LMFDB - Embedded newform 1110.2.i.n.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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, 4]))

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

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

chi := DirichletCharacter("1110.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1110.121
Dual form			1110.2.i.n.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-1.36603 - 2.36603i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-1.36603 - 2.36603i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -0.464102 q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.23205 - 5.59808i) q^{13} -2.73205 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.86603 + 6.69615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(1.73205 + 3.00000i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.36603 - 2.36603i) q^{21} +(-0.232051 + 0.401924i) q^{22} -4.92820 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -6.46410 q^{26} -1.00000 q^{27} +(-1.36603 + 2.36603i) q^{28} +5.19615 q^{29} +(-0.500000 - 0.866025i) q^{30} -3.46410 q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.232051 - 0.401924i) q^{33} +(3.86603 + 6.69615i) q^{34} +(-1.36603 + 2.36603i) q^{35} +1.00000 q^{36} +(-4.69615 + 3.86603i) q^{37} +3.46410 q^{38} +(3.23205 - 5.59808i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.36603 - 9.29423i) q^{41} +(-1.36603 - 2.36603i) q^{42} -8.39230 q^{43} +(0.232051 + 0.401924i) q^{44} +1.00000 q^{45} +(-2.46410 + 4.26795i) q^{46} +4.46410 q^{47} -1.00000 q^{48} +(-0.232051 + 0.401924i) q^{49} +(0.500000 + 0.866025i) q^{50} -7.73205 q^{51} +(-3.23205 + 5.59808i) q^{52} +(3.36603 - 5.83013i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.232051 + 0.401924i) q^{55} +(1.36603 + 2.36603i) q^{56} +(-1.73205 + 3.00000i) q^{57} +(2.59808 - 4.50000i) q^{58} +(3.23205 - 5.59808i) q^{59} -1.00000 q^{60} +(-2.83013 - 4.90192i) q^{61} +(-1.73205 + 3.00000i) q^{62} +2.73205 q^{63} +1.00000 q^{64} +(-3.23205 + 5.59808i) q^{65} -0.464102 q^{66} +(-3.86603 - 6.69615i) q^{67} +7.73205 q^{68} +(-2.46410 - 4.26795i) q^{69} +(1.36603 + 2.36603i) q^{70} +(3.36603 + 5.83013i) q^{71} +(0.500000 - 0.866025i) q^{72} +(1.00000 + 6.00000i) q^{74} -1.00000 q^{75} +(1.73205 - 3.00000i) q^{76} +(0.633975 + 1.09808i) q^{77} +(-3.23205 - 5.59808i) q^{78} +(-2.00000 - 3.46410i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} -10.7321 q^{82} +(1.83013 - 3.16987i) q^{83} -2.73205 q^{84} +7.73205 q^{85} +(-4.19615 + 7.26795i) q^{86} +(2.59808 + 4.50000i) q^{87} +0.464102 q^{88} +(-1.73205 + 3.00000i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-8.83013 + 15.2942i) q^{91} +(2.46410 + 4.26795i) q^{92} +(-1.73205 - 3.00000i) q^{93} +(2.23205 - 3.86603i) q^{94} +(1.73205 - 3.00000i) q^{95} +(-0.500000 + 0.866025i) q^{96} -4.92820 q^{97} +(0.232051 + 0.401924i) q^{98} +(0.232051 - 0.401924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{10} + 12 q^{11} + 2 q^{12} - 6 q^{13} - 4 q^{14} + 2 q^{15} - 2 q^{16} - 12 q^{17} + 2 q^{18} - 2 q^{20} + 2 q^{21} + 6 q^{22} + 8 q^{23} - 2 q^{24} - 2 q^{25} - 12 q^{26} - 4 q^{27} - 2 q^{28} - 2 q^{30} + 2 q^{32} + 6 q^{33} + 12 q^{34} - 2 q^{35} + 4 q^{36} + 2 q^{37} + 6 q^{39} + 2 q^{40} - 18 q^{41} - 2 q^{42} + 8 q^{43} - 6 q^{44} + 4 q^{45} + 4 q^{46} + 4 q^{47} - 4 q^{48} + 6 q^{49} + 2 q^{50} - 24 q^{51} - 6 q^{52} + 10 q^{53} - 2 q^{54} - 6 q^{55} + 2 q^{56} + 6 q^{59} - 4 q^{60} + 6 q^{61} + 4 q^{63} + 4 q^{64} - 6 q^{65} + 12 q^{66} - 12 q^{67} + 24 q^{68} + 4 q^{69} + 2 q^{70} + 10 q^{71} + 2 q^{72} + 4 q^{74} - 4 q^{75} + 6 q^{77} - 6 q^{78} - 8 q^{79} + 4 q^{80} - 2 q^{81} - 36 q^{82} - 10 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} - 12 q^{88} + 2 q^{90} - 18 q^{91} - 4 q^{92} + 2 q^{94} - 2 q^{96} + 8 q^{97} - 6 q^{98} - 6 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 - 4 * q^10 + 12 * q^11 + 2 * q^12 - 6 * q^13 - 4 * q^14 + 2 * q^15 - 2 * q^16 - 12 * q^17 + 2 * q^18 - 2 * q^20 + 2 * q^21 + 6 * q^22 + 8 * q^23 - 2 * q^24 - 2 * q^25 - 12 * q^26 - 4 * q^27 - 2 * q^28 - 2 * q^30 + 2 * q^32 + 6 * q^33 + 12 * q^34 - 2 * q^35 + 4 * q^36 + 2 * q^37 + 6 * q^39 + 2 * q^40 - 18 * q^41 - 2 * q^42 + 8 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 4 * q^47 - 4 * q^48 + 6 * q^49 + 2 * q^50 - 24 * q^51 - 6 * q^52 + 10 * q^53 - 2 * q^54 - 6 * q^55 + 2 * q^56 + 6 * q^59 - 4 * q^60 + 6 * q^61 + 4 * q^63 + 4 * q^64 - 6 * q^65 + 12 * q^66 - 12 * q^67 + 24 * q^68 + 4 * q^69 + 2 * q^70 + 10 * q^71 + 2 * q^72 + 4 * q^74 - 4 * q^75 + 6 * q^77 - 6 * q^78 - 8 * q^79 + 4 * q^80 - 2 * q^81 - 36 * q^82 - 10 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 - 12 * q^88 + 2 * q^90 - 18 * q^91 - 4 * q^92 + 2 * q^94 - 2 * q^96 + 8 * q^97 - 6 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.00000			0.408248
$7$	−1.36603	−	2.36603i	−0.516309	−	0.894274i	−0.999821	−	0.0189356i	$-0.993972\pi$
$7$	−1.36603	−	2.36603i	−0.516309	−	0.894274i	0.483512	−	0.875338i	$-0.339361\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000			−0.316228
$11$	−0.464102			−0.139932			−0.0699660	−	0.997549i	$-0.522289\pi$
$11$	−0.464102			−0.139932			−0.0699660	+	0.997549i	$0.522289\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−3.23205	−	5.59808i	−0.896410	−	1.55263i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−3.23205	−	5.59808i	−0.896410	−	1.55263i	−0.0643593	−	0.997927i	$-0.520500\pi$
$14$	−2.73205			−0.730171
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.86603	+	6.69615i	−0.937649	+	1.62406i	−0.167808	+	0.985820i	$0.553669\pi$
$17$	−3.86603	+	6.69615i	−0.937649	+	1.62406i	−0.769841	+	0.638236i	$0.779664\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	1.73205	+	3.00000i	0.397360	+	0.688247i	0.993399	−	0.114708i	$-0.0365932\pi$
$19$	1.73205	+	3.00000i	0.397360	+	0.688247i	−0.596040	+	0.802955i	$0.703260\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	1.36603	−	2.36603i	0.298091	−	0.516309i
$22$	−0.232051	+	0.401924i	−0.0494734	+	0.0856904i
$23$	−4.92820			−1.02760			−0.513801	−	0.857910i	$-0.671763\pi$
$23$	−4.92820			−1.02760			−0.513801	+	0.857910i	$0.671763\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−6.46410			−1.26771
$27$	−1.00000			−0.192450
$28$	−1.36603	+	2.36603i	−0.258155	+	0.447137i
$29$	5.19615			0.964901			0.482451	−	0.875923i	$-0.339747\pi$
$29$	5.19615			0.964901			0.482451	+	0.875923i	$0.339747\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−3.46410			−0.622171			−0.311086	−	0.950382i	$-0.600693\pi$
$31$	−3.46410			−0.622171			−0.311086	+	0.950382i	$0.600693\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.232051	−	0.401924i	−0.0403949	−	0.0699660i
$34$	3.86603	+	6.69615i	0.663018	+	1.14838i
$35$	−1.36603	+	2.36603i	−0.230900	+	0.399931i
$36$	1.00000			0.166667
$37$	−4.69615	+	3.86603i	−0.772043	+	0.635571i
$37$	−4.69615	+	3.86603i	−0.772043	+	0.635571i
$38$	3.46410			0.561951
$39$	3.23205	−	5.59808i	0.517542	−	0.896410i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−5.36603	−	9.29423i	−0.838032	−	1.45151i	−0.891537	−	0.452947i	$-0.850373\pi$
$41$	−5.36603	−	9.29423i	−0.838032	−	1.45151i	0.0535050	−	0.998568i	$-0.482961\pi$
$42$	−1.36603	−	2.36603i	−0.210782	−	0.365086i
$43$	−8.39230			−1.27981			−0.639907	−	0.768452i	$-0.721027\pi$
$43$	−8.39230			−1.27981			−0.639907	+	0.768452i	$0.721027\pi$
$44$	0.232051	+	0.401924i	0.0349830	+	0.0605923i
$45$	1.00000			0.149071
$46$	−2.46410	+	4.26795i	−0.363312	+	0.629275i
$47$	4.46410			0.651156			0.325578	−	0.945515i	$-0.394441\pi$
$47$	4.46410			0.651156			0.325578	+	0.945515i	$0.394441\pi$
$48$	−1.00000			−0.144338
$49$	−0.232051	+	0.401924i	−0.0331501	+	0.0574177i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−7.73205			−1.08270
$52$	−3.23205	+	5.59808i	−0.448205	+	0.776313i
$53$	3.36603	−	5.83013i	0.462359	−	0.800830i	−0.536719	−	0.843761i	$-0.680336\pi$
$53$	3.36603	−	5.83013i	0.462359	−	0.800830i	0.999078	+	0.0429316i	$0.0136698\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	0.232051	+	0.401924i	0.0312897	+	0.0541954i
$56$	1.36603	+	2.36603i	0.182543	+	0.316173i
$57$	−1.73205	+	3.00000i	−0.229416	+	0.397360i
$58$	2.59808	−	4.50000i	0.341144	−	0.590879i
$59$	3.23205	−	5.59808i	0.420777	−	0.728807i	−0.575239	−	0.817986i	$-0.695091\pi$
$59$	3.23205	−	5.59808i	0.420777	−	0.728807i	0.996016	+	0.0891783i	$0.0284241\pi$
$60$	−1.00000			−0.129099
$61$	−2.83013	−	4.90192i	−0.362361	−	0.627627i	0.625988	−	0.779832i	$-0.284696\pi$
$61$	−2.83013	−	4.90192i	−0.362361	−	0.627627i	−0.988349	+	0.152205i	$0.951362\pi$
$62$	−1.73205	+	3.00000i	−0.219971	+	0.381000i
$63$	2.73205			0.344206
$64$	1.00000			0.125000
$65$	−3.23205	+	5.59808i	−0.400887	+	0.694356i
$66$	−0.464102			−0.0571270
$67$	−3.86603	−	6.69615i	−0.472310	−	0.818065i	0.527188	−	0.849749i	$-0.323246\pi$
$67$	−3.86603	−	6.69615i	−0.472310	−	0.818065i	−0.999498	+	0.0316836i	$0.989913\pi$
$68$	7.73205			0.937649
$69$	−2.46410	−	4.26795i	−0.296643	−	0.513801i
$70$	1.36603	+	2.36603i	0.163271	+	0.282794i
$71$	3.36603	+	5.83013i	0.399474	+	0.691909i	0.993661	−	0.112418i	$-0.0358595\pi$
$71$	3.36603	+	5.83013i	0.399474	+	0.691909i	−0.594187	+	0.804327i	$0.702526\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	1.00000	+	6.00000i	0.116248	+	0.697486i
$75$	−1.00000			−0.115470
$76$	1.73205	−	3.00000i	0.198680	−	0.344124i
$77$	0.633975	+	1.09808i	0.0722481	+	0.125137i
$78$	−3.23205	−	5.59808i	−0.365958	−	0.633857i
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$	1.00000			0.111803
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.7321			−1.18516
$83$	1.83013	−	3.16987i	0.200883	−	0.347939i	−0.747930	−	0.663777i	$-0.768952\pi$
$83$	1.83013	−	3.16987i	0.200883	−	0.347939i	0.948813	+	0.315838i	$0.102286\pi$
$84$	−2.73205			−0.298091
$85$	7.73205			0.838659
$86$	−4.19615	+	7.26795i	−0.452483	+	0.783723i
$87$	2.59808	+	4.50000i	0.278543	+	0.482451i
$88$	0.464102			0.0494734
$89$	−1.73205	+	3.00000i	−0.183597	+	0.317999i	−0.943103	−	0.332501i	$-0.892107\pi$
$89$	−1.73205	+	3.00000i	−0.183597	+	0.317999i	0.759506	+	0.650500i	$0.225441\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$	−8.83013	+	15.2942i	−0.925649	+	1.60327i
$92$	2.46410	+	4.26795i	0.256900	+	0.444964i
$93$	−1.73205	−	3.00000i	−0.179605	−	0.311086i
$94$	2.23205	−	3.86603i	0.230218	−	0.398750i
$95$	1.73205	−	3.00000i	0.177705	−	0.307794i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−4.92820			−0.500383			−0.250192	−	0.968196i	$-0.580494\pi$
$97$	−4.92820			−0.500383			−0.250192	+	0.968196i	$0.580494\pi$
$98$	0.232051	+	0.401924i	0.0234407	+	0.0406004i
$99$	0.232051	−	0.401924i	0.0233220	−	0.0403949i
$100$	1.00000			0.100000
$101$	8.12436			0.808404			0.404202	−	0.914670i	$-0.367549\pi$
$101$	8.12436			0.808404			0.404202	+	0.914670i	$0.367549\pi$
$102$	−3.86603	+	6.69615i	−0.382794	+	0.663018i
$103$	7.66025			0.754787			0.377394	−	0.926053i	$-0.376820\pi$
$103$	7.66025			0.754787			0.377394	+	0.926053i	$0.376820\pi$
$104$	3.23205	+	5.59808i	0.316929	+	0.548937i
$105$	−2.73205			−0.266621
$106$	−3.36603	−	5.83013i	−0.326937	−	0.566272i
$107$	−1.63397	−	2.83013i	−0.157962	−	0.273599i	0.776171	−	0.630522i	$-0.217159\pi$
$107$	−1.63397	−	2.83013i	−0.157962	−	0.273599i	−0.934134	+	0.356923i	$0.883826\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−0.169873	+	0.294229i	−0.0162709	+	0.0281820i	−0.874046	−	0.485843i	$-0.838513\pi$
$109$	−0.169873	+	0.294229i	−0.0162709	+	0.0281820i	0.857775	+	0.514025i	$0.171846\pi$
$110$	0.464102			0.0442504
$111$	−5.69615	−	2.13397i	−0.540655	−	0.202548i
$112$	2.73205			0.258155
$113$	−0.133975	+	0.232051i	−0.0126033	+	0.0218295i	−0.872258	−	0.489046i	$-0.837345\pi$
$113$	−0.133975	+	0.232051i	−0.0126033	+	0.0218295i	0.859655	+	0.510875i	$0.170679\pi$
$114$	1.73205	+	3.00000i	0.162221	+	0.280976i
$115$	2.46410	+	4.26795i	0.229779	+	0.397988i
$116$	−2.59808	−	4.50000i	−0.241225	−	0.417815i
$117$	6.46410			0.597606
$118$	−3.23205	−	5.59808i	−0.297534	−	0.515345i
$119$	21.1244			1.93647
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	−10.7846			−0.980419
$122$	−5.66025			−0.512455
$123$	5.36603	−	9.29423i	0.483838	−	0.838032i
$124$	1.73205	+	3.00000i	0.155543	+	0.269408i
$125$	1.00000			0.0894427
$126$	1.36603	−	2.36603i	0.121695	−	0.210782i
$127$	9.56218	−	16.5622i	0.848506	−	1.46966i	−0.0340352	−	0.999421i	$-0.510836\pi$
$127$	9.56218	−	16.5622i	0.848506	−	1.46966i	0.882541	−	0.470235i	$-0.155831\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.19615	−	7.26795i	−0.369451	−	0.639907i
$130$	3.23205	+	5.59808i	0.283470	+	0.490984i
$131$	6.69615	−	11.5981i	0.585046	−	1.01333i	−0.409824	−	0.912165i	$-0.634410\pi$
$131$	6.69615	−	11.5981i	0.585046	−	1.01333i	0.994870	−	0.101164i	$-0.0322567\pi$
$132$	−0.232051	+	0.401924i	−0.0201974	+	0.0349830i
$133$	4.73205	−	8.19615i	0.410321	−	0.710697i
$134$	−7.73205			−0.667947
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	3.86603	−	6.69615i	0.331509	−	0.574190i
$137$	−2.26795			−0.193764			−0.0968820	−	0.995296i	$-0.530887\pi$
$137$	−2.26795			−0.193764			−0.0968820	+	0.995296i	$0.530887\pi$
$138$	−4.92820			−0.419517
$139$	−1.26795	+	2.19615i	−0.107546	+	0.186275i	−0.914776	−	0.403962i	$-0.867633\pi$
$139$	−1.26795	+	2.19615i	−0.107546	+	0.186275i	0.807230	+	0.590238i	$0.200966\pi$
$140$	2.73205			0.230900
$141$	2.23205	+	3.86603i	0.187973	+	0.325578i
$142$	6.73205			0.564941
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−2.59808	−	4.50000i	−0.215758	−	0.373705i
$146$		0			0
$147$	−0.464102			−0.0382785
$148$	5.69615	+	2.13397i	0.468221	+	0.175412i
$149$	−7.73205			−0.633434			−0.316717	−	0.948520i	$-0.602581\pi$
$149$	−7.73205			−0.633434			−0.316717	+	0.948520i	$0.602581\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	4.92820	+	8.53590i	0.401051	+	0.694642i	0.993853	−	0.110707i	$-0.0353115\pi$
$151$	4.92820	+	8.53590i	0.401051	+	0.694642i	−0.592802	+	0.805349i	$0.701978\pi$
$152$	−1.73205	−	3.00000i	−0.140488	−	0.243332i
$153$	−3.86603	−	6.69615i	−0.312550	−	0.541352i
$154$	1.26795			0.102174
$155$	1.73205	+	3.00000i	0.139122	+	0.240966i
$156$	−6.46410			−0.517542
$157$	4.96410	−	8.59808i	0.396178	−	0.686201i	−0.597072	−	0.802187i	$-0.703669\pi$
$157$	4.96410	−	8.59808i	0.396178	−	0.686201i	0.993251	+	0.115986i	$0.0370028\pi$
$158$	−4.00000			−0.318223
$159$	6.73205			0.533886
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	6.73205	+	11.6603i	0.530560	+	0.918957i
$162$	−1.00000			−0.0785674
$163$	−11.0622	+	19.1603i	−0.866457	+	1.50075i	−0.000863114		1.00000i	$0.500275\pi$
$163$	−11.0622	+	19.1603i	−0.866457	+	1.50075i	−0.865594	+	0.500747i	$0.833059\pi$
$164$	−5.36603	+	9.29423i	−0.419016	+	0.725757i
$165$	−0.232051	+	0.401924i	−0.0180651	+	0.0312897i
$166$	−1.83013	−	3.16987i	−0.142045	−	0.246030i
$167$	9.69615	+	16.7942i	0.750311	+	1.29958i	0.947672	+	0.319246i	$0.103429\pi$
$167$	9.69615	+	16.7942i	0.750311	+	1.29958i	−0.197361	+	0.980331i	$0.563237\pi$
$168$	−1.36603	+	2.36603i	−0.105391	+	0.182543i
$169$	−14.3923	+	24.9282i	−1.10710	+	1.91755i
$170$	3.86603	−	6.69615i	0.296511	−	0.513571i
$171$	−3.46410			−0.264906
$172$	4.19615	+	7.26795i	0.319954	+	0.554176i
$173$	−6.63397	+	11.4904i	−0.504372	+	0.873597i	0.495615	+	0.868542i	$0.334943\pi$
$173$	−6.63397	+	11.4904i	−0.504372	+	0.873597i	−0.999987	+	0.00505544i	$0.998391\pi$
$174$	5.19615			0.393919
$175$	2.73205			0.206524
$176$	0.232051	−	0.401924i	0.0174915	−	0.0302961i
$177$	6.46410			0.485872
$178$	1.73205	+	3.00000i	0.129823	+	0.224860i
$179$	19.8564			1.48414			0.742069	−	0.670324i	$-0.233845\pi$
$179$	19.8564			1.48414			0.742069	+	0.670324i	$0.233845\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−3.53590	−	6.12436i	−0.262821	−	0.455220i	0.704169	−	0.710032i	$-0.251320\pi$
$181$	−3.53590	−	6.12436i	−0.262821	−	0.455220i	−0.966991	+	0.254812i	$0.917986\pi$
$182$	8.83013	+	15.2942i	0.654533	+	1.13368i
$183$	2.83013	−	4.90192i	0.209209	−	0.362361i
$184$	4.92820			0.363312
$185$	5.69615	+	2.13397i	0.418789	+	0.156893i
$186$	−3.46410			−0.254000
$187$	1.79423	−	3.10770i	0.131207	−	0.227257i
$188$	−2.23205	−	3.86603i	−0.162789	−	0.281959i
$189$	1.36603	+	2.36603i	0.0993637	+	0.172103i
$190$	−1.73205	−	3.00000i	−0.125656	−	0.217643i
$191$	−2.87564			−0.208074			−0.104037	−	0.994573i	$-0.533176\pi$
$191$	−2.87564			−0.208074			−0.104037	+	0.994573i	$0.533176\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−11.2679			−0.811085			−0.405542	−	0.914076i	$-0.632917\pi$
$193$	−11.2679			−0.811085			−0.405542	+	0.914076i	$0.632917\pi$
$194$	−2.46410	+	4.26795i	−0.176912	+	0.306421i
$195$	−6.46410			−0.462904
$196$	0.464102			0.0331501
$197$	4.26795	−	7.39230i	0.304079	−	0.526680i	−0.672977	−	0.739663i	$-0.734985\pi$
$197$	4.26795	−	7.39230i	0.304079	−	0.526680i	0.977056	+	0.212983i	$0.0683181\pi$
$198$	−0.232051	−	0.401924i	−0.0164911	−	0.0285635i
$199$	23.5885			1.67214			0.836071	−	0.548622i	$-0.184847\pi$
$199$	23.5885			1.67214			0.836071	+	0.548622i	$0.184847\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	3.86603	−	6.69615i	0.272688	−	0.472310i
$202$	4.06218	−	7.03590i	0.285814	−	0.495044i
$203$	−7.09808	−	12.2942i	−0.498187	−	0.862886i
$204$	3.86603	+	6.69615i	0.270676	+	0.468824i
$205$	−5.36603	+	9.29423i	−0.374779	+	0.649137i
$206$	3.83013	−	6.63397i	0.266858	−	0.462211i
$207$	2.46410	−	4.26795i	0.171267	−	0.296643i
$208$	6.46410			0.448205
$209$	−0.803848	−	1.39230i	−0.0556033	−	0.0963077i
$210$	−1.36603	+	2.36603i	−0.0942647	+	0.163271i
$211$	2.53590			0.174578			0.0872892	−	0.996183i	$-0.472180\pi$
$211$	2.53590			0.174578			0.0872892	+	0.996183i	$0.472180\pi$
$212$	−6.73205			−0.462359
$213$	−3.36603	+	5.83013i	−0.230636	+	0.399474i
$214$	−3.26795			−0.223392
$215$	4.19615	+	7.26795i	0.286175	+	0.495670i
$216$	1.00000			0.0680414
$217$	4.73205	+	8.19615i	0.321233	+	0.556391i
$218$	0.169873	+	0.294229i	0.0115053	+	0.0199277i
$219$		0			0
$220$	0.232051	−	0.401924i	0.0156449	−	0.0270977i
$221$	49.9808			3.36207
$222$	−4.69615	+	3.86603i	−0.315185	+	0.259471i
$223$	−5.85641			−0.392174			−0.196087	−	0.980587i	$-0.562823\pi$
$223$	−5.85641			−0.392174			−0.196087	+	0.980587i	$0.562823\pi$
$224$	1.36603	−	2.36603i	0.0912714	−	0.158087i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	0.133975	+	0.232051i	0.00891186	+	0.0154358i
$227$	−0.901924	−	1.56218i	−0.0598628	−	0.103685i	0.834541	−	0.550946i	$-0.185733\pi$
$227$	−0.901924	−	1.56218i	−0.0598628	−	0.103685i	−0.894404	+	0.447261i	$0.852400\pi$
$228$	3.46410			0.229416
$229$	−7.90192	−	13.6865i	−0.522174	−	0.904432i	−0.999667	−	0.0257963i	$-0.991788\pi$
$229$	−7.90192	−	13.6865i	−0.522174	−	0.904432i	0.477493	−	0.878635i	$-0.341545\pi$
$230$	4.92820			0.324956
$231$	−0.633975	+	1.09808i	−0.0417125	+	0.0722481i
$232$	−5.19615			−0.341144
$233$	3.07180			0.201240			0.100620	−	0.994925i	$-0.467917\pi$
$233$	3.07180			0.201240			0.100620	+	0.994925i	$0.467917\pi$
$234$	3.23205	−	5.59808i	0.211286	−	0.365958i
$235$	−2.23205	−	3.86603i	−0.145603	−	0.252192i
$236$	−6.46410			−0.420777
$237$	2.00000	−	3.46410i	0.129914	−	0.225018i
$238$	10.5622	−	18.2942i	0.684644	−	1.18584i
$239$	−7.26795	+	12.5885i	−0.470125	+	0.814280i	−0.999416	−	0.0341602i	$-0.989124\pi$
$239$	−7.26795	+	12.5885i	−0.470125	+	0.814280i	0.529292	+	0.848440i	$0.322458\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−13.6244	−	23.5981i	−0.877622	−	1.52009i	−0.853943	−	0.520366i	$-0.825795\pi$
$241$	−13.6244	−	23.5981i	−0.877622	−	1.52009i	−0.0236786	−	0.999720i	$-0.507538\pi$
$242$	−5.39230	+	9.33975i	−0.346630	+	0.600382i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.83013	+	4.90192i	−0.181180	+	0.313814i
$245$	0.464102			0.0296504
$246$	−5.36603	−	9.29423i	−0.342125	−	0.592578i
$247$	11.1962	−	19.3923i	0.712394	−	1.23390i
$248$	3.46410			0.219971
$249$	3.66025			0.231959
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	6.46410			0.408010			0.204005	−	0.978970i	$-0.434604\pi$
$251$	6.46410			0.408010			0.204005	+	0.978970i	$0.434604\pi$
$252$	−1.36603	−	2.36603i	−0.0860515	−	0.149046i
$253$	2.28719			0.143794
$254$	−9.56218	−	16.5622i	−0.599984	−	1.03920i
$255$	3.86603	+	6.69615i	0.242100	+	0.419329i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.06218	+	12.2321i	−0.440527	+	0.763014i	−0.997729	−	0.0673626i	$-0.978542\pi$
$257$	−7.06218	+	12.2321i	−0.440527	+	0.763014i	0.557202	+	0.830377i	$0.311875\pi$
$258$	−8.39230			−0.522482
$259$	15.5622	+	5.83013i	0.966987	+	0.362266i
$260$	6.46410			0.400887
$261$	−2.59808	+	4.50000i	−0.160817	+	0.278543i
$262$	−6.69615	−	11.5981i	−0.413690	−	0.716532i
$263$	−15.1962	−	26.3205i	−0.937035	−	1.62299i	−0.770964	−	0.636878i	$-0.780225\pi$
$263$	−15.1962	−	26.3205i	−0.937035	−	1.62299i	−0.166070	−	0.986114i	$-0.553108\pi$
$264$	0.232051	+	0.401924i	0.0142817	+	0.0247367i
$265$	−6.73205			−0.413547
$266$	−4.73205	−	8.19615i	−0.290141	−	0.502538i
$267$	−3.46410			−0.212000
$268$	−3.86603	+	6.69615i	−0.236155	+	0.409033i
$269$	25.3205			1.54382			0.771909	−	0.635733i	$-0.219302\pi$
$269$	25.3205			1.54382			0.771909	+	0.635733i	$0.219302\pi$
$270$	1.00000			0.0608581
$271$	2.06218	−	3.57180i	0.125268	−	0.216971i	−0.796569	−	0.604547i	$-0.793354\pi$
$271$	2.06218	−	3.57180i	0.125268	−	0.216971i	0.921838	+	0.387576i	$0.126687\pi$
$272$	−3.86603	−	6.69615i	−0.234412	−	0.406014i
$273$	−17.6603			−1.06885
$274$	−1.13397	+	1.96410i	−0.0685059	+	0.118656i
$275$	0.232051	−	0.401924i	0.0139932	−	0.0242369i
$276$	−2.46410	+	4.26795i	−0.148321	+	0.256900i
$277$	−10.4282	−	18.0622i	−0.626570	−	1.08525i	−0.988235	−	0.152943i	$-0.951125\pi$
$277$	−10.4282	−	18.0622i	−0.626570	−	1.08525i	0.361665	−	0.932308i	$-0.382208\pi$
$278$	1.26795	+	2.19615i	0.0760465	+	0.131716i
$279$	1.73205	−	3.00000i	0.103695	−	0.179605i
$280$	1.36603	−	2.36603i	0.0816356	−	0.141397i
$281$	2.66025	−	4.60770i	0.158697	−	0.274872i	−0.775702	−	0.631100i	$-0.782604\pi$
$281$	2.66025	−	4.60770i	0.158697	−	0.274872i	0.934399	+	0.356228i	$0.115937\pi$
$282$	4.46410			0.265833
$283$	6.13397	+	10.6244i	0.364627	+	0.631552i	0.988716	−	0.149801i	$-0.0478632\pi$
$283$	6.13397	+	10.6244i	0.364627	+	0.631552i	−0.624089	+	0.781353i	$0.714530\pi$
$284$	3.36603	−	5.83013i	0.199737	−	0.345954i
$285$	3.46410			0.205196
$286$	3.00000			0.177394
$287$	−14.6603	+	25.3923i	−0.865367	+	1.49886i
$288$	−1.00000			−0.0589256
$289$	−21.3923	−	37.0526i	−1.25837	−	2.17956i
$290$	−5.19615			−0.305129
$291$	−2.46410	−	4.26795i	−0.144448	−	0.250192i
$292$		0			0
$293$	−5.19615	−	9.00000i	−0.303562	−	0.525786i	0.673378	−	0.739299i	$-0.264843\pi$
$293$	−5.19615	−	9.00000i	−0.303562	−	0.525786i	−0.976940	+	0.213513i	$0.931509\pi$
$294$	−0.232051	+	0.401924i	−0.0135335	+	0.0234407i
$295$	−6.46410			−0.376355
$296$	4.69615	−	3.86603i	0.272958	−	0.224708i
$297$	0.464102			0.0269299
$298$	−3.86603	+	6.69615i	−0.223953	+	0.387898i
$299$	15.9282	+	27.5885i	0.921152	+	1.59548i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	11.4641	+	19.8564i	0.660780	+	1.14450i
$302$	9.85641			0.567172
$303$	4.06218	+	7.03590i	0.233366	+	0.404202i
$304$	−3.46410			−0.198680
$305$	−2.83013	+	4.90192i	−0.162053	+	0.280683i
$306$	−7.73205			−0.442012
$307$	19.4641			1.11087			0.555437	−	0.831558i	$-0.312551\pi$
$307$	19.4641			1.11087			0.555437	+	0.831558i	$0.312551\pi$
$308$	0.633975	−	1.09808i	0.0361241	−	0.0625687i
$309$	3.83013	+	6.63397i	0.217888	+	0.377394i
$310$	3.46410			0.196748
$311$	2.09808	−	3.63397i	0.118971	−	0.206064i	−0.800389	−	0.599481i	$-0.795374\pi$
$311$	2.09808	−	3.63397i	0.118971	−	0.206064i	0.919360	+	0.393417i	$0.128707\pi$
$312$	−3.23205	+	5.59808i	−0.182979	+	0.316929i
$313$	1.19615	−	2.07180i	0.0676105	−	0.117105i	−0.830238	−	0.557408i	$-0.811796\pi$
$313$	1.19615	−	2.07180i	0.0676105	−	0.117105i	0.897849	+	0.440303i	$0.145129\pi$
$314$	−4.96410	−	8.59808i	−0.280140	−	0.485218i
$315$	−1.36603	−	2.36603i	−0.0769668	−	0.133310i
$316$	−2.00000	+	3.46410i	−0.112509	+	0.194871i
$317$	−8.83013	+	15.2942i	−0.495949	+	0.859009i	−0.999989	−	0.00467100i	$-0.998513\pi$
$317$	−8.83013	+	15.2942i	−0.495949	+	0.859009i	0.504040	+	0.863680i	$0.331847\pi$
$318$	3.36603	−	5.83013i	0.188757	−	0.326937i
$319$	−2.41154			−0.135020
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	1.63397	−	2.83013i	0.0911996	−	0.157962i
$322$	13.4641			0.750325
$323$	−26.7846			−1.49034
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	6.46410			0.358564
$326$	11.0622	+	19.1603i	0.612677	+	1.06119i
$327$	−0.339746			−0.0187880
$328$	5.36603	+	9.29423i	0.296289	+	0.513188i
$329$	−6.09808	−	10.5622i	−0.336198	−	0.582312i
$330$	0.232051	+	0.401924i	0.0127740	+	0.0221252i
$331$	8.36603	−	14.4904i	0.459838	−	0.796463i	−0.539114	−	0.842233i	$-0.681241\pi$
$331$	8.36603	−	14.4904i	0.459838	−	0.796463i	0.998952	+	0.0457696i	$0.0145740\pi$
$332$	−3.66025			−0.200883
$333$	−1.00000	−	6.00000i	−0.0547997	−	0.328798i
$334$	19.3923			1.06110
$335$	−3.86603	+	6.69615i	−0.211224	+	0.365850i
$336$	1.36603	+	2.36603i	0.0745228	+	0.129077i
$337$	10.9019	+	18.8827i	0.593866	+	1.02861i	0.993706	+	0.112021i	$0.0357323\pi$
$337$	10.9019	+	18.8827i	0.593866	+	1.02861i	−0.399840	+	0.916585i	$0.630934\pi$
$338$	14.3923	+	24.9282i	0.782838	+	1.35592i
$339$	−0.267949			−0.0145530
$340$	−3.86603	−	6.69615i	−0.209665	−	0.363150i
$341$	1.60770			0.0870616
$342$	−1.73205	+	3.00000i	−0.0936586	+	0.162221i
$343$	−17.8564			−0.964155
$344$	8.39230			0.452483
$345$	−2.46410	+	4.26795i	−0.132663	+	0.229779i
$346$	6.63397	+	11.4904i	0.356645	+	0.617727i
$347$	−16.9282			−0.908754			−0.454377	−	0.890810i	$-0.650138\pi$
$347$	−16.9282			−0.908754			−0.454377	+	0.890810i	$0.650138\pi$
$348$	2.59808	−	4.50000i	0.139272	−	0.241225i
$349$	−17.8564	+	30.9282i	−0.955832	+	1.65555i	−0.223378	+	0.974732i	$0.571708\pi$
$349$	−17.8564	+	30.9282i	−0.955832	+	1.65555i	−0.732454	+	0.680817i	$0.761625\pi$
$350$	1.36603	−	2.36603i	0.0730171	−	0.126469i
$351$	3.23205	+	5.59808i	0.172514	+	0.298803i
$352$	−0.232051	−	0.401924i	−0.0123683	−	0.0214226i
$353$	16.4641	−	28.5167i	0.876296	−	1.51779i	0.0209197	−	0.999781i	$-0.493341\pi$
$353$	16.4641	−	28.5167i	0.876296	−	1.51779i	0.855376	−	0.518008i	$-0.173326\pi$
$354$	3.23205	−	5.59808i	0.171782	−	0.297534i
$355$	3.36603	−	5.83013i	0.178650	−	0.309431i
$356$	3.46410			0.183597
$357$	10.5622	+	18.2942i	0.559010	+	0.968233i
$358$	9.92820	−	17.1962i	0.524722	−	0.908845i
$359$	2.39230			0.126261			0.0631305	−	0.998005i	$-0.479892\pi$
$359$	2.39230			0.126261			0.0631305	+	0.998005i	$0.479892\pi$
$360$	−1.00000			−0.0527046
$361$	3.50000	−	6.06218i	0.184211	−	0.319062i
$362$	−7.07180			−0.371685
$363$	−5.39230	−	9.33975i	−0.283023	−	0.490210i
$364$	17.6603			0.925649
$365$		0			0
$366$	−2.83013	−	4.90192i	−0.147933	−	0.256228i
$367$	−7.66025	−	13.2679i	−0.399862	−	0.692581i	0.593847	−	0.804578i	$-0.297609\pi$
$367$	−7.66025	−	13.2679i	−0.399862	−	0.692581i	−0.993709	+	0.111997i	$0.964275\pi$
$368$	2.46410	−	4.26795i	0.128450	−	0.222482i
$369$	10.7321			0.558688
$370$	4.69615	−	3.86603i	0.244141	−	0.200985i
$371$	−18.3923			−0.954881
$372$	−1.73205	+	3.00000i	−0.0898027	+	0.155543i
$373$	−18.7321	−	32.4449i	−0.969909	−	1.67993i	−0.695804	−	0.718231i	$-0.744952\pi$
$373$	−18.7321	−	32.4449i	−0.969909	−	1.67993i	−0.274105	−	0.961700i	$-0.588381\pi$
$374$	−1.79423	−	3.10770i	−0.0927774	−	0.160695i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−4.46410			−0.230218
$377$	−16.7942	−	29.0885i	−0.864947	−	1.49813i
$378$	2.73205			0.140522
$379$	5.90192	−	10.2224i	0.303161	−	0.525091i	−0.673689	−	0.739015i	$-0.735291\pi$
$379$	5.90192	−	10.2224i	0.303161	−	0.525091i	0.976850	+	0.213924i	$0.0686245\pi$
$380$	−3.46410			−0.177705
$381$	19.1244			0.979770
$382$	−1.43782	+	2.49038i	−0.0735654	+	0.127419i
$383$	−12.2321	−	21.1865i	−0.625029	−	1.08258i	−0.988535	−	0.150990i	$-0.951754\pi$
$383$	−12.2321	−	21.1865i	−0.625029	−	1.08258i	0.363507	−	0.931592i	$-0.381579\pi$
$384$	1.00000			0.0510310
$385$	0.633975	−	1.09808i	0.0323103	−	0.0559631i
$386$	−5.63397	+	9.75833i	−0.286762	+	0.496686i
$387$	4.19615	−	7.26795i	0.213302	−	0.369451i
$388$	2.46410	+	4.26795i	0.125096	+	0.216672i
$389$	10.2679	+	17.7846i	0.520606	+	0.901716i	0.999713	+	0.0239591i	$0.00762716\pi$
$389$	10.2679	+	17.7846i	0.520606	+	0.901716i	−0.479107	+	0.877756i	$0.659040\pi$
$390$	−3.23205	+	5.59808i	−0.163661	+	0.283470i
$391$	19.0526	−	33.0000i	0.963529	−	1.66888i
$392$	0.232051	−	0.401924i	0.0117203	−	0.0203002i
$393$	13.3923			0.675552
$394$	−4.26795	−	7.39230i	−0.215016	−	0.372419i
$395$	−2.00000	+	3.46410i	−0.100631	+	0.174298i
$396$	−0.464102			−0.0233220
$397$	−14.0718			−0.706243			−0.353122	−	0.935577i	$-0.614880\pi$
$397$	−14.0718			−0.706243			−0.353122	+	0.935577i	$0.614880\pi$
$398$	11.7942	−	20.4282i	0.591191	−	1.02397i
$399$	9.46410			0.473798
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	0.196152			0.00979538			0.00489769	−	0.999988i	$-0.498441\pi$
$401$	0.196152			0.00979538			0.00489769	+	0.999988i	$0.498441\pi$
$402$	−3.86603	−	6.69615i	−0.192820	−	0.333974i
$403$	11.1962	+	19.3923i	0.557720	+	0.966000i
$404$	−4.06218	−	7.03590i	−0.202101	−	0.350049i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	−14.1962			−0.704543
$407$	2.17949	−	1.79423i	0.108033	−	0.0889366i
$408$	7.73205			0.382794
$409$	−10.6244	+	18.4019i	−0.525341	+	0.909917i	0.474224	+	0.880404i	$0.342729\pi$
$409$	−10.6244	+	18.4019i	−0.525341	+	0.909917i	−0.999564	+	0.0295123i	$0.990605\pi$
$410$	5.36603	+	9.29423i	0.265009	+	0.459009i
$411$	−1.13397	−	1.96410i	−0.0559348	−	0.0968820i
$412$	−3.83013	−	6.63397i	−0.188697	−	0.326832i
$413$	−17.6603			−0.869004
$414$	−2.46410	−	4.26795i	−0.121104	−	0.209758i
$415$	−3.66025			−0.179675
$416$	3.23205	−	5.59808i	0.158464	−	0.274468i
$417$	−2.53590			−0.124183
$418$	−1.60770			−0.0786349
$419$	−15.0000	+	25.9808i	−0.732798	+	1.26924i	0.222885	+	0.974845i	$0.428453\pi$
$419$	−15.0000	+	25.9808i	−0.732798	+	1.26924i	−0.955683	+	0.294398i	$0.904881\pi$
$420$	1.36603	+	2.36603i	0.0666552	+	0.115450i
$421$	−40.1962			−1.95904			−0.979520	−	0.201345i	$-0.935469\pi$
$421$	−40.1962			−1.95904			−0.979520	+	0.201345i	$0.935469\pi$
$422$	1.26795	−	2.19615i	0.0617228	−	0.106907i
$423$	−2.23205	+	3.86603i	−0.108526	+	0.187973i
$424$	−3.36603	+	5.83013i	−0.163469	+	0.283136i
$425$	−3.86603	−	6.69615i	−0.187530	−	0.324811i
$426$	3.36603	+	5.83013i	0.163084	+	0.282471i
$427$	−7.73205	+	13.3923i	−0.374180	+	0.648099i
$428$	−1.63397	+	2.83013i	−0.0789811	+	0.136799i
$429$	−1.50000	+	2.59808i	−0.0724207	+	0.125436i
$430$	8.39230			0.404713
$431$	−5.56218	−	9.63397i	−0.267921	−	0.464052i	0.700404	−	0.713747i	$-0.253003\pi$
$431$	−5.56218	−	9.63397i	−0.267921	−	0.464052i	−0.968325	+	0.249694i	$0.919670\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−10.9282			−0.525176			−0.262588	−	0.964908i	$-0.584576\pi$
$433$	−10.9282			−0.525176			−0.262588	+	0.964908i	$0.584576\pi$
$434$	9.46410			0.454291
$435$	2.59808	−	4.50000i	0.124568	−	0.215758i
$436$	0.339746			0.0162709
$437$	−8.53590	−	14.7846i	−0.408327	−	0.707244i
$438$		0			0
$439$	19.9904	+	34.6244i	0.954089	+	1.65253i	0.736440	+	0.676503i	$0.236506\pi$
$439$	19.9904	+	34.6244i	0.954089	+	1.65253i	0.217649	+	0.976027i	$0.430161\pi$
$440$	−0.232051	−	0.401924i	−0.0110626	−	0.0191610i
$441$	−0.232051	−	0.401924i	−0.0110500	−	0.0191392i
$442$	24.9904	−	43.2846i	1.18867	−	2.05884i
$443$	29.8038			1.41602			0.708012	−	0.706201i	$-0.249592\pi$
$443$	29.8038			1.41602			0.708012	+	0.706201i	$0.249592\pi$
$444$	1.00000	+	6.00000i	0.0474579	+	0.284747i
$445$	3.46410			0.164214
$446$	−2.92820	+	5.07180i	−0.138654	+	0.240157i
$447$	−3.86603	−	6.69615i	−0.182857	−	0.316717i
$448$	−1.36603	−	2.36603i	−0.0645386	−	0.111784i
$449$	14.9282	+	25.8564i	0.704505	+	1.22024i	0.966870	+	0.255270i	$0.0821645\pi$
$449$	14.9282	+	25.8564i	0.704505	+	1.22024i	−0.262364	+	0.964969i	$0.584502\pi$
$450$	−1.00000			−0.0471405
$451$	2.49038	+	4.31347i	0.117267	+	0.203113i
$452$	0.267949			0.0126033
$453$	−4.92820	+	8.53590i	−0.231547	+	0.401051i
$454$	−1.80385			−0.0846588
$455$	17.6603			0.827925
$456$	1.73205	−	3.00000i	0.0811107	−	0.140488i
$457$	−8.19615	−	14.1962i	−0.383400	−	0.664068i	0.608146	−	0.793825i	$-0.291914\pi$
$457$	−8.19615	−	14.1962i	−0.383400	−	0.664068i	−0.991546	+	0.129757i	$0.958580\pi$
$458$	−15.8038			−0.738465
$459$	3.86603	−	6.69615i	0.180451	−	0.312550i
$460$	2.46410	−	4.26795i	0.114889	−	0.198994i
$461$	−10.5263	+	18.2321i	−0.490258	+	0.849151i	−0.999937	−	0.0112131i	$-0.996431\pi$
$461$	−10.5263	+	18.2321i	−0.490258	+	0.849151i	0.509679	+	0.860364i	$0.329764\pi$
$462$	0.633975	+	1.09808i	0.0294952	+	0.0510871i
$463$	−2.07180	−	3.58846i	−0.0962846	−	0.166770i	0.813859	−	0.581062i	$-0.197363\pi$
$463$	−2.07180	−	3.58846i	−0.0962846	−	0.166770i	−0.910144	+	0.414292i	$0.864029\pi$
$464$	−2.59808	+	4.50000i	−0.120613	+	0.208907i
$465$	−1.73205	+	3.00000i	−0.0803219	+	0.139122i
$466$	1.53590	−	2.66025i	0.0711491	−	0.123234i
$467$	11.4641			0.530495			0.265248	−	0.964180i	$-0.414546\pi$
$467$	11.4641			0.530495			0.265248	+	0.964180i	$0.414546\pi$
$468$	−3.23205	−	5.59808i	−0.149402	−	0.258771i
$469$	−10.5622	+	18.2942i	−0.487716	+	0.844749i
$470$	−4.46410			−0.205914
$471$	9.92820			0.457467
$472$	−3.23205	+	5.59808i	−0.148767	+	0.257672i
$473$	3.89488			0.179087
$474$	−2.00000	−	3.46410i	−0.0918630	−	0.159111i
$475$	−3.46410			−0.158944
$476$	−10.5622	−	18.2942i	−0.484117	−	0.838515i
$477$	3.36603	+	5.83013i	0.154120	+	0.266943i
$478$	7.26795	+	12.5885i	0.332428	+	0.575783i
$479$	19.0000	−	32.9090i	0.868132	−	1.50365i	0.00422900	−	0.999991i	$-0.498654\pi$
$479$	19.0000	−	32.9090i	0.868132	−	1.50365i	0.863903	−	0.503658i	$-0.168013\pi$
$480$	1.00000			0.0456435
$481$	36.8205	+	13.7942i	1.67887	+	0.628963i
$482$	−27.2487			−1.24114
$483$	−6.73205	+	11.6603i	−0.306319	+	0.530560i
$484$	5.39230	+	9.33975i	0.245105	+	0.424534i
$485$	2.46410	+	4.26795i	0.111889	+	0.193798i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	14.3923			0.652178			0.326089	−	0.945339i	$-0.394269\pi$
$487$	14.3923			0.652178			0.326089	+	0.945339i	$0.394269\pi$
$488$	2.83013	+	4.90192i	0.128114	+	0.221900i
$489$	−22.1244			−1.00050
$490$	0.232051	−	0.401924i	0.0104830	−	0.0181571i
$491$	25.7128			1.16040			0.580202	−	0.814473i	$-0.302974\pi$
$491$	25.7128			1.16040			0.580202	+	0.814473i	$0.302974\pi$
$492$	−10.7321			−0.483838
$493$	−20.0885	+	34.7942i	−0.904739	+	1.56705i
$494$	−11.1962	−	19.3923i	−0.503739	−	0.872501i
$495$	−0.464102			−0.0208598
$496$	1.73205	−	3.00000i	0.0777714	−	0.134704i
$497$	9.19615	−	15.9282i	0.412504	−	0.714478i
$498$	1.83013	−	3.16987i	0.0820100	−	0.142045i
$499$	9.09808	+	15.7583i	0.407286	+	0.705440i	0.994585	−	0.103931i	$-0.0331420\pi$
$499$	9.09808	+	15.7583i	0.407286	+	0.705440i	−0.587299	+	0.809370i	$0.699809\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−9.69615	+	16.7942i	−0.433192	+	0.750311i
$502$	3.23205	−	5.59808i	0.144253	−	0.249854i
$503$	−19.6244	+	33.9904i	−0.875007	+	1.51556i	−0.0182512	+	0.999833i	$0.505810\pi$
$503$	−19.6244	+	33.9904i	−0.875007	+	1.51556i	−0.856756	+	0.515723i	$0.827523\pi$
$504$	−2.73205			−0.121695
$505$	−4.06218	−	7.03590i	−0.180765	−	0.313093i
$506$	1.14359	−	1.98076i	0.0508389	−	0.0880556i
$507$	−28.7846			−1.27837
$508$	−19.1244			−0.848506
$509$	−16.3923	+	28.3923i	−0.726576	+	1.25847i	0.231746	+	0.972776i	$0.425556\pi$
$509$	−16.3923	+	28.3923i	−0.726576	+	1.25847i	−0.958322	+	0.285690i	$0.907777\pi$
$510$	7.73205			0.342381
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−1.73205	−	3.00000i	−0.0764719	−	0.132453i
$514$	7.06218	+	12.2321i	0.311499	+	0.539533i
$515$	−3.83013	−	6.63397i	−0.168776	−	0.292328i
$516$	−4.19615	+	7.26795i	−0.184725	+	0.319954i
$517$	−2.07180			−0.0911175
$518$	12.8301	−	10.5622i	0.563723	−	0.464075i
$519$	−13.2679			−0.582398
$520$	3.23205	−	5.59808i	0.141735	−	0.245492i
$521$	−22.1962	−	38.4449i	−0.972431	−	1.68430i	−0.688164	−	0.725555i	$-0.741583\pi$
$521$	−22.1962	−	38.4449i	−0.972431	−	1.68430i	−0.284267	−	0.958745i	$-0.591750\pi$
$522$	2.59808	+	4.50000i	0.113715	+	0.196960i
$523$	3.66025	+	6.33975i	0.160052	+	0.277218i	0.934887	−	0.354945i	$-0.115501\pi$
$523$	3.66025	+	6.33975i	0.160052	+	0.277218i	−0.774835	+	0.632163i	$0.782167\pi$
$524$	−13.3923			−0.585046
$525$	1.36603	+	2.36603i	0.0596182	+	0.103262i
$526$	−30.3923			−1.32517
$527$	13.3923	−	23.1962i	0.583378	−	1.01044i
$528$	0.464102			0.0201974
$529$	1.28719			0.0559647
$530$	−3.36603	+	5.83013i	−0.146211	+	0.253245i
$531$	3.23205	+	5.59808i	0.140259	+	0.242936i
$532$	−9.46410			−0.410321
$533$	−34.6865	+	60.0788i	−1.50244	+	2.60230i
$534$	−1.73205	+	3.00000i	−0.0749532	+	0.129823i
$535$	−1.63397	+	2.83013i	−0.0706429	+	0.122357i
$536$	3.86603	+	6.69615i	0.166987	+	0.289230i
$537$	9.92820	+	17.1962i	0.428434	+	0.742069i
$538$	12.6603	−	21.9282i	0.545822	−	0.945392i
$539$	0.107695	−	0.186533i	0.00463876	−	0.00803457i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	−30.0526			−1.29206			−0.646030	−	0.763312i	$-0.723572\pi$
$541$	−30.0526			−1.29206			−0.646030	+	0.763312i	$0.723572\pi$
$542$	−2.06218	−	3.57180i	−0.0885781	−	0.153422i
$543$	3.53590	−	6.12436i	0.151740	−	0.262821i
$544$	−7.73205			−0.331509
$545$	0.339746			0.0145531
$546$	−8.83013	+	15.2942i	−0.377895	+	0.654533i
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$	1.13397	+	1.96410i	0.0484410	+	0.0839023i
$549$	5.66025			0.241574
$550$	−0.232051	−	0.401924i	−0.00989468	−	0.0171381i
$551$	9.00000	+	15.5885i	0.383413	+	0.664091i
$552$	2.46410	+	4.26795i	0.104879	+	0.181656i
$553$	−5.46410	+	9.46410i	−0.232357	+	0.402455i
$554$	−20.8564			−0.886104
$555$	1.00000	+	6.00000i	0.0424476	+	0.254686i
$556$	2.53590			0.107546
$557$	−6.07180	+	10.5167i	−0.257270	+	0.445605i	−0.965510	−	0.260367i	$-0.916156\pi$
$557$	−6.07180	+	10.5167i	−0.257270	+	0.445605i	0.708239	+	0.705972i	$0.249490\pi$
$558$	−1.73205	−	3.00000i	−0.0733236	−	0.127000i
$559$	27.1244	+	46.9808i	1.14724	+	1.98707i
$560$	−1.36603	−	2.36603i	−0.0577251	−	0.0999828i
$561$	3.58846			0.151505
$562$	−2.66025	−	4.60770i	−0.112216	−	0.194364i
$563$	−2.33975			−0.0986085			−0.0493043	−	0.998784i	$-0.515700\pi$
$563$	−2.33975			−0.0986085			−0.0493043	+	0.998784i	$0.515700\pi$
$564$	2.23205	−	3.86603i	0.0939863	−	0.162789i
$565$	0.267949			0.0112727
$566$	12.2679			0.515660
$567$	−1.36603	+	2.36603i	−0.0573677	+	0.0993637i
$568$	−3.36603	−	5.83013i	−0.141235	−	0.244627i
$569$	0.196152			0.00822314			0.00411157	−	0.999992i	$-0.498691\pi$
$569$	0.196152			0.00822314			0.00411157	+	0.999992i	$0.498691\pi$
$570$	1.73205	−	3.00000i	0.0725476	−	0.125656i
$571$	−4.46410	+	7.73205i	−0.186817	+	0.323576i	−0.944187	−	0.329409i	$-0.893150\pi$
$571$	−4.46410	+	7.73205i	−0.186817	+	0.323576i	0.757370	+	0.652986i	$0.226484\pi$
$572$	1.50000	−	2.59808i	0.0627182	−	0.108631i
$573$	−1.43782	−	2.49038i	−0.0600659	−	0.104037i
$574$	14.6603	+	25.3923i	0.611907	+	1.05985i
$575$	2.46410	−	4.26795i	0.102760	−	0.177986i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−15.7583	+	27.2942i	−0.656028	+	1.13627i	0.325607	+	0.945505i	$0.394431\pi$
$577$	−15.7583	+	27.2942i	−0.656028	+	1.13627i	−0.981635	+	0.190768i	$0.938902\pi$
$578$	−42.7846			−1.77961
$579$	−5.63397	−	9.75833i	−0.234140	−	0.405542i
$580$	−2.59808	+	4.50000i	−0.107879	+	0.186852i
$581$	−10.0000			−0.414870
$582$	−4.92820			−0.204281
$583$	−1.56218	+	2.70577i	−0.0646988	+	0.112062i
$584$		0			0
$585$	−3.23205	−	5.59808i	−0.133629	−	0.231452i
$586$	−10.3923			−0.429302
$587$	14.7583	+	25.5622i	0.609141	+	1.05506i	0.991382	+	0.131001i	$0.0418192\pi$
$587$	14.7583	+	25.5622i	0.609141	+	1.05506i	−0.382241	+	0.924063i	$0.624847\pi$
$588$	0.232051	+	0.401924i	0.00956961	+	0.0165751i
$589$	−6.00000	−	10.3923i	−0.247226	−	0.428207i
$590$	−3.23205	+	5.59808i	−0.133061	+	0.230469i
$591$	8.53590			0.351120
$592$	−1.00000	−	6.00000i	−0.0410997	−	0.246598i
$593$	−15.3397			−0.629928			−0.314964	−	0.949104i	$-0.601992\pi$
$593$	−15.3397			−0.629928			−0.314964	+	0.949104i	$0.601992\pi$
$594$	0.232051	−	0.401924i	0.00952116	−	0.0164911i
$595$	−10.5622	−	18.2942i	−0.433007	−	0.749990i
$596$	3.86603	+	6.69615i	0.158359	+	0.274285i
$597$	11.7942	+	20.4282i	0.482706	+	0.836071i
$598$	31.8564			1.30271
$599$	−17.8301	−	30.8827i	−0.728519	−	1.26183i	−0.957509	−	0.288403i	$-0.906876\pi$
$599$	−17.8301	−	30.8827i	−0.728519	−	1.26183i	0.228990	−	0.973429i	$-0.426458\pi$
$600$	1.00000			0.0408248
$601$	−4.96410	+	8.59808i	−0.202490	+	0.350723i	−0.949330	−	0.314281i	$-0.898237\pi$
$601$	−4.96410	+	8.59808i	−0.202490	+	0.350723i	0.746840	+	0.665004i	$0.231570\pi$
$602$	22.9282			0.934484
$603$	7.73205			0.314873
$604$	4.92820	−	8.53590i	0.200526	−	0.347321i
$605$	5.39230	+	9.33975i	0.219228	+	0.379715i
$606$	8.12436			0.330029
$607$	21.7846	−	37.7321i	0.884210	−	1.53150i	0.0375936	−	0.999293i	$-0.488031\pi$
$607$	21.7846	−	37.7321i	0.884210	−	1.53150i	0.846616	−	0.532204i	$-0.178636\pi$
$608$	−1.73205	+	3.00000i	−0.0702439	+	0.121666i
$609$	7.09808	−	12.2942i	0.287629	−	0.498187i
$610$	2.83013	+	4.90192i	0.114588	+	0.198473i
$611$	−14.4282	−	24.9904i	−0.583703	−	1.01100i
$612$	−3.86603	+	6.69615i	−0.156275	+	0.270676i
$613$	−0.892305	+	1.54552i	−0.0360399	+	0.0624229i	−0.883483	−	0.468464i	$-0.844808\pi$
$613$	−0.892305	+	1.54552i	−0.0360399	+	0.0624229i	0.847443	+	0.530887i	$0.178141\pi$
$614$	9.73205	−	16.8564i	0.392754	−	0.680269i
$615$	−10.7321			−0.432758
$616$	−0.633975	−	1.09808i	−0.0255436	−	0.0442428i
$617$	−10.7942	+	18.6962i	−0.434559	+	0.752679i	−0.997260	−	0.0739822i	$-0.976429\pi$
$617$	−10.7942	+	18.6962i	−0.434559	+	0.752679i	0.562700	+	0.826661i	$0.309763\pi$
$618$	7.66025			0.308141
$619$	−26.7321			−1.07445			−0.537226	−	0.843438i	$-0.680528\pi$
$619$	−26.7321			−1.07445			−0.537226	+	0.843438i	$0.680528\pi$
$620$	1.73205	−	3.00000i	0.0695608	−	0.120483i
$621$	4.92820			0.197762
$622$	−2.09808	−	3.63397i	−0.0841252	−	0.145709i
$623$	9.46410			0.379171
$624$	3.23205	+	5.59808i	0.129386	+	0.224102i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.19615	−	2.07180i	−0.0478079	−	0.0828057i
$627$	0.803848	−	1.39230i	0.0321026	−	0.0556033i
$628$	−9.92820			−0.396178
$629$	−7.73205	−	46.3923i	−0.308297	−	1.84978i
$630$	−2.73205			−0.108848
$631$	−1.59808	+	2.76795i	−0.0636184	+	0.110190i	−0.896080	−	0.443892i	$-0.853597\pi$
$631$	−1.59808	+	2.76795i	−0.0636184	+	0.110190i	0.832462	+	0.554082i	$0.186931\pi$
$632$	2.00000	+	3.46410i	0.0795557	+	0.137795i
$633$	1.26795	+	2.19615i	0.0503965	+	0.0872892i
$634$	8.83013	+	15.2942i	0.350689	+	0.607411i
$635$	−19.1244			−0.758927
$636$	−3.36603	−	5.83013i	−0.133472	−	0.231180i
$637$	3.00000			0.118864
$638$	−1.20577	+	2.08846i	−0.0477369	+	0.0826828i
$639$	−6.73205			−0.266316
$640$	−1.00000			−0.0395285
$641$	−20.0263	+	34.6865i	−0.790990	+	1.37004i	0.134364	+	0.990932i	$0.457101\pi$
$641$	−20.0263	+	34.6865i	−0.790990	+	1.37004i	−0.925354	+	0.379104i	$0.876232\pi$
$642$	−1.63397	−	2.83013i	−0.0644878	−	0.111696i
$643$	−22.1244			−0.872499			−0.436250	−	0.899826i	$-0.643694\pi$
$643$	−22.1244			−0.872499			−0.436250	+	0.899826i	$0.643694\pi$
$644$	6.73205	−	11.6603i	0.265280	−	0.459478i
$645$	−4.19615	+	7.26795i	−0.165223	+	0.286175i
$646$	−13.3923	+	23.1962i	−0.526913	+	0.912640i
$647$	4.83975	+	8.38269i	0.190270	+	0.329557i	0.945340	−	0.326087i	$-0.105730\pi$
$647$	4.83975	+	8.38269i	0.190270	+	0.329557i	−0.755070	+	0.655645i	$0.772397\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−1.50000	+	2.59808i	−0.0588802	+	0.101983i
$650$	3.23205	−	5.59808i	0.126771	−	0.219575i
$651$	−4.73205	+	8.19615i	−0.185464	+	0.321233i
$652$	22.1244			0.866457
$653$	7.26795	+	12.5885i	0.284417	+	0.492624i	0.972468	−	0.233038i	$-0.0748667\pi$
$653$	7.26795	+	12.5885i	0.284417	+	0.492624i	−0.688051	+	0.725663i	$0.741533\pi$
$654$	−0.169873	+	0.294229i	−0.00664256	+	0.0115053i
$655$	−13.3923			−0.523281
$656$	10.7321			0.419016
$657$		0			0
$658$	−12.1962			−0.475456
$659$	−14.3038	−	24.7750i	−0.557199	−	0.965097i	−0.997729	−	0.0673587i	$-0.978543\pi$
$659$	−14.3038	−	24.7750i	−0.557199	−	0.965097i	0.440530	−	0.897738i	$-0.354791\pi$
$660$	0.464102			0.0180651
$661$	16.1962	+	28.0526i	0.629957	+	1.09112i	0.987560	+	0.157244i	$0.0502610\pi$
$661$	16.1962	+	28.0526i	0.629957	+	1.09112i	−0.357602	+	0.933874i	$0.616406\pi$
$662$	−8.36603	−	14.4904i	−0.325155	−	0.563185i
$663$	24.9904	+	43.2846i	0.970546	+	1.68103i
$664$	−1.83013	+	3.16987i	−0.0710227	+	0.123015i
$665$	−9.46410			−0.367002
$666$	−5.69615	−	2.13397i	−0.220721	−	0.0826898i
$667$	−25.6077			−0.991534
$668$	9.69615	−	16.7942i	0.375155	−	0.649788i
$669$	−2.92820	−	5.07180i	−0.113211	−	0.196087i
$670$	3.86603	+	6.69615i	0.149358	+	0.258695i
$671$	1.31347	+	2.27499i	0.0507058	+	0.0878250i
$672$	2.73205			0.105391
$673$	−24.9545	−	43.2224i	−0.961925	−	1.66610i	−0.717660	−	0.696394i	$-0.754787\pi$
$673$	−24.9545	−	43.2224i	−0.961925	−	1.66610i	−0.244265	−	0.969709i	$-0.578547\pi$
$674$	21.8038			0.839853
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	28.7846			1.10710
$677$	11.2679			0.433062			0.216531	−	0.976276i	$-0.430526\pi$
$677$	11.2679			0.433062			0.216531	+	0.976276i	$0.430526\pi$
$678$	−0.133975	+	0.232051i	−0.00514526	+	0.00891186i
$679$	6.73205	+	11.6603i	0.258352	+	0.447479i
$680$	−7.73205			−0.296511
$681$	0.901924	−	1.56218i	0.0345618	−	0.0598628i
$682$	0.803848	−	1.39230i	0.0307809	−	0.0533141i
$683$	−8.26795	+	14.3205i	−0.316364	+	0.547959i	−0.979727	−	0.200339i	$-0.935796\pi$
$683$	−8.26795	+	14.3205i	−0.316364	+	0.547959i	0.663362	+	0.748298i	$0.269129\pi$
$684$	1.73205	+	3.00000i	0.0662266	+	0.114708i
$685$	1.13397	+	1.96410i	0.0433269	+	0.0750445i
$686$	−8.92820	+	15.4641i	−0.340880	+	0.590422i
$687$	7.90192	−	13.6865i	0.301477	−	0.522174i
$688$	4.19615	−	7.26795i	0.159977	−	0.277088i
$689$	−43.5167			−1.65785
$690$	2.46410	+	4.26795i	0.0938067	+	0.162478i
$691$	5.33975	−	9.24871i	0.203134	−	0.351838i	−0.746403	−	0.665494i	$-0.768221\pi$
$691$	5.33975	−	9.24871i	0.203134	−	0.351838i	0.949536	+	0.313657i	$0.101554\pi$
$692$	13.2679			0.504372
$693$	−1.26795			−0.0481654
$694$	−8.46410	+	14.6603i	−0.321293	+	0.556496i
$695$	2.53590			0.0961921
$696$	−2.59808	−	4.50000i	−0.0984798	−	0.170572i
$697$	82.9808			3.14312
$698$	17.8564	+	30.9282i	0.675875	+	1.17065i
$699$	1.53590	+	2.66025i	0.0580930	+	0.100620i
$700$	−1.36603	−	2.36603i	−0.0516309	−	0.0894274i
$701$	−12.2583	+	21.2321i	−0.462991	+	0.801923i	−0.999108	−	0.0422198i	$-0.986557\pi$
$701$	−12.2583	+	21.2321i	−0.462991	+	0.801923i	0.536118	+	0.844143i	$0.319890\pi$
$702$	6.46410			0.243972
$703$	−19.7321	−	7.39230i	−0.744208	−	0.278806i
$704$	−0.464102			−0.0174915
$705$	2.23205	−	3.86603i	0.0840639	−	0.145603i
$706$	−16.4641	−	28.5167i	−0.619635	−	1.07324i
$707$	−11.0981	−	19.2224i	−0.417386	−	0.722934i
$708$	−3.23205	−	5.59808i	−0.121468	−	0.210389i
$709$	−2.73205			−0.102604			−0.0513022	−	0.998683i	$-0.516337\pi$
$709$	−2.73205			−0.102604			−0.0513022	+	0.998683i	$0.516337\pi$
$710$	−3.36603	−	5.83013i	−0.126325	−	0.218801i
$711$	4.00000			0.150012
$712$	1.73205	−	3.00000i	0.0649113	−	0.112430i
$713$	17.0718			0.639344
$714$	21.1244			0.790559
$715$	1.50000	−	2.59808i	0.0560968	−	0.0971625i
$716$	−9.92820	−	17.1962i	−0.371034	−	0.642650i
$717$	−14.5359			−0.542853
$718$	1.19615	−	2.07180i	0.0446400	−	0.0773188i
$719$	−16.5622	+	28.6865i	−0.617665	+	1.06983i	0.372246	+	0.928134i	$0.378588\pi$
$719$	−16.5622	+	28.6865i	−0.617665	+	1.06983i	−0.989911	+	0.141693i	$0.954745\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$	−10.4641	−	18.1244i	−0.389704	−	0.674986i
$722$	−3.50000	−	6.06218i	−0.130257	−	0.225611i
$723$	13.6244	−	23.5981i	0.506695	−	0.877622i
$724$	−3.53590	+	6.12436i	−0.131411	+	0.227610i
$725$	−2.59808	+	4.50000i	−0.0964901	+	0.167126i
$726$	−10.7846			−0.400254
$727$	−7.66025	−	13.2679i	−0.284103	−	0.492081i	0.688288	−	0.725437i	$-0.258362\pi$
$727$	−7.66025	−	13.2679i	−0.284103	−	0.492081i	−0.972391	+	0.233356i	$0.925029\pi$
$728$	8.83013	−	15.2942i	0.327266	−	0.566842i
$729$	1.00000			0.0370370
$730$		0			0
$731$	32.4449	−	56.1962i	1.20002	−	2.07849i
$732$	−5.66025			−0.209209
$733$	18.5526	+	32.1340i	0.685254	+	1.18690i	0.973357	+	0.229296i	$0.0736423\pi$
$733$	18.5526	+	32.1340i	0.685254	+	1.18690i	−0.288102	+	0.957600i	$0.593024\pi$
$734$	−15.3205			−0.565490
$735$	0.232051	+	0.401924i	0.00855932	+	0.0148252i
$736$	−2.46410	−	4.26795i	−0.0908280	−	0.157319i
$737$	1.79423	+	3.10770i	0.0660913	+	0.114473i
$738$	5.36603	−	9.29423i	0.197526	−	0.342125i
$739$	−20.5359			−0.755425			−0.377713	−	0.925923i	$-0.623289\pi$
$739$	−20.5359			−0.755425			−0.377713	+	0.925923i	$0.623289\pi$
$740$	−1.00000	−	6.00000i	−0.0367607	−	0.220564i
$741$	22.3923			0.822602
$742$	−9.19615	+	15.9282i	−0.337601	+	0.584743i
$743$	−23.0885	−	39.9904i	−0.847033	−	1.46710i	−0.883844	−	0.467783i	$-0.845053\pi$
$743$	−23.0885	−	39.9904i	−0.847033	−	1.46710i	0.0368103	−	0.999322i	$-0.488280\pi$
$744$	1.73205	+	3.00000i	0.0635001	+	0.109985i
$745$	3.86603	+	6.69615i	0.141640	+	0.245328i
$746$	−37.4641			−1.37166
$747$	1.83013	+	3.16987i	0.0669608	+	0.115980i
$748$	−3.58846			−0.131207
$749$	−4.46410	+	7.73205i	−0.163115	+	0.282523i
$750$	1.00000			0.0365148
$751$	27.0526			0.987162			0.493581	−	0.869700i	$-0.335688\pi$
$751$	27.0526			0.987162			0.493581	+	0.869700i	$0.335688\pi$
$752$	−2.23205	+	3.86603i	−0.0813945	+	0.140979i
$753$	3.23205	+	5.59808i	0.117782	+	0.204005i
$754$	−33.5885			−1.22322
$755$	4.92820	−	8.53590i	0.179356	−	0.310653i
$756$	1.36603	−	2.36603i	0.0496819	−	0.0860515i
$757$	13.0000	−	22.5167i	0.472493	−	0.818382i	−0.527011	−	0.849858i	$-0.676688\pi$
$757$	13.0000	−	22.5167i	0.472493	−	0.818382i	0.999505	+	0.0314762i	$0.0100208\pi$
$758$	−5.90192	−	10.2224i	−0.214368	−	0.371295i
$759$	1.14359	+	1.98076i	0.0415098	+	0.0718971i
$760$	−1.73205	+	3.00000i	−0.0628281	+	0.108821i
$761$	−4.22243	+	7.31347i	−0.153063	+	0.265113i	−0.932352	−	0.361552i	$-0.882247\pi$
$761$	−4.22243	+	7.31347i	−0.153063	+	0.265113i	0.779289	+	0.626665i	$0.215580\pi$
$762$	9.56218	−	16.5622i	0.346401	−	0.599984i
$763$	0.928203			0.0336032
$764$	1.43782	+	2.49038i	0.0520186	+	0.0900988i
$765$	−3.86603	+	6.69615i	−0.139776	+	0.242100i
$766$	−24.4641			−0.883924
$767$	−41.7846			−1.50875
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	37.5359			1.35358			0.676790	−	0.736177i	$-0.263371\pi$
$769$	37.5359			1.35358			0.676790	+	0.736177i	$0.263371\pi$
$770$	−0.633975	−	1.09808i	−0.0228469	−	0.0395719i
$771$	−14.1244			−0.508676
$772$	5.63397	+	9.75833i	0.202771	+	0.351210i
$773$	−0.0980762	−	0.169873i	−0.00352756	−	0.00610991i	0.864256	−	0.503052i	$-0.167790\pi$
$773$	−0.0980762	−	0.169873i	−0.00352756	−	0.00610991i	−0.867784	+	0.496942i	$0.834456\pi$
$774$	−4.19615	−	7.26795i	−0.150828	−	0.261241i
$775$	1.73205	−	3.00000i	0.0622171	−	0.107763i
$776$	4.92820			0.176912
$777$	2.73205	+	16.3923i	0.0980118	+	0.588071i
$778$	20.5359			0.736248
$779$	18.5885	−	32.1962i	0.666001	−	1.15355i
$780$	3.23205	+	5.59808i	0.115726	+	0.200443i
$781$	−1.56218	−	2.70577i	−0.0558991	−	0.0968201i
$782$	−19.0526	−	33.0000i	−0.681318	−	1.18008i
$783$	−5.19615			−0.185695
$784$	−0.232051	−	0.401924i	−0.00828753	−	0.0143544i
$785$	−9.92820			−0.354353
$786$	6.69615	−	11.5981i	0.238844	−	0.413690i
$787$	18.5167			0.660048			0.330024	−	0.943973i	$-0.392943\pi$
$787$	18.5167			0.660048			0.330024	+	0.943973i	$0.392943\pi$
$788$	−8.53590			−0.304079
$789$	15.1962	−	26.3205i	0.540997	−	0.937035i
$790$	2.00000	+	3.46410i	0.0711568	+	0.123247i
$791$	0.732051			0.0260287
$792$	−0.232051	+	0.401924i	−0.00824557	+	0.0142817i
$793$	−18.2942	+	31.6865i	−0.649647	+	1.12522i
$794$	−7.03590	+	12.1865i	−0.249695	+	0.432484i
$795$	−3.36603	−	5.83013i	−0.119381	−	0.206773i
$796$	−11.7942	−	20.4282i	−0.418035	−	0.724058i
$797$	10.9282	−	18.9282i	0.387097	−	0.670471i	−0.604961	−	0.796255i	$-0.706811\pi$
$797$	10.9282	−	18.9282i	0.387097	−	0.670471i	0.992058	+	0.125784i	$0.0401446\pi$
$798$	4.73205	−	8.19615i	0.167513	−	0.290141i
$799$	−17.2583	+	29.8923i	−0.610556	+	1.05751i
$800$	−1.00000			−0.0353553
$801$	−1.73205	−	3.00000i	−0.0611990	−	0.106000i
$802$	0.0980762	−	0.169873i	0.00346319	−	0.00599842i
$803$		0			0
$804$	−7.73205			−0.272688
$805$	6.73205	−	11.6603i	0.237274	−	0.410970i
$806$	22.3923			0.788735
$807$	12.6603	+	21.9282i	0.445662	+	0.771909i
$808$	−8.12436			−0.285814
$809$	−23.5885	−	40.8564i	−0.829326	−	1.43643i	−0.898568	−	0.438835i	$-0.855391\pi$
$809$	−23.5885	−	40.8564i	−0.829326	−	1.43643i	0.0692417	−	0.997600i	$-0.477942\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	21.6865	+	37.5622i	0.761517	+	1.31899i	0.942068	+	0.335421i	$0.108879\pi$
$811$	21.6865	+	37.5622i	0.761517	+	1.31899i	−0.180551	+	0.983566i	$0.557788\pi$
$812$	−7.09808	+	12.2942i	−0.249094	+	0.431443i
$813$	4.12436			0.144647
$814$	−0.464102	−	2.78461i	−0.0162668	−	0.0976005i
$815$	22.1244			0.774982
$816$	3.86603	−	6.69615i	0.135338	−	0.234412i
$817$	−14.5359	−	25.1769i	−0.508547	−	0.880829i
$818$	10.6244	+	18.4019i	0.371472	+	0.643408i
$819$	−8.83013	−	15.2942i	−0.308550	−	0.534424i
$820$	10.7321			0.374779
$821$	−2.79423	−	4.83975i	−0.0975193	−	0.168908i	0.813138	−	0.582071i	$-0.197757\pi$
$821$	−2.79423	−	4.83975i	−0.0975193	−	0.168908i	−0.910657	+	0.413163i	$0.864424\pi$
$822$	−2.26795			−0.0791038
$823$	−5.70577	+	9.88269i	−0.198891	+	0.344489i	−0.948169	−	0.317766i	$-0.897067\pi$
$823$	−5.70577	+	9.88269i	−0.198891	+	0.344489i	0.749278	+	0.662255i	$0.230401\pi$
$824$	−7.66025			−0.266858
$825$	0.464102			0.0161579
$826$	−8.83013	+	15.2942i	−0.307239	+	0.532154i
$827$	−19.7846	−	34.2679i	−0.687978	−	1.19161i	−0.972491	−	0.232941i	$-0.925165\pi$
$827$	−19.7846	−	34.2679i	−0.687978	−	1.19161i	0.284513	−	0.958672i	$-0.408168\pi$
$828$	−4.92820			−0.171267
$829$	23.8301	−	41.2750i	0.827655	−	1.43354i	−0.0722190	−	0.997389i	$-0.523008\pi$
$829$	23.8301	−	41.2750i	0.827655	−	1.43354i	0.899874	−	0.436151i	$-0.143659\pi$
$830$	−1.83013	+	3.16987i	−0.0635246	+	0.110028i
$831$	10.4282	−	18.0622i	0.361750	−	0.626570i
$832$	−3.23205	−	5.59808i	−0.112051	−	0.194078i
$833$	−1.79423	−	3.10770i	−0.0621663	−	0.107675i
$834$	−1.26795	+	2.19615i	−0.0439055	+	0.0760465i
$835$	9.69615	−	16.7942i	0.335549	−	0.581188i
$836$	−0.803848	+	1.39230i	−0.0278016	+	0.0481539i
$837$	3.46410			0.119737
$838$	15.0000	+	25.9808i	0.518166	+	0.897491i
$839$	14.8301	−	25.6865i	0.511993	−	0.886798i	−0.487910	−	0.872894i	$-0.662241\pi$
$839$	14.8301	−	25.6865i	0.511993	−	0.886798i	0.999903	−	0.0139040i	$-0.00442591\pi$
$840$	2.73205			0.0942647
$841$	−2.00000			−0.0689655
$842$	−20.0981	+	34.8109i	−0.692625	+	1.19966i
$843$	5.32051			0.183248
$844$	−1.26795	−	2.19615i	−0.0436446	−	0.0755947i
$845$	28.7846			0.990221
$846$	2.23205	+	3.86603i	0.0767395	+	0.132917i
$847$	14.7321	+	25.5167i	0.506199	+	0.876763i
$848$	3.36603	+	5.83013i	0.115590	+	0.200207i
$849$	−6.13397	+	10.6244i	−0.210517	+	0.364627i
$850$	−7.73205			−0.265207
$851$	23.1436	−	19.0526i	0.793352	−	0.653113i
$852$	6.73205			0.230636
$853$	13.6962	−	23.7224i	0.468947	−	0.812241i	−0.530423	−	0.847733i	$-0.677967\pi$
$853$	13.6962	−	23.7224i	0.468947	−	0.812241i	0.999370	+	0.0354928i	$0.0113001\pi$
$854$	7.73205	+	13.3923i	0.264585	+	0.458275i
$855$	1.73205	+	3.00000i	0.0592349	+	0.102598i
$856$	1.63397	+	2.83013i	0.0558481	+	0.0967318i
$857$	17.8756			0.610620			0.305310	−	0.952253i	$-0.401240\pi$
$857$	17.8756			0.610620			0.305310	+	0.952253i	$0.401240\pi$
$858$	1.50000	+	2.59808i	0.0512092	+	0.0886969i
$859$	−1.94744			−0.0664458			−0.0332229	−	0.999448i	$-0.510577\pi$
$859$	−1.94744			−0.0664458			−0.0332229	+	0.999448i	$0.510577\pi$
$860$	4.19615	−	7.26795i	0.143088	−	0.247835i
$861$	−29.3205			−0.999240
$862$	−11.1244			−0.378897
$863$	22.1603	−	38.3827i	0.754344	−	1.30656i	−0.191356	−	0.981521i	$-0.561289\pi$
$863$	22.1603	−	38.3827i	0.754344	−	1.30656i	0.945700	−	0.325041i	$-0.105378\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	13.2679			0.451124
$866$	−5.46410	+	9.46410i	−0.185678	+	0.321603i
$867$	21.3923	−	37.0526i	0.726521	−	1.25837i
$868$	4.73205	−	8.19615i	0.160616	−	0.278196i
$869$	0.928203	+	1.60770i	0.0314871	+	0.0545373i
$870$	−2.59808	−	4.50000i	−0.0880830	−	0.152564i
$871$	−24.9904	+	43.2846i	−0.846767	+	1.46664i
$872$	0.169873	−	0.294229i	0.00575263	−	0.00996384i
$873$	2.46410	−	4.26795i	0.0833972	−	0.144448i
$874$	−17.0718			−0.577462
$875$	−1.36603	−	2.36603i	−0.0461801	−	0.0799863i
$876$		0			0
$877$	−10.2154			−0.344949			−0.172475	−	0.985014i	$-0.555176\pi$
$877$	−10.2154			−0.344949			−0.172475	+	0.985014i	$0.555176\pi$
$878$	39.9808			1.34929
$879$	5.19615	−	9.00000i	0.175262	−	0.303562i
$880$	−0.464102			−0.0156449
$881$	−16.3923	−	28.3923i	−0.552271	−	0.956561i	−0.998110	−	0.0614481i	$-0.980428\pi$
$881$	−16.3923	−	28.3923i	−0.552271	−	0.956561i	0.445839	−	0.895113i	$-0.352905\pi$
$882$	−0.464102			−0.0156271
$883$	14.9904	+	25.9641i	0.504466	+	0.873762i	0.999987	+	0.00516516i	$0.00164413\pi$
$883$	14.9904	+	25.9641i	0.504466	+	0.873762i	−0.495520	+	0.868596i	$0.665023\pi$
$884$	−24.9904	−	43.2846i	−0.840517	−	1.45582i
$885$	−3.23205	−	5.59808i	−0.108644	−	0.188177i
$886$	14.9019	−	25.8109i	0.500640	−	0.867134i
$887$	9.21539			0.309423			0.154711	−	0.987960i	$-0.450555\pi$
$887$	9.21539			0.309423			0.154711	+	0.987960i	$0.450555\pi$
$888$	5.69615	+	2.13397i	0.191150	+	0.0716115i
$889$	−52.2487			−1.75237
$890$	1.73205	−	3.00000i	0.0580585	−	0.100560i
$891$	0.232051	+	0.401924i	0.00777399	+	0.0134650i
$892$	2.92820	+	5.07180i	0.0980435	+	0.169816i
$893$	7.73205	+	13.3923i	0.258743	+	0.448156i
$894$	−7.73205			−0.258598
$895$	−9.92820	−	17.1962i	−0.331863	−	0.574804i
$896$	−2.73205			−0.0912714
$897$	−15.9282	+	27.5885i	−0.531827	+	0.921152i
$898$	29.8564			0.996321
$899$	−18.0000			−0.600334
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	26.0263	+	45.0788i	0.867061	+	1.50179i
$902$	4.98076			0.165841
$903$	−11.4641	+	19.8564i	−0.381501	+	0.660780i
$904$	0.133975	−	0.232051i	0.00445593	−	0.00771790i
$905$	−3.53590	+	6.12436i	−0.117537	+	0.203580i
$906$	4.92820	+	8.53590i	0.163729	+	0.283586i
$907$	8.53590	+	14.7846i	0.283430	+	0.490915i	0.972227	−	0.234039i	$-0.0751944\pi$
$907$	8.53590	+	14.7846i	0.283430	+	0.490915i	−0.688797	+	0.724954i	$0.741861\pi$
$908$	−0.901924	+	1.56218i	−0.0299314	+	0.0518427i
$909$	−4.06218	+	7.03590i	−0.134734	+	0.233366i
$910$	8.83013	−	15.2942i	0.292716	−	0.506999i
$911$	5.32051			0.176276			0.0881381	−	0.996108i	$-0.471908\pi$
$911$	5.32051			0.176276			0.0881381	+	0.996108i	$0.471908\pi$
$912$	−1.73205	−	3.00000i	−0.0573539	−	0.0993399i
$913$	−0.849365	+	1.47114i	−0.0281099	+	0.0486877i
$914$	−16.3923			−0.542209
$915$	−5.66025			−0.187122
$916$	−7.90192	+	13.6865i	−0.261087	+	0.452216i
$917$	−36.5885			−1.20826
$918$	−3.86603	−	6.69615i	−0.127598	−	0.221006i
$919$	6.26795			0.206761			0.103380	−	0.994642i	$-0.467034\pi$
$919$	6.26795			0.206761			0.103380	+	0.994642i	$0.467034\pi$
$920$	−2.46410	−	4.26795i	−0.0812390	−	0.140710i
$921$	9.73205	+	16.8564i	0.320682	+	0.555437i
$922$	10.5263	+	18.2321i	0.346665	+	0.600441i
$923$	21.7583	−	37.6865i	0.716184	−	1.24047i
$924$	1.26795			0.0417125
$925$	−1.00000	−	6.00000i	−0.0328798	−	0.197279i
$926$	−4.14359			−0.136167
$927$	−3.83013	+	6.63397i	−0.125798	+	0.217888i
$928$	2.59808	+	4.50000i	0.0852860	+	0.147720i
$929$	23.6603	+	40.9808i	0.776268	+	1.34454i	0.934079	+	0.357066i	$0.116223\pi$
$929$	23.6603	+	40.9808i	0.776268	+	1.34454i	−0.157811	+	0.987469i	$0.550444\pi$
$930$	1.73205	+	3.00000i	0.0567962	+	0.0983739i
$931$	−1.60770			−0.0526901
$932$	−1.53590	−	2.66025i	−0.0503100	−	0.0871395i
$933$	4.19615			0.137376
$934$	5.73205	−	9.92820i	0.187558	−	0.324861i
$935$	−3.58846			−0.117355
$936$	−6.46410			−0.211286
$937$	11.6865	−	20.2417i	0.381782	−	0.661267i	−0.609535	−	0.792759i	$-0.708644\pi$
$937$	11.6865	−	20.2417i	0.381782	−	0.661267i	0.991317	+	0.131493i	$0.0419770\pi$
$938$	10.5622	+	18.2942i	0.344867	+	0.597328i
$939$	2.39230			0.0780699
$940$	−2.23205	+	3.86603i	−0.0728015	+	0.126096i
$941$	26.7846	−	46.3923i	0.873153	−	1.51235i	0.0144363	−	0.999896i	$-0.495405\pi$
$941$	26.7846	−	46.3923i	0.873153	−	1.51235i	0.858717	−	0.512450i	$-0.171262\pi$
$942$	4.96410	−	8.59808i	0.161739	−	0.280140i
$943$	26.4449	+	45.8038i	0.861163	+	1.49158i
$944$	3.23205	+	5.59808i	0.105194	+	0.182202i
$945$	1.36603	−	2.36603i	0.0444368	−	0.0769668i
$946$	1.94744	−	3.37307i	0.0633168	−	0.109668i
$947$	−25.3923	+	43.9808i	−0.825139	+	1.42918i	0.0766740	+	0.997056i	$0.475570\pi$
$947$	−25.3923	+	43.9808i	−0.825139	+	1.42918i	−0.901813	+	0.432127i	$0.857763\pi$
$948$	−4.00000			−0.129914
$949$		0			0
$950$	−1.73205	+	3.00000i	−0.0561951	+	0.0973329i
$951$	−17.6603			−0.572673
$952$	−21.1244			−0.684644
$953$	16.6699	−	28.8731i	0.539990	−	0.935290i	−0.458914	−	0.888481i	$-0.651761\pi$
$953$	16.6699	−	28.8731i	0.539990	−	0.935290i	0.998904	−	0.0468095i	$-0.0149054\pi$
$954$	6.73205			0.217958
$955$	1.43782	+	2.49038i	0.0465268	+	0.0805868i
$956$	14.5359			0.470125
$957$	−1.20577	−	2.08846i	−0.0389771	−	0.0675102i
$958$	−19.0000	−	32.9090i	−0.613862	−	1.06324i
$959$	3.09808	+	5.36603i	0.100042	+	0.173278i
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	−19.0000			−0.612903
$962$	30.3564	−	24.9904i	0.978730	−	0.805722i
$963$	3.26795			0.105308
$964$	−13.6244	+	23.5981i	−0.438811	+	0.760043i
$965$	5.63397	+	9.75833i	0.181364	+	0.314132i
$966$	6.73205	+	11.6603i	0.216600	+	0.375163i
$967$	−29.6147	−	51.2942i	−0.952346	−	1.64951i	−0.740329	−	0.672245i	$-0.765330\pi$
$967$	−29.6147	−	51.2942i	−0.952346	−	1.64951i	−0.212017	−	0.977266i	$-0.568003\pi$
$968$	10.7846			0.346630
$969$	−13.3923	−	23.1962i	−0.430223	−	0.745168i
$970$	4.92820			0.158235
$971$	−27.5885	+	47.7846i	−0.885356	+	1.53348i	−0.0400503	+	0.999198i	$0.512752\pi$
$971$	−27.5885	+	47.7846i	−0.885356	+	1.53348i	−0.845305	+	0.534283i	$0.820582\pi$
$972$	−1.00000			−0.0320750
$973$	6.92820			0.222108
$974$	7.19615	−	12.4641i	0.230580	−	0.399376i
$975$	3.23205	+	5.59808i	0.103508	+	0.179282i
$976$	5.66025			0.181180
$977$	−15.9378	+	27.6051i	−0.509896	+	0.883166i	0.490038	+	0.871701i	$0.336983\pi$
$977$	−15.9378	+	27.6051i	−0.509896	+	0.883166i	−0.999934	+	0.0114650i	$0.996351\pi$
$978$	−11.0622	+	19.1603i	−0.353729	+	0.612677i
$979$	0.803848	−	1.39230i	0.0256911	−	0.0444983i
$980$	−0.232051	−	0.401924i	−0.00741259	−	0.0128390i
$981$	−0.169873	−	0.294229i	−0.00542363	−	0.00939400i
$982$	12.8564	−	22.2679i	0.410264	−	0.710599i
$983$	22.8564	−	39.5885i	0.729006	−	1.26268i	−0.228298	−	0.973591i	$-0.573316\pi$
$983$	22.8564	−	39.5885i	0.729006	−	1.26268i	0.957304	−	0.289084i	$-0.0933508\pi$
$984$	−5.36603	+	9.29423i	−0.171063	+	0.296289i
$985$	−8.53590			−0.271976
$986$	20.0885	+	34.7942i	0.639747	+	1.10807i
$987$	6.09808	−	10.5622i	0.194104	−	0.336198i
$988$	−22.3923			−0.712394
$989$	41.3590			1.31514
$990$	−0.232051	+	0.401924i	−0.00737506	+	0.0127740i
$991$	−43.0526			−1.36761			−0.683805	−	0.729665i	$-0.739676\pi$
$991$	−43.0526			−1.36761			−0.683805	+	0.729665i	$0.739676\pi$
$992$	−1.73205	−	3.00000i	−0.0549927	−	0.0952501i
$993$	16.7321			0.530976
$994$	−9.19615	−	15.9282i	−0.291684	−	0.505212i
$995$	−11.7942	−	20.4282i	−0.373902	−	0.647618i
$996$	−1.83013	−	3.16987i	−0.0579898	−	0.100441i
$997$	26.0885	−	45.1865i	0.826230	−	1.43107i	−0.0747461	−	0.997203i	$-0.523815\pi$
$997$	26.0885	−	45.1865i	0.826230	−	1.43107i	0.900976	−	0.433869i	$-0.142852\pi$
$998$	18.1962			0.575989
$999$	4.69615	−	3.86603i	0.148580	−	0.122316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.n.121.1	✓	4
37.26	even	3	inner	1110.2.i.n.211.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.n.121.1	✓	4	1.1	even	1	trivial
1110.2.i.n.211.1	yes	4	37.26	even	3	inner

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-1.36603 - 2.36603i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-1.36603 - 2.36603i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -0.464102 q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.23205 - 5.59808i) q^{13} -2.73205 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.86603 + 6.69615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(1.73205 + 3.00000i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.36603 - 2.36603i) q^{21} +(-0.232051 + 0.401924i) q^{22} -4.92820 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -6.46410 q^{26} -1.00000 q^{27} +(-1.36603 + 2.36603i) q^{28} +5.19615 q^{29} +(-0.500000 - 0.866025i) q^{30} -3.46410 q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.232051 - 0.401924i) q^{33} +(3.86603 + 6.69615i) q^{34} +(-1.36603 + 2.36603i) q^{35} +1.00000 q^{36} +(-4.69615 + 3.86603i) q^{37} +3.46410 q^{38} +(3.23205 - 5.59808i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.36603 - 9.29423i) q^{41} +(-1.36603 - 2.36603i) q^{42} -8.39230 q^{43} +(0.232051 + 0.401924i) q^{44} +1.00000 q^{45} +(-2.46410 + 4.26795i) q^{46} +4.46410 q^{47} -1.00000 q^{48} +(-0.232051 + 0.401924i) q^{49} +(0.500000 + 0.866025i) q^{50} -7.73205 q^{51} +(-3.23205 + 5.59808i) q^{52} +(3.36603 - 5.83013i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.232051 + 0.401924i) q^{55} +(1.36603 + 2.36603i) q^{56} +(-1.73205 + 3.00000i) q^{57} +(2.59808 - 4.50000i) q^{58} +(3.23205 - 5.59808i) q^{59} -1.00000 q^{60} +(-2.83013 - 4.90192i) q^{61} +(-1.73205 + 3.00000i) q^{62} +2.73205 q^{63} +1.00000 q^{64} +(-3.23205 + 5.59808i) q^{65} -0.464102 q^{66} +(-3.86603 - 6.69615i) q^{67} +7.73205 q^{68} +(-2.46410 - 4.26795i) q^{69} +(1.36603 + 2.36603i) q^{70} +(3.36603 + 5.83013i) q^{71} +(0.500000 - 0.866025i) q^{72} +(1.00000 + 6.00000i) q^{74} -1.00000 q^{75} +(1.73205 - 3.00000i) q^{76} +(0.633975 + 1.09808i) q^{77} +(-3.23205 - 5.59808i) q^{78} +(-2.00000 - 3.46410i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} -10.7321 q^{82} +(1.83013 - 3.16987i) q^{83} -2.73205 q^{84} +7.73205 q^{85} +(-4.19615 + 7.26795i) q^{86} +(2.59808 + 4.50000i) q^{87} +0.464102 q^{88} +(-1.73205 + 3.00000i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-8.83013 + 15.2942i) q^{91} +(2.46410 + 4.26795i) q^{92} +(-1.73205 - 3.00000i) q^{93} +(2.23205 - 3.86603i) q^{94} +(1.73205 - 3.00000i) q^{95} +(-0.500000 + 0.866025i) q^{96} -4.92820 q^{97} +(0.232051 + 0.401924i) q^{98} +(0.232051 - 0.401924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{10} + 12 q^{11} + 2 q^{12} - 6 q^{13} - 4 q^{14} + 2 q^{15} - 2 q^{16} - 12 q^{17} + 2 q^{18} - 2 q^{20} + 2 q^{21} + 6 q^{22} + 8 q^{23} - 2 q^{24} - 2 q^{25} - 12 q^{26} - 4 q^{27} - 2 q^{28} - 2 q^{30} + 2 q^{32} + 6 q^{33} + 12 q^{34} - 2 q^{35} + 4 q^{36} + 2 q^{37} + 6 q^{39} + 2 q^{40} - 18 q^{41} - 2 q^{42} + 8 q^{43} - 6 q^{44} + 4 q^{45} + 4 q^{46} + 4 q^{47} - 4 q^{48} + 6 q^{49} + 2 q^{50} - 24 q^{51} - 6 q^{52} + 10 q^{53} - 2 q^{54} - 6 q^{55} + 2 q^{56} + 6 q^{59} - 4 q^{60} + 6 q^{61} + 4 q^{63} + 4 q^{64} - 6 q^{65} + 12 q^{66} - 12 q^{67} + 24 q^{68} + 4 q^{69} + 2 q^{70} + 10 q^{71} + 2 q^{72} + 4 q^{74} - 4 q^{75} + 6 q^{77} - 6 q^{78} - 8 q^{79} + 4 q^{80} - 2 q^{81} - 36 q^{82} - 10 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} - 12 q^{88} + 2 q^{90} - 18 q^{91} - 4 q^{92} + 2 q^{94} - 2 q^{96} + 8 q^{97} - 6 q^{98} - 6 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 - 4 * q^10 + 12 * q^11 + 2 * q^12 - 6 * q^13 - 4 * q^14 + 2 * q^15 - 2 * q^16 - 12 * q^17 + 2 * q^18 - 2 * q^20 + 2 * q^21 + 6 * q^22 + 8 * q^23 - 2 * q^24 - 2 * q^25 - 12 * q^26 - 4 * q^27 - 2 * q^28 - 2 * q^30 + 2 * q^32 + 6 * q^33 + 12 * q^34 - 2 * q^35 + 4 * q^36 + 2 * q^37 + 6 * q^39 + 2 * q^40 - 18 * q^41 - 2 * q^42 + 8 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 4 * q^47 - 4 * q^48 + 6 * q^49 + 2 * q^50 - 24 * q^51 - 6 * q^52 + 10 * q^53 - 2 * q^54 - 6 * q^55 + 2 * q^56 + 6 * q^59 - 4 * q^60 + 6 * q^61 + 4 * q^63 + 4 * q^64 - 6 * q^65 + 12 * q^66 - 12 * q^67 + 24 * q^68 + 4 * q^69 + 2 * q^70 + 10 * q^71 + 2 * q^72 + 4 * q^74 - 4 * q^75 + 6 * q^77 - 6 * q^78 - 8 * q^79 + 4 * q^80 - 2 * q^81 - 36 * q^82 - 10 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 - 12 * q^88 + 2 * q^90 - 18 * q^91 - 4 * q^92 + 2 * q^94 - 2 * q^96 + 8 * q^97 - 6 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more