LMFDB - Embedded newform 483.2.i.b.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	483.277
Dual form			483.2.i.b.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(1.00000 + 1.73205i) q^{12} +5.00000 q^{13} +(-2.00000 - 3.46410i) q^{16} +(3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(0.500000 + 0.866025i) q^{23} +(2.50000 - 4.33013i) q^{25} +1.00000 q^{27} +(4.00000 - 3.46410i) q^{28} +6.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-3.00000 - 5.19615i) q^{33} -2.00000 q^{36} +(3.50000 + 6.06218i) q^{37} +(-2.50000 + 4.33013i) q^{39} -1.00000 q^{43} +(6.00000 + 10.3923i) q^{44} +(-3.00000 - 5.19615i) q^{47} +4.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{51} +(5.00000 - 8.66025i) q^{52} +(-6.00000 + 10.3923i) q^{53} -1.00000 q^{57} +(3.00000 - 5.19615i) q^{59} +(-7.00000 - 12.1244i) q^{61} +(-0.500000 - 2.59808i) q^{63} -8.00000 q^{64} +(-2.50000 + 4.33013i) q^{67} +(-6.00000 - 10.3923i) q^{68} -1.00000 q^{69} -6.00000 q^{71} +(3.50000 - 6.06218i) q^{73} +(2.50000 + 4.33013i) q^{75} +2.00000 q^{76} +(-12.0000 + 10.3923i) q^{77} +(-2.50000 - 4.33013i) q^{79} +(-0.500000 + 0.866025i) q^{81} -12.0000 q^{83} +(1.00000 + 5.19615i) q^{84} +(-3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{89} +(12.5000 + 4.33013i) q^{91} +2.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} -10.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 2 q^{4} + 5 q^{7} - q^{9}+O(q^{10}) $ 2 * q - q^3 + 2 * q^4 + 5 * q^7 - q^9	$ 2 q - q^{3} + 2 q^{4} + 5 q^{7} - q^{9} - 6 q^{11} + 2 q^{12} + 10 q^{13} - 4 q^{16} + 6 q^{17} + q^{19} - 4 q^{21} + q^{23} + 5 q^{25} + 2 q^{27} + 8 q^{28} + 12 q^{29} - 5 q^{31} - 6 q^{33} - 4 q^{36} + 7 q^{37} - 5 q^{39} - 2 q^{43} + 12 q^{44} - 6 q^{47} + 8 q^{48} + 11 q^{49} + 6 q^{51} + 10 q^{52} - 12 q^{53} - 2 q^{57} + 6 q^{59} - 14 q^{61} - q^{63} - 16 q^{64} - 5 q^{67} - 12 q^{68} - 2 q^{69} - 12 q^{71} + 7 q^{73} + 5 q^{75} + 4 q^{76} - 24 q^{77} - 5 q^{79} - q^{81} - 24 q^{83} + 2 q^{84} - 6 q^{87} + 6 q^{89} + 25 q^{91} + 4 q^{92} - 5 q^{93} - 20 q^{97} + 12 q^{99}+O(q^{100}) $ 2 * q - q^3 + 2 * q^4 + 5 * q^7 - q^9 - 6 * q^11 + 2 * q^12 + 10 * q^13 - 4 * q^16 + 6 * q^17 + q^19 - 4 * q^21 + q^23 + 5 * q^25 + 2 * q^27 + 8 * q^28 + 12 * q^29 - 5 * q^31 - 6 * q^33 - 4 * q^36 + 7 * q^37 - 5 * q^39 - 2 * q^43 + 12 * q^44 - 6 * q^47 + 8 * q^48 + 11 * q^49 + 6 * q^51 + 10 * q^52 - 12 * q^53 - 2 * q^57 + 6 * q^59 - 14 * q^61 - q^63 - 16 * q^64 - 5 * q^67 - 12 * q^68 - 2 * q^69 - 12 * q^71 + 7 * q^73 + 5 * q^75 + 4 * q^76 - 24 * q^77 - 5 * q^79 - q^81 - 24 * q^83 + 2 * q^84 - 6 * q^87 + 6 * q^89 + 25 * q^91 + 4 * q^92 - 5 * q^93 - 20 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$	1.00000	+	1.73205i	0.288675	+	0.500000i
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$		0			0
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$		0			0
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$		0			0
$27$	1.00000			0.192450
$28$	4.00000	−	3.46410i	0.755929	−	0.654654i
$29$	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
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$		0			0
$33$	−3.00000	−	5.19615i	−0.522233	−	0.904534i
$34$		0			0
$35$		0			0
$36$	−2.00000			−0.333333
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$		0			0
$39$	−2.50000	+	4.33013i	−0.400320	+	0.693375i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	6.00000	+	10.3923i	0.904534	+	1.56670i
$45$		0			0
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$	4.00000			0.577350
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$	3.00000	+	5.19615i	0.420084	+	0.727607i
$52$	5.00000	−	8.66025i	0.693375	−	1.20096i
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.00000			−0.132453
$58$		0			0
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.0640184	−	0.997949i	$-0.520392\pi$
$62$		0			0
$63$	−0.500000	−	2.59808i	−0.0629941	−	0.327327i
$64$	−8.00000			−1.00000
$65$		0			0
$66$		0			0
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$	−6.00000	−	10.3923i	−0.727607	−	1.26025i
$69$	−1.00000			−0.120386
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$		0			0
$75$	2.50000	+	4.33013i	0.288675	+	0.500000i
$76$	2.00000			0.229416
$77$	−12.0000	+	10.3923i	−1.36753	+	1.18431i
$78$		0			0
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	0.690426	−	0.723403i	$-0.257423\pi$
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	−0.971698	+	0.236225i	$0.924090\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$	1.00000	+	5.19615i	0.109109	+	0.566947i
$85$		0			0
$86$		0			0
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$		0			0
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	12.5000	+	4.33013i	1.31036	+	0.453921i
$92$	2.00000			0.208514
$93$	−2.50000	−	4.33013i	−0.259238	−	0.449013i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$	−5.00000	−	8.66025i	−0.500000	−	0.866025i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	−5.50000	−	9.52628i	−0.541931	−	0.938652i	−0.998793	−	0.0491146i	$-0.984360\pi$
$103$	−5.50000	−	9.52628i	−0.541931	−	0.938652i	0.456862	−	0.889538i	$-0.348973\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$	1.00000	−	1.73205i	0.0962250	−	0.166667i
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$		0			0
$111$	−7.00000			−0.664411
$112$	−2.00000	−	10.3923i	−0.188982	−	0.981981i
$113$	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
$117$	−2.50000	−	4.33013i	−0.231125	−	0.400320i
$118$		0			0
$119$	12.0000	−	10.3923i	1.10004	−	0.952661i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$		0			0
$123$		0			0
$124$	5.00000	+	8.66025i	0.449013	+	0.777714i
$125$		0			0
$126$		0			0
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$		0			0
$129$	0.500000	−	0.866025i	0.0440225	−	0.0762493i
$130$		0			0
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$	−12.0000			−1.04447
$133$	0.500000	+	2.59808i	0.0433555	+	0.225282i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$		0			0
$143$	−15.0000	+	25.9808i	−1.25436	+	2.17262i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$		0			0
$146$		0			0
$147$	−6.50000	+	2.59808i	−0.536111	+	0.214286i
$148$	14.0000			1.15079
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	0.0964061	+	0.995342i	$0.469265\pi$
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	−0.910195	+	0.414181i	$0.864068\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$		0			0
$155$		0			0
$156$	5.00000	+	8.66025i	0.400320	+	0.693375i
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$		0			0
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$		0			0
$161$	0.500000	+	2.59808i	0.0394055	+	0.204757i
$162$		0			0
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	0.500000	−	0.866025i	0.0382360	−	0.0662266i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	10.0000	−	8.66025i	0.755929	−	0.654654i
$176$	24.0000			1.80907
$177$	3.00000	+	5.19615i	0.225494	+	0.390567i
$178$		0			0
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$		0			0
$181$	23.0000			1.70958			0.854788	−	0.518977i	$-0.173687\pi$
$181$	23.0000			1.70958			0.854788	+	0.518977i	$0.173687\pi$
$182$		0			0
$183$	14.0000			1.03491
$184$		0			0
$185$		0			0
$186$		0			0
$187$	18.0000	+	31.1769i	1.31629	+	2.27988i
$188$	−12.0000			−0.875190
$189$	2.50000	+	0.866025i	0.181848	+	0.0629941i
$190$		0			0
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$	4.00000	−	6.92820i	0.288675	−	0.500000i
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	−0.993215	−	0.116289i	$-0.962900\pi$
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	0.597317	+	0.802005i	$0.296234\pi$
$194$		0			0
$195$		0			0
$196$	13.0000	−	5.19615i	0.928571	−	0.371154i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$		0			0
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	−0.429745	−	0.902950i	$-0.641397\pi$
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	0.996850	−	0.0793045i	$-0.0252700\pi$
$200$		0			0
$201$	−2.50000	−	4.33013i	−0.176336	−	0.305424i
$202$		0			0
$203$	15.0000	+	5.19615i	1.05279	+	0.364698i
$204$	12.0000			0.840168
$205$		0			0
$206$		0			0
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	−10.0000	−	17.3205i	−0.693375	−	1.20096i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	12.0000	+	20.7846i	0.824163	+	1.42749i
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−10.0000	+	8.66025i	−0.678844	+	0.587896i
$218$		0			0
$219$	3.50000	+	6.06218i	0.236508	+	0.409644i
$220$		0			0
$221$	15.0000	−	25.9808i	1.00901	−	1.74766i
$222$		0			0
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$		0			0
$225$	−5.00000			−0.333333
$226$		0			0
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	−0.749125	−	0.662428i	$-0.769526\pi$
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	0.948242	+	0.317547i	$0.102859\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	0.996832	−	0.0795401i	$-0.0253452\pi$
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	−0.567300	+	0.823511i	$0.692012\pi$
$230$		0			0
$231$	−3.00000	−	15.5885i	−0.197386	−	1.02565i
$232$		0			0
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	−0.994283	−	0.106773i	$-0.965948\pi$
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	0.404674	−	0.914461i	$-0.367385\pi$
$234$		0			0
$235$		0			0
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$	5.00000			0.324785
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−28.0000			−1.79252
$245$		0			0
$246$		0			0
$247$	2.50000	+	4.33013i	0.159071	+	0.275519i
$248$		0			0
$249$	6.00000	−	10.3923i	0.380235	−	0.658586i
$250$		0			0
$251$	30.0000			1.89358			0.946792	−	0.321847i	$-0.104304\pi$
$251$	30.0000			1.89358			0.946792	+	0.321847i	$0.104304\pi$
$252$	−5.00000	−	1.73205i	−0.314970	−	0.109109i
$253$	−6.00000			−0.377217
$254$		0			0
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	0.615948	−	0.787787i	$-0.288773\pi$
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	−0.990217	+	0.139533i	$0.955440\pi$
$258$		0			0
$259$	3.50000	+	18.1865i	0.217479	+	1.13006i
$260$		0			0
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.00000			−0.367194
$268$	5.00000	+	8.66025i	0.305424	+	0.529009i
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	−0.224523	−	0.974469i	$-0.572083\pi$
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	0.956176	−	0.292791i	$-0.0945841\pi$
$270$		0			0
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	0.880812	+	0.473466i	$0.156997\pi$
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	−24.0000			−1.45521
$273$	−10.0000	+	8.66025i	−0.605228	+	0.524142i
$274$		0			0
$275$	15.0000	+	25.9808i	0.904534	+	1.56670i
$276$	−1.00000	+	1.73205i	−0.0601929	+	0.104257i
$277$	15.5000	−	26.8468i	0.931305	−	1.61307i	0.150210	−	0.988654i	$-0.452005\pi$
$277$	15.5000	−	26.8468i	0.931305	−	1.61307i	0.781094	−	0.624413i	$-0.214662\pi$
$278$		0			0
$279$	5.00000			0.299342
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	6.50000	−	11.2583i	0.386385	−	0.669238i	−0.605575	−	0.795788i	$-0.707057\pi$
$283$	6.50000	−	11.2583i	0.386385	−	0.669238i	0.991960	+	0.126550i	$0.0403903\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$	5.00000	−	8.66025i	0.293105	−	0.507673i
$292$	−7.00000	−	12.1244i	−0.409644	−	0.709524i
$293$	18.0000			1.05157			0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000			1.05157			0.525786	+	0.850617i	$0.323771\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.00000	+	5.19615i	−0.174078	+	0.301511i
$298$		0			0
$299$	2.50000	+	4.33013i	0.144579	+	0.250418i
$300$	10.0000			0.577350
$301$	−2.50000	−	0.866025i	−0.144098	−	0.0499169i
$302$		0			0
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$		0			0
$306$		0			0
$307$	−13.0000			−0.741949			−0.370975	−	0.928643i	$-0.620976\pi$
$307$	−13.0000			−0.741949			−0.370975	+	0.928643i	$0.620976\pi$
$308$	6.00000	+	31.1769i	0.341882	+	1.77647i
$309$	11.0000			0.625768
$310$		0			0
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	0.999065	+	0.0432311i	$0.0137652\pi$
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	−0.462093	+	0.886831i	$0.652902\pi$
$314$		0			0
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$		0			0
$319$	−18.0000	+	31.1769i	−1.00781	+	1.74557i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.00000			0.333849
$324$	1.00000	+	1.73205i	0.0555556	+	0.0962250i
$325$	12.5000	−	21.6506i	0.693375	−	1.20096i
$326$		0			0
$327$	−5.50000	−	9.52628i	−0.304151	−	0.526804i
$328$		0			0
$329$	−3.00000	−	15.5885i	−0.165395	−	0.859419i
$330$		0			0
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	0.674351	−	0.738411i	$-0.264424\pi$
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	−0.976658	+	0.214799i	$0.931090\pi$
$332$	−12.0000	+	20.7846i	−0.658586	+	1.14070i
$333$	3.50000	−	6.06218i	0.191799	−	0.332205i
$334$		0			0
$335$		0			0
$336$	10.0000	+	3.46410i	0.545545	+	0.188982i
$337$	−25.0000			−1.36184			−0.680918	−	0.732359i	$-0.738419\pi$
$337$	−25.0000			−1.36184			−0.680918	+	0.732359i	$0.738419\pi$
$338$		0			0
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$		0			0
$341$	−15.0000	−	25.9808i	−0.812296	−	1.40694i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$	6.00000	+	10.3923i	0.321634	+	0.557086i
$349$	−22.0000			−1.17763			−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000			−1.17763			−0.588817	+	0.808267i	$0.700406\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$		0			0
$353$	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
$355$		0			0
$356$	12.0000			0.635999
$357$	3.00000	+	15.5885i	0.158777	+	0.825029i
$358$		0			0
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	0.999590	−	0.0286287i	$-0.00911406\pi$
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	−0.524588	+	0.851356i	$0.675781\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	25.0000			1.31216
$364$	20.0000	−	17.3205i	1.04828	−	0.907841i
$365$		0			0
$366$		0			0
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$		0			0
$370$		0			0
$371$	−24.0000	+	20.7846i	−1.24602	+	1.07908i
$372$	−10.0000			−0.518476
$373$	15.5000	+	26.8468i	0.802560	+	1.39007i	0.917926	+	0.396751i	$0.129862\pi$
$373$	15.5000	+	26.8468i	0.802560	+	1.39007i	−0.115367	+	0.993323i	$0.536804\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	30.0000			1.54508
$378$		0			0
$379$	−7.00000			−0.359566			−0.179783	−	0.983706i	$-0.557540\pi$
$379$	−7.00000			−0.359566			−0.179783	+	0.983706i	$0.557540\pi$
$380$		0			0
$381$	3.50000	−	6.06218i	0.179310	−	0.310575i
$382$		0			0
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	0.932436	−	0.361335i	$-0.117679\pi$
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	−0.779143	+	0.626846i	$0.784346\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.500000	+	0.866025i	0.0254164	+	0.0440225i
$388$	−10.0000	+	17.3205i	−0.507673	+	0.879316i
$389$	−18.0000	+	31.1769i	−0.912636	+	1.58073i	−0.102311	+	0.994753i	$0.532624\pi$
$389$	−18.0000	+	31.1769i	−0.912636	+	1.58073i	−0.810326	+	0.585980i	$0.800710\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$	6.00000	−	10.3923i	0.301511	−	0.522233i
$397$	12.5000	+	21.6506i	0.627357	+	1.08661i	0.988080	+	0.153941i	$0.0491966\pi$
$397$	12.5000	+	21.6506i	0.627357	+	1.08661i	−0.360723	+	0.932673i	$0.617470\pi$
$398$		0			0
$399$	−2.50000	−	0.866025i	−0.125157	−	0.0433555i
$400$	−20.0000			−1.00000
$401$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$401$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$402$		0			0
$403$	−12.5000	+	21.6506i	−0.622669	+	1.07849i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−42.0000			−2.08186
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$		0			0
$411$	−6.00000	−	10.3923i	−0.295958	−	0.512615i
$412$	−22.0000			−1.08386
$413$	12.0000	−	10.3923i	0.590481	−	0.511372i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.50000	+	4.33013i	−0.122426	+	0.212047i
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	−13.0000			−0.633581			−0.316791	−	0.948495i	$-0.602605\pi$
$421$	−13.0000			−0.633581			−0.316791	+	0.948495i	$0.602605\pi$
$422$		0			0
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$	−15.0000	−	25.9808i	−0.727607	−	1.26025i
$426$		0			0
$427$	−7.00000	−	36.3731i	−0.338754	−	1.76022i
$428$		0			0
$429$	−15.0000	−	25.9808i	−0.724207	−	1.25436i
$430$		0			0
$431$	18.0000	−	31.1769i	0.867029	−	1.50174i	0.00201168	−	0.999998i	$-0.499360\pi$
$431$	18.0000	−	31.1769i	0.867029	−	1.50174i	0.865018	−	0.501741i	$-0.167307\pi$
$432$	−2.00000	−	3.46410i	−0.0962250	−	0.166667i
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$		0			0
$435$		0			0
$436$	11.0000	+	19.0526i	0.526804	+	0.912452i
$437$	−0.500000	+	0.866025i	−0.0239182	+	0.0414276i
$438$		0			0
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$		0			0
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	0.569057	−	0.822298i	$-0.307309\pi$
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	−0.996660	+	0.0816684i	$0.973975\pi$
$444$	−7.00000	+	12.1244i	−0.332205	+	0.575396i
$445$		0			0
$446$		0			0
$447$	18.0000			0.851371
$448$	−20.0000	−	6.92820i	−0.944911	−	0.327327i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$		0			0
$452$	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
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	0.877483	−	0.479608i	$-0.159221\pi$
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	−0.854094	+	0.520119i	$0.825888\pi$
$458$		0			0
$459$	3.00000	−	5.19615i	0.140028	−	0.242536i
$460$		0			0
$461$	−42.0000			−1.95614			−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−42.0000			−1.95614			−0.978068	+	0.208288i	$0.933211\pi$
$462$		0			0
$463$	−13.0000			−0.604161			−0.302081	−	0.953282i	$-0.597681\pi$
$463$	−13.0000			−0.604161			−0.302081	+	0.953282i	$0.597681\pi$
$464$	−12.0000	−	20.7846i	−0.557086	−	0.964901i
$465$		0			0
$466$		0			0
$467$	9.00000	+	15.5885i	0.416470	+	0.721348i	0.995582	−	0.0939008i	$-0.0299336\pi$
$467$	9.00000	+	15.5885i	0.416470	+	0.721348i	−0.579111	+	0.815249i	$0.696600\pi$
$468$	−10.0000			−0.462250
$469$	−10.0000	+	8.66025i	−0.461757	+	0.399893i
$470$		0			0
$471$	−7.00000	−	12.1244i	−0.322543	−	0.558661i
$472$		0			0
$473$	3.00000	−	5.19615i	0.137940	−	0.238919i
$474$		0			0
$475$	5.00000			0.229416
$476$	−6.00000	−	31.1769i	−0.275010	−	1.42899i
$477$	12.0000			0.549442
$478$		0			0
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	−0.789314	−	0.613990i	$-0.789564\pi$
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	0.926388	+	0.376571i	$0.122897\pi$
$480$		0			0
$481$	17.5000	+	30.3109i	0.797931	+	1.38206i
$482$		0			0
$483$	−2.50000	−	0.866025i	−0.113754	−	0.0394055i
$484$	−50.0000			−2.27273
$485$		0			0
$486$		0			0
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	−0.680335	−	0.732901i	$-0.738166\pi$
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	0.974879	+	0.222737i	$0.0714992\pi$
$488$		0			0
$489$	−4.00000			−0.180886
$490$		0			0
$491$	30.0000			1.35388			0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000			1.35388			0.676941	+	0.736038i	$0.263305\pi$
$492$		0			0
$493$	18.0000	−	31.1769i	0.810679	−	1.40414i
$494$		0			0
$495$		0			0
$496$	20.0000			0.898027
$497$	−15.0000	−	5.19615i	−0.672842	−	0.233079i
$498$		0			0
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	0.804627	−	0.593780i	$-0.202365\pi$
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	−0.916542	+	0.399937i	$0.869032\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$	−7.00000	+	12.1244i	−0.310575	+	0.537931i
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	0.967811	−	0.251679i	$-0.0809826\pi$
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	−0.701866	+	0.712309i	$0.747649\pi$
$510$		0			0
$511$	14.0000	−	12.1244i	0.619324	−	0.536350i
$512$		0			0
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$		0			0
$515$		0			0
$516$	−1.00000	−	1.73205i	−0.0440225	−	0.0762493i
$517$	36.0000			1.58328
$518$		0			0
$519$	6.00000			0.263371
$520$		0			0
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	0.324185	+	0.945994i	$0.394910\pi$
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	−0.981347	+	0.192244i	$0.938423\pi$
$522$		0			0
$523$	−20.5000	−	35.5070i	−0.896402	−	1.55261i	−0.832059	−	0.554687i	$-0.812838\pi$
$523$	−20.5000	−	35.5070i	−0.896402	−	1.55261i	−0.0643431	−	0.997928i	$-0.520495\pi$
$524$		0			0
$525$	2.50000	+	12.9904i	0.109109	+	0.566947i
$526$		0			0
$527$	15.0000	+	25.9808i	0.653410	+	1.13174i
$528$	−12.0000	+	20.7846i	−0.522233	+	0.904534i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$		0			0
$531$	−6.00000			−0.260378
$532$	5.00000	+	1.73205i	0.216777	+	0.0750939i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$		0			0
$539$	−39.0000	+	15.5885i	−1.67985	+	0.671442i
$540$		0			0
$541$	15.5000	+	26.8468i	0.666397	+	1.15423i	0.978905	+	0.204318i	$0.0654977\pi$
$541$	15.5000	+	26.8468i	0.666397	+	1.15423i	−0.312507	+	0.949915i	$0.601169\pi$
$542$		0			0
$543$	−11.5000	+	19.9186i	−0.493512	+	0.854788i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	44.0000			1.88130			0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000			1.88130			0.940652	+	0.339372i	$0.110215\pi$
$548$	12.0000	+	20.7846i	0.512615	+	0.887875i
$549$	−7.00000	+	12.1244i	−0.298753	+	0.517455i
$550$		0			0
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$		0			0
$553$	−2.50000	−	12.9904i	−0.106311	−	0.552407i
$554$		0			0
$555$		0			0
$556$	5.00000	−	8.66025i	0.212047	−	0.367277i
$557$	3.00000	−	5.19615i	0.127114	−	0.220168i	−0.795443	−	0.606028i	$-0.792762\pi$
$557$	3.00000	−	5.19615i	0.127114	−	0.220168i	0.922557	+	0.385860i	$0.126095\pi$
$558$		0			0
$559$	−5.00000			−0.211477
$560$		0			0
$561$	−36.0000			−1.51992
$562$		0			0
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	0.943560	−	0.331202i	$-0.107454\pi$
$564$	6.00000	−	10.3923i	0.252646	−	0.437595i
$565$		0			0
$566$		0			0
$567$	−2.00000	+	1.73205i	−0.0839921	+	0.0727393i
$568$		0			0
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	0.999994	+	0.00354413i	$0.00112814\pi$
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	−0.496928	+	0.867792i	$0.665539\pi$
$570$		0			0
$571$	6.50000	−	11.2583i	0.272017	−	0.471146i	−0.697362	−	0.716720i	$-0.745643\pi$
$571$	6.50000	−	11.2583i	0.272017	−	0.471146i	0.969378	+	0.245573i	$0.0789761\pi$
$572$	30.0000	+	51.9615i	1.25436	+	2.17262i
$573$	18.0000			0.751961
$574$		0			0
$575$	5.00000			0.208514
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	6.50000	−	11.2583i	0.270599	−	0.468690i	−0.698417	−	0.715691i	$-0.746112\pi$
$577$	6.50000	−	11.2583i	0.270599	−	0.468690i	0.969015	+	0.247001i	$0.0794451\pi$
$578$		0			0
$579$	−5.50000	−	9.52628i	−0.228572	−	0.395899i
$580$		0			0
$581$	−30.0000	−	10.3923i	−1.24461	−	0.431145i
$582$		0			0
$583$	−36.0000	−	62.3538i	−1.49097	−	2.58243i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−30.0000			−1.23823			−0.619116	−	0.785299i	$-0.712509\pi$
$587$	−30.0000			−1.23823			−0.619116	+	0.785299i	$0.712509\pi$
$588$	−2.00000	+	13.8564i	−0.0824786	+	0.571429i
$589$	−5.00000			−0.206021
$590$		0			0
$591$	6.00000	−	10.3923i	0.246807	−	0.427482i
$592$	14.0000	−	24.2487i	0.575396	−	0.996616i
$593$	−15.0000	−	25.9808i	−0.615976	−	1.06690i	−0.990212	−	0.139569i	$-0.955428\pi$
$593$	−15.0000	−	25.9808i	−0.615976	−	1.06690i	0.374236	−	0.927333i	$-0.377905\pi$
$594$		0			0
$595$		0			0
$596$	−36.0000			−1.47462
$597$	8.00000	+	13.8564i	0.327418	+	0.567105i
$598$		0			0
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$		0			0
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$		0			0
$603$	5.00000			0.203616
$604$	20.0000	+	34.6410i	0.813788	+	1.40952i
$605$		0			0
$606$		0			0
$607$	12.5000	+	21.6506i	0.507359	+	0.878772i	0.999964	+	0.00851879i	$0.00271165\pi$
$607$	12.5000	+	21.6506i	0.507359	+	0.878772i	−0.492604	+	0.870253i	$0.663955\pi$
$608$		0			0
$609$	−12.0000	+	10.3923i	−0.486265	+	0.421117i
$610$		0			0
$611$	−15.0000	−	25.9808i	−0.606835	−	1.05107i
$612$	−6.00000	+	10.3923i	−0.242536	+	0.420084i
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	0.474509	+	0.880251i	$0.342626\pi$
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	−0.999574	+	0.0291886i	$0.990708\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.0000			−0.724653			−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000			−0.724653			−0.362326	+	0.932051i	$0.618017\pi$
$618$		0			0
$619$	9.50000	−	16.4545i	0.381837	−	0.661361i	−0.609488	−	0.792796i	$-0.708625\pi$
$619$	9.50000	−	16.4545i	0.381837	−	0.661361i	0.991325	+	0.131434i	$0.0419582\pi$
$620$		0			0
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$		0			0
$623$	3.00000	+	15.5885i	0.120192	+	0.624538i
$624$	20.0000			0.800641
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$		0			0
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$	14.0000	+	24.2487i	0.558661	+	0.967629i
$629$	42.0000			1.67465
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$	2.00000	−	3.46410i	0.0794929	−	0.137686i
$634$		0			0
$635$		0			0
$636$	−24.0000			−0.951662
$637$	27.5000	+	21.6506i	1.08959	+	0.857829i
$638$		0			0
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$	−13.0000			−0.512670			−0.256335	−	0.966588i	$-0.582515\pi$
$643$	−13.0000			−0.512670			−0.256335	+	0.966588i	$0.582515\pi$
$644$	5.00000	+	1.73205i	0.197028	+	0.0682524i
$645$		0			0
$646$		0			0
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	−0.986916	−	0.161233i	$-0.948453\pi$
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	0.633090	+	0.774078i	$0.281786\pi$
$648$		0			0
$649$	18.0000	+	31.1769i	0.706562	+	1.22380i
$650$		0			0
$651$	−2.50000	−	12.9904i	−0.0979827	−	0.509133i
$652$	8.00000			0.313304
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	0.904345	+	0.426801i	$0.140360\pi$
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	−0.0825519	+	0.996587i	$0.526307\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−7.00000			−0.273096
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	15.5000	−	26.8468i	0.602880	−	1.04422i	−0.389503	−	0.921025i	$-0.627353\pi$
$661$	15.5000	−	26.8468i	0.602880	−	1.04422i	0.992383	−	0.123194i	$-0.0393136\pi$
$662$		0			0
$663$	15.0000	+	25.9808i	0.582552	+	1.00901i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.00000	+	5.19615i	0.116160	+	0.201196i
$668$		0			0
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$		0			0
$671$	84.0000			3.24278
$672$		0			0
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$		0			0
$675$	2.50000	−	4.33013i	0.0962250	−	0.166667i
$676$	12.0000	−	20.7846i	0.461538	−	0.799408i
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	0.985517	−	0.169580i	$-0.0542410\pi$
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	−0.639618	+	0.768693i	$0.720908\pi$
$678$		0			0
$679$	−25.0000	−	8.66025i	−0.959412	−	0.332350i
$680$		0			0
$681$	3.00000	+	5.19615i	0.114960	+	0.199117i
$682$		0			0
$683$	18.0000	−	31.1769i	0.688751	−	1.19295i	−0.283491	−	0.958975i	$-0.591493\pi$
$683$	18.0000	−	31.1769i	0.688751	−	1.19295i	0.972242	−	0.233977i	$-0.0751739\pi$
$684$	−1.00000	−	1.73205i	−0.0382360	−	0.0662266i
$685$		0			0
$686$		0			0
$687$	−13.0000			−0.495981
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−30.0000	+	51.9615i	−1.14291	+	1.97958i
$690$		0			0
$691$	6.50000	+	11.2583i	0.247272	+	0.428287i	0.962768	−	0.270330i	$-0.0871327\pi$
$691$	6.50000	+	11.2583i	0.247272	+	0.428287i	−0.715496	+	0.698617i	$0.753799\pi$
$692$	−12.0000			−0.456172
$693$	15.0000	+	5.19615i	0.569803	+	0.197386i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$	18.0000			0.680823
$700$	−5.00000	−	25.9808i	−0.188982	−	0.981981i
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	−3.50000	+	6.06218i	−0.132005	+	0.228639i
$704$	24.0000	−	41.5692i	0.904534	−	1.56670i
$705$		0			0
$706$		0			0
$707$		0			0
$708$	12.0000			0.450988
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$	−2.50000	+	4.33013i	−0.0937573	+	0.162392i
$712$		0			0
$713$	−5.00000			−0.187251
$714$		0			0
$715$		0			0
$716$	12.0000	+	20.7846i	0.448461	+	0.776757i
$717$	−12.0000	+	20.7846i	−0.448148	+	0.776215i
$718$		0			0
$719$	−21.0000	−	36.3731i	−0.783168	−	1.35649i	−0.930087	−	0.367338i	$-0.880269\pi$
$719$	−21.0000	−	36.3731i	−0.783168	−	1.35649i	0.146920	−	0.989148i	$-0.453064\pi$
$720$		0			0
$721$	−5.50000	−	28.5788i	−0.204831	−	1.06433i
$722$		0			0
$723$	−1.00000	−	1.73205i	−0.0371904	−	0.0644157i
$724$	23.0000	−	39.8372i	0.854788	−	1.48054i
$725$	15.0000	−	25.9808i	0.557086	−	0.964901i
$726$		0			0
$727$	5.00000			0.185440			0.0927199	−	0.995692i	$-0.470444\pi$
$727$	5.00000			0.185440			0.0927199	+	0.995692i	$0.470444\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−3.00000	+	5.19615i	−0.110959	+	0.192187i
$732$	14.0000	−	24.2487i	0.517455	−	0.896258i
$733$	−11.5000	−	19.9186i	−0.424762	−	0.735710i	0.571636	−	0.820507i	$-0.306309\pi$
$733$	−11.5000	−	19.9186i	−0.424762	−	0.735710i	−0.996398	+	0.0847976i	$0.972976\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−15.0000	−	25.9808i	−0.552532	−	0.957014i
$738$		0			0
$739$	−14.5000	+	25.1147i	−0.533391	+	0.923861i	0.465848	+	0.884865i	$0.345749\pi$
$739$	−14.5000	+	25.1147i	−0.533391	+	0.923861i	−0.999239	+	0.0389959i	$0.987584\pi$
$740$		0			0
$741$	−5.00000			−0.183680
$742$		0			0
$743$	24.0000			0.880475			0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000			0.880475			0.440237	+	0.897881i	$0.354894\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	6.00000	+	10.3923i	0.219529	+	0.380235i
$748$	72.0000			2.63258
$749$		0			0
$750$		0			0
$751$	0.500000	+	0.866025i	0.0182453	+	0.0316017i	0.875004	−	0.484116i	$-0.160859\pi$
$751$	0.500000	+	0.866025i	0.0182453	+	0.0316017i	−0.856759	+	0.515718i	$0.827525\pi$
$752$	−12.0000	+	20.7846i	−0.437595	+	0.757937i
$753$	−15.0000	+	25.9808i	−0.546630	+	0.946792i
$754$		0			0
$755$		0			0
$756$	4.00000	−	3.46410i	0.145479	−	0.125988i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$		0			0
$759$	3.00000	−	5.19615i	0.108893	−	0.188608i
$760$		0			0
$761$	−15.0000	−	25.9808i	−0.543750	−	0.941802i	−0.998684	−	0.0512772i	$-0.983671\pi$
$761$	−15.0000	−	25.9808i	−0.543750	−	0.941802i	0.454935	−	0.890525i	$-0.349663\pi$
$762$		0			0
$763$	−22.0000	+	19.0526i	−0.796453	+	0.689749i
$764$	−36.0000			−1.30243
$765$		0			0
$766$		0			0
$767$	15.0000	−	25.9808i	0.541619	−	0.938111i
$768$	−8.00000	−	13.8564i	−0.288675	−	0.500000i
$769$	17.0000			0.613036			0.306518	−	0.951865i	$-0.400836\pi$
$769$	17.0000			0.613036			0.306518	+	0.951865i	$0.400836\pi$
$770$		0			0
$771$	12.0000			0.432169
$772$	11.0000	+	19.0526i	0.395899	+	0.685717i
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	−0.981250	−	0.192740i	$-0.938263\pi$
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	0.657542	+	0.753418i	$0.271596\pi$
$774$		0			0
$775$	12.5000	+	21.6506i	0.449013	+	0.777714i
$776$		0			0
$777$	−17.5000	−	6.06218i	−0.627809	−	0.217479i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$		0			0
$783$	6.00000			0.214423
$784$	4.00000	−	27.7128i	0.142857	−	0.989743i
$785$		0			0
$786$		0			0
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	0.426193	+	0.904632i	$0.359855\pi$
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	−0.996531	+	0.0832226i	$0.973479\pi$
$788$	−12.0000	+	20.7846i	−0.427482	+	0.740421i
$789$		0			0
$790$		0			0
$791$	15.0000	+	5.19615i	0.533339	+	0.184754i
$792$		0			0
$793$	−35.0000	−	60.6218i	−1.24289	−	2.15274i
$794$		0			0
$795$		0			0
$796$	−16.0000	−	27.7128i	−0.567105	−	0.982255i
$797$	36.0000			1.27519			0.637593	−	0.770374i	$-0.279930\pi$
$797$	36.0000			1.27519			0.637593	+	0.770374i	$0.279930\pi$
$798$		0			0
$799$	−36.0000			−1.27359
$800$		0			0
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$		0			0
$803$	21.0000	+	36.3731i	0.741074	+	1.28358i
$804$	−10.0000			−0.352673
$805$		0			0
$806$		0			0
$807$	12.0000	+	20.7846i	0.422420	+	0.731653i
$808$		0			0
$809$	−24.0000	+	41.5692i	−0.843795	+	1.46150i	0.0428684	+	0.999081i	$0.486350\pi$
$809$	−24.0000	+	41.5692i	−0.843795	+	1.46150i	−0.886664	+	0.462415i	$0.846983\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	24.0000	−	20.7846i	0.842235	−	0.729397i
$813$	−28.0000			−0.982003
$814$		0			0
$815$		0			0
$816$	12.0000	−	20.7846i	0.420084	−	0.727607i
$817$	−0.500000	−	0.866025i	−0.0174928	−	0.0302984i
$818$		0			0
$819$	−2.50000	−	12.9904i	−0.0873571	−	0.453921i
$820$		0			0
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$		0			0
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$		0			0
$825$	−30.0000			−1.04447
$826$		0			0
$827$	24.0000			0.834562			0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000			0.834562			0.417281	+	0.908778i	$0.362983\pi$
$828$	−1.00000	−	1.73205i	−0.0347524	−	0.0601929i
$829$	9.50000	−	16.4545i	0.329949	−	0.571488i	−0.652553	−	0.757743i	$-0.726302\pi$
$829$	9.50000	−	16.4545i	0.329949	−	0.571488i	0.982501	+	0.186256i	$0.0596352\pi$
$830$		0			0
$831$	15.5000	+	26.8468i	0.537689	+	0.931305i
$832$	−40.0000			−1.38675
$833$	39.0000	−	15.5885i	1.35127	−	0.540108i
$834$		0			0
$835$		0			0
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$	−2.50000	+	4.33013i	−0.0864126	+	0.149671i
$838$		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
$843$	−9.00000	+	15.5885i	−0.309976	+	0.536895i
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$		0			0
$846$		0			0
$847$	−12.5000	−	64.9519i	−0.429505	−	2.23177i
$848$	48.0000			1.64833
$849$	6.50000	+	11.2583i	0.223079	+	0.386385i
$850$		0			0
$851$	−3.50000	+	6.06218i	−0.119978	+	0.207809i
$852$	−6.00000	−	10.3923i	−0.205557	−	0.356034i
$853$	−1.00000			−0.0342393			−0.0171197	−	0.999853i	$-0.505450\pi$
$853$	−1.00000			−0.0342393			−0.0171197	+	0.999853i	$0.505450\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−24.0000	+	41.5692i	−0.819824	+	1.41998i	0.0859870	+	0.996296i	$0.472596\pi$
$857$	−24.0000	+	41.5692i	−0.819824	+	1.41998i	−0.905811	+	0.423681i	$0.860738\pi$
$858$		0			0
$859$	26.0000	+	45.0333i	0.887109	+	1.53652i	0.843278	+	0.537478i	$0.180623\pi$
$859$	26.0000	+	45.0333i	0.887109	+	1.53652i	0.0438309	+	0.999039i	$0.486044\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−21.0000	−	36.3731i	−0.714848	−	1.23815i	−0.963018	−	0.269437i	$-0.913162\pi$
$863$	−21.0000	−	36.3731i	−0.714848	−	1.23815i	0.248170	−	0.968717i	$-0.420171\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	19.0000			0.645274
$868$	5.00000	+	25.9808i	0.169711	+	0.881845i
$869$	30.0000			1.01768
$870$		0			0
$871$	−12.5000	+	21.6506i	−0.423546	+	0.733604i
$872$		0			0
$873$	5.00000	+	8.66025i	0.169224	+	0.293105i
$874$		0			0
$875$		0			0
$876$	14.0000			0.473016
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$		0			0
$879$	−9.00000	+	15.5885i	−0.303562	+	0.525786i
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	−1.00000			−0.0336527			−0.0168263	−	0.999858i	$-0.505356\pi$
$883$	−1.00000			−0.0336527			−0.0168263	+	0.999858i	$0.505356\pi$
$884$	−30.0000	−	51.9615i	−1.00901	−	1.74766i
$885$		0			0
$886$		0			0
$887$	27.0000	+	46.7654i	0.906571	+	1.57023i	0.818794	+	0.574087i	$0.194643\pi$
$887$	27.0000	+	46.7654i	0.906571	+	1.57023i	0.0877772	+	0.996140i	$0.472024\pi$
$888$		0			0
$889$	−17.5000	−	6.06218i	−0.586931	−	0.203319i
$890$		0			0
$891$	−3.00000	−	5.19615i	−0.100504	−	0.174078i
$892$	−16.0000	+	27.7128i	−0.535720	+	0.927894i
$893$	3.00000	−	5.19615i	0.100391	−	0.173883i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−5.00000			−0.166945
$898$		0			0
$899$	−15.0000	+	25.9808i	−0.500278	+	0.866507i
$900$	−5.00000	+	8.66025i	−0.166667	+	0.288675i
$901$	36.0000	+	62.3538i	1.19933	+	2.07731i
$902$		0			0
$903$	2.00000	−	1.73205i	0.0665558	−	0.0576390i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−14.5000	+	25.1147i	−0.481465	+	0.833921i	−0.999774	−	0.0212722i	$-0.993228\pi$
$907$	−14.5000	+	25.1147i	−0.481465	+	0.833921i	0.518309	+	0.855193i	$0.326562\pi$
$908$	−6.00000	−	10.3923i	−0.199117	−	0.344881i
$909$		0			0
$910$		0			0
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$	2.00000	+	3.46410i	0.0662266	+	0.114708i
$913$	36.0000	−	62.3538i	1.19143	−	2.06361i
$914$		0			0
$915$		0			0
$916$	26.0000			0.859064
$917$		0			0
$918$		0			0
$919$	−2.50000	−	4.33013i	−0.0824674	−	0.142838i	0.821842	−	0.569716i	$-0.192947\pi$
$919$	−2.50000	−	4.33013i	−0.0824674	−	0.142838i	−0.904309	+	0.426878i	$0.859613\pi$
$920$		0			0
$921$	6.50000	−	11.2583i	0.214182	−	0.370975i
$922$		0			0
$923$	−30.0000			−0.987462
$924$	−30.0000	−	10.3923i	−0.986928	−	0.341882i
$925$	35.0000			1.15079
$926$		0			0
$927$	−5.50000	+	9.52628i	−0.180644	+	0.312884i
$928$		0			0
$929$	−6.00000	−	10.3923i	−0.196854	−	0.340960i	0.750653	−	0.660697i	$-0.229739\pi$
$929$	−6.00000	−	10.3923i	−0.196854	−	0.340960i	−0.947507	+	0.319736i	$0.896406\pi$
$930$		0			0
$931$	−1.00000	+	6.92820i	−0.0327737	+	0.227063i
$932$	−36.0000			−1.17922
$933$	3.00000	+	5.19615i	0.0982156	+	0.170114i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−43.0000			−1.40475			−0.702374	−	0.711808i	$-0.747877\pi$
$937$	−43.0000			−1.40475			−0.702374	+	0.711808i	$0.747877\pi$
$938$		0			0
$939$	−19.0000			−0.620042
$940$		0			0
$941$	18.0000	−	31.1769i	0.586783	−	1.01634i	−0.407867	−	0.913041i	$-0.633727\pi$
$941$	18.0000	−	31.1769i	0.586783	−	1.01634i	0.994651	−	0.103297i	$-0.0329393\pi$
$942$		0			0
$943$		0			0
$944$	−24.0000			−0.781133
$945$		0			0
$946$		0			0
$947$	−3.00000	−	5.19615i	−0.0974869	−	0.168852i	0.813157	−	0.582045i	$-0.197747\pi$
$947$	−3.00000	−	5.19615i	−0.0974869	−	0.168852i	−0.910644	+	0.413192i	$0.864414\pi$
$948$	5.00000	−	8.66025i	0.162392	−	0.281272i
$949$	17.5000	−	30.3109i	0.568074	−	0.983933i
$950$		0			0
$951$	18.0000			0.583690
$952$		0			0
$953$	−30.0000			−0.971795			−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000			−0.971795			−0.485898	+	0.874016i	$0.661507\pi$
$954$		0			0
$955$		0			0
$956$	24.0000	−	41.5692i	0.776215	−	1.34444i
$957$	−18.0000	−	31.1769i	−0.581857	−	1.00781i
$958$		0			0
$959$	−24.0000	+	20.7846i	−0.775000	+	0.671170i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$		0			0
$963$		0			0
$964$	2.00000	+	3.46410i	0.0644157	+	0.111571i
$965$		0			0
$966$		0			0
$967$	11.0000			0.353736			0.176868	−	0.984235i	$-0.443403\pi$
$967$	11.0000			0.353736			0.176868	+	0.984235i	$0.443403\pi$
$968$		0			0
$969$	−3.00000	+	5.19615i	−0.0963739	+	0.166924i
$970$		0			0
$971$	21.0000	+	36.3731i	0.673922	+	1.16727i	0.976783	+	0.214232i	$0.0687250\pi$
$971$	21.0000	+	36.3731i	0.673922	+	1.16727i	−0.302861	+	0.953035i	$0.597942\pi$
$972$	−2.00000			−0.0641500
$973$	12.5000	+	4.33013i	0.400732	+	0.138817i
$974$		0			0
$975$	12.5000	+	21.6506i	0.400320	+	0.693375i
$976$	−28.0000	+	48.4974i	−0.896258	+	1.55236i
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	0.305530	+	0.952183i	$0.401167\pi$
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	−0.977379	+	0.211495i	$0.932167\pi$
$978$		0			0
$979$	−36.0000			−1.15056
$980$		0			0
$981$	11.0000			0.351203
$982$		0			0
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	15.0000	+	5.19615i	0.477455	+	0.165395i
$988$	10.0000			0.318142
$989$	−0.500000	−	0.866025i	−0.0158991	−	0.0275380i
$990$		0			0
$991$	15.5000	−	26.8468i	0.492374	−	0.852816i	−0.507588	−	0.861600i	$-0.669463\pi$
$991$	15.5000	−	26.8468i	0.492374	−	0.852816i	0.999961	+	0.00878379i	$0.00279600\pi$
$992$		0			0
$993$	11.0000			0.349074
$994$		0			0
$995$		0			0
$996$	−12.0000	−	20.7846i	−0.380235	−	0.658586i
$997$	0.500000	−	0.866025i	0.0158352	−	0.0274273i	−0.857999	−	0.513651i	$-0.828293\pi$
$997$	0.500000	−	0.866025i	0.0158352	−	0.0274273i	0.873834	+	0.486224i	$0.161626\pi$
$998$		0			0
$999$	3.50000	+	6.06218i	0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.b.277.1	✓	2
7.2	even	3	inner	483.2.i.b.415.1	yes	2
7.3	odd	6		3381.2.a.g.1.1		1
7.4	even	3		3381.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.b.277.1	✓	2	1.1	even	1	trivial
483.2.i.b.415.1	yes	2	7.2	even	3	inner
3381.2.a.g.1.1		1	7.3	odd	6
3381.2.a.j.1.1		1	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(1.00000 + 1.73205i) q^{12} +5.00000 q^{13} +(-2.00000 - 3.46410i) q^{16} +(3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(0.500000 + 0.866025i) q^{23} +(2.50000 - 4.33013i) q^{25} +1.00000 q^{27} +(4.00000 - 3.46410i) q^{28} +6.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-3.00000 - 5.19615i) q^{33} -2.00000 q^{36} +(3.50000 + 6.06218i) q^{37} +(-2.50000 + 4.33013i) q^{39} -1.00000 q^{43} +(6.00000 + 10.3923i) q^{44} +(-3.00000 - 5.19615i) q^{47} +4.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{51} +(5.00000 - 8.66025i) q^{52} +(-6.00000 + 10.3923i) q^{53} -1.00000 q^{57} +(3.00000 - 5.19615i) q^{59} +(-7.00000 - 12.1244i) q^{61} +(-0.500000 - 2.59808i) q^{63} -8.00000 q^{64} +(-2.50000 + 4.33013i) q^{67} +(-6.00000 - 10.3923i) q^{68} -1.00000 q^{69} -6.00000 q^{71} +(3.50000 - 6.06218i) q^{73} +(2.50000 + 4.33013i) q^{75} +2.00000 q^{76} +(-12.0000 + 10.3923i) q^{77} +(-2.50000 - 4.33013i) q^{79} +(-0.500000 + 0.866025i) q^{81} -12.0000 q^{83} +(1.00000 + 5.19615i) q^{84} +(-3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{89} +(12.5000 + 4.33013i) q^{91} +2.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} -10.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 2 q^{4} + 5 q^{7} - q^{9}+O(q^{10}) \) 2 * q - q^3 + 2 * q^4 + 5 * q^7 - q^9	\( 2 q - q^{3} + 2 q^{4} + 5 q^{7} - q^{9} - 6 q^{11} + 2 q^{12} + 10 q^{13} - 4 q^{16} + 6 q^{17} + q^{19} - 4 q^{21} + q^{23} + 5 q^{25} + 2 q^{27} + 8 q^{28} + 12 q^{29} - 5 q^{31} - 6 q^{33} - 4 q^{36} + 7 q^{37} - 5 q^{39} - 2 q^{43} + 12 q^{44} - 6 q^{47} + 8 q^{48} + 11 q^{49} + 6 q^{51} + 10 q^{52} - 12 q^{53} - 2 q^{57} + 6 q^{59} - 14 q^{61} - q^{63} - 16 q^{64} - 5 q^{67} - 12 q^{68} - 2 q^{69} - 12 q^{71} + 7 q^{73} + 5 q^{75} + 4 q^{76} - 24 q^{77} - 5 q^{79} - q^{81} - 24 q^{83} + 2 q^{84} - 6 q^{87} + 6 q^{89} + 25 q^{91} + 4 q^{92} - 5 q^{93} - 20 q^{97} + 12 q^{99}+O(q^{100}) \) 2 * q - q^3 + 2 * q^4 + 5 * q^7 - q^9 - 6 * q^11 + 2 * q^12 + 10 * q^13 - 4 * q^16 + 6 * q^17 + q^19 - 4 * q^21 + q^23 + 5 * q^25 + 2 * q^27 + 8 * q^28 + 12 * q^29 - 5 * q^31 - 6 * q^33 - 4 * q^36 + 7 * q^37 - 5 * q^39 - 2 * q^43 + 12 * q^44 - 6 * q^47 + 8 * q^48 + 11 * q^49 + 6 * q^51 + 10 * q^52 - 12 * q^53 - 2 * q^57 + 6 * q^59 - 14 * q^61 - q^63 - 16 * q^64 - 5 * q^67 - 12 * q^68 - 2 * q^69 - 12 * q^71 + 7 * q^73 + 5 * q^75 + 4 * q^76 - 24 * q^77 - 5 * q^79 - q^81 - 24 * q^83 + 2 * q^84 - 6 * q^87 + 6 * q^89 + 25 * q^91 + 4 * q^92 - 5 * q^93 - 20 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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