LMFDB - Embedded newform 288.2.bf.a.131.29

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [288,2,Mod(11,288)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(288, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 15, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("288.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			131.29
Character	$\chi$	$=$	288.131
Dual form			288.2.bf.a.11.29

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.365445 - 1.36618i) q^{2} +(-0.140380 + 1.72635i) q^{3} +(-1.73290 - 0.998528i) q^{4} +(-0.152157 + 1.15575i) q^{5} +(2.30721 + 0.822672i) q^{6} +(-0.496625 + 1.85343i) q^{7} +(-1.99745 + 2.00255i) q^{8} +(-2.96059 - 0.484692i) q^{9} +(1.52335 + 0.630235i) q^{10} +(3.87378 + 2.97246i) q^{11} +(1.96708 - 2.85142i) q^{12} +(1.63147 + 2.12617i) q^{13} +(2.35063 + 1.35581i) q^{14} +(-1.97386 - 0.424920i) q^{15} +(2.00588 + 3.46070i) q^{16} -4.48513 q^{17} +(-1.74411 + 3.86757i) q^{18} +(1.00431 + 0.415998i) q^{19} +(1.41772 - 1.85086i) q^{20} +(-3.12996 - 1.11753i) q^{21} +(5.47657 - 4.20602i) q^{22} +(-0.329076 + 0.0881758i) q^{23} +(-3.17670 - 3.72942i) q^{24} +(3.51703 + 0.942386i) q^{25} +(3.50095 - 1.45188i) q^{26} +(1.25236 - 5.04298i) q^{27} +(2.71130 - 2.71591i) q^{28} +(-5.80978 + 0.764873i) q^{29} +(-1.30186 + 2.54137i) q^{30} +(4.83932 + 2.79398i) q^{31} +(5.46098 - 1.47570i) q^{32} +(-5.67531 + 6.27024i) q^{33} +(-1.63907 + 6.12750i) q^{34} +(-2.06653 - 0.855983i) q^{35} +(4.64642 + 3.79615i) q^{36} +(-2.90428 - 7.01154i) q^{37} +(0.935348 - 1.22004i) q^{38} +(-3.89955 + 2.51802i) q^{39} +(-2.01051 - 2.61324i) q^{40} +(-0.987619 - 3.68584i) q^{41} +(-2.67058 + 3.86769i) q^{42} +(7.23706 - 9.43152i) q^{43} +(-3.74479 - 9.01905i) q^{44} +(1.01065 - 3.34793i) q^{45} +(0.000204623 + 0.481801i) q^{46} +(-3.25721 + 1.88055i) q^{47} +(-6.25597 + 2.97705i) q^{48} +(2.87362 + 1.65908i) q^{49} +(2.57275 - 4.46051i) q^{50} +(0.629624 - 7.74292i) q^{51} +(-0.704130 - 5.31352i) q^{52} +(-3.91618 - 9.45448i) q^{53} +(-6.43195 - 3.55388i) q^{54} +(-4.02483 + 4.02483i) q^{55} +(-2.71959 - 4.69665i) q^{56} +(-0.859144 + 1.67539i) q^{57} +(-1.07820 + 8.21673i) q^{58} +(0.952686 + 0.125424i) q^{59} +(2.99621 + 2.70730i) q^{60} +(1.55814 + 11.8353i) q^{61} +(5.58560 - 5.59034i) q^{62} +(2.36864 - 5.24653i) q^{63} +(-0.0203858 - 7.99997i) q^{64} +(-2.70555 + 1.56205i) q^{65} +(6.49227 + 10.0449i) q^{66} +(1.54211 + 2.00972i) q^{67} +(7.77228 + 4.47853i) q^{68} +(-0.106027 - 0.580480i) q^{69} +(-1.92463 + 2.51043i) q^{70} +(-6.68291 + 6.68291i) q^{71} +(6.88424 - 4.96056i) q^{72} +(-0.787037 - 0.787037i) q^{73} +(-10.6404 + 1.40543i) q^{74} +(-2.12061 + 5.93935i) q^{75} +(-1.32498 - 1.72371i) q^{76} +(-7.43306 + 5.70358i) q^{77} +(2.01500 + 6.24769i) q^{78} +(3.18314 + 5.51337i) q^{79} +(-4.30489 + 1.79172i) q^{80} +(8.53015 + 2.86994i) q^{81} +(-5.39645 + 0.00229190i) q^{82} +(17.9192 - 2.35911i) q^{83} +(4.30801 + 5.06192i) q^{84} +(0.682443 - 5.18367i) q^{85} +(-10.2404 - 13.3338i) q^{86} +(-0.504860 - 10.1371i) q^{87} +(-13.6902 + 1.82009i) q^{88} +(-2.96906 - 2.96906i) q^{89} +(-4.20455 - 2.60422i) q^{90} +(-4.75094 + 1.96790i) q^{91} +(0.658302 + 0.175792i) q^{92} +(-5.50275 + 7.96216i) q^{93} +(1.37884 + 5.13718i) q^{94} +(-0.633600 + 1.09743i) q^{95} +(1.78097 + 9.63474i) q^{96} +(-1.67561 - 2.90224i) q^{97} +(3.31676 - 3.31958i) q^{98} +(-10.0279 - 10.6778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21}+ \cdots - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.365445	−	1.36618i	0.258409	−	0.966036i
$2$	0.365445	−	1.36618i	0.258409	−	0.966036i
$3$	−0.140380	+	1.72635i	−0.0810486	+	0.996710i
$3$	−0.140380	+	1.72635i	−0.0810486	+	0.996710i
$4$	−1.73290	−	0.998528i	−0.866450	−	0.499264i
$5$	−0.152157	+	1.15575i	−0.0680466	+	0.516865i	0.923147	+	0.384446i	$0.125608\pi$
$5$	−0.152157	+	1.15575i	−0.0680466	+	0.516865i	−0.991194	+	0.132419i	$0.957726\pi$
$6$	2.30721	+	0.822672i	0.941914	+	0.335855i
$7$	−0.496625	+	1.85343i	−0.187706	+	0.700530i	0.806328	+	0.591468i	$0.201451\pi$
$7$	−0.496625	+	1.85343i	−0.187706	+	0.700530i	−0.994035	+	0.109062i	$0.965215\pi$
$8$	−1.99745	+	2.00255i	−0.706205	+	0.708007i
$9$	−2.96059	−	0.484692i	−0.986862	−	0.161564i
$10$	1.52335	+	0.630235i	0.481726	+	0.199298i
$11$	3.87378	+	2.97246i	1.16799	+	0.896230i	0.996043	−	0.0888763i	$-0.0283276\pi$
$11$	3.87378	+	2.97246i	1.16799	+	0.896230i	0.171947	+	0.985106i	$0.444994\pi$
$12$	1.96708	−	2.85142i	0.567846	−	0.823135i
$13$	1.63147	+	2.12617i	0.452489	+	0.589695i	0.962773	−	0.270311i	$-0.0871265\pi$
$13$	1.63147	+	2.12617i	0.452489	+	0.589695i	−0.510284	+	0.860006i	$0.670460\pi$
$14$	2.35063	+	1.35581i	0.628232	+	0.362354i
$15$	−1.97386	−	0.424920i	−0.509649	−	0.109714i
$16$	2.00588	+	3.46070i	0.501470	+	0.865175i
$17$	−4.48513			−1.08780			−0.543902	−	0.839149i	$-0.683054\pi$
$17$	−4.48513			−1.08780			−0.543902	+	0.839149i	$0.683054\pi$
$18$	−1.74411	+	3.86757i	−0.411090	+	0.911595i
$19$	1.00431	+	0.415998i	0.230404	+	0.0954365i	0.494899	−	0.868951i	$-0.335205\pi$
$19$	1.00431	+	0.415998i	0.230404	+	0.0954365i	−0.264495	+	0.964387i	$0.585205\pi$
$20$	1.41772	−	1.85086i	0.317011	−	0.413864i
$21$	−3.12996	−	1.11753i	−0.683012	−	0.243866i
$22$	5.47657	−	4.20602i	1.16761	−	0.896726i
$23$	−0.329076	+	0.0881758i	−0.0686172	+	0.0183859i	−0.292964	−	0.956123i	$-0.594642\pi$
$23$	−0.329076	+	0.0881758i	−0.0686172	+	0.0183859i	0.224347	+	0.974509i	$0.427975\pi$
$24$	−3.17670	−	3.72942i	−0.648441	−	0.761265i
$25$	3.51703	+	0.942386i	0.703407	+	0.188477i
$26$	3.50095	−	1.45188i	0.686593	−	0.284738i
$27$	1.25236	−	5.04298i	0.241016	−	0.970521i
$28$	2.71130	−	2.71591i	0.512388	−	0.513259i
$29$	−5.80978	+	0.764873i	−1.07885	+	0.142033i	−0.648941	−	0.760839i	$-0.724788\pi$
$29$	−5.80978	+	0.764873i	−1.07885	+	0.142033i	−0.429909	+	0.902872i	$0.641454\pi$
$30$	−1.30186	+	2.54137i	−0.237685	+	0.463989i
$31$	4.83932	+	2.79398i	0.869168	+	0.501814i	0.867072	−	0.498183i	$-0.165999\pi$
$31$	4.83932	+	2.79398i	0.869168	+	0.501814i	0.00209645	+	0.999998i	$0.499333\pi$
$32$	5.46098	−	1.47570i	0.965374	−	0.260870i
$33$	−5.67531	+	6.27024i	−0.987945	+	1.09151i
$34$	−1.63907	+	6.12750i	−0.281098	+	1.05086i
$35$	−2.06653	−	0.855983i	−0.349307	−	0.144688i
$36$	4.64642	+	3.79615i	0.774403	+	0.632692i
$37$	−2.90428	−	7.01154i	−0.477460	−	1.15269i	−0.960796	−	0.277255i	$-0.910575\pi$
$37$	−2.90428	−	7.01154i	−0.477460	−	1.15269i	0.483336	−	0.875435i	$-0.339425\pi$
$38$	0.935348	−	1.22004i	0.151733	−	0.197917i
$39$	−3.89955	+	2.51802i	−0.624428	+	0.403206i
$40$	−2.01051	−	2.61324i	−0.317889	−	0.413190i
$41$	−0.987619	−	3.68584i	−0.154240	−	0.575632i	−0.999169	−	0.0407537i	$-0.987024\pi$
$41$	−0.987619	−	3.68584i	−0.154240	−	0.575632i	0.844929	−	0.534878i	$-0.179643\pi$
$42$	−2.67058	+	3.86769i	−0.412080	+	0.596797i
$43$	7.23706	−	9.43152i	1.10364	−	1.43829i	0.216802	−	0.976216i	$-0.430437\pi$
$43$	7.23706	−	9.43152i	1.10364	−	1.43829i	0.886839	−	0.462078i	$-0.152896\pi$
$44$	−3.74479	−	9.01905i	−0.564549	−	1.35967i
$45$	1.01065	−	3.34793i	0.150659	−	0.499081i
$46$	0.000204623		0.481801i	3.01700e−5		0.0710377i
$47$	−3.25721	+	1.88055i	−0.475114	+	0.274307i	−0.718378	−	0.695653i	$-0.755115\pi$
$47$	−3.25721	+	1.88055i	−0.475114	+	0.274307i	0.243264	+	0.969960i	$0.421782\pi$
$48$	−6.25597	+	2.97705i	−0.902972	+	0.429700i
$49$	2.87362	+	1.65908i	0.410517	+	0.237012i
$50$	2.57275	−	4.46051i	0.363842	−	0.630812i
$51$	0.629624	−	7.74292i	0.0881650	−	1.08423i
$52$	−0.704130	−	5.31352i	−0.0976452	−	0.736852i
$53$	−3.91618	−	9.45448i	−0.537928	−	1.29867i	−0.926167	−	0.377114i	$-0.876916\pi$
$53$	−3.91618	−	9.45448i	−0.537928	−	1.29867i	0.388239	−	0.921559i	$-0.373084\pi$
$54$	−6.43195	−	3.55388i	−0.875277	−	0.483621i
$55$	−4.02483	+	4.02483i	−0.542708	+	0.542708i
$56$	−2.71959	−	4.69665i	−0.363421	−	0.627616i
$57$	−0.859144	+	1.67539i	−0.113796	+	0.221911i
$58$	−1.07820	+	8.21673i	−0.141575	+	1.07891i
$59$	0.952686	+	0.125424i	0.124029	+	0.0163288i	0.192285	−	0.981339i	$-0.438410\pi$
$59$	0.952686	+	0.125424i	0.124029	+	0.0163288i	−0.0682560	+	0.997668i	$0.521743\pi$
$60$	2.99621	+	2.70730i	0.386809	+	0.349511i
$61$	1.55814	+	11.8353i	0.199500	+	1.51535i	0.739196	+	0.673491i	$0.235206\pi$
$61$	1.55814	+	11.8353i	0.199500	+	1.51535i	−0.539696	+	0.841860i	$0.681461\pi$
$62$	5.58560	−	5.59034i	0.709371	−	0.709974i
$63$	2.36864	−	5.24653i	0.298421	−	0.661000i
$64$	−0.0203858	−	7.99997i	−0.00254822	−	0.999997i
$65$	−2.70555	+	1.56205i	−0.335583	+	0.193749i
$66$	6.49227	+	10.0449i	0.799143	+	1.23645i
$67$	1.54211	+	2.00972i	0.188399	+	0.245527i	0.877997	−	0.478666i	$-0.158879\pi$
$67$	1.54211	+	2.00972i	0.188399	+	0.245527i	−0.689598	+	0.724192i	$0.742213\pi$
$68$	7.77228	+	4.47853i	0.942528	+	0.543102i
$69$	−0.106027	−	0.580480i	−0.0127641	−	0.0698816i
$70$	−1.92463	+	2.51043i	−0.230037	+	0.300054i
$71$	−6.68291	+	6.68291i	−0.793115	+	0.793115i	−0.981999	−	0.188884i	$-0.939513\pi$
$71$	−6.68291	+	6.68291i	−0.793115	+	0.793115i	0.188884	+	0.981999i	$0.439513\pi$
$72$	6.88424	−	4.96056i	0.811316	−	0.584608i
$73$	−0.787037	−	0.787037i	−0.0921157	−	0.0921157i	0.659547	−	0.751663i	$-0.270748\pi$
$73$	−0.787037	−	0.787037i	−0.0921157	−	0.0921157i	−0.751663	+	0.659547i	$0.770748\pi$
$74$	−10.6404	+	1.40543i	−1.23692	+	0.163378i
$75$	−2.12061	+	5.93935i	−0.244867	+	0.685817i
$76$	−1.32498	−	1.72371i	−0.151986	−	0.197723i
$77$	−7.43306	+	5.70358i	−0.847075	+	0.649984i
$78$	2.01500	+	6.24769i	0.228154	+	0.707412i
$79$	3.18314	+	5.51337i	0.358132	+	0.620302i	0.987649	−	0.156684i	$-0.0500805\pi$
$79$	3.18314	+	5.51337i	0.358132	+	0.620302i	−0.629517	+	0.776987i	$0.716747\pi$
$80$	−4.30489	+	1.79172i	−0.481302	+	0.200320i
$81$	8.53015	+	2.86994i	0.947794	+	0.318883i
$82$	−5.39645	+	0.00229190i	−0.595938	+	0.000253098i
$83$	17.9192	−	2.35911i	1.96689	−	0.258946i	0.966896	−	0.255170i	$-0.0821315\pi$
$83$	17.9192	−	2.35911i	1.96689	−	0.258946i	0.999993	−	0.00377576i	$-0.00120186\pi$
$84$	4.30801	+	5.06192i	0.470042	+	0.552301i
$85$	0.682443	−	5.18367i	0.0740213	−	0.562248i
$86$	−10.2404	−	13.3338i	−1.10425	−	1.43782i
$87$	−0.504860	−	10.1371i	−0.0541267	−	1.08681i
$88$	−13.6902	+	1.82009i	−1.45938	+	0.194023i
$89$	−2.96906	−	2.96906i	−0.314720	−	0.314720i	0.532015	−	0.846735i	$-0.321435\pi$
$89$	−2.96906	−	2.96906i	−0.314720	−	0.314720i	−0.846735	+	0.532015i	$0.821435\pi$
$90$	−4.20455	−	2.60422i	−0.443198	−	0.274509i
$91$	−4.75094	+	1.96790i	−0.498034	+	0.206292i
$92$	0.658302	+	0.175792i	0.0686328	+	0.0183276i
$93$	−5.50275	+	7.96216i	−0.570608	+	0.825637i
$94$	1.37884	+	5.13718i	0.142217	+	0.529860i
$95$	−0.633600	+	1.09743i	−0.0650060	+	0.112594i
$96$	1.78097	+	9.63474i	0.181769	+	0.983341i
$97$	−1.67561	−	2.90224i	−0.170132	−	0.294678i	0.768334	−	0.640049i	$-0.221086\pi$
$97$	−1.67561	−	2.90224i	−0.170132	−	0.294678i	−0.938466	+	0.345372i	$0.887753\pi$
$98$	3.31676	−	3.31958i	0.335043	−	0.335328i
$99$	−10.0279	−	10.6778i	−1.00785	−	1.07316i
$100$	−5.15367	−	5.14492i	−0.515367	−	0.514492i
$101$	9.93629	+	7.62438i	0.988698	+	0.758654i	0.970481	−	0.241180i	$-0.0775343\pi$
$101$	9.93629	+	7.62438i	0.988698	+	0.758654i	0.0182173	+	0.999834i	$0.494201\pi$
$102$	−10.3481	−	3.68979i	−1.02462	−	0.365344i
$103$	−3.80296	+	1.01900i	−0.374717	+	0.100405i	−0.441262	−	0.897378i	$-0.645469\pi$
$103$	−3.80296	+	1.01900i	−0.374717	+	0.100405i	0.0665452	+	0.997783i	$0.478802\pi$
$104$	−7.51654	−	0.979831i	−0.737058	−	0.0960803i
$105$	1.76783	−	3.44739i	0.172522	−	0.336431i
$106$	−14.3477	+	1.89511i	−1.39357	+	0.184069i
$107$	10.9410	−	4.53190i	1.05770	−	0.438115i	0.215068	−	0.976599i	$-0.431003\pi$
$107$	10.9410	−	4.53190i	1.05770	−	0.438115i	0.842636	+	0.538484i	$0.181003\pi$
$108$	−7.20576	+	7.48846i	−0.693375	+	0.720577i
$109$	5.21100	−	12.5805i	0.499124	−	1.20499i	−0.450833	−	0.892608i	$-0.648873\pi$
$109$	5.21100	−	12.5805i	0.499124	−	1.20499i	0.949956	−	0.312383i	$-0.101127\pi$
$110$	4.02779	+	6.96949i	0.384034	+	0.664515i
$111$	12.5121	−	4.02952i	1.18760	−	0.382465i
$112$	−7.41033	+	1.99909i	−0.700210	+	0.188896i
$113$	−1.89610	+	3.28415i	−0.178370	+	0.308947i	−0.941323	−	0.337508i	$-0.890416\pi$
$113$	−1.89610	+	3.28415i	−0.178370	+	0.308947i	0.762952	+	0.646455i	$0.223749\pi$
$114$	1.97492	+	1.78601i	0.184968	+	0.167275i
$115$	−0.0518375	−	0.393745i	−0.00483387	−	0.0367169i
$116$	10.8315	+	4.47579i	1.00568	+	0.415566i
$117$	−3.79957	−	7.08548i	−0.351270	−	0.655053i
$118$	0.519506	−	1.25571i	0.0478244	−	0.115597i
$119$	2.22743	−	8.31287i	0.204188	−	0.762040i
$120$	4.79362	−	3.10400i	0.437595	−	0.283355i
$121$	3.32368	+	12.4041i	0.302152	+	1.12765i
$122$	16.7385	+	2.19644i	1.51544	+	0.198856i
$123$	6.50171	−	1.18756i	0.586239	−	0.107079i
$124$	−5.59619	−	9.67390i	−0.502553	−	0.868742i
$125$	−3.85480	+	9.30632i	−0.344784	+	0.832383i
$126$	−6.30209	−	5.15331i	−0.561435	−	0.459093i
$127$		−	0.602538i		−	0.0534666i	−0.999643	−	0.0267333i	$-0.991490\pi$
$127$		−	0.602538i		−	0.0534666i	0.999643	−	0.0267333i	$-0.00851049\pi$
$128$	−10.9369	−	2.89570i	−0.966691	−	0.255946i
$129$	15.2662	+	13.8177i	1.34411	+	1.21658i
$130$	1.14531	+	4.26712i	0.100451	+	0.374251i
$131$	5.60471	−	4.30064i	0.489685	−	0.375749i	−0.334203	−	0.942501i	$-0.608467\pi$
$131$	5.60471	−	4.30064i	0.489685	−	0.375749i	0.823888	+	0.566752i	$0.191800\pi$
$132$	16.0958	−	5.19874i	1.40096	−	0.452492i
$133$	−1.26979	+	1.65482i	−0.110104	+	0.143491i
$134$	3.30920	−	1.37236i	0.285872	−	0.118554i
$135$	5.63784	+	2.21473i	0.485228	+	0.190613i
$136$	8.95883	−	8.98168i	0.768213	−	0.770173i
$137$	13.7801	+	3.69237i	1.17731	+	0.315461i	0.793861	−	0.608099i	$-0.208068\pi$
$137$	13.7801	+	3.69237i	1.17731	+	0.315461i	0.383454	+	0.923560i	$0.374734\pi$
$138$	−0.831788	−	0.0672822i	−0.0708065	−	0.00572744i
$139$	7.76450	+	1.02222i	0.658576	+	0.0867032i	0.452405	−	0.891813i	$-0.350566\pi$
$139$	7.76450	+	1.02222i	0.658576	+	0.0867032i	0.206171	+	0.978516i	$0.433900\pi$
$140$	2.72636	+	3.54682i	0.230419	+	0.299761i
$141$	−2.78925	−	5.88709i	−0.234897	−	0.495783i
$142$	6.68782	+	11.5723i	0.561230	+	0.971126i
$143$			13.0858i			1.09429i
$144$	−4.26121	−	11.2179i	−0.355101	−	0.934828i
$145$		−	6.83101i		−	0.567285i
$146$	−1.36285	+	0.787615i	−0.112791	+	0.0651835i
$147$	−3.26756	+	4.72797i	−0.269504	+	0.389957i
$148$	−1.96841	+	15.0503i	−0.161802	+	1.23713i
$149$	−16.4859	−	2.17041i	−1.35058	−	0.177807i	−0.579720	−	0.814815i	$-0.696838\pi$
$149$	−16.4859	−	2.17041i	−1.35058	−	0.177807i	−0.770857	+	0.637009i	$0.780172\pi$
$150$	7.33925	+	5.06765i	0.599248	+	0.413772i
$151$	−9.68466	−	2.59500i	−0.788127	−	0.211178i	−0.157762	−	0.987477i	$-0.550428\pi$
$151$	−9.68466	−	2.59500i	−0.788127	−	0.211178i	−0.630365	+	0.776299i	$0.717095\pi$
$152$	−2.83911	+	1.18024i	−0.230282	+	0.0957300i
$153$	13.2786	+	2.17391i	1.07351	+	0.175750i
$154$	5.07575	+	12.2392i	0.409016	+	0.986266i
$155$	−3.96547	+	5.16790i	−0.318514	+	0.415096i
$156$	9.27185	−	0.469663i	0.742342	−	0.0376031i
$157$	17.8272	−	13.6793i	1.42277	−	1.09173i	0.441894	−	0.897067i	$-0.354307\pi$
$157$	17.8272	−	13.6793i	1.42277	−	1.09173i	0.980871	−	0.194659i	$-0.0623600\pi$
$158$	8.69552	−	2.33392i	0.691779	−	0.185676i
$159$	16.8715	−	5.43348i	1.33800	−	0.430903i
$160$	0.874610	+	6.53604i	0.0691440	+	0.516719i
$161$		−	0.653710i		−	0.0515196i
$162$	7.03816	−	10.6049i	0.552970	−	0.833201i
$163$	−3.18448	+	7.68801i	−0.249428	+	0.602171i	−0.998156	−	0.0607058i	$-0.980665\pi$
$163$	−3.18448	+	7.68801i	−0.249428	+	0.602171i	0.748728	+	0.662877i	$0.230665\pi$
$164$	−1.96898	+	7.37336i	−0.153751	+	0.575763i
$165$	−6.38326	−	7.51328i	−0.496936	−	0.584908i
$166$	3.32552	−	25.3430i	0.258110	−	1.96700i
$167$	−1.78966	−	6.67910i	−0.138488	−	0.516844i	−0.999959	−	0.00903759i	$-0.997123\pi$
$167$	−1.78966	−	6.67910i	−0.138488	−	0.516844i	0.861471	−	0.507806i	$-0.169543\pi$
$168$	8.48984	−	4.03566i	0.655006	−	0.311358i
$169$	1.50573	−	5.61945i	0.115825	−	0.432266i
$170$	−6.83243	−	2.82669i	−0.524024	−	0.216797i
$171$	−2.77171	−	1.71838i	−0.211958	−	0.131408i
$172$	−21.9587	+	9.11747i	−1.67434	+	0.695200i
$173$	−0.986445	−	7.49279i	−0.0749980	−	0.569666i	−0.987148	−	0.159810i	$-0.948912\pi$
$173$	−0.986445	−	7.49279i	−0.0749980	−	0.569666i	0.912150	−	0.409857i	$-0.134421\pi$
$174$	−14.0336	−	3.01483i	−1.06389	−	0.228553i
$175$	−3.49329	+	6.05056i	−0.264068	+	0.457379i
$176$	−2.51643	+	19.3684i	−0.189683	+	1.45995i
$177$	−0.350264	+	1.62707i	−0.0263274	+	0.122298i
$178$	−5.14130	+	2.97124i	−0.385357	+	0.222704i
$179$	−8.90629	+	21.5017i	−0.665688	+	1.60711i	0.123063	+	0.992399i	$0.460728\pi$
$179$	−8.90629	+	21.5017i	−0.665688	+	1.60711i	−0.788751	+	0.614713i	$0.789272\pi$
$180$	−5.09437	+	4.79247i	−0.379712	+	0.357210i
$181$	23.2328	−	9.62335i	1.72688	−	0.715298i	0.727302	−	0.686318i	$-0.240774\pi$
$181$	23.2328	−	9.62335i	1.72688	−	0.715298i	0.999580	−	0.0289797i	$-0.00922581\pi$
$182$	0.952304	+	7.20980i	0.0705895	+	0.534426i
$183$	−20.6506	+	1.02846i	−1.52653	+	0.0760263i
$184$	0.480738	−	0.835118i	0.0354405	−	0.0615657i
$185$	8.54546	−	2.28975i	0.628275	−	0.168346i
$186$	8.86679	+	10.4275i	0.650145	+	0.764580i
$187$	−17.3744	−	13.3319i	−1.27054	−	0.974923i
$188$	7.52221	−	0.00638943i	0.548614	−	0.000465997i
$189$	8.72484	+	4.82562i	0.634639	+	0.351012i
$190$	1.26774	+	1.26666i	0.0919714	+	0.0918933i
$191$	−2.34881	−	4.06825i	−0.169954	−	0.294369i	0.768450	−	0.639910i	$-0.221029\pi$
$191$	−2.34881	−	4.06825i	−0.169954	−	0.294369i	−0.938403	+	0.345542i	$0.887695\pi$
$192$	13.8136	+	1.08785i	0.996913	+	0.0785085i
$193$	5.59933	−	9.69833i	0.403049	−	0.698101i	−0.591043	−	0.806640i	$-0.701284\pi$
$193$	5.59933	−	9.69833i	0.403049	−	0.698101i	0.994092	+	0.108539i	$0.0346171\pi$
$194$	−4.57733	+	1.22857i	−0.328633	+	0.0882065i
$195$	−2.31685	−	4.89002i	−0.165913	−	0.350182i
$196$	−3.32305	−	5.74441i	−0.237360	−	0.410315i
$197$	−10.2796	+	4.25796i	−0.732394	+	0.303367i	−0.717535	−	0.696522i	$-0.754730\pi$
$197$	−10.2796	+	4.25796i	−0.732394	+	0.303367i	−0.0148585	+	0.999890i	$0.504730\pi$
$198$	−18.2525	+	9.79783i	−1.29715	+	0.696301i
$199$	12.0444	+	12.0444i	0.853803	+	0.853803i	0.990599	−	0.136796i	$-0.0436806\pi$
$199$	12.0444	+	12.0444i	0.853803	+	0.853803i	−0.136796	+	0.990599i	$0.543681\pi$
$200$	−8.91227	+	5.16065i	−0.630193	+	0.364913i
$201$	−3.68597	+	2.38011i	−0.259989	+	0.167880i
$202$	14.0475	−	10.7885i	0.988375	−	0.759074i
$203$	1.46765	−	11.1479i	0.103009	−	0.782427i
$204$	−8.82260	+	12.7890i	−0.617705	+	0.895409i
$205$	4.41017	−	0.580610i	0.308020	−	0.0405515i
$206$	0.00236472	+	5.56792i	0.000164758	+	0.387935i
$207$	1.01700	−	0.101551i	0.0706862	−	0.00705830i
$208$	−4.08551	+	9.91088i	−0.283279	+	0.687196i
$209$	2.65393	+	4.59675i	0.183576	+	0.317964i
$210$	−4.06371	−	3.67501i	−0.280423	−	0.253599i
$211$	−16.2026	+	12.4327i	−1.11543	+	0.855901i	−0.990670	−	0.136285i	$-0.956484\pi$
$211$	−16.2026	+	12.4327i	−1.11543	+	0.855901i	−0.124763	+	0.992187i	$0.539817\pi$
$212$	−2.65423	+	20.2941i	−0.182293	+	1.39380i
$213$	−10.5989	−	12.4752i	−0.726225	−	0.854787i
$214$	−2.19307	−	16.6035i	−0.149915	−	1.13499i
$215$	9.79927	+	9.79927i	0.668305	+	0.668305i
$216$	7.59727	+	12.5810i	0.516929	+	0.856028i
$217$	−7.58178	+	7.58178i	−0.514685	+	0.514685i
$218$	−15.2829	−	11.7166i	−1.03509	−	0.793551i
$219$	1.46919	−	1.24822i	0.0992785	−	0.0843468i
$220$	10.9935	−	2.95572i	0.741183	−	0.199274i
$221$	−7.31736	−	9.53617i	−0.492219	−	0.641472i
$222$	−0.932569	−	18.5664i	−0.0625899	−	1.24609i
$223$	−11.0201	+	6.36245i	−0.737960	+	0.426061i	−0.821327	−	0.570457i	$-0.806766\pi$
$223$	−11.0201	+	6.36245i	−0.737960	+	0.426061i	0.0833671	+	0.996519i	$0.473433\pi$
$224$	0.0230496	+	10.8544i	0.00154007	+	0.725241i
$225$	−9.95572	−	4.49469i	−0.663714	−	0.299646i
$226$	3.79382	+	3.79060i	0.252361	+	0.252147i
$227$	2.99712	+	22.7654i	0.198926	+	1.51099i	0.741481	+	0.670974i	$0.234124\pi$
$227$	2.99712	+	22.7654i	0.198926	+	1.51099i	−0.542555	+	0.840020i	$0.682543\pi$
$228$	3.16174	−	2.04541i	0.209391	−	0.135460i
$229$	−14.8209	−	1.95121i	−0.979393	−	0.128940i	−0.376203	−	0.926537i	$-0.622771\pi$
$229$	−14.8209	−	1.95121i	−0.979393	−	0.128940i	−0.603190	+	0.797598i	$0.706104\pi$
$230$	−0.556871	−	0.0730728i	−0.0367190	−	0.00481828i
$231$	−8.80294	−	13.6327i	−0.579191	−	0.896969i
$232$	10.0731	−	13.1622i	0.661329	−	0.864138i
$233$	7.68982	−	7.68982i	0.503777	−	0.503777i	−0.408833	−	0.912609i	$-0.634064\pi$
$233$	7.68982	−	7.68982i	0.503777	−	0.503777i	0.912609	+	0.408833i	$0.134064\pi$
$234$	−11.0686	+	2.60155i	−0.723576	+	0.170068i
$235$	−1.67783	−	4.05065i	−0.109450	−	0.264235i
$236$	−1.52567	−	1.16863i	−0.0993127	−	0.0760714i
$237$	−9.96487	+	4.72126i	−0.647288	+	0.306679i
$238$	−10.5429	−	6.08097i	−0.683393	−	0.394171i
$239$	3.38369	+	1.95358i	0.218873	+	0.126366i	0.605428	−	0.795900i	$-0.293002\pi$
$239$	3.38369	+	1.95358i	0.218873	+	0.126366i	−0.386555	+	0.922266i	$0.626335\pi$
$240$	−2.48882	−	7.68329i	−0.160652	−	0.495954i
$241$	−24.7577	+	14.2939i	−1.59479	+	0.920751i	−0.602318	+	0.798257i	$0.705756\pi$
$241$	−24.7577	+	14.2939i	−1.59479	+	0.920751i	−0.992469	+	0.122494i	$0.960911\pi$
$242$	18.1609	−	0.00771302i	1.16743	−	0.000495812i
$243$	−6.15200	+	14.3232i	−0.394651	+	0.918831i
$244$	9.11775	−	22.0652i	0.583704	−	1.41258i
$245$	−2.35472	+	3.06873i	−0.150437	+	0.196054i
$246$	0.753599	−	9.31650i	0.0480477	−	0.593998i
$247$	0.754015	+	2.81402i	0.0479768	+	0.179052i
$248$	−15.2614	+	4.11013i	−0.969099	+	0.260993i
$249$	1.55715	+	31.2661i	0.0986803	+	1.98141i
$250$	11.3054	+	8.66731i	0.715016	+	0.548169i
$251$	−2.34809	−	5.66878i	−0.148210	−	0.357810i	0.832287	−	0.554345i	$-0.187031\pi$
$251$	−2.34809	−	5.66878i	−0.148210	−	0.357810i	−0.980497	+	0.196535i	$0.937031\pi$
$252$	−9.34342	+	6.72655i	−0.588580	+	0.423733i
$253$	−1.53687	−	0.636592i	−0.0966222	−	0.0400222i
$254$	−0.823176	−	0.220195i	−0.0516507	−	0.0138162i
$255$	8.85304	+	1.90582i	0.554399	+	0.119347i
$256$	−7.95287	+	13.8835i	−0.497055	+	0.867719i
$257$	−8.35257	−	4.82236i	−0.521019	−	0.300810i	0.216333	−	0.976320i	$-0.430590\pi$
$257$	−8.35257	−	4.82236i	−0.521019	−	0.300810i	−0.737351	+	0.675509i	$0.763924\pi$
$258$	24.4565	−	15.8068i	1.52259	−	0.984086i
$259$	14.4377	−	1.90076i	0.897117	−	0.118108i
$260$	6.24821	−	0.00530728i	0.387497	−	0.000329144i
$261$	17.5711	+	0.551484i	1.08762	+	0.0341360i
$262$	−3.82724	−	9.22869i	−0.236448	−	0.570150i
$263$	−30.5078	−	8.17454i	−1.88119	−	0.504063i	−0.999479	−	0.0322745i	$-0.989725\pi$
$263$	−30.5078	−	8.17454i	−1.88119	−	0.504063i	−0.881712	−	0.471789i	$-0.843608\pi$
$264$	−1.22029	−	23.8896i	−0.0751038	−	1.47030i
$265$	11.5228	−	3.08754i	0.707843	−	0.189666i
$266$	1.79674	+	2.33950i	0.110165	+	0.143444i
$267$	5.54244	−	4.70885i	0.339192	−	0.288177i
$268$	−0.665564	−	5.02249i	−0.0406558	−	0.306798i
$269$	21.1423	+	8.75744i	1.28907	+	0.533951i	0.918708	−	0.394937i	$-0.129233\pi$
$269$	21.1423	+	8.75744i	1.28907	+	0.533951i	0.370362	+	0.928887i	$0.379233\pi$
$270$	5.08604	−	6.89295i	0.309527	−	0.419491i
$271$	−11.0776			−0.672917			−0.336459	−	0.941698i	$-0.609229\pi$
$271$	−11.0776			−0.672917			−0.336459	+	0.941698i	$0.609229\pi$
$272$	−8.99664	−	15.5217i	−0.545502	−	0.941141i
$273$	−2.73036	−	8.47805i	−0.165249	−	0.513115i
$274$	10.0803	−	17.4768i	0.608975	−	1.05581i
$275$	10.8230	+	14.1048i	0.652653	+	0.850554i
$276$	−0.395892	+	1.11178i	−0.0238299	+	0.0669215i
$277$	−4.19306	−	3.21745i	−0.251937	−	0.193318i	0.475070	−	0.879948i	$-0.342423\pi$
$277$	−4.19306	−	3.21745i	−0.251937	−	0.193318i	−0.727007	+	0.686630i	$0.759089\pi$
$278$	4.23403	−	10.2341i	0.253940	−	0.613803i
$279$	−12.9730	−	10.6174i	−0.776674	−	0.635648i
$280$	5.84193	−	2.42853i	0.349122	−	0.145133i
$281$	7.51836	−	28.0589i	0.448508	−	1.67385i	−0.257997	−	0.966146i	$-0.583062\pi$
$281$	7.51836	−	28.0589i	0.448508	−	1.67385i	0.706505	−	0.707708i	$-0.250271\pi$
$282$	−9.06215	+	1.65921i	−0.539643	+	0.0988045i
$283$	1.55835	−	11.8369i	0.0926345	−	0.703629i	−0.880608	−	0.473846i	$-0.842865\pi$
$283$	1.55835	−	11.8369i	0.0926345	−	0.703629i	0.973242	−	0.229782i	$-0.0738015\pi$
$284$	18.2539	−	4.90773i	1.08317	−	0.291220i
$285$	−1.80560	−	1.24787i	−0.106955	−	0.0739177i
$286$	17.8776	+	4.78215i	1.05712	+	0.282774i
$287$	7.32192			0.432200
$288$	−16.8830	+	1.72205i	−0.994838	+	0.101473i
$289$	3.11640			0.183318
$290$	−9.33240	−	2.49636i	−0.548017	−	0.146591i
$291$	5.24551	−	2.48527i	0.307497	−	0.145689i
$292$	0.577977	+	2.14973i	0.0338235	+	0.125804i
$293$	1.49049	−	11.3214i	0.0870756	−	0.661405i	−0.891127	−	0.453753i	$-0.850085\pi$
$293$	1.49049	−	11.3214i	0.0870756	−	0.661405i	0.978203	−	0.207651i	$-0.0665820\pi$
$294$	5.26515	+	6.19189i	0.307070	+	0.361119i
$295$	−0.289915	+	1.08198i	−0.0168795	+	0.0629952i
$296$	19.8421	+	8.18926i	1.15330	+	0.475991i
$297$	19.8414	−	15.8128i	1.15131	−	0.917552i
$298$	−8.98986	+	21.7295i	−0.520769	+	1.25876i
$299$	−0.724356	−	0.555818i	−0.0418906	−	0.0321438i
$300$	9.60542	−	8.17480i	0.554569	−	0.471972i
$301$	13.8865	+	18.0973i	0.800407	+	1.04311i
$302$	−7.08445	+	12.2827i	−0.407664	+	0.706788i
$303$	−14.5572	+	16.0832i	−0.836291	+	0.923957i
$304$	0.574879	+	4.31005i	0.0329716	+	0.247198i
$305$	−13.9156			−0.796807
$306$	7.82256	−	17.3466i	0.447186	−	0.991636i
$307$	−30.1275	−	12.4792i	−1.71947	−	0.712228i	−0.999840	−	0.0178696i	$-0.994312\pi$
$307$	−30.1275	−	12.4792i	−1.71947	−	0.712228i	−0.719630	−	0.694358i	$-0.755688\pi$
$308$	18.5759	−	2.46162i	1.05846	−	0.140264i
$309$	−1.22529	−	6.70829i	−0.0697044	−	0.381622i
$310$	5.61113	+	7.30613i	0.318691	+	0.414961i
$311$	3.57862	−	0.958889i	0.202925	−	0.0543736i	−0.155925	−	0.987769i	$-0.549836\pi$
$311$	3.57862	−	0.958889i	0.202925	−	0.0543736i	0.358850	+	0.933395i	$0.383169\pi$
$312$	2.74671	−	12.8387i	0.155502	−	0.726846i
$313$	−4.60631	−	1.23426i	−0.260364	−	0.0697643i	0.126276	−	0.991995i	$-0.459698\pi$
$313$	−4.60631	−	1.23426i	−0.260364	−	0.0697643i	−0.386640	+	0.922231i	$0.626364\pi$
$314$	−12.1735	−	29.3542i	−0.686991	−	1.65655i
$315$	5.70324	+	3.53584i	0.321341	+	0.199222i
$316$	−0.0108152	−	12.7326i	−0.000608400	−	0.716263i
$317$	−3.12929	+	0.411979i	−0.175758	+	0.0231390i	−0.217892	−	0.975973i	$-0.569918\pi$
$317$	−3.12929	+	0.411979i	−0.175758	+	0.0231390i	0.0421332	+	0.999112i	$0.486585\pi$
$318$	−1.25749	−	25.0352i	−0.0705166	−	1.40390i
$319$	−24.7794	−	14.3064i	−1.38738	−	0.801004i
$320$	9.24903	+	1.19369i	0.517037	+	0.0667293i
$321$	6.28776	+	19.5242i	0.350949	+	1.08973i
$322$	−0.893086	−	0.238895i	−0.0497697	−	0.0133131i
$323$	−4.50445	−	1.86581i	−0.250634	−	0.103816i
$324$	−11.9162	−	13.4909i	−0.662009	−	0.749496i
$325$	3.73426	+	9.01530i	0.207139	+	0.500079i
$326$	9.33946	+	7.16012i	0.517265	+	0.396562i
$327$	20.9868	+	10.7621i	1.16057	+	0.595144i
$328$	9.35379	+	5.38454i	0.516477	+	0.297311i
$329$	−1.86786	−	6.97094i	−0.102978	−	0.384321i
$330$	−12.5972	+	5.97500i	−0.693455	+	0.328913i
$331$	10.9540	−	14.2755i	0.602085	−	0.784652i	−0.388515	−	0.921442i	$-0.627012\pi$
$331$	10.9540	−	14.2755i	0.602085	−	0.784652i	0.990600	+	0.136790i	$0.0436786\pi$
$332$	−33.4078	−	13.8047i	−1.83349	−	0.757634i
$333$	5.19992	+	22.1660i	0.284954	+	1.21469i
$334$	−9.77887	+	0.00415313i	−0.535076	+	0.000227249i
$335$	−2.55737	+	1.47650i	−0.139724	+	0.0806697i
$336$	−2.41087	−	13.0735i	−0.131524	−	0.713216i
$337$	−21.5782	−	12.4582i	−1.17544	−	0.678641i	−0.220485	−	0.975390i	$-0.570764\pi$
$337$	−21.5782	−	12.4582i	−1.17544	−	0.678641i	−0.954955	+	0.296750i	$0.904097\pi$
$338$	−7.12693	−	4.11070i	−0.387654	−	0.223593i
$339$	−5.40342	−	3.73437i	−0.293474	−	0.202823i
$340$	−6.35865	+	8.30134i	−0.344846	+	0.450203i
$341$	10.4415	+	25.2080i	0.565438	+	1.36509i
$342$	−3.36052	+	3.15868i	−0.181716	+	0.170802i
$343$	−13.9997	+	13.9997i	−0.755914	+	0.755914i
$344$	4.43139	+	33.3315i	0.238925	+	1.79712i
$345$	0.687020	−	0.0342158i	0.0369879	−	0.00184212i
$346$	−10.5970	−	1.39054i	−0.569698	−	0.0747560i
$347$	−23.5985	−	3.10680i	−1.26683	−	0.166782i	−0.533001	−	0.846114i	$-0.678936\pi$
$347$	−23.5985	−	3.10680i	−1.26683	−	0.166782i	−0.733830	+	0.679333i	$0.762269\pi$
$348$	−9.24732	+	18.0707i	−0.495708	+	0.968692i
$349$	0.937142	+	7.11830i	0.0501641	+	0.381034i	0.998050	+	0.0624233i	$0.0198829\pi$
$349$	0.937142	+	7.11830i	0.0501641	+	0.381034i	−0.947886	+	0.318611i	$0.896784\pi$
$350$	6.98955	+	6.98362i	0.373607	+	0.373290i
$351$	12.7654	−	5.56474i	0.681368	−	0.297024i
$352$	25.5411	+	10.5160i	1.36135	+	0.560504i
$353$	4.86328	−	2.80781i	0.258846	−	0.149445i	−0.364962	−	0.931022i	$-0.618918\pi$
$353$	4.86328	−	2.80781i	0.258846	−	0.149445i	0.623808	+	0.781578i	$0.285585\pi$
$354$	2.09486	+	1.07313i	0.111341	+	0.0570360i
$355$	−6.70689	−	8.74059i	−0.355965	−	0.463902i
$356$	2.18039	+	8.10978i	0.115561	+	0.429817i
$357$	14.0383	+	5.01229i	0.742983	+	0.265278i
$358$	26.1204	+	20.0253i	1.38051	+	1.05837i
$359$	10.4889	−	10.4889i	0.553582	−	0.553582i	−0.373891	−	0.927473i	$-0.621977\pi$
$359$	10.4889	−	10.4889i	0.553582	−	0.553582i	0.927473	+	0.373891i	$0.121977\pi$
$360$	4.68567	+	8.71121i	0.246956	+	0.459121i
$361$	−12.5994	−	12.5994i	−0.663129	−	0.663129i
$362$	−4.65691	−	35.2570i	−0.244762	−	1.85307i
$363$	−21.8805	+	3.99654i	−1.14843	+	0.209764i
$364$	10.1979	+	1.33377i	0.534516	+	0.0699085i
$365$	1.02937	−	0.789861i	0.0538795	−	0.0413432i
$366$	−6.14159	+	28.5883i	−0.321026	+	1.49433i
$367$	4.13255	+	7.15779i	0.215718	+	0.373634i	0.953494	−	0.301411i	$-0.0974576\pi$
$367$	4.13255	+	7.15779i	0.215718	+	0.373634i	−0.737777	+	0.675045i	$0.764124\pi$
$368$	−0.965238	−	0.961964i	−0.0503165	−	0.0501459i
$369$	1.13743	+	11.3910i	0.0592124	+	0.592989i
$370$	−0.00531366	−	12.5114i	−0.000276244	−	0.650438i
$371$	19.4681	−	2.56302i	1.01073	−	0.133065i
$372$	17.4862	−	8.30297i	0.906615	−	0.430489i
$373$	−2.80109	+	21.2764i	−0.145035	+	1.10165i	0.751833	+	0.659353i	$0.229170\pi$
$373$	−2.80109	+	21.2764i	−0.145035	+	1.10165i	−0.896868	+	0.442298i	$0.854163\pi$
$374$	−24.5631	+	18.8645i	−1.27013	+	0.975462i
$375$	−15.5249	−	7.96118i	−0.801700	−	0.411113i
$376$	2.74023	−	10.2790i	0.141316	−	0.530101i
$377$	−11.1047	−	11.1047i	−0.571924	−	0.571924i
$378$	9.78112	−	10.1562i	0.503087	−	0.522379i
$379$	15.8866	−	6.58044i	0.816039	−	0.338015i	0.0646786	−	0.997906i	$-0.479398\pi$
$379$	15.8866	−	6.58044i	0.816039	−	0.338015i	0.751361	+	0.659892i	$0.229398\pi$
$380$	2.19378	−	1.26906i	0.112538	−	0.0651016i
$381$	1.04019	+	0.0845845i	0.0532907	+	0.00433340i
$382$	−6.41633	+	1.72217i	−0.328288	+	0.0881140i
$383$	2.44422	−	4.23351i	0.124894	−	0.216322i	−0.796798	−	0.604246i	$-0.793474\pi$
$383$	2.44422	−	4.23351i	0.124894	−	0.216322i	0.921691	+	0.387924i	$0.126808\pi$
$384$	6.53432	−	18.4744i	0.333453	−	0.942767i
$385$	−5.46090	−	9.45856i	−0.278313	−	0.482053i
$386$	−11.2034	−	11.1939i	−0.570239	−	0.569755i
$387$	−25.9973	+	24.4151i	−1.32152	+	1.24109i
$388$	0.00569310	+	6.70243i	0.000289024	+	0.340264i
$389$	22.3831	+	17.1751i	1.13487	+	0.870813i	0.992887	−	0.119057i	$-0.0379870\pi$
$389$	22.3831	+	17.1751i	1.13487	+	0.870813i	0.141978	+	0.989870i	$0.454654\pi$
$390$	−7.52734	+	1.37820i	−0.381161	+	0.0697877i
$391$	1.47595	−	0.395480i	0.0746420	−	0.0200003i
$392$	−9.06230	+	2.44061i	−0.457715	+	0.123270i
$393$	6.63763	+	10.2794i	0.334824	+	0.518528i
$394$	2.06051	+	15.5999i	0.103807	+	0.785911i
$395$	−6.85638	+	2.84001i	−0.344982	+	0.142896i
$396$	6.71532	+	28.5168i	0.337458	+	1.43302i
$397$	3.45578	−	8.34299i	0.173441	−	0.418723i	−0.813125	−	0.582089i	$-0.802235\pi$
$397$	3.45578	−	8.34299i	0.173441	−	0.418723i	0.986565	+	0.163367i	$0.0522354\pi$
$398$	20.8563	−	12.0532i	1.04543	−	0.604174i
$399$	−2.67855	−	2.42440i	−0.134095	−	0.121372i
$400$	3.79344	+	14.0617i	0.189672	+	0.703086i
$401$	−8.90316	+	15.4207i	−0.444602	+	0.770074i	−0.998024	−	0.0628271i	$-0.979988\pi$
$401$	−8.90316	+	15.4207i	−0.444602	+	0.770074i	0.553422	+	0.832901i	$0.313322\pi$
$402$	1.90464	+	5.90550i	0.0949946	+	0.294540i
$403$	1.95472	+	14.8475i	0.0973714	+	0.739609i
$404$	−9.60543	−	23.1340i	−0.477888	−	1.15096i
$405$	−4.61484	+	9.42200i	−0.229313	+	0.468183i
$406$	−14.6937	−	6.07901i	−0.729235	−	0.301696i
$407$	9.59098	−	35.7940i	0.475407	−	1.77424i
$408$	14.2479	+	16.7269i	0.705377	+	0.828107i
$409$	0.569267	+	2.12454i	0.0281485	+	0.105052i	0.978571	−	0.205910i	$-0.0660155\pi$
$409$	0.569267	+	2.12454i	0.0281485	+	0.105052i	−0.950422	+	0.310962i	$0.899349\pi$
$410$	0.818457	−	6.23727i	0.0404207	−	0.308037i
$411$	−8.30879	+	23.2710i	−0.409843	+	1.14787i
$412$	7.60764	+	2.03154i	0.374802	+	0.100087i
$413$	−0.705591	+	1.70345i	−0.0347199	+	0.0838212i
$414$	0.232919	−	1.42651i	0.0114474	−	0.0701093i
$415$			21.0690i			1.03424i
$416$	12.0470	+	9.20343i	0.590654	+	0.451235i
$417$	−2.85469	+	13.2608i	−0.139795	+	0.649382i
$418$	7.24986	−	1.94589i	0.354602	−	0.0951768i
$419$	20.3284	−	15.5986i	0.993109	−	0.762039i	0.0217758	−	0.999763i	$-0.493068\pi$
$419$	20.3284	−	15.5986i	0.993109	−	0.762039i	0.971333	+	0.237724i	$0.0764013\pi$
$420$	−6.50579	+	4.20875i	−0.317450	+	0.205366i
$421$	−4.74051	+	6.17795i	−0.231038	+	0.301095i	−0.894457	−	0.447153i	$-0.852438\pi$
$421$	−4.74051	+	6.17795i	−0.231038	+	0.301095i	0.663419	+	0.748248i	$0.269105\pi$
$422$	11.0641	+	26.6791i	0.538594	+	1.29872i
$423$	10.5548	−	3.98880i	0.513190	−	0.193942i
$424$	26.7554	+	11.0425i	1.29936	+	0.536273i
$425$	−15.7744	−	4.22673i	−0.765169	−	0.205026i
$426$	−20.9167	+	9.92102i	−1.01342	+	0.480675i
$427$	−22.7096	−	2.98978i	−1.09900	−	0.144686i
$428$	−23.4848	−	3.07155i	−1.13518	−	0.148469i
$429$	−22.5907	−	1.83699i	−1.09069	−	0.0886908i
$430$	16.9687	−	9.80648i	0.818302	−	0.472910i
$431$			5.95516i			0.286850i	0.989661	+	0.143425i	$0.0458116\pi$
$431$			5.95516i			0.286850i	−0.989661	+	0.143425i	$0.954188\pi$
$432$	19.9643	−	5.78158i	0.960533	−	0.278166i
$433$		−	0.651090i		−	0.0312894i	−0.999878	−	0.0156447i	$-0.995020\pi$
$433$		−	0.651090i		−	0.0312894i	0.999878	−	0.0156447i	$-0.00498007\pi$
$434$	7.58736	+	13.1288i	0.364205	+	0.630203i
$435$	11.7927	+	0.958940i	0.565418	+	0.0459776i
$436$	−21.5921	+	16.5974i	−1.03407	+	0.794870i
$437$	−0.367175	−	0.0483395i	−0.0175644	−	0.00231239i
$438$	−1.16838	−	2.46333i	−0.0558276	−	0.117702i
$439$	34.0762	+	9.13069i	1.62637	+	0.435784i	0.952864	−	0.303399i	$-0.0981214\pi$
$439$	34.0762	+	9.13069i	1.62637	+	0.435784i	0.673505	+	0.739183i	$0.264788\pi$
$440$	−0.0205123	−	16.0993i	−0.000977887	−	0.767504i
$441$	−7.70345	−	6.30468i	−0.366831	−	0.300223i
$442$	−15.7022	+	6.51189i	−0.746879	+	0.309739i
$443$	8.30070	−	10.8177i	0.394378	−	0.513964i	−0.553391	−	0.832922i	$-0.686666\pi$
$443$	8.30070	−	10.8177i	0.394378	−	0.513964i	0.947769	+	0.318958i	$0.103333\pi$
$444$	−25.7058	−	5.51093i	−1.21994	−	0.261537i
$445$	3.88324	−	2.97972i	0.184083	−	0.141252i
$446$	4.66502	+	17.3806i	0.220895	+	0.822994i
$447$	6.06119	−	28.1558i	0.286684	−	1.33172i
$448$	14.8375	+	3.93520i	0.701006	+	0.185921i
$449$		−	26.8384i		−	1.26658i	−0.773914	−	0.633291i	$-0.781704\pi$
$449$		−	26.8384i		−	1.26658i	0.773914	−	0.633291i	$-0.218296\pi$
$450$	−9.77883	+	11.9587i	−0.460979	+	0.563741i
$451$	7.13020	−	17.2138i	0.335748	−	0.810567i
$452$	6.56507	−	3.79779i	0.308795	−	0.178633i
$453$	5.83942	−	16.3549i	0.274360	−	0.768418i
$454$	32.1970	+	4.22490i	1.51108	+	0.198284i
$455$	−1.55151	−	5.79031i	−0.0727358	−	0.271454i
$456$	−1.63895	−	5.06699i	−0.0767510	−	0.237283i
$457$	−4.47630	+	16.7058i	−0.209392	+	0.781463i	0.778673	+	0.627430i	$0.215893\pi$
$457$	−4.47630	+	16.7058i	−0.209392	+	0.781463i	−0.988066	+	0.154033i	$0.950774\pi$
$458$	−8.08193	+	19.5350i	−0.377644	+	0.912810i
$459$	−5.61699	+	22.6184i	−0.262178	+	1.05574i
$460$	−0.303336	+	0.734082i	−0.0141431	+	0.0342267i
$461$	−0.427534	−	3.24745i	−0.0199123	−	0.151249i	0.978600	−	0.205770i	$-0.0659700\pi$
$461$	−0.427534	−	3.24745i	−0.0199123	−	0.151249i	−0.998513	+	0.0545216i	$0.982637\pi$
$462$	−21.8418	+	7.04439i	−1.01617	+	0.327735i
$463$	13.4759	−	23.3409i	0.626277	−	1.08474i	−0.362016	−	0.932172i	$-0.617911\pi$
$463$	13.4759	−	23.3409i	0.626277	−	1.08474i	0.988293	−	0.152571i	$-0.0487552\pi$
$464$	−14.3007	−	18.5717i	−0.663895	−	0.862168i
$465$	−8.36495	−	7.57127i	−0.387915	−	0.351109i
$466$	−7.69548	−	13.3159i	−0.356486	−	0.616847i
$467$	6.67811	−	16.1224i	0.309026	−	0.746055i	−0.690711	−	0.723131i	$-0.742702\pi$
$467$	6.67811	−	16.1224i	0.309026	−	0.746055i	0.999737	−	0.0229242i	$-0.00729765\pi$
$468$	−0.490781	+	16.0724i	−0.0226864	+	0.742947i
$469$	−4.49073	+	1.86012i	−0.207363	+	0.0858924i
$470$	−6.14707	+	0.811934i	−0.283543	+	0.0374517i
$471$	21.1127	+	32.6963i	0.972821	+	1.50657i
$472$	−2.15411	+	1.65727i	−0.0991509	+	0.0762821i
$473$	56.0696	−	15.0238i	2.57808	−	0.690795i
$474$	2.80848	+	15.3392i	0.128998	+	0.704551i
$475$	3.14015	+	2.40952i	0.144080	+	0.110557i
$476$	−12.1605	+	12.1812i	−0.557378	+	0.558325i
$477$	7.01167	+	29.8890i	0.321042	+	1.36852i
$478$	3.90549	−	3.90881i	0.178633	−	0.178785i
$479$	9.05406	+	15.6821i	0.413691	+	0.716533i	0.995290	−	0.0969423i	$-0.0309062\pi$
$479$	9.05406	+	15.6821i	0.413691	+	0.716533i	−0.581599	+	0.813475i	$0.697573\pi$
$480$	−11.4063	+	0.592354i	−0.520623	+	0.0270371i
$481$	10.1695	−	17.6141i	0.463690	−	0.803135i
$482$	10.4804	+	39.0472i	0.477371	+	1.77855i
$483$	1.12853	+	0.0917680i	0.0513501	+	0.00417559i
$484$	6.62628	−	24.8139i	0.301195	−	1.12790i
$485$	3.60920	−	1.49498i	0.163885	−	0.0678836i
$486$	17.3198	+	13.6391i	0.785642	+	0.618681i
$487$	22.7577	+	22.7577i	1.03125	+	1.03125i	0.999496	+	0.0317527i	$0.0101089\pi$
$487$	22.7577	+	22.7577i	1.03125	+	1.03125i	0.0317527	+	0.999496i	$0.489891\pi$
$488$	−26.8130	−	20.5201i	−1.21377	−	0.928902i
$489$	−12.8252	−	6.57678i	−0.579975	−	0.297412i
$490$	3.33192	+	4.33842i	0.150521	+	0.195990i
$491$	1.33643	−	10.1512i	0.0603121	−	0.458116i	−0.934466	−	0.356053i	$-0.884122\pi$
$491$	1.33643	−	10.1512i	0.0603121	−	0.458116i	0.994778	−	0.102063i	$-0.0325443\pi$
$492$	−12.4526	−	4.43422i	−0.561407	−	0.199910i
$493$	26.0576	−	3.43055i	1.17358	−	0.154504i
$494$	4.12001	−	0.00174979i	0.185368	−	7.87267e-5i
$495$	13.8666	−	9.96505i	0.623260	−	0.447896i
$496$	0.0379717	+	22.3518i	0.00170498	+	1.00363i
$497$	−9.06740	−	15.7052i	−0.406728	−	0.704474i
$498$	43.2841	+	9.29868i	1.93961	+	0.416684i
$499$	−6.69096	+	5.13416i	−0.299529	+	0.229836i	−0.747581	−	0.664171i	$-0.768785\pi$
$499$	−6.69096	+	5.13416i	−0.299529	+	0.229836i	0.448052	+	0.894008i	$0.352118\pi$
$500$	15.9726	−	12.2778i	0.714317	−	0.549079i
$501$	11.7817	−	2.15197i	0.526368	−	0.0961428i
$502$	−8.60267	+	1.13628i	−0.383956	+	0.0507147i
$503$	−23.0958	−	23.0958i	−1.02979	−	1.02979i	−0.999542	−	0.0302472i	$-0.990371\pi$
$503$	−23.0958	−	23.0958i	−1.02979	−	1.02979i	−0.0302472	−	0.999542i	$-0.509629\pi$
$504$	5.77517	+	15.2230i	0.257246	+	0.678086i
$505$	−10.3237	+	10.3237i	−0.459399	+	0.459399i
$506$	−1.43134	+	1.86700i	−0.0636309	+	0.0829984i
$507$	9.48978	+	3.38828i	0.421456	+	0.150479i
$508$	−0.601652	+	1.04414i	−0.0266940	+	0.0463261i
$509$	−20.5757	−	26.8147i	−0.912000	−	1.18854i	−0.981597	−	0.190966i	$-0.938838\pi$
$509$	−20.5757	−	26.8147i	−0.912000	−	1.18854i	0.0695967	−	0.997575i	$-0.477829\pi$
$510$	5.83900	−	11.3984i	0.258555	−	0.504729i
$511$	1.84958	−	1.06785i	0.0818205	−	0.0472391i
$512$	16.0610	+	15.9387i	0.709804	+	0.704399i
$513$	3.35562	−	4.54372i	0.148154	−	0.200610i
$514$	−9.64062	+	9.64881i	−0.425229	+	0.425591i
$515$	−0.599058	−	4.55030i	−0.0263977	−	0.200510i
$516$	−12.6574	−	39.1884i	−0.557211	−	1.72518i
$517$	−18.2076	−	2.39708i	−0.800770	−	0.105423i
$518$	2.67941	−	20.4192i	0.117727	−	0.897167i
$519$	13.0737	−	0.651111i	0.573871	−	0.0285806i
$520$	2.27613	−	8.53812i	0.0998148	−	0.374421i
$521$	−6.84957	+	6.84957i	−0.300085	+	0.300085i	−0.841047	−	0.540962i	$-0.818060\pi$
$521$	−6.84957	+	6.84957i	−0.300085	+	0.300085i	0.540962	+	0.841047i	$0.318060\pi$
$522$	7.17470	−	23.8038i	0.314028	−	1.04186i
$523$	15.0066	+	36.2292i	0.656193	+	1.58419i	0.803637	+	0.595120i	$0.202896\pi$
$523$	15.0066	+	36.2292i	0.656193	+	1.58419i	−0.147443	+	0.989071i	$0.547104\pi$
$524$	−14.0067	+	1.85612i	−0.611886	+	0.0810851i
$525$	−9.95501	−	6.88003i	−0.434472	−	0.300269i
$526$	−22.3168	+	38.6918i	−0.973059	+	1.68704i
$527$	−21.7050	−	12.5314i	−0.945485	−	0.545876i
$528$	−33.0834	−	7.06319i	−1.43977	−	0.307386i
$529$	−19.8181	+	11.4420i	−0.861655	+	0.497477i
$530$	−0.00716503	−	16.8706i	−0.000311229	−	0.732813i
$531$	−2.75972	−	0.833086i	−0.119762	−	0.0361529i
$532$	3.85280	−	1.59972i	0.167040	−	0.0693565i
$533$	6.22547	−	8.11320i	0.269655	−	0.351422i
$534$	−4.40768	−	9.29281i	−0.190739	−	0.402139i
$535$	3.57298	+	13.3345i	0.154473	+	0.576503i
$536$	−7.10486	−	0.926165i	−0.306883	−	0.0400042i
$537$	−35.8692	−	18.3938i	−1.54787	−	0.793752i
$538$	19.6906	−	25.6839i	0.848923	−	1.10731i
$539$	6.20021	+	14.9686i	0.267062	+	0.644745i
$540$	−7.55834	−	9.46745i	−0.325259	−	0.407414i
$541$	16.0481	+	6.64736i	0.689963	+	0.285792i	0.699985	−	0.714158i	$-0.253190\pi$
$541$	16.0481	+	6.64736i	0.689963	+	0.285792i	−0.0100216	+	0.999950i	$0.503190\pi$
$542$	−4.04826	+	15.1340i	−0.173888	+	0.650062i
$543$	13.3519	+	41.4590i	0.572983	+	1.77917i
$544$	−24.4932	+	6.61871i	−1.05014	+	0.283775i
$545$	13.7469	+	7.93680i	0.588854	+	0.339975i
$546$	−12.5804	+	0.631898i	−0.538389	+	0.0270427i
$547$	−17.9515	+	2.36335i	−0.767549	+	0.101050i	−0.504125	−	0.863630i	$-0.668185\pi$
$547$	−17.9515	+	2.36335i	−0.767549	+	0.101050i	−0.263424	+	0.964680i	$0.584852\pi$
$548$	−20.1926	−	20.1583i	−0.862586	−	0.861122i
$549$	1.12344	−	35.7946i	0.0479474	−	1.52767i
$550$	23.2250	−	9.63166i	0.990316	−	0.410695i
$551$	−6.15300	−	1.64869i	−0.262127	−	0.0702366i
$552$	1.37422	+	0.947157i	0.0584907	+	0.0403137i
$553$	−11.7995	+	3.16166i	−0.501764	+	0.134447i
$554$	−5.92796	+	4.55268i	−0.251855	+	0.193425i
$555$	2.75330	+	15.0739i	0.116871	+	0.639852i
$556$	−12.4344	−	9.52447i	−0.527335	−	0.403927i
$557$	−5.47199	−	2.26657i	−0.231856	−	0.0960377i	0.263731	−	0.964596i	$-0.415047\pi$
$557$	−5.47199	−	2.26657i	−0.231856	−	0.0960377i	−0.495587	+	0.868559i	$0.665047\pi$
$558$	−19.2462	+	13.8434i	−0.814758	+	0.586038i
$559$	31.8601			1.34754
$560$	−1.18291	−	8.86863i	−0.0499870	−	0.374768i
$561$	25.4545	−	28.1229i	1.07469	−	1.18735i
$562$	−35.5860	−	20.5254i	−1.50110	−	0.865813i
$563$	1.84247	+	2.40115i	0.0776508	+	0.101197i	0.830564	−	0.556924i	$-0.188018\pi$
$563$	1.84247	+	2.40115i	0.0776508	+	0.101197i	−0.752913	+	0.658120i	$0.771352\pi$
$564$	−1.04494	+	12.9869i	−0.0439999	+	0.546847i
$565$	−3.50713	−	2.69112i	−0.147546	−	0.113216i
$566$	−15.6018	−	6.45472i	−0.655793	−	0.271312i
$567$	−9.55552	+	14.3847i	−0.401294	+	0.604102i
$568$	−0.0340591	−	26.7316i	−0.00142909	−	1.12163i
$569$	−1.32295	+	4.93731i	−0.0554608	+	0.206983i	−0.988096	−	0.153838i	$-0.950837\pi$
$569$	−1.32295	+	4.93731i	−0.0554608	+	0.206983i	0.932635	+	0.360821i	$0.117503\pi$
$570$	−2.36467	+	2.01075i	−0.0990451	+	0.0842210i
$571$	2.82734	−	21.4758i	0.118321	−	0.898734i	−0.824600	−	0.565716i	$-0.808600\pi$
$571$	2.82734	−	21.4758i	0.118321	−	0.898734i	0.942921	−	0.333018i	$-0.108067\pi$
$572$	13.0666	−	22.6764i	0.546340	−	0.948148i
$573$	7.35297	−	3.48377i	0.307175	−	0.145536i
$574$	2.67576	−	10.0031i	0.111684	−	0.417520i
$575$	−1.24047			−0.0517311
$576$	−3.81717	+	23.6945i	−0.159049	+	0.987271i
$577$	−14.1206			−0.587847			−0.293924	−	0.955829i	$-0.594961\pi$
$577$	−14.1206			−0.587847			−0.293924	+	0.955829i	$0.594961\pi$
$578$	1.13887	−	4.25757i	0.0473709	−	0.177091i
$579$	15.9567	+	11.0279i	0.663138	+	0.458303i
$580$	−6.82096	+	11.8375i	−0.283225	+	0.491524i
$581$	−4.52668	+	34.3836i	−0.187798	+	1.42647i
$582$	−1.47839	−	8.07454i	−0.0612811	−	0.334701i
$583$	12.9326	−	48.2653i	0.535615	−	1.99894i
$584$	3.14814	−	0.00401109i	0.130271	−	0.000165980i
$585$	8.76714	−	3.31323i	0.362477	−	0.136985i
$586$	−14.9224	−	6.17365i	−0.616440	−	0.255031i
$587$	19.9235	+	15.2878i	0.822331	+	0.630997i	0.931791	−	0.362994i	$-0.118246\pi$
$587$	19.9235	+	15.2878i	0.822331	+	0.630997i	−0.109460	+	0.993991i	$0.534912\pi$
$588$	10.3834	−	4.93035i	0.428203	−	0.203324i
$589$	3.69788	+	4.81917i	0.152368	+	0.198570i
$590$	1.37223	+	0.791480i	0.0564938	+	0.0325847i
$591$	−5.90769	−	18.3440i	−0.243010	−	0.754572i
$592$	18.4392	−	24.1151i	0.757846	−	0.991126i
$593$	7.37102			0.302692			0.151346	−	0.988481i	$-0.451639\pi$
$593$	7.37102			0.302692			0.151346	+	0.988481i	$0.451639\pi$
$594$	−14.3522	−	32.8856i	−0.588879	−	1.34931i
$595$	9.26864	+	3.83920i	0.379977	+	0.157392i
$596$	26.4012	+	20.2227i	1.08143	+	0.828356i
$597$	−22.4836	+	19.1020i	−0.920193	+	0.781794i
$598$	−1.02406	+	0.786480i	−0.0418769	+	0.0321615i
$599$	8.50790	−	2.27969i	0.347623	−	0.0931454i	−0.0807826	−	0.996732i	$-0.525742\pi$
$599$	8.50790	−	2.27969i	0.347623	−	0.0931454i	0.428406	+	0.903586i	$0.359075\pi$
$600$	−7.65800	−	16.1102i	−0.312637	−	0.657695i
$601$	10.5441	+	2.82530i	0.430105	+	0.115246i	0.467375	−	0.884059i	$-0.345200\pi$
$601$	10.5441	+	2.82530i	0.430105	+	0.115246i	−0.0372706	+	0.999305i	$0.511866\pi$
$602$	29.7990	−	12.3580i	1.21451	−	0.503673i
$603$	−3.59147	−	6.69741i	−0.146256	−	0.272740i
$604$	14.1914	+	14.1673i	0.577439	+	0.576459i
$605$	−14.8417	+	1.95395i	−0.603402	+	0.0794394i
$606$	16.6527	+	25.7653i	0.676471	+	1.04665i
$607$	−28.7961	−	16.6254i	−1.16880	−	0.674805i	−0.215400	−	0.976526i	$-0.569106\pi$
$607$	−28.7961	−	16.6254i	−1.16880	−	0.674805i	−0.953396	+	0.301721i	$0.902439\pi$
$608$	6.09839	+	0.789698i	0.247323	+	0.0320265i
$609$	19.0391	+	4.09862i	0.771505	+	0.166084i
$610$	−5.08540	+	19.0113i	−0.205902	+	0.769744i
$611$	−9.31243	−	3.85734i	−0.376741	−	0.156051i
$612$	−20.8398	−	17.0262i	−0.842399	−	0.688245i
$613$	−14.8026	−	35.7366i	−0.597871	−	1.44339i	−0.875747	−	0.482770i	$-0.839631\pi$
$613$	−14.8026	−	35.7366i	−0.597871	−	1.44339i	0.277876	−	0.960617i	$-0.410369\pi$
$614$	−28.0589	+	36.5992i	−1.13236	+	1.47702i
$615$	0.383236	+	7.69501i	0.0154536	+	0.310293i
$616$	3.42546	−	26.2777i	0.138016	−	1.05876i
$617$	8.76394	+	32.7075i	0.352823	+	1.31675i	0.883202	+	0.468992i	$0.155383\pi$
$617$	8.76394	+	32.7075i	0.352823	+	1.31675i	−0.530380	+	0.847760i	$0.677951\pi$
$618$	−9.61252	−	0.777544i	−0.386672	−	0.0312774i
$619$	25.8219	−	33.6518i	1.03787	−	1.35258i	0.104157	−	0.994561i	$-0.466785\pi$
$619$	25.8219	−	33.6518i	1.03787	−	1.35258i	0.933714	−	0.358020i	$-0.116548\pi$
$620$	12.0321	−	4.99582i	0.483219	−	0.200637i
$621$	0.0325469	+	1.76995i	0.00130606	+	0.0710257i
$622$	−0.00222522	−	5.23947i	−8.92234e−5	−	0.210083i
$623$	6.97745	−	4.02843i	0.279546	−	0.161396i
$624$	−16.5362	−	8.44433i	−0.661976	−	0.338044i
$625$	5.59723	+	3.23156i	0.223889	+	0.129263i
$626$	−3.36957	+	5.84200i	−0.134675	+	0.233493i
$627$	−8.30817	+	3.93633i	−0.331796	+	0.157202i
$628$	−44.5519	+	5.90387i	−1.77781	+	0.235590i
$629$	13.0261	+	31.4477i	0.519383	+	1.25390i
$630$	6.91482	−	6.49950i	0.275493	−	0.258946i
$631$	12.5592	−	12.5592i	0.499973	−	0.499973i	−0.411457	−	0.911429i	$-0.634980\pi$
$631$	12.5592	−	12.5592i	0.499973	−	0.499973i	0.911429	+	0.411457i	$0.134980\pi$
$632$	−17.3989	−	4.63828i	−0.692093	−	0.184501i
$633$	−19.1887	−	29.7167i	−0.762681	−	1.18113i
$634$	−0.580746	+	4.42573i	−0.0230644	+	0.175768i
$635$	0.696381	+	0.0916803i	0.0276350	+	0.00363822i
$636$	−34.6621	−	7.43103i	−1.37444	−	0.294660i
$637$	1.16072	+	8.81655i	0.0459895	+	0.349325i
$638$	−28.6006	+	28.6249i	−1.13231	+	1.13327i
$639$	23.0245	−	16.5462i	0.910834	−	0.654557i
$640$	5.01081	−	12.1996i	0.198070	−	0.482232i
$641$	−28.9745	+	16.7284i	−1.14442	+	0.660733i	−0.947522	−	0.319690i	$-0.896421\pi$
$641$	−28.9745	+	16.7284i	−1.14442	+	0.660733i	−0.196901	+	0.980423i	$0.563088\pi$
$642$	28.9714	−	1.45520i	1.14341	−	0.0574323i
$643$	13.7211	+	17.8817i	0.541108	+	0.705186i	0.981249	−	0.192742i	$-0.0617382\pi$
$643$	13.7211	+	17.8817i	0.541108	+	0.705186i	−0.440141	+	0.897929i	$0.645072\pi$
$644$	−0.652748	+	1.13281i	−0.0257219	+	0.0446391i
$645$	−18.2926	+	15.5414i	−0.720271	+	0.611941i
$646$	−4.19516	+	5.47205i	−0.165056	+	0.215295i
$647$	6.25883	−	6.25883i	0.246060	−	0.246060i	−0.573291	−	0.819352i	$-0.694334\pi$
$647$	6.25883	−	6.25883i	0.246060	−	0.246060i	0.819352	+	0.573291i	$0.194334\pi$
$648$	−22.7857	+	11.3494i	−0.895109	+	0.445848i
$649$	3.31768	+	3.31768i	0.130230	+	0.130230i
$650$	13.6812	−	1.80708i	0.536621	−	0.0708793i
$651$	−12.0245	−	14.1532i	−0.471277	−	0.554706i
$652$	13.1951	−	10.1428i	0.516759	−	0.397221i
$653$	38.4898	−	29.5343i	1.50622	−	1.15577i	0.561691	−	0.827347i	$-0.310151\pi$
$653$	38.4898	−	29.5343i	1.50622	−	1.15577i	0.944532	−	0.328419i	$-0.106516\pi$
$654$	22.3725	−	24.7388i	0.874833	−	0.967365i
$655$	4.11765	+	7.13198i	0.160890	+	0.278670i
$656$	10.7745	−	10.8112i	0.420675	−	0.422107i
$657$	1.94862	+	2.71156i	0.0760229	+	0.105788i
$658$	−10.2062	+	0.00433460i	−0.397878	+	0.000168980i
$659$	6.25640	−	0.823671i	0.243715	−	0.0320857i	−0.00767915	−	0.999971i	$-0.502444\pi$
$659$	6.25640	−	0.823671i	0.243715	−	0.0320857i	0.251394	+	0.967885i	$0.419111\pi$
$660$	3.55933	+	19.3936i	0.138547	+	0.754896i
$661$	−1.88948	+	14.3520i	−0.0734924	+	0.558230i	0.914599	+	0.404362i	$0.132506\pi$
$661$	−1.88948	+	14.3520i	−0.0734924	+	0.558230i	−0.988091	+	0.153868i	$0.950827\pi$
$662$	−15.4998	−	20.1820i	−0.602418	−	0.784396i
$663$	17.4900	−	11.2937i	0.679256	−	0.438609i
$664$	−31.0685	+	40.5963i	−1.20569	+	1.57544i
$665$	−1.71934	−	1.71934i	−0.0666732	−	0.0666732i
$666$	32.1830	+	0.996409i	1.24707	+	0.0386101i
$667$	1.84442	−	0.763984i	0.0714162	−	0.0295816i
$668$	−3.56797	+	13.3612i	−0.138049	+	0.516961i
$669$	−9.43684	−	19.9177i	−0.364849	−	0.770064i
$670$	1.08259	+	4.03341i	0.0418239	+	0.155824i
$671$	−29.1439	+	50.4788i	−1.12509	+	1.94871i
$672$	−18.7418	−	1.48395i	−0.722979	−	0.0572447i
$673$	−15.4497	−	26.7596i	−0.595541	−	1.03151i	−0.993470	−	0.114091i	$-0.963605\pi$
$673$	−15.4497	−	26.7596i	−0.595541	−	1.03151i	0.397930	−	0.917416i	$-0.369729\pi$
$674$	−24.9058	+	24.9270i	−0.959335	+	0.960150i
$675$	9.15701	−	16.5561i	0.352454	−	0.637245i
$676$	−8.22046	+	8.23444i	−0.316172	+	0.316709i
$677$	−0.624072	−	0.478867i	−0.0239850	−	0.0184044i	0.596699	−	0.802465i	$-0.296478\pi$
$677$	−0.624072	−	0.478867i	−0.0239850	−	0.0184044i	−0.620684	+	0.784061i	$0.713145\pi$
$678$	−7.07648	+	6.01734i	−0.271771	+	0.231095i
$679$	6.21124	−	1.66430i	0.238366	−	0.0638698i
$680$	9.01739	+	11.7207i	0.345801	+	0.449470i
$681$	−39.7219	+	1.97828i	−1.52215	+	0.0758077i
$682$	38.2544	−	5.05282i	1.46484	−	0.193483i
$683$	−23.0089	+	9.53060i	−0.880411	+	0.364678i	−0.776656	−	0.629925i	$-0.783086\pi$
$683$	−23.0089	+	9.53060i	−0.880411	+	0.364678i	−0.103755	+	0.994603i	$0.533086\pi$
$684$	3.08725	+	5.74541i	0.118044	+	0.219681i
$685$	−6.36418	+	15.3645i	−0.243163	+	0.587047i
$686$	14.0100	+	24.2423i	0.534905	+	0.925575i
$687$	5.44904	−	25.3122i	0.207894	−	0.965721i
$688$	47.1563	+	6.12677i	1.79782	+	0.233581i
$689$	13.7128	−	23.7512i	0.522414	−	0.904848i
$690$	0.204323	−	0.951097i	0.00777845	−	0.0362076i
$691$	1.33597	+	10.1477i	0.0508228	+	0.386038i	0.997886	+	0.0649902i	$0.0207016\pi$
$691$	1.33597	+	10.1477i	0.0508228	+	0.386038i	−0.947063	+	0.321048i	$0.895965\pi$
$692$	−5.77235	+	13.9692i	−0.219432	+	0.531031i
$693$	24.7707	−	13.2832i	0.940961	−	0.504588i
$694$	−12.8684	+	31.1044i	−0.488477	+	1.18071i
$695$	−2.36284	+	8.81824i	−0.0896277	+	0.334495i
$696$	21.3085	+	19.2374i	0.807695	+	0.729190i
$697$	4.42960	+	16.5315i	0.167783	+	0.626175i
$698$	10.0674	+	1.32104i	0.381055	+	0.0500022i
$699$	12.1958	+	14.3548i	0.461289	+	0.542950i
$700$	12.0952	−	6.99686i	0.457155	−	0.264456i
$701$	−9.41659	+	22.7336i	−0.355660	+	0.858638i	0.640240	+	0.768175i	$0.278835\pi$
$701$	−9.41659	+	22.7336i	−0.355660	+	0.858638i	−0.995900	+	0.0904633i	$0.971165\pi$
$702$	−2.93737	−	19.4735i	−0.110864	−	0.734979i
$703$		−	8.24992i		−	0.311152i
$704$	23.7006	−	31.0508i	0.893251	−	1.17027i
$705$	7.22838	−	2.32790i	0.272237	−	0.0876738i
$706$	−2.05872	−	7.67022i	−0.0774810	−	0.288672i
$707$	−19.0659	+	14.6297i	−0.717045	+	0.550208i
$708$	2.23164	−	2.46979i	0.0838703	−	0.0928205i
$709$	2.64015	−	3.44071i	0.0991530	−	0.129219i	−0.741142	−	0.671349i	$-0.765715\pi$
$709$	2.64015	−	3.44071i	0.0991530	−	0.129219i	0.840295	+	0.542130i	$0.182382\pi$
$710$	−14.3922	+	5.96862i	−0.540131	+	0.223998i
$711$	−6.75169	−	17.8656i	−0.253208	−	0.670014i
$712$	11.8762	−	0.0151317i	0.445081	−	0.000567083i
$713$	−1.83887	−	0.492723i	−0.0688662	−	0.0184526i
$714$	11.9779	−	17.3471i	0.448262	−	0.649198i
$715$	−15.1239	−	1.99110i	−0.565601	−	0.0744627i
$716$	36.9038	−	28.3671i	1.37916	−	1.06013i
$717$	−3.84757	+	5.56720i	−0.143690	+	0.207911i
$718$	−10.4966	−	18.1628i	−0.391729	−	0.677830i
$719$		−	31.9312i		−	1.19083i	−0.803418	−	0.595416i	$-0.796987\pi$
$719$		−	31.9312i		−	1.19083i	0.803418	−	0.595416i	$-0.203013\pi$
$720$	13.6134	−	3.21799i	0.507343	−	0.119928i
$721$		−	7.55457i		−	0.281347i
$722$	−21.8175	+	12.6087i	−0.811964	+	0.469248i
$723$	−21.2008	−	44.7472i	−0.788466	−	1.66417i
$724$	−49.8693	−	6.52233i	−1.85338	−	0.242401i
$725$	−21.1540	−	2.78498i	−0.785640	−	0.103432i
$726$	−2.53612	+	31.3532i	−0.0941242	+	1.16363i
$727$	−34.0277	−	9.11768i	−1.26202	−	0.338156i	−0.435049	−	0.900407i	$-0.643269\pi$
$727$	−34.0277	−	9.11768i	−1.26202	−	0.338156i	−0.826967	+	0.562251i	$0.809936\pi$
$728$	5.54895	−	13.4448i	0.205658	−	0.498296i
$729$	−23.8632	−	12.6312i	−0.883822	−	0.467823i
$730$	−0.702916	−	1.69495i	−0.0260161	−	0.0627330i
$731$	−32.4592	+	42.3016i	−1.20055	+	1.56458i
$732$	36.8123	+	18.8380i	1.36062	+	0.696271i
$733$	16.4635	−	12.6329i	0.608093	−	0.466606i	−0.258235	−	0.966082i	$-0.583141\pi$
$733$	16.4635	−	12.6329i	0.608093	−	0.466606i	0.866328	+	0.499476i	$0.166474\pi$
$734$	11.2891	−	3.03003i	0.416687	−	0.111841i
$735$	−4.96715	−	4.49586i	−0.183216	−	0.165832i
$736$	−1.66696	+	0.967145i	−0.0614449	+	0.0356494i
$737$			12.3691i			0.455622i
$738$	15.9778	+	2.60883i	0.588150	+	0.0960324i
$739$	4.30694	−	10.3979i	0.158433	−	0.382492i	−0.824652	−	0.565641i	$-0.808629\pi$
$739$	4.30694	−	10.3979i	0.158433	−	0.382492i	0.983085	+	0.183149i	$0.0586289\pi$
$740$	−17.0948	−	4.56498i	−0.628417	−	0.167812i
$741$	−4.96384	+	0.906662i	−0.182351	+	0.0333071i
$742$	3.61297	−	27.5336i	0.132636	−	1.01079i
$743$	6.01956	+	22.4653i	0.220836	+	0.824172i	0.984030	+	0.178003i	$0.0569635\pi$
$743$	6.01956	+	22.4653i	0.220836	+	0.824172i	−0.763194	+	0.646170i	$0.776370\pi$
$744$	−4.95313	−	26.9235i	−0.181590	−	0.987064i
$745$	5.01688	−	18.7233i	0.183804	−	0.685967i
$746$	28.0438	+	11.6022i	1.02676	+	0.424785i
$747$	−54.1948	−	1.70095i	−1.98288	−	0.0622345i
$748$	16.7959	+	40.4516i	0.614118	+	1.47906i
$749$	2.96600	+	22.5290i	0.108375	+	0.823191i
$750$	−16.5499	+	18.3004i	−0.604316	+	0.668235i
$751$	23.4640	−	40.6409i	0.856214	−	1.48301i	−0.0193005	−	0.999814i	$-0.506144\pi$
$751$	23.4640	−	40.6409i	0.856214	−	1.48301i	0.875514	−	0.483192i	$-0.160523\pi$
$752$	−13.0416	−	7.50007i	−0.475579	−	0.273499i
$753$	10.1159	−	3.25784i	0.368645	−	0.118722i
$754$	−19.2293	+	11.1129i	−0.700289	+	0.404708i
$755$	4.47274	−	10.7982i	0.162780	−	0.392985i
$756$	−10.3008	−	17.0743i	−0.374635	−	0.620987i
$757$	−23.1447	+	9.58685i	−0.841209	+	0.348440i	−0.761330	−	0.648364i	$-0.775453\pi$
$757$	−23.1447	+	9.58685i	−0.841209	+	0.348440i	−0.0798788	+	0.996805i	$0.525453\pi$
$758$	−3.18439	−	24.1087i	−0.115662	−	0.875669i
$759$	1.31473	−	2.56381i	0.0477216	−	0.0930605i
$760$	−0.932065	−	3.46087i	−0.0338095	−	0.125539i
$761$	0.0980316	−	0.0262675i	0.00355364	−	0.000952196i	−0.257042	−	0.966400i	$-0.582748\pi$
$761$	0.0980316	−	0.0262675i	0.00355364	−	0.000952196i	0.260595	+	0.965448i	$0.416081\pi$
$762$	0.495691	−	1.39018i	0.0179570	−	0.0503610i
$763$	20.7291	+	15.9060i	0.750444	+	0.575836i
$764$	0.00798039	+	9.39523i	0.000288720	+	0.339907i
$765$	−4.53291	+	15.0159i	−0.163888	+	0.542902i
$766$	−4.89051	−	4.88636i	−0.176701	−	0.176551i
$767$	1.28761	+	2.23020i	0.0464928	+	0.0805279i
$768$	−22.8514	−	15.6784i	−0.824579	−	0.565747i
$769$	−15.1755	+	26.2847i	−0.547241	+	0.947850i	0.451221	+	0.892412i	$0.350989\pi$
$769$	−15.1755	+	26.2847i	−0.547241	+	0.947850i	−0.998462	+	0.0554374i	$0.982345\pi$
$770$	−14.9178	+	4.00399i	−0.537599	+	0.144294i
$771$	9.49762	−	13.7425i	0.342049	−	0.494924i
$772$	−19.3871	+	11.2151i	−0.697759	+	0.403642i
$773$	10.1380	−	4.19928i	0.364637	−	0.151038i	−0.192839	−	0.981230i	$-0.561770\pi$
$773$	10.1380	−	4.19928i	0.364637	−	0.151038i	0.557477	+	0.830193i	$0.311770\pi$
$774$	23.8548	+	44.4394i	0.857444	+	1.59734i
$775$	14.3871	+	14.3871i	0.516798	+	0.516798i
$776$	9.15881	+	2.44159i	0.328782	+	0.0876481i
$777$	1.25461	+	25.1914i	0.0450090	+	0.903738i
$778$	31.6441	−	24.3027i	1.13450	−	0.871295i
$779$	0.541430	−	4.11257i	0.0193987	−	0.147348i
$780$	−0.867963	+	10.7874i	−0.0310781	+	0.386249i
$781$	−45.7528	+	6.02347i	−1.63716	+	0.215537i
$782$	−0.000917762	−	2.16094i	−3.28191e−5	−	0.0772751i
$783$	−3.41869	+	30.2565i	−0.122174	+	1.08128i
$784$	0.0225478	+	13.2726i	0.000805279	+	0.474023i
$785$	13.0972	+	22.6851i	0.467461	+	0.809666i
$786$	16.4692	−	5.31164i	0.587438	−	0.189460i
$787$	−14.1342	+	10.8456i	−0.503830	+	0.386602i	−0.829171	−	0.558994i	$-0.811187\pi$
$787$	−14.1342	+	10.8456i	−0.503830	+	0.386602i	0.325342	+	0.945597i	$0.394521\pi$
$788$	22.0653	+	2.88588i	0.786043	+	0.102805i
$789$	18.3948	−	51.5196i	0.654873	−	1.83415i
$790$	1.37433	+	10.4049i	0.0488965	+	0.370191i
$791$	−5.14528	−	5.14528i	−0.182945	−	0.182945i
$792$	41.4131	+	1.24697i	1.47155	+	0.0443092i
$793$	−22.6218	+	22.6218i	−0.803323	+	0.803323i
$794$	−10.1351	−	7.77012i	−0.359682	−	0.275751i
$795$	3.71260	+	20.3259i	0.131672	+	0.720886i
$796$	−8.84504	−	32.8983i	−0.313504	−	1.16605i
$797$	−0.293764	−	0.382841i	−0.0104057	−	0.0135609i	0.788122	−	0.615520i	$-0.211054\pi$
$797$	−0.293764	−	0.382841i	−0.0104057	−	0.0135609i	−0.798527	+	0.601959i	$0.794387\pi$
$798$	−4.29104	+	2.77339i	−0.151901	+	0.0981770i
$799$	14.6090	−	8.43453i	0.516830	−	0.298392i
$800$	20.5971	−	0.0437385i	0.728219	−	0.00154639i
$801$	7.35108	+	10.2292i	0.259738	+	0.361432i
$802$	17.8139	+	17.7987i	0.629030	+	0.628496i
$803$	−0.709376	−	5.38824i	−0.0250333	−	0.190147i
$804$	8.76403	−	0.443940i	0.309083	−	0.0156565i
$805$	0.755522	+	0.0994664i	0.0266287	+	0.00350573i
$806$	20.9988	+	2.75547i	0.739650	+	0.0970573i
$807$	−18.0864	+	35.2697i	−0.636671	+	1.24155i
$808$	−35.1154	+	4.66856i	−1.23536	+	0.164239i
$809$	−2.96581	+	2.96581i	−0.104272	+	0.104272i	−0.757318	−	0.653046i	$-0.773491\pi$
$809$	−2.96581	+	2.96581i	−0.104272	+	0.104272i	0.653046	+	0.757318i	$0.273491\pi$
$810$	11.1857	+	9.74793i	0.393025	+	0.342508i
$811$	2.73876	+	6.61195i	0.0961709	+	0.232177i	0.964642	−	0.263562i	$-0.0848973\pi$
$811$	2.73876	+	6.61195i	0.0961709	+	0.232177i	−0.868472	+	0.495739i	$0.834897\pi$
$812$	−13.6748	+	17.8527i	−0.479890	+	0.626506i
$813$	1.55508	−	19.1239i	0.0545390	−	0.670703i
$814$	−45.3961	−	26.1838i	−1.59113	−	0.917741i
$815$	−8.40084	−	4.85023i	−0.294269	−	0.169896i
$816$	28.0589	−	13.3524i	0.982257	−	0.467429i
$817$	11.1917	−	6.46155i	0.391549	−	0.226061i
$818$	3.11054	−	0.00132106i	0.108757	−	4.61897e-5i
$819$	15.0194	−	3.52341i	0.524820	−	0.123118i
$820$	−8.22214	−	3.39754i	−0.287129	−	0.118647i
$821$	21.2304	−	27.6680i	0.740945	−	0.965619i	−0.259054	−	0.965863i	$-0.583411\pi$
$821$	21.2304	−	27.6680i	0.740945	−	0.965619i	1.00000		0.000243759i	$7.75908e-5\pi$
$822$	28.7560	+	19.8556i	1.00298	+	0.692543i
$823$	9.68278	+	36.1366i	0.337520	+	1.25964i	0.901111	+	0.433589i	$0.142753\pi$
$823$	9.68278	+	36.1366i	0.337520	+	1.25964i	−0.563590	+	0.826054i	$0.690580\pi$
$824$	5.55563	−	9.65100i	0.193539	−	0.336209i
$825$	−25.8693	+	16.7043i	−0.900652	+	0.581569i
$826$	2.06936	+	1.58648i	0.0720023	+	0.0552008i
$827$	−2.02392	−	4.88617i	−0.0703785	−	0.169909i	0.884776	−	0.466016i	$-0.154311\pi$
$827$	−2.02392	−	4.88617i	−0.0703785	−	0.169909i	−0.955155	+	0.296108i	$0.904311\pi$
$828$	−1.86376	−	0.839523i	−0.0647700	−	0.0291754i
$829$	−49.1995	−	20.3791i	−1.70877	−	0.707795i	−0.999997	−	0.00235766i	$-0.999250\pi$
$829$	−49.1995	−	20.3791i	−1.70877	−	0.707795i	−0.708772	−	0.705438i	$-0.750750\pi$
$830$	28.7841	+	7.69956i	0.999109	+	0.267256i
$831$	6.14308	−	6.78704i	0.213101	−	0.235440i
$832$	16.9761	−	13.0951i	0.588540	−	0.453990i
$833$	−12.8885	−	7.44121i	−0.446562	−	0.257822i
$834$	17.0734	+	8.74610i	0.591202	+	0.302853i
$835$	7.99164	−	1.05212i	0.276562	−	0.0364101i
$836$	−0.00901710	−	10.6157i	−0.000311863	−	0.367153i
$837$	20.1506	−	20.9055i	0.696505	−	0.722601i
$838$	−13.8815	−	33.4727i	−0.479529	−	1.15630i
$839$	−26.1888	−	7.01726i	−0.904137	−	0.242263i	−0.223345	−	0.974739i	$-0.571698\pi$
$839$	−26.1888	−	7.01726i	−0.904137	−	0.242263i	−0.680792	+	0.732477i	$0.738364\pi$
$840$	3.37241	+	10.4261i	0.116359	+	0.359736i
$841$	5.15671	−	1.38174i	0.177818	−	0.0476461i
$842$	6.70780	+	8.73409i	0.231166	+	0.300997i
$843$	47.3841	+	16.9183i	1.63200	+	0.582696i
$844$	40.4919	−	5.36585i	1.39379	−	0.184700i
$845$	6.26555	+	2.59528i	0.215541	+	0.0892802i
$846$	−1.59223	−	15.8774i	−0.0547421	−	0.545876i
$847$	−24.6408			−0.846668
$848$	24.8637	−	32.5173i	0.853824	−	1.11665i
$849$	20.2158	+	4.35193i	0.693806	+	0.149358i
$850$	−11.5391	+	20.0060i	−0.395789	+	0.686200i
$851$	1.57398	+	2.05125i	0.0539552	+	0.0703158i
$852$	5.90999	+	32.2016i	0.202473	+	1.10321i
$853$	25.0743	+	19.2402i	0.858528	+	0.658772i	0.941217	−	0.337804i	$-0.109684\pi$
$853$	25.0743	+	19.2402i	0.858528	+	0.658772i	−0.0826883	+	0.996575i	$0.526351\pi$
$854$	−12.3837	+	29.9329i	−0.423762	+	1.02428i
$855$	2.40774	−	2.94193i	0.0823430	−	0.100612i
$856$	−12.7787	+	30.9621i	−0.436767	+	1.05826i
$857$	−6.40709	+	23.9116i	−0.218862	+	0.816804i	0.765909	+	0.642949i	$0.222289\pi$
$857$	−6.40709	+	23.9116i	−0.218862	+	0.816804i	−0.984771	+	0.173855i	$0.944378\pi$
$858$	−10.7653	+	30.1917i	−0.367523	+	1.03073i
$859$	0.403091	−	3.06178i	0.0137533	−	0.104466i	−0.983191	−	0.182578i	$-0.941556\pi$
$859$	0.403091	−	3.06178i	0.0137533	−	0.104466i	0.996945	+	0.0781117i	$0.0248891\pi$
$860$	−7.19630	−	26.7660i	−0.245392	−	0.912713i
$861$	−1.02785	+	12.6402i	−0.0350292	+	0.430778i
$862$	8.13583	+	2.17629i	0.277107	+	0.0741246i
$863$	38.7531			1.31917			0.659585	−	0.751630i	$-0.270732\pi$
$863$	38.7531			1.31917			0.659585	+	0.751630i	$0.270732\pi$
$864$	−0.602828	−	29.3877i	−0.0205086	−	0.999790i
$865$	8.80985			0.299544
$866$	−0.889507	−	0.237938i	−0.0302267	−	0.00808546i
$867$	−0.437482	+	5.38001i	−0.0148577	+	0.182715i
$868$	20.7091	−	5.56784i	0.702912	−	0.188985i
$869$	−4.05744	+	30.8194i	−0.137639	+	1.04547i
$870$	5.61968	−	15.7606i	0.190525	−	0.534333i
$871$	−1.75711	+	6.55761i	−0.0595373	+	0.222196i
$872$	14.7843	+	35.5641i	0.500658	+	1.20435i
$873$	3.55409	+	9.40448i	0.120288	+	0.318293i
$874$	−0.200223	+	0.483962i	−0.00677264	+	0.0163703i
$875$	−15.3342	−	11.7664i	−0.518391	−	0.397775i
$876$	−3.79234	+	0.696012i	−0.128131	+	0.0235161i
$877$	6.81089	+	8.87612i	0.229987	+	0.299725i	0.894064	−	0.447939i	$-0.147842\pi$
$877$	6.81089	+	8.87612i	0.229987	+	0.299725i	−0.664077	+	0.747664i	$0.731175\pi$
$878$	24.9272	−	43.2175i	0.841251	−	1.45852i
$879$	19.3355	+	4.16243i	0.652172	+	0.140395i
$880$	−22.0020	−	5.85539i	−0.741689	−	0.197385i
$881$	33.1806			1.11788			0.558941	−	0.829208i	$-0.311208\pi$
$881$	33.1806			1.11788			0.558941	+	0.829208i	$0.311208\pi$
$882$	−11.4285	+	8.22028i	−0.384818	+	0.276791i
$883$	−16.9677	−	7.02823i	−0.571007	−	0.236519i	0.0784488	−	0.996918i	$-0.475003\pi$
$883$	−16.9677	−	7.02823i	−0.571007	−	0.236519i	−0.649456	+	0.760399i	$0.725003\pi$
$884$	3.15811	+	23.8318i	0.106219	+	0.801551i
$885$	−1.82718	−	0.652384i	−0.0614199	−	0.0219297i
$886$	−11.7455	−	15.2935i	−0.394596	−	0.513796i
$887$	24.3228	−	6.51728i	0.816681	−	0.218829i	0.173786	−	0.984783i	$-0.444400\pi$
$887$	24.3228	−	6.51728i	0.816681	−	0.218829i	0.642895	+	0.765955i	$0.277733\pi$
$888$	−16.9230	+	33.1048i	−0.567898	+	1.11093i
$889$	1.11676	+	0.299235i	0.0374550	+	0.0100360i
$890$	−2.65172	−	6.39413i	−0.0888858	−	0.214332i
$891$	24.5131	+	36.4731i	0.821221	+	1.22189i
$892$	25.4498	−	0.0216173i	0.852123	−	0.000723801i
$893$	−4.05355	+	0.533660i	−0.135647	+	0.0178583i
$894$	−36.2509	−	18.5701i	−1.21241	−	0.621076i
$895$	−23.4953	−	13.5650i	−0.785362	−	0.453429i
$896$	10.7985	−	18.8326i	0.360752	−	0.629153i
$897$	1.06122	−	1.17247i	0.0354332	−	0.0391475i
$898$	−36.6661	−	9.80796i	−1.22356	−	0.327296i
$899$	−30.2525	−	12.5310i	−1.00898	−	0.417932i
$900$	12.7642	+	17.7299i	0.425473	+	0.590997i
$901$	17.5646	+	42.4046i	0.585160	+	1.41270i
$902$	−20.9115	−	16.0318i	−0.696276	−	0.533802i
$903$	−33.1917	+	21.4326i	−1.10455	+	0.713231i
$904$	−2.78929	−	10.3570i	−0.0927703	−	0.344467i
$905$	7.58711	+	28.3155i	0.252204	+	0.941238i
$906$	−20.2097	−	13.9545i	−0.671423	−	0.463607i
$907$	−2.26032	+	2.94571i	−0.0750529	+	0.0978108i	−0.829371	−	0.558698i	$-0.811301\pi$
$907$	−2.26032	+	2.94571i	−0.0750529	+	0.0978108i	0.754318	+	0.656509i	$0.227968\pi$
$908$	17.5382	−	42.4429i	0.582026	−	1.40852i
$909$	−25.7218	−	27.3887i	−0.853137	−	0.908425i
$910$	−8.47760	+	0.00360047i	−0.281030	+	0.000119355i
$911$	−41.0434	+	23.6964i	−1.35983	+	0.785098i	−0.989601	−	0.143843i	$-0.954054\pi$
$911$	−41.0434	+	23.6964i	−1.35983	+	0.785098i	−0.370229	+	0.928941i	$0.620721\pi$
$912$	−7.52137	+	0.387398i	−0.249057	+	0.0128280i
$913$	76.4275	+	44.1254i	2.52938	+	1.46034i
$914$	21.1873	+	12.2205i	0.700812	+	0.404217i
$915$	1.95348	−	24.0233i	0.0645801	−	0.794186i
$916$	23.7348	+	18.1803i	0.784220	+	0.600696i
$917$	5.18750	+	12.5237i	0.171306	+	0.413570i
$918$	28.8481	+	15.9396i	0.952130	+	0.526085i
$919$	18.4084	−	18.4084i	0.607235	−	0.607235i	−0.334987	−	0.942223i	$-0.608732\pi$
$919$	18.4084	−	18.4084i	0.607235	−	0.607235i	0.942223	+	0.334987i	$0.108732\pi$
$920$	0.892036	+	0.682679i	0.0294095	+	0.0225073i
$921$	25.7729	−	50.2589i	0.849245	−	1.65609i
$922$	−4.59284	−	0.602674i	−0.151257	−	0.0198480i
$923$	−25.1120	−	3.30606i	−0.826571	−	0.108820i
$924$	1.64193	+	32.4142i	0.0540156	+	1.06635i
$925$	−3.60685	−	27.3968i	−0.118593	−	0.900800i
$926$	−26.9632	−	26.9403i	−0.886065	−	0.885313i
$927$	11.7529	−	1.17357i	0.386016	−	0.0385452i
$928$	−30.5984	+	12.7505i	−1.00444	+	0.418554i
$929$	−16.1678	+	9.33448i	−0.530448	+	0.306254i	−0.741199	−	0.671285i	$-0.765742\pi$
$929$	−16.1678	+	9.33448i	−0.530448	+	0.306254i	0.210751	+	0.977540i	$0.432409\pi$
$930$	−13.4007	+	8.66114i	−0.439425	+	0.284010i
$931$	2.19582	+	2.86165i	0.0719651	+	0.0937868i
$932$	−21.0042	+	5.64718i	−0.688015	+	0.184980i
$933$	1.15301	+	6.31257i	0.0377479	+	0.206664i
$934$	−19.5856	−	15.0154i	−0.640861	−	0.491317i
$935$	18.0519	−	18.0519i	0.590359	−	0.590359i
$936$	21.7785	+	6.54408i	0.711851	+	0.213900i
$937$	3.70266	+	3.70266i	0.120961	+	0.120961i	0.764996	−	0.644035i	$-0.222741\pi$
$937$	3.70266	+	3.70266i	0.120961	+	0.120961i	−0.644035	+	0.764996i	$0.722741\pi$
$938$	0.900146	+	6.81492i	0.0293908	+	0.222515i
$939$	2.77740	−	7.77885i	0.0906370	−	0.253853i
$940$	−1.13717	+	8.69473i	−0.0370904	+	0.283591i
$941$	−37.1844	+	28.5326i	−1.21218	+	0.930136i	−0.998902	−	0.0468567i	$-0.985080\pi$
$941$	−37.1844	+	28.5326i	−1.21218	+	0.930136i	−0.213275	+	0.976992i	$0.568413\pi$
$942$	52.3846	−	16.8950i	1.70678	−	0.550470i
$943$	0.650004	+	1.12584i	0.0211670	+	0.0366624i
$944$	1.47692	+	3.54854i	0.0480697	+	0.115495i
$945$	−6.90473	+	9.34945i	−0.224611	+	0.304137i
$946$	−0.0348647	−	82.0916i	−0.00113355	−	2.66903i
$947$	22.5521	−	2.96904i	0.732845	−	0.0964808i	0.245138	−	0.969488i	$-0.421167\pi$
$947$	22.5521	−	2.96904i	0.732845	−	0.0964808i	0.487707	+	0.873007i	$0.337833\pi$
$948$	21.9824	+	1.76873i	0.713956	+	0.0574457i
$949$	0.389350	−	2.95740i	0.0126388	−	0.0960014i
$950$	4.43940	−	3.40947i	0.144033	−	0.110618i
$951$	−0.271930	−	5.46009i	−0.00881793	−	0.177056i
$952$	12.1977	+	21.0651i	0.395331	+	0.682723i
$953$	−20.1825	−	20.1825i	−0.653774	−	0.653774i	0.300126	−	0.953900i	$-0.402971\pi$
$953$	−20.1825	−	20.1825i	−0.653774	−	0.653774i	−0.953900	+	0.300126i	$0.902971\pi$
$954$	43.3961	+	1.34357i	1.40500	+	0.0434998i
$955$	5.05925	−	2.09561i	0.163714	−	0.0678124i
$956$	−3.91290	−	6.76407i	−0.126552	−	0.218766i
$957$	28.1764	−	40.7696i	0.910814	−	1.31790i
$958$	24.7333	−	6.63854i	0.799098	−	0.214481i
$959$	−13.6871	+	23.7067i	−0.441979	+	0.765531i
$960$	−3.35911	+	15.7995i	−0.108415	+	0.509927i
$961$	0.112702	+	0.195206i	0.00363555	+	0.00629696i
$962$	−20.3477	−	20.3304i	−0.656035	−	0.655478i
$963$	−34.5883	+	8.11408i	−1.11459	+	0.261473i
$964$	57.1756	−	0.0485654i	1.84150	−	0.00156419i
$965$	10.3568	+	7.94707i	0.333398	+	0.255825i
$966$	0.537789	−	1.50825i	0.0173031	−	0.0485270i
$967$	−17.8839	+	4.79197i	−0.575107	+	0.154100i	−0.534638	−	0.845081i	$-0.679552\pi$
$967$	−17.8839	+	4.79197i	−0.575107	+	0.154100i	−0.0404694	+	0.999181i	$0.512885\pi$
$968$	−31.4787	−	18.1208i	−1.01176	−	0.582425i
$969$	3.85337	−	7.51435i	0.123788	−	0.241396i
$970$	−0.723448	−	5.47716i	−0.0232285	−	0.175861i
$971$	−38.0099	+	15.7442i	−1.21979	+	0.505255i	−0.897344	−	0.441331i	$-0.854506\pi$
$971$	−38.0099	+	15.7442i	−1.21979	+	0.505255i	−0.322450	+	0.946586i	$0.604506\pi$
$972$	24.9629	−	18.6776i	0.800685	−	0.599086i
$973$	−5.75065	+	13.8833i	−0.184357	+	0.445078i
$974$	39.4078	−	22.7744i	1.26271	−	0.729739i
$975$	−16.0878	+	5.18108i	−0.515222	+	0.165927i
$976$	−37.8329	+	29.1324i	−1.21100	+	0.932506i
$977$	−6.97197	+	12.0758i	−0.223053	+	0.386339i	−0.955734	−	0.294233i	$-0.904936\pi$
$977$	−6.97197	+	12.0758i	−0.223053	+	0.386339i	0.732680	+	0.680573i	$0.238269\pi$
$978$	−13.6720	+	15.1181i	−0.437181	+	0.483422i
$979$	−2.67609	−	20.3269i	−0.0855281	−	0.649651i
$980$	7.14470	−	2.96654i	0.228229	−	0.0947628i
$981$	−21.5253	+	34.7199i	−0.687249	+	1.10852i
$982$	−13.3799	−	5.53549i	−0.426971	−	0.176645i
$983$	−8.81570	+	32.9007i	−0.281177	+	1.04937i	0.670410	+	0.741990i	$0.266118\pi$
$983$	−8.81570	+	32.9007i	−0.281177	+	1.04937i	−0.951588	+	0.307377i	$0.900549\pi$
$984$	−10.6087	+	15.3921i	−0.338193	+	0.490681i
$985$	−3.35701	−	12.5285i	−0.106963	−	0.399192i
$986$	4.83588	−	36.8531i	0.154006	−	1.17364i
$987$	12.2965	−	2.24600i	0.391402	−	0.0714909i
$988$	1.50325	−	5.62932i	0.0478247	−	0.179093i
$989$	−1.54991	+	3.74182i	−0.0492844	+	0.118983i
$990$	−8.54656	−	22.5860i	−0.271627	−	0.717831i
$991$		−	18.4826i		−	0.587119i	−0.955941	−	0.293560i	$-0.905160\pi$
$991$		−	18.4826i		−	0.587119i	0.955941	−	0.293560i	$-0.0948399\pi$
$992$	30.5505	+	8.11650i	0.969981	+	0.257699i
$993$	23.1068	+	20.9144i	0.733273	+	0.663699i
$994$	−24.7698	+	6.64831i	−0.785649	+	0.210872i
$995$	−15.7529	+	12.0876i	−0.499399	+	0.383202i
$996$	28.5217	−	55.7358i	0.903743	−	1.76606i
$997$	−2.97562	+	3.87790i	−0.0942388	+	0.122814i	−0.838093	−	0.545528i	$-0.816329\pi$
$997$	−2.97562	+	3.87790i	−0.0942388	+	0.122814i	0.743854	+	0.668342i	$0.232996\pi$
$998$	4.56901	+	11.0173i	0.144629	+	0.348747i
$999$	−38.9962	+	5.86523i	−1.23379	+	0.185568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.131.29	yes	368
3.2	odd	2		864.2.bn.a.611.18		368
9.2	odd	6	inner	288.2.bf.a.227.44	yes	368
9.7	even	3		864.2.bn.a.35.3		368
32.11	odd	8	inner	288.2.bf.a.203.44	yes	368
96.11	even	8		864.2.bn.a.395.3		368
288.11	even	24	inner	288.2.bf.a.11.29	✓	368
288.43	odd	24		864.2.bn.a.683.18		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.29	✓	368	288.11	even	24	inner
288.2.bf.a.131.29	yes	368	1.1	even	1	trivial
288.2.bf.a.203.44	yes	368	32.11	odd	8	inner
288.2.bf.a.227.44	yes	368	9.2	odd	6	inner
864.2.bn.a.35.3		368	9.7	even	3
864.2.bn.a.395.3		368	96.11	even	8
864.2.bn.a.611.18		368	3.2	odd	2
864.2.bn.a.683.18		368	288.43	odd	24

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.365445 - 1.36618i) q^{2} +(-0.140380 + 1.72635i) q^{3} +(-1.73290 - 0.998528i) q^{4} +(-0.152157 + 1.15575i) q^{5} +(2.30721 + 0.822672i) q^{6} +(-0.496625 + 1.85343i) q^{7} +(-1.99745 + 2.00255i) q^{8} +(-2.96059 - 0.484692i) q^{9} +(1.52335 + 0.630235i) q^{10} +(3.87378 + 2.97246i) q^{11} +(1.96708 - 2.85142i) q^{12} +(1.63147 + 2.12617i) q^{13} +(2.35063 + 1.35581i) q^{14} +(-1.97386 - 0.424920i) q^{15} +(2.00588 + 3.46070i) q^{16} -4.48513 q^{17} +(-1.74411 + 3.86757i) q^{18} +(1.00431 + 0.415998i) q^{19} +(1.41772 - 1.85086i) q^{20} +(-3.12996 - 1.11753i) q^{21} +(5.47657 - 4.20602i) q^{22} +(-0.329076 + 0.0881758i) q^{23} +(-3.17670 - 3.72942i) q^{24} +(3.51703 + 0.942386i) q^{25} +(3.50095 - 1.45188i) q^{26} +(1.25236 - 5.04298i) q^{27} +(2.71130 - 2.71591i) q^{28} +(-5.80978 + 0.764873i) q^{29} +(-1.30186 + 2.54137i) q^{30} +(4.83932 + 2.79398i) q^{31} +(5.46098 - 1.47570i) q^{32} +(-5.67531 + 6.27024i) q^{33} +(-1.63907 + 6.12750i) q^{34} +(-2.06653 - 0.855983i) q^{35} +(4.64642 + 3.79615i) q^{36} +(-2.90428 - 7.01154i) q^{37} +(0.935348 - 1.22004i) q^{38} +(-3.89955 + 2.51802i) q^{39} +(-2.01051 - 2.61324i) q^{40} +(-0.987619 - 3.68584i) q^{41} +(-2.67058 + 3.86769i) q^{42} +(7.23706 - 9.43152i) q^{43} +(-3.74479 - 9.01905i) q^{44} +(1.01065 - 3.34793i) q^{45} +(0.000204623 + 0.481801i) q^{46} +(-3.25721 + 1.88055i) q^{47} +(-6.25597 + 2.97705i) q^{48} +(2.87362 + 1.65908i) q^{49} +(2.57275 - 4.46051i) q^{50} +(0.629624 - 7.74292i) q^{51} +(-0.704130 - 5.31352i) q^{52} +(-3.91618 - 9.45448i) q^{53} +(-6.43195 - 3.55388i) q^{54} +(-4.02483 + 4.02483i) q^{55} +(-2.71959 - 4.69665i) q^{56} +(-0.859144 + 1.67539i) q^{57} +(-1.07820 + 8.21673i) q^{58} +(0.952686 + 0.125424i) q^{59} +(2.99621 + 2.70730i) q^{60} +(1.55814 + 11.8353i) q^{61} +(5.58560 - 5.59034i) q^{62} +(2.36864 - 5.24653i) q^{63} +(-0.0203858 - 7.99997i) q^{64} +(-2.70555 + 1.56205i) q^{65} +(6.49227 + 10.0449i) q^{66} +(1.54211 + 2.00972i) q^{67} +(7.77228 + 4.47853i) q^{68} +(-0.106027 - 0.580480i) q^{69} +(-1.92463 + 2.51043i) q^{70} +(-6.68291 + 6.68291i) q^{71} +(6.88424 - 4.96056i) q^{72} +(-0.787037 - 0.787037i) q^{73} +(-10.6404 + 1.40543i) q^{74} +(-2.12061 + 5.93935i) q^{75} +(-1.32498 - 1.72371i) q^{76} +(-7.43306 + 5.70358i) q^{77} +(2.01500 + 6.24769i) q^{78} +(3.18314 + 5.51337i) q^{79} +(-4.30489 + 1.79172i) q^{80} +(8.53015 + 2.86994i) q^{81} +(-5.39645 + 0.00229190i) q^{82} +(17.9192 - 2.35911i) q^{83} +(4.30801 + 5.06192i) q^{84} +(0.682443 - 5.18367i) q^{85} +(-10.2404 - 13.3338i) q^{86} +(-0.504860 - 10.1371i) q^{87} +(-13.6902 + 1.82009i) q^{88} +(-2.96906 - 2.96906i) q^{89} +(-4.20455 - 2.60422i) q^{90} +(-4.75094 + 1.96790i) q^{91} +(0.658302 + 0.175792i) q^{92} +(-5.50275 + 7.96216i) q^{93} +(1.37884 + 5.13718i) q^{94} +(-0.633600 + 1.09743i) q^{95} +(1.78097 + 9.63474i) q^{96} +(-1.67561 - 2.90224i) q^{97} +(3.31676 - 3.31958i) q^{98} +(-10.0279 - 10.6778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21}+ \cdots - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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