LMFDB - Embedded newform 114.2.e.b.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [114,2,Mod(7,114)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(114, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("114.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$114 = 2 \cdot 3 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	114.e (of order $3$ , degree $2$ , 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:	$0.910294583043$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	114.49
Dual form			114.2.e.b.7.1

$q$ -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^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -2.00000 q^{11} -1.00000 q^{12} +(1.50000 + 2.59808i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} -1.00000 q^{18} +(4.00000 + 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +3.00000 q^{26} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} -3.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(2.00000 + 3.46410i) q^{34} +(-0.500000 + 0.866025i) q^{36} -5.00000 q^{37} +(3.50000 - 2.59808i) q^{38} +3.00000 q^{39} +(-2.00000 + 3.46410i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(4.50000 - 7.79423i) q^{43} +(1.00000 + 1.73205i) q^{44} -4.00000 q^{46} +(-5.00000 - 8.66025i) q^{47} +(0.500000 + 0.866025i) q^{48} -6.00000 q^{49} +5.00000 q^{50} +(2.00000 + 3.46410i) q^{51} +(1.50000 - 2.59808i) q^{52} +(2.00000 + 3.46410i) q^{53} +(-0.500000 + 0.866025i) q^{54} -1.00000 q^{56} +(3.50000 - 2.59808i) q^{57} +(7.00000 - 12.1244i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(-1.50000 + 2.59808i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{66} +(-1.50000 - 2.59808i) q^{67} +4.00000 q^{68} -4.00000 q^{69} +(-7.00000 + 12.1244i) q^{71} +(0.500000 + 0.866025i) q^{72} +(5.50000 - 9.52628i) q^{73} +(-2.50000 + 4.33013i) q^{74} +5.00000 q^{75} +(-0.500000 - 4.33013i) q^{76} -2.00000 q^{77} +(1.50000 - 2.59808i) q^{78} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.00000 + 3.46410i) q^{82} +8.00000 q^{83} -1.00000 q^{84} +(-4.50000 - 7.79423i) q^{86} +2.00000 q^{88} +(7.00000 + 12.1244i) q^{89} +(1.50000 + 2.59808i) q^{91} +(-2.00000 + 3.46410i) q^{92} +(-1.50000 + 2.59808i) q^{93} -10.0000 q^{94} +1.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(1.00000 + 1.73205i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q + q^{2} + q^{3} - q^{4} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9} - 4 q^{11} - 2 q^{12} + 3 q^{13} + q^{14} - q^{16} - 4 q^{17} - 2 q^{18} + 8 q^{19} + q^{21} - 2 q^{22} - 4 q^{23} - q^{24} + 5 q^{25}+ \cdots + 2 q^{99}+O(q^{100})$ 2 * q + q^2 + q^3 - q^4 - q^6 + 2 * q^7 - 2 * q^8 - q^9 - 4 * q^11 - 2 * q^12 + 3 * q^13 + q^14 - q^16 - 4 * q^17 - 2 * q^18 + 8 * q^19 + q^21 - 2 * q^22 - 4 * q^23 - q^24 + 5 * q^25 + 6 * q^26 - 2 * q^27 - q^28 - 6 * q^31 + q^32 - 2 * q^33 + 4 * q^34 - q^36 - 10 * q^37 + 7 * q^38 + 6 * q^39 - 4 * q^41 - q^42 + 9 * q^43 + 2 * q^44 - 8 * q^46 - 10 * q^47 + q^48 - 12 * q^49 + 10 * q^50 + 4 * q^51 + 3 * q^52 + 4 * q^53 - q^54 - 2 * q^56 + 7 * q^57 + 14 * q^59 - 11 * q^61 - 3 * q^62 - q^63 + 2 * q^64 + 2 * q^66 - 3 * q^67 + 8 * q^68 - 8 * q^69 - 14 * q^71 + q^72 + 11 * q^73 - 5 * q^74 + 10 * q^75 - q^76 - 4 * q^77 + 3 * q^78 - q^79 - q^81 + 4 * q^82 + 16 * q^83 - 2 * q^84 - 9 * q^86 + 4 * q^88 + 14 * q^89 + 3 * q^91 - 4 * q^92 - 3 * q^93 - 20 * q^94 + 2 * q^96 - 2 * q^97 - 6 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$ .

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	1.00000			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$	−1.00000			−0.288675
$13$	1.50000	+	2.59808i	0.416025	+	0.720577i	0.995535	−	0.0943882i	$-0.0300895\pi$
$13$	1.50000	+	2.59808i	0.416025	+	0.720577i	−0.579510	+	0.814965i	$0.696756\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$	−1.00000			−0.235702
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$20$		0			0
$21$	0.500000	−	0.866025i	0.109109	−	0.188982i
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	3.00000			0.588348
$27$	−1.00000			−0.192450
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$	−3.00000			−0.538816			−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000			−0.538816			−0.269408	+	0.963026i	$0.586828\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	2.00000	+	3.46410i	0.342997	+	0.594089i
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−5.00000			−0.821995			−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000			−0.821995			−0.410997	+	0.911636i	$0.634819\pi$
$38$	3.50000	−	2.59808i	0.567775	−	0.421464i
$39$	3.00000			0.480384
$40$		0			0
$41$	−2.00000	+	3.46410i	−0.312348	+	0.541002i	−0.978870	−	0.204483i	$-0.934449\pi$
$41$	−2.00000	+	3.46410i	−0.312348	+	0.541002i	0.666523	+	0.745485i	$0.267782\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$	4.50000	−	7.79423i	0.686244	−	1.18861i	−0.286801	−	0.957990i	$-0.592592\pi$
$43$	4.50000	−	7.79423i	0.686244	−	1.18861i	0.973044	−	0.230618i	$-0.0740749\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$		0			0
$46$	−4.00000			−0.589768
$47$	−5.00000	−	8.66025i	−0.729325	−	1.26323i	−0.957169	−	0.289530i	$-0.906501\pi$
$47$	−5.00000	−	8.66025i	−0.729325	−	1.26323i	0.227844	−	0.973698i	$-0.426832\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−6.00000			−0.857143
$50$	5.00000			0.707107
$51$	2.00000	+	3.46410i	0.280056	+	0.485071i
$52$	1.50000	−	2.59808i	0.208013	−	0.360288i
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	0.970065	−	0.242846i	$-0.0780811\pi$
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	−0.695344	+	0.718677i	$0.744748\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	−1.00000			−0.133631
$57$	3.50000	−	2.59808i	0.463586	−	0.344124i
$58$		0			0
$59$	7.00000	−	12.1244i	0.911322	−	1.57846i	0.0991242	−	0.995075i	$-0.468396\pi$
$59$	7.00000	−	12.1244i	0.911322	−	1.57846i	0.812198	−	0.583382i	$-0.198271\pi$
$60$		0			0
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	−0.966978	−	0.254858i	$-0.917971\pi$
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	0.262776	−	0.964857i	$-0.415362\pi$
$62$	−1.50000	+	2.59808i	−0.190500	+	0.329956i
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.00000	+	1.73205i	0.123091	+	0.213201i
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	0.759733	−	0.650236i	$-0.225330\pi$
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	−0.942987	+	0.332830i	$0.891996\pi$
$68$	4.00000			0.485071
$69$	−4.00000			−0.481543
$70$		0			0
$71$	−7.00000	+	12.1244i	−0.830747	+	1.43890i	0.0666994	+	0.997773i	$0.478753\pi$
$71$	−7.00000	+	12.1244i	−0.830747	+	1.43890i	−0.897447	+	0.441123i	$0.854580\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	−0.340868	−	0.940111i	$-0.610721\pi$
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	0.984594	−	0.174855i	$-0.0559458\pi$
$74$	−2.50000	+	4.33013i	−0.290619	+	0.503367i
$75$	5.00000			0.577350
$76$	−0.500000	−	4.33013i	−0.0573539	−	0.496700i
$77$	−2.00000			−0.227921
$78$	1.50000	−	2.59808i	0.169842	−	0.294174i
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	−0.892781	−	0.450490i	$-0.851249\pi$
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	0.836527	+	0.547926i	$0.184582\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.00000	+	3.46410i	0.220863	+	0.382546i
$83$	8.00000			0.878114			0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000			0.878114			0.439057	+	0.898459i	$0.355313\pi$
$84$	−1.00000			−0.109109
$85$		0			0
$86$	−4.50000	−	7.79423i	−0.485247	−	0.840473i
$87$		0			0
$88$	2.00000			0.213201
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	0.951584	+	0.307389i	$0.0994552\pi$
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	−0.209585	+	0.977790i	$0.567211\pi$
$90$		0			0
$91$	1.50000	+	2.59808i	0.157243	+	0.272352i
$92$	−2.00000	+	3.46410i	−0.208514	+	0.361158i
$93$	−1.50000	+	2.59808i	−0.155543	+	0.269408i
$94$	−10.0000			−1.03142
$95$		0			0
$96$	1.00000			0.102062
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$	1.00000	+	1.73205i	0.100504	+	0.174078i
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$	4.00000			0.396059
$103$	−3.00000			−0.295599			−0.147799	−	0.989017i	$-0.547219\pi$
$103$	−3.00000			−0.295599			−0.147799	+	0.989017i	$0.547219\pi$
$104$	−1.50000	−	2.59808i	−0.147087	−	0.254762i
$105$		0			0
$106$	4.00000			0.388514
$107$	−10.0000			−0.966736			−0.483368	−	0.875417i	$-0.660587\pi$
$107$	−10.0000			−0.966736			−0.483368	+	0.875417i	$0.660587\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$		0			0
$111$	−2.50000	+	4.33013i	−0.237289	+	0.410997i
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$	−0.500000	−	4.33013i	−0.0468293	−	0.405554i
$115$		0			0
$116$		0			0
$117$	1.50000	−	2.59808i	0.138675	−	0.240192i
$118$	−7.00000	−	12.1244i	−0.644402	−	1.11614i
$119$	−2.00000	+	3.46410i	−0.183340	+	0.317554i
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−11.0000			−0.995893
$123$	2.00000	+	3.46410i	0.180334	+	0.312348i
$124$	1.50000	+	2.59808i	0.134704	+	0.233314i
$125$		0			0
$126$	−1.00000			−0.0890871
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	0.987108	−	0.160055i	$-0.0511671\pi$
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	−0.632166	+	0.774833i	$0.717834\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.50000	−	7.79423i	−0.396203	−	0.686244i
$130$		0			0
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$	2.00000			0.174078
$133$	4.00000	+	1.73205i	0.346844	+	0.150188i
$134$	−3.00000			−0.259161
$135$		0			0
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$	−2.00000	+	3.46410i	−0.170251	+	0.294884i
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	0.915764	+	0.401718i	$0.131587\pi$
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	−0.109984	+	0.993933i	$0.535080\pi$
$140$		0			0
$141$	−10.0000			−0.842152
$142$	7.00000	+	12.1244i	0.587427	+	1.01745i
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−5.50000	−	9.52628i	−0.455183	−	0.788400i
$147$	−3.00000	+	5.19615i	−0.247436	+	0.428571i
$148$	2.50000	+	4.33013i	0.205499	+	0.355934i
$149$	11.0000	−	19.0526i	0.901155	−	1.56085i	0.0751583	−	0.997172i	$-0.476054\pi$
$149$	11.0000	−	19.0526i	0.901155	−	1.56085i	0.825997	−	0.563675i	$-0.190613\pi$
$150$	2.50000	−	4.33013i	0.204124	−	0.353553i
$151$	−20.0000			−1.62758			−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000			−1.62758			−0.813788	+	0.581161i	$0.802599\pi$
$152$	−4.00000	−	1.73205i	−0.324443	−	0.140488i
$153$	4.00000			0.323381
$154$	−1.00000	+	1.73205i	−0.0805823	+	0.139573i
$155$		0			0
$156$	−1.50000	−	2.59808i	−0.120096	−	0.208013i
$157$	10.5000	−	18.1865i	0.837991	−	1.45144i	−0.0535803	−	0.998564i	$-0.517063\pi$
$157$	10.5000	−	18.1865i	0.837991	−	1.45144i	0.891572	−	0.452880i	$-0.149603\pi$
$158$	0.500000	+	0.866025i	0.0397779	+	0.0688973i
$159$	4.00000			0.317221
$160$		0			0
$161$	−2.00000	−	3.46410i	−0.157622	−	0.273009i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	11.0000			0.861586			0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000			0.861586			0.430793	+	0.902451i	$0.358234\pi$
$164$	4.00000			0.312348
$165$		0			0
$166$	4.00000	−	6.92820i	0.310460	−	0.537733i
$167$	−3.00000	−	5.19615i	−0.232147	−	0.402090i	0.726293	−	0.687386i	$-0.241242\pi$
$167$	−3.00000	−	5.19615i	−0.232147	−	0.402090i	−0.958440	+	0.285295i	$0.907908\pi$
$168$	−0.500000	+	0.866025i	−0.0385758	+	0.0668153i
$169$	2.00000	−	3.46410i	0.153846	−	0.266469i
$170$		0			0
$171$	−0.500000	−	4.33013i	−0.0382360	−	0.331133i
$172$	−9.00000			−0.686244
$173$	12.0000	−	20.7846i	0.912343	−	1.58022i	0.101598	−	0.994826i	$-0.467605\pi$
$173$	12.0000	−	20.7846i	0.912343	−	1.58022i	0.810745	−	0.585399i	$-0.199062\pi$
$174$		0			0
$175$	2.50000	+	4.33013i	0.188982	+	0.327327i
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$	−7.00000	−	12.1244i	−0.526152	−	0.911322i
$178$	14.0000			1.04934
$179$	4.00000			0.298974			0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000			0.298974			0.149487	+	0.988764i	$0.452238\pi$
$180$		0			0
$181$	9.00000	+	15.5885i	0.668965	+	1.15868i	0.978194	+	0.207693i	$0.0665956\pi$
$181$	9.00000	+	15.5885i	0.668965	+	1.15868i	−0.309229	+	0.950988i	$0.600071\pi$
$182$	3.00000			0.222375
$183$	−11.0000			−0.813143
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$		0			0
$186$	1.50000	+	2.59808i	0.109985	+	0.190500i
$187$	4.00000	−	6.92820i	0.292509	−	0.506640i
$188$	−5.00000	+	8.66025i	−0.364662	+	0.631614i
$189$	−1.00000			−0.0727393
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	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	$0.0116845\pi$
$194$	1.00000	+	1.73205i	0.0717958	+	0.124354i
$195$		0			0
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$	2.00000			0.142134
$199$	−2.50000	−	4.33013i	−0.177220	−	0.306955i	0.763707	−	0.645563i	$-0.223377\pi$
$199$	−2.50000	−	4.33013i	−0.177220	−	0.306955i	−0.940927	+	0.338608i	$0.890044\pi$
$200$	−2.50000	−	4.33013i	−0.176777	−	0.306186i
$201$	−3.00000			−0.211604
$202$	10.0000			0.703598
$203$		0			0
$204$	2.00000	−	3.46410i	0.140028	−	0.242536i
$205$		0			0
$206$	−1.50000	+	2.59808i	−0.104510	+	0.181017i
$207$	−2.00000	+	3.46410i	−0.139010	+	0.240772i
$208$	−3.00000			−0.208013
$209$	−8.00000	−	3.46410i	−0.553372	−	0.239617i
$210$		0			0
$211$	−12.5000	+	21.6506i	−0.860535	+	1.49049i	0.0108774	+	0.999941i	$0.496538\pi$
$211$	−12.5000	+	21.6506i	−0.860535	+	1.49049i	−0.871413	+	0.490550i	$0.836796\pi$
$212$	2.00000	−	3.46410i	0.137361	−	0.237915i
$213$	7.00000	+	12.1244i	0.479632	+	0.830747i
$214$	−5.00000	+	8.66025i	−0.341793	+	0.592003i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−3.00000			−0.203653
$218$	7.00000	+	12.1244i	0.474100	+	0.821165i
$219$	−5.50000	−	9.52628i	−0.371656	−	0.643726i
$220$		0			0
$221$	−12.0000			−0.807207
$222$	2.50000	+	4.33013i	0.167789	+	0.290619i
$223$	−4.50000	+	7.79423i	−0.301342	+	0.521940i	−0.976440	−	0.215788i	$-0.930768\pi$
$223$	−4.50000	+	7.79423i	−0.301342	+	0.521940i	0.675098	+	0.737728i	$0.264101\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	2.50000	−	4.33013i	0.166667	−	0.288675i
$226$	5.00000	−	8.66025i	0.332595	−	0.576072i
$227$	8.00000			0.530979			0.265489	−	0.964114i	$-0.414466\pi$
$227$	8.00000			0.530979			0.265489	+	0.964114i	$0.414466\pi$
$228$	−4.00000	−	1.73205i	−0.264906	−	0.114708i
$229$	−11.0000			−0.726900			−0.363450	−	0.931614i	$-0.618401\pi$
$229$	−11.0000			−0.726900			−0.363450	+	0.931614i	$0.618401\pi$
$230$		0			0
$231$	−1.00000	+	1.73205i	−0.0657952	+	0.113961i
$232$		0			0
$233$	−9.00000	+	15.5885i	−0.589610	+	1.02123i	0.404674	+	0.914461i	$0.367385\pi$
$233$	−9.00000	+	15.5885i	−0.589610	+	1.02123i	−0.994283	+	0.106773i	$0.965948\pi$
$234$	−1.50000	−	2.59808i	−0.0980581	−	0.169842i
$235$		0			0
$236$	−14.0000			−0.911322
$237$	0.500000	+	0.866025i	0.0324785	+	0.0562544i
$238$	2.00000	+	3.46410i	0.129641	+	0.224544i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	−12.5000	−	21.6506i	−0.805196	−	1.39464i	−0.916159	−	0.400815i	$-0.868727\pi$
$241$	−12.5000	−	21.6506i	−0.805196	−	1.39464i	0.110963	−	0.993825i	$-0.464606\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−5.50000	+	9.52628i	−0.352101	+	0.609858i
$245$		0			0
$246$	4.00000			0.255031
$247$	1.50000	+	12.9904i	0.0954427	+	0.826558i
$248$	3.00000			0.190500
$249$	4.00000	−	6.92820i	0.253490	−	0.439057i
$250$		0			0
$251$	9.00000	+	15.5885i	0.568075	+	0.983935i	0.996756	+	0.0804789i	$0.0256450\pi$
$251$	9.00000	+	15.5885i	0.568075	+	0.983935i	−0.428681	+	0.903456i	$0.641022\pi$
$252$	−0.500000	+	0.866025i	−0.0314970	+	0.0545545i
$253$	4.00000	+	6.92820i	0.251478	+	0.435572i
$254$	8.00000			0.501965
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	0.990217	−	0.139533i	$-0.0445601\pi$
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	−0.615948	+	0.787787i	$0.711227\pi$
$258$	−9.00000			−0.560316
$259$	−5.00000			−0.310685
$260$		0			0
$261$		0			0
$262$	−3.00000	−	5.19615i	−0.185341	−	0.321019i
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$	1.00000	−	1.73205i	0.0615457	−	0.106600i
$265$		0			0
$266$	3.50000	−	2.59808i	0.214599	−	0.159298i
$267$	14.0000			0.856786
$268$	−1.50000	+	2.59808i	−0.0916271	+	0.158703i
$269$	−1.00000	+	1.73205i	−0.0609711	+	0.105605i	−0.894900	−	0.446267i	$-0.852753\pi$
$269$	−1.00000	+	1.73205i	−0.0609711	+	0.105605i	0.833929	+	0.551872i	$0.186086\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	−2.00000	−	3.46410i	−0.121268	−	0.210042i
$273$	3.00000			0.181568
$274$	6.00000			0.362473
$275$	−5.00000	−	8.66025i	−0.301511	−	0.522233i
$276$	2.00000	+	3.46410i	0.120386	+	0.208514i
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$	19.0000			1.13954
$279$	1.50000	+	2.59808i	0.0898027	+	0.155543i
$280$		0			0
$281$	4.00000	+	6.92820i	0.238620	+	0.413302i	0.960319	−	0.278906i	$-0.0899716\pi$
$281$	4.00000	+	6.92820i	0.238620	+	0.413302i	−0.721699	+	0.692207i	$0.756638\pi$
$282$	−5.00000	+	8.66025i	−0.297746	+	0.515711i
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	−0.399188	−	0.916869i	$-0.630708\pi$
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	0.993626	−	0.112728i	$-0.0359589\pi$
$284$	14.0000			0.830747
$285$		0			0
$286$	−6.00000			−0.354787
$287$	−2.00000	+	3.46410i	−0.118056	+	0.204479i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$	1.00000	+	1.73205i	0.0586210	+	0.101535i
$292$	−11.0000			−0.643726
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$	3.00000	+	5.19615i	0.174964	+	0.303046i
$295$		0			0
$296$	5.00000			0.290619
$297$	2.00000			0.116052
$298$	−11.0000	−	19.0526i	−0.637213	−	1.10369i
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$	−2.50000	−	4.33013i	−0.144338	−	0.250000i
$301$	4.50000	−	7.79423i	0.259376	−	0.449252i
$302$	−10.0000	+	17.3205i	−0.575435	+	0.996683i
$303$	10.0000			0.574485
$304$	−3.50000	+	2.59808i	−0.200739	+	0.149010i
$305$		0			0
$306$	2.00000	−	3.46410i	0.114332	−	0.198030i
$307$	6.00000	−	10.3923i	0.342438	−	0.593120i	−0.642447	−	0.766330i	$-0.722081\pi$
$307$	6.00000	−	10.3923i	0.342438	−	0.593120i	0.984885	+	0.173210i	$0.0554140\pi$
$308$	1.00000	+	1.73205i	0.0569803	+	0.0986928i
$309$	−1.50000	+	2.59808i	−0.0853320	+	0.147799i
$310$		0			0
$311$	10.0000			0.567048			0.283524	−	0.958965i	$-0.408496\pi$
$311$	10.0000			0.567048			0.283524	+	0.958965i	$0.408496\pi$
$312$	−3.00000			−0.169842
$313$	−3.00000	−	5.19615i	−0.169570	−	0.293704i	0.768699	−	0.639611i	$-0.220905\pi$
$313$	−3.00000	−	5.19615i	−0.169570	−	0.293704i	−0.938269	+	0.345907i	$0.887571\pi$
$314$	−10.5000	−	18.1865i	−0.592549	−	1.02633i
$315$		0			0
$316$	1.00000			0.0562544
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$	2.00000	−	3.46410i	0.112154	−	0.194257i
$319$		0			0
$320$		0			0
$321$	−5.00000	+	8.66025i	−0.279073	+	0.483368i
$322$	−4.00000			−0.222911
$323$	−14.0000	+	10.3923i	−0.778981	+	0.578243i
$324$	1.00000			0.0555556
$325$	−7.50000	+	12.9904i	−0.416025	+	0.720577i
$326$	5.50000	−	9.52628i	0.304617	−	0.527612i
$327$	7.00000	+	12.1244i	0.387101	+	0.670478i
$328$	2.00000	−	3.46410i	0.110432	−	0.191273i
$329$	−5.00000	−	8.66025i	−0.275659	−	0.477455i
$330$		0			0
$331$	15.0000			0.824475			0.412237	−	0.911077i	$-0.364747\pi$
$331$	15.0000			0.824475			0.412237	+	0.911077i	$0.364747\pi$
$332$	−4.00000	−	6.92820i	−0.219529	−	0.380235i
$333$	2.50000	+	4.33013i	0.136999	+	0.237289i
$334$	−6.00000			−0.328305
$335$		0			0
$336$	0.500000	+	0.866025i	0.0272772	+	0.0472456i
$337$	9.50000	−	16.4545i	0.517498	−	0.896333i	−0.482295	−	0.876009i	$-0.660197\pi$
$337$	9.50000	−	16.4545i	0.517498	−	0.896333i	0.999793	−	0.0203242i	$-0.00646983\pi$
$338$	−2.00000	−	3.46410i	−0.108786	−	0.188422i
$339$	5.00000	−	8.66025i	0.271563	−	0.470360i
$340$		0			0
$341$	6.00000			0.324918
$342$	−4.00000	−	1.73205i	−0.216295	−	0.0936586i
$343$	−13.0000			−0.701934
$344$	−4.50000	+	7.79423i	−0.242624	+	0.420237i
$345$		0			0
$346$	−12.0000	−	20.7846i	−0.645124	−	1.11739i
$347$	−8.00000	+	13.8564i	−0.429463	+	0.743851i	−0.996826	−	0.0796169i	$-0.974630\pi$
$347$	−8.00000	+	13.8564i	−0.429463	+	0.743851i	0.567363	+	0.823468i	$0.307964\pi$
$348$		0			0
$349$	−29.0000			−1.55233			−0.776167	−	0.630527i	$-0.782839\pi$
$349$	−29.0000			−1.55233			−0.776167	+	0.630527i	$0.782839\pi$
$350$	5.00000			0.267261
$351$	−1.50000	−	2.59808i	−0.0800641	−	0.138675i
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$	−12.0000			−0.638696			−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000			−0.638696			−0.319348	+	0.947638i	$0.603464\pi$
$354$	−14.0000			−0.744092
$355$		0			0
$356$	7.00000	−	12.1244i	0.370999	−	0.642590i
$357$	2.00000	+	3.46410i	0.105851	+	0.183340i
$358$	2.00000	−	3.46410i	0.105703	−	0.183083i
$359$	18.0000	−	31.1769i	0.950004	−	1.64545i	0.204595	−	0.978847i	$-0.434412\pi$
$359$	18.0000	−	31.1769i	0.950004	−	1.64545i	0.745409	−	0.666608i	$-0.232254\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$	18.0000			0.946059
$363$	−3.50000	+	6.06218i	−0.183702	+	0.318182i
$364$	1.50000	−	2.59808i	0.0786214	−	0.136176i
$365$		0			0
$366$	−5.50000	+	9.52628i	−0.287490	+	0.497947i
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	−0.992776	−	0.119982i	$-0.961716\pi$
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	0.392481	−	0.919760i	$-0.371617\pi$
$368$	4.00000			0.208514
$369$	4.00000			0.208232
$370$		0			0
$371$	2.00000	+	3.46410i	0.103835	+	0.179847i
$372$	3.00000			0.155543
$373$	26.0000			1.34623			0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000			1.34623			0.673114	+	0.739538i	$0.264956\pi$
$374$	−4.00000	−	6.92820i	−0.206835	−	0.358249i
$375$		0			0
$376$	5.00000	+	8.66025i	0.257855	+	0.446619i
$377$		0			0
$378$	−0.500000	+	0.866025i	−0.0257172	+	0.0445435i
$379$	−13.0000			−0.667765			−0.333883	−	0.942615i	$-0.608359\pi$
$379$	−13.0000			−0.667765			−0.333883	+	0.942615i	$0.608359\pi$
$380$		0			0
$381$	8.00000			0.409852
$382$	−4.00000	+	6.92820i	−0.204658	+	0.354478i
$383$	−7.00000	+	12.1244i	−0.357683	+	0.619526i	−0.987573	−	0.157159i	$-0.949767\pi$
$383$	−7.00000	+	12.1244i	−0.357683	+	0.619526i	0.629890	+	0.776684i	$0.283100\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	−6.50000	−	11.2583i	−0.330841	−	0.573034i
$387$	−9.00000			−0.457496
$388$	2.00000			0.101535
$389$	8.00000	+	13.8564i	0.405616	+	0.702548i	0.994393	−	0.105748i	$-0.0337237\pi$
$389$	8.00000	+	13.8564i	0.405616	+	0.702548i	−0.588777	+	0.808296i	$0.700390\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	6.00000			0.303046
$393$	−3.00000	−	5.19615i	−0.151330	−	0.262111i
$394$	−1.00000	+	1.73205i	−0.0503793	+	0.0872595i
$395$		0			0
$396$	1.00000	−	1.73205i	0.0502519	−	0.0870388i
$397$	−7.50000	+	12.9904i	−0.376414	+	0.651969i	−0.990538	−	0.137241i	$-0.956176\pi$
$397$	−7.50000	+	12.9904i	−0.376414	+	0.651969i	0.614123	+	0.789210i	$0.289510\pi$
$398$	−5.00000			−0.250627
$399$	3.50000	−	2.59808i	0.175219	−	0.130066i
$400$	−5.00000			−0.250000
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$	−1.50000	+	2.59808i	−0.0748132	+	0.129580i
$403$	−4.50000	−	7.79423i	−0.224161	−	0.388258i
$404$	5.00000	−	8.66025i	0.248759	−	0.430864i
$405$		0			0
$406$		0			0
$407$	10.0000			0.495682
$408$	−2.00000	−	3.46410i	−0.0990148	−	0.171499i
$409$	15.0000	+	25.9808i	0.741702	+	1.28467i	0.951720	+	0.306968i	$0.0993146\pi$
$409$	15.0000	+	25.9808i	0.741702	+	1.28467i	−0.210017	+	0.977698i	$0.567352\pi$
$410$		0			0
$411$	6.00000			0.295958
$412$	1.50000	+	2.59808i	0.0738997	+	0.127998i
$413$	7.00000	−	12.1244i	0.344447	−	0.596601i
$414$	2.00000	+	3.46410i	0.0982946	+	0.170251i
$415$		0			0
$416$	−1.50000	+	2.59808i	−0.0735436	+	0.127381i
$417$	19.0000			0.930434
$418$	−7.00000	+	5.19615i	−0.342381	+	0.254152i
$419$	18.0000			0.879358			0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000			0.879358			0.439679	+	0.898155i	$0.355092\pi$
$420$		0			0
$421$	−5.00000	+	8.66025i	−0.243685	+	0.422075i	−0.961761	−	0.273890i	$-0.911690\pi$
$421$	−5.00000	+	8.66025i	−0.243685	+	0.422075i	0.718076	+	0.695965i	$0.245023\pi$
$422$	12.5000	+	21.6506i	0.608490	+	1.05394i
$423$	−5.00000	+	8.66025i	−0.243108	+	0.421076i
$424$	−2.00000	−	3.46410i	−0.0971286	−	0.168232i
$425$	−20.0000			−0.970143
$426$	14.0000			0.678302
$427$	−5.50000	−	9.52628i	−0.266164	−	0.461009i
$428$	5.00000	+	8.66025i	0.241684	+	0.418609i
$429$	−6.00000			−0.289683
$430$		0			0
$431$	5.00000	+	8.66025i	0.240842	+	0.417150i	0.960954	−	0.276707i	$-0.0892433\pi$
$431$	5.00000	+	8.66025i	0.240842	+	0.417150i	−0.720113	+	0.693857i	$0.755910\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	4.50000	+	7.79423i	0.216256	+	0.374567i	0.953660	−	0.300885i	$-0.0972820\pi$
$433$	4.50000	+	7.79423i	0.216256	+	0.374567i	−0.737404	+	0.675452i	$0.763949\pi$
$434$	−1.50000	+	2.59808i	−0.0720023	+	0.124712i
$435$		0			0
$436$	14.0000			0.670478
$437$	−2.00000	−	17.3205i	−0.0956730	−	0.828552i
$438$	−11.0000			−0.525600
$439$	−9.50000	+	16.4545i	−0.453410	+	0.785330i	−0.998595	−	0.0529862i	$-0.983126\pi$
$439$	−9.50000	+	16.4545i	−0.453410	+	0.785330i	0.545185	+	0.838316i	$0.316459\pi$
$440$		0			0
$441$	3.00000	+	5.19615i	0.142857	+	0.247436i
$442$	−6.00000	+	10.3923i	−0.285391	+	0.494312i
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$	5.00000			0.237289
$445$		0			0
$446$	4.50000	+	7.79423i	0.213081	+	0.369067i
$447$	−11.0000	−	19.0526i	−0.520282	−	0.901155i
$448$	1.00000			0.0472456
$449$	−36.0000			−1.69895			−0.849473	−	0.527633i	$-0.823080\pi$
$449$	−36.0000			−1.69895			−0.849473	+	0.527633i	$0.823080\pi$
$450$	−2.50000	−	4.33013i	−0.117851	−	0.204124i
$451$	4.00000	−	6.92820i	0.188353	−	0.326236i
$452$	−5.00000	−	8.66025i	−0.235180	−	0.407344i
$453$	−10.0000	+	17.3205i	−0.469841	+	0.813788i
$454$	4.00000	−	6.92820i	0.187729	−	0.325157i
$455$		0			0
$456$	−3.50000	+	2.59808i	−0.163903	+	0.121666i
$457$	5.00000			0.233890			0.116945	−	0.993138i	$-0.462690\pi$
$457$	5.00000			0.233890			0.116945	+	0.993138i	$0.462690\pi$
$458$	−5.50000	+	9.52628i	−0.256998	+	0.445134i
$459$	2.00000	−	3.46410i	0.0933520	−	0.161690i
$460$		0			0
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	−0.927392	−	0.374091i	$-0.877955\pi$
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	0.787668	+	0.616100i	$0.211288\pi$
$462$	1.00000	+	1.73205i	0.0465242	+	0.0805823i
$463$	−9.00000			−0.418265			−0.209133	−	0.977887i	$-0.567064\pi$
$463$	−9.00000			−0.418265			−0.209133	+	0.977887i	$0.567064\pi$
$464$		0			0
$465$		0			0
$466$	9.00000	+	15.5885i	0.416917	+	0.722121i
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$	−3.00000			−0.138675
$469$	−1.50000	−	2.59808i	−0.0692636	−	0.119968i
$470$		0			0
$471$	−10.5000	−	18.1865i	−0.483814	−	0.837991i
$472$	−7.00000	+	12.1244i	−0.322201	+	0.558069i
$473$	−9.00000	+	15.5885i	−0.413820	+	0.716758i
$474$	1.00000			0.0459315
$475$	2.50000	+	21.6506i	0.114708	+	0.993399i
$476$	4.00000			0.183340
$477$	2.00000	−	3.46410i	0.0915737	−	0.158610i
$478$	−6.00000	+	10.3923i	−0.274434	+	0.475333i
$479$	−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
$481$	−7.50000	−	12.9904i	−0.341971	−	0.592310i
$482$	−25.0000			−1.13872
$483$	−4.00000			−0.182006
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$		0			0
$486$	1.00000			0.0453609
$487$	32.0000			1.45006			0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000			1.45006			0.725029	+	0.688718i	$0.241826\pi$
$488$	5.50000	+	9.52628i	0.248973	+	0.431234i
$489$	5.50000	−	9.52628i	0.248719	−	0.430793i
$490$		0			0
$491$	−15.0000	+	25.9808i	−0.676941	+	1.17250i	0.298957	+	0.954267i	$0.403361\pi$
$491$	−15.0000	+	25.9808i	−0.676941	+	1.17250i	−0.975898	+	0.218229i	$0.929972\pi$
$492$	2.00000	−	3.46410i	0.0901670	−	0.156174i
$493$		0			0
$494$	12.0000	+	5.19615i	0.539906	+	0.233786i
$495$		0			0
$496$	1.50000	−	2.59808i	0.0673520	−	0.116657i
$497$	−7.00000	+	12.1244i	−0.313993	+	0.543852i
$498$	−4.00000	−	6.92820i	−0.179244	−	0.310460i
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	−0.916542	−	0.399937i	$-0.869032\pi$
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	0.804627	+	0.593780i	$0.202365\pi$
$500$		0			0
$501$	−6.00000			−0.268060
$502$	18.0000			0.803379
$503$	−8.00000	−	13.8564i	−0.356702	−	0.617827i	0.630705	−	0.776022i	$-0.282766\pi$
$503$	−8.00000	−	13.8564i	−0.356702	−	0.617827i	−0.987408	+	0.158196i	$0.949432\pi$
$504$	0.500000	+	0.866025i	0.0222718	+	0.0385758i
$505$		0			0
$506$	8.00000			0.355643
$507$	−2.00000	−	3.46410i	−0.0888231	−	0.153846i
$508$	4.00000	−	6.92820i	0.177471	−	0.307389i
$509$	−13.0000	−	22.5167i	−0.576215	−	0.998033i	−0.995908	−	0.0903676i	$-0.971196\pi$
$509$	−13.0000	−	22.5167i	−0.576215	−	0.998033i	0.419694	−	0.907666i	$-0.362138\pi$
$510$		0			0
$511$	5.50000	−	9.52628i	0.243306	−	0.421418i
$512$	−1.00000			−0.0441942
$513$	−4.00000	−	1.73205i	−0.176604	−	0.0764719i
$514$	12.0000			0.529297
$515$		0			0
$516$	−4.50000	+	7.79423i	−0.198101	+	0.343122i
$517$	10.0000	+	17.3205i	0.439799	+	0.761755i
$518$	−2.50000	+	4.33013i	−0.109844	+	0.190255i
$519$	−12.0000	−	20.7846i	−0.526742	−	0.912343i
$520$		0			0
$521$	34.0000			1.48957			0.744784	−	0.667306i	$-0.232553\pi$
$521$	34.0000			1.48957			0.744784	+	0.667306i	$0.232553\pi$
$522$		0			0
$523$	−18.5000	−	32.0429i	−0.808949	−	1.40114i	−0.913593	−	0.406630i	$-0.866704\pi$
$523$	−18.5000	−	32.0429i	−0.808949	−	1.40114i	0.104644	−	0.994510i	$-0.466630\pi$
$524$	−6.00000			−0.262111
$525$	5.00000			0.218218
$526$	9.00000	+	15.5885i	0.392419	+	0.679689i
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$	−1.00000	−	1.73205i	−0.0435194	−	0.0753778i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	−14.0000			−0.607548
$532$	−0.500000	−	4.33013i	−0.0216777	−	0.187735i
$533$	−12.0000			−0.519778
$534$	7.00000	−	12.1244i	0.302920	−	0.524672i
$535$		0			0
$536$	1.50000	+	2.59808i	0.0647901	+	0.112220i
$537$	2.00000	−	3.46410i	0.0863064	−	0.149487i
$538$	1.00000	+	1.73205i	0.0431131	+	0.0746740i
$539$	12.0000			0.516877
$540$		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	$0.601169\pi$
$542$	−8.00000	−	13.8564i	−0.343629	−	0.595184i
$543$	18.0000			0.772454
$544$	−4.00000			−0.171499
$545$		0			0
$546$	1.50000	−	2.59808i	0.0641941	−	0.111187i
$547$	−5.50000	−	9.52628i	−0.235163	−	0.407314i	0.724157	−	0.689635i	$-0.242229\pi$
$547$	−5.50000	−	9.52628i	−0.235163	−	0.407314i	−0.959320	+	0.282321i	$0.908896\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$	−5.50000	+	9.52628i	−0.234734	+	0.406572i
$550$	−10.0000			−0.426401
$551$		0			0
$552$	4.00000			0.170251
$553$	−0.500000	+	0.866025i	−0.0212622	+	0.0368271i
$554$	−1.00000	+	1.73205i	−0.0424859	+	0.0735878i
$555$		0			0
$556$	9.50000	−	16.4545i	0.402890	−	0.697826i
$557$	−17.0000	−	29.4449i	−0.720313	−	1.24762i	−0.960874	−	0.276985i	$-0.910665\pi$
$557$	−17.0000	−	29.4449i	−0.720313	−	1.24762i	0.240561	−	0.970634i	$-0.422669\pi$
$558$	3.00000			0.127000
$559$	27.0000			1.14198
$560$		0			0
$561$	−4.00000	−	6.92820i	−0.168880	−	0.292509i
$562$	8.00000			0.337460
$563$	−6.00000			−0.252870			−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000			−0.252870			−0.126435	+	0.991975i	$0.540353\pi$
$564$	5.00000	+	8.66025i	0.210538	+	0.364662i
$565$		0			0
$566$	−10.0000	−	17.3205i	−0.420331	−	0.728035i
$567$	−0.500000	+	0.866025i	−0.0209980	+	0.0363696i
$568$	7.00000	−	12.1244i	0.293713	−	0.508727i
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$	−3.00000	+	5.19615i	−0.125436	+	0.217262i
$573$	−4.00000	+	6.92820i	−0.167102	+	0.289430i
$574$	2.00000	+	3.46410i	0.0834784	+	0.144589i
$575$	10.0000	−	17.3205i	0.417029	−	0.722315i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−14.0000			−0.582828			−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000			−0.582828			−0.291414	+	0.956597i	$0.594126\pi$
$578$	1.00000			0.0415945
$579$	−6.50000	−	11.2583i	−0.270131	−	0.467880i
$580$		0			0
$581$	8.00000			0.331896
$582$	2.00000			0.0829027
$583$	−4.00000	−	6.92820i	−0.165663	−	0.286937i
$584$	−5.50000	+	9.52628i	−0.227592	+	0.394200i
$585$		0			0
$586$	7.00000	−	12.1244i	0.289167	−	0.500853i
$587$	1.00000	−	1.73205i	0.0412744	−	0.0714894i	−0.844650	−	0.535319i	$-0.820192\pi$
$587$	1.00000	−	1.73205i	0.0412744	−	0.0714894i	0.885925	+	0.463829i	$0.153525\pi$
$588$	6.00000			0.247436
$589$	−12.0000	−	5.19615i	−0.494451	−	0.214104i
$590$		0			0
$591$	−1.00000	+	1.73205i	−0.0411345	+	0.0712470i
$592$	2.50000	−	4.33013i	0.102749	−	0.177967i
$593$	−17.0000	−	29.4449i	−0.698106	−	1.20916i	−0.969122	−	0.246581i	$-0.920693\pi$
$593$	−17.0000	−	29.4449i	−0.698106	−	1.20916i	0.271016	−	0.962575i	$-0.412640\pi$
$594$	1.00000	−	1.73205i	0.0410305	−	0.0710669i
$595$		0			0
$596$	−22.0000			−0.901155
$597$	−5.00000			−0.204636
$598$	−6.00000	−	10.3923i	−0.245358	−	0.424973i
$599$	23.0000	+	39.8372i	0.939755	+	1.62770i	0.765928	+	0.642926i	$0.222280\pi$
$599$	23.0000	+	39.8372i	0.939755	+	1.62770i	0.173826	+	0.984776i	$0.444387\pi$
$600$	−5.00000			−0.204124
$601$	27.0000			1.10135			0.550676	−	0.834719i	$-0.314370\pi$
$601$	27.0000			1.10135			0.550676	+	0.834719i	$0.314370\pi$
$602$	−4.50000	−	7.79423i	−0.183406	−	0.317669i
$603$	−1.50000	+	2.59808i	−0.0610847	+	0.105802i
$604$	10.0000	+	17.3205i	0.406894	+	0.704761i
$605$		0			0
$606$	5.00000	−	8.66025i	0.203111	−	0.351799i
$607$	5.00000			0.202944			0.101472	−	0.994838i	$-0.467645\pi$
$607$	5.00000			0.202944			0.101472	+	0.994838i	$0.467645\pi$
$608$	0.500000	+	4.33013i	0.0202777	+	0.175610i
$609$		0			0
$610$		0			0
$611$	15.0000	−	25.9808i	0.606835	−	1.05107i
$612$	−2.00000	−	3.46410i	−0.0808452	−	0.140028i
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$	−6.00000	−	10.3923i	−0.242140	−	0.419399i
$615$		0			0
$616$	2.00000			0.0805823
$617$	21.0000	+	36.3731i	0.845428	+	1.46432i	0.885249	+	0.465118i	$0.153988\pi$
$617$	21.0000	+	36.3731i	0.845428	+	1.46432i	−0.0398207	+	0.999207i	$0.512679\pi$
$618$	1.50000	+	2.59808i	0.0603388	+	0.104510i
$619$	1.00000			0.0401934			0.0200967	−	0.999798i	$-0.493603\pi$
$619$	1.00000			0.0401934			0.0200967	+	0.999798i	$0.493603\pi$
$620$		0			0
$621$	2.00000	+	3.46410i	0.0802572	+	0.139010i
$622$	5.00000	−	8.66025i	0.200482	−	0.347245i
$623$	7.00000	+	12.1244i	0.280449	+	0.485752i
$624$	−1.50000	+	2.59808i	−0.0600481	+	0.104006i
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	−6.00000			−0.239808
$627$	−7.00000	+	5.19615i	−0.279553	+	0.207514i
$628$	−21.0000			−0.837991
$629$	10.0000	−	17.3205i	0.398726	−	0.690614i
$630$		0			0
$631$	−8.50000	−	14.7224i	−0.338380	−	0.586091i	0.645748	−	0.763550i	$-0.276545\pi$
$631$	−8.50000	−	14.7224i	−0.338380	−	0.586091i	−0.984128	+	0.177459i	$0.943212\pi$
$632$	0.500000	−	0.866025i	0.0198889	−	0.0344486i
$633$	12.5000	+	21.6506i	0.496830	+	0.860535i
$634$	−12.0000			−0.476581
$635$		0			0
$636$	−2.00000	−	3.46410i	−0.0793052	−	0.137361i
$637$	−9.00000	−	15.5885i	−0.356593	−	0.617637i
$638$		0			0
$639$	14.0000			0.553831
$640$		0			0
$641$	7.00000	−	12.1244i	0.276483	−	0.478883i	−0.694025	−	0.719951i	$-0.744164\pi$
$641$	7.00000	−	12.1244i	0.276483	−	0.478883i	0.970508	+	0.241068i	$0.0774976\pi$
$642$	5.00000	+	8.66025i	0.197334	+	0.341793i
$643$	−18.5000	+	32.0429i	−0.729569	+	1.26365i	0.227497	+	0.973779i	$0.426946\pi$
$643$	−18.5000	+	32.0429i	−0.729569	+	1.26365i	−0.957066	+	0.289871i	$0.906387\pi$
$644$	−2.00000	+	3.46410i	−0.0788110	+	0.136505i
$645$		0			0
$646$	2.00000	+	17.3205i	0.0786889	+	0.681466i
$647$	48.0000			1.88707			0.943537	−	0.331266i	$-0.107476\pi$
$647$	48.0000			1.88707			0.943537	+	0.331266i	$0.107476\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−14.0000	+	24.2487i	−0.549548	+	0.951845i
$650$	7.50000	+	12.9904i	0.294174	+	0.509525i
$651$	−1.50000	+	2.59808i	−0.0587896	+	0.101827i
$652$	−5.50000	−	9.52628i	−0.215397	−	0.373078i
$653$	−42.0000			−1.64359			−0.821794	−	0.569785i	$-0.807026\pi$
$653$	−42.0000			−1.64359			−0.821794	+	0.569785i	$0.807026\pi$
$654$	14.0000			0.547443
$655$		0			0
$656$	−2.00000	−	3.46410i	−0.0780869	−	0.135250i
$657$	−11.0000			−0.429151
$658$	−10.0000			−0.389841
$659$	7.00000	+	12.1244i	0.272681	+	0.472298i	0.969548	−	0.244903i	$-0.0787562\pi$
$659$	7.00000	+	12.1244i	0.272681	+	0.472298i	−0.696866	+	0.717201i	$0.745423\pi$
$660$		0			0
$661$	−5.00000	−	8.66025i	−0.194477	−	0.336845i	0.752252	−	0.658876i	$-0.228968\pi$
$661$	−5.00000	−	8.66025i	−0.194477	−	0.336845i	−0.946729	+	0.322031i	$0.895634\pi$
$662$	7.50000	−	12.9904i	0.291496	−	0.504885i
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$	−8.00000			−0.310460
$665$		0			0
$666$	5.00000			0.193746
$667$		0			0
$668$	−3.00000	+	5.19615i	−0.116073	+	0.201045i
$669$	4.50000	+	7.79423i	0.173980	+	0.301342i
$670$		0			0
$671$	11.0000	+	19.0526i	0.424650	+	0.735516i
$672$	1.00000			0.0385758
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$	−9.50000	−	16.4545i	−0.365926	−	0.633803i
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$	−4.00000			−0.153846
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$	−5.00000	−	8.66025i	−0.192024	−	0.332595i
$679$	−1.00000	+	1.73205i	−0.0383765	+	0.0664700i
$680$		0			0
$681$	4.00000	−	6.92820i	0.153280	−	0.265489i
$682$	3.00000	−	5.19615i	0.114876	−	0.198971i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$	−3.50000	+	2.59808i	−0.133826	+	0.0993399i
$685$		0			0
$686$	−6.50000	+	11.2583i	−0.248171	+	0.429845i
$687$	−5.50000	+	9.52628i	−0.209838	+	0.363450i
$688$	4.50000	+	7.79423i	0.171561	+	0.297152i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	4.00000			0.152167			0.0760836	−	0.997101i	$-0.475758\pi$
$691$	4.00000			0.152167			0.0760836	+	0.997101i	$0.475758\pi$
$692$	−24.0000			−0.912343
$693$	1.00000	+	1.73205i	0.0379869	+	0.0657952i
$694$	8.00000	+	13.8564i	0.303676	+	0.525982i
$695$		0			0
$696$		0			0
$697$	−8.00000	−	13.8564i	−0.303022	−	0.524849i
$698$	−14.5000	+	25.1147i	−0.548833	+	0.950607i
$699$	9.00000	+	15.5885i	0.340411	+	0.589610i
$700$	2.50000	−	4.33013i	0.0944911	−	0.163663i
$701$	22.0000	−	38.1051i	0.830929	−	1.43921i	−0.0663742	−	0.997795i	$-0.521143\pi$
$701$	22.0000	−	38.1051i	0.830929	−	1.43921i	0.897303	−	0.441416i	$-0.145524\pi$
$702$	−3.00000			−0.113228
$703$	−20.0000	−	8.66025i	−0.754314	−	0.326628i
$704$	−2.00000			−0.0753778
$705$		0			0
$706$	−6.00000	+	10.3923i	−0.225813	+	0.391120i
$707$	5.00000	+	8.66025i	0.188044	+	0.325702i
$708$	−7.00000	+	12.1244i	−0.263076	+	0.455661i
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	0.995228	+	0.0975728i	$0.0311079\pi$
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	−0.413114	+	0.910679i	$0.635559\pi$
$710$		0			0
$711$	1.00000			0.0375029
$712$	−7.00000	−	12.1244i	−0.262336	−	0.454379i
$713$	6.00000	+	10.3923i	0.224702	+	0.389195i
$714$	4.00000			0.149696
$715$		0			0
$716$	−2.00000	−	3.46410i	−0.0747435	−	0.129460i
$717$	−6.00000	+	10.3923i	−0.224074	+	0.388108i
$718$	−18.0000	−	31.1769i	−0.671754	−	1.16351i
$719$	−20.0000	+	34.6410i	−0.745874	+	1.29189i	0.203911	+	0.978989i	$0.434635\pi$
$719$	−20.0000	+	34.6410i	−0.745874	+	1.29189i	−0.949785	+	0.312903i	$0.898699\pi$
$720$		0			0
$721$	−3.00000			−0.111726
$722$	18.5000	−	4.33013i	0.688499	−	0.161151i
$723$	−25.0000			−0.929760
$724$	9.00000	−	15.5885i	0.334482	−	0.579340i
$725$		0			0
$726$	3.50000	+	6.06218i	0.129897	+	0.224989i
$727$	−8.50000	+	14.7224i	−0.315248	+	0.546025i	−0.979490	−	0.201492i	$-0.935421\pi$
$727$	−8.50000	+	14.7224i	−0.315248	+	0.546025i	0.664243	+	0.747517i	$0.268754\pi$
$728$	−1.50000	−	2.59808i	−0.0555937	−	0.0962911i
$729$	1.00000			0.0370370
$730$		0			0
$731$	18.0000	+	31.1769i	0.665754	+	1.15312i
$732$	5.50000	+	9.52628i	0.203286	+	0.352101i
$733$	−2.00000			−0.0738717			−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000			−0.0738717			−0.0369358	+	0.999318i	$0.511760\pi$
$734$	−23.0000			−0.848945
$735$		0			0
$736$	2.00000	−	3.46410i	0.0737210	−	0.127688i
$737$	3.00000	+	5.19615i	0.110506	+	0.191403i
$738$	2.00000	−	3.46410i	0.0736210	−	0.127515i
$739$	2.50000	−	4.33013i	0.0919640	−	0.159286i	−0.816373	−	0.577524i	$-0.804019\pi$
$739$	2.50000	−	4.33013i	0.0919640	−	0.159286i	0.908337	+	0.418238i	$0.137352\pi$
$740$		0			0
$741$	12.0000	+	5.19615i	0.440831	+	0.190885i
$742$	4.00000			0.146845
$743$	9.00000	−	15.5885i	0.330178	−	0.571885i	−0.652369	−	0.757902i	$-0.726225\pi$
$743$	9.00000	−	15.5885i	0.330178	−	0.571885i	0.982547	+	0.186017i	$0.0595579\pi$
$744$	1.50000	−	2.59808i	0.0549927	−	0.0952501i
$745$		0			0
$746$	13.0000	−	22.5167i	0.475964	−	0.824394i
$747$	−4.00000	−	6.92820i	−0.146352	−	0.253490i
$748$	−8.00000			−0.292509
$749$	−10.0000			−0.365392
$750$		0			0
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	0.722718	−	0.691143i	$-0.242893\pi$
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	−0.959906	+	0.280321i	$0.909559\pi$
$752$	10.0000			0.364662
$753$	18.0000			0.655956
$754$		0			0
$755$		0			0
$756$	0.500000	+	0.866025i	0.0181848	+	0.0314970i
$757$	−2.50000	+	4.33013i	−0.0908640	+	0.157381i	−0.907875	−	0.419241i	$-0.862296\pi$
$757$	−2.50000	+	4.33013i	−0.0908640	+	0.157381i	0.817011	+	0.576622i	$0.195630\pi$
$758$	−6.50000	+	11.2583i	−0.236091	+	0.408921i
$759$	8.00000			0.290382
$760$		0			0
$761$	−34.0000			−1.23250			−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000			−1.23250			−0.616250	+	0.787551i	$0.711349\pi$
$762$	4.00000	−	6.92820i	0.144905	−	0.250982i
$763$	−7.00000	+	12.1244i	−0.253417	+	0.438931i
$764$	4.00000	+	6.92820i	0.144715	+	0.250654i
$765$		0			0
$766$	7.00000	+	12.1244i	0.252920	+	0.438071i
$767$	42.0000			1.51653
$768$	−1.00000			−0.0360844
$769$	−13.5000	−	23.3827i	−0.486822	−	0.843201i	0.513063	−	0.858351i	$-0.328511\pi$
$769$	−13.5000	−	23.3827i	−0.486822	−	0.843201i	−0.999885	+	0.0151499i	$0.995177\pi$
$770$		0			0
$771$	12.0000			0.432169
$772$	−13.0000			−0.467880
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$	−4.50000	+	7.79423i	−0.161749	+	0.280158i
$775$	−7.50000	−	12.9904i	−0.269408	−	0.466628i
$776$	1.00000	−	1.73205i	0.0358979	−	0.0621770i
$777$	−2.50000	+	4.33013i	−0.0896870	+	0.155342i
$778$	16.0000			0.573628
$779$	−14.0000	+	10.3923i	−0.501602	+	0.372343i
$780$		0			0
$781$	14.0000	−	24.2487i	0.500959	−	0.867687i
$782$	8.00000	−	13.8564i	0.286079	−	0.495504i
$783$		0			0
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$		0			0
$786$	−6.00000			−0.214013
$787$	−47.0000			−1.67537			−0.837685	−	0.546154i	$-0.816091\pi$
$787$	−47.0000			−1.67537			−0.837685	+	0.546154i	$0.816091\pi$
$788$	1.00000	+	1.73205i	0.0356235	+	0.0617018i
$789$	9.00000	+	15.5885i	0.320408	+	0.554964i
$790$		0			0
$791$	10.0000			0.355559
$792$	−1.00000	−	1.73205i	−0.0355335	−	0.0615457i
$793$	16.5000	−	28.5788i	0.585932	−	1.01486i
$794$	7.50000	+	12.9904i	0.266165	+	0.461011i
$795$		0			0
$796$	−2.50000	+	4.33013i	−0.0886102	+	0.153477i
$797$	26.0000			0.920967			0.460484	−	0.887668i	$-0.347676\pi$
$797$	26.0000			0.920967			0.460484	+	0.887668i	$0.347676\pi$
$798$	−0.500000	−	4.33013i	−0.0176998	−	0.153285i
$799$	40.0000			1.41510
$800$	−2.50000	+	4.33013i	−0.0883883	+	0.153093i
$801$	7.00000	−	12.1244i	0.247333	−	0.428393i
$802$	9.00000	+	15.5885i	0.317801	+	0.550448i
$803$	−11.0000	+	19.0526i	−0.388182	+	0.672350i
$804$	1.50000	+	2.59808i	0.0529009	+	0.0916271i
$805$		0			0
$806$	−9.00000			−0.317011
$807$	1.00000	+	1.73205i	0.0352017	+	0.0609711i
$808$	−5.00000	−	8.66025i	−0.175899	−	0.304667i
$809$		0			0			−	1.00000i	$-0.5\pi$
$809$		0			0				1.00000i	$0.5\pi$
$810$		0			0
$811$	−2.00000	−	3.46410i	−0.0702295	−	0.121641i	0.828772	−	0.559586i	$-0.189040\pi$
$811$	−2.00000	−	3.46410i	−0.0702295	−	0.121641i	−0.899002	+	0.437945i	$0.855706\pi$
$812$		0			0
$813$	−8.00000	−	13.8564i	−0.280572	−	0.485965i
$814$	5.00000	−	8.66025i	0.175250	−	0.303542i
$815$		0			0
$816$	−4.00000			−0.140028
$817$	31.5000	−	23.3827i	1.10205	−	0.818057i
$818$	30.0000			1.04893
$819$	1.50000	−	2.59808i	0.0524142	−	0.0907841i
$820$		0			0
$821$	−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	$-0.482712\pi$
$822$	3.00000	−	5.19615i	0.104637	−	0.181237i
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	0.829060	−	0.559159i	$-0.188876\pi$
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	−0.898776	+	0.438408i	$0.855543\pi$
$824$	3.00000			0.104510
$825$	−10.0000			−0.348155
$826$	−7.00000	−	12.1244i	−0.243561	−	0.421860i
$827$	−18.0000	−	31.1769i	−0.625921	−	1.08413i	−0.988362	−	0.152121i	$-0.951390\pi$
$827$	−18.0000	−	31.1769i	−0.625921	−	1.08413i	0.362441	−	0.932007i	$-0.381944\pi$
$828$	4.00000			0.139010
$829$	−31.0000			−1.07667			−0.538337	−	0.842729i	$-0.680947\pi$
$829$	−31.0000			−1.07667			−0.538337	+	0.842729i	$0.680947\pi$
$830$		0			0
$831$	−1.00000	+	1.73205i	−0.0346896	+	0.0600842i
$832$	1.50000	+	2.59808i	0.0520031	+	0.0900721i
$833$	12.0000	−	20.7846i	0.415775	−	0.720144i
$834$	9.50000	−	16.4545i	0.328958	−	0.569772i
$835$		0			0
$836$	1.00000	+	8.66025i	0.0345857	+	0.299521i
$837$	3.00000			0.103695
$838$	9.00000	−	15.5885i	0.310900	−	0.538494i
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	−0.743670	−	0.668546i	$-0.766917\pi$
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	0.950813	+	0.309764i	$0.100250\pi$
$840$		0			0
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	5.00000	+	8.66025i	0.172311	+	0.298452i
$843$	8.00000			0.275535
$844$	25.0000			0.860535
$845$		0			0
$846$	5.00000	+	8.66025i	0.171904	+	0.297746i
$847$	−7.00000			−0.240523
$848$	−4.00000			−0.137361
$849$	−10.0000	−	17.3205i	−0.343199	−	0.594438i
$850$	−10.0000	+	17.3205i	−0.342997	+	0.594089i
$851$	10.0000	+	17.3205i	0.342796	+	0.593739i
$852$	7.00000	−	12.1244i	0.239816	−	0.415374i
$853$	−1.50000	+	2.59808i	−0.0513590	+	0.0889564i	−0.890562	−	0.454862i	$-0.849689\pi$
$853$	−1.50000	+	2.59808i	−0.0513590	+	0.0889564i	0.839203	+	0.543818i	$0.183022\pi$
$854$	−11.0000			−0.376412
$855$		0			0
$856$	10.0000			0.341793
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	0.244701	+	0.969599i	$0.421310\pi$
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	−0.962048	+	0.272882i	$0.912023\pi$
$858$	−3.00000	+	5.19615i	−0.102418	+	0.177394i
$859$	−3.50000	−	6.06218i	−0.119418	−	0.206839i	0.800119	−	0.599841i	$-0.204770\pi$
$859$	−3.50000	−	6.06218i	−0.119418	−	0.206839i	−0.919537	+	0.393003i	$0.871436\pi$
$860$		0			0
$861$	2.00000	+	3.46410i	0.0681598	+	0.118056i
$862$	10.0000			0.340601
$863$	−22.0000			−0.748889			−0.374444	−	0.927249i	$-0.622167\pi$
$863$	−22.0000			−0.748889			−0.374444	+	0.927249i	$0.622167\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	9.00000			0.305832
$867$	1.00000			0.0339618
$868$	1.50000	+	2.59808i	0.0509133	+	0.0881845i
$869$	1.00000	−	1.73205i	0.0339227	−	0.0587558i
$870$		0			0
$871$	4.50000	−	7.79423i	0.152477	−	0.264097i
$872$	7.00000	−	12.1244i	0.237050	−	0.410582i
$873$	2.00000			0.0676897
$874$	−16.0000	−	6.92820i	−0.541208	−	0.234350i
$875$		0			0
$876$	−5.50000	+	9.52628i	−0.185828	+	0.321863i
$877$	12.5000	−	21.6506i	0.422095	−	0.731090i	−0.574049	−	0.818821i	$-0.694628\pi$
$877$	12.5000	−	21.6506i	0.422095	−	0.731090i	0.996144	+	0.0877308i	$0.0279615\pi$
$878$	9.50000	+	16.4545i	0.320609	+	0.555312i
$879$	7.00000	−	12.1244i	0.236104	−	0.408944i
$880$		0			0
$881$	36.0000			1.21287			0.606435	−	0.795133i	$-0.292599\pi$
$881$	36.0000			1.21287			0.606435	+	0.795133i	$0.292599\pi$
$882$	6.00000			0.202031
$883$	4.50000	+	7.79423i	0.151437	+	0.262297i	0.931756	−	0.363085i	$-0.118277\pi$
$883$	4.50000	+	7.79423i	0.151437	+	0.262297i	−0.780319	+	0.625382i	$0.784943\pi$
$884$	6.00000	+	10.3923i	0.201802	+	0.349531i
$885$		0			0
$886$	−24.0000			−0.806296
$887$	−9.00000	−	15.5885i	−0.302190	−	0.523409i	0.674441	−	0.738328i	$-0.264385\pi$
$887$	−9.00000	−	15.5885i	−0.302190	−	0.523409i	−0.976632	+	0.214919i	$0.931051\pi$
$888$	2.50000	−	4.33013i	0.0838945	−	0.145310i
$889$	4.00000	+	6.92820i	0.134156	+	0.232364i
$890$		0			0
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$	9.00000			0.301342
$893$	−5.00000	−	43.3013i	−0.167319	−	1.44902i
$894$	−22.0000			−0.735790
$895$		0			0
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$	−6.00000	−	10.3923i	−0.200334	−	0.346989i
$898$	−18.0000	+	31.1769i	−0.600668	+	1.04039i
$899$		0			0
$900$	−5.00000			−0.166667
$901$	−16.0000			−0.533037
$902$	−4.00000	−	6.92820i	−0.133185	−	0.230684i
$903$	−4.50000	−	7.79423i	−0.149751	−	0.259376i
$904$	−10.0000			−0.332595
$905$		0			0
$906$	10.0000	+	17.3205i	0.332228	+	0.575435i
$907$	−26.0000	+	45.0333i	−0.863316	+	1.49531i	0.00539395	+	0.999985i	$0.498283\pi$
$907$	−26.0000	+	45.0333i	−0.863316	+	1.49531i	−0.868710	+	0.495321i	$0.835050\pi$
$908$	−4.00000	−	6.92820i	−0.132745	−	0.229920i
$909$	5.00000	−	8.66025i	0.165840	−	0.287242i
$910$		0			0
$911$	−60.0000			−1.98789			−0.993944	−	0.109885i	$-0.964952\pi$
$911$	−60.0000			−1.98789			−0.993944	+	0.109885i	$0.964952\pi$
$912$	0.500000	+	4.33013i	0.0165567	+	0.143385i
$913$	−16.0000			−0.529523
$914$	2.50000	−	4.33013i	0.0826927	−	0.143228i
$915$		0			0
$916$	5.50000	+	9.52628i	0.181725	+	0.314757i
$917$	3.00000	−	5.19615i	0.0990687	−	0.171592i
$918$	−2.00000	−	3.46410i	−0.0660098	−	0.114332i
$919$	55.0000			1.81428			0.907141	−	0.420826i	$-0.138260\pi$
$919$	55.0000			1.81428			0.907141	+	0.420826i	$0.138260\pi$
$920$		0			0
$921$	−6.00000	−	10.3923i	−0.197707	−	0.342438i
$922$	3.00000	+	5.19615i	0.0987997	+	0.171126i
$923$	−42.0000			−1.38245
$924$	2.00000			0.0657952
$925$	−12.5000	−	21.6506i	−0.410997	−	0.711868i
$926$	−4.50000	+	7.79423i	−0.147879	+	0.256134i
$927$	1.50000	+	2.59808i	0.0492665	+	0.0853320i
$928$		0			0
$929$	−6.00000	+	10.3923i	−0.196854	+	0.340960i	−0.947507	−	0.319736i	$-0.896406\pi$
$929$	−6.00000	+	10.3923i	−0.196854	+	0.340960i	0.750653	+	0.660697i	$0.229739\pi$
$930$		0			0
$931$	−24.0000	−	10.3923i	−0.786568	−	0.340594i
$932$	18.0000			0.589610
$933$	5.00000	−	8.66025i	0.163693	−	0.283524i
$934$	4.00000	−	6.92820i	0.130884	−	0.226698i
$935$		0			0
$936$	−1.50000	+	2.59808i	−0.0490290	+	0.0849208i
$937$	12.5000	+	21.6506i	0.408357	+	0.707295i	0.994706	−	0.102763i	$-0.0327685\pi$
$937$	12.5000	+	21.6506i	0.408357	+	0.707295i	−0.586349	+	0.810059i	$0.699435\pi$
$938$	−3.00000			−0.0979535
$939$	−6.00000			−0.195803
$940$		0			0
$941$	16.0000	+	27.7128i	0.521585	+	0.903412i	0.999685	+	0.0251063i	$0.00799243\pi$
$941$	16.0000	+	27.7128i	0.521585	+	0.903412i	−0.478100	+	0.878306i	$0.658674\pi$
$942$	−21.0000			−0.684217
$943$	16.0000			0.521032
$944$	7.00000	+	12.1244i	0.227831	+	0.394614i
$945$		0			0
$946$	9.00000	+	15.5885i	0.292615	+	0.506824i
$947$	−5.00000	+	8.66025i	−0.162478	+	0.281420i	−0.935757	−	0.352646i	$-0.885282\pi$
$947$	−5.00000	+	8.66025i	−0.162478	+	0.281420i	0.773279	+	0.634066i	$0.218615\pi$
$948$	0.500000	−	0.866025i	0.0162392	−	0.0281272i
$949$	33.0000			1.07123
$950$	20.0000	+	8.66025i	0.648886	+	0.280976i
$951$	−12.0000			−0.389127
$952$	2.00000	−	3.46410i	0.0648204	−	0.112272i
$953$	15.0000	−	25.9808i	0.485898	−	0.841599i	−0.513971	−	0.857808i	$-0.671826\pi$
$953$	15.0000	−	25.9808i	0.485898	−	0.841599i	0.999869	+	0.0162081i	$0.00515944\pi$
$954$	−2.00000	−	3.46410i	−0.0647524	−	0.112154i
$955$		0			0
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$		0			0
$958$	−6.00000			−0.193851
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$		0			0
$961$	−22.0000			−0.709677
$962$	−15.0000			−0.483619
$963$	5.00000	+	8.66025i	0.161123	+	0.279073i
$964$	−12.5000	+	21.6506i	−0.402598	+	0.697320i
$965$		0			0
$966$	−2.00000	+	3.46410i	−0.0643489	+	0.111456i
$967$	−25.5000	+	44.1673i	−0.820025	+	1.42032i	0.0856383	+	0.996326i	$0.472707\pi$
$967$	−25.5000	+	44.1673i	−0.820025	+	1.42032i	−0.905663	+	0.423998i	$0.860626\pi$
$968$	7.00000			0.224989
$969$	2.00000	+	17.3205i	0.0642493	+	0.556415i
$970$		0			0
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	−0.910140	−	0.414301i	$-0.864026\pi$
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	0.813865	+	0.581054i	$0.197359\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	9.50000	+	16.4545i	0.304556	+	0.527506i
$974$	16.0000	−	27.7128i	0.512673	−	0.887976i
$975$	7.50000	+	12.9904i	0.240192	+	0.416025i
$976$	11.0000			0.352101
$977$	−42.0000			−1.34370			−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000			−1.34370			−0.671850	+	0.740688i	$0.734500\pi$
$978$	−5.50000	−	9.52628i	−0.175871	−	0.304617i
$979$	−14.0000	−	24.2487i	−0.447442	−	0.774992i
$980$		0			0
$981$	14.0000			0.446986
$982$	15.0000	+	25.9808i	0.478669	+	0.829079i
$983$	3.00000	−	5.19615i	0.0956851	−	0.165732i	−0.814209	−	0.580572i	$-0.802829\pi$
$983$	3.00000	−	5.19615i	0.0956851	−	0.165732i	0.909894	+	0.414840i	$0.136162\pi$
$984$	−2.00000	−	3.46410i	−0.0637577	−	0.110432i
$985$		0			0
$986$		0			0
$987$	−10.0000			−0.318304
$988$	10.5000	−	7.79423i	0.334050	−	0.247967i
$989$	−36.0000			−1.14473
$990$		0			0
$991$	8.50000	−	14.7224i	0.270011	−	0.467673i	−0.698853	−	0.715265i	$-0.746306\pi$
$991$	8.50000	−	14.7224i	0.270011	−	0.467673i	0.968864	+	0.247592i	$0.0796392\pi$
$992$	−1.50000	−	2.59808i	−0.0476250	−	0.0824890i
$993$	7.50000	−	12.9904i	0.238005	−	0.412237i
$994$	7.00000	+	12.1244i	0.222027	+	0.384561i
$995$		0			0
$996$	−8.00000			−0.253490
$997$	24.5000	+	42.4352i	0.775923	+	1.34394i	0.934274	+	0.356555i	$0.116049\pi$
$997$	24.5000	+	42.4352i	0.775923	+	1.34394i	−0.158352	+	0.987383i	$0.550618\pi$
$998$	2.50000	+	4.33013i	0.0791361	+	0.137068i
$999$	5.00000			0.158193

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	114.2.e.b.49.1	yes	2
3.2	odd	2		342.2.g.c.163.1		2
4.3	odd	2		912.2.q.b.49.1		2
12.11	even	2		2736.2.s.k.1873.1		2
19.7	even	3	inner	114.2.e.b.7.1	✓	2
19.8	odd	6		2166.2.a.h.1.1		1
19.11	even	3		2166.2.a.b.1.1		1
57.8	even	6		6498.2.a.g.1.1		1
57.11	odd	6		6498.2.a.u.1.1		1
57.26	odd	6		342.2.g.c.235.1		2
76.7	odd	6		912.2.q.b.577.1		2
228.83	even	6		2736.2.s.k.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.e.b.7.1	✓	2	19.7	even	3	inner
114.2.e.b.49.1	yes	2	1.1	even	1	trivial
342.2.g.c.163.1		2	3.2	odd	2
342.2.g.c.235.1		2	57.26	odd	6
912.2.q.b.49.1		2	4.3	odd	2
912.2.q.b.577.1		2	76.7	odd	6
2166.2.a.b.1.1		1	19.11	even	3
2166.2.a.h.1.1		1	19.8	odd	6
2736.2.s.k.577.1		2	228.83	even	6
2736.2.s.k.1873.1		2	12.11	even	2
6498.2.a.g.1.1		1	57.8	even	6
6498.2.a.u.1.1		1	57.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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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	114.2.e.b.49.1

Level	$114$
Weight	$2$
Character	114.49
Analytic conductor	$0.910$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$