LMFDB - Embedded newform 270.2.e.a.91.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [270,2,Mod(91,270)] 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("270.91"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(270, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$270 = 2 \cdot 3^{3} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	270.e (of order $3$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.15596085457$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			91.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	270.91
Dual form			270.2.e.a.181.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} -1.00000 q^{10} +(1.50000 + 2.59808i) q^{11} +(2.00000 - 3.46410i) q^{13} +(2.00000 - 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} -3.00000 q^{17} +5.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(1.50000 - 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{25} -4.00000 q^{26} -4.00000 q^{28} +(3.00000 + 5.19615i) q^{29} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{34} +4.00000 q^{35} -4.00000 q^{37} +(-2.50000 - 4.33013i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(-5.50000 - 9.52628i) q^{43} -3.00000 q^{44} -6.00000 q^{46} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(2.00000 + 3.46410i) q^{52} -6.00000 q^{53} +3.00000 q^{55} +(2.00000 + 3.46410i) q^{56} +(3.00000 - 5.19615i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(5.00000 + 8.66025i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-2.50000 + 4.33013i) q^{67} +(1.50000 - 2.59808i) q^{68} +(-2.00000 - 3.46410i) q^{70} -6.00000 q^{71} -7.00000 q^{73} +(2.00000 + 3.46410i) q^{74} +(-2.50000 + 4.33013i) q^{76} +(-6.00000 + 10.3923i) q^{77} +(-7.00000 - 12.1244i) q^{79} -1.00000 q^{80} +3.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(-1.50000 + 2.59808i) q^{85} +(-5.50000 + 9.52628i) q^{86} +(1.50000 + 2.59808i) q^{88} -6.00000 q^{89} +16.0000 q^{91} +(3.00000 + 5.19615i) q^{92} +(2.50000 - 4.33013i) q^{95} +(-5.50000 - 9.52628i) q^{97} +9.00000 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - q^{2} - q^{4} + q^{5} + 4 q^{7} + 2 q^{8} - 2 q^{10} + 3 q^{11} + 4 q^{13} + 4 q^{14} - q^{16} - 6 q^{17} + 10 q^{19} + q^{20} + 3 q^{22} + 6 q^{23} - q^{25} - 8 q^{26} - 8 q^{28} + 6 q^{29}+ \cdots + 18 q^{98}+O(q^{100})$ 2 * q - q^2 - q^4 + q^5 + 4 * q^7 + 2 * q^8 - 2 * q^10 + 3 * q^11 + 4 * q^13 + 4 * q^14 - q^16 - 6 * q^17 + 10 * q^19 + q^20 + 3 * q^22 + 6 * q^23 - q^25 - 8 * q^26 - 8 * q^28 + 6 * q^29 - 2 * q^31 - q^32 + 3 * q^34 + 8 * q^35 - 8 * q^37 - 5 * q^38 + q^40 - 3 * q^41 - 11 * q^43 - 6 * q^44 - 12 * q^46 - 9 * q^49 - q^50 + 4 * q^52 - 12 * q^53 + 6 * q^55 + 4 * q^56 + 6 * q^58 - 3 * q^59 + 10 * q^61 + 4 * q^62 + 2 * q^64 - 4 * q^65 - 5 * q^67 + 3 * q^68 - 4 * q^70 - 12 * q^71 - 14 * q^73 + 4 * q^74 - 5 * q^76 - 12 * q^77 - 14 * q^79 - 2 * q^80 + 6 * q^82 + 12 * q^83 - 3 * q^85 - 11 * q^86 + 3 * q^88 - 12 * q^89 + 32 * q^91 + 6 * q^92 + 5 * q^95 - 11 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$ .

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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

)

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	0.944911	+	0.327327i	$0.106148\pi$
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.00000			−0.316228
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$	2.00000	−	3.46410i	0.534522	−	0.925820i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$		0			0
$19$	5.00000			1.14708			0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000			1.14708			0.573539	+	0.819178i	$0.305570\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−4.00000			−0.784465
$27$		0			0
$28$	−4.00000			−0.755929
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	1.50000	+	2.59808i	0.257248	+	0.445566i
$35$	4.00000			0.676123
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$	−2.50000	−	4.33013i	−0.405554	−	0.702439i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	−0.890947	−	0.454108i	$-0.849958\pi$
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	0.0522047	−	0.998636i	$-0.483375\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	−6.00000			−0.884652
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	3.00000			0.404520
$56$	2.00000	+	3.46410i	0.267261	+	0.462910i
$57$		0			0
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		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	$0.265465\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$	−2.00000	−	3.46410i	−0.239046	−	0.414039i
$71$	−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
$73$	−7.00000			−0.819288			−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000			−0.819288			−0.409644	+	0.912245i	$0.634347\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$		0			0
$76$	−2.50000	+	4.33013i	−0.286770	+	0.496700i
$77$	−6.00000	+	10.3923i	−0.683763	+	1.18431i
$78$		0			0
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	−0.927457	−	0.373930i	$-0.878010\pi$
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	0.139895	−	0.990166i	$-0.455323\pi$
$80$	−1.00000			−0.111803
$81$		0			0
$82$	3.00000			0.331295
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$		0			0
$85$	−1.50000	+	2.59808i	−0.162698	+	0.281801i
$86$	−5.50000	+	9.52628i	−0.593080	+	1.02725i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	16.0000			1.67726
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$		0			0
$94$		0			0
$95$	2.50000	−	4.33013i	0.256495	−	0.444262i
$96$		0			0
$97$	−5.50000	−	9.52628i	−0.558440	−	0.967247i	−0.997627	−	0.0688512i	$-0.978067\pi$
$97$	−5.50000	−	9.52628i	−0.558440	−	0.967247i	0.439187	−	0.898396i	$-0.355267\pi$
$98$	9.00000			0.909137
$99$		0			0
$100$	1.00000			0.100000
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$		0			0
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	2.00000	−	3.46410i	0.196116	−	0.339683i
$105$		0			0
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	9.00000			0.870063			0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000			0.870063			0.435031	+	0.900415i	$0.356737\pi$
$108$		0			0
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$	−1.50000	−	2.59808i	−0.143019	−	0.247717i
$111$		0			0
$112$	2.00000	−	3.46410i	0.188982	−	0.327327i
$113$	9.00000	−	15.5885i	0.846649	−	1.46644i	−0.0375328	−	0.999295i	$-0.511950\pi$
$113$	9.00000	−	15.5885i	0.846649	−	1.46644i	0.884182	−	0.467143i	$-0.154717\pi$
$114$		0			0
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$	−6.00000			−0.557086
$117$		0			0
$118$	3.00000			0.276172
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	5.00000	−	8.66025i	0.452679	−	0.784063i
$123$		0			0
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.00000	+	3.46410i	−0.175412	+	0.303822i
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$	10.0000	+	17.3205i	0.867110	+	1.50188i
$134$	5.00000			0.431934
$135$		0			0
$136$	−3.00000			−0.257248
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$		0			0
$139$	0.500000	−	0.866025i	0.0424094	−	0.0734553i	−0.844042	−	0.536278i	$-0.819830\pi$
$139$	0.500000	−	0.866025i	0.0424094	−	0.0734553i	0.886451	+	0.462822i	$0.153163\pi$
$140$	−2.00000	+	3.46410i	−0.169031	+	0.292770i
$141$		0			0
$142$	3.00000	+	5.19615i	0.251754	+	0.436051i
$143$	12.0000			1.00349
$144$		0			0
$145$	6.00000			0.498273
$146$	3.50000	+	6.06218i	0.289662	+	0.501709i
$147$		0			0
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		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	$0.699945\pi$
$152$	5.00000			0.405554
$153$		0			0
$154$	12.0000			0.966988
$155$	1.00000	+	1.73205i	0.0803219	+	0.139122i
$156$		0			0
$157$	−4.00000	+	6.92820i	−0.319235	+	0.552931i	−0.980329	−	0.197372i	$-0.936759\pi$
$157$	−4.00000	+	6.92820i	−0.319235	+	0.552931i	0.661094	+	0.750303i	$0.270093\pi$
$158$	−7.00000	+	12.1244i	−0.556890	+	0.964562i
$159$		0			0
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	24.0000			1.89146
$162$		0			0
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	0.273252	+	0.961943i	$0.411901\pi$
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	−0.969693	+	0.244328i	$0.921432\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	3.00000			0.230089
$171$		0			0
$172$	11.0000			0.838742
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$		0			0
$175$	2.00000	−	3.46410i	0.151186	−	0.261861i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$		0			0
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	−8.00000	−	13.8564i	−0.592999	−	1.02711i
$183$		0			0
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$		0			0
$187$	−4.50000	−	7.79423i	−0.329073	−	0.569970i
$188$		0			0
$189$		0			0
$190$	−5.00000			−0.362738
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	6.50000	−	11.2583i	0.467880	−	0.810392i	−0.531446	−	0.847092i	$-0.678351\pi$
$193$	6.50000	−	11.2583i	0.467880	−	0.810392i	0.999326	+	0.0366998i	$0.0116845\pi$
$194$	−5.50000	+	9.52628i	−0.394877	+	0.683947i
$195$		0			0
$196$	−4.50000	−	7.79423i	−0.321429	−	0.556731i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	−6.00000	+	10.3923i	−0.422159	+	0.731200i
$203$	−12.0000	+	20.7846i	−0.842235	+	1.45879i
$204$		0			0
$205$	1.50000	+	2.59808i	0.104765	+	0.181458i
$206$	−4.00000			−0.278693
$207$		0			0
$208$	−4.00000			−0.277350
$209$	7.50000	+	12.9904i	0.518786	+	0.898563i
$210$		0			0
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$		0			0
$214$	−4.50000	−	7.79423i	−0.307614	−	0.532803i
$215$	−11.0000			−0.750194
$216$		0			0
$217$	−8.00000			−0.543075
$218$	2.00000	+	3.46410i	0.135457	+	0.234619i
$219$		0			0
$220$	−1.50000	+	2.59808i	−0.101130	+	0.175162i
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$		0			0
$223$	11.0000	+	19.0526i	0.736614	+	1.27585i	0.954011	+	0.299770i	$0.0969101\pi$
$223$	11.0000	+	19.0526i	0.736614	+	1.27585i	−0.217397	+	0.976083i	$0.569757\pi$
$224$	−4.00000			−0.267261
$225$		0			0
$226$	−18.0000			−1.19734
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	0.811943	−	0.583736i	$-0.198410\pi$
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	−0.911502	+	0.411296i	$0.865076\pi$
$228$		0			0
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	0.319582	+	0.947559i	$0.396457\pi$
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	−0.980401	+	0.197013i	$0.936876\pi$
$230$	−3.00000	+	5.19615i	−0.197814	+	0.342624i
$231$		0			0
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	−21.0000			−1.37576			−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000			−1.37576			−0.687878	+	0.725826i	$0.741458\pi$
$234$		0			0
$235$		0			0
$236$	−1.50000	−	2.59808i	−0.0976417	−	0.169120i
$237$		0			0
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	−0.752536	−	0.658551i	$-0.771170\pi$
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	0.946590	+	0.322440i	$0.104503\pi$
$240$		0			0
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	0.450910	−	0.892570i	$-0.351100\pi$
$242$	−2.00000			−0.128565
$243$		0			0
$244$	−10.0000			−0.640184
$245$	4.50000	+	7.79423i	0.287494	+	0.497955i
$246$		0			0
$247$	10.0000	−	17.3205i	0.636285	−	1.10208i
$248$	−1.00000	+	1.73205i	−0.0635001	+	0.109985i
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	21.0000			1.32551			0.662754	−	0.748837i	$-0.269387\pi$
$251$	21.0000			1.32551			0.662754	+	0.748837i	$0.269387\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$	−1.00000	−	1.73205i	−0.0627456	−	0.108679i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.50000	−	7.79423i	0.280702	−	0.486191i	−0.690856	−	0.722993i	$-0.742766\pi$
$257$	4.50000	−	7.79423i	0.280702	−	0.486191i	0.971558	+	0.236802i	$0.0760993\pi$
$258$		0			0
$259$	−8.00000	−	13.8564i	−0.497096	−	0.860995i
$260$	4.00000			0.248069
$261$		0			0
$262$	−12.0000			−0.741362
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	0.952517	+	0.304487i	$0.0984850\pi$
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$264$		0			0
$265$	−3.00000	+	5.19615i	−0.184289	+	0.319197i
$266$	10.0000	−	17.3205i	0.613139	−	1.06199i
$267$		0			0
$268$	−2.50000	−	4.33013i	−0.152712	−	0.264505i
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$		0			0
$274$	−4.50000	+	7.79423i	−0.271855	+	0.470867i
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$		0			0
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	0.980373	+	0.197153i	$0.0631696\pi$
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	−0.319447	+	0.947604i	$0.603497\pi$
$278$	−1.00000			−0.0599760
$279$		0			0
$280$	4.00000			0.239046
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	0.762561	−	0.646916i	$-0.223942\pi$
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	−0.941526	+	0.336939i	$0.890608\pi$
$282$		0			0
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	0.399188	+	0.916869i	$0.369292\pi$
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	−0.993626	+	0.112728i	$0.964041\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.354787	−	0.614510i
$287$	−12.0000			−0.708338
$288$		0			0
$289$	−8.00000			−0.470588
$290$	−3.00000	−	5.19615i	−0.176166	−	0.305129i
$291$		0			0
$292$	3.50000	−	6.06218i	0.204822	−	0.354762i
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	0.473763	+	0.880652i	$0.342895\pi$
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	−0.999549	+	0.0300351i	$0.990438\pi$
$294$		0			0
$295$	1.50000	+	2.59808i	0.0873334	+	0.151266i
$296$	−4.00000			−0.232495
$297$		0			0
$298$		0			0
$299$	−12.0000	−	20.7846i	−0.693978	−	1.20201i
$300$		0			0
$301$	22.0000	−	38.1051i	1.26806	−	2.19634i
$302$	5.00000	−	8.66025i	0.287718	−	0.498342i
$303$		0			0
$304$	−2.50000	−	4.33013i	−0.143385	−	0.248350i
$305$	10.0000			0.572598
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$	−6.00000	−	10.3923i	−0.341882	−	0.592157i
$309$		0			0
$310$	1.00000	−	1.73205i	0.0567962	−	0.0983739i
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	−0.938460	−	0.345389i	$-0.887747\pi$
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	0.768345	+	0.640036i	$0.221080\pi$
$312$		0			0
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	0.879810	−	0.475325i	$-0.157669\pi$
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	−0.851549	+	0.524276i	$0.824336\pi$
$314$	8.00000			0.451466
$315$		0			0
$316$	14.0000			0.787562
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	0.976764	+	0.214318i	$0.0687530\pi$
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	−0.302777	+	0.953062i	$0.597914\pi$
$318$		0			0
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	−12.0000	−	20.7846i	−0.668734	−	1.15828i
$323$	−15.0000			−0.834622
$324$		0			0
$325$	−4.00000			−0.221880
$326$	8.00000	+	13.8564i	0.443079	+	0.767435i
$327$		0			0
$328$	−1.50000	+	2.59808i	−0.0828236	+	0.143455i
$329$		0			0
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	−12.0000			−0.658586
$333$		0			0
$334$	18.0000			0.984916
$335$	2.50000	+	4.33013i	0.136590	+	0.236580i
$336$		0			0
$337$	15.5000	−	26.8468i	0.844339	−	1.46244i	−0.0418554	−	0.999124i	$-0.513327\pi$
$337$	15.5000	−	26.8468i	0.844339	−	1.46244i	0.886194	−	0.463314i	$-0.153340\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$		0			0
$340$	−1.50000	−	2.59808i	−0.0813489	−	0.140900i
$341$	−6.00000			−0.324918
$342$		0			0
$343$	−8.00000			−0.431959
$344$	−5.50000	−	9.52628i	−0.296540	−	0.513623i
$345$		0			0
$346$	−9.00000	+	15.5885i	−0.483843	+	0.838041i
$347$	10.5000	−	18.1865i	0.563670	−	0.976304i	−0.433503	−	0.901152i	$-0.642722\pi$
$347$	10.5000	−	18.1865i	0.563670	−	0.976304i	0.997172	−	0.0751519i	$-0.0239442\pi$
$348$		0			0
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	0.996716	−	0.0809766i	$-0.0258039\pi$
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	−0.568486	+	0.822693i	$0.692471\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	−3.00000			−0.159901
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	0.960574	−	0.278024i	$-0.0896796\pi$
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	−0.721063	+	0.692869i	$0.756346\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$	3.00000	−	5.19615i	0.159000	−	0.275396i
$357$		0			0
$358$		0			0
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	6.00000			0.315789
$362$	8.00000	+	13.8564i	0.420471	+	0.728277i
$363$		0			0
$364$	−8.00000	+	13.8564i	−0.419314	+	0.726273i
$365$	−3.50000	+	6.06218i	−0.183198	+	0.317309i
$366$		0			0
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	−6.00000			−0.312772
$369$		0			0
$370$	4.00000			0.207950
$371$	−12.0000	−	20.7846i	−0.623009	−	1.07908i
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	−4.50000	+	7.79423i	−0.232689	+	0.403030i
$375$		0			0
$376$		0			0
$377$	24.0000			1.23606
$378$		0			0
$379$	29.0000			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$380$	2.50000	+	4.33013i	0.128247	+	0.222131i
$381$		0			0
$382$		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
$385$	6.00000	+	10.3923i	0.305788	+	0.529641i
$386$	−13.0000			−0.661683
$387$		0			0
$388$	11.0000			0.558440
$389$	18.0000	+	31.1769i	0.912636	+	1.58073i	0.810326	+	0.585980i	$0.199290\pi$
$389$	18.0000	+	31.1769i	0.912636	+	1.58073i	0.102311	+	0.994753i	$0.467376\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.455150	+	0.788342i
$392$	−4.50000	+	7.79423i	−0.227284	+	0.393668i
$393$		0			0
$394$		0			0
$395$	−14.0000			−0.704416
$396$		0			0
$397$	8.00000			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$398$	−10.0000	−	17.3205i	−0.501255	−	0.868199i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	−0.0787327	−	0.996896i	$-0.525087\pi$
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	0.902703	−	0.430263i	$-0.141579\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	12.0000			0.597022
$405$		0			0
$406$	24.0000			1.19110
$407$	−6.00000	−	10.3923i	−0.297409	−	0.515127i
$408$		0			0
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	0.939490	−	0.342578i	$-0.111300\pi$
$410$	1.50000	−	2.59808i	0.0740797	−	0.128310i
$411$		0			0
$412$	2.00000	+	3.46410i	0.0985329	+	0.170664i
$413$	−12.0000			−0.590481
$414$		0			0
$415$	12.0000			0.589057
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$		0			0
$418$	7.50000	−	12.9904i	0.366837	−	0.635380i
$419$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$419$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$420$		0			0
$421$	−1.00000	−	1.73205i	−0.0487370	−	0.0844150i	0.840628	−	0.541613i	$-0.182186\pi$
$421$	−1.00000	−	1.73205i	−0.0487370	−	0.0844150i	−0.889365	+	0.457198i	$0.848853\pi$
$422$	−4.00000			−0.194717
$423$		0			0
$424$	−6.00000			−0.291386
$425$	1.50000	+	2.59808i	0.0727607	+	0.126025i
$426$		0			0
$427$	−20.0000	+	34.6410i	−0.967868	+	1.67640i
$428$	−4.50000	+	7.79423i	−0.217516	+	0.376748i
$429$		0			0
$430$	5.50000	+	9.52628i	0.265234	+	0.459398i
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$		0			0
$433$	−13.0000			−0.624740			−0.312370	−	0.949960i	$-0.601123\pi$
$433$	−13.0000			−0.624740			−0.312370	+	0.949960i	$0.601123\pi$
$434$	4.00000	+	6.92820i	0.192006	+	0.332564i
$435$		0			0
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$	15.0000	−	25.9808i	0.717547	−	1.24283i
$438$		0			0
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	0.960323	−	0.278889i	$-0.0899661\pi$
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	−0.721686	+	0.692220i	$0.756633\pi$
$440$	3.00000			0.143019
$441$		0			0
$442$	12.0000			0.570782
$443$	1.50000	+	2.59808i	0.0712672	+	0.123438i	0.899457	−	0.437009i	$-0.143962\pi$
$443$	1.50000	+	2.59808i	0.0712672	+	0.123438i	−0.828190	+	0.560448i	$0.810629\pi$
$444$		0			0
$445$	−3.00000	+	5.19615i	−0.142214	+	0.246321i
$446$	11.0000	−	19.0526i	0.520865	−	0.902165i
$447$		0			0
$448$	2.00000	+	3.46410i	0.0944911	+	0.163663i
$449$	15.0000			0.707894			0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000			0.707894			0.353947	+	0.935266i	$0.384839\pi$
$450$		0			0
$451$	−9.00000			−0.423793
$452$	9.00000	+	15.5885i	0.423324	+	0.733219i
$453$		0			0
$454$	−1.50000	+	2.59808i	−0.0703985	+	0.121934i
$455$	8.00000	−	13.8564i	0.375046	−	0.649598i
$456$		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	$0.825888\pi$
$458$	20.0000			0.934539
$459$		0			0
$460$	6.00000			0.279751
$461$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$461$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$462$		0			0
$463$	−10.0000	+	17.3205i	−0.464739	+	0.804952i	−0.999190	−	0.0402476i	$-0.987185\pi$
$463$	−10.0000	+	17.3205i	−0.464739	+	0.804952i	0.534450	+	0.845200i	$0.320519\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$		0			0
$466$	10.5000	+	18.1865i	0.486403	+	0.842475i
$467$	−21.0000			−0.971764			−0.485882	−	0.874024i	$-0.661502\pi$
$467$	−21.0000			−0.971764			−0.485882	+	0.874024i	$0.661502\pi$
$468$		0			0
$469$	−20.0000			−0.923514
$470$		0			0
$471$		0			0
$472$	−1.50000	+	2.59808i	−0.0690431	+	0.119586i
$473$	16.5000	−	28.5788i	0.758671	−	1.31406i
$474$		0			0
$475$	−2.50000	−	4.33013i	−0.114708	−	0.198680i
$476$	12.0000			0.550019
$477$		0			0
$478$	−6.00000			−0.274434
$479$	−3.00000	−	5.19615i	−0.137073	−	0.237418i	0.789314	−	0.613990i	$-0.210436\pi$
$479$	−3.00000	−	5.19615i	−0.137073	−	0.237418i	−0.926388	+	0.376571i	$0.877103\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$	−8.50000	+	14.7224i	−0.387164	+	0.670588i
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−11.0000			−0.499484
$486$		0			0
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	5.00000	+	8.66025i	0.226339	+	0.392031i
$489$		0			0
$490$	4.50000	−	7.79423i	0.203289	−	0.352107i
$491$	−16.5000	+	28.5788i	−0.744635	+	1.28974i	0.205731	+	0.978609i	$0.434043\pi$
$491$	−16.5000	+	28.5788i	−0.744635	+	1.28974i	−0.950365	+	0.311136i	$0.899290\pi$
$492$		0			0
$493$	−9.00000	−	15.5885i	−0.405340	−	0.702069i
$494$	−20.0000			−0.899843
$495$		0			0
$496$	2.00000			0.0898027
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$		0			0
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	−0.276683	−	0.960961i	$-0.589235\pi$
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	0.970558	−	0.240866i	$-0.0774314\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−10.5000	−	18.1865i	−0.468638	−	0.811705i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$	−12.0000			−0.533993
$506$	−9.00000	−	15.5885i	−0.400099	−	0.692991i
$507$		0			0
$508$	−1.00000	+	1.73205i	−0.0443678	+	0.0768473i
$509$	−6.00000	+	10.3923i	−0.265945	+	0.460631i	−0.967811	−	0.251679i	$-0.919017\pi$
$509$	−6.00000	+	10.3923i	−0.265945	+	0.460631i	0.701866	+	0.712309i	$0.252351\pi$
$510$		0			0
$511$	−14.0000	−	24.2487i	−0.619324	−	1.07270i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−9.00000			−0.396973
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$		0			0
$517$		0			0
$518$	−8.00000	+	13.8564i	−0.351500	+	0.608816i
$519$		0			0
$520$	−2.00000	−	3.46410i	−0.0877058	−	0.151911i
$521$	3.00000			0.131432			0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000			0.131432			0.0657162	+	0.997838i	$0.479067\pi$
$522$		0			0
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	6.00000	+	10.3923i	0.262111	+	0.453990i
$525$		0			0
$526$	12.0000	−	20.7846i	0.523225	−	0.906252i
$527$	3.00000	−	5.19615i	0.130682	−	0.226348i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	6.00000			0.260623
$531$		0			0
$532$	−20.0000			−0.867110
$533$	6.00000	+	10.3923i	0.259889	+	0.450141i
$534$		0			0
$535$	4.50000	−	7.79423i	0.194552	−	0.336974i
$536$	−2.50000	+	4.33013i	−0.107984	+	0.187033i
$537$		0			0
$538$	3.00000	+	5.19615i	0.129339	+	0.224022i
$539$	−27.0000			−1.16297
$540$		0			0
$541$	8.00000			0.343947			0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000			0.343947			0.171973	+	0.985102i	$0.444986\pi$
$542$	8.00000	+	13.8564i	0.343629	+	0.595184i
$543$		0			0
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$	−2.00000	+	3.46410i	−0.0856706	+	0.148386i
$546$		0			0
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	0.876517	−	0.481371i	$-0.159861\pi$
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	−0.855138	+	0.518400i	$0.826528\pi$
$548$	9.00000			0.384461
$549$		0			0
$550$	−3.00000			−0.127920
$551$	15.0000	+	25.9808i	0.639021	+	1.10682i
$552$		0			0
$553$	28.0000	−	48.4974i	1.19068	−	2.06232i
$554$	11.0000	−	19.0526i	0.467345	−	0.809466i
$555$		0			0
$556$	0.500000	+	0.866025i	0.0212047	+	0.0367277i
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$		0			0
$559$	−44.0000			−1.86100
$560$	−2.00000	−	3.46410i	−0.0845154	−	0.146385i
$561$		0			0
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	−1.50000	+	2.59808i	−0.0632175	+	0.109496i	−0.895902	−	0.444252i	$-0.853470\pi$
$563$	−1.50000	+	2.59808i	−0.0632175	+	0.109496i	0.832684	+	0.553748i	$0.186803\pi$
$564$		0			0
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$	20.0000			0.840663
$567$		0			0
$568$	−6.00000			−0.251754
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	−0.907532	−	0.419984i	$-0.862036\pi$
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	0.0900490	−	0.995937i	$-0.471298\pi$
$570$		0			0
$571$	−14.5000	+	25.1147i	−0.606806	+	1.05102i	0.384957	+	0.922934i	$0.374216\pi$
$571$	−14.5000	+	25.1147i	−0.606806	+	1.05102i	−0.991763	+	0.128085i	$0.959117\pi$
$572$	−6.00000	+	10.3923i	−0.250873	+	0.434524i
$573$		0			0
$574$	6.00000	+	10.3923i	0.250435	+	0.433766i
$575$	−6.00000			−0.250217
$576$		0			0
$577$	−7.00000			−0.291414			−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000			−0.291414			−0.145707	+	0.989328i	$0.546546\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$		0			0
$580$	−3.00000	+	5.19615i	−0.124568	+	0.215758i
$581$	−24.0000	+	41.5692i	−0.995688	+	1.72458i
$582$		0			0
$583$	−9.00000	−	15.5885i	−0.372742	−	0.645608i
$584$	−7.00000			−0.289662
$585$		0			0
$586$	18.0000			0.743573
$587$	19.5000	+	33.7750i	0.804851	+	1.39404i	0.916392	+	0.400283i	$0.131088\pi$
$587$	19.5000	+	33.7750i	0.804851	+	1.39404i	−0.111540	+	0.993760i	$0.535578\pi$
$588$		0			0
$589$	−5.00000	+	8.66025i	−0.206021	+	0.356840i
$590$	1.50000	−	2.59808i	0.0617540	−	0.106961i
$591$		0			0
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	18.0000			0.739171			0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000			0.739171			0.369586	+	0.929197i	$0.379500\pi$
$594$		0			0
$595$	−12.0000			−0.491952
$596$		0			0
$597$		0			0
$598$	−12.0000	+	20.7846i	−0.490716	+	0.849946i
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	0.999934	+	0.0114528i	$0.00364562\pi$
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	−0.490049	+	0.871695i	$0.663021\pi$
$602$	−44.0000			−1.79331
$603$		0			0
$604$	−10.0000			−0.406894
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$		0			0
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	−0.935713	−	0.352763i	$-0.885242\pi$
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	0.773358	+	0.633970i	$0.218576\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$		0			0
$610$	−5.00000	−	8.66025i	−0.202444	−	0.350643i
$611$		0			0
$612$		0			0
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$	3.50000	+	6.06218i	0.141249	+	0.244650i
$615$		0			0
$616$	−6.00000	+	10.3923i	−0.241747	+	0.418718i
$617$	−19.5000	+	33.7750i	−0.785040	+	1.35973i	0.143934	+	0.989587i	$0.454025\pi$
$617$	−19.5000	+	33.7750i	−0.785040	+	1.35973i	−0.928975	+	0.370143i	$0.879309\pi$
$618$		0			0
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	0.991325	−	0.131434i	$-0.0419582\pi$
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	−0.609488	+	0.792796i	$0.708625\pi$
$620$	−2.00000			−0.0803219
$621$		0			0
$622$	6.00000			0.240578
$623$	−12.0000	−	20.7846i	−0.480770	−	0.832718i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.500000	−	0.866025i	0.0199840	−	0.0346133i
$627$		0			0
$628$	−4.00000	−	6.92820i	−0.159617	−	0.276465i
$629$	12.0000			0.478471
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$	−7.00000	−	12.1244i	−0.278445	−	0.482281i
$633$		0			0
$634$	12.0000	−	20.7846i	0.476581	−	0.825462i
$635$	1.00000	−	1.73205i	0.0396838	−	0.0687343i
$636$		0			0
$637$	18.0000	+	31.1769i	0.713186	+	1.23527i
$638$	18.0000			0.712627
$639$		0			0
$640$	−1.00000			−0.0395285
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$		0			0
$643$	−11.5000	+	19.9186i	−0.453516	+	0.785512i	−0.998602	−	0.0528680i	$-0.983164\pi$
$643$	−11.5000	+	19.9186i	−0.453516	+	0.785512i	0.545086	+	0.838380i	$0.316497\pi$
$644$	−12.0000	+	20.7846i	−0.472866	+	0.819028i
$645$		0			0
$646$	7.50000	+	12.9904i	0.295084	+	0.511100i
$647$	−6.00000			−0.235884			−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000			−0.235884			−0.117942	+	0.993020i	$0.537630\pi$
$648$		0			0
$649$	−9.00000			−0.353281
$650$	2.00000	+	3.46410i	0.0784465	+	0.135873i
$651$		0			0
$652$	8.00000	−	13.8564i	0.313304	−	0.542659i
$653$	21.0000	−	36.3731i	0.821794	−	1.42339i	−0.0825519	−	0.996587i	$-0.526307\pi$
$653$	21.0000	−	36.3731i	0.821794	−	1.42339i	0.904345	−	0.426801i	$-0.140360\pi$
$654$		0			0
$655$	−6.00000	−	10.3923i	−0.234439	−	0.406061i
$656$	3.00000			0.117130
$657$		0			0
$658$		0			0
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	−0.968052	−	0.250748i	$-0.919323\pi$
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	0.266872	−	0.963732i	$-0.414010\pi$
$660$		0			0
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	0.366723	+	0.930330i	$0.380480\pi$
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	−0.989051	+	0.147573i	$0.952854\pi$
$662$	2.00000	−	3.46410i	0.0777322	−	0.134636i
$663$		0			0
$664$	6.00000	+	10.3923i	0.232845	+	0.403300i
$665$	20.0000			0.775567
$666$		0			0
$667$	36.0000			1.39393
$668$	−9.00000	−	15.5885i	−0.348220	−	0.603136i
$669$		0			0
$670$	2.50000	−	4.33013i	0.0965834	−	0.167287i
$671$	−15.0000	+	25.9808i	−0.579069	+	1.00298i
$672$		0			0
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	0.698988	−	0.715134i	$-0.253634\pi$
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	−0.968818	+	0.247774i	$0.920301\pi$
$674$	−31.0000			−1.19408
$675$		0			0
$676$	3.00000			0.115385
$677$	−18.0000	−	31.1769i	−0.691796	−	1.19823i	−0.971249	−	0.238067i	$-0.923486\pi$
$677$	−18.0000	−	31.1769i	−0.691796	−	1.19823i	0.279453	−	0.960159i	$-0.409847\pi$
$678$		0			0
$679$	22.0000	−	38.1051i	0.844283	−	1.46234i
$680$	−1.50000	+	2.59808i	−0.0575224	+	0.0996317i
$681$		0			0
$682$	3.00000	+	5.19615i	0.114876	+	0.198971i
$683$	21.0000			0.803543			0.401771	−	0.915740i	$-0.368395\pi$
$683$	21.0000			0.803543			0.401771	+	0.915740i	$0.368395\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$	4.00000	+	6.92820i	0.152721	+	0.264520i
$687$		0			0
$688$	−5.50000	+	9.52628i	−0.209686	+	0.363186i
$689$	−12.0000	+	20.7846i	−0.457164	+	0.791831i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	18.0000			0.684257
$693$		0			0
$694$	−21.0000			−0.797149
$695$	−0.500000	−	0.866025i	−0.0189661	−	0.0328502i
$696$		0			0
$697$	4.50000	−	7.79423i	0.170450	−	0.295227i
$698$	8.00000	−	13.8564i	0.302804	−	0.524473i
$699$		0			0
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	−20.0000			−0.754314
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	4.50000	−	7.79423i	0.169360	−	0.293340i
$707$	24.0000	−	41.5692i	0.902613	−	1.56337i
$708$		0			0
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	0.985773	+	0.168080i	$0.0537568\pi$
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	−0.347325	+	0.937745i	$0.612910\pi$
$710$	6.00000			0.225176
$711$		0			0
$712$	−6.00000			−0.224860
$713$	6.00000	+	10.3923i	0.224702	+	0.389195i
$714$		0			0
$715$	6.00000	−	10.3923i	0.224387	−	0.388650i
$716$		0			0
$717$		0			0
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	16.0000			0.595871
$722$	−3.00000	−	5.19615i	−0.111648	−	0.193381i
$723$		0			0
$724$	8.00000	−	13.8564i	0.297318	−	0.514969i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$		0			0
$727$	14.0000	+	24.2487i	0.519231	+	0.899335i	0.999750	+	0.0223506i	$0.00711500\pi$
$727$	14.0000	+	24.2487i	0.519231	+	0.899335i	−0.480519	+	0.876984i	$0.659552\pi$
$728$	16.0000			0.592999
$729$		0			0
$730$	7.00000			0.259082
$731$	16.5000	+	28.5788i	0.610275	+	1.05703i
$732$		0			0
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	0.403128	+	0.915144i	$0.367923\pi$
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	−0.994102	+	0.108453i	$0.965410\pi$
$734$	−4.00000	+	6.92820i	−0.147643	+	0.255725i
$735$		0			0
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	−15.0000			−0.552532
$738$		0			0
$739$	29.0000			1.06678			0.533391	−	0.845869i	$-0.320917\pi$
$739$	29.0000			1.06678			0.533391	+	0.845869i	$0.320917\pi$
$740$	−2.00000	−	3.46410i	−0.0735215	−	0.127343i
$741$		0			0
$742$	−12.0000	+	20.7846i	−0.440534	+	0.763027i
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	−0.915794	−	0.401648i	$-0.868437\pi$
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	0.805735	+	0.592277i	$0.201771\pi$
$744$		0			0
$745$		0			0
$746$	−10.0000			−0.366126
$747$		0			0
$748$	9.00000			0.329073
$749$	18.0000	+	31.1769i	0.657706	+	1.13918i
$750$		0			0
$751$	14.0000	−	24.2487i	0.510867	−	0.884848i	−0.489053	−	0.872254i	$-0.662658\pi$
$751$	14.0000	−	24.2487i	0.510867	−	0.884848i	0.999921	−	0.0125942i	$-0.00400897\pi$
$752$		0			0
$753$		0			0
$754$	−12.0000	−	20.7846i	−0.437014	−	0.756931i
$755$	10.0000			0.363937
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	−14.5000	−	25.1147i	−0.526664	−	0.912208i
$759$		0			0
$760$	2.50000	−	4.33013i	0.0906845	−	0.157070i
$761$	9.00000	−	15.5885i	0.326250	−	0.565081i	−0.655515	−	0.755182i	$-0.727548\pi$
$761$	9.00000	−	15.5885i	0.326250	−	0.565081i	0.981764	+	0.190101i	$0.0608816\pi$
$762$		0			0
$763$	−8.00000	−	13.8564i	−0.289619	−	0.501636i
$764$		0			0
$765$		0			0
$766$	−12.0000			−0.433578
$767$	6.00000	+	10.3923i	0.216647	+	0.375244i
$768$		0			0
$769$	−25.0000	+	43.3013i	−0.901523	+	1.56148i	−0.0760054	+	0.997107i	$0.524217\pi$
$769$	−25.0000	+	43.3013i	−0.901523	+	1.56148i	−0.825518	+	0.564376i	$0.809117\pi$
$770$	6.00000	−	10.3923i	0.216225	−	0.374513i
$771$		0			0
$772$	6.50000	+	11.2583i	0.233940	+	0.405196i
$773$	30.0000			1.07903			0.539513	−	0.841978i	$-0.318609\pi$
$773$	30.0000			1.07903			0.539513	+	0.841978i	$0.318609\pi$
$774$		0			0
$775$	2.00000			0.0718421
$776$	−5.50000	−	9.52628i	−0.197438	−	0.341974i
$777$		0			0
$778$	18.0000	−	31.1769i	0.645331	−	1.11775i
$779$	−7.50000	+	12.9904i	−0.268715	+	0.465429i
$780$		0			0
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$	18.0000			0.643679
$783$		0			0
$784$	9.00000			0.321429
$785$	4.00000	+	6.92820i	0.142766	+	0.247278i
$786$		0			0
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	−0.828176	−	0.560469i	$-0.810621\pi$
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	0.899468	+	0.436987i	$0.143954\pi$
$788$		0			0
$789$		0			0
$790$	7.00000	+	12.1244i	0.249049	+	0.431365i
$791$	72.0000			2.56003
$792$		0			0
$793$	40.0000			1.42044
$794$	−4.00000	−	6.92820i	−0.141955	−	0.245873i
$795$		0			0
$796$	−10.0000	+	17.3205i	−0.354441	+	0.613909i
$797$	−24.0000	+	41.5692i	−0.850124	+	1.47246i	0.0309726	+	0.999520i	$0.490140\pi$
$797$	−24.0000	+	41.5692i	−0.850124	+	1.47246i	−0.881096	+	0.472937i	$0.843194\pi$
$798$		0			0
$799$		0			0
$800$	1.00000			0.0353553
$801$		0			0
$802$	−33.0000			−1.16527
$803$	−10.5000	−	18.1865i	−0.370537	−	0.641789i
$804$		0			0
$805$	12.0000	−	20.7846i	0.422944	−	0.732561i
$806$	4.00000	−	6.92820i	0.140894	−	0.244036i
$807$		0			0
$808$	−6.00000	−	10.3923i	−0.211079	−	0.365600i
$809$	39.0000			1.37117			0.685583	−	0.727994i	$-0.259547\pi$
$809$	39.0000			1.37117			0.685583	+	0.727994i	$0.259547\pi$
$810$		0			0
$811$	35.0000			1.22902			0.614508	−	0.788911i	$-0.289355\pi$
$811$	35.0000			1.22902			0.614508	+	0.788911i	$0.289355\pi$
$812$	−12.0000	−	20.7846i	−0.421117	−	0.729397i
$813$		0			0
$814$	−6.00000	+	10.3923i	−0.210300	+	0.364250i
$815$	−8.00000	+	13.8564i	−0.280228	+	0.485369i
$816$		0			0
$817$	−27.5000	−	47.6314i	−0.962103	−	1.66641i
$818$	−31.0000			−1.08389
$819$		0			0
$820$	−3.00000			−0.104765
$821$	−24.0000	−	41.5692i	−0.837606	−	1.45078i	−0.891891	−	0.452250i	$-0.850621\pi$
$821$	−24.0000	−	41.5692i	−0.837606	−	1.45078i	0.0542853	−	0.998525i	$-0.482712\pi$
$822$		0			0
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	−0.829060	−	0.559159i	$-0.811124\pi$
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	0.898776	+	0.438408i	$0.144457\pi$
$824$	2.00000	−	3.46410i	0.0696733	−	0.120678i
$825$		0			0
$826$	6.00000	+	10.3923i	0.208767	+	0.361595i
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$		0			0
$829$	44.0000			1.52818			0.764092	−	0.645108i	$-0.223188\pi$
$829$	44.0000			1.52818			0.764092	+	0.645108i	$0.223188\pi$
$830$	−6.00000	−	10.3923i	−0.208263	−	0.360722i
$831$		0			0
$832$	2.00000	−	3.46410i	0.0693375	−	0.120096i
$833$	13.5000	−	23.3827i	0.467747	−	0.810162i
$834$		0			0
$835$	9.00000	+	15.5885i	0.311458	+	0.539461i
$836$	−15.0000			−0.518786
$837$		0			0
$838$		0			0
$839$	−15.0000	−	25.9808i	−0.517858	−	0.896956i	−0.999785	−	0.0207443i	$-0.993396\pi$
$839$	−15.0000	−	25.9808i	−0.517858	−	0.896956i	0.481927	−	0.876211i	$-0.339937\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−1.00000	+	1.73205i	−0.0344623	+	0.0596904i
$843$		0			0
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$	−3.00000			−0.103203
$846$		0			0
$847$	8.00000			0.274883
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$		0			0
$850$	1.50000	−	2.59808i	0.0514496	−	0.0891133i
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$		0			0
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	−0.946232	−	0.323489i	$-0.895144\pi$
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	0.192966	−	0.981205i	$-0.438189\pi$
$854$	40.0000			1.36877
$855$		0			0
$856$	9.00000			0.307614
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$		0			0
$859$	9.50000	−	16.4545i	0.324136	−	0.561420i	−0.657201	−	0.753715i	$-0.728260\pi$
$859$	9.50000	−	16.4545i	0.324136	−	0.561420i	0.981337	+	0.192295i	$0.0615932\pi$
$860$	5.50000	−	9.52628i	0.187548	−	0.324843i
$861$		0			0
$862$	12.0000	+	20.7846i	0.408722	+	0.707927i
$863$	6.00000			0.204242			0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$864$		0			0
$865$	−18.0000			−0.612018
$866$	6.50000	+	11.2583i	0.220879	+	0.382574i
$867$		0			0
$868$	4.00000	−	6.92820i	0.135769	−	0.235159i
$869$	21.0000	−	36.3731i	0.712376	−	1.23387i
$870$		0			0
$871$	10.0000	+	17.3205i	0.338837	+	0.586883i
$872$	−4.00000			−0.135457
$873$		0			0
$874$	−30.0000			−1.01477
$875$	−2.00000	−	3.46410i	−0.0676123	−	0.117108i
$876$		0			0
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	−0.882415	−	0.470471i	$-0.844084\pi$
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	0.848648	+	0.528958i	$0.177417\pi$
$878$	5.00000	−	8.66025i	0.168742	−	0.292269i
$879$		0			0
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	−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
$883$	41.0000			1.37976			0.689880	−	0.723924i	$-0.257663\pi$
$883$	41.0000			1.37976			0.689880	+	0.723924i	$0.257663\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$		0			0
$886$	1.50000	−	2.59808i	0.0503935	−	0.0872841i
$887$	−21.0000	+	36.3731i	−0.705111	+	1.22129i	0.261540	+	0.965193i	$0.415770\pi$
$887$	−21.0000	+	36.3731i	−0.705111	+	1.22129i	−0.966651	+	0.256096i	$0.917564\pi$
$888$		0			0
$889$	4.00000	+	6.92820i	0.134156	+	0.232364i
$890$	6.00000			0.201120
$891$		0			0
$892$	−22.0000			−0.736614
$893$		0			0
$894$		0			0
$895$		0			0
$896$	2.00000	−	3.46410i	0.0668153	−	0.115728i
$897$		0			0
$898$	−7.50000	−	12.9904i	−0.250278	−	0.433495i
$899$	−12.0000			−0.400222
$900$		0			0
$901$	18.0000			0.599667
$902$	4.50000	+	7.79423i	0.149834	+	0.259519i
$903$		0			0
$904$	9.00000	−	15.5885i	0.299336	−	0.518464i
$905$	−8.00000	+	13.8564i	−0.265929	+	0.460603i
$906$		0			0
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	0.821531	−	0.570164i	$-0.193120\pi$
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	−0.904542	+	0.426385i	$0.859787\pi$
$908$	3.00000			0.0995585
$909$		0			0
$910$	−16.0000			−0.530395
$911$	−15.0000	−	25.9808i	−0.496972	−	0.860781i	0.503022	−	0.864274i	$-0.332222\pi$
$911$	−15.0000	−	25.9808i	−0.496972	−	0.860781i	−0.999994	+	0.00349271i	$0.998888\pi$
$912$		0			0
$913$	−18.0000	+	31.1769i	−0.595713	+	1.03181i
$914$	0.500000	−	0.866025i	0.0165385	−	0.0286456i
$915$		0			0
$916$	−10.0000	−	17.3205i	−0.330409	−	0.572286i
$917$	48.0000			1.58510
$918$		0			0
$919$	−34.0000			−1.12156			−0.560778	−	0.827966i	$-0.689498\pi$
$919$	−34.0000			−1.12156			−0.560778	+	0.827966i	$0.689498\pi$
$920$	−3.00000	−	5.19615i	−0.0989071	−	0.171312i
$921$		0			0
$922$		0			0
$923$	−12.0000	+	20.7846i	−0.394985	+	0.684134i
$924$		0			0
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$	20.0000			0.657241
$927$		0			0
$928$	−6.00000			−0.196960
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	0.999959	−	0.00905914i	$-0.00288365\pi$
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	−0.507825	+	0.861460i	$0.669550\pi$
$930$		0			0
$931$	−22.5000	+	38.9711i	−0.737408	+	1.27723i
$932$	10.5000	−	18.1865i	0.343939	−	0.595720i
$933$		0			0
$934$	10.5000	+	18.1865i	0.343570	+	0.595082i
$935$	−9.00000			−0.294331
$936$		0			0
$937$	−10.0000			−0.326686			−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000			−0.326686			−0.163343	+	0.986569i	$0.552228\pi$
$938$	10.0000	+	17.3205i	0.326512	+	0.565535i
$939$		0			0
$940$		0			0
$941$	12.0000	−	20.7846i	0.391189	−	0.677559i	−0.601418	−	0.798935i	$-0.705397\pi$
$941$	12.0000	−	20.7846i	0.391189	−	0.677559i	0.992607	+	0.121376i	$0.0387306\pi$
$942$		0			0
$943$	9.00000	+	15.5885i	0.293080	+	0.507630i
$944$	3.00000			0.0976417
$945$		0			0
$946$	−33.0000			−1.07292
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	0.997589	−	0.0694014i	$-0.0221089\pi$
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	−0.558898	+	0.829237i	$0.688776\pi$
$948$		0			0
$949$	−14.0000	+	24.2487i	−0.454459	+	0.787146i
$950$	−2.50000	+	4.33013i	−0.0811107	+	0.140488i
$951$		0			0
$952$	−6.00000	−	10.3923i	−0.194461	−	0.336817i
$953$	−51.0000			−1.65205			−0.826026	−	0.563632i	$-0.809404\pi$
$953$	−51.0000			−1.65205			−0.826026	+	0.563632i	$0.809404\pi$
$954$		0			0
$955$		0			0
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$		0			0
$958$	−3.00000	+	5.19615i	−0.0969256	+	0.167880i
$959$	18.0000	−	31.1769i	0.581250	−	1.00676i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	16.0000			0.515861
$963$		0			0
$964$	17.0000			0.547533
$965$	−6.50000	−	11.2583i	−0.209242	−	0.362418i
$966$		0			0
$967$	11.0000	−	19.0526i	0.353736	−	0.612689i	−0.633165	−	0.774017i	$-0.718244\pi$
$967$	11.0000	−	19.0526i	0.353736	−	0.612689i	0.986901	+	0.161328i	$0.0515777\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$		0			0
$970$	5.50000	+	9.52628i	0.176594	+	0.305870i
$971$	−60.0000			−1.92549			−0.962746	−	0.270408i	$-0.912841\pi$
$971$	−60.0000			−1.92549			−0.962746	+	0.270408i	$0.912841\pi$
$972$		0			0
$973$	4.00000			0.128234
$974$	−1.00000	−	1.73205i	−0.0320421	−	0.0554985i
$975$		0			0
$976$	5.00000	−	8.66025i	0.160046	−	0.277208i
$977$	−4.50000	+	7.79423i	−0.143968	+	0.249359i	−0.928987	−	0.370111i	$-0.879319\pi$
$977$	−4.50000	+	7.79423i	−0.143968	+	0.249359i	0.785020	+	0.619471i	$0.212653\pi$
$978$		0			0
$979$	−9.00000	−	15.5885i	−0.287641	−	0.498209i
$980$	−9.00000			−0.287494
$981$		0			0
$982$	33.0000			1.05307
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	0.996138	+	0.0878058i	$0.0279855\pi$
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	−0.422027	+	0.906583i	$0.638681\pi$
$984$		0			0
$985$		0			0
$986$	−9.00000	+	15.5885i	−0.286618	+	0.496438i
$987$		0			0
$988$	10.0000	+	17.3205i	0.318142	+	0.551039i
$989$	−66.0000			−2.09868
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	−1.00000	−	1.73205i	−0.0317500	−	0.0549927i
$993$		0			0
$994$	−12.0000	+	20.7846i	−0.380617	+	0.659248i
$995$	10.0000	−	17.3205i	0.317021	−	0.549097i
$996$		0			0
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$	−31.0000			−0.981288
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.e.a.91.1		2
3.2	odd	2		90.2.e.b.31.1	✓	2
4.3	odd	2		2160.2.q.d.1441.1		2
5.2	odd	4		1350.2.j.c.199.2		4
5.3	odd	4		1350.2.j.c.199.1		4
5.4	even	2		1350.2.e.g.901.1		2
9.2	odd	6		90.2.e.b.61.1	yes	2
9.4	even	3		810.2.a.e.1.1		1
9.5	odd	6		810.2.a.a.1.1		1
9.7	even	3	inner	270.2.e.a.181.1		2
12.11	even	2		720.2.q.c.481.1		2
15.2	even	4		450.2.j.a.49.1		4
15.8	even	4		450.2.j.a.49.2		4
15.14	odd	2		450.2.e.d.301.1		2
36.7	odd	6		2160.2.q.d.721.1		2
36.11	even	6		720.2.q.c.241.1		2
36.23	even	6		6480.2.a.z.1.1		1
36.31	odd	6		6480.2.a.l.1.1		1
45.2	even	12		450.2.j.a.349.2		4
45.4	even	6		4050.2.a.q.1.1		1
45.7	odd	12		1350.2.j.c.1099.1		4
45.13	odd	12		4050.2.c.d.649.1		2
45.14	odd	6		4050.2.a.bi.1.1		1
45.22	odd	12		4050.2.c.d.649.2		2
45.23	even	12		4050.2.c.p.649.2		2
45.29	odd	6		450.2.e.d.151.1		2
45.32	even	12		4050.2.c.p.649.1		2
45.34	even	6		1350.2.e.g.451.1		2
45.38	even	12		450.2.j.a.349.1		4
45.43	odd	12		1350.2.j.c.1099.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.b.31.1	✓	2	3.2	odd	2
90.2.e.b.61.1	yes	2	9.2	odd	6
270.2.e.a.91.1		2	1.1	even	1	trivial
270.2.e.a.181.1		2	9.7	even	3	inner
450.2.e.d.151.1		2	45.29	odd	6
450.2.e.d.301.1		2	15.14	odd	2
450.2.j.a.49.1		4	15.2	even	4
450.2.j.a.49.2		4	15.8	even	4
450.2.j.a.349.1		4	45.38	even	12
450.2.j.a.349.2		4	45.2	even	12
720.2.q.c.241.1		2	36.11	even	6
720.2.q.c.481.1		2	12.11	even	2
810.2.a.a.1.1		1	9.5	odd	6
810.2.a.e.1.1		1	9.4	even	3
1350.2.e.g.451.1		2	45.34	even	6
1350.2.e.g.901.1		2	5.4	even	2
1350.2.j.c.199.1		4	5.3	odd	4
1350.2.j.c.199.2		4	5.2	odd	4
1350.2.j.c.1099.1		4	45.7	odd	12
1350.2.j.c.1099.2		4	45.43	odd	12
2160.2.q.d.721.1		2	36.7	odd	6
2160.2.q.d.1441.1		2	4.3	odd	2
4050.2.a.q.1.1		1	45.4	even	6
4050.2.a.bi.1.1		1	45.14	odd	6
4050.2.c.d.649.1		2	45.13	odd	12
4050.2.c.d.649.2		2	45.22	odd	12
4050.2.c.p.649.1		2	45.32	even	12
4050.2.c.p.649.2		2	45.23	even	12
6480.2.a.l.1.1		1	36.31	odd	6
6480.2.a.z.1.1		1	36.23	even	6

Overview	Random
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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	270.2.e.a.91.1

Level	$270$
Weight	$2$
Character	270.91
Analytic conductor	$2.156$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$