LMFDB - Embedded newform 1218.2.p.b.1159.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(289,1218)] 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("1218.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1218 = 2 \cdot 3 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1218.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1159.18
Character	$\chi$	$=$	1218.1159
Dual form			1218.2.p.b.289.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.110464 + 0.191328i) q^{5} -1.00000 q^{6} +(-1.52713 + 2.16053i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.191328 + 0.110464i) q^{10} +(-0.274800 - 0.158656i) q^{11} +(-0.866025 + 0.500000i) q^{12} -1.21353 q^{13} +(-0.242272 + 2.63464i) q^{14} -0.220927i q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.46212 + 2.57621i) q^{17} +(0.866025 + 0.500000i) q^{18} +(6.73813 - 3.89026i) q^{19} +0.220927 q^{20} +(2.40280 - 1.10750i) q^{21} -0.317311 q^{22} +(1.31488 + 2.27743i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.47560 - 4.28786i) q^{25} +(-1.05094 + 0.606763i) q^{26} -1.00000i q^{27} +(1.10750 + 2.40280i) q^{28} +(2.08334 - 4.96585i) q^{29} +(-0.110464 - 0.191328i) q^{30} +(7.64677 + 4.41486i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.158656 + 0.274800i) q^{33} +5.15241 q^{34} +(-0.582062 - 0.0535244i) q^{35} +1.00000 q^{36} +(-3.27121 + 1.88863i) q^{37} +(3.89026 - 6.73813i) q^{38} +(1.05094 + 0.606763i) q^{39} +(0.191328 - 0.110464i) q^{40} -6.58939i q^{41} +(1.52713 - 2.16053i) q^{42} +11.1579i q^{43} +(-0.274800 + 0.158656i) q^{44} +(-0.110464 + 0.191328i) q^{45} +(2.27743 + 1.31488i) q^{46} +(9.94369 - 5.74099i) q^{47} +1.00000i q^{48} +(-2.33574 - 6.59881i) q^{49} -4.95119i q^{50} +(-2.57621 - 4.46212i) q^{51} +(-0.606763 + 1.05094i) q^{52} +(-3.70604 + 6.41905i) q^{53} +(-0.500000 - 0.866025i) q^{54} -0.0701026i q^{55} +(2.16053 + 1.52713i) q^{56} -7.78053 q^{57} +(-0.678700 - 5.34222i) q^{58} +(0.748385 - 1.29624i) q^{59} +(-0.191328 - 0.110464i) q^{60} +(-2.42457 + 1.39983i) q^{61} +8.82973 q^{62} +(-2.63464 - 0.242272i) q^{63} -1.00000 q^{64} +(-0.134050 - 0.232182i) q^{65} +(0.274800 + 0.158656i) q^{66} +(-4.08337 + 7.07261i) q^{67} +(4.46212 - 2.57621i) q^{68} -2.62975i q^{69} +(-0.530843 + 0.244678i) q^{70} +1.43010 q^{71} +(0.866025 - 0.500000i) q^{72} +(-1.82300 - 1.05251i) q^{73} +(-1.88863 + 3.27121i) q^{74} +(-4.28786 + 2.47560i) q^{75} -7.78053i q^{76} +(0.762434 - 0.351424i) q^{77} +1.21353 q^{78} +(8.74395 - 5.04832i) q^{79} +(0.110464 - 0.191328i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.29469 - 5.70658i) q^{82} +4.86994 q^{83} +(0.242272 - 2.63464i) q^{84} +1.13831i q^{85} +(5.57896 + 9.66304i) q^{86} +(-4.28715 + 3.25888i) q^{87} +(-0.158656 + 0.274800i) q^{88} +(-3.63682 + 2.09972i) q^{89} +0.220927i q^{90} +(1.85321 - 2.62185i) q^{91} +2.62975 q^{92} +(-4.41486 - 7.64677i) q^{93} +(5.74099 - 9.94369i) q^{94} +(1.48864 + 0.859465i) q^{95} +(0.500000 + 0.866025i) q^{96} -5.41085i q^{97} +(-5.32222 - 4.54687i) q^{98} -0.317311i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 22 q^{4} - 44 q^{6} - 8 q^{7} + 22 q^{9} - 16 q^{13} - 22 q^{16} - 4 q^{23} - 22 q^{24} - 22 q^{25} - 4 q^{28} + 4 q^{29} - 16 q^{34} - 10 q^{35} + 44 q^{36} + 4 q^{38} + 8 q^{42} - 52 q^{49} + 8 q^{51}+ \cdots + 22 q^{96}+O(q^{100}) $ 44 * q + 22 * q^4 - 44 * q^6 - 8 * q^7 + 22 * q^9 - 16 * q^13 - 22 * q^16 - 4 * q^23 - 22 * q^24 - 22 * q^25 - 4 * q^28 + 4 * q^29 - 16 * q^34 - 10 * q^35 + 44 * q^36 + 4 * q^38 + 8 * q^42 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 6 * q^53 - 22 * q^54 - 8 * q^57 + 14 * q^58 + 24 * q^59 + 16 * q^62 - 4 * q^63 - 44 * q^64 - 24 * q^65 + 28 * q^67 - 24 * q^71 - 16 * q^74 + 16 * q^78 - 22 * q^81 - 28 * q^83 + 4 * q^86 + 14 * q^87 + 112 * q^91 - 8 * q^92 - 8 * q^93 - 36 * q^94 + 22 * q^96

Character values

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

$n$	$379$	$407$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.110464	+	0.191328i	0.0494008	+	0.0855647i	0.889668	−	0.456607i	$-0.150936\pi$
$5$	0.110464	+	0.191328i	0.0494008	+	0.0855647i	−0.840268	+	0.542172i	$0.817602\pi$
$6$	−1.00000			−0.408248
$7$	−1.52713	+	2.16053i	−0.577201	+	0.816602i
$7$	−1.52713	+	2.16053i	−0.577201	+	0.816602i
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.191328	+	0.110464i	0.0605034	+	0.0349316i
$11$	−0.274800	−	0.158656i	−0.0828552	−	0.0478365i	0.458000	−	0.888952i	$-0.348566\pi$
$11$	−0.274800	−	0.158656i	−0.0828552	−	0.0478365i	−0.540855	+	0.841116i	$0.681899\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	−1.21353			−0.336572			−0.168286	−	0.985738i	$-0.553823\pi$
$13$	−1.21353			−0.336572			−0.168286	+	0.985738i	$0.553823\pi$
$14$	−0.242272	+	2.63464i	−0.0647498	+	0.704136i
$15$		−	0.220927i		−	0.0570431i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.46212	+	2.57621i	1.08222	+	0.624822i	0.931495	−	0.363754i	$-0.118505\pi$
$17$	4.46212	+	2.57621i	1.08222	+	0.624822i	0.150728	+	0.988575i	$0.451838\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	6.73813	−	3.89026i	1.54583	−	0.892488i	0.547381	−	0.836884i	$-0.315625\pi$
$19$	6.73813	−	3.89026i	1.54583	−	0.892488i	0.998453	−	0.0556040i	$-0.0177084\pi$
$20$	0.220927			0.0494008
$21$	2.40280	−	1.10750i	0.524333	−	0.241677i
$22$	−0.317311			−0.0676510
$23$	1.31488	+	2.27743i	0.274171	+	0.474878i	0.969926	−	0.243402i	$-0.0782633\pi$
$23$	1.31488	+	2.27743i	0.274171	+	0.474878i	−0.695755	+	0.718279i	$0.744930\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	2.47560	−	4.28786i	0.495119	−	0.857571i
$26$	−1.05094	+	0.606763i	−0.206107	+	0.118996i
$27$		−	1.00000i		−	0.192450i
$28$	1.10750	+	2.40280i	0.209299	+	0.454086i
$29$	2.08334	−	4.96585i	0.386867	−	0.922136i
$29$	2.08334	−	4.96585i	0.386867	−	0.922136i
$30$	−0.110464	−	0.191328i	−0.0201678	−	0.0349316i
$31$	7.64677	+	4.41486i	1.37340	+	0.792933i	0.991354	−	0.131211i	$-0.0418865\pi$
$31$	7.64677	+	4.41486i	1.37340	+	0.792933i	0.382045	+	0.924144i	$0.375220\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	0.158656	+	0.274800i	0.0276184	+	0.0478365i
$34$	5.15241			0.883631
$35$	−0.582062	−	0.0535244i	−0.0983865	−	0.00904727i
$36$	1.00000			0.166667
$37$	−3.27121	+	1.88863i	−0.537784	+	0.310489i	−0.744180	−	0.667979i	$-0.767160\pi$
$37$	−3.27121	+	1.88863i	−0.537784	+	0.310489i	0.206397	+	0.978468i	$0.433826\pi$
$38$	3.89026	−	6.73813i	0.631084	−	1.09307i
$39$	1.05094	+	0.606763i	0.168286	+	0.0971599i
$40$	0.191328	−	0.110464i	0.0302517	−	0.0174658i
$41$		−	6.58939i		−	1.02909i	−0.857464	−	0.514545i	$-0.827961\pi$
$41$		−	6.58939i		−	1.02909i	0.857464	−	0.514545i	$-0.172039\pi$
$42$	1.52713	−	2.16053i	0.235641	−	0.333376i
$43$			11.1579i			1.70157i	0.525516	+	0.850783i	$0.323872\pi$
$43$			11.1579i			1.70157i	−0.525516	+	0.850783i	$0.676128\pi$
$44$	−0.274800	+	0.158656i	−0.0414276	+	0.0239182i
$45$	−0.110464	+	0.191328i	−0.0164669	+	0.0285216i
$46$	2.27743	+	1.31488i	0.335789	+	0.193868i
$47$	9.94369	−	5.74099i	1.45044	−	0.837410i	0.451931	−	0.892053i	$-0.350735\pi$
$47$	9.94369	−	5.74099i	1.45044	−	0.837410i	0.998506	+	0.0546430i	$0.0174021\pi$
$48$			1.00000i			0.144338i
$49$	−2.33574	−	6.59881i	−0.333677	−	0.942687i
$50$		−	4.95119i		−	0.700204i
$51$	−2.57621	−	4.46212i	−0.360741	−	0.624822i
$52$	−0.606763	+	1.05094i	−0.0841429	+	0.145740i
$53$	−3.70604	+	6.41905i	−0.509064	+	0.881725i	0.490881	+	0.871227i	$0.336675\pi$
$53$	−3.70604	+	6.41905i	−0.509064	+	0.881725i	−0.999945	+	0.0104982i	$0.996658\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		−	0.0701026i		−	0.00945264i
$56$	2.16053	+	1.52713i	0.288712	+	0.204071i
$57$	−7.78053			−1.03056
$58$	−0.678700	−	5.34222i	−0.0891176	−	0.701468i
$59$	0.748385	−	1.29624i	0.0974314	−	0.168756i	−0.813189	−	0.581999i	$-0.802271\pi$
$59$	0.748385	−	1.29624i	0.0974314	−	0.168756i	0.910621	+	0.413243i	$0.135604\pi$
$60$	−0.191328	−	0.110464i	−0.0247004	−	0.0142608i
$61$	−2.42457	+	1.39983i	−0.310434	+	0.179229i	−0.647121	−	0.762387i	$-0.724027\pi$
$61$	−2.42457	+	1.39983i	−0.310434	+	0.179229i	0.336687	+	0.941617i	$0.390694\pi$
$62$	8.82973			1.12138
$63$	−2.63464	−	0.242272i	−0.331933	−	0.0305234i
$64$	−1.00000			−0.125000
$65$	−0.134050	−	0.232182i	−0.0166269	−	0.0287986i
$66$	0.274800	+	0.158656i	0.0338255	+	0.0195292i
$67$	−4.08337	+	7.07261i	−0.498863	+	0.864057i	−0.999999	−	0.00131209i	$-0.999582\pi$
$67$	−4.08337	+	7.07261i	−0.498863	+	0.864057i	0.501136	+	0.865369i	$0.332916\pi$
$68$	4.46212	−	2.57621i	0.541111	−	0.312411i
$69$		−	2.62975i		−	0.316585i
$70$	−0.530843	+	0.244678i	−0.0634479	+	0.0292446i
$71$	1.43010			0.169722			0.0848610	−	0.996393i	$-0.472955\pi$
$71$	1.43010			0.169722			0.0848610	+	0.996393i	$0.472955\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−1.82300	−	1.05251i	−0.213366	−	0.123187i	0.389509	−	0.921023i	$-0.372645\pi$
$73$	−1.82300	−	1.05251i	−0.213366	−	0.123187i	−0.602875	+	0.797836i	$0.705978\pi$
$74$	−1.88863	+	3.27121i	−0.219549	+	0.380270i
$75$	−4.28786	+	2.47560i	−0.495119	+	0.285857i
$76$		−	7.78053i		−	0.892488i
$77$	0.762434	−	0.351424i	0.0868875	−	0.0400484i
$78$	1.21353			0.137405
$79$	8.74395	−	5.04832i	0.983771	−	0.567980i	0.0803645	−	0.996766i	$-0.474392\pi$
$79$	8.74395	−	5.04832i	0.983771	−	0.567980i	0.903407	+	0.428785i	$0.141058\pi$
$80$	0.110464	−	0.191328i	0.0123502	−	0.0213912i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.29469	−	5.70658i	−0.363838	−	0.630186i
$83$	4.86994			0.534545			0.267273	−	0.963621i	$-0.413878\pi$
$83$	4.86994			0.534545			0.267273	+	0.963621i	$0.413878\pi$
$84$	0.242272	−	2.63464i	0.0264340	−	0.287462i
$85$			1.13831i			0.123467i
$86$	5.57896	+	9.66304i	0.601595	+	1.04199i
$87$	−4.28715	+	3.25888i	−0.459631	+	0.349389i
$88$	−0.158656	+	0.274800i	−0.0169127	+	0.0292937i
$89$	−3.63682	+	2.09972i	−0.385502	+	0.222570i	−0.680209	−	0.733018i	$-0.738111\pi$
$89$	−3.63682	+	2.09972i	−0.385502	+	0.222570i	0.294707	+	0.955588i	$0.404778\pi$
$90$			0.220927i			0.0232878i
$91$	1.85321	−	2.62185i	0.194270	−	0.274845i
$92$	2.62975			0.274171
$93$	−4.41486	−	7.64677i	−0.457800	−	0.792933i
$94$	5.74099	−	9.94369i	0.592138	−	1.02561i
$95$	1.48864	+	0.859465i	0.152731	+	0.0881792i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$		−	5.41085i		−	0.549389i	−0.961532	−	0.274694i	$-0.911423\pi$
$97$		−	5.41085i		−	0.549389i	0.961532	−	0.274694i	$-0.0885767\pi$
$98$	−5.32222	−	4.54687i	−0.537625	−	0.459303i
$99$		−	0.317311i		−	0.0318910i
$100$	−2.47560	−	4.28786i	−0.247560	−	0.428786i
$101$	9.02235	+	5.20906i	0.897757	+	0.518320i	0.876472	−	0.481453i	$-0.159891\pi$
$101$	9.02235	+	5.20906i	0.897757	+	0.518320i	0.0212854	+	0.999773i	$0.493224\pi$
$102$	−4.46212	−	2.57621i	−0.441816	−	0.255082i
$103$	−2.33496	−	4.04426i	−0.230070	−	0.398493i	0.727758	−	0.685834i	$-0.240562\pi$
$103$	−2.33496	−	4.04426i	−0.230070	−	0.398493i	−0.957829	+	0.287340i	$0.907229\pi$
$104$			1.21353i			0.118996i
$105$	0.477319	+	0.337385i	0.0465815	+	0.0329254i
$106$			7.41209i			0.719925i
$107$	3.83354	+	6.63989i	0.370602	+	0.641902i	0.989658	−	0.143445i	$-0.0458179\pi$
$107$	3.83354	+	6.63989i	0.370602	+	0.641902i	−0.619056	+	0.785347i	$0.712485\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	−1.47989	+	2.56325i	−0.141748	+	0.245515i	−0.928155	−	0.372194i	$-0.878606\pi$
$109$	−1.47989	+	2.56325i	−0.141748	+	0.245515i	0.786407	+	0.617709i	$0.211939\pi$
$110$	−0.0350513	−	0.0607107i	−0.00334201	−	0.00578853i
$111$	3.77727			0.358522
$112$	2.63464	+	0.242272i	0.248950	+	0.0228925i
$113$		−	10.1377i		−	0.953678i	−0.878991	−	0.476839i	$-0.841782\pi$
$113$		−	10.1377i		−	0.953678i	0.878991	−	0.476839i	$-0.158218\pi$
$114$	−6.73813	+	3.89026i	−0.631084	+	0.364357i
$115$	−0.290492	+	0.503147i	−0.0270885	+	0.0469187i
$116$	−3.25888	−	4.28715i	−0.302580	−	0.398052i
$117$	−0.606763	−	1.05094i	−0.0560953	−	0.0971599i
$118$		−	1.49677i		−	0.137789i
$119$	−12.3802	+	5.70632i	−1.13489	+	0.523097i
$120$	−0.220927			−0.0201678
$121$	−5.44966	−	9.43908i	−0.495423	−	0.858098i
$122$	−1.39983	+	2.42457i	−0.126734	+	0.219510i
$123$	−3.29469	+	5.70658i	−0.297072	+	0.514545i
$124$	7.64677	−	4.41486i	0.686700	−	0.396466i
$125$	2.19849			0.196639
$126$	−2.40280	+	1.10750i	−0.214058	+	0.0986643i
$127$			1.54515i			0.137110i	0.997647	+	0.0685551i	$0.0218389\pi$
$127$			1.54515i			0.137110i	−0.997647	+	0.0685551i	$0.978161\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	5.57896	−	9.66304i	0.491200	−	0.850783i
$130$	−0.232182	−	0.134050i	−0.0203637	−	0.0117570i
$131$	5.14271	−	2.96914i	0.449320	−	0.259415i	−0.258223	−	0.966085i	$-0.583137\pi$
$131$	5.14271	−	2.96914i	0.449320	−	0.259415i	0.707543	+	0.706670i	$0.249804\pi$
$132$	0.317311			0.0276184
$133$	−1.88500	+	20.4989i	−0.163450	+	1.77748i
$134$			8.16674i			0.705499i
$135$	0.191328	−	0.110464i	0.0164669	−	0.00950719i
$136$	2.57621	−	4.46212i	0.220908	−	0.382624i
$137$	3.36335	+	1.94183i	0.287351	+	0.165902i	0.636746	−	0.771073i	$-0.280280\pi$
$137$	3.36335	+	1.94183i	0.287351	+	0.165902i	−0.349396	+	0.936975i	$0.613613\pi$
$138$	−1.31488	−	2.27743i	−0.111930	−	0.193868i
$139$	−20.8867			−1.77158			−0.885792	−	0.464082i	$-0.846384\pi$
$139$	−20.8867			−1.77158			−0.885792	+	0.464082i	$0.846384\pi$
$140$	−0.337385	+	0.477319i	−0.0285142	+	0.0403408i
$141$	−11.4820			−0.966958
$142$	1.23851	−	0.715052i	0.103933	−	0.0600058i
$143$	0.333476	+	0.192533i	0.0278867	+	0.0161004i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	1.18024	−	0.149943i	0.0980138	−	0.0124521i
$146$	−2.10502			−0.174212
$147$	−1.27659	+	6.88261i	−0.105292	+	0.567668i
$148$			3.77727i			0.310489i
$149$	−4.46307	−	7.73027i	−0.365629	−	0.633288i	0.623248	−	0.782024i	$-0.285813\pi$
$149$	−4.46307	−	7.73027i	−0.365629	−	0.633288i	−0.988877	+	0.148736i	$0.952479\pi$
$150$	−2.47560	+	4.28786i	−0.202132	+	0.350102i
$151$	−9.20482	+	15.9432i	−0.749077	+	1.29744i	0.199188	+	0.979961i	$0.436170\pi$
$151$	−9.20482	+	15.9432i	−0.749077	+	1.29744i	−0.948265	+	0.317479i	$0.897164\pi$
$152$	−3.89026	−	6.73813i	−0.315542	−	0.546535i
$153$			5.15241i			0.416548i
$154$	0.484576	−	0.685559i	0.0390482	−	0.0552439i
$155$			1.95073i			0.156686i
$156$	1.05094	−	0.606763i	0.0841429	−	0.0485799i
$157$	7.19216	+	4.15240i	0.573997	+	0.331397i	0.758744	−	0.651389i	$-0.225813\pi$
$157$	7.19216	+	4.15240i	0.573997	+	0.331397i	−0.184747	+	0.982786i	$0.559147\pi$
$158$	5.04832	−	8.74395i	0.401623	−	0.695631i
$159$	6.41905	−	3.70604i	0.509064	−	0.293908i
$160$		−	0.220927i		−	0.0174658i
$161$	−6.92845	−	0.637115i	−0.546038	−	0.0502117i
$162$			1.00000i			0.0785674i
$163$	−17.9970	+	10.3906i	−1.40963	+	0.813851i	−0.995352	−	0.0962987i	$-0.969300\pi$
$163$	−17.9970	+	10.3906i	−1.40963	+	0.813851i	−0.414279	+	0.910150i	$0.635966\pi$
$164$	−5.70658	−	3.29469i	−0.445609	−	0.257272i
$165$	−0.0350513	+	0.0607107i	−0.00272874	+	0.00472632i
$166$	4.21749	−	2.43497i	0.327341	−	0.188990i
$167$	17.1162			1.32449			0.662247	−	0.749286i	$-0.269603\pi$
$167$	17.1162			1.32449			0.662247	+	0.749286i	$0.269603\pi$
$168$	−1.10750	−	2.40280i	−0.0854458	−	0.185380i
$169$	−11.5274			−0.886720
$170$	0.569154	+	0.985803i	0.0436521	+	0.0756076i
$171$	6.73813	+	3.89026i	0.515278	+	0.297496i
$172$	9.66304	+	5.57896i	0.736800	+	0.425392i
$173$	5.90310	+	10.2245i	0.448804	+	0.777352i	0.998309	−	0.0581389i	$-0.0185166\pi$
$173$	5.90310	+	10.2245i	0.448804	+	0.777352i	−0.549504	+	0.835491i	$0.685183\pi$
$174$	−2.08334	+	4.96585i	−0.157938	+	0.376460i
$175$	5.48347	+	11.8967i	0.414511	+	0.899307i
$176$			0.317311i			0.0239182i
$177$	−1.29624	+	0.748385i	−0.0974314	+	0.0562520i
$178$	−2.09972	+	3.63682i	−0.157381	+	0.272591i
$179$	−5.38113	+	9.32038i	−0.402204	+	0.696638i	−0.993992	−	0.109456i	$-0.965089\pi$
$179$	−5.38113	+	9.32038i	−0.402204	+	0.696638i	0.591787	+	0.806094i	$0.298422\pi$
$180$	0.110464	+	0.191328i	0.00823347	+	0.0142608i
$181$	13.7491			1.02196			0.510982	−	0.859591i	$-0.329282\pi$
$181$	13.7491			1.02196			0.510982	+	0.859591i	$0.329282\pi$
$182$	0.294003	−	3.19720i	0.0217929	−	0.236992i
$183$	2.79965			0.206956
$184$	2.27743	−	1.31488i	0.167895	−	0.0969340i
$185$	−0.722699	−	0.417250i	−0.0531339	−	0.0306769i
$186$	−7.64677	−	4.41486i	−0.560688	−	0.323713i
$187$	−0.817459	−	1.41588i	−0.0597785	−	0.103539i
$188$		−	11.4820i		−	0.837410i
$189$	2.16053	+	1.52713i	0.157155	+	0.111082i
$190$	1.71893			0.124704
$191$	7.01329	−	4.04913i	0.507464	−	0.292984i	−0.224327	−	0.974514i	$-0.572018\pi$
$191$	7.01329	−	4.04913i	0.507464	−	0.292984i	0.731791	+	0.681530i	$0.238685\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−20.9307	−	12.0843i	−1.50662	−	0.869850i	−0.999970	−	0.00769983i	$-0.997549\pi$
$193$	−20.9307	−	12.0843i	−1.50662	−	0.869850i	−0.506653	−	0.862150i	$-0.669118\pi$
$194$	−2.70543	−	4.68594i	−0.194238	−	0.336431i
$195$			0.268101i			0.0191991i
$196$	−6.88261	−	1.27659i	−0.491615	−	0.0911853i
$197$	27.2623			1.94236			0.971180	−	0.238349i	$-0.0766061\pi$
$197$	27.2623			1.94236			0.971180	+	0.238349i	$0.0766061\pi$
$198$	−0.158656	−	0.274800i	−0.0112752	−	0.0195292i
$199$	3.70741	−	6.42143i	0.262812	−	0.455203i	−0.704176	−	0.710025i	$-0.748684\pi$
$199$	3.70741	−	6.42143i	0.262812	−	0.455203i	0.966988	+	0.254822i	$0.0820169\pi$
$200$	−4.28786	−	2.47560i	−0.303197	−	0.175051i
$201$	7.07261	−	4.08337i	0.498863	−	0.288019i
$202$	10.4181			0.733016
$203$	7.54732	+	12.0846i	0.529718	+	0.848174i
$204$	−5.15241			−0.360741
$205$	1.26074	−	0.727887i	0.0880537	−	0.0508378i
$206$	−4.04426	−	2.33496i	−0.281777	−	0.162684i
$207$	−1.31488	+	2.27743i	−0.0913903	+	0.158293i
$208$	0.606763	+	1.05094i	0.0420715	+	0.0728699i
$209$	−2.46885			−0.170774
$210$	0.582062	+	0.0535244i	0.0401661	+	0.00369353i
$211$		−	3.11259i		−	0.214280i	−0.994244	−	0.107140i	$-0.965831\pi$
$211$		−	3.11259i		−	0.214280i	0.994244	−	0.107140i	$-0.0341693\pi$
$212$	3.70604	+	6.41905i	0.254532	+	0.440862i
$213$	−1.23851	−	0.715052i	−0.0848610	−	0.0489945i
$214$	6.63989	+	3.83354i	0.453893	+	0.262055i
$215$	−2.13483	+	1.23254i	−0.145594	+	0.0840588i
$216$	−1.00000			−0.0680414
$217$	−21.2160	+	9.77896i	−1.44024	+	0.663839i
$218$			2.95979i			0.200462i
$219$	1.05251	+	1.82300i	0.0711220	+	0.123187i
$220$	−0.0607107	−	0.0350513i	−0.00409311	−	0.00236316i
$221$	−5.41490	−	3.12629i	−0.364245	−	0.210297i
$222$	3.27121	−	1.88863i	0.219549	−	0.126757i
$223$	9.49845			0.636063			0.318032	−	0.948080i	$-0.396978\pi$
$223$	9.49845			0.636063			0.318032	+	0.948080i	$0.396978\pi$
$224$	2.40280	−	1.10750i	0.160544	−	0.0739983i
$225$	4.95119			0.330079
$226$	−5.06887	−	8.77954i	−0.337176	−	0.584006i
$227$	−10.5170	+	18.2160i	−0.698040	+	1.20904i	0.271105	+	0.962550i	$0.412611\pi$
$227$	−10.5170	+	18.2160i	−0.698040	+	1.20904i	−0.969145	+	0.246491i	$0.920722\pi$
$228$	−3.89026	+	6.73813i	−0.257639	+	0.446244i
$229$	−22.1527	+	12.7898i	−1.46389	+	0.845176i	−0.999188	−	0.0402915i	$-0.987171\pi$
$229$	−22.1527	+	12.7898i	−1.46389	+	0.845176i	−0.464701	+	0.885468i	$0.653838\pi$
$230$			0.580984i			0.0383090i
$231$	−0.835999	−	0.0768755i	−0.0550047	−	0.00505804i
$232$	−4.96585	−	2.08334i	−0.326024	−	0.136778i
$233$	−3.81968	−	6.61588i	−0.250236	−	0.433421i	0.713355	−	0.700803i	$-0.247175\pi$
$233$	−3.81968	−	6.61588i	−0.250236	−	0.433421i	−0.963591	+	0.267382i	$0.913841\pi$
$234$	−1.05094	−	0.606763i	−0.0687024	−	0.0396653i
$235$	2.19683	+	1.26834i	0.143305	+	0.0827374i
$236$	−0.748385	−	1.29624i	−0.0487157	−	0.0843781i
$237$	−10.0966			−0.655847
$238$	−7.86841	+	11.1319i	−0.510033	+	0.721575i
$239$	0.712097			0.0460617			0.0230309	−	0.999735i	$-0.492668\pi$
$239$	0.712097			0.0460617			0.0230309	+	0.999735i	$0.492668\pi$
$240$	−0.191328	+	0.110464i	−0.0123502	+	0.00713039i
$241$	−13.8541	+	23.9959i	−0.892418	+	1.54571i	−0.0554500	+	0.998461i	$0.517659\pi$
$241$	−13.8541	+	23.9959i	−0.892418	+	1.54571i	−0.836968	+	0.547252i	$0.815674\pi$
$242$	−9.43908	−	5.44966i	−0.606767	−	0.350317i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$			2.79965i			0.179229i
$245$	1.00453	−	1.17582i	0.0641768	−	0.0751205i
$246$			6.58939i			0.420124i
$247$	−8.17690	+	4.72094i	−0.520284	+	0.300386i
$248$	4.41486	−	7.64677i	0.280344	−	0.485570i
$249$	−4.21749	−	2.43497i	−0.267273	−	0.154310i
$250$	1.90395	−	1.09924i	0.120416	−	0.0695223i
$251$			15.1349i			0.955308i	0.878548	+	0.477654i	$0.158513\pi$
$251$			15.1349i			0.955308i	−0.878548	+	0.477654i	$0.841487\pi$
$252$	−1.52713	+	2.16053i	−0.0962002	+	0.136100i
$253$		−	0.834451i		−	0.0524615i
$254$	0.772576	+	1.33814i	0.0484757	+	0.0839624i
$255$	0.569154	−	0.985803i	0.0356418	−	0.0617334i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.9550	−	20.7067i	−0.745735	−	1.29165i	−0.949851	−	0.312704i	$-0.898765\pi$
$257$	−11.9550	−	20.7067i	−0.745735	−	1.29165i	0.204116	−	0.978947i	$-0.434568\pi$
$258$		−	11.1579i		−	0.694662i
$259$	0.915125	−	9.95172i	0.0568631	−	0.618370i
$260$	−0.268101			−0.0166269
$261$	5.34222	−	0.678700i	0.330675	−	0.0420105i
$262$	2.96914	−	5.14271i	0.183434	−	0.317718i
$263$	−27.2423	−	15.7284i	−1.67983	−	0.969852i	−0.961764	−	0.273881i	$-0.911693\pi$
$263$	−27.2423	−	15.7284i	−1.67983	−	0.969852i	−0.718070	−	0.695971i	$-0.754974\pi$
$264$	0.274800	−	0.158656i	0.0169127	−	0.00976458i
$265$	−1.63753			−0.100593
$266$	8.61697	+	18.6950i	0.528340	+	1.14627i
$267$	4.19944			0.257001
$268$	4.08337	+	7.07261i	0.249432	+	0.432028i
$269$	−12.6806	−	7.32116i	−0.773152	−	0.446379i	0.0608462	−	0.998147i	$-0.480620\pi$
$269$	−12.6806	−	7.32116i	−0.773152	−	0.446379i	−0.833998	+	0.551768i	$0.813953\pi$
$270$	0.110464	−	0.191328i	0.00672260	−	0.0116439i
$271$	4.59414	−	2.65243i	0.279074	−	0.161123i	−0.353930	−	0.935272i	$-0.615155\pi$
$271$	4.59414	−	2.65243i	0.279074	−	0.161123i	0.633004	+	0.774148i	$0.281822\pi$
$272$		−	5.15241i		−	0.312411i
$273$	−2.91586	+	1.34399i	−0.176476	+	0.0813417i
$274$	3.88367			0.234621
$275$	−1.36059	+	0.785534i	−0.0820464	+	0.0473695i
$276$	−2.27743	−	1.31488i	−0.137085	−	0.0791463i
$277$	−13.7879	+	23.8814i	−0.828437	+	1.43489i	0.0708274	+	0.997489i	$0.477436\pi$
$277$	−13.7879	+	23.8814i	−0.828437	+	1.43489i	−0.899264	+	0.437406i	$0.855897\pi$
$278$	−18.0884	+	10.4433i	−1.08487	+	0.626350i
$279$			8.82973i			0.528622i
$280$	−0.0535244	+	0.582062i	−0.00319869	+	0.0347849i
$281$	15.5471			0.927465			0.463732	−	0.885975i	$-0.346510\pi$
$281$	15.5471			0.927465			0.463732	+	0.885975i	$0.346510\pi$
$282$	−9.94369	+	5.74099i	−0.592138	+	0.341871i
$283$	10.0635	−	17.4305i	0.598213	−	1.03613i	−0.394872	−	0.918736i	$-0.629211\pi$
$283$	10.0635	−	17.4305i	0.598213	−	1.03613i	0.993085	−	0.117398i	$-0.0374555\pi$
$284$	0.715052	−	1.23851i	0.0424305	−	0.0734918i
$285$	−0.859465	−	1.48864i	−0.0509103	−	0.0881792i
$286$	0.385065			0.0227694
$287$	14.2365	+	10.0629i	0.840356	+	0.593992i
$288$		−	1.00000i		−	0.0589256i
$289$	4.77367	+	8.26824i	0.280804	+	0.486367i
$290$	0.947148	−	0.719976i	0.0556185	−	0.0422784i
$291$	−2.70543	+	4.68594i	−0.158595	+	0.274694i
$292$	−1.82300	+	1.05251i	−0.106683	+	0.0615934i
$293$		−	21.8552i		−	1.27679i	−0.769707	−	0.638397i	$-0.779598\pi$
$293$		−	21.8552i		−	1.27679i	0.769707	−	0.638397i	$-0.220402\pi$
$294$	2.33574	+	6.59881i	0.136223	+	0.384851i
$295$	0.330677			0.0192528
$296$	1.88863	+	3.27121i	0.109775	+	0.190135i
$297$	−0.158656	+	0.274800i	−0.00920613	+	0.0159455i
$298$	−7.73027	−	4.46307i	−0.447802	−	0.258539i
$299$	−1.59564	−	2.76373i	−0.0922781	−	0.159830i
$300$			4.95119i			0.285857i
$301$	−24.1070	−	17.0396i	−1.38950	−	0.982147i
$302$			18.4096i			1.05936i
$303$	−5.20906	−	9.02235i	−0.299252	−	0.518320i
$304$	−6.73813	−	3.89026i	−0.386458	−	0.223122i
$305$	−0.535653	−	0.309259i	−0.0306714	−	0.0177081i
$306$	2.57621	+	4.46212i	0.147272	+	0.255082i
$307$		−	29.8609i		−	1.70425i	−0.523336	−	0.852126i	$-0.675313\pi$
$307$		−	29.8609i		−	1.70425i	0.523336	−	0.852126i	$-0.324687\pi$
$308$	0.0768755	−	0.835999i	0.00438039	−	0.0476355i
$309$			4.66991i			0.265662i
$310$	0.975363	+	1.68938i	0.0553969	+	0.0959502i
$311$	−8.03916	−	4.64141i	−0.455859	−	0.263190i	0.254442	−	0.967088i	$-0.418108\pi$
$311$	−8.03916	−	4.64141i	−0.455859	−	0.263190i	−0.710302	+	0.703898i	$0.751441\pi$
$312$	0.606763	−	1.05094i	0.0343512	−	0.0594980i
$313$	7.84599	+	13.5897i	0.443482	+	0.768133i	0.997945	−	0.0640754i	$-0.0204098\pi$
$313$	7.84599	+	13.5897i	0.443482	+	0.768133i	−0.554463	+	0.832208i	$0.687076\pi$
$314$	8.30479			0.468667
$315$	−0.244678	−	0.530843i	−0.0137860	−	0.0299096i
$316$		−	10.0966i		−	0.567980i
$317$	6.68217	−	3.85795i	0.375308	−	0.216684i	−0.300467	−	0.953792i	$-0.597142\pi$
$317$	6.68217	−	3.85795i	0.375308	−	0.216684i	0.675775	+	0.737108i	$0.263809\pi$
$318$	3.70604	−	6.41905i	0.207825	−	0.359963i
$319$	−1.36036	+	1.03408i	−0.0761656	+	0.0578974i
$320$	−0.110464	−	0.191328i	−0.00617510	−	0.0106956i
$321$		−	7.66708i		−	0.427935i
$322$	−6.31877	+	2.91246i	−0.352131	+	0.162305i
$323$	40.0885			2.23058
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−3.00420	+	5.20343i	−0.166643	+	0.288634i
$326$	−10.3906	+	17.9970i	−0.575480	+	0.996760i
$327$	2.56325	−	1.47989i	0.141748	−	0.0818383i
$328$	−6.58939			−0.363838
$329$	−2.78176	+	30.2509i	−0.153363	+	1.66778i
$330$			0.0701026i			0.00385902i
$331$	3.81163	−	2.20065i	0.209506	−	0.120958i	−0.391576	−	0.920146i	$-0.628070\pi$
$331$	3.81163	−	2.20065i	0.209506	−	0.120958i	0.601082	+	0.799187i	$0.294737\pi$
$332$	2.43497	−	4.21749i	0.133636	−	0.231465i
$333$	−3.27121	−	1.88863i	−0.179261	−	0.103496i
$334$	14.8231	−	8.55811i	0.811083	−	0.468279i
$335$	−1.80425			−0.0985770
$336$	−2.16053	−	1.52713i	−0.117866	−	0.0833118i
$337$			20.9678i			1.14219i	0.820885	+	0.571093i	$0.193481\pi$
$337$			20.9678i			1.14219i	−0.820885	+	0.571093i	$0.806519\pi$
$338$	−9.98298	+	5.76368i	−0.543003	+	0.313503i
$339$	−5.06887	+	8.77954i	−0.275303	+	0.476839i
$340$	0.985803	+	0.569154i	0.0534627	+	0.0308667i
$341$	−1.40089	−	2.42640i	−0.0758622	−	0.131397i
$342$	7.78053			0.420723
$343$	17.8239	+	5.03082i	0.962399	+	0.271639i
$344$	11.1579			0.601595
$345$	0.503147	−	0.290492i	0.0270885	−	0.0156396i
$346$	10.2245	+	5.90310i	0.549671	+	0.317353i
$347$	−5.98823	+	10.3719i	−0.321465	+	0.556794i	−0.980791	−	0.195064i	$-0.937509\pi$
$347$	−5.98823	+	10.3719i	−0.321465	+	0.556794i	0.659326	+	0.751858i	$0.270842\pi$
$348$	0.678700	+	5.34222i	0.0363821	+	0.286373i
$349$	−15.4664			−0.827899			−0.413949	−	0.910300i	$-0.635851\pi$
$349$	−15.4664			−0.827899			−0.413949	+	0.910300i	$0.635851\pi$
$350$	10.6972	+	7.56112i	0.571788	+	0.404159i
$351$			1.21353i			0.0647732i
$352$	0.158656	+	0.274800i	0.00845637	+	0.0146469i
$353$	11.1355	−	19.2873i	0.592683	−	1.02656i	−0.401186	−	0.915997i	$-0.631402\pi$
$353$	11.1355	−	19.2873i	0.592683	−	1.02656i	0.993869	−	0.110561i	$-0.0352647\pi$
$354$	−0.748385	+	1.29624i	−0.0397762	+	0.0688944i
$355$	0.157974	+	0.273620i	0.00838441	+	0.0145222i
$356$			4.19944i			0.222570i
$357$	13.5747	+	1.24828i	0.718451	+	0.0660661i
$358$			10.7623i			0.568803i
$359$	20.0728	−	11.5890i	1.05940	−	0.611646i	0.134136	−	0.990963i	$-0.457174\pi$
$359$	20.0728	−	11.5890i	1.05940	−	0.611646i	0.925267	+	0.379317i	$0.123841\pi$
$360$	0.191328	+	0.110464i	0.0100839	+	0.00582194i
$361$	20.7683	−	35.9717i	1.09307	−	1.89325i
$362$	11.9071	−	6.87456i	0.625823	−	0.361319i
$363$			10.8993i			0.572066i
$364$	−1.34399	−	2.91586i	−0.0704440	−	0.152832i
$365$		−	0.465055i		−	0.0243421i
$366$	2.42457	−	1.39983i	0.126734	−	0.0731701i
$367$	−20.0834	−	11.5952i	−1.04835	−	0.605263i	−0.126160	−	0.992010i	$-0.540265\pi$
$367$	−20.0834	−	11.5952i	−1.04835	−	0.605263i	−0.922186	+	0.386747i	$0.873599\pi$
$368$	1.31488	−	2.27743i	0.0685427	−	0.118719i
$369$	5.70658	−	3.29469i	0.297072	−	0.171515i
$370$	−0.834501			−0.0433836
$371$	−8.20892	−	17.8097i	−0.426186	−	0.924636i
$372$	−8.82973			−0.457800
$373$	−11.3787	−	19.7084i	−0.589165	−	1.02046i	−0.994342	−	0.106226i	$-0.966123\pi$
$373$	−11.3787	−	19.7084i	−0.589165	−	1.02046i	0.405177	−	0.914238i	$-0.367210\pi$
$374$	−1.41588	−	0.817459i	−0.0732134	−	0.0422698i
$375$	−1.90395	−	1.09924i	−0.0983194	−	0.0567647i
$376$	−5.74099	−	9.94369i	−0.296069	−	0.512807i
$377$	−2.52819	+	6.02619i	−0.130208	+	0.310365i
$378$	2.63464	+	0.242272i	0.135511	+	0.0124611i
$379$		−	1.86376i		−	0.0957350i	−0.998854	−	0.0478675i	$-0.984757\pi$
$379$		−	1.86376i		−	0.0957350i	0.998854	−	0.0478675i	$-0.0152425\pi$
$380$	1.48864	−	0.859465i	0.0763654	−	0.0440896i
$381$	0.772576	−	1.33814i	0.0395803	−	0.0685551i
$382$	4.04913	−	7.01329i	0.207171	−	0.358831i
$383$	17.1755	+	29.7489i	0.877628	+	1.52010i	0.853937	+	0.520377i	$0.174208\pi$
$383$	17.1755	+	29.7489i	0.877628	+	1.52010i	0.0236910	+	0.999719i	$0.492458\pi$
$384$	1.00000			0.0510310
$385$	0.151459	+	0.107056i	0.00771904	+	0.00545607i
$386$	−24.1687			−1.23015
$387$	−9.66304	+	5.57896i	−0.491200	+	0.283594i
$388$	−4.68594	−	2.70543i	−0.237892	−	0.137347i
$389$	−24.6108	−	14.2091i	−1.24782	−	0.720428i	−0.277144	−	0.960829i	$-0.589388\pi$
$389$	−24.6108	−	14.2091i	−1.24782	−	0.720428i	−0.970674	+	0.240401i	$0.922721\pi$
$390$	0.134050	+	0.232182i	0.00678791	+	0.0117570i
$391$			13.5496i			0.685232i
$392$	−6.59881	+	2.33574i	−0.333290	+	0.117973i
$393$	−5.93829			−0.299547
$394$	23.6099	−	13.6312i	1.18945	−	0.686728i
$395$	1.93177	+	1.11531i	0.0971981	+	0.0561174i
$396$	−0.274800	−	0.158656i	−0.0138092	−	0.00797274i
$397$	9.94309	+	17.2219i	0.499029	+	0.864344i	0.999999	−	0.00112060i	$-0.000356698\pi$
$397$	9.94309	+	17.2219i	0.499029	+	0.864344i	−0.500970	+	0.865465i	$0.667023\pi$
$398$		−	7.41483i		−	0.371672i
$399$	11.8819	−	16.8100i	0.594838	−	0.841554i
$400$	−4.95119			−0.247560
$401$	−8.82036	−	15.2773i	−0.440468	−	0.762912i	0.557257	−	0.830340i	$-0.311854\pi$
$401$	−8.82036	−	15.2773i	−0.440468	−	0.762912i	−0.997724	+	0.0674282i	$0.978521\pi$
$402$	4.08337	−	7.07261i	0.203660	−	0.352750i
$403$	−9.27955	−	5.35755i	−0.462247	−	0.266879i
$404$	9.02235	−	5.20906i	0.448879	−	0.259160i
$405$	−0.220927			−0.0109780
$406$	12.5785	+	6.69193i	0.624259	+	0.332115i
$407$	1.19857			0.0594109
$408$	−4.46212	+	2.57621i	−0.220908	+	0.127541i
$409$	−2.93279	−	1.69324i	−0.145017	−	0.0837256i	0.425736	−	0.904847i	$-0.360015\pi$
$409$	−2.93279	−	1.69324i	−0.145017	−	0.0837256i	−0.570753	+	0.821122i	$0.693349\pi$
$410$	0.727887	−	1.26074i	0.0359478	−	0.0622634i
$411$	−1.94183	−	3.36335i	−0.0957836	−	0.165902i
$412$	−4.66991			−0.230070
$413$	1.65768	+	3.59643i	0.0815690	+	0.176969i
$414$			2.62975i			0.129245i
$415$	0.537951	+	0.931758i	0.0264070	+	0.0457382i
$416$	1.05094	+	0.606763i	0.0515268	+	0.0297490i
$417$	18.0884	+	10.4433i	0.885792	+	0.511412i
$418$	−2.13809	+	1.23442i	−0.104577	+	0.0603777i
$419$	−4.65875			−0.227595			−0.113797	−	0.993504i	$-0.536301\pi$
$419$	−4.65875			−0.227595			−0.113797	+	0.993504i	$0.536301\pi$
$420$	0.530843	−	0.244678i	0.0259025	−	0.0119391i
$421$			13.7311i			0.669214i	0.942358	+	0.334607i	$0.108604\pi$
$421$			13.7311i			0.669214i	−0.942358	+	0.334607i	$0.891396\pi$
$422$	−1.55630	−	2.69558i	−0.0757593	−	0.131219i
$423$	9.94369	+	5.74099i	0.483479	+	0.279137i
$424$	6.41905	+	3.70604i	0.311737	+	0.179981i
$425$	22.0928	−	12.7553i	1.07166	−	0.618722i
$426$	−1.43010			−0.0692887
$427$	0.678276	−	7.37606i	0.0328241	−	0.356953i
$428$	7.66708			0.370602
$429$	−0.192533	−	0.333476i	−0.00929557	−	0.0161004i
$430$	−1.23254	+	2.13483i	−0.0594385	+	0.102951i
$431$	0.0345413	−	0.0598273i	0.00166380	−	0.00288178i	−0.865192	−	0.501440i	$-0.832804\pi$
$431$	0.0345413	−	0.0598273i	0.00166380	−	0.00288178i	0.866856	+	0.498558i	$0.166137\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$		−	25.5734i		−	1.22898i	−0.788924	−	0.614491i	$-0.789362\pi$
$433$		−	25.5734i		−	1.22898i	0.788924	−	0.614491i	$-0.210638\pi$
$434$	−13.4841	+	19.0768i	−0.647260	+	0.915718i
$435$	−1.09709	−	0.460267i	−0.0526015	−	0.0220681i
$436$	1.47989	+	2.56325i	0.0708741	+	0.122758i
$437$	17.7196	+	10.2304i	0.847645	+	0.489388i
$438$	1.82300	+	1.05251i	0.0871062	+	0.0502908i
$439$	13.8168	+	23.9314i	0.659441	+	1.14219i	0.980761	+	0.195215i	$0.0625403\pi$
$439$	13.8168	+	23.9314i	0.659441	+	1.14219i	−0.321319	+	0.946971i	$0.604126\pi$
$440$	−0.0701026			−0.00334201
$441$	4.54687	−	5.32222i	0.216518	−	0.253439i
$442$	−6.25259			−0.297405
$443$	−10.8619	+	6.27111i	−0.516063	+	0.297949i	−0.735322	−	0.677717i	$-0.762969\pi$
$443$	−10.8619	+	6.27111i	−0.516063	+	0.297949i	0.219259	+	0.975667i	$0.429636\pi$
$444$	1.88863	−	3.27121i	0.0896306	−	0.155245i
$445$	−0.803472	−	0.463885i	−0.0380882	−	0.0219903i
$446$	8.22590	−	4.74922i	0.389508	−	0.224882i
$447$			8.92615i			0.422192i
$448$	1.52713	−	2.16053i	0.0721502	−	0.102075i
$449$			30.7618i			1.45174i	0.687832	+	0.725870i	$0.258563\pi$
$449$			30.7618i			1.45174i	−0.687832	+	0.725870i	$0.741437\pi$
$450$	4.28786	−	2.47560i	0.202132	−	0.116701i
$451$	−1.04544	+	1.81076i	−0.0492280	+	0.0852654i
$452$	−8.77954	−	5.06887i	−0.412955	−	0.238420i
$453$	15.9432	−	9.20482i	0.749077	−	0.432480i
$454$			21.0341i			0.987178i
$455$	0.706348	+	0.0649532i	0.0331141	+	0.00304505i
$456$			7.78053i			0.364357i
$457$	−5.35170	−	9.26942i	−0.250342	−	0.433605i	0.713278	−	0.700881i	$-0.247210\pi$
$457$	−5.35170	−	9.26942i	−0.250342	−	0.433605i	−0.963620	+	0.267276i	$0.913876\pi$
$458$	−12.7898	+	22.1527i	−0.597630	+	1.03513i
$459$	2.57621	−	4.46212i	0.120247	−	0.208274i
$460$	0.290492	+	0.503147i	0.0135443	+	0.0234593i
$461$		−	24.7437i		−	1.15243i	−0.817299	−	0.576214i	$-0.804530\pi$
$461$		−	24.7437i		−	1.15243i	0.817299	−	0.576214i	$-0.195470\pi$
$462$	−0.762434	+	0.351424i	−0.0354717	+	0.0163497i
$463$	12.6567			0.588209			0.294104	−	0.955773i	$-0.404979\pi$
$463$	12.6567			0.588209			0.294104	+	0.955773i	$0.404979\pi$
$464$	−5.34222	+	0.678700i	−0.248007	+	0.0315078i
$465$	0.975363	−	1.68938i	0.0452314	−	0.0783430i
$466$	−6.61588	−	3.81968i	−0.306475	−	0.176943i
$467$	14.3675	−	8.29506i	0.664847	−	0.383850i	−0.129274	−	0.991609i	$-0.541265\pi$
$467$	14.3675	−	8.29506i	0.664847	−	0.383850i	0.794121	+	0.607759i	$0.207931\pi$
$468$	−1.21353			−0.0560953
$469$	−9.04470	−	19.6230i	−0.417646	−	0.906107i
$470$	2.53668			0.117008
$471$	−4.15240	−	7.19216i	−0.191332	−	0.331397i
$472$	−1.29624	−	0.748385i	−0.0596643	−	0.0344472i
$473$	1.77027	−	3.06619i	0.0813969	−	0.140984i
$474$	−8.74395	+	5.04832i	−0.401623	+	0.231877i
$475$		−	38.5229i		−	1.76755i
$476$	−1.24828	+	13.5747i	−0.0572150	+	0.622196i
$477$	−7.41209			−0.339376
$478$	0.616694	−	0.356049i	0.0282069	−	0.0162853i
$479$	8.83435	+	5.10051i	0.403652	+	0.233048i	0.688058	−	0.725655i	$-0.258463\pi$
$479$	8.83435	+	5.10051i	0.403652	+	0.233048i	−0.284407	+	0.958704i	$0.591797\pi$
$480$	−0.110464	+	0.191328i	−0.00504195	+	0.00873291i
$481$	3.96970	−	2.29191i	0.181003	−	0.104502i
$482$			27.7081i			1.26207i
$483$	5.68165	+	4.01598i	0.258524	+	0.182733i
$484$	−10.8993			−0.495423
$485$	1.03525	−	0.597702i	0.0470083	−	0.0271403i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−8.21529	+	14.2293i	−0.372270	+	0.644791i	−0.989914	−	0.141667i	$-0.954754\pi$
$487$	−8.21529	+	14.2293i	−0.372270	+	0.644791i	0.617644	+	0.786458i	$0.288087\pi$
$488$	1.39983	+	2.42457i	0.0633671	+	0.109755i
$489$	20.7811			0.939754
$490$	0.282034	−	1.52055i	0.0127410	−	0.0686917i
$491$		−	25.4101i		−	1.14674i	−0.819295	−	0.573372i	$-0.805635\pi$
$491$		−	25.4101i		−	1.14674i	0.819295	−	0.573372i	$-0.194365\pi$
$492$	3.29469	+	5.70658i	0.148536	+	0.257272i
$493$	22.0892	−	16.7911i	0.994846	−	0.756233i
$494$	−4.72094	+	8.17690i	−0.212405	+	0.367896i
$495$	0.0607107	−	0.0350513i	0.00272874	−	0.00157544i
$496$		−	8.82973i		−	0.396466i
$497$	−2.18396	+	3.08978i	−0.0979638	+	0.138595i
$498$	−4.86994			−0.218227
$499$	−4.72862	−	8.19021i	−0.211682	−	0.366644i	0.740559	−	0.671991i	$-0.234561\pi$
$499$	−4.72862	−	8.19021i	−0.211682	−	0.366644i	−0.952241	+	0.305347i	$0.901227\pi$
$500$	1.09924	−	1.90395i	0.0491597	−	0.0851471i
$501$	−14.8231	−	8.55811i	−0.662247	−	0.382348i
$502$	7.56746	+	13.1072i	0.337752	+	0.585004i
$503$			31.1591i			1.38931i	0.719341	+	0.694657i	$0.244444\pi$
$503$			31.1591i			1.38931i	−0.719341	+	0.694657i	$0.755556\pi$
$504$	−0.242272	+	2.63464i	−0.0107916	+	0.117356i
$505$			2.30164i			0.102422i
$506$	−0.417225	−	0.722655i	−0.0185479	−	0.0321260i
$507$	9.98298	+	5.76368i	0.443360	+	0.255974i
$508$	1.33814	+	0.772576i	0.0593704	+	0.0342775i
$509$	−14.4714	−	25.0652i	−0.641434	−	1.11100i	−0.985113	−	0.171909i	$-0.945007\pi$
$509$	−14.4714	−	25.0652i	−0.641434	−	1.11100i	0.343679	−	0.939087i	$-0.388327\pi$
$510$		−	1.13831i		−	0.0504051i
$511$	5.05793	−	2.33132i	0.223750	−	0.103131i
$512$			1.00000i			0.0441942i
$513$	−3.89026	−	6.73813i	−0.171759	−	0.297496i
$514$	−20.7067	−	11.9550i	−0.913335	−	0.527314i
$515$	0.515855	−	0.893487i	0.0227313	−	0.0393718i
$516$	−5.57896	−	9.66304i	−0.245600	−	0.425392i
$517$	−3.64336			−0.160235
$518$	−4.18334	−	9.07601i	−0.183805	−	0.398777i
$519$		−	11.8062i		−	0.518235i
$520$	−0.232182	+	0.134050i	−0.0101819	+	0.00587850i
$521$	−6.22505	+	10.7821i	−0.272724	+	0.472373i	−0.969559	−	0.244860i	$-0.921258\pi$
$521$	−6.22505	+	10.7821i	−0.272724	+	0.472373i	0.696834	+	0.717232i	$0.254591\pi$
$522$	4.28715	−	3.25888i	0.187644	−	0.142637i
$523$	−13.0842	−	22.6625i	−0.572133	−	0.990963i	−0.996347	−	0.0854009i	$-0.972783\pi$
$523$	−13.0842	−	22.6625i	−0.572133	−	0.990963i	0.424214	−	0.905562i	$-0.360550\pi$
$524$		−	5.93829i		−	0.259415i
$525$	1.19953	−	13.0446i	0.0523519	−	0.569312i
$526$	−31.4567			−1.37158
$527$	22.7472	+	39.3993i	0.990883	+	1.71626i
$528$	0.158656	−	0.274800i	0.00690460	−	0.0119591i
$529$	8.04220	−	13.9295i	0.349661	−	0.605630i
$530$	−1.41814	+	0.818765i	−0.0616002	+	0.0355649i
$531$	1.49677			0.0649543
$532$	16.8100	+	11.8819i	0.728807	+	0.515145i
$533$			7.99639i			0.346362i
$534$	3.63682	−	2.09972i	0.157381	−	0.0908637i
$535$	−0.846933	+	1.46693i	−0.0366161	+	0.0634210i
$536$	7.07261	+	4.08337i	0.305490	+	0.176375i
$537$	9.32038	−	5.38113i	0.402204	−	0.232213i
$538$	−14.6423			−0.631276
$539$	−0.405078	+	2.18393i	−0.0174479	+	0.0940685i
$540$		−	0.220927i		−	0.00950719i
$541$	−30.1452	+	17.4044i	−1.29604	+	0.748272i	−0.979719	−	0.200379i	$-0.935783\pi$
$541$	−30.1452	+	17.4044i	−1.29604	+	0.748272i	−0.316326	+	0.948650i	$0.602449\pi$
$542$	2.65243	−	4.59414i	0.113931	−	0.197335i
$543$	−11.9071	−	6.87456i	−0.510982	−	0.295016i
$544$	−2.57621	−	4.46212i	−0.110454	−	0.191312i
$545$	−0.653897			−0.0280099
$546$	−1.85321	+	2.62185i	−0.0793102	+	0.112205i
$547$	−1.93713			−0.0828258			−0.0414129	−	0.999142i	$-0.513186\pi$
$547$	−1.93713			−0.0828258			−0.0414129	+	0.999142i	$0.513186\pi$
$548$	3.36335	−	1.94183i	0.143675	−	0.0829510i
$549$	−2.42457	−	1.39983i	−0.103478	−	0.0597431i
$550$	−0.785534	+	1.36059i	−0.0334953	+	0.0580155i
$551$	−5.28064	−	41.5653i	−0.224963	−	1.77074i
$552$	−2.62975			−0.111930
$553$	−2.44613	+	26.6010i	−0.104020	+	1.13119i
$554$			27.5759i			1.17159i
$555$	0.417250	+	0.722699i	0.0177113	+	0.0306769i
$556$	−10.4433	+	18.0884i	−0.442896	+	0.767119i
$557$	6.40858	−	11.1000i	0.271540	−	0.470322i	−0.697716	−	0.716374i	$-0.745800\pi$
$557$	6.40858	−	11.1000i	0.271540	−	0.470322i	0.969256	+	0.246053i	$0.0791336\pi$
$558$	4.41486	+	7.64677i	0.186896	+	0.323713i
$559$		−	13.5404i		−	0.572699i
$560$	0.244678	+	0.530843i	0.0103395	+	0.0224322i
$561$			1.63492i			0.0690263i
$562$	13.4642	−	7.77357i	0.567954	−	0.327908i
$563$	23.6196	+	13.6368i	0.995448	+	0.574722i	0.906898	−	0.421350i	$-0.138443\pi$
$563$	23.6196	+	13.6368i	0.995448	+	0.574722i	0.0885496	+	0.996072i	$0.471777\pi$
$564$	−5.74099	+	9.94369i	−0.241739	+	0.418705i
$565$	1.93964	−	1.11985i	0.0816012	−	0.0471125i
$566$		−	20.1270i		−	0.846000i
$567$	−1.10750	−	2.40280i	−0.0465108	−	0.100908i
$568$		−	1.43010i		−	0.0600058i
$569$	15.8085	−	9.12706i	0.662728	−	0.382626i	−0.130588	−	0.991437i	$-0.541686\pi$
$569$	15.8085	−	9.12706i	0.662728	−	0.382626i	0.793316	+	0.608811i	$0.208353\pi$
$570$	−1.48864	−	0.859465i	−0.0623521	−	0.0359990i
$571$	−8.84380	+	15.3179i	−0.370101	+	0.641035i	−0.989581	−	0.143978i	$-0.954010\pi$
$571$	−8.84380	+	15.3179i	−0.370101	+	0.641035i	0.619479	+	0.785013i	$0.287344\pi$
$572$	0.333476	−	0.192533i	0.0139434	−	0.00805020i
$573$	−8.09825			−0.338309
$574$	17.3606	+	1.59642i	0.724619	+	0.0666333i
$575$	13.0204			0.542989
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	9.37504	+	5.41268i	0.390288	+	0.225333i	0.682285	−	0.731086i	$-0.260986\pi$
$577$	9.37504	+	5.41268i	0.390288	+	0.225333i	−0.291997	+	0.956419i	$0.594320\pi$
$578$	8.26824	+	4.77367i	0.343913	+	0.198558i
$579$	12.0843	+	20.9307i	0.502208	+	0.869850i
$580$	0.460267	−	1.09709i	0.0191115	−	0.0455542i
$581$	−7.43703	+	10.5216i	−0.308540	+	0.436511i
$582$			5.41085i			0.224287i
$583$	2.03684	−	1.17597i	0.0843572	−	0.0487037i
$584$	−1.05251	+	1.82300i	−0.0435531	+	0.0754362i
$585$	0.134050	−	0.232182i	0.00554230	−	0.00959955i
$586$	−10.9276	−	18.9272i	−0.451415	−	0.781874i
$587$	−31.4402			−1.29767			−0.648837	−	0.760927i	$-0.724744\pi$
$587$	−31.4402			−1.29767			−0.648837	+	0.760927i	$0.724744\pi$
$588$	5.32222	+	4.54687i	0.219485	+	0.187510i
$589$	68.6999			2.83073
$590$	0.286375	−	0.165338i	0.0117899	−	0.00680688i
$591$	−23.6099	−	13.6312i	−0.971180	−	0.560711i
$592$	3.27121	+	1.88863i	0.134446	+	0.0776224i
$593$	−17.8946	−	30.9944i	−0.734844	−	1.27279i	−0.954792	−	0.297276i	$-0.903922\pi$
$593$	−17.8946	−	30.9944i	−0.734844	−	1.27279i	0.219947	−	0.975512i	$-0.429411\pi$
$594$			0.317311i			0.0130194i
$595$	−2.45934	−	1.73834i	−0.100823	−	0.0712652i
$596$	−8.92615			−0.365629
$597$	−6.42143	+	3.70741i	−0.262812	+	0.151734i
$598$	−2.76373	−	1.59564i	−0.113017	−	0.0652505i
$599$	−7.53261	−	4.34896i	−0.307774	−	0.177694i	0.338156	−	0.941090i	$-0.390197\pi$
$599$	−7.53261	−	4.34896i	−0.307774	−	0.177694i	−0.645930	+	0.763397i	$0.723530\pi$
$600$	2.47560	+	4.28786i	0.101066	+	0.175051i
$601$			3.25920i			0.132945i	0.997788	+	0.0664727i	$0.0211745\pi$
$601$			3.25920i			0.132945i	−0.997788	+	0.0664727i	$0.978825\pi$
$602$	−29.3971	−	2.70325i	−1.19813	−	0.110176i
$603$	−8.16674			−0.332576
$604$	9.20482	+	15.9432i	0.374539	+	0.648720i
$605$	1.20398	−	2.08535i	0.0489486	−	0.0847815i
$606$	−9.02235	−	5.20906i	−0.366508	−	0.211603i
$607$	−9.20875	+	5.31668i	−0.373772	+	0.215797i	−0.675105	−	0.737722i	$-0.735902\pi$
$607$	−9.20875	+	5.31668i	−0.373772	+	0.215797i	0.301333	+	0.953519i	$0.402568\pi$
$608$	−7.78053			−0.315542
$609$	−0.493857	−	14.2392i	−0.0200121	−	0.577003i
$610$	−0.618519			−0.0250431
$611$	−12.0669	+	6.96685i	−0.488176	+	0.281848i
$612$	4.46212	+	2.57621i	0.180370	+	0.104137i
$613$	−9.46520	+	16.3942i	−0.382296	+	0.662156i	−0.991390	−	0.130942i	$-0.958200\pi$
$613$	−9.46520	+	16.3942i	−0.382296	+	0.662156i	0.609094	+	0.793098i	$0.291533\pi$
$614$	−14.9305	−	25.8603i	−0.602544	−	1.04364i
$615$	−1.45577			−0.0587025
$616$	−0.351424	−	0.762434i	−0.0141593	−	0.0307194i
$617$		−	36.8579i		−	1.48384i	−0.670486	−	0.741922i	$-0.733914\pi$
$617$		−	36.8579i		−	1.48384i	0.670486	−	0.741922i	$-0.266086\pi$
$618$	2.33496	+	4.04426i	0.0939257	+	0.162684i
$619$	31.8324	+	18.3785i	1.27945	+	0.738693i	0.976748	−	0.214391i	$-0.0687767\pi$
$619$	31.8324	+	18.3785i	1.27945	+	0.738693i	0.302706	+	0.953084i	$0.402110\pi$
$620$	1.68938	+	0.975363i	0.0678470	+	0.0391715i
$621$	2.27743	−	1.31488i	0.0913903	−	0.0527642i
$622$	−9.28283			−0.372207
$623$	1.01740	−	11.0640i	0.0407615	−	0.443269i
$624$		−	1.21353i		−	0.0485799i
$625$	−12.1351	−	21.0187i	−0.485405	−	0.840746i
$626$	13.5897	+	7.84599i	0.543152	+	0.313589i
$627$	2.13809	+	1.23442i	0.0853869	+	0.0492981i
$628$	7.19216	−	4.15240i	0.286999	−	0.165699i
$629$	−19.4620			−0.776002
$630$	−0.477319	−	0.337385i	−0.0190168	−	0.0134417i
$631$	−23.3835			−0.930882			−0.465441	−	0.885079i	$-0.654104\pi$
$631$	−23.3835			−0.930882			−0.465441	+	0.885079i	$0.654104\pi$
$632$	−5.04832	−	8.74395i	−0.200811	−	0.347816i
$633$	−1.55630	+	2.69558i	−0.0618572	+	0.107140i
$634$	3.85795	−	6.68217i	0.153219	−	0.265383i
$635$	−0.295632	+	0.170683i	−0.0117318	+	0.00677335i
$636$		−	7.41209i		−	0.293908i
$637$	2.83448	+	8.00783i	0.112306	+	0.317282i
$638$	−0.661067	+	1.57572i	−0.0261719	+	0.0623834i
$639$	0.715052	+	1.23851i	0.0282870	+	0.0489945i
$640$	−0.191328	−	0.110464i	−0.00756292	−	0.00436646i
$641$	32.7553	+	18.9113i	1.29376	+	0.746951i	0.979318	−	0.202327i	$-0.0648504\pi$
$641$	32.7553	+	18.9113i	1.29376	+	0.746951i	0.314439	+	0.949278i	$0.398184\pi$
$642$	−3.83354	−	6.63989i	−0.151298	−	0.262055i
$643$	−37.2243			−1.46798			−0.733992	−	0.679158i	$-0.762345\pi$
$643$	−37.2243			−1.46798			−0.733992	+	0.679158i	$0.762345\pi$
$644$	−4.01598	+	5.68165i	−0.158252	+	0.223888i
$645$	2.46509			0.0970627
$646$	34.7176	−	20.0442i	1.36595	−	0.788630i
$647$	−9.23054	+	15.9878i	−0.362890	+	0.628544i	−0.988435	−	0.151644i	$-0.951543\pi$
$647$	−9.23054	+	15.9878i	−0.362890	+	0.628544i	0.625545	+	0.780188i	$0.284877\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−0.411312	+	0.237471i	−0.0161454	+	0.00932155i
$650$			6.00840i			0.235669i
$651$	23.2631	+	2.13919i	0.911753	+	0.0838415i
$652$			20.7811i			0.813851i
$653$	5.09880	−	2.94379i	0.199532	−	0.115200i	−0.396905	−	0.917860i	$-0.629916\pi$
$653$	5.09880	−	2.94379i	0.199532	−	0.115200i	0.596437	+	0.802660i	$0.296583\pi$
$654$	1.47989	−	2.56325i	0.0578684	−	0.100231i
$655$	1.13616	+	0.655964i	0.0443936	+	0.0256306i
$656$	−5.70658	+	3.29469i	−0.222804	+	0.128636i
$657$		−	2.10502i		−	0.0821246i
$658$	12.7164	+	27.5889i	0.495735	+	1.07553i
$659$			13.9253i			0.542453i	0.962516	+	0.271227i	$0.0874292\pi$
$659$			13.9253i			0.542453i	−0.962516	+	0.271227i	$0.912571\pi$
$660$	0.0350513	+	0.0607107i	0.00136437	+	0.00236316i
$661$	16.2651	−	28.1720i	0.632639	−	1.09576i	−0.354371	−	0.935105i	$-0.615305\pi$
$661$	16.2651	−	28.1720i	0.632639	−	1.09576i	0.987010	−	0.160658i	$-0.0513617\pi$
$662$	2.20065	−	3.81163i	0.0855306	−	0.148143i
$663$	3.12629	+	5.41490i	0.121415	+	0.210297i
$664$		−	4.86994i		−	0.188990i
$665$	−4.13024	+	1.90372i	−0.160164	+	0.0738232i
$666$	−3.77727			−0.146366
$667$	14.0487	−	1.78481i	0.543969	−	0.0691083i
$668$	8.55811	−	14.8231i	0.331123	−	0.573522i
$669$	−8.22590	−	4.74922i	−0.318032	−	0.183616i
$670$	−1.56253	+	0.902127i	−0.0603658	+	0.0348522i
$671$	0.888361			0.0342948
$672$	−2.63464	−	0.242272i	−0.101633	−	0.00934583i
$673$	15.9346			0.614235			0.307117	−	0.951672i	$-0.400636\pi$
$673$	15.9346			0.614235			0.307117	+	0.951672i	$0.400636\pi$
$674$	10.4839	+	18.1586i	0.403824	+	0.699444i
$675$	−4.28786	−	2.47560i	−0.165040	−	0.0952857i
$676$	−5.76368	+	9.98298i	−0.221680	+	0.383961i
$677$	−23.9884	+	13.8497i	−0.921947	+	0.532287i	−0.884256	−	0.467003i	$-0.845334\pi$
$677$	−23.9884	+	13.8497i	−0.921947	+	0.532287i	−0.0376916	+	0.999289i	$0.512000\pi$
$678$			10.1377i			0.389338i
$679$	11.6903	+	8.26308i	0.448632	+	0.317108i
$680$	1.13831			0.0436521
$681$	18.2160	−	10.5170i	0.698040	−	0.403014i
$682$	−2.42640	−	1.40089i	−0.0929118	−	0.0536427i
$683$	20.1638	−	34.9248i	0.771548	−	1.33636i	−0.165167	−	0.986266i	$-0.552816\pi$
$683$	20.1638	−	34.9248i	0.771548	−	1.33636i	0.936714	−	0.350094i	$-0.113850\pi$
$684$	6.73813	−	3.89026i	0.257639	−	0.148748i
$685$			0.858007i			0.0327828i
$686$	17.9513	−	4.55512i	0.685386	−	0.173915i
$687$	25.5797			0.975926
$688$	9.66304	−	5.57896i	0.368400	−	0.212696i
$689$	4.49738	−	7.78969i	0.171337	−	0.296764i
$690$	0.290492	−	0.503147i	0.0110588	−	0.0191545i
$691$	8.77453	+	15.1979i	0.333799	+	0.578156i	0.983253	−	0.182244i	$-0.0583361\pi$
$691$	8.77453	+	15.1979i	0.333799	+	0.578156i	−0.649455	+	0.760400i	$0.725003\pi$
$692$	11.8062			0.448804
$693$	0.685559	+	0.484576i	0.0260422	+	0.0184075i
$694$			11.9765i			0.454620i
$695$	−2.30722	−	3.99622i	−0.0875177	−	0.151585i
$696$	3.25888	+	4.28715i	0.123528	+	0.162504i
$697$	16.9756	−	29.4026i	0.642997	−	1.11370i
$698$	−13.3943	+	7.73321i	−0.506982	+	0.292706i
$699$			7.63937i			0.288947i
$700$	13.0446	+	1.19953i	0.493039	+	0.0453381i
$701$	−19.6096			−0.740645			−0.370322	−	0.928903i	$-0.620753\pi$
$701$	−19.6096			−0.740645			−0.370322	+	0.928903i	$0.620753\pi$
$702$	0.606763	+	1.05094i	0.0229008	+	0.0396653i
$703$	−14.6946	+	25.4517i	−0.554216	+	0.959930i
$704$	0.274800	+	0.158656i	0.0103569	+	0.00597956i
$705$	−1.26834	−	2.19683i	−0.0477685	−	0.0827374i
$706$		−	22.2710i		−	0.838181i
$707$	−25.0326	+	11.5381i	−0.941448	+	0.433935i
$708$			1.49677i			0.0562520i
$709$	−8.62267	−	14.9349i	−0.323831	−	0.560892i	0.657444	−	0.753503i	$-0.271638\pi$
$709$	−8.62267	−	14.9349i	−0.323831	−	0.560892i	−0.981275	+	0.192611i	$0.938304\pi$
$710$	0.273620	+	0.157974i	0.0102688	+	0.00592867i
$711$	8.74395	+	5.04832i	0.327924	+	0.189327i
$712$	2.09972	+	3.63682i	0.0786903	+	0.136296i
$713$			23.2200i			0.869596i
$714$	12.3802	−	5.70632i	0.463317	−	0.213554i
$715$			0.0850714i			0.00318149i
$716$	5.38113	+	9.32038i	0.201102	+	0.348319i
$717$	−0.616694	−	0.356049i	−0.0230309	−	0.0132969i
$718$	11.5890	−	20.0728i	0.432499	−	0.749111i
$719$	−9.43716	−	16.3456i	−0.351947	−	0.609590i	0.634644	−	0.772805i	$-0.281147\pi$
$719$	−9.43716	−	16.3456i	−0.351947	−	0.609590i	−0.986590	+	0.163215i	$0.947813\pi$
$720$	0.220927			0.00823347
$721$	12.3035	+	1.13139i	0.458207	+	0.0421351i
$722$		−	41.5366i		−	1.54583i
$723$	23.9959	−	13.8541i	0.892418	−	0.515238i
$724$	6.87456	−	11.9071i	0.255491	−	0.442524i
$725$	−16.1354	−	21.2265i	−0.599252	−	0.788333i
$726$	5.44966	+	9.43908i	0.202256	+	0.350317i
$727$			1.20134i			0.0445552i	0.999752	+	0.0222776i	$0.00709177\pi$
$727$			1.20134i			0.0445552i	−0.999752	+	0.0222776i	$0.992908\pi$
$728$	−2.62185	−	1.85321i	−0.0971724	−	0.0686847i
$729$	−1.00000			−0.0370370
$730$	−0.232528	−	0.402750i	−0.00860624	−	0.0149064i
$731$	−28.7451	+	49.7880i	−1.06318	+	1.84147i
$732$	1.39983	−	2.42457i	0.0517390	−	0.0896146i
$733$	33.7365	−	19.4778i	1.24609	−	0.719428i	0.275759	−	0.961227i	$-0.411071\pi$
$733$	33.7365	−	19.4778i	1.24609	−	0.719428i	0.970326	+	0.241799i	$0.0777375\pi$
$734$	−23.1903			−0.855970
$735$	−1.45786	+	0.516028i	−0.0537738	+	0.0190340i
$736$		−	2.62975i		−	0.0969340i
$737$	2.24422	−	1.29570i	0.0826668	−	0.0477277i
$738$	3.29469	−	5.70658i	0.121279	−	0.210062i
$739$	9.02586	+	5.21108i	0.332022	+	0.191693i	0.656738	−	0.754119i	$-0.271936\pi$
$739$	9.02586	+	5.21108i	0.332022	+	0.191693i	−0.324717	+	0.945811i	$0.605269\pi$
$740$	−0.722699	+	0.417250i	−0.0265669	+	0.0153384i
$741$	9.44187			0.346856
$742$	−16.0140	−	11.3192i	−0.587892	−	0.415542i
$743$		−	27.1753i		−	0.996964i	−0.866900	−	0.498482i	$-0.833891\pi$
$743$		−	27.1753i		−	0.996964i	0.866900	−	0.498482i	$-0.166109\pi$
$744$	−7.64677	+	4.41486i	−0.280344	+	0.161857i
$745$	0.986014	−	1.70783i	0.0361247	−	0.0625699i
$746$	−19.7084	−	11.3787i	−0.721577	−	0.416603i
$747$	2.43497	+	4.21749i	0.0890908	+	0.154310i
$748$	−1.63492			−0.0597785
$749$	−20.2000	−	1.85752i	−0.738091	−	0.0678722i
$750$	−2.19849			−0.0802774
$751$	28.0247	−	16.1801i	1.02264	−	0.590420i	0.107770	−	0.994176i	$-0.465629\pi$
$751$	28.0247	−	16.1801i	1.02264	−	0.590420i	0.914867	+	0.403756i	$0.132296\pi$
$752$	−9.94369	−	5.74099i	−0.362609	−	0.209353i
$753$	7.56746	−	13.1072i	0.275774	−	0.477654i
$754$	0.823620	+	6.48293i	0.0299945	+	0.236094i
$755$	−4.06719			−0.148020
$756$	2.40280	−	1.10750i	0.0873889	−	0.0402795i
$757$			34.2475i			1.24475i	0.782721	+	0.622373i	$0.213831\pi$
$757$			34.2475i			1.24475i	−0.782721	+	0.622373i	$0.786169\pi$
$758$	−0.931881	−	1.61406i	−0.0338474	−	0.0586255i
$759$	−0.417225	+	0.722655i	−0.0151443	+	0.0262307i
$760$	0.859465	−	1.48864i	0.0311761	−	0.0539985i
$761$	−16.7499	−	29.0118i	−0.607185	−	1.05168i	−0.991702	−	0.128557i	$-0.958965\pi$
$761$	−16.7499	−	29.0118i	−0.607185	−	1.05168i	0.384517	−	0.923118i	$-0.374368\pi$
$762$		−	1.54515i		−	0.0559750i
$763$	−3.27798	−	7.11177i	−0.118671	−	0.257463i
$764$		−	8.09825i		−	0.292984i
$765$	−0.985803	+	0.569154i	−0.0356418	+	0.0205778i
$766$	29.7489	+	17.1755i	1.07487	+	0.620577i
$767$	−0.908184	+	1.57302i	−0.0327926	+	0.0567985i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$			3.74841i			0.135171i	0.997713	+	0.0675856i	$0.0215296\pi$
$769$			3.74841i			0.135171i	−0.997713	+	0.0675856i	$0.978470\pi$
$770$	0.184695	+	0.0169839i	0.00665594	+	0.000612057i
$771$			23.9101i			0.861100i
$772$	−20.9307	+	12.0843i	−0.753312	+	0.434925i
$773$	−11.3798	−	6.57011i	−0.409302	−	0.236310i	0.281188	−	0.959653i	$-0.409272\pi$
$773$	−11.3798	−	6.57011i	−0.409302	−	0.236310i	−0.690490	+	0.723342i	$0.742605\pi$
$774$	−5.57896	+	9.66304i	−0.200532	+	0.347331i
$775$	37.8606	−	21.8588i	1.35999	−	0.785192i
$776$	−5.41085			−0.194238
$777$	−5.76838	+	8.16088i	−0.206940	+	0.292770i
$778$	−28.4181			−1.01884
$779$	−25.6344	−	44.4002i	−0.918449	−	1.59080i
$780$	0.232182	+	0.134050i	0.00831345	+	0.00479977i
$781$	−0.392992	−	0.226894i	−0.0140624	−	0.00811890i
$782$	6.77479	+	11.7343i	0.242266	+	0.419617i
$783$	−4.96585	−	2.08334i	−0.177465	−	0.0744525i
$784$	−4.54687	+	5.32222i	−0.162388	+	0.190079i
$785$			1.83475i			0.0654852i
$786$	−5.14271	+	2.96914i	−0.183434	+	0.105906i
$787$	−4.44260	+	7.69481i	−0.158362	+	0.274291i	−0.934278	−	0.356545i	$-0.883955\pi$
$787$	−4.44260	+	7.69481i	−0.158362	+	0.274291i	0.775916	+	0.630836i	$0.217288\pi$
$788$	13.6312	−	23.6099i	0.485590	−	0.841066i
$789$	15.7284	+	27.2423i	0.559944	+	0.969852i
$790$	2.23062			0.0793620
$791$	21.9028	+	15.4817i	0.778775	+	0.550464i
$792$	−0.317311			−0.0112752
$793$	2.94228	−	1.69872i	0.104483	−	0.0603235i
$794$	17.2219	+	9.94309i	0.611183	+	0.352867i
$795$	1.41814	+	0.818765i	0.0502964	+	0.0290386i
$796$	−3.70741	−	6.42143i	−0.131406	−	0.227601i
$797$			49.4813i			1.75272i	0.481657	+	0.876360i	$0.340035\pi$
$797$			49.4813i			1.75272i	−0.481657	+	0.876360i	$0.659965\pi$
$798$	1.88500	−	20.4989i	0.0667283	−	0.725651i
$799$	59.1599			2.09293
$800$	−4.28786	+	2.47560i	−0.151599	+	0.0875255i
$801$	−3.63682	−	2.09972i	−0.128501	−	0.0741899i
$802$	−15.2773	−	8.82036i	−0.539460	−	0.311458i
$803$	0.333973	+	0.578458i	0.0117856	+	0.0204133i
$804$		−	8.16674i		−	0.288019i
$805$	−0.643442	−	1.39599i	−0.0226784	−	0.0492021i
$806$	−10.7151			−0.377423
$807$	7.32116	+	12.6806i	0.257717	+	0.446379i
$808$	5.20906	−	9.02235i	0.183254	−	0.317405i
$809$	−12.6119	−	7.28146i	−0.443409	−	0.256002i	0.261634	−	0.965167i	$-0.415739\pi$
$809$	−12.6119	−	7.28146i	−0.443409	−	0.256002i	−0.705043	+	0.709165i	$0.749072\pi$
$810$	−0.191328	+	0.110464i	−0.00672260	+	0.00388129i
$811$	−7.36893			−0.258758			−0.129379	−	0.991595i	$-0.541298\pi$
$811$	−7.36893			−0.258758			−0.129379	+	0.991595i	$0.541298\pi$
$812$	14.2392	−	0.493857i	0.499700	−	0.0173310i
$813$	−5.30485			−0.186049
$814$	1.03799	−	0.599285i	0.0363816	−	0.0210049i
$815$	−3.97602	−	2.29556i	−0.139274	−	0.0804098i
$816$	−2.57621	+	4.46212i	−0.0901852	+	0.156205i
$817$	43.4072	+	75.1836i	1.51863	+	2.63034i
$818$	−3.38649			−0.118406
$819$	3.19720	+	0.294003i	0.111719	+	0.0102733i
$820$		−	1.45577i		−	0.0508378i
$821$	15.1963	+	26.3208i	0.530356	+	0.918603i	0.999373	+	0.0354139i	$0.0112749\pi$
$821$	15.1963	+	26.3208i	0.530356	+	0.918603i	−0.469017	+	0.883189i	$0.655392\pi$
$822$	−3.36335	−	1.94183i	−0.117310	−	0.0677292i
$823$	−34.7221	−	20.0468i	−1.21034	−	0.698788i	−0.247504	−	0.968887i	$-0.579610\pi$
$823$	−34.7221	−	20.0468i	−1.21034	−	0.698788i	−0.962833	+	0.270098i	$0.912944\pi$
$824$	−4.04426	+	2.33496i	−0.140889	+	0.0813421i
$825$	1.57107			0.0546976
$826$	3.23381	+	2.28576i	0.112519	+	0.0795319i
$827$			37.9109i			1.31829i	0.752015	+	0.659146i	$0.229082\pi$
$827$			37.9109i			1.31829i	−0.752015	+	0.659146i	$0.770918\pi$
$828$	1.31488	+	2.27743i	0.0456951	+	0.0791463i
$829$	12.7764	+	7.37648i	0.443744	+	0.256196i	0.705184	−	0.709024i	$-0.250864\pi$
$829$	12.7764	+	7.37648i	0.443744	+	0.256196i	−0.261440	+	0.965220i	$0.584198\pi$
$830$	0.931758	+	0.537951i	0.0323418	+	0.0186725i
$831$	23.8814	−	13.7879i	0.828437	−	0.478298i
$832$	1.21353			0.0420715
$833$	6.57754	−	35.4620i	0.227898	−	1.22869i
$834$	20.8867			0.723246
$835$	1.89072	+	3.27482i	0.0654310	+	0.113330i
$836$	−1.23442	+	2.13809i	−0.0426934	+	0.0739472i
$837$	4.41486	−	7.64677i	0.152600	−	0.264311i
$838$	−4.03459	+	2.32937i	−0.139373	+	0.0804669i
$839$		−	1.10674i		−	0.0382089i	−0.999817	−	0.0191044i	$-0.993918\pi$
$839$		−	1.10674i		−	0.0382089i	0.999817	−	0.0191044i	$-0.00608151\pi$
$840$	0.337385	−	0.477319i	0.0116409	−	0.0164691i
$841$	−20.3194	−	20.6911i	−0.700668	−	0.713487i
$842$	6.86556	+	11.8915i	0.236603	+	0.409808i
$843$	−13.4642	−	7.77357i	−0.463732	−	0.267736i
$844$	−2.69558	−	1.55630i	−0.0927858	−	0.0535699i
$845$	−1.27335	−	2.20551i	−0.0438047	−	0.0758719i
$846$	11.4820			0.394759
$847$	28.7157	+	2.64059i	0.986684	+	0.0907319i
$848$	7.41209			0.254532
$849$	−17.4305	+	10.0635i	−0.598213	+	0.345378i
$850$	12.7553	−	22.0928i	0.437503	−	0.757777i
$851$	−8.60248	−	4.96664i	−0.294889	−	0.170254i
$852$	−1.23851	+	0.715052i	−0.0424305	+	0.0244973i
$853$			3.91179i			0.133937i	0.997755	+	0.0669686i	$0.0213327\pi$
$853$			3.91179i			0.133937i	−0.997755	+	0.0669686i	$0.978667\pi$
$854$	−3.10063	−	6.72699i	−0.106101	−	0.230193i
$855$			1.71893i			0.0587861i
$856$	6.63989	−	3.83354i	0.226947	−	0.131028i
$857$	−6.32818	+	10.9607i	−0.216167	+	0.374412i	−0.953633	−	0.300972i	$-0.902689\pi$
$857$	−6.32818	+	10.9607i	−0.216167	+	0.374412i	0.737466	+	0.675384i	$0.236022\pi$
$858$	−0.333476	−	0.192533i	−0.0113847	−	0.00657296i
$859$	−8.15026	+	4.70555i	−0.278083	+	0.160551i	−0.632555	−	0.774515i	$-0.717994\pi$
$859$	−8.15026	+	4.70555i	−0.278083	+	0.160551i	0.354472	+	0.935067i	$0.384661\pi$
$860$			2.46509i			0.0840588i
$861$	−7.29777	−	15.8330i	−0.248707	−	0.539586i
$862$		−	0.0690826i		−	0.00235296i
$863$	−16.0061	−	27.7234i	−0.544854	−	0.943715i	−0.998616	−	0.0525923i	$-0.983252\pi$
$863$	−16.0061	−	27.7234i	−0.544854	−	0.943715i	0.453762	−	0.891123i	$-0.350082\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−1.30415	+	2.25886i	−0.0443426	+	0.0768036i
$866$	−12.7867	−	22.1472i	−0.434510	−	0.752594i
$867$		−	9.54734i		−	0.324245i
$868$	−2.13919	+	23.2631i	−0.0726089	+	0.789601i
$869$	−3.20378			−0.108681
$870$	−1.18024	+	0.149943i	−0.0400140	+	0.00508355i
$871$	4.95528	−	8.58279i	0.167903	−	0.290817i
$872$	2.56325	+	1.47989i	0.0868027	+	0.0501155i
$873$	4.68594	−	2.70543i	0.158595	−	0.0915648i
$874$	20.4609			0.692099
$875$	−3.35738	+	4.74989i	−0.113500	+	0.160576i
$876$	2.10502			0.0711220
$877$	−2.19989	−	3.81032i	−0.0742850	−	0.128665i	0.826490	−	0.562951i	$-0.190334\pi$
$877$	−2.19989	−	3.81032i	−0.0742850	−	0.128665i	−0.900775	+	0.434286i	$0.857001\pi$
$878$	23.9314	+	13.8168i	0.807647	+	0.466295i
$879$	−10.9276	+	18.9272i	−0.368579	+	0.638397i
$880$	−0.0607107	+	0.0350513i	−0.00204656	+	0.00118158i
$881$		−	28.4837i		−	0.959639i	−0.877367	−	0.479820i	$-0.840702\pi$
$881$		−	28.4837i		−	0.959639i	0.877367	−	0.479820i	$-0.159298\pi$
$882$	1.27659	−	6.88261i	0.0429852	−	0.231749i
$883$	22.2152			0.747603			0.373801	−	0.927509i	$-0.378054\pi$
$883$	22.2152			0.747603			0.373801	+	0.927509i	$0.378054\pi$
$884$	−5.41490	+	3.12629i	−0.182123	+	0.105149i
$885$	−0.286375	−	0.165338i	−0.00962638	−	0.00555779i
$886$	−6.27111	+	10.8619i	−0.210682	+	0.364912i
$887$	−23.4567	+	13.5427i	−0.787598	+	0.454720i	−0.839116	−	0.543952i	$-0.816927\pi$
$887$	−23.4567	+	13.5427i	−0.787598	+	0.454720i	0.0515181	+	0.998672i	$0.483594\pi$
$888$		−	3.77727i		−	0.126757i
$889$	−3.33834	−	2.35965i	−0.111964	−	0.0791401i
$890$	−0.927770			−0.0310989
$891$	0.274800	−	0.158656i	0.00920613	−	0.00531516i
$892$	4.74922	−	8.22590i	0.159016	−	0.275423i
$893$	44.6680	−	77.3672i	1.49476	−	2.58899i
$894$	4.46307	+	7.73027i	0.149267	+	0.258539i
$895$	−2.37767			−0.0794768
$896$	0.242272	−	2.63464i	0.00809373	−	0.0880170i
$897$			3.19128i			0.106554i
$898$	15.3809	+	26.6405i	0.513268	+	0.889005i
$899$	37.8544	−	28.7750i	1.26251	−	0.959702i
$900$	2.47560	−	4.28786i	0.0825199	−	0.142929i
$901$	−33.0736	+	19.0951i	−1.10184	+	0.636149i
$902$			2.09089i			0.0696189i
$903$	12.3574	+	26.8102i	0.411230	+	0.892188i
$904$	−10.1377			−0.337176
$905$	1.51878	+	2.63060i	0.0504859	+	0.0874441i
$906$	9.20482	−	15.9432i	0.305810	−	0.529678i
$907$	0.492048	+	0.284084i	0.0163382	+	0.00943286i	0.508147	−	0.861270i	$-0.330331\pi$
$907$	0.492048	+	0.284084i	0.0163382	+	0.00943286i	−0.491809	+	0.870703i	$0.663664\pi$
$908$	10.5170	+	18.2160i	0.349020	+	0.604521i
$909$			10.4181i			0.345547i
$910$	0.644192	−	0.296923i	0.0213548	−	0.00984290i
$911$		−	50.6095i		−	1.67677i	−0.545080	−	0.838384i	$-0.683501\pi$
$911$		−	50.6095i		−	1.67677i	0.545080	−	0.838384i	$-0.316499\pi$
$912$	3.89026	+	6.73813i	0.128819	+	0.223122i
$913$	−1.33826	−	0.772643i	−0.0442898	−	0.0255707i
$914$	−9.26942	−	5.35170i	−0.306605	−	0.177019i
$915$	0.309259	+	0.535653i	0.0102238	+	0.0177081i
$916$			25.5797i			0.845176i
$917$	−1.43868	+	15.6452i	−0.0475093	+	0.516651i
$918$		−	5.15241i		−	0.170055i
$919$	10.5652	+	18.2994i	0.348513	+	0.603642i	0.985985	−	0.166831i	$-0.0533534\pi$
$919$	10.5652	+	18.2994i	0.348513	+	0.603642i	−0.637473	+	0.770473i	$0.720020\pi$
$920$	0.503147	+	0.290492i	0.0165883	+	0.00957724i
$921$	−14.9305	+	25.8603i	−0.491975	+	0.852126i
$922$	−12.3718	−	21.4286i	−0.407445	−	0.705715i
$923$	−1.73547			−0.0571236
$924$	−0.484576	+	0.685559i	−0.0159414	+	0.0225532i
$925$			18.7020i			0.614917i
$926$	10.9611	−	6.32837i	0.360203	−	0.207963i
$927$	2.33496	−	4.04426i	0.0766900	−	0.132831i
$928$	−4.28715	+	3.25888i	−0.140733	+	0.106978i
$929$	−11.1044	−	19.2334i	−0.364324	−	0.631028i	0.624343	−	0.781150i	$-0.285367\pi$
$929$	−11.1044	−	19.2334i	−0.364324	−	0.631028i	−0.988667	+	0.150122i	$0.952033\pi$
$930$		−	1.95073i		−	0.0639668i
$931$	−41.4096	−	35.3770i	−1.35715	−	1.15944i
$932$	−7.63937			−0.250236
$933$	4.64141	+	8.03916i	0.151953	+	0.263190i
$934$	8.29506	−	14.3675i	0.271423	−	0.470118i
$935$	0.180599	−	0.312806i	0.00590621	−	0.0102299i
$936$	−1.05094	+	0.606763i	−0.0343512	+	0.0198327i
$937$	−24.6024			−0.803727			−0.401863	−	0.915700i	$-0.631637\pi$
$937$	−24.6024			−0.803727			−0.401863	+	0.915700i	$0.631637\pi$
$938$	−17.6445	−	12.4717i	−0.576112	−	0.407215i
$939$		−	15.6920i		−	0.512088i
$940$	2.19683	−	1.26834i	0.0716527	−	0.0413687i
$941$	−25.0471	+	43.3828i	−0.816512	+	1.41424i	0.0917257	+	0.995784i	$0.470762\pi$
$941$	−25.0471	+	43.3828i	−0.816512	+	1.41424i	−0.908237	+	0.418455i	$0.862572\pi$
$942$	−7.19216	−	4.15240i	−0.234333	−	0.135292i
$943$	15.0069	−	8.66423i	0.488692	−	0.282146i
$944$	−1.49677			−0.0487157
$945$	−0.0535244	+	0.582062i	−0.00174115	+	0.0189345i
$946$		−	3.54053i		−	0.115113i
$947$	−12.0583	+	6.96186i	−0.391842	+	0.226230i	−0.682958	−	0.730458i	$-0.739307\pi$
$947$	−12.0583	+	6.96186i	−0.391842	+	0.226230i	0.291116	+	0.956688i	$0.405973\pi$
$948$	−5.04832	+	8.74395i	−0.163962	+	0.283990i
$949$	2.21226	+	1.27725i	0.0718129	+	0.0414612i
$950$	−19.2614	−	33.3618i	−0.624924	−	1.08240i
$951$	−7.71591			−0.250205
$952$	5.70632	+	12.3802i	0.184943	+	0.401245i
$953$	24.4214			0.791085			0.395543	−	0.918448i	$-0.370557\pi$
$953$	24.4214			0.791085			0.395543	+	0.918448i	$0.370557\pi$
$954$	−6.41905	+	3.70604i	−0.207825	+	0.119988i
$955$	1.54943	+	0.894562i	0.0501383	+	0.0289473i
$956$	0.356049	−	0.616694i	0.0115154	−	0.0199453i
$957$	1.69515	−	0.215359i	0.0547963	−	0.00696157i
$958$	10.2010			0.329580
$959$	−9.33166	+	4.30118i	−0.301335	+	0.138892i
$960$			0.220927i			0.00713039i
$961$	23.4820	+	40.6721i	0.757485	+	1.31200i
$962$	2.29191	−	3.96970i	0.0738940	−	0.127988i
$963$	−3.83354	+	6.63989i	−0.123534	+	0.213967i
$964$	13.8541	+	23.9959i	0.446209	+	0.772857i
$965$		−	5.33952i		−	0.171885i
$966$	6.92845	+	0.637115i	0.222919	+	0.0204988i
$967$		−	23.9578i		−	0.770430i	−0.922827	−	0.385215i	$-0.874127\pi$
$967$		−	23.9578i		−	0.770430i	0.922827	−	0.385215i	$-0.125873\pi$
$968$	−9.43908	+	5.44966i	−0.303384	+	0.175159i
$969$	−34.7176	−	20.0442i	−1.11529	−	0.643914i
$970$	0.597702	−	1.03525i	0.0191911	−	0.0332399i
$971$	−25.1230	+	14.5048i	−0.806235	+	0.465480i	−0.845647	−	0.533743i	$-0.820785\pi$
$971$	−25.1230	+	14.5048i	−0.806235	+	0.465480i	0.0394117	+	0.999223i	$0.487452\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	31.8967	−	45.1262i	1.02256	−	1.44668i
$974$			16.4306i			0.526470i
$975$	5.20343	−	3.00420i	0.166643	−	0.0962114i
$976$	2.42457	+	1.39983i	0.0776086	+	0.0448073i
$977$	−18.0239	+	31.2183i	−0.576636	+	0.998762i	0.419226	+	0.907882i	$0.362301\pi$
$977$	−18.0239	+	31.2183i	−0.576636	+	0.998762i	−0.995862	+	0.0908805i	$0.971032\pi$
$978$	17.9970	−	10.3906i	0.575480	−	0.332253i
$979$	1.33253			0.0425878
$980$	−0.516028	−	1.45786i	−0.0164839	−	0.0465695i
$981$	−2.95979			−0.0944988
$982$	−12.7051	−	22.0058i	−0.405435	−	0.702234i
$983$	14.2590	+	8.23244i	0.454792	+	0.262574i	0.709852	−	0.704351i	$-0.248762\pi$
$983$	14.2590	+	8.23244i	0.454792	+	0.262574i	−0.255060	+	0.966925i	$0.582095\pi$
$984$	5.70658	+	3.29469i	0.181919	+	0.105031i
$985$	3.01149	+	5.21606i	0.0959541	+	0.166197i
$986$	10.7342	−	25.5861i	0.341848	−	0.814828i
$987$	17.5345	−	24.8071i	0.558129	−	0.789620i
$988$			9.44187i			0.300386i
$989$	−25.4114	+	14.6713i	−0.808037	+	0.466520i
$990$	0.0350513	−	0.0607107i	0.00111400	−	0.00192951i
$991$	−11.0076	+	19.0657i	−0.349667	+	0.605641i	−0.986190	−	0.165616i	$-0.947039\pi$
$991$	−11.0076	+	19.0657i	−0.349667	+	0.605641i	0.636523	+	0.771258i	$0.280372\pi$
$992$	−4.41486	−	7.64677i	−0.140172	−	0.242785i
$993$	−4.40129			−0.139671
$994$	−0.346474	+	3.76780i	−0.0109895	+	0.119507i
$995$	1.63814			0.0519324
$996$	−4.21749	+	2.43497i	−0.133636	+	0.0771549i
$997$	38.4928	+	22.2238i	1.21908	+	0.703836i	0.964721	−	0.263274i	$-0.0848023\pi$
$997$	38.4928	+	22.2238i	1.21908	+	0.703836i	0.254359	+	0.967110i	$0.418136\pi$
$998$	−8.19021	−	4.72862i	−0.259257	−	0.149682i
$999$	1.88863	+	3.27121i	0.0597537	+	0.103496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.p.b.1159.18	yes	44
7.2	even	3	inner	1218.2.p.b.289.7	✓	44
29.28	even	2	inner	1218.2.p.b.1159.7	yes	44
203.86	even	6	inner	1218.2.p.b.289.18	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.p.b.289.7	✓	44	7.2	even	3	inner
1218.2.p.b.289.18	yes	44	203.86	even	6	inner
1218.2.p.b.1159.7	yes	44	29.28	even	2	inner
1218.2.p.b.1159.18	yes	44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.110464 + 0.191328i) q^{5} -1.00000 q^{6} +(-1.52713 + 2.16053i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.191328 + 0.110464i) q^{10} +(-0.274800 - 0.158656i) q^{11} +(-0.866025 + 0.500000i) q^{12} -1.21353 q^{13} +(-0.242272 + 2.63464i) q^{14} -0.220927i q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.46212 + 2.57621i) q^{17} +(0.866025 + 0.500000i) q^{18} +(6.73813 - 3.89026i) q^{19} +0.220927 q^{20} +(2.40280 - 1.10750i) q^{21} -0.317311 q^{22} +(1.31488 + 2.27743i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.47560 - 4.28786i) q^{25} +(-1.05094 + 0.606763i) q^{26} -1.00000i q^{27} +(1.10750 + 2.40280i) q^{28} +(2.08334 - 4.96585i) q^{29} +(-0.110464 - 0.191328i) q^{30} +(7.64677 + 4.41486i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.158656 + 0.274800i) q^{33} +5.15241 q^{34} +(-0.582062 - 0.0535244i) q^{35} +1.00000 q^{36} +(-3.27121 + 1.88863i) q^{37} +(3.89026 - 6.73813i) q^{38} +(1.05094 + 0.606763i) q^{39} +(0.191328 - 0.110464i) q^{40} -6.58939i q^{41} +(1.52713 - 2.16053i) q^{42} +11.1579i q^{43} +(-0.274800 + 0.158656i) q^{44} +(-0.110464 + 0.191328i) q^{45} +(2.27743 + 1.31488i) q^{46} +(9.94369 - 5.74099i) q^{47} +1.00000i q^{48} +(-2.33574 - 6.59881i) q^{49} -4.95119i q^{50} +(-2.57621 - 4.46212i) q^{51} +(-0.606763 + 1.05094i) q^{52} +(-3.70604 + 6.41905i) q^{53} +(-0.500000 - 0.866025i) q^{54} -0.0701026i q^{55} +(2.16053 + 1.52713i) q^{56} -7.78053 q^{57} +(-0.678700 - 5.34222i) q^{58} +(0.748385 - 1.29624i) q^{59} +(-0.191328 - 0.110464i) q^{60} +(-2.42457 + 1.39983i) q^{61} +8.82973 q^{62} +(-2.63464 - 0.242272i) q^{63} -1.00000 q^{64} +(-0.134050 - 0.232182i) q^{65} +(0.274800 + 0.158656i) q^{66} +(-4.08337 + 7.07261i) q^{67} +(4.46212 - 2.57621i) q^{68} -2.62975i q^{69} +(-0.530843 + 0.244678i) q^{70} +1.43010 q^{71} +(0.866025 - 0.500000i) q^{72} +(-1.82300 - 1.05251i) q^{73} +(-1.88863 + 3.27121i) q^{74} +(-4.28786 + 2.47560i) q^{75} -7.78053i q^{76} +(0.762434 - 0.351424i) q^{77} +1.21353 q^{78} +(8.74395 - 5.04832i) q^{79} +(0.110464 - 0.191328i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.29469 - 5.70658i) q^{82} +4.86994 q^{83} +(0.242272 - 2.63464i) q^{84} +1.13831i q^{85} +(5.57896 + 9.66304i) q^{86} +(-4.28715 + 3.25888i) q^{87} +(-0.158656 + 0.274800i) q^{88} +(-3.63682 + 2.09972i) q^{89} +0.220927i q^{90} +(1.85321 - 2.62185i) q^{91} +2.62975 q^{92} +(-4.41486 - 7.64677i) q^{93} +(5.74099 - 9.94369i) q^{94} +(1.48864 + 0.859465i) q^{95} +(0.500000 + 0.866025i) q^{96} -5.41085i q^{97} +(-5.32222 - 4.54687i) q^{98} -0.317311i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 22 q^{4} - 44 q^{6} - 8 q^{7} + 22 q^{9} - 16 q^{13} - 22 q^{16} - 4 q^{23} - 22 q^{24} - 22 q^{25} - 4 q^{28} + 4 q^{29} - 16 q^{34} - 10 q^{35} + 44 q^{36} + 4 q^{38} + 8 q^{42} - 52 q^{49} + 8 q^{51}+ \cdots + 22 q^{96}+O(q^{100}) \) 44 * q + 22 * q^4 - 44 * q^6 - 8 * q^7 + 22 * q^9 - 16 * q^13 - 22 * q^16 - 4 * q^23 - 22 * q^24 - 22 * q^25 - 4 * q^28 + 4 * q^29 - 16 * q^34 - 10 * q^35 + 44 * q^36 + 4 * q^38 + 8 * q^42 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 6 * q^53 - 22 * q^54 - 8 * q^57 + 14 * q^58 + 24 * q^59 + 16 * q^62 - 4 * q^63 - 44 * q^64 - 24 * q^65 + 28 * q^67 - 24 * q^71 - 16 * q^74 + 16 * q^78 - 22 * q^81 - 28 * q^83 + 4 * q^86 + 14 * q^87 + 112 * q^91 - 8 * q^92 - 8 * q^93 - 36 * q^94 + 22 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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