LMFDB - Embedded newform 1110.2.x.b.841.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			841.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.b.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +1.00000i q^{6} +(-0.366025 - 0.633975i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +1.00000i q^{6} +(-0.366025 - 0.633975i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +0.267949 q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.50000 - 0.866025i) q^{13} -0.732051i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.23205 + 3.59808i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(1.73205 - 1.00000i) q^{19} +(0.866025 + 0.500000i) q^{20} +(0.366025 - 0.633975i) q^{21} +(0.232051 + 0.133975i) q^{22} +2.00000i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} +1.73205 q^{26} -1.00000 q^{27} +(0.366025 - 0.633975i) q^{28} +4.26795i q^{29} +(0.500000 + 0.866025i) q^{30} +6.92820i q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.133975 + 0.232051i) q^{33} +(3.59808 + 6.23205i) q^{34} +(-0.633975 - 0.366025i) q^{35} -1.00000 q^{36} +(-0.500000 + 6.06218i) q^{37} +2.00000 q^{38} +(1.50000 + 0.866025i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-4.09808 - 7.09808i) q^{41} +(0.633975 - 0.366025i) q^{42} -0.535898i q^{43} +(0.133975 + 0.232051i) q^{44} +1.00000i q^{45} +(-1.00000 + 1.73205i) q^{46} -1.73205 q^{47} -1.00000 q^{48} +(3.23205 - 5.59808i) q^{49} +(0.866025 - 0.500000i) q^{50} +7.19615i q^{51} +(1.50000 + 0.866025i) q^{52} +(4.09808 - 7.09808i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(0.232051 - 0.133975i) q^{55} +(0.633975 - 0.366025i) q^{56} +(1.73205 + 1.00000i) q^{57} +(-2.13397 + 3.69615i) q^{58} +(-0.401924 - 0.232051i) q^{59} +1.00000i q^{60} +(1.09808 - 0.633975i) q^{61} +(-3.46410 + 6.00000i) q^{62} +0.732051 q^{63} -1.00000 q^{64} +(0.866025 - 1.50000i) q^{65} +0.267949i q^{66} +(-5.33013 - 9.23205i) q^{67} +7.19615i q^{68} +(-1.73205 + 1.00000i) q^{69} +(-0.366025 - 0.633975i) q^{70} +(-4.09808 - 7.09808i) q^{71} +(-0.866025 - 0.500000i) q^{72} -12.3923 q^{73} +(-3.46410 + 5.00000i) q^{74} +1.00000 q^{75} +(1.73205 + 1.00000i) q^{76} +(-0.0980762 - 0.169873i) q^{77} +(0.866025 + 1.50000i) q^{78} +(-4.26795 + 2.46410i) q^{79} +1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -8.19615i q^{82} +(3.09808 - 5.36603i) q^{83} +0.732051 q^{84} +7.19615 q^{85} +(0.267949 - 0.464102i) q^{86} +(-3.69615 + 2.13397i) q^{87} +0.267949i q^{88} +(11.1962 + 6.46410i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-1.09808 - 0.633975i) q^{91} +(-1.73205 + 1.00000i) q^{92} +(-6.00000 + 3.46410i) q^{93} +(-1.50000 - 0.866025i) q^{94} +(1.00000 - 1.73205i) q^{95} +(-0.866025 - 0.500000i) q^{96} +11.4641i q^{97} +(5.59808 - 3.23205i) q^{98} +(-0.133975 + 0.232051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} + 2 q^{7} - 2 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{12} + 6 q^{13} - 2 q^{16} + 18 q^{17} - 2 q^{21} - 6 q^{22} + 2 q^{25} - 4 q^{27} - 2 q^{28} + 2 q^{30} + 4 q^{33} + 4 q^{34} - 6 q^{35} - 4 q^{36} - 2 q^{37} + 8 q^{38} + 6 q^{39} + 2 q^{40} - 6 q^{41} + 6 q^{42} + 4 q^{44} - 4 q^{46} - 4 q^{48} + 6 q^{49} + 6 q^{52} + 6 q^{53} - 6 q^{55} + 6 q^{56} - 12 q^{58} - 12 q^{59} - 6 q^{61} - 4 q^{63} - 4 q^{64} - 4 q^{67} + 2 q^{70} - 6 q^{71} - 8 q^{73} + 4 q^{75} + 10 q^{77} - 24 q^{79} - 2 q^{81} + 2 q^{83} - 4 q^{84} + 8 q^{85} + 8 q^{86} + 6 q^{87} + 24 q^{89} - 2 q^{90} + 6 q^{91} - 24 q^{93} - 6 q^{94} + 4 q^{95} + 12 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^7 - 2 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^12 + 6 * q^13 - 2 * q^16 + 18 * q^17 - 2 * q^21 - 6 * q^22 + 2 * q^25 - 4 * q^27 - 2 * q^28 + 2 * q^30 + 4 * q^33 + 4 * q^34 - 6 * q^35 - 4 * q^36 - 2 * q^37 + 8 * q^38 + 6 * q^39 + 2 * q^40 - 6 * q^41 + 6 * q^42 + 4 * q^44 - 4 * q^46 - 4 * q^48 + 6 * q^49 + 6 * q^52 + 6 * q^53 - 6 * q^55 + 6 * q^56 - 12 * q^58 - 12 * q^59 - 6 * q^61 - 4 * q^63 - 4 * q^64 - 4 * q^67 + 2 * q^70 - 6 * q^71 - 8 * q^73 + 4 * q^75 + 10 * q^77 - 24 * q^79 - 2 * q^81 + 2 * q^83 - 4 * q^84 + 8 * q^85 + 8 * q^86 + 6 * q^87 + 24 * q^89 - 2 * q^90 + 6 * q^91 - 24 * q^93 - 6 * q^94 + 4 * q^95 + 12 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$			1.00000i			0.408248i
$7$	−0.366025	−	0.633975i	−0.138345	−	0.239620i	0.788526	−	0.615002i	$-0.210845\pi$
$7$	−0.366025	−	0.633975i	−0.138345	−	0.239620i	−0.926870	+	0.375382i	$0.877511\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	0.267949			0.0807897			0.0403949	−	0.999184i	$-0.487138\pi$
$11$	0.267949			0.0807897			0.0403949	+	0.999184i	$0.487138\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.50000	−	0.866025i	0.416025	−	0.240192i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	1.50000	−	0.866025i	0.416025	−	0.240192i	0.693375	+	0.720577i	$0.256123\pi$
$14$		−	0.732051i		−	0.195649i
$15$	0.866025	+	0.500000i	0.223607	+	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.23205	+	3.59808i	1.51149	+	0.872662i	0.999910	+	0.0134287i	$0.00427461\pi$
$17$	6.23205	+	3.59808i	1.51149	+	0.872662i	0.511585	+	0.859233i	$0.329059\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	1.73205	−	1.00000i	0.397360	−	0.229416i	−0.287984	−	0.957635i	$-0.592985\pi$
$19$	1.73205	−	1.00000i	0.397360	−	0.229416i	0.685344	+	0.728219i	$0.259652\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	0.366025	−	0.633975i	0.0798733	−	0.138345i
$22$	0.232051	+	0.133975i	0.0494734	+	0.0285635i
$23$			2.00000i			0.417029i	0.978019	+	0.208514i	$0.0668628\pi$
$23$			2.00000i			0.417029i	−0.978019	+	0.208514i	$0.933137\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.73205			0.339683
$27$	−1.00000			−0.192450
$28$	0.366025	−	0.633975i	0.0691723	−	0.119810i
$29$			4.26795i			0.792538i	0.918134	+	0.396269i	$0.129695\pi$
$29$			4.26795i			0.792538i	−0.918134	+	0.396269i	$0.870305\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$			6.92820i			1.24434i	0.782881	+	0.622171i	$0.213749\pi$
$31$			6.92820i			1.24434i	−0.782881	+	0.622171i	$0.786251\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.133975	+	0.232051i	0.0233220	+	0.0403949i
$34$	3.59808	+	6.23205i	0.617065	+	1.06879i
$35$	−0.633975	−	0.366025i	−0.107161	−	0.0618696i
$36$	−1.00000			−0.166667
$37$	−0.500000	+	6.06218i	−0.0821995	+	0.996616i
$37$	−0.500000	+	6.06218i	−0.0821995	+	0.996616i
$38$	2.00000			0.324443
$39$	1.50000	+	0.866025i	0.240192	+	0.138675i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−4.09808	−	7.09808i	−0.640012	−	1.10853i	−0.985430	−	0.170084i	$-0.945596\pi$
$41$	−4.09808	−	7.09808i	−0.640012	−	1.10853i	0.345418	−	0.938449i	$-0.387737\pi$
$42$	0.633975	−	0.366025i	0.0978244	−	0.0564789i
$43$		−	0.535898i		−	0.0817237i	−0.999165	−	0.0408619i	$-0.986990\pi$
$43$		−	0.535898i		−	0.0817237i	0.999165	−	0.0408619i	$-0.0130104\pi$
$44$	0.133975	+	0.232051i	0.0201974	+	0.0349830i
$45$			1.00000i			0.149071i
$46$	−1.00000	+	1.73205i	−0.147442	+	0.255377i
$47$	−1.73205			−0.252646			−0.126323	−	0.991989i	$-0.540318\pi$
$47$	−1.73205			−0.252646			−0.126323	+	0.991989i	$0.540318\pi$
$48$	−1.00000			−0.144338
$49$	3.23205	−	5.59808i	0.461722	−	0.799725i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$			7.19615i			1.00766i
$52$	1.50000	+	0.866025i	0.208013	+	0.120096i
$53$	4.09808	−	7.09808i	0.562914	−	0.974996i	−0.434326	−	0.900756i	$-0.643014\pi$
$53$	4.09808	−	7.09808i	0.562914	−	0.974996i	0.997240	−	0.0742402i	$-0.0236531\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	0.232051	−	0.133975i	0.0312897	−	0.0180651i
$56$	0.633975	−	0.366025i	0.0847184	−	0.0489122i
$57$	1.73205	+	1.00000i	0.229416	+	0.132453i
$58$	−2.13397	+	3.69615i	−0.280205	+	0.485329i
$59$	−0.401924	−	0.232051i	−0.0523260	−	0.0302104i	0.473609	−	0.880735i	$-0.342951\pi$
$59$	−0.401924	−	0.232051i	−0.0523260	−	0.0302104i	−0.525935	+	0.850525i	$0.676284\pi$
$60$			1.00000i			0.129099i
$61$	1.09808	−	0.633975i	0.140594	−	0.0811721i	−0.428053	−	0.903754i	$-0.640800\pi$
$61$	1.09808	−	0.633975i	0.140594	−	0.0811721i	0.568647	+	0.822582i	$0.307467\pi$
$62$	−3.46410	+	6.00000i	−0.439941	+	0.762001i
$63$	0.732051			0.0922297
$64$	−1.00000			−0.125000
$65$	0.866025	−	1.50000i	0.107417	−	0.186052i
$66$			0.267949i			0.0329823i
$67$	−5.33013	−	9.23205i	−0.651179	−	1.12787i	−0.982837	−	0.184475i	$-0.940942\pi$
$67$	−5.33013	−	9.23205i	−0.651179	−	1.12787i	0.331659	−	0.943399i	$-0.392392\pi$
$68$			7.19615i			0.872662i
$69$	−1.73205	+	1.00000i	−0.208514	+	0.120386i
$70$	−0.366025	−	0.633975i	−0.0437484	−	0.0757745i
$71$	−4.09808	−	7.09808i	−0.486352	−	0.842387i	0.513525	−	0.858075i	$-0.328339\pi$
$71$	−4.09808	−	7.09808i	−0.486352	−	0.842387i	−0.999877	+	0.0156881i	$0.995006\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	−12.3923			−1.45041			−0.725205	−	0.688533i	$-0.758255\pi$
$73$	−12.3923			−1.45041			−0.725205	+	0.688533i	$0.758255\pi$
$74$	−3.46410	+	5.00000i	−0.402694	+	0.581238i
$75$	1.00000			0.115470
$76$	1.73205	+	1.00000i	0.198680	+	0.114708i
$77$	−0.0980762	−	0.169873i	−0.0111768	−	0.0193588i
$78$	0.866025	+	1.50000i	0.0980581	+	0.169842i
$79$	−4.26795	+	2.46410i	−0.480182	+	0.277233i	−0.720492	−	0.693463i	$-0.756084\pi$
$79$	−4.26795	+	2.46410i	−0.480182	+	0.277233i	0.240310	+	0.970696i	$0.422751\pi$
$80$			1.00000i			0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	8.19615i		−	0.905114i
$83$	3.09808	−	5.36603i	0.340058	−	0.588998i	−0.644385	−	0.764701i	$-0.722887\pi$
$83$	3.09808	−	5.36603i	0.340058	−	0.588998i	0.984443	+	0.175703i	$0.0562199\pi$
$84$	0.732051			0.0798733
$85$	7.19615			0.780532
$86$	0.267949	−	0.464102i	0.0288937	−	0.0500454i
$87$	−3.69615	+	2.13397i	−0.396269	+	0.228786i
$88$			0.267949i			0.0285635i
$89$	11.1962	+	6.46410i	1.18679	+	0.685193i	0.957575	−	0.288183i	$-0.0930510\pi$
$89$	11.1962	+	6.46410i	1.18679	+	0.685193i	0.229214	+	0.973376i	$0.426384\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	−1.09808	−	0.633975i	−0.115110	−	0.0664586i
$92$	−1.73205	+	1.00000i	−0.180579	+	0.104257i
$93$	−6.00000	+	3.46410i	−0.622171	+	0.359211i
$94$	−1.50000	−	0.866025i	−0.154713	−	0.0893237i
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$			11.4641i			1.16400i	0.813188	+	0.582002i	$0.197730\pi$
$97$			11.4641i			1.16400i	−0.813188	+	0.582002i	$0.802270\pi$
$98$	5.59808	−	3.23205i	0.565491	−	0.326486i
$99$	−0.133975	+	0.232051i	−0.0134650	+	0.0233220i
$100$	1.00000			0.100000
$101$	8.46410			0.842210			0.421105	−	0.907012i	$-0.361642\pi$
$101$	8.46410			0.842210			0.421105	+	0.907012i	$0.361642\pi$
$102$	−3.59808	+	6.23205i	−0.356263	+	0.617065i
$103$		−	10.1962i		−	1.00466i	−0.864677	−	0.502328i	$-0.832477\pi$
$103$		−	10.1962i		−	1.00466i	0.864677	−	0.502328i	$-0.167523\pi$
$104$	0.866025	+	1.50000i	0.0849208	+	0.147087i
$105$		−	0.732051i		−	0.0714408i
$106$	7.09808	−	4.09808i	0.689426	−	0.398040i
$107$	0.901924	+	1.56218i	0.0871923	+	0.151021i	0.906323	−	0.422585i	$-0.138877\pi$
$107$	0.901924	+	1.56218i	0.0871923	+	0.151021i	−0.819131	+	0.573606i	$0.805544\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	2.83013	+	1.63397i	0.271077	+	0.156506i	0.629377	−	0.777100i	$-0.283310\pi$
$109$	2.83013	+	1.63397i	0.271077	+	0.156506i	−0.358300	+	0.933607i	$0.616643\pi$
$110$	0.267949			0.0255480
$111$	−5.50000	+	2.59808i	−0.522037	+	0.246598i
$112$	0.732051			0.0691723
$113$	−12.6962	−	7.33013i	−1.19435	−	0.689560i	−0.235063	−	0.971980i	$-0.575530\pi$
$113$	−12.6962	−	7.33013i	−1.19435	−	0.689560i	−0.959291	+	0.282420i	$0.908863\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$	1.00000	+	1.73205i	0.0932505	+	0.161515i
$116$	−3.69615	+	2.13397i	−0.343179	+	0.198135i
$117$			1.73205i			0.160128i
$118$	−0.232051	−	0.401924i	−0.0213620	−	0.0370001i
$119$		−	5.26795i		−	0.482912i
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	−10.9282			−0.993473
$122$	1.26795			0.114795
$123$	4.09808	−	7.09808i	0.369511	−	0.640012i
$124$	−6.00000	+	3.46410i	−0.538816	+	0.311086i
$125$		−	1.00000i		−	0.0894427i
$126$	0.633975	+	0.366025i	0.0564789	+	0.0326081i
$127$	−0.366025	+	0.633975i	−0.0324795	+	0.0562561i	−0.881808	−	0.471608i	$-0.843674\pi$
$127$	−0.366025	+	0.633975i	−0.0324795	+	0.0562561i	0.849329	+	0.527864i	$0.177007\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	0.464102	−	0.267949i	0.0408619	−	0.0235916i
$130$	1.50000	−	0.866025i	0.131559	−	0.0759555i
$131$	−8.13397	−	4.69615i	−0.710669	−	0.410305i	0.100640	−	0.994923i	$-0.467911\pi$
$131$	−8.13397	−	4.69615i	−0.710669	−	0.410305i	−0.811309	+	0.584618i	$0.801244\pi$
$132$	−0.133975	+	0.232051i	−0.0116610	+	0.0201974i
$133$	−1.26795	−	0.732051i	−0.109945	−	0.0634769i
$134$		−	10.6603i		−	0.920906i
$135$	−0.866025	+	0.500000i	−0.0745356	+	0.0430331i
$136$	−3.59808	+	6.23205i	−0.308532	+	0.534394i
$137$	11.0000			0.939793			0.469897	−	0.882721i	$-0.344291\pi$
$137$	11.0000			0.939793			0.469897	+	0.882721i	$0.344291\pi$
$138$	−2.00000			−0.170251
$139$	−8.19615	+	14.1962i	−0.695189	+	1.20410i	0.274929	+	0.961465i	$0.411346\pi$
$139$	−8.19615	+	14.1962i	−0.695189	+	1.20410i	−0.970117	+	0.242637i	$0.921988\pi$
$140$		−	0.732051i		−	0.0618696i
$141$	−0.866025	−	1.50000i	−0.0729325	−	0.126323i
$142$		−	8.19615i		−	0.687806i
$143$	0.401924	−	0.232051i	0.0336106	−	0.0194051i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	2.13397	+	3.69615i	0.177217	+	0.306949i
$146$	−10.7321	−	6.19615i	−0.888191	−	0.512797i
$147$	6.46410			0.533150
$148$	−5.50000	+	2.59808i	−0.452097	+	0.213561i
$149$	3.92820			0.321811			0.160905	−	0.986970i	$-0.448559\pi$
$149$	3.92820			0.321811			0.160905	+	0.986970i	$0.448559\pi$
$150$	0.866025	+	0.500000i	0.0707107	+	0.0408248i
$151$	2.53590	+	4.39230i	0.206368	+	0.357441i	0.950568	−	0.310517i	$-0.100502\pi$
$151$	2.53590	+	4.39230i	0.206368	+	0.357441i	−0.744199	+	0.667958i	$0.767169\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	−6.23205	+	3.59808i	−0.503831	+	0.290887i
$154$		−	0.196152i		−	0.0158064i
$155$	3.46410	+	6.00000i	0.278243	+	0.481932i
$156$			1.73205i			0.138675i
$157$	11.2321	−	19.4545i	0.896415	−	1.55264i	0.0643720	−	0.997926i	$-0.479496\pi$
$157$	11.2321	−	19.4545i	0.896415	−	1.55264i	0.832043	−	0.554711i	$-0.187171\pi$
$158$	−4.92820			−0.392067
$159$	8.19615			0.649997
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	1.26795	−	0.732051i	0.0999284	−	0.0576937i
$162$		−	1.00000i		−	0.0785674i
$163$	−19.4545	−	11.2321i	−1.52379	−	0.879762i	−0.999603	−	0.0281603i	$-0.991035\pi$
$163$	−19.4545	−	11.2321i	−1.52379	−	0.879762i	−0.524189	−	0.851602i	$-0.675632\pi$
$164$	4.09808	−	7.09808i	0.320006	−	0.554267i
$165$	0.232051	+	0.133975i	0.0180651	+	0.0104299i
$166$	5.36603	−	3.09808i	0.416484	−	0.240457i
$167$	15.4019	−	8.89230i	1.19184	−	0.688107i	0.233114	−	0.972449i	$-0.425109\pi$
$167$	15.4019	−	8.89230i	1.19184	−	0.688107i	0.958723	+	0.284342i	$0.0917752\pi$
$168$	0.633975	+	0.366025i	0.0489122	+	0.0282395i
$169$	−5.00000	+	8.66025i	−0.384615	+	0.666173i
$170$	6.23205	+	3.59808i	0.477976	+	0.275960i
$171$			2.00000i			0.152944i
$172$	0.464102	−	0.267949i	0.0353874	−	0.0204309i
$173$	8.83013	−	15.2942i	0.671342	−	1.16280i	−0.306182	−	0.951973i	$-0.599051\pi$
$173$	8.83013	−	15.2942i	0.671342	−	1.16280i	0.977524	−	0.210826i	$-0.0676152\pi$
$174$	−4.26795			−0.323552
$175$	−0.732051			−0.0553378
$176$	−0.133975	+	0.232051i	−0.0100987	+	0.0174915i
$177$		−	0.464102i		−	0.0348840i
$178$	6.46410	+	11.1962i	0.484505	+	0.839187i
$179$		−	8.92820i		−	0.667325i	−0.942693	−	0.333663i	$-0.891715\pi$
$179$		−	8.92820i		−	0.667325i	0.942693	−	0.333663i	$-0.108285\pi$
$180$	−0.866025	+	0.500000i	−0.0645497	+	0.0372678i
$181$	1.00000	+	1.73205i	0.0743294	+	0.128742i	0.900794	−	0.434246i	$-0.142985\pi$
$181$	1.00000	+	1.73205i	0.0743294	+	0.128742i	−0.826465	+	0.562988i	$0.809652\pi$
$182$	−0.633975	−	1.09808i	−0.0469933	−	0.0813948i
$183$	1.09808	+	0.633975i	0.0811721	+	0.0468648i
$184$	−2.00000			−0.147442
$185$	2.59808	+	5.50000i	0.191014	+	0.404368i
$186$	−6.92820			−0.508001
$187$	1.66987	+	0.964102i	0.122113	+	0.0705021i
$188$	−0.866025	−	1.50000i	−0.0631614	−	0.109399i
$189$	0.366025	+	0.633975i	0.0266244	+	0.0461149i
$190$	1.73205	−	1.00000i	0.125656	−	0.0725476i
$191$		−	0.196152i		−	0.0141931i	−0.999975	−	0.00709655i	$-0.997741\pi$
$191$		−	0.196152i		−	0.0141931i	0.999975	−	0.00709655i	$-0.00225892\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$		−	10.1962i		−	0.733935i	−0.930234	−	0.366968i	$-0.880396\pi$
$193$		−	10.1962i		−	0.733935i	0.930234	−	0.366968i	$-0.119604\pi$
$194$	−5.73205	+	9.92820i	−0.411537	+	0.712803i
$195$	1.73205			0.124035
$196$	6.46410			0.461722
$197$	2.46410	−	4.26795i	0.175560	−	0.304079i	−0.764795	−	0.644274i	$-0.777160\pi$
$197$	2.46410	−	4.26795i	0.175560	−	0.304079i	0.940355	+	0.340195i	$0.110493\pi$
$198$	−0.232051	+	0.133975i	−0.0164911	+	0.00952116i
$199$		−	8.32051i		−	0.589825i	−0.955524	−	0.294913i	$-0.904709\pi$
$199$		−	8.32051i		−	0.589825i	0.955524	−	0.294913i	$-0.0952905\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	5.33013	−	9.23205i	0.375958	−	0.651179i
$202$	7.33013	+	4.23205i	0.515746	+	0.297766i
$203$	2.70577	−	1.56218i	0.189908	−	0.109643i
$204$	−6.23205	+	3.59808i	−0.436331	+	0.251916i
$205$	−7.09808	−	4.09808i	−0.495751	−	0.286222i
$206$	5.09808	−	8.83013i	0.355200	−	0.615224i
$207$	−1.73205	−	1.00000i	−0.120386	−	0.0695048i
$208$			1.73205i			0.120096i
$209$	0.464102	−	0.267949i	0.0321026	−	0.0185344i
$210$	0.366025	−	0.633975i	0.0252582	−	0.0437484i
$211$	−23.3205			−1.60545			−0.802725	−	0.596349i	$-0.796617\pi$
$211$	−23.3205			−1.60545			−0.802725	+	0.596349i	$0.796617\pi$
$212$	8.19615			0.562914
$213$	4.09808	−	7.09808i	0.280796	−	0.486352i
$214$			1.80385i			0.123308i
$215$	−0.267949	−	0.464102i	−0.0182740	−	0.0316515i
$216$		−	1.00000i		−	0.0680414i
$217$	4.39230	−	2.53590i	0.298169	−	0.172148i
$218$	1.63397	+	2.83013i	0.110667	+	0.191680i
$219$	−6.19615	−	10.7321i	−0.418697	−	0.725205i
$220$	0.232051	+	0.133975i	0.0156449	+	0.00903257i
$221$	12.4641			0.838426
$222$	−6.06218	−	0.500000i	−0.406867	−	0.0335578i
$223$	−14.5359			−0.973396			−0.486698	−	0.873570i	$-0.661799\pi$
$223$	−14.5359			−0.973396			−0.486698	+	0.873570i	$0.661799\pi$
$224$	0.633975	+	0.366025i	0.0423592	+	0.0244561i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	−7.33013	−	12.6962i	−0.487593	−	0.844535i
$227$	−1.09808	+	0.633975i	−0.0728819	+	0.0420784i	−0.535998	−	0.844219i	$-0.680065\pi$
$227$	−1.09808	+	0.633975i	−0.0728819	+	0.0420784i	0.463116	+	0.886298i	$0.346731\pi$
$228$			2.00000i			0.132453i
$229$	8.02628	+	13.9019i	0.530391	+	0.918665i	0.999371	+	0.0354561i	$0.0112884\pi$
$229$	8.02628	+	13.9019i	0.530391	+	0.918665i	−0.468980	+	0.883209i	$0.655378\pi$
$230$			2.00000i			0.131876i
$231$	0.0980762	−	0.169873i	0.00645294	−	0.0111768i
$232$	−4.26795			−0.280205
$233$	−2.53590			−0.166132			−0.0830661	−	0.996544i	$-0.526471\pi$
$233$	−2.53590			−0.166132			−0.0830661	+	0.996544i	$0.526471\pi$
$234$	−0.866025	+	1.50000i	−0.0566139	+	0.0980581i
$235$	−1.50000	+	0.866025i	−0.0978492	+	0.0564933i
$236$		−	0.464102i		−	0.0302104i
$237$	−4.26795	−	2.46410i	−0.277233	−	0.160061i
$238$	2.63397	−	4.56218i	0.170735	−	0.295722i
$239$	12.5885	+	7.26795i	0.814280	+	0.470125i	0.848440	−	0.529292i	$-0.177542\pi$
$239$	12.5885	+	7.26795i	0.814280	+	0.470125i	−0.0341602	+	0.999416i	$0.510876\pi$
$240$	−0.866025	+	0.500000i	−0.0559017	+	0.0322749i
$241$	−3.23205	+	1.86603i	−0.208195	+	0.120201i	−0.600472	−	0.799646i	$-0.705021\pi$
$241$	−3.23205	+	1.86603i	−0.208195	+	0.120201i	0.392277	+	0.919847i	$0.371687\pi$
$242$	−9.46410	−	5.46410i	−0.608375	−	0.351246i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.09808	+	0.633975i	0.0702971	+	0.0405861i
$245$		−	6.46410i		−	0.412976i
$246$	7.09808	−	4.09808i	0.452557	−	0.261284i
$247$	1.73205	−	3.00000i	0.110208	−	0.190885i
$248$	−6.92820			−0.439941
$249$	6.19615			0.392665
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$		−	8.32051i		−	0.525186i	−0.964907	−	0.262593i	$-0.915422\pi$
$251$		−	8.32051i		−	0.525186i	0.964907	−	0.262593i	$-0.0845776\pi$
$252$	0.366025	+	0.633975i	0.0230574	+	0.0399366i
$253$			0.535898i			0.0336916i
$254$	−0.633975	+	0.366025i	−0.0397791	+	0.0229665i
$255$	3.59808	+	6.23205i	0.225320	+	0.390266i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.76795	−	3.33013i	−0.359795	−	0.207728i	0.309196	−	0.950998i	$-0.399940\pi$
$257$	−5.76795	−	3.33013i	−0.359795	−	0.207728i	−0.668991	+	0.743271i	$0.733273\pi$
$258$	0.535898			0.0333636
$259$	4.02628	−	1.90192i	0.250181	−	0.118180i
$260$	1.73205			0.107417
$261$	−3.69615	−	2.13397i	−0.228786	−	0.132090i
$262$	−4.69615	−	8.13397i	−0.290129	−	0.502519i
$263$	−11.6603	−	20.1962i	−0.719002	−	1.24535i	−0.961396	−	0.275170i	$-0.911266\pi$
$263$	−11.6603	−	20.1962i	−0.719002	−	1.24535i	0.242393	−	0.970178i	$-0.422068\pi$
$264$	−0.232051	+	0.133975i	−0.0142817	+	0.00824557i
$265$		−	8.19615i		−	0.503486i
$266$	−0.732051	−	1.26795i	−0.0448849	−	0.0777430i
$267$			12.9282i			0.791193i
$268$	5.33013	−	9.23205i	0.325589	−	0.563937i
$269$	−1.07180			−0.0653486			−0.0326743	−	0.999466i	$-0.510402\pi$
$269$	−1.07180			−0.0653486			−0.0326743	+	0.999466i	$0.510402\pi$
$270$	−1.00000			−0.0608581
$271$	2.66987	−	4.62436i	0.162183	−	0.280910i	−0.773468	−	0.633835i	$-0.781480\pi$
$271$	2.66987	−	4.62436i	0.162183	−	0.280910i	0.935651	+	0.352926i	$0.114813\pi$
$272$	−6.23205	+	3.59808i	−0.377874	+	0.218165i
$273$		−	1.26795i		−	0.0767398i
$274$	9.52628	+	5.50000i	0.575504	+	0.332267i
$275$	0.133975	−	0.232051i	0.00807897	−	0.0139932i
$276$	−1.73205	−	1.00000i	−0.104257	−	0.0601929i
$277$	13.1603	−	7.59808i	0.790723	−	0.456524i	−0.0494940	−	0.998774i	$-0.515761\pi$
$277$	13.1603	−	7.59808i	0.790723	−	0.456524i	0.840217	+	0.542250i	$0.182428\pi$
$278$	−14.1962	+	8.19615i	−0.851429	+	0.491573i
$279$	−6.00000	−	3.46410i	−0.359211	−	0.207390i
$280$	0.366025	−	0.633975i	0.0218742	−	0.0378872i
$281$	−3.00000	−	1.73205i	−0.178965	−	0.103325i	0.407841	−	0.913053i	$-0.366282\pi$
$281$	−3.00000	−	1.73205i	−0.178965	−	0.103325i	−0.586806	+	0.809727i	$0.699615\pi$
$282$		−	1.73205i		−	0.103142i
$283$	−26.3827	+	15.2321i	−1.56829	+	0.905451i	−0.571919	+	0.820310i	$0.693801\pi$
$283$	−26.3827	+	15.2321i	−1.56829	+	0.905451i	−0.996369	+	0.0851413i	$0.972866\pi$
$284$	4.09808	−	7.09808i	0.243176	−	0.421193i
$285$	2.00000			0.118470
$286$	0.464102			0.0274429
$287$	−3.00000	+	5.19615i	−0.177084	+	0.306719i
$288$		−	1.00000i		−	0.0589256i
$289$	17.3923	+	30.1244i	1.02308	+	1.77202i
$290$			4.26795i			0.250623i
$291$	−9.92820	+	5.73205i	−0.582002	+	0.336019i
$292$	−6.19615	−	10.7321i	−0.362602	−	0.628046i
$293$	1.73205	+	3.00000i	0.101187	+	0.175262i	0.912174	−	0.409803i	$-0.134402\pi$
$293$	1.73205	+	3.00000i	0.101187	+	0.175262i	−0.810987	+	0.585065i	$0.801069\pi$
$294$	5.59808	+	3.23205i	0.326486	+	0.188497i
$295$	−0.464102			−0.0270210
$296$	−6.06218	−	0.500000i	−0.352357	−	0.0290619i
$297$	−0.267949			−0.0155480
$298$	3.40192	+	1.96410i	0.197068	+	0.113777i
$299$	1.73205	+	3.00000i	0.100167	+	0.173494i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	−0.339746	+	0.196152i	−0.0195826	+	0.0113060i
$302$			5.07180i			0.291849i
$303$	4.23205	+	7.33013i	0.243125	+	0.421105i
$304$			2.00000i			0.114708i
$305$	0.633975	−	1.09808i	0.0363013	−	0.0628757i
$306$	−7.19615			−0.411377
$307$	−19.4641			−1.11087			−0.555437	−	0.831558i	$-0.687449\pi$
$307$	−19.4641			−1.11087			−0.555437	+	0.831558i	$0.687449\pi$
$308$	0.0980762	−	0.169873i	0.00558841	−	0.00967941i
$309$	8.83013	−	5.09808i	0.502328	−	0.290019i
$310$			6.92820i			0.393496i
$311$	−4.09808	−	2.36603i	−0.232381	−	0.134165i	0.379289	−	0.925278i	$-0.376169\pi$
$311$	−4.09808	−	2.36603i	−0.232381	−	0.134165i	−0.611670	+	0.791113i	$0.709502\pi$
$312$	−0.866025	+	1.50000i	−0.0490290	+	0.0849208i
$313$	4.26795	+	2.46410i	0.241239	+	0.139279i	0.615746	−	0.787945i	$-0.288855\pi$
$313$	4.26795	+	2.46410i	0.241239	+	0.139279i	−0.374507	+	0.927224i	$0.622188\pi$
$314$	19.4545	−	11.2321i	1.09788	−	0.633861i
$315$	0.633975	−	0.366025i	0.0357204	−	0.0206232i
$316$	−4.26795	−	2.46410i	−0.240091	−	0.138617i
$317$	2.63397	−	4.56218i	0.147939	−	0.256237i	−0.782527	−	0.622617i	$-0.786069\pi$
$317$	2.63397	−	4.56218i	0.147939	−	0.256237i	0.930465	+	0.366380i	$0.119403\pi$
$318$	7.09808	+	4.09808i	0.398040	+	0.229809i
$319$			1.14359i			0.0640289i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$	−0.901924	+	1.56218i	−0.0503405	+	0.0871923i
$322$	1.46410			0.0815912
$323$	14.3923			0.800809
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$		−	1.73205i		−	0.0960769i
$326$	−11.2321	−	19.4545i	−0.622086	−	1.07748i
$327$			3.26795i			0.180718i
$328$	7.09808	−	4.09808i	0.391926	−	0.226278i
$329$	0.633975	+	1.09808i	0.0349522	+	0.0605389i
$330$	0.133975	+	0.232051i	0.00737506	+	0.0127740i
$331$	23.9545	+	13.8301i	1.31666	+	0.760173i	0.983189	−	0.182589i	$-0.0584477\pi$
$331$	23.9545	+	13.8301i	1.31666	+	0.760173i	0.333468	+	0.942761i	$0.391781\pi$
$332$	6.19615			0.340058
$333$	−5.00000	−	3.46410i	−0.273998	−	0.189832i
$334$	17.7846			0.973131
$335$	−9.23205	−	5.33013i	−0.504401	−	0.291216i
$336$	0.366025	+	0.633975i	0.0199683	+	0.0345861i
$337$	−4.83013	−	8.36603i	−0.263114	−	0.455726i	0.703954	−	0.710246i	$-0.251416\pi$
$337$	−4.83013	−	8.36603i	−0.263114	−	0.455726i	−0.967068	+	0.254519i	$0.918083\pi$
$338$	−8.66025	+	5.00000i	−0.471056	+	0.271964i
$339$		−	14.6603i		−	0.796236i
$340$	3.59808	+	6.23205i	0.195133	+	0.337980i
$341$			1.85641i			0.100530i
$342$	−1.00000	+	1.73205i	−0.0540738	+	0.0936586i
$343$	−9.85641			−0.532196
$344$	0.535898			0.0288937
$345$	−1.00000	+	1.73205i	−0.0538382	+	0.0932505i
$346$	15.2942	−	8.83013i	0.822223	−	0.474711i
$347$			28.9282i			1.55295i	0.630150	+	0.776474i	$0.282994\pi$
$347$			28.9282i			1.55295i	−0.630150	+	0.776474i	$0.717006\pi$
$348$	−3.69615	−	2.13397i	−0.198135	−	0.114393i
$349$	−2.19615	+	3.80385i	−0.117557	+	0.203615i	−0.918799	−	0.394725i	$-0.870840\pi$
$349$	−2.19615	+	3.80385i	−0.117557	+	0.203615i	0.801242	+	0.598341i	$0.204173\pi$
$350$	−0.633975	−	0.366025i	−0.0338874	−	0.0195649i
$351$	−1.50000	+	0.866025i	−0.0800641	+	0.0462250i
$352$	−0.232051	+	0.133975i	−0.0123683	+	0.00714087i
$353$	−17.1962	−	9.92820i	−0.915259	−	0.528425i	−0.0331394	−	0.999451i	$-0.510551\pi$
$353$	−17.1962	−	9.92820i	−0.915259	−	0.528425i	−0.882119	+	0.471026i	$0.843884\pi$
$354$	0.232051	−	0.401924i	0.0123334	−	0.0213620i
$355$	−7.09808	−	4.09808i	−0.376727	−	0.217503i
$356$			12.9282i			0.685193i
$357$	4.56218	−	2.63397i	0.241456	−	0.139405i
$358$	4.46410	−	7.73205i	0.235935	−	0.408652i
$359$	18.0000			0.950004			0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000			0.950004			0.475002	+	0.879985i	$0.342447\pi$
$360$	−1.00000			−0.0527046
$361$	−7.50000	+	12.9904i	−0.394737	+	0.683704i
$362$			2.00000i			0.105118i
$363$	−5.46410	−	9.46410i	−0.286791	−	0.496737i
$364$		−	1.26795i		−	0.0664586i
$365$	−10.7321	+	6.19615i	−0.561741	+	0.324321i
$366$	0.633975	+	1.09808i	0.0331384	+	0.0573974i
$367$	−0.196152	−	0.339746i	−0.0102391	−	0.0177346i	0.860860	−	0.508841i	$-0.169926\pi$
$367$	−0.196152	−	0.339746i	−0.0102391	−	0.0177346i	−0.871100	+	0.491106i	$0.836593\pi$
$368$	−1.73205	−	1.00000i	−0.0902894	−	0.0521286i
$369$	8.19615			0.426675
$370$	−0.500000	+	6.06218i	−0.0259938	+	0.315158i
$371$	−6.00000			−0.311504
$372$	−6.00000	−	3.46410i	−0.311086	−	0.179605i
$373$	−7.80385	−	13.5167i	−0.404068	−	0.699866i	0.590145	−	0.807298i	$-0.299071\pi$
$373$	−7.80385	−	13.5167i	−0.404068	−	0.699866i	−0.994212	+	0.107431i	$0.965737\pi$
$374$	0.964102	+	1.66987i	0.0498525	+	0.0863471i
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$		−	1.73205i		−	0.0893237i
$377$	3.69615	+	6.40192i	0.190362	+	0.329716i
$378$			0.732051i			0.0376526i
$379$	−10.7583	+	18.6340i	−0.552618	+	0.957163i	0.445466	+	0.895299i	$0.353038\pi$
$379$	−10.7583	+	18.6340i	−0.552618	+	0.957163i	−0.998085	+	0.0618643i	$0.980295\pi$
$380$	2.00000			0.102598
$381$	−0.732051			−0.0375041
$382$	0.0980762	−	0.169873i	0.00501802	−	0.00869146i
$383$	28.3301	−	16.3564i	1.44760	−	0.835773i	0.449264	−	0.893399i	$-0.351686\pi$
$383$	28.3301	−	16.3564i	1.44760	−	0.835773i	0.998338	+	0.0576259i	$0.0183531\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−0.169873	−	0.0980762i	−0.00865753	−	0.00499843i
$386$	5.09808	−	8.83013i	0.259485	−	0.449442i
$387$	0.464102	+	0.267949i	0.0235916	+	0.0136206i
$388$	−9.92820	+	5.73205i	−0.504028	+	0.291001i
$389$	−19.3923	+	11.1962i	−0.983229	+	0.567667i	−0.903243	−	0.429129i	$-0.858821\pi$
$389$	−19.3923	+	11.1962i	−0.983229	+	0.567667i	−0.0799855	+	0.996796i	$0.525487\pi$
$390$	1.50000	+	0.866025i	0.0759555	+	0.0438529i
$391$	−7.19615	+	12.4641i	−0.363925	+	0.630337i
$392$	5.59808	+	3.23205i	0.282746	+	0.163243i
$393$		−	9.39230i		−	0.473779i
$394$	4.26795	−	2.46410i	0.215016	−	0.124140i
$395$	−2.46410	+	4.26795i	−0.123982	+	0.214744i
$396$	−0.267949			−0.0134650
$397$	−11.5359			−0.578970			−0.289485	−	0.957183i	$-0.593484\pi$
$397$	−11.5359			−0.578970			−0.289485	+	0.957183i	$0.593484\pi$
$398$	4.16025	−	7.20577i	0.208535	−	0.361193i
$399$		−	1.46410i		−	0.0732968i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$		−	33.1244i		−	1.65415i	−0.562091	−	0.827076i	$-0.690003\pi$
$401$		−	33.1244i		−	1.65415i	0.562091	−	0.827076i	$-0.309997\pi$
$402$	9.23205	−	5.33013i	0.460453	−	0.265843i
$403$	6.00000	+	10.3923i	0.298881	+	0.517678i
$404$	4.23205	+	7.33013i	0.210552	+	0.364687i
$405$	−0.866025	−	0.500000i	−0.0430331	−	0.0248452i
$406$	3.12436			0.155059
$407$	−0.133975	+	1.62436i	−0.00664087	+	0.0805163i
$408$	−7.19615			−0.356263
$409$	1.83975	+	1.06218i	0.0909696	+	0.0525213i	0.544795	−	0.838569i	$-0.316608\pi$
$409$	1.83975	+	1.06218i	0.0909696	+	0.0525213i	−0.453825	+	0.891091i	$0.649941\pi$
$410$	−4.09808	−	7.09808i	−0.202390	−	0.350549i
$411$	5.50000	+	9.52628i	0.271295	+	0.469897i
$412$	8.83013	−	5.09808i	0.435029	−	0.251164i
$413$			0.339746i			0.0167178i
$414$	−1.00000	−	1.73205i	−0.0491473	−	0.0851257i
$415$		−	6.19615i		−	0.304157i
$416$	−0.866025	+	1.50000i	−0.0424604	+	0.0735436i
$417$	−16.3923			−0.802735
$418$	0.535898			0.0262116
$419$	−5.07180	+	8.78461i	−0.247773	+	0.429156i	−0.962908	−	0.269831i	$-0.913032\pi$
$419$	−5.07180	+	8.78461i	−0.247773	+	0.429156i	0.715134	+	0.698987i	$0.246366\pi$
$420$	0.633975	−	0.366025i	0.0309348	−	0.0178602i
$421$			29.6603i			1.44555i	0.691082	+	0.722776i	$0.257134\pi$
$421$			29.6603i			1.44555i	−0.691082	+	0.722776i	$0.742866\pi$
$422$	−20.1962	−	11.6603i	−0.983133	−	0.567612i
$423$	0.866025	−	1.50000i	0.0421076	−	0.0729325i
$424$	7.09808	+	4.09808i	0.344713	+	0.199020i
$425$	6.23205	−	3.59808i	0.302299	−	0.174532i
$426$	7.09808	−	4.09808i	0.343903	−	0.198552i
$427$	−0.803848	−	0.464102i	−0.0389009	−	0.0224595i
$428$	−0.901924	+	1.56218i	−0.0435961	+	0.0755107i
$429$	0.401924	+	0.232051i	0.0194051	+	0.0112035i
$430$		−	0.535898i		−	0.0258433i
$431$	−8.24167	+	4.75833i	−0.396987	+	0.229201i	−0.685183	−	0.728371i	$-0.740278\pi$
$431$	−8.24167	+	4.75833i	−0.396987	+	0.229201i	0.288196	+	0.957571i	$0.406945\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	26.9282			1.29409			0.647043	−	0.762453i	$-0.276005\pi$
$433$	26.9282			1.29409			0.647043	+	0.762453i	$0.276005\pi$
$434$	5.07180			0.243454
$435$	−2.13397	+	3.69615i	−0.102316	+	0.177217i
$436$			3.26795i			0.156506i
$437$	2.00000	+	3.46410i	0.0956730	+	0.165710i
$438$		−	12.3923i		−	0.592127i
$439$	−32.0429	+	18.5000i	−1.52933	+	0.882957i	−0.529936	+	0.848038i	$0.677784\pi$
$439$	−32.0429	+	18.5000i	−1.52933	+	0.882957i	−0.999390	+	0.0349192i	$0.988883\pi$
$440$	0.133975	+	0.232051i	0.00638699	+	0.0110626i
$441$	3.23205	+	5.59808i	0.153907	+	0.266575i
$442$	10.7942	+	6.23205i	0.513429	+	0.296428i
$443$	−35.3731			−1.68063			−0.840313	−	0.542102i	$-0.817629\pi$
$443$	−35.3731			−1.68063			−0.840313	+	0.542102i	$0.817629\pi$
$444$	−5.00000	−	3.46410i	−0.237289	−	0.164399i
$445$	12.9282			0.612856
$446$	−12.5885	−	7.26795i	−0.596081	−	0.344147i
$447$	1.96410	+	3.40192i	0.0928988	+	0.160905i
$448$	0.366025	+	0.633975i	0.0172931	+	0.0299525i
$449$	21.4641	−	12.3923i	1.01295	−	0.584829i	0.100898	−	0.994897i	$-0.467828\pi$
$449$	21.4641	−	12.3923i	1.01295	−	0.584829i	0.912055	+	0.410068i	$0.134495\pi$
$450$			1.00000i			0.0471405i
$451$	−1.09808	−	1.90192i	−0.0517064	−	0.0895581i
$452$		−	14.6603i		−	0.689560i
$453$	−2.53590	+	4.39230i	−0.119147	+	0.206368i
$454$	−1.26795			−0.0595078
$455$	−1.26795			−0.0594424
$456$	−1.00000	+	1.73205i	−0.0468293	+	0.0811107i
$457$	13.2679	−	7.66025i	0.620648	−	0.358332i	−0.156473	−	0.987682i	$-0.550012\pi$
$457$	13.2679	−	7.66025i	0.620648	−	0.358332i	0.777121	+	0.629351i	$0.216679\pi$
$458$			16.0526i			0.750087i
$459$	−6.23205	−	3.59808i	−0.290887	−	0.167944i
$460$	−1.00000	+	1.73205i	−0.0466252	+	0.0807573i
$461$	−3.82051	−	2.20577i	−0.177939	−	0.102733i	0.408385	−	0.912810i	$-0.366092\pi$
$461$	−3.82051	−	2.20577i	−0.177939	−	0.102733i	−0.586324	+	0.810077i	$0.699425\pi$
$462$	0.169873	−	0.0980762i	0.00790321	−	0.00456292i
$463$	−0.464102	+	0.267949i	−0.0215686	+	0.0124527i	−0.510746	−	0.859732i	$-0.670631\pi$
$463$	−0.464102	+	0.267949i	−0.0215686	+	0.0124527i	0.489177	+	0.872185i	$0.337297\pi$
$464$	−3.69615	−	2.13397i	−0.171590	−	0.0990673i
$465$	−3.46410	+	6.00000i	−0.160644	+	0.278243i
$466$	−2.19615	−	1.26795i	−0.101735	−	0.0587366i
$467$			15.8564i			0.733747i	0.930271	+	0.366873i	$0.119572\pi$
$467$			15.8564i			0.733747i	−0.930271	+	0.366873i	$0.880428\pi$
$468$	−1.50000	+	0.866025i	−0.0693375	+	0.0400320i
$469$	−3.90192	+	6.75833i	−0.180174	+	0.312071i
$470$	−1.73205			−0.0798935
$471$	22.4641			1.03509
$472$	0.232051	−	0.401924i	0.0106810	−	0.0185000i
$473$		−	0.143594i		−	0.00660244i
$474$	−2.46410	−	4.26795i	−0.113180	−	0.196033i
$475$		−	2.00000i		−	0.0917663i
$476$	4.56218	−	2.63397i	0.209107	−	0.120728i
$477$	4.09808	+	7.09808i	0.187638	+	0.324999i
$478$	7.26795	+	12.5885i	0.332428	+	0.575783i
$479$	14.0718	+	8.12436i	0.642957	+	0.371211i	0.785753	−	0.618541i	$-0.212276\pi$
$479$	14.0718	+	8.12436i	0.642957	+	0.371211i	−0.142796	+	0.989752i	$0.545609\pi$
$480$	−1.00000			−0.0456435
$481$	4.50000	+	9.52628i	0.205182	+	0.434361i
$482$	−3.73205			−0.169990
$483$	1.26795	+	0.732051i	0.0576937	+	0.0333095i
$484$	−5.46410	−	9.46410i	−0.248368	−	0.430186i
$485$	5.73205	+	9.92820i	0.260279	+	0.450816i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$		−	11.0718i		−	0.501711i	−0.968025	−	0.250856i	$-0.919288\pi$
$487$		−	11.0718i		−	0.501711i	0.968025	−	0.250856i	$-0.0807119\pi$
$488$	0.633975	+	1.09808i	0.0286987	+	0.0497076i
$489$		−	22.4641i		−	1.01586i
$490$	3.23205	−	5.59808i	0.146009	−	0.252895i
$491$	16.0000			0.722070			0.361035	−	0.932552i	$-0.382424\pi$
$491$	16.0000			0.722070			0.361035	+	0.932552i	$0.382424\pi$
$492$	8.19615			0.369511
$493$	−15.3564	+	26.5981i	−0.691618	+	1.19792i
$494$	3.00000	−	1.73205i	0.134976	−	0.0779287i
$495$			0.267949i			0.0120434i
$496$	−6.00000	−	3.46410i	−0.269408	−	0.155543i
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$	5.36603	+	3.09808i	0.240457	+	0.138828i
$499$	24.6340	−	14.2224i	1.10277	−	0.636683i	0.165821	−	0.986156i	$-0.446972\pi$
$499$	24.6340	−	14.2224i	1.10277	−	0.636683i	0.936947	+	0.349472i	$0.113639\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	15.4019	+	8.89230i	0.688107	+	0.397279i
$502$	4.16025	−	7.20577i	0.185681	−	0.321609i
$503$	−15.4019	−	8.89230i	−0.686738	−	0.396488i	0.115651	−	0.993290i	$-0.463105\pi$
$503$	−15.4019	−	8.89230i	−0.686738	−	0.396488i	−0.802389	+	0.596802i	$0.796438\pi$
$504$			0.732051i			0.0326081i
$505$	7.33013	−	4.23205i	0.326186	−	0.188324i
$506$	−0.267949	+	0.464102i	−0.0119118	+	0.0206318i
$507$	−10.0000			−0.444116
$508$	−0.732051			−0.0324795
$509$	3.39230	−	5.87564i	0.150361	−	0.260433i	−0.780999	−	0.624532i	$-0.785290\pi$
$509$	3.39230	−	5.87564i	0.150361	−	0.260433i	0.931360	+	0.364099i	$0.118623\pi$
$510$			7.19615i			0.318651i
$511$	4.53590	+	7.85641i	0.200656	+	0.347547i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.73205	+	1.00000i	−0.0764719	+	0.0441511i
$514$	−3.33013	−	5.76795i	−0.146886	−	0.254413i
$515$	−5.09808	−	8.83013i	−0.224648	−	0.389102i
$516$	0.464102	+	0.267949i	0.0204309	+	0.0117958i
$517$	−0.464102			−0.0204112
$518$	4.43782	+	0.366025i	0.194987	+	0.0160822i
$519$	17.6603			0.775199
$520$	1.50000	+	0.866025i	0.0657794	+	0.0379777i
$521$	2.19615	+	3.80385i	0.0962152	+	0.166650i	0.910115	−	0.414355i	$-0.135993\pi$
$521$	2.19615	+	3.80385i	0.0962152	+	0.166650i	−0.813900	+	0.581005i	$0.802660\pi$
$522$	−2.13397	−	3.69615i	−0.0934015	−	0.161776i
$523$	−22.8564	+	13.1962i	−0.999441	+	0.577027i	−0.908083	−	0.418791i	$-0.862454\pi$
$523$	−22.8564	+	13.1962i	−0.999441	+	0.577027i	−0.0913581	+	0.995818i	$0.529121\pi$
$524$		−	9.39230i		−	0.410305i
$525$	−0.366025	−	0.633975i	−0.0159747	−	0.0276689i
$526$		−	23.3205i		−	1.01682i
$527$	−24.9282	+	43.1769i	−1.08589	+	1.88082i
$528$	−0.267949			−0.0116610
$529$	19.0000			0.826087
$530$	4.09808	−	7.09808i	0.178009	−	0.308321i
$531$	0.401924	−	0.232051i	0.0174420	−	0.0100701i
$532$		−	1.46410i		−	0.0634769i
$533$	−12.2942	−	7.09808i	−0.532522	−	0.307452i
$534$	−6.46410	+	11.1962i	−0.279729	+	0.484505i
$535$	1.56218	+	0.901924i	0.0675388	+	0.0389936i
$536$	9.23205	−	5.33013i	0.398764	−	0.230226i
$537$	7.73205	−	4.46410i	0.333663	−	0.192640i
$538$	−0.928203	−	0.535898i	−0.0400177	−	0.0231042i
$539$	0.866025	−	1.50000i	0.0373024	−	0.0646096i
$540$	−0.866025	−	0.500000i	−0.0372678	−	0.0215166i
$541$			7.41154i			0.318647i	0.987226	+	0.159324i	$0.0509313\pi$
$541$			7.41154i			0.318647i	−0.987226	+	0.159324i	$0.949069\pi$
$542$	4.62436	−	2.66987i	0.198633	−	0.114681i
$543$	−1.00000	+	1.73205i	−0.0429141	+	0.0743294i
$544$	−7.19615			−0.308532
$545$	3.26795			0.139984
$546$	0.633975	−	1.09808i	0.0271316	−	0.0469933i
$547$		−	15.0718i		−	0.644423i	−0.946668	−	0.322212i	$-0.895574\pi$
$547$		−	15.0718i		−	0.644423i	0.946668	−	0.322212i	$-0.104426\pi$
$548$	5.50000	+	9.52628i	0.234948	+	0.406942i
$549$			1.26795i			0.0541148i
$550$	0.232051	−	0.133975i	0.00989468	−	0.00571270i
$551$	4.26795	+	7.39230i	0.181821	+	0.314923i
$552$	−1.00000	−	1.73205i	−0.0425628	−	0.0737210i
$553$	3.12436	+	1.80385i	0.132861	+	0.0767074i
$554$	15.1962			0.645623
$555$	−3.46410	+	5.00000i	−0.147043	+	0.212238i
$556$	−16.3923			−0.695189
$557$	36.3731	+	21.0000i	1.54118	+	0.889799i	0.998765	+	0.0496855i	$0.0158219\pi$
$557$	36.3731	+	21.0000i	1.54118	+	0.889799i	0.542411	+	0.840113i	$0.317511\pi$
$558$	−3.46410	−	6.00000i	−0.146647	−	0.254000i
$559$	−0.464102	−	0.803848i	−0.0196294	−	0.0339991i
$560$	0.633975	−	0.366025i	0.0267903	−	0.0154674i
$561$			1.92820i			0.0814088i
$562$	−1.73205	−	3.00000i	−0.0730622	−	0.126547i
$563$			23.6603i			0.997161i	0.866843	+	0.498580i	$0.166145\pi$
$563$			23.6603i			0.997161i	−0.866843	+	0.498580i	$0.833855\pi$
$564$	0.866025	−	1.50000i	0.0364662	−	0.0631614i
$565$	−14.6603			−0.616762
$566$	−30.4641			−1.28050
$567$	−0.366025	+	0.633975i	−0.0153716	+	0.0266244i
$568$	7.09808	−	4.09808i	0.297829	−	0.171951i
$569$			10.9808i			0.460337i	0.973151	+	0.230169i	$0.0739278\pi$
$569$			10.9808i			0.460337i	−0.973151	+	0.230169i	$0.926072\pi$
$570$	1.73205	+	1.00000i	0.0725476	+	0.0418854i
$571$	7.53590	−	13.0526i	0.315368	−	0.546233i	−0.664148	−	0.747601i	$-0.731206\pi$
$571$	7.53590	−	13.0526i	0.315368	−	0.546233i	0.979516	+	0.201369i	$0.0645389\pi$
$572$	0.401924	+	0.232051i	0.0168053	+	0.00970253i
$573$	0.169873	−	0.0980762i	0.00709655	−	0.00409719i
$574$	−5.19615	+	3.00000i	−0.216883	+	0.125218i
$575$	1.73205	+	1.00000i	0.0722315	+	0.0417029i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−21.8827	−	12.6340i	−0.910988	−	0.525959i	−0.0302392	−	0.999543i	$-0.509627\pi$
$577$	−21.8827	−	12.6340i	−0.910988	−	0.525959i	−0.880749	+	0.473583i	$0.842960\pi$
$578$			34.7846i			1.44685i
$579$	8.83013	−	5.09808i	0.366968	−	0.211869i
$580$	−2.13397	+	3.69615i	−0.0886085	+	0.153474i
$581$	−4.53590			−0.188181
$582$	−11.4641			−0.475202
$583$	1.09808	−	1.90192i	0.0454777	−	0.0787696i
$584$		−	12.3923i		−	0.512797i
$585$	0.866025	+	1.50000i	0.0358057	+	0.0620174i
$586$			3.46410i			0.143101i
$587$	−21.6340	+	12.4904i	−0.892930	+	0.515533i	−0.874900	−	0.484304i	$-0.839073\pi$
$587$	−21.6340	+	12.4904i	−0.892930	+	0.515533i	−0.0180300	+	0.999837i	$0.505739\pi$
$588$	3.23205	+	5.59808i	0.133288	+	0.230861i
$589$	6.92820	+	12.0000i	0.285472	+	0.494451i
$590$	−0.401924	−	0.232051i	−0.0165469	−	0.00955338i
$591$	4.92820			0.202719
$592$	−5.00000	−	3.46410i	−0.205499	−	0.142374i
$593$	−18.0718			−0.742120			−0.371060	−	0.928609i	$-0.621006\pi$
$593$	−18.0718			−0.742120			−0.371060	+	0.928609i	$0.621006\pi$
$594$	−0.232051	−	0.133975i	−0.00952116	−	0.00549704i
$595$	−2.63397	−	4.56218i	−0.107982	−	0.187031i
$596$	1.96410	+	3.40192i	0.0804527	+	0.139348i
$597$	7.20577	−	4.16025i	0.294913	−	0.170268i
$598$			3.46410i			0.141658i
$599$	3.29423	+	5.70577i	0.134599	+	0.233131i	0.925444	−	0.378884i	$-0.123692\pi$
$599$	3.29423	+	5.70577i	0.134599	+	0.233131i	−0.790845	+	0.612016i	$0.790359\pi$
$600$			1.00000i			0.0408248i
$601$	−2.57180	+	4.45448i	−0.104906	+	0.181702i	−0.913700	−	0.406390i	$-0.866787\pi$
$601$	−2.57180	+	4.45448i	−0.104906	+	0.181702i	0.808794	+	0.588092i	$0.200121\pi$
$602$	−0.392305			−0.0159892
$603$	10.6603			0.434119
$604$	−2.53590	+	4.39230i	−0.103184	+	0.178720i
$605$	−9.46410	+	5.46410i	−0.384770	+	0.222147i
$606$			8.46410i			0.343831i
$607$	3.00000	+	1.73205i	0.121766	+	0.0703018i	0.559646	−	0.828732i	$-0.310937\pi$
$607$	3.00000	+	1.73205i	0.121766	+	0.0703018i	−0.437880	+	0.899034i	$0.644270\pi$
$608$	−1.00000	+	1.73205i	−0.0405554	+	0.0702439i
$609$	2.70577	+	1.56218i	0.109643	+	0.0633026i
$610$	1.09808	−	0.633975i	0.0444598	−	0.0256689i
$611$	−2.59808	+	1.50000i	−0.105107	+	0.0606835i
$612$	−6.23205	−	3.59808i	−0.251916	−	0.145444i
$613$	4.69615	−	8.13397i	0.189676	−	0.328528i	−0.755466	−	0.655187i	$-0.772590\pi$
$613$	4.69615	−	8.13397i	0.189676	−	0.328528i	0.945142	+	0.326659i	$0.105923\pi$
$614$	−16.8564	−	9.73205i	−0.680269	−	0.392754i
$615$		−	8.19615i		−	0.330501i
$616$	0.169873	−	0.0980762i	0.00684438	−	0.00395160i
$617$	−10.6244	+	18.4019i	−0.427720	+	0.740834i	−0.996670	−	0.0815388i	$-0.974017\pi$
$617$	−10.6244	+	18.4019i	−0.427720	+	0.740834i	0.568950	+	0.822372i	$0.307350\pi$
$618$	10.1962			0.410149
$619$	26.1962			1.05291			0.526456	−	0.850202i	$-0.323520\pi$
$619$	26.1962			1.05291			0.526456	+	0.850202i	$0.323520\pi$
$620$	−3.46410	+	6.00000i	−0.139122	+	0.240966i
$621$		−	2.00000i		−	0.0802572i
$622$	−2.36603	−	4.09808i	−0.0948690	−	0.164318i
$623$		−	9.46410i		−	0.379171i
$624$	−1.50000	+	0.866025i	−0.0600481	+	0.0346688i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.46410	+	4.26795i	0.0984853	+	0.170582i
$627$	0.464102	+	0.267949i	0.0185344	+	0.0107009i
$628$	22.4641			0.896415
$629$	−24.9282	+	35.9808i	−0.993953	+	1.43465i
$630$	0.732051			0.0291656
$631$	11.9378	+	6.89230i	0.475237	+	0.274378i	0.718430	−	0.695600i	$-0.244861\pi$
$631$	11.9378	+	6.89230i	0.475237	+	0.274378i	−0.243192	+	0.969978i	$0.578195\pi$
$632$	−2.46410	−	4.26795i	−0.0980167	−	0.169770i
$633$	−11.6603	−	20.1962i	−0.463453	−	0.802725i
$634$	4.56218	−	2.63397i	0.181187	−	0.104608i
$635$			0.732051i			0.0290506i
$636$	4.09808	+	7.09808i	0.162499	+	0.281457i
$637$		−	11.1962i		−	0.443608i
$638$	−0.571797	+	0.990381i	−0.0226377	+	0.0392096i
$639$	8.19615			0.324235
$640$	−1.00000			−0.0395285
$641$	−2.02628	+	3.50962i	−0.0800332	+	0.138622i	−0.903264	−	0.429085i	$-0.858836\pi$
$641$	−2.02628	+	3.50962i	−0.0800332	+	0.138622i	0.823231	+	0.567707i	$0.192169\pi$
$642$	−1.56218	+	0.901924i	−0.0616542	+	0.0355961i
$643$			14.6077i			0.576071i	0.957620	+	0.288036i	$0.0930022\pi$
$643$			14.6077i			0.576071i	−0.957620	+	0.288036i	$0.906998\pi$
$644$	1.26795	+	0.732051i	0.0499642	+	0.0288468i
$645$	0.267949	−	0.464102i	0.0105505	−	0.0182740i
$646$	12.4641	+	7.19615i	0.490394	+	0.283129i
$647$	−36.1865	+	20.8923i	−1.42264	+	0.821361i	−0.996524	−	0.0833075i	$-0.973452\pi$
$647$	−36.1865	+	20.8923i	−1.42264	+	0.821361i	−0.426116	+	0.904669i	$0.640118\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−0.107695	−	0.0621778i	−0.00422740	−	0.00244069i
$650$	0.866025	−	1.50000i	0.0339683	−	0.0588348i
$651$	4.39230	+	2.53590i	0.172148	+	0.0993897i
$652$		−	22.4641i		−	0.879762i
$653$	39.7128	−	22.9282i	1.55408	−	0.897250i	0.556280	−	0.830995i	$-0.312228\pi$
$653$	39.7128	−	22.9282i	1.55408	−	0.897250i	0.997803	−	0.0662548i	$-0.0211050\pi$
$654$	−1.63397	+	2.83013i	−0.0638935	+	0.110667i
$655$	−9.39230			−0.366988
$656$	8.19615			0.320006
$657$	6.19615	−	10.7321i	0.241735	−	0.418697i
$658$			1.26795i			0.0494298i
$659$	13.0622	+	22.6244i	0.508830	+	0.881320i	0.999948	+	0.0102264i	$0.00325523\pi$
$659$	13.0622	+	22.6244i	0.508830	+	0.881320i	−0.491118	+	0.871093i	$0.663411\pi$
$660$			0.267949i			0.0104299i
$661$	26.4449	−	15.2679i	1.02859	−	0.593854i	0.112007	−	0.993707i	$-0.464272\pi$
$661$	26.4449	−	15.2679i	1.02859	−	0.593854i	0.916579	+	0.399853i	$0.130939\pi$
$662$	13.8301	+	23.9545i	0.537523	+	0.931017i
$663$	6.23205	+	10.7942i	0.242033	+	0.419213i
$664$	5.36603	+	3.09808i	0.208242	+	0.120229i
$665$	−1.46410			−0.0567754
$666$	−2.59808	−	5.50000i	−0.100673	−	0.213121i
$667$	−8.53590			−0.330511
$668$	15.4019	+	8.89230i	0.595918	+	0.344054i
$669$	−7.26795	−	12.5885i	−0.280995	−	0.486698i
$670$	−5.33013	−	9.23205i	−0.205921	−	0.356665i
$671$	0.294229	−	0.169873i	0.0113586	−	0.00655787i
$672$			0.732051i			0.0282395i
$673$	8.43782	+	14.6147i	0.325254	+	0.563357i	0.981564	−	0.191135i	$-0.0612168\pi$
$673$	8.43782	+	14.6147i	0.325254	+	0.563357i	−0.656310	+	0.754492i	$0.727883\pi$
$674$		−	9.66025i		−	0.372099i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−10.0000			−0.384615
$677$	0.339746			0.0130575			0.00652875	−	0.999979i	$-0.497922\pi$
$677$	0.339746			0.0130575			0.00652875	+	0.999979i	$0.497922\pi$
$678$	7.33013	−	12.6962i	0.281512	−	0.487593i
$679$	7.26795	−	4.19615i	0.278918	−	0.161034i
$680$			7.19615i			0.275960i
$681$	−1.09808	−	0.633975i	−0.0420784	−	0.0242940i
$682$	−0.928203	+	1.60770i	−0.0355427	+	0.0615618i
$683$	31.0526	+	17.9282i	1.18819	+	0.686004i	0.957896	−	0.287117i	$-0.0926967\pi$
$683$	31.0526	+	17.9282i	1.18819	+	0.686004i	0.230298	+	0.973120i	$0.426030\pi$
$684$	−1.73205	+	1.00000i	−0.0662266	+	0.0382360i
$685$	9.52628	−	5.50000i	0.363980	−	0.210144i
$686$	−8.53590	−	4.92820i	−0.325902	−	0.188160i
$687$	−8.02628	+	13.9019i	−0.306222	+	0.530391i
$688$	0.464102	+	0.267949i	0.0176937	+	0.0102155i
$689$		−	14.1962i		−	0.540830i
$690$	−1.73205	+	1.00000i	−0.0659380	+	0.0380693i
$691$	−7.19615	+	12.4641i	−0.273755	+	0.474157i	−0.969820	−	0.243821i	$-0.921599\pi$
$691$	−7.19615	+	12.4641i	−0.273755	+	0.474157i	0.696066	+	0.717978i	$0.254932\pi$
$692$	17.6603			0.671342
$693$	0.196152			0.00745121
$694$	−14.4641	+	25.0526i	−0.549050	+	0.950982i
$695$			16.3923i			0.621796i
$696$	−2.13397	−	3.69615i	−0.0808881	−	0.140102i
$697$		−	58.9808i		−	2.23406i
$698$	−3.80385	+	2.19615i	−0.143978	+	0.0831256i
$699$	−1.26795	−	2.19615i	−0.0479582	−	0.0830661i
$700$	−0.366025	−	0.633975i	−0.0138345	−	0.0239620i
$701$	13.9641	+	8.06218i	0.527417	+	0.304504i	0.739964	−	0.672647i	$-0.234843\pi$
$701$	13.9641	+	8.06218i	0.527417	+	0.304504i	−0.212547	+	0.977151i	$0.568176\pi$
$702$	−1.73205			−0.0653720
$703$	5.19615	+	11.0000i	0.195977	+	0.414873i
$704$	−0.267949			−0.0100987
$705$	−1.50000	−	0.866025i	−0.0564933	−	0.0326164i
$706$	−9.92820	−	17.1962i	−0.373653	−	0.647186i
$707$	−3.09808	−	5.36603i	−0.116515	−	0.201810i
$708$	0.401924	−	0.232051i	0.0151052	−	0.00872100i
$709$			13.6603i			0.513022i	0.966541	+	0.256511i	$0.0825729\pi$
$709$			13.6603i			0.513022i	−0.966541	+	0.256511i	$0.917427\pi$
$710$	−4.09808	−	7.09808i	−0.153798	−	0.266386i
$711$		−	4.92820i		−	0.184822i
$712$	−6.46410	+	11.1962i	−0.242252	+	0.419594i
$713$	−13.8564			−0.518927
$714$	5.26795			0.197148
$715$	0.232051	−	0.401924i	0.00867821	−	0.0150311i
$716$	7.73205	−	4.46410i	0.288960	−	0.166831i
$717$			14.5359i			0.542853i
$718$	15.5885	+	9.00000i	0.581756	+	0.335877i
$719$	−21.8827	+	37.9019i	−0.816086	+	1.41350i	0.0924587	+	0.995717i	$0.470527\pi$
$719$	−21.8827	+	37.9019i	−0.816086	+	1.41350i	−0.908545	+	0.417787i	$0.862806\pi$
$720$	−0.866025	−	0.500000i	−0.0322749	−	0.0186339i
$721$	−6.46410	+	3.73205i	−0.240736	+	0.138989i
$722$	−12.9904	+	7.50000i	−0.483452	+	0.279121i
$723$	−3.23205	−	1.86603i	−0.120201	−	0.0693982i
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	3.69615	+	2.13397i	0.137272	+	0.0792538i
$726$		−	10.9282i		−	0.405584i
$727$	−7.26795	+	4.19615i	−0.269553	+	0.155627i	−0.628685	−	0.777660i	$-0.716406\pi$
$727$	−7.26795	+	4.19615i	−0.269553	+	0.155627i	0.359131	+	0.933287i	$0.383073\pi$
$728$	0.633975	−	1.09808i	0.0234967	−	0.0406974i
$729$	1.00000			0.0370370
$730$	−12.3923			−0.458660
$731$	1.92820	−	3.33975i	0.0713172	−	0.123525i
$732$			1.26795i			0.0468648i
$733$	−14.5000	−	25.1147i	−0.535570	−	0.927634i	−0.999136	−	0.0415715i	$-0.986764\pi$
$733$	−14.5000	−	25.1147i	−0.535570	−	0.927634i	0.463566	−	0.886062i	$-0.346570\pi$
$734$		−	0.392305i		−	0.0144802i
$735$	5.59808	−	3.23205i	0.206488	−	0.119216i
$736$	−1.00000	−	1.73205i	−0.0368605	−	0.0638442i
$737$	−1.42820	−	2.47372i	−0.0526085	−	0.0911207i
$738$	7.09808	+	4.09808i	0.261284	+	0.150852i
$739$	−10.0000			−0.367856			−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000			−0.367856			−0.183928	+	0.982940i	$0.558881\pi$
$740$	−3.46410	+	5.00000i	−0.127343	+	0.183804i
$741$	3.46410			0.127257
$742$	−5.19615	−	3.00000i	−0.190757	−	0.110133i
$743$	3.25833	+	5.64359i	0.119537	+	0.207043i	0.919584	−	0.392893i	$-0.128526\pi$
$743$	3.25833	+	5.64359i	0.119537	+	0.207043i	−0.800048	+	0.599937i	$0.795192\pi$
$744$	−3.46410	−	6.00000i	−0.127000	−	0.219971i
$745$	3.40192	−	1.96410i	0.124637	−	0.0719591i
$746$		−	15.6077i		−	0.571438i
$747$	3.09808	+	5.36603i	0.113353	+	0.196333i
$748$			1.92820i			0.0705021i
$749$	0.660254	−	1.14359i	0.0241252	−	0.0417860i
$750$	1.00000			0.0365148
$751$	−11.4449			−0.417629			−0.208815	−	0.977955i	$-0.566960\pi$
$751$	−11.4449			−0.417629			−0.208815	+	0.977955i	$0.566960\pi$
$752$	0.866025	−	1.50000i	0.0315807	−	0.0546994i
$753$	7.20577	−	4.16025i	0.262593	−	0.151608i
$754$			7.39230i			0.269212i
$755$	4.39230	+	2.53590i	0.159852	+	0.0922908i
$756$	−0.366025	+	0.633975i	−0.0133122	+	0.0230574i
$757$	30.0000	+	17.3205i	1.09037	+	0.629525i	0.933675	−	0.358123i	$-0.116583\pi$
$757$	30.0000	+	17.3205i	1.09037	+	0.629525i	0.156694	+	0.987647i	$0.449916\pi$
$758$	−18.6340	+	10.7583i	−0.676816	+	0.390760i
$759$	−0.464102	+	0.267949i	−0.0168458	+	0.00972594i
$760$	1.73205	+	1.00000i	0.0628281	+	0.0362738i
$761$	−11.0981	+	19.2224i	−0.402305	+	0.696813i	−0.994004	−	0.109347i	$-0.965124\pi$
$761$	−11.0981	+	19.2224i	−0.402305	+	0.696813i	0.591699	+	0.806159i	$0.298458\pi$
$762$	−0.633975	−	0.366025i	−0.0229665	−	0.0132597i
$763$		−	2.39230i		−	0.0866073i
$764$	0.169873	−	0.0980762i	0.00614579	−	0.00354827i
$765$	−3.59808	+	6.23205i	−0.130089	+	0.225320i
$766$	32.7128			1.18196
$767$	−0.803848			−0.0290253
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$			12.8038i			0.461719i	0.972987	+	0.230859i	$0.0741537\pi$
$769$			12.8038i			0.461719i	−0.972987	+	0.230859i	$0.925846\pi$
$770$	−0.0980762	−	0.169873i	−0.00353442	−	0.00612180i
$771$		−	6.66025i		−	0.239863i
$772$	8.83013	−	5.09808i	0.317803	−	0.183484i
$773$	8.29423	+	14.3660i	0.298323	+	0.516710i	0.975752	−	0.218878i	$-0.0702395\pi$
$773$	8.29423	+	14.3660i	0.298323	+	0.516710i	−0.677430	+	0.735588i	$0.736906\pi$
$774$	0.267949	+	0.464102i	0.00963123	+	0.0166818i
$775$	6.00000	+	3.46410i	0.215526	+	0.124434i
$776$	−11.4641			−0.411537
$777$	3.66025	+	2.53590i	0.131311	+	0.0909748i
$778$	−22.3923			−0.802803
$779$	−14.1962	−	8.19615i	−0.508630	−	0.293658i
$780$	0.866025	+	1.50000i	0.0310087	+	0.0537086i
$781$	−1.09808	−	1.90192i	−0.0392923	−	0.0680562i
$782$	−12.4641	+	7.19615i	−0.445715	+	0.257334i
$783$		−	4.26795i		−	0.152524i
$784$	3.23205	+	5.59808i	0.115430	+	0.199931i
$785$		−	22.4641i		−	0.801778i
$786$	4.69615	−	8.13397i	0.167506	−	0.290129i
$787$	−48.3731			−1.72431			−0.862157	−	0.506642i	$-0.830887\pi$
$787$	−48.3731			−1.72431			−0.862157	+	0.506642i	$0.830887\pi$
$788$	4.92820			0.175560
$789$	11.6603	−	20.1962i	0.415116	−	0.719002i
$790$	−4.26795	+	2.46410i	−0.151847	+	0.0876688i
$791$			10.7321i			0.381588i
$792$	−0.232051	−	0.133975i	−0.00824557	−	0.00476058i
$793$	1.09808	−	1.90192i	0.0389938	−	0.0675393i
$794$	−9.99038	−	5.76795i	−0.354545	−	0.204697i
$795$	7.09808	−	4.09808i	0.251743	−	0.145344i
$796$	7.20577	−	4.16025i	0.255402	−	0.147456i
$797$	−28.3923	−	16.3923i	−1.00571	−	0.580645i	−0.0957752	−	0.995403i	$-0.530533\pi$
$797$	−28.3923	−	16.3923i	−1.00571	−	0.580645i	−0.909932	+	0.414758i	$0.863866\pi$
$798$	0.732051	−	1.26795i	0.0259143	−	0.0448849i
$799$	−10.7942	−	6.23205i	−0.381872	−	0.220474i
$800$			1.00000i			0.0353553i
$801$	−11.1962	+	6.46410i	−0.395597	+	0.228398i
$802$	16.5622	−	28.6865i	0.584831	−	1.01296i
$803$	−3.32051			−0.117178
$804$	10.6603			0.375958
$805$	0.732051	−	1.26795i	0.0258014	−	0.0446893i
$806$			12.0000i			0.422682i
$807$	−0.535898	−	0.928203i	−0.0188645	−	0.0326743i
$808$			8.46410i			0.297766i
$809$	−24.8038	+	14.3205i	−0.872057	+	0.503482i	−0.868031	−	0.496510i	$-0.834615\pi$
$809$	−24.8038	+	14.3205i	−0.872057	+	0.503482i	−0.00402564	+	0.999992i	$0.501281\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	3.16987	+	5.49038i	0.111309	+	0.192793i	0.916298	−	0.400496i	$-0.131162\pi$
$811$	3.16987	+	5.49038i	0.111309	+	0.192793i	−0.804989	+	0.593290i	$0.797829\pi$
$812$	2.70577	+	1.56218i	0.0949540	+	0.0548217i
$813$	5.33975			0.187273
$814$	−0.928203	+	1.33975i	−0.0325335	+	0.0469581i
$815$	−22.4641			−0.786883
$816$	−6.23205	−	3.59808i	−0.218165	−	0.125958i
$817$	−0.535898	−	0.928203i	−0.0187487	−	0.0324737i
$818$	1.06218	+	1.83975i	0.0371382	+	0.0643252i
$819$	1.09808	−	0.633975i	0.0383699	−	0.0221529i
$820$		−	8.19615i		−	0.286222i
$821$	21.8205	+	37.7942i	0.761541	+	1.31903i	0.942056	+	0.335455i	$0.108890\pi$
$821$	21.8205	+	37.7942i	0.761541	+	1.31903i	−0.180515	+	0.983572i	$0.557776\pi$
$822$			11.0000i			0.383669i
$823$	4.22243	−	7.31347i	0.147185	−	0.254931i	−0.783001	−	0.622020i	$-0.786312\pi$
$823$	4.22243	−	7.31347i	0.147185	−	0.254931i	0.930186	+	0.367089i	$0.119645\pi$
$824$	10.1962			0.355200
$825$	0.267949			0.00932879
$826$	−0.169873	+	0.294229i	−0.00591064	+	0.0102375i
$827$	27.0000	−	15.5885i	0.938882	−	0.542064i	0.0492723	−	0.998785i	$-0.484310\pi$
$827$	27.0000	−	15.5885i	0.938882	−	0.542064i	0.889610	+	0.456722i	$0.150976\pi$
$828$		−	2.00000i		−	0.0695048i
$829$	9.41858	+	5.43782i	0.327121	+	0.188863i	0.654562	−	0.756008i	$-0.272853\pi$
$829$	9.41858	+	5.43782i	0.327121	+	0.188863i	−0.327441	+	0.944872i	$0.606186\pi$
$830$	3.09808	−	5.36603i	0.107536	−	0.186257i
$831$	13.1603	+	7.59808i	0.456524	+	0.263574i
$832$	−1.50000	+	0.866025i	−0.0520031	+	0.0300240i
$833$	40.2846	−	23.2583i	1.39578	−	0.805853i
$834$	−14.1962	−	8.19615i	−0.491573	−	0.283810i
$835$	8.89230	−	15.4019i	0.307731	−	0.533006i
$836$	0.464102	+	0.267949i	0.0160513	+	0.00926722i
$837$		−	6.92820i		−	0.239474i
$838$	−8.78461	+	5.07180i	−0.303459	+	0.175202i
$839$	20.6865	−	35.8301i	0.714178	−	1.23699i	−0.249097	−	0.968479i	$-0.580134\pi$
$839$	20.6865	−	35.8301i	0.714178	−	1.23699i	0.963276	−	0.268515i	$-0.0865328\pi$
$840$	0.732051			0.0252582
$841$	10.7846			0.371883
$842$	−14.8301	+	25.6865i	−0.511080	+	0.885216i
$843$		−	3.46410i		−	0.119310i
$844$	−11.6603	−	20.1962i	−0.401362	−	0.695180i
$845$			10.0000i			0.344010i
$846$	1.50000	−	0.866025i	0.0515711	−	0.0297746i
$847$	4.00000	+	6.92820i	0.137442	+	0.238056i
$848$	4.09808	+	7.09808i	0.140729	+	0.243749i
$849$	−26.3827	−	15.2321i	−0.905451	−	0.522763i
$850$	7.19615			0.246826
$851$	−12.1244	−	1.00000i	−0.415618	−	0.0342796i
$852$	8.19615			0.280796
$853$	42.6051	+	24.5981i	1.45877	+	0.842222i	0.998951	−	0.0457899i	$-0.0145805\pi$
$853$	42.6051	+	24.5981i	1.45877	+	0.842222i	0.459820	+	0.888012i	$0.347914\pi$
$854$	−0.464102	−	0.803848i	−0.0158812	−	0.0275071i
$855$	1.00000	+	1.73205i	0.0341993	+	0.0592349i
$856$	−1.56218	+	0.901924i	−0.0533941	+	0.0308271i
$857$		−	6.12436i		−	0.209204i	−0.994514	−	0.104602i	$-0.966643\pi$
$857$		−	6.12436i		−	0.209204i	0.994514	−	0.104602i	$-0.0333569\pi$
$858$	0.232051	+	0.401924i	0.00792208	+	0.0137215i
$859$		−	24.9808i		−	0.852333i	−0.904645	−	0.426166i	$-0.859864\pi$
$859$		−	24.9808i		−	0.852333i	0.904645	−	0.426166i	$-0.140136\pi$
$860$	0.267949	−	0.464102i	0.00913699	−	0.0158257i
$861$	−6.00000			−0.204479
$862$	−9.51666			−0.324139
$863$	1.66987	−	2.89230i	0.0568431	−	0.0984552i	−0.836204	−	0.548419i	$-0.815230\pi$
$863$	1.66987	−	2.89230i	0.0568431	−	0.0984552i	0.893047	+	0.449964i	$0.148563\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		−	17.6603i		−	0.600467i
$866$	23.3205	+	13.4641i	0.792463	+	0.457529i
$867$	−17.3923	+	30.1244i	−0.590674	+	1.02308i
$868$	4.39230	+	2.53590i	0.149085	+	0.0860740i
$869$	−1.14359	+	0.660254i	−0.0387938	+	0.0223976i
$870$	−3.69615	+	2.13397i	−0.125311	+	0.0723485i
$871$	−15.9904	−	9.23205i	−0.541813	−	0.312816i
$872$	−1.63397	+	2.83013i	−0.0553334	+	0.0958402i
$873$	−9.92820	−	5.73205i	−0.336019	−	0.194001i
$874$			4.00000i			0.135302i
$875$	−0.633975	+	0.366025i	−0.0214323	+	0.0123739i
$876$	6.19615	−	10.7321i	0.209349	−	0.362602i
$877$	18.1769			0.613791			0.306895	−	0.951743i	$-0.400710\pi$
$877$	18.1769			0.613791			0.306895	+	0.951743i	$0.400710\pi$
$878$	−37.0000			−1.24869
$879$	−1.73205	+	3.00000i	−0.0584206	+	0.101187i
$880$			0.267949i			0.00903257i
$881$	14.9282	+	25.8564i	0.502944	+	0.871124i	0.999994	+	0.00340272i	$0.00108312\pi$
$881$	14.9282	+	25.8564i	0.502944	+	0.871124i	−0.497050	+	0.867722i	$0.665584\pi$
$882$			6.46410i			0.217658i
$883$	23.2583	−	13.4282i	0.782705	−	0.451895i	−0.0546830	−	0.998504i	$-0.517415\pi$
$883$	23.2583	−	13.4282i	0.782705	−	0.451895i	0.837388	+	0.546609i	$0.184081\pi$
$884$	6.23205	+	10.7942i	0.209607	+	0.363049i
$885$	−0.232051	−	0.401924i	−0.00780030	−	0.0135105i
$886$	−30.6340	−	17.6865i	−1.02917	−	0.594191i
$887$	−15.2154			−0.510883			−0.255441	−	0.966825i	$-0.582221\pi$
$887$	−15.2154			−0.510883			−0.255441	+	0.966825i	$0.582221\pi$
$888$	−2.59808	−	5.50000i	−0.0871857	−	0.184568i
$889$	0.535898			0.0179735
$890$	11.1962	+	6.46410i	0.375296	+	0.216677i
$891$	−0.133975	−	0.232051i	−0.00448832	−	0.00777399i
$892$	−7.26795	−	12.5885i	−0.243349	−	0.421493i
$893$	−3.00000	+	1.73205i	−0.100391	+	0.0579609i
$894$			3.92820i			0.131379i
$895$	−4.46410	−	7.73205i	−0.149218	−	0.258454i
$896$			0.732051i			0.0244561i
$897$	−1.73205	+	3.00000i	−0.0578315	+	0.100167i
$898$	24.7846			0.827073
$899$	−29.5692			−0.986189
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	51.0788	−	29.4904i	1.70168	−	0.982467i
$902$		−	2.19615i		−	0.0731239i
$903$	−0.339746	−	0.196152i	−0.0113060	−	0.00652754i
$904$	7.33013	−	12.6962i	0.243796	−	0.422268i
$905$	1.73205	+	1.00000i	0.0575753	+	0.0332411i
$906$	−4.39230	+	2.53590i	−0.145925	+	0.0842496i
$907$	−24.1244	+	13.9282i	−0.801036	+	0.462478i	−0.843833	−	0.536605i	$-0.819706\pi$
$907$	−24.1244	+	13.9282i	−0.801036	+	0.462478i	0.0427972	+	0.999084i	$0.486373\pi$
$908$	−1.09808	−	0.633975i	−0.0364409	−	0.0210392i
$909$	−4.23205	+	7.33013i	−0.140368	+	0.243125i
$910$	−1.09808	−	0.633975i	−0.0364009	−	0.0210161i
$911$			47.5692i			1.57604i	0.615651	+	0.788019i	$0.288893\pi$
$911$			47.5692i			1.57604i	−0.615651	+	0.788019i	$0.711107\pi$
$912$	−1.73205	+	1.00000i	−0.0573539	+	0.0331133i
$913$	0.830127	−	1.43782i	0.0274732	−	0.0475850i
$914$	15.3205			0.506757
$915$	1.26795			0.0419171
$916$	−8.02628	+	13.9019i	−0.265196	+	0.459332i
$917$			6.87564i			0.227054i
$918$	−3.59808	−	6.23205i	−0.118754	−	0.205688i
$919$		−	55.2487i		−	1.82249i	−0.411868	−	0.911243i	$-0.635124\pi$
$919$		−	55.2487i		−	1.82249i	0.411868	−	0.911243i	$-0.364876\pi$
$920$	−1.73205	+	1.00000i	−0.0571040	+	0.0329690i
$921$	−9.73205	−	16.8564i	−0.320682	−	0.555437i
$922$	−2.20577	−	3.82051i	−0.0726432	−	0.125822i
$923$	−12.2942	−	7.09808i	−0.404669	−	0.233636i
$924$	0.196152			0.00645294
$925$	5.00000	+	3.46410i	0.164399	+	0.113899i
$926$	−0.535898			−0.0176107
$927$	8.83013	+	5.09808i	0.290019	+	0.167443i
$928$	−2.13397	−	3.69615i	−0.0700511	−	0.121332i
$929$	−13.8564	−	24.0000i	−0.454614	−	0.787414i	0.544052	−	0.839052i	$-0.316889\pi$
$929$	−13.8564	−	24.0000i	−0.454614	−	0.787414i	−0.998666	+	0.0516371i	$0.983556\pi$
$930$	−6.00000	+	3.46410i	−0.196748	+	0.113592i
$931$		−	12.9282i		−	0.423705i
$932$	−1.26795	−	2.19615i	−0.0415331	−	0.0719374i
$933$		−	4.73205i		−	0.154920i
$934$	−7.92820	+	13.7321i	−0.259419	+	0.449326i
$935$	1.92820			0.0630590
$936$	−1.73205			−0.0566139
$937$	22.2942	−	38.6147i	0.728321	−	1.26149i	−0.229272	−	0.973362i	$-0.573634\pi$
$937$	22.2942	−	38.6147i	0.728321	−	1.26149i	0.957593	−	0.288126i	$-0.0930322\pi$
$938$	−6.75833	+	3.90192i	−0.220667	+	0.127402i
$939$			4.92820i			0.160826i
$940$	−1.50000	−	0.866025i	−0.0489246	−	0.0282466i
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.0290288	−	0.999579i	$-0.490759\pi$
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.851146	−	0.524929i	$-0.175908\pi$
$942$	19.4545	+	11.2321i	0.633861	+	0.365960i
$943$	14.1962	−	8.19615i	0.462290	−	0.266903i
$944$	0.401924	−	0.232051i	0.0130815	−	0.00755261i
$945$	0.633975	+	0.366025i	0.0206232	+	0.0119068i
$946$	0.0717968	−	0.124356i	0.00233431	−	0.00404315i
$947$	39.2487	+	22.6603i	1.27541	+	0.736359i	0.976001	−	0.217765i	$-0.0698767\pi$
$947$	39.2487	+	22.6603i	1.27541	+	0.736359i	0.299411	+	0.954124i	$0.403210\pi$
$948$		−	4.92820i		−	0.160061i
$949$	−18.5885	+	10.7321i	−0.603407	+	0.348377i
$950$	1.00000	−	1.73205i	0.0324443	−	0.0561951i
$951$	5.26795			0.170825
$952$	5.26795			0.170735
$953$	1.16025	−	2.00962i	0.0375843	−	0.0650979i	−0.846621	−	0.532196i	$-0.821367\pi$
$953$	1.16025	−	2.00962i	0.0375843	−	0.0650979i	0.884206	+	0.467098i	$0.154700\pi$
$954$			8.19615i			0.265360i
$955$	−0.0980762	−	0.169873i	−0.00317367	−	0.00549696i
$956$			14.5359i			0.470125i
$957$	−0.990381	+	0.571797i	−0.0320145	+	0.0184836i
$958$	8.12436	+	14.0718i	0.262486	+	0.454639i
$959$	−4.02628	−	6.97372i	−0.130015	−	0.225193i
$960$	−0.866025	−	0.500000i	−0.0279508	−	0.0161374i
$961$	−17.0000			−0.548387
$962$	−0.866025	+	10.5000i	−0.0279218	+	0.338534i
$963$	−1.80385			−0.0581282
$964$	−3.23205	−	1.86603i	−0.104097	−	0.0601006i
$965$	−5.09808	−	8.83013i	−0.164113	−	0.284252i
$966$	0.732051	+	1.26795i	0.0235533	+	0.0407956i
$967$	38.6147	−	22.2942i	1.24177	−	0.716934i	0.272313	−	0.962209i	$-0.412212\pi$
$967$	38.6147	−	22.2942i	1.24177	−	0.716934i	0.969454	+	0.245275i	$0.0788782\pi$
$968$		−	10.9282i		−	0.351246i
$969$	7.19615	+	12.4641i	0.231174	+	0.400405i
$970$			11.4641i			0.368090i
$971$	1.26795	−	2.19615i	0.0406904	−	0.0704779i	−0.844963	−	0.534825i	$-0.820378\pi$
$971$	1.26795	−	2.19615i	0.0406904	−	0.0704779i	0.885653	+	0.464347i	$0.153711\pi$
$972$	1.00000			0.0320750
$973$	12.0000			0.384702
$974$	5.53590	−	9.58846i	0.177382	−	0.307234i
$975$	1.50000	−	0.866025i	0.0480384	−	0.0277350i
$976$			1.26795i			0.0405861i
$977$	−38.6769	−	22.3301i	−1.23738	−	0.714404i	−0.268825	−	0.963189i	$-0.586635\pi$
$977$	−38.6769	−	22.3301i	−1.23738	−	0.714404i	−0.968559	+	0.248785i	$0.919969\pi$
$978$	11.2321	−	19.4545i	0.359161	−	0.622086i
$979$	3.00000	+	1.73205i	0.0958804	+	0.0553566i
$980$	5.59808	−	3.23205i	0.178824	−	0.103244i
$981$	−2.83013	+	1.63397i	−0.0903590	+	0.0521688i
$982$	13.8564	+	8.00000i	0.442176	+	0.255290i
$983$	5.46410	−	9.46410i	0.174278	−	0.301858i	−0.765633	−	0.643277i	$-0.777574\pi$
$983$	5.46410	−	9.46410i	0.174278	−	0.301858i	0.939911	+	0.341419i	$0.110908\pi$
$984$	7.09808	+	4.09808i	0.226278	+	0.130642i
$985$		−	4.92820i		−	0.157026i
$986$	−26.5981	+	15.3564i	−0.847055	+	0.489048i
$987$	−0.633975	+	1.09808i	−0.0201796	+	0.0349522i
$988$	3.46410			0.110208
$989$	1.07180			0.0340812
$990$	−0.133975	+	0.232051i	−0.00425799	+	0.00737506i
$991$		−	46.1769i		−	1.46686i	−0.679766	−	0.733429i	$-0.737919\pi$
$991$		−	46.1769i		−	1.46686i	0.679766	−	0.733429i	$-0.262081\pi$
$992$	−3.46410	−	6.00000i	−0.109985	−	0.190500i
$993$			27.6603i			0.877772i
$994$	−5.19615	+	3.00000i	−0.164812	+	0.0951542i
$995$	−4.16025	−	7.20577i	−0.131889	−	0.228438i
$996$	3.09808	+	5.36603i	0.0981663	+	0.170029i
$997$	12.8205	+	7.40192i	0.406030	+	0.234421i	0.689082	−	0.724683i	$-0.258014\pi$
$997$	12.8205	+	7.40192i	0.406030	+	0.234421i	−0.283053	+	0.959104i	$0.591347\pi$
$998$	28.4449			0.900406
$999$	0.500000	−	6.06218i	0.0158193	−	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.b.841.2	yes	4
37.11	even	6	inner	1110.2.x.b.751.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.b.751.2	✓	4	37.11	even	6	inner
1110.2.x.b.841.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +1.00000i q^{6} +(-0.366025 - 0.633975i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +1.00000i q^{6} +(-0.366025 - 0.633975i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +0.267949 q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.50000 - 0.866025i) q^{13} -0.732051i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.23205 + 3.59808i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(1.73205 - 1.00000i) q^{19} +(0.866025 + 0.500000i) q^{20} +(0.366025 - 0.633975i) q^{21} +(0.232051 + 0.133975i) q^{22} +2.00000i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} +1.73205 q^{26} -1.00000 q^{27} +(0.366025 - 0.633975i) q^{28} +4.26795i q^{29} +(0.500000 + 0.866025i) q^{30} +6.92820i q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.133975 + 0.232051i) q^{33} +(3.59808 + 6.23205i) q^{34} +(-0.633975 - 0.366025i) q^{35} -1.00000 q^{36} +(-0.500000 + 6.06218i) q^{37} +2.00000 q^{38} +(1.50000 + 0.866025i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-4.09808 - 7.09808i) q^{41} +(0.633975 - 0.366025i) q^{42} -0.535898i q^{43} +(0.133975 + 0.232051i) q^{44} +1.00000i q^{45} +(-1.00000 + 1.73205i) q^{46} -1.73205 q^{47} -1.00000 q^{48} +(3.23205 - 5.59808i) q^{49} +(0.866025 - 0.500000i) q^{50} +7.19615i q^{51} +(1.50000 + 0.866025i) q^{52} +(4.09808 - 7.09808i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(0.232051 - 0.133975i) q^{55} +(0.633975 - 0.366025i) q^{56} +(1.73205 + 1.00000i) q^{57} +(-2.13397 + 3.69615i) q^{58} +(-0.401924 - 0.232051i) q^{59} +1.00000i q^{60} +(1.09808 - 0.633975i) q^{61} +(-3.46410 + 6.00000i) q^{62} +0.732051 q^{63} -1.00000 q^{64} +(0.866025 - 1.50000i) q^{65} +0.267949i q^{66} +(-5.33013 - 9.23205i) q^{67} +7.19615i q^{68} +(-1.73205 + 1.00000i) q^{69} +(-0.366025 - 0.633975i) q^{70} +(-4.09808 - 7.09808i) q^{71} +(-0.866025 - 0.500000i) q^{72} -12.3923 q^{73} +(-3.46410 + 5.00000i) q^{74} +1.00000 q^{75} +(1.73205 + 1.00000i) q^{76} +(-0.0980762 - 0.169873i) q^{77} +(0.866025 + 1.50000i) q^{78} +(-4.26795 + 2.46410i) q^{79} +1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -8.19615i q^{82} +(3.09808 - 5.36603i) q^{83} +0.732051 q^{84} +7.19615 q^{85} +(0.267949 - 0.464102i) q^{86} +(-3.69615 + 2.13397i) q^{87} +0.267949i q^{88} +(11.1962 + 6.46410i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-1.09808 - 0.633975i) q^{91} +(-1.73205 + 1.00000i) q^{92} +(-6.00000 + 3.46410i) q^{93} +(-1.50000 - 0.866025i) q^{94} +(1.00000 - 1.73205i) q^{95} +(-0.866025 - 0.500000i) q^{96} +11.4641i q^{97} +(5.59808 - 3.23205i) q^{98} +(-0.133975 + 0.232051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} + 2 q^{7} - 2 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{12} + 6 q^{13} - 2 q^{16} + 18 q^{17} - 2 q^{21} - 6 q^{22} + 2 q^{25} - 4 q^{27} - 2 q^{28} + 2 q^{30} + 4 q^{33} + 4 q^{34} - 6 q^{35} - 4 q^{36} - 2 q^{37} + 8 q^{38} + 6 q^{39} + 2 q^{40} - 6 q^{41} + 6 q^{42} + 4 q^{44} - 4 q^{46} - 4 q^{48} + 6 q^{49} + 6 q^{52} + 6 q^{53} - 6 q^{55} + 6 q^{56} - 12 q^{58} - 12 q^{59} - 6 q^{61} - 4 q^{63} - 4 q^{64} - 4 q^{67} + 2 q^{70} - 6 q^{71} - 8 q^{73} + 4 q^{75} + 10 q^{77} - 24 q^{79} - 2 q^{81} + 2 q^{83} - 4 q^{84} + 8 q^{85} + 8 q^{86} + 6 q^{87} + 24 q^{89} - 2 q^{90} + 6 q^{91} - 24 q^{93} - 6 q^{94} + 4 q^{95} + 12 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^7 - 2 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^12 + 6 * q^13 - 2 * q^16 + 18 * q^17 - 2 * q^21 - 6 * q^22 + 2 * q^25 - 4 * q^27 - 2 * q^28 + 2 * q^30 + 4 * q^33 + 4 * q^34 - 6 * q^35 - 4 * q^36 - 2 * q^37 + 8 * q^38 + 6 * q^39 + 2 * q^40 - 6 * q^41 + 6 * q^42 + 4 * q^44 - 4 * q^46 - 4 * q^48 + 6 * q^49 + 6 * q^52 + 6 * q^53 - 6 * q^55 + 6 * q^56 - 12 * q^58 - 12 * q^59 - 6 * q^61 - 4 * q^63 - 4 * q^64 - 4 * q^67 + 2 * q^70 - 6 * q^71 - 8 * q^73 + 4 * q^75 + 10 * q^77 - 24 * q^79 - 2 * q^81 + 2 * q^83 - 4 * q^84 + 8 * q^85 + 8 * q^86 + 6 * q^87 + 24 * q^89 - 2 * q^90 + 6 * q^91 - 24 * q^93 - 6 * q^94 + 4 * q^95 + 12 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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