LMFDB - Embedded newform 65.2.l.a.4.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [65,2,Mod(4,65)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("65.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(65, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.l (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.3
Root			$0.228425 - 1.39564i$ of defining polynomial
Character	$\chi$	$=$	65.4
Dual form			65.2.l.a.49.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.228425 - 0.395644i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.895644 + 1.55130i) q^{4} +(-2.18890 - 0.456850i) q^{5} +(0.395644 - 0.228425i) q^{6} +(-0.866025 - 1.50000i) q^{7} +1.73205 q^{8} +(-1.00000 - 1.73205i) q^{9} +(-0.680750 + 0.761669i) q^{10} +(-2.29129 - 1.32288i) q^{11} +1.79129i q^{12} +(3.46410 + 1.00000i) q^{13} -0.791288 q^{14} +(-1.66722 - 1.49009i) q^{15} +(-1.39564 + 2.41733i) q^{16} +(-3.96863 + 2.29129i) q^{17} -0.913701 q^{18} +(-1.50000 + 0.866025i) q^{19} +(-1.25176 - 3.80482i) q^{20} -1.73205i q^{21} +(-1.04678 + 0.604356i) q^{22} +(3.96863 + 2.29129i) q^{23} +(1.50000 + 0.866025i) q^{24} +(4.58258 + 2.00000i) q^{25} +(1.18693 - 1.14213i) q^{26} -5.00000i q^{27} +(1.55130 - 2.68693i) q^{28} +(2.29129 - 3.96863i) q^{29} +(-0.970381 + 0.319250i) q^{30} +6.20520i q^{31} +(2.36965 + 4.10436i) q^{32} +(-1.32288 - 2.29129i) q^{33} +2.09355i q^{34} +(1.21037 + 3.67900i) q^{35} +(1.79129 - 3.10260i) q^{36} +(3.96863 - 6.87386i) q^{37} +0.791288i q^{38} +(2.50000 + 2.59808i) q^{39} +(-3.79129 - 0.791288i) q^{40} +(2.29129 + 1.32288i) q^{41} +(-0.685275 - 0.395644i) q^{42} +(-9.16478 + 5.29129i) q^{43} -4.73930i q^{44} +(1.39761 + 4.24814i) q^{45} +(1.81307 - 1.04678i) q^{46} +1.82740 q^{47} +(-2.41733 + 1.39564i) q^{48} +(2.00000 - 3.46410i) q^{49} +(1.83806 - 1.35622i) q^{50} -4.58258 q^{51} +(1.55130 + 6.26951i) q^{52} -7.58258i q^{53} +(-1.97822 - 1.14213i) q^{54} +(4.41105 + 3.94242i) q^{55} +(-1.50000 - 2.59808i) q^{56} -1.73205 q^{57} +(-1.04678 - 1.81307i) q^{58} +(-12.0826 + 6.97588i) q^{59} +(0.818350 - 3.92095i) q^{60} +(0.708712 + 1.22753i) q^{61} +(2.45505 + 1.41742i) q^{62} +(-1.73205 + 3.00000i) q^{63} -3.41742 q^{64} +(-7.12573 - 3.77148i) q^{65} -1.20871 q^{66} +(-0.504525 + 0.873864i) q^{67} +(-7.10895 - 4.10436i) q^{68} +(2.29129 + 3.96863i) q^{69} +(1.73205 + 0.361500i) q^{70} +(6.08258 - 3.51178i) q^{71} +(-1.73205 - 3.00000i) q^{72} +(-1.81307 - 3.14033i) q^{74} +(2.96863 + 4.02334i) q^{75} +(-2.68693 - 1.55130i) q^{76} +4.58258i q^{77} +(1.59898 - 0.395644i) q^{78} +6.00000 q^{79} +(4.15928 - 4.65369i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.04678 - 0.604356i) q^{82} -6.01450 q^{83} +(2.68693 - 1.55130i) q^{84} +(9.73371 - 3.20233i) q^{85} +4.83465i q^{86} +(3.96863 - 2.29129i) q^{87} +(-3.96863 - 2.29129i) q^{88} +(8.29129 + 4.78698i) q^{89} +(2.00000 + 0.417424i) q^{90} +(-1.50000 - 6.06218i) q^{91} +8.20871i q^{92} +(-3.10260 + 5.37386i) q^{93} +(0.417424 - 0.723000i) q^{94} +(3.67900 - 1.21037i) q^{95} +4.73930i q^{96} +(-5.70068 - 9.87386i) q^{97} +(-0.913701 - 1.58258i) q^{98} +5.29150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 6 q^{6} - 8 q^{9} - 4 q^{10} + 12 q^{14} - 6 q^{15} - 2 q^{16} - 12 q^{19} + 24 q^{20} + 12 q^{24} - 18 q^{26} - 10 q^{30} + 6 q^{35} - 4 q^{36} + 20 q^{39} - 12 q^{40} + 12 q^{45} + 42 q^{46}+ \cdots - 6 q^{95}+O(q^{100}) $ 8 * q - 2 * q^4 - 6 * q^6 - 8 * q^9 - 4 * q^10 + 12 * q^14 - 6 * q^15 - 2 * q^16 - 12 * q^19 + 24 * q^20 + 12 * q^24 - 18 * q^26 - 10 * q^30 + 6 * q^35 - 4 * q^36 + 20 * q^39 - 12 * q^40 + 12 * q^45 + 42 * q^46 + 16 * q^49 - 12 * q^50 + 30 * q^54 - 14 * q^55 - 12 * q^56 - 60 * q^59 + 24 * q^61 - 64 * q^64 - 24 * q^65 - 28 * q^66 + 12 * q^71 - 42 * q^74 - 8 * q^75 + 6 * q^76 + 48 * q^79 + 18 * q^80 - 4 * q^81 - 6 * q^84 + 42 * q^85 + 48 * q^89 + 16 * q^90 - 12 * q^91 + 40 * q^94 - 6 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.228425	−	0.395644i	0.161521	−	0.279763i	−0.773893	−	0.633316i	$-0.781693\pi$
$2$	0.228425	−	0.395644i	0.161521	−	0.279763i	0.935414	+	0.353553i	$0.115027\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	0.728714	−	0.684819i	$-0.240119\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	−0.228714	+	0.973494i	$0.573452\pi$
$4$	0.895644	+	1.55130i	0.447822	+	0.775650i
$5$	−2.18890	−	0.456850i	−0.978906	−	0.204310i
$5$	−2.18890	−	0.456850i	−0.978906	−	0.204310i
$6$	0.395644	−	0.228425i	0.161521	−	0.0932542i
$7$	−0.866025	−	1.50000i	−0.327327	−	0.566947i	0.654654	−	0.755929i	$-0.272814\pi$
$7$	−0.866025	−	1.50000i	−0.327327	−	0.566947i	−0.981981	+	0.188982i	$0.939481\pi$
$8$	1.73205			0.612372
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$	−0.680750	+	0.761669i	−0.215272	+	0.240861i
$11$	−2.29129	−	1.32288i	−0.690849	−	0.398862i	0.113081	−	0.993586i	$-0.463928\pi$
$11$	−2.29129	−	1.32288i	−0.690849	−	0.398862i	−0.803930	+	0.594724i	$0.797261\pi$
$12$			1.79129i			0.517100i
$13$	3.46410	+	1.00000i	0.960769	+	0.277350i
$13$	3.46410	+	1.00000i	0.960769	+	0.277350i
$14$	−0.791288			−0.211481
$15$	−1.66722	−	1.49009i	−0.430474	−	0.384741i
$16$	−1.39564	+	2.41733i	−0.348911	+	0.604332i
$17$	−3.96863	+	2.29129i	−0.962533	+	0.555719i	−0.896952	−	0.442128i	$-0.854224\pi$
$17$	−3.96863	+	2.29129i	−0.962533	+	0.555719i	−0.0655816	+	0.997847i	$0.520890\pi$
$18$	−0.913701			−0.215361
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	−0.662094	−	0.749421i	$-0.730332\pi$
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	0.317970	+	0.948101i	$0.396999\pi$
$20$	−1.25176	−	3.80482i	−0.279903	−	0.850783i
$21$		−	1.73205i		−	0.377964i
$22$	−1.04678	+	0.604356i	−0.223173	+	0.128849i
$23$	3.96863	+	2.29129i	0.827516	+	0.477767i	0.853001	−	0.521909i	$-0.174780\pi$
$23$	3.96863	+	2.29129i	0.827516	+	0.477767i	−0.0254855	+	0.999675i	$0.508113\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	4.58258	+	2.00000i	0.916515	+	0.400000i
$26$	1.18693	−	1.14213i	0.232776	−	0.223989i
$27$		−	5.00000i		−	0.962250i
$28$	1.55130	−	2.68693i	0.293168	−	0.507782i
$29$	2.29129	−	3.96863i	0.425481	−	0.736956i	−0.570984	−	0.820961i	$-0.693438\pi$
$29$	2.29129	−	3.96863i	0.425481	−	0.736956i	0.996465	+	0.0840058i	$0.0267714\pi$
$30$	−0.970381	+	0.319250i	−0.177167	+	0.0582868i
$31$			6.20520i			1.11449i	0.830349	+	0.557244i	$0.188141\pi$
$31$			6.20520i			1.11449i	−0.830349	+	0.557244i	$0.811859\pi$
$32$	2.36965	+	4.10436i	0.418899	+	0.725555i
$33$	−1.32288	−	2.29129i	−0.230283	−	0.398862i
$34$			2.09355i			0.359041i
$35$	1.21037	+	3.67900i	0.204590	+	0.621864i
$36$	1.79129	−	3.10260i	0.298548	−	0.517100i
$37$	3.96863	−	6.87386i	0.652438	−	1.13006i	−0.330091	−	0.943949i	$-0.607080\pi$
$37$	3.96863	−	6.87386i	0.652438	−	1.13006i	0.982529	−	0.186107i	$-0.0595872\pi$
$38$			0.791288i			0.128364i
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$	−3.79129	−	0.791288i	−0.599455	−	0.125114i
$41$	2.29129	+	1.32288i	0.357839	+	0.206598i	0.668132	−	0.744042i	$-0.267094\pi$
$41$	2.29129	+	1.32288i	0.357839	+	0.206598i	−0.310293	+	0.950641i	$0.600427\pi$
$42$	−0.685275	−	0.395644i	−0.105740	−	0.0610492i
$43$	−9.16478	+	5.29129i	−1.39762	+	0.806914i	−0.994142	−	0.108078i	$-0.965531\pi$
$43$	−9.16478	+	5.29129i	−1.39762	+	0.806914i	−0.403473	+	0.914991i	$0.632197\pi$
$44$		−	4.73930i		−	0.714477i
$45$	1.39761	+	4.24814i	0.208344	+	0.633275i
$46$	1.81307	−	1.04678i	0.267322	−	0.154339i
$47$	1.82740			0.266554			0.133277	−	0.991079i	$-0.457450\pi$
$47$	1.82740			0.266554			0.133277	+	0.991079i	$0.457450\pi$
$48$	−2.41733	+	1.39564i	−0.348911	+	0.201444i
$49$	2.00000	−	3.46410i	0.285714	−	0.494872i
$50$	1.83806	−	1.35622i	0.259941	−	0.191798i
$51$	−4.58258			−0.641689
$52$	1.55130	+	6.26951i	0.215127	+	0.869424i
$53$		−	7.58258i		−	1.04155i	−0.853695	−	0.520773i	$-0.825644\pi$
$53$		−	7.58258i		−	1.04155i	0.853695	−	0.520773i	$-0.174356\pi$
$54$	−1.97822	−	1.14213i	−0.269202	−	0.155424i
$55$	4.41105	+	3.94242i	0.594785	+	0.531596i
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$	−1.73205			−0.229416
$58$	−1.04678	−	1.81307i	−0.137448	−	0.238068i
$59$	−12.0826	+	6.97588i	−1.57302	+	0.908182i	−0.577221	+	0.816588i	$0.695863\pi$
$59$	−12.0826	+	6.97588i	−1.57302	+	0.908182i	−0.995796	+	0.0915940i	$0.970804\pi$
$60$	0.818350	−	3.92095i	0.105649	−	0.506193i
$61$	0.708712	+	1.22753i	0.0907413	+	0.157169i	0.907823	−	0.419353i	$-0.137743\pi$
$61$	0.708712	+	1.22753i	0.0907413	+	0.157169i	−0.817082	+	0.576522i	$0.804410\pi$
$62$	2.45505	+	1.41742i	0.311792	+	0.180013i
$63$	−1.73205	+	3.00000i	−0.218218	+	0.377964i
$64$	−3.41742			−0.427178
$65$	−7.12573	−	3.77148i	−0.883837	−	0.467794i
$66$	−1.20871			−0.148782
$67$	−0.504525	+	0.873864i	−0.0616376	+	0.106759i	−0.895198	−	0.445670i	$-0.852966\pi$
$67$	−0.504525	+	0.873864i	−0.0616376	+	0.106759i	0.833560	+	0.552429i	$0.186299\pi$
$68$	−7.10895	−	4.10436i	−0.862087	−	0.497726i
$69$	2.29129	+	3.96863i	0.275839	+	0.477767i
$70$	1.73205	+	0.361500i	0.207020	+	0.0432075i
$71$	6.08258	−	3.51178i	0.721869	−	0.416771i	−0.0935712	−	0.995613i	$-0.529828\pi$
$71$	6.08258	−	3.51178i	0.721869	−	0.416771i	0.815440	+	0.578841i	$0.196495\pi$
$72$	−1.73205	−	3.00000i	−0.204124	−	0.353553i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	−1.81307	−	3.14033i	−0.210765	−	0.365056i
$75$	2.96863	+	4.02334i	0.342788	+	0.464575i
$76$	−2.68693	−	1.55130i	−0.308212	−	0.177946i
$77$			4.58258i			0.522233i
$78$	1.59898	−	0.395644i	0.181048	−	0.0447979i
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$	4.15928	−	4.65369i	0.465022	−	0.520298i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.04678	−	0.604356i	0.115597	−	0.0667400i
$83$	−6.01450			−0.660177			−0.330089	−	0.943950i	$-0.607079\pi$
$83$	−6.01450			−0.660177			−0.330089	+	0.943950i	$0.607079\pi$
$84$	2.68693	−	1.55130i	0.293168	−	0.169261i
$85$	9.73371	−	3.20233i	1.05577	−	0.347342i
$86$			4.83465i			0.521334i
$87$	3.96863	−	2.29129i	0.425481	−	0.245652i
$88$	−3.96863	−	2.29129i	−0.423057	−	0.244252i
$89$	8.29129	+	4.78698i	0.878875	+	0.507419i	0.870287	−	0.492545i	$-0.163933\pi$
$89$	8.29129	+	4.78698i	0.878875	+	0.507419i	0.00858752	+	0.999963i	$0.497266\pi$
$90$	2.00000	+	0.417424i	0.210819	+	0.0440004i
$91$	−1.50000	−	6.06218i	−0.157243	−	0.635489i
$92$			8.20871i			0.855817i
$93$	−3.10260	+	5.37386i	−0.321725	+	0.557244i
$94$	0.417424	−	0.723000i	0.0430540	−	0.0745718i
$95$	3.67900	−	1.21037i	0.377457	−	0.124181i
$96$			4.73930i			0.483703i
$97$	−5.70068	−	9.87386i	−0.578816	−	1.00254i	−0.995615	−	0.0935404i	$-0.970182\pi$
$97$	−5.70068	−	9.87386i	−0.578816	−	1.00254i	0.416799	−	0.908999i	$-0.363152\pi$
$98$	−0.913701	−	1.58258i	−0.0922977	−	0.159864i
$99$			5.29150i			0.531816i
$100$	1.00175	+	8.90024i	0.100175	+	0.890024i
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	−0.998240	−	0.0592978i	$-0.981114\pi$
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	0.550474	+	0.834853i	$0.314447\pi$
$102$	−1.04678	+	1.81307i	−0.103646	+	0.179521i
$103$		−	3.16515i		−	0.311872i	−0.987767	−	0.155936i	$-0.950161\pi$
$103$		−	3.16515i		−	0.311872i	0.987767	−	0.155936i	$-0.0498393\pi$
$104$	6.00000	+	1.73205i	0.588348	+	0.169842i
$105$	−0.791288	+	3.79129i	−0.0772218	+	0.369992i
$106$	−3.00000	−	1.73205i	−0.291386	−	0.168232i
$107$	9.16478	+	5.29129i	0.885993	+	0.511528i	0.872630	−	0.488383i	$-0.162413\pi$
$107$	9.16478	+	5.29129i	0.885993	+	0.511528i	0.0133631	+	0.999911i	$0.495746\pi$
$108$	7.75650	−	4.47822i	0.746370	−	0.430917i
$109$		−	13.1334i		−	1.25795i	−0.777425	−	0.628976i	$-0.783474\pi$
$109$		−	13.1334i		−	1.25795i	0.777425	−	0.628976i	$-0.216526\pi$
$110$	2.56739	−	0.844656i	0.244791	−	0.0805348i
$111$	6.87386	−	3.96863i	0.652438	−	0.376685i
$112$	4.83465			0.456832
$113$	6.42368	−	3.70871i	0.604289	−	0.348886i	−0.166438	−	0.986052i	$-0.553227\pi$
$113$	6.42368	−	3.70871i	0.604289	−	0.348886i	0.770727	+	0.637166i	$0.219893\pi$
$114$	−0.395644	+	0.685275i	−0.0370554	+	0.0641819i
$115$	−7.64016	−	6.82847i	−0.712448	−	0.636758i
$116$	8.20871			0.762160
$117$	−1.73205	−	7.00000i	−0.160128	−	0.647150i
$118$			6.37386i			0.586762i
$119$	6.87386	+	3.96863i	0.630126	+	0.363803i
$120$	−2.88771	−	2.58092i	−0.263610	−	0.235605i
$121$	−2.00000	−	3.46410i	−0.181818	−	0.314918i
$122$	0.647551			0.0586265
$123$	1.32288	+	2.29129i	0.119280	+	0.206598i
$124$	−9.62614	+	5.55765i	−0.864453	+	0.499092i
$125$	−9.11710	−	6.47135i	−0.815459	−	0.578815i
$126$	0.791288	+	1.37055i	0.0704935	+	0.122098i
$127$	−15.3700	−	8.87386i	−1.36387	−	0.787428i	−0.373729	−	0.927538i	$-0.621921\pi$
$127$	−15.3700	−	8.87386i	−1.36387	−	0.787428i	−0.990136	+	0.140110i	$0.955254\pi$
$128$	−5.51993	+	9.56080i	−0.487897	+	0.845063i
$129$	−10.5826			−0.931744
$130$	−3.11986	+	1.95775i	−0.273630	+	0.171706i
$131$	−7.58258			−0.662493			−0.331246	−	0.943544i	$-0.607469\pi$
$131$	−7.58258			−0.662493			−0.331246	+	0.943544i	$0.607469\pi$
$132$	2.36965	−	4.10436i	0.206252	−	0.357238i
$133$	2.59808	+	1.50000i	0.225282	+	0.130066i
$134$	0.230493	+	0.399225i	0.0199115	+	0.0344878i
$135$	−2.28425	+	10.9445i	−0.196597	+	0.941953i
$136$	−6.87386	+	3.96863i	−0.589429	+	0.340307i
$137$	5.24383	+	9.08258i	0.448010	+	0.775977i	0.998256	−	0.0590258i	$-0.0187994\pi$
$137$	5.24383	+	9.08258i	0.448010	+	0.775977i	−0.550246	+	0.835003i	$0.685466\pi$
$138$	2.09355			0.178215
$139$	−10.8739	−	18.8341i	−0.922309	−	1.59749i	−0.795833	−	0.605517i	$-0.792967\pi$
$139$	−10.8739	−	18.8341i	−0.922309	−	1.59749i	−0.126476	−	0.991970i	$-0.540367\pi$
$140$	−4.62317	+	5.17272i	−0.390729	+	0.437174i
$141$	1.58258	+	0.913701i	0.133277	+	0.0769475i
$142$		−	3.20871i		−	0.269269i
$143$	−6.61438	−	6.87386i	−0.553122	−	0.574821i
$144$	5.58258			0.465215
$145$	−6.82847	+	7.64016i	−0.567074	+	0.634480i
$146$		0			0
$147$	3.46410	−	2.00000i	0.285714	−	0.164957i
$148$	14.2179			1.16870
$149$	−14.4564	+	8.34643i	−1.18432	+	0.683766i	−0.957009	−	0.290057i	$-0.906326\pi$
$149$	−14.4564	+	8.34643i	−1.18432	+	0.683766i	−0.227308	+	0.973823i	$0.572992\pi$
$150$	2.26992	−	0.255488i	0.185338	−	0.0208605i
$151$		−	9.66930i		−	0.786877i	−0.919351	−	0.393438i	$-0.871285\pi$
$151$		−	9.66930i		−	0.786877i	0.919351	−	0.393438i	$-0.128715\pi$
$152$	−2.59808	+	1.50000i	−0.210732	+	0.121666i
$153$	7.93725	+	4.58258i	0.641689	+	0.370479i
$154$	1.81307	+	1.04678i	0.146101	+	0.0843516i
$155$	2.83485	−	13.5826i	0.227701	−	1.09098i
$156$	−1.79129	+	6.20520i	−0.143418	+	0.496814i
$157$			9.16515i			0.731459i	0.930721	+	0.365729i	$0.119180\pi$
$157$			9.16515i			0.731459i	−0.930721	+	0.365729i	$0.880820\pi$
$158$	1.37055	−	2.37386i	0.109035	−	0.188854i
$159$	3.79129	−	6.56670i	0.300669	−	0.520773i
$160$	−3.31186	−	10.0666i	−0.261825	−	0.795835i
$161$		−	7.93725i		−	0.625543i
$162$	0.228425	+	0.395644i	0.0179468	+	0.0310847i
$163$	10.5353	+	18.2477i	0.825191	+	1.42927i	0.901773	+	0.432209i	$0.142266\pi$
$163$	10.5353	+	18.2477i	0.825191	+	1.42927i	−0.0765827	+	0.997063i	$0.524401\pi$
$164$			4.73930i			0.370077i
$165$	1.84887	+	5.61976i	0.143934	+	0.437498i
$166$	−1.37386	+	2.37960i	−0.106632	+	0.184693i
$167$	−4.78698	+	8.29129i	−0.370427	+	0.641599i	−0.989631	−	0.143631i	$-0.954122\pi$
$167$	−4.78698	+	8.29129i	−0.370427	+	0.641599i	0.619204	+	0.785230i	$0.287455\pi$
$168$		−	3.00000i		−	0.231455i
$169$	11.0000	+	6.92820i	0.846154	+	0.532939i
$170$	0.956439	−	4.58258i	0.0733555	−	0.351468i
$171$	3.00000	+	1.73205i	0.229416	+	0.132453i
$172$	−16.4168	−	9.47822i	−1.25177	−	0.722707i
$173$	14.3609	−	8.29129i	1.09184	−	0.630375i	0.157775	−	0.987475i	$-0.449568\pi$
$173$	14.3609	−	8.29129i	1.09184	−	0.630375i	0.934066	+	0.357100i	$0.116234\pi$
$174$		−	2.09355i		−	0.158712i
$175$	−0.968627	−	8.60591i	−0.0732213	−	0.650546i
$176$	6.39564	−	3.69253i	0.482090	−	0.278335i
$177$	−13.9518			−1.04868
$178$	3.78788	−	2.18693i	0.283913	−	0.163917i
$179$	9.08258	−	15.7315i	0.678864	−	1.17583i	−0.296460	−	0.955045i	$-0.595806\pi$
$179$	9.08258	−	15.7315i	0.678864	−	1.17583i	0.975323	−	0.220781i	$-0.0708606\pi$
$180$	−5.33838	+	5.97294i	−0.397899	+	0.445196i
$181$	8.74773			0.650213			0.325107	−	0.945677i	$-0.394600\pi$
$181$	8.74773			0.650213			0.325107	+	0.945677i	$0.394600\pi$
$182$	−2.74110	−	0.791288i	−0.203184	−	0.0586542i
$183$			1.41742i			0.104779i
$184$	6.87386	+	3.96863i	0.506748	+	0.292571i
$185$	−11.8273	+	13.2331i	−0.869557	+	0.972920i
$186$	1.41742	+	2.45505i	0.103931	+	0.180013i
$187$	12.1244			0.886621
$188$	1.63670	+	2.83485i	0.119369	+	0.206753i
$189$	−7.50000	+	4.33013i	−0.545545	+	0.314970i
$190$	0.361500	−	1.73205i	0.0262260	−	0.125656i
$191$	8.29129	+	14.3609i	0.599937	+	1.03912i	0.992830	+	0.119536i	$0.0381408\pi$
$191$	8.29129	+	14.3609i	0.599937	+	1.03912i	−0.392893	+	0.919584i	$0.628526\pi$
$192$	−2.95958	−	1.70871i	−0.213589	−	0.123316i
$193$	7.43273	−	12.8739i	0.535020	−	0.926681i	−0.464143	−	0.885760i	$-0.653638\pi$
$193$	7.43273	−	12.8739i	0.535020	−	0.926681i	0.999162	−	0.0409206i	$-0.0130291\pi$
$194$	−5.20871			−0.373964
$195$	−4.28532	−	6.82906i	−0.306878	−	0.489039i
$196$	7.16515			0.511797
$197$	−7.33738	+	12.7087i	−0.522767	+	0.905458i	0.476882	+	0.878967i	$0.341767\pi$
$197$	−7.33738	+	12.7087i	−0.522767	+	0.905458i	−0.999649	+	0.0264912i	$0.991567\pi$
$198$	2.09355	+	1.20871i	0.148782	+	0.0858994i
$199$	5.29129	+	9.16478i	0.375089	+	0.649674i	0.990340	−	0.138657i	$-0.0442787\pi$
$199$	5.29129	+	9.16478i	0.375089	+	0.649674i	−0.615251	+	0.788331i	$0.710945\pi$
$200$	7.93725	+	3.46410i	0.561249	+	0.244949i
$201$	−0.873864	+	0.504525i	−0.0616376	+	0.0355865i
$202$	2.05583	+	3.56080i	0.144647	+	0.250537i
$203$	−7.93725			−0.557086
$204$	−4.10436	−	7.10895i	−0.287362	−	0.497726i
$205$	−4.41105	−	3.94242i	−0.308081	−	0.275351i
$206$	−1.25227	−	0.723000i	−0.0872500	−	0.0503738i
$207$		−	9.16515i		−	0.637022i
$208$	−7.25198	+	6.97822i	−0.502834	+	0.483852i
$209$	4.58258			0.316983
$210$	1.31925	+	1.17909i	0.0910369	+	0.0813652i
$211$	0.0825757	−	0.143025i	0.00568475	−	0.00984627i	−0.863169	−	0.504915i	$-0.831524\pi$
$211$	0.0825757	−	0.143025i	0.00568475	−	0.00984627i	0.868854	+	0.495069i	$0.164857\pi$
$212$	11.7629	−	6.79129i	0.807876	−	0.466428i
$213$	7.02355			0.481246
$214$	4.18693	−	2.41733i	0.286213	−	0.165245i
$215$	22.4781	−	7.39517i	1.53300	−	0.504347i
$216$		−	8.66025i		−	0.589256i
$217$	9.30780	−	5.37386i	0.631855	−	0.364802i
$218$	−5.19615	−	3.00000i	−0.351928	−	0.203186i
$219$		0			0
$220$	−2.16515	+	10.3739i	−0.145974	+	0.699406i
$221$	−16.0390	+	3.96863i	−1.07890	+	0.266959i
$222$		−	3.62614i		−	0.243370i
$223$	−4.33013	+	7.50000i	−0.289967	+	0.502237i	−0.973801	−	0.227400i	$-0.926978\pi$
$223$	−4.33013	+	7.50000i	−0.289967	+	0.502237i	0.683835	+	0.729637i	$0.260311\pi$
$224$	4.10436	−	7.10895i	0.274234	−	0.474987i
$225$	−1.11847	−	9.93725i	−0.0745649	−	0.662484i
$226$		−	3.38865i		−	0.225410i
$227$	0.409175	+	0.708712i	0.0271579	+	0.0470389i	0.879285	−	0.476296i	$-0.158021\pi$
$227$	0.409175	+	0.708712i	0.0271579	+	0.0470389i	−0.852127	+	0.523335i	$0.824688\pi$
$228$	−1.55130	−	2.68693i	−0.102737	−	0.177946i
$229$			26.2668i			1.73576i	0.496774	+	0.867880i	$0.334518\pi$
$229$			26.2668i			1.73576i	−0.496774	+	0.867880i	$0.665482\pi$
$230$	−4.44685	+	1.46299i	−0.293216	+	0.0964665i
$231$	−2.29129	+	3.96863i	−0.150756	+	0.261116i
$232$	3.96863	−	6.87386i	0.260553	−	0.451291i
$233$		−	2.83485i		−	0.185717i	−0.995679	−	0.0928586i	$-0.970400\pi$
$233$		−	2.83485i		−	0.185717i	0.995679	−	0.0928586i	$-0.0296004\pi$
$234$	−3.16515	−	0.913701i	−0.206912	−	0.0597305i
$235$	−4.00000	−	0.834849i	−0.260931	−	0.0544595i
$236$	−21.6434	−	12.4958i	−1.40886	−	0.813408i
$237$	5.19615	+	3.00000i	0.337526	+	0.194871i
$238$	3.14033	−	1.81307i	0.203557	−	0.117524i
$239$			0.190700i			0.0123354i	0.999981	+	0.00616769i	$0.00196325\pi$
$239$			0.190700i			0.0123354i	−0.999981	+	0.00616769i	$0.998037\pi$
$240$	5.92889	−	1.95057i	0.382708	−	0.125909i
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	0.450910	+	0.892570i	$0.351100\pi$
$242$	−1.82740			−0.117470
$243$	−13.8564	+	8.00000i	−0.888889	+	0.513200i
$244$	−1.26951	+	2.19885i	−0.0812719	+	0.140767i
$245$	−5.96038	+	6.66888i	−0.380795	+	0.426059i
$246$	1.20871			0.0770647
$247$	−6.06218	+	1.50000i	−0.385727	+	0.0954427i
$248$			10.7477i			0.682481i
$249$	−5.20871	−	3.00725i	−0.330089	−	0.190577i
$250$	−4.64293	+	2.12891i	−0.293644	+	0.134644i
$251$	0.0825757	+	0.143025i	0.00521213	+	0.00902768i	0.868620	−	0.495479i	$-0.165008\pi$
$251$	0.0825757	+	0.143025i	0.00521213	+	0.00902768i	−0.863408	+	0.504507i	$0.831674\pi$
$252$	−6.20520			−0.390891
$253$	−6.06218	−	10.5000i	−0.381126	−	0.660129i
$254$	−7.02178	+	4.05403i	−0.440586	+	0.254372i
$255$	10.0308	+	2.09355i	0.628153	+	0.131103i
$256$	−0.895644	−	1.55130i	−0.0559777	−	0.0969563i
$257$	15.7315	+	9.08258i	0.981303	+	0.566556i	0.902663	−	0.430348i	$-0.141609\pi$
$257$	15.7315	+	9.08258i	0.981303	+	0.566556i	0.0786397	+	0.996903i	$0.474942\pi$
$258$	−2.41733	+	4.18693i	−0.150496	+	0.260667i
$259$	−13.7477			−0.854242
$260$	−0.531418	−	14.4320i	−0.0329571	−	0.895037i
$261$	−9.16515			−0.567309
$262$	−1.73205	+	3.00000i	−0.107006	+	0.185341i
$263$	7.79423	+	4.50000i	0.480613	+	0.277482i	0.720672	−	0.693276i	$-0.243833\pi$
$263$	7.79423	+	4.50000i	0.480613	+	0.277482i	−0.240059	+	0.970758i	$0.577167\pi$
$264$	−2.29129	−	3.96863i	−0.141019	−	0.244252i
$265$	−3.46410	+	16.5975i	−0.212798	+	1.01958i
$266$	1.18693	−	0.685275i	0.0727755	−	0.0420169i
$267$	4.78698	+	8.29129i	0.292958	+	0.507419i
$268$	−1.80750			−0.110411
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	0.541533	−	0.840679i	$-0.317844\pi$
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	−0.998816	+	0.0486418i	$0.984511\pi$
$270$	3.80835	+	3.40375i	0.231769	+	0.207146i
$271$	7.50000	+	4.33013i	0.455593	+	0.263036i	0.710189	−	0.704011i	$-0.248609\pi$
$271$	7.50000	+	4.33013i	0.455593	+	0.263036i	−0.254597	+	0.967047i	$0.581943\pi$
$272$		−	12.7913i		−	0.775586i
$273$	1.73205	−	6.00000i	0.104828	−	0.363137i
$274$	4.79129			0.289452
$275$	−7.85425	−	10.6448i	−0.473629	−	0.641903i
$276$	−4.10436	+	7.10895i	−0.247053	+	0.427909i
$277$	−6.42368	+	3.70871i	−0.385961	+	0.222835i	−0.680409	−	0.732833i	$-0.738198\pi$
$277$	−6.42368	+	3.70871i	−0.385961	+	0.222835i	0.294447	+	0.955668i	$0.404864\pi$
$278$	−9.93545			−0.595889
$279$	10.7477	−	6.20520i	0.643450	−	0.371496i
$280$	2.09642	+	6.37221i	0.125285	+	0.380812i
$281$			3.65480i			0.218027i	0.994040	+	0.109014i	$0.0347692\pi$
$281$			3.65480i			0.218027i	−0.994040	+	0.109014i	$0.965231\pi$
$282$	0.723000	−	0.417424i	0.0430540	−	0.0248573i
$283$	−24.0302	−	13.8739i	−1.42845	−	0.824716i	−0.431451	−	0.902136i	$-0.641998\pi$
$283$	−24.0302	−	13.8739i	−1.42845	−	0.824716i	−0.996998	+	0.0774209i	$0.975331\pi$
$284$	10.8956	+	6.29060i	0.646538	+	0.373279i
$285$	3.79129	+	0.791288i	0.224577	+	0.0468718i
$286$	−4.23049	+	1.04678i	−0.250154	+	0.0618971i
$287$		−	4.58258i		−	0.270501i
$288$	4.73930	−	8.20871i	0.279266	−	0.483703i
$289$	2.00000	−	3.46410i	0.117647	−	0.203771i
$290$	1.46299	+	4.44685i	0.0859096	+	0.261128i
$291$		−	11.4014i		−	0.668359i
$292$		0			0
$293$	−9.06943	−	15.7087i	−0.529842	−	0.917713i	−0.999394	−	0.0348081i	$-0.988918\pi$
$293$	−9.06943	−	15.7087i	−0.529842	−	0.917713i	0.469552	−	0.882905i	$-0.344415\pi$
$294$		−	1.82740i		−	0.106576i
$295$	29.6345	−	9.74958i	1.72539	−	0.567642i
$296$	6.87386	−	11.9059i	0.399535	−	0.692015i
$297$	−6.61438	+	11.4564i	−0.383805	+	0.664770i
$298$			7.62614i			0.441770i
$299$	11.4564	+	11.9059i	0.662543	+	0.688535i
$300$	−3.58258	+	8.20871i	−0.206840	+	0.473930i
$301$	15.8739	+	9.16478i	0.914954	+	0.528249i
$302$	−3.82560	−	2.20871i	−0.220139	−	0.127097i
$303$	−7.79423	+	4.50000i	−0.447767	+	0.258518i
$304$		−	4.83465i		−	0.277286i
$305$	−0.990505	−	3.01071i	−0.0567162	−	0.172393i
$306$	3.62614	−	2.09355i	0.207292	−	0.119680i
$307$	24.2487			1.38395			0.691974	−	0.721923i	$-0.256741\pi$
$307$	24.2487			1.38395			0.691974	+	0.721923i	$0.256741\pi$
$308$	−7.10895	+	4.10436i	−0.405070	+	0.233867i
$309$	1.58258	−	2.74110i	0.0900296	−	0.155936i
$310$	−4.72631	−	4.22419i	−0.268437	−	0.239918i
$311$	7.58258			0.429968			0.214984	−	0.976618i	$-0.431030\pi$
$311$	7.58258			0.429968			0.214984	+	0.976618i	$0.431030\pi$
$312$	4.33013	+	4.50000i	0.245145	+	0.254762i
$313$			3.25227i			0.183829i	0.995767	+	0.0919147i	$0.0292987\pi$
$313$			3.25227i			0.183829i	−0.995767	+	0.0919147i	$0.970701\pi$
$314$	3.62614	+	2.09355i	0.204635	+	0.118146i
$315$	5.16184	−	5.77542i	0.290837	−	0.325408i
$316$	5.37386	+	9.30780i	0.302303	+	0.523605i
$317$	−0.190700			−0.0107108			−0.00535540	−	0.999986i	$-0.501705\pi$
$317$	−0.190700			−0.0107108			−0.00535540	+	0.999986i	$0.501705\pi$
$318$	−1.73205	−	3.00000i	−0.0971286	−	0.168232i
$319$	−10.5000	+	6.06218i	−0.587887	+	0.339417i
$320$	7.48040	+	1.56125i	0.418167	+	0.0872766i
$321$	5.29129	+	9.16478i	0.295331	+	0.511528i
$322$	−3.14033	−	1.81307i	−0.175004	−	0.101038i
$323$	3.96863	−	6.87386i	0.220820	−	0.382472i
$324$	−1.79129			−0.0995160
$325$	13.8745	+	11.5108i	0.769619	+	0.638503i
$326$	9.62614			0.533142
$327$	6.56670	−	11.3739i	0.363140	−	0.628976i
$328$	3.96863	+	2.29129i	0.219131	+	0.126515i
$329$	−1.58258	−	2.74110i	−0.0872502	−	0.151122i
$330$	2.64575	+	0.552200i	0.145644	+	0.0303976i
$331$	−3.87386	+	2.23658i	−0.212927	+	0.122933i	−0.602671	−	0.797990i	$-0.705897\pi$
$331$	−3.87386	+	2.23658i	−0.212927	+	0.122933i	0.389744	+	0.920923i	$0.372563\pi$
$332$	−5.38685	−	9.33030i	−0.295642	−	0.512067i
$333$	−15.8745			−0.869918
$334$	2.18693	+	3.78788i	0.119664	+	0.207263i
$335$	1.50358	−	1.68231i	0.0821494	−	0.0919143i
$336$	4.18693	+	2.41733i	0.228416	+	0.131876i
$337$			30.7477i			1.67494i	0.546487	+	0.837468i	$0.315965\pi$
$337$			30.7477i			1.67494i	−0.546487	+	0.837468i	$0.684035\pi$
$338$	5.25378	−	2.76951i	0.285768	−	0.150641i
$339$	7.41742			0.402859
$340$	13.6857	+	12.2318i	0.742212	+	0.663360i
$341$	8.20871	−	14.2179i	0.444527	−	0.769943i
$342$	1.37055	−	0.791288i	0.0741109	−	0.0427879i
$343$	−19.0526			−1.02874
$344$	−15.8739	+	9.16478i	−0.855861	+	0.494132i
$345$	−3.20233	−	9.73371i	−0.172408	−	0.524045i
$346$		−	7.57575i		−	0.407275i
$347$	−18.4726	+	10.6652i	−0.991660	+	0.572535i	−0.905770	−	0.423769i	$-0.860707\pi$
$347$	−18.4726	+	10.6652i	−0.991660	+	0.572535i	−0.0858901	+	0.996305i	$0.527373\pi$
$348$	7.10895	+	4.10436i	0.381080	+	0.220017i
$349$	2.12614	+	1.22753i	0.113809	+	0.0657079i	0.555824	−	0.831300i	$-0.312403\pi$
$349$	2.12614	+	1.22753i	0.113809	+	0.0657079i	−0.442015	+	0.897008i	$0.645736\pi$
$350$	−3.62614	−	1.58258i	−0.193825	−	0.0845922i
$351$	5.00000	−	17.3205i	0.266880	−	0.924500i
$352$		−	12.5390i		−	0.668332i
$353$	3.41643	−	5.91742i	0.181838	−	0.314953i	−0.760668	−	0.649141i	$-0.775129\pi$
$353$	3.41643	−	5.91742i	0.181838	−	0.314953i	0.942506	+	0.334188i	$0.108462\pi$
$354$	−3.18693	+	5.51993i	−0.169384	+	0.293381i
$355$	−14.9185	+	4.90811i	−0.791792	+	0.260495i
$356$			17.1497i			0.908933i
$357$	3.96863	+	6.87386i	0.210042	+	0.363803i
$358$	−4.14938	−	7.18693i	−0.219301	−	0.379841i
$359$		−	19.5293i		−	1.03072i	−0.856975	−	0.515359i	$-0.827659\pi$
$359$		−	19.5293i		−	1.03072i	0.856975	−	0.515359i	$-0.172341\pi$
$360$	2.42074	+	7.35799i	0.127584	+	0.387800i
$361$	−8.00000	+	13.8564i	−0.421053	+	0.729285i
$362$	1.99820	−	3.46099i	0.105023	−	0.181905i
$363$		−	4.00000i		−	0.209946i
$364$	8.06080	−	7.75650i	0.422500	−	0.406551i
$365$		0			0
$366$	0.560795	+	0.323775i	0.0293132	+	0.0169240i
$367$	1.51358	+	0.873864i	0.0790080	+	0.0456153i	0.538984	−	0.842316i	$-0.318808\pi$
$367$	1.51358	+	0.873864i	0.0790080	+	0.0456153i	−0.459976	+	0.887932i	$0.652142\pi$
$368$	−11.0776	+	6.39564i	−0.577459	+	0.333396i
$369$		−	5.29150i		−	0.275465i
$370$	2.53397	+	7.70216i	0.131735	+	0.400416i
$371$	−11.3739	+	6.56670i	−0.590502	+	0.340926i
$372$	−11.1153			−0.576302
$373$	11.2583	−	6.50000i	0.582934	−	0.336557i	−0.179364	−	0.983783i	$-0.557404\pi$
$373$	11.2583	−	6.50000i	0.582934	−	0.336557i	0.762299	+	0.647225i	$0.224071\pi$
$374$	2.76951	−	4.79693i	0.143208	−	0.248043i
$375$	−4.65997	−	10.1629i	−0.240640	−	0.524810i
$376$	3.16515			0.163230
$377$	11.9059	−	11.4564i	0.613184	−	0.590037i
$378$			3.95644i			0.203497i
$379$	−9.24773	−	5.33918i	−0.475024	−	0.274255i	0.243317	−	0.969947i	$-0.421765\pi$
$379$	−9.24773	−	5.33918i	−0.475024	−	0.274255i	−0.718340	+	0.695692i	$0.755098\pi$
$380$	5.17272	+	4.62317i	0.265355	+	0.237164i
$381$	−8.87386	−	15.3700i	−0.454622	−	0.787428i
$382$	7.57575			0.387609
$383$	11.8105	+	20.4564i	0.603490	+	1.04528i	0.992288	+	0.123952i	$0.0395570\pi$
$383$	11.8105	+	20.4564i	0.603490	+	1.04528i	−0.388798	+	0.921323i	$0.627110\pi$
$384$	−9.56080	+	5.51993i	−0.487897	+	0.281688i
$385$	2.09355	−	10.0308i	0.106697	−	0.511217i
$386$	−3.39564	−	5.88143i	−0.172834	−	0.299357i
$387$	18.3296	+	10.5826i	0.931744	+	0.537943i
$388$	10.2116	−	17.6869i	0.518413	−	0.897918i
$389$	3.16515			0.160480			0.0802398	−	0.996776i	$-0.474431\pi$
$389$	3.16515			0.160480			0.0802398	+	0.996776i	$0.474431\pi$
$390$	−3.68075	+	0.135533i	−0.186382	+	0.00686297i
$391$	−21.0000			−1.06202
$392$	3.46410	−	6.00000i	0.174964	−	0.303046i
$393$	−6.56670	−	3.79129i	−0.331246	−	0.191245i
$394$	3.35208	+	5.80598i	0.168876	+	0.292501i
$395$	−13.1334	−	2.74110i	−0.660813	−	0.137920i
$396$	−8.20871	+	4.73930i	−0.412503	+	0.238159i
$397$	−10.1738	−	17.6216i	−0.510610	−	0.884402i	−0.999924	−	0.0122949i	$-0.996086\pi$
$397$	−10.1738	−	17.6216i	−0.510610	−	0.884402i	0.489315	−	0.872107i	$-0.337247\pi$
$398$	4.83465			0.242339
$399$	1.50000	+	2.59808i	0.0750939	+	0.130066i
$400$	−11.2303	+	8.28629i	−0.561515	+	0.414315i
$401$	−25.8303	−	14.9131i	−1.28990	−	0.744726i	−0.311267	−	0.950323i	$-0.600753\pi$
$401$	−25.8303	−	14.9131i	−1.28990	−	0.744726i	−0.978637	+	0.205596i	$0.934087\pi$
$402$			0.460985i			0.0229918i
$403$	−6.20520	+	21.4955i	−0.309103	+	1.07076i
$404$	−16.1216			−0.802079
$405$	1.49009	−	1.66722i	0.0740434	−	0.0828448i
$406$	−1.81307	+	3.14033i	−0.0899811	+	0.155852i
$407$	−18.1865	+	10.5000i	−0.901473	+	0.520466i
$408$	−7.93725			−0.392953
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	−0.302979	−	0.952997i	$-0.597981\pi$
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	0.673830	+	0.738886i	$0.264648\pi$
$410$	−2.56739	+	0.844656i	−0.126794	+	0.0417146i
$411$			10.4877i			0.517318i
$412$	4.91010	−	2.83485i	0.241903	−	0.139663i
$413$	20.9276	+	12.0826i	1.02978	+	0.594545i
$414$	−3.62614	−	2.09355i	−0.178215	−	0.102892i
$415$	13.1652	+	2.74773i	0.646252	+	0.134881i
$416$	4.10436	+	16.5876i	0.201233	+	0.813272i
$417$		−	21.7477i		−	1.06499i
$418$	1.04678	−	1.81307i	0.0511995	−	0.0886801i
$419$	−2.91742	+	5.05313i	−0.142526	+	0.246861i	−0.928447	−	0.371465i	$-0.878856\pi$
$419$	−2.91742	+	5.05313i	−0.142526	+	0.246861i	0.785922	+	0.618326i	$0.212189\pi$
$420$	−6.59014	+	2.16812i	−0.321566	+	0.105793i
$421$			5.48220i			0.267186i	0.991036	+	0.133593i	$0.0426515\pi$
$421$			5.48220i			0.267186i	−0.991036	+	0.133593i	$0.957348\pi$
$422$	−0.0377247	−	0.0653411i	−0.00183641	−	0.00318076i
$423$	−1.82740	−	3.16515i	−0.0888513	−	0.153895i
$424$		−	13.1334i		−	0.637815i
$425$	−22.7691	+	2.56275i	−1.10446	+	0.124311i
$426$	1.60436	−	2.77883i	0.0777313	−	0.134635i
$427$	1.22753	−	2.12614i	0.0594041	−	0.102891i
$428$			18.9564i			0.916294i
$429$	−2.29129	−	9.26013i	−0.110624	−	0.447083i
$430$	2.20871	−	10.5826i	0.106514	−	0.510337i
$431$	7.33485	+	4.23478i	0.353307	+	0.203982i	0.666141	−	0.745826i	$-0.267945\pi$
$431$	7.33485	+	4.23478i	0.353307	+	0.203982i	−0.312834	+	0.949808i	$0.601278\pi$
$432$	12.0866	+	6.97822i	0.581518	+	0.335740i
$433$	−8.44178	+	4.87386i	−0.405686	+	0.234223i	−0.688934	−	0.724824i	$-0.741921\pi$
$433$	−8.44178	+	4.87386i	−0.405686	+	0.234223i	0.283248	+	0.959047i	$0.408588\pi$
$434$		−	4.91010i		−	0.235692i
$435$	−9.73371	+	3.20233i	−0.466696	+	0.153540i
$436$	20.3739	−	11.7629i	0.975731	−	0.563339i
$437$	−7.93725			−0.379690
$438$		0			0
$439$	−7.24773	+	12.5534i	−0.345915	+	0.599143i	−0.985520	−	0.169562i	$-0.945765\pi$
$439$	−7.24773	+	12.5534i	−0.345915	+	0.599143i	0.639604	+	0.768704i	$0.279098\pi$
$440$	7.64016	+	6.82847i	0.364230	+	0.325535i
$441$	−8.00000			−0.380952
$442$	−2.09355	+	7.25227i	−0.0995801	+	0.344955i
$443$		−	19.9129i		−	0.946089i	−0.881038	−	0.473045i	$-0.843155\pi$
$443$		−	19.9129i		−	0.946089i	0.881038	−	0.473045i	$-0.156845\pi$
$444$	12.3131	+	7.10895i	0.584352	+	0.337376i
$445$	−15.9619	−	14.2661i	−0.756666	−	0.676278i
$446$	1.97822	+	3.42638i	0.0936714	+	0.162244i
$447$	−16.6929			−0.789545
$448$	2.95958	+	5.12614i	0.139827	+	0.242187i
$449$	9.54356	−	5.50998i	0.450388	−	0.260032i	−0.257606	−	0.966250i	$-0.582934\pi$
$449$	9.54356	−	5.50998i	0.450388	−	0.260032i	0.707994	+	0.706218i	$0.249600\pi$
$450$	−4.18710	−	1.82740i	−0.197382	−	0.0861445i
$451$	−3.50000	−	6.06218i	−0.164809	−	0.285457i
$452$	11.5067	+	6.64337i	0.541228	+	0.312478i
$453$	4.83465	−	8.37386i	0.227152	−	0.393438i
$454$	0.373864			0.0175463
$455$	0.513844	+	13.9548i	0.0240894	+	0.654210i
$456$	−3.00000			−0.140488
$457$	0.866025	−	1.50000i	0.0405110	−	0.0701670i	−0.845059	−	0.534673i	$-0.820435\pi$
$457$	0.866025	−	1.50000i	0.0405110	−	0.0701670i	0.885570	+	0.464506i	$0.153768\pi$
$458$	10.3923	+	6.00000i	0.485601	+	0.280362i
$459$	11.4564	+	19.8431i	0.534741	+	0.926198i
$460$	3.75015	−	17.9681i	0.174852	−	0.837765i
$461$	31.0390	−	17.9204i	1.44563	−	0.834635i	0.447414	−	0.894327i	$-0.352345\pi$
$461$	31.0390	−	17.9204i	1.44563	−	0.834635i	0.998217	+	0.0596914i	$0.0190117\pi$
$462$	1.04678	+	1.81307i	0.0487004	+	0.0843516i
$463$	39.4002			1.83108			0.915542	−	0.402223i	$-0.131762\pi$
$463$	39.4002			1.83108			0.915542	+	0.402223i	$0.131762\pi$
$464$	6.39564	+	11.0776i	0.296910	+	0.514264i
$465$	9.24634	−	10.3454i	0.428789	−	0.479758i
$466$	−1.12159	−	0.647551i	−0.0519567	−	0.0299972i
$467$		−	24.3303i		−	1.12587i	−0.826500	−	0.562936i	$-0.809672\pi$
$467$		−	24.3303i		−	1.12587i	0.826500	−	0.562936i	$-0.190328\pi$
$468$	9.30780	−	8.95644i	0.430253	−	0.414012i
$469$	1.74773			0.0807025
$470$	−1.24400	+	1.39188i	−0.0573816	+	0.0642024i
$471$	−4.58258	+	7.93725i	−0.211154	+	0.365729i
$472$	−20.9276	+	12.0826i	−0.963272	+	0.556146i
$473$	27.9989			1.28739
$474$	2.37386	−	1.37055i	0.109035	−	0.0629515i
$475$	−8.60591	+	0.968627i	−0.394866	+	0.0444437i
$476$			14.2179i			0.651677i
$477$	−13.1334	+	7.58258i	−0.601337	+	0.347182i
$478$	0.0754495	+	0.0435608i	0.00345098	+	0.00199242i
$479$	4.03901	+	2.33193i	0.184547	+	0.106548i	0.589427	−	0.807821i	$-0.299353\pi$
$479$	4.03901	+	2.33193i	0.184547	+	0.106548i	−0.404880	+	0.914370i	$0.632687\pi$
$480$	2.16515	−	10.3739i	0.0988252	−	0.473500i
$481$	20.6216	−	19.8431i	0.940264	−	0.904769i
$482$			0.791288i			0.0360422i
$483$	3.96863	−	6.87386i	0.180579	−	0.312772i
$484$	3.58258	−	6.20520i	0.162844	−	0.282055i
$485$	7.96734	+	24.2173i	0.361778	+	1.09965i
$486$			7.30960i			0.331570i
$487$	5.33918	+	9.24773i	0.241941	+	0.419055i	0.961267	−	0.275618i	$-0.0888825\pi$
$487$	5.33918	+	9.24773i	0.241941	+	0.419055i	−0.719326	+	0.694673i	$0.755549\pi$
$488$	1.22753	+	2.12614i	0.0555675	+	0.0962457i
$489$			21.0707i			0.952848i
$490$	1.27700	+	3.88153i	0.0576890	+	0.175349i
$491$	−9.70871	+	16.8160i	−0.438148	+	0.758895i	−0.997547	−	0.0700041i	$-0.977699\pi$
$491$	−9.70871	+	16.8160i	−0.438148	+	0.758895i	0.559399	+	0.828899i	$0.311032\pi$
$492$	−2.36965	+	4.10436i	−0.106832	+	0.185039i
$493$			21.0000i			0.945792i
$494$	−0.791288	+	2.74110i	−0.0356017	+	0.123328i
$495$	2.41742	−	11.5826i	0.108655	−	0.520598i
$496$	−15.0000	−	8.66025i	−0.673520	−	0.388857i
$497$	−10.5353	−	6.08258i	−0.472574	−	0.272841i
$498$	−2.37960	+	1.37386i	−0.106632	+	0.0615643i
$499$			0.723000i			0.0323659i	0.999869	+	0.0161830i	$0.00515142\pi$
$499$			0.723000i			0.0323659i	−0.999869	+	0.0161830i	$0.994849\pi$
$500$	1.87334	−	19.9394i	0.0837781	−	0.891717i
$501$	−8.29129	+	4.78698i	−0.370427	+	0.213866i
$502$	0.0754495			0.00336747
$503$	−0.143025	+	0.0825757i	−0.00637718	+	0.00368187i	−0.503185	−	0.864179i	$-0.667839\pi$
$503$	−0.143025	+	0.0825757i	−0.00637718	+	0.00368187i	0.496808	+	0.867860i	$0.334505\pi$
$504$	−3.00000	+	5.19615i	−0.133631	+	0.231455i
$505$	13.4109	−	15.0050i	0.596775	−	0.667712i
$506$	−5.53901			−0.246239
$507$	6.06218	+	11.5000i	0.269231	+	0.510733i
$508$		−	31.7913i		−	1.41051i
$509$	−7.33485	−	4.23478i	−0.325111	−	0.187703i	0.328557	−	0.944484i	$-0.393438\pi$
$509$	−7.33485	−	4.23478i	−0.325111	−	0.187703i	−0.653669	+	0.756781i	$0.726771\pi$
$510$	3.11959	−	3.49041i	0.138138	−	0.154558i
$511$		0			0
$512$	−22.8981			−1.01196
$513$	4.33013	+	7.50000i	0.191180	+	0.331133i
$514$	7.18693	−	4.14938i	0.317002	−	0.183021i
$515$	−1.44600	+	6.92820i	−0.0637184	+	0.305293i
$516$	−9.47822	−	16.4168i	−0.417255	−	0.722707i
$517$	−4.18710	−	2.41742i	−0.184149	−	0.106318i
$518$	−3.14033	+	5.43920i	−0.137978	+	0.238985i
$519$	16.5826			0.727894
$520$	−12.3421	−	6.53239i	−0.541238	−	0.286464i
$521$	27.4955			1.20460			0.602299	−	0.798271i	$-0.294252\pi$
$521$	27.4955			1.20460			0.602299	+	0.798271i	$0.294252\pi$
$522$	−2.09355	+	3.62614i	−0.0916322	+	0.158712i
$523$	0.143025	+	0.0825757i	0.00625406	+	0.00361078i	0.503124	−	0.864214i	$-0.332184\pi$
$523$	0.143025	+	0.0825757i	0.00625406	+	0.00361078i	−0.496870	+	0.867825i	$0.665517\pi$
$524$	−6.79129	−	11.7629i	−0.296679	−	0.513863i
$525$	3.46410	−	7.93725i	0.151186	−	0.346410i
$526$	3.56080	−	2.05583i	0.155258	−	0.0896383i
$527$	−14.2179	−	24.6261i	−0.619342	−	1.07273i
$528$	7.38505			0.321393
$529$	−1.00000	−	1.73205i	−0.0434783	−	0.0753066i
$530$	5.77542	+	5.16184i	0.250868	+	0.224216i
$531$	24.1652	+	13.9518i	1.04868	+	0.605455i
$532$			5.37386i			0.232987i
$533$	6.61438	+	6.87386i	0.286501	+	0.297740i
$534$	4.37386			0.189276
$535$	−17.6435	−	15.7690i	−0.762794	−	0.681755i
$536$	−0.873864	+	1.51358i	−0.0377452	+	0.0653765i
$537$	15.7315	−	9.08258i	0.678864	−	0.391942i
$538$	−6.85275			−0.295443
$539$	−9.16515	+	5.29150i	−0.394771	+	0.227921i
$540$	−19.0241	+	6.25882i	−0.818667	+	0.269337i
$541$		−	10.3923i		−	0.446800i	−0.974727	−	0.223400i	$-0.928284\pi$
$541$		−	10.3923i		−	0.446800i	0.974727	−	0.223400i	$-0.0717156\pi$
$542$	3.42638	−	1.97822i	0.147175	−	0.0849718i
$543$	7.57575	+	4.37386i	0.325107	+	0.187700i
$544$	−18.8085	−	10.8591i	−0.806409	−	0.465580i
$545$	−6.00000	+	28.7477i	−0.257012	+	1.23142i
$546$	−1.97822	−	2.05583i	−0.0846600	−	0.0879812i
$547$			28.7477i			1.22916i	0.788853	+	0.614582i	$0.210675\pi$
$547$			28.7477i			1.22916i	−0.788853	+	0.614582i	$0.789325\pi$
$548$	−9.39320	+	16.2695i	−0.401258	+	0.694999i
$549$	1.41742	−	2.45505i	0.0604942	−	0.104779i
$550$	−6.00564	+	0.675957i	−0.256081	+	0.0288229i
$551$			7.93725i			0.338138i
$552$	3.96863	+	6.87386i	0.168916	+	0.292571i
$553$	−5.19615	−	9.00000i	−0.220963	−	0.382719i
$554$			3.38865i			0.143970i
$555$	−16.8593	+	5.54661i	−0.715636	+	0.235440i
$556$	19.4782	−	33.7373i	0.826061	−	1.43078i
$557$	3.87328	−	6.70871i	0.164116	−	0.284257i	−0.772225	−	0.635349i	$-0.780856\pi$
$557$	3.87328	−	6.70871i	0.164116	−	0.284257i	0.936341	+	0.351092i	$0.114190\pi$
$558$		−	5.66970i		−	0.240017i
$559$	−37.0390	+	9.16478i	−1.56658	+	0.387629i
$560$	−10.5826	−	2.20871i	−0.447195	−	0.0933351i
$561$	10.5000	+	6.06218i	0.443310	+	0.255945i
$562$	1.44600	+	0.834849i	0.0609958	+	0.0352160i
$563$	7.79423	−	4.50000i	0.328488	−	0.189652i	−0.326682	−	0.945134i	$-0.605931\pi$
$563$	7.79423	−	4.50000i	0.328488	−	0.189652i	0.655169	+	0.755482i	$0.272597\pi$
$564$			3.27340i			0.137835i
$565$	−15.7551	+	5.18335i	−0.662823	+	0.218065i
$566$	−10.9782	+	6.33828i	−0.461449	+	0.266418i
$567$	1.73205			0.0727393
$568$	10.5353	−	6.08258i	0.442053	−	0.255219i
$569$	3.87386	−	6.70973i	0.162401	−	0.281286i	−0.773328	−	0.634006i	$-0.781410\pi$
$569$	3.87386	−	6.70973i	0.162401	−	0.281286i	0.935729	+	0.352719i	$0.114743\pi$
$570$	1.17909	−	1.31925i	0.0493868	−	0.0552573i
$571$	−35.0780			−1.46797			−0.733985	−	0.679166i	$-0.762342\pi$
$571$	−35.0780			−1.46797			−0.733985	+	0.679166i	$0.762342\pi$
$572$	4.73930	−	16.4174i	0.198160	−	0.686447i
$573$			16.5826i			0.692747i
$574$	−1.81307	−	1.04678i	−0.0756760	−	0.0436916i
$575$	13.6040	+	18.4373i	0.567324	+	0.768887i
$576$	3.41742	+	5.91915i	0.142393	+	0.246631i
$577$	−6.92820			−0.288425			−0.144212	−	0.989547i	$-0.546065\pi$
$577$	−6.92820			−0.288425			−0.144212	+	0.989547i	$0.546065\pi$
$578$	−0.913701	−	1.58258i	−0.0380049	−	0.0658265i
$579$	12.8739	−	7.43273i	0.535020	−	0.308894i
$580$	−17.9681	−	3.75015i	−0.746083	−	0.155717i
$581$	5.20871	+	9.02175i	0.216094	+	0.374285i
$582$	−4.51088	−	2.60436i	−0.186982	−	0.107954i
$583$	−10.0308	+	17.3739i	−0.415433	+	0.719552i
$584$		0			0
$585$	0.593336	+	16.1136i	0.0245314	+	0.666215i
$586$	−8.28674			−0.342322
$587$	19.7478	−	34.2042i	0.815078	−	1.41176i	−0.0941934	−	0.995554i	$-0.530027\pi$
$587$	19.7478	−	34.2042i	0.815078	−	1.41176i	0.909272	−	0.416203i	$-0.136639\pi$
$588$	6.20520	+	3.58258i	0.255898	+	0.147743i
$589$	−5.37386	−	9.30780i	−0.221426	−	0.383521i
$590$	2.91190	−	13.9518i	0.119881	−	0.574385i
$591$	−12.7087	+	7.33738i	−0.522767	+	0.301819i
$592$	11.0776	+	19.1869i	0.455286	+	0.788578i
$593$	−21.1660			−0.869184			−0.434592	−	0.900627i	$-0.643107\pi$
$593$	−21.1660			−0.869184			−0.434592	+	0.900627i	$0.643107\pi$
$594$	3.02178	+	5.23388i	0.123985	+	0.214749i
$595$	−13.2331	−	11.8273i	−0.542506	−	0.484870i
$596$	−25.8956	−	14.9509i	−1.06073	−	0.612411i
$597$			10.5826i			0.433116i
$598$	7.32743	−	1.81307i	0.299641	−	0.0741419i
$599$	−15.4955			−0.633127			−0.316564	−	0.948571i	$-0.602529\pi$
$599$	−15.4955			−0.633127			−0.316564	+	0.948571i	$0.602529\pi$
$600$	5.14181	+	6.96863i	0.209914	+	0.284493i
$601$	−8.45644	+	14.6470i	−0.344945	+	0.597463i	−0.985344	−	0.170580i	$-0.945436\pi$
$601$	−8.45644	+	14.6470i	−0.344945	+	0.597463i	0.640398	+	0.768043i	$0.278769\pi$
$602$	7.25198	−	4.18693i	0.295569	−	0.170647i
$603$	2.01810			0.0821834
$604$	15.0000	−	8.66025i	0.610341	−	0.352381i
$605$	2.79523	+	8.49628i	0.113642	+	0.345423i
$606$			4.11165i			0.167024i
$607$	6.70973	−	3.87386i	0.272339	−	0.157235i	−0.357611	−	0.933871i	$-0.616409\pi$
$607$	6.70973	−	3.87386i	0.272339	−	0.157235i	0.629950	+	0.776635i	$0.283075\pi$
$608$	−7.10895	−	4.10436i	−0.288306	−	0.166454i
$609$	−6.87386	−	3.96863i	−0.278543	−	0.160817i
$610$	−1.41742	−	0.295834i	−0.0573898	−	0.0119780i
$611$	6.33030	+	1.82740i	0.256097	+	0.0739287i
$612$			16.4174i			0.663635i
$613$	−2.95958	+	5.12614i	−0.119536	+	0.207043i	−0.919584	−	0.392894i	$-0.871474\pi$
$613$	−2.95958	+	5.12614i	−0.119536	+	0.207043i	0.800048	+	0.599936i	$0.204807\pi$
$614$	5.53901	−	9.59386i	0.223536	−	0.387176i
$615$	−1.84887	−	5.61976i	−0.0745536	−	0.226611i
$616$			7.93725i			0.319801i
$617$	−6.97588	−	12.0826i	−0.280838	−	0.486426i	0.690753	−	0.723091i	$-0.257279\pi$
$617$	−6.97588	−	12.0826i	−0.280838	−	0.486426i	−0.971591	+	0.236664i	$0.923946\pi$
$618$	−0.723000	−	1.25227i	−0.0290833	−	0.0503738i
$619$		−	29.7309i		−	1.19499i	−0.801874	−	0.597493i	$-0.796164\pi$
$619$		−	29.7309i		−	1.19499i	0.801874	−	0.597493i	$-0.203836\pi$
$620$	23.6097	−	7.76745i	0.948187	−	0.311948i
$621$	11.4564	−	19.8431i	0.459731	−	0.796278i
$622$	1.73205	−	3.00000i	0.0694489	−	0.120289i
$623$		−	16.5826i		−	0.664367i
$624$	−9.76951	+	2.41733i	−0.391093	+	0.0967705i
$625$	17.0000	+	18.3303i	0.680000	+	0.733212i
$626$	1.28674	+	0.742901i	0.0514286	+	0.0296923i
$627$	3.96863	+	2.29129i	0.158492	+	0.0915052i
$628$	−14.2179	+	8.20871i	−0.567356	+	0.327563i
$629$			36.3731i			1.45029i
$630$	−1.10591	−	3.36150i	−0.0440607	−	0.133925i
$631$	−5.12614	+	2.95958i	−0.204068	+	0.117819i	−0.598552	−	0.801084i	$-0.704257\pi$
$631$	−5.12614	+	2.95958i	−0.204068	+	0.117819i	0.394483	+	0.918903i	$0.370924\pi$
$632$	10.3923			0.413384
$633$	0.143025	−	0.0825757i	0.00568475	−	0.00328209i
$634$	−0.0435608	+	0.0754495i	−0.00173002	+	0.00299648i
$635$	29.5893	+	26.4458i	1.17422	+	1.04947i
$636$	13.5826			0.538584
$637$	10.3923	−	10.0000i	0.411758	−	0.396214i
$638$			5.53901i			0.219292i
$639$	−12.1652	−	7.02355i	−0.481246	−	0.277847i
$640$	16.4504	−	18.4059i	0.650260	−	0.727555i
$641$	−9.08258	−	15.7315i	−0.358740	−	0.621356i	0.629010	−	0.777397i	$-0.283460\pi$
$641$	−9.08258	−	15.7315i	−0.358740	−	0.621356i	−0.987751	+	0.156041i	$0.950127\pi$
$642$	4.83465			0.190809
$643$	−10.8968	−	18.8739i	−0.429729	−	0.744313i	0.567120	−	0.823635i	$-0.308058\pi$
$643$	−10.8968	−	18.8739i	−0.429729	−	0.744313i	−0.996849	+	0.0793227i	$0.974724\pi$
$644$	12.3131	−	7.10895i	0.485203	−	0.280132i
$645$	23.1642	+	4.83465i	0.912090	+	0.190364i
$646$	−1.81307	−	3.14033i	−0.0713342	−	0.123554i
$647$	−23.3827	−	13.5000i	−0.919268	−	0.530740i	−0.0358667	−	0.999357i	$-0.511419\pi$
$647$	−23.3827	−	13.5000i	−0.919268	−	0.530740i	−0.883402	+	0.468617i	$0.844753\pi$
$648$	−0.866025	+	1.50000i	−0.0340207	+	0.0589256i
$649$	36.9129			1.44896
$650$	7.72346	−	2.86001i	0.302939	−	0.112179i
$651$	10.7477			0.421237
$652$	−18.8718	+	32.6869i	−0.739077	+	1.28012i
$653$	−37.0882	−	21.4129i	−1.45137	−	0.837951i	−0.452814	−	0.891605i	$-0.649580\pi$
$653$	−37.0882	−	21.4129i	−1.45137	−	0.837951i	−0.998560	+	0.0536545i	$0.982913\pi$
$654$	−3.00000	−	5.19615i	−0.117309	−	0.203186i
$655$	16.5975	+	3.46410i	0.648518	+	0.135354i
$656$	−6.39564	+	3.69253i	−0.249708	+	0.144169i
$657$		0			0
$658$	−1.44600			−0.0563710
$659$	15.2477	+	26.4098i	0.593967	+	1.02878i	0.993692	+	0.112146i	$0.0357724\pi$
$659$	15.2477	+	26.4098i	0.593967	+	1.02878i	−0.399725	+	0.916635i	$0.630894\pi$
$660$	−7.06201	+	7.90145i	−0.274888	+	0.307564i
$661$	15.8739	+	9.16478i	0.617422	+	0.356469i	0.775865	−	0.630900i	$-0.217314\pi$
$661$	15.8739	+	9.16478i	0.617422	+	0.356469i	−0.158443	+	0.987368i	$0.550647\pi$
$662$			2.04356i			0.0794252i
$663$	−15.8745	−	4.58258i	−0.616515	−	0.177972i
$664$	−10.4174			−0.404274
$665$	−5.00166	−	4.47028i	−0.193956	−	0.173350i
$666$	−3.62614	+	6.28065i	−0.140510	+	0.243370i
$667$	18.1865	−	10.5000i	0.704185	−	0.406562i
$668$	−17.1497			−0.663542
$669$	−7.50000	+	4.33013i	−0.289967	+	0.167412i
$670$	−0.322139	−	0.979164i	−0.0124453	−	0.0378284i
$671$		−	3.75015i		−	0.144773i
$672$	7.10895	−	4.10436i	0.274234	−	0.158329i
$673$	−20.9276	−	12.0826i	−0.806701	−	0.465749i	0.0391079	−	0.999235i	$-0.487548\pi$
$673$	−20.9276	−	12.0826i	−0.806701	−	0.465749i	−0.845809	+	0.533486i	$0.820882\pi$
$674$	12.1652	+	7.02355i	0.468584	+	0.270537i
$675$	10.0000	−	22.9129i	0.384900	−	0.881917i
$676$	−0.895644	+	23.2695i	−0.0344478	+	0.894981i
$677$		−	2.83485i		−	0.108952i	−0.998515	−	0.0544760i	$-0.982651\pi$
$677$		−	2.83485i		−	0.108952i	0.998515	−	0.0544760i	$-0.0173489\pi$
$678$	1.69433	−	2.93466i	0.0650702	−	0.112705i
$679$	−9.87386	+	17.1020i	−0.378924	+	0.656316i
$680$	16.8593	−	5.54661i	0.646524	−	0.212703i
$681$			0.818350i			0.0313593i
$682$	−3.75015	−	6.49545i	−0.143601	−	0.248724i
$683$	16.5498	+	28.6652i	0.633262	+	1.09684i	0.986881	+	0.161452i	$0.0516177\pi$
$683$	16.5498	+	28.6652i	0.633262	+	1.09684i	−0.353619	+	0.935390i	$0.615049\pi$
$684$			6.20520i			0.237262i
$685$	−7.32884	−	22.2765i	−0.280021	−	0.851141i
$686$	−4.35208	+	7.53803i	−0.166163	+	0.287803i
$687$	−13.1334	+	22.7477i	−0.501071	+	0.867880i
$688$		−	29.5390i		−	1.12616i
$689$	7.58258	−	26.2668i	0.288873	−	1.00069i
$690$	−4.58258	−	0.956439i	−0.174456	−	0.0364110i
$691$	17.1261	+	9.88778i	0.651509	+	0.376149i	0.789034	−	0.614349i	$-0.210581\pi$
$691$	17.1261	+	9.88778i	0.651509	+	0.376149i	−0.137525	+	0.990498i	$0.543915\pi$
$692$	25.7246	+	14.8521i	0.977901	+	0.564591i
$693$	7.93725	−	4.58258i	0.301511	−	0.174078i
$694$			9.74475i			0.369906i
$695$	15.1975	+	46.1937i	0.576472	+	1.75223i
$696$	6.87386	−	3.96863i	0.260553	−	0.150430i
$697$	−12.1244			−0.459243
$698$	0.971326	−	0.560795i	0.0367652	−	0.0212264i
$699$	1.41742	−	2.45505i	0.0536119	−	0.0928586i
$700$	12.4828	−	9.21047i	0.471806	−	0.348123i
$701$	−21.1652			−0.799397			−0.399698	−	0.916647i	$-0.630885\pi$
$701$	−21.1652			−0.799397			−0.399698	+	0.916647i	$0.630885\pi$
$702$	−5.71063	−	5.93466i	−0.215534	−	0.223989i
$703$			13.7477i			0.518505i
$704$	7.83030	+	4.52083i	0.295116	+	0.170385i
$705$	−3.04668	−	2.72300i	−0.114745	−	0.102554i
$706$	−1.56080	−	2.70338i	−0.0587413	−	0.101743i
$707$	15.5885			0.586264
$708$	−12.4958	−	21.6434i	−0.469621	−	0.813408i
$709$	31.5000	−	18.1865i	1.18301	−	0.683010i	0.226299	−	0.974058i	$-0.427337\pi$
$709$	31.5000	−	18.1865i	1.18301	−	0.683010i	0.956708	+	0.291048i	$0.0940040\pi$
$710$	−1.46590	+	7.02355i	−0.0550143	+	0.263589i
$711$	−6.00000	−	10.3923i	−0.225018	−	0.389742i
$712$	14.3609	+	8.29129i	0.538199	+	0.310729i
$713$	−14.2179	+	24.6261i	−0.532465	+	0.922256i
$714$	3.62614			0.135705
$715$	11.3379	+	18.0680i	0.424013	+	0.675704i
$716$	32.5390			1.21604
$717$	−0.0953502	+	0.165151i	−0.00356092	+	0.00616769i
$718$	−7.72665	−	4.46099i	−0.288356	−	0.166482i
$719$	−12.2477	−	21.2137i	−0.456763	−	0.791137i	0.542025	−	0.840363i	$-0.317658\pi$
$719$	−12.2477	−	21.2137i	−0.456763	−	0.791137i	−0.998788	+	0.0492257i	$0.984325\pi$
$720$	−12.2197	−	2.55040i	−0.455402	−	0.0950478i
$721$	−4.74773	+	2.74110i	−0.176815	+	0.102084i
$722$	3.65480	+	6.33030i	0.136018	+	0.235589i
$723$	−1.73205			−0.0644157
$724$	7.83485	+	13.5704i	0.291180	+	0.504338i
$725$	18.4373	−	13.6040i	0.684742	−	0.505238i
$726$	−1.58258	−	0.913701i	−0.0587349	−	0.0339106i
$727$		−	15.2523i		−	0.565675i	−0.959168	−	0.282838i	$-0.908724\pi$
$727$		−	15.2523i		−	0.565675i	0.959168	−	0.282838i	$-0.0912758\pi$
$728$	−2.59808	−	10.5000i	−0.0962911	−	0.389156i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	24.2477	−	41.9983i	0.896835	−	1.55336i
$732$	−2.19885	+	1.26951i	−0.0812719	+	0.0469223i
$733$	22.8027			0.842237			0.421119	−	0.907006i	$-0.361638\pi$
$733$	22.8027			0.842237			0.421119	+	0.907006i	$0.361638\pi$
$734$	0.691478	−	0.399225i	0.0255229	−	0.0147357i
$735$	−8.49628	+	2.79523i	−0.313390	+	0.103103i
$736$			21.7182i			0.800544i
$737$	2.31203	−	1.33485i	0.0851646	−	0.0491698i
$738$	−2.09355	−	1.20871i	−0.0770647	−	0.0444933i
$739$	−14.7523	−	8.51723i	−0.542671	−	0.313311i	0.203490	−	0.979077i	$-0.434772\pi$
$739$	−14.7523	−	8.51723i	−0.542671	−	0.313311i	−0.746161	+	0.665766i	$0.768105\pi$
$740$	−31.1216	−	6.49545i	−1.14405	−	0.238778i
$741$	−6.00000	−	1.73205i	−0.220416	−	0.0636285i
$742$			6.00000i			0.220267i
$743$	2.86423	−	4.96099i	0.105078	−	0.182001i	−0.808692	−	0.588232i	$-0.799824\pi$
$743$	2.86423	−	4.96099i	0.105078	−	0.182001i	0.913770	+	0.406232i	$0.133157\pi$
$744$	−5.37386	+	9.30780i	−0.197015	+	0.341241i
$745$	35.4568	−	11.6651i	1.29904	−	0.427375i
$746$		−	5.93905i		−	0.217444i
$747$	6.01450	+	10.4174i	0.220059	+	0.381154i
$748$	10.8591	+	18.8085i	0.397048	+	0.687708i
$749$		−	18.3296i		−	0.669748i
$750$	−5.08535	−	0.477776i	−0.185691	−	0.0174459i
$751$	−5.87386	+	10.1738i	−0.214340	+	0.371248i	−0.953068	−	0.302755i	$-0.902093\pi$
$751$	−5.87386	+	10.1738i	−0.214340	+	0.371248i	0.738728	+	0.674004i	$0.235427\pi$
$752$	−2.55040	+	4.41742i	−0.0930036	+	0.161087i
$753$			0.165151i			0.00601845i
$754$	−1.81307	−	7.32743i	−0.0660281	−	0.266849i
$755$	−4.41742	+	21.1652i	−0.160767	+	0.770279i
$756$	−13.4347	−	7.75650i	−0.488614	−	0.282101i
$757$	−8.44178	−	4.87386i	−0.306822	−	0.177144i	0.338682	−	0.940901i	$-0.390019\pi$
$757$	−8.44178	−	4.87386i	−0.306822	−	0.177144i	−0.645503	+	0.763757i	$0.723352\pi$
$758$	−4.22483	+	2.43920i	−0.153453	+	0.0885959i
$759$		−	12.1244i		−	0.440086i
$760$	6.37221	−	2.09642i	0.231144	−	0.0760451i
$761$	−30.7087	+	17.7297i	−1.11319	+	0.642701i	−0.939654	−	0.342127i	$-0.888853\pi$
$761$	−30.7087	+	17.7297i	−1.11319	+	0.642701i	−0.173536	+	0.984827i	$0.555519\pi$
$762$	−8.10805			−0.293724
$763$	−19.7001	+	11.3739i	−0.713192	+	0.411762i
$764$	−14.8521	+	25.7246i	−0.537330	+	0.930682i
$765$	−15.2803	−	13.6569i	−0.552461	−	0.493768i
$766$	10.7913			0.389905
$767$	−48.8311	+	12.0826i	−1.76319	+	0.436277i
$768$		−	1.79129i		−	0.0646375i
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	0.236433	−	0.971648i	$-0.424022\pi$
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	−0.723255	+	0.690581i	$0.757355\pi$
$770$	−3.49041	−	3.11959i	−0.125786	−	0.112422i
$771$	9.08258	+	15.7315i	0.327101	+	0.566556i
$772$	26.6283			0.958374
$773$	−12.0767	−	20.9174i	−0.434368	−	0.752347i	0.562876	−	0.826541i	$-0.309695\pi$
$773$	−12.0767	−	20.9174i	−0.434368	−	0.752347i	−0.997244	+	0.0741940i	$0.976362\pi$
$774$	8.37386	−	4.83465i	0.300992	−	0.173778i
$775$	−12.4104	+	28.4358i	−0.445795	+	1.02144i
$776$	−9.87386	−	17.1020i	−0.354451	−	0.613927i
$777$	−11.9059	−	6.87386i	−0.427121	−	0.246598i
$778$	0.723000	−	1.25227i	0.0259208	−	0.0448962i
$779$	−4.58258			−0.164188
$780$	6.75580	−	12.7642i	0.241896	−	0.457033i
$781$	−18.5826			−0.664937
$782$	−4.79693	+	8.30852i	−0.171538	+	0.297112i
$783$	−19.8431	−	11.4564i	−0.709136	−	0.409420i
$784$	5.58258	+	9.66930i	0.199378	+	0.345332i
$785$	4.18710	−	20.0616i	0.149444	−	0.716030i
$786$	−3.00000	+	1.73205i	−0.107006	+	0.0617802i
$787$	8.15573	+	14.1261i	0.290720	+	0.503542i	0.973980	−	0.226633i	$-0.0727717\pi$
$787$	8.15573	+	14.1261i	0.290720	+	0.503542i	−0.683260	+	0.730175i	$0.739438\pi$
$788$	−26.2867			−0.936425
$789$	4.50000	+	7.79423i	0.160204	+	0.277482i
$790$	−4.08450	+	4.57002i	−0.145320	+	0.162594i
$791$	−11.1261	−	6.42368i	−0.395600	−	0.228400i
$792$			9.16515i			0.325669i
$793$	1.22753	+	4.96099i	0.0435907	+	0.176170i
$794$	−9.29583			−0.329897
$795$	−11.2988	+	12.6418i	−0.400726	+	0.448359i
$796$	−9.47822	+	16.4168i	−0.335947	+	0.581877i
$797$	38.1727	−	22.0390i	1.35215	−	0.780662i	0.363596	−	0.931557i	$-0.381549\pi$
$797$	38.1727	−	22.0390i	1.35215	−	0.780662i	0.988550	+	0.150895i	$0.0482154\pi$
$798$	1.37055			0.0485170
$799$	−7.25227	+	4.18710i	−0.256567	+	0.148129i
$800$	2.65039	+	23.5478i	0.0937056	+	0.832541i
$801$		−	19.1479i		−	0.676558i
$802$	−11.8006	+	6.81307i	−0.416693	+	0.240578i
$803$		0			0
$804$	−1.56534	−	0.903750i	−0.0552053	−	0.0318728i
$805$	−3.62614	+	17.3739i	−0.127805	+	0.612348i
$806$	7.08712	+	7.36515i	0.249633	+	0.259426i
$807$		−	15.0000i		−	0.528025i
$808$	−7.79423	+	13.5000i	−0.274200	+	0.474928i
$809$	−27.4129	+	47.4805i	−0.963785	+	1.66933i	−0.250942	+	0.968002i	$0.580740\pi$
$809$	−27.4129	+	47.4805i	−0.963785	+	1.66933i	−0.712843	+	0.701323i	$0.752593\pi$
$810$	−0.319250	−	0.970381i	−0.0112173	−	0.0340957i
$811$		−	50.5155i		−	1.77384i	−0.461923	−	0.886920i	$-0.652840\pi$
$811$		−	50.5155i		−	1.77384i	0.461923	−	0.886920i	$-0.347160\pi$
$812$	−7.10895	−	12.3131i	−0.249475	−	0.432104i
$813$	4.33013	+	7.50000i	0.151864	+	0.263036i
$814$			9.59386i			0.336264i
$815$	−14.7243	−	44.7555i	−0.515770	−	1.56772i
$816$	6.39564	−	11.0776i	0.223892	−	0.387793i
$817$	9.16478	−	15.8739i	0.320635	−	0.555356i
$818$		−	3.95644i		−	0.138334i
$819$	−9.00000	+	8.66025i	−0.314485	+	0.302614i
$820$	2.16515	−	10.3739i	0.0756104	−	0.362271i
$821$	15.7087	+	9.06943i	0.548238	+	0.316525i	0.748411	−	0.663235i	$-0.230817\pi$
$821$	15.7087	+	9.06943i	0.548238	+	0.316525i	−0.200173	+	0.979761i	$0.564150\pi$
$822$	4.14938	+	2.39564i	0.144726	+	0.0835577i
$823$	27.2083	−	15.7087i	0.948421	−	0.547571i	0.0558311	−	0.998440i	$-0.482219\pi$
$823$	27.2083	−	15.7087i	0.948421	−	0.547571i	0.892590	+	0.450869i	$0.148886\pi$
$824$		−	5.48220i		−	0.190982i
$825$	−1.47960	−	13.1458i	−0.0515131	−	0.457676i
$826$	9.56080	−	5.51993i	0.332663	−	0.192063i
$827$	10.7737			0.374638			0.187319	−	0.982299i	$-0.440020\pi$
$827$	10.7737			0.374638			0.187319	+	0.982299i	$0.440020\pi$
$828$	14.2179	−	8.20871i	0.494106	−	0.285272i
$829$	−16.6652	+	28.8649i	−0.578805	+	1.00252i	0.416812	+	0.908993i	$0.363147\pi$
$829$	−16.6652	+	28.8649i	−0.578805	+	1.00252i	−0.995617	+	0.0935264i	$0.970186\pi$
$830$	4.09437	−	4.58106i	0.142118	−	0.159011i
$831$	−7.41742			−0.257308
$832$	−11.8383	−	3.41742i	−0.410419	−	0.118478i
$833$			18.3303i			0.635107i
$834$	−8.60436	−	4.96773i	−0.297944	−	0.172018i
$835$	14.2661	−	15.9619i	0.493699	−	0.552384i
$836$	4.10436	+	7.10895i	0.141952	+	0.245868i
$837$	31.0260			1.07242
$838$	1.33283	+	2.30852i	0.0460417	+	0.0797466i
$839$	37.8303	−	21.8413i	1.30605	−	0.754047i	0.324613	−	0.945847i	$-0.394766\pi$
$839$	37.8303	−	21.8413i	1.30605	−	0.754047i	0.981434	+	0.191800i	$0.0614326\pi$
$840$	−1.37055	+	6.56670i	−0.0472885	+	0.226573i
$841$	4.00000	+	6.92820i	0.137931	+	0.238904i
$842$	2.16900	+	1.25227i	0.0747487	+	0.0431562i
$843$	−1.82740	+	3.16515i	−0.0629390	+	0.109014i
$844$	0.295834			0.0101830
$845$	−20.9128	−	20.1905i	−0.719421	−	0.694574i
$846$	−1.66970			−0.0574054
$847$	−3.46410	+	6.00000i	−0.119028	+	0.206162i
$848$	18.3296	+	10.5826i	0.629440	+	0.363407i
$849$	−13.8739	−	24.0302i	−0.476150	−	0.824716i
$850$	−4.18710	+	9.59386i	−0.143616	+	0.329067i
$851$	31.5000	−	18.1865i	1.07981	−	0.623426i
$852$	6.29060	+	10.8956i	0.215513	+	0.373279i
$853$	−5.63310			−0.192874			−0.0964369	−	0.995339i	$-0.530745\pi$
$853$	−5.63310			−0.192874			−0.0964369	+	0.995339i	$0.530745\pi$
$854$	−0.560795	−	0.971326i	−0.0191900	−	0.0332381i
$855$	−5.77542	−	5.16184i	−0.197515	−	0.176531i
$856$	15.8739	+	9.16478i	0.542557	+	0.313246i
$857$		−	4.74773i		−	0.162179i	−0.996707	−	0.0810896i	$-0.974160\pi$
$857$		−	4.74773i		−	0.162179i	0.996707	−	0.0810896i	$-0.0258400\pi$
$858$	−4.18710	−	1.20871i	−0.142945	−	0.0412648i
$859$	44.2432			1.50956			0.754779	−	0.655979i	$-0.227744\pi$
$859$	44.2432			1.50956			0.754779	+	0.655979i	$0.227744\pi$
$860$	31.6045	+	28.2469i	1.07771	+	0.963211i
$861$	2.29129	−	3.96863i	0.0780869	−	0.135250i
$862$	3.35093	−	1.93466i	0.114133	−	0.0658947i
$863$	13.6657			0.465186			0.232593	−	0.972574i	$-0.425279\pi$
$863$	13.6657			0.465186			0.232593	+	0.972574i	$0.425279\pi$
$864$	20.5218	−	11.8483i	0.698165	−	0.403086i
$865$	−35.2225	+	11.5880i	−1.19760	+	0.394004i
$866$			4.45325i			0.151328i
$867$	3.46410	−	2.00000i	0.117647	−	0.0679236i
$868$	16.6730	+	9.62614i	0.565917	+	0.326732i
$869$	−13.7477	−	7.93725i	−0.466360	−	0.269253i
$870$	−0.956439	+	4.58258i	−0.0324263	+	0.155364i
$871$	−2.62159	+	2.52263i	−0.0888292	+	0.0854759i
$872$		−	22.7477i		−	0.770335i
$873$	−11.4014	+	19.7477i	−0.385877	+	0.668359i
$874$	−1.81307	+	3.14033i	−0.0613279	+	0.106223i
$875$	−1.81139	+	19.2800i	−0.0612360	+	0.651783i
$876$		0			0
$877$	−3.96863	−	6.87386i	−0.134011	−	0.232114i	0.791208	−	0.611547i	$-0.209452\pi$
$877$	−3.96863	−	6.87386i	−0.134011	−	0.232114i	−0.925219	+	0.379433i	$0.876119\pi$
$878$	3.31113	+	5.73504i	0.111745	+	0.193548i
$879$		−	18.1389i		−	0.611809i
$880$	−15.6864	+	5.16072i	−0.528787	+	0.173968i
$881$	−18.2477	+	31.6060i	−0.614782	+	1.06483i	0.375641	+	0.926765i	$0.377422\pi$
$881$	−18.2477	+	31.6060i	−0.614782	+	1.06483i	−0.990423	+	0.138068i	$0.955911\pi$
$882$	−1.82740	+	3.16515i	−0.0615318	+	0.106576i
$883$		−	36.2432i		−	1.21968i	−0.792524	−	0.609840i	$-0.791234\pi$
$883$		−	36.2432i		−	1.21968i	0.792524	−	0.609840i	$-0.208766\pi$
$884$	−20.5218	−	21.3269i	−0.690222	−	0.717300i
$885$	30.5390	+	6.37386i	1.02656	+	0.214255i
$886$	−7.87841	−	4.54860i	−0.264680	−	0.152813i
$887$	−47.1944	−	27.2477i	−1.58463	−	0.914889i	−0.994170	−	0.107826i	$-0.965611\pi$
$887$	−47.1944	−	27.2477i	−1.58463	−	0.914889i	−0.590465	−	0.807064i	$-0.701055\pi$
$888$	11.9059	−	6.87386i	0.399535	−	0.230672i
$889$			30.7400i			1.03099i
$890$	−9.29039	+	3.05648i	−0.311415	+	0.102454i
$891$	2.29129	−	1.32288i	0.0767610	−	0.0443180i
$892$	−15.5130			−0.519414
$893$	−2.74110	+	1.58258i	−0.0917275	+	0.0529589i
$894$	−3.81307	+	6.60443i	−0.127528	+	0.220885i
$895$	−27.0678	+	30.2853i	−0.904776	+	1.01233i
$896$	19.1216			0.638808
$897$	3.96863	+	16.0390i	0.132509	+	0.535527i
$898$		−	5.03447i		−	0.168002i
$899$	24.6261	+	14.2179i	0.821328	+	0.474194i
$900$	14.4139	−	10.6353i	0.480464	−	0.354511i
$901$	17.3739	+	30.0924i	0.578807	+	1.00252i
$902$	−3.19795			−0.106480
$903$	9.16478	+	15.8739i	0.304985	+	0.528249i
$904$	11.1261	−	6.42368i	0.370050	−	0.213648i
$905$	−19.1479	−	3.99640i	−0.636498	−	0.132845i
$906$	−2.20871	−	3.82560i	−0.0733795	−	0.127097i
$907$	5.41463	+	3.12614i	0.179790	+	0.103802i	0.587194	−	0.809446i	$-0.300233\pi$
$907$	5.41463	+	3.12614i	0.179790	+	0.103802i	−0.407404	+	0.913248i	$0.633566\pi$
$908$	−0.732950	+	1.26951i	−0.0243238	+	0.0421301i
$909$	18.0000			0.597022
$910$	5.63850	+	2.98432i	0.186914	+	0.0989294i
$911$	−7.91288			−0.262165			−0.131083	−	0.991371i	$-0.541845\pi$
$911$	−7.91288			−0.262165			−0.131083	+	0.991371i	$0.541845\pi$
$912$	2.41733	−	4.18693i	0.0800457	−	0.138643i
$913$	13.7810	+	7.95644i	0.456083	+	0.263320i
$914$	−0.395644	−	0.685275i	−0.0130867	−	0.0226669i
$915$	0.647551	−	3.10260i	0.0214074	−	0.102569i
$916$	−40.7477	+	23.5257i	−1.34634	+	0.777311i
$917$	6.56670	+	11.3739i	0.216852	+	0.375598i
$918$	10.4678			0.345487
$919$	27.0826	+	46.9084i	0.893372	+	1.54737i	0.835807	+	0.549023i	$0.185000\pi$
$919$	27.0826	+	46.9084i	0.893372	+	1.54737i	0.0575648	+	0.998342i	$0.481666\pi$
$920$	−13.2331	−	11.8273i	−0.436284	−	0.389933i
$921$	21.0000	+	12.1244i	0.691974	+	0.399511i
$922$		−	16.3739i		−	0.539244i
$923$	24.5824	−	6.08258i	0.809141	−	0.200210i
$924$	−8.20871			−0.270047
$925$	31.9343	−	23.5627i	1.04999	−	0.774738i
$926$	9.00000	−	15.5885i	0.295758	−	0.512268i
$927$	−5.48220	+	3.16515i	−0.180059	+	0.103957i
$928$	21.7182			0.712935
$929$	22.8303	−	13.1811i	0.749038	−	0.432457i	−0.0763082	−	0.997084i	$-0.524313\pi$
$929$	22.8303	−	13.1811i	0.749038	−	0.432457i	0.825346	+	0.564627i	$0.190980\pi$
$930$	−1.98101	−	6.02141i	−0.0649599	−	0.197450i
$931$			6.92820i			0.227063i
$932$	4.39770	−	2.53901i	0.144052	−	0.0831682i
$933$	6.56670	+	3.79129i	0.214984	+	0.124121i
$934$	−9.62614	−	5.55765i	−0.314977	−	0.181852i
$935$	−26.5390	−	5.53901i	−0.867919	−	0.181145i
$936$	−3.00000	−	12.1244i	−0.0980581	−	0.396297i
$937$			31.4955i			1.02891i	0.857517	+	0.514456i	$0.172006\pi$
$937$			31.4955i			1.02891i	−0.857517	+	0.514456i	$0.827994\pi$
$938$	0.399225	−	0.691478i	0.0130352	−	0.0225775i
$939$	−1.62614	+	2.81655i	−0.0530670	+	0.0919147i
$940$	−2.28747	−	6.95293i	−0.0746092	−	0.226780i
$941$		−	26.4575i		−	0.862490i	−0.902235	−	0.431245i	$-0.858074\pi$
$941$		−	26.4575i		−	0.862490i	0.902235	−	0.431245i	$-0.141926\pi$
$942$	2.09355	+	3.62614i	0.0682116	+	0.118146i
$943$	6.06218	+	10.5000i	0.197412	+	0.341927i
$944$		−	38.9434i		−	1.26750i
$945$	18.3950	−	6.05184i	0.598389	−	0.196866i
$946$	6.39564	−	11.0776i	0.207940	−	0.360163i
$947$	7.16658	−	12.4129i	0.232883	−	0.403364i	−0.725773	−	0.687935i	$-0.758518\pi$
$947$	7.16658	−	12.4129i	0.232883	−	0.403364i	0.958655	+	0.284570i	$0.0918509\pi$
$948$			10.7477i			0.349070i
$949$		0			0
$950$	−1.58258	+	3.62614i	−0.0513455	+	0.117647i
$951$	−0.165151	−	0.0953502i	−0.00535540	−	0.00309194i
$952$	11.9059	+	6.87386i	0.385872	+	0.222783i
$953$	6.99578	−	4.03901i	0.226616	−	0.130837i	−0.382394	−	0.923999i	$-0.624900\pi$
$953$	6.99578	−	4.03901i	0.226616	−	0.130837i	0.609010	+	0.793163i	$0.291567\pi$
$954$			6.92820i			0.224309i
$955$	−11.5880	−	35.2225i	−0.374979	−	1.13977i
$956$	−0.295834	+	0.170800i	−0.00956794	+	0.00552406i
$957$	−12.1244			−0.391925
$958$	1.84522	−	1.06534i	0.0596165	−	0.0344196i
$959$	9.08258	−	15.7315i	0.293292	−	0.507996i
$960$	5.69759	+	5.09229i	0.183889	+	0.164353i
$961$	−7.50455			−0.242082
$962$	−3.14033	−	12.6915i	−0.101248	−	0.409190i
$963$		−	21.1652i		−	0.682037i
$964$	−2.68693	−	1.55130i	−0.0865402	−	0.0499640i
$965$	−22.1509	+	24.7840i	−0.713064	+	0.797824i
$966$	−1.81307	−	3.14033i	−0.0583345	−	0.101038i
$967$	−37.3821			−1.20213			−0.601064	−	0.799201i	$-0.705256\pi$
$967$	−37.3821			−1.20213			−0.601064	+	0.799201i	$0.705256\pi$
$968$	−3.46410	−	6.00000i	−0.111340	−	0.192847i
$969$	6.87386	−	3.96863i	0.220820	−	0.127491i
$970$	11.4014	+	2.37960i	0.366075	+	0.0764044i
$971$	9.24773	+	16.0175i	0.296774	+	0.514027i	0.975396	−	0.220460i	$-0.0707560\pi$
$971$	9.24773	+	16.0175i	0.296774	+	0.514027i	−0.678622	+	0.734487i	$0.737423\pi$
$972$	−24.8208	−	14.3303i	−0.796128	−	0.459645i
$973$	−18.8341	+	32.6216i	−0.603793	+	1.04580i
$974$	4.87841			0.156314
$975$	6.26029	+	16.9059i	0.200490	+	0.541421i
$976$	−3.95644			−0.126643
$977$	−17.6542	+	30.5780i	−0.564809	+	0.978278i	0.432258	+	0.901750i	$0.357717\pi$
$977$	−17.6542	+	30.5780i	−0.564809	+	0.978278i	−0.997067	+	0.0765281i	$0.975617\pi$
$978$	8.33648	+	4.81307i	0.266571	+	0.153905i
$979$	−12.6652	−	21.9367i	−0.404780	−	0.701100i
$980$	−15.6838	−	3.27340i	−0.501001	−	0.104565i
$981$	−22.7477	+	13.1334i	−0.726279	+	0.419317i
$982$	4.43543	+	7.68239i	0.141540	+	0.245155i
$983$	55.0840			1.75691			0.878454	−	0.477827i	$-0.158576\pi$
$983$	55.0840			1.75691			0.878454	+	0.477827i	$0.158576\pi$
$984$	2.29129	+	3.96863i	0.0730436	+	0.126515i
$985$	21.8668	−	24.4660i	0.696733	−	0.779553i
$986$	8.30852	+	4.79693i	0.264597	+	0.152765i
$987$		−	3.16515i		−	0.100748i
$988$	−7.75650	−	8.06080i	−0.246767	−	0.256448i
$989$	−48.4955			−1.54207
$990$	−4.03038	−	3.60219i	−0.128094	−	0.114485i
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	−0.744124	−	0.668042i	$-0.767133\pi$
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	0.950603	+	0.310409i	$0.100466\pi$
$992$	−25.4684	+	14.7042i	−0.808621	+	0.466858i
$993$	−4.47315			−0.141951
$994$	−4.81307	+	2.77883i	−0.152661	+	0.0881390i
$995$	−7.39517	−	22.4781i	−0.234443	−	0.712604i
$996$		−	10.7737i		−	0.341378i
$997$	0.143025	−	0.0825757i	0.00452966	−	0.00261520i	−0.497733	−	0.867330i	$-0.665834\pi$
$997$	0.143025	−	0.0825757i	0.00452966	−	0.00261520i	0.502263	+	0.864715i	$0.332501\pi$
$998$	0.286051	+	0.165151i	0.00905477	+	0.00522778i
$999$	−34.3693	−	19.8431i	−1.08740	−	0.627809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.l.a.4.3	yes	8
3.2	odd	2		585.2.bf.a.199.2		8
4.3	odd	2		1040.2.df.b.849.1		8
5.2	odd	4		325.2.n.b.251.2		4
5.3	odd	4		325.2.n.c.251.1		4
5.4	even	2	inner	65.2.l.a.4.2	✓	8
13.2	odd	12		845.2.n.c.484.3		8
13.3	even	3		845.2.l.c.699.3		8
13.4	even	6		845.2.d.c.844.5		8
13.5	odd	4		845.2.n.d.529.2		8
13.6	odd	12		845.2.b.f.339.5		8
13.7	odd	12		845.2.b.f.339.3		8
13.8	odd	4		845.2.n.c.529.4		8
13.9	even	3		845.2.d.c.844.3		8
13.10	even	6	inner	65.2.l.a.49.2	yes	8
13.11	odd	12		845.2.n.d.484.1		8
13.12	even	2		845.2.l.c.654.2		8
15.14	odd	2		585.2.bf.a.199.3		8
20.19	odd	2		1040.2.df.b.849.4		8
39.23	odd	6		585.2.bf.a.244.3		8
52.23	odd	6		1040.2.df.b.49.4		8
65.4	even	6		845.2.d.c.844.4		8
65.7	even	12		4225.2.a.bj.1.3		4
65.9	even	6		845.2.d.c.844.6		8
65.19	odd	12		845.2.b.f.339.4		8
65.23	odd	12		325.2.n.c.101.1		4
65.24	odd	12		845.2.n.c.484.4		8
65.29	even	6		845.2.l.c.699.2		8
65.32	even	12		4225.2.a.bj.1.2		4
65.33	even	12		4225.2.a.bk.1.2		4
65.34	odd	4		845.2.n.d.529.1		8
65.44	odd	4		845.2.n.c.529.3		8
65.49	even	6	inner	65.2.l.a.49.3	yes	8
65.54	odd	12		845.2.n.d.484.2		8
65.58	even	12		4225.2.a.bk.1.3		4
65.59	odd	12		845.2.b.f.339.6		8
65.62	odd	12		325.2.n.b.101.2		4
65.64	even	2		845.2.l.c.654.3		8
195.179	odd	6		585.2.bf.a.244.2		8
260.179	odd	6		1040.2.df.b.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.2	✓	8	5.4	even	2	inner
65.2.l.a.4.3	yes	8	1.1	even	1	trivial
65.2.l.a.49.2	yes	8	13.10	even	6	inner
65.2.l.a.49.3	yes	8	65.49	even	6	inner
325.2.n.b.101.2		4	65.62	odd	12
325.2.n.b.251.2		4	5.2	odd	4
325.2.n.c.101.1		4	65.23	odd	12
325.2.n.c.251.1		4	5.3	odd	4
585.2.bf.a.199.2		8	3.2	odd	2
585.2.bf.a.199.3		8	15.14	odd	2
585.2.bf.a.244.2		8	195.179	odd	6
585.2.bf.a.244.3		8	39.23	odd	6
845.2.b.f.339.3		8	13.7	odd	12
845.2.b.f.339.4		8	65.19	odd	12
845.2.b.f.339.5		8	13.6	odd	12
845.2.b.f.339.6		8	65.59	odd	12
845.2.d.c.844.3		8	13.9	even	3
845.2.d.c.844.4		8	65.4	even	6
845.2.d.c.844.5		8	13.4	even	6
845.2.d.c.844.6		8	65.9	even	6
845.2.l.c.654.2		8	13.12	even	2
845.2.l.c.654.3		8	65.64	even	2
845.2.l.c.699.2		8	65.29	even	6
845.2.l.c.699.3		8	13.3	even	3
845.2.n.c.484.3		8	13.2	odd	12
845.2.n.c.484.4		8	65.24	odd	12
845.2.n.c.529.3		8	65.44	odd	4
845.2.n.c.529.4		8	13.8	odd	4
845.2.n.d.484.1		8	13.11	odd	12
845.2.n.d.484.2		8	65.54	odd	12
845.2.n.d.529.1		8	65.34	odd	4
845.2.n.d.529.2		8	13.5	odd	4
1040.2.df.b.49.1		8	260.179	odd	6
1040.2.df.b.49.4		8	52.23	odd	6
1040.2.df.b.849.1		8	4.3	odd	2
1040.2.df.b.849.4		8	20.19	odd	2
4225.2.a.bj.1.2		4	65.32	even	12
4225.2.a.bj.1.3		4	65.7	even	12
4225.2.a.bk.1.2		4	65.33	even	12
4225.2.a.bk.1.3		4	65.58	even	12

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.228425 - 0.395644i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.895644 + 1.55130i) q^{4} +(-2.18890 - 0.456850i) q^{5} +(0.395644 - 0.228425i) q^{6} +(-0.866025 - 1.50000i) q^{7} +1.73205 q^{8} +(-1.00000 - 1.73205i) q^{9} +(-0.680750 + 0.761669i) q^{10} +(-2.29129 - 1.32288i) q^{11} +1.79129i q^{12} +(3.46410 + 1.00000i) q^{13} -0.791288 q^{14} +(-1.66722 - 1.49009i) q^{15} +(-1.39564 + 2.41733i) q^{16} +(-3.96863 + 2.29129i) q^{17} -0.913701 q^{18} +(-1.50000 + 0.866025i) q^{19} +(-1.25176 - 3.80482i) q^{20} -1.73205i q^{21} +(-1.04678 + 0.604356i) q^{22} +(3.96863 + 2.29129i) q^{23} +(1.50000 + 0.866025i) q^{24} +(4.58258 + 2.00000i) q^{25} +(1.18693 - 1.14213i) q^{26} -5.00000i q^{27} +(1.55130 - 2.68693i) q^{28} +(2.29129 - 3.96863i) q^{29} +(-0.970381 + 0.319250i) q^{30} +6.20520i q^{31} +(2.36965 + 4.10436i) q^{32} +(-1.32288 - 2.29129i) q^{33} +2.09355i q^{34} +(1.21037 + 3.67900i) q^{35} +(1.79129 - 3.10260i) q^{36} +(3.96863 - 6.87386i) q^{37} +0.791288i q^{38} +(2.50000 + 2.59808i) q^{39} +(-3.79129 - 0.791288i) q^{40} +(2.29129 + 1.32288i) q^{41} +(-0.685275 - 0.395644i) q^{42} +(-9.16478 + 5.29129i) q^{43} -4.73930i q^{44} +(1.39761 + 4.24814i) q^{45} +(1.81307 - 1.04678i) q^{46} +1.82740 q^{47} +(-2.41733 + 1.39564i) q^{48} +(2.00000 - 3.46410i) q^{49} +(1.83806 - 1.35622i) q^{50} -4.58258 q^{51} +(1.55130 + 6.26951i) q^{52} -7.58258i q^{53} +(-1.97822 - 1.14213i) q^{54} +(4.41105 + 3.94242i) q^{55} +(-1.50000 - 2.59808i) q^{56} -1.73205 q^{57} +(-1.04678 - 1.81307i) q^{58} +(-12.0826 + 6.97588i) q^{59} +(0.818350 - 3.92095i) q^{60} +(0.708712 + 1.22753i) q^{61} +(2.45505 + 1.41742i) q^{62} +(-1.73205 + 3.00000i) q^{63} -3.41742 q^{64} +(-7.12573 - 3.77148i) q^{65} -1.20871 q^{66} +(-0.504525 + 0.873864i) q^{67} +(-7.10895 - 4.10436i) q^{68} +(2.29129 + 3.96863i) q^{69} +(1.73205 + 0.361500i) q^{70} +(6.08258 - 3.51178i) q^{71} +(-1.73205 - 3.00000i) q^{72} +(-1.81307 - 3.14033i) q^{74} +(2.96863 + 4.02334i) q^{75} +(-2.68693 - 1.55130i) q^{76} +4.58258i q^{77} +(1.59898 - 0.395644i) q^{78} +6.00000 q^{79} +(4.15928 - 4.65369i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.04678 - 0.604356i) q^{82} -6.01450 q^{83} +(2.68693 - 1.55130i) q^{84} +(9.73371 - 3.20233i) q^{85} +4.83465i q^{86} +(3.96863 - 2.29129i) q^{87} +(-3.96863 - 2.29129i) q^{88} +(8.29129 + 4.78698i) q^{89} +(2.00000 + 0.417424i) q^{90} +(-1.50000 - 6.06218i) q^{91} +8.20871i q^{92} +(-3.10260 + 5.37386i) q^{93} +(0.417424 - 0.723000i) q^{94} +(3.67900 - 1.21037i) q^{95} +4.73930i q^{96} +(-5.70068 - 9.87386i) q^{97} +(-0.913701 - 1.58258i) q^{98} +5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 6 q^{6} - 8 q^{9} - 4 q^{10} + 12 q^{14} - 6 q^{15} - 2 q^{16} - 12 q^{19} + 24 q^{20} + 12 q^{24} - 18 q^{26} - 10 q^{30} + 6 q^{35} - 4 q^{36} + 20 q^{39} - 12 q^{40} + 12 q^{45} + 42 q^{46}+ \cdots - 6 q^{95}+O(q^{100}) \) 8 * q - 2 * q^4 - 6 * q^6 - 8 * q^9 - 4 * q^10 + 12 * q^14 - 6 * q^15 - 2 * q^16 - 12 * q^19 + 24 * q^20 + 12 * q^24 - 18 * q^26 - 10 * q^30 + 6 * q^35 - 4 * q^36 + 20 * q^39 - 12 * q^40 + 12 * q^45 + 42 * q^46 + 16 * q^49 - 12 * q^50 + 30 * q^54 - 14 * q^55 - 12 * q^56 - 60 * q^59 + 24 * q^61 - 64 * q^64 - 24 * q^65 - 28 * q^66 + 12 * q^71 - 42 * q^74 - 8 * q^75 + 6 * q^76 + 48 * q^79 + 18 * q^80 - 4 * q^81 - 6 * q^84 + 42 * q^85 + 48 * q^89 + 16 * q^90 - 12 * q^91 + 40 * q^94 - 6 * q^95

Introduction

L-functions

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