LMFDB - Embedded newform 64.2.i.a.13.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [64,2,Mod(5,64)] 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("64.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(64, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, 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:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	64.13
Dual form			64.2.i.a.5.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0973444 - 1.41086i) q^{2} +(0.306211 - 0.204603i) q^{3} +(-1.98105 - 0.274678i) q^{4} +(1.42470 - 0.283390i) q^{5} +(-0.258859 - 0.451937i) q^{6} +(-0.666723 - 1.60961i) q^{7} +(-0.580376 + 2.76824i) q^{8} +(-1.09615 + 2.64634i) q^{9} +(-0.261137 - 2.03763i) q^{10} +(-1.65860 + 2.48226i) q^{11} +(-0.662818 + 0.321220i) q^{12} +(5.03569 + 1.00166i) q^{13} +(-2.33584 + 0.783966i) q^{14} +(0.378274 - 0.378274i) q^{15} +(3.84910 + 1.08830i) q^{16} +(-1.55248 - 1.55248i) q^{17} +(3.62690 + 1.80412i) q^{18} +(-0.0359002 + 0.180483i) q^{19} +(-2.90023 + 0.170075i) q^{20} +(-0.533490 - 0.356467i) q^{21} +(3.34067 + 2.58168i) q^{22} +(-6.50946 - 2.69631i) q^{23} +(0.388674 + 0.966412i) q^{24} +(-2.66995 + 1.10593i) q^{25} +(1.90340 - 7.00714i) q^{26} +(0.421339 + 2.11821i) q^{27} +(0.878685 + 3.37185i) q^{28} +(0.0389072 + 0.0582287i) q^{29} +(-0.496869 - 0.570515i) q^{30} -6.25272i q^{31} +(1.91013 - 5.32460i) q^{32} +1.09945i q^{33} +(-2.34146 + 2.03921i) q^{34} +(-1.40602 - 2.10426i) q^{35} +(2.89841 - 4.94143i) q^{36} +(-1.63291 - 8.20918i) q^{37} +(0.251141 + 0.0682192i) q^{38} +(1.74693 - 0.723600i) q^{39} +(-0.0423689 + 4.10837i) q^{40} +(-6.98521 - 2.89337i) q^{41} +(-0.554857 + 0.717979i) q^{42} +(9.23959 + 6.17369i) q^{43} +(3.96758 - 4.46190i) q^{44} +(-0.811733 + 4.08086i) q^{45} +(-4.43777 + 8.92146i) q^{46} +(7.84283 + 7.84283i) q^{47} +(1.40131 - 0.454290i) q^{48} +(2.80342 - 2.80342i) q^{49} +(1.30041 + 3.87458i) q^{50} +(-0.793030 - 0.157743i) q^{51} +(-9.70081 - 3.36753i) q^{52} +(-1.21975 + 1.82549i) q^{53} +(3.02951 - 0.388253i) q^{54} +(-1.65955 + 4.00650i) q^{55} +(4.84275 - 0.911470i) q^{56} +(0.0259343 + 0.0626110i) q^{57} +(0.0859400 - 0.0492244i) q^{58} +(-8.31975 + 1.65490i) q^{59} +(-0.853284 + 0.645476i) q^{60} +(-3.29205 + 2.19968i) q^{61} +(-8.82172 - 0.608668i) q^{62} +4.99040 q^{63} +(-7.32633 - 3.21324i) q^{64} +7.45818 q^{65} +(1.55117 + 0.107025i) q^{66} +(13.1855 - 8.81029i) q^{67} +(2.64911 + 3.50197i) q^{68} +(-2.54494 + 0.506220i) q^{69} +(-3.10569 + 1.77886i) q^{70} +(1.13245 + 2.73397i) q^{71} +(-6.68952 - 4.57027i) q^{72} +(-3.74820 + 9.04896i) q^{73} +(-11.7410 + 1.50469i) q^{74} +(-0.591290 + 0.884929i) q^{75} +(0.120695 - 0.347684i) q^{76} +(5.10131 + 1.01471i) q^{77} +(-0.850845 - 2.53510i) q^{78} +(-1.58284 + 1.58284i) q^{79} +(5.79221 + 0.459704i) q^{80} +(-5.51384 - 5.51384i) q^{81} +(-4.76211 + 9.57349i) q^{82} +(-1.12345 + 5.64796i) q^{83} +(0.958956 + 0.852716i) q^{84} +(-2.65177 - 1.77186i) q^{85} +(9.60964 - 12.4348i) q^{86} +(0.0238276 + 0.00986972i) q^{87} +(-5.90890 - 6.03204i) q^{88} +(14.5341 - 6.02023i) q^{89} +(5.67850 + 1.54249i) q^{90} +(-1.74513 - 8.77334i) q^{91} +(12.1549 + 7.12952i) q^{92} +(-1.27933 - 1.91465i) q^{93} +(11.8286 - 10.3017i) q^{94} +0.267307i q^{95} +(-0.504530 - 2.02127i) q^{96} +5.25588i q^{97} +(-3.68233 - 4.22812i) q^{98} +(-4.75084 - 7.11013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20}+ \cdots + 16 q^{99}+O(q^{100}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{15}{16}\right)$	$1$

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 $

$2$	0.0973444	−	1.41086i	0.0688329	−	0.997628i
$2$	0.0973444	−	1.41086i	0.0688329	−	0.997628i
$3$	0.306211	−	0.204603i	0.176791	−	0.118128i	−0.464026	−	0.885821i	$-0.653596\pi$
$3$	0.306211	−	0.204603i	0.176791	−	0.118128i	0.640817	+	0.767694i	$0.278596\pi$
$4$	−1.98105	−	0.274678i	−0.990524	−	0.137339i
$5$	1.42470	−	0.283390i	0.637143	−	0.126736i	0.134059	−	0.990973i	$-0.457199\pi$
$5$	1.42470	−	0.283390i	0.637143	−	0.126736i	0.503084	+	0.864238i	$0.332199\pi$
$6$	−0.258859	−	0.451937i	−0.105679	−	0.184503i
$7$	−0.666723	−	1.60961i	−0.251998	−	0.608376i	0.746367	−	0.665534i	$-0.231796\pi$
$7$	−0.666723	−	1.60961i	−0.251998	−	0.608376i	−0.998365	+	0.0571578i	$0.981796\pi$
$8$	−0.580376	+	2.76824i	−0.205194	+	0.978721i
$9$	−1.09615	+	2.64634i	−0.365383	+	0.882112i
$10$	−0.261137	−	2.03763i	−0.0825787	−	0.644356i
$11$	−1.65860	+	2.48226i	−0.500086	+	0.748431i	−0.992542	−	0.121906i	$-0.961099\pi$
$11$	−1.65860	+	2.48226i	−0.500086	+	0.748431i	0.492456	+	0.870337i	$0.336099\pi$
$12$	−0.662818	+	0.321220i	−0.191339	+	0.0927282i
$13$	5.03569	+	1.00166i	1.39665	+	0.277811i	0.835312	−	0.549776i	$-0.185287\pi$
$13$	5.03569	+	1.00166i	1.39665	+	0.277811i	0.561337	+	0.827587i	$0.310287\pi$
$14$	−2.33584	+	0.783966i	−0.624279	+	0.209524i
$15$	0.378274	−	0.378274i	0.0976700	−	0.0976700i
$16$	3.84910	+	1.08830i	0.962276	+	0.272076i
$17$	−1.55248	−	1.55248i	−0.376532	−	0.376532i	0.493317	−	0.869849i	$-0.335784\pi$
$17$	−1.55248	−	1.55248i	−0.376532	−	0.376532i	−0.869849	+	0.493317i	$0.835784\pi$
$18$	3.62690	+	1.80412i	0.854869	+	0.425234i
$19$	−0.0359002	+	0.180483i	−0.00823608	+	0.0414056i	−0.984685	−	0.174344i	$-0.944220\pi$
$19$	−0.0359002	+	0.180483i	−0.00823608	+	0.0414056i	0.976449	+	0.215750i	$0.0692195\pi$
$20$	−2.90023	+	0.170075i	−0.648511	+	0.0380300i
$21$	−0.533490	−	0.356467i	−0.116417	−	0.0777874i
$22$	3.34067	+	2.58168i	0.712233	+	0.550416i
$23$	−6.50946	−	2.69631i	−1.35732	−	0.562219i	−0.418997	−	0.907988i	$-0.637618\pi$
$23$	−6.50946	−	2.69631i	−1.35732	−	0.562219i	−0.938320	+	0.345769i	$0.887618\pi$
$24$	0.388674	+	0.966412i	0.0793378	+	0.197268i
$25$	−2.66995	+	1.10593i	−0.533990	+	0.221186i
$26$	1.90340	−	7.00714i	0.373287	−	1.37421i
$27$	0.421339	+	2.11821i	0.0810866	+	0.407650i
$28$	0.878685	+	3.37185i	0.166056	+	0.637221i
$29$	0.0389072	+	0.0582287i	0.00722489	+	0.0108128i	0.835064	−	0.550152i	$-0.185430\pi$
$29$	0.0389072	+	0.0582287i	0.00722489	+	0.0108128i	−0.827840	+	0.560965i	$0.810430\pi$
$30$	−0.496869	−	0.570515i	−0.0907155	−	0.104161i
$31$		−	6.25272i		−	1.12302i	−0.827469	−	0.561511i	$-0.810220\pi$
$31$		−	6.25272i		−	1.12302i	0.827469	−	0.561511i	$-0.189780\pi$
$32$	1.91013	−	5.32460i	0.337666	−	0.941266i
$33$			1.09945i			0.191390i
$34$	−2.34146	+	2.03921i	−0.401557	+	0.349721i
$35$	−1.40602	−	2.10426i	−0.237662	−	0.355686i
$36$	2.89841	−	4.94143i	0.483069	−	0.823572i
$37$	−1.63291	−	8.20918i	−0.268448	−	1.34958i	−0.845981	−	0.533213i	$-0.820984\pi$
$37$	−1.63291	−	8.20918i	−0.268448	−	1.34958i	0.577532	−	0.816368i	$-0.304016\pi$
$38$	0.251141	+	0.0682192i	0.0407405	+	0.0110666i
$39$	1.74693	−	0.723600i	0.279732	−	0.115869i
$40$	−0.0423689	+	4.10837i	−0.00669911	+	0.649591i
$41$	−6.98521	−	2.89337i	−1.09091	−	0.451868i	−0.236584	−	0.971611i	$-0.576028\pi$
$41$	−6.98521	−	2.89337i	−1.09091	−	0.451868i	−0.854323	+	0.519743i	$0.826028\pi$
$42$	−0.554857	+	0.717979i	−0.0856162	+	0.110787i
$43$	9.23959	+	6.17369i	1.40902	+	0.941480i	0.999575	+	0.0291463i	$0.00927887\pi$
$43$	9.23959	+	6.17369i	1.40902	+	0.941480i	0.409449	+	0.912333i	$0.365721\pi$
$44$	3.96758	−	4.46190i	0.598136	−	0.672657i
$45$	−0.811733	+	4.08086i	−0.121006	+	0.608338i
$46$	−4.43777	+	8.92146i	−0.654313	+	1.31540i
$47$	7.84283	+	7.84283i	1.14399	+	1.14399i	0.987713	+	0.156281i	$0.0499507\pi$
$47$	7.84283	+	7.84283i	1.14399	+	1.14399i	0.156281	+	0.987713i	$0.450049\pi$
$48$	1.40131	−	0.454290i	0.202261	−	0.0655711i
$49$	2.80342	−	2.80342i	0.400488	−	0.400488i
$50$	1.30041	+	3.87458i	0.183905	+	0.547948i
$51$	−0.793030	−	0.157743i	−0.111046	−	0.0220885i
$52$	−9.70081	−	3.36753i	−1.34526	−	0.466993i
$53$	−1.21975	+	1.82549i	−0.167546	+	0.250750i	−0.905736	−	0.423843i	$-0.860681\pi$
$53$	−1.21975	+	1.82549i	−0.167546	+	0.250750i	0.738190	+	0.674593i	$0.235681\pi$
$54$	3.02951	−	0.388253i	0.412265	−	0.0528346i
$55$	−1.65955	+	4.00650i	−0.223773	+	0.540236i
$56$	4.84275	−	0.911470i	0.647139	−	0.121800i
$57$	0.0259343	+	0.0626110i	0.00343509	+	0.00829304i
$58$	0.0859400	−	0.0492244i	0.0112845	−	0.00646347i
$59$	−8.31975	+	1.65490i	−1.08314	+	0.215450i	−0.704221	−	0.709981i	$-0.748704\pi$
$59$	−8.31975	+	1.65490i	−1.08314	+	0.215450i	−0.378918	+	0.925430i	$0.623704\pi$
$60$	−0.853284	+	0.645476i	−0.110158	+	0.0833306i
$61$	−3.29205	+	2.19968i	−0.421504	+	0.281640i	−0.748179	−	0.663497i	$-0.769072\pi$
$61$	−3.29205	+	2.19968i	−0.421504	+	0.281640i	0.326675	+	0.945137i	$0.394072\pi$
$62$	−8.82172	−	0.608668i	−1.12036	−	0.0773009i
$63$	4.99040			0.628731
$64$	−7.32633	−	3.21324i	−0.915791	−	0.401656i
$65$	7.45818			0.925074
$66$	1.55117	+	0.107025i	0.190936	+	0.0131739i
$67$	13.1855	−	8.81029i	1.61087	−	1.07635i	0.667497	−	0.744612i	$-0.267366\pi$
$67$	13.1855	−	8.81029i	1.61087	−	1.07635i	0.943372	−	0.331736i	$-0.107634\pi$
$68$	2.64911	+	3.50197i	0.321252	+	0.424677i
$69$	−2.54494	+	0.506220i	−0.306375	+	0.0609417i
$70$	−3.10569	+	1.77886i	−0.371201	+	0.212615i
$71$	1.13245	+	2.73397i	0.134397	+	0.324462i	0.976723	−	0.214506i	$-0.0688142\pi$
$71$	1.13245	+	2.73397i	0.134397	+	0.324462i	−0.842326	+	0.538968i	$0.818814\pi$
$72$	−6.68952	−	4.57027i	−0.788367	−	0.538612i
$73$	−3.74820	+	9.04896i	−0.438694	+	1.05910i	0.537706	+	0.843132i	$0.319291\pi$
$73$	−3.74820	+	9.04896i	−0.438694	+	1.05910i	−0.976400	+	0.215969i	$0.930709\pi$
$74$	−11.7410	+	1.50469i	−1.36486	+	0.174916i
$75$	−0.591290	+	0.884929i	−0.0682763	+	0.102183i
$76$	0.120695	−	0.347684i	0.0138446	−	0.0398821i
$77$	5.10131	+	1.01471i	0.581348	+	0.115637i
$78$	−0.850845	−	2.53510i	−0.0963392	−	0.287044i
$79$	−1.58284	+	1.58284i	−0.178083	+	0.178083i	−0.790520	−	0.612436i	$-0.790190\pi$
$79$	−1.58284	+	1.58284i	−0.178083	+	0.178083i	0.612436	+	0.790520i	$0.290190\pi$
$80$	5.79221	+	0.459704i	0.647589	+	0.0513964i
$81$	−5.51384	−	5.51384i	−0.612649	−	0.612649i
$82$	−4.76211	+	9.57349i	−0.525887	+	1.05722i
$83$	−1.12345	+	5.64796i	−0.123314	+	0.619944i	0.868857	+	0.495063i	$0.164855\pi$
$83$	−1.12345	+	5.64796i	−0.123314	+	0.619944i	−0.992172	+	0.124881i	$0.960145\pi$
$84$	0.958956	+	0.852716i	0.104631	+	0.0930389i
$85$	−2.65177	−	1.77186i	−0.287625	−	0.192185i
$86$	9.60964	−	12.4348i	1.03623	−	1.34088i
$87$	0.0238276	+	0.00986972i	0.00255459	+	0.00105814i
$88$	−5.90890	−	6.03204i	−0.629891	−	0.643018i
$89$	14.5341	−	6.02023i	1.54061	−	0.638143i	0.559024	−	0.829151i	$-0.311176\pi$
$89$	14.5341	−	6.02023i	1.54061	−	0.638143i	0.981588	+	0.191009i	$0.0611759\pi$
$90$	5.67850	+	1.54249i	0.598566	+	0.162593i
$91$	−1.74513	−	8.77334i	−0.182939	−	0.919696i
$92$	12.1549	+	7.12952i	1.26724	+	0.743304i
$93$	−1.27933	−	1.91465i	−0.132660	−	0.198540i
$94$	11.8286	−	10.3017i	1.22003	−	1.06254i
$95$			0.267307i			0.0274251i
$96$	−0.504530	−	2.02127i	−0.0514934	−	0.206295i
$97$			5.25588i			0.533654i	0.963744	+	0.266827i	$0.0859753\pi$
$97$			5.25588i			0.533654i	−0.963744	+	0.266827i	$0.914025\pi$
$98$	−3.68233	−	4.22812i	−0.371971	−	0.427105i
$99$	−4.75084	−	7.11013i	−0.477477	−	0.714595i
$100$	5.59308	−	1.45752i	0.559308	−	0.145752i
$101$	−0.994080	−	4.99758i	−0.0989146	−	0.497278i	−0.998203	−	0.0599215i	$-0.980915\pi$
$101$	−0.994080	−	4.99758i	−0.0989146	−	0.497278i	0.899288	−	0.437356i	$-0.144085\pi$
$102$	−0.299751	+	1.10350i	−0.0296797	+	0.109263i
$103$	0.990660	−	0.410345i	0.0976127	−	0.0404325i	−0.333343	−	0.942806i	$-0.608177\pi$
$103$	0.990660	−	0.410345i	0.0976127	−	0.0404325i	0.430955	+	0.902373i	$0.358177\pi$
$104$	−5.69544	+	13.3587i	−0.558483	+	1.30993i
$105$	−0.861080	−	0.356671i	−0.0840328	−	0.0348075i
$106$	2.45677	+	1.89860i	0.238623	+	0.184409i
$107$	−3.35832	−	2.24396i	−0.324661	−	0.216932i	0.382549	−	0.923935i	$-0.375046\pi$
$107$	−3.35832	−	2.24396i	−0.324661	−	0.216932i	−0.707210	+	0.707004i	$0.750046\pi$
$108$	−0.252865	−	4.31201i	−0.0243319	−	0.414924i
$109$	0.692578	−	3.48183i	0.0663370	−	0.333498i	−0.933338	−	0.358999i	$-0.883118\pi$
$109$	0.692578	−	3.48183i	0.0663370	−	0.333498i	0.999675	+	0.0255008i	$0.00811805\pi$
$110$	5.49106	+	2.73140i	0.523552	+	0.260428i
$111$	−2.17964	−	2.17964i	−0.206882	−	0.206882i
$112$	−0.814542	−	6.92116i	−0.0769670	−	0.653988i
$113$	5.12191	−	5.12191i	0.481829	−	0.481829i	−0.423886	−	0.905715i	$-0.639334\pi$
$113$	5.12191	−	5.12191i	0.481829	−	0.481829i	0.905715	+	0.423886i	$0.139334\pi$
$114$	0.0908599	−	0.0304949i	0.00850981	−	0.00285611i
$115$	−10.0381	−	1.99670i	−0.936058	−	0.186194i
$116$	−0.0610829	−	0.126041i	−0.00567140	−	0.0117026i
$117$	−8.17059	+	12.2282i	−0.755371	+	1.13049i
$118$	1.52495	+	11.8991i	0.140383	+	1.09540i
$119$	−1.46382	+	3.53397i	−0.134188	+	0.323958i
$120$	0.827614	+	1.26670i	0.0755504	+	0.115633i
$121$	0.798822	+	1.92853i	0.0726202	+	0.175321i
$122$	2.78297	+	4.85874i	0.251958	+	0.439890i
$123$	−2.73094	+	0.543217i	−0.246240	+	0.0489803i
$124$	−1.71749	+	12.3869i	−0.154235	+	1.11238i
$125$	−9.52945	+	6.36737i	−0.852340	+	0.569515i
$126$	0.485787	−	7.04075i	0.0432774	−	0.627240i
$127$	−2.94406			−0.261243			−0.130622	−	0.991432i	$-0.541697\pi$
$127$	−2.94406			−0.261243			−0.130622	+	0.991432i	$0.541697\pi$
$128$	−5.24661	+	10.0236i	−0.463739	+	0.885972i
$129$	4.09242			0.360317
$130$	0.726012	−	10.5224i	0.0636755	−	0.922880i
$131$	−6.41752	+	4.28805i	−0.560701	+	0.374648i	−0.803388	−	0.595456i	$-0.796971\pi$
$131$	−6.41752	+	4.28805i	−0.560701	+	0.374648i	0.242687	+	0.970105i	$0.421971\pi$
$132$	0.301995	−	2.17806i	0.0262853	−	0.189576i
$133$	0.314443	−	0.0625465i	0.0272656	−	0.00542347i
$134$	−11.1465	−	19.4606i	−0.962915	−	1.68114i
$135$	1.20056	+	2.89840i	0.103328	+	0.249455i
$136$	5.19867	−	3.39662i	0.445782	−	0.291258i
$137$	1.69028	−	4.08071i	0.144411	−	0.348638i	−0.835080	−	0.550129i	$-0.814579\pi$
$137$	1.69028	−	4.08071i	0.144411	−	0.348638i	0.979490	+	0.201491i	$0.0645786\pi$
$138$	0.466470	+	3.63983i	0.0397085	+	0.309843i
$139$	4.34787	−	6.50705i	0.368782	−	0.551921i	−0.599948	−	0.800039i	$-0.704812\pi$
$139$	4.34787	−	6.50705i	0.368782	−	0.551921i	0.968730	+	0.248118i	$0.0798121\pi$
$140$	2.20741	+	4.55485i	0.186560	+	0.384955i
$141$	4.00623	+	0.796888i	0.337385	+	0.0671101i
$142$	3.96748	−	1.33159i	0.332944	−	0.111744i
$143$	−10.8386	+	10.8386i	−0.906366	+	0.906366i
$144$	−7.09920	+	8.99308i	−0.591600	+	0.749423i
$145$	0.0719323	+	0.0719323i	0.00597365	+	0.00597365i
$146$	12.4019	+	6.16905i	1.02639	+	0.510554i
$147$	0.284847	−	1.43202i	0.0234938	−	0.118111i
$148$	0.979984	+	16.7113i	0.0805542	+	1.37366i
$149$	10.7964	+	7.21395i	0.884479	+	0.590990i	0.912708	−	0.408612i	$-0.133987\pi$
$149$	10.7964	+	7.21395i	0.884479	+	0.590990i	−0.0282295	+	0.999601i	$0.508987\pi$
$150$	1.19095	+	0.920370i	0.0972407	+	0.0751479i
$151$	−9.79563	−	4.05748i	−0.797157	−	0.330193i	−0.0533397	−	0.998576i	$-0.516987\pi$
$151$	−9.79563	−	4.05748i	−0.797157	−	0.330193i	−0.743817	+	0.668383i	$0.766987\pi$
$152$	−0.478784	−	0.204128i	−0.0388345	−	0.0165570i
$153$	5.81014	−	2.40664i	0.469722	−	0.194565i
$154$	1.92820	−	7.09845i	0.155379	−	0.572010i
$155$	−1.77196	−	8.90823i	−0.142327	−	0.715526i
$156$	−3.65950	+	0.953644i	−0.292995	+	0.0763526i
$157$	−4.31959	−	6.46472i	−0.344741	−	0.515941i	0.618068	−	0.786124i	$-0.287916\pi$
$157$	−4.31959	−	6.46472i	−0.344741	−	0.515941i	−0.962809	+	0.270184i	$0.912916\pi$
$158$	2.07908	+	2.38724i	0.165403	+	0.189919i
$159$			0.808550i			0.0641222i
$160$	1.21242	−	8.12725i	0.0958499	−	0.642515i
$161$			12.2754i			0.967437i
$162$	−8.31599	+	7.24251i	−0.653366	+	0.569025i
$163$	0.437112	+	0.654184i	0.0342372	+	0.0512396i	0.848193	−	0.529687i	$-0.177690\pi$
$163$	0.437112	+	0.654184i	0.0342372	+	0.0512396i	−0.813956	+	0.580926i	$0.802690\pi$
$164$	13.0433	+	7.65059i	1.01851	+	0.597410i
$165$	0.311573	+	1.56638i	0.0242559	+	0.121943i
$166$	7.85911	+	2.13482i	0.609985	+	0.165695i
$167$	17.5845	−	7.28375i	1.36073	−	0.563633i	0.421472	−	0.906841i	$-0.361514\pi$
$167$	17.5845	−	7.28375i	1.36073	−	0.563633i	0.939259	+	0.343208i	$0.111514\pi$
$168$	1.29641	−	1.26994i	0.100020	−	0.0979784i
$169$	12.3444	+	5.11322i	0.949570	+	0.393325i
$170$	−2.75798	+	3.56879i	−0.211527	+	0.273714i
$171$	−0.438266	−	0.292840i	−0.0335150	−	0.0223940i
$172$	−16.6083	−	14.7683i	−1.26637	−	1.12607i
$173$	0.285668	−	1.43615i	0.0217189	−	0.109188i	−0.968405	−	0.249382i	$-0.919773\pi$
$173$	0.285668	−	1.43615i	0.0217189	−	0.109188i	0.990124	+	0.140194i	$0.0447725\pi$
$174$	0.0162443	−	0.0326566i	0.00123147	−	0.00247569i
$175$	3.56024	+	3.56024i	0.269129	+	0.269129i
$176$	−9.08556	+	7.74944i	−0.684850	+	0.584136i
$177$	−2.20900	+	2.20900i	−0.166038	+	0.166038i
$178$	−7.07888	−	21.0916i	−0.530584	−	1.58088i
$179$	9.41568	+	1.87290i	0.703761	+	0.139987i	0.533983	−	0.845496i	$-0.320695\pi$
$179$	9.41568	+	1.87290i	0.703761	+	0.139987i	0.169778	+	0.985482i	$0.445695\pi$
$180$	2.72901	−	7.86141i	0.203408	−	0.585955i
$181$	1.23999	−	1.85578i	0.0921677	−	0.137939i	−0.782520	−	0.622625i	$-0.786066\pi$
$181$	1.23999	−	1.85578i	0.0921677	−	0.137939i	0.874688	+	0.484686i	$0.161066\pi$
$182$	−12.5478	+	1.60809i	−0.930107	+	0.119200i
$183$	−0.557999	+	1.34713i	−0.0412485	+	0.0995826i
$184$	11.2420	−	16.4549i	0.828769	−	1.21307i
$185$	−4.65279	−	11.2328i	−0.342080	−	0.825854i
$186$	−2.82584	+	1.61857i	−0.207201	+	0.118680i
$187$	6.42861	−	1.27873i	0.470107	−	0.0935100i
$188$	−13.3828	−	17.6913i	−0.976038	−	1.29027i
$189$	3.12858	−	2.09045i	0.227571	−	0.152058i
$190$	0.377132	+	0.0260208i	0.0273600	+	0.00188775i
$191$	−13.2544			−0.959054			−0.479527	−	0.877527i	$-0.659192\pi$
$191$	−13.2544			−0.959054			−0.479527	+	0.877527i	$0.659192\pi$
$192$	−2.90084	+	0.515062i	−0.209350	+	0.0371714i
$193$	−9.34813			−0.672893			−0.336447	−	0.941703i	$-0.609225\pi$
$193$	−9.34813			−0.672893			−0.336447	+	0.941703i	$0.609225\pi$
$194$	7.41531	+	0.511631i	0.532388	+	0.0367329i
$195$	2.28378	−	1.52597i	0.163545	−	0.109277i
$196$	−6.32374	+	4.78366i	−0.451696	+	0.341690i
$197$	16.0043	−	3.18345i	1.14026	−	0.226812i	0.411387	−	0.911461i	$-0.365045\pi$
$197$	16.0043	−	3.18345i	1.14026	−	0.226812i	0.728873	+	0.684649i	$0.240045\pi$
$198$	−10.4939	+	6.01063i	−0.745766	+	0.427157i
$199$	2.57784	+	6.22346i	0.182738	+	0.441170i	0.988529	−	0.151031i	$-0.0482593\pi$
$199$	2.57784	+	6.22346i	0.182738	+	0.441170i	−0.805791	+	0.592201i	$0.798259\pi$
$200$	−1.51190	−	8.03292i	−0.106908	−	0.568014i
$201$	2.23494	−	5.39561i	0.157640	−	0.380577i
$202$	−7.14765	+	0.916021i	−0.502907	+	0.0644510i
$203$	0.0677854	−	0.101448i	0.00475760	−	0.00712025i
$204$	1.52770	+	0.530325i	0.106960	+	0.0371302i
$205$	−10.7717	−	2.14263i	−0.752331	−	0.149648i
$206$	−0.482504	−	1.43763i	−0.0336176	−	0.100164i
$207$	14.2707	−	14.2707i	0.991880	−	0.991880i
$208$	18.2928	+	9.33585i	1.26838	+	0.647325i
$209$	−0.388462	−	0.388462i	−0.0268705	−	0.0268705i
$210$	−0.587034	+	1.18014i	−0.0405092	+	0.0814376i
$211$	−4.14756	+	20.8512i	−0.285530	+	1.43546i	0.525671	+	0.850688i	$0.323814\pi$
$211$	−4.14756	+	20.8512i	−0.285530	+	1.43546i	−0.811201	+	0.584768i	$0.801186\pi$
$212$	2.91781	−	3.28134i	0.200396	−	0.225364i
$213$	0.906147	+	0.605468i	0.0620881	+	0.0414860i
$214$	−3.49282	+	4.51968i	−0.238765	+	0.308959i
$215$	14.9132	+	6.17723i	1.01707	+	0.421284i
$216$	−6.10826	−	0.0629934i	−0.415614	−	0.00428616i
$217$	−10.0645	+	4.16884i	−0.683220	+	0.282999i
$218$	−4.84495	−	1.31607i	−0.328141	−	0.0891353i
$219$	0.703709	+	3.53778i	0.0475522	+	0.239061i
$220$	4.38814	−	7.48123i	0.295848	−	0.504384i
$221$	−6.26276	−	9.37288i	−0.421279	−	0.630488i
$222$	−3.28734	+	2.86299i	−0.220632	+	0.192151i
$223$		−	18.1448i		−	1.21507i	−0.794294	−	0.607533i	$-0.792159\pi$
$223$		−	18.1448i		−	1.21507i	0.794294	−	0.607533i	$-0.207841\pi$
$224$	−9.84408	+	0.475468i	−0.657735	+	0.0317686i
$225$		−	8.27785i		−	0.551856i
$226$	−6.72771	−	7.72489i	−0.447521	−	0.513852i
$227$	13.5289	+	20.2475i	0.897946	+	1.34387i	0.938712	+	0.344703i	$0.112020\pi$
$227$	13.5289	+	20.2475i	0.897946	+	1.34387i	−0.0407657	+	0.999169i	$0.512980\pi$
$228$	−0.0341793	−	0.131159i	−0.00226358	−	0.00868622i
$229$	3.24498	+	16.3136i	0.214434	+	1.07803i	0.926607	+	0.376031i	$0.122711\pi$
$229$	3.24498	+	16.3136i	0.214434	+	1.07803i	−0.712173	+	0.702004i	$0.752289\pi$
$230$	−3.79422	+	13.9680i	−0.250183	+	0.921022i
$231$	1.76969	−	0.733029i	0.116437	−	0.0482298i
$232$	−0.183772	+	0.0739100i	−0.0120652	+	0.00485243i
$233$	−7.94074	−	3.28916i	−0.520215	−	0.215480i	0.107096	−	0.994249i	$-0.465845\pi$
$233$	−7.94074	−	3.28916i	−0.520215	−	0.215480i	−0.627311	+	0.778769i	$0.715845\pi$
$234$	16.4568	+	12.7179i	1.07582	+	0.831395i
$235$	13.3962	+	8.95106i	0.873873	+	0.583903i
$236$	16.9364	−	0.993183i	1.10246	−	0.0646507i
$237$	−0.160828	+	0.808537i	−0.0104469	+	0.0525201i
$238$	4.84344	+	2.40925i	0.313954	+	0.156169i
$239$	−10.9591	−	10.9591i	−0.708886	−	0.708886i	0.257415	−	0.966301i	$-0.417129\pi$
$239$	−10.9591	−	10.9591i	−0.708886	−	0.708886i	−0.966301	+	0.257415i	$0.917129\pi$
$240$	1.86769	−	1.04434i	0.120559	−	0.0674119i
$241$	−20.9147	+	20.9147i	−1.34723	+	1.34723i	−0.458584	+	0.888651i	$0.651643\pi$
$241$	−20.9147	+	20.9147i	−1.34723	+	1.34723i	−0.888651	+	0.458584i	$0.848357\pi$
$242$	2.79864	−	0.939294i	0.179903	−	0.0603801i
$243$	−9.17118	−	1.82426i	−0.588332	−	0.117026i
$244$	7.12591	−	3.45341i	0.456190	−	0.221082i
$245$	3.19955	−	4.78847i	0.204412	−	0.305924i
$246$	0.500562	+	3.90585i	0.0319147	+	0.249028i
$247$	−0.361565	+	0.872895i	−0.0230058	+	0.0555410i
$248$	17.3091	+	3.62893i	1.09913	+	0.230438i
$249$	0.811579	+	1.95933i	0.0514318	+	0.124167i
$250$	8.05583	+	14.0645i	0.509495	+	0.889520i
$251$	5.57057	−	1.10806i	0.351611	−	0.0699398i	−0.0161250	−	0.999870i	$-0.505133\pi$
$251$	5.57057	−	1.10806i	0.351611	−	0.0699398i	0.367736	+	0.929930i	$0.380133\pi$
$252$	−9.88622	−	1.37076i	−0.622774	−	0.0863495i
$253$	17.4895	−	11.6861i	1.09956	−	0.734700i
$254$	−0.286588	+	4.15365i	−0.0179821	+	0.260623i
$255$	−1.17453			−0.0735518
$256$	13.6312	+	8.37798i	0.851950	+	0.523624i
$257$	−18.3131			−1.14234			−0.571171	−	0.820831i	$-0.693511\pi$
$257$	−18.3131			−1.14234			−0.571171	+	0.820831i	$0.693511\pi$
$258$	0.398374	−	5.77383i	0.0248017	−	0.359463i
$259$	−12.1249	+	8.10160i	−0.753405	+	0.503409i
$260$	−14.7750	−	2.04860i	−0.916308	−	0.127049i
$261$	−0.196741	+	0.0391342i	−0.0121780	+	0.00242235i
$262$	5.42512	+	9.47163i	0.335165	+	0.585159i
$263$	−5.81316	−	14.0342i	−0.358455	−	0.865387i	−0.995518	−	0.0945749i	$-0.969851\pi$
$263$	−5.81316	−	14.0342i	−0.358455	−	0.865387i	0.637063	−	0.770812i	$-0.280149\pi$
$264$	−3.04354	−	0.638095i	−0.187317	−	0.0392720i
$265$	−1.22045	+	2.94643i	−0.0749718	+	0.180998i
$266$	−0.0576352	−	0.449723i	−0.00353384	−	0.0275743i
$267$	3.21874	−	4.81719i	0.196984	−	0.294807i
$268$	−28.5412	+	13.8318i	−1.74343	+	0.844914i
$269$	−13.7633	−	2.73769i	−0.839162	−	0.166920i	−0.243244	−	0.969965i	$-0.578212\pi$
$269$	−13.7633	−	2.73769i	−0.839162	−	0.166920i	−0.595918	+	0.803045i	$0.703212\pi$
$270$	4.20611	−	1.41168i	0.255976	−	0.0859118i
$271$	−17.1462	+	17.1462i	−1.04156	+	1.04156i	−0.0424570	+	0.999098i	$0.513519\pi$
$271$	−17.1462	+	17.1462i	−1.04156	+	1.04156i	−0.999098	+	0.0424570i	$0.986481\pi$
$272$	−4.28609	−	7.66523i	−0.259883	−	0.464773i
$273$	−2.32943	−	2.32943i	−0.140984	−	0.140984i
$274$	−5.59276	−	2.78199i	−0.337871	−	0.168066i
$275$	1.68316	−	8.46181i	0.101498	−	0.510267i
$276$	5.18070	−	0.303806i	0.311841	−	0.0182870i
$277$	−5.37310	−	3.59019i	−0.322838	−	0.215714i	0.383581	−	0.923507i	$-0.374691\pi$
$277$	−5.37310	−	3.59019i	−0.322838	−	0.215714i	−0.706419	+	0.707794i	$0.749691\pi$
$278$	−8.75729	−	6.76766i	−0.525228	−	0.405897i
$279$	16.5468	+	6.85391i	0.990631	+	0.410333i
$280$	6.64114	−	2.67095i	0.396884	−	0.159620i
$281$	2.20599	−	0.913752i	0.131598	−	0.0545099i	−0.315912	−	0.948788i	$-0.602311\pi$
$281$	2.20599	−	0.913752i	0.131598	−	0.0545099i	0.447511	+	0.894279i	$0.352311\pi$
$282$	1.51428	−	5.57465i	0.0901741	−	0.331966i
$283$	1.14821	+	5.77245i	0.0682541	+	0.343137i	0.999790	−	0.0205138i	$-0.00653021\pi$
$283$	1.14821	+	5.77245i	0.0682541	+	0.343137i	−0.931535	+	0.363651i	$0.881530\pi$
$284$	−1.49247	−	5.72718i	−0.0885618	−	0.339846i
$285$	0.0546919	+	0.0818521i	0.00323967	+	0.00484850i
$286$	14.2366	+	16.3468i	0.841829	+	0.966604i
$287$			13.1726i			0.777551i
$288$	11.9969	+	10.8914i	0.706924	+	0.641782i
$289$		−	12.1796i		−	0.716447i
$290$	0.108489	−	0.0944842i	0.00637067	−	0.00554830i
$291$	1.07537	+	1.60941i	0.0630394	+	0.0943452i
$292$	9.91093	−	16.8969i	0.579993	−	0.988815i
$293$	−0.402515	−	2.02358i	−0.0235152	−	0.118219i	0.967245	−	0.253845i	$-0.0816953\pi$
$293$	−0.402515	−	2.02358i	−0.0235152	−	0.118219i	−0.990760	+	0.135626i	$0.956695\pi$
$294$	−1.99266	−	0.541279i	−0.116214	−	0.0315680i
$295$	−11.3841	+	4.71546i	−0.662809	+	0.274545i
$296$	23.6727	+	0.244132i	1.37595	+	0.0141899i
$297$	−5.95679	−	2.46738i	−0.345648	−	0.143172i
$298$	11.2288	−	14.5300i	0.650469	−	0.841702i
$299$	−30.0788	−	20.0980i	−1.73950	−	1.16230i
$300$	1.41445	−	1.59067i	0.0816630	−	0.0918375i
$301$	3.77701	−	18.9883i	0.217703	−	1.09447i
$302$	−6.67808	+	13.4253i	−0.384281	+	0.772538i
$303$	−1.32692	−	1.32692i	−0.0762295	−	0.0762295i
$304$	−0.334604	+	0.655626i	−0.0191908	+	0.0376027i
$305$	−4.06680	+	4.06680i	−0.232864	+	0.232864i
$306$	−2.82984	−	8.43156i	−0.161771	−	0.482000i
$307$	19.1912	+	3.81736i	1.09530	+	0.217868i	0.709493	−	0.704712i	$-0.248924\pi$
$307$	19.1912	+	3.81736i	1.09530	+	0.217868i	0.385804	+	0.922581i	$0.373924\pi$
$308$	−9.82722	−	3.41142i	−0.559958	−	0.194383i
$309$	0.219393	−	0.328344i	0.0124808	−	0.0186789i
$310$	−12.7407	+	1.63282i	−0.723626	+	0.0927377i
$311$	11.9287	−	28.7984i	0.676414	−	1.63301i	−0.0940829	−	0.995564i	$-0.529992\pi$
$311$	11.9287	−	28.7984i	0.676414	−	1.63301i	0.770497	−	0.637444i	$-0.220008\pi$
$312$	0.989226	+	5.25587i	0.0560039	+	0.297555i
$313$	3.76527	+	9.09016i	0.212825	+	0.513806i	0.993855	−	0.110688i	$-0.0353053\pi$
$313$	3.76527	+	9.09016i	0.212825	+	0.513806i	−0.781030	+	0.624494i	$0.785305\pi$
$314$	−9.54129	+	5.46502i	−0.538446	+	0.308409i
$315$	7.10980	−	1.41423i	0.400592	−	0.0796827i
$316$	3.57045	−	2.70091i	0.200854	−	0.151938i
$317$	−6.34804	+	4.24162i	−0.356541	+	0.238233i	−0.720921	−	0.693017i	$-0.756281\pi$
$317$	−6.34804	+	4.24162i	−0.356541	+	0.238233i	0.364380	+	0.931250i	$0.381281\pi$
$318$	1.14075	+	0.0787078i	0.0639701	+	0.00441372i
$319$	−0.209070			−0.0117057
$320$	−11.3484	−	2.50169i	−0.634394	−	0.139849i
$321$	−1.48748			−0.0830228
$322$	17.3189	+	1.19494i	0.965143	+	0.0665915i
$323$	0.335931	−	0.224462i	0.0186917	−	0.0124894i
$324$	9.40865	+	12.4377i	0.522703	+	0.690984i
$325$	−14.5528	+	2.89473i	−0.807245	+	0.160571i
$326$	0.965512	−	0.553022i	0.0534747	−	0.0306290i
$327$	−0.500319	−	1.20788i	−0.0276677	−	0.0667957i
$328$	12.0636	−	17.6575i	0.666100	−	0.974972i
$329$	7.39492	−	17.8529i	0.407695	−	0.984263i
$330$	2.24027	−	0.287107i	0.123323	−	0.0158047i
$331$	−3.00110	+	4.49147i	−0.164956	+	0.246873i	−0.904734	−	0.425977i	$-0.859930\pi$
$331$	−3.00110	+	4.49147i	−0.164956	+	0.246873i	0.739778	+	0.672851i	$0.234930\pi$
$332$	3.77698	−	10.8803i	0.207289	−	0.597133i
$333$	23.5142	+	4.67726i	1.28857	+	0.256312i
$334$	−8.56459	−	25.5183i	−0.468634	−	1.39630i
$335$	16.2886	−	16.2886i	0.889943	−	0.889943i
$336$	−1.66551	−	1.95268i	−0.0908613	−	0.106527i
$337$	9.39328	+	9.39328i	0.511684	+	0.511684i	0.915042	−	0.403358i	$-0.132157\pi$
$337$	9.39328	+	9.39328i	0.511684	+	0.511684i	−0.403358	+	0.915042i	$0.632157\pi$
$338$	8.41570	−	16.9185i	0.457754	−	0.920244i
$339$	0.520424	−	2.61635i	0.0282655	−	0.142100i
$340$	4.76659	+	4.23852i	0.258505	+	0.229866i
$341$	15.5209	+	10.3707i	0.840505	+	0.561607i
$342$	−0.455818	+	0.589825i	−0.0246478	+	0.0318941i
$343$	−17.6488	−	7.31037i	−0.952946	−	0.394723i
$344$	−22.4527	+	21.9943i	−1.21057	+	1.18586i
$345$	−3.48231	+	1.44242i	−0.187481	+	0.0776572i
$346$	−1.99839	−	0.542838i	−0.107434	−	0.0291831i
$347$	2.30495	+	11.5878i	0.123736	+	0.622064i	0.992029	+	0.126011i	$0.0402176\pi$
$347$	2.30495	+	11.5878i	0.123736	+	0.622064i	−0.868293	+	0.496052i	$0.834782\pi$
$348$	−0.0444926	−	0.0260973i	−0.00238506	−	0.00139896i
$349$	14.7665	+	22.0997i	0.790435	+	1.18297i	0.979587	+	0.201021i	$0.0644261\pi$
$349$	14.7665	+	22.0997i	0.790435	+	1.18297i	−0.189152	+	0.981948i	$0.560574\pi$
$350$	5.36956	−	4.67642i	0.287015	−	0.249965i
$351$			11.0887i			0.591871i
$352$	10.0489	+	13.5728i	0.535610	+	0.723433i
$353$			10.7979i			0.574714i	0.957824	+	0.287357i	$0.0927766\pi$
$353$			10.7979i			0.574714i	−0.957824	+	0.287357i	$0.907223\pi$
$354$	2.90155	+	3.33162i	0.154216	+	0.177073i
$355$	2.38817	+	3.57415i	0.126751	+	0.189696i
$356$	−30.4464	+	7.93415i	−1.61366	+	0.420509i
$357$	0.274826	+	1.38164i	0.0145453	+	0.0731242i
$358$	3.55895	−	13.1019i	0.188097	−	0.692456i
$359$	−13.1862	+	5.46192i	−0.695943	+	0.288269i	−0.702474	−	0.711710i	$-0.747921\pi$
$359$	−13.1862	+	5.46192i	−0.695943	+	0.288269i	0.00653056	+	0.999979i	$0.497921\pi$
$360$	−10.8257	−	4.61551i	−0.570564	−	0.243259i
$361$	17.5224	+	7.25803i	0.922233	+	0.382001i
$362$	−2.49753	−	1.93010i	−0.131267	−	0.101444i
$363$	0.639191	+	0.427094i	0.0335488	+	0.0224166i
$364$	1.04733	+	17.8598i	0.0548951	+	0.936106i
$365$	−2.77567	+	13.9542i	−0.145285	+	0.730397i
$366$	1.84629	+	0.918394i	0.0965072	+	0.0480052i
$367$	−17.9142	−	17.9142i	−0.935116	−	0.935116i	0.0629039	−	0.998020i	$-0.479964\pi$
$367$	−17.9142	−	17.9142i	−0.935116	−	0.935116i	−0.998020	+	0.0629039i	$0.979964\pi$
$368$	−22.1212	−	17.4626i	−1.15315	−	0.910302i
$369$	15.3136	−	15.3136i	0.797196	−	0.797196i
$370$	−16.3009	+	5.47098i	−0.847442	+	0.284423i
$371$	3.75157	+	0.746234i	0.194772	+	0.0387425i
$372$	2.00850	+	4.14442i	0.104136	+	0.214878i
$373$	16.1231	−	24.1299i	0.834820	−	1.24940i	−0.131310	−	0.991341i	$-0.541918\pi$
$373$	16.1231	−	24.1299i	0.834820	−	1.24940i	0.966130	−	0.258056i	$-0.0830818\pi$
$374$	−1.17832	−	9.19434i	−0.0609294	−	0.475428i
$375$	−1.61523	+	3.89952i	−0.0834102	+	0.201370i
$376$	−26.2626	+	17.1591i	−1.35439	+	0.884911i
$377$	0.137599	+	0.332194i	0.00708672	+	0.0171088i
$378$	−2.64479	−	4.61749i	−0.136033	−	0.237498i
$379$	−5.13105	+	1.02063i	−0.263564	+	0.0524262i	−0.325103	−	0.945678i	$-0.605399\pi$
$379$	−5.13105	+	1.02063i	−0.263564	+	0.0524262i	0.0615391	+	0.998105i	$0.480399\pi$
$380$	0.0734234	−	0.529547i	0.00376654	−	0.0271652i
$381$	−0.901502	+	0.602365i	−0.0461854	+	0.0308601i
$382$	−1.29024	+	18.7001i	−0.0660144	+	0.956779i
$383$	8.64365			0.441670			0.220835	−	0.975311i	$-0.429122\pi$
$383$	8.64365			0.441670			0.220835	+	0.975311i	$0.429122\pi$
$384$	0.444299	+	4.14282i	0.0226730	+	0.211412i
$385$	7.55537			0.385057
$386$	−0.909988	+	13.1889i	−0.0463172	+	0.671297i
$387$	−26.4656	+	17.6838i	−1.34532	+	0.898916i
$388$	1.44368	−	10.4122i	0.0732916	−	0.528597i
$389$	−3.11633	+	0.619876i	−0.158004	+	0.0314290i	−0.273458	−	0.961884i	$-0.588168\pi$
$389$	−3.11633	+	0.619876i	−0.158004	+	0.0314290i	0.115454	+	0.993313i	$0.463168\pi$
$390$	−1.93062	−	3.37063i	−0.0977606	−	0.170679i
$391$	5.91985	+	14.2918i	0.299380	+	0.722767i
$392$	6.13350	+	9.38757i	0.309788	+	0.474144i
$393$	−1.08776	+	2.62609i	−0.0548704	+	0.132469i
$394$	−2.93348	−	22.8897i	−0.147786	−	1.15317i
$395$	−1.80650	+	2.70362i	−0.0908950	+	0.136034i
$396$	7.45864	+	15.3905i	0.374811	+	0.773400i
$397$	−19.5057	−	3.87993i	−0.978963	−	0.194728i	−0.320424	−	0.947274i	$-0.603825\pi$
$397$	−19.5057	−	3.87993i	−0.978963	−	0.194728i	−0.658539	+	0.752546i	$0.728825\pi$
$398$	9.03137	−	3.03115i	0.452702	−	0.151938i
$399$	0.0834885	−	0.0834885i	0.00417965	−	0.00417965i
$400$	−11.4805	+	1.35112i	−0.574025	+	0.0675562i
$401$	12.9963	+	12.9963i	0.649006	+	0.649006i	0.952753	−	0.303747i	$-0.0982376\pi$
$401$	12.9963	+	12.9963i	0.649006	+	0.649006i	−0.303747	+	0.952753i	$0.598238\pi$
$402$	−7.39489	−	3.67841i	−0.368824	−	0.183463i
$403$	6.26311	−	31.4868i	0.311988	−	1.56847i
$404$	0.596594	+	10.1735i	0.0296816	+	0.506150i
$405$	−9.41811	−	6.29298i	−0.467989	−	0.312701i
$406$	−0.136530	−	0.105511i	−0.00677589	−	0.00523642i
$407$	23.0857	+	9.56241i	1.14432	+	0.473991i
$408$	0.896928	−	2.10375i	0.0444045	−	0.104151i
$409$	−10.3447	+	4.28490i	−0.511510	+	0.211874i	−0.623483	−	0.781837i	$-0.714283\pi$
$409$	−10.3447	+	4.28490i	−0.511510	+	0.211874i	0.111973	+	0.993711i	$0.464283\pi$
$410$	−4.07152	+	14.9888i	−0.201078	+	0.740246i
$411$	−0.317344	−	1.59539i	−0.0156534	−	0.0786950i
$412$	−2.07526	+	0.540800i	−0.102241	+	0.0266433i
$413$	8.21072	+	12.2882i	0.404023	+	0.604663i
$414$	−18.7447	−	21.5231i	−0.921253	−	1.05780i
$415$			8.36499i			0.410621i
$416$	14.9523	−	24.8997i	0.733095	−	1.22081i
$417$		−	2.88212i		−	0.141138i
$418$	−0.585880	+	0.510250i	−0.0286563	+	0.0249572i
$419$	−16.9150	−	25.3152i	−0.826354	−	1.23673i	−0.969027	−	0.246957i	$-0.920570\pi$
$419$	−16.9150	−	25.3152i	−0.826354	−	1.23673i	0.142672	−	0.989770i	$-0.454430\pi$
$420$	1.60787	+	0.943102i	0.0784560	+	0.0460187i
$421$	4.45310	+	22.3872i	0.217031	+	1.09109i	0.923575	+	0.383418i	$0.125253\pi$
$421$	4.45310	+	22.3872i	0.217031	+	1.09109i	−0.706544	+	0.707669i	$0.749747\pi$
$422$	29.0144	+	7.88137i	1.41240	+	0.383659i
$423$	−29.3516	+	12.1579i	−1.42713	+	0.591135i
$424$	−4.34548	−	4.43604i	−0.211035	−	0.215433i
$425$	5.86199	+	2.42811i	0.284348	+	0.117781i
$426$	0.942438	−	1.21951i	0.0456613	−	0.0590853i
$427$	5.73551	+	3.83235i	0.277561	+	0.185460i
$428$	6.03663	+	5.36785i	0.291792	+	0.259465i
$429$	−1.10128	+	5.53649i	−0.0531701	+	0.267304i
$430$	10.1669	−	20.4390i	0.490292	−	0.985658i
$431$	9.97751	+	9.97751i	0.480600	+	0.480600i	0.905323	−	0.424723i	$-0.139629\pi$
$431$	9.97751	+	9.97751i	0.480600	+	0.480600i	−0.424723	+	0.905323i	$0.639629\pi$
$432$	−0.683479	+	8.61176i	−0.0328839	+	0.414334i
$433$	9.49988	−	9.49988i	0.456535	−	0.456535i	−0.440981	−	0.897516i	$-0.645369\pi$
$433$	9.49988	−	9.49988i	0.456535	−	0.456535i	0.897516	+	0.440981i	$0.145369\pi$
$434$	4.90192	+	14.6054i	0.235300	+	0.701079i
$435$	0.0367440	+	0.00730885i	0.00176174	+	0.000350432i
$436$	−2.32841	+	6.70743i	−0.111511	+	0.321228i
$437$	0.720328	−	1.07805i	0.0344580	−	0.0515700i
$438$	5.05982	−	0.648451i	0.241767	−	0.0309842i
$439$	−3.51252	+	8.47998i	−0.167643	+	0.404727i	−0.985266	−	0.171027i	$-0.945291\pi$
$439$	−3.51252	+	8.47998i	−0.167643	+	0.404727i	0.817623	+	0.575754i	$0.195291\pi$
$440$	−10.1278	−	6.91930i	−0.482824	−	0.329865i
$441$	4.34582	+	10.4917i	0.206944	+	0.499606i
$442$	−13.8335	+	7.92347i	−0.657990	+	0.376881i
$443$	4.35418	−	0.866101i	0.206874	−	0.0411497i	−0.0905656	−	0.995890i	$-0.528867\pi$
$443$	4.35418	−	0.866101i	0.206874	−	0.0411497i	0.297439	+	0.954741i	$0.403867\pi$
$444$	3.71927	+	4.91667i	0.176509	+	0.233335i
$445$	19.0006	−	12.6958i	0.900715	−	0.601839i
$446$	−25.5998	−	1.76630i	−1.21218	−	0.0836365i
$447$	4.78198			0.226180
$448$	−0.287447	+	13.9349i	−0.0135806	+	0.658362i
$449$	12.3670			0.583636			0.291818	−	0.956474i	$-0.405740\pi$
$449$	12.3670			0.583636			0.291818	+	0.956474i	$0.405740\pi$
$450$	−11.6789	−	0.805802i	−0.550548	−	0.0379859i
$451$	18.7677	−	12.5402i	0.883738	−	0.590495i
$452$	−11.5536	+	8.73988i	−0.543437	+	0.411089i
$453$	−3.82970	+	0.761775i	−0.179935	+	0.0357913i
$454$	29.8833	−	17.1164i	1.40249	−	0.803314i
$455$	−4.97254	−	12.0048i	−0.233116	−	0.562793i
$456$	−0.188374	+	0.0354546i	−0.00882143	+	0.00166031i
$457$	5.19687	−	12.5463i	0.243099	−	0.586893i	−0.754488	−	0.656314i	$-0.772115\pi$
$457$	5.19687	−	12.5463i	0.243099	−	0.586893i	0.997588	+	0.0694200i	$0.0221149\pi$
$458$	23.3321	−	2.99017i	1.09024	−	0.139722i
$459$	2.63437	−	3.94261i	0.122962	−	0.184025i
$460$	19.3375	+	6.71282i	0.901616	+	0.312987i
$461$	−31.3777	−	6.24141i	−1.46140	−	0.290691i	−0.600568	−	0.799573i	$-0.705059\pi$
$461$	−31.3777	−	6.24141i	−1.46140	−	0.290691i	−0.860836	+	0.508882i	$0.830059\pi$
$462$	−0.861932	−	2.56814i	−0.0401007	−	0.119481i
$463$	20.2752	−	20.2752i	0.942266	−	0.942266i	−0.0561556	−	0.998422i	$-0.517884\pi$
$463$	20.2752	−	20.2752i	0.942266	−	0.942266i	0.998422	+	0.0561556i	$0.0178843\pi$
$464$	0.0863874	+	0.266471i	0.00401043	+	0.0123706i
$465$	−2.36525	−	2.36525i	−0.109686	−	0.109686i
$466$	−5.41353	+	10.8831i	−0.250777	+	0.504149i
$467$	1.24791	−	6.27365i	0.0577463	−	0.290310i	−0.941111	−	0.338097i	$-0.890217\pi$
$467$	1.24791	−	6.27365i	0.0577463	−	0.290310i	0.998858	+	0.0477869i	$0.0152168\pi$
$468$	19.5451	−	21.9803i	0.903475	−	1.01604i
$469$	−22.9723	−	15.3496i	−1.06076	−	0.708777i
$470$	13.9327	−	18.0288i	0.642669	−	0.831608i
$471$	−2.64541	−	1.09576i	−0.121894	−	0.0504901i
$472$	0.247420	−	23.9915i	0.0113884	−	1.10430i
$473$	−30.6495	+	12.6954i	−1.40926	+	0.583737i
$474$	1.12508	+	0.305612i	0.0516764	+	0.0140372i
$475$	−0.103749	−	0.521583i	−0.00476035	−	0.0239319i
$476$	3.87060	−	6.59888i	0.177409	−	0.302459i
$477$	−3.49383	−	5.22888i	−0.159971	−	0.239414i
$478$	−16.5286	+	14.3950i	−0.755999	+	0.658410i
$479$			38.2671i			1.74847i	0.485503	+	0.874235i	$0.338636\pi$
$479$			38.2671i			1.74847i	−0.485503	+	0.874235i	$0.661364\pi$
$480$	−1.29161	−	2.73671i	−0.0589536	−	0.124913i
$481$		−	42.9745i		−	1.95947i
$482$	27.4718	+	31.5436i	1.25131	+	1.43677i
$483$	2.51159	+	3.75886i	0.114281	+	0.171034i
$484$	−1.05278	−	4.03992i	−0.0478536	−	0.183633i
$485$	1.48946	+	7.48803i	0.0676330	+	0.340014i
$486$	−3.46654	+	12.7617i	−0.157245	+	0.578881i
$487$	−0.702848	+	0.291129i	−0.0318491	+	0.0131923i	−0.398551	−	0.917146i	$-0.630487\pi$
$487$	−0.702848	+	0.291129i	−0.0318491	+	0.0131923i	0.366702	+	0.930338i	$0.380487\pi$
$488$	−4.17861	−	10.3898i	−0.189157	−	0.470325i
$489$	0.267696	+	0.110884i	0.0121057	+	0.00501433i
$490$	−6.44440	−	4.98025i	−0.291128	−	0.224985i
$491$	−16.0938	−	10.7535i	−0.726303	−	0.485300i	0.136628	−	0.990622i	$-0.456374\pi$
$491$	−16.0938	−	10.7535i	−0.726303	−	0.485300i	−0.862931	+	0.505322i	$0.831374\pi$
$492$	5.55933	−	0.326010i	0.250634	−	0.0146977i
$493$	0.0299963	−	0.150802i	0.00135097	−	0.00679177i
$494$	1.19634	+	0.595089i	0.0538257	+	0.0267743i
$495$	−8.78343	−	8.78343i	−0.394786	−	0.394786i
$496$	6.80486	−	24.0674i	0.305547	−	1.08066i
$497$	3.64560	−	3.64560i	0.163528	−	0.163528i
$498$	2.84334	−	0.954295i	0.127413	−	0.0427630i
$499$	−27.5562	−	5.48127i	−1.23359	−	0.245376i	−0.465109	−	0.885253i	$-0.653985\pi$
$499$	−27.5562	−	5.48127i	−1.23359	−	0.245376i	−0.768477	+	0.639878i	$0.778985\pi$
$500$	20.6273	−	9.99654i	0.922480	−	0.447059i
$501$	3.89429	−	5.82822i	0.173984	−	0.260386i
$502$	−1.02105	−	7.96715i	−0.0455715	−	0.355591i
$503$	0.279297	−	0.674282i	0.0124532	−	0.0300647i	−0.917531	−	0.397665i	$-0.869821\pi$
$503$	0.279297	−	0.674282i	0.0124532	−	0.0300647i	0.929984	+	0.367600i	$0.119821\pi$
$504$	−2.89631	+	13.8146i	−0.129012	+	0.615353i
$505$	−2.83252	−	6.83831i	−0.126046	−	0.304301i
$506$	−14.7850	−	25.8128i	−0.657272	−	1.14752i
$507$	4.82617	−	0.959986i	0.214338	−	0.0426345i
$508$	5.83232	+	0.808670i	0.258767	+	0.0358789i
$509$	−14.6162	+	9.76623i	−0.647851	+	0.432880i	−0.835601	−	0.549336i	$-0.814881\pi$
$509$	−14.6162	+	9.76623i	−0.647851	+	0.432880i	0.187750	+	0.982217i	$0.439881\pi$
$510$	−0.114334	+	1.65709i	−0.00506278	+	0.0733774i
$511$	17.0643			0.754882
$512$	13.1471	−	18.4162i	0.581024	−	0.813887i
$513$	−0.397427			−0.0175468
$514$	−1.78268	+	25.8373i	−0.0786307	+	1.13963i
$515$	1.29510	−	0.865359i	0.0570690	−	0.0381323i
$516$	−8.10728	−	1.12410i	−0.356903	−	0.0494857i
$517$	−32.4761	+	6.45989i	−1.42830	+	0.284106i
$518$	10.2499	+	17.8952i	0.450356	+	0.786269i
$519$	−0.206366	−	0.498212i	−0.00905848	−	0.0218691i
$520$	−4.32855	+	20.6461i	−0.189820	+	0.905389i
$521$	0.465084	−	1.12281i	0.0203757	−	0.0491913i	−0.913364	−	0.407143i	$-0.866525\pi$
$521$	0.465084	−	1.12281i	0.0203757	−	0.0491913i	0.933740	+	0.357952i	$0.116525\pi$
$522$	0.0360612	+	0.281383i	0.00157836	+	0.0123158i
$523$	−16.7116	+	25.0106i	−0.730746	+	1.09364i	0.260990	+	0.965341i	$0.415951\pi$
$523$	−16.7116	+	25.0106i	−0.730746	+	1.09364i	−0.991736	+	0.128297i	$0.959049\pi$
$524$	13.8912	−	6.73207i	0.606842	−	0.294092i
$525$	1.81862	+	0.361746i	0.0793710	+	0.0157879i
$526$	−20.3662	+	6.83540i	−0.888008	+	0.298038i
$527$	−9.70724	+	9.70724i	−0.422854	+	0.422854i
$528$	−1.19653	+	4.23190i	−0.0520725	+	0.184170i
$529$	18.8396	+	18.8396i	0.819111	+	0.819111i
$530$	4.03820	+	2.00871i	0.175408	+	0.0872526i
$531$	4.74025	−	23.8308i	0.205709	−	1.03417i
$532$	−0.640106	+	0.0375371i	−0.0277521	+	0.00162744i
$533$	−32.2772	−	21.5669i	−1.39808	−	0.934167i
$534$	−6.48305	−	5.01012i	−0.280549	−	0.216809i
$535$	−5.42050	−	2.24524i	−0.234349	−	0.0970704i
$536$	16.7364	+	41.6140i	0.722904	+	1.79745i
$537$	3.26638	−	1.35298i	0.140955	−	0.0583854i
$538$	−5.20227	+	19.1516i	−0.224286	+	0.825682i
$539$	2.30908	+	11.6086i	0.0994593	+	0.500016i
$540$	−1.58223	−	6.07165i	−0.0680885	−	0.261282i
$541$	12.6138	+	18.8780i	0.542312	+	0.811627i	0.996867	−	0.0790916i	$-0.0252019\pi$
$541$	12.6138	+	18.8780i	0.542312	+	0.811627i	−0.454556	+	0.890718i	$0.650202\pi$
$542$	22.5217	+	25.8599i	0.967392	+	1.11078i
$543$		−	0.821964i		−	0.0352739i
$544$	−11.2318	+	5.30091i	−0.481559	+	0.227275i
$545$		−	5.15681i		−	0.220893i
$546$	−3.51326	+	3.05974i	−0.150354	+	0.130945i
$547$	−17.7222	−	26.5232i	−0.757748	−	1.13405i	−0.987006	−	0.160684i	$-0.948630\pi$
$547$	−17.7222	−	26.5232i	−0.757748	−	1.13405i	0.229258	−	0.973366i	$-0.426370\pi$
$548$	−4.46942	+	7.61979i	−0.190924	+	0.325501i
$549$	−2.21251	−	11.1230i	−0.0944276	−	0.474720i
$550$	−11.7746	−	3.19841i	−0.502070	−	0.136381i
$551$	−0.0119061	+	0.00493165i	−0.000507215	+	0.000210095i
$552$	0.0756838	−	7.33881i	0.00322132	−	0.312360i
$553$	3.60307	+	1.49244i	0.153218	+	0.0634651i
$554$	−5.58830	+	7.23121i	−0.237424	+	0.307224i
$555$	−3.72301	−	2.48764i	−0.158033	−	0.105594i
$556$	−10.4007	+	11.6965i	−0.441088	+	0.496043i
$557$	−5.25641	+	26.4258i	−0.222721	+	1.11970i	0.693940	+	0.720032i	$0.255873\pi$
$557$	−5.25641	+	26.4258i	−0.222721	+	1.11970i	−0.916662	+	0.399664i	$0.869127\pi$
$558$	11.2806	−	22.6780i	0.477548	−	0.960037i
$559$	40.3437	+	40.3437i	1.70636	+	1.70636i
$560$	−3.12186	−	9.62971i	−0.131923	−	0.406930i
$561$	1.70688	−	1.70688i	0.0720644	−	0.0720644i
$562$	−1.07443	−	3.20129i	−0.0453223	−	0.135038i
$563$	37.9592	+	7.55055i	1.59979	+	0.318218i	0.912786	−	0.408437i	$-0.133926\pi$
$563$	37.9592	+	7.55055i	1.59979	+	0.318218i	0.687002	+	0.726655i	$0.258926\pi$
$564$	−7.71764	−	2.67910i	−0.324971	−	0.112810i
$565$	5.84567	−	8.74866i	0.245929	−	0.368059i
$566$	8.25589	−	1.05805i	0.347021	−	0.0444732i
$567$	−5.19894	+	12.5514i	−0.218335	+	0.527107i
$568$	−8.22553	+	1.54816i	−0.345136	+	0.0649592i
$569$	−2.03813	−	4.92049i	−0.0854431	−	0.206278i	0.875383	−	0.483430i	$-0.160609\pi$
$569$	−2.03813	−	4.92049i	−0.0854431	−	0.206278i	−0.960826	+	0.277152i	$0.910609\pi$
$570$	0.120806	−	0.0691947i	0.00506000	−	0.00289825i
$571$	14.3880	−	2.86195i	0.602118	−	0.119769i	0.115387	−	0.993321i	$-0.463189\pi$
$571$	14.3880	−	2.86195i	0.602118	−	0.119769i	0.486731	+	0.873552i	$0.338189\pi$
$572$	24.4488	−	18.4946i	1.02226	−	0.773298i
$573$	−4.05864	+	2.71189i	−0.169552	+	0.113291i
$574$	18.5846	+	1.28227i	0.775707	+	0.0535211i
$575$	20.3619			0.849149
$576$	16.5341	−	15.8657i	0.688919	−	0.661072i
$577$	−10.2313			−0.425936			−0.212968	−	0.977059i	$-0.568313\pi$
$577$	−10.2313			−0.425936			−0.212968	+	0.977059i	$0.568313\pi$
$578$	−17.1837	−	1.18562i	−0.714748	−	0.0493151i
$579$	−2.86250	+	1.91266i	−0.118961	+	0.0794874i
$580$	−0.122743	−	0.162260i	−0.00509663	−	0.00673747i
$581$	9.84005	−	1.95731i	0.408234	−	0.0812028i
$582$	2.37533	−	1.36053i	0.0984606	−	0.0563959i
$583$	−2.50827	−	6.05550i	−0.103882	−	0.250793i
$584$	−22.8743	−	15.6277i	−0.946547	−	0.646680i
$585$	−8.17527	+	19.7369i	−0.338006	+	0.816018i
$586$	−2.89417	+	0.370908i	−0.119557	+	0.0153221i
$587$	15.0588	−	22.5371i	0.621543	−	0.930206i	−0.378446	−	0.925623i	$-0.623541\pi$
$587$	15.0588	−	22.5371i	0.621543	−	0.930206i	0.999990	−	0.00458217i	$-0.00145855\pi$
$588$	−0.957642	+	2.75867i	−0.0394925	+	0.113766i
$589$	1.12851	+	0.224474i	0.0464994	+	0.00924930i
$590$	5.54467	+	16.5204i	0.228270	+	0.680135i
$591$	4.24934	−	4.24934i	0.174795	−	0.174795i
$592$	2.64884	−	33.3751i	0.108867	−	1.37171i
$593$	9.24907	+	9.24907i	0.379814	+	0.379814i	0.871035	−	0.491221i	$-0.163449\pi$
$593$	9.24907	+	9.24907i	0.379814	+	0.379814i	−0.491221	+	0.871035i	$0.663449\pi$
$594$	−4.06099	+	8.16401i	−0.166625	+	0.334973i
$595$	−1.08400	+	5.44966i	−0.0444399	+	0.223414i
$596$	−19.4068	−	17.2567i	−0.794932	−	0.706863i
$597$	2.06270	+	1.37826i	0.0844209	+	0.0564082i
$598$	−31.2835	+	40.4806i	−1.27928	+	1.65537i
$599$	5.52517	+	2.28860i	0.225752	+	0.0935097i	0.492693	−	0.870203i	$-0.336013\pi$
$599$	5.52517	+	2.28860i	0.225752	+	0.0935097i	−0.266940	+	0.963713i	$0.586013\pi$
$600$	−2.10653	−	2.15043i	−0.0859985	−	0.0877908i
$601$	−16.7410	+	6.93436i	−0.682880	+	0.282858i	−0.697030	−	0.717042i	$-0.745496\pi$
$601$	−16.7410	+	6.93436i	−0.682880	+	0.282858i	0.0141501	+	0.999900i	$0.495496\pi$
$602$	−26.4221	−	7.17723i	−1.07689	−	0.292522i
$603$	8.86169	+	44.5507i	0.360876	+	1.81425i
$604$	18.2911	+	10.7287i	0.744254	+	0.436545i
$605$	1.68460	+	2.52119i	0.0684888	+	0.102501i
$606$	−2.00126	+	1.74293i	−0.0812958	+	0.0708016i
$607$		−	7.72029i		−	0.313357i	−0.987650	−	0.156679i	$-0.949921\pi$
$607$		−	7.72029i		−	0.313357i	0.987650	−	0.156679i	$-0.0500787\pi$
$608$	0.892425	+	0.535900i	0.0361926	+	0.0217336i
$609$		−	0.0449336i		−	0.00182080i
$610$	5.34180	+	6.13356i	0.216283	+	0.248341i
$611$	31.6382	+	47.3499i	1.27994	+	1.91557i
$612$	−12.1712	+	3.17175i	−0.491992	+	0.128210i
$613$	−5.99511	−	30.1394i	−0.242140	−	1.21732i	−0.890143	−	0.455682i	$-0.849395\pi$
$613$	−5.99511	−	30.1394i	−0.242140	−	1.21732i	0.648003	−	0.761638i	$-0.275605\pi$
$614$	7.25391	−	26.7044i	0.292744	−	1.07770i
$615$	−3.73681	+	1.54784i	−0.150683	+	0.0624149i
$616$	−5.76965	+	13.5327i	−0.232466	+	0.545250i
$617$	−17.6517	−	7.31159i	−0.710632	−	0.294353i	−0.00206586	−	0.999998i	$-0.500658\pi$
$617$	−17.6517	−	7.31159i	−0.710632	−	0.294353i	−0.708566	+	0.705644i	$0.750658\pi$
$618$	−0.441891	−	0.341495i	−0.0177755	−	0.0137369i
$619$	−9.76932	−	6.52765i	−0.392662	−	0.262368i	0.343529	−	0.939142i	$-0.388378\pi$
$619$	−9.76932	−	6.52765i	−0.392662	−	0.262368i	−0.736191	+	0.676774i	$0.763378\pi$
$620$	1.06343	+	18.1343i	0.0427085	+	0.728293i
$621$	2.96866	−	14.9245i	0.119128	−	0.598899i
$622$	−39.4693	−	19.6331i	−1.58258	−	0.787214i
$623$	−19.3805	−	19.3805i	−0.776462	−	0.776462i
$624$	7.51159	−	0.884029i	0.300704	−	0.0353895i
$625$	−1.55466	+	1.55466i	−0.0621862	+	0.0621862i
$626$	13.1915	−	4.42739i	0.527237	−	0.176954i
$627$	−0.198432	−	0.0394705i	−0.00792460	−	0.00157630i
$628$	6.78159	+	13.9934i	0.270615	+	0.558398i
$629$	−10.2095	+	15.2797i	−0.407081	+	0.609240i
$630$	−1.30318	−	10.1686i	−0.0519198	−	0.405127i
$631$	4.61559	−	11.1430i	0.183744	−	0.443596i	−0.804989	−	0.593290i	$-0.797829\pi$
$631$	4.61559	−	11.1430i	0.183744	−	0.443596i	0.988732	+	0.149694i	$0.0478287\pi$
$632$	−3.46304	−	5.30032i	−0.137752	−	0.210836i
$633$	2.99620	+	7.23347i	0.119088	+	0.287504i
$634$	5.36639	+	9.36909i	0.213127	+	0.372094i
$635$	−4.19439	+	0.834315i	−0.166449	+	0.0331088i
$636$	0.222091	−	1.60178i	0.00880650	−	0.0635146i
$637$	16.9252	−	11.3091i	0.670601	−	0.448081i
$638$	−0.0203518	+	0.294969i	−0.000805737	+	0.0116779i
$639$	−8.47633			−0.335318
$640$	−4.63424	+	15.7674i	−0.183184	+	0.623263i
$641$	6.70997			0.265028			0.132514	−	0.991181i	$-0.457695\pi$
$641$	6.70997			0.265028			0.132514	+	0.991181i	$0.457695\pi$
$642$	−0.144797	+	2.09862i	−0.00571470	+	0.0828259i
$643$	0.990370	−	0.661744i	0.0390564	−	0.0260966i	−0.535889	−	0.844289i	$-0.680023\pi$
$643$	0.990370	−	0.661744i	0.0390564	−	0.0260966i	0.574945	+	0.818192i	$0.305023\pi$
$644$	3.37179	−	24.3182i	0.132867	−	0.958270i
$645$	5.83045	−	1.15975i	0.229574	−	0.0456651i
$646$	−0.283983	−	0.495801i	−0.0111732	−	0.0195070i
$647$	−3.48816	−	8.42116i	−0.137134	−	0.331070i	0.840362	−	0.542026i	$-0.182342\pi$
$647$	−3.48816	−	8.42116i	−0.137134	−	0.331070i	−0.977496	+	0.210956i	$0.932342\pi$
$648$	18.4637	−	12.0635i	0.725324	−	0.473901i
$649$	9.69120	−	23.3966i	0.380413	−	0.918398i
$650$	2.66743	+	20.8138i	0.104625	+	0.816383i
$651$	−2.22889	+	3.33577i	−0.0873570	+	0.130739i
$652$	−0.686249	−	1.41603i	−0.0268756	−	0.0554562i
$653$	32.8825	+	6.54074i	1.28679	+	0.255959i	0.790643	−	0.612278i	$-0.209747\pi$
$653$	32.8825	+	6.54074i	1.28679	+	0.255959i	0.496150	+	0.868237i	$0.334747\pi$
$654$	−1.75285	+	0.588299i	−0.0685417	+	0.0230043i
$655$	−7.92782	+	7.92782i	−0.309765	+	0.309765i
$656$	−23.7379	−	18.7389i	−0.926810	−	0.731631i
$657$	−19.8380	−	19.8380i	−0.773954	−	0.773954i
$658$	−24.4681	−	12.1711i	−0.953865	−	0.474478i
$659$	5.99601	−	30.1440i	0.233571	−	1.17424i	−0.668853	−	0.743395i	$-0.733214\pi$
$659$	5.99601	−	30.1440i	0.233571	−	1.17424i	0.902424	−	0.430848i	$-0.141786\pi$
$660$	−0.186989	−	3.18866i	−0.00727855	−	0.124118i
$661$	37.6753	+	25.1739i	1.46540	+	0.979149i	0.995331	+	0.0965199i	$0.0307712\pi$
$661$	37.6753	+	25.1739i	1.46540	+	0.979149i	0.470069	+	0.882629i	$0.344229\pi$
$662$	6.04469	+	4.67135i	0.234934	+	0.181557i
$663$	−3.83545	−	1.58869i	−0.148956	−	0.0616997i
$664$	−14.9829	−	6.38792i	−0.581449	−	0.247899i
$665$	0.430260	−	0.178220i	0.0166848	−	0.00691106i
$666$	8.88792	−	32.7199i	0.344400	−	1.26787i
$667$	−0.0962624	−	0.483944i	−0.00372729	−	0.0187384i
$668$	−36.8365	+	9.59937i	−1.42525	+	0.371411i
$669$	−3.71249	−	5.55614i	−0.143533	−	0.214813i
$670$	−21.3954	−	24.5666i	−0.826575	−	0.949089i
$671$		−	11.8201i		−	0.456310i
$672$	−2.91708	+	2.15973i	−0.112529	+	0.0833132i
$673$		−	32.2882i		−	1.24462i	−0.782771	−	0.622310i	$-0.786194\pi$
$673$		−	32.2882i		−	1.24462i	0.782771	−	0.622310i	$-0.213806\pi$
$674$	14.1670	−	12.3382i	0.545692	−	0.475250i
$675$	−3.46755	−	5.18955i	−0.133466	−	0.199746i
$676$	−23.0504	−	13.5203i	−0.886553	−	0.520011i
$677$	1.07518	+	5.40530i	0.0413225	+	0.207742i	0.995931	−	0.0901220i	$-0.0287257\pi$
$677$	1.07518	+	5.40530i	0.0413225	+	0.207742i	−0.954608	+	0.297864i	$0.903726\pi$
$678$	−3.64064	−	0.988931i	−0.139818	−	0.0379797i
$679$	8.45994	−	3.50422i	0.324663	−	0.134480i
$680$	6.44395	−	6.31240i	0.247114	−	0.242069i
$681$	8.28540	+	3.43193i	0.317497	+	0.131512i
$682$	16.1425	−	20.8883i	0.618130	−	0.799854i
$683$	16.8416	+	11.2532i	0.644427	+	0.430592i	0.834371	−	0.551203i	$-0.185831\pi$
$683$	16.8416	+	11.2532i	0.644427	+	0.430592i	−0.189945	+	0.981795i	$0.560831\pi$
$684$	0.787789	+	0.700512i	0.0301219	+	0.0267847i
$685$	1.25171	−	6.29277i	0.0478254	−	0.240435i
$686$	−12.0319	+	24.1884i	−0.459381	+	0.923516i
$687$	4.33147	+	4.33147i	0.165256	+	0.165256i
$688$	28.8453	+	33.8187i	1.09972	+	1.28932i
$689$	−7.97082	+	7.97082i	−0.303664	+	0.303664i
$690$	1.69607	+	5.05346i	0.0645682	+	0.192382i
$691$	−17.9592	−	3.57231i	−0.683201	−	0.135897i	−0.158726	−	0.987323i	$-0.550739\pi$
$691$	−17.9592	−	3.57231i	−0.683201	−	0.135897i	−0.524476	+	0.851425i	$0.675739\pi$
$692$	−0.960400	+	2.76661i	−0.0365089	+	0.105171i
$693$	−8.27706	+	12.3875i	−0.314419	+	0.470562i
$694$	16.5731	−	2.12396i	0.629106	−	0.0806243i
$695$	4.35036	−	10.5027i	0.165019	−	0.398390i
$696$	−0.0411507	+	0.0602324i	−0.00155981	+	0.00228310i
$697$	6.35251	+	15.3363i	0.240618	+	0.580904i
$698$	32.6170	−	18.6822i	1.23457	−	0.707133i
$699$	−3.10451	+	0.617526i	−0.117423	+	0.0233570i
$700$	−6.07508	−	8.03092i	−0.229616	−	0.303540i
$701$	11.9298	−	7.97124i	0.450583	−	0.301070i	−0.309496	−	0.950901i	$-0.600160\pi$
$701$	11.9298	−	7.97124i	0.450583	−	0.301070i	0.760079	+	0.649831i	$0.225160\pi$
$702$	15.6446	+	1.07942i	0.590467	+	0.0407402i
$703$	1.54024			0.0580911
$704$	20.1275	−	12.8564i	0.758585	−	0.484544i
$705$	5.93348			0.223468
$706$	15.2343	+	1.05111i	0.573351	+	0.0395592i
$707$	−7.38139	+	4.93208i	−0.277606	+	0.185490i
$708$	4.98289	−	3.76937i	0.187269	−	0.141661i
$709$	8.17031	−	1.62518i	0.306843	−	0.0610348i	−0.0392674	−	0.999229i	$-0.512502\pi$
$709$	8.17031	−	1.62518i	0.306843	−	0.0610348i	0.346110	+	0.938194i	$0.387502\pi$
$710$	5.27510	−	3.02145i	0.197971	−	0.113393i
$711$	−2.45370	−	5.92375i	−0.0920208	−	0.222158i
$712$	8.23018	+	43.7279i	0.308439	+	1.63877i
$713$	−16.8593	+	40.7019i	−0.631385	+	1.52430i
$714$	1.97605	−	0.253245i	0.0739520	−	0.00947746i
$715$	−12.3701	+	18.5132i	−0.462616	+	0.692354i
$716$	−18.1385	−	6.29658i	−0.677866	−	0.235314i
$717$	−5.59807	−	1.11353i	−0.209064	−	0.0415854i
$718$	6.42240	+	19.1356i	0.239682	+	0.714135i
$719$	14.9481	−	14.9481i	0.557471	−	0.557471i	−0.371116	−	0.928587i	$-0.621025\pi$
$719$	14.9481	−	14.9481i	0.557471	−	0.557471i	0.928587	+	0.371116i	$0.121025\pi$
$720$	−7.56565	+	14.8242i	−0.281955	+	0.552467i
$721$	−1.32099	−	1.32099i	−0.0491963	−	0.0491963i
$722$	11.9458	−	24.0152i	0.444575	−	0.893751i
$723$	−2.12509	+	10.6835i	−0.0790328	+	0.397325i
$724$	−2.96622	+	3.33578i	−0.110239	+	0.123973i
$725$	−0.168277	−	0.112439i	−0.00624966	−	0.00417589i
$726$	0.664791	−	0.860233i	0.0246727	−	0.0319263i
$727$	−12.1904	−	5.04943i	−0.452117	−	0.187273i	0.144992	−	0.989433i	$-0.453684\pi$
$727$	−12.1904	−	5.04943i	−0.452117	−	0.187273i	−0.597110	+	0.802160i	$0.703684\pi$
$728$	25.2996	+	0.260910i	0.937664	+	0.00966996i
$729$	18.4310	−	7.63436i	0.682629	−	0.282754i
$730$	19.4172	+	5.27444i	0.718664	+	0.195216i
$731$	−4.75974	−	23.9288i	−0.176045	−	0.885040i
$732$	1.47545	−	2.51546i	0.0545342	−	0.0929740i
$733$	8.53401	+	12.7721i	0.315211	+	0.471746i	0.954917	−	0.296873i	$-0.0959439\pi$
$733$	8.53401	+	12.7721i	0.315211	+	0.471746i	−0.639706	+	0.768620i	$0.720944\pi$
$734$	−27.0183	+	23.5306i	−0.997264	+	0.868531i
$735$		−	2.12092i		−	0.0782313i
$736$	−26.7907	+	29.5100i	−0.987518	+	1.08775i
$737$			47.3427i			1.74389i
$738$	−20.1147	−	23.0961i	−0.740432	−	0.850179i
$739$	8.82990	+	13.2149i	0.324813	+	0.486117i	0.957557	−	0.288244i	$-0.0930714\pi$
$739$	8.82990	+	13.2149i	0.324813	+	0.486117i	−0.632744	+	0.774361i	$0.718071\pi$
$740$	6.13199	+	23.5308i	0.225416	+	0.865010i
$741$	0.0678823	+	0.341267i	0.00249372	+	0.0125368i
$742$	1.41802	−	5.22030i	0.0520573	−	0.191643i
$743$	−19.6016	+	8.11923i	−0.719112	+	0.297866i	−0.712069	−	0.702109i	$-0.752242\pi$
$743$	−19.6016	+	8.11923i	−0.719112	+	0.297866i	−0.00704260	+	0.999975i	$0.502242\pi$
$744$	6.04271	−	2.43027i	0.221537	−	0.0890982i
$745$	17.4260	+	7.21808i	0.638439	+	0.264450i
$746$	−32.4744	−	25.0963i	−1.18897	−	0.918840i
$747$	−13.7149	−	9.16402i	−0.501803	−	0.335294i
$748$	−13.0866	+	0.767425i	−0.478494	+	0.0280599i
$749$	−1.37283	+	6.90170i	−0.0501622	+	0.252183i
$750$	5.34443	+	2.65846i	0.195151	+	0.0970733i
$751$	−35.0649	−	35.0649i	−1.27954	−	1.27954i	−0.940928	−	0.338608i	$-0.890044\pi$
$751$	−35.0649	−	35.0649i	−1.27954	−	1.27954i	−0.338608	−	0.940928i	$-0.609956\pi$
$752$	21.6525	+	38.7232i	0.789585	+	1.41209i
$753$	1.47906	−	1.47906i	0.0538998	−	0.0538998i
$754$	0.482073	−	0.161796i	0.0175561	−	0.00589226i
$755$	−15.1056	−	3.00470i	−0.549750	−	0.109352i
$756$	−6.77208	+	3.28193i	−0.246298	+	0.119363i
$757$	4.47197	−	6.69277i	0.162536	−	0.243253i	−0.741258	−	0.671221i	$-0.765770\pi$
$757$	4.47197	−	6.69277i	0.162536	−	0.243253i	0.903794	+	0.427968i	$0.140770\pi$
$758$	0.940485	+	7.33854i	0.0341600	+	0.266548i
$759$	2.96446	−	7.15683i	0.107603	−	0.259776i
$760$	−0.739969	−	0.155138i	−0.0268415	−	0.00562746i
$761$	−14.8692	−	35.8975i	−0.539009	−	1.30128i	−0.925415	−	0.378955i	$-0.876284\pi$
$761$	−14.8692	−	35.8975i	−0.539009	−	1.30128i	0.386406	−	0.922329i	$-0.373716\pi$
$762$	0.762096	+	1.33053i	0.0276078	+	0.0482000i
$763$	−6.06615	+	1.20663i	−0.219609	+	0.0436830i
$764$	26.2576	+	3.64070i	0.949966	+	0.131716i
$765$	7.59566	−	5.07526i	0.274622	−	0.183496i
$766$	0.841411	−	12.1950i	0.0304014	−	0.440623i
$767$	−43.5533			−1.57262
$768$	5.88818	−	0.223564i	0.212471	−	0.00806716i
$769$	−8.75459			−0.315699			−0.157849	−	0.987463i	$-0.550456\pi$
$769$	−8.75459			−0.315699			−0.157849	+	0.987463i	$0.550456\pi$
$770$	0.735473	−	10.6596i	0.0265046	−	0.384144i
$771$	−5.60768	+	3.74693i	−0.201956	+	0.134942i
$772$	18.5191	+	2.56773i	0.666517	+	0.0924146i
$773$	22.8691	−	4.54895i	0.822544	−	0.163614i	0.234162	−	0.972197i	$-0.424765\pi$
$773$	22.8691	−	4.54895i	0.822544	−	0.163614i	0.588382	+	0.808583i	$0.299765\pi$
$774$	22.3730	+	39.0607i	0.804182	+	1.40401i
$775$	6.91507	+	16.6945i	0.248397	+	0.599683i
$776$	−14.5496	−	3.05039i	−0.522299	−	0.109503i
$777$	−2.05516	+	4.96159i	−0.0737284	+	0.177996i
$778$	0.571201	+	4.45704i	0.0204786	+	0.159793i
$779$	0.772974	−	1.15684i	0.0276947	−	0.0414480i
$780$	−4.94342	+	2.39572i	−0.177003	+	0.0857804i
$781$	−8.66470	−	1.72352i	−0.310048	−	0.0616723i
$782$	20.7400	−	6.96085i	0.741660	−	0.248920i
$783$	−0.106948	+	0.106948i	−0.00382200	+	0.00382200i
$784$	13.8416	−	7.73967i	0.494343	−	0.276417i
$785$	−7.98613	−	7.98613i	−0.285037	−	0.285037i
$786$	3.59916	+	1.79032i	0.128378	+	0.0638584i
$787$	−7.15249	+	35.9580i	−0.254959	+	1.28176i	0.614956	+	0.788561i	$0.289174\pi$
$787$	−7.15249	+	35.9580i	−0.254959	+	1.28176i	−0.869915	+	0.493202i	$0.835826\pi$
$788$	−32.5797	+	1.91054i	−1.16060	+	0.0680601i
$789$	−4.65150	−	3.10803i	−0.165598	−	0.110649i
$790$	3.63858	+	2.81190i	0.129455	+	0.100043i
$791$	−11.6592	−	4.82940i	−0.414553	−	0.171714i
$792$	22.4398	−	9.02491i	0.797365	−	0.320686i
$793$	−18.7811	+	7.77937i	−0.666935	+	0.276254i
$794$	−7.37280	+	27.1421i	−0.261651	+	0.963238i
$795$	0.229135	+	1.15194i	0.00812657	+	0.0408550i
$796$	−3.39738	−	13.0371i	−0.120417	−	0.462086i
$797$	−22.6473	−	33.8941i	−0.802209	−	1.20059i	−0.976419	−	0.215882i	$-0.930737\pi$
$797$	−22.6473	−	33.8941i	−0.802209	−	1.20059i	0.174210	−	0.984708i	$-0.444263\pi$
$798$	−0.109663	−	0.125918i	−0.00388204	−	0.00445744i
$799$		−	24.3517i		−	0.861501i
$800$	0.788685	+	16.3289i	0.0278842	+	0.577314i
$801$			45.0612i			1.59216i
$802$	19.6011	−	17.0709i	0.692140	−	0.602794i
$803$	−16.2452	−	24.3126i	−0.573279	−	0.857973i
$804$	−5.90957	+	10.0751i	−0.208415	+	0.355321i
$805$	3.47872	+	17.4887i	0.122609	+	0.616396i
$806$	−43.8137	−	11.9014i	−1.54327	−	0.419210i
$807$	−4.77460	+	1.97771i	−0.168074	+	0.0696185i
$808$	14.4114	+	0.148623i	0.506993	+	0.00522852i
$809$	−20.5884	−	8.52801i	−0.723851	−	0.299829i	−0.00982829	−	0.999952i	$-0.503128\pi$
$809$	−20.5884	−	8.52801i	−0.723851	−	0.299829i	−0.714022	+	0.700123i	$0.753128\pi$
$810$	−9.79530	+	12.6750i	−0.344172	+	0.445355i
$811$	28.5660	+	19.0872i	1.00309	+	0.670241i	0.944660	−	0.328050i	$-0.106392\pi$
$811$	28.5660	+	19.0872i	1.00309	+	0.670241i	0.0584267	+	0.998292i	$0.481392\pi$
$812$	−0.162152	+	0.182354i	−0.00569041	+	0.00639938i
$813$	−1.74217	+	8.75850i	−0.0611007	+	0.307174i
$814$	15.7385	−	31.6398i	0.551633	−	1.10898i
$815$	0.808140	+	0.808140i	0.0283079	+	0.0283079i
$816$	−2.88078	−	1.47023i	−0.100847	−	0.0514682i
$817$	−1.44595	+	1.44595i	−0.0505873	+	0.0505873i
$818$	5.03839	+	15.0120i	0.176163	+	0.524881i
$819$	25.1301	+	4.99869i	0.878117	+	0.174668i
$820$	20.7508	+	7.20342i	0.724650	+	0.251554i
$821$	18.1775	−	27.2045i	0.634398	−	0.949444i	−0.365429	−	0.930839i	$-0.619078\pi$
$821$	18.1775	−	27.2045i	0.634398	−	0.949444i	0.999827	−	0.0186046i	$-0.00592238\pi$
$822$	−2.28177	+	0.292425i	−0.0795858	+	0.0101995i
$823$	−13.8958	+	33.5474i	−0.484377	+	1.16939i	0.473134	+	0.880991i	$0.343123\pi$
$823$	−13.8958	+	33.5474i	−0.484377	+	1.16939i	−0.957511	+	0.288398i	$0.906877\pi$
$824$	0.560978	+	2.98054i	0.0195426	+	0.103832i
$825$	−1.21591	−	2.93548i	−0.0423327	−	0.102200i
$826$	18.1362	−	10.3880i	0.631039	−	0.361444i
$827$	−31.3707	+	6.24001i	−1.09087	+	0.216987i	−0.707573	−	0.706641i	$-0.750210\pi$
$827$	−31.3707	+	6.24001i	−1.09087	+	0.216987i	−0.383292	+	0.923627i	$0.625210\pi$
$828$	−32.1907	+	24.3510i	−1.11870	+	0.846257i
$829$	−28.9138	+	19.3196i	−1.00422	+	0.670997i	−0.944940	−	0.327244i	$-0.893880\pi$
$829$	−28.9138	+	19.3196i	−1.00422	+	0.670997i	−0.0592783	+	0.998241i	$0.518880\pi$
$830$	11.8018	+	0.814285i	0.409647	+	0.0282642i
$831$	−2.37987			−0.0825567
$832$	−33.6745	−	23.5194i	−1.16745	−	0.815389i
$833$	−8.70450			−0.301593
$834$	−4.06626	−	0.280558i	−0.140803	−	0.00971493i
$835$	22.9885	−	15.3604i	0.795548	−	0.531568i
$836$	0.662859	+	0.876264i	0.0229255	+	0.0303062i
$837$	13.2446	−	2.63451i	0.457800	−	0.0910621i
$838$	−37.3627	+	21.4005i	−1.29067	+	0.739267i
$839$	−4.77355	−	11.5244i	−0.164801	−	0.397865i	0.819807	−	0.572639i	$-0.194080\pi$
$839$	−4.77355	−	11.5244i	−0.164801	−	0.397865i	−0.984609	+	0.174774i	$0.944080\pi$
$840$	1.48710	−	2.17667i	0.0513099	−	0.0751024i
$841$	11.0959	−	26.7880i	0.382619	−	0.923723i
$842$	32.0187	−	4.10342i	1.10344	−	0.141413i
$843$	0.488541	−	0.731154i	0.0168263	−	0.0251823i
$844$	13.9439	−	40.1680i	0.479969	−	1.38264i
$845$	19.0361	+	3.78651i	0.654860	+	0.130260i
$846$	14.2958	+	42.5945i	0.491500	+	1.46443i
$847$	2.57159	−	2.57159i	0.0883608	−	0.0883608i
$848$	−6.68164	+	5.69904i	−0.229449	+	0.195706i
$849$	1.53266	+	1.53266i	0.0526007	+	0.0526007i
$850$	3.99636	−	8.03407i	0.137074	−	0.275566i
$851$	−11.5051	+	57.8402i	−0.394391	+	1.98274i
$852$	−1.62881	−	1.44836i	−0.0558022	−	0.0496200i
$853$	15.0593	+	10.0623i	0.515620	+	0.344526i	0.785999	−	0.618228i	$-0.212149\pi$
$853$	15.0593	+	10.0623i	0.515620	+	0.344526i	−0.270379	+	0.962754i	$0.587149\pi$
$854$	5.96522	−	7.71894i	0.204126	−	0.264137i
$855$	−0.707383	−	0.293008i	−0.0241920	−	0.0100206i
$856$	8.16091	−	7.99431i	0.278934	−	0.273240i
$857$	45.1567	−	18.7045i	1.54252	−	0.638933i	0.560577	−	0.828102i	$-0.310579\pi$
$857$	45.1567	−	18.7045i	1.54252	−	0.638933i	0.981945	+	0.189169i	$0.0605793\pi$
$858$	7.70401	+	2.09269i	0.263010	+	0.0714433i
$859$	−10.5662	−	53.1197i	−0.360513	−	1.81242i	−0.555385	−	0.831593i	$-0.687429\pi$
$859$	−10.5662	−	53.1197i	−0.360513	−	1.81242i	0.194872	−	0.980829i	$-0.437571\pi$
$860$	−27.8469	−	16.3337i	−0.949572	−	0.556975i
$861$	2.69515	+	4.03358i	0.0918505	+	0.137464i
$862$	15.0481	−	13.1056i	0.512541	−	0.446379i
$863$		−	9.30109i		−	0.316613i	−0.987390	−	0.158306i	$-0.949397\pi$
$863$		−	9.30109i		−	0.316613i	0.987390	−	0.158306i	$-0.0506034\pi$
$864$	12.0835	+	1.80260i	0.411087	+	0.0613257i
$865$		−	2.12703i		−	0.0723211i
$866$	−12.4782	−	14.3278i	−0.424028	−	0.486877i
$867$	−2.49199	−	3.72952i	−0.0846324	−	0.126661i
$868$	21.0833	−	5.49418i	0.715613	−	0.186485i
$869$	−1.30373	−	6.55432i	−0.0442262	−	0.222340i
$870$	0.0138886	−	0.0511292i	0.000470867	−	0.00173344i
$871$	75.2232	−	31.1585i	2.54884	−	1.05576i
$872$	9.23658	+	3.93799i	0.312790	+	0.133357i
$873$	−13.9088	−	5.76123i	−0.470743	−	0.194988i
$874$	−1.45085	−	1.12122i	−0.0490758	−	0.0379259i
$875$	16.6025	+	11.0934i	0.561267	+	0.375027i
$876$	−0.422329	−	7.20181i	−0.0142692	−	0.243327i
$877$	4.03688	−	20.2948i	0.136316	−	0.685306i	−0.850824	−	0.525450i	$-0.823897\pi$
$877$	4.03688	−	20.2948i	0.136316	−	0.685306i	0.987140	−	0.159856i	$-0.0511030\pi$
$878$	11.6221	+	5.78115i	0.392228	+	0.195104i
$879$	−0.537286	−	0.537286i	−0.0181222	−	0.0181222i
$880$	−10.7480	+	13.6153i	−0.362317	+	0.458973i
$881$	−21.4492	+	21.4492i	−0.722643	+	0.722643i	−0.969143	−	0.246500i	$-0.920719\pi$
$881$	−21.4492	+	21.4492i	−0.722643	+	0.722643i	0.246500	+	0.969143i	$0.420719\pi$
$882$	15.2254	−	5.11003i	0.512666	−	0.172064i
$883$	−34.4043	−	6.84345i	−1.15780	−	0.230300i	−0.421417	−	0.906867i	$-0.638467\pi$
$883$	−34.4043	−	6.84345i	−1.15780	−	0.230300i	−0.736381	+	0.676567i	$0.763467\pi$
$884$	9.83229	+	20.2884i	0.330696	+	0.682372i
$885$	−2.52114	+	3.77315i	−0.0847472	+	0.126833i
$886$	−0.798091	−	6.22745i	−0.0268124	−	0.209215i
$887$	8.28163	−	19.9936i	0.278070	−	0.671320i	−0.721712	−	0.692193i	$-0.756645\pi$
$887$	8.28163	−	19.9936i	0.278070	−	0.671320i	0.999782	+	0.0208730i	$0.00664455\pi$
$888$	7.29878	−	4.76876i	0.244931	−	0.160029i
$889$	1.96287	+	4.73879i	0.0658326	+	0.158934i
$890$	−16.0624	−	28.0431i	−0.538412	−	0.940005i
$891$	22.8320	−	4.54158i	0.764902	−	0.152148i
$892$	−4.98399	+	35.9458i	−0.166876	+	1.20355i
$893$	−1.69705	+	1.13394i	−0.0567898	+	0.0379457i
$894$	0.465499	−	6.74671i	0.0155686	−	0.225644i
$895$	13.9452			0.466138
$896$	19.6322	+	1.76203i	0.655865	+	0.0588653i
$897$	−13.3226			−0.444828
$898$	1.20386	−	17.4481i	0.0401733	−	0.582252i
$899$	0.364088	−	0.243276i	0.0121430	−	0.00811371i
$900$	−2.27375	+	16.3988i	−0.0757915	+	0.546627i
$901$	4.72769	−	0.940395i	0.157502	−	0.0313291i
$902$	−15.8655	−	27.6994i	−0.528264	−	0.922288i
$903$	−2.72851	−	6.58721i	−0.0907992	−	0.219209i
$904$	11.2061	+	17.1513i	0.372708	+	0.570445i
$905$	1.24070	−	2.99531i	0.0412423	−	0.0995676i
$906$	0.701957	+	5.47732i	0.0233210	+	0.181972i
$907$	18.4680	−	27.6393i	0.613220	−	0.917748i	−0.386771	−	0.922176i	$-0.626409\pi$
$907$	18.4680	−	27.6393i	0.613220	−	0.917748i	0.999990	+	0.00442801i	$0.00140948\pi$
$908$	−21.2399	−	43.8273i	−0.704871	−	1.45446i
$909$	14.3149	+	2.84742i	0.474796	+	0.0944428i
$910$	−17.4211	+	5.84696i	−0.577504	+	0.193825i
$911$	−38.1083	+	38.1083i	−1.26258	+	1.26258i	−0.312748	+	0.949836i	$0.601249\pi$
$911$	−38.1083	+	38.1083i	−1.26258	+	1.26258i	−0.949836	+	0.312748i	$0.898751\pi$
$912$	0.0316842	+	0.269221i	0.00104917	+	0.00891479i
$913$	−12.1564	−	12.1564i	−0.402317	−	0.402317i
$914$	−17.1952	−	8.55337i	−0.568768	−	0.282920i
$915$	−0.413216	+	2.07738i	−0.0136605	+	0.0686760i
$916$	−1.94746	−	33.2094i	−0.0643460	−	1.09727i
$917$	11.1808	+	7.47077i	0.369223	+	0.246707i
$918$	−5.30602	−	4.10051i	−0.175125	−	0.135337i
$919$	4.18590	+	1.73385i	0.138080	+	0.0571946i	0.450653	−	0.892699i	$-0.351191\pi$
$919$	4.18590	+	1.73385i	0.138080	+	0.0571946i	−0.312573	+	0.949894i	$0.601191\pi$
$920$	11.3532	−	26.6291i	0.374305	−	0.877934i
$921$	6.65758	−	2.75766i	0.219375	−	0.0908680i
$922$	−11.8602	+	43.6619i	−0.390595	+	1.43793i
$923$	2.96414	+	14.9017i	0.0975659	+	0.490497i
$924$	−3.70719	+	0.966071i	−0.121957	+	0.0317814i
$925$	13.4386	+	20.1122i	0.441857	+	0.661286i
$926$	−26.6317	−	30.5791i	−0.875173	−	1.00489i
$927$			3.07142i			0.100879i
$928$	0.384363	−	0.0959410i	0.0126173	−	0.00314942i
$929$			6.50934i			0.213564i	0.994282	+	0.106782i	$0.0340548\pi$
$929$			6.50934i			0.213564i	−0.994282	+	0.106782i	$0.965945\pi$
$930$	−3.56727	+	3.10679i	−0.116975	+	0.101876i
$931$	0.405325	+	0.606611i	0.0132840	+	0.0198809i
$932$	14.8275	+	8.69713i	0.485691	+	0.284884i
$933$	−2.23956	−	11.2590i	−0.0733199	−	0.368604i
$934$	−8.72977	−	2.37133i	−0.285647	−	0.0775922i
$935$	8.79643	−	3.64360i	0.287674	−	0.119159i
$936$	−29.1085	−	29.7151i	−0.951440	−	0.971269i
$937$	−19.5113	−	8.08185i	−0.637407	−	0.264023i	0.0404894	−	0.999180i	$-0.487108\pi$
$937$	−19.5113	−	8.08185i	−0.637407	−	0.264023i	−0.677897	+	0.735157i	$0.737108\pi$
$938$	−23.8923	+	30.9164i	−0.780111	+	1.00946i
$939$	3.01284	+	2.01312i	0.0983204	+	0.0656956i
$940$	−24.0799	−	21.4121i	−0.785399	−	0.698387i
$941$	10.7030	−	53.8075i	0.348907	−	1.75408i	−0.264573	−	0.964366i	$-0.585231\pi$
$941$	10.7030	−	53.8075i	0.348907	−	1.75408i	0.613480	−	0.789710i	$-0.289769\pi$
$942$	−1.80348	+	3.62563i	−0.0587607	+	0.118129i
$943$	37.6685	+	37.6685i	1.22666	+	1.22666i
$944$	−33.8246	−	2.68452i	−1.10090	−	0.0873735i
$945$	3.86487	−	3.86487i	0.125724	−	0.125724i
$946$	14.9279	+	44.4779i	0.485348	+	1.44610i
$947$	42.5123	+	8.45622i	1.38146	+	0.274790i	0.829234	−	0.558901i	$-0.188777\pi$
$947$	42.5123	+	8.45622i	1.38146	+	0.274790i	0.552230	+	0.833692i	$0.313777\pi$
$948$	0.540695	−	1.55757i	0.0175610	−	0.0505876i
$949$	−27.9388	+	41.8133i	−0.906931	+	1.35732i
$950$	−0.745980	+	0.0956025i	−0.0242028	+	0.00310176i
$951$	−1.07599	+	2.59766i	−0.0348913	+	0.0842349i
$952$	−8.93332	−	6.10324i	−0.289530	−	0.197807i
$953$	11.3628	+	27.4322i	0.368077	+	0.888616i	0.994065	+	0.108784i	$0.0346956\pi$
$953$	11.3628	+	27.4322i	0.368077	+	0.888616i	−0.625989	+	0.779832i	$0.715304\pi$
$954$	−7.71732	+	4.42030i	−0.249858	+	0.143112i
$955$	−18.8835	+	3.75616i	−0.611055	+	0.121546i
$956$	18.7003	+	24.7208i	0.604811	+	0.799527i
$957$	−0.0640196	+	0.0427765i	−0.00206946	+	0.00138277i
$958$	53.9895	+	3.72509i	1.74432	+	0.120352i
$959$	−7.69531			−0.248494
$960$	−3.98685	+	1.55587i	−0.128675	+	0.0502156i
$961$	−8.09657			−0.261180
$962$	−60.6310	−	4.18333i	−1.95482	−	0.134876i
$963$	9.61949	−	6.42754i	0.309984	−	0.207124i
$964$	47.1779	−	35.6882i	1.51950	−	1.14944i
$965$	−13.3182	+	2.64916i	−0.428729	+	0.0852795i
$966$	5.54771	−	3.17760i	0.178495	−	0.102237i
$967$	12.7234	+	30.7169i	0.409155	+	0.987788i	0.985361	+	0.170483i	$0.0545329\pi$
$967$	12.7234	+	30.7169i	0.409155	+	0.987788i	−0.576205	+	0.817305i	$0.695467\pi$
$968$	−5.80225	+	1.09206i	−0.186491	+	0.0351002i
$969$	0.0569399	−	0.137465i	0.00182917	−	0.00441602i
$970$	10.7096	−	1.37250i	0.343863	−	0.0440684i
$971$	1.52250	−	2.27858i	0.0488594	−	0.0731232i	−0.806236	−	0.591594i	$-0.798499\pi$
$971$	1.52250	−	2.27858i	0.0488594	−	0.0731232i	0.855095	+	0.518471i	$0.173499\pi$
$972$	17.6675	+	6.13308i	0.566684	+	0.196719i
$973$	−13.3727	−	2.65999i	−0.428708	−	0.0852753i
$974$	0.342324	+	1.01996i	0.0109688	+	0.0326816i
$975$	−3.86395	+	3.86395i	−0.123746	+	0.123746i
$976$	−15.0653	+	4.88404i	−0.482230	+	0.156334i
$977$	−24.7249	−	24.7249i	−0.791018	−	0.791018i	0.190642	−	0.981660i	$-0.438943\pi$
$977$	−24.7249	−	24.7249i	−0.791018	−	0.791018i	−0.981660	+	0.190642i	$0.938943\pi$
$978$	0.182500	−	0.366888i	0.00583570	−	0.0117318i
$979$	−9.16243	+	46.0626i	−0.292832	+	1.47217i
$980$	−7.65376	+	8.60734i	−0.244490	+	0.274951i
$981$	8.45491	+	5.64939i	0.269944	+	0.180371i
$982$	−16.7384	+	21.6593i	−0.534143	+	0.691176i
$983$	8.66961	+	3.59107i	0.276517	+	0.114537i	0.516633	−	0.856207i	$-0.327185\pi$
$983$	8.66961	+	3.59107i	0.276517	+	0.114537i	−0.240115	+	0.970744i	$0.577185\pi$
$984$	0.0812152	−	7.87517i	0.00258905	−	0.251051i
$985$	21.8991	−	9.07090i	0.697763	−	0.289023i
$986$	−0.209840	−	0.0570003i	−0.00668267	−	0.00181526i
$987$	−1.38836	−	6.97978i	−0.0441921	−	0.222169i
$988$	0.956043	−	1.62993i	0.0304158	−	0.0518551i
$989$	−43.4986	−	65.1002i	−1.38317	−	2.07007i
$990$	−13.2472	+	11.5372i	−0.421024	+	0.366675i
$991$		−	39.1011i		−	1.24209i	−0.783776	−	0.621044i	$-0.786709\pi$
$991$		−	39.1011i		−	1.24209i	0.783776	−	0.621044i	$-0.213291\pi$
$992$	−33.2933	−	11.9435i	−1.05706	−	0.379207i
$993$			1.98937i			0.0631308i
$994$	−4.78855	−	5.49831i	−0.151884	−	0.174396i
$995$	5.43630	+	8.13600i	0.172342	+	0.257929i
$996$	−1.06959	−	4.10444i	−0.0338914	−	0.130054i
$997$	7.93159	+	39.8748i	0.251196	+	1.26285i	0.876094	+	0.482140i	$0.160140\pi$
$997$	7.93159	+	39.8748i	0.251196	+	1.26285i	−0.624898	+	0.780706i	$0.714860\pi$
$998$	−10.4157	+	38.3444i	−0.329705	+	1.21377i
$999$	16.7008	−	6.91769i	0.528389	−	0.218866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.13.4	yes	56
3.2	odd	2		576.2.bd.a.397.4		56
4.3	odd	2		256.2.i.a.145.3		56
8.3	odd	2		512.2.i.a.33.5		56
8.5	even	2		512.2.i.b.33.3		56
64.5	even	16	inner	64.2.i.a.5.4	✓	56
64.27	odd	16		512.2.i.a.481.5		56
64.37	even	16		512.2.i.b.481.3		56
64.59	odd	16		256.2.i.a.113.3		56
192.5	odd	16		576.2.bd.a.325.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.4	✓	56	64.5	even	16	inner
64.2.i.a.13.4	yes	56	1.1	even	1	trivial
256.2.i.a.113.3		56	64.59	odd	16
256.2.i.a.145.3		56	4.3	odd	2
512.2.i.a.33.5		56	8.3	odd	2
512.2.i.a.481.5		56	64.27	odd	16
512.2.i.b.33.3		56	8.5	even	2
512.2.i.b.481.3		56	64.37	even	16
576.2.bd.a.325.4		56	192.5	odd	16
576.2.bd.a.397.4		56	3.2	odd	2

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0973444 - 1.41086i) q^{2} +(0.306211 - 0.204603i) q^{3} +(-1.98105 - 0.274678i) q^{4} +(1.42470 - 0.283390i) q^{5} +(-0.258859 - 0.451937i) q^{6} +(-0.666723 - 1.60961i) q^{7} +(-0.580376 + 2.76824i) q^{8} +(-1.09615 + 2.64634i) q^{9} +(-0.261137 - 2.03763i) q^{10} +(-1.65860 + 2.48226i) q^{11} +(-0.662818 + 0.321220i) q^{12} +(5.03569 + 1.00166i) q^{13} +(-2.33584 + 0.783966i) q^{14} +(0.378274 - 0.378274i) q^{15} +(3.84910 + 1.08830i) q^{16} +(-1.55248 - 1.55248i) q^{17} +(3.62690 + 1.80412i) q^{18} +(-0.0359002 + 0.180483i) q^{19} +(-2.90023 + 0.170075i) q^{20} +(-0.533490 - 0.356467i) q^{21} +(3.34067 + 2.58168i) q^{22} +(-6.50946 - 2.69631i) q^{23} +(0.388674 + 0.966412i) q^{24} +(-2.66995 + 1.10593i) q^{25} +(1.90340 - 7.00714i) q^{26} +(0.421339 + 2.11821i) q^{27} +(0.878685 + 3.37185i) q^{28} +(0.0389072 + 0.0582287i) q^{29} +(-0.496869 - 0.570515i) q^{30} -6.25272i q^{31} +(1.91013 - 5.32460i) q^{32} +1.09945i q^{33} +(-2.34146 + 2.03921i) q^{34} +(-1.40602 - 2.10426i) q^{35} +(2.89841 - 4.94143i) q^{36} +(-1.63291 - 8.20918i) q^{37} +(0.251141 + 0.0682192i) q^{38} +(1.74693 - 0.723600i) q^{39} +(-0.0423689 + 4.10837i) q^{40} +(-6.98521 - 2.89337i) q^{41} +(-0.554857 + 0.717979i) q^{42} +(9.23959 + 6.17369i) q^{43} +(3.96758 - 4.46190i) q^{44} +(-0.811733 + 4.08086i) q^{45} +(-4.43777 + 8.92146i) q^{46} +(7.84283 + 7.84283i) q^{47} +(1.40131 - 0.454290i) q^{48} +(2.80342 - 2.80342i) q^{49} +(1.30041 + 3.87458i) q^{50} +(-0.793030 - 0.157743i) q^{51} +(-9.70081 - 3.36753i) q^{52} +(-1.21975 + 1.82549i) q^{53} +(3.02951 - 0.388253i) q^{54} +(-1.65955 + 4.00650i) q^{55} +(4.84275 - 0.911470i) q^{56} +(0.0259343 + 0.0626110i) q^{57} +(0.0859400 - 0.0492244i) q^{58} +(-8.31975 + 1.65490i) q^{59} +(-0.853284 + 0.645476i) q^{60} +(-3.29205 + 2.19968i) q^{61} +(-8.82172 - 0.608668i) q^{62} +4.99040 q^{63} +(-7.32633 - 3.21324i) q^{64} +7.45818 q^{65} +(1.55117 + 0.107025i) q^{66} +(13.1855 - 8.81029i) q^{67} +(2.64911 + 3.50197i) q^{68} +(-2.54494 + 0.506220i) q^{69} +(-3.10569 + 1.77886i) q^{70} +(1.13245 + 2.73397i) q^{71} +(-6.68952 - 4.57027i) q^{72} +(-3.74820 + 9.04896i) q^{73} +(-11.7410 + 1.50469i) q^{74} +(-0.591290 + 0.884929i) q^{75} +(0.120695 - 0.347684i) q^{76} +(5.10131 + 1.01471i) q^{77} +(-0.850845 - 2.53510i) q^{78} +(-1.58284 + 1.58284i) q^{79} +(5.79221 + 0.459704i) q^{80} +(-5.51384 - 5.51384i) q^{81} +(-4.76211 + 9.57349i) q^{82} +(-1.12345 + 5.64796i) q^{83} +(0.958956 + 0.852716i) q^{84} +(-2.65177 - 1.77186i) q^{85} +(9.60964 - 12.4348i) q^{86} +(0.0238276 + 0.00986972i) q^{87} +(-5.90890 - 6.03204i) q^{88} +(14.5341 - 6.02023i) q^{89} +(5.67850 + 1.54249i) q^{90} +(-1.74513 - 8.77334i) q^{91} +(12.1549 + 7.12952i) q^{92} +(-1.27933 - 1.91465i) q^{93} +(11.8286 - 10.3017i) q^{94} +0.267307i q^{95} +(-0.504530 - 2.02127i) q^{96} +5.25588i q^{97} +(-3.68233 - 4.22812i) q^{98} +(-4.75084 - 7.11013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20}+ \cdots + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more