923i	0.248069	+	0.429669i
$586$		0			0
$587$	−45.0000			−1.85735			−0.928674	−	0.370896i	$-0.879051\pi$
$587$	−45.0000			−1.85735			−0.928674	+	0.370896i	$0.879051\pi$
$588$		0			0
$589$	−4.00000			−0.164817
$590$		0			0
$591$	−18.0000	−	31.1769i	−0.740421	−	1.28245i
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	0.00727173	+	0.999974i	$0.497685\pi$
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	−0.869638	+	0.493689i	$0.835648\pi$
$594$		0			0
$595$		0			0
$596$	−42.0000			−1.72039
$597$	11.0000	−	19.0526i	0.450200	−	0.779769i
$598$		0			0
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	0.954521	+	0.298143i	$0.0963673\pi$
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	−0.219061	+	0.975711i	$0.570299\pi$
$600$		0			0
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$	−10.0000	+	17.3205i	−0.406894	+	0.704761i
$605$	−3.00000	−	5.19615i	−0.121967	−	0.211254i
$606$		0			0
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	−0.333842	−	0.942629i	$-0.608345\pi$
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	0.983262	−	0.182199i	$-0.0583216\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$	3.00000	+	5.19615i	0.121268	+	0.210042i
$613$	−14.5000	−	25.1147i	−0.585649	−	1.01437i	−0.994794	−	0.101905i	$-0.967506\pi$
$613$	−14.5000	−	25.1147i	−0.585649	−	1.01437i	0.409145	−	0.912470i	$-0.365827\pi$
$614$		0			0
$615$	−36.0000			−1.45166
$616$		0			0
$617$	9.00000			0.362326			0.181163	−	0.983453i	$-0.442014\pi$
$617$	9.00000			0.362326			0.181163	+	0.983453i	$0.442014\pi$
$618$		0			0
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.846566	+	0.532284i	$0.178666\pi$
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.0376891	+	0.999290i	$0.488000\pi$
$620$	−12.0000	−	20.7846i	−0.481932	−	0.834730i
$621$		0			0
$622$		0			0
$623$		0			0
$624$	32.0000			1.28103
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$	3.00000	+	5.19615i	0.119808	+	0.207514i
$628$	−14.0000	+	24.2487i	−0.558661	+	0.967629i
$629$	6.00000			0.239236
$630$		0			0
$631$	11.0000			0.437903			0.218952	−	0.975736i	$-0.429736\pi$
$631$	11.0000			0.437903			0.218952	+	0.975736i	$0.429736\pi$
$632$		0			0
$633$	−14.0000	−	24.2487i	−0.556450	−	0.963800i
$634$		0			0
$635$	3.00000	−	5.19615i	0.119051	−	0.206203i
$636$	−48.0000			−1.90332
$637$		0			0
$638$		0			0
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$641$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$642$		0			0
$643$	13.0000			0.512670			0.256335	−	0.966588i	$-0.417485\pi$
$643$	13.0000			0.512670			0.256335	+	0.966588i	$0.417485\pi$
$644$		0			0
$645$	6.00000			0.236250
$646$		0			0
$647$	13.5000	+	23.3827i	0.530740	+	0.919268i	0.999357	+	0.0358667i	$0.0114192\pi$
$647$	13.5000	+	23.3827i	0.530740	+	0.919268i	−0.468617	+	0.883402i	$0.655247\pi$
$648$		0			0
$649$	−9.00000	+	15.5885i	−0.353281	+	0.611900i
$650$		0			0
$651$		0			0
$652$	−40.0000			−1.56652
$653$	19.5000	−	33.7750i	0.763094	−	1.32172i	−0.178154	−	0.984003i	$-0.557013\pi$
$653$	19.5000	−	33.7750i	0.763094	−	1.32172i	0.941248	−	0.337715i	$-0.109654\pi$
$654$		0			0
$655$	22.5000	+	38.9711i	0.879148	+	1.52273i
$656$	−12.0000	+	20.7846i	−0.468521	+	0.811503i
$657$	7.00000			0.273096
$658$		0			0
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$	−18.0000	+	31.1769i	−0.700649	+	1.21356i
$661$	16.0000	+	27.7128i	0.622328	+	1.07790i	0.989051	+	0.147573i	$0.0471463\pi$
$661$	16.0000	+	27.7128i	0.622328	+	1.07790i	−0.366723	+	0.930330i	$0.619520\pi$
$662$		0			0
$663$	−12.0000	+	20.7846i	−0.466041	+	0.807207i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	18.0000	+	31.1769i	0.696441	+	1.20627i
$669$	−10.0000	−	17.3205i	−0.386622	−	0.669650i
$670$		0			0
$671$	3.00000			0.115814
$672$		0			0
$673$	−10.0000			−0.385472			−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000			−0.385472			−0.192736	+	0.981251i	$0.561736\pi$
$674$		0			0
$675$	8.00000	+	13.8564i	0.307920	+	0.533333i
$676$	3.00000	+	5.19615i	0.115385	+	0.199852i
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	0.107772	+	0.994176i	$0.465628\pi$
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	−0.914867	+	0.403755i	$0.867705\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	12.0000	−	20.7846i	0.459841	−	0.796468i
$682$		0			0
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	−0.972242	−	0.233977i	$-0.924826\pi$
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	0.283491	−	0.958975i	$-0.408507\pi$
$684$	−1.00000	+	1.73205i	−0.0382360	+	0.0662266i
$685$	9.00000			0.343872
$686$		0			0
$687$	−10.0000			−0.381524
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−24.0000	−	41.5692i	−0.914327	−	1.58366i
$690$		0			0
$691$	8.50000	−	14.7224i	0.323355	−	0.560068i	−0.657823	−	0.753173i	$-0.728522\pi$
$691$	8.50000	−	14.7224i	0.323355	−	0.560068i	0.981178	+	0.193105i	$0.0618558\pi$
$692$	−36.0000			−1.36851
$693$		0			0
$694$		0			0
$695$	19.5000	−	33.7750i	0.739677	−	1.28116i
$696$		0			0
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$		0			0
$699$	−42.0000			−1.58859
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$	1.00000	+	1.73205i	0.0377157	+	0.0653255i
$704$	12.0000	+	20.7846i	0.452267	+	0.783349i
$705$	9.00000	−	15.5885i	0.338960	−	0.587095i
$706$		0			0
$707$		0			0
$708$	−24.0000			−0.901975
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$		0			0
$711$	−4.00000	−	6.92820i	−0.150012	−	0.259828i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−36.0000			−1.34632
$716$	−18.0000	+	31.1769i	−0.672692	+	1.16514i
$717$	−15.0000	−	25.9808i	−0.560185	−	0.970269i
$718$		0			0
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	−0.691608	−	0.722273i	$-0.743097\pi$
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	0.971311	+	0.237814i	$0.0764307\pi$
$720$	−12.0000			−0.447214
$721$		0			0
$722$		0			0
$723$	−10.0000	+	17.3205i	−0.371904	+	0.644157i
$724$	−2.00000	−	3.46410i	−0.0743294	−	0.128742i
$725$	−12.0000	−	20.7846i	−0.445669	−	0.771921i
$726$		0			0
$727$	19.0000			0.704671			0.352335	−	0.935874i	$-0.385388\pi$
$727$	19.0000			0.704671			0.352335	+	0.935874i	$0.385388\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$	2.00000	+	3.46410i	0.0739221	+	0.128037i
$733$	−11.0000	+	19.0526i	−0.406294	+	0.703722i	−0.994471	−	0.105010i	$-0.966513\pi$
$733$	−11.0000	+	19.0526i	−0.406294	+	0.703722i	0.588177	+	0.808732i	$0.299846\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$		0			0
$739$	−5.50000	−	9.52628i	−0.202321	−	0.350430i	0.746955	−	0.664875i	$-0.231515\pi$
$739$	−5.50000	−	9.52628i	−0.202321	−	0.350430i	−0.949276	+	0.314445i	$0.898182\pi$
$740$	−6.00000	+	10.3923i	−0.220564	+	0.382029i
$741$	−8.00000			−0.293887
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$		0			0
$745$	31.5000	+	54.5596i	1.15407	+	1.99891i
$746$		0			0
$747$	6.00000	−	10.3923i	0.219529	−	0.380235i
$748$	−18.0000			−0.658145
$749$		0			0
$750$		0			0
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$	−6.00000	−	10.3923i	−0.218797	−	0.378968i
$753$	21.0000	+	36.3731i	0.765283	+	1.32551i
$754$		0			0
$755$	30.0000			1.09181
$756$		0			0
$757$	−25.0000			−0.908640			−0.454320	−	0.890838i	$-0.650118\pi$
$757$	−25.0000			−0.908640			−0.454320	+	0.890838i	$0.650118\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	16.5000	−	28.5788i	0.598125	−	1.03598i	−0.394973	−	0.918693i	$-0.629246\pi$
$761$	16.5000	−	28.5788i	0.598125	−	1.03598i	0.993098	−	0.117289i	$-0.0374205\pi$
$762$		0			0
$763$		0			0
$764$	−6.00000			−0.217072
$765$	4.50000	−	7.79423i	0.162698	−	0.281801i
$766$		0			0
$767$	−12.0000	−	20.7846i	−0.433295	−	0.750489i
$768$	−16.0000	+	27.7128i	−0.577350	+	1.00000i
$769$	−23.0000			−0.829401			−0.414701	−	0.909958i	$-0.636114\pi$
$769$	−23.0000			−0.829401			−0.414701	+	0.909958i	$0.636114\pi$
$770$		0			0
$771$		0			0
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	0.807018	−	0.590527i	$-0.201080\pi$
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	−0.914920	+	0.403634i	$0.867747\pi$
$774$		0			0
$775$	−8.00000	+	13.8564i	−0.287368	+	0.497737i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.00000	−	5.19615i	0.107486	−	0.186171i
$780$	−24.0000	−	41.5692i	−0.859338	−	1.48842i
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$		0			0
$783$	−24.0000			−0.857690
$784$		0			0
$785$	42.0000			1.49904
$786$		0			0
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	18.0000	+	31.1769i	0.641223	+	1.11063i
$789$	−9.00000	+	15.5885i	−0.320408	+	0.554964i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2.00000	+	3.46410i	−0.0710221	+	0.123014i
$794$		0			0
$795$	36.0000	+	62.3538i	1.27679	+	2.21146i
$796$	−11.0000	+	19.0526i	−0.389885	+	0.675300i
$797$	12.0000			0.425062			0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$		0			0
$799$	9.00000			0.318397
$800$		0			0
$801$	6.00000	+	10.3923i	0.212000	+	0.367194i
$802$		0			0
$803$	−10.5000	+	18.1865i	−0.370537	+	0.641789i
$804$	16.0000			0.564276
$805$		0			0
$806$		0			0
$807$	24.0000	−	41.5692i	0.844840	−	1.46331i
$808$		0			0
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	0.934224	−	0.356687i	$-0.116094\pi$
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	−0.776012	+	0.630718i	$0.782761\pi$
$810$		0			0
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$	32.0000			1.12229
$814$		0			0
$815$	30.0000	+	51.9615i	1.05085	+	1.82013i
$816$	−12.0000	−	20.7846i	−0.420084	−	0.727607i
$817$	−0.500000	+	0.866025i	−0.0174928	+	0.0302984i
$818$		0			0
$819$		0			0
$820$	36.0000			1.25717
$821$	−16.5000	+	28.5788i	−0.575854	+	0.997408i	0.420094	+	0.907480i	$0.361997\pi$
$821$	−16.5000	+	28.5788i	−0.575854	+	0.997408i	−0.995948	+	0.0899279i	$0.971336\pi$
$822$		0			0
$823$	24.5000	+	42.4352i	0.854016	+	1.47920i	0.877555	+	0.479477i	$0.159174\pi$
$823$	24.5000	+	42.4352i	0.854016	+	1.47920i	−0.0235383	+	0.999723i	$0.507493\pi$
$824$		0			0
$825$	24.0000			0.835573
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−8.00000	−	13.8564i	−0.277851	−	0.481253i	0.692999	−	0.720938i	$-0.256289\pi$
$829$	−8.00000	−	13.8564i	−0.277851	−	0.481253i	−0.970851	+	0.239686i	$0.922956\pi$
$830$		0			0
$831$	19.0000	−	32.9090i	0.659103	−	1.14160i
$832$	−32.0000			−1.10940
$833$		0			0
$834$		0			0
$835$	27.0000	−	46.7654i	0.934374	−	1.61838i
$836$	−3.00000	−	5.19615i	−0.103757	−	0.179713i
$837$	8.00000	+	13.8564i	0.276520	+	0.478947i
$838$		0			0
$839$	−18.0000			−0.621429			−0.310715	−	0.950503i	$-0.600568\pi$
$839$	−18.0000			−0.621429			−0.310715	+	0.950503i	$0.600568\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	−6.00000	−	10.3923i	−0.206651	−	0.357930i
$844$	14.0000	+	24.2487i	0.481900	+	0.834675i
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$		0			0
$847$		0			0
$848$	48.0000			1.64833
$849$	−13.0000	+	22.5167i	−0.446159	+	0.772770i
$850$		0			0
$851$		0			0
$852$	12.0000	−	20.7846i	0.411113	−	0.712069i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$		0			0
$855$	3.00000			0.102598
$856$		0			0
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	0.977800	−	0.209539i	$-0.0671963\pi$
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	−0.670366	+	0.742030i	$0.733863\pi$
$858$		0			0
$859$	−24.5000	+	42.4352i	−0.835929	+	1.44787i	0.0573424	+	0.998355i	$0.481737\pi$
$859$	−24.5000	+	42.4352i	−0.835929	+	1.44787i	−0.893272	+	0.449517i	$0.851596\pi$
$860$	−6.00000			−0.204598
$861$		0			0
$862$		0			0
$863$	−9.00000	+	15.5885i	−0.306364	+	0.530637i	−0.977564	−	0.210639i	$-0.932446\pi$
$863$	−9.00000	+	15.5885i	−0.306364	+	0.530637i	0.671200	+	0.741276i	$0.265779\pi$
$864$		0			0
$865$	27.0000	+	46.7654i	0.918028	+	1.59007i
$866$		0			0
$867$	−16.0000			−0.543388
$868$		0			0
$869$	24.0000			0.814144
$870$		0			0
$871$	8.00000	+	13.8564i	0.271070	+	0.469506i
$872$		0			0
$873$	4.00000	−	6.92820i	0.135379	−	0.234484i
$874$		0			0
$875$		0			0
$876$	−28.0000			−0.946032
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$		0			0
$879$	−12.0000	−	20.7846i	−0.404750	−	0.701047i
$880$	18.0000	−	31.1769i	0.606780	−	1.05097i
$881$	27.0000			0.909653			0.454827	−	0.890580i	$-0.349701\pi$
$881$	27.0000			0.909653			0.454827	+	0.890580i	$0.349701\pi$
$882$		0			0
$883$	47.0000			1.58168			0.790838	−	0.612026i	$-0.209645\pi$
$883$	47.0000			1.58168			0.790838	+	0.612026i	$0.209645\pi$
$884$	12.0000	−	20.7846i	0.403604	−	0.699062i
$885$	18.0000	+	31.1769i	0.605063	+	1.04800i
$886$		0			0
$887$	9.00000	−	15.5885i	0.302190	−	0.523409i	−0.674441	−	0.738328i	$-0.735615\pi$
$887$	9.00000	−	15.5885i	0.302190	−	0.523409i	0.976632	+	0.214919i	$0.0689488\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	16.5000	−	28.5788i	0.552771	−	0.957427i
$892$	10.0000	+	17.3205i	0.334825	+	0.579934i
$893$	1.50000	+	2.59808i	0.0501956	+	0.0869413i
$894$		0			0
$895$	54.0000			1.80502
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$	4.00000	+	6.92820i	0.133333	+	0.230940i
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.00000	+	5.19615i	−0.0997234	+	0.172726i
$906$		0			0
$907$	−4.00000	−	6.92820i	−0.132818	−	0.230047i	0.791944	−	0.610594i	$-0.209069\pi$
$907$	−4.00000	−	6.92820i	−0.132818	−	0.230047i	−0.924762	+	0.380547i	$0.875736\pi$
$908$	−12.0000	+	20.7846i	−0.398234	+	0.689761i
$909$	−6.00000			−0.199007
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$	4.00000	−	6.92820i	0.132453	−	0.229416i
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$		0			0
$915$	3.00000	−	5.19615i	0.0991769	−	0.171780i
$916$	10.0000			0.330409
$917$		0			0
$918$		0			0
$919$	−10.0000	+	17.3205i	−0.329870	+	0.571351i	−0.982486	−	0.186338i	$-0.940338\pi$
$919$	−10.0000	+	17.3205i	−0.329870	+	0.571351i	0.652616	+	0.757689i	$0.273671\pi$
$920$		0			0
$921$	20.0000	+	34.6410i	0.659022	+	1.14146i
$922$		0			0
$923$	24.0000			0.789970
$924$		0			0
$925$	8.00000			0.263038
$926$		0			0
$927$	7.00000	+	12.1244i	0.229910	+	0.398216i
$928$		0			0
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	−0.975050	−	0.221985i	$-0.928746\pi$
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	0.679770	+	0.733426i	$0.262080\pi$
$930$		0			0
$931$		0			0
$932$	42.0000			1.37576
$933$	−3.00000	+	5.19615i	−0.0982156	+	0.170114i
$934$		0			0
$935$	13.5000	+	23.3827i	0.441497	+	0.764696i
$936$		0			0
$937$	7.00000			0.228680			0.114340	−	0.993442i	$-0.463525\pi$
$937$	7.00000			0.228680			0.114340	+	0.993442i	$0.463525\pi$
$938$		0			0
$939$	20.0000			0.652675
$940$	−9.00000	+	15.5885i	−0.293548	+	0.508439i
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	0.681218	−	0.732081i	$-0.261451\pi$
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	−0.974609	+	0.223912i	$0.928117\pi$
$942$		0			0
$943$		0			0
$944$	24.0000			0.781133
$945$		0			0
$946$		0			0
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	−0.409964	−	0.912102i	$-0.634459\pi$
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	0.994885	−	0.101012i	$-0.0322080\pi$
$948$	16.0000	+	27.7128i	0.519656	+	0.900070i
$949$	−14.0000	−	24.2487i	−0.454459	−	0.787146i
$950$		0			0
$951$	12.0000			0.389127
$952$		0			0
$953$	−48.0000			−1.55487			−0.777436	−	0.628962i	$-0.783480\pi$
$953$	−48.0000			−1.55487			−0.777436	+	0.628962i	$0.783480\pi$
$954$		0			0
$955$	4.50000	+	7.79423i	0.145617	+	0.252215i
$956$	15.0000	+	25.9808i	0.485135	+	0.840278i
$957$	−18.0000	+	31.1769i	−0.581857	+	1.00781i
$958$		0			0
$959$		0			0
$960$	48.0000			1.54919
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	9.00000	+	15.5885i	0.290021	+	0.502331i
$964$	10.0000	−	17.3205i	0.322078	−	0.557856i
$965$	12.0000			0.386294
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$		0			0
$969$	3.00000	+	5.19615i	0.0963739	+	0.166924i
$970$		0			0
$971$	30.0000	−	51.9615i	0.962746	−	1.66752i	0.247193	−	0.968966i	$-0.420492\pi$
$971$	30.0000	−	51.9615i	0.962746	−	1.66752i	0.715553	−	0.698558i	$-0.246175\pi$
$972$	20.0000			0.641500
$973$		0			0
$974$		0			0
$975$	−16.0000	+	27.7128i	−0.512410	+	0.887520i
$976$	−2.00000	−	3.46410i	−0.0640184	−	0.110883i
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	0.607704	−	0.794164i	$-0.292091\pi$
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	−0.991618	+	0.129205i	$0.958757\pi$
$978$		0			0
$979$	−36.0000			−1.15056
$980$		0			0
$981$	−16.0000			−0.510841
$982$		0			0
$983$	−18.0000	−	31.1769i	−0.574111	−	0.994389i	−0.996138	−	0.0878058i	$-0.972015\pi$
$983$	−18.0000	−	31.1769i	−0.574111	−	0.994389i	0.422027	−	0.906583i	$-0.361319\pi$
$984$		0			0
$985$	27.0000	−	46.7654i	0.860292	−	1.49007i
$986$		0			0
$987$		0			0
$988$	8.00000			0.254514
$989$		0			0
$990$		0			0
$991$	17.0000	+	29.4449i	0.540023	+	0.935347i	0.998902	+	0.0468483i	$0.0149177\pi$
$991$	17.0000	+	29.4449i	0.540023	+	0.935347i	−0.458879	+	0.888499i	$0.651749\pi$
$992$		0			0
$993$	−56.0000			−1.77711
$994$		0			0
$995$	33.0000			1.04617
$996$	−24.0000	+	41.5692i	−0.760469	+	1.31717i
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	0.968655	−	0.248410i	$-0.0799082\pi$
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	−0.699457	+	0.714675i	$0.746575\pi$
$998$		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	931.2.f.b.324.1		2
7.2	even	3		931.2.a.a.1.1		1
7.3	odd	6		931.2.f.c.704.1		2
7.4	even	3	inner	931.2.f.b.704.1		2
7.5	odd	6		19.2.a.a.1.1	✓	1
7.6	odd	2		931.2.f.c.324.1		2
21.2	odd	6		8379.2.a.j.1.1		1
21.5	even	6		171.2.a.b.1.1		1
28.19	even	6		304.2.a.f.1.1		1
35.12	even	12		475.2.b.a.324.2		2
35.19	odd	6		475.2.a.b.1.1		1
35.33	even	12		475.2.b.a.324.1		2
56.5	odd	6		1216.2.a.o.1.1		1
56.19	even	6		1216.2.a.b.1.1		1
77.54	even	6		2299.2.a.b.1.1		1
84.47	odd	6		2736.2.a.c.1.1		1
91.12	odd	6		3211.2.a.a.1.1		1
105.89	even	6		4275.2.a.i.1.1		1
119.33	odd	6		5491.2.a.b.1.1		1
133.5	odd	18		361.2.e.d.234.1		6
133.12	even	6		361.2.c.a.68.1		2
133.26	odd	6		361.2.c.c.68.1		2
133.33	even	18		361.2.e.e.234.1		6
133.40	even	18		361.2.e.e.99.1		6
133.47	odd	18		361.2.e.d.62.1		6
133.54	odd	18		361.2.e.d.28.1		6
133.61	odd	18		361.2.e.d.54.1		6
133.68	odd	6		361.2.c.c.292.1		2
133.75	even	6		361.2.a.b.1.1		1
133.82	odd	18		361.2.e.d.245.1		6
133.89	even	18		361.2.e.e.245.1		6
133.103	even	6		361.2.c.a.292.1		2
133.110	even	18		361.2.e.e.54.1		6
133.117	even	18		361.2.e.e.28.1		6
133.124	even	18		361.2.e.e.62.1		6
133.131	odd	18		361.2.e.d.99.1		6
140.19	even	6		7600.2.a.c.1.1		1
399.341	odd	6		3249.2.a.d.1.1		1
532.75	odd	6		5776.2.a.c.1.1		1
665.474	even	6		9025.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.a.a.1.1	✓	1	7.5	odd	6
171.2.a.b.1.1		1	21.5	even	6
304.2.a.f.1.1		1	28.19	even	6
361.2.a.b.1.1		1	133.75	even	6
361.2.c.a.68.1		2	133.12	even	6
361.2.c.a.292.1		2	133.103	even	6
361.2.c.c.68.1		2	133.26	odd	6
361.2.c.c.292.1		2	133.68	odd	6
361.2.e.d.28.1		6	133.54	odd	18
361.2.e.d.54.1		6	133.61	odd	18
361.2.e.d.62.1		6	133.47	odd	18
361.2.e.d.99.1		6	133.131	odd	18
361.2.e.d.234.1		6	133.5	odd	18
361.2.e.d.245.1		6	133.82	odd	18
361.2.e.e.28.1		6	133.117	even	18
361.2.e.e.54.1		6	133.110	even	18
361.2.e.e.62.1		6	133.124	even	18
361.2.e.e.99.1		6	133.40	even	18
361.2.e.e.234.1		6	133.33	even	18
361.2.e.e.245.1		6	133.89	even	18
475.2.a.b.1.1		1	35.19	odd	6
475.2.b.a.324.1		2	35.33	even	12
475.2.b.a.324.2		2	35.12	even	12
931.2.a.a.1.1		1	7.2	even	3
931.2.f.b.324.1		2	1.1	even	1	trivial
931.2.f.b.704.1		2	7.4	even	3	inner
931.2.f.c.324.1		2	7.6	odd	2
931.2.f.c.704.1		2	7.3	odd	6
1216.2.a.b.1.1		1	56.19	even	6
1216.2.a.o.1.1		1	56.5	odd	6
2299.2.a.b.1.1		1	77.54	even	6
2736.2.a.c.1.1		1	84.47	odd	6
3211.2.a.a.1.1		1	91.12	odd	6
3249.2.a.d.1.1		1	399.341	odd	6
4275.2.a.i.1.1		1	105.89	even	6
5491.2.a.b.1.1		1	119.33	odd	6
5776.2.a.c.1.1		1	532.75	odd	6
7600.2.a.c.1.1		1	140.19	even	6
8379.2.a.j.1.1		1	21.2	odd	6
9025.2.a.d.1.1		1	665.474	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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(2.00000 - 3.46410i) q^{12} +4.00000 q^{13} -6.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{19} +6.00000 q^{20} +(-2.00000 - 3.46410i) q^{25} -4.00000 q^{27} +6.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-3.00000 + 5.19615i) q^{33} -2.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(-4.00000 - 6.92820i) q^{39} +6.00000 q^{41} -1.00000 q^{43} +(3.00000 - 5.19615i) q^{44} +(1.50000 + 2.59808i) q^{45} +(-1.50000 + 2.59808i) q^{47} +8.00000 q^{48} +(-3.00000 + 5.19615i) q^{51} +(4.00000 + 6.92820i) q^{52} +(-6.00000 - 10.3923i) q^{53} -9.00000 q^{55} -2.00000 q^{57} +(-3.00000 - 5.19615i) q^{59} +(-6.00000 - 10.3923i) q^{60} +(-0.500000 + 0.866025i) q^{61} -8.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{68} +6.00000 q^{71} +(-3.50000 - 6.06218i) q^{73} +(-4.00000 + 6.92820i) q^{75} +2.00000 q^{76} +(-4.00000 + 6.92820i) q^{79} +(6.00000 + 10.3923i) q^{80} +(5.50000 + 9.52628i) q^{81} -12.0000 q^{83} -9.00000 q^{85} +(-6.00000 - 10.3923i) q^{87} +(6.00000 - 10.3923i) q^{89} +(-4.00000 + 6.92820i) q^{93} +(-1.50000 - 2.59808i) q^{95} -8.00000 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{4} + 3 q^{5} - q^{9} - 3 q^{11} + 4 q^{12} + 8 q^{13} - 12 q^{15} - 4 q^{16} - 3 q^{17} + q^{19} + 12 q^{20} - 4 q^{25} - 8 q^{27} + 12 q^{29} - 4 q^{31} - 6 q^{33} - 4 q^{36} - 2 q^{37}+ \cdots + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^4 + 3 * q^5 - q^9 - 3 * q^11 + 4 * q^12 + 8 * q^13 - 12 * q^15 - 4 * q^16 - 3 * q^17 + q^19 + 12 * q^20 - 4 * q^25 - 8 * q^27 + 12 * q^29 - 4 * q^31 - 6 * q^33 - 4 * q^36 - 2 * q^37 - 8 * q^39 + 12 * q^41 - 2 * q^43 + 6 * q^44 + 3 * q^45 - 3 * q^47 + 16 * q^48 - 6 * q^51 + 8 * q^52 - 12 * q^53 - 18 * q^55 - 4 * q^57 - 6 * q^59 - 12 * q^60 - q^61 - 16 * q^64 + 12 * q^65 + 4 * q^67 + 6 * q^68 + 12 * q^71 - 7 * q^73 - 8 * q^75 + 4 * q^76 - 8 * q^79 + 12 * q^80 + 11 * q^81 - 24 * q^83 - 18 * q^85 - 12 * q^87 + 12 * q^89 - 8 * q^93 - 3 * q^95 - 16 * q^97 + 6 * q^99

Introduction

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