LMFDB - Embedded newform 1218.2.i.a.1045.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(697,1218)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1218.697"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1218 = 2 \cdot 3 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1218.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,-3,-3,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1045.1
Root			$-0.623490 + 1.07992i$ of defining polynomial
Character	$\chi$	$=$	1218.1045
Dual form			1218.2.i.a.697.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.623490 + 1.07992i) q^{5} +1.00000 q^{6} +(0.167563 - 2.64044i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.623490 - 1.07992i) q^{10} +(1.22252 + 2.11747i) q^{11} +(-0.500000 + 0.866025i) q^{12} -4.13706 q^{13} +(2.20291 + 1.46533i) q^{14} +1.24698 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.955927 + 1.65571i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.92543 - 3.33494i) q^{19} +1.24698 q^{20} +(-2.37047 + 1.17511i) q^{21} -2.44504 q^{22} +(3.48039 - 6.02820i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.72252 + 2.98349i) q^{25} +(2.06853 - 3.58280i) q^{26} +1.00000 q^{27} +(-2.37047 + 1.17511i) q^{28} -1.00000 q^{29} +(-0.623490 + 1.07992i) q^{30} +(-4.44989 - 7.70743i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.22252 - 2.11747i) q^{33} -1.91185 q^{34} +(2.74698 + 1.82724i) q^{35} +1.00000 q^{36} +(-2.91939 + 5.05653i) q^{37} +(1.92543 + 3.33494i) q^{38} +(2.06853 + 3.58280i) q^{39} +(-0.623490 + 1.07992i) q^{40} -6.47219 q^{41} +(0.167563 - 2.64044i) q^{42} -12.7017 q^{43} +(1.22252 - 2.11747i) q^{44} +(-0.623490 - 1.07992i) q^{45} +(3.48039 + 6.02820i) q^{46} +(-0.900969 + 1.56052i) q^{47} +1.00000 q^{48} +(-6.94385 - 0.884879i) q^{49} -3.44504 q^{50} +(0.955927 - 1.65571i) q^{51} +(2.06853 + 3.58280i) q^{52} +(-2.29590 - 3.97661i) q^{53} +(-0.500000 + 0.866025i) q^{54} -3.04892 q^{55} +(0.167563 - 2.64044i) q^{56} -3.85086 q^{57} +(0.500000 - 0.866025i) q^{58} +(-3.55496 - 6.15737i) q^{59} +(-0.623490 - 1.07992i) q^{60} +(2.59030 - 4.48653i) q^{61} +8.89977 q^{62} +(2.20291 + 1.46533i) q^{63} +1.00000 q^{64} +(2.57942 - 4.46768i) q^{65} +(1.22252 + 2.11747i) q^{66} +(0.0196143 + 0.0339730i) q^{67} +(0.955927 - 1.65571i) q^{68} -6.96077 q^{69} +(-2.95593 + 1.46533i) q^{70} -3.36227 q^{71} +(-0.500000 + 0.866025i) q^{72} +(2.01357 + 3.48761i) q^{73} +(-2.91939 - 5.05653i) q^{74} +(1.72252 - 2.98349i) q^{75} -3.85086 q^{76} +(5.79590 - 2.87318i) q^{77} -4.13706 q^{78} +(4.36778 - 7.56522i) q^{79} +(-0.623490 - 1.07992i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.23609 - 5.60508i) q^{82} -6.04892 q^{83} +(2.20291 + 1.46533i) q^{84} -2.38404 q^{85} +(6.35086 - 11.0000i) q^{86} +(0.500000 + 0.866025i) q^{87} +(1.22252 + 2.11747i) q^{88} +(5.62833 - 9.74856i) q^{89} +1.24698 q^{90} +(-0.693218 + 10.9237i) q^{91} -6.96077 q^{92} +(-4.44989 + 7.70743i) q^{93} +(-0.900969 - 1.56052i) q^{94} +(2.40097 + 4.15860i) q^{95} +(-0.500000 + 0.866025i) q^{96} -11.6528 q^{97} +(4.23825 - 5.57111i) q^{98} -2.44504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + q^{5} + 6 q^{6} + 6 q^{8} - 3 q^{9} + q^{10} + 7 q^{11} - 3 q^{12} - 14 q^{13} - 2 q^{15} - 3 q^{16} + 2 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{20} - 14 q^{22} + 8 q^{23}+ \cdots - 14 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + q^5 + 6 * q^6 + 6 * q^8 - 3 * q^9 + q^10 + 7 * q^11 - 3 * q^12 - 14 * q^13 - 2 * q^15 - 3 * q^16 + 2 * q^17 - 3 * q^18 - 2 * q^19 - 2 * q^20 - 14 * q^22 + 8 * q^23 - 3 * q^24 + 10 * q^25 + 7 * q^26 + 6 * q^27 - 6 * q^29 + q^30 - 4 * q^31 - 3 * q^32 + 7 * q^33 - 4 * q^34 + 7 * q^35 + 6 * q^36 + 15 * q^37 - 2 * q^38 + 7 * q^39 + q^40 - 26 * q^41 - 22 * q^43 + 7 * q^44 + q^45 + 8 * q^46 - q^47 + 6 * q^48 - 20 * q^50 + 2 * q^51 + 7 * q^52 + 14 * q^53 - 3 * q^54 + 4 * q^57 + 3 * q^58 - 22 * q^59 + q^60 + 4 * q^61 + 8 * q^62 + 6 * q^64 + 7 * q^65 + 7 * q^66 + 13 * q^67 + 2 * q^68 - 16 * q^69 - 14 * q^70 - 6 * q^71 - 3 * q^72 + 6 * q^73 + 15 * q^74 + 10 * q^75 + 4 * q^76 + 7 * q^77 - 14 * q^78 + 15 * q^79 + q^80 - 3 * q^81 + 13 * q^82 - 18 * q^83 + 6 * q^85 + 11 * q^86 + 3 * q^87 + 7 * q^88 + 7 * q^89 - 2 * q^90 - 35 * q^91 - 16 * q^92 - 4 * q^93 - q^94 + 10 * q^95 - 3 * q^96 - 34 * q^97 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1218\mathbb{Z}\right)^\times$.

$n$	$379$	$407$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.623490	+	1.07992i	−0.278833	+	0.482953i	−0.971095	−	0.238693i	$-0.923281\pi$
$5$	−0.623490	+	1.07992i	−0.278833	+	0.482953i	0.692262	+	0.721646i	$0.256614\pi$
$6$	1.00000			0.408248
$7$	0.167563	−	2.64044i	0.0633328	−	0.997992i
$7$	0.167563	−	2.64044i	0.0633328	−	0.997992i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.623490	−	1.07992i	−0.197165	−	0.341499i
$11$	1.22252	+	2.11747i	0.368604	+	0.638441i	0.989348	−	0.145573i	$-0.0465025\pi$
$11$	1.22252	+	2.11747i	0.368604	+	0.638441i	−0.620744	+	0.784014i	$0.713169\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−4.13706			−1.14741			−0.573707	−	0.819060i	$-0.694495\pi$
$13$	−4.13706			−1.14741			−0.573707	+	0.819060i	$0.694495\pi$
$14$	2.20291	+	1.46533i	0.588752	+	0.391627i
$15$	1.24698			0.321969
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.955927	+	1.65571i	0.231846	+	0.401570i	0.958351	−	0.285591i	$-0.0921900\pi$
$17$	0.955927	+	1.65571i	0.231846	+	0.401570i	−0.726505	+	0.687161i	$0.758857\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.92543	−	3.33494i	0.441723	−	0.765087i	−0.556094	−	0.831119i	$-0.687701\pi$
$19$	1.92543	−	3.33494i	0.441723	−	0.765087i	0.997818	+	0.0660320i	$0.0210339\pi$
$20$	1.24698			0.278833
$21$	−2.37047	+	1.17511i	−0.517279	+	0.256429i
$22$	−2.44504			−0.521285
$23$	3.48039	−	6.02820i	0.725711	−	1.25697i	−0.232970	−	0.972484i	$-0.574844\pi$
$23$	3.48039	−	6.02820i	0.725711	−	1.25697i	0.958681	−	0.284484i	$-0.0918222\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	1.72252	+	2.98349i	0.344504	+	0.596699i
$26$	2.06853	−	3.58280i	0.405672	−	0.702645i
$27$	1.00000			0.192450
$28$	−2.37047	+	1.17511i	−0.447977	+	0.222074i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$	−0.623490	+	1.07992i	−0.113833	+	0.197165i
$31$	−4.44989	−	7.70743i	−0.799223	−	1.38430i	−0.920123	−	0.391630i	$-0.871911\pi$
$31$	−4.44989	−	7.70743i	−0.799223	−	1.38430i	0.120899	−	0.992665i	$-0.461422\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.22252	−	2.11747i	0.212814	−	0.368604i
$34$	−1.91185			−0.327880
$35$	2.74698	+	1.82724i	0.464324	+	0.308860i
$36$	1.00000			0.166667
$37$	−2.91939	+	5.05653i	−0.479944	+	0.831288i	−0.999735	−	0.0230056i	$-0.992676\pi$
$37$	−2.91939	+	5.05653i	−0.479944	+	0.831288i	0.519791	+	0.854293i	$0.326010\pi$
$38$	1.92543	+	3.33494i	0.312346	+	0.540998i
$39$	2.06853	+	3.58280i	0.331230	+	0.573707i
$40$	−0.623490	+	1.07992i	−0.0985824	+	0.170750i
$41$	−6.47219			−1.01079			−0.505393	−	0.862889i	$-0.668652\pi$
$41$	−6.47219			−1.01079			−0.505393	+	0.862889i	$0.668652\pi$
$42$	0.167563	−	2.64044i	0.0258555	−	0.407429i
$43$	−12.7017			−1.93699			−0.968496	−	0.249028i	$-0.919889\pi$
$43$	−12.7017			−1.93699			−0.968496	+	0.249028i	$0.919889\pi$
$44$	1.22252	−	2.11747i	0.184302	−	0.319220i
$45$	−0.623490	−	1.07992i	−0.0929444	−	0.160984i
$46$	3.48039	+	6.02820i	0.513155	+	0.888810i
$47$	−0.900969	+	1.56052i	−0.131420	+	0.227626i	−0.924224	−	0.381851i	$-0.875287\pi$
$47$	−0.900969	+	1.56052i	−0.131420	+	0.227626i	0.792804	+	0.609476i	$0.208620\pi$
$48$	1.00000			0.144338
$49$	−6.94385	−	0.884879i	−0.991978	−	0.126411i
$50$	−3.44504			−0.487202
$51$	0.955927	−	1.65571i	0.133857	−	0.231846i
$52$	2.06853	+	3.58280i	0.286854	+	0.496845i
$53$	−2.29590	−	3.97661i	−0.315366	−	0.546229i	0.664149	−	0.747600i	$-0.268794\pi$
$53$	−2.29590	−	3.97661i	−0.315366	−	0.546229i	−0.979515	+	0.201370i	$0.935461\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−3.04892			−0.411116
$56$	0.167563	−	2.64044i	0.0223915	−	0.352844i
$57$	−3.85086			−0.510058
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	−3.55496	−	6.15737i	−0.462816	−	0.801621i	0.536284	−	0.844038i	$-0.319828\pi$
$59$	−3.55496	−	6.15737i	−0.462816	−	0.801621i	−0.999100	+	0.0424166i	$0.986494\pi$
$60$	−0.623490	−	1.07992i	−0.0804922	−	0.139417i
$61$	2.59030	−	4.48653i	0.331654	−	0.574442i	−0.651182	−	0.758921i	$-0.725727\pi$
$61$	2.59030	−	4.48653i	0.331654	−	0.574442i	0.982836	+	0.184480i	$0.0590600\pi$
$62$	8.89977			1.13027
$63$	2.20291	+	1.46533i	0.277540	+	0.184615i
$64$	1.00000			0.125000
$65$	2.57942	−	4.46768i	0.319937	−	0.554148i
$66$	1.22252	+	2.11747i	0.150482	+	0.260642i
$67$	0.0196143	+	0.0339730i	0.00239627	+	0.00415046i	0.867221	−	0.497923i	$-0.165904\pi$
$67$	0.0196143	+	0.0339730i	0.00239627	+	0.00415046i	−0.864825	+	0.502074i	$0.832571\pi$
$68$	0.955927	−	1.65571i	0.115923	−	0.200785i
$69$	−6.96077			−0.837978
$70$	−2.95593	+	1.46533i	−0.353301	+	0.175141i
$71$	−3.36227			−0.399028			−0.199514	−	0.979895i	$-0.563936\pi$
$71$	−3.36227			−0.399028			−0.199514	+	0.979895i	$0.563936\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	2.01357	+	3.48761i	0.235671	+	0.408194i	0.959467	−	0.281819i	$-0.0909379\pi$
$73$	2.01357	+	3.48761i	0.235671	+	0.408194i	−0.723797	+	0.690013i	$0.757605\pi$
$74$	−2.91939	−	5.05653i	−0.339372	−	0.587809i
$75$	1.72252	−	2.98349i	0.198900	−	0.344504i
$76$	−3.85086			−0.441723
$77$	5.79590	−	2.87318i	0.660504	−	0.327430i
$78$	−4.13706			−0.468430
$79$	4.36778	−	7.56522i	0.491414	−	0.851154i	−0.508537	−	0.861040i	$-0.669814\pi$
$79$	4.36778	−	7.56522i	0.491414	−	0.851154i	0.999951	+	0.00988633i	$0.00314697\pi$
$80$	−0.623490	−	1.07992i	−0.0697083	−	0.120738i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.23609	−	5.60508i	0.357367	−	0.618978i
$83$	−6.04892			−0.663955			−0.331977	−	0.943287i	$-0.607716\pi$
$83$	−6.04892			−0.663955			−0.331977	+	0.943287i	$0.607716\pi$
$84$	2.20291	+	1.46533i	0.240357	+	0.159881i
$85$	−2.38404			−0.258586
$86$	6.35086	−	11.0000i	0.684830	−	1.18616i
$87$	0.500000	+	0.866025i	0.0536056	+	0.0928477i
$88$	1.22252	+	2.11747i	0.130321	+	0.225723i
$89$	5.62833	−	9.74856i	0.596602	−	1.03335i	−0.396716	−	0.917941i	$-0.629850\pi$
$89$	5.62833	−	9.74856i	0.596602	−	1.03335i	0.993319	−	0.115404i	$-0.0368163\pi$
$90$	1.24698			0.131443
$91$	−0.693218	+	10.9237i	−0.0726690	+	1.14511i
$92$	−6.96077			−0.725711
$93$	−4.44989	+	7.70743i	−0.461432	+	0.799223i
$94$	−0.900969	−	1.56052i	−0.0929278	−	0.160956i
$95$	2.40097	+	4.15860i	0.246334	+	0.426663i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−11.6528			−1.18316			−0.591581	−	0.806246i	$-0.701496\pi$
$97$	−11.6528			−1.18316			−0.591581	+	0.806246i	$0.701496\pi$
$98$	4.23825	−	5.57111i	0.428128	−	0.562767i
$99$	−2.44504			−0.245736
$100$	1.72252	−	2.98349i	0.172252	−	0.298349i
$101$	−9.31431	−	16.1329i	−0.926809	−	1.60528i	−0.788626	−	0.614874i	$-0.789207\pi$
$101$	−9.31431	−	16.1329i	−0.926809	−	1.60528i	−0.138183	−	0.990407i	$-0.544126\pi$
$102$	0.955927	+	1.65571i	0.0946509	+	0.163940i
$103$	1.46681	−	2.54059i	0.144529	−	0.250332i	−0.784668	−	0.619916i	$-0.787167\pi$
$103$	1.46681	−	2.54059i	0.144529	−	0.250332i	0.929197	+	0.369584i	$0.120500\pi$
$104$	−4.13706			−0.405672
$105$	0.208947	−	3.29257i	0.0203912	−	0.321322i
$106$	4.59179			0.445994
$107$	0.236094	−	0.408928i	0.0228241	−	0.0395325i	−0.854388	−	0.519636i	$-0.826068\pi$
$107$	0.236094	−	0.408928i	0.0228241	−	0.0395325i	0.877212	+	0.480103i	$0.159401\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−4.76540	−	8.25391i	−0.456442	−	0.790581i	0.542328	−	0.840167i	$-0.317543\pi$
$109$	−4.76540	−	8.25391i	−0.456442	−	0.790581i	−0.998770	+	0.0495859i	$0.984210\pi$
$110$	1.52446	−	2.64044i	0.145351	−	0.251756i
$111$	5.83877			0.554192
$112$	2.20291	+	1.46533i	0.208155	+	0.138461i
$113$	1.77479			0.166958			0.0834791	−	0.996510i	$-0.473397\pi$
$113$	1.77479			0.166958			0.0834791	+	0.996510i	$0.473397\pi$
$114$	1.92543	−	3.33494i	0.180333	−	0.312346i
$115$	4.33997	+	7.51705i	0.404704	+	0.700968i
$116$	0.500000	+	0.866025i	0.0464238	+	0.0804084i
$117$	2.06853	−	3.58280i	0.191236	−	0.331230i
$118$	7.10992			0.654521
$119$	4.53199	−	2.24663i	0.415447	−	0.205948i
$120$	1.24698			0.113833
$121$	2.51089	−	4.34898i	0.228262	−	0.395362i
$122$	2.59030	+	4.48653i	0.234515	+	0.406192i
$123$	3.23609	+	5.60508i	0.291789	+	0.505393i
$124$	−4.44989	+	7.70743i	−0.399612	+	0.692148i
$125$	−10.5308			−0.941903
$126$	−2.37047	+	1.17511i	−0.211178	+	0.104687i
$127$	−9.97046			−0.884735			−0.442368	−	0.896834i	$-0.645861\pi$
$127$	−9.97046			−0.884735			−0.442368	+	0.896834i	$0.645861\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	6.35086	+	11.0000i	0.559162	+	0.968496i
$130$	2.57942	+	4.46768i	0.226230	+	0.391842i
$131$	−1.69537	+	2.93647i	−0.148126	+	0.256561i	−0.930535	−	0.366204i	$-0.880657\pi$
$131$	−1.69537	+	2.93647i	−0.148126	+	0.256561i	0.782409	+	0.622765i	$0.213991\pi$
$132$	−2.44504			−0.212814
$133$	−8.48307	−	5.64279i	−0.735576	−	0.489292i
$134$	−0.0392287			−0.00338884
$135$	−0.623490	+	1.07992i	−0.0536615	+	0.0929444i
$136$	0.955927	+	1.65571i	0.0819701	+	0.141976i
$137$	11.3068	+	19.5839i	0.966004	+	1.67317i	0.706894	+	0.707319i	$0.250096\pi$
$137$	11.3068	+	19.5839i	0.966004	+	1.67317i	0.259109	+	0.965848i	$0.416571\pi$
$138$	3.48039	−	6.02820i	0.296270	−	0.513155i
$139$	−9.10752			−0.772490			−0.386245	−	0.922396i	$-0.626228\pi$
$139$	−9.10752			−0.772490			−0.386245	+	0.922396i	$0.626228\pi$
$140$	0.208947	−	3.29257i	0.0176593	−	0.278273i
$141$	1.80194			0.151751
$142$	1.68114	−	2.91181i	0.141078	−	0.244354i
$143$	−5.05765	−	8.76010i	−0.422942	−	0.732556i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.623490	−	1.07992i	0.0517780	−	0.0896821i
$146$	−4.02715			−0.333289
$147$	2.70560	+	6.45599i	0.223154	+	0.532481i
$148$	5.83877			0.479944
$149$	1.61529	−	2.79777i	0.132330	−	0.229202i	−0.792244	−	0.610204i	$-0.791087\pi$
$149$	1.61529	−	2.79777i	0.132330	−	0.229202i	0.924574	+	0.381002i	$0.124421\pi$
$150$	1.72252	+	2.98349i	0.140643	+	0.243601i
$151$	−3.28501	−	5.68981i	−0.267330	−	0.463030i	0.700841	−	0.713317i	$-0.252808\pi$
$151$	−3.28501	−	5.68981i	−0.267330	−	0.463030i	−0.968172	+	0.250287i	$0.919475\pi$
$152$	1.92543	−	3.33494i	0.156173	−	0.270499i
$153$	−1.91185			−0.154564
$154$	−0.409698	+	6.45599i	−0.0330144	+	0.520238i
$155$	11.0978			0.891400
$156$	2.06853	−	3.58280i	0.165615	−	0.286854i
$157$	−5.68814	−	9.85214i	−0.453963	−	0.786287i	0.544665	−	0.838654i	$-0.316657\pi$
$157$	−5.68814	−	9.85214i	−0.453963	−	0.786287i	−0.998628	+	0.0523671i	$0.983323\pi$
$158$	4.36778	+	7.56522i	0.347482	+	0.601856i
$159$	−2.29590	+	3.97661i	−0.182076	+	0.315366i
$160$	1.24698			0.0985824
$161$	−15.3339	−	10.1999i	−1.20848	−	0.803861i
$162$	1.00000			0.0785674
$163$	−6.89373	+	11.9403i	−0.539959	+	0.935236i	0.458947	+	0.888464i	$0.348227\pi$
$163$	−6.89373	+	11.9403i	−0.539959	+	0.935236i	−0.998906	+	0.0467722i	$0.985107\pi$
$164$	3.23609	+	5.60508i	0.252697	+	0.437683i
$165$	1.52446	+	2.64044i	0.118679	+	0.205558i
$166$	3.02446	−	5.23852i	0.234744	−	0.406588i
$167$	24.8485			1.92283			0.961416	−	0.275099i	$-0.0887107\pi$
$167$	24.8485			1.92283			0.961416	+	0.275099i	$0.0887107\pi$
$168$	−2.37047	+	1.17511i	−0.182886	+	0.0906614i
$169$	4.11529			0.316561
$170$	1.19202	−	2.06464i	0.0914239	−	0.158351i
$171$	1.92543	+	3.33494i	0.147241	+	0.255029i
$172$	6.35086	+	11.0000i	0.484248	+	0.838742i
$173$	−7.45257	+	12.9082i	−0.566609	+	0.981395i	0.430289	+	0.902691i	$0.358412\pi$
$173$	−7.45257	+	12.9082i	−0.566609	+	0.981395i	−0.996898	+	0.0787041i	$0.974922\pi$
$174$	−1.00000			−0.0758098
$175$	8.16637	−	4.04829i	0.617319	−	0.306022i
$176$	−2.44504			−0.184302
$177$	−3.55496	+	6.15737i	−0.267207	+	0.462816i
$178$	5.62833	+	9.74856i	0.421861	+	0.730686i
$179$	12.5843	+	21.7966i	0.940592	+	1.62915i	0.764346	+	0.644807i	$0.223062\pi$
$179$	12.5843	+	21.7966i	0.940592	+	1.62915i	0.176246	+	0.984346i	$0.443605\pi$
$180$	−0.623490	+	1.07992i	−0.0464722	+	0.0804922i
$181$	4.71140			0.350196			0.175098	−	0.984551i	$-0.443976\pi$
$181$	4.71140			0.350196			0.175098	+	0.984551i	$0.443976\pi$
$182$	−9.11356	−	6.06218i	−0.675542	−	0.449359i
$183$	−5.18060			−0.382961
$184$	3.48039	−	6.02820i	0.256577	−	0.444405i
$185$	−3.64042	−	6.30538i	−0.267649	−	0.463581i
$186$	−4.44989	−	7.70743i	−0.326281	−	0.565136i
$187$	−2.33728	+	4.04829i	−0.170919	+	0.296040i
$188$	1.80194			0.131420
$189$	0.167563	−	2.64044i	0.0121884	−	0.192064i
$190$	−4.80194			−0.348369
$191$	9.50753	−	16.4675i	0.687941	−	1.19155i	−0.284562	−	0.958658i	$-0.591848\pi$
$191$	9.50753	−	16.4675i	0.687941	−	1.19155i	0.972503	−	0.232891i	$-0.0748185\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−4.39828	−	7.61805i	−0.316595	−	0.548359i	0.663180	−	0.748460i	$-0.269206\pi$
$193$	−4.39828	−	7.61805i	−0.316595	−	0.548359i	−0.979775	+	0.200101i	$0.935873\pi$
$194$	5.82640	−	10.0916i	0.418311	−	0.724536i
$195$	−5.15883			−0.369432
$196$	2.70560	+	6.45599i	0.193257	+	0.461142i
$197$	−5.93900			−0.423136			−0.211568	−	0.977363i	$-0.567857\pi$
$197$	−5.93900			−0.423136			−0.211568	+	0.977363i	$0.567857\pi$
$198$	1.22252	−	2.11747i	0.0868808	−	0.150482i
$199$	10.4107	+	18.0318i	0.737992	+	1.27824i	0.953398	+	0.301715i	$0.0975591\pi$
$199$	10.4107	+	18.0318i	0.737992	+	1.27824i	−0.215406	+	0.976525i	$0.569108\pi$
$200$	1.72252	+	2.98349i	0.121801	+	0.210965i
$201$	0.0196143	−	0.0339730i	0.00138349	−	0.00239627i
$202$	18.6286			1.31071
$203$	−0.167563	+	2.64044i	−0.0117606	+	0.185323i
$204$	−1.91185			−0.133857
$205$	4.03534	−	6.98942i	0.281841	−	0.488162i
$206$	1.46681	+	2.54059i	0.102198	+	0.177012i
$207$	3.48039	+	6.02820i	0.241904	+	0.418989i
$208$	2.06853	−	3.58280i	0.143427	−	0.248423i
$209$	9.41550			0.651284
$210$	2.74698	+	1.82724i	0.189560	+	0.126092i
$211$	15.9366			1.09712			0.548561	−	0.836111i	$-0.315176\pi$
$211$	15.9366			1.09712			0.548561	+	0.836111i	$0.315176\pi$
$212$	−2.29590	+	3.97661i	−0.157683	+	0.273115i
$213$	1.68114	+	2.91181i	0.115190	+	0.199514i
$214$	0.236094	+	0.408928i	0.0161391	+	0.0279537i
$215$	7.91939	−	13.7168i	0.540098	−	0.935477i
$216$	1.00000			0.0680414
$217$	−21.0966	+	10.4582i	−1.43213	+	0.709947i
$218$	9.53079			0.645507
$219$	2.01357	−	3.48761i	0.136065	−	0.235671i
$220$	1.52446	+	2.64044i	0.102779	+	0.178018i
$221$	−3.95473	−	6.84979i	−0.266024	−	0.460767i
$222$	−2.91939	+	5.05653i	−0.195936	+	0.339372i
$223$	17.0465			1.14152			0.570760	−	0.821117i	$-0.306649\pi$
$223$	17.0465			1.14152			0.570760	+	0.821117i	$0.306649\pi$
$224$	−2.37047	+	1.17511i	−0.158384	+	0.0785151i
$225$	−3.44504			−0.229669
$226$	−0.887395	+	1.53701i	−0.0590287	+	0.102241i
$227$	−0.111113	−	0.192453i	−0.00737481	−	0.0127735i	0.862314	−	0.506373i	$-0.169014\pi$
$227$	−0.111113	−	0.192453i	−0.00737481	−	0.0127735i	−0.869689	+	0.493600i	$0.835681\pi$
$228$	1.92543	+	3.33494i	0.127515	+	0.220862i
$229$	−9.89104	+	17.1318i	−0.653619	+	1.13210i	0.328620	+	0.944462i	$0.393417\pi$
$229$	−9.89104	+	17.1318i	−0.653619	+	1.13210i	−0.982238	+	0.187638i	$0.939917\pi$
$230$	−8.67994			−0.572338
$231$	−5.38620	−	3.58280i	−0.354386	−	0.235731i
$232$	−1.00000			−0.0656532
$233$	1.91670	−	3.31982i	0.125567	−	0.217489i	−0.796387	−	0.604787i	$-0.793258\pi$
$233$	1.91670	−	3.31982i	0.125567	−	0.217489i	0.921954	+	0.387298i	$0.126592\pi$
$234$	2.06853	+	3.58280i	0.135224	+	0.234215i
$235$	−1.12349	−	1.94594i	−0.0732884	−	0.126939i
$236$	−3.55496	+	6.15737i	−0.231408	+	0.400811i
$237$	−8.73556			−0.567436
$238$	−0.320356	+	5.04814i	−0.0207656	+	0.327222i
$239$	−6.64310			−0.429707			−0.214853	−	0.976646i	$-0.568927\pi$
$239$	−6.64310			−0.429707			−0.214853	+	0.976646i	$0.568927\pi$
$240$	−0.623490	+	1.07992i	−0.0402461	+	0.0697083i
$241$	−4.32036	−	7.48308i	−0.278299	−	0.482027i	0.692663	−	0.721261i	$-0.256437\pi$
$241$	−4.32036	−	7.48308i	−0.278299	−	0.482027i	−0.970962	+	0.239234i	$0.923104\pi$
$242$	2.51089	+	4.34898i	0.161406	+	0.279563i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−5.18060			−0.331654
$245$	5.28501	−	6.94706i	0.337647	−	0.443831i
$246$	−6.47219			−0.412652
$247$	−7.96562	+	13.7969i	−0.506840	+	0.877873i
$248$	−4.44989	−	7.70743i	−0.282568	−	0.489422i
$249$	3.02446	+	5.23852i	0.191667	+	0.331977i
$250$	5.26540	−	9.11994i	0.333013	−	0.576795i
$251$	1.47757			0.0932631			0.0466316	−	0.998912i	$-0.485151\pi$
$251$	1.47757			0.0932631			0.0466316	+	0.998912i	$0.485151\pi$
$252$	0.167563	−	2.64044i	0.0105555	−	0.166332i
$253$	17.0194			1.07000
$254$	4.98523	−	8.63467i	0.312801	−	0.541787i
$255$	1.19202	+	2.06464i	0.0746473	+	0.129293i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.16003	−	5.47333i	0.197117	−	0.341417i	−0.750475	−	0.660899i	$-0.770175\pi$
$257$	3.16003	−	5.47333i	0.197117	−	0.341417i	0.947593	+	0.319481i	$0.103509\pi$
$258$	−12.7017			−0.790774
$259$	12.8623	+	8.55575i	0.799223	+	0.531628i
$260$	−5.15883			−0.319937
$261$	0.500000	−	0.866025i	0.0309492	−	0.0536056i
$262$	−1.69537	−	2.93647i	−0.104741	−	0.181416i
$263$	5.08211	+	8.80246i	0.313376	+	0.542783i	0.979091	−	0.203423i	$-0.0652066\pi$
$263$	5.08211	+	8.80246i	0.313376	+	0.542783i	−0.665715	+	0.746206i	$0.731873\pi$
$264$	1.22252	−	2.11747i	0.0752410	−	0.130321i
$265$	5.72587			0.351738
$266$	9.12833	−	4.52516i	0.559694	−	0.277456i
$267$	−11.2567			−0.688897
$268$	0.0196143	−	0.0339730i	0.00119814	−	0.00207523i
$269$	−1.67360	−	2.89877i	−0.102041	−	0.176741i	0.810484	−	0.585761i	$-0.199204\pi$
$269$	−1.67360	−	2.89877i	−0.102041	−	0.176741i	−0.912526	+	0.409020i	$0.865871\pi$
$270$	−0.623490	−	1.07992i	−0.0379444	−	0.0657216i
$271$	−3.68060	+	6.37499i	−0.223581	+	0.387253i	−0.955893	−	0.293716i	$-0.905108\pi$
$271$	−3.68060	+	6.37499i	−0.223581	+	0.387253i	0.732312	+	0.680969i	$0.238441\pi$
$272$	−1.91185			−0.115923
$273$	9.80678	−	4.86149i	0.593533	−	0.294231i
$274$	−22.6136			−1.36614
$275$	−4.21164	+	7.29477i	−0.253971	+	0.439891i
$276$	3.48039	+	6.02820i	0.209495	+	0.362855i
$277$	12.5722	+	21.7757i	0.755389	+	1.30837i	0.945181	+	0.326548i	$0.105885\pi$
$277$	12.5722	+	21.7757i	0.755389	+	1.30837i	−0.189792	+	0.981824i	$0.560781\pi$
$278$	4.55376	−	7.88735i	0.273116	−	0.473052i
$279$	8.89977			0.532815
$280$	2.74698	+	1.82724i	0.164163	+	0.109199i
$281$	14.5646			0.868854			0.434427	−	0.900707i	$-0.356951\pi$
$281$	14.5646			0.868854			0.434427	+	0.900707i	$0.356951\pi$
$282$	−0.900969	+	1.56052i	−0.0536519	+	0.0929278i
$283$	−13.8828	−	24.0458i	−0.825250	−	1.42937i	−0.901728	−	0.432303i	$-0.857701\pi$
$283$	−13.8828	−	24.0458i	−0.825250	−	1.42937i	0.0764789	−	0.997071i	$-0.475632\pi$
$284$	1.68114	+	2.91181i	0.0997571	+	0.172784i
$285$	2.40097	−	4.15860i	0.142221	−	0.246334i
$286$	10.1153			0.598130
$287$	−1.08450	+	17.0894i	−0.0640159	+	1.00876i
$288$	1.00000			0.0589256
$289$	6.67241	−	11.5569i	0.392495	−	0.679820i
$290$	0.623490	+	1.07992i	0.0366126	+	0.0634149i
$291$	5.82640	+	10.0916i	0.341549	+	0.591581i
$292$	2.01357	−	3.48761i	0.117835	−	0.204097i
$293$	29.4873			1.72266			0.861332	−	0.508043i	$-0.169631\pi$
$293$	29.4873			1.72266			0.861332	+	0.508043i	$0.169631\pi$
$294$	−6.94385	−	0.884879i	−0.404973	−	0.0516072i
$295$	8.86592			0.516194
$296$	−2.91939	+	5.05653i	−0.169686	+	0.293905i
$297$	1.22252	+	2.11747i	0.0709379	+	0.122868i
$298$	1.61529	+	2.79777i	0.0935714	+	0.162070i
$299$	−14.3986	+	24.9391i	−0.832691	+	1.44226i
$300$	−3.44504			−0.198900
$301$	−2.12833	+	33.5381i	−0.122675	+	1.93310i
$302$	6.57002			0.378062
$303$	−9.31431	+	16.1329i	−0.535093	+	0.926809i
$304$	1.92543	+	3.33494i	0.110431	+	0.191272i
$305$	3.23005	+	5.59462i	0.184952	+	0.320347i
$306$	0.955927	−	1.65571i	0.0546467	−	0.0946509i
$307$	−2.39373			−0.136617			−0.0683087	−	0.997664i	$-0.521760\pi$
$307$	−2.39373			−0.136617			−0.0683087	+	0.997664i	$0.521760\pi$
$308$	−5.38620	−	3.58280i	−0.306907	−	0.204149i
$309$	−2.93362			−0.166888
$310$	−5.54892	+	9.61101i	−0.315157	+	0.545869i
$311$	−7.21044	−	12.4888i	−0.408867	−	0.708178i	0.585897	−	0.810386i	$-0.300743\pi$
$311$	−7.21044	−	12.4888i	−0.408867	−	0.708178i	−0.994763	+	0.102208i	$0.967409\pi$
$312$	2.06853	+	3.58280i	0.117108	+	0.202836i
$313$	−9.34146	+	16.1799i	−0.528011	+	0.914541i	0.471456	+	0.881890i	$0.343729\pi$
$313$	−9.34146	+	16.1799i	−0.528011	+	0.914541i	−0.999467	+	0.0326518i	$0.989605\pi$
$314$	11.3763			0.642000
$315$	−2.95593	+	1.46533i	−0.166548	+	0.0825622i
$316$	−8.73556			−0.491414
$317$	−10.6201	+	18.3946i	−0.596486	+	1.03314i	0.396849	+	0.917884i	$0.370104\pi$
$317$	−10.6201	+	18.3946i	−0.596486	+	1.03314i	−0.993335	+	0.115261i	$0.963230\pi$
$318$	−2.29590	−	3.97661i	−0.128748	−	0.222997i
$319$	−1.22252	−	2.11747i	−0.0684480	−	0.118555i
$320$	−0.623490	+	1.07992i	−0.0348541	+	0.0603691i
$321$	−0.472189			−0.0263550
$322$	16.5003	−	8.17965i	0.919526	−	0.455834i
$323$	7.36227			0.409648
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−7.12618	−	12.3429i	−0.395289	−	0.684661i
$326$	−6.89373	−	11.9403i	−0.381808	−	0.661312i
$327$	−4.76540	+	8.25391i	−0.263527	+	0.456442i
$328$	−6.47219			−0.357367
$329$	3.96950	+	2.64044i	0.218846	+	0.145572i
$330$	−3.04892			−0.167837
$331$	5.33997	−	9.24910i	0.293511	−	0.508376i	−0.681126	−	0.732166i	$-0.738510\pi$
$331$	5.33997	−	9.24910i	0.293511	−	0.508376i	0.974637	+	0.223790i	$0.0718428\pi$
$332$	3.02446	+	5.23852i	0.165989	+	0.287501i
$333$	−2.91939	−	5.05653i	−0.159981	−	0.277096i
$334$	−12.4242	+	21.5194i	−0.679824	+	1.17749i
$335$	−0.0489173			−0.00267264
$336$	0.167563	−	2.64044i	0.00914130	−	0.144048i
$337$	−26.9028			−1.46549			−0.732743	−	0.680505i	$-0.761760\pi$
$337$	−26.9028			−1.46549			−0.732743	+	0.680505i	$0.761760\pi$
$338$	−2.05765	+	3.56395i	−0.111921	+	0.193853i
$339$	−0.887395	−	1.53701i	−0.0481967	−	0.0834791i
$340$	1.19202	+	2.06464i	0.0646464	+	0.111971i
$341$	10.8802	−	18.8450i	0.589194	−	1.02051i
$342$	−3.85086			−0.208230
$343$	−3.50000	+	18.1865i	−0.188982	+	0.981981i
$344$	−12.7017			−0.684830
$345$	4.33997	−	7.51705i	0.233656	−	0.404704i
$346$	−7.45257	−	12.9082i	−0.400653	−	0.693951i
$347$	8.72252	+	15.1078i	0.468249	+	0.811032i	0.999342	−	0.0362822i	$-0.0115515\pi$
$347$	8.72252	+	15.1078i	0.468249	+	0.811032i	−0.531092	+	0.847314i	$0.678218\pi$
$348$	0.500000	−	0.866025i	0.0268028	−	0.0464238i
$349$	−19.1564			−1.02542			−0.512710	−	0.858562i	$-0.671359\pi$
$349$	−19.1564			−1.02542			−0.512710	+	0.858562i	$0.671359\pi$
$350$	−0.577261	+	9.09643i	−0.0308559	+	0.486224i
$351$	−4.13706			−0.220820
$352$	1.22252	−	2.11747i	0.0651606	−	0.112861i
$353$	−15.6479	−	27.1030i	−0.832856	−	1.44255i	−0.895764	−	0.444530i	$-0.853371\pi$
$353$	−15.6479	−	27.1030i	−0.832856	−	1.44255i	0.0629077	−	0.998019i	$-0.479963\pi$
$354$	−3.55496	−	6.15737i	−0.188944	−	0.327260i
$355$	2.09634	−	3.63097i	0.111262	−	0.192712i
$356$	−11.2567			−0.596602
$357$	−4.21164	−	2.80150i	−0.222903	−	0.148271i
$358$	−25.1685			−1.33020
$359$	−17.2337	+	29.8496i	−0.909560	+	1.57540i	−0.0948835	+	0.995488i	$0.530248\pi$
$359$	−17.2337	+	29.8496i	−0.909560	+	1.57540i	−0.814676	+	0.579916i	$0.803085\pi$
$360$	−0.623490	−	1.07992i	−0.0328608	−	0.0569166i
$361$	2.08546	+	3.61212i	0.109761	+	0.190112i
$362$	−2.35570	+	4.08019i	−0.123813	+	0.214450i
$363$	−5.02177			−0.263575
$364$	9.80678	−	4.86149i	0.514015	−	0.254811i
$365$	−5.02177			−0.262851
$366$	2.59030	−	4.48653i	0.135397	−	0.234515i
$367$	−1.85809	−	3.21831i	−0.0969916	−	0.167994i	0.813446	−	0.581640i	$-0.197589\pi$
$367$	−1.85809	−	3.21831i	−0.0969916	−	0.167994i	−0.910438	+	0.413645i	$0.864255\pi$
$368$	3.48039	+	6.02820i	0.181428	+	0.314242i
$369$	3.23609	−	5.60508i	0.168464	−	0.291789i
$370$	7.28083			0.378512
$371$	−10.8847	+	5.39585i	−0.565106	+	0.280138i
$372$	8.89977			0.461432
$373$	4.37800	−	7.58292i	0.226684	−	0.392629i	−0.730139	−	0.683299i	$-0.760545\pi$
$373$	4.37800	−	7.58292i	0.226684	−	0.392629i	0.956823	+	0.290670i	$0.0938781\pi$
$374$	−2.33728	−	4.04829i	−0.120858	−	0.209332i
$375$	5.26540	+	9.11994i	0.271904	+	0.470951i
$376$	−0.900969	+	1.56052i	−0.0464639	+	0.0804779i
$377$	4.13706			0.213070
$378$	2.20291	+	1.46533i	0.113305	+	0.0753686i
$379$	−18.7584			−0.963554			−0.481777	−	0.876294i	$-0.660008\pi$
$379$	−18.7584			−0.963554			−0.481777	+	0.876294i	$0.660008\pi$
$380$	2.40097	−	4.15860i	0.123167	−	0.213332i
$381$	4.98523	+	8.63467i	0.255401	+	0.442368i
$382$	9.50753	+	16.4675i	0.486448	+	0.842552i
$383$	6.69567	−	11.5972i	0.342133	−	0.592591i	−0.642696	−	0.766121i	$-0.722184\pi$
$383$	6.69567	−	11.5972i	0.342133	−	0.592591i	0.984829	+	0.173530i	$0.0555174\pi$
$384$	1.00000			0.0510310
$385$	−0.510885	+	8.05048i	−0.0260371	+	0.410291i
$386$	8.79656			0.447733
$387$	6.35086	−	11.0000i	0.322832	−	0.559162i
$388$	5.82640	+	10.0916i	0.295790	+	0.512324i
$389$	12.3443	+	21.3809i	0.625880	+	1.08406i	0.988370	+	0.152068i	$0.0485933\pi$
$389$	12.3443	+	21.3809i	0.625880	+	1.08406i	−0.362490	+	0.931988i	$0.618073\pi$
$390$	2.57942	−	4.46768i	0.130614	−	0.226230i
$391$	13.3080			0.673013
$392$	−6.94385	−	0.884879i	−0.350717	−	0.0446931i
$393$	3.39075			0.171041
$394$	2.96950	−	5.14333i	0.149601	−	0.259117i
$395$	5.44653	+	9.43367i	0.274045	+	0.474660i
$396$	1.22252	+	2.11747i	0.0614340	+	0.106407i
$397$	19.7669	−	34.2373i	0.992072	−	1.71832i	0.387200	−	0.921996i	$-0.373442\pi$
$397$	19.7669	−	34.2373i	0.992072	−	1.71832i	0.604872	−	0.796323i	$-0.293224\pi$
$398$	−20.8213			−1.04368
$399$	−0.645260	+	10.1680i	−0.0323034	+	0.509034i
$400$	−3.44504			−0.172252
$401$	12.1468	−	21.0388i	0.606580	−	1.05063i	−0.385220	−	0.922825i	$-0.625874\pi$
$401$	12.1468	−	21.0388i	0.606580	−	1.05063i	0.991800	−	0.127802i	$-0.0407923\pi$
$402$	0.0196143	+	0.0339730i	0.000978274	+	0.00169442i
$403$	18.4095	+	31.8861i	0.917041	+	1.58836i
$404$	−9.31431	+	16.1329i	−0.463404	+	0.802640i
$405$	1.24698			0.0619629
$406$	−2.20291	−	1.46533i	−0.109328	−	0.0727233i
$407$	−14.2760			−0.707637
$408$	0.955927	−	1.65571i	0.0473254	−	0.0819701i
$409$	−4.08211	−	7.07041i	−0.201847	−	0.349609i	0.747276	−	0.664513i	$-0.231361\pi$
$409$	−4.08211	−	7.07041i	−0.201847	−	0.349609i	−0.949124	+	0.314904i	$0.898028\pi$
$410$	4.03534	+	6.98942i	0.199291	+	0.345183i
$411$	11.3068	−	19.5839i	0.557722	−	0.966004i
$412$	−2.93362			−0.144529
$413$	−16.8538	+	8.35491i	−0.829323	+	0.411118i
$414$	−6.96077			−0.342103
$415$	3.77144	−	6.53232i	0.185133	−	0.320659i
$416$	2.06853	+	3.58280i	0.101418	+	0.175661i
$417$	4.55376	+	7.88735i	0.222999	+	0.386245i
$418$	−4.70775	+	8.15406i	−0.230264	+	0.398828i
$419$	−23.2218			−1.13446			−0.567228	−	0.823561i	$-0.691984\pi$
$419$	−23.2218			−1.13446			−0.567228	+	0.823561i	$0.691984\pi$
$420$	−2.95593	+	1.46533i	−0.144234	+	0.0715010i
$421$	39.7861			1.93906			0.969529	−	0.244977i	$-0.0787805\pi$
$421$	39.7861			1.93906			0.969529	+	0.244977i	$0.0787805\pi$
$422$	−7.96830	+	13.8015i	−0.387891	+	0.671847i
$423$	−0.900969	−	1.56052i	−0.0438066	−	0.0758753i
$424$	−2.29590	−	3.97661i	−0.111499	−	0.193121i
$425$	−3.29321	+	5.70400i	−0.159744	+	0.276685i
$426$	−3.36227			−0.162903
$427$	−11.4124	−	7.59131i	−0.552284	−	0.367369i
$428$	−0.472189			−0.0228241
$429$	−5.05765	+	8.76010i	−0.244185	+	0.422942i
$430$	7.91939	+	13.7168i	0.381907	+	0.661482i
$431$	7.19537	+	12.4628i	0.346589	+	0.600310i	0.985641	−	0.168854i	$-0.0540065\pi$
$431$	7.19537	+	12.4628i	0.346589	+	0.600310i	−0.639052	+	0.769163i	$0.720673\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	0.411190			0.0197605			0.00988027	−	0.999951i	$-0.496855\pi$
$433$	0.411190			0.0197605			0.00988027	+	0.999951i	$0.496855\pi$
$434$	1.49127	−	23.4993i	0.0715833	−	1.12800i
$435$	−1.24698			−0.0597881
$436$	−4.76540	+	8.25391i	−0.228221	+	0.395291i
$437$	−13.4025	−	23.2137i	−0.641127	−	1.11046i
$438$	2.01357	+	3.48761i	0.0962123	+	0.166645i
$439$	17.0688	−	29.5641i	0.814651	−	1.41102i	−0.0949278	−	0.995484i	$-0.530262\pi$
$439$	17.0688	−	29.5641i	0.814651	−	1.41102i	0.909578	−	0.415532i	$-0.136405\pi$
$440$	−3.04892			−0.145351
$441$	4.23825	−	5.57111i	0.201821	−	0.265291i
$442$	7.90946			0.376215
$443$	−5.32586	+	9.22467i	−0.253039	+	0.438277i	−0.964361	−	0.264589i	$-0.914764\pi$
$443$	−5.32586	+	9.22467i	−0.253039	+	0.438277i	0.711322	+	0.702867i	$0.248097\pi$
$444$	−2.91939	−	5.05653i	−0.138548	−	0.239972i
$445$	7.01842	+	12.1563i	0.332705	+	0.576262i
$446$	−8.52326	+	14.7627i	−0.403588	+	0.699035i
$447$	−3.23059			−0.152801
$448$	0.167563	−	2.64044i	0.00791660	−	0.124749i
$449$	15.4179			0.727615			0.363808	−	0.931474i	$-0.381477\pi$
$449$	15.4179			0.727615			0.363808	+	0.931474i	$0.381477\pi$
$450$	1.72252	−	2.98349i	0.0812004	−	0.140643i
$451$	−7.91239	−	13.7047i	−0.372580	−	0.645327i
$452$	−0.887395	−	1.53701i	−0.0417396	−	0.0722950i
$453$	−3.28501	+	5.68981i	−0.154343	+	0.267330i
$454$	0.222225			0.0104296
$455$	−11.3644	−	7.55941i	−0.532773	−	0.354391i
$456$	−3.85086			−0.180333
$457$	−9.86563	+	17.0878i	−0.461494	+	0.799332i	−0.999036	−	0.0439056i	$-0.986020\pi$
$457$	−9.86563	+	17.0878i	−0.461494	+	0.799332i	0.537541	+	0.843237i	$0.319353\pi$
$458$	−9.89104	−	17.1318i	−0.462178	−	0.800516i
$459$	0.955927	+	1.65571i	0.0446189	+	0.0772821i
$460$	4.33997	−	7.51705i	0.202352	−	0.350484i
$461$	16.9312			0.788566			0.394283	−	0.918989i	$-0.370993\pi$
$461$	16.9312			0.788566			0.394283	+	0.918989i	$0.370993\pi$
$462$	5.79590	−	2.87318i	0.269650	−	0.133673i
$463$	−9.79763			−0.455334			−0.227667	−	0.973739i	$-0.573110\pi$
$463$	−9.79763			−0.455334			−0.227667	+	0.973739i	$0.573110\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$	−5.54892	−	9.61101i	−0.257325	−	0.445700i
$466$	1.91670	+	3.31982i	0.0887893	+	0.153788i
$467$	−5.71260	+	9.89451i	−0.264347	+	0.457863i	−0.967392	−	0.253282i	$-0.918490\pi$
$467$	−5.71260	+	9.89451i	−0.264347	+	0.457863i	0.703045	+	0.711145i	$0.251823\pi$
$468$	−4.13706			−0.191236
$469$	0.0929903	−	0.0460978i	0.00429389	−	0.00212860i
$470$	2.24698			0.103645
$471$	−5.68814	+	9.85214i	−0.262096	+	0.453963i
$472$	−3.55496	−	6.15737i	−0.163630	−	0.283416i
$473$	−15.5281	−	26.8955i	−0.713983	−	1.23666i
$474$	4.36778	−	7.56522i	0.200619	−	0.347482i
$475$	13.2664			0.608702
$476$	−4.21164	−	2.80150i	−0.193040	−	0.128407i
$477$	4.59179			0.210244
$478$	3.32155	−	5.75310i	0.151924	−	0.263141i
$479$	16.5221	+	28.6171i	0.754912	+	1.30755i	0.945418	+	0.325861i	$0.105654\pi$
$479$	16.5221	+	28.6171i	0.754912	+	1.30755i	−0.190505	+	0.981686i	$0.561013\pi$
$480$	−0.623490	−	1.07992i	−0.0284583	−	0.0492912i
$481$	12.0777	−	20.9192i	0.550695	−	0.953832i
$482$	8.64071			0.393574
$483$	−1.16637	+	18.3795i	−0.0530715	+	0.836296i
$484$	−5.02177			−0.228262
$485$	7.26540	−	12.5840i	0.329905	−	0.571412i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−20.4007	−	35.3351i	−0.924445	−	1.60119i	−0.792451	−	0.609936i	$-0.791195\pi$
$487$	−20.4007	−	35.3351i	−0.924445	−	1.60119i	−0.131995	−	0.991250i	$-0.542138\pi$
$488$	2.59030	−	4.48653i	0.117257	−	0.203096i
$489$	13.7875			0.623491
$490$	3.37382	+	8.05048i	0.152414	+	0.363684i
$491$	25.5555			1.15331			0.576653	−	0.816989i	$-0.304359\pi$
$491$	25.5555			1.15331			0.576653	+	0.816989i	$0.304359\pi$
$492$	3.23609	−	5.60508i	0.145894	−	0.252697i
$493$	−0.955927	−	1.65571i	−0.0430528	−	0.0745696i
$494$	−7.96562	−	13.7969i	−0.358390	−	0.620750i
$495$	1.52446	−	2.64044i	0.0685193	−	0.118679i
$496$	8.89977			0.399612
$497$	−0.563392	+	8.87788i	−0.0252716	+	0.398227i
$498$	−6.04892			−0.271058
$499$	3.44451	−	5.96607i	0.154197	−	0.267078i	−0.778569	−	0.627559i	$-0.784054\pi$
$499$	3.44451	−	5.96607i	0.154197	−	0.267078i	0.932766	+	0.360481i	$0.117387\pi$
$500$	5.26540	+	9.11994i	0.235476	+	0.407856i
$501$	−12.4242	−	21.5194i	−0.555074	−	0.961416i
$502$	−0.738783	+	1.27961i	−0.0329735	+	0.0571118i
$503$	−9.42758			−0.420355			−0.210178	−	0.977663i	$-0.567404\pi$
$503$	−9.42758			−0.420355			−0.210178	+	0.977663i	$0.567404\pi$
$504$	2.20291	+	1.46533i	0.0981253	+	0.0652711i
$505$	23.2295			1.03370
$506$	−8.50969	+	14.7392i	−0.378302	+	0.655238i
$507$	−2.05765	−	3.56395i	−0.0913833	−	0.158281i
$508$	4.98523	+	8.63467i	0.221184	+	0.383102i
$509$	5.62833	−	9.74856i	0.249472	−	0.432097i	−0.713908	−	0.700240i	$-0.753076\pi$
$509$	5.62833	−	9.74856i	0.249472	−	0.432097i	0.963379	+	0.268142i	$0.0864098\pi$
$510$	−2.38404			−0.105567
$511$	9.54623	−	4.73233i	0.422300	−	0.209346i
$512$	1.00000			0.0441942
$513$	1.92543	−	3.33494i	0.0850097	−	0.147241i
$514$	3.16003	+	5.47333i	0.139383	+	0.241418i
$515$	1.82908	+	3.16807i	0.0805991	+	0.139602i
$516$	6.35086	−	11.0000i	0.279581	−	0.484248i
$517$	−4.40581			−0.193767
$518$	−13.8406	+	6.86118i	−0.608123	+	0.301463i
$519$	14.9051			0.654263
$520$	2.57942	−	4.46768i	0.113115	−	0.195921i
$521$	−13.8828	−	24.0458i	−0.608219	−	1.05347i	−0.991534	−	0.129848i	$-0.958551\pi$
$521$	−13.8828	−	24.0458i	−0.608219	−	1.05347i	0.383315	−	0.923618i	$-0.374782\pi$
$522$	0.500000	+	0.866025i	0.0218844	+	0.0379049i
$523$	17.3823	−	30.1071i	0.760076	−	1.31649i	−0.182736	−	0.983162i	$-0.558495\pi$
$523$	17.3823	−	30.1071i	0.760076	−	1.31649i	0.942811	−	0.333327i	$-0.108171\pi$
$524$	3.39075			0.148126
$525$	−7.58911	−	5.04814i	−0.331216	−	0.220319i
$526$	−10.1642			−0.443181
$527$	8.50753	−	14.7355i	0.370594	−	0.641888i
$528$	1.22252	+	2.11747i	0.0532034	+	0.0921510i
$529$	−12.7262	−	22.0424i	−0.553312	−	0.958364i
$530$	−2.86294	+	4.95875i	−0.124358	+	0.215394i
$531$	7.10992			0.308544
$532$	−0.645260	+	10.1680i	−0.0279756	+	0.440837i
$533$	26.7759			1.15979
$534$	5.62833	−	9.74856i	0.243562	−	0.421861i
$535$	0.294405	+	0.509924i	0.0127282	+	0.0220460i
$536$	0.0196143	+	0.0339730i	0.000847210	+	0.00146741i
$537$	12.5843	−	21.7966i	0.543051	−	0.940592i
$538$	3.34721			0.144308
$539$	−6.61529	−	15.7852i	−0.284941	−	0.679915i
$540$	1.24698			0.0536615
$541$	12.4933	−	21.6390i	0.537129	−	0.930334i	−0.461928	−	0.886917i	$-0.652842\pi$
$541$	12.4933	−	21.6390i	0.537129	−	0.930334i	0.999057	−	0.0434170i	$-0.0138244\pi$
$542$	−3.68060	−	6.37499i	−0.158095	−	0.273829i
$543$	−2.35570	−	4.08019i	−0.101093	−	0.175098i
$544$	0.955927	−	1.65571i	0.0409850	−	0.0709882i
$545$	11.8847			0.509085
$546$	−0.693218	+	10.9237i	−0.0296670	+	0.467490i
$547$	−1.07846			−0.0461115			−0.0230558	−	0.999734i	$-0.507340\pi$
$547$	−1.07846			−0.0461115			−0.0230558	+	0.999734i	$0.507340\pi$
$548$	11.3068	−	19.5839i	0.483002	−	0.836584i
$549$	2.59030	+	4.48653i	0.110551	+	0.191481i
$550$	−4.21164	−	7.29477i	−0.179585	−	0.311050i
$551$	−1.92543	+	3.33494i	−0.0820260	+	0.142073i
$552$	−6.96077			−0.296270
$553$	−19.2436	−	12.8005i	−0.818322	−	0.544333i
$554$	−25.1444			−1.06828
$555$	−3.64042	+	6.30538i	−0.154527	+	0.267649i
$556$	4.55376	+	7.88735i	0.193123	+	0.334498i
$557$	−10.0429	−	17.3948i	−0.425530	−	0.737040i	0.570939	−	0.820992i	$-0.306579\pi$
$557$	−10.0429	−	17.3948i	−0.425530	−	0.737040i	−0.996470	+	0.0839520i	$0.973246\pi$
$558$	−4.44989	+	7.70743i	−0.188379	+	0.326281i
$559$	52.5478			2.22253
$560$	−2.95593	+	1.46533i	−0.124911	+	0.0619216i
$561$	4.67456			0.197360
$562$	−7.28232	+	12.6134i	−0.307186	+	0.532062i
$563$	1.44116	+	2.49616i	0.0607375	+	0.105200i	0.894795	−	0.446477i	$-0.147321\pi$
$563$	1.44116	+	2.49616i	0.0607375	+	0.105200i	−0.834058	+	0.551677i	$0.813988\pi$
$564$	−0.900969	−	1.56052i	−0.0379376	−	0.0657099i
$565$	−1.10656	+	1.91662i	−0.0465535	+	0.0806330i
$566$	27.7657			1.16708
$567$	−2.37047	+	1.17511i	−0.0995504	+	0.0493498i
$568$	−3.36227			−0.141078
$569$	−7.93685	+	13.7470i	−0.332730	+	0.576305i	−0.983046	−	0.183359i	$-0.941303\pi$
$569$	−7.93685	+	13.7470i	−0.332730	+	0.576305i	0.650316	+	0.759664i	$0.274636\pi$
$570$	2.40097	+	4.15860i	0.100566	+	0.174185i
$571$	−17.1548	−	29.7130i	−0.717907	−	1.24345i	−0.961828	−	0.273656i	$-0.911767\pi$
$571$	−17.1548	−	29.7130i	−0.717907	−	1.24345i	0.243921	−	0.969795i	$-0.421566\pi$
$572$	−5.05765	+	8.76010i	−0.211471	+	0.366278i
$573$	−19.0151			−0.794366
$574$	−14.2576	−	9.48392i	−0.595102	−	0.395851i
$575$	23.9801			1.00004
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−0.631687	−	1.09411i	−0.0262975	−	0.0455485i	0.852577	−	0.522601i	$-0.175038\pi$
$577$	−0.631687	−	1.09411i	−0.0262975	−	0.0455485i	−0.878875	+	0.477053i	$0.841705\pi$
$578$	6.67241	+	11.5569i	0.277536	+	0.480706i
$579$	−4.39828	+	7.61805i	−0.182786	+	0.316595i
$580$	−1.24698			−0.0517780
$581$	−1.01357	+	15.9718i	−0.0420501	+	0.662622i
$582$	−11.6528			−0.483024
$583$	5.61356	−	9.72298i	0.232490	−	0.402685i
$584$	2.01357	+	3.48761i	0.0833223	+	0.144318i
$585$	2.57942	+	4.46768i	0.106646	+	0.184716i
$586$	−14.7436	+	25.5367i	−0.609054	+	1.05491i
$587$	−2.10082			−0.0867101			−0.0433550	−	0.999060i	$-0.513805\pi$
$587$	−2.10082			−0.0867101			−0.0433550	+	0.999060i	$0.513805\pi$
$588$	4.23825	−	5.57111i	0.174783	−	0.229749i
$589$	−34.2717			−1.41214
$590$	−4.43296	+	7.67811i	−0.182502	+	0.316103i
$591$	2.96950	+	5.14333i	0.122149	+	0.211568i
$592$	−2.91939	−	5.05653i	−0.119986	−	0.207822i
$593$	4.43512	−	7.68185i	0.182128	−	0.315456i	−0.760477	−	0.649365i	$-0.775035\pi$
$593$	4.43512	−	7.68185i	0.182128	−	0.315456i	0.942605	+	0.333910i	$0.108368\pi$
$594$	−2.44504			−0.100321
$595$	−0.399477	+	6.29492i	−0.0163770	+	0.258067i
$596$	−3.23059			−0.132330
$597$	10.4107	−	18.0318i	0.426080	−	0.737992i
$598$	−14.3986	−	24.9391i	−0.588802	−	1.01983i
$599$	8.92639	+	15.4610i	0.364722	+	0.631718i	0.988732	−	0.149699i	$-0.0478306\pi$
$599$	8.92639	+	15.4610i	0.364722	+	0.631718i	−0.624009	+	0.781417i	$0.714497\pi$
$600$	1.72252	−	2.98349i	0.0703216	−	0.121801i
$601$	−9.43834			−0.384998			−0.192499	−	0.981297i	$-0.561659\pi$
$601$	−9.43834			−0.384998			−0.192499	+	0.981297i	$0.561659\pi$
$602$	−27.9807	−	18.6122i	−1.14041	−	0.758578i
$603$	−0.0392287			−0.00159751
$604$	−3.28501	+	5.68981i	−0.133665	+	0.231515i
$605$	3.13102	+	5.42309i	0.127294	+	0.220480i
$606$	−9.31431	−	16.1329i	−0.378368	−	0.655353i
$607$	14.4858	−	25.0901i	0.587959	−	1.01837i	−0.406540	−	0.913633i	$-0.633265\pi$
$607$	14.4858	−	25.0901i	0.587959	−	1.01837i	0.994499	−	0.104742i	$-0.0334017\pi$
$608$	−3.85086			−0.156173
$609$	2.37047	−	1.17511i	0.0960563	−	0.0476177i
$610$	−6.46011			−0.261562
$611$	3.72737	−	6.45599i	0.150793	−	0.261181i
$612$	0.955927	+	1.65571i	0.0386411	+	0.0669283i
$613$	−4.36294	−	7.55683i	−0.176217	−	0.305217i	0.764365	−	0.644784i	$-0.223053\pi$
$613$	−4.36294	−	7.55683i	−0.176217	−	0.305217i	−0.940582	+	0.339567i	$0.889719\pi$
$614$	1.19687	−	2.07303i	0.0483016	−	0.0836608i
$615$	−8.07069			−0.325442
$616$	5.79590	−	2.87318i	0.233523	−	0.115764i
$617$	11.1357			0.448308			0.224154	−	0.974554i	$-0.428038\pi$
$617$	11.1357			0.448308			0.224154	+	0.974554i	$0.428038\pi$
$618$	1.46681	−	2.54059i	0.0590038	−	0.102198i
$619$	−2.78568	−	4.82493i	−0.111966	−	0.193930i	0.804597	−	0.593821i	$-0.202381\pi$
$619$	−2.78568	−	4.82493i	−0.111966	−	0.193930i	−0.916563	+	0.399891i	$0.869048\pi$
$620$	−5.54892	−	9.61101i	−0.222850	−	0.385987i
$621$	3.48039	−	6.02820i	0.139663	−	0.241904i
$622$	14.4209			0.578225
$623$	−24.7974	−	16.4948i	−0.993486	−	0.660849i
$624$	−4.13706			−0.165615
$625$	−2.04676	+	3.54509i	−0.0818705	+	0.141804i
$626$	−9.34146	−	16.1799i	−0.373360	−	0.646678i
$627$	−4.70775	−	8.15406i	−0.188009	−	0.325642i
$628$	−5.68814	+	9.85214i	−0.226981	+	0.393143i
$629$	−11.1629			−0.445093
$630$	0.208947	−	3.29257i	0.00832466	−	0.131179i
$631$	3.31229			0.131860			0.0659301	−	0.997824i	$-0.478999\pi$
$631$	3.31229			0.131860			0.0659301	+	0.997824i	$0.478999\pi$
$632$	4.36778	−	7.56522i	0.173741	−	0.300928i
$633$	−7.96830	−	13.8015i	−0.316712	−	0.548561i
$634$	−10.6201	−	18.3946i	−0.421780	−	0.730544i
$635$	6.21648	−	10.7673i	0.246693	−	0.427286i
$636$	4.59179			0.182076
$637$	28.7271	+	3.66080i	1.13821	+	0.145046i
$638$	2.44504			0.0968001
$639$	1.68114	−	2.91181i	0.0665047	−	0.115190i
$640$	−0.623490	−	1.07992i	−0.0246456	−	0.0426874i
$641$	22.8599	+	39.5945i	0.902911	+	1.56389i	0.823697	+	0.567030i	$0.191908\pi$
$641$	22.8599	+	39.5945i	0.902911	+	1.56389i	0.0792138	+	0.996858i	$0.474759\pi$
$642$	0.236094	−	0.408928i	0.00931791	−	0.0161391i
$643$	−8.08336			−0.318777			−0.159388	−	0.987216i	$-0.550952\pi$
$643$	−8.08336			−0.318777			−0.159388	+	0.987216i	$0.550952\pi$
$644$	−1.16637	+	18.3795i	−0.0459613	+	0.724254i
$645$	−15.8388			−0.623651
$646$	−3.68114	+	6.37592i	−0.144832	+	0.250857i
$647$	2.53856	+	4.39692i	0.0998013	+	0.172861i	0.911602	−	0.411073i	$-0.134846\pi$
$647$	2.53856	+	4.39692i	0.0998013	+	0.172861i	−0.811801	+	0.583934i	$0.801513\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	8.69202	−	15.0550i	0.341192	−	0.590961i
$650$	14.2524			0.559023
$651$	19.6054	+	13.0411i	0.768395	+	0.511122i
$652$	13.7875			0.539959
$653$	−6.16972	+	10.6863i	−0.241440	+	0.418186i	−0.961125	−	0.276115i	$-0.910953\pi$
$653$	−6.16972	+	10.6863i	−0.241440	+	0.418186i	0.719685	+	0.694301i	$0.244286\pi$
$654$	−4.76540	−	8.25391i	−0.186342	−	0.322753i
$655$	−2.11410	−	3.66172i	−0.0826046	−	0.143075i
$656$	3.23609	−	5.60508i	0.126348	−	0.218842i
$657$	−4.02715			−0.157114
$658$	−4.27144	+	2.11747i	−0.166518	+	0.0825475i
$659$	−25.1444			−0.979485			−0.489743	−	0.871867i	$-0.662909\pi$
$659$	−25.1444			−0.979485			−0.489743	+	0.871867i	$0.662909\pi$
$660$	1.52446	−	2.64044i	0.0593395	−	0.102779i
$661$	−0.185981	−	0.322128i	−0.00723381	−	0.0125293i	0.862386	−	0.506252i	$-0.168969\pi$
$661$	−0.185981	−	0.322128i	−0.00723381	−	0.0125293i	−0.869620	+	0.493722i	$0.835636\pi$
$662$	5.33997	+	9.24910i	0.207544	+	0.359476i
$663$	−3.95473	+	6.84979i	−0.153589	+	0.266024i
$664$	−6.04892			−0.234744
$665$	11.3828	−	5.64279i	0.441408	−	0.218818i
$666$	5.83877			0.226248
$667$	−3.48039	+	6.02820i	−0.134761	+	0.233413i
$668$	−12.4242	−	21.5194i	−0.480708	−	0.832611i
$669$	−8.52326	−	14.7627i	−0.329528	−	0.570760i
$670$	0.0244587	−	0.0423637i	0.000944921	−	0.00163665i
$671$	12.6668			0.488996
$672$	2.20291	+	1.46533i	0.0849790	+	0.0565265i
$673$	14.3418			0.552837			0.276418	−	0.961037i	$-0.410852\pi$
$673$	14.3418			0.552837			0.276418	+	0.961037i	$0.410852\pi$
$674$	13.4514	−	23.2985i	0.518128	−	0.897424i
$675$	1.72252	+	2.98349i	0.0662999	+	0.114835i
$676$	−2.05765	−	3.56395i	−0.0791403	−	0.137075i
$677$	−15.2256	+	26.3716i	−0.585169	+	1.01354i	0.409686	+	0.912227i	$0.365638\pi$
$677$	−15.2256	+	26.3716i	−0.585169	+	1.01354i	−0.994854	+	0.101315i	$0.967695\pi$
$678$	1.77479			0.0681604
$679$	−1.95257	+	30.7685i	−0.0749329	+	1.18079i
$680$	−2.38404			−0.0914239
$681$	−0.111113	+	0.192453i	−0.00425785	+	0.00737481i
$682$	10.8802	+	18.8450i	0.416623	+	0.721612i
$683$	−11.9291	−	20.6618i	−0.456453	−	0.790600i	0.542317	−	0.840174i	$-0.317547\pi$
$683$	−11.9291	−	20.6618i	−0.456453	−	0.790600i	−0.998770	+	0.0495734i	$0.984214\pi$
$684$	1.92543	−	3.33494i	0.0736206	−	0.127515i
$685$	−28.1987			−1.07742
$686$	−14.0000	−	12.1244i	−0.534522	−	0.462910i
$687$	19.7821			0.754734
$688$	6.35086	−	11.0000i	0.242124	−	0.419371i
$689$	9.49827	+	16.4515i	0.361855	+	0.626752i
$690$	4.33997	+	7.51705i	0.165220	+	0.286169i
$691$	−2.62780	+	4.55149i	−0.0999663	+	0.173147i	−0.911670	−	0.410922i	$-0.865207\pi$
$691$	−2.62780	+	4.55149i	−0.0999663	+	0.173147i	0.811704	+	0.584069i	$0.198540\pi$
$692$	14.9051			0.566609
$693$	−0.409698	+	6.45599i	−0.0155631	+	0.245243i
$694$	−17.4450			−0.662205
$695$	5.67845	−	9.83536i	0.215396	−	0.373076i
$696$	0.500000	+	0.866025i	0.0189525	+	0.0328266i
$697$	−6.18694	−	10.7161i	−0.234347	−	0.405901i
$698$	9.57822	−	16.5900i	0.362541	−	0.627939i
$699$	−3.83340			−0.144992
$700$	−7.58911	−	5.04814i	−0.286841	−	0.190802i
$701$	−31.6243			−1.19443			−0.597217	−	0.802080i	$-0.703727\pi$
$701$	−31.6243			−1.19443			−0.597217	+	0.802080i	$0.703727\pi$
$702$	2.06853	−	3.58280i	0.0780717	−	0.135224i
$703$	11.2421	+	19.4719i	0.424005	+	0.734398i
$704$	1.22252	+	2.11747i	0.0460755	+	0.0798051i
$705$	−1.12349	+	1.94594i	−0.0423131	+	0.0732884i
$706$	31.2959			1.17784
$707$	−44.1586	+	21.8906i	−1.66075	+	0.823281i
$708$	7.10992			0.267207
$709$	−2.25398	+	3.90401i	−0.0846500	+	0.146618i	−0.905242	−	0.424896i	$-0.860311\pi$
$709$	−2.25398	+	3.90401i	−0.0846500	+	0.146618i	0.820592	+	0.571514i	$0.193644\pi$
$710$	2.09634	+	3.63097i	0.0786743	+	0.136268i
$711$	4.36778	+	7.56522i	0.163805	+	0.283718i
$712$	5.62833	−	9.74856i	0.210931	−	0.365343i
$713$	−61.9493			−2.32002
$714$	4.53199	−	2.24663i	0.169606	−	0.0840781i
$715$	12.6136			0.471721
$716$	12.5843	−	21.7966i	0.470296	−	0.814576i
$717$	3.32155	+	5.75310i	0.124046	+	0.214853i
$718$	−17.2337	−	29.8496i	−0.643156	−	1.11398i
$719$	−15.4894	+	26.8284i	−0.577658	+	1.00053i	0.418090	+	0.908406i	$0.362700\pi$
$719$	−15.4894	+	26.8284i	−0.577658	+	1.00053i	−0.995747	+	0.0921265i	$0.970634\pi$
$720$	1.24698			0.0464722
$721$	−6.46250	−	4.29874i	−0.240676	−	0.160093i
$722$	−4.17092			−0.155225
$723$	−4.32036	+	7.48308i	−0.160676	+	0.278299i
$724$	−2.35570	−	4.08019i	−0.0875489	−	0.151639i
$725$	−1.72252	−	2.98349i	−0.0639728	−	0.110804i
$726$	2.51089	−	4.34898i	0.0931877	−	0.161406i
$727$	39.5646			1.46737			0.733686	−	0.679489i	$-0.237798\pi$
$727$	39.5646			1.46737			0.733686	+	0.679489i	$0.237798\pi$
$728$	−0.693218	+	10.9237i	−0.0256924	+	0.404858i
$729$	1.00000			0.0370370
$730$	2.51089	−	4.34898i	0.0929320	−	0.160963i
$731$	−12.1419	−	21.0304i	−0.449085	−	0.777837i
$732$	2.59030	+	4.48653i	0.0957403	+	0.165827i
$733$	−10.4405	+	18.0835i	−0.385628	+	0.667928i	−0.991856	−	0.127363i	$-0.959349\pi$
$733$	−10.4405	+	18.0835i	−0.385628	+	0.667928i	0.606228	+	0.795291i	$0.292682\pi$
$734$	3.71618			0.137167
$735$	−8.65883	−	1.10343i	−0.319386	−	0.0407005i
$736$	−6.96077			−0.256577
$737$	−0.0479579	+	0.0830654i	−0.00176655	+	0.00305976i
$738$	3.23609	+	5.60508i	0.119122	+	0.206326i
$739$	17.1998	+	29.7910i	0.632707	+	1.09588i	0.986996	+	0.160744i	$0.0513895\pi$
$739$	17.1998	+	29.7910i	0.632707	+	1.09588i	−0.354289	+	0.935136i	$0.615277\pi$
$740$	−3.64042	+	6.30538i	−0.133824	+	0.231791i
$741$	15.9312			0.585248
$742$	0.769414	−	12.1244i	0.0282461	−	0.445099i
$743$	−39.2059			−1.43833			−0.719163	−	0.694841i	$-0.755475\pi$
$743$	−39.2059			−1.43833			−0.719163	+	0.694841i	$0.755475\pi$
$744$	−4.44989	+	7.70743i	−0.163141	+	0.282568i
$745$	2.01424	+	3.48876i	0.0737960	+	0.127818i
$746$	4.37800	+	7.58292i	0.160290	+	0.277631i
$747$	3.02446	−	5.23852i	0.110659	−	0.191667i
$748$	4.67456			0.170919
$749$	−1.04019	−	0.691914i	−0.0380076	−	0.0252820i
$750$	−10.5308			−0.384530
$751$	21.6036	−	37.4186i	0.788328	−	1.36542i	−0.138663	−	0.990340i	$-0.544280\pi$
$751$	21.6036	−	37.4186i	0.788328	−	1.36542i	0.926991	−	0.375084i	$-0.122386\pi$
$752$	−0.900969	−	1.56052i	−0.0328550	−	0.0569064i
$753$	−0.738783	−	1.27961i	−0.0269227	−	0.0466316i
$754$	−2.06853	+	3.58280i	−0.0753315	+	0.130478i
$755$	8.19269			0.298162
$756$	−2.37047	+	1.17511i	−0.0862131	+	0.0427382i
$757$	−23.8780			−0.867861			−0.433930	−	0.900946i	$-0.642874\pi$
$757$	−23.8780			−0.867861			−0.433930	+	0.900946i	$0.642874\pi$
$758$	9.37920	−	16.2452i	0.340668	−	0.590054i
$759$	−8.50969	−	14.7392i	−0.308882	−	0.535000i
$760$	2.40097	+	4.15860i	0.0870923	+	0.150848i
$761$	−15.7763	+	27.3253i	−0.571890	+	0.990542i	0.424482	+	0.905436i	$0.360456\pi$
$761$	−15.7763	+	27.3253i	−0.571890	+	0.990542i	−0.996372	+	0.0851059i	$0.972877\pi$
$762$	−9.97046			−0.361192
$763$	−22.5925	+	11.1997i	−0.817902	+	0.405456i
$764$	−19.0151			−0.687941
$765$	1.19202	−	2.06464i	0.0430976	−	0.0746473i
$766$	6.69567	+	11.5972i	0.241924	+	0.419025i
$767$	14.7071	+	25.4734i	0.531042	+	0.919792i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−13.1196			−0.473105			−0.236553	−	0.971619i	$-0.576018\pi$
$769$	−13.1196			−0.473105			−0.236553	+	0.971619i	$0.576018\pi$
$770$	−6.71648	−	4.46768i	−0.242045	−	0.161004i
$771$	−6.32006			−0.227611
$772$	−4.39828	+	7.61805i	−0.158298	+	0.274179i
$773$	16.6521	+	28.8423i	0.598935	+	1.03739i	0.992979	+	0.118295i	$0.0377427\pi$
$773$	16.6521	+	28.8423i	0.598935	+	1.03739i	−0.394043	+	0.919092i	$0.628924\pi$
$774$	6.35086	+	11.0000i	0.228277	+	0.395387i
$775$	15.3300	−	26.5524i	0.550671	−	0.953791i
$776$	−11.6528			−0.418311
$777$	0.978361	−	15.4169i	0.0350985	−	0.553079i
$778$	−24.6886			−0.885128
$779$	−12.4617	+	21.5844i	−0.446488	+	0.773340i
$780$	2.57942	+	4.46768i	0.0923579	+	0.159969i
$781$	−4.11045	−	7.11951i	−0.147083	−	0.254756i
$782$	−6.65399	+	11.5250i	−0.237946	+	0.412135i
$783$	−1.00000			−0.0357371
$784$	4.23825	−	5.57111i	0.151366	−	0.198968i
$785$	14.1860			0.506319
$786$	−1.69537	+	2.93647i	−0.0604720	+	0.104741i
$787$	14.4933	+	25.1031i	0.516630	+	0.894830i	0.999814	+	0.0193105i	$0.00614712\pi$
$787$	14.4933	+	25.1031i	0.516630	+	0.894830i	−0.483183	+	0.875519i	$0.660520\pi$
$788$	2.96950	+	5.14333i	0.105784	+	0.183223i
$789$	5.08211	−	8.80246i	0.180928	−	0.313376i
$790$	−10.8931			−0.387558
$791$	0.297389	−	4.68623i	0.0105739	−	0.166623i
$792$	−2.44504			−0.0868808
$793$	−10.7162	+	18.5611i	−0.380545	+	0.659123i
$794$	19.7669	+	34.2373i	0.701501	+	1.21503i
$795$	−2.86294	−	4.95875i	−0.101538	−	0.175869i
$796$	10.4107	−	18.0318i	0.368996	−	0.639120i
$797$	34.5163			1.22263			0.611315	−	0.791387i	$-0.290641\pi$
$797$	34.5163			1.22263			0.611315	+	0.791387i	$0.290641\pi$
$798$	−8.48307	−	5.64279i	−0.300298	−	0.199753i
$799$	−3.44504			−0.121877
$800$	1.72252	−	2.98349i	0.0609003	−	0.105482i
$801$	5.62833	+	9.74856i	0.198867	+	0.344448i
$802$	12.1468	+	21.0388i	0.428917	+	0.742906i
$803$	−4.92327	+	8.52736i	−0.173738	+	0.300924i
$804$	−0.0392287			−0.00138349
$805$	20.5755	−	10.1999i	0.725192	−	0.359498i
$806$	−36.8189			−1.29689
$807$	−1.67360	+	2.89877i	−0.0589136	+	0.102041i
$808$	−9.31431	−	16.1329i	−0.327676	−	0.567552i
$809$	−3.32789	−	5.76407i	−0.117002	−	0.202654i	0.801576	−	0.597893i	$-0.203995\pi$
$809$	−3.32789	−	5.76407i	−0.117002	−	0.202654i	−0.918578	+	0.395239i	$0.870662\pi$
$810$	−0.623490	+	1.07992i	−0.0219072	+	0.0379444i
$811$	36.9057			1.29594			0.647968	−	0.761668i	$-0.275619\pi$
$811$	36.9057			1.29594			0.647968	+	0.761668i	$0.275619\pi$
$812$	2.37047	−	1.17511i	0.0831872	−	0.0412381i
$813$	7.36121			0.258169
$814$	7.13802	−	12.3634i	0.250188	−	0.433338i
$815$	−8.59634	−	14.8893i	−0.301117	−	0.521550i
$816$	0.955927	+	1.65571i	0.0334641	+	0.0579616i
$817$	−24.4562	+	42.3594i	−0.855615	+	1.48197i
$818$	8.16421			0.285455
$819$	−9.11356	−	6.06218i	−0.318454	−	0.211830i
$820$	−8.07069			−0.281841
$821$	10.6326	−	18.4163i	0.371082	−	0.642733i	−0.618650	−	0.785666i	$-0.712320\pi$
$821$	10.6326	−	18.4163i	0.371082	−	0.642733i	0.989732	+	0.142934i	$0.0456536\pi$
$822$	11.3068	+	19.5839i	0.394369	+	0.683068i
$823$	−19.9520	−	34.5580i	−0.695484	−	1.20461i	−0.970017	−	0.243037i	$-0.921856\pi$
$823$	−19.9520	−	34.5580i	−0.695484	−	1.20461i	0.274533	−	0.961578i	$-0.411477\pi$
$824$	1.46681	−	2.54059i	0.0510988	−	0.0885058i
$825$	8.42327			0.293261
$826$	1.19136	−	18.7733i	0.0414526	−	0.653207i
$827$	18.3037			0.636481			0.318240	−	0.948010i	$-0.396908\pi$
$827$	18.3037			0.636481			0.318240	+	0.948010i	$0.396908\pi$
$828$	3.48039	−	6.02820i	0.120952	−	0.209495i
$829$	−1.08977	−	1.88754i	−0.0378493	−	0.0655568i	0.846480	−	0.532420i	$-0.178717\pi$
$829$	−1.08977	−	1.88754i	−0.0378493	−	0.0655568i	−0.884329	+	0.466863i	$0.845384\pi$
$830$	3.77144	+	6.53232i	0.130909	+	0.226740i
$831$	12.5722	−	21.7757i	0.436124	−	0.755389i
$832$	−4.13706			−0.143427
$833$	−5.17270	−	12.3429i	−0.179224	−	0.427656i
$834$	−9.10752			−0.315368
$835$	−15.4928	+	26.8343i	−0.536149	+	0.928638i
$836$	−4.70775	−	8.15406i	−0.162821	−	0.282014i
$837$	−4.44989	−	7.70743i	−0.153811	−	0.266408i
$838$	11.6109	−	20.1106i	0.401091	−	0.694710i
$839$	6.88876			0.237826			0.118913	−	0.992905i	$-0.462059\pi$
$839$	6.88876			0.237826			0.118913	+	0.992905i	$0.462059\pi$
$840$	0.208947	−	3.29257i	0.00720937	−	0.113605i
$841$	1.00000			0.0344828
$842$	−19.8931	+	34.4558i	−0.685560	+	1.18743i
$843$	−7.28232	−	12.6134i	−0.250817	−	0.434427i
$844$	−7.96830	−	13.8015i	−0.274280	−	0.475067i
$845$	−2.56584	+	4.44417i	−0.0882677	+	0.152884i
$846$	1.80194			0.0619519
$847$	−11.0625	−	7.35857i	−0.380112	−	0.252843i
$848$	4.59179			0.157683
$849$	−13.8828	+	24.0458i	−0.476458	+	0.825250i
$850$	−3.29321	−	5.70400i	−0.112956	−	0.195646i
$851$	20.3212	+	35.1973i	0.696601	+	1.20655i
$852$	1.68114	−	2.91181i	0.0575948	−	0.0997571i
$853$	−35.0828			−1.20121			−0.600606	−	0.799545i	$-0.705074\pi$
$853$	−35.0828			−1.20121			−0.600606	+	0.799545i	$0.705074\pi$
$854$	12.2805	−	6.08776i	0.420229	−	0.208319i
$855$	−4.80194			−0.164223
$856$	0.236094	−	0.408928i	0.00806954	−	0.0139769i
$857$	−18.0308	−	31.2303i	−0.615920	−	1.06681i	−0.990222	−	0.139498i	$-0.955451\pi$
$857$	−18.0308	−	31.2303i	−0.615920	−	1.06681i	0.374302	−	0.927307i	$-0.377882\pi$
$858$	−5.05765	−	8.76010i	−0.172665	−	0.299065i
$859$	21.4361	−	37.1284i	0.731389	−	1.26680i	−0.224900	−	0.974382i	$-0.572206\pi$
$859$	21.4361	−	37.1284i	0.731389	−	1.26680i	0.956289	−	0.292422i	$-0.0944611\pi$
$860$	−15.8388			−0.540098
$861$	15.3421	−	7.60551i	0.522858	−	0.259195i
$862$	−14.3907			−0.490151
$863$	0.973385	−	1.68595i	0.0331344	−	0.0573905i	−0.848983	−	0.528421i	$-0.822784\pi$
$863$	0.973385	−	1.68595i	0.0331344	−	0.0573905i	0.882117	+	0.471030i	$0.156118\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−9.29321	−	16.0963i	−0.315979	−	0.547291i
$866$	−0.205595	+	0.356101i	−0.00698640	+	0.0121008i
$867$	−13.3448			−0.453214
$868$	19.6054	+	13.0411i	0.665450	+	0.442645i
$869$	21.3588			0.724548
$870$	0.623490	−	1.07992i	0.0211383	−	0.0366126i
$871$	−0.0811457	−	0.140549i	−0.00274952	−	0.00476230i
$872$	−4.76540	−	8.25391i	−0.161377	−	0.279513i
$873$	5.82640	−	10.0916i	0.197194	−	0.341549i
$874$	26.8049			0.906690
$875$	−1.76457	+	27.8059i	−0.0596533	+	0.940012i
$876$	−4.02715			−0.136065
$877$	19.6196	−	33.9822i	0.662507	−	1.14750i	−0.317448	−	0.948276i	$-0.602826\pi$
$877$	19.6196	−	33.9822i	0.662507	−	1.14750i	0.979955	−	0.199220i	$-0.0638408\pi$
$878$	17.0688	+	29.5641i	0.576045	+	0.997739i
$879$	−14.7436	−	25.5367i	−0.497290	−	0.861332i
$880$	1.52446	−	2.64044i	0.0513895	−	0.0890092i
$881$	−40.1584			−1.35297			−0.676485	−	0.736457i	$-0.736498\pi$
$881$	−40.1584			−1.35297			−0.676485	+	0.736457i	$0.736498\pi$
$882$	2.70560	+	6.45599i	0.0911021	+	0.217384i
$883$	−31.4596			−1.05870			−0.529350	−	0.848403i	$-0.677564\pi$
$883$	−31.4596			−1.05870			−0.529350	+	0.848403i	$0.677564\pi$
$884$	−3.95473	+	6.84979i	−0.133012	+	0.230384i
$885$	−4.43296	−	7.67811i	−0.149012	−	0.258097i
$886$	−5.32586	−	9.22467i	−0.178926	−	0.309909i
$887$	−7.23609	+	12.5333i	−0.242964	+	0.420826i	−0.961557	−	0.274604i	$-0.911453\pi$
$887$	−7.23609	+	12.5333i	−0.242964	+	0.420826i	0.718593	+	0.695431i	$0.244786\pi$
$888$	5.83877			0.195936
$889$	−1.67068	+	26.3264i	−0.0560327	+	0.882959i
$890$	−14.0368			−0.470516
$891$	1.22252	−	2.11747i	0.0409560	−	0.0709379i
$892$	−8.52326	−	14.7627i	−0.285380	−	0.494293i
$893$	3.46950	+	6.00935i	0.116102	+	0.201095i
$894$	1.61529	−	2.79777i	0.0540235	−	0.0935714i
$895$	−31.3846			−1.04907
$896$	2.20291	+	1.46533i	0.0735939	+	0.0489534i
$897$	28.7972			0.961509
$898$	−7.70895	+	13.3523i	−0.257251	+	0.445572i
$899$	4.44989	+	7.70743i	0.148412	+	0.257057i
$900$	1.72252	+	2.98349i	0.0574174	+	0.0994498i
$901$	4.38942	−	7.60270i	0.146233	−	0.253283i
$902$	15.8248			0.526907
$903$	30.1090	−	14.9259i	1.00197	−	0.496702i
$904$	1.77479			0.0590287
$905$	−2.93751	+	5.08792i	−0.0976461	+	0.169128i
$906$	−3.28501	−	5.68981i	−0.109137	−	0.189031i
$907$	27.9294	+	48.3751i	0.927380	+	1.60627i	0.787689	+	0.616073i	$0.211277\pi$
$907$	27.9294	+	48.3751i	0.927380	+	1.60627i	0.139691	+	0.990195i	$0.455389\pi$
$908$	−0.111113	+	0.192453i	−0.00368741	+	0.00638677i
$909$	18.6286			0.617873
$910$	12.2289	−	6.06218i	0.405383	−	0.200959i
$911$	29.3201			0.971417			0.485708	−	0.874121i	$-0.338562\pi$
$911$	29.3201			0.971417			0.485708	+	0.874121i	$0.338562\pi$
$912$	1.92543	−	3.33494i	0.0637573	−	0.110431i
$913$	−7.39493	−	12.8084i	−0.244736	−	0.423896i
$914$	−9.86563	−	17.0878i	−0.326326	−	0.565213i
$915$	3.23005	−	5.59462i	0.106782	−	0.184952i
$916$	19.7821			0.653619
$917$	7.46950	+	4.96858i	0.246665	+	0.164077i
$918$	−1.91185			−0.0631006
$919$	10.6884	−	18.5129i	0.352579	−	0.610684i	−0.634122	−	0.773233i	$-0.718638\pi$
$919$	10.6884	−	18.5129i	0.352579	−	0.610684i	0.986701	+	0.162549i	$0.0519715\pi$
$920$	4.33997	+	7.51705i	0.143085	+	0.247830i
$921$	1.19687	+	2.07303i	0.0394381	+	0.0683087i
$922$	−8.46562	+	14.6629i	−0.278800	+	0.482896i
$923$	13.9099			0.457851
$924$	−0.409698	+	6.45599i	−0.0134781	+	0.212386i
$925$	−20.1148			−0.661371
$926$	4.89881	−	8.48499i	0.160985	−	0.278834i
$927$	1.46681	+	2.54059i	0.0481764	+	0.0834440i
$928$	0.500000	+	0.866025i	0.0164133	+	0.0284287i
$929$	13.3756	−	23.1672i	0.438840	−	0.760092i	−0.558761	−	0.829329i	$-0.688723\pi$
$929$	13.3756	−	23.1672i	0.438840	−	0.760092i	0.997600	+	0.0692366i	$0.0220563\pi$
$930$	11.0978			0.363912
$931$	−16.3209	+	21.4535i	−0.534896	+	0.703111i
$932$	−3.83340			−0.125567
$933$	−7.21044	+	12.4888i	−0.236059	+	0.408867i
$934$	−5.71260	−	9.89451i	−0.186922	−	0.323758i
$935$	−2.91454	−	5.04814i	−0.0953157	−	0.165092i
$936$	2.06853	−	3.58280i	0.0676121	−	0.117108i
$937$	16.2983			0.532442			0.266221	−	0.963912i	$-0.414225\pi$
$937$	16.2983			0.532442			0.266221	+	0.963912i	$0.414225\pi$
$938$	−0.00657326	+	0.103581i	−0.000214625	+	0.00338204i
$939$	18.6829			0.609694
$940$	−1.12349	+	1.94594i	−0.0366442	+	0.0634696i
$941$	15.9100	+	27.5569i	0.518651	+	0.898330i	0.999765	+	0.0216719i	$0.00689891\pi$
$941$	15.9100	+	27.5569i	0.518651	+	0.898330i	−0.481114	+	0.876658i	$0.659768\pi$
$942$	−5.68814	−	9.85214i	−0.185330	−	0.321000i
$943$	−22.5257	+	39.0157i	−0.733538	+	1.27053i
$944$	7.10992			0.231408
$945$	2.74698	+	1.82724i	0.0893593	+	0.0594402i
$946$	31.0562			1.00972
$947$	−18.5155	+	32.0698i	−0.601673	+	1.04213i	0.390895	+	0.920435i	$0.372165\pi$
$947$	−18.5155	+	32.0698i	−0.601673	+	1.04213i	−0.992568	+	0.121692i	$0.961168\pi$
$948$	4.36778	+	7.56522i	0.141859	+	0.245707i
$949$	−8.33028	−	14.4285i	−0.270412	−	0.468368i
$950$	−6.63318	+	11.4890i	−0.215209	+	0.372752i
$951$	21.2403			0.688763
$952$	4.53199	−	2.24663i	0.146883	−	0.0728138i
$953$	47.7904			1.54808			0.774042	−	0.633134i	$-0.218232\pi$
$953$	47.7904			1.54808			0.774042	+	0.633134i	$0.218232\pi$
$954$	−2.29590	+	3.97661i	−0.0743324	+	0.128748i
$955$	11.8557	+	20.5347i	0.383641	+	0.664486i
$956$	3.32155	+	5.75310i	0.107427	+	0.186068i
$957$	−1.22252	+	2.11747i	−0.0395185	+	0.0684480i
$958$	−33.0441			−1.06761
$959$	53.6048	−	26.5733i	1.73099	−	0.858098i
$960$	1.24698			0.0402461
$961$	−24.1030	+	41.7476i	−0.777515	+	1.34670i
$962$	12.0777	+	20.9192i	0.389400	+	0.674461i
$963$	0.236094	+	0.408928i	0.00760804	+	0.0131775i
$964$	−4.32036	+	7.48308i	−0.139149	+	0.241014i
$965$	10.9691			0.353109
$966$	−15.3339	−	10.1999i	−0.493361	−	0.328175i
$967$	−12.8522			−0.413298			−0.206649	−	0.978415i	$-0.566256\pi$
$967$	−12.8522			−0.413298			−0.206649	+	0.978415i	$0.566256\pi$
$968$	2.51089	−	4.34898i	0.0807029	−	0.139782i
$969$	−3.68114	−	6.37592i	−0.118255	−	0.204824i
$970$	7.26540	+	12.5840i	0.233278	+	0.404049i
$971$	23.9983	−	41.5662i	0.770141	−	1.33392i	−0.167344	−	0.985899i	$-0.553519\pi$
$971$	23.9983	−	41.5662i	0.770141	−	1.33392i	0.937485	−	0.348025i	$-0.113148\pi$
$972$	1.00000			0.0320750
$973$	−1.52608	+	24.0479i	−0.0489239	+	0.770939i
$974$	40.8015			1.30736
$975$	−7.12618	+	12.3429i	−0.228220	+	0.395289i
$976$	2.59030	+	4.48653i	0.0829135	+	0.143610i
$977$	−19.8666	−	34.4099i	−0.635588	−	1.10087i	−0.986390	−	0.164422i	$-0.947424\pi$
$977$	−19.8666	−	34.4099i	−0.635588	−	1.10087i	0.350802	−	0.936450i	$-0.385909\pi$
$978$	−6.89373	+	11.9403i	−0.220437	+	0.381808i
$979$	27.5230			0.879640
$980$	−8.65883	−	1.10343i	−0.276596	−	0.0352477i
$981$	9.53079			0.304295
$982$	−12.7778	+	22.1318i	−0.407755	+	0.706253i
$983$	−12.2959	−	21.2971i	−0.392178	−	0.679273i	0.600558	−	0.799581i	$-0.294945\pi$
$983$	−12.2959	−	21.2971i	−0.392178	−	0.679273i	−0.992737	+	0.120308i	$0.961612\pi$
$984$	3.23609	+	5.60508i	0.103163	+	0.178683i
$985$	3.70291	−	6.41362i	0.117984	−	0.204355i
$986$	1.91185			0.0608858
$987$	0.301938	−	4.75791i	0.00961078	−	0.151446i
$988$	15.9312			0.506840
$989$	−44.2068	+	76.5685i	−1.40570	+	2.43474i
$990$	1.52446	+	2.64044i	0.0484505	+	0.0839187i
$991$	−6.70613	−	11.6154i	−0.213027	−	0.368974i	0.739633	−	0.673010i	$-0.234999\pi$
$991$	−6.70613	−	11.6154i	−0.213027	−	0.368974i	−0.952660	+	0.304036i	$0.901666\pi$
$992$	−4.44989	+	7.70743i	−0.141284	+	0.244711i
$993$	−10.6799			−0.338918
$994$	−7.40677	−	4.92685i	−0.234929	−	0.156270i
$995$	−25.9638			−0.823106
$996$	3.02446	−	5.23852i	0.0958336	−	0.165989i
$997$	24.4746	+	42.3913i	0.775120	+	1.34255i	0.934727	+	0.355366i	$0.115644\pi$
$997$	24.4746	+	42.3913i	0.775120	+	1.34255i	−0.159608	+	0.987181i	$0.551023\pi$
$998$	3.44451	+	5.96607i	0.109034	+	0.188852i
$999$	−2.91939	+	5.05653i	−0.0923653	+	0.159981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.i.a.1045.1	yes	6
7.2	even	3		8526.2.a.cb.1.3		3
7.4	even	3	inner	1218.2.i.a.697.1	✓	6
7.5	odd	6		8526.2.a.bz.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.i.a.697.1	✓	6	7.4	even	3	inner
1218.2.i.a.1045.1	yes	6	1.1	even	1	trivial
8526.2.a.bz.1.1		3	7.5	odd	6
8526.2.a.cb.1.3		3	7.2	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:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.623490 + 1.07992i) q^{5} +1.00000 q^{6} +(0.167563 - 2.64044i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.623490 - 1.07992i) q^{10} +(1.22252 + 2.11747i) q^{11} +(-0.500000 + 0.866025i) q^{12} -4.13706 q^{13} +(2.20291 + 1.46533i) q^{14} +1.24698 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.955927 + 1.65571i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.92543 - 3.33494i) q^{19} +1.24698 q^{20} +(-2.37047 + 1.17511i) q^{21} -2.44504 q^{22} +(3.48039 - 6.02820i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.72252 + 2.98349i) q^{25} +(2.06853 - 3.58280i) q^{26} +1.00000 q^{27} +(-2.37047 + 1.17511i) q^{28} -1.00000 q^{29} +(-0.623490 + 1.07992i) q^{30} +(-4.44989 - 7.70743i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.22252 - 2.11747i) q^{33} -1.91185 q^{34} +(2.74698 + 1.82724i) q^{35} +1.00000 q^{36} +(-2.91939 + 5.05653i) q^{37} +(1.92543 + 3.33494i) q^{38} +(2.06853 + 3.58280i) q^{39} +(-0.623490 + 1.07992i) q^{40} -6.47219 q^{41} +(0.167563 - 2.64044i) q^{42} -12.7017 q^{43} +(1.22252 - 2.11747i) q^{44} +(-0.623490 - 1.07992i) q^{45} +(3.48039 + 6.02820i) q^{46} +(-0.900969 + 1.56052i) q^{47} +1.00000 q^{48} +(-6.94385 - 0.884879i) q^{49} -3.44504 q^{50} +(0.955927 - 1.65571i) q^{51} +(2.06853 + 3.58280i) q^{52} +(-2.29590 - 3.97661i) q^{53} +(-0.500000 + 0.866025i) q^{54} -3.04892 q^{55} +(0.167563 - 2.64044i) q^{56} -3.85086 q^{57} +(0.500000 - 0.866025i) q^{58} +(-3.55496 - 6.15737i) q^{59} +(-0.623490 - 1.07992i) q^{60} +(2.59030 - 4.48653i) q^{61} +8.89977 q^{62} +(2.20291 + 1.46533i) q^{63} +1.00000 q^{64} +(2.57942 - 4.46768i) q^{65} +(1.22252 + 2.11747i) q^{66} +(0.0196143 + 0.0339730i) q^{67} +(0.955927 - 1.65571i) q^{68} -6.96077 q^{69} +(-2.95593 + 1.46533i) q^{70} -3.36227 q^{71} +(-0.500000 + 0.866025i) q^{72} +(2.01357 + 3.48761i) q^{73} +(-2.91939 - 5.05653i) q^{74} +(1.72252 - 2.98349i) q^{75} -3.85086 q^{76} +(5.79590 - 2.87318i) q^{77} -4.13706 q^{78} +(4.36778 - 7.56522i) q^{79} +(-0.623490 - 1.07992i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.23609 - 5.60508i) q^{82} -6.04892 q^{83} +(2.20291 + 1.46533i) q^{84} -2.38404 q^{85} +(6.35086 - 11.0000i) q^{86} +(0.500000 + 0.866025i) q^{87} +(1.22252 + 2.11747i) q^{88} +(5.62833 - 9.74856i) q^{89} +1.24698 q^{90} +(-0.693218 + 10.9237i) q^{91} -6.96077 q^{92} +(-4.44989 + 7.70743i) q^{93} +(-0.900969 - 1.56052i) q^{94} +(2.40097 + 4.15860i) q^{95} +(-0.500000 + 0.866025i) q^{96} -11.6528 q^{97} +(4.23825 - 5.57111i) q^{98} -2.44504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + q^{5} + 6 q^{6} + 6 q^{8} - 3 q^{9} + q^{10} + 7 q^{11} - 3 q^{12} - 14 q^{13} - 2 q^{15} - 3 q^{16} + 2 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{20} - 14 q^{22} + 8 q^{23}+ \cdots - 14 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + q^5 + 6 * q^6 + 6 * q^8 - 3 * q^9 + q^10 + 7 * q^11 - 3 * q^12 - 14 * q^13 - 2 * q^15 - 3 * q^16 + 2 * q^17 - 3 * q^18 - 2 * q^19 - 2 * q^20 - 14 * q^22 + 8 * q^23 - 3 * q^24 + 10 * q^25 + 7 * q^26 + 6 * q^27 - 6 * q^29 + q^30 - 4 * q^31 - 3 * q^32 + 7 * q^33 - 4 * q^34 + 7 * q^35 + 6 * q^36 + 15 * q^37 - 2 * q^38 + 7 * q^39 + q^40 - 26 * q^41 - 22 * q^43 + 7 * q^44 + q^45 + 8 * q^46 - q^47 + 6 * q^48 - 20 * q^50 + 2 * q^51 + 7 * q^52 + 14 * q^53 - 3 * q^54 + 4 * q^57 + 3 * q^58 - 22 * q^59 + q^60 + 4 * q^61 + 8 * q^62 + 6 * q^64 + 7 * q^65 + 7 * q^66 + 13 * q^67 + 2 * q^68 - 16 * q^69 - 14 * q^70 - 6 * q^71 - 3 * q^72 + 6 * q^73 + 15 * q^74 + 10 * q^75 + 4 * q^76 + 7 * q^77 - 14 * q^78 + 15 * q^79 + q^80 - 3 * q^81 + 13 * q^82 - 18 * q^83 + 6 * q^85 + 11 * q^86 + 3 * q^87 + 7 * q^88 + 7 * q^89 - 2 * q^90 - 35 * q^91 - 16 * q^92 - 4 * q^93 - q^94 + 10 * q^95 - 3 * q^96 - 34 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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