LMFDB - Embedded newform 114.2.e.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(7,114)]

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

lf = mfeigenbasis(mf)

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")

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

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.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} -3.00000 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} -3.00000 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{10} +2.00000 q^{11} -1.00000 q^{12} +(3.50000 + 6.06218i) q^{13} +(1.50000 - 2.59808i) q^{14} +(-2.00000 - 3.46410i) q^{15} +(-0.500000 + 0.866025i) q^{16} +1.00000 q^{18} +(-4.00000 + 1.73205i) q^{19} -4.00000 q^{20} +(-1.50000 + 2.59808i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-5.50000 - 9.52628i) q^{25} -7.00000 q^{26} -1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +(-2.00000 - 3.46410i) q^{29} +4.00000 q^{30} +1.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} +(-6.00000 + 10.3923i) q^{35} +(-0.500000 + 0.866025i) q^{36} +7.00000 q^{37} +(0.500000 - 4.33013i) q^{38} +7.00000 q^{39} +(2.00000 - 3.46410i) q^{40} +(-2.00000 + 3.46410i) q^{41} +(-1.50000 - 2.59808i) q^{42} +(-3.50000 + 6.06218i) q^{43} +(-1.00000 - 1.73205i) q^{44} -4.00000 q^{45} -4.00000 q^{46} +(-1.00000 - 1.73205i) q^{47} +(0.500000 + 0.866025i) q^{48} +2.00000 q^{49} +11.0000 q^{50} +(3.50000 - 6.06218i) q^{52} +(2.00000 + 3.46410i) q^{53} +(0.500000 - 0.866025i) q^{54} +(4.00000 - 6.92820i) q^{55} -3.00000 q^{56} +(-0.500000 + 4.33013i) q^{57} +4.00000 q^{58} +(3.00000 - 5.19615i) q^{59} +(-2.00000 + 3.46410i) q^{60} +(0.500000 + 0.866025i) q^{61} +(-0.500000 + 0.866025i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +28.0000 q^{65} +(1.00000 + 1.73205i) q^{66} +(-1.50000 - 2.59808i) q^{67} +4.00000 q^{69} +(-6.00000 - 10.3923i) q^{70} +(-1.00000 + 1.73205i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.50000 - 2.59808i) q^{73} +(-3.50000 + 6.06218i) q^{74} -11.0000 q^{75} +(3.50000 + 2.59808i) q^{76} -6.00000 q^{77} +(-3.50000 + 6.06218i) q^{78} +(-2.50000 + 4.33013i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.00000 - 3.46410i) q^{82} -12.0000 q^{83} +3.00000 q^{84} +(-3.50000 - 6.06218i) q^{86} -4.00000 q^{87} +2.00000 q^{88} +(-9.00000 - 15.5885i) q^{89} +(2.00000 - 3.46410i) q^{90} +(-10.5000 - 18.1865i) q^{91} +(2.00000 - 3.46410i) q^{92} +(0.500000 - 0.866025i) q^{93} +2.00000 q^{94} +(-2.00000 + 17.3205i) q^{95} -1.00000 q^{96} +(-5.00000 + 8.66025i) q^{97} +(-1.00000 + 1.73205i) q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} + 4 q^{5} + q^{6} - 6 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 + 4 * q^5 + q^6 - 6 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} + 4 q^{5} + q^{6} - 6 q^{7} + 2 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 2 q^{12} + 7 q^{13} + 3 q^{14} - 4 q^{15} - q^{16} + 2 q^{18} - 8 q^{19} - 8 q^{20} - 3 q^{21} - 2 q^{22} + 4 q^{23} + q^{24} - 11 q^{25} - 14 q^{26} - 2 q^{27} + 3 q^{28} - 4 q^{29} + 8 q^{30} + 2 q^{31} - q^{32} + 2 q^{33} - 12 q^{35} - q^{36} + 14 q^{37} + q^{38} + 14 q^{39} + 4 q^{40} - 4 q^{41} - 3 q^{42} - 7 q^{43} - 2 q^{44} - 8 q^{45} - 8 q^{46} - 2 q^{47} + q^{48} + 4 q^{49} + 22 q^{50} + 7 q^{52} + 4 q^{53} + q^{54} + 8 q^{55} - 6 q^{56} - q^{57} + 8 q^{58} + 6 q^{59} - 4 q^{60} + q^{61} - q^{62} + 3 q^{63} + 2 q^{64} + 56 q^{65} + 2 q^{66} - 3 q^{67} + 8 q^{69} - 12 q^{70} - 2 q^{71} - q^{72} + 3 q^{73} - 7 q^{74} - 22 q^{75} + 7 q^{76} - 12 q^{77} - 7 q^{78} - 5 q^{79} + 4 q^{80} - q^{81} - 4 q^{82} - 24 q^{83} + 6 q^{84} - 7 q^{86} - 8 q^{87} + 4 q^{88} - 18 q^{89} + 4 q^{90} - 21 q^{91} + 4 q^{92} + q^{93} + 4 q^{94} - 4 q^{95} - 2 q^{96} - 10 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 + 4 * q^5 + q^6 - 6 * q^7 + 2 * q^8 - q^9 + 4 * q^10 + 4 * q^11 - 2 * q^12 + 7 * q^13 + 3 * q^14 - 4 * q^15 - q^16 + 2 * q^18 - 8 * q^19 - 8 * q^20 - 3 * q^21 - 2 * q^22 + 4 * q^23 + q^24 - 11 * q^25 - 14 * q^26 - 2 * q^27 + 3 * q^28 - 4 * q^29 + 8 * q^30 + 2 * q^31 - q^32 + 2 * q^33 - 12 * q^35 - q^36 + 14 * q^37 + q^38 + 14 * q^39 + 4 * q^40 - 4 * q^41 - 3 * q^42 - 7 * q^43 - 2 * q^44 - 8 * q^45 - 8 * q^46 - 2 * q^47 + q^48 + 4 * q^49 + 22 * q^50 + 7 * q^52 + 4 * q^53 + q^54 + 8 * q^55 - 6 * q^56 - q^57 + 8 * q^58 + 6 * q^59 - 4 * q^60 + q^61 - q^62 + 3 * q^63 + 2 * q^64 + 56 * q^65 + 2 * q^66 - 3 * q^67 + 8 * q^69 - 12 * q^70 - 2 * q^71 - q^72 + 3 * q^73 - 7 * q^74 - 22 * q^75 + 7 * q^76 - 12 * q^77 - 7 * q^78 - 5 * q^79 + 4 * q^80 - q^81 - 4 * q^82 - 24 * q^83 + 6 * q^84 - 7 * q^86 - 8 * q^87 + 4 * q^88 - 18 * q^89 + 4 * q^90 - 21 * q^91 + 4 * q^92 + q^93 + 4 * q^94 - 4 * q^95 - 2 * q^96 - 10 * q^97 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

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
$5$	2.00000	−	3.46410i	0.894427	−	1.54919i	0.0599153	−	0.998203i	$-0.480917\pi$
$5$	2.00000	−	3.46410i	0.894427	−	1.54919i	0.834512	−	0.550990i	$-0.185750\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.00000	+	3.46410i	0.632456	+	1.09545i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.00000			−0.288675
$13$	3.50000	+	6.06218i	0.970725	+	1.68135i	0.693375	+	0.720577i	$0.256123\pi$
$13$	3.50000	+	6.06218i	0.970725	+	1.68135i	0.277350	+	0.960769i	$0.410544\pi$
$14$	1.50000	−	2.59808i	0.400892	−	0.694365i
$15$	−2.00000	−	3.46410i	−0.516398	−	0.894427i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	1.00000			0.235702
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$20$	−4.00000			−0.894427
$21$	−1.50000	+	2.59808i	−0.327327	+	0.566947i
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−5.50000	−	9.52628i	−1.10000	−	1.90526i
$26$	−7.00000			−1.37281
$27$	−1.00000			−0.192450
$28$	1.50000	+	2.59808i	0.283473	+	0.490990i
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	0.618389	−	0.785872i	$-0.287786\pi$
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	−0.989780	+	0.142605i	$0.954452\pi$
$30$	4.00000			0.730297
$31$	1.00000			0.179605			0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000			0.179605			0.0898027	+	0.995960i	$0.471376\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.00000	−	1.73205i	0.174078	−	0.301511i
$34$		0			0
$35$	−6.00000	+	10.3923i	−1.01419	+	1.75662i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	7.00000			1.15079			0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000			1.15079			0.575396	+	0.817875i	$0.304848\pi$
$38$	0.500000	−	4.33013i	0.0811107	−	0.702439i
$39$	7.00000			1.12090
$40$	2.00000	−	3.46410i	0.316228	−	0.547723i
$41$	−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	$0.267782\pi$
$42$	−1.50000	−	2.59808i	−0.231455	−	0.400892i
$43$	−3.50000	+	6.06218i	−0.533745	+	0.924473i	0.465478	+	0.885059i	$0.345882\pi$
$43$	−3.50000	+	6.06218i	−0.533745	+	0.924473i	−0.999223	+	0.0394140i	$0.987451\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$	−4.00000			−0.596285
$46$	−4.00000			−0.589768
$47$	−1.00000	−	1.73205i	−0.145865	−	0.252646i	0.783830	−	0.620975i	$-0.213263\pi$
$47$	−1.00000	−	1.73205i	−0.145865	−	0.252646i	−0.929695	+	0.368329i	$0.879930\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	2.00000			0.285714
$50$	11.0000			1.55563
$51$		0			0
$52$	3.50000	−	6.06218i	0.485363	−	0.840673i
$53$	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
$55$	4.00000	−	6.92820i	0.539360	−	0.934199i
$56$	−3.00000			−0.400892
$57$	−0.500000	+	4.33013i	−0.0662266	+	0.573539i
$58$	4.00000			0.525226
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$	−2.00000	+	3.46410i	−0.258199	+	0.447214i
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	−0.500000	+	0.866025i	−0.0635001	+	0.109985i
$63$	1.50000	+	2.59808i	0.188982	+	0.327327i
$64$	1.00000			0.125000
$65$	28.0000			3.47297
$66$	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	$0.891996\pi$
$68$		0			0
$69$	4.00000			0.481543
$70$	−6.00000	−	10.3923i	−0.717137	−	1.24212i
$71$	−1.00000	+	1.73205i	−0.118678	+	0.205557i	−0.919244	−	0.393688i	$-0.871199\pi$
$71$	−1.00000	+	1.73205i	−0.118678	+	0.205557i	0.800566	+	0.599245i	$0.204532\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	−0.764794	−	0.644275i	$-0.777159\pi$
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	0.940356	+	0.340193i	$0.110493\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$	−11.0000			−1.27017
$76$	3.50000	+	2.59808i	0.401478	+	0.298020i
$77$	−6.00000			−0.683763
$78$	−3.50000	+	6.06218i	−0.396297	+	0.686406i
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$	2.00000	+	3.46410i	0.223607	+	0.387298i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.00000	−	3.46410i	−0.220863	−	0.382546i
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$	3.00000			0.327327
$85$		0			0
$86$	−3.50000	−	6.06218i	−0.377415	−	0.653701i
$87$	−4.00000			−0.428845
$88$	2.00000			0.213201
$89$	−9.00000	−	15.5885i	−0.953998	−	1.65237i	−0.736644	−	0.676280i	$-0.763591\pi$
$89$	−9.00000	−	15.5885i	−0.953998	−	1.65237i	−0.217354	−	0.976093i	$-0.569742\pi$
$90$	2.00000	−	3.46410i	0.210819	−	0.365148i
$91$	−10.5000	−	18.1865i	−1.10070	−	1.90647i
$92$	2.00000	−	3.46410i	0.208514	−	0.361158i
$93$	0.500000	−	0.866025i	0.0518476	−	0.0898027i
$94$	2.00000			0.206284
$95$	−2.00000	+	17.3205i	−0.205196	+	1.77705i
$96$	−1.00000			−0.102062
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	0.492287	+	0.870433i	$0.336161\pi$
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	−0.999961	+	0.00888289i	$0.997172\pi$
$98$	−1.00000	+	1.73205i	−0.101015	+	0.174964i
$99$	−1.00000	−	1.73205i	−0.100504	−	0.174078i
$100$	−5.50000	+	9.52628i	−0.550000	+	0.952628i
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	0.811976	−	0.583691i	$-0.198392\pi$
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	−0.911479	+	0.411346i	$0.865059\pi$
$102$		0			0
$103$	9.00000			0.886796			0.443398	−	0.896325i	$-0.353773\pi$
$103$	9.00000			0.886796			0.443398	+	0.896325i	$0.353773\pi$
$104$	3.50000	+	6.06218i	0.343203	+	0.594445i
$105$	6.00000	+	10.3923i	0.585540	+	1.01419i
$106$	−4.00000			−0.388514
$107$	2.00000			0.193347			0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000			0.193347			0.0966736	+	0.995316i	$0.469180\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−3.00000	+	5.19615i	−0.287348	+	0.497701i	−0.973176	−	0.230063i	$-0.926107\pi$
$109$	−3.00000	+	5.19615i	−0.287348	+	0.497701i	0.685828	+	0.727764i	$0.259440\pi$
$110$	4.00000	+	6.92820i	0.381385	+	0.660578i
$111$	3.50000	−	6.06218i	0.332205	−	0.575396i
$112$	1.50000	−	2.59808i	0.141737	−	0.245495i
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$	−3.50000	−	2.59808i	−0.327805	−	0.243332i
$115$	16.0000			1.49201
$116$	−2.00000	+	3.46410i	−0.185695	+	0.321634i
$117$	3.50000	−	6.06218i	0.323575	−	0.560449i
$118$	3.00000	+	5.19615i	0.276172	+	0.478345i
$119$		0			0
$120$	−2.00000	−	3.46410i	−0.182574	−	0.316228i
$121$	−7.00000			−0.636364
$122$	−1.00000			−0.0905357
$123$	2.00000	+	3.46410i	0.180334	+	0.312348i
$124$	−0.500000	−	0.866025i	−0.0449013	−	0.0777714i
$125$	−24.0000			−2.14663
$126$	−3.00000			−0.267261
$127$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$127$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	3.50000	+	6.06218i	0.308158	+	0.533745i
$130$	−14.0000	+	24.2487i	−1.22788	+	2.12675i
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$	−2.00000			−0.174078
$133$	12.0000	−	5.19615i	1.04053	−	0.450564i
$134$	3.00000			0.259161
$135$	−2.00000	+	3.46410i	−0.172133	+	0.298142i
$136$		0			0
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$	−2.00000	+	3.46410i	−0.170251	+	0.294884i
$139$	−10.5000	−	18.1865i	−0.890598	−	1.54256i	−0.839159	−	0.543885i	$-0.816953\pi$
$139$	−10.5000	−	18.1865i	−0.890598	−	1.54256i	−0.0514389	−	0.998676i	$-0.516381\pi$
$140$	12.0000			1.01419
$141$	−2.00000			−0.168430
$142$	−1.00000	−	1.73205i	−0.0839181	−	0.145350i
$143$	7.00000	+	12.1244i	0.585369	+	1.01389i
$144$	1.00000			0.0833333
$145$	−16.0000			−1.32873
$146$	1.50000	+	2.59808i	0.124141	+	0.215018i
$147$	1.00000	−	1.73205i	0.0824786	−	0.142857i
$148$	−3.50000	−	6.06218i	−0.287698	−	0.498308i
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	−0.216394	−	0.976306i	$-0.569430\pi$
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	0.953703	−	0.300750i	$-0.0972370\pi$
$150$	5.50000	−	9.52628i	0.449073	−	0.777817i
$151$	20.0000			1.62758			0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000			1.62758			0.813788	+	0.581161i	$0.197401\pi$
$152$	−4.00000	+	1.73205i	−0.324443	+	0.140488i
$153$		0			0
$154$	3.00000	−	5.19615i	0.241747	−	0.418718i
$155$	2.00000	−	3.46410i	0.160644	−	0.278243i
$156$	−3.50000	−	6.06218i	−0.280224	−	0.485363i
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$	−2.50000	−	4.33013i	−0.198889	−	0.344486i
$159$	4.00000			0.317221
$160$	−4.00000			−0.316228
$161$	−6.00000	−	10.3923i	−0.472866	−	0.819028i
$162$	−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
$165$	−4.00000	−	6.92820i	−0.311400	−	0.539360i
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	−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	$0.907908\pi$
$168$	−1.50000	+	2.59808i	−0.115728	+	0.200446i
$169$	−18.0000	+	31.1769i	−1.38462	+	2.39822i
$170$		0			0
$171$	3.50000	+	2.59808i	0.267652	+	0.198680i
$172$	7.00000			0.533745
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	−0.998755	−	0.0498898i	$-0.984113\pi$
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	0.542583	+	0.840002i	$0.317446\pi$
$174$	2.00000	−	3.46410i	0.151620	−	0.262613i
$175$	16.5000	+	28.5788i	1.24728	+	2.16036i
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	−3.00000	−	5.19615i	−0.225494	−	0.390567i
$178$	18.0000			1.34916
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	2.00000	+	3.46410i	0.149071	+	0.258199i
$181$	1.00000	+	1.73205i	0.0743294	+	0.128742i	0.900794	−	0.434246i	$-0.142985\pi$
$181$	1.00000	+	1.73205i	0.0743294	+	0.128742i	−0.826465	+	0.562988i	$0.809652\pi$
$182$	21.0000			1.55662
$183$	1.00000			0.0739221
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	14.0000	−	24.2487i	1.02930	−	1.78280i
$186$	0.500000	+	0.866025i	0.0366618	+	0.0635001i
$187$		0			0
$188$	−1.00000	+	1.73205i	−0.0729325	+	0.126323i
$189$	3.00000			0.218218
$190$	−14.0000	−	10.3923i	−1.01567	−	0.753937i
$191$	−20.0000			−1.44715			−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000			−1.44715			−0.723575	+	0.690246i	$0.757502\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	10.5000	−	18.1865i	0.755807	−	1.30910i	−0.189166	−	0.981945i	$-0.560578\pi$
$193$	10.5000	−	18.1865i	0.755807	−	1.30910i	0.944972	−	0.327150i	$-0.106088\pi$
$194$	−5.00000	−	8.66025i	−0.358979	−	0.621770i
$195$	14.0000	−	24.2487i	1.00256	−	1.73649i
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$	−10.0000			−0.712470			−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000			−0.712470			−0.356235	+	0.934396i	$0.615940\pi$
$198$	2.00000			0.142134
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	0.963001	−	0.269498i	$-0.0868577\pi$
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	−0.714893	+	0.699234i	$0.753524\pi$
$200$	−5.50000	−	9.52628i	−0.388909	−	0.673610i
$201$	−3.00000			−0.211604
$202$	2.00000			0.140720
$203$	6.00000	+	10.3923i	0.421117	+	0.729397i
$204$		0			0
$205$	8.00000	+	13.8564i	0.558744	+	0.967773i
$206$	−4.50000	+	7.79423i	−0.313530	+	0.543050i
$207$	2.00000	−	3.46410i	0.139010	−	0.240772i
$208$	−7.00000			−0.485363
$209$	−8.00000	+	3.46410i	−0.553372	+	0.239617i
$210$	−12.0000			−0.828079
$211$	−4.50000	+	7.79423i	−0.309793	+	0.536577i	−0.978317	−	0.207114i	$-0.933593\pi$
$211$	−4.50000	+	7.79423i	−0.309793	+	0.536577i	0.668524	+	0.743690i	$0.266926\pi$
$212$	2.00000	−	3.46410i	0.137361	−	0.237915i
$213$	1.00000	+	1.73205i	0.0685189	+	0.118678i
$214$	−1.00000	+	1.73205i	−0.0683586	+	0.118401i
$215$	14.0000	+	24.2487i	0.954792	+	1.65375i
$216$	−1.00000			−0.0680414
$217$	−3.00000			−0.203653
$218$	−3.00000	−	5.19615i	−0.203186	−	0.351928i
$219$	−1.50000	−	2.59808i	−0.101361	−	0.175562i
$220$	−8.00000			−0.539360
$221$		0			0
$222$	3.50000	+	6.06218i	0.234905	+	0.406867i
$223$	−2.50000	+	4.33013i	−0.167412	+	0.289967i	−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−2.50000	+	4.33013i	−0.167412	+	0.289967i	0.770097	+	0.637927i	$0.220208\pi$
$224$	1.50000	+	2.59808i	0.100223	+	0.173591i
$225$	−5.50000	+	9.52628i	−0.366667	+	0.635085i
$226$	−1.00000	+	1.73205i	−0.0665190	+	0.115214i
$227$	4.00000			0.265489			0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000			0.265489			0.132745	+	0.991150i	$0.457621\pi$
$228$	4.00000	−	1.73205i	0.264906	−	0.114708i
$229$	−7.00000			−0.462573			−0.231287	−	0.972886i	$-0.574293\pi$
$229$	−7.00000			−0.462573			−0.231287	+	0.972886i	$0.574293\pi$
$230$	−8.00000	+	13.8564i	−0.527504	+	0.913664i
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$	−2.00000	−	3.46410i	−0.131306	−	0.227429i
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	3.50000	+	6.06218i	0.228802	+	0.396297i
$235$	−8.00000			−0.521862
$236$	−6.00000			−0.390567
$237$	2.50000	+	4.33013i	0.162392	+	0.281272i
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$	4.00000			0.258199
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	0.849472	−	0.527633i	$-0.176921\pi$
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	−0.881680	+	0.471848i	$0.843587\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.500000	−	0.866025i	0.0320092	−	0.0554416i
$245$	4.00000	−	6.92820i	0.255551	−	0.442627i
$246$	−4.00000			−0.255031
$247$	−24.5000	−	18.1865i	−1.55890	−	1.15718i
$248$	1.00000			0.0635001
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$	12.0000	−	20.7846i	0.758947	−	1.31453i
$251$	−7.00000	−	12.1244i	−0.441836	−	0.765283i	0.555990	−	0.831189i	$-0.312339\pi$
$251$	−7.00000	−	12.1244i	−0.441836	−	0.765283i	−0.997826	+	0.0659066i	$0.979006\pi$
$252$	1.50000	−	2.59808i	0.0944911	−	0.163663i
$253$	4.00000	+	6.92820i	0.251478	+	0.435572i
$254$		0			0
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.0000	+	24.2487i	0.873296	+	1.51259i	0.858567	+	0.512702i	$0.171355\pi$
$257$	14.0000	+	24.2487i	0.873296	+	1.51259i	0.0147291	+	0.999892i	$0.495311\pi$
$258$	−7.00000			−0.435801
$259$	−21.0000			−1.30488
$260$	−14.0000	−	24.2487i	−0.868243	−	1.50384i
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	9.00000	+	15.5885i	0.556022	+	0.963058i
$263$	9.00000	−	15.5885i	0.554964	−	0.961225i	−0.442943	−	0.896550i	$-0.646065\pi$
$263$	9.00000	−	15.5885i	0.554964	−	0.961225i	0.997906	−	0.0646755i	$-0.0206012\pi$
$264$	1.00000	−	1.73205i	0.0615457	−	0.106600i
$265$	16.0000			0.982872
$266$	−1.50000	+	12.9904i	−0.0919709	+	0.796491i
$267$	−18.0000			−1.10158
$268$	−1.50000	+	2.59808i	−0.0916271	+	0.158703i
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	−2.00000	−	3.46410i	−0.121716	−	0.210819i
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	−0.718580	−	0.695444i	$-0.755208\pi$
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	0.961563	+	0.274586i	$0.0885408\pi$
$272$		0			0
$273$	−21.0000			−1.27098
$274$	−2.00000			−0.120824
$275$	−11.0000	−	19.0526i	−0.663325	−	1.14891i
$276$	−2.00000	−	3.46410i	−0.120386	−	0.208514i
$277$	−26.0000			−1.56219			−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000			−1.56219			−0.781094	+	0.624413i	$0.785338\pi$
$278$	21.0000			1.25950
$279$	−0.500000	−	0.866025i	−0.0299342	−	0.0518476i
$280$	−6.00000	+	10.3923i	−0.358569	+	0.621059i
$281$	−2.00000	−	3.46410i	−0.119310	−	0.206651i	0.800184	−	0.599754i	$-0.204735\pi$
$281$	−2.00000	−	3.46410i	−0.119310	−	0.206651i	−0.919494	+	0.393103i	$0.871402\pi$
$282$	1.00000	−	1.73205i	0.0595491	−	0.103142i
$283$	6.00000	−	10.3923i	0.356663	−	0.617758i	−0.630738	−	0.775996i	$-0.717248\pi$
$283$	6.00000	−	10.3923i	0.356663	−	0.617758i	0.987401	+	0.158237i	$0.0505811\pi$
$284$	2.00000			0.118678
$285$	14.0000	+	10.3923i	0.829288	+	0.615587i
$286$	−14.0000			−0.827837
$287$	6.00000	−	10.3923i	0.354169	−	0.613438i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	8.00000	−	13.8564i	0.469776	−	0.813676i
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$	−3.00000			−0.175562
$293$	−18.0000			−1.05157			−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000			−1.05157			−0.525786	+	0.850617i	$0.676229\pi$
$294$	1.00000	+	1.73205i	0.0583212	+	0.101015i
$295$	−12.0000	−	20.7846i	−0.698667	−	1.21013i
$296$	7.00000			0.406867
$297$	−2.00000			−0.116052
$298$	9.00000	+	15.5885i	0.521356	+	0.903015i
$299$	−14.0000	+	24.2487i	−0.809641	+	1.40234i
$300$	5.50000	+	9.52628i	0.317543	+	0.550000i
$301$	10.5000	−	18.1865i	0.605210	−	1.04825i
$302$	−10.0000	+	17.3205i	−0.575435	+	0.996683i
$303$	−2.00000			−0.114897
$304$	0.500000	−	4.33013i	0.0286770	−	0.248350i
$305$	4.00000			0.229039
$306$		0			0
$307$	−6.00000	+	10.3923i	−0.342438	+	0.593120i	−0.984885	−	0.173210i	$-0.944586\pi$
$307$	−6.00000	+	10.3923i	−0.342438	+	0.593120i	0.642447	+	0.766330i	$0.277919\pi$
$308$	3.00000	+	5.19615i	0.170941	+	0.296078i
$309$	4.50000	−	7.79423i	0.255996	−	0.443398i
$310$	2.00000	+	3.46410i	0.113592	+	0.196748i
$311$	34.0000			1.92796			0.963982	−	0.265969i	$-0.0856919\pi$
$311$	34.0000			1.92796			0.963982	+	0.265969i	$0.0856919\pi$
$312$	7.00000			0.396297
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	0.597522	−	0.801852i	$-0.296152\pi$
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	−0.993186	+	0.116543i	$0.962819\pi$
$314$	−3.50000	−	6.06218i	−0.197516	−	0.342108i
$315$	12.0000			0.676123
$316$	5.00000			0.281272
$317$	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	$0.597914\pi$
$318$	−2.00000	+	3.46410i	−0.112154	+	0.194257i
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$	2.00000	−	3.46410i	0.111803	−	0.193649i
$321$	1.00000	−	1.73205i	0.0558146	−	0.0966736i
$322$	12.0000			0.668734
$323$		0			0
$324$	1.00000			0.0555556
$325$	38.5000	−	66.6840i	2.13560	−	3.69896i
$326$	−5.50000	+	9.52628i	−0.304617	+	0.527612i
$327$	3.00000	+	5.19615i	0.165900	+	0.287348i
$328$	−2.00000	+	3.46410i	−0.110432	+	0.191273i
$329$	3.00000	+	5.19615i	0.165395	+	0.286473i
$330$	8.00000			0.440386
$331$	23.0000			1.26419			0.632097	−	0.774889i	$-0.282194\pi$
$331$	23.0000			1.26419			0.632097	+	0.774889i	$0.282194\pi$
$332$	6.00000	+	10.3923i	0.329293	+	0.570352i
$333$	−3.50000	−	6.06218i	−0.191799	−	0.332205i
$334$	6.00000			0.328305
$335$	−12.0000			−0.655630
$336$	−1.50000	−	2.59808i	−0.0818317	−	0.141737i
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	−0.986960	−	0.160968i	$-0.948538\pi$
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	0.632882	+	0.774248i	$0.281872\pi$
$338$	−18.0000	−	31.1769i	−0.979071	−	1.69580i
$339$	1.00000	−	1.73205i	0.0543125	−	0.0940721i
$340$		0			0
$341$	2.00000			0.108306
$342$	−4.00000	+	1.73205i	−0.216295	+	0.0936586i
$343$	15.0000			0.809924
$344$	−3.50000	+	6.06218i	−0.188707	+	0.326851i
$345$	8.00000	−	13.8564i	0.430706	−	0.746004i
$346$	−6.00000	−	10.3923i	−0.322562	−	0.558694i
$347$	−14.0000	+	24.2487i	−0.751559	+	1.30174i	0.195507	+	0.980702i	$0.437365\pi$
$347$	−14.0000	+	24.2487i	−0.751559	+	1.30174i	−0.947067	+	0.321037i	$0.895969\pi$
$348$	2.00000	+	3.46410i	0.107211	+	0.185695i
$349$	31.0000			1.65939			0.829696	−	0.558216i	$-0.188514\pi$
$349$	31.0000			1.65939			0.829696	+	0.558216i	$0.188514\pi$
$350$	−33.0000			−1.76392
$351$	−3.50000	−	6.06218i	−0.186816	−	0.323575i
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$		0			0			−	1.00000i	$-0.5\pi$
$353$		0			0				1.00000i	$0.5\pi$
$354$	6.00000			0.318896
$355$	4.00000	+	6.92820i	0.212298	+	0.367711i
$356$	−9.00000	+	15.5885i	−0.476999	+	0.826187i
$357$		0			0
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	−0.663123	−	0.748511i	$-0.730769\pi$
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	0.979791	+	0.200026i	$0.0641026\pi$
$360$	−4.00000			−0.210819
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$	−2.00000			−0.105118
$363$	−3.50000	+	6.06218i	−0.183702	+	0.318182i
$364$	−10.5000	+	18.1865i	−0.550350	+	0.953233i
$365$	−6.00000	−	10.3923i	−0.314054	−	0.543958i
$366$	−0.500000	+	0.866025i	−0.0261354	+	0.0452679i
$367$	−9.50000	−	16.4545i	−0.495896	−	0.858917i	0.504093	−	0.863649i	$-0.331827\pi$
$367$	−9.50000	−	16.4545i	−0.495896	−	0.858917i	−0.999989	+	0.00473247i	$0.998494\pi$
$368$	−4.00000			−0.208514
$369$	4.00000			0.208232
$370$	14.0000	+	24.2487i	0.727825	+	1.26063i
$371$	−6.00000	−	10.3923i	−0.311504	−	0.539542i
$372$	−1.00000			−0.0518476
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$	−12.0000	+	20.7846i	−0.619677	+	1.07331i
$376$	−1.00000	−	1.73205i	−0.0515711	−	0.0893237i
$377$	14.0000	−	24.2487i	0.721037	−	1.24887i
$378$	−1.50000	+	2.59808i	−0.0771517	+	0.133631i
$379$	−21.0000			−1.07870			−0.539349	−	0.842082i	$-0.681330\pi$
$379$	−21.0000			−1.07870			−0.539349	+	0.842082i	$0.681330\pi$
$380$	16.0000	−	6.92820i	0.820783	−	0.355409i
$381$		0			0
$382$	10.0000	−	17.3205i	0.511645	−	0.886194i
$383$	7.00000	−	12.1244i	0.357683	−	0.619526i	−0.629890	−	0.776684i	$-0.716900\pi$
$383$	7.00000	−	12.1244i	0.357683	−	0.619526i	0.987573	+	0.157159i	$0.0502334\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−12.0000	+	20.7846i	−0.611577	+	1.05928i
$386$	10.5000	+	18.1865i	0.534436	+	0.925670i
$387$	7.00000			0.355830
$388$	10.0000			0.507673
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	0.991500	+	0.130105i	$0.0415314\pi$
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	−0.383076	+	0.923717i	$0.625135\pi$
$390$	14.0000	+	24.2487i	0.708918	+	1.22788i
$391$		0			0
$392$	2.00000			0.101015
$393$	−9.00000	−	15.5885i	−0.453990	−	0.786334i
$394$	5.00000	−	8.66025i	0.251896	−	0.436297i
$395$	10.0000	+	17.3205i	0.503155	+	0.871489i
$396$	−1.00000	+	1.73205i	−0.0502519	+	0.0870388i
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	−0.655534	−	0.755166i	$-0.727556\pi$
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	0.981760	+	0.190126i	$0.0608897\pi$
$398$	−7.00000			−0.350878
$399$	1.50000	−	12.9904i	0.0750939	−	0.650332i
$400$	11.0000			0.550000
$401$	−5.00000	+	8.66025i	−0.249688	+	0.432472i	−0.963439	−	0.267927i	$-0.913661\pi$
$401$	−5.00000	+	8.66025i	−0.249688	+	0.432472i	0.713751	+	0.700399i	$0.246995\pi$
$402$	1.50000	−	2.59808i	0.0748132	−	0.129580i
$403$	3.50000	+	6.06218i	0.174347	+	0.301979i
$404$	−1.00000	+	1.73205i	−0.0497519	+	0.0861727i
$405$	2.00000	+	3.46410i	0.0993808	+	0.172133i
$406$	−12.0000			−0.595550
$407$	14.0000			0.693954
$408$		0			0
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$	−16.0000			−0.790184
$411$	2.00000			0.0986527
$412$	−4.50000	−	7.79423i	−0.221699	−	0.383994i
$413$	−9.00000	+	15.5885i	−0.442861	+	0.767058i
$414$	2.00000	+	3.46410i	0.0982946	+	0.170251i
$415$	−24.0000	+	41.5692i	−1.17811	+	2.04055i
$416$	3.50000	−	6.06218i	0.171602	−	0.297223i
$417$	−21.0000			−1.02837
$418$	1.00000	−	8.66025i	0.0489116	−	0.423587i
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$	6.00000	−	10.3923i	0.292770	−	0.507093i
$421$	−13.0000	+	22.5167i	−0.633581	+	1.09739i	0.353233	+	0.935536i	$0.385082\pi$
$421$	−13.0000	+	22.5167i	−0.633581	+	1.09739i	−0.986814	+	0.161859i	$0.948251\pi$
$422$	−4.50000	−	7.79423i	−0.219057	−	0.379417i
$423$	−1.00000	+	1.73205i	−0.0486217	+	0.0842152i
$424$	2.00000	+	3.46410i	0.0971286	+	0.168232i
$425$		0			0
$426$	−2.00000			−0.0969003
$427$	−1.50000	−	2.59808i	−0.0725901	−	0.125730i
$428$	−1.00000	−	1.73205i	−0.0483368	−	0.0837218i
$429$	14.0000			0.675926
$430$	−28.0000			−1.35028
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	0.784683	−	0.619897i	$-0.212826\pi$
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	−0.929188	+	0.369607i	$0.879492\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−11.5000	−	19.9186i	−0.552655	−	0.957226i	−0.998082	−	0.0619079i	$-0.980282\pi$
$433$	−11.5000	−	19.9186i	−0.552655	−	0.957226i	0.445427	−	0.895318i	$-0.353052\pi$
$434$	1.50000	−	2.59808i	0.0720023	−	0.124712i
$435$	−8.00000	+	13.8564i	−0.383571	+	0.664364i
$436$	6.00000			0.287348
$437$	−14.0000	−	10.3923i	−0.669711	−	0.497131i
$438$	3.00000			0.143346
$439$	−11.5000	+	19.9186i	−0.548865	+	0.950662i	0.449488	+	0.893287i	$0.351607\pi$
$439$	−11.5000	+	19.9186i	−0.548865	+	0.950662i	−0.998353	+	0.0573756i	$0.981727\pi$
$440$	4.00000	−	6.92820i	0.190693	−	0.330289i
$441$	−1.00000	−	1.73205i	−0.0476190	−	0.0824786i
$442$		0			0
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	0.814595	−	0.580030i	$-0.196959\pi$
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	−0.909618	+	0.415445i	$0.863626\pi$
$444$	−7.00000			−0.332205
$445$	−72.0000			−3.41313
$446$	−2.50000	−	4.33013i	−0.118378	−	0.205037i
$447$	−9.00000	−	15.5885i	−0.425685	−	0.737309i
$448$	−3.00000			−0.141737
$449$	16.0000			0.755087			0.377543	−	0.925992i	$-0.376769\pi$
$449$	16.0000			0.755087			0.377543	+	0.925992i	$0.376769\pi$
$450$	−5.50000	−	9.52628i	−0.259272	−	0.449073i
$451$	−4.00000	+	6.92820i	−0.188353	+	0.326236i
$452$	−1.00000	−	1.73205i	−0.0470360	−	0.0814688i
$453$	10.0000	−	17.3205i	0.469841	−	0.813788i
$454$	−2.00000	+	3.46410i	−0.0938647	+	0.162578i
$455$	−84.0000			−3.93798
$456$	−0.500000	+	4.33013i	−0.0234146	+	0.202777i
$457$	29.0000			1.35656			0.678281	−	0.734802i	$-0.262725\pi$
$457$	29.0000			1.35656			0.678281	+	0.734802i	$0.262725\pi$
$458$	3.50000	−	6.06218i	0.163544	−	0.283267i
$459$		0			0
$460$	−8.00000	−	13.8564i	−0.373002	−	0.646058i
$461$	17.0000	−	29.4449i	0.791769	−	1.37138i	−0.133102	−	0.991102i	$-0.542494\pi$
$461$	17.0000	−	29.4449i	0.791769	−	1.37138i	0.924871	−	0.380282i	$-0.124173\pi$
$462$	−3.00000	−	5.19615i	−0.139573	−	0.241747i
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$	4.00000			0.185695
$465$	−2.00000	−	3.46410i	−0.0927478	−	0.160644i
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$	−7.00000			−0.323575
$469$	4.50000	+	7.79423i	0.207791	+	0.359904i
$470$	4.00000	−	6.92820i	0.184506	−	0.319574i
$471$	3.50000	+	6.06218i	0.161271	+	0.279330i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$	−7.00000	+	12.1244i	−0.321860	+	0.557478i
$474$	−5.00000			−0.229658
$475$	38.5000	+	28.5788i	1.76650	+	1.31129i
$476$		0			0
$477$	2.00000	−	3.46410i	0.0915737	−	0.158610i
$478$	−12.0000	+	20.7846i	−0.548867	+	0.950666i
$479$	−17.0000	−	29.4449i	−0.776750	−	1.34537i	−0.933806	−	0.357780i	$-0.883534\pi$
$479$	−17.0000	−	29.4449i	−0.776750	−	1.34537i	0.157056	−	0.987590i	$-0.449800\pi$
$480$	−2.00000	+	3.46410i	−0.0912871	+	0.158114i
$481$	24.5000	+	42.4352i	1.11710	+	1.93488i
$482$	1.00000			0.0455488
$483$	−12.0000			−0.546019
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	20.0000	+	34.6410i	0.908153	+	1.57297i
$486$	−1.00000			−0.0453609
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$	0.500000	+	0.866025i	0.0226339	+	0.0392031i
$489$	5.50000	−	9.52628i	0.248719	−	0.430793i
$490$	4.00000	+	6.92820i	0.180702	+	0.312984i
$491$	−13.0000	+	22.5167i	−0.586682	+	1.01616i	0.407982	+	0.912990i	$0.366233\pi$
$491$	−13.0000	+	22.5167i	−0.586682	+	1.01616i	−0.994663	+	0.103173i	$0.967101\pi$
$492$	2.00000	−	3.46410i	0.0901670	−	0.156174i
$493$		0			0
$494$	28.0000	−	12.1244i	1.25978	−	0.545501i
$495$	−8.00000			−0.359573
$496$	−0.500000	+	0.866025i	−0.0224507	+	0.0388857i
$497$	3.00000	−	5.19615i	0.134568	−	0.233079i
$498$	−6.00000	−	10.3923i	−0.268866	−	0.465690i
$499$	5.50000	−	9.52628i	0.246214	−	0.426455i	−0.716258	−	0.697835i	$-0.754147\pi$
$499$	5.50000	−	9.52628i	0.246214	−	0.426455i	0.962472	+	0.271380i	$0.0874801\pi$
$500$	12.0000	+	20.7846i	0.536656	+	0.929516i
$501$	−6.00000			−0.268060
$502$	14.0000			0.624851
$503$	6.00000	+	10.3923i	0.267527	+	0.463370i	0.968223	−	0.250090i	$-0.0804603\pi$
$503$	6.00000	+	10.3923i	0.267527	+	0.463370i	−0.700696	+	0.713460i	$0.747127\pi$
$504$	1.50000	+	2.59808i	0.0668153	+	0.115728i
$505$	−8.00000			−0.355995
$506$	−8.00000			−0.355643
$507$	18.0000	+	31.1769i	0.799408	+	1.38462i
$508$		0			0
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$	−4.50000	+	7.79423i	−0.199068	+	0.344796i
$512$	1.00000			0.0441942
$513$	4.00000	−	1.73205i	0.176604	−	0.0764719i
$514$	−28.0000			−1.23503
$515$	18.0000	−	31.1769i	0.793175	−	1.37382i
$516$	3.50000	−	6.06218i	0.154079	−	0.266872i
$517$	−2.00000	−	3.46410i	−0.0879599	−	0.152351i
$518$	10.5000	−	18.1865i	0.461344	−	0.799070i
$519$	6.00000	+	10.3923i	0.263371	+	0.456172i
$520$	28.0000			1.22788
$521$	38.0000			1.66481			0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000			1.66481			0.832405	+	0.554168i	$0.186963\pi$
$522$	−2.00000	−	3.46410i	−0.0875376	−	0.151620i
$523$	−14.5000	−	25.1147i	−0.634041	−	1.09819i	−0.986718	−	0.162446i	$-0.948062\pi$
$523$	−14.5000	−	25.1147i	−0.634041	−	1.09819i	0.352677	−	0.935745i	$-0.385272\pi$
$524$	−18.0000			−0.786334
$525$	33.0000			1.44024
$526$	9.00000	+	15.5885i	0.392419	+	0.679689i
$527$		0			0
$528$	1.00000	+	1.73205i	0.0435194	+	0.0753778i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−8.00000	+	13.8564i	−0.347498	+	0.601884i
$531$	−6.00000			−0.260378
$532$	−10.5000	−	7.79423i	−0.455233	−	0.337923i
$533$	−28.0000			−1.21281
$534$	9.00000	−	15.5885i	0.389468	−	0.674579i
$535$	4.00000	−	6.92820i	0.172935	−	0.299532i
$536$	−1.50000	−	2.59808i	−0.0647901	−	0.112220i
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$	−9.00000	−	15.5885i	−0.388018	−	0.672066i
$539$	4.00000			0.172292
$540$	4.00000			0.172133
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	0.994715	−	0.102677i	$-0.0327407\pi$
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	−0.586278	+	0.810110i	$0.699407\pi$
$542$	4.00000	+	6.92820i	0.171815	+	0.297592i
$543$	2.00000			0.0858282
$544$		0			0
$545$	12.0000	+	20.7846i	0.514024	+	0.890315i
$546$	10.5000	−	18.1865i	0.449359	−	0.778312i
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	0.989490	+	0.144604i	$0.0461907\pi$
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	−0.369514	+	0.929225i	$0.620476\pi$
$548$	1.00000	−	1.73205i	0.0427179	−	0.0739895i
$549$	0.500000	−	0.866025i	0.0213395	−	0.0369611i
$550$	22.0000			0.938083
$551$	14.0000	+	10.3923i	0.596420	+	0.442727i
$552$	4.00000			0.170251
$553$	7.50000	−	12.9904i	0.318932	−	0.552407i
$554$	13.0000	−	22.5167i	0.552317	−	0.956641i
$555$	−14.0000	−	24.2487i	−0.594267	−	1.02930i
$556$	−10.5000	+	18.1865i	−0.445299	+	0.771281i
$557$	−11.0000	−	19.0526i	−0.466085	−	0.807283i	0.533165	−	0.846011i	$-0.321003\pi$
$557$	−11.0000	−	19.0526i	−0.466085	−	0.807283i	−0.999250	+	0.0387286i	$0.987669\pi$
$558$	1.00000			0.0423334
$559$	−49.0000			−2.07248
$560$	−6.00000	−	10.3923i	−0.253546	−	0.439155i
$561$		0			0
$562$	4.00000			0.168730
$563$	−42.0000			−1.77009			−0.885044	−	0.465506i	$-0.845872\pi$
$563$	−42.0000			−1.77009			−0.885044	+	0.465506i	$0.845872\pi$
$564$	1.00000	+	1.73205i	0.0421076	+	0.0729325i
$565$	4.00000	−	6.92820i	0.168281	−	0.291472i
$566$	6.00000	+	10.3923i	0.252199	+	0.436821i
$567$	1.50000	−	2.59808i	0.0629941	−	0.109109i
$568$	−1.00000	+	1.73205i	−0.0419591	+	0.0726752i
$569$	16.0000			0.670755			0.335377	−	0.942084i	$-0.391136\pi$
$569$	16.0000			0.670755			0.335377	+	0.942084i	$0.391136\pi$
$570$	−16.0000	+	6.92820i	−0.670166	+	0.290191i
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$	7.00000	−	12.1244i	0.292685	−	0.506945i
$573$	−10.0000	+	17.3205i	−0.417756	+	0.723575i
$574$	6.00000	+	10.3923i	0.250435	+	0.433766i
$575$	22.0000	−	38.1051i	0.917463	−	1.58909i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	−17.0000			−0.707107
$579$	−10.5000	−	18.1865i	−0.436365	−	0.755807i
$580$	8.00000	+	13.8564i	0.332182	+	0.575356i
$581$	36.0000			1.49353
$582$	−10.0000			−0.414513
$583$	4.00000	+	6.92820i	0.165663	+	0.286937i
$584$	1.50000	−	2.59808i	0.0620704	−	0.107509i
$585$	−14.0000	−	24.2487i	−0.578829	−	1.00256i
$586$	9.00000	−	15.5885i	0.371787	−	0.643953i
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	−0.618322	−	0.785925i	$-0.712187\pi$
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	0.989792	+	0.142520i	$0.0455206\pi$
$588$	−2.00000			−0.0824786
$589$	−4.00000	+	1.73205i	−0.164817	+	0.0713679i
$590$	24.0000			0.988064
$591$	−5.00000	+	8.66025i	−0.205673	+	0.356235i
$592$	−3.50000	+	6.06218i	−0.143849	+	0.249154i
$593$	−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
$596$	−18.0000			−0.737309
$597$	7.00000			0.286491
$598$	−14.0000	−	24.2487i	−0.572503	−	0.991604i
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	−0.990752	−	0.135686i	$-0.956676\pi$
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	0.377869	−	0.925859i	$-0.376657\pi$
$600$	−11.0000			−0.449073
$601$	19.0000			0.775026			0.387513	−	0.921864i	$-0.373334\pi$
$601$	19.0000			0.775026			0.387513	+	0.921864i	$0.373334\pi$
$602$	10.5000	+	18.1865i	0.427948	+	0.741228i
$603$	−1.50000	+	2.59808i	−0.0610847	+	0.105802i
$604$	−10.0000	−	17.3205i	−0.406894	−	0.704761i
$605$	−14.0000	+	24.2487i	−0.569181	+	0.985850i
$606$	1.00000	−	1.73205i	0.0406222	−	0.0703598i
$607$	41.0000			1.66414			0.832069	−	0.554672i	$-0.187156\pi$
$607$	41.0000			1.66414			0.832069	+	0.554672i	$0.187156\pi$
$608$	3.50000	+	2.59808i	0.141944	+	0.105366i
$609$	12.0000			0.486265
$610$	−2.00000	+	3.46410i	−0.0809776	+	0.140257i
$611$	7.00000	−	12.1244i	0.283190	−	0.490499i
$612$		0			0
$613$	19.0000	−	32.9090i	0.767403	−	1.32918i	−0.171564	−	0.985173i	$-0.554882\pi$
$613$	19.0000	−	32.9090i	0.767403	−	1.32918i	0.938967	−	0.344008i	$-0.111785\pi$
$614$	−6.00000	−	10.3923i	−0.242140	−	0.419399i
$615$	16.0000			0.645182
$616$	−6.00000			−0.241747
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	0.626017	−	0.779809i	$-0.284684\pi$
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	−0.988343	+	0.152242i	$0.951351\pi$
$618$	4.50000	+	7.79423i	0.181017	+	0.313530i
$619$	−23.0000			−0.924448			−0.462224	−	0.886763i	$-0.652948\pi$
$619$	−23.0000			−0.924448			−0.462224	+	0.886763i	$0.652948\pi$
$620$	−4.00000			−0.160644
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$	−17.0000	+	29.4449i	−0.681638	+	1.18063i
$623$	27.0000	+	46.7654i	1.08173	+	1.87362i
$624$	−3.50000	+	6.06218i	−0.140112	+	0.242681i
$625$	−20.5000	+	35.5070i	−0.820000	+	1.42028i
$626$	14.0000			0.559553
$627$	−1.00000	+	8.66025i	−0.0399362	+	0.345857i
$628$	7.00000			0.279330
$629$		0			0
$630$	−6.00000	+	10.3923i	−0.239046	+	0.414039i
$631$	9.50000	+	16.4545i	0.378189	+	0.655043i	0.990799	−	0.135343i	$-0.0432136\pi$
$631$	9.50000	+	16.4545i	0.378189	+	0.655043i	−0.612610	+	0.790386i	$0.709880\pi$
$632$	−2.50000	+	4.33013i	−0.0994447	+	0.172243i
$633$	4.50000	+	7.79423i	0.178859	+	0.309793i
$634$	−24.0000			−0.953162
$635$		0			0
$636$	−2.00000	−	3.46410i	−0.0793052	−	0.137361i
$637$	7.00000	+	12.1244i	0.277350	+	0.480384i
$638$	8.00000			0.316723
$639$	2.00000			0.0791188
$640$	2.00000	+	3.46410i	0.0790569	+	0.136931i
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$	1.00000	+	1.73205i	0.0394669	+	0.0683586i
$643$	−6.50000	+	11.2583i	−0.256335	+	0.443985i	−0.965257	−	0.261301i	$-0.915848\pi$
$643$	−6.50000	+	11.2583i	−0.256335	+	0.443985i	0.708922	+	0.705287i	$0.249182\pi$
$644$	−6.00000	+	10.3923i	−0.236433	+	0.409514i
$645$	28.0000			1.10250
$646$		0			0
$647$	−28.0000			−1.10079			−0.550397	−	0.834903i	$-0.685524\pi$
$647$	−28.0000			−1.10079			−0.550397	+	0.834903i	$0.685524\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	6.00000	−	10.3923i	0.235521	−	0.407934i
$650$	38.5000	+	66.6840i	1.51009	+	2.61556i
$651$	−1.50000	+	2.59808i	−0.0587896	+	0.101827i
$652$	−5.50000	−	9.52628i	−0.215397	−	0.373078i
$653$	−30.0000			−1.17399			−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000			−1.17399			−0.586995	+	0.809590i	$0.699689\pi$
$654$	−6.00000			−0.234619
$655$	−36.0000	−	62.3538i	−1.40664	−	2.43637i
$656$	−2.00000	−	3.46410i	−0.0780869	−	0.135250i
$657$	−3.00000			−0.117041
$658$	−6.00000			−0.233904
$659$	5.00000	+	8.66025i	0.194772	+	0.337356i	0.946826	−	0.321746i	$-0.104270\pi$
$659$	5.00000	+	8.66025i	0.194772	+	0.337356i	−0.752054	+	0.659102i	$0.770937\pi$
$660$	−4.00000	+	6.92820i	−0.155700	+	0.269680i
$661$	−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	$0.895634\pi$
$662$	−11.5000	+	19.9186i	−0.446960	+	0.774158i
$663$		0			0
$664$	−12.0000			−0.465690
$665$	6.00000	−	51.9615i	0.232670	−	2.01498i
$666$	7.00000			0.271244
$667$	8.00000	−	13.8564i	0.309761	−	0.536522i
$668$	−3.00000	+	5.19615i	−0.116073	+	0.201045i
$669$	2.50000	+	4.33013i	0.0966556	+	0.167412i
$670$	6.00000	−	10.3923i	0.231800	−	0.401490i
$671$	1.00000	+	1.73205i	0.0386046	+	0.0668651i
$672$	3.00000			0.115728
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$	−6.50000	−	11.2583i	−0.250371	−	0.433655i
$675$	5.50000	+	9.52628i	0.211695	+	0.366667i
$676$	36.0000			1.38462
$677$	−38.0000			−1.46046			−0.730229	−	0.683202i	$-0.760587\pi$
$677$	−38.0000			−1.46046			−0.730229	+	0.683202i	$0.760587\pi$
$678$	1.00000	+	1.73205i	0.0384048	+	0.0665190i
$679$	15.0000	−	25.9808i	0.575647	−	0.997050i
$680$		0			0
$681$	2.00000	−	3.46410i	0.0766402	−	0.132745i
$682$	−1.00000	+	1.73205i	−0.0382920	+	0.0663237i
$683$	40.0000			1.53056			0.765279	−	0.643699i	$-0.222601\pi$
$683$	40.0000			1.53056			0.765279	+	0.643699i	$0.222601\pi$
$684$	0.500000	−	4.33013i	0.0191180	−	0.165567i
$685$	8.00000			0.305664
$686$	−7.50000	+	12.9904i	−0.286351	+	0.495975i
$687$	−3.50000	+	6.06218i	−0.133533	+	0.231287i
$688$	−3.50000	−	6.06218i	−0.133436	−	0.231118i
$689$	−14.0000	+	24.2487i	−0.533358	+	0.923802i
$690$	8.00000	+	13.8564i	0.304555	+	0.527504i
$691$	12.0000			0.456502			0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000			0.456502			0.228251	+	0.973602i	$0.426699\pi$
$692$	12.0000			0.456172
$693$	3.00000	+	5.19615i	0.113961	+	0.197386i
$694$	−14.0000	−	24.2487i	−0.531433	−	0.920468i
$695$	−84.0000			−3.18630
$696$	−4.00000			−0.151620
$697$		0			0
$698$	−15.5000	+	26.8468i	−0.586684	+	1.01617i
$699$	3.00000	+	5.19615i	0.113470	+	0.196537i
$700$	16.5000	−	28.5788i	0.623641	−	1.08018i
$701$	−4.00000	+	6.92820i	−0.151078	+	0.261675i	−0.931624	−	0.363424i	$-0.881608\pi$
$701$	−4.00000	+	6.92820i	−0.151078	+	0.261675i	0.780546	+	0.625098i	$0.214941\pi$
$702$	7.00000			0.264198
$703$	−28.0000	+	12.1244i	−1.05604	+	0.457279i
$704$	2.00000			0.0753778
$705$	−4.00000	+	6.92820i	−0.150649	+	0.260931i
$706$		0			0
$707$	3.00000	+	5.19615i	0.112827	+	0.195421i
$708$	−3.00000	+	5.19615i	−0.112747	+	0.195283i
$709$	1.50000	+	2.59808i	0.0563337	+	0.0975728i	0.892817	−	0.450420i	$-0.148726\pi$
$709$	1.50000	+	2.59808i	0.0563337	+	0.0975728i	−0.836483	+	0.547992i	$0.815392\pi$
$710$	−8.00000			−0.300235
$711$	5.00000			0.187515
$712$	−9.00000	−	15.5885i	−0.337289	−	0.584202i
$713$	2.00000	+	3.46410i	0.0749006	+	0.129732i
$714$		0			0
$715$	56.0000			2.09428
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$	12.0000	−	20.7846i	0.448148	−	0.776215i
$718$	6.00000	+	10.3923i	0.223918	+	0.387837i
$719$	−8.00000	+	13.8564i	−0.298350	+	0.516757i	−0.975759	−	0.218850i	$-0.929769\pi$
$719$	−8.00000	+	13.8564i	−0.298350	+	0.516757i	0.677409	+	0.735607i	$0.263103\pi$
$720$	2.00000	−	3.46410i	0.0745356	−	0.129099i
$721$	−27.0000			−1.00553
$722$	5.50000	+	18.1865i	0.204689	+	0.676833i
$723$	−1.00000			−0.0371904
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$	−22.0000	+	38.1051i	−0.817059	+	1.41519i
$726$	−3.50000	−	6.06218i	−0.129897	−	0.224989i
$727$	−18.5000	+	32.0429i	−0.686127	+	1.18841i	0.286954	+	0.957944i	$0.407357\pi$
$727$	−18.5000	+	32.0429i	−0.686127	+	1.18841i	−0.973081	+	0.230463i	$0.925976\pi$
$728$	−10.5000	−	18.1865i	−0.389156	−	0.674038i
$729$	1.00000			0.0370370
$730$	12.0000			0.444140
$731$		0			0
$732$	−0.500000	−	0.866025i	−0.0184805	−	0.0320092i
$733$	30.0000			1.10808			0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000			1.10808			0.554038	+	0.832492i	$0.313086\pi$
$734$	19.0000			0.701303
$735$	−4.00000	−	6.92820i	−0.147542	−	0.255551i
$736$	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
$739$	−17.5000	+	30.3109i	−0.643748	+	1.11500i	0.340841	+	0.940121i	$0.389288\pi$
$739$	−17.5000	+	30.3109i	−0.643748	+	1.11500i	−0.984589	+	0.174883i	$0.944045\pi$
$740$	−28.0000			−1.02930
$741$	−28.0000	+	12.1244i	−1.02861	+	0.445399i
$742$	12.0000			0.440534
$743$	−13.0000	+	22.5167i	−0.476924	+	0.826056i	−0.999650	−	0.0264443i	$-0.991582\pi$
$743$	−13.0000	+	22.5167i	−0.476924	+	0.826056i	0.522727	+	0.852500i	$0.324915\pi$
$744$	0.500000	−	0.866025i	0.0183309	−	0.0317500i
$745$	−36.0000	−	62.3538i	−1.31894	−	2.28447i
$746$	11.0000	−	19.0526i	0.402739	−	0.697564i
$747$	6.00000	+	10.3923i	0.219529	+	0.380235i
$748$		0			0
$749$	−6.00000			−0.219235
$750$	−12.0000	−	20.7846i	−0.438178	−	0.758947i
$751$	15.5000	+	26.8468i	0.565603	+	0.979653i	0.996993	+	0.0774878i	$0.0246899\pi$
$751$	15.5000	+	26.8468i	0.565603	+	0.979653i	−0.431390	+	0.902165i	$0.641977\pi$
$752$	2.00000			0.0729325
$753$	−14.0000			−0.510188
$754$	14.0000	+	24.2487i	0.509850	+	0.883086i
$755$	40.0000	−	69.2820i	1.45575	−	2.52143i
$756$	−1.50000	−	2.59808i	−0.0545545	−	0.0944911i
$757$	11.5000	−	19.9186i	0.417975	−	0.723953i	−0.577761	−	0.816206i	$-0.696073\pi$
$757$	11.5000	−	19.9186i	0.417975	−	0.723953i	0.995736	+	0.0922527i	$0.0294068\pi$
$758$	10.5000	−	18.1865i	0.381377	−	0.660565i
$759$	8.00000			0.290382
$760$	−2.00000	+	17.3205i	−0.0725476	+	0.628281i
$761$	−42.0000			−1.52250			−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000			−1.52250			−0.761249	+	0.648459i	$0.775414\pi$
$762$		0			0
$763$	9.00000	−	15.5885i	0.325822	−	0.564340i
$764$	10.0000	+	17.3205i	0.361787	+	0.626634i
$765$		0			0
$766$	7.00000	+	12.1244i	0.252920	+	0.438071i
$767$	42.0000			1.51653
$768$	−1.00000			−0.0360844
$769$	2.50000	+	4.33013i	0.0901523	+	0.156148i	0.907575	−	0.419890i	$-0.137931\pi$
$769$	2.50000	+	4.33013i	0.0901523	+	0.156148i	−0.817423	+	0.576038i	$0.804598\pi$
$770$	−12.0000	−	20.7846i	−0.432450	−	0.749025i
$771$	28.0000			1.00840
$772$	−21.0000			−0.755807
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	0.807018	−	0.590527i	$-0.201080\pi$
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	−0.914920	+	0.403634i	$0.867747\pi$
$774$	−3.50000	+	6.06218i	−0.125805	+	0.217900i
$775$	−5.50000	−	9.52628i	−0.197566	−	0.342194i
$776$	−5.00000	+	8.66025i	−0.179490	+	0.310885i
$777$	−10.5000	+	18.1865i	−0.376685	+	0.652438i
$778$	−24.0000			−0.860442
$779$	2.00000	−	17.3205i	0.0716574	−	0.620572i
$780$	−28.0000			−1.00256
$781$	−2.00000	+	3.46410i	−0.0715656	+	0.123955i
$782$		0			0
$783$	2.00000	+	3.46410i	0.0714742	+	0.123797i
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$	14.0000	+	24.2487i	0.499681	+	0.865474i
$786$	18.0000			0.642039
$787$	49.0000			1.74666			0.873331	−	0.487128i	$-0.161955\pi$
$787$	49.0000			1.74666			0.873331	+	0.487128i	$0.161955\pi$
$788$	5.00000	+	8.66025i	0.178118	+	0.308509i
$789$	−9.00000	−	15.5885i	−0.320408	−	0.554964i
$790$	−20.0000			−0.711568
$791$	−6.00000			−0.213335
$792$	−1.00000	−	1.73205i	−0.0355335	−	0.0615457i
$793$	−3.50000	+	6.06218i	−0.124289	+	0.215274i
$794$	6.50000	+	11.2583i	0.230676	+	0.399543i
$795$	8.00000	−	13.8564i	0.283731	−	0.491436i
$796$	3.50000	−	6.06218i	0.124054	−	0.214868i
$797$	6.00000			0.212531			0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000			0.212531			0.106265	+	0.994338i	$0.466111\pi$
$798$	10.5000	+	7.79423i	0.371696	+	0.275913i
$799$		0			0
$800$	−5.50000	+	9.52628i	−0.194454	+	0.336805i
$801$	−9.00000	+	15.5885i	−0.317999	+	0.550791i
$802$	−5.00000	−	8.66025i	−0.176556	−	0.305804i
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$	1.50000	+	2.59808i	0.0529009	+	0.0916271i
$805$	−48.0000			−1.69178
$806$	−7.00000			−0.246564
$807$	9.00000	+	15.5885i	0.316815	+	0.548740i
$808$	−1.00000	−	1.73205i	−0.0351799	−	0.0609333i
$809$	36.0000			1.26569			0.632846	−	0.774277i	$-0.281886\pi$
$809$	36.0000			1.26569			0.632846	+	0.774277i	$0.281886\pi$
$810$	−4.00000			−0.140546
$811$	−18.0000	−	31.1769i	−0.632065	−	1.09477i	−0.987129	−	0.159927i	$-0.948874\pi$
$811$	−18.0000	−	31.1769i	−0.632065	−	1.09477i	0.355063	−	0.934842i	$-0.384459\pi$
$812$	6.00000	−	10.3923i	0.210559	−	0.364698i
$813$	−4.00000	−	6.92820i	−0.140286	−	0.242983i
$814$	−7.00000	+	12.1244i	−0.245350	+	0.424958i
$815$	22.0000	−	38.1051i	0.770626	−	1.33476i
$816$		0			0
$817$	3.50000	−	30.3109i	0.122449	−	1.06044i
$818$	10.0000			0.349642
$819$	−10.5000	+	18.1865i	−0.366900	+	0.635489i
$820$	8.00000	−	13.8564i	0.279372	−	0.483887i
$821$	−6.00000	−	10.3923i	−0.209401	−	0.362694i	0.742125	−	0.670262i	$-0.233818\pi$
$821$	−6.00000	−	10.3923i	−0.209401	−	0.362694i	−0.951526	+	0.307568i	$0.900485\pi$
$822$	−1.00000	+	1.73205i	−0.0348790	+	0.0604122i
$823$	−22.0000	−	38.1051i	−0.766872	−	1.32826i	−0.939251	−	0.343230i	$-0.888479\pi$
$823$	−22.0000	−	38.1051i	−0.766872	−	1.32826i	0.172379	−	0.985031i	$-0.444854\pi$
$824$	9.00000			0.313530
$825$	−22.0000			−0.765942
$826$	−9.00000	−	15.5885i	−0.313150	−	0.542392i
$827$	−4.00000	−	6.92820i	−0.139094	−	0.240917i	0.788060	−	0.615598i	$-0.211086\pi$
$827$	−4.00000	−	6.92820i	−0.139094	−	0.240917i	−0.927154	+	0.374681i	$0.877752\pi$
$828$	−4.00000			−0.139010
$829$	45.0000			1.56291			0.781457	−	0.623959i	$-0.214477\pi$
$829$	45.0000			1.56291			0.781457	+	0.623959i	$0.214477\pi$
$830$	−24.0000	−	41.5692i	−0.833052	−	1.44289i
$831$	−13.0000	+	22.5167i	−0.450965	+	0.781094i
$832$	3.50000	+	6.06218i	0.121341	+	0.210168i
$833$		0			0
$834$	10.5000	−	18.1865i	0.363585	−	0.629748i
$835$	−24.0000			−0.830554
$836$	7.00000	+	5.19615i	0.242100	+	0.179713i
$837$	−1.00000			−0.0345651
$838$	−15.0000	+	25.9808i	−0.518166	+	0.897491i
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	−0.281205	−	0.959648i	$-0.590734\pi$
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	0.971682	−	0.236293i	$-0.0759325\pi$
$840$	6.00000	+	10.3923i	0.207020	+	0.358569i
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	−13.0000	−	22.5167i	−0.448010	−	0.775975i
$843$	−4.00000			−0.137767
$844$	9.00000			0.309793
$845$	72.0000	+	124.708i	2.47688	+	4.29007i
$846$	−1.00000	−	1.73205i	−0.0343807	−	0.0595491i
$847$	21.0000			0.721569
$848$	−4.00000			−0.137361
$849$	−6.00000	−	10.3923i	−0.205919	−	0.356663i
$850$		0			0
$851$	14.0000	+	24.2487i	0.479914	+	0.831235i
$852$	1.00000	−	1.73205i	0.0342594	−	0.0593391i
$853$	4.50000	−	7.79423i	0.154077	−	0.266869i	−0.778646	−	0.627464i	$-0.784093\pi$
$853$	4.50000	−	7.79423i	0.154077	−	0.266869i	0.932723	+	0.360595i	$0.117426\pi$
$854$	3.00000			0.102658
$855$	16.0000	−	6.92820i	0.547188	−	0.236940i
$856$	2.00000			0.0683586
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	−0.810227	−	0.586116i	$-0.800656\pi$
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	0.912705	+	0.408619i	$0.133990\pi$
$858$	−7.00000	+	12.1244i	−0.238976	+	0.413919i
$859$	−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	$0.871436\pi$
$860$	14.0000	−	24.2487i	0.477396	−	0.826874i
$861$	−6.00000	−	10.3923i	−0.204479	−	0.354169i
$862$	6.00000			0.204361
$863$	−6.00000			−0.204242			−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000			−0.204242			−0.102121	+	0.994772i	$0.532563\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	24.0000	+	41.5692i	0.816024	+	1.41340i
$866$	23.0000			0.781572
$867$	17.0000			0.577350
$868$	1.50000	+	2.59808i	0.0509133	+	0.0881845i
$869$	−5.00000	+	8.66025i	−0.169613	+	0.293779i
$870$	−8.00000	−	13.8564i	−0.271225	−	0.469776i
$871$	10.5000	−	18.1865i	0.355779	−	0.616227i
$872$	−3.00000	+	5.19615i	−0.101593	+	0.175964i
$873$	10.0000			0.338449
$874$	16.0000	−	6.92820i	0.541208	−	0.234350i
$875$	72.0000			2.43404
$876$	−1.50000	+	2.59808i	−0.0506803	+	0.0877809i
$877$	−9.50000	+	16.4545i	−0.320792	+	0.555628i	−0.980652	−	0.195761i	$-0.937282\pi$
$877$	−9.50000	+	16.4545i	−0.320792	+	0.555628i	0.659860	+	0.751389i	$0.270616\pi$
$878$	−11.5000	−	19.9186i	−0.388106	−	0.672220i
$879$	−9.00000	+	15.5885i	−0.303562	+	0.525786i
$880$	4.00000	+	6.92820i	0.134840	+	0.233550i
$881$	−24.0000			−0.808581			−0.404290	−	0.914631i	$-0.632481\pi$
$881$	−24.0000			−0.808581			−0.404290	+	0.914631i	$0.632481\pi$
$882$	2.00000			0.0673435
$883$	20.5000	+	35.5070i	0.689880	+	1.19491i	0.971876	+	0.235492i	$0.0756700\pi$
$883$	20.5000	+	35.5070i	0.689880	+	1.19491i	−0.281996	+	0.959415i	$0.590997\pi$
$884$		0			0
$885$	−24.0000			−0.806751
$886$	4.00000			0.134383
$887$	−5.00000	−	8.66025i	−0.167884	−	0.290783i	0.769792	−	0.638295i	$-0.220360\pi$
$887$	−5.00000	−	8.66025i	−0.167884	−	0.290783i	−0.937676	+	0.347512i	$0.887027\pi$
$888$	3.50000	−	6.06218i	0.117452	−	0.203433i
$889$		0			0
$890$	36.0000	−	62.3538i	1.20672	−	2.09011i
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$	5.00000			0.167412
$893$	7.00000	+	5.19615i	0.234246	+	0.173883i
$894$	18.0000			0.602010
$895$	−24.0000	+	41.5692i	−0.802232	+	1.38951i
$896$	1.50000	−	2.59808i	0.0501115	−	0.0867956i
$897$	14.0000	+	24.2487i	0.467446	+	0.809641i
$898$	−8.00000	+	13.8564i	−0.266963	+	0.462394i
$899$	−2.00000	−	3.46410i	−0.0667037	−	0.115534i
$900$	11.0000			0.366667
$901$		0			0
$902$	−4.00000	−	6.92820i	−0.133185	−	0.230684i
$903$	−10.5000	−	18.1865i	−0.349418	−	0.605210i
$904$	2.00000			0.0665190
$905$	8.00000			0.265929
$906$	10.0000	+	17.3205i	0.332228	+	0.575435i
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	−0.982913	−	0.184073i	$-0.941072\pi$
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	0.650868	+	0.759191i	$0.274405\pi$
$908$	−2.00000	−	3.46410i	−0.0663723	−	0.114960i
$909$	−1.00000	+	1.73205i	−0.0331679	+	0.0574485i
$910$	42.0000	−	72.7461i	1.39229	−	2.41151i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	−3.50000	−	2.59808i	−0.115897	−	0.0860309i
$913$	−24.0000			−0.794284
$914$	−14.5000	+	25.1147i	−0.479617	+	0.830722i
$915$	2.00000	−	3.46410i	0.0661180	−	0.114520i
$916$	3.50000	+	6.06218i	0.115643	+	0.200300i
$917$	−27.0000	+	46.7654i	−0.891619	+	1.54433i
$918$		0			0
$919$	11.0000			0.362857			0.181428	−	0.983404i	$-0.441928\pi$
$919$	11.0000			0.362857			0.181428	+	0.983404i	$0.441928\pi$
$920$	16.0000			0.527504
$921$	6.00000	+	10.3923i	0.197707	+	0.342438i
$922$	17.0000	+	29.4449i	0.559865	+	0.969715i
$923$	−14.0000			−0.460816
$924$	6.00000			0.197386
$925$	−38.5000	−	66.6840i	−1.26587	−	2.19255i
$926$	−9.50000	+	16.4545i	−0.312189	+	0.540728i
$927$	−4.50000	−	7.79423i	−0.147799	−	0.255996i
$928$	−2.00000	+	3.46410i	−0.0656532	+	0.113715i
$929$	−4.00000	+	6.92820i	−0.131236	+	0.227307i	−0.924153	−	0.382022i	$-0.875228\pi$
$929$	−4.00000	+	6.92820i	−0.131236	+	0.227307i	0.792917	+	0.609329i	$0.208561\pi$
$930$	4.00000			0.131165
$931$	−8.00000	+	3.46410i	−0.262189	+	0.113531i
$932$	6.00000			0.196537
$933$	17.0000	−	29.4449i	0.556555	−	0.963982i
$934$	4.00000	−	6.92820i	0.130884	−	0.226698i
$935$		0			0
$936$	3.50000	−	6.06218i	0.114401	−	0.198148i
$937$	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	$0.699435\pi$
$938$	−9.00000			−0.293860
$939$	−14.0000			−0.456873
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	−8.00000	−	13.8564i	−0.260793	−	0.451706i	0.705660	−	0.708550i	$-0.250651\pi$
$941$	−8.00000	−	13.8564i	−0.260793	−	0.451706i	−0.966453	+	0.256844i	$0.917317\pi$
$942$	−7.00000			−0.228072
$943$	−16.0000			−0.521032
$944$	3.00000	+	5.19615i	0.0976417	+	0.169120i
$945$	6.00000	−	10.3923i	0.195180	−	0.338062i
$946$	−7.00000	−	12.1244i	−0.227590	−	0.394197i
$947$	−27.0000	+	46.7654i	−0.877382	+	1.51967i	−0.0231788	+	0.999731i	$0.507379\pi$
$947$	−27.0000	+	46.7654i	−0.877382	+	1.51967i	−0.854203	+	0.519939i	$0.825955\pi$
$948$	2.50000	−	4.33013i	0.0811962	−	0.140636i
$949$	21.0000			0.681689
$950$	−44.0000	+	19.0526i	−1.42755	+	0.618147i
$951$	24.0000			0.778253
$952$		0			0
$953$	5.00000	−	8.66025i	0.161966	−	0.280533i	−0.773608	−	0.633665i	$-0.781550\pi$
$953$	5.00000	−	8.66025i	0.161966	−	0.280533i	0.935574	+	0.353132i	$0.114883\pi$
$954$	2.00000	+	3.46410i	0.0647524	+	0.112154i
$955$	−40.0000	+	69.2820i	−1.29437	+	2.24191i
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$	−8.00000			−0.258603
$958$	34.0000			1.09849
$959$	−3.00000	−	5.19615i	−0.0968751	−	0.167793i
$960$	−2.00000	−	3.46410i	−0.0645497	−	0.111803i
$961$	−30.0000			−0.967742
$962$	−49.0000			−1.57982
$963$	−1.00000	−	1.73205i	−0.0322245	−	0.0558146i
$964$	−0.500000	+	0.866025i	−0.0161039	+	0.0278928i
$965$	−42.0000	−	72.7461i	−1.35203	−	2.34178i
$966$	6.00000	−	10.3923i	0.193047	−	0.334367i
$967$	4.50000	−	7.79423i	0.144710	−	0.250645i	−0.784555	−	0.620060i	$-0.787108\pi$
$967$	4.50000	−	7.79423i	0.144710	−	0.250645i	0.929265	+	0.369414i	$0.120442\pi$
$968$	−7.00000			−0.224989
$969$		0			0
$970$	−40.0000			−1.28432
$971$	−7.00000	+	12.1244i	−0.224641	+	0.389089i	−0.956212	−	0.292676i	$-0.905454\pi$
$971$	−7.00000	+	12.1244i	−0.224641	+	0.389089i	0.731571	+	0.681765i	$0.238788\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	31.5000	+	54.5596i	1.00984	+	1.74910i
$974$	−8.00000	+	13.8564i	−0.256337	+	0.443988i
$975$	−38.5000	−	66.6840i	−1.23299	−	2.13560i
$976$	−1.00000			−0.0320092
$977$	14.0000			0.447900			0.223950	−	0.974601i	$-0.428105\pi$
$977$	14.0000			0.447900			0.223950	+	0.974601i	$0.428105\pi$
$978$	5.50000	+	9.52628i	0.175871	+	0.304617i
$979$	−18.0000	−	31.1769i	−0.575282	−	0.996419i
$980$	−8.00000			−0.255551
$981$	6.00000			0.191565
$982$	−13.0000	−	22.5167i	−0.414847	−	0.718536i
$983$	−3.00000	+	5.19615i	−0.0956851	+	0.165732i	−0.909894	−	0.414840i	$-0.863838\pi$
$983$	−3.00000	+	5.19615i	−0.0956851	+	0.165732i	0.814209	+	0.580572i	$0.197171\pi$
$984$	2.00000	+	3.46410i	0.0637577	+	0.110432i
$985$	−20.0000	+	34.6410i	−0.637253	+	1.10375i
$986$		0			0
$987$	6.00000			0.190982
$988$	−3.50000	+	30.3109i	−0.111350	+	0.964318i
$989$	−28.0000			−0.890348
$990$	4.00000	−	6.92820i	0.127128	−	0.220193i
$991$	14.5000	−	25.1147i	0.460608	−	0.797796i	−0.538384	−	0.842700i	$-0.680965\pi$
$991$	14.5000	−	25.1147i	0.460608	−	0.797796i	0.998991	+	0.0449040i	$0.0142982\pi$
$992$	−0.500000	−	0.866025i	−0.0158750	−	0.0274963i
$993$	11.5000	−	19.9186i	0.364941	−	0.632097i
$994$	3.00000	+	5.19615i	0.0951542	+	0.164812i
$995$	28.0000			0.887660
$996$	12.0000			0.380235
$997$	26.5000	+	45.8993i	0.839263	+	1.45365i	0.890511	+	0.454961i	$0.150347\pi$
$997$	26.5000	+	45.8993i	0.839263	+	1.45365i	−0.0512480	+	0.998686i	$0.516320\pi$
$998$	5.50000	+	9.52628i	0.174099	+	0.301549i
$999$	−7.00000			−0.221470

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} -3.00000 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} -3.00000 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{10} +2.00000 q^{11} -1.00000 q^{12} +(3.50000 + 6.06218i) q^{13} +(1.50000 - 2.59808i) q^{14} +(-2.00000 - 3.46410i) q^{15} +(-0.500000 + 0.866025i) q^{16} +1.00000 q^{18} +(-4.00000 + 1.73205i) q^{19} -4.00000 q^{20} +(-1.50000 + 2.59808i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-5.50000 - 9.52628i) q^{25} -7.00000 q^{26} -1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +(-2.00000 - 3.46410i) q^{29} +4.00000 q^{30} +1.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} +(-6.00000 + 10.3923i) q^{35} +(-0.500000 + 0.866025i) q^{36} +7.00000 q^{37} +(0.500000 - 4.33013i) q^{38} +7.00000 q^{39} +(2.00000 - 3.46410i) q^{40} +(-2.00000 + 3.46410i) q^{41} +(-1.50000 - 2.59808i) q^{42} +(-3.50000 + 6.06218i) q^{43} +(-1.00000 - 1.73205i) q^{44} -4.00000 q^{45} -4.00000 q^{46} +(-1.00000 - 1.73205i) q^{47} +(0.500000 + 0.866025i) q^{48} +2.00000 q^{49} +11.0000 q^{50} +(3.50000 - 6.06218i) q^{52} +(2.00000 + 3.46410i) q^{53} +(0.500000 - 0.866025i) q^{54} +(4.00000 - 6.92820i) q^{55} -3.00000 q^{56} +(-0.500000 + 4.33013i) q^{57} +4.00000 q^{58} +(3.00000 - 5.19615i) q^{59} +(-2.00000 + 3.46410i) q^{60} +(0.500000 + 0.866025i) q^{61} +(-0.500000 + 0.866025i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +28.0000 q^{65} +(1.00000 + 1.73205i) q^{66} +(-1.50000 - 2.59808i) q^{67} +4.00000 q^{69} +(-6.00000 - 10.3923i) q^{70} +(-1.00000 + 1.73205i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.50000 - 2.59808i) q^{73} +(-3.50000 + 6.06218i) q^{74} -11.0000 q^{75} +(3.50000 + 2.59808i) q^{76} -6.00000 q^{77} +(-3.50000 + 6.06218i) q^{78} +(-2.50000 + 4.33013i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.00000 - 3.46410i) q^{82} -12.0000 q^{83} +3.00000 q^{84} +(-3.50000 - 6.06218i) q^{86} -4.00000 q^{87} +2.00000 q^{88} +(-9.00000 - 15.5885i) q^{89} +(2.00000 - 3.46410i) q^{90} +(-10.5000 - 18.1865i) q^{91} +(2.00000 - 3.46410i) q^{92} +(0.500000 - 0.866025i) q^{93} +2.00000 q^{94} +(-2.00000 + 17.3205i) q^{95} -1.00000 q^{96} +(-5.00000 + 8.66025i) q^{97} +(-1.00000 + 1.73205i) q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} + 4 q^{5} + q^{6} - 6 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 + 4 * q^5 + q^6 - 6 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} + 4 q^{5} + q^{6} - 6 q^{7} + 2 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 2 q^{12} + 7 q^{13} + 3 q^{14} - 4 q^{15} - q^{16} + 2 q^{18} - 8 q^{19} - 8 q^{20} - 3 q^{21} - 2 q^{22} + 4 q^{23} + q^{24} - 11 q^{25} - 14 q^{26} - 2 q^{27} + 3 q^{28} - 4 q^{29} + 8 q^{30} + 2 q^{31} - q^{32} + 2 q^{33} - 12 q^{35} - q^{36} + 14 q^{37} + q^{38} + 14 q^{39} + 4 q^{40} - 4 q^{41} - 3 q^{42} - 7 q^{43} - 2 q^{44} - 8 q^{45} - 8 q^{46} - 2 q^{47} + q^{48} + 4 q^{49} + 22 q^{50} + 7 q^{52} + 4 q^{53} + q^{54} + 8 q^{55} - 6 q^{56} - q^{57} + 8 q^{58} + 6 q^{59} - 4 q^{60} + q^{61} - q^{62} + 3 q^{63} + 2 q^{64} + 56 q^{65} + 2 q^{66} - 3 q^{67} + 8 q^{69} - 12 q^{70} - 2 q^{71} - q^{72} + 3 q^{73} - 7 q^{74} - 22 q^{75} + 7 q^{76} - 12 q^{77} - 7 q^{78} - 5 q^{79} + 4 q^{80} - q^{81} - 4 q^{82} - 24 q^{83} + 6 q^{84} - 7 q^{86} - 8 q^{87} + 4 q^{88} - 18 q^{89} + 4 q^{90} - 21 q^{91} + 4 q^{92} + q^{93} + 4 q^{94} - 4 q^{95} - 2 q^{96} - 10 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 + 4 * q^5 + q^6 - 6 * q^7 + 2 * q^8 - q^9 + 4 * q^10 + 4 * q^11 - 2 * q^12 + 7 * q^13 + 3 * q^14 - 4 * q^15 - q^16 + 2 * q^18 - 8 * q^19 - 8 * q^20 - 3 * q^21 - 2 * q^22 + 4 * q^23 + q^24 - 11 * q^25 - 14 * q^26 - 2 * q^27 + 3 * q^28 - 4 * q^29 + 8 * q^30 + 2 * q^31 - q^32 + 2 * q^33 - 12 * q^35 - q^36 + 14 * q^37 + q^38 + 14 * q^39 + 4 * q^40 - 4 * q^41 - 3 * q^42 - 7 * q^43 - 2 * q^44 - 8 * q^45 - 8 * q^46 - 2 * q^47 + q^48 + 4 * q^49 + 22 * q^50 + 7 * q^52 + 4 * q^53 + q^54 + 8 * q^55 - 6 * q^56 - q^57 + 8 * q^58 + 6 * q^59 - 4 * q^60 + q^61 - q^62 + 3 * q^63 + 2 * q^64 + 56 * q^65 + 2 * q^66 - 3 * q^67 + 8 * q^69 - 12 * q^70 - 2 * q^71 - q^72 + 3 * q^73 - 7 * q^74 - 22 * q^75 + 7 * q^76 - 12 * q^77 - 7 * q^78 - 5 * q^79 + 4 * q^80 - q^81 - 4 * q^82 - 24 * q^83 + 6 * q^84 - 7 * q^86 - 8 * q^87 + 4 * q^88 - 18 * q^89 + 4 * q^90 - 21 * q^91 + 4 * q^92 + q^93 + 4 * q^94 - 4 * q^95 - 2 * q^96 - 10 * q^97 - 2 * q^98 - 2 * q^99

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