LMFDB - Embedded newform 64.2.i.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			5.4
Character	$\chi$	$=$	64.5
Dual form			64.2.i.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0973444 + 1.41086i) q^{2} +(0.306211 + 0.204603i) q^{3} +(-1.98105 + 0.274678i) q^{4} +(1.42470 + 0.283390i) q^{5} +(-0.258859 + 0.451937i) q^{6} +(-0.666723 + 1.60961i) q^{7} +(-0.580376 - 2.76824i) q^{8} +(-1.09615 - 2.64634i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 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	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.640817	−	0.767694i	$-0.278596\pi$
$3$	0.306211	+	0.204603i	0.176791	+	0.118128i	−0.464026	+	0.885821i	$0.653596\pi$
$4$	−1.98105	+	0.274678i	−0.990524	+	0.137339i
$5$	1.42470	+	0.283390i	0.637143	+	0.126736i	0.503084	−	0.864238i	$-0.332199\pi$
$5$	1.42470	+	0.283390i	0.637143	+	0.126736i	0.134059	+	0.990973i	$0.457199\pi$
$6$	−0.258859	+	0.451937i	−0.105679	+	0.184503i
$7$	−0.666723	+	1.60961i	−0.251998	+	0.608376i	−0.998365	−	0.0571578i	$-0.981796\pi$
$7$	−0.666723	+	1.60961i	−0.251998	+	0.608376i	0.746367	+	0.665534i	$0.231796\pi$
$8$	−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	0.492456	−	0.870337i	$-0.336099\pi$
$11$	−1.65860	−	2.48226i	−0.500086	−	0.748431i	−0.992542	+	0.121906i	$0.961099\pi$
$12$	−0.662818	−	0.321220i	−0.191339	−	0.0927282i
$13$	5.03569	−	1.00166i	1.39665	−	0.277811i	0.561337	−	0.827587i	$-0.310287\pi$
$13$	5.03569	−	1.00166i	1.39665	−	0.277811i	0.835312	+	0.549776i	$0.185287\pi$
$14$	−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	−0.869849	−	0.493317i	$-0.835784\pi$
$17$	−1.55248	+	1.55248i	−0.376532	+	0.376532i	0.493317	+	0.869849i	$0.335784\pi$
$18$	3.62690	−	1.80412i	0.854869	−	0.425234i
$19$	−0.0359002	−	0.180483i	−0.00823608	−	0.0414056i	0.976449	−	0.215750i	$-0.0692195\pi$
$19$	−0.0359002	−	0.180483i	−0.00823608	−	0.0414056i	−0.984685	+	0.174344i	$0.944220\pi$
$20$	−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	−0.938320	−	0.345769i	$-0.887618\pi$
$23$	−6.50946	+	2.69631i	−1.35732	+	0.562219i	−0.418997	+	0.907988i	$0.637618\pi$
$24$	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	−0.827840	−	0.560965i	$-0.810430\pi$
$29$	0.0389072	−	0.0582287i	0.00722489	−	0.0108128i	0.835064	+	0.550152i	$0.185430\pi$
$30$	−0.496869	+	0.570515i	−0.0907155	+	0.104161i
$31$			6.25272i			1.12302i	0.827469	+	0.561511i	$0.189780\pi$
$31$			6.25272i			1.12302i	−0.827469	+	0.561511i	$0.810220\pi$
$32$	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	0.577532	+	0.816368i	$0.304016\pi$
$37$	−1.63291	+	8.20918i	−0.268448	+	1.34958i	−0.845981	+	0.533213i	$0.820984\pi$
$38$	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	−0.854323	−	0.519743i	$-0.826028\pi$
$41$	−6.98521	+	2.89337i	−1.09091	+	0.451868i	−0.236584	+	0.971611i	$0.576028\pi$
$42$	−0.554857	−	0.717979i	−0.0856162	−	0.110787i
$43$	9.23959	−	6.17369i	1.40902	−	0.941480i	0.409449	−	0.912333i	$-0.365721\pi$
$43$	9.23959	−	6.17369i	1.40902	−	0.941480i	0.999575	−	0.0291463i	$-0.00927887\pi$
$44$	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	0.156281	−	0.987713i	$-0.450049\pi$
$47$	7.84283	−	7.84283i	1.14399	−	1.14399i	0.987713	−	0.156281i	$-0.0499507\pi$
$48$	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	0.738190	−	0.674593i	$-0.235681\pi$
$53$	−1.21975	−	1.82549i	−0.167546	−	0.250750i	−0.905736	+	0.423843i	$0.860681\pi$
$54$	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	−0.378918	−	0.925430i	$-0.623704\pi$
$59$	−8.31975	−	1.65490i	−1.08314	−	0.215450i	−0.704221	+	0.709981i	$0.748704\pi$
$60$	−0.853284	−	0.645476i	−0.110158	−	0.0833306i
$61$	−3.29205	−	2.19968i	−0.421504	−	0.281640i	0.326675	−	0.945137i	$-0.394072\pi$
$61$	−3.29205	−	2.19968i	−0.421504	−	0.281640i	−0.748179	+	0.663497i	$0.769072\pi$
$62$	−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	0.943372	+	0.331736i	$0.107634\pi$
$67$	13.1855	+	8.81029i	1.61087	+	1.07635i	0.667497	+	0.744612i	$0.267366\pi$
$68$	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	−0.842326	−	0.538968i	$-0.818814\pi$
$71$	1.13245	−	2.73397i	0.134397	−	0.324462i	0.976723	+	0.214506i	$0.0688142\pi$
$72$	−6.68952	+	4.57027i	−0.788367	+	0.538612i
$73$	−3.74820	−	9.04896i	−0.438694	−	1.05910i	−0.976400	−	0.215969i	$-0.930709\pi$
$73$	−3.74820	−	9.04896i	−0.438694	−	1.05910i	0.537706	−	0.843132i	$-0.319291\pi$
$74$	−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	0.612436	−	0.790520i	$-0.290190\pi$
$79$	−1.58284	−	1.58284i	−0.178083	−	0.178083i	−0.790520	+	0.612436i	$0.790190\pi$
$80$	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	−0.992172	−	0.124881i	$-0.960145\pi$
$83$	−1.12345	−	5.64796i	−0.123314	−	0.619944i	0.868857	−	0.495063i	$-0.164855\pi$
$84$	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	0.981588	−	0.191009i	$-0.0611759\pi$
$89$	14.5341	+	6.02023i	1.54061	+	0.638143i	0.559024	+	0.829151i	$0.311176\pi$
$90$	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	$-0.914025\pi$
$97$		−	5.25588i		−	0.533654i	0.963744	−	0.266827i	$-0.0859753\pi$
$98$	−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	0.899288	+	0.437356i	$0.144085\pi$
$101$	−0.994080	+	4.99758i	−0.0989146	+	0.497278i	−0.998203	+	0.0599215i	$0.980915\pi$
$102$	−0.299751	−	1.10350i	−0.0296797	−	0.109263i
$103$	0.990660	+	0.410345i	0.0976127	+	0.0404325i	0.430955	−	0.902373i	$-0.358177\pi$
$103$	0.990660	+	0.410345i	0.0976127	+	0.0404325i	−0.333343	+	0.942806i	$0.608177\pi$
$104$	−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	−0.707210	−	0.707004i	$-0.750046\pi$
$107$	−3.35832	+	2.24396i	−0.324661	+	0.216932i	0.382549	+	0.923935i	$0.375046\pi$
$108$	−0.252865	+	4.31201i	−0.0243319	+	0.414924i
$109$	0.692578	+	3.48183i	0.0663370	+	0.333498i	0.999675	−	0.0255008i	$-0.00811805\pi$
$109$	0.692578	+	3.48183i	0.0663370	+	0.333498i	−0.933338	+	0.358999i	$0.883118\pi$
$110$	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	0.905715	−	0.423886i	$-0.139334\pi$
$113$	5.12191	+	5.12191i	0.481829	+	0.481829i	−0.423886	+	0.905715i	$0.639334\pi$
$114$	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	0.242687	−	0.970105i	$-0.421971\pi$
$131$	−6.41752	−	4.28805i	−0.560701	−	0.374648i	−0.803388	+	0.595456i	$0.796971\pi$
$132$	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	0.979490	−	0.201491i	$-0.0645786\pi$
$137$	1.69028	+	4.08071i	0.144411	+	0.348638i	−0.835080	+	0.550129i	$0.814579\pi$
$138$	0.466470	−	3.63983i	0.0397085	−	0.309843i
$139$	4.34787	+	6.50705i	0.368782	+	0.551921i	0.968730	−	0.248118i	$-0.0798121\pi$
$139$	4.34787	+	6.50705i	0.368782	+	0.551921i	−0.599948	+	0.800039i	$0.704812\pi$
$140$	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	−0.0282295	−	0.999601i	$-0.508987\pi$
$149$	10.7964	−	7.21395i	0.884479	−	0.590990i	0.912708	+	0.408612i	$0.133987\pi$
$150$	1.19095	−	0.920370i	0.0972407	−	0.0751479i
$151$	−9.79563	+	4.05748i	−0.797157	+	0.330193i	−0.743817	−	0.668383i	$-0.766987\pi$
$151$	−9.79563	+	4.05748i	−0.797157	+	0.330193i	−0.0533397	+	0.998576i	$0.516987\pi$
$152$	−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	−0.962809	−	0.270184i	$-0.912916\pi$
$157$	−4.31959	+	6.46472i	−0.344741	+	0.515941i	0.618068	+	0.786124i	$0.287916\pi$
$158$	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	−0.813956	−	0.580926i	$-0.802690\pi$
$163$	0.437112	−	0.654184i	0.0342372	−	0.0512396i	0.848193	+	0.529687i	$0.177690\pi$
$164$	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	0.939259	−	0.343208i	$-0.111514\pi$
$167$	17.5845	+	7.28375i	1.36073	+	0.563633i	0.421472	+	0.906841i	$0.361514\pi$
$168$	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	0.990124	−	0.140194i	$-0.0447725\pi$
$173$	0.285668	+	1.43615i	0.0217189	+	0.109188i	−0.968405	+	0.249382i	$0.919773\pi$
$174$	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	0.169778	−	0.985482i	$-0.445695\pi$
$179$	9.41568	−	1.87290i	0.703761	−	0.139987i	0.533983	+	0.845496i	$0.320695\pi$
$180$	2.72901	+	7.86141i	0.203408	+	0.585955i
$181$	1.23999	+	1.85578i	0.0921677	+	0.137939i	0.874688	−	0.484686i	$-0.161066\pi$
$181$	1.23999	+	1.85578i	0.0921677	+	0.137939i	−0.782520	+	0.622625i	$0.786066\pi$
$182$	−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	0.728873	−	0.684649i	$-0.240045\pi$
$197$	16.0043	+	3.18345i	1.14026	+	0.226812i	0.411387	+	0.911461i	$0.365045\pi$
$198$	−10.4939	−	6.01063i	−0.745766	−	0.427157i
$199$	2.57784	−	6.22346i	0.182738	−	0.441170i	−0.805791	−	0.592201i	$-0.798259\pi$
$199$	2.57784	−	6.22346i	0.182738	−	0.441170i	0.988529	+	0.151031i	$0.0482593\pi$
$200$	−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	−0.811201	−	0.584768i	$-0.801186\pi$
$211$	−4.14756	−	20.8512i	−0.285530	−	1.43546i	0.525671	−	0.850688i	$-0.323814\pi$
$212$	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	$0.207841\pi$
$223$			18.1448i			1.21507i	−0.794294	+	0.607533i	$0.792159\pi$
$224$	−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	−0.0407657	−	0.999169i	$-0.512980\pi$
$227$	13.5289	−	20.2475i	0.897946	−	1.34387i	0.938712	−	0.344703i	$-0.112020\pi$
$228$	−0.0341793	+	0.131159i	−0.00226358	+	0.00868622i
$229$	3.24498	−	16.3136i	0.214434	−	1.07803i	−0.712173	−	0.702004i	$-0.752289\pi$
$229$	3.24498	−	16.3136i	0.214434	−	1.07803i	0.926607	−	0.376031i	$-0.122711\pi$
$230$	−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	−0.627311	−	0.778769i	$-0.715845\pi$
$233$	−7.94074	+	3.28916i	−0.520215	+	0.215480i	0.107096	+	0.994249i	$0.465845\pi$
$234$	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	−0.966301	−	0.257415i	$-0.917129\pi$
$239$	−10.9591	+	10.9591i	−0.708886	+	0.708886i	0.257415	+	0.966301i	$0.417129\pi$
$240$	1.86769	+	1.04434i	0.120559	+	0.0674119i
$241$	−20.9147	−	20.9147i	−1.34723	−	1.34723i	−0.888651	−	0.458584i	$-0.848357\pi$
$241$	−20.9147	−	20.9147i	−1.34723	−	1.34723i	−0.458584	−	0.888651i	$-0.651643\pi$
$242$	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	0.367736	−	0.929930i	$-0.380133\pi$
$251$	5.57057	+	1.10806i	0.351611	+	0.0699398i	−0.0161250	+	0.999870i	$0.505133\pi$
$252$	−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	0.637063	+	0.770812i	$0.280149\pi$
$263$	−5.81316	+	14.0342i	−0.358455	+	0.865387i	−0.995518	+	0.0945749i	$0.969851\pi$
$264$	−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	−0.595918	−	0.803045i	$-0.703212\pi$
$269$	−13.7633	+	2.73769i	−0.839162	+	0.166920i	−0.243244	+	0.969965i	$0.578212\pi$
$270$	4.20611	+	1.41168i	0.255976	+	0.0859118i
$271$	−17.1462	−	17.1462i	−1.04156	−	1.04156i	−0.999098	−	0.0424570i	$-0.986481\pi$
$271$	−17.1462	−	17.1462i	−1.04156	−	1.04156i	−0.0424570	−	0.999098i	$-0.513519\pi$
$272$	−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	−0.706419	−	0.707794i	$-0.749691\pi$
$277$	−5.37310	+	3.59019i	−0.322838	+	0.215714i	0.383581	+	0.923507i	$0.374691\pi$
$278$	−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	0.447511	−	0.894279i	$-0.352311\pi$
$281$	2.20599	+	0.913752i	0.131598	+	0.0545099i	−0.315912	+	0.948788i	$0.602311\pi$
$282$	1.51428	+	5.57465i	0.0901741	+	0.331966i
$283$	1.14821	−	5.77245i	0.0682541	−	0.343137i	−0.931535	−	0.363651i	$-0.881530\pi$
$283$	1.14821	−	5.77245i	0.0682541	−	0.343137i	0.999790	+	0.0205138i	$0.00653021\pi$
$284$	−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	−0.990760	−	0.135626i	$-0.956695\pi$
$293$	−0.402515	+	2.02358i	−0.0235152	+	0.118219i	0.967245	+	0.253845i	$0.0816953\pi$
$294$	−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	0.385804	−	0.922581i	$-0.373924\pi$
$307$	19.1912	−	3.81736i	1.09530	−	0.217868i	0.709493	+	0.704712i	$0.248924\pi$
$308$	−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	0.770497	+	0.637444i	$0.220008\pi$
$311$	11.9287	+	28.7984i	0.676414	+	1.63301i	−0.0940829	+	0.995564i	$0.529992\pi$
$312$	0.989226	−	5.25587i	0.0560039	−	0.297555i
$313$	3.76527	−	9.09016i	0.212825	−	0.513806i	−0.781030	−	0.624494i	$-0.785305\pi$
$313$	3.76527	−	9.09016i	0.212825	−	0.513806i	0.993855	+	0.110688i	$0.0353053\pi$
$314$	−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	0.364380	−	0.931250i	$-0.381281\pi$
$317$	−6.34804	−	4.24162i	−0.356541	−	0.238233i	−0.720921	+	0.693017i	$0.756281\pi$
$318$	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	0.739778	−	0.672851i	$-0.234930\pi$
$331$	−3.00110	−	4.49147i	−0.164956	−	0.246873i	−0.904734	+	0.425977i	$0.859930\pi$
$332$	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	−0.403358	−	0.915042i	$-0.632157\pi$
$337$	9.39328	−	9.39328i	0.511684	−	0.511684i	0.915042	+	0.403358i	$0.132157\pi$
$338$	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	−0.868293	−	0.496052i	$-0.834782\pi$
$347$	2.30495	−	11.5878i	0.123736	−	0.622064i	0.992029	−	0.126011i	$-0.0402176\pi$
$348$	−0.0444926	+	0.0260973i	−0.00238506	+	0.00139896i
$349$	14.7665	−	22.0997i	0.790435	−	1.18297i	−0.189152	−	0.981948i	$-0.560574\pi$
$349$	14.7665	−	22.0997i	0.790435	−	1.18297i	0.979587	−	0.201021i	$-0.0644261\pi$
$350$	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	$-0.907223\pi$
$353$		−	10.7979i		−	0.574714i	0.957824	−	0.287357i	$-0.0927766\pi$
$354$	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	0.00653056	−	0.999979i	$-0.497921\pi$
$359$	−13.1862	−	5.46192i	−0.695943	−	0.288269i	−0.702474	+	0.711710i	$0.747921\pi$
$360$	−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	−0.998020	−	0.0629039i	$-0.979964\pi$
$367$	−17.9142	+	17.9142i	−0.935116	+	0.935116i	0.0629039	+	0.998020i	$0.479964\pi$
$368$	−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	0.966130	+	0.258056i	$0.0830818\pi$
$373$	16.1231	+	24.1299i	0.834820	+	1.24940i	−0.131310	+	0.991341i	$0.541918\pi$
$374$	−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	0.0615391	−	0.998105i	$-0.480399\pi$
$379$	−5.13105	−	1.02063i	−0.263564	−	0.0524262i	−0.325103	+	0.945678i	$0.605399\pi$
$380$	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	0.115454	−	0.993313i	$-0.463168\pi$
$389$	−3.11633	−	0.619876i	−0.158004	−	0.0314290i	−0.273458	+	0.961884i	$0.588168\pi$
$390$	−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	−0.658539	−	0.752546i	$-0.728825\pi$
$397$	−19.5057	+	3.87993i	−0.978963	+	0.194728i	−0.320424	+	0.947274i	$0.603825\pi$
$398$	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	−0.303747	−	0.952753i	$-0.598238\pi$
$401$	12.9963	−	12.9963i	0.649006	−	0.649006i	0.952753	+	0.303747i	$0.0982376\pi$
$402$	−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	0.111973	−	0.993711i	$-0.464283\pi$
$409$	−10.3447	−	4.28490i	−0.511510	−	0.211874i	−0.623483	+	0.781837i	$0.714283\pi$
$410$	−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	0.142672	+	0.989770i	$0.454430\pi$
$419$	−16.9150	+	25.3152i	−0.826354	+	1.23673i	−0.969027	+	0.246957i	$0.920570\pi$
$420$	1.60787	−	0.943102i	0.0784560	−	0.0460187i
$421$	4.45310	−	22.3872i	0.217031	−	1.09109i	−0.706544	−	0.707669i	$-0.749747\pi$
$421$	4.45310	−	22.3872i	0.217031	−	1.09109i	0.923575	−	0.383418i	$-0.125253\pi$
$422$	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	−0.424723	−	0.905323i	$-0.639629\pi$
$431$	9.97751	−	9.97751i	0.480600	−	0.480600i	0.905323	+	0.424723i	$0.139629\pi$
$432$	−0.683479	−	8.61176i	−0.0328839	−	0.414334i
$433$	9.49988	+	9.49988i	0.456535	+	0.456535i	0.897516	−	0.440981i	$-0.145369\pi$
$433$	9.49988	+	9.49988i	0.456535	+	0.456535i	−0.440981	+	0.897516i	$0.645369\pi$
$434$	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	0.817623	−	0.575754i	$-0.195291\pi$
$439$	−3.51252	−	8.47998i	−0.167643	−	0.404727i	−0.985266	+	0.171027i	$0.945291\pi$
$440$	−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	0.297439	−	0.954741i	$-0.403867\pi$
$443$	4.35418	+	0.866101i	0.206874	+	0.0411497i	−0.0905656	+	0.995890i	$0.528867\pi$
$444$	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	0.997588	−	0.0694200i	$-0.0221149\pi$
$457$	5.19687	+	12.5463i	0.243099	+	0.586893i	−0.754488	+	0.656314i	$0.772115\pi$
$458$	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	−0.860836	−	0.508882i	$-0.830059\pi$
$461$	−31.3777	+	6.24141i	−1.46140	+	0.290691i	−0.600568	+	0.799573i	$0.705059\pi$
$462$	−0.861932	+	2.56814i	−0.0401007	+	0.119481i
$463$	20.2752	+	20.2752i	0.942266	+	0.942266i	0.998422	−	0.0561556i	$-0.0178843\pi$
$463$	20.2752	+	20.2752i	0.942266	+	0.942266i	−0.0561556	+	0.998422i	$0.517884\pi$
$464$	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	0.998858	−	0.0477869i	$-0.0152168\pi$
$467$	1.24791	+	6.27365i	0.0577463	+	0.290310i	−0.941111	+	0.338097i	$0.890217\pi$
$468$	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	$-0.661364\pi$
$479$		−	38.2671i		−	1.74847i	0.485503	−	0.874235i	$-0.338636\pi$
$480$	−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	0.366702	−	0.930338i	$-0.380487\pi$
$487$	−0.702848	−	0.291129i	−0.0318491	−	0.0131923i	−0.398551	+	0.917146i	$0.630487\pi$
$488$	−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	−0.862931	−	0.505322i	$-0.831374\pi$
$491$	−16.0938	+	10.7535i	−0.726303	+	0.485300i	0.136628	+	0.990622i	$0.456374\pi$
$492$	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	−0.768477	−	0.639878i	$-0.778985\pi$
$499$	−27.5562	+	5.48127i	−1.23359	+	0.245376i	−0.465109	+	0.885253i	$0.653985\pi$
$500$	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	0.929984	−	0.367600i	$-0.119821\pi$
$503$	0.279297	+	0.674282i	0.0124532	+	0.0300647i	−0.917531	+	0.397665i	$0.869821\pi$
$504$	−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	0.187750	−	0.982217i	$-0.439881\pi$
$509$	−14.6162	−	9.76623i	−0.647851	−	0.432880i	−0.835601	+	0.549336i	$0.814881\pi$
$510$	−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	0.933740	−	0.357952i	$-0.116525\pi$
$521$	0.465084	+	1.12281i	0.0203757	+	0.0491913i	−0.913364	+	0.407143i	$0.866525\pi$
$522$	0.0360612	−	0.281383i	0.00157836	−	0.0123158i
$523$	−16.7116	−	25.0106i	−0.730746	−	1.09364i	−0.991736	−	0.128297i	$-0.959049\pi$
$523$	−16.7116	−	25.0106i	−0.730746	−	1.09364i	0.260990	−	0.965341i	$-0.415951\pi$
$524$	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	−0.454556	−	0.890718i	$-0.650202\pi$
$541$	12.6138	−	18.8780i	0.542312	−	0.811627i	0.996867	+	0.0790916i	$0.0252019\pi$
$542$	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	0.229258	+	0.973366i	$0.426370\pi$
$547$	−17.7222	+	26.5232i	−0.757748	+	1.13405i	−0.987006	+	0.160684i	$0.948630\pi$
$548$	−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	−0.916662	−	0.399664i	$-0.869127\pi$
$557$	−5.25641	−	26.4258i	−0.222721	−	1.11970i	0.693940	−	0.720032i	$-0.255873\pi$
$558$	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	0.687002	−	0.726655i	$-0.258926\pi$
$563$	37.9592	−	7.55055i	1.59979	−	0.318218i	0.912786	+	0.408437i	$0.133926\pi$
$564$	−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	−0.960826	−	0.277152i	$-0.910609\pi$
$569$	−2.03813	+	4.92049i	−0.0854431	+	0.206278i	0.875383	+	0.483430i	$0.160609\pi$
$570$	0.120806	+	0.0691947i	0.00506000	+	0.00289825i
$571$	14.3880	+	2.86195i	0.602118	+	0.119769i	0.486731	−	0.873552i	$-0.338189\pi$
$571$	14.3880	+	2.86195i	0.602118	+	0.119769i	0.115387	+	0.993321i	$0.463189\pi$
$572$	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	0.999990	+	0.00458217i	$0.00145855\pi$
$587$	15.0588	+	22.5371i	0.621543	+	0.930206i	−0.378446	+	0.925623i	$0.623541\pi$
$588$	−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	−0.491221	−	0.871035i	$-0.663449\pi$
$593$	9.24907	−	9.24907i	0.379814	−	0.379814i	0.871035	+	0.491221i	$0.163449\pi$
$594$	−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	−0.266940	−	0.963713i	$-0.586013\pi$
$599$	5.52517	−	2.28860i	0.225752	−	0.0935097i	0.492693	+	0.870203i	$0.336013\pi$
$600$	−2.10653	+	2.15043i	−0.0859985	+	0.0877908i
$601$	−16.7410	−	6.93436i	−0.682880	−	0.282858i	0.0141501	−	0.999900i	$-0.495496\pi$
$601$	−16.7410	−	6.93436i	−0.682880	−	0.282858i	−0.697030	+	0.717042i	$0.745496\pi$
$602$	−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	$0.0500787\pi$
$607$			7.72029i			0.313357i	−0.987650	+	0.156679i	$0.949921\pi$
$608$	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	0.648003	+	0.761638i	$0.275605\pi$
$613$	−5.99511	+	30.1394i	−0.242140	+	1.21732i	−0.890143	+	0.455682i	$0.849395\pi$
$614$	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	−0.708566	−	0.705644i	$-0.750658\pi$
$617$	−17.6517	+	7.31159i	−0.710632	+	0.294353i	−0.00206586	+	0.999998i	$0.500658\pi$
$618$	−0.441891	+	0.341495i	−0.0177755	+	0.0137369i
$619$	−9.76932	+	6.52765i	−0.392662	+	0.262368i	−0.736191	−	0.676774i	$-0.763378\pi$
$619$	−9.76932	+	6.52765i	−0.392662	+	0.262368i	0.343529	+	0.939142i	$0.388378\pi$
$620$	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	0.988732	−	0.149694i	$-0.0478287\pi$
$631$	4.61559	+	11.1430i	0.183744	+	0.443596i	−0.804989	+	0.593290i	$0.797829\pi$
$632$	−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	0.574945	−	0.818192i	$-0.305023\pi$
$643$	0.990370	+	0.661744i	0.0390564	+	0.0260966i	−0.535889	+	0.844289i	$0.680023\pi$
$644$	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	−0.977496	−	0.210956i	$-0.932342\pi$
$647$	−3.48816	+	8.42116i	−0.137134	+	0.331070i	0.840362	+	0.542026i	$0.182342\pi$
$648$	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	0.496150	−	0.868237i	$-0.334747\pi$
$653$	32.8825	−	6.54074i	1.28679	−	0.255959i	0.790643	+	0.612278i	$0.209747\pi$
$654$	−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	0.902424	+	0.430848i	$0.141786\pi$
$659$	5.99601	+	30.1440i	0.233571	+	1.17424i	−0.668853	+	0.743395i	$0.733214\pi$
$660$	−0.186989	+	3.18866i	−0.00727855	+	0.124118i
$661$	37.6753	−	25.1739i	1.46540	−	0.979149i	0.470069	−	0.882629i	$-0.344229\pi$
$661$	37.6753	−	25.1739i	1.46540	−	0.979149i	0.995331	−	0.0965199i	$-0.0307712\pi$
$662$	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	$0.213806\pi$
$673$			32.2882i			1.24462i	−0.782771	+	0.622310i	$0.786194\pi$
$674$	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	−0.954608	−	0.297864i	$-0.903726\pi$
$677$	1.07518	−	5.40530i	0.0413225	−	0.207742i	0.995931	+	0.0901220i	$0.0287257\pi$
$678$	−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	−0.189945	−	0.981795i	$-0.560831\pi$
$683$	16.8416	−	11.2532i	0.644427	−	0.430592i	0.834371	+	0.551203i	$0.185831\pi$
$684$	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	−0.524476	−	0.851425i	$-0.675739\pi$
$691$	−17.9592	+	3.57231i	−0.683201	+	0.135897i	−0.158726	+	0.987323i	$0.550739\pi$
$692$	−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	0.760079	−	0.649831i	$-0.225160\pi$
$701$	11.9298	+	7.97124i	0.450583	+	0.301070i	−0.309496	+	0.950901i	$0.600160\pi$
$702$	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	0.346110	−	0.938194i	$-0.387502\pi$
$709$	8.17031	+	1.62518i	0.306843	+	0.0610348i	−0.0392674	+	0.999229i	$0.512502\pi$
$710$	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	0.928587	−	0.371116i	$-0.121025\pi$
$719$	14.9481	+	14.9481i	0.557471	+	0.557471i	−0.371116	+	0.928587i	$0.621025\pi$
$720$	−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	−0.597110	−	0.802160i	$-0.703684\pi$
$727$	−12.1904	+	5.04943i	−0.452117	+	0.187273i	0.144992	+	0.989433i	$0.453684\pi$
$728$	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	−0.639706	−	0.768620i	$-0.720944\pi$
$733$	8.53401	−	12.7721i	0.315211	−	0.471746i	0.954917	+	0.296873i	$0.0959439\pi$
$734$	−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	−0.632744	−	0.774361i	$-0.718071\pi$
$739$	8.82990	−	13.2149i	0.324813	−	0.486117i	0.957557	+	0.288244i	$0.0930714\pi$
$740$	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	−0.00704260	−	0.999975i	$-0.502242\pi$
$743$	−19.6016	−	8.11923i	−0.719112	−	0.297866i	−0.712069	+	0.702109i	$0.752242\pi$
$744$	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	−0.338608	+	0.940928i	$0.609956\pi$
$751$	−35.0649	+	35.0649i	−1.27954	+	1.27954i	−0.940928	+	0.338608i	$0.890044\pi$
$752$	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	0.903794	−	0.427968i	$-0.140770\pi$
$757$	4.47197	+	6.69277i	0.162536	+	0.243253i	−0.741258	+	0.671221i	$0.765770\pi$
$758$	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	0.386406	+	0.922329i	$0.373716\pi$
$761$	−14.8692	+	35.8975i	−0.539009	+	1.30128i	−0.925415	+	0.378955i	$0.876284\pi$
$762$	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	0.588382	−	0.808583i	$-0.299765\pi$
$773$	22.8691	+	4.54895i	0.822544	+	0.163614i	0.234162	+	0.972197i	$0.424765\pi$
$774$	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	−0.869915	−	0.493202i	$-0.835826\pi$
$787$	−7.15249	−	35.9580i	−0.254959	−	1.28176i	0.614956	−	0.788561i	$-0.289174\pi$
$788$	−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	0.174210	+	0.984708i	$0.444263\pi$
$797$	−22.6473	+	33.8941i	−0.802209	+	1.20059i	−0.976419	+	0.215882i	$0.930737\pi$
$798$	−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	−0.714022	−	0.700123i	$-0.753128\pi$
$809$	−20.5884	+	8.52801i	−0.723851	+	0.299829i	−0.00982829	+	0.999952i	$0.503128\pi$
$810$	−9.79530	−	12.6750i	−0.344172	−	0.445355i
$811$	28.5660	−	19.0872i	1.00309	−	0.670241i	0.0584267	−	0.998292i	$-0.481392\pi$
$811$	28.5660	−	19.0872i	1.00309	−	0.670241i	0.944660	+	0.328050i	$0.106392\pi$
$812$	−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	0.999827	+	0.0186046i	$0.00592238\pi$
$821$	18.1775	+	27.2045i	0.634398	+	0.949444i	−0.365429	+	0.930839i	$0.619078\pi$
$822$	−2.28177	−	0.292425i	−0.0795858	−	0.0101995i
$823$	−13.8958	−	33.5474i	−0.484377	−	1.16939i	−0.957511	−	0.288398i	$-0.906877\pi$
$823$	−13.8958	−	33.5474i	−0.484377	−	1.16939i	0.473134	−	0.880991i	$-0.343123\pi$
$824$	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	−0.383292	−	0.923627i	$-0.625210\pi$
$827$	−31.3707	−	6.24001i	−1.09087	−	0.216987i	−0.707573	+	0.706641i	$0.750210\pi$
$828$	−32.1907	−	24.3510i	−1.11870	−	0.846257i
$829$	−28.9138	−	19.3196i	−1.00422	−	0.670997i	−0.0592783	−	0.998241i	$-0.518880\pi$
$829$	−28.9138	−	19.3196i	−1.00422	−	0.670997i	−0.944940	+	0.327244i	$0.893880\pi$
$830$	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	−0.984609	−	0.174774i	$-0.944080\pi$
$839$	−4.77355	+	11.5244i	−0.164801	+	0.397865i	0.819807	+	0.572639i	$0.194080\pi$
$840$	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	−0.270379	−	0.962754i	$-0.587149\pi$
$853$	15.0593	−	10.0623i	0.515620	−	0.344526i	0.785999	+	0.618228i	$0.212149\pi$
$854$	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	0.981945	−	0.189169i	$-0.0605793\pi$
$857$	45.1567	+	18.7045i	1.54252	+	0.638933i	0.560577	+	0.828102i	$0.310579\pi$
$858$	7.70401	−	2.09269i	0.263010	−	0.0714433i
$859$	−10.5662	+	53.1197i	−0.360513	+	1.81242i	0.194872	+	0.980829i	$0.437571\pi$
$859$	−10.5662	+	53.1197i	−0.360513	+	1.81242i	−0.555385	+	0.831593i	$0.687429\pi$
$860$	−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	$0.0506034\pi$
$863$			9.30109i			0.316613i	−0.987390	+	0.158306i	$0.949397\pi$
$864$	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	0.987140	+	0.159856i	$0.0511030\pi$
$877$	4.03688	+	20.2948i	0.136316	+	0.685306i	−0.850824	+	0.525450i	$0.823897\pi$
$878$	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	0.246500	−	0.969143i	$-0.420719\pi$
$881$	−21.4492	−	21.4492i	−0.722643	−	0.722643i	−0.969143	+	0.246500i	$0.920719\pi$
$882$	15.2254	+	5.11003i	0.512666	+	0.172064i
$883$	−34.4043	+	6.84345i	−1.15780	+	0.230300i	−0.736381	−	0.676567i	$-0.763467\pi$
$883$	−34.4043	+	6.84345i	−1.15780	+	0.230300i	−0.421417	+	0.906867i	$0.638467\pi$
$884$	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	0.999782	−	0.0208730i	$-0.00664455\pi$
$887$	8.28163	+	19.9936i	0.278070	+	0.671320i	−0.721712	+	0.692193i	$0.756645\pi$
$888$	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	0.999990	−	0.00442801i	$-0.00140948\pi$
$907$	18.4680	+	27.6393i	0.613220	+	0.917748i	−0.386771	+	0.922176i	$0.626409\pi$
$908$	−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	−0.949836	−	0.312748i	$-0.898751\pi$
$911$	−38.1083	−	38.1083i	−1.26258	−	1.26258i	−0.312748	−	0.949836i	$-0.601249\pi$
$912$	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	−0.312573	−	0.949894i	$-0.601191\pi$
$919$	4.18590	−	1.73385i	0.138080	−	0.0571946i	0.450653	+	0.892699i	$0.351191\pi$
$920$	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	$-0.965945\pi$
$929$		−	6.50934i		−	0.213564i	0.994282	−	0.106782i	$-0.0340548\pi$
$930$	−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	−0.677897	−	0.735157i	$-0.737108\pi$
$937$	−19.5113	+	8.08185i	−0.637407	+	0.264023i	0.0404894	+	0.999180i	$0.487108\pi$
$938$	−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	0.613480	+	0.789710i	$0.289769\pi$
$941$	10.7030	+	53.8075i	0.348907	+	1.75408i	−0.264573	+	0.964366i	$0.585231\pi$
$942$	−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	0.552230	−	0.833692i	$-0.313777\pi$
$947$	42.5123	−	8.45622i	1.38146	−	0.274790i	0.829234	+	0.558901i	$0.188777\pi$
$948$	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	−0.625989	−	0.779832i	$-0.715304\pi$
$953$	11.3628	−	27.4322i	0.368077	−	0.888616i	0.994065	−	0.108784i	$-0.0346956\pi$
$954$	−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	−0.576205	−	0.817305i	$-0.695467\pi$
$967$	12.7234	−	30.7169i	0.409155	−	0.987788i	0.985361	−	0.170483i	$-0.0545329\pi$
$968$	−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	0.855095	−	0.518471i	$-0.173499\pi$
$971$	1.52250	+	2.27858i	0.0488594	+	0.0731232i	−0.806236	+	0.591594i	$0.798499\pi$
$972$	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	−0.981660	−	0.190642i	$-0.938943\pi$
$977$	−24.7249	+	24.7249i	−0.791018	+	0.791018i	0.190642	+	0.981660i	$0.438943\pi$
$978$	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	−0.240115	−	0.970744i	$-0.577185\pi$
$983$	8.66961	−	3.59107i	0.276517	−	0.114537i	0.516633	+	0.856207i	$0.327185\pi$
$984$	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	$0.213291\pi$
$991$			39.1011i			1.24209i	−0.783776	+	0.621044i	$0.786709\pi$
$992$	−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	−0.624898	−	0.780706i	$-0.714860\pi$
$997$	7.93159	−	39.8748i	0.251196	−	1.26285i	0.876094	−	0.482140i	$-0.160140\pi$
$998$	−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.5.4	✓	56
3.2	odd	2		576.2.bd.a.325.4		56
4.3	odd	2		256.2.i.a.113.3		56
8.3	odd	2		512.2.i.a.481.5		56
8.5	even	2		512.2.i.b.481.3		56
64.13	even	16	inner	64.2.i.a.13.4	yes	56
64.19	odd	16		512.2.i.a.33.5		56
64.45	even	16		512.2.i.b.33.3		56
64.51	odd	16		256.2.i.a.145.3		56
192.77	odd	16		576.2.bd.a.397.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.4	✓	56	1.1	even	1	trivial
64.2.i.a.13.4	yes	56	64.13	even	16	inner
256.2.i.a.113.3		56	4.3	odd	2
256.2.i.a.145.3		56	64.51	odd	16
512.2.i.a.33.5		56	64.19	odd	16
512.2.i.a.481.5		56	8.3	odd	2
512.2.i.b.33.3		56	64.45	even	16
512.2.i.b.481.3		56	8.5	even	2
576.2.bd.a.325.4		56	3.2	odd	2
576.2.bd.a.397.4		56	192.77	odd	16

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.0973444 + 1.41086i) q^{2} +(0.306211 + 0.204603i) q^{3} +(-1.98105 + 0.274678i) q^{4} +(1.42470 + 0.283390i) q^{5} +(-0.258859 + 0.451937i) q^{6} +(-0.666723 + 1.60961i) q^{7} +(-0.580376 - 2.76824i) q^{8} +(-1.09615 - 2.64634i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 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	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 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

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Database

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