LMFDB - Embedded newform 483.2.i.e.277.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(277,483)] 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("483.277"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,1,-2,-5,1,-2,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.1
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	483.277
Dual form			483.2.i.e.415.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.780776 - 1.35234i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.219224 + 0.379706i) q^{4} +(-0.780776 - 1.35234i) q^{5} +1.56155 q^{6} +(2.50000 + 0.866025i) q^{7} -2.43845 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.21922 + 2.11176i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-0.219224 - 0.379706i) q^{12} -6.12311 q^{13} +(-0.780776 - 4.05703i) q^{14} +1.56155 q^{15} +(2.34233 + 4.05703i) q^{16} +(3.78078 - 6.54850i) q^{17} +(-0.780776 + 1.35234i) q^{18} +(-0.719224 - 1.24573i) q^{19} +0.684658 q^{20} +(-2.00000 + 1.73205i) q^{21} -3.12311 q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.21922 - 2.11176i) q^{24} +(1.28078 - 2.21837i) q^{25} +(4.78078 + 8.28055i) q^{26} +1.00000 q^{27} +(-0.876894 + 0.759413i) q^{28} -9.12311 q^{29} +(-1.21922 - 2.11176i) q^{30} +(-2.84233 + 4.92306i) q^{31} +(1.21922 - 2.11176i) q^{32} +(1.00000 + 1.73205i) q^{33} -11.8078 q^{34} +(-0.780776 - 4.05703i) q^{35} +0.438447 q^{36} +(-1.71922 - 2.97778i) q^{37} +(-1.12311 + 1.94528i) q^{38} +(3.06155 - 5.30277i) q^{39} +(1.90388 + 3.29762i) q^{40} -10.2462 q^{41} +(3.90388 + 1.35234i) q^{42} -0.315342 q^{43} +(0.438447 + 0.759413i) q^{44} +(-0.780776 + 1.35234i) q^{45} +(-0.780776 + 1.35234i) q^{46} +(-3.34233 - 5.78908i) q^{47} -4.68466 q^{48} +(5.50000 + 4.33013i) q^{49} -4.00000 q^{50} +(3.78078 + 6.54850i) q^{51} +(1.34233 - 2.32498i) q^{52} +(3.90388 - 6.76172i) q^{53} +(-0.780776 - 1.35234i) q^{54} -3.12311 q^{55} +(-6.09612 - 2.11176i) q^{56} +1.43845 q^{57} +(7.12311 + 12.3376i) q^{58} +(-4.56155 + 7.90084i) q^{59} +(-0.342329 + 0.592932i) q^{60} +(-3.00000 - 5.19615i) q^{61} +8.87689 q^{62} +(-0.500000 - 2.59808i) q^{63} +5.56155 q^{64} +(4.78078 + 8.28055i) q^{65} +(1.56155 - 2.70469i) q^{66} +(7.06155 - 12.2310i) q^{67} +(1.65767 + 2.87117i) q^{68} +1.00000 q^{69} +(-4.87689 + 4.22351i) q^{70} +13.8078 q^{71} +(1.21922 + 2.11176i) q^{72} +(-2.93845 + 5.08954i) q^{73} +(-2.68466 + 4.64996i) q^{74} +(1.28078 + 2.21837i) q^{75} +0.630683 q^{76} +(4.00000 - 3.46410i) q^{77} -9.56155 q^{78} +(2.71922 + 4.70983i) q^{79} +(3.65767 - 6.33527i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(8.00000 + 13.8564i) q^{82} +4.87689 q^{83} +(-0.219224 - 1.13912i) q^{84} -11.8078 q^{85} +(0.246211 + 0.426450i) q^{86} +(4.56155 - 7.90084i) q^{87} +(-2.43845 + 4.22351i) q^{88} +(5.00000 + 8.66025i) q^{89} +2.43845 q^{90} +(-15.3078 - 5.30277i) q^{91} +0.438447 q^{92} +(-2.84233 - 4.92306i) q^{93} +(-5.21922 + 9.03996i) q^{94} +(-1.12311 + 1.94528i) q^{95} +(1.21922 + 2.11176i) q^{96} +15.3693 q^{97} +(1.56155 - 10.8188i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} - 5 q^{4} + q^{5} - 2 q^{6} + 10 q^{7} - 18 q^{8} - 2 q^{9} - 9 q^{10} + 4 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 2 q^{15} - 3 q^{16} + 11 q^{17} + q^{18} - 7 q^{19} - 22 q^{20}+ \cdots - 8 q^{99}+O(q^{100}) $ 4 * q + q^2 - 2 * q^3 - 5 * q^4 + q^5 - 2 * q^6 + 10 * q^7 - 18 * q^8 - 2 * q^9 - 9 * q^10 + 4 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 2 * q^15 - 3 * q^16 + 11 * q^17 + q^18 - 7 * q^19 - 22 * q^20 - 8 * q^21 + 4 * q^22 - 2 * q^23 + 9 * q^24 + q^25 + 15 * q^26 + 4 * q^27 - 20 * q^28 - 20 * q^29 - 9 * q^30 + q^31 + 9 * q^32 + 4 * q^33 - 6 * q^34 + q^35 + 10 * q^36 - 11 * q^37 + 12 * q^38 + 4 * q^39 - 13 * q^40 - 8 * q^41 - 5 * q^42 - 26 * q^43 + 10 * q^44 + q^45 + q^46 - q^47 + 6 * q^48 + 22 * q^49 - 16 * q^50 + 11 * q^51 - 7 * q^52 - 5 * q^53 + q^54 + 4 * q^55 - 45 * q^56 + 14 * q^57 + 12 * q^58 - 10 * q^59 + 11 * q^60 - 12 * q^61 + 52 * q^62 - 2 * q^63 + 14 * q^64 + 15 * q^65 - 2 * q^66 + 20 * q^67 + 19 * q^68 + 4 * q^69 - 36 * q^70 + 14 * q^71 + 9 * q^72 - 20 * q^73 + 14 * q^74 + q^75 + 52 * q^76 + 16 * q^77 - 30 * q^78 + 15 * q^79 + 27 * q^80 - 2 * q^81 + 32 * q^82 + 36 * q^83 - 5 * q^84 - 6 * q^85 - 32 * q^86 + 10 * q^87 - 18 * q^88 + 20 * q^89 + 18 * q^90 - 20 * q^91 + 10 * q^92 + q^93 - 25 * q^94 + 12 * q^95 + 9 * q^96 + 12 * q^97 - 2 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.780776	−	1.35234i	−0.552092	−	0.956252i	−0.998123	−	0.0612344i	$-0.980496\pi$
$2$	−0.780776	−	1.35234i	−0.552092	−	0.956252i	0.446031	−	0.895017i	$-0.352837\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.219224	+	0.379706i	−0.109612	+	0.189853i
$5$	−0.780776	−	1.35234i	−0.349174	−	0.604787i	0.636929	−	0.770922i	$-0.280204\pi$
$5$	−0.780776	−	1.35234i	−0.349174	−	0.604787i	−0.986103	+	0.166136i	$0.946871\pi$
$6$	1.56155			0.637501
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$	−2.43845			−0.862121
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.21922	+	2.11176i	−0.385552	+	0.667796i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	−0.219224	−	0.379706i	−0.0632844	−	0.109612i
$13$	−6.12311			−1.69824			−0.849122	−	0.528197i	$-0.822868\pi$
$13$	−6.12311			−1.69824			−0.849122	+	0.528197i	$0.822868\pi$
$14$	−0.780776	−	4.05703i	−0.208671	−	1.08429i
$15$	1.56155			0.403191
$16$	2.34233	+	4.05703i	0.585582	+	1.01426i
$17$	3.78078	−	6.54850i	0.916973	−	1.58824i	0.112986	−	0.993597i	$-0.463958\pi$
$17$	3.78078	−	6.54850i	0.916973	−	1.58824i	0.803987	−	0.594647i	$-0.202708\pi$
$18$	−0.780776	+	1.35234i	−0.184031	+	0.318751i
$19$	−0.719224	−	1.24573i	−0.165001	−	0.285790i	0.771655	−	0.636042i	$-0.219429\pi$
$19$	−0.719224	−	1.24573i	−0.165001	−	0.285790i	−0.936656	+	0.350251i	$0.886096\pi$
$20$	0.684658			0.153094
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$	−3.12311			−0.665848
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	1.21922	−	2.11176i	0.248873	−	0.431061i
$25$	1.28078	−	2.21837i	0.256155	−	0.443674i
$26$	4.78078	+	8.28055i	0.937587	+	1.62395i
$27$	1.00000			0.192450
$28$	−0.876894	+	0.759413i	−0.165717	+	0.143516i
$29$	−9.12311			−1.69412			−0.847059	−	0.531499i	$-0.821629\pi$
$29$	−9.12311			−1.69412			−0.847059	+	0.531499i	$0.821629\pi$
$30$	−1.21922	−	2.11176i	−0.222599	−	0.385552i
$31$	−2.84233	+	4.92306i	−0.510497	+	0.884207i	0.489429	+	0.872043i	$0.337205\pi$
$31$	−2.84233	+	4.92306i	−0.510497	+	0.884207i	−0.999926	+	0.0121641i	$0.996128\pi$
$32$	1.21922	−	2.11176i	0.215530	−	0.373309i
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$	−11.8078			−2.02501
$35$	−0.780776	−	4.05703i	−0.131975	−	0.685764i
$36$	0.438447			0.0730745
$37$	−1.71922	−	2.97778i	−0.282639	−	0.489544i	0.689395	−	0.724385i	$-0.257876\pi$
$37$	−1.71922	−	2.97778i	−0.282639	−	0.489544i	−0.972034	+	0.234841i	$0.924543\pi$
$38$	−1.12311	+	1.94528i	−0.182192	+	0.315565i
$39$	3.06155	−	5.30277i	0.490241	−	0.849122i
$40$	1.90388	+	3.29762i	0.301030	+	0.521400i
$41$	−10.2462			−1.60019			−0.800095	−	0.599874i	$-0.795217\pi$
$41$	−10.2462			−1.60019			−0.800095	+	0.599874i	$0.795217\pi$
$42$	3.90388	+	1.35234i	0.602382	+	0.208671i
$43$	−0.315342			−0.0480891			−0.0240446	−	0.999711i	$-0.507654\pi$
$43$	−0.315342			−0.0480891			−0.0240446	+	0.999711i	$0.507654\pi$
$44$	0.438447	+	0.759413i	0.0660984	+	0.114486i
$45$	−0.780776	+	1.35234i	−0.116391	+	0.201596i
$46$	−0.780776	+	1.35234i	−0.115119	+	0.199392i
$47$	−3.34233	−	5.78908i	−0.487529	−	0.844425i	0.512368	−	0.858766i	$-0.328768\pi$
$47$	−3.34233	−	5.78908i	−0.487529	−	0.844425i	−0.999897	+	0.0143411i	$0.995435\pi$
$48$	−4.68466			−0.676172
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−4.00000			−0.565685
$51$	3.78078	+	6.54850i	0.529415	+	0.916973i
$52$	1.34233	−	2.32498i	0.186148	−	0.322417i
$53$	3.90388	−	6.76172i	0.536239	−	0.928794i	−0.462863	−	0.886430i	$-0.653178\pi$
$53$	3.90388	−	6.76172i	0.536239	−	0.928794i	0.999102	−	0.0423640i	$-0.0134889\pi$
$54$	−0.780776	−	1.35234i	−0.106250	−	0.184031i
$55$	−3.12311			−0.421119
$56$	−6.09612	−	2.11176i	−0.814628	−	0.282195i
$57$	1.43845			0.190527
$58$	7.12311	+	12.3376i	0.935310	+	1.62000i
$59$	−4.56155	+	7.90084i	−0.593864	+	1.02860i	0.399843	+	0.916584i	$0.369065\pi$
$59$	−4.56155	+	7.90084i	−0.593864	+	1.02860i	−0.993706	+	0.112018i	$0.964269\pi$
$60$	−0.342329	+	0.592932i	−0.0441945	+	0.0765471i
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	0.607535	−	0.794293i	$-0.292159\pi$
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	−0.991645	+	0.128994i	$0.958825\pi$
$62$	8.87689			1.12737
$63$	−0.500000	−	2.59808i	−0.0629941	−	0.327327i
$64$	5.56155			0.695194
$65$	4.78078	+	8.28055i	0.592982	+	1.02708i
$66$	1.56155	−	2.70469i	0.192214	−	0.332924i
$67$	7.06155	−	12.2310i	0.862706	−	1.49425i	−0.00660110	−	0.999978i	$-0.502101\pi$
$67$	7.06155	−	12.2310i	0.862706	−	1.49425i	0.869307	−	0.494272i	$-0.164565\pi$
$68$	1.65767	+	2.87117i	0.201022	+	0.348181i
$69$	1.00000			0.120386
$70$	−4.87689	+	4.22351i	−0.582900	+	0.504807i
$71$	13.8078			1.63868			0.819340	−	0.573308i	$-0.194340\pi$
$71$	13.8078			1.63868			0.819340	+	0.573308i	$0.194340\pi$
$72$	1.21922	+	2.11176i	0.143687	+	0.248873i
$73$	−2.93845	+	5.08954i	−0.343919	+	0.595686i	−0.985157	−	0.171657i	$-0.945088\pi$
$73$	−2.93845	+	5.08954i	−0.343919	+	0.595686i	0.641238	+	0.767342i	$0.278421\pi$
$74$	−2.68466	+	4.64996i	−0.312085	+	0.540547i
$75$	1.28078	+	2.21837i	0.147891	+	0.256155i
$76$	0.630683			0.0723443
$77$	4.00000	−	3.46410i	0.455842	−	0.394771i
$78$	−9.56155			−1.08263
$79$	2.71922	+	4.70983i	0.305937	+	0.529898i	0.977469	−	0.211077i	$-0.0676971\pi$
$79$	2.71922	+	4.70983i	0.305937	+	0.529898i	−0.671533	+	0.740975i	$0.734364\pi$
$80$	3.65767	−	6.33527i	0.408940	−	0.708305i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	8.00000	+	13.8564i	0.883452	+	1.53018i
$83$	4.87689			0.535309			0.267654	−	0.963515i	$-0.413751\pi$
$83$	4.87689			0.535309			0.267654	+	0.963515i	$0.413751\pi$
$84$	−0.219224	−	1.13912i	−0.0239193	−	0.124288i
$85$	−11.8078			−1.28073
$86$	0.246211	+	0.426450i	0.0265496	+	0.0459853i
$87$	4.56155	−	7.90084i	0.489050	−	0.847059i
$88$	−2.43845	+	4.22351i	−0.259939	+	0.450228i
$89$	5.00000	+	8.66025i	0.529999	+	0.917985i	0.999388	+	0.0349934i	$0.0111410\pi$
$89$	5.00000	+	8.66025i	0.529999	+	0.917985i	−0.469389	+	0.882992i	$0.655526\pi$
$90$	2.43845			0.257035
$91$	−15.3078	−	5.30277i	−1.60469	−	0.555881i
$92$	0.438447			0.0457113
$93$	−2.84233	−	4.92306i	−0.294736	−	0.510497i
$94$	−5.21922	+	9.03996i	−0.538322	+	0.932401i
$95$	−1.12311	+	1.94528i	−0.115228	+	0.199581i
$96$	1.21922	+	2.11176i	0.124436	+	0.215530i
$97$	15.3693			1.56052			0.780259	−	0.625457i	$-0.215087\pi$
$97$	15.3693			1.56052			0.780259	+	0.625457i	$0.215087\pi$
$98$	1.56155	−	10.8188i	0.157741	−	1.09286i
$99$	−2.00000			−0.201008
$100$	0.561553	+	0.972638i	0.0561553	+	0.0972638i
$101$	0.438447	−	0.759413i	0.0436271	−	0.0755644i	−0.843387	−	0.537306i	$-0.819442\pi$
$101$	0.438447	−	0.759413i	0.0436271	−	0.0755644i	0.887014	+	0.461742i	$0.152775\pi$
$102$	5.90388	−	10.2258i	0.584571	−	1.01251i
$103$	−7.06155	−	12.2310i	−0.695795	−	1.20515i	−0.969912	−	0.243457i	$-0.921719\pi$
$103$	−7.06155	−	12.2310i	−0.695795	−	1.20515i	0.274116	−	0.961697i	$-0.411615\pi$
$104$	14.9309			1.46409
$105$	3.90388	+	1.35234i	0.380980	+	0.131975i
$106$	−12.1922			−1.18421
$107$	3.12311	+	5.40938i	0.301922	+	0.522944i	0.976571	−	0.215194i	$-0.0690384\pi$
$107$	3.12311	+	5.40938i	0.301922	+	0.522944i	−0.674649	+	0.738138i	$0.735705\pi$
$108$	−0.219224	+	0.379706i	−0.0210948	+	0.0365373i
$109$	5.28078	−	9.14657i	0.505807	−	0.876083i	−0.494171	−	0.869365i	$-0.664528\pi$
$109$	5.28078	−	9.14657i	0.505807	−	0.876083i	0.999977	−	0.00671796i	$-0.00213841\pi$
$110$	2.43845	+	4.22351i	0.232497	+	0.402696i
$111$	3.43845			0.326363
$112$	2.34233	+	12.1711i	0.221329	+	1.15006i
$113$	9.80776			0.922637			0.461318	−	0.887235i	$-0.347377\pi$
$113$	9.80776			0.922637			0.461318	+	0.887235i	$0.347377\pi$
$114$	−1.12311	−	1.94528i	−0.105188	−	0.182192i
$115$	−0.780776	+	1.35234i	−0.0728078	+	0.126107i
$116$	2.00000	−	3.46410i	0.185695	−	0.321634i
$117$	3.06155	+	5.30277i	0.283041	+	0.490241i
$118$	14.2462			1.31147
$119$	15.1231	−	13.0970i	1.38633	−	1.20060i
$120$	−3.80776			−0.347600
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−4.68466	+	8.11407i	−0.424129	+	0.734613i
$123$	5.12311	−	8.87348i	0.461935	−	0.800095i
$124$	−1.24621	−	2.15850i	−0.111913	−	0.193839i
$125$	−11.8078			−1.05612
$126$	−3.12311	+	2.70469i	−0.278228	+	0.240953i
$127$	1.68466			0.149489			0.0747446	−	0.997203i	$-0.476186\pi$
$127$	1.68466			0.149489			0.0747446	+	0.997203i	$0.476186\pi$
$128$	−6.78078	−	11.7446i	−0.599342	−	1.03809i
$129$	0.157671	−	0.273094i	0.0138821	−	0.0240446i
$130$	7.46543	−	12.9305i	0.654762	−	1.13408i
$131$	−6.34233	−	10.9852i	−0.554132	−	0.959785i	−0.997971	−	0.0636778i	$-0.979717\pi$
$131$	−6.34233	−	10.9852i	−0.554132	−	0.959785i	0.443839	−	0.896107i	$-0.353616\pi$
$132$	−0.876894			−0.0763239
$133$	−0.719224	−	3.73720i	−0.0623646	−	0.324056i
$134$	−22.0540			−1.90517
$135$	−0.780776	−	1.35234i	−0.0671985	−	0.116391i
$136$	−9.21922	+	15.9682i	−0.790542	+	1.36926i
$137$	3.90388	−	6.76172i	0.333531	−	0.577693i	−0.649670	−	0.760216i	$-0.725093\pi$
$137$	3.90388	−	6.76172i	0.333531	−	0.577693i	0.983202	+	0.182523i	$0.0584264\pi$
$138$	−0.780776	−	1.35234i	−0.0664641	−	0.115119i
$139$	11.9309			1.01196			0.505982	−	0.862544i	$-0.331130\pi$
$139$	11.9309			1.01196			0.505982	+	0.862544i	$0.331130\pi$
$140$	1.71165	+	0.592932i	0.144660	+	0.0501119i
$141$	6.68466			0.562950
$142$	−10.7808	−	18.6729i	−0.904703	−	1.56699i
$143$	−6.12311	+	10.6055i	−0.512040	+	0.886879i
$144$	2.34233	−	4.05703i	0.195194	−	0.338086i
$145$	7.12311	+	12.3376i	0.591542	+	1.02458i
$146$	9.17708			0.759501
$147$	−6.50000	+	2.59808i	−0.536111	+	0.214286i
$148$	1.50758			0.123922
$149$	0.657671	+	1.13912i	0.0538785	+	0.0933203i	0.891707	−	0.452614i	$-0.149508\pi$
$149$	0.657671	+	1.13912i	0.0538785	+	0.0933203i	−0.837828	+	0.545934i	$0.816175\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	9.12311	−	15.8017i	0.742428	−	1.28592i	−0.208959	−	0.977924i	$-0.567008\pi$
$151$	9.12311	−	15.8017i	0.742428	−	1.28592i	0.951387	−	0.307998i	$-0.0996591\pi$
$152$	1.75379	+	3.03765i	0.142251	+	0.246386i
$153$	−7.56155			−0.611315
$154$	−7.80776	−	2.70469i	−0.629168	−	0.217950i
$155$	8.87689			0.713009
$156$	1.34233	+	2.32498i	0.107472	+	0.186148i
$157$	−2.12311	+	3.67733i	−0.169442	+	0.293483i	−0.938224	−	0.346029i	$-0.887530\pi$
$157$	−2.12311	+	3.67733i	−0.169442	+	0.293483i	0.768782	+	0.639511i	$0.220863\pi$
$158$	4.24621	−	7.35465i	0.337810	−	0.585105i
$159$	3.90388	+	6.76172i	0.309598	+	0.536239i
$160$	−3.80776			−0.301030
$161$	−0.500000	−	2.59808i	−0.0394055	−	0.204757i
$162$	1.56155			0.122687
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	2.24621	−	3.89055i	0.175400	−	0.303801i
$165$	1.56155	−	2.70469i	0.121567	−	0.210560i
$166$	−3.80776	−	6.59524i	−0.295540	−	0.511890i
$167$	−3.31534			−0.256549			−0.128274	−	0.991739i	$-0.540944\pi$
$167$	−3.31534			−0.256549			−0.128274	+	0.991739i	$0.540944\pi$
$168$	4.87689	−	4.22351i	0.376261	−	0.325851i
$169$	24.4924			1.88403
$170$	9.21922	+	15.9682i	0.707082	+	1.22470i
$171$	−0.719224	+	1.24573i	−0.0550004	+	0.0952635i
$172$	0.0691303	−	0.119737i	0.00527114	−	0.00912988i
$173$	11.6847	+	20.2384i	0.888368	+	1.53870i	0.841804	+	0.539783i	$0.181494\pi$
$173$	11.6847	+	20.2384i	0.888368	+	1.53870i	0.0465642	+	0.998915i	$0.485173\pi$
$174$	−14.2462			−1.08000
$175$	5.12311	−	4.43674i	0.387270	−	0.335386i
$176$	9.36932			0.706239
$177$	−4.56155	−	7.90084i	−0.342867	−	0.593864i
$178$	7.80776	−	13.5234i	0.585217	−	1.01362i
$179$	−3.46543	+	6.00231i	−0.259019	+	0.448634i	−0.965979	−	0.258619i	$-0.916732\pi$
$179$	−3.46543	+	6.00231i	−0.259019	+	0.448634i	0.706961	+	0.707253i	$0.250066\pi$
$180$	−0.342329	−	0.592932i	−0.0255157	−	0.0441945i
$181$	−7.93087			−0.589497			−0.294748	−	0.955575i	$-0.595236\pi$
$181$	−7.93087			−0.589497			−0.294748	+	0.955575i	$0.595236\pi$
$182$	4.78078	+	24.8416i	0.354375	+	1.84139i
$183$	6.00000			0.443533
$184$	1.21922	+	2.11176i	0.0898824	+	0.155681i
$185$	−2.68466	+	4.64996i	−0.197380	+	0.341872i
$186$	−4.43845	+	7.68762i	−0.325443	+	0.563683i
$187$	−7.56155	−	13.0970i	−0.552956	−	0.957747i
$188$	2.93087			0.213756
$189$	2.50000	+	0.866025i	0.181848	+	0.0629941i
$190$	3.50758			0.254466
$191$	0.561553	+	0.972638i	0.0406325	+	0.0703776i	0.885626	−	0.464398i	$-0.153729\pi$
$191$	0.561553	+	0.972638i	0.0406325	+	0.0703776i	−0.844994	+	0.534776i	$0.820396\pi$
$192$	−2.78078	+	4.81645i	−0.200685	+	0.347597i
$193$	−3.93845	+	6.82159i	−0.283496	+	0.491029i	−0.972243	−	0.233972i	$-0.924827\pi$
$193$	−3.93845	+	6.82159i	−0.283496	+	0.491029i	0.688748	+	0.725001i	$0.258161\pi$
$194$	−12.0000	−	20.7846i	−0.861550	−	1.49225i
$195$	−9.56155			−0.684717
$196$	−2.84991	+	1.13912i	−0.203565	+	0.0813657i
$197$	−21.3693			−1.52250			−0.761250	−	0.648458i	$-0.775414\pi$
$197$	−21.3693			−1.52250			−0.761250	+	0.648458i	$0.775414\pi$
$198$	1.56155	+	2.70469i	0.110975	+	0.192214i
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$	−3.12311	+	5.40938i	−0.220837	+	0.382501i
$201$	7.06155	+	12.2310i	0.498084	+	0.862706i
$202$	−1.36932			−0.0963448
$203$	−22.8078	−	7.90084i	−1.60079	−	0.554530i
$204$	−3.31534			−0.232120
$205$	8.00000	+	13.8564i	0.558744	+	0.967773i
$206$	−11.0270	+	19.0993i	−0.768287	+	1.33071i
$207$	−0.500000	+	0.866025i	−0.0347524	+	0.0601929i
$208$	−14.3423	−	24.8416i	−0.994462	−	1.72246i
$209$	−2.87689			−0.198999
$210$	−1.21922	−	6.33527i	−0.0841344	−	0.437175i
$211$	−7.12311			−0.490375			−0.245187	−	0.969476i	$-0.578849\pi$
$211$	−7.12311			−0.490375			−0.245187	+	0.969476i	$0.578849\pi$
$212$	1.71165	+	2.96466i	0.117556	+	0.203614i
$213$	−6.90388	+	11.9579i	−0.473046	+	0.819340i
$214$	4.87689	−	8.44703i	0.333378	−	0.577427i
$215$	0.246211	+	0.426450i	0.0167915	+	0.0290837i
$216$	−2.43845			−0.165915
$217$	−11.3693	+	9.84612i	−0.771800	+	0.668398i
$218$	−16.4924			−1.11701
$219$	−2.93845	−	5.08954i	−0.198562	−	0.343919i
$220$	0.684658	−	1.18586i	0.0461597	−	0.0799509i
$221$	−23.1501	+	40.0971i	−1.55724	+	2.69723i
$222$	−2.68466	−	4.64996i	−0.180182	−	0.312085i
$223$	−20.4924			−1.37227			−0.686137	−	0.727472i	$-0.740695\pi$
$223$	−20.4924			−1.37227			−0.686137	+	0.727472i	$0.740695\pi$
$224$	4.87689	−	4.22351i	0.325851	−	0.282195i
$225$	−2.56155			−0.170770
$226$	−7.65767	−	13.2635i	−0.509381	−	0.882273i
$227$	−1.00000	+	1.73205i	−0.0663723	+	0.114960i	−0.897302	−	0.441417i	$-0.854476\pi$
$227$	−1.00000	+	1.73205i	−0.0663723	+	0.114960i	0.830930	+	0.556378i	$0.187809\pi$
$228$	−0.315342	+	0.546188i	−0.0208840	+	0.0361722i
$229$	14.6501	+	25.3747i	0.968105	+	1.67681i	0.701030	+	0.713132i	$0.252724\pi$
$229$	14.6501	+	25.3747i	0.968105	+	1.67681i	0.267076	+	0.963675i	$0.413943\pi$
$230$	2.43845			0.160786
$231$	1.00000	+	5.19615i	0.0657952	+	0.341882i
$232$	22.2462			1.46054
$233$	5.43845	+	9.41967i	0.356285	+	0.617103i	0.987337	−	0.158637i	$-0.0507101\pi$
$233$	5.43845	+	9.41967i	0.356285	+	0.617103i	−0.631052	+	0.775740i	$0.717377\pi$
$234$	4.78078	−	8.28055i	0.312529	−	0.541316i
$235$	−5.21922	+	9.03996i	−0.340465	+	0.589702i
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$	−5.43845			−0.353265
$238$	−29.5194	−	10.2258i	−1.91346	−	0.662842i
$239$	−18.2462			−1.18025			−0.590125	−	0.807312i	$-0.700921\pi$
$239$	−18.2462			−1.18025			−0.590125	+	0.807312i	$0.700921\pi$
$240$	3.65767	+	6.33527i	0.236102	+	0.408940i
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$	5.46543	−	9.46641i	0.351331	−	0.608524i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	2.63068			0.168412
$245$	1.56155	−	10.8188i	0.0997639	−	0.691185i
$246$	−16.0000			−1.02012
$247$	4.40388	+	7.62775i	0.280212	+	0.485342i
$248$	6.93087	−	12.0046i	0.440111	−	0.762294i
$249$	−2.43845	+	4.22351i	−0.154530	+	0.267654i
$250$	9.21922	+	15.9682i	0.583075	+	1.00992i
$251$	2.00000			0.126239			0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000			0.126239			0.0631194	+	0.998006i	$0.479895\pi$
$252$	1.09612	+	0.379706i	0.0690489	+	0.0239193i
$253$	−2.00000			−0.125739
$254$	−1.31534	−	2.27824i	−0.0825319	−	0.142949i
$255$	5.90388	−	10.2258i	0.369715	−	0.640366i
$256$	−5.02699	+	8.70700i	−0.314187	+	0.544187i
$257$	3.31534	+	5.74234i	0.206805	+	0.358197i	0.950706	−	0.310092i	$-0.100360\pi$
$257$	3.31534	+	5.74234i	0.206805	+	0.358197i	−0.743901	+	0.668290i	$0.767027\pi$
$258$	−0.492423			−0.0306569
$259$	−1.71922	−	8.93335i	−0.106827	−	0.555091i
$260$	−4.19224			−0.259991
$261$	4.56155	+	7.90084i	0.282353	+	0.489050i
$262$	−9.90388	+	17.1540i	−0.611864	+	1.05978i
$263$	−2.24621	+	3.89055i	−0.138507	+	0.239902i	−0.926932	−	0.375230i	$-0.877564\pi$
$263$	−2.24621	+	3.89055i	−0.138507	+	0.239902i	0.788424	+	0.615132i	$0.210897\pi$
$264$	−2.43845	−	4.22351i	−0.150076	−	0.259939i
$265$	−12.1922			−0.748963
$266$	−4.49242	+	3.89055i	−0.275448	+	0.238545i
$267$	−10.0000			−0.611990
$268$	3.09612	+	5.36263i	0.189126	+	0.327575i
$269$	4.24621	−	7.35465i	0.258896	−	0.448421i	−0.707050	−	0.707163i	$-0.749975\pi$
$269$	4.24621	−	7.35465i	0.258896	−	0.448421i	0.965946	+	0.258742i	$0.0833080\pi$
$270$	−1.21922	+	2.11176i	−0.0741996	+	0.128517i
$271$	9.80776	+	16.9875i	0.595779	+	1.03192i	0.993436	+	0.114386i	$0.0364900\pi$
$271$	9.80776	+	16.9875i	0.595779	+	1.03192i	−0.397657	+	0.917534i	$0.630177\pi$
$272$	35.4233			2.14785
$273$	12.2462	−	10.6055i	0.741174	−	0.641876i
$274$	−12.1922			−0.736560
$275$	−2.56155	−	4.43674i	−0.154467	−	0.267545i
$276$	−0.219224	+	0.379706i	−0.0131957	+	0.0228556i
$277$	14.6231	−	25.3280i	0.878617	−	1.52181i	0.0257584	−	0.999668i	$-0.491800\pi$
$277$	14.6231	−	25.3280i	0.878617	−	1.52181i	0.852859	−	0.522142i	$-0.174867\pi$
$278$	−9.31534	−	16.1346i	−0.558697	−	0.967692i
$279$	5.68466			0.340332
$280$	1.90388	+	9.89286i	0.113779	+	0.591212i
$281$	19.5616			1.16694			0.583472	−	0.812133i	$-0.301694\pi$
$281$	19.5616			1.16694			0.583472	+	0.812133i	$0.301694\pi$
$282$	−5.21922	−	9.03996i	−0.310800	−	0.538322i
$283$	12.0616	−	20.8912i	0.716985	−	1.24185i	−0.245204	−	0.969471i	$-0.578855\pi$
$283$	12.0616	−	20.8912i	0.716985	−	1.24185i	0.962189	−	0.272383i	$-0.0878117\pi$
$284$	−3.02699	+	5.24290i	−0.179619	+	0.311109i
$285$	−1.12311	−	1.94528i	−0.0665270	−	0.115228i
$286$	19.1231			1.13077
$287$	−25.6155	−	8.87348i	−1.51204	−	0.523785i
$288$	−2.43845			−0.143687
$289$	−20.0885	−	34.7944i	−1.18168	−	2.04673i
$290$	11.1231	−	19.2658i	0.653171	−	1.13133i
$291$	−7.68466	+	13.3102i	−0.450483	+	0.780259i
$292$	−1.28835	−	2.23149i	−0.0753952	−	0.130588i
$293$	24.0540			1.40525			0.702624	−	0.711561i	$-0.252012\pi$
$293$	24.0540			1.40525			0.702624	+	0.711561i	$0.252012\pi$
$294$	8.58854	+	6.76172i	0.500894	+	0.394352i
$295$	14.2462			0.829446
$296$	4.19224	+	7.26117i	0.243669	+	0.422047i
$297$	1.00000	−	1.73205i	0.0580259	−	0.100504i
$298$	1.02699	−	1.77879i	0.0594918	−	0.103043i
$299$	3.06155	+	5.30277i	0.177054	+	0.306667i
$300$	−1.12311			−0.0648425
$301$	−0.788354	−	0.273094i	−0.0454400	−	0.0157409i
$302$	−28.4924			−1.63955
$303$	0.438447	+	0.759413i	0.0251881	+	0.0436271i
$304$	3.36932	−	5.83583i	0.193244	−	0.334708i
$305$	−4.68466	+	8.11407i	−0.268243	+	0.464610i
$306$	5.90388	+	10.2258i	0.337502	+	0.584571i
$307$	11.6847			0.666879			0.333439	−	0.942772i	$-0.391791\pi$
$307$	11.6847			0.666879			0.333439	+	0.942772i	$0.391791\pi$
$308$	0.438447	+	2.27824i	0.0249828	+	0.129815i
$309$	14.1231			0.803435
$310$	−6.93087	−	12.0046i	−0.393647	−	0.681817i
$311$	−3.78078	+	6.54850i	−0.214388	+	0.371331i	−0.953083	−	0.302709i	$-0.902109\pi$
$311$	−3.78078	+	6.54850i	−0.214388	+	0.371331i	0.738695	+	0.674040i	$0.235442\pi$
$312$	−7.46543	+	12.9305i	−0.422647	+	0.732046i
$313$	−14.6501	−	25.3747i	−0.828072	−	1.43426i	−0.899549	−	0.436821i	$-0.856104\pi$
$313$	−14.6501	−	25.3747i	−0.828072	−	1.43426i	0.0714763	−	0.997442i	$-0.477229\pi$
$314$	6.63068			0.374191
$315$	−3.12311	+	2.70469i	−0.175967	+	0.152392i
$316$	−2.38447			−0.134137
$317$	5.87689	+	10.1791i	0.330079	+	0.571714i	0.982527	−	0.186120i	$-0.0595912\pi$
$317$	5.87689	+	10.1791i	0.330079	+	0.571714i	−0.652448	+	0.757834i	$0.726258\pi$
$318$	6.09612	−	10.5588i	0.341853	−	0.592107i
$319$	−9.12311	+	15.8017i	−0.510796	+	0.884724i
$320$	−4.34233	−	7.52113i	−0.242744	−	0.420444i
$321$	−6.24621			−0.348630
$322$	−3.12311	+	2.70469i	−0.174044	+	0.150726i
$323$	−10.8769			−0.605207
$324$	−0.219224	−	0.379706i	−0.0121791	−	0.0210948i
$325$	−7.84233	+	13.5833i	−0.435014	+	0.753467i
$326$	−3.12311	+	5.40938i	−0.172973	+	0.299598i
$327$	5.28078	+	9.14657i	0.292028	+	0.505807i
$328$	24.9848			1.37956
$329$	−3.34233	−	17.3673i	−0.184269	−	0.957488i
$330$	−4.87689			−0.268464
$331$	7.71922	+	13.3701i	0.424287	+	0.734886i	0.996354	−	0.0853207i	$-0.0271915\pi$
$331$	7.71922	+	13.3701i	0.424287	+	0.734886i	−0.572067	+	0.820207i	$0.693858\pi$
$332$	−1.06913	+	1.85179i	−0.0586761	+	0.101630i
$333$	−1.71922	+	2.97778i	−0.0942129	+	0.163181i
$334$	2.58854	+	4.48348i	0.141639	+	0.245325i
$335$	−22.0540			−1.20494
$336$	−11.7116	−	4.05703i	−0.638923	−	0.221329i
$337$	−20.8078			−1.13347			−0.566736	−	0.823900i	$-0.691794\pi$
$337$	−20.8078			−1.13347			−0.566736	+	0.823900i	$0.691794\pi$
$338$	−19.1231	−	33.1222i	−1.04016	−	1.80161i
$339$	−4.90388	+	8.49377i	−0.266342	+	0.461318i
$340$	2.58854	−	4.48348i	0.140383	−	0.243151i
$341$	5.68466	+	9.84612i	0.307842	+	0.533197i
$342$	2.24621			0.121461
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	0.768944			0.0414587
$345$	−0.780776	−	1.35234i	−0.0420356	−	0.0728078i
$346$	18.2462	−	31.6034i	0.980922	−	1.69901i
$347$	6.34233	−	10.9852i	0.340474	−	0.589718i	−0.644047	−	0.764986i	$-0.722746\pi$
$347$	6.34233	−	10.9852i	0.340474	−	0.589718i	0.984521	+	0.175268i	$0.0560791\pi$
$348$	2.00000	+	3.46410i	0.107211	+	0.185695i
$349$	0.930870			0.0498283			0.0249142	−	0.999690i	$-0.492069\pi$
$349$	0.930870			0.0498283			0.0249142	+	0.999690i	$0.492069\pi$
$350$	−10.0000	−	3.46410i	−0.534522	−	0.185164i
$351$	−6.12311			−0.326827
$352$	−2.43845	−	4.22351i	−0.129970	−	0.225114i
$353$	3.68466	−	6.38202i	0.196115	−	0.339680i	−0.751151	−	0.660131i	$-0.770501\pi$
$353$	3.68466	−	6.38202i	0.196115	−	0.339680i	0.947265	+	0.320450i	$0.103834\pi$
$354$	−7.12311	+	12.3376i	−0.378589	+	0.655735i
$355$	−10.7808	−	18.6729i	−0.572184	−	0.991052i
$356$	−4.38447			−0.232377
$357$	3.78078	+	19.6455i	0.200100	+	1.03975i
$358$	10.8229			0.572009
$359$	−6.36932	−	11.0320i	−0.336160	−	0.582246i	0.647547	−	0.762025i	$-0.275795\pi$
$359$	−6.36932	−	11.0320i	−0.336160	−	0.582246i	−0.983707	+	0.179780i	$0.942462\pi$
$360$	1.90388	−	3.29762i	0.100343	−	0.173800i
$361$	8.46543	−	14.6626i	0.445549	−	0.771714i
$362$	6.19224	+	10.7253i	0.325457	+	0.563708i
$363$	−7.00000			−0.367405
$364$	5.36932	−	4.64996i	0.281429	−	0.243724i
$365$	9.17708			0.480350
$366$	−4.68466	−	8.11407i	−0.244871	−	0.424129i
$367$	4.18466	−	7.24804i	0.218437	−	0.378345i	−0.735893	−	0.677098i	$-0.763237\pi$
$367$	4.18466	−	7.24804i	0.218437	−	0.378345i	0.954330	+	0.298753i	$0.0965707\pi$
$368$	2.34233	−	4.05703i	0.122102	−	0.211487i
$369$	5.12311	+	8.87348i	0.266698	+	0.461935i
$370$	8.38447			0.435888
$371$	15.6155	−	13.5234i	0.810718	−	0.702102i
$372$	2.49242			0.129226
$373$	−4.84233	−	8.38716i	−0.250726	−	0.434271i	0.713000	−	0.701164i	$-0.247336\pi$
$373$	−4.84233	−	8.38716i	−0.250726	−	0.434271i	−0.963726	+	0.266894i	$0.914003\pi$
$374$	−11.8078	+	20.4516i	−0.610565	+	1.05753i
$375$	5.90388	−	10.2258i	0.304875	−	0.528059i
$376$	8.15009	+	14.1164i	0.420309	+	0.727996i
$377$	55.8617			2.87703
$378$	−0.780776	−	4.05703i	−0.0401588	−	0.208671i
$379$	8.61553			0.442550			0.221275	−	0.975211i	$-0.428978\pi$
$379$	8.61553			0.442550			0.221275	+	0.975211i	$0.428978\pi$
$380$	−0.492423	−	0.852901i	−0.0252607	−	0.0437529i
$381$	−0.842329	+	1.45896i	−0.0431538	+	0.0747446i
$382$	0.876894	−	1.51883i	0.0448658	−	0.0777099i
$383$	−2.12311	−	3.67733i	−0.108486	−	0.187903i	0.806671	−	0.591000i	$-0.201267\pi$
$383$	−2.12311	−	3.67733i	−0.108486	−	0.187903i	−0.915157	+	0.403098i	$0.867933\pi$
$384$	13.5616			0.692060
$385$	−7.80776	−	2.70469i	−0.397921	−	0.137844i
$386$	12.3002			0.626063
$387$	0.157671	+	0.273094i	0.00801486	+	0.0138821i
$388$	−3.36932	+	5.83583i	−0.171051	+	0.296269i
$389$	−7.80776	+	13.5234i	−0.395869	+	0.685666i	−0.993212	−	0.116321i	$-0.962890\pi$
$389$	−7.80776	+	13.5234i	−0.395869	+	0.685666i	0.597342	+	0.801986i	$0.296223\pi$
$390$	7.46543	+	12.9305i	0.378027	+	0.654762i
$391$	−7.56155			−0.382404
$392$	−13.4115	−	10.5588i	−0.677381	−	0.533299i
$393$	12.6847			0.639856
$394$	16.6847	+	28.8987i	0.840561	+	1.45589i
$395$	4.24621	−	7.35465i	0.213650	−	0.370053i
$396$	0.438447	−	0.759413i	0.0220328	−	0.0381619i
$397$	−11.3078	−	19.5856i	−0.567520	−	0.982974i	−0.996810	−	0.0798074i	$-0.974569\pi$
$397$	−11.3078	−	19.5856i	−0.567520	−	0.982974i	0.429290	−	0.903167i	$-0.358764\pi$
$398$	−12.4924			−0.626189
$399$	3.59612	+	1.24573i	0.180031	+	0.0623646i
$400$	12.0000			0.600000
$401$	0.342329	+	0.592932i	0.0170951	+	0.0296096i	0.874446	−	0.485122i	$-0.161225\pi$
$401$	0.342329	+	0.592932i	0.0170951	+	0.0296096i	−0.857351	+	0.514732i	$0.827892\pi$
$402$	11.0270	−	19.0993i	0.549976	−	0.952587i
$403$	17.4039	−	30.1444i	0.866949	−	1.50160i
$404$	0.192236	+	0.332962i	0.00956410	+	0.0165655i
$405$	1.56155			0.0775942
$406$	7.12311	+	37.0127i	0.353514	+	1.83691i
$407$	−6.87689			−0.340875
$408$	−9.21922	−	15.9682i	−0.456420	−	0.790542i
$409$	−9.43087	+	16.3347i	−0.466326	+	0.807701i	−0.999260	−	0.0384558i	$-0.987756\pi$
$409$	−9.43087	+	16.3347i	−0.466326	+	0.807701i	0.532934	+	0.846157i	$0.321089\pi$
$410$	12.4924	−	21.6375i	0.616957	−	1.06860i
$411$	3.90388	+	6.76172i	0.192564	+	0.333531i
$412$	6.19224			0.305070
$413$	−18.2462	+	15.8017i	−0.897837	+	0.777550i
$414$	1.56155			0.0767461
$415$	−3.80776	−	6.59524i	−0.186916	−	0.323748i
$416$	−7.46543	+	12.9305i	−0.366023	+	0.633971i
$417$	−5.96543	+	10.3324i	−0.292129	+	0.505982i
$418$	2.24621	+	3.89055i	0.109866	+	0.190293i
$419$	−28.4924			−1.39195			−0.695973	−	0.718068i	$-0.745027\pi$
$419$	−28.4924			−1.39195			−0.695973	+	0.718068i	$0.745027\pi$
$420$	−1.36932	+	1.18586i	−0.0668158	+	0.0578642i
$421$	−4.31534			−0.210317			−0.105158	−	0.994455i	$-0.533535\pi$
$421$	−4.31534			−0.210317			−0.105158	+	0.994455i	$0.533535\pi$
$422$	5.56155	+	9.63289i	0.270732	+	0.468922i
$423$	−3.34233	+	5.78908i	−0.162510	+	0.281475i
$424$	−9.51941	+	16.4881i	−0.462303	+	0.800733i
$425$	−9.68466	−	16.7743i	−0.469775	−	0.813674i
$426$	21.5616			1.04466
$427$	−3.00000	−	15.5885i	−0.145180	−	0.754378i
$428$	−2.73863			−0.132377
$429$	−6.12311	−	10.6055i	−0.295626	−	0.512040i
$430$	0.384472	−	0.665925i	0.0185409	−	0.0321137i
$431$	−4.00000	+	6.92820i	−0.192673	+	0.333720i	−0.946135	−	0.323772i	$-0.895049\pi$
$431$	−4.00000	+	6.92820i	−0.192673	+	0.333720i	0.753462	+	0.657491i	$0.228382\pi$
$432$	2.34233	+	4.05703i	0.112695	+	0.195194i
$433$	−6.80776			−0.327160			−0.163580	−	0.986530i	$-0.552304\pi$
$433$	−6.80776			−0.327160			−0.163580	+	0.986530i	$0.552304\pi$
$434$	22.1922	+	7.68762i	1.06526	+	0.369017i
$435$	−14.2462			−0.683054
$436$	2.31534	+	4.01029i	0.110885	+	0.192058i
$437$	−0.719224	+	1.24573i	−0.0344051	+	0.0595914i
$438$	−4.58854	+	7.94759i	−0.219249	+	0.379750i
$439$	−7.80776	−	13.5234i	−0.372644	−	0.645439i	0.617327	−	0.786707i	$-0.288215\pi$
$439$	−7.80776	−	13.5234i	−0.372644	−	0.645439i	−0.989971	+	0.141268i	$0.954882\pi$
$440$	7.61553			0.363056
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	72.3002			3.43897
$443$	−6.65767	−	11.5314i	−0.316315	−	0.547874i	0.663401	−	0.748264i	$-0.269112\pi$
$443$	−6.65767	−	11.5314i	−0.316315	−	0.547874i	−0.979716	+	0.200390i	$0.935779\pi$
$444$	−0.753789	+	1.30560i	−0.0357732	+	0.0619611i
$445$	7.80776	−	13.5234i	0.370124	−	0.641073i
$446$	16.0000	+	27.7128i	0.757622	+	1.31224i
$447$	−1.31534			−0.0622135
$448$	13.9039	+	4.81645i	0.656897	+	0.227556i
$449$	−14.0000			−0.660701			−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000			−0.660701			−0.330350	+	0.943858i	$0.607167\pi$
$450$	2.00000	+	3.46410i	0.0942809	+	0.163299i
$451$	−10.2462	+	17.7470i	−0.482475	+	0.835672i
$452$	−2.15009	+	3.72407i	−0.101132	+	0.175166i
$453$	9.12311	+	15.8017i	0.428641	+	0.742428i
$454$	3.12311			0.146575
$455$	4.78078	+	24.8416i	0.224126	+	1.16459i
$456$	−3.50758			−0.164257
$457$	−0.719224	−	1.24573i	−0.0336439	−	0.0582729i	0.848713	−	0.528853i	$-0.177378\pi$
$457$	−0.719224	−	1.24573i	−0.0336439	−	0.0582729i	−0.882357	+	0.470581i	$0.844045\pi$
$458$	22.8769	−	39.6239i	1.06897	−	1.85151i
$459$	3.78078	−	6.54850i	0.176472	−	0.305658i
$460$	−0.342329	−	0.592932i	−0.0159612	−	0.0276456i
$461$	−4.24621			−0.197766			−0.0988829	−	0.995099i	$-0.531527\pi$
$461$	−4.24621			−0.197766			−0.0988829	+	0.995099i	$0.531527\pi$
$462$	6.24621	−	5.40938i	0.290600	−	0.251667i
$463$	19.6847			0.914824			0.457412	−	0.889255i	$-0.348777\pi$
$463$	19.6847			0.914824			0.457412	+	0.889255i	$0.348777\pi$
$464$	−21.3693	−	37.0127i	−0.992046	−	1.71827i
$465$	−4.43845	+	7.68762i	−0.205828	+	0.356505i
$466$	8.49242	−	14.7093i	0.393404	−	0.681396i
$467$	−0.561553	−	0.972638i	−0.0259856	−	0.0450083i	0.852740	−	0.522335i	$-0.174939\pi$
$467$	−0.561553	−	0.972638i	−0.0259856	−	0.0450083i	−0.878726	+	0.477327i	$0.841606\pi$
$468$	−2.68466			−0.124098
$469$	28.2462	−	24.4619i	1.30429	−	1.12955i
$470$	16.3002			0.751872
$471$	−2.12311	−	3.67733i	−0.0978275	−	0.169442i
$472$	11.1231	−	19.2658i	0.511982	−	0.886780i
$473$	−0.315342	+	0.546188i	−0.0144994	+	0.0251137i
$474$	4.24621	+	7.35465i	0.195035	+	0.337810i
$475$	−3.68466			−0.169064
$476$	1.65767	+	8.61351i	0.0759792	+	0.394800i
$477$	−7.80776			−0.357493
$478$	14.2462	+	24.6752i	0.651607	+	1.12862i
$479$	9.68466	−	16.7743i	0.442503	−	0.766438i	−0.555371	−	0.831603i	$-0.687424\pi$
$479$	9.68466	−	16.7743i	0.442503	−	0.766438i	0.997875	+	0.0651643i	$0.0207571\pi$
$480$	1.90388	−	3.29762i	0.0868999	−	0.150515i
$481$	10.5270	+	18.2333i	0.479989	+	0.831366i
$482$	3.12311			0.142254
$483$	2.50000	+	0.866025i	0.113754	+	0.0394055i
$484$	−3.06913			−0.139506
$485$	−12.0000	−	20.7846i	−0.544892	−	0.943781i
$486$	−0.780776	+	1.35234i	−0.0354167	+	0.0613436i
$487$	−11.2116	+	19.4191i	−0.508048	+	0.879965i	0.491908	+	0.870647i	$0.336299\pi$
$487$	−11.2116	+	19.4191i	−0.508048	+	0.879965i	−0.999957	+	0.00931830i	$0.997034\pi$
$488$	7.31534	+	12.6705i	0.331150	+	0.573569i
$489$	4.00000			0.180886
$490$	−15.8499	+	6.33527i	−0.716026	+	0.286198i
$491$	−30.6847			−1.38478			−0.692390	−	0.721524i	$-0.743442\pi$
$491$	−30.6847			−1.38478			−0.692390	+	0.721524i	$0.743442\pi$
$492$	2.24621	+	3.89055i	0.101267	+	0.175400i
$493$	−34.4924	+	59.7426i	−1.55346	+	2.69067i
$494$	6.87689	−	11.9111i	0.309406	−	0.535907i
$495$	1.56155	+	2.70469i	0.0701866	+	0.121567i
$496$	−26.6307			−1.19575
$497$	34.5194	+	11.9579i	1.54841	+	0.536384i
$498$	7.61553			0.341260
$499$	17.8423	+	30.9038i	0.798732	+	1.38345i	0.920442	+	0.390879i	$0.127829\pi$
$499$	17.8423	+	30.9038i	0.798732	+	1.38345i	−0.121710	+	0.992566i	$0.538838\pi$
$500$	2.58854	−	4.48348i	0.115763	−	0.200507i
$501$	1.65767	−	2.87117i	0.0740593	−	0.128274i
$502$	−1.56155	−	2.70469i	−0.0696955	−	0.120716i
$503$	9.36932			0.417757			0.208879	−	0.977942i	$-0.433019\pi$
$503$	9.36932			0.417757			0.208879	+	0.977942i	$0.433019\pi$
$504$	1.21922	+	6.33527i	0.0543085	+	0.282195i
$505$	−1.36932			−0.0609338
$506$	1.56155	+	2.70469i	0.0694195	+	0.120238i
$507$	−12.2462	+	21.2111i	−0.543873	+	0.942016i
$508$	−0.369317	+	0.639676i	−0.0163858	+	0.0283810i
$509$	−2.43845	−	4.22351i	−0.108082	−	0.187204i	0.806911	−	0.590673i	$-0.201138\pi$
$509$	−2.43845	−	4.22351i	−0.108082	−	0.187204i	−0.914993	+	0.403469i	$0.867804\pi$
$510$	−18.4384			−0.816468
$511$	−11.7538	+	10.1791i	−0.519957	+	0.450296i
$512$	−11.4233			−0.504843
$513$	−0.719224	−	1.24573i	−0.0317545	−	0.0550004i
$514$	5.17708	−	8.96697i	0.228351	−	0.395516i
$515$	−11.0270	+	19.0993i	−0.485907	+	0.841616i
$516$	0.0691303	+	0.119737i	0.00304329	+	0.00527114i
$517$	−13.3693			−0.587982
$518$	−10.7386	+	9.29993i	−0.471828	+	0.408615i
$519$	−23.3693			−1.02580
$520$	−11.6577	−	20.1917i	−0.511223	−	0.885464i
$521$	15.3423	−	26.5737i	0.672160	−	1.16421i	−0.305131	−	0.952310i	$-0.598700\pi$
$521$	15.3423	−	26.5737i	0.672160	−	1.16421i	0.977290	−	0.211904i	$-0.0679665\pi$
$522$	7.12311	−	12.3376i	0.311770	−	0.540001i
$523$	−9.18466	−	15.9083i	−0.401617	−	0.695621i	0.592304	−	0.805714i	$-0.298218\pi$
$523$	−9.18466	−	15.9083i	−0.401617	−	0.695621i	−0.993921	+	0.110093i	$0.964885\pi$
$524$	5.56155			0.242958
$525$	1.28078	+	6.65511i	0.0558977	+	0.290453i
$526$	7.01515			0.305875
$527$	21.4924	+	37.2260i	0.936225	+	1.62159i
$528$	−4.68466	+	8.11407i	−0.203874	+	0.353119i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	9.51941	+	16.4881i	0.413497	+	0.716197i
$531$	9.12311			0.395909
$532$	1.57671	+	0.546188i	0.0683590	+	0.0236802i
$533$	62.7386			2.71751
$534$	7.80776	+	13.5234i	0.337875	+	0.585217i
$535$	4.87689	−	8.44703i	0.210847	−	0.365197i
$536$	−17.2192	+	29.8246i	−0.743757	+	1.28823i
$537$	−3.46543	−	6.00231i	−0.149545	−	0.259019i
$538$	−13.2614			−0.571738
$539$	13.0000	−	5.19615i	0.559950	−	0.223814i
$540$	0.684658			0.0294630
$541$	−1.86932	−	3.23775i	−0.0803682	−	0.139202i	0.823040	−	0.567984i	$-0.192276\pi$
$541$	−1.86932	−	3.23775i	−0.0803682	−	0.139202i	−0.903408	+	0.428782i	$0.858943\pi$
$542$	15.3153	−	26.5269i	0.657850	−	1.13943i
$543$	3.96543	−	6.86833i	0.170173	−	0.294748i
$544$	−9.21922	−	15.9682i	−0.395271	−	0.684629i
$545$	−16.4924			−0.706458
$546$	−23.9039	−	8.28055i	−1.02299	−	0.354375i
$547$	29.3693			1.25574			0.627871	−	0.778318i	$-0.283927\pi$
$547$	29.3693			1.25574			0.627871	+	0.778318i	$0.283927\pi$
$548$	1.71165	+	2.96466i	0.0731179	+	0.126644i
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$	−4.00000	+	6.92820i	−0.170561	+	0.295420i
$551$	6.56155	+	11.3649i	0.279532	+	0.484163i
$552$	−2.43845			−0.103787
$553$	2.71922	+	14.1295i	0.115633	+	0.600847i
$554$	−45.6695			−1.94031
$555$	−2.68466	−	4.64996i	−0.113957	−	0.197380i
$556$	−2.61553	+	4.53023i	−0.110923	+	0.192124i
$557$	−16.1231	+	27.9260i	−0.683158	+	1.18326i	0.290854	+	0.956767i	$0.406061\pi$
$557$	−16.1231	+	27.9260i	−0.683158	+	1.18326i	−0.974012	+	0.226497i	$0.927273\pi$
$558$	−4.43845	−	7.68762i	−0.187894	−	0.325443i
$559$	1.93087			0.0816671
$560$	14.6307	−	12.6705i	0.618259	−	0.535428i
$561$	15.1231			0.638498
$562$	−15.2732	−	26.4540i	−0.644261	−	1.11589i
$563$	7.12311	−	12.3376i	0.300203	−	0.519967i	−0.675979	−	0.736921i	$-0.736279\pi$
$563$	7.12311	−	12.3376i	0.300203	−	0.519967i	0.976182	+	0.216954i	$0.0696122\pi$
$564$	−1.46543	+	2.53821i	−0.0617059	+	0.106878i
$565$	−7.65767	−	13.2635i	−0.322161	−	0.557999i
$566$	−37.6695			−1.58337
$567$	−2.00000	+	1.73205i	−0.0839921	+	0.0727393i
$568$	−33.6695			−1.41274
$569$	12.5885	+	21.8040i	0.527739	+	0.914071i	0.999477	+	0.0323322i	$0.0102934\pi$
$569$	12.5885	+	21.8040i	0.527739	+	0.914071i	−0.471738	+	0.881739i	$0.656373\pi$
$570$	−1.75379	+	3.03765i	−0.0734581	+	0.127233i
$571$	−20.4309	+	35.3873i	−0.855005	+	1.48091i	0.0216348	+	0.999766i	$0.493113\pi$
$571$	−20.4309	+	35.3873i	−0.855005	+	1.48091i	−0.876640	+	0.481147i	$0.840220\pi$
$572$	−2.68466	−	4.64996i	−0.112251	−	0.194425i
$573$	−1.12311			−0.0469184
$574$	8.00000	+	41.5692i	0.333914	+	1.73507i
$575$	−2.56155			−0.106824
$576$	−2.78078	−	4.81645i	−0.115866	−	0.200685i
$577$	−5.15767	+	8.93335i	−0.214717	+	0.371900i	−0.953185	−	0.302388i	$-0.902216\pi$
$577$	−5.15767	+	8.93335i	−0.214717	+	0.371900i	0.738468	+	0.674288i	$0.235549\pi$
$578$	−31.3693	+	54.3333i	−1.30479	+	2.25997i
$579$	−3.93845	−	6.82159i	−0.163676	−	0.283496i
$580$	−6.24621			−0.259360
$581$	12.1922	+	4.22351i	0.505819	+	0.175221i
$582$	24.0000			0.994832
$583$	−7.80776	−	13.5234i	−0.323365	−	0.560084i
$584$	7.16525	−	12.4106i	0.296500	−	0.513553i
$585$	4.78078	−	8.28055i	0.197661	−	0.342359i
$586$	−18.7808	−	32.5293i	−0.775827	−	1.34377i
$587$	0.438447			0.0180967			0.00904833	−	0.999959i	$-0.497120\pi$
$587$	0.438447			0.0180967			0.00904833	+	0.999959i	$0.497120\pi$
$588$	0.438447	−	3.03765i	0.0180813	−	0.125271i
$589$	8.17708			0.336931
$590$	−11.1231	−	19.2658i	−0.457931	−	0.793160i
$591$	10.6847	−	18.5064i	0.439508	−	0.761250i
$592$	8.05398	−	13.9499i	0.331016	−	0.573337i
$593$	5.00000	+	8.66025i	0.205325	+	0.355634i	0.950236	−	0.311530i	$-0.100841\pi$
$593$	5.00000	+	8.66025i	0.205325	+	0.355634i	−0.744911	+	0.667164i	$0.767508\pi$
$594$	−3.12311			−0.128143
$595$	−29.5194	−	10.2258i	−1.21018	−	0.419218i
$596$	−0.576708			−0.0236229
$597$	4.00000	+	6.92820i	0.163709	+	0.283552i
$598$	4.78078	−	8.28055i	0.195500	−	0.338617i
$599$	18.5885	−	32.1963i	0.759507	−	1.31551i	−0.183595	−	0.983002i	$-0.558773\pi$
$599$	18.5885	−	32.1963i	0.759507	−	1.31551i	0.943102	−	0.332503i	$-0.107893\pi$
$600$	−3.12311	−	5.40938i	−0.127500	−	0.220837i
$601$	5.05398			0.206156			0.103078	−	0.994673i	$-0.467131\pi$
$601$	5.05398			0.206156			0.103078	+	0.994673i	$0.467131\pi$
$602$	0.246211	+	1.27935i	0.0100348	+	0.0521425i
$603$	−14.1231			−0.575137
$604$	4.00000	+	6.92820i	0.162758	+	0.281905i
$605$	5.46543	−	9.46641i	0.222202	−	0.384864i
$606$	0.684658	−	1.18586i	0.0278123	−	0.0481724i
$607$	−21.4039	−	37.0726i	−0.868757	−	1.50473i	−0.863268	−	0.504746i	$-0.831586\pi$
$607$	−21.4039	−	37.0726i	−0.868757	−	1.50473i	−0.00548883	−	0.999985i	$-0.501747\pi$
$608$	−3.50758			−0.142251
$609$	18.2462	−	15.8017i	0.739374	−	0.640316i
$610$	14.6307			0.592379
$611$	20.4654	+	35.4472i	0.827943	+	1.43404i
$612$	1.65767	−	2.87117i	0.0670074	−	0.116060i
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	0.474509	+	0.880251i	$0.342626\pi$
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	−0.999574	+	0.0291886i	$0.990708\pi$
$614$	−9.12311	−	15.8017i	−0.368179	−	0.637704i
$615$	−16.0000			−0.645182
$616$	−9.75379	+	8.44703i	−0.392991	+	0.340340i
$617$	−0.930870			−0.0374754			−0.0187377	−	0.999824i	$-0.505965\pi$
$617$	−0.930870			−0.0374754			−0.0187377	+	0.999824i	$0.505965\pi$
$618$	−11.0270	−	19.0993i	−0.443570	−	0.768287i
$619$	11.0616	−	19.1592i	0.444601	−	0.770072i	−0.553423	−	0.832900i	$-0.686679\pi$
$619$	11.0616	−	19.1592i	0.444601	−	0.770072i	0.998024	+	0.0628282i	$0.0200120\pi$
$620$	−1.94602	+	3.37061i	−0.0781542	+	0.135367i
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	11.8078			0.473448
$623$	5.00000	+	25.9808i	0.200321	+	1.04090i
$624$	28.6847			1.14831
$625$	2.81534	+	4.87631i	0.112614	+	0.195053i
$626$	−22.8769	+	39.6239i	−0.914345	+	1.58369i
$627$	1.43845	−	2.49146i	0.0574460	−	0.0994995i
$628$	−0.930870	−	1.61231i	−0.0371457	−	0.0643383i
$629$	−26.0000			−1.03669
$630$	6.09612	+	2.11176i	0.242875	+	0.0841344i
$631$	5.94602			0.236708			0.118354	−	0.992971i	$-0.462238\pi$
$631$	5.94602			0.236708			0.118354	+	0.992971i	$0.462238\pi$
$632$	−6.63068	−	11.4847i	−0.263754	−	0.456836i
$633$	3.56155	−	6.16879i	0.141559	−	0.245187i
$634$	9.17708	−	15.8952i	0.364468	−	0.631278i
$635$	−1.31534	−	2.27824i	−0.0521977	−	0.0904091i
$636$	−3.42329			−0.135742
$637$	−33.6771	−	26.5138i	−1.33433	−	1.05052i
$638$	28.4924			1.12803
$639$	−6.90388	−	11.9579i	−0.273113	−	0.473046i
$640$	−10.5885	+	18.3399i	−0.418549	+	0.724948i
$641$	17.2192	−	29.8246i	0.680118	−	1.17800i	−0.294826	−	0.955551i	$-0.595262\pi$
$641$	17.2192	−	29.8246i	0.680118	−	1.17800i	0.974944	−	0.222449i	$-0.0714050\pi$
$642$	4.87689	+	8.44703i	0.192476	+	0.333378i
$643$	37.4384			1.47643			0.738214	−	0.674566i	$-0.235669\pi$
$643$	37.4384			1.47643			0.738214	+	0.674566i	$0.235669\pi$
$644$	1.09612	+	0.379706i	0.0431931	+	0.0149625i
$645$	−0.492423			−0.0193891
$646$	8.49242	+	14.7093i	0.334130	+	0.578730i
$647$	−0.315342	+	0.546188i	−0.0123974	+	0.0214729i	−0.872158	−	0.489225i	$-0.837280\pi$
$647$	−0.315342	+	0.546188i	−0.0123974	+	0.0214729i	0.859760	+	0.510698i	$0.170613\pi$
$648$	1.21922	−	2.11176i	0.0478956	−	0.0829577i
$649$	9.12311	+	15.8017i	0.358113	+	0.620270i
$650$	24.4924			0.960672
$651$	−2.84233	−	14.7692i	−0.111400	−	0.578850i
$652$	1.75379			0.0686837
$653$	−5.24621	−	9.08670i	−0.205300	−	0.355590i	0.744928	−	0.667145i	$-0.232484\pi$
$653$	−5.24621	−	9.08670i	−0.205300	−	0.355590i	−0.950228	+	0.311554i	$0.899150\pi$
$654$	8.24621	−	14.2829i	0.322452	−	0.558504i
$655$	−9.90388	+	17.1540i	−0.386977	+	0.670263i
$656$	−24.0000	−	41.5692i	−0.937043	−	1.62301i
$657$	5.87689			0.229279
$658$	−20.8769	+	18.0799i	−0.813866	+	0.704829i
$659$	−0.384472			−0.0149769			−0.00748845	−	0.999972i	$-0.502384\pi$
$659$	−0.384472			−0.0149769			−0.00748845	+	0.999972i	$0.502384\pi$
$660$	0.684658	+	1.18586i	0.0266503	+	0.0461597i
$661$	−14.4039	+	24.9483i	−0.560246	+	0.970375i	0.437229	+	0.899350i	$0.355960\pi$
$661$	−14.4039	+	24.9483i	−0.560246	+	0.970375i	−0.997475	+	0.0710242i	$0.977373\pi$
$662$	12.0540	−	20.8781i	0.468491	−	0.811450i
$663$	−23.1501	−	40.0971i	−0.899075	−	1.55724i
$664$	−11.8920			−0.461501
$665$	−4.49242	+	3.89055i	−0.174209	+	0.150869i
$666$	5.36932			0.208057
$667$	4.56155	+	7.90084i	0.176624	+	0.305922i
$668$	0.726801	−	1.25886i	0.0281208	−	0.0487066i
$669$	10.2462	−	17.7470i	0.396141	−	0.686137i
$670$	17.2192	+	29.8246i	0.665237	+	1.15222i
$671$	−12.0000			−0.463255
$672$	1.21922	+	6.33527i	0.0470326	+	0.244388i
$673$	−1.68466			−0.0649388			−0.0324694	−	0.999473i	$-0.510337\pi$
$673$	−1.68466			−0.0649388			−0.0324694	+	0.999473i	$0.510337\pi$
$674$	16.2462	+	28.1393i	0.625781	+	1.08388i
$675$	1.28078	−	2.21837i	0.0492971	−	0.0853851i
$676$	−5.36932	+	9.29993i	−0.206512	+	0.357690i
$677$	−20.4654	−	35.4472i	−0.786551	−	1.36235i	−0.928068	−	0.372410i	$-0.878532\pi$
$677$	−20.4654	−	35.4472i	−0.786551	−	1.36235i	0.141518	−	0.989936i	$-0.454802\pi$
$678$	15.3153			0.588182
$679$	38.4233	+	13.3102i	1.47455	+	0.510799i
$680$	28.7926			1.10415
$681$	−1.00000	−	1.73205i	−0.0383201	−	0.0663723i
$682$	8.87689	−	15.3752i	0.339914	−	0.588748i
$683$	7.02699	−	12.1711i	0.268880	−	0.465714i	−0.699693	−	0.714444i	$-0.746680\pi$
$683$	7.02699	−	12.1711i	0.268880	−	0.465714i	0.968573	+	0.248730i	$0.0800131\pi$
$684$	−0.315342	−	0.546188i	−0.0120574	−	0.0208840i
$685$	−12.1922			−0.465841
$686$	13.2732	−	25.6945i	0.506773	−	0.981022i
$687$	−29.3002			−1.11787
$688$	−0.738634	−	1.27935i	−0.0281601	−	0.0487748i
$689$	−23.9039	+	41.4027i	−0.910665	+	1.57732i
$690$	−1.21922	+	2.11176i	−0.0464150	+	0.0803932i
$691$	−7.40388	−	12.8239i	−0.281657	−	0.487844i	0.690136	−	0.723680i	$-0.257551\pi$
$691$	−7.40388	−	12.8239i	−0.281657	−	0.487844i	−0.971793	+	0.235836i	$0.924217\pi$
$692$	−10.2462			−0.389503
$693$	−5.00000	−	1.73205i	−0.189934	−	0.0657952i
$694$	−19.8078			−0.751892
$695$	−9.31534	−	16.1346i	−0.353351	−	0.612022i
$696$	−11.1231	+	19.2658i	−0.421620	+	0.730268i
$697$	−38.7386	+	67.0973i	−1.46733	+	2.54149i
$698$	−0.726801	−	1.25886i	−0.0275098	−	0.0476484i
$699$	−10.8769			−0.411402
$700$	0.561553	+	2.91791i	0.0212247	+	0.110287i
$701$	7.17708			0.271075			0.135537	−	0.990772i	$-0.456724\pi$
$701$	7.17708			0.271075			0.135537	+	0.990772i	$0.456724\pi$
$702$	4.78078	+	8.28055i	0.180439	+	0.312529i
$703$	−2.47301	+	4.28338i	−0.0932714	+	0.161551i
$704$	5.56155	−	9.63289i	0.209609	−	0.363053i
$705$	−5.21922	−	9.03996i	−0.196567	−	0.340465i
$706$	−11.5076			−0.433093
$707$	1.75379	−	1.51883i	0.0659580	−	0.0571213i
$708$	4.00000			0.150329
$709$	−10.3153	−	17.8667i	−0.387401	−	0.670998i	0.604698	−	0.796455i	$-0.293294\pi$
$709$	−10.3153	−	17.8667i	−0.387401	−	0.670998i	−0.992099	+	0.125457i	$0.959960\pi$
$710$	−16.8348	+	29.1586i	−0.631797	+	1.09430i
$711$	2.71922	−	4.70983i	0.101979	−	0.176633i
$712$	−12.1922	−	21.1176i	−0.456923	−	0.791414i
$713$	5.68466			0.212892
$714$	23.6155	−	20.4516i	0.883789	−	0.765384i
$715$	19.1231			0.715164
$716$	−1.51941	−	2.63170i	−0.0567830	−	0.0983511i
$717$	9.12311	−	15.8017i	0.340709	−	0.590125i
$718$	−9.94602	+	17.2270i	−0.371182	+	0.642907i
$719$	18.2732	+	31.6501i	0.681475	+	1.18035i	0.974531	+	0.224254i	$0.0719947\pi$
$719$	18.2732	+	31.6501i	0.681475	+	1.18035i	−0.293055	+	0.956095i	$0.594672\pi$
$720$	−7.31534			−0.272627
$721$	−7.06155	−	36.6929i	−0.262986	−	1.36652i
$722$	−26.4384			−0.983937
$723$	−1.00000	−	1.73205i	−0.0371904	−	0.0644157i
$724$	1.73863	−	3.01140i	0.0646158	−	0.111918i
$725$	−11.6847	+	20.2384i	−0.433957	+	0.751636i
$726$	5.46543	+	9.46641i	0.202841	+	0.351331i
$727$	28.3153			1.05016			0.525079	−	0.851054i	$-0.324036\pi$
$727$	28.3153			1.05016			0.525079	+	0.851054i	$0.324036\pi$
$728$	37.3272	+	12.9305i	1.38344	+	0.479237i
$729$	1.00000			0.0370370
$730$	−7.16525	−	12.4106i	−0.265198	−	0.459336i
$731$	−1.19224	+	2.06501i	−0.0440964	+	0.0763773i
$732$	−1.31534	+	2.27824i	−0.0486164	+	0.0842061i
$733$	0.650093	+	1.12599i	0.0240117	+	0.0415896i	0.877782	−	0.479061i	$-0.159023\pi$
$733$	0.650093	+	1.12599i	0.0240117	+	0.0415896i	−0.853770	+	0.520651i	$0.825689\pi$
$734$	−13.0691			−0.482390
$735$	8.58854	+	6.76172i	0.316793	+	0.249410i
$736$	−2.43845			−0.0898824
$737$	−14.1231	−	24.4619i	−0.520231	−	0.901067i
$738$	8.00000	−	13.8564i	0.294484	−	0.510061i
$739$	14.3348	−	24.8285i	0.527312	−	0.913332i	−0.472181	−	0.881502i	$-0.656533\pi$
$739$	14.3348	−	24.8285i	0.527312	−	0.913332i	0.999493	−	0.0318302i	$-0.0101336\pi$
$740$	−1.17708	−	2.03876i	−0.0432704	−	0.0749465i
$741$	−8.80776			−0.323561
$742$	−30.4806	−	10.5588i	−1.11898	−	0.387625i
$743$	27.6155			1.01312			0.506558	−	0.862206i	$-0.330918\pi$
$743$	27.6155			1.01312			0.506558	+	0.862206i	$0.330918\pi$
$744$	6.93087	+	12.0046i	0.254098	+	0.440111i
$745$	1.02699	−	1.77879i	0.0376259	−	0.0651700i
$746$	−7.56155	+	13.0970i	−0.276848	+	0.479515i
$747$	−2.43845	−	4.22351i	−0.0892181	−	0.154530i
$748$	6.63068			0.242442
$749$	3.12311	+	16.2281i	0.114116	+	0.592963i
$750$	−18.4384			−0.673277
$751$	−14.9654	−	25.9209i	−0.546096	−	0.945867i	−0.998537	−	0.0540723i	$-0.982780\pi$
$751$	−14.9654	−	25.9209i	−0.546096	−	0.945867i	0.452441	−	0.891795i	$-0.350553\pi$
$752$	15.6577	−	27.1199i	0.570977	−	0.988960i
$753$	−1.00000	+	1.73205i	−0.0364420	+	0.0631194i
$754$	−43.6155	−	75.5443i	−1.58838	−	2.75116i
$755$	−28.4924			−1.03695
$756$	−0.876894	+	0.759413i	−0.0318923	+	0.0276196i
$757$	−21.6155			−0.785630			−0.392815	−	0.919618i	$-0.628499\pi$
$757$	−21.6155			−0.785630			−0.392815	+	0.919618i	$0.628499\pi$
$758$	−6.72680	−	11.6512i	−0.244328	−	0.423189i
$759$	1.00000	−	1.73205i	0.0362977	−	0.0628695i
$760$	2.73863	−	4.74345i	0.0993407	−	0.172063i
$761$	3.19224	+	5.52911i	0.115718	+	0.200430i	0.918067	−	0.396426i	$-0.129750\pi$
$761$	3.19224	+	5.52911i	0.115718	+	0.200430i	−0.802348	+	0.596856i	$0.796416\pi$
$762$	2.63068			0.0952996
$763$	21.1231	−	18.2931i	0.764708	−	0.662256i
$764$	−0.492423			−0.0178152
$765$	5.90388	+	10.2258i	0.213455	+	0.369715i
$766$	−3.31534	+	5.74234i	−0.119788	+	0.207479i
$767$	27.9309	−	48.3777i	1.00853	−	1.74682i
$768$	−5.02699	−	8.70700i	−0.181396	−	0.314187i
$769$	−18.8078			−0.678225			−0.339113	−	0.940746i	$-0.610127\pi$
$769$	−18.8078			−0.678225			−0.339113	+	0.940746i	$0.610127\pi$
$770$	2.43845	+	12.6705i	0.0878755	+	0.456615i
$771$	−6.63068			−0.238798
$772$	−1.72680	−	2.99091i	−0.0621489	−	0.107645i
$773$	15.1501	−	26.2407i	0.544911	−	0.943814i	−0.453702	−	0.891154i	$-0.649897\pi$
$773$	15.1501	−	26.2407i	0.544911	−	0.943814i	0.998613	−	0.0526598i	$-0.0167699\pi$
$774$	0.246211	−	0.426450i	0.00884988	−	0.0153284i
$775$	7.28078	+	12.6107i	0.261533	+	0.452989i
$776$	−37.4773			−1.34536
$777$	8.59612	+	2.97778i	0.308384	+	0.106827i
$778$	24.3845			0.874226
$779$	7.36932	+	12.7640i	0.264033	+	0.457319i
$780$	2.09612	−	3.63058i	0.0750531	−	0.129996i
$781$	13.8078	−	23.9157i	0.494081	−	0.855773i
$782$	5.90388	+	10.2258i	0.211122	+	0.365675i
$783$	−9.12311			−0.326033
$784$	−4.68466	+	32.4563i	−0.167309	+	1.15915i
$785$	6.63068			0.236659
$786$	−9.90388	−	17.1540i	−0.353260	−	0.611864i
$787$	22.7808	−	39.4575i	0.812047	−	1.40651i	−0.0993821	−	0.995049i	$-0.531687\pi$
$787$	22.7808	−	39.4575i	0.812047	−	1.40651i	0.911429	−	0.411457i	$-0.134980\pi$
$788$	4.68466	−	8.11407i	0.166884	−	0.289052i
$789$	−2.24621	−	3.89055i	−0.0799672	−	0.138507i
$790$	−13.2614			−0.471818
$791$	24.5194	+	8.49377i	0.871810	+	0.302004i
$792$	4.87689			0.173293
$793$	18.3693	+	31.8166i	0.652314	+	1.12984i
$794$	−17.6577	+	30.5840i	−0.626647	+	1.08538i
$795$	6.09612	−	10.5588i	0.216207	−	0.374482i
$796$	1.75379	+	3.03765i	0.0621614	+	0.107667i
$797$	−30.0540			−1.06457			−0.532283	−	0.846566i	$-0.678666\pi$
$797$	−30.0540			−1.06457			−0.532283	+	0.846566i	$0.678666\pi$
$798$	−1.12311	−	5.83583i	−0.0397575	−	0.206586i
$799$	−50.5464			−1.78820
$800$	−3.12311	−	5.40938i	−0.110418	−	0.191250i
$801$	5.00000	−	8.66025i	0.176666	−	0.305995i
$802$	0.534565	−	0.925894i	0.0188762	−	0.0326945i
$803$	5.87689	+	10.1791i	0.207391	+	0.359212i
$804$	−6.19224			−0.218383
$805$	−3.12311	+	2.70469i	−0.110075	+	0.0953278i
$806$	−54.3542			−1.91454
$807$	4.24621	+	7.35465i	0.149474	+	0.258896i
$808$	−1.06913	+	1.85179i	−0.0376119	+	0.0651457i
$809$	9.31534	−	16.1346i	0.327510	−	0.567264i	−0.654507	−	0.756056i	$-0.727124\pi$
$809$	9.31534	−	16.1346i	0.327510	−	0.567264i	0.982017	+	0.188792i	$0.0604572\pi$
$810$	−1.21922	−	2.11176i	−0.0428392	−	0.0741996i
$811$	−19.6155			−0.688794			−0.344397	−	0.938824i	$-0.611917\pi$
$811$	−19.6155			−0.688794			−0.344397	+	0.938824i	$0.611917\pi$
$812$	8.00000	−	6.92820i	0.280745	−	0.243132i
$813$	−19.6155			−0.687947
$814$	5.36932	+	9.29993i	0.188194	+	0.325962i
$815$	−3.12311	+	5.40938i	−0.109398	+	0.189482i
$816$	−17.7116	+	30.6775i	−0.620032	+	1.07393i
$817$	0.226801	+	0.392831i	0.00793477	+	0.0137434i
$818$	29.4536			1.02982
$819$	3.06155	+	15.9083i	0.106979	+	0.555881i
$820$	−7.01515			−0.244980
$821$	6.36932	+	11.0320i	0.222291	+	0.385019i	0.955503	−	0.294981i	$-0.0953133\pi$
$821$	6.36932	+	11.0320i	0.222291	+	0.385019i	−0.733212	+	0.680000i	$0.761980\pi$
$822$	6.09612	−	10.5588i	0.212627	−	0.368280i
$823$	−14.9309	+	25.8610i	−0.520457	+	0.901459i	0.479260	+	0.877673i	$0.340905\pi$
$823$	−14.9309	+	25.8610i	−0.520457	+	0.901459i	−0.999717	+	0.0237855i	$0.992428\pi$
$824$	17.2192	+	29.8246i	0.599860	+	1.03899i
$825$	5.12311			0.178364
$826$	35.6155	+	12.3376i	1.23922	+	0.429279i
$827$	22.7386			0.790700			0.395350	−	0.918531i	$-0.370623\pi$
$827$	22.7386			0.790700			0.395350	+	0.918531i	$0.370623\pi$
$828$	−0.219224	−	0.379706i	−0.00761855	−	0.0131957i
$829$	−0.746211	+	1.29248i	−0.0259170	+	0.0448895i	−0.878693	−	0.477387i	$-0.841584\pi$
$829$	−0.746211	+	1.29248i	−0.0259170	+	0.0448895i	0.852776	+	0.522277i	$0.174917\pi$
$830$	−5.94602	+	10.2988i	−0.206390	+	0.357477i
$831$	14.6231	+	25.3280i	0.507270	+	0.878617i
$832$	−34.0540			−1.18061
$833$	49.1501	−	19.6455i	1.70295	−	0.680676i
$834$	18.6307			0.645128
$835$	2.58854	+	4.48348i	0.0895801	+	0.155157i
$836$	0.630683	−	1.09238i	0.0218126	−	0.0377806i
$837$	−2.84233	+	4.92306i	−0.0982453	+	0.170166i
$838$	22.2462	+	38.5316i	0.768483	+	1.33105i
$839$	−20.6307			−0.712250			−0.356125	−	0.934438i	$-0.615902\pi$
$839$	−20.6307			−0.712250			−0.356125	+	0.934438i	$0.615902\pi$
$840$	−9.51941	−	3.29762i	−0.328451	−	0.113779i
$841$	54.2311			1.87004
$842$	3.36932	+	5.83583i	0.116114	+	0.201116i
$843$	−9.78078	+	16.9408i	−0.336868	+	0.583472i
$844$	1.56155	−	2.70469i	0.0537509	−	0.0930992i
$845$	−19.1231	−	33.1222i	−0.657855	−	1.13944i
$846$	10.4384			0.358881
$847$	3.50000	+	18.1865i	0.120261	+	0.624897i
$848$	36.5767			1.25605
$849$	12.0616	+	20.8912i	0.413951	+	0.716985i
$850$	−15.1231	+	26.1940i	−0.518718	+	0.898446i
$851$	−1.71922	+	2.97778i	−0.0589342	+	0.102077i
$852$	−3.02699	−	5.24290i	−0.103703	−	0.179619i
$853$	−31.9309			−1.09329			−0.546646	−	0.837364i	$-0.684096\pi$
$853$	−31.9309			−1.09329			−0.546646	+	0.837364i	$0.684096\pi$
$854$	−18.7386	+	16.2281i	−0.641223	+	0.555315i
$855$	2.24621			0.0768188
$856$	−7.61553	−	13.1905i	−0.260293	−	0.450841i
$857$	−8.68466	+	15.0423i	−0.296662	+	0.513834i	−0.975370	−	0.220574i	$-0.929207\pi$
$857$	−8.68466	+	15.0423i	−0.296662	+	0.513834i	0.678708	+	0.734408i	$0.262540\pi$
$858$	−9.56155	+	16.5611i	−0.326426	+	0.565386i
$859$	13.1231	+	22.7299i	0.447755	+	0.775534i	0.998240	−	0.0593114i	$-0.0188905\pi$
$859$	13.1231	+	22.7299i	0.447755	+	0.775534i	−0.550485	+	0.834845i	$0.685557\pi$
$860$	−0.215901			−0.00736217
$861$	20.4924	−	17.7470i	0.698380	−	0.604815i
$862$	12.4924			0.425494
$863$	3.15009	+	5.45612i	0.107230	+	0.185729i	0.914647	−	0.404253i	$-0.132468\pi$
$863$	3.15009	+	5.45612i	0.107230	+	0.185729i	−0.807417	+	0.589981i	$0.799135\pi$
$864$	1.21922	−	2.11176i	0.0414788	−	0.0718434i
$865$	18.2462	−	31.6034i	0.620390	−	1.07455i
$866$	5.31534	+	9.20644i	0.180623	+	0.312848i
$867$	40.1771			1.36449
$868$	−1.24621	−	6.47550i	−0.0422992	−	0.219793i
$869$	10.8769			0.368973
$870$	11.1231	+	19.2658i	0.377109	+	0.653171i
$871$	−43.2386	+	74.8915i	−1.46509	+	2.53760i
$872$	−12.8769	+	22.3034i	−0.436067	+	0.755290i
$873$	−7.68466	−	13.3102i	−0.260086	−	0.450483i
$874$	2.24621			0.0759792
$875$	−29.5194	−	10.2258i	−0.997938	−	0.345696i
$876$	2.57671			0.0870589
$877$	12.0270	+	20.8314i	0.406123	+	0.703425i	0.994451	−	0.105197i	$-0.0335473\pi$
$877$	12.0270	+	20.8314i	0.406123	+	0.703425i	−0.588329	+	0.808622i	$0.700214\pi$
$878$	−12.1922	+	21.1176i	−0.411468	+	0.712684i
$879$	−12.0270	+	20.8314i	−0.405660	+	0.702624i
$880$	−7.31534	−	12.6705i	−0.246600	−	0.427124i
$881$	5.31534			0.179078			0.0895392	−	0.995983i	$-0.471461\pi$
$881$	5.31534			0.179078			0.0895392	+	0.995983i	$0.471461\pi$
$882$	−10.1501	+	4.05703i	−0.341771	+	0.136607i
$883$	−2.06913			−0.0696318			−0.0348159	−	0.999394i	$-0.511084\pi$
$883$	−2.06913			−0.0696318			−0.0348159	+	0.999394i	$0.511084\pi$
$884$	−10.1501	−	17.5805i	−0.341385	−	0.591295i
$885$	−7.12311	+	12.3376i	−0.239441	+	0.414723i
$886$	−10.3963	+	18.0069i	−0.349271	+	0.604955i
$887$	−0.315342	−	0.546188i	−0.0105881	−	0.0183392i	0.860683	−	0.509142i	$-0.170037\pi$
$887$	−0.315342	−	0.546188i	−0.0105881	−	0.0183392i	−0.871271	+	0.490802i	$0.836704\pi$
$888$	−8.38447			−0.281364
$889$	4.21165	+	1.45896i	0.141254	+	0.0489318i
$890$	−24.3845			−0.817369
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	4.49242	−	7.78110i	0.150417	−	0.260531i
$893$	−4.80776	+	8.32729i	−0.160886	+	0.278662i
$894$	1.02699	+	1.77879i	0.0343476	+	0.0594918i
$895$	10.8229			0.361770
$896$	−6.78078	−	35.2339i	−0.226530	−	1.17708i
$897$	−6.12311			−0.204445
$898$	10.9309	+	18.9328i	0.364768	+	0.631796i
$899$	25.9309	−	44.9136i	0.864843	−	1.49795i
$900$	0.561553	−	0.972638i	0.0187184	−	0.0324213i
$901$	−29.5194	−	51.1291i	−0.983434	−	1.70336i
$902$	32.0000			1.06548
$903$	0.630683	−	0.546188i	0.0209878	−	0.0181760i
$904$	−23.9157			−0.795425
$905$	6.19224	+	10.7253i	0.205837	+	0.356520i
$906$	14.2462	−	24.6752i	0.473299	−	0.819777i
$907$	−3.86932	+	6.70185i	−0.128479	+	0.222531i	−0.923087	−	0.384590i	$-0.874343\pi$
$907$	−3.86932	+	6.70185i	−0.128479	+	0.222531i	0.794609	+	0.607122i	$0.207676\pi$
$908$	−0.438447	−	0.759413i	−0.0145504	−	0.0252020i
$909$	−0.876894			−0.0290848
$910$	29.8617	−	25.8610i	0.989907	−	0.857285i
$911$	40.4924			1.34157			0.670787	−	0.741650i	$-0.265957\pi$
$911$	40.4924			1.34157			0.670787	+	0.741650i	$0.265957\pi$
$912$	3.36932	+	5.83583i	0.111569	+	0.193244i
$913$	4.87689	−	8.44703i	0.161402	−	0.279556i
$914$	−1.12311	+	1.94528i	−0.0371490	+	0.0643440i
$915$	−4.68466	−	8.11407i	−0.154870	−	0.268243i
$916$	−12.8466			−0.424463
$917$	−6.34233	−	32.9557i	−0.209442	−	1.08829i
$918$	−11.8078			−0.389714
$919$	19.7462	+	34.2014i	0.651367	+	1.12820i	0.982791	+	0.184719i	$0.0591377\pi$
$919$	19.7462	+	34.2014i	0.651367	+	1.12820i	−0.331424	+	0.943482i	$0.607529\pi$
$920$	1.90388	−	3.29762i	0.0627691	−	0.108719i
$921$	−5.84233	+	10.1192i	−0.192511	+	0.333439i
$922$	3.31534	+	5.74234i	0.109185	+	0.189114i
$923$	−84.5464			−2.78288
$924$	−2.19224	−	0.759413i	−0.0721193	−	0.0249828i
$925$	−8.80776			−0.289597
$926$	−15.3693	−	26.6204i	−0.505067	−	0.874802i
$927$	−7.06155	+	12.2310i	−0.231932	+	0.401718i
$928$	−11.1231	+	19.2658i	−0.365134	+	0.632430i
$929$	−1.75379	−	3.03765i	−0.0575399	−	0.0996621i	0.835821	−	0.549003i	$-0.184992\pi$
$929$	−1.75379	−	3.03765i	−0.0575399	−	0.0996621i	−0.893361	+	0.449341i	$0.851659\pi$
$930$	13.8617			0.454544
$931$	1.43845	−	9.96585i	0.0471432	−	0.326618i
$932$	−4.76894			−0.156212
$933$	−3.78078	−	6.54850i	−0.123777	−	0.214388i
$934$	−0.876894	+	1.51883i	−0.0286929	+	0.0496975i
$935$	−11.8078	+	20.4516i	−0.386155	+	0.668840i
$936$	−7.46543	−	12.9305i	−0.244015	−	0.422647i
$937$	−1.93087			−0.0630788			−0.0315394	−	0.999503i	$-0.510041\pi$
$937$	−1.93087			−0.0630788			−0.0315394	+	0.999503i	$0.510041\pi$
$938$	−55.1349	−	19.0993i	−1.80022	−	0.623614i
$939$	29.3002			0.956175
$940$	−2.28835	−	3.96355i	−0.0746379	−	0.129277i
$941$	7.56155	−	13.0970i	0.246500	−	0.426950i	−0.716053	−	0.698046i	$-0.754053\pi$
$941$	7.56155	−	13.0970i	0.246500	−	0.426950i	0.962552	+	0.271097i	$0.0873863\pi$
$942$	−3.31534	+	5.74234i	−0.108020	+	0.187096i
$943$	5.12311	+	8.87348i	0.166831	+	0.288960i
$944$	−42.7386			−1.39102
$945$	−0.780776	−	4.05703i	−0.0253987	−	0.131975i
$946$	0.984845			0.0320201
$947$	8.65767	+	14.9955i	0.281336	+	0.487289i	0.971714	−	0.236160i	$-0.0758890\pi$
$947$	8.65767	+	14.9955i	0.281336	+	0.487289i	−0.690378	+	0.723449i	$0.742556\pi$
$948$	1.19224	−	2.06501i	0.0387220	−	0.0670685i
$949$	17.9924	−	31.1638i	0.584059	−	1.01162i
$950$	2.87689	+	4.98293i	0.0933388	+	0.161668i
$951$	−11.7538			−0.381143
$952$	−36.8769	+	31.9363i	−1.19519	+	1.03506i
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	6.09612	+	10.5588i	0.197369	+	0.341853i
$955$	0.876894	−	1.51883i	0.0283756	−	0.0491480i
$956$	4.00000	−	6.92820i	0.129369	−	0.224074i
$957$	−9.12311	−	15.8017i	−0.294908	−	0.510796i
$958$	−30.2462			−0.977211
$959$	15.6155	−	13.5234i	0.504252	−	0.436695i
$960$	8.68466			0.280296
$961$	−0.657671	−	1.13912i	−0.0212152	−	0.0367458i
$962$	16.4384	−	28.4722i	0.529997	−	0.917981i
$963$	3.12311	−	5.40938i	0.100641	−	0.174315i
$964$	−0.438447	−	0.759413i	−0.0141214	−	0.0244590i
$965$	12.3002			0.395957
$966$	−0.780776	−	4.05703i	−0.0251211	−	0.130533i
$967$	−40.8078			−1.31229			−0.656145	−	0.754635i	$-0.727814\pi$
$967$	−40.8078			−1.31229			−0.656145	+	0.754635i	$0.727814\pi$
$968$	−8.53457	−	14.7823i	−0.274311	−	0.475121i
$969$	5.43845	−	9.41967i	0.174708	−	0.302603i
$970$	−18.7386	+	32.4563i	−0.601661	+	1.04211i
$971$	4.56155	+	7.90084i	0.146387	+	0.253550i	0.929890	−	0.367839i	$-0.119902\pi$
$971$	4.56155	+	7.90084i	0.146387	+	0.253550i	−0.783502	+	0.621389i	$0.786569\pi$
$972$	0.438447			0.0140632
$973$	29.8272	+	10.3324i	0.956215	+	0.331243i
$974$	35.0152			1.12196
$975$	−7.84233	−	13.5833i	−0.251156	−	0.435014i
$976$	14.0540	−	24.3422i	0.449857	−	0.779175i
$977$	4.21922	−	7.30791i	0.134985	−	0.233801i	−0.790607	−	0.612324i	$-0.790235\pi$
$977$	4.21922	−	7.30791i	0.134985	−	0.233801i	0.925592	+	0.378523i	$0.123568\pi$
$978$	−3.12311	−	5.40938i	−0.0998659	−	0.172973i
$979$	20.0000			0.639203
$980$	3.76562	+	2.96466i	0.120288	+	0.0947025i
$981$	−10.5616			−0.337204
$982$	23.9579	+	41.4962i	0.764526	+	1.32420i
$983$	−2.68466	+	4.64996i	−0.0856273	+	0.148311i	−0.905658	−	0.424008i	$-0.860623\pi$
$983$	−2.68466	+	4.64996i	−0.0856273	+	0.148311i	0.820031	+	0.572319i	$0.193956\pi$
$984$	−12.4924	+	21.6375i	−0.398244	+	0.689779i
$985$	16.6847	+	28.8987i	0.531617	+	0.920788i
$986$	107.723			3.43061
$987$	16.7116	+	5.78908i	0.531938	+	0.184269i
$988$	−3.86174			−0.122858
$989$	0.157671	+	0.273094i	0.00501364	+	0.00868388i
$990$	2.43845	−	4.22351i	0.0774989	−	0.134232i
$991$	3.65009	−	6.32215i	0.115949	−	0.200830i	−0.802210	−	0.597042i	$-0.796342\pi$
$991$	3.65009	−	6.32215i	0.115949	−	0.200830i	0.918159	+	0.396213i	$0.129676\pi$
$992$	6.93087	+	12.0046i	0.220055	+	0.381147i
$993$	−15.4384			−0.489924
$994$	−10.7808	−	56.0186i	−0.341945	−	1.77680i
$995$	−12.4924			−0.396036
$996$	−1.06913	−	1.85179i	−0.0338767	−	0.0586761i
$997$	−15.6501	+	27.1068i	−0.495643	+	0.858480i	−0.999987	−	0.00502325i	$-0.998401\pi$
$997$	−15.6501	+	27.1068i	−0.495643	+	0.858480i	0.504344	+	0.863503i	$0.331734\pi$
$998$	27.8617	−	48.2579i	0.881948	−	1.52758i
$999$	−1.71922	−	2.97778i	−0.0543938	−	0.0942129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.e.277.1	✓	4
7.2	even	3	inner	483.2.i.e.415.1	yes	4
7.3	odd	6		3381.2.a.q.1.2		2
7.4	even	3		3381.2.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.e.277.1	✓	4	1.1	even	1	trivial
483.2.i.e.415.1	yes	4	7.2	even	3	inner
3381.2.a.q.1.2		2	7.3	odd	6
3381.2.a.s.1.2		2	7.4	even	3

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.780776 - 1.35234i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.219224 + 0.379706i) q^{4} +(-0.780776 - 1.35234i) q^{5} +1.56155 q^{6} +(2.50000 + 0.866025i) q^{7} -2.43845 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.21922 + 2.11176i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-0.219224 - 0.379706i) q^{12} -6.12311 q^{13} +(-0.780776 - 4.05703i) q^{14} +1.56155 q^{15} +(2.34233 + 4.05703i) q^{16} +(3.78078 - 6.54850i) q^{17} +(-0.780776 + 1.35234i) q^{18} +(-0.719224 - 1.24573i) q^{19} +0.684658 q^{20} +(-2.00000 + 1.73205i) q^{21} -3.12311 q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.21922 - 2.11176i) q^{24} +(1.28078 - 2.21837i) q^{25} +(4.78078 + 8.28055i) q^{26} +1.00000 q^{27} +(-0.876894 + 0.759413i) q^{28} -9.12311 q^{29} +(-1.21922 - 2.11176i) q^{30} +(-2.84233 + 4.92306i) q^{31} +(1.21922 - 2.11176i) q^{32} +(1.00000 + 1.73205i) q^{33} -11.8078 q^{34} +(-0.780776 - 4.05703i) q^{35} +0.438447 q^{36} +(-1.71922 - 2.97778i) q^{37} +(-1.12311 + 1.94528i) q^{38} +(3.06155 - 5.30277i) q^{39} +(1.90388 + 3.29762i) q^{40} -10.2462 q^{41} +(3.90388 + 1.35234i) q^{42} -0.315342 q^{43} +(0.438447 + 0.759413i) q^{44} +(-0.780776 + 1.35234i) q^{45} +(-0.780776 + 1.35234i) q^{46} +(-3.34233 - 5.78908i) q^{47} -4.68466 q^{48} +(5.50000 + 4.33013i) q^{49} -4.00000 q^{50} +(3.78078 + 6.54850i) q^{51} +(1.34233 - 2.32498i) q^{52} +(3.90388 - 6.76172i) q^{53} +(-0.780776 - 1.35234i) q^{54} -3.12311 q^{55} +(-6.09612 - 2.11176i) q^{56} +1.43845 q^{57} +(7.12311 + 12.3376i) q^{58} +(-4.56155 + 7.90084i) q^{59} +(-0.342329 + 0.592932i) q^{60} +(-3.00000 - 5.19615i) q^{61} +8.87689 q^{62} +(-0.500000 - 2.59808i) q^{63} +5.56155 q^{64} +(4.78078 + 8.28055i) q^{65} +(1.56155 - 2.70469i) q^{66} +(7.06155 - 12.2310i) q^{67} +(1.65767 + 2.87117i) q^{68} +1.00000 q^{69} +(-4.87689 + 4.22351i) q^{70} +13.8078 q^{71} +(1.21922 + 2.11176i) q^{72} +(-2.93845 + 5.08954i) q^{73} +(-2.68466 + 4.64996i) q^{74} +(1.28078 + 2.21837i) q^{75} +0.630683 q^{76} +(4.00000 - 3.46410i) q^{77} -9.56155 q^{78} +(2.71922 + 4.70983i) q^{79} +(3.65767 - 6.33527i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(8.00000 + 13.8564i) q^{82} +4.87689 q^{83} +(-0.219224 - 1.13912i) q^{84} -11.8078 q^{85} +(0.246211 + 0.426450i) q^{86} +(4.56155 - 7.90084i) q^{87} +(-2.43845 + 4.22351i) q^{88} +(5.00000 + 8.66025i) q^{89} +2.43845 q^{90} +(-15.3078 - 5.30277i) q^{91} +0.438447 q^{92} +(-2.84233 - 4.92306i) q^{93} +(-5.21922 + 9.03996i) q^{94} +(-1.12311 + 1.94528i) q^{95} +(1.21922 + 2.11176i) q^{96} +15.3693 q^{97} +(1.56155 - 10.8188i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} - 5 q^{4} + q^{5} - 2 q^{6} + 10 q^{7} - 18 q^{8} - 2 q^{9} - 9 q^{10} + 4 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 2 q^{15} - 3 q^{16} + 11 q^{17} + q^{18} - 7 q^{19} - 22 q^{20}+ \cdots - 8 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 - 5 * q^4 + q^5 - 2 * q^6 + 10 * q^7 - 18 * q^8 - 2 * q^9 - 9 * q^10 + 4 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 2 * q^15 - 3 * q^16 + 11 * q^17 + q^18 - 7 * q^19 - 22 * q^20 - 8 * q^21 + 4 * q^22 - 2 * q^23 + 9 * q^24 + q^25 + 15 * q^26 + 4 * q^27 - 20 * q^28 - 20 * q^29 - 9 * q^30 + q^31 + 9 * q^32 + 4 * q^33 - 6 * q^34 + q^35 + 10 * q^36 - 11 * q^37 + 12 * q^38 + 4 * q^39 - 13 * q^40 - 8 * q^41 - 5 * q^42 - 26 * q^43 + 10 * q^44 + q^45 + q^46 - q^47 + 6 * q^48 + 22 * q^49 - 16 * q^50 + 11 * q^51 - 7 * q^52 - 5 * q^53 + q^54 + 4 * q^55 - 45 * q^56 + 14 * q^57 + 12 * q^58 - 10 * q^59 + 11 * q^60 - 12 * q^61 + 52 * q^62 - 2 * q^63 + 14 * q^64 + 15 * q^65 - 2 * q^66 + 20 * q^67 + 19 * q^68 + 4 * q^69 - 36 * q^70 + 14 * q^71 + 9 * q^72 - 20 * q^73 + 14 * q^74 + q^75 + 52 * q^76 + 16 * q^77 - 30 * q^78 + 15 * q^79 + 27 * q^80 - 2 * q^81 + 32 * q^82 + 36 * q^83 - 5 * q^84 - 6 * q^85 - 32 * q^86 + 10 * q^87 - 18 * q^88 + 20 * q^89 + 18 * q^90 - 20 * q^91 + 10 * q^92 + q^93 - 25 * q^94 + 12 * q^95 + 9 * q^96 + 12 * q^97 - 2 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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