LMFDB - Embedded newform 966.2.i.d.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.d.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} +(-0.500000 + 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} -6.00000 q^{13} +(2.00000 + 1.73205i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} -3.00000 q^{20} +(-0.500000 + 2.59808i) q^{21} +1.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(3.00000 + 5.19615i) q^{26} -1.00000 q^{27} +(0.500000 - 2.59808i) q^{28} -7.00000 q^{29} +(-1.50000 - 2.59808i) q^{30} +(-3.50000 + 6.06218i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} -2.00000 q^{34} +(-6.00000 - 5.19615i) q^{35} +1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-3.00000 + 5.19615i) q^{39} +(1.50000 + 2.59808i) q^{40} -10.0000 q^{41} +(2.50000 - 0.866025i) q^{42} +2.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.50000 - 2.59808i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-3.00000 - 5.19615i) q^{47} -1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +4.00000 q^{50} +(-1.00000 - 1.73205i) q^{51} +(3.00000 - 5.19615i) q^{52} +(-5.50000 + 9.52628i) q^{53} +(0.500000 + 0.866025i) q^{54} -3.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +2.00000 q^{57} +(3.50000 + 6.06218i) q^{58} +(-7.50000 + 12.9904i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(1.00000 + 1.73205i) q^{61} +7.00000 q^{62} +(2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-9.00000 - 15.5885i) q^{65} +(0.500000 - 0.866025i) q^{66} +(-1.00000 + 1.73205i) q^{67} +(1.00000 + 1.73205i) q^{68} +1.00000 q^{69} +(-1.50000 + 7.79423i) q^{70} +(-0.500000 - 0.866025i) q^{72} +(5.00000 - 8.66025i) q^{73} +(1.00000 - 1.73205i) q^{74} +(2.00000 + 3.46410i) q^{75} -2.00000 q^{76} +(0.500000 - 2.59808i) q^{77} +6.00000 q^{78} +(5.50000 + 9.52628i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.00000 + 8.66025i) q^{82} +13.0000 q^{83} +(-2.00000 - 1.73205i) q^{84} +6.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(-3.50000 + 6.06218i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-4.00000 - 6.92820i) q^{89} -3.00000 q^{90} +(15.0000 - 5.19615i) q^{91} -1.00000 q^{92} +(3.50000 + 6.06218i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{96} +1.00000 q^{97} +(-6.50000 - 2.59808i) q^{98} +1.00000 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	\( 2 q - q^{2} + q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 5 q^{7} + 2 q^{8} - q^{9} + 3 q^{10} - q^{11} + q^{12} - 12 q^{13} + 4 q^{14} + 6 q^{15} - q^{16} + 2 q^{17} - q^{18} + 2 q^{19} - 6 q^{20} - q^{21} + 2 q^{22} + q^{23} + q^{24} - 4 q^{25} + 6 q^{26} - 2 q^{27} + q^{28} - 14 q^{29} - 3 q^{30} - 7 q^{31} - q^{32} + q^{33} - 4 q^{34} - 12 q^{35} + 2 q^{36} + 2 q^{37} + 2 q^{38} - 6 q^{39} + 3 q^{40} - 20 q^{41} + 5 q^{42} + 4 q^{43} - q^{44} + 3 q^{45} + q^{46} - 6 q^{47} - 2 q^{48} + 11 q^{49} + 8 q^{50} - 2 q^{51} + 6 q^{52} - 11 q^{53} + q^{54} - 6 q^{55} - 5 q^{56} + 4 q^{57} + 7 q^{58} - 15 q^{59} - 3 q^{60} + 2 q^{61} + 14 q^{62} + 4 q^{63} + 2 q^{64} - 18 q^{65} + q^{66} - 2 q^{67} + 2 q^{68} + 2 q^{69} - 3 q^{70} - q^{72} + 10 q^{73} + 2 q^{74} + 4 q^{75} - 4 q^{76} + q^{77} + 12 q^{78} + 11 q^{79} + 3 q^{80} - q^{81} + 10 q^{82} + 26 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} - 7 q^{87} - q^{88} - 8 q^{89} - 6 q^{90} + 30 q^{91} - 2 q^{92} + 7 q^{93} - 6 q^{94} - 6 q^{95} + q^{96} + 2 q^{97} - 13 q^{98} + 2 q^{99}+O(q^{100}) \) 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 - q^11 + q^12 - 12 * q^13 + 4 * q^14 + 6 * q^15 - q^16 + 2 * q^17 - q^18 + 2 * q^19 - 6 * q^20 - q^21 + 2 * q^22 + q^23 + q^24 - 4 * q^25 + 6 * q^26 - 2 * q^27 + q^28 - 14 * q^29 - 3 * q^30 - 7 * q^31 - q^32 + q^33 - 4 * q^34 - 12 * q^35 + 2 * q^36 + 2 * q^37 + 2 * q^38 - 6 * q^39 + 3 * q^40 - 20 * q^41 + 5 * q^42 + 4 * q^43 - q^44 + 3 * q^45 + q^46 - 6 * q^47 - 2 * q^48 + 11 * q^49 + 8 * q^50 - 2 * q^51 + 6 * q^52 - 11 * q^53 + q^54 - 6 * q^55 - 5 * q^56 + 4 * q^57 + 7 * q^58 - 15 * q^59 - 3 * q^60 + 2 * q^61 + 14 * q^62 + 4 * q^63 + 2 * q^64 - 18 * q^65 + q^66 - 2 * q^67 + 2 * q^68 + 2 * q^69 - 3 * q^70 - q^72 + 10 * q^73 + 2 * q^74 + 4 * q^75 - 4 * q^76 + q^77 + 12 * q^78 + 11 * q^79 + 3 * q^80 - q^81 + 10 * q^82 + 26 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 - 7 * q^87 - q^88 - 8 * q^89 - 6 * q^90 + 30 * q^91 - 2 * q^92 + 7 * q^93 - 6 * q^94 - 6 * q^95 + q^96 + 2 * q^97 - 13 * q^98 + 2 * 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
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−6.00000			−1.66410			−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000			−1.66410			−0.832050	+	0.554700i	$0.812833\pi$
$14$	2.00000	+	1.73205i	0.534522	+	0.462910i
$15$	3.00000			0.774597
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	−3.00000			−0.670820
$21$	−0.500000	+	2.59808i	−0.109109	+	0.566947i
$22$	1.00000			0.213201
$23$	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
$26$	3.00000	+	5.19615i	0.588348	+	1.01905i
$27$	−1.00000			−0.192450
$28$	0.500000	−	2.59808i	0.0944911	−	0.490990i
$29$	−7.00000			−1.29987			−0.649934	−	0.759991i	$-0.725203\pi$
$29$	−7.00000			−1.29987			−0.649934	+	0.759991i	$0.725203\pi$
$30$	−1.50000	−	2.59808i	−0.273861	−	0.474342i
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	0.359211	+	0.933257i	$0.383046\pi$
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	−2.00000			−0.342997
$35$	−6.00000	−	5.19615i	−1.01419	−	0.878310i
$36$	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	$0.780765\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$	−3.00000	+	5.19615i	−0.480384	+	0.832050i
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$	−10.0000			−1.56174			−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000			−1.56174			−0.780869	+	0.624695i	$0.785223\pi$
$42$	2.50000	−	0.866025i	0.385758	−	0.133631i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$	−1.00000			−0.144338
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	4.00000			0.565685
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	3.00000	−	5.19615i	0.416025	−	0.720577i
$53$	−5.50000	+	9.52628i	−0.755483	+	1.30854i	0.189651	+	0.981852i	$0.439264\pi$
$53$	−5.50000	+	9.52628i	−0.755483	+	1.30854i	−0.945134	+	0.326683i	$0.894069\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−3.00000			−0.404520
$56$	−2.50000	+	0.866025i	−0.334077	+	0.115728i
$57$	2.00000			0.264906
$58$	3.50000	+	6.06218i	0.459573	+	0.796003i
$59$	−7.50000	+	12.9904i	−0.976417	+	1.69120i	−0.301239	+	0.953549i	$0.597400\pi$
$59$	−7.50000	+	12.9904i	−0.976417	+	1.69120i	−0.675178	+	0.737655i	$0.735933\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	7.00000			0.889001
$63$	2.00000	+	1.73205i	0.251976	+	0.218218i
$64$	1.00000			0.125000
$65$	−9.00000	−	15.5885i	−1.11631	−	1.93351i
$66$	0.500000	−	0.866025i	0.0615457	−	0.106600i
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	1.00000	+	1.73205i	0.121268	+	0.210042i
$69$	1.00000			0.120386
$70$	−1.50000	+	7.79423i	−0.179284	+	0.931589i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	5.00000	−	8.66025i	0.585206	−	1.01361i	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	5.00000	−	8.66025i	0.585206	−	1.01361i	0.994850	−	0.101361i	$-0.0323196\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$	−2.00000			−0.229416
$77$	0.500000	−	2.59808i	0.0569803	−	0.296078i
$78$	6.00000			0.679366
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	0.989705	+	0.143120i	$0.0457135\pi$
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.00000	+	8.66025i	0.552158	+	0.956365i
$83$	13.0000			1.42694			0.713468	−	0.700688i	$-0.247124\pi$
$83$	13.0000			1.42694			0.713468	+	0.700688i	$0.247124\pi$
$84$	−2.00000	−	1.73205i	−0.218218	−	0.188982i
$85$	6.00000			0.650791
$86$	−1.00000	−	1.73205i	−0.107833	−	0.186772i
$87$	−3.50000	+	6.06218i	−0.375239	+	0.649934i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−4.00000	−	6.92820i	−0.423999	−	0.734388i	0.572327	−	0.820025i	$-0.306041\pi$
$89$	−4.00000	−	6.92820i	−0.423999	−	0.734388i	−0.996326	+	0.0856373i	$0.972707\pi$
$90$	−3.00000			−0.316228
$91$	15.0000	−	5.19615i	1.57243	−	0.544705i
$92$	−1.00000			−0.104257
$93$	3.50000	+	6.06218i	0.362933	+	0.628619i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	1.00000			0.101535			0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000			0.101535			0.0507673	+	0.998711i	$0.483833\pi$
$98$	−6.50000	−	2.59808i	−0.656599	−	0.262445i
$99$	1.00000			0.100504
$100$	−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	$0.000911295\pi$
$102$	−1.00000	+	1.73205i	−0.0990148	+	0.171499i
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$	−6.00000			−0.588348
$105$	−7.50000	+	2.59808i	−0.731925	+	0.253546i
$106$	11.0000			1.06841
$107$	8.50000	+	14.7224i	0.821726	+	1.42327i	0.904396	+	0.426694i	$0.140322\pi$
$107$	8.50000	+	14.7224i	0.821726	+	1.42327i	−0.0826699	+	0.996577i	$0.526345\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	−0.307290	−	0.951616i	$-0.599422\pi$
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	0.977769	−	0.209687i	$-0.0672444\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$	2.00000			0.189832
$112$	2.00000	+	1.73205i	0.188982	+	0.163663i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$	3.50000	−	6.06218i	0.324967	−	0.562859i
$117$	3.00000	+	5.19615i	0.277350	+	0.480384i
$118$	15.0000			1.38086
$119$	−1.00000	+	5.19615i	−0.0916698	+	0.476331i
$120$	3.00000			0.273861
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	1.00000	−	1.73205i	0.0905357	−	0.156813i
$123$	−5.00000	+	8.66025i	−0.450835	+	0.780869i
$124$	−3.50000	−	6.06218i	−0.314309	−	0.544400i
$125$	3.00000			0.268328
$126$	0.500000	−	2.59808i	0.0445435	−	0.231455i
$127$	17.0000			1.50851			0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000			1.50851			0.754253	+	0.656584i	$0.227999\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$	−9.00000	+	15.5885i	−0.789352	+	1.36720i
$131$	−3.50000	−	6.06218i	−0.305796	−	0.529655i	0.671642	−	0.740876i	$-0.265589\pi$
$131$	−3.50000	−	6.06218i	−0.305796	−	0.529655i	−0.977438	+	0.211221i	$0.932256\pi$
$132$	−1.00000			−0.0870388
$133$	−4.00000	−	3.46410i	−0.346844	−	0.300376i
$134$	2.00000			0.172774
$135$	−1.50000	−	2.59808i	−0.129099	−	0.223607i
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	−0.905577	−	0.424182i	$-0.860562\pi$
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	0.820141	+	0.572161i	$0.193895\pi$
$138$	−0.500000	−	0.866025i	−0.0425628	−	0.0737210i
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$	7.50000	−	2.59808i	0.633866	−	0.219578i
$141$	−6.00000			−0.505291
$142$		0			0
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−10.5000	−	18.1865i	−0.871978	−	1.51031i
$146$	−10.0000			−0.827606
$147$	−1.00000	−	6.92820i	−0.0824786	−	0.571429i
$148$	−2.00000			−0.164399
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	0.162758	+	0.986666i	$0.447961\pi$
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	−2.00000			−0.161690
$154$	−2.50000	+	0.866025i	−0.201456	+	0.0697863i
$155$	−21.0000			−1.68676
$156$	−3.00000	−	5.19615i	−0.240192	−	0.416025i
$157$	−11.0000	+	19.0526i	−0.877896	+	1.52056i	−0.0242497	+	0.999706i	$0.507720\pi$
$157$	−11.0000	+	19.0526i	−0.877896	+	1.52056i	−0.853646	+	0.520854i	$0.825614\pi$
$158$	5.50000	−	9.52628i	0.437557	−	0.757870i
$159$	5.50000	+	9.52628i	0.436178	+	0.755483i
$160$	−3.00000			−0.237171
$161$	−2.00000	−	1.73205i	−0.157622	−	0.136505i
$162$	1.00000			0.0785674
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	0.601035	−	0.799223i	$-0.294755\pi$
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	−0.992665	+	0.120900i	$0.961422\pi$
$164$	5.00000	−	8.66025i	0.390434	−	0.676252i
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$	−6.50000	−	11.2583i	−0.504498	−	0.873816i
$167$	6.00000			0.464294			0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000			0.464294			0.232147	+	0.972681i	$0.425425\pi$
$168$	−0.500000	+	2.59808i	−0.0385758	+	0.200446i
$169$	23.0000			1.76923
$170$	−3.00000	−	5.19615i	−0.230089	−	0.398527i
$171$	1.00000	−	1.73205i	0.0764719	−	0.132453i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−5.00000	−	8.66025i	−0.380143	−	0.658427i	0.610939	−	0.791677i	$-0.290792\pi$
$173$	−5.00000	−	8.66025i	−0.380143	−	0.658427i	−0.991082	+	0.133250i	$0.957459\pi$
$174$	7.00000			0.530669
$175$	2.00000	−	10.3923i	0.151186	−	0.785584i
$176$	1.00000			0.0753778
$177$	7.50000	+	12.9904i	0.563735	+	0.976417i
$178$	−4.00000	+	6.92820i	−0.299813	+	0.519291i
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	−0.931038	−	0.364922i	$-0.881096\pi$
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	0.781551	+	0.623841i	$0.214429\pi$
$180$	1.50000	+	2.59808i	0.111803	+	0.193649i
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	−12.0000	−	10.3923i	−0.889499	−	0.770329i
$183$	2.00000			0.147844
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$	3.50000	−	6.06218i	0.256632	−	0.444500i
$187$	1.00000	+	1.73205i	0.0731272	+	0.126660i
$188$	6.00000			0.437595
$189$	2.50000	−	0.866025i	0.181848	−	0.0629941i
$190$	6.00000			0.435286
$191$	−13.0000	−	22.5167i	−0.940647	−	1.62925i	−0.764241	−	0.644931i	$-0.776886\pi$
$191$	−13.0000	−	22.5167i	−0.940647	−	1.62925i	−0.176406	−	0.984317i	$-0.556447\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	0.899770	−	0.436365i	$-0.143734\pi$
$194$	−0.500000	−	0.866025i	−0.0358979	−	0.0621770i
$195$	−18.0000			−1.28901
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$	−0.500000	−	0.866025i	−0.0355335	−	0.0615457i
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	0.256391	+	0.966573i	$0.417466\pi$
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	−0.965272	+	0.261245i	$0.915867\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$	1.00000	+	1.73205i	0.0705346	+	0.122169i
$202$	−10.0000			−0.703598
$203$	17.5000	−	6.06218i	1.22826	−	0.425481i
$204$	2.00000			0.140028
$205$	−15.0000	−	25.9808i	−1.04765	−	1.81458i
$206$		0			0
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	3.00000	+	5.19615i	0.208013	+	0.360288i
$209$	−2.00000			−0.138343
$210$	6.00000	+	5.19615i	0.414039	+	0.358569i
$211$	6.00000			0.413057			0.206529	−	0.978441i	$-0.433783\pi$
$211$	6.00000			0.413057			0.206529	+	0.978441i	$0.433783\pi$
$212$	−5.50000	−	9.52628i	−0.377742	−	0.654268i
$213$		0			0
$214$	8.50000	−	14.7224i	0.581048	−	1.00640i
$215$	3.00000	+	5.19615i	0.204598	+	0.354375i
$216$	−1.00000			−0.0680414
$217$	3.50000	−	18.1865i	0.237595	−	1.23458i
$218$	−14.0000			−0.948200
$219$	−5.00000	−	8.66025i	−0.337869	−	0.585206i
$220$	1.50000	−	2.59808i	0.101130	−	0.175162i
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$	−1.00000	−	1.73205i	−0.0671156	−	0.116248i
$223$	21.0000			1.40626			0.703132	−	0.711059i	$-0.251784\pi$
$223$	21.0000			1.40626			0.703132	+	0.711059i	$0.251784\pi$
$224$	0.500000	−	2.59808i	0.0334077	−	0.173591i
$225$	4.00000			0.266667
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	6.50000	−	11.2583i	0.431420	−	0.747242i	−0.565576	−	0.824696i	$-0.691346\pi$
$227$	6.50000	−	11.2583i	0.431420	−	0.747242i	0.996996	+	0.0774548i	$0.0246793\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$	3.00000			0.197814
$231$	−2.00000	−	1.73205i	−0.131590	−	0.113961i
$232$	−7.00000			−0.459573
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	−0.994283	−	0.106773i	$-0.965948\pi$
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	0.404674	−	0.914461i	$-0.367385\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$	9.00000	−	15.5885i	0.587095	−	1.01688i
$236$	−7.50000	−	12.9904i	−0.488208	−	0.845602i
$237$	11.0000			0.714527
$238$	5.00000	−	1.73205i	0.324102	−	0.112272i
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$	−1.50000	−	2.59808i	−0.0968246	−	0.167705i
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	−0.731001	−	0.682376i	$-0.760947\pi$
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	0.956456	+	0.291877i	$0.0942799\pi$
$242$	5.00000	−	8.66025i	0.321412	−	0.556702i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−2.00000			−0.128037
$245$	19.5000	+	7.79423i	1.24581	+	0.497955i
$246$	10.0000			0.637577
$247$	−6.00000	−	10.3923i	−0.381771	−	0.661247i
$248$	−3.50000	+	6.06218i	−0.222250	+	0.384949i
$249$	6.50000	−	11.2583i	0.411921	−	0.713468i
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	−15.0000			−0.946792			−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000			−0.946792			−0.473396	+	0.880850i	$0.656972\pi$
$252$	−2.50000	+	0.866025i	−0.157485	+	0.0545545i
$253$	−1.00000			−0.0628695
$254$	−8.50000	−	14.7224i	−0.533337	−	0.923768i
$255$	3.00000	−	5.19615i	0.187867	−	0.325396i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	0.990217	−	0.139533i	$-0.0445601\pi$
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	−0.615948	+	0.787787i	$0.711227\pi$
$258$	−2.00000			−0.124515
$259$	−4.00000	−	3.46410i	−0.248548	−	0.215249i
$260$	18.0000			1.11631
$261$	3.50000	+	6.06218i	0.216645	+	0.375239i
$262$	−3.50000	+	6.06218i	−0.216231	+	0.374523i
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	−0.943572	−	0.331166i	$-0.892558\pi$
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	0.758585	+	0.651575i	$0.225891\pi$
$264$	0.500000	+	0.866025i	0.0307729	+	0.0533002i
$265$	−33.0000			−2.02717
$266$	−1.00000	+	5.19615i	−0.0613139	+	0.318597i
$267$	−8.00000			−0.489592
$268$	−1.00000	−	1.73205i	−0.0610847	−	0.105802i
$269$	−14.5000	+	25.1147i	−0.884081	+	1.53127i	−0.0373168	+	0.999303i	$0.511881\pi$
$269$	−14.5000	+	25.1147i	−0.884081	+	1.53127i	−0.846764	+	0.531969i	$0.821452\pi$
$270$	−1.50000	+	2.59808i	−0.0912871	+	0.158114i
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	0.880812	−	0.473466i	$-0.156997\pi$
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	−0.850439	+	0.526073i	$0.823664\pi$
$272$	−2.00000			−0.121268
$273$	3.00000	−	15.5885i	0.181568	−	0.943456i
$274$	2.00000			0.120824
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$	−0.500000	+	0.866025i	−0.0300965	+	0.0521286i
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	1.00000	+	1.73205i	0.0599760	+	0.103882i
$279$	7.00000			0.419079
$280$	−6.00000	−	5.19615i	−0.358569	−	0.310530i
$281$	20.0000			1.19310			0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000			1.19310			0.596550	+	0.802576i	$0.296538\pi$
$282$	3.00000	+	5.19615i	0.178647	+	0.309426i
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$		0			0
$285$	3.00000	+	5.19615i	0.177705	+	0.307794i
$286$	−6.00000			−0.354787
$287$	25.0000	−	8.66025i	1.47570	−	0.511199i
$288$	1.00000			0.0589256
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−10.5000	+	18.1865i	−0.616581	+	1.06795i
$291$	0.500000	−	0.866025i	0.0293105	−	0.0507673i
$292$	5.00000	+	8.66025i	0.292603	+	0.506803i
$293$	−1.00000			−0.0584206			−0.0292103	−	0.999573i	$-0.509299\pi$
$293$	−1.00000			−0.0584206			−0.0292103	+	0.999573i	$0.509299\pi$
$294$	−5.50000	+	4.33013i	−0.320767	+	0.252538i
$295$	−45.0000			−2.62000
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	−5.00000	+	8.66025i	−0.289642	+	0.501675i
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$	−4.00000			−0.230940
$301$	−5.00000	+	1.73205i	−0.288195	+	0.0998337i
$302$	19.0000			1.09333
$303$	−5.00000	−	8.66025i	−0.287242	−	0.497519i
$304$	1.00000	−	1.73205i	0.0573539	−	0.0993399i
$305$	−3.00000	+	5.19615i	−0.171780	+	0.297531i
$306$	1.00000	+	1.73205i	0.0571662	+	0.0990148i
$307$	6.00000			0.342438			0.171219	−	0.985233i	$-0.445229\pi$
$307$	6.00000			0.342438			0.171219	+	0.985233i	$0.445229\pi$
$308$	2.00000	+	1.73205i	0.113961	+	0.0986928i
$309$		0			0
$310$	10.5000	+	18.1865i	0.596360	+	1.03293i
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	−0.938460	−	0.345389i	$-0.887747\pi$
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	0.768345	+	0.640036i	$0.221080\pi$
$312$	−3.00000	+	5.19615i	−0.169842	+	0.294174i
$313$	−13.5000	−	23.3827i	−0.763065	−	1.32167i	−0.941263	−	0.337673i	$-0.890360\pi$
$313$	−13.5000	−	23.3827i	−0.763065	−	1.32167i	0.178198	−	0.983995i	$-0.442973\pi$
$314$	22.0000			1.24153
$315$	−1.50000	+	7.79423i	−0.0845154	+	0.439155i
$316$	−11.0000			−0.618798
$317$	7.50000	+	12.9904i	0.421242	+	0.729612i	0.996061	−	0.0886679i	$-0.0282610\pi$
$317$	7.50000	+	12.9904i	0.421242	+	0.729612i	−0.574819	+	0.818280i	$0.694928\pi$
$318$	5.50000	−	9.52628i	0.308425	−	0.534207i
$319$	3.50000	−	6.06218i	0.195962	−	0.339417i
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$	17.0000			0.948847
$322$	−0.500000	+	2.59808i	−0.0278639	+	0.144785i
$323$	4.00000			0.222566
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	12.0000	−	20.7846i	0.665640	−	1.15292i
$326$	−5.00000	+	8.66025i	−0.276924	+	0.479647i
$327$	−7.00000	−	12.1244i	−0.387101	−	0.670478i
$328$	−10.0000			−0.552158
$329$	12.0000	+	10.3923i	0.661581	+	0.572946i
$330$	3.00000			0.165145
$331$	7.00000	+	12.1244i	0.384755	+	0.666415i	0.991735	−	0.128302i	$-0.0409527\pi$
$331$	7.00000	+	12.1244i	0.384755	+	0.666415i	−0.606980	+	0.794717i	$0.707619\pi$
$332$	−6.50000	+	11.2583i	−0.356734	+	0.617881i
$333$	1.00000	−	1.73205i	0.0547997	−	0.0949158i
$334$	−3.00000	−	5.19615i	−0.164153	−	0.284321i
$335$	−6.00000			−0.327815
$336$	2.50000	−	0.866025i	0.136386	−	0.0472456i
$337$	35.0000			1.90657			0.953286	−	0.302070i	$-0.0976776\pi$
$337$	35.0000			1.90657			0.953286	+	0.302070i	$0.0976776\pi$
$338$	−11.5000	−	19.9186i	−0.625518	−	1.08343i
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−3.50000	−	6.06218i	−0.189536	−	0.328285i
$342$	−2.00000			−0.108148
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	2.00000			0.107833
$345$	1.50000	+	2.59808i	0.0807573	+	0.139876i
$346$	−5.00000	+	8.66025i	−0.268802	+	0.465578i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$	−3.50000	−	6.06218i	−0.187620	−	0.324967i
$349$	−24.0000			−1.28469			−0.642345	−	0.766415i	$-0.722038\pi$
$349$	−24.0000			−1.28469			−0.642345	+	0.766415i	$0.722038\pi$
$350$	−10.0000	+	3.46410i	−0.534522	+	0.185164i
$351$	6.00000			0.320256
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	−0.989960	−	0.141344i	$-0.954858\pi$
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	0.617388	+	0.786659i	$0.288191\pi$
$354$	7.50000	−	12.9904i	0.398621	−	0.690431i
$355$		0			0
$356$	8.00000			0.423999
$357$	4.00000	+	3.46410i	0.211702	+	0.183340i
$358$	4.00000			0.211407
$359$	−3.00000	−	5.19615i	−0.158334	−	0.274242i	0.775934	−	0.630814i	$-0.217279\pi$
$359$	−3.00000	−	5.19615i	−0.158334	−	0.274242i	−0.934268	+	0.356572i	$0.883946\pi$
$360$	1.50000	−	2.59808i	0.0790569	−	0.136931i
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	8.00000	+	13.8564i	0.420471	+	0.728277i
$363$	10.0000			0.524864
$364$	−3.00000	+	15.5885i	−0.157243	+	0.817057i
$365$	30.0000			1.57027
$366$	−1.00000	−	1.73205i	−0.0522708	−	0.0905357i
$367$	−5.50000	+	9.52628i	−0.287098	+	0.497268i	−0.973116	−	0.230317i	$-0.926024\pi$
$367$	−5.50000	+	9.52628i	−0.287098	+	0.497268i	0.686018	+	0.727585i	$0.259357\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	5.00000	+	8.66025i	0.260290	+	0.450835i
$370$	6.00000			0.311925
$371$	5.50000	−	28.5788i	0.285546	−	1.48374i
$372$	−7.00000			−0.362933
$373$	−8.00000	−	13.8564i	−0.414224	−	0.717458i	0.581122	−	0.813816i	$-0.302614\pi$
$373$	−8.00000	−	13.8564i	−0.414224	−	0.717458i	−0.995347	+	0.0963587i	$0.969280\pi$
$374$	1.00000	−	1.73205i	0.0517088	−	0.0895622i
$375$	1.50000	−	2.59808i	0.0774597	−	0.134164i
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	42.0000			2.16311
$378$	−2.00000	−	1.73205i	−0.102869	−	0.0890871i
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$	−3.00000	−	5.19615i	−0.153897	−	0.266557i
$381$	8.50000	−	14.7224i	0.435468	−	0.754253i
$382$	−13.0000	+	22.5167i	−0.665138	+	1.15205i
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	0.585973	−	0.810331i	$-0.300713\pi$
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	−0.994753	+	0.102302i	$0.967379\pi$
$384$	−1.00000			−0.0510310
$385$	7.50000	−	2.59808i	0.382235	−	0.132410i
$386$	−23.0000			−1.17067
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$	−0.500000	+	0.866025i	−0.0253837	+	0.0439658i
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$	9.00000	+	15.5885i	0.455733	+	0.789352i
$391$	2.00000			0.101144
$392$	5.50000	−	4.33013i	0.277792	−	0.218704i
$393$	−7.00000			−0.353103
$394$	1.00000	+	1.73205i	0.0503793	+	0.0872595i
$395$	−16.5000	+	28.5788i	−0.830205	+	1.43796i
$396$	−0.500000	+	0.866025i	−0.0251259	+	0.0435194i
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	20.0000			1.00251
$399$	−5.00000	+	1.73205i	−0.250313	+	0.0867110i
$400$	4.00000			0.200000
$401$	−2.00000	−	3.46410i	−0.0998752	−	0.172989i	0.811758	−	0.583994i	$-0.198511\pi$
$401$	−2.00000	−	3.46410i	−0.0998752	−	0.172989i	−0.911633	+	0.411005i	$0.865178\pi$
$402$	1.00000	−	1.73205i	0.0498755	−	0.0863868i
$403$	21.0000	−	36.3731i	1.04608	−	1.81187i
$404$	5.00000	+	8.66025i	0.248759	+	0.430864i
$405$	−3.00000			−0.149071
$406$	−14.0000	−	12.1244i	−0.694808	−	0.601722i
$407$	−2.00000			−0.0991363
$408$	−1.00000	−	1.73205i	−0.0495074	−	0.0857493i
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	−0.999402	−	0.0345902i	$-0.988987\pi$
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	0.529657	+	0.848212i	$0.322321\pi$
$410$	−15.0000	+	25.9808i	−0.740797	+	1.28310i
$411$	1.00000	+	1.73205i	0.0493264	+	0.0854358i
$412$		0			0
$413$	7.50000	−	38.9711i	0.369051	−	1.91764i
$414$	−1.00000			−0.0491473
$415$	19.5000	+	33.7750i	0.957217	+	1.65795i
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$	−1.00000	+	1.73205i	−0.0489702	+	0.0848189i
$418$	1.00000	+	1.73205i	0.0489116	+	0.0847174i
$419$	4.00000			0.195413			0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000			0.195413			0.0977064	+	0.995215i	$0.468849\pi$
$420$	1.50000	−	7.79423i	0.0731925	−	0.380319i
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	−3.00000	−	5.19615i	−0.146038	−	0.252945i
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$	−5.50000	+	9.52628i	−0.267104	+	0.462637i
$425$	4.00000	+	6.92820i	0.194029	+	0.336067i
$426$		0			0
$427$	−4.00000	−	3.46410i	−0.193574	−	0.167640i
$428$	−17.0000			−0.821726
$429$	−3.00000	−	5.19615i	−0.144841	−	0.250873i
$430$	3.00000	−	5.19615i	0.144673	−	0.250581i
$431$	−8.00000	+	13.8564i	−0.385346	+	0.667440i	−0.991817	−	0.127666i	$-0.959251\pi$
$431$	−8.00000	+	13.8564i	−0.385346	+	0.667440i	0.606471	+	0.795106i	$0.292585\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−26.0000			−1.24948			−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000			−1.24948			−0.624740	+	0.780833i	$0.714795\pi$
$434$	−17.5000	+	6.06218i	−0.840027	+	0.290994i
$435$	−21.0000			−1.00687
$436$	7.00000	+	12.1244i	0.335239	+	0.580651i
$437$	−1.00000	+	1.73205i	−0.0478365	+	0.0828552i
$438$	−5.00000	+	8.66025i	−0.238909	+	0.413803i
$439$	14.5000	+	25.1147i	0.692047	+	1.19866i	0.971166	+	0.238404i	$0.0766244\pi$
$439$	14.5000	+	25.1147i	0.692047	+	1.19866i	−0.279119	+	0.960257i	$0.590042\pi$
$440$	−3.00000			−0.143019
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$	12.0000			0.570782
$443$	−5.50000	−	9.52628i	−0.261313	−	0.452607i	0.705278	−	0.708931i	$-0.250822\pi$
$443$	−5.50000	−	9.52628i	−0.261313	−	0.452607i	−0.966591	+	0.256323i	$0.917489\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$	12.0000	−	20.7846i	0.568855	−	0.985285i
$446$	−10.5000	−	18.1865i	−0.497189	−	0.861157i
$447$	−10.0000			−0.472984
$448$	−2.50000	+	0.866025i	−0.118114	+	0.0409159i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	−2.00000	−	3.46410i	−0.0942809	−	0.163299i
$451$	5.00000	−	8.66025i	0.235441	−	0.407795i
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$	9.50000	+	16.4545i	0.446349	+	0.773099i
$454$	−13.0000			−0.610120
$455$	36.0000	+	31.1769i	1.68771	+	1.46160i
$456$	2.00000			0.0936586
$457$	5.50000	+	9.52628i	0.257279	+	0.445621i	0.965512	−	0.260358i	$-0.0838407\pi$
$457$	5.50000	+	9.52628i	0.257279	+	0.445621i	−0.708233	+	0.705979i	$0.750507\pi$
$458$	5.00000	−	8.66025i	0.233635	−	0.404667i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$	−1.50000	−	2.59808i	−0.0699379	−	0.121136i
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$	−0.500000	+	2.59808i	−0.0232621	+	0.120873i
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	3.50000	+	6.06218i	0.162483	+	0.281430i
$465$	−10.5000	+	18.1865i	−0.486926	+	0.843380i
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$	10.0000	+	17.3205i	0.462745	+	0.801498i	0.999097	−	0.0424970i	$-0.0135313\pi$
$467$	10.0000	+	17.3205i	0.462745	+	0.801498i	−0.536352	+	0.843995i	$0.680198\pi$
$468$	−6.00000			−0.277350
$469$	1.00000	−	5.19615i	0.0461757	−	0.239936i
$470$	−18.0000			−0.830278
$471$	11.0000	+	19.0526i	0.506853	+	0.877896i
$472$	−7.50000	+	12.9904i	−0.345215	+	0.597931i
$473$	−1.00000	+	1.73205i	−0.0459800	+	0.0796398i
$474$	−5.50000	−	9.52628i	−0.252623	−	0.437557i
$475$	−8.00000			−0.367065
$476$	−4.00000	−	3.46410i	−0.183340	−	0.158777i
$477$	11.0000			0.503655
$478$	−10.0000	−	17.3205i	−0.457389	−	0.792222i
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	−0.998796	−	0.0490589i	$-0.984378\pi$
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	0.541884	+	0.840453i	$0.317711\pi$
$480$	−1.50000	+	2.59808i	−0.0684653	+	0.118585i
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$	−7.00000			−0.318841
$483$	−2.50000	+	0.866025i	−0.113754	+	0.0394055i
$484$	−10.0000			−0.454545
$485$	1.50000	+	2.59808i	0.0681115	+	0.117973i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−0.500000	+	0.866025i	−0.0226572	+	0.0392434i	−0.877132	−	0.480250i	$-0.840546\pi$
$487$	−0.500000	+	0.866025i	−0.0226572	+	0.0392434i	0.854475	+	0.519493i	$0.173879\pi$
$488$	1.00000	+	1.73205i	0.0452679	+	0.0784063i
$489$	−10.0000			−0.452216
$490$	−3.00000	−	20.7846i	−0.135526	−	0.938953i
$491$	−29.0000			−1.30875			−0.654376	−	0.756169i	$-0.727069\pi$
$491$	−29.0000			−1.30875			−0.654376	+	0.756169i	$0.727069\pi$
$492$	−5.00000	−	8.66025i	−0.225417	−	0.390434i
$493$	−7.00000	+	12.1244i	−0.315264	+	0.546054i
$494$	−6.00000	+	10.3923i	−0.269953	+	0.467572i
$495$	1.50000	+	2.59808i	0.0674200	+	0.116775i
$496$	7.00000			0.314309
$497$		0			0
$498$	−13.0000			−0.582544
$499$	5.00000	+	8.66025i	0.223831	+	0.387686i	0.955968	−	0.293471i	$-0.0948104\pi$
$499$	5.00000	+	8.66025i	0.223831	+	0.387686i	−0.732137	+	0.681157i	$0.761477\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	3.00000	−	5.19615i	0.134030	−	0.232147i
$502$	7.50000	+	12.9904i	0.334741	+	0.579789i
$503$	−28.0000			−1.24846			−0.624229	−	0.781241i	$-0.714587\pi$
$503$	−28.0000			−1.24846			−0.624229	+	0.781241i	$0.714587\pi$
$504$	2.00000	+	1.73205i	0.0890871	+	0.0771517i
$505$	30.0000			1.33498
$506$	0.500000	+	0.866025i	0.0222277	+	0.0384995i
$507$	11.5000	−	19.9186i	0.510733	−	0.884615i
$508$	−8.50000	+	14.7224i	−0.377127	+	0.653202i
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	0.982988	−	0.183669i	$-0.0587976\pi$
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	−0.650556	+	0.759458i	$0.725464\pi$
$510$	−6.00000			−0.265684
$511$	−5.00000	+	25.9808i	−0.221187	+	1.14932i
$512$	1.00000			0.0441942
$513$	−1.00000	−	1.73205i	−0.0441511	−	0.0764719i
$514$	6.00000	−	10.3923i	0.264649	−	0.458385i
$515$		0			0
$516$	1.00000	+	1.73205i	0.0440225	+	0.0762493i
$517$	6.00000			0.263880
$518$	−1.00000	+	5.19615i	−0.0439375	+	0.228306i
$519$	−10.0000			−0.438951
$520$	−9.00000	−	15.5885i	−0.394676	−	0.683599i
$521$	−19.0000	+	32.9090i	−0.832405	+	1.44177i	0.0637207	+	0.997968i	$0.479703\pi$
$521$	−19.0000	+	32.9090i	−0.832405	+	1.44177i	−0.896126	+	0.443800i	$0.853630\pi$
$522$	3.50000	−	6.06218i	0.153191	−	0.265334i
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	0.818980	−	0.573822i	$-0.194540\pi$
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	−0.906434	+	0.422347i	$0.861206\pi$
$524$	7.00000			0.305796
$525$	−8.00000	−	6.92820i	−0.349149	−	0.302372i
$526$	6.00000			0.261612
$527$	7.00000	+	12.1244i	0.304925	+	0.528145i
$528$	0.500000	−	0.866025i	0.0217597	−	0.0376889i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	16.5000	+	28.5788i	0.716714	+	1.24139i
$531$	15.0000			0.650945
$532$	5.00000	−	1.73205i	0.216777	−	0.0750939i
$533$	60.0000			2.59889
$534$	4.00000	+	6.92820i	0.173097	+	0.299813i
$535$	−25.5000	+	44.1673i	−1.10246	+	1.90952i
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$	2.00000	+	3.46410i	0.0863064	+	0.149487i
$538$	29.0000			1.25028
$539$	1.00000	+	6.92820i	0.0430730	+	0.298419i
$540$	3.00000			0.129099
$541$	16.0000	+	27.7128i	0.687894	+	1.19147i	0.972518	+	0.232828i	$0.0747978\pi$
$541$	16.0000	+	27.7128i	0.687894	+	1.19147i	−0.284624	+	0.958639i	$0.591869\pi$
$542$	0.500000	−	0.866025i	0.0214768	−	0.0371990i
$543$	−8.00000	+	13.8564i	−0.343313	+	0.594635i
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$	42.0000			1.79908
$546$	−15.0000	+	5.19615i	−0.641941	+	0.222375i
$547$	18.0000			0.769624			0.384812	−	0.922995i	$-0.374266\pi$
$547$	18.0000			0.769624			0.384812	+	0.922995i	$0.374266\pi$
$548$	−1.00000	−	1.73205i	−0.0427179	−	0.0739895i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$	−7.00000	−	12.1244i	−0.298210	−	0.516515i
$552$	1.00000			0.0425628
$553$	−22.0000	−	19.0526i	−0.935535	−	0.810197i
$554$	8.00000			0.339887
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$	1.00000	−	1.73205i	0.0424094	−	0.0734553i
$557$	13.5000	−	23.3827i	0.572013	−	0.990756i	−0.424346	−	0.905500i	$-0.639496\pi$
$557$	13.5000	−	23.3827i	0.572013	−	0.990756i	0.996359	−	0.0852559i	$-0.0271708\pi$
$558$	−3.50000	−	6.06218i	−0.148167	−	0.256632i
$559$	−12.0000			−0.507546
$560$	−1.50000	+	7.79423i	−0.0633866	+	0.329366i
$561$	2.00000			0.0844401
$562$	−10.0000	−	17.3205i	−0.421825	−	0.730622i
$563$	−20.5000	+	35.5070i	−0.863972	+	1.49644i	0.00409232	+	0.999992i	$0.498697\pi$
$563$	−20.5000	+	35.5070i	−0.863972	+	1.49644i	−0.868064	+	0.496452i	$0.834636\pi$
$564$	3.00000	−	5.19615i	0.126323	−	0.218797i
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$	14.0000			0.588464
$567$	0.500000	−	2.59808i	0.0209980	−	0.109109i
$568$		0			0
$569$	−6.00000	−	10.3923i	−0.251533	−	0.435668i	0.712415	−	0.701758i	$-0.247601\pi$
$569$	−6.00000	−	10.3923i	−0.251533	−	0.435668i	−0.963948	+	0.266090i	$0.914268\pi$
$570$	3.00000	−	5.19615i	0.125656	−	0.217643i
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	−0.963827	−	0.266529i	$-0.914123\pi$
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	0.712735	+	0.701434i	$0.247456\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$	−26.0000			−1.08617
$574$	−20.0000	−	17.3205i	−0.834784	−	0.722944i
$575$	−4.00000			−0.166812
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	12.5000	−	21.6506i	0.520382	−	0.901328i	−0.479337	−	0.877631i	$-0.659123\pi$
$577$	12.5000	−	21.6506i	0.520382	−	0.901328i	0.999719	−	0.0236970i	$-0.00754370\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$	−11.5000	−	19.9186i	−0.477924	−	0.827788i
$580$	21.0000			0.871978
$581$	−32.5000	+	11.2583i	−1.34833	+	0.467074i
$582$	−1.00000			−0.0414513
$583$	−5.50000	−	9.52628i	−0.227787	−	0.394538i
$584$	5.00000	−	8.66025i	0.206901	−	0.358364i
$585$	−9.00000	+	15.5885i	−0.372104	+	0.644503i
$586$	0.500000	+	0.866025i	0.0206548	+	0.0357752i
$587$	−3.00000			−0.123823			−0.0619116	−	0.998082i	$-0.519720\pi$
$587$	−3.00000			−0.123823			−0.0619116	+	0.998082i	$0.519720\pi$
$588$	6.50000	+	2.59808i	0.268055	+	0.107143i
$589$	−14.0000			−0.576860
$590$	22.5000	+	38.9711i	0.926310	+	1.60442i
$591$	−1.00000	+	1.73205i	−0.0411345	+	0.0712470i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	−10.0000	−	17.3205i	−0.410651	−	0.711268i	0.584310	−	0.811530i	$-0.301365\pi$
$593$	−10.0000	−	17.3205i	−0.410651	−	0.711268i	−0.994961	+	0.100262i	$0.968032\pi$
$594$	−1.00000			−0.0410305
$595$	−15.0000	+	5.19615i	−0.614940	+	0.213021i
$596$	10.0000			0.409616
$597$	10.0000	+	17.3205i	0.409273	+	0.708881i
$598$	−3.00000	+	5.19615i	−0.122679	+	0.212486i
$599$	−8.00000	+	13.8564i	−0.326871	+	0.566157i	−0.981889	−	0.189456i	$-0.939328\pi$
$599$	−8.00000	+	13.8564i	−0.326871	+	0.566157i	0.655018	+	0.755613i	$0.272661\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	−17.0000			−0.693444			−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000			−0.693444			−0.346722	+	0.937968i	$0.612705\pi$
$602$	4.00000	+	3.46410i	0.163028	+	0.141186i
$603$	2.00000			0.0814463
$604$	−9.50000	−	16.4545i	−0.386550	−	0.669523i
$605$	−15.0000	+	25.9808i	−0.609837	+	1.05627i
$606$	−5.00000	+	8.66025i	−0.203111	+	0.351799i
$607$	9.50000	+	16.4545i	0.385593	+	0.667867i	0.991851	−	0.127401i	$-0.0406635\pi$
$607$	9.50000	+	16.4545i	0.385593	+	0.667867i	−0.606258	+	0.795268i	$0.707330\pi$
$608$	−2.00000			−0.0811107
$609$	3.50000	−	18.1865i	0.141827	−	0.736956i
$610$	6.00000			0.242933
$611$	18.0000	+	31.1769i	0.728202	+	1.26128i
$612$	1.00000	−	1.73205i	0.0404226	−	0.0700140i
$613$	14.0000	−	24.2487i	0.565455	−	0.979396i	−0.431553	−	0.902088i	$-0.642034\pi$
$613$	14.0000	−	24.2487i	0.565455	−	0.979396i	0.997007	−	0.0773084i	$-0.0246326\pi$
$614$	−3.00000	−	5.19615i	−0.121070	−	0.209700i
$615$	−30.0000			−1.20972
$616$	0.500000	−	2.59808i	0.0201456	−	0.104679i
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$		0			0
$619$	20.0000	−	34.6410i	0.803868	−	1.39234i	−0.113185	−	0.993574i	$-0.536105\pi$
$619$	20.0000	−	34.6410i	0.803868	−	1.39234i	0.917053	−	0.398766i	$-0.130561\pi$
$620$	10.5000	−	18.1865i	0.421690	−	0.730389i
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	6.00000			0.240578
$623$	16.0000	+	13.8564i	0.641026	+	0.555145i
$624$	6.00000			0.240192
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−13.5000	+	23.3827i	−0.539569	+	0.934560i
$627$	−1.00000	+	1.73205i	−0.0399362	+	0.0691714i
$628$	−11.0000	−	19.0526i	−0.438948	−	0.760280i
$629$	4.00000			0.159490
$630$	7.50000	−	2.59808i	0.298807	−	0.103510i
$631$	−21.0000			−0.835997			−0.417998	−	0.908448i	$-0.637268\pi$
$631$	−21.0000			−0.835997			−0.417998	+	0.908448i	$0.637268\pi$
$632$	5.50000	+	9.52628i	0.218778	+	0.378935i
$633$	3.00000	−	5.19615i	0.119239	−	0.206529i
$634$	7.50000	−	12.9904i	0.297863	−	0.515914i
$635$	25.5000	+	44.1673i	1.01194	+	1.75273i
$636$	−11.0000			−0.436178
$637$	−33.0000	+	25.9808i	−1.30751	+	1.02940i
$638$	−7.00000			−0.277133
$639$		0			0
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	10.0000	−	17.3205i	0.394976	−	0.684119i	−0.598122	−	0.801405i	$-0.704086\pi$
$641$	10.0000	−	17.3205i	0.394976	−	0.684119i	0.993098	+	0.117286i	$0.0374195\pi$
$642$	−8.50000	−	14.7224i	−0.335468	−	0.581048i
$643$	44.0000			1.73519			0.867595	−	0.497271i	$-0.165665\pi$
$643$	44.0000			1.73519			0.867595	+	0.497271i	$0.165665\pi$
$644$	2.50000	−	0.866025i	0.0985138	−	0.0341262i
$645$	6.00000			0.236250
$646$	−2.00000	−	3.46410i	−0.0786889	−	0.136293i
$647$	−11.0000	+	19.0526i	−0.432455	+	0.749033i	−0.997084	−	0.0763112i	$-0.975686\pi$
$647$	−11.0000	+	19.0526i	−0.432455	+	0.749033i	0.564629	+	0.825345i	$0.309019\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−7.50000	−	12.9904i	−0.294401	−	0.509917i
$650$	−24.0000			−0.941357
$651$	−14.0000	−	12.1244i	−0.548703	−	0.475191i
$652$	10.0000			0.391630
$653$	18.5000	+	32.0429i	0.723961	+	1.25394i	0.959400	+	0.282048i	$0.0910138\pi$
$653$	18.5000	+	32.0429i	0.723961	+	1.25394i	−0.235439	+	0.971889i	$0.575653\pi$
$654$	−7.00000	+	12.1244i	−0.273722	+	0.474100i
$655$	10.5000	−	18.1865i	0.410269	−	0.710607i
$656$	5.00000	+	8.66025i	0.195217	+	0.338126i
$657$	−10.0000			−0.390137
$658$	3.00000	−	15.5885i	0.116952	−	0.607701i
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	−1.50000	−	2.59808i	−0.0583874	−	0.101130i
$661$	25.0000	−	43.3013i	0.972387	−	1.68422i	0.284087	−	0.958799i	$-0.408310\pi$
$661$	25.0000	−	43.3013i	0.972387	−	1.68422i	0.688301	−	0.725426i	$-0.258357\pi$
$662$	7.00000	−	12.1244i	0.272063	−	0.471226i
$663$	6.00000	+	10.3923i	0.233021	+	0.403604i
$664$	13.0000			0.504498
$665$	3.00000	−	15.5885i	0.116335	−	0.604494i
$666$	−2.00000			−0.0774984
$667$	−3.50000	−	6.06218i	−0.135521	−	0.234728i
$668$	−3.00000	+	5.19615i	−0.116073	+	0.201045i
$669$	10.5000	−	18.1865i	0.405953	−	0.703132i
$670$	3.00000	+	5.19615i	0.115900	+	0.200745i
$671$	−2.00000			−0.0772091
$672$	−2.00000	−	1.73205i	−0.0771517	−	0.0668153i
$673$	−7.00000			−0.269830			−0.134915	−	0.990857i	$-0.543076\pi$
$673$	−7.00000			−0.269830			−0.134915	+	0.990857i	$0.543076\pi$
$674$	−17.5000	−	30.3109i	−0.674075	−	1.16753i
$675$	2.00000	−	3.46410i	0.0769800	−	0.133333i
$676$	−11.5000	+	19.9186i	−0.442308	+	0.766099i
$677$	11.5000	+	19.9186i	0.441981	+	0.765533i	0.997836	−	0.0657455i	$-0.0209426\pi$
$677$	11.5000	+	19.9186i	0.441981	+	0.765533i	−0.555856	+	0.831279i	$0.687609\pi$
$678$	6.00000			0.230429
$679$	−2.50000	+	0.866025i	−0.0959412	+	0.0332350i
$680$	6.00000			0.230089
$681$	−6.50000	−	11.2583i	−0.249081	−	0.431420i
$682$	−3.50000	+	6.06218i	−0.134022	+	0.232133i
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	−0.939184	−	0.343413i	$-0.888417\pi$
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	0.766997	+	0.641651i	$0.221750\pi$
$684$	1.00000	+	1.73205i	0.0382360	+	0.0662266i
$685$	−6.00000			−0.229248
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$	10.0000			0.381524
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$	33.0000	−	57.1577i	1.25720	−	2.17753i
$690$	1.50000	−	2.59808i	0.0571040	−	0.0989071i
$691$	23.0000	+	39.8372i	0.874961	+	1.51548i	0.856804	+	0.515642i	$0.172447\pi$
$691$	23.0000	+	39.8372i	0.874961	+	1.51548i	0.0181572	+	0.999835i	$0.494220\pi$
$692$	10.0000			0.380143
$693$	−2.50000	+	0.866025i	−0.0949671	+	0.0328976i
$694$	−12.0000			−0.455514
$695$	−3.00000	−	5.19615i	−0.113796	−	0.197101i
$696$	−3.50000	+	6.06218i	−0.132667	+	0.229786i
$697$	−10.0000	+	17.3205i	−0.378777	+	0.656061i
$698$	12.0000	+	20.7846i	0.454207	+	0.786709i
$699$	−18.0000			−0.680823
$700$	8.00000	+	6.92820i	0.302372	+	0.261861i
$701$	−5.00000			−0.188847			−0.0944237	−	0.995532i	$-0.530101\pi$
$701$	−5.00000			−0.188847			−0.0944237	+	0.995532i	$0.530101\pi$
$702$	−3.00000	−	5.19615i	−0.113228	−	0.196116i
$703$	−2.00000	+	3.46410i	−0.0754314	+	0.130651i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	−9.00000	−	15.5885i	−0.338960	−	0.587095i
$706$	14.0000			0.526897
$707$	−5.00000	+	25.9808i	−0.188044	+	0.977107i
$708$	−15.0000			−0.563735
$709$	2.00000	+	3.46410i	0.0751116	+	0.130097i	0.901135	−	0.433539i	$-0.142735\pi$
$709$	2.00000	+	3.46410i	0.0751116	+	0.130097i	−0.826023	+	0.563636i	$0.809402\pi$
$710$		0			0
$711$	5.50000	−	9.52628i	0.206266	−	0.357263i
$712$	−4.00000	−	6.92820i	−0.149906	−	0.259645i
$713$	−7.00000			−0.262152
$714$	1.00000	−	5.19615i	0.0374241	−	0.194461i
$715$	18.0000			0.673162
$716$	−2.00000	−	3.46410i	−0.0747435	−	0.129460i
$717$	10.0000	−	17.3205i	0.373457	−	0.646846i
$718$	−3.00000	+	5.19615i	−0.111959	+	0.193919i
$719$	−25.0000	−	43.3013i	−0.932343	−	1.61486i	−0.779305	−	0.626644i	$-0.784428\pi$
$719$	−25.0000	−	43.3013i	−0.932343	−	1.61486i	−0.153037	−	0.988220i	$-0.548906\pi$
$720$	−3.00000			−0.111803
$721$		0			0
$722$	−15.0000			−0.558242
$723$	−3.50000	−	6.06218i	−0.130166	−	0.225455i
$724$	8.00000	−	13.8564i	0.297318	−	0.514969i
$725$	14.0000	−	24.2487i	0.519947	−	0.900575i
$726$	−5.00000	−	8.66025i	−0.185567	−	0.321412i
$727$	1.00000			0.0370879			0.0185440	−	0.999828i	$-0.494097\pi$
$727$	1.00000			0.0370879			0.0185440	+	0.999828i	$0.494097\pi$
$728$	15.0000	−	5.19615i	0.555937	−	0.192582i
$729$	1.00000			0.0370370
$730$	−15.0000	−	25.9808i	−0.555175	−	0.961591i
$731$	2.00000	−	3.46410i	0.0739727	−	0.128124i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	10.0000	+	17.3205i	0.369358	+	0.639748i	0.989465	−	0.144770i	$-0.0462441\pi$
$733$	10.0000	+	17.3205i	0.369358	+	0.639748i	−0.620107	+	0.784517i	$0.712911\pi$
$734$	11.0000			0.406017
$735$	16.5000	−	12.9904i	0.608612	−	0.479157i
$736$	−1.00000			−0.0368605
$737$	−1.00000	−	1.73205i	−0.0368355	−	0.0638009i
$738$	5.00000	−	8.66025i	0.184053	−	0.318788i
$739$	7.00000	−	12.1244i	0.257499	−	0.446002i	−0.708072	−	0.706140i	$-0.750435\pi$
$739$	7.00000	−	12.1244i	0.257499	−	0.446002i	0.965571	+	0.260138i	$0.0837682\pi$
$740$	−3.00000	−	5.19615i	−0.110282	−	0.191014i
$741$	−12.0000			−0.440831
$742$	−27.5000	+	9.52628i	−1.00956	+	0.349721i
$743$	24.0000			0.880475			0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000			0.880475			0.440237	+	0.897881i	$0.354894\pi$
$744$	3.50000	+	6.06218i	0.128316	+	0.222250i
$745$	15.0000	−	25.9808i	0.549557	−	0.951861i
$746$	−8.00000	+	13.8564i	−0.292901	+	0.507319i
$747$	−6.50000	−	11.2583i	−0.237823	−	0.411921i
$748$	−2.00000			−0.0731272
$749$	−34.0000	−	29.4449i	−1.24233	−	1.07589i
$750$	−3.00000			−0.109545
$751$	−23.5000	−	40.7032i	−0.857527	−	1.48528i	−0.874281	−	0.485421i	$-0.838666\pi$
$751$	−23.5000	−	40.7032i	−0.857527	−	1.48528i	0.0167534	−	0.999860i	$-0.494667\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$	−7.50000	+	12.9904i	−0.273315	+	0.473396i
$754$	−21.0000	−	36.3731i	−0.764775	−	1.32463i
$755$	−57.0000			−2.07444
$756$	−0.500000	+	2.59808i	−0.0181848	+	0.0944911i
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$	2.00000	+	3.46410i	0.0726433	+	0.125822i
$759$	−0.500000	+	0.866025i	−0.0181489	+	0.0314347i
$760$	−3.00000	+	5.19615i	−0.108821	+	0.188484i
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	−0.942207	−	0.335032i	$-0.891253\pi$
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	0.180957	−	0.983491i	$-0.442080\pi$
$762$	−17.0000			−0.615845
$763$	−7.00000	+	36.3731i	−0.253417	+	1.31679i
$764$	26.0000			0.940647
$765$	−3.00000	−	5.19615i	−0.108465	−	0.187867i
$766$	−8.00000	+	13.8564i	−0.289052	+	0.500652i
$767$	45.0000	−	77.9423i	1.62486	−	2.81433i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−29.0000			−1.04577			−0.522883	−	0.852404i	$-0.675144\pi$
$769$	−29.0000			−1.04577			−0.522883	+	0.852404i	$0.675144\pi$
$770$	−6.00000	−	5.19615i	−0.216225	−	0.187256i
$771$	12.0000			0.432169
$772$	11.5000	+	19.9186i	0.413894	+	0.716886i
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	−0.712241	−	0.701935i	$-0.752320\pi$
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	0.964014	+	0.265852i	$0.0856532\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$	−14.0000	−	24.2487i	−0.502895	−	0.871039i
$776$	1.00000			0.0358979
$777$	−5.00000	+	1.73205i	−0.179374	+	0.0621370i
$778$	6.00000			0.215110
$779$	−10.0000	−	17.3205i	−0.358287	−	0.620572i
$780$	9.00000	−	15.5885i	0.322252	−	0.558156i
$781$		0			0
$782$	−1.00000	−	1.73205i	−0.0357599	−	0.0619380i
$783$	7.00000			0.250160
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$	−66.0000			−2.35564
$786$	3.50000	+	6.06218i	0.124841	+	0.216231i
$787$	27.0000	−	46.7654i	0.962446	−	1.66701i	0.246121	−	0.969239i	$-0.420844\pi$
$787$	27.0000	−	46.7654i	0.962446	−	1.66701i	0.716326	−	0.697766i	$-0.245823\pi$
$788$	1.00000	−	1.73205i	0.0356235	−	0.0617018i
$789$	3.00000	+	5.19615i	0.106803	+	0.184988i
$790$	33.0000			1.17409
$791$	15.0000	−	5.19615i	0.533339	−	0.184754i
$792$	1.00000			0.0355335
$793$	−6.00000	−	10.3923i	−0.213066	−	0.369042i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$	−16.5000	+	28.5788i	−0.585195	+	1.01359i
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	21.0000			0.743858			0.371929	−	0.928261i	$-0.378696\pi$
$797$	21.0000			0.743858			0.371929	+	0.928261i	$0.378696\pi$
$798$	4.00000	+	3.46410i	0.141598	+	0.122628i
$799$	−12.0000			−0.424529
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$	−4.00000	+	6.92820i	−0.141333	+	0.244796i
$802$	−2.00000	+	3.46410i	−0.0706225	+	0.122322i
$803$	5.00000	+	8.66025i	0.176446	+	0.305614i
$804$	−2.00000			−0.0705346
$805$	1.50000	−	7.79423i	0.0528681	−	0.274710i
$806$	−42.0000			−1.47939
$807$	14.5000	+	25.1147i	0.510424	+	0.884081i
$808$	5.00000	−	8.66025i	0.175899	−	0.304667i
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	−0.764644	−	0.644453i	$-0.777085\pi$
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	0.940435	+	0.339975i	$0.110418\pi$
$810$	1.50000	+	2.59808i	0.0527046	+	0.0912871i
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$	−3.50000	+	18.1865i	−0.122826	+	0.638222i
$813$	1.00000			0.0350715
$814$	1.00000	+	1.73205i	0.0350500	+	0.0607083i
$815$	15.0000	−	25.9808i	0.525427	−	0.910066i
$816$	−1.00000	+	1.73205i	−0.0350070	+	0.0606339i
$817$	2.00000	+	3.46410i	0.0699711	+	0.121194i
$818$	19.0000			0.664319
$819$	−12.0000	−	10.3923i	−0.419314	−	0.363137i
$820$	30.0000			1.04765
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	0.966708	−	0.255884i	$-0.0823665\pi$
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	−0.704956	+	0.709251i	$0.749033\pi$
$822$	1.00000	−	1.73205i	0.0348790	−	0.0604122i
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$		0			0
$825$	−4.00000			−0.139262
$826$	−37.5000	+	12.9904i	−1.30479	+	0.451993i
$827$	−23.0000			−0.799788			−0.399894	−	0.916561i	$-0.630953\pi$
$827$	−23.0000			−0.799788			−0.399894	+	0.916561i	$0.630953\pi$
$828$	0.500000	+	0.866025i	0.0173762	+	0.0300965i
$829$	−6.00000	+	10.3923i	−0.208389	+	0.360940i	−0.951207	−	0.308553i	$-0.900155\pi$
$829$	−6.00000	+	10.3923i	−0.208389	+	0.360940i	0.742818	+	0.669493i	$0.233489\pi$
$830$	19.5000	−	33.7750i	0.676855	−	1.17235i
$831$	4.00000	+	6.92820i	0.138758	+	0.240337i
$832$	−6.00000			−0.208013
$833$	−2.00000	−	13.8564i	−0.0692959	−	0.480096i
$834$	2.00000			0.0692543
$835$	9.00000	+	15.5885i	0.311458	+	0.539461i
$836$	1.00000	−	1.73205i	0.0345857	−	0.0599042i
$837$	3.50000	−	6.06218i	0.120978	−	0.209540i
$838$	−2.00000	−	3.46410i	−0.0690889	−	0.119665i
$839$	54.0000			1.86429			0.932144	−	0.362089i	$-0.117936\pi$
$839$	54.0000			1.86429			0.932144	+	0.362089i	$0.117936\pi$
$840$	−7.50000	+	2.59808i	−0.258775	+	0.0896421i
$841$	20.0000			0.689655
$842$	−11.0000	−	19.0526i	−0.379085	−	0.656595i
$843$	10.0000	−	17.3205i	0.344418	−	0.596550i
$844$	−3.00000	+	5.19615i	−0.103264	+	0.178859i
$845$	34.5000	+	59.7558i	1.18684	+	2.05566i
$846$	6.00000			0.206284
$847$	−20.0000	−	17.3205i	−0.687208	−	0.595140i
$848$	11.0000			0.377742
$849$	7.00000	+	12.1244i	0.240239	+	0.416107i
$850$	4.00000	−	6.92820i	0.137199	−	0.237635i
$851$	−1.00000	+	1.73205i	−0.0342796	+	0.0593739i
$852$		0			0
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$	−1.00000	+	5.19615i	−0.0342193	+	0.177809i
$855$	6.00000			0.205196
$856$	8.50000	+	14.7224i	0.290524	+	0.503202i
$857$	−20.0000	+	34.6410i	−0.683187	+	1.18331i	0.290816	+	0.956779i	$0.406073\pi$
$857$	−20.0000	+	34.6410i	−0.683187	+	1.18331i	−0.974003	+	0.226536i	$0.927260\pi$
$858$	−3.00000	+	5.19615i	−0.102418	+	0.177394i
$859$	24.0000	+	41.5692i	0.818869	+	1.41832i	0.906516	+	0.422172i	$0.138732\pi$
$859$	24.0000	+	41.5692i	0.818869	+	1.41832i	−0.0876464	+	0.996152i	$0.527935\pi$
$860$	−6.00000			−0.204598
$861$	5.00000	−	25.9808i	0.170400	−	0.885422i
$862$	16.0000			0.544962
$863$	−4.00000	−	6.92820i	−0.136162	−	0.235839i	0.789879	−	0.613263i	$-0.210143\pi$
$863$	−4.00000	−	6.92820i	−0.136162	−	0.235839i	−0.926041	+	0.377424i	$0.876810\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	15.0000	−	25.9808i	0.510015	−	0.883372i
$866$	13.0000	+	22.5167i	0.441758	+	0.765147i
$867$	13.0000			0.441503
$868$	14.0000	+	12.1244i	0.475191	+	0.411527i
$869$	−11.0000			−0.373149
$870$	10.5000	+	18.1865i	0.355983	+	0.616581i
$871$	6.00000	−	10.3923i	0.203302	−	0.352130i
$872$	7.00000	−	12.1244i	0.237050	−	0.410582i
$873$	−0.500000	−	0.866025i	−0.0169224	−	0.0293105i
$874$	2.00000			0.0676510
$875$	−7.50000	+	2.59808i	−0.253546	+	0.0878310i
$876$	10.0000			0.337869
$877$	−5.00000	−	8.66025i	−0.168838	−	0.292436i	0.769174	−	0.639040i	$-0.220668\pi$
$877$	−5.00000	−	8.66025i	−0.168838	−	0.292436i	−0.938012	+	0.346604i	$0.887335\pi$
$878$	14.5000	−	25.1147i	0.489351	−	0.847581i
$879$	−0.500000	+	0.866025i	−0.0168646	+	0.0292103i
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$	1.00000	+	6.92820i	0.0336718	+	0.233285i
$883$	−54.0000			−1.81724			−0.908622	−	0.417619i	$-0.862865\pi$
$883$	−54.0000			−1.81724			−0.908622	+	0.417619i	$0.862865\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$	−22.5000	+	38.9711i	−0.756329	+	1.31000i
$886$	−5.50000	+	9.52628i	−0.184776	+	0.320042i
$887$	−14.0000	−	24.2487i	−0.470074	−	0.814192i	0.529340	−	0.848410i	$-0.322439\pi$
$887$	−14.0000	−	24.2487i	−0.470074	−	0.814192i	−0.999414	+	0.0342175i	$0.989106\pi$
$888$	2.00000			0.0671156
$889$	−42.5000	+	14.7224i	−1.42540	+	0.493775i
$890$	−24.0000			−0.804482
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	−10.5000	+	18.1865i	−0.351566	+	0.608930i
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$	5.00000	+	8.66025i	0.167225	+	0.289642i
$895$	−12.0000			−0.401116
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$	−6.00000			−0.200334
$898$	3.00000	+	5.19615i	0.100111	+	0.173398i
$899$	24.5000	−	42.4352i	0.817121	−	1.41529i
$900$	−2.00000	+	3.46410i	−0.0666667	+	0.115470i
$901$	11.0000	+	19.0526i	0.366463	+	0.634733i
$902$	−10.0000			−0.332964
$903$	−1.00000	+	5.19615i	−0.0332779	+	0.172917i
$904$	−6.00000			−0.199557
$905$	−24.0000	−	41.5692i	−0.797787	−	1.38181i
$906$	9.50000	−	16.4545i	0.315616	−	0.546664i
$907$	−23.0000	+	39.8372i	−0.763702	+	1.32277i	0.177227	+	0.984170i	$0.443287\pi$
$907$	−23.0000	+	39.8372i	−0.763702	+	1.32277i	−0.940930	+	0.338602i	$0.890046\pi$
$908$	6.50000	+	11.2583i	0.215710	+	0.373621i
$909$	−10.0000			−0.331679
$910$	9.00000	−	46.7654i	0.298347	−	1.55026i
$911$	14.0000			0.463841			0.231920	−	0.972735i	$-0.425499\pi$
$911$	14.0000			0.463841			0.231920	+	0.972735i	$0.425499\pi$
$912$	−1.00000	−	1.73205i	−0.0331133	−	0.0573539i
$913$	−6.50000	+	11.2583i	−0.215119	+	0.372596i
$914$	5.50000	−	9.52628i	0.181924	−	0.315101i
$915$	3.00000	+	5.19615i	0.0991769	+	0.171780i
$916$	−10.0000			−0.330409
$917$	14.0000	+	12.1244i	0.462321	+	0.400381i
$918$	2.00000			0.0660098
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	0.597365	−	0.801970i	$-0.296214\pi$
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	−0.993208	+	0.116348i	$0.962881\pi$
$920$	−1.50000	+	2.59808i	−0.0494535	+	0.0856560i
$921$	3.00000	−	5.19615i	0.0988534	−	0.171219i
$922$	15.0000	+	25.9808i	0.493999	+	0.855631i
$923$		0			0
$924$	2.50000	−	0.866025i	0.0822440	−	0.0284901i
$925$	−8.00000			−0.263038
$926$	−4.00000	−	6.92820i	−0.131448	−	0.227675i
$927$		0			0
$928$	3.50000	−	6.06218i	0.114893	−	0.199001i
$929$	20.0000	+	34.6410i	0.656179	+	1.13653i	0.981597	+	0.190965i	$0.0611616\pi$
$929$	20.0000	+	34.6410i	0.656179	+	1.13653i	−0.325418	+	0.945570i	$0.605505\pi$
$930$	21.0000			0.688617
$931$	13.0000	+	5.19615i	0.426058	+	0.170297i
$932$	18.0000			0.589610
$933$	3.00000	+	5.19615i	0.0982156	+	0.170114i
$934$	10.0000	−	17.3205i	0.327210	−	0.566744i
$935$	−3.00000	+	5.19615i	−0.0981105	+	0.169932i
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	1.00000			0.0326686			0.0163343	−	0.999867i	$-0.494800\pi$
$937$	1.00000			0.0326686			0.0163343	+	0.999867i	$0.494800\pi$
$938$	−5.00000	+	1.73205i	−0.163256	+	0.0565535i
$939$	−27.0000			−0.881112
$940$	9.00000	+	15.5885i	0.293548	+	0.508439i
$941$	−18.5000	+	32.0429i	−0.603083	+	1.04457i	0.389269	+	0.921124i	$0.372728\pi$
$941$	−18.5000	+	32.0429i	−0.603083	+	1.04457i	−0.992351	+	0.123446i	$0.960606\pi$
$942$	11.0000	−	19.0526i	0.358399	−	0.620766i
$943$	−5.00000	−	8.66025i	−0.162822	−	0.282017i
$944$	15.0000			0.488208
$945$	6.00000	+	5.19615i	0.195180	+	0.169031i
$946$	2.00000			0.0650256
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	0.992442	−	0.122714i	$-0.0391598\pi$
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	−0.602494	+	0.798123i	$0.705826\pi$
$948$	−5.50000	+	9.52628i	−0.178632	+	0.309399i
$949$	−30.0000	+	51.9615i	−0.973841	+	1.68674i
$950$	4.00000	+	6.92820i	0.129777	+	0.224781i
$951$	15.0000			0.486408
$952$	−1.00000	+	5.19615i	−0.0324102	+	0.168408i
$953$	−18.0000			−0.583077			−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000			−0.583077			−0.291539	+	0.956559i	$0.594167\pi$
$954$	−5.50000	−	9.52628i	−0.178069	−	0.308425i
$955$	39.0000	−	67.5500i	1.26201	−	2.18587i
$956$	−10.0000	+	17.3205i	−0.323423	+	0.560185i
$957$	−3.50000	−	6.06218i	−0.113139	−	0.195962i
$958$	20.0000			0.646171
$959$	1.00000	−	5.19615i	0.0322917	−	0.167793i
$960$	3.00000			0.0968246
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$	−6.00000	+	10.3923i	−0.193448	+	0.335061i
$963$	8.50000	−	14.7224i	0.273909	−	0.474424i
$964$	3.50000	+	6.06218i	0.112727	+	0.195250i
$965$	69.0000			2.22119
$966$	2.00000	+	1.73205i	0.0643489	+	0.0557278i
$967$	3.00000			0.0964735			0.0482367	−	0.998836i	$-0.484640\pi$
$967$	3.00000			0.0964735			0.0482367	+	0.998836i	$0.484640\pi$
$968$	5.00000	+	8.66025i	0.160706	+	0.278351i
$969$	2.00000	−	3.46410i	0.0642493	−	0.111283i
$970$	1.50000	−	2.59808i	0.0481621	−	0.0834192i
$971$	10.5000	+	18.1865i	0.336961	+	0.583634i	0.983860	−	0.178942i	$-0.0572676\pi$
$971$	10.5000	+	18.1865i	0.336961	+	0.583634i	−0.646899	+	0.762576i	$0.723934\pi$
$972$	−1.00000			−0.0320750
$973$	5.00000	−	1.73205i	0.160293	−	0.0555270i
$974$	1.00000			0.0320421
$975$	−12.0000	−	20.7846i	−0.384308	−	0.665640i
$976$	1.00000	−	1.73205i	0.0320092	−	0.0554416i
$977$	−19.0000	+	32.9090i	−0.607864	+	1.05285i	0.383728	+	0.923446i	$0.374640\pi$
$977$	−19.0000	+	32.9090i	−0.607864	+	1.05285i	−0.991592	+	0.129405i	$0.958693\pi$
$978$	5.00000	+	8.66025i	0.159882	+	0.276924i
$979$	8.00000			0.255681
$980$	−16.5000	+	12.9904i	−0.527073	+	0.414963i
$981$	−14.0000			−0.446986
$982$	14.5000	+	25.1147i	0.462714	+	0.801443i
$983$	−15.0000	+	25.9808i	−0.478426	+	0.828658i	−0.999694	−	0.0247352i	$-0.992126\pi$
$983$	−15.0000	+	25.9808i	−0.478426	+	0.828658i	0.521268	+	0.853393i	$0.325459\pi$
$984$	−5.00000	+	8.66025i	−0.159394	+	0.276079i
$985$	−3.00000	−	5.19615i	−0.0955879	−	0.165563i
$986$	14.0000			0.445851
$987$	15.0000	−	5.19615i	0.477455	−	0.165395i
$988$	12.0000			0.381771
$989$	1.00000	+	1.73205i	0.0317982	+	0.0550760i
$990$	1.50000	−	2.59808i	0.0476731	−	0.0825723i
$991$	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	$0.0142982\pi$
$992$	−3.50000	−	6.06218i	−0.111125	−	0.192474i
$993$	14.0000			0.444277
$994$		0			0
$995$	−60.0000			−1.90213
$996$	6.50000	+	11.2583i	0.205960	+	0.356734i
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	−0.997938	−	0.0641836i	$-0.979556\pi$
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	0.554554	+	0.832148i	$0.312889\pi$
$998$	5.00000	−	8.66025i	0.158272	−	0.274136i
$999$	−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.d.277.1	✓	2
7.2	even	3	inner	966.2.i.d.415.1	yes	2
7.3	odd	6		6762.2.a.bm.1.1		1
7.4	even	3		6762.2.a.x.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.d.277.1	✓	2	1.1	even	1	trivial
966.2.i.d.415.1	yes	2	7.2	even	3	inner
6762.2.a.x.1.1		1	7.4	even	3
6762.2.a.bm.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} +(-0.500000 + 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} -6.00000 q^{13} +(2.00000 + 1.73205i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} -3.00000 q^{20} +(-0.500000 + 2.59808i) q^{21} +1.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(3.00000 + 5.19615i) q^{26} -1.00000 q^{27} +(0.500000 - 2.59808i) q^{28} -7.00000 q^{29} +(-1.50000 - 2.59808i) q^{30} +(-3.50000 + 6.06218i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} -2.00000 q^{34} +(-6.00000 - 5.19615i) q^{35} +1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-3.00000 + 5.19615i) q^{39} +(1.50000 + 2.59808i) q^{40} -10.0000 q^{41} +(2.50000 - 0.866025i) q^{42} +2.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.50000 - 2.59808i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-3.00000 - 5.19615i) q^{47} -1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +4.00000 q^{50} +(-1.00000 - 1.73205i) q^{51} +(3.00000 - 5.19615i) q^{52} +(-5.50000 + 9.52628i) q^{53} +(0.500000 + 0.866025i) q^{54} -3.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +2.00000 q^{57} +(3.50000 + 6.06218i) q^{58} +(-7.50000 + 12.9904i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(1.00000 + 1.73205i) q^{61} +7.00000 q^{62} +(2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-9.00000 - 15.5885i) q^{65} +(0.500000 - 0.866025i) q^{66} +(-1.00000 + 1.73205i) q^{67} +(1.00000 + 1.73205i) q^{68} +1.00000 q^{69} +(-1.50000 + 7.79423i) q^{70} +(-0.500000 - 0.866025i) q^{72} +(5.00000 - 8.66025i) q^{73} +(1.00000 - 1.73205i) q^{74} +(2.00000 + 3.46410i) q^{75} -2.00000 q^{76} +(0.500000 - 2.59808i) q^{77} +6.00000 q^{78} +(5.50000 + 9.52628i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.00000 + 8.66025i) q^{82} +13.0000 q^{83} +(-2.00000 - 1.73205i) q^{84} +6.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(-3.50000 + 6.06218i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-4.00000 - 6.92820i) q^{89} -3.00000 q^{90} +(15.0000 - 5.19615i) q^{91} -1.00000 q^{92} +(3.50000 + 6.06218i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{96} +1.00000 q^{97} +(-6.50000 - 2.59808i) q^{98} +1.00000 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	\( 2 q - q^{2} + q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 5 q^{7} + 2 q^{8} - q^{9} + 3 q^{10} - q^{11} + q^{12} - 12 q^{13} + 4 q^{14} + 6 q^{15} - q^{16} + 2 q^{17} - q^{18} + 2 q^{19} - 6 q^{20} - q^{21} + 2 q^{22} + q^{23} + q^{24} - 4 q^{25} + 6 q^{26} - 2 q^{27} + q^{28} - 14 q^{29} - 3 q^{30} - 7 q^{31} - q^{32} + q^{33} - 4 q^{34} - 12 q^{35} + 2 q^{36} + 2 q^{37} + 2 q^{38} - 6 q^{39} + 3 q^{40} - 20 q^{41} + 5 q^{42} + 4 q^{43} - q^{44} + 3 q^{45} + q^{46} - 6 q^{47} - 2 q^{48} + 11 q^{49} + 8 q^{50} - 2 q^{51} + 6 q^{52} - 11 q^{53} + q^{54} - 6 q^{55} - 5 q^{56} + 4 q^{57} + 7 q^{58} - 15 q^{59} - 3 q^{60} + 2 q^{61} + 14 q^{62} + 4 q^{63} + 2 q^{64} - 18 q^{65} + q^{66} - 2 q^{67} + 2 q^{68} + 2 q^{69} - 3 q^{70} - q^{72} + 10 q^{73} + 2 q^{74} + 4 q^{75} - 4 q^{76} + q^{77} + 12 q^{78} + 11 q^{79} + 3 q^{80} - q^{81} + 10 q^{82} + 26 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} - 7 q^{87} - q^{88} - 8 q^{89} - 6 q^{90} + 30 q^{91} - 2 q^{92} + 7 q^{93} - 6 q^{94} - 6 q^{95} + q^{96} + 2 q^{97} - 13 q^{98} + 2 q^{99}+O(q^{100}) \) 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 - q^11 + q^12 - 12 * q^13 + 4 * q^14 + 6 * q^15 - q^16 + 2 * q^17 - q^18 + 2 * q^19 - 6 * q^20 - q^21 + 2 * q^22 + q^23 + q^24 - 4 * q^25 + 6 * q^26 - 2 * q^27 + q^28 - 14 * q^29 - 3 * q^30 - 7 * q^31 - q^32 + q^33 - 4 * q^34 - 12 * q^35 + 2 * q^36 + 2 * q^37 + 2 * q^38 - 6 * q^39 + 3 * q^40 - 20 * q^41 + 5 * q^42 + 4 * q^43 - q^44 + 3 * q^45 + q^46 - 6 * q^47 - 2 * q^48 + 11 * q^49 + 8 * q^50 - 2 * q^51 + 6 * q^52 - 11 * q^53 + q^54 - 6 * q^55 - 5 * q^56 + 4 * q^57 + 7 * q^58 - 15 * q^59 - 3 * q^60 + 2 * q^61 + 14 * q^62 + 4 * q^63 + 2 * q^64 - 18 * q^65 + q^66 - 2 * q^67 + 2 * q^68 + 2 * q^69 - 3 * q^70 - q^72 + 10 * q^73 + 2 * q^74 + 4 * q^75 - 4 * q^76 + q^77 + 12 * q^78 + 11 * q^79 + 3 * q^80 - q^81 + 10 * q^82 + 26 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 - 7 * q^87 - q^88 - 8 * q^89 - 6 * q^90 + 30 * q^91 - 2 * q^92 + 7 * q^93 - 6 * q^94 - 6 * q^95 + q^96 + 2 * q^97 - 13 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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