LMFDB - Embedded newform 936.2.ca.b.589.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(205,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.205"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.ca (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			589.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	936.589
Dual form			936.2.ca.b.205.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(-0.133975 + 0.232051i) q^{5} +(1.73205 + 1.73205i) q^{6} +(1.50000 + 0.866025i) q^{7} +(-2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +(-0.366025 + 0.0980762i) q^{10} -5.46410 q^{11} +3.46410i q^{12} +(3.46410 + 1.00000i) q^{13} +(0.633975 + 2.36603i) q^{14} +(-0.232051 + 0.401924i) q^{15} -4.00000 q^{16} +(0.232051 + 0.401924i) q^{17} +(3.00000 + 3.00000i) q^{18} +(2.59808 + 4.50000i) q^{19} +(-0.464102 - 0.267949i) q^{20} +(2.59808 + 1.50000i) q^{21} +(-5.46410 - 5.46410i) q^{22} +(-3.23205 - 5.59808i) q^{23} +(-3.46410 + 3.46410i) q^{24} +(2.46410 + 4.26795i) q^{25} +(2.46410 + 4.46410i) q^{26} +5.19615 q^{27} +(-1.73205 + 3.00000i) q^{28} +(-0.633975 + 0.169873i) q^{30} +(1.50000 + 0.866025i) q^{31} +(-4.00000 - 4.00000i) q^{32} -9.46410 q^{33} +(-0.169873 + 0.633975i) q^{34} +(-0.401924 + 0.232051i) q^{35} +6.00000i q^{36} +(2.13397 - 3.69615i) q^{37} +(-1.90192 + 7.09808i) q^{38} +(6.00000 + 1.73205i) q^{39} +(-0.196152 - 0.732051i) q^{40} +(4.96410 - 2.86603i) q^{41} +(1.09808 + 4.09808i) q^{42} +(-5.59808 - 3.23205i) q^{43} -10.9282i q^{44} +(-0.401924 + 0.696152i) q^{45} +(2.36603 - 8.83013i) q^{46} +(7.16025 - 4.13397i) q^{47} -6.92820 q^{48} +(-2.00000 - 3.46410i) q^{49} +(-1.80385 + 6.73205i) q^{50} +(0.401924 + 0.696152i) q^{51} +(-2.00000 + 6.92820i) q^{52} +(5.19615 + 5.19615i) q^{54} +(0.732051 - 1.26795i) q^{55} +(-4.73205 + 1.26795i) q^{56} +(4.50000 + 7.79423i) q^{57} -7.46410 q^{59} +(-0.803848 - 0.464102i) q^{60} +(-9.86603 - 5.69615i) q^{61} +(0.633975 + 2.36603i) q^{62} +(4.50000 + 2.59808i) q^{63} -8.00000i q^{64} +(-0.696152 + 0.669873i) q^{65} +(-9.46410 - 9.46410i) q^{66} +(3.86603 + 6.69615i) q^{67} +(-0.803848 + 0.464102i) q^{68} +(-5.59808 - 9.69615i) q^{69} +(-0.633975 - 0.169873i) q^{70} +(11.4282 - 6.59808i) q^{71} +(-6.00000 + 6.00000i) q^{72} +8.53590i q^{73} +(5.83013 - 1.56218i) q^{74} +(4.26795 + 7.39230i) q^{75} +(-9.00000 + 5.19615i) q^{76} +(-8.19615 - 4.73205i) q^{77} +(4.26795 + 7.73205i) q^{78} +(-7.96410 - 13.7942i) q^{79} +(0.535898 - 0.928203i) q^{80} +9.00000 q^{81} +(7.83013 + 2.09808i) q^{82} +(7.06218 + 12.2321i) q^{83} +(-3.00000 + 5.19615i) q^{84} -0.124356 q^{85} +(-2.36603 - 8.83013i) q^{86} +(10.9282 - 10.9282i) q^{88} +(0.571797 + 0.330127i) q^{89} +(-1.09808 + 0.294229i) q^{90} +(4.33013 + 4.50000i) q^{91} +(11.1962 - 6.46410i) q^{92} +(2.59808 + 1.50000i) q^{93} +(11.2942 + 3.02628i) q^{94} -1.39230 q^{95} +(-6.92820 - 6.92820i) q^{96} +(-2.30385 - 1.33013i) q^{97} +(1.46410 - 5.46410i) q^{98} -16.3923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{5} + 6 q^{7} - 8 q^{8} + 12 q^{9} + 2 q^{10} - 8 q^{11} + 6 q^{14} + 6 q^{15} - 16 q^{16} - 6 q^{17} + 12 q^{18} + 12 q^{20} - 8 q^{22} - 6 q^{23} - 4 q^{25} - 4 q^{26} - 6 q^{30} + 6 q^{31}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^5 + 6 * q^7 - 8 * q^8 + 12 * q^9 + 2 * q^10 - 8 * q^11 + 6 * q^14 + 6 * q^15 - 16 * q^16 - 6 * q^17 + 12 * q^18 + 12 * q^20 - 8 * q^22 - 6 * q^23 - 4 * q^25 - 4 * q^26 - 6 * q^30 + 6 * q^31 - 16 * q^32 - 24 * q^33 - 18 * q^34 - 12 * q^35 + 12 * q^37 - 18 * q^38 + 24 * q^39 + 20 * q^40 + 6 * q^41 - 6 * q^42 - 12 * q^43 - 12 * q^45 + 6 * q^46 - 6 * q^47 - 8 * q^49 - 28 * q^50 + 12 * q^51 - 8 * q^52 - 4 * q^55 - 12 * q^56 + 18 * q^57 - 16 * q^59 - 24 * q^60 - 36 * q^61 + 6 * q^62 + 18 * q^63 + 18 * q^65 - 24 * q^66 + 12 * q^67 - 24 * q^68 - 12 * q^69 - 6 * q^70 + 18 * q^71 - 24 * q^72 + 6 * q^74 + 24 * q^75 - 36 * q^76 - 12 * q^77 + 24 * q^78 - 18 * q^79 + 16 * q^80 + 36 * q^81 + 14 * q^82 + 4 * q^83 - 12 * q^84 + 48 * q^85 - 6 * q^86 + 16 * q^88 + 30 * q^89 + 6 * q^90 + 24 * q^92 + 14 * q^94 + 36 * q^95 - 30 * q^97 - 8 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

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 $

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$	1.73205			1.00000
$3$	1.73205			1.00000
$4$			2.00000i			1.00000i
$5$	−0.133975	+	0.232051i	−0.0599153	+	0.103776i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	−0.133975	+	0.232051i	−0.0599153	+	0.103776i	0.834512	+	0.550990i	$0.185750\pi$
$6$	1.73205	+	1.73205i	0.707107	+	0.707107i
$7$	1.50000	+	0.866025i	0.566947	+	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	1.50000	+	0.866025i	0.566947	+	0.327327i	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	3.00000			1.00000
$10$	−0.366025	+	0.0980762i	−0.115747	+	0.0310144i
$11$	−5.46410			−1.64749			−0.823744	−	0.566961i	$-0.808119\pi$
$11$	−5.46410			−1.64749			−0.823744	+	0.566961i	$0.808119\pi$
$12$			3.46410i			1.00000i
$13$	3.46410	+	1.00000i	0.960769	+	0.277350i
$13$	3.46410	+	1.00000i	0.960769	+	0.277350i
$14$	0.633975	+	2.36603i	0.169437	+	0.632347i
$15$	−0.232051	+	0.401924i	−0.0599153	+	0.103776i
$16$	−4.00000			−1.00000
$17$	0.232051	+	0.401924i	0.0562806	+	0.0974808i	0.892793	−	0.450467i	$-0.148743\pi$
$17$	0.232051	+	0.401924i	0.0562806	+	0.0974808i	−0.836512	+	0.547948i	$0.815409\pi$
$18$	3.00000	+	3.00000i	0.707107	+	0.707107i
$19$	2.59808	+	4.50000i	0.596040	+	1.03237i	0.993399	+	0.114708i	$0.0365932\pi$
$19$	2.59808	+	4.50000i	0.596040	+	1.03237i	−0.397360	+	0.917663i	$0.630073\pi$
$20$	−0.464102	−	0.267949i	−0.103776	−	0.0599153i
$21$	2.59808	+	1.50000i	0.566947	+	0.327327i
$22$	−5.46410	−	5.46410i	−1.16495	−	1.16495i
$23$	−3.23205	−	5.59808i	−0.673929	−	1.16728i	−0.976781	−	0.214242i	$-0.931272\pi$
$23$	−3.23205	−	5.59808i	−0.673929	−	1.16728i	0.302851	−	0.953038i	$-0.402061\pi$
$24$	−3.46410	+	3.46410i	−0.707107	+	0.707107i
$25$	2.46410	+	4.26795i	0.492820	+	0.853590i
$26$	2.46410	+	4.46410i	0.483250	+	0.875482i
$27$	5.19615			1.00000
$28$	−1.73205	+	3.00000i	−0.327327	+	0.566947i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	−0.633975	+	0.169873i	−0.115747	+	0.0310144i
$31$	1.50000	+	0.866025i	0.269408	+	0.155543i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	1.50000	+	0.866025i	0.269408	+	0.155543i	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	−9.46410			−1.64749
$34$	−0.169873	+	0.633975i	−0.0291330	+	0.108726i
$35$	−0.401924	+	0.232051i	−0.0679375	+	0.0392237i
$36$			6.00000i			1.00000i
$37$	2.13397	−	3.69615i	0.350823	−	0.607644i	−0.635571	−	0.772043i	$-0.719235\pi$
$37$	2.13397	−	3.69615i	0.350823	−	0.607644i	0.986394	+	0.164399i	$0.0525685\pi$
$38$	−1.90192	+	7.09808i	−0.308533	+	1.15146i
$39$	6.00000	+	1.73205i	0.960769	+	0.277350i
$40$	−0.196152	−	0.732051i	−0.0310144	−	0.115747i
$41$	4.96410	−	2.86603i	0.775262	−	0.447598i	−0.0594862	−	0.998229i	$-0.518946\pi$
$41$	4.96410	−	2.86603i	0.775262	−	0.447598i	0.834749	+	0.550631i	$0.185613\pi$
$42$	1.09808	+	4.09808i	0.169437	+	0.632347i
$43$	−5.59808	−	3.23205i	−0.853699	−	0.492883i	0.00819845	−	0.999966i	$-0.497390\pi$
$43$	−5.59808	−	3.23205i	−0.853699	−	0.492883i	−0.861897	+	0.507083i	$0.830724\pi$
$44$		−	10.9282i		−	1.64749i
$45$	−0.401924	+	0.696152i	−0.0599153	+	0.103776i
$46$	2.36603	−	8.83013i	0.348851	−	1.30193i
$47$	7.16025	−	4.13397i	1.04443	−	0.603002i	0.123345	−	0.992364i	$-0.460638\pi$
$47$	7.16025	−	4.13397i	1.04443	−	0.603002i	0.921085	+	0.389362i	$0.127304\pi$
$48$	−6.92820			−1.00000
$49$	−2.00000	−	3.46410i	−0.285714	−	0.494872i
$50$	−1.80385	+	6.73205i	−0.255103	+	0.952056i
$51$	0.401924	+	0.696152i	0.0562806	+	0.0974808i
$52$	−2.00000	+	6.92820i	−0.277350	+	0.960769i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	5.19615	+	5.19615i	0.707107	+	0.707107i
$55$	0.732051	−	1.26795i	0.0987097	−	0.170970i
$56$	−4.73205	+	1.26795i	−0.632347	+	0.169437i
$57$	4.50000	+	7.79423i	0.596040	+	1.03237i
$58$		0			0
$59$	−7.46410			−0.971743			−0.485872	−	0.874030i	$-0.661498\pi$
$59$	−7.46410			−0.971743			−0.485872	+	0.874030i	$0.661498\pi$
$60$	−0.803848	−	0.464102i	−0.103776	−	0.0599153i
$61$	−9.86603	−	5.69615i	−1.26322	−	0.729318i	−0.289520	−	0.957172i	$-0.593496\pi$
$61$	−9.86603	−	5.69615i	−1.26322	−	0.729318i	−0.973695	+	0.227854i	$0.926829\pi$
$62$	0.633975	+	2.36603i	0.0805149	+	0.300486i
$63$	4.50000	+	2.59808i	0.566947	+	0.327327i
$64$		−	8.00000i		−	1.00000i
$65$	−0.696152	+	0.669873i	−0.0863471	+	0.0830875i
$66$	−9.46410	−	9.46410i	−1.16495	−	1.16495i
$67$	3.86603	+	6.69615i	0.472310	+	0.818065i	0.999498	−	0.0316836i	$-0.0100869\pi$
$67$	3.86603	+	6.69615i	0.472310	+	0.818065i	−0.527188	+	0.849749i	$0.676754\pi$
$68$	−0.803848	+	0.464102i	−0.0974808	+	0.0562806i
$69$	−5.59808	−	9.69615i	−0.673929	−	1.16728i
$70$	−0.633975	−	0.169873i	−0.0757745	−	0.0203037i
$71$	11.4282	−	6.59808i	1.35628	−	0.783048i	0.367158	−	0.930159i	$-0.380331\pi$
$71$	11.4282	−	6.59808i	1.35628	−	0.783048i	0.989120	+	0.147111i	$0.0469974\pi$
$72$	−6.00000	+	6.00000i	−0.707107	+	0.707107i
$73$			8.53590i			0.999051i	0.866299	+	0.499526i	$0.166492\pi$
$73$			8.53590i			0.999051i	−0.866299	+	0.499526i	$0.833508\pi$
$74$	5.83013	−	1.56218i	0.677738	−	0.181599i
$75$	4.26795	+	7.39230i	0.492820	+	0.853590i
$76$	−9.00000	+	5.19615i	−1.03237	+	0.596040i
$77$	−8.19615	−	4.73205i	−0.934038	−	0.539267i
$78$	4.26795	+	7.73205i	0.483250	+	0.875482i
$79$	−7.96410	−	13.7942i	−0.896031	−	1.55197i	−0.832523	−	0.553991i	$-0.813104\pi$
$79$	−7.96410	−	13.7942i	−0.896031	−	1.55197i	−0.0635086	−	0.997981i	$-0.520229\pi$
$80$	0.535898	−	0.928203i	0.0599153	−	0.103776i
$81$	9.00000			1.00000
$82$	7.83013	+	2.09808i	0.864693	+	0.231694i
$83$	7.06218	+	12.2321i	0.775175	+	1.34264i	0.934696	+	0.355448i	$0.115672\pi$
$83$	7.06218	+	12.2321i	0.775175	+	1.34264i	−0.159522	+	0.987194i	$0.550995\pi$
$84$	−3.00000	+	5.19615i	−0.327327	+	0.566947i
$85$	−0.124356			−0.0134883
$86$	−2.36603	−	8.83013i	−0.255135	−	0.952177i
$87$		0			0
$88$	10.9282	−	10.9282i	1.16495	−	1.16495i
$89$	0.571797	+	0.330127i	0.0606103	+	0.0349934i	0.529999	−	0.847998i	$-0.322192\pi$
$89$	0.571797	+	0.330127i	0.0606103	+	0.0349934i	−0.469389	+	0.882992i	$0.655526\pi$
$90$	−1.09808	+	0.294229i	−0.115747	+	0.0310144i
$91$	4.33013	+	4.50000i	0.453921	+	0.471728i
$92$	11.1962	−	6.46410i	1.16728	−	0.673929i
$93$	2.59808	+	1.50000i	0.269408	+	0.155543i
$94$	11.2942	+	3.02628i	1.16491	+	0.312137i
$95$	−1.39230			−0.142847
$96$	−6.92820	−	6.92820i	−0.707107	−	0.707107i
$97$	−2.30385	−	1.33013i	−0.233920	−	0.135054i	0.378459	−	0.925618i	$-0.376454\pi$
$97$	−2.30385	−	1.33013i	−0.233920	−	0.135054i	−0.612379	+	0.790564i	$0.709787\pi$
$98$	1.46410	−	5.46410i	0.147897	−	0.551958i
$99$	−16.3923			−1.64749
$100$	−8.53590	+	4.92820i	−0.853590	+	0.492820i
$101$		−	9.46410i		−	0.941713i	−0.882210	−	0.470857i	$-0.843945\pi$
$101$		−	9.46410i		−	0.941713i	0.882210	−	0.470857i	$-0.156055\pi$
$102$	−0.294229	+	1.09808i	−0.0291330	+	0.108726i
$103$	−2.69615	+	4.66987i	−0.265660	+	0.460136i	−0.967736	−	0.251965i	$-0.918923\pi$
$103$	−2.69615	+	4.66987i	−0.265660	+	0.460136i	0.702076	+	0.712102i	$0.252256\pi$
$104$	−8.92820	+	4.92820i	−0.875482	+	0.483250i
$105$	−0.696152	+	0.401924i	−0.0679375	+	0.0392237i
$106$		0			0
$107$	−15.9904	−	9.23205i	−1.54585	−	0.892496i	−0.998452	−	0.0556227i	$-0.982286\pi$
$107$	−15.9904	−	9.23205i	−1.54585	−	0.892496i	−0.547397	−	0.836873i	$-0.684381\pi$
$108$			10.3923i			1.00000i
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$	2.00000	−	0.535898i	0.190693	−	0.0510959i
$111$	3.69615	−	6.40192i	0.350823	−	0.607644i
$112$	−6.00000	−	3.46410i	−0.566947	−	0.327327i
$113$	13.8564			1.30350			0.651751	−	0.758433i	$-0.274035\pi$
$113$	13.8564			1.30350			0.651751	+	0.758433i	$0.274035\pi$
$114$	−3.29423	+	12.2942i	−0.308533	+	1.15146i
$115$	1.73205			0.161515
$116$		0			0
$117$	10.3923	+	3.00000i	0.960769	+	0.277350i
$118$	−7.46410	−	7.46410i	−0.687126	−	0.687126i
$119$			0.803848i			0.0736886i
$120$	−0.339746	−	1.26795i	−0.0310144	−	0.115747i
$121$	18.8564			1.71422
$122$	−4.16987	−	15.5622i	−0.377523	−	1.40893i
$123$	8.59808	−	4.96410i	0.775262	−	0.447598i
$124$	−1.73205	+	3.00000i	−0.155543	+	0.269408i
$125$	−2.66025			−0.237940
$126$	1.90192	+	7.09808i	0.169437	+	0.632347i
$127$	7.16025	−	12.4019i	0.635370	−	1.10049i	−0.351067	−	0.936350i	$-0.614181\pi$
$127$	7.16025	−	12.4019i	0.635370	−	1.10049i	0.986437	−	0.164142i	$-0.0524857\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$	−9.69615	−	5.59808i	−0.853699	−	0.492883i
$130$	−1.36603	−	0.0262794i	−0.119808	−	0.00230486i
$131$	−10.7942	−	6.23205i	−0.943096	−	0.544497i	−0.0521666	−	0.998638i	$-0.516613\pi$
$131$	−10.7942	−	6.23205i	−0.943096	−	0.544497i	−0.890930	+	0.454142i	$0.849946\pi$
$132$		−	18.9282i		−	1.64749i
$133$			9.00000i			0.780399i
$134$	−2.83013	+	10.5622i	−0.244486	+	0.912433i
$135$	−0.696152	+	1.20577i	−0.0599153	+	0.103776i
$136$	−1.26795	−	0.339746i	−0.108726	−	0.0291330i
$137$	−2.42820	−	1.40192i	−0.207455	−	0.119774i	0.392673	−	0.919678i	$-0.371550\pi$
$137$	−2.42820	−	1.40192i	−0.207455	−	0.119774i	−0.600128	+	0.799904i	$0.704884\pi$
$138$	4.09808	−	15.2942i	0.348851	−	1.30193i
$139$			7.85641i			0.666372i	0.942861	+	0.333186i	$0.108124\pi$
$139$			7.85641i			0.666372i	−0.942861	+	0.333186i	$0.891876\pi$
$140$	−0.464102	−	0.803848i	−0.0392237	−	0.0679375i
$141$	12.4019	−	7.16025i	1.04443	−	0.603002i
$142$	18.0263	+	4.83013i	1.51273	+	0.405335i
$143$	−18.9282	−	5.46410i	−1.58286	−	0.456931i
$144$	−12.0000			−1.00000
$145$		0			0
$146$	−8.53590	+	8.53590i	−0.706436	+	0.706436i
$147$	−3.46410	−	6.00000i	−0.285714	−	0.494872i
$148$	7.39230	+	4.26795i	0.607644	+	0.350823i
$149$	−15.8564			−1.29901			−0.649504	−	0.760358i	$-0.725023\pi$
$149$	−15.8564			−1.29901			−0.649504	+	0.760358i	$0.725023\pi$
$150$	−3.12436	+	11.6603i	−0.255103	+	0.952056i
$151$	−0.696152	+	0.401924i	−0.0566521	+	0.0327081i	−0.528059	−	0.849208i	$-0.677080\pi$
$151$	−0.696152	+	0.401924i	−0.0566521	+	0.0327081i	0.471406	+	0.881916i	$0.343747\pi$
$152$	−14.1962	−	3.80385i	−1.15146	−	0.308533i
$153$	0.696152	+	1.20577i	0.0562806	+	0.0974808i
$154$	−3.46410	−	12.9282i	−0.279145	−	1.04178i
$155$	−0.401924	+	0.232051i	−0.0322833	+	0.0186388i
$156$	−3.46410	+	12.0000i	−0.277350	+	0.960769i
$157$	7.79423	+	4.50000i	0.622047	+	0.359139i	0.777666	−	0.628678i	$-0.216404\pi$
$157$	7.79423	+	4.50000i	0.622047	+	0.359139i	−0.155618	+	0.987817i	$0.549737\pi$
$158$	5.83013	−	21.7583i	0.463820	−	1.73100i
$159$		0			0
$160$	1.46410	−	0.392305i	0.115747	−	0.0310144i
$161$		−	11.1962i		−	0.882380i
$162$	9.00000	+	9.00000i	0.707107	+	0.707107i
$163$	−11.5981	−	20.0885i	−0.908431	−	1.57345i	−0.816244	−	0.577708i	$-0.803947\pi$
$163$	−11.5981	−	20.0885i	−0.908431	−	1.57345i	−0.0921878	−	0.995742i	$-0.529386\pi$
$164$	5.73205	+	9.92820i	0.447598	+	0.775262i
$165$	1.26795	−	2.19615i	0.0987097	−	0.170970i
$166$	−5.16987	+	19.2942i	−0.401260	+	1.49752i
$167$	−0.232051	+	0.133975i	−0.0179566	+	0.0103673i	−0.508951	−	0.860795i	$-0.669967\pi$
$167$	−0.232051	+	0.133975i	−0.0179566	+	0.0103673i	0.490995	+	0.871162i	$0.336633\pi$
$168$	−8.19615	+	2.19615i	−0.632347	+	0.169437i
$169$	11.0000	+	6.92820i	0.846154	+	0.532939i
$170$	−0.124356	−	0.124356i	−0.00953764	−	0.00953764i
$171$	7.79423	+	13.5000i	0.596040	+	1.03237i
$172$	6.46410	−	11.1962i	0.492883	−	0.853699i
$173$	19.7942	+	11.4282i	1.50493	+	0.868870i	0.999984	+	0.00571791i	$0.00182008\pi$
$173$	19.7942	+	11.4282i	1.50493	+	0.868870i	0.504944	+	0.863152i	$0.331513\pi$
$174$		0			0
$175$			8.53590i			0.645253i
$176$	21.8564			1.64749
$177$	−12.9282			−0.971743
$178$	0.241670	+	0.901924i	0.0181139	+	0.0676020i
$179$	1.79423	+	1.03590i	0.134107	+	0.0774267i	0.565552	−	0.824712i	$-0.308663\pi$
$179$	1.79423	+	1.03590i	0.134107	+	0.0774267i	−0.431446	+	0.902139i	$0.641996\pi$
$180$	−1.39230	−	0.803848i	−0.103776	−	0.0599153i
$181$			14.5359i			1.08044i	0.841522	+	0.540222i	$0.181660\pi$
$181$			14.5359i			1.08044i	−0.841522	+	0.540222i	$0.818340\pi$
$182$	−0.169873	+	8.83013i	−0.0125918	+	0.654533i
$183$	−17.0885	−	9.86603i	−1.26322	−	0.729318i
$184$	17.6603	+	4.73205i	1.30193	+	0.348851i
$185$	0.571797	+	0.990381i	0.0420393	+	0.0728143i
$186$	1.09808	+	4.09808i	0.0805149	+	0.300486i
$187$	−1.26795	−	2.19615i	−0.0927216	−	0.160599i
$188$	8.26795	+	14.3205i	0.603002	+	1.04443i
$189$	7.79423	+	4.50000i	0.566947	+	0.327327i
$190$	−1.39230	−	1.39230i	−0.101008	−	0.101008i
$191$	−9.23205	+	15.9904i	−0.668008	+	1.15702i	0.310453	+	0.950589i	$0.399519\pi$
$191$	−9.23205	+	15.9904i	−0.668008	+	1.15702i	−0.978460	+	0.206435i	$0.933814\pi$
$192$		−	13.8564i		−	1.00000i
$193$	3.69615	−	2.13397i	0.266055	−	0.153607i	−0.361039	−	0.932551i	$-0.617578\pi$
$193$	3.69615	−	2.13397i	0.266055	−	0.153607i	0.627093	+	0.778944i	$0.284244\pi$
$194$	−0.973721	−	3.63397i	−0.0699091	−	0.260904i
$195$	−1.20577	+	1.16025i	−0.0863471	+	0.0830875i
$196$	6.92820	−	4.00000i	0.494872	−	0.285714i
$197$	7.86603	−	13.6244i	0.560431	−	0.970695i	−0.437028	−	0.899448i	$-0.643969\pi$
$197$	7.86603	−	13.6244i	0.560431	−	0.970695i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$	−16.3923	−	16.3923i	−1.16495	−	1.16495i
$199$	−3.69615	−	6.40192i	−0.262013	−	0.453820i	0.704764	−	0.709442i	$-0.251053\pi$
$199$	−3.69615	−	6.40192i	−0.262013	−	0.453820i	−0.966777	+	0.255622i	$0.917720\pi$
$200$	−13.4641	−	3.60770i	−0.952056	−	0.255103i
$201$	6.69615	+	11.5981i	0.472310	+	0.818065i
$202$	9.46410	−	9.46410i	0.665892	−	0.665892i
$203$		0			0
$204$	−1.39230	+	0.803848i	−0.0974808	+	0.0562806i
$205$			1.53590i			0.107272i
$206$	−7.36603	+	1.97372i	−0.513215	+	0.137516i
$207$	−9.69615	−	16.7942i	−0.673929	−	1.16728i
$208$	−13.8564	−	4.00000i	−0.960769	−	0.277350i
$209$	−14.1962	−	24.5885i	−0.981968	−	1.70082i
$210$	−1.09808	−	0.294229i	−0.0757745	−	0.0203037i
$211$	−8.13397	+	4.69615i	−0.559966	+	0.323296i	−0.753132	−	0.657870i	$-0.771458\pi$
$211$	−8.13397	+	4.69615i	−0.559966	+	0.323296i	0.193166	+	0.981166i	$0.438124\pi$
$212$		0			0
$213$	19.7942	−	11.4282i	1.35628	−	0.783048i
$214$	−6.75833	−	25.2224i	−0.461990	−	1.72417i
$215$	1.50000	−	0.866025i	0.102299	−	0.0590624i
$216$	−10.3923	+	10.3923i	−0.707107	+	0.707107i
$217$	1.50000	+	2.59808i	0.101827	+	0.176369i
$218$	6.00000	+	6.00000i	0.406371	+	0.406371i
$219$			14.7846i			0.999051i
$220$	2.53590	+	1.46410i	0.170970	+	0.0987097i
$221$	0.401924	+	1.62436i	0.0270363	+	0.109266i
$222$	10.0981	−	2.70577i	0.677738	−	0.181599i
$223$			5.32051i			0.356288i	0.984004	+	0.178144i	$0.0570092\pi$
$223$			5.32051i			0.356288i	−0.984004	+	0.178144i	$0.942991\pi$
$224$	−2.53590	−	9.46410i	−0.169437	−	0.632347i
$225$	7.39230	+	12.8038i	0.492820	+	0.853590i
$226$	13.8564	+	13.8564i	0.921714	+	0.921714i
$227$	−6.59808	+	11.4282i	−0.437930	+	0.758516i	−0.997530	−	0.0702464i	$-0.977621\pi$
$227$	−6.59808	+	11.4282i	−0.437930	+	0.758516i	0.559600	+	0.828763i	$0.310955\pi$
$228$	−15.5885	+	9.00000i	−1.03237	+	0.596040i
$229$	−0.401924	+	0.696152i	−0.0265599	+	0.0460030i	−0.879000	−	0.476822i	$-0.841789\pi$
$229$	−0.401924	+	0.696152i	−0.0265599	+	0.0460030i	0.852440	+	0.522825i	$0.175122\pi$
$230$	1.73205	+	1.73205i	0.114208	+	0.114208i
$231$	−14.1962	−	8.19615i	−0.934038	−	0.539267i
$232$		0			0
$233$	7.85641			0.514690			0.257345	−	0.966320i	$-0.417152\pi$
$233$	7.85641			0.514690			0.257345	+	0.966320i	$0.417152\pi$
$234$	7.39230	+	13.3923i	0.483250	+	0.875482i
$235$			2.21539i			0.144516i
$236$		−	14.9282i		−	0.971743i
$237$	−13.7942	−	23.8923i	−0.896031	−	1.55197i
$238$	−0.803848	+	0.803848i	−0.0521057	+	0.0521057i
$239$	−2.42820	−	1.40192i	−0.157067	−	0.0906829i	0.419406	−	0.907799i	$-0.362238\pi$
$239$	−2.42820	−	1.40192i	−0.157067	−	0.0906829i	−0.576474	+	0.817116i	$0.695572\pi$
$240$	0.928203	−	1.60770i	0.0599153	−	0.103776i
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	−0.450910	+	0.892570i	$0.648900\pi$
$242$	18.8564	+	18.8564i	1.21214	+	1.21214i
$243$	15.5885			1.00000
$244$	11.3923	−	19.7321i	0.729318	−	1.26322i
$245$	1.07180			0.0684746
$246$	13.5622	+	3.63397i	0.864693	+	0.231694i
$247$	4.50000	+	18.1865i	0.286328	+	1.15718i
$248$	−4.73205	+	1.26795i	−0.300486	+	0.0805149i
$249$	12.2321	+	21.1865i	0.775175	+	1.34264i
$250$	−2.66025	−	2.66025i	−0.168249	−	0.168249i
$251$	−19.7942	+	11.4282i	−1.24940	+	0.721342i	−0.970990	−	0.239120i	$-0.923141\pi$
$251$	−19.7942	+	11.4282i	−1.24940	+	0.721342i	−0.278411	+	0.960462i	$0.589808\pi$
$252$	−5.19615	+	9.00000i	−0.327327	+	0.566947i
$253$	17.6603	+	30.5885i	1.11029	+	1.92308i
$254$	19.5622	−	5.24167i	1.22744	−	0.328892i
$255$	−0.215390			−0.0134883
$256$	16.0000			1.00000
$257$	−3.23205	−	5.59808i	−0.201610	−	0.349198i	0.747437	−	0.664332i	$-0.231284\pi$
$257$	−3.23205	−	5.59808i	−0.201610	−	0.349198i	−0.949047	+	0.315134i	$0.897951\pi$
$258$	−4.09808	−	15.2942i	−0.255135	−	0.952177i
$259$	6.40192	−	3.69615i	0.397796	−	0.229668i
$260$	−1.33975	−	1.39230i	−0.0830875	−	0.0863471i
$261$		0			0
$262$	−4.56218	−	17.0263i	−0.281852	−	1.05189i
$263$	−3.46410			−0.213606			−0.106803	−	0.994280i	$-0.534061\pi$
$263$	−3.46410			−0.213606			−0.106803	+	0.994280i	$0.534061\pi$
$264$	18.9282	−	18.9282i	1.16495	−	1.16495i
$265$		0			0
$266$	−9.00000	+	9.00000i	−0.551825	+	0.551825i
$267$	0.990381	+	0.571797i	0.0606103	+	0.0349934i
$268$	−13.3923	+	7.73205i	−0.818065	+	0.472310i
$269$	11.5981	−	6.69615i	0.707147	−	0.408272i	−0.102857	−	0.994696i	$-0.532798\pi$
$269$	11.5981	−	6.69615i	0.707147	−	0.408272i	0.810004	+	0.586425i	$0.199465\pi$
$270$	−1.90192	+	0.509619i	−0.115747	+	0.0310144i
$271$	−14.0885	−	8.13397i	−0.855813	−	0.494104i	0.00679505	−	0.999977i	$-0.497837\pi$
$271$	−14.0885	−	8.13397i	−0.855813	−	0.494104i	−0.862608	+	0.505873i	$0.831170\pi$
$272$	−0.928203	−	1.60770i	−0.0562806	−	0.0974808i
$273$	7.50000	+	7.79423i	0.453921	+	0.471728i
$274$	−1.02628	−	3.83013i	−0.0619998	−	0.231386i
$275$	−13.4641	−	23.3205i	−0.811916	−	1.40628i
$276$	19.3923	−	11.1962i	1.16728	−	0.673929i
$277$	−24.1865	−	13.9641i	−1.45323	−	0.839022i	−0.454565	−	0.890714i	$-0.650205\pi$
$277$	−24.1865	−	13.9641i	−1.45323	−	0.839022i	−0.998663	+	0.0516921i	$0.983539\pi$
$278$	−7.85641	+	7.85641i	−0.471196	+	0.471196i
$279$	4.50000	+	2.59808i	0.269408	+	0.155543i
$280$	0.339746	−	1.26795i	0.0203037	−	0.0757745i
$281$	−18.2321	+	10.5263i	−1.08763	+	0.627945i	−0.932945	−	0.360018i	$-0.882770\pi$
$281$	−18.2321	+	10.5263i	−1.08763	+	0.627945i	−0.154688	+	0.987963i	$0.549437\pi$
$282$	19.5622	+	5.24167i	1.16491	+	0.312137i
$283$	27.5263	−	15.8923i	1.63627	−	0.944699i	0.654165	−	0.756352i	$-0.273020\pi$
$283$	27.5263	−	15.8923i	1.63627	−	0.944699i	0.982102	−	0.188348i	$-0.0603132\pi$
$284$	13.1962	+	22.8564i	0.783048	+	1.35628i
$285$	−2.41154			−0.142847
$286$	−13.4641	−	24.3923i	−0.796149	−	1.44235i
$287$	9.92820			0.586043
$288$	−12.0000	−	12.0000i	−0.707107	−	0.707107i
$289$	8.39230	−	14.5359i	0.493665	−	0.855053i
$290$		0			0
$291$	−3.99038	−	2.30385i	−0.233920	−	0.135054i
$292$	−17.0718			−0.999051
$293$	4.92820			0.287909			0.143954	−	0.989584i	$-0.454018\pi$
$293$	4.92820			0.287909			0.143954	+	0.989584i	$0.454018\pi$
$294$	2.53590	−	9.46410i	0.147897	−	0.551958i
$295$	1.00000	−	1.73205i	0.0582223	−	0.100844i
$296$	3.12436	+	11.6603i	0.181599	+	0.677738i
$297$	−28.3923			−1.64749
$298$	−15.8564	−	15.8564i	−0.918537	−	0.918537i
$299$	−5.59808	−	22.6244i	−0.323745	−	1.30840i
$300$	−14.7846	+	8.53590i	−0.853590	+	0.492820i
$301$	−5.59808	−	9.69615i	−0.322668	−	0.558877i
$302$	−1.09808	−	0.294229i	−0.0631872	−	0.0169310i
$303$		−	16.3923i		−	0.941713i
$304$	−10.3923	−	18.0000i	−0.596040	−	1.03237i
$305$	2.64359	−	1.52628i	0.151372	−	0.0873945i
$306$	−0.509619	+	1.90192i	−0.0291330	+	0.108726i
$307$	5.07180			0.289463			0.144731	−	0.989471i	$-0.453768\pi$
$307$	5.07180			0.289463			0.144731	+	0.989471i	$0.453768\pi$
$308$	9.46410	−	16.3923i	0.539267	−	0.934038i
$309$	−4.66987	+	8.08846i	−0.265660	+	0.460136i
$310$	−0.633975	−	0.169873i	−0.0360073	−	0.00964814i
$311$	−4.96410	+	8.59808i	−0.281488	+	0.487552i	−0.971752	−	0.236006i	$-0.924161\pi$
$311$	−4.96410	+	8.59808i	−0.281488	+	0.487552i	0.690263	+	0.723558i	$0.257495\pi$
$312$	−15.4641	+	8.53590i	−0.875482	+	0.483250i
$313$	6.69615	+	11.5981i	0.378489	+	0.655562i	0.990843	−	0.135022i	$-0.0431105\pi$
$313$	6.69615	+	11.5981i	0.378489	+	0.655562i	−0.612354	+	0.790584i	$0.709777\pi$
$314$	3.29423	+	12.2942i	0.185904	+	0.693803i
$315$	−1.20577	+	0.696152i	−0.0679375	+	0.0392237i
$316$	27.5885	−	15.9282i	1.55197	−	0.896031i
$317$	2.52628	+	4.37564i	0.141890	+	0.245761i	0.928208	−	0.372061i	$-0.121349\pi$
$317$	2.52628	+	4.37564i	0.141890	+	0.245761i	−0.786318	+	0.617822i	$0.788015\pi$
$318$		0			0
$319$		0			0
$320$	1.85641	+	1.07180i	0.103776	+	0.0599153i
$321$	−27.6962	−	15.9904i	−1.54585	−	0.892496i
$322$	11.1962	−	11.1962i	0.623937	−	0.623937i
$323$	−1.20577	+	2.08846i	−0.0670909	+	0.116205i
$324$			18.0000i			1.00000i
$325$	4.26795	+	17.2487i	0.236743	+	0.956786i
$326$	8.49038	−	31.6865i	0.470239	−	1.75495i
$327$	10.3923			0.574696
$328$	−4.19615	+	15.6603i	−0.231694	+	0.864693i
$329$	14.3205			0.789515
$330$	3.46410	−	0.928203i	0.190693	−	0.0510959i
$331$	−8.25833	+	14.3038i	−0.453919	+	0.786211i	−0.998625	−	0.0524162i	$-0.983308\pi$
$331$	−8.25833	+	14.3038i	−0.453919	+	0.786211i	0.544706	+	0.838627i	$0.316641\pi$
$332$	−24.4641	+	14.1244i	−1.34264	+	0.775175i
$333$	6.40192	−	11.0885i	0.350823	−	0.607644i
$334$	−0.366025	−	0.0980762i	−0.0200280	−	0.00536649i
$335$	−2.07180			−0.113194
$336$	−10.3923	−	6.00000i	−0.566947	−	0.327327i
$337$	−4.96410	+	8.59808i	−0.270412	+	0.468367i	−0.968967	−	0.247189i	$-0.920493\pi$
$337$	−4.96410	+	8.59808i	−0.270412	+	0.468367i	0.698555	+	0.715556i	$0.253827\pi$
$338$	4.07180	+	17.9282i	0.221477	+	0.975166i
$339$	24.0000			1.30350
$340$		−	0.248711i		−	0.0134883i
$341$	−8.19615	−	4.73205i	−0.443847	−	0.256255i
$342$	−5.70577	+	21.2942i	−0.308533	+	1.15146i
$343$		−	19.0526i		−	1.02874i
$344$	17.6603	−	4.73205i	0.952177	−	0.255135i
$345$	3.00000			0.161515
$346$	8.36603	+	31.2224i	0.449760	+	1.67853i
$347$			7.85641i			0.421754i	0.977513	+	0.210877i	$0.0676320\pi$
$347$			7.85641i			0.421754i	−0.977513	+	0.210877i	$0.932368\pi$
$348$		0			0
$349$	14.7846			0.791402			0.395701	−	0.918379i	$-0.370502\pi$
$349$	14.7846			0.791402			0.395701	+	0.918379i	$0.370502\pi$
$350$	−8.53590	+	8.53590i	−0.456263	+	0.456263i
$351$	18.0000	+	5.19615i	0.960769	+	0.277350i
$352$	21.8564	+	21.8564i	1.16495	+	1.16495i
$353$			2.00000i			0.106449i	0.998583	+	0.0532246i	$0.0169499\pi$
$353$			2.00000i			0.106449i	−0.998583	+	0.0532246i	$0.983050\pi$
$354$	−12.9282	−	12.9282i	−0.687126	−	0.687126i
$355$			3.53590i			0.187666i
$356$	−0.660254	+	1.14359i	−0.0349934	+	0.0606103i
$357$			1.39230i			0.0736886i
$358$	0.758330	+	2.83013i	0.0400790	+	0.149577i
$359$			13.0718i			0.689903i	0.938621	+	0.344952i	$0.112105\pi$
$359$			13.0718i			0.689903i	−0.938621	+	0.344952i	$0.887895\pi$
$360$	−0.588457	−	2.19615i	−0.0310144	−	0.115747i
$361$	−4.00000	+	6.92820i	−0.210526	+	0.364642i
$362$	−14.5359	+	14.5359i	−0.763990	+	0.763990i
$363$	32.6603			1.71422
$364$	−9.00000	+	8.66025i	−0.471728	+	0.453921i
$365$	−1.98076	−	1.14359i	−0.103678	−	0.0598584i
$366$	−7.22243	−	26.9545i	−0.377523	−	1.40893i
$367$	5.60770			0.292719			0.146360	−	0.989231i	$-0.453244\pi$
$367$	5.60770			0.292719			0.146360	+	0.989231i	$0.453244\pi$
$368$	12.9282	+	22.3923i	0.673929	+	1.16728i
$369$	14.8923	−	8.59808i	0.775262	−	0.447598i
$370$	−0.418584	+	1.56218i	−0.0217612	+	0.0812138i
$371$		0			0
$372$	−3.00000	+	5.19615i	−0.155543	+	0.269408i
$373$			12.3923i			0.641649i	0.947139	+	0.320825i	$0.103960\pi$
$373$			12.3923i			0.641649i	−0.947139	+	0.320825i	$0.896040\pi$
$374$	0.928203	−	3.46410i	0.0479962	−	0.179124i
$375$	−4.60770			−0.237940
$376$	−6.05256	+	22.5885i	−0.312137	+	1.16491i
$377$		0			0
$378$	3.29423	+	12.2942i	0.169437	+	0.632347i
$379$	16.3301	−	28.2846i	0.838822	−	1.45288i	−0.0520577	−	0.998644i	$-0.516578\pi$
$379$	16.3301	−	28.2846i	0.838822	−	1.45288i	0.890880	−	0.454239i	$-0.150089\pi$
$380$		−	2.78461i		−	0.142847i
$381$	12.4019	−	21.4808i	0.635370	−	1.10049i
$382$	−25.2224	+	6.75833i	−1.29049	+	0.345786i
$383$			38.2487i			1.95442i	0.212280	+	0.977209i	$0.431911\pi$
$383$			38.2487i			1.95442i	−0.212280	+	0.977209i	$0.568089\pi$
$384$	13.8564	−	13.8564i	0.707107	−	0.707107i
$385$	2.19615	−	1.26795i	0.111926	−	0.0646207i
$386$	5.83013	+	1.56218i	0.296746	+	0.0795128i
$387$	−16.7942	−	9.69615i	−0.853699	−	0.492883i
$388$	2.66025	−	4.60770i	0.135054	−	0.233920i
$389$	−7.20577	+	4.16025i	−0.365347	+	0.210933i	−0.671424	−	0.741074i	$-0.734317\pi$
$389$	−7.20577	+	4.16025i	−0.365347	+	0.210933i	0.306077	+	0.952007i	$0.400984\pi$
$390$	−2.36603	−	0.0455173i	−0.119808	−	0.00230486i
$391$	1.50000	−	2.59808i	0.0758583	−	0.131390i
$392$	10.9282	+	2.92820i	0.551958	+	0.147897i
$393$	−18.6962	−	10.7942i	−0.943096	−	0.544497i
$394$	21.4904	−	5.75833i	1.08267	−	0.290100i
$395$	4.26795			0.214744
$396$		−	32.7846i		−	1.64749i
$397$	9.86603	+	17.0885i	0.495162	+	0.857645i	0.999984	−	0.00557790i	$-0.00177551\pi$
$397$	9.86603	+	17.0885i	0.495162	+	0.857645i	−0.504823	+	0.863223i	$0.668442\pi$
$398$	2.70577	−	10.0981i	0.135628	−	0.506171i
$399$			15.5885i			0.780399i
$400$	−9.85641	−	17.0718i	−0.492820	−	0.853590i
$401$	−25.6244	+	14.7942i	−1.27962	+	0.738789i	−0.976778	−	0.214253i	$-0.931268\pi$
$401$	−25.6244	+	14.7942i	−1.27962	+	0.738789i	−0.302841	+	0.953041i	$0.597935\pi$
$402$	−4.90192	+	18.2942i	−0.244486	+	0.912433i
$403$	4.33013	+	4.50000i	0.215699	+	0.224161i
$404$	18.9282			0.941713
$405$	−1.20577	+	2.08846i	−0.0599153	+	0.103776i
$406$		0			0
$407$	−11.6603	+	20.1962i	−0.577977	+	1.00109i
$408$	−2.19615	−	0.588457i	−0.108726	−	0.0291330i
$409$		−	17.0718i		−	0.844146i	−0.906562	−	0.422073i	$-0.861303\pi$
$409$		−	17.0718i		−	0.844146i	0.906562	−	0.422073i	$-0.138697\pi$
$410$	−1.53590	+	1.53590i	−0.0758526	+	0.0758526i
$411$	−4.20577	−	2.42820i	−0.207455	−	0.119774i
$412$	−9.33975	−	5.39230i	−0.460136	−	0.265660i
$413$	−11.1962	−	6.46410i	−0.550927	−	0.318078i
$414$	7.09808	−	26.4904i	0.348851	−	1.30193i
$415$	−3.78461			−0.185779
$416$	−9.85641	−	17.8564i	−0.483250	−	0.875482i
$417$			13.6077i			0.666372i
$418$	10.3923	−	38.7846i	0.508304	−	1.89702i
$419$	−9.18653	+	5.30385i	−0.448792	+	0.259110i	−0.707320	−	0.706894i	$-0.750096\pi$
$419$	−9.18653	+	5.30385i	−0.448792	+	0.259110i	0.258528	+	0.966004i	$0.416763\pi$
$420$	−0.803848	−	1.39230i	−0.0392237	−	0.0679375i
$421$	0.866025	+	1.50000i	0.0422075	+	0.0731055i	0.886357	−	0.463002i	$-0.153228\pi$
$421$	0.866025	+	1.50000i	0.0422075	+	0.0731055i	−0.844150	+	0.536107i	$0.819894\pi$
$422$	−12.8301	−	3.43782i	−0.624561	−	0.167351i
$423$	21.4808	−	12.4019i	1.04443	−	0.603002i
$424$		0			0
$425$	−1.14359	+	1.98076i	−0.0554724	+	0.0960811i
$426$	31.2224	+	8.36603i	1.51273	+	0.405335i
$427$	−9.86603	−	17.0885i	−0.477450	−	0.826968i
$428$	18.4641	−	31.9808i	0.892496	−	1.54585i
$429$	−32.7846	−	9.46410i	−1.58286	−	0.456931i
$430$	2.36603	+	0.633975i	0.114100	+	0.0305730i
$431$	14.5526	+	8.40192i	0.700972	+	0.404706i	0.807709	−	0.589581i	$-0.200707\pi$
$431$	14.5526	+	8.40192i	0.700972	+	0.404706i	−0.106737	+	0.994287i	$0.534040\pi$
$432$	−20.7846			−1.00000
$433$	4.16025	+	7.20577i	0.199929	+	0.346287i	0.948505	−	0.316762i	$-0.102595\pi$
$433$	4.16025	+	7.20577i	0.199929	+	0.346287i	−0.748576	+	0.663049i	$0.769262\pi$
$434$	−1.09808	+	4.09808i	−0.0527093	+	0.196714i
$435$		0			0
$436$			12.0000i			0.574696i
$437$	16.7942	−	29.0885i	0.803377	−	1.39149i
$438$	−14.7846	+	14.7846i	−0.706436	+	0.706436i
$439$	−38.3923			−1.83236			−0.916182	−	0.400762i	$-0.868746\pi$
$439$	−38.3923			−1.83236			−0.916182	+	0.400762i	$0.868746\pi$
$440$	1.07180	+	4.00000i	0.0510959	+	0.190693i
$441$	−6.00000	−	10.3923i	−0.285714	−	0.494872i
$442$	−1.22243	+	2.02628i	−0.0581452	+	0.0963803i
$443$	−36.1865	+	20.8923i	−1.71927	+	0.992623i	−0.799018	+	0.601308i	$0.794647\pi$
$443$	−36.1865	+	20.8923i	−1.71927	+	0.992623i	−0.920256	+	0.391316i	$0.872020\pi$
$444$	12.8038	+	7.39230i	0.607644	+	0.350823i
$445$	−0.153212	+	0.0884573i	−0.00726297	+	0.00419328i
$446$	−5.32051	+	5.32051i	−0.251933	+	0.251933i
$447$	−27.4641			−1.29901
$448$	6.92820	−	12.0000i	0.327327	−	0.566947i
$449$	−7.83975	+	4.52628i	−0.369980	+	0.213608i	−0.673450	−	0.739233i	$-0.735188\pi$
$449$	−7.83975	+	4.52628i	−0.369980	+	0.213608i	0.303469	+	0.952841i	$0.401855\pi$
$450$	−5.41154	+	20.1962i	−0.255103	+	0.952056i
$451$	−27.1244	+	15.6603i	−1.27724	+	0.737413i
$452$			27.7128i			1.30350i
$453$	−1.20577	+	0.696152i	−0.0566521	+	0.0327081i
$454$	−18.0263	+	4.83013i	−0.846015	+	0.226689i
$455$	−1.62436	+	0.401924i	−0.0761510	+	0.0188425i
$456$	−24.5885	−	6.58846i	−1.15146	−	0.308533i
$457$			32.5359i			1.52197i	0.648772	+	0.760983i	$0.275283\pi$
$457$			32.5359i			1.52197i	−0.648772	+	0.760983i	$0.724717\pi$
$458$	−1.09808	+	0.294229i	−0.0513097	+	0.0137484i
$459$	1.20577	+	2.08846i	0.0562806	+	0.0974808i
$460$			3.46410i			0.161515i
$461$	0.205771	−	0.356406i	0.00958373	−	0.0165995i	−0.861194	−	0.508277i	$-0.830283\pi$
$461$	0.205771	−	0.356406i	0.00958373	−	0.0165995i	0.870777	+	0.491677i	$0.163616\pi$
$462$	−6.00000	−	22.3923i	−0.279145	−	1.04178i
$463$	−25.5000	−	14.7224i	−1.18509	−	0.684209i	−0.227900	−	0.973685i	$-0.573186\pi$
$463$	−25.5000	−	14.7224i	−1.18509	−	0.684209i	−0.957186	+	0.289475i	$0.906519\pi$
$464$		0			0
$465$	−0.696152	+	0.401924i	−0.0322833	+	0.0186388i
$466$	7.85641	+	7.85641i	0.363941	+	0.363941i
$467$		−	20.5359i		−	0.950288i	−0.879908	−	0.475144i	$-0.842396\pi$
$467$		−	20.5359i		−	0.950288i	0.879908	−	0.475144i	$-0.157604\pi$
$468$	−6.00000	+	20.7846i	−0.277350	+	0.960769i
$469$			13.3923i			0.618399i
$470$	−2.21539	+	2.21539i	−0.102188	+	0.102188i
$471$	13.5000	+	7.79423i	0.622047	+	0.359139i
$472$	14.9282	−	14.9282i	0.687126	−	0.687126i
$473$	30.5885	+	17.6603i	1.40646	+	0.812019i
$474$	10.0981	−	37.6865i	0.463820	−	1.73100i
$475$	−12.8038	+	22.1769i	−0.587481	+	1.01755i
$476$	−1.60770			−0.0736886
$477$		0			0
$478$	−1.02628	−	3.83013i	−0.0469409	−	0.175186i
$479$			39.3205i			1.79660i	0.439383	+	0.898300i	$0.355197\pi$
$479$			39.3205i			1.79660i	−0.439383	+	0.898300i	$0.644803\pi$
$480$	2.53590	−	0.679492i	0.115747	−	0.0310144i
$481$	11.0885	−	10.6699i	0.505590	−	0.486504i
$482$	0.633975	+	2.36603i	0.0288768	+	0.107770i
$483$		−	19.3923i		−	0.882380i
$484$			37.7128i			1.71422i
$485$	0.617314	−	0.356406i	0.0280308	−	0.0161836i
$486$	15.5885	+	15.5885i	0.707107	+	0.707107i
$487$	−36.4808	+	21.0622i	−1.65310	+	0.954418i	−0.677315	+	0.735694i	$0.736856\pi$
$487$	−36.4808	+	21.0622i	−1.65310	+	0.954418i	−0.975787	+	0.218725i	$0.929810\pi$
$488$	31.1244	−	8.33975i	1.40893	−	0.377523i
$489$	−20.0885	−	34.7942i	−0.908431	−	1.57345i
$490$	1.07180	+	1.07180i	0.0484188	+	0.0484188i
$491$	−8.59808	+	4.96410i	−0.388026	+	0.224027i	−0.681304	−	0.732000i	$-0.738587\pi$
$491$	−8.59808	+	4.96410i	−0.388026	+	0.224027i	0.293279	+	0.956027i	$0.405254\pi$
$492$	9.92820	+	17.1962i	0.447598	+	0.775262i
$493$		0			0
$494$	−13.6865	+	22.6865i	−0.615786	+	1.02072i
$495$	2.19615	−	3.80385i	0.0987097	−	0.170970i
$496$	−6.00000	−	3.46410i	−0.269408	−	0.155543i
$497$	22.8564			1.02525
$498$	−8.95448	+	33.4186i	−0.401260	+	1.49752i
$499$	−1.79423	+	3.10770i	−0.0803207	+	0.139120i	−0.903388	−	0.428825i	$-0.858928\pi$
$499$	−1.79423	+	3.10770i	−0.0803207	+	0.139120i	0.823067	+	0.567944i	$0.192261\pi$
$500$		−	5.32051i		−	0.237940i
$501$	−0.401924	+	0.232051i	−0.0179566	+	0.0103673i
$502$	−31.2224	−	8.36603i	−1.39353	−	0.373394i
$503$	−13.1603	−	22.7942i	−0.586787	−	1.01634i	−0.994650	−	0.103301i	$-0.967059\pi$
$503$	−13.1603	−	22.7942i	−0.586787	−	1.01634i	0.407863	−	0.913043i	$-0.366274\pi$
$504$	−14.1962	+	3.80385i	−0.632347	+	0.169437i
$505$	2.19615	+	1.26795i	0.0977275	+	0.0564230i
$506$	−12.9282	+	48.2487i	−0.574729	+	2.14492i
$507$	19.0526	+	12.0000i	0.846154	+	0.532939i
$508$	24.8038	+	14.3205i	1.10049	+	0.635370i
$509$	10.0622	+	17.4282i	0.445998	+	0.772492i	0.998121	−	0.0612712i	$-0.0195154\pi$
$509$	10.0622	+	17.4282i	0.445998	+	0.772492i	−0.552123	+	0.833763i	$0.686182\pi$
$510$	−0.215390	−	0.215390i	−0.00953764	−	0.00953764i
$511$	−7.39230	+	12.8038i	−0.327016	+	0.566409i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	13.5000	+	23.3827i	0.596040	+	1.03237i
$514$	2.36603	−	8.83013i	0.104361	−	0.389480i
$515$	−0.722432	−	1.25129i	−0.0318342	−	0.0551384i
$516$	11.1962	−	19.3923i	0.492883	−	0.853699i
$517$	−39.1244	+	22.5885i	−1.72069	+	0.993439i
$518$	10.0981	+	2.70577i	0.443684	+	0.118885i
$519$	34.2846	+	19.7942i	1.50493	+	0.868870i
$520$	0.0525589	−	2.73205i	0.00230486	−	0.119808i
$521$	−18.2487			−0.799491			−0.399745	−	0.916626i	$-0.630901\pi$
$521$	−18.2487			−0.799491			−0.399745	+	0.916626i	$0.630901\pi$
$522$		0			0
$523$	14.3827	+	8.30385i	0.628911	+	0.363102i	0.780330	−	0.625368i	$-0.215051\pi$
$523$	14.3827	+	8.30385i	0.628911	+	0.363102i	−0.151419	+	0.988470i	$0.548384\pi$
$524$	12.4641	−	21.5885i	0.544497	−	0.943096i
$525$			14.7846i			0.645253i
$526$	−3.46410	−	3.46410i	−0.151042	−	0.151042i
$527$			0.803848i			0.0350162i
$528$	37.8564			1.64749
$529$	−9.39230	+	16.2679i	−0.408361	+	0.707302i
$530$		0			0
$531$	−22.3923			−0.971743
$532$	−18.0000			−0.780399
$533$	20.0622	−	4.96410i	0.868989	−	0.215019i
$534$	0.418584	+	1.56218i	0.0181139	+	0.0676020i
$535$	4.28461	−	2.47372i	0.185240	−	0.106948i
$536$	−21.1244	−	5.66025i	−0.912433	−	0.244486i
$537$	3.10770	+	1.79423i	0.134107	+	0.0774267i
$538$	18.2942	+	4.90192i	0.788720	+	0.211337i
$539$	10.9282	+	18.9282i	0.470711	+	0.815295i
$540$	−2.41154	−	1.39230i	−0.103776	−	0.0599153i
$541$	−37.8564			−1.62757			−0.813787	−	0.581163i	$-0.802598\pi$
$541$	−37.8564			−1.62757			−0.813787	+	0.581163i	$0.802598\pi$
$542$	−5.95448	−	22.2224i	−0.255767	−	0.954535i
$543$			25.1769i			1.08044i
$544$	0.679492	−	2.53590i	0.0291330	−	0.108726i
$545$	−0.803848	+	1.39230i	−0.0344330	+	0.0596398i
$546$	−0.294229	+	15.2942i	−0.0125918	+	0.654533i
$547$	−17.5981	+	10.1603i	−0.752439	+	0.434421i	−0.826575	−	0.562827i	$-0.809714\pi$
$547$	−17.5981	+	10.1603i	−0.752439	+	0.434421i	0.0741352	+	0.997248i	$0.476380\pi$
$548$	2.80385	−	4.85641i	0.119774	−	0.207455i
$549$	−29.5981	−	17.0885i	−1.26322	−	0.729318i
$550$	9.85641	−	36.7846i	0.420279	−	1.56850i
$551$		0			0
$552$	30.5885	+	8.19615i	1.30193	+	0.348851i
$553$		−	27.5885i		−	1.17318i
$554$	−10.2224	−	38.1506i	−0.434310	−	1.62087i
$555$	0.990381	+	1.71539i	0.0420393	+	0.0728143i
$556$	−15.7128			−0.666372
$557$	−13.1340	+	22.7487i	−0.556504	+	0.963894i	0.441280	+	0.897369i	$0.354524\pi$
$557$	−13.1340	+	22.7487i	−0.556504	+	0.963894i	−0.997785	+	0.0665246i	$0.978809\pi$
$558$	1.90192	+	7.09808i	0.0805149	+	0.300486i
$559$	−16.1603	−	16.7942i	−0.683506	−	0.710320i
$560$	1.60770	−	0.928203i	0.0679375	−	0.0392237i
$561$	−2.19615	−	3.80385i	−0.0927216	−	0.160599i
$562$	−28.7583	−	7.70577i	−1.21310	−	0.325048i
$563$		−	12.9282i		−	0.544859i	−0.962176	−	0.272429i	$-0.912173\pi$
$563$		−	12.9282i		−	0.544859i	0.962176	−	0.272429i	$-0.0878271\pi$
$564$	14.3205	+	24.8038i	0.603002	+	1.04443i
$565$	−1.85641	+	3.21539i	−0.0780996	+	0.135272i
$566$	43.4186	+	11.6340i	1.82502	+	0.489012i
$567$	13.5000	+	7.79423i	0.566947	+	0.327327i
$568$	−9.66025	+	36.0526i	−0.405335	+	1.51273i
$569$	−42.9282			−1.79964			−0.899822	−	0.436257i	$-0.856304\pi$
$569$	−42.9282			−1.79964			−0.899822	+	0.436257i	$0.856304\pi$
$570$	−2.41154	−	2.41154i	−0.101008	−	0.101008i
$571$	15.0622	+	8.69615i	0.630333	+	0.363923i	0.780881	−	0.624680i	$-0.214771\pi$
$571$	15.0622	+	8.69615i	0.630333	+	0.363923i	−0.150548	+	0.988603i	$0.548104\pi$
$572$	10.9282	−	37.8564i	0.456931	−	1.58286i
$573$	−15.9904	+	27.6962i	−0.668008	+	1.15702i
$574$	9.92820	+	9.92820i	0.414395	+	0.414395i
$575$	15.9282	−	27.5885i	0.664252	−	1.15052i
$576$		−	24.0000i		−	1.00000i
$577$			6.00000i			0.249783i	0.992170	+	0.124892i	$0.0398583\pi$
$577$			6.00000i			0.249783i	−0.992170	+	0.124892i	$0.960142\pi$
$578$	22.9282	−	6.14359i	0.953688	−	0.255540i
$579$	6.40192	−	3.69615i	0.266055	−	0.153607i
$580$		0			0
$581$			24.4641i			1.01494i
$582$	−1.68653	−	6.29423i	−0.0699091	−	0.260904i
$583$		0			0
$584$	−17.0718	−	17.0718i	−0.706436	−	0.706436i
$585$	−2.08846	+	2.00962i	−0.0863471	+	0.0830875i
$586$	4.92820	+	4.92820i	0.203582	+	0.203582i
$587$	−11.6077			−0.479101			−0.239550	−	0.970884i	$-0.577000\pi$
$587$	−11.6077			−0.479101			−0.239550	+	0.970884i	$0.577000\pi$
$588$	12.0000	−	6.92820i	0.494872	−	0.285714i
$589$			9.00000i			0.370839i
$590$	2.73205	−	0.732051i	0.112477	−	0.0301381i
$591$	13.6244	−	23.5981i	0.560431	−	0.970695i
$592$	−8.53590	+	14.7846i	−0.350823	+	0.607644i
$593$		−	16.2487i		−	0.667255i	−0.942705	−	0.333627i	$-0.891727\pi$
$593$		−	16.2487i		−	0.667255i	0.942705	−	0.333627i	$-0.108273\pi$
$594$	−28.3923	−	28.3923i	−1.16495	−	1.16495i
$595$	−0.186533	−	0.107695i	−0.00764713	−	0.00441507i
$596$		−	31.7128i		−	1.29901i
$597$	−6.40192	−	11.0885i	−0.262013	−	0.453820i
$598$	17.0263	−	28.2224i	0.696256	−	1.15410i
$599$	2.76795	−	4.79423i	0.113095	−	0.195887i	−0.803921	−	0.594736i	$-0.797257\pi$
$599$	2.76795	−	4.79423i	0.113095	−	0.195887i	0.917017	+	0.398849i	$0.130590\pi$
$600$	−23.3205	−	6.24871i	−0.952056	−	0.255103i
$601$	−11.3205			−0.461773			−0.230887	−	0.972981i	$-0.574163\pi$
$601$	−11.3205			−0.461773			−0.230887	+	0.972981i	$0.574163\pi$
$602$	4.09808	−	15.2942i	0.167025	−	0.623346i
$603$	11.5981	+	20.0885i	0.472310	+	0.818065i
$604$	−0.803848	−	1.39230i	−0.0327081	−	0.0566521i
$605$	−2.52628	+	4.37564i	−0.102708	+	0.177895i
$606$	16.3923	−	16.3923i	0.665892	−	0.665892i
$607$	18.3923			0.746521			0.373260	−	0.927727i	$-0.378240\pi$
$607$	18.3923			0.746521			0.373260	+	0.927727i	$0.378240\pi$
$608$	7.60770	−	28.3923i	0.308533	−	1.15146i
$609$		0			0
$610$	4.16987	+	1.11731i	0.168833	+	0.0452387i
$611$	28.9378	−	7.16025i	1.17070	−	0.289673i
$612$	−2.41154	+	1.39230i	−0.0974808	+	0.0562806i
$613$	9.52628	−	16.5000i	0.384763	−	0.666429i	−0.606973	−	0.794722i	$-0.707617\pi$
$613$	9.52628	−	16.5000i	0.384763	−	0.666429i	0.991736	+	0.128293i	$0.0409499\pi$
$614$	5.07180	+	5.07180i	0.204681	+	0.204681i
$615$			2.66025i			0.107272i
$616$	25.8564	−	6.92820i	1.04178	−	0.279145i
$617$			5.60770i			0.225757i	0.993609	+	0.112879i	$0.0360071\pi$
$617$			5.60770i			0.225757i	−0.993609	+	0.112879i	$0.963993\pi$
$618$	−12.7583	+	3.41858i	−0.513215	+	0.137516i
$619$	2.93782	+	5.08846i	0.118081	+	0.204522i	0.919007	−	0.394241i	$-0.128992\pi$
$619$	2.93782	+	5.08846i	0.118081	+	0.204522i	−0.800926	+	0.598763i	$0.795659\pi$
$620$	−0.464102	−	0.803848i	−0.0186388	−	0.0322833i
$621$	−16.7942	−	29.0885i	−0.673929	−	1.16728i
$622$	−13.5622	+	3.63397i	−0.543794	+	0.145709i
$623$	0.571797	+	0.990381i	0.0229086	+	0.0396788i
$624$	−24.0000	−	6.92820i	−0.960769	−	0.277350i
$625$	−11.9641	+	20.7224i	−0.478564	+	0.828897i
$626$	−4.90192	+	18.2942i	−0.195920	+	0.731184i
$627$	−24.5885	−	42.5885i	−0.981968	−	1.70082i
$628$	−9.00000	+	15.5885i	−0.359139	+	0.622047i
$629$	1.98076			0.0789782
$630$	−1.90192	−	0.509619i	−0.0757745	−	0.0203037i
$631$	2.89230	−	1.66987i	0.115141	−	0.0664766i	−0.441324	−	0.897348i	$-0.645491\pi$
$631$	2.89230	−	1.66987i	0.115141	−	0.0664766i	0.556464	+	0.830871i	$0.312158\pi$
$632$	43.5167	+	11.6603i	1.73100	+	0.463820i
$633$	−14.0885	+	8.13397i	−0.559966	+	0.323296i
$634$	−1.84936	+	6.90192i	−0.0734477	+	0.274110i
$635$	1.91858	+	3.32309i	0.0761367	+	0.131873i
$636$		0			0
$637$	−3.46410	−	14.0000i	−0.137253	−	0.554700i
$638$		0			0
$639$	34.2846	−	19.7942i	1.35628	−	0.783048i
$640$	0.784610	+	2.92820i	0.0310144	+	0.115747i
$641$	18.3564	−	31.7942i	0.725034	−	1.25580i	−0.233925	−	0.972255i	$-0.575157\pi$
$641$	18.3564	−	31.7942i	0.725034	−	1.25580i	0.958960	−	0.283542i	$-0.0915095\pi$
$642$	−11.7058	−	43.6865i	−0.461990	−	1.72417i
$643$	−3.46410			−0.136611			−0.0683054	−	0.997664i	$-0.521759\pi$
$643$	−3.46410			−0.136611			−0.0683054	+	0.997664i	$0.521759\pi$
$644$	22.3923			0.882380
$645$	2.59808	−	1.50000i	0.102299	−	0.0590624i
$646$	−3.29423	+	0.882686i	−0.129610	+	0.0347288i
$647$	10.0359	−	17.3827i	0.394552	−	0.683384i	−0.598492	−	0.801129i	$-0.704233\pi$
$647$	10.0359	−	17.3827i	0.394552	−	0.683384i	0.993044	+	0.117745i	$0.0375665\pi$
$648$	−18.0000	+	18.0000i	−0.707107	+	0.707107i
$649$	40.7846			1.60094
$650$	−12.9808	+	21.5167i	−0.509147	+	0.843953i
$651$	2.59808	+	4.50000i	0.101827	+	0.176369i
$652$	40.1769	−	23.1962i	1.57345	−	0.908431i
$653$	9.40192	−	5.42820i	0.367926	−	0.212422i	−0.304626	−	0.952472i	$-0.598532\pi$
$653$	9.40192	−	5.42820i	0.367926	−	0.212422i	0.672552	+	0.740050i	$0.265198\pi$
$654$	10.3923	+	10.3923i	0.406371	+	0.406371i
$655$	2.89230	−	1.66987i	0.113012	−	0.0652473i
$656$	−19.8564	+	11.4641i	−0.775262	+	0.447598i
$657$			25.6077i			0.999051i
$658$	14.3205	+	14.3205i	0.558272	+	0.558272i
$659$	4.79423	+	2.76795i	0.186757	+	0.107824i	0.590463	−	0.807064i	$-0.298945\pi$
$659$	4.79423	+	2.76795i	0.186757	+	0.107824i	−0.403707	+	0.914888i	$0.632278\pi$
$660$	4.39230	+	2.53590i	0.170970	+	0.0987097i
$661$	1.33013	+	2.30385i	0.0517359	+	0.0896093i	0.890734	−	0.454526i	$-0.150191\pi$
$661$	1.33013	+	2.30385i	0.0517359	+	0.0896093i	−0.838998	+	0.544135i	$0.816858\pi$
$662$	−22.5622	+	6.04552i	−0.876904	+	0.234966i
$663$	0.696152	+	2.81347i	0.0270363	+	0.109266i
$664$	−38.5885	−	10.3397i	−1.49752	−	0.401260i
$665$	−2.08846	−	1.20577i	−0.0809869	−	0.0467578i
$666$	17.4904	−	4.68653i	0.677738	−	0.181599i
$667$		0			0
$668$	−0.267949	−	0.464102i	−0.0103673	−	0.0179566i
$669$			9.21539i			0.356288i
$670$	−2.07180	−	2.07180i	−0.0800405	−	0.0800405i
$671$	53.9090	+	31.1244i	2.08113	+	1.20154i
$672$	−4.39230	−	16.3923i	−0.169437	−	0.632347i
$673$	−12.3923			−0.477688			−0.238844	−	0.971058i	$-0.576768\pi$
$673$	−12.3923			−0.477688			−0.238844	+	0.971058i	$0.576768\pi$
$674$	−13.5622	+	3.63397i	−0.522396	+	0.139975i
$675$	12.8038	+	22.1769i	0.492820	+	0.853590i
$676$	−13.8564	+	22.0000i	−0.532939	+	0.846154i
$677$	26.3827	−	15.2321i	1.01397	−	0.585415i	0.101618	−	0.994824i	$-0.467598\pi$
$677$	26.3827	−	15.2321i	1.01397	−	0.585415i	0.912351	+	0.409408i	$0.134265\pi$
$678$	24.0000	+	24.0000i	0.921714	+	0.921714i
$679$	−2.30385	−	3.99038i	−0.0884136	−	0.153137i
$680$	0.248711	−	0.248711i	0.00953764	−	0.00953764i
$681$	−11.4282	+	19.7942i	−0.437930	+	0.758516i
$682$	−3.46410	−	12.9282i	−0.132647	−	0.495046i
$683$	15.4545	+	26.7679i	0.591349	+	1.02425i	0.994051	+	0.108916i	$0.0347379\pi$
$683$	15.4545	+	26.7679i	0.591349	+	1.02425i	−0.402702	+	0.915331i	$0.631929\pi$
$684$	−27.0000	+	15.5885i	−1.03237	+	0.596040i
$685$	0.650635	−	0.375644i	0.0248595	−	0.0143526i
$686$	19.0526	−	19.0526i	0.727430	−	0.727430i
$687$	−0.696152	+	1.20577i	−0.0265599	+	0.0460030i
$688$	22.3923	+	12.9282i	0.853699	+	0.492883i
$689$		0			0
$690$	3.00000	+	3.00000i	0.114208	+	0.114208i
$691$	32.5359			1.23772			0.618862	−	0.785500i	$-0.287594\pi$
$691$	32.5359			1.23772			0.618862	+	0.785500i	$0.287594\pi$
$692$	−22.8564	+	39.5885i	−0.868870	+	1.50493i
$693$	−24.5885	−	14.1962i	−0.934038	−	0.539267i
$694$	−7.85641	+	7.85641i	−0.298225	+	0.298225i
$695$	−1.82309	−	1.05256i	−0.0691536	−	0.0399258i
$696$		0			0
$697$	2.30385	+	1.33013i	0.0872644	+	0.0503822i
$698$	14.7846	+	14.7846i	0.559606	+	0.559606i
$699$	13.6077			0.514690
$700$	−17.0718			−0.645253
$701$		−	28.3923i		−	1.07236i	−0.844103	−	0.536181i	$-0.819866\pi$
$701$		−	28.3923i		−	1.07236i	0.844103	−	0.536181i	$-0.180134\pi$
$702$	12.8038	+	23.1962i	0.483250	+	0.875482i
$703$	22.1769			0.836418
$704$			43.7128i			1.64749i
$705$			3.83717i			0.144516i
$706$	−2.00000	+	2.00000i	−0.0752710	+	0.0752710i
$707$	8.19615	−	14.1962i	0.308248	−	0.533901i
$708$		−	25.8564i		−	0.971743i
$709$	16.3301	−	28.2846i	0.613291	−	1.06225i	−0.377391	−	0.926054i	$-0.623179\pi$
$709$	16.3301	−	28.2846i	0.613291	−	1.06225i	0.990682	−	0.136197i	$-0.0434880\pi$
$710$	−3.53590	+	3.53590i	−0.132700	+	0.132700i
$711$	−23.8923	−	41.3827i	−0.896031	−	1.55197i
$712$	−1.80385	+	0.483340i	−0.0676020	+	0.0181139i
$713$		−	11.1962i		−	0.419299i
$714$	−1.39230	+	1.39230i	−0.0521057	+	0.0521057i
$715$	3.80385	−	3.66025i	0.142256	−	0.136886i
$716$	−2.07180	+	3.58846i	−0.0774267	+	0.134107i
$717$	−4.20577	−	2.42820i	−0.157067	−	0.0906829i
$718$	−13.0718	+	13.0718i	−0.487835	+	0.487835i
$719$	−3.69615	−	6.40192i	−0.137843	−	0.238751i	0.788837	−	0.614603i	$-0.210684\pi$
$719$	−3.69615	−	6.40192i	−0.137843	−	0.238751i	−0.926680	+	0.375851i	$0.877350\pi$
$720$	1.60770	−	2.78461i	0.0599153	−	0.103776i
$721$	−8.08846	+	4.66987i	−0.301230	+	0.173915i
$722$	−10.9282	+	2.92820i	−0.406706	+	0.108976i
$723$	2.59808	+	1.50000i	0.0966235	+	0.0557856i
$724$	−29.0718			−1.08044
$725$		0			0
$726$	32.6603	+	32.6603i	1.21214	+	1.21214i
$727$	−24.3564	−	42.1865i	−0.903329	−	1.56461i	−0.823145	−	0.567832i	$-0.807782\pi$
$727$	−24.3564	−	42.1865i	−0.903329	−	1.56461i	−0.0801846	−	0.996780i	$-0.525551\pi$
$728$	−17.6603	−	0.339746i	−0.654533	−	0.0125918i
$729$	27.0000			1.00000
$730$	−0.837169	−	3.12436i	−0.0309850	−	0.115638i
$731$		−	3.00000i		−	0.110959i
$732$	19.7321	−	34.1769i	0.729318	−	1.26322i
$733$	2.13397	−	3.69615i	0.0788202	−	0.136521i	−0.823921	−	0.566705i	$-0.808218\pi$
$733$	2.13397	−	3.69615i	0.0788202	−	0.136521i	0.902741	+	0.430184i	$0.141551\pi$
$734$	5.60770	+	5.60770i	0.206984	+	0.206984i
$735$	1.85641			0.0684746
$736$	−9.46410	+	35.3205i	−0.348851	+	1.30193i
$737$	−21.1244	−	36.5885i	−0.778126	−	1.34775i
$738$	23.4904	+	6.29423i	0.864693	+	0.231694i
$739$	24.6506	−	42.6962i	0.906788	−	1.57060i	0.0882897	−	0.996095i	$-0.471860\pi$
$739$	24.6506	−	42.6962i	0.906788	−	1.57060i	0.818499	−	0.574509i	$-0.194807\pi$
$740$	−1.98076	+	1.14359i	−0.0728143	+	0.0420393i
$741$	7.79423	+	31.5000i	0.286328	+	1.15718i
$742$		0			0
$743$	−8.64359	+	4.99038i	−0.317103	+	0.183079i	−0.650100	−	0.759848i	$-0.725273\pi$
$743$	−8.64359	+	4.99038i	−0.317103	+	0.183079i	0.332998	+	0.942928i	$0.391940\pi$
$744$	−8.19615	+	2.19615i	−0.300486	+	0.0805149i
$745$	2.12436	−	3.67949i	0.0778304	−	0.134806i
$746$	−12.3923	+	12.3923i	−0.453715	+	0.453715i
$747$	21.1865	+	36.6962i	0.775175	+	1.34264i
$748$	4.39230	−	2.53590i	0.160599	−	0.0927216i
$749$	−15.9904	−	27.6962i	−0.584276	−	1.01200i
$750$	−4.60770	−	4.60770i	−0.168249	−	0.168249i
$751$	25.4808	+	44.1340i	0.929806	+	1.61047i	0.783643	+	0.621211i	$0.213359\pi$
$751$	25.4808	+	44.1340i	0.929806	+	1.61047i	0.146163	+	0.989261i	$0.453308\pi$
$752$	−28.6410	+	16.5359i	−1.04443	+	0.603002i
$753$	−34.2846	+	19.7942i	−1.24940	+	0.721342i
$754$		0			0
$755$		−	0.215390i		−	0.00783886i
$756$	−9.00000	+	15.5885i	−0.327327	+	0.566947i
$757$	24.0622	+	13.8923i	0.874555	+	0.504924i	0.868859	−	0.495059i	$-0.164854\pi$
$757$	24.0622	+	13.8923i	0.874555	+	0.504924i	0.00569558	+	0.999984i	$0.498187\pi$
$758$	44.6147	−	11.9545i	1.62048	−	0.434206i
$759$	30.5885	+	52.9808i	1.11029	+	1.92308i
$760$	2.78461	−	2.78461i	0.101008	−	0.101008i
$761$		−	26.3923i		−	0.956720i	−0.878164	−	0.478360i	$-0.841231\pi$
$761$		−	26.3923i		−	0.956720i	0.878164	−	0.478360i	$-0.158769\pi$
$762$	33.8827	−	9.07884i	1.22744	−	0.328892i
$763$	9.00000	+	5.19615i	0.325822	+	0.188113i
$764$	−31.9808	−	18.4641i	−1.15702	−	0.668008i
$765$	−0.373067			−0.0134883
$766$	−38.2487	+	38.2487i	−1.38198	+	1.38198i
$767$	−25.8564	−	7.46410i	−0.933621	−	0.269513i
$768$	27.7128			1.00000
$769$	−28.2846	+	16.3301i	−1.01997	+	0.588879i	−0.914095	−	0.405500i	$-0.867097\pi$
$769$	−28.2846	+	16.3301i	−1.01997	+	0.588879i	−0.105874	+	0.994380i	$0.533764\pi$
$770$	3.46410	+	0.928203i	0.124838	+	0.0334501i
$771$	−5.59808	−	9.69615i	−0.201610	−	0.349198i
$772$	4.26795	+	7.39230i	0.153607	+	0.266055i
$773$	14.9904	+	25.9641i	0.539167	+	0.933864i	0.998949	+	0.0458323i	$0.0145940\pi$
$773$	14.9904	+	25.9641i	0.539167	+	0.933864i	−0.459783	+	0.888032i	$0.652073\pi$
$774$	−7.09808	−	26.4904i	−0.255135	−	0.952177i
$775$			8.53590i			0.306619i
$776$	7.26795	−	1.94744i	0.260904	−	0.0699091i
$777$	11.0885	−	6.40192i	0.397796	−	0.229668i
$778$	−11.3660	−	3.04552i	−0.407492	−	0.109187i
$779$	25.7942	+	14.8923i	0.924174	+	0.533572i
$780$	−2.32051	−	2.41154i	−0.0830875	−	0.0863471i
$781$	−62.4449	+	36.0526i	−2.23445	+	1.29006i
$782$	4.09808	−	1.09808i	0.146547	−	0.0392671i
$783$		0			0
$784$	8.00000	+	13.8564i	0.285714	+	0.494872i
$785$	−2.08846	+	1.20577i	−0.0745402	+	0.0430358i
$786$	−7.90192	−	29.4904i	−0.281852	−	1.05189i
$787$	−49.1769			−1.75297			−0.876484	−	0.481431i	$-0.840117\pi$
$787$	−49.1769			−1.75297			−0.876484	+	0.481431i	$0.840117\pi$
$788$	27.2487	+	15.7321i	0.970695	+	0.560431i
$789$	−6.00000			−0.213606
$790$	4.26795	+	4.26795i	0.151847	+	0.151847i
$791$	20.7846	+	12.0000i	0.739016	+	0.426671i
$792$	32.7846	−	32.7846i	1.16495	−	1.16495i
$793$	−28.4808	−	29.5981i	−1.01138	−	1.05106i
$794$	−7.22243	+	26.9545i	−0.256315	+	0.956579i
$795$		0			0
$796$	12.8038	−	7.39230i	0.453820	−	0.262013i
$797$			16.3923i			0.580645i	0.956929	+	0.290323i	$0.0937626\pi$
$797$			16.3923i			0.580645i	−0.956929	+	0.290323i	$0.906237\pi$
$798$	−15.5885	+	15.5885i	−0.551825	+	0.551825i
$799$	3.32309	+	1.91858i	0.117562	+	0.0678746i
$800$	7.21539	−	26.9282i	0.255103	−	0.952056i
$801$	1.71539	+	0.990381i	0.0606103	+	0.0349934i
$802$	−40.4186	−	10.8301i	−1.42723	−	0.382425i
$803$		−	46.6410i		−	1.64593i
$804$	−23.1962	+	13.3923i	−0.818065	+	0.472310i
$805$	2.59808	+	1.50000i	0.0915702	+	0.0528681i
$806$	−0.169873	+	8.83013i	−0.00598352	+	0.311028i
$807$	20.0885	−	11.5981i	0.707147	−	0.408272i
$808$	18.9282	+	18.9282i	0.665892	+	0.665892i
$809$	0.571797	−	0.990381i	0.0201033	−	0.0348199i	−0.855799	−	0.517309i	$-0.826934\pi$
$809$	0.571797	−	0.990381i	0.0201033	−	0.0348199i	0.875902	+	0.482489i	$0.160267\pi$
$810$	−3.29423	+	0.882686i	−0.115747	+	0.0310144i
$811$	19.6077			0.688519			0.344260	−	0.938874i	$-0.388130\pi$
$811$	19.6077			0.688519			0.344260	+	0.938874i	$0.388130\pi$
$812$		0			0
$813$	−24.4019	−	14.0885i	−0.855813	−	0.494104i
$814$	−31.8564	+	8.53590i	−1.11657	+	0.299183i
$815$	6.21539			0.217716
$816$	−1.60770	−	2.78461i	−0.0562806	−	0.0974808i
$817$		−	33.5885i		−	1.17511i
$818$	17.0718	−	17.0718i	0.596901	−	0.596901i
$819$	12.9904	+	13.5000i	0.453921	+	0.471728i
$820$	−3.07180			−0.107272
$821$	−1.32051			−0.0460860			−0.0230430	−	0.999734i	$-0.507335\pi$
$821$	−1.32051			−0.0460860			−0.0230430	+	0.999734i	$0.507335\pi$
$822$	−1.77757	−	6.63397i	−0.0619998	−	0.231386i
$823$	26.0000			0.906303			0.453152	−	0.891434i	$-0.350300\pi$
$823$	26.0000			0.906303			0.453152	+	0.891434i	$0.350300\pi$
$824$	−3.94744	−	14.7321i	−0.137516	−	0.513215i
$825$	−23.3205	−	40.3923i	−0.811916	−	1.40628i
$826$	−4.73205	−	17.6603i	−0.164649	−	0.614479i
$827$	38.9282			1.35367			0.676833	−	0.736136i	$-0.263352\pi$
$827$	38.9282			1.35367			0.676833	+	0.736136i	$0.263352\pi$
$828$	33.5885	−	19.3923i	1.16728	−	0.673929i
$829$	−7.11474	−	4.10770i	−0.247105	−	0.142666i	0.371333	−	0.928500i	$-0.378901\pi$
$829$	−7.11474	−	4.10770i	−0.247105	−	0.142666i	−0.618438	+	0.785834i	$0.712234\pi$
$830$	−3.78461	−	3.78461i	−0.131366	−	0.131366i
$831$	−41.8923	−	24.1865i	−1.45323	−	0.839022i
$832$	8.00000	−	27.7128i	0.277350	−	0.960769i
$833$	0.928203	−	1.60770i	0.0321603	−	0.0557033i
$834$	−13.6077	+	13.6077i	−0.471196	+	0.471196i
$835$		−	0.0717968i		−	0.00248463i
$836$	49.1769	−	28.3923i	1.70082	−	0.981968i
$837$	7.79423	+	4.50000i	0.269408	+	0.155543i
$838$	−14.4904	−	3.88269i	−0.500562	−	0.134125i
$839$	−13.1603	−	7.59808i	−0.454342	−	0.262315i	0.255320	−	0.966857i	$-0.417819\pi$
$839$	−13.1603	−	7.59808i	−0.454342	−	0.262315i	−0.709662	+	0.704542i	$0.751153\pi$
$840$	0.588457	−	2.19615i	0.0203037	−	0.0757745i
$841$	29.0000			1.00000
$842$	−0.633975	+	2.36603i	−0.0218482	+	0.0815386i
$843$	−31.5788	+	18.2321i	−1.08763	+	0.627945i
$844$	−9.39230	−	16.2679i	−0.323296	−	0.559966i
$845$	−3.08142	+	1.62436i	−0.106004	+	0.0558795i
$846$	33.8827	+	9.07884i	1.16491	+	0.312137i
$847$	28.2846	+	16.3301i	0.971871	+	0.561110i
$848$		0			0
$849$	47.6769	−	27.5263i	1.63627	−	0.944699i
$850$	−3.12436	+	0.837169i	−0.107165	+	0.0287146i
$851$	−27.5885			−0.945720
$852$	22.8564	+	39.5885i	0.783048	+	1.35628i
$853$	−11.7224	−	20.3038i	−0.401368	−	0.695191i	0.592523	−	0.805554i	$-0.298132\pi$
$853$	−11.7224	−	20.3038i	−0.401368	−	0.695191i	−0.993891	+	0.110363i	$0.964799\pi$
$854$	7.22243	−	26.9545i	0.247147	−	0.922363i
$855$	−4.17691			−0.142847
$856$	50.4449	−	13.5167i	1.72417	−	0.461990i
$857$	19.6244	+	33.9904i	0.670355	+	1.16109i	0.977803	+	0.209524i	$0.0671916\pi$
$857$	19.6244	+	33.9904i	0.670355	+	1.16109i	−0.307448	+	0.951565i	$0.599475\pi$
$858$	−23.3205	−	42.2487i	−0.796149	−	1.44235i
$859$	30.3109	+	17.5000i	1.03419	+	0.597092i	0.918183	−	0.396156i	$-0.129656\pi$
$859$	30.3109	+	17.5000i	1.03419	+	0.597092i	0.116011	+	0.993248i	$0.462989\pi$
$860$	1.73205	+	3.00000i	0.0590624	+	0.102299i
$861$	17.1962			0.586043
$862$	6.15064	+	22.9545i	0.209491	+	0.781833i
$863$		−	22.1051i		−	0.752467i	−0.926525	−	0.376233i	$-0.877219\pi$
$863$		−	22.1051i		−	0.752467i	0.926525	−	0.376233i	$-0.122781\pi$
$864$	−20.7846	−	20.7846i	−0.707107	−	0.707107i
$865$	−5.30385	+	3.06218i	−0.180336	+	0.104117i
$866$	−3.04552	+	11.3660i	−0.103491	+	0.386233i
$867$	14.5359	−	25.1769i	0.493665	−	0.855053i
$868$	−5.19615	+	3.00000i	−0.176369	+	0.101827i
$869$	43.5167	+	75.3731i	1.47620	+	2.55686i
$870$		0			0
$871$	6.69615	+	27.0622i	0.226890	+	0.916967i
$872$	−12.0000	+	12.0000i	−0.406371	+	0.406371i
$873$	−6.91154	−	3.99038i	−0.233920	−	0.135054i
$874$	45.8827	−	12.2942i	1.55201	−	0.415858i
$875$	−3.99038	−	2.30385i	−0.134900	−	0.0778843i
$876$	−29.5692			−0.999051
$877$	−46.3923			−1.56656			−0.783278	−	0.621671i	$-0.786454\pi$
$877$	−46.3923			−1.56656			−0.783278	+	0.621671i	$0.786454\pi$
$878$	−38.3923	−	38.3923i	−1.29568	−	1.29568i
$879$	8.53590			0.287909
$880$	−2.92820	+	5.07180i	−0.0987097	+	0.170970i
$881$	13.9641	−	24.1865i	0.470463	−	0.814865i	−0.528967	−	0.848642i	$-0.677420\pi$
$881$	13.9641	−	24.1865i	0.470463	−	0.814865i	0.999429	+	0.0337775i	$0.0107537\pi$
$882$	4.39230	−	16.3923i	0.147897	−	0.551958i
$883$		−	40.7846i		−	1.37251i	−0.727360	−	0.686256i	$-0.759253\pi$
$883$		−	40.7846i		−	1.37251i	0.727360	−	0.686256i	$-0.240747\pi$
$884$	−3.24871	+	0.803848i	−0.109266	+	0.0270363i
$885$	1.73205	−	3.00000i	0.0582223	−	0.100844i
$886$	−57.0788	−	15.2942i	−1.91760	−	0.513820i
$887$	23.0885	+	39.9904i	0.775235	+	1.34275i	0.934663	+	0.355536i	$0.115702\pi$
$887$	23.0885	+	39.9904i	0.775235	+	1.34275i	−0.159428	+	0.987210i	$0.550965\pi$
$888$	5.41154	+	20.1962i	0.181599	+	0.677738i
$889$	21.4808	−	12.4019i	0.720442	−	0.415947i
$890$	−0.241670	−	0.0647552i	−0.00810079	−	0.00217060i
$891$	−49.1769			−1.64749
$892$	−10.6410			−0.356288
$893$	37.2058	+	21.4808i	1.24504	+	0.718826i
$894$	−27.4641	−	27.4641i	−0.918537	−	0.918537i
$895$	−0.480762	+	0.277568i	−0.0160701	+	0.00927808i
$896$	18.9282	−	5.07180i	0.632347	−	0.169437i
$897$	−9.69615	−	39.1865i	−0.323745	−	1.30840i
$898$	−12.3660	−	3.31347i	−0.412660	−	0.110572i
$899$		0			0
$900$	−25.6077	+	14.7846i	−0.853590	+	0.492820i
$901$		0			0
$902$	−42.7846	−	11.4641i	−1.42457	−	0.381713i
$903$	−9.69615	−	16.7942i	−0.322668	−	0.558877i
$904$	−27.7128	+	27.7128i	−0.921714	+	0.921714i
$905$	−3.37307	−	1.94744i	−0.112125	−	0.0647351i
$906$	−1.90192	−	0.509619i	−0.0631872	−	0.0169310i
$907$		−	51.1769i		−	1.69930i	−0.527346	−	0.849651i	$-0.676813\pi$
$907$		−	51.1769i		−	1.69930i	0.527346	−	0.849651i	$-0.323187\pi$
$908$	−22.8564	−	13.1962i	−0.758516	−	0.437930i
$909$		−	28.3923i		−	0.941713i
$910$	−2.02628	−	1.22243i	−0.0671705	−	0.0405232i
$911$	−4.03590	−	6.99038i	−0.133715	−	0.231602i	0.791391	−	0.611311i	$-0.209357\pi$
$911$	−4.03590	−	6.99038i	−0.133715	−	0.231602i	−0.925106	+	0.379709i	$0.876024\pi$
$912$	−18.0000	−	31.1769i	−0.596040	−	1.03237i
$913$	−38.5885	−	66.8372i	−1.27709	−	2.21199i
$914$	−32.5359	+	32.5359i	−1.07619	+	1.07619i
$915$	4.57884	−	2.64359i	0.151372	−	0.0873945i
$916$	−1.39230	−	0.803848i	−0.0460030	−	0.0265599i
$917$	−10.7942	−	18.6962i	−0.356457	−	0.617401i
$918$	−0.882686	+	3.29423i	−0.0291330	+	0.108726i
$919$	4.37564	+	7.57884i	0.144339	+	0.250003i	0.929126	−	0.369763i	$-0.120561\pi$
$919$	4.37564	+	7.57884i	0.144339	+	0.250003i	−0.784787	+	0.619766i	$0.787228\pi$
$920$	−3.46410	+	3.46410i	−0.114208	+	0.114208i
$921$	8.78461			0.289463
$922$	0.562178	−	0.150635i	0.0185143	−	0.00496090i
$923$	46.1865	−	11.4282i	1.52025	−	0.376164i
$924$	16.3923	−	28.3923i	0.539267	−	0.934038i
$925$	21.0333			0.691571
$926$	−10.7776	−	40.2224i	−0.354173	−	1.32179i
$927$	−8.08846	+	14.0096i	−0.265660	+	0.460136i
$928$		0			0
$929$	−18.0167	−	10.4019i	−0.591107	−	0.341276i	0.174428	−	0.984670i	$-0.444192\pi$
$929$	−18.0167	−	10.4019i	−0.591107	−	0.341276i	−0.765535	+	0.643394i	$0.777526\pi$
$930$	−1.09808	−	0.294229i	−0.0360073	−	0.00964814i
$931$	10.3923	−	18.0000i	0.340594	−	0.589926i
$932$			15.7128i			0.514690i
$933$	−8.59808	+	14.8923i	−0.281488	+	0.487552i
$934$	20.5359	−	20.5359i	0.671955	−	0.671955i
$935$	0.679492			0.0222218
$936$	−26.7846	+	14.7846i	−0.875482	+	0.483250i
$937$	−18.2487			−0.596159			−0.298080	−	0.954541i	$-0.596346\pi$
$937$	−18.2487			−0.596159			−0.298080	+	0.954541i	$0.596346\pi$
$938$	−13.3923	+	13.3923i	−0.437274	+	0.437274i
$939$	11.5981	+	20.0885i	0.378489	+	0.655562i
$940$	−4.43078			−0.144516
$941$	16.1865	−	28.0359i	0.527666	−	0.913944i	−0.471814	−	0.881698i	$-0.656401\pi$
$941$	16.1865	−	28.0359i	0.527666	−	0.913944i	0.999480	−	0.0322461i	$-0.0102660\pi$
$942$	5.70577	+	21.2942i	0.185904	+	0.693803i
$943$	−32.0885	−	18.5263i	−1.04494	−	0.603299i
$944$	29.8564			0.971743
$945$	−2.08846	+	1.20577i	−0.0679375	+	0.0392237i
$946$	12.9282	+	48.2487i	0.420332	+	1.56870i
$947$	19.3205			0.627832			0.313916	−	0.949451i	$-0.398359\pi$
$947$	19.3205			0.627832			0.313916	+	0.949451i	$0.398359\pi$
$948$	47.7846	−	27.5885i	1.55197	−	0.896031i
$949$	−8.53590	+	29.5692i	−0.277087	+	0.959857i
$950$	−34.9808	+	9.37307i	−1.13493	+	0.304102i
$951$	4.37564	+	7.57884i	0.141890	+	0.245761i
$952$	−1.60770	−	1.60770i	−0.0521057	−	0.0521057i
$953$	4.16025	+	7.20577i	0.134764	+	0.233418i	0.925507	−	0.378730i	$-0.123639\pi$
$953$	4.16025	+	7.20577i	0.134764	+	0.233418i	−0.790743	+	0.612148i	$0.790306\pi$
$954$		0			0
$955$	−2.47372	−	4.28461i	−0.0800477	−	0.138647i
$956$	2.80385	−	4.85641i	0.0906829	−	0.157067i
$957$		0			0
$958$	−39.3205	+	39.3205i	−1.27039	+	1.27039i
$959$	−2.42820	−	4.20577i	−0.0784108	−	0.135811i
$960$	3.21539	+	1.85641i	0.103776	+	0.0599153i
$961$	−14.0000	−	24.2487i	−0.451613	−	0.782216i
$962$	21.7583	+	0.418584i	0.701517	+	0.0134957i
$963$	−47.9711	−	27.6962i	−1.54585	−	0.892496i
$964$	−1.73205	+	3.00000i	−0.0557856	+	0.0966235i
$965$			1.14359i			0.0368136i
$966$	19.3923	−	19.3923i	0.623937	−	0.623937i
$967$	−35.6769	−	20.5981i	−1.14729	−	0.662389i	−0.199066	−	0.979986i	$-0.563791\pi$
$967$	−35.6769	−	20.5981i	−1.14729	−	0.662389i	−0.948226	+	0.317597i	$0.897124\pi$
$968$	−37.7128	+	37.7128i	−1.21214	+	1.21214i
$969$	−2.08846	+	3.61731i	−0.0670909	+	0.116205i
$970$	0.973721	+	0.260908i	0.0312643	+	0.00837724i
$971$	36.9904	−	21.3564i	1.18708	−	0.685360i	0.229437	−	0.973324i	$-0.426312\pi$
$971$	36.9904	−	21.3564i	1.18708	−	0.685360i	0.957641	+	0.287964i	$0.0929783\pi$
$972$			31.1769i			1.00000i
$973$	−6.80385	+	11.7846i	−0.218121	+	0.377797i
$974$	−57.5429	−	15.4186i	−1.84379	−	0.494043i
$975$	7.39230	+	29.8756i	0.236743	+	0.956786i
$976$	39.4641	+	22.7846i	1.26322	+	0.729318i
$977$	7.83975	−	4.52628i	0.250816	−	0.144809i	−0.369322	−	0.929301i	$-0.620410\pi$
$977$	7.83975	−	4.52628i	0.250816	−	0.144809i	0.620138	+	0.784493i	$0.287077\pi$
$978$	14.7058	−	54.8827i	0.470239	−	1.75495i
$979$	−3.12436	−	1.80385i	−0.0998548	−	0.0576512i
$980$			2.14359i			0.0684746i
$981$	18.0000			0.574696
$982$	−13.5622	−	3.63397i	−0.432786	−	0.115965i
$983$	32.5526	−	18.7942i	1.03827	−	0.599443i	0.118924	−	0.992903i	$-0.462056\pi$
$983$	32.5526	−	18.7942i	1.03827	−	0.599443i	0.919341	+	0.393461i	$0.128722\pi$
$984$	−7.26795	+	27.1244i	−0.231694	+	0.864693i
$985$	2.10770	+	3.65064i	0.0671568	+	0.116319i
$986$		0			0
$987$	24.8038			0.789515
$988$	−36.3731	+	9.00000i	−1.15718	+	0.286328i
$989$			41.7846i			1.32867i
$990$	6.00000	−	1.60770i	0.190693	−	0.0510959i
$991$	3.89230	−	6.74167i	0.123643	−	0.214156i	−0.797559	−	0.603241i	$-0.793876\pi$
$991$	3.89230	−	6.74167i	0.123643	−	0.214156i	0.921202	+	0.389085i	$0.127209\pi$
$992$	−2.53590	−	9.46410i	−0.0805149	−	0.300486i
$993$	−14.3038	+	24.7750i	−0.453919	+	0.786211i
$994$	22.8564	+	22.8564i	0.724961	+	0.724961i
$995$	1.98076			0.0627944
$996$	−42.3731	+	24.4641i	−1.34264	+	0.775175i
$997$	4.79423	+	2.76795i	0.151835	+	0.0876618i	0.573993	−	0.818861i	$-0.305394\pi$
$997$	4.79423	+	2.76795i	0.151835	+	0.0876618i	−0.422158	+	0.906522i	$0.638727\pi$
$998$	−4.90192	+	1.31347i	−0.155168	+	0.0415771i
$999$	11.0885	−	19.2058i	0.350823	−	0.607644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.ca.b.589.2	yes	4
8.5	even	2		936.2.ca.a.589.2	yes	4
9.7	even	3		936.2.bk.a.277.2	✓	4
13.10	even	6		936.2.bk.b.517.2	yes	4
72.61	even	6		936.2.bk.b.277.2	yes	4
104.101	even	6		936.2.bk.a.517.2	yes	4
117.88	even	6		936.2.ca.a.205.1	yes	4
936.205	even	6	inner	936.2.ca.b.205.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.bk.a.277.2	✓	4	9.7	even	3
936.2.bk.a.517.2	yes	4	104.101	even	6
936.2.bk.b.277.2	yes	4	72.61	even	6
936.2.bk.b.517.2	yes	4	13.10	even	6
936.2.ca.a.205.1	yes	4	117.88	even	6
936.2.ca.a.589.2	yes	4	8.5	even	2
936.2.ca.b.205.1	yes	4	936.205	even	6	inner
936.2.ca.b.589.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(-0.133975 + 0.232051i) q^{5} +(1.73205 + 1.73205i) q^{6} +(1.50000 + 0.866025i) q^{7} +(-2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +(-0.366025 + 0.0980762i) q^{10} -5.46410 q^{11} +3.46410i q^{12} +(3.46410 + 1.00000i) q^{13} +(0.633975 + 2.36603i) q^{14} +(-0.232051 + 0.401924i) q^{15} -4.00000 q^{16} +(0.232051 + 0.401924i) q^{17} +(3.00000 + 3.00000i) q^{18} +(2.59808 + 4.50000i) q^{19} +(-0.464102 - 0.267949i) q^{20} +(2.59808 + 1.50000i) q^{21} +(-5.46410 - 5.46410i) q^{22} +(-3.23205 - 5.59808i) q^{23} +(-3.46410 + 3.46410i) q^{24} +(2.46410 + 4.26795i) q^{25} +(2.46410 + 4.46410i) q^{26} +5.19615 q^{27} +(-1.73205 + 3.00000i) q^{28} +(-0.633975 + 0.169873i) q^{30} +(1.50000 + 0.866025i) q^{31} +(-4.00000 - 4.00000i) q^{32} -9.46410 q^{33} +(-0.169873 + 0.633975i) q^{34} +(-0.401924 + 0.232051i) q^{35} +6.00000i q^{36} +(2.13397 - 3.69615i) q^{37} +(-1.90192 + 7.09808i) q^{38} +(6.00000 + 1.73205i) q^{39} +(-0.196152 - 0.732051i) q^{40} +(4.96410 - 2.86603i) q^{41} +(1.09808 + 4.09808i) q^{42} +(-5.59808 - 3.23205i) q^{43} -10.9282i q^{44} +(-0.401924 + 0.696152i) q^{45} +(2.36603 - 8.83013i) q^{46} +(7.16025 - 4.13397i) q^{47} -6.92820 q^{48} +(-2.00000 - 3.46410i) q^{49} +(-1.80385 + 6.73205i) q^{50} +(0.401924 + 0.696152i) q^{51} +(-2.00000 + 6.92820i) q^{52} +(5.19615 + 5.19615i) q^{54} +(0.732051 - 1.26795i) q^{55} +(-4.73205 + 1.26795i) q^{56} +(4.50000 + 7.79423i) q^{57} -7.46410 q^{59} +(-0.803848 - 0.464102i) q^{60} +(-9.86603 - 5.69615i) q^{61} +(0.633975 + 2.36603i) q^{62} +(4.50000 + 2.59808i) q^{63} -8.00000i q^{64} +(-0.696152 + 0.669873i) q^{65} +(-9.46410 - 9.46410i) q^{66} +(3.86603 + 6.69615i) q^{67} +(-0.803848 + 0.464102i) q^{68} +(-5.59808 - 9.69615i) q^{69} +(-0.633975 - 0.169873i) q^{70} +(11.4282 - 6.59808i) q^{71} +(-6.00000 + 6.00000i) q^{72} +8.53590i q^{73} +(5.83013 - 1.56218i) q^{74} +(4.26795 + 7.39230i) q^{75} +(-9.00000 + 5.19615i) q^{76} +(-8.19615 - 4.73205i) q^{77} +(4.26795 + 7.73205i) q^{78} +(-7.96410 - 13.7942i) q^{79} +(0.535898 - 0.928203i) q^{80} +9.00000 q^{81} +(7.83013 + 2.09808i) q^{82} +(7.06218 + 12.2321i) q^{83} +(-3.00000 + 5.19615i) q^{84} -0.124356 q^{85} +(-2.36603 - 8.83013i) q^{86} +(10.9282 - 10.9282i) q^{88} +(0.571797 + 0.330127i) q^{89} +(-1.09808 + 0.294229i) q^{90} +(4.33013 + 4.50000i) q^{91} +(11.1962 - 6.46410i) q^{92} +(2.59808 + 1.50000i) q^{93} +(11.2942 + 3.02628i) q^{94} -1.39230 q^{95} +(-6.92820 - 6.92820i) q^{96} +(-2.30385 - 1.33013i) q^{97} +(1.46410 - 5.46410i) q^{98} -16.3923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{5} + 6 q^{7} - 8 q^{8} + 12 q^{9} + 2 q^{10} - 8 q^{11} + 6 q^{14} + 6 q^{15} - 16 q^{16} - 6 q^{17} + 12 q^{18} + 12 q^{20} - 8 q^{22} - 6 q^{23} - 4 q^{25} - 4 q^{26} - 6 q^{30} + 6 q^{31}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^5 + 6 * q^7 - 8 * q^8 + 12 * q^9 + 2 * q^10 - 8 * q^11 + 6 * q^14 + 6 * q^15 - 16 * q^16 - 6 * q^17 + 12 * q^18 + 12 * q^20 - 8 * q^22 - 6 * q^23 - 4 * q^25 - 4 * q^26 - 6 * q^30 + 6 * q^31 - 16 * q^32 - 24 * q^33 - 18 * q^34 - 12 * q^35 + 12 * q^37 - 18 * q^38 + 24 * q^39 + 20 * q^40 + 6 * q^41 - 6 * q^42 - 12 * q^43 - 12 * q^45 + 6 * q^46 - 6 * q^47 - 8 * q^49 - 28 * q^50 + 12 * q^51 - 8 * q^52 - 4 * q^55 - 12 * q^56 + 18 * q^57 - 16 * q^59 - 24 * q^60 - 36 * q^61 + 6 * q^62 + 18 * q^63 + 18 * q^65 - 24 * q^66 + 12 * q^67 - 24 * q^68 - 12 * q^69 - 6 * q^70 + 18 * q^71 - 24 * q^72 + 6 * q^74 + 24 * q^75 - 36 * q^76 - 12 * q^77 + 24 * q^78 - 18 * q^79 + 16 * q^80 + 36 * q^81 + 14 * q^82 + 4 * q^83 - 12 * q^84 + 48 * q^85 - 6 * q^86 + 16 * q^88 + 30 * q^89 + 6 * q^90 + 24 * q^92 + 14 * q^94 + 36 * q^95 - 30 * q^97 - 8 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more