LMFDB - Embedded newform 288.2.bf.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.749302 - 1.19939i) q^{2} +(0.475486 - 1.66551i) q^{3} +(-0.877093 + 1.79742i) q^{4} +(-0.384557 - 2.92100i) q^{5} +(-2.35388 + 0.677673i) q^{6} +(-0.163982 - 0.611989i) q^{7} +(2.81302 - 0.294828i) q^{8} +(-2.54783 - 1.58385i) q^{9} +O(q^{10})$	\(q+(-0.749302 - 1.19939i) q^{2} +(0.475486 - 1.66551i) q^{3} +(-0.877093 + 1.79742i) q^{4} +(-0.384557 - 2.92100i) q^{5} +(-2.35388 + 0.677673i) q^{6} +(-0.163982 - 0.611989i) q^{7} +(2.81302 - 0.294828i) q^{8} +(-2.54783 - 1.58385i) q^{9} +(-3.21528 + 2.64995i) q^{10} +(0.939959 - 0.721256i) q^{11} +(2.57657 + 2.31545i) q^{12} +(-1.82995 + 2.38483i) q^{13} +(-0.611144 + 0.655244i) q^{14} +(-5.04780 - 0.748413i) q^{15} +(-2.46142 - 3.15300i) q^{16} +2.02378 q^{17} +(0.00943085 + 4.24263i) q^{18} +(0.630742 - 0.261262i) q^{19} +(5.58755 + 1.87078i) q^{20} +(-1.09724 - 0.0178791i) q^{21} +(-1.56938 - 0.586943i) q^{22} +(-7.40463 - 1.98407i) q^{23} +(0.846512 - 4.82529i) q^{24} +(-3.55474 + 0.952490i) q^{25} +(4.23153 + 0.407867i) q^{26} +(-3.84937 + 3.49032i) q^{27} +(1.24383 + 0.242027i) q^{28} +(10.5335 + 1.38676i) q^{29} +(2.88469 + 6.61509i) q^{30} +(-2.48302 + 1.43357i) q^{31} +(-1.93735 + 5.31476i) q^{32} +(-0.754319 - 1.90845i) q^{33} +(-1.51642 - 2.42731i) q^{34} +(-1.72456 + 0.714337i) q^{35} +(5.08152 - 3.19032i) q^{36} +(1.08845 - 2.62775i) q^{37} +(-0.785972 - 0.560744i) q^{38} +(3.10184 + 4.18174i) q^{39} +(-1.94296 - 8.10346i) q^{40} +(0.258552 - 0.964929i) q^{41} +(0.800723 + 1.32942i) q^{42} +(1.27177 + 1.65740i) q^{43} +(0.471966 + 2.32211i) q^{44} +(-3.64664 + 8.05129i) q^{45} +(3.16863 + 10.3677i) q^{46} +(-8.68027 - 5.01155i) q^{47} +(-6.42172 + 2.60030i) q^{48} +(5.71454 - 3.29929i) q^{49} +(3.80598 + 3.54983i) q^{50} +(0.962280 - 3.37062i) q^{51} +(-2.68150 - 5.38089i) q^{52} +(4.08933 - 9.87251i) q^{53} +(7.07061 + 2.00160i) q^{54} +(-2.46826 - 2.46826i) q^{55} +(-0.641716 - 1.67319i) q^{56} +(-0.135225 - 1.17473i) q^{57} +(-6.22948 - 13.6729i) q^{58} +(9.92768 - 1.30700i) q^{59} +(5.77260 - 8.41658i) q^{60} +(-0.353716 + 2.68674i) q^{61} +(3.57994 + 1.90394i) q^{62} +(-0.551501 + 1.81896i) q^{63} +(7.82615 - 1.65871i) q^{64} +(7.66982 + 4.42817i) q^{65} +(-1.72378 + 2.33474i) q^{66} +(1.27668 - 1.66380i) q^{67} +(-1.77504 + 3.63758i) q^{68} +(-6.82527 + 11.3891i) q^{69} +(2.14899 + 1.53317i) q^{70} +(-6.54986 - 6.54986i) q^{71} +(-7.63405 - 3.70423i) q^{72} +(9.76835 - 9.76835i) q^{73} +(-3.96729 + 0.663499i) q^{74} +(-0.103851 + 6.37334i) q^{75} +(-0.0836227 + 1.36286i) q^{76} +(-0.595537 - 0.456972i) q^{77} +(2.69134 - 6.85372i) q^{78} +(1.39820 - 2.42176i) q^{79} +(-8.26337 + 8.40231i) q^{80} +(3.98284 + 8.07075i) q^{81} +(-1.35106 + 0.412918i) q^{82} +(14.3756 + 1.89259i) q^{83} +(0.994520 - 1.95652i) q^{84} +(-0.778260 - 5.91147i) q^{85} +(1.03494 - 2.76725i) q^{86} +(7.31817 - 16.8842i) q^{87} +(2.43148 - 2.30603i) q^{88} +(8.61931 - 8.61931i) q^{89} +(12.3891 - 1.65908i) q^{90} +(1.75957 + 0.728837i) q^{91} +(10.0607 - 11.5690i) q^{92} +(1.20698 + 4.81712i) q^{93} +(0.493313 + 14.1662i) q^{94} +(-1.00570 - 1.74193i) q^{95} +(7.93059 + 5.75376i) q^{96} +(-5.48891 + 9.50707i) q^{97} +(-8.23906 - 4.38182i) q^{98} +(-3.53721 + 0.348881i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.749302	−	1.19939i	−0.529837	−	0.848100i
$2$	−0.749302	−	1.19939i	−0.529837	−	0.848100i
$3$	0.475486	−	1.66551i	0.274522	−	0.961581i
$3$	0.475486	−	1.66551i	0.274522	−	0.961581i
$4$	−0.877093	+	1.79742i	−0.438546	+	0.898709i
$5$	−0.384557	−	2.92100i	−0.171979	−	1.30631i	−0.831879	−	0.554958i	$-0.812734\pi$
$5$	−0.384557	−	2.92100i	−0.171979	−	1.30631i	0.659899	−	0.751354i	$-0.270599\pi$
$6$	−2.35388	+	0.677673i	−0.960968	+	0.276659i
$7$	−0.163982	−	0.611989i	−0.0619794	−	0.231310i	0.927987	−	0.372612i	$-0.121538\pi$
$7$	−0.163982	−	0.611989i	−0.0619794	−	0.231310i	−0.989967	+	0.141302i	$0.954871\pi$
$8$	2.81302	−	0.294828i	0.994552	−	0.104238i
$9$	−2.54783	−	1.58385i	−0.849275	−	0.527950i
$10$	−3.21528	+	2.64995i	−1.01676	+	0.837987i
$11$	0.939959	−	0.721256i	0.283408	−	0.217467i	−0.457268	−	0.889329i	$-0.651172\pi$
$11$	0.939959	−	0.721256i	0.283408	−	0.217467i	0.740676	+	0.671862i	$0.234505\pi$
$12$	2.57657	+	2.31545i	0.743790	+	0.668413i
$13$	−1.82995	+	2.38483i	−0.507536	+	0.661433i	−0.974903	−	0.222630i	$-0.928536\pi$
$13$	−1.82995	+	2.38483i	−0.507536	+	0.661433i	0.467367	+	0.884063i	$0.345203\pi$
$14$	−0.611144	+	0.655244i	−0.163335	+	0.175121i
$15$	−5.04780	−	0.748413i	−1.30334	−	0.193239i
$16$	−2.46142	−	3.15300i	−0.615354	−	0.788251i
$17$	2.02378			0.490839			0.245420	−	0.969417i	$-0.421074\pi$
$17$	2.02378			0.490839			0.245420	+	0.969417i	$0.421074\pi$
$18$	0.00943085	+	4.24263i	0.00222287	+	0.999998i
$19$	0.630742	−	0.261262i	0.144702	−	0.0599376i	−0.309157	−	0.951011i	$-0.600047\pi$
$19$	0.630742	−	0.261262i	0.144702	−	0.0599376i	0.453859	+	0.891073i	$0.350047\pi$
$20$	5.58755	+	1.87078i	1.24941	+	0.418319i
$21$	−1.09724	−	0.0178791i	−0.239438	−	0.00390153i
$22$	−1.56938	−	0.586943i	−0.334594	−	0.125137i
$23$	−7.40463	−	1.98407i	−1.54397	−	0.413706i	−0.616426	−	0.787413i	$-0.711420\pi$
$23$	−7.40463	−	1.98407i	−1.54397	−	0.413706i	−0.927547	+	0.373707i	$0.878087\pi$
$24$	0.846512	−	4.82529i	0.172794	−	0.984958i
$25$	−3.55474	+	0.952490i	−0.710948	+	0.190498i
$26$	4.23153	+	0.407867i	0.829872	+	0.0799893i
$27$	−3.84937	+	3.49032i	−0.740811	+	0.671713i
$28$	1.24383	+	0.242027i	0.235061	+	0.0457389i
$29$	10.5335	+	1.38676i	1.95602	+	0.257514i	0.999425	−	0.0339178i	$-0.0107985\pi$
$29$	10.5335	+	1.38676i	1.95602	+	0.257514i	0.956591	+	0.291432i	$0.0941318\pi$
$30$	2.88469	+	6.61509i	0.526669	+	1.20774i
$31$	−2.48302	+	1.43357i	−0.445963	+	0.257477i	−0.706124	−	0.708089i	$-0.749558\pi$
$31$	−2.48302	+	1.43357i	−0.445963	+	0.257477i	0.260161	+	0.965565i	$0.416224\pi$
$32$	−1.93735	+	5.31476i	−0.342478	+	0.939526i
$33$	−0.754319	−	1.90845i	−0.131310	−	0.332219i
$34$	−1.51642	−	2.42731i	−0.260065	−	0.416281i
$35$	−1.72456	+	0.714337i	−0.291504	+	0.120745i
$36$	5.08152	−	3.19032i	0.846920	−	0.531720i
$37$	1.08845	−	2.62775i	0.178940	−	0.432000i	−0.808805	−	0.588078i	$-0.799885\pi$
$37$	1.08845	−	2.62775i	0.178940	−	0.432000i	0.987745	+	0.156078i	$0.0498850\pi$
$38$	−0.785972	−	0.560744i	−0.127502	−	0.0909647i
$39$	3.10184	+	4.18174i	0.496692	+	0.669614i
$40$	−1.94296	−	8.10346i	−0.307209	−	1.28127i
$41$	0.258552	−	0.964929i	0.0403790	−	0.150697i	−0.942793	−	0.333379i	$-0.891811\pi$
$41$	0.258552	−	0.964929i	0.0403790	−	0.150697i	0.983172	+	0.182682i	$0.0584779\pi$
$42$	0.800723	+	1.32942i	0.123554	+	0.205135i
$43$	1.27177	+	1.65740i	0.193943	+	0.252752i	0.880195	−	0.474612i	$-0.157412\pi$
$43$	1.27177	+	1.65740i	0.193943	+	0.252752i	−0.686252	+	0.727364i	$0.740745\pi$
$44$	0.471966	+	2.32211i	0.0711516	+	0.350071i
$45$	−3.64664	+	8.05129i	−0.543610	+	1.20021i
$46$	3.16863	+	10.3677i	0.467189	+	1.52864i
$47$	−8.68027	−	5.01155i	−1.26615	−	0.731010i	−0.291890	−	0.956452i	$-0.594284\pi$
$47$	−8.68027	−	5.01155i	−1.26615	−	0.731010i	−0.974257	+	0.225441i	$0.927618\pi$
$48$	−6.42172	+	2.60030i	−0.926895	+	0.375321i
$49$	5.71454	−	3.29929i	0.816362	−	0.471327i
$50$	3.80598	+	3.54983i	0.538247	+	0.502022i
$51$	0.962280	−	3.37062i	0.134746	−	0.471982i
$52$	−2.68150	−	5.38089i	−0.371858	−	0.746196i
$53$	4.08933	−	9.87251i	0.561712	−	1.35609i	−0.346683	−	0.937982i	$-0.612692\pi$
$53$	4.08933	−	9.87251i	0.561712	−	1.35609i	0.908396	−	0.418111i	$-0.137308\pi$
$54$	7.07061	+	2.00160i	0.962189	+	0.272384i
$55$	−2.46826	−	2.46826i	−0.332820	−	0.332820i
$56$	−0.641716	−	1.67319i	−0.0857529	−	0.223590i
$57$	−0.135225	−	1.17473i	−0.0179109	−	0.155597i
$58$	−6.22948	−	13.6729i	−0.817971	−	1.79534i
$59$	9.92768	−	1.30700i	1.29247	−	0.170157i	0.547249	−	0.836970i	$-0.315675\pi$
$59$	9.92768	−	1.30700i	1.29247	−	0.170157i	0.745225	+	0.666813i	$0.232342\pi$
$60$	5.77260	−	8.41658i	0.745239	−	1.08658i
$61$	−0.353716	+	2.68674i	−0.0452888	+	0.344002i	0.953767	+	0.300548i	$0.0971696\pi$
$61$	−0.353716	+	2.68674i	−0.0452888	+	0.344002i	−0.999055	+	0.0434542i	$0.986164\pi$
$62$	3.57994	+	1.90394i	0.454653	+	0.241800i
$63$	−0.551501	+	1.81896i	−0.0694827	+	0.229168i
$64$	7.82615	−	1.65871i	0.978269	−	0.207339i
$65$	7.66982	+	4.42817i	0.951324	+	0.549247i
$66$	−1.72378	+	2.33474i	−0.212182	+	0.287386i
$67$	1.27668	−	1.66380i	0.155972	−	0.203266i	−0.708831	−	0.705379i	$-0.750777\pi$
$67$	1.27668	−	1.66380i	0.155972	−	0.203266i	0.864802	+	0.502112i	$0.167444\pi$
$68$	−1.77504	+	3.63758i	−0.215256	+	0.441121i
$69$	−6.82527	+	11.3891i	−0.821666	+	1.37108i
$70$	2.14899	+	1.53317i	0.256853	+	0.183249i
$71$	−6.54986	−	6.54986i	−0.777325	−	0.777325i	0.202050	−	0.979375i	$-0.435240\pi$
$71$	−6.54986	−	6.54986i	−0.777325	−	0.777325i	−0.979375	+	0.202050i	$0.935240\pi$
$72$	−7.63405	−	3.70423i	−0.899681	−	0.436548i
$73$	9.76835	−	9.76835i	1.14330	−	1.14330i	0.155456	−	0.987843i	$-0.450315\pi$
$73$	9.76835	−	9.76835i	1.14330	−	1.14330i	0.987843	−	0.155456i	$-0.0496845\pi$
$74$	−3.96729	+	0.663499i	−0.461188	+	0.0771302i
$75$	−0.103851	+	6.37334i	−0.0119916	+	0.735930i
$76$	−0.0836227	+	1.36286i	−0.00959218	+	0.156330i
$77$	−0.595537	−	0.456972i	−0.0678677	−	0.0520767i
$78$	2.69134	−	6.85372i	0.304734	−	0.776030i
$79$	1.39820	−	2.42176i	0.157310	−	0.272469i	−0.776588	−	0.630009i	$-0.783051\pi$
$79$	1.39820	−	2.42176i	0.157310	−	0.272469i	0.933898	+	0.357540i	$0.116384\pi$
$80$	−8.26337	+	8.40231i	−0.923873	+	0.939407i
$81$	3.98284	+	8.07075i	0.442538	+	0.896750i
$82$	−1.35106	+	0.412918i	−0.149200	+	0.0455991i
$83$	14.3756	+	1.89259i	1.57793	+	0.207739i	0.868012	−	0.496544i	$-0.165398\pi$
$83$	14.3756	+	1.89259i	1.57793	+	0.207739i	0.709920	+	0.704282i	$0.248731\pi$
$84$	0.994520	−	1.95652i	0.108511	−	0.213474i
$85$	−0.778260	−	5.91147i	−0.0844141	−	0.641189i
$86$	1.03494	−	2.76725i	0.111601	−	0.298400i
$87$	7.31817	−	16.8842i	0.784590	−	1.81017i
$88$	2.43148	−	2.30603i	0.259196	−	0.245824i
$89$	8.61931	−	8.61931i	0.913645	−	0.913645i	−0.0829117	−	0.996557i	$-0.526422\pi$
$89$	8.61931	−	8.61931i	0.913645	−	0.913645i	0.996557	+	0.0829117i	$0.0264219\pi$
$90$	12.3891	−	1.65908i	1.30593	−	0.174883i
$91$	1.75957	+	0.728837i	0.184453	+	0.0764029i
$92$	10.0607	−	11.5690i	1.04891	−	1.20615i
$93$	1.20698	+	4.81712i	0.125158	+	0.499512i
$94$	0.493313	+	14.1662i	0.0508813	+	1.46113i
$95$	−1.00570	−	1.74193i	−0.103183	−	0.178718i
$96$	7.93059	+	5.75376i	0.809412	+	0.587241i
$97$	−5.48891	+	9.50707i	−0.557314	+	0.965297i	0.440405	+	0.897799i	$0.354835\pi$
$97$	−5.48891	+	9.50707i	−0.557314	+	0.965297i	−0.997719	+	0.0674974i	$0.978499\pi$
$98$	−8.23906	−	4.38182i	−0.832271	−	0.442630i
$99$	−3.53721	+	0.348881i	−0.355503	+	0.0350638i
$100$	1.40582	−	7.22477i	0.140582	−	0.722477i
$101$	−8.90279	+	6.83135i	−0.885861	+	0.679745i	−0.947982	−	0.318324i	$-0.896880\pi$
$101$	−8.90279	+	6.83135i	−0.885861	+	0.679745i	0.0621212	+	0.998069i	$0.480213\pi$
$102$	−4.76374	+	1.37146i	−0.471681	+	0.135795i
$103$	3.72337	+	0.997673i	0.366874	+	0.0983036i	0.437546	−	0.899196i	$-0.355848\pi$
$103$	3.72337	+	0.997673i	0.366874	+	0.0983036i	−0.0706720	+	0.997500i	$0.522514\pi$
$104$	−4.44456	+	7.24810i	−0.435825	+	0.710734i
$105$	0.369728	+	3.21193i	0.0360818	+	0.313452i
$106$	−14.9052	+	2.49278i	−1.44772	+	0.242120i
$107$	−16.6930	−	6.91445i	−1.61377	−	0.668445i	−0.620493	−	0.784212i	$-0.713067\pi$
$107$	−16.6930	−	6.91445i	−1.61377	−	0.668445i	−0.993276	+	0.115767i	$0.963067\pi$
$108$	−2.89731	−	9.98026i	−0.278794	−	0.960351i
$109$	5.19946	+	12.5526i	0.498018	+	1.20232i	0.950549	+	0.310574i	$0.100521\pi$
$109$	5.19946	+	12.5526i	0.498018	+	1.20232i	−0.452531	+	0.891749i	$0.649479\pi$
$110$	−1.11094	+	4.80988i	−0.105924	+	0.458604i
$111$	−3.85900	−	3.06228i	−0.366280	−	0.290659i
$112$	−1.52598	+	2.02340i	−0.144191	+	0.191193i
$113$	6.49957	+	11.2576i	0.611428	+	1.05902i	0.991000	+	0.133862i	$0.0427379\pi$
$113$	6.49957	+	11.2576i	0.611428	+	1.05902i	−0.379572	+	0.925162i	$0.623929\pi$
$114$	−1.30764	+	1.04242i	−0.122472	+	0.0976312i
$115$	−2.94795	+	22.3919i	−0.274898	+	2.08806i
$116$	−11.7314	+	17.7167i	−1.08923	+	1.64496i
$117$	8.43960	−	3.17778i	0.780241	−	0.293786i
$118$	−9.00644	−	10.9279i	−0.829110	−	1.00599i
$119$	−0.331864	−	1.23853i	−0.0304219	−	0.113536i
$120$	−14.4202	−	0.617065i	−1.31638	−	0.0563301i
$121$	−2.48370	+	9.26928i	−0.225791	+	0.842662i
$122$	3.48751	−	1.58894i	0.315744	−	0.143856i
$123$	−1.48416	−	0.889430i	−0.133822	−	0.0801972i
$124$	−0.398888	−	5.72039i	−0.0358212	−	0.513706i
$125$	−1.48810	−	3.59259i	−0.133100	−	0.321331i
$126$	2.59490	−	0.701487i	0.231172	−	0.0624934i
$127$			13.3962i			1.18872i	0.804200	+	0.594359i	$0.202594\pi$
$127$			13.3962i			1.18872i	−0.804200	+	0.594359i	$0.797406\pi$
$128$	−7.85361	−	8.14376i	−0.694167	−	0.719814i
$129$	3.36513	−	1.33007i	0.296283	−	0.117106i
$130$	−0.435887	−	12.5172i	−0.0382298	−	1.09783i
$131$	−8.55153	−	6.56182i	−0.747150	−	0.573309i	0.163472	−	0.986548i	$-0.447731\pi$
$131$	−8.55153	−	6.56182i	−0.747150	−	0.573309i	−0.910622	+	0.413239i	$0.864397\pi$
$132$	4.09190	+	0.318066i	0.356154	+	0.0276841i
$133$	−0.263320	−	0.343165i	−0.0228327	−	0.0297562i
$134$	−2.95218	−	0.284553i	−0.255029	−	0.0245816i
$135$	11.6755	+	9.90178i	1.00487	+	0.852210i
$136$	5.69294	−	0.596668i	0.488165	−	0.0511639i
$137$	−7.31178	+	1.95919i	−0.624687	+	0.167384i	−0.557258	−	0.830340i	$-0.688146\pi$
$137$	−7.31178	+	1.95919i	−0.624687	+	0.167384i	−0.0674296	+	0.997724i	$0.521480\pi$
$138$	18.7742	−	0.347662i	1.59816	−	0.0295949i
$139$	5.05465	−	0.665457i	0.428730	−	0.0564434i	0.0869262	−	0.996215i	$-0.472296\pi$
$139$	5.05465	−	0.665457i	0.428730	−	0.0564434i	0.341804	+	0.939771i	$0.388962\pi$
$140$	0.228639	−	3.72630i	0.0193236	−	0.314929i
$141$	−12.4741	+	12.0741i	−1.05051	+	1.01682i
$142$	−2.94804	+	12.7637i	−0.247394	+	1.07110i
$143$			3.56150i			0.297828i
$144$	1.27738	+	11.9318i	0.106448	+	0.994318i
$145$		−	31.3016i		−	2.59945i
$146$	−19.0355	−	4.39666i	−1.57539	−	0.363870i
$147$	−2.77781	−	11.0864i	−0.229110	−	0.914388i
$148$	3.76850	+	4.26118i	0.309769	+	0.350267i
$149$	−13.0422	+	1.71704i	−1.06846	+	0.140665i	−0.644186	−	0.764869i	$-0.722804\pi$
$149$	−13.0422	+	1.71704i	−1.06846	+	0.140665i	−0.424273	+	0.905534i	$0.639470\pi$
$150$	7.72196	−	4.65100i	0.630495	−	0.379752i
$151$	17.0816	−	4.57700i	1.39008	−	0.372471i	0.515308	−	0.857005i	$-0.327678\pi$
$151$	17.0816	−	4.57700i	1.39008	−	0.372471i	0.874772	+	0.484534i	$0.161011\pi$
$152$	1.69726	−	0.920895i	0.137666	−	0.0746945i
$153$	−5.15624	−	3.20537i	−0.416858	−	0.259139i
$154$	−0.101852	+	1.05669i	−0.00820747	+	0.0851508i
$155$	5.14232	+	6.70161i	0.413041	+	0.538286i
$156$	−10.2369	+	1.90753i	−0.819611	+	0.152724i
$157$	−6.72449	−	5.15988i	−0.536673	−	0.411804i	0.304547	−	0.952497i	$-0.401495\pi$
$157$	−6.72449	−	5.15988i	−0.536673	−	0.411804i	−0.841219	+	0.540694i	$0.818162\pi$
$158$	−3.95232	+	0.137632i	−0.314430	+	0.0109494i
$159$	−14.4983	−	11.5050i	−1.14979	−	0.912409i
$160$	16.2694	+	3.61517i	1.28621	+	0.285805i
$161$			4.85691i			0.382778i
$162$	6.69566	−	10.8244i	0.526061	−	0.850447i
$163$	5.14413	+	12.4190i	0.402920	+	0.972734i	0.986954	+	0.161005i	$0.0514734\pi$
$163$	5.14413	+	12.4190i	0.402920	+	0.972734i	−0.584034	+	0.811729i	$0.698527\pi$
$164$	1.50761	+	1.31106i	0.117724	+	0.102376i
$165$	−5.28452	+	2.93728i	−0.411399	+	0.228667i
$166$	−8.50174	−	18.6602i	−0.659863	−	1.44831i
$167$	0.592672	−	2.21188i	0.0458624	−	0.171161i	−0.939196	−	0.343382i	$-0.888428\pi$
$167$	0.592672	−	2.21188i	0.0458624	−	0.171161i	0.985058	+	0.172221i	$0.0550943\pi$
$168$	−3.09184	+	0.273204i	−0.238540	+	0.0210782i
$169$	1.02593	+	3.82881i	0.0789175	+	0.294524i
$170$	−6.50703	+	5.36292i	−0.499067	+	0.411317i
$171$	−2.02082	−	0.333351i	−0.154536	−	0.0254920i
$172$	−4.09451	+	0.832206i	−0.312203	+	0.0634551i
$173$	0.109832	−	0.834260i	0.00835041	−	0.0634276i	−0.986762	−	0.162173i	$-0.948150\pi$
$173$	0.109832	−	0.834260i	0.00835041	−	0.0634276i	0.995113	+	0.0987456i	$0.0314830\pi$
$174$	−25.7343	+	3.87398i	−1.95091	+	0.293686i
$175$	1.16583	+	2.01927i	0.0881282	+	0.152643i
$176$	−4.58775	−	1.18838i	−0.345815	−	0.0895777i
$177$	2.54365	−	17.1561i	0.191192	−	1.28953i
$178$	−16.7964	−	3.87948i	−1.25894	−	0.290780i
$179$	6.02840	+	14.5538i	0.450584	+	1.08781i	0.972101	+	0.234564i	$0.0753664\pi$
$179$	6.02840	+	14.5538i	0.450584	+	1.08781i	−0.521517	+	0.853241i	$0.674634\pi$
$180$	−11.2731	−	13.6163i	−0.840245	−	1.01490i
$181$	7.39901	+	3.06477i	0.549964	+	0.227802i	0.640322	−	0.768107i	$-0.278801\pi$
$181$	7.39901	+	3.06477i	0.549964	+	0.227802i	−0.0903579	+	0.995909i	$0.528801\pi$
$182$	−0.444285	−	2.65654i	−0.0329326	−	0.196916i
$183$	4.30660	+	1.86663i	0.318353	+	0.137985i
$184$	−21.4143	−	3.39812i	−1.57869	−	0.250513i
$185$	−8.09425	−	2.16885i	−0.595101	−	0.159457i
$186$	4.87324	−	5.05713i	0.357323	−	0.370807i
$187$	1.90227	−	1.45966i	0.139108	−	0.106741i
$188$	16.6213	−	11.2065i	1.21223	−	0.817315i
$189$	2.76727	+	1.78342i	0.201289	+	0.129725i
$190$	−1.33568	+	2.51146i	−0.0969007	+	0.182201i
$191$	−12.7388	+	22.0642i	−0.921746	+	1.59651i	−0.125033	+	0.992153i	$0.539904\pi$
$191$	−12.7388	+	22.0642i	−0.921746	+	1.59651i	−0.796713	+	0.604358i	$0.793430\pi$
$192$	0.958624	−	13.8232i	0.0691827	−	0.997604i
$193$	−8.34520	−	14.4543i	−0.600701	−	1.04044i	−0.992715	−	0.120485i	$-0.961555\pi$
$193$	−8.34520	−	14.4543i	−0.600701	−	1.04044i	0.392014	−	0.919959i	$-0.371778\pi$
$194$	15.5156	−	0.540301i	1.11395	−	0.0387913i
$195$	11.0220	−	10.6686i	0.789305	−	0.763994i
$196$	0.918020	+	13.1652i	0.0655728	+	0.940371i
$197$	13.2585	+	5.49187i	0.944632	+	0.391279i	0.801211	−	0.598382i	$-0.204190\pi$
$197$	13.2585	+	5.49187i	0.944632	+	0.391279i	0.143421	+	0.989662i	$0.454190\pi$
$198$	3.06889	+	3.98110i	0.218096	+	0.282924i
$199$	−5.46648	+	5.46648i	−0.387508	+	0.387508i	−0.873798	−	0.486289i	$-0.838350\pi$
$199$	−5.46648	+	5.46648i	−0.387508	+	0.387508i	0.486289	+	0.873798i	$0.338350\pi$
$200$	−9.71873	+	3.72741i	−0.687218	+	0.263568i
$201$	−2.16403	−	2.91744i	−0.152639	−	0.205780i
$202$	14.8644	+	5.55921i	1.04585	+	0.391145i
$203$	−0.878619	−	6.67377i	−0.0616669	−	0.468407i
$204$	5.21441	+	4.68597i	0.365081	+	0.328083i
$205$	−2.91799	−	0.384160i	−0.203801	−	0.0268309i
$206$	−1.59332	−	5.21334i	−0.111012	−	0.363231i
$207$	15.7233	+	16.7829i	1.09284	+	1.16649i
$208$	12.0236	−	0.100239i	0.833689	−	0.00695029i
$209$	0.404435	−	0.700502i	0.0279753	−	0.0484547i
$210$	3.57533	−	2.85015i	0.246721	−	0.196679i
$211$	15.4182	+	11.8308i	1.06143	+	0.814467i	0.983212	−	0.182469i	$-0.0584090\pi$
$211$	15.4182	+	11.8308i	1.06143	+	0.814467i	0.0782220	+	0.996936i	$0.475076\pi$
$212$	14.1583	+	16.0093i	0.972396	+	1.09953i
$213$	−14.0232	+	7.79447i	−0.960853	+	0.534068i
$214$	4.21492	+	25.2024i	0.288126	+	1.72280i
$215$	4.35221	−	4.35221i	0.296818	−	0.296818i
$216$	−9.79930	+	10.9532i	−0.666758	+	0.745274i
$217$	1.28450	+	1.28450i	0.0871975	+	0.0871975i
$218$	11.1596	−	15.6419i	0.755821	−	1.05940i
$219$	−11.6245	−	20.9140i	−0.785513	−	1.41323i
$220$	6.60138	−	2.27160i	0.445065	−	0.153151i
$221$	−3.70341	+	4.82638i	−0.249118	+	0.324657i
$222$	−0.781329	+	6.92304i	−0.0524393	+	0.464644i
$223$	−3.78187	−	2.18347i	−0.253253	−	0.146216i	0.368000	−	0.929826i	$-0.380043\pi$
$223$	−3.78187	−	2.18347i	−0.253253	−	0.146216i	−0.621253	+	0.783610i	$0.713376\pi$
$224$	3.57027	+	0.314112i	0.238548	+	0.0209875i
$225$	10.5655	+	3.20340i	0.704364	+	0.213560i
$226$	8.63214	−	16.2309i	0.574201	−	1.07966i
$227$	−1.58889	+	12.0688i	−0.105458	+	0.801037i	0.854215	+	0.519920i	$0.174038\pi$
$227$	−1.58889	+	12.0688i	−0.105458	+	0.801037i	−0.959674	+	0.281117i	$0.909295\pi$
$228$	2.23009	+	0.787294i	0.147691	+	0.0521398i
$229$	29.1533	−	3.83810i	1.92650	−	0.253629i	0.932344	−	0.361572i	$-0.117760\pi$
$229$	29.1533	−	3.83810i	1.92650	−	0.253629i	0.994157	+	0.107944i	$0.0344266\pi$
$230$	29.0657	−	13.2426i	1.91653	−	0.873189i
$231$	−1.04426	+	0.774587i	−0.0687072	+	0.0509641i
$232$	30.0397	+	0.795411i	1.97220	+	0.0522213i
$233$	−4.41732	−	4.41732i	−0.289388	−	0.289388i	0.547450	−	0.836838i	$-0.315599\pi$
$233$	−4.41732	−	4.41732i	−0.289388	−	0.289388i	−0.836838	+	0.547450i	$0.815599\pi$
$234$	−10.1352	−	7.74129i	−0.662560	−	0.506064i
$235$	−11.3007	+	27.2823i	−0.737176	+	1.77970i
$236$	−6.35827	+	18.9905i	−0.413888	+	1.23618i
$237$	−3.36863	−	3.48023i	−0.218816	−	0.226065i
$238$	−1.23682	+	1.32607i	−0.0801713	+	0.0859564i
$239$	−0.591936	+	0.341754i	−0.0382891	+	0.0221062i	−0.519022	−	0.854761i	$-0.673704\pi$
$239$	−0.591936	+	0.341754i	−0.0382891	+	0.0221062i	0.480733	+	0.876867i	$0.340371\pi$
$240$	10.0650	+	17.7579i	0.649692	+	1.14627i
$241$	−5.86601	−	3.38674i	−0.377863	−	0.218159i	0.299025	−	0.954245i	$-0.403339\pi$
$241$	−5.86601	−	3.38674i	−0.377863	−	0.218159i	−0.676888	+	0.736086i	$0.736672\pi$
$242$	12.9786	−	3.96656i	0.834294	−	0.254980i
$243$	15.3357	−	2.79592i	0.983784	−	0.179358i
$244$	−4.51896	−	2.99230i	−0.289297	−	0.191562i
$245$	−11.8348	−	15.4234i	−0.756098	−	0.985365i
$246$	0.0453053	+	2.44654i	0.00288856	+	0.155986i
$247$	−0.531158	+	1.98231i	−0.0337968	+	0.126131i
$248$	−6.56212	+	4.76472i	−0.416695	+	0.302560i
$249$	9.98753	−	23.0428i	0.632934	−	1.46028i
$250$	−3.19389	+	4.47675i	−0.202000	+	0.283135i
$251$	6.32538	−	15.2708i	0.399254	−	0.963886i	−0.588589	−	0.808433i	$-0.700316\pi$
$251$	6.32538	−	15.2708i	0.399254	−	0.963886i	0.987843	−	0.155453i	$-0.0496837\pi$
$252$	−2.78572	−	2.58668i	−0.175484	−	0.162945i
$253$	−8.39107	+	3.47569i	−0.527542	+	0.218515i
$254$	16.0673	−	10.0378i	1.00815	−	0.629827i
$255$	−10.2156	−	1.51462i	−0.639729	−	0.0948494i
$256$	−3.88286	+	15.5217i	−0.242679	+	0.970107i
$257$	12.0627	−	6.96440i	0.752451	−	0.434428i	−0.0741281	−	0.997249i	$-0.523617\pi$
$257$	12.0627	−	6.96440i	0.752451	−	0.434428i	0.826579	+	0.562821i	$0.190284\pi$
$258$	−4.11678	−	3.03949i	−0.256299	−	0.189230i
$259$	−1.78664	−	0.235216i	−0.111017	−	0.0146156i
$260$	−14.6864	+	9.90194i	−0.910813	+	0.614092i
$261$	−24.6410	−	20.2167i	−1.52524	−	1.25138i
$262$	−1.46253	+	15.1734i	−0.0903553	+	0.937418i
$263$	−7.98028	+	2.13831i	−0.492085	+	0.131854i	−0.496324	−	0.868137i	$-0.665317\pi$
$263$	−7.98028	+	2.13831i	−0.492085	+	0.131854i	0.00423929	+	0.999991i	$0.498651\pi$
$264$	−2.68458	−	5.14612i	−0.165225	−	0.316722i
$265$	−30.4102	−	8.14839i	−1.86808	−	0.500552i
$266$	−0.214284	+	0.572958i	−0.0131386	+	0.0351303i
$267$	−10.2572	−	18.4539i	−0.627728	−	1.12936i
$268$	1.87078	+	3.75404i	0.114276	+	0.229315i
$269$	18.6408	−	7.72126i	1.13655	−	0.470773i	0.266546	−	0.963822i	$-0.414118\pi$
$269$	18.6408	−	7.72126i	1.13655	−	0.470773i	0.870002	+	0.493049i	$0.164118\pi$
$270$	3.12763	−	21.4230i	0.190342	−	1.30376i
$271$	12.7899			0.776930			0.388465	−	0.921464i	$-0.373005\pi$
$271$	12.7899			0.776930			0.388465	+	0.921464i	$0.373005\pi$
$272$	−4.98137	−	6.38099i	−0.302040	−	0.386904i
$273$	2.05053	−	2.58402i	0.124104	−	0.156392i
$274$	7.82857	+	7.30168i	0.472941	+	0.441111i
$275$	−2.65432	+	3.45918i	−0.160062	+	0.208596i
$276$	−14.4845	−	22.2571i	−0.871865	−	1.33972i
$277$	4.25340	−	3.26375i	0.255562	−	0.196100i	−0.473032	−	0.881045i	$-0.656841\pi$
$277$	4.25340	−	3.26375i	0.255562	−	0.196100i	0.728594	+	0.684945i	$0.240174\pi$
$278$	−4.58561	−	5.56389i	−0.275026	−	0.333700i
$279$	8.59685	+	0.280238i	0.514680	+	0.0167774i
$280$	−4.64062	+	2.51789i	−0.277330	+	0.150473i
$281$	1.08798	+	4.06041i	0.0649037	+	0.242224i	0.990755	−	0.135664i	$-0.0433169\pi$
$281$	1.08798	+	4.06041i	0.0649037	+	0.242224i	−0.925851	+	0.377889i	$0.876650\pi$
$282$	23.8285	+	5.91423i	1.41897	+	0.352187i
$283$	−2.05451	−	15.6056i	−0.122128	−	0.927654i	−0.937322	−	0.348466i	$-0.886703\pi$
$283$	−2.05451	−	15.6056i	−0.122128	−	0.927654i	0.815194	−	0.579189i	$-0.196631\pi$
$284$	17.5177	−	6.02799i	1.03948	−	0.357695i
$285$	−3.37939	+	0.846743i	−0.200178	+	0.0501567i
$286$	4.27164	−	2.66864i	0.252588	−	0.157800i
$287$	−0.632924			−0.0373603
$288$	13.3538	−	10.4726i	0.786881	−	0.617105i
$289$	−12.9043			−0.759077
$290$	−37.5429	+	23.4543i	−2.20460	+	1.37729i
$291$	13.2242	+	13.6623i	0.775216	+	0.800898i
$292$	8.99005	+	26.1255i	0.526103	+	1.52888i
$293$	0.831252	+	6.31399i	0.0485623	+	0.368867i	0.998420	+	0.0561857i	$0.0178939\pi$
$293$	0.831252	+	6.31399i	0.0485623	+	0.368867i	−0.949858	+	0.312681i	$0.898773\pi$
$294$	−11.2155	+	11.6387i	−0.654102	+	0.678784i
$295$	−7.63552	−	28.4962i	−0.444557	−	1.65911i
$296$	2.28710	−	7.71283i	0.132935	−	0.448299i
$297$	−1.10083	+	6.05714i	−0.0638767	+	0.351471i
$298$	11.8320	+	14.3562i	0.685407	+	0.831630i
$299$	18.2817	−	14.0281i	1.05726	−	0.811264i
$300$	−11.3645	−	5.77667i	−0.656127	−	0.333516i
$301$	0.805766	−	1.05009i	0.0464436	−	0.0605265i
$302$	−18.2889	−	17.0580i	−1.05241	−	0.981578i
$303$	7.14451	+	18.0759i	0.410442	+	1.03843i
$304$	−2.37628	−	1.34566i	−0.136289	−	0.0771787i
$305$	7.98401			0.457163
$306$	0.0190860	+	8.58616i	0.00109107	+	0.490838i
$307$	8.25442	−	3.41909i	0.471105	−	0.195138i	−0.134484	−	0.990916i	$-0.542938\pi$
$307$	8.25442	−	3.41909i	0.471105	−	0.195138i	0.605589	+	0.795778i	$0.292938\pi$
$308$	1.34371	−	0.669622i	0.0765650	−	0.0381552i
$309$	3.43204	−	5.72691i	0.195242	−	0.325793i
$310$	4.18471	−	11.1892i	0.237676	−	0.635504i
$311$	−16.2361	−	4.35044i	−0.920663	−	0.246691i	−0.232794	−	0.972526i	$-0.574787\pi$
$311$	−16.2361	−	4.35044i	−0.920663	−	0.246691i	−0.687869	+	0.725835i	$0.741454\pi$
$312$	9.95843	+	10.8488i	0.563785	+	0.614193i
$313$	−23.3646	+	6.26053i	−1.32065	+	0.353866i	−0.849220	−	0.528040i	$-0.822927\pi$
$313$	−23.3646	+	6.26053i	−1.32065	+	0.353866i	−0.471426	+	0.881906i	$0.656260\pi$
$314$	−1.15006	+	11.9316i	−0.0649016	+	0.673341i
$315$	5.52528	+	0.911441i	0.311315	+	0.0513539i
$316$	3.12656	+	4.63727i	0.175883	+	0.260867i
$317$	13.8447	+	1.82269i	0.777597	+	0.102373i	0.508870	−	0.860844i	$-0.330063\pi$
$317$	13.8447	+	1.82269i	0.777597	+	0.102373i	0.268728	+	0.963216i	$0.413397\pi$
$318$	−2.93546	+	26.0099i	−0.164613	+	1.45857i
$319$	10.9012	−	6.29383i	0.610352	−	0.352387i
$320$	−7.85471	−	22.2223i	−0.439092	−	1.24227i
$321$	−19.4533	+	24.5145i	−1.08578	+	1.36827i
$322$	5.82534	−	3.63929i	0.324634	−	0.202810i
$323$	1.27648	−	0.528737i	0.0710255	−	0.0294197i
$324$	−17.9998	+	0.0800232i	−0.999990	+	0.00444573i
$325$	4.23345	−	10.2205i	0.234830	−	0.566929i
$326$	11.0408	−	15.4754i	0.611494	−	0.857106i
$327$	23.3787	−	2.69115i	1.29285	−	0.148821i
$328$	0.442823	−	2.79059i	0.0244508	−	0.154085i
$329$	−1.64361	+	6.13403i	−0.0906151	+	0.338180i
$330$	7.48266	+	4.13732i	0.411907	+	0.227752i
$331$	−11.8418	−	15.4325i	−0.650884	−	0.848249i	0.345027	−	0.938593i	$-0.387870\pi$
$331$	−11.8418	−	15.4325i	−0.650884	−	0.848249i	−0.995911	+	0.0903444i	$0.971203\pi$
$332$	−16.0105	+	24.1790i	−0.878693	+	1.32700i
$333$	−6.93515	+	4.97112i	−0.380044	+	0.272416i
$334$	−3.09701	+	0.946521i	−0.169461	+	0.0517913i
$335$	−5.35093	−	3.08936i	−0.292353	−	0.168790i
$336$	2.64440	+	3.50362i	0.144264	+	0.191138i
$337$	−1.34414	+	0.776042i	−0.0732202	+	0.0422737i	−0.536163	−	0.844114i	$-0.680127\pi$
$337$	−1.34414	+	0.776042i	−0.0732202	+	0.0422737i	0.462943	+	0.886388i	$0.346793\pi$
$338$	3.82353	−	4.09943i	0.207972	−	0.222979i
$339$	21.8400	−	5.47225i	1.18619	−	0.297212i
$340$	11.3080	+	3.78605i	0.613262	+	0.205327i
$341$	−1.29996	+	3.13839i	−0.0703969	+	0.169953i
$342$	1.11439	+	2.67354i	0.0602591	+	0.144569i
$343$	−6.09226	−	6.09226i	−0.328951	−	0.328951i
$344$	4.06617	+	4.28736i	0.219233	+	0.231159i
$345$	35.8922	+	15.5569i	1.93237	+	0.837555i
$346$	−1.08290	+	0.493381i	−0.0582173	+	0.0265243i
$347$	−9.56611	+	1.25940i	−0.513535	+	0.0676082i	−0.382841	−	0.923814i	$-0.625054\pi$
$347$	−9.56611	+	1.25940i	−0.513535	+	0.0676082i	−0.130695	+	0.991423i	$0.541721\pi$
$348$	23.9292	+	27.9628i	1.28274	+	1.49896i
$349$	−1.16021	+	8.81265i	−0.0621045	+	0.471730i	0.931928	+	0.362644i	$0.118126\pi$
$349$	−1.16021	+	8.81265i	−0.0621045	+	0.471730i	−0.994032	+	0.109086i	$0.965207\pi$
$350$	1.54835	−	2.91133i	0.0827625	−	0.155617i
$351$	−1.27970	−	15.5672i	−0.0683053	−	0.830916i
$352$	2.01227	+	6.39298i	0.107254	+	0.340747i
$353$	4.69231	+	2.70910i	0.249746	+	0.144191i	0.619648	−	0.784880i	$-0.287275\pi$
$353$	4.69231	+	2.70910i	0.249746	+	0.144191i	−0.369902	+	0.929071i	$0.620609\pi$
$354$	−22.4829	+	9.80425i	−1.19495	+	0.521090i
$355$	−16.6133	+	21.6509i	−0.881745	+	1.14911i
$356$	7.93256	+	23.0524i	0.420425	+	1.22178i
$357$	−2.22058	−	0.0361833i	−0.117526	−	0.00191503i
$358$	12.9387	−	18.1357i	0.683832	−	0.958499i
$359$	11.7607	+	11.7607i	0.620705	+	0.620705i	0.945712	−	0.325007i	$-0.105367\pi$
$359$	11.7607	+	11.7607i	0.620705	+	0.620705i	−0.325007	+	0.945712i	$0.605367\pi$
$360$	−7.88433	+	23.7236i	−0.415541	+	1.25034i
$361$	−13.1055	+	13.1055i	−0.689761	+	0.689761i
$362$	−1.86822	−	11.1708i	−0.0981917	−	0.587122i
$363$	14.2571	+	8.54403i	0.748303	+	0.448445i
$364$	−2.85333	+	2.52342i	−0.149555	+	0.132263i
$365$	−32.2898	−	24.7769i	−1.69013	−	1.29688i
$366$	−0.988126	−	6.56398i	−0.0516502	−	0.343105i
$367$	13.5355	−	23.4442i	0.706547	−	1.22378i	−0.259583	−	0.965721i	$-0.583585\pi$
$367$	13.5355	−	23.4442i	0.706547	−	1.22378i	0.966130	−	0.258055i	$-0.0830816\pi$
$368$	11.9701	+	28.2304i	0.623986	+	1.47161i
$369$	−2.18705	+	2.04896i	−0.113853	+	0.106665i
$370$	3.46373	+	11.3333i	0.180071	+	0.589191i
$371$	−6.71245	−	0.883710i	−0.348493	−	0.0458799i
$372$	−9.71701	−	2.05561i	−0.503804	−	0.106579i
$373$	0.242150	+	1.83932i	0.0125381	+	0.0952361i	0.996570	−	0.0827575i	$-0.0263727\pi$
$373$	0.242150	+	1.83932i	0.0125381	+	0.0952361i	−0.984032	+	0.177994i	$0.943039\pi$
$374$	−3.17609	−	1.18784i	−0.164232	−	0.0614219i
$375$	−6.69105	+	0.770214i	−0.345524	+	0.0397737i
$376$	−25.8953	−	11.5384i	−1.33545	−	0.595048i
$377$	−22.5829	+	22.5829i	−1.16308	+	1.16308i
$378$	0.0655064	−	4.65537i	0.00336928	−	0.239446i
$379$	−27.4416	−	11.3667i	−1.40958	−	0.583867i	−0.457359	−	0.889282i	$-0.651205\pi$
$379$	−27.4416	−	11.3667i	−1.40958	−	0.583867i	−0.952219	+	0.305415i	$0.901205\pi$
$380$	4.01307	−	0.279834i	0.205866	−	0.0143552i
$381$	22.3114	+	6.36969i	1.14305	+	0.326329i
$382$	36.0089	−	1.25394i	1.84237	−	0.0641573i
$383$	12.1738	+	21.0857i	0.622055	+	1.07743i	0.989103	+	0.147228i	$0.0470352\pi$
$383$	12.1738	+	21.0857i	0.622055	+	1.07743i	−0.367048	+	0.930202i	$0.619631\pi$
$384$	−17.2978	+	9.20799i	−0.882723	+	0.469893i
$385$	−1.10580	+	1.91530i	−0.0563566	+	0.0976125i
$386$	−11.0833	+	20.8398i	−0.564127	+	1.06072i
$387$	−0.615172	−	6.23707i	−0.0312709	−	0.317048i
$388$	−12.2739	−	18.2044i	−0.623112	−	0.924190i
$389$	2.81058	−	2.15664i	0.142502	−	0.109346i	−0.535050	−	0.844820i	$-0.679707\pi$
$389$	2.81058	−	2.15664i	0.142502	−	0.109346i	0.677552	+	0.735474i	$0.263041\pi$
$390$	−21.0547	−	5.22577i	−1.06615	−	0.264617i
$391$	−14.9854	−	4.01532i	−0.757842	−	0.203063i
$392$	15.1024	−	10.9658i	0.762785	−	0.553855i
$393$	−14.9949	+	11.1226i	−0.756392	+	0.561060i
$394$	−3.34774	−	20.0173i	−0.168657	−	1.00846i
$395$	−7.61166	−	3.15285i	−0.382984	−	0.158637i
$396$	2.47538	−	6.66385i	0.124393	−	0.334871i
$397$	−3.99497	−	9.64470i	−0.200502	−	0.484054i	0.791364	−	0.611346i	$-0.209372\pi$
$397$	−3.99497	−	9.64470i	−0.200502	−	0.484054i	−0.991865	+	0.127292i	$0.959372\pi$
$398$	10.6525	+	2.46042i	0.533962	+	0.123330i
$399$	−0.696749	+	0.275391i	−0.0348811	+	0.0137868i
$400$	11.7529	+	8.86363i	0.587645	+	0.443182i
$401$	17.8921	+	30.9900i	0.893488	+	1.54757i	0.835664	+	0.549241i	$0.185083\pi$
$401$	17.8921	+	30.9900i	0.893488	+	1.54757i	0.0578241	+	0.998327i	$0.481584\pi$
$402$	−1.87764	+	4.78157i	−0.0936484	+	0.238483i
$403$	1.12496	−	8.54493i	0.0560383	−	0.425653i
$404$	−4.47021	−	21.9938i	−0.222401	−	1.09423i
$405$	22.0430	−	14.7375i	1.09533	−	0.732314i
$406$	−7.34613	+	6.05448i	−0.364582	+	0.300479i
$407$	−0.872183	−	3.25503i	−0.0432325	−	0.161346i
$408$	1.71316	−	9.76533i	0.0848139	−	0.483456i
$409$	−3.59107	+	13.4021i	−0.177567	+	0.662689i	0.818533	+	0.574459i	$0.194788\pi$
$409$	−3.59107	+	13.4021i	−0.177567	+	0.662689i	−0.996100	+	0.0882297i	$0.971879\pi$
$410$	1.72569	+	3.78767i	0.0852260	+	0.187060i
$411$	−0.213611	+	13.1094i	−0.0105367	+	0.646638i
$412$	−5.05897	+	5.81739i	−0.249238	+	0.286602i
$413$	−2.42783	−	5.86131i	−0.119466	−	0.288416i
$414$	8.34782	−	31.4338i	0.410273	−	1.54489i
$415$		−	42.7191i		−	2.09700i
$416$	−9.12956	−	14.3460i	−0.447614	−	0.703369i
$417$	1.29509	−	8.73497i	0.0634209	−	0.427753i
$418$	−1.14322	+	0.0398106i	−0.0559168	+	0.00194720i
$419$	−15.3297	−	11.7629i	−0.748907	−	0.574657i	0.162233	−	0.986752i	$-0.448130\pi$
$419$	−15.3297	−	11.7629i	−0.748907	−	0.574657i	−0.911141	+	0.412096i	$0.864797\pi$
$420$	−6.09746	−	2.15260i	−0.297525	−	0.105036i
$421$	4.80753	+	6.26530i	0.234305	+	0.305352i	0.895676	−	0.444706i	$-0.146692\pi$
$421$	4.80753	+	6.26530i	0.234305	+	0.305352i	−0.661372	+	0.750058i	$0.730025\pi$
$422$	2.63691	−	27.3574i	0.128363	−	1.33174i
$423$	14.1783	+	26.5168i	0.689371	+	1.28929i
$424$	8.59266	−	28.9772i	0.417297	−	1.40726i
$425$	−7.19402	+	1.92763i	−0.348961	+	0.0935038i
$426$	19.8562	+	10.9789i	0.962038	+	0.531931i
$427$	1.70226	−	0.224107i	0.0823782	−	0.0108453i
$428$	27.0694	−	23.9396i	1.30845	−	1.15716i
$429$	5.93171	+	1.69344i	0.286385	+	0.0817602i
$430$	−8.48114	−	1.95890i	−0.408997	−	0.0944664i
$431$			11.7304i			0.565033i	0.959263	+	0.282516i	$0.0911691\pi$
$431$			11.7304i			0.565033i	−0.959263	+	0.282516i	$0.908831\pi$
$432$	20.4799	+	3.54593i	0.985340	+	0.170604i
$433$		−	5.97268i		−	0.287029i	−0.989648	−	0.143514i	$-0.954160\pi$
$433$		−	5.97268i		−	0.287029i	0.989648	−	0.143514i	$-0.0458403\pi$
$434$	0.578143	−	2.50310i	0.0277518	−	0.120153i
$435$	−52.1330	−	14.8835i	−2.49959	−	0.713607i
$436$	−27.1227	−	1.66421i	−1.29894	−	0.0797010i
$437$	−5.18877	+	0.683115i	−0.248213	+	0.0326778i
$438$	−16.3738	+	29.6133i	−0.782370	+	1.41498i
$439$	8.97073	−	2.40370i	0.428150	−	0.114722i	−0.0383077	−	0.999266i	$-0.512197\pi$
$439$	8.97073	−	2.40370i	0.428150	−	0.114722i	0.466458	+	0.884544i	$0.345530\pi$
$440$	−7.67097	−	6.21554i	−0.365699	−	0.296314i
$441$	−19.7852	−	0.644954i	−0.942154	−	0.0307121i
$442$	8.56370	+	0.825434i	0.407334	+	0.0392619i
$443$	15.2830	+	19.9172i	0.726116	+	0.946293i	0.999880	−	0.0155039i	$-0.00493523\pi$
$443$	15.2830	+	19.9172i	0.726116	+	0.946293i	−0.273764	+	0.961797i	$0.588269\pi$
$444$	8.88890	−	4.25032i	0.421849	−	0.201711i
$445$	−28.4916	−	21.8624i	−1.35063	−	1.03638i
$446$	0.214930	+	6.17203i	0.0101772	+	0.292254i
$447$	−3.34164	+	22.5383i	−0.158054	+	1.06603i
$448$	−2.29846	−	4.51752i	−0.108592	−	0.213433i
$449$			11.5900i			0.546968i	0.961877	+	0.273484i	$0.0881760\pi$
$449$			11.5900i			0.546968i	−0.961877	+	0.273484i	$0.911824\pi$
$450$	−4.07459	−	15.0725i	−0.192078	−	0.710523i
$451$	−0.452932	−	1.09348i	−0.0213278	−	0.0514898i
$452$	−25.9353	+	1.80849i	−1.21989	+	0.0850642i
$453$	0.499034	−	30.6258i	0.0234466	−	1.43893i
$454$	15.6658	−	7.13749i	0.735235	−	0.334979i
$455$	1.45228	−	5.41998i	0.0680840	−	0.254093i
$456$	−0.726733	−	3.26467i	−0.0340324	−	0.152882i
$457$	−6.56261	−	24.4920i	−0.306986	−	1.14569i	−0.931222	−	0.364452i	$-0.881256\pi$
$457$	−6.56261	−	24.4920i	−0.306986	−	1.14569i	0.624236	−	0.781236i	$-0.285410\pi$
$458$	−26.4480	−	32.0903i	−1.23583	−	1.49948i
$459$	−7.79028	+	7.06365i	−0.363619	+	0.329703i
$460$	−37.6620	−	24.9385i	−1.75600	−	1.16276i
$461$	1.43061	−	10.8666i	0.0666301	−	0.506106i	−0.925292	−	0.379256i	$-0.876180\pi$
$461$	1.43061	−	10.8666i	0.0666301	−	0.506106i	0.991922	−	0.126850i	$-0.0404867\pi$
$462$	1.71150	+	0.672078i	0.0796262	+	0.0312679i
$463$	−0.589636	−	1.02128i	−0.0274027	−	0.0474629i	0.851999	−	0.523544i	$-0.175390\pi$
$463$	−0.589636	−	1.02128i	−0.0274027	−	0.0474629i	−0.879402	+	0.476081i	$0.842057\pi$
$464$	−21.5548	−	36.6255i	−1.00066	−	1.70029i
$465$	13.6067	−	5.37806i	0.630994	−	0.249401i
$466$	−1.98820	+	8.60801i	−0.0921016	+	0.398759i
$467$	−1.82869	−	4.41486i	−0.0846219	−	0.204295i	0.875904	−	0.482485i	$-0.160266\pi$
$467$	−1.82869	−	4.41486i	−0.0846219	−	0.204295i	−0.960526	+	0.278190i	$0.910266\pi$
$468$	−1.69052	+	17.9567i	−0.0781444	+	0.830048i
$469$	−1.22758	−	0.508482i	−0.0566845	−	0.0234795i
$470$	41.1899	−	6.88869i	1.89995	−	0.317752i
$471$	−11.7912	+	8.74624i	−0.543311	+	0.403005i
$472$	27.5414	−	6.60359i	1.26770	−	0.303955i
$473$	2.39083	+	0.640620i	0.109930	+	0.0294557i
$474$	−1.65005	+	6.64807i	−0.0757892	+	0.305356i
$475$	−1.99327	+	1.52949i	−0.0914577	+	0.0701780i
$476$	2.51723	+	0.489810i	0.115377	+	0.0224504i
$477$	−26.0555	+	18.6766i	−1.19300	+	0.855141i
$478$	0.853437	+	0.453887i	0.0390353	+	0.0207603i
$479$	−6.23270	+	10.7954i	−0.284779	+	0.493252i	−0.972556	−	0.232670i	$-0.925254\pi$
$479$	−6.23270	+	10.7954i	−0.284779	+	0.493252i	0.687776	+	0.725923i	$0.258587\pi$
$480$	13.7570	−	25.3779i	0.627918	−	1.15834i
$481$	4.27494	+	7.40442i	0.194921	+	0.337612i
$482$	0.333374	+	9.57335i	0.0151848	+	0.436054i
$483$	8.08921	+	2.30939i	0.368072	+	0.105081i
$484$	−14.4823	−	12.5943i	−0.658288	−	0.572466i
$485$	29.8810	+	12.3771i	1.35682	+	0.562015i
$486$	−14.8445	−	16.2985i	−0.673358	−	0.739316i
$487$	−18.2953	+	18.2953i	−0.829039	+	0.829039i	−0.987384	−	0.158345i	$-0.949384\pi$
$487$	−18.2953	+	18.2953i	−0.829039	+	0.829039i	0.158345	+	0.987384i	$0.449384\pi$
$488$	−0.202883	+	7.66215i	−0.00918410	+	0.346849i
$489$	23.1299	−	2.66251i	1.04597	−	0.120403i
$490$	−9.63091	+	25.7514i	−0.435080	+	1.16333i
$491$	3.93750	+	29.9083i	0.177697	+	1.34974i	0.815149	+	0.579252i	$0.196655\pi$
$491$	3.93750	+	29.9083i	0.177697	+	1.34974i	−0.637452	+	0.770490i	$0.720011\pi$
$492$	2.90042	−	1.88754i	0.130761	−	0.0850968i
$493$	21.3174	+	2.80649i	0.960089	+	0.126398i
$494$	2.77557	−	0.848280i	0.124879	−	0.0381659i
$495$	2.37934	+	10.1980i	0.106943	+	0.458368i
$496$	10.6318	+	4.30035i	0.477381	+	0.193091i
$497$	−2.93438	+	5.08250i	−0.131625	+	0.227981i
$498$	−35.1211	+	5.28705i	−1.57381	+	0.236918i
$499$	3.07761	+	2.36154i	0.137773	+	0.105717i	0.675349	−	0.737499i	$-0.263993\pi$
$499$	3.07761	+	2.36154i	0.137773	+	0.105717i	−0.537576	+	0.843215i	$0.680660\pi$
$500$	7.76258	+	0.476299i	0.347153	+	0.0213008i
$501$	−3.40210	−	2.03882i	−0.151995	−	0.0910877i
$502$	−23.0554	+	3.85583i	−1.02901	+	0.172094i
$503$	10.2603	−	10.2603i	0.457486	−	0.457486i	−0.440344	−	0.897829i	$-0.645143\pi$
$503$	10.2603	−	10.2603i	0.457486	−	0.457486i	0.897829	+	0.440344i	$0.145143\pi$
$504$	−1.01510	+	5.27938i	−0.0452162	+	0.235162i
$505$	23.3780	+	23.3780i	1.04031	+	1.04031i
$506$	10.4562	+	7.45985i	0.464834	+	0.331631i
$507$	6.86473	+	0.111858i	0.304873	+	0.00496777i
$508$	−24.0785	−	11.7497i	−1.06831	−	0.521308i
$509$	4.33821	−	5.65367i	0.192288	−	0.250594i	−0.687253	−	0.726418i	$-0.741183\pi$
$509$	4.33821	−	5.65367i	0.192288	−	0.250594i	0.879540	+	0.475824i	$0.157850\pi$
$510$	5.83797	+	13.3875i	0.258510	+	0.592808i
$511$	−7.57995	−	4.37629i	−0.335317	−	0.193596i
$512$	21.5261	−	6.97337i	0.951327	−	0.308182i
$513$	−1.51607	+	3.20719i	−0.0669361	+	0.141601i
$514$	−17.3917	−	9.24949i	−0.767114	−	0.407978i
$515$	1.48236	−	11.2596i	0.0653205	−	0.496158i
$516$	−0.560837	+	7.21513i	−0.0246895	+	0.317629i
$517$	−11.7737	+	1.55004i	−0.517807	+	0.0681706i
$518$	1.05662	+	2.31914i	0.0464252	+	0.101897i
$519$	−1.33724	−	0.579606i	−0.0586984	−	0.0254419i
$520$	22.8809	+	10.1952i	1.00339	+	0.447091i
$521$	−0.310594	−	0.310594i	−0.0136074	−	0.0136074i	0.700270	−	0.713878i	$-0.253063\pi$
$521$	−0.310594	−	0.310594i	−0.0136074	−	0.0136074i	−0.713878	+	0.700270i	$0.753063\pi$
$522$	−5.78416	+	44.7027i	−0.253166	+	1.95658i
$523$	−6.00563	+	14.4989i	−0.262608	+	0.633991i	−0.999098	−	0.0424566i	$-0.986482\pi$
$523$	−6.00563	+	14.4989i	−0.262608	+	0.633991i	0.736491	+	0.676448i	$0.236482\pi$
$524$	19.2948	−	9.61534i	0.842897	−	0.420048i
$525$	3.91744	−	0.981557i	0.170971	−	0.0428387i
$526$	8.54431	+	7.96926i	0.372550	+	0.347476i
$527$	−5.02508	+	2.90123i	−0.218896	+	0.126380i
$528$	−4.16067	+	7.07587i	−0.181070	+	0.307938i
$529$	30.9735	+	17.8826i	1.34667	+	0.777502i
$530$	13.0133	+	42.5794i	0.565262	+	1.84953i
$531$	−27.3641	−	12.3939i	−1.18750	−	0.537851i
$532$	0.847767	−	0.172308i	0.0367553	−	0.00747049i
$533$	1.82806	+	2.38237i	0.0791819	+	0.103192i
$534$	−14.4478	+	26.1299i	−0.625216	+	1.13075i
$535$	−13.7777	+	51.4192i	−0.595663	+	2.22304i
$536$	3.10080	−	5.05672i	0.133934	−	0.218417i
$537$	27.1060	−	3.12019i	1.16971	−	0.134646i
$538$	−23.2284	−	16.5721i	−1.00145	−	0.714473i
$539$	2.99180	−	7.22284i	0.128866	−	0.311110i
$540$	−28.0382	+	12.3010i	−1.20657	+	0.529352i
$541$	42.2351	−	17.4944i	1.81583	−	0.752141i	0.837081	−	0.547079i	$-0.184260\pi$
$541$	42.2351	−	17.4944i	1.81583	−	0.752141i	0.978749	−	0.205063i	$-0.0657399\pi$
$542$	−9.58348	−	15.3401i	−0.411646	−	0.658914i
$543$	8.62252	−	10.8658i	0.370028	−	0.466298i
$544$	−3.92077	+	10.7559i	−0.168102	+	0.461156i
$545$	34.6667	−	20.0148i	1.48496	−	0.857342i
$546$	−4.63573	−	0.523185i	−0.198391	−	0.0223903i
$547$	10.2782	+	1.35315i	0.439464	+	0.0578565i	0.347012	−	0.937861i	$-0.387196\pi$
$547$	10.2782	+	1.35315i	0.439464	+	0.0578565i	0.0924518	+	0.995717i	$0.470530\pi$
$548$	2.89164	−	14.8607i	0.123525	−	0.634818i
$549$	5.15661	−	6.28512i	0.220079	−	0.268242i
$550$	6.13780	+	0.591607i	0.261717	+	0.0252262i
$551$	7.00621	−	1.87731i	0.298474	−	0.0799760i
$552$	−15.8418	+	34.0500i	−0.674272	+	1.44926i
$553$	−1.71137	−	0.458561i	−0.0727749	−	0.0195000i
$554$	−7.10161	−	2.65597i	−0.301718	−	0.112841i
$555$	−7.46093	+	12.4498i	−0.316699	+	0.528463i
$556$	−3.23729	+	9.66898i	−0.137292	+	0.410056i
$557$	−25.6193	+	10.6118i	−1.08552	+	0.449638i	−0.852443	−	0.522820i	$-0.824880\pi$
$557$	−25.6193	+	10.6118i	−1.08552	+	0.449638i	−0.233079	+	0.972458i	$0.574880\pi$
$558$	−6.10552	−	10.5210i	−0.258467	−	0.445389i
$559$	−6.27990			−0.265612
$560$	6.49717	+	3.67927i	0.274555	+	0.155477i
$561$	−1.52658	−	3.86230i	−0.0644521	−	0.163066i
$562$	4.05481	−	4.34740i	0.171042	−	0.183384i
$563$	−18.4467	+	24.0402i	−0.777437	+	1.01318i	0.221837	+	0.975084i	$0.428795\pi$
$563$	−18.4467	+	24.0402i	−0.777437	+	1.01318i	−0.999274	+	0.0380920i	$0.987872\pi$
$564$	−10.7613	−	33.0113i	−0.453131	−	1.39003i
$565$	30.3840	−	23.3144i	1.27826	−	0.980846i
$566$	−17.1778	+	14.1574i	−0.722036	+	0.595082i
$567$	4.28610	−	3.76091i	0.179999	−	0.157943i
$568$	−20.3560	−	16.4938i	−0.854117	−	0.692064i
$569$	3.64833	+	13.6157i	0.152946	+	0.570801i	0.999273	+	0.0381373i	$0.0121424\pi$
$569$	3.64833	+	13.6157i	0.152946	+	0.570801i	−0.846327	+	0.532664i	$0.821191\pi$
$570$	3.54776	+	3.41876i	0.148599	+	0.143196i
$571$	−2.84392	−	21.6017i	−0.119015	−	0.904005i	−0.941922	−	0.335830i	$-0.890983\pi$
$571$	−2.84392	−	21.6017i	−0.119015	−	0.904005i	0.822908	−	0.568175i	$-0.192350\pi$
$572$	−6.40150	−	3.12377i	−0.267660	−	0.130611i
$573$	30.6910	+	31.7077i	1.28213	+	1.32461i
$574$	0.474251	+	0.759125i	0.0197949	+	0.0316853i
$575$	28.2113			1.17649
$576$	−22.5668	−	8.16934i	−0.940285	−	0.340389i
$577$	12.1248			0.504762			0.252381	−	0.967628i	$-0.418786\pi$
$577$	12.1248			0.504762			0.252381	+	0.967628i	$0.418786\pi$
$578$	9.66922	+	15.4774i	0.402187	+	0.643773i
$579$	−28.0418	+	7.02617i	−1.16538	+	0.291998i
$580$	56.2620	+	27.4544i	2.33615	+	1.13998i
$581$	−1.19910	−	9.10809i	−0.0497472	−	0.377867i
$582$	6.47756	−	26.0982i	0.268504	−	1.08181i
$583$	−3.27681	−	12.2292i	−0.135711	−	0.506482i
$584$	24.5986	−	30.3585i	1.01790	−	1.25624i
$585$	−12.5278	−	23.4300i	−0.517961	−	0.968713i
$586$	6.95010	−	5.72808i	0.287106	−	0.236625i
$587$	25.0341	−	19.2094i	1.03327	−	0.792855i	0.0546435	−	0.998506i	$-0.482598\pi$
$587$	25.0341	−	19.2094i	1.03327	−	0.792855i	0.978625	+	0.205651i	$0.0659311\pi$
$588$	22.3632	+	4.73089i	0.922244	+	0.195099i
$589$	−1.19161	+	1.55293i	−0.0490992	+	0.0639874i
$590$	−28.4568	+	30.5102i	−1.17155	+	1.25609i
$591$	15.4510	−	19.4709i	0.635569	−	0.800925i
$592$	−10.9644	+	3.03611i	−0.450636	+	0.124783i
$593$	−42.1432			−1.73061			−0.865306	−	0.501244i	$-0.832876\pi$
$593$	−42.1432			−1.73061			−0.865306	+	0.501244i	$0.832876\pi$
$594$	8.08975	−	3.21830i	0.331927	−	0.132048i
$595$	−3.49014	+	1.44566i	−0.143082	+	0.0592663i
$596$	8.35299	−	24.9483i	0.342152	−	1.02192i
$597$	6.50522	+	11.7037i	0.266241	+	0.479000i
$598$	−30.5237	−	11.4157i	−1.24821	−	0.466825i
$599$	−22.2691	−	5.96698i	−0.909889	−	0.243804i	−0.226631	−	0.973981i	$-0.572771\pi$
$599$	−22.2691	−	5.96698i	−0.909889	−	0.243804i	−0.683258	+	0.730177i	$0.739438\pi$
$600$	1.58691	+	17.9589i	0.0647852	+	0.733171i
$601$	−13.9859	+	3.74752i	−0.570498	+	0.152865i	−0.532525	−	0.846414i	$-0.678757\pi$
$601$	−13.9859	+	3.74752i	−0.570498	+	0.152865i	−0.0379732	+	0.999279i	$0.512090\pi$
$602$	−1.86324	−	0.179593i	−0.0759400	−	0.00731966i
$603$	−5.88798	+	2.21701i	−0.239777	+	0.0902837i
$604$	−6.75537	+	34.7172i	−0.274872	+	1.41262i
$605$	28.0307	+	3.69031i	1.13961	+	0.150033i
$606$	16.3267	−	22.1134i	0.663227	−	0.898294i
$607$	32.0940	−	18.5295i	1.30266	−	0.752089i	0.321798	−	0.946808i	$-0.395713\pi$
$607$	32.0940	−	18.5295i	1.30266	−	0.752089i	0.980859	+	0.194719i	$0.0623795\pi$
$608$	0.166577	+	3.85840i	0.00675557	+	0.156479i
$609$	−11.5330	−	1.70994i	−0.467340	−	0.0692902i
$610$	−5.98243	−	9.57597i	−0.242222	−	0.387720i
$611$	27.8361	−	11.5301i	1.12613	−	0.466458i
$612$	10.2839	−	6.45652i	0.415701	−	0.260989i
$613$	−9.25181	+	22.3358i	−0.373677	+	0.902136i	0.619444	+	0.785041i	$0.287358\pi$
$613$	−9.25181	+	22.3358i	−0.373677	+	0.902136i	−0.993121	+	0.117095i	$0.962642\pi$
$614$	−10.2859	−	7.33837i	−0.415105	−	0.296153i
$615$	−2.02728	+	4.67727i	−0.0817480	+	0.188606i
$616$	−1.80999	−	1.10989i	−0.0729264	−	0.0447187i
$617$	−2.19546	+	8.19357i	−0.0883859	+	0.329861i	−0.995934	−	0.0900878i	$-0.971285\pi$
$617$	−2.19546	+	8.19357i	−0.0883859	+	0.329861i	0.907548	+	0.419949i	$0.137952\pi$
$618$	−9.44046	+	0.174819i	−0.379751	+	0.00703226i
$619$	8.13657	+	10.6038i	0.327036	+	0.426202i	0.927715	−	0.373288i	$-0.121770\pi$
$619$	8.13657	+	10.6038i	0.327036	+	0.426202i	−0.600679	+	0.799490i	$0.705103\pi$
$620$	−16.5559	+	3.36497i	−0.664900	+	0.135140i
$621$	35.4282	−	18.2072i	1.42168	−	0.730628i
$622$	6.94783	+	22.7332i	0.278582	+	0.911520i
$623$	−6.68834	−	3.86151i	−0.267963	−	0.154708i
$624$	5.55012	−	20.0731i	0.222183	−	0.803568i
$625$	−25.8572	+	14.9286i	−1.03429	+	0.597146i
$626$	25.0160	+	23.3323i	0.999840	+	0.932548i
$627$	−0.974387	−	1.00667i	−0.0389133	−	0.0402024i
$628$	15.1725	−	7.56102i	0.605447	−	0.301718i
$629$	2.20279	−	5.31800i	0.0878309	−	0.212043i
$630$	−3.04693	−	7.30994i	−0.121393	−	0.291235i
$631$	26.8014	+	26.8014i	1.06695	+	1.06695i	0.997592	+	0.0693528i	$0.0220934\pi$
$631$	26.8014	+	26.8014i	1.06695	+	1.06695i	0.0693528	+	0.997592i	$0.477907\pi$
$632$	3.21917	−	7.22469i	0.128052	−	0.287383i
$633$	27.0354	−	20.0538i	1.07456	−	0.797065i
$634$	−8.18776	−	17.9710i	−0.325177	−	0.713721i
$635$	39.1303	−	5.15160i	1.55284	−	0.204435i
$636$	33.3957	−	15.9685i	1.32423	−	0.633193i
$637$	−2.58904	+	19.6657i	−0.102582	+	0.779185i
$638$	−15.7171	−	8.35890i	−0.622246	−	0.330932i
$639$	6.31390	+	27.0619i	0.249774	+	1.07055i
$640$	−20.7678	+	26.0721i	−0.820919	+	1.03059i
$641$	−41.6687	−	24.0574i	−1.64581	−	0.950211i	−0.978710	−	0.205246i	$-0.934200\pi$
$641$	−41.6687	−	24.0574i	−1.64581	−	0.950211i	−0.667104	−	0.744965i	$-0.732466\pi$
$642$	43.9790	+	4.96344i	1.73571	+	0.195891i
$643$	5.98708	−	7.80251i	0.236107	−	0.307701i	−0.660239	−	0.751056i	$-0.729545\pi$
$643$	5.98708	−	7.80251i	0.236107	−	0.307701i	0.896346	+	0.443354i	$0.146212\pi$
$644$	−8.72989	−	4.25996i	−0.344006	−	0.167866i
$645$	−5.17923	−	9.31806i	−0.203932	−	0.366898i
$646$	−1.59064	−	1.13482i	−0.0625827	−	0.0446490i
$647$	0.196754	+	0.196754i	0.00773518	+	0.00773518i	0.710964	−	0.703229i	$-0.248259\pi$
$647$	0.196754	+	0.196754i	0.00773518	+	0.00773518i	−0.703229	+	0.710964i	$0.748259\pi$
$648$	13.5833	+	21.5289i	0.533602	+	0.845736i
$649$	8.38893	−	8.38893i	0.329294	−	0.329294i
$650$	−15.4305	+	2.58063i	−0.605234	+	0.101221i
$651$	2.75010	−	1.52858i	0.107785	−	0.0599098i
$652$	−26.8341	−	1.64649i	−1.05090	−	0.0644817i
$653$	11.4274	+	8.76859i	0.447191	+	0.343141i	0.807679	−	0.589622i	$-0.200723\pi$
$653$	11.4274	+	8.76859i	0.447191	+	0.343141i	−0.360489	+	0.932764i	$0.617390\pi$
$654$	−20.7455	−	26.0238i	−0.811213	−	1.01761i
$655$	−15.8785	+	27.5024i	−0.620425	+	1.07461i
$656$	−3.67883	+	1.55988i	−0.143634	+	0.0609030i
$657$	−40.3596	+	9.41645i	−1.57458	+	0.367371i
$658$	8.58868	−	2.62491i	0.334822	−	0.102330i
$659$	−10.5960	−	1.39499i	−0.412760	−	0.0543409i	−0.0787133	−	0.996897i	$-0.525081\pi$
$659$	−10.5960	−	1.39499i	−0.412760	−	0.0543409i	−0.334047	+	0.942556i	$0.608414\pi$
$660$	−0.644498	−	12.0748i	−0.0250870	−	0.470009i
$661$	3.49389	+	26.5388i	0.135897	+	1.03224i	0.914461	+	0.404673i	$0.132615\pi$
$661$	3.49389	+	26.5388i	0.135897	+	1.03224i	−0.778565	+	0.627565i	$0.784052\pi$
$662$	−9.63660	+	25.7666i	−0.374537	+	1.00145i
$663$	6.27745	+	8.46293i	0.243796	+	0.328673i
$664$	40.9969	+	1.08554i	1.59099	+	0.0421273i
$665$	−0.901124	+	0.901124i	−0.0349441	+	0.0349441i
$666$	11.1589	+	4.59311i	0.432397	+	0.177980i
$667$	−75.2451	−	31.1675i	−2.91350	−	1.20681i
$668$	3.45585	+	3.00531i	0.133711	+	0.116279i
$669$	−5.43481	+	5.26053i	−0.210122	+	0.203384i
$670$	0.304102	+	8.73275i	0.0117485	+	0.337375i
$671$	1.60535	+	2.78055i	0.0619739	+	0.107342i
$672$	2.22077	−	5.79695i	0.0856679	−	0.223622i
$673$	15.2215	−	26.3645i	0.586747	−	1.01628i	−0.407908	−	0.913023i	$-0.633742\pi$
$673$	15.2215	−	26.3645i	0.586747	−	1.01628i	0.994655	−	0.103252i	$-0.0329249\pi$
$674$	1.93795	+	1.03067i	0.0746471	+	0.0396999i
$675$	10.3590	−	16.0737i	0.398718	−	0.618676i
$676$	−7.78181	−	1.51420i	−0.299300	−	0.0582387i
$677$	−6.02806	+	4.62549i	−0.231677	+	0.177772i	−0.718076	−	0.695965i	$-0.754977\pi$
$677$	−6.02806	+	4.62549i	−0.231677	+	0.177772i	0.486399	+	0.873737i	$0.338310\pi$
$678$	−22.9282	−	22.0944i	−0.880551	−	0.848532i
$679$	6.71830	+	1.80016i	0.257825	+	0.0690840i
$680$	−3.93213	−	16.3996i	−0.150790	−	0.628897i
$681$	19.3452	+	8.38487i	0.741311	+	0.321309i
$682$	4.73823	−	0.792432i	0.181436	−	0.0303438i
$683$	16.5877	+	6.87083i	0.634709	+	0.262905i	0.676752	−	0.736211i	$-0.263387\pi$
$683$	16.5877	+	6.87083i	0.634709	+	0.262905i	−0.0420433	+	0.999116i	$0.513387\pi$
$684$	2.37162	−	3.33988i	0.0906811	−	0.127703i
$685$	8.53458	+	20.6043i	0.326090	+	0.787250i
$686$	−2.74208	+	11.8720i	−0.104693	+	0.453274i
$687$	7.46958	−	50.3799i	0.284982	−	1.92211i
$688$	2.09544	−	8.08946i	0.0798880	−	0.308408i
$689$	16.0610	+	27.8185i	0.611876	+	1.05980i
$690$	−8.23527	−	54.7057i	−0.313511	−	2.08261i
$691$	0.372785	−	2.83158i	0.0141814	−	0.107718i	−0.982890	−	0.184193i	$-0.941033\pi$
$691$	0.372785	−	2.83158i	0.0141814	−	0.107718i	0.997072	+	0.0764742i	$0.0243663\pi$
$692$	1.40318	+	0.929139i	0.0533409	+	0.0353206i
$693$	0.793550	+	2.10753i	0.0301445	+	0.0800583i
$694$	8.67842	+	10.5299i	0.329428	+	0.399708i
$695$	−3.88760	−	14.5087i	−0.147465	−	0.550348i
$696$	15.6082	−	49.6531i	0.591628	−	1.88210i
$697$	0.523253	−	1.95281i	0.0198196	−	0.0739678i
$698$	11.4392	−	5.21179i	0.432980	−	0.197269i
$699$	−9.45745	+	5.25670i	−0.357714	+	0.198827i
$700$	−4.65201	+	0.324389i	−0.175829	+	0.0122607i
$701$	−18.7603	−	45.2914i	−0.708567	−	1.71063i	−0.703552	−	0.710643i	$-0.748404\pi$
$701$	−18.7603	−	45.2914i	−0.708567	−	1.71063i	−0.00501422	−	0.999987i	$-0.501596\pi$
$702$	−17.7123	+	13.1994i	−0.668509	+	0.498179i
$703$		−	1.94181i		−	0.0732366i
$704$	6.15990	−	7.20378i	0.232160	−	0.271503i
$705$	40.0655	+	31.7937i	1.50896	+	1.19742i
$706$	−0.266671	−	7.65786i	−0.0100363	−	0.288207i
$707$	5.64061	+	4.32819i	0.212137	+	0.162778i
$708$	28.6056	+	19.6195i	1.07506	+	0.737345i
$709$	21.3812	+	27.8645i	0.802987	+	1.04647i	0.997843	+	0.0656416i	$0.0209094\pi$
$709$	21.3812	+	27.8645i	0.802987	+	1.04647i	−0.194856	+	0.980832i	$0.562424\pi$
$710$	38.4164	+	3.70286i	1.44174	+	0.138966i
$711$	−7.39809	+	3.95568i	−0.277450	+	0.148350i
$712$	21.7051	−	26.7875i	0.813432	−	1.00390i
$713$	21.2301	−	5.68859i	0.795074	−	0.213040i
$714$	1.62049	+	2.69046i	0.0606452	+	0.100688i
$715$	10.4032	−	1.36960i	0.389056	−	0.0512202i
$716$	−31.4468	−	1.92952i	−1.17522	−	0.0721097i
$717$	0.287737	+	1.14837i	0.0107457	+	0.0428868i
$718$	5.29339	−	22.9180i	0.197547	−	0.855292i
$719$			25.3597i			0.945758i	0.881127	+	0.472879i	$0.156785\pi$
$719$			25.3597i			0.945758i	−0.881127	+	0.472879i	$0.843215\pi$
$720$	34.3616	−	8.31969i	1.28058	−	0.310056i
$721$		−	2.44226i		−	0.0909545i
$722$	25.5385	+	5.89866i	0.950446	+	0.219525i
$723$	−8.42985	+	8.15953i	−0.313509	+	0.303456i
$724$	−11.9983	+	10.6110i	−0.445913	+	0.394355i
$725$	−38.7646	+	5.10346i	−1.43968	+	0.189538i
$726$	−0.435211	−	23.5019i	−0.0161522	−	0.872238i
$727$	−12.4483	+	3.33550i	−0.461681	+	0.123707i	−0.482160	−	0.876083i	$-0.660148\pi$
$727$	−12.4483	+	3.33550i	−0.461681	+	0.123707i	0.0204790	+	0.999790i	$0.493481\pi$
$728$	5.16458	+	1.53146i	0.191412	+	0.0567598i
$729$	2.63528	−	26.8711i	0.0976030	−	0.995225i
$730$	−5.52239	+	57.2936i	−0.204393	+	2.12053i
$731$	2.57379	+	3.35423i	0.0951950	+	0.124060i
$732$	−7.13240	+	6.10356i	−0.263621	+	0.225594i
$733$	−20.5652	−	15.7803i	−0.759594	−	0.582857i	0.154674	−	0.987965i	$-0.450567\pi$
$733$	−20.5652	−	15.7803i	−0.759594	−	0.582857i	−0.914269	+	0.405108i	$0.867234\pi$
$734$	−38.2610	+	1.33237i	−1.41224	+	0.0491786i
$735$	−31.3151	+	12.3773i	−1.15507	+	0.456544i
$736$	24.8902	−	35.5100i	0.917465	−	1.30892i
$737$		−	2.48472i		−	0.0915259i
$738$	4.09628	+	1.08784i	0.150786	+	0.0400440i
$739$	−17.9759	−	43.3976i	−0.661253	−	1.59641i	−0.795841	−	0.605505i	$-0.792971\pi$
$739$	−17.9759	−	43.3976i	−0.661253	−	1.59641i	0.134588	−	0.990902i	$-0.457029\pi$
$740$	10.9977	−	12.6465i	0.404284	−	0.464893i
$741$	3.04899	+	1.82721i	0.112007	+	0.0671241i
$742$	3.96973	+	8.71303i	0.145733	+	0.319866i
$743$	9.09414	−	33.9398i	0.333632	−	1.24513i	−0.571713	−	0.820454i	$-0.693721\pi$
$743$	9.09414	−	33.9398i	0.333632	−	1.24513i	0.905345	−	0.424677i	$-0.139612\pi$
$744$	4.81549	+	13.1948i	0.176544	+	0.483745i
$745$	10.0309	+	37.4360i	0.367505	+	1.37155i
$746$	2.02462	−	1.66864i	0.0741266	−	0.0610931i
$747$	−33.6291	−	27.5908i	−1.23042	−	1.00950i
$748$	0.955157	+	4.69944i	0.0349240	+	0.171828i
$749$	−1.49422	+	11.3498i	−0.0545977	+	0.414711i
$750$	5.93741	+	7.44808i	0.216803	+	0.271966i
$751$	4.92929	+	8.53777i	0.179872	+	0.311548i	0.941837	−	0.336071i	$-0.109098\pi$
$751$	4.92929	+	8.53777i	0.179872	+	0.311548i	−0.761964	+	0.647619i	$0.775765\pi$
$752$	5.56430	+	39.7044i	0.202909	+	1.44787i
$753$	−22.4260	−	17.7960i	−0.817250	−	0.648523i
$754$	44.0071	+	10.1644i	1.60265	+	0.370164i
$755$	−19.9383	−	48.1353i	−0.725628	−	1.75182i
$756$	−5.63270	+	3.40971i	−0.204859	+	0.124010i
$757$	−0.819058	−	0.339265i	−0.0297692	−	0.0123308i	0.367749	−	0.929925i	$-0.380128\pi$
$757$	−0.819058	−	0.339265i	−0.0297692	−	0.0123308i	−0.397518	+	0.917594i	$0.630128\pi$
$758$	6.92890	+	41.4303i	0.251669	+	1.50482i
$759$	1.79896	+	15.6280i	0.0652980	+	0.567261i
$760$	−3.34263	−	4.60357i	−0.121250	−	0.166989i
$761$	−43.1448	−	11.5606i	−1.56400	−	0.419072i	−0.630070	−	0.776538i	$-0.716974\pi$
$761$	−43.1448	−	11.5606i	−1.56400	−	0.419072i	−0.933926	+	0.357466i	$0.883641\pi$
$762$	−9.07822	−	31.5330i	−0.328869	−	1.14232i
$763$	6.82945	−	5.24042i	0.247243	−	0.189716i
$764$	−28.4855	−	42.2493i	−1.03057	−	1.52852i
$765$	−7.38001	+	16.2940i	−0.266825	+	0.589112i
$766$	16.1682	−	30.4008i	0.584181	−	1.09843i
$767$	−15.0501	+	26.0676i	−0.543429	+	0.941246i
$768$	24.0053	+	13.8473i	0.866215	+	0.499671i
$769$	−3.42270	−	5.92829i	−0.123426	−	0.213780i	0.797691	−	0.603067i	$-0.206055\pi$
$769$	−3.42270	−	5.92829i	−0.123426	−	0.213780i	−0.921117	+	0.389287i	$0.872721\pi$
$770$	3.12577	−	0.108849i	0.112645	−	0.00392265i
$771$	−5.86362	−	23.4020i	−0.211173	−	0.842802i
$772$	33.2999	−	2.32203i	1.19849	−	0.0835718i
$773$	−20.0574	−	8.30804i	−0.721414	−	0.298820i	−0.00839566	−	0.999965i	$-0.502672\pi$
$773$	−20.0574	−	8.30804i	−0.721414	−	0.298820i	−0.713018	+	0.701145i	$0.752672\pi$
$774$	−7.01976	+	5.41129i	−0.252320	+	0.194505i
$775$	7.46102	−	7.46102i	0.268008	−	0.268008i
$776$	−12.6375	+	28.3618i	−0.453658	+	1.01813i
$777$	−1.24128	+	2.86382i	−0.0445306	+	0.102739i
$778$	−4.69263	−	1.75502i	−0.168239	−	0.0629207i
$779$	−0.0890196	−	0.676171i	−0.00318946	−	0.0242263i
$780$	9.50857	+	29.1686i	0.340461	+	1.04440i
$781$	−10.8807	−	1.43247i	−0.389343	−	0.0512579i
$782$	6.41262	+	20.9820i	0.229315	+	0.750316i
$783$	−45.3874	+	31.4271i	−1.62201	+	1.12311i
$784$	−24.4685	−	9.89703i	−0.873876	−	0.353465i
$785$	−12.4861	+	21.6265i	−0.445647	+	0.771884i
$786$	24.5760	+	9.65061i	0.876598	+	0.344226i
$787$	31.1280	+	23.8854i	1.10959	+	0.851422i	0.989953	−	0.141395i	$-0.0451587\pi$
$787$	31.1280	+	23.8854i	1.10959	+	0.851422i	0.119642	+	0.992817i	$0.461825\pi$
$788$	−21.5001	+	19.0143i	−0.765911	+	0.677355i
$789$	−0.233141	+	14.3079i	−0.00830005	+	0.509376i
$790$	1.92192	+	11.4918i	0.0683788	+	0.408861i
$791$	5.82371	−	5.82371i	0.207067	−	0.207067i
$792$	−9.84739	+	2.02428i	−0.349912	+	0.0719296i
$793$	−5.76015	−	5.76015i	−0.204549	−	0.204549i
$794$	−8.57437	+	12.0183i	−0.304293	+	0.426515i
$795$	−28.0308	+	46.7740i	−0.994151	+	1.65890i
$796$	−5.03093	−	14.6202i	−0.178317	−	0.518198i
$797$	25.1860	−	32.8230i	0.892133	−	1.16265i	−0.0938131	−	0.995590i	$-0.529906\pi$
$797$	25.1860	−	32.8230i	0.892133	−	1.16265i	0.985947	−	0.167061i	$-0.0534277\pi$
$798$	0.852377	+	0.629325i	0.0301738	+	0.0222779i
$799$	−17.5670	−	10.1423i	−0.621475	−	0.358808i
$800$	1.82452	−	20.7379i	0.0645065	−	0.733195i
$801$	−35.6122	+	8.30881i	−1.25830	+	0.293577i
$802$	23.7627	−	44.6806i	0.839089	−	1.57773i
$803$	2.13637	−	16.2273i	0.0753908	−	0.572650i
$804$	7.14191	−	1.33081i	0.251876	−	0.0469339i
$805$	14.1870	−	1.86776i	0.500027	−	0.0658298i
$806$	−11.0917	+	5.05346i	−0.390688	+	0.178001i
$807$	−3.99639	−	34.7177i	−0.140679	−	1.22212i
$808$	−23.0296	+	21.8415i	−0.810180	+	0.768382i
$809$	−5.55838	−	5.55838i	−0.195422	−	0.195422i	0.602612	−	0.798034i	$-0.294127\pi$
$809$	−5.55838	−	5.55838i	−0.195422	−	0.195422i	−0.798034	+	0.602612i	$0.794127\pi$
$810$	−34.1930	−	15.3954i	−1.20142	−	0.540940i
$811$	3.10476	−	7.49555i	0.109023	−	0.263204i	−0.859947	−	0.510383i	$-0.829504\pi$
$811$	3.10476	−	7.49555i	0.109023	−	0.263204i	0.968970	+	0.247179i	$0.0795035\pi$
$812$	12.7662	+	4.27427i	0.448005	+	0.149998i
$813$	6.08141	−	21.3016i	0.213284	−	0.747081i
$814$	−3.25054	+	3.48509i	−0.113931	+	0.122152i
$815$	34.2978	−	19.8018i	1.20140	−	0.693629i
$816$	−12.9962	+	5.26243i	−0.454956	+	0.184222i
$817$	1.23518	+	0.713129i	0.0432133	+	0.0249492i
$818$	18.7651	−	5.73508i	0.656108	−	0.200522i
$819$	−3.32871	−	4.64384i	−0.116314	−	0.162269i
$820$	3.24984	−	4.90790i	0.113489	−	0.171391i
$821$	18.2526	+	23.7872i	0.637020	+	0.830180i	0.994609	−	0.103699i	$-0.0330678\pi$
$821$	18.2526	+	23.7872i	0.637020	+	0.830180i	−0.357589	+	0.933879i	$0.616401\pi$
$822$	15.8834	−	9.56668i	0.553996	−	0.333676i
$823$	0.0495592	−	0.184958i	0.00172753	−	0.00644721i	−0.965057	−	0.262041i	$-0.915604\pi$
$823$	0.0495592	−	0.184958i	0.00172753	−	0.00644721i	0.966784	+	0.255594i	$0.0822710\pi$
$824$	10.7680	+	1.70872i	0.375122	+	0.0595261i
$825$	4.49919	+	6.06558i	0.156642	+	0.211176i
$826$	−5.21084	+	7.30382i	−0.181308	+	0.254132i
$827$	−8.69011	+	20.9798i	−0.302185	+	0.729538i	0.697729	+	0.716362i	$0.254194\pi$
$827$	−8.69011	+	20.9798i	−0.302185	+	0.729538i	−0.999913	+	0.0131760i	$0.995806\pi$
$828$	−43.9566	+	13.5411i	−1.52760	+	0.470586i
$829$	−26.8336	+	11.1148i	−0.931969	+	0.386034i	−0.796425	−	0.604737i	$-0.793278\pi$
$829$	−26.8336	+	11.1148i	−0.931969	+	0.386034i	−0.135544	+	0.990771i	$0.543278\pi$
$830$	−51.2370	+	32.0095i	−1.77846	+	1.11107i
$831$	−3.41337	−	8.63594i	−0.118408	−	0.299577i
$832$	−10.3657	+	21.6994i	−0.359365	+	0.752292i
$833$	11.5650	−	6.67704i	0.400703	−	0.231346i
$834$	−11.4471	+	4.99181i	−0.396380	+	0.172852i
$835$	−6.68883	−	0.880601i	−0.231477	−	0.0304745i
$836$	0.904367	+	1.34134i	0.0312782	+	0.0463913i
$837$	4.55442	−	14.1849i	0.157424	−	0.490301i
$838$	−2.62178	+	27.2004i	−0.0905678	+	0.939622i
$839$	31.1153	−	8.33732i	1.07422	−	0.287836i	0.321994	−	0.946742i	$-0.395647\pi$
$839$	31.1153	−	8.33732i	1.07422	−	0.287836i	0.752226	+	0.658905i	$0.228980\pi$
$840$	1.98702	+	8.92620i	0.0685586	+	0.307983i
$841$	81.0190	+	21.7090i	2.79376	+	0.748586i
$842$	3.91227	−	10.4607i	0.134826	−	0.360500i
$843$	7.27997	+	0.118624i	0.250736	+	0.00408562i
$844$	−34.7881	+	17.3362i	−1.19746	+	0.596738i
$845$	10.7894	−	4.46913i	0.371168	−	0.153743i
$846$	21.1803	−	36.8744i	0.728194	−	1.26777i
$847$	6.07998			0.208911
$848$	−41.1936	+	11.4067i	−1.41459	+	0.391707i
$849$	−26.9681	−	3.99842i	−0.925541	−	0.137225i
$850$	7.70248	+	7.18408i	0.264193	+	0.246412i
$851$	−13.2732	+	17.2980i	−0.455000	+	0.592968i
$852$	−1.71026	−	32.0420i	−0.0585926	−	1.09774i
$853$	−36.3410	+	27.8854i	−1.24429	+	0.954778i	−0.999889	−	0.0148964i	$-0.995258\pi$
$853$	−36.3410	+	27.8854i	−1.24429	+	0.954778i	−0.244401	+	0.969674i	$0.578591\pi$
$854$	−1.54430	−	1.87376i	−0.0528449	−	0.0641187i
$855$	−0.196597	+	6.03101i	−0.00672349	+	0.206256i
$856$	−48.9962	−	14.5289i	−1.67466	−	0.496588i
$857$	−10.7153	−	39.9899i	−0.366026	−	1.36603i	−0.866024	−	0.500002i	$-0.833333\pi$
$857$	−10.7153	−	39.9899i	−0.366026	−	1.36603i	0.499998	−	0.866027i	$-0.333334\pi$
$858$	−2.41353	−	8.38335i	−0.0823966	−	0.286203i
$859$	4.60379	+	34.9692i	0.157079	+	1.19314i	0.870417	+	0.492315i	$0.163849\pi$
$859$	4.60379	+	34.9692i	0.157079	+	1.19314i	−0.713338	+	0.700820i	$0.752818\pi$
$860$	4.00545	+	11.6400i	0.136585	+	0.396922i
$861$	−0.300946	+	1.05414i	−0.0102562	+	0.0359250i
$862$	14.0694	−	8.78960i	0.479204	−	0.299375i
$863$	−12.7564			−0.434232			−0.217116	−	0.976146i	$-0.569665\pi$
$863$	−12.7564			−0.434232			−0.217116	+	0.976146i	$0.569665\pi$
$864$	−11.0927	−	27.2204i	−0.377380	−	0.926059i
$865$	−2.47911			−0.0842924
$866$	−7.16360	+	4.47534i	−0.243429	+	0.152078i
$867$	−6.13582	+	21.4922i	−0.208383	+	0.729914i
$868$	−3.43541	+	1.18216i	−0.116605	+	0.0401250i
$869$	−0.432455	−	3.28482i	−0.0146700	−	0.111430i
$870$	21.2122	+	73.6802i	0.719162	+	2.49799i
$871$	1.63163	+	6.08934i	0.0552858	+	0.206330i
$872$	18.3271	+	33.7778i	0.620633	+	1.14386i
$873$	29.0426	−	15.5288i	0.982942	−	0.525569i
$874$	4.70728	+	5.71153i	0.159226	+	0.193195i
$875$	−1.95460	+	1.49982i	−0.0660777	+	0.0507032i
$876$	47.7869	−	2.55066i	1.61457	−	0.0861787i
$877$	6.60053	−	8.60198i	0.222884	−	0.290468i	−0.668505	−	0.743708i	$-0.733065\pi$
$877$	6.60053	−	8.60198i	0.222884	−	0.290468i	0.891389	+	0.453240i	$0.149732\pi$
$878$	−9.60477	−	8.95835i	−0.324145	−	0.302330i
$879$	10.9112	+	1.61776i	0.368027	+	0.0545656i
$880$	−1.70701	+	13.8578i	−0.0575435	+	0.467147i
$881$	−13.1678			−0.443635			−0.221818	−	0.975088i	$-0.571199\pi$
$881$	−13.1678			−0.443635			−0.221818	+	0.975088i	$0.571199\pi$
$882$	14.0516	+	24.2136i	0.473141	+	0.815313i
$883$	11.8697	−	4.91661i	0.399449	−	0.165457i	−0.173910	−	0.984762i	$-0.555640\pi$
$883$	11.8697	−	4.91661i	0.399449	−	0.165457i	0.573359	+	0.819305i	$0.305640\pi$
$884$	−5.42678	−	10.8898i	−0.182522	−	0.366262i
$885$	−51.0911	−	0.832506i	−1.71741	−	0.0279844i
$886$	12.4370	−	33.2543i	0.417828	−	1.11720i
$887$	10.9054	+	2.92210i	0.366168	+	0.0981144i	0.437211	−	0.899359i	$-0.355966\pi$
$887$	10.9054	+	2.92210i	0.366168	+	0.0981144i	−0.0710433	+	0.997473i	$0.522633\pi$
$888$	−11.7583	−	7.47652i	−0.394582	−	0.250896i
$889$	8.19832	−	2.19673i	0.274963	−	0.0736760i
$890$	−4.87280	+	50.5543i	−0.163337	+	1.69458i
$891$	9.56478	+	4.71353i	0.320432	+	0.157909i
$892$	7.24165	−	4.88250i	0.242469	−	0.163478i
$893$	−6.78434	−	0.893175i	−0.227029	−	0.0298890i
$894$	29.5362	−	12.8801i	0.987839	−	0.430773i
$895$	40.1935	−	23.2058i	1.34352	−	0.775683i
$896$	−3.69605	+	6.14175i	−0.123476	+	0.205182i
$897$	−14.6711	−	37.1185i	−0.489855	−	1.23935i
$898$	13.9010	−	8.68444i	0.463883	−	0.289803i
$899$	−28.1428	+	11.6571i	−0.938615	+	0.388787i
$900$	−15.0247	+	16.1809i	−0.500824	+	0.539362i
$901$	8.27591	−	19.9798i	0.275710	−	0.665624i
$902$	−0.972125	+	1.36259i	−0.0323682	+	0.0453692i
$903$	−1.36581	−	1.84131i	−0.0454513	−	0.0612751i
$904$	21.6025	+	29.7515i	0.718487	+	0.989521i
$905$	6.10685	−	22.7911i	0.202999	−	0.757601i
$906$	−37.1063	+	22.3494i	−1.23278	+	0.742511i
$907$	−30.4632	−	39.7004i	−1.01151	−	1.31823i	−0.947319	−	0.320293i	$-0.896219\pi$
$907$	−30.4632	−	39.7004i	−1.01151	−	1.31823i	−0.0641952	−	0.997937i	$-0.520448\pi$
$908$	−20.2991	−	13.4414i	−0.673650	−	0.446068i
$909$	33.5026	−	3.30441i	1.11121	−	0.109600i
$910$	−7.58890	+	2.31935i	−0.251569	+	0.0768857i
$911$	−46.6854	−	26.9538i	−1.54675	−	0.893019i	−0.998387	−	0.0567822i	$-0.981916\pi$
$911$	−46.6854	−	26.9538i	−1.54675	−	0.893019i	−0.548368	−	0.836237i	$-0.684751\pi$
$912$	−3.37109	+	3.31787i	−0.111628	+	0.109866i
$913$	14.8776	−	8.58956i	0.492375	−	0.284273i
$914$	−24.4582	+	26.2231i	−0.809005	+	0.867382i
$915$	3.79628	−	13.2974i	0.125501	−	0.439599i
$916$	−18.6714	+	55.7669i	−0.616922	+	1.84259i
$917$	−2.61346	+	6.30946i	−0.0863042	+	0.208357i
$918$	14.3094	+	4.05081i	0.472280	+	0.133697i
$919$	−14.1720	−	14.1720i	−0.467491	−	0.467491i	0.433610	−	0.901101i	$-0.357240\pi$
$919$	−14.1720	−	14.1720i	−0.467491	−	0.467491i	−0.901101	+	0.433610i	$0.857240\pi$
$920$	−1.69088	+	63.8581i	−0.0557466	+	2.10534i
$921$	−1.76966	−	15.3735i	−0.0583124	−	0.506575i
$922$	−14.1052	+	6.42647i	−0.464531	+	0.211644i
$923$	27.6062	−	3.63442i	0.908669	−	0.119628i
$924$	−0.476345	−	2.55635i	−0.0156706	−	0.0840979i
$925$	−1.36625	+	10.3777i	−0.0449221	+	0.341217i
$926$	−0.783101	+	1.47245i	−0.0257343	+	0.0483878i
$927$	−7.90632	−	8.43915i	−0.259678	−	0.277178i
$928$	−27.7773	+	53.2962i	−0.911834	+	1.74953i
$929$	8.11541	+	4.68544i	0.266258	+	0.153724i	0.627186	−	0.778870i	$-0.284207\pi$
$929$	8.11541	+	4.68544i	0.266258	+	0.153724i	−0.360928	+	0.932594i	$0.617540\pi$
$930$	−16.6459	−	12.2900i	−0.545841	−	0.403004i
$931$	2.74242	−	3.57399i	0.0898792	−	0.117133i
$932$	11.8142	−	4.06537i	0.386986	−	0.133165i
$933$	−14.9657	+	24.9727i	−0.489955	+	0.817570i
$934$	−3.92491	+	5.50139i	−0.128427	+	0.180011i
$935$	−4.99521	−	4.99521i	−0.163361	−	0.163361i
$936$	22.8039	−	11.4274i	0.745367	−	0.373516i
$937$	−18.9743	+	18.9743i	−0.619863	+	0.619863i	−0.945496	−	0.325633i	$-0.894422\pi$
$937$	−18.9743	+	18.9743i	−0.619863	+	0.619863i	0.325633	+	0.945496i	$0.394422\pi$
$938$	0.309961	+	1.85336i	0.0101206	+	0.0605144i
$939$	−0.682590	+	41.8907i	−0.0222755	+	1.36705i
$940$	−39.1259	−	44.2412i	−1.27615	−	1.44299i
$941$	−24.5774	−	18.8589i	−0.801202	−	0.614784i	0.124852	−	0.992175i	$-0.460154\pi$
$941$	−24.5774	−	18.8589i	−0.801202	−	0.614784i	−0.926054	+	0.377392i	$0.876821\pi$
$942$	19.3254	+	7.58875i	0.629655	+	0.247255i
$943$	−3.82896	+	6.63196i	−0.124688	+	0.215966i
$944$	−28.5571	−	28.0849i	−0.929456	−	0.914087i
$945$	4.14521	−	8.76902i	0.134844	−	0.285256i
$946$	−1.02309	−	3.34756i	−0.0332637	−	0.108839i
$947$	−18.9501	−	2.49483i	−0.615795	−	0.0810710i	−0.183825	−	0.982959i	$-0.558848\pi$
$947$	−18.9501	−	2.49483i	−0.615795	−	0.0810710i	−0.431970	+	0.901888i	$0.642181\pi$
$948$	9.21003	−	3.00235i	0.299128	−	0.0975119i
$949$	5.42032	+	41.1714i	0.175951	+	1.33648i
$950$	3.32803	+	1.24467i	0.107976	+	0.0403824i
$951$	9.61868	−	22.1918i	0.311907	−	0.719619i
$952$	−1.29869	−	3.38617i	−0.0420909	−	0.109746i
$953$	−35.7423	+	35.7423i	−1.15781	+	1.15781i	−0.172860	+	0.984946i	$0.555301\pi$
$953$	−35.7423	+	35.7423i	−1.15781	+	1.15781i	−0.984946	+	0.172860i	$0.944699\pi$
$954$	41.9240	+	17.2564i	1.35734	+	0.558697i
$955$	69.3484	+	28.7250i	2.24406	+	0.929521i
$956$	−0.0950923	−	1.36371i	−0.00307551	−	0.0441054i
$957$	−5.29903	−	21.1487i	−0.171293	−	0.683641i
$958$	17.6181	−	0.613516i	0.569214	−	0.0198218i
$959$	2.39800	+	4.15346i	0.0774355	+	0.134122i
$960$	−40.7463	+	2.51567i	−1.31508	+	0.0811929i
$961$	−11.3898	+	19.7276i	−0.367411	+	0.636375i
$962$	5.67759	−	10.6755i	0.183053	−	0.344192i
$963$	31.5793	+	44.0560i	1.01763	+	1.41968i
$964$	11.2324	−	7.57318i	0.361772	−	0.243916i
$965$	−39.0119	+	29.9349i	−1.25584	+	0.963637i
$966$	−3.29139	−	11.4326i	−0.105899	−	0.367837i
$967$	6.15960	+	1.65046i	0.198079	+	0.0530752i	0.356495	−	0.934297i	$-0.383972\pi$
$967$	6.15960	+	1.65046i	0.198079	+	0.0530752i	−0.158415	+	0.987373i	$0.550638\pi$
$968$	−4.25384	+	26.8069i	−0.136724	+	0.861607i
$969$	−0.273665	−	2.37740i	−0.00879138	−	0.0763731i
$970$	−7.54485	−	45.1132i	−0.242250	−	1.44850i
$971$	−31.0937	−	12.8795i	−0.997846	−	0.413321i	−0.176839	−	0.984240i	$-0.556587\pi$
$971$	−31.0937	−	12.8795i	−0.997846	−	0.413321i	−0.821007	+	0.570919i	$0.806587\pi$
$972$	−8.42538	+	30.0169i	−0.270244	+	0.962792i
$973$	−1.23612	−	2.98427i	−0.0396283	−	0.0956712i
$974$	35.6520	+	8.23457i	1.14236	+	0.263853i
$975$	−15.0093	−	11.9105i	−0.480682	−	0.381442i
$976$	9.34195	−	5.49792i	0.299029	−	0.175984i
$977$	−20.9015	−	36.2025i	−0.668698	−	1.15822i	−0.978268	−	0.207343i	$-0.933519\pi$
$977$	−20.9015	−	36.2025i	−0.668698	−	1.15822i	0.309570	−	0.950877i	$-0.399815\pi$
$978$	−20.5247	−	25.7469i	−0.656308	−	0.823295i
$979$	1.88507	−	14.3185i	0.0602471	−	0.457622i
$980$	38.1025	−	7.74431i	1.21714	−	0.247383i
$981$	6.63413	−	40.2171i	0.211812	−	1.28403i
$982$	32.9215	−	27.1330i	1.05057	−	0.865848i
$983$	2.98722	+	11.1485i	0.0952777	+	0.355581i	0.997061	−	0.0766065i	$-0.0244085\pi$
$983$	2.98722	+	11.1485i	0.0952777	+	0.355581i	−0.901784	+	0.432188i	$0.857742\pi$
$984$	−4.43719	−	2.06441i	−0.141453	−	0.0658111i
$985$	10.9431	−	40.8402i	0.348676	−	1.30128i
$986$	−12.6071	−	27.6709i	−0.401492	−	0.881222i
$987$	9.43476	+	5.65409i	0.300312	+	0.179972i
$988$	−3.09716	−	2.69338i	−0.0985338	−	0.0856879i
$989$	−6.12860	−	14.7957i	−0.194878	−	0.470477i
$990$	10.4486	−	10.4952i	0.332079	−	0.333559i
$991$		−	5.21640i		−	0.165704i	−0.996562	−	0.0828521i	$-0.973597\pi$
$991$		−	5.21640i		−	0.165704i	0.996562	−	0.0828521i	$-0.0264029\pi$
$992$	−2.80861	−	15.9740i	−0.0891735	−	0.507174i
$993$	−31.3336	+	12.3846i	−0.994342	+	0.393015i
$994$	8.29466	−	0.288846i	0.263091	−	0.00916164i
$995$	18.0698	+	13.8654i	0.572850	+	0.439563i
$996$	32.6576	+	38.1625i	1.03480	+	1.20922i
$997$	−13.4127	−	17.4798i	−0.424784	−	0.553590i	0.531109	−	0.847303i	$-0.321775\pi$
$997$	−13.4127	−	17.4798i	−0.424784	−	0.553590i	−0.955893	+	0.293714i	$0.905109\pi$
$998$	0.526350	−	5.46078i	0.0166613	−	0.172858i
$999$	4.98186	+	13.9142i	0.157619	+	0.440227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.15	✓	368
3.2	odd	2		864.2.bn.a.683.32		368
9.4	even	3		864.2.bn.a.395.45		368
9.5	odd	6	inner	288.2.bf.a.203.2	yes	368
32.3	odd	8	inner	288.2.bf.a.227.2	yes	368
96.35	even	8		864.2.bn.a.35.45		368
288.67	odd	24		864.2.bn.a.611.32		368
288.131	even	24	inner	288.2.bf.a.131.15	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.15	✓	368	1.1	even	1	trivial
288.2.bf.a.131.15	yes	368	288.131	even	24	inner
288.2.bf.a.203.2	yes	368	9.5	odd	6	inner
288.2.bf.a.227.2	yes	368	32.3	odd	8	inner
864.2.bn.a.35.45		368	96.35	even	8
864.2.bn.a.395.45		368	9.4	even	3
864.2.bn.a.611.32		368	288.67	odd	24
864.2.bn.a.683.32		368	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.749302 - 1.19939i) q^{2} +(0.475486 - 1.66551i) q^{3} +(-0.877093 + 1.79742i) q^{4} +(-0.384557 - 2.92100i) q^{5} +(-2.35388 + 0.677673i) q^{6} +(-0.163982 - 0.611989i) q^{7} +(2.81302 - 0.294828i) q^{8} +(-2.54783 - 1.58385i) q^{9} +O(q^{10})\)	\(q+(-0.749302 - 1.19939i) q^{2} +(0.475486 - 1.66551i) q^{3} +(-0.877093 + 1.79742i) q^{4} +(-0.384557 - 2.92100i) q^{5} +(-2.35388 + 0.677673i) q^{6} +(-0.163982 - 0.611989i) q^{7} +(2.81302 - 0.294828i) q^{8} +(-2.54783 - 1.58385i) q^{9} +(-3.21528 + 2.64995i) q^{10} +(0.939959 - 0.721256i) q^{11} +(2.57657 + 2.31545i) q^{12} +(-1.82995 + 2.38483i) q^{13} +(-0.611144 + 0.655244i) q^{14} +(-5.04780 - 0.748413i) q^{15} +(-2.46142 - 3.15300i) q^{16} +2.02378 q^{17} +(0.00943085 + 4.24263i) q^{18} +(0.630742 - 0.261262i) q^{19} +(5.58755 + 1.87078i) q^{20} +(-1.09724 - 0.0178791i) q^{21} +(-1.56938 - 0.586943i) q^{22} +(-7.40463 - 1.98407i) q^{23} +(0.846512 - 4.82529i) q^{24} +(-3.55474 + 0.952490i) q^{25} +(4.23153 + 0.407867i) q^{26} +(-3.84937 + 3.49032i) q^{27} +(1.24383 + 0.242027i) q^{28} +(10.5335 + 1.38676i) q^{29} +(2.88469 + 6.61509i) q^{30} +(-2.48302 + 1.43357i) q^{31} +(-1.93735 + 5.31476i) q^{32} +(-0.754319 - 1.90845i) q^{33} +(-1.51642 - 2.42731i) q^{34} +(-1.72456 + 0.714337i) q^{35} +(5.08152 - 3.19032i) q^{36} +(1.08845 - 2.62775i) q^{37} +(-0.785972 - 0.560744i) q^{38} +(3.10184 + 4.18174i) q^{39} +(-1.94296 - 8.10346i) q^{40} +(0.258552 - 0.964929i) q^{41} +(0.800723 + 1.32942i) q^{42} +(1.27177 + 1.65740i) q^{43} +(0.471966 + 2.32211i) q^{44} +(-3.64664 + 8.05129i) q^{45} +(3.16863 + 10.3677i) q^{46} +(-8.68027 - 5.01155i) q^{47} +(-6.42172 + 2.60030i) q^{48} +(5.71454 - 3.29929i) q^{49} +(3.80598 + 3.54983i) q^{50} +(0.962280 - 3.37062i) q^{51} +(-2.68150 - 5.38089i) q^{52} +(4.08933 - 9.87251i) q^{53} +(7.07061 + 2.00160i) q^{54} +(-2.46826 - 2.46826i) q^{55} +(-0.641716 - 1.67319i) q^{56} +(-0.135225 - 1.17473i) q^{57} +(-6.22948 - 13.6729i) q^{58} +(9.92768 - 1.30700i) q^{59} +(5.77260 - 8.41658i) q^{60} +(-0.353716 + 2.68674i) q^{61} +(3.57994 + 1.90394i) q^{62} +(-0.551501 + 1.81896i) q^{63} +(7.82615 - 1.65871i) q^{64} +(7.66982 + 4.42817i) q^{65} +(-1.72378 + 2.33474i) q^{66} +(1.27668 - 1.66380i) q^{67} +(-1.77504 + 3.63758i) q^{68} +(-6.82527 + 11.3891i) q^{69} +(2.14899 + 1.53317i) q^{70} +(-6.54986 - 6.54986i) q^{71} +(-7.63405 - 3.70423i) q^{72} +(9.76835 - 9.76835i) q^{73} +(-3.96729 + 0.663499i) q^{74} +(-0.103851 + 6.37334i) q^{75} +(-0.0836227 + 1.36286i) q^{76} +(-0.595537 - 0.456972i) q^{77} +(2.69134 - 6.85372i) q^{78} +(1.39820 - 2.42176i) q^{79} +(-8.26337 + 8.40231i) q^{80} +(3.98284 + 8.07075i) q^{81} +(-1.35106 + 0.412918i) q^{82} +(14.3756 + 1.89259i) q^{83} +(0.994520 - 1.95652i) q^{84} +(-0.778260 - 5.91147i) q^{85} +(1.03494 - 2.76725i) q^{86} +(7.31817 - 16.8842i) q^{87} +(2.43148 - 2.30603i) q^{88} +(8.61931 - 8.61931i) q^{89} +(12.3891 - 1.65908i) q^{90} +(1.75957 + 0.728837i) q^{91} +(10.0607 - 11.5690i) q^{92} +(1.20698 + 4.81712i) q^{93} +(0.493313 + 14.1662i) q^{94} +(-1.00570 - 1.74193i) q^{95} +(7.93059 + 5.75376i) q^{96} +(-5.48891 + 9.50707i) q^{97} +(-8.23906 - 4.38182i) q^{98} +(-3.53721 + 0.348881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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