LMFDB - Embedded newform 966.2.i.g.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(277,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
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			277.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	966.277
Dual form			966.2.i.g.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(1.00000 - 1.73205i) q^{11} +(0.500000 + 0.866025i) q^{12} +3.00000 q^{13} +(0.500000 + 2.59808i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{18} -3.00000 q^{20} +(2.00000 - 1.73205i) q^{21} +2.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(1.50000 + 2.59808i) q^{26} -1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} -8.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(-5.00000 + 8.66025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +3.00000 q^{34} +(1.50000 + 7.79423i) q^{35} +1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(1.50000 - 2.59808i) q^{39} +(-1.50000 - 2.59808i) q^{40} +8.00000 q^{41} +(2.50000 + 0.866025i) q^{42} -4.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(1.50000 - 2.59808i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-4.50000 - 7.79423i) q^{47} -1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -4.00000 q^{50} +(-1.50000 - 2.59808i) q^{51} +(-1.50000 + 2.59808i) q^{52} +(4.50000 - 7.79423i) q^{53} +(-0.500000 - 0.866025i) q^{54} +6.00000 q^{55} +(-2.50000 - 0.866025i) q^{56} +(-4.00000 - 6.92820i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(3.00000 + 5.19615i) q^{61} -10.0000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(4.50000 + 7.79423i) q^{65} +(1.00000 - 1.73205i) q^{66} +(-1.50000 + 2.59808i) q^{67} +(1.50000 + 2.59808i) q^{68} +1.00000 q^{69} +(-6.00000 + 5.19615i) q^{70} +7.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-1.50000 + 2.59808i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(2.00000 + 3.46410i) q^{75} +(4.00000 - 3.46410i) q^{77} +3.00000 q^{78} +(-2.00000 - 3.46410i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.00000 + 6.92820i) q^{82} -14.0000 q^{83} +(0.500000 + 2.59808i) q^{84} +9.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(-4.00000 + 6.92820i) q^{87} +(-1.00000 + 1.73205i) q^{88} +(-5.00000 - 8.66025i) q^{89} +3.00000 q^{90} +(7.50000 + 2.59808i) q^{91} -1.00000 q^{92} +(5.00000 + 8.66025i) q^{93} +(4.50000 - 7.79423i) q^{94} +(-0.500000 - 0.866025i) q^{96} +4.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + 3 q^{5} + 2 q^{6} + 5 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + 3 * q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} + 3 q^{5} + 2 q^{6} + 5 q^{7} - 2 q^{8} - q^{9} - 3 q^{10} + 2 q^{11} + q^{12} + 6 q^{13} + q^{14} + 6 q^{15} - q^{16} + 3 q^{17} + q^{18} - 6 q^{20} + 4 q^{21} + 4 q^{22} + q^{23} - q^{24} - 4 q^{25} + 3 q^{26} - 2 q^{27} - 4 q^{28} - 16 q^{29} + 3 q^{30} - 10 q^{31} + q^{32} - 2 q^{33} + 6 q^{34} + 3 q^{35} + 2 q^{36} + 2 q^{37} + 3 q^{39} - 3 q^{40} + 16 q^{41} + 5 q^{42} - 8 q^{43} + 2 q^{44} + 3 q^{45} - q^{46} - 9 q^{47} - 2 q^{48} + 11 q^{49} - 8 q^{50} - 3 q^{51} - 3 q^{52} + 9 q^{53} - q^{54} + 12 q^{55} - 5 q^{56} - 8 q^{58} - 4 q^{59} - 3 q^{60} + 6 q^{61} - 20 q^{62} - q^{63} + 2 q^{64} + 9 q^{65} + 2 q^{66} - 3 q^{67} + 3 q^{68} + 2 q^{69} - 12 q^{70} + 14 q^{71} + q^{72} - 3 q^{73} - 2 q^{74} + 4 q^{75} + 8 q^{77} + 6 q^{78} - 4 q^{79} + 3 q^{80} - q^{81} + 8 q^{82} - 28 q^{83} + q^{84} + 18 q^{85} - 4 q^{86} - 8 q^{87} - 2 q^{88} - 10 q^{89} + 6 q^{90} + 15 q^{91} - 2 q^{92} + 10 q^{93} + 9 q^{94} - q^{96} + 8 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + 3 * q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 - q^9 - 3 * q^10 + 2 * q^11 + q^12 + 6 * q^13 + q^14 + 6 * q^15 - q^16 + 3 * q^17 + q^18 - 6 * q^20 + 4 * q^21 + 4 * q^22 + q^23 - q^24 - 4 * q^25 + 3 * q^26 - 2 * q^27 - 4 * q^28 - 16 * q^29 + 3 * q^30 - 10 * q^31 + q^32 - 2 * q^33 + 6 * q^34 + 3 * q^35 + 2 * q^36 + 2 * q^37 + 3 * q^39 - 3 * q^40 + 16 * q^41 + 5 * q^42 - 8 * q^43 + 2 * q^44 + 3 * q^45 - q^46 - 9 * q^47 - 2 * q^48 + 11 * q^49 - 8 * q^50 - 3 * q^51 - 3 * q^52 + 9 * q^53 - q^54 + 12 * q^55 - 5 * q^56 - 8 * q^58 - 4 * q^59 - 3 * q^60 + 6 * q^61 - 20 * q^62 - q^63 + 2 * q^64 + 9 * q^65 + 2 * q^66 - 3 * q^67 + 3 * q^68 + 2 * q^69 - 12 * q^70 + 14 * q^71 + q^72 - 3 * q^73 - 2 * q^74 + 4 * q^75 + 8 * q^77 + 6 * q^78 - 4 * q^79 + 3 * q^80 - q^81 + 8 * q^82 - 28 * q^83 + q^84 + 18 * q^85 - 4 * q^86 - 8 * q^87 - 2 * q^88 - 10 * q^89 + 6 * q^90 + 15 * q^91 - 2 * q^92 + 10 * q^93 + 9 * q^94 - q^96 + 8 * q^97 - 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	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
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$	1.00000			0.408248
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	3.00000			0.832050			0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000			0.832050			0.416025	+	0.909353i	$0.363423\pi$
$14$	0.500000	+	2.59808i	0.133631	+	0.694365i
$15$	3.00000			0.774597
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	−3.00000			−0.670820
$21$	2.00000	−	1.73205i	0.436436	−	0.377964i
$22$	2.00000			0.426401
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	1.50000	+	2.59808i	0.294174	+	0.509525i
$27$	−1.00000			−0.192450
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$	1.50000	+	2.59808i	0.273861	+	0.474342i
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.0680129	+	0.997684i	$0.521666\pi$
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.830014	+	0.557743i	$0.811667\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	3.00000			0.514496
$35$	1.50000	+	7.79423i	0.253546	+	1.31747i
$36$	1.00000			0.166667
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$		0			0
$39$	1.50000	−	2.59808i	0.240192	−	0.416025i
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	8.00000			1.24939			0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000			1.24939			0.624695	+	0.780869i	$0.285223\pi$
$42$	2.50000	+	0.866025i	0.385758	+	0.133631i
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	−0.981543	−	0.191243i	$-0.938748\pi$
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	0.325150	−	0.945662i	$-0.394585\pi$
$48$	−1.00000			−0.144338
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−4.00000			−0.565685
$51$	−1.50000	−	2.59808i	−0.210042	−	0.363803i
$52$	−1.50000	+	2.59808i	−0.208013	+	0.360288i
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	−0.371706	−	0.928351i	$-0.621227\pi$
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	0.989828	−	0.142269i	$-0.0454398\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	6.00000			0.809040
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$		0			0
$58$	−4.00000	−	6.92820i	−0.525226	−	0.909718i
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	−10.0000			−1.27000
$63$	−0.500000	−	2.59808i	−0.0629941	−	0.327327i
$64$	1.00000			0.125000
$65$	4.50000	+	7.79423i	0.558156	+	0.966755i
$66$	1.00000	−	1.73205i	0.123091	−	0.213201i
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	−0.942987	−	0.332830i	$-0.891996\pi$
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	0.759733	+	0.650236i	$0.225330\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	1.00000			0.120386
$70$	−6.00000	+	5.19615i	−0.717137	+	0.621059i
$71$	7.00000			0.830747			0.415374	−	0.909651i	$-0.363651\pi$
$71$	7.00000			0.830747			0.415374	+	0.909651i	$0.363651\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	−0.940356	−	0.340193i	$-0.889507\pi$
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	0.764794	+	0.644275i	$0.222841\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$		0			0
$77$	4.00000	−	3.46410i	0.455842	−	0.394771i
$78$	3.00000			0.339683
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.00000	+	6.92820i	0.441726	+	0.765092i
$83$	−14.0000			−1.53670			−0.768350	−	0.640030i	$-0.778922\pi$
$83$	−14.0000			−1.53670			−0.768350	+	0.640030i	$0.778922\pi$
$84$	0.500000	+	2.59808i	0.0545545	+	0.283473i
$85$	9.00000			0.976187
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$	−4.00000	+	6.92820i	−0.428845	+	0.742781i
$88$	−1.00000	+	1.73205i	−0.106600	+	0.184637i
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	0.469389	−	0.882992i	$-0.344474\pi$
$90$	3.00000			0.316228
$91$	7.50000	+	2.59808i	0.786214	+	0.272352i
$92$	−1.00000			−0.104257
$93$	5.00000	+	8.66025i	0.518476	+	0.898027i
$94$	4.50000	−	7.79423i	0.464140	−	0.803913i
$95$		0			0
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	4.00000			0.406138			0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000			0.406138			0.203069	+	0.979164i	$0.434908\pi$
$98$	−1.00000	+	6.92820i	−0.101015	+	0.699854i
$99$	−2.00000			−0.201008
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$	1.50000	−	2.59808i	0.148522	−	0.257248i
$103$	−8.50000	−	14.7224i	−0.837530	−	1.45064i	−0.891954	−	0.452126i	$-0.850666\pi$
$103$	−8.50000	−	14.7224i	−0.837530	−	1.45064i	0.0544240	−	0.998518i	$-0.482668\pi$
$104$	−3.00000			−0.294174
$105$	7.50000	+	2.59808i	0.731925	+	0.253546i
$106$	9.00000			0.874157
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	0.992003	−	0.126217i	$-0.0402834\pi$
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	−0.605308	+	0.795991i	$0.706950\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−4.00000	+	6.92820i	−0.383131	+	0.663602i	−0.991508	−	0.130046i	$-0.958487\pi$
$109$	−4.00000	+	6.92820i	−0.383131	+	0.663602i	0.608377	+	0.793648i	$0.291821\pi$
$110$	3.00000	+	5.19615i	0.286039	+	0.495434i
$111$	2.00000			0.189832
$112$	−0.500000	−	2.59808i	−0.0472456	−	0.245495i
$113$	−5.00000			−0.470360			−0.235180	−	0.971952i	$-0.575568\pi$
$113$	−5.00000			−0.470360			−0.235180	+	0.971952i	$0.575568\pi$
$114$		0			0
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$	4.00000	−	6.92820i	0.371391	−	0.643268i
$117$	−1.50000	−	2.59808i	−0.138675	−	0.240192i
$118$	−4.00000			−0.368230
$119$	6.00000	−	5.19615i	0.550019	−	0.476331i
$120$	−3.00000			−0.273861
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−3.00000	+	5.19615i	−0.271607	+	0.470438i
$123$	4.00000	−	6.92820i	0.360668	−	0.624695i
$124$	−5.00000	−	8.66025i	−0.449013	−	0.777714i
$125$	3.00000			0.268328
$126$	2.00000	−	1.73205i	0.178174	−	0.154303i
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−2.00000	+	3.46410i	−0.176090	+	0.304997i
$130$	−4.50000	+	7.79423i	−0.394676	+	0.683599i
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	−0.981824	−	0.189794i	$-0.939218\pi$
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	0.326546	−	0.945181i	$-0.394115\pi$
$132$	2.00000			0.174078
$133$		0			0
$134$	−3.00000			−0.259161
$135$	−1.50000	−	2.59808i	−0.129099	−	0.223607i
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	−9.50000	+	16.4545i	−0.811640	+	1.40580i	0.100076	+	0.994980i	$0.468091\pi$
$137$	−9.50000	+	16.4545i	−0.811640	+	1.40580i	−0.911716	+	0.410822i	$0.865242\pi$
$138$	0.500000	+	0.866025i	0.0425628	+	0.0737210i
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$	−7.50000	−	2.59808i	−0.633866	−	0.219578i
$141$	−9.00000			−0.757937
$142$	3.50000	+	6.06218i	0.293713	+	0.508727i
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−12.0000	−	20.7846i	−0.996546	−	1.72607i
$146$	−3.00000			−0.248282
$147$	6.50000	−	2.59808i	0.536111	−	0.214286i
$148$	−2.00000			−0.164399
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	−0.871742	−	0.489966i	$-0.837009\pi$
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	0.0115483	−	0.999933i	$-0.496324\pi$
$150$	−2.00000	+	3.46410i	−0.163299	+	0.282843i
$151$	10.0000	−	17.3205i	0.813788	−	1.40952i	−0.0964061	−	0.995342i	$-0.530735\pi$
$151$	10.0000	−	17.3205i	0.813788	−	1.40952i	0.910195	−	0.414181i	$-0.135932\pi$
$152$		0			0
$153$	−3.00000			−0.242536
$154$	5.00000	+	1.73205i	0.402911	+	0.139573i
$155$	−30.0000			−2.40966
$156$	1.50000	+	2.59808i	0.120096	+	0.208013i
$157$	9.00000	−	15.5885i	0.718278	−	1.24409i	−0.243403	−	0.969925i	$-0.578264\pi$
$157$	9.00000	−	15.5885i	0.718278	−	1.24409i	0.961681	−	0.274169i	$-0.0884028\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$	−4.50000	−	7.79423i	−0.356873	−	0.618123i
$160$	3.00000			0.237171
$161$	0.500000	+	2.59808i	0.0394055	+	0.204757i
$162$	−1.00000			−0.0785674
$163$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$163$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$164$	−4.00000	+	6.92820i	−0.312348	+	0.541002i
$165$	3.00000	−	5.19615i	0.233550	−	0.404520i
$166$	−7.00000	−	12.1244i	−0.543305	−	0.941033i
$167$	−21.0000			−1.62503			−0.812514	−	0.582941i	$-0.801902\pi$
$167$	−21.0000			−1.62503			−0.812514	+	0.582941i	$0.801902\pi$
$168$	−2.00000	+	1.73205i	−0.154303	+	0.133631i
$169$	−4.00000			−0.307692
$170$	4.50000	+	7.79423i	0.345134	+	0.597790i
$171$		0			0
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−10.0000	−	17.3205i	−0.760286	−	1.31685i	−0.942703	−	0.333633i	$-0.891725\pi$
$173$	−10.0000	−	17.3205i	−0.760286	−	1.31685i	0.182417	−	0.983221i	$-0.441608\pi$
$174$	−8.00000			−0.606478
$175$	−8.00000	+	6.92820i	−0.604743	+	0.523723i
$176$	−2.00000			−0.150756
$177$	2.00000	+	3.46410i	0.150329	+	0.260378i
$178$	5.00000	−	8.66025i	0.374766	−	0.649113i
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	0.436870	+	0.899525i	$0.356087\pi$
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	−0.997446	+	0.0714220i	$0.977246\pi$
$180$	1.50000	+	2.59808i	0.111803	+	0.193649i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	1.50000	+	7.79423i	0.111187	+	0.577747i
$183$	6.00000			0.443533
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$	−5.00000	+	8.66025i	−0.366618	+	0.635001i
$187$	−3.00000	−	5.19615i	−0.219382	−	0.379980i
$188$	9.00000			0.656392
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$		0			0
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$	2.00000	+	3.46410i	0.143592	+	0.248708i
$195$	9.00000			0.644503
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	−1.00000	−	1.73205i	−0.0710669	−	0.123091i
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$	1.50000	+	2.59808i	0.105802	+	0.183254i
$202$	10.0000			0.703598
$203$	−20.0000	−	6.92820i	−1.40372	−	0.486265i
$204$	3.00000			0.210042
$205$	12.0000	+	20.7846i	0.838116	+	1.45166i
$206$	8.50000	−	14.7224i	0.592223	−	1.02576i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	−1.50000	−	2.59808i	−0.104006	−	0.180144i
$209$		0			0
$210$	1.50000	+	7.79423i	0.103510	+	0.537853i
$211$	−6.00000			−0.413057			−0.206529	−	0.978441i	$-0.566217\pi$
$211$	−6.00000			−0.413057			−0.206529	+	0.978441i	$0.566217\pi$
$212$	4.50000	+	7.79423i	0.309061	+	0.535310i
$213$	3.50000	−	6.06218i	0.239816	−	0.415374i
$214$	−4.00000	+	6.92820i	−0.273434	+	0.473602i
$215$	−6.00000	−	10.3923i	−0.409197	−	0.708749i
$216$	1.00000			0.0680414
$217$	−20.0000	+	17.3205i	−1.35769	+	1.17579i
$218$	−8.00000			−0.541828
$219$	1.50000	+	2.59808i	0.101361	+	0.175562i
$220$	−3.00000	+	5.19615i	−0.202260	+	0.350325i
$221$	4.50000	−	7.79423i	0.302703	−	0.524297i
$222$	1.00000	+	1.73205i	0.0671156	+	0.116248i
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$	2.00000	−	1.73205i	0.133631	−	0.115728i
$225$	4.00000			0.266667
$226$	−2.50000	−	4.33013i	−0.166298	−	0.288036i
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	−0.534577	−	0.845120i	$-0.679529\pi$
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	0.999184	+	0.0403978i	$0.0128625\pi$
$228$		0			0
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	0.980401	+	0.197013i	$0.0631241\pi$
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	−0.319582	+	0.947559i	$0.603543\pi$
$230$	−3.00000			−0.197814
$231$	−1.00000	−	5.19615i	−0.0657952	−	0.341882i
$232$	8.00000			0.525226
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	0.924072	−	0.382219i	$-0.124840\pi$
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	−0.793047	+	0.609160i	$0.791507\pi$
$234$	1.50000	−	2.59808i	0.0980581	−	0.169842i
$235$	13.5000	−	23.3827i	0.880643	−	1.52532i
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$	−4.00000			−0.259828
$238$	7.50000	+	2.59808i	0.486153	+	0.168408i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−1.50000	−	2.59808i	−0.0968246	−	0.167705i
$241$	3.00000	−	5.19615i	0.193247	−	0.334714i	−0.753077	−	0.657932i	$-0.771431\pi$
$241$	3.00000	−	5.19615i	0.193247	−	0.334714i	0.946324	+	0.323218i	$0.104765\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−6.00000			−0.384111
$245$	−3.00000	+	20.7846i	−0.191663	+	1.32788i
$246$	8.00000			0.510061
$247$		0			0
$248$	5.00000	−	8.66025i	0.317500	−	0.549927i
$249$	−7.00000	+	12.1244i	−0.443607	+	0.768350i
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	−26.0000			−1.64111			−0.820553	−	0.571571i	$-0.806334\pi$
$251$	−26.0000			−1.64111			−0.820553	+	0.571571i	$0.806334\pi$
$252$	2.50000	+	0.866025i	0.157485	+	0.0545545i
$253$	2.00000			0.125739
$254$	−1.00000	−	1.73205i	−0.0627456	−	0.108679i
$255$	4.50000	−	7.79423i	0.281801	−	0.488094i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	0.560781	−	0.827964i	$-0.310501\pi$
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	−0.997429	+	0.0716680i	$0.977168\pi$
$258$	−4.00000			−0.249029
$259$	1.00000	+	5.19615i	0.0621370	+	0.322873i
$260$	−9.00000			−0.558156
$261$	4.00000	+	6.92820i	0.247594	+	0.428845i
$262$	7.50000	−	12.9904i	0.463352	−	0.802548i
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$	1.00000	+	1.73205i	0.0615457	+	0.106600i
$265$	27.0000			1.65860
$266$		0			0
$267$	−10.0000			−0.611990
$268$	−1.50000	−	2.59808i	−0.0916271	−	0.158703i
$269$	10.0000	−	17.3205i	0.609711	−	1.05605i	−0.381577	−	0.924337i	$-0.624619\pi$
$269$	10.0000	−	17.3205i	0.609711	−	1.05605i	0.991288	−	0.131713i	$-0.0420477\pi$
$270$	1.50000	−	2.59808i	0.0912871	−	0.158114i
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	0.760405	−	0.649449i	$-0.225000\pi$
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	−0.942642	+	0.333805i	$0.891667\pi$
$272$	−3.00000			−0.181902
$273$	6.00000	−	5.19615i	0.363137	−	0.314485i
$274$	−19.0000			−1.14783
$275$	4.00000	+	6.92820i	0.241209	+	0.417786i
$276$	−0.500000	+	0.866025i	−0.0300965	+	0.0521286i
$277$	−4.50000	+	7.79423i	−0.270379	+	0.468310i	−0.968959	−	0.247222i	$-0.920482\pi$
$277$	−4.50000	+	7.79423i	−0.270379	+	0.468310i	0.698580	+	0.715532i	$0.253816\pi$
$278$	5.00000	+	8.66025i	0.299880	+	0.519408i
$279$	10.0000			0.598684
$280$	−1.50000	−	7.79423i	−0.0896421	−	0.465794i
$281$	7.00000			0.417585			0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000			0.417585			0.208792	+	0.977960i	$0.433047\pi$
$282$	−4.50000	−	7.79423i	−0.267971	−	0.464140i
$283$	3.50000	−	6.06218i	0.208053	−	0.360359i	−0.743048	−	0.669238i	$-0.766621\pi$
$283$	3.50000	−	6.06218i	0.208053	−	0.360359i	0.951101	+	0.308879i	$0.0999539\pi$
$284$	−3.50000	+	6.06218i	−0.207687	+	0.359724i
$285$		0			0
$286$	6.00000			0.354787
$287$	20.0000	+	6.92820i	1.18056	+	0.408959i
$288$	−1.00000			−0.0589256
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	12.0000	−	20.7846i	0.704664	−	1.22051i
$291$	2.00000	−	3.46410i	0.117242	−	0.203069i
$292$	−1.50000	−	2.59808i	−0.0877809	−	0.152041i
$293$	−13.0000			−0.759468			−0.379734	−	0.925096i	$-0.623985\pi$
$293$	−13.0000			−0.759468			−0.379734	+	0.925096i	$0.623985\pi$
$294$	5.50000	+	4.33013i	0.320767	+	0.252538i
$295$	−12.0000			−0.698667
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	10.5000	−	18.1865i	0.608249	−	1.05352i
$299$	1.50000	+	2.59808i	0.0867472	+	0.150251i
$300$	−4.00000			−0.230940
$301$	−10.0000	−	3.46410i	−0.576390	−	0.199667i
$302$	20.0000			1.15087
$303$	−5.00000	−	8.66025i	−0.287242	−	0.497519i
$304$		0			0
$305$	−9.00000	+	15.5885i	−0.515339	+	0.892592i
$306$	−1.50000	−	2.59808i	−0.0857493	−	0.148522i
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$	1.00000	+	5.19615i	0.0569803	+	0.296078i
$309$	−17.0000			−0.967096
$310$	−15.0000	−	25.9808i	−0.851943	−	1.47561i
$311$	6.50000	−	11.2583i	0.368581	−	0.638401i	−0.620763	−	0.783998i	$-0.713177\pi$
$311$	6.50000	−	11.2583i	0.368581	−	0.638401i	0.989344	+	0.145597i	$0.0465103\pi$
$312$	−1.50000	+	2.59808i	−0.0849208	+	0.147087i
$313$	14.0000	+	24.2487i	0.791327	+	1.37062i	0.925146	+	0.379612i	$0.123943\pi$
$313$	14.0000	+	24.2487i	0.791327	+	1.37062i	−0.133819	+	0.991006i	$0.542724\pi$
$314$	18.0000			1.01580
$315$	6.00000	−	5.19615i	0.338062	−	0.292770i
$316$	4.00000			0.225018
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$	4.50000	−	7.79423i	0.252347	−	0.437079i
$319$	−8.00000	+	13.8564i	−0.447914	+	0.775810i
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$	8.00000			0.446516
$322$	−2.00000	+	1.73205i	−0.111456	+	0.0965234i
$323$		0			0
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−6.00000	+	10.3923i	−0.332820	+	0.576461i
$326$		0			0
$327$	4.00000	+	6.92820i	0.221201	+	0.383131i
$328$	−8.00000			−0.441726
$329$	−4.50000	−	23.3827i	−0.248093	−	1.28913i
$330$	6.00000			0.330289
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$	7.00000	−	12.1244i	0.384175	−	0.665410i
$333$	1.00000	−	1.73205i	0.0547997	−	0.0949158i
$334$	−10.5000	−	18.1865i	−0.574534	−	0.995123i
$335$	−9.00000			−0.491723
$336$	−2.50000	−	0.866025i	−0.136386	−	0.0472456i
$337$	16.0000			0.871576			0.435788	−	0.900049i	$-0.356470\pi$
$337$	16.0000			0.871576			0.435788	+	0.900049i	$0.356470\pi$
$338$	−2.00000	−	3.46410i	−0.108786	−	0.188422i
$339$	−2.50000	+	4.33013i	−0.135781	+	0.235180i
$340$	−4.50000	+	7.79423i	−0.244047	+	0.422701i
$341$	10.0000	+	17.3205i	0.541530	+	0.937958i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	4.00000			0.215666
$345$	1.50000	+	2.59808i	0.0807573	+	0.139876i
$346$	10.0000	−	17.3205i	0.537603	−	0.931156i
$347$	7.50000	−	12.9904i	0.402621	−	0.697360i	−0.591420	−	0.806363i	$-0.701433\pi$
$347$	7.50000	−	12.9904i	0.402621	−	0.697360i	0.994041	+	0.109003i	$0.0347659\pi$
$348$	−4.00000	−	6.92820i	−0.214423	−	0.371391i
$349$	−25.0000			−1.33822			−0.669110	−	0.743164i	$-0.733324\pi$
$349$	−25.0000			−1.33822			−0.669110	+	0.743164i	$0.733324\pi$
$350$	−10.0000	−	3.46410i	−0.534522	−	0.185164i
$351$	−3.00000			−0.160128
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$	−2.00000	+	3.46410i	−0.106449	+	0.184376i	−0.914329	−	0.404971i	$-0.867282\pi$
$353$	−2.00000	+	3.46410i	−0.106449	+	0.184376i	0.807880	+	0.589347i	$0.200615\pi$
$354$	−2.00000	+	3.46410i	−0.106299	+	0.184115i
$355$	10.5000	+	18.1865i	0.557282	+	0.965241i
$356$	10.0000			0.529999
$357$	−1.50000	−	7.79423i	−0.0793884	−	0.412514i
$358$	−15.0000			−0.792775
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	−0.775934	+	0.630814i	$0.782721\pi$
$360$	−1.50000	+	2.59808i	−0.0790569	+	0.136931i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	3.00000	+	5.19615i	0.157676	+	0.273104i
$363$	7.00000			0.367405
$364$	−6.00000	+	5.19615i	−0.314485	+	0.272352i
$365$	−9.00000			−0.471082
$366$	3.00000	+	5.19615i	0.156813	+	0.271607i
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	−0.724345	−	0.689438i	$-0.757858\pi$
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	0.959243	+	0.282582i	$0.0911910\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	−4.00000	−	6.92820i	−0.208232	−	0.360668i
$370$	−6.00000			−0.311925
$371$	18.0000	−	15.5885i	0.934513	−	0.809312i
$372$	−10.0000			−0.518476
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	0.707055	−	0.707159i	$-0.250023\pi$
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	−0.965945	+	0.258748i	$0.916690\pi$
$374$	3.00000	−	5.19615i	0.155126	−	0.268687i
$375$	1.50000	−	2.59808i	0.0774597	−	0.134164i
$376$	4.50000	+	7.79423i	0.232070	+	0.401957i
$377$	−24.0000			−1.23606
$378$	−0.500000	−	2.59808i	−0.0257172	−	0.133631i
$379$	−29.0000			−1.48963			−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000			−1.48963			−0.744815	+	0.667271i	$0.767462\pi$
$380$		0			0
$381$	−1.00000	+	1.73205i	−0.0512316	+	0.0887357i
$382$	−4.00000	+	6.92820i	−0.204658	+	0.354478i
$383$	11.0000	+	19.0526i	0.562074	+	0.973540i	0.997315	+	0.0732266i	$0.0233296\pi$
$383$	11.0000	+	19.0526i	0.562074	+	0.973540i	−0.435242	+	0.900314i	$0.643337\pi$
$384$	1.00000			0.0510310
$385$	15.0000	+	5.19615i	0.764471	+	0.264820i
$386$	−5.00000			−0.254493
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$	−2.00000	+	3.46410i	−0.101535	+	0.175863i
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	−0.964490	−	0.264120i	$-0.914918\pi$
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	0.710980	+	0.703213i	$0.248252\pi$
$390$	4.50000	+	7.79423i	0.227866	+	0.394676i
$391$	3.00000			0.151717
$392$	−5.50000	−	4.33013i	−0.277792	−	0.218704i
$393$	−15.0000			−0.756650
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	6.00000	−	10.3923i	0.301893	−	0.522894i
$396$	1.00000	−	1.73205i	0.0502519	−	0.0870388i
$397$	−4.50000	−	7.79423i	−0.225849	−	0.391181i	0.730725	−	0.682672i	$-0.239182\pi$
$397$	−4.50000	−	7.79423i	−0.225849	−	0.391181i	−0.956574	+	0.291491i	$0.905849\pi$
$398$	8.00000			0.401004
$399$		0			0
$400$	4.00000			0.200000
$401$	19.5000	+	33.7750i	0.973784	+	1.68664i	0.683892	+	0.729583i	$0.260286\pi$
$401$	19.5000	+	33.7750i	0.973784	+	1.68664i	0.289891	+	0.957060i	$0.406381\pi$
$402$	−1.50000	+	2.59808i	−0.0748132	+	0.129580i
$403$	−15.0000	+	25.9808i	−0.747203	+	1.29419i
$404$	5.00000	+	8.66025i	0.248759	+	0.430864i
$405$	−3.00000			−0.149071
$406$	−4.00000	−	20.7846i	−0.198517	−	1.03152i
$407$	4.00000			0.198273
$408$	1.50000	+	2.59808i	0.0742611	+	0.128624i
$409$	−19.5000	+	33.7750i	−0.964213	+	1.67007i	−0.252498	+	0.967597i	$0.581252\pi$
$409$	−19.5000	+	33.7750i	−0.964213	+	1.67007i	−0.711715	+	0.702468i	$0.752081\pi$
$410$	−12.0000	+	20.7846i	−0.592638	+	1.02648i
$411$	9.50000	+	16.4545i	0.468600	+	0.811640i
$412$	17.0000			0.837530
$413$	−8.00000	+	6.92820i	−0.393654	+	0.340915i
$414$	1.00000			0.0491473
$415$	−21.0000	−	36.3731i	−1.03085	−	1.78548i
$416$	1.50000	−	2.59808i	0.0735436	−	0.127381i
$417$	5.00000	−	8.66025i	0.244851	−	0.424094i
$418$		0			0
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$	−6.00000	+	5.19615i	−0.292770	+	0.253546i
$421$	−4.00000			−0.194948			−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000			−0.194948			−0.0974740	+	0.995238i	$0.531076\pi$
$422$	−3.00000	−	5.19615i	−0.146038	−	0.252945i
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$	−4.50000	+	7.79423i	−0.218539	+	0.378521i
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$	7.00000			0.339151
$427$	3.00000	+	15.5885i	0.145180	+	0.754378i
$428$	−8.00000			−0.386695
$429$	−3.00000	−	5.19615i	−0.144841	−	0.250873i
$430$	6.00000	−	10.3923i	0.289346	−	0.501161i
$431$	−18.0000	+	31.1769i	−0.867029	+	1.50174i	−0.00201168	+	0.999998i	$0.500640\pi$
$431$	−18.0000	+	31.1769i	−0.867029	+	1.50174i	−0.865018	+	0.501741i	$0.832693\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−18.0000			−0.865025			−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000			−0.865025			−0.432512	+	0.901628i	$0.642373\pi$
$434$	−25.0000	−	8.66025i	−1.20004	−	0.415705i
$435$	−24.0000			−1.15071
$436$	−4.00000	−	6.92820i	−0.191565	−	0.331801i
$437$		0			0
$438$	−1.50000	+	2.59808i	−0.0716728	+	0.124141i
$439$	−13.0000	−	22.5167i	−0.620456	−	1.07466i	−0.989401	−	0.145210i	$-0.953614\pi$
$439$	−13.0000	−	22.5167i	−0.620456	−	1.07466i	0.368945	−	0.929451i	$-0.379719\pi$
$440$	−6.00000			−0.286039
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	9.00000			0.428086
$443$	8.50000	+	14.7224i	0.403847	+	0.699484i	0.994187	−	0.107671i	$-0.0343394\pi$
$443$	8.50000	+	14.7224i	0.403847	+	0.699484i	−0.590339	+	0.807155i	$0.701006\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$	15.0000	−	25.9808i	0.711068	−	1.23161i
$446$	4.00000	+	6.92820i	0.189405	+	0.328060i
$447$	−21.0000			−0.993266
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	2.00000	+	3.46410i	0.0942809	+	0.163299i
$451$	8.00000	−	13.8564i	0.376705	−	0.652473i
$452$	2.50000	−	4.33013i	0.117590	−	0.203672i
$453$	−10.0000	−	17.3205i	−0.469841	−	0.813788i
$454$	14.0000			0.657053
$455$	4.50000	+	23.3827i	0.210963	+	1.09620i
$456$		0			0
$457$	14.0000	+	24.2487i	0.654892	+	1.13431i	0.981921	+	0.189292i	$0.0606194\pi$
$457$	14.0000	+	24.2487i	0.654892	+	1.13431i	−0.327028	+	0.945015i	$0.606047\pi$
$458$	−10.0000	+	17.3205i	−0.467269	+	0.809334i
$459$	−1.50000	+	2.59808i	−0.0700140	+	0.121268i
$460$	−1.50000	−	2.59808i	−0.0699379	−	0.121136i
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$	4.00000	−	3.46410i	0.186097	−	0.161165i
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	4.00000	+	6.92820i	0.185695	+	0.321634i
$465$	−15.0000	+	25.9808i	−0.695608	+	1.20483i
$466$	−2.00000	+	3.46410i	−0.0926482	+	0.160471i
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	0.970799	−	0.239892i	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$	3.00000			0.138675
$469$	−6.00000	+	5.19615i	−0.277054	+	0.239936i
$470$	27.0000			1.24542
$471$	−9.00000	−	15.5885i	−0.414698	−	0.718278i
$472$	2.00000	−	3.46410i	0.0920575	−	0.159448i
$473$	−4.00000	+	6.92820i	−0.183920	+	0.318559i
$474$	−2.00000	−	3.46410i	−0.0918630	−	0.159111i
$475$		0			0
$476$	1.50000	+	7.79423i	0.0687524	+	0.357248i
$477$	−9.00000			−0.412082
$478$		0			0
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	1.50000	−	2.59808i	0.0684653	−	0.118585i
$481$	3.00000	+	5.19615i	0.136788	+	0.236924i
$482$	6.00000			0.273293
$483$	2.50000	+	0.866025i	0.113754	+	0.0394055i
$484$	−7.00000			−0.318182
$485$	6.00000	+	10.3923i	0.272446	+	0.471890i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	10.0000	−	17.3205i	0.453143	−	0.784867i	−0.545436	−	0.838152i	$-0.683636\pi$
$487$	10.0000	−	17.3205i	0.453143	−	0.784867i	0.998579	+	0.0532853i	$0.0169693\pi$
$488$	−3.00000	−	5.19615i	−0.135804	−	0.235219i
$489$		0			0
$490$	−19.5000	+	7.79423i	−0.880920	+	0.352107i
$491$	−29.0000			−1.30875			−0.654376	−	0.756169i	$-0.727069\pi$
$491$	−29.0000			−1.30875			−0.654376	+	0.756169i	$0.727069\pi$
$492$	4.00000	+	6.92820i	0.180334	+	0.312348i
$493$	−12.0000	+	20.7846i	−0.540453	+	0.936092i
$494$		0			0
$495$	−3.00000	−	5.19615i	−0.134840	−	0.233550i
$496$	10.0000			0.449013
$497$	17.5000	+	6.06218i	0.784982	+	0.271926i
$498$	−14.0000			−0.627355
$499$	20.0000	+	34.6410i	0.895323	+	1.55074i	0.833404	+	0.552664i	$0.186389\pi$
$499$	20.0000	+	34.6410i	0.895323	+	1.55074i	0.0619186	+	0.998081i	$0.480278\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	−10.5000	+	18.1865i	−0.469105	+	0.812514i
$502$	−13.0000	−	22.5167i	−0.580218	−	1.00497i
$503$	−2.00000			−0.0891756			−0.0445878	−	0.999005i	$-0.514197\pi$
$503$	−2.00000			−0.0891756			−0.0445878	+	0.999005i	$0.514197\pi$
$504$	0.500000	+	2.59808i	0.0222718	+	0.115728i
$505$	30.0000			1.33498
$506$	1.00000	+	1.73205i	0.0444554	+	0.0769991i
$507$	−2.00000	+	3.46410i	−0.0888231	+	0.153846i
$508$	1.00000	−	1.73205i	0.0443678	−	0.0768473i
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$	9.00000			0.398527
$511$	−6.00000	+	5.19615i	−0.265424	+	0.229864i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	7.00000	−	12.1244i	0.308757	−	0.534782i
$515$	25.5000	−	44.1673i	1.12366	−	1.94624i
$516$	−2.00000	−	3.46410i	−0.0880451	−	0.152499i
$517$	−18.0000			−0.791639
$518$	−4.00000	+	3.46410i	−0.175750	+	0.152204i
$519$	−20.0000			−0.877903
$520$	−4.50000	−	7.79423i	−0.197338	−	0.341800i
$521$	20.5000	−	35.5070i	0.898121	−	1.55559i	0.0682279	−	0.997670i	$-0.478266\pi$
$521$	20.5000	−	35.5070i	0.898121	−	1.55559i	0.829893	−	0.557922i	$-0.188401\pi$
$522$	−4.00000	+	6.92820i	−0.175075	+	0.303239i
$523$	−11.5000	−	19.9186i	−0.502860	−	0.870979i	−0.999995	−	0.00330547i	$-0.998948\pi$
$523$	−11.5000	−	19.9186i	−0.502860	−	0.870979i	0.497135	−	0.867673i	$-0.334385\pi$
$524$	15.0000			0.655278
$525$	2.00000	+	10.3923i	0.0872872	+	0.453557i
$526$	12.0000			0.523225
$527$	15.0000	+	25.9808i	0.653410	+	1.13174i
$528$	−1.00000	+	1.73205i	−0.0435194	+	0.0753778i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	13.5000	+	23.3827i	0.586403	+	1.01568i
$531$	4.00000			0.173585
$532$		0			0
$533$	24.0000			1.03956
$534$	−5.00000	−	8.66025i	−0.216371	−	0.374766i
$535$	−12.0000	+	20.7846i	−0.518805	+	0.898597i
$536$	1.50000	−	2.59808i	0.0647901	−	0.112220i
$537$	7.50000	+	12.9904i	0.323649	+	0.560576i
$538$	20.0000			0.862261
$539$	13.0000	−	5.19615i	0.559950	−	0.223814i
$540$	3.00000			0.129099
$541$	7.50000	+	12.9904i	0.322450	+	0.558500i	0.980993	−	0.194043i	$-0.0621602\pi$
$541$	7.50000	+	12.9904i	0.322450	+	0.558500i	−0.658543	+	0.752543i	$0.728827\pi$
$542$	3.00000	−	5.19615i	0.128861	−	0.223194i
$543$	3.00000	−	5.19615i	0.128742	−	0.222988i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	−24.0000			−1.02805
$546$	7.50000	+	2.59808i	0.320970	+	0.111187i
$547$	−26.0000			−1.11168			−0.555840	−	0.831289i	$-0.687603\pi$
$547$	−26.0000			−1.11168			−0.555840	+	0.831289i	$0.687603\pi$
$548$	−9.50000	−	16.4545i	−0.405820	−	0.702901i
$549$	3.00000	−	5.19615i	0.128037	−	0.221766i
$550$	−4.00000	+	6.92820i	−0.170561	+	0.295420i
$551$		0			0
$552$	−1.00000			−0.0425628
$553$	−2.00000	−	10.3923i	−0.0850487	−	0.441926i
$554$	−9.00000			−0.382373
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$	−5.00000	+	8.66025i	−0.212047	+	0.367277i
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	−0.991254	−	0.131965i	$-0.957871\pi$
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	0.609912	+	0.792469i	$0.291205\pi$
$558$	5.00000	+	8.66025i	0.211667	+	0.366618i
$559$	−12.0000			−0.507546
$560$	6.00000	−	5.19615i	0.253546	−	0.219578i
$561$	−6.00000			−0.253320
$562$	3.50000	+	6.06218i	0.147639	+	0.255718i
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$	4.50000	−	7.79423i	0.189484	−	0.328196i
$565$	−7.50000	−	12.9904i	−0.315527	−	0.546509i
$566$	7.00000			0.294232
$567$	−2.00000	+	1.73205i	−0.0839921	+	0.0727393i
$568$	−7.00000			−0.293713
$569$	−2.50000	−	4.33013i	−0.104805	−	0.181528i	0.808853	−	0.588011i	$-0.200089\pi$
$569$	−2.50000	−	4.33013i	−0.104805	−	0.181528i	−0.913659	+	0.406482i	$0.866755\pi$
$570$		0			0
$571$	−12.5000	+	21.6506i	−0.523109	+	0.906051i	0.476530	+	0.879158i	$0.341895\pi$
$571$	−12.5000	+	21.6506i	−0.523109	+	0.906051i	−0.999638	+	0.0268925i	$0.991439\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$	8.00000			0.334205
$574$	4.00000	+	20.7846i	0.166957	+	0.867533i
$575$	−4.00000			−0.166812
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	−0.844459	−	0.535620i	$-0.820078\pi$
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	0.886090	+	0.463513i	$0.153411\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	2.50000	+	4.33013i	0.103896	+	0.179954i
$580$	24.0000			0.996546
$581$	−35.0000	−	12.1244i	−1.45204	−	0.503003i
$582$	4.00000			0.165805
$583$	−9.00000	−	15.5885i	−0.372742	−	0.645608i
$584$	1.50000	−	2.59808i	0.0620704	−	0.107509i
$585$	4.50000	−	7.79423i	0.186052	−	0.322252i
$586$	−6.50000	−	11.2583i	−0.268513	−	0.465077i
$587$	25.0000			1.03186			0.515930	−	0.856631i	$-0.327446\pi$
$587$	25.0000			1.03186			0.515930	+	0.856631i	$0.327446\pi$
$588$	−1.00000	+	6.92820i	−0.0412393	+	0.285714i
$589$		0			0
$590$	−6.00000	−	10.3923i	−0.247016	−	0.427844i
$591$	9.00000	−	15.5885i	0.370211	−	0.641223i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	9.00000	+	15.5885i	0.369586	+	0.640141i	0.989501	−	0.144528i	$-0.0461663\pi$
$593$	9.00000	+	15.5885i	0.369586	+	0.640141i	−0.619915	+	0.784669i	$0.712833\pi$
$594$	−2.00000			−0.0820610
$595$	22.5000	+	7.79423i	0.922410	+	0.319532i
$596$	21.0000			0.860194
$597$	−4.00000	−	6.92820i	−0.163709	−	0.283552i
$598$	−1.50000	+	2.59808i	−0.0613396	+	0.106243i
$599$	−4.50000	+	7.79423i	−0.183865	+	0.318464i	−0.943193	−	0.332244i	$-0.892194\pi$
$599$	−4.50000	+	7.79423i	−0.183865	+	0.318464i	0.759328	+	0.650708i	$0.225528\pi$
$600$	−2.00000	−	3.46410i	−0.0816497	−	0.141421i
$601$	18.0000			0.734235			0.367118	−	0.930175i	$-0.380345\pi$
$601$	18.0000			0.734235			0.367118	+	0.930175i	$0.380345\pi$
$602$	−2.00000	−	10.3923i	−0.0815139	−	0.423559i
$603$	3.00000			0.122169
$604$	10.0000	+	17.3205i	0.406894	+	0.704761i
$605$	−10.5000	+	18.1865i	−0.426886	+	0.739388i
$606$	5.00000	−	8.66025i	0.203111	−	0.351799i
$607$	19.0000	+	32.9090i	0.771186	+	1.33573i	0.936913	+	0.349562i	$0.113670\pi$
$607$	19.0000	+	32.9090i	0.771186	+	1.33573i	−0.165727	+	0.986172i	$0.552997\pi$
$608$		0			0
$609$	−16.0000	+	13.8564i	−0.648353	+	0.561490i
$610$	−18.0000			−0.728799
$611$	−13.5000	−	23.3827i	−0.546152	−	0.945962i
$612$	1.50000	−	2.59808i	0.0606339	−	0.105021i
$613$	21.0000	−	36.3731i	0.848182	−	1.46909i	−0.0346469	−	0.999400i	$-0.511031\pi$
$613$	21.0000	−	36.3731i	0.848182	−	1.46909i	0.882829	−	0.469695i	$-0.155636\pi$
$614$	8.00000	+	13.8564i	0.322854	+	0.559199i
$615$	24.0000			0.967773
$616$	−4.00000	+	3.46410i	−0.161165	+	0.139573i
$617$	−9.00000			−0.362326			−0.181163	−	0.983453i	$-0.557986\pi$
$617$	−9.00000			−0.362326			−0.181163	+	0.983453i	$0.557986\pi$
$618$	−8.50000	−	14.7224i	−0.341920	−	0.592223i
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	−0.991325	−	0.131434i	$-0.958042\pi$
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	0.609488	+	0.792796i	$0.291375\pi$
$620$	15.0000	−	25.9808i	0.602414	−	1.04341i
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	13.0000			0.521253
$623$	−5.00000	−	25.9808i	−0.200321	−	1.04090i
$624$	−3.00000			−0.120096
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−14.0000	+	24.2487i	−0.559553	+	0.969173i
$627$		0			0
$628$	9.00000	+	15.5885i	0.359139	+	0.622047i
$629$	6.00000			0.239236
$630$	7.50000	+	2.59808i	0.298807	+	0.103510i
$631$	−23.0000			−0.915616			−0.457808	−	0.889051i	$-0.651365\pi$
$631$	−23.0000			−0.915616			−0.457808	+	0.889051i	$0.651365\pi$
$632$	2.00000	+	3.46410i	0.0795557	+	0.137795i
$633$	−3.00000	+	5.19615i	−0.119239	+	0.206529i
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$	−3.00000	−	5.19615i	−0.119051	−	0.206203i
$636$	9.00000			0.356873
$637$	16.5000	+	12.9904i	0.653754	+	0.514698i
$638$	−16.0000			−0.633446
$639$	−3.50000	−	6.06218i	−0.138458	−	0.239816i
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−18.5000	+	32.0429i	−0.730706	+	1.26562i	0.225876	+	0.974156i	$0.427476\pi$
$641$	−18.5000	+	32.0429i	−0.730706	+	1.26562i	−0.956582	+	0.291464i	$0.905858\pi$
$642$	4.00000	+	6.92820i	0.157867	+	0.273434i
$643$	−20.0000			−0.788723			−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000			−0.788723			−0.394362	+	0.918955i	$0.629034\pi$
$644$	−2.50000	−	0.866025i	−0.0985138	−	0.0341262i
$645$	−12.0000			−0.472500
$646$		0			0
$647$	24.0000	−	41.5692i	0.943537	−	1.63425i	0.184884	−	0.982760i	$-0.440809\pi$
$647$	24.0000	−	41.5692i	0.943537	−	1.63425i	0.758654	−	0.651494i	$-0.225858\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	4.00000	+	6.92820i	0.157014	+	0.271956i
$650$	−12.0000			−0.470679
$651$	5.00000	+	25.9808i	0.195965	+	1.01827i
$652$		0			0
$653$	−5.00000	−	8.66025i	−0.195665	−	0.338902i	0.751453	−	0.659786i	$-0.229353\pi$
$653$	−5.00000	−	8.66025i	−0.195665	−	0.338902i	−0.947118	+	0.320884i	$0.896020\pi$
$654$	−4.00000	+	6.92820i	−0.156412	+	0.270914i
$655$	22.5000	−	38.9711i	0.879148	−	1.52273i
$656$	−4.00000	−	6.92820i	−0.156174	−	0.270501i
$657$	3.00000			0.117041
$658$	18.0000	−	15.5885i	0.701713	−	0.607701i
$659$	−2.00000			−0.0779089			−0.0389545	−	0.999241i	$-0.512403\pi$
$659$	−2.00000			−0.0779089			−0.0389545	+	0.999241i	$0.512403\pi$
$660$	3.00000	+	5.19615i	0.116775	+	0.202260i
$661$	−20.0000	+	34.6410i	−0.777910	+	1.34738i	0.155235	+	0.987878i	$0.450387\pi$
$661$	−20.0000	+	34.6410i	−0.777910	+	1.34738i	−0.933144	+	0.359502i	$0.882947\pi$
$662$	5.00000	−	8.66025i	0.194331	−	0.336590i
$663$	−4.50000	−	7.79423i	−0.174766	−	0.302703i
$664$	14.0000			0.543305
$665$		0			0
$666$	2.00000			0.0774984
$667$	−4.00000	−	6.92820i	−0.154881	−	0.268261i
$668$	10.5000	−	18.1865i	0.406257	−	0.703658i
$669$	4.00000	−	6.92820i	0.154649	−	0.267860i
$670$	−4.50000	−	7.79423i	−0.173850	−	0.301117i
$671$	12.0000			0.463255
$672$	−0.500000	−	2.59808i	−0.0192879	−	0.100223i
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$	8.00000	+	13.8564i	0.308148	+	0.533729i
$675$	2.00000	−	3.46410i	0.0769800	−	0.133333i
$676$	2.00000	−	3.46410i	0.0769231	−	0.133235i
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	0.999760	+	0.0219013i	$0.00697196\pi$
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	−0.480913	+	0.876768i	$0.659695\pi$
$678$	−5.00000			−0.192024
$679$	10.0000	+	3.46410i	0.383765	+	0.132940i
$680$	−9.00000			−0.345134
$681$	−7.00000	−	12.1244i	−0.268241	−	0.464606i
$682$	−10.0000	+	17.3205i	−0.382920	+	0.663237i
$683$	18.5000	−	32.0429i	0.707883	−	1.22609i	−0.257758	−	0.966209i	$-0.582984\pi$
$683$	18.5000	−	32.0429i	0.707883	−	1.22609i	0.965641	−	0.259880i	$-0.0836829\pi$
$684$		0			0
$685$	−57.0000			−2.17786
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$	20.0000			0.763048
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	13.5000	−	23.3827i	0.514309	−	0.890809i
$690$	−1.50000	+	2.59808i	−0.0571040	+	0.0989071i
$691$	3.00000	+	5.19615i	0.114125	+	0.197671i	0.917430	−	0.397898i	$-0.130260\pi$
$691$	3.00000	+	5.19615i	0.114125	+	0.197671i	−0.803304	+	0.595569i	$0.796927\pi$
$692$	20.0000			0.760286
$693$	−5.00000	−	1.73205i	−0.189934	−	0.0657952i
$694$	15.0000			0.569392
$695$	15.0000	+	25.9808i	0.568982	+	0.985506i
$696$	4.00000	−	6.92820i	0.151620	−	0.262613i
$697$	12.0000	−	20.7846i	0.454532	−	0.787273i
$698$	−12.5000	−	21.6506i	−0.473132	−	0.819489i
$699$	4.00000			0.151294
$700$	−2.00000	−	10.3923i	−0.0755929	−	0.392792i
$701$	33.0000			1.24639			0.623196	−	0.782065i	$-0.285834\pi$
$701$	33.0000			1.24639			0.623196	+	0.782065i	$0.285834\pi$
$702$	−1.50000	−	2.59808i	−0.0566139	−	0.0980581i
$703$		0			0
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$	−13.5000	−	23.3827i	−0.508439	−	0.880643i
$706$	−4.00000			−0.150542
$707$	20.0000	−	17.3205i	0.752177	−	0.651405i
$708$	−4.00000			−0.150329
$709$	−2.00000	−	3.46410i	−0.0751116	−	0.130097i	0.826023	−	0.563636i	$-0.190598\pi$
$709$	−2.00000	−	3.46410i	−0.0751116	−	0.130097i	−0.901135	+	0.433539i	$0.857265\pi$
$710$	−10.5000	+	18.1865i	−0.394058	+	0.682528i
$711$	−2.00000	+	3.46410i	−0.0750059	+	0.129914i
$712$	5.00000	+	8.66025i	0.187383	+	0.324557i
$713$	−10.0000			−0.374503
$714$	6.00000	−	5.19615i	0.224544	−	0.194461i
$715$	18.0000			0.673162
$716$	−7.50000	−	12.9904i	−0.280288	−	0.485473i
$717$		0			0
$718$	−3.00000	+	5.19615i	−0.111959	+	0.193919i
$719$	−20.5000	−	35.5070i	−0.764521	−	1.32419i	−0.940499	−	0.339795i	$-0.889642\pi$
$719$	−20.5000	−	35.5070i	−0.764521	−	1.32419i	0.175978	−	0.984394i	$-0.443691\pi$
$720$	−3.00000			−0.111803
$721$	−8.50000	−	44.1673i	−0.316557	−	1.64488i
$722$	19.0000			0.707107
$723$	−3.00000	−	5.19615i	−0.111571	−	0.193247i
$724$	−3.00000	+	5.19615i	−0.111494	+	0.193113i
$725$	16.0000	−	27.7128i	0.594225	−	1.02923i
$726$	3.50000	+	6.06218i	0.129897	+	0.224989i
$727$	−40.0000			−1.48352			−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000			−1.48352			−0.741759	+	0.670667i	$0.766008\pi$
$728$	−7.50000	−	2.59808i	−0.277968	−	0.0962911i
$729$	1.00000			0.0370370
$730$	−4.50000	−	7.79423i	−0.166552	−	0.288477i
$731$	−6.00000	+	10.3923i	−0.221918	+	0.384373i
$732$	−3.00000	+	5.19615i	−0.110883	+	0.192055i
$733$	12.0000	+	20.7846i	0.443230	+	0.767697i	0.997927	−	0.0643554i	$-0.0204991\pi$
$733$	12.0000	+	20.7846i	0.443230	+	0.767697i	−0.554697	+	0.832052i	$0.687166\pi$
$734$	9.00000			0.332196
$735$	16.5000	+	12.9904i	0.608612	+	0.479157i
$736$	1.00000			0.0368605
$737$	3.00000	+	5.19615i	0.110506	+	0.191403i
$738$	4.00000	−	6.92820i	0.147242	−	0.255031i
$739$	12.0000	−	20.7846i	0.441427	−	0.764574i	−0.556369	−	0.830936i	$-0.687806\pi$
$739$	12.0000	−	20.7846i	0.441427	−	0.764574i	0.997796	+	0.0663614i	$0.0211390\pi$
$740$	−3.00000	−	5.19615i	−0.110282	−	0.191014i
$741$		0			0
$742$	22.5000	+	7.79423i	0.826001	+	0.286135i
$743$	14.0000			0.513610			0.256805	−	0.966463i	$-0.417330\pi$
$743$	14.0000			0.513610			0.256805	+	0.966463i	$0.417330\pi$
$744$	−5.00000	−	8.66025i	−0.183309	−	0.317500i
$745$	31.5000	−	54.5596i	1.15407	−	1.99891i
$746$	5.00000	−	8.66025i	0.183063	−	0.317074i
$747$	7.00000	+	12.1244i	0.256117	+	0.443607i
$748$	6.00000			0.219382
$749$	4.00000	+	20.7846i	0.146157	+	0.759453i
$750$	3.00000			0.109545
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	0.997526	−	0.0702946i	$-0.0223939\pi$
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	−0.559640	+	0.828736i	$0.689061\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	−13.0000	+	22.5167i	−0.473746	+	0.820553i
$754$	−12.0000	−	20.7846i	−0.437014	−	0.756931i
$755$	60.0000			2.18362
$756$	2.00000	−	1.73205i	0.0727393	−	0.0629941i
$757$	−40.0000			−1.45382			−0.726912	−	0.686730i	$-0.759045\pi$
$757$	−40.0000			−1.45382			−0.726912	+	0.686730i	$0.759045\pi$
$758$	−14.5000	−	25.1147i	−0.526664	−	0.912208i
$759$	1.00000	−	1.73205i	0.0362977	−	0.0628695i
$760$		0			0
$761$	2.00000	+	3.46410i	0.0724999	+	0.125574i	0.899996	−	0.435897i	$-0.143569\pi$
$761$	2.00000	+	3.46410i	0.0724999	+	0.125574i	−0.827496	+	0.561471i	$0.810236\pi$
$762$	−2.00000			−0.0724524
$763$	−16.0000	+	13.8564i	−0.579239	+	0.501636i
$764$	−8.00000			−0.289430
$765$	−4.50000	−	7.79423i	−0.162698	−	0.281801i
$766$	−11.0000	+	19.0526i	−0.397446	+	0.688397i
$767$	−6.00000	+	10.3923i	−0.216647	+	0.375244i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$	3.00000	+	15.5885i	0.108112	+	0.561769i
$771$	−14.0000			−0.504198
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	−8.50000	+	14.7224i	−0.305724	+	0.529529i	−0.977422	−	0.211296i	$-0.932232\pi$
$773$	−8.50000	+	14.7224i	−0.305724	+	0.529529i	0.671698	+	0.740825i	$0.265565\pi$
$774$	−2.00000	+	3.46410i	−0.0718885	+	0.124515i
$775$	−20.0000	−	34.6410i	−0.718421	−	1.24434i
$776$	−4.00000			−0.143592
$777$	5.00000	+	1.73205i	0.179374	+	0.0621370i
$778$	−10.0000			−0.358517
$779$		0			0
$780$	−4.50000	+	7.79423i	−0.161126	+	0.279078i
$781$	7.00000	−	12.1244i	0.250480	−	0.433844i
$782$	1.50000	+	2.59808i	0.0536399	+	0.0929070i
$783$	8.00000			0.285897
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	54.0000			1.92734
$786$	−7.50000	−	12.9904i	−0.267516	−	0.463352i
$787$	−26.5000	+	45.8993i	−0.944623	+	1.63614i	−0.188119	+	0.982146i	$0.560239\pi$
$787$	−26.5000	+	45.8993i	−0.944623	+	1.63614i	−0.756504	+	0.653989i	$0.773094\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$	−6.00000	−	10.3923i	−0.213606	−	0.369976i
$790$	12.0000			0.426941
$791$	−12.5000	−	4.33013i	−0.444449	−	0.153962i
$792$	2.00000			0.0710669
$793$	9.00000	+	15.5885i	0.319599	+	0.553562i
$794$	4.50000	−	7.79423i	0.159699	−	0.276607i
$795$	13.5000	−	23.3827i	0.478796	−	0.829298i
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	11.0000			0.389640			0.194820	−	0.980839i	$-0.437588\pi$
$797$	11.0000			0.389640			0.194820	+	0.980839i	$0.437588\pi$
$798$		0			0
$799$	−27.0000			−0.955191
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	−5.00000	+	8.66025i	−0.176666	+	0.305995i
$802$	−19.5000	+	33.7750i	−0.688569	+	1.19264i
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$	−3.00000			−0.105802
$805$	−6.00000	+	5.19615i	−0.211472	+	0.183140i
$806$	−30.0000			−1.05670
$807$	−10.0000	−	17.3205i	−0.352017	−	0.609711i
$808$	−5.00000	+	8.66025i	−0.175899	+	0.304667i
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	−0.808458	−	0.588555i	$-0.799697\pi$
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	0.913932	+	0.405868i	$0.133031\pi$
$810$	−1.50000	−	2.59808i	−0.0527046	−	0.0912871i
$811$	−46.0000			−1.61528			−0.807639	−	0.589677i	$-0.799255\pi$
$811$	−46.0000			−1.61528			−0.807639	+	0.589677i	$0.799255\pi$
$812$	16.0000	−	13.8564i	0.561490	−	0.486265i
$813$	−6.00000			−0.210429
$814$	2.00000	+	3.46410i	0.0701000	+	0.121417i
$815$		0			0
$816$	−1.50000	+	2.59808i	−0.0525105	+	0.0909509i
$817$		0			0
$818$	−39.0000			−1.36360
$819$	−1.50000	−	7.79423i	−0.0524142	−	0.272352i
$820$	−24.0000			−0.838116
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$	−9.50000	+	16.4545i	−0.331351	+	0.573916i
$823$	13.0000	−	22.5167i	0.453152	−	0.784881i	−0.545428	−	0.838157i	$-0.683633\pi$
$823$	13.0000	−	22.5167i	0.453152	−	0.784881i	0.998580	+	0.0532760i	$0.0169663\pi$
$824$	8.50000	+	14.7224i	0.296112	+	0.512880i
$825$	8.00000			0.278524
$826$	−10.0000	−	3.46410i	−0.347945	−	0.120532i
$827$	−48.0000			−1.66912			−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000			−1.66912			−0.834562	+	0.550914i	$0.814279\pi$
$828$	0.500000	+	0.866025i	0.0173762	+	0.0300965i
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	−0.997225	−	0.0744432i	$-0.976282\pi$
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	0.563082	+	0.826401i	$0.309615\pi$
$830$	21.0000	−	36.3731i	0.728921	−	1.26253i
$831$	4.50000	+	7.79423i	0.156103	+	0.270379i
$832$	3.00000			0.104006
$833$	19.5000	−	7.79423i	0.675635	−	0.270054i
$834$	10.0000			0.346272
$835$	−31.5000	−	54.5596i	−1.09010	−	1.88811i
$836$		0			0
$837$	5.00000	−	8.66025i	0.172825	−	0.299342i
$838$	14.0000	+	24.2487i	0.483622	+	0.837658i
$839$	−12.0000			−0.414286			−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000			−0.414286			−0.207143	+	0.978311i	$0.566417\pi$
$840$	−7.50000	−	2.59808i	−0.258775	−	0.0896421i
$841$	35.0000			1.20690
$842$	−2.00000	−	3.46410i	−0.0689246	−	0.119381i
$843$	3.50000	−	6.06218i	0.120546	−	0.208792i
$844$	3.00000	−	5.19615i	0.103264	−	0.178859i
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$	−9.00000			−0.309426
$847$	3.50000	+	18.1865i	0.120261	+	0.624897i
$848$	−9.00000			−0.309061
$849$	−3.50000	−	6.06218i	−0.120120	−	0.208053i
$850$	−6.00000	+	10.3923i	−0.205798	+	0.356453i
$851$	−1.00000	+	1.73205i	−0.0342796	+	0.0593739i
$852$	3.50000	+	6.06218i	0.119908	+	0.207687i
$853$	38.0000			1.30110			0.650548	−	0.759465i	$-0.274539\pi$
$853$	38.0000			1.30110			0.650548	+	0.759465i	$0.274539\pi$
$854$	−12.0000	+	10.3923i	−0.410632	+	0.355617i
$855$		0			0
$856$	−4.00000	−	6.92820i	−0.136717	−	0.236801i
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$	3.00000	−	5.19615i	0.102418	−	0.177394i
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	−0.974249	−	0.225475i	$-0.927607\pi$
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	0.291858	−	0.956462i	$-0.405727\pi$
$860$	12.0000			0.409197
$861$	16.0000	−	13.8564i	0.545279	−	0.472225i
$862$	−36.0000			−1.22616
$863$	25.5000	+	44.1673i	0.868030	+	1.50347i	0.864007	+	0.503480i	$0.167947\pi$
$863$	25.5000	+	44.1673i	0.868030	+	1.50347i	0.00402340	+	0.999992i	$0.498719\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	30.0000	−	51.9615i	1.02003	−	1.76674i
$866$	−9.00000	−	15.5885i	−0.305832	−	0.529717i
$867$	8.00000			0.271694
$868$	−5.00000	−	25.9808i	−0.169711	−	0.881845i
$869$	−8.00000			−0.271381
$870$	−12.0000	−	20.7846i	−0.406838	−	0.704664i
$871$	−4.50000	+	7.79423i	−0.152477	+	0.264097i
$872$	4.00000	−	6.92820i	0.135457	−	0.234619i
$873$	−2.00000	−	3.46410i	−0.0676897	−	0.117242i
$874$		0			0
$875$	7.50000	+	2.59808i	0.253546	+	0.0878310i
$876$	−3.00000			−0.101361
$877$	20.5000	+	35.5070i	0.692236	+	1.19899i	0.971104	+	0.238658i	$0.0767075\pi$
$877$	20.5000	+	35.5070i	0.692236	+	1.19899i	−0.278868	+	0.960329i	$0.589959\pi$
$878$	13.0000	−	22.5167i	0.438729	−	0.759900i
$879$	−6.50000	+	11.2583i	−0.219240	+	0.379734i
$880$	−3.00000	−	5.19615i	−0.101130	−	0.175162i
$881$	35.0000			1.17918			0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000			1.17918			0.589590	+	0.807703i	$0.299289\pi$
$882$	6.50000	−	2.59808i	0.218866	−	0.0874818i
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$	4.50000	+	7.79423i	0.151351	+	0.262148i
$885$	−6.00000	+	10.3923i	−0.201688	+	0.349334i
$886$	−8.50000	+	14.7224i	−0.285563	+	0.494610i
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	0.791026	−	0.611783i	$-0.209547\pi$
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	−0.925332	+	0.379157i	$0.876214\pi$
$888$	−2.00000			−0.0671156
$889$	−5.00000	−	1.73205i	−0.167695	−	0.0580911i
$890$	30.0000			1.00560
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	−4.00000	+	6.92820i	−0.133930	+	0.231973i
$893$		0			0
$894$	−10.5000	−	18.1865i	−0.351173	−	0.608249i
$895$	−45.0000			−1.50418
$896$	0.500000	+	2.59808i	0.0167038	+	0.0867956i
$897$	3.00000			0.100167
$898$	3.00000	+	5.19615i	0.100111	+	0.173398i
$899$	40.0000	−	69.2820i	1.33407	−	2.31069i
$900$	−2.00000	+	3.46410i	−0.0666667	+	0.115470i
$901$	−13.5000	−	23.3827i	−0.449750	−	0.778990i
$902$	16.0000			0.532742
$903$	−8.00000	+	6.92820i	−0.266223	+	0.230556i
$904$	5.00000			0.166298
$905$	9.00000	+	15.5885i	0.299170	+	0.518178i
$906$	10.0000	−	17.3205i	0.332228	−	0.575435i
$907$	−14.5000	+	25.1147i	−0.481465	+	0.833921i	−0.999774	−	0.0212722i	$-0.993228\pi$
$907$	−14.5000	+	25.1147i	−0.481465	+	0.833921i	0.518309	+	0.855193i	$0.326562\pi$
$908$	7.00000	+	12.1244i	0.232303	+	0.402361i
$909$	−10.0000			−0.331679
$910$	−18.0000	+	15.5885i	−0.596694	+	0.516752i
$911$	−4.00000			−0.132526			−0.0662630	−	0.997802i	$-0.521108\pi$
$911$	−4.00000			−0.132526			−0.0662630	+	0.997802i	$0.521108\pi$
$912$		0			0
$913$	−14.0000	+	24.2487i	−0.463332	+	0.802515i
$914$	−14.0000	+	24.2487i	−0.463079	+	0.802076i
$915$	9.00000	+	15.5885i	0.297531	+	0.515339i
$916$	−20.0000			−0.660819
$917$	−7.50000	−	38.9711i	−0.247672	−	1.28694i
$918$	−3.00000			−0.0990148
$919$	−22.5000	−	38.9711i	−0.742207	−	1.28554i	−0.951489	−	0.307684i	$-0.900446\pi$
$919$	−22.5000	−	38.9711i	−0.742207	−	1.28554i	0.209282	−	0.977855i	$-0.432887\pi$
$920$	1.50000	−	2.59808i	0.0494535	−	0.0856560i
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$	−9.00000	−	15.5885i	−0.296399	−	0.513378i
$923$	21.0000			0.691223
$924$	5.00000	+	1.73205i	0.164488	+	0.0569803i
$925$	−8.00000			−0.263038
$926$	−2.00000	−	3.46410i	−0.0657241	−	0.113837i
$927$	−8.50000	+	14.7224i	−0.279177	+	0.483548i
$928$	−4.00000	+	6.92820i	−0.131306	+	0.227429i
$929$	18.0000	+	31.1769i	0.590561	+	1.02288i	0.994157	+	0.107944i	$0.0344268\pi$
$929$	18.0000	+	31.1769i	0.590561	+	1.02288i	−0.403596	+	0.914937i	$0.632240\pi$
$930$	−30.0000			−0.983739
$931$		0			0
$932$	−4.00000			−0.131024
$933$	−6.50000	−	11.2583i	−0.212800	−	0.368581i
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$	9.00000	−	15.5885i	0.294331	−	0.509797i
$936$	1.50000	+	2.59808i	0.0490290	+	0.0849208i
$937$	52.0000			1.69877			0.849383	−	0.527777i	$-0.176974\pi$
$937$	52.0000			1.69877			0.849383	+	0.527777i	$0.176974\pi$
$938$	−7.50000	−	2.59808i	−0.244884	−	0.0848302i
$939$	28.0000			0.913745
$940$	13.5000	+	23.3827i	0.440321	+	0.762659i
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	−0.974609	−	0.223912i	$-0.928117\pi$
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	0.681218	+	0.732081i	$0.261451\pi$
$942$	9.00000	−	15.5885i	0.293236	−	0.507899i
$943$	4.00000	+	6.92820i	0.130258	+	0.225613i
$944$	4.00000			0.130189
$945$	−1.50000	−	7.79423i	−0.0487950	−	0.253546i
$946$	−8.00000			−0.260102
$947$	1.50000	+	2.59808i	0.0487435	+	0.0844261i	0.889368	−	0.457193i	$-0.151145\pi$
$947$	1.50000	+	2.59808i	0.0487435	+	0.0844261i	−0.840624	+	0.541619i	$0.817812\pi$
$948$	2.00000	−	3.46410i	0.0649570	−	0.112509i
$949$	−4.50000	+	7.79423i	−0.146076	+	0.253011i
$950$		0			0
$951$	6.00000			0.194563
$952$	−6.00000	+	5.19615i	−0.194461	+	0.168408i
$953$	−46.0000			−1.49009			−0.745043	−	0.667016i	$-0.767571\pi$
$953$	−46.0000			−1.49009			−0.745043	+	0.667016i	$0.767571\pi$
$954$	−4.50000	−	7.79423i	−0.145693	−	0.252347i
$955$	−12.0000	+	20.7846i	−0.388311	+	0.672574i
$956$		0			0
$957$	8.00000	+	13.8564i	0.258603	+	0.447914i
$958$		0			0
$959$	−38.0000	+	32.9090i	−1.22708	+	1.06269i
$960$	3.00000			0.0968246
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	−3.00000	+	5.19615i	−0.0967239	+	0.167531i
$963$	4.00000	−	6.92820i	0.128898	−	0.223258i
$964$	3.00000	+	5.19615i	0.0966235	+	0.167357i
$965$	−15.0000			−0.482867
$966$	0.500000	+	2.59808i	0.0160872	+	0.0835917i
$967$	16.0000			0.514525			0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000			0.514525			0.257263	+	0.966342i	$0.417179\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$		0			0
$970$	−6.00000	+	10.3923i	−0.192648	+	0.333677i
$971$	20.0000	+	34.6410i	0.641831	+	1.11168i	0.985024	+	0.172418i	$0.0551581\pi$
$971$	20.0000	+	34.6410i	0.641831	+	1.11168i	−0.343193	+	0.939265i	$0.611509\pi$
$972$	−1.00000			−0.0320750
$973$	25.0000	+	8.66025i	0.801463	+	0.277635i
$974$	20.0000			0.640841
$975$	6.00000	+	10.3923i	0.192154	+	0.332820i
$976$	3.00000	−	5.19615i	0.0960277	−	0.166325i
$977$	18.5000	−	32.0429i	0.591867	−	1.02514i	−0.402113	−	0.915590i	$-0.631724\pi$
$977$	18.5000	−	32.0429i	0.591867	−	1.02514i	0.993981	−	0.109555i	$-0.0349424\pi$
$978$		0			0
$979$	−20.0000			−0.639203
$980$	−16.5000	−	12.9904i	−0.527073	−	0.414963i
$981$	8.00000			0.255420
$982$	−14.5000	−	25.1147i	−0.462714	−	0.801443i
$983$	5.00000	−	8.66025i	0.159475	−	0.276219i	−0.775204	−	0.631711i	$-0.782353\pi$
$983$	5.00000	−	8.66025i	0.159475	−	0.276219i	0.934680	+	0.355491i	$0.115686\pi$
$984$	−4.00000	+	6.92820i	−0.127515	+	0.220863i
$985$	27.0000	+	46.7654i	0.860292	+	1.49007i
$986$	−24.0000			−0.764316
$987$	−22.5000	−	7.79423i	−0.716183	−	0.248093i
$988$		0			0
$989$	−2.00000	−	3.46410i	−0.0635963	−	0.110152i
$990$	3.00000	−	5.19615i	0.0953463	−	0.165145i
$991$	−7.00000	+	12.1244i	−0.222362	+	0.385143i	−0.955525	−	0.294911i	$-0.904710\pi$
$991$	−7.00000	+	12.1244i	−0.222362	+	0.385143i	0.733163	+	0.680053i	$0.238043\pi$
$992$	5.00000	+	8.66025i	0.158750	+	0.274963i
$993$	−10.0000			−0.317340
$994$	3.50000	+	18.1865i	0.111013	+	0.576842i
$995$	24.0000			0.760851
$996$	−7.00000	−	12.1244i	−0.221803	−	0.384175i
$997$	19.0000	−	32.9090i	0.601736	−	1.04224i	−0.390822	−	0.920466i	$-0.627809\pi$
$997$	19.0000	−	32.9090i	0.601736	−	1.04224i	0.992558	−	0.121771i	$-0.0388574\pi$
$998$	−20.0000	+	34.6410i	−0.633089	+	1.09654i
$999$	−1.00000	−	1.73205i	−0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.g.277.1	✓	2
7.2	even	3	inner	966.2.i.g.415.1	yes	2
7.3	odd	6		6762.2.a.u.1.1		1
7.4	even	3		6762.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.g.277.1	✓	2	1.1	even	1	trivial
966.2.i.g.415.1	yes	2	7.2	even	3	inner
6762.2.a.b.1.1		1	7.4	even	3
6762.2.a.u.1.1		1	7.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(1.00000 - 1.73205i) q^{11} +(0.500000 + 0.866025i) q^{12} +3.00000 q^{13} +(0.500000 + 2.59808i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{18} -3.00000 q^{20} +(2.00000 - 1.73205i) q^{21} +2.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(1.50000 + 2.59808i) q^{26} -1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} -8.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(-5.00000 + 8.66025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +3.00000 q^{34} +(1.50000 + 7.79423i) q^{35} +1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(1.50000 - 2.59808i) q^{39} +(-1.50000 - 2.59808i) q^{40} +8.00000 q^{41} +(2.50000 + 0.866025i) q^{42} -4.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(1.50000 - 2.59808i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-4.50000 - 7.79423i) q^{47} -1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -4.00000 q^{50} +(-1.50000 - 2.59808i) q^{51} +(-1.50000 + 2.59808i) q^{52} +(4.50000 - 7.79423i) q^{53} +(-0.500000 - 0.866025i) q^{54} +6.00000 q^{55} +(-2.50000 - 0.866025i) q^{56} +(-4.00000 - 6.92820i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(3.00000 + 5.19615i) q^{61} -10.0000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(4.50000 + 7.79423i) q^{65} +(1.00000 - 1.73205i) q^{66} +(-1.50000 + 2.59808i) q^{67} +(1.50000 + 2.59808i) q^{68} +1.00000 q^{69} +(-6.00000 + 5.19615i) q^{70} +7.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-1.50000 + 2.59808i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(2.00000 + 3.46410i) q^{75} +(4.00000 - 3.46410i) q^{77} +3.00000 q^{78} +(-2.00000 - 3.46410i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.00000 + 6.92820i) q^{82} -14.0000 q^{83} +(0.500000 + 2.59808i) q^{84} +9.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(-4.00000 + 6.92820i) q^{87} +(-1.00000 + 1.73205i) q^{88} +(-5.00000 - 8.66025i) q^{89} +3.00000 q^{90} +(7.50000 + 2.59808i) q^{91} -1.00000 q^{92} +(5.00000 + 8.66025i) q^{93} +(4.50000 - 7.79423i) q^{94} +(-0.500000 - 0.866025i) q^{96} +4.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + 3 q^{5} + 2 q^{6} + 5 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + 3 * q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + 3 q^{5} + 2 q^{6} + 5 q^{7} - 2 q^{8} - q^{9} - 3 q^{10} + 2 q^{11} + q^{12} + 6 q^{13} + q^{14} + 6 q^{15} - q^{16} + 3 q^{17} + q^{18} - 6 q^{20} + 4 q^{21} + 4 q^{22} + q^{23} - q^{24} - 4 q^{25} + 3 q^{26} - 2 q^{27} - 4 q^{28} - 16 q^{29} + 3 q^{30} - 10 q^{31} + q^{32} - 2 q^{33} + 6 q^{34} + 3 q^{35} + 2 q^{36} + 2 q^{37} + 3 q^{39} - 3 q^{40} + 16 q^{41} + 5 q^{42} - 8 q^{43} + 2 q^{44} + 3 q^{45} - q^{46} - 9 q^{47} - 2 q^{48} + 11 q^{49} - 8 q^{50} - 3 q^{51} - 3 q^{52} + 9 q^{53} - q^{54} + 12 q^{55} - 5 q^{56} - 8 q^{58} - 4 q^{59} - 3 q^{60} + 6 q^{61} - 20 q^{62} - q^{63} + 2 q^{64} + 9 q^{65} + 2 q^{66} - 3 q^{67} + 3 q^{68} + 2 q^{69} - 12 q^{70} + 14 q^{71} + q^{72} - 3 q^{73} - 2 q^{74} + 4 q^{75} + 8 q^{77} + 6 q^{78} - 4 q^{79} + 3 q^{80} - q^{81} + 8 q^{82} - 28 q^{83} + q^{84} + 18 q^{85} - 4 q^{86} - 8 q^{87} - 2 q^{88} - 10 q^{89} + 6 q^{90} + 15 q^{91} - 2 q^{92} + 10 q^{93} + 9 q^{94} - q^{96} + 8 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 3 * q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 - q^9 - 3 * q^10 + 2 * q^11 + q^12 + 6 * q^13 + q^14 + 6 * q^15 - q^16 + 3 * q^17 + q^18 - 6 * q^20 + 4 * q^21 + 4 * q^22 + q^23 - q^24 - 4 * q^25 + 3 * q^26 - 2 * q^27 - 4 * q^28 - 16 * q^29 + 3 * q^30 - 10 * q^31 + q^32 - 2 * q^33 + 6 * q^34 + 3 * q^35 + 2 * q^36 + 2 * q^37 + 3 * q^39 - 3 * q^40 + 16 * q^41 + 5 * q^42 - 8 * q^43 + 2 * q^44 + 3 * q^45 - q^46 - 9 * q^47 - 2 * q^48 + 11 * q^49 - 8 * q^50 - 3 * q^51 - 3 * q^52 + 9 * q^53 - q^54 + 12 * q^55 - 5 * q^56 - 8 * q^58 - 4 * q^59 - 3 * q^60 + 6 * q^61 - 20 * q^62 - q^63 + 2 * q^64 + 9 * q^65 + 2 * q^66 - 3 * q^67 + 3 * q^68 + 2 * q^69 - 12 * q^70 + 14 * q^71 + q^72 - 3 * q^73 - 2 * q^74 + 4 * q^75 + 8 * q^77 + 6 * q^78 - 4 * q^79 + 3 * q^80 - q^81 + 8 * q^82 - 28 * q^83 + q^84 + 18 * q^85 - 4 * q^86 - 8 * q^87 - 2 * q^88 - 10 * q^89 + 6 * q^90 + 15 * q^91 - 2 * q^92 + 10 * q^93 + 9 * q^94 - q^96 + 8 * q^97 - 2 * q^98 - 4 * q^99

Introduction

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